From 96309eb56861333d6e3111c5a3cb54c9426a1d61 Mon Sep 17 00:00:00 2001 From: jthorn Date: Tue, 15 Apr 2003 17:12:59 +0000 Subject: new machine-generated coefficient files for this interpolator (with Lagrange now split into tensor-product and maximum-degree interpolators) git-svn-id: http://svn.cactuscode.org/arrangements/CactusBase/LocalInterp/trunk@144 df1f8a13-aa1d-4dd4-9681-27ded5b42416 --- .../1d.cube.order1.smooth0/coeffs-I.compute.c | 2 + .../1d.cube.order1.smooth0/coeffs-dx.compute.c | 2 + .../1d.cube.order2.smooth0/coeffs-I.compute.c | 9 + .../1d.cube.order2.smooth0/coeffs-dx.compute.c | 3 + .../1d.cube.order2.smooth0/coeffs-dxx.compute.c | 5 + .../1d.cube.order3.smooth0/coeffs-I.compute.c | 16 + .../1d.cube.order3.smooth0/coeffs-dx.compute.c | 8 + .../1d.cube.order3.smooth0/coeffs-dxx.compute.c | 6 + .../1d.cube.order4.smooth0/coeffs-I.compute.c | 24 + .../1d.cube.order4.smooth0/coeffs-dx.compute.c | 17 + .../1d.cube.order4.smooth0/coeffs-dxx.compute.c | 13 + .../1d.cube.order5.smooth0/coeffs-I.compute.c | 28 + .../1d.cube.order5.smooth0/coeffs-dx.compute.c | 21 + .../1d.cube.order5.smooth0/coeffs-dxx.compute.c | 17 + .../1d.cube.order6.smooth0/coeffs-I.compute.c | 41 + .../1d.cube.order6.smooth0/coeffs-dx.compute.c | 32 + .../1d.cube.order6.smooth0/coeffs-dxx.compute.c | 24 + .../1d.cube.order1.smooth0.c | 57 + .../1d.cube.order2.smooth0.c | 58 + .../1d.cube.order3.smooth0.c | 58 + .../1d.cube.order4.smooth0.c | 58 + .../1d.cube.order5.smooth0.c | 58 + .../1d.cube.order6.smooth0.c | 58 + .../Lagrange-maximum-degree/1d.log | 2264 + .../Lagrange-maximum-degree/1d.maple | 166 + .../2d.cube.order1.smooth0/coeffs-I.compute.c | 18 + .../2d.cube.order1.smooth0/coeffs-dx.compute.c | 8 + .../2d.cube.order1.smooth0/coeffs-dy.compute.c | 8 + .../2d.cube.order2.smooth0/coeffs-I.compute.c | 53 + .../2d.cube.order2.smooth0/coeffs-dx.compute.c | 21 + .../2d.cube.order2.smooth0/coeffs-dxx.compute.c | 13 + .../2d.cube.order2.smooth0/coeffs-dxy.compute.c | 15 + .../2d.cube.order2.smooth0/coeffs-dy.compute.c | 21 + .../2d.cube.order2.smooth0/coeffs-dyy.compute.c | 13 + .../2d.cube.order3.smooth0/coeffs-I.compute.c | 190 + .../2d.cube.order3.smooth0/coeffs-dx.compute.c | 97 + .../2d.cube.order3.smooth0/coeffs-dxx.compute.c | 40 + .../2d.cube.order3.smooth0/coeffs-dxy.compute.c | 52 + .../2d.cube.order3.smooth0/coeffs-dy.compute.c | 97 + .../2d.cube.order3.smooth0/coeffs-dyy.compute.c | 40 + .../2d.cube.order4.smooth0/coeffs-I.compute.c | 239 + .../2d.cube.order4.smooth0/coeffs-dx.compute.c | 155 + .../2d.cube.order4.smooth0/coeffs-dxx.compute.c | 107 + .../2d.cube.order4.smooth0/coeffs-dxy.compute.c | 119 + .../2d.cube.order4.smooth0/coeffs-dy.compute.c | 147 + .../2d.cube.order4.smooth0/coeffs-dyy.compute.c | 107 + .../2d.cube.order1.smooth0.c | 59 + .../2d.cube.order2.smooth0.c | 64 + .../2d.cube.order3.smooth0.c | 64 + .../2d.cube.order4.smooth0.c | 64 + .../Lagrange-maximum-degree/2d.log | 4728 + .../Lagrange-maximum-degree/2d.maple | 170 + .../3d.cube.order1.smooth0/coeffs-I.compute.c | 34 + .../3d.cube.order1.smooth0/coeffs-dx.compute.c | 12 + .../3d.cube.order1.smooth0/coeffs-dy.compute.c | 12 + .../3d.cube.order1.smooth0/coeffs-dz.compute.c | 12 + .../3d.cube.order2.smooth0/coeffs-I.compute.c | 153 + .../3d.cube.order2.smooth0/coeffs-dx.compute.c | 65 + .../3d.cube.order2.smooth0/coeffs-dxx.compute.c | 31 + .../3d.cube.order2.smooth0/coeffs-dxy.compute.c | 33 + .../3d.cube.order2.smooth0/coeffs-dxz.compute.c | 33 + .../3d.cube.order2.smooth0/coeffs-dy.compute.c | 59 + .../3d.cube.order2.smooth0/coeffs-dyy.compute.c | 31 + .../3d.cube.order2.smooth0/coeffs-dyz.compute.c | 33 + .../3d.cube.order2.smooth0/coeffs-dz.compute.c | 63 + .../3d.cube.order2.smooth0/coeffs-dzz.compute.c | 31 + .../3d.cube.order3.smooth0/coeffs-I.compute.c | 938 + .../3d.cube.order3.smooth0/coeffs-dx.compute.c | 518 + .../3d.cube.order3.smooth0/coeffs-dxx.compute.c | 182 + .../3d.cube.order3.smooth0/coeffs-dxy.compute.c | 208 + .../3d.cube.order3.smooth0/coeffs-dxz.compute.c | 202 + .../3d.cube.order3.smooth0/coeffs-dy.compute.c | 510 + .../3d.cube.order3.smooth0/coeffs-dyy.compute.c | 186 + .../3d.cube.order3.smooth0/coeffs-dyz.compute.c | 210 + .../3d.cube.order3.smooth0/coeffs-dz.compute.c | 502 + .../3d.cube.order3.smooth0/coeffs-dzz.compute.c | 192 + .../3d.cube.order4.smooth0/coeffs-I.compute.c | 1615 + .../3d.cube.order4.smooth0/coeffs-dx.compute.c | 977 + .../3d.cube.order4.smooth0/coeffs-dxx.compute.c | 593 + .../3d.cube.order4.smooth0/coeffs-dxy.compute.c | 511 + .../3d.cube.order4.smooth0/coeffs-dxz.compute.c | 523 + .../3d.cube.order4.smooth0/coeffs-dy.compute.c | 961 + .../3d.cube.order4.smooth0/coeffs-dyy.compute.c | 605 + .../3d.cube.order4.smooth0/coeffs-dyz.compute.c | 507 + .../3d.cube.order4.smooth0/coeffs-dz.compute.c | 985 + .../3d.cube.order4.smooth0/coeffs-dzz.compute.c | 621 + .../3d.cube.order1.smooth0.c | 61 + .../3d.cube.order2.smooth0.c | 71 + .../3d.cube.order3.smooth0.c | 71 + .../3d.cube.order4.smooth0.c | 71 + .../Lagrange-maximum-degree/3d.log | 40709 ++++ .../Lagrange-maximum-degree/3d.maple | 248 + .../Lagrange-maximum-degree/README | 62 + .../Lagrange-maximum-degree/all_prototypes.h | 72 + .../Lagrange-maximum-degree/fns.maple | 266 + .../Lagrange-maximum-degree/make.code.defn | 22 + .../Lagrange-maximum-degree/makefile | 72 + .../1d.cube.order1.smooth0/coeffs-I.compute.c | 2 + .../1d.cube.order1.smooth0/coeffs-dx.compute.c | 2 + .../1d.cube.order2.smooth0/coeffs-I.compute.c | 9 + .../1d.cube.order2.smooth0/coeffs-dx.compute.c | 3 + .../1d.cube.order2.smooth0/coeffs-dxx.compute.c | 5 + .../1d.cube.order3.smooth0/coeffs-I.compute.c | 16 + .../1d.cube.order3.smooth0/coeffs-dx.compute.c | 8 + .../1d.cube.order3.smooth0/coeffs-dxx.compute.c | 6 + .../1d.cube.order4.smooth0/coeffs-I.compute.c | 24 + .../1d.cube.order4.smooth0/coeffs-dx.compute.c | 17 + .../1d.cube.order4.smooth0/coeffs-dxx.compute.c | 13 + .../1d.cube.order5.smooth0/coeffs-I.compute.c | 28 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| 35 + .../2d.cube.order2.smooth0/coeffs-dyy.compute.c | 21 + .../2d.cube.order3.smooth0/coeffs-I.compute.c | 162 + .../2d.cube.order3.smooth0/coeffs-dx.compute.c | 131 + .../2d.cube.order3.smooth0/coeffs-dxx.compute.c | 74 + .../2d.cube.order3.smooth0/coeffs-dxy.compute.c | 87 + .../2d.cube.order3.smooth0/coeffs-dy.compute.c | 114 + .../2d.cube.order3.smooth0/coeffs-dyy.compute.c | 71 + .../2d.cube.order4.smooth0/coeffs-I.compute.c | 287 + .../2d.cube.order4.smooth0/coeffs-dx.compute.c | 261 + .../2d.cube.order4.smooth0/coeffs-dxx.compute.c | 224 + .../2d.cube.order4.smooth0/coeffs-dxy.compute.c | 256 + .../2d.cube.order4.smooth0/coeffs-dy.compute.c | 255 + .../2d.cube.order4.smooth0/coeffs-dyy.compute.c | 223 + .../2d.cube.order1.smooth0.c | 59 + .../2d.cube.order2.smooth0.c | 64 + .../2d.cube.order3.smooth0.c | 64 + .../2d.cube.order4.smooth0.c | 64 + .../Lagrange-tensor-product/2d.log | 6898 + .../Lagrange-tensor-product/2d.maple | 170 + .../3d.cube.order1.smooth0/coeffs-I.compute.c | 22 + .../3d.cube.order1.smooth0/coeffs-dx.compute.c | 16 + .../3d.cube.order1.smooth0/coeffs-dy.compute.c | 16 + .../3d.cube.order1.smooth0/coeffs-dz.compute.c | 16 + .../3d.cube.order2.smooth0/coeffs-I.compute.c | 245 + .../3d.cube.order2.smooth0/coeffs-dx.compute.c | 186 + .../3d.cube.order2.smooth0/coeffs-dxx.compute.c | 120 + .../3d.cube.order2.smooth0/coeffs-dxy.compute.c | 170 + .../3d.cube.order2.smooth0/coeffs-dxz.compute.c | 152 + .../3d.cube.order2.smooth0/coeffs-dy.compute.c | 203 + .../3d.cube.order2.smooth0/coeffs-dyy.compute.c | 116 + .../3d.cube.order2.smooth0/coeffs-dyz.compute.c | 164 + .../3d.cube.order2.smooth0/coeffs-dz.compute.c | 196 + .../3d.cube.order2.smooth0/coeffs-dzz.compute.c | 120 + .../3d.cube.order3.smooth0/coeffs-I.compute.c | 1421 + .../3d.cube.order3.smooth0/coeffs-dx.compute.c | 1251 + .../3d.cube.order3.smooth0/coeffs-dxx.compute.c | 891 + .../3d.cube.order3.smooth0/coeffs-dxy.compute.c | 1084 + .../3d.cube.order3.smooth0/coeffs-dxz.compute.c | 1094 + .../3d.cube.order3.smooth0/coeffs-dy.compute.c | 1268 + .../3d.cube.order3.smooth0/coeffs-dyy.compute.c | 889 + .../3d.cube.order3.smooth0/coeffs-dyz.compute.c | 1098 + .../3d.cube.order3.smooth0/coeffs-dz.compute.c | 1264 + .../3d.cube.order3.smooth0/coeffs-dzz.compute.c | 869 + .../3d.cube.order4.smooth0/coeffs-I.compute.c | 2724 + .../3d.cube.order4.smooth0/coeffs-dx.compute.c | 2720 + .../3d.cube.order4.smooth0/coeffs-dxx.compute.c | 2321 + .../3d.cube.order4.smooth0/coeffs-dxy.compute.c | 2557 + .../3d.cube.order4.smooth0/coeffs-dxz.compute.c | 2488 + .../3d.cube.order4.smooth0/coeffs-dy.compute.c | 2721 + .../3d.cube.order4.smooth0/coeffs-dyy.compute.c | 2265 + .../3d.cube.order4.smooth0/coeffs-dyz.compute.c | 2550 + .../3d.cube.order4.smooth0/coeffs-dz.compute.c | 2737 + .../3d.cube.order4.smooth0/coeffs-dzz.compute.c | 2341 + .../3d.cube.order1.smooth0.c | 61 + .../3d.cube.order2.smooth0.c | 71 + .../3d.cube.order3.smooth0.c | 71 + .../3d.cube.order4.smooth0.c | 71 + .../Lagrange-tensor-product/3d.log | 200156 ++++++++++++++++++ .../Lagrange-tensor-product/3d.maple | 248 + .../Lagrange-tensor-product/README | 62 + .../Lagrange-tensor-product/all_prototypes.h | 72 + .../Lagrange-tensor-product/fns.maple | 306 + .../Lagrange-tensor-product/make.code.defn | 22 + .../Lagrange-tensor-product/makefile | 72 + 194 files changed, 315853 insertions(+) create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order1.smooth0/coeffs-I.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order1.smooth0/coeffs-dx.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-I.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-dx.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-dxx.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-I.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-dx.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-dxx.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-I.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-dx.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-dxx.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-I.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-dx.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-dxx.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-I.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-dx.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-dxx.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order1.smooth0.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order2.smooth0.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order3.smooth0.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order4.smooth0.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order5.smooth0.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order6.smooth0.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.log create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.maple create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c create mode 100644 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create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/fns.maple create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/make.code.defn create mode 100644 src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/makefile diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order1.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order1.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..c8a5114 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order1.smooth0/coeffs-I.compute.c @@ -0,0 +1,2 @@ + coeffs_I->coeff_0 = RATIONAL(1.0,1.0)-x; + coeffs_I->coeff_p1 = x; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order1.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order1.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..583278a --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order1.smooth0/coeffs-dx.compute.c @@ -0,0 +1,2 @@ + coeffs_dx->coeff_0 = RATIONAL(-1.0,1.0); + coeffs_dx->coeff_p1 = RATIONAL(1.0,1.0); diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..6e17264 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-I.compute.c @@ -0,0 +1,9 @@ +fp t3; +fp t2; +fp t1; + t3 = x*x; + t2 = RATIONAL(1.0,2.0); + t1 = t2*t3; + coeffs_I->coeff_m1 = RATIONAL(-1.0,2.0)*x+t1; + coeffs_I->coeff_0 = RATIONAL(1.0,1.0)-t3; + coeffs_I->coeff_p1 = t2*x+t1; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..5647f75 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-dx.compute.c @@ -0,0 +1,3 @@ + coeffs_dx->coeff_m1 = x+RATIONAL(-1.0,2.0); + coeffs_dx->coeff_0 = RATIONAL(-2.0,1.0)*x; + coeffs_dx->coeff_p1 = RATIONAL(1.0,2.0)+x; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..19689e7 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,5 @@ +fp t4; + t4 = RATIONAL(1.0,1.0); + coeffs_dxx->coeff_m1 = t4; + coeffs_dxx->coeff_0 = RATIONAL(-2.0,1.0); + coeffs_dxx->coeff_p1 = t4; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..6ee0b5a --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-I.compute.c @@ -0,0 +1,16 @@ +fp t10; +fp t9; +fp t8; +fp t7; +fp t6; +fp t5; + t10 = x*x; + t9 = x*t10; + t8 = RATIONAL(-1.0,2.0); + t7 = RATIONAL(1.0,2.0); + t6 = RATIONAL(-1.0,6.0); + t5 = t7*t10; + coeffs_I->coeff_m1 = RATIONAL(-1.0,3.0)*x+t5+t6*t9; + coeffs_I->coeff_0 = RATIONAL(1.0,1.0)+t8*x-t10+t7*t9; + coeffs_I->coeff_p1 = x+t5+t8*t9; + coeffs_I->coeff_p2 = t6*x+RATIONAL(1.0,6.0)*t9; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..1cf3fc6 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-dx.compute.c @@ -0,0 +1,8 @@ +fp t13; +fp t12; + t13 = x*x; + t12 = RATIONAL(-1.0,2.0); + coeffs_dx->coeff_m1 = x+t12*t13+RATIONAL(-1.0,3.0); + coeffs_dx->coeff_0 = t12+RATIONAL(-2.0,1.0)*x+RATIONAL(3.0,2.0)*t13; + coeffs_dx->coeff_p1 = x+RATIONAL(1.0,1.0)+RATIONAL(-3.0,2.0)*t13; + coeffs_dx->coeff_p2 = RATIONAL(1.0,2.0)*t13+RATIONAL(-1.0,6.0); diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..470882c --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,6 @@ +fp t14; + t14 = RATIONAL(1.0,1.0); + coeffs_dxx->coeff_m1 = t14-x; + coeffs_dxx->coeff_0 = RATIONAL(-2.0,1.0)+RATIONAL(3.0,1.0)*x; + coeffs_dxx->coeff_p1 = t14+RATIONAL(-3.0,1.0)*x; + coeffs_dxx->coeff_p2 = x; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..c30526f --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-I.compute.c @@ -0,0 +1,24 @@ +fp t25; +fp t23; +fp t29; +fp t21; +fp t22; +fp t28; +fp t24; +fp t20; +fp t19; + t25 = x*x; + t23 = t25*t25; + t29 = RATIONAL(1.0,24.0)*t23+RATIONAL(-1.0,24.0)*t25; + t21 = RATIONAL(-1.0,6.0); + t22 = RATIONAL(2.0,3.0); + t28 = t21*t23+t22*t25; + t24 = x*t25; + t20 = RATIONAL(1.0,12.0); + t19 = RATIONAL(-1.0,12.0); + coeffs_I->coeff_m2 = t20*x+t19*t24+t29; + coeffs_I->coeff_m1 = RATIONAL(-2.0,3.0)*x+RATIONAL(1.0,6.0)*t24+t28; + coeffs_I->coeff_0 = RATIONAL(-5.0,4.0)*t25+RATIONAL(1.0,1.0)+RATIONAL(1.0 +,4.0)*t23; + coeffs_I->coeff_p1 = t21*t24+t22*x+t28; + coeffs_I->coeff_p2 = t20*t24+t19*x+t29; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..14b1551 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-dx.compute.c @@ -0,0 +1,17 @@ +fp t34; +fp t37; +fp t36; +fp t40; +fp t35; +fp t39; + t34 = RATIONAL(-1.0,12.0); + t37 = x*x; + t36 = x*t37; + t40 = RATIONAL(1.0,6.0)*t36+t34*x; + t35 = RATIONAL(-2.0,3.0); + t39 = t35*t36+RATIONAL(4.0,3.0)*x; + coeffs_dx->coeff_m2 = RATIONAL(-1.0,4.0)*t37+RATIONAL(1.0,12.0)+t40; + coeffs_dx->coeff_m1 = t35+RATIONAL(1.0,2.0)*t37+t39; + coeffs_dx->coeff_0 = t36+RATIONAL(-5.0,2.0)*x; + coeffs_dx->coeff_p1 = RATIONAL(-1.0,2.0)*t37+RATIONAL(2.0,3.0)+t39; + coeffs_dx->coeff_p2 = t34+RATIONAL(1.0,4.0)*t37+t40; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..6f78a84 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,13 @@ +fp t46; +fp t48; +fp t44; +fp t47; + t46 = x*x; + t48 = RATIONAL(-2.0,1.0)*t46+RATIONAL(4.0,3.0); + t44 = RATIONAL(1.0,2.0); + t47 = t44*t46+RATIONAL(-1.0,12.0); + coeffs_dxx->coeff_m2 = RATIONAL(-1.0,2.0)*x+t47; + coeffs_dxx->coeff_m1 = x+t48; + coeffs_dxx->coeff_0 = RATIONAL(-5.0,2.0)+RATIONAL(3.0,1.0)*t46; + coeffs_dxx->coeff_p1 = -x+t48; + coeffs_dxx->coeff_p2 = t44*x+t47; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..2fe57b6 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-I.compute.c @@ -0,0 +1,28 @@ +fp t54; +fp t55; +fp t57; +fp t58; +fp t64; +fp t63; +fp t60; +fp t59; +fp t51; + t54 = RATIONAL(1.0,24.0); + t55 = RATIONAL(-1.0,24.0); + t57 = x*x; + t58 = t57*t57; + t64 = t54*t58+t55*t57; + t63 = RATIONAL(-1.0,6.0)*t58+RATIONAL(2.0,3.0)*t57; + t60 = x*t57; + t59 = t60*t57; + t51 = t55*t60; + coeffs_I->coeff_m2 = RATIONAL(1.0,20.0)*x+t51+RATIONAL(-1.0,120.0)*t59+ +t64; + coeffs_I->coeff_m1 = RATIONAL(-1.0,2.0)*x+t51+t54*t59+t63; + coeffs_I->coeff_0 = RATIONAL(1.0,1.0)+RATIONAL(-1.0,3.0)*x+RATIONAL(-5.0, +4.0)*t57+RATIONAL(5.0,12.0)*t60+RATIONAL(1.0,4.0)*t58+RATIONAL(-1.0,12.0)*t59; + coeffs_I->coeff_p1 = x+RATIONAL(-7.0,12.0)*t60+RATIONAL(1.0,12.0)*t59+t63 +; + coeffs_I->coeff_p2 = RATIONAL(-1.0,4.0)*x+RATIONAL(7.0,24.0)*t60+t55*t59+ +t64; + coeffs_I->coeff_p3 = RATIONAL(1.0,30.0)*x+RATIONAL(1.0,120.0)*t59+t51; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..0fc33a0 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-dx.compute.c @@ -0,0 +1,21 @@ +fp t71; +fp t70; +fp t76; +fp t75; +fp t72; +fp t67; + t71 = x*x; + t70 = t71*x; + t76 = RATIONAL(-2.0,3.0)*t70+RATIONAL(4.0,3.0)*x; + t75 = RATIONAL(-1.0,12.0)*x+RATIONAL(1.0,6.0)*t70; + t72 = t71*t71; + t67 = RATIONAL(-1.0,8.0)*t71; + coeffs_dx->coeff_m2 = RATIONAL(-1.0,24.0)*t72+RATIONAL(1.0,20.0)+t67+t75; + coeffs_dx->coeff_m1 = t67+RATIONAL(-1.0,2.0)+RATIONAL(5.0,24.0)*t72+t76; + coeffs_dx->coeff_0 = RATIONAL(-5.0,2.0)*x+t70+RATIONAL(-5.0,12.0)*t72+ +RATIONAL(-1.0,3.0)+RATIONAL(5.0,4.0)*t71; + coeffs_dx->coeff_p1 = RATIONAL(5.0,12.0)*t72+RATIONAL(-7.0,4.0)*t71+ +RATIONAL(1.0,1.0)+t76; + coeffs_dx->coeff_p2 = RATIONAL(7.0,8.0)*t71+RATIONAL(-1.0,4.0)+RATIONAL( +-5.0,24.0)*t72+t75; + coeffs_dx->coeff_p3 = RATIONAL(1.0,24.0)*t72+t67+RATIONAL(1.0,30.0); diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..2382d07 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,17 @@ +fp t83; +fp t86; +fp t85; +fp t82; +fp t78; + t83 = x*x; + t86 = RATIONAL(1.0,2.0)*t83+RATIONAL(-1.0,12.0); + t85 = RATIONAL(-2.0,1.0)*t83+RATIONAL(4.0,3.0); + t82 = x*t83; + t78 = RATIONAL(-1.0,4.0)*x; + coeffs_dxx->coeff_m2 = RATIONAL(-1.0,6.0)*t82+t78+t86; + coeffs_dxx->coeff_m1 = RATIONAL(5.0,6.0)*t82+t78+t85; + coeffs_dxx->coeff_0 = RATIONAL(-5.0,3.0)*t82+RATIONAL(5.0,2.0)*x+RATIONAL +(3.0,1.0)*t83+RATIONAL(-5.0,2.0); + coeffs_dxx->coeff_p1 = RATIONAL(5.0,3.0)*t82+RATIONAL(-7.0,2.0)*x+t85; + coeffs_dxx->coeff_p2 = RATIONAL(-5.0,6.0)*t82+RATIONAL(7.0,4.0)*x+t86; + coeffs_dxx->coeff_p3 = t78+RATIONAL(1.0,6.0)*t82; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..28b9679 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-I.compute.c @@ -0,0 +1,41 @@ +fp t103; +fp t106; +fp t107; +fp t105; +fp t113; +fp t112; +fp t100; +fp t96; +fp t101; +fp t111; +fp t104; +fp t99; +fp t98; +fp t97; + t103 = x*x; + t106 = t103*t103; + t107 = x*t103; + t105 = t107*t107; + t113 = RATIONAL(1.0,720.0)*t105+RATIONAL(1.0,180.0)*t103+RATIONAL(-1.0, +144.0)*t106; + t112 = RATIONAL(-1.0,120.0)*t105+RATIONAL(-3.0,40.0)*t103+RATIONAL(1.0, +12.0)*t106; + t100 = RATIONAL(1.0,48.0); + t96 = RATIONAL(-13.0,48.0); + t101 = RATIONAL(3.0,4.0); + t111 = t100*t105+t96*t106+t101*t103; + t104 = t107*t103; + t99 = RATIONAL(-1.0,60.0); + t98 = RATIONAL(1.0,60.0); + t97 = RATIONAL(-1.0,48.0); + coeffs_I->coeff_m3 = t99*x+t100*t107+RATIONAL(-1.0,240.0)*t104+t113; + coeffs_I->coeff_m2 = RATIONAL(3.0,20.0)*x+RATIONAL(-1.0,6.0)*t107+t98* +t104+t112; + coeffs_I->coeff_m1 = RATIONAL(-3.0,4.0)*x+RATIONAL(13.0,48.0)*t107+t97* +t104+t111; + coeffs_I->coeff_0 = RATIONAL(7.0,18.0)*t106+RATIONAL(-49.0,36.0)*t103+ +RATIONAL(1.0,1.0)+RATIONAL(-1.0,36.0)*t105; + coeffs_I->coeff_p1 = t96*t107+t101*x+t100*t104+t111; + coeffs_I->coeff_p2 = RATIONAL(1.0,6.0)*t107+RATIONAL(-3.0,20.0)*x+t99* +t104+t112; + coeffs_I->coeff_p3 = t97*t107+t98*x+RATIONAL(1.0,240.0)*t104+t113; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..d4d1004 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-dx.compute.c @@ -0,0 +1,32 @@ +fp t123; +fp t125; +fp t128; +fp t126; +fp t133; +fp t132; +fp t131; +fp t127; + t123 = RATIONAL(-3.0,20.0); + t125 = x*x; + t128 = x*t125; + t126 = t128*t125; + t133 = t123*x+RATIONAL(-1.0,20.0)*t126+RATIONAL(1.0,3.0)*t128; + t132 = RATIONAL(1.0,120.0)*t126+RATIONAL(1.0,90.0)*x+RATIONAL(-1.0,36.0)* +t128; + t131 = RATIONAL(3.0,2.0)*x+RATIONAL(-13.0,12.0)*t128+RATIONAL(1.0,8.0)* +t126; + t127 = t125*t125; + coeffs_dx->coeff_m3 = RATIONAL(-1.0,48.0)*t127+RATIONAL(-1.0,60.0)+ +RATIONAL(1.0,16.0)*t125+t132; + coeffs_dx->coeff_m2 = RATIONAL(-1.0,2.0)*t125+RATIONAL(3.0,20.0)+RATIONAL +(1.0,12.0)*t127+t133; + coeffs_dx->coeff_m1 = RATIONAL(-5.0,48.0)*t127+RATIONAL(13.0,16.0)*t125+ +RATIONAL(-3.0,4.0)+t131; + coeffs_dx->coeff_0 = RATIONAL(-1.0,6.0)*t126+RATIONAL(14.0,9.0)*t128+ +RATIONAL(-49.0,18.0)*x; + coeffs_dx->coeff_p1 = RATIONAL(5.0,48.0)*t127+RATIONAL(3.0,4.0)+RATIONAL( +-13.0,16.0)*t125+t131; + coeffs_dx->coeff_p2 = RATIONAL(1.0,2.0)*t125+RATIONAL(-1.0,12.0)*t127+ +t123+t133; + coeffs_dx->coeff_p3 = RATIONAL(-1.0,16.0)*t125+RATIONAL(1.0,60.0)+ +RATIONAL(1.0,48.0)*t127+t132; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..02aa677 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,24 @@ +fp t144; +fp t145; +fp t150; +fp t149; +fp t141; +fp t148; +fp t143; + t144 = x*x; + t145 = t144*t144; + t150 = RATIONAL(-13.0,4.0)*t144+RATIONAL(3.0,2.0)+RATIONAL(5.0,8.0)*t145; + t149 = t144+RATIONAL(-3.0,20.0)+RATIONAL(-1.0,4.0)*t145; + t141 = RATIONAL(-1.0,12.0); + t148 = RATIONAL(1.0,90.0)+RATIONAL(1.0,24.0)*t145+t141*t144; + t143 = x*t144; + coeffs_dxx->coeff_m3 = RATIONAL(1.0,8.0)*x+t141*t143+t148; + coeffs_dxx->coeff_m2 = -x+RATIONAL(1.0,3.0)*t143+t149; + coeffs_dxx->coeff_m1 = RATIONAL(-5.0,12.0)*t143+RATIONAL(13.0,8.0)*x+t150 +; + coeffs_dxx->coeff_0 = RATIONAL(14.0,3.0)*t144+RATIONAL(-5.0,6.0)*t145+ +RATIONAL(-49.0,18.0); + coeffs_dxx->coeff_p1 = RATIONAL(5.0,12.0)*t143+RATIONAL(-13.0,8.0)*x+t150 +; + coeffs_dxx->coeff_p2 = x+RATIONAL(-1.0,3.0)*t143+t149; + coeffs_dxx->coeff_p3 = RATIONAL(-1.0,8.0)*x+RATIONAL(1.0,12.0)*t143+t148; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order1.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order1.smooth0.c new file mode 100644 index 0000000..20523da --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order1.smooth0.c @@ -0,0 +1,57 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrMD_1d_cube10 +#include "../template.h" + +#define N_DIMS 1 +#define MOLECULE_MIN_M 0 +#define MOLECULE_MAX_M 1 +#define MOLECULE_SIZE 2 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +/* n.b. no 2nd derivatives for linear interpolation! */ + +#define XYZ x +#define FP_XYZ fp x +#define STRIDE_IJK stride_i +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride + +#define DATA_STRUCT data_struct_1d_cube_size2 +#define COEFFS_STRUCT coeffs_struct_1d_cube_size2 + +#define FETCH_DATA_REAL LocalInterp_fetch_1d_cube2_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_1d_cube2_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_1d_cube2_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_1d_cube2_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_1d_cube2_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_1d_cube2_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_1d_cube2_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_1d_cube2_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_1d_cube2 + +#define STORE_COEFFS LocalInterp_store_1d_cube2 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order1.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order1.smooth0/coeffs-dx.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order2.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order2.smooth0.c new file mode 100644 index 0000000..bf2ca11 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order2.smooth0.c @@ -0,0 +1,58 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrMD_1d_cube20 +#include "../template.h" + +#define N_DIMS 1 +#define MOLECULE_MIN_M -1 +#define MOLECULE_MAX_M 1 +#define MOLECULE_SIZE 3 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DXX + +#define XYZ x +#define FP_XYZ fp x +#define STRIDE_IJK stride_i +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride + +#define DATA_STRUCT data_struct_1d_cube_size3 +#define COEFFS_STRUCT coeffs_struct_1d_cube_size3 + +#define FETCH_DATA_REAL LocalInterp_fetch_1d_cube3_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_1d_cube3_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_1d_cube3_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_1d_cube3_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_1d_cube3_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_1d_cube3_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_1d_cube3_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_1d_cube3_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_1d_cube3 + +#define STORE_COEFFS LocalInterp_store_1d_cube3 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-dx.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order2.smooth0/coeffs-dxx.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order3.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order3.smooth0.c new file mode 100644 index 0000000..a25fa0c --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order3.smooth0.c @@ -0,0 +1,58 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrMD_1d_cube30 +#include "../template.h" + +#define N_DIMS 1 +#define MOLECULE_MIN_M -1 +#define MOLECULE_MAX_M 2 +#define MOLECULE_SIZE 4 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DXX + +#define XYZ x +#define FP_XYZ fp x +#define STRIDE_IJK stride_i +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride + +#define DATA_STRUCT data_struct_1d_cube_size4 +#define COEFFS_STRUCT coeffs_struct_1d_cube_size4 + +#define FETCH_DATA_REAL LocalInterp_fetch_1d_cube4_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_1d_cube4_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_1d_cube4_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_1d_cube4_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_1d_cube4_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_1d_cube4_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_1d_cube4_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_1d_cube4_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_1d_cube4 + +#define STORE_COEFFS LocalInterp_store_1d_cube4 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-dx.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order3.smooth0/coeffs-dxx.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order4.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order4.smooth0.c new file mode 100644 index 0000000..e578c26 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order4.smooth0.c @@ -0,0 +1,58 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrMD_1d_cube40 +#include "../template.h" + +#define N_DIMS 1 +#define MOLECULE_MIN_M -2 +#define MOLECULE_MAX_M 2 +#define MOLECULE_SIZE 5 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DXX + +#define XYZ x +#define FP_XYZ fp x +#define STRIDE_IJK stride_i +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride + +#define DATA_STRUCT data_struct_1d_cube_size5 +#define COEFFS_STRUCT coeffs_struct_1d_cube_size5 + +#define FETCH_DATA_REAL LocalInterp_fetch_1d_cube5_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_1d_cube5_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_1d_cube5_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_1d_cube5_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_1d_cube5_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_1d_cube5_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_1d_cube5_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_1d_cube5_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_1d_cube5 + +#define STORE_COEFFS LocalInterp_store_1d_cube5 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-dx.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order4.smooth0/coeffs-dxx.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order5.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order5.smooth0.c new file mode 100644 index 0000000..148d4d2 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order5.smooth0.c @@ -0,0 +1,58 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrMD_1d_cube50 +#include "../template.h" + +#define N_DIMS 1 +#define MOLECULE_MIN_M -2 +#define MOLECULE_MAX_M 3 +#define MOLECULE_SIZE 6 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DXX + +#define XYZ x +#define FP_XYZ fp x +#define STRIDE_IJK stride_i +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride + +#define DATA_STRUCT data_struct_1d_cube_size6 +#define COEFFS_STRUCT coeffs_struct_1d_cube_size6 + +#define FETCH_DATA_REAL LocalInterp_fetch_1d_cube6_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_1d_cube6_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_1d_cube6_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_1d_cube6_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_1d_cube6_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_1d_cube6_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_1d_cube6_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_1d_cube6_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_1d_cube6 + +#define STORE_COEFFS LocalInterp_store_1d_cube6 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-dx.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order5.smooth0/coeffs-dxx.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order6.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order6.smooth0.c new file mode 100644 index 0000000..4e7b49c --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.cube.order6.smooth0.c @@ -0,0 +1,58 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrMD_1d_cube60 +#include "../template.h" + +#define N_DIMS 1 +#define MOLECULE_MIN_M -3 +#define MOLECULE_MAX_M 3 +#define MOLECULE_SIZE 7 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DXX + +#define XYZ x +#define FP_XYZ fp x +#define STRIDE_IJK stride_i +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride + +#define DATA_STRUCT data_struct_1d_cube_size7 +#define COEFFS_STRUCT coeffs_struct_1d_cube_size7 + +#define FETCH_DATA_REAL LocalInterp_fetch_1d_cube7_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_1d_cube7_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_1d_cube7_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_1d_cube7_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_1d_cube7_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_1d_cube7_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_1d_cube7_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_1d_cube7_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_1d_cube7 + +#define STORE_COEFFS LocalInterp_store_1d_cube7 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-dx.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/1d.coeffs/1d.cube.order6.smooth0/coeffs-dxx.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.log b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.log new file mode 100644 index 0000000..4fbd840 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.log @@ -0,0 +1,2264 @@ + |\^/| Maple 7 (IBM INTEL LINUX) +._|\| |/|_. Copyright (c) 2001 by Waterloo Maple Inc. + \ MAPLE / All rights reserved. Maple is a registered trademark of + <____ ____> Waterloo Maple Inc. + | Type ? for help. +# util.maple -- misc utility routines +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/util.maple,v 1.4 2002/08/20 16:46:06 jthorn Exp $ +> +# +# fix_rationals - convert numbers to RATIONAL() calls +# nonmatching_names - find names in a list which *don't* have a specified prefix +# sprint_numeric_list - convert a numeric list to a valid C identifier suffix +# print_name_list_dcl - print C declarations for a list of names +# +# hypercube_points - compute all (integer) points in an N-dimensional hypercube +# +# ftruncate - truncate a file to zero length +# +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function converts all {integer, rational} subexpressions of its +# input except integer exponents and -1 factors in products, into function +# calls +# RATIONAL(num,den) +# This is useful in conjunction with the C() library function, since +# +# C( (1/3) * foo * bar ) +# t0 = foo*bar/3; +# +# generates a (slow) division (and runs the risk of mixed-mode-arithmetic +# problems), while +# +# C((1.0/3.0) * foo * bar); +# t0 = 0.3333333333*foo*bar; +# +# suffers from roundoff error. With this function, +# +# fix_rationals((1/3) * foo * bar); +# RATIONAL(1,3) foo bar +# C(%); +# t0 = RATIONAL(1.0,3.0)*foo*bar; +# +# which a C preprocessor macro can easily convert to the desired +# +# t0 = (1.0/3.0)*foo*bar; +# +# Additionally, this function can be told to leave certain types of +# subexpressions unconverged. For example, +# fix_rationals(expr, type, specfunc(integer, DATA)); +# will leave all subexpressions of the form DATA(integer arguments) +# unconverted. +# +# Arguments: +# expr = (in) The expression to be converted. +# inert_fn = (optional in) +# If specified, this argument should be a Boolean procedure +# or the name of a Boolean procedure. This procedure should +# take one or more argument, and return true if and only if +# the first argument should *not* be converted, i.e. if we +# should leave this expression unchanged. See the last +# example above. +# ... = (optional in) +# Any further arguments are passed as additional arguments to +# the inert_fn procedure. +# +> fix_rationals := +> proc( +> expr::{ +> algebraic, name = algebraic, +> list({algebraic, name = algebraic}), +> set ({algebraic, name = algebraic}) +> }, +> inert_fn::{name, procedure} +> ) +> local nn, k, +> base, power, fbase, fpower, +> fn, fn_args_list, +> num, den, mult; +> +# do we want to convert this expression? +> if ((nargs >= 2) and inert_fn(expr, args[3..nargs])) +> then return expr; +> end if; +> +# recurse over lists and sets +> if (type(expr, {list,set})) +> then return map(fix_rationals, expr, args[2..nargs]); +> end if; +> +# recurse over equation right hand sides +> if (type(expr, name = algebraic)) +> then return ( lhs(expr) = fix_rationals(rhs(expr), args[2..nargs]) ); +> end if; +> +# recurse over functions other than RATIONAL() +> if (type(expr, function)) +> then +> fn := op(0, expr); +> if (fn <> 'RATIONAL') +> then +> fn_args_list := [op(expr)]; +> fn_args_list := map(fix_rationals, fn_args_list, args[2..nargs]); +> fn; return '%'( op(fn_args_list) ); +> end if; +> end if; +> +> nn := nops(expr); +> +# recurse over sums +> if (type(expr, `+`)) +> then return sum('fix_rationals(op(k,expr), args[2..nargs])', 'k'=1..nn); +> end if; +> +# recurse over products +# ... leaving leading -1 factors intact, i.e. not converted to RATIONAL(-1,1) +> if (type(expr, `*`)) +> then +> if (op(1, expr) = -1) +> then return -1*fix_rationals(remove(type, expr, 'identical(-1)'), +> args[2..nargs]); +> else return product('fix_rationals(op(k,expr), args[2..nargs])', +> 'k'=1..nn); +> end if; +> end if; +> +# recurse over powers +# ... leaving integer exponents intact +> if (type(expr, `^`)) +> then +> base := op(1, expr); +> power := op(2, expr); +> +> fbase := fix_rationals(base, args[2..nargs]); +> if (type(power, integer)) +> then fpower := power; +> else fpower := fix_rationals(power, args[2..nargs]); +> end if; +> return fbase ^ fpower; +> end if; +> +# fix integers and fractions +> if (type(expr, integer)) +> then return 'RATIONAL'(expr, 1); +> end if; +> if (type(expr, fraction)) +> then +> num := op(1, expr); +> den := op(2, expr); +> +> return 'RATIONAL'(num, den); +> end if; +> +# turn Maple floating-point into integer fraction, then recursively fix that +> if (type(expr, float)) +> then +> mult := op(1, expr); +> power := op(2, expr); +> return fix_rationals(mult * 10^power, args[2..nargs]); +> end if; +> +# identity op on names +> if (type(expr, name)) +> then return expr; +> end if; +> +# unknown type +> error "%0", +> "unknown type for expr!", +> " whattype(expr) = ", whattype(expr), +> " expr = ", expr; +> end proc; +fix_rationals := proc(expr::{algebraic, name = algebraic, +list({algebraic, name = algebraic}), set({algebraic, name = algebraic})}, +inert_fn::{procedure, name}) +local nn, k, base, power, fbase, fpower, fn, fn_args_list, num, den, mult; + if 2 <= nargs and inert_fn(expr, args[3 .. nargs]) then return expr + end if; + if type(expr, {set, list}) then + return map(fix_rationals, expr, args[2 .. nargs]) + end if; + if type(expr, name = algebraic) then + return lhs(expr) = fix_rationals(rhs(expr), args[2 .. nargs]) + end if; + if type(expr, function) then + fn := op(0, expr); + if fn <> 'RATIONAL' then + fn_args_list := [op(expr)]; + fn_args_list := + map(fix_rationals, fn_args_list, args[2 .. nargs]); + fn; + return '%'(op(fn_args_list)) + end if + end if; + nn := nops(expr); + if type(expr, `+`) then return + sum('fix_rationals(op(k, expr), args[2 .. nargs])', 'k' = 1 .. nn) + end if; + if type(expr, `*`) then + if op(1, expr) = -1 then return -fix_rationals( + remove(type, expr, 'identical(-1)'), args[2 .. nargs]) + else return product('fix_rationals(op(k, expr), args[2 .. nargs])', + 'k' = 1 .. nn) + end if + end if; + if type(expr, `^`) then + base := op(1, expr); + power := op(2, expr); + fbase := fix_rationals(base, args[2 .. nargs]); + if type(power, integer) then fpower := power + else fpower := fix_rationals(power, args[2 .. nargs]) + end if; + return fbase^fpower + end if; + if type(expr, integer) then return 'RATIONAL'(expr, 1) end if; + if type(expr, fraction) then + num := op(1, expr); den := op(2, expr); return 'RATIONAL'(num, den) + end if; + if type(expr, float) then + mult := op(1, expr); + power := op(2, expr); + return fix_rationals(mult*10^power, args[2 .. nargs]) + end if; + if type(expr, name) then return expr end if; + error "%0", "unknown type for expr!", " whattype(expr) = ", + whattype(expr), " expr = ", expr +end proc + +> +################################################################################ +> +# +# This function finds names in a list which *don't* have a specified prefix. +# +# Arguments: +# name_list = A list of the names. +# prefix = The prefix we want to filter out. +# +# Results: +# This function returns the subset list of names which don't have the +# specified prefix. +# +> nonmatching_names := +> proc( name_list::list({name,string}), prefix::{name,string} ) +> +> select( proc(n) +> evalb(not StringTools[IsPrefix](prefix,n)); +> end proc +> , +> name_list +> ); +> end proc; +nonmatching_names := proc( +name_list::list({name, string}), prefix::{name, string}) + select(proc(n) evalb(not StringTools[IsPrefix](prefix, n)) end proc, + name_list) +end proc + +> +################################################################################ +> +# +# This function converts a numeric list to a string which is a valid +# C identifier suffix: elements are separated by "_", decimal points are +# replaced by "x", and all nonzero values have explicit +/- signs, which +# are replaced by "p"/"m". +# +# For example, [0,-3.5,+4] --> "0_m3x5_p4". +# +> sprint_numeric_list := +> proc(nlist::list(numeric)) +> +# generate preliminary string, eg "+0_-3.5_+4" +> map2(sprintf, "%+a", nlist); +> ListTools[Join](%, "_"); +> cat(op(%)); +> +# fixup bad characters +> StringTools[SubstituteAll](%, "+0", "0"); +> StringTools[CharacterMap](".+-", "xpm", %); +> +> return %; +> end proc; +sprint_numeric_list := proc(nlist::list(numeric)) + map2(sprintf, "%+a", nlist); + ListTools[Join](%, "_"); + cat(op(%)); + StringTools[SubstituteAll](%, "+0", "0"); + StringTools[CharacterMap](".+-", "xpm", %); + return % +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C declarations for a list of names. +# +# Argument: +# name_list = A list of the names. +# type_name = The C type of the names, eg. "double". +# file_name = The file name to write the declaration to. This is +# truncated before writing. +# +> print_name_list_dcl := +> proc( name_list::list({name,string}), +> type_name::string, +> file_name::string ) +> local blanks, separator_string; +> +> ftruncate(file_name); +> +> map( +> proc(var::{name,string}) +> fprintf(file_name, +> "%s %s;\n", +> type_name, var); +> end proc +> , +> name_list +> ); +> +> fclose(file_name); +> NULL; +> end proc; +print_name_list_dcl := proc( +name_list::list({name, string}), type_name::string, file_name::string) +local blanks, separator_string; + ftruncate(file_name); + map(proc(var::{name, string}) + fprintf(file_name, "%s %s;\n", type_name, var) + end proc, name_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes a list of all the (integer) points in an +# N-dimensional hypercube, in lexicographic order. The present +# implementation requires N <= 4. +# +# Arguments: +# cmin,cmax = N-element lists of cube minimum/maximum coordinates. +# +# Results: +# The function returns a set of d-element lists giving the coordinates. +# For example, +# hypercube([0,0], [2,1] +# returns +# { [0,0], [0,1], [1,0], [1,1], [2,0], [2,1] } +> hypercube_points := +> proc(cmin::list(integer), cmax::list(integer)) +> local N, i,j,k,l; +> +> N := nops(cmin); +> if (nops(cmax) <> N) +> then error +> "must have same number of dimensions for min and max coordinates!"; +> fi; +> +> if (N = 1) +> then return [seq([i], i=cmin[1]..cmax[1])]; +> elif (N = 2) +> then return [ +> seq( +> seq([i,j], j=cmin[2]..cmax[2]), +> i=cmin[1]..cmax[1]) +> ]; +> elif (N = 3) +> then return [ +> seq( +> seq( +> seq([i,j,k], k=cmin[3]..cmax[3]), +> j=cmin[2]..cmax[2] ), +> i=cmin[1]..cmax[1]) +> ]; +> elif (N = 4) +> then return [ +> seq( +> seq( +> seq( +> seq([i,j,k,l], l=cmin[4]..cmax[4]), +> k=cmin[3]..cmax[3] ), +> j=cmin[2]..cmax[2]), +> i=cmin[1]..cmax[1]) +> ]; +> else +> error "implementation restriction: must have N <= 4, got %1!", N; +> fi; +> end proc; +hypercube_points := proc(cmin::list(integer), cmax::list(integer)) +local N, i, j, k, l; + N := nops(cmin); + if nops(cmax) <> N then error + "must have same number of dimensions for min and max coordinates!" + end if; + if N = 1 then return [seq([i], i = cmin[1] .. cmax[1])] + elif N = 2 then return + [seq(seq([i, j], j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] + elif N = 3 then return [seq( + seq(seq([i, j, k], k = cmin[3] .. cmax[3]), j = cmin[2] .. cmax[2]) + , i = cmin[1] .. cmax[1])] + elif N = 4 then return [seq(seq(seq( + seq([i, j, k, l], l = cmin[4] .. cmax[4]), k = cmin[3] .. cmax[3]), + j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] + else error "implementation restriction: must have N <= 4, got %1!", N + end if +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function truncates a file to 0 length if it exists, or creates +# it at that length if it doesn't exist. +# +# Arguments: +# file_name = (in) The name of the file. +# +> ftruncate := +> proc(file_name::string) +> fopen(file_name, 'WRITE'); +> fclose(%); +> NULL; +> end proc; +ftruncate := + + proc(file_name::string) fopen(file_name, 'WRITE'); fclose(%); NULL end proc + +# interpolate.maple -- compute interpolation formulas/coefficients +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/interpolate.maple,v 1.10 2002/08/28 11:31:09 jthorn Exp $ +> +# +# <<>> +# Lagrange_polynomial_interpolant - compute Lagrange polynomial interpolant +# Hermite_polynomial_interpolant - compute Hermite polynomial interpolant +# coeffs_as_lc_of_data - coefficients of ... (linear combination of data) +# +# print_coeffs__lc_of_data - print C code to compute coefficients +# print_fetch_data - print C code to fetch input array chunk into struct data +# print_store_coeffs - print C code to store struct coeffs "somewhere" +# print_interp_cmpt__lc_of_data - print C code for computation of interpolant +# +# coeff_name - name of coefficient of data at a given [m] coordinate +# data_var_name - name of variable storing data value at a given [m] coordinate +# +> +################################################################################ +> +# +# ***** representation of numbers, data values, etc ***** +# +# We use RATIONAL(p.0,q.0) to denote the rational number p/q. +# +# We use DATA(...) to represent the data values being interpolated at a +# specified [m] coordinate, where the arguments are the [m] coordinates. +# +# We use COEFF(...) to represent the molecule coefficient at a specified +# [m] coordinate, where the arguments are the [m] coordinates. +# +# For example, the usual 1-D centered 2nd order 1st derivative molecule +# would be written +# RATIONAL(-1.0,2.0)*DATA(-1) + RATIONA(1.0,2.0)*DATA(1) +# and its coefficients as +# COEFF(-1) = RATIONAL(-1.0,2.0) +# COEFF(1) = RATIONAL(1.0,2.0) +# +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes a Lagrange polynomial interpolant in any +# number of dimensions. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) c00 + c10*x + c01*y end proc +# coeff_list = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example [c00, c10, c01]. +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# posn_list = A list of positions (each a list of numeric values) where the +# interpolant is to use data, for example hypercube([0,0], [1,1]). +# Any positions may be used; if they're redundant (as in the +# example) the least-squares interpolant is computed. +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Lagrange_polynomial_interpolant := +> proc( +> fn::procedure, coeff_list::list(name), +> coord_list::list(name), posn_list::list(list(numeric)) +> ) +> local posn, data_eqns, coeff_eqns; +> +# coefficients of interpolating polynomial +> data_eqns := { seq( fn(op(posn))='DATA'(op(posn)) , posn=posn_list ) }; +> coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); +> if (has(coeff_eqns, '_t')) +> then error "interpolation coefficients aren't uniquely determined!"; +> end if; +> +# interpolant as a polynomial in the coordinates +> return subs(coeff_eqns, eval(fn))(op(coord_list)); +> end proc; +Lagrange_polynomial_interpolant := proc(fn::procedure, coeff_list::list(name), +coord_list::list(name), posn_list::list(list(numeric))) +local posn, data_eqns, coeff_eqns; + data_eqns := {seq(fn(op(posn)) = 'DATA'(op(posn)), posn = posn_list)}; + coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); + if has(coeff_eqns, '_t') then + error "interpolation coefficients aren't uniquely determined!" + end if; + return subs(coeff_eqns, eval(fn))(op(coord_list)) +end proc + +> +################################################################################ +> +# +# This function computes a Hermite polynomial interpolant in any +# number of dimensions. This is a polynomial which +# * has values which match the given data DATA() at a specified set of +# points, and +# * has derivatives which match the specified finite-difference derivatives +# of the given data DATA() at a specified set of points +# +# For the derivative matching, we actually match all possible products +# of 1st derivatives, i.e. in 2-D we match dx, dy, and dxy, in 3-D we +# match dx, dy, dz, dxy, dxz, dyz, and dxyz, etc etc. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) +# + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 +# + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 +# + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +# + c00 + c10*x + c20*x^2 + c30*x^3 +# end proc; +# coeff_set = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example +# { +# c03, c13, c23, c33, +# c02, c12, c22, c32, +# c01, c11, c21, c31, +# c00, c10, c20, c30 +# } +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# deriv_set = A set of equations of the form +# {coords} = proc +# giving the derivatives which are to be matched, and the +# procedures to compute their finite-difference approximations. +# Each procedure should take N_dims integer arguments specifying +# an evaluation point, and return a suitable linear combination +# of the DATA() for the derivative at that point. For example +# { +# {x} = proc(i::integer, j::integer) +# - 1/2*DATA(i-1,j) + 1/2*DATA(i+1,j) +# end proc +# , +# {y} = proc(i::integer, j::integer) +# - 1/2*DATA(i,j-1) + 1/2*DATA(i,j+1) +# end proc +# , +# {x,y} = proc(i::integer, j::integer) +# - 1/4*DATA(i-1,j+1) + 1/4*DATA(i+1,j+1) +# + 1/4*DATA(i-1,j-1) - 1/4*DATA(i+1,j-1) +# end proc +# } +# fn_posn_set = A set of positions (each a list of numeric values) +# where the interpolant is to match the given data DATA(), +# for example +# {[0,0], [0,1], [1,0], [1,1]} +# deriv_posn_set = A list of positions (each a list of numeric values) +# where the interpolant is to match the derivatives +# specified by deriv_set , for example +# {[0,0], [0,1], [1,0], [1,1]} +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Hermite_polynomial_interpolant := +> proc( +> fn::procedure, +> coeff_set::set(name), +> coord_list::list(name), +> deriv_set::set(set(name) = procedure), +> fn_posn_set::set(list(numeric)), +> deriv_posn_set::set(list(numeric)) +> ) +> local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; +> +> +# +# compute a set of equations +# {fn(posn) = DATA(posn)} +# giving the function values to be matched +# +> fn_eqnset := map( +> # return equation that fn(posn) = DATA(posn) +> proc(posn::list(integer)) +> fn(op(posn)) = 'DATA'(op(posn)); +> end proc +> , +> fn_posn_set +> ); +> +> +# +# compute a set of equations +# { diff(fn,coords)(posn) = DERIV(coords)(posn) } +# giving the derivative values to be matched, where DERIV(coords) +# is a placeholder for the appropriate derivative +# +> map( +> # return set of equations for this particular derivative +> proc(deriv_coords::set(name)) +> local deriv_fn; +> fn(op(coord_list)); +> diff(%, op(deriv_coords)); +> deriv_fn := unapply(%, op(coord_list)); +> map( +> proc(posn::list(integer)) +> deriv_fn(op(posn)) = 'DERIV'(op(deriv_coords))(op(posn)); +> end proc +> , +> deriv_posn_set +> ); +> end proc +> , +> map(lhs, deriv_set) +> ); +> deriv_eqnset := `union`(op(%)); +> +> +# +# solve overall set of equations for coefficients +# in terms of DATA() and DERIV() values +# +> coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); +> if (indets(map(rhs,%)) <> {}) +> then error "no unique solution for coefficients -- %1 eqns for %2 coeffs", +> nops(fn_eqnset union deriv_eqnset), +> nops(coeff_set); +> fi; +> +> +# +# compute a set of substitution equations +# {'DERIV'(coords) = procedure} +# +> subs_eqnset := map( +> proc(eqn::set(name) = procedure) +> 'DERIV'(op(lhs(eqn))) = rhs(eqn); +> end proc +> , +> deriv_set +> ); +> +> +# +# compute the coefficients in terms of the DATA() values +# +> subs(subs_eqnset, coeff_eqns); +> eval(%); +> +# +# compute the interpolant as a polynomial in the coordinates +# +> subs(%, fn(op(coord_list))); +> end proc; +Hermite_polynomial_interpolant := proc(fn::procedure, coeff_set::set(name), +coord_list::list(name), deriv_set::set(set(name) = procedure), +fn_posn_set::set(list(numeric)), deriv_posn_set::set(list(numeric))) +local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; + fn_eqnset := map( + proc(posn::list(integer)) fn(op(posn)) = 'DATA'(op(posn)) end proc, + fn_posn_set); + map(proc(deriv_coords::set(name)) + local deriv_fn; + fn(op(coord_list)); + diff(%, op(deriv_coords)); + deriv_fn := unapply(%, op(coord_list)); + map(proc(posn::list(integer)) + deriv_fn(op(posn)) = + 'DERIV'(op(deriv_coords))(op(posn)) + end proc, deriv_posn_set) + end proc, map(lhs, deriv_set)); + deriv_eqnset := `union`(op(%)); + coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); + if indets(map(rhs, %)) <> {} then error + "no unique solution for coefficients -- %1 eqns for %2 coeffs", + nops(fn_eqnset union deriv_eqnset), nops(coeff_set) + end if; + subs_eqnset := map(proc(eqn::(set(name) = procedure)) + 'DERIV'(op(lhs(eqn))) = rhs(eqn) + end proc, deriv_set); + subs(subs_eqnset, coeff_eqns); + eval(%); + subs(%, fn(op(coord_list))) +end proc + +> +################################################################################ +> +# +# This function takes as input an interpolating polynomial, expresses +# it as a linear combination of the data values, and returns the coefficeints +# of that form. +# +# Arguments: +# interpolant = The interpolating polynomial (an algebraic expression +# in the coordinates and the data values). +# posn_list = The same list of data positions used in the interpolant. +# +# Results: +# This function returns the coefficients, as a list of equations of the +# form COEFF(...) = value , where each value is a polynomial in the +# coordinates. The order of the list matches that of posn_list. +# +> coeffs_as_lc_of_data := +> proc( +> interpolant::algebraic, +> posn_list::list(list(numeric)) +> ) +> local data_list, interpolant_as_lc_of_data; +> +# interpolant as a linear combination of the data values +> data_list := [ seq( 'DATA'(op(posn)) , posn=posn_list ) ]; +> interpolant_as_lc_of_data := collect(interpolant, data_list); +> +# coefficients of the data values in the linear combination +> return map( +> proc(posn::list(numeric)) +> coeff(interpolant_as_lc_of_data, DATA(op(posn))); +> 'COEFF'(op(posn)) = %; +> end proc +> , +> posn_list +> ); +> end proc; +coeffs_as_lc_of_data := proc( +interpolant::algebraic, posn_list::list(list(numeric))) +local data_list, interpolant_as_lc_of_data; + data_list := [seq('DATA'(op(posn)), posn = posn_list)]; + interpolant_as_lc_of_data := collect(interpolant, data_list); + return map(proc(posn::list(numeric)) + coeff(interpolant_as_lc_of_data, DATA(op(posn))); + 'COEFF'(op(posn)) = % + end proc, posn_list) +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function prints C expressions for the coefficients of an +# interpolating polynomial. (The polynomial is expressed as linear +# combinations of the data values with coefficients which are +# RATIONAL(p,q) calls.) +# +# Arguments: +# coeff_list = A list of the coefficients, as returned from +# coeffs_as_lc_of_data() . +# coeff_name_prefix = A prefix string for the coefficient names. +# temp_name_type = The C type to be used for Maple-introduced temporary +# names, eg. "double". +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_coeffs__lc_of_data := +> proc( coeff_list::list(specfunc(numeric,COEFF) = algebraic), +> coeff_name_prefix::string, +> temp_name_type::string, +> file_name::string ) +> global `codegen/C/function/informed`; +> local coeff_list2, cmpt_list, temp_name_list; +> +# convert LHS of each equation from a COEFF() call (eg COEFF(-1,+1)) +# to a Maple/C variable name (eg coeff_I_m1_p1) +> coeff_list2 := map( +> proc(coeff_eqn::specfunc(numeric,COEFF) = algebraic) +> local posn; +> posn := [op(lhs(coeff_eqn))]; +> coeff_name(posn,coeff_name_prefix); +> convert(%, name); # codegen[C] wants LHS +> # to be an actual Maple *name* +> % = fix_rationals(rhs(coeff_eqn)); +> end proc +> , +> coeff_list +> ); +> +# +# generate the C code +# +> +# tell codegen[C] not to warn about unknown RATIONAL() and DATA() "fn calls" +# via undocumented :( global table +> `codegen/C/function/informed`['RATIONAL'] := true; +> `codegen/C/function/informed`['DATA'] := true; +> +> ftruncate(file_name); +> +# optimized computation sequence for all the coefficients +# (may use local variables t0,t1,t2,...) +> cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; +> +# list of the t0,t1,t2,... local variables +> temp_name_list := nonmatching_names(map(lhs,cmpt_list), coeff_name_prefix); +> +# declare the t0,t1,t2,... local variables (if there are any) +> if (nops(temp_name_list) > 0) +> then print_name_list_dcl(%, temp_name_type, file_name); +> fi; +> +# now print the optimized computation sequence +> codegen[C](cmpt_list, filename=file_name); +> +> fclose(file_name); +> +> NULL; +> end proc; +print_coeffs__lc_of_data := proc( +coeff_list::list(specfunc(numeric, COEFF) = algebraic), +coeff_name_prefix::string, temp_name_type::string, file_name::string) +local coeff_list2, cmpt_list, temp_name_list; +global `codegen/C/function/informed`; + coeff_list2 := map(proc( + coeff_eqn::(specfunc(numeric, COEFF) = algebraic)) + local posn; + posn := [op(lhs(coeff_eqn))]; + coeff_name(posn, coeff_name_prefix); + convert(%, name); + % = fix_rationals(rhs(coeff_eqn)) + end proc, coeff_list); + `codegen/C/function/informed`['RATIONAL'] := true; + `codegen/C/function/informed`['DATA'] := true; + ftruncate(file_name); + cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; + temp_name_list := + nonmatching_names(map(lhs, cmpt_list), coeff_name_prefix); + if 0 < nops(temp_name_list) then + print_name_list_dcl(%, temp_name_type, file_name) + end if; + codegen[C](cmpt_list, filename = file_name); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C expression to assign the data-value +# variables, eg +# data->data_m1_p1 = DATA(-1,1); +# +# Arguments: +# posn_list = The same list of positions as was used to compute the +# interpolating polynomial. +# data_var_name_prefix = A prefix string for the data variable names. +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_fetch_data := +> proc( +> posn_list::list(list(numeric)), +> data_var_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> map( +> proc(posn::list(numeric)) +> fprintf(file_name, +> "%s = %a;\n", +> data_var_name(posn,data_var_name_prefix), +> DATA(op(posn))); +> end proc +> , +> posn_list +> ); +> fclose(file_name); +> +> NULL; +> end proc; +print_fetch_data := proc(posn_list::list(list(numeric)), +data_var_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + fprintf(file_name, "%s = %a;\n", + data_var_name(posn, data_var_name_prefix), DATA(op(posn))) + end proc, posn_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C expression to store the interpolation +# coefficients in COEFF(...) expressions, eg +# COEFF(1,-1) = factor * coeffs->coeff_p1_m1; +# +# Arguments: +# posn_list = The list of positions in the molecule. +# coeff_name_prefix = A prefix string for the coefficient names, +# eg "factor * coeffs->coeff_" +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_store_coeffs := +> proc( +> posn_list::list(list(numeric)), +> coeff_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> map( +> proc(posn::list(numeric)) +> fprintf(file_name, +> "%a = %s;\n", +> 'COEFF'(op(posn)), +> coeff_name(posn,coeff_name_prefix)); +> end proc +> , +> posn_list +> ); +> fclose(file_name); +> +> NULL; +> end proc; +print_store_coeffs := proc(posn_list::list(list(numeric)), +coeff_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + fprintf(file_name, "%a = %s;\n", 'COEFF'(op(posn)), + coeff_name(posn, coeff_name_prefix)) + end proc, posn_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a C expression to evaluate a molecule, i.e. +# to compute the molecule as a linear combination of the data values. +# +# Arguments: +# posn_list = The list of positions in the molecule. +# coeff_name_prefix = A prefix string for the coefficient names. +# data_var_name_prefix = A prefix string for the data variable names. +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_evaluate_molecule := +> proc( +> posn_list::list(list(numeric)), +> coeff_name_prefix::string, +> data_var_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> +# list of "coeff*data_var" terms +> map( +> proc(posn::list(numeric)) +> sprintf("%s*%s", +> coeff_name(posn,coeff_name_prefix), +> data_var_name(posn,data_var_name_prefix)); +> end proc +> , +> posn_list +> ); +> +> ListTools[Join](%, "\n + "); +> cat(op(%)); +> fprintf(file_name, " %s;\n", %); +> +> fclose(file_name); +> +> NULL; +> end proc; +print_evaluate_molecule := proc(posn_list::list(list(numeric)), +coeff_name_prefix::string, data_var_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + sprintf("%s*%s", coeff_name(posn, coeff_name_prefix), + data_var_name(posn, data_var_name_prefix)) + end proc, posn_list); + ListTools[Join](%, "\n + "); + cat(op(%)); + fprintf(file_name, " %s;\n", %); + fclose(file_name); + NULL +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes the name of the coefficient of the data at a +# given [m] position, i.e. it encapsulates our naming convention for this. +# +# Arguments: +# posn = (in) The [m] coordinates. +# name_prefix = A prefix string for the coefficient name. +# +# Results: +# The function returns the coefficient, as a Maple string. +# +> coeff_name := +> proc(posn::list(numeric), name_prefix::string) +> cat(name_prefix, sprint_numeric_list(posn)); +> end proc; +coeff_name := proc(posn::list(numeric), name_prefix::string) + cat(name_prefix, sprint_numeric_list(posn)) +end proc + +> +################################################################################ +> +# +# This function computes the name of the variable in which the C code +# will store the input data at a given [m] position, i.e. it encapsulates +# our naming convention for this. +# +# Arguments: +# posn = (in) The [m] coordinates. +# name_prefix = A prefix string for the variable name. +# +# Results: +# The function returns the variable name, as a Maple string. +# +> data_var_name := +> proc(posn::list(numeric), name_prefix::string) +> cat(name_prefix, sprint_numeric_list(posn)); +> end proc; +data_var_name := proc(posn::list(numeric), name_prefix::string) + cat(name_prefix, sprint_numeric_list(posn)) +end proc + +# Maple code to compute lists of point positions in hypercube-shaped molecules +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/common/cube_posns.maple,v 1.3 2002/08/20 16:56:41 jthorn Exp $ +> +################################################################################ +> +# +# 1D interpolation points +# +> posn_list_1d_size2 := hypercube_points([ 0], [+1]); + posn_list_1d_size2 := [[0], [1]] + +> posn_list_1d_size3 := hypercube_points([-1], [+1]); + posn_list_1d_size3 := [[-1], [0], [1]] + +> posn_list_1d_size4 := hypercube_points([-1], [+2]); + posn_list_1d_size4 := [[-1], [0], [1], [2]] + +> posn_list_1d_size5 := hypercube_points([-2], [+2]); + posn_list_1d_size5 := [[-2], [-1], [0], [1], [2]] + +> posn_list_1d_size6 := hypercube_points([-2], [+3]); + posn_list_1d_size6 := [[-2], [-1], [0], [1], [2], [3]] + +> posn_list_1d_size7 := hypercube_points([-3], [+3]); + posn_list_1d_size7 := [[-3], [-2], [-1], [0], [1], [2], [3]] + +> +################################################################################ +> +# +# 2D interpolation points (Fortran ordering) +# +> posn_list_2d_size2 := map(ListTools[Reverse], +> hypercube_points([ 0, 0], [+1,+1])); + posn_list_2d_size2 := [[0, 0], [1, 0], [0, 1], [1, 1]] + +> posn_list_2d_size3 := map(ListTools[Reverse], +> hypercube_points([-1,-1], [+1,+1])); +posn_list_2d_size3 := [[-1, -1], [0, -1], [1, -1], [-1, 0], [0, 0], [1, 0], + + [-1, 1], [0, 1], [1, 1]] + +> posn_list_2d_size4 := map(ListTools[Reverse], +> hypercube_points([-1,-1], [+2,+2])); +posn_list_2d_size4 := [[-1, -1], [0, -1], [1, -1], [2, -1], [-1, 0], [0, 0], + + [1, 0], [2, 0], [-1, 1], [0, 1], [1, 1], [2, 1], [-1, 2], [0, 2], [1, 2], + + [2, 2]] + +> posn_list_2d_size5 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+2,+2])); +posn_list_2d_size5 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [-2, -1], + + [-1, -1], [0, -1], [1, -1], [2, -1], [-2, 0], [-1, 0], [0, 0], [1, 0], + + [2, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], [-2, 2], [-1, 2], [0, 2], + + [1, 2], [2, 2]] + +> posn_list_2d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+3,+3])); +posn_list_2d_size6 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [3, -2], + + [-2, -1], [-1, -1], [0, -1], [1, -1], [2, -1], [3, -1], [-2, 0], [-1, 0], + + [0, 0], [1, 0], [2, 0], [3, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], + + [3, 1], [-2, 2], [-1, 2], [0, 2], [1, 2], [2, 2], [3, 2], [-2, 3], [-1, 3], + + [0, 3], [1, 3], [2, 3], [3, 3]] + +> +################################################################################ +> +# +# 3D interpolation points (Fortran ordering) +# +> posn_list_3d_size2 := map(ListTools[Reverse], +> hypercube_points([ 0, 0, 0], [+1,+1,+1])); +posn_list_3d_size2 := [[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], + + [1, 0, 1], [0, 1, 1], [1, 1, 1]] + +> posn_list_3d_size3 := map(ListTools[Reverse], +> hypercube_points([-1,-1,-1], [+1,+1,+1])); +posn_list_3d_size3 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [-1, 0, -1], + + [0, 0, -1], [1, 0, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], [-1, -1, 0], + + [0, -1, 0], [1, -1, 0], [-1, 0, 0], [0, 0, 0], [1, 0, 0], [-1, 1, 0], + + [0, 1, 0], [1, 1, 0], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [-1, 0, 1], + + [0, 0, 1], [1, 0, 1], [-1, 1, 1], [0, 1, 1], [1, 1, 1]] + +> posn_list_3d_size4 := map(ListTools[Reverse], +> hypercube_points([-1,-1,-1], [+2,+2,+2])); +posn_list_3d_size4 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [2, -1, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [-1, 1, -1], [0, 1, -1], + + [1, 1, -1], [2, 1, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-1, 0, 0], [0, 0, 0], + + [1, 0, 0], [2, 0, 0], [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [-1, -1, 1], [0, -1, 1], + + [1, -1, 1], [2, -1, 1], [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [-1, 2, 1], [0, 2, 1], + + [1, 2, 1], [2, 2, 1], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-1, 1, 2], [0, 1, 2], + + [1, 1, 2], [2, 1, 2], [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2]] + +> posn_list_3d_size5 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+2,+2,+2])); +posn_list_3d_size5 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], [1, -1, -2], + + [2, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], [1, 0, -2], [2, 0, -2], + + [-2, 1, -2], [-1, 1, -2], [0, 1, -2], [1, 1, -2], [2, 1, -2], [-2, 2, -2], + + [-1, 2, -2], [0, 2, -2], [1, 2, -2], [2, 2, -2], [-2, -2, -1], [-1, -2, -1], + + [0, -2, -1], [1, -2, -1], [2, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [-2, 0, -1], [-1, 0, -1], [0, 0, -1], + + [1, 0, -1], [2, 0, -1], [-2, 1, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], + + [2, 1, -1], [-2, 2, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], + + [-2, -2, 0], [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-2, 0, 0], [-1, 0, 0], + + [0, 0, 0], [1, 0, 0], [2, 0, 0], [-2, 1, 0], [-1, 1, 0], [0, 1, 0], + + [1, 1, 0], [2, 1, 0], [-2, 2, 0], [-1, 2, 0], [0, 2, 0], [1, 2, 0], + + [2, 2, 0], [-2, -2, 1], [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], + + [-2, -1, 1], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [-2, 1, 1], [-1, 1, 1], + + [0, 1, 1], [1, 1, 1], [2, 1, 1], [-2, 2, 1], [-1, 2, 1], [0, 2, 1], + + [1, 2, 1], [2, 2, 1], [-2, -2, 2], [-1, -2, 2], [0, -2, 2], [1, -2, 2], + + [2, -2, 2], [-2, -1, 2], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], + + [-2, 0, 2], [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [-2, 2, 2], [-1, 2, 2], + + [0, 2, 2], [1, 2, 2], [2, 2, 2]] + +> posn_list_3d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+3,+3,+3])); +posn_list_3d_size6 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [3, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], + + [1, -1, -2], [2, -1, -2], [3, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], + + [1, 0, -2], [2, 0, -2], [3, 0, -2], [-2, 1, -2], [-1, 1, -2], [0, 1, -2], + + [1, 1, -2], [2, 1, -2], [3, 1, -2], [-2, 2, -2], [-1, 2, -2], [0, 2, -2], + + [1, 2, -2], [2, 2, -2], [3, 2, -2], [-2, 3, -2], [-1, 3, -2], [0, 3, -2], + + [1, 3, -2], [2, 3, -2], [3, 3, -2], [-2, -2, -1], [-1, -2, -1], [0, -2, -1], + + [1, -2, -1], [2, -2, -1], [3, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [3, -1, -1], [-2, 0, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [3, 0, -1], [-2, 1, -1], + + [-1, 1, -1], [0, 1, -1], [1, 1, -1], [2, 1, -1], [3, 1, -1], [-2, 2, -1], + + [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], [3, 2, -1], [-2, 3, -1], + + [-1, 3, -1], [0, 3, -1], [1, 3, -1], [2, 3, -1], [3, 3, -1], [-2, -2, 0], + + [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [3, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [3, -1, 0], [-2, 0, 0], + + [-1, 0, 0], [0, 0, 0], [1, 0, 0], [2, 0, 0], [3, 0, 0], [-2, 1, 0], + + [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [3, 1, 0], [-2, 2, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [3, 2, 0], [-2, 3, 0], + + [-1, 3, 0], [0, 3, 0], [1, 3, 0], [2, 3, 0], [3, 3, 0], [-2, -2, 1], + + [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], [3, -2, 1], [-2, -1, 1], + + [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [3, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [3, 0, 1], [-2, 1, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [3, 1, 1], [-2, 2, 1], + + [-1, 2, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [3, 2, 1], [-2, 3, 1], + + [-1, 3, 1], [0, 3, 1], [1, 3, 1], [2, 3, 1], [3, 3, 1], [-2, -2, 2], + + [-1, -2, 2], [0, -2, 2], [1, -2, 2], [2, -2, 2], [3, -2, 2], [-2, -1, 2], + + [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], [3, -1, 2], [-2, 0, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [3, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [3, 1, 2], [-2, 2, 2], + + [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2], [3, 2, 2], [-2, 3, 2], + + [-1, 3, 2], [0, 3, 2], [1, 3, 2], [2, 3, 2], [3, 3, 2], [-2, -2, 3], + + [-1, -2, 3], [0, -2, 3], [1, -2, 3], [2, -2, 3], [3, -2, 3], [-2, -1, 3], + + [-1, -1, 3], [0, -1, 3], [1, -1, 3], [2, -1, 3], [3, -1, 3], [-2, 0, 3], + + [-1, 0, 3], [0, 0, 3], [1, 0, 3], [2, 0, 3], [3, 0, 3], [-2, 1, 3], + + [-1, 1, 3], [0, 1, 3], [1, 1, 3], [2, 1, 3], [3, 1, 3], [-2, 2, 3], + + [-1, 2, 3], [0, 2, 3], [1, 2, 3], [2, 2, 3], [3, 2, 3], [-2, 3, 3], + + [-1, 3, 3], [0, 3, 3], [1, 3, 3], [2, 3, 3], [3, 3, 3]] + +# Maple code to define Lagrange interpolating functions/coords/coeffs +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple,v 1.2 2002/08/20 16:31:24 jthorn Exp $ +> +################################################################################ +> +# +# 1-D interpolating functions +# +> +> fn_1d_order1 := +> proc(x) +> + c0 + c1*x +> end proc; + fn_1d_order1 := proc(x) c0 + c1*x end proc + +> +> fn_1d_order2 := +> proc(x) +> + c0 + c1*x + c2*x^2 +> end proc; + fn_1d_order2 := proc(x) c0 + c1*x + c2*x^2 end proc + +> +> fn_1d_order3 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 +> end proc; + fn_1d_order3 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 end proc + +> +> fn_1d_order4 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 +> end; + fn_1d_order4 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 end proc + +> +> fn_1d_order5 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 +> end; + fn_1d_order5 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 end proc + +> +> fn_1d_order6 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 +> end; +fn_1d_order6 := + + proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 end proc + +> +######################################## +> +# coordinates for 1-D interpolating functions +> coords_list_1d := [x]; + coords_list_1d := [x] + +> +######################################## +> +# +# coefficients in 1-D interpolating functions +# +> +> coeffs_list_1d_order1 := [c0, c1]; + coeffs_list_1d_order1 := [c0, c1] + +> coeffs_list_1d_order2 := [c0, c1, c2]; + coeffs_list_1d_order2 := [c0, c1, c2] + +> coeffs_list_1d_order3 := [c0, c1, c2, c3]; + coeffs_list_1d_order3 := [c0, c1, c2, c3] + +> coeffs_list_1d_order4 := [c0, c1, c2, c3, c4]; + coeffs_list_1d_order4 := [c0, c1, c2, c3, c4] + +> coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5]; + coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5] + +> coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6]; + coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6] + +> +################################################################################ +> +# +# 2-D interpolating functions +# +> +> fn_2d_order1 := +> proc(x,y) +> + c01*y +> + c00 + c10*x +> end proc; + fn_2d_order1 := proc(x, y) c01*y + c00 + c10*x end proc + +> +> fn_2d_order2 := +> proc(x,y) +> + c02*y^2 +> + c01*y + c11*x*y +> + c00 + c10*x + c20*x^2 +> end proc; +fn_2d_order2 := + + proc(x, y) c02*y^2 + c01*y + c11*x*y + c00 + c10*x + c20*x^2 end proc + +> +> fn_2d_order3 := +> proc(x,y) +> + c03*y^3 +> + c02*y^2 + c12*x*y^2 +> + c01*y + c11*x*y + c21*x^2*y +> + c00 + c10*x + c20*x^2 + c30*x^3 +> end proc; +fn_2d_order3 := proc(x, y) + c03*y^3 + c02*y^2 + c12*x*y^2 + c01*y + c11*x*y + c21*x^2*y + c00 + + c10*x + c20*x^2 + c30*x^3 +end proc + +> +> fn_2d_order4 := +> proc(x,y) +> + c04*y^4 +> + c03*y^3 + c13*x*y^3 +> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 +> + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +> + c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 +> end; +fn_2d_order4 := proc(x, y) + c04*y^4 + c03*y^3 + c13*x*y^3 + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + c00 + c10*x + c20*x^2 + + c30*x^3 + c40*x^4 +end proc + +> +######################################## +> +# coordinates for 2-D interpolating functions +> coords_list_2d := [x,y]; + coords_list_2d := [x, y] + +> +######################################## +> +# +# coefficients in 2-D interpolating functions +# +> +> coeffs_list_2d_order1 := [ +> c01, +> c00, c10 +> ]; + coeffs_list_2d_order1 := [c01, c00, c10] + +> coeffs_list_2d_order2 := [ +> c02, +> c01, c11, +> c00, c10, c20 +> ]; + coeffs_list_2d_order2 := [c02, c01, c11, c00, c10, c20] + +> coeffs_list_2d_order3 := [ +> c03, +> c02, c12, +> c01, c11, c21, +> c00, c10, c20, c30 +> ]; + coeffs_list_2d_order3 := [c03, c02, c12, c01, c11, c21, c00, c10, c20, c30] + +> coeffs_list_2d_order4 := [ +> c04, +> c03, c13, +> c02, c12, c22, +> c01, c11, c21, c31, +> c00, c10, c20, c30, c40 +> ]; +coeffs_list_2d_order4 := + + [c04, c03, c13, c02, c12, c22, c01, c11, c21, c31, c00, c10, c20, c30, c40] + +> +################################################################################ +> +# +# 3-D interpolating functions +# +> +> fn_3d_order1 := +> proc(x,y,z) +# z^0 ----------- +> + c010*y +> + c000 + c100*x +# z^1 ----------- +> + c001*z +> end proc; + fn_3d_order1 := proc(x, y, z) c010*y + c000 + c100*x + c001*z end proc + +> +> fn_3d_order2 := +> proc(x,y,z) +# z^0 -------------------------- +> + c020*y^2 +> + c010*y + c110*x*y +> + c000 + c100*x + c200*x^2 +# z^1 -------------------------- +> + c011*y*z +> + c001*z + c101*x*z +# z^2 -------------------------- +> + c002*z^2 +> end proc; +fn_3d_order2 := proc(x, y, z) + c020*y^2 + c010*y + c110*x*y + c000 + c100*x + c200*x^2 + c011*y*z + + c001*z + c101*x*z + c002*z^2 +end proc + +> +> fn_3d_order3 := +> proc(x,y,z) +# z^0 ------------------------------------------- +> + c030*y^3 +> + c020*y^2 + c120*x*y^2 +> + c010*y + c110*x*y + c210*x^2*y +> + c000 + c100*x + c200*x^2 + c300*x^3 +# z^1 ------------------------------------------- +> + c021*y^2*z +> + c011*y *z + c111*x*y*z +> + c001 *z + c101*x *z + c201*x^2*z +# z^2 ------------------------------------------- +> + c012*y*z^2 +> + c002 *z^2 + c102*x*z^2 +# z^3 ------------------------------------------- +> + c003 *z^3 +> end proc; +fn_3d_order3 := proc(x, y, z) + c030*y^3 + c020*y^2 + c120*x*y^2 + c010*y + c110*x*y + c210*x^2*y + + c000 + c100*x + c200*x^2 + c300*x^3 + c021*y^2*z + c011*y*z + + c111*x*y*z + c001*z + c101*x*z + c201*x^2*z + c012*y*z^2 + c002*z^2 + + c102*x*z^2 + c003*z^3 +end proc + +> +> fn_3d_order4 := +> proc(x,y,z) +# z^0 -------------------------------------------------------- +> + c040*y^4 +> + c030*y^3 + c130*x*y^3 +> + c020*y^2 + c120*x*y^2 + c220*x^2*y^2 +> + c010*y + c110*x*y + c210*x^2*y + c310*x^3*y +> + c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 +# z^1 ------------------------------------------- +> + c031*y^3*z +> + c021*y^2*z + c121*x*y^2*z +> + c011*y *z + c111*x*y *z + c211*x^2*y*z +> + c001 *z + c101*x *z + c201*x^2 *z + c301*x^3*z +# z^2 ------------------------------------------- +> + c022*y^2*z^2 +> + c012*y *z^2 + c112*x*y*z^2 +> + c002 *z^2 + c102*x *z^2 + c202*x^2*z^2 +# z^3 ------------------------------------------- +> + c013*y *z^3 +> + c003 *z^3 + c103*x *z^3 +# z^4 ------------------------------------------- +> + c004 *z^4 +> end; +fn_3d_order4 := proc(x, y, z) + c102*x*z^2 + c012*y*z^2 + c111*x*y*z + c121*x*y^2*z + c211*x^2*y*z + + c112*x*y*z^2 + c010*y + c110*x*y + c011*y*z + c101*x*z + c120*x*y^2 + + c210*x^2*y + c021*y^2*z + c201*x^2*z + c130*x*y^3 + c220*x^2*y^2 + + c310*x^3*y + c031*y^3*z + c301*x^3*z + c022*y^2*z^2 + c202*x^2*z^2 + + c013*y*z^3 + c103*x*z^3 + c000 + c100*x + c001*z + c020*y^2 + + c200*x^2 + c002*z^2 + c030*y^3 + c300*x^3 + c003*z^3 + c040*y^4 + + c400*x^4 + c004*z^4 +end proc + +> +######################################## +> +# coordinates for 3-D interpolating functions +> coords_list_3d := [x,y,z]; + coords_list_3d := [x, y, z] + +> +######################################## +> +# +# coefficients in 3-D interpolating functions +# +> +> coeffs_list_3d_order1 := [ +> # z^0 ----- +> c010, +> c000, c100, +> # z^1 ----- +> c001 +> ]; + coeffs_list_3d_order1 := [c010, c000, c100, c001] + +> coeffs_list_3d_order2 := [ +> # z^0 ----------- +> c020, +> c010, c110, +> c000, c100, c200, +> # z^1 ----------- +> c011, +> c001, c101, +> # z^2 ----------- +> c002 +> ]; +coeffs_list_3d_order2 := + + [c020, c010, c110, c000, c100, c200, c011, c001, c101, c002] + +> coeffs_list_3d_order3 := [ +> # z^0 ---------------- +> c030, +> c020, c120, +> c010, c110, c210, +> c000, c100, c200, c300, +> # z^1 ---------------- +> c021, +> c011, c111, +> c001, c101, c201, +> # z^2 ---------------- +> c012, +> c002, c102, +> # z^3 ---------------- +> c003 +> ]; +coeffs_list_3d_order3 := [c030, c020, c120, c010, c110, c210, c000, c100, c200, + + c300, c021, c011, c111, c001, c101, c201, c012, c002, c102, c003] + +> coeffs_list_3d_order4 := [ +> # z^0 ----------------------- +> c040, +> c030, c130, +> c020, c120, c220, +> c010, c110, c210, c310, +> c000, c100, c200, c300, c400, +> # z^1 ----------------------- +> c031, +> c021, c121, +> c011, c111, c211, +> c001, c101, c201, c301, +> # z^2 ----------------------- +> c022, +> c012, c112, +> c002, c102, c202, +> # z^3 ----------------------- +> c013, +> c003, c103, +> # z^4 ----------------------- +> c004 +> ]; +coeffs_list_3d_order4 := [c040, c030, c130, c020, c120, c220, c010, c110, c210, + + c310, c000, c100, c200, c300, c400, c031, c021, c121, c011, c111, c211, + + c001, c101, c201, c301, c022, c012, c112, c002, c102, c202, c013, c003, + + c103, c004] + +> +################################################################################ +# 1d.maple -- compute Lagrange interpolation coefficients in 1-D +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/1d.maple,v 1.2 2002/08/20 16:31:22 jthorn Exp $ +> +################################################################################ +> +# +# 1d, cube, order=1, smoothing=0 (size=2) +# +> +# interpolating polynomial +> interp_1d_cube_order1_smooth0 +> := Lagrange_polynomial_interpolant(fn_1d_order1, coeffs_list_1d_order1, +> coords_list_1d, posn_list_1d_size2); + interp_1d_cube_order1_smooth0 := DATA(0) + (DATA(1) - DATA(0)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_1d_size2); + [COEFF(0) = 1 - x, COEFF(1) = x] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "1d.coeffs/1d.cube.order1.smooth0/coeffs-I.compute.c"); +bytes used=1000428, alloc=917336, time=0.07 +> +# d/dx +> simplify( diff(interp_1d_cube_order1_smooth0,x) ); + DATA(1) - DATA(0) + +> coeffs_as_lc_of_data(%, posn_list_1d_size2); + [COEFF(0) = -1, COEFF(1) = 1] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "1d.coeffs/1d.cube.order1.smooth0/coeffs-dx.compute.c"); +> +################################################################################ +> +# +# 1d, cube, order=2, smoothing=0 (size=3) +# +> +# interpolating polynomial +> interp_1d_cube_order2_smooth0 +> := Lagrange_polynomial_interpolant(fn_1d_order2, coeffs_list_1d_order2, +> coords_list_1d, posn_list_1d_size3); +interp_1d_cube_order2_smooth0 := DATA(0) + (- 1/2 DATA(-1) + 1/2 DATA(1)) x + + 2 + + (1/2 DATA(-1) + 1/2 DATA(1) - DATA(0)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_1d_size3); + 2 2 2 + [COEFF(-1) = - 1/2 x + 1/2 x , COEFF(0) = 1 - x , COEFF(1) = 1/2 x + 1/2 x ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "1d.coeffs/1d.cube.order2.smooth0/coeffs-I.compute.c"); +> +# d/dx +> simplify( diff(interp_1d_cube_order2_smooth0,x) ); + - 1/2 DATA(-1) + 1/2 DATA(1) + x DATA(-1) + DATA(1) x - 2 x DATA(0) + +> coeffs_as_lc_of_data(%, posn_list_1d_size3); + [COEFF(-1) = x - 1/2, COEFF(0) = -2 x, COEFF(1) = 1/2 + x] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "1d.coeffs/1d.cube.order2.smooth0/coeffs-dx.compute.c"); +> +# d^2/dx^2 +> simplify( diff(interp_1d_cube_order2_smooth0,x,x) ); +bytes used=2000692, alloc=1441528, time=0.11 + DATA(-1) + DATA(1) - 2 DATA(0) + +> coeffs_as_lc_of_data(%, posn_list_1d_size3); + [COEFF(-1) = 1, COEFF(0) = -2, COEFF(1) = 1] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "1d.coeffs/1d.cube.order2.smooth0/coeffs-dxx.compute.c"); +> +################################################################################ +> +# +# 1d, cube, order=3, smoothing=0 (size=4) +# +> +# interpolating polynomial +> interp_1d_cube_order3_smooth0 +> := Lagrange_polynomial_interpolant(fn_1d_order3, coeffs_list_1d_order3, +> coords_list_1d, posn_list_1d_size4); +interp_1d_cube_order3_smooth0 := DATA(0) + + + (- 1/2 DATA(0) - 1/3 DATA(-1) + DATA(1) - 1/6 DATA(2)) x + + 2 + + (1/2 DATA(-1) + 1/2 DATA(1) - DATA(0)) x + + 3 + + (1/2 DATA(0) - 1/6 DATA(-1) - 1/2 DATA(1) + 1/6 DATA(2)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_1d_size4); + 2 3 2 3 +[COEFF(-1) = - 1/3 x + 1/2 x - 1/6 x , COEFF(0) = 1 - 1/2 x - x + 1/2 x , + + 2 3 3 + COEFF(1) = x + 1/2 x - 1/2 x , COEFF(2) = - 1/6 x + 1/6 x ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "1d.coeffs/1d.cube.order3.smooth0/coeffs-I.compute.c"); +> +# d/dx +> simplify( diff(interp_1d_cube_order3_smooth0,x) ); +bytes used=3001280, alloc=1769148, time=0.17 +- 1/2 DATA(0) - 1/3 DATA(-1) + DATA(1) - 1/6 DATA(2) + x DATA(-1) + x DATA(1) + + 2 2 2 + - 2 x DATA(0) + 3/2 x DATA(0) - 1/2 x DATA(-1) - 3/2 x DATA(1) + + 2 + + 1/2 x DATA(2) + +> coeffs_as_lc_of_data(%, posn_list_1d_size4); + 2 2 +[COEFF(-1) = x - 1/2 x - 1/3, COEFF(0) = - 1/2 - 2 x + 3/2 x , + + 2 2 + COEFF(1) = x + 1 - 3/2 x , COEFF(2) = 1/2 x - 1/6] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "1d.coeffs/1d.cube.order3.smooth0/coeffs-dx.compute.c"); +> +# d^2/dx^2 +> simplify( diff(interp_1d_cube_order3_smooth0,x,x) ); +DATA(-1) + DATA(1) - 2 DATA(0) + 3 x DATA(0) - x DATA(-1) - 3 x DATA(1) + + + x DATA(2) + +> coeffs_as_lc_of_data(%, posn_list_1d_size4); + [COEFF(-1) = 1 - x, COEFF(0) = -2 + 3 x, COEFF(1) = 1 - 3 x, COEFF(2) = x] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "1d.coeffs/1d.cube.order3.smooth0/coeffs-dxx.compute.c"); +> +################################################################################ +> +# +# 1d, cube, order=4, smoothing=0 (size=5) +# +> +# interpolating polynomial +> interp_1d_cube_order4_smooth0 +> := Lagrange_polynomial_interpolant(fn_1d_order4, coeffs_list_1d_order4, +> coords_list_1d, posn_list_1d_size5); +bytes used=4001452, alloc=1834672, time=0.27 +interp_1d_cube_order4_smooth0 := DATA(0) + + + (- 1/12 DATA(2) + 1/12 DATA(-2) - 2/3 DATA(-1) + 2/3 DATA(1)) x + + + (2/3 DATA(1) - 5/4 DATA(0) - 1/24 DATA(-2) + 2/3 DATA(-1) - 1/24 DATA(2)) + + 2 3 + x + (1/12 DATA(2) - 1/12 DATA(-2) + 1/6 DATA(-1) - 1/6 DATA(1)) x + + + (- 1/6 DATA(1) + 1/4 DATA(0) + 1/24 DATA(-2) - 1/6 DATA(-1) + 1/24 DATA(2)) + + 4 + x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_1d_size5); + 2 3 4 +[COEFF(-2) = 1/12 x - 1/24 x - 1/12 x + 1/24 x , + + 2 3 4 + COEFF(-1) = - 2/3 x + 2/3 x + 1/6 x - 1/6 x , + + 2 4 + COEFF(0) = - 5/4 x + 1 + 1/4 x , + + 3 2 4 + COEFF(1) = - 1/6 x + 2/3 x + 2/3 x - 1/6 x , + + 3 2 4 + COEFF(2) = 1/12 x - 1/12 x - 1/24 x + 1/24 x ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "1d.coeffs/1d.cube.order4.smooth0/coeffs-I.compute.c"); +bytes used=5001648, alloc=1900196, time=0.34 +> +# d/dx +> simplify( diff(interp_1d_cube_order4_smooth0,x) ); +- 1/12 DATA(2) + 1/12 DATA(-2) - 2/3 DATA(-1) + 2/3 DATA(1) + 4/3 x DATA(1) + + - 5/2 x DATA(0) - 1/12 x DATA(-2) + 4/3 x DATA(-1) - 1/12 x DATA(2) + + 2 2 2 2 + + 1/4 x DATA(2) - 1/4 x DATA(-2) + 1/2 x DATA(-1) - 1/2 x DATA(1) + + 3 3 3 3 + - 2/3 x DATA(1) + x DATA(0) + 1/6 x DATA(-2) - 2/3 x DATA(-1) + + 3 + + 1/6 x DATA(2) + +> coeffs_as_lc_of_data(%, posn_list_1d_size5); + 2 3 +[COEFF(-2) = - 1/12 x - 1/4 x + 1/12 + 1/6 x , + + 3 2 3 + COEFF(-1) = - 2/3 + 4/3 x - 2/3 x + 1/2 x , COEFF(0) = x - 5/2 x, + + 3 2 + COEFF(1) = 4/3 x - 2/3 x - 1/2 x + 2/3, + + 2 3 + COEFF(2) = - 1/12 - 1/12 x + 1/4 x + 1/6 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "1d.coeffs/1d.cube.order4.smooth0/coeffs-dx.compute.c"); +bytes used=6001824, alloc=1900196, time=0.42 +> +# d^2/dx^2 +> simplify( diff(interp_1d_cube_order4_smooth0,x,x) ); +4/3 DATA(1) - 5/2 DATA(0) - 1/12 DATA(-2) + 4/3 DATA(-1) - 1/12 DATA(2) + + 2 + + 1/2 x DATA(2) - 1/2 x DATA(-2) + x DATA(-1) - x DATA(1) - 2 x DATA(1) + + 2 2 2 2 + + 3 x DATA(0) + 1/2 x DATA(-2) - 2 x DATA(-1) + 1/2 x DATA(2) + +> coeffs_as_lc_of_data(%, posn_list_1d_size5); + 2 2 +[COEFF(-2) = - 1/12 - 1/2 x + 1/2 x , COEFF(-1) = 4/3 - 2 x + x, + + 2 2 + COEFF(0) = - 5/2 + 3 x , COEFF(1) = -x + 4/3 - 2 x , + + 2 + COEFF(2) = - 1/12 + 1/2 x + 1/2 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "1d.coeffs/1d.cube.order4.smooth0/coeffs-dxx.compute.c"); +bytes used=7002056, alloc=1900196, time=0.50 +> +################################################################################ +> +# +# 1d, cube, order=5, smoothing=0 (size=6) +# +> +# interpolating polynomial +> interp_1d_cube_order5_smooth0 +> := Lagrange_polynomial_interpolant(fn_1d_order5, coeffs_list_1d_order5, +> coords_list_1d, posn_list_1d_size6); +bytes used=8002252, alloc=1900196, time=0.55 +interp_1d_cube_order5_smooth0 := DATA(0) + (- 1/2 DATA(-1) - 1/4 DATA(2) + + - 1/3 DATA(0) + 1/20 DATA(-2) + DATA(1) + 1/30 DATA(3)) x + + + (2/3 DATA(1) - 5/4 DATA(0) - 1/24 DATA(-2) + 2/3 DATA(-1) - 1/24 DATA(2)) + + 2 + x + (- 1/24 DATA(-1) + 7/24 DATA(2) + 5/12 DATA(0) - 1/24 DATA(-2) + + 3 + - 7/12 DATA(1) - 1/24 DATA(3)) x + + + (- 1/6 DATA(1) + 1/4 DATA(0) + 1/24 DATA(-2) - 1/6 DATA(-1) + 1/24 DATA(2)) + + 4 + x + (1/24 DATA(-1) - 1/24 DATA(2) - 1/12 DATA(0) - 1/120 DATA(-2) + + 5 + + 1/12 DATA(1) + 1/120 DATA(3)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_1d_size6); + 2 3 4 5 +[COEFF(-2) = 1/20 x - 1/24 x - 1/24 x + 1/24 x - 1/120 x , + + 2 3 4 5 + COEFF(-1) = - 1/2 x + 2/3 x - 1/24 x - 1/6 x + 1/24 x , + + 2 3 4 5 + COEFF(0) = 1 - 1/3 x - 5/4 x + 5/12 x + 1/4 x - 1/12 x , + + 2 3 4 5 + COEFF(1) = x + 2/3 x - 7/12 x - 1/6 x + 1/12 x , + + 3 4 2 5 + COEFF(2) = - 1/4 x + 7/24 x + 1/24 x - 1/24 x - 1/24 x , + + 5 3 + COEFF(3) = 1/30 x + 1/120 x - 1/24 x ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "1d.coeffs/1d.cube.order5.smooth0/coeffs-I.compute.c"); +bytes used=9004240, alloc=1965720, time=0.63 +> +# d/dx +> simplify( diff(interp_1d_cube_order5_smooth0,x) ); +- 1/3 DATA(0) + DATA(1) - 1/4 DATA(2) - 1/2 DATA(-1) + 1/30 DATA(3) + + 4 4 4 4 + + 5/24 x DATA(-1) - 5/24 x DATA(2) - 5/12 x DATA(0) - 1/24 x DATA(-2) + + 4 4 + + 5/12 x DATA(1) + 1/24 x DATA(3) + 4/3 x DATA(1) - 5/2 x DATA(0) + + 2 + - 1/12 x DATA(-2) + 4/3 x DATA(-1) - 1/12 x DATA(2) - 1/8 x DATA(-1) + + 2 2 2 2 + + 7/8 x DATA(2) + 5/4 x DATA(0) - 1/8 x DATA(-2) - 7/4 x DATA(1) + + 2 3 3 3 + - 1/8 x DATA(3) - 2/3 x DATA(1) + x DATA(0) + 1/6 x DATA(-2) + + 3 3 + - 2/3 x DATA(-1) + 1/6 x DATA(2) + 1/20 DATA(-2) + +> coeffs_as_lc_of_data(%, posn_list_1d_size6); + 4 3 2 +[COEFF(-2) = - 1/12 x - 1/24 x + 1/6 x + 1/20 - 1/8 x , + + 3 2 4 + COEFF(-1) = - 2/3 x - 1/8 x - 1/2 + 5/24 x + 4/3 x, + + 3 4 2 + COEFF(0) = - 5/2 x + x - 5/12 x - 1/3 + 5/4 x , + + 4 3 2 + COEFF(1) = 5/12 x - 2/3 x + 4/3 x - 7/4 x + 1, + + 3 2 4 + COEFF(2) = 1/6 x - 1/12 x + 7/8 x - 1/4 - 5/24 x , + + 4 2 + COEFF(3) = 1/24 x - 1/8 x + 1/30] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "1d.coeffs/1d.cube.order5.smooth0/coeffs-dx.compute.c"); +bytes used=10004620, alloc=1965720, time=0.72 +bytes used=11005012, alloc=1965720, time=0.81 +> +# d^2/dx^2 +> simplify( diff(interp_1d_cube_order5_smooth0,x,x) ); +4/3 DATA(1) - 5/2 DATA(0) - 1/12 DATA(-2) + 4/3 DATA(-1) - 1/12 DATA(2) + + - 1/4 x DATA(-1) + 7/4 x DATA(2) + 5/2 x DATA(0) - 1/4 x DATA(-2) + + 2 2 + - 7/2 x DATA(1) - 1/4 x DATA(3) - 2 x DATA(1) + 3 x DATA(0) + + 2 2 2 3 + + 1/2 x DATA(-2) - 2 x DATA(-1) + 1/2 x DATA(2) + 5/6 x DATA(-1) + + 3 3 3 3 + - 5/6 x DATA(2) - 5/3 x DATA(0) - 1/6 x DATA(-2) + 5/3 x DATA(1) + + 3 + + 1/6 x DATA(3) + +> coeffs_as_lc_of_data(%, posn_list_1d_size6); + 2 3 +[COEFF(-2) = - 1/12 + 1/2 x - 1/6 x - 1/4 x, + + 2 3 + COEFF(-1) = -2 x + 5/6 x + 4/3 - 1/4 x, + + 3 2 + COEFF(0) = - 5/3 x + 5/2 x + 3 x - 5/2, + + 2 3 + COEFF(1) = 4/3 - 2 x + 5/3 x - 7/2 x, + + 3 2 3 + COEFF(2) = - 5/6 x + 1/2 x - 1/12 + 7/4 x, COEFF(3) = - 1/4 x + 1/6 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "1d.coeffs/1d.cube.order5.smooth0/coeffs-dxx.compute.c"); +bytes used=12005228, alloc=1965720, time=0.88 +> +################################################################################ +> +# +# 1d, cube, order=6, smoothing=0 (size=7) +# +> +# interpolating polynomial +> interp_1d_cube_order6_smooth0 +> := Lagrange_polynomial_interpolant(fn_1d_order6, coeffs_list_1d_order6, +> coords_list_1d, posn_list_1d_size7); +bytes used=13005380, alloc=1965720, time=0.95 +interp_1d_cube_order6_smooth0 := DATA(0) + (3/20 DATA(-2) + 3/4 DATA(1) + + / + + 1/60 DATA(3) - 1/60 DATA(-3) - 3/4 DATA(-1) - 3/20 DATA(2)) x + | + \ + + 1/180 DATA(-3) + 3/4 DATA(1) - 3/40 DATA(-2) + 1/180 DATA(3) + 3/4 DATA(-1) + + 49 \ 2 / 13 + - -- DATA(0) - 3/40 DATA(2)| x + |- 1/6 DATA(-2) - -- DATA(1) + 36 / \ 48 + + 13 \ 3 / + - 1/48 DATA(3) + 1/48 DATA(-3) + -- DATA(-1) + 1/6 DATA(2)| x + | + 48 / \ + + 13 13 + - 1/144 DATA(-3) - -- DATA(1) + 1/12 DATA(-2) - 1/144 DATA(3) - -- DATA(-1) + 48 48 + + \ 4 + + 7/18 DATA(0) + 1/12 DATA(2)| x + (1/60 DATA(-2) + 1/48 DATA(1) + / + + 5 + + 1/240 DATA(3) - 1/240 DATA(-3) - 1/48 DATA(-1) - 1/60 DATA(2)) x + ( + + 1/720 DATA(-3) + 1/48 DATA(1) - 1/120 DATA(-2) + 1/720 DATA(3) + + 6 + + 1/48 DATA(-1) - 1/36 DATA(0) - 1/120 DATA(2)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_1d_size7); + 2 3 4 5 6 +[COEFF(-3) = - 1/60 x + 1/180 x + 1/48 x - 1/144 x - 1/240 x + 1/720 x , + + 2 3 4 5 6 + COEFF(-2) = 3/20 x - 3/40 x - 1/6 x + 1/12 x + 1/60 x - 1/120 x , + + 2 13 3 13 4 5 6 + COEFF(-1) = - 3/4 x + 3/4 x + -- x - -- x - 1/48 x + 1/48 x , + 48 48 + + 4 49 2 6 + COEFF(0) = 7/18 x - -- x + 1 - 1/36 x , + 36 + + 13 3 2 5 6 13 4 + COEFF(1) = - -- x + 3/4 x + 3/4 x + 1/48 x + 1/48 x - -- x , + 48 48 + + 3 2 5 6 4 + COEFF(2) = 1/6 x - 3/20 x - 3/40 x - 1/60 x - 1/120 x + 1/12 x , + + 3 2 5 6 4 + COEFF(3) = - 1/48 x + 1/60 x + 1/180 x + 1/240 x + 1/720 x - 1/144 x ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "1d.coeffs/1d.cube.order6.smooth0/coeffs-I.compute.c"); +bytes used=14005568, alloc=1965720, time=1.03 +bytes used=15005724, alloc=1965720, time=1.12 +> +# d/dx +> simplify( diff(interp_1d_cube_order6_smooth0,x) ); +3/4 DATA(1) - 3/20 DATA(2) - 3/4 DATA(-1) - 1/60 DATA(-3) + 1/60 DATA(3) + + 13 3 3 3 3 + - -- x DATA(1) - 1/36 x DATA(-3) + 1/3 x DATA(-2) - 1/36 x DATA(3) + 12 + + 13 3 3 3 4 + - -- x DATA(-1) + 14/9 x DATA(0) + 1/3 x DATA(2) + 1/12 x DATA(-2) + 12 + + 4 4 4 4 + + 5/48 x DATA(1) + 1/48 x DATA(3) - 1/48 x DATA(-3) - 5/48 x DATA(-1) + + 4 5 5 5 + - 1/12 x DATA(2) + 1/120 x DATA(-3) + 1/8 x DATA(1) - 1/20 x DATA(-2) + + 5 5 5 5 + + 1/120 x DATA(3) + 1/8 x DATA(-1) - 1/6 x DATA(0) - 1/20 x DATA(2) + + + 1/90 x DATA(-3) + 3/2 x DATA(1) - 3/20 x DATA(-2) + 1/90 x DATA(3) + + 49 2 13 2 + + 3/2 x DATA(-1) - -- x DATA(0) - 1/2 x DATA(-2) - -- x DATA(1) + 18 16 + + 2 2 13 2 2 + - 1/16 x DATA(3) + 1/16 x DATA(-3) + -- x DATA(-1) + 1/2 x DATA(2) + 16 + + - 3/20 x DATA(2) + 3/20 DATA(-2) + +> coeffs_as_lc_of_data(%, posn_list_1d_size7); +bytes used=16005892, alloc=1965720, time=1.20 + 3 5 4 2 +[COEFF(-3) = - 1/36 x + 1/120 x - 1/48 x - 1/60 + 1/90 x + 1/16 x , + + 2 5 3 4 + COEFF(-2) = - 1/2 x - 1/20 x + 1/3 x + 3/20 - 3/20 x + 1/12 x , + + 4 13 2 13 3 5 + COEFF(-1) = 3/2 x - 5/48 x + -- x - -- x + 1/8 x - 3/4, + 16 12 + + 5 3 49 + COEFF(0) = - 1/6 x + 14/9 x - -- x, + 18 + + 4 5 13 2 13 3 + COEFF(1) = 5/48 x + 3/4 + 1/8 x + 3/2 x - -- x - -- x , + 16 12 + + 5 3 2 4 + COEFF(2) = - 1/20 x + 1/3 x + 1/2 x - 1/12 x - 3/20 - 3/20 x, + + 3 2 4 5 + COEFF(3) = - 1/36 x + 1/90 x - 1/16 x + 1/60 + 1/48 x + 1/120 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "1d.coeffs/1d.cube.order6.smooth0/coeffs-dx.compute.c"); +bytes used=17006200, alloc=1965720, time=1.29 +> +# d^2/dx^2 +> simplify( diff(interp_1d_cube_order6_smooth0,x,x) ); +bytes used=18007928, alloc=1965720, time=1.39 + 49 +- -- DATA(0) + 3/2 DATA(1) - 3/20 DATA(2) + 3/2 DATA(-1) + 1/90 DATA(-3) + 18 + + 3 3 3 + + 1/90 DATA(3) + 5/12 x DATA(1) - 1/12 x DATA(-3) + 1/3 x DATA(-2) + + 3 3 3 4 + + 1/12 x DATA(3) - 5/12 x DATA(-1) - 1/3 x DATA(2) - 1/4 x DATA(-2) + + 4 4 4 4 + + 5/8 x DATA(1) + 1/24 x DATA(3) + 1/24 x DATA(-3) + 5/8 x DATA(-1) + + 4 + - 1/4 x DATA(2) + 1/8 x DATA(-3) - 13/8 x DATA(1) - x DATA(-2) + + 2 2 + - 1/8 x DATA(3) + 13/8 x DATA(-1) + x DATA(-2) - 13/4 x DATA(1) + + 2 2 2 2 + - 1/12 x DATA(3) - 1/12 x DATA(-3) - 13/4 x DATA(-1) + x DATA(2) + + 2 4 + + x DATA(2) - 3/20 DATA(-2) + 14/3 x DATA(0) - 5/6 x DATA(0) + +> coeffs_as_lc_of_data(%, posn_list_1d_size7); + 2 4 3 +[COEFF(-3) = - 1/12 x + 1/24 x + 1/90 + 1/8 x - 1/12 x , + + 4 2 3 + COEFF(-2) = -x - 1/4 x - 3/20 + x + 1/3 x , + + 4 3 2 + COEFF(-1) = 5/8 x + 3/2 - 5/12 x + 13/8 x - 13/4 x , + + 2 4 49 + COEFF(0) = 14/3 x - 5/6 x - --, + 18 + + 2 3 4 + COEFF(1) = - 13/4 x + 5/12 x - 13/8 x + 5/8 x + 3/2, + + 2 4 3 + COEFF(2) = - 3/20 + x + x - 1/4 x - 1/3 x , + + 4 2 3 + COEFF(3) = 1/90 + 1/24 x - 1/8 x - 1/12 x + 1/12 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "1d.coeffs/1d.cube.order6.smooth0/coeffs-dxx.compute.c"); +bytes used=19008116, alloc=1965720, time=1.47 +> +################################################################################ +> quit +bytes used=19802260, alloc=1965720, time=1.53 diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.maple b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.maple new file mode 100644 index 0000000..cdf1494 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/1d.maple @@ -0,0 +1,166 @@ +# 1d.maple -- compute Lagrange interpolation coefficients in 1-D +# $Header$ + +################################################################################ + +# +# 1d, cube, order=1, smoothing=0 (size=2) +# + +# interpolating polynomial +interp_1d_cube_order1_smooth0 + := Lagrange_polynomial_interpolant(fn_1d_order1, coeffs_list_1d_order1, + coords_list_1d, posn_list_1d_size2); + +# I +coeffs_as_lc_of_data(%, posn_list_1d_size2); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "1d.coeffs/1d.cube.order1.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_1d_cube_order1_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size2); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "1d.coeffs/1d.cube.order1.smooth0/coeffs-dx.compute.c"); + +################################################################################ + +# +# 1d, cube, order=2, smoothing=0 (size=3) +# + +# interpolating polynomial +interp_1d_cube_order2_smooth0 + := Lagrange_polynomial_interpolant(fn_1d_order2, coeffs_list_1d_order2, + coords_list_1d, posn_list_1d_size3); + +# I +coeffs_as_lc_of_data(%, posn_list_1d_size3); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "1d.coeffs/1d.cube.order2.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_1d_cube_order2_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size3); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "1d.coeffs/1d.cube.order2.smooth0/coeffs-dx.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_1d_cube_order2_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size3); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "1d.coeffs/1d.cube.order2.smooth0/coeffs-dxx.compute.c"); + +################################################################################ + +# +# 1d, cube, order=3, smoothing=0 (size=4) +# + +# interpolating polynomial +interp_1d_cube_order3_smooth0 + := Lagrange_polynomial_interpolant(fn_1d_order3, coeffs_list_1d_order3, + coords_list_1d, posn_list_1d_size4); + +# I +coeffs_as_lc_of_data(%, posn_list_1d_size4); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "1d.coeffs/1d.cube.order3.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_1d_cube_order3_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size4); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "1d.coeffs/1d.cube.order3.smooth0/coeffs-dx.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_1d_cube_order3_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size4); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "1d.coeffs/1d.cube.order3.smooth0/coeffs-dxx.compute.c"); + +################################################################################ + +# +# 1d, cube, order=4, smoothing=0 (size=5) +# + +# interpolating polynomial +interp_1d_cube_order4_smooth0 + := Lagrange_polynomial_interpolant(fn_1d_order4, coeffs_list_1d_order4, + coords_list_1d, posn_list_1d_size5); + +# I +coeffs_as_lc_of_data(%, posn_list_1d_size5); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "1d.coeffs/1d.cube.order4.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_1d_cube_order4_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size5); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "1d.coeffs/1d.cube.order4.smooth0/coeffs-dx.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_1d_cube_order4_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size5); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "1d.coeffs/1d.cube.order4.smooth0/coeffs-dxx.compute.c"); + +################################################################################ + +# +# 1d, cube, order=5, smoothing=0 (size=6) +# + +# interpolating polynomial +interp_1d_cube_order5_smooth0 + := Lagrange_polynomial_interpolant(fn_1d_order5, coeffs_list_1d_order5, + coords_list_1d, posn_list_1d_size6); + +# I +coeffs_as_lc_of_data(%, posn_list_1d_size6); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "1d.coeffs/1d.cube.order5.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_1d_cube_order5_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size6); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "1d.coeffs/1d.cube.order5.smooth0/coeffs-dx.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_1d_cube_order5_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size6); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "1d.coeffs/1d.cube.order5.smooth0/coeffs-dxx.compute.c"); + +################################################################################ + +# +# 1d, cube, order=6, smoothing=0 (size=7) +# + +# interpolating polynomial +interp_1d_cube_order6_smooth0 + := Lagrange_polynomial_interpolant(fn_1d_order6, coeffs_list_1d_order6, + coords_list_1d, posn_list_1d_size7); + +# I +coeffs_as_lc_of_data(%, posn_list_1d_size7); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "1d.coeffs/1d.cube.order6.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_1d_cube_order6_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size7); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "1d.coeffs/1d.cube.order6.smooth0/coeffs-dx.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_1d_cube_order6_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size7); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "1d.coeffs/1d.cube.order6.smooth0/coeffs-dxx.compute.c"); + +################################################################################ diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..cda1593 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c @@ -0,0 +1,18 @@ +fp t7; +fp t6; +fp t5; +fp t4; +fp t3; +fp t2; +fp t1; + t7 = RATIONAL(-1.0,2.0); + t6 = RATIONAL(1.0,4.0); + t5 = RATIONAL(1.0,2.0); + t4 = t7*y; + t3 = t7*x; + t2 = t5*x; + t1 = t5*y; + coeffs_I->coeff_0_0 = RATIONAL(3.0,4.0)+t4+t3; + coeffs_I->coeff_p1_0 = t6+t4+t2; + coeffs_I->coeff_0_p1 = t3+t6+t1; + coeffs_I->coeff_p1_p1 = t1+RATIONAL(-1.0,4.0)+t2; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..cf806b2 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c @@ -0,0 +1,8 @@ +fp t9; +fp t8; + t9 = RATIONAL(-1.0,2.0); + t8 = RATIONAL(1.0,2.0); + coeffs_dx->coeff_0_0 = t9; + coeffs_dx->coeff_p1_0 = t8; + coeffs_dx->coeff_0_p1 = t9; + coeffs_dx->coeff_p1_p1 = t8; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..e5bb3a5 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c @@ -0,0 +1,8 @@ +fp t11; +fp t10; + t11 = RATIONAL(-1.0,2.0); + t10 = RATIONAL(1.0,2.0); + coeffs_dy->coeff_0_0 = t11; + coeffs_dy->coeff_p1_0 = t11; + coeffs_dy->coeff_0_p1 = t10; + coeffs_dy->coeff_p1_p1 = t10; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..c5e53d7 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c @@ -0,0 +1,53 @@ +fp t27; +fp t25; +fp t18; +fp t28; +fp t21; +fp t34; +fp t33; +fp t22; +fp t17; +fp t23; +fp t32; +fp t15; +fp t31; +fp t14; +fp t30; +fp t24; +fp t20; +fp t29; +fp t19; +fp t16; +fp t13; +fp t12; + t27 = x*x; + t25 = RATIONAL(1.0,6.0); + t18 = t25*t27; + t28 = y*y; + t21 = t25*t28; + t34 = t18+t21+RATIONAL(-1.0,9.0); + t33 = x*y; + t22 = RATIONAL(-1.0,3.0); + t17 = t22*t27; + t23 = RATIONAL(2.0,9.0); + t32 = t17+t21+t23; + t15 = t22*t28; + t31 = t15+t18+t23; + t14 = t25*y; + t30 = t14+t34; + t24 = RATIONAL(-1.0,6.0); + t20 = t24*y; + t29 = t20+t34; + t19 = t24*x; + t16 = t25*x; + t13 = RATIONAL(-1.0,4.0)*t33; + t12 = RATIONAL(1.0,4.0)*t33; + coeffs_I->coeff_m1_m1 = t19+t12+t29; + coeffs_I->coeff_0_m1 = t20+t32; + coeffs_I->coeff_p1_m1 = t13+t16+t29; + coeffs_I->coeff_m1_0 = t19+t31; + coeffs_I->coeff_0_0 = t15+t17+RATIONAL(5.0,9.0); + coeffs_I->coeff_p1_0 = t16+t31; + coeffs_I->coeff_m1_p1 = t19+t13+t30; + coeffs_I->coeff_0_p1 = t14+t32; + coeffs_I->coeff_p1_p1 = t16+t12+t30; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..7c930d7 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c @@ -0,0 +1,21 @@ +fp t36; +fp t42; +fp t41; +fp t40; +fp t39; +fp t37; + t36 = RATIONAL(1.0,3.0)*x; + t42 = RATIONAL(1.0,4.0)*y+t36; + t41 = t36+RATIONAL(-1.0,4.0)*y; + t40 = RATIONAL(1.0,6.0); + t39 = RATIONAL(-1.0,6.0); + t37 = RATIONAL(-2.0,3.0)*x; + coeffs_dx->coeff_m1_m1 = t39+t42; + coeffs_dx->coeff_0_m1 = t37; + coeffs_dx->coeff_p1_m1 = t40+t41; + coeffs_dx->coeff_m1_0 = t36+t39; + coeffs_dx->coeff_0_0 = t37; + coeffs_dx->coeff_p1_0 = t36+t40; + coeffs_dx->coeff_m1_p1 = t39+t41; + coeffs_dx->coeff_0_p1 = t37; + coeffs_dx->coeff_p1_p1 = t40+t42; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..0831674 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,13 @@ +fp t52; +fp t51; + t52 = RATIONAL(-2.0,3.0); + t51 = RATIONAL(1.0,3.0); + coeffs_dxx->coeff_m1_m1 = t51; + coeffs_dxx->coeff_0_m1 = t52; + coeffs_dxx->coeff_p1_m1 = t51; + coeffs_dxx->coeff_m1_0 = t51; + coeffs_dxx->coeff_0_0 = t52; + coeffs_dxx->coeff_p1_0 = t51; + coeffs_dxx->coeff_m1_p1 = t51; + coeffs_dxx->coeff_0_p1 = t52; + coeffs_dxx->coeff_p1_p1 = t51; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c new file mode 100644 index 0000000..f886764 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c @@ -0,0 +1,15 @@ +fp t55; +fp t54; +fp t53; + t55 = RATIONAL(0.0,1.0); + t54 = RATIONAL(1.0,4.0); + t53 = RATIONAL(-1.0,4.0); + coeffs_dxy->coeff_m1_m1 = t54; + coeffs_dxy->coeff_0_m1 = t55; + coeffs_dxy->coeff_p1_m1 = t53; + coeffs_dxy->coeff_m1_0 = t55; + coeffs_dxy->coeff_0_0 = t55; + coeffs_dxy->coeff_p1_0 = t55; + coeffs_dxy->coeff_m1_p1 = t53; + coeffs_dxy->coeff_0_p1 = t55; + coeffs_dxy->coeff_p1_p1 = t54; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..f18c6ef --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c @@ -0,0 +1,21 @@ +fp t46; +fp t50; +fp t49; +fp t48; +fp t47; +fp t43; + t46 = RATIONAL(1.0,3.0)*y; + t50 = RATIONAL(-1.0,4.0)*x+t46; + t49 = RATIONAL(1.0,4.0)*x+t46; + t48 = RATIONAL(1.0,6.0); + t47 = RATIONAL(-1.0,6.0); + t43 = RATIONAL(-2.0,3.0)*y; + coeffs_dy->coeff_m1_m1 = t47+t49; + coeffs_dy->coeff_0_m1 = t47+t46; + coeffs_dy->coeff_p1_m1 = t47+t50; + coeffs_dy->coeff_m1_0 = t43; + coeffs_dy->coeff_0_0 = t43; + coeffs_dy->coeff_p1_0 = t43; + coeffs_dy->coeff_m1_p1 = t48+t50; + coeffs_dy->coeff_0_p1 = t46+t48; + coeffs_dy->coeff_p1_p1 = t48+t49; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c new file mode 100644 index 0000000..47224b8 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c @@ -0,0 +1,13 @@ +fp t57; +fp t56; + t57 = RATIONAL(-2.0,3.0); + t56 = RATIONAL(1.0,3.0); + coeffs_dyy->coeff_m1_m1 = t56; + coeffs_dyy->coeff_0_m1 = t56; + coeffs_dyy->coeff_p1_m1 = t56; + coeffs_dyy->coeff_m1_0 = t57; + coeffs_dyy->coeff_0_0 = t57; + coeffs_dyy->coeff_p1_0 = t57; + coeffs_dyy->coeff_m1_p1 = t56; + coeffs_dyy->coeff_0_p1 = t56; + coeffs_dyy->coeff_p1_p1 = t56; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..ac11344 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c @@ -0,0 +1,190 @@ +fp t158; +fp t131; +fp t157; +fp t132; +fp t156; +fp t117; +fp t63; +fp t129; +fp t130; +fp t84; +fp t155; +fp t154; +fp t128; +fp t87; +fp t153; +fp t126; +fp t64; +fp t133; +fp t116; +fp t76; +fp t152; +fp t67; +fp t86; +fp t151; +fp t123; +fp t71; +fp t150; +fp t124; +fp t65; +fp t149; +fp t125; +fp t81; +fp t148; +fp t85; +fp t147; +fp t146; +fp t112; +fp t69; +fp t145; +fp t110; +fp t66; +fp t144; +fp t143; +fp t70; +fp t120; +fp t142; +fp t122; +fp t141; +fp t140; +fp t101; +fp t139; +fp t138; +fp t137; +fp t136; +fp t127; +fp t121; +fp t118; +fp t115; +fp t113; +fp t109; +fp t107; +fp t106; +fp t104; +fp t103; +fp t102; +fp t100; +fp t98; +fp t97; +fp t96; +fp t95; +fp t94; +fp t93; +fp t92; +fp t91; +fp t90; +fp t89; +fp t88; +fp t83; +fp t82; +fp t80; +fp t78; +fp t77; +fp t74; +fp t73; + t158 = x*y; + t131 = x*x; + t157 = t131*y; + t132 = y*y; + t156 = x*t132; + t117 = RATIONAL(1.0,40.0); + t63 = t117*t157; + t129 = RATIONAL(1.0,8.0); + t130 = t132*y; + t84 = t129*t130; + t155 = t63+t84; + t154 = RATIONAL(-1.0,100.0)*t158+RATIONAL(37.0,200.0); + t128 = RATIONAL(-1.0,8.0); + t87 = t128*t130; + t153 = t63+t87; + t126 = RATIONAL(-3.0,40.0); + t64 = t126*t156; + t133 = t131*x; + t116 = RATIONAL(1.0,24.0); + t76 = t116*t133; + t152 = t64+t76; + t67 = t117*t156; + t86 = t129*t133; + t151 = t67+t86; + t123 = RATIONAL(-1.0,40.0); + t71 = t123*t156; + t150 = t71+t86; + t124 = RATIONAL(3.0,40.0); + t65 = t124*t156; + t149 = t65+t76; + t125 = RATIONAL(-1.0,24.0); + t81 = t125*t133; + t148 = t64+t81; + t85 = t128*t133; + t147 = t71+t85; + t146 = t65+t81; + t112 = RATIONAL(13.0,80.0); + t69 = t126*t157; + t145 = t69+t112*t131; + t110 = RATIONAL(11.0,80.0); + t66 = t123*t157; + t144 = t66+t110*t131; + t143 = t67+t85; + t70 = t124*t157; + t120 = RATIONAL(7.0,80.0); + t142 = t70+t120*t131; + t122 = RATIONAL(-1.0,50.0); + t141 = t122+RATIONAL(-13.0,100.0)*t158; + t140 = RATIONAL(2.0,25.0)*t158+RATIONAL(-2.0,25.0); + t101 = RATIONAL(-17.0,200.0); + t139 = RATIONAL(-9.0,100.0)*t158+t101; + t138 = RATIONAL(11.0,50.0)+t122*t158; + t137 = RATIONAL(7.0,100.0)*t158+RATIONAL(13.0,100.0); + t136 = t131+t132; + t127 = RATIONAL(1.0,80.0); + t121 = RATIONAL(9.0,80.0); + t118 = RATIONAL(-1.0,80.0); + t115 = RATIONAL(3.0,80.0); + t113 = RATIONAL(-17.0,80.0); + t109 = RATIONAL(-23.0,80.0); + t107 = RATIONAL(-19.0,80.0); + t106 = RATIONAL(-63.0,400.0); + t104 = RATIONAL(-49.0,400.0); + t103 = RATIONAL(-31.0,400.0); + t102 = RATIONAL(69.0,400.0); + t100 = RATIONAL(-57.0,400.0); + t98 = RATIONAL(117.0,400.0); + t97 = RATIONAL(43.0,1200.0); + t96 = RATIONAL(103.0,400.0); + t95 = RATIONAL(111.0,400.0); + t94 = RATIONAL(37.0,1200.0); + t93 = RATIONAL(89.0,1200.0); + t92 = RATIONAL(-109.0,1200.0); + t91 = RATIONAL(-223.0,1200.0); + t90 = RATIONAL(-157.0,1200.0); + t89 = RATIONAL(-131.0,1200.0); + t88 = RATIONAL(-149.0,1200.0); + t83 = t121*t131; + t82 = t125*t130; + t80 = t121*t132; + t78 = t116*t130; + t77 = t120*t132; + t74 = t112*t132; + t73 = t110*t132; + coeffs_I->coeff_m1_m1 = t74+t82+t92*y+RATIONAL(-23.0,200.0)+(t92+RATIONAL +(6.0,25.0)*y)*x+t145+t148; + coeffs_I->coeff_0_m1 = t70+t91*y+t73+t103*x+t82+t109*t131+t138+t150; + coeffs_I->coeff_p1_m1 = t80+t82+t95*x+t90*y+t141+t142+t143; + coeffs_I->coeff_p2_m1 = t93*y+t89*x+t77+t82+t69+t115*t131+t139+t149; + coeffs_I->coeff_m1_0 = t109*t132+t84+t91*x+t103*y+t138+t144+t146; + coeffs_I->coeff_0_0 = RATIONAL(93.0,200.0)+t100*y+t136*RATIONAL(-21.0, +80.0)+(t100+RATIONAL(-1.0,25.0)*y)*x+t151+t155; + coeffs_I->coeff_p1_0 = t107*t132+t106*y+t83+t98*x+t147+t154+t155; + coeffs_I->coeff_p2_0 = t66+t113*t132+t127*t131+t84+t104*y+t97*x+t137+t152 +; + coeffs_I->coeff_m1_p1 = t95*y+t90*x+t77+t83+t141+t146+t153; + coeffs_I->coeff_0_p1 = t87+t106*x+t66+t80+t98*y+t107*t131+t151+t154; + coeffs_I->coeff_p1_p1 = t87+t73+t101+t96*y+(t96+RATIONAL(3.0,50.0)*y)*x+ +t144+t147; + coeffs_I->coeff_p2_p1 = t118*t131+t102*y+t74+t94*x+t140+t152+t153; + coeffs_I->coeff_m1_p2 = t93*x+t89*y+t115*t132+t78+t139+t142+t148; + coeffs_I->coeff_0_p2 = t97*y+t69+t127*t132+t113*t131+t78+t104*x+t137+t150 +; + coeffs_I->coeff_p1_p2 = t102*x+t94*y+t78+t118*t132+t140+t143+t145; + coeffs_I->coeff_p2_p2 = t70+t88*y+t78+RATIONAL(7.0,200.0)+t136*RATIONAL( +-3.0,80.0)+(t88+RATIONAL(-3.0,50.0)*y)*x+t149; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..0ea2d65 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c @@ -0,0 +1,97 @@ +fp t199; +fp t185; +fp t178; +fp t181; +fp t186; +fp t173; +fp t198; +fp t159; +fp t197; +fp t182; +fp t175; +fp t196; +fp t161; +fp t195; +fp t162; +fp t194; +fp t160; +fp t193; +fp t179; +fp t184; +fp t176; +fp t192; +fp t183; +fp t171; +fp t191; +fp t180; +fp t190; +fp t189; +fp t177; +fp t188; +fp t187; +fp t174; +fp t169; +fp t167; +fp t165; +fp t164; +fp t163; + t199 = x*y; + t185 = x*x; + t178 = RATIONAL(-3.0,8.0)*t185; + t181 = RATIONAL(1.0,40.0); + t186 = y*y; + t173 = t181*t186; + t198 = t178+t173; + t159 = RATIONAL(-3.0,20.0)*t199; + t197 = RATIONAL(13.0,40.0)*x+t159; + t182 = RATIONAL(-1.0,40.0); + t175 = t182*t186; + t196 = t178+t175; + t161 = RATIONAL(-1.0,20.0)*t199; + t195 = t161+RATIONAL(11.0,40.0)*x; + t162 = RATIONAL(3.0,20.0)*t199; + t194 = RATIONAL(7.0,40.0)*x+t162; + t160 = RATIONAL(1.0,20.0)*t199; + t193 = RATIONAL(9.0,40.0)*x+t160; + t179 = RATIONAL(-1.0,8.0)*t185; + t184 = RATIONAL(-3.0,40.0); + t176 = t184*t186; + t192 = t179+t176; + t183 = RATIONAL(3.0,40.0); + t171 = t183*t186; + t191 = t179+t171; + t180 = RATIONAL(3.0,8.0)*t185; + t190 = t180+t175; + t189 = t180+t173; + t177 = RATIONAL(1.0,8.0)*t185; + t188 = t171+t177; + t187 = t176+t177; + t174 = RATIONAL(-1.0,50.0)*y; + t169 = RATIONAL(2.0,25.0)*y; + t167 = RATIONAL(-9.0,100.0)*y; + t165 = RATIONAL(-1.0,100.0)*y; + t164 = RATIONAL(7.0,100.0)*y; + t163 = RATIONAL(-13.0,100.0)*y; + coeffs_dx->coeff_m1_m1 = RATIONAL(6.0,25.0)*y+RATIONAL(-109.0,1200.0)+ +t192+t197; + coeffs_dx->coeff_0_m1 = t162+t174+RATIONAL(-31.0,400.0)+RATIONAL(-23.0, +40.0)*x+t190; + coeffs_dx->coeff_p1_m1 = RATIONAL(111.0,400.0)+t163+t194+t198; + coeffs_dx->coeff_p2_m1 = t183*x+RATIONAL(-131.0,1200.0)+t167+t159+t188; + coeffs_dx->coeff_m1_0 = RATIONAL(-223.0,1200.0)+t174+t191+t195; + coeffs_dx->coeff_0_0 = RATIONAL(-1.0,25.0)*y+t160+RATIONAL(-21.0,40.0)*x+ +RATIONAL(-57.0,400.0)+t189; + coeffs_dx->coeff_p1_0 = t165+RATIONAL(117.0,400.0)+t193+t196; + coeffs_dx->coeff_p2_0 = t161+t181*x+RATIONAL(43.0,1200.0)+t164+t187; + coeffs_dx->coeff_m1_p1 = RATIONAL(-157.0,1200.0)+t163+t191+t193; + coeffs_dx->coeff_0_p1 = RATIONAL(-63.0,400.0)+t165+t161+RATIONAL(-19.0, +40.0)*x+t189; + coeffs_dx->coeff_p1_p1 = RATIONAL(103.0,400.0)+RATIONAL(3.0,50.0)*y+t195+ +t196; + coeffs_dx->coeff_p2_p1 = t160+t169+RATIONAL(37.0,1200.0)+t182*x+t187; + coeffs_dx->coeff_m1_p2 = RATIONAL(89.0,1200.0)+t167+t192+t194; + coeffs_dx->coeff_0_p2 = t159+t164+RATIONAL(-17.0,40.0)*x+RATIONAL(-49.0, +400.0)+t190; + coeffs_dx->coeff_p1_p2 = RATIONAL(69.0,400.0)+t169+t197+t198; + coeffs_dx->coeff_p2_p2 = RATIONAL(-149.0,1200.0)+t162+RATIONAL(-3.0,50.0) +*y+t184*x+t188; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..ba139bf --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,40 @@ +fp t244; +fp t256; +fp t242; +fp t255; +fp t241; +fp t254; +fp t243; +fp t253; +fp t248; +fp t247; +fp t246; +fp t245; + t244 = RATIONAL(-3.0,20.0)*y; + t256 = t244+RATIONAL(13.0,40.0); + t242 = RATIONAL(-1.0,20.0)*y; + t255 = t242+RATIONAL(11.0,40.0); + t241 = RATIONAL(1.0,20.0)*y; + t254 = t241+RATIONAL(9.0,40.0); + t243 = RATIONAL(3.0,20.0)*y; + t253 = t243+RATIONAL(7.0,40.0); + t248 = RATIONAL(-1.0,4.0)*x; + t247 = RATIONAL(1.0,4.0)*x; + t246 = RATIONAL(-3.0,4.0)*x; + t245 = RATIONAL(3.0,4.0)*x; + coeffs_dxx->coeff_m1_m1 = t248+t256; + coeffs_dxx->coeff_0_m1 = t245+t243+RATIONAL(-23.0,40.0); + coeffs_dxx->coeff_p1_m1 = t246+t253; + coeffs_dxx->coeff_p2_m1 = t244+RATIONAL(3.0,40.0)+t247; + coeffs_dxx->coeff_m1_0 = t248+t255; + coeffs_dxx->coeff_0_0 = RATIONAL(-21.0,40.0)+t241+t245; + coeffs_dxx->coeff_p1_0 = t246+t254; + coeffs_dxx->coeff_p2_0 = t247+t242+RATIONAL(1.0,40.0); + coeffs_dxx->coeff_m1_p1 = t248+t254; + coeffs_dxx->coeff_0_p1 = RATIONAL(-19.0,40.0)+t242+t245; + coeffs_dxx->coeff_p1_p1 = t246+t255; + coeffs_dxx->coeff_p2_p1 = RATIONAL(-1.0,40.0)+t241+t247; + coeffs_dxx->coeff_m1_p2 = t248+t253; + coeffs_dxx->coeff_0_p2 = t244+t245+RATIONAL(-17.0,40.0); + coeffs_dxx->coeff_p1_p2 = t246+t256; + coeffs_dxx->coeff_p2_p2 = RATIONAL(-3.0,40.0)+t247+t243; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c new file mode 100644 index 0000000..e9208a2 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c @@ -0,0 +1,52 @@ +fp t274; +fp t273; +fp t272; +fp t271; +fp t270; +fp t269; +fp t268; +fp t267; +fp t266; +fp t265; +fp t264; +fp t263; +fp t262; +fp t261; +fp t260; +fp t259; +fp t258; +fp t257; + t274 = RATIONAL(-3.0,20.0); + t273 = RATIONAL(3.0,20.0); + t272 = RATIONAL(2.0,25.0); + t271 = RATIONAL(-1.0,20.0); + t270 = RATIONAL(1.0,20.0); + t269 = RATIONAL(-1.0,50.0); + t268 = RATIONAL(-1.0,100.0); + t267 = RATIONAL(7.0,100.0); + t266 = RATIONAL(-9.0,100.0); + t265 = RATIONAL(-13.0,100.0); + t264 = t274*x; + t263 = t273*x; + t262 = t271*x; + t261 = t274*y; + t260 = t270*x; + t259 = t273*y; + t258 = t271*y; + t257 = t270*y; + coeffs_dxy->coeff_m1_m1 = t264+RATIONAL(6.0,25.0)+t261; + coeffs_dxy->coeff_0_m1 = t263+t269+t258; + coeffs_dxy->coeff_p1_m1 = t257+t265+t263; + coeffs_dxy->coeff_p2_m1 = t259+t264+t266; + coeffs_dxy->coeff_m1_0 = t259+t262+t269; + coeffs_dxy->coeff_0_0 = t260+RATIONAL(-1.0,25.0)+t257; + coeffs_dxy->coeff_p1_0 = t258+t268+t260; + coeffs_dxy->coeff_p2_0 = t261+t262+t267; + coeffs_dxy->coeff_m1_p1 = t259+t265+t260; + coeffs_dxy->coeff_0_p1 = t262+t257+t268; + coeffs_dxy->coeff_p1_p1 = t262+RATIONAL(3.0,50.0)+t258; + coeffs_dxy->coeff_p2_p1 = t261+t260+t272; + coeffs_dxy->coeff_m1_p2 = t266+t261+t263; + coeffs_dxy->coeff_0_p2 = t267+t258+t264; + coeffs_dxy->coeff_p1_p2 = t264+t257+t272; + coeffs_dxy->coeff_p2_p2 = t263+t259+RATIONAL(-3.0,50.0); diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..c12d9d1 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c @@ -0,0 +1,97 @@ +fp t240; +fp t227; +fp t219; +fp t226; +fp t222; +fp t211; +fp t239; +fp t201; +fp t238; +fp t223; +fp t213; +fp t237; +fp t200; +fp t236; +fp t203; +fp t235; +fp t202; +fp t234; +fp t224; +fp t216; +fp t221; +fp t233; +fp t225; +fp t217; +fp t232; +fp t218; +fp t231; +fp t230; +fp t220; +fp t229; +fp t228; +fp t215; +fp t210; +fp t207; +fp t206; +fp t205; +fp t204; + t240 = x*y; + t227 = y*y; + t219 = RATIONAL(-3.0,8.0)*t227; + t226 = x*x; + t222 = RATIONAL(1.0,40.0); + t211 = t222*t226; + t239 = t219+t211; + t201 = RATIONAL(1.0,20.0)*t240; + t238 = t201+RATIONAL(9.0,40.0)*y; + t223 = RATIONAL(-1.0,40.0); + t213 = t223*t226; + t237 = t219+t213; + t200 = RATIONAL(3.0,20.0)*t240; + t236 = t200+RATIONAL(7.0,40.0)*y; + t203 = RATIONAL(-3.0,20.0)*t240; + t235 = t203+RATIONAL(13.0,40.0)*y; + t202 = RATIONAL(-1.0,20.0)*t240; + t234 = t202+RATIONAL(11.0,40.0)*y; + t224 = RATIONAL(3.0,40.0); + t216 = t224*t226; + t221 = RATIONAL(-1.0,8.0)*t227; + t233 = t216+t221; + t225 = RATIONAL(-3.0,40.0); + t217 = t225*t226; + t232 = t217+t221; + t218 = RATIONAL(1.0,8.0)*t227; + t231 = t218+t217; + t230 = t216+t218; + t220 = RATIONAL(3.0,8.0)*t227; + t229 = t220+t213; + t228 = t220+t211; + t215 = RATIONAL(-1.0,50.0)*x; + t210 = RATIONAL(2.0,25.0)*x; + t207 = RATIONAL(-9.0,100.0)*x; + t206 = RATIONAL(-1.0,100.0)*x; + t205 = RATIONAL(7.0,100.0)*x; + t204 = RATIONAL(-13.0,100.0)*x; + coeffs_dy->coeff_m1_m1 = RATIONAL(6.0,25.0)*x+RATIONAL(-109.0,1200.0)+ +t232+t235; + coeffs_dy->coeff_0_m1 = t215+RATIONAL(-223.0,1200.0)+t233+t234; + coeffs_dy->coeff_p1_m1 = RATIONAL(-157.0,1200.0)+t204+t233+t238; + coeffs_dy->coeff_p2_m1 = t207+RATIONAL(89.0,1200.0)+t232+t236; + coeffs_dy->coeff_m1_0 = RATIONAL(-23.0,40.0)*y+RATIONAL(-31.0,400.0)+t200 ++t215+t229; + coeffs_dy->coeff_0_0 = RATIONAL(-21.0,40.0)*y+RATIONAL(-57.0,400.0)+ +RATIONAL(-1.0,25.0)*x+t201+t228; + coeffs_dy->coeff_p1_0 = t202+RATIONAL(-19.0,40.0)*y+RATIONAL(-63.0,400.0) ++t206+t228; + coeffs_dy->coeff_p2_0 = t203+RATIONAL(-49.0,400.0)+RATIONAL(-17.0,40.0)*y ++t205+t229; + coeffs_dy->coeff_m1_p1 = t204+RATIONAL(111.0,400.0)+t236+t239; + coeffs_dy->coeff_0_p1 = t206+RATIONAL(117.0,400.0)+t237+t238; + coeffs_dy->coeff_p1_p1 = RATIONAL(3.0,50.0)*x+RATIONAL(103.0,400.0)+t234+ +t237; + coeffs_dy->coeff_p2_p1 = t210+RATIONAL(69.0,400.0)+t235+t239; + coeffs_dy->coeff_m1_p2 = t207+t203+RATIONAL(-131.0,1200.0)+t224*y+t230; + coeffs_dy->coeff_0_p2 = t205+t202+t222*y+RATIONAL(43.0,1200.0)+t231; + coeffs_dy->coeff_p1_p2 = t201+RATIONAL(37.0,1200.0)+t223*y+t210+t231; + coeffs_dy->coeff_p2_p2 = t225*y+t200+RATIONAL(-3.0,50.0)*x+RATIONAL( +-149.0,1200.0)+t230; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c new file mode 100644 index 0000000..6bbdde7 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c @@ -0,0 +1,40 @@ +fp t276; +fp t290; +fp t277; +fp t289; +fp t278; +fp t288; +fp t275; +fp t287; +fp t282; +fp t281; +fp t280; +fp t279; + t276 = RATIONAL(-1.0,20.0)*x; + t290 = t276+RATIONAL(11.0,40.0); + t277 = RATIONAL(3.0,20.0)*x; + t289 = RATIONAL(7.0,40.0)+t277; + t278 = RATIONAL(-3.0,20.0)*x; + t288 = t278+RATIONAL(13.0,40.0); + t275 = RATIONAL(1.0,20.0)*x; + t287 = t275+RATIONAL(9.0,40.0); + t282 = RATIONAL(1.0,4.0)*y; + t281 = RATIONAL(-1.0,4.0)*y; + t280 = RATIONAL(3.0,4.0)*y; + t279 = RATIONAL(-3.0,4.0)*y; + coeffs_dyy->coeff_m1_m1 = t281+t288; + coeffs_dyy->coeff_0_m1 = t281+t290; + coeffs_dyy->coeff_p1_m1 = t281+t287; + coeffs_dyy->coeff_p2_m1 = t281+t289; + coeffs_dyy->coeff_m1_0 = t277+t280+RATIONAL(-23.0,40.0); + coeffs_dyy->coeff_0_0 = t280+t275+RATIONAL(-21.0,40.0); + coeffs_dyy->coeff_p1_0 = t280+RATIONAL(-19.0,40.0)+t276; + coeffs_dyy->coeff_p2_0 = RATIONAL(-17.0,40.0)+t280+t278; + coeffs_dyy->coeff_m1_p1 = t279+t289; + coeffs_dyy->coeff_0_p1 = t279+t287; + coeffs_dyy->coeff_p1_p1 = t279+t290; + coeffs_dyy->coeff_p2_p1 = t279+t288; + coeffs_dyy->coeff_m1_p2 = t278+t282+RATIONAL(3.0,40.0); + coeffs_dyy->coeff_0_p2 = t282+RATIONAL(1.0,40.0)+t276; + coeffs_dyy->coeff_p1_p2 = t275+t282+RATIONAL(-1.0,40.0); + coeffs_dyy->coeff_p2_p2 = t277+RATIONAL(-3.0,40.0)+t282; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..51bec8d --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c @@ -0,0 +1,239 @@ +fp t411; +fp t412; +fp t464; +fp t414; +fp t404; +fp t356; +fp t413; +fp t360; +fp t433; +fp t442; +fp t463; +fp t407; +fp t365; +fp t364; +fp t436; +fp t462; +fp t435; +fp t461; +fp t438; +fp t389; +fp t398; +fp t406; +fp t362; +fp t460; +fp t401; +fp t368; +fp t395; +fp t397; +fp t459; +fp t439; +fp t359; +fp t458; +fp t370; +fp t291; +fp t396; +fp t440; +fp t457; +fp t405; +fp t322; +fp t409; +fp t456; +fp t402; +fp t400; +fp t327; +fp t455; +fp t383; +fp t454; +fp t311; +fp t453; +fp t390; +fp t307; +fp t452; +fp t451; +fp t384; +fp t408; +fp t318; +fp t450; +fp t399; +fp t296; +fp t449; +fp t448; +fp t387; +fp t403; +fp t330; +fp t447; +fp t416; +fp t354; +fp t415; +fp t355; +fp t314; +fp t446; +fp t369; +fp t358; +fp t445; +fp t376; +fp t379; +fp t444; +fp t443; +fp t441; +fp t437; +fp t434; +fp t410; +fp t366; +fp t394; +fp t372; +fp t432; +fp t371; +fp t431; +fp t391; +fp t393; +fp t430; +fp t429; +fp t428; +fp t306; +fp t427; +fp t426; +fp t316; +fp t425; +fp t424; +fp t423; +fp t422; +fp t421; +fp t392; +fp t386; +fp t385; +fp t382; + t411 = x*x; + t412 = y*y; + t464 = t411+t412; + t414 = t411*x; + t404 = RATIONAL(-1.0,60.0); + t356 = t404*t414; + t413 = y*t412; + t360 = t404*t413; + t433 = y*t356+x*t360; + t442 = x*y; + t463 = RATIONAL(11.0,150.0)*t442+t433; + t407 = RATIONAL(1.0,60.0); + t365 = t407*t414; + t364 = t407*t413; + t436 = x*t364+y*t365; + t462 = RATIONAL(-11.0,150.0)*t442+t436; + t435 = t411*t412; + t461 = RATIONAL(-99.0,1225.0)+RATIONAL(-1.0,98.0)*t435; + t438 = y*t411; + t389 = RATIONAL(31.0,210.0); + t398 = RATIONAL(-1.0,140.0); + t406 = RATIONAL(-1.0,30.0); + t362 = t406*t413; + t460 = t389*y+t398*t438+t362; + t401 = RATIONAL(1.0,30.0); + t368 = t401*t413; + t395 = RATIONAL(-31.0,210.0); + t397 = RATIONAL(1.0,140.0); + t459 = t368+t395*y+t397*t438; + t439 = x*t412; + t359 = t401*t414; + t458 = t395*x+t397*t439+t359; + t370 = t406*t414; + t291 = RATIONAL(21.0,200.0)*t442; + t396 = RATIONAL(1.0,120.0); + t440 = x*t413; + t457 = t291+t396*t440+y*t370; + t405 = RATIONAL(-1.0,70.0); + t322 = t405*t438; + t409 = RATIONAL(1.0,84.0); + t456 = t322+t409*y+t364; + t402 = RATIONAL(-1.0,84.0); + t400 = RATIONAL(1.0,70.0); + t327 = t400*t439; + t455 = t327+t356+t402*x; + t383 = RATIONAL(-11.0,105.0); + t454 = t368+t322+t383*y; + t311 = t405*t439; + t453 = t409*x+t311+t365; + t390 = RATIONAL(11.0,105.0); + t307 = t400*t438; + t452 = t307+t390*y+t362; + t451 = t307+t402*y+t360; + t384 = RATIONAL(31.0,420.0); + t408 = RATIONAL(-1.0,35.0); + t318 = t408*t439; + t450 = t384*x+t356+t318; + t399 = RATIONAL(-1.0,120.0); + t296 = RATIONAL(-21.0,200.0)*t442; + t449 = y*t359+t399*t440+t296; + t448 = t389*x+t370+t398*t439; + t387 = RATIONAL(-31.0,420.0); + t403 = RATIONAL(1.0,35.0); + t330 = t403*t439; + t447 = t330+t387*x+t365; + t416 = t412*t412; + t354 = t396*t416; + t415 = t411*t411; + t355 = t396*t415; + t314 = RATIONAL(1.0,49.0)*t435; + t446 = RATIONAL(51.0,1225.0)+t314+t354+t355+t464*RATIONAL(-289.0,5880.0); + t369 = t406*t416; + t358 = t406*t415; + t445 = RATIONAL(1.0,196.0)*t435+t369+RATIONAL(-24.0,1225.0)+t358+t464* +RATIONAL(181.0,1470.0); + t376 = RATIONAL(71.0,5880.0); + t379 = RATIONAL(113.0,735.0); + t444 = t376*t412+t379*t411+t354+t358+t461; + t443 = t369+t376*t411+t379*t412+t355+t461; + t441 = t414*y; + t437 = RATIONAL(-1.0,49.0)*t435+RATIONAL(96.0,1225.0); + t434 = RATIONAL(1.0,98.0)*t435+RATIONAL(246.0,1225.0); + t410 = RATIONAL(1.0,20.0); + t366 = t410*t416; + t394 = RATIONAL(-41.0,196.0); + t372 = RATIONAL(191.0,5880.0); + t432 = t366+t372*t411+t355+t394*t412+t437; + t371 = t410*t415; + t431 = t371+t394*t411+t372*t412+t354+t437; + t391 = RATIONAL(83.0,735.0); + t393 = RATIONAL(-53.0,196.0); + t430 = t369+t391*t412+t371+t393*t411+t434; + t429 = t366+t393*t412+t391*t411+t358+t434; + t428 = RATIONAL(-37.0,300.0)*t442+t436+t445; + t306 = t403*t438; + t427 = t306+t387*y+t364+t446; + t426 = RATIONAL(37.0,300.0)*t442+t433+t445; + t316 = t408*t438; + t425 = t384*y+t360+t316+t446; + t424 = t390*x+t370+t327+t444; + t423 = t383*x+t311+t359+t444; + t422 = x*t368+t296+t399*t441+t443; + t421 = t396*t441+t291+x*t362+t443; + t392 = RATIONAL(-17.0,105.0); + t386 = RATIONAL(17.0,105.0); + t385 = RATIONAL(17.0,420.0); + t382 = RATIONAL(-17.0,420.0); + coeffs_I->coeff_m2_m2 = t425+t450+t462; + coeffs_I->coeff_m1_m2 = t423+t451+t457; + coeffs_I->coeff_0_m2 = t306+t382*y+t360+t431; + coeffs_I->coeff_p1_m2 = t424+t449+t451; + coeffs_I->coeff_p2_m2 = t425+t447+t463; + coeffs_I->coeff_m2_m1 = t421+t454+t455; + coeffs_I->coeff_m1_m1 = t426+t458+t459; + coeffs_I->coeff_0_m1 = t392*y+t368+t307+t430; + coeffs_I->coeff_p1_m1 = t428+t448+t459; + coeffs_I->coeff_p2_m1 = t422+t453+t454; + coeffs_I->coeff_m2_0 = t356+t330+t382*x+t432; + coeffs_I->coeff_m1_0 = t359+t392*x+t327+t429; + coeffs_I->coeff_0_0 = RATIONAL(541.0,1225.0)+t366+t314+t371+t464*RATIONAL +(-57.0,196.0); + coeffs_I->coeff_p1_0 = t311+t370+t386*x+t429; + coeffs_I->coeff_p2_0 = t318+t365+t385*x+t432; + coeffs_I->coeff_m2_p1 = t422+t452+t455; + coeffs_I->coeff_m1_p1 = t428+t458+t460; + coeffs_I->coeff_0_p1 = t386*y+t362+t322+t430; + coeffs_I->coeff_p1_p1 = t426+t448+t460; + coeffs_I->coeff_p2_p1 = t421+t452+t453; + coeffs_I->coeff_m2_p2 = t427+t450+t463; + coeffs_I->coeff_m1_p2 = t423+t449+t456; + coeffs_I->coeff_0_p2 = t316+t364+t385*y+t431; + coeffs_I->coeff_p1_p2 = t424+t456+t457; + coeffs_I->coeff_p2_p2 = t427+t447+t462; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..295e9c5 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c @@ -0,0 +1,155 @@ +fp t532; +fp t503; +fp t533; +fp t534; +fp t551; +fp t569; +fp t511; +fp t550; +fp t568; +fp t557; +fp t567; +fp t522; +fp t535; +fp t507; +fp t566; +fp t481; +fp t565; +fp t526; +fp t512; +fp t564; +fp t505; +fp t491; +fp t563; +fp t506; +fp t490; +fp t562; +fp t556; +fp t561; +fp t524; +fp t501; +fp t560; +fp t559; +fp t558; +fp t508; +fp t555; +fp t554; +fp t482; +fp t525; +fp t509; +fp t553; +fp t521; +fp t504; +fp t552; +fp t475; +fp t549; +fp t467; +fp t548; +fp t514; +fp t547; +fp t546; +fp t545; +fp t544; +fp t486; +fp t543; +fp t542; +fp t541; +fp t540; +fp t539; +fp t538; +fp t483; +fp t479; +fp t473; +fp t469; +fp t466; +fp t465; + t532 = x*x; + t503 = RATIONAL(1.0,20.0)*t532; + t533 = y*y; + t534 = y*t533; + t551 = y*t503+RATIONAL(1.0,60.0)*t534; + t569 = t551+RATIONAL(-37.0,300.0)*y; + t511 = RATIONAL(-1.0,20.0)*t532; + t550 = RATIONAL(-1.0,60.0)*t534+y*t511; + t568 = t550+RATIONAL(37.0,300.0)*y; + t557 = x*t533; + t567 = RATIONAL(1.0,98.0)*t557+RATIONAL(181.0,735.0)*x; + t522 = RATIONAL(1.0,30.0); + t535 = x*t532; + t507 = t522*t535; + t566 = RATIONAL(71.0,2940.0)*x+t507; + t481 = RATIONAL(2.0,49.0)*t557; + t565 = RATIONAL(-289.0,2940.0)*x+t481+t507; + t526 = RATIONAL(-1.0,35.0); + t512 = t526*t533; + t564 = t511+t512+RATIONAL(31.0,420.0); + t505 = RATIONAL(-1.0,10.0)*t532; + t491 = RATIONAL(21.0,200.0)*y; + t563 = y*t505+t491+RATIONAL(1.0,120.0)*t534; + t506 = RATIONAL(1.0,10.0)*t532; + t490 = RATIONAL(-21.0,200.0)*y; + t562 = t490+RATIONAL(-1.0,120.0)*t534+y*t506; + t556 = y*t532; + t561 = RATIONAL(1.0,40.0)*t556+t491+RATIONAL(-1.0,30.0)*t534; + t524 = RATIONAL(1.0,35.0); + t501 = t524*t533; + t560 = t503+RATIONAL(-31.0,420.0)+t501; + t559 = RATIONAL(-1.0,40.0)*t556+t490+t522*t534; + t558 = x*y; + t508 = RATIONAL(-2.0,15.0)*t535; + t555 = t506+t508; + t554 = t505+t508; + t482 = RATIONAL(-1.0,49.0)*t557; + t525 = RATIONAL(-1.0,70.0); + t509 = t525*t533; + t553 = t482+t509; + t521 = RATIONAL(1.0,70.0); + t504 = t521*t533; + t552 = t504+t482; + t475 = RATIONAL(-2.0,49.0)*t557; + t549 = t475+RATIONAL(191.0,2940.0)*x+t507; + t467 = RATIONAL(1.0,49.0)*t557; + t548 = t508+RATIONAL(166.0,735.0)*x+t467; + t514 = RATIONAL(1.0,5.0)*t535; + t547 = t475+t514+RATIONAL(-41.0,98.0)*x; + t546 = t467+RATIONAL(-53.0,98.0)*x+t514; + t545 = t511+RATIONAL(-1.0,84.0)+t552+t566; + t544 = t503+RATIONAL(1.0,84.0)+t553+t566; + t486 = RATIONAL(226.0,735.0)*x; + t543 = t486+RATIONAL(-11.0,105.0)+t553+t555; + t542 = RATIONAL(1.0,140.0)*t533+RATIONAL(-31.0,210.0)+t555+t567; + t541 = t486+RATIONAL(11.0,105.0)+t552+t554; + t540 = RATIONAL(-1.0,140.0)*t533+RATIONAL(31.0,210.0)+t554+t567; + t539 = RATIONAL(-11.0,150.0)*y+t551+t565; + t538 = RATIONAL(11.0,150.0)*y+t550+t565; + t483 = t524*t558; + t479 = RATIONAL(-2.0,35.0)*t558; + t473 = RATIONAL(2.0,35.0)*t558; + t469 = t526*t558; + t466 = t521*t558; + t465 = t525*t558; + coeffs_dx->coeff_m2_m2 = t479+t539+t564; + coeffs_dx->coeff_m1_m2 = t483+t543+t563; + coeffs_dx->coeff_0_m2 = t473+t547; + coeffs_dx->coeff_p1_m2 = t483+t541+t562; + coeffs_dx->coeff_p2_m2 = t479+t538+t560; + coeffs_dx->coeff_m2_m1 = t469+t545+t561; + coeffs_dx->coeff_m1_m1 = t466+t542+t568; + coeffs_dx->coeff_0_m1 = t483+t546; + coeffs_dx->coeff_p1_m1 = t466+t540+t569; + coeffs_dx->coeff_p2_m1 = t469+t544+t559; + coeffs_dx->coeff_m2_0 = t501+t511+RATIONAL(-17.0,420.0)+t549; + coeffs_dx->coeff_m1_0 = t504+RATIONAL(-17.0,105.0)+t506+t548; + coeffs_dx->coeff_0_0 = t514+RATIONAL(-57.0,98.0)*x+t481; + coeffs_dx->coeff_p1_0 = t509+RATIONAL(17.0,105.0)+t505+t548; + coeffs_dx->coeff_p2_0 = RATIONAL(17.0,420.0)+t512+t503+t549; + coeffs_dx->coeff_m2_p1 = t483+t545+t559; + coeffs_dx->coeff_m1_p1 = t465+t542+t569; + coeffs_dx->coeff_0_p1 = t469+t546; + coeffs_dx->coeff_p1_p1 = t465+t540+t568; + coeffs_dx->coeff_p2_p1 = t483+t544+t561; + coeffs_dx->coeff_m2_p2 = t473+t538+t564; + coeffs_dx->coeff_m1_p2 = t469+t543+t562; + coeffs_dx->coeff_0_p2 = t479+t547; + coeffs_dx->coeff_p1_p2 = t469+t541+t563; + coeffs_dx->coeff_p2_p2 = t473+t539+t560; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..c1b3b65 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,107 @@ +fp t704; +fp t708; +fp t685; +fp t709; +fp t688; +fp t726; +fp t683; +fp t695; +fp t725; +fp t724; +fp t723; +fp t722; +fp t679; +fp t692; +fp t694; +fp t687; +fp t681; +fp t721; +fp t693; +fp t720; +fp t686; +fp t719; +fp t718; +fp t682; +fp t717; +fp t678; +fp t716; +fp t684; +fp t715; +fp t714; +fp t713; +fp t712; +fp t689; +fp t711; +fp t710; +fp t677; +fp t676; +fp t675; +fp t674; +fp t673; +fp t672; + t704 = RATIONAL(1.0,10.0); + t708 = x*x; + t685 = t704*t708; + t709 = y*y; + t688 = RATIONAL(2.0,49.0)*t709; + t726 = t685+t688+RATIONAL(-289.0,2940.0); + t683 = RATIONAL(-1.0,49.0)*t709; + t695 = RATIONAL(-2.0,5.0)*t708; + t725 = t683+t695+RATIONAL(226.0,735.0); + t724 = RATIONAL(1.0,98.0)*t709+t695+RATIONAL(181.0,735.0); + t723 = t683+t685+RATIONAL(71.0,2940.0); + t722 = x*y; + t679 = t704*x; + t692 = RATIONAL(-1.0,5.0)*x; + t694 = RATIONAL(1.0,5.0)*x; + t687 = RATIONAL(-1.0,10.0)*x; + t681 = RATIONAL(-2.0,49.0)*t709; + t721 = t681+t685+RATIONAL(191.0,2940.0); + t693 = RATIONAL(3.0,5.0)*t708; + t720 = t681+t693+RATIONAL(-41.0,98.0); + t686 = RATIONAL(1.0,49.0)*t709; + t719 = t686+t695+RATIONAL(166.0,735.0); + t718 = t686+t693+RATIONAL(-53.0,98.0); + t682 = RATIONAL(2.0,35.0)*y; + t717 = t682+t726; + t678 = RATIONAL(-1.0,35.0)*y; + t716 = t678+t725; + t684 = RATIONAL(1.0,35.0)*y; + t715 = t684+t725; + t714 = t679+t723; + t713 = t687+t723; + t712 = RATIONAL(-1.0,70.0)*y+t724; + t689 = RATIONAL(-2.0,35.0)*y; + t711 = t689+t726; + t710 = RATIONAL(1.0,70.0)*y+t724; + t677 = y*t692; + t676 = y*t694; + t675 = RATIONAL(1.0,20.0)*t722; + t674 = y*t687; + t673 = RATIONAL(-1.0,20.0)*t722; + t672 = y*t679; + coeffs_dxx->coeff_m2_m2 = t672+t687+t711; + coeffs_dxx->coeff_m1_m2 = t677+t694+t715; + coeffs_dxx->coeff_0_m2 = t682+t720; + coeffs_dxx->coeff_p1_m2 = t676+t692+t715; + coeffs_dxx->coeff_p2_m2 = t674+t679+t711; + coeffs_dxx->coeff_m2_m1 = t675+t678+t713; + coeffs_dxx->coeff_m1_m1 = t694+t674+t710; + coeffs_dxx->coeff_0_m1 = t684+t718; + coeffs_dxx->coeff_p1_m1 = t692+t672+t710; + coeffs_dxx->coeff_p2_m1 = t678+t673+t714; + coeffs_dxx->coeff_m2_0 = t687+t721; + coeffs_dxx->coeff_m1_0 = t694+t719; + coeffs_dxx->coeff_0_0 = t693+RATIONAL(-57.0,98.0)+t688; + coeffs_dxx->coeff_p1_0 = t692+t719; + coeffs_dxx->coeff_p2_0 = t679+t721; + coeffs_dxx->coeff_m2_p1 = t684+t673+t713; + coeffs_dxx->coeff_m1_p1 = t672+t694+t712; + coeffs_dxx->coeff_0_p1 = t678+t718; + coeffs_dxx->coeff_p1_p1 = t692+t674+t712; + coeffs_dxx->coeff_p2_p1 = t684+t675+t714; + coeffs_dxx->coeff_m2_p2 = t687+t674+t717; + coeffs_dxx->coeff_m1_p2 = t694+t676+t716; + coeffs_dxx->coeff_0_p2 = t689+t720; + coeffs_dxx->coeff_p1_p2 = t677+t692+t716; + coeffs_dxx->coeff_p2_p2 = t679+t672+t717; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c new file mode 100644 index 0000000..dd9a747 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c @@ -0,0 +1,119 @@ +fp t774; +fp t775; +fp t793; +fp t763; +fp t747; +fp t765; +fp t732; +fp t792; +fp t740; +fp t753; +fp t791; +fp t767; +fp t771; +fp t790; +fp t789; +fp t788; +fp t787; +fp t786; +fp t731; +fp t785; +fp t784; +fp t728; +fp t783; +fp t730; +fp t782; +fp t768; +fp t773; +fp t781; +fp t780; +fp t779; +fp t778; +fp t777; +fp t776; +fp t770; +fp t766; +fp t764; +fp t762; +fp t755; +fp t754; +fp t751; +fp t746; +fp t745; +fp t742; +fp t736; +fp t733; +fp t729; +fp t727; + t774 = x*x; + t775 = y*y; + t793 = t774+t775; + t763 = RATIONAL(1.0,35.0); + t747 = t763*x; + t765 = RATIONAL(-1.0,35.0); + t732 = t765*y; + t792 = t747+t732; + t740 = t765*x; + t753 = t763*y; + t791 = t740+t753; + t767 = RATIONAL(1.0,10.0); + t771 = RATIONAL(-1.0,40.0); + t790 = t767*t775+t771*t774; + t789 = t767*t774+t771*t775; + t788 = x*y; + t787 = t793*RATIONAL(-1.0,20.0); + t786 = t793*RATIONAL(1.0,20.0); + t731 = RATIONAL(-2.0,49.0)*t788; + t785 = t731+RATIONAL(21.0,200.0); + t784 = t731+RATIONAL(-21.0,200.0); + t728 = RATIONAL(1.0,49.0)*t788; + t783 = t728+RATIONAL(-37.0,300.0)+t786; + t730 = RATIONAL(4.0,49.0)*t788; + t782 = t730+RATIONAL(-11.0,150.0)+t786; + t768 = RATIONAL(-1.0,10.0); + t773 = RATIONAL(1.0,40.0); + t781 = t773*t775+t768*t774+t785; + t780 = t768*t775+t773*t774+t785; + t779 = t740+t732+t784; + t778 = t730+RATIONAL(11.0,150.0)+t787; + t777 = t747+t753+t784; + t776 = t728+RATIONAL(37.0,300.0)+t787; + t770 = RATIONAL(-2.0,35.0); + t766 = RATIONAL(2.0,35.0); + t764 = RATIONAL(-1.0,70.0); + t762 = RATIONAL(1.0,70.0); + t755 = t762*y; + t754 = t770*y; + t751 = t770*x; + t746 = t766*y; + t745 = t766*x; + t742 = t764*y; + t736 = t762*x; + t733 = t764*x; + t729 = RATIONAL(-4.0,49.0)*t788; + t727 = RATIONAL(2.0,49.0)*t788; + coeffs_dxy->coeff_m2_m2 = t754+t751+t782; + coeffs_dxy->coeff_m1_m2 = t781+t792; + coeffs_dxy->coeff_0_m2 = t729+t745; + coeffs_dxy->coeff_p1_m2 = t777+t789; + coeffs_dxy->coeff_p2_m2 = t746+t751+t778; + coeffs_dxy->coeff_m2_m1 = t780+t791; + coeffs_dxy->coeff_m1_m1 = t755+t736+t776; + coeffs_dxy->coeff_0_m1 = t727+t747; + coeffs_dxy->coeff_p1_m1 = t742+t736+t783; + coeffs_dxy->coeff_p2_m1 = t779+t790; + coeffs_dxy->coeff_m2_0 = t746+t729; + coeffs_dxy->coeff_m1_0 = t727+t753; + coeffs_dxy->coeff_0_0 = t730; + coeffs_dxy->coeff_p1_0 = t732+t727; + coeffs_dxy->coeff_p2_0 = t754+t729; + coeffs_dxy->coeff_m2_p1 = t777+t790; + coeffs_dxy->coeff_m1_p1 = t733+t755+t783; + coeffs_dxy->coeff_0_p1 = t727+t740; + coeffs_dxy->coeff_p1_p1 = t733+t742+t776; + coeffs_dxy->coeff_p2_p1 = t780+t792; + coeffs_dxy->coeff_m2_p2 = t745+t754+t778; + coeffs_dxy->coeff_m1_p2 = t779+t789; + coeffs_dxy->coeff_0_p2 = t729+t751; + coeffs_dxy->coeff_p1_p2 = t781+t791; + coeffs_dxy->coeff_p2_p2 = t745+t746+t782; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..a1b62b5 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c @@ -0,0 +1,147 @@ +fp t638; +fp t617; +fp t637; +fp t640; +fp t655; +fp t671; +fp t613; +fp t656; +fp t670; +fp t658; +fp t586; +fp t627; +fp t639; +fp t614; +fp t669; +fp t587; +fp t608; +fp t668; +fp t667; +fp t666; +fp t596; +fp t657; +fp t665; +fp t631; +fp t618; +fp t664; +fp t629; +fp t611; +fp t663; +fp t597; +fp t662; +fp t607; +fp t630; +fp t606; +fp t661; +fp t626; +fp t612; +fp t605; +fp t660; +fp t659; +fp t572; +fp t654; +fp t581; +fp t653; +fp t619; +fp t652; +fp t651; +fp t650; +fp t649; +fp t648; +fp t647; +fp t646; +fp t645; +fp t644; +fp t643; +fp t584; +fp t582; +fp t577; +fp t576; +fp t573; +fp t571; + t638 = y*y; + t617 = RATIONAL(-1.0,20.0)*t638; + t637 = x*x; + t640 = x*t637; + t655 = x*t617+RATIONAL(-1.0,60.0)*t640; + t671 = t655+RATIONAL(37.0,300.0)*x; + t613 = RATIONAL(1.0,20.0)*t638; + t656 = x*t613+RATIONAL(1.0,60.0)*t640; + t670 = RATIONAL(-37.0,300.0)*x+t656; + t658 = y*t637; + t586 = RATIONAL(2.0,49.0)*t658; + t627 = RATIONAL(1.0,30.0); + t639 = y*t638; + t614 = t627*t639; + t669 = RATIONAL(-289.0,2940.0)*y+t586+t614; + t587 = RATIONAL(-1.0,49.0)*t658; + t608 = RATIONAL(-2.0,15.0)*t639; + t668 = t587+RATIONAL(226.0,735.0)*y+t608; + t667 = t587+t614+RATIONAL(71.0,2940.0)*y; + t666 = RATIONAL(1.0,98.0)*t658+RATIONAL(181.0,735.0)*y+t608; + t596 = RATIONAL(-21.0,200.0)*x; + t657 = x*t638; + t665 = t627*t640+RATIONAL(-1.0,40.0)*t657+t596; + t631 = RATIONAL(-1.0,35.0); + t618 = t631*t637; + t664 = t617+t618+RATIONAL(31.0,420.0); + t629 = RATIONAL(1.0,35.0); + t611 = t629*t637; + t663 = t611+t613+RATIONAL(-31.0,420.0); + t597 = RATIONAL(21.0,200.0)*x; + t662 = RATIONAL(1.0,40.0)*t657+RATIONAL(-1.0,30.0)*t640+t597; + t607 = RATIONAL(1.0,10.0)*t638; + t630 = RATIONAL(-1.0,70.0); + t606 = t630*t637; + t661 = RATIONAL(-11.0,105.0)+t607+t606; + t626 = RATIONAL(1.0,70.0); + t612 = t626*t637; + t605 = RATIONAL(-1.0,10.0)*t638; + t660 = t612+t605+RATIONAL(11.0,105.0); + t659 = x*y; + t572 = RATIONAL(1.0,49.0)*t658; + t654 = t572+RATIONAL(166.0,735.0)*y+t608; + t581 = RATIONAL(-2.0,49.0)*t658; + t653 = RATIONAL(191.0,2940.0)*y+t581+t614; + t619 = RATIONAL(1.0,5.0)*t639; + t652 = t581+t619+RATIONAL(-41.0,98.0)*y; + t651 = t572+t619+RATIONAL(-53.0,98.0)*y; + t650 = RATIONAL(-11.0,150.0)*x+t656+t669; + t649 = RATIONAL(1.0,140.0)*t637+t607+RATIONAL(-31.0,210.0)+t666; + t648 = x*t607+t596+RATIONAL(-1.0,120.0)*t640+t668; + t647 = x*t605+t597+RATIONAL(1.0,120.0)*t640+t668; + t646 = RATIONAL(-1.0,140.0)*t637+t605+RATIONAL(31.0,210.0)+t666; + t645 = t612+t617+RATIONAL(-1.0,84.0)+t667; + t644 = t613+t606+RATIONAL(1.0,84.0)+t667; + t643 = RATIONAL(11.0,150.0)*x+t655+t669; + t584 = RATIONAL(-2.0,35.0)*t659; + t582 = t631*t659; + t577 = t629*t659; + t576 = RATIONAL(2.0,35.0)*t659; + t573 = t626*t659; + t571 = t630*t659; + coeffs_dy->coeff_m2_m2 = t584+t650+t664; + coeffs_dy->coeff_m1_m2 = t582+t645+t662; + coeffs_dy->coeff_0_m2 = t611+t617+RATIONAL(-17.0,420.0)+t653; + coeffs_dy->coeff_p1_m2 = t577+t645+t665; + coeffs_dy->coeff_p2_m2 = t576+t643+t664; + coeffs_dy->coeff_m2_m1 = t577+t647+t661; + coeffs_dy->coeff_m1_m1 = t573+t649+t671; + coeffs_dy->coeff_0_m1 = RATIONAL(-17.0,105.0)+t607+t612+t654; + coeffs_dy->coeff_p1_m1 = t571+t649+t670; + coeffs_dy->coeff_p2_m1 = t582+t648+t661; + coeffs_dy->coeff_m2_0 = t576+t652; + coeffs_dy->coeff_m1_0 = t577+t651; + coeffs_dy->coeff_0_0 = RATIONAL(-57.0,98.0)*y+t619+t586; + coeffs_dy->coeff_p1_0 = t582+t651; + coeffs_dy->coeff_p2_0 = t584+t652; + coeffs_dy->coeff_m2_p1 = t577+t648+t660; + coeffs_dy->coeff_m1_p1 = t573+t646+t670; + coeffs_dy->coeff_0_p1 = RATIONAL(17.0,105.0)+t606+t605+t654; + coeffs_dy->coeff_p1_p1 = t571+t646+t671; + coeffs_dy->coeff_p2_p1 = t582+t647+t660; + coeffs_dy->coeff_m2_p2 = t584+t643+t663; + coeffs_dy->coeff_m1_p2 = t582+t644+t665; + coeffs_dy->coeff_0_p2 = t618+RATIONAL(17.0,420.0)+t613+t653; + coeffs_dy->coeff_p1_p2 = t577+t644+t662; + coeffs_dy->coeff_p2_p2 = t576+t650+t663; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c new file mode 100644 index 0000000..29eef2a --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c @@ -0,0 +1,107 @@ +fp t831; +fp t817; +fp t830; +fp t848; +fp t808; +fp t826; +fp t811; +fp t847; +fp t846; +fp t813; +fp t845; +fp t844; +fp t814; +fp t816; +fp t800; +fp t812; +fp t807; +fp t843; +fp t815; +fp t842; +fp t801; +fp t841; +fp t840; +fp t839; +fp t838; +fp t806; +fp t837; +fp t809; +fp t836; +fp t835; +fp t834; +fp t833; +fp t832; +fp t810; +fp t805; +fp t799; +fp t798; +fp t797; +fp t796; +fp t795; +fp t794; + t831 = y*y; + t817 = RATIONAL(-2.0,5.0)*t831; + t830 = x*x; + t848 = RATIONAL(1.0,98.0)*t830+t817+RATIONAL(181.0,735.0); + t808 = RATIONAL(-1.0,49.0)*t830; + t826 = RATIONAL(1.0,10.0); + t811 = t826*t831; + t847 = t808+t811+RATIONAL(71.0,2940.0); + t846 = t808+t817+RATIONAL(226.0,735.0); + t813 = RATIONAL(2.0,49.0)*t830; + t845 = t811+t813+RATIONAL(-289.0,2940.0); + t844 = x*y; + t814 = RATIONAL(-1.0,5.0)*y; + t816 = RATIONAL(1.0,5.0)*y; + t800 = t826*y; + t812 = RATIONAL(-1.0,10.0)*y; + t807 = RATIONAL(-2.0,49.0)*t830; + t843 = t807+t811+RATIONAL(191.0,2940.0); + t815 = RATIONAL(3.0,5.0)*t831; + t842 = t807+t815+RATIONAL(-41.0,98.0); + t801 = RATIONAL(1.0,49.0)*t830; + t841 = t801+t815+RATIONAL(-53.0,98.0); + t840 = t801+RATIONAL(166.0,735.0)+t817; + t839 = t800+t845; + t838 = t812+t845; + t806 = RATIONAL(1.0,35.0)*x; + t837 = t806+t847; + t809 = RATIONAL(-1.0,35.0)*x; + t836 = t809+t847; + t835 = t814+t846; + t834 = t816+t846; + t833 = RATIONAL(1.0,70.0)*x+t848; + t832 = RATIONAL(-1.0,70.0)*x+t848; + t810 = RATIONAL(-2.0,35.0)*x; + t805 = RATIONAL(2.0,35.0)*x; + t799 = x*t814; + t798 = x*t816; + t797 = RATIONAL(1.0,20.0)*t844; + t796 = x*t812; + t795 = RATIONAL(-1.0,20.0)*t844; + t794 = x*t800; + coeffs_dyy->coeff_m2_m2 = t810+t794+t838; + coeffs_dyy->coeff_m1_m2 = t797+t812+t836; + coeffs_dyy->coeff_0_m2 = t812+t843; + coeffs_dyy->coeff_p1_m2 = t812+t795+t837; + coeffs_dyy->coeff_p2_m2 = t796+t805+t838; + coeffs_dyy->coeff_m2_m1 = t799+t806+t834; + coeffs_dyy->coeff_m1_m1 = t796+t816+t833; + coeffs_dyy->coeff_0_m1 = t816+t840; + coeffs_dyy->coeff_p1_m1 = t794+t816+t832; + coeffs_dyy->coeff_p2_m1 = t809+t798+t834; + coeffs_dyy->coeff_m2_0 = t805+t842; + coeffs_dyy->coeff_m1_0 = t806+t841; + coeffs_dyy->coeff_0_0 = t813+t815+RATIONAL(-57.0,98.0); + coeffs_dyy->coeff_p1_0 = t809+t841; + coeffs_dyy->coeff_p2_0 = t810+t842; + coeffs_dyy->coeff_m2_p1 = t806+t798+t835; + coeffs_dyy->coeff_m1_p1 = t794+t814+t833; + coeffs_dyy->coeff_0_p1 = t814+t840; + coeffs_dyy->coeff_p1_p1 = t814+t796+t832; + coeffs_dyy->coeff_p2_p1 = t799+t809+t835; + coeffs_dyy->coeff_m2_p2 = t796+t810+t839; + coeffs_dyy->coeff_m1_p2 = t795+t800+t836; + coeffs_dyy->coeff_0_p2 = t800+t843; + coeffs_dyy->coeff_p1_p2 = t800+t797+t837; + coeffs_dyy->coeff_p2_p2 = t794+t805+t839; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.cube.order1.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.cube.order1.smooth0.c new file mode 100644 index 0000000..ee1c6bf --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.cube.order1.smooth0.c @@ -0,0 +1,59 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrMD_2d_cube10 +#include "../template.h" + +#define N_DIMS 2 +#define MOLECULE_MIN_M 0 +#define MOLECULE_MAX_M 1 +#define MOLECULE_SIZE 2 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +/* n.b. no 2nd derivatives for linear interpolation! */ + +#define XYZ x, y +#define FP_XYZ fp x, fp y +#define STRIDE_IJK stride_i, stride_j +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride + +#define DATA_STRUCT data_struct_2d_cube_size2 +#define COEFFS_STRUCT coeffs_struct_2d_cube_size2 + +#define FETCH_DATA_REAL LocalInterp_fetch_2d_cube2_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_2d_cube2_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_2d_cube2_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_2d_cube2_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_2d_cube2_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_2d_cube2_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_2d_cube2_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_2d_cube2_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_2d_cube2 + +#define STORE_COEFFS LocalInterp_store_2d_cube2 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.cube.order2.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.cube.order2.smooth0.c new file mode 100644 index 0000000..f2173b4 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.cube.order2.smooth0.c @@ -0,0 +1,64 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrMD_2d_cube20 +#include "../template.h" + +#define N_DIMS 2 +#define MOLECULE_MIN_M -1 +#define MOLECULE_MAX_M 1 +#define MOLECULE_SIZE 3 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +#define HAVE_OP_DXX +#define HAVE_OP_DXY +#define HAVE_OP_DYY + +#define XYZ x, y +#define FP_XYZ fp x, fp y +#define STRIDE_IJK stride_i, stride_j +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride + +#define DATA_STRUCT data_struct_2d_cube_size3 +#define COEFFS_STRUCT coeffs_struct_2d_cube_size3 + +#define FETCH_DATA_REAL LocalInterp_fetch_2d_cube3_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_2d_cube3_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_2d_cube3_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_2d_cube3_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_2d_cube3_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_2d_cube3_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_2d_cube3_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_2d_cube3_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_2d_cube3 + +#define STORE_COEFFS LocalInterp_store_2d_cube3 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c" +#define COEFFS_DXY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c" +#define COEFFS_DYY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.cube.order3.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.cube.order3.smooth0.c new file mode 100644 index 0000000..904a122 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.cube.order3.smooth0.c @@ -0,0 +1,64 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrMD_2d_cube30 +#include "../template.h" + +#define N_DIMS 2 +#define MOLECULE_MIN_M -1 +#define MOLECULE_MAX_M 2 +#define MOLECULE_SIZE 4 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +#define HAVE_OP_DXX +#define HAVE_OP_DXY +#define HAVE_OP_DYY + +#define XYZ x, y +#define FP_XYZ fp x, fp y +#define STRIDE_IJK stride_i, stride_j +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride + +#define DATA_STRUCT data_struct_2d_cube_size4 +#define COEFFS_STRUCT coeffs_struct_2d_cube_size4 + +#define FETCH_DATA_REAL LocalInterp_fetch_2d_cube4_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_2d_cube4_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_2d_cube4_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_2d_cube4_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_2d_cube4_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_2d_cube4_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_2d_cube4_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_2d_cube4_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_2d_cube4 + +#define STORE_COEFFS LocalInterp_store_2d_cube4 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c" +#define COEFFS_DXY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c" +#define COEFFS_DYY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.cube.order4.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.cube.order4.smooth0.c new file mode 100644 index 0000000..9d50ba2 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.cube.order4.smooth0.c @@ -0,0 +1,64 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrMD_2d_cube40 +#include "../template.h" + +#define N_DIMS 2 +#define MOLECULE_MIN_M -2 +#define MOLECULE_MAX_M 2 +#define MOLECULE_SIZE 5 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +#define HAVE_OP_DXX +#define HAVE_OP_DXY +#define HAVE_OP_DYY + +#define XYZ x, y +#define FP_XYZ fp x, fp y +#define STRIDE_IJK stride_i, stride_j +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride + +#define DATA_STRUCT data_struct_2d_cube_size5 +#define COEFFS_STRUCT coeffs_struct_2d_cube_size5 + +#define FETCH_DATA_REAL LocalInterp_fetch_2d_cube5_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_2d_cube5_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_2d_cube5_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_2d_cube5_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_2d_cube5_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_2d_cube5_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_2d_cube5_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_2d_cube5_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_2d_cube5 + +#define STORE_COEFFS LocalInterp_store_2d_cube5 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c" +#define COEFFS_DXY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c" +#define COEFFS_DYY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.log b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.log new file mode 100644 index 0000000..84b0264 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.log @@ -0,0 +1,4728 @@ + |\^/| Maple 7 (IBM INTEL LINUX) +._|\| |/|_. Copyright (c) 2001 by Waterloo Maple Inc. + \ MAPLE / All rights reserved. Maple is a registered trademark of + <____ ____> Waterloo Maple Inc. + | Type ? for help. +# util.maple -- misc utility routines +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/util.maple,v 1.4 2002/08/20 16:46:06 jthorn Exp $ +> +# +# fix_rationals - convert numbers to RATIONAL() calls +# nonmatching_names - find names in a list which *don't* have a specified prefix +# sprint_numeric_list - convert a numeric list to a valid C identifier suffix +# print_name_list_dcl - print C declarations for a list of names +# +# hypercube_points - compute all (integer) points in an N-dimensional hypercube +# +# ftruncate - truncate a file to zero length +# +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function converts all {integer, rational} subexpressions of its +# input except integer exponents and -1 factors in products, into function +# calls +# RATIONAL(num,den) +# This is useful in conjunction with the C() library function, since +# +# C( (1/3) * foo * bar ) +# t0 = foo*bar/3; +# +# generates a (slow) division (and runs the risk of mixed-mode-arithmetic +# problems), while +# +# C((1.0/3.0) * foo * bar); +# t0 = 0.3333333333*foo*bar; +# +# suffers from roundoff error. With this function, +# +# fix_rationals((1/3) * foo * bar); +# RATIONAL(1,3) foo bar +# C(%); +# t0 = RATIONAL(1.0,3.0)*foo*bar; +# +# which a C preprocessor macro can easily convert to the desired +# +# t0 = (1.0/3.0)*foo*bar; +# +# Additionally, this function can be told to leave certain types of +# subexpressions unconverged. For example, +# fix_rationals(expr, type, specfunc(integer, DATA)); +# will leave all subexpressions of the form DATA(integer arguments) +# unconverted. +# +# Arguments: +# expr = (in) The expression to be converted. +# inert_fn = (optional in) +# If specified, this argument should be a Boolean procedure +# or the name of a Boolean procedure. This procedure should +# take one or more argument, and return true if and only if +# the first argument should *not* be converted, i.e. if we +# should leave this expression unchanged. See the last +# example above. +# ... = (optional in) +# Any further arguments are passed as additional arguments to +# the inert_fn procedure. +# +> fix_rationals := +> proc( +> expr::{ +> algebraic, name = algebraic, +> list({algebraic, name = algebraic}), +> set ({algebraic, name = algebraic}) +> }, +> inert_fn::{name, procedure} +> ) +> local nn, k, +> base, power, fbase, fpower, +> fn, fn_args_list, +> num, den, mult; +> +# do we want to convert this expression? +> if ((nargs >= 2) and inert_fn(expr, args[3..nargs])) +> then return expr; +> end if; +> +# recurse over lists and sets +> if (type(expr, {list,set})) +> then return map(fix_rationals, expr, args[2..nargs]); +> end if; +> +# recurse over equation right hand sides +> if (type(expr, name = algebraic)) +> then return ( lhs(expr) = fix_rationals(rhs(expr), args[2..nargs]) ); +> end if; +> +# recurse over functions other than RATIONAL() +> if (type(expr, function)) +> then +> fn := op(0, expr); +> if (fn <> 'RATIONAL') +> then +> fn_args_list := [op(expr)]; +> fn_args_list := map(fix_rationals, fn_args_list, args[2..nargs]); +> fn; return '%'( op(fn_args_list) ); +> end if; +> end if; +> +> nn := nops(expr); +> +# recurse over sums +> if (type(expr, `+`)) +> then return sum('fix_rationals(op(k,expr), args[2..nargs])', 'k'=1..nn); +> end if; +> +# recurse over products +# ... leaving leading -1 factors intact, i.e. not converted to RATIONAL(-1,1) +> if (type(expr, `*`)) +> then +> if (op(1, expr) = -1) +> then return -1*fix_rationals(remove(type, expr, 'identical(-1)'), +> args[2..nargs]); +> else return product('fix_rationals(op(k,expr), args[2..nargs])', +> 'k'=1..nn); +> end if; +> end if; +> +# recurse over powers +# ... leaving integer exponents intact +> if (type(expr, `^`)) +> then +> base := op(1, expr); +> power := op(2, expr); +> +> fbase := fix_rationals(base, args[2..nargs]); +> if (type(power, integer)) +> then fpower := power; +> else fpower := fix_rationals(power, args[2..nargs]); +> end if; +> return fbase ^ fpower; +> end if; +> +# fix integers and fractions +> if (type(expr, integer)) +> then return 'RATIONAL'(expr, 1); +> end if; +> if (type(expr, fraction)) +> then +> num := op(1, expr); +> den := op(2, expr); +> +> return 'RATIONAL'(num, den); +> end if; +> +# turn Maple floating-point into integer fraction, then recursively fix that +> if (type(expr, float)) +> then +> mult := op(1, expr); +> power := op(2, expr); +> return fix_rationals(mult * 10^power, args[2..nargs]); +> end if; +> +# identity op on names +> if (type(expr, name)) +> then return expr; +> end if; +> +# unknown type +> error "%0", +> "unknown type for expr!", +> " whattype(expr) = ", whattype(expr), +> " expr = ", expr; +> end proc; +fix_rationals := proc(expr::{algebraic, name = algebraic, +list({algebraic, name = algebraic}), set({algebraic, name = algebraic})}, +inert_fn::{procedure, name}) +local nn, k, base, power, fbase, fpower, fn, fn_args_list, num, den, mult; + if 2 <= nargs and inert_fn(expr, args[3 .. nargs]) then return expr + end if; + if type(expr, {set, list}) then + return map(fix_rationals, expr, args[2 .. nargs]) + end if; + if type(expr, name = algebraic) then + return lhs(expr) = fix_rationals(rhs(expr), args[2 .. nargs]) + end if; + if type(expr, function) then + fn := op(0, expr); + if fn <> 'RATIONAL' then + fn_args_list := [op(expr)]; + fn_args_list := + map(fix_rationals, fn_args_list, args[2 .. nargs]); + fn; + return '%'(op(fn_args_list)) + end if + end if; + nn := nops(expr); + if type(expr, `+`) then return + sum('fix_rationals(op(k, expr), args[2 .. nargs])', 'k' = 1 .. nn) + end if; + if type(expr, `*`) then + if op(1, expr) = -1 then return -fix_rationals( + remove(type, expr, 'identical(-1)'), args[2 .. nargs]) + else return product('fix_rationals(op(k, expr), args[2 .. nargs])', + 'k' = 1 .. nn) + end if + end if; + if type(expr, `^`) then + base := op(1, expr); + power := op(2, expr); + fbase := fix_rationals(base, args[2 .. nargs]); + if type(power, integer) then fpower := power + else fpower := fix_rationals(power, args[2 .. nargs]) + end if; + return fbase^fpower + end if; + if type(expr, integer) then return 'RATIONAL'(expr, 1) end if; + if type(expr, fraction) then + num := op(1, expr); den := op(2, expr); return 'RATIONAL'(num, den) + end if; + if type(expr, float) then + mult := op(1, expr); + power := op(2, expr); + return fix_rationals(mult*10^power, args[2 .. nargs]) + end if; + if type(expr, name) then return expr end if; + error "%0", "unknown type for expr!", " whattype(expr) = ", + whattype(expr), " expr = ", expr +end proc + +> +################################################################################ +> +# +# This function finds names in a list which *don't* have a specified prefix. +# +# Arguments: +# name_list = A list of the names. +# prefix = The prefix we want to filter out. +# +# Results: +# This function returns the subset list of names which don't have the +# specified prefix. +# +> nonmatching_names := +> proc( name_list::list({name,string}), prefix::{name,string} ) +> +> select( proc(n) +> evalb(not StringTools[IsPrefix](prefix,n)); +> end proc +> , +> name_list +> ); +> end proc; +nonmatching_names := proc( +name_list::list({name, string}), prefix::{name, string}) + select(proc(n) evalb(not StringTools[IsPrefix](prefix, n)) end proc, + name_list) +end proc + +> +################################################################################ +> +# +# This function converts a numeric list to a string which is a valid +# C identifier suffix: elements are separated by "_", decimal points are +# replaced by "x", and all nonzero values have explicit +/- signs, which +# are replaced by "p"/"m". +# +# For example, [0,-3.5,+4] --> "0_m3x5_p4". +# +> sprint_numeric_list := +> proc(nlist::list(numeric)) +> +# generate preliminary string, eg "+0_-3.5_+4" +> map2(sprintf, "%+a", nlist); +> ListTools[Join](%, "_"); +> cat(op(%)); +> +# fixup bad characters +> StringTools[SubstituteAll](%, "+0", "0"); +> StringTools[CharacterMap](".+-", "xpm", %); +> +> return %; +> end proc; +sprint_numeric_list := proc(nlist::list(numeric)) + map2(sprintf, "%+a", nlist); + ListTools[Join](%, "_"); + cat(op(%)); + StringTools[SubstituteAll](%, "+0", "0"); + StringTools[CharacterMap](".+-", "xpm", %); + return % +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C declarations for a list of names. +# +# Argument: +# name_list = A list of the names. +# type_name = The C type of the names, eg. "double". +# file_name = The file name to write the declaration to. This is +# truncated before writing. +# +> print_name_list_dcl := +> proc( name_list::list({name,string}), +> type_name::string, +> file_name::string ) +> local blanks, separator_string; +> +> ftruncate(file_name); +> +> map( +> proc(var::{name,string}) +> fprintf(file_name, +> "%s %s;\n", +> type_name, var); +> end proc +> , +> name_list +> ); +> +> fclose(file_name); +> NULL; +> end proc; +print_name_list_dcl := proc( +name_list::list({name, string}), type_name::string, file_name::string) +local blanks, separator_string; + ftruncate(file_name); + map(proc(var::{name, string}) + fprintf(file_name, "%s %s;\n", type_name, var) + end proc, name_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes a list of all the (integer) points in an +# N-dimensional hypercube, in lexicographic order. The present +# implementation requires N <= 4. +# +# Arguments: +# cmin,cmax = N-element lists of cube minimum/maximum coordinates. +# +# Results: +# The function returns a set of d-element lists giving the coordinates. +# For example, +# hypercube([0,0], [2,1] +# returns +# { [0,0], [0,1], [1,0], [1,1], [2,0], [2,1] } +> hypercube_points := +> proc(cmin::list(integer), cmax::list(integer)) +> local N, i,j,k,l; +> +> N := nops(cmin); +> if (nops(cmax) <> N) +> then error +> "must have same number of dimensions for min and max coordinates!"; +> fi; +> +> if (N = 1) +> then return [seq([i], i=cmin[1]..cmax[1])]; +> elif (N = 2) +> then return [ +> seq( +> seq([i,j], j=cmin[2]..cmax[2]), +> i=cmin[1]..cmax[1]) +> ]; +> elif (N = 3) +> then return [ +> seq( +> seq( +> seq([i,j,k], k=cmin[3]..cmax[3]), +> j=cmin[2]..cmax[2] ), +> i=cmin[1]..cmax[1]) +> ]; +> elif (N = 4) +> then return [ +> seq( +> seq( +> seq( +> seq([i,j,k,l], l=cmin[4]..cmax[4]), +> k=cmin[3]..cmax[3] ), +> j=cmin[2]..cmax[2]), +> i=cmin[1]..cmax[1]) +> ]; +> else +> error "implementation restriction: must have N <= 4, got %1!", N; +> fi; +> end proc; +hypercube_points := proc(cmin::list(integer), cmax::list(integer)) +local N, i, j, k, l; + N := nops(cmin); + if nops(cmax) <> N then error + "must have same number of dimensions for min and max coordinates!" + end if; + if N = 1 then return [seq([i], i = cmin[1] .. cmax[1])] + elif N = 2 then return + [seq(seq([i, j], j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] + elif N = 3 then return [seq( + seq(seq([i, j, k], k = cmin[3] .. cmax[3]), j = cmin[2] .. cmax[2]) + , i = cmin[1] .. cmax[1])] + elif N = 4 then return [seq(seq(seq( + seq([i, j, k, l], l = cmin[4] .. cmax[4]), k = cmin[3] .. cmax[3]), + j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] + else error "implementation restriction: must have N <= 4, got %1!", N + end if +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function truncates a file to 0 length if it exists, or creates +# it at that length if it doesn't exist. +# +# Arguments: +# file_name = (in) The name of the file. +# +> ftruncate := +> proc(file_name::string) +> fopen(file_name, 'WRITE'); +> fclose(%); +> NULL; +> end proc; +ftruncate := + + proc(file_name::string) fopen(file_name, 'WRITE'); fclose(%); NULL end proc + +# interpolate.maple -- compute interpolation formulas/coefficients +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/interpolate.maple,v 1.10 2002/08/28 11:31:09 jthorn Exp $ +> +# +# <<>> +# Lagrange_polynomial_interpolant - compute Lagrange polynomial interpolant +# Hermite_polynomial_interpolant - compute Hermite polynomial interpolant +# coeffs_as_lc_of_data - coefficients of ... (linear combination of data) +# +# print_coeffs__lc_of_data - print C code to compute coefficients +# print_fetch_data - print C code to fetch input array chunk into struct data +# print_store_coeffs - print C code to store struct coeffs "somewhere" +# print_interp_cmpt__lc_of_data - print C code for computation of interpolant +# +# coeff_name - name of coefficient of data at a given [m] coordinate +# data_var_name - name of variable storing data value at a given [m] coordinate +# +> +################################################################################ +> +# +# ***** representation of numbers, data values, etc ***** +# +# We use RATIONAL(p.0,q.0) to denote the rational number p/q. +# +# We use DATA(...) to represent the data values being interpolated at a +# specified [m] coordinate, where the arguments are the [m] coordinates. +# +# We use COEFF(...) to represent the molecule coefficient at a specified +# [m] coordinate, where the arguments are the [m] coordinates. +# +# For example, the usual 1-D centered 2nd order 1st derivative molecule +# would be written +# RATIONAL(-1.0,2.0)*DATA(-1) + RATIONA(1.0,2.0)*DATA(1) +# and its coefficients as +# COEFF(-1) = RATIONAL(-1.0,2.0) +# COEFF(1) = RATIONAL(1.0,2.0) +# +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes a Lagrange polynomial interpolant in any +# number of dimensions. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) c00 + c10*x + c01*y end proc +# coeff_list = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example [c00, c10, c01]. +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# posn_list = A list of positions (each a list of numeric values) where the +# interpolant is to use data, for example hypercube([0,0], [1,1]). +# Any positions may be used; if they're redundant (as in the +# example) the least-squares interpolant is computed. +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Lagrange_polynomial_interpolant := +> proc( +> fn::procedure, coeff_list::list(name), +> coord_list::list(name), posn_list::list(list(numeric)) +> ) +> local posn, data_eqns, coeff_eqns; +> +# coefficients of interpolating polynomial +> data_eqns := { seq( fn(op(posn))='DATA'(op(posn)) , posn=posn_list ) }; +> coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); +> if (has(coeff_eqns, '_t')) +> then error "interpolation coefficients aren't uniquely determined!"; +> end if; +> +# interpolant as a polynomial in the coordinates +> return subs(coeff_eqns, eval(fn))(op(coord_list)); +> end proc; +Lagrange_polynomial_interpolant := proc(fn::procedure, coeff_list::list(name), +coord_list::list(name), posn_list::list(list(numeric))) +local posn, data_eqns, coeff_eqns; + data_eqns := {seq(fn(op(posn)) = 'DATA'(op(posn)), posn = posn_list)}; + coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); + if has(coeff_eqns, '_t') then + error "interpolation coefficients aren't uniquely determined!" + end if; + return subs(coeff_eqns, eval(fn))(op(coord_list)) +end proc + +> +################################################################################ +> +# +# This function computes a Hermite polynomial interpolant in any +# number of dimensions. This is a polynomial which +# * has values which match the given data DATA() at a specified set of +# points, and +# * has derivatives which match the specified finite-difference derivatives +# of the given data DATA() at a specified set of points +# +# For the derivative matching, we actually match all possible products +# of 1st derivatives, i.e. in 2-D we match dx, dy, and dxy, in 3-D we +# match dx, dy, dz, dxy, dxz, dyz, and dxyz, etc etc. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) +# + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 +# + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 +# + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +# + c00 + c10*x + c20*x^2 + c30*x^3 +# end proc; +# coeff_set = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example +# { +# c03, c13, c23, c33, +# c02, c12, c22, c32, +# c01, c11, c21, c31, +# c00, c10, c20, c30 +# } +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# deriv_set = A set of equations of the form +# {coords} = proc +# giving the derivatives which are to be matched, and the +# procedures to compute their finite-difference approximations. +# Each procedure should take N_dims integer arguments specifying +# an evaluation point, and return a suitable linear combination +# of the DATA() for the derivative at that point. For example +# { +# {x} = proc(i::integer, j::integer) +# - 1/2*DATA(i-1,j) + 1/2*DATA(i+1,j) +# end proc +# , +# {y} = proc(i::integer, j::integer) +# - 1/2*DATA(i,j-1) + 1/2*DATA(i,j+1) +# end proc +# , +# {x,y} = proc(i::integer, j::integer) +# - 1/4*DATA(i-1,j+1) + 1/4*DATA(i+1,j+1) +# + 1/4*DATA(i-1,j-1) - 1/4*DATA(i+1,j-1) +# end proc +# } +# fn_posn_set = A set of positions (each a list of numeric values) +# where the interpolant is to match the given data DATA(), +# for example +# {[0,0], [0,1], [1,0], [1,1]} +# deriv_posn_set = A list of positions (each a list of numeric values) +# where the interpolant is to match the derivatives +# specified by deriv_set , for example +# {[0,0], [0,1], [1,0], [1,1]} +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Hermite_polynomial_interpolant := +> proc( +> fn::procedure, +> coeff_set::set(name), +> coord_list::list(name), +> deriv_set::set(set(name) = procedure), +> fn_posn_set::set(list(numeric)), +> deriv_posn_set::set(list(numeric)) +> ) +> local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; +> +> +# +# compute a set of equations +# {fn(posn) = DATA(posn)} +# giving the function values to be matched +# +> fn_eqnset := map( +> # return equation that fn(posn) = DATA(posn) +> proc(posn::list(integer)) +> fn(op(posn)) = 'DATA'(op(posn)); +> end proc +> , +> fn_posn_set +> ); +> +> +# +# compute a set of equations +# { diff(fn,coords)(posn) = DERIV(coords)(posn) } +# giving the derivative values to be matched, where DERIV(coords) +# is a placeholder for the appropriate derivative +# +> map( +> # return set of equations for this particular derivative +> proc(deriv_coords::set(name)) +> local deriv_fn; +> fn(op(coord_list)); +> diff(%, op(deriv_coords)); +> deriv_fn := unapply(%, op(coord_list)); +> map( +> proc(posn::list(integer)) +> deriv_fn(op(posn)) = 'DERIV'(op(deriv_coords))(op(posn)); +> end proc +> , +> deriv_posn_set +> ); +> end proc +> , +> map(lhs, deriv_set) +> ); +> deriv_eqnset := `union`(op(%)); +> +> +# +# solve overall set of equations for coefficients +# in terms of DATA() and DERIV() values +# +> coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); +> if (indets(map(rhs,%)) <> {}) +> then error "no unique solution for coefficients -- %1 eqns for %2 coeffs", +> nops(fn_eqnset union deriv_eqnset), +> nops(coeff_set); +> fi; +> +> +# +# compute a set of substitution equations +# {'DERIV'(coords) = procedure} +# +> subs_eqnset := map( +> proc(eqn::set(name) = procedure) +> 'DERIV'(op(lhs(eqn))) = rhs(eqn); +> end proc +> , +> deriv_set +> ); +> +> +# +# compute the coefficients in terms of the DATA() values +# +> subs(subs_eqnset, coeff_eqns); +> eval(%); +> +# +# compute the interpolant as a polynomial in the coordinates +# +> subs(%, fn(op(coord_list))); +> end proc; +Hermite_polynomial_interpolant := proc(fn::procedure, coeff_set::set(name), +coord_list::list(name), deriv_set::set(set(name) = procedure), +fn_posn_set::set(list(numeric)), deriv_posn_set::set(list(numeric))) +local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; + fn_eqnset := map( + proc(posn::list(integer)) fn(op(posn)) = 'DATA'(op(posn)) end proc, + fn_posn_set); + map(proc(deriv_coords::set(name)) + local deriv_fn; + fn(op(coord_list)); + diff(%, op(deriv_coords)); + deriv_fn := unapply(%, op(coord_list)); + map(proc(posn::list(integer)) + deriv_fn(op(posn)) = + 'DERIV'(op(deriv_coords))(op(posn)) + end proc, deriv_posn_set) + end proc, map(lhs, deriv_set)); + deriv_eqnset := `union`(op(%)); + coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); + if indets(map(rhs, %)) <> {} then error + "no unique solution for coefficients -- %1 eqns for %2 coeffs", + nops(fn_eqnset union deriv_eqnset), nops(coeff_set) + end if; + subs_eqnset := map(proc(eqn::(set(name) = procedure)) + 'DERIV'(op(lhs(eqn))) = rhs(eqn) + end proc, deriv_set); + subs(subs_eqnset, coeff_eqns); + eval(%); + subs(%, fn(op(coord_list))) +end proc + +> +################################################################################ +> +# +# This function takes as input an interpolating polynomial, expresses +# it as a linear combination of the data values, and returns the coefficeints +# of that form. +# +# Arguments: +# interpolant = The interpolating polynomial (an algebraic expression +# in the coordinates and the data values). +# posn_list = The same list of data positions used in the interpolant. +# +# Results: +# This function returns the coefficients, as a list of equations of the +# form COEFF(...) = value , where each value is a polynomial in the +# coordinates. The order of the list matches that of posn_list. +# +> coeffs_as_lc_of_data := +> proc( +> interpolant::algebraic, +> posn_list::list(list(numeric)) +> ) +> local data_list, interpolant_as_lc_of_data; +> +# interpolant as a linear combination of the data values +> data_list := [ seq( 'DATA'(op(posn)) , posn=posn_list ) ]; +> interpolant_as_lc_of_data := collect(interpolant, data_list); +> +# coefficients of the data values in the linear combination +> return map( +> proc(posn::list(numeric)) +> coeff(interpolant_as_lc_of_data, DATA(op(posn))); +> 'COEFF'(op(posn)) = %; +> end proc +> , +> posn_list +> ); +> end proc; +coeffs_as_lc_of_data := proc( +interpolant::algebraic, posn_list::list(list(numeric))) +local data_list, interpolant_as_lc_of_data; + data_list := [seq('DATA'(op(posn)), posn = posn_list)]; + interpolant_as_lc_of_data := collect(interpolant, data_list); + return map(proc(posn::list(numeric)) + coeff(interpolant_as_lc_of_data, DATA(op(posn))); + 'COEFF'(op(posn)) = % + end proc, posn_list) +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function prints C expressions for the coefficients of an +# interpolating polynomial. (The polynomial is expressed as linear +# combinations of the data values with coefficients which are +# RATIONAL(p,q) calls.) +# +# Arguments: +# coeff_list = A list of the coefficients, as returned from +# coeffs_as_lc_of_data() . +# coeff_name_prefix = A prefix string for the coefficient names. +# temp_name_type = The C type to be used for Maple-introduced temporary +# names, eg. "double". +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_coeffs__lc_of_data := +> proc( coeff_list::list(specfunc(numeric,COEFF) = algebraic), +> coeff_name_prefix::string, +> temp_name_type::string, +> file_name::string ) +> global `codegen/C/function/informed`; +> local coeff_list2, cmpt_list, temp_name_list; +> +# convert LHS of each equation from a COEFF() call (eg COEFF(-1,+1)) +# to a Maple/C variable name (eg coeff_I_m1_p1) +> coeff_list2 := map( +> proc(coeff_eqn::specfunc(numeric,COEFF) = algebraic) +> local posn; +> posn := [op(lhs(coeff_eqn))]; +> coeff_name(posn,coeff_name_prefix); +> convert(%, name); # codegen[C] wants LHS +> # to be an actual Maple *name* +> % = fix_rationals(rhs(coeff_eqn)); +> end proc +> , +> coeff_list +> ); +> +# +# generate the C code +# +> +# tell codegen[C] not to warn about unknown RATIONAL() and DATA() "fn calls" +# via undocumented :( global table +> `codegen/C/function/informed`['RATIONAL'] := true; +> `codegen/C/function/informed`['DATA'] := true; +> +> ftruncate(file_name); +> +# optimized computation sequence for all the coefficients +# (may use local variables t0,t1,t2,...) +> cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; +> +# list of the t0,t1,t2,... local variables +> temp_name_list := nonmatching_names(map(lhs,cmpt_list), coeff_name_prefix); +> +# declare the t0,t1,t2,... local variables (if there are any) +> if (nops(temp_name_list) > 0) +> then print_name_list_dcl(%, temp_name_type, file_name); +> fi; +> +# now print the optimized computation sequence +> codegen[C](cmpt_list, filename=file_name); +> +> fclose(file_name); +> +> NULL; +> end proc; +print_coeffs__lc_of_data := proc( +coeff_list::list(specfunc(numeric, COEFF) = algebraic), +coeff_name_prefix::string, temp_name_type::string, file_name::string) +local coeff_list2, cmpt_list, temp_name_list; +global `codegen/C/function/informed`; + coeff_list2 := map(proc( + coeff_eqn::(specfunc(numeric, COEFF) = algebraic)) + local posn; + posn := [op(lhs(coeff_eqn))]; + coeff_name(posn, coeff_name_prefix); + convert(%, name); + % = fix_rationals(rhs(coeff_eqn)) + end proc, coeff_list); + `codegen/C/function/informed`['RATIONAL'] := true; + `codegen/C/function/informed`['DATA'] := true; + ftruncate(file_name); + cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; + temp_name_list := + nonmatching_names(map(lhs, cmpt_list), coeff_name_prefix); + if 0 < nops(temp_name_list) then + print_name_list_dcl(%, temp_name_type, file_name) + end if; + codegen[C](cmpt_list, filename = file_name); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C expression to assign the data-value +# variables, eg +# data->data_m1_p1 = DATA(-1,1); +# +# Arguments: +# posn_list = The same list of positions as was used to compute the +# interpolating polynomial. +# data_var_name_prefix = A prefix string for the data variable names. +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_fetch_data := +> proc( +> posn_list::list(list(numeric)), +> data_var_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> map( +> proc(posn::list(numeric)) +> fprintf(file_name, +> "%s = %a;\n", +> data_var_name(posn,data_var_name_prefix), +> DATA(op(posn))); +> end proc +> , +> posn_list +> ); +> fclose(file_name); +> +> NULL; +> end proc; +print_fetch_data := proc(posn_list::list(list(numeric)), +data_var_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + fprintf(file_name, "%s = %a;\n", + data_var_name(posn, data_var_name_prefix), DATA(op(posn))) + end proc, posn_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C expression to store the interpolation +# coefficients in COEFF(...) expressions, eg +# COEFF(1,-1) = factor * coeffs->coeff_p1_m1; +# +# Arguments: +# posn_list = The list of positions in the molecule. +# coeff_name_prefix = A prefix string for the coefficient names, +# eg "factor * coeffs->coeff_" +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_store_coeffs := +> proc( +> posn_list::list(list(numeric)), +> coeff_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> map( +> proc(posn::list(numeric)) +> fprintf(file_name, +> "%a = %s;\n", +> 'COEFF'(op(posn)), +> coeff_name(posn,coeff_name_prefix)); +> end proc +> , +> posn_list +> ); +> fclose(file_name); +> +> NULL; +> end proc; +print_store_coeffs := proc(posn_list::list(list(numeric)), +coeff_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + fprintf(file_name, "%a = %s;\n", 'COEFF'(op(posn)), + coeff_name(posn, coeff_name_prefix)) + end proc, posn_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a C expression to evaluate a molecule, i.e. +# to compute the molecule as a linear combination of the data values. +# +# Arguments: +# posn_list = The list of positions in the molecule. +# coeff_name_prefix = A prefix string for the coefficient names. +# data_var_name_prefix = A prefix string for the data variable names. +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_evaluate_molecule := +> proc( +> posn_list::list(list(numeric)), +> coeff_name_prefix::string, +> data_var_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> +# list of "coeff*data_var" terms +> map( +> proc(posn::list(numeric)) +> sprintf("%s*%s", +> coeff_name(posn,coeff_name_prefix), +> data_var_name(posn,data_var_name_prefix)); +> end proc +> , +> posn_list +> ); +> +> ListTools[Join](%, "\n + "); +> cat(op(%)); +> fprintf(file_name, " %s;\n", %); +> +> fclose(file_name); +> +> NULL; +> end proc; +print_evaluate_molecule := proc(posn_list::list(list(numeric)), +coeff_name_prefix::string, data_var_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + sprintf("%s*%s", coeff_name(posn, coeff_name_prefix), + data_var_name(posn, data_var_name_prefix)) + end proc, posn_list); + ListTools[Join](%, "\n + "); + cat(op(%)); + fprintf(file_name, " %s;\n", %); + fclose(file_name); + NULL +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes the name of the coefficient of the data at a +# given [m] position, i.e. it encapsulates our naming convention for this. +# +# Arguments: +# posn = (in) The [m] coordinates. +# name_prefix = A prefix string for the coefficient name. +# +# Results: +# The function returns the coefficient, as a Maple string. +# +> coeff_name := +> proc(posn::list(numeric), name_prefix::string) +> cat(name_prefix, sprint_numeric_list(posn)); +> end proc; +coeff_name := proc(posn::list(numeric), name_prefix::string) + cat(name_prefix, sprint_numeric_list(posn)) +end proc + +> +################################################################################ +> +# +# This function computes the name of the variable in which the C code +# will store the input data at a given [m] position, i.e. it encapsulates +# our naming convention for this. +# +# Arguments: +# posn = (in) The [m] coordinates. +# name_prefix = A prefix string for the variable name. +# +# Results: +# The function returns the variable name, as a Maple string. +# +> data_var_name := +> proc(posn::list(numeric), name_prefix::string) +> cat(name_prefix, sprint_numeric_list(posn)); +> end proc; +data_var_name := proc(posn::list(numeric), name_prefix::string) + cat(name_prefix, sprint_numeric_list(posn)) +end proc + +# Maple code to compute lists of point positions in hypercube-shaped molecules +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/common/cube_posns.maple,v 1.3 2002/08/20 16:56:41 jthorn Exp $ +> +################################################################################ +> +# +# 1D interpolation points +# +> posn_list_1d_size2 := hypercube_points([ 0], [+1]); + posn_list_1d_size2 := [[0], [1]] + +> posn_list_1d_size3 := hypercube_points([-1], [+1]); + posn_list_1d_size3 := [[-1], [0], [1]] + +> posn_list_1d_size4 := hypercube_points([-1], [+2]); + posn_list_1d_size4 := [[-1], [0], [1], [2]] + +> posn_list_1d_size5 := hypercube_points([-2], [+2]); + posn_list_1d_size5 := [[-2], [-1], [0], [1], [2]] + +> posn_list_1d_size6 := hypercube_points([-2], [+3]); + posn_list_1d_size6 := [[-2], [-1], [0], [1], [2], [3]] + +> posn_list_1d_size7 := hypercube_points([-3], [+3]); + posn_list_1d_size7 := [[-3], [-2], [-1], [0], [1], [2], [3]] + +> +################################################################################ +> +# +# 2D interpolation points (Fortran ordering) +# +> posn_list_2d_size2 := map(ListTools[Reverse], +> hypercube_points([ 0, 0], [+1,+1])); + posn_list_2d_size2 := [[0, 0], [1, 0], [0, 1], [1, 1]] + +> posn_list_2d_size3 := map(ListTools[Reverse], +> hypercube_points([-1,-1], [+1,+1])); +posn_list_2d_size3 := [[-1, -1], [0, -1], [1, -1], [-1, 0], [0, 0], [1, 0], + + [-1, 1], [0, 1], [1, 1]] + +> posn_list_2d_size4 := map(ListTools[Reverse], +> hypercube_points([-1,-1], [+2,+2])); +posn_list_2d_size4 := [[-1, -1], [0, -1], [1, -1], [2, -1], [-1, 0], [0, 0], + + [1, 0], [2, 0], [-1, 1], [0, 1], [1, 1], [2, 1], [-1, 2], [0, 2], [1, 2], + + [2, 2]] + +> posn_list_2d_size5 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+2,+2])); +posn_list_2d_size5 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [-2, -1], + + [-1, -1], [0, -1], [1, -1], [2, -1], [-2, 0], [-1, 0], [0, 0], [1, 0], + + [2, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], [-2, 2], [-1, 2], [0, 2], + + [1, 2], [2, 2]] + +> posn_list_2d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+3,+3])); +posn_list_2d_size6 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [3, -2], + + [-2, -1], [-1, -1], [0, -1], [1, -1], [2, -1], [3, -1], [-2, 0], [-1, 0], + + [0, 0], [1, 0], [2, 0], [3, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], + + [3, 1], [-2, 2], [-1, 2], [0, 2], [1, 2], [2, 2], [3, 2], [-2, 3], [-1, 3], + + [0, 3], [1, 3], [2, 3], [3, 3]] + +> +################################################################################ +> +# +# 3D interpolation points (Fortran ordering) +# +> posn_list_3d_size2 := map(ListTools[Reverse], +> hypercube_points([ 0, 0, 0], [+1,+1,+1])); +posn_list_3d_size2 := [[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], + + [1, 0, 1], [0, 1, 1], [1, 1, 1]] + +> posn_list_3d_size3 := map(ListTools[Reverse], +> hypercube_points([-1,-1,-1], [+1,+1,+1])); +posn_list_3d_size3 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [-1, 0, -1], + + [0, 0, -1], [1, 0, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], [-1, -1, 0], + + [0, -1, 0], [1, -1, 0], [-1, 0, 0], [0, 0, 0], [1, 0, 0], [-1, 1, 0], + + [0, 1, 0], [1, 1, 0], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [-1, 0, 1], + + [0, 0, 1], [1, 0, 1], [-1, 1, 1], [0, 1, 1], [1, 1, 1]] + +> posn_list_3d_size4 := map(ListTools[Reverse], +> hypercube_points([-1,-1,-1], [+2,+2,+2])); +posn_list_3d_size4 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [2, -1, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [-1, 1, -1], [0, 1, -1], + + [1, 1, -1], [2, 1, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-1, 0, 0], [0, 0, 0], + + [1, 0, 0], [2, 0, 0], [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [-1, -1, 1], [0, -1, 1], + + [1, -1, 1], [2, -1, 1], [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [-1, 2, 1], [0, 2, 1], + + [1, 2, 1], [2, 2, 1], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-1, 1, 2], [0, 1, 2], + + [1, 1, 2], [2, 1, 2], [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2]] + +> posn_list_3d_size5 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+2,+2,+2])); +posn_list_3d_size5 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], [1, -1, -2], + + [2, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], [1, 0, -2], [2, 0, -2], + + [-2, 1, -2], [-1, 1, -2], [0, 1, -2], [1, 1, -2], [2, 1, -2], [-2, 2, -2], + + [-1, 2, -2], [0, 2, -2], [1, 2, -2], [2, 2, -2], [-2, -2, -1], [-1, -2, -1], + + [0, -2, -1], [1, -2, -1], [2, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [-2, 0, -1], [-1, 0, -1], [0, 0, -1], + + [1, 0, -1], [2, 0, -1], [-2, 1, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], + + [2, 1, -1], [-2, 2, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], + + [-2, -2, 0], [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-2, 0, 0], [-1, 0, 0], + + [0, 0, 0], [1, 0, 0], [2, 0, 0], [-2, 1, 0], [-1, 1, 0], [0, 1, 0], + + [1, 1, 0], [2, 1, 0], [-2, 2, 0], [-1, 2, 0], [0, 2, 0], [1, 2, 0], + + [2, 2, 0], [-2, -2, 1], [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], + + [-2, -1, 1], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [-2, 1, 1], [-1, 1, 1], + + [0, 1, 1], [1, 1, 1], [2, 1, 1], [-2, 2, 1], [-1, 2, 1], [0, 2, 1], + + [1, 2, 1], [2, 2, 1], [-2, -2, 2], [-1, -2, 2], [0, -2, 2], [1, -2, 2], + + [2, -2, 2], [-2, -1, 2], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], + + [-2, 0, 2], [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [-2, 2, 2], [-1, 2, 2], + + [0, 2, 2], [1, 2, 2], [2, 2, 2]] + +> posn_list_3d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+3,+3,+3])); +posn_list_3d_size6 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [3, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], + + [1, -1, -2], [2, -1, -2], [3, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], + + [1, 0, -2], [2, 0, -2], [3, 0, -2], [-2, 1, -2], [-1, 1, -2], [0, 1, -2], + + [1, 1, -2], [2, 1, -2], [3, 1, -2], [-2, 2, -2], [-1, 2, -2], [0, 2, -2], + + [1, 2, -2], [2, 2, -2], [3, 2, -2], [-2, 3, -2], [-1, 3, -2], [0, 3, -2], + + [1, 3, -2], [2, 3, -2], [3, 3, -2], [-2, -2, -1], [-1, -2, -1], [0, -2, -1], + + [1, -2, -1], [2, -2, -1], [3, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [3, -1, -1], [-2, 0, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [3, 0, -1], [-2, 1, -1], + + [-1, 1, -1], [0, 1, -1], [1, 1, -1], [2, 1, -1], [3, 1, -1], [-2, 2, -1], + + [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], [3, 2, -1], [-2, 3, -1], + + [-1, 3, -1], [0, 3, -1], [1, 3, -1], [2, 3, -1], [3, 3, -1], [-2, -2, 0], + + [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [3, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [3, -1, 0], [-2, 0, 0], + + [-1, 0, 0], [0, 0, 0], [1, 0, 0], [2, 0, 0], [3, 0, 0], [-2, 1, 0], + + [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [3, 1, 0], [-2, 2, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [3, 2, 0], [-2, 3, 0], + + [-1, 3, 0], [0, 3, 0], [1, 3, 0], [2, 3, 0], [3, 3, 0], [-2, -2, 1], + + [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], [3, -2, 1], [-2, -1, 1], + + [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [3, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [3, 0, 1], [-2, 1, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [3, 1, 1], [-2, 2, 1], + + [-1, 2, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [3, 2, 1], [-2, 3, 1], + + [-1, 3, 1], [0, 3, 1], [1, 3, 1], [2, 3, 1], [3, 3, 1], [-2, -2, 2], + + [-1, -2, 2], [0, -2, 2], [1, -2, 2], [2, -2, 2], [3, -2, 2], [-2, -1, 2], + + [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], [3, -1, 2], [-2, 0, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [3, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [3, 1, 2], [-2, 2, 2], + + [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2], [3, 2, 2], [-2, 3, 2], + + [-1, 3, 2], [0, 3, 2], [1, 3, 2], [2, 3, 2], [3, 3, 2], [-2, -2, 3], + + [-1, -2, 3], [0, -2, 3], [1, -2, 3], [2, -2, 3], [3, -2, 3], [-2, -1, 3], + + [-1, -1, 3], [0, -1, 3], [1, -1, 3], [2, -1, 3], [3, -1, 3], [-2, 0, 3], + + [-1, 0, 3], [0, 0, 3], [1, 0, 3], [2, 0, 3], [3, 0, 3], [-2, 1, 3], + + [-1, 1, 3], [0, 1, 3], [1, 1, 3], [2, 1, 3], [3, 1, 3], [-2, 2, 3], + + [-1, 2, 3], [0, 2, 3], [1, 2, 3], [2, 2, 3], [3, 2, 3], [-2, 3, 3], + + [-1, 3, 3], [0, 3, 3], [1, 3, 3], [2, 3, 3], [3, 3, 3]] + +# Maple code to define Lagrange interpolating functions/coords/coeffs +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple,v 1.2 2002/08/20 16:31:24 jthorn Exp $ +> +################################################################################ +> +# +# 1-D interpolating functions +# +> +> fn_1d_order1 := +> proc(x) +> + c0 + c1*x +> end proc; + fn_1d_order1 := proc(x) c0 + c1*x end proc + +> +> fn_1d_order2 := +> proc(x) +> + c0 + c1*x + c2*x^2 +> end proc; + fn_1d_order2 := proc(x) c0 + c1*x + c2*x^2 end proc + +> +> fn_1d_order3 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 +> end proc; + fn_1d_order3 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 end proc + +> +> fn_1d_order4 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 +> end; + fn_1d_order4 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 end proc + +> +> fn_1d_order5 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 +> end; + fn_1d_order5 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 end proc + +> +> fn_1d_order6 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 +> end; +fn_1d_order6 := + + proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 end proc + +> +######################################## +> +# coordinates for 1-D interpolating functions +> coords_list_1d := [x]; + coords_list_1d := [x] + +> +######################################## +> +# +# coefficients in 1-D interpolating functions +# +> +> coeffs_list_1d_order1 := [c0, c1]; + coeffs_list_1d_order1 := [c0, c1] + +> coeffs_list_1d_order2 := [c0, c1, c2]; + coeffs_list_1d_order2 := [c0, c1, c2] + +> coeffs_list_1d_order3 := [c0, c1, c2, c3]; + coeffs_list_1d_order3 := [c0, c1, c2, c3] + +> coeffs_list_1d_order4 := [c0, c1, c2, c3, c4]; + coeffs_list_1d_order4 := [c0, c1, c2, c3, c4] + +> coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5]; + coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5] + +> coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6]; + coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6] + +> +################################################################################ +> +# +# 2-D interpolating functions +# +> +> fn_2d_order1 := +> proc(x,y) +> + c01*y +> + c00 + c10*x +> end proc; + fn_2d_order1 := proc(x, y) c01*y + c00 + c10*x end proc + +> +> fn_2d_order2 := +> proc(x,y) +> + c02*y^2 +> + c01*y + c11*x*y +> + c00 + c10*x + c20*x^2 +> end proc; +fn_2d_order2 := + + proc(x, y) c02*y^2 + c01*y + c11*x*y + c00 + c10*x + c20*x^2 end proc + +> +> fn_2d_order3 := +> proc(x,y) +> + c03*y^3 +> + c02*y^2 + c12*x*y^2 +> + c01*y + c11*x*y + c21*x^2*y +> + c00 + c10*x + c20*x^2 + c30*x^3 +> end proc; +fn_2d_order3 := proc(x, y) + c03*y^3 + c02*y^2 + c12*x*y^2 + c01*y + c11*x*y + c21*x^2*y + c00 + + c10*x + c20*x^2 + c30*x^3 +end proc + +> +> fn_2d_order4 := +> proc(x,y) +> + c04*y^4 +> + c03*y^3 + c13*x*y^3 +> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 +> + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +> + c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 +> end; +fn_2d_order4 := proc(x, y) + c04*y^4 + c03*y^3 + c13*x*y^3 + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + c00 + c10*x + c20*x^2 + + c30*x^3 + c40*x^4 +end proc + +> +######################################## +> +# coordinates for 2-D interpolating functions +> coords_list_2d := [x,y]; + coords_list_2d := [x, y] + +> +######################################## +> +# +# coefficients in 2-D interpolating functions +# +> +> coeffs_list_2d_order1 := [ +> c01, +> c00, c10 +> ]; + coeffs_list_2d_order1 := [c01, c00, c10] + +> coeffs_list_2d_order2 := [ +> c02, +> c01, c11, +> c00, c10, c20 +> ]; + coeffs_list_2d_order2 := [c02, c01, c11, c00, c10, c20] + +> coeffs_list_2d_order3 := [ +> c03, +> c02, c12, +> c01, c11, c21, +> c00, c10, c20, c30 +> ]; + coeffs_list_2d_order3 := [c03, c02, c12, c01, c11, c21, c00, c10, c20, c30] + +> coeffs_list_2d_order4 := [ +> c04, +> c03, c13, +> c02, c12, c22, +> c01, c11, c21, c31, +> c00, c10, c20, c30, c40 +> ]; +coeffs_list_2d_order4 := + + [c04, c03, c13, c02, c12, c22, c01, c11, c21, c31, c00, c10, c20, c30, c40] + +> +################################################################################ +> +# +# 3-D interpolating functions +# +> +> fn_3d_order1 := +> proc(x,y,z) +# z^0 ----------- +> + c010*y +> + c000 + c100*x +# z^1 ----------- +> + c001*z +> end proc; + fn_3d_order1 := proc(x, y, z) c010*y + c000 + c100*x + c001*z end proc + +> +> fn_3d_order2 := +> proc(x,y,z) +# z^0 -------------------------- +> + c020*y^2 +> + c010*y + c110*x*y +> + c000 + c100*x + c200*x^2 +# z^1 -------------------------- +> + c011*y*z +> + c001*z + c101*x*z +# z^2 -------------------------- +> + c002*z^2 +> end proc; +fn_3d_order2 := proc(x, y, z) + c020*y^2 + c010*y + c110*x*y + c000 + c100*x + c200*x^2 + c011*y*z + + c001*z + c101*x*z + c002*z^2 +end proc + +> +> fn_3d_order3 := +> proc(x,y,z) +# z^0 ------------------------------------------- +> + c030*y^3 +> + c020*y^2 + c120*x*y^2 +> + c010*y + c110*x*y + c210*x^2*y +> + c000 + c100*x + c200*x^2 + c300*x^3 +# z^1 ------------------------------------------- +> + c021*y^2*z +> + c011*y *z + c111*x*y*z +> + c001 *z + c101*x *z + c201*x^2*z +# z^2 ------------------------------------------- +> + c012*y*z^2 +> + c002 *z^2 + c102*x*z^2 +# z^3 ------------------------------------------- +> + c003 *z^3 +> end proc; +fn_3d_order3 := proc(x, y, z) + c030*y^3 + c020*y^2 + c120*x*y^2 + c010*y + c110*x*y + c210*x^2*y + + c000 + c100*x + c200*x^2 + c300*x^3 + c021*y^2*z + c011*y*z + + c111*x*y*z + c001*z + c101*x*z + c201*x^2*z + c012*y*z^2 + c002*z^2 + + c102*x*z^2 + c003*z^3 +end proc + +> +> fn_3d_order4 := +> proc(x,y,z) +# z^0 -------------------------------------------------------- +> + c040*y^4 +> + c030*y^3 + c130*x*y^3 +> + c020*y^2 + c120*x*y^2 + c220*x^2*y^2 +> + c010*y + c110*x*y + c210*x^2*y + c310*x^3*y +> + c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 +# z^1 ------------------------------------------- +> + c031*y^3*z +> + c021*y^2*z + c121*x*y^2*z +> + c011*y *z + c111*x*y *z + c211*x^2*y*z +> + c001 *z + c101*x *z + c201*x^2 *z + c301*x^3*z +# z^2 ------------------------------------------- +> + c022*y^2*z^2 +> + c012*y *z^2 + c112*x*y*z^2 +> + c002 *z^2 + c102*x *z^2 + c202*x^2*z^2 +# z^3 ------------------------------------------- +> + c013*y *z^3 +> + c003 *z^3 + c103*x *z^3 +# z^4 ------------------------------------------- +> + c004 *z^4 +> end; +fn_3d_order4 := proc(x, y, z) + c102*x*z^2 + c012*y*z^2 + c111*x*y*z + c121*x*y^2*z + c211*x^2*y*z + + c112*x*y*z^2 + c010*y + c110*x*y + c011*y*z + c101*x*z + c120*x*y^2 + + c210*x^2*y + c021*y^2*z + c201*x^2*z + c130*x*y^3 + c220*x^2*y^2 + + c310*x^3*y + c031*y^3*z + c301*x^3*z + c022*y^2*z^2 + c202*x^2*z^2 + + c013*y*z^3 + c103*x*z^3 + c000 + c100*x + c001*z + c020*y^2 + + c200*x^2 + c002*z^2 + c030*y^3 + c300*x^3 + c003*z^3 + c040*y^4 + + c400*x^4 + c004*z^4 +end proc + +> +######################################## +> +# coordinates for 3-D interpolating functions +> coords_list_3d := [x,y,z]; + coords_list_3d := [x, y, z] + +> +######################################## +> +# +# coefficients in 3-D interpolating functions +# +> +> coeffs_list_3d_order1 := [ +> # z^0 ----- +> c010, +> c000, c100, +> # z^1 ----- +> c001 +> ]; + coeffs_list_3d_order1 := [c010, c000, c100, c001] + +> coeffs_list_3d_order2 := [ +> # z^0 ----------- +> c020, +> c010, c110, +> c000, c100, c200, +> # z^1 ----------- +> c011, +> c001, c101, +> # z^2 ----------- +> c002 +> ]; +coeffs_list_3d_order2 := + + [c020, c010, c110, c000, c100, c200, c011, c001, c101, c002] + +> coeffs_list_3d_order3 := [ +> # z^0 ---------------- +> c030, +> c020, c120, +> c010, c110, c210, +> c000, c100, c200, c300, +> # z^1 ---------------- +> c021, +> c011, c111, +> c001, c101, c201, +> # z^2 ---------------- +> c012, +> c002, c102, +> # z^3 ---------------- +> c003 +> ]; +coeffs_list_3d_order3 := [c030, c020, c120, c010, c110, c210, c000, c100, c200, + + c300, c021, c011, c111, c001, c101, c201, c012, c002, c102, c003] + +> coeffs_list_3d_order4 := [ +> # z^0 ----------------------- +> c040, +> c030, c130, +> c020, c120, c220, +> c010, c110, c210, c310, +> c000, c100, c200, c300, c400, +> # z^1 ----------------------- +> c031, +> c021, c121, +> c011, c111, c211, +> c001, c101, c201, c301, +> # z^2 ----------------------- +> c022, +> c012, c112, +> c002, c102, c202, +> # z^3 ----------------------- +> c013, +> c003, c103, +> # z^4 ----------------------- +> c004 +> ]; +coeffs_list_3d_order4 := [c040, c030, c130, c020, c120, c220, c010, c110, c210, + + c310, c000, c100, c200, c300, c400, c031, c021, c121, c011, c111, c211, + + c001, c101, c201, c301, c022, c012, c112, c002, c102, c202, c013, c003, + + c103, c004] + +> +################################################################################ +# 2d.maple -- compute Lagrange interpolation coefficients in 2-D +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/2d.maple,v 1.2 2002/08/20 16:31:24 jthorn Exp $ +> +################################################################################ +> +# +# 2d, cube, order=1, smoothing=0 (size=2) +# +> +# interpolating polynomial +> interp_2d_cube_order1_smooth0 +> := Lagrange_polynomial_interpolant(fn_2d_order1, coeffs_list_2d_order1, +> coords_list_2d, posn_list_2d_size2); +interp_2d_cube_order1_smooth0 := + + (1/2 DATA(1, 1) - 1/2 DATA(0, 0) - 1/2 DATA(1, 0) + 1/2 DATA(0, 1)) y + + - 1/4 DATA(1, 1) + 3/4 DATA(0, 0) + 1/4 DATA(1, 0) + 1/4 DATA(0, 1) + + + (1/2 DATA(1, 1) - 1/2 DATA(0, 0) + 1/2 DATA(1, 0) - 1/2 DATA(0, 1)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_2d_size2); +[COEFF(0, 0) = 3/4 - 1/2 y - 1/2 x, COEFF(1, 0) = 1/4 - 1/2 y + 1/2 x, + + COEFF(0, 1) = - 1/2 x + 1/4 + 1/2 y, COEFF(1, 1) = 1/2 y - 1/4 + 1/2 x] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c"); +bytes used=1000980, alloc=917336, time=0.08 +> +# d/dx +> simplify( diff(interp_2d_cube_order1_smooth0,x) ); + 1/2 DATA(1, 1) - 1/2 DATA(0, 0) + 1/2 DATA(1, 0) - 1/2 DATA(0, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size2); + [COEFF(0, 0) = -1/2, COEFF(1, 0) = 1/2, COEFF(0, 1) = -1/2, COEFF(1, 1) = 1/2] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c"); +> +# d/dy +> simplify( diff(interp_2d_cube_order1_smooth0,y) ); + 1/2 DATA(1, 1) - 1/2 DATA(0, 0) - 1/2 DATA(1, 0) + 1/2 DATA(0, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size2); +bytes used=2001372, alloc=1376004, time=0.15 + [COEFF(0, 0) = -1/2, COEFF(1, 0) = -1/2, COEFF(0, 1) = 1/2, COEFF(1, 1) = 1/2] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c"); +> +################################################################################ +> +# +# 2d, cube, order=2, smoothing=0 (size=3) +# +> +# interpolating polynomial +> interp_2d_cube_order2_smooth0 +> := Lagrange_polynomial_interpolant(fn_2d_order2, coeffs_list_2d_order2, +> coords_list_2d, posn_list_2d_size3); +interp_2d_cube_order2_smooth0 := (1/6 DATA(0, 1) + 1/6 DATA(1, -1) + + + 1/6 DATA(0, -1) - 1/3 DATA(0, 0) + 1/6 DATA(-1, -1) + 1/6 DATA(1, 1) + + 2 + - 1/3 DATA(-1, 0) - 1/3 DATA(1, 0) + 1/6 DATA(-1, 1)) y + ( + + 1/6 DATA(-1, 1) - 1/6 DATA(-1, -1) - 1/6 DATA(0, -1) - 1/6 DATA(1, -1) + + + 1/6 DATA(1, 1) + 1/6 DATA(0, 1)) y + + + (1/4 DATA(1, 1) + 1/4 DATA(-1, -1) - 1/4 DATA(1, -1) - 1/4 DATA(-1, 1)) x y + + + 2/9 DATA(0, 1) - 1/9 DATA(1, -1) + 2/9 DATA(0, -1) + 5/9 DATA(0, 0) + + - 1/9 DATA(-1, -1) - 1/9 DATA(1, 1) + 2/9 DATA(-1, 0) + 2/9 DATA(1, 0) + + - 1/9 DATA(-1, 1) + (1/6 DATA(1, 0) - 1/6 DATA(-1, -1) + 1/6 DATA(1, -1) + + - 1/6 DATA(-1, 0) - 1/6 DATA(-1, 1) + 1/6 DATA(1, 1)) x + ( + + - 1/3 DATA(0, 1) + 1/6 DATA(1, -1) - 1/3 DATA(0, -1) - 1/3 DATA(0, 0) + + + 1/6 DATA(-1, -1) + 1/6 DATA(1, 1) + 1/6 DATA(-1, 0) + 1/6 DATA(1, 0) + + 2 + + 1/6 DATA(-1, 1)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_2d_size3); + 2 2 +[COEFF(-1, -1) = - 1/9 + 1/6 y - 1/6 y - 1/6 x + 1/4 x y + 1/6 x , + + 2 2 + COEFF(0, -1) = 2/9 - 1/6 y + 1/6 y - 1/3 x , + + 2 2 + COEFF(1, -1) = - 1/6 y - 1/4 x y - 1/9 + 1/6 x + 1/6 y + 1/6 x , + + 2 2 + COEFF(-1, 0) = - 1/3 y - 1/6 x + 1/6 x + 2/9, + + 2 2 + COEFF(0, 0) = - 1/3 y - 1/3 x + 5/9, + + 2 2 + COEFF(1, 0) = - 1/3 y + 1/6 x + 2/9 + 1/6 x , + + 2 2 + COEFF(-1, 1) = 1/6 y + 1/6 y + 1/6 x - 1/6 x - 1/4 x y - 1/9, + + 2 2 + COEFF(0, 1) = 1/6 y + 1/6 y - 1/3 x + 2/9, + + 2 2 + COEFF(1, 1) = 1/6 y + 1/6 x - 1/9 + 1/6 y + 1/6 x + 1/4 x y] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c"); +bytes used=3001624, alloc=1769148, time=0.22 +bytes used=4001856, alloc=1834672, time=0.29 +> +# d/dx +> simplify( diff(interp_2d_cube_order2_smooth0,x) ); +1/4 y DATA(1, 1) + 1/4 y DATA(-1, -1) - 1/4 y DATA(1, -1) - 1/4 y DATA(-1, 1) + + + 1/6 DATA(1, 0) - 1/6 DATA(-1, -1) + 1/6 DATA(1, -1) - 1/6 DATA(-1, 0) + + - 1/6 DATA(-1, 1) + 1/6 DATA(1, 1) - 2/3 x DATA(0, 1) + 1/3 x DATA(1, -1) + + - 2/3 x DATA(0, -1) - 2/3 x DATA(0, 0) + 1/3 x DATA(-1, -1) + + + 1/3 x DATA(1, 1) + 1/3 x DATA(-1, 0) + 1/3 x DATA(1, 0) + + + 1/3 x DATA(-1, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); +[COEFF(-1, -1) = 1/3 x + 1/4 y - 1/6, COEFF(0, -1) = - 2/3 x, + + COEFF(1, -1) = - 1/4 y + 1/3 x + 1/6, COEFF(-1, 0) = 1/3 x - 1/6, + + COEFF(0, 0) = - 2/3 x, COEFF(1, 0) = 1/3 x + 1/6, + + COEFF(-1, 1) = - 1/4 y - 1/6 + 1/3 x, COEFF(0, 1) = - 2/3 x, + + COEFF(1, 1) = 1/4 y + 1/6 + 1/3 x] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c"); +bytes used=5002008, alloc=1834672, time=0.37 +> +# d/dy +> simplify( diff(interp_2d_cube_order2_smooth0,y) ); +1/3 y DATA(0, 1) + 1/3 y DATA(1, -1) + 1/3 y DATA(0, -1) - 2/3 y DATA(0, 0) + + + 1/3 y DATA(-1, -1) + 1/3 y DATA(1, 1) - 2/3 y DATA(-1, 0) + + - 2/3 y DATA(1, 0) + 1/3 y DATA(-1, 1) + 1/6 DATA(-1, 1) + + - 1/6 DATA(-1, -1) - 1/6 DATA(0, -1) - 1/6 DATA(1, -1) + 1/6 DATA(1, 1) + + + 1/6 DATA(0, 1) + 1/4 x DATA(1, 1) + 1/4 x DATA(-1, -1) + + - 1/4 x DATA(1, -1) - 1/4 x DATA(-1, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); +[COEFF(-1, -1) = 1/4 x + 1/3 y - 1/6, COEFF(0, -1) = - 1/6 + 1/3 y, + + COEFF(1, -1) = - 1/6 - 1/4 x + 1/3 y, COEFF(-1, 0) = - 2/3 y, + + COEFF(0, 0) = - 2/3 y, COEFF(1, 0) = - 2/3 y, + + COEFF(-1, 1) = 1/3 y + 1/6 - 1/4 x, COEFF(0, 1) = 1/3 y + 1/6, + + COEFF(1, 1) = 1/3 y + 1/4 x + 1/6] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c"); +> +# d^2/dx^2 +> simplify( diff(interp_2d_cube_order2_smooth0,x,x) ); +bytes used=6002212, alloc=1834672, time=0.42 +- 2/3 DATA(0, 1) + 1/3 DATA(1, -1) - 2/3 DATA(0, -1) - 2/3 DATA(0, 0) + + + 1/3 DATA(-1, -1) + 1/3 DATA(1, 1) + 1/3 DATA(-1, 0) + 1/3 DATA(1, 0) + + + 1/3 DATA(-1, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); +[COEFF(-1, -1) = 1/3, COEFF(0, -1) = -2/3, COEFF(1, -1) = 1/3, + + COEFF(-1, 0) = 1/3, COEFF(0, 0) = -2/3, COEFF(1, 0) = 1/3, + + COEFF(-1, 1) = 1/3, COEFF(0, 1) = -2/3, COEFF(1, 1) = 1/3] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c"); +> +# d^2/dxdy +> simplify( diff(interp_2d_cube_order2_smooth0,x,y) ); + 1/4 DATA(1, 1) + 1/4 DATA(-1, -1) - 1/4 DATA(1, -1) - 1/4 DATA(-1, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); +[COEFF(-1, -1) = 1/4, COEFF(0, -1) = 0, COEFF(1, -1) = -1/4, COEFF(-1, 0) = 0, + + COEFF(0, 0) = 0, COEFF(1, 0) = 0, COEFF(-1, 1) = -1/4, COEFF(0, 1) = 0, + + COEFF(1, 1) = 1/4] + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c"); +> +# d^2/dy^2 +> simplify( diff(interp_2d_cube_order2_smooth0,y,y) ); +1/3 DATA(0, 1) + 1/3 DATA(1, -1) + 1/3 DATA(0, -1) - 2/3 DATA(0, 0) + + + 1/3 DATA(-1, -1) + 1/3 DATA(1, 1) - 2/3 DATA(-1, 0) - 2/3 DATA(1, 0) + + + 1/3 DATA(-1, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); +[COEFF(-1, -1) = 1/3, COEFF(0, -1) = 1/3, COEFF(1, -1) = 1/3, + + COEFF(-1, 0) = -2/3, COEFF(0, 0) = -2/3, COEFF(1, 0) = -2/3, + + COEFF(-1, 1) = 1/3, COEFF(0, 1) = 1/3, COEFF(1, 1) = 1/3] + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c"); +bytes used=7002528, alloc=1834672, time=0.52 +> +################################################################################ +> +# +# 2d, cube, order=3, smoothing=0 (size=4) +# +> +# interpolating polynomial +> interp_2d_cube_order3_smooth0 +> := Lagrange_polynomial_interpolant(fn_2d_order3, coeffs_list_2d_order3, +> coords_list_2d, posn_list_2d_size4); +bytes used=8002908, alloc=1900196, time=0.59 +bytes used=9003224, alloc=1900196, time=0.65 +bytes used=10004308, alloc=1965720, time=0.71 +bytes used=11004468, alloc=1965720, time=0.77 +interp_2d_cube_order3_smooth0 := (- 3/40 DATA(2, 0) + 1/40 DATA(0, 0) + + - 1/40 DATA(1, 0) + 1/40 DATA(0, 1) - 1/40 DATA(1, 1) - 1/40 DATA(0, -1) + + - 3/40 DATA(-1, -1) + 1/40 DATA(1, -1) + 3/40 DATA(-1, 0) + + + 3/40 DATA(-1, 1) + 3/40 DATA(2, -1) - 1/40 DATA(0, 2) - 3/40 DATA(-1, 2) + + 2 / + - 3/40 DATA(2, 1) + 1/40 DATA(1, 2) + 3/40 DATA(2, 2)) x y + | + \ + + 7/100 DATA(2, 0) - 1/25 DATA(0, 0) - 1/100 DATA(1, 0) - 1/100 DATA(0, 1) + + 13 + + 3/50 DATA(1, 1) - 1/50 DATA(0, -1) + 6/25 DATA(-1, -1) - --- DATA(1, -1) + 100 + + 13 + - 1/50 DATA(-1, 0) - --- DATA(-1, 1) - 9/100 DATA(2, -1) + 100 + + + 7/100 DATA(0, 2) - 9/100 DATA(-1, 2) + 2/25 DATA(2, 1) + 2/25 DATA(1, 2) + + \ + - 3/50 DATA(2, 2)| x y + (- 1/40 DATA(2, 0) + 1/40 DATA(0, 0) + / + + + 1/40 DATA(1, 0) - 1/40 DATA(0, 1) - 1/40 DATA(1, 1) + 3/40 DATA(0, -1) + + - 3/40 DATA(-1, -1) + 3/40 DATA(1, -1) - 1/40 DATA(-1, 0) + + + 1/40 DATA(-1, 1) - 3/40 DATA(2, -1) - 3/40 DATA(0, 2) + 3/40 DATA(-1, 2) + + 2 + + 1/40 DATA(2, 1) - 3/40 DATA(1, 2) + 3/40 DATA(2, 2)) x y + + 13 93 37 37 + + --- DATA(2, 0) + --- DATA(0, 0) + --- DATA(1, 0) + --- DATA(0, 1) + 100 200 200 200 + + 17 11 23 + - --- DATA(1, 1) + -- DATA(0, -1) - --- DATA(-1, -1) - 1/50 DATA(1, -1) + 200 50 200 + + 11 17 13 + + -- DATA(-1, 0) - 1/50 DATA(-1, 1) - --- DATA(2, -1) + --- DATA(0, 2) + 50 200 100 + + 17 + - --- DATA(-1, 2) - 2/25 DATA(2, 1) - 2/25 DATA(1, 2) + 7/200 DATA(2, 2) + 200 + + + (1/8 DATA(2, 0) + 1/8 DATA(0, 0) + 1/8 DATA(1, 0) - 1/8 DATA(0, 1) + + - 1/8 DATA(1, 1) - 1/24 DATA(0, -1) - 1/24 DATA(-1, -1) - 1/24 DATA(1, -1) + + + 1/8 DATA(-1, 0) - 1/8 DATA(-1, 1) - 1/24 DATA(2, -1) + 1/24 DATA(0, 2) + + + 1/24 DATA(-1, 2) - 1/8 DATA(2, 1) + 1/24 DATA(1, 2) + 1/24 DATA(2, 2)) + + 3 / 49 57 63 117 + y + |- --- DATA(2, 0) - --- DATA(0, 0) - --- DATA(1, 0) + --- DATA(0, 1) + \ 400 400 400 400 + + 103 223 109 157 + + --- DATA(1, 1) - ---- DATA(0, -1) - ---- DATA(-1, -1) - ---- DATA(1, -1) + 400 1200 1200 1200 + + 31 111 89 43 + - --- DATA(-1, 0) + --- DATA(-1, 1) + ---- DATA(2, -1) + ---- DATA(0, 2) + 400 400 1200 1200 + + 131 69 37 149 \ + - ---- DATA(-1, 2) + --- DATA(2, 1) + ---- DATA(1, 2) - ---- DATA(2, 2)| y + 1200 400 1200 1200 / + + / 43 57 117 63 + + |---- DATA(2, 0) - --- DATA(0, 0) + --- DATA(1, 0) - --- DATA(0, 1) + \1200 400 400 400 + + 103 31 109 111 + + --- DATA(1, 1) - --- DATA(0, -1) - ---- DATA(-1, -1) + --- DATA(1, -1) + 400 400 1200 400 + + 223 157 131 49 + - ---- DATA(-1, 0) - ---- DATA(-1, 1) - ---- DATA(2, -1) - --- DATA(0, 2) + 1200 1200 1200 400 + + 89 37 69 149 \ + + ---- DATA(-1, 2) + ---- DATA(2, 1) + --- DATA(1, 2) - ---- DATA(2, 2)| x + 1200 1200 400 1200 / + + / 21 19 + + |1/80 DATA(2, 0) - -- DATA(0, 0) + 9/80 DATA(1, 0) - -- DATA(0, 1) + \ 80 80 + + 11 23 13 + + -- DATA(1, 1) - -- DATA(0, -1) + -- DATA(-1, -1) + 7/80 DATA(1, -1) + 80 80 80 + + 11 17 + + -- DATA(-1, 0) + 9/80 DATA(-1, 1) + 3/80 DATA(2, -1) - -- DATA(0, 2) + 80 80 + + 13 \ 2 + + 7/80 DATA(-1, 2) - 1/80 DATA(2, 1) + -- DATA(1, 2) - 3/80 DATA(2, 2)| x + 80 / + + + (1/24 DATA(2, 0) + 1/8 DATA(0, 0) - 1/8 DATA(1, 0) + 1/8 DATA(0, 1) + + - 1/8 DATA(1, 1) + 1/8 DATA(0, -1) - 1/24 DATA(-1, -1) - 1/8 DATA(1, -1) + + - 1/24 DATA(-1, 0) - 1/24 DATA(-1, 1) + 1/24 DATA(2, -1) + 1/8 DATA(0, 2) + + - 1/24 DATA(-1, 2) + 1/24 DATA(2, 1) - 1/8 DATA(1, 2) + 1/24 DATA(2, 2)) + + 3 / 17 21 19 + x + |- -- DATA(2, 0) - -- DATA(0, 0) - -- DATA(1, 0) + 9/80 DATA(0, 1) + \ 80 80 80 + + 11 11 13 + + -- DATA(1, 1) + -- DATA(0, -1) + -- DATA(-1, -1) + 9/80 DATA(1, -1) + 80 80 80 + + 23 + - -- DATA(-1, 0) + 7/80 DATA(-1, 1) + 7/80 DATA(2, -1) + 1/80 DATA(0, 2) + 80 + + 13 \ 2 + + 3/80 DATA(-1, 2) + -- DATA(2, 1) - 1/80 DATA(1, 2) - 3/80 DATA(2, 2)| y + 80 / + +> +# I +> coeffs_as_lc_of_data(%, posn_list_2d_size4); +bytes used=12010172, alloc=1965720, time=0.82 + 2 13 2 13 2 2 109 +[COEFF(-1, -1) = - 3/40 x y + -- y + -- x - 3/40 x y - ---- x + 6/25 x y + 80 80 1200 + + 109 23 3 3 2 2 + - ---- y - --- - 1/24 y - 1/24 x , COEFF(0, -1) = 3/40 x y - 1/40 x y + 1200 200 + + 223 11 11 2 3 31 3 23 2 + - ---- y + -- + -- y + 1/8 x - --- x - 1/50 x y - 1/24 y - -- x , + 1200 50 80 400 80 + + 2 3 2 2 2 + COEFF(1, -1) = 9/80 y - 1/50 - 1/24 y + 7/80 x + 1/40 x y + 3/40 x y + + 111 157 13 3 89 131 + + --- x - ---- y - --- x y - 1/8 x , COEFF(2, -1) = ---- y - ---- x + 400 1200 100 1200 1200 + + 17 2 3 2 2 2 + - 9/100 x y - --- + 7/80 y - 1/24 y - 3/40 x y + 3/40 x y + 3/80 x + 200 + + 3 2 23 2 11 2 11 2 + + 1/24 x , COEFF(-1, 0) = - 1/40 x y - -- y + -- x + -- + 3/40 x y + 80 80 50 + + 3 3 223 31 3 93 + - 1/50 x y - 1/24 x + 1/8 y - ---- x - --- y, COEFF(0, 0) = 1/8 y + --- + 1200 400 200 + + 2 2 57 21 2 57 21 2 + + 1/40 x y + 1/40 x y - 1/25 x y - --- y - -- x - --- x - -- y + 400 80 400 80 + + 3 37 19 2 3 3 63 2 + + 1/8 x , COEFF(1, 0) = --- - -- y - 1/8 x + 1/8 y - --- y - 1/40 x y + 200 80 400 + + 2 117 2 2 13 + + 9/80 x - 1/100 x y + --- x + 1/40 x y, COEFF(2, 0) = - 1/40 x y + --- + 400 100 + + 17 2 3 2 3 49 2 + - -- y + 1/24 x + 7/100 x y + 1/80 x + 1/8 y - --- y - 3/40 x y + 80 400 + + 43 2 3 13 111 + + ---- x, COEFF(-1, 1) = - 1/50 + 1/40 x y - 1/24 x - --- x y + --- y + 1200 100 400 + + 157 3 2 2 2 3 + - ---- x - 1/8 y + 7/80 y + 9/80 x + 3/40 x y , COEFF(0, 1) = - 1/8 y + 1200 + + 63 2 2 3 37 2 + - 1/100 x y - --- x - 1/40 x y + 1/40 x y + 1/8 x + --- + 9/80 y + 400 200 + + 117 19 2 3 3 11 2 + + --- y - -- x , COEFF(1, 1) = 3/50 x y - 1/8 x - 1/8 y + -- y + 400 80 80 + + 2 103 103 11 2 17 2 + - 1/40 x y + --- y + --- x + -- x - --- - 1/40 x y , COEFF(2, 1) = + 400 400 80 200 + + 2 2 69 3 3 13 2 + 1/40 x y - 2/25 - 1/80 x + --- y + 2/25 x y - 1/8 y + 1/24 x + -- y + 400 80 + + 2 37 2 17 2 + - 3/40 x y + ---- x, COEFF(-1, 2) = 3/40 x y - --- - 9/100 x y + 7/80 x + 1200 200 + + 89 131 3 2 2 3 + + ---- x - ---- y - 1/24 x - 3/40 x y + 3/80 y + 1/24 y , COEFF(0, 2) + 1200 1200 + + 43 3 2 13 2 17 2 + = ---- y + 1/8 x - 3/40 x y + 7/100 x y + --- + 1/80 y - -- x + 1200 100 80 + + 3 49 2 13 2 69 + + 1/24 y - --- x - 1/40 x y , COEFF(1, 2) = 2/25 x y + -- x + --- x + 400 80 400 + + 2 3 37 3 2 2 + - 3/40 x y - 1/8 x - 2/25 + ---- y + 1/24 y + 1/40 x y - 1/80 y , + 1200 + + 2 2 149 3 2 + COEFF(2, 2) = 3/40 x y - 3/80 y - ---- y + 1/24 y + 3/40 x y - 3/50 x y + 1200 + + 2 149 3 + - 3/80 x - ---- x + 7/200 + 1/24 x ] + 1200 + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c"); +bytes used=13010356, alloc=2031244, time=0.89 +bytes used=14014296, alloc=2031244, time=0.96 +bytes used=15017972, alloc=2031244, time=1.06 +bytes used=16018212, alloc=2031244, time=1.13 +bytes used=17018832, alloc=2031244, time=1.22 +bytes used=18019192, alloc=2031244, time=1.30 +bytes used=19019652, alloc=2031244, time=1.40 +bytes used=20019840, alloc=2031244, time=1.46 +> +# d/dx +> simplify( diff(interp_2d_cube_order3_smooth0,x) ); +bytes used=21020004, alloc=2031244, time=1.52 +3/20 x y DATA(1, -1) - 1/20 x y DATA(-1, 0) + 1/20 x y DATA(-1, 1) + + - 3/20 x y DATA(2, -1) - 3/20 x y DATA(0, 2) + 3/20 x y DATA(-1, 2) + + + 1/20 x y DATA(2, 1) - 3/20 x y DATA(1, 2) + 3/20 x y DATA(2, 2) + + - 1/20 x y DATA(1, 1) - 1/20 x y DATA(2, 0) + 1/20 x y DATA(0, 0) + + 43 + + 1/20 x y DATA(1, 0) - 1/20 x y DATA(0, 1) + ---- DATA(2, 0) + 1200 + + 21 11 11 + - -- x DATA(0, 0) + -- x DATA(1, 1) + -- x DATA(-1, 0) + 40 40 40 + + 13 23 + + 7/40 x DATA(1, -1) + -- x DATA(-1, -1) - -- x DATA(0, -1) + 40 40 + + 19 + + 9/40 x DATA(1, 0) - -- x DATA(0, 1) - 3/50 y DATA(2, 2) + 40 + + + 1/40 x DATA(2, 0) - 1/25 y DATA(0, 0) + 7/100 y DATA(2, 0) + + + 7/100 y DATA(0, 2) - 9/100 y DATA(2, -1) - 9/100 y DATA(-1, 2) + + + 2/25 y DATA(1, 2) + 2/25 y DATA(2, 1) - 1/50 y DATA(0, -1) + + 13 13 + - --- y DATA(1, -1) + 6/25 y DATA(-1, -1) - --- y DATA(-1, 1) + 100 100 + + - 1/50 y DATA(-1, 0) - 1/100 y DATA(0, 1) - 1/100 y DATA(1, 0) + + 2 + + 3/40 y DATA(2, 2) + 3/50 y DATA(1, 1) + 3/40 x DATA(2, -1) + + 2 2 2 + + 1/40 y DATA(1, 2) - 3/40 y DATA(2, 1) - 3/40 y DATA(-1, 2) + + 17 2 + + 9/40 x DATA(-1, 1) - -- x DATA(0, 2) - 3/8 x DATA(1, 0) + 40 + + 2 + + 3/8 x DATA(0, 1) - 3/40 x DATA(2, 2) + 7/40 x DATA(-1, 2) + + 13 2 + + -- x DATA(1, 2) - 1/40 x DATA(2, 1) + 1/8 x DATA(2, 0) + 40 + + 2 2 2 + + 3/8 x DATA(0, 0) + 1/8 x DATA(2, -1) - 3/8 x DATA(1, -1) + + 2 2 2 + - 1/8 x DATA(-1, 0) - 3/8 x DATA(1, 1) - 1/8 x DATA(-1, 2) + + 2 2 2 + - 1/8 x DATA(-1, 1) - 3/8 x DATA(1, 2) + 3/8 x DATA(0, 2) + + 2 2 2 + + 1/8 x DATA(2, 2) + 1/8 x DATA(2, 1) + 3/8 x DATA(0, -1) + + 2 2 2 + - 1/8 x DATA(-1, -1) - 3/40 y DATA(-1, -1) + 1/40 y DATA(1, -1) + + 2 2 2 + - 1/40 y DATA(0, -1) + 1/40 y DATA(0, 1) - 1/40 y DATA(1, 1) + + 2 2 2 + + 3/40 y DATA(-1, 0) + 3/40 y DATA(-1, 1) + 3/40 y DATA(2, -1) + + 2 2 2 + - 1/40 y DATA(0, 2) - 3/40 y DATA(2, 0) - 1/40 y DATA(1, 0) + + 2 + + 1/40 y DATA(0, 0) + 3/20 x y DATA(0, -1) - 3/20 x y DATA(-1, -1) + + 57 117 63 103 + - --- DATA(0, 0) + --- DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1) + 400 400 400 400 + + 31 109 111 223 + - --- DATA(0, -1) - ---- DATA(-1, -1) + --- DATA(1, -1) - ---- DATA(-1, 0) + 400 1200 400 1200 + + 157 131 49 89 + - ---- DATA(-1, 1) - ---- DATA(2, -1) - --- DATA(0, 2) + ---- DATA(-1, 2) + 1200 1200 400 1200 + + 37 69 149 + + ---- DATA(2, 1) + --- DATA(1, 2) - ---- DATA(2, 2) + 1200 400 1200 + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); +bytes used=22023600, alloc=2096768, time=1.59 + 2 13 109 2 +[COEFF(-1, -1) = - 3/20 x y - 3/40 y + -- x + 6/25 y - ---- - 1/8 x , + 40 1200 + + 2 31 23 2 + COEFF(0, -1) = 3/8 x + 3/20 x y - 1/50 y - --- - -- x - 1/40 y , + 400 40 + + 111 2 13 2 + COEFF(1, -1) = --- + 1/40 y - --- y + 3/20 x y - 3/8 x + 7/40 x, + 400 100 + + 2 131 2 + COEFF(2, -1) = 1/8 x + 3/40 x - ---- - 9/100 y + 3/40 y - 3/20 x y, + 1200 + + 2 223 2 11 + COEFF(-1, 0) = 3/40 y - 1/20 x y - ---- - 1/8 x - 1/50 y + -- x, + 1200 40 + + 2 21 57 2 + COEFF(0, 0) = - 1/25 y + 1/20 x y + 1/40 y - -- x - --- + 3/8 x , + 40 400 + + 2 2 117 + COEFF(1, 0) = - 1/40 y + 1/20 x y - 1/100 y - 3/8 x + 9/40 x + ---, + 400 + + 2 2 43 + COEFF(2, 0) = - 1/20 x y + 1/8 x - 3/40 y + 1/40 x + ---- + 7/100 y, + 1200 + + 157 2 13 2 + COEFF(-1, 1) = - ---- + 3/40 y - --- y + 9/40 x - 1/8 x + 1/20 x y, + 1200 100 + + 2 63 2 19 + COEFF(0, 1) = 1/40 y - --- + 3/8 x - 1/100 y - 1/20 x y - -- x, + 400 40 + + 103 2 2 11 + COEFF(1, 1) = - 1/20 x y + --- - 3/8 x + 3/50 y - 1/40 y + -- x, + 400 40 + + 2 2 37 + COEFF(2, 1) = 1/20 x y - 3/40 y + 1/8 x + 2/25 y + ---- - 1/40 x, + 1200 + + 2 89 2 + COEFF(-1, 2) = - 1/8 x + ---- + 7/40 x - 3/40 y + 3/20 x y - 9/100 y, + 1200 + + 2 2 17 49 + COEFF(0, 2) = - 1/40 y - 3/20 x y + 7/100 y + 3/8 x - -- x - ---, + 40 400 + + 69 13 2 2 + COEFF(1, 2) = --- + -- x + 1/40 y - 3/8 x + 2/25 y - 3/20 x y, + 400 40 + + 2 149 2 + COEFF(2, 2) = 3/40 y - ---- + 3/20 x y - 3/50 y + 1/8 x - 3/40 x] + 1200 + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c"); +bytes used=23023764, alloc=2096768, time=1.67 +bytes used=24024212, alloc=2096768, time=1.75 +bytes used=25024544, alloc=2096768, time=1.84 +> +# d/dy +> simplify( diff(interp_2d_cube_order3_smooth0,y) ); +bytes used=26024784, alloc=2096768, time=1.94 +bytes used=27025040, alloc=2096768, time=2.00 +1/20 x y DATA(1, -1) + 3/20 x y DATA(-1, 0) + 3/20 x y DATA(-1, 1) + + + 3/20 x y DATA(2, -1) - 1/20 x y DATA(0, 2) - 3/20 x y DATA(-1, 2) + + - 3/20 x y DATA(2, 1) + 1/20 x y DATA(1, 2) + 3/20 x y DATA(2, 2) + + - 1/20 x y DATA(1, 1) - 3/20 x y DATA(2, 0) + 1/20 x y DATA(0, 0) + + 49 + - 1/20 x y DATA(1, 0) + 1/20 x y DATA(0, 1) - --- DATA(2, 0) + 400 + + - 1/25 x DATA(0, 0) + 3/50 x DATA(1, 1) - 1/50 x DATA(-1, 0) + + 13 + - --- x DATA(1, -1) + 6/25 x DATA(-1, -1) - 1/50 x DATA(0, -1) + 100 + + - 1/100 x DATA(1, 0) - 1/100 x DATA(0, 1) - 3/40 y DATA(2, 2) + + 21 17 + + 7/100 x DATA(2, 0) - -- y DATA(0, 0) - -- y DATA(2, 0) + 40 40 + + + 1/40 y DATA(0, 2) + 7/40 y DATA(2, -1) + 3/40 y DATA(-1, 2) + + 13 11 + - 1/40 y DATA(1, 2) + -- y DATA(2, 1) + -- y DATA(0, -1) + 40 40 + + 13 + + 9/40 y DATA(1, -1) + -- y DATA(-1, -1) + 7/40 y DATA(-1, 1) + 40 + + 23 19 + - -- y DATA(-1, 0) + 9/40 y DATA(0, 1) - -- y DATA(1, 0) + 40 40 + + 2 11 + + 1/8 y DATA(2, 2) + -- y DATA(1, 1) - 9/100 x DATA(2, -1) + 40 + + 2 2 2 + + 1/8 y DATA(1, 2) - 3/8 y DATA(2, 1) + 1/8 y DATA(-1, 2) + + 13 2 + - --- x DATA(-1, 1) + 7/100 x DATA(0, 2) + 1/40 x DATA(1, 0) + 100 + + 2 + - 1/40 x DATA(0, 1) - 3/50 x DATA(2, 2) - 9/100 x DATA(-1, 2) + + 2 + + 2/25 x DATA(1, 2) + 2/25 x DATA(2, 1) - 1/40 x DATA(2, 0) + + 2 2 2 + + 1/40 x DATA(0, 0) - 3/40 x DATA(2, -1) + 3/40 x DATA(1, -1) + + 2 2 2 + - 1/40 x DATA(-1, 0) - 1/40 x DATA(1, 1) + 3/40 x DATA(-1, 2) + + 2 2 2 + + 1/40 x DATA(-1, 1) - 3/40 x DATA(1, 2) - 3/40 x DATA(0, 2) + + 2 2 2 + + 3/40 x DATA(2, 2) + 1/40 x DATA(2, 1) + 3/40 x DATA(0, -1) + + 2 2 2 + - 3/40 x DATA(-1, -1) - 1/8 y DATA(-1, -1) - 1/8 y DATA(1, -1) + + 2 2 2 + - 1/8 y DATA(0, -1) - 3/8 y DATA(0, 1) - 3/8 y DATA(1, 1) + + 2 2 2 + + 3/8 y DATA(-1, 0) - 3/8 y DATA(-1, 1) - 1/8 y DATA(2, -1) + + 2 2 2 + + 1/8 y DATA(0, 2) + 3/8 y DATA(2, 0) + 3/8 y DATA(1, 0) + + 2 + + 3/8 y DATA(0, 0) - 1/20 x y DATA(0, -1) - 3/20 x y DATA(-1, -1) + + 57 63 117 103 + - --- DATA(0, 0) - --- DATA(1, 0) + --- DATA(0, 1) + --- DATA(1, 1) + 400 400 400 400 + + 223 109 157 + - ---- DATA(0, -1) - ---- DATA(-1, -1) - ---- DATA(1, -1) + 1200 1200 1200 + + 31 111 89 43 + - --- DATA(-1, 0) + --- DATA(-1, 1) + ---- DATA(2, -1) + ---- DATA(0, 2) + 400 400 1200 1200 + + 131 69 37 149 + - ---- DATA(-1, 2) + --- DATA(2, 1) + ---- DATA(1, 2) - ---- DATA(2, 2) + 1200 400 1200 1200 + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); + 2 2 109 13 +[COEFF(-1, -1) = - 1/8 y - 3/40 x + 6/25 x - 3/20 x y - ---- + -- y, + 1200 40 + + 2 2 223 11 + COEFF(0, -1) = - 1/20 x y - 1/50 x + 3/40 x - 1/8 y - ---- + -- y, + 1200 40 + + 2 157 2 13 + COEFF(1, -1) = 1/20 x y - 1/8 y - ---- + 9/40 y + 3/40 x - --- x, + 1200 100 + + 2 89 2 + COEFF(2, -1) = - 9/100 x - 3/40 x + 7/40 y + 3/20 x y + ---- - 1/8 y , + 1200 + + 23 2 31 2 + COEFF(-1, 0) = - -- y - 1/40 x - --- + 3/20 x y + 3/8 y - 1/50 x, + 40 400 + + 21 57 2 2 + COEFF(0, 0) = - -- y - --- - 1/25 x + 1/20 x y + 3/8 y + 1/40 x , + 40 400 + + 2 19 63 2 + COEFF(1, 0) = 1/40 x - 1/20 x y - -- y - --- - 1/100 x + 3/8 y , + 40 400 + + 49 2 2 17 + COEFF(2, 0) = - 3/20 x y - --- + 3/8 y - 1/40 x - -- y + 7/100 x, + 400 40 + + 13 111 2 2 + COEFF(-1, 1) = - --- x + 7/40 y + --- + 1/40 x - 3/8 y + 3/20 x y, + 100 400 + + 2 2 117 + COEFF(0, 1) = - 1/40 x + 1/20 x y + 9/40 y - 3/8 y - 1/100 x + ---, + 400 + + 11 2 2 103 + COEFF(1, 1) = -- y + 3/50 x - 1/40 x - 3/8 y - 1/20 x y + ---, + 40 400 + + 2 13 2 69 + COEFF(2, 1) = 2/25 x + 1/40 x + -- y - 3/20 x y - 3/8 y + ---, + 40 400 + + 2 2 131 + COEFF(-1, 2) = 1/8 y + 3/40 x - 9/100 x - 3/20 x y - ---- + 3/40 y, + 1200 + + 2 2 43 + COEFF(0, 2) = 7/100 x - 1/20 x y - 3/40 x + 1/8 y + 1/40 y + ----, + 1200 + + 2 37 2 + COEFF(1, 2) = 1/20 x y - 3/40 x + ---- + 1/8 y - 1/40 y + 2/25 x, + 1200 + + 2 149 2 + COEFF(2, 2) = 1/8 y - 3/40 y + 3/20 x y - 3/50 x - ---- + 3/40 x ] + 1200 + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c"); +bytes used=28025200, alloc=2162292, time=2.08 +bytes used=29025372, alloc=2162292, time=2.17 +bytes used=30025660, alloc=2162292, time=2.26 +bytes used=31025832, alloc=2162292, time=2.37 +> +# d^2/dx^2 +> simplify( diff(interp_2d_cube_order3_smooth0,x,x) ); +1/40 DATA(2, 0) + 3/4 x DATA(0, 0) - 3/4 x DATA(1, 1) - 1/4 x DATA(-1, 0) + + - 3/4 x DATA(1, -1) - 1/4 x DATA(-1, -1) + 3/4 x DATA(0, -1) + + - 3/4 x DATA(1, 0) + 3/4 x DATA(0, 1) + 3/20 y DATA(2, 2) + + + 1/4 x DATA(2, 0) + 1/20 y DATA(0, 0) - 1/20 y DATA(2, 0) + + - 3/20 y DATA(0, 2) - 3/20 y DATA(2, -1) + 3/20 y DATA(-1, 2) + + - 3/20 y DATA(1, 2) + 1/20 y DATA(2, 1) + 3/20 y DATA(0, -1) + + + 3/20 y DATA(1, -1) - 3/20 y DATA(-1, -1) + 1/20 y DATA(-1, 1) + + - 1/20 y DATA(-1, 0) - 1/20 y DATA(0, 1) + 1/20 y DATA(1, 0) + + - 1/20 y DATA(1, 1) + 1/4 x DATA(2, -1) - 1/4 x DATA(-1, 1) + + + 3/4 x DATA(0, 2) + 1/4 x DATA(2, 2) - 1/4 x DATA(-1, 2) + + 21 + - 3/4 x DATA(1, 2) + 1/4 x DATA(2, 1) - -- DATA(0, 0) + 9/40 DATA(1, 0) + 40 + + 19 11 23 13 + - -- DATA(0, 1) + -- DATA(1, 1) - -- DATA(0, -1) + -- DATA(-1, -1) + 40 40 40 40 + + 11 + + 7/40 DATA(1, -1) + -- DATA(-1, 0) + 9/40 DATA(-1, 1) + 3/40 DATA(2, -1) + 40 + + 17 13 + - -- DATA(0, 2) + 7/40 DATA(-1, 2) - 1/40 DATA(2, 1) + -- DATA(1, 2) + 40 40 + + - 3/40 DATA(2, 2) + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); + 13 23 +[COEFF(-1, -1) = - 1/4 x - 3/20 y + --, COEFF(0, -1) = 3/4 x + 3/20 y - --, + 40 40 + + COEFF(1, -1) = 7/40 + 3/20 y - 3/4 x, + + 11 + COEFF(2, -1) = - 3/20 y + 3/40 + 1/4 x, COEFF(-1, 0) = -- - 1/20 y - 1/4 x, + 40 + + 21 + COEFF(0, 0) = - -- + 1/20 y + 3/4 x, COEFF(1, 0) = - 3/4 x + 1/20 y + 9/40, + 40 + + COEFF(2, 0) = 1/4 x - 1/20 y + 1/40, COEFF(-1, 1) = 9/40 - 1/4 x + 1/20 y, + + 19 11 + COEFF(0, 1) = - -- - 1/20 y + 3/4 x, COEFF(1, 1) = - 1/20 y + -- - 3/4 x, + 40 40 + + COEFF(2, 1) = - 1/40 + 1/20 y + 1/4 x, + + 17 + COEFF(-1, 2) = - 1/4 x + 7/40 + 3/20 y, COEFF(0, 2) = - 3/20 y + 3/4 x - --, + 40 + + 13 + COEFF(1, 2) = - 3/20 y - 3/4 x + --, COEFF(2, 2) = - 3/40 + 1/4 x + 3/20 y] + 40 + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c"); +bytes used=32026056, alloc=2162292, time=2.48 +bytes used=33027468, alloc=2162292, time=2.58 +> +# d^2/dxdy +> simplify( diff(interp_2d_cube_order3_smooth0,x,y) ); +7/100 DATA(2, 0) + 1/20 x DATA(0, 0) - 1/20 x DATA(1, 1) - 1/20 x DATA(-1, 0) + + + 3/20 x DATA(1, -1) - 3/20 x DATA(-1, -1) + 3/20 x DATA(0, -1) + + + 1/20 x DATA(1, 0) - 1/20 x DATA(0, 1) + 3/20 y DATA(2, 2) + + - 1/20 x DATA(2, 0) + 1/20 y DATA(0, 0) - 3/20 y DATA(2, 0) + + - 1/20 y DATA(0, 2) + 3/20 y DATA(2, -1) - 3/20 y DATA(-1, 2) + + + 1/20 y DATA(1, 2) - 3/20 y DATA(2, 1) - 1/20 y DATA(0, -1) + + + 1/20 y DATA(1, -1) - 3/20 y DATA(-1, -1) + 3/20 y DATA(-1, 1) + + + 3/20 y DATA(-1, 0) + 1/20 y DATA(0, 1) - 1/20 y DATA(1, 0) + + - 1/20 y DATA(1, 1) - 3/20 x DATA(2, -1) + 1/20 x DATA(-1, 1) + + - 3/20 x DATA(0, 2) + 3/20 x DATA(2, 2) + 3/20 x DATA(-1, 2) + + - 3/20 x DATA(1, 2) + 1/20 x DATA(2, 1) - 1/25 DATA(0, 0) + + - 1/100 DATA(1, 0) - 1/100 DATA(0, 1) + 3/50 DATA(1, 1) - 1/50 DATA(0, -1) + + 13 13 + + 6/25 DATA(-1, -1) - --- DATA(1, -1) - 1/50 DATA(-1, 0) - --- DATA(-1, 1) + 100 100 + + - 9/100 DATA(2, -1) + 7/100 DATA(0, 2) - 9/100 DATA(-1, 2) + + + 2/25 DATA(2, 1) + 2/25 DATA(1, 2) - 3/50 DATA(2, 2) + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); +bytes used=34028660, alloc=2162292, time=2.68 +[COEFF(-1, -1) = - 3/20 x + 6/25 - 3/20 y, + + 13 + COEFF(0, -1) = 3/20 x - 1/50 - 1/20 y, COEFF(1, -1) = 1/20 y - --- + 3/20 x, + 100 + + COEFF(2, -1) = 3/20 y - 3/20 x - 9/100, + + COEFF(-1, 0) = 3/20 y - 1/20 x - 1/50, COEFF(0, 0) = 1/20 x - 1/25 + 1/20 y, + + COEFF(1, 0) = - 1/20 y - 1/100 + 1/20 x, + + COEFF(2, 0) = - 3/20 y - 1/20 x + 7/100, + + 13 + COEFF(-1, 1) = 3/20 y - --- + 1/20 x, + 100 + + COEFF(0, 1) = - 1/20 x + 1/20 y - 1/100, + + COEFF(1, 1) = - 1/20 x + 3/50 - 1/20 y, + + COEFF(2, 1) = - 3/20 y + 1/20 x + 2/25, + + COEFF(-1, 2) = - 9/100 - 3/20 y + 3/20 x, + + COEFF(0, 2) = 7/100 - 1/20 y - 3/20 x, + + COEFF(1, 2) = - 3/20 x + 1/20 y + 2/25, + + COEFF(2, 2) = 3/20 x + 3/20 y - 3/50] + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c"); +bytes used=35028816, alloc=2162292, time=2.75 +> +# d^2/dy^2 +> simplify( diff(interp_2d_cube_order3_smooth0,y,y) ); + 17 +- -- DATA(2, 0) + 1/20 x DATA(0, 0) - 1/20 x DATA(1, 1) + 3/20 x DATA(-1, 0) + 40 + + + 1/20 x DATA(1, -1) - 3/20 x DATA(-1, -1) - 1/20 x DATA(0, -1) + + - 1/20 x DATA(1, 0) + 1/20 x DATA(0, 1) + 1/4 y DATA(2, 2) + + - 3/20 x DATA(2, 0) + 3/4 y DATA(0, 0) + 3/4 y DATA(2, 0) + + + 1/4 y DATA(0, 2) - 1/4 y DATA(2, -1) + 1/4 y DATA(-1, 2) + + + 1/4 y DATA(1, 2) - 3/4 y DATA(2, 1) - 1/4 y DATA(0, -1) + + - 1/4 y DATA(1, -1) - 1/4 y DATA(-1, -1) - 3/4 y DATA(-1, 1) + + + 3/4 y DATA(-1, 0) - 3/4 y DATA(0, 1) + 3/4 y DATA(1, 0) + + - 3/4 y DATA(1, 1) + 3/20 x DATA(2, -1) + 3/20 x DATA(-1, 1) + + - 1/20 x DATA(0, 2) + 3/20 x DATA(2, 2) - 3/20 x DATA(-1, 2) + + 21 19 + + 1/20 x DATA(1, 2) - 3/20 x DATA(2, 1) - -- DATA(0, 0) - -- DATA(1, 0) + 40 40 + + 11 11 13 + + 9/40 DATA(0, 1) + -- DATA(1, 1) + -- DATA(0, -1) + -- DATA(-1, -1) + 40 40 40 + + 23 + + 9/40 DATA(1, -1) - -- DATA(-1, 0) + 7/40 DATA(-1, 1) + 7/40 DATA(2, -1) + 40 + + 13 + + 1/40 DATA(0, 2) + 3/40 DATA(-1, 2) + -- DATA(2, 1) - 1/40 DATA(1, 2) + 40 + + - 3/40 DATA(2, 2) + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); + 13 11 +[COEFF(-1, -1) = - 1/4 y - 3/20 x + --, COEFF(0, -1) = -- - 1/4 y - 1/20 x, + 40 40 + + COEFF(1, -1) = - 1/4 y + 9/40 + 1/20 x, + + 23 + COEFF(2, -1) = 7/40 + 3/20 x - 1/4 y, COEFF(-1, 0) = 3/20 x + 3/4 y - --, + 40 + + 21 19 + COEFF(0, 0) = 3/4 y + 1/20 x - --, COEFF(1, 0) = 3/4 y - -- - 1/20 x, + 40 40 + + 17 + COEFF(2, 0) = - -- + 3/4 y - 3/20 x, COEFF(-1, 1) = - 3/4 y + 3/20 x + 7/40, + 40 + + 11 + COEFF(0, 1) = - 3/4 y + 1/20 x + 9/40, COEFF(1, 1) = - 3/4 y - 1/20 x + --, + 40 + + 13 + COEFF(2, 1) = - 3/20 x + -- - 3/4 y, COEFF(-1, 2) = - 3/20 x + 1/4 y + 3/40, + 40 + + COEFF(0, 2) = 1/4 y + 1/40 - 1/20 x, COEFF(1, 2) = 1/20 x + 1/4 y - 1/40, + + COEFF(2, 2) = 3/20 x - 3/40 + 1/4 y] + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c"); +bytes used=36029536, alloc=2162292, time=2.85 +bytes used=37029756, alloc=2162292, time=2.94 +> +################################################################################ +> +# +# 2d, cube, order=4, smoothing=0 (size=5) +# +> +# interpolating polynomial +> interp_2d_cube_order4_smooth0 +> := Lagrange_polynomial_interpolant(fn_2d_order4, coeffs_list_2d_order4, +> coords_list_2d, posn_list_2d_size5); +bytes used=38029976, alloc=2162292, time=3.04 +bytes used=39030204, alloc=2162292, time=3.10 +bytes used=40030440, alloc=2162292, time=3.16 +bytes used=41032164, alloc=2162292, time=3.22 +bytes used=42032408, alloc=2162292, time=3.28 +bytes used=43032708, alloc=2162292, time=3.34 +interp_2d_cube_order4_smooth0 := (- 1/60 DATA(1, 1) - 1/60 DATA(-1, -1) + + + 1/60 DATA(1, -1) + 1/60 DATA(-1, 1) + 1/30 DATA(2, -1) + + - 1/120 DATA(-1, 2) - 1/30 DATA(2, 1) + 1/120 DATA(-1, -2) + + + 1/60 DATA(-2, -2) + 1/120 DATA(1, 2) + 1/60 DATA(2, 2) + + - 1/60 DATA(-2, 2) + 1/30 DATA(-2, 1) - 1/120 DATA(1, -2) + + 3 + - 1/60 DATA(2, -2) - 1/30 DATA(-2, -1)) x y + (- 1/35 DATA(2, 0) + + - 1/70 DATA(1, 0) - 1/140 DATA(1, 1) + 1/140 DATA(-1, -1) + + - 1/140 DATA(1, -1) + 1/70 DATA(-1, 0) + 1/140 DATA(-1, 1) + + - 1/70 DATA(2, -1) - 1/70 DATA(-1, 2) - 1/70 DATA(2, 1) + + - 1/70 DATA(-1, -2) - 1/35 DATA(-2, -2) + 1/70 DATA(1, 2) + + + 1/35 DATA(2, 2) - 1/35 DATA(-2, 2) + 1/70 DATA(-2, 1) + 1/35 DATA(-2, 0) + + 2 + + 1/70 DATA(1, -2) + 1/35 DATA(2, -2) + 1/70 DATA(-2, -1)) x y + ( + + - 1/49 DATA(2, 0) + 1/49 DATA(0, 0) + 1/98 DATA(1, 0) + 1/98 DATA(0, 1) + + + 1/196 DATA(1, 1) + 1/98 DATA(0, -1) + 1/196 DATA(-1, -1) + + + 1/196 DATA(1, -1) + 1/98 DATA(-1, 0) + 1/196 DATA(-1, 1) + + - 1/98 DATA(2, -1) - 1/49 DATA(0, 2) - 1/98 DATA(-1, 2) - 1/98 DATA(2, 1) + + - 1/98 DATA(-1, -2) - 1/49 DATA(0, -2) + 1/49 DATA(-2, -2) + + - 1/98 DATA(1, 2) + 1/49 DATA(2, 2) + 1/49 DATA(-2, 2) - 1/98 DATA(-2, 1) + + - 1/49 DATA(-2, 0) - 1/98 DATA(1, -2) + 1/49 DATA(2, -2) + + 2 2 /37 37 + - 1/98 DATA(-2, -1)) x y + |--- DATA(1, 1) + --- DATA(-1, -1) + \300 300 + + 37 37 21 21 + - --- DATA(1, -1) - --- DATA(-1, 1) - --- DATA(2, -1) - --- DATA(-1, 2) + 300 300 200 200 + + 21 21 11 21 + + --- DATA(2, 1) + --- DATA(-1, -2) - --- DATA(-2, -2) + --- DATA(1, 2) + 200 200 150 200 + + 11 11 21 21 + - --- DATA(2, 2) + --- DATA(-2, 2) - --- DATA(-2, 1) - --- DATA(1, -2) + 150 150 200 200 + + 11 21 \ + + --- DATA(2, -2) + --- DATA(-2, -1)| x y + (- 1/70 DATA(0, 1) + 150 200 / + + - 1/140 DATA(1, 1) + 1/70 DATA(0, -1) + 1/140 DATA(-1, -1) + + + 1/140 DATA(1, -1) - 1/140 DATA(-1, 1) - 1/70 DATA(2, -1) + + - 1/35 DATA(0, 2) - 1/70 DATA(-1, 2) + 1/70 DATA(2, 1) + 1/70 DATA(-1, -2) + + + 1/35 DATA(0, -2) - 1/35 DATA(-2, -2) - 1/70 DATA(1, 2) + 1/35 DATA(2, 2) + + + 1/35 DATA(-2, 2) + 1/70 DATA(-2, 1) + 1/70 DATA(1, -2) + + 2 + - 1/35 DATA(2, -2) - 1/70 DATA(-2, -1)) x y + (- 1/60 DATA(1, 1) + + - 1/60 DATA(-1, -1) + 1/60 DATA(1, -1) + 1/60 DATA(-1, 1) + + - 1/120 DATA(2, -1) + 1/30 DATA(-1, 2) + 1/120 DATA(2, 1) + + - 1/30 DATA(-1, -2) + 1/60 DATA(-2, -2) - 1/30 DATA(1, 2) + + + 1/60 DATA(2, 2) - 1/60 DATA(-2, 2) - 1/120 DATA(-2, 1) + + 3 + + 1/30 DATA(1, -2) - 1/60 DATA(2, -2) + 1/120 DATA(-2, -1)) x y + + 96 541 246 246 + + ---- DATA(2, 0) + ---- DATA(0, 0) + ---- DATA(1, 0) + ---- DATA(0, 1) + 1225 1225 1225 1225 + + 24 + - ---- DATA(1, 1) + (1/60 DATA(2, 0) - 1/30 DATA(1, 0) - 1/30 DATA(1, 1) + 1225 + + + 1/30 DATA(-1, -1) - 1/30 DATA(1, -1) + 1/30 DATA(-1, 0) + + + 1/30 DATA(-1, 1) + 1/60 DATA(2, -1) + 1/30 DATA(-1, 2) + 1/60 DATA(2, 1) + + + 1/30 DATA(-1, -2) - 1/60 DATA(-2, -2) - 1/30 DATA(1, 2) + + + 1/60 DATA(2, 2) - 1/60 DATA(-2, 2) - 1/60 DATA(-2, 1) - 1/60 DATA(-2, 0) + + 3 + - 1/30 DATA(1, -2) + 1/60 DATA(2, -2) - 1/60 DATA(-2, -1)) x + ( + + 1/120 DATA(2, 0) + 1/20 DATA(0, 0) - 1/30 DATA(1, 0) + 1/20 DATA(0, 1) + + - 1/30 DATA(1, 1) + 1/20 DATA(0, -1) - 1/30 DATA(-1, -1) + + - 1/30 DATA(1, -1) - 1/30 DATA(-1, 0) - 1/30 DATA(-1, 1) + + + 1/120 DATA(2, -1) + 1/20 DATA(0, 2) - 1/30 DATA(-1, 2) + + + 1/120 DATA(2, 1) - 1/30 DATA(-1, -2) + 1/20 DATA(0, -2) + + + 1/120 DATA(-2, -2) - 1/30 DATA(1, 2) + 1/120 DATA(2, 2) + + + 1/120 DATA(-2, 2) + 1/120 DATA(-2, 1) + 1/120 DATA(-2, 0) + + 4 + - 1/30 DATA(1, -2) + 1/120 DATA(2, -2) + 1/120 DATA(-2, -1)) x + ( + + 1/20 DATA(2, 0) + 1/20 DATA(0, 0) + 1/20 DATA(1, 0) - 1/30 DATA(0, 1) + + - 1/30 DATA(1, 1) - 1/30 DATA(0, -1) - 1/30 DATA(-1, -1) + + - 1/30 DATA(1, -1) + 1/20 DATA(-1, 0) - 1/30 DATA(-1, 1) + + - 1/30 DATA(2, -1) + 1/120 DATA(0, 2) + 1/120 DATA(-1, 2) + + - 1/30 DATA(2, 1) + 1/120 DATA(-1, -2) + 1/120 DATA(0, -2) + + + 1/120 DATA(-2, -2) + 1/120 DATA(1, 2) + 1/120 DATA(2, 2) + + + 1/120 DATA(-2, 2) - 1/30 DATA(-2, 1) + 1/20 DATA(-2, 0) + + 4 + + 1/120 DATA(1, -2) + 1/120 DATA(2, -2) - 1/30 DATA(-2, -1)) y + ( + + - 1/30 DATA(0, 1) - 1/30 DATA(1, 1) + 1/30 DATA(0, -1) + 1/30 DATA(-1, -1) + + + 1/30 DATA(1, -1) - 1/30 DATA(-1, 1) + 1/30 DATA(2, -1) + 1/60 DATA(0, 2) + + + 1/60 DATA(-1, 2) - 1/30 DATA(2, 1) - 1/60 DATA(-1, -2) + + - 1/60 DATA(0, -2) - 1/60 DATA(-2, -2) + 1/60 DATA(1, 2) + 1/60 DATA(2, 2) + + + 1/60 DATA(-2, 2) - 1/30 DATA(-2, 1) - 1/60 DATA(1, -2) + + 3 / 41 + - 1/60 DATA(2, -2) + 1/30 DATA(-2, -1)) y + |- --- DATA(2, 0) + \ 196 + + 57 53 83 181 + - --- DATA(0, 0) - --- DATA(1, 0) + --- DATA(0, 1) + ---- DATA(1, 1) + 196 196 735 1470 + + 83 181 181 53 + + --- DATA(0, -1) + ---- DATA(-1, -1) + ---- DATA(1, -1) - --- DATA(-1, 0) + 735 1470 1470 196 + + 181 113 191 71 + + ---- DATA(-1, 1) + --- DATA(2, -1) + ---- DATA(0, 2) + ---- DATA(-1, 2) + 1470 735 5880 5880 + + 113 71 191 + + --- DATA(2, 1) + ---- DATA(-1, -2) + ---- DATA(0, -2) + 735 5880 5880 + + 289 71 289 289 + - ---- DATA(-2, -2) + ---- DATA(1, 2) - ---- DATA(2, 2) - ---- DATA(-2, 2) + 5880 5880 5880 5880 + + 113 41 71 289 + + --- DATA(-2, 1) - --- DATA(-2, 0) + ---- DATA(1, -2) - ---- DATA(2, -2) + 735 196 5880 5880 + + 113 \ 2 /17 31 + + --- DATA(-2, -1)| y + |--- DATA(0, 1) + --- DATA(1, 1) + 735 / \105 210 + + 17 31 31 31 + - --- DATA(0, -1) - --- DATA(-1, -1) - --- DATA(1, -1) + --- DATA(-1, 1) + 105 210 210 210 + + 11 17 11 + - --- DATA(2, -1) + --- DATA(0, 2) + 1/84 DATA(-1, 2) + --- DATA(2, 1) + 105 420 105 + + 17 31 + - 1/84 DATA(-1, -2) - --- DATA(0, -2) + --- DATA(-2, -2) + 1/84 DATA(1, 2) + 420 420 + + 31 31 11 + - --- DATA(2, 2) - --- DATA(-2, 2) + --- DATA(-2, 1) - 1/84 DATA(1, -2) + 420 420 105 + + 31 11 \ /17 17 + + --- DATA(2, -2) - --- DATA(-2, -1)| y + |--- DATA(2, 0) + --- DATA(1, 0) + 420 105 / \420 105 + + 31 31 31 17 + + --- DATA(1, 1) - --- DATA(-1, -1) + --- DATA(1, -1) - --- DATA(-1, 0) + 210 210 210 105 + + 31 11 + - --- DATA(-1, 1) + 1/84 DATA(2, -1) - --- DATA(-1, 2) + 1/84 DATA(2, 1) + 210 105 + + 11 31 11 31 + - --- DATA(-1, -2) + --- DATA(-2, -2) + --- DATA(1, 2) - --- DATA(2, 2) + 105 420 105 420 + + 31 17 11 + + --- DATA(-2, 2) - 1/84 DATA(-2, 1) - --- DATA(-2, 0) + --- DATA(1, -2) + 420 420 105 + + 31 \ /191 + - --- DATA(2, -2) - 1/84 DATA(-2, -1)| x + |---- DATA(2, 0) + 420 / \5880 + + 57 83 53 181 + - --- DATA(0, 0) + --- DATA(1, 0) - --- DATA(0, 1) + ---- DATA(1, 1) + 196 735 196 1470 + + 53 181 181 83 + - --- DATA(0, -1) + ---- DATA(-1, -1) + ---- DATA(1, -1) + --- DATA(-1, 0) + 196 1470 1470 735 + + 181 71 41 113 + + ---- DATA(-1, 1) + ---- DATA(2, -1) - --- DATA(0, 2) + --- DATA(-1, 2) + 1470 5880 196 735 + + 71 113 41 289 + + ---- DATA(2, 1) + --- DATA(-1, -2) - --- DATA(0, -2) - ---- DATA(-2, -2) + 5880 735 196 5880 + + 113 289 289 71 + + --- DATA(1, 2) - ---- DATA(2, 2) - ---- DATA(-2, 2) + ---- DATA(-2, 1) + 735 5880 5880 5880 + + 191 113 289 + + ---- DATA(-2, 0) + --- DATA(1, -2) - ---- DATA(2, -2) + 5880 735 5880 + + 71 \ 2 246 24 + + ---- DATA(-2, -1)| x + ---- DATA(0, -1) - ---- DATA(-1, -1) + 5880 / 1225 1225 + + 24 246 24 + - ---- DATA(1, -1) + ---- DATA(-1, 0) - ---- DATA(-1, 1) + 1225 1225 1225 + + 99 96 99 99 + - ---- DATA(2, -1) + ---- DATA(0, 2) - ---- DATA(-1, 2) - ---- DATA(2, 1) + 1225 1225 1225 1225 + + 99 96 51 + - ---- DATA(-1, -2) + ---- DATA(0, -2) + ---- DATA(-2, -2) + 1225 1225 1225 + + 99 51 51 99 + - ---- DATA(1, 2) + ---- DATA(2, 2) + ---- DATA(-2, 2) - ---- DATA(-2, 1) + 1225 1225 1225 1225 + + 96 99 51 + + ---- DATA(-2, 0) - ---- DATA(1, -2) + ---- DATA(2, -2) + 1225 1225 1225 + + 99 + - ---- DATA(-2, -1) + 1225 + +> +# I +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=44034460, alloc=2162292, time=3.41 + 2 2 3 3 4 2 +[COEFF(-2, -2) = 1/49 x y + 1/60 x y + 1/60 x y + 1/120 x - 1/35 x y + + 2 3 11 289 2 3 289 2 51 + - 1/35 x y - 1/60 y - --- x y - ---- y - 1/60 x - ---- x + ---- + 150 5880 5880 1225 + + 31 4 31 2 2 3 + + --- x + 1/120 y + --- y, COEFF(-1, -2) = - 1/98 x y - 1/30 x y + 420 420 + + 21 2 3 4 113 2 3 3 + + --- x y - 1/70 x y + 1/120 x y + 1/120 y + --- x - 1/60 y + 1/30 x + 200 735 + + 71 2 4 2 11 99 + + ---- y - 1/30 x - 1/84 y + 1/70 x y - --- x - ----, COEFF(0, -2) = + 5880 105 1225 + + 2 191 2 17 4 4 2 2 3 + 1/35 x y + ---- y - --- y + 1/20 x + 1/120 y - 1/49 x y - 1/60 y + 5880 420 + + 96 41 2 21 2 3 + + ---- - --- x , COEFF(1, -2) = - --- x y + 1/70 x y - 1/120 x y + 1225 196 200 + + 3 3 11 4 2 2 2 + - 1/30 x - 1/60 y + --- x + 1/120 y - 1/98 x y - 1/84 y + 1/70 x y + 105 + + 71 2 99 113 2 3 4 31 + + ---- y - ---- + --- x + 1/30 x y - 1/30 x , COEFF(2, -2) = - --- x + 5880 1225 735 420 + + 3 2 51 3 4 2 2 289 2 + + 1/60 x + 1/35 x y + ---- - 1/60 x y + 1/120 x + 1/49 x y - ---- x + 1225 5880 + + 31 11 4 2 289 2 3 3 + + --- y + --- x y + 1/120 y - 1/35 x y - ---- y - 1/60 x y - 1/60 y , + 420 150 5880 + + 3 4 99 11 3 3 + COEFF(-2, -1) = - 1/60 x - 1/30 y - ---- - --- y - 1/30 x y + 1/30 y + 1225 105 + + 4 113 2 2 71 2 2 2 21 + + 1/120 x + --- y + 1/70 x y + ---- x - 1/98 x y + --- x y + 735 5880 200 + + 3 2 2 4 + + 1/120 x y - 1/84 x - 1/70 x y, COEFF(-1, -1) = 1/140 x y - 1/30 x + + 2 2 3 181 2 3 4 181 2 + + 1/196 x y + 1/30 y + ---- x - 1/60 x y - 1/30 y + ---- y + 1470 1470 + + 3 31 2 3 37 31 24 + - 1/60 x y - --- x + 1/140 x y + 1/30 x + --- x y - --- y - ----, + 210 300 210 1225 + + 83 2 17 3 246 53 2 2 2 + COEFF(0, -1) = --- y - --- y + 1/30 y + ---- - --- x + 1/98 x y + 735 105 1225 196 + + 4 2 4 24 2 + + 1/20 x + 1/70 x y - 1/30 y , COEFF(1, -1) = - ---- - 1/140 x y + 1225 + + 181 2 2 31 3 3 3 181 2 + + ---- y + 1/140 x y - --- y + 1/60 x y + 1/30 y + 1/60 x y + ---- x + 1470 210 1470 + + 37 4 31 4 3 2 2 + - --- x y - 1/30 x + --- x - 1/30 y - 1/30 x + 1/196 x y , + 300 210 + + 2 3 3 11 2 + COEFF(2, -1) = - 1/70 x y - 1/120 x y + 1/30 y - --- y - 1/70 x y + 105 + + 99 3 3 4 113 2 4 71 2 + - ---- + 1/30 x y + 1/60 x - 1/30 y + --- y + 1/120 x + ---- x + 1225 735 5880 + + 2 2 21 191 2 96 41 2 + - 1/98 x y + 1/84 x - --- x y, COEFF(-2, 0) = ---- x + ---- - --- y + 200 5880 1225 196 + + 3 2 2 2 4 17 4 + - 1/60 x + 1/35 x y - 1/49 x y + 1/120 x - --- x + 1/20 y , + 420 + + 246 3 17 83 2 4 2 + COEFF(-1, 0) = ---- + 1/30 x - --- x + --- x + 1/20 y + 1/70 x y + 1225 105 735 + + 4 2 2 53 2 + - 1/30 x + 1/98 x y - --- y , + 196 + + 57 2 4 2 2 4 541 57 2 + COEFF(0, 0) = - --- x + 1/20 y + 1/49 x y + 1/20 x + ---- - --- y , + 196 1225 196 + + 4 2 2 53 2 83 2 4 246 + COEFF(1, 0) = 1/20 y + 1/98 x y - --- y + --- x - 1/30 x + ---- + 196 735 1225 + + 2 3 17 96 2 191 2 + - 1/70 x y - 1/30 x + --- x, COEFF(2, 0) = ---- - 1/35 x y + ---- x + 105 1225 5880 + + 41 2 3 17 2 2 4 4 + - --- y + 1/60 x + --- x - 1/49 x y + 1/120 x + 1/20 y , COEFF(-2, 1) + 196 420 + + 21 3 2 3 71 2 11 3 + = - --- x y - 1/60 x + 1/70 x y - 1/30 y + ---- x + --- y - 1/120 x y + 200 5880 105 + + 2 2 3 4 2 113 2 4 99 + - 1/98 x y + 1/30 x y + 1/120 x + 1/70 x y + --- y - 1/30 y - ---- + 735 1225 + + 3 37 3 2 + - 1/84 x, COEFF(-1, 1) = 1/60 x y - --- x y + 1/60 x y - 1/140 x y + 300 + + 4 3 181 2 2 24 31 181 2 + - 1/30 x + 1/30 x + ---- x + 1/140 x y - ---- - --- x + ---- y + 1470 1225 210 1470 + + 3 4 2 2 31 83 2 53 2 + - 1/30 y - 1/30 y + 1/196 x y + --- y, COEFF(0, 1) = --- y - --- x + 210 735 196 + + 2 2 17 3 4 4 246 2 + + 1/98 x y + --- y - 1/30 y + 1/20 x - 1/30 y + ---- - 1/70 x y, + 105 1225 + + 3 2 3 181 2 3 + COEFF(1, 1) = - 1/60 x y - 1/140 x y - 1/60 x y + ---- x - 1/30 x + 1470 + + 24 181 2 37 3 2 2 2 31 + - ---- + ---- y + --- x y - 1/30 y + 1/196 x y - 1/140 x y + --- x + 1225 1470 300 210 + + 4 31 4 3 3 + - 1/30 y + --- y - 1/30 x , COEFF(2, 1) = - 1/30 x y - 1/30 y + 1/84 x + 210 + + 2 21 71 2 4 113 2 2 2 + + 1/70 x y + --- x y + ---- x - 1/30 y + --- y - 1/98 x y + 200 5880 735 + + 3 4 99 3 2 11 + + 1/120 x y + 1/120 x - ---- + 1/60 x - 1/70 x y + --- y, COEFF(-2, 2) + 1225 105 + + 2 31 3 51 3 11 289 2 + = - 1/35 x y + --- x - 1/60 x y + ---- - 1/60 x y + --- x y - ---- y + 420 1225 150 5880 + + 3 2 31 289 2 4 4 2 2 + + 1/60 y + 1/35 x y - --- y - ---- x + 1/120 x + 1/120 y + 1/49 x y + 420 5880 + + 3 3 2 71 2 3 + - 1/60 x , COEFF(-1, 2) = - 1/120 x y - 1/70 x y + ---- y + 1/60 y + 5880 + + 4 21 3 11 2 2 113 2 3 + + 1/120 y - --- x y + 1/30 x - --- x - 1/98 x y + --- x + 1/30 x y + 200 105 735 + + 99 2 4 41 2 191 2 + - ---- - 1/70 x y + 1/84 y - 1/30 x , COEFF(0, 2) = - --- x + ---- y + 1225 196 5880 + + 4 4 96 2 3 2 2 17 + + 1/120 y + 1/20 x + ---- - 1/35 x y + 1/60 y - 1/49 x y + --- y, + 1225 420 + + 99 71 2 3 3 4 21 + COEFF(1, 2) = - ---- + ---- y + 1/120 x y - 1/30 x + 1/120 y + --- x y + 1225 5880 200 + + 11 2 2 113 2 3 3 2 + + --- x - 1/98 x y + --- x + 1/60 y - 1/30 x y + 1/70 x y + 105 735 + + 2 4 3 289 2 + - 1/70 x y + 1/84 y - 1/30 x , COEFF(2, 2) = 1/60 x y - ---- x + 5880 + + 289 2 11 31 3 4 3 2 + - ---- y - --- x y - --- x + 1/60 x + 1/120 y + 1/60 y + 1/35 x y + 5880 150 420 + + 2 2 2 31 3 51 4 + + 1/49 x y + 1/35 x y - --- y + 1/60 x y + ---- + 1/120 x ] + 420 1225 + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c"); +bytes used=45034944, alloc=2162292, time=3.47 +bytes used=46035108, alloc=2162292, time=3.54 +bytes used=47035352, alloc=2162292, time=3.60 +bytes used=48052304, alloc=2162292, time=3.67 +bytes used=49052696, alloc=2227816, time=3.74 +bytes used=50052952, alloc=2227816, time=3.86 +bytes used=51053208, alloc=2227816, time=3.97 +bytes used=52055716, alloc=2227816, time=4.04 +bytes used=53062388, alloc=2227816, time=4.13 +bytes used=54063168, alloc=2227816, time=4.27 +bytes used=55063348, alloc=2227816, time=4.36 +bytes used=56070108, alloc=2227816, time=4.45 +bytes used=57070308, alloc=2227816, time=4.57 +bytes used=58070564, alloc=2227816, time=4.72 +bytes used=59070836, alloc=2227816, time=4.78 +bytes used=60071040, alloc=2227816, time=4.91 +bytes used=61071296, alloc=2227816, time=5.05 +bytes used=62071508, alloc=2227816, time=5.13 +bytes used=63071660, alloc=2227816, time=5.27 +bytes used=64071832, alloc=2227816, time=5.34 +bytes used=65072432, alloc=2227816, time=5.51 +bytes used=66072588, alloc=2227816, time=5.61 +> +# d/dx +> simplify( diff(interp_2d_cube_order4_smooth0,x) ); +bytes used=67072804, alloc=2358864, time=5.68 +bytes used=68073096, alloc=2358864, time=5.74 +bytes used=69073300, alloc=2424388, time=5.81 +17 17 31 31 +--- DATA(2, 0) + --- DATA(1, 0) + --- DATA(1, 1) - --- DATA(-1, -1) +420 105 210 210 + + 31 17 31 + + --- DATA(1, -1) - --- DATA(-1, 0) - --- DATA(-1, 1) + 1/84 DATA(2, -1) + 210 105 210 + + 2 2 2 + - 1/10 x DATA(1, 2) + 1/20 x DATA(2, 2) - 1/20 x DATA(-2, 2) + + 2 2 + - 1/20 x DATA(-2, 1) + 1/40 x y DATA(2, 1) + 1/35 x y DATA(2, 1) + + 11 11 31 + - --- DATA(-1, 2) + 1/84 DATA(2, 1) - --- DATA(-1, -2) + --- DATA(-2, -2) + 105 105 420 + + 2 2 2 + + 1/20 x y DATA(-1, 1) - 1/40 x y DATA(-2, 1) + 1/10 x y DATA(-1, 2) + + 2 + + 1/35 x y DATA(0, -1) + 1/20 x y DATA(-2, -2) - 1/70 x y DATA(-1, 1) + + 2 2 + - 1/35 x y DATA(2, -1) + 1/20 x y DATA(2, 2) + 1/10 x y DATA(1, -2) + + 2 3 + + 1/40 x y DATA(-2, -1) - 2/35 x y DATA(0, 2) + 1/120 y DATA(1, 2) + + 3 3 3 + - 1/60 y DATA(1, 1) - 1/60 y DATA(-1, -1) + 1/30 x DATA(-2, -1) + + 3 3 3 + + 1/5 x DATA(0, -1) + 1/5 x DATA(0, 1) + 1/60 y DATA(-1, 1) + + 2 2 2 + - 1/35 y DATA(2, 0) - 1/70 y DATA(1, 0) - 1/140 y DATA(1, 1) + + 3 3 3 + - 1/30 y DATA(-2, -1) + 1/60 y DATA(-2, -2) + 1/60 y DATA(2, 2) + + 3 3 3 + - 1/60 y DATA(-2, 2) + 1/30 y DATA(-2, 1) - 1/120 y DATA(1, -2) + + 3 2 2 + - 1/60 y DATA(2, -2) + 1/140 y DATA(-1, -1) - 1/140 y DATA(1, -1) + + 2 2 2 + + 1/70 y DATA(-1, 0) + 1/140 y DATA(-1, 1) - 1/70 y DATA(2, -1) + + 2 2 3 + - 1/70 y DATA(-1, 2) - 1/70 y DATA(2, 1) + 1/60 y DATA(1, -1) + + 3 3 3 + + 1/30 y DATA(2, -1) - 1/120 y DATA(-1, 2) - 1/30 y DATA(2, 1) + + 3 2 37 + + 1/120 y DATA(-1, -2) + 1/70 y DATA(-2, -1) + --- y DATA(1, 1) + 300 + + 37 2 2 + + --- y DATA(-1, -1) - 1/70 y DATA(-1, -2) + 1/70 y DATA(1, 2) + 300 + + 2 2 2 + + 1/35 y DATA(2, 2) - 1/35 y DATA(-2, 2) + 1/70 y DATA(-2, 1) + + 2 2 21 + - 1/35 y DATA(-2, -2) - 1/20 x y DATA(1, 1) + --- y DATA(1, 2) + 200 + + 11 11 21 + - --- y DATA(2, 2) + --- y DATA(-2, 2) - --- y DATA(-2, 1) + 150 150 200 + + 21 11 21 + - --- y DATA(1, -2) + --- y DATA(2, -2) + --- y DATA(-2, -1) + 200 150 200 + + 37 2 2 + - --- y DATA(-1, 1) + 1/35 y DATA(-2, 0) + 1/70 y DATA(1, -2) + 300 + + 2 2 + + 1/35 y DATA(2, -2) - 1/10 x y DATA(1, 2) - 1/35 x y DATA(0, 1) + + 2 + - 1/10 x y DATA(-1, -2) + 1/70 x y DATA(1, -1) - 1/35 x y DATA(-1, 2) + + 11 2 2 + + --- DATA(1, 2) - 2/49 x y DATA(0, -2) + 1/49 x y DATA(1, 0) + 105 + + 2 + + 1/49 x y DATA(-1, 0) + 1/35 x y DATA(-2, 1) - 2/35 x y DATA(2, -2) + + - 1/35 x y DATA(-2, -1) + 1/35 x y DATA(1, -2) + 1/35 x y DATA(-1, -2) + + + 2/35 x y DATA(0, -2) - 2/35 x y DATA(-2, -2) - 1/35 x y DATA(1, 2) + + 2 + + 2/35 x y DATA(2, 2) + 2/35 x y DATA(-2, 2) - 1/49 x y DATA(1, -2) + + 2 2 2 + + 2/49 x y DATA(2, -2) - 1/49 x y DATA(-2, -1) + 1/49 x y DATA(0, 1) + + 2 2 31 + + 1/49 x y DATA(0, -1) - 2/49 x y DATA(0, 2) - --- DATA(2, 2) + 420 + + 2 2 2 + + 2/49 x y DATA(2, 2) + 2/49 x y DATA(-2, 2) + 1/98 x y DATA(-1, -1) + + 2 2 2 + + 1/98 x y DATA(1, -1) + 1/98 x y DATA(1, 1) - 2/49 x y DATA(2, 0) + + 2 3 3 + + 2/49 x y DATA(0, 0) - 2/15 x DATA(1, 1) + 1/30 x DATA(-2, 1) + + 3 3 3 + - 2/15 x DATA(-1, -2) + 1/30 x DATA(-2, -2) - 2/15 x DATA(1, 2) + + 3 3 3 + + 1/30 x DATA(2, 2) + 1/30 x DATA(-2, 2) - 2/15 x DATA(-1, -1) + + 3 3 3 + - 2/15 x DATA(1, -1) - 2/15 x DATA(-1, 1) + 1/30 x DATA(2, -1) + + 3 3 3 + - 2/15 x DATA(-1, 2) + 1/30 x DATA(2, 0) + 1/5 x DATA(0, 0) + + 3 3 37 + - 2/15 x DATA(1, -2) + 1/30 x DATA(2, -2) - --- y DATA(1, -1) + 300 + + 21 21 21 + - --- y DATA(2, -1) - --- y DATA(-1, 2) + --- y DATA(2, 1) + 200 200 200 + + 21 11 2 + + --- y DATA(-1, -2) - --- y DATA(-2, -2) + 1/98 x y DATA(-1, 1) + 200 150 + + 53 3 181 + - -- x DATA(0, 1) + 1/30 x DATA(2, 1) + --- x DATA(1, 1) + 98 735 + + 191 57 226 + + ---- x DATA(2, 0) - -- x DATA(0, 0) + --- x DATA(1, -2) + 2940 98 735 + + 3 3 3 + + 1/5 x DATA(0, 2) + 1/5 x DATA(0, -2) - 2/15 x DATA(1, 0) + + 3 3 71 + - 2/15 x DATA(-1, 0) + 1/30 x DATA(-2, 0) + ---- x DATA(-2, -1) + 2940 + + 191 71 226 + + ---- x DATA(-2, 0) + ---- x DATA(-2, 1) + --- x DATA(-1, -2) + 2940 2940 735 + + 289 226 289 + - ---- x DATA(-2, -2) + --- x DATA(1, 2) - ---- x DATA(2, 2) + 2940 735 2940 + + 289 2 2 + - ---- x DATA(2, -2) - 1/49 x y DATA(2, -1) - 1/10 x DATA(1, 1) + 2940 + + 2 2 2 + + 1/10 x DATA(-1, -1) - 1/10 x DATA(1, -1) + 1/10 x DATA(-1, 0) + + 2 2 2 + + 1/10 x DATA(-1, 1) + 1/20 x DATA(2, -1) + 1/10 x DATA(-1, 2) + + 2 289 181 + + 1/20 x DATA(2, 1) - ---- x DATA(-2, 2) + --- x DATA(1, -1) + 2940 735 + + 181 71 226 + + --- x DATA(-1, 1) + ---- x DATA(2, -1) + --- x DATA(-1, 2) + 735 2940 735 + + 71 181 53 + + ---- x DATA(2, 1) + --- x DATA(-1, -1) - -- x DATA(0, -1) + 2940 735 98 + + 41 41 166 + - -- x DATA(0, 2) - -- x DATA(0, -2) + --- x DATA(1, 0) + 98 98 735 + + 166 2 2 + + --- x DATA(-1, 0) - 1/20 x DATA(-2, 0) - 1/10 x DATA(1, -2) + 735 + + 2 2 2 + + 1/20 x DATA(2, -2) - 1/20 x DATA(-2, -1) + 1/20 x DATA(2, 0) + + 2 2 2 + - 1/10 x DATA(1, 0) - 1/49 x y DATA(-1, 2) - 1/40 x y DATA(2, -1) + + 2 2 2 + - 1/20 x y DATA(-1, -1) + 1/20 x y DATA(1, -1) - 1/49 x y DATA(2, 1) + + 2 2 2 + - 2/49 x y DATA(-2, 0) - 1/49 x y DATA(-2, 1) - 1/49 x y DATA(-1, -2) + + 2 2 + + 2/49 x y DATA(-2, -2) - 1/49 x y DATA(1, 2) + 1/70 x y DATA(-1, -1) + + 2 2 + - 1/20 x y DATA(2, -2) - 1/20 x y DATA(-2, 2) - 1/70 x y DATA(1, 1) + + 2 2 31 + + 1/10 x DATA(-1, -2) - 1/20 x DATA(-2, -2) + --- DATA(-2, 2) + 420 + + 17 11 31 + - 1/84 DATA(-2, 1) - --- DATA(-2, 0) + --- DATA(1, -2) - --- DATA(2, -2) + 420 105 420 + + - 1/84 DATA(-2, -1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=70074076, alloc=2489912, time=5.88 + 11 289 3 2 2 +[COEFF(-2, -2) = - --- y - ---- x - 2/35 x y + 1/60 y - 1/20 x + 1/20 x y + 150 2940 + + 2 31 3 2 3 11 + - 1/35 y + --- + 1/30 x + 2/49 x y , COEFF(-1, -2) = - 2/15 x - --- + 420 105 + + 21 2 2 2 2 226 + + --- y - 1/70 y + 1/35 x y - 1/49 x y + 1/10 x - 1/10 x y + --- x + 200 735 + + 3 2 3 41 + + 1/120 y , COEFF(0, -2) = - 2/49 x y + 2/35 x y + 1/5 x - -- x, + 98 + + 11 2 226 2 3 + COEFF(1, -2) = 1/35 x y + --- - 1/49 x y + --- x + 1/10 x y - 1/120 y + 105 735 + + 2 21 3 2 2 + - 1/10 x - --- y - 2/15 x + 1/70 y , COEFF(2, -2) = - 1/20 x y + 200 + + 2 31 3 2 2 11 + - 2/35 x y + 1/35 y - --- - 1/60 y + 2/49 x y + 1/20 x + --- y + 420 150 + + 289 3 21 2 + - ---- x + 1/30 x , COEFF(-2, -1) = --- y + 1/40 x y - 1/84 - 1/35 x y + 2940 200 + + 2 71 2 3 3 2 + - 1/49 x y + ---- x - 1/20 x + 1/30 x - 1/30 y + 1/70 y , + 2940 + + 3 2 2 3 + COEFF(-1, -1) = - 2/15 x + 1/10 x - 1/20 x y + 1/70 x y - 1/60 y + + 2 37 181 31 2 + + 1/140 y + --- y + --- x - --- + 1/98 x y , + 300 735 210 + + 2 53 3 + COEFF(0, -1) = 1/49 x y - -- x + 1/5 x + 1/35 x y, COEFF(1, -1) = + 98 + + 2 2 3 181 37 31 2 + - 1/10 x + 1/98 x y + 1/60 y + --- x + 1/70 x y - --- y + --- - 1/140 y + 735 300 210 + + 2 3 3 71 2 + + 1/20 x y - 2/15 x , COEFF(2, -1) = 1/30 y + 1/84 + ---- x - 1/40 x y + 2940 + + 2 21 2 2 3 + - 1/49 x y - --- y - 1/35 x y + 1/20 x - 1/70 y + 1/30 x , + 200 + + 191 2 2 2 3 17 + COEFF(-2, 0) = ---- x + 1/35 y - 2/49 x y - 1/20 x + 1/30 x - ---, + 2940 420 + + 3 2 17 2 166 2 + COEFF(-1, 0) = - 2/15 x + 1/70 y - --- + 1/49 x y + --- x + 1/10 x , + 105 735 + + 3 57 2 + COEFF(0, 0) = 1/5 x - -- x + 2/49 x y , + 98 + + 2 2 17 2 3 166 + COEFF(1, 0) = 1/49 x y - 1/70 y + --- - 1/10 x - 2/15 x + --- x, + 105 735 + + 2 17 3 191 2 2 + COEFF(2, 0) = - 2/49 x y + --- + 1/30 x + ---- x - 1/35 y + 1/20 x , + 420 2940 + + 3 2 71 21 2 + COEFF(-2, 1) = 1/30 x - 1/40 x y + ---- x - --- y - 1/20 x + 1/35 x y + 2940 200 + + 2 2 3 3 2 + + 1/70 y - 1/84 - 1/49 x y + 1/30 y , COEFF(-1, 1) = 1/60 y + 1/98 x y + + 2 31 2 181 3 37 + + 1/140 y - --- + 1/20 x y + --- x - 2/15 x - 1/70 x y - --- y + 210 735 300 + + 2 3 2 53 + + 1/10 x , COEFF(0, 1) = 1/5 x - 1/35 x y + 1/49 x y - -- x, COEFF(1, 1) + 98 + + 3 181 2 2 2 + = - 1/60 y - 1/70 x y + --- x + 1/98 x y - 1/20 x y - 1/140 y + 735 + + 3 37 31 2 2 2 + - 2/15 x + --- y + --- - 1/10 x , COEFF(2, 1) = - 1/49 x y + 1/40 x y + 300 210 + + 21 71 3 3 2 2 + + 1/35 x y + --- y + 1/84 + ---- x + 1/30 x - 1/30 y + 1/20 x - 1/70 y + 200 2940 + + 31 2 3 11 2 + , COEFF(-2, 2) = --- - 1/20 x y + 1/30 x + 2/35 x y + --- y + 2/49 x y + 420 150 + + 3 2 289 2 + - 1/60 y - 1/35 y - ---- x - 1/20 x , COEFF(-1, 2) = - 1/35 x y + 2940 + + 2 3 11 3 2 2 21 + - 1/70 y - 2/15 x - --- - 1/120 y - 1/49 x y + 1/10 x y - --- y + 105 200 + + 226 2 2 3 41 + + --- x + 1/10 x , COEFF(0, 2) = - 2/49 x y + 1/5 x - 2/35 x y - -- x, + 735 98 + + 2 21 3 3 2 + COEFF(1, 2) = - 1/35 x y - 1/10 x + --- y + 1/120 y - 2/15 x - 1/49 x y + 200 + + 2 11 2 226 2 31 3 + + 1/70 y + --- - 1/10 x y + --- x, COEFF(2, 2) = 1/20 x - --- + 1/60 y + 105 735 420 + + 2 2 11 289 2 3 + + 1/20 x y + 2/49 x y - --- y + 2/35 x y - ---- x + 1/35 y + 1/30 x ] + 150 2940 + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c"); +bytes used=71074548, alloc=2489912, time=5.96 +bytes used=72074804, alloc=2489912, time=6.03 +bytes used=73076960, alloc=2489912, time=6.10 +bytes used=74077744, alloc=2489912, time=6.24 +bytes used=75078056, alloc=2489912, time=6.32 +bytes used=76078252, alloc=2489912, time=6.46 +bytes used=77078548, alloc=2489912, time=6.53 +bytes used=78078716, alloc=2489912, time=6.69 +bytes used=79078944, alloc=2489912, time=6.78 +bytes used=80079564, alloc=2489912, time=6.91 +> +# d/dy +> simplify( diff(interp_2d_cube_order4_smooth0,y) ); +bytes used=81080236, alloc=2489912, time=7.01 +bytes used=82080460, alloc=2489912, time=7.07 +bytes used=83081684, alloc=2489912, time=7.13 +17 31 17 31 +--- DATA(0, 1) + --- DATA(1, 1) - --- DATA(0, -1) - --- DATA(-1, -1) +105 210 105 210 + + 31 2 2 + - --- DATA(1, -1) + 1/35 x DATA(0, -2) - 1/35 x DATA(0, 2) + 210 + + 2 2 2 + + 1/70 x DATA(0, -1) + 1/10 y DATA(0, -1) - 1/20 y DATA(0, -2) + + 2 2 53 + - 1/10 y DATA(0, 1) + 1/20 y DATA(0, 2) - -- y DATA(-1, 0) + 98 + + 166 41 2 + + --- y DATA(0, -1) - -- y DATA(-2, 0) - 2/49 x y DATA(0, 2) + 735 98 + + 2 2 2 + + 1/49 x y DATA(0, -1) - 2/49 x y DATA(0, -2) - 2/49 x y DATA(2, 0) + + 2 2 2 + + 2/49 x y DATA(0, 0) + 1/49 x y DATA(1, 0) + 1/49 x y DATA(-1, 0) + + 2 + - 2/49 x y DATA(-2, 0) - 2/35 x y DATA(2, 0) - 1/35 x y DATA(1, 0) + + 2 + + 1/49 x y DATA(0, 1) + 2/35 x y DATA(-2, 0) + 1/35 x y DATA(-1, 0) + + 2 53 41 57 + - 1/70 x DATA(0, 1) - -- y DATA(1, 0) - -- y DATA(2, 0) - -- y DATA(0, 0) + 98 98 98 + + 191 191 3 + + ---- y DATA(0, -2) + ---- y DATA(0, 2) + 1/5 y DATA(1, 0) + 2940 2940 + + 3 3 3 + + 1/5 y DATA(-1, 0) + 1/5 y DATA(-2, 0) - 2/15 y DATA(0, -1) + + 3 166 3 + + 1/30 y DATA(0, 2) + --- y DATA(0, 1) + 1/30 y DATA(0, -2) + 735 + + 3 3 3 + + 1/5 y DATA(2, 0) + 1/5 y DATA(0, 0) - 2/15 y DATA(0, 1) + + 31 11 2 + + --- DATA(-1, 1) - --- DATA(2, -1) - 1/70 x DATA(1, 2) + 210 105 + + 2 2 2 + + 1/35 x DATA(2, 2) + 1/35 x DATA(-2, 2) + 1/70 x DATA(-2, 1) + + 2 17 + - 1/49 x y DATA(2, 1) - 1/35 x y DATA(2, 1) + --- DATA(0, 2) + 420 + + 11 17 + + 1/84 DATA(-1, 2) + --- DATA(2, 1) - 1/84 DATA(-1, -2) - --- DATA(0, -2) + 105 420 + + 31 2 2 + + --- DATA(-2, -2) + 1/98 x y DATA(-1, 1) - 1/49 x y DATA(-2, 1) + 420 + + 2 2 + - 1/49 x y DATA(-1, 2) + 2/49 x y DATA(-2, -2) + 1/70 x y DATA(-1, 1) + + 2 2 + - 1/35 x y DATA(2, -1) + 2/49 x y DATA(2, 2) - 1/49 x y DATA(1, -2) + + 2 3 3 + - 1/49 x y DATA(-2, -1) + 1/30 y DATA(1, 2) - 2/15 y DATA(1, 1) + + 3 3 3 + - 2/15 y DATA(-1, -1) + 1/120 x DATA(-2, -1) - 2/15 y DATA(-1, 1) + + 2 3 3 + - 1/10 y DATA(1, 1) - 2/15 y DATA(-2, -1) + 1/30 y DATA(-2, -2) + + 3 3 3 + + 1/30 y DATA(2, 2) + 1/30 y DATA(-2, 2) - 2/15 y DATA(-2, 1) + + 3 3 2 + + 1/30 y DATA(1, -2) + 1/30 y DATA(2, -2) + 1/10 y DATA(-1, -1) + + 2 2 2 + + 1/10 y DATA(1, -1) - 1/10 y DATA(-1, 1) + 1/10 y DATA(2, -1) + + 2 2 3 + + 1/20 y DATA(-1, 2) - 1/10 y DATA(2, 1) - 2/15 y DATA(1, -1) + + 3 3 3 + - 2/15 y DATA(2, -1) + 1/30 y DATA(-1, 2) - 2/15 y DATA(2, 1) + + 3 2 181 + + 1/30 y DATA(-1, -2) + 1/10 y DATA(-2, -1) + --- y DATA(1, 1) + 735 + + 181 2 2 + + --- y DATA(-1, -1) - 1/20 y DATA(-1, -2) + 1/20 y DATA(1, 2) + 735 + + 2 2 2 + + 1/20 y DATA(2, 2) + 1/20 y DATA(-2, 2) - 1/10 y DATA(-2, 1) + + 2 2 71 + - 1/20 y DATA(-2, -2) + 1/98 x y DATA(1, 1) + ---- y DATA(1, 2) + 2940 + + 289 289 226 + - ---- y DATA(2, 2) - ---- y DATA(-2, 2) + --- y DATA(-2, 1) + 2940 2940 735 + + 71 289 226 + + ---- y DATA(1, -2) - ---- y DATA(2, -2) + --- y DATA(-2, -1) + 2940 2940 735 + + 181 2 2 + + --- y DATA(-1, 1) - 1/20 y DATA(1, -2) - 1/20 y DATA(2, -2) + 735 + + 2 2 + - 1/49 x y DATA(1, 2) - 1/49 x y DATA(-1, -2) - 1/70 x y DATA(1, -1) + + - 1/35 x y DATA(-1, 2) + 1/84 DATA(1, 2) + 1/35 x y DATA(-2, 1) + + + 2/35 x y DATA(2, -2) + 1/35 x y DATA(-2, -1) + 1/35 x y DATA(1, -2) + + - 1/35 x y DATA(-1, -2) - 2/35 x y DATA(-2, -2) + 1/35 x y DATA(1, 2) + + 2 + + 2/35 x y DATA(2, 2) - 2/35 x y DATA(-2, 2) - 1/40 x y DATA(1, -2) + + 2 2 31 + - 1/20 x y DATA(2, -2) - 1/10 x y DATA(-2, -1) - --- DATA(2, 2) + 420 + + 2 2 2 + + 1/20 x y DATA(2, 2) - 1/20 x y DATA(-2, 2) - 1/20 x y DATA(-1, -1) + + 2 2 3 + + 1/20 x y DATA(1, -1) - 1/20 x y DATA(1, 1) - 1/60 x DATA(1, 1) + + 3 3 3 + - 1/120 x DATA(-2, 1) - 1/30 x DATA(-1, -2) + 1/60 x DATA(-2, -2) + + 3 3 3 + - 1/30 x DATA(1, 2) + 1/60 x DATA(2, 2) - 1/60 x DATA(-2, 2) + + 3 3 3 + - 1/60 x DATA(-1, -1) + 1/60 x DATA(1, -1) + 1/60 x DATA(-1, 1) + + 3 3 3 + - 1/120 x DATA(2, -1) + 1/30 x DATA(-1, 2) + 1/30 x DATA(1, -2) + + 3 181 226 + - 1/60 x DATA(2, -2) + --- y DATA(1, -1) + --- y DATA(2, -1) + 735 735 + + 71 226 71 + + ---- y DATA(-1, 2) + --- y DATA(2, 1) + ---- y DATA(-1, -2) + 2940 735 2940 + + 289 2 3 + - ---- y DATA(-2, -2) + 1/20 x y DATA(-1, 1) + 1/120 x DATA(2, 1) + 2940 + + 37 21 21 + + --- x DATA(1, 1) - --- x DATA(1, -2) + --- x DATA(-2, -1) + 300 200 200 + + 21 21 11 + - --- x DATA(-2, 1) + --- x DATA(-1, -2) - --- x DATA(-2, -2) + 200 200 150 + + 21 11 11 + + --- x DATA(1, 2) - --- x DATA(2, 2) + --- x DATA(2, -2) + 200 150 150 + + 2 2 2 + + 1/10 x y DATA(2, -1) - 1/140 x DATA(1, 1) + 1/140 x DATA(-1, -1) + + 2 2 2 + + 1/140 x DATA(1, -1) - 1/140 x DATA(-1, 1) - 1/70 x DATA(2, -1) + + 2 2 11 + - 1/70 x DATA(-1, 2) + 1/70 x DATA(2, 1) + --- x DATA(-2, 2) + 150 + + 37 37 21 + - --- x DATA(1, -1) - --- x DATA(-1, 1) - --- x DATA(2, -1) + 300 300 200 + + 21 21 37 + - --- x DATA(-1, 2) + --- x DATA(2, 1) + --- x DATA(-1, -1) + 200 200 300 + + 2 2 2 + + 1/70 x DATA(1, -2) - 1/35 x DATA(2, -2) - 1/70 x DATA(-2, -1) + + 2 2 2 + - 1/40 x y DATA(-1, 2) - 1/49 x y DATA(2, -1) + 1/98 x y DATA(-1, -1) + + 2 2 2 + + 1/98 x y DATA(1, -1) - 1/10 x y DATA(2, 1) + 1/10 x y DATA(-2, 1) + + 2 2 2 + + 1/40 x y DATA(-1, -2) + 1/20 x y DATA(-2, -2) + 1/40 x y DATA(1, 2) + + 2 2 + + 1/70 x y DATA(-1, -1) + 2/49 x y DATA(2, -2) + 2/49 x y DATA(-2, 2) + + 2 2 + - 1/70 x y DATA(1, 1) + 1/70 x DATA(-1, -2) - 1/35 x DATA(-2, -2) + + 31 11 31 + - --- DATA(-2, 2) + --- DATA(-2, 1) - 1/84 DATA(1, -2) + --- DATA(2, -2) + 420 105 420 + + 11 + - --- DATA(-2, -1) + 105 + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=84082964, alloc=2555436, time=7.20 + 289 2 31 11 2 +[COEFF(-2, -2) = - ---- y - 1/35 x + --- - --- x - 2/35 x y + 1/20 x y + 2940 420 150 + + 2 2 3 3 3 + + 2/49 x y - 1/20 y + 1/30 y + 1/60 x , COEFF(-1, -2) = - 1/30 x + + 2 2 2 3 21 2 + - 1/49 x y + 1/40 x y - 1/20 y + 1/30 y + --- x + 1/70 x - 1/84 + 200 + + 71 + + ---- y - 1/35 x y, + 2940 + + 3 191 2 2 17 2 + COEFF(0, -2) = 1/30 y + ---- y + 1/35 x - 1/20 y - --- - 2/49 x y, + 2940 420 + + 2 2 21 71 3 + COEFF(1, -2) = - 1/20 y - 1/40 x y - --- x + ---- y + 1/30 y + 1/35 x y + 200 2940 + + 2 3 2 2 + - 1/49 x y - 1/84 + 1/30 x + 1/70 x , COEFF(2, -2) = - 1/20 y + + 2 11 289 3 2 3 + - 1/20 x y + --- x - ---- y - 1/60 x - 1/35 x + 2/35 x y + 1/30 y + 150 2940 + + 31 2 2 2 11 21 + + --- + 2/49 x y, COEFF(-2, -1) = 1/10 y - 1/49 x y - --- + --- x + 420 105 200 + + 3 226 3 2 2 + + 1/35 x y - 2/15 y + --- y + 1/120 x - 1/10 x y - 1/70 x , + 735 + + 3 3 2 2 2 + COEFF(-1, -1) = - 1/60 x - 2/15 y + 1/140 x + 1/10 y + 1/98 x y + + 2 37 31 181 + - 1/20 x y + --- x - --- + --- y + 1/70 x y, + 300 210 735 + + 17 2 2 3 2 166 + COEFF(0, -1) = - --- + 1/10 y + 1/70 x - 2/15 y + 1/49 x y + --- y, + 105 735 + + 181 2 2 2 31 37 + COEFF(1, -1) = --- y + 1/10 y + 1/20 x y + 1/140 x - --- - --- x + 735 210 300 + + 2 3 3 2 + + 1/98 x y - 1/70 x y - 2/15 y + 1/60 x , COEFF(2, -1) = 1/10 x y + + 3 3 2 2 226 2 + - 1/120 x - 2/15 y - 1/70 x - 1/49 x y + --- y - 1/35 x y + 1/10 y + 735 + + 11 21 3 41 2 + - --- - --- x, COEFF(-2, 0) = 1/5 y - -- y + 2/35 x y - 2/49 x y, + 105 200 98 + + 53 2 3 + COEFF(-1, 0) = - -- y + 1/49 x y + 1/5 y + 1/35 x y, + 98 + + 57 3 2 + COEFF(0, 0) = - -- y + 1/5 y + 2/49 x y, + 98 + + 3 2 53 + COEFF(1, 0) = - 1/35 x y + 1/5 y + 1/49 x y - -- y, + 98 + + 41 3 2 226 + COEFF(2, 0) = - -- y + 1/5 y - 2/35 x y - 2/49 x y, COEFF(-2, 1) = --- y + 98 735 + + 2 3 2 2 2 3 11 + - 1/10 y - 2/15 y + 1/70 x + 1/10 x y - 1/49 x y - 1/120 x + --- + 105 + + 21 2 3 3 + - --- x + 1/35 x y, COEFF(-1, 1) = - 1/10 y + 1/60 x - 2/15 y + 200 + + 37 2 31 2 2 181 + + 1/70 x y - --- x + 1/98 x y + --- + 1/20 x y - 1/140 x + --- y, + 300 210 735 + + 17 2 3 2 166 2 + COEFF(0, 1) = --- - 1/70 x - 2/15 y + 1/49 x y + --- y - 1/10 y , + 105 735 + + 2 37 3 3 2 2 + COEFF(1, 1) = - 1/20 x y + --- x - 1/60 x - 2/15 y + 1/98 x y - 1/10 y + 300 + + 31 181 2 2 3 + + --- + --- y - 1/70 x y - 1/140 x , COEFF(2, 1) = - 1/10 y + 1/120 x + 210 735 + + 11 2 2 226 3 21 + + --- - 1/10 x y + 1/70 x + --- y - 1/35 x y - 2/15 y + --- x + 105 735 200 + + 2 2 2 3 3 + - 1/49 x y, COEFF(-2, 2) = 2/49 x y + 1/20 y - 1/60 x + 1/30 y + + 2 11 31 289 2 + + 1/35 x + --- x - --- - ---- y - 2/35 x y - 1/20 x y , COEFF(-1, 2) = + 150 420 2940 + + 2 2 3 71 2 + - 1/40 x y - 1/35 x y + 1/20 y + 1/30 x + 1/84 + ---- y - 1/70 x + 2940 + + 2 3 21 + - 1/49 x y + 1/30 y - --- x, + 200 + + 2 17 3 2 191 2 + COEFF(0, 2) = - 1/35 x + --- + 1/30 y - 2/49 x y + ---- y + 1/20 y , + 420 2940 + + 3 2 2 3 + COEFF(1, 2) = 1/84 + 1/30 y - 1/49 x y - 1/70 x - 1/30 x + 1/35 x y + + 2 2 21 71 3 + + 1/20 y + 1/40 x y + --- x + ---- y, COEFF(2, 2) = 2/35 x y + 1/30 y + 200 2940 + + 11 31 289 2 2 3 2 + - --- x - --- - ---- y + 1/35 x + 2/49 x y + 1/60 x + 1/20 x y + 150 420 2940 + + 2 + + 1/20 y ] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c"); +bytes used=85083136, alloc=2555436, time=7.28 +bytes used=86083376, alloc=2555436, time=7.35 +bytes used=87083652, alloc=2555436, time=7.44 +bytes used=88083808, alloc=2555436, time=7.60 +bytes used=89087088, alloc=2555436, time=7.68 +bytes used=90087256, alloc=2555436, time=7.86 +bytes used=91087488, alloc=2555436, time=7.95 +bytes used=92087708, alloc=2555436, time=8.14 +bytes used=93087872, alloc=2555436, time=8.22 +bytes used=94088076, alloc=2555436, time=8.41 +> +# d^2/dx^2 +> simplify( diff(interp_2d_cube_order4_smooth0,x,x) ); +bytes used=95088296, alloc=2555436, time=8.51 +bytes used=96088500, alloc=2555436, time=8.57 +191 57 166 53 +---- DATA(2, 0) - -- DATA(0, 0) + --- DATA(1, 0) - -- DATA(0, 1) +2940 98 735 98 + + 181 53 181 181 + + --- DATA(1, 1) - -- DATA(0, -1) + --- DATA(-1, -1) + --- DATA(1, -1) + 735 98 735 735 + + 166 2 2 + + --- DATA(-1, 0) + 3/5 x DATA(0, -2) + 3/5 x DATA(0, 2) + 735 + + 2 2 2 + + 3/5 x DATA(0, -1) + 1/49 y DATA(0, -1) - 2/49 y DATA(0, -2) + + 2 2 + + 1/49 y DATA(0, 1) - 2/49 y DATA(0, 2) + 1/35 y DATA(0, -1) + + 2 + + 3/5 x DATA(0, 1) + 2/35 y DATA(0, -2) - 2/35 y DATA(0, 2) + + 181 71 + - 1/35 y DATA(0, 1) + --- DATA(-1, 1) + ---- DATA(2, -1) + 735 2940 + + 2 2 + + 1/5 x DATA(-1, 0) - 2/5 x DATA(1, 2) + 1/10 x DATA(2, 2) + + 2 2 + + 1/10 x DATA(-2, 2) + 1/10 x DATA(-2, 1) + 1/20 x y DATA(2, 1) + + 41 226 71 + - -- DATA(0, 2) + --- DATA(-1, 2) + ---- DATA(2, 1) + 1/10 x DATA(2, 0) + 98 735 2940 + + 226 41 289 + - 1/5 x DATA(1, 0) + --- DATA(-1, -2) - -- DATA(0, -2) - ---- DATA(-2, -2) + 735 98 2940 + + 2 + + 1/10 x y DATA(-1, 1) - 1/20 x y DATA(2, -1) + 1/98 y DATA(1, 1) + + 2 2 2 + + 1/98 y DATA(-1, -1) + 1/98 y DATA(1, -1) + 1/98 y DATA(-1, 1) + + 2 2 2 + - 1/49 y DATA(2, -1) - 1/49 y DATA(-1, 2) - 1/49 y DATA(2, 1) + + 2 + - 1/49 y DATA(-2, -1) - 1/70 y DATA(1, 1) + 1/70 y DATA(-1, -1) + + 2 2 2 + - 1/49 y DATA(-1, -2) - 1/49 y DATA(1, 2) + 2/49 y DATA(2, 2) + + 2 2 2 + + 2/49 y DATA(-2, 2) - 1/49 y DATA(-2, 1) + 2/49 y DATA(-2, -2) + + - 1/35 y DATA(1, 2) + 2/35 y DATA(2, 2) + 2/35 y DATA(-2, 2) + + + 1/35 y DATA(-2, 1) + 1/35 y DATA(1, -2) - 2/35 y DATA(2, -2) + + 2 + - 1/35 y DATA(-2, -1) - 1/70 y DATA(-1, 1) - 1/49 y DATA(1, -2) + + 2 + + 2/49 y DATA(2, -2) + 1/10 x y DATA(1, -1) + 1/5 x y DATA(-1, 2) + + 226 + + --- DATA(1, 2) - 1/20 x y DATA(-2, 1) - 1/10 x y DATA(2, -2) + 735 + + + 1/20 x y DATA(-2, -1) + 1/5 x y DATA(1, -2) - 1/5 x y DATA(-1, -2) + + + 1/10 x y DATA(-2, -2) - 1/5 x y DATA(1, 2) + 1/10 x y DATA(2, 2) + + 289 + - 1/10 x y DATA(-2, 2) - ---- DATA(2, 2) + 1/70 y DATA(1, -1) + 2940 + + - 1/35 y DATA(2, -1) - 1/35 y DATA(-1, 2) + 1/35 y DATA(2, 1) + + + 1/35 y DATA(-1, -2) - 2/35 y DATA(-2, -2) - 1/5 x DATA(1, 1) + + - 1/5 x DATA(1, -2) - 1/10 x DATA(-2, -1) - 1/10 x DATA(-2, 1) + + + 1/5 x DATA(-1, -2) - 1/10 x DATA(-2, -2) - 1/5 x DATA(1, 2) + + 2 + + 1/10 x DATA(2, 2) + 1/10 x DATA(2, -2) - 2/5 x DATA(1, 1) + + 2 2 + - 2/5 x DATA(-1, -1) - 2/5 x DATA(1, -1) - 1/10 x DATA(-2, 0) + + 2 2 2 + - 2/5 x DATA(-1, 1) + 1/10 x DATA(2, -1) - 2/5 x DATA(-1, 2) + + 2 + + 1/10 x DATA(2, 1) - 1/10 x DATA(-2, 2) - 1/5 x DATA(1, -1) + + + 1/5 x DATA(-1, 1) + 1/10 x DATA(2, -1) + 1/5 x DATA(-1, 2) + + 2 + + 1/10 x DATA(2, 1) + 1/5 x DATA(-1, -1) - 2/5 x DATA(1, -2) + + 2 2 + + 1/10 x DATA(2, -2) + 1/10 x DATA(-2, -1) - 1/10 x y DATA(-1, -1) + + 2 2 + - 1/10 x y DATA(1, 1) - 2/5 x DATA(-1, -2) + 1/10 x DATA(-2, -2) + + 2 289 71 + + 2/49 y DATA(0, 0) - ---- DATA(-2, 2) + ---- DATA(-2, 1) + 2940 2940 + + 191 226 289 + + ---- DATA(-2, 0) + --- DATA(1, -2) - ---- DATA(2, -2) + 2940 735 2940 + + 71 2 2 + + ---- DATA(-2, -1) - 2/49 y DATA(2, 0) + 1/49 y DATA(-1, 0) + 2940 + + 2 2 2 + - 2/49 y DATA(-2, 0) + 1/49 y DATA(1, 0) - 2/5 x DATA(1, 0) + + 2 2 2 + - 2/5 x DATA(-1, 0) + 1/10 x DATA(-2, 0) + 3/5 x DATA(0, 0) + + 2 + + 1/10 x DATA(2, 0) + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=97091392, alloc=2555436, time=8.63 + 2 289 2 +[COEFF(-2, -2) = 2/49 y - 2/35 y + 1/10 x y - ---- - 1/10 x + 1/10 x , + 2940 + + 2 226 2 + COEFF(-1, -2) = 1/35 y - 2/5 x + --- - 1/5 x y + 1/5 x - 1/49 y , + 735 + + 41 2 2 + COEFF(0, -2) = - -- + 2/35 y + 3/5 x - 2/49 y , + 98 + + 2 226 2 + COEFF(1, -2) = 1/35 y - 2/5 x + --- - 1/49 y + 1/5 x y - 1/5 x, + 735 + + 2 289 2 + COEFF(2, -2) = - 2/35 y + 1/10 x - 1/10 x y + 1/10 x - ---- + 2/49 y , + 2940 + + 2 2 71 + COEFF(-2, -1) = - 1/49 y + 1/10 x + 1/20 x y - 1/10 x - 1/35 y + ----, + 2940 + + 2 181 2 + COEFF(-1, -1) = 1/70 y + 1/5 x - 1/10 x y + 1/98 y + --- - 2/5 x , + 735 + + 2 2 53 + COEFF(0, -1) = 3/5 x + 1/49 y + 1/35 y - --, + 98 + + 181 2 2 + COEFF(1, -1) = --- + 1/98 y - 1/5 x - 2/5 x + 1/10 x y + 1/70 y, + 735 + + 2 2 71 + COEFF(2, -1) = - 1/35 y + 1/10 x - 1/49 y + ---- + 1/10 x - 1/20 x y, + 2940 + + 2 2 191 + COEFF(-2, 0) = 1/10 x - 2/49 y + ---- - 1/10 x, + 2940 + + 166 2 2 + COEFF(-1, 0) = 1/5 x + --- + 1/49 y - 2/5 x , + 735 + + 2 57 2 + COEFF(0, 0) = 3/5 x - -- + 2/49 y , + 98 + + 166 2 2 + COEFF(1, 0) = - 1/5 x + --- + 1/49 y - 2/5 x , + 735 + + 2 2 191 + COEFF(2, 0) = 1/10 x - 2/49 y + 1/10 x + ----, + 2940 + + 2 2 71 + COEFF(-2, 1) = - 1/10 x - 1/49 y + 1/10 x + 1/35 y - 1/20 x y + ----, + 2940 + + 181 2 2 + COEFF(-1, 1) = --- - 1/70 y + 1/98 y + 1/10 x y - 2/5 x + 1/5 x, + 735 + + 53 2 2 + COEFF(0, 1) = - 1/35 y - -- + 3/5 x + 1/49 y , + 98 + + 2 2 181 + COEFF(1, 1) = - 1/5 x + 1/98 y - 1/10 x y - 2/5 x + --- - 1/70 y, + 735 + + 2 71 2 + COEFF(2, 1) = 1/35 y - 1/49 y + ---- + 1/10 x + 1/20 x y + 1/10 x , + 2940 + + 2 289 2 + COEFF(-2, 2) = 1/10 x - ---- + 2/35 y - 1/10 x + 2/49 y - 1/10 x y, + 2940 + + 2 2 226 + COEFF(-1, 2) = - 2/5 x - 1/49 y + 1/5 x - 1/35 y + --- + 1/5 x y, + 735 + + 2 2 41 + COEFF(0, 2) = - 2/49 y - 2/35 y + 3/5 x - --, + 98 + + 2 226 2 + COEFF(1, 2) = - 1/5 x y - 1/5 x - 2/5 x - 1/35 y + --- - 1/49 y , + 735 + + 2 2 289 + COEFF(2, 2) = 2/49 y + 2/35 y + 1/10 x + 1/10 x - ---- + 1/10 x y] + 2940 + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c"); +bytes used=98091548, alloc=2555436, time=8.70 +bytes used=99091708, alloc=2555436, time=8.83 +bytes used=100092244, alloc=2555436, time=8.91 +bytes used=101092436, alloc=2555436, time=9.07 +bytes used=102092596, alloc=2555436, time=9.25 +bytes used=103092832, alloc=2555436, time=9.38 +> +# d^2/dxdy +> simplify( diff(interp_2d_cube_order4_smooth0,x,y) ); +bytes used=104093572, alloc=2555436, time=9.47 + 37 37 37 +1/35 x DATA(0, -1) + --- DATA(1, 1) + --- DATA(-1, -1) - --- DATA(1, -1) + 300 300 300 + + 37 21 2 + - --- DATA(-1, 1) - --- DATA(2, -1) - 1/10 x DATA(1, 2) + 300 200 + + 2 2 2 + + 1/20 x DATA(2, 2) - 1/20 x DATA(-2, 2) - 1/40 x DATA(-2, 1) + + 21 21 + - 2/49 x y DATA(2, 1) - --- DATA(-1, 2) + --- DATA(2, 1) + 200 200 + + 21 11 + + --- DATA(-1, -2) - --- DATA(-2, -2) + 1/49 x y DATA(-1, 1) + 200 150 + + 2 2 + - 2/49 x y DATA(2, -1) - 1/20 y DATA(1, 1) - 1/20 y DATA(-1, -1) + + 2 2 2 + + 1/20 y DATA(1, -1) + 1/20 y DATA(-1, 1) + 1/10 y DATA(2, -1) + + 2 2 2 + - 1/40 y DATA(-1, 2) - 1/10 y DATA(2, 1) - 1/10 y DATA(-2, -1) + + 2 + - 1/70 y DATA(1, 1) + 1/70 y DATA(-1, -1) + 1/40 y DATA(-1, -2) + + 2 2 2 + + 1/40 y DATA(1, 2) + 1/20 y DATA(2, 2) - 1/20 y DATA(-2, 2) + + 2 2 + + 1/10 y DATA(-2, 1) + 1/20 y DATA(-2, -2) + 1/35 y DATA(1, 2) + + + 2/35 y DATA(2, 2) - 2/35 y DATA(-2, 2) + 1/35 y DATA(-2, 1) + + + 1/35 y DATA(1, -2) + 2/35 y DATA(2, -2) + 1/35 y DATA(-2, -1) + + 2 2 + + 1/70 y DATA(-1, 1) - 1/40 y DATA(1, -2) - 1/20 y DATA(2, -2) + + 21 + + 1/49 x y DATA(1, -1) - 2/49 x y DATA(-1, 2) + --- DATA(1, 2) + 200 + + - 2/49 x y DATA(-2, 1) + 4/49 x y DATA(2, -2) - 2/49 x y DATA(-2, -1) + + - 2/49 x y DATA(1, -2) - 2/49 x y DATA(-1, -2) + 4/49 x y DATA(-2, -2) + + - 2/49 x y DATA(1, 2) + 4/49 x y DATA(2, 2) + 4/49 x y DATA(-2, 2) + + 11 + - --- DATA(2, 2) - 1/70 y DATA(1, -1) - 1/35 y DATA(2, -1) + 150 + + - 1/35 y DATA(-1, 2) - 1/35 y DATA(2, 1) - 1/35 y DATA(-1, -2) + + - 2/35 y DATA(-2, -2) - 1/70 x DATA(1, 1) + 1/35 x DATA(1, -2) + + - 1/35 x DATA(-2, -1) + 1/35 x DATA(-2, 1) + 1/35 x DATA(-1, -2) + + - 2/35 x DATA(-2, -2) - 1/35 x DATA(1, 2) + 2/35 x DATA(2, 2) + + 2 2 + - 2/35 x DATA(2, -2) - 1/20 x DATA(1, 1) - 1/20 x DATA(-1, -1) + + 2 2 2 + + 1/20 x DATA(1, -1) + 1/20 x DATA(-1, 1) - 1/40 x DATA(2, -1) + + 2 2 + + 1/10 x DATA(-1, 2) + 1/40 x DATA(2, 1) + 2/35 x DATA(-2, 2) + + + 1/70 x DATA(1, -1) - 1/70 x DATA(-1, 1) - 1/35 x DATA(2, -1) + + - 1/35 x DATA(-1, 2) + 1/35 x DATA(2, 1) + 1/70 x DATA(-1, -1) + + 2 2 2 + + 1/10 x DATA(1, -2) - 1/20 x DATA(2, -2) + 1/40 x DATA(-2, -1) + + 2 + + 1/49 x y DATA(-1, -1) + 1/49 x y DATA(1, 1) - 1/10 x DATA(-1, -2) + + 2 11 21 + + 1/20 x DATA(-2, -2) + --- DATA(-2, 2) - --- DATA(-2, 1) + 150 200 + + 21 11 21 + - --- DATA(1, -2) + --- DATA(2, -2) + --- DATA(-2, -1) + 200 150 200 + + + 2/49 x y DATA(-1, 0) - 2/35 y DATA(2, 0) - 1/35 y DATA(1, 0) + + + 1/35 y DATA(-1, 0) + 2/49 x y DATA(0, -1) + 2/35 y DATA(-2, 0) + + - 4/49 x y DATA(2, 0) - 1/35 x DATA(0, 1) - 2/35 x DATA(0, 2) + + + 2/35 x DATA(0, -2) - 4/49 x y DATA(0, -2) + 2/49 x y DATA(1, 0) + + + 2/49 x y DATA(0, 1) + 4/49 x y DATA(0, 0) - 4/49 x y DATA(-2, 0) + + - 4/49 x y DATA(0, 2) + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=105096984, alloc=2555436, time=9.52 + 2 11 2 +[COEFF(-2, -2) = 4/49 x y + 1/20 y - 2/35 y - 2/35 x - --- + 1/20 x , + 150 + + 2 2 21 + COEFF(-1, -2) = 1/35 x - 1/10 x - 2/49 x y - 1/35 y + 1/40 y + ---, + 200 + + COEFF(0, -2) = - 4/49 x y + 2/35 x, + + 21 2 2 + COEFF(1, -2) = - 2/49 x y + 1/35 x - --- + 1/10 x + 1/35 y - 1/40 y , + 200 + + 2 11 2 + COEFF(2, -2) = - 1/20 y + --- + 2/35 y - 2/35 x + 4/49 x y - 1/20 x , + 150 + + 2 21 2 + COEFF(-2, -1) = 1/40 x + --- - 1/35 x - 1/10 y + 1/35 y - 2/49 x y, + 200 + + 2 37 2 + COEFF(-1, -1) = - 1/20 y + 1/49 x y + --- + 1/70 y + 1/70 x - 1/20 x , + 300 + + COEFF(0, -1) = 2/49 x y + 1/35 x, + + 2 2 37 + COEFF(1, -1) = - 1/70 y + 1/20 x + 1/20 y + 1/49 x y + 1/70 x - ---, + 300 + + 2 21 2 + COEFF(2, -1) = - 1/35 x - 1/35 y + 1/10 y - 2/49 x y - --- - 1/40 x , + 200 + + COEFF(-2, 0) = 2/35 y - 4/49 x y, COEFF(-1, 0) = 2/49 x y + 1/35 y, + + COEFF(0, 0) = 4/49 x y, COEFF(1, 0) = - 1/35 y + 2/49 x y, + + COEFF(2, 0) = - 2/35 y - 4/49 x y, + + 2 21 2 + COEFF(-2, 1) = - 1/40 x + 1/35 x - --- + 1/10 y + 1/35 y - 2/49 x y, + 200 + + 37 2 2 + COEFF(-1, 1) = - --- - 1/70 x + 1/20 x + 1/70 y + 1/20 y + 1/49 x y, + 300 + + COEFF(0, 1) = 2/49 x y - 1/35 x, + + 37 2 2 + COEFF(1, 1) = - 1/70 x + --- - 1/20 x + 1/49 x y - 1/20 y - 1/70 y, + 300 + + 2 21 2 + COEFF(2, 1) = - 1/35 y - 1/10 y + 1/35 x - 2/49 x y + --- + 1/40 x , + 200 + + 2 2 11 + COEFF(-2, 2) = 2/35 x - 1/20 x - 1/20 y + 4/49 x y + --- - 2/35 y, + 150 + + 2 2 21 + COEFF(-1, 2) = - 1/35 x - 1/40 y + 1/10 x - --- - 1/35 y - 2/49 x y, + 200 + + COEFF(0, 2) = - 4/49 x y - 2/35 x, + + 2 2 21 + COEFF(1, 2) = 1/40 y - 2/49 x y - 1/10 x + 1/35 y - 1/35 x + ---, + 200 + + 2 2 11 + COEFF(2, 2) = 1/20 y + 1/20 x - --- + 2/35 x + 2/35 y + 4/49 x y] + 150 + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c"); +bytes used=106097284, alloc=2555436, time=9.59 +bytes used=107097536, alloc=2555436, time=9.71 +bytes used=108099596, alloc=2555436, time=9.81 +bytes used=109099792, alloc=2555436, time=9.98 +bytes used=110100132, alloc=2555436, time=10.14 +bytes used=111100580, alloc=2555436, time=10.31 +bytes used=112100732, alloc=2555436, time=10.47 +> +# d^2/dy^2 +> simplify( diff(interp_2d_cube_order4_smooth0,y,y) ); +bytes used=113100928, alloc=2555436, time=10.54 + 41 57 53 166 +- -- DATA(2, 0) - -- DATA(0, 0) - -- DATA(1, 0) + --- DATA(0, 1) + 98 98 98 735 + + 181 + + --- DATA(1, 1) + 1/5 y DATA(0, -1) + 2/35 x DATA(-2, 0) + 735 + + 166 + - 2/35 x DATA(2, 0) - 1/5 y DATA(0, 1) + --- DATA(0, -1) + 735 + + 181 181 53 181 + + --- DATA(-1, -1) + --- DATA(1, -1) - -- DATA(-1, 0) + --- DATA(-1, 1) + 735 735 98 735 + + 226 2 2 + + --- DATA(2, -1) - 1/49 x DATA(1, 2) + 2/49 x DATA(2, 2) + 735 + + 2 2 + + 2/49 x DATA(-2, 2) - 1/49 x DATA(-2, 1) - 1/5 x y DATA(2, 1) + + 191 71 226 71 + + ---- DATA(0, 2) + ---- DATA(-1, 2) + --- DATA(2, 1) + ---- DATA(-1, -2) + 2940 2940 735 2940 + + 191 289 + + ---- DATA(0, -2) - ---- DATA(-2, -2) + 1/10 x y DATA(-1, 1) + 2940 2940 + + 2 2 + + 1/5 x y DATA(2, -1) - 2/5 y DATA(1, 1) - 2/5 y DATA(-1, -1) + + 2 2 2 + - 2/5 y DATA(1, -1) - 2/5 y DATA(-1, 1) - 2/5 y DATA(2, -1) + + 2 2 2 + + 1/10 y DATA(-1, 2) - 2/5 y DATA(2, 1) - 2/5 y DATA(-2, -1) + + 2 + - 1/5 y DATA(1, 1) + 1/5 y DATA(-1, -1) + 1/10 y DATA(-1, -2) + + 2 2 2 + + 1/10 y DATA(1, 2) + 1/10 y DATA(2, 2) + 1/10 y DATA(-2, 2) + + 2 2 + - 2/5 y DATA(-2, 1) + 1/10 y DATA(-2, -2) + 1/10 y DATA(1, 2) + + + 1/10 y DATA(2, 2) + 1/10 y DATA(-2, 2) - 1/5 y DATA(-2, 1) + + - 1/10 y DATA(1, -2) - 1/10 y DATA(2, -2) + 1/5 y DATA(-2, -1) + + 2 2 + - 1/5 y DATA(-1, 1) + 1/10 y DATA(1, -2) + 1/10 y DATA(2, -2) + + 71 + + 1/10 x y DATA(1, -1) - 1/20 x y DATA(-1, 2) + ---- DATA(1, 2) + 2940 + + + 1/5 x y DATA(-2, 1) - 1/10 x y DATA(2, -2) - 1/5 x y DATA(-2, -1) + + - 1/20 x y DATA(1, -2) + 1/20 x y DATA(-1, -2) + 1/10 x y DATA(-2, -2) + + + 1/20 x y DATA(1, 2) + 1/10 x y DATA(2, 2) - 1/10 x y DATA(-2, 2) + + 289 + - ---- DATA(2, 2) + 1/5 y DATA(1, -1) + 1/5 y DATA(2, -1) + 2940 + + + 1/10 y DATA(-1, 2) - 1/5 y DATA(2, 1) - 1/10 y DATA(-1, -2) + + - 1/10 y DATA(-2, -2) - 1/70 x DATA(1, 1) + 1/35 x DATA(1, -2) + + + 1/35 x DATA(-2, -1) + 1/35 x DATA(-2, 1) - 1/35 x DATA(-1, -2) + + - 2/35 x DATA(-2, -2) + 1/35 x DATA(1, 2) + 2/35 x DATA(2, 2) + + 2 2 + + 2/35 x DATA(2, -2) + 1/98 x DATA(1, 1) + 1/98 x DATA(-1, -1) + + 2 2 2 + + 1/98 x DATA(1, -1) + 1/98 x DATA(-1, 1) - 1/49 x DATA(2, -1) + + 2 2 + - 1/49 x DATA(-1, 2) - 1/49 x DATA(2, 1) - 2/35 x DATA(-2, 2) + + - 1/70 x DATA(1, -1) + 1/70 x DATA(-1, 1) - 1/35 x DATA(2, -1) + + - 1/35 x DATA(-1, 2) - 1/35 x DATA(2, 1) + 1/70 x DATA(-1, -1) + + 2 2 2 + - 1/49 x DATA(1, -2) + 2/49 x DATA(2, -2) - 1/49 x DATA(-2, -1) + + 2 + - 1/10 x y DATA(-1, -1) - 1/10 x y DATA(1, 1) - 1/49 x DATA(-1, -2) + + 2 289 226 + + 2/49 x DATA(-2, -2) - ---- DATA(-2, 2) + --- DATA(-2, 1) + 2940 735 + + 41 71 + - -- DATA(-2, 0) - 1/10 y DATA(0, -2) + ---- DATA(1, -2) + 98 2940 + + 289 226 + - ---- DATA(2, -2) + --- DATA(-2, -1) + 1/10 y DATA(0, 2) + 2940 735 + + 2 2 2 + + 3/5 y DATA(0, 0) - 2/5 y DATA(0, -1) + 3/5 y DATA(-1, 0) + + 2 2 2 + + 3/5 y DATA(1, 0) + 1/10 y DATA(0, 2) + 1/10 y DATA(0, -2) + + 2 2 2 + - 2/5 y DATA(0, 1) + 1/49 x DATA(1, 0) - 2/49 x DATA(0, 2) + + 2 2 2 + - 2/49 x DATA(0, -2) + 1/49 x DATA(0, 1) + 3/5 y DATA(-2, 0) + + 2 2 2 + + 3/5 y DATA(2, 0) - 2/49 x DATA(-2, 0) + 2/49 x DATA(0, 0) + + 2 2 + + 1/49 x DATA(0, -1) + 1/49 x DATA(-1, 0) + 1/35 x DATA(-1, 0) + + 2 + - 1/35 x DATA(1, 0) - 2/49 x DATA(2, 0) + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=114101228, alloc=2555436, time=10.61 + 2 289 2 +[COEFF(-2, -2) = - 2/35 x + 1/10 y - ---- - 1/10 y + 1/10 x y + 2/49 x , + 2940 + + 2 71 2 + COEFF(-1, -2) = 1/10 y + ---- - 1/35 x + 1/20 x y - 1/49 x - 1/10 y, + 2940 + + 2 191 2 + COEFF(0, -2) = 1/10 y + ---- - 2/49 x - 1/10 y, + 2940 + + 2 71 2 + COEFF(1, -2) = - 1/49 x + ---- + 1/10 y - 1/10 y + 1/35 x - 1/20 x y, + 2940 + + 289 2 2 + COEFF(2, -2) = - 1/10 y - 1/10 x y + 2/35 x - ---- + 2/49 x + 1/10 y , + 2940 + + 226 2 2 + COEFF(-2, -1) = - 1/5 x y + --- + 1/5 y + 1/35 x - 1/49 x - 2/5 y , + 735 + + 181 2 2 + COEFF(-1, -1) = --- - 1/10 x y + 1/98 x + 1/5 y - 2/5 y + 1/70 x, + 735 + + 2 2 166 + COEFF(0, -1) = 1/5 y - 2/5 y + 1/49 x + ---, + 735 + + 181 2 2 + COEFF(1, -1) = - 1/70 x + 1/10 x y + --- + 1/5 y + 1/98 x - 2/5 y , + 735 + + 2 226 2 + COEFF(2, -1) = - 1/35 x - 2/5 y + 1/5 x y + --- - 1/49 x + 1/5 y, + 735 + + 41 2 2 + COEFF(-2, 0) = - -- + 2/35 x - 2/49 x + 3/5 y , + 98 + + 53 2 2 + COEFF(-1, 0) = - -- + 3/5 y + 1/35 x + 1/49 x , + 98 + + 2 2 57 + COEFF(0, 0) = 2/49 x + 3/5 y - --, + 98 + + 2 2 53 + COEFF(1, 0) = 3/5 y + 1/49 x - -- - 1/35 x, + 98 + + 41 2 2 + COEFF(2, 0) = - -- + 3/5 y - 2/35 x - 2/49 x , + 98 + + 2 2 226 + COEFF(-2, 1) = 1/35 x - 1/5 y + 1/5 x y - 1/49 x - 2/5 y + ---, + 735 + + 2 2 181 + COEFF(-1, 1) = 1/10 x y + 1/70 x - 2/5 y - 1/5 y + 1/98 x + ---, + 735 + + 2 166 2 + COEFF(0, 1) = - 1/5 y - 2/5 y + --- + 1/49 x , + 735 + + 181 2 2 + COEFF(1, 1) = - 1/5 y + --- - 1/70 x + 1/98 x - 2/5 y - 1/10 x y, + 735 + + 2 2 226 + COEFF(2, 1) = - 2/5 y - 1/49 x + --- - 1/5 x y - 1/5 y - 1/35 x, + 735 + + 2 2 289 + COEFF(-2, 2) = 2/49 x + 1/10 y - 1/10 x y + 1/10 y - 2/35 x - ----, + 2940 + + 2 71 2 + COEFF(-1, 2) = 1/10 y + ---- - 1/20 x y + 1/10 y - 1/35 x - 1/49 x , + 2940 + + 2 2 191 + COEFF(0, 2) = 1/10 y - 2/49 x + 1/10 y + ----, + 2940 + + 71 2 2 + COEFF(1, 2) = 1/35 x + 1/10 y + ---- + 1/20 x y + 1/10 y - 1/49 x , + 2940 + + 2 2 289 + COEFF(2, 2) = 2/49 x + 1/10 y + 1/10 y + 1/10 x y - ---- + 2/35 x] + 2940 + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c"); +bytes used=115101596, alloc=2555436, time=10.70 +bytes used=116101756, alloc=2555436, time=10.85 +bytes used=117101948, alloc=2555436, time=10.94 +bytes used=118102268, alloc=2555436, time=11.10 +bytes used=119102436, alloc=2555436, time=11.27 +bytes used=120102772, alloc=2555436, time=11.41 +> +################################################################################ +> quit +bytes used=120843640, alloc=2555436, time=11.51 diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.maple b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.maple new file mode 100644 index 0000000..a5b197c --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.maple @@ -0,0 +1,170 @@ +# 2d.maple -- compute Lagrange interpolation coefficients in 2-D +# $Header$ + +################################################################################ + +# +# 2d, cube, order=1, smoothing=0 (size=2) +# + +# interpolating polynomial +interp_2d_cube_order1_smooth0 + := Lagrange_polynomial_interpolant(fn_2d_order1, coeffs_list_2d_order1, + coords_list_2d, posn_list_2d_size2); + +# I +coeffs_as_lc_of_data(%, posn_list_2d_size2); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_2d_cube_order1_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size2); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_2d_cube_order1_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size2); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c"); + +################################################################################ + +# +# 2d, cube, order=2, smoothing=0 (size=3) +# + +# interpolating polynomial +interp_2d_cube_order2_smooth0 + := Lagrange_polynomial_interpolant(fn_2d_order2, coeffs_list_2d_order2, + coords_list_2d, posn_list_2d_size3); + +# I +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_2d_cube_order2_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_2d_cube_order2_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_2d_cube_order2_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_2d_cube_order2_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_2d_cube_order2_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c"); + +################################################################################ + +# +# 2d, cube, order=3, smoothing=0 (size=4) +# + +# interpolating polynomial +interp_2d_cube_order3_smooth0 + := Lagrange_polynomial_interpolant(fn_2d_order3, coeffs_list_2d_order3, + coords_list_2d, posn_list_2d_size4); + +# I +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_2d_cube_order3_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_2d_cube_order3_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_2d_cube_order3_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_2d_cube_order3_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_2d_cube_order3_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c"); + +################################################################################ + +# +# 2d, cube, order=4, smoothing=0 (size=5) +# + +# interpolating polynomial +interp_2d_cube_order4_smooth0 + := Lagrange_polynomial_interpolant(fn_2d_order4, coeffs_list_2d_order4, + coords_list_2d, posn_list_2d_size5); + +# I +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_2d_cube_order4_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_2d_cube_order4_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_2d_cube_order4_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_2d_cube_order4_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_2d_cube_order4_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c"); + +################################################################################ diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..f4187d3 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-I.compute.c @@ -0,0 +1,34 @@ +fp t8; +fp t2; +fp t7; +fp t4; +fp t13; +fp t1; +fp t6; +fp t12; +fp t11; +fp t10; +fp t5; +fp t9; +fp t3; + t8 = RATIONAL(1.0,4.0); + t2 = t8*y; + t7 = RATIONAL(-1.0,4.0); + t4 = t7*z; + t13 = t2+t4; + t1 = t8*z; + t6 = t7*y; + t12 = t1+t6; + t11 = t1+t2; + t10 = t4+t6; + t5 = t7*x; + t9 = t5+t8; + t3 = t8*x; + coeffs_I->coeff_0_0_0 = t5+RATIONAL(1.0,2.0)+t10; + coeffs_I->coeff_p1_0_0 = t8+t3+t10; + coeffs_I->coeff_0_p1_0 = t9+t13; + coeffs_I->coeff_p1_p1_0 = t3+t13; + coeffs_I->coeff_0_0_p1 = t9+t12; + coeffs_I->coeff_p1_0_p1 = t3+t12; + coeffs_I->coeff_0_p1_p1 = t5+t11; + coeffs_I->coeff_p1_p1_p1 = t3+t7+t11; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..0f61ed0 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-dx.compute.c @@ -0,0 +1,12 @@ +fp t15; +fp t14; + t15 = RATIONAL(1.0,4.0); + t14 = RATIONAL(-1.0,4.0); + coeffs_dx->coeff_0_0_0 = t14; + coeffs_dx->coeff_p1_0_0 = t15; + coeffs_dx->coeff_0_p1_0 = t14; + coeffs_dx->coeff_p1_p1_0 = t15; + coeffs_dx->coeff_0_0_p1 = t14; + coeffs_dx->coeff_p1_0_p1 = t15; + coeffs_dx->coeff_0_p1_p1 = t14; + coeffs_dx->coeff_p1_p1_p1 = t15; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..ccabcbd --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-dy.compute.c @@ -0,0 +1,12 @@ +fp t17; +fp t16; + t17 = RATIONAL(1.0,4.0); + t16 = RATIONAL(-1.0,4.0); + coeffs_dy->coeff_0_0_0 = t16; + coeffs_dy->coeff_p1_0_0 = t16; + coeffs_dy->coeff_0_p1_0 = t17; + coeffs_dy->coeff_p1_p1_0 = t17; + coeffs_dy->coeff_0_0_p1 = t16; + coeffs_dy->coeff_p1_0_p1 = t16; + coeffs_dy->coeff_0_p1_p1 = t17; + coeffs_dy->coeff_p1_p1_p1 = t17; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-dz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-dz.compute.c new file mode 100644 index 0000000..9f25875 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-dz.compute.c @@ -0,0 +1,12 @@ +fp t19; +fp t18; + t19 = RATIONAL(1.0,4.0); + t18 = RATIONAL(-1.0,4.0); + coeffs_dz->coeff_0_0_0 = t18; + coeffs_dz->coeff_p1_0_0 = t18; + coeffs_dz->coeff_0_p1_0 = t18; + coeffs_dz->coeff_p1_p1_0 = t18; + coeffs_dz->coeff_0_0_p1 = t19; + coeffs_dz->coeff_p1_0_p1 = t19; + coeffs_dz->coeff_0_p1_p1 = t19; + coeffs_dz->coeff_p1_p1_p1 = t19; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..7cd1009 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-I.compute.c @@ -0,0 +1,153 @@ +fp t43; +fp t47; +fp t31; +fp t46; +fp t32; +fp t85; +fp t26; +fp t84; +fp t48; +fp t29; +fp t83; +fp t45; +fp t37; +fp t40; +fp t82; +fp t38; +fp t28; +fp t42; +fp t24; +fp t81; +fp t27; +fp t41; +fp t71; +fp t25; +fp t80; +fp t72; +fp t21; +fp t34; +fp t79; +fp t36; +fp t68; +fp t69; +fp t78; +fp t77; +fp t76; +fp t35; +fp t67; +fp t75; +fp t22; +fp t30; +fp t74; +fp t73; +fp t39; +fp t70; +fp t66; +fp t33; +fp t63; +fp t62; +fp t61; +fp t60; +fp t59; +fp t58; +fp t57; +fp t56; +fp t55; +fp t54; +fp t53; +fp t52; +fp t51; +fp t50; +fp t49; +fp t23; +fp t20; + t43 = RATIONAL(1.0,18.0); + t47 = z*z; + t31 = t43*t47; + t46 = y*y; + t32 = t43*t46; + t85 = t31+t32; + t26 = t43*y; + t84 = t26+t85; + t48 = x*x; + t29 = t43*t48; + t83 = t29+RATIONAL(-2.0,27.0); + t45 = RATIONAL(-1.0,9.0); + t37 = t45*t48; + t40 = RATIONAL(1.0,27.0); + t82 = t37+t40; + t38 = RATIONAL(-1.0,18.0); + t28 = t38*x; + t42 = RATIONAL(1.0,12.0); + t24 = t42*x*z; + t81 = t28+t24; + t27 = t43*x; + t41 = RATIONAL(-1.0,12.0); + t71 = z*t41; + t25 = x*t71; + t80 = t27+t25; + t72 = y*t42; + t21 = z*t72; + t34 = t43*z; + t79 = t21+t34; + t36 = t45*t46; + t68 = t31+t36; + t69 = t29+t40; + t78 = t68+t69; + t77 = t27+t24; + t76 = t28+t25; + t35 = t45*t47; + t67 = t35+t32; + t75 = t67+t69; + t22 = y*t71; + t30 = t38*z; + t74 = t22+t30; + t73 = t83+t84; + t39 = RATIONAL(4.0,27.0); + t70 = t37+t39; + t66 = t35+t36; + t33 = t38*y; + t63 = t33+t85; + t62 = t68+t70; + t61 = t67+t70; + t60 = t29+t39+t66; + t59 = t30+t21+t63; + t58 = t82+t84; + t57 = t27+t75; + t56 = t24+t78; + t55 = t28+t75; + t54 = t25+t78; + t53 = t22+t34+t63; + t52 = t73+t79; + t51 = t53+t83; + t50 = t73+t74; + t49 = t59+t83; + t23 = t41*x*y; + t20 = x*t72; + coeffs_I->coeff_m1_m1_m1 = t20+t49+t81; + coeffs_I->coeff_0_m1_m1 = t59+t82; + coeffs_I->coeff_p1_m1_m1 = t23+t49+t80; + coeffs_I->coeff_m1_0_m1 = t28+t30+t56; + coeffs_I->coeff_0_0_m1 = t30+t62; + coeffs_I->coeff_p1_0_m1 = t27+t30+t54; + coeffs_I->coeff_m1_p1_m1 = t23+t50+t81; + coeffs_I->coeff_0_p1_m1 = t58+t74; + coeffs_I->coeff_p1_p1_m1 = t20+t50+t80; + coeffs_I->coeff_m1_m1_0 = t20+t33+t55; + coeffs_I->coeff_0_m1_0 = t33+t61; + coeffs_I->coeff_p1_m1_0 = t33+t23+t57; + coeffs_I->coeff_m1_0_0 = t28+t60; + coeffs_I->coeff_0_0_0 = t37+RATIONAL(7.0,27.0)+t66; + coeffs_I->coeff_p1_0_0 = t27+t60; + coeffs_I->coeff_m1_p1_0 = t23+t26+t55; + coeffs_I->coeff_0_p1_0 = t26+t61; + coeffs_I->coeff_p1_p1_0 = t20+t26+t57; + coeffs_I->coeff_m1_m1_p1 = t20+t51+t76; + coeffs_I->coeff_0_m1_p1 = t53+t82; + coeffs_I->coeff_p1_m1_p1 = t23+t51+t77; + coeffs_I->coeff_m1_0_p1 = t28+t34+t54; + coeffs_I->coeff_0_0_p1 = t34+t62; + coeffs_I->coeff_p1_0_p1 = t34+t27+t56; + coeffs_I->coeff_m1_p1_p1 = t23+t52+t76; + coeffs_I->coeff_0_p1_p1 = t58+t79; + coeffs_I->coeff_p1_p1_p1 = t20+t52+t77; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..9f29978 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dx.compute.c @@ -0,0 +1,65 @@ +fp t91; +fp t95; +fp t104; +fp t94; +fp t86; +fp t103; +fp t93; +fp t88; +fp t102; +fp t89; +fp t101; +fp t92; +fp t100; +fp t99; +fp t87; +fp t98; +fp t97; +fp t96; +fp t90; + t91 = RATIONAL(1.0,9.0)*x; + t95 = RATIONAL(1.0,18.0); + t104 = t91+t95; + t94 = RATIONAL(1.0,12.0); + t86 = t94*y; + t103 = t91+t86; + t93 = RATIONAL(-1.0,12.0); + t88 = t93*y; + t102 = t91+t88; + t89 = t94*z; + t101 = t91+t89; + t92 = RATIONAL(-1.0,18.0); + t100 = t92+t91; + t99 = t86+t101; + t87 = t93*z; + t98 = t87+t103; + t97 = t87+t102; + t96 = t88+t101; + t90 = RATIONAL(-2.0,9.0)*x; + coeffs_dx->coeff_m1_m1_m1 = t92+t99; + coeffs_dx->coeff_0_m1_m1 = t90; + coeffs_dx->coeff_p1_m1_m1 = t95+t97; + coeffs_dx->coeff_m1_0_m1 = t89+t100; + coeffs_dx->coeff_0_0_m1 = t90; + coeffs_dx->coeff_p1_0_m1 = t87+t104; + coeffs_dx->coeff_m1_p1_m1 = t92+t96; + coeffs_dx->coeff_0_p1_m1 = t90; + coeffs_dx->coeff_p1_p1_m1 = t95+t98; + coeffs_dx->coeff_m1_m1_0 = t86+t100; + coeffs_dx->coeff_0_m1_0 = t90; + coeffs_dx->coeff_p1_m1_0 = t95+t102; + coeffs_dx->coeff_m1_0_0 = t100; + coeffs_dx->coeff_0_0_0 = t90; + coeffs_dx->coeff_p1_0_0 = t104; + coeffs_dx->coeff_m1_p1_0 = t88+t100; + coeffs_dx->coeff_0_p1_0 = t90; + coeffs_dx->coeff_p1_p1_0 = t95+t103; + coeffs_dx->coeff_m1_m1_p1 = t92+t98; + coeffs_dx->coeff_0_m1_p1 = t90; + coeffs_dx->coeff_p1_m1_p1 = t95+t96; + coeffs_dx->coeff_m1_0_p1 = t87+t100; + coeffs_dx->coeff_0_0_p1 = t90; + coeffs_dx->coeff_p1_0_p1 = t95+t101; + coeffs_dx->coeff_m1_p1_p1 = t92+t97; + coeffs_dx->coeff_0_p1_p1 = t90; + coeffs_dx->coeff_p1_p1_p1 = t95+t99; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..ab4ef30 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,31 @@ +fp t143; +fp t142; + t143 = RATIONAL(1.0,9.0); + t142 = RATIONAL(-2.0,9.0); + coeffs_dxx->coeff_m1_m1_m1 = t143; + coeffs_dxx->coeff_0_m1_m1 = t142; + coeffs_dxx->coeff_p1_m1_m1 = t143; + coeffs_dxx->coeff_m1_0_m1 = t143; + coeffs_dxx->coeff_0_0_m1 = t142; + coeffs_dxx->coeff_p1_0_m1 = t143; + coeffs_dxx->coeff_m1_p1_m1 = t143; + coeffs_dxx->coeff_0_p1_m1 = t142; + coeffs_dxx->coeff_p1_p1_m1 = t143; + coeffs_dxx->coeff_m1_m1_0 = t143; + coeffs_dxx->coeff_0_m1_0 = t142; + coeffs_dxx->coeff_p1_m1_0 = t143; + coeffs_dxx->coeff_m1_0_0 = t143; + coeffs_dxx->coeff_0_0_0 = t142; + coeffs_dxx->coeff_p1_0_0 = t143; + coeffs_dxx->coeff_m1_p1_0 = t143; + coeffs_dxx->coeff_0_p1_0 = t142; + coeffs_dxx->coeff_p1_p1_0 = t143; + coeffs_dxx->coeff_m1_m1_p1 = t143; + coeffs_dxx->coeff_0_m1_p1 = t142; + coeffs_dxx->coeff_p1_m1_p1 = t143; + coeffs_dxx->coeff_m1_0_p1 = t143; + coeffs_dxx->coeff_0_0_p1 = t142; + coeffs_dxx->coeff_p1_0_p1 = t143; + coeffs_dxx->coeff_m1_p1_p1 = t143; + coeffs_dxx->coeff_0_p1_p1 = t142; + coeffs_dxx->coeff_p1_p1_p1 = t143; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxy.compute.c new file mode 100644 index 0000000..d22213d --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxy.compute.c @@ -0,0 +1,33 @@ +fp t146; +fp t145; +fp t144; + t146 = RATIONAL(0.0,1.0); + t145 = RATIONAL(-1.0,12.0); + t144 = RATIONAL(1.0,12.0); + coeffs_dxy->coeff_m1_m1_m1 = t144; + coeffs_dxy->coeff_0_m1_m1 = t146; + coeffs_dxy->coeff_p1_m1_m1 = t145; + coeffs_dxy->coeff_m1_0_m1 = t146; + coeffs_dxy->coeff_0_0_m1 = t146; + coeffs_dxy->coeff_p1_0_m1 = t146; + coeffs_dxy->coeff_m1_p1_m1 = t145; + coeffs_dxy->coeff_0_p1_m1 = t146; + coeffs_dxy->coeff_p1_p1_m1 = t144; + coeffs_dxy->coeff_m1_m1_0 = t144; + coeffs_dxy->coeff_0_m1_0 = t146; + coeffs_dxy->coeff_p1_m1_0 = t145; + coeffs_dxy->coeff_m1_0_0 = t146; + coeffs_dxy->coeff_0_0_0 = t146; + coeffs_dxy->coeff_p1_0_0 = t146; + coeffs_dxy->coeff_m1_p1_0 = t145; + coeffs_dxy->coeff_0_p1_0 = t146; + coeffs_dxy->coeff_p1_p1_0 = t144; + coeffs_dxy->coeff_m1_m1_p1 = t144; + coeffs_dxy->coeff_0_m1_p1 = t146; + coeffs_dxy->coeff_p1_m1_p1 = t145; + coeffs_dxy->coeff_m1_0_p1 = t146; + coeffs_dxy->coeff_0_0_p1 = t146; + coeffs_dxy->coeff_p1_0_p1 = t146; + coeffs_dxy->coeff_m1_p1_p1 = t145; + coeffs_dxy->coeff_0_p1_p1 = t146; + coeffs_dxy->coeff_p1_p1_p1 = t144; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxz.compute.c new file mode 100644 index 0000000..d968dcd --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxz.compute.c @@ -0,0 +1,33 @@ +fp t149; +fp t148; +fp t147; + t149 = RATIONAL(0.0,1.0); + t148 = RATIONAL(-1.0,12.0); + t147 = RATIONAL(1.0,12.0); + coeffs_dxz->coeff_m1_m1_m1 = t147; + coeffs_dxz->coeff_0_m1_m1 = t149; + coeffs_dxz->coeff_p1_m1_m1 = t148; + coeffs_dxz->coeff_m1_0_m1 = t147; + coeffs_dxz->coeff_0_0_m1 = t149; + coeffs_dxz->coeff_p1_0_m1 = t148; + coeffs_dxz->coeff_m1_p1_m1 = t147; + coeffs_dxz->coeff_0_p1_m1 = t149; + coeffs_dxz->coeff_p1_p1_m1 = t148; + coeffs_dxz->coeff_m1_m1_0 = t149; + coeffs_dxz->coeff_0_m1_0 = t149; + coeffs_dxz->coeff_p1_m1_0 = t149; + coeffs_dxz->coeff_m1_0_0 = t149; + coeffs_dxz->coeff_0_0_0 = t149; + coeffs_dxz->coeff_p1_0_0 = t149; + coeffs_dxz->coeff_m1_p1_0 = t149; + coeffs_dxz->coeff_0_p1_0 = t149; + coeffs_dxz->coeff_p1_p1_0 = t149; + coeffs_dxz->coeff_m1_m1_p1 = t148; + coeffs_dxz->coeff_0_m1_p1 = t149; + coeffs_dxz->coeff_p1_m1_p1 = t147; + coeffs_dxz->coeff_m1_0_p1 = t148; + coeffs_dxz->coeff_0_0_p1 = t149; + coeffs_dxz->coeff_p1_0_p1 = t147; + coeffs_dxz->coeff_m1_p1_p1 = t148; + coeffs_dxz->coeff_0_p1_p1 = t149; + coeffs_dxz->coeff_p1_p1_p1 = t147; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..e3774d8 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dy.compute.c @@ -0,0 +1,59 @@ +fp t110; +fp t122; +fp t121; +fp t113; +fp t108; +fp t120; +fp t112; +fp t106; +fp t119; +fp t105; +fp t118; +fp t117; +fp t116; +fp t107; +fp t115; +fp t109; + t110 = RATIONAL(1.0,9.0)*y; + t122 = RATIONAL(-1.0,18.0)+t110; + t121 = t110+RATIONAL(1.0,18.0); + t113 = RATIONAL(1.0,12.0); + t108 = t113*x; + t120 = t108+t122; + t112 = RATIONAL(-1.0,12.0); + t106 = t112*x; + t119 = t106+t122; + t105 = t112*z; + t118 = t105+t122; + t117 = t106+t121; + t116 = t108+t121; + t107 = t113*z; + t115 = t107+t121; + t109 = RATIONAL(-2.0,9.0)*y; + coeffs_dy->coeff_m1_m1_m1 = t107+t120; + coeffs_dy->coeff_0_m1_m1 = t107+t122; + coeffs_dy->coeff_p1_m1_m1 = t107+t119; + coeffs_dy->coeff_m1_0_m1 = t109; + coeffs_dy->coeff_0_0_m1 = t109; + coeffs_dy->coeff_p1_0_m1 = t109; + coeffs_dy->coeff_m1_p1_m1 = t105+t117; + coeffs_dy->coeff_0_p1_m1 = t105+t121; + coeffs_dy->coeff_p1_p1_m1 = t105+t116; + coeffs_dy->coeff_m1_m1_0 = t120; + coeffs_dy->coeff_0_m1_0 = t122; + coeffs_dy->coeff_p1_m1_0 = t119; + coeffs_dy->coeff_m1_0_0 = t109; + coeffs_dy->coeff_0_0_0 = t109; + coeffs_dy->coeff_p1_0_0 = t109; + coeffs_dy->coeff_m1_p1_0 = t117; + coeffs_dy->coeff_0_p1_0 = t121; + coeffs_dy->coeff_p1_p1_0 = t116; + coeffs_dy->coeff_m1_m1_p1 = t108+t118; + coeffs_dy->coeff_0_m1_p1 = t118; + coeffs_dy->coeff_p1_m1_p1 = t106+t118; + coeffs_dy->coeff_m1_0_p1 = t109; + coeffs_dy->coeff_0_0_p1 = t109; + coeffs_dy->coeff_p1_0_p1 = t109; + coeffs_dy->coeff_m1_p1_p1 = t106+t115; + coeffs_dy->coeff_0_p1_p1 = t115; + coeffs_dy->coeff_p1_p1_p1 = t108+t115; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyy.compute.c new file mode 100644 index 0000000..f9a66c9 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyy.compute.c @@ -0,0 +1,31 @@ +fp t151; +fp t150; + t151 = RATIONAL(-2.0,9.0); + t150 = RATIONAL(1.0,9.0); + coeffs_dyy->coeff_m1_m1_m1 = t150; + coeffs_dyy->coeff_0_m1_m1 = t150; + coeffs_dyy->coeff_p1_m1_m1 = t150; + coeffs_dyy->coeff_m1_0_m1 = t151; + coeffs_dyy->coeff_0_0_m1 = t151; + coeffs_dyy->coeff_p1_0_m1 = t151; + coeffs_dyy->coeff_m1_p1_m1 = t150; + coeffs_dyy->coeff_0_p1_m1 = t150; + coeffs_dyy->coeff_p1_p1_m1 = t150; + coeffs_dyy->coeff_m1_m1_0 = t150; + coeffs_dyy->coeff_0_m1_0 = t150; + coeffs_dyy->coeff_p1_m1_0 = t150; + coeffs_dyy->coeff_m1_0_0 = t151; + coeffs_dyy->coeff_0_0_0 = t151; + coeffs_dyy->coeff_p1_0_0 = t151; + coeffs_dyy->coeff_m1_p1_0 = t150; + coeffs_dyy->coeff_0_p1_0 = t150; + coeffs_dyy->coeff_p1_p1_0 = t150; + coeffs_dyy->coeff_m1_m1_p1 = t150; + coeffs_dyy->coeff_0_m1_p1 = t150; + coeffs_dyy->coeff_p1_m1_p1 = t150; + coeffs_dyy->coeff_m1_0_p1 = t151; + coeffs_dyy->coeff_0_0_p1 = t151; + coeffs_dyy->coeff_p1_0_p1 = t151; + coeffs_dyy->coeff_m1_p1_p1 = t150; + coeffs_dyy->coeff_0_p1_p1 = t150; + coeffs_dyy->coeff_p1_p1_p1 = t150; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyz.compute.c new file mode 100644 index 0000000..93b8620 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyz.compute.c @@ -0,0 +1,33 @@ +fp t154; +fp t153; +fp t152; + t154 = RATIONAL(0.0,1.0); + t153 = RATIONAL(-1.0,12.0); + t152 = RATIONAL(1.0,12.0); + coeffs_dyz->coeff_m1_m1_m1 = t152; + coeffs_dyz->coeff_0_m1_m1 = t152; + coeffs_dyz->coeff_p1_m1_m1 = t152; + coeffs_dyz->coeff_m1_0_m1 = t154; + coeffs_dyz->coeff_0_0_m1 = t154; + coeffs_dyz->coeff_p1_0_m1 = t154; + coeffs_dyz->coeff_m1_p1_m1 = t153; + coeffs_dyz->coeff_0_p1_m1 = t153; + coeffs_dyz->coeff_p1_p1_m1 = t153; + coeffs_dyz->coeff_m1_m1_0 = t154; + coeffs_dyz->coeff_0_m1_0 = t154; + coeffs_dyz->coeff_p1_m1_0 = t154; + coeffs_dyz->coeff_m1_0_0 = t154; + coeffs_dyz->coeff_0_0_0 = t154; + coeffs_dyz->coeff_p1_0_0 = t154; + coeffs_dyz->coeff_m1_p1_0 = t154; + coeffs_dyz->coeff_0_p1_0 = t154; + coeffs_dyz->coeff_p1_p1_0 = t154; + coeffs_dyz->coeff_m1_m1_p1 = t153; + coeffs_dyz->coeff_0_m1_p1 = t153; + coeffs_dyz->coeff_p1_m1_p1 = t153; + coeffs_dyz->coeff_m1_0_p1 = t154; + coeffs_dyz->coeff_0_0_p1 = t154; + coeffs_dyz->coeff_p1_0_p1 = t154; + coeffs_dyz->coeff_m1_p1_p1 = t152; + coeffs_dyz->coeff_0_p1_p1 = t152; + coeffs_dyz->coeff_p1_p1_p1 = t152; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dz.compute.c new file mode 100644 index 0000000..ab8dae1 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dz.compute.c @@ -0,0 +1,63 @@ +fp t127; +fp t132; +fp t141; +fp t131; +fp t123; +fp t140; +fp t129; +fp t139; +fp t130; +fp t126; +fp t138; +fp t137; +fp t124; +fp t136; +fp t135; +fp t134; +fp t133; +fp t128; + t127 = RATIONAL(1.0,9.0)*z; + t132 = RATIONAL(1.0,18.0); + t141 = t132+t127; + t131 = RATIONAL(1.0,12.0); + t123 = t131*y; + t140 = t123+t127; + t129 = RATIONAL(-1.0,18.0); + t139 = t129+t127; + t130 = RATIONAL(-1.0,12.0); + t126 = t130*x; + t138 = t126+t127; + t137 = t130*y+t127; + t124 = t131*x; + t136 = t124+t140; + t135 = t123+t138; + t134 = t126+t137; + t133 = t124+t137; + t128 = RATIONAL(-2.0,9.0)*z; + coeffs_dz->coeff_m1_m1_m1 = t129+t136; + coeffs_dz->coeff_0_m1_m1 = t123+t139; + coeffs_dz->coeff_p1_m1_m1 = t129+t135; + coeffs_dz->coeff_m1_0_m1 = t124+t139; + coeffs_dz->coeff_0_0_m1 = t139; + coeffs_dz->coeff_p1_0_m1 = t129+t138; + coeffs_dz->coeff_m1_p1_m1 = t129+t133; + coeffs_dz->coeff_0_p1_m1 = t129+t137; + coeffs_dz->coeff_p1_p1_m1 = t129+t134; + coeffs_dz->coeff_m1_m1_0 = t128; + coeffs_dz->coeff_0_m1_0 = t128; + coeffs_dz->coeff_p1_m1_0 = t128; + coeffs_dz->coeff_m1_0_0 = t128; + coeffs_dz->coeff_0_0_0 = t128; + coeffs_dz->coeff_p1_0_0 = t128; + coeffs_dz->coeff_m1_p1_0 = t128; + coeffs_dz->coeff_0_p1_0 = t128; + coeffs_dz->coeff_p1_p1_0 = t128; + coeffs_dz->coeff_m1_m1_p1 = t132+t134; + coeffs_dz->coeff_0_m1_p1 = t132+t137; + coeffs_dz->coeff_p1_m1_p1 = t132+t133; + coeffs_dz->coeff_m1_0_p1 = t132+t138; + coeffs_dz->coeff_0_0_p1 = t141; + coeffs_dz->coeff_p1_0_p1 = t124+t141; + coeffs_dz->coeff_m1_p1_p1 = t132+t135; + coeffs_dz->coeff_0_p1_p1 = t132+t140; + coeffs_dz->coeff_p1_p1_p1 = t132+t136; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dzz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dzz.compute.c new file mode 100644 index 0000000..0f833a6 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dzz.compute.c @@ -0,0 +1,31 @@ +fp t156; +fp t155; + t156 = RATIONAL(-2.0,9.0); + t155 = RATIONAL(1.0,9.0); + coeffs_dzz->coeff_m1_m1_m1 = t155; + coeffs_dzz->coeff_0_m1_m1 = t155; + coeffs_dzz->coeff_p1_m1_m1 = t155; + coeffs_dzz->coeff_m1_0_m1 = t155; + coeffs_dzz->coeff_0_0_m1 = t155; + coeffs_dzz->coeff_p1_0_m1 = t155; + coeffs_dzz->coeff_m1_p1_m1 = t155; + coeffs_dzz->coeff_0_p1_m1 = t155; + coeffs_dzz->coeff_p1_p1_m1 = t155; + coeffs_dzz->coeff_m1_m1_0 = t156; + coeffs_dzz->coeff_0_m1_0 = t156; + coeffs_dzz->coeff_p1_m1_0 = t156; + coeffs_dzz->coeff_m1_0_0 = t156; + coeffs_dzz->coeff_0_0_0 = t156; + coeffs_dzz->coeff_p1_0_0 = t156; + coeffs_dzz->coeff_m1_p1_0 = t156; + coeffs_dzz->coeff_0_p1_0 = t156; + coeffs_dzz->coeff_p1_p1_0 = t156; + coeffs_dzz->coeff_m1_m1_p1 = t155; + coeffs_dzz->coeff_0_m1_p1 = t155; + coeffs_dzz->coeff_p1_m1_p1 = t155; + coeffs_dzz->coeff_m1_0_p1 = t155; + coeffs_dzz->coeff_0_0_p1 = t155; + coeffs_dzz->coeff_p1_0_p1 = t155; + coeffs_dzz->coeff_m1_p1_p1 = t155; + coeffs_dzz->coeff_0_p1_p1 = t155; + coeffs_dzz->coeff_p1_p1_p1 = t155; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..cb38b59 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-I.compute.c @@ -0,0 +1,938 @@ +fp t652; +fp t401; +fp t470; +fp t748; +fp t509; +fp t489; +fp t341; +fp t260; +fp t510; +fp t506; +fp t498; +fp t378; +fp t490; +fp t511; +fp t346; +fp t233; +fp t747; +fp t642; +fp t746; +fp t448; +fp t451; +fp t638; +fp t745; +fp t493; +fp t607; +fp t274; +fp t508; +fp t497; +fp t365; +fp t744; +fp t612; +fp t265; +fp t375; +fp t743; +fp t350; +fp t237; +fp t502; +fp t364; +fp t742; +fp t407; +fp t482; +fp t339; +fp t483; +fp t631; +fp t741; +fp t349; +fp t740; +fp t433; +fp t495; +fp t466; +fp t649; +fp t739; +fp t738; +fp t501; +fp t380; +fp t654; +fp t737; +fp t384; +fp t226; +fp t601; +fp t736; +fp t611; +fp t256; +fp t735; +fp t481; +fp t352; +fp t276; +fp t734; +fp t353; +fp t232; +fp t733; +fp t253; +fp t351; +fp t230; +fp t507; +fp t363; +fp t732; +fp t347; +fp t249; +fp t586; +fp t731; +fp t467; +fp t206; +fp t160; +fp t730; +fp t651; +fp t616; +fp t164; +fp t729; +fp t157; +fp t728; +fp t505; +fp t374; +fp t727; +fp t726; +fp t392; +fp t725; +fp t245; +fp t724; +fp t438; +fp t723; +fp t418; +fp t462; +fp t722; +fp t376; +fp t721; +fp t261; +fp t610; +fp t720; +fp t719; +fp t718; +fp t336; +fp t251; +fp t717; +fp t453; +fp t476; +fp t639; +fp t214; +fp t163; +fp t716; +fp t429; +fp t405; +fp t715; +fp t258; +fp t590; +fp t714; +fp t367; +fp t345; +fp t243; +fp t713; +fp t712; +fp t469; +fp t473; +fp t711; +fp t248; +fp t278; +fp t604; +fp t389; +fp t710; +fp t262; +fp t263; +fp t709; +fp t707; +fp t706; +fp t270; +fp t705; +fp t161; +fp t704; +fp t463; +fp t194; +fp t158; +fp t703; +fp t640; +fp t702; +fp t641; +fp t216; +fp t162; +fp t701; +fp t630; +fp t700; +fp t159; +fp t699; +fp t577; +fp t698; +fp t697; +fp t488; +fp t628; +fp t396; +fp t696; +fp t695; +fp t694; +fp t693; +fp t264; +fp t582; +fp t354; +fp t692; +fp t472; +fp t643; +fp t397; +fp t691; +fp t447; +fp t168; +fp t480; +fp t494; +fp t690; +fp t404; +fp t689; +fp t503; +fp t382; +fp t443; +fp t459; +fp t619; +fp t688; +fp t632; +fp t195; +fp t687; +fp t446; +fp t622; +fp t182; +fp t458; +fp t499; +fp t379; +fp t686; +fp t492; +fp t393; +fp t685; +fp t636; +fp t684; +fp t383; +fp t454; +fp t436; +fp t634; +fp t683; +fp t464; +fp t330; +fp t478; +fp t621; +fp t402; +fp t682; +fp t414; +fp t372; +fp t487; +fp t681; +fp t440; +fp t449; +fp t626; +fp t496; +fp t680; +fp t427; +fp t633; +fp t403; +fp t679; +fp t678; +fp t391; +fp t624; +fp t677; +fp t676; +fp t355; +fp t675; +fp t387; +fp t185; +fp t674; +fp t183; +fp t362; +fp t673; +fp t672; +fp t366; +fp t671; +fp t670; +fp t629; +fp t669; +fp t668; +fp t667; +fp t500; +fp t360; +fp t644; +fp t666; +fp t333; +fp t665; +fp t664; +fp t356; +fp t663; +fp t662; +fp t661; +fp t332; +fp t660; +fp t659; +fp t450; +fp t658; +fp t439; +fp t484; +fp t348; +fp t657; +fp t406; +fp t340; +fp t656; +fp t409; +fp t655; +fp t653; +fp t431; +fp t650; +fp t435; +fp t648; +fp t434; +fp t647; +fp t491; +fp t646; +fp t475; +fp t645; +fp t417; +fp t637; +fp t428; +fp t635; +fp t627; +fp t442; +fp t625; +fp t411; +fp t623; +fp t441; +fp t620; +fp t479; +fp t618; +fp t452; +fp t617; +fp t239; +fp t614; +fp t342; +fp t343; +fp t609; +fp t605; +fp t603; +fp t602; +fp t600; +fp t369; +fp t599; +fp t598; +fp t597; +fp t596; +fp t595; +fp t594; +fp t593; +fp t592; +fp t588; +fp t587; +fp t585; +fp t584; +fp t381; +fp t583; +fp t581; +fp t579; +fp t578; +fp t575; +fp t574; +fp t573; +fp t572; +fp t571; +fp t570; +fp t569; +fp t568; +fp t567; +fp t566; +fp t565; +fp t564; +fp t563; +fp t562; +fp t561; +fp t560; +fp t559; +fp t558; +fp t486; +fp t557; +fp t556; +fp t555; +fp t554; +fp t553; +fp t552; +fp t551; +fp t550; +fp t549; +fp t548; +fp t547; +fp t546; +fp t545; +fp t544; +fp t432; +fp t197; +fp t543; +fp t542; +fp t541; +fp t540; +fp t539; +fp t538; +fp t537; +fp t536; +fp t474; +fp t535; +fp t534; +fp t533; +fp t532; +fp t457; +fp t531; +fp t530; +fp t529; +fp t528; +fp t421; +fp t527; +fp t526; +fp t525; +fp t394; +fp t524; +fp t523; +fp t522; +fp t521; +fp t520; +fp t444; +fp t519; +fp t518; +fp t517; +fp t516; +fp t515; +fp t504; +fp t485; +fp t477; +fp t471; +fp t468; +fp t465; +fp t456; +fp t455; +fp t430; +fp t424; +fp t422; +fp t420; +fp t419; +fp t416; +fp t413; +fp t412; +fp t408; +fp t400; +fp t399; +fp t398; +fp t395; +fp t390; +fp t388; +fp t386; +fp t199; +fp t181; +fp t179; + t652 = y*z; + t401 = RATIONAL(-607.0,12000.0); + t470 = RATIONAL(-1.0,2000.0); + t748 = t401*x+t470*t652; + t509 = z*z; + t489 = RATIONAL(1.0,160.0); + t341 = t489*t509; + t260 = x*t341; + t510 = x*x; + t506 = t510*x; + t498 = RATIONAL(-1.0,32.0); + t378 = t498*t506; + t490 = RATIONAL(-1.0,160.0); + t511 = y*y; + t346 = t490*t511; + t233 = x*t346; + t747 = t260+t378+t233; + t642 = x*t470; + t746 = t401*y+z*t642; + t448 = RATIONAL(-97.0,3000.0); + t451 = RATIONAL(-37.0,1000.0); + t638 = y*t451; + t745 = t448*x+z*t638; + t493 = RATIONAL(-3.0,160.0); + t607 = t493*t510; + t274 = y*t607; + t508 = t511*y; + t497 = RATIONAL(1.0,96.0); + t365 = t497*t508; + t744 = t274+t365; + t612 = t511*t493; + t265 = x*t612; + t375 = t497*t506; + t743 = t265+t375; + t350 = t490*t509; + t237 = y*t350; + t502 = RATIONAL(1.0,32.0); + t364 = t502*t508; + t742 = t237+t364; + t407 = RATIONAL(-137.0,4000.0); + t482 = RATIONAL(-9.0,160.0); + t339 = t482*t511; + t483 = RATIONAL(2.0,125.0); + t631 = z*t483; + t741 = x*t631+t339+t407*y; + t349 = t482*t510; + t740 = t349+y*t631+t407*x; + t433 = RATIONAL(-49.0,2000.0); + t495 = RATIONAL(-3.0,40.0); + t466 = RATIONAL(-7.0,2000.0); + t649 = y*t466; + t739 = t495*t509+t433*z+x*t649; + t738 = t433*x+z*t649+t495*t510; + t501 = RATIONAL(3.0,80.0); + t380 = t501*t511; + t654 = x*z; + t737 = t451*t654+t448*y+t380; + t384 = t502*t506; + t226 = x*t350; + t601 = t233+t226; + t736 = t384+t601; + t611 = t493*t509; + t256 = x*t611; + t735 = t256+t743; + t481 = RATIONAL(3.0,160.0); + t352 = t481*t509; + t276 = y*t352; + t734 = t276+t744; + t353 = t489*t510; + t232 = y*t353; + t733 = t232+t742; + t253 = z*t353; + t351 = t489*t511; + t230 = z*t351; + t507 = t509*z; + t363 = t498*t507; + t732 = t253+t230+t363; + t347 = t481*t510; + t249 = y*t347; + t586 = t249+t276; + t731 = t365+t586; + t467 = RATIONAL(-3.0,1000.0); + t206 = t467*t654; + t160 = y*t206; + t730 = t160+RATIONAL(49.0,4000.0); + t651 = x*y; + t616 = z*t651; + t164 = RATIONAL(1.0,1000.0)*t616; + t729 = RATIONAL(397.0,4000.0)+t164; + t157 = RATIONAL(27.0,1000.0)*t616; + t728 = t157+RATIONAL(-59.0,1000.0); + t505 = RATIONAL(-1.0,96.0); + t374 = t505*t508; + t727 = t274+t374; + t726 = t260+t384; + t392 = t505*t506; + t725 = t256+t392; + t245 = y*t341; + t724 = t245+t747; + t438 = RATIONAL(-87.0,2000.0); + t723 = t438*y+t206; + t418 = RATIONAL(183.0,4000.0); + t462 = RATIONAL(37.0,2000.0); + t722 = t462*t654+t418*y; + t376 = t502*t507; + t721 = t253+t376; + t261 = x*t351; + t610 = t260+t261; + t720 = t610+t378; + t719 = t265+t392; + t718 = t384+t261+t226; + t336 = t481*t511; + t251 = x*t336; + t717 = t251+t375; + t453 = RATIONAL(49.0,2000.0); + t476 = RATIONAL(-1.0,1000.0); + t639 = x*t476; + t214 = z*t639; + t163 = y*t214; + t716 = t453+t163; + t429 = RATIONAL(-31.0,1000.0); + t405 = RATIONAL(141.0,2000.0); + t715 = t429*t651+t405*z; + t258 = x*t352; + t590 = t251+t258; + t714 = t392+t590; + t367 = t498*t508; + t345 = t490*t510; + t243 = y*t345; + t713 = t367+t243; + t712 = t365+t249; + t469 = RATIONAL(-9.0,1000.0); + t473 = RATIONAL(-41.0,750.0); + t711 = t473*x+t469*t652; + t248 = z*t347; + t278 = z*t612; + t604 = t248+t278; + t389 = t505*t507; + t710 = t604+t389; + t262 = z*t345; + t263 = z*t346; + t709 = t262+t263+t376; + t707 = t245+t364; + t706 = t376+t230; + t270 = y*t611; + t705 = t249+t270+t374; + t161 = RATIONAL(9.0,1000.0)*t616; + t704 = RATIONAL(73.0,4000.0)+t161; + t463 = RATIONAL(-27.0,1000.0); + t194 = t463*t654; + t158 = y*t194; + t703 = t158+RATIONAL(-59.0,4000.0); + t640 = z*t429; + t702 = t405*x+y*t640; + t641 = x*t469; + t216 = z*t641; + t162 = y*t216; + t701 = RATIONAL(-59.0,2000.0)+t162; + t630 = y*t462; + t700 = t418*x+z*t630; + t159 = RATIONAL(3.0,1000.0)*t616; + t699 = t159+RATIONAL(49.0,1000.0); + t577 = t274+t270; + t698 = t365+t577; + t697 = y*t641+t473*z; + t488 = RATIONAL(-9.0,250.0); + t628 = z*t488; + t396 = RATIONAL(281.0,12000.0); + t696 = t396*y+x*t628; + t695 = t375+t258; + t694 = t263+t363; + t693 = t262+t226; + t264 = z*t607; + t582 = t278+t264; + t354 = t497*t507; + t692 = t582+t354; + t472 = RATIONAL(11.0,500.0); + t643 = x*t472; + t397 = RATIONAL(-167.0,12000.0); + t691 = t397*y+z*t643+t346; + t447 = RATIONAL(31.0,2000.0); + t168 = t447*t654; + t480 = RATIONAL(-4.0,375.0); + t494 = RATIONAL(-1.0,80.0); + t690 = t168+t480*y+t494*t511; + t404 = RATIONAL(53.0,12000.0); + t689 = t453*t652+t404*x+t347; + t503 = RATIONAL(1.0,40.0); + t382 = t503*t509; + t443 = RATIONAL(-29.0,6000.0); + t459 = RATIONAL(13.0,1000.0); + t619 = y*t459; + t688 = t382+x*t619+t443*z; + t632 = y*t447; + t195 = z*t632; + t687 = t480*x+t195+t494*t510; + t446 = RATIONAL(-19.0,2000.0); + t622 = y*t446; + t182 = z*t622; + t458 = RATIONAL(-17.0,3000.0); + t499 = RATIONAL(1.0,80.0); + t379 = t499*t510; + t686 = t182+t458*x+t379; + t492 = RATIONAL(-7.0,250.0); + t393 = RATIONAL(-137.0,12000.0); + t685 = t341+t393*z+t492*t651; + t636 = x*t453; + t684 = t336+z*t636+t404*y; + t383 = t501*t509; + t454 = RATIONAL(53.0,1000.0); + t436 = RATIONAL(19.0,1000.0); + t634 = y*t436; + t683 = t383+x*t634+t454*z; + t464 = RATIONAL(-11.0,160.0); + t330 = t464*t511; + t478 = RATIONAL(-17.0,500.0); + t621 = z*t478; + t402 = RATIONAL(-107.0,4000.0); + t682 = t402*y+t330+x*t621; + t414 = RATIONAL(299.0,4000.0); + t372 = t502*t509; + t487 = RATIONAL(-1.0,500.0); + t681 = t372+t414*z+t487*t651; + t440 = RATIONAL(-79.0,2000.0); + t449 = RATIONAL(43.0,2000.0); + t626 = y*t449; + t496 = RATIONAL(-1.0,20.0); + t680 = z*t626+t496*t510+t440*x; + t427 = RATIONAL(-13.0,2000.0); + t633 = x*t427; + t403 = RATIONAL(323.0,4000.0); + t679 = t352+t403*z+y*t633; + t678 = t454*y+t436*t654+t380; + t391 = t502*t510; + t624 = z*t487; + t677 = t414*x+t391+y*t624; + t676 = t352+y*t636+t404*z; + t355 = t503*t510; + t675 = t355+t443*x+z*t619; + t387 = t499*t509; + t185 = x*t622; + t674 = t387+t458*z+t185; + t183 = t446*t654; + t362 = t499*t511; + t673 = t458*y+t183+t362; + t672 = t496*t511+t440*y+t449*t654; + t366 = t501*t510; + t671 = t366+t454*x+z*t634; + t670 = t427*t652+t403*x+t347; + t629 = z*t492; + t669 = t393*x+y*t629+t353; + t668 = t336+t403*y+z*t633; + t667 = x*t626+t496*t509+t440*z; + t500 = RATIONAL(-1.0,16.0); + t360 = t500*t509; + t644 = y*t467; + t666 = t360+t438*z+x*t644; + t333 = t464*t509; + t665 = t402*z+t478*t651+t333; + t664 = t351+x*t629+t393*y; + t356 = t503*t511; + t663 = t443*y+t356+t459*t654; + t662 = t396*x+t391+y*t628; + t661 = t472*t652+t345+t397*x; + t332 = t464*t510; + t660 = t402*x+y*t621+t332; + t659 = t382+t355+t356+RATIONAL(-61.0,4000.0); + t450 = RATIONAL(-97.0,4000.0); + t658 = t448*z+t450+t161+x*t638; + t439 = RATIONAL(71.0,2000.0); + t484 = RATIONAL(7.0,160.0); + t348 = t484*t509; + t657 = y*t642+t401*z+t439+t348+t162; + t406 = RATIONAL(143.0,2000.0); + t340 = t482*t509; + t656 = t406+t159+t340+t407*z+t483*t651; + t409 = RATIONAL(469.0,4000.0); + t655 = t466*t654+t409+t160+t495*t511+t433*y; + t653 = y+z; + t431 = RATIONAL(-17.0,2000.0); + t650 = y*t431; + t435 = RATIONAL(-23.0,2000.0); + t648 = x*t435; + t434 = RATIONAL(-39.0,2000.0); + t647 = y*t434; + t491 = RATIONAL(-9.0,500.0); + t646 = y*t491; + t475 = RATIONAL(-3.0,2000.0); + t645 = t475*z; + t417 = RATIONAL(111.0,2000.0); + t637 = y*t417; + t428 = RATIONAL(33.0,2000.0); + t635 = x*t428; + t627 = y*t463; + t442 = RATIONAL(93.0,2000.0); + t625 = x*t442; + t411 = RATIONAL(129.0,2000.0); + t623 = x*t411; + t441 = RATIONAL(-21.0,2000.0); + t620 = t441*y; + t479 = RATIONAL(-1.0,250.0); + t618 = y*t479; + t452 = RATIONAL(27.0,2000.0); + t617 = x*t452; + t239 = z*t336; + t614 = t239+t264; + t342 = t484*t510; + t343 = t484*t511; + t609 = t342+t343; + t605 = t232+t245; + t603 = t237+t243; + t602 = t239+t265; + t600 = t256+t276; + t369 = t502*t511; + t599 = t369+t367; + t598 = t261+t263; + t597 = t369+t374; + t596 = t262+t232; + t595 = t372+t389; + t594 = t270+t258; + t593 = t253+t243; + t592 = t230+t233; + t588 = t256+t270; + t587 = t248+t239; + t585 = t384+t500*t510; + t584 = t253+t232; + t381 = t500*t511; + t583 = t364+t381; + t581 = t263+t233; + t579 = t248+t243; + t578 = t251+t278; + t575 = t383+t366+t367; + t574 = t160+t374+t586; + t573 = t161+t732; + t572 = t159+t692; + t571 = t712+t719; + t570 = t367+t232+t743; + t569 = t262+t363+t726; + t568 = t248+t354+t725; + t567 = t706+t707; + t566 = t717+t727; + t565 = t162+t709; + t564 = t378+t226+t721; + t563 = t264+t389+t695; + t562 = t719+t727; + t561 = t694+t707; + t560 = t237+t367+t706; + t559 = t261+t378+t744; + t558 = t378+t363+t693; + t486 = RATIONAL(7.0,250.0); + t557 = t350+t397*z+t486+y*t643+t354+t162; + t556 = t571+t594; + t555 = t569+t592; + t554 = t354+t614+t705; + t553 = t710+t734; + t552 = t568+t602; + t551 = t251+t389+t614+t725; + t550 = t560+t596; + t549 = t718+t733; + t548 = t564+t598; + t547 = t563+t602; + t546 = t354+t375+t587+t590; + t545 = t262+t243+t567; + t544 = t564+t592; + t432 = RATIONAL(-67.0,4000.0); + t197 = x*t632; + t543 = t354+t494*t509+t480*z+t161+t432+t197; + t542 = t245+t713+t718; + t541 = t588+t712+t717; + t540 = t561+t593; + t539 = t733+t747; + t538 = t705+t710; + t537 = t558+t581; + t536 = t276+t258+t562; + t474 = RATIONAL(-23.0,500.0); + t535 = t474+t159+x*t630+t418*z+t363+t348; + t534 = t581+t721+t726; + t533 = t566+t600; + t532 = t568+t578; + t457 = RATIONAL(79.0,3000.0); + t531 = t457*z+y*t639+t692+t730; + t530 = t457*y+t214+t698+t730; + t529 = t473*y+t216+t703+t731; + t528 = t457*x+t476*t652+t730+t735; + t421 = RATIONAL(191.0,4000.0); + t527 = t372+t421*z+x*t646+t701+t732; + t526 = t438*x+z*t644+t585+t610+t729; + t525 = x*t640+t160+t367+t405*y+t659; + t394 = RATIONAL(-691.0,12000.0); + t524 = t479*t654+t394*y+t586+t597+t699; + t523 = t491*t654+t421*y+t599+t605+t701; + t522 = t394*x+t391+z*t618+t699+t714; + t521 = x*t618+t394*z+t587+t595+t699; + t520 = t396*z+t488*t651+t582+t595+t728; + t444 = RATIONAL(-33.0,2000.0); + t519 = t360+t444*z+x*t627+t704+t709; + t518 = t444*x+z*t627+t585+t601+t704; + t517 = z*t646+t391+t421*x+t701+t720; + t516 = t194+t444*y+t583+t603+t704; + t515 = t414*y+x*t624+t599+t603+t716; + t504 = RATIONAL(1.0,20.0); + t485 = RATIONAL(-7.0,160.0); + t477 = RATIONAL(-13.0,160.0); + t471 = RATIONAL(21.0,250.0); + t468 = RATIONAL(13.0,500.0); + t465 = RATIONAL(-17.0,375.0); + t456 = RATIONAL(-39.0,4000.0); + t455 = RATIONAL(-47.0,1500.0); + t430 = RATIONAL(29.0,2000.0); + t424 = RATIONAL(-57.0,2000.0); + t422 = RATIONAL(133.0,2000.0); + t420 = RATIONAL(147.0,2000.0); + t419 = RATIONAL(307.0,6000.0); + t416 = RATIONAL(157.0,2000.0); + t413 = RATIONAL(-129.0,4000.0); + t412 = RATIONAL(-191.0,4000.0); + t408 = RATIONAL(-437.0,6000.0); + t400 = RATIONAL(319.0,12000.0); + t399 = RATIONAL(-539.0,12000.0); + t398 = RATIONAL(-449.0,12000.0); + t395 = RATIONAL(349.0,12000.0); + t390 = t504*t510; + t388 = t504*t511; + t386 = t504*t509; + t199 = t441*t654; + t181 = x*t620; + t179 = z*t620; + coeffs_I->coeff_m1_m1_m1 = RATIONAL(-269.0,4000.0)+t390+t158+t386+t389+ +t455*z+t388+(t420*z+t455)*y+(t455+t653*t420)*x+t562+t582+t588; + coeffs_I->coeff_0_m1_m1 = t477*t510+t456*x+t411*t652+t538+t343+t657+t736+ +t746; + coeffs_I->coeff_p1_m1_m1 = t383+t416*x+z*t637+t538+t379+t658+t720+t737; + coeffs_I->coeff_p2_m1_m1 = t442*t652+t369+t398*x+t520+t347+t566+t594+t696 +; + coeffs_I->coeff_m1_0_m1 = t477*t511+t456*y+z*t623+t342+t551+t364+t603+ +t657+t748; + coeffs_I->coeff_0_0_m1 = t383+t408*z+t549+t389+x*t650+t587+t655+t738; + coeffs_I->coeff_p1_0_m1 = t521+t539+t670+t682; + coeffs_I->coeff_p2_0_m1 = t516+t547+t686+t688; + coeffs_I->coeff_m1_p1_m1 = t416*y+t417*t654+t362+t551+t575+t605+t658+t745 +; + coeffs_I->coeff_0_p1_m1 = t521+t542+t660+t668; + coeffs_I->coeff_p1_p1_m1 = t239+t525+y*t635+t389+t465*z+t579+t702+t724; + coeffs_I->coeff_p2_p1_m1 = t523+t547+t669+t676; + coeffs_I->coeff_m1_p2_m1 = z*t625+t398*y+t336+t520+t571+t600+t662; + coeffs_I->coeff_0_p2_m1 = t518+t553+t673+t688; + coeffs_I->coeff_p1_p2_m1 = t517+t553+t664+t676; + coeffs_I->coeff_p2_p2_m1 = t387+t475*t651+t419*z+t529+t563+t578+t711; + coeffs_I->coeff_m1_m1_0 = t477*t509+t536+t456*z+y*t623+t439+t565+t609+ +t746+t748; + coeffs_I->coeff_0_m1_0 = t534+t408*y+t409+t380+t431*t654+t574+t738+t739; + coeffs_I->coeff_p1_m1_0 = t524+t548+t665+t670; + coeffs_I->coeff_p2_m1_0 = t519+t533+t663+t686; + coeffs_I->coeff_m1_0_0 = t545+t366+t408*x+z*t650+t655+t714+t739; + coeffs_I->coeff_0_0_0 = RATIONAL(177.0,1000.0)+t163+t384+t183+t333+t332+ +t185+t182+t330+(x+t653)*RATIONAL(-161.0,4000.0)+t567+t584+t610; + coeffs_I->coeff_p1_0_0 = t179+t355+t544+t471*x+t583+t605+t666+t723+t729; + coeffs_I->coeff_p2_0_0 = t545+t353+t435*t652+t395*x+t656+t735+t741; + coeffs_I->coeff_m1_p1_0 = t522+t550+t665+t668; + coeffs_I->coeff_0_p1_0 = t356+t526+t471*y+t199+t560+t593+t666; + coeffs_I->coeff_p1_p1_0 = t412*z+t340+t515+t197+t544+t677; + coeffs_I->coeff_p2_p1_0 = t528+t550+t667+t678; + coeffs_I->coeff_m1_p2_0 = t519+t556+t673+t675; + coeffs_I->coeff_0_p2_0 = t534+t351+z*t648+t395*y+t656+t698+t740; + coeffs_I->coeff_p1_p2_0 = t530+t548+t667+t671; + coeffs_I->coeff_p2_p2_0 = t413*z+t485*t509+t181+t486+t541+t565+t661+t691; + coeffs_I->coeff_m1_m1_p1 = t366+t450+t536+t387+t416*z+x*t637+t573+t737+ +t745; + coeffs_I->coeff_0_m1_p1 = t524+t555+t660+t679; + coeffs_I->coeff_p1_m1_p1 = t261+t558+z*t635+t230+t465*y+t574+t659+t702+ +t715; + coeffs_I->coeff_p2_m1_p1 = t527+t533+t669+t684; + coeffs_I->coeff_m1_0_p1 = t522+t540+t679+t682; + coeffs_I->coeff_0_0_p1 = t382+t181+t526+t381+t471*z+t561+t596+t723; + coeffs_I->coeff_p1_0_p1 = t168+t412*y+t537+t339+t364+t605+t677+t681+t716; + coeffs_I->coeff_p2_0_p1 = t528+t540+t672+t683; + coeffs_I->coeff_m1_p1_p1 = t237+t525+t428*t652+t465*x+t584+t694+t714+t715 +; + coeffs_I->coeff_0_p1_p1 = t349+t412*x+t515+t195+t569+t598+t681; + coeffs_I->coeff_p1_p1_p1 = RATIONAL(-193.0,4000.0)+t422*z+t164+t380+(t430 +*z+t422)*y+(t422+t653*t430)*x+t537+t575+t603; + coeffs_I->coeff_p2_p1_p1 = t237+t263+t345+t253+t535+t256+t452*t652+t343+ +t400*x+t570+t722; + coeffs_I->coeff_m1_p2_p1 = t527+t556+t664+t689; + coeffs_I->coeff_0_p2_p1 = t530+t555+t680+t683; + coeffs_I->coeff_p1_p2_p1 = t535+t270+z*t617+t342+t400*y+t346+t230+t559+ +t693+t700; + coeffs_I->coeff_p2_p2_p1 = t386+t468*z+x*t647+t432+t541+t573+t687+t690; + coeffs_I->coeff_m1_m1_p2 = t352+y*t625+t398*z+t552+t577+t597+t662+t696+ +t728; + coeffs_I->coeff_0_m1_p2 = t518+t554+t663+t674; + coeffs_I->coeff_p1_m1_p2 = t517+t554+t684+t685; + coeffs_I->coeff_p2_m1_p2 = t419*y+x*t645+t546+t374+t362+t577+t697+t703+ +t711; + coeffs_I->coeff_m1_0_p2 = t516+t532+t674+t675; + coeffs_I->coeff_0_0_p2 = t406+t341+t549+y*t648+t395*z+t572+t740+t741; + coeffs_I->coeff_p1_0_p2 = t531+t539+t671+t672; + coeffs_I->coeff_p2_0_p2 = t557+t413*y+t485*t511+t265+t278+t199+t579+t661+ +t695+t742; + coeffs_I->coeff_m1_p1_p2 = t523+t532+t685+t689; + coeffs_I->coeff_0_p1_p2 = t531+t542+t678+t680; + coeffs_I->coeff_p1_p1_p2 = t474+t350+y*t617+t400*z+t572+t609+t700+t713+ +t722+t724; + coeffs_I->coeff_p2_p1_p2 = t543+t468*y+t388+t434*t654+t258+t245+t570+t604 ++t687; + coeffs_I->coeff_m1_p2_p2 = t419*x+y*t645+t379+t529+t552+t697; + coeffs_I->coeff_0_p2_p2 = t179+t413*x+t485*t510+t557+t614+t691+t734+t736; + coeffs_I->coeff_p1_p2_p2 = t260+t543+t390+t468*x+z*t647+t276+t559+t614+ +t690; + coeffs_I->coeff_p2_p2_p2 = RATIONAL(77.0,2000.0)+t399*z+t157+(t424*z+t399 +)*y+(t509+t510+t511)*t493+(t399+t653*t424)*x+t546+t731; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..1753d9b --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dx.compute.c @@ -0,0 +1,518 @@ +fp t911; +fp t898; +fp t808; +fp t913; +fp t809; +fp t1006; +fp t912; +fp t826; +fp t906; +fp t804; +fp t962; +fp t1005; +fp t840; +fp t1004; +fp t888; +fp t797; +fp t755; +fp t1003; +fp t829; +fp t1002; +fp t903; +fp t812; +fp t803; +fp t837; +fp t1001; +fp t834; +fp t805; +fp t963; +fp t1000; +fp t999; +fp t998; +fp t997; +fp t833; +fp t996; +fp t835; +fp t995; +fp t832; +fp t759; +fp t994; +fp t993; +fp t902; +fp t816; +fp t958; +fp t813; +fp t992; +fp t838; +fp t961; +fp t991; +fp t827; +fp t990; +fp t989; +fp t822; +fp t988; +fp t987; +fp t986; +fp t985; +fp t984; +fp t983; +fp t982; +fp t886; +fp t783; +fp t889; +fp t799; +fp t894; +fp t793; +fp t758; +fp t760; +fp t981; +fp t757; +fp t762; +fp t980; +fp t979; +fp t978; +fp t761; +fp t764; +fp t976; +fp t763; +fp t975; +fp t974; +fp t973; +fp t971; +fp t970; +fp t969; +fp t967; +fp t966; +fp t965; +fp t964; +fp t960; +fp t957; +fp t955; +fp t954; +fp t751; +fp t953; +fp t756; +fp t952; +fp t951; +fp t950; +fp t830; +fp t949; +fp t752; +fp t948; +fp t947; +fp t946; +fp t836; +fp t945; +fp t944; +fp t943; +fp t753; +fp t942; +fp t941; +fp t940; +fp t939; +fp t938; +fp t749; +fp t937; +fp t754; +fp t936; +fp t935; +fp t934; +fp t933; +fp t932; +fp t750; +fp t931; +fp t930; +fp t929; +fp t928; +fp t927; +fp t926; +fp t925; +fp t924; +fp t923; +fp t922; +fp t921; +fp t920; +fp t841; +fp t919; +fp t918; +fp t824; +fp t917; +fp t916; +fp t915; +fp t914; +fp t905; +fp t904; +fp t901; +fp t900; +fp t899; +fp t896; +fp t895; +fp t893; +fp t891; +fp t890; +fp t887; +fp t885; +fp t884; +fp t880; +fp t879; +fp t878; +fp t877; +fp t875; +fp t874; +fp t871; +fp t870; +fp t867; +fp t866; +fp t865; +fp t863; +fp t861; +fp t860; +fp t859; +fp t855; +fp t854; +fp t852; +fp t849; +fp t848; +fp t846; +fp t823; +fp t821; +fp t820; +fp t819; +fp t818; +fp t817; +fp t815; +fp t814; +fp t811; +fp t810; +fp t807; +fp t806; +fp t802; +fp t801; +fp t800; +fp t798; +fp t796; +fp t795; +fp t794; +fp t792; +fp t791; +fp t790; +fp t789; +fp t788; +fp t787; +fp t786; +fp t785; +fp t784; +fp t782; +fp t781; +fp t780; +fp t779; +fp t778; +fp t777; +fp t776; +fp t775; +fp t774; +fp t773; +fp t772; +fp t771; +fp t770; +fp t769; +fp t768; +fp t767; +fp t766; +fp t765; + t911 = z*z; + t898 = RATIONAL(3.0,160.0); + t808 = t898*t911; + t913 = y*y; + t809 = t898*t913; + t1006 = t808+t809; + t912 = x*x; + t826 = RATIONAL(-1.0,32.0)*t912; + t906 = RATIONAL(-3.0,160.0); + t804 = t906*t913; + t962 = t808+t804; + t1005 = t826+t962; + t840 = RATIONAL(3.0,40.0)*x; + t1004 = t840+RATIONAL(-97.0,3000.0); + t888 = RATIONAL(-3.0,1000.0); + t797 = t888*y; + t755 = z*t797; + t1003 = RATIONAL(53.0,1000.0)+t840+t755; + t829 = RATIONAL(-1.0,80.0)*x; + t1002 = RATIONAL(-167.0,12000.0)+t829; + t903 = RATIONAL(-1.0,160.0); + t812 = t903*t913; + t803 = t903*t911; + t837 = RATIONAL(-3.0,32.0)*t912; + t1001 = t812+t837+t803; + t834 = RATIONAL(1.0,32.0)*t912; + t805 = t906*t911; + t963 = t804+t805; + t1000 = t834+t963; + t999 = t834+t1006; + t998 = RATIONAL(-79.0,2000.0)+RATIONAL(-1.0,10.0)*x; + t997 = t834+t962; + t833 = RATIONAL(-9.0,80.0)*x; + t996 = RATIONAL(-137.0,4000.0)+t833; + t835 = RATIONAL(1.0,40.0)*x; + t995 = RATIONAL(-17.0,3000.0)+t835; + t832 = RATIONAL(3.0,80.0)*x; + t759 = y*t832; + t994 = t759+t832; + t993 = RATIONAL(-49.0,2000.0)+RATIONAL(-3.0,20.0)*x; + t902 = RATIONAL(1.0,160.0); + t816 = t902*t913; + t958 = t816+t837; + t813 = t902*t911; + t992 = t958+t813; + t838 = RATIONAL(3.0,32.0)*t912; + t961 = t803+t838; + t991 = t812+t961; + t827 = RATIONAL(1.0,80.0)*x; + t990 = RATIONAL(-137.0,12000.0)+t827; + t989 = t826+t1006; + t822 = RATIONAL(-11.0,80.0)*x; + t988 = RATIONAL(-107.0,4000.0)+t822; + t987 = RATIONAL(-4.0,375.0)+RATIONAL(-1.0,40.0)*x; + t986 = t816+t813+t838; + t985 = t826+t963; + t984 = y+z; + t983 = y*z; + t982 = RATIONAL(-3.0,80.0)*x; + t886 = RATIONAL(-27.0,1000.0); + t783 = t886*y; + t889 = RATIONAL(-9.0,1000.0); + t799 = t889*y; + t894 = RATIONAL(-1.0,1000.0); + t793 = t894*z; + t758 = z*t832; + t760 = y*t829; + t981 = t758+t760; + t757 = y*t982; + t762 = z*t827; + t980 = t757+t762; + t979 = t816+t803; + t978 = t809+t805; + t761 = y*t827; + t764 = z*t982; + t976 = t761+t764; + t763 = z*t829; + t975 = t760+t763; + t974 = t758+t761; + t973 = t757+t764; + t971 = t757+t763; + t970 = t759+t763; + t969 = t759+t762; + t967 = t760+t764; + t966 = t761+t763; + t965 = t758+t759; + t964 = t760+t762; + t960 = t759+t764; + t957 = t761+t762; + t955 = t757+t758; + t954 = t812+t813; + t751 = z*t799; + t953 = t751+t978; + t756 = RATIONAL(3.0,1000.0)*t983; + t952 = t756+t954; + t951 = RATIONAL(1.0,10.0)*x+t973; + t950 = t832+t974; + t830 = RATIONAL(7.0,80.0)*x; + t949 = t830+t971; + t752 = RATIONAL(9.0,1000.0)*t983; + t948 = t752+t978; + t947 = t840+t975; + t946 = t756+t979; + t836 = RATIONAL(1.0,20.0)*x; + t945 = t836+t957; + t944 = t835+t965; + t943 = t751+t991; + t753 = y*t793; + t942 = t753+t986; + t941 = t838+t952; + t940 = t755+t989; + t939 = t762+t803+t958; + t938 = t834+t953; + t749 = z*t783; + t937 = t749+t985; + t754 = RATIONAL(1.0,1000.0)*t983; + t936 = t754+t1001; + t935 = t764+t997; + t934 = t762+t1005; + t933 = t758+t997; + t932 = t755+t838+t954; + t750 = RATIONAL(27.0,1000.0)*t983; + t931 = t750+t999; + t930 = t755+t816+t961; + t929 = t756+t1000; + t928 = t752+t826+t836+RATIONAL(-29.0,6000.0); + t927 = t755+RATIONAL(141.0,2000.0)+t836+t837; + t926 = t764+t837+t954; + t925 = t826+t953; + t924 = t834+t948; + t923 = t752+t992; + t922 = t838+t946; + t921 = t755+RATIONAL(79.0,3000.0)+t1000; + t920 = RATIONAL(-41.0,750.0)+t749+t999; + t841 = RATIONAL(-1.0,8.0)*x; + t919 = t752+RATIONAL(-33.0,2000.0)+t841+t991; + t918 = t841+RATIONAL(-87.0,2000.0)+t754+t986; + t824 = RATIONAL(1.0,16.0)*x; + t917 = t756+RATIONAL(-691.0,12000.0)+t824+t989; + t916 = t753+RATIONAL(299.0,4000.0)+t824+t1001; + t915 = RATIONAL(281.0,12000.0)+t750+t824+t985; + t914 = t751+t824+RATIONAL(191.0,4000.0)+t992; + t905 = RATIONAL(-7.0,250.0); + t904 = RATIONAL(-9.0,500.0); + t901 = RATIONAL(-9.0,250.0); + t900 = RATIONAL(-1.0,500.0); + t899 = RATIONAL(2.0,125.0); + t896 = RATIONAL(-1.0,250.0); + t895 = RATIONAL(-17.0,500.0); + t893 = RATIONAL(-3.0,2000.0); + t891 = RATIONAL(11.0,500.0); + t890 = RATIONAL(-1.0,2000.0); + t887 = RATIONAL(-7.0,2000.0); + t885 = RATIONAL(37.0,2000.0); + t884 = RATIONAL(13.0,1000.0); + t880 = RATIONAL(49.0,2000.0); + t879 = RATIONAL(27.0,2000.0); + t878 = RATIONAL(-37.0,1000.0); + t877 = RATIONAL(43.0,2000.0); + t875 = RATIONAL(31.0,2000.0); + t874 = RATIONAL(-19.0,2000.0); + t871 = RATIONAL(93.0,2000.0); + t870 = RATIONAL(-21.0,2000.0); + t867 = RATIONAL(19.0,1000.0); + t866 = RATIONAL(-23.0,2000.0); + t865 = RATIONAL(-39.0,2000.0); + t863 = RATIONAL(-17.0,2000.0); + t861 = RATIONAL(-31.0,1000.0); + t860 = RATIONAL(33.0,2000.0); + t859 = RATIONAL(-13.0,2000.0); + t855 = RATIONAL(183.0,4000.0); + t854 = RATIONAL(111.0,2000.0); + t852 = RATIONAL(129.0,2000.0); + t849 = RATIONAL(53.0,12000.0); + t848 = RATIONAL(323.0,4000.0); + t846 = RATIONAL(-607.0,12000.0); + t823 = t900*y; + t821 = t896*z; + t820 = t905*y; + t819 = t904*y; + t818 = t899*z; + t817 = t899*y; + t815 = t905*z; + t814 = t900*z; + t811 = t901*y; + t810 = t901*z; + t807 = t904*z; + t806 = t896*y; + t802 = t887*y; + t801 = t895*y; + t800 = t890*z; + t798 = t888*z; + t796 = t894*y; + t795 = t891*y; + t794 = t889*z; + t792 = t891*z; + t791 = t887*z; + t790 = t895*z; + t789 = t890*y; + t788 = t875*z; + t787 = t885*z; + t786 = t859*z; + t785 = t885*y; + t784 = t877*z; + t782 = t884*z; + t781 = t861*y; + t780 = t874*y; + t779 = t874*z; + t778 = t867*y; + t777 = t861*z; + t776 = t880*z; + t775 = t870*z; + t774 = t878*y; + t773 = t875*y; + t772 = t877*y; + t771 = t878*z; + t770 = t867*z; + t769 = t870*y; + t768 = t880*y; + t767 = t884*y; + t766 = t886*z; + t765 = t859*y; + coeffs_dx->coeff_m1_m1_m1 = RATIONAL(-47.0,1500.0)+t984*RATIONAL(147.0, +2000.0)+t937+t951; + coeffs_dx->coeff_0_m1_m1 = RATIONAL(-39.0,4000.0)+t789+t800+RATIONAL( +-13.0,80.0)*x+t943+t965; + coeffs_dx->coeff_p1_m1_m1 = RATIONAL(157.0,2000.0)+t774+t771+t923+t944; + coeffs_dx->coeff_p2_m1_m1 = t811+t832+t810+RATIONAL(-449.0,12000.0)+t931+ +t973; + coeffs_dx->coeff_m1_0_m1 = t830+t846+t852*z+t789+t925+t967; + coeffs_dx->coeff_0_0_m1 = t863*y+t791+t930+t974+t993; + coeffs_dx->coeff_p1_0_m1 = t837+t790+t806+t848+t950+t952; + coeffs_dx->coeff_p2_0_m1 = t766+t760+t767+t752+t935+t995; + coeffs_dx->coeff_m1_p1_m1 = t854*z+t774+t826+t948+t976+t1004; + coeffs_dx->coeff_0_p1_m1 = t786+t806+t922+t981+t988; + coeffs_dx->coeff_p1_p1_m1 = t777+t860*y+t927+t954+t981; + coeffs_dx->coeff_p2_p1_m1 = t761+t807+t751+t768+t935+t990; + coeffs_dx->coeff_m1_p2_m1 = t811+t871*z+t915+t960; + coeffs_dx->coeff_0_p2_m1 = t767+t779+t919+t955; + coeffs_dx->coeff_p1_p2_m1 = t815+t768+t914+t955; + coeffs_dx->coeff_p2_p2_m1 = t794+t893*y+t920+t960; + coeffs_dx->coeff_m1_m1_0 = t751+t852*y+t846+t800+t949+t1005; + coeffs_dx->coeff_0_m1_0 = t802+t863*z+t932+t969+t993; + coeffs_dx->coeff_p1_m1_0 = t821+t756+t801+t848+t939+t994; + coeffs_dx->coeff_p2_m1_0 = t783+t782+t924+t971+t995; + coeffs_dx->coeff_m1_0_0 = t791+RATIONAL(-437.0,6000.0)+t802+t940+t947; + coeffs_dx->coeff_0_0_0 = RATIONAL(-161.0,4000.0)+t822+t779+t780+t942+t957 +; + coeffs_dx->coeff_p1_0_0 = RATIONAL(21.0,250.0)+t797+t798+t936+t945; + coeffs_dx->coeff_p2_0_0 = t827+t817+RATIONAL(349.0,12000.0)+t818+t929+ +t975; + coeffs_dx->coeff_m1_p1_0 = t786+t801+t917+t966; + coeffs_dx->coeff_0_p1_0 = t775+t797+t918+t964; + coeffs_dx->coeff_p1_p1_0 = t773+t814+t916+t964; + coeffs_dx->coeff_p2_p1_0 = t772+t770+t921+t966; + coeffs_dx->coeff_m1_p2_0 = t783+t779+t928+t962+t970; + coeffs_dx->coeff_0_p2_0 = t817+t866*z+t941+t980+t996; + coeffs_dx->coeff_p1_p2_0 = t772+t757+t793+t939+t1003; + coeffs_dx->coeff_p2_p2_0 = t792+t769+t938+t970+t1002; + coeffs_dx->coeff_m1_m1_p1 = t752+t757+t854*y+t771+t934+t1004; + coeffs_dx->coeff_0_m1_p1 = t765+t821+t941+t970+t988; + coeffs_dx->coeff_p1_m1_p1 = t860*z+t781+t927+t970+t979; + coeffs_dx->coeff_p2_m1_p1 = t819+t776+t938+t980+t990; + coeffs_dx->coeff_m1_0_p1 = t790+t765+t917+t964; + coeffs_dx->coeff_0_0_p1 = t769+t798+t918+t966; + coeffs_dx->coeff_p1_0_p1 = t823+t788+t916+t966; + coeffs_dx->coeff_p2_0_p1 = t778+t784+t921+t964; + coeffs_dx->coeff_m1_p1_p1 = RATIONAL(-17.0,375.0)+t777+t781+t940+t945; + coeffs_dx->coeff_0_p1_p1 = RATIONAL(-191.0,4000.0)+t833+t814+t823+t942+ +t975; + coeffs_dx->coeff_p1_p1_p1 = RATIONAL(133.0,2000.0)+t984*RATIONAL(29.0, +2000.0)+t936+t947; + coeffs_dx->coeff_p2_p1_p1 = RATIONAL(319.0,12000.0)+t829+t787+t785+t929+ +t957; + coeffs_dx->coeff_m1_p2_p1 = t849+t819+t751+t815+t934+t994; + coeffs_dx->coeff_0_p2_p1 = t793+t778+t932+t971+t998; + coeffs_dx->coeff_p1_p2_p1 = t855+t837+t879*z+t785+t946+t949; + coeffs_dx->coeff_p2_p2_p1 = t865*y+t788+t924+t969+t987; + coeffs_dx->coeff_m1_m1_p2 = t810+t871*y+t915+t955; + coeffs_dx->coeff_0_m1_p2 = t780+t782+t919+t960; + coeffs_dx->coeff_p1_m1_p2 = t776+t820+t914+t960; + coeffs_dx->coeff_p2_m1_p2 = t799+t893*z+t920+t955; + coeffs_dx->coeff_m1_0_p2 = t780+t766+t928+t978+t981; + coeffs_dx->coeff_0_0_p2 = t866*y+t818+t922+t976+t996; + coeffs_dx->coeff_p1_0_p2 = t796+t761+t784+t926+t1003; + coeffs_dx->coeff_p2_0_p2 = t775+t795+t760+t751+t933+t1002; + coeffs_dx->coeff_m1_p1_p2 = t849+t820+t807+t925+t950; + coeffs_dx->coeff_0_p1_p2 = t770+t796+t930+t967+t998; + coeffs_dx->coeff_p1_p1_p2 = t879*y+t760+t855+t830+t756+t787+t926; + coeffs_dx->coeff_p2_p1_p2 = t761+t752+t865*z+t773+t933+t987; + coeffs_dx->coeff_m1_p2_p2 = t794+RATIONAL(307.0,6000.0)+t799+t937+t944; + coeffs_dx->coeff_0_p2_p2 = t792+t795+RATIONAL(-7.0,80.0)*x+RATIONAL( +-129.0,4000.0)+t943+t973; + coeffs_dx->coeff_p1_p2_p2 = RATIONAL(13.0,500.0)+t788+t773+t923+t951; + coeffs_dx->coeff_p2_p2_p2 = RATIONAL(-539.0,12000.0)+t982+t984*RATIONAL( +-57.0,2000.0)+t931+t965; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..cd2e06d --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,182 @@ +fp t1543; +fp t1525; +fp t1539; +fp t1578; +fp t1531; +fp t1519; +fp t1529; +fp t1577; +fp t1518; +fp t1538; +fp t1527; +fp t1576; +fp t1524; +fp t1528; +fp t1575; +fp t1574; +fp t1573; +fp t1521; +fp t1572; +fp t1571; +fp t1540; +fp t1520; +fp t1570; +fp t1569; +fp t1568; +fp t1567; +fp t1526; +fp t1566; +fp t1565; +fp t1564; +fp t1563; +fp t1562; +fp t1533; +fp t1561; +fp t1544; +fp t1560; +fp t1541; +fp t1559; +fp t1558; +fp t1557; +fp t1556; +fp t1555; +fp t1554; +fp t1553; +fp t1552; +fp t1551; +fp t1550; +fp t1535; +fp t1549; +fp t1548; +fp t1547; +fp t1546; +fp t1545; +fp t1542; +fp t1537; +fp t1534; +fp t1530; +fp t1523; +fp t1522; + t1543 = RATIONAL(1.0,16.0); + t1525 = t1543*x; + t1539 = RATIONAL(1.0,80.0); + t1578 = t1525+t1539; + t1531 = RATIONAL(-3.0,80.0); + t1519 = t1531*y; + t1529 = t1531*z; + t1577 = t1519+t1529; + t1518 = t1539*y; + t1538 = RATIONAL(-1.0,80.0); + t1527 = t1538*z; + t1576 = t1518+t1527; + t1524 = t1538*y; + t1528 = t1539*z; + t1575 = t1524+t1528; + t1574 = t1518+t1528; + t1573 = t1518+t1529; + t1521 = RATIONAL(3.0,16.0)*x; + t1572 = t1518+t1521; + t1571 = t1521+t1528; + t1540 = RATIONAL(3.0,80.0); + t1520 = t1540*y; + t1570 = t1520+t1525; + t1569 = t1524+t1529; + t1568 = t1521+RATIONAL(-1.0,10.0); + t1567 = t1519+t1527; + t1526 = t1540*z; + t1566 = t1525+t1526; + t1565 = t1520+t1521; + t1564 = t1524+t1527; + t1563 = t1521+t1526; + t1562 = t1519+t1525; + t1533 = RATIONAL(3.0,40.0); + t1561 = t1519+t1528+t1533; + t1544 = RATIONAL(1.0,20.0); + t1560 = t1544+t1574; + t1541 = RATIONAL(1.0,40.0); + t1559 = t1520+t1526+t1541; + t1558 = t1520+t1527+t1544; + t1557 = RATIONAL(1.0,10.0)+t1577; + t1556 = t1524+t1526+t1544; + t1555 = t1519+t1526+t1543; + t1554 = t1533+t1573; + t1553 = t1518+t1526+t1540; + t1552 = t1520+t1528+t1540; + t1551 = t1520+t1529+t1543; + t1550 = t1543+t1575; + t1535 = RATIONAL(7.0,80.0); + t1549 = t1535+t1569; + t1548 = t1533+t1564; + t1547 = t1543+t1576; + t1546 = t1535+t1567; + t1545 = RATIONAL(-1.0,8.0); + t1542 = RATIONAL(-1.0,40.0); + t1537 = RATIONAL(-9.0,80.0); + t1534 = RATIONAL(-3.0,20.0); + t1530 = RATIONAL(-11.0,80.0); + t1523 = RATIONAL(-3.0,16.0)*x; + t1522 = RATIONAL(-1.0,16.0)*x; + coeffs_dxx->coeff_m1_m1_m1 = t1522+t1557; + coeffs_dxx->coeff_0_m1_m1 = RATIONAL(-13.0,80.0)+t1520+t1563; + coeffs_dxx->coeff_p1_m1_m1 = t1523+t1559; + coeffs_dxx->coeff_p2_m1_m1 = t1540+t1529+t1562; + coeffs_dxx->coeff_m1_0_m1 = t1522+t1549; + coeffs_dxx->coeff_0_0_m1 = t1534+t1518+t1563; + coeffs_dxx->coeff_p1_0_m1 = t1523+t1553; + coeffs_dxx->coeff_p2_0_m1 = t1525+t1541+t1569; + coeffs_dxx->coeff_m1_p1_m1 = t1522+t1554; + coeffs_dxx->coeff_0_p1_m1 = t1524+t1530+t1563; + coeffs_dxx->coeff_p1_p1_m1 = t1523+t1556; + coeffs_dxx->coeff_p2_p1_m1 = t1573+t1578; + coeffs_dxx->coeff_m1_p2_m1 = t1522+t1551; + coeffs_dxx->coeff_0_p2_m1 = t1545+t1519+t1563; + coeffs_dxx->coeff_p1_p2_m1 = t1523+t1555; + coeffs_dxx->coeff_p2_p2_m1 = t1529+t1570; + coeffs_dxx->coeff_m1_m1_0 = t1522+t1546; + coeffs_dxx->coeff_0_m1_0 = t1528+t1534+t1565; + coeffs_dxx->coeff_p1_m1_0 = t1523+t1552; + coeffs_dxx->coeff_p2_m1_0 = t1541+t1527+t1562; + coeffs_dxx->coeff_m1_0_0 = t1522+t1548; + coeffs_dxx->coeff_0_0_0 = t1530+t1518+t1571; + coeffs_dxx->coeff_p1_0_0 = t1523+t1560; + coeffs_dxx->coeff_p2_0_0 = t1564+t1578; + coeffs_dxx->coeff_m1_p1_0 = t1522+t1547; + coeffs_dxx->coeff_0_p1_0 = t1524+t1545+t1571; + coeffs_dxx->coeff_p1_p1_0 = t1523+t1550; + coeffs_dxx->coeff_p2_p1_0 = t1525+t1576; + coeffs_dxx->coeff_m1_p2_0 = t1522+t1558; + coeffs_dxx->coeff_0_p2_0 = t1537+t1519+t1571; + coeffs_dxx->coeff_p1_p2_0 = t1523+t1561; + coeffs_dxx->coeff_p2_p2_0 = t1527+t1538+t1570; + coeffs_dxx->coeff_m1_m1_p1 = t1522+t1561; + coeffs_dxx->coeff_0_m1_p1 = t1527+t1530+t1565; + coeffs_dxx->coeff_p1_m1_p1 = t1523+t1558; + coeffs_dxx->coeff_p2_m1_p1 = t1528+t1539+t1562; + coeffs_dxx->coeff_m1_0_p1 = t1522+t1550; + coeffs_dxx->coeff_0_0_p1 = t1545+t1527+t1572; + coeffs_dxx->coeff_p1_0_p1 = t1523+t1547; + coeffs_dxx->coeff_p2_0_p1 = t1525+t1575; + coeffs_dxx->coeff_m1_p1_p1 = t1522+t1560; + coeffs_dxx->coeff_0_p1_p1 = t1537+t1521+t1564; + coeffs_dxx->coeff_p1_p1_p1 = t1523+t1548; + coeffs_dxx->coeff_p2_p1_p1 = t1538+t1525+t1574; + coeffs_dxx->coeff_m1_p2_p1 = t1522+t1552; + coeffs_dxx->coeff_0_p2_p1 = t1567+t1568; + coeffs_dxx->coeff_p1_p2_p1 = t1523+t1546; + coeffs_dxx->coeff_p2_p2_p1 = t1528+t1542+t1570; + coeffs_dxx->coeff_m1_m1_p2 = t1522+t1555; + coeffs_dxx->coeff_0_m1_p2 = t1545+t1529+t1565; + coeffs_dxx->coeff_p1_m1_p2 = t1523+t1551; + coeffs_dxx->coeff_p2_m1_p2 = t1526+t1562; + coeffs_dxx->coeff_m1_0_p2 = t1522+t1556; + coeffs_dxx->coeff_0_0_p2 = t1529+t1537+t1572; + coeffs_dxx->coeff_p1_0_p2 = t1523+t1554; + coeffs_dxx->coeff_p2_0_p2 = t1538+t1524+t1566; + coeffs_dxx->coeff_m1_p1_p2 = t1522+t1553; + coeffs_dxx->coeff_0_p1_p2 = t1568+t1569; + coeffs_dxx->coeff_p1_p1_p2 = t1523+t1549; + coeffs_dxx->coeff_p2_p1_p2 = t1542+t1518+t1566; + coeffs_dxx->coeff_m1_p2_p2 = t1522+t1559; + coeffs_dxx->coeff_0_p2_p2 = RATIONAL(-7.0,80.0)+t1521+t1577; + coeffs_dxx->coeff_p1_p2_p2 = t1523+t1557; + coeffs_dxx->coeff_p2_p2_p2 = t1531+t1520+t1566; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxy.compute.c new file mode 100644 index 0000000..e7d150e --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxy.compute.c @@ -0,0 +1,208 @@ +fp t1622; +fp t1588; +fp t1590; +fp t1660; +fp t1611; +fp t1584; +fp t1659; +fp t1621; +fp t1587; +fp t1658; +fp t1583; +fp t1657; +fp t1613; +fp t1585; +fp t1656; +fp t1586; +fp t1599; +fp t1655; +fp t1581; +fp t1593; +fp t1654; +fp t1653; +fp t1623; +fp t1594; +fp t1652; +fp t1651; +fp t1650; +fp t1649; +fp t1648; +fp t1647; +fp t1603; +fp t1580; +fp t1646; +fp t1645; +fp t1589; +fp t1644; +fp t1643; +fp t1642; +fp t1620; +fp t1591; +fp t1592; +fp t1641; +fp t1640; +fp t1639; +fp t1638; +fp t1637; +fp t1636; +fp t1635; +fp t1634; +fp t1633; +fp t1632; +fp t1579; +fp t1631; +fp t1630; +fp t1629; +fp t1628; +fp t1627; +fp t1607; +fp t1582; +fp t1626; +fp t1625; +fp t1624; +fp t1618; +fp t1616; +fp t1612; +fp t1609; +fp t1604; +fp t1602; +fp t1601; +fp t1598; +fp t1597; +fp t1595; + t1622 = RATIONAL(1.0,80.0); + t1588 = t1622*y; + t1590 = t1622*x; + t1660 = t1588+t1590; + t1611 = RATIONAL(-3.0,1000.0); + t1584 = t1611*z; + t1659 = t1584+RATIONAL(-31.0,1000.0); + t1621 = RATIONAL(-1.0,80.0); + t1587 = t1621*x; + t1658 = t1587+t1588; + t1583 = RATIONAL(3.0,1000.0)*z; + t1657 = t1583+RATIONAL(37.0,2000.0); + t1613 = RATIONAL(-9.0,1000.0); + t1585 = t1613*z; + t1656 = t1585+RATIONAL(49.0,2000.0); + t1586 = RATIONAL(9.0,1000.0)*z; + t1599 = RATIONAL(-19.0,2000.0); + t1655 = t1586+t1599; + t1581 = RATIONAL(1.0,1000.0)*z; + t1593 = t1621*y; + t1654 = t1581+t1593; + t1653 = t1583+RATIONAL(-17.0,500.0); + t1623 = RATIONAL(3.0,80.0); + t1594 = t1623*x; + t1652 = t1594+t1593; + t1651 = t1583+RATIONAL(-1.0,250.0); + t1650 = t1584+t1593; + t1649 = t1584+t1587; + t1648 = t1583+RATIONAL(2.0,125.0); + t1647 = t1581+t1588; + t1603 = RATIONAL(-27.0,1000.0); + t1580 = t1603*z; + t1646 = t1580+t1613; + t1645 = t1585+RATIONAL(-9.0,500.0); + t1589 = t1623*y; + t1644 = t1589+t1594; + t1643 = t1585+RATIONAL(-7.0,250.0); + t1642 = t1585+t1594; + t1620 = RATIONAL(-3.0,80.0); + t1591 = t1620*x; + t1592 = t1620*y; + t1641 = t1591+t1592; + t1640 = t1589+t1590; + t1639 = t1586+t1589; + t1638 = t1588+t1594; + t1637 = t1592+t1594; + t1636 = t1590+t1592; + t1635 = t1588+t1591; + t1634 = t1591+t1593; + t1633 = t1584+t1591; + t1632 = t1589+t1591; + t1579 = RATIONAL(27.0,1000.0)*z; + t1631 = t1592+t1579; + t1630 = t1587+t1592; + t1629 = t1586+t1592; + t1628 = t1585+RATIONAL(11.0,500.0); + t1627 = t1586+t1591; + t1607 = RATIONAL(-1.0,1000.0); + t1582 = t1607*z; + t1626 = t1582+t1593; + t1625 = t1583+RATIONAL(-13.0,2000.0); + t1624 = t1587+t1589; + t1618 = RATIONAL(-1.0,500.0); + t1616 = RATIONAL(-9.0,250.0); + t1612 = RATIONAL(-1.0,2000.0); + t1609 = RATIONAL(-7.0,2000.0); + t1604 = RATIONAL(19.0,1000.0); + t1602 = RATIONAL(-37.0,1000.0); + t1601 = RATIONAL(13.0,1000.0); + t1598 = RATIONAL(43.0,2000.0); + t1597 = RATIONAL(31.0,2000.0); + t1595 = RATIONAL(-21.0,2000.0); + coeffs_dxy->coeff_m1_m1_m1 = t1580+RATIONAL(147.0,2000.0)+t1641; + coeffs_dxy->coeff_0_m1_m1 = t1593+t1612+t1642; + coeffs_dxy->coeff_p1_m1_m1 = t1586+t1602+t1638; + coeffs_dxy->coeff_p2_m1_m1 = t1579+t1616+t1632; + coeffs_dxy->coeff_m1_0_m1 = t1585+t1612+t1624; + coeffs_dxy->coeff_0_0_m1 = t1584+RATIONAL(-17.0,2000.0)+t1660; + coeffs_dxy->coeff_p1_0_m1 = t1593+t1590+t1651; + coeffs_dxy->coeff_p2_0_m1 = t1587+t1601+t1629; + coeffs_dxy->coeff_m1_p1_m1 = t1602+t1590+t1639; + coeffs_dxy->coeff_0_p1_m1 = t1651+t1658; + coeffs_dxy->coeff_p1_p1_m1 = RATIONAL(33.0,2000.0)+t1593+t1649; + coeffs_dxy->coeff_p2_p1_m1 = t1636+t1656; + coeffs_dxy->coeff_m1_p2_m1 = t1594+t1616+t1631; + coeffs_dxy->coeff_0_p2_m1 = t1601+t1593+t1627; + coeffs_dxy->coeff_p1_p2_m1 = t1635+t1656; + coeffs_dxy->coeff_p2_p2_m1 = RATIONAL(-3.0,2000.0)+t1580+t1644; + coeffs_dxy->coeff_m1_m1_0 = RATIONAL(129.0,2000.0)+t1585+t1641; + coeffs_dxy->coeff_0_m1_0 = t1609+t1594+t1650; + coeffs_dxy->coeff_p1_m1_0 = t1638+t1653; + coeffs_dxy->coeff_p2_m1_0 = t1589+t1603+t1627; + coeffs_dxy->coeff_m1_0_0 = t1609+t1584+t1624; + coeffs_dxy->coeff_0_0_0 = t1599+t1582+t1660; + coeffs_dxy->coeff_p1_0_0 = t1611+t1590+t1654; + coeffs_dxy->coeff_p2_0_0 = t1630+t1648; + coeffs_dxy->coeff_m1_p1_0 = t1640+t1653; + coeffs_dxy->coeff_0_p1_0 = t1587+t1611+t1647; + coeffs_dxy->coeff_p1_p1_0 = t1587+t1597+t1626; + coeffs_dxy->coeff_p2_p1_0 = t1598+t1584+t1636; + coeffs_dxy->coeff_m1_p2_0 = t1603+t1594+t1629; + coeffs_dxy->coeff_0_p2_0 = t1634+t1648; + coeffs_dxy->coeff_p1_p2_0 = t1588+t1598+t1633; + coeffs_dxy->coeff_p2_p2_0 = t1595+t1589+t1642; + coeffs_dxy->coeff_m1_m1_p1 = t1592+RATIONAL(111.0,2000.0)+t1627; + coeffs_dxy->coeff_0_m1_p1 = t1625+t1652; + coeffs_dxy->coeff_p1_m1_p1 = t1638+t1659; + coeffs_dxy->coeff_p2_m1_p1 = t1632+t1645; + coeffs_dxy->coeff_m1_0_p1 = t1624+t1625; + coeffs_dxy->coeff_0_0_p1 = t1590+t1595+t1647; + coeffs_dxy->coeff_p1_0_p1 = t1618+t1590+t1626; + coeffs_dxy->coeff_p2_0_p1 = t1584+t1604+t1630; + coeffs_dxy->coeff_m1_p1_p1 = t1640+t1659; + coeffs_dxy->coeff_0_p1_p1 = t1582+t1618+t1658; + coeffs_dxy->coeff_p1_p1_p1 = t1587+RATIONAL(29.0,2000.0)+t1654; + coeffs_dxy->coeff_p2_p1_p1 = t1636+t1657; + coeffs_dxy->coeff_m1_p2_p1 = t1637+t1645; + coeffs_dxy->coeff_0_p2_p1 = t1604+t1593+t1633; + coeffs_dxy->coeff_p1_p2_p1 = t1635+t1657; + coeffs_dxy->coeff_p2_p2_p1 = t1594+RATIONAL(-39.0,2000.0)+t1639; + coeffs_dxy->coeff_m1_m1_p2 = t1591+RATIONAL(93.0,2000.0)+t1631; + coeffs_dxy->coeff_0_m1_p2 = t1652+t1655; + coeffs_dxy->coeff_p1_m1_p2 = t1638+t1643; + coeffs_dxy->coeff_p2_m1_p2 = t1632+t1646; + coeffs_dxy->coeff_m1_0_p2 = t1624+t1655; + coeffs_dxy->coeff_0_0_p2 = RATIONAL(-23.0,2000.0)+t1583+t1660; + coeffs_dxy->coeff_p1_0_p2 = t1590+t1607+t1650; + coeffs_dxy->coeff_p2_0_p2 = t1628+t1630; + coeffs_dxy->coeff_m1_p1_p2 = t1640+t1643; + coeffs_dxy->coeff_0_p1_p2 = t1607+t1588+t1649; + coeffs_dxy->coeff_p1_p1_p2 = t1593+RATIONAL(27.0,2000.0)+t1583+t1587; + coeffs_dxy->coeff_p2_p1_p2 = t1590+t1597+t1629; + coeffs_dxy->coeff_m1_p2_p2 = t1637+t1646; + coeffs_dxy->coeff_0_p2_p2 = t1628+t1634; + coeffs_dxy->coeff_p1_p2_p2 = t1597+t1588+t1627; + coeffs_dxy->coeff_p2_p2_p2 = t1579+RATIONAL(-57.0,2000.0)+t1644; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxz.compute.c new file mode 100644 index 0000000..1f44ca7 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxz.compute.c @@ -0,0 +1,202 @@ +fp t1695; +fp t1666; +fp t1741; +fp t1685; +fp t1662; +fp t1740; +fp t1739; +fp t1661; +fp t1738; +fp t1737; +fp t1689; +fp t1664; +fp t1703; +fp t1674; +fp t1736; +fp t1705; +fp t1670; +fp t1671; +fp t1735; +fp t1734; +fp t1702; +fp t1676; +fp t1673; +fp t1733; +fp t1667; +fp t1732; +fp t1731; +fp t1730; +fp t1665; +fp t1729; +fp t1675; +fp t1728; +fp t1663; +fp t1704; +fp t1672; +fp t1727; +fp t1693; +fp t1668; +fp t1726; +fp t1725; +fp t1724; +fp t1723; +fp t1722; +fp t1679; +fp t1721; +fp t1669; +fp t1720; +fp t1719; +fp t1718; +fp t1717; +fp t1716; +fp t1715; +fp t1714; +fp t1713; +fp t1712; +fp t1711; +fp t1710; +fp t1709; +fp t1708; +fp t1707; +fp t1706; +fp t1700; +fp t1697; +fp t1691; +fp t1688; +fp t1686; +fp t1681; +fp t1678; +fp t1677; + t1695 = RATIONAL(-9.0,1000.0); + t1666 = t1695*y; + t1741 = t1666+RATIONAL(11.0,500.0); + t1685 = RATIONAL(-27.0,1000.0); + t1662 = t1685*y; + t1740 = t1695+t1662; + t1739 = t1666+RATIONAL(-7.0,250.0); + t1661 = RATIONAL(27.0,1000.0)*y; + t1738 = t1661+RATIONAL(-9.0,250.0); + t1737 = t1666+RATIONAL(-9.0,500.0); + t1689 = RATIONAL(-1.0,1000.0); + t1664 = t1689*y; + t1703 = RATIONAL(-1.0,80.0); + t1674 = t1703*z; + t1736 = t1664+t1674; + t1705 = RATIONAL(3.0,80.0); + t1670 = t1705*z; + t1671 = t1703*x; + t1735 = t1670+t1671; + t1734 = t1666+RATIONAL(-1.0,2000.0); + t1702 = RATIONAL(-3.0,80.0); + t1676 = t1702*z; + t1673 = t1705*x; + t1733 = t1676+t1673; + t1667 = RATIONAL(3.0,1000.0)*y; + t1732 = t1667+t1674; + t1731 = t1666+RATIONAL(49.0,2000.0); + t1730 = t1670+t1673; + t1665 = RATIONAL(9.0,1000.0)*y; + t1729 = t1665+t1673; + t1675 = t1702*x; + t1728 = t1670+t1675; + t1663 = RATIONAL(1.0,1000.0)*y; + t1704 = RATIONAL(1.0,80.0); + t1672 = t1704*z; + t1727 = t1663+t1672; + t1693 = RATIONAL(-3.0,1000.0); + t1668 = t1693*y; + t1726 = RATIONAL(43.0,2000.0)+t1668; + t1725 = t1664+t1672; + t1724 = RATIONAL(-37.0,1000.0)+t1665; + t1723 = t1672+t1675; + t1722 = t1663+t1674; + t1679 = RATIONAL(31.0,2000.0); + t1721 = t1679+t1665; + t1669 = t1704*x; + t1720 = t1669+t1670; + t1719 = t1667+t1672; + t1718 = t1672+t1673; + t1717 = t1667+t1669; + t1716 = RATIONAL(-31.0,1000.0)+t1668; + t1715 = t1676+t1675; + t1714 = t1667+RATIONAL(2.0,125.0); + t1713 = t1674+t1675; + t1712 = RATIONAL(13.0,1000.0)+t1665; + t1711 = t1676+t1671; + t1710 = t1667+RATIONAL(-17.0,500.0); + t1709 = t1668+t1674; + t1708 = t1668+t1671; + t1707 = t1676+t1669; + t1706 = t1685+t1665; + t1700 = RATIONAL(-1.0,500.0); + t1697 = RATIONAL(-1.0,250.0); + t1691 = RATIONAL(-7.0,2000.0); + t1688 = RATIONAL(37.0,2000.0); + t1686 = RATIONAL(19.0,1000.0); + t1681 = RATIONAL(-19.0,2000.0); + t1678 = RATIONAL(-13.0,2000.0); + t1677 = RATIONAL(-21.0,2000.0); + coeffs_dxz->coeff_m1_m1_m1 = RATIONAL(147.0,2000.0)+t1662+t1715; + coeffs_dxz->coeff_0_m1_m1 = t1673+t1674+t1734; + coeffs_dxz->coeff_p1_m1_m1 = t1718+t1724; + coeffs_dxz->coeff_p2_m1_m1 = t1728+t1738; + coeffs_dxz->coeff_m1_0_m1 = RATIONAL(129.0,2000.0)+t1666+t1715; + coeffs_dxz->coeff_0_0_m1 = t1691+t1673+t1709; + coeffs_dxz->coeff_p1_0_m1 = t1710+t1718; + coeffs_dxz->coeff_p2_0_m1 = t1706+t1728; + coeffs_dxz->coeff_m1_p1_m1 = RATIONAL(111.0,2000.0)+t1665+t1715; + coeffs_dxz->coeff_0_p1_m1 = t1673+t1678+t1732; + coeffs_dxz->coeff_p1_p1_m1 = t1716+t1718; + coeffs_dxz->coeff_p2_p1_m1 = t1728+t1737; + coeffs_dxz->coeff_m1_p2_m1 = RATIONAL(93.0,2000.0)+t1661+t1715; + coeffs_dxz->coeff_0_p2_m1 = t1674+t1681+t1729; + coeffs_dxz->coeff_p1_p2_m1 = t1718+t1739; + coeffs_dxz->coeff_p2_p2_m1 = t1728+t1740; + coeffs_dxz->coeff_m1_m1_0 = t1734+t1735; + coeffs_dxz->coeff_0_m1_0 = t1669+t1668+t1672+RATIONAL(-17.0,2000.0); + coeffs_dxz->coeff_p1_m1_0 = t1674+t1697+t1717; + coeffs_dxz->coeff_p2_m1_0 = t1711+t1712; + coeffs_dxz->coeff_m1_0_0 = t1691+t1670+t1708; + coeffs_dxz->coeff_0_0_0 = t1669+t1681+t1725; + coeffs_dxz->coeff_p1_0_0 = t1693+t1669+t1722; + coeffs_dxz->coeff_p2_0_0 = t1711+t1714; + coeffs_dxz->coeff_m1_p1_0 = t1678+t1667+t1735; + coeffs_dxz->coeff_0_p1_0 = t1669+t1677+t1727; + coeffs_dxz->coeff_p1_p1_0 = t1700+t1669+t1736; + coeffs_dxz->coeff_p2_p1_0 = t1676+t1686+t1708; + coeffs_dxz->coeff_m1_p2_0 = t1665+t1681+t1735; + coeffs_dxz->coeff_0_p2_0 = t1672+RATIONAL(-23.0,2000.0)+t1717; + coeffs_dxz->coeff_p1_p2_0 = t1689+t1669+t1709; + coeffs_dxz->coeff_p2_p2_0 = t1711+t1741; + coeffs_dxz->coeff_m1_m1_p1 = t1720+t1724; + coeffs_dxz->coeff_0_m1_p1 = t1671+t1697+t1719; + coeffs_dxz->coeff_p1_m1_p1 = RATIONAL(33.0,2000.0)+t1674+t1708; + coeffs_dxz->coeff_p2_m1_p1 = t1707+t1731; + coeffs_dxz->coeff_m1_0_p1 = t1710+t1720; + coeffs_dxz->coeff_0_0_p1 = t1671+t1693+t1727; + coeffs_dxz->coeff_p1_0_p1 = t1671+t1679+t1736; + coeffs_dxz->coeff_p2_0_p1 = t1707+t1726; + coeffs_dxz->coeff_m1_p1_p1 = t1716+t1720; + coeffs_dxz->coeff_0_p1_p1 = t1700+t1671+t1725; + coeffs_dxz->coeff_p1_p1_p1 = RATIONAL(29.0,2000.0)+t1671+t1722; + coeffs_dxz->coeff_p2_p1_p1 = t1667+t1688+t1707; + coeffs_dxz->coeff_m1_p2_p1 = t1720+t1739; + coeffs_dxz->coeff_0_p2_p1 = t1689+t1672+t1708; + coeffs_dxz->coeff_p1_p2_p1 = RATIONAL(27.0,2000.0)+t1671+t1732; + coeffs_dxz->coeff_p2_p2_p1 = t1707+t1721; + coeffs_dxz->coeff_m1_m1_p2 = t1733+t1738; + coeffs_dxz->coeff_0_m1_p2 = t1712+t1713; + coeffs_dxz->coeff_p1_m1_p2 = t1723+t1731; + coeffs_dxz->coeff_p2_m1_p2 = t1662+RATIONAL(-3.0,2000.0)+t1730; + coeffs_dxz->coeff_m1_0_p2 = t1706+t1733; + coeffs_dxz->coeff_0_0_p2 = t1713+t1714; + coeffs_dxz->coeff_p1_0_p2 = t1723+t1726; + coeffs_dxz->coeff_p2_0_p2 = t1666+t1677+t1730; + coeffs_dxz->coeff_m1_p1_p2 = t1733+t1737; + coeffs_dxz->coeff_0_p1_p2 = t1686+t1675+t1709; + coeffs_dxz->coeff_p1_p1_p2 = t1688+t1675+t1719; + coeffs_dxz->coeff_p2_p1_p2 = RATIONAL(-39.0,2000.0)+t1670+t1729; + coeffs_dxz->coeff_m1_p2_p2 = t1733+t1740; + coeffs_dxz->coeff_0_p2_p2 = t1713+t1741; + coeffs_dxz->coeff_p1_p2_p2 = t1721+t1723; + coeffs_dxz->coeff_p2_p2_p2 = RATIONAL(-57.0,2000.0)+t1661+t1730; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..c483dac --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dy.compute.c @@ -0,0 +1,510 @@ +fp t1156; +fp t1170; +fp t1069; +fp t1164; +fp t1169; +fp t1076; +fp t1237; +fp t1078; +fp t1073; +fp t1231; +fp t1171; +fp t1086; +fp t1160; +fp t1065; +fp t1265; +fp t1063; +fp t1264; +fp t1085; +fp t1263; +fp t1094; +fp t1262; +fp t1091; +fp t1261; +fp t1216; +fp t1260; +fp t1259; +fp t1080; +fp t1258; +fp t1161; +fp t1068; +fp t1070; +fp t1230; +fp t1257; +fp t1154; +fp t1017; +fp t1256; +fp t1255; +fp t1254; +fp t1082; +fp t1253; +fp t1162; +fp t1147; +fp t1051; +fp t1014; +fp t1252; +fp t1098; +fp t1251; +fp t1226; +fp t1250; +fp t1093; +fp t1249; +fp t1248; +fp t1096; +fp t1247; +fp t1246; +fp t1088; +fp t1245; +fp t1083; +fp t1244; +fp t1240; +fp t1013; +fp t1243; +fp t1242; +fp t1241; +fp t1144; +fp t1027; +fp t1146; +fp t1050; +fp t1239; +fp t1152; +fp t1057; +fp t1021; +fp t1016; +fp t1238; +fp t1022; +fp t1019; +fp t1236; +fp t1020; +fp t1235; +fp t1015; +fp t1234; +fp t1018; +fp t1233; +fp t1232; +fp t1229; +fp t1228; +fp t1227; +fp t1225; +fp t1224; +fp t1223; +fp t1217; +fp t1090; +fp t1215; +fp t1214; +fp t1089; +fp t1213; +fp t1212; +fp t1211; +fp t1210; +fp t1209; +fp t1208; +fp t1012; +fp t1207; +fp t1097; +fp t1206; +fp t1205; +fp t1011; +fp t1204; +fp t1203; +fp t1202; +fp t1201; +fp t1008; +fp t1200; +fp t1199; +fp t1009; +fp t1198; +fp t1197; +fp t1196; +fp t1007; +fp t1195; +fp t1194; +fp t1010; +fp t1193; +fp t1192; +fp t1191; +fp t1190; +fp t1189; +fp t1188; +fp t1187; +fp t1186; +fp t1185; +fp t1184; +fp t1183; +fp t1182; +fp t1181; +fp t1180; +fp t1179; +fp t1178; +fp t1177; +fp t1099; +fp t1176; +fp t1175; +fp t1174; +fp t1173; +fp t1172; +fp t1163; +fp t1159; +fp t1158; +fp t1157; +fp t1153; +fp t1151; +fp t1149; +fp t1148; +fp t1145; +fp t1143; +fp t1142; +fp t1138; +fp t1137; +fp t1136; +fp t1135; +fp t1133; +fp t1132; +fp t1129; +fp t1128; +fp t1125; +fp t1124; +fp t1123; +fp t1121; +fp t1119; +fp t1118; +fp t1117; +fp t1112; +fp t1110; +fp t1081; +fp t1079; +fp t1077; +fp t1075; +fp t1074; +fp t1072; +fp t1067; +fp t1064; +fp t1062; +fp t1060; +fp t1059; +fp t1058; +fp t1056; +fp t1055; +fp t1054; +fp t1053; +fp t1052; +fp t1049; +fp t1048; +fp t1047; +fp t1046; +fp t1045; +fp t1044; +fp t1043; +fp t1042; +fp t1041; +fp t1040; +fp t1039; +fp t1038; +fp t1037; +fp t1036; +fp t1035; +fp t1034; +fp t1033; +fp t1032; +fp t1031; +fp t1030; +fp t1029; +fp t1028; +fp t1026; +fp t1025; +fp t1024; +fp t1023; + t1156 = RATIONAL(3.0,160.0); + t1170 = x*x; + t1069 = t1156*t1170; + t1164 = RATIONAL(-3.0,160.0); + t1169 = z*z; + t1076 = t1164*t1169; + t1237 = t1069+t1076; + t1078 = t1164*t1170; + t1073 = t1156*t1169; + t1231 = t1078+t1073; + t1171 = y*y; + t1086 = RATIONAL(3.0,32.0)*t1171; + t1160 = RATIONAL(1.0,160.0); + t1065 = t1160*t1170; + t1265 = t1086+t1065; + t1063 = RATIONAL(-11.0,80.0)*y; + t1264 = t1063+RATIONAL(-107.0,4000.0); + t1085 = RATIONAL(7.0,80.0)*y; + t1263 = RATIONAL(183.0,4000.0)+t1085; + t1094 = RATIONAL(3.0,80.0)*y; + t1262 = RATIONAL(53.0,12000.0)+t1094; + t1091 = RATIONAL(1.0,32.0)*t1171; + t1261 = t1091+t1237; + t1216 = t1078+t1076; + t1260 = t1216+t1091; + t1259 = RATIONAL(-79.0,2000.0)+RATIONAL(-1.0,10.0)*y; + t1080 = t1160*t1169; + t1258 = t1080+t1265; + t1161 = RATIONAL(-1.0,160.0); + t1068 = t1161*t1170; + t1070 = t1161*t1169; + t1230 = t1068+t1070; + t1257 = t1086+t1230; + t1154 = RATIONAL(-1.0,250.0); + t1017 = z*t1094; + t1256 = t1154*x+t1017; + t1255 = t1070+t1265; + t1254 = RATIONAL(323.0,4000.0)+t1094; + t1082 = RATIONAL(-9.0,80.0)*y; + t1253 = RATIONAL(-137.0,4000.0)+t1082; + t1162 = RATIONAL(-9.0,500.0); + t1147 = RATIONAL(-9.0,1000.0); + t1051 = t1147*x; + t1014 = z*t1051; + t1252 = t1162*x+t1014; + t1098 = RATIONAL(3.0,40.0)*y; + t1251 = t1098+RATIONAL(53.0,1000.0); + t1226 = t1069+t1073; + t1250 = t1226+t1091; + t1093 = RATIONAL(1.0,20.0)*y; + t1249 = t1093+RATIONAL(141.0,2000.0); + t1248 = RATIONAL(-3.0,20.0)*y+RATIONAL(-49.0,2000.0); + t1096 = RATIONAL(-3.0,32.0)*t1171; + t1247 = t1096+t1065+t1070; + t1246 = t1091+t1231; + t1088 = RATIONAL(1.0,80.0)*y; + t1245 = t1088+RATIONAL(-137.0,12000.0); + t1083 = RATIONAL(-1.0,80.0)*y; + t1244 = RATIONAL(-167.0,12000.0)+t1014+t1083; + t1240 = x*z; + t1013 = RATIONAL(9.0,1000.0)*t1240; + t1243 = t1093+t1013+RATIONAL(-29.0,6000.0); + t1242 = RATIONAL(-1.0,40.0)*y+t1013+RATIONAL(-4.0,375.0); + t1241 = z+x; + t1144 = RATIONAL(-27.0,1000.0); + t1027 = t1144*x; + t1146 = RATIONAL(-3.0,1000.0); + t1050 = t1146*x; + t1239 = RATIONAL(-3.0,80.0)*y; + t1152 = RATIONAL(-1.0,1000.0); + t1057 = t1152*z; + t1021 = x*t1094; + t1016 = z*t1088; + t1238 = t1021+t1016; + t1022 = x*t1083; + t1019 = z*t1239; + t1236 = t1022+t1019; + t1020 = x*t1239; + t1235 = t1019+t1020; + t1015 = x*t1088; + t1234 = t1015+t1016; + t1018 = z*t1083; + t1233 = t1018+t1020; + t1232 = t1015+t1019; + t1229 = t1017+t1020; + t1228 = t1021+t1018; + t1227 = t1065+t1080; + t1225 = t1068+t1080; + t1224 = t1021+t1019; + t1223 = t1021+t1017; + t1217 = t1016+t1022; + t1090 = RATIONAL(-1.0,32.0)*t1171; + t1215 = t1069+t1090; + t1214 = t1016+t1020; + t1089 = RATIONAL(1.0,16.0)*y; + t1213 = t1096+t1089; + t1212 = t1015+t1018; + t1211 = t1022+t1018; + t1210 = t1089+t1090; + t1209 = t1014+t1015+t1162*z; + t1208 = RATIONAL(1.0,10.0)*y+t1235; + t1012 = RATIONAL(3.0,1000.0)*t1240; + t1207 = t1012+t1225; + t1097 = RATIONAL(1.0,40.0)*y; + t1206 = t1097+t1223; + t1205 = t1093+t1234; + t1011 = z*t1050; + t1204 = t1011+t1225; + t1203 = t1098+t1211; + t1202 = t1015+t1255; + t1201 = t1098+RATIONAL(-97.0,3000.0)+t1013+t1090; + t1008 = RATIONAL(27.0,1000.0)*t1240; + t1200 = t1008+t1250; + t1199 = t1017+t1246; + t1009 = RATIONAL(1.0,1000.0)*t1240; + t1198 = t1009+t1096+t1230; + t1197 = t1096+t1013+t1227; + t1196 = t1096+t1207; + t1007 = z*t1027; + t1195 = t1090+t1007+t1216; + t1194 = t1086+t1207; + t1010 = x*t1057; + t1193 = t1010+t1258; + t1192 = t1011+t1073+t1215; + t1191 = t1022+t1255; + t1190 = t1016+t1261; + t1189 = t1096+t1204; + t1188 = t1017+t1076+t1215; + t1187 = t1021+t1090+t1231; + t1186 = t1011+t1247; + t1185 = t1012+t1247; + t1184 = t1012+t1260; + t1183 = RATIONAL(-17.0,3000.0)+t1097+t1013+t1091; + t1182 = t1086+t1204; + t1181 = t1014+t1257; + t1180 = RATIONAL(-607.0,12000.0)+t1014+t1090+t1085; + t1179 = RATIONAL(-41.0,750.0)+t1007+t1250; + t1178 = RATIONAL(79.0,3000.0)+t1011+t1260; + t1177 = t1014+RATIONAL(191.0,4000.0)+t1213+t1227; + t1099 = RATIONAL(-1.0,8.0)*y; + t1176 = t1009+t1099+RATIONAL(-87.0,2000.0)+t1258; + t1175 = t1008+RATIONAL(281.0,12000.0)+t1210+t1216; + t1174 = t1099+t1013+RATIONAL(-33.0,2000.0)+t1257; + t1173 = RATIONAL(-691.0,12000.0)+t1012+t1210+t1226; + t1172 = t1010+RATIONAL(299.0,4000.0)+t1213+t1230; + t1163 = RATIONAL(-7.0,250.0); + t1159 = RATIONAL(-9.0,250.0); + t1158 = RATIONAL(-1.0,500.0); + t1157 = RATIONAL(2.0,125.0); + t1153 = RATIONAL(-17.0,500.0); + t1151 = RATIONAL(-3.0,2000.0); + t1149 = RATIONAL(11.0,500.0); + t1148 = RATIONAL(-1.0,2000.0); + t1145 = RATIONAL(-7.0,2000.0); + t1143 = RATIONAL(37.0,2000.0); + t1142 = RATIONAL(13.0,1000.0); + t1138 = RATIONAL(49.0,2000.0); + t1137 = RATIONAL(27.0,2000.0); + t1136 = RATIONAL(-37.0,1000.0); + t1135 = RATIONAL(43.0,2000.0); + t1133 = RATIONAL(31.0,2000.0); + t1132 = RATIONAL(-19.0,2000.0); + t1129 = RATIONAL(93.0,2000.0); + t1128 = RATIONAL(-21.0,2000.0); + t1125 = RATIONAL(19.0,1000.0); + t1124 = RATIONAL(-23.0,2000.0); + t1123 = RATIONAL(-39.0,2000.0); + t1121 = RATIONAL(-17.0,2000.0); + t1119 = RATIONAL(-31.0,1000.0); + t1118 = RATIONAL(33.0,2000.0); + t1117 = RATIONAL(-13.0,2000.0); + t1112 = RATIONAL(111.0,2000.0); + t1110 = RATIONAL(129.0,2000.0); + t1081 = t1158*x; + t1079 = t1157*z; + t1077 = t1158*z; + t1075 = t1163*z; + t1074 = t1159*z; + t1072 = t1159*x; + t1067 = t1163*x; + t1064 = t1157*x; + t1062 = t1154*z; + t1060 = t1153*z; + t1059 = t1147*z; + t1058 = t1148*x; + t1056 = t1145*x; + t1055 = t1153*x; + t1054 = t1148*z; + t1053 = t1149*z; + t1052 = t1145*z; + t1049 = t1152*x; + t1048 = t1149*x; + t1047 = t1146*z; + t1046 = t1117*z; + t1045 = t1132*z; + t1044 = t1142*x; + t1043 = t1136*z; + t1042 = t1125*x; + t1041 = t1119*z; + t1040 = t1133*z; + t1039 = t1138*x; + t1038 = t1117*x; + t1037 = t1133*x; + t1036 = t1125*z; + t1035 = t1143*x; + t1034 = t1144*z; + t1033 = t1138*z; + t1032 = t1135*z; + t1031 = t1143*z; + t1030 = t1119*x; + t1029 = t1135*x; + t1028 = t1142*z; + t1026 = t1128*x; + t1025 = t1132*x; + t1024 = t1136*x; + t1023 = t1128*z; + coeffs_dy->coeff_m1_m1_m1 = RATIONAL(-47.0,1500.0)+t1241*RATIONAL(147.0, +2000.0)+t1195+t1208; + coeffs_dy->coeff_0_m1_m1 = t1058+t1110*z+t1180+t1236+t1237; + coeffs_dy->coeff_p1_m1_m1 = t1024+t1112*z+t1201+t1232+t1237; + coeffs_dy->coeff_p2_m1_m1 = t1129*z+t1072+t1175+t1224; + coeffs_dy->coeff_m1_0_m1 = RATIONAL(-13.0,80.0)*y+t1058+t1054+RATIONAL( +-39.0,4000.0)+t1181+t1223; + coeffs_dy->coeff_0_0_m1 = t1017+t1121*x+t1052+t1011+t1202+t1248; + coeffs_dy->coeff_p1_0_m1 = t1046+t1012+t1191+t1256+t1264; + coeffs_dy->coeff_p2_0_m1 = t1045+t1044+t1174+t1229; + coeffs_dy->coeff_m1_p1_m1 = t1043+t1024+RATIONAL(157.0,2000.0)+t1197+ +t1206; + coeffs_dy->coeff_0_p1_m1 = t1060+t1015+t1196+t1254+t1256; + coeffs_dy->coeff_p1_p1_m1 = t1022+t1017+t1041+t1118*x+t1189+t1249; + coeffs_dy->coeff_p2_p1_m1 = t1039+t1075+t1177+t1229; + coeffs_dy->coeff_m1_p2_m1 = t1074+t1072+RATIONAL(-449.0,12000.0)+t1094+ +t1200+t1235; + coeffs_dy->coeff_0_p2_m1 = t1044+t1034+t1183+t1231+t1236; + coeffs_dy->coeff_p1_p2_m1 = t1019+t1039+t1209+t1245+t1246; + coeffs_dy->coeff_p2_p2_m1 = t1059+t1151*x+t1179+t1224; + coeffs_dy->coeff_m1_m1_0 = t1054+t1110*x+t1180+t1231+t1233; + coeffs_dy->coeff_0_m1_0 = t1052+RATIONAL(-437.0,6000.0)+t1056+t1192+t1203 +; + coeffs_dy->coeff_p1_m1_0 = t1055+t1046+t1173+t1212; + coeffs_dy->coeff_p2_m1_0 = t1027+t1045+t1018+t1187+t1243; + coeffs_dy->coeff_m1_0_0 = t1121*z+t1056+t1182+t1238+t1248; + coeffs_dy->coeff_0_0_0 = t1025+t1063+t1045+RATIONAL(-161.0,4000.0)+t1193+ +t1234; + coeffs_dy->coeff_p1_0_0 = t1050+t1023+t1176+t1217; + coeffs_dy->coeff_p2_0_0 = t1124*z+t1064+t1194+t1214+t1253; + coeffs_dy->coeff_m1_p1_0 = t1055+t1062+t1185+t1238+t1254; + coeffs_dy->coeff_0_p1_0 = t1050+t1047+RATIONAL(21.0,250.0)+t1198+t1205; + coeffs_dy->coeff_p1_p1_0 = t1077+t1037+t1172+t1217; + coeffs_dy->coeff_p2_p1_0 = t1057+t1029+t1186+t1214+t1251; + coeffs_dy->coeff_m1_p2_0 = t1028+t1027+t1183+t1233+t1237; + coeffs_dy->coeff_0_p2_0 = t1064+t1088+t1079+RATIONAL(349.0,12000.0)+t1184 ++t1211; + coeffs_dy->coeff_p1_p2_0 = t1036+t1029+t1178+t1212; + coeffs_dy->coeff_p2_p2_0 = t1026+t1053+t1228+t1244+t1261; + coeffs_dy->coeff_m1_m1_p1 = t1043+t1112*x+t1201+t1214+t1231; + coeffs_dy->coeff_0_m1_p1 = t1060+t1038+t1173+t1217; + coeffs_dy->coeff_p1_m1_p1 = RATIONAL(-17.0,375.0)+t1041+t1030+t1192+t1205 +; + coeffs_dy->coeff_p2_m1_p1 = t1075+t1016+t1187+t1252+t1262; + coeffs_dy->coeff_m1_0_p1 = t1062+t1038+t1194+t1228+t1264; + coeffs_dy->coeff_0_0_p1 = t1026+t1047+t1176+t1212; + coeffs_dy->coeff_p1_0_p1 = t1077+t1082+RATIONAL(-191.0,4000.0)+t1081+ +t1193+t1211; + coeffs_dy->coeff_p2_0_p1 = t1057+t1042+t1182+t1233+t1259; + coeffs_dy->coeff_m1_p1_p1 = t1030+t1118*z+t1186+t1228+t1249; + coeffs_dy->coeff_0_p1_p1 = t1081+t1040+t1172+t1212; + coeffs_dy->coeff_p1_p1_p1 = RATIONAL(133.0,2000.0)+t1241*RATIONAL(29.0, +2000.0)+t1198+t1203; + coeffs_dy->coeff_p2_p1_p1 = t1137*z+t1035+t1185+t1233+t1263; + coeffs_dy->coeff_m1_p2_p1 = t1020+t1033+t1190+t1245+t1252; + coeffs_dy->coeff_0_p2_p1 = t1042+t1032+t1178+t1217; + coeffs_dy->coeff_p1_p2_p1 = t1035+RATIONAL(319.0,12000.0)+t1031+t1083+ +t1184+t1234; + coeffs_dy->coeff_p2_p2_p1 = t1021+t1040+t1123*x+t1190+t1242; + coeffs_dy->coeff_m1_m1_p2 = t1074+t1129*x+t1175+t1229; + coeffs_dy->coeff_0_m1_p2 = t1025+t1034+t1022+t1188+t1243; + coeffs_dy->coeff_p1_m1_p2 = t1067+t1188+t1209+t1262; + coeffs_dy->coeff_p2_m1_p2 = t1059+t1051+RATIONAL(307.0,6000.0)+t1195+ +t1206; + coeffs_dy->coeff_m1_0_p2 = t1025+t1028+t1174+t1224; + coeffs_dy->coeff_0_0_p2 = t1079+t1124*x+t1019+t1012+t1202+t1253; + coeffs_dy->coeff_p1_0_p2 = t1011+t1036+t1049+t1019+t1191+t1259; + coeffs_dy->coeff_p2_0_p2 = t1048+t1053+RATIONAL(-129.0,4000.0)+RATIONAL( +-7.0,80.0)*y+t1181+t1235; + coeffs_dy->coeff_m1_p1_p2 = t1033+t1067+t1177+t1224; + coeffs_dy->coeff_0_p1_p2 = t1049+t1032+t1189+t1232+t1251; + coeffs_dy->coeff_p1_p1_p2 = t1031+t1137*x+t1196+t1236+t1263; + coeffs_dy->coeff_p2_p1_p2 = t1040+t1037+RATIONAL(13.0,500.0)+t1197+t1208; + coeffs_dy->coeff_m1_p2_p2 = t1151*z+t1051+t1179+t1229; + coeffs_dy->coeff_0_p2_p2 = t1023+t1022+t1048+t1199+t1244; + coeffs_dy->coeff_p1_p2_p2 = t1037+t1123*z+t1015+t1199+t1242; + coeffs_dy->coeff_p2_p2_p2 = t1239+RATIONAL(-539.0,12000.0)+t1241*RATIONAL +(-57.0,2000.0)+t1200+t1223; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyy.compute.c new file mode 100644 index 0000000..52494e5 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyy.compute.c @@ -0,0 +1,186 @@ +fp t1761; +fp t1745; +fp t1755; +fp t1751; +fp t1804; +fp t1756; +fp t1744; +fp t1752; +fp t1803; +fp t1753; +fp t1802; +fp t1801; +fp t1760; +fp t1749; +fp t1800; +fp t1769; +fp t1746; +fp t1799; +fp t1798; +fp t1747; +fp t1797; +fp t1796; +fp t1795; +fp t1794; +fp t1743; +fp t1793; +fp t1792; +fp t1791; +fp t1762; +fp t1748; +fp t1790; +fp t1789; +fp t1788; +fp t1787; +fp t1786; +fp t1785; +fp t1784; +fp t1783; +fp t1768; +fp t1782; +fp t1763; +fp t1781; +fp t1780; +fp t1779; +fp t1778; +fp t1777; +fp t1776; +fp t1775; +fp t1765; +fp t1774; +fp t1773; +fp t1772; +fp t1766; +fp t1771; +fp t1770; +fp t1764; +fp t1758; +fp t1757; +fp t1754; +fp t1750; +fp t1742; + t1761 = RATIONAL(3.0,80.0); + t1745 = t1761*z; + t1755 = RATIONAL(-3.0,80.0); + t1751 = t1755*x; + t1804 = t1745+t1751; + t1756 = RATIONAL(-1.0,80.0); + t1744 = t1756*z; + t1752 = t1756*x; + t1803 = t1744+t1752; + t1753 = t1755*z; + t1802 = t1752+t1753; + t1801 = t1751+t1753; + t1760 = RATIONAL(1.0,80.0); + t1749 = t1760*x; + t1800 = t1745+t1749; + t1769 = RATIONAL(-1.0,8.0); + t1746 = RATIONAL(3.0,16.0)*y; + t1799 = t1769+t1746; + t1798 = t1744+t1751; + t1747 = t1761*x; + t1797 = t1746+t1747; + t1796 = t1744+t1749; + t1795 = t1745+t1752; + t1794 = t1746+t1752; + t1743 = t1760*z; + t1793 = t1743+t1746; + t1792 = t1743+t1752; + t1791 = t1749+t1753; + t1762 = RATIONAL(1.0,16.0); + t1748 = t1762*y; + t1790 = t1748+t1749; + t1789 = t1747+t1748; + t1788 = t1746+RATIONAL(-1.0,10.0); + t1787 = t1748+t1751; + t1786 = t1743+t1748; + t1785 = t1743+t1747+t1761; + t1784 = RATIONAL(1.0,10.0)+t1801; + t1783 = t1761+t1800; + t1768 = RATIONAL(1.0,40.0); + t1782 = t1768+t1745+t1747; + t1763 = RATIONAL(3.0,40.0); + t1781 = t1763+t1791; + t1780 = t1747+t1753+t1762; + t1779 = t1762+t1804; + t1778 = t1762+t1792; + t1777 = t1762+t1796; + t1776 = t1763+t1803; + t1775 = t1743+t1751+t1763; + t1765 = RATIONAL(1.0,20.0); + t1774 = t1765+t1795; + t1773 = t1743+t1749+t1765; + t1772 = t1744+t1747+t1765; + t1766 = RATIONAL(7.0,80.0); + t1771 = t1766+t1802; + t1770 = t1766+t1798; + t1764 = RATIONAL(-9.0,80.0); + t1758 = RATIONAL(-3.0,20.0); + t1757 = RATIONAL(-1.0,40.0); + t1754 = RATIONAL(-11.0,80.0); + t1750 = RATIONAL(-1.0,16.0)*y; + t1742 = RATIONAL(-3.0,16.0)*y; + coeffs_dyy->coeff_m1_m1_m1 = t1750+t1784; + coeffs_dyy->coeff_0_m1_m1 = t1750+t1771; + coeffs_dyy->coeff_p1_m1_m1 = t1750+t1781; + coeffs_dyy->coeff_p2_m1_m1 = t1750+t1780; + coeffs_dyy->coeff_m1_0_m1 = RATIONAL(-13.0,80.0)+t1745+t1797; + coeffs_dyy->coeff_0_0_m1 = t1746+t1758+t1800; + coeffs_dyy->coeff_p1_0_m1 = t1754+t1745+t1794; + coeffs_dyy->coeff_p2_0_m1 = t1799+t1804; + coeffs_dyy->coeff_m1_p1_m1 = t1742+t1782; + coeffs_dyy->coeff_0_p1_m1 = t1742+t1783; + coeffs_dyy->coeff_p1_p1_m1 = t1742+t1774; + coeffs_dyy->coeff_p2_p1_m1 = t1742+t1779; + coeffs_dyy->coeff_m1_p2_m1 = t1753+t1761+t1787; + coeffs_dyy->coeff_0_p2_m1 = t1748+t1768+t1802; + coeffs_dyy->coeff_p1_p2_m1 = t1753+t1760+t1790; + coeffs_dyy->coeff_p2_p2_m1 = t1753+t1789; + coeffs_dyy->coeff_m1_m1_0 = t1750+t1770; + coeffs_dyy->coeff_0_m1_0 = t1750+t1776; + coeffs_dyy->coeff_p1_m1_0 = t1750+t1777; + coeffs_dyy->coeff_p2_m1_0 = t1750+t1772; + coeffs_dyy->coeff_m1_0_0 = t1747+t1758+t1793; + coeffs_dyy->coeff_0_0_0 = t1749+t1754+t1793; + coeffs_dyy->coeff_p1_0_0 = t1792+t1799; + coeffs_dyy->coeff_p2_0_0 = t1751+t1764+t1793; + coeffs_dyy->coeff_m1_p1_0 = t1742+t1785; + coeffs_dyy->coeff_0_p1_0 = t1742+t1773; + coeffs_dyy->coeff_p1_p1_0 = t1742+t1778; + coeffs_dyy->coeff_p2_p1_0 = t1742+t1775; + coeffs_dyy->coeff_m1_p2_0 = t1744+t1768+t1787; + coeffs_dyy->coeff_0_p2_0 = t1748+t1760+t1803; + coeffs_dyy->coeff_p1_p2_0 = t1744+t1790; + coeffs_dyy->coeff_p2_p2_0 = t1744+t1756+t1789; + coeffs_dyy->coeff_m1_m1_p1 = t1750+t1775; + coeffs_dyy->coeff_0_m1_p1 = t1750+t1778; + coeffs_dyy->coeff_p1_m1_p1 = t1750+t1773; + coeffs_dyy->coeff_p2_m1_p1 = t1750+t1785; + coeffs_dyy->coeff_m1_0_p1 = t1744+t1754+t1797; + coeffs_dyy->coeff_0_0_p1 = t1796+t1799; + coeffs_dyy->coeff_p1_0_p1 = t1744+t1764+t1794; + coeffs_dyy->coeff_p2_0_p1 = t1788+t1798; + coeffs_dyy->coeff_m1_p1_p1 = t1742+t1772; + coeffs_dyy->coeff_0_p1_p1 = t1742+t1777; + coeffs_dyy->coeff_p1_p1_p1 = t1742+t1776; + coeffs_dyy->coeff_p2_p1_p1 = t1742+t1770; + coeffs_dyy->coeff_m1_p2_p1 = t1760+t1751+t1786; + coeffs_dyy->coeff_0_p2_p1 = t1752+t1786; + coeffs_dyy->coeff_p1_p2_p1 = t1749+t1756+t1786; + coeffs_dyy->coeff_p2_p2_p1 = t1757+t1747+t1786; + coeffs_dyy->coeff_m1_m1_p2 = t1750+t1779; + coeffs_dyy->coeff_0_m1_p2 = t1750+t1774; + coeffs_dyy->coeff_p1_m1_p2 = t1750+t1783; + coeffs_dyy->coeff_p2_m1_p2 = t1750+t1782; + coeffs_dyy->coeff_m1_0_p2 = t1769+t1753+t1797; + coeffs_dyy->coeff_0_0_p2 = t1746+t1764+t1791; + coeffs_dyy->coeff_p1_0_p2 = t1788+t1802; + coeffs_dyy->coeff_p2_0_p2 = RATIONAL(-7.0,80.0)+t1746+t1801; + coeffs_dyy->coeff_m1_p1_p2 = t1742+t1780; + coeffs_dyy->coeff_0_p1_p2 = t1742+t1781; + coeffs_dyy->coeff_p1_p1_p2 = t1742+t1771; + coeffs_dyy->coeff_p2_p1_p2 = t1742+t1784; + coeffs_dyy->coeff_m1_p2_p2 = t1745+t1787; + coeffs_dyy->coeff_0_p2_p2 = t1756+t1748+t1795; + coeffs_dyy->coeff_p1_p2_p2 = t1745+t1757+t1790; + coeffs_dyy->coeff_p2_p2_p2 = t1755+t1745+t1789; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyz.compute.c new file mode 100644 index 0000000..8af310e --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyz.compute.c @@ -0,0 +1,210 @@ +fp t1848; +fp t1813; +fp t1847; +fp t1815; +fp t1883; +fp t1809; +fp t1882; +fp t1846; +fp t1819; +fp t1820; +fp t1881; +fp t1849; +fp t1816; +fp t1880; +fp t1879; +fp t1807; +fp t1834; +fp t1878; +fp t1814; +fp t1877; +fp t1822; +fp t1811; +fp t1876; +fp t1838; +fp t1824; +fp t1806; +fp t1875; +fp t1817; +fp t1874; +fp t1818; +fp t1873; +fp t1833; +fp t1808; +fp t1872; +fp t1871; +fp t1870; +fp t1869; +fp t1868; +fp t1812; +fp t1867; +fp t1866; +fp t1865; +fp t1864; +fp t1863; +fp t1862; +fp t1861; +fp t1860; +fp t1810; +fp t1859; +fp t1858; +fp t1857; +fp t1856; +fp t1855; +fp t1854; +fp t1805; +fp t1853; +fp t1852; +fp t1851; +fp t1850; +fp t1843; +fp t1841; +fp t1840; +fp t1839; +fp t1837; +fp t1836; +fp t1835; +fp t1832; +fp t1831; +fp t1829; +fp t1828; +fp t1827; +fp t1823; +fp t1821; + t1848 = RATIONAL(1.0,80.0); + t1813 = t1848*y; + t1847 = RATIONAL(-1.0,80.0); + t1815 = t1847*z; + t1883 = t1813+t1815; + t1809 = RATIONAL(3.0,1000.0)*x; + t1882 = RATIONAL(-1.0,250.0)+t1809; + t1846 = RATIONAL(-3.0,80.0); + t1819 = t1846*z; + t1820 = t1846*y; + t1881 = t1819+t1820; + t1849 = RATIONAL(3.0,80.0); + t1816 = t1849*y; + t1880 = t1819+t1816; + t1879 = RATIONAL(2.0,125.0)+t1809; + t1807 = RATIONAL(1.0,1000.0)*x; + t1834 = RATIONAL(-3.0,1000.0); + t1878 = t1807+t1834; + t1814 = t1847*y; + t1877 = t1819+t1814; + t1822 = RATIONAL(-19.0,2000.0); + t1811 = RATIONAL(9.0,1000.0)*x; + t1876 = t1822+t1811; + t1838 = RATIONAL(-9.0,1000.0); + t1824 = RATIONAL(-27.0,1000.0); + t1806 = t1824*x; + t1875 = t1838+t1806; + t1817 = t1849*z; + t1874 = t1817+t1816; + t1818 = t1848*z; + t1873 = t1818+t1814; + t1833 = RATIONAL(-1.0,1000.0); + t1808 = t1833*x; + t1872 = RATIONAL(-1.0,500.0)+t1808; + t1871 = t1817+t1809; + t1870 = t1819+t1813; + t1869 = RATIONAL(37.0,2000.0)+t1809; + t1868 = t1809+t1816; + t1812 = t1838*x; + t1867 = t1812+t1816; + t1866 = t1818+t1820; + t1865 = t1814+t1815; + t1864 = t1811+t1813; + t1863 = t1824+t1811; + t1862 = t1817+t1820; + t1861 = RATIONAL(13.0,1000.0)+t1811; + t1860 = t1820+t1815; + t1810 = t1834*x; + t1859 = t1810+t1815; + t1858 = t1820+t1812; + t1857 = t1817+t1812; + t1856 = RATIONAL(49.0,2000.0)+t1812; + t1855 = t1810+t1814; + t1854 = t1818+t1813; + t1805 = RATIONAL(27.0,1000.0)*x; + t1853 = t1819+t1805; + t1852 = t1810+t1813; + t1851 = t1818+t1810; + t1850 = t1817+t1805; + t1843 = RATIONAL(-7.0,250.0); + t1841 = RATIONAL(-9.0,250.0); + t1840 = RATIONAL(-9.0,500.0); + t1839 = RATIONAL(-17.0,500.0); + t1837 = RATIONAL(11.0,500.0); + t1836 = RATIONAL(-1.0,2000.0); + t1835 = RATIONAL(-7.0,2000.0); + t1832 = RATIONAL(-37.0,1000.0); + t1831 = RATIONAL(-31.0,1000.0); + t1829 = RATIONAL(19.0,1000.0); + t1828 = RATIONAL(31.0,2000.0); + t1827 = RATIONAL(43.0,2000.0); + t1823 = RATIONAL(-13.0,2000.0); + t1821 = RATIONAL(-21.0,2000.0); + coeffs_dyz->coeff_m1_m1_m1 = t1806+RATIONAL(147.0,2000.0)+t1881; + coeffs_dyz->coeff_0_m1_m1 = RATIONAL(129.0,2000.0)+t1819+t1858; + coeffs_dyz->coeff_p1_m1_m1 = t1811+RATIONAL(111.0,2000.0)+t1881; + coeffs_dyz->coeff_p2_m1_m1 = t1820+RATIONAL(93.0,2000.0)+t1853; + coeffs_dyz->coeff_m1_0_m1 = t1836+t1815+t1867; + coeffs_dyz->coeff_0_0_m1 = t1835+t1816+t1859; + coeffs_dyz->coeff_p1_0_m1 = t1815+t1823+t1868; + coeffs_dyz->coeff_p2_0_m1 = t1815+t1816+t1876; + coeffs_dyz->coeff_m1_p1_m1 = t1811+t1832+t1818+t1816; + coeffs_dyz->coeff_0_p1_m1 = t1818+t1839+t1868; + coeffs_dyz->coeff_p1_p1_m1 = t1816+t1831+t1851; + coeffs_dyz->coeff_p2_p1_m1 = t1843+t1818+t1867; + coeffs_dyz->coeff_m1_p2_m1 = t1820+t1841+t1850; + coeffs_dyz->coeff_0_p2_m1 = t1862+t1863; + coeffs_dyz->coeff_p1_p2_m1 = t1840+t1820+t1857; + coeffs_dyz->coeff_p2_p2_m1 = t1862+t1875; + coeffs_dyz->coeff_m1_m1_0 = t1814+t1836+t1857; + coeffs_dyz->coeff_0_m1_0 = t1817+t1835+t1855; + coeffs_dyz->coeff_p1_m1_0 = t1823+t1814+t1871; + coeffs_dyz->coeff_p2_m1_0 = t1814+t1817+t1876; + coeffs_dyz->coeff_m1_0_0 = t1813+RATIONAL(-17.0,2000.0)+t1851; + coeffs_dyz->coeff_0_0_0 = t1822+t1808+t1854; + coeffs_dyz->coeff_p1_0_0 = t1821+t1807+t1854; + coeffs_dyz->coeff_p2_0_0 = t1809+RATIONAL(-23.0,2000.0)+t1854; + coeffs_dyz->coeff_m1_p1_0 = t1882+t1883; + coeffs_dyz->coeff_0_p1_0 = t1878+t1883; + coeffs_dyz->coeff_p1_p1_0 = t1872+t1883; + coeffs_dyz->coeff_p2_p1_0 = t1815+t1833+t1852; + coeffs_dyz->coeff_m1_p2_0 = t1861+t1877; + coeffs_dyz->coeff_0_p2_0 = t1877+t1879; + coeffs_dyz->coeff_p1_p2_0 = t1829+t1819+t1855; + coeffs_dyz->coeff_p2_p2_0 = t1812+t1837+t1877; + coeffs_dyz->coeff_m1_m1_p1 = t1817+t1832+t1864; + coeffs_dyz->coeff_0_m1_p1 = t1813+t1839+t1871; + coeffs_dyz->coeff_p1_m1_p1 = t1817+t1831+t1852; + coeffs_dyz->coeff_p2_m1_p1 = t1843+t1813+t1857; + coeffs_dyz->coeff_m1_0_p1 = t1873+t1882; + coeffs_dyz->coeff_0_0_p1 = t1873+t1878; + coeffs_dyz->coeff_p1_0_p1 = t1872+t1873; + coeffs_dyz->coeff_p2_0_p1 = t1833+t1814+t1851; + coeffs_dyz->coeff_m1_p1_p1 = t1815+RATIONAL(33.0,2000.0)+t1855; + coeffs_dyz->coeff_0_p1_p1 = t1828+t1808+t1865; + coeffs_dyz->coeff_p1_p1_p1 = RATIONAL(29.0,2000.0)+t1807+t1865; + coeffs_dyz->coeff_p2_p1_p1 = RATIONAL(27.0,2000.0)+t1809+t1865; + coeffs_dyz->coeff_m1_p2_p1 = t1856+t1870; + coeffs_dyz->coeff_0_p2_p1 = t1819+t1827+t1852; + coeffs_dyz->coeff_p1_p2_p1 = t1869+t1870; + coeffs_dyz->coeff_p2_p2_p1 = t1819+t1828+t1864; + coeffs_dyz->coeff_m1_m1_p2 = t1841+t1816+t1853; + coeffs_dyz->coeff_0_m1_p2 = t1863+t1880; + coeffs_dyz->coeff_p1_m1_p2 = t1840+t1819+t1867; + coeffs_dyz->coeff_p2_m1_p2 = t1875+t1880; + coeffs_dyz->coeff_m1_0_p2 = t1860+t1861; + coeffs_dyz->coeff_0_0_p2 = t1860+t1879; + coeffs_dyz->coeff_p1_0_p2 = t1829+t1820+t1859; + coeffs_dyz->coeff_p2_0_p2 = t1837+t1815+t1858; + coeffs_dyz->coeff_m1_p1_p2 = t1856+t1866; + coeffs_dyz->coeff_0_p1_p2 = t1827+t1820+t1851; + coeffs_dyz->coeff_p1_p1_p2 = t1866+t1869; + coeffs_dyz->coeff_p2_p1_p2 = t1828+t1811+t1866; + coeffs_dyz->coeff_m1_p2_p2 = RATIONAL(-3.0,2000.0)+t1806+t1874; + coeffs_dyz->coeff_0_p2_p2 = t1821+t1816+t1857; + coeffs_dyz->coeff_p1_p2_p2 = t1811+RATIONAL(-39.0,2000.0)+t1874; + coeffs_dyz->coeff_p2_p2_p2 = t1816+RATIONAL(-57.0,2000.0)+t1850; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dz.compute.c new file mode 100644 index 0000000..dc79363 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dz.compute.c @@ -0,0 +1,502 @@ +fp t1423; +fp t1429; +fp t1339; +fp t1430; +fp t1336; +fp t1477; +fp t1352; +fp t1517; +fp t1516; +fp t1337; +fp t1515; +fp t1428; +fp t1342; +fp t1419; +fp t1320; +fp t1328; +fp t1514; +fp t1348; +fp t1513; +fp t1356; +fp t1420; +fp t1321; +fp t1322; +fp t1512; +fp t1344; +fp t1511; +fp t1403; +fp t1500; +fp t1270; +fp t1510; +fp t1341; +fp t1509; +fp t1351; +fp t1508; +fp t1468; +fp t1507; +fp t1467; +fp t1506; +fp t1405; +fp t1306; +fp t1268; +fp t1505; +fp t1415; +fp t1331; +fp t1335; +fp t1469; +fp t1504; +fp t1347; +fp t1406; +fp t1308; +fp t1269; +fp t1503; +fp t1353; +fp t1502; +fp t1271; +fp t1345; +fp t1501; +fp t1499; +fp t1411; +fp t1319; +fp t1498; +fp t1346; +fp t1297; +fp t1280; +fp t1281; +fp t1497; +fp t1277; +fp t1496; +fp t1275; +fp t1276; +fp t1495; +fp t1279; +fp t1494; +fp t1493; +fp t1491; +fp t1489; +fp t1488; +fp t1278; +fp t1487; +fp t1350; +fp t1354; +fp t1486; +fp t1485; +fp t1484; +fp t1483; +fp t1482; +fp t1481; +fp t1274; +fp t1480; +fp t1479; +fp t1478; +fp t1475; +fp t1474; +fp t1472; +fp t1471; +fp t1470; +fp t1466; +fp t1465; +fp t1464; +fp t1463; +fp t1462; +fp t1461; +fp t1266; +fp t1460; +fp t1273; +fp t1459; +fp t1458; +fp t1457; +fp t1456; +fp t1455; +fp t1454; +fp t1453; +fp t1452; +fp t1267; +fp t1451; +fp t1450; +fp t1449; +fp t1448; +fp t1447; +fp t1446; +fp t1445; +fp t1444; +fp t1443; +fp t1442; +fp t1441; +fp t1272; +fp t1440; +fp t1439; +fp t1438; +fp t1437; +fp t1436; +fp t1435; +fp t1358; +fp t1434; +fp t1433; +fp t1432; +fp t1431; +fp t1422; +fp t1421; +fp t1418; +fp t1417; +fp t1416; +fp t1413; +fp t1412; +fp t1410; +fp t1408; +fp t1407; +fp t1404; +fp t1402; +fp t1401; +fp t1397; +fp t1396; +fp t1395; +fp t1394; +fp t1392; +fp t1391; +fp t1388; +fp t1387; +fp t1384; +fp t1383; +fp t1382; +fp t1380; +fp t1378; +fp t1377; +fp t1376; +fp t1371; +fp t1369; +fp t1340; +fp t1338; +fp t1334; +fp t1333; +fp t1332; +fp t1330; +fp t1329; +fp t1327; +fp t1326; +fp t1325; +fp t1324; +fp t1323; +fp t1318; +fp t1317; +fp t1316; +fp t1315; +fp t1314; +fp t1313; +fp t1312; +fp t1311; +fp t1310; +fp t1309; +fp t1307; +fp t1305; +fp t1304; +fp t1303; +fp t1302; +fp t1301; +fp t1300; +fp t1299; +fp t1298; +fp t1296; +fp t1295; +fp t1294; +fp t1293; +fp t1292; +fp t1291; +fp t1290; +fp t1289; +fp t1288; +fp t1287; +fp t1285; +fp t1284; +fp t1283; +fp t1282; + t1423 = RATIONAL(-3.0,160.0); + t1429 = x*x; + t1339 = t1423*t1429; + t1430 = y*y; + t1336 = t1423*t1430; + t1477 = t1339+t1336; + t1352 = RATIONAL(-9.0,80.0)*z; + t1517 = t1352+RATIONAL(-137.0,4000.0); + t1516 = RATIONAL(-4.0,375.0)+RATIONAL(-1.0,40.0)*z; + t1337 = RATIONAL(-11.0,80.0)*z; + t1515 = t1337+RATIONAL(-107.0,4000.0); + t1428 = z*z; + t1342 = RATIONAL(3.0,32.0)*t1428; + t1419 = RATIONAL(1.0,160.0); + t1320 = t1419*t1429; + t1328 = t1419*t1430; + t1514 = t1342+t1328+t1320; + t1348 = RATIONAL(1.0,20.0)*z; + t1513 = RATIONAL(-29.0,6000.0)+t1348; + t1356 = RATIONAL(-3.0,32.0)*t1428; + t1420 = RATIONAL(-1.0,160.0); + t1321 = t1420*t1430; + t1322 = t1420*t1429; + t1512 = t1356+t1321+t1322; + t1344 = RATIONAL(1.0,40.0)*z; + t1511 = RATIONAL(-17.0,3000.0)+t1344; + t1403 = RATIONAL(-27.0,1000.0); + t1500 = x*y; + t1270 = RATIONAL(9.0,1000.0)*t1500; + t1510 = t1403*y+t1270; + t1341 = RATIONAL(1.0,32.0)*t1428; + t1509 = t1341+t1477; + t1351 = RATIONAL(3.0,40.0)*z; + t1508 = RATIONAL(-97.0,3000.0)+t1351; + t1468 = t1342+t1321; + t1507 = t1322+t1468; + t1467 = t1320+t1356; + t1506 = t1467+t1328; + t1405 = RATIONAL(-3.0,1000.0); + t1306 = t1405*y; + t1268 = x*t1306; + t1505 = RATIONAL(53.0,1000.0)+t1351+t1268; + t1415 = RATIONAL(3.0,160.0); + t1331 = t1415*t1430; + t1335 = t1415*t1429; + t1469 = t1341+t1335; + t1504 = t1331+t1469; + t1347 = RATIONAL(1.0,80.0)*z; + t1406 = RATIONAL(-9.0,1000.0); + t1308 = t1406*x; + t1269 = y*t1308; + t1503 = t1347+t1269+RATIONAL(-137.0,12000.0); + t1353 = RATIONAL(7.0,80.0)*z; + t1502 = t1353+t1269+RATIONAL(-607.0,12000.0); + t1271 = RATIONAL(3.0,1000.0)*t1500; + t1345 = RATIONAL(3.0,80.0)*z; + t1501 = t1271+RATIONAL(323.0,4000.0)+t1345; + t1499 = y+x; + t1411 = RATIONAL(-1.0,1000.0); + t1319 = t1411*x; + t1498 = RATIONAL(-3.0,80.0)*z; + t1346 = RATIONAL(-1.0,80.0)*z; + t1297 = t1403*x; + t1280 = x*t1345; + t1281 = y*t1345; + t1497 = t1280+t1281; + t1277 = y*t1346; + t1496 = t1280+t1277; + t1275 = y*t1347; + t1276 = x*t1498; + t1495 = t1275+t1276; + t1279 = x*t1347; + t1494 = t1279+t1275; + t1493 = t1279+t1281; + t1491 = t1320+t1321; + t1489 = t1280+t1275; + t1488 = t1281+t1276; + t1278 = y*t1498; + t1487 = t1279+t1278; + t1350 = RATIONAL(1.0,16.0)*z; + t1354 = RATIONAL(-1.0,32.0)*t1428; + t1486 = t1350+t1354; + t1485 = t1322+t1328; + t1484 = t1280+t1278; + t1483 = t1279+t1277; + t1482 = t1342+t1268; + t1481 = t1276+t1278; + t1274 = x*t1346; + t1480 = t1275+t1274; + t1479 = t1276+t1277; + t1478 = t1335+t1336; + t1475 = t1278+t1274; + t1474 = t1339+t1331; + t1472 = t1331+t1335; + t1471 = t1277+t1274; + t1470 = t1281+t1274; + t1466 = t1344+t1497; + t1465 = t1270+t1478; + t1464 = t1348+t1494; + t1463 = t1270+t1474; + t1462 = t1351+t1471; + t1461 = RATIONAL(1.0,10.0)*z+t1481; + t1266 = RATIONAL(27.0,1000.0)*t1500; + t1460 = t1266+t1504; + t1273 = y*t1319; + t1459 = t1273+t1514; + t1458 = t1275+t1321+t1467; + t1457 = t1342+t1271+t1485; + t1456 = t1271+t1509; + t1455 = t1354+t1269+RATIONAL(53.0,12000.0)+t1345; + t1454 = t1279+t1356+t1485; + t1453 = t1269+t1507; + t1452 = RATIONAL(-3.0,20.0)*z+RATIONAL(-49.0,2000.0)+t1482; + t1267 = y*t1297; + t1451 = t1267+t1354+t1477; + t1450 = t1341+t1465; + t1449 = t1354+t1268+t1472; + t1448 = t1341+t1278+t1474; + t1447 = RATIONAL(-1.0,10.0)*z+RATIONAL(-79.0,2000.0)+t1482; + t1446 = t1270+t1506; + t1445 = t1356+t1268+t1348+RATIONAL(141.0,2000.0); + t1444 = t1354+t1276+t1474; + t1443 = t1346+t1341+t1269+RATIONAL(-167.0,12000.0); + t1442 = t1354+t1274+t1478; + t1441 = t1320+t1271+t1468; + t1272 = RATIONAL(1.0,1000.0)*t1500; + t1440 = t1272+t1512; + t1439 = t1353+t1356+t1271+RATIONAL(183.0,4000.0); + t1438 = RATIONAL(79.0,3000.0)+t1268+t1509; + t1437 = RATIONAL(-41.0,750.0)+t1267+t1504; + t1436 = RATIONAL(-691.0,12000.0)+t1271+t1472+t1486; + t1435 = t1266+RATIONAL(281.0,12000.0)+t1477+t1486; + t1358 = RATIONAL(-1.0,8.0)*z; + t1434 = RATIONAL(-33.0,2000.0)+t1358+t1270+t1507; + t1433 = t1350+RATIONAL(299.0,4000.0)+t1273+t1512; + t1432 = t1358+t1272+RATIONAL(-87.0,2000.0)+t1514; + t1431 = t1350+t1269+RATIONAL(191.0,4000.0)+t1506; + t1422 = RATIONAL(-7.0,250.0); + t1421 = RATIONAL(-9.0,500.0); + t1418 = RATIONAL(-9.0,250.0); + t1417 = RATIONAL(-1.0,500.0); + t1416 = RATIONAL(2.0,125.0); + t1413 = RATIONAL(-1.0,250.0); + t1412 = RATIONAL(-17.0,500.0); + t1410 = RATIONAL(-3.0,2000.0); + t1408 = RATIONAL(11.0,500.0); + t1407 = RATIONAL(-1.0,2000.0); + t1404 = RATIONAL(-7.0,2000.0); + t1402 = RATIONAL(37.0,2000.0); + t1401 = RATIONAL(13.0,1000.0); + t1397 = RATIONAL(49.0,2000.0); + t1396 = RATIONAL(27.0,2000.0); + t1395 = RATIONAL(-37.0,1000.0); + t1394 = RATIONAL(43.0,2000.0); + t1392 = RATIONAL(31.0,2000.0); + t1391 = RATIONAL(-19.0,2000.0); + t1388 = RATIONAL(93.0,2000.0); + t1387 = RATIONAL(-21.0,2000.0); + t1384 = RATIONAL(19.0,1000.0); + t1383 = RATIONAL(-23.0,2000.0); + t1382 = RATIONAL(-39.0,2000.0); + t1380 = RATIONAL(-17.0,2000.0); + t1378 = RATIONAL(-31.0,1000.0); + t1377 = RATIONAL(33.0,2000.0); + t1376 = RATIONAL(-13.0,2000.0); + t1371 = RATIONAL(111.0,2000.0); + t1369 = RATIONAL(129.0,2000.0); + t1340 = t1416*y; + t1338 = t1413*x; + t1334 = t1417*y; + t1333 = t1417*x; + t1332 = t1418*x; + t1330 = t1416*x; + t1329 = t1413*y; + t1327 = t1421*x; + t1326 = t1418*y; + t1325 = t1422*y; + t1324 = t1422*x; + t1323 = t1421*y; + t1318 = t1408*x; + t1317 = t1408*y; + t1316 = t1407*x; + t1315 = t1405*x; + t1314 = t1407*y; + t1313 = t1404*y; + t1312 = t1404*x; + t1311 = t1412*x; + t1310 = t1412*y; + t1309 = t1411*y; + t1307 = t1406*y; + t1305 = t1384*y; + t1304 = t1387*y; + t1303 = t1395*x; + t1302 = t1397*x; + t1301 = t1392*x; + t1300 = t1376*y; + t1299 = t1384*x; + t1298 = t1391*y; + t1296 = t1401*x; + t1295 = t1395*y; + t1294 = t1394*x; + t1293 = t1378*x; + t1292 = t1392*y; + t1291 = t1376*x; + t1290 = t1378*y; + t1289 = t1402*x; + t1288 = t1401*y; + t1287 = t1397*y; + t1285 = t1391*x; + t1284 = t1387*x; + t1283 = t1394*y; + t1282 = t1402*y; + coeffs_dz->coeff_m1_m1_m1 = RATIONAL(-47.0,1500.0)+t1499*RATIONAL(147.0, +2000.0)+t1451+t1461; + coeffs_dz->coeff_0_m1_m1 = t1316+t1278+t1369*y+t1442+t1502; + coeffs_dz->coeff_p1_m1_m1 = t1371*y+t1354+t1303+t1465+t1487+t1508; + coeffs_dz->coeff_p2_m1_m1 = t1388*y+t1332+t1435+t1484; + coeffs_dz->coeff_m1_0_m1 = t1277+t1314+t1369*x+t1444+t1502; + coeffs_dz->coeff_0_0_m1 = t1312+t1313+RATIONAL(-437.0,6000.0)+t1449+t1462 +; + coeffs_dz->coeff_p1_0_m1 = t1311+t1300+t1436+t1483; + coeffs_dz->coeff_p2_0_m1 = t1354+t1297+t1298+t1463+t1496+t1513; + coeffs_dz->coeff_m1_p1_m1 = t1270+t1371*x+t1275+t1295+t1444+t1508; + coeffs_dz->coeff_0_p1_m1 = t1310+t1291+t1436+t1480; + coeffs_dz->coeff_p1_p1_m1 = RATIONAL(-17.0,375.0)+t1293+t1290+t1449+t1464 +; + coeffs_dz->coeff_p2_p1_m1 = t1327+t1325+t1455+t1474+t1489; + coeffs_dz->coeff_m1_p2_m1 = t1326+t1388*x+t1435+t1488; + coeffs_dz->coeff_0_p2_m1 = t1285+t1281+t1442+t1510+t1513; + coeffs_dz->coeff_p1_p2_m1 = t1324+t1323+t1455+t1478+t1493; + coeffs_dz->coeff_p2_p2_m1 = t1308+RATIONAL(307.0,6000.0)+t1307+t1451+ +t1466; + coeffs_dz->coeff_m1_m1_0 = t1316+t1314+RATIONAL(-39.0,4000.0)+RATIONAL( +-13.0,80.0)*z+t1453+t1497; + coeffs_dz->coeff_0_m1_0 = t1380*x+t1313+t1452+t1491+t1493; + coeffs_dz->coeff_p1_m1_0 = t1338+t1300+t1441+t1470+t1515; + coeffs_dz->coeff_p2_m1_0 = t1298+t1296+t1434+t1488; + coeffs_dz->coeff_m1_0_0 = t1380*y+t1312+t1452+t1485+t1489; + coeffs_dz->coeff_0_0_0 = t1337+t1298+RATIONAL(-161.0,4000.0)+t1285+t1459+ +t1494; + coeffs_dz->coeff_p1_0_0 = t1315+t1304+t1432+t1480; + coeffs_dz->coeff_p2_0_0 = t1383*y+t1330+t1457+t1495+t1517; + coeffs_dz->coeff_m1_p1_0 = t1329+t1291+t1457+t1496+t1515; + coeffs_dz->coeff_0_p1_0 = t1284+t1306+t1432+t1483; + coeffs_dz->coeff_p1_p1_0 = t1352+RATIONAL(-191.0,4000.0)+t1334+t1333+ +t1459+t1471; + coeffs_dz->coeff_p2_p1_0 = t1299+t1309+t1447+t1479+t1485; + coeffs_dz->coeff_m1_p2_0 = t1285+t1288+t1434+t1484; + coeffs_dz->coeff_0_p2_0 = t1383*x+t1340+t1441+t1487+t1517; + coeffs_dz->coeff_p1_p2_0 = t1305+t1319+t1447+t1475+t1491; + coeffs_dz->coeff_p2_p2_0 = t1318+RATIONAL(-7.0,80.0)*z+t1317+RATIONAL( +-129.0,4000.0)+t1453+t1481; + coeffs_dz->coeff_m1_m1_p1 = t1303+t1295+RATIONAL(157.0,2000.0)+t1446+ +t1466; + coeffs_dz->coeff_0_m1_p1 = t1281+t1310+t1338+t1454+t1501; + coeffs_dz->coeff_p1_m1_p1 = t1377*x+t1290+t1445+t1470+t1485; + coeffs_dz->coeff_p2_m1_p1 = t1302+t1325+t1431+t1488; + coeffs_dz->coeff_m1_0_p1 = t1280+t1329+t1311+t1458+t1501; + coeffs_dz->coeff_0_0_p1 = RATIONAL(21.0,250.0)+t1315+t1306+t1440+t1464; + coeffs_dz->coeff_p1_0_p1 = t1334+t1301+t1433+t1480; + coeffs_dz->coeff_p2_0_p1 = t1309+t1294+t1276+t1458+t1505; + coeffs_dz->coeff_m1_p1_p1 = t1377*y+t1293+t1445+t1491+t1496; + coeffs_dz->coeff_0_p1_p1 = t1292+t1333+t1433+t1483; + coeffs_dz->coeff_p1_p1_p1 = RATIONAL(133.0,2000.0)+t1499*RATIONAL(29.0, +2000.0)+t1440+t1462; + coeffs_dz->coeff_p2_p1_p1 = t1289+t1396*y+t1439+t1479+t1491; + coeffs_dz->coeff_m1_p2_p1 = t1287+t1324+t1431+t1484; + coeffs_dz->coeff_0_p2_p1 = t1319+t1283+t1278+t1454+t1505; + coeffs_dz->coeff_p1_p2_p1 = t1396*x+t1282+t1439+t1475+t1485; + coeffs_dz->coeff_p2_p2_p1 = t1301+RATIONAL(13.0,500.0)+t1292+t1446+t1461; + coeffs_dz->coeff_m1_m1_p2 = t1345+t1326+t1332+RATIONAL(-449.0,12000.0)+ +t1460+t1481; + coeffs_dz->coeff_0_m1_p2 = t1274+t1296+t1448+t1510+t1511; + coeffs_dz->coeff_p1_m1_p2 = t1302+t1323+t1279+t1448+t1503; + coeffs_dz->coeff_p2_m1_p2 = t1410*x+t1307+t1437+t1484; + coeffs_dz->coeff_m1_0_p2 = t1288+t1297+t1450+t1479+t1511; + coeffs_dz->coeff_0_0_p2 = RATIONAL(349.0,12000.0)+t1347+t1340+t1330+t1456 ++t1471; + coeffs_dz->coeff_p1_0_p2 = t1305+t1294+t1438+t1483; + coeffs_dz->coeff_p2_0_p2 = t1284+t1317+t1443+t1478+t1496; + coeffs_dz->coeff_m1_p1_p2 = t1327+t1336+t1287+t1469+t1495+t1503; + coeffs_dz->coeff_0_p1_p2 = t1283+t1299+t1438+t1480; + coeffs_dz->coeff_p1_p1_p2 = t1282+RATIONAL(319.0,12000.0)+t1346+t1289+ +t1456+t1494; + coeffs_dz->coeff_p2_p1_p2 = t1382*x+t1292+t1450+t1489+t1516; + coeffs_dz->coeff_m1_p2_p2 = t1308+t1410*y+t1437+t1488; + coeffs_dz->coeff_0_p2_p2 = t1304+t1318+t1443+t1470+t1474; + coeffs_dz->coeff_p1_p2_p2 = t1382*y+t1341+t1301+t1463+t1493+t1516; + coeffs_dz->coeff_p2_p2_p2 = t1498+RATIONAL(-539.0,12000.0)+t1499*RATIONAL +(-57.0,2000.0)+t1460+t1497; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dzz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dzz.compute.c new file mode 100644 index 0000000..8de80ca --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dzz.compute.c @@ -0,0 +1,192 @@ +fp t1886; +fp t1896; +fp t1949; +fp t1897; +fp t1884; +fp t1905; +fp t1892; +fp t1948; +fp t1885; +fp t1900; +fp t1888; +fp t1947; +fp t1906; +fp t1890; +fp t1946; +fp t1895; +fp t1945; +fp t1903; +fp t1889; +fp t1944; +fp t1894; +fp t1943; +fp t1942; +fp t1891; +fp t1941; +fp t1901; +fp t1940; +fp t1939; +fp t1938; +fp t1937; +fp t1936; +fp t1935; +fp t1934; +fp t1933; +fp t1932; +fp t1931; +fp t1930; +fp t1929; +fp t1928; +fp t1907; +fp t1927; +fp t1910; +fp t1926; +fp t1925; +fp t1924; +fp t1923; +fp t1922; +fp t1921; +fp t1920; +fp t1919; +fp t1904; +fp t1918; +fp t1917; +fp t1916; +fp t1915; +fp t1914; +fp t1913; +fp t1912; +fp t1911; +fp t1909; +fp t1899; +fp t1898; +fp t1893; +fp t1887; + t1886 = RATIONAL(3.0,16.0)*z; + t1896 = RATIONAL(-11.0,80.0); + t1949 = t1886+t1896; + t1897 = RATIONAL(-3.0,80.0); + t1884 = t1897*y; + t1905 = RATIONAL(1.0,80.0); + t1892 = t1905*x; + t1948 = t1884+t1892; + t1885 = t1897*x; + t1900 = RATIONAL(-1.0,80.0); + t1888 = t1900*y; + t1947 = t1885+t1888; + t1906 = RATIONAL(3.0,80.0); + t1890 = t1906*x; + t1946 = t1884+t1890; + t1895 = t1905*y; + t1945 = t1890+t1895; + t1903 = RATIONAL(1.0,16.0); + t1889 = t1903*z; + t1944 = t1889+t1900; + t1894 = t1900*x; + t1943 = t1895+t1894; + t1942 = t1888+t1892; + t1891 = t1906*y; + t1941 = t1889+t1891; + t1901 = RATIONAL(1.0,40.0); + t1940 = t1889+t1901; + t1939 = t1885+t1895; + t1938 = t1886+t1885; + t1937 = t1886+RATIONAL(-1.0,10.0); + t1936 = t1888+t1894; + t1935 = t1886+t1894; + t1934 = t1886+t1892; + t1933 = t1884+t1894; + t1932 = t1885+t1884; + t1931 = t1888+t1890; + t1930 = t1889+t1905; + t1929 = t1890+t1891; + t1928 = t1892+t1895; + t1907 = RATIONAL(7.0,80.0); + t1927 = t1907+t1933; + t1910 = RATIONAL(1.0,20.0); + t1926 = t1910+t1891+t1894; + t1925 = t1907+t1947; + t1924 = t1903+t1942; + t1923 = t1901+t1929; + t1922 = RATIONAL(1.0,10.0)+t1932; + t1921 = t1903+t1946; + t1920 = t1885+t1891+t1903; + t1919 = t1903+t1943; + t1904 = RATIONAL(3.0,40.0); + t1918 = t1904+t1939; + t1917 = t1904+t1948; + t1916 = t1904+t1936; + t1915 = t1910+t1931; + t1914 = t1910+t1928; + t1913 = t1891+t1892+t1906; + t1912 = t1906+t1945; + t1911 = RATIONAL(-1.0,8.0); + t1909 = RATIONAL(-9.0,80.0); + t1899 = RATIONAL(-3.0,20.0); + t1898 = RATIONAL(-1.0,40.0); + t1893 = RATIONAL(-3.0,16.0)*z; + t1887 = RATIONAL(-1.0,16.0)*z; + coeffs_dzz->coeff_m1_m1_m1 = t1887+t1922; + coeffs_dzz->coeff_0_m1_m1 = t1887+t1927; + coeffs_dzz->coeff_p1_m1_m1 = t1887+t1917; + coeffs_dzz->coeff_p2_m1_m1 = t1887+t1921; + coeffs_dzz->coeff_m1_0_m1 = t1887+t1925; + coeffs_dzz->coeff_0_0_m1 = t1887+t1916; + coeffs_dzz->coeff_p1_0_m1 = t1887+t1924; + coeffs_dzz->coeff_p2_0_m1 = t1887+t1915; + coeffs_dzz->coeff_m1_p1_m1 = t1887+t1918; + coeffs_dzz->coeff_0_p1_m1 = t1887+t1919; + coeffs_dzz->coeff_p1_p1_m1 = t1887+t1914; + coeffs_dzz->coeff_p2_p1_m1 = t1887+t1912; + coeffs_dzz->coeff_m1_p2_m1 = t1887+t1920; + coeffs_dzz->coeff_0_p2_m1 = t1887+t1926; + coeffs_dzz->coeff_p1_p2_m1 = t1887+t1913; + coeffs_dzz->coeff_p2_p2_m1 = t1887+t1923; + coeffs_dzz->coeff_m1_m1_0 = RATIONAL(-13.0,80.0)+t1886+t1929; + coeffs_dzz->coeff_0_m1_0 = t1899+t1891+t1934; + coeffs_dzz->coeff_p1_m1_0 = t1896+t1891+t1935; + coeffs_dzz->coeff_p2_m1_0 = t1911+t1891+t1938; + coeffs_dzz->coeff_m1_0_0 = t1886+t1899+t1945; + coeffs_dzz->coeff_0_0_0 = t1928+t1949; + coeffs_dzz->coeff_p1_0_0 = t1911+t1895+t1935; + coeffs_dzz->coeff_p2_0_0 = t1909+t1895+t1938; + coeffs_dzz->coeff_m1_p1_0 = t1931+t1949; + coeffs_dzz->coeff_0_p1_0 = t1911+t1888+t1934; + coeffs_dzz->coeff_p1_p1_0 = t1888+t1909+t1935; + coeffs_dzz->coeff_p2_p1_0 = t1937+t1947; + coeffs_dzz->coeff_m1_p2_0 = t1886+t1911+t1946; + coeffs_dzz->coeff_0_p2_0 = t1884+t1909+t1934; + coeffs_dzz->coeff_p1_p2_0 = t1933+t1937; + coeffs_dzz->coeff_p2_p2_0 = t1886+RATIONAL(-7.0,80.0)+t1932; + coeffs_dzz->coeff_m1_m1_p1 = t1893+t1923; + coeffs_dzz->coeff_0_m1_p1 = t1893+t1913; + coeffs_dzz->coeff_p1_m1_p1 = t1893+t1926; + coeffs_dzz->coeff_p2_m1_p1 = t1893+t1920; + coeffs_dzz->coeff_m1_0_p1 = t1893+t1912; + coeffs_dzz->coeff_0_0_p1 = t1893+t1914; + coeffs_dzz->coeff_p1_0_p1 = t1893+t1919; + coeffs_dzz->coeff_p2_0_p1 = t1893+t1918; + coeffs_dzz->coeff_m1_p1_p1 = t1893+t1915; + coeffs_dzz->coeff_0_p1_p1 = t1893+t1924; + coeffs_dzz->coeff_p1_p1_p1 = t1893+t1916; + coeffs_dzz->coeff_p2_p1_p1 = t1893+t1925; + coeffs_dzz->coeff_m1_p2_p1 = t1893+t1921; + coeffs_dzz->coeff_0_p2_p1 = t1893+t1917; + coeffs_dzz->coeff_p1_p2_p1 = t1893+t1927; + coeffs_dzz->coeff_p2_p2_p1 = t1893+t1922; + coeffs_dzz->coeff_m1_m1_p2 = t1889+t1906+t1932; + coeffs_dzz->coeff_0_m1_p2 = t1933+t1940; + coeffs_dzz->coeff_p1_m1_p2 = t1930+t1948; + coeffs_dzz->coeff_p2_m1_p2 = t1889+t1946; + coeffs_dzz->coeff_m1_0_p2 = t1940+t1947; + coeffs_dzz->coeff_0_0_p2 = t1930+t1936; + coeffs_dzz->coeff_p1_0_p2 = t1889+t1942; + coeffs_dzz->coeff_p2_0_p2 = t1931+t1944; + coeffs_dzz->coeff_m1_p1_p2 = t1930+t1939; + coeffs_dzz->coeff_0_p1_p2 = t1889+t1943; + coeffs_dzz->coeff_p1_p1_p2 = t1928+t1944; + coeffs_dzz->coeff_p2_p1_p2 = t1898+t1889+t1945; + coeffs_dzz->coeff_m1_p2_p2 = t1885+t1941; + coeffs_dzz->coeff_0_p2_p2 = t1900+t1894+t1941; + coeffs_dzz->coeff_p1_p2_p2 = t1898+t1892+t1941; + coeffs_dzz->coeff_p2_p2_p2 = t1897+t1889+t1929; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..762444a --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-I.compute.c @@ -0,0 +1,1615 @@ +fp t2339; +fp t2337; +fp t2338; +fp t2834; +fp t2309; +fp t2503; +fp t2075; +fp t2324; +fp t2227; +fp t2833; +fp t2326; +fp t2246; +fp t2310; +fp t2512; +fp t2041; +fp t2832; +fp t2294; +fp t2303; +fp t2465; +fp t2060; +fp t2831; +fp t2292; +fp t2307; +fp t2515; +fp t2131; +fp t2830; +fp t2458; +fp t2083; +fp t2313; +fp t2205; +fp t2829; +fp t2200; +fp t2116; +fp t2828; +fp t2261; +fp t2495; +fp t2323; +fp t2095; +fp t2827; +fp t2330; +fp t2231; +fp t2539; +fp t2538; +fp t1960; +fp t2826; +fp t2825; +fp t2824; +fp t2254; +fp t2114; +fp t2320; +fp t2823; +fp t2325; +fp t2452; +fp t2031; +fp t2331; +fp t2304; +fp t2193; +fp t2822; +fp t2467; +fp t2108; +fp t2298; +fp t2178; +fp t2821; +fp t2302; +fp t2477; +fp t2107; +fp t1961; +fp t2249; +fp t2528; +fp t2820; +fp t2262; +fp t2537; +fp t2521; +fp t2076; +fp t1964; +fp t2819; +fp t2260; +fp t2534; +fp t2000; +fp t2336; +fp t2211; +fp t2334; +fp t2209; +fp t2510; +fp t2818; +fp t2333; +fp t2229; +fp t2043; +fp t2817; +fp t2335; +fp t2212; +fp t2499; +fp t2002; +fp t2816; +fp t2281; +fp t2216; +fp t2815; +fp t2277; +fp t2149; +fp t2814; +fp t2311; +fp t2513; +fp t2210; +fp t2813; +fp t2173; +fp t2459; +fp t2065; +fp t2812; +fp t2273; +fp t2811; +fp t2322; +fp t2230; +fp t2810; +fp t2256; +fp t2527; +fp t2809; +fp t2478; +fp t2192; +fp t2808; +fp t2475; +fp t2104; +fp t2807; +fp t2516; +fp t2208; +fp t2806; +fp t2287; +fp t2308; +fp t2464; +fp t2122; +fp t2457; +fp t2120; +fp t2461; +fp t2805; +fp t2258; +fp t2535; +fp t2010; +fp t2203; +fp t2202; +fp t2462; +fp t2804; +fp t2121; +fp t2803; +fp t2051; +fp t1992; +fp t2271; +fp t2524; +fp t2802; +fp t2270; +fp t2522; +fp t2519; +fp t2059; +fp t1959; +fp t2801; +fp t2541; +fp t2511; +fp t2046; +fp t1988; +fp t2800; +fp t2257; +fp t2507; +fp t2130; +fp t2799; +fp t2540; +fp t1982; +fp t2798; +fp t2797; +fp t2318; +fp t2204; +fp t2316; +fp t2470; +fp t2106; +fp t2284; +fp t2483; +fp t2796; +fp t2054; +fp t1973; +fp t2795; +fp t2067; +fp t2794; +fp t2072; +fp t2793; +fp t2312; +fp t2081; +fp t2332; +fp t2226; +fp t2792; +fp t2317; +fp t2508; +fp t2791; +fp t2194; +fp t2790; +fp t2016; +fp t2520; +fp t2789; +fp t2486; +fp t2039; +fp t1966; +fp t2290; +fp t2788; +fp t2518; +fp t2787; +fp t2196; +fp t2786; +fp t2228; +fp t2454; +fp t2785; +fp t2321; +fp t2489; +fp t2094; +fp t2207; +fp t2784; +fp t2263; +fp t2783; +fp t2493; +fp t2782; +fp t2291; +fp t2781; +fp t2780; +fp t2485; +fp t2097; +fp t1962; +fp t2779; +fp t2267; +fp t2533; +fp t2006; +fp t2453; +fp t2049; +fp t1975; +fp t2778; +fp t2328; +fp t2045; +fp t2777; +fp t1989; +fp t2776; +fp t2775; +fp t2481; +fp t2100; +fp t2774; +fp t2086; +fp t1958; +fp t2773; +fp t2480; +fp t2460; +fp t2772; +fp t2771; +fp t2466; +fp t2293; +fp t1951; +fp t2770; +fp t2030; +fp t2769; +fp t2768; +fp t2255; +fp t2531; +fp t2767; +fp t2529; +fp t2766; +fp t2272; +fp t2036; +fp t2765; +fp t2098; +fp t2482; +fp t2223; +fp t2764; +fp t2253; +fp t2523; +fp t2763; +fp t2468; +fp t2762; +fp t2761; +fp t2115; +fp t2760; +fp t2759; +fp t2758; +fp t2327; +fp t2757; +fp t2756; +fp t2755; +fp t2754; +fp t2451; +fp t2063; +fp t2753; +fp t2752; +fp t2751; +fp t2033; +fp t2750; +fp t2265; +fp t2264; +fp t2749; +fp t2103; +fp t2748; +fp t2259; +fp t2530; +fp t1996; +fp t2747; +fp t2247; +fp t2746; +fp t2745; +fp t2744; +fp t2473; +fp t2073; +fp t2743; +fp t2145; +fp t2742; +fp t2741; +fp t2525; +fp t2740; +fp t2014; +fp t2487; +fp t2739; +fp t2738; +fp t2737; +fp t2736; +fp t1981; +fp t2735; +fp t2734; +fp t2733; +fp t2732; +fp t2299; +fp t2731; +fp t2730; +fp t2729; +fp t2728; +fp t2206; +fp t2727; +fp t2048; +fp t2726; +fp t2105; +fp t2725; +fp t2724; +fp t2723; +fp t2722; +fp t2721; +fp t2720; +fp t2719; +fp t2718; +fp t2032; +fp t2717; +fp t2716; +fp t2068; +fp t2715; +fp t2714; +fp t2111; +fp t2713; +fp t2712; +fp t1991; +fp t2711; +fp t2235; +fp t2710; +fp t2709; +fp t2062; +fp t2708; +fp t2278; +fp t2526; +fp t2707; +fp t2056; +fp t2706; +fp t2705; +fp t1994; +fp t2704; +fp t2282; +fp t2152; +fp t2703; +fp t2702; +fp t2701; +fp t2276; +fp t2157; +fp t2700; +fp t2314; +fp t2213; +fp t2088; +fp t2092; +fp t2491; +fp t2699; +fp t2463; +fp t1956; +fp t2698; +fp t2697; +fp t2696; +fp t1987; +fp t2695; +fp t2289; +fp t2153; +fp t2694; +fp t2693; +fp t2306; +fp t2692; +fp t1986; +fp t2691; +fp t2139; +fp t2109; +fp t2690; +fp t1963; +fp t2689; +fp t2288; +fp t2532; +fp t2688; +fp t2329; +fp t2237; +fp t2687; +fp t2295; +fp t1955; +fp t2686; +fp t2685; +fp t2684; +fp t2456; +fp t2683; +fp t2147; +fp t2682; +fp t2681; +fp t2040; +fp t2504; +fp t2168; +fp t2680; +fp t1980; +fp t2679; +fp t2279; +fp t2536; +fp t2678; +fp t1993; +fp t2677; +fp t2248; +fp t2676; +fp t2019; +fp t2675; +fp t2674; +fp t2673; +fp t2672; +fp t1984; +fp t2671; +fp t2280; +fp t2156; +fp t2670; +fp t2669; +fp t2668; +fp t2667; +fp t2666; +fp t2665; +fp t2148; +fp t2664; +fp t2166; +fp t2663; +fp t2476; +fp t2662; +fp t2661; +fp t2474; +fp t2660; +fp t2243; +fp t2659; +fp t2658; +fp t2657; +fp t2656; +fp t2655; +fp t2001; +fp t2654; +fp t2653; +fp t2652; +fp t2651; +fp t2650; +fp t2649; +fp t2158; +fp t2648; +fp t2647; +fp t2646; +fp t2146; +fp t2645; +fp t2144; +fp t2644; +fp t2643; +fp t2642; +fp t2641; +fp t2640; +fp t2301; +fp t2639; +fp t2638; +fp t2637; +fp t2636; +fp t2635; +fp t2184; +fp t2634; +fp t2241; +fp t2129; +fp t2319; +fp t2201; +fp t2633; +fp t2632; +fp t2631; +fp t2630; +fp t2629; +fp t2628; +fp t2224; +fp t2245; +fp t2627; +fp t2626; +fp t2625; +fp t2242; +fp t2624; +fp t2623; +fp t2233; +fp t2622; +fp t2621; +fp t2620; +fp t2619; +fp t2618; +fp t2617; +fp t2616; +fp t2132; +fp t2297; +fp t2615; +fp t2614; +fp t2219; +fp t2613; +fp t2612; +fp t2170; +fp t2611; +fp t2238; +fp t2610; +fp t2214; +fp t2609; +fp t2608; +fp t2607; +fp t2250; +fp t2136; +fp t2606; +fp t2605; +fp t2604; +fp t2603; +fp t2602; +fp t2601; +fp t2600; +fp t2599; +fp t2598; +fp t2597; +fp t2239; +fp t2596; +fp t2300; +fp t2222; +fp t2218; +fp t2595; +fp t2594; +fp t2593; +fp t2592; +fp t2591; +fp t2590; +fp t2589; +fp t2588; +fp t2587; +fp t2134; +fp t2586; +fp t2585; +fp t2161; +fp t2584; +fp t2583; +fp t2582; +fp t2220; +fp t2581; +fp t2580; +fp t2579; +fp t2578; +fp t2577; +fp t2576; +fp t2575; +fp t2574; +fp t2573; +fp t2572; +fp t2571; +fp t2570; +fp t2118; +fp t2569; +fp t2568; +fp t2567; +fp t2566; +fp t2565; +fp t2564; +fp t2563; +fp t2562; +fp t2225; +fp t2561; +fp t2560; +fp t2559; +fp t2558; +fp t2557; +fp t2506; +fp t2556; +fp t2555; +fp t2554; +fp t2553; +fp t2502; +fp t2552; +fp t2551; +fp t2550; +fp t2549; +fp t2548; +fp t2547; +fp t2546; +fp t2545; +fp t2544; +fp t2543; +fp t2418; +fp t2542; +fp t2517; +fp t2514; +fp t2505; +fp t2501; +fp t2500; +fp t2498; +fp t2497; +fp t2496; +fp t2494; +fp t2490; +fp t2488; +fp t2484; +fp t2479; +fp t2472; +fp t2471; +fp t2455; +fp t2450; +fp t2449; +fp t2448; +fp t2447; +fp t2446; +fp t2445; +fp t2444; +fp t2443; +fp t2442; +fp t2441; +fp t2440; +fp t2439; +fp t2438; +fp t2266; +fp t2437; +fp t2436; +fp t2269; +fp t2435; +fp t2434; +fp t2433; +fp t2432; +fp t2431; +fp t2430; +fp t2429; +fp t2428; +fp t2427; +fp t2426; +fp t2425; +fp t2424; +fp t2423; +fp t2422; +fp t2421; +fp t2420; +fp t2419; +fp t2417; +fp t2416; +fp t2415; +fp t2414; +fp t2413; +fp t2412; +fp t2411; +fp t2410; +fp t2409; +fp t2408; +fp t2251; +fp t2407; +fp t2182; +fp t2285; +fp t2406; +fp t2405; +fp t2404; +fp t2403; +fp t2402; +fp t2151; +fp t2401; +fp t2400; +fp t2399; +fp t2215; +fp t2398; +fp t2397; +fp t2396; +fp t2395; +fp t1970; +fp t2394; +fp t2154; +fp t2393; +fp t2392; +fp t2159; +fp t2391; +fp t2390; +fp t2389; +fp t2388; +fp t2387; +fp t2386; +fp t2385; +fp t2384; +fp t2383; +fp t1971; +fp t2382; +fp t2381; +fp t2380; +fp t2379; +fp t2378; +fp t2377; +fp t2376; +fp t2375; +fp t2374; +fp t2197; +fp t2373; +fp t2372; +fp t2371; +fp t1953; +fp t2370; +fp t2369; +fp t2368; +fp t2367; +fp t2366; +fp t2365; +fp t2364; +fp t2363; +fp t2362; +fp t2361; +fp t1954; +fp t1950; +fp t2360; +fp t2359; +fp t2358; +fp t2357; +fp t2356; +fp t2355; +fp t2354; +fp t2353; +fp t2352; +fp t2351; +fp t2350; +fp t2349; +fp t2348; +fp t2347; +fp t2346; +fp t2315; +fp t2305; +fp t2286; +fp t2283; +fp t1990; +fp t1985; +fp t1972; +fp t1957; +fp t1952; + t2339 = y*y; + t2337 = z*z; + t2338 = x*x; + t2834 = t2338+t2339+t2337; + t2309 = RATIONAL(1.0,175.0); + t2503 = t2339*t2309; + t2075 = x*t2503; + t2324 = RATIONAL(1.0,300.0); + t2227 = t2324*x; + t2833 = t2075+t2227; + t2326 = RATIONAL(-2.0,75.0); + t2246 = t2326*y; + t2310 = RATIONAL(1.0,350.0); + t2512 = t2310*t2337; + t2041 = y*t2512; + t2832 = t2246+t2041; + t2294 = RATIONAL(-17.0,525.0); + t2303 = RATIONAL(1.0,700.0); + t2465 = t2338*t2303; + t2060 = z*t2465; + t2831 = t2294*z+t2060; + t2292 = RATIONAL(11.0,420.0); + t2307 = RATIONAL(-1.0,175.0); + t2515 = t2307*t2339; + t2131 = x*t2515; + t2830 = t2292*x+t2131; + t2458 = t2307*t2337; + t2083 = y*t2458; + t2313 = RATIONAL(-1.0,300.0); + t2205 = t2313*y; + t2829 = t2083+t2205; + t2200 = t2313*x; + t2116 = x*t2458; + t2828 = t2200+t2116; + t2261 = RATIONAL(151.0,7350.0); + t2495 = t2337*t2338; + t2323 = RATIONAL(1.0,490.0); + t2095 = t2323*t2495; + t2827 = t2095+t2261*t2339; + t2330 = RATIONAL(1.0,42.0); + t2231 = t2330*z; + t2539 = x*z; + t2538 = y*t2539; + t1960 = RATIONAL(1.0,500.0)*t2538; + t2826 = t2231+t1960; + t2825 = RATIONAL(202.0,6125.0)+t2834*RATIONAL(-529.0,29400.0); + t2824 = RATIONAL(-23.0,6125.0)+t2834*RATIONAL(83.0,3675.0); + t2254 = RATIONAL(-169.0,29400.0); + t2114 = t2254*t2339; + t2320 = RATIONAL(-2.0,125.0); + t2823 = t2114+t2320; + t2325 = RATIONAL(-1.0,490.0); + t2452 = t2325*t2339; + t2031 = t2338*t2452; + t2331 = t2339*t2339; + t2304 = RATIONAL(-1.0,150.0); + t2193 = t2304*t2331; + t2822 = t2031+t2193; + t2467 = t2338*t2309; + t2108 = z*t2467; + t2298 = RATIONAL(-11.0,420.0); + t2178 = t2298*z; + t2821 = t2108+t2178; + t2302 = RATIONAL(-1.0,700.0); + t2477 = t2339*t2302; + t2107 = z*t2477; + t1961 = x*t2107; + t2249 = RATIONAL(289.0,10500.0); + t2528 = z*t2249; + t2820 = x*t2528+t1961; + t2262 = RATIONAL(-187.0,7000.0); + t2537 = y*t2262; + t2521 = t2310*t2338; + t2076 = y*t2521; + t1964 = z*t2076; + t2819 = z*t2537+t1964; + t2260 = RATIONAL(137.0,5250.0); + t2534 = x*t2260; + t2000 = z*t2534; + t2336 = t2338*x; + t2211 = t2313*t2336; + t2334 = t2337*z; + t2209 = t2313*t2334; + t2510 = z*t2211+x*t2209; + t2818 = t2000+t2510; + t2333 = t2337*t2337; + t2229 = t2304*t2333; + t2043 = t2337*t2452; + t2817 = t2229+t2043; + t2335 = t2339*y; + t2212 = t2313*t2335; + t2499 = y*t2211+x*t2212; + t2002 = y*t2534; + t2816 = t2499+t2002; + t2281 = RATIONAL(29.0,2100.0); + t2216 = t2324*t2335; + t2815 = t2216+t2281*y; + t2277 = RATIONAL(19.0,2100.0); + t2149 = t2277*x; + t2814 = t2149+t2131; + t2311 = RATIONAL(1.0,600.0); + t2513 = t2311*t2335; + t2210 = t2304*t2336; + t2813 = x*t2513+y*t2210; + t2173 = t2294*y; + t2459 = t2337*t2303; + t2065 = y*t2459; + t2812 = t2173+t2065; + t2273 = RATIONAL(167.0,7000.0); + t2811 = t1961+t2273*t2539; + t2322 = RATIONAL(1.0,150.0); + t2230 = t2322*t2334; + t2810 = t2326*z+t2230; + t2256 = RATIONAL(-229.0,10500.0); + t2527 = z*t2256; + t2809 = t1961+x*t2527; + t2478 = t2311*t2334; + t2192 = t2304*t2335; + t2808 = z*t2192+y*t2478; + t2475 = t2337*t2309; + t2104 = y*t2475; + t2807 = t2212+t2104; + t2516 = t2041+t2043; + t2208 = t2311*t2333; + t2806 = t2516+t2208; + t2287 = RATIONAL(17.0,2100.0); + t2308 = RATIONAL(-1.0,350.0); + t2464 = t2308*t2338; + t2122 = z*t2464; + t2457 = t2308*t2339; + t2120 = z*t2457; + t2461 = t2122+t2120; + t2805 = t2461+t2287*z; + t2258 = RATIONAL(-137.0,5250.0); + t2535 = z*t2258; + t2010 = x*t2535; + t2203 = t2324*t2334; + t2202 = t2324*t2336; + t2462 = x*t2203+z*t2202; + t2804 = t2010+t2462; + t2121 = x*t2477; + t2803 = t2121+t2210; + t2051 = y*t2464; + t1992 = z*t2051; + t2271 = RATIONAL(187.0,7000.0); + t2524 = z*t2271; + t2802 = t1992+y*t2524; + t2270 = RATIONAL(-167.0,7000.0); + t2522 = x*t2270; + t2519 = t2339*t2303; + t2059 = z*t2519; + t1959 = x*t2059; + t2801 = t1959+z*t2522; + t2541 = x*y; + t2511 = t2337*t2302; + t2046 = x*t2511; + t1988 = y*t2046; + t2800 = t2256*t2541+t1988; + t2257 = RATIONAL(311.0,29400.0); + t2507 = t2339*t2338; + t2130 = t2323*t2507; + t2799 = t2257*t2337+t2130; + t2540 = y*z; + t1982 = y*t2060; + t2798 = t1982+t2270*t2540; + t2797 = t2060+t2230; + t2318 = RATIONAL(1.0,100.0); + t2204 = t2318*t2333; + t2316 = RATIONAL(-1.0,245.0); + t2470 = t2337*t2316; + t2106 = t2338*t2470; + t2284 = RATIONAL(47.0,6125.0); + t2483 = t2106+t2284; + t2796 = t2204+t2483; + t2054 = x*t2457; + t1973 = z*t2054; + t2795 = x*t2524+t1973; + t2067 = y*t2511; + t2794 = t2192+t2067; + t2072 = x*t2475; + t2793 = t2211+t2072; + t2312 = RATIONAL(1.0,980.0); + t2081 = t2312*t2507; + t2332 = t2338*t2338; + t2226 = t2304*t2332; + t2792 = t2081+t2226; + t2317 = RATIONAL(-1.0,600.0); + t2508 = t2335*t2317; + t2791 = z*t2508+y*t2230; + t2194 = t2322*t2335; + t2790 = t2051+t2194; + t2016 = y*t2535; + t2520 = z*t2216+y*t2203; + t2789 = t2016+t2520; + t2486 = t2310*t2339; + t2039 = z*t2486; + t1966 = x*t2039; + t2290 = RATIONAL(47.0,5250.0); + t2788 = t2290*t2539+t1966; + t2518 = t2317*t2336; + t2787 = x*t2194+y*t2518; + t2196 = t2304*t2334; + t2786 = t2196+t2122; + t2228 = t2322*t2336; + t2454 = t2334*t2317; + t2785 = z*t2228+x*t2454; + t2321 = RATIONAL(1.0,245.0); + t2489 = t2338*t2321; + t2094 = t2339*t2489; + t2207 = t2311*t2331; + t2784 = t2094+t2207; + t2263 = RATIONAL(272.0,6125.0); + t2783 = t2263+t2261*t2338; + t2493 = z*t2212+y*t2209; + t2782 = t2260*t2540+t2493; + t2291 = RATIONAL(-29.0,2100.0); + t2781 = t2212+t2291*y; + t2780 = t2202+t2131; + t2485 = t2338*t2302; + t2097 = y*t2485; + t1962 = z*t2097; + t2779 = y*t2527+t1962; + t2267 = RATIONAL(-107.0,7000.0); + t2533 = t2267*y; + t2006 = x*t2533; + t2453 = t2308*t2337; + t2049 = y*t2453; + t1975 = x*t2049; + t2778 = t2006+t1975; + t2328 = RATIONAL(2.0,75.0); + t2045 = t2339*t2470; + t2777 = t2284+t2045+t2328*t2338; + t1989 = z*t2075; + t2776 = t2010+t1989; + t2775 = t2192+t2097; + t2481 = t2307*t2338; + t2100 = z*t2481; + t2774 = t2100+t2203; + t2086 = x*t2459; + t1958 = y*t2086; + t2773 = t1958+y*t2522; + t2480 = t2194+t2193; + t2460 = t2049+t2043; + t2772 = t2480+t2460; + t2771 = t1973+t2267*t2539; + t2466 = t2338*t2540; + t2293 = RATIONAL(1.0,1400.0); + t1951 = t2293*t2466; + t2770 = t2016+t1951; + t2030 = x*t2519; + t2769 = t2030+t2228; + t2768 = t2271*t2541+t1975; + t2255 = RATIONAL(229.0,10500.0); + t2531 = x*t2255; + t2767 = z*t2531+t1959; + t2529 = y*t2273; + t2766 = t1962+z*t2529; + t2272 = RATIONAL(128.0,3675.0); + t2036 = t2254*t2338; + t2765 = t2036+t2272*t2337; + t2098 = t2316*t2507; + t2482 = t2284+t2098; + t2223 = t2318*t2332; + t2764 = t2482+t2223; + t2253 = RATIONAL(-289.0,10500.0); + t2523 = z*t2253; + t2763 = x*t2523+t1959; + t2468 = t2311*t2336; + t2762 = z*t2468+x*t2196; + t2761 = t2211+t2116; + t2115 = t2254*t2337; + t2760 = t2115+t2320; + t2759 = t2075+t2202; + t2758 = t1966+t2262*t2539; + t2327 = RATIONAL(-1.0,20.0); + t2757 = t2327*t2338+t2045; + t2756 = y*t2228+x*t2508; + t2755 = t2207+t2223; + t2754 = y*t2196+z*t2513; + t2451 = t2312*t2337; + t2063 = t2339*t2451; + t2753 = t2063+t2193; + t2752 = t2228+t2086; + t2751 = x*t2230+z*t2518; + t2033 = z*t2503; + t2750 = t2209+t2033; + t2265 = RATIONAL(-173.0,6125.0); + t2264 = RATIONAL(211.0,7350.0); + t2749 = t2265+t2264*t2339; + t2103 = y*t2467; + t2748 = t2216+t2103; + t2259 = RATIONAL(107.0,7000.0); + t2530 = t2259*y; + t1996 = z*t2530; + t2747 = t1996+t1964; + t2247 = t2330*x; + t2746 = t2210+t2247; + t2745 = t2108+t2203; + t2744 = t2194+t2065; + t2473 = t2339*t2337; + t2073 = t2323*t2473; + t2743 = t2229+t2073; + t2145 = t2277*z; + t2742 = t2145+t2209; + t2741 = z*t2210+x*t2478; + t2525 = y*t2290; + t2740 = t2493+z*t2525; + t2014 = t2258*t2541; + t2487 = x*t2216+y*t2202; + t2739 = t2014+t2487; + t2738 = t2327*t2339+t2106; + t2737 = t2030+t2294*x; + t2736 = z*t2194+y*t2454; + t1981 = x*t2104; + t2735 = t1981+t2014; + t2734 = t2095+t2257*t2339; + t2733 = t1966+t2259*t2539; + t2732 = t2059+t2230; + t2299 = RATIONAL(-61.0,980.0); + t2731 = t2299*t2338+t2223; + t2730 = t2192+t2076; + t2729 = t2116+t2202; + t2728 = t2054+t2228; + t2206 = t2311*t2332; + t2727 = t2206+t2094; + t2048 = t2325*t2495; + t2726 = t2226+t2048; + t2105 = z*t2515; + t2725 = t2105+t2108; + t2724 = t2072+t2298*x; + t2723 = t2212+t2083; + t2722 = t2031+t2226; + t2721 = t2317*t2338+t2045; + t2720 = t2216+t2104; + t2719 = t1988+x*t2529; + t2718 = t1982+t2255*t2540; + t2032 = y*t2465; + t2717 = t2194+t2032; + t2716 = t2108+t2209; + t2068 = z*t2485; + t2715 = t2196+t2068; + t2714 = t2203+t2033; + t2111 = t2337*t2489; + t2713 = t2111+t2204; + t2712 = t2249*t2541+t1988; + t1991 = x*t2041; + t2711 = x*t2537+t1991; + t2235 = t2330*y; + t2710 = t2235+t2067; + t2709 = t2111+t2208; + t2062 = x*t2453; + t2708 = t2210+t2062; + t2278 = RATIONAL(-47.0,5250.0); + t2526 = x*t2278; + t2707 = t1973+z*t2526; + t2056 = y*t2481; + t2706 = t2083+t2056; + t2705 = y*t2468+x*t2192; + t1994 = z*t2533; + t2704 = t1994+t1992; + t2282 = RATIONAL(37.0,1050.0); + t2152 = t2282*z; + t2703 = t2152+t2715; + t2702 = t2487+t2800; + t2701 = t2105+t2742; + t2276 = RATIONAL(-19.0,2100.0); + t2157 = t2276*y; + t2700 = t2157+t2720; + t2314 = RATIONAL(8.0,525.0); + t2213 = t2314*x; + t2088 = x*t2512; + t2092 = x*t2486; + t2491 = t2088+t2092; + t2699 = t2210+t2213+t2491; + t2463 = t2339*t2539; + t1956 = t2293*t2463; + t2698 = t1956+t2804; + t2697 = t2203+t2805; + t2696 = t2121+t2746; + t1987 = y*t2108; + t2695 = t1987+t2789; + t2289 = RATIONAL(-17.0,2100.0); + t2153 = t2289*x; + t2694 = t2211+t2153+t2491; + t2693 = t1958+t2803; + t2306 = RATIONAL(-8.0,525.0); + t2692 = t2461+t2230+t2306*z; + t1986 = RATIONAL(-1.0,500.0)*t2538; + t2691 = t1986+t2231+t2196; + t2139 = t2272*t2338; + t2109 = t2321*t2473; + t2690 = t2139+t2115+t2109; + t1963 = z*t2056; + t2689 = t1963+t2782; + t2288 = RATIONAL(-17.0,5250.0); + t2532 = y*t2288; + t2688 = t1963+t2520+z*t2532; + t2329 = RATIONAL(-1.0,42.0); + t2237 = t2329*z; + t2687 = t2237+t2797; + t2295 = RATIONAL(-1.0,1400.0); + t1955 = t2295*t2466; + t2686 = t1955+t2782; + t2685 = t2229+t2753; + t2684 = t1964+t2740; + t2456 = t2049+t2051; + t2683 = t2216+t2287*y+t2456; + t2147 = t2277*y; + t2682 = t2147+t2723; + t2681 = y*t2526+t2765; + t2040 = z*t2521; + t2504 = t2039+t2040; + t2168 = t2289*z; + t2680 = t2504+t2168+t2209; + t1980 = y*t2531; + t2679 = t1958+t2499+t1980; + t2279 = RATIONAL(17.0,5250.0); + t2536 = y*t2279; + t2678 = z*t2536+t1987+t2493; + t1993 = RATIONAL(-1.0,250.0)*t2538; + t2677 = t1993+t2788; + t2248 = t2329*x; + t2676 = t2248+t2769; + t2019 = t2278*t2540; + t2675 = t1992+t2019+t2520; + t2674 = t1994+t2736; + t2673 = t2100+t2742; + t2672 = t2006+t2756; + t1984 = RATIONAL(1.0,250.0)*t2538; + t2671 = t1984+t2707; + t2280 = RATIONAL(-37.0,1050.0); + t2156 = t2280*z; + t2670 = t2156+t2797; + t2669 = t2208+t2726; + t2668 = t2272*t2339+t2111+t2036; + t2667 = t2207+t2109+t2033; + t2666 = t2043+t2754; + t2665 = t2504+t2196+t2314*z; + t2148 = t2276*z; + t2664 = t2148+t2714; + t2166 = t2280*x; + t2663 = t2166+t2769; + t2476 = t2041+t2076; + t2662 = t2212+t2289*y+t2476; + t2661 = t2235+t2775; + t2474 = t2054+t2062; + t2660 = t2474+t2202+t2287*x; + t2243 = t2329*y; + t2659 = t2243+t2717; + t2658 = t2207+t2823; + t2657 = t2493+t2718; + t2656 = t2228+t2306*x+t2474; + t2655 = t2206+t2709; + t2001 = x*t2530; + t2654 = t2001+t2705; + t2653 = t2761+t2830; + t2652 = t2248+t2086+t2728; + t2651 = t2094+x*t2525+t2765; + t2650 = t2046+t2092+t2746; + t2649 = t1984+t2510+t2788; + t2158 = t2281*x; + t2648 = t2158+t2062+t2780; + t2647 = t2001+t1991+t2813; + t2646 = t2049+t2056+t2815; + t2146 = t2276*x; + t2645 = t2054+t2146+t2072+t2202; + t2144 = t2291*x; + t2644 = t2075+t2211+t2088+t2144; + t2643 = t2040+t2120+t2810; + t2642 = t2715+t2826; + t2641 = t2762+t2795; + t2640 = t2741+t2811; + t2301 = RATIONAL(17.0,525.0); + t2639 = t2107+t2301*z+t2715; + t2638 = t2802+t2808; + t2637 = t2083+t2051+t2815; + t2636 = t2200+t2072+t2780; + t2635 = t2762+t2811; + t2184 = t2298*y; + t2634 = t2184+t2103+t2720; + t2241 = t2328*t2339; + t2129 = t2257*t2338; + t2319 = RATIONAL(-9.0,196.0); + t2201 = t2319*t2337; + t2633 = t2241+t2129+t2073+t2201; + t2632 = t1984+t2692; + t2631 = t2766+t2808; + t2630 = t2227+t2131+t2793; + t2629 = t2732+t2794; + t2628 = t2785+t2801; + t2224 = t2319*t2338; + t2245 = t2328*t2337; + t2627 = t2224+t2245+t2734; + t2626 = t2076+t2104+t2781; + t2625 = t2105+t2100+t2292*z+t2209; + t2242 = t2328*z; + t2624 = t2039+t2242+t2786; + t2623 = t2301*y+t2067+t2775; + t2233 = t2328*x; + t2622 = t2092+t2233+t2708; + t2621 = t2212+t2056+t2759; + t2620 = t2041+t2103+t2781; + t2619 = t2732+t2831; + t2618 = t2736+t2819; + t2617 = t2046+t2301*x+t2803; + t2616 = t2208+t2690; + t2132 = t2261*t2337; + t2297 = RATIONAL(-57.0,980.0); + t2615 = t2132+t2297*t2339+t2783; + t2614 = t2056+t2205+t2720; + t2219 = t2324*z; + t2613 = t2219+t2100+t2750; + t2612 = t1986+t2687; + t2170 = t2291*z; + t2611 = t2170+t2040+t2750; + t2238 = t2326*x; + t2610 = t2228+t2238+t2062+t2092; + t2214 = t2319*t2339; + t2609 = t2214+t2245+t2129+t2482; + t2608 = t2238+t2088+t2728; + t2607 = t1984+t2665; + t2250 = RATIONAL(191.0,29400.0); + t2136 = t2264*t2338; + t2606 = t2136+t2250*t2337+t2749; + t2605 = t2705+t2768; + t2604 = t1993+t2692; + t2603 = t2039+t2170+t2716; + t2602 = t2732+t2744; + t2601 = t2722+t2813; + t2600 = t2771+t2785; + t2599 = t2733+t2741; + t2598 = t2747+t2808; + t2597 = t2748+t2759; + t2239 = t2328*y; + t2596 = t2239+t2049+t2730; + t2300 = RATIONAL(-33.0,980.0); + t2222 = t2317*t2337; + t2218 = t2317*t2339; + t2595 = t2106+t2222+t2218+t2300*t2338; + t2594 = t2722+t2756; + t2593 = t2737+t2752; + t2592 = t1975+t2672; + t2591 = t2107+t2196+t2744; + t2590 = t2300*t2337+t2218+t2721; + t2589 = t2229+t2666; + t2588 = t2724+t2759; + t2587 = t1993+t2665; + t2134 = t2264*t2337; + t2586 = t2250*t2338+t2134+t2749; + t2585 = t2751+t2758; + t2161 = t2281*z; + t2584 = t2161+t2120+t2774; + t2583 = t2292*y+t2212+t2706; + t2582 = t2736+t2798; + t2220 = t2324*y; + t2581 = t2220+t2103+t2723; + t2580 = t2462+t1993+t2707; + t2579 = t2054+t2210+t2088+t2233; + t2578 = t2105+t2203+t2122+t2161; + t2577 = t2745+t2761; + t2576 = t2751+t2801; + t2575 = t2705+t2719; + t2574 = t2787+t2790; + t2573 = t2733+t2823; + t2572 = t2668+t2760; + t2571 = t1960+t2120+t2687; + t2570 = t2039+t2068+t2691; + t2118 = t2338*t2451; + t2569 = t2118+t2824; + t2568 = t2118+t2136+t2250*t2339+t2134+t2265; + t2567 = t2031+t2586; + t2566 = t2109+t2825; + t2565 = t2073+t2204+t2297*t2337+t2783+t2827; + t2564 = t2314*y+t2572; + t2563 = t2130+t2263+t2132+t2297*t2338+t2223+t2827; + t2562 = t2791+t2798+t2809; + t2225 = t2318*t2331; + t2561 = t2214+t2225+t2777+t2799; + t2560 = t2754+t2766+t2767; + t2559 = t2224+t2241+t2483+t2223+t2799; + t2558 = t2204+t2201+t2734+t2777; + t2557 = t2225+t2222+t2300*t2339+t2482+t2721; + t2506 = t2049+t2088; + t2556 = t2157+t2211+t2506+t2748+t2814; + t2555 = t2081+t2043+t2193+t2606; + t2554 = t2650+t2662; + t2553 = t2566+t2784; + t2502 = t2041+t2062; + t2552 = t2146+t2502+t2147+t2621; + t2551 = t2569+t2792; + t2550 = t2568+t2773; + t2549 = t1992+t2673+t2674; + t2548 = t2652+t2683; + t2547 = t2148+t2598+t2745; + t2546 = t2149+t1991+t2092+t2654+t2761; + t2545 = t2645+t2778+t2787; + t2544 = t2704+t2751+t2771+t2791; + t2543 = t2733+t2747+t2754+t2762; + t2418 = t2207+t2601; + t2542 = t2418+t2568+t2719+t2817; + t2517 = t2209+t2208; + t2514 = t2039+t2206; + t2505 = t2192+t2193; + t2501 = t2076+t2122; + t2500 = t2210+t2226; + t2498 = t2122+t2048; + t2497 = t2051+t2040; + t2496 = t2206+t1991; + t2494 = t2211+t2206; + t2490 = t2088+t2048; + t2488 = t2031+t2076; + t2484 = t2073+t2130; + t2479 = t2051+t2031; + t2472 = t2203+t2208; + t2471 = t2048+t2040; + t2455 = t2337*t2541; + t2450 = t2225+t2094+t2223; + t2449 = t2039+t2510; + t2448 = t2229+t2487; + t2447 = t2039+t2462; + t2446 = t2062+t2487; + t2445 = t2120+t2462; + t2444 = t2120+t2510; + t2443 = t2229+t2499; + t2442 = t2225+t2743; + t2441 = t2122+t2520; + t2440 = t2088+t2499; + t2439 = t2482+t2755; + t2438 = t2206+t2796; + t2266 = RATIONAL(292.0,6125.0); + t2437 = t2204+t2327*t2337+t2098+t2266; + t2436 = t2062+t2048+t2460; + t2269 = RATIONAL(592.0,6125.0); + t2435 = t2269+t2299*t2339+t2095+t2225; + t2434 = t2229+t2118+t2226+t2752; + t2433 = t2207+t2487+t2727; + t2432 = t2505+t2806; + t2431 = t2669+t2741; + t2430 = t2472+t2667; + t2429 = t2208+t2772; + t2428 = t2462+t2655; + t2427 = t2097+t2505+t2792; + t2426 = t2032+t2480+t2792; + t2425 = t2092+t2494+t2822; + t2424 = t2493+t2685; + t2423 = t2207+t2594; + t2422 = t2229+t2206+t2196+t2471; + t2421 = t2207+t2791+t2817; + t2420 = t2226+t2471+t2517; + t2419 = t2510+t2655; + t2417 = t2520+t2685; + t2416 = t2789+t2816; + t2415 = t2804+t2816; + t2414 = t2739+t2818; + t2413 = t2782+t2818; + t2412 = t1991+t1964+t2048+t2658+t2771; + t2411 = t2212+t1975+t2147+t2490+t2658; + t2410 = t1992+t2148+t2472+t2479+t2760; + t2409 = t2433+t2597; + t2408 = t2425+t2730+t2787; + t2251 = RATIONAL(431.0,29400.0); + t2407 = t2206+t2225+t2251*t2338+t2109+t2437+t2738; + t2182 = t2299*t2337; + t2285 = RATIONAL(68.0,3675.0); + t2406 = t2182+t2204+t2285*t2338+t2226+t2109+t2130+t2435; + t2405 = t2111+t2251*t2339+t2437+t2755+t2757; + t2404 = t2251*t2337+t2266+t2208+t2450+t2738+t2757; + t2403 = t2269+t2182+t2285*t2339+t2193+t2484+t2713+t2731; + t2402 = t2094+t2285*t2337+t2435+t2731+t2743; + t2151 = t2280*y; + t2401 = t2041+t2151+t2426+t2565; + t2400 = t2225+t2166+t2092+t2434+t2484+t2615; + t2399 = y*t2523+t1982+t2417+t2563; + t2215 = t2313*z; + t2398 = t2215+t2100+t2430+t2595+t2764; + t2397 = t2442+t2498+t2514+t2609+t2810; + t2396 = t2561+t2669+t2758+t2785; + t2395 = t2219+t2109+t2439+t2517+t2595+t2725; + t1970 = x*t2105; + t2394 = t1970+t2288*t2539+t2428+t2557; + t2154 = t2282*y; + t2393 = t2049+t2154+t2427+t2565; + t2392 = t2431+t2561+t2795; + t2159 = t2282*x; + t2391 = t2054+t2118+t2046+t2159+t2130+t2442+t2500+t2615; + t2390 = t2279*t2539+t1989+t2419+t2557; + t2389 = t2239+t2051+t2432+t2559; + t2388 = t1981+x*t2536+t2438+t2499+t2590+t2784; + t2387 = t2439+t2589+t2627+t2802; + t2386 = t1962+y*t2528+t2424+t2563; + t2385 = t2423+t2558+t2711; + t2384 = t2421+t2627+t2764+t2819; + t2383 = t2418+t2558+t2768; + t1971 = y*t2116; + t2382 = x*t2532+t1971+t2433+t2590+t2796; + t2381 = t2225+t2242+t2073+t2120+t2422+t2609; + t2380 = t2246+t2076+t2429+t2559; + t2379 = t2072+t2144+t2425+t2633+t2796; + t2378 = t2054+t2158+t2438+t2633+t2729+t2822; + t2377 = t2424+t2206+t2243+t2237+t2479+t2498+t2586+t2602+t2718; + t2376 = t2105+t2031+t2207+t2145+t2420+t2573+t2656+t2690+t2741; + t2375 = t2107+t2231+t2422+t2567+t2635+t2660+t2753; + t2374 = t2550+t2421+t2510+t2594+t2767+t2798; + t2197 = t2306*y; + t2373 = t2197+t2429+t2479+t2514+t2572+t2598+t2673; + t2372 = t2056+t2411+t2094+t2448+t2494+t2516+t2681+t2814; + t2371 = t2184+t2104+t2409+t2566+t2709+t2724+t2735; + t1953 = t2293*t2455; + t2370 = t1953+t2014+t2426+t2063+t2448+t2569+t2617+t2812; + t2369 = t2542+t2652+t2662; + t2368 = t2039+t2555+t2088+t2168+t2420+t2628+t2696; + t2367 = t2229+t2408+t2063+t2153+t2490+t2586+t2710+t2773; + t2366 = t2551+t2417+t2619+t2623+t2770; + t2365 = t2206+t2048+t2417+t2567+t2575+t2576+t2779; + t2364 = t2542+t2650+t2683; + t2363 = t2431+t2555+t2582+t2702+t2811; + t2362 = t2001+t2412+t2601+t2616+t2740+t2785; + t2361 = t2081+t2434+t2639+t2698+t2737+t2753+t2824; + t1954 = t2295*t2463; + t1950 = t2295*t2455; + t2360 = t1954+t1955+t2413+t1950+t2002+t2443+t2551+t2753; + t2359 = t2149+t2408+t2116+t2564+t2778+t2806; + t2358 = t2553+t2428+t2625+t2653+t2776; + t2357 = t2550+t2462+t2423+t2589+t2766+t2809; + t2356 = t2083+t2411+t2213+t2092+t2488+t2500+t2616+t2672; + t2355 = t2426+t2243+t2208+t2436+t2606+t2676+t2679; + t2354 = t2111+t2430+t2583+t2689+t2727+t2821+t2825; + t2353 = t2421+t2048+t2496+t2499+t2573+t2651+t2704+t2762; + t2352 = t2206+t1996+t2412+t2443+t2651+t2666+t2751; + t2351 = t2229+t2157+t1975+t2146+t2409+t2436+t2681+t2823; + t2350 = t2197+t2206+t2108+t2410+t2120+t2668+t2674+t2772; + t2349 = t2235+t2427+t2048+t2472+t2516+t2606+t2631+t2805; + t2348 = t1971+t2000+t1970+t1987+t2416+t2419+t2553; + t2347 = t2432+t2488+t2496+t2564+t2645+t2654; + t2346 = t2019+t2114+t2410+t2139+t2441+t2667+t2700+t2726; + t2315 = RATIONAL(-4.0,105.0); + t2305 = RATIONAL(4.0,105.0); + t2286 = RATIONAL(41.0,2100.0); + t2283 = RATIONAL(-41.0,2100.0); + t1990 = RATIONAL(-1.0,125.0)*t2538; + t1985 = RATIONAL(1.0,125.0)*t2538; + t1972 = t2253*t2541; + t1957 = RATIONAL(1.0,1000.0)*t2538; + t1952 = RATIONAL(-1.0,1000.0)*t2538; + coeffs_I->coeff_m2_m2_m2 = t1990+t2358+t2487+t2583+t2695+t2735; + coeffs_I->coeff_m1_m2_m2 = t2376+t2076+t1993+t2647+t2675+t2682; + coeffs_I->coeff_0_m2_m2 = t2395+t2581+t2688; + coeffs_I->coeff_p1_m2_m2 = t2356+t1984+t2040+t2600+t2675+t2701; + coeffs_I->coeff_p2_m2_m2 = t1985+t2348+t2583+t2588+t2625; + coeffs_I->coeff_m2_m1_m2 = t2373+t2546+t2580; + coeffs_I->coeff_m1_m1_m2 = t2355+t1986+t2631+t2640+t2680; + coeffs_I->coeff_0_m1_m2 = t2380+t2603+t2638; + coeffs_I->coeff_p1_m1_m2 = t2049+t1960+t2368+t2631+t2659+t2702; + coeffs_I->coeff_p2_m1_m2 = t2373+t2545+t2649; + coeffs_I->coeff_m2_0_m2 = t2394+t2613+t2761+t2833; + coeffs_I->coeff_m1_0_m2 = t2392+t2610+t2611; + coeffs_I->coeff_0_0_m2 = t2404+t2283*z+t2033+t2716; + coeffs_I->coeff_p1_0_m2 = t2396+t2579+t2611; + coeffs_I->coeff_p2_0_m2 = t2390+t2613+t2636; + coeffs_I->coeff_m2_p1_m2 = t2359+t2447+t2549+t2671; + coeffs_I->coeff_m1_p1_m2 = t2363+t1960+t2502+t2661+t2676+t2680; + coeffs_I->coeff_0_p1_m2 = t2389+t2603+t2618; + coeffs_I->coeff_p1_p1_m2 = t1986+t2041+t2368+t2582+t2661+t2679; + coeffs_I->coeff_p2_p1_m2 = t2347+t2449+t2549+t2677; + coeffs_I->coeff_m2_p2_m2 = t1971+t1985+t2358+t2634+t2689+t2816; + coeffs_I->coeff_m1_p2_m2 = t2376+t1984+t2051+t2592+t2684+t2700; + coeffs_I->coeff_0_p2_m2 = t2395+t2614+t2678; + coeffs_I->coeff_p1_p2_m2 = t2362+t1993+t2497+t2699+t2700+t2701; + coeffs_I->coeff_p2_p2_m2 = t1990+t1970+t2371+t1963+t2413+t2625; + coeffs_I->coeff_m2_m2_m1 = t2372+t2543+t2604; + coeffs_I->coeff_m1_m2_m1 = t2369+t2444+t2560+t2612; + coeffs_I->coeff_0_m2_m1 = t2387+t2620+t2643; + coeffs_I->coeff_p1_m2_m1 = t2357+t2554+t2571; + coeffs_I->coeff_p2_m2_m1 = t2352+t2552+t2632; + coeffs_I->coeff_m2_m1_m1 = t1986+t2377+t2575+t2635+t2694; + coeffs_I->coeff_m1_m1_m1 = t2173+t2360+t1952+t2032+t2593+t2602+t2831; + coeffs_I->coeff_0_m1_m1 = t2386+t2076+t2156+t2151+t2040+t2602; + coeffs_I->coeff_p1_m1_m1 = t1957+t2370+t2619+t2686+t2698; + coeffs_I->coeff_p2_m1_m1 = t2377+t1960+t2576+t2660+t2773+t2787; + coeffs_I->coeff_m2_0_m1 = t2397+t2641+t2644; + coeffs_I->coeff_m1_0_m1 = t2400+t2449+t2670+t2820; + coeffs_I->coeff_0_0_m1 = t2230+t2315*z+t2402+t2504; + coeffs_I->coeff_p1_0_m1 = t2391+t2447+t2670+t2763; + coeffs_I->coeff_p2_0_m1 = t2397+t2585+t2648; + coeffs_I->coeff_m2_p1_m1 = t1960+t2367+t2237+t2441+t2635+t2732+t2779; + coeffs_I->coeff_m1_p1_m1 = t1953+t1957+t1954+t2366+t2414+t2593; + coeffs_I->coeff_0_p1_m1 = t2399+t2156+t2154+t2497+t2629; + coeffs_I->coeff_p1_p1_m1 = t1956+t1952+t2366+t1950+t2415+t2617; + coeffs_I->coeff_p2_p1_m1 = t1986+t2235+t2365+t2237+t2501+t2629+t2660; + coeffs_I->coeff_m2_p2_m1 = t2353+t2556+t2632; + coeffs_I->coeff_m1_p2_m1 = t2374+t2548+t2571; + coeffs_I->coeff_0_p2_m1 = t2384+t2643+t2646; + coeffs_I->coeff_p1_p2_m1 = t2364+t2445+t2562+t2612; + coeffs_I->coeff_p2_p2_m1 = t2351+t2544+t2604; + coeffs_I->coeff_m2_m2_0 = t2382+t2220+t2056+t2630+t2807; + coeffs_I->coeff_m1_m2_0 = t2383+t2608+t2626; + coeffs_I->coeff_0_m2_0 = t2405+t2283*y+t2103+t2807; + coeffs_I->coeff_p1_m2_0 = t2385+t2622+t2626; + coeffs_I->coeff_p2_m2_0 = t2220+t2104+t2388+t2621+t2828; + coeffs_I->coeff_m2_m1_0 = t2379+t2605+t2790+t2832; + coeffs_I->coeff_m1_m1_0 = t2401+t2440+t2663+t2712; + coeffs_I->coeff_0_m1_0 = t2194+t2315*y+t2403+t2476; + coeffs_I->coeff_p1_m1_0 = t2401+t1972+t2159+t2446+t2693; + coeffs_I->coeff_p2_m1_0 = t2378+t2574+t2711+t2832; + coeffs_I->coeff_m2_0_0 = t2075+t2407+t2283*x+t2793; + coeffs_I->coeff_m1_0_0 = t2228+t2406+t2315*x+t2491; + coeffs_I->coeff_0_0_0 = RATIONAL(937.0,6125.0)+t2109+t2834*RATIONAL(-13.0 +,196.0)+t2450+t2713; + coeffs_I->coeff_p1_0_0 = t2305*x+t2210+t2406+t2474; + coeffs_I->coeff_p2_0_0 = t2286*x+t2407+t2131+t2729; + coeffs_I->coeff_m2_p1_0 = t2379+t2596+t2711+t2787; + coeffs_I->coeff_m1_p1_0 = t1958+t2393+t1972+t2088+t2487+t2663; + coeffs_I->coeff_0_p1_0 = t2305*y+t2192+t2403+t2456; + coeffs_I->coeff_p1_p1_0 = t2393+t2121+t2159+t2499+t2708+t2712; + coeffs_I->coeff_p2_p1_0 = t2378+t2596+t2605; + coeffs_I->coeff_m2_p2_0 = t2388+t2630+t2748+t2829; + coeffs_I->coeff_m1_p2_0 = t2385+t2608+t2637; + coeffs_I->coeff_0_p2_0 = t2286*y+t2405+t2216+t2706; + coeffs_I->coeff_p1_p2_0 = t2383+t2622+t2637; + coeffs_I->coeff_p2_p2_0 = t2382+t2597+t2828+t2829; + coeffs_I->coeff_m2_m2_p1 = t2372+t2544+t2607; + coeffs_I->coeff_m1_m2_p1 = t2369+t2447+t2562+t2642; + coeffs_I->coeff_0_m2_p1 = t2384+t2620+t2624; + coeffs_I->coeff_p1_m2_p1 = t2374+t2554+t2570; + coeffs_I->coeff_p2_m2_p1 = t2353+t2552+t2587; + coeffs_I->coeff_m2_m1_p1 = t2365+t2243+t2497+t2591+t2694+t2826; + coeffs_I->coeff_m1_m1_p1 = t1957+t2361+t1951+t1950+t2416+t2717+t2812; + coeffs_I->coeff_0_m1_p1 = t2399+t2152+t2151+t2501+t2591; + coeffs_I->coeff_p1_m1_p1 = t1954+t2370+t1952+t2520+t2639+t2770+t2818; + coeffs_I->coeff_p2_m1_p1 = t1986+t2375+t2065+t2243+t2520+t2574+t2773+ +t2779; + coeffs_I->coeff_m2_0_p1 = t2381+t2585+t2644; + coeffs_I->coeff_m1_0_p1 = t2400+t2445+t2703+t2763; + coeffs_I->coeff_0_0_p1 = t2305*z+t2196+t2402+t2461; + coeffs_I->coeff_p1_0_p1 = t2391+t2444+t2703+t2820; + coeffs_I->coeff_p2_0_p1 = t2381+t2641+t2648; + coeffs_I->coeff_m2_p1_p1 = t2107+t2367+t2040+t2576+t2657+t2691; + coeffs_I->coeff_m1_p1_p1 = t1953+t2361+t1952+t2623+t2686+t2739; + coeffs_I->coeff_0_p1_p1 = t2107+t2051+t2386+t2154+t2152+t2786+t2794; + coeffs_I->coeff_p1_p1_p1 = t1957+t2360+t2617+t2623+t2639; + coeffs_I->coeff_p2_p1_p1 = t2375+t1960+t2575+t2657+t2710+t2730; + coeffs_I->coeff_m2_p2_p1 = t2352+t2556+t2587; + coeffs_I->coeff_m1_p2_p1 = t2357+t2548+t2570; + coeffs_I->coeff_0_p2_p1 = t2387+t2624+t2646; + coeffs_I->coeff_p1_p2_p1 = t2364+t2449+t2560+t2642; + coeffs_I->coeff_p2_p2_p1 = t2351+t2543+t2607; + coeffs_I->coeff_m2_m2_p2 = t1970+t1981+t1985+t2354+t2414+t2653; + coeffs_I->coeff_m1_m2_p2 = t1984+t2362+t2501+t2656+t2664+t2682; + coeffs_I->coeff_0_m2_p2 = t2398+t2581+t2678; + coeffs_I->coeff_p1_m2_p2 = t2356+t2122+t1993+t2599+t2664+t2684; + coeffs_I->coeff_p2_m2_p2 = t1990+t1971+t1989+t2354+t2415+t2588; + coeffs_I->coeff_m2_m1_p2 = t2350+t2546+t2649; + coeffs_I->coeff_m1_m1_p2 = t2355+t1960+t2582+t2628+t2697; + coeffs_I->coeff_0_m1_p2 = t2380+t2584+t2618; + coeffs_I->coeff_p1_m1_p2 = t1986+t2363+t2506+t2659+t2696+t2697; + coeffs_I->coeff_p2_m1_p2 = t2350+t2545+t2580; + coeffs_I->coeff_m2_0_p2 = t2105+t2215+t2390+t2577+t2833; + coeffs_I->coeff_m1_0_p2 = t2396+t2578+t2610; + coeffs_I->coeff_0_0_p2 = t2404+t2286*z+t2105+t2774; + coeffs_I->coeff_p1_0_p2 = t2392+t2578+t2579; + coeffs_I->coeff_p2_0_p2 = t2215+t2203+t2394+t2636+t2725; + coeffs_I->coeff_m2_p1_p2 = t2359+t2444+t2547+t2677; + coeffs_I->coeff_m1_p1_p2 = t1986+t2349+t2446+t2628+t2676+t2800; + coeffs_I->coeff_0_p1_p2 = t2389+t2584+t2638; + coeffs_I->coeff_p1_p1_p2 = t1980+t1960+t2349+t2247+t2440+t2640+t2693; + coeffs_I->coeff_p2_p1_p2 = t2347+t2445+t2547+t2671; + coeffs_I->coeff_m2_p2_p2 = t1990+t2178+t2348+t2033+t2577+t2634+t2830; + coeffs_I->coeff_m1_p2_p2 = t2346+t1993+t2592+t2600+t2656; + coeffs_I->coeff_0_p2_p2 = t2398+t2614+t2688; + coeffs_I->coeff_p1_p2_p2 = t1984+t2346+t2599+t2647+t2699; + coeffs_I->coeff_p2_p2_p2 = t1985+t2371+t2462+t2695+t2714+t2776+t2821; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..27bf601 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dx.compute.c @@ -0,0 +1,977 @@ +fp t3003; +fp t3033; +fp t3046; +fp t3044; +fp t2963; +fp t3047; +fp t3043; +fp t2965; +fp t3026; +fp t3157; +fp t3183; +fp t3024; +fp t2865; +fp t3123; +fp t3334; +fp t3011; +fp t2973; +fp t3041; +fp t3333; +fp t3332; +fp t2985; +fp t3035; +fp t2952; +fp t3148; +fp t3139; +fp t3045; +fp t3187; +fp t3006; +fp t3331; +fp t3008; +fp t2987; +fp t2911; +fp t3137; +fp t3330; +fp t3012; +fp t2970; +fp t3329; +fp t3032; +fp t2900; +fp t2975; +fp t3328; +fp t3017; +fp t2960; +fp t2976; +fp t3274; +fp t3040; +fp t3327; +fp t3156; +fp t3326; +fp t3042; +fp t2974; +fp t3025; +fp t3325; +fp t2863; +fp t3324; +fp t3020; +fp t2956; +fp t2877; +fp t3181; +fp t3029; +fp t2882; +fp t3323; +fp t3191; +fp t2904; +fp t3016; +fp t3180; +fp t2851; +fp t3322; +fp t3151; +fp t3013; +fp t3321; +fp t2988; +fp t3320; +fp t3018; +fp t2951; +fp t2887; +fp t3319; +fp t2849; +fp t3185; +fp t2875; +fp t3318; +fp t3186; +fp t2879; +fp t3317; +fp t3190; +fp t2836; +fp t2843; +fp t3316; +fp t2923; +fp t2903; +fp t3315; +fp t3030; +fp t3314; +fp t3313; +fp t3038; +fp t3312; +fp t2979; +fp t3311; +fp t3184; +fp t2891; +fp t2883; +fp t3310; +fp t2948; +fp t3309; +fp t2964; +fp t3015; +fp t2870; +fp t3308; +fp t3307; +fp t3306; +fp t3034; +fp t2906; +fp t3305; +fp t2962; +fp t2868; +fp t2991; +fp t3304; +fp t3303; +fp t2837; +fp t2893; +fp t3302; +fp t2853; +fp t2873; +fp t2839; +fp t3301; +fp t3300; +fp t2947; +fp t3299; +fp t2854; +fp t3298; +fp t2957; +fp t2880; +fp t3297; +fp t3189; +fp t2909; +fp t2841; +fp t2954; +fp t2905; +fp t3296; +fp t2898; +fp t2990; +fp t2928; +fp t3295; +fp t2860; +fp t3294; +fp t3293; +fp t3292; +fp t3291; +fp t2852; +fp t3290; +fp t3164; +fp t3289; +fp t2847; +fp t2835; +fp t3288; +fp t2989; +fp t2912; +fp t2881; +fp t3287; +fp t2901; +fp t3286; +fp t2910; +fp t2966; +fp t2858; +fp t3285; +fp t3284; +fp t3283; +fp t2914; +fp t3282; +fp t3281; +fp t3280; +fp t3279; +fp t3149; +fp t2894; +fp t3278; +fp t3277; +fp t2986; +fp t2916; +fp t3276; +fp t2992; +fp t2929; +fp t3275; +fp t2876; +fp t3273; +fp t2922; +fp t2885; +fp t3272; +fp t3271; +fp t2897; +fp t3270; +fp t3269; +fp t3268; +fp t3267; +fp t3266; +fp t3265; +fp t2913; +fp t3264; +fp t3263; +fp t2980; +fp t3262; +fp t2878; +fp t2915; +fp t3118; +fp t3261; +fp t3002; +fp t3173; +fp t3260; +fp t3163; +fp t3259; +fp t3258; +fp t2892; +fp t3146; +fp t3257; +fp t2919; +fp t3256; +fp t2902; +fp t3255; +fp t2983; +fp t3254; +fp t3182; +fp t2869; +fp t3253; +fp t3028; +fp t3252; +fp t3001; +fp t3251; +fp t2995; +fp t3250; +fp t3249; +fp t3248; +fp t3000; +fp t3247; +fp t3246; +fp t3245; +fp t3244; +fp t3243; +fp t3242; +fp t3241; +fp t3240; +fp t2996; +fp t3239; +fp t2895; +fp t3238; +fp t3237; +fp t2984; +fp t2977; +fp t3134; +fp t3236; +fp t2866; +fp t3235; +fp t2993; +fp t3234; +fp t3233; +fp t3232; +fp t2997; +fp t3231; +fp t2994; +fp t3230; +fp t3229; +fp t3039; +fp t3228; +fp t2884; +fp t2842; +fp t2935; +fp t3227; +fp t2999; +fp t3226; +fp t3225; +fp t3224; +fp t3223; +fp t3222; +fp t3188; +fp t3221; +fp t3220; +fp t3219; +fp t3218; +fp t3217; +fp t3216; +fp t3215; +fp t2840; +fp t3214; +fp t3213; +fp t3212; +fp t3211; +fp t2890; +fp t2864; +fp t3210; +fp t2918; +fp t3126; +fp t3209; +fp t3208; +fp t3207; +fp t3150; +fp t3116; +fp t3206; +fp t3205; +fp t2838; +fp t3204; +fp t3203; +fp t3202; +fp t2934; +fp t3201; +fp t3200; +fp t3199; +fp t3198; +fp t3197; +fp t3196; +fp t3129; +fp t3195; +fp t3194; +fp t3193; +fp t3192; +fp t2888; +fp t3179; +fp t3178; +fp t3177; +fp t3176; +fp t3175; +fp t3174; +fp t3172; +fp t3171; +fp t3170; +fp t3169; +fp t3168; +fp t3167; +fp t3166; +fp t3165; +fp t3161; +fp t3160; +fp t3159; +fp t3158; +fp t3155; +fp t3154; +fp t3153; +fp t3147; +fp t3145; +fp t3144; +fp t3143; +fp t3142; +fp t3141; +fp t3140; +fp t3133; +fp t3132; +fp t3131; +fp t2943; +fp t3130; +fp t3128; +fp t3127; +fp t2978; +fp t3125; +fp t3124; +fp t3122; +fp t3121; +fp t3120; +fp t3119; +fp t3117; +fp t3115; +fp t3114; +fp t3113; +fp t3112; +fp t3111; +fp t3110; +fp t3109; +fp t3108; +fp t3107; +fp t3106; +fp t3105; +fp t3104; +fp t3103; +fp t3102; +fp t3101; +fp t3100; +fp t3099; +fp t2953; +fp t3098; +fp t3097; +fp t2982; +fp t3096; +fp t3095; +fp t3094; +fp t3093; +fp t3092; +fp t3091; +fp t3090; +fp t3089; +fp t2981; +fp t3088; +fp t3087; +fp t3086; +fp t3085; +fp t3084; +fp t3083; +fp t3082; +fp t3081; +fp t2850; +fp t3080; +fp t3079; +fp t3078; +fp t3077; +fp t3076; +fp t3075; +fp t3074; +fp t3073; +fp t3072; +fp t3071; +fp t3070; +fp t3069; +fp t3068; +fp t3067; +fp t3066; +fp t3065; +fp t3064; +fp t3063; +fp t3062; +fp t3061; +fp t3060; +fp t3059; +fp t3058; +fp t3057; +fp t3056; +fp t3055; +fp t3054; +fp t3053; +fp t3052; +fp t3051; +fp t2907; + t3003 = RATIONAL(47.0,5250.0); + t3033 = RATIONAL(1.0,150.0); + t3046 = x*x; + t3044 = t3046*x; + t2963 = t3033*t3044; + t3047 = y*y; + t3043 = t3047*y; + t2965 = RATIONAL(-1.0,100.0)*t3046; + t3026 = RATIONAL(-1.0,300.0); + t3157 = t3026*t3043+y*t2965; + t3183 = x*t3047; + t3024 = RATIONAL(2.0,245.0); + t2865 = t3024*t3183; + t3123 = t2963+t2865+t3157; + t3334 = t3123+t3003*y; + t3011 = RATIONAL(-1.0,700.0); + t2973 = t3011*t3047; + t3041 = RATIONAL(1.0,42.0); + t3333 = t2973+t3041; + t3332 = t2973+RATIONAL(17.0,525.0); + t2985 = RATIONAL(-137.0,5250.0); + t3035 = RATIONAL(1.0,300.0); + t2952 = RATIONAL(1.0,100.0)*t3046; + t3148 = t3035*t3043+y*t2952; + t3139 = t2985*y+t3148; + t3045 = z*z; + t3187 = y*t3045; + t3006 = RATIONAL(1.0,1400.0); + t3331 = t3006*t3187+t3139; + t3008 = RATIONAL(-1.0,1400.0); + t2987 = RATIONAL(137.0,5250.0); + t2911 = t2987*y; + t3137 = t2911+t3157; + t3330 = t3008*t3187+t3137; + t3012 = RATIONAL(1.0,700.0); + t2970 = t3012*t3047; + t3329 = RATIONAL(-17.0,525.0)+t2970; + t3032 = RATIONAL(1.0,245.0); + t2900 = t3032*t3183; + t2975 = RATIONAL(1.0,25.0)*t3044; + t3328 = t2900+t2975; + t3017 = RATIONAL(-1.0,350.0); + t2960 = t3017*t3045; + t2976 = RATIONAL(1.0,50.0)*t3046; + t3274 = t2976+t2970; + t3040 = RATIONAL(-1.0,42.0); + t3327 = t2960+t3274+t3040; + t3156 = t3046*RATIONAL(-1.0,200.0); + t3326 = y*t3156+t3033*t3043; + t3042 = t3045*z; + t2974 = RATIONAL(-1.0,50.0)*t3046; + t3025 = RATIONAL(1.0,600.0); + t3325 = t3025*t3042+z*t2974; + t2863 = RATIONAL(311.0,14700.0)*x; + t3324 = RATIONAL(29.0,2100.0)+t2863; + t3020 = RATIONAL(1.0,350.0); + t2956 = t3020*t3045; + t2877 = y*t2956; + t3181 = x*t3045; + t3029 = RATIONAL(-1.0,245.0); + t2882 = t3029*t3181; + t3323 = t2877+t2882; + t3191 = y*z; + t2904 = RATIONAL(-1.0,500.0)*t3191; + t3016 = RATIONAL(-1.0,175.0); + t3180 = x*t3016; + t2851 = y*t3180; + t3322 = t2904+t2851; + t3151 = t3046*RATIONAL(1.0,200.0); + t3013 = RATIONAL(-1.0,150.0); + t3321 = z*t3151+t3013*t3042; + t2988 = RATIONAL(-187.0,7000.0); + t3320 = t2877+t2988*y; + t3018 = RATIONAL(1.0,175.0); + t2951 = t3018*t3045; + t2887 = y*t2951; + t3319 = t2887+t3139; + t2849 = RATIONAL(1.0,250.0)*t3191; + t3185 = x*RATIONAL(2.0,175.0); + t2875 = z*t3185; + t3318 = t2849+t2875; + t3186 = x*t3018; + t2879 = y*t3186; + t3317 = t2879+t2904; + t3190 = x*t3191; + t2836 = t3012*t3190; + t2843 = RATIONAL(-1.0,1000.0)*t3191; + t3316 = t2836+t2843; + t2923 = RATIONAL(211.0,3675.0)*x; + t2903 = z*t2973; + t3315 = t2923+t2903; + t3030 = RATIONAL(-1.0,600.0); + t3314 = t3030*t3043+y*t2976; + t3313 = t2976+RATIONAL(-8.0,525.0); + t3038 = RATIONAL(-2.0,75.0); + t3312 = t2976+t3038; + t2979 = RATIONAL(4.0,75.0)*x; + t3311 = t2900+t2979; + t3184 = x*RATIONAL(-2.0,175.0); + t2891 = z*t3184; + t2883 = RATIONAL(-1.0,250.0)*t3191; + t3310 = t2891+t2883; + t2948 = t3018*t3047; + t3309 = t2952+t2948; + t2964 = t3016*t3045; + t3015 = RATIONAL(-2.0,245.0); + t2870 = t3015*t3181; + t3308 = t2964+t2870; + t3307 = t2879+t2883; + t3306 = t3025*t3043+y*t2974; + t3034 = RATIONAL(1.0,490.0); + t2906 = t3034*t3183; + t3305 = RATIONAL(166.0,3675.0)*x+t2906; + t2962 = t3017*t3047; + t2868 = z*t2962; + t2991 = RATIONAL(187.0,7000.0); + t3304 = t2868+t2991*z; + t3303 = t2974+t2956; + t2837 = y*t2891; + t2893 = RATIONAL(-1.0,125.0)*t3191; + t3302 = t2837+t2893; + t2853 = RATIONAL(1.0,125.0)*t3191; + t2873 = y*t3185; + t2839 = z*t2873; + t3301 = t2853+t2839; + t3300 = t2964+t2965; + t2947 = t3011*t3045; + t3299 = t2974+t2947; + t2854 = y*t2964; + t3298 = t3137+t2854; + t2957 = t3020*t3047; + t2880 = z*t2957; + t3297 = t2988*z+t2880; + t3189 = x*t3020; + t2909 = y*t3189; + t2841 = z*t2909; + t2954 = t3012*t3045; + t2905 = y*t2954; + t3296 = t2841+t2905; + t2898 = z*t2970; + t2990 = RATIONAL(-167.0,7000.0); + t2928 = t2990*z; + t3295 = t2898+t2928; + t2860 = y*t2960; + t3294 = t2860+t2991*y; + t3293 = t3013*t3043+y*t3151; + t3292 = t3157+t2906; + t3291 = t2923+t2898; + t2852 = RATIONAL(-169.0,14700.0)*x; + t3290 = t2852+t2880; + t3164 = t3026*t3042+z*t2965; + t3289 = t3003*z+t3164; + t2847 = RATIONAL(1.0,1000.0)*t3191; + t2835 = t3011*t3190; + t3288 = t2847+t2835; + t2989 = RATIONAL(-107.0,7000.0); + t2912 = t2989*y; + t2881 = t3029*t3183; + t3287 = t2912+t2881; + t2901 = RATIONAL(1.0,500.0)*t3191; + t3286 = t2901+t2851; + t2910 = t2987*z; + t2966 = t3016*t3047; + t2858 = z*t2966; + t3285 = t2910+t3164+t2858; + t3284 = t2863+RATIONAL(-29.0,2100.0); + t3283 = t2849+t2851; + t2914 = RATIONAL(151.0,3675.0)*x; + t3282 = t2900+t2914; + t3281 = z*t2976+t3030*t3042; + t3280 = t2843+t2835; + t3279 = t2962+t2956; + t3149 = z*t2952+t3035*t3042; + t2894 = t3034*t3181; + t3278 = t3149+t2894; + t3277 = t2836+t2847; + t2986 = RATIONAL(107.0,7000.0); + t2916 = t2986*y; + t3276 = t2877+t2916; + t2992 = RATIONAL(167.0,7000.0); + t2929 = t2992*z; + t3275 = t2903+t2929; + t2876 = t3015*t3183; + t3273 = t2948+t2876; + t2922 = t2985*z; + t2885 = z*t2948; + t3272 = t2885+t2922+t3149; + t3271 = t3033*t3042+z*t3156; + t2897 = y*t2947; + t3270 = t2882+t2897; + t3269 = t2966+t2865; + t3268 = t2960+t2974; + t3267 = t2901+t2879; + t3266 = t2951+t2952; + t3265 = t2976+t2954; + t2913 = t2989*z; + t3264 = t2868+t2913; + t3263 = RATIONAL(-33.0,490.0)*x+t2870+t2876+t2975; + t2980 = RATIONAL(-9.0,98.0)*x; + t3262 = t2980+t2870+t3328; + t2878 = RATIONAL(191.0,14700.0)*x; + t2915 = t2992*y; + t3118 = t2963+t2881+t3293; + t3261 = t2878+t2915+t3118; + t3002 = RATIONAL(-17.0,2100.0); + t3173 = t2957+t2956; + t3260 = t3002+t3173+t2965; + t3163 = t2960+t2962; + t3259 = t3163+t3313; + t3258 = t2875+t3272; + t2892 = t3032*t3181; + t3146 = t2892+t2975; + t3257 = t3146+t2980+t2876; + t2919 = t2986*z; + t3256 = t2919+t3321; + t2902 = z*t3180; + t3255 = t2902+t3303; + t2983 = RATIONAL(229.0,10500.0); + t3254 = t2983*z+t3291; + t3182 = x*t3017; + t2869 = y*t3182; + t3253 = t2869+t3331; + t3028 = RATIONAL(8.0,525.0); + t3252 = t3173+t2974+t3028; + t3001 = RATIONAL(-17.0,5250.0); + t3251 = t3001*y+t3148+t2854; + t2995 = RATIONAL(-47.0,5250.0); + t3250 = t2882+t3148+t2865+t2995*y; + t3249 = t2869+t3330; + t3248 = t3146+t2900+RATIONAL(-57.0,490.0)*x; + t3000 = RATIONAL(17.0,2100.0); + t3247 = t3000+t3163+t2952; + t3246 = t2983*y+t3292; + t3245 = t2909+t3331; + t3244 = t2852+t3276; + t3243 = t2891+t3285; + t3242 = t2909+t3330; + t3241 = t2852+t3271; + t3240 = t2881+t3314; + t2996 = RATIONAL(17.0,5250.0); + t3239 = t2887+t3157+t2996*y; + t2895 = z*t3189; + t3238 = t2895+t3299; + t3237 = t2882+t3325; + t2984 = RATIONAL(-229.0,10500.0); + t2977 = t3038*t3044; + t3134 = t2977+t2906+t3148; + t3236 = t2923+t2984*y+t3134; + t2866 = z*t3182; + t3235 = t2866+t3265; + t2993 = RATIONAL(-19.0,2100.0); + t3234 = t2962+t2993+t3266; + t3233 = t3320+t3326; + t3232 = t2915+t2897+t3306; + t2997 = RATIONAL(-37.0,1050.0); + t3231 = t2957+t2997+t3265; + t2994 = RATIONAL(19.0,2100.0); + t3230 = t2957+t2994+t3300; + t3229 = t3271+t3297; + t3039 = RATIONAL(2.0,75.0); + t3228 = t2974+t3039+t3279; + t2884 = z*t3186; + t2842 = y*t2884; + t2935 = t2995*z; + t3227 = t3149+t2868+t2842+t2935; + t2999 = RATIONAL(37.0,1050.0); + t3226 = t2999+t2962+t3299; + t3225 = t2957+t2960+t3312; + t3224 = t3304+t3321; + t3223 = t2966+t3026+t3266; + t3222 = t2960+t2993+t3309; + t3188 = z*t3047; + t3221 = t3008*t3188+t2910+t3305; + t3220 = t2999+t2973+t3268; + t3219 = t3293+t3294; + t3218 = t3271+t3295; + t3217 = t3035+t2948+t3300; + t3216 = t2965+t2966+t2994+t2956; + t3215 = t3279+t3312; + t2840 = z*t2851; + t3214 = t2880+t2840+t3289; + t3213 = t2956+t2997+t3274; + t3212 = t2957+t3039+t3268; + t3211 = t3275+t3321; + t2890 = t3024*t3181; + t2864 = RATIONAL(-529.0,14700.0)*x; + t3210 = RATIONAL(-11.0,420.0)+t2890+t2864+t2951; + t2918 = RATIONAL(256.0,3675.0)*x; + t3126 = t2977+t3237; + t3209 = t2880+t2919+t2918+t3126; + t3208 = t2884+t3303+t3333; + t3207 = t2909+t3327; + t3150 = t2963+t2965; + t3116 = t2890+t2964+t3150; + t3206 = t2864+RATIONAL(11.0,420.0)+t3116+t3269; + t3205 = t3040+t2962+t3235; + t2838 = z*t2869; + t3204 = t2838+t3232; + t3203 = t2849+t3222; + t3202 = t2860+t2842+t2912+t3314; + t2934 = t2990*y; + t3201 = t2878+t2934+t2905+t3326; + t3200 = t2849+t3216; + t3199 = t2883+t3216; + t3198 = t2883+t3222; + t3197 = t2934+t3296+t3314; + t3196 = t2840+t3276+t3306; + t3129 = t2977+t3278; + t3195 = t3006*t3188+t2922+t3129+t3305; + t3194 = t3255+t3333; + t3193 = t2869+t3327; + t3192 = t2957+t3041+t3238; + t2888 = y*t3184; + t3179 = t2839+t2888; + t3178 = t2891+t2851; + t3177 = t2963+t2952; + t3176 = t2873+t2884; + t3175 = t2837+t2888; + t3174 = t2838+t2884; + t3172 = t2957+t2881; + t3171 = t2888+t2884; + t3170 = t2875+t2851; + t3169 = t2879+t2875; + t3168 = t2839+t2873; + t3167 = t2860+t2963; + t3166 = t2884+t2851; + t3165 = t2891+t2879; + t3161 = t2838+t2902; + t3160 = t2902+t2879; + t3159 = t2902+t2841; + t3158 = t2888+t2902; + t3155 = t2879+t2884; + t3154 = t2977+t2892; + t3153 = t2837+t2873; + t3147 = t2865+t2975; + t3145 = t2902+t2851; + t3144 = t2890+t2876; + t3143 = t2902+t2873; + t3142 = t2960+t2882; + t3141 = t2881+t2962; + t3140 = t2841+t2884; + t3133 = t2977+t2881+t3306; + t3132 = t2900+RATIONAL(136.0,3675.0)*x+t3154; + t3131 = t2951+t2870+t3150; + t2943 = RATIONAL(-61.0,490.0)*x; + t3130 = t2890+t2943+t3328; + t3128 = t2865+t2948+t3177; + t3127 = t2977+t2894+t3164; + t2978 = RATIONAL(-1.0,10.0)*x; + t3125 = t2978+t2870+t3147; + t3124 = t2978+t2975+t3144; + t3122 = t2943+t2865+t3146; + t3121 = t2977+t2882+t3281; + t3120 = t3141+t3177; + t3119 = t2966+t2876+t3177; + t3117 = t2963+t2890+t3149; + t3115 = t2882+t2956+t3150; + t3114 = t2842+t3167+t3290; + t3113 = t2842+t3264+t3323; + t3112 = t2884+t3257; + t3111 = t2840+t3262; + t3110 = t2891+t3263; + t3109 = t2838+t3270+t3295; + t3108 = t2851+t3248; + t3107 = t2841+t3270+t3275; + t3106 = t2838+t2977+t2905+t3315; + t3105 = t2860+t2868+t2840+t3287; + t3104 = t2902+t3257; + t3103 = t2879+t3248; + t3102 = t2875+t3263; + t3101 = t2842+t3262; + t3100 = t2866+t3127+t3299; + t3099 = t2895+t3127+t3265; + t2953 = t3026*x; + t3098 = t2953+t3026+t3128+t3308; + t3097 = t3115+t3273+t3284; + t2982 = RATIONAL(-289.0,10500.0); + t3096 = t2982*y+t2914+t2892+t2905+t3134; + t3095 = t2963+t2953+t2996*z+t2885+t3144+t3164; + t3094 = t3126+t3304+t3311; + t3093 = t3121+t3297+t3311; + t3092 = t2982*z+t2898+t3129+t3282; + t3091 = t3131+t3172+t3284; + t3090 = t3035+t2953+t3131+t3269; + t3089 = t3119+t3142+t3324; + t2981 = RATIONAL(289.0,10500.0); + t3088 = t2914+t2981*y+t2897+t3154+t3292; + t3087 = t3120+t3308+t3324; + t3086 = t3001*z+t2953+t2876+t2858+t3117; + t3085 = t2903+t2981*z+t3127+t3282; + t3084 = t2979+t3154+t3240+t3320; + t3083 = t2892+t2979+t3133+t3294; + t3082 = t2994+t2851+t3116+t3172+t3244+t3293; + t3081 = t2918+t2916+t3113+t3133+t3281; + t2850 = t2984*z; + t3080 = t2934+t2850+t3106+t3240+t3278; + t3079 = t2928+t3121+t3246+t3291+t3296; + t3078 = t2891+t3206+t3272; + t3077 = t2960+t2884+t3141+t3209+t3313; + t3076 = t3109+t3261+t3271; + t3075 = t3100+t3221+t3332; + t3074 = t2890+t3114+t3287+t3289+t3326; + t3073 = t2840+t3167+t3241+t3250+t3264; + t3072 = t3107+t3236+t3325; + t3071 = t3028+t3172+t3209+t3255; + t3070 = t2881+t2841+t2850+t3129+t3232+t3315; + t3069 = t3107+t3261+t3321; + t3068 = t2840+t3256+t3290+t3323+t3334; + t3067 = t2918+t2913+t3105+t3121+t3314; + t3066 = t3113+t3241+t3334; + t3065 = t3195+t3238+t3332; + t3064 = t3040+t3099+t3141+t3254; + t3063 = t2890+t2879+t3118+t3234+t3244; + t3062 = t3109+t3236+t3281; + t3061 = t2875+t3206+t3285; + t3060 = t2929+t3106+t3237+t3246; + t3059 = t2873+t3128+t3210+t3319; + t3058 = t3000+t2851+t3120+t3142+t3201; + t3057 = t3195+t3235+t3329; + t3056 = t2852+t2935+t3105+t3117+t3326; + t3055 = t3041+t3100+t3172+t3254; + t3054 = t3114+t3250+t3256; + t3053 = t2888+t2854+t2911+t3123+t3210+t3309; + t3052 = t3002+t2879+t3115+t3172+t3201; + t3051 = t3099+t3221+t3329; + t2907 = RATIONAL(431.0,14700.0)*x; + coeffs_dx->coeff_m2_m2_m2 = t2893+t3078+t3179+t3319; + coeffs_dx->coeff_m1_m2_m2 = t3077+t3196+t3307; + coeffs_dx->coeff_0_m2_m2 = t3102+t3153; + coeffs_dx->coeff_p1_m2_m2 = t3067+t2849+t3155+t3252; + coeffs_dx->coeff_p2_m2_m2 = t3053+t3243+t3301; + coeffs_dx->coeff_m2_m1_m2 = t3082+t3227+t3310; + coeffs_dx->coeff_m1_m1_m2 = t3060+t2904+t2884+t3207; + coeffs_dx->coeff_0_m1_m2 = t3111+t3169; + coeffs_dx->coeff_p1_m1_m2 = t2909+t2901+t3062+t3208; + coeffs_dx->coeff_p2_m1_m2 = t3074+t2849+t3178+t3234; + coeffs_dx->coeff_m2_0_m2 = t2891+t3086+t3217; + coeffs_dx->coeff_m1_0_m2 = t2884+t3094+t3225; + coeffs_dx->coeff_0_0_m2 = t2875+t3125; + coeffs_dx->coeff_p1_0_m2 = t2884+t3093+t3228; + coeffs_dx->coeff_p2_0_m2 = t2891+t3095+t3223; + coeffs_dx->coeff_m2_p1_m2 = t3056+t2849+t3165+t3230; + coeffs_dx->coeff_m1_p1_m2 = t3072+t2901+t2884+t3193; + coeffs_dx->coeff_0_p1_m2 = t3101+t3170; + coeffs_dx->coeff_p1_p1_m2 = t2869+t2904+t3079+t3208; + coeffs_dx->coeff_p2_p1_m2 = t3063+t3214+t3310; + coeffs_dx->coeff_m2_p2_m2 = t2853+t3078+t3153+t3298; + coeffs_dx->coeff_m1_p2_m2 = t3077+t3202+t3283; + coeffs_dx->coeff_0_p2_m2 = t3102+t3179; + coeffs_dx->coeff_p1_p2_m2 = t2883+t3081+t3166+t3252; + coeffs_dx->coeff_p2_p2_m2 = t3059+t3243+t3302; + coeffs_dx->coeff_m2_m2_m1 = t3054+t3158+t3199; + coeffs_dx->coeff_m1_m2_m1 = t3064+t3204+t3317; + coeffs_dx->coeff_0_m2_m1 = t2873+t2840+t3112; + coeffs_dx->coeff_p1_m2_m1 = t3080+t3192+t3267; + coeffs_dx->coeff_p2_m2_m1 = t3066+t3158+t3203; + coeffs_dx->coeff_m2_m1_m1 = t2904+t3069+t3145+t3260; + coeffs_dx->coeff_m1_m1_m1 = t3051+t3242+t3280; + coeffs_dx->coeff_0_m1_m1 = t3103+t3174; + coeffs_dx->coeff_p1_m1_m1 = t3065+t3245+t3288; + coeffs_dx->coeff_p2_m1_m1 = t2901+t3058+t3159+t3218; + coeffs_dx->coeff_m2_0_m1 = t2902+t3097+t3224; + coeffs_dx->coeff_m1_0_m1 = t2895+t3085+t3231; + coeffs_dx->coeff_0_0_m1 = t2884+t3122; + coeffs_dx->coeff_p1_0_m1 = t2895+t3092+t3226; + coeffs_dx->coeff_p2_0_m1 = t2902+t3089+t3229; + coeffs_dx->coeff_m2_p1_m1 = t2901+t3052+t3161+t3211; + coeffs_dx->coeff_m1_p1_m1 = t3051+t3253+t3277; + coeffs_dx->coeff_0_p1_m1 = t3108+t3140; + coeffs_dx->coeff_p1_p1_m1 = t3065+t3249+t3316; + coeffs_dx->coeff_p2_p1_m1 = t3076+t2904+t3160+t3247; + coeffs_dx->coeff_m2_p2_m1 = t3068+t3143+t3200; + coeffs_dx->coeff_m1_p2_m1 = t3064+t3197+t3286; + coeffs_dx->coeff_0_p2_m1 = t2888+t2842+t3112; + coeffs_dx->coeff_p1_p2_m1 = t3070+t3192+t3322; + coeffs_dx->coeff_p2_p2_m1 = t3073+t3143+t3198; + coeffs_dx->coeff_m2_m2_0 = t2888+t3090+t3251; + coeffs_dx->coeff_m1_m2_0 = t2879+t3083+t3215; + coeffs_dx->coeff_0_m2_0 = t2873+t3124; + coeffs_dx->coeff_p1_m2_0 = t2879+t3084+t3212; + coeffs_dx->coeff_p2_m2_0 = t2888+t3098+t3239; + coeffs_dx->coeff_m2_m1_0 = t2851+t3091+t3219; + coeffs_dx->coeff_m1_m1_0 = t2909+t3088+t3213; + coeffs_dx->coeff_0_m1_0 = t2879+t3130; + coeffs_dx->coeff_p1_m1_0 = t2909+t3096+t3220; + coeffs_dx->coeff_p2_m1_0 = t2851+t3087+t3233; + coeffs_dx->coeff_m2_0_0 = RATIONAL(-41.0,2100.0)+t2907+t3131+t3273; + coeffs_dx->coeff_m1_0_0 = RATIONAL(-4.0,105.0)+t2976+t3132+t3173; + coeffs_dx->coeff_0_0_0 = t2890+RATIONAL(-13.0,98.0)*x+t3147; + coeffs_dx->coeff_p1_0_0 = t2974+RATIONAL(4.0,105.0)+t3132+t3163; + coeffs_dx->coeff_p2_0_0 = RATIONAL(41.0,2100.0)+t2907+t3119+t3308; + coeffs_dx->coeff_m2_p1_0 = t2879+t3091+t3233; + coeffs_dx->coeff_m1_p1_0 = t2869+t3096+t3213; + coeffs_dx->coeff_0_p1_0 = t2851+t3130; + coeffs_dx->coeff_p1_p1_0 = t2869+t3088+t3220; + coeffs_dx->coeff_p2_p1_0 = t2879+t3087+t3219; + coeffs_dx->coeff_m2_p2_0 = t2873+t3090+t3239; + coeffs_dx->coeff_m1_p2_0 = t2851+t3084+t3215; + coeffs_dx->coeff_0_p2_0 = t2888+t3124; + coeffs_dx->coeff_p1_p2_0 = t2851+t3083+t3212; + coeffs_dx->coeff_p2_p2_0 = t2873+t3098+t3251; + coeffs_dx->coeff_m2_m2_p1 = t3073+t3171+t3200; + coeffs_dx->coeff_m1_m2_p1 = t3070+t3205+t3267; + coeffs_dx->coeff_0_m2_p1 = t2842+t2873+t3104; + coeffs_dx->coeff_p1_m2_p1 = t3055+t3197+t3317; + coeffs_dx->coeff_p2_m2_p1 = t3068+t3171+t3198; + coeffs_dx->coeff_m2_m1_p1 = t2901+t3076+t3166+t3260; + coeffs_dx->coeff_m1_m1_p1 = t3057+t3242+t3277; + coeffs_dx->coeff_0_m1_p1 = t3103+t3159; + coeffs_dx->coeff_p1_m1_p1 = t3075+t3245+t3316; + coeffs_dx->coeff_p2_m1_p1 = t2904+t3058+t3174+t3211; + coeffs_dx->coeff_m2_0_p1 = t2884+t3097+t3229; + coeffs_dx->coeff_m1_0_p1 = t2866+t3092+t3231; + coeffs_dx->coeff_0_0_p1 = t2902+t3122; + coeffs_dx->coeff_p1_0_p1 = t2866+t3085+t3226; + coeffs_dx->coeff_p2_0_p1 = t2884+t3089+t3224; + coeffs_dx->coeff_m2_p1_p1 = t3052+t2904+t3140+t3218; + coeffs_dx->coeff_m1_p1_p1 = t3057+t3253+t3280; + coeffs_dx->coeff_0_p1_p1 = t3108+t3161; + coeffs_dx->coeff_p1_p1_p1 = t3075+t3249+t3288; + coeffs_dx->coeff_p2_p1_p1 = t2901+t3069+t3155+t3247; + coeffs_dx->coeff_m2_p2_p1 = t3066+t3176+t3199; + coeffs_dx->coeff_m1_p2_p1 = t3080+t3205+t3322; + coeffs_dx->coeff_0_p2_p1 = t2840+t2888+t3104; + coeffs_dx->coeff_p1_p2_p1 = t3055+t3204+t3286; + coeffs_dx->coeff_p2_p2_p1 = t3054+t3176+t3203; + coeffs_dx->coeff_m2_m2_p2 = t3061+t2853+t3175+t3319; + coeffs_dx->coeff_m1_m2_p2 = t2849+t3081+t3160+t3259; + coeffs_dx->coeff_0_m2_p2 = t3110+t3168; + coeffs_dx->coeff_p1_m2_p2 = t3071+t3202+t3307; + coeffs_dx->coeff_p2_m2_p2 = t3053+t3258+t3302; + coeffs_dx->coeff_m2_m1_p2 = t3082+t3214+t3318; + coeffs_dx->coeff_m1_m1_p2 = t2901+t2902+t3079+t3207; + coeffs_dx->coeff_0_m1_p2 = t3101+t3165; + coeffs_dx->coeff_p1_m1_p2 = t2909+t3072+t2904+t3194; + coeffs_dx->coeff_p2_m1_p2 = t3056+t2883+t3170+t3234; + coeffs_dx->coeff_m2_0_p2 = t2875+t3095+t3217; + coeffs_dx->coeff_m1_0_p2 = t2902+t3093+t3225; + coeffs_dx->coeff_0_0_p2 = t2891+t3125; + coeffs_dx->coeff_p1_0_p2 = t2902+t3094+t3228; + coeffs_dx->coeff_p2_0_p2 = t2875+t3086+t3223; + coeffs_dx->coeff_m2_p1_p2 = t3074+t2883+t3169+t3230; + coeffs_dx->coeff_m1_p1_p2 = t3062+t2902+t2904+t3193; + coeffs_dx->coeff_0_p1_p2 = t3111+t3178; + coeffs_dx->coeff_p1_p1_p2 = t3060+t2869+t2901+t3194; + coeffs_dx->coeff_p2_p1_p2 = t3063+t3227+t3318; + coeffs_dx->coeff_m2_p2_p2 = t3061+t2893+t3168+t3298; + coeffs_dx->coeff_m1_p2_p2 = t3067+t2883+t3145+t3259; + coeffs_dx->coeff_0_p2_p2 = t3110+t3175; + coeffs_dx->coeff_p1_p2_p2 = t3071+t3196+t3283; + coeffs_dx->coeff_p2_p2_p2 = t3059+t3258+t3301; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..e1a20d4 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,593 @@ +fp t4416; +fp t4431; +fp t4367; +fp t4398; +fp t4594; +fp t4423; +fp t4389; +fp t4360; +fp t4541; +fp t4353; +fp t4593; +fp t4411; +fp t4380; +fp t4418; +fp t4429; +fp t4381; +fp t4395; +fp t4592; +fp t4408; +fp t4379; +fp t4420; +fp t4382; +fp t4591; +fp t4391; +fp t4412; +fp t4370; +fp t4590; +fp t4539; +fp t4347; +fp t4589; +fp t4409; +fp t4372; +fp t4588; +fp t4430; +fp t4388; +fp t4587; +fp t4540; +fp t4348; +fp t4586; +fp t4368; +fp t4376; +fp t4585; +fp t4396; +fp t4584; +fp t4357; +fp t4390; +fp t4364; +fp t4583; +fp t4361; +fp t4393; +fp t4582; +fp t4417; +fp t4581; +fp t4363; +fp t4580; +fp t4375; +fp t4579; +fp t4402; +fp t4410; +fp t4378; +fp t4355; +fp t4578; +fp t4415; +fp t4373; +fp t4577; +fp t4387; +fp t4352; +fp t4576; +fp t4385; +fp t4575; +fp t4574; +fp t4573; +fp t4414; +fp t4374; +fp t4572; +fp t4358; +fp t4571; +fp t4401; +fp t4570; +fp t4569; +fp t4384; +fp t4568; +fp t4421; +fp t4386; +fp t4567; +fp t4566; +fp t4365; +fp t4565; +fp t4564; +fp t4563; +fp t4400; +fp t4562; +fp t4354; +fp t4561; +fp t4560; +fp t4559; +fp t4558; +fp t4557; +fp t4426; +fp t4556; +fp t4362; +fp t4555; +fp t4394; +fp t4554; +fp t4369; +fp t4553; +fp t4552; +fp t4551; +fp t4527; +fp t4550; +fp t4549; +fp t4548; +fp t4517; +fp t4547; +fp t4392; +fp t4546; +fp t4516; +fp t4545; +fp t4366; +fp t4544; +fp t4543; +fp t4497; +fp t4542; +fp t4383; +fp t4377; +fp t4538; +fp t4537; +fp t4350; +fp t4536; +fp t4535; +fp t4533; +fp t4532; +fp t4371; +fp t4530; +fp t4529; +fp t4528; +fp t4526; +fp t4525; +fp t4524; +fp t4523; +fp t4356; +fp t4522; +fp t4521; +fp t4520; +fp t4519; +fp t4518; +fp t4515; +fp t4514; +fp t4513; +fp t4512; +fp t4510; +fp t4509; +fp t4508; +fp t4507; +fp t4359; +fp t4506; +fp t4505; +fp t4504; +fp t4503; +fp t4502; +fp t4501; +fp t4500; +fp t4499; +fp t4498; +fp t4496; +fp t4495; +fp t4405; +fp t4494; +fp t4493; +fp t4492; +fp t4491; +fp t4490; +fp t4489; +fp t4351; +fp t4488; +fp t4487; +fp t4486; +fp t4485; +fp t4484; +fp t4483; +fp t4482; +fp t4481; +fp t4480; +fp t4349; +fp t4479; +fp t4478; +fp t4477; +fp t4476; +fp t4475; +fp t4474; +fp t4473; +fp t4472; +fp t4471; +fp t4470; +fp t4469; +fp t4468; +fp t4467; +fp t4466; +fp t4465; +fp t4464; +fp t4463; +fp t4462; +fp t4461; +fp t4460; +fp t4459; +fp t4458; +fp t4457; +fp t4456; +fp t4455; +fp t4454; +fp t4453; +fp t4452; +fp t4451; +fp t4346; +fp t4399; +fp t4450; +fp t4449; +fp t4448; +fp t4447; +fp t4446; +fp t4445; +fp t4444; +fp t4443; +fp t4442; +fp t4441; +fp t4440; +fp t4439; +fp t4438; +fp t4437; +fp t4436; +fp t4435; +fp t4434; +fp t4433; +fp t4432; + t4416 = RATIONAL(2.0,245.0); + t4431 = y*y; + t4367 = t4416*t4431; + t4398 = RATIONAL(-529.0,14700.0); + t4594 = t4367+t4398; + t4423 = RATIONAL(1.0,50.0); + t4389 = t4423*x; + t4360 = z*t4389; + t4541 = y*z; + t4353 = RATIONAL(1.0,700.0)*t4541; + t4593 = t4360+t4353; + t4411 = RATIONAL(1.0,175.0); + t4380 = t4411*z; + t4418 = RATIONAL(-1.0,245.0); + t4429 = z*z; + t4381 = t4418*t4429; + t4395 = RATIONAL(-169.0,14700.0); + t4592 = t4380+t4381+t4395; + t4408 = RATIONAL(-2.0,245.0); + t4379 = t4408*t4429; + t4420 = RATIONAL(1.0,245.0); + t4382 = t4420*t4431; + t4591 = t4379+t4382; + t4391 = RATIONAL(-1.0,25.0)*x; + t4412 = RATIONAL(1.0,350.0); + t4370 = t4412*z; + t4590 = t4391+t4370; + t4539 = x*RATIONAL(-1.0,100.0); + t4347 = z*t4539; + t4589 = t4347+t4380; + t4409 = RATIONAL(-1.0,175.0); + t4372 = t4409*z; + t4588 = t4391+t4372; + t4430 = x*x; + t4388 = t4423*t4430; + t4587 = t4367+t4388; + t4540 = x*RATIONAL(1.0,100.0); + t4348 = z*t4540; + t4586 = t4380+t4348; + t4368 = t4420*t4429; + t4376 = t4408*t4431; + t4585 = t4368+t4376; + t4396 = RATIONAL(311.0,14700.0); + t4584 = t4376+t4396; + t4357 = RATIONAL(-1.0,700.0)*t4541; + t4390 = RATIONAL(-1.0,50.0)*x; + t4364 = z*t4390; + t4583 = t4357+t4364; + t4361 = y*t4391; + t4393 = RATIONAL(1.0,25.0)*x; + t4582 = t4361+t4393; + t4417 = RATIONAL(-1.0,300.0); + t4581 = t4417+t4379; + t4363 = z*t4391; + t4580 = t4381+t4363; + t4375 = t4416*t4429; + t4579 = t4375+t4398; + t4402 = RATIONAL(211.0,3675.0); + t4410 = RATIONAL(-1.0,350.0); + t4378 = t4410*y; + t4355 = z*t4378; + t4578 = t4402+t4355; + t4415 = RATIONAL(-2.0,175.0); + t4373 = z*t4415; + t4577 = t4373+t4360; + t4387 = t4412*y; + t4352 = z*t4387; + t4576 = t4352+t4370; + t4385 = t4418*t4431; + t4575 = t4385+t4395; + t4574 = t4375+t4388; + t4573 = t4380+t4391; + t4414 = RATIONAL(2.0,175.0); + t4374 = z*t4414; + t4572 = t4374+t4364; + t4358 = y*t4389; + t4571 = t4358+t4389; + t4401 = RATIONAL(256.0,3675.0); + t4570 = t4401+t4385; + t4569 = t4381+t4388; + t4384 = t4410*z; + t4568 = t4384+t4391; + t4421 = RATIONAL(1.0,490.0); + t4386 = t4421*t4431; + t4567 = t4358+t4386; + t4566 = t4358+t4390; + t4365 = y*t4390; + t4565 = t4365+t4390; + t4564 = t4391+t4378; + t4563 = t4348+t4390; + t4400 = RATIONAL(151.0,3675.0); + t4562 = t4400+t4386; + t4354 = y*t4539; + t4561 = t4389+t4354; + t4560 = t4387+t4393; + t4559 = t4384+t4355; + t4558 = t4365+t4389; + t4557 = t4393+t4378; + t4426 = RATIONAL(4.0,75.0); + t4556 = t4426+t4382; + t4362 = y*t4393; + t4555 = t4362+t4391; + t4394 = RATIONAL(-2.0,25.0)*t4430; + t4554 = t4386+t4394; + t4369 = t4421*t4429; + t4553 = RATIONAL(166.0,3675.0)+t4369; + t4552 = t4347+t4372; + t4551 = t4373+t4389; + t4527 = t4381+t4372; + t4550 = t4527+t4395; + t4549 = t4393+t4372; + t4548 = t4417+t4376; + t4517 = t4382+t4394; + t4547 = t4400+t4369+t4517; + t4392 = RATIONAL(3.0,25.0)*t4430; + t4546 = t4379+t4376+RATIONAL(-33.0,490.0)+t4392; + t4516 = t4382+t4368; + t4545 = RATIONAL(-57.0,490.0)+t4516+t4392; + t4366 = t4409*y; + t4544 = t4402+t4366+t4369; + t4543 = t4358+t4554+t4553; + t4497 = t4365+t4554; + t4542 = t4497+t4553; + t4383 = t4411*y; + t4377 = t4414*y; + t4538 = t4402+t4394; + t4537 = t4380+t4366; + t4350 = z*t4366; + t4536 = t4350+t4366; + t4535 = t4393+t4394; + t4533 = t4383+t4350; + t4532 = t4383+t4385; + t4371 = t4415*y; + t4530 = t4374+t4371; + t4529 = t4373+t4377; + t4528 = t4385+t4355; + t4526 = t4388+t4390; + t4525 = t4383+t4372; + t4524 = t4367+t4392; + t4523 = t4379+t4388; + t4356 = z*t4383; + t4522 = t4356+t4383; + t4521 = RATIONAL(-1.0,10.0)+t4392; + t4520 = RATIONAL(-9.0,98.0)+t4392; + t4519 = t4368+t4394; + t4518 = t4381+t4352; + t4515 = t4356+t4366; + t4514 = t4360+t4574; + t4513 = t4356+t4520; + t4512 = t4385+t4535; + t4510 = t4381+t4526; + t4509 = t4364+t4574; + t4508 = t4385+t4366+t4388; + t4507 = t4389+t4569; + t4359 = z*t4393; + t4506 = t4359+t4381+t4394; + t4505 = t4385+t4391+t4394; + t4504 = t4371+t4587; + t4503 = t4352+t4538; + t4502 = t4391+t4519; + t4501 = t4350+t4520; + t4500 = t4381+t4535; + t4499 = t4377+t4587; + t4498 = t4375+t4526; + t4496 = t4376+RATIONAL(431.0,14700.0)+t4523; + t4495 = t4375+t4376+t4521; + t4405 = RATIONAL(-61.0,490.0); + t4494 = t4375+t4382+t4405+t4392; + t4493 = t4405+t4368+t4524; + t4492 = t4379+t4367+t4521; + t4491 = RATIONAL(136.0,3675.0)+t4394+t4516; + t4490 = t4379+t4396+t4508; + t4489 = t4393+t4519+t4562; + t4351 = z*t4377; + t4488 = t4351+t4546; + t4487 = t4501+t4585; + t4486 = t4509+t4551; + t4485 = t4509+t4548; + t4484 = t4426+t4385+t4502; + t4483 = t4374+t4389+t4514; + t4482 = t4513+t4585; + t4481 = t4513+t4591; + t4480 = t4506+t4573; + t4349 = y*t4373; + t4479 = t4349+t4546; + t4478 = t4504+t4566; + t4477 = t4507+t4584; + t4476 = t4364+t4547; + t4475 = t4355+t4545; + t4474 = t4510+t4584; + t4473 = t4396+t4523+t4532; + t4472 = t4498+t4577; + t4471 = t4352+t4545; + t4470 = t4360+t4547; + t4469 = t4501+t4591; + t4468 = t4499+t4581; + t4467 = t4359+t4372+t4500; + t4466 = t4502+t4562; + t4465 = t4426+t4368+t4512; + t4464 = t4426+t4517+t4580; + t4463 = t4486+t4594; + t4462 = t4497+t4578+t4580; + t4461 = t4486+t4575; + t4460 = t4478+t4579; + t4459 = t4350+t4499+t4550; + t4458 = t4383+t4369+t4370+t4528+t4538; + t4457 = t4506+t4567+t4578; + t4456 = t4356+t4504+t4550; + t4455 = t4374+t4351+t4499+t4579; + t4454 = t4380+t4363+t4500+t4570; + t4453 = t4472+t4575; + t4452 = t4384+t4369+t4503+t4532; + t4451 = t4498+t4572+t4575; + t4346 = y*t4540; + t4399 = RATIONAL(191.0,14700.0); + t4450 = t4346+t4399+t4507+t4532; + t4449 = t4385+t4399+t4510+t4589; + t4448 = t4364+t4353+t4543; + t4447 = t4356+t4499+t4592; + t4446 = t4350+t4504+t4592; + t4445 = t4357+t4360+t4543; + t4444 = t4480+t4570; + t4443 = t4483+t4575; + t4442 = t4348+t4354+t4399+t4528+t4569; + t4441 = t4401+t4363+t4505+t4527; + t4440 = t4361+t4505+t4544; + t4439 = t4542+t4560; + t4438 = t4402+t4359+t4497+t4518; + t4437 = t4362+t4512+t4544; + t4436 = t4467+t4570; + t4435 = t4372+t4399+t4508+t4518; + t4434 = t4542+t4564; + t4433 = t4503+t4567+t4580; + t4432 = t4349+t4365+t4514+t4594; + coeffs_dxx->coeff_m2_m2_m2 = t4351+t4460+t4577; + coeffs_dxx->coeff_m1_m2_m2 = t4361+t4454+t4533; + coeffs_dxx->coeff_0_m2_m2 = t4374+t4377+t4479; + coeffs_dxx->coeff_p1_m2_m2 = t4362+t4444+t4533; + coeffs_dxx->coeff_p2_m2_m2 = t4371+t4351+t4365+t4463; + coeffs_dxx->coeff_m2_m1_m2 = t4346+t4453+t4515; + coeffs_dxx->coeff_m1_m1_m2 = t4380+t4462+t4560; + coeffs_dxx->coeff_0_m1_m2 = t4383+t4374+t4469; + coeffs_dxx->coeff_p1_m1_m2 = t4387+t4457+t4573; + coeffs_dxx->coeff_p2_m1_m2 = t4354+t4461+t4515; + coeffs_dxx->coeff_m2_0_m2 = t4472+t4548; + coeffs_dxx->coeff_m1_0_m2 = t4393+t4380+t4464; + coeffs_dxx->coeff_0_0_m2 = t4374+t4492; + coeffs_dxx->coeff_p1_0_m2 = t4480+t4556; + coeffs_dxx->coeff_p2_0_m2 = t4485+t4551; + coeffs_dxx->coeff_m2_p1_m2 = t4354+t4453+t4533; + coeffs_dxx->coeff_m1_p1_m2 = t4380+t4433+t4557; + coeffs_dxx->coeff_0_p1_m2 = t4374+t4366+t4481; + coeffs_dxx->coeff_p1_p1_m2 = t4380+t4438+t4564; + coeffs_dxx->coeff_p2_p1_m2 = t4346+t4461+t4533; + coeffs_dxx->coeff_m2_p2_m2 = t4390+t4432+t4529; + coeffs_dxx->coeff_m1_p2_m2 = t4362+t4454+t4515; + coeffs_dxx->coeff_0_p2_m2 = t4488+t4530; + coeffs_dxx->coeff_p1_p2_m2 = t4361+t4444+t4515; + coeffs_dxx->coeff_p2_p2_m2 = t4377+t4358+t4349+t4463; + coeffs_dxx->coeff_m2_m2_m1 = t4358+t4456+t4563; + coeffs_dxx->coeff_m1_m2_m1 = t4364+t4458+t4582; + coeffs_dxx->coeff_0_m2_m1 = t4380+t4377+t4487; + coeffs_dxx->coeff_p1_m2_m1 = t4360+t4458+t4555; + coeffs_dxx->coeff_p2_m2_m1 = t4347+t4456+t4558; + coeffs_dxx->coeff_m2_m1_m1 = t4346+t4435+t4563; + coeffs_dxx->coeff_m1_m1_m1 = t4370+t4439+t4583; + coeffs_dxx->coeff_0_m1_m1 = t4383+t4380+t4475; + coeffs_dxx->coeff_p1_m1_m1 = t4387+t4445+t4590; + coeffs_dxx->coeff_p2_m1_m1 = t4347+t4435+t4561; + coeffs_dxx->coeff_m2_0_m1 = t4348+t4372+t4474; + coeffs_dxx->coeff_m1_0_m1 = t4370+t4393+t4476; + coeffs_dxx->coeff_0_0_m1 = t4380+t4493; + coeffs_dxx->coeff_p1_0_m1 = t4470+t4590; + coeffs_dxx->coeff_p2_0_m1 = t4477+t4552; + coeffs_dxx->coeff_m2_p1_m1 = t4390+t4442+t4525; + coeffs_dxx->coeff_m1_p1_m1 = t4370+t4448+t4557; + coeffs_dxx->coeff_0_p1_m1 = t4471+t4537; + coeffs_dxx->coeff_p1_p1_m1 = t4370+t4434+t4593; + coeffs_dxx->coeff_p2_p1_m1 = t4355+t4450+t4552; + coeffs_dxx->coeff_m2_p2_m1 = t4365+t4459+t4563; + coeffs_dxx->coeff_m1_p2_m1 = t4364+t4437+t4576; + coeffs_dxx->coeff_0_p2_m1 = t4380+t4371+t4482; + coeffs_dxx->coeff_p1_p2_m1 = t4360+t4440+t4576; + coeffs_dxx->coeff_p2_p2_m1 = t4347+t4459+t4571; + coeffs_dxx->coeff_m2_m2_0 = t4478+t4581; + coeffs_dxx->coeff_m1_m2_0 = t4361+t4383+t4465; + coeffs_dxx->coeff_0_m2_0 = t4377+t4495; + coeffs_dxx->coeff_p1_m2_0 = t4362+t4383+t4484; + coeffs_dxx->coeff_p2_m2_0 = t4504+t4558+t4581; + coeffs_dxx->coeff_m2_m1_0 = t4346+t4390+t4490; + coeffs_dxx->coeff_m1_m1_0 = t4387+t4365+t4489; + coeffs_dxx->coeff_0_m1_0 = t4383+t4494; + coeffs_dxx->coeff_p1_m1_0 = t4387+t4358+t4466; + coeffs_dxx->coeff_p2_m1_0 = t4490+t4561; + coeffs_dxx->coeff_m2_0_0 = t4390+t4496; + coeffs_dxx->coeff_m1_0_0 = t4393+t4491; + coeffs_dxx->coeff_0_0_0 = RATIONAL(-13.0,98.0)+t4375+t4524; + coeffs_dxx->coeff_p1_0_0 = t4391+t4491; + coeffs_dxx->coeff_p2_0_0 = t4389+t4496; + coeffs_dxx->coeff_m2_p1_0 = t4354+t4390+t4473; + coeffs_dxx->coeff_m1_p1_0 = t4358+t4378+t4489; + coeffs_dxx->coeff_0_p1_0 = t4366+t4494; + coeffs_dxx->coeff_p1_p1_0 = t4378+t4365+t4466; + coeffs_dxx->coeff_p2_p1_0 = t4389+t4346+t4473; + coeffs_dxx->coeff_m2_p2_0 = t4468+t4565; + coeffs_dxx->coeff_m1_p2_0 = t4362+t4366+t4465; + coeffs_dxx->coeff_0_p2_0 = t4371+t4495; + coeffs_dxx->coeff_p1_p2_0 = t4366+t4361+t4484; + coeffs_dxx->coeff_p2_p2_0 = t4468+t4571; + coeffs_dxx->coeff_m2_m2_p1 = t4347+t4446+t4566; + coeffs_dxx->coeff_m1_m2_p1 = t4360+t4452+t4582; + coeffs_dxx->coeff_0_m2_p1 = t4372+t4377+t4482; + coeffs_dxx->coeff_p1_m2_p1 = t4364+t4452+t4555; + coeffs_dxx->coeff_p2_m2_p1 = t4348+t4446+t4558; + coeffs_dxx->coeff_m2_m1_p1 = t4346+t4355+t4366+t4449; + coeffs_dxx->coeff_m1_m1_p1 = t4384+t4439+t4593; + coeffs_dxx->coeff_0_m1_p1 = t4471+t4525; + coeffs_dxx->coeff_p1_m1_p1 = t4387+t4448+t4568; + coeffs_dxx->coeff_p2_m1_p1 = t4389+t4442+t4537; + coeffs_dxx->coeff_m2_0_p1 = t4474+t4589; + coeffs_dxx->coeff_m1_0_p1 = t4384+t4393+t4470; + coeffs_dxx->coeff_0_0_p1 = t4372+t4493; + coeffs_dxx->coeff_p1_0_p1 = t4476+t4568; + coeffs_dxx->coeff_p2_0_p1 = t4477+t4586; + coeffs_dxx->coeff_m2_p1_p1 = t4352+t4354+t4383+t4449; + coeffs_dxx->coeff_m1_p1_p1 = t4384+t4445+t4557; + coeffs_dxx->coeff_0_p1_p1 = t4366+t4372+t4475; + coeffs_dxx->coeff_p1_p1_p1 = t4384+t4434+t4583; + coeffs_dxx->coeff_p2_p1_p1 = t4352+t4450+t4586; + coeffs_dxx->coeff_m2_p2_p1 = t4347+t4447+t4565; + coeffs_dxx->coeff_m1_p2_p1 = t4360+t4437+t4559; + coeffs_dxx->coeff_0_p2_p1 = t4372+t4371+t4487; + coeffs_dxx->coeff_p1_p2_p1 = t4364+t4440+t4559; + coeffs_dxx->coeff_p2_p2_p1 = t4348+t4447+t4571; + coeffs_dxx->coeff_m2_m2_p2 = t4349+t4460+t4572; + coeffs_dxx->coeff_m1_m2_p2 = t4361+t4436+t4522; + coeffs_dxx->coeff_0_m2_p2 = t4488+t4529; + coeffs_dxx->coeff_p1_m2_p2 = t4362+t4441+t4522; + coeffs_dxx->coeff_p2_m2_p2 = t4389+t4432+t4530; + coeffs_dxx->coeff_m2_m1_p2 = t4346+t4451+t4536; + coeffs_dxx->coeff_m1_m1_p2 = t4387+t4438+t4549; + coeffs_dxx->coeff_0_m1_p2 = t4373+t4383+t4481; + coeffs_dxx->coeff_p1_m1_p2 = t4387+t4433+t4588; + coeffs_dxx->coeff_p2_m1_p2 = t4354+t4443+t4536; + coeffs_dxx->coeff_m2_0_p2 = t4374+t4390+t4485; + coeffs_dxx->coeff_m1_0_p2 = t4467+t4556; + coeffs_dxx->coeff_0_0_p2 = t4373+t4492; + coeffs_dxx->coeff_p1_0_p2 = t4464+t4588; + coeffs_dxx->coeff_p2_0_p2 = t4483+t4548; + coeffs_dxx->coeff_m2_p1_p2 = t4354+t4451+t4522; + coeffs_dxx->coeff_m1_p1_p2 = t4378+t4457+t4549; + coeffs_dxx->coeff_0_p1_p2 = t4366+t4373+t4469; + coeffs_dxx->coeff_p1_p1_p2 = t4372+t4462+t4564; + coeffs_dxx->coeff_p2_p1_p2 = t4346+t4443+t4522; + coeffs_dxx->coeff_m2_p2_p2 = t4364+t4455+t4565; + coeffs_dxx->coeff_m1_p2_p2 = t4362+t4436+t4536; + coeffs_dxx->coeff_0_p2_p2 = t4371+t4373+t4479; + coeffs_dxx->coeff_p1_p2_p2 = t4361+t4441+t4536; + coeffs_dxx->coeff_p2_p2_p2 = t4360+t4455+t4571; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxy.compute.c new file mode 100644 index 0000000..c4beea7 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxy.compute.c @@ -0,0 +1,511 @@ +fp t4781; +fp t4604; +fp t4687; +fp t4688; +fp t4819; +fp t4763; +fp t4747; +fp t4749; +fp t4612; +fp t4744; +fp t4682; +fp t4775; +fp t4598; +fp t4681; +fp t4776; +fp t4603; +fp t4818; +fp t4679; +fp t4647; +fp t4677; +fp t4627; +fp t4817; +fp t4637; +fp t4622; +fp t4816; +fp t4642; +fp t4649; +fp t4815; +fp t4777; +fp t4610; +fp t4648; +fp t4606; +fp t4761; +fp t4814; +fp t4678; +fp t4686; +fp t4644; +fp t4813; +fp t4629; +fp t4812; +fp t4684; +fp t4672; +fp t4811; +fp t4685; +fp t4673; +fp t4810; +fp t4676; +fp t4624; +fp t4809; +fp t4674; +fp t4635; +fp t4808; +fp t4807; +fp t4675; +fp t4646; +fp t4806; +fp t4779; +fp t4614; +fp t4768; +fp t4611; +fp t4805; +fp t4602; +fp t4595; +fp t4804; +fp t4645; +fp t4752; +fp t4803; +fp t4630; +fp t4802; +fp t4660; +fp t4801; +fp t4773; +fp t4800; +fp t4641; +fp t4799; +fp t4798; +fp t4797; +fp t4619; +fp t4796; +fp t4795; +fp t4632; +fp t4794; +fp t4616; +fp t4793; +fp t4792; +fp t4791; +fp t4634; +fp t4651; +fp t4790; +fp t4789; +fp t4636; +fp t4628; +fp t4788; +fp t4663; +fp t4740; +fp t4787; +fp t4786; +fp t4785; +fp t4601; +fp t4784; +fp t4741; +fp t4783; +fp t4782; +fp t4780; +fp t4778; +fp t4774; +fp t4631; +fp t4599; +fp t4772; +fp t4613; +fp t4771; +fp t4597; +fp t4770; +fp t4769; +fp t4767; +fp t4766; +fp t4765; +fp t4596; +fp t4626; +fp t4764; +fp t4615; +fp t4762; +fp t4760; +fp t4759; +fp t4758; +fp t4757; +fp t4756; +fp t4755; +fp t4754; +fp t4753; +fp t4751; +fp t4750; +fp t4748; +fp t4746; +fp t4743; +fp t4739; +fp t4600; +fp t4738; +fp t4737; +fp t4736; +fp t4735; +fp t4734; +fp t4733; +fp t4732; +fp t4731; +fp t4730; +fp t4729; +fp t4728; +fp t4727; +fp t4726; +fp t4725; +fp t4724; +fp t4723; +fp t4722; +fp t4721; +fp t4720; +fp t4719; +fp t4718; +fp t4717; +fp t4716; +fp t4715; +fp t4714; +fp t4713; +fp t4712; +fp t4607; +fp t4605; +fp t4711; +fp t4710; +fp t4709; +fp t4609; +fp t4608; +fp t4708; +fp t4707; +fp t4706; +fp t4705; +fp t4704; +fp t4703; +fp t4702; +fp t4701; +fp t4700; +fp t4699; +fp t4698; +fp t4697; +fp t4696; +fp t4695; +fp t4694; +fp t4693; +fp t4692; +fp t4691; +fp t4690; +fp t4689; +fp t4639; +fp t4623; + t4781 = x*y; + t4604 = RATIONAL(4.0,245.0)*t4781; + t4687 = x*x; + t4688 = y*y; + t4819 = t4688+t4687; + t4763 = t4819*RATIONAL(1.0,100.0); + t4747 = t4604+t4763; + t4749 = t4819*RATIONAL(-1.0,100.0); + t4612 = RATIONAL(1.0,245.0)*t4781; + t4744 = t4612+t4749; + t4682 = RATIONAL(-2.0,175.0); + t4775 = z*t4682; + t4598 = x*t4775; + t4681 = RATIONAL(2.0,175.0); + t4776 = z*t4681; + t4603 = y*t4776; + t4818 = t4598+t4603; + t4679 = RATIONAL(1.0,350.0); + t4647 = t4679*x; + t4677 = RATIONAL(-1.0,350.0); + t4627 = t4677*y; + t4817 = t4647+t4627; + t4637 = t4682*x; + t4622 = t4681*y; + t4816 = t4637+t4622; + t4642 = t4677*x; + t4649 = t4679*y; + t4815 = t4642+t4649; + t4777 = z*t4679; + t4610 = y*t4777; + t4648 = RATIONAL(-1.0,500.0)*z; + t4606 = x*t4777; + t4761 = t4648+t4606; + t4814 = t4610+t4761; + t4678 = RATIONAL(1.0,175.0); + t4686 = z*z; + t4644 = t4678*t4686; + t4813 = RATIONAL(17.0,5250.0)+t4644; + t4629 = t4677*t4686; + t4812 = RATIONAL(187.0,7000.0)+t4629; + t4684 = RATIONAL(1.0,50.0); + t4672 = RATIONAL(-1.0,200.0); + t4811 = t4684*t4687+t4672*t4688; + t4685 = RATIONAL(-1.0,50.0); + t4673 = RATIONAL(1.0,200.0); + t4810 = t4673*t4688+t4685*t4687; + t4676 = RATIONAL(-1.0,175.0); + t4624 = t4676*t4686; + t4809 = t4624+RATIONAL(-17.0,5250.0); + t4674 = RATIONAL(-1.0,700.0); + t4635 = t4674*t4686; + t4808 = RATIONAL(167.0,7000.0)+t4635; + t4807 = t4629+RATIONAL(-47.0,5250.0); + t4675 = RATIONAL(1.0,700.0); + t4646 = t4675*t4686; + t4806 = RATIONAL(-167.0,7000.0)+t4646; + t4779 = t4677*z; + t4614 = x*t4779; + t4768 = t4614+t4648; + t4611 = y*t4779; + t4805 = t4768+t4611; + t4602 = x*t4776; + t4595 = y*t4775; + t4804 = t4602+t4595; + t4645 = RATIONAL(1.0,500.0)*z; + t4752 = t4614+t4645; + t4803 = t4752+t4611; + t4630 = t4681*x; + t4802 = t4630+t4622; + t4660 = RATIONAL(137.0,5250.0); + t4801 = t4660+t4624; + t4773 = t4645+t4606; + t4800 = t4610+t4773; + t4641 = t4682*y; + t4799 = t4630+t4641; + t4798 = t4637+t4641; + t4797 = t4646+RATIONAL(229.0,10500.0); + t4619 = RATIONAL(-1.0,1000.0)*z; + t4796 = t4642+t4619; + t4795 = t4673*t4687+t4685*t4688; + t4632 = t4679*t4686; + t4794 = RATIONAL(107.0,7000.0)+t4632; + t4616 = RATIONAL(1.0,1000.0)*z; + t4793 = t4616+t4642; + t4792 = t4635+RATIONAL(289.0,10500.0); + t4791 = t4672*t4687+t4684*t4688; + t4634 = t4676*y; + t4651 = t4676*x; + t4790 = t4634+t4651; + t4789 = t4647+t4649; + t4636 = t4678*x; + t4628 = t4678*y; + t4788 = t4636+t4628; + t4663 = RATIONAL(-137.0,5250.0); + t4740 = t4612+t4763; + t4787 = t4663+t4740+RATIONAL(1.0,1400.0)*t4686; + t4786 = t4644+t4663+t4747; + t4785 = t4660+RATIONAL(-1.0,1400.0)*t4686+t4744; + t4601 = RATIONAL(-2.0,245.0)*t4781; + t4784 = RATIONAL(-107.0,7000.0)+t4629+t4601; + t4741 = t4604+t4749; + t4783 = t4741+t4632+RATIONAL(47.0,5250.0); + t4782 = t4740+t4635+RATIONAL(-229.0,10500.0); + t4780 = z*t4675; + t4778 = t4678*z; + t4774 = z*t4674; + t4631 = RATIONAL(-1.0,250.0)*z; + t4599 = y*t4778; + t4772 = t4631+t4599; + t4613 = RATIONAL(2.0,245.0)*t4781; + t4771 = t4634+t4613; + t4597 = RATIONAL(-4.0,245.0)*t4781; + t4770 = t4597+t4637; + t4769 = t4630+t4597; + t4767 = t4613+t4628; + t4766 = t4597+t4641; + t4765 = t4601+t4628; + t4596 = z*t4634; + t4626 = RATIONAL(1.0,250.0)*z; + t4764 = t4596+t4626; + t4615 = x*t4778; + t4762 = t4615+t4597; + t4760 = t4634+t4601; + t4759 = t4599+t4626; + t4758 = t4596+t4631; + t4757 = t4597+t4622; + t4756 = t4599+t4613; + t4755 = t4613+t4651; + t4754 = t4597+t4595; + t4753 = t4597+t4598; + t4751 = t4610+t4613; + t4750 = t4613+t4636; + t4748 = t4651+t4765; + t4746 = RATIONAL(-187.0,7000.0)+t4632+t4601; + t4743 = t4636+t4760; + t4739 = t4741+t4816; + t4600 = z*t4651; + t4738 = t4596+t4600+t4784; + t4737 = t4747+t4798; + t4736 = t4748+t4812; + t4735 = t4746+t4811; + t4734 = t4615+t4599+t4784; + t4733 = t4747+t4802; + t4732 = t4646+RATIONAL(-289.0,10500.0)+t4740; + t4731 = t4651+t4760+t4806; + t4730 = t4746+t4791; + t4729 = t4642+t4627+t4744; + t4728 = t4748+t4794; + t4727 = t4743+t4812; + t4726 = t4744+t4789; + t4725 = t4743+t4808; + t4724 = t4743+t4794; + t4723 = t4636+t4765+t4806; + t4722 = t4748+t4808; + t4721 = t4741+t4799; + t4720 = t4739+t4801; + t4719 = t4602+t4603+t4786; + t4718 = t4596+t4615+t4783; + t4717 = t4599+t4600+t4783; + t4716 = t4737+t4807; + t4715 = t4733+t4807; + t4714 = t4598+t4595+t4786; + t4713 = t4726+t4797; + t4712 = t4729+t4797; + t4607 = y*t4780; + t4605 = x*t4780; + t4711 = t4607+t4605+t4785; + t4710 = t4611+t4606+t4782; + t4709 = t4614+t4610+t4782; + t4609 = y*t4774; + t4608 = x*t4774; + t4708 = t4609+t4608+t4785; + t4707 = t4607+t4608+t4787; + t4706 = t4609+t4605+t4787; + t4705 = t4721+t4801; + t4704 = t4610+t4722+t4752; + t4703 = t4723+t4814; + t4702 = t4731+t4805; + t4701 = t4631+t4738+t4790; + t4700 = t4611+t4725+t4773; + t4699 = t4626+t4738+t4788; + t4698 = t4626+t4734+t4790; + t4697 = t4600+t4728+t4759; + t4696 = t4731+t4800; + t4695 = t4615+t4728+t4758; + t4694 = t4610+t4725+t4768; + t4693 = t4600+t4724+t4772; + t4692 = t4615+t4724+t4764; + t4691 = t4631+t4734+t4788; + t4690 = t4723+t4803; + t4689 = t4611+t4722+t4761; + t4639 = RATIONAL(-1.0,125.0)*z; + t4623 = RATIONAL(1.0,125.0)*z; + coeffs_dxy->coeff_m2_m2_m2 = t4639+t4719+t4798; + coeffs_dxy->coeff_m1_m2_m2 = t4693+t4810; + coeffs_dxy->coeff_0_m2_m2 = t4630+t4753; + coeffs_dxy->coeff_p1_m2_m2 = t4699+t4811; + coeffs_dxy->coeff_p2_m2_m2 = t4623+t4720+t4804; + coeffs_dxy->coeff_m2_m1_m2 = t4695+t4795; + coeffs_dxy->coeff_m1_m1_m2 = t4713+t4805; + coeffs_dxy->coeff_0_m1_m2 = t4600+t4750; + coeffs_dxy->coeff_p1_m1_m2 = t4645+t4709+t4817; + coeffs_dxy->coeff_p2_m1_m2 = t4698+t4791; + coeffs_dxy->coeff_m2_0_m2 = t4622+t4754; + coeffs_dxy->coeff_m1_0_m2 = t4596+t4767; + coeffs_dxy->coeff_0_0_m2 = t4604; + coeffs_dxy->coeff_p1_0_m2 = t4634+t4756; + coeffs_dxy->coeff_p2_0_m2 = t4603+t4766; + coeffs_dxy->coeff_m2_p1_m2 = t4699+t4791; + coeffs_dxy->coeff_m1_p1_m2 = t4645+t4710+t4815; + coeffs_dxy->coeff_0_p1_m2 = t4615+t4755; + coeffs_dxy->coeff_p1_p1_m2 = t4712+t4814; + coeffs_dxy->coeff_p2_p1_m2 = t4693+t4795; + coeffs_dxy->coeff_m2_p2_m2 = t4623+t4705+t4818; + coeffs_dxy->coeff_m1_p2_m2 = t4698+t4811; + coeffs_dxy->coeff_0_p2_m2 = t4602+t4770; + coeffs_dxy->coeff_p1_p2_m2 = t4695+t4810; + coeffs_dxy->coeff_p2_p2_m2 = t4639+t4714+t4802; + coeffs_dxy->coeff_m2_m2_m1 = t4615+t4716+t4772; + coeffs_dxy->coeff_m1_m2_m1 = t4694+t4810; + coeffs_dxy->coeff_0_m2_m1 = t4600+t4769; + coeffs_dxy->coeff_p1_m2_m1 = t4690+t4811; + coeffs_dxy->coeff_p2_m2_m1 = t4626+t4718+t4816; + coeffs_dxy->coeff_m2_m1_m1 = t4689+t4795; + coeffs_dxy->coeff_m1_m1_m1 = t4619+t4708+t4789; + coeffs_dxy->coeff_0_m1_m1 = t4614+t4750; + coeffs_dxy->coeff_p1_m1_m1 = t4616+t4707+t4817; + coeffs_dxy->coeff_p2_m1_m1 = t4696+t4791; + coeffs_dxy->coeff_m2_0_m1 = t4596+t4757; + coeffs_dxy->coeff_m1_0_m1 = t4611+t4767; + coeffs_dxy->coeff_0_0_m1 = t4604; + coeffs_dxy->coeff_p1_0_m1 = t4634+t4751; + coeffs_dxy->coeff_p2_0_m1 = t4599+t4766; + coeffs_dxy->coeff_m2_p1_m1 = t4690+t4791; + coeffs_dxy->coeff_m1_p1_m1 = t4649+t4706+t4793; + coeffs_dxy->coeff_0_p1_m1 = t4606+t4755; + coeffs_dxy->coeff_p1_p1_m1 = t4627+t4711+t4796; + coeffs_dxy->coeff_p2_p1_m1 = t4694+t4795; + coeffs_dxy->coeff_m2_p2_m1 = t4626+t4717+t4799; + coeffs_dxy->coeff_m1_p2_m1 = t4696+t4811; + coeffs_dxy->coeff_0_p2_m1 = t4637+t4762; + coeffs_dxy->coeff_p1_p2_m1 = t4689+t4810; + coeffs_dxy->coeff_p2_p2_m1 = t4600+t4715+t4758; + coeffs_dxy->coeff_m2_m2_0 = t4737+t4809; + coeffs_dxy->coeff_m1_m2_0 = t4727+t4810; + coeffs_dxy->coeff_0_m2_0 = t4769; + coeffs_dxy->coeff_p1_m2_0 = t4735+t4788; + coeffs_dxy->coeff_p2_m2_0 = t4739+t4813; + coeffs_dxy->coeff_m2_m1_0 = t4736+t4795; + coeffs_dxy->coeff_m1_m1_0 = t4726+t4792; + coeffs_dxy->coeff_0_m1_0 = t4750; + coeffs_dxy->coeff_p1_m1_0 = t4732+t4817; + coeffs_dxy->coeff_p2_m1_0 = t4730+t4790; + coeffs_dxy->coeff_m2_0_0 = t4757; + coeffs_dxy->coeff_m1_0_0 = t4767; + coeffs_dxy->coeff_0_0_0 = t4604; + coeffs_dxy->coeff_p1_0_0 = t4771; + coeffs_dxy->coeff_p2_0_0 = t4766; + coeffs_dxy->coeff_m2_p1_0 = t4730+t4788; + coeffs_dxy->coeff_m1_p1_0 = t4732+t4815; + coeffs_dxy->coeff_0_p1_0 = t4755; + coeffs_dxy->coeff_p1_p1_0 = t4729+t4792; + coeffs_dxy->coeff_p2_p1_0 = t4727+t4795; + coeffs_dxy->coeff_m2_p2_0 = t4721+t4813; + coeffs_dxy->coeff_m1_p2_0 = t4735+t4790; + coeffs_dxy->coeff_0_p2_0 = t4770; + coeffs_dxy->coeff_p1_p2_0 = t4736+t4810; + coeffs_dxy->coeff_p2_p2_0 = t4733+t4809; + coeffs_dxy->coeff_m2_m2_p1 = t4600+t4716+t4764; + coeffs_dxy->coeff_m1_m2_p1 = t4700+t4810; + coeffs_dxy->coeff_0_m2_p1 = t4630+t4762; + coeffs_dxy->coeff_p1_m2_p1 = t4703+t4811; + coeffs_dxy->coeff_p2_m2_p1 = t4631+t4717+t4816; + coeffs_dxy->coeff_m2_m1_p1 = t4704+t4795; + coeffs_dxy->coeff_m1_m1_p1 = t4616+t4711+t4789; + coeffs_dxy->coeff_0_m1_p1 = t4606+t4750; + coeffs_dxy->coeff_p1_m1_p1 = t4619+t4706+t4817; + coeffs_dxy->coeff_p2_m1_p1 = t4702+t4791; + coeffs_dxy->coeff_m2_0_p1 = t4599+t4757; + coeffs_dxy->coeff_m1_0_p1 = t4628+t4751; + coeffs_dxy->coeff_0_0_p1 = t4604; + coeffs_dxy->coeff_p1_0_p1 = t4611+t4771; + coeffs_dxy->coeff_p2_0_p1 = t4596+t4766; + coeffs_dxy->coeff_m2_p1_p1 = t4703+t4791; + coeffs_dxy->coeff_m1_p1_p1 = t4649+t4707+t4796; + coeffs_dxy->coeff_0_p1_p1 = t4614+t4755; + coeffs_dxy->coeff_p1_p1_p1 = t4627+t4708+t4793; + coeffs_dxy->coeff_p2_p1_p1 = t4700+t4795; + coeffs_dxy->coeff_m2_p2_p1 = t4631+t4718+t4799; + coeffs_dxy->coeff_m1_p2_p1 = t4702+t4811; + coeffs_dxy->coeff_0_p2_p1 = t4600+t4770; + coeffs_dxy->coeff_p1_p2_p1 = t4704+t4810; + coeffs_dxy->coeff_p2_p2_p1 = t4615+t4715+t4759; + coeffs_dxy->coeff_m2_m2_p2 = t4623+t4714+t4798; + coeffs_dxy->coeff_m1_m2_p2 = t4692+t4810; + coeffs_dxy->coeff_0_m2_p2 = t4602+t4769; + coeffs_dxy->coeff_p1_m2_p2 = t4691+t4811; + coeffs_dxy->coeff_p2_m2_p2 = t4639+t4720+t4818; + coeffs_dxy->coeff_m2_m1_p2 = t4697+t4795; + coeffs_dxy->coeff_m1_m1_p2 = t4713+t4800; + coeffs_dxy->coeff_0_m1_p2 = t4615+t4750; + coeffs_dxy->coeff_p1_m1_p2 = t4648+t4710+t4817; + coeffs_dxy->coeff_p2_m1_p2 = t4701+t4791; + coeffs_dxy->coeff_m2_0_p2 = t4603+t4757; + coeffs_dxy->coeff_m1_0_p2 = t4628+t4756; + coeffs_dxy->coeff_0_0_p2 = t4604; + coeffs_dxy->coeff_p1_0_p2 = t4596+t4771; + coeffs_dxy->coeff_p2_0_p2 = t4641+t4754; + coeffs_dxy->coeff_m2_p1_p2 = t4691+t4791; + coeffs_dxy->coeff_m1_p1_p2 = t4648+t4709+t4815; + coeffs_dxy->coeff_0_p1_p2 = t4600+t4755; + coeffs_dxy->coeff_p1_p1_p2 = t4712+t4803; + coeffs_dxy->coeff_p2_p1_p2 = t4692+t4795; + coeffs_dxy->coeff_m2_p2_p2 = t4639+t4705+t4804; + coeffs_dxy->coeff_m1_p2_p2 = t4701+t4811; + coeffs_dxy->coeff_0_p2_p2 = t4637+t4753; + coeffs_dxy->coeff_p1_p2_p2 = t4697+t4810; + coeffs_dxy->coeff_p2_p2_p2 = t4623+t4719+t4802; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxz.compute.c new file mode 100644 index 0000000..8770b03 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxz.compute.c @@ -0,0 +1,523 @@ +fp t4903; +fp t4845; +fp t4837; +fp t4873; +fp t4820; +fp t5056; +fp t4901; +fp t4853; +fp t4828; +fp t4847; +fp t4830; +fp t5055; +fp t4911; +fp t4912; +fp t5054; +fp t4904; +fp t5004; +fp t4835; +fp t4862; +fp t5053; +fp t4827; +fp t4864; +fp t5052; +fp t4900; +fp t4913; +fp t4861; +fp t5051; +fp t4902; +fp t5005; +fp t4833; +fp t4982; +fp t4832; +fp t5050; +fp t4906; +fp t4869; +fp t4824; +fp t4875; +fp t4825; +fp t5049; +fp t5048; +fp t5047; +fp t5046; +fp t5045; +fp t4885; +fp t5044; +fp t4874; +fp t5043; +fp t4854; +fp t5042; +fp t4907; +fp t4856; +fp t4836; +fp t4858; +fp t4840; +fp t5041; +fp t4897; +fp t4909; +fp t5040; +fp t5039; +fp t4888; +fp t4859; +fp t5038; +fp t5037; +fp t5007; +fp t4823; +fp t5036; +fp t4849; +fp t4848; +fp t5035; +fp t4899; +fp t5003; +fp t4838; +fp t4839; +fp t5034; +fp t4870; +fp t5033; +fp t5032; +fp t4898; +fp t4910; +fp t5031; +fp t5030; +fp t5029; +fp t5028; +fp t4978; +fp t5027; +fp t5026; +fp t4876; +fp t5025; +fp t4863; +fp t5024; +fp t4987; +fp t4826; +fp t4970; +fp t5023; +fp t5022; +fp t5021; +fp t5020; +fp t5019; +fp t5018; +fp t4867; +fp t5017; +fp t5016; +fp t5006; +fp t4834; +fp t4831; +fp t5015; +fp t4852; +fp t5014; +fp t5013; +fp t5012; +fp t5011; +fp t5010; +fp t4822; +fp t4980; +fp t4966; +fp t5009; +fp t5008; +fp t4829; +fp t5002; +fp t5001; +fp t5000; +fp t4998; +fp t4994; +fp t4993; +fp t4992; +fp t4821; +fp t4990; +fp t4988; +fp t4986; +fp t4985; +fp t4984; +fp t4981; +fp t4977; +fp t4976; +fp t4851; +fp t4975; +fp t4974; +fp t4973; +fp t4972; +fp t4971; +fp t4969; +fp t4968; +fp t4967; +fp t4965; +fp t4964; +fp t4963; +fp t4962; +fp t4961; +fp t4960; +fp t4959; +fp t4958; +fp t4957; +fp t4956; +fp t4955; +fp t4954; +fp t4953; +fp t4952; +fp t4951; +fp t4950; +fp t4949; +fp t4948; +fp t4947; +fp t4946; +fp t4945; +fp t4944; +fp t4943; +fp t4942; +fp t4941; +fp t4940; +fp t4939; +fp t4938; +fp t4937; +fp t4936; +fp t4935; +fp t4934; +fp t4933; +fp t4932; +fp t4931; +fp t4930; +fp t4929; +fp t4928; +fp t4927; +fp t4926; +fp t4925; +fp t4924; +fp t4923; +fp t4922; +fp t4921; +fp t4920; +fp t4919; +fp t4918; +fp t4917; +fp t4916; +fp t4915; +fp t4914; +fp t4866; +fp t4857; +fp t4844; +fp t4843; + t4903 = RATIONAL(1.0,175.0); + t4845 = t4903*x; + t4837 = y*t4845; + t4873 = t4903*z; + t4820 = y*t4873; + t5056 = t4837+t4820; + t4901 = RATIONAL(-1.0,175.0); + t4853 = t4901*x; + t4828 = y*t4853; + t4847 = t4901*z; + t4830 = y*t4847; + t5055 = t4828+t4830; + t4911 = z*z; + t4912 = x*x; + t5054 = t4911+t4912; + t4904 = RATIONAL(1.0,350.0); + t5004 = y*t4904; + t4835 = z*t5004; + t4862 = RATIONAL(1.0,500.0)*y; + t5053 = t4835+t4862; + t4827 = x*t5004; + t4864 = RATIONAL(-1.0,500.0)*y; + t5052 = t4827+t4864; + t4900 = RATIONAL(1.0,700.0); + t4913 = y*y; + t4861 = t4900*t4913; + t5051 = RATIONAL(-167.0,7000.0)+t4861; + t4902 = RATIONAL(-1.0,350.0); + t5005 = y*t4902; + t4833 = x*t5005; + t4982 = t4833+t4864; + t4832 = z*t5005; + t5050 = t4982+t4832; + t4906 = RATIONAL(2.0,175.0); + t4869 = t4906*z; + t4824 = y*t4869; + t4875 = t4906*x; + t4825 = y*t4875; + t5049 = t4824+t4825; + t5048 = t4847+t4853; + t5047 = t4982+t4835; + t5046 = RATIONAL(229.0,10500.0)+t4861; + t5045 = t4833+t5053; + t4885 = RATIONAL(137.0,5250.0); + t5044 = t4885+RATIONAL(-1.0,1400.0)*t4913; + t4874 = t4902*t4913; + t5043 = RATIONAL(-107.0,7000.0)+t4874; + t4854 = RATIONAL(-1.0,250.0)*y; + t5042 = t4854+t5055; + t4907 = RATIONAL(-2.0,175.0); + t4856 = t4907*x; + t4836 = y*t4856; + t4858 = t4907*z; + t4840 = y*t4858; + t5041 = t4836+t4840; + t4897 = RATIONAL(-1.0,200.0); + t4909 = RATIONAL(1.0,50.0); + t5040 = t4897*t4912+t4909*t4911; + t5039 = t4873+t4845; + t4888 = RATIONAL(-137.0,5250.0); + t4859 = t4903*t4913; + t5038 = t4888+t4859; + t5037 = t4827+t5053; + t5007 = x*z; + t4823 = RATIONAL(-2.0,245.0)*t5007; + t5036 = t4823+RATIONAL(107.0,7000.0); + t4849 = t4904*x; + t4848 = t4904*z; + t5035 = t4849+t4848; + t4899 = RATIONAL(-1.0,700.0); + t5003 = y*t4899; + t4838 = x*t5003; + t4839 = z*t5003; + t5034 = t4838+t4839; + t4870 = RATIONAL(1.0,250.0)*y; + t5033 = t4870+t5055; + t5032 = t4870+t5056; + t4898 = RATIONAL(1.0,200.0); + t4910 = RATIONAL(-1.0,50.0); + t5031 = t4910*t4911+t4898*t4912; + t5030 = t4874+RATIONAL(-47.0,5250.0); + t5029 = t4835+t5052; + t5028 = t4875+t4858; + t4978 = t4862+t4832; + t5027 = t4827+t4978; + t5026 = t4856+t4869; + t4876 = t4902*z; + t5025 = t4849+t4876; + t4863 = t4899*t4913; + t5024 = RATIONAL(167.0,7000.0)+t4863; + t4987 = t5054*RATIONAL(-1.0,100.0); + t4826 = RATIONAL(4.0,245.0)*t5007; + t4970 = t4826+t4987; + t5023 = RATIONAL(47.0,5250.0)+t4970; + t5022 = t4873+t4853; + t5021 = t4832+t5052; + t5020 = t4909*t4912+t4897*t4911; + t5019 = RATIONAL(-229.0,10500.0)+t4863; + t5018 = t4833+t4978; + t4867 = t4901*t4913; + t5017 = RATIONAL(-17.0,5250.0)+t4867; + t5016 = t4847+t4845; + t5006 = y*t4900; + t4834 = z*t5006; + t4831 = x*t5006; + t5015 = t4834+t4831; + t4852 = t4902*x; + t5014 = t4848+t4852; + t5013 = t4854+t5056; + t5012 = RATIONAL(-289.0,10500.0)+t4861; + t5011 = t4876+t4852; + t5010 = t4898*t4911+t4910*t4912; + t4822 = RATIONAL(1.0,245.0)*t5007; + t4980 = t5054*RATIONAL(1.0,100.0); + t4966 = t4822+t4980; + t5009 = t4888+t4966+RATIONAL(1.0,1400.0)*t4913; + t5008 = t4885+t4970+t4867; + t4829 = RATIONAL(-4.0,245.0)*t5007; + t5002 = t4875+t4829; + t5001 = t4856+t4829; + t5000 = t4858+t4829; + t4998 = t4873+t4823; + t4994 = t4829+t4825; + t4993 = t4847+t4823; + t4992 = t4829+t4837; + t4821 = RATIONAL(2.0,245.0)*t5007; + t4990 = t4820+t4821; + t4988 = t4828+t4829; + t4986 = t4821+t4830; + t4985 = t4821+t4832; + t4984 = t4835+t4821; + t4981 = t4869+t4829; + t4977 = t4821+t4853; + t4976 = t4845+t4821; + t4851 = t4904*t4913; + t4975 = t4828+t4820+t4851; + t4974 = t4845+t4998; + t4973 = t4826+t4980; + t4972 = t4837+t4830+t4851; + t4971 = RATIONAL(-187.0,7000.0)+t4823+t4851; + t4969 = t4822+t4987; + t4968 = t4874+RATIONAL(187.0,7000.0)+t4823; + t4967 = t4853+t4993; + t4965 = t4971+t5020; + t4964 = t4966+t5025; + t4963 = t4975+t5036; + t4962 = t4853+t4998+t5024; + t4961 = t4845+t4993+t5024; + t4960 = t4972+t5036; + t4959 = t4967+t5051; + t4958 = t4971+t5040; + t4957 = t4974+t5043; + t4956 = t4974+t5051; + t4955 = t4856+t4858+t4973; + t4954 = t4969+t5011; + t4953 = t4969+t5035; + t4952 = t4863+RATIONAL(289.0,10500.0)+t4969; + t4951 = t4875+t4869+t4973; + t4950 = t4968+t5022; + t4949 = t4967+t5043; + t4948 = t4966+t5014; + t4947 = t4968+t5016; + t4946 = RATIONAL(17.0,5250.0)+t4859+t4970; + t4945 = t4964+t5019; + t4944 = t4955+t5030; + t4943 = t4975+t5023; + t4942 = t4951+t5030; + t4941 = t4955+t5038; + t4940 = t4953+t5044; + t4939 = t4836+t4824+t5008; + t4938 = t4972+t5023; + t4937 = t4954+t5046; + t4936 = t4840+t4825+t5008; + t4935 = t4953+t5046; + t4934 = t4951+t5038; + t4933 = t4834+t4838+t5009; + t4932 = t4948+t5019; + t4931 = t4954+t5044; + t4930 = t4831+t4839+t5009; + t4929 = t4854+t4963+t5016; + t4928 = t4957+t5033; + t4927 = t4957+t5013; + t4926 = t4962+t5045; + t4925 = t4962+t5021; + t4924 = t4870+t4963+t5022; + t4923 = t4961+t5027; + t4922 = t4949+t5032; + t4921 = t4959+t5050; + t4920 = t4961+t5047; + t4919 = t4854+t4960+t5022; + t4918 = t4959+t5037; + t4917 = t4870+t4960+t5016; + t4916 = t4956+t5029; + t4915 = t4956+t5018; + t4914 = t4949+t5042; + t4866 = RATIONAL(1.0,125.0)*y; + t4857 = RATIONAL(-1.0,125.0)*y; + t4844 = RATIONAL(1.0,1000.0)*y; + t4843 = RATIONAL(-1.0,1000.0)*y; + coeffs_dxz->coeff_m2_m2_m2 = t4857+t4941+t5049; + coeffs_dxz->coeff_m1_m2_m2 = t4929+t5010; + coeffs_dxz->coeff_0_m2_m2 = t4836+t5002; + coeffs_dxz->coeff_p1_m2_m2 = t4928+t5020; + coeffs_dxz->coeff_p2_m2_m2 = t4866+t4936+t5026; + coeffs_dxz->coeff_m2_m1_m2 = t4944+t5013; + coeffs_dxz->coeff_m1_m1_m2 = t4920+t5010; + coeffs_dxz->coeff_0_m1_m2 = t4875+t4988; + coeffs_dxz->coeff_p1_m1_m2 = t4915+t5020; + coeffs_dxz->coeff_p2_m1_m2 = t4870+t4938+t5026; + coeffs_dxz->coeff_m2_0_m2 = t4955+t5017; + coeffs_dxz->coeff_m1_0_m2 = t4947+t5010; + coeffs_dxz->coeff_0_0_m2 = t5002; + coeffs_dxz->coeff_p1_0_m2 = t4965+t5039; + coeffs_dxz->coeff_p2_0_m2 = t4946+t5026; + coeffs_dxz->coeff_m2_p1_m2 = t4944+t5033; + coeffs_dxz->coeff_m1_p1_m2 = t4923+t5010; + coeffs_dxz->coeff_0_p1_m2 = t4875+t4992; + coeffs_dxz->coeff_p1_p1_m2 = t4916+t5020; + coeffs_dxz->coeff_p2_p1_m2 = t4854+t4943+t5026; + coeffs_dxz->coeff_m2_p2_m2 = t4866+t4941+t5041; + coeffs_dxz->coeff_m1_p2_m2 = t4917+t5010; + coeffs_dxz->coeff_0_p2_m2 = t4875+t4994; + coeffs_dxz->coeff_p1_p2_m2 = t4927+t5020; + coeffs_dxz->coeff_p2_p2_m2 = t4857+t4939+t5026; + coeffs_dxz->coeff_m2_m2_m1 = t4919+t5031; + coeffs_dxz->coeff_m1_m2_m1 = t4935+t5050; + coeffs_dxz->coeff_0_m2_m1 = t4828+t4976; + coeffs_dxz->coeff_p1_m2_m1 = t4945+t5045; + coeffs_dxz->coeff_p2_m2_m1 = t4922+t5040; + coeffs_dxz->coeff_m2_m1_m1 = t4925+t5031; + coeffs_dxz->coeff_m1_m1_m1 = t4843+t4940+t5034; + coeffs_dxz->coeff_0_m1_m1 = t4833+t4976; + coeffs_dxz->coeff_p1_m1_m1 = t4844+t4933+t5025; + coeffs_dxz->coeff_p2_m1_m1 = t4918+t5040; + coeffs_dxz->coeff_m2_0_m1 = t4950+t5031; + coeffs_dxz->coeff_m1_0_m1 = t4952+t5035; + coeffs_dxz->coeff_0_0_m1 = t4976; + coeffs_dxz->coeff_p1_0_m1 = t4964+t5012; + coeffs_dxz->coeff_p2_0_m1 = t4958+t5048; + coeffs_dxz->coeff_m2_p1_m1 = t4926+t5031; + coeffs_dxz->coeff_m1_p1_m1 = t4844+t4940+t5015; + coeffs_dxz->coeff_0_p1_m1 = t4827+t4976; + coeffs_dxz->coeff_p1_p1_m1 = t4843+t4930+t5025; + coeffs_dxz->coeff_p2_p1_m1 = t4921+t5040; + coeffs_dxz->coeff_m2_p2_m1 = t4924+t5031; + coeffs_dxz->coeff_m1_p2_m1 = t4935+t5037; + coeffs_dxz->coeff_0_p2_m1 = t4837+t4976; + coeffs_dxz->coeff_p1_p2_m1 = t4945+t5021; + coeffs_dxz->coeff_p2_p2_m1 = t4914+t5040; + coeffs_dxz->coeff_m2_m2_0 = t4840+t4981; + coeffs_dxz->coeff_m1_m2_0 = t4873+t4986; + coeffs_dxz->coeff_0_m2_0 = t4826; + coeffs_dxz->coeff_p1_m2_0 = t4847+t4990; + coeffs_dxz->coeff_p2_m2_0 = t4824+t5000; + coeffs_dxz->coeff_m2_m1_0 = t4830+t4981; + coeffs_dxz->coeff_m1_m1_0 = t4873+t4985; + coeffs_dxz->coeff_0_m1_0 = t4826; + coeffs_dxz->coeff_p1_m1_0 = t4847+t4984; + coeffs_dxz->coeff_p2_m1_0 = t4820+t5000; + coeffs_dxz->coeff_m2_0_0 = t4981; + coeffs_dxz->coeff_m1_0_0 = t4821+t4873; + coeffs_dxz->coeff_0_0_0 = t4826; + coeffs_dxz->coeff_p1_0_0 = t4821+t4847; + coeffs_dxz->coeff_p2_0_0 = t5000; + coeffs_dxz->coeff_m2_p1_0 = t4820+t4981; + coeffs_dxz->coeff_m1_p1_0 = t4873+t4984; + coeffs_dxz->coeff_0_p1_0 = t4826; + coeffs_dxz->coeff_p1_p1_0 = t4847+t4985; + coeffs_dxz->coeff_p2_p1_0 = t4830+t5000; + coeffs_dxz->coeff_m2_p2_0 = t4824+t4981; + coeffs_dxz->coeff_m1_p2_0 = t4873+t4990; + coeffs_dxz->coeff_0_p2_0 = t4826; + coeffs_dxz->coeff_p1_p2_0 = t4847+t4986; + coeffs_dxz->coeff_p2_p2_0 = t4840+t5000; + coeffs_dxz->coeff_m2_m2_p1 = t4928+t5040; + coeffs_dxz->coeff_m1_m2_p1 = t4932+t5027; + coeffs_dxz->coeff_0_m2_p1 = t4837+t4977; + coeffs_dxz->coeff_p1_m2_p1 = t4937+t5029; + coeffs_dxz->coeff_p2_m2_p1 = t4929+t5031; + coeffs_dxz->coeff_m2_m1_p1 = t4915+t5040; + coeffs_dxz->coeff_m1_m1_p1 = t4844+t4930+t5014; + coeffs_dxz->coeff_0_m1_p1 = t4827+t4977; + coeffs_dxz->coeff_p1_m1_p1 = t4843+t4931+t5015; + coeffs_dxz->coeff_p2_m1_p1 = t4920+t5031; + coeffs_dxz->coeff_m2_0_p1 = t4958+t5039; + coeffs_dxz->coeff_m1_0_p1 = t4948+t5012; + coeffs_dxz->coeff_0_0_p1 = t4977; + coeffs_dxz->coeff_p1_0_p1 = t4952+t5011; + coeffs_dxz->coeff_p2_0_p1 = t4947+t5031; + coeffs_dxz->coeff_m2_p1_p1 = t4916+t5040; + coeffs_dxz->coeff_m1_p1_p1 = t4843+t4933+t5014; + coeffs_dxz->coeff_0_p1_p1 = t4833+t4977; + coeffs_dxz->coeff_p1_p1_p1 = t4844+t4931+t5034; + coeffs_dxz->coeff_p2_p1_p1 = t4923+t5031; + coeffs_dxz->coeff_m2_p2_p1 = t4927+t5040; + coeffs_dxz->coeff_m1_p2_p1 = t4932+t5047; + coeffs_dxz->coeff_0_p2_p1 = t4828+t4977; + coeffs_dxz->coeff_p1_p2_p1 = t4937+t5018; + coeffs_dxz->coeff_p2_p2_p1 = t4917+t5031; + coeffs_dxz->coeff_m2_m2_p2 = t4866+t4939+t5028; + coeffs_dxz->coeff_m1_m2_p2 = t4922+t5020; + coeffs_dxz->coeff_0_m2_p2 = t4856+t4994; + coeffs_dxz->coeff_p1_m2_p2 = t4919+t5010; + coeffs_dxz->coeff_p2_m2_p2 = t4857+t4934+t5041; + coeffs_dxz->coeff_m2_m1_p2 = t4870+t4943+t5028; + coeffs_dxz->coeff_m1_m1_p2 = t4918+t5020; + coeffs_dxz->coeff_0_m1_p2 = t4856+t4992; + coeffs_dxz->coeff_p1_m1_p2 = t4925+t5010; + coeffs_dxz->coeff_p2_m1_p2 = t4942+t5042; + coeffs_dxz->coeff_m2_0_p2 = t4946+t5028; + coeffs_dxz->coeff_m1_0_p2 = t4965+t5048; + coeffs_dxz->coeff_0_0_p2 = t5001; + coeffs_dxz->coeff_p1_0_p2 = t4950+t5010; + coeffs_dxz->coeff_p2_0_p2 = t4951+t5017; + coeffs_dxz->coeff_m2_p1_p2 = t4854+t4938+t5028; + coeffs_dxz->coeff_m1_p1_p2 = t4921+t5020; + coeffs_dxz->coeff_0_p1_p2 = t4856+t4988; + coeffs_dxz->coeff_p1_p1_p2 = t4926+t5010; + coeffs_dxz->coeff_p2_p1_p2 = t4942+t5032; + coeffs_dxz->coeff_m2_p2_p2 = t4857+t4936+t5028; + coeffs_dxz->coeff_m1_p2_p2 = t4914+t5020; + coeffs_dxz->coeff_0_p2_p2 = t4836+t5001; + coeffs_dxz->coeff_p1_p2_p2 = t4924+t5010; + coeffs_dxz->coeff_p2_p2_p2 = t4866+t4934+t5049; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..dd418fa --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dy.compute.c @@ -0,0 +1,961 @@ +fp t3545; +fp t3684; +fp t3408; +fp t3547; +fp t3543; +fp t3533; +fp t3456; +fp t3797; +fp t3642; +fp t3542; +fp t3815; +fp t3490; +fp t3429; +fp t3841; +fp t3459; +fp t3526; +fp t3668; +fp t3487; +fp t3840; +fp t3520; +fp t3546; +fp t3453; +fp t3353; +fp t3486; +fp t3789; +fp t3538; +fp t3474; +fp t3476; +fp t3525; +fp t3791; +fp t3624; +fp t3839; +fp t3492; +fp t3419; +fp t3673; +fp t3513; +fp t3793; +fp t3838; +fp t3682; +fp t3377; +fp t3395; +fp t3647; +fp t3688; +fp t3532; +fp t3370; +fp t3475; +fp t3837; +fp t3511; +fp t3446; +fp t3782; +fp t3541; +fp t3836; +fp t3477; +fp t3512; +fp t3466; +fp t3803; +fp t3540; +fp t3517; +fp t3471; +fp t3835; +fp t3516; +fp t3685; +fp t3381; +fp t3340; +fp t3692; +fp t3373; +fp t3834; +fp t3400; +fp t3432; +fp t3833; +fp t3679; +fp t3359; +fp t3335; +fp t3468; +fp t3351; +fp t3832; +fp t3544; +fp t3530; +fp t3831; +fp t3363; +fp t3830; +fp t3382; +fp t3489; +fp t3829; +fp t3828; +fp t3491; +fp t3827; +fp t3479; +fp t3690; +fp t3402; +fp t3826; +fp t3680; +fp t3386; +fp t3368; +fp t3825; +fp t3824; +fp t3372; +fp t3823; +fp t3534; +fp t3404; +fp t3822; +fp t3821; +fp t3485; +fp t3535; +fp t3454; +fp t3661; +fp t3637; +fp t3518; +fp t3455; +fp t3385; +fp t3820; +fp t3819; +fp t3681; +fp t3349; +fp t3341; +fp t3818; +fp t3508; +fp t3678; +fp t3817; +fp t3691; +fp t3336; +fp t3683; +fp t3346; +fp t3816; +fp t3814; +fp t3813; +fp t3503; +fp t3652; +fp t3812; +fp t3811; +fp t3352; +fp t3810; +fp t3409; +fp t3391; +fp t3809; +fp t3426; +fp t3808; +fp t3687; +fp t3406; +fp t3342; +fp t3807; +fp t3806; +fp t3462; +fp t3805; +fp t3804; +fp t3802; +fp t3801; +fp t3415; +fp t3639; +fp t3457; +fp t3358; +fp t3800; +fp t3799; +fp t3686; +fp t3388; +fp t3384; +fp t3798; +fp t3488; +fp t3796; +fp t3689; +fp t3361; +fp t3362; +fp t3795; +fp t3473; +fp t3794; +fp t3792; +fp t3464; +fp t3403; +fp t3790; +fp t3407; +fp t3788; +fp t3451; +fp t3787; +fp t3786; +fp t3398; +fp t3785; +fp t3784; +fp t3783; +fp t3781; +fp t3643; +fp t3636; +fp t3506; +fp t3780; +fp t3779; +fp t3778; +fp t3417; +fp t3777; +fp t3776; +fp t3374; +fp t3775; +fp t3420; +fp t3774; +fp t3773; +fp t3772; +fp t3771; +fp t3387; +fp t3770; +fp t3337; +fp t3769; +fp t3405; +fp t3768; +fp t3501; +fp t3767; +fp t3766; +fp t3389; +fp t3338; +fp t3765; +fp t3360; +fp t3645; +fp t3764; +fp t3763; +fp t3364; +fp t3413; +fp t3762; +fp t3761; +fp t3366; +fp t3760; +fp t3465; +fp t3663; +fp t3759; +fp t3480; +fp t3758; +fp t3757; +fp t3401; +fp t3756; +fp t3755; +fp t3666; +fp t3754; +fp t3753; +fp t3752; +fp t3496; +fp t3751; +fp t3750; +fp t3749; +fp t3635; +fp t3484; +fp t3748; +fp t3375; +fp t3394; +fp t3747; +fp t3746; +fp t3483; +fp t3745; +fp t3482; +fp t3744; +fp t3495; +fp t3743; +fp t3742; +fp t3741; +fp t3481; +fp t3740; +fp t3739; +fp t3497; +fp t3738; +fp t3737; +fp t3736; +fp t3735; +fp t3378; +fp t3734; +fp t3733; +fp t3732; +fp t3731; +fp t3730; +fp t3641; +fp t3618; +fp t3729; +fp t3504; +fp t3728; +fp t3499; +fp t3727; +fp t3498; +fp t3726; +fp t3725; +fp t3505; +fp t3724; +fp t3441; +fp t3723; +fp t3539; +fp t3722; +fp t3721; +fp t3720; +fp t3719; +fp t3718; +fp t3717; +fp t3716; +fp t3715; +fp t3714; +fp t3713; +fp t3712; +fp t3711; +fp t3710; +fp t3709; +fp t3708; +fp t3707; +fp t3706; +fp t3626; +fp t3705; +fp t3658; +fp t3704; +fp t3703; +fp t3350; +fp t3702; +fp t3701; +fp t3700; +fp t3699; +fp t3430; +fp t3698; +fp t3697; +fp t3696; +fp t3695; +fp t3694; +fp t3693; +fp t3677; +fp t3383; +fp t3676; +fp t3675; +fp t3672; +fp t3671; +fp t3670; +fp t3669; +fp t3667; +fp t3665; +fp t3664; +fp t3662; +fp t3660; +fp t3659; +fp t3657; +fp t3655; +fp t3654; +fp t3650; +fp t3649; +fp t3646; +fp t3644; +fp t3638; +fp t3633; +fp t3632; +fp t3631; +fp t3630; +fp t3628; +fp t3627; +fp t3450; +fp t3625; +fp t3623; +fp t3622; +fp t3621; +fp t3617; +fp t3616; +fp t3615; +fp t3614; +fp t3613; +fp t3612; +fp t3611; +fp t3610; +fp t3609; +fp t3608; +fp t3607; +fp t3606; +fp t3605; +fp t3604; +fp t3603; +fp t3602; +fp t3601; +fp t3600; +fp t3599; +fp t3598; +fp t3597; +fp t3596; +fp t3422; +fp t3595; +fp t3594; +fp t3593; +fp t3592; +fp t3591; +fp t3590; +fp t3589; +fp t3588; +fp t3587; +fp t3586; +fp t3585; +fp t3584; +fp t3583; +fp t3582; +fp t3581; +fp t3580; +fp t3579; +fp t3392; +fp t3578; +fp t3577; +fp t3576; +fp t3357; +fp t3575; +fp t3574; +fp t3573; +fp t3572; +fp t3571; +fp t3570; +fp t3569; +fp t3568; +fp t3567; +fp t3566; +fp t3565; +fp t3564; +fp t3563; +fp t3562; +fp t3561; +fp t3560; +fp t3559; +fp t3558; +fp t3557; +fp t3556; +fp t3555; +fp t3339; +fp t3554; +fp t3553; +fp t3552; +fp t3551; +fp t3347; +fp t3343; + t3545 = z*z; + t3684 = y*RATIONAL(-1.0,245.0); + t3408 = t3545*t3684; + t3547 = y*y; + t3543 = t3547*y; + t3533 = RATIONAL(1.0,150.0); + t3456 = t3533*t3543; + t3797 = t3408+t3456; + t3642 = t3547*RATIONAL(-1.0,200.0); + t3542 = t3545*z; + t3815 = t3533*t3542+z*t3642; + t3490 = RATIONAL(-167.0,7000.0); + t3429 = t3490*z; + t3841 = t3797+t3815+t3429; + t3459 = RATIONAL(-1.0,100.0)*t3547; + t3526 = RATIONAL(-1.0,300.0); + t3668 = z*t3459+t3526*t3542; + t3487 = RATIONAL(137.0,5250.0); + t3840 = t3487*z+t3668; + t3520 = RATIONAL(1.0,350.0); + t3546 = x*x; + t3453 = t3520*t3546; + t3353 = z*t3453; + t3486 = RATIONAL(107.0,7000.0); + t3789 = t3353+t3486*z; + t3538 = RATIONAL(-2.0,75.0); + t3474 = t3538*t3543; + t3476 = RATIONAL(-1.0,50.0)*t3547; + t3525 = RATIONAL(1.0,600.0); + t3791 = z*t3476+t3525*t3542; + t3624 = t3474+t3408+t3791; + t3839 = t3789+t3624; + t3492 = RATIONAL(167.0,7000.0); + t3419 = t3492*z; + t3673 = t3547*RATIONAL(1.0,200.0); + t3513 = RATIONAL(-1.0,150.0); + t3793 = t3513*t3542+z*t3673; + t3838 = t3419+t3793+t3797; + t3682 = y*RATIONAL(2.0,245.0); + t3377 = t3546*t3682; + t3395 = t3545*t3682; + t3647 = t3377+t3395; + t3688 = y*t3545; + t3532 = RATIONAL(1.0,245.0); + t3370 = t3532*t3688; + t3475 = RATIONAL(1.0,25.0)*t3543; + t3837 = t3370+t3475; + t3511 = RATIONAL(-1.0,700.0); + t3446 = t3511*t3545; + t3782 = t3476+t3453; + t3541 = RATIONAL(1.0,42.0); + t3836 = t3446+t3782+t3541; + t3477 = RATIONAL(1.0,50.0)*t3547; + t3512 = RATIONAL(1.0,700.0); + t3466 = t3512*t3545; + t3803 = t3477+t3466; + t3540 = RATIONAL(-1.0,42.0); + t3517 = RATIONAL(-1.0,350.0); + t3471 = t3517*t3546; + t3835 = t3803+t3540+t3471; + t3516 = RATIONAL(-1.0,175.0); + t3685 = y*t3516; + t3381 = x*t3685; + t3340 = z*t3381; + t3692 = x*z; + t3373 = RATIONAL(-1.0,250.0)*t3692; + t3834 = t3340+t3373; + t3400 = x*t3446; + t3432 = RATIONAL(211.0,3675.0)*y; + t3833 = t3432+t3400+t3474; + t3679 = y*t3517; + t3359 = z*t3679; + t3335 = x*t3359; + t3468 = t3512*t3546; + t3351 = z*t3468; + t3832 = t3335+t3351; + t3544 = t3546*x; + t3530 = RATIONAL(-1.0,600.0); + t3831 = x*t3477+t3530*t3544; + t3363 = RATIONAL(1.0,250.0)*t3692; + t3830 = t3363+t3340; + t3382 = z*t3471; + t3489 = RATIONAL(-107.0,7000.0); + t3829 = t3489*z+t3382; + t3828 = x*t3476+t3525*t3544; + t3491 = RATIONAL(187.0,7000.0); + t3827 = t3382+t3491*z; + t3479 = RATIONAL(4.0,75.0)*y; + t3690 = y*t3546; + t3402 = t3532*t3690; + t3826 = t3479+t3402; + t3680 = y*RATIONAL(-2.0,245.0); + t3386 = t3545*t3680; + t3368 = RATIONAL(311.0,14700.0)*y; + t3825 = t3386+t3368; + t3824 = t3386+RATIONAL(431.0,14700.0)*y; + t3372 = RATIONAL(-169.0,14700.0)*y; + t3823 = t3372+RATIONAL(-19.0,2100.0); + t3534 = RATIONAL(1.0,490.0); + t3404 = t3534*t3690; + t3822 = t3474+t3404; + t3821 = t3530*t3542+z*t3477; + t3485 = RATIONAL(-137.0,5250.0); + t3535 = RATIONAL(1.0,300.0); + t3454 = RATIONAL(1.0,100.0)*t3547; + t3661 = t3535*t3544+x*t3454; + t3637 = t3485*x+t3661; + t3518 = RATIONAL(1.0,175.0); + t3455 = t3518*t3545; + t3385 = x*t3455; + t3820 = t3637+t3385; + t3819 = t3372+RATIONAL(19.0,2100.0); + t3681 = y*t3518; + t3349 = x*t3681; + t3341 = z*t3349; + t3818 = t3363+t3341; + t3508 = RATIONAL(-1.0,1400.0); + t3678 = z*t3546; + t3817 = t3508*t3678+t3840; + t3691 = y*t3692; + t3336 = t3511*t3691; + t3683 = x*t3545; + t3346 = t3508*t3683; + t3816 = t3336+t3346; + t3814 = RATIONAL(-17.0,525.0)+t3466; + t3813 = t3477+t3468; + t3503 = RATIONAL(47.0,5250.0); + t3652 = x*t3459+t3526*t3544; + t3812 = t3652+t3503*x; + t3811 = x*t3673+t3513*t3544; + t3352 = t3534*t3688; + t3810 = t3352+RATIONAL(166.0,3675.0)*y; + t3409 = z*t3681; + t3391 = RATIONAL(1.0,500.0)*t3692; + t3809 = t3409+t3391; + t3426 = RATIONAL(151.0,3675.0)*y; + t3808 = t3426+t3402; + t3687 = y*t3520; + t3406 = x*t3687; + t3342 = z*t3406; + t3807 = t3351+t3342; + t3806 = t3446+RATIONAL(17.0,525.0); + t3462 = t3516*t3546; + t3805 = t3377+t3462; + t3804 = t3373+t3341; + t3802 = t3462+t3455; + t3801 = t3352+t3474; + t3415 = t3487*x; + t3639 = t3415+t3652; + t3457 = t3516*t3545; + t3358 = x*t3457; + t3800 = t3639+t3358; + t3799 = t3426+t3370; + t3686 = y*RATIONAL(-2.0,175.0); + t3388 = x*t3686; + t3384 = RATIONAL(-1.0,125.0)*t3692; + t3798 = t3388+t3384; + t3488 = RATIONAL(-187.0,7000.0); + t3796 = t3353+t3488*z; + t3689 = y*RATIONAL(2.0,175.0); + t3361 = x*t3689; + t3362 = RATIONAL(1.0,125.0)*t3692; + t3795 = t3361+t3362; + t3473 = t3517*t3545; + t3794 = t3473+t3477; + t3792 = t3476+t3471; + t3464 = t3511*t3546; + t3403 = z*t3464; + t3790 = t3403+t3342; + t3407 = RATIONAL(-1.0,500.0)*t3692; + t3788 = t3407+t3409; + t3451 = t3518*t3546; + t3787 = t3457+t3451; + t3786 = t3403+t3335; + t3398 = z*t3685; + t3785 = t3398+t3391; + t3784 = t3533*t3544+x*t3642; + t3783 = t3464+t3476; + t3781 = t3377+t3451; + t3643 = t3535*t3542+z*t3454; + t3636 = t3485*z+t3643; + t3506 = RATIONAL(1.0,1400.0); + t3780 = t3506*t3678+t3636; + t3779 = t3407+t3398; + t3778 = t3506*t3683+t3637; + t3417 = t3489*x; + t3777 = t3417+t3784; + t3776 = t3408+t3821; + t3374 = t3546*t3684; + t3775 = t3374+t3828; + t3420 = t3486*x; + t3774 = t3420+t3811; + t3773 = t3374+t3831; + t3772 = t3353+t3668+t3503*z; + t3771 = t3429+t3821; + t3387 = RATIONAL(191.0,14700.0)*y; + t3770 = t3387+t3784; + t3337 = z*t3388; + t3769 = t3337+t3800; + t3405 = x*t3466; + t3768 = t3490*x+t3374+t3405; + t3501 = RATIONAL(-17.0,5250.0); + t3767 = t3501*x+t3358+t3661; + t3766 = t3374+t3471+t3395+t3455; + t3389 = z*t3689; + t3338 = x*t3389; + t3765 = t3338+t3820; + t3360 = t3546*t3680; + t3645 = t3386+t3475; + t3764 = t3360+RATIONAL(-33.0,490.0)*y+t3645; + t3763 = t3432+t3831; + t3364 = x*t3473; + t3413 = RATIONAL(256.0,3675.0)*y; + t3762 = t3364+t3413+t3417; + t3761 = t3336+t3780; + t3366 = z*t3462; + t3760 = t3501*z+t3643+t3366; + t3465 = t3520*t3545; + t3663 = t3465+t3453; + t3759 = t3476+t3663+RATIONAL(8.0,525.0); + t3480 = RATIONAL(-9.0,98.0)*y; + t3758 = t3645+t3402+t3480; + t3757 = t3359+t3817; + t3401 = x*t3679; + t3756 = t3401+t3778; + t3755 = RATIONAL(-11.0,420.0)+t3451+t3455; + t3666 = t3473+t3471; + t3754 = RATIONAL(17.0,2100.0)+t3454+t3666; + t3753 = t3401+t3783; + t3752 = RATIONAL(-17.0,2100.0)+t3663+t3459; + t3496 = RATIONAL(17.0,5250.0); + t3751 = t3652+t3496*x+t3385; + t3750 = RATIONAL(-57.0,490.0)*y+t3402+t3837; + t3749 = t3406+t3813; + t3635 = t3408+t3661; + t3484 = RATIONAL(-229.0,10500.0); + t3748 = t3484*x+t3635+t3404; + t3375 = RATIONAL(-529.0,14700.0)*y; + t3394 = z*t3451; + t3747 = t3636+t3375+t3394; + t3746 = t3419+t3791; + t3483 = RATIONAL(229.0,10500.0); + t3745 = t3432+t3483*x+t3405; + t3482 = RATIONAL(-289.0,10500.0); + t3744 = t3482*x+t3661+t3405; + t3495 = RATIONAL(-47.0,5250.0); + t3743 = t3382+t3643+t3495*z; + t3742 = t3668+t3496*z+t3394; + t3741 = t3477+RATIONAL(-8.0,525.0)+t3666; + t3481 = RATIONAL(289.0,10500.0); + t3740 = t3400+t3652+t3481*x; + t3739 = t3360+t3480+t3837; + t3497 = RATIONAL(-37.0,1050.0); + t3738 = t3453+t3497+t3803; + t3737 = t3363+t3743; + t3736 = t3363+t3741; + t3735 = t3815+t3829; + t3378 = x*t3465; + t3734 = t3378+t3361+t3812; + t3733 = t3363+t3772; + t3732 = t3477+t3538+t3465+t3471; + t3731 = t3796+t3815; + t3730 = t3793+t3827; + t3641 = t3459+t3456; + t3618 = t3457+t3395+t3641; + t3729 = t3618+t3453+t3374+t3819; + t3504 = RATIONAL(-29.0,2100.0); + t3728 = t3504+t3459+t3453+t3455; + t3499 = RATIONAL(37.0,1050.0); + t3727 = t3499+t3446+t3792; + t3498 = RATIONAL(29.0,2100.0); + t3726 = t3498+t3457+t3454+t3471; + t3725 = t3454+t3755; + t3505 = RATIONAL(11.0,420.0); + t3724 = t3457+t3462+t3459+t3505; + t3441 = t3495*x; + t3723 = t3388+t3364+t3441+t3661; + t3539 = RATIONAL(2.0,75.0); + t3722 = t3473+t3539+t3782; + t3721 = t3363+t3759; + t3720 = t3806+t3810; + t3719 = t3391+t3754; + t3718 = t3373+t3759; + t3717 = t3407+t3752; + t3716 = t3391+t3752; + t3715 = t3407+t3754; + t3714 = t3789+t3793; + t3713 = t3538+t3453+t3794; + t3712 = t3373+t3772; + t3711 = t3465+t3539+t3792; + t3710 = t3373+t3741; + t3709 = t3373+t3743; + t3708 = t3398+t3735; + t3707 = t3359+t3835; + t3706 = t3381+t3836; + t3626 = t3813+t3822; + t3705 = t3626+t3810+t3814; + t3658 = t3465+t3408; + t3704 = t3641+t3658+t3805+t3819; + t3703 = t3401+t3540+t3468+t3794; + t3350 = z*t3687; + t3702 = t3350+t3835; + t3701 = t3409+t3714; + t3700 = t3746+t3786; + t3699 = t3366+t3375+t3456+t3647+t3840; + t3430 = t3492*x; + t3698 = t3352+t3430+t3775; + t3697 = t3465+t3541+t3406+t3783; + t3696 = t3349+t3836; + t3695 = t3771+t3807; + t3694 = t3400+t3374+t3430+t3387+t3811; + t3693 = t3378+t3420+t3413+t3775; + t3677 = RATIONAL(-61.0,490.0)*y+t3475; + t3383 = z*t3686; + t3676 = t3361+t3383; + t3675 = t3383+t3341; + t3672 = t3360+t3395; + t3671 = t3398+t3349; + t3670 = t3388+t3389; + t3669 = t3454+t3456; + t3667 = t3340+t3389; + t3665 = t3378+t3456; + t3664 = t3398+t3381; + t3662 = t3388+t3383; + t3660 = t3473+t3408; + t3659 = t3341+t3389; + t3657 = t3386+t3377; + t3655 = t3340+t3383; + t3654 = t3361+t3389; + t3650 = t3409+t3381; + t3649 = t3409+t3349; + t3646 = t3474+t3370; + t3644 = RATIONAL(-1.0,10.0)*y+t3475; + t3638 = t3491*x+t3364+t3374; + t3633 = t3395+t3402+t3677; + t3632 = t3474+t3776; + t3631 = t3474+t3773; + t3630 = t3668+t3801; + t3628 = t3643+t3801; + t3627 = t3360+t3462+t3669; + t3450 = t3526*y; + t3625 = t3450+t3526+t3669; + t3623 = t3644+t3657; + t3622 = t3783+t3822; + t3621 = t3402+RATIONAL(136.0,3675.0)*y+t3646; + t3617 = t3644+t3672; + t3616 = t3360+t3451+t3641; + t3615 = t3652+t3822; + t3614 = t3535+t3450+t3641; + t3613 = t3377+t3370+t3677; + t3612 = t3409+t3750; + t3611 = t3364+t3669+t3823; + t3610 = t3768+t3786; + t3609 = t3338+t3764; + t3608 = t3768+t3807; + t3607 = t3340+t3739; + t3606 = t3398+t3750; + t3605 = t3337+t3764; + t3604 = t3832+t3833; + t3603 = t3381+t3758; + t3602 = t3341+t3739; + t3601 = t3790+t3833; + t3600 = t3454+t3665+t3823; + t3599 = t3349+t3758; + t3598 = t3615+t3753; + t3597 = t3614+t3672+t3787; + t3596 = t3624+t3826+t3827; + t3422 = t3488*x; + t3595 = t3422+t3374+t3665+t3784+t3825; + t3594 = t3465+t3497+t3626+t3799; + t3593 = t3498+t3368+t3627+t3660; + t3592 = t3456+t3638+t3811+t3825; + t3591 = t3481*z+t3403+t3630+t3808; + t3590 = t3614+t3657+t3802; + t3589 = t3482*z+t3351+t3628+t3808; + t3588 = t3378+t3422+t3479+t3370+t3631; + t3587 = t3499+t3473+t3622+t3799; + t3586 = t3625+t3672+t3802; + t3585 = t3368+t3504+t3616+t3658; + t3584 = t3625+t3657+t3787; + t3583 = t3479+t3638+t3646+t3828; + t3582 = t3632+t3796+t3826; + t3581 = t3540+t3615+t3660+t3745+t3749; + t3580 = t3389+t3647+t3669+t3747+t3755; + t3579 = t3349+t3600+t3766+t3774; + t3392 = t3483*z; + t3578 = t3392+t3608+t3630+t3763; + t3577 = t3608+t3770+t3841; + t3576 = t3381+t3611+t3766+t3777; + t3357 = t3484*z; + t3575 = t3357+t3610+t3628+t3763; + t3574 = t3340+t3693+t3839; + t3573 = t3473+t3361+t3441+t3611+t3635+t3781; + t3572 = t3392+t3604+t3668+t3698; + t3571 = t3364+t3349+t3729+t3777; + t3570 = t3340+t3631+t3762+t3776+t3829; + t3569 = t3338+t3699+t3800; + t3568 = t3604+t3748+t3771; + t3567 = t3694+t3790+t3838; + t3566 = t3341+t3632+t3693+t3829; + t3565 = t3378+t3381+t3729+t3774; + t3564 = t3398+t3704+t3714; + t3563 = t3601+t3746+t3748; + t3562 = t3341+t3762+t3773+t3839; + t3561 = t3337+t3699+t3820; + t3560 = t3610+t3770+t3838; + t3559 = t3406+t3622+t3720+t3778; + t3558 = t3541+t3598+t3658+t3745; + t3557 = t3694+t3832+t3841; + t3556 = t3350+t3705+t3817; + t3555 = t3409+t3704+t3735; + t3339 = t3512*t3691; + t3554 = t3339+t3415+t3346+t3615+t3780+t3810; + t3553 = t3383+t3505+t3618+t3747+t3805; + t3552 = t3388+t3600+t3660+t3781+t3812; + t3551 = t3357+t3601+t3643+t3698; + t3347 = RATIONAL(-1.0,1000.0)*t3692; + t3343 = RATIONAL(1.0,1000.0)*t3692; + coeffs_dy->coeff_m2_m2_m2 = t3553+t3765+t3798; + coeffs_dy->coeff_m1_m2_m2 = t3565+t3675+t3709; + coeffs_dy->coeff_0_m2_m2 = t3383+t3597+t3760; + coeffs_dy->coeff_p1_m2_m2 = t3571+t3655+t3737; + coeffs_dy->coeff_p2_m2_m2 = t3553+t3769+t3795; + coeffs_dy->coeff_m2_m1_m2 = t3574+t3649+t3710; + coeffs_dy->coeff_m1_m1_m2 = t3581+t3700+t3788; + coeffs_dy->coeff_0_m1_m2 = t3409+t3596+t3713; + coeffs_dy->coeff_p1_m1_m2 = t3563+t3703+t3809; + coeffs_dy->coeff_p2_m1_m2 = t3562+t3650+t3736; + coeffs_dy->coeff_m2_0_m2 = t3605+t3654; + coeffs_dy->coeff_m1_0_m2 = t3599+t3667; + coeffs_dy->coeff_0_0_m2 = t3389+t3623; + coeffs_dy->coeff_p1_0_m2 = t3603+t3659; + coeffs_dy->coeff_p2_0_m2 = t3609+t3670; + coeffs_dy->coeff_m2_p1_m2 = t3570+t3649+t3721; + coeffs_dy->coeff_m1_p1_m2 = t3568+t3697+t3809; + coeffs_dy->coeff_0_p1_m2 = t3409+t3582+t3711; + coeffs_dy->coeff_p1_p1_m2 = t3558+t3695+t3788; + coeffs_dy->coeff_p2_p1_m2 = t3566+t3650+t3718; + coeffs_dy->coeff_m2_p2_m2 = t3362+t3569+t3662+t3725; + coeffs_dy->coeff_m1_p2_m2 = t3576+t3675+t3733; + coeffs_dy->coeff_0_p2_m2 = t3383+t3586+t3742; + coeffs_dy->coeff_p1_p2_m2 = t3579+t3655+t3712; + coeffs_dy->coeff_p2_p2_m2 = t3561+t3384+t3676+t3725; + coeffs_dy->coeff_m2_m2_m1 = t3564+t3723+t3804; + coeffs_dy->coeff_m1_m2_m1 = t3567+t3664+t3717; + coeffs_dy->coeff_0_m2_m1 = t3398+t3585+t3730; + coeffs_dy->coeff_p1_m2_m1 = t3560+t3671+t3716; + coeffs_dy->coeff_p2_m2_m1 = t3564+t3734+t3830; + coeffs_dy->coeff_m2_m1_m1 = t3572+t3407+t3349+t3702; + coeffs_dy->coeff_m1_m1_m1 = t3347+t3556+t3406+t3639+t3816; + coeffs_dy->coeff_0_m1_m1 = t3350+t3591+t3738; + coeffs_dy->coeff_p1_m1_m1 = t3339+t3343+t3556+t3756; + coeffs_dy->coeff_p2_m1_m1 = t3381+t3391+t3578+t3702; + coeffs_dy->coeff_m2_0_m1 = t3409+t3361+t3607; + coeffs_dy->coeff_m1_0_m1 = t3349+t3335+t3612; + coeffs_dy->coeff_0_0_m1 = t3409+t3613; + coeffs_dy->coeff_p1_0_m1 = t3342+t3381+t3612; + coeffs_dy->coeff_p2_0_m1 = t3388+t3409+t3602; + coeffs_dy->coeff_m2_p1_m1 = t3575+t3391+t3350+t3696; + coeffs_dy->coeff_m1_p1_m1 = t3343+t3350+t3559+t3761; + coeffs_dy->coeff_0_p1_m1 = t3350+t3589+t3727; + coeffs_dy->coeff_p1_p1_m1 = t3347+t3554+t3350+t3753+t3806; + coeffs_dy->coeff_p2_p1_m1 = t3551+t3407+t3350+t3706; + coeffs_dy->coeff_m2_p2_m1 = t3552+t3708+t3818; + coeffs_dy->coeff_m1_p2_m1 = t3577+t3664+t3719; + coeffs_dy->coeff_0_p2_m1 = t3398+t3593+t3731; + coeffs_dy->coeff_p1_p2_m1 = t3557+t3671+t3715; + coeffs_dy->coeff_p2_p2_m1 = t3573+t3708+t3834; + coeffs_dy->coeff_m2_m2_0 = t3388+t3590+t3767; + coeffs_dy->coeff_m1_m2_0 = t3381+t3592+t3728; + coeffs_dy->coeff_0_m2_0 = t3455+RATIONAL(-41.0,2100.0)+t3616+t3824; + coeffs_dy->coeff_p1_m2_0 = t3349+t3595+t3728; + coeffs_dy->coeff_p2_m2_0 = t3361+t3590+t3751; + coeffs_dy->coeff_m2_m1_0 = t3349+t3583+t3732; + coeffs_dy->coeff_m1_m1_0 = t3406+t3594+t3740; + coeffs_dy->coeff_0_m1_0 = RATIONAL(-4.0,105.0)+t3477+t3621+t3663; + coeffs_dy->coeff_p1_m1_0 = t3401+t3594+t3744; + coeffs_dy->coeff_p2_m1_0 = t3381+t3588+t3732; + coeffs_dy->coeff_m2_0_0 = t3361+t3617; + coeffs_dy->coeff_m1_0_0 = t3349+t3633; + coeffs_dy->coeff_0_0_0 = RATIONAL(-13.0,98.0)*y+t3475+t3647; + coeffs_dy->coeff_p1_0_0 = t3381+t3633; + coeffs_dy->coeff_p2_0_0 = t3388+t3617; + coeffs_dy->coeff_m2_p1_0 = t3349+t3588+t3722; + coeffs_dy->coeff_m1_p1_0 = t3406+t3587+t3744; + coeffs_dy->coeff_0_p1_0 = RATIONAL(4.0,105.0)+t3476+t3621+t3666; + coeffs_dy->coeff_p1_p1_0 = t3401+t3587+t3740; + coeffs_dy->coeff_p2_p1_0 = t3381+t3583+t3722; + coeffs_dy->coeff_m2_p2_0 = t3388+t3584+t3751; + coeffs_dy->coeff_m1_p2_0 = t3381+t3595+t3726; + coeffs_dy->coeff_0_p2_0 = RATIONAL(41.0,2100.0)+t3457+t3627+t3824; + coeffs_dy->coeff_p1_p2_0 = t3349+t3592+t3726; + coeffs_dy->coeff_p2_p2_0 = t3361+t3584+t3767; + coeffs_dy->coeff_m2_m2_p1 = t3555+t3723+t3830; + coeffs_dy->coeff_m1_m2_p1 = t3557+t3650+t3716; + coeffs_dy->coeff_0_m2_p1 = t3409+t3585+t3731; + coeffs_dy->coeff_p1_m2_p1 = t3577+t3649+t3717; + coeffs_dy->coeff_p2_m2_p1 = t3555+t3734+t3804; + coeffs_dy->coeff_m2_m1_p1 = t3551+t3391+t3349+t3707; + coeffs_dy->coeff_m1_m1_p1 = t3554+t3343+t3359+t3749+t3814; + coeffs_dy->coeff_0_m1_p1 = t3359+t3589+t3738; + coeffs_dy->coeff_p1_m1_p1 = t3347+t3359+t3705+t3756+t3761; + coeffs_dy->coeff_p2_m1_p1 = t3407+t3575+t3381+t3707; + coeffs_dy->coeff_m2_0_p1 = t3361+t3398+t3602; + coeffs_dy->coeff_m1_0_p1 = t3349+t3342+t3606; + coeffs_dy->coeff_0_0_p1 = t3398+t3613; + coeffs_dy->coeff_p1_0_p1 = t3335+t3381+t3606; + coeffs_dy->coeff_p2_0_p1 = t3398+t3388+t3607; + coeffs_dy->coeff_m2_p1_p1 = t3407+t3578+t3359+t3696; + coeffs_dy->coeff_m1_p1_p1 = t3347+t3339+t3559+t3757; + coeffs_dy->coeff_0_p1_p1 = t3359+t3591+t3727; + coeffs_dy->coeff_p1_p1_p1 = t3343+t3598+t3415+t3720+t3757+t3816; + coeffs_dy->coeff_p2_p1_p1 = t3572+t3391+t3359+t3706; + coeffs_dy->coeff_m2_p2_p1 = t3552+t3701+t3834; + coeffs_dy->coeff_m1_p2_p1 = t3560+t3650+t3715; + coeffs_dy->coeff_0_p2_p1 = t3409+t3593+t3730; + coeffs_dy->coeff_p1_p2_p1 = t3567+t3649+t3719; + coeffs_dy->coeff_p2_p2_p1 = t3573+t3701+t3818; + coeffs_dy->coeff_m2_m2_p2 = t3561+t3362+t3670+t3724; + coeffs_dy->coeff_m1_m2_p2 = t3565+t3667+t3733; + coeffs_dy->coeff_0_m2_p2 = t3389+t3597+t3742; + coeffs_dy->coeff_p1_m2_p2 = t3571+t3659+t3712; + coeffs_dy->coeff_p2_m2_p2 = t3569+t3384+t3654+t3724; + coeffs_dy->coeff_m2_m1_p2 = t3566+t3671+t3736; + coeffs_dy->coeff_m1_m1_p2 = t3581+t3695+t3785; + coeffs_dy->coeff_0_m1_p2 = t3398+t3582+t3713; + coeffs_dy->coeff_p1_m1_p2 = t3568+t3703+t3779; + coeffs_dy->coeff_p2_m1_p2 = t3570+t3664+t3710; + coeffs_dy->coeff_m2_0_p2 = t3609+t3676; + coeffs_dy->coeff_m1_0_p2 = t3599+t3675; + coeffs_dy->coeff_0_0_p2 = t3383+t3623; + coeffs_dy->coeff_p1_0_p2 = t3603+t3655; + coeffs_dy->coeff_p2_0_p2 = t3605+t3662; + coeffs_dy->coeff_m2_p1_p2 = t3562+t3671+t3718; + coeffs_dy->coeff_m1_p1_p2 = t3563+t3697+t3779; + coeffs_dy->coeff_0_p1_p2 = t3398+t3596+t3711; + coeffs_dy->coeff_p1_p1_p2 = t3558+t3700+t3785; + coeffs_dy->coeff_p2_p1_p2 = t3574+t3664+t3721; + coeffs_dy->coeff_m2_p2_p2 = t3580+t3769+t3798; + coeffs_dy->coeff_m1_p2_p2 = t3576+t3667+t3709; + coeffs_dy->coeff_0_p2_p2 = t3389+t3586+t3760; + coeffs_dy->coeff_p1_p2_p2 = t3579+t3659+t3737; + coeffs_dy->coeff_p2_p2_p2 = t3580+t3765+t3795; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyy.compute.c new file mode 100644 index 0000000..b88054d --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyy.compute.c @@ -0,0 +1,605 @@ +fp t5135; +fp t5142; +fp t5105; +fp t5110; +fp t5308; +fp t5127; +fp t5140; +fp t5094; +fp t5307; +fp t5104; +fp t5069; +fp t5123; +fp t5082; +fp t5063; +fp t5306; +fp t5122; +fp t5086; +fp t5103; +fp t5305; +fp t5113; +fp t5128; +fp t5141; +fp t5084; +fp t5304; +fp t5119; +fp t5079; +fp t5129; +fp t5303; +fp t5133; +fp t5132; +fp t5083; +fp t5302; +fp t5096; +fp t5126; +fp t5097; +fp t5301; +fp t5115; +fp t5300; +fp t5299; +fp t5100; +fp t5071; +fp t5298; +fp t5297; +fp t5091; +fp t5296; +fp t5131; +fp t5088; +fp t5295; +fp t5099; +fp t5294; +fp t5137; +fp t5098; +fp t5293; +fp t5261; +fp t5058; +fp t5292; +fp t5121; +fp t5080; +fp t5291; +fp t5089; +fp t5073; +fp t5290; +fp t5262; +fp t5057; +fp t5289; +fp t5076; +fp t5288; +fp t5109; +fp t5287; +fp t5286; +fp t5120; +fp t5077; +fp t5285; +fp t5284; +fp t5102; +fp t5283; +fp t5282; +fp t5281; +fp t5280; +fp t5075; +fp t5279; +fp t5107; +fp t5278; +fp t5277; +fp t5062; +fp t5276; +fp t5275; +fp t5074; +fp t5274; +fp t5273; +fp t5272; +fp t5271; +fp t5081; +fp t5270; +fp t5085; +fp t5225; +fp t5112; +fp t5269; +fp t5268; +fp t5101; +fp t5267; +fp t5230; +fp t5266; +fp t5125; +fp t5078; +fp t5210; +fp t5265; +fp t5070; +fp t5226; +fp t5264; +fp t5263; +fp t5260; +fp t5259; +fp t5092; +fp t5258; +fp t5257; +fp t5256; +fp t5255; +fp t5254; +fp t5087; +fp t5060; +fp t5253; +fp t5059; +fp t5252; +fp t5067; +fp t5251; +fp t5090; +fp t5250; +fp t5249; +fp t5093; +fp t5248; +fp t5247; +fp t5246; +fp t5245; +fp t5244; +fp t5243; +fp t5242; +fp t5241; +fp t5240; +fp t5239; +fp t5238; +fp t5237; +fp t5236; +fp t5095; +fp t5235; +fp t5065; +fp t5234; +fp t5233; +fp t5232; +fp t5231; +fp t5229; +fp t5227; +fp t5224; +fp t5223; +fp t5222; +fp t5221; +fp t5220; +fp t5219; +fp t5218; +fp t5072; +fp t5217; +fp t5216; +fp t5215; +fp t5214; +fp t5213; +fp t5212; +fp t5211; +fp t5209; +fp t5134; +fp t5208; +fp t5207; +fp t5206; +fp t5205; +fp t5204; +fp t5203; +fp t5202; +fp t5201; +fp t5200; +fp t5199; +fp t5198; +fp t5197; +fp t5196; +fp t5195; +fp t5194; +fp t5193; +fp t5192; +fp t5191; +fp t5190; +fp t5189; +fp t5188; +fp t5187; +fp t5186; +fp t5185; +fp t5184; +fp t5183; +fp t5182; +fp t5181; +fp t5180; +fp t5179; +fp t5178; +fp t5177; +fp t5176; +fp t5175; +fp t5066; +fp t5174; +fp t5173; +fp t5172; +fp t5171; +fp t5170; +fp t5169; +fp t5168; +fp t5114; +fp t5167; +fp t5166; +fp t5165; +fp t5164; +fp t5163; +fp t5162; +fp t5161; +fp t5160; +fp t5064; +fp t5159; +fp t5158; +fp t5157; +fp t5156; +fp t5155; +fp t5154; +fp t5153; +fp t5152; +fp t5151; +fp t5150; +fp t5149; +fp t5148; +fp t5147; +fp t5146; +fp t5145; +fp t5144; +fp t5143; +fp t5068; +fp t5061; + t5135 = RATIONAL(1.0,50.0); + t5142 = y*y; + t5105 = t5135*t5142; + t5110 = RATIONAL(191.0,14700.0); + t5308 = t5105+t5110; + t5127 = RATIONAL(2.0,245.0); + t5140 = z*z; + t5094 = t5127*t5140; + t5307 = t5105+t5094; + t5104 = RATIONAL(-1.0,50.0)*y; + t5069 = x*t5104; + t5123 = RATIONAL(1.0,350.0); + t5082 = t5123*z; + t5063 = x*t5082; + t5306 = t5069+t5063; + t5122 = RATIONAL(1.0,175.0); + t5086 = t5122*z; + t5103 = RATIONAL(1.0,25.0)*y; + t5305 = t5086+t5103; + t5113 = RATIONAL(211.0,3675.0); + t5128 = RATIONAL(1.0,490.0); + t5141 = x*x; + t5084 = t5128*t5141; + t5304 = t5113+t5084; + t5119 = RATIONAL(-2.0,245.0); + t5079 = t5119*t5140; + t5129 = RATIONAL(-1.0,300.0); + t5303 = t5079+t5129; + t5133 = RATIONAL(-9.0,98.0); + t5132 = RATIONAL(1.0,245.0); + t5083 = t5132*t5141; + t5302 = t5133+t5083; + t5096 = t5127*t5141; + t5126 = RATIONAL(-2.0,175.0); + t5097 = t5126*x; + t5301 = t5096+t5097; + t5115 = RATIONAL(151.0,3675.0); + t5300 = t5115+t5083; + t5299 = RATIONAL(-529.0,14700.0)+t5096; + t5100 = RATIONAL(-1.0,25.0)*y; + t5071 = x*t5100; + t5298 = t5071+t5103; + t5297 = t5071+t5100; + t5091 = t5119*t5141; + t5296 = t5129+t5091; + t5131 = RATIONAL(-1.0,245.0); + t5088 = t5131*t5140; + t5295 = t5088+t5110; + t5099 = t5135*y; + t5294 = t5069+t5099; + t5137 = RATIONAL(4.0,75.0); + t5098 = t5132*t5140; + t5293 = t5137+t5098; + t5261 = y*RATIONAL(-1.0,100.0); + t5058 = x*t5261; + t5292 = t5104+t5058; + t5121 = RATIONAL(-1.0,350.0); + t5080 = t5121*x; + t5291 = t5084+t5080; + t5089 = t5121*z; + t5073 = z*t5099; + t5290 = t5089+t5073; + t5262 = y*RATIONAL(1.0,100.0); + t5057 = x*t5262; + t5289 = t5057+t5099; + t5076 = x*t5103; + t5288 = t5076+t5100; + t5109 = RATIONAL(311.0,14700.0); + t5287 = t5079+t5109; + t5286 = t5057+t5094; + t5120 = RATIONAL(-1.0,175.0); + t5077 = t5120*z; + t5285 = t5100+t5077; + t5284 = t5103+t5077; + t5102 = RATIONAL(-2.0,25.0)*t5142; + t5283 = t5102+t5088; + t5282 = t5082+t5073; + t5281 = t5105+t5096; + t5280 = t5058+t5094; + t5075 = x*t5099; + t5279 = t5104+t5075; + t5107 = RATIONAL(-169.0,14700.0); + t5278 = t5088+t5107; + t5277 = t5086+t5100; + t5062 = x*t5089; + t5276 = t5075+t5062; + t5275 = RATIONAL(-33.0,490.0)+t5091; + t5074 = z*t5104; + t5274 = t5089+t5074; + t5273 = t5137+t5083; + t5272 = t5082+t5074; + t5271 = t5113+t5082; + t5081 = t5128*t5140; + t5270 = t5113+t5081+t5089; + t5085 = t5123*x; + t5225 = t5102+t5084+t5085; + t5112 = RATIONAL(166.0,3675.0); + t5269 = t5081+t5225+t5112; + t5268 = t5112+t5291; + t5101 = RATIONAL(3.0,25.0)*t5142; + t5267 = RATIONAL(-57.0,490.0)+t5101+t5083+t5098; + t5230 = t5101+t5091; + t5266 = t5133+t5230+t5098; + t5125 = RATIONAL(2.0,175.0); + t5078 = t5125*z; + t5210 = t5078+t5307; + t5265 = t5210+t5299; + t5070 = z*t5100; + t5226 = t5070+t5283; + t5264 = t5226+t5304; + t5263 = x*z; + t5260 = t5073+t5075; + t5259 = t5086+t5088; + t5092 = t5131*t5141; + t5258 = t5074+t5092; + t5257 = t5077+t5063; + t5256 = t5069+t5073; + t5255 = t5102+t5103; + t5254 = t5073+t5092; + t5087 = t5125*x; + t5060 = z*t5097; + t5253 = t5087+t5060; + t5059 = x*t5077; + t5252 = t5059+t5077; + t5067 = x*t5078; + t5251 = t5067+t5097; + t5090 = t5122*x; + t5250 = t5090+t5092; + t5249 = t5102+t5098; + t5093 = t5120*x; + t5248 = t5093+t5063; + t5247 = t5060+t5097; + t5246 = t5067+t5087; + t5245 = t5086+t5063; + t5244 = t5092+t5093; + t5243 = t5079+t5101; + t5242 = t5090+t5062; + t5241 = t5093+t5078; + t5240 = t5105+t5091; + t5239 = t5090+t5078; + t5238 = t5086+t5062; + t5237 = t5074+t5075; + t5236 = t5105+t5107; + t5095 = t5126*z; + t5235 = t5090+t5095; + t5065 = x*t5086; + t5234 = t5065+t5093; + t5233 = t5086+t5065; + t5232 = t5093+t5095; + t5231 = t5069+t5074; + t5229 = t5090+t5059; + t5227 = RATIONAL(-61.0,490.0)+t5101; + t5224 = t5088+t5250; + t5223 = t5105+t5058+t5092; + t5222 = t5078+t5243; + t5221 = t5081+t5102+t5100; + t5220 = t5087+t5281; + t5219 = t5105+t5109+t5099; + t5218 = t5102+t5244; + t5072 = z*t5103; + t5217 = t5072+t5283; + t5216 = t5095+t5243; + t5215 = t5059+t5236; + t5214 = t5065+t5236; + t5213 = t5102+t5250; + t5212 = t5095+t5307; + t5211 = t5081+t5255; + t5209 = t5092+t5255; + t5134 = RATIONAL(-1.0,10.0); + t5208 = t5134+t5096+t5243; + t5207 = t5134+t5094+t5230; + t5206 = t5077+t5224; + t5205 = t5079+RATIONAL(431.0,14700.0)+t5240; + t5204 = t5083+RATIONAL(136.0,3675.0)+t5249; + t5203 = t5094+t5083+t5227; + t5202 = t5096+t5098+t5227; + t5201 = t5097+t5281+t5303; + t5200 = t5090+t5267; + t5199 = t5104+t5088+t5109+t5240; + t5198 = t5211+t5300; + t5197 = t5226+t5273; + t5196 = t5069+t5104+t5220; + t5195 = t5075+t5099+t5220; + t5194 = t5104+t5073+t5212; + t5193 = t5222+t5275; + t5192 = t5104+t5105+t5057+t5244; + t5191 = t5222+t5302; + t5190 = t5209+t5293; + t5189 = t5216+t5275; + t5188 = t5088+t5091+t5219; + t5187 = t5210+t5296; + t5186 = t5218+t5297; + t5185 = t5217+t5277; + t5184 = t5216+t5302; + t5183 = t5093+t5267; + t5182 = t5217+t5284; + t5181 = t5079+t5092+t5219; + t5180 = t5115+t5098+t5225; + t5179 = t5221+t5300; + t5178 = t5097+t5266; + t5177 = t5115+t5249+t5291; + t5176 = t5087+t5266; + t5175 = t5074+t5099+t5212; + t5066 = RATIONAL(-1.0,700.0)*t5263; + t5174 = t5082+t5066+t5269; + t5173 = t5215+t5258+t5286; + t5172 = t5075+t5063+t5264; + t5171 = t5194+t5299; + t5170 = t5062+t5218+t5270; + t5169 = t5069+t5062+t5264; + t5168 = t5215+t5259+t5301; + t5114 = RATIONAL(256.0,3675.0); + t5167 = t5114+t5102+t5065+t5206; + t5166 = t5063+t5213+t5270; + t5165 = t5175+t5299; + t5164 = t5221+t5254+t5271; + t5163 = t5214+t5258+t5280; + t5162 = t5247+t5265; + t5161 = t5246+t5265; + t5160 = t5195+t5278; + t5064 = RATIONAL(1.0,700.0)*t5263; + t5159 = t5064+t5089+t5269; + t5158 = t5224+t5245+t5308; + t5157 = t5093+t5099+t5223+t5295; + t5156 = t5114+t5088+t5186; + t5155 = t5081+t5074+t5209+t5271; + t5154 = t5069+t5221+t5268; + t5153 = t5182+t5304; + t5152 = t5215+t5254+t5280; + t5151 = t5214+t5254+t5286; + t5150 = t5062+t5206+t5308; + t5149 = t5114+t5076+t5059+t5092+t5217; + t5148 = t5075+t5211+t5268; + t5147 = t5192+t5295; + t5146 = t5196+t5278; + t5145 = t5185+t5304; + t5144 = t5114+t5070+t5209+t5259; + t5143 = t5088+t5077+t5214+t5301; + t5068 = z*t5262; + t5061 = z*t5261; + coeffs_dyy->coeff_m2_m2_m2 = t5075+t5171+t5251; + coeffs_dyy->coeff_m1_m2_m2 = t5104+t5151+t5232; + coeffs_dyy->coeff_0_m2_m2 = t5194+t5296; + coeffs_dyy->coeff_p1_m2_m2 = t5104+t5152+t5235; + coeffs_dyy->coeff_p2_m2_m2 = t5069+t5171+t5253; + coeffs_dyy->coeff_m2_m1_m2 = t5071+t5144+t5229; + coeffs_dyy->coeff_m1_m1_m2 = t5085+t5169+t5305; + coeffs_dyy->coeff_0_m1_m2 = t5197+t5305; + coeffs_dyy->coeff_p1_m1_m2 = t5080+t5172+t5305; + coeffs_dyy->coeff_p2_m1_m2 = t5076+t5144+t5234; + coeffs_dyy->coeff_m2_0_m2 = t5193+t5253; + coeffs_dyy->coeff_m1_0_m2 = t5191+t5229; + coeffs_dyy->coeff_0_0_m2 = t5078+t5208; + coeffs_dyy->coeff_p1_0_m2 = t5191+t5234; + coeffs_dyy->coeff_p2_0_m2 = t5193+t5251; + coeffs_dyy->coeff_m2_p1_m2 = t5090+t5149+t5277; + coeffs_dyy->coeff_m1_p1_m2 = t5085+t5145+t5276; + coeffs_dyy->coeff_0_p1_m2 = t5185+t5273; + coeffs_dyy->coeff_p1_p1_m2 = t5080+t5145+t5306; + coeffs_dyy->coeff_p2_p1_m2 = t5072+t5156+t5233; + coeffs_dyy->coeff_m2_p2_m2 = t5069+t5165+t5251; + coeffs_dyy->coeff_m1_p2_m2 = t5099+t5163+t5232; + coeffs_dyy->coeff_0_p2_m2 = t5175+t5296; + coeffs_dyy->coeff_p1_p2_m2 = t5099+t5173+t5235; + coeffs_dyy->coeff_p2_p2_m2 = t5075+t5165+t5253; + coeffs_dyy->coeff_m2_m2_m1 = t5068+t5143+t5279; + coeffs_dyy->coeff_m1_m2_m1 = t5068+t5147+t5257; + coeffs_dyy->coeff_0_m2_m1 = t5077+t5068+t5199; + coeffs_dyy->coeff_p1_m2_m1 = t5068+t5150+t5292; + coeffs_dyy->coeff_p2_m2_m1 = t5068+t5146+t5252; + coeffs_dyy->coeff_m2_m1_m1 = t5071+t5155+t5242; + coeffs_dyy->coeff_m1_m1_m1 = t5103+t5174+t5231; + coeffs_dyy->coeff_0_m1_m1 = t5198+t5272; + coeffs_dyy->coeff_p1_m1_m1 = t5064+t5148+t5272; + coeffs_dyy->coeff_p2_m1_m1 = t5076+t5155+t5248; + coeffs_dyy->coeff_m2_0_m1 = t5059+t5086+t5176; + coeffs_dyy->coeff_m1_0_m1 = t5200+t5238; + coeffs_dyy->coeff_0_0_m1 = t5086+t5202; + coeffs_dyy->coeff_p1_0_m1 = t5183+t5245; + coeffs_dyy->coeff_p2_0_m1 = t5178+t5233; + coeffs_dyy->coeff_m2_p1_m1 = t5076+t5164+t5242; + coeffs_dyy->coeff_m1_p1_m1 = t5100+t5174+t5260; + coeffs_dyy->coeff_0_p1_m1 = t5179+t5282; + coeffs_dyy->coeff_p1_p1_m1 = t5064+t5154+t5282; + coeffs_dyy->coeff_p2_p1_m1 = t5071+t5164+t5248; + coeffs_dyy->coeff_m2_p2_m1 = t5061+t5143+t5294; + coeffs_dyy->coeff_m1_p2_m1 = t5061+t5157+t5257; + coeffs_dyy->coeff_0_p2_m1 = t5061+t5077+t5188; + coeffs_dyy->coeff_p1_p2_m1 = t5061+t5150+t5289; + coeffs_dyy->coeff_p2_p2_m1 = t5061+t5160+t5252; + coeffs_dyy->coeff_m2_m2_0 = t5201+t5279; + coeffs_dyy->coeff_m1_m2_0 = t5192+t5287; + coeffs_dyy->coeff_0_m2_0 = t5104+t5205; + coeffs_dyy->coeff_p1_m2_0 = t5104+t5090+t5223+t5287; + coeffs_dyy->coeff_p2_m2_0 = t5196+t5303; + coeffs_dyy->coeff_m2_m1_0 = t5071+t5090+t5190; + coeffs_dyy->coeff_m1_m1_0 = t5103+t5069+t5180; + coeffs_dyy->coeff_0_m1_0 = t5103+t5204; + coeffs_dyy->coeff_p1_m1_0 = t5075+t5103+t5177; + coeffs_dyy->coeff_p2_m1_0 = t5076+t5093+t5190; + coeffs_dyy->coeff_m2_0_0 = t5087+t5207; + coeffs_dyy->coeff_m1_0_0 = t5090+t5203; + coeffs_dyy->coeff_0_0_0 = t5101+t5094+t5096+RATIONAL(-13.0,98.0); + coeffs_dyy->coeff_p1_0_0 = t5093+t5203; + coeffs_dyy->coeff_p2_0_0 = t5097+t5207; + coeffs_dyy->coeff_m2_p1_0 = t5213+t5288+t5293; + coeffs_dyy->coeff_m1_p1_0 = t5100+t5075+t5180; + coeffs_dyy->coeff_0_p1_0 = t5100+t5204; + coeffs_dyy->coeff_p1_p1_0 = t5100+t5069+t5177; + coeffs_dyy->coeff_p2_p1_0 = t5186+t5293; + coeffs_dyy->coeff_m2_p2_0 = t5201+t5294; + coeffs_dyy->coeff_m1_p2_0 = t5058+t5093+t5181; + coeffs_dyy->coeff_0_p2_0 = t5099+t5205; + coeffs_dyy->coeff_p1_p2_0 = t5090+t5057+t5181; + coeffs_dyy->coeff_p2_p2_0 = t5195+t5303; + coeffs_dyy->coeff_m2_m2_p1 = t5061+t5168+t5279; + coeffs_dyy->coeff_m1_m2_p1 = t5061+t5147+t5238; + coeffs_dyy->coeff_0_m2_p1 = t5086+t5061+t5199; + coeffs_dyy->coeff_p1_m2_p1 = t5061+t5158+t5292; + coeffs_dyy->coeff_p2_m2_p1 = t5061+t5146+t5233; + coeffs_dyy->coeff_m2_m1_p1 = t5073+t5166+t5298; + coeffs_dyy->coeff_m1_m1_p1 = t5103+t5159+t5256; + coeffs_dyy->coeff_0_m1_p1 = t5198+t5290; + coeffs_dyy->coeff_p1_m1_p1 = t5066+t5148+t5290; + coeffs_dyy->coeff_p2_m1_p1 = t5076+t5103+t5073+t5170; + coeffs_dyy->coeff_m2_0_p1 = t5077+t5065+t5176; + coeffs_dyy->coeff_m1_0_p1 = t5200+t5257; + coeffs_dyy->coeff_0_0_p1 = t5077+t5202; + coeffs_dyy->coeff_p1_0_p1 = t5062+t5077+t5183; + coeffs_dyy->coeff_p2_0_p1 = t5178+t5252; + coeffs_dyy->coeff_m2_p1_p1 = t5074+t5166+t5288; + coeffs_dyy->coeff_m1_p1_p1 = t5100+t5159+t5237; + coeffs_dyy->coeff_0_p1_p1 = t5179+t5274; + coeffs_dyy->coeff_p1_p1_p1 = t5066+t5154+t5274; + coeffs_dyy->coeff_p2_p1_p1 = t5074+t5170+t5297; + coeffs_dyy->coeff_m2_p2_p1 = t5068+t5168+t5294; + coeffs_dyy->coeff_m1_p2_p1 = t5068+t5157+t5238; + coeffs_dyy->coeff_0_p2_p1 = t5086+t5068+t5188; + coeffs_dyy->coeff_p1_p2_p1 = t5068+t5158+t5289; + coeffs_dyy->coeff_p2_p2_p1 = t5068+t5160+t5233; + coeffs_dyy->coeff_m2_m2_p2 = t5104+t5162+t5237; + coeffs_dyy->coeff_m1_m2_p2 = t5104+t5173+t5241; + coeffs_dyy->coeff_0_m2_p2 = t5074+t5104+t5187; + coeffs_dyy->coeff_p1_m2_p2 = t5104+t5163+t5239; + coeffs_dyy->coeff_p2_m2_p2 = t5104+t5161+t5231; + coeffs_dyy->coeff_m2_m1_p2 = t5072+t5167+t5298; + coeffs_dyy->coeff_m1_m1_p2 = t5085+t5153+t5306; + coeffs_dyy->coeff_0_m1_p2 = t5182+t5273; + coeffs_dyy->coeff_p1_m1_p2 = t5080+t5153+t5276; + coeffs_dyy->coeff_p2_m1_p2 = t5093+t5149+t5284; + coeffs_dyy->coeff_m2_0_p2 = t5189+t5246; + coeffs_dyy->coeff_m1_0_p2 = t5090+t5065+t5184; + coeffs_dyy->coeff_0_0_p2 = t5095+t5208; + coeffs_dyy->coeff_p1_0_p2 = t5093+t5059+t5184; + coeffs_dyy->coeff_p2_0_p2 = t5189+t5247; + coeffs_dyy->coeff_m2_p1_p2 = t5070+t5167+t5288; + coeffs_dyy->coeff_m1_p1_p2 = t5085+t5172+t5285; + coeffs_dyy->coeff_0_p1_p2 = t5197+t5285; + coeffs_dyy->coeff_p1_p1_p2 = t5080+t5169+t5285; + coeffs_dyy->coeff_p2_p1_p2 = t5070+t5156+t5252; + coeffs_dyy->coeff_m2_p2_p2 = t5099+t5162+t5256; + coeffs_dyy->coeff_m1_p2_p2 = t5099+t5152+t5241; + coeffs_dyy->coeff_0_p2_p2 = t5073+t5099+t5187; + coeffs_dyy->coeff_p1_p2_p2 = t5099+t5151+t5239; + coeffs_dyy->coeff_p2_p2_p2 = t5099+t5161+t5260; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyz.compute.c new file mode 100644 index 0000000..0b62f5c --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyz.compute.c @@ -0,0 +1,507 @@ +fp t5390; +fp t5365; +fp t5320; +fp t5392; +fp t5351; +fp t5322; +fp t5533; +fp t5400; +fp t5402; +fp t5532; +fp t5466; +fp t5490; +fp t5324; +fp t5462; +fp t5473; +fp t5460; +fp t5401; +fp t5356; +fp t5323; +fp t5531; +fp t5530; +fp t5357; +fp t5349; +fp t5529; +fp t5387; +fp t5337; +fp t5528; +fp t5394; +fp t5340; +fp t5395; +fp t5362; +fp t5527; +fp t5526; +fp t5332; +fp t5525; +fp t5314; +fp t5341; +fp t5469; +fp t5524; +fp t5343; +fp t5523; +fp t5364; +fp t5522; +fp t5315; +fp t5479; +fp t5521; +fp t5520; +fp t5388; +fp t5398; +fp t5519; +fp t5389; +fp t5355; +fp t5518; +fp t5517; +fp t5386; +fp t5345; +fp t5516; +fp t5350; +fp t5515; +fp t5396; +fp t5399; +fp t5514; +fp t5513; +fp t5512; +fp t5511; +fp t5391; +fp t5338; +fp t5353; +fp t5510; +fp t5336; +fp t5359; +fp t5509; +fp t5344; +fp t5508; +fp t5346; +fp t5507; +fp t5506; +fp t5505; +fp t5504; +fp t5503; +fp t5502; +fp t5501; +fp t5330; +fp t5500; +fp t5499; +fp t5498; +fp t5360; +fp t5381; +fp t5319; +fp t5457; +fp t5497; +fp t5496; +fp t5495; +fp t5374; +fp t5494; +fp t5458; +fp t5347; +fp t5493; +fp t5492; +fp t5491; +fp t5489; +fp t5488; +fp t5312; +fp t5486; +fp t5485; +fp t5484; +fp t5329; +fp t5482; +fp t5328; +fp t5481; +fp t5316; +fp t5358; +fp t5478; +fp t5352; +fp t5477; +fp t5311; +fp t5476; +fp t5325; +fp t5475; +fp t5474; +fp t5327; +fp t5471; +fp t5313; +fp t5470; +fp t5468; +fp t5467; +fp t5465; +fp t5464; +fp t5463; +fp t5456; +fp t5455; +fp t5454; +fp t5453; +fp t5452; +fp t5451; +fp t5450; +fp t5449; +fp t5448; +fp t5447; +fp t5446; +fp t5445; +fp t5444; +fp t5443; +fp t5375; +fp t5442; +fp t5380; +fp t5441; +fp t5440; +fp t5439; +fp t5438; +fp t5437; +fp t5436; +fp t5435; +fp t5434; +fp t5433; +fp t5432; +fp t5431; +fp t5318; +fp t5430; +fp t5317; +fp t5309; +fp t5429; +fp t5321; +fp t5310; +fp t5428; +fp t5427; +fp t5426; +fp t5425; +fp t5326; +fp t5424; +fp t5423; +fp t5422; +fp t5421; +fp t5420; +fp t5419; +fp t5418; +fp t5417; +fp t5416; +fp t5415; +fp t5414; +fp t5413; +fp t5412; +fp t5411; +fp t5410; +fp t5409; +fp t5408; +fp t5407; +fp t5406; +fp t5405; +fp t5404; +fp t5403; + t5390 = RATIONAL(-1.0,350.0); + t5365 = t5390*y; + t5320 = x*t5365; + t5392 = RATIONAL(1.0,350.0); + t5351 = t5392*z; + t5322 = x*t5351; + t5533 = t5320+t5322; + t5400 = z*z; + t5402 = y*y; + t5532 = t5400+t5402; + t5466 = t5532*RATIONAL(-1.0,100.0); + t5490 = y*z; + t5324 = RATIONAL(1.0,245.0)*t5490; + t5462 = t5324+t5466; + t5473 = t5532*RATIONAL(1.0,100.0); + t5460 = t5324+t5473; + t5401 = x*x; + t5356 = t5390*t5401; + t5323 = RATIONAL(-2.0,245.0)*t5490; + t5531 = t5356+t5323; + t5530 = t5365+t5351; + t5357 = t5390*z; + t5349 = t5392*y; + t5529 = t5357+t5349; + t5387 = RATIONAL(1.0,700.0); + t5337 = t5387*t5401; + t5528 = RATIONAL(-289.0,10500.0)+t5337; + t5394 = RATIONAL(2.0,175.0); + t5340 = t5394*y; + t5395 = RATIONAL(-2.0,175.0); + t5362 = t5395*z; + t5527 = t5340+t5362; + t5526 = t5357+t5365; + t5332 = RATIONAL(-1.0,1000.0)*x; + t5525 = t5357+t5332; + t5314 = x*t5357; + t5341 = RATIONAL(1.0,500.0)*x; + t5469 = t5314+t5341; + t5524 = t5469+t5320; + t5343 = RATIONAL(-1.0,500.0)*x; + t5523 = t5320+t5314+t5343; + t5364 = RATIONAL(-1.0,125.0)*x; + t5522 = t5364+t5362; + t5315 = x*t5349; + t5479 = t5343+t5315; + t5521 = t5322+t5479; + t5520 = RATIONAL(-167.0,7000.0)+t5337; + t5388 = RATIONAL(-1.0,200.0); + t5398 = RATIONAL(1.0,50.0); + t5519 = t5388*t5400+t5398*t5402; + t5389 = RATIONAL(-1.0,175.0); + t5355 = t5389*t5401; + t5518 = t5355+RATIONAL(-17.0,5250.0); + t5517 = t5469+t5315; + t5386 = RATIONAL(-1.0,700.0); + t5345 = t5386*t5401; + t5516 = RATIONAL(-229.0,10500.0)+t5345; + t5350 = RATIONAL(1.0,125.0)*x; + t5515 = t5350+t5362; + t5396 = RATIONAL(1.0,200.0); + t5399 = RATIONAL(-1.0,50.0); + t5514 = t5399*t5402+t5396*t5400; + t5513 = t5341+t5322+t5315; + t5512 = t5343+t5533; + t5511 = t5345+RATIONAL(167.0,7000.0); + t5391 = RATIONAL(1.0,175.0); + t5338 = t5391*z; + t5353 = t5389*y; + t5510 = t5338+t5353; + t5336 = t5394*z; + t5359 = t5395*y; + t5509 = t5336+t5359; + t5344 = t5389*z; + t5508 = t5344+t5353; + t5346 = t5391*y; + t5507 = t5346+t5338; + t5506 = t5314+t5479; + t5505 = t5399*t5400+t5396*t5402; + t5504 = t5344+t5346; + t5503 = t5349+t5351; + t5502 = t5341+t5533; + t5501 = t5356+RATIONAL(-47.0,5250.0); + t5330 = RATIONAL(1.0,1000.0)*x; + t5500 = t5330+t5365; + t5499 = t5336+t5340; + t5498 = t5398*t5400+t5388*t5402; + t5360 = t5391*t5401; + t5381 = RATIONAL(-137.0,5250.0); + t5319 = RATIONAL(4.0,245.0)*t5490; + t5457 = t5319+t5473; + t5497 = t5360+t5381+t5457; + t5496 = RATIONAL(-107.0,7000.0)+t5531; + t5495 = RATIONAL(1.0,1400.0)*t5401+t5381+t5460; + t5374 = RATIONAL(137.0,5250.0); + t5494 = RATIONAL(-1.0,1400.0)*t5401+t5374+t5462; + t5458 = t5319+t5466; + t5347 = t5392*t5401; + t5493 = RATIONAL(47.0,5250.0)+t5458+t5347; + t5492 = t5462+RATIONAL(229.0,10500.0)+t5337; + t5491 = t5374+t5355+t5458; + t5489 = x*t5386; + t5488 = x*t5387; + t5312 = RATIONAL(-4.0,245.0)*t5490; + t5486 = t5340+t5312; + t5485 = t5336+t5312; + t5484 = t5359+t5312; + t5329 = x*t5340; + t5482 = t5312+t5329; + t5328 = x*t5346; + t5481 = t5328+t5312; + t5316 = x*t5338; + t5358 = RATIONAL(-1.0,250.0)*x; + t5478 = t5316+t5358; + t5352 = RATIONAL(1.0,250.0)*x; + t5477 = t5352+t5328; + t5311 = RATIONAL(2.0,245.0)*t5490; + t5476 = t5311+t5344; + t5325 = x*t5344; + t5475 = t5358+t5325; + t5474 = t5311+t5346; + t5327 = x*t5353; + t5471 = t5327+t5352; + t5313 = x*t5359; + t5470 = t5313+t5312; + t5468 = t5323+t5353; + t5467 = t5338+t5311; + t5465 = t5311+t5353; + t5464 = t5323+t5346; + t5463 = t5362+t5312; + t5456 = t5344+t5323+t5347; + t5455 = t5338+t5468; + t5454 = t5338+t5464; + t5453 = RATIONAL(187.0,7000.0)+t5531; + t5452 = t5457+t5499; + t5451 = t5453+t5505; + t5450 = t5453+t5514; + t5449 = t5316+t5328+t5496; + t5448 = t5344+t5464+t5511; + t5447 = t5455+t5511; + t5446 = t5460+t5530; + t5445 = t5325+t5327+t5496; + t5444 = t5344+t5468+t5520; + t5443 = t5359+t5362+t5457; + t5375 = RATIONAL(-187.0,7000.0); + t5442 = t5375+t5353+t5456; + t5380 = RATIONAL(107.0,7000.0); + t5441 = t5380+t5347+t5455; + t5440 = t5454+t5520; + t5439 = t5360+RATIONAL(17.0,5250.0)+t5458; + t5438 = t5460+t5529; + t5437 = t5380+t5346+t5456; + t5436 = RATIONAL(289.0,10500.0)+t5345+t5462; + t5435 = t5375+t5347+t5454; + t5434 = t5492+t5526; + t5433 = t5446+t5516; + t5432 = t5443+t5501; + t5431 = t5452+t5501; + t5318 = x*t5336; + t5430 = t5313+t5318+t5491; + t5317 = z*t5488; + t5309 = y*t5488; + t5429 = t5317+t5309+t5494; + t5321 = z*t5489; + t5310 = y*t5489; + t5428 = t5321+t5310+t5494; + t5427 = t5438+t5516; + t5426 = t5317+t5310+t5495; + t5425 = t5321+t5309+t5495; + t5326 = x*t5362; + t5424 = t5313+t5326+t5497; + t5423 = t5316+t5327+t5493; + t5422 = t5318+t5329+t5497; + t5421 = t5492+t5503; + t5420 = t5326+t5329+t5491; + t5419 = t5325+t5328+t5493; + t5418 = t5447+t5506; + t5417 = t5358+t5449+t5507; + t5416 = t5352+t5449+t5508; + t5415 = t5448+t5512; + t5414 = t5447+t5502; + t5413 = t5358+t5445+t5508; + t5412 = t5352+t5445+t5507; + t5411 = t5444+t5513; + t5410 = t5448+t5517; + t5409 = t5444+t5523; + t5408 = t5316+t5441+t5471; + t5407 = t5328+t5441+t5475; + t5406 = t5440+t5524; + t5405 = t5325+t5437+t5477; + t5404 = t5327+t5437+t5478; + t5403 = t5440+t5521; + coeffs_dyz->coeff_m2_m2_m2 = t5359+t5422+t5522; + coeffs_dyz->coeff_m1_m2_m2 = t5328+t5432+t5478; + coeffs_dyz->coeff_0_m2_m2 = t5443+t5518; + coeffs_dyz->coeff_p1_m2_m2 = t5325+t5432+t5471; + coeffs_dyz->coeff_p2_m2_m2 = t5359+t5424+t5515; + coeffs_dyz->coeff_m2_m1_m2 = t5404+t5514; + coeffs_dyz->coeff_m1_m1_m2 = t5415+t5514; + coeffs_dyz->coeff_0_m1_m2 = t5450+t5504; + coeffs_dyz->coeff_p1_m1_m2 = t5410+t5514; + coeffs_dyz->coeff_p2_m1_m2 = t5405+t5514; + coeffs_dyz->coeff_m2_0_m2 = t5340+t5470; + coeffs_dyz->coeff_m1_0_m2 = t5327+t5486; + coeffs_dyz->coeff_0_0_m2 = t5486; + coeffs_dyz->coeff_p1_0_m2 = t5340+t5481; + coeffs_dyz->coeff_p2_0_m2 = t5340+t5482; + coeffs_dyz->coeff_m2_p1_m2 = t5412+t5519; + coeffs_dyz->coeff_m1_p1_m2 = t5406+t5519; + coeffs_dyz->coeff_0_p1_m2 = t5435+t5519; + coeffs_dyz->coeff_p1_p1_m2 = t5403+t5519; + coeffs_dyz->coeff_p2_p1_m2 = t5417+t5519; + coeffs_dyz->coeff_m2_p2_m2 = t5350+t5420+t5509; + coeffs_dyz->coeff_m1_p2_m2 = t5352+t5419+t5509; + coeffs_dyz->coeff_0_p2_m2 = t5439+t5509; + coeffs_dyz->coeff_p1_p2_m2 = t5358+t5423+t5509; + coeffs_dyz->coeff_p2_p2_m2 = t5364+t5430+t5509; + coeffs_dyz->coeff_m2_m2_m1 = t5407+t5505; + coeffs_dyz->coeff_m1_m2_m1 = t5418+t5505; + coeffs_dyz->coeff_0_m2_m1 = t5451+t5510; + coeffs_dyz->coeff_p1_m2_m1 = t5414+t5505; + coeffs_dyz->coeff_p2_m2_m1 = t5408+t5505; + coeffs_dyz->coeff_m2_m1_m1 = t5421+t5523; + coeffs_dyz->coeff_m1_m1_m1 = t5332+t5428+t5503; + coeffs_dyz->coeff_0_m1_m1 = t5436+t5503; + coeffs_dyz->coeff_p1_m1_m1 = t5330+t5429+t5503; + coeffs_dyz->coeff_p2_m1_m1 = t5421+t5513; + coeffs_dyz->coeff_m2_0_m1 = t5327+t5474; + coeffs_dyz->coeff_m1_0_m1 = t5320+t5474; + coeffs_dyz->coeff_0_0_m1 = t5474; + coeffs_dyz->coeff_p1_0_m1 = t5315+t5474; + coeffs_dyz->coeff_p2_0_m1 = t5328+t5474; + coeffs_dyz->coeff_m2_p1_m1 = t5427+t5502; + coeffs_dyz->coeff_m1_p1_m1 = t5330+t5426+t5529; + coeffs_dyz->coeff_0_p1_m1 = t5438+t5528; + coeffs_dyz->coeff_p1_p1_m1 = t5349+t5425+t5525; + coeffs_dyz->coeff_p2_p1_m1 = t5427+t5506; + coeffs_dyz->coeff_m2_p2_m1 = t5416+t5498; + coeffs_dyz->coeff_m1_p2_m1 = t5411+t5498; + coeffs_dyz->coeff_0_p2_m1 = t5442+t5498; + coeffs_dyz->coeff_p1_p2_m1 = t5409+t5498; + coeffs_dyz->coeff_p2_p2_m1 = t5413+t5498; + coeffs_dyz->coeff_m2_m2_0 = t5326+t5485; + coeffs_dyz->coeff_m1_m2_0 = t5325+t5485; + coeffs_dyz->coeff_0_m2_0 = t5485; + coeffs_dyz->coeff_p1_m2_0 = t5316+t5485; + coeffs_dyz->coeff_p2_m2_0 = t5318+t5485; + coeffs_dyz->coeff_m2_m1_0 = t5325+t5467; + coeffs_dyz->coeff_m1_m1_0 = t5314+t5467; + coeffs_dyz->coeff_0_m1_0 = t5467; + coeffs_dyz->coeff_p1_m1_0 = t5322+t5467; + coeffs_dyz->coeff_p2_m1_0 = t5316+t5467; + coeffs_dyz->coeff_m2_0_0 = t5319; + coeffs_dyz->coeff_m1_0_0 = t5319; + coeffs_dyz->coeff_0_0_0 = t5319; + coeffs_dyz->coeff_p1_0_0 = t5319; + coeffs_dyz->coeff_p2_0_0 = t5319; + coeffs_dyz->coeff_m2_p1_0 = t5316+t5476; + coeffs_dyz->coeff_m1_p1_0 = t5322+t5476; + coeffs_dyz->coeff_0_p1_0 = t5476; + coeffs_dyz->coeff_p1_p1_0 = t5314+t5476; + coeffs_dyz->coeff_p2_p1_0 = t5325+t5476; + coeffs_dyz->coeff_m2_p2_0 = t5318+t5463; + coeffs_dyz->coeff_m1_p2_0 = t5316+t5463; + coeffs_dyz->coeff_0_p2_0 = t5463; + coeffs_dyz->coeff_p1_p2_0 = t5325+t5463; + coeffs_dyz->coeff_p2_p2_0 = t5326+t5463; + coeffs_dyz->coeff_m2_m2_p1 = t5412+t5498; + coeffs_dyz->coeff_m1_m2_p1 = t5406+t5498; + coeffs_dyz->coeff_0_m2_p1 = t5435+t5498; + coeffs_dyz->coeff_p1_m2_p1 = t5403+t5498; + coeffs_dyz->coeff_p2_m2_p1 = t5417+t5498; + coeffs_dyz->coeff_m2_m1_p1 = t5433+t5517; + coeffs_dyz->coeff_m1_m1_p1 = t5351+t5425+t5500; + coeffs_dyz->coeff_0_m1_p1 = t5446+t5528; + coeffs_dyz->coeff_p1_m1_p1 = t5332+t5426+t5530; + coeffs_dyz->coeff_p2_m1_p1 = t5433+t5512; + coeffs_dyz->coeff_m2_0_p1 = t5328+t5465; + coeffs_dyz->coeff_m1_0_p1 = t5315+t5465; + coeffs_dyz->coeff_0_0_p1 = t5465; + coeffs_dyz->coeff_p1_0_p1 = t5320+t5465; + coeffs_dyz->coeff_p2_0_p1 = t5327+t5465; + coeffs_dyz->coeff_m2_p1_p1 = t5434+t5521; + coeffs_dyz->coeff_m1_p1_p1 = t5365+t5429+t5525; + coeffs_dyz->coeff_0_p1_p1 = t5436+t5526; + coeffs_dyz->coeff_p1_p1_p1 = t5357+t5428+t5500; + coeffs_dyz->coeff_p2_p1_p1 = t5434+t5524; + coeffs_dyz->coeff_m2_p2_p1 = t5404+t5505; + coeffs_dyz->coeff_m1_p2_p1 = t5415+t5505; + coeffs_dyz->coeff_0_p2_p1 = t5451+t5504; + coeffs_dyz->coeff_p1_p2_p1 = t5410+t5505; + coeffs_dyz->coeff_p2_p2_p1 = t5405+t5505; + coeffs_dyz->coeff_m2_m2_p2 = t5340+t5430+t5515; + coeffs_dyz->coeff_m1_m2_p2 = t5352+t5423+t5527; + coeffs_dyz->coeff_0_m2_p2 = t5439+t5527; + coeffs_dyz->coeff_p1_m2_p2 = t5358+t5419+t5527; + coeffs_dyz->coeff_p2_m2_p2 = t5340+t5420+t5522; + coeffs_dyz->coeff_m2_m1_p2 = t5416+t5519; + coeffs_dyz->coeff_m1_m1_p2 = t5411+t5519; + coeffs_dyz->coeff_0_m1_p2 = t5442+t5519; + coeffs_dyz->coeff_p1_m1_p2 = t5409+t5519; + coeffs_dyz->coeff_p2_m1_p2 = t5413+t5519; + coeffs_dyz->coeff_m2_0_p2 = t5359+t5482; + coeffs_dyz->coeff_m1_0_p2 = t5359+t5481; + coeffs_dyz->coeff_0_0_p2 = t5484; + coeffs_dyz->coeff_p1_0_p2 = t5327+t5484; + coeffs_dyz->coeff_p2_0_p2 = t5359+t5470; + coeffs_dyz->coeff_m2_p1_p2 = t5407+t5514; + coeffs_dyz->coeff_m1_p1_p2 = t5418+t5514; + coeffs_dyz->coeff_0_p1_p2 = t5450+t5510; + coeffs_dyz->coeff_p1_p1_p2 = t5414+t5514; + coeffs_dyz->coeff_p2_p1_p2 = t5408+t5514; + coeffs_dyz->coeff_m2_p2_p2 = t5364+t5424+t5499; + coeffs_dyz->coeff_m1_p2_p2 = t5327+t5431+t5475; + coeffs_dyz->coeff_0_p2_p2 = t5452+t5518; + coeffs_dyz->coeff_p1_p2_p2 = t5316+t5431+t5477; + coeffs_dyz->coeff_p2_p2_p2 = t5350+t5422+t5499; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dz.compute.c new file mode 100644 index 0000000..c48ec4e --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dz.compute.c @@ -0,0 +1,985 @@ +fp t4052; +fp t4049; +fp t3983; +fp t4054; +fp t4198; +fp t3864; +fp t4345; +fp t4201; +fp t4036; +fp t3905; +fp t4040; +fp t3962; +fp t4291; +fp t4050; +fp t4020; +fp t4174; +fp t4326; +fp t4122; +fp t4053; +fp t4018; +fp t3968; +fp t3887; +fp t3999; +fp t4302; +fp t4344; +fp t4206; +fp t3857; +fp t4343; +fp t4192; +fp t4338; +fp t4134; +fp t4019; +fp t3973; +fp t3878; +fp t3997; +fp t4304; +fp t4342; +fp t4010; +fp t3965; +fp t4051; +fp t4033; +fp t4168; +fp t4341; +fp t3966; +fp t3894; +fp t4340; +fp t4209; +fp t3911; +fp t4197; +fp t3912; +fp t4339; +fp t3866; +fp t4337; +fp t3984; +fp t4336; +fp t3985; +fp t4039; +fp t3909; +fp t4335; +fp t4025; +fp t3972; +fp t4334; +fp t3856; +fp t4333; +fp t3956; +fp t4332; +fp t4045; +fp t3987; +fp t4041; +fp t3882; +fp t4331; +fp t4031; +fp t3868; +fp t4330; +fp t3854; +fp t4024; +fp t4204; +fp t3901; +fp t4329; +fp t4328; +fp t3888; +fp t4023; +fp t3963; +fp t4327; +fp t4027; +fp t4205; +fp t3898; +fp t4325; +fp t3877; +fp t4207; +fp t3867; +fp t4324; +fp t4323; +fp t3995; +fp t3957; +fp t3896; +fp t4322; +fp t3842; +fp t3900; +fp t4321; +fp t3879; +fp t3922; +fp t4320; +fp t3986; +fp t4319; +fp t4032; +fp t4318; +fp t3870; +fp t4000; +fp t4317; +fp t4316; +fp t4037; +fp t4315; +fp t3993; +fp t3941; +fp t4314; +fp t3953; +fp t3859; +fp t4313; +fp t3885; +fp t3851; +fp t4312; +fp t3998; +fp t3978; +fp t3863; +fp t4311; +fp t3982; +fp t3860; +fp t4310; +fp t4309; +fp t4308; +fp t4307; +fp t3961; +fp t4306; +fp t3915; +fp t4305; +fp t3971; +fp t3954; +fp t4303; +fp t4301; +fp t3874; +fp t4300; +fp t4299; +fp t4298; +fp t3979; +fp t3858; +fp t4002; +fp t4297; +fp t4202; +fp t3862; +fp t3848; +fp t4296; +fp t4295; +fp t4042; +fp t4191; +fp t3992; +fp t3920; +fp t4149; +fp t4013; +fp t4199; +fp t4294; +fp t4293; +fp t4292; +fp t4290; +fp t4289; +fp t4001; +fp t4288; +fp t3924; +fp t4287; +fp t3996; +fp t3927; +fp t4286; +fp t4203; +fp t3886; +fp t3846; +fp t4285; +fp t4284; +fp t3990; +fp t4283; +fp t3872; +fp t4282; +fp t3937; +fp t4281; +fp t3895; +fp t3890; +fp t3847; +fp t4280; +fp t4279; +fp t4170; +fp t3988; +fp t4278; +fp t3883; +fp t4003; +fp t4277; +fp t3913; +fp t3845; +fp t4276; +fp t4155; +fp t4275; +fp t4167; +fp t4274; +fp t4176; +fp t4273; +fp t4272; +fp t4271; +fp t4270; +fp t4269; +fp t3944; +fp t4268; +fp t3930; +fp t4267; +fp t4015; +fp t3852; +fp t4208; +fp t3843; +fp t3994; +fp t3932; +fp t4144; +fp t4266; +fp t3919; +fp t4265; +fp t4008; +fp t3861; +fp t4264; +fp t3844; +fp t4263; +fp t3880; +fp t4262; +fp t3989; +fp t4261; +fp t3908; +fp t4260; +fp t4259; +fp t4258; +fp t3876; +fp t3849; +fp t4257; +fp t3991; +fp t4256; +fp t4047; +fp t4255; +fp t4254; +fp t3943; +fp t4253; +fp t3938; +fp t4252; +fp t4251; +fp t4250; +fp t4005; +fp t4249; +fp t4248; +fp t4012; +fp t4247; +fp t4246; +fp t4245; +fp t4244; +fp t4243; +fp t4242; +fp t3899; +fp t4241; +fp t4240; +fp t4239; +fp t4004; +fp t4238; +fp t4237; +fp t4236; +fp t4235; +fp t4046; +fp t4234; +fp t4200; +fp t3936; +fp t4233; +fp t4232; +fp t4231; +fp t4230; +fp t4229; +fp t4228; +fp t4016; +fp t4227; +fp t4006; +fp t4226; +fp t4011; +fp t4225; +fp t4224; +fp t4223; +fp t3916; +fp t4222; +fp t3902; +fp t4221; +fp t4220; +fp t4219; +fp t4218; +fp t4217; +fp t4216; +fp t4215; +fp t4214; +fp t4213; +fp t4212; +fp t4211; +fp t4210; +fp t4196; +fp t4195; +fp t4194; +fp t4193; +fp t4190; +fp t4189; +fp t4188; +fp t4187; +fp t4186; +fp t4185; +fp t4184; +fp t4183; +fp t4182; +fp t4181; +fp t4180; +fp t4179; +fp t4178; +fp t4177; +fp t4175; +fp t4173; +fp t4172; +fp t4171; +fp t4169; +fp t4166; +fp t4165; +fp t4164; +fp t4163; +fp t4162; +fp t4161; +fp t4160; +fp t4159; +fp t4157; +fp t4156; +fp t4154; +fp t4153; +fp t4152; +fp t4150; +fp t4148; +fp t3923; +fp t4147; +fp t4146; +fp t4143; +fp t4142; +fp t4141; +fp t4140; +fp t4139; +fp t4138; +fp t4137; +fp t4136; +fp t4135; +fp t4133; +fp t4132; +fp t4131; +fp t4130; +fp t4129; +fp t4128; +fp t4127; +fp t4126; +fp t3955; +fp t4125; +fp t4124; +fp t4123; +fp t4121; +fp t4120; +fp t4119; +fp t4118; +fp t4117; +fp t4116; +fp t4115; +fp t4048; +fp t4114; +fp t4113; +fp t4112; +fp t4111; +fp t4110; +fp t4109; +fp t4108; +fp t4107; +fp t4106; +fp t4105; +fp t4104; +fp t4103; +fp t4102; +fp t4101; +fp t4100; +fp t4099; +fp t4098; +fp t4097; +fp t4096; +fp t4095; +fp t4094; +fp t4093; +fp t4092; +fp t4091; +fp t4090; +fp t4089; +fp t4088; +fp t4087; +fp t4086; +fp t4085; +fp t4084; +fp t4083; +fp t4082; +fp t3893; +fp t4081; +fp t4080; +fp t4079; +fp t4078; +fp t4077; +fp t4076; +fp t4075; +fp t4074; +fp t4073; +fp t4072; +fp t4071; +fp t4070; +fp t4069; +fp t4068; +fp t4067; +fp t3850; +fp t4066; +fp t4065; +fp t4064; +fp t4063; +fp t4062; +fp t4061; +fp t4060; +fp t4059; +fp t4058; +fp t3889; + t4052 = z*z; + t4049 = t4052*z; + t3983 = RATIONAL(1.0,25.0)*t4049; + t4054 = y*y; + t4198 = z*RATIONAL(-2.0,245.0); + t3864 = t4054*t4198; + t4345 = t3983+t3864; + t4201 = z*t4054; + t4036 = RATIONAL(-1.0,245.0); + t3905 = t4036*t4201; + t4040 = RATIONAL(1.0,150.0); + t3962 = t4040*t4049; + t4291 = t3905+t3962; + t4050 = y*t4054; + t4020 = RATIONAL(-1.0,150.0); + t4174 = t4052*RATIONAL(1.0,200.0); + t4326 = y*t4174+t4020*t4050; + t4122 = t4291+t4326; + t4053 = x*x; + t4018 = RATIONAL(-1.0,700.0); + t3968 = t4018*t4053; + t3887 = y*t3968; + t3999 = RATIONAL(167.0,7000.0); + t4302 = t3999*y+t3887; + t4344 = t4122+t4302; + t4206 = z*t4053; + t3857 = t4036*t4206; + t4343 = t3857+RATIONAL(191.0,14700.0)*z; + t4192 = t4052*RATIONAL(-1.0,200.0); + t4338 = t4040*t4050+y*t4192; + t4134 = t4291+t4338; + t4019 = RATIONAL(1.0,700.0); + t3973 = t4019*t4053; + t3878 = y*t3973; + t3997 = RATIONAL(-167.0,7000.0); + t4304 = t3997*y+t3878; + t4342 = t4134+t4304; + t4010 = RATIONAL(47.0,5250.0); + t3965 = RATIONAL(-1.0,100.0)*t4052; + t4051 = t4053*x; + t4033 = RATIONAL(-1.0,300.0); + t4168 = t4033*t4051+x*t3965; + t4341 = t4168+t4010*x; + t3966 = t4019*t4054; + t3894 = x*t3966; + t4340 = t3894+t3997*x; + t4209 = x*y; + t3911 = RATIONAL(1.0,125.0)*t4209; + t4197 = z*RATIONAL(2.0,175.0); + t3912 = y*t4197; + t4339 = t3911+t3912; + t3866 = RATIONAL(-1.0,250.0)*t4209; + t4337 = t3866+t3912; + t3984 = RATIONAL(-1.0,50.0)*t4052; + t4336 = t3984+t3968; + t3985 = RATIONAL(4.0,75.0)*z; + t4039 = RATIONAL(1.0,245.0); + t3909 = t4039*t4201; + t4335 = t3985+t3909; + t4025 = RATIONAL(1.0,175.0); + t3972 = t4025*t4054; + t4334 = t3972+t3864; + t3856 = t4039*t4206; + t4333 = RATIONAL(-57.0,490.0)*z+t3856; + t3956 = t4018*t4054; + t4332 = RATIONAL(17.0,525.0)+t3956; + t4045 = RATIONAL(-2.0,75.0); + t3987 = t4045*t4049; + t4041 = RATIONAL(1.0,490.0); + t3882 = t4041*t4206; + t4331 = t3987+t3882; + t4031 = RATIONAL(2.0,245.0); + t3868 = t4031*t4201; + t4330 = t3868+t3962; + t3854 = RATIONAL(-1.0,1000.0)*t4209; + t4024 = RATIONAL(-1.0,350.0); + t4204 = z*t4024; + t3901 = y*t4204; + t4329 = t3854+t3901; + t4328 = t3985+t3856; + t3888 = t4031*t4206; + t4023 = RATIONAL(-1.0,175.0); + t3963 = t4023*t4053; + t4327 = t3888+t3963; + t4027 = RATIONAL(1.0,350.0); + t4205 = z*t4027; + t3898 = x*t4205; + t4325 = t3968+t3898; + t3877 = RATIONAL(-1.0,125.0)*t4209; + t4207 = z*RATIONAL(-2.0,175.0); + t3867 = y*t4207; + t4324 = t3877+t3867; + t4323 = x*t4174+t4020*t4051; + t3995 = RATIONAL(-187.0,7000.0); + t3957 = t4027*t4053; + t3896 = y*t3957; + t4322 = t3995*y+t3896; + t3842 = y*t3898; + t3900 = RATIONAL(-1.0,500.0)*t4209; + t4321 = t3842+t3900; + t3879 = t4041*t4201; + t3922 = RATIONAL(151.0,3675.0)*z; + t4320 = t3879+t3922; + t3986 = RATIONAL(1.0,50.0)*t4052; + t4319 = t3986+t3973; + t4032 = RATIONAL(1.0,600.0); + t4318 = y*t3984+t4032*t4050; + t3870 = RATIONAL(-169.0,14700.0)*z; + t4000 = RATIONAL(-19.0,2100.0); + t4317 = t3870+t4000; + t4316 = t3966+RATIONAL(-17.0,525.0); + t4037 = RATIONAL(-1.0,600.0); + t4315 = y*t3986+t4037*t4050; + t3993 = RATIONAL(107.0,7000.0); + t3941 = t3993*y; + t4314 = t3941+t3896; + t3953 = t4027*t4054; + t3859 = x*t3953; + t4313 = t3995*x+t3859; + t3885 = y*t4205; + t3851 = RATIONAL(1.0,1000.0)*t4209; + t4312 = t3885+t3851; + t3998 = RATIONAL(187.0,7000.0); + t3978 = t4024*t4053; + t3863 = y*t3978; + t4311 = t3863+t3998*y; + t3982 = RATIONAL(-9.0,98.0)*z; + t3860 = t4053*t4198; + t4310 = t3982+t3860; + t4309 = t3885+t3854; + t4308 = t3851+t3901; + t4307 = t3905+t3987; + t3961 = t4023*t4054; + t4306 = t3961+t3864; + t3915 = RATIONAL(1.0,250.0)*t4209; + t4305 = t3915+t3867; + t3971 = RATIONAL(1.0,100.0)*t4052; + t3954 = t4025*t4053; + t4303 = t3971+t3954; + t4301 = RATIONAL(136.0,3675.0)*z+t3909; + t3874 = RATIONAL(-529.0,14700.0)*z; + t4300 = t3874+t3888; + t4299 = t4032*t4051+x*t3984; + t4298 = t3868+t3961; + t3979 = t4024*t4054; + t3858 = x*t3979; + t4002 = RATIONAL(-47.0,5250.0); + t4297 = t3858+t4002*x; + t4202 = z*t4023; + t3862 = x*t4202; + t3848 = y*t3862; + t4296 = t3915+t3848; + t4295 = t3909+t3922; + t4042 = RATIONAL(1.0,300.0); + t4191 = t4042*t4050+y*t3971; + t3992 = RATIONAL(-137.0,5250.0); + t3920 = t3992*y; + t4149 = t3920+t4191; + t4013 = RATIONAL(1.0,1400.0); + t4199 = y*t4053; + t4294 = t4149+t4013*t4199; + t4293 = t3858+t3998*x; + t4292 = x*t3986+t4037*t4051; + t4290 = x*t4192+t4040*t4051; + t4289 = t3965+t3961; + t4001 = RATIONAL(19.0,2100.0); + t4288 = t3870+t4001; + t3924 = RATIONAL(166.0,3675.0)*z; + t4287 = t3879+t3924; + t3996 = RATIONAL(-107.0,7000.0); + t3927 = t3996*y; + t4286 = t3927+t3863; + t4203 = z*t4025; + t3886 = y*t4203; + t3846 = x*t3886; + t4285 = t3866+t3846; + t4284 = t3868+t3972; + t3990 = RATIONAL(229.0,10500.0); + t4283 = t3878+t3990*y; + t3872 = RATIONAL(311.0,14700.0)*z; + t4282 = t3860+t3872; + t3937 = RATIONAL(211.0,3675.0)*z; + t4281 = t3879+t3937; + t3895 = RATIONAL(1.0,500.0)*t4209; + t3890 = x*t4204; + t3847 = y*t3890; + t4280 = t3895+t3847; + t4279 = t3860+RATIONAL(-33.0,490.0)*z+t4345; + t4170 = y*t3965+t4033*t4050; + t3988 = RATIONAL(289.0,10500.0); + t4278 = t3988*y+t3887+t4170; + t3883 = y*t3954; + t4003 = RATIONAL(17.0,5250.0); + t4277 = t3883+t4170+t4003*y; + t3913 = x*t4197; + t3845 = y*t3913; + t4276 = t4149+t3883+t3845; + t4155 = t3979+t3978; + t4275 = t3986+t4155+RATIONAL(-8.0,525.0); + t4167 = t3957+t3953; + t4274 = t3965+RATIONAL(-17.0,2100.0)+t4167; + t4176 = t4042*t4051+x*t3971; + t4273 = t4176+t4297; + t4272 = t3982+t3856+t4345; + t4271 = t3858+t3857+t3996*x; + t4270 = t3971+RATIONAL(17.0,2100.0)+t4155; + t4269 = t3990*x+t3894+t3937; + t3944 = t4010*y; + t4268 = t3944+t4170+t3896; + t3930 = t3999*x; + t4267 = t3930+t4299; + t4015 = RATIONAL(-1.0,1400.0); + t3852 = t4015*t4199; + t4208 = z*t4209; + t3843 = t4018*t4208; + t3994 = RATIONAL(137.0,5250.0); + t3932 = t3994*y; + t4144 = t3932+t4170; + t4266 = t3852+t3843+t4144; + t3919 = t3993*x; + t4265 = t3919+t4323; + t4008 = RATIONAL(-17.0,5250.0); + t3861 = y*t3963; + t4264 = t4191+t3861+t4008*y; + t3844 = t4019*t4208; + t4263 = t3844+t4294; + t3880 = x*t3972; + t4262 = t4003*x+t3880+t4168; + t3989 = RATIONAL(-289.0,10500.0); + t4261 = t4191+t3878+t3989*y; + t3908 = x*t3961; + t4260 = t3908+t4008*x+t4176; + t4259 = t3859+t4341; + t4258 = t3984+t4167+RATIONAL(8.0,525.0); + t3876 = x*t4207; + t3849 = y*t3876; + t4257 = t3849+t3861+t4144; + t3991 = RATIONAL(-229.0,10500.0); + t4256 = t4191+t3887+t3991*y; + t4047 = RATIONAL(-1.0,42.0); + t4255 = t3986+t4047+t3937; + t4254 = t3870+t4290; + t3943 = t4002*y; + t4253 = t3943+t4191+t3863; + t3938 = RATIONAL(256.0,3675.0)*z; + t4252 = t3938+t4292; + t4251 = t3979+t4045+t3957+t3986; + t4250 = t4293+t4323; + t4005 = RATIONAL(29.0,2100.0); + t4249 = t4005+t3971+t3979+t3963; + t4248 = t4290+t4313; + t4012 = RATIONAL(11.0,420.0); + t4247 = t4012+t3963+t4289; + t4246 = t3895+t4274; + t4245 = t4293+t4299; + t4244 = t3915+t4258; + t4243 = t3900+t4270; + t4242 = t3915+t4275; + t3899 = x*t3956; + t4241 = t3899+t4267; + t4240 = t3885+t4256; + t4239 = t4302+t4318; + t4004 = RATIONAL(-37.0,1050.0); + t4238 = t4004+t3953+t4319; + t4237 = t3900+t4274; + t4236 = t3866+t4275; + t4235 = t4304+t4315; + t4046 = RATIONAL(2.0,75.0); + t4234 = t3984+t4046+t3953+t3978; + t4200 = x*t4054; + t3936 = t3994*x; + t4233 = t4015*t4200+t3936+t4287; + t4232 = t3936+t4168+t3908+t4300; + t4231 = t4292+t4313; + t4230 = t3895+t4270; + t4229 = t4170+t3901+t4283; + t4228 = t3866+t4258; + t4016 = RATIONAL(-11.0,420.0); + t4227 = t4016+t3972+t4303; + t4006 = RATIONAL(37.0,1050.0); + t4226 = t4006+t3979+t4336; + t4011 = RATIONAL(-29.0,2100.0); + t4225 = t3965+t3954+t4011+t3953; + t4224 = t4292+t4340; + t4223 = t3895+t4235; + t3916 = x*t4203; + t4222 = t3916+t3957+t4001+t4289; + t3902 = y*t4202; + t4221 = t3902+t4314+t4326; + t4220 = t3984+t4325+t4332; + t4219 = t3900+t4239; + t4218 = t3886+t4286+t4338; + t4217 = t3895+t4239; + t4216 = t3890+t4316+t4319; + t4215 = t3900+t4235; + t4214 = t3971+t3972+t3862+t4000+t3978; + t4213 = t3899+t3930+t4323+t4343; + t4212 = t3979+t3888+t4303+t4317; + t4211 = t4290+t4340+t4343; + t4210 = t3857+t3938+t3919+t3859+t4299; + t4196 = t3886+t3862; + t4195 = t3876+t3846; + t4194 = t3888+t3864; + t4193 = t3857+t3978; + t4190 = t3857+t3957; + t4189 = t3905+t3953; + t4188 = t3913+t3846; + t4187 = t3965+t3962; + t4186 = t3886+t3847; + t4185 = t3916+t3886; + t4184 = t3916+t3847; + t4183 = t3916+t3842; + t4182 = t3842+t3902; + t4181 = t3916+t3902; + t4180 = t3867+t3848; + t4179 = t3842+t3862; + t4178 = t3867+t3846; + t4177 = t3886+t3842; + t4175 = t3913+t3867; + t4173 = t3913+t3912; + t4172 = t3868+t3860; + t4171 = t3983+t3909; + t4169 = t3913+t3848; + t4166 = t3957+t3987; + t4165 = t3876+t3912; + t4164 = t3876+t3848; + t4163 = t3876+t3867; + t4162 = t3862+t3902; + t4161 = t3847+t3902; + t4160 = t3847+t3862; + t4159 = t3987+t3978; + t4157 = t3979+t3905; + t4156 = t3971+t3962; + t4154 = t3848+t3912; + t4153 = t3983+RATIONAL(-1.0,10.0)*z; + t4152 = t3912+t3846; + t4150 = t3983+RATIONAL(-61.0,490.0)*z; + t4148 = t3862+t4190; + t3923 = t3992*x; + t4147 = t3923+t4176; + t4146 = t3902+t4171; + t4143 = t3886+t4171; + t4142 = t4191+t4330; + t4141 = t3868+t3856+t4150; + t4140 = t4153+t4194; + t4139 = t3857+t3986+t4159; + t4138 = t4307+t4318; + t4137 = t4187+t4334; + t4136 = t4307+t4315; + t4135 = t4153+t4172; + t4133 = t3984+t3857+t4166; + t4132 = t4176+t4331; + t4131 = t4156+t4284; + t4130 = t4187+t4327; + t4129 = t3986+t3856+t4166; + t4128 = t3879+t3987+t4170; + t4127 = t4170+t4330; + t4126 = t4168+t4331; + t3955 = t4033*z; + t4125 = t3954+t3955+t3961+t3962; + t4124 = t3984+t3856+t4159; + t4123 = t3860+t3963+t4156; + t4121 = t3888+t3909+t4150; + t4120 = t3916+t4272; + t4119 = t4143+t4333; + t4118 = t3859+t4187+t4288; + t4117 = t3845+t4279; + t4116 = t3896+t3846+t4271; + t4115 = t4146+t4310; + t4048 = RATIONAL(1.0,42.0); + t4114 = t3984+t4048+t3899+t3987+t3937; + t4113 = t3848+t3863+t4271; + t4112 = t4146+t4333; + t4111 = t3849+t4279; + t4110 = t3862+t4272; + t4109 = t4143+t4310; + t4108 = t3876+t4130+t4176; + t4107 = t3890+t4126+t4336; + t4106 = t3898+t4126+t4319; + t4105 = t3955+t4033+t4123+t4284; + t4104 = t4042+t3955+t4130+t4334; + t4103 = t4005+t3872+t4156+t4193+t4306; + t4102 = t3989*x+t3894+t4132+t4295; + t4101 = t4138+t4311+t4328; + t4100 = t4045+t3953+t4139+t4335; + t4099 = t4136+t4322+t4328; + t4098 = t4004+t3966+t4129+t4320; + t4097 = t3988*x+t3899+t4126+t4295; + t4096 = t3971+t4033+t4125+t4194; + t4095 = t3979+t4046+t4133+t4335; + t4094 = t4006+t3956+t4124+t4320; + t4093 = t3965+t4042+t4125+t4172; + t4092 = t4011+t3872+t4137+t4190; + t4091 = t4134+t4282+t4322; + t4090 = t4122+t4282+t4311; + t4089 = t3883+t3849+t3920+t4142+t4232; + t4088 = t3842+t4211+t4342; + t4087 = t3916+t3859+t4131+t4193+t4265+t4317; + t4086 = t3941+t4116+t4138+t4252; + t4085 = t3874+t4012+t3880+t3923+t4108+t4298; + t4084 = t3879+t3956+t4114+t4148+t4267; + t4083 = t3944+t4116+t4127+t4254; + t4082 = t3847+t4211+t4344; + t3893 = t3991*x; + t4081 = t3893+t3973+t3899+t3890+t4132+t4157+t4255; + t4080 = t3886+t4122+t4212+t4314; + t4079 = t3902+t4134+t4212+t4286; + t4078 = t3943+t4113+t4142+t4254; + t4077 = t4047+t4106+t4157+t4269; + t4076 = t3848+t4138+t4210+t4314; + t4075 = t3954+t4016+t3913+t3880+t4131+t4147+t4300; + t4074 = t4048+t4107+t4189+t4269; + t4073 = t3966+t4047+t3901+t4139+t4256+t4281; + t4072 = t3842+t4213+t4344; + t4071 = t4106+t4233+t4316; + t4070 = t3927+t4113+t4136+t4252; + t4069 = t3847+t4213+t4342; + t4068 = t3893+t3882+t4114+t4176+t4189+t4325; + t4067 = t3846+t4136+t4210+t4286; + t3850 = t4013*t4200; + t4066 = t3850+t3843+t3923+t4132+t4287+t4294; + t4065 = t3913+t4118+t4189+t4327+t4341; + t4064 = t3932+t3845+t3861+t4127+t4232; + t4063 = t3916+t4048+t3956+t4133+t4224+t4281; + t4062 = t4108+t4189+t4288+t4297; + t4061 = t3850+t3844+t3852+t3932+t3924+t3882+t4128+t4147; + t4060 = t4118+t4148+t4265+t4298; + t4059 = t4107+t4233+t4332; + t4058 = t3966+t3885+t4128+t4193+t4255+t4283; + t3889 = RATIONAL(431.0,14700.0)*z; + coeffs_dz->coeff_m2_m2_m2 = t4085+t4276+t4324; + coeffs_dz->coeff_m1_m2_m2 = t4060+t3866+t4178+t4253; + coeffs_dz->coeff_0_m2_m2 = t3867+t4093+t4264; + coeffs_dz->coeff_p1_m2_m2 = t4078+t4222+t4305; + coeffs_dz->coeff_p2_m2_m2 = t4089+t3911+t4175+t4247; + coeffs_dz->coeff_m2_m1_m2 = t4062+t4221+t4285; + coeffs_dz->coeff_m1_m1_m2 = t4072+t4162+t4237; + coeffs_dz->coeff_0_m1_m2 = t3902+t4090+t4225; + coeffs_dz->coeff_p1_m1_m2 = t4082+t4181+t4246; + coeffs_dz->coeff_p2_m1_m2 = t4065+t4221+t4296; + coeffs_dz->coeff_m2_0_m2 = t3876+t4104+t4260; + coeffs_dz->coeff_m1_0_m2 = t3862+t4092+t4250; + coeffs_dz->coeff_0_0_m2 = RATIONAL(-41.0,2100.0)+t3860+t3889+t3954+t4137; + coeffs_dz->coeff_p1_0_m2 = t3916+t4092+t4248; + coeffs_dz->coeff_p2_0_m2 = t3913+t4104+t4262; + coeffs_dz->coeff_m2_p1_m2 = t4062+t4218+t4296; + coeffs_dz->coeff_m1_p1_m2 = t4069+t4196+t4246; + coeffs_dz->coeff_0_p1_m2 = t3886+t4091+t4225; + coeffs_dz->coeff_p1_p1_m2 = t4088+t4185+t4237; + coeffs_dz->coeff_p2_p1_m2 = t4065+t4218+t4285; + coeffs_dz->coeff_m2_p2_m2 = t4085+t4257+t4339; + coeffs_dz->coeff_m1_p2_m2 = t4060+t3915+t4154+t4268; + coeffs_dz->coeff_0_p2_m2 = t3912+t4093+t4277; + coeffs_dz->coeff_p1_p2_m2 = t4083+t4222+t4337; + coeffs_dz->coeff_p2_p2_m2 = t3877+t4064+t4173+t4247; + coeffs_dz->coeff_m2_m2_m1 = t4076+t4185+t4236; + coeffs_dz->coeff_m1_m2_m1 = t4077+t4186+t4219; + coeffs_dz->coeff_0_m2_m1 = t3886+t4101+t4251; + coeffs_dz->coeff_p1_m2_m1 = t4081+t4177+t4217; + coeffs_dz->coeff_p2_m2_m1 = t4086+t4196+t4242; + coeffs_dz->coeff_m2_m1_m1 = t4058+t3900+t4184+t4241; + coeffs_dz->coeff_m1_m1_m1 = t4071+t4266+t4309; + coeffs_dz->coeff_0_m1_m1 = t3885+t4098+t4278; + coeffs_dz->coeff_p1_m1_m1 = t4061+t4216+t4312; + coeffs_dz->coeff_p2_m1_m1 = t4058+t3895+t4179+t4224; + coeffs_dz->coeff_m2_0_m1 = t3916+t4100+t4245; + coeffs_dz->coeff_m1_0_m1 = t3898+t4097+t4238; + coeffs_dz->coeff_0_0_m1 = RATIONAL(-4.0,105.0)+t3953+t4129+t4301; + coeffs_dz->coeff_p1_0_m1 = t3890+t4102+t4238; + coeffs_dz->coeff_p2_0_m1 = t3862+t4100+t4231; + coeffs_dz->coeff_m2_p1_m1 = t3895+t4073+t4183+t4241; + coeffs_dz->coeff_m1_p1_m1 = t4071+t4263+t4308; + coeffs_dz->coeff_0_p1_m1 = t3901+t4098+t4261; + coeffs_dz->coeff_p1_p1_m1 = t4066+t4216+t4329; + coeffs_dz->coeff_p2_p1_m1 = t3900+t4073+t4160+t4224; + coeffs_dz->coeff_m2_p2_m1 = t4067+t4181+t4242; + coeffs_dz->coeff_m1_p2_m1 = t4077+t4182+t4223; + coeffs_dz->coeff_0_p2_m1 = t3902+t4099+t4251; + coeffs_dz->coeff_p1_p2_m1 = t4081+t4161+t4215; + coeffs_dz->coeff_p2_p2_m1 = t4070+t4162+t4236; + coeffs_dz->coeff_m2_m2_0 = t4111+t4173; + coeffs_dz->coeff_m1_m2_0 = t4120+t4154; + coeffs_dz->coeff_0_m2_0 = t3912+t4140; + coeffs_dz->coeff_p1_m2_0 = t4110+t4152; + coeffs_dz->coeff_p2_m2_0 = t4117+t4165; + coeffs_dz->coeff_m2_m1_0 = t4109+t4169; + coeffs_dz->coeff_m1_m1_0 = t4119+t4184; + coeffs_dz->coeff_0_m1_0 = t3886+t4121; + coeffs_dz->coeff_p1_m1_0 = t4119+t4179; + coeffs_dz->coeff_p2_m1_0 = t4109+t4195; + coeffs_dz->coeff_m2_0_0 = t3913+t4135; + coeffs_dz->coeff_m1_0_0 = t3916+t4141; + coeffs_dz->coeff_0_0_0 = t3983+t3868+RATIONAL(-13.0,98.0)*z+t3888; + coeffs_dz->coeff_p1_0_0 = t3862+t4141; + coeffs_dz->coeff_p2_0_0 = t3876+t4135; + coeffs_dz->coeff_m2_p1_0 = t4115+t4188; + coeffs_dz->coeff_m1_p1_0 = t4112+t4183; + coeffs_dz->coeff_0_p1_0 = t3902+t4121; + coeffs_dz->coeff_p1_p1_0 = t4112+t4160; + coeffs_dz->coeff_p2_p1_0 = t4115+t4164; + coeffs_dz->coeff_m2_p2_0 = t4117+t4175; + coeffs_dz->coeff_m1_p2_0 = t4120+t4178; + coeffs_dz->coeff_0_p2_0 = t3867+t4140; + coeffs_dz->coeff_p1_p2_0 = t4110+t4180; + coeffs_dz->coeff_p2_p2_0 = t4111+t4163; + coeffs_dz->coeff_m2_m2_p1 = t4070+t4185+t4244; + coeffs_dz->coeff_m1_m2_p1 = t4068+t4186+t4223; + coeffs_dz->coeff_0_m2_p1 = t3886+t4099+t4234; + coeffs_dz->coeff_p1_m2_p1 = t4074+t4177+t4215; + coeffs_dz->coeff_p2_m2_p1 = t4067+t4196+t4228; + coeffs_dz->coeff_m2_m1_p1 = t4063+t4240+t4280; + coeffs_dz->coeff_m1_m1_p1 = t4066+t4220+t4312; + coeffs_dz->coeff_0_m1_p1 = t3885+t4094+t4261; + coeffs_dz->coeff_p1_m1_p1 = t4059+t4263+t4309; + coeffs_dz->coeff_p2_m1_p1 = t4084+t4240+t4321; + coeffs_dz->coeff_m2_0_p1 = t3916+t4095+t4231; + coeffs_dz->coeff_m1_0_p1 = t3898+t4102+t4226; + coeffs_dz->coeff_0_0_p1 = t3979+RATIONAL(4.0,105.0)+t4124+t4301; + coeffs_dz->coeff_p1_0_p1 = t3890+t4097+t4226; + coeffs_dz->coeff_p2_0_p1 = t3862+t4095+t4245; + coeffs_dz->coeff_m2_p1_p1 = t4063+t4229+t4321; + coeffs_dz->coeff_m1_p1_p1 = t4061+t4220+t4329; + coeffs_dz->coeff_0_p1_p1 = t3901+t4094+t4278; + coeffs_dz->coeff_p1_p1_p1 = t4059+t4266+t4308; + coeffs_dz->coeff_p2_p1_p1 = t4084+t4229+t4280; + coeffs_dz->coeff_m2_p2_p1 = t4086+t4181+t4228; + coeffs_dz->coeff_m1_p2_p1 = t4068+t4182+t4219; + coeffs_dz->coeff_0_p2_p1 = t3902+t4101+t4234; + coeffs_dz->coeff_p1_p2_p1 = t4074+t4161+t4217; + coeffs_dz->coeff_p2_p2_p1 = t4076+t4162+t4244; + coeffs_dz->coeff_m2_m2_p2 = t4064+t3911+t4163+t4227; + coeffs_dz->coeff_m1_m2_p2 = t4083+t4214+t4305; + coeffs_dz->coeff_0_m2_p2 = t3867+t4105+t4277; + coeffs_dz->coeff_p1_m2_p2 = t3866+t4087+t4180+t4268; + coeffs_dz->coeff_p2_m2_p2 = t4075+t4257+t4324; + coeffs_dz->coeff_m2_m1_p2 = t3915+t4079+t4195+t4259; + coeffs_dz->coeff_m1_m1_p2 = t4088+t4162+t4230; + coeffs_dz->coeff_0_m1_p2 = t3902+t4091+t4249; + coeffs_dz->coeff_p1_m1_p2 = t4069+t4181+t4243; + coeffs_dz->coeff_p2_m1_p2 = t3866+t4079+t4169+t4273; + coeffs_dz->coeff_m2_0_p2 = t3876+t4096+t4262; + coeffs_dz->coeff_m1_0_p2 = t3862+t4103+t4248; + coeffs_dz->coeff_0_0_p2 = t3889+RATIONAL(41.0,2100.0)+t4123+t4306; + coeffs_dz->coeff_p1_0_p2 = t3916+t4103+t4250; + coeffs_dz->coeff_p2_0_p2 = t3913+t4096+t4260; + coeffs_dz->coeff_m2_p1_p2 = t3866+t4080+t4164+t4259; + coeffs_dz->coeff_m1_p1_p2 = t4082+t4196+t4243; + coeffs_dz->coeff_0_p1_p2 = t3886+t4090+t4249; + coeffs_dz->coeff_p1_p1_p2 = t4072+t4185+t4230; + coeffs_dz->coeff_p2_p1_p2 = t4080+t3915+t4188+t4273; + coeffs_dz->coeff_m2_p2_p2 = t4089+t3877+t4165+t4227; + coeffs_dz->coeff_m1_p2_p2 = t4078+t4214+t4337; + coeffs_dz->coeff_0_p2_p2 = t3912+t4105+t4264; + coeffs_dz->coeff_p1_p2_p2 = t3915+t4087+t4152+t4253; + coeffs_dz->coeff_p2_p2_p2 = t4075+t4276+t4339; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dzz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dzz.compute.c new file mode 100644 index 0000000..9edb5fe --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dzz.compute.c @@ -0,0 +1,621 @@ +fp t5617; +fp t5576; +fp t5609; +fp t5618; +fp t5574; +fp t5791; +fp t5578; +fp t5608; +fp t5619; +fp t5560; +fp t5790; +fp t5592; +fp t5789; +fp t5597; +fp t5558; +fp t5606; +fp t5788; +fp t5596; +fp t5559; +fp t5589; +fp t5787; +fp t5568; +fp t5584; +fp t5786; +fp t5557; +fp t5785; +fp t5588; +fp t5784; +fp t5598; +fp t5561; +fp t5582; +fp t5551; +fp t5783; +fp t5552; +fp t5782; +fp t5605; +fp t5572; +fp t5586; +fp t5781; +fp t5577; +fp t5546; +fp t5600; +fp t5555; +fp t5780; +fp t5614; +fp t5579; +fp t5549; +fp t5779; +fp t5567; +fp t5581; +fp t5778; +fp t5729; +fp t5538; +fp t5777; +fp t5616; +fp t5571; +fp t5776; +fp t5775; +fp t5580; +fp t5604; +fp t5573; +fp t5774; +fp t5601; +fp t5575; +fp t5773; +fp t5772; +fp t5556; +fp t5771; +fp t5770; +fp t5730; +fp t5542; +fp t5769; +fp t5768; +fp t5767; +fp t5599; +fp t5563; +fp t5544; +fp t5766; +fp t5765; +fp t5603; +fp t5554; +fp t5545; +fp t5553; +fp t5764; +fp t5548; +fp t5763; +fp t5570; +fp t5762; +fp t5534; +fp t5761; +fp t5547; +fp t5760; +fp t5759; +fp t5758; +fp t5541; +fp t5757; +fp t5566; +fp t5756; +fp t5564; +fp t5755; +fp t5587; +fp t5754; +fp t5753; +fp t5752; +fp t5751; +fp t5750; +fp t5749; +fp t5748; +fp t5747; +fp t5550; +fp t5746; +fp t5745; +fp t5744; +fp t5590; +fp t5743; +fp t5742; +fp t5562; +fp t5741; +fp t5539; +fp t5740; +fp t5585; +fp t5739; +fp t5738; +fp t5688; +fp t5737; +fp t5706; +fp t5736; +fp t5611; +fp t5735; +fp t5734; +fp t5733; +fp t5716; +fp t5732; +fp t5731; +fp t5537; +fp t5728; +fp t5727; +fp t5726; +fp t5725; +fp t5724; +fp t5540; +fp t5565; +fp t5723; +fp t5722; +fp t5721; +fp t5569; +fp t5720; +fp t5719; +fp t5718; +fp t5717; +fp t5715; +fp t5714; +fp t5713; +fp t5712; +fp t5711; +fp t5710; +fp t5709; +fp t5708; +fp t5705; +fp t5704; +fp t5703; +fp t5702; +fp t5701; +fp t5700; +fp t5699; +fp t5698; +fp t5697; +fp t5696; +fp t5695; +fp t5694; +fp t5693; +fp t5535; +fp t5692; +fp t5691; +fp t5690; +fp t5689; +fp t5687; +fp t5593; +fp t5686; +fp t5610; +fp t5685; +fp t5684; +fp t5683; +fp t5682; +fp t5681; +fp t5680; +fp t5679; +fp t5678; +fp t5677; +fp t5676; +fp t5675; +fp t5674; +fp t5673; +fp t5672; +fp t5671; +fp t5670; +fp t5669; +fp t5668; +fp t5667; +fp t5666; +fp t5665; +fp t5664; +fp t5663; +fp t5662; +fp t5661; +fp t5660; +fp t5659; +fp t5658; +fp t5657; +fp t5656; +fp t5655; +fp t5654; +fp t5653; +fp t5652; +fp t5536; +fp t5651; +fp t5650; +fp t5649; +fp t5648; +fp t5647; +fp t5646; +fp t5645; +fp t5644; +fp t5643; +fp t5543; +fp t5642; +fp t5641; +fp t5640; +fp t5639; +fp t5638; +fp t5637; +fp t5636; +fp t5635; +fp t5634; +fp t5633; +fp t5632; +fp t5631; +fp t5630; +fp t5629; +fp t5628; +fp t5627; +fp t5626; +fp t5625; +fp t5624; +fp t5623; +fp t5622; +fp t5621; +fp t5620; + t5617 = z*z; + t5576 = RATIONAL(3.0,25.0)*t5617; + t5609 = RATIONAL(1.0,245.0); + t5618 = x*x; + t5574 = t5609*t5618; + t5791 = t5576+t5574; + t5578 = RATIONAL(-2.0,25.0)*t5617; + t5608 = RATIONAL(-1.0,245.0); + t5619 = y*y; + t5560 = t5608*t5619; + t5790 = t5578+t5560; + t5592 = RATIONAL(211.0,3675.0); + t5789 = t5560+t5592; + t5597 = RATIONAL(-2.0,245.0); + t5558 = t5597*t5619; + t5606 = RATIONAL(-1.0,300.0); + t5788 = t5558+t5606; + t5596 = RATIONAL(1.0,490.0); + t5559 = t5596*t5618; + t5589 = RATIONAL(166.0,3675.0); + t5787 = t5559+t5589; + t5568 = t5608*t5618; + t5584 = RATIONAL(191.0,14700.0); + t5786 = t5568+t5584; + t5557 = t5596*t5619; + t5785 = t5557+t5592; + t5588 = RATIONAL(151.0,3675.0); + t5784 = t5588+t5574; + t5598 = RATIONAL(-1.0,175.0); + t5561 = t5598*y; + t5582 = RATIONAL(-1.0,25.0)*z; + t5551 = y*t5582; + t5783 = t5561+t5551; + t5552 = x*t5582; + t5782 = t5582+t5552; + t5605 = RATIONAL(2.0,245.0); + t5572 = t5605*t5618; + t5586 = RATIONAL(-169.0,14700.0); + t5781 = t5572+t5586; + t5577 = RATIONAL(1.0,25.0)*z; + t5546 = y*t5577; + t5600 = RATIONAL(1.0,175.0); + t5555 = t5600*y; + t5780 = t5546+t5555; + t5614 = RATIONAL(1.0,50.0); + t5579 = t5614*z; + t5549 = y*t5579; + t5779 = t5549+t5577; + t5567 = t5605*t5619; + t5581 = t5614*t5617; + t5778 = t5567+t5581; + t5729 = z*RATIONAL(-1.0,100.0); + t5538 = x*t5729; + t5777 = t5568+t5538; + t5616 = RATIONAL(4.0,75.0); + t5571 = t5609*t5619; + t5776 = t5616+t5571; + t5775 = t5549+t5579; + t5580 = RATIONAL(-1.0,50.0)*z; + t5604 = RATIONAL(-2.0,175.0); + t5573 = t5604*x; + t5774 = t5580+t5573; + t5601 = RATIONAL(1.0,350.0); + t5575 = t5601*x; + t5773 = t5582+t5575; + t5772 = t5546+t5561; + t5556 = t5601*y; + t5771 = t5549+t5556; + t5770 = t5571+t5588; + t5730 = z*RATIONAL(1.0,100.0); + t5542 = y*t5730; + t5769 = t5542+t5579; + t5768 = t5568+t5586; + t5767 = t5542+t5580; + t5599 = RATIONAL(-1.0,350.0); + t5563 = t5599*y; + t5544 = x*t5563; + t5766 = t5544+t5546; + t5765 = t5551+t5555; + t5603 = RATIONAL(2.0,175.0); + t5554 = t5603*y; + t5545 = x*t5554; + t5553 = y*t5580; + t5764 = t5545+t5553; + t5548 = x*t5577; + t5763 = t5548+t5582; + t5570 = t5604*y; + t5762 = t5580+t5570; + t5534 = x*t5555; + t5761 = t5534+t5586; + t5547 = x*t5580; + t5760 = t5547+t5572; + t5759 = t5616+t5574; + t5758 = t5577+t5575; + t5541 = y*t5729; + t5757 = t5541+t5560; + t5566 = t5597*t5618; + t5756 = t5566+t5606; + t5564 = t5599*x; + t5755 = t5564+t5582; + t5587 = RATIONAL(-529.0,14700.0); + t5754 = t5567+t5587; + t5753 = t5563+t5553; + t5752 = t5547+t5559; + t5751 = t5577+t5552; + t5750 = t5580+t5553; + t5749 = t5563+t5577; + t5748 = t5568+t5592; + t5747 = t5582+t5553; + t5550 = x*t5579; + t5746 = t5541+t5550; + t5745 = t5578+t5557; + t5744 = t5550+t5572; + t5590 = RATIONAL(256.0,3675.0); + t5743 = t5568+t5590; + t5742 = t5577+t5553; + t5562 = t5603*x; + t5741 = t5579+t5562; + t5539 = x*t5570; + t5740 = t5549+t5539; + t5585 = RATIONAL(311.0,14700.0); + t5739 = t5566+t5585; + t5738 = t5564+t5550; + t5688 = t5554+t5778; + t5737 = t5688+t5768; + t5706 = t5576+t5571; + t5736 = RATIONAL(-57.0,490.0)+t5706+t5574; + t5611 = RATIONAL(-9.0,98.0); + t5735 = t5566+t5611+t5706; + t5734 = t5558+t5611+t5791; + t5733 = t5587+t5744; + t5716 = t5576+t5566; + t5732 = t5558+RATIONAL(-33.0,490.0)+t5716; + t5731 = x*y; + t5537 = x*t5561; + t5728 = t5537+t5573; + t5727 = t5561+t5573; + t5726 = t5537+t5562; + t5725 = t5562+t5555; + t5724 = t5576+t5572; + t5540 = y*t5575; + t5565 = t5600*x; + t5723 = t5540+t5565; + t5722 = t5565+t5537; + t5721 = t5565+t5555; + t5569 = t5598*x; + t5720 = t5534+t5569; + t5719 = t5569+t5555; + t5718 = t5568+t5569; + t5717 = t5544+t5565; + t5715 = t5540+t5569; + t5714 = t5544+t5569; + t5713 = t5565+t5534; + t5712 = t5565+t5561; + t5711 = t5561+t5560; + t5710 = t5569+t5537; + t5709 = t5558+t5581; + t5708 = t5561+t5569; + t5705 = t5563+t5745; + t5704 = t5581+t5744; + t5703 = t5553+t5778; + t5702 = t5559+t5578+t5550; + t5701 = t5549+t5778; + t5700 = t5578+t5752; + t5699 = t5581+t5760; + t5698 = t5556+t5745; + t5697 = t5582+t5790; + t5696 = t5565+t5578+t5568; + t5695 = t5578+t5718; + t5694 = t5581+t5560+t5555; + t5693 = t5581+t5757; + t5535 = x*t5730; + t5692 = t5535+t5568+t5581; + t5691 = t5577+t5790; + t5690 = t5581+t5711; + t5689 = t5551+t5790; + t5687 = t5549+t5745; + t5593 = RATIONAL(-61.0,490.0); + t5686 = t5593+t5572+t5706; + t5610 = RATIONAL(-1.0,10.0); + t5685 = t5558+t5610+t5724; + t5684 = t5567+t5610+t5716; + t5683 = t5593+t5567+t5791; + t5682 = RATIONAL(136.0,3675.0)+t5578+t5571+t5574; + t5681 = t5566+RATIONAL(431.0,14700.0)+t5709; + t5680 = t5702+t5773; + t5679 = t5555+t5735; + t5678 = t5701+t5762; + t5677 = t5537+t5734; + t5676 = t5580+t5562+t5699; + t5675 = t5702+t5770; + t5674 = t5704+t5788; + t5673 = t5696+t5763; + t5672 = t5544+t5736; + t5671 = t5697+t5759; + t5670 = t5585+t5709+t5777; + t5669 = t5558+t5585+t5692; + t5668 = t5540+t5736; + t5667 = t5534+t5734; + t5666 = t5700+t5770; + t5665 = t5693+t5739; + t5664 = t5690+t5767; + t5663 = t5554+t5732; + t5662 = t5579+t5573+t5699; + t5661 = t5688+t5756; + t5660 = t5695+t5776; + t5659 = t5698+t5742; + t5658 = t5691+t5759; + t5657 = t5698+t5784; + t5656 = t5570+t5732; + t5655 = t5705+t5784; + t5654 = t5694+t5769; + t5653 = t5579+t5570+t5703; + t5652 = t5561+t5735; + t5536 = RATIONAL(-1.0,700.0)*t5731; + t5651 = t5564+t5536+t5705+t5787; + t5650 = t5542+t5560+t5704+t5761; + t5649 = t5678+t5768; + t5648 = t5559+t5592+t5691+t5738; + t5647 = t5697+t5743+t5780; + t5646 = t5693+t5760+t5761; + t5645 = t5737+t5750; + t5644 = t5680+t5789; + t5643 = t5653+t5768; + t5543 = RATIONAL(1.0,700.0)*t5731; + t5642 = t5543+t5589+t5687+t5752; + t5641 = t5676+t5754; + t5640 = t5664+t5786; + t5639 = t5695+t5782+t5785; + t5638 = t5534+t5590+t5696+t5711; + t5637 = t5687+t5748+t5749; + t5636 = t5548+t5590+t5691+t5718; + t5635 = t5737+t5775; + t5634 = t5673+t5785; + t5633 = t5694+t5728+t5781; + t5632 = t5544+t5584+t5692+t5757; + t5631 = t5539+t5703+t5733; + t5630 = t5662+t5754; + t5629 = t5540+t5584+t5693+t5777; + t5628 = t5690+t5726+t5781; + t5627 = t5544+t5592+t5689+t5752; + t5626 = t5552+t5537+t5689+t5743; + t5625 = t5654+t5786; + t5624 = t5545+t5701+t5733; + t5623 = t5557+t5589+t5680; + t5622 = t5546+t5540+t5700+t5789; + t5621 = t5659+t5748; + t5620 = t5659+t5787; + coeffs_dzz->coeff_m2_m2_m2 = t5573+t5624+t5762; + coeffs_dzz->coeff_m1_m2_m2 = t5535+t5649+t5720; + coeffs_dzz->coeff_0_m2_m2 = t5678+t5756; + coeffs_dzz->coeff_p1_m2_m2 = t5538+t5649+t5722; + coeffs_dzz->coeff_p2_m2_m2 = t5570+t5641+t5740; + coeffs_dzz->coeff_m2_m1_m2 = t5580+t5650+t5727; + coeffs_dzz->coeff_m1_m1_m2 = t5535+t5640+t5715; + coeffs_dzz->coeff_0_m1_m2 = t5664+t5739; + coeffs_dzz->coeff_p1_m1_m2 = t5538+t5640+t5717; + coeffs_dzz->coeff_p2_m1_m2 = t5547+t5628+t5767; + coeffs_dzz->coeff_m2_0_m2 = t5674+t5774; + coeffs_dzz->coeff_m1_0_m2 = t5569+t5580+t5669; + coeffs_dzz->coeff_0_0_m2 = t5580+t5681; + coeffs_dzz->coeff_p1_0_m2 = t5580+t5565+t5670; + coeffs_dzz->coeff_p2_0_m2 = t5676+t5788; + coeffs_dzz->coeff_m2_p1_m2 = t5580+t5633+t5746; + coeffs_dzz->coeff_m1_p1_m2 = t5580+t5632+t5719; + coeffs_dzz->coeff_0_p1_m2 = t5555+t5580+t5665; + coeffs_dzz->coeff_p1_p1_m2 = t5580+t5629+t5721; + coeffs_dzz->coeff_p2_p1_m2 = t5580+t5646+t5725; + coeffs_dzz->coeff_m2_p2_m2 = t5554+t5631+t5774; + coeffs_dzz->coeff_m1_p2_m2 = t5535+t5645+t5710; + coeffs_dzz->coeff_0_p2_m2 = t5661+t5750; + coeffs_dzz->coeff_p1_p2_m2 = t5538+t5645+t5713; + coeffs_dzz->coeff_p2_p2_m2 = t5554+t5641+t5764; + coeffs_dzz->coeff_m2_m2_m1 = t5577+t5626+t5721; + coeffs_dzz->coeff_m1_m2_m1 = t5555+t5627+t5758; + coeffs_dzz->coeff_0_m2_m1 = t5658+t5765; + coeffs_dzz->coeff_p1_m2_m1 = t5540+t5648+t5765; + coeffs_dzz->coeff_p2_m2_m1 = t5534+t5636+t5765; + coeffs_dzz->coeff_m2_m1_m1 = t5552+t5621+t5717; + coeffs_dzz->coeff_m1_m1_m1 = t5536+t5547+t5575+t5620; + coeffs_dzz->coeff_0_m1_m1 = t5657+t5742; + coeffs_dzz->coeff_p1_m1_m1 = t5543+t5620+t5738; + coeffs_dzz->coeff_p2_m1_m1 = t5548+t5621+t5715; + coeffs_dzz->coeff_m2_0_m1 = t5696+t5751+t5776; + coeffs_dzz->coeff_m1_0_m1 = t5666+t5758; + coeffs_dzz->coeff_0_0_m1 = t5577+t5682; + coeffs_dzz->coeff_p1_0_m1 = t5564+t5577+t5675; + coeffs_dzz->coeff_p2_0_m1 = t5577+t5548+t5660; + coeffs_dzz->coeff_m2_p1_m1 = t5552+t5637+t5723; + coeffs_dzz->coeff_m1_p1_m1 = t5575+t5642+t5749; + coeffs_dzz->coeff_0_p1_m1 = t5655+t5779; + coeffs_dzz->coeff_p1_p1_m1 = t5550+t5651+t5779; + coeffs_dzz->coeff_p2_p1_m1 = t5548+t5637+t5714; + coeffs_dzz->coeff_m2_p2_m1 = t5546+t5638+t5751; + coeffs_dzz->coeff_m1_p2_m1 = t5561+t5622+t5758; + coeffs_dzz->coeff_0_p2_m1 = t5658+t5772; + coeffs_dzz->coeff_p1_p2_m1 = t5561+t5648+t5766; + coeffs_dzz->coeff_p2_p2_m1 = t5537+t5636+t5772; + coeffs_dzz->coeff_m2_m2_0 = t5539+t5562+t5663; + coeffs_dzz->coeff_m1_m2_0 = t5565+t5554+t5677; + coeffs_dzz->coeff_0_m2_0 = t5554+t5685; + coeffs_dzz->coeff_p1_m2_0 = t5569+t5554+t5667; + coeffs_dzz->coeff_p2_m2_0 = t5573+t5545+t5663; + coeffs_dzz->coeff_m2_m1_0 = t5679+t5726; + coeffs_dzz->coeff_m1_m1_0 = t5672+t5721; + coeffs_dzz->coeff_0_m1_0 = t5555+t5686; + coeffs_dzz->coeff_p1_m1_0 = t5668+t5719; + coeffs_dzz->coeff_p2_m1_0 = t5573+t5534+t5679; + coeffs_dzz->coeff_m2_0_0 = t5562+t5684; + coeffs_dzz->coeff_m1_0_0 = t5565+t5683; + coeffs_dzz->coeff_0_0_0 = t5567+RATIONAL(-13.0,98.0)+t5724; + coeffs_dzz->coeff_p1_0_0 = t5569+t5683; + coeffs_dzz->coeff_p2_0_0 = t5573+t5684; + coeffs_dzz->coeff_m2_p1_0 = t5534+t5562+t5652; + coeffs_dzz->coeff_m1_p1_0 = t5668+t5712; + coeffs_dzz->coeff_0_p1_0 = t5561+t5686; + coeffs_dzz->coeff_p1_p1_0 = t5672+t5708; + coeffs_dzz->coeff_p2_p1_0 = t5652+t5728; + coeffs_dzz->coeff_m2_p2_0 = t5545+t5562+t5656; + coeffs_dzz->coeff_m1_p2_0 = t5570+t5565+t5667; + coeffs_dzz->coeff_0_p2_0 = t5570+t5685; + coeffs_dzz->coeff_p1_p2_0 = t5570+t5569+t5677; + coeffs_dzz->coeff_p2_p2_0 = t5573+t5539+t5656; + coeffs_dzz->coeff_m2_m2_p1 = t5548+t5647+t5722; + coeffs_dzz->coeff_m1_m2_p1 = t5555+t5644+t5766; + coeffs_dzz->coeff_0_m2_p1 = t5671+t5780; + coeffs_dzz->coeff_p1_m2_p1 = t5555+t5622+t5755; + coeffs_dzz->coeff_p2_m2_p1 = t5552+t5647+t5720; + coeffs_dzz->coeff_m2_m1_p1 = t5544+t5634+t5771; + coeffs_dzz->coeff_m1_m1_p1 = t5536+t5623+t5771; + coeffs_dzz->coeff_0_m1_p1 = t5582+t5549+t5657; + coeffs_dzz->coeff_p1_m1_p1 = t5556+t5642+t5755; + coeffs_dzz->coeff_p2_m1_p1 = t5540+t5639+t5771; + coeffs_dzz->coeff_m2_0_p1 = t5673+t5776; + coeffs_dzz->coeff_m1_0_p1 = t5675+t5773; + coeffs_dzz->coeff_0_0_p1 = t5582+t5682; + coeffs_dzz->coeff_p1_0_p1 = t5666+t5755; + coeffs_dzz->coeff_p2_0_p1 = t5660+t5782; + coeffs_dzz->coeff_m2_p1_p1 = t5540+t5634+t5753; + coeffs_dzz->coeff_m1_p1_p1 = t5543+t5623+t5753; + coeffs_dzz->coeff_0_p1_p1 = t5655+t5747; + coeffs_dzz->coeff_p1_p1_p1 = t5547+t5651+t5747; + coeffs_dzz->coeff_p2_p1_p1 = t5544+t5639+t5753; + coeffs_dzz->coeff_m2_p2_p1 = t5551+t5638+t5763; + coeffs_dzz->coeff_m1_p2_p1 = t5540+t5644+t5783; + coeffs_dzz->coeff_0_p2_p1 = t5671+t5783; + coeffs_dzz->coeff_p1_p2_p1 = t5561+t5627+t5755; + coeffs_dzz->coeff_p2_p2_p1 = t5582+t5626+t5708; + coeffs_dzz->coeff_m2_m2_p2 = t5570+t5630+t5764; + coeffs_dzz->coeff_m1_m2_p2 = t5538+t5643+t5720; + coeffs_dzz->coeff_0_m2_p2 = t5653+t5756; + coeffs_dzz->coeff_p1_m2_p2 = t5535+t5643+t5722; + coeffs_dzz->coeff_p2_m2_p2 = t5570+t5631+t5741; + coeffs_dzz->coeff_m2_m1_p2 = t5579+t5646+t5727; + coeffs_dzz->coeff_m1_m1_p2 = t5579+t5629+t5708; + coeffs_dzz->coeff_0_m1_p2 = t5579+t5561+t5665; + coeffs_dzz->coeff_p1_m1_p2 = t5579+t5632+t5712; + coeffs_dzz->coeff_p2_m1_p2 = t5579+t5628+t5746; + coeffs_dzz->coeff_m2_0_p2 = t5662+t5788; + coeffs_dzz->coeff_m1_0_p2 = t5569+t5579+t5670; + coeffs_dzz->coeff_0_0_p2 = t5579+t5681; + coeffs_dzz->coeff_p1_0_p2 = t5565+t5579+t5669; + coeffs_dzz->coeff_p2_0_p2 = t5674+t5741; + coeffs_dzz->coeff_m2_p1_p2 = t5547+t5633+t5769; + coeffs_dzz->coeff_m1_p1_p2 = t5538+t5625+t5714; + coeffs_dzz->coeff_0_p1_p2 = t5654+t5739; + coeffs_dzz->coeff_p1_p1_p2 = t5535+t5625+t5723; + coeffs_dzz->coeff_p2_p1_p2 = t5579+t5650+t5725; + coeffs_dzz->coeff_m2_p2_p2 = t5554+t5630+t5740; + coeffs_dzz->coeff_m1_p2_p2 = t5538+t5635+t5710; + coeffs_dzz->coeff_0_p2_p2 = t5661+t5775; + coeffs_dzz->coeff_p1_p2_p2 = t5535+t5635+t5713; + coeffs_dzz->coeff_p2_p2_p2 = t5554+t5624+t5741; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.cube.order1.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.cube.order1.smooth0.c new file mode 100644 index 0000000..6b9b2e2 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.cube.order1.smooth0.c @@ -0,0 +1,61 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrMD_3d_cube10 +#include "../template.h" + +#define N_DIMS 3 +#define MOLECULE_MIN_M 0 +#define MOLECULE_MAX_M 1 +#define MOLECULE_SIZE 2 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +#define HAVE_OP_DZ +/* n.b. no 2nd derivatives for linear interpolation! */ + +#define XYZ x, y, z +#define FP_XYZ fp x, fp y, fp z +#define STRIDE_IJK stride_i, stride_j, stride_k +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride, Jacobian_mk_stride + +#define DATA_STRUCT data_struct_3d_cube_size2 +#define COEFFS_STRUCT coeffs_struct_3d_cube_size2 + +#define FETCH_DATA_REAL LocalInterp_fetch_3d_cube2_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_3d_cube2_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_3d_cube2_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_3d_cube2_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_3d_cube2_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_3d_cube2_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_3d_cube2_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_3d_cube2_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_3d_cube2 + +#define STORE_COEFFS LocalInterp_store_3d_cube2 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-dy.compute.c" +#define COEFFS_DZ_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order1.smooth0/coeffs-dz.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.cube.order2.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.cube.order2.smooth0.c new file mode 100644 index 0000000..02ebe11 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.cube.order2.smooth0.c @@ -0,0 +1,71 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrMD_3d_cube20 +#include "../template.h" + +#define N_DIMS 3 +#define MOLECULE_MIN_M -1 +#define MOLECULE_MAX_M 1 +#define MOLECULE_SIZE 3 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +#define HAVE_OP_DZ +#define HAVE_OP_DXX +#define HAVE_OP_DXY +#define HAVE_OP_DXZ +#define HAVE_OP_DYY +#define HAVE_OP_DYZ +#define HAVE_OP_DZZ + +#define XYZ x, y, z +#define FP_XYZ fp x, fp y, fp z +#define STRIDE_IJK stride_i, stride_j, stride_k +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride, Jacobian_mk_stride + +#define DATA_STRUCT data_struct_3d_cube_size3 +#define COEFFS_STRUCT coeffs_struct_3d_cube_size3 + +#define FETCH_DATA_REAL LocalInterp_fetch_3d_cube3_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_3d_cube3_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_3d_cube3_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_3d_cube3_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_3d_cube3_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_3d_cube3_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_3d_cube3_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_3d_cube3_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_3d_cube3 + +#define STORE_COEFFS LocalInterp_store_3d_cube3 + +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dy.compute.c" +#define COEFFS_DZ_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dz.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxx.compute.c" +#define COEFFS_DXY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxy.compute.c" +#define COEFFS_DXZ_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxz.compute.c" +#define COEFFS_DYY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyy.compute.c" +#define COEFFS_DYZ_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyz.compute.c" +#define COEFFS_DZZ_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order2.smooth0/coeffs-dzz.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.cube.order3.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.cube.order3.smooth0.c new file mode 100644 index 0000000..6abed55 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.cube.order3.smooth0.c @@ -0,0 +1,71 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrMD_3d_cube30 +#include "../template.h" + +#define N_DIMS 3 +#define MOLECULE_MIN_M -1 +#define MOLECULE_MAX_M 2 +#define MOLECULE_SIZE 4 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +#define HAVE_OP_DZ +#define HAVE_OP_DXX +#define HAVE_OP_DXY +#define HAVE_OP_DXZ +#define HAVE_OP_DYY +#define HAVE_OP_DYZ +#define HAVE_OP_DZZ + +#define XYZ x, y, z +#define FP_XYZ fp x, fp y, fp z +#define STRIDE_IJK stride_i, stride_j, stride_k +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride, Jacobian_mk_stride + +#define DATA_STRUCT data_struct_3d_cube_size4 +#define COEFFS_STRUCT coeffs_struct_3d_cube_size4 + +#define FETCH_DATA_REAL LocalInterp_fetch_3d_cube4_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_3d_cube4_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_3d_cube4_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_3d_cube4_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_3d_cube4_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_3d_cube4_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_3d_cube4_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_3d_cube4_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_3d_cube4 + +#define STORE_COEFFS LocalInterp_store_3d_cube4 + +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dy.compute.c" +#define COEFFS_DZ_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dz.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxx.compute.c" +#define COEFFS_DXY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxy.compute.c" +#define COEFFS_DXZ_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxz.compute.c" +#define COEFFS_DYY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyy.compute.c" +#define COEFFS_DYZ_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyz.compute.c" +#define COEFFS_DZZ_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order3.smooth0/coeffs-dzz.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.cube.order4.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.cube.order4.smooth0.c new file mode 100644 index 0000000..97f5e23 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.cube.order4.smooth0.c @@ -0,0 +1,71 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrMD_3d_cube40 +#include "../template.h" + +#define N_DIMS 3 +#define MOLECULE_MIN_M -2 +#define MOLECULE_MAX_M 2 +#define MOLECULE_SIZE 5 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +#define HAVE_OP_DZ +#define HAVE_OP_DXX +#define HAVE_OP_DXY +#define HAVE_OP_DXZ +#define HAVE_OP_DYY +#define HAVE_OP_DYZ +#define HAVE_OP_DZZ + +#define XYZ x, y, z +#define FP_XYZ fp x, fp y, fp z +#define STRIDE_IJK stride_i, stride_j, stride_k +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride, Jacobian_mk_stride + +#define DATA_STRUCT data_struct_3d_cube_size5 +#define COEFFS_STRUCT coeffs_struct_3d_cube_size5 + +#define FETCH_DATA_REAL LocalInterp_fetch_3d_cube5_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_3d_cube5_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_3d_cube5_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_3d_cube5_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_3d_cube5_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_3d_cube5_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_3d_cube5_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_3d_cube5_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_3d_cube5 + +#define STORE_COEFFS LocalInterp_store_3d_cube5 + +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dy.compute.c" +#define COEFFS_DZ_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dz.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxx.compute.c" +#define COEFFS_DXY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxy.compute.c" +#define COEFFS_DXZ_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxz.compute.c" +#define COEFFS_DYY_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyy.compute.c" +#define COEFFS_DYZ_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyz.compute.c" +#define COEFFS_DZZ_COMPUTE_FILE_NAME "Lagrange-maximum-degree/3d.coeffs/3d.cube.order4.smooth0/coeffs-dzz.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.log b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.log new file mode 100644 index 0000000..93faeb6 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.log @@ -0,0 +1,40709 @@ + |\^/| Maple 7 (IBM INTEL LINUX) +._|\| |/|_. Copyright (c) 2001 by Waterloo Maple Inc. + \ MAPLE / All rights reserved. Maple is a registered trademark of + <____ ____> Waterloo Maple Inc. + | Type ? for help. +# util.maple -- misc utility routines +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/util.maple,v 1.4 2002/08/20 16:46:06 jthorn Exp $ +> +# +# fix_rationals - convert numbers to RATIONAL() calls +# nonmatching_names - find names in a list which *don't* have a specified prefix +# sprint_numeric_list - convert a numeric list to a valid C identifier suffix +# print_name_list_dcl - print C declarations for a list of names +# +# hypercube_points - compute all (integer) points in an N-dimensional hypercube +# +# ftruncate - truncate a file to zero length +# +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function converts all {integer, rational} subexpressions of its +# input except integer exponents and -1 factors in products, into function +# calls +# RATIONAL(num,den) +# This is useful in conjunction with the C() library function, since +# +# C( (1/3) * foo * bar ) +# t0 = foo*bar/3; +# +# generates a (slow) division (and runs the risk of mixed-mode-arithmetic +# problems), while +# +# C((1.0/3.0) * foo * bar); +# t0 = 0.3333333333*foo*bar; +# +# suffers from roundoff error. With this function, +# +# fix_rationals((1/3) * foo * bar); +# RATIONAL(1,3) foo bar +# C(%); +# t0 = RATIONAL(1.0,3.0)*foo*bar; +# +# which a C preprocessor macro can easily convert to the desired +# +# t0 = (1.0/3.0)*foo*bar; +# +# Additionally, this function can be told to leave certain types of +# subexpressions unconverged. For example, +# fix_rationals(expr, type, specfunc(integer, DATA)); +# will leave all subexpressions of the form DATA(integer arguments) +# unconverted. +# +# Arguments: +# expr = (in) The expression to be converted. +# inert_fn = (optional in) +# If specified, this argument should be a Boolean procedure +# or the name of a Boolean procedure. This procedure should +# take one or more argument, and return true if and only if +# the first argument should *not* be converted, i.e. if we +# should leave this expression unchanged. See the last +# example above. +# ... = (optional in) +# Any further arguments are passed as additional arguments to +# the inert_fn procedure. +# +> fix_rationals := +> proc( +> expr::{ +> algebraic, name = algebraic, +> list({algebraic, name = algebraic}), +> set ({algebraic, name = algebraic}) +> }, +> inert_fn::{name, procedure} +> ) +> local nn, k, +> base, power, fbase, fpower, +> fn, fn_args_list, +> num, den, mult; +> +# do we want to convert this expression? +> if ((nargs >= 2) and inert_fn(expr, args[3..nargs])) +> then return expr; +> end if; +> +# recurse over lists and sets +> if (type(expr, {list,set})) +> then return map(fix_rationals, expr, args[2..nargs]); +> end if; +> +# recurse over equation right hand sides +> if (type(expr, name = algebraic)) +> then return ( lhs(expr) = fix_rationals(rhs(expr), args[2..nargs]) ); +> end if; +> +# recurse over functions other than RATIONAL() +> if (type(expr, function)) +> then +> fn := op(0, expr); +> if (fn <> 'RATIONAL') +> then +> fn_args_list := [op(expr)]; +> fn_args_list := map(fix_rationals, fn_args_list, args[2..nargs]); +> fn; return '%'( op(fn_args_list) ); +> end if; +> end if; +> +> nn := nops(expr); +> +# recurse over sums +> if (type(expr, `+`)) +> then return sum('fix_rationals(op(k,expr), args[2..nargs])', 'k'=1..nn); +> end if; +> +# recurse over products +# ... leaving leading -1 factors intact, i.e. not converted to RATIONAL(-1,1) +> if (type(expr, `*`)) +> then +> if (op(1, expr) = -1) +> then return -1*fix_rationals(remove(type, expr, 'identical(-1)'), +> args[2..nargs]); +> else return product('fix_rationals(op(k,expr), args[2..nargs])', +> 'k'=1..nn); +> end if; +> end if; +> +# recurse over powers +# ... leaving integer exponents intact +> if (type(expr, `^`)) +> then +> base := op(1, expr); +> power := op(2, expr); +> +> fbase := fix_rationals(base, args[2..nargs]); +> if (type(power, integer)) +> then fpower := power; +> else fpower := fix_rationals(power, args[2..nargs]); +> end if; +> return fbase ^ fpower; +> end if; +> +# fix integers and fractions +> if (type(expr, integer)) +> then return 'RATIONAL'(expr, 1); +> end if; +> if (type(expr, fraction)) +> then +> num := op(1, expr); +> den := op(2, expr); +> +> return 'RATIONAL'(num, den); +> end if; +> +# turn Maple floating-point into integer fraction, then recursively fix that +> if (type(expr, float)) +> then +> mult := op(1, expr); +> power := op(2, expr); +> return fix_rationals(mult * 10^power, args[2..nargs]); +> end if; +> +# identity op on names +> if (type(expr, name)) +> then return expr; +> end if; +> +# unknown type +> error "%0", +> "unknown type for expr!", +> " whattype(expr) = ", whattype(expr), +> " expr = ", expr; +> end proc; +fix_rationals := proc(expr::{algebraic, name = algebraic, +list({algebraic, name = algebraic}), set({algebraic, name = algebraic})}, +inert_fn::{procedure, name}) +local nn, k, base, power, fbase, fpower, fn, fn_args_list, num, den, mult; + if 2 <= nargs and inert_fn(expr, args[3 .. nargs]) then return expr + end if; + if type(expr, {set, list}) then + return map(fix_rationals, expr, args[2 .. nargs]) + end if; + if type(expr, name = algebraic) then + return lhs(expr) = fix_rationals(rhs(expr), args[2 .. nargs]) + end if; + if type(expr, function) then + fn := op(0, expr); + if fn <> 'RATIONAL' then + fn_args_list := [op(expr)]; + fn_args_list := + map(fix_rationals, fn_args_list, args[2 .. nargs]); + fn; + return '%'(op(fn_args_list)) + end if + end if; + nn := nops(expr); + if type(expr, `+`) then return + sum('fix_rationals(op(k, expr), args[2 .. nargs])', 'k' = 1 .. nn) + end if; + if type(expr, `*`) then + if op(1, expr) = -1 then return -fix_rationals( + remove(type, expr, 'identical(-1)'), args[2 .. nargs]) + else return product('fix_rationals(op(k, expr), args[2 .. nargs])', + 'k' = 1 .. nn) + end if + end if; + if type(expr, `^`) then + base := op(1, expr); + power := op(2, expr); + fbase := fix_rationals(base, args[2 .. nargs]); + if type(power, integer) then fpower := power + else fpower := fix_rationals(power, args[2 .. nargs]) + end if; + return fbase^fpower + end if; + if type(expr, integer) then return 'RATIONAL'(expr, 1) end if; + if type(expr, fraction) then + num := op(1, expr); den := op(2, expr); return 'RATIONAL'(num, den) + end if; + if type(expr, float) then + mult := op(1, expr); + power := op(2, expr); + return fix_rationals(mult*10^power, args[2 .. nargs]) + end if; + if type(expr, name) then return expr end if; + error "%0", "unknown type for expr!", " whattype(expr) = ", + whattype(expr), " expr = ", expr +end proc + +> +################################################################################ +> +# +# This function finds names in a list which *don't* have a specified prefix. +# +# Arguments: +# name_list = A list of the names. +# prefix = The prefix we want to filter out. +# +# Results: +# This function returns the subset list of names which don't have the +# specified prefix. +# +> nonmatching_names := +> proc( name_list::list({name,string}), prefix::{name,string} ) +> +> select( proc(n) +> evalb(not StringTools[IsPrefix](prefix,n)); +> end proc +> , +> name_list +> ); +> end proc; +nonmatching_names := proc( +name_list::list({name, string}), prefix::{name, string}) + select(proc(n) evalb(not StringTools[IsPrefix](prefix, n)) end proc, + name_list) +end proc + +> +################################################################################ +> +# +# This function converts a numeric list to a string which is a valid +# C identifier suffix: elements are separated by "_", decimal points are +# replaced by "x", and all nonzero values have explicit +/- signs, which +# are replaced by "p"/"m". +# +# For example, [0,-3.5,+4] --> "0_m3x5_p4". +# +> sprint_numeric_list := +> proc(nlist::list(numeric)) +> +# generate preliminary string, eg "+0_-3.5_+4" +> map2(sprintf, "%+a", nlist); +> ListTools[Join](%, "_"); +> cat(op(%)); +> +# fixup bad characters +> StringTools[SubstituteAll](%, "+0", "0"); +> StringTools[CharacterMap](".+-", "xpm", %); +> +> return %; +> end proc; +sprint_numeric_list := proc(nlist::list(numeric)) + map2(sprintf, "%+a", nlist); + ListTools[Join](%, "_"); + cat(op(%)); + StringTools[SubstituteAll](%, "+0", "0"); + StringTools[CharacterMap](".+-", "xpm", %); + return % +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C declarations for a list of names. +# +# Argument: +# name_list = A list of the names. +# type_name = The C type of the names, eg. "double". +# file_name = The file name to write the declaration to. This is +# truncated before writing. +# +> print_name_list_dcl := +> proc( name_list::list({name,string}), +> type_name::string, +> file_name::string ) +> local blanks, separator_string; +> +> ftruncate(file_name); +> +> map( +> proc(var::{name,string}) +> fprintf(file_name, +> "%s %s;\n", +> type_name, var); +> end proc +> , +> name_list +> ); +> +> fclose(file_name); +> NULL; +> end proc; +print_name_list_dcl := proc( +name_list::list({name, string}), type_name::string, file_name::string) +local blanks, separator_string; + ftruncate(file_name); + map(proc(var::{name, string}) + fprintf(file_name, "%s %s;\n", type_name, var) + end proc, name_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes a list of all the (integer) points in an +# N-dimensional hypercube, in lexicographic order. The present +# implementation requires N <= 4. +# +# Arguments: +# cmin,cmax = N-element lists of cube minimum/maximum coordinates. +# +# Results: +# The function returns a set of d-element lists giving the coordinates. +# For example, +# hypercube([0,0], [2,1] +# returns +# { [0,0], [0,1], [1,0], [1,1], [2,0], [2,1] } +> hypercube_points := +> proc(cmin::list(integer), cmax::list(integer)) +> local N, i,j,k,l; +> +> N := nops(cmin); +> if (nops(cmax) <> N) +> then error +> "must have same number of dimensions for min and max coordinates!"; +> fi; +> +> if (N = 1) +> then return [seq([i], i=cmin[1]..cmax[1])]; +> elif (N = 2) +> then return [ +> seq( +> seq([i,j], j=cmin[2]..cmax[2]), +> i=cmin[1]..cmax[1]) +> ]; +> elif (N = 3) +> then return [ +> seq( +> seq( +> seq([i,j,k], k=cmin[3]..cmax[3]), +> j=cmin[2]..cmax[2] ), +> i=cmin[1]..cmax[1]) +> ]; +> elif (N = 4) +> then return [ +> seq( +> seq( +> seq( +> seq([i,j,k,l], l=cmin[4]..cmax[4]), +> k=cmin[3]..cmax[3] ), +> j=cmin[2]..cmax[2]), +> i=cmin[1]..cmax[1]) +> ]; +> else +> error "implementation restriction: must have N <= 4, got %1!", N; +> fi; +> end proc; +hypercube_points := proc(cmin::list(integer), cmax::list(integer)) +local N, i, j, k, l; + N := nops(cmin); + if nops(cmax) <> N then error + "must have same number of dimensions for min and max coordinates!" + end if; + if N = 1 then return [seq([i], i = cmin[1] .. cmax[1])] + elif N = 2 then return + [seq(seq([i, j], j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] + elif N = 3 then return [seq( + seq(seq([i, j, k], k = cmin[3] .. cmax[3]), j = cmin[2] .. cmax[2]) + , i = cmin[1] .. cmax[1])] + elif N = 4 then return [seq(seq(seq( + seq([i, j, k, l], l = cmin[4] .. cmax[4]), k = cmin[3] .. cmax[3]), + j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] + else error "implementation restriction: must have N <= 4, got %1!", N + end if +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function truncates a file to 0 length if it exists, or creates +# it at that length if it doesn't exist. +# +# Arguments: +# file_name = (in) The name of the file. +# +> ftruncate := +> proc(file_name::string) +> fopen(file_name, 'WRITE'); +> fclose(%); +> NULL; +> end proc; +ftruncate := + + proc(file_name::string) fopen(file_name, 'WRITE'); fclose(%); NULL end proc + +# interpolate.maple -- compute interpolation formulas/coefficients +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/interpolate.maple,v 1.10 2002/08/28 11:31:09 jthorn Exp $ +> +# +# <<>> +# Lagrange_polynomial_interpolant - compute Lagrange polynomial interpolant +# Hermite_polynomial_interpolant - compute Hermite polynomial interpolant +# coeffs_as_lc_of_data - coefficients of ... (linear combination of data) +# +# print_coeffs__lc_of_data - print C code to compute coefficients +# print_fetch_data - print C code to fetch input array chunk into struct data +# print_store_coeffs - print C code to store struct coeffs "somewhere" +# print_interp_cmpt__lc_of_data - print C code for computation of interpolant +# +# coeff_name - name of coefficient of data at a given [m] coordinate +# data_var_name - name of variable storing data value at a given [m] coordinate +# +> +################################################################################ +> +# +# ***** representation of numbers, data values, etc ***** +# +# We use RATIONAL(p.0,q.0) to denote the rational number p/q. +# +# We use DATA(...) to represent the data values being interpolated at a +# specified [m] coordinate, where the arguments are the [m] coordinates. +# +# We use COEFF(...) to represent the molecule coefficient at a specified +# [m] coordinate, where the arguments are the [m] coordinates. +# +# For example, the usual 1-D centered 2nd order 1st derivative molecule +# would be written +# RATIONAL(-1.0,2.0)*DATA(-1) + RATIONA(1.0,2.0)*DATA(1) +# and its coefficients as +# COEFF(-1) = RATIONAL(-1.0,2.0) +# COEFF(1) = RATIONAL(1.0,2.0) +# +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes a Lagrange polynomial interpolant in any +# number of dimensions. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) c00 + c10*x + c01*y end proc +# coeff_list = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example [c00, c10, c01]. +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# posn_list = A list of positions (each a list of numeric values) where the +# interpolant is to use data, for example hypercube([0,0], [1,1]). +# Any positions may be used; if they're redundant (as in the +# example) the least-squares interpolant is computed. +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Lagrange_polynomial_interpolant := +> proc( +> fn::procedure, coeff_list::list(name), +> coord_list::list(name), posn_list::list(list(numeric)) +> ) +> local posn, data_eqns, coeff_eqns; +> +# coefficients of interpolating polynomial +> data_eqns := { seq( fn(op(posn))='DATA'(op(posn)) , posn=posn_list ) }; +> coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); +> if (has(coeff_eqns, '_t')) +> then error "interpolation coefficients aren't uniquely determined!"; +> end if; +> +# interpolant as a polynomial in the coordinates +> return subs(coeff_eqns, eval(fn))(op(coord_list)); +> end proc; +Lagrange_polynomial_interpolant := proc(fn::procedure, coeff_list::list(name), +coord_list::list(name), posn_list::list(list(numeric))) +local posn, data_eqns, coeff_eqns; + data_eqns := {seq(fn(op(posn)) = 'DATA'(op(posn)), posn = posn_list)}; + coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); + if has(coeff_eqns, '_t') then + error "interpolation coefficients aren't uniquely determined!" + end if; + return subs(coeff_eqns, eval(fn))(op(coord_list)) +end proc + +> +################################################################################ +> +# +# This function computes a Hermite polynomial interpolant in any +# number of dimensions. This is a polynomial which +# * has values which match the given data DATA() at a specified set of +# points, and +# * has derivatives which match the specified finite-difference derivatives +# of the given data DATA() at a specified set of points +# +# For the derivative matching, we actually match all possible products +# of 1st derivatives, i.e. in 2-D we match dx, dy, and dxy, in 3-D we +# match dx, dy, dz, dxy, dxz, dyz, and dxyz, etc etc. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) +# + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 +# + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 +# + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +# + c00 + c10*x + c20*x^2 + c30*x^3 +# end proc; +# coeff_set = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example +# { +# c03, c13, c23, c33, +# c02, c12, c22, c32, +# c01, c11, c21, c31, +# c00, c10, c20, c30 +# } +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# deriv_set = A set of equations of the form +# {coords} = proc +# giving the derivatives which are to be matched, and the +# procedures to compute their finite-difference approximations. +# Each procedure should take N_dims integer arguments specifying +# an evaluation point, and return a suitable linear combination +# of the DATA() for the derivative at that point. For example +# { +# {x} = proc(i::integer, j::integer) +# - 1/2*DATA(i-1,j) + 1/2*DATA(i+1,j) +# end proc +# , +# {y} = proc(i::integer, j::integer) +# - 1/2*DATA(i,j-1) + 1/2*DATA(i,j+1) +# end proc +# , +# {x,y} = proc(i::integer, j::integer) +# - 1/4*DATA(i-1,j+1) + 1/4*DATA(i+1,j+1) +# + 1/4*DATA(i-1,j-1) - 1/4*DATA(i+1,j-1) +# end proc +# } +# fn_posn_set = A set of positions (each a list of numeric values) +# where the interpolant is to match the given data DATA(), +# for example +# {[0,0], [0,1], [1,0], [1,1]} +# deriv_posn_set = A list of positions (each a list of numeric values) +# where the interpolant is to match the derivatives +# specified by deriv_set , for example +# {[0,0], [0,1], [1,0], [1,1]} +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Hermite_polynomial_interpolant := +> proc( +> fn::procedure, +> coeff_set::set(name), +> coord_list::list(name), +> deriv_set::set(set(name) = procedure), +> fn_posn_set::set(list(numeric)), +> deriv_posn_set::set(list(numeric)) +> ) +> local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; +> +> +# +# compute a set of equations +# {fn(posn) = DATA(posn)} +# giving the function values to be matched +# +> fn_eqnset := map( +> # return equation that fn(posn) = DATA(posn) +> proc(posn::list(integer)) +> fn(op(posn)) = 'DATA'(op(posn)); +> end proc +> , +> fn_posn_set +> ); +> +> +# +# compute a set of equations +# { diff(fn,coords)(posn) = DERIV(coords)(posn) } +# giving the derivative values to be matched, where DERIV(coords) +# is a placeholder for the appropriate derivative +# +> map( +> # return set of equations for this particular derivative +> proc(deriv_coords::set(name)) +> local deriv_fn; +> fn(op(coord_list)); +> diff(%, op(deriv_coords)); +> deriv_fn := unapply(%, op(coord_list)); +> map( +> proc(posn::list(integer)) +> deriv_fn(op(posn)) = 'DERIV'(op(deriv_coords))(op(posn)); +> end proc +> , +> deriv_posn_set +> ); +> end proc +> , +> map(lhs, deriv_set) +> ); +> deriv_eqnset := `union`(op(%)); +> +> +# +# solve overall set of equations for coefficients +# in terms of DATA() and DERIV() values +# +> coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); +> if (indets(map(rhs,%)) <> {}) +> then error "no unique solution for coefficients -- %1 eqns for %2 coeffs", +> nops(fn_eqnset union deriv_eqnset), +> nops(coeff_set); +> fi; +> +> +# +# compute a set of substitution equations +# {'DERIV'(coords) = procedure} +# +> subs_eqnset := map( +> proc(eqn::set(name) = procedure) +> 'DERIV'(op(lhs(eqn))) = rhs(eqn); +> end proc +> , +> deriv_set +> ); +> +> +# +# compute the coefficients in terms of the DATA() values +# +> subs(subs_eqnset, coeff_eqns); +> eval(%); +> +# +# compute the interpolant as a polynomial in the coordinates +# +> subs(%, fn(op(coord_list))); +> end proc; +Hermite_polynomial_interpolant := proc(fn::procedure, coeff_set::set(name), +coord_list::list(name), deriv_set::set(set(name) = procedure), +fn_posn_set::set(list(numeric)), deriv_posn_set::set(list(numeric))) +local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; + fn_eqnset := map( + proc(posn::list(integer)) fn(op(posn)) = 'DATA'(op(posn)) end proc, + fn_posn_set); + map(proc(deriv_coords::set(name)) + local deriv_fn; + fn(op(coord_list)); + diff(%, op(deriv_coords)); + deriv_fn := unapply(%, op(coord_list)); + map(proc(posn::list(integer)) + deriv_fn(op(posn)) = + 'DERIV'(op(deriv_coords))(op(posn)) + end proc, deriv_posn_set) + end proc, map(lhs, deriv_set)); + deriv_eqnset := `union`(op(%)); + coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); + if indets(map(rhs, %)) <> {} then error + "no unique solution for coefficients -- %1 eqns for %2 coeffs", + nops(fn_eqnset union deriv_eqnset), nops(coeff_set) + end if; + subs_eqnset := map(proc(eqn::(set(name) = procedure)) + 'DERIV'(op(lhs(eqn))) = rhs(eqn) + end proc, deriv_set); + subs(subs_eqnset, coeff_eqns); + eval(%); + subs(%, fn(op(coord_list))) +end proc + +> +################################################################################ +> +# +# This function takes as input an interpolating polynomial, expresses +# it as a linear combination of the data values, and returns the coefficeints +# of that form. +# +# Arguments: +# interpolant = The interpolating polynomial (an algebraic expression +# in the coordinates and the data values). +# posn_list = The same list of data positions used in the interpolant. +# +# Results: +# This function returns the coefficients, as a list of equations of the +# form COEFF(...) = value , where each value is a polynomial in the +# coordinates. The order of the list matches that of posn_list. +# +> coeffs_as_lc_of_data := +> proc( +> interpolant::algebraic, +> posn_list::list(list(numeric)) +> ) +> local data_list, interpolant_as_lc_of_data; +> +# interpolant as a linear combination of the data values +> data_list := [ seq( 'DATA'(op(posn)) , posn=posn_list ) ]; +> interpolant_as_lc_of_data := collect(interpolant, data_list); +> +# coefficients of the data values in the linear combination +> return map( +> proc(posn::list(numeric)) +> coeff(interpolant_as_lc_of_data, DATA(op(posn))); +> 'COEFF'(op(posn)) = %; +> end proc +> , +> posn_list +> ); +> end proc; +coeffs_as_lc_of_data := proc( +interpolant::algebraic, posn_list::list(list(numeric))) +local data_list, interpolant_as_lc_of_data; + data_list := [seq('DATA'(op(posn)), posn = posn_list)]; + interpolant_as_lc_of_data := collect(interpolant, data_list); + return map(proc(posn::list(numeric)) + coeff(interpolant_as_lc_of_data, DATA(op(posn))); + 'COEFF'(op(posn)) = % + end proc, posn_list) +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function prints C expressions for the coefficients of an +# interpolating polynomial. (The polynomial is expressed as linear +# combinations of the data values with coefficients which are +# RATIONAL(p,q) calls.) +# +# Arguments: +# coeff_list = A list of the coefficients, as returned from +# coeffs_as_lc_of_data() . +# coeff_name_prefix = A prefix string for the coefficient names. +# temp_name_type = The C type to be used for Maple-introduced temporary +# names, eg. "double". +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_coeffs__lc_of_data := +> proc( coeff_list::list(specfunc(numeric,COEFF) = algebraic), +> coeff_name_prefix::string, +> temp_name_type::string, +> file_name::string ) +> global `codegen/C/function/informed`; +> local coeff_list2, cmpt_list, temp_name_list; +> +# convert LHS of each equation from a COEFF() call (eg COEFF(-1,+1)) +# to a Maple/C variable name (eg coeff_I_m1_p1) +> coeff_list2 := map( +> proc(coeff_eqn::specfunc(numeric,COEFF) = algebraic) +> local posn; +> posn := [op(lhs(coeff_eqn))]; +> coeff_name(posn,coeff_name_prefix); +> convert(%, name); # codegen[C] wants LHS +> # to be an actual Maple *name* +> % = fix_rationals(rhs(coeff_eqn)); +> end proc +> , +> coeff_list +> ); +> +# +# generate the C code +# +> +# tell codegen[C] not to warn about unknown RATIONAL() and DATA() "fn calls" +# via undocumented :( global table +> `codegen/C/function/informed`['RATIONAL'] := true; +> `codegen/C/function/informed`['DATA'] := true; +> +> ftruncate(file_name); +> +# optimized computation sequence for all the coefficients +# (may use local variables t0,t1,t2,...) +> cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; +> +# list of the t0,t1,t2,... local variables +> temp_name_list := nonmatching_names(map(lhs,cmpt_list), coeff_name_prefix); +> +# declare the t0,t1,t2,... local variables (if there are any) +> if (nops(temp_name_list) > 0) +> then print_name_list_dcl(%, temp_name_type, file_name); +> fi; +> +# now print the optimized computation sequence +> codegen[C](cmpt_list, filename=file_name); +> +> fclose(file_name); +> +> NULL; +> end proc; +print_coeffs__lc_of_data := proc( +coeff_list::list(specfunc(numeric, COEFF) = algebraic), +coeff_name_prefix::string, temp_name_type::string, file_name::string) +local coeff_list2, cmpt_list, temp_name_list; +global `codegen/C/function/informed`; + coeff_list2 := map(proc( + coeff_eqn::(specfunc(numeric, COEFF) = algebraic)) + local posn; + posn := [op(lhs(coeff_eqn))]; + coeff_name(posn, coeff_name_prefix); + convert(%, name); + % = fix_rationals(rhs(coeff_eqn)) + end proc, coeff_list); + `codegen/C/function/informed`['RATIONAL'] := true; + `codegen/C/function/informed`['DATA'] := true; + ftruncate(file_name); + cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; + temp_name_list := + nonmatching_names(map(lhs, cmpt_list), coeff_name_prefix); + if 0 < nops(temp_name_list) then + print_name_list_dcl(%, temp_name_type, file_name) + end if; + codegen[C](cmpt_list, filename = file_name); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C expression to assign the data-value +# variables, eg +# data->data_m1_p1 = DATA(-1,1); +# +# Arguments: +# posn_list = The same list of positions as was used to compute the +# interpolating polynomial. +# data_var_name_prefix = A prefix string for the data variable names. +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_fetch_data := +> proc( +> posn_list::list(list(numeric)), +> data_var_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> map( +> proc(posn::list(numeric)) +> fprintf(file_name, +> "%s = %a;\n", +> data_var_name(posn,data_var_name_prefix), +> DATA(op(posn))); +> end proc +> , +> posn_list +> ); +> fclose(file_name); +> +> NULL; +> end proc; +print_fetch_data := proc(posn_list::list(list(numeric)), +data_var_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + fprintf(file_name, "%s = %a;\n", + data_var_name(posn, data_var_name_prefix), DATA(op(posn))) + end proc, posn_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C expression to store the interpolation +# coefficients in COEFF(...) expressions, eg +# COEFF(1,-1) = factor * coeffs->coeff_p1_m1; +# +# Arguments: +# posn_list = The list of positions in the molecule. +# coeff_name_prefix = A prefix string for the coefficient names, +# eg "factor * coeffs->coeff_" +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_store_coeffs := +> proc( +> posn_list::list(list(numeric)), +> coeff_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> map( +> proc(posn::list(numeric)) +> fprintf(file_name, +> "%a = %s;\n", +> 'COEFF'(op(posn)), +> coeff_name(posn,coeff_name_prefix)); +> end proc +> , +> posn_list +> ); +> fclose(file_name); +> +> NULL; +> end proc; +print_store_coeffs := proc(posn_list::list(list(numeric)), +coeff_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + fprintf(file_name, "%a = %s;\n", 'COEFF'(op(posn)), + coeff_name(posn, coeff_name_prefix)) + end proc, posn_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a C expression to evaluate a molecule, i.e. +# to compute the molecule as a linear combination of the data values. +# +# Arguments: +# posn_list = The list of positions in the molecule. +# coeff_name_prefix = A prefix string for the coefficient names. +# data_var_name_prefix = A prefix string for the data variable names. +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_evaluate_molecule := +> proc( +> posn_list::list(list(numeric)), +> coeff_name_prefix::string, +> data_var_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> +# list of "coeff*data_var" terms +> map( +> proc(posn::list(numeric)) +> sprintf("%s*%s", +> coeff_name(posn,coeff_name_prefix), +> data_var_name(posn,data_var_name_prefix)); +> end proc +> , +> posn_list +> ); +> +> ListTools[Join](%, "\n + "); +> cat(op(%)); +> fprintf(file_name, " %s;\n", %); +> +> fclose(file_name); +> +> NULL; +> end proc; +print_evaluate_molecule := proc(posn_list::list(list(numeric)), +coeff_name_prefix::string, data_var_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + sprintf("%s*%s", coeff_name(posn, coeff_name_prefix), + data_var_name(posn, data_var_name_prefix)) + end proc, posn_list); + ListTools[Join](%, "\n + "); + cat(op(%)); + fprintf(file_name, " %s;\n", %); + fclose(file_name); + NULL +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes the name of the coefficient of the data at a +# given [m] position, i.e. it encapsulates our naming convention for this. +# +# Arguments: +# posn = (in) The [m] coordinates. +# name_prefix = A prefix string for the coefficient name. +# +# Results: +# The function returns the coefficient, as a Maple string. +# +> coeff_name := +> proc(posn::list(numeric), name_prefix::string) +> cat(name_prefix, sprint_numeric_list(posn)); +> end proc; +coeff_name := proc(posn::list(numeric), name_prefix::string) + cat(name_prefix, sprint_numeric_list(posn)) +end proc + +> +################################################################################ +> +# +# This function computes the name of the variable in which the C code +# will store the input data at a given [m] position, i.e. it encapsulates +# our naming convention for this. +# +# Arguments: +# posn = (in) The [m] coordinates. +# name_prefix = A prefix string for the variable name. +# +# Results: +# The function returns the variable name, as a Maple string. +# +> data_var_name := +> proc(posn::list(numeric), name_prefix::string) +> cat(name_prefix, sprint_numeric_list(posn)); +> end proc; +data_var_name := proc(posn::list(numeric), name_prefix::string) + cat(name_prefix, sprint_numeric_list(posn)) +end proc + +# Maple code to compute lists of point positions in hypercube-shaped molecules +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/common/cube_posns.maple,v 1.3 2002/08/20 16:56:41 jthorn Exp $ +> +################################################################################ +> +# +# 1D interpolation points +# +> posn_list_1d_size2 := hypercube_points([ 0], [+1]); + posn_list_1d_size2 := [[0], [1]] + +> posn_list_1d_size3 := hypercube_points([-1], [+1]); + posn_list_1d_size3 := [[-1], [0], [1]] + +> posn_list_1d_size4 := hypercube_points([-1], [+2]); + posn_list_1d_size4 := [[-1], [0], [1], [2]] + +> posn_list_1d_size5 := hypercube_points([-2], [+2]); + posn_list_1d_size5 := [[-2], [-1], [0], [1], [2]] + +> posn_list_1d_size6 := hypercube_points([-2], [+3]); + posn_list_1d_size6 := [[-2], [-1], [0], [1], [2], [3]] + +> posn_list_1d_size7 := hypercube_points([-3], [+3]); + posn_list_1d_size7 := [[-3], [-2], [-1], [0], [1], [2], [3]] + +> +################################################################################ +> +# +# 2D interpolation points (Fortran ordering) +# +> posn_list_2d_size2 := map(ListTools[Reverse], +> hypercube_points([ 0, 0], [+1,+1])); + posn_list_2d_size2 := [[0, 0], [1, 0], [0, 1], [1, 1]] + +> posn_list_2d_size3 := map(ListTools[Reverse], +> hypercube_points([-1,-1], [+1,+1])); +posn_list_2d_size3 := [[-1, -1], [0, -1], [1, -1], [-1, 0], [0, 0], [1, 0], + + [-1, 1], [0, 1], [1, 1]] + +> posn_list_2d_size4 := map(ListTools[Reverse], +> hypercube_points([-1,-1], [+2,+2])); +posn_list_2d_size4 := [[-1, -1], [0, -1], [1, -1], [2, -1], [-1, 0], [0, 0], + + [1, 0], [2, 0], [-1, 1], [0, 1], [1, 1], [2, 1], [-1, 2], [0, 2], [1, 2], + + [2, 2]] + +> posn_list_2d_size5 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+2,+2])); +posn_list_2d_size5 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [-2, -1], + + [-1, -1], [0, -1], [1, -1], [2, -1], [-2, 0], [-1, 0], [0, 0], [1, 0], + + [2, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], [-2, 2], [-1, 2], [0, 2], + + [1, 2], [2, 2]] + +> posn_list_2d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+3,+3])); +posn_list_2d_size6 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [3, -2], + + [-2, -1], [-1, -1], [0, -1], [1, -1], [2, -1], [3, -1], [-2, 0], [-1, 0], + + [0, 0], [1, 0], [2, 0], [3, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], + + [3, 1], [-2, 2], [-1, 2], [0, 2], [1, 2], [2, 2], [3, 2], [-2, 3], [-1, 3], + + [0, 3], [1, 3], [2, 3], [3, 3]] + +> +################################################################################ +> +# +# 3D interpolation points (Fortran ordering) +# +> posn_list_3d_size2 := map(ListTools[Reverse], +> hypercube_points([ 0, 0, 0], [+1,+1,+1])); +posn_list_3d_size2 := [[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], + + [1, 0, 1], [0, 1, 1], [1, 1, 1]] + +> posn_list_3d_size3 := map(ListTools[Reverse], +> hypercube_points([-1,-1,-1], [+1,+1,+1])); +posn_list_3d_size3 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [-1, 0, -1], + + [0, 0, -1], [1, 0, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], [-1, -1, 0], + + [0, -1, 0], [1, -1, 0], [-1, 0, 0], [0, 0, 0], [1, 0, 0], [-1, 1, 0], + + [0, 1, 0], [1, 1, 0], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [-1, 0, 1], + + [0, 0, 1], [1, 0, 1], [-1, 1, 1], [0, 1, 1], [1, 1, 1]] + +> posn_list_3d_size4 := map(ListTools[Reverse], +> hypercube_points([-1,-1,-1], [+2,+2,+2])); +posn_list_3d_size4 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [2, -1, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [-1, 1, -1], [0, 1, -1], + + [1, 1, -1], [2, 1, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-1, 0, 0], [0, 0, 0], + + [1, 0, 0], [2, 0, 0], [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [-1, -1, 1], [0, -1, 1], + + [1, -1, 1], [2, -1, 1], [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [-1, 2, 1], [0, 2, 1], + + [1, 2, 1], [2, 2, 1], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-1, 1, 2], [0, 1, 2], + + [1, 1, 2], [2, 1, 2], [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2]] + +> posn_list_3d_size5 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+2,+2,+2])); +posn_list_3d_size5 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], [1, -1, -2], + + [2, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], [1, 0, -2], [2, 0, -2], + + [-2, 1, -2], [-1, 1, -2], [0, 1, -2], [1, 1, -2], [2, 1, -2], [-2, 2, -2], + + [-1, 2, -2], [0, 2, -2], [1, 2, -2], [2, 2, -2], [-2, -2, -1], [-1, -2, -1], + + [0, -2, -1], [1, -2, -1], [2, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [-2, 0, -1], [-1, 0, -1], [0, 0, -1], + + [1, 0, -1], [2, 0, -1], [-2, 1, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], + + [2, 1, -1], [-2, 2, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], + + [-2, -2, 0], [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-2, 0, 0], [-1, 0, 0], + + [0, 0, 0], [1, 0, 0], [2, 0, 0], [-2, 1, 0], [-1, 1, 0], [0, 1, 0], + + [1, 1, 0], [2, 1, 0], [-2, 2, 0], [-1, 2, 0], [0, 2, 0], [1, 2, 0], + + [2, 2, 0], [-2, -2, 1], [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], + + [-2, -1, 1], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [-2, 1, 1], [-1, 1, 1], + + [0, 1, 1], [1, 1, 1], [2, 1, 1], [-2, 2, 1], [-1, 2, 1], [0, 2, 1], + + [1, 2, 1], [2, 2, 1], [-2, -2, 2], [-1, -2, 2], [0, -2, 2], [1, -2, 2], + + [2, -2, 2], [-2, -1, 2], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], + + [-2, 0, 2], [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [-2, 2, 2], [-1, 2, 2], + + [0, 2, 2], [1, 2, 2], [2, 2, 2]] + +> posn_list_3d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+3,+3,+3])); +posn_list_3d_size6 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [3, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], + + [1, -1, -2], [2, -1, -2], [3, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], + + [1, 0, -2], [2, 0, -2], [3, 0, -2], [-2, 1, -2], [-1, 1, -2], [0, 1, -2], + + [1, 1, -2], [2, 1, -2], [3, 1, -2], [-2, 2, -2], [-1, 2, -2], [0, 2, -2], + + [1, 2, -2], [2, 2, -2], [3, 2, -2], [-2, 3, -2], [-1, 3, -2], [0, 3, -2], + + [1, 3, -2], [2, 3, -2], [3, 3, -2], [-2, -2, -1], [-1, -2, -1], [0, -2, -1], + + [1, -2, -1], [2, -2, -1], [3, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [3, -1, -1], [-2, 0, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [3, 0, -1], [-2, 1, -1], + + [-1, 1, -1], [0, 1, -1], [1, 1, -1], [2, 1, -1], [3, 1, -1], [-2, 2, -1], + + [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], [3, 2, -1], [-2, 3, -1], + + [-1, 3, -1], [0, 3, -1], [1, 3, -1], [2, 3, -1], [3, 3, -1], [-2, -2, 0], + + [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [3, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [3, -1, 0], [-2, 0, 0], + + [-1, 0, 0], [0, 0, 0], [1, 0, 0], [2, 0, 0], [3, 0, 0], [-2, 1, 0], + + [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [3, 1, 0], [-2, 2, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [3, 2, 0], [-2, 3, 0], + + [-1, 3, 0], [0, 3, 0], [1, 3, 0], [2, 3, 0], [3, 3, 0], [-2, -2, 1], + + [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], [3, -2, 1], [-2, -1, 1], + + [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [3, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [3, 0, 1], [-2, 1, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [3, 1, 1], [-2, 2, 1], + + [-1, 2, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [3, 2, 1], [-2, 3, 1], + + [-1, 3, 1], [0, 3, 1], [1, 3, 1], [2, 3, 1], [3, 3, 1], [-2, -2, 2], + + [-1, -2, 2], [0, -2, 2], [1, -2, 2], [2, -2, 2], [3, -2, 2], [-2, -1, 2], + + [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], [3, -1, 2], [-2, 0, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [3, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [3, 1, 2], [-2, 2, 2], + + [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2], [3, 2, 2], [-2, 3, 2], + + [-1, 3, 2], [0, 3, 2], [1, 3, 2], [2, 3, 2], [3, 3, 2], [-2, -2, 3], + + [-1, -2, 3], [0, -2, 3], [1, -2, 3], [2, -2, 3], [3, -2, 3], [-2, -1, 3], + + [-1, -1, 3], [0, -1, 3], [1, -1, 3], [2, -1, 3], [3, -1, 3], [-2, 0, 3], + + [-1, 0, 3], [0, 0, 3], [1, 0, 3], [2, 0, 3], [3, 0, 3], [-2, 1, 3], + + [-1, 1, 3], [0, 1, 3], [1, 1, 3], [2, 1, 3], [3, 1, 3], [-2, 2, 3], + + [-1, 2, 3], [0, 2, 3], [1, 2, 3], [2, 2, 3], [3, 2, 3], [-2, 3, 3], + + [-1, 3, 3], [0, 3, 3], [1, 3, 3], [2, 3, 3], [3, 3, 3]] + +# Maple code to define Lagrange interpolating functions/coords/coeffs +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple,v 1.2 2002/08/20 16:31:24 jthorn Exp $ +> +################################################################################ +> +# +# 1-D interpolating functions +# +> +> fn_1d_order1 := +> proc(x) +> + c0 + c1*x +> end proc; + fn_1d_order1 := proc(x) c0 + c1*x end proc + +> +> fn_1d_order2 := +> proc(x) +> + c0 + c1*x + c2*x^2 +> end proc; + fn_1d_order2 := proc(x) c0 + c1*x + c2*x^2 end proc + +> +> fn_1d_order3 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 +> end proc; + fn_1d_order3 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 end proc + +> +> fn_1d_order4 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 +> end; + fn_1d_order4 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 end proc + +> +> fn_1d_order5 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 +> end; + fn_1d_order5 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 end proc + +> +> fn_1d_order6 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 +> end; +fn_1d_order6 := + + proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 end proc + +> +######################################## +> +# coordinates for 1-D interpolating functions +> coords_list_1d := [x]; + coords_list_1d := [x] + +> +######################################## +> +# +# coefficients in 1-D interpolating functions +# +> +> coeffs_list_1d_order1 := [c0, c1]; + coeffs_list_1d_order1 := [c0, c1] + +> coeffs_list_1d_order2 := [c0, c1, c2]; + coeffs_list_1d_order2 := [c0, c1, c2] + +> coeffs_list_1d_order3 := [c0, c1, c2, c3]; + coeffs_list_1d_order3 := [c0, c1, c2, c3] + +> coeffs_list_1d_order4 := [c0, c1, c2, c3, c4]; + coeffs_list_1d_order4 := [c0, c1, c2, c3, c4] + +> coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5]; + coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5] + +> coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6]; + coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6] + +> +################################################################################ +> +# +# 2-D interpolating functions +# +> +> fn_2d_order1 := +> proc(x,y) +> + c01*y +> + c00 + c10*x +> end proc; + fn_2d_order1 := proc(x, y) c01*y + c00 + c10*x end proc + +> +> fn_2d_order2 := +> proc(x,y) +> + c02*y^2 +> + c01*y + c11*x*y +> + c00 + c10*x + c20*x^2 +> end proc; +fn_2d_order2 := + + proc(x, y) c02*y^2 + c01*y + c11*x*y + c00 + c10*x + c20*x^2 end proc + +> +> fn_2d_order3 := +> proc(x,y) +> + c03*y^3 +> + c02*y^2 + c12*x*y^2 +> + c01*y + c11*x*y + c21*x^2*y +> + c00 + c10*x + c20*x^2 + c30*x^3 +> end proc; +fn_2d_order3 := proc(x, y) + c03*y^3 + c02*y^2 + c12*x*y^2 + c01*y + c11*x*y + c21*x^2*y + c00 + + c10*x + c20*x^2 + c30*x^3 +end proc + +> +> fn_2d_order4 := +> proc(x,y) +> + c04*y^4 +> + c03*y^3 + c13*x*y^3 +> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 +> + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +> + c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 +> end; +fn_2d_order4 := proc(x, y) + c04*y^4 + c03*y^3 + c13*x*y^3 + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + c00 + c10*x + c20*x^2 + + c30*x^3 + c40*x^4 +end proc + +> +######################################## +> +# coordinates for 2-D interpolating functions +> coords_list_2d := [x,y]; + coords_list_2d := [x, y] + +> +######################################## +> +# +# coefficients in 2-D interpolating functions +# +> +> coeffs_list_2d_order1 := [ +> c01, +> c00, c10 +> ]; + coeffs_list_2d_order1 := [c01, c00, c10] + +> coeffs_list_2d_order2 := [ +> c02, +> c01, c11, +> c00, c10, c20 +> ]; + coeffs_list_2d_order2 := [c02, c01, c11, c00, c10, c20] + +> coeffs_list_2d_order3 := [ +> c03, +> c02, c12, +> c01, c11, c21, +> c00, c10, c20, c30 +> ]; + coeffs_list_2d_order3 := [c03, c02, c12, c01, c11, c21, c00, c10, c20, c30] + +> coeffs_list_2d_order4 := [ +> c04, +> c03, c13, +> c02, c12, c22, +> c01, c11, c21, c31, +> c00, c10, c20, c30, c40 +> ]; +coeffs_list_2d_order4 := + + [c04, c03, c13, c02, c12, c22, c01, c11, c21, c31, c00, c10, c20, c30, c40] + +> +################################################################################ +> +# +# 3-D interpolating functions +# +> +> fn_3d_order1 := +> proc(x,y,z) +# z^0 ----------- +> + c010*y +> + c000 + c100*x +# z^1 ----------- +> + c001*z +> end proc; + fn_3d_order1 := proc(x, y, z) c010*y + c000 + c100*x + c001*z end proc + +> +> fn_3d_order2 := +> proc(x,y,z) +# z^0 -------------------------- +> + c020*y^2 +> + c010*y + c110*x*y +> + c000 + c100*x + c200*x^2 +# z^1 -------------------------- +> + c011*y*z +> + c001*z + c101*x*z +# z^2 -------------------------- +> + c002*z^2 +> end proc; +fn_3d_order2 := proc(x, y, z) + c020*y^2 + c010*y + c110*x*y + c000 + c100*x + c200*x^2 + c011*y*z + + c001*z + c101*x*z + c002*z^2 +end proc + +> +> fn_3d_order3 := +> proc(x,y,z) +# z^0 ------------------------------------------- +> + c030*y^3 +> + c020*y^2 + c120*x*y^2 +> + c010*y + c110*x*y + c210*x^2*y +> + c000 + c100*x + c200*x^2 + c300*x^3 +# z^1 ------------------------------------------- +> + c021*y^2*z +> + c011*y *z + c111*x*y*z +> + c001 *z + c101*x *z + c201*x^2*z +# z^2 ------------------------------------------- +> + c012*y*z^2 +> + c002 *z^2 + c102*x*z^2 +# z^3 ------------------------------------------- +> + c003 *z^3 +> end proc; +fn_3d_order3 := proc(x, y, z) + c030*y^3 + c020*y^2 + c120*x*y^2 + c010*y + c110*x*y + c210*x^2*y + + c000 + c100*x + c200*x^2 + c300*x^3 + c021*y^2*z + c011*y*z + + c111*x*y*z + c001*z + c101*x*z + c201*x^2*z + c012*y*z^2 + c002*z^2 + + c102*x*z^2 + c003*z^3 +end proc + +> +> fn_3d_order4 := +> proc(x,y,z) +# z^0 -------------------------------------------------------- +> + c040*y^4 +> + c030*y^3 + c130*x*y^3 +> + c020*y^2 + c120*x*y^2 + c220*x^2*y^2 +> + c010*y + c110*x*y + c210*x^2*y + c310*x^3*y +> + c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 +# z^1 ------------------------------------------- +> + c031*y^3*z +> + c021*y^2*z + c121*x*y^2*z +> + c011*y *z + c111*x*y *z + c211*x^2*y*z +> + c001 *z + c101*x *z + c201*x^2 *z + c301*x^3*z +# z^2 ------------------------------------------- +> + c022*y^2*z^2 +> + c012*y *z^2 + c112*x*y*z^2 +> + c002 *z^2 + c102*x *z^2 + c202*x^2*z^2 +# z^3 ------------------------------------------- +> + c013*y *z^3 +> + c003 *z^3 + c103*x *z^3 +# z^4 ------------------------------------------- +> + c004 *z^4 +> end; +fn_3d_order4 := proc(x, y, z) + c102*x*z^2 + c012*y*z^2 + c111*x*y*z + c121*x*y^2*z + c211*x^2*y*z + + c112*x*y*z^2 + c010*y + c110*x*y + c011*y*z + c101*x*z + c120*x*y^2 + + c210*x^2*y + c021*y^2*z + c201*x^2*z + c130*x*y^3 + c220*x^2*y^2 + + c310*x^3*y + c031*y^3*z + c301*x^3*z + c022*y^2*z^2 + c202*x^2*z^2 + + c013*y*z^3 + c103*x*z^3 + c000 + c100*x + c001*z + c020*y^2 + + c200*x^2 + c002*z^2 + c030*y^3 + c300*x^3 + c003*z^3 + c040*y^4 + + c400*x^4 + c004*z^4 +end proc + +> +######################################## +> +# coordinates for 3-D interpolating functions +> coords_list_3d := [x,y,z]; + coords_list_3d := [x, y, z] + +> +######################################## +> +# +# coefficients in 3-D interpolating functions +# +> +> coeffs_list_3d_order1 := [ +> # z^0 ----- +> c010, +> c000, c100, +> # z^1 ----- +> c001 +> ]; + coeffs_list_3d_order1 := [c010, c000, c100, c001] + +> coeffs_list_3d_order2 := [ +> # z^0 ----------- +> c020, +> c010, c110, +> c000, c100, c200, +> # z^1 ----------- +> c011, +> c001, c101, +> # z^2 ----------- +> c002 +> ]; +coeffs_list_3d_order2 := + + [c020, c010, c110, c000, c100, c200, c011, c001, c101, c002] + +> coeffs_list_3d_order3 := [ +> # z^0 ---------------- +> c030, +> c020, c120, +> c010, c110, c210, +> c000, c100, c200, c300, +> # z^1 ---------------- +> c021, +> c011, c111, +> c001, c101, c201, +> # z^2 ---------------- +> c012, +> c002, c102, +> # z^3 ---------------- +> c003 +> ]; +coeffs_list_3d_order3 := [c030, c020, c120, c010, c110, c210, c000, c100, c200, + + c300, c021, c011, c111, c001, c101, c201, c012, c002, c102, c003] + +> coeffs_list_3d_order4 := [ +> # z^0 ----------------------- +> c040, +> c030, c130, +> c020, c120, c220, +> c010, c110, c210, c310, +> c000, c100, c200, c300, c400, +> # z^1 ----------------------- +> c031, +> c021, c121, +> c011, c111, c211, +> c001, c101, c201, c301, +> # z^2 ----------------------- +> c022, +> c012, c112, +> c002, c102, c202, +> # z^3 ----------------------- +> c013, +> c003, c103, +> # z^4 ----------------------- +> c004 +> ]; +coeffs_list_3d_order4 := [c040, c030, c130, c020, c120, c220, c010, c110, c210, + + c310, c000, c100, c200, c300, c400, c031, c021, c121, c011, c111, c211, + + c001, c101, c201, c301, c022, c012, c112, c002, c102, c202, c013, c003, + + c103, c004] + +> +################################################################################ +# 3d.maple -- compute Lagrange interpolation coefficients in 3-D +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/3d.maple,v 1.2 2002/08/20 16:31:24 jthorn Exp $ +> +################################################################################ +> +# +# 3d, cube, order=1, smoothing=0 (size=2) +# +> +# interpolating polynomial +> interp_3d_cube_order1_smooth0 +> := Lagrange_polynomial_interpolant(fn_3d_order1, coeffs_list_3d_order1, +> coords_list_3d, posn_list_3d_size2); +bytes used=1000768, alloc=917336, time=0.07 +interp_3d_cube_order1_smooth0 := (- 1/4 DATA(0, 0, 0) - 1/4 DATA(1, 0, 0) + + + 1/4 DATA(0, 1, 0) + 1/4 DATA(1, 1, 0) - 1/4 DATA(0, 0, 1) + + - 1/4 DATA(1, 0, 1) + 1/4 DATA(0, 1, 1) + 1/4 DATA(1, 1, 1)) y + + + 1/4 DATA(0, 0, 1) + 1/4 DATA(0, 1, 0) + 1/4 DATA(1, 0, 0) + + + 1/2 DATA(0, 0, 0) - 1/4 DATA(1, 1, 1) + (- 1/4 DATA(0, 0, 1) + + - 1/4 DATA(0, 1, 0) + 1/4 DATA(1, 0, 0) - 1/4 DATA(0, 0, 0) + + + 1/4 DATA(1, 0, 1) + 1/4 DATA(1, 1, 0) - 1/4 DATA(0, 1, 1) + + + 1/4 DATA(1, 1, 1)) x + (1/4 DATA(0, 0, 1) - 1/4 DATA(0, 1, 0) + + - 1/4 DATA(1, 0, 0) - 1/4 DATA(0, 0, 0) + 1/4 DATA(1, 0, 1) + + - 1/4 DATA(1, 1, 0) + 1/4 DATA(0, 1, 1) + 1/4 DATA(1, 1, 1)) z + +> +# I +> coeffs_as_lc_of_data(%, posn_list_3d_size2); +[COEFF(0, 0, 0) = - 1/4 y - 1/4 x + 1/2 - 1/4 z, + + COEFF(1, 0, 0) = - 1/4 y + 1/4 - 1/4 z + 1/4 x, + + COEFF(0, 1, 0) = - 1/4 z + 1/4 y + 1/4 - 1/4 x, + + COEFF(1, 1, 0) = 1/4 y - 1/4 z + 1/4 x, + + COEFF(0, 0, 1) = - 1/4 y + 1/4 + 1/4 z - 1/4 x, + + COEFF(1, 0, 1) = 1/4 z - 1/4 y + 1/4 x, + + COEFF(0, 1, 1) = - 1/4 x + 1/4 y + 1/4 z, + + COEFF(1, 1, 1) = 1/4 y + 1/4 z + 1/4 x - 1/4] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "3d.coeffs/3d.cube.order1.smooth0/coeffs-I.compute.c"); +bytes used=2001036, alloc=1376004, time=0.15 +> +# d/dx +> simplify( diff(interp_3d_cube_order1_smooth0,x) ); +- 1/4 DATA(0, 0, 1) - 1/4 DATA(0, 1, 0) + 1/4 DATA(1, 0, 0) - 1/4 DATA(0, 0, 0) + + + 1/4 DATA(1, 0, 1) + 1/4 DATA(1, 1, 0) - 1/4 DATA(0, 1, 1) + + + 1/4 DATA(1, 1, 1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size2); +[COEFF(0, 0, 0) = -1/4, COEFF(1, 0, 0) = 1/4, COEFF(0, 1, 0) = -1/4, + + COEFF(1, 1, 0) = 1/4, COEFF(0, 0, 1) = -1/4, COEFF(1, 0, 1) = 1/4, + + COEFF(0, 1, 1) = -1/4, COEFF(1, 1, 1) = 1/4] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "3d.coeffs/3d.cube.order1.smooth0/coeffs-dx.compute.c"); +> +# d/dy +> simplify( diff(interp_3d_cube_order1_smooth0,y) ); +bytes used=3001348, alloc=1507052, time=0.20 +- 1/4 DATA(0, 0, 0) - 1/4 DATA(1, 0, 0) + 1/4 DATA(0, 1, 0) + 1/4 DATA(1, 1, 0) + + - 1/4 DATA(0, 0, 1) - 1/4 DATA(1, 0, 1) + 1/4 DATA(0, 1, 1) + + + 1/4 DATA(1, 1, 1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size2); +[COEFF(0, 0, 0) = -1/4, COEFF(1, 0, 0) = -1/4, COEFF(0, 1, 0) = 1/4, + + COEFF(1, 1, 0) = 1/4, COEFF(0, 0, 1) = -1/4, COEFF(1, 0, 1) = -1/4, + + COEFF(0, 1, 1) = 1/4, COEFF(1, 1, 1) = 1/4] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "3d.coeffs/3d.cube.order1.smooth0/coeffs-dy.compute.c"); +> +# d/dz +> simplify( diff(interp_3d_cube_order1_smooth0,z) ); +1/4 DATA(0, 0, 1) - 1/4 DATA(0, 1, 0) - 1/4 DATA(1, 0, 0) - 1/4 DATA(0, 0, 0) + + + 1/4 DATA(1, 0, 1) - 1/4 DATA(1, 1, 0) + 1/4 DATA(0, 1, 1) + + + 1/4 DATA(1, 1, 1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size2); +[COEFF(0, 0, 0) = -1/4, COEFF(1, 0, 0) = -1/4, COEFF(0, 1, 0) = -1/4, + + COEFF(1, 1, 0) = -1/4, COEFF(0, 0, 1) = 1/4, COEFF(1, 0, 1) = 1/4, + + COEFF(0, 1, 1) = 1/4, COEFF(1, 1, 1) = 1/4] + +> print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", +> "3d.coeffs/3d.cube.order1.smooth0/coeffs-dz.compute.c"); +> +################################################################################ +> +# +# 3d, cube, order=2, smoothing=0 (size=3) +# +> +# interpolating polynomial +> interp_3d_cube_order2_smooth0 +> := Lagrange_polynomial_interpolant(fn_3d_order2, coeffs_list_3d_order2, +> coords_list_3d, posn_list_3d_size3); +bytes used=4001600, alloc=1834672, time=0.27 +bytes used=5003968, alloc=1900196, time=0.33 +interp_3d_cube_order2_smooth0 := 1/27 DATA(-1, 0, -1) + 7/27 DATA(0, 0, 0) + + + 4/27 DATA(1, 0, 0) + 4/27 DATA(0, 1, 0) + 1/27 DATA(1, 1, 0) + + + 4/27 DATA(0, 0, 1) + 1/27 DATA(1, 0, 1) + 1/27 DATA(0, 1, 1) + + - 2/27 DATA(1, 1, 1) + (1/18 DATA(1, 0, -1) - 1/18 DATA(-1, 0, -1) + + + 1/18 DATA(1, 0, 0) + 1/18 DATA(1, 1, 0) + 1/18 DATA(1, 0, 1) + + + 1/18 DATA(1, 1, 1) + 1/18 DATA(1, -1, 0) - 1/18 DATA(-1, 0, 0) + + - 1/18 DATA(-1, 1, 0) - 1/18 DATA(-1, -1, 1) + 1/18 DATA(1, -1, 1) + + - 1/18 DATA(-1, 0, 1) - 1/18 DATA(-1, 1, 1) - 1/18 DATA(-1, -1, -1) + + - 1/18 DATA(-1, 1, -1) + 1/18 DATA(1, 1, -1) - 1/18 DATA(-1, -1, 0) + + + 1/18 DATA(1, -1, -1)) x + (1/18 DATA(-1, 0, -1) - 1/9 DATA(0, 0, 0) + + + 1/18 DATA(1, 0, 0) - 1/9 DATA(0, 1, 0) + 1/18 DATA(1, 1, 0) + + - 1/9 DATA(0, 0, 1) + 1/18 DATA(1, 0, 1) - 1/9 DATA(0, 1, 1) + + + 1/18 DATA(1, 1, 1) - 1/9 DATA(0, -1, 0) + 1/18 DATA(1, -1, 0) + + + 1/18 DATA(-1, 0, 0) + 1/18 DATA(-1, 1, 0) + 1/18 DATA(-1, -1, 1) + + - 1/9 DATA(0, -1, 1) + 1/18 DATA(1, -1, 1) + 1/18 DATA(-1, 0, 1) + + + 1/18 DATA(-1, 1, 1) - 1/9 DATA(0, 0, -1) + 1/18 DATA(1, 0, -1) + + + 1/18 DATA(-1, 1, -1) - 1/9 DATA(0, 1, -1) + 1/18 DATA(1, 1, -1) + + + 1/18 DATA(-1, -1, 0) + 1/18 DATA(-1, -1, -1) - 1/9 DATA(0, -1, -1) + + 2 + + 1/18 DATA(1, -1, -1)) x + (- 1/18 DATA(-1, 1, -1) + + - 1/18 DATA(-1, 0, -1) + 1/18 DATA(0, 0, 1) + 1/18 DATA(1, 0, 1) + + + 1/18 DATA(0, 1, 1) + 1/18 DATA(1, 1, 1) + 1/18 DATA(-1, -1, 1) + + + 1/18 DATA(0, -1, 1) + 1/18 DATA(1, -1, 1) + 1/18 DATA(-1, 0, 1) + + + 1/18 DATA(-1, 1, 1) - 1/18 DATA(0, 0, -1) - 1/18 DATA(1, 0, -1) + + - 1/18 DATA(0, -1, -1) - 1/18 DATA(0, 1, -1) - 1/18 DATA(1, 1, -1) + + - 1/18 DATA(-1, -1, -1) - 1/18 DATA(1, -1, -1)) z + (1/18 DATA(-1, 0, -1) + + - 1/9 DATA(0, 0, 0) - 1/9 DATA(1, 0, 0) - 1/9 DATA(0, 1, 0) + + - 1/9 DATA(1, 1, 0) + 1/18 DATA(0, 0, 1) + 1/18 DATA(1, 0, 1) + + + 1/18 DATA(0, 1, 1) + 1/18 DATA(1, 1, 1) - 1/9 DATA(0, -1, 0) + + - 1/9 DATA(1, -1, 0) - 1/9 DATA(-1, 0, 0) - 1/9 DATA(-1, 1, 0) + + + 1/18 DATA(-1, -1, 1) + 1/18 DATA(0, -1, 1) + 1/18 DATA(1, -1, 1) + + + 1/18 DATA(-1, 0, 1) + 1/18 DATA(-1, 1, 1) + 1/18 DATA(0, 0, -1) + + + 1/18 DATA(1, 0, -1) + 1/18 DATA(-1, 1, -1) + 1/18 DATA(0, 1, -1) + + + 1/18 DATA(1, 1, -1) - 1/9 DATA(-1, -1, 0) + 1/18 DATA(-1, -1, -1) + + 2 + + 1/18 DATA(0, -1, -1) + 1/18 DATA(1, -1, -1)) z + (- 1/9 DATA(-1, 0, -1) + + - 1/9 DATA(0, 0, 0) - 1/9 DATA(1, 0, 0) + 1/18 DATA(0, 1, 0) + + + 1/18 DATA(1, 1, 0) - 1/9 DATA(0, 0, 1) - 1/9 DATA(1, 0, 1) + + + 1/18 DATA(0, 1, 1) + 1/18 DATA(1, 1, 1) + 1/18 DATA(0, -1, 0) + + + 1/18 DATA(1, -1, 0) - 1/9 DATA(-1, 0, 0) + 1/18 DATA(-1, 1, 0) + + + 1/18 DATA(-1, -1, 1) + 1/18 DATA(0, -1, 1) + 1/18 DATA(1, -1, 1) + + - 1/9 DATA(-1, 0, 1) + 1/18 DATA(-1, 1, 1) - 1/9 DATA(0, 0, -1) + + - 1/9 DATA(1, 0, -1) + 1/18 DATA(-1, 1, -1) + 1/18 DATA(0, 1, -1) + + + 1/18 DATA(1, 1, -1) + 1/18 DATA(-1, -1, 0) + 1/18 DATA(-1, -1, -1) + + 2 + + 1/18 DATA(0, -1, -1) + 1/18 DATA(1, -1, -1)) y + (1/18 DATA(0, 1, -1) + + + 1/18 DATA(0, 1, 0) + 1/18 DATA(1, 1, 0) + 1/18 DATA(0, 1, 1) + + + 1/18 DATA(1, 1, 1) - 1/18 DATA(0, -1, 0) - 1/18 DATA(1, -1, 0) + + + 1/18 DATA(-1, 1, 0) - 1/18 DATA(-1, -1, 1) - 1/18 DATA(0, -1, 1) + + - 1/18 DATA(1, -1, 1) + 1/18 DATA(-1, 1, 1) + 1/18 DATA(-1, 1, -1) + + - 1/18 DATA(0, -1, -1) + 1/18 DATA(1, 1, -1) - 1/18 DATA(-1, -1, 0) + + - 1/18 DATA(-1, -1, -1) - 1/18 DATA(1, -1, -1)) y + ( + + - 1/12 DATA(-1, -1, 1) + 1/12 DATA(-1, 0, -1) + 1/12 DATA(1, 0, 1) + + + 1/12 DATA(1, 1, 1) - 1/12 DATA(1, 0, -1) + 1/12 DATA(1, -1, 1) + + - 1/12 DATA(-1, 0, 1) - 1/12 DATA(-1, 1, 1) - 1/12 DATA(1, -1, -1) + + + 1/12 DATA(-1, 1, -1) - 1/12 DATA(1, 1, -1) + 1/12 DATA(-1, -1, -1)) x z + + + (- 1/12 DATA(-1, 1, 0) + 1/12 DATA(1, 1, 0) + 1/12 DATA(1, 1, 1) + + - 1/12 DATA(1, -1, 0) - 1/12 DATA(-1, 1, -1) + 1/12 DATA(-1, -1, 1) + + - 1/12 DATA(1, -1, 1) - 1/12 DATA(-1, 1, 1) - 1/12 DATA(1, -1, -1) + + + 1/12 DATA(1, 1, -1) + 1/12 DATA(-1, -1, 0) + 1/12 DATA(-1, -1, -1)) x y + + + (- 1/12 DATA(0, -1, 1) + 1/12 DATA(0, 1, 1) + 1/12 DATA(1, 1, 1) + + - 1/12 DATA(-1, -1, 1) - 1/12 DATA(0, 1, -1) - 1/12 DATA(1, -1, 1) + + + 1/12 DATA(-1, 1, 1) - 1/12 DATA(-1, 1, -1) + 1/12 DATA(1, -1, -1) + + - 1/12 DATA(1, 1, -1) + 1/12 DATA(-1, -1, -1) + 1/12 DATA(0, -1, -1)) y z + + + 4/27 DATA(0, -1, 0) + 1/27 DATA(1, -1, 0) + 4/27 DATA(-1, 0, 0) + + + 1/27 DATA(-1, 1, 0) - 2/27 DATA(-1, -1, 1) + 1/27 DATA(0, -1, 1) + + - 2/27 DATA(1, -1, 1) + 1/27 DATA(-1, 0, 1) - 2/27 DATA(-1, 1, 1) + + + 4/27 DATA(0, 0, -1) + 1/27 DATA(1, 0, -1) - 2/27 DATA(-1, 1, -1) + + + 1/27 DATA(0, 1, -1) - 2/27 DATA(1, 1, -1) + 1/27 DATA(-1, -1, 0) + + - 2/27 DATA(-1, -1, -1) + 1/27 DATA(0, -1, -1) - 2/27 DATA(1, -1, -1) + +> +# I +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +bytes used=6016752, alloc=1900196, time=0.40 + 2 +[COEFF(-1, -1, -1) = 1/12 x y + 1/12 y z + 1/18 z - 1/18 z - 1/18 y - 2/27 + + 2 2 + + 1/18 y - 1/18 x + 1/12 x z + 1/18 x , COEFF(0, -1, -1) = + + 2 2 2 + 1/12 y z - 1/9 x - 1/18 z - 1/18 y + 1/18 y + 1/18 z + 1/27, + + 2 2 2 + COEFF(1, -1, -1) = - 1/12 x z + 1/18 y + 1/18 z - 1/18 y + 1/18 x - 2/27 + + - 1/18 z - 1/12 x y + 1/12 y z + 1/18 x, COEFF(-1, 0, -1) = + + 2 2 2 + 1/18 x + 1/18 z - 1/9 y - 1/18 x + 1/27 + 1/12 x z - 1/18 z, + + 2 2 2 + COEFF(0, 0, -1) = - 1/9 x + 1/18 z + 4/27 - 1/9 y - 1/18 z, + + COEFF(1, 0, -1) = + + 2 2 2 + 1/18 x + 1/18 x + 1/18 z - 1/18 z + 1/27 - 1/9 y - 1/12 x z, + + 2 2 + COEFF(-1, 1, -1) = - 1/12 y z - 1/18 z + 1/18 y + 1/18 z + 1/18 y + + 2 + - 1/18 x - 1/12 x y + 1/18 x - 2/27 + 1/12 x z, COEFF(0, 1, -1) = + + 2 2 2 + - 1/18 z + 1/18 y + 1/18 y + 1/18 z - 1/12 y z - 1/9 x + 1/27, + + 2 2 + COEFF(1, 1, -1) = 1/18 x - 1/18 z + 1/12 x y + 1/18 z - 1/12 x z + 1/18 x + + 2 + - 2/27 + 1/18 y - 1/12 y z + 1/18 y , COEFF(-1, -1, 0) = + + 2 2 2 + 1/12 x y - 1/9 z + 1/18 x + 1/27 + 1/18 y - 1/18 x - 1/18 y, + + 2 2 2 + COEFF(0, -1, 0) = - 1/9 z - 1/9 x + 4/27 - 1/18 y + 1/18 y , + + COEFF(1, -1, 0) = + + 2 2 2 + - 1/9 z - 1/18 y + 1/27 - 1/12 x y + 1/18 y + 1/18 x + 1/18 x, + + 2 2 2 + COEFF(-1, 0, 0) = 4/27 + 1/18 x - 1/9 z - 1/18 x - 1/9 y , + + 2 2 2 + COEFF(0, 0, 0) = - 1/9 x - 1/9 z - 1/9 y + 7/27, + + 2 2 2 + COEFF(1, 0, 0) = - 1/9 y + 1/18 x + 1/18 x - 1/9 z + 4/27, + + COEFF(-1, 1, 0) = + + 2 2 2 + 1/27 + 1/18 y - 1/18 x - 1/12 x y + 1/18 y - 1/9 z + 1/18 x , + + 2 2 2 + COEFF(0, 1, 0) = 1/18 y + 1/18 y + 4/27 - 1/9 z - 1/9 x , COEFF(1, 1, 0) + + 2 2 2 + = 1/12 x y - 1/9 z + 1/27 + 1/18 y + 1/18 x + 1/18 y + 1/18 x, + + 2 + COEFF(-1, -1, 1) = 1/12 x y + 1/18 x - 1/12 y z + 1/18 z - 1/18 y + + 2 2 + - 1/12 x z + 1/18 y - 1/18 x - 2/27 + 1/18 z , COEFF(0, -1, 1) = + + 2 2 2 + - 1/12 y z + 1/18 z + 1/18 z + 1/18 y - 1/18 y - 1/9 x + 1/27, + + 2 + COEFF(1, -1, 1) = - 1/12 y z + 1/12 x z + 1/18 x - 1/12 x y + 1/18 z + + 2 2 + + 1/18 y + 1/18 x + 1/18 z - 1/18 y - 2/27, COEFF(-1, 0, 1) = + + 2 2 2 + - 1/12 x z - 1/18 x + 1/18 z + 1/18 z - 1/9 y + 1/18 x + 1/27, + + 2 2 2 + COEFF(0, 0, 1) = 1/18 z - 1/9 x + 1/18 z + 4/27 - 1/9 y , COEFF(1, 0, 1) + + 2 2 2 + = - 1/9 y + 1/12 x z + 1/18 z + 1/18 z + 1/18 x + 1/18 x + 1/27, + + 2 2 + COEFF(-1, 1, 1) = - 2/27 + 1/18 y + 1/18 y - 1/12 x y + 1/18 x + 1/18 z + + 2 + - 1/12 x z - 1/18 x + 1/12 y z + 1/18 z , COEFF(0, 1, 1) = + + 2 2 2 + - 1/9 x + 1/18 y + 1/18 z + 1/18 y + 1/12 y z + 1/18 z + 1/27, + + 2 + COEFF(1, 1, 1) = 1/12 x y + 1/12 y z + 1/18 x + 1/18 z + 1/18 x + 1/12 x z + + 2 2 + + 1/18 y - 2/27 + 1/18 y + 1/18 z ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-I.compute.c"); +bytes used=7016988, alloc=1965720, time=0.47 +bytes used=8017216, alloc=1965720, time=0.54 +bytes used=9017496, alloc=1965720, time=0.61 +bytes used=10017692, alloc=1965720, time=0.68 +bytes used=11017876, alloc=1965720, time=0.76 +bytes used=12018432, alloc=1965720, time=0.83 +bytes used=13018804, alloc=1965720, time=0.92 +bytes used=14019172, alloc=1965720, time=1.01 +> +# d/dx +> simplify( diff(interp_3d_cube_order2_smooth0,x) ); +- 1/18 DATA(-1, 0, -1) + 1/18 DATA(1, 0, 0) + 1/18 DATA(1, 1, 0) + + + 1/18 DATA(1, 0, 1) + 1/18 DATA(1, 1, 1) + 1/18 DATA(1, -1, 0) + + - 1/18 DATA(-1, 0, 0) - 1/18 DATA(-1, 1, 0) - 1/18 DATA(-1, -1, 1) + + + 1/18 DATA(1, -1, 1) - 1/18 DATA(-1, 0, 1) - 1/18 DATA(-1, 1, 1) + + + 1/18 DATA(1, 0, -1) - 1/18 DATA(-1, 1, -1) + 1/18 DATA(1, 1, -1) + + - 1/18 DATA(-1, -1, 0) - 1/18 DATA(-1, -1, -1) + 1/18 DATA(1, -1, -1) + + + 1/12 y DATA(1, 1, -1) + 1/12 y DATA(-1, -1, -1) + 1/12 y DATA(-1, -1, 0) + + + 1/9 x DATA(1, 0, -1) - 1/12 y DATA(1, -1, 0) + 1/12 y DATA(-1, -1, 1) + + - 1/12 y DATA(-1, 1, -1) - 1/12 y DATA(1, -1, 1) - 1/12 y DATA(1, -1, -1) + + - 1/12 y DATA(-1, 1, 1) - 1/12 y DATA(-1, 1, 0) + 1/12 y DATA(1, 1, 1) + + + 1/12 y DATA(1, 1, 0) + 1/9 x DATA(1, 0, 1) + 1/9 x DATA(1, 1, 1) + + + 1/9 x DATA(1, -1, 0) + 1/9 x DATA(-1, 0, 0) + 1/9 x DATA(-1, 1, 0) + + + 1/9 x DATA(-1, -1, 1) + 1/9 x DATA(1, -1, 1) + 1/9 x DATA(-1, 0, 1) + + + 1/9 x DATA(-1, 1, 1) + 1/9 x DATA(-1, -1, -1) + 1/9 x DATA(-1, 1, -1) + + + 1/9 x DATA(1, 1, -1) + 1/9 x DATA(-1, -1, 0) + 1/9 x DATA(1, -1, -1) + + - 2/9 x DATA(0, 0, 0) - 2/9 x DATA(0, 1, 0) - 2/9 x DATA(0, 0, 1) + + - 2/9 x DATA(0, 1, 1) - 2/9 x DATA(0, -1, 0) - 2/9 x DATA(0, -1, 1) + + - 2/9 x DATA(0, 0, -1) - 2/9 x DATA(0, 1, -1) - 2/9 x DATA(0, -1, -1) + + + 1/9 x DATA(1, 0, 0) - 1/12 z DATA(-1, -1, 1) + 1/12 z DATA(-1, 0, -1) + + + 1/12 z DATA(1, 0, 1) + 1/12 z DATA(1, 1, 1) - 1/12 z DATA(1, 0, -1) + + + 1/12 z DATA(1, -1, 1) - 1/12 z DATA(-1, 0, 1) - 1/12 z DATA(-1, 1, 1) + + - 1/12 z DATA(1, -1, -1) + 1/12 z DATA(-1, 1, -1) - 1/12 z DATA(1, 1, -1) + + + 1/12 z DATA(-1, -1, -1) + 1/9 x DATA(-1, 0, -1) + 1/9 x DATA(1, 1, 0) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +bytes used=15019376, alloc=1965720, time=1.08 +[COEFF(-1, -1, -1) = - 1/18 + 1/9 x + 1/12 z + 1/12 y, + + COEFF(0, -1, -1) = - 2/9 x, + + COEFF(1, -1, -1) = - 1/12 z - 1/12 y + 1/18 + 1/9 x, + + COEFF(-1, 0, -1) = 1/9 x - 1/18 + 1/12 z, COEFF(0, 0, -1) = - 2/9 x, + + COEFF(1, 0, -1) = 1/18 - 1/12 z + 1/9 x, + + COEFF(-1, 1, -1) = 1/9 x + 1/12 z - 1/18 - 1/12 y, + + COEFF(0, 1, -1) = - 2/9 x, COEFF(1, 1, -1) = 1/12 y + 1/9 x + 1/18 - 1/12 z, + + COEFF(-1, -1, 0) = 1/12 y - 1/18 + 1/9 x, COEFF(0, -1, 0) = - 2/9 x, + + COEFF(1, -1, 0) = 1/9 x + 1/18 - 1/12 y, COEFF(-1, 0, 0) = - 1/18 + 1/9 x, + + COEFF(0, 0, 0) = - 2/9 x, COEFF(1, 0, 0) = 1/9 x + 1/18, + + COEFF(-1, 1, 0) = 1/9 x - 1/12 y - 1/18, COEFF(0, 1, 0) = - 2/9 x, + + COEFF(1, 1, 0) = 1/12 y + 1/9 x + 1/18, + + COEFF(-1, -1, 1) = - 1/12 z - 1/18 + 1/9 x + 1/12 y, + + COEFF(0, -1, 1) = - 2/9 x, COEFF(1, -1, 1) = 1/12 z + 1/18 - 1/12 y + 1/9 x, + + COEFF(-1, 0, 1) = 1/9 x - 1/12 z - 1/18, COEFF(0, 0, 1) = - 2/9 x, + + COEFF(1, 0, 1) = 1/9 x + 1/12 z + 1/18, + + COEFF(-1, 1, 1) = - 1/12 y + 1/9 x - 1/18 - 1/12 z, + + COEFF(0, 1, 1) = - 2/9 x, COEFF(1, 1, 1) = 1/18 + 1/9 x + 1/12 y + 1/12 z] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dx.compute.c"); +bytes used=16019688, alloc=1965720, time=1.14 +bytes used=17019864, alloc=1965720, time=1.22 +> +# d/dy +> simplify( diff(interp_3d_cube_order2_smooth0,y) ); +1/18 DATA(0, 1, 0) + 1/18 DATA(1, 1, 0) + 1/18 DATA(0, 1, 1) + + + 1/18 DATA(1, 1, 1) + 1/9 y DATA(0, 1, 1) + 1/9 y DATA(0, -1, 0) + + - 2/9 y DATA(0, 0, 1) + 1/9 y DATA(0, -1, -1) - 2/9 y DATA(1, 0, 0) + + - 2/9 y DATA(0, 0, 0) + 1/9 y DATA(0, 1, 0) - 2/9 y DATA(-1, 0, -1) + + - 1/12 z DATA(0, -1, 1) + 1/12 z DATA(0, 1, 1) - 1/12 z DATA(0, 1, -1) + + + 1/12 z DATA(0, -1, -1) - 2/9 y DATA(1, 0, 1) - 2/9 y DATA(-1, 0, 0) + + + 1/9 y DATA(0, -1, 1) - 2/9 y DATA(-1, 0, 1) - 2/9 y DATA(0, 0, -1) + + - 2/9 y DATA(1, 0, -1) + 1/9 y DATA(0, 1, -1) - 1/18 DATA(0, -1, 0) + + - 1/18 DATA(1, -1, 0) + 1/18 DATA(-1, 1, 0) - 1/18 DATA(-1, -1, 1) + + - 1/18 DATA(0, -1, 1) - 1/18 DATA(1, -1, 1) + 1/18 DATA(-1, 1, 1) + + + 1/18 DATA(-1, 1, -1) + 1/18 DATA(0, 1, -1) + 1/18 DATA(1, 1, -1) + + - 1/18 DATA(-1, -1, 0) - 1/18 DATA(-1, -1, -1) - 1/18 DATA(0, -1, -1) + + - 1/18 DATA(1, -1, -1) + 1/9 y DATA(1, 1, -1) + 1/9 y DATA(-1, -1, -1) + + + 1/9 y DATA(-1, -1, 0) + 1/9 y DATA(1, -1, 0) + 1/9 y DATA(-1, -1, 1) + + + 1/9 y DATA(-1, 1, -1) + 1/9 y DATA(1, -1, 1) + 1/9 y DATA(1, -1, -1) + + + 1/9 y DATA(-1, 1, 1) + 1/9 y DATA(-1, 1, 0) + 1/9 y DATA(1, 1, 1) + + + 1/9 y DATA(1, 1, 0) + 1/12 x DATA(1, 1, 1) - 1/12 x DATA(1, -1, 0) + + - 1/12 x DATA(-1, 1, 0) + 1/12 x DATA(-1, -1, 1) - 1/12 x DATA(1, -1, 1) + + - 1/12 x DATA(-1, 1, 1) + 1/12 x DATA(-1, -1, -1) - 1/12 x DATA(-1, 1, -1) + + + 1/12 x DATA(1, 1, -1) + 1/12 x DATA(-1, -1, 0) - 1/12 x DATA(1, -1, -1) + + - 1/12 z DATA(-1, -1, 1) + 1/12 z DATA(1, 1, 1) - 1/12 z DATA(1, -1, 1) + + + 1/12 z DATA(-1, 1, 1) + 1/12 z DATA(1, -1, -1) - 1/12 z DATA(-1, 1, -1) + + - 1/12 z DATA(1, 1, -1) + 1/12 z DATA(-1, -1, -1) + 1/12 x DATA(1, 1, 0) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +bytes used=18021124, alloc=1965720, time=1.32 +[COEFF(-1, -1, -1) = 1/12 z + 1/9 y + 1/12 x - 1/18, + + COEFF(0, -1, -1) = - 1/18 + 1/12 z + 1/9 y, + + COEFF(1, -1, -1) = 1/9 y + 1/12 z - 1/18 - 1/12 x, + + COEFF(-1, 0, -1) = - 2/9 y, COEFF(0, 0, -1) = - 2/9 y, + + COEFF(1, 0, -1) = - 2/9 y, + + COEFF(-1, 1, -1) = - 1/12 x + 1/9 y + 1/18 - 1/12 z, + + COEFF(0, 1, -1) = 1/9 y - 1/12 z + 1/18, + + COEFF(1, 1, -1) = - 1/12 z + 1/18 + 1/12 x + 1/9 y, + + COEFF(-1, -1, 0) = 1/12 x - 1/18 + 1/9 y, COEFF(0, -1, 0) = - 1/18 + 1/9 y, + + COEFF(1, -1, 0) = 1/9 y - 1/18 - 1/12 x, COEFF(-1, 0, 0) = - 2/9 y, + + COEFF(0, 0, 0) = - 2/9 y, COEFF(1, 0, 0) = - 2/9 y, + + COEFF(-1, 1, 0) = - 1/12 x + 1/18 + 1/9 y, COEFF(0, 1, 0) = 1/9 y + 1/18, + + COEFF(1, 1, 0) = 1/9 y + 1/12 x + 1/18, + + COEFF(-1, -1, 1) = - 1/12 z + 1/12 x - 1/18 + 1/9 y, + + COEFF(0, -1, 1) = - 1/12 z - 1/18 + 1/9 y, + + COEFF(1, -1, 1) = - 1/18 + 1/9 y - 1/12 z - 1/12 x, + + COEFF(-1, 0, 1) = - 2/9 y, COEFF(0, 0, 1) = - 2/9 y, + + COEFF(1, 0, 1) = - 2/9 y, COEFF(-1, 1, 1) = 1/12 z - 1/12 x + 1/9 y + 1/18, + + COEFF(0, 1, 1) = 1/12 z + 1/18 + 1/9 y, + + COEFF(1, 1, 1) = 1/12 x + 1/9 y + 1/12 z + 1/18] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dy.compute.c"); +bytes used=19021332, alloc=2031244, time=1.40 +bytes used=20021760, alloc=2031244, time=1.48 +> +# d/dz +> simplify( diff(interp_3d_cube_order2_smooth0,z) ); +- 1/18 DATA(-1, 0, -1) + 1/18 DATA(0, 0, 1) + 1/18 DATA(1, 0, 1) + + + 1/18 DATA(0, 1, 1) + 1/18 DATA(1, 1, 1) + 1/12 y DATA(0, 1, 1) + + + 1/12 y DATA(0, -1, -1) + 1/9 z DATA(0, -1, 1) + 1/9 z DATA(0, 1, 1) + + + 1/9 z DATA(0, 1, -1) + 1/9 z DATA(0, -1, -1) - 1/12 y DATA(0, -1, 1) + + - 1/12 y DATA(0, 1, -1) + 1/9 z DATA(0, 0, -1) + 1/9 z DATA(1, 0, -1) + + + 1/9 z DATA(0, 0, 1) - 2/9 z DATA(0, 0, 0) + 1/9 z DATA(-1, 0, 1) + + + 1/9 z DATA(-1, 0, -1) - 2/9 z DATA(-1, -1, 0) - 2/9 z DATA(0, 1, 0) + + - 2/9 z DATA(1, 1, 0) - 2/9 z DATA(0, -1, 0) - 2/9 z DATA(1, -1, 0) + + - 2/9 z DATA(-1, 0, 0) + 1/12 x DATA(-1, 0, -1) - 1/12 x DATA(1, 0, -1) + + - 1/12 x DATA(-1, 0, 1) + 1/9 z DATA(1, 0, 1) + 1/12 x DATA(1, 0, 1) + + - 2/9 z DATA(-1, 1, 0) - 2/9 z DATA(1, 0, 0) + 1/18 DATA(-1, -1, 1) + + + 1/18 DATA(0, -1, 1) + 1/18 DATA(1, -1, 1) + 1/18 DATA(-1, 0, 1) + + + 1/18 DATA(-1, 1, 1) - 1/18 DATA(0, 0, -1) - 1/18 DATA(1, 0, -1) + + - 1/18 DATA(-1, 1, -1) - 1/18 DATA(0, 1, -1) - 1/18 DATA(1, 1, -1) + + - 1/18 DATA(-1, -1, -1) - 1/18 DATA(0, -1, -1) - 1/18 DATA(1, -1, -1) + + - 1/12 y DATA(1, 1, -1) + 1/12 y DATA(-1, -1, -1) - 1/12 y DATA(-1, -1, 1) + + - 1/12 y DATA(-1, 1, -1) - 1/12 y DATA(1, -1, 1) + 1/12 y DATA(1, -1, -1) + + + 1/12 y DATA(-1, 1, 1) + 1/12 y DATA(1, 1, 1) + 1/12 x DATA(1, 1, 1) + + - 1/12 x DATA(-1, -1, 1) + 1/12 x DATA(1, -1, 1) - 1/12 x DATA(-1, 1, 1) + + + 1/12 x DATA(-1, -1, -1) + 1/12 x DATA(-1, 1, -1) - 1/12 x DATA(1, 1, -1) + + - 1/12 x DATA(1, -1, -1) + 1/9 z DATA(-1, -1, 1) + 1/9 z DATA(1, 1, 1) + + + 1/9 z DATA(1, -1, 1) + 1/9 z DATA(-1, 1, 1) + 1/9 z DATA(1, -1, -1) + + + 1/9 z DATA(-1, 1, -1) + 1/9 z DATA(1, 1, -1) + 1/9 z DATA(-1, -1, -1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +[COEFF(-1, -1, -1) = 1/12 y + 1/9 z - 1/18 + 1/12 x, + + COEFF(0, -1, -1) = - 1/18 + 1/9 z + 1/12 y, + + COEFF(1, -1, -1) = - 1/12 x - 1/18 + 1/9 z + 1/12 y, + + COEFF(-1, 0, -1) = 1/9 z + 1/12 x - 1/18, COEFF(0, 0, -1) = - 1/18 + 1/9 z, + + COEFF(1, 0, -1) = - 1/12 x - 1/18 + 1/9 z, + + COEFF(-1, 1, -1) = - 1/18 - 1/12 y + 1/12 x + 1/9 z, + + COEFF(0, 1, -1) = - 1/12 y - 1/18 + 1/9 z, + + COEFF(1, 1, -1) = - 1/12 y + 1/9 z - 1/18 - 1/12 x, + + COEFF(-1, -1, 0) = - 2/9 z, COEFF(0, -1, 0) = - 2/9 z, + + COEFF(1, -1, 0) = - 2/9 z, COEFF(-1, 0, 0) = - 2/9 z, + + COEFF(0, 0, 0) = - 2/9 z, COEFF(1, 0, 0) = - 2/9 z, + + COEFF(-1, 1, 0) = - 2/9 z, COEFF(0, 1, 0) = - 2/9 z, + + COEFF(1, 1, 0) = - 2/9 z, COEFF(-1, -1, 1) = 1/9 z - 1/12 x + 1/18 - 1/12 y, + + COEFF(0, -1, 1) = 1/18 + 1/9 z - 1/12 y, + + COEFF(1, -1, 1) = - 1/12 y + 1/18 + 1/9 z + 1/12 x, + + COEFF(-1, 0, 1) = - 1/12 x + 1/18 + 1/9 z, COEFF(0, 0, 1) = 1/18 + 1/9 z, + + COEFF(1, 0, 1) = 1/9 z + 1/18 + 1/12 x, + + COEFF(-1, 1, 1) = 1/18 + 1/9 z + 1/12 y - 1/12 x, + + COEFF(0, 1, 1) = 1/9 z + 1/18 + 1/12 y, + + COEFF(1, 1, 1) = 1/18 + 1/9 z + 1/12 y + 1/12 x] + +> print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dz.compute.c"); +bytes used=21021920, alloc=2031244, time=1.55 +bytes used=22022152, alloc=2031244, time=1.64 +> +# d^2/dx^2 +> simplify( diff(interp_3d_cube_order2_smooth0,x,x) ); +bytes used=23022556, alloc=2031244, time=1.74 +1/9 DATA(-1, 0, -1) - 2/9 DATA(0, 0, 0) + 1/9 DATA(1, 0, 0) - 2/9 DATA(0, 1, 0) + + + 1/9 DATA(1, 1, 0) - 2/9 DATA(0, 0, 1) + 1/9 DATA(1, 0, 1) + + - 2/9 DATA(0, 1, 1) + 1/9 DATA(1, 1, 1) - 2/9 DATA(0, -1, 0) + + + 1/9 DATA(1, -1, 0) + 1/9 DATA(-1, 0, 0) + 1/9 DATA(-1, 1, 0) + + + 1/9 DATA(-1, -1, 1) - 2/9 DATA(0, -1, 1) + 1/9 DATA(1, -1, 1) + + + 1/9 DATA(-1, 0, 1) + 1/9 DATA(-1, 1, 1) - 2/9 DATA(0, 0, -1) + + + 1/9 DATA(1, 0, -1) + 1/9 DATA(-1, 1, -1) - 2/9 DATA(0, 1, -1) + + + 1/9 DATA(1, 1, -1) + 1/9 DATA(-1, -1, 0) + 1/9 DATA(-1, -1, -1) + + - 2/9 DATA(0, -1, -1) + 1/9 DATA(1, -1, -1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +[COEFF(-1, -1, -1) = 1/9, COEFF(0, -1, -1) = -2/9, COEFF(1, -1, -1) = 1/9, + + COEFF(-1, 0, -1) = 1/9, COEFF(0, 0, -1) = -2/9, COEFF(1, 0, -1) = 1/9, + + COEFF(-1, 1, -1) = 1/9, COEFF(0, 1, -1) = -2/9, COEFF(1, 1, -1) = 1/9, + + COEFF(-1, -1, 0) = 1/9, COEFF(0, -1, 0) = -2/9, COEFF(1, -1, 0) = 1/9, + + COEFF(-1, 0, 0) = 1/9, COEFF(0, 0, 0) = -2/9, COEFF(1, 0, 0) = 1/9, + + COEFF(-1, 1, 0) = 1/9, COEFF(0, 1, 0) = -2/9, COEFF(1, 1, 0) = 1/9, + + COEFF(-1, -1, 1) = 1/9, COEFF(0, -1, 1) = -2/9, COEFF(1, -1, 1) = 1/9, + + COEFF(-1, 0, 1) = 1/9, COEFF(0, 0, 1) = -2/9, COEFF(1, 0, 1) = 1/9, + + COEFF(-1, 1, 1) = 1/9, COEFF(0, 1, 1) = -2/9, COEFF(1, 1, 1) = 1/9] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxx.compute.c"); +bytes used=24022828, alloc=2031244, time=1.85 +> +# d^2/dxdy +> simplify( diff(interp_3d_cube_order2_smooth0,x,y) ); +- 1/12 DATA(-1, 1, 0) + 1/12 DATA(1, 1, 0) + 1/12 DATA(1, 1, 1) + + - 1/12 DATA(1, -1, 0) - 1/12 DATA(-1, 1, -1) + 1/12 DATA(-1, -1, 1) + + - 1/12 DATA(1, -1, 1) - 1/12 DATA(-1, 1, 1) - 1/12 DATA(1, -1, -1) + + + 1/12 DATA(1, 1, -1) + 1/12 DATA(-1, -1, 0) + 1/12 DATA(-1, -1, -1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); + -1 +[COEFF(-1, -1, -1) = 1/12, COEFF(0, -1, -1) = 0, COEFF(1, -1, -1) = --, + 12 + + COEFF(-1, 0, -1) = 0, COEFF(0, 0, -1) = 0, COEFF(1, 0, -1) = 0, + + -1 + COEFF(-1, 1, -1) = --, COEFF(0, 1, -1) = 0, COEFF(1, 1, -1) = 1/12, + 12 + + -1 + COEFF(-1, -1, 0) = 1/12, COEFF(0, -1, 0) = 0, COEFF(1, -1, 0) = --, + 12 + + COEFF(-1, 0, 0) = 0, COEFF(0, 0, 0) = 0, COEFF(1, 0, 0) = 0, + + -1 + COEFF(-1, 1, 0) = --, COEFF(0, 1, 0) = 0, COEFF(1, 1, 0) = 1/12, + 12 + + -1 + COEFF(-1, -1, 1) = 1/12, COEFF(0, -1, 1) = 0, COEFF(1, -1, 1) = --, + 12 + + COEFF(-1, 0, 1) = 0, COEFF(0, 0, 1) = 0, COEFF(1, 0, 1) = 0, + + -1 + COEFF(-1, 1, 1) = --, COEFF(0, 1, 1) = 0, COEFF(1, 1, 1) = 1/12] + 12 + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxy.compute.c"); +bytes used=25023044, alloc=2031244, time=1.94 +> +# d^2/dxdz +> simplify( diff(interp_3d_cube_order2_smooth0,x,z) ); +- 1/12 DATA(-1, -1, 1) + 1/12 DATA(-1, 0, -1) + 1/12 DATA(1, 0, 1) + + + 1/12 DATA(1, 1, 1) - 1/12 DATA(1, 0, -1) + 1/12 DATA(1, -1, 1) + + - 1/12 DATA(-1, 0, 1) - 1/12 DATA(-1, 1, 1) - 1/12 DATA(1, -1, -1) + + + 1/12 DATA(-1, 1, -1) - 1/12 DATA(1, 1, -1) + 1/12 DATA(-1, -1, -1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); + -1 +[COEFF(-1, -1, -1) = 1/12, COEFF(0, -1, -1) = 0, COEFF(1, -1, -1) = --, + 12 + + -1 + COEFF(-1, 0, -1) = 1/12, COEFF(0, 0, -1) = 0, COEFF(1, 0, -1) = --, + 12 + + -1 + COEFF(-1, 1, -1) = 1/12, COEFF(0, 1, -1) = 0, COEFF(1, 1, -1) = --, + 12 + + COEFF(-1, -1, 0) = 0, COEFF(0, -1, 0) = 0, COEFF(1, -1, 0) = 0, + + COEFF(-1, 0, 0) = 0, COEFF(0, 0, 0) = 0, COEFF(1, 0, 0) = 0, + + COEFF(-1, 1, 0) = 0, COEFF(0, 1, 0) = 0, COEFF(1, 1, 0) = 0, + + -1 + COEFF(-1, -1, 1) = --, COEFF(0, -1, 1) = 0, COEFF(1, -1, 1) = 1/12, + 12 + + -1 + COEFF(-1, 0, 1) = --, COEFF(0, 0, 1) = 0, COEFF(1, 0, 1) = 1/12, + 12 + + -1 + COEFF(-1, 1, 1) = --, COEFF(0, 1, 1) = 0, COEFF(1, 1, 1) = 1/12] + 12 + +> print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxz.compute.c"); +> +# d^2/dy^2 +> simplify( diff(interp_3d_cube_order2_smooth0,y,y) ); +bytes used=26023408, alloc=2031244, time=2.02 +- 2/9 DATA(-1, 0, -1) - 2/9 DATA(0, 0, 0) - 2/9 DATA(1, 0, 0) + + + 1/9 DATA(0, 1, 0) + 1/9 DATA(1, 1, 0) - 2/9 DATA(0, 0, 1) + + - 2/9 DATA(1, 0, 1) + 1/9 DATA(0, 1, 1) + 1/9 DATA(1, 1, 1) + + + 1/9 DATA(0, -1, 0) + 1/9 DATA(1, -1, 0) - 2/9 DATA(-1, 0, 0) + + + 1/9 DATA(-1, 1, 0) + 1/9 DATA(-1, -1, 1) + 1/9 DATA(0, -1, 1) + + + 1/9 DATA(1, -1, 1) - 2/9 DATA(-1, 0, 1) + 1/9 DATA(-1, 1, 1) + + - 2/9 DATA(0, 0, -1) - 2/9 DATA(1, 0, -1) + 1/9 DATA(-1, 1, -1) + + + 1/9 DATA(0, 1, -1) + 1/9 DATA(1, 1, -1) + 1/9 DATA(-1, -1, 0) + + + 1/9 DATA(-1, -1, -1) + 1/9 DATA(0, -1, -1) + 1/9 DATA(1, -1, -1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +[COEFF(-1, -1, -1) = 1/9, COEFF(0, -1, -1) = 1/9, COEFF(1, -1, -1) = 1/9, + + COEFF(-1, 0, -1) = -2/9, COEFF(0, 0, -1) = -2/9, COEFF(1, 0, -1) = -2/9, + + COEFF(-1, 1, -1) = 1/9, COEFF(0, 1, -1) = 1/9, COEFF(1, 1, -1) = 1/9, + + COEFF(-1, -1, 0) = 1/9, COEFF(0, -1, 0) = 1/9, COEFF(1, -1, 0) = 1/9, + + COEFF(-1, 0, 0) = -2/9, COEFF(0, 0, 0) = -2/9, COEFF(1, 0, 0) = -2/9, + + COEFF(-1, 1, 0) = 1/9, COEFF(0, 1, 0) = 1/9, COEFF(1, 1, 0) = 1/9, + + COEFF(-1, -1, 1) = 1/9, COEFF(0, -1, 1) = 1/9, COEFF(1, -1, 1) = 1/9, + + COEFF(-1, 0, 1) = -2/9, COEFF(0, 0, 1) = -2/9, COEFF(1, 0, 1) = -2/9, + + COEFF(-1, 1, 1) = 1/9, COEFF(0, 1, 1) = 1/9, COEFF(1, 1, 1) = 1/9] + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dyy.compute.c"); +bytes used=27023608, alloc=2031244, time=2.11 +> +# d^2/dydz +> simplify( diff(interp_3d_cube_order2_smooth0,y,z) ); +- 1/12 DATA(0, -1, 1) + 1/12 DATA(0, 1, 1) + 1/12 DATA(1, 1, 1) + + - 1/12 DATA(-1, -1, 1) - 1/12 DATA(0, 1, -1) - 1/12 DATA(1, -1, 1) + + + 1/12 DATA(-1, 1, 1) - 1/12 DATA(-1, 1, -1) + 1/12 DATA(1, -1, -1) + + - 1/12 DATA(1, 1, -1) + 1/12 DATA(-1, -1, -1) + 1/12 DATA(0, -1, -1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +[COEFF(-1, -1, -1) = 1/12, COEFF(0, -1, -1) = 1/12, COEFF(1, -1, -1) = 1/12, + + COEFF(-1, 0, -1) = 0, COEFF(0, 0, -1) = 0, COEFF(1, 0, -1) = 0, + + -1 -1 -1 + COEFF(-1, 1, -1) = --, COEFF(0, 1, -1) = --, COEFF(1, 1, -1) = --, + 12 12 12 + + COEFF(-1, -1, 0) = 0, COEFF(0, -1, 0) = 0, COEFF(1, -1, 0) = 0, + + COEFF(-1, 0, 0) = 0, COEFF(0, 0, 0) = 0, COEFF(1, 0, 0) = 0, + + COEFF(-1, 1, 0) = 0, COEFF(0, 1, 0) = 0, COEFF(1, 1, 0) = 0, + + -1 -1 -1 + COEFF(-1, -1, 1) = --, COEFF(0, -1, 1) = --, COEFF(1, -1, 1) = --, + 12 12 12 + + COEFF(-1, 0, 1) = 0, COEFF(0, 0, 1) = 0, COEFF(1, 0, 1) = 0, + + COEFF(-1, 1, 1) = 1/12, COEFF(0, 1, 1) = 1/12, COEFF(1, 1, 1) = 1/12] + +> print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dyz.compute.c"); +> +# d^2/dz^2 +> simplify( diff(interp_3d_cube_order2_smooth0,z,z) ); +bytes used=28023908, alloc=2031244, time=2.23 +1/9 DATA(-1, 0, -1) - 2/9 DATA(0, 0, 0) - 2/9 DATA(1, 0, 0) - 2/9 DATA(0, 1, 0) + + - 2/9 DATA(1, 1, 0) + 1/9 DATA(0, 0, 1) + 1/9 DATA(1, 0, 1) + + + 1/9 DATA(0, 1, 1) + 1/9 DATA(1, 1, 1) - 2/9 DATA(0, -1, 0) + + - 2/9 DATA(1, -1, 0) - 2/9 DATA(-1, 0, 0) - 2/9 DATA(-1, 1, 0) + + + 1/9 DATA(-1, -1, 1) + 1/9 DATA(0, -1, 1) + 1/9 DATA(1, -1, 1) + + + 1/9 DATA(-1, 0, 1) + 1/9 DATA(-1, 1, 1) + 1/9 DATA(0, 0, -1) + + + 1/9 DATA(1, 0, -1) + 1/9 DATA(-1, 1, -1) + 1/9 DATA(0, 1, -1) + + + 1/9 DATA(1, 1, -1) - 2/9 DATA(-1, -1, 0) + 1/9 DATA(-1, -1, -1) + + + 1/9 DATA(0, -1, -1) + 1/9 DATA(1, -1, -1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +[COEFF(-1, -1, -1) = 1/9, COEFF(0, -1, -1) = 1/9, COEFF(1, -1, -1) = 1/9, + + COEFF(-1, 0, -1) = 1/9, COEFF(0, 0, -1) = 1/9, COEFF(1, 0, -1) = 1/9, + + COEFF(-1, 1, -1) = 1/9, COEFF(0, 1, -1) = 1/9, COEFF(1, 1, -1) = 1/9, + + COEFF(-1, -1, 0) = -2/9, COEFF(0, -1, 0) = -2/9, COEFF(1, -1, 0) = -2/9, + + COEFF(-1, 0, 0) = -2/9, COEFF(0, 0, 0) = -2/9, COEFF(1, 0, 0) = -2/9, + + COEFF(-1, 1, 0) = -2/9, COEFF(0, 1, 0) = -2/9, COEFF(1, 1, 0) = -2/9, + + COEFF(-1, -1, 1) = 1/9, COEFF(0, -1, 1) = 1/9, COEFF(1, -1, 1) = 1/9, + + COEFF(-1, 0, 1) = 1/9, COEFF(0, 0, 1) = 1/9, COEFF(1, 0, 1) = 1/9, + + COEFF(-1, 1, 1) = 1/9, COEFF(0, 1, 1) = 1/9, COEFF(1, 1, 1) = 1/9] + +> print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dzz.compute.c"); +bytes used=29024060, alloc=2031244, time=2.32 +> +################################################################################ +> +# +# 3d, cube, order=3, smoothing=0 (size=4) +# +> +# interpolating polynomial +> interp_3d_cube_order3_smooth0 +> := Lagrange_polynomial_interpolant(fn_3d_order3, coeffs_list_3d_order3, +> coords_list_3d, posn_list_3d_size4); +bytes used=30024284, alloc=2031244, time=2.40 +bytes used=31110904, alloc=2162292, time=2.47 +bytes used=32111568, alloc=2227816, time=2.52 +bytes used=33116552, alloc=2293340, time=2.59 +bytes used=34116684, alloc=2293340, time=2.65 +bytes used=35117004, alloc=2293340, time=2.71 +bytes used=36117340, alloc=2293340, time=2.76 +bytes used=37121600, alloc=2293340, time=2.83 +bytes used=38126188, alloc=2293340, time=2.88 +bytes used=39126460, alloc=2358864, time=2.96 +bytes used=40126588, alloc=2358864, time=3.02 +bytes used=41126744, alloc=2358864, time=3.09 +bytes used=42127236, alloc=2358864, time=3.15 +bytes used=43129196, alloc=2358864, time=3.22 +bytes used=44129324, alloc=2358864, time=3.28 +bytes used=45129992, alloc=2358864, time=3.34 +bytes used=46130308, alloc=2358864, time=3.40 +bytes used=47130556, alloc=2358864, time=3.47 +bytes used=48131000, alloc=2358864, time=3.53 +bytes used=49136704, alloc=2358864, time=3.60 +bytes used=50136984, alloc=2424388, time=3.66 +bytes used=51137164, alloc=2424388, time=3.72 +bytes used=52137360, alloc=2424388, time=3.78 +bytes used=53138544, alloc=2424388, time=3.85 +bytes used=54139880, alloc=2424388, time=3.91 +bytes used=55140028, alloc=2424388, time=3.97 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used=98223204, alloc=2424388, time=6.61 + 73 73 +interp_3d_cube_order3_smooth0 := ---- DATA(0, 2, -1) + ---- DATA(2, 0, -1) + 4000 4000 + + 73 49 + + ---- DATA(0, -1, 2) + 7/250 DATA(0, 2, 2) + ---- DATA(1, 0, 2) + 4000 4000 + + 71 59 177 + + ---- DATA(-1, 0, -1) - ---- DATA(2, -1, -1) + ---- DATA(0, 0, 0) + 2000 1000 1000 + + 397 397 49 + + ---- DATA(1, 0, 0) + ---- DATA(0, 1, 0) + ---- DATA(1, 1, 0) + 4000 4000 2000 + + 397 49 49 + + ---- DATA(0, 0, 1) + ---- DATA(1, 0, 1) + ---- DATA(0, 1, 1) + 4000 2000 2000 + + 193 59 59 + - ---- DATA(1, 1, 1) - ---- DATA(2, 2, -1) - ---- DATA(1, 2, -1) + 4000 4000 2000 + + 59 59 143 + - ---- DATA(-1, 2, -1) - ---- DATA(2, 1, -1) + ---- DATA(2, 0, 0) + 1000 2000 2000 + + 73 + + ---- DATA(2, -1, 0) + (3/160 DATA(0, 2, -1) - 1/160 DATA(2, 0, -1) + 4000 + + - 3/160 DATA(0, -1, 2) + 3/160 DATA(0, 2, 2) - 1/160 DATA(1, 0, 2) + + - 1/160 DATA(-1, 0, -1) - 3/160 DATA(2, -1, -1) + 1/160 DATA(0, 0, 0) + + + 1/160 DATA(1, 0, 0) - 1/160 DATA(0, 1, 0) - 1/160 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1/160 DATA(-1, 0, 1) + + - 1/160 DATA(-1, 1, 1) - 1/160 DATA(0, 0, -1) - 1/160 DATA(1, 0, -1) + + + 1/160 DATA(-1, 1, -1) + 1/160 DATA(0, 1, -1) + 1/160 DATA(1, 1, -1) + + + 3/160 DATA(-1, -1, 0) - 3/160 DATA(-1, -1, -1) - 3/160 DATA(0, -1, -1) + + 2 49 + - 3/160 DATA(1, -1, -1) + 3/160 DATA(2, 2, 2)) y z + ---- DATA(1, 2, 0) + 4000 + + 143 73 49 + + ---- DATA(0, 2, 0) + ---- DATA(-1, 2, 0) + ---- DATA(2, 1, 0) + ( + 2000 4000 4000 + + - 1/160 DATA(0, 2, -1) + 3/160 DATA(2, 0, -1) - 1/160 DATA(0, -1, 2) + + - 1/160 DATA(0, 2, 2) + 1/160 DATA(1, 0, 2) - 3/160 DATA(-1, 0, -1) + + + 3/160 DATA(2, -1, -1) + 1/160 DATA(0, 0, 0) - 1/160 DATA(1, 0, 0) + + + 1/160 DATA(0, 1, 0) - 1/160 DATA(1, 1, 0) + 1/160 DATA(0, 0, 1) + + - 1/160 DATA(1, 0, 1) + 1/160 DATA(0, 1, 1) - 1/160 DATA(1, 1, 1) + + + 3/160 DATA(2, 2, -1) + 1/160 DATA(1, 2, -1) - 3/160 DATA(-1, 2, -1) + + + 3/160 DATA(2, 1, -1) - 3/160 DATA(2, 0, 0) - 3/160 DATA(2, -1, 0) + + - 1/160 DATA(1, 2, 0) + 1/160 DATA(0, 2, 0) + 3/160 DATA(-1, 2, 0) + + - 3/160 DATA(2, 1, 0) - 3/160 DATA(2, 2, 0) - 3/160 DATA(2, -1, 1) + + - 3/160 DATA(2, 0, 1) + 3/160 DATA(-1, 2, 1) - 3/160 DATA(2, 1, 1) + + - 1/160 DATA(1, 2, 1) + 1/160 DATA(0, 2, 1) - 3/160 DATA(-1, -1, 2) + + - 3/160 DATA(2, 2, 1) + 1/160 DATA(1, -1, 2) + 3/160 DATA(2, 0, 2) + + - 1/160 DATA(0, 0, 2) - 3/160 DATA(-1, 0, 2) + 3/160 DATA(2, -1, 2) + + + 1/160 DATA(1, 1, 2) - 1/160 DATA(0, 1, 2) - 3/160 DATA(-1, 1, 2) + + - 3/160 DATA(-1, 2, 2) + 3/160 DATA(2, 1, 2) + 1/160 DATA(1, 2, 2) + + + 1/160 DATA(0, -1, 0) - 1/160 DATA(1, -1, 0) + 3/160 DATA(-1, 0, 0) + + + 3/160 DATA(-1, 1, 0) + 3/160 DATA(-1, -1, 1) + 1/160 DATA(0, -1, 1) + + - 1/160 DATA(1, -1, 1) + 3/160 DATA(-1, 0, 1) + 3/160 DATA(-1, 1, 1) + + - 1/160 DATA(0, 0, -1) + 1/160 DATA(1, 0, -1) - 3/160 DATA(-1, 1, -1) + + - 1/160 DATA(0, 1, -1) + 1/160 DATA(1, 1, -1) + 3/160 DATA(-1, -1, 0) + + - 3/160 DATA(-1, -1, -1) - 1/160 DATA(0, -1, -1) + 1/160 DATA(1, -1, -1) + + 2 + + 3/160 DATA(2, 2, 2)) x z + (3/160 DATA(0, 2, -1) - 3/160 DATA(2, 0, -1) + + - 3/160 DATA(0, -1, 2) - 3/160 DATA(0, 2, 2) - 3/160 DATA(1, 0, 2) + + - 3/160 DATA(-1, 0, -1) - 3/160 DATA(2, -1, -1) + 1/160 DATA(0, 0, 0) + + + 1/160 DATA(1, 0, 0) + 1/160 DATA(0, 1, 0) + 1/160 DATA(1, 1, 0) + + - 1/160 DATA(0, 0, 1) - 1/160 DATA(1, 0, 1) - 1/160 DATA(0, 1, 1) + + - 1/160 DATA(1, 1, 1) - 3/160 DATA(2, 2, -1) + 3/160 DATA(1, 2, -1) + + - 3/160 DATA(-1, 2, -1) - 3/160 DATA(2, 1, -1) - 1/160 DATA(2, 0, 0) + + - 1/160 DATA(2, -1, 0) + 1/160 DATA(1, 2, 0) + 1/160 DATA(0, 2, 0) + + - 1/160 DATA(-1, 2, 0) - 1/160 DATA(2, 1, 0) - 1/160 DATA(2, 2, 0) + + + 1/160 DATA(2, -1, 1) + 1/160 DATA(2, 0, 1) + 1/160 DATA(-1, 2, 1) + + + 1/160 DATA(2, 1, 1) - 1/160 DATA(1, 2, 1) - 1/160 DATA(0, 2, 1) + + + 3/160 DATA(-1, -1, 2) + 1/160 DATA(2, 2, 1) - 3/160 DATA(1, -1, 2) + + + 3/160 DATA(2, 0, 2) - 3/160 DATA(0, 0, 2) + 3/160 DATA(-1, 0, 2) + + + 3/160 DATA(2, -1, 2) - 3/160 DATA(1, 1, 2) - 3/160 DATA(0, 1, 2) + + + 3/160 DATA(-1, 1, 2) + 3/160 DATA(-1, 2, 2) + 3/160 DATA(2, 1, 2) + + - 3/160 DATA(1, 2, 2) + 1/160 DATA(0, -1, 0) + 1/160 DATA(1, -1, 0) + + - 1/160 DATA(-1, 0, 0) - 1/160 DATA(-1, 1, 0) + 1/160 DATA(-1, -1, 1) + + - 1/160 DATA(0, -1, 1) - 1/160 DATA(1, -1, 1) + 1/160 DATA(-1, 0, 1) + + + 1/160 DATA(-1, 1, 1) + 3/160 DATA(0, 0, -1) + 3/160 DATA(1, 0, -1) + + - 3/160 DATA(-1, 1, -1) + 3/160 DATA(0, 1, -1) + 3/160 DATA(1, 1, -1) + + - 1/160 DATA(-1, -1, 0) - 3/160 DATA(-1, -1, -1) + 3/160 DATA(0, -1, -1) + + 2 + + 3/160 DATA(1, -1, -1) + 3/160 DATA(2, 2, 2)) x z + 7/250 DATA(2, 2, 0) + + 59 / 13 13 + - ---- DATA(2, -1, 1) + |---- DATA(0, 2, -1) + ---- DATA(2, 0, -1) + 2000 \1000 1000 + + 19 11 + - ---- DATA(0, -1, 2) + --- DATA(0, 2, 2) - 1/1000 DATA(1, 0, 2) + 2000 500 + + 19 + - 1/2000 DATA(-1, 0, -1) - 9/250 DATA(2, -1, -1) - ---- DATA(0, 0, 0) + 2000 + + 31 + - 3/1000 DATA(1, 0, 0) - 3/1000 DATA(0, 1, 0) + ---- DATA(1, 1, 0) + 2000 + + 21 + - ---- DATA(0, 0, 1) - 1/500 DATA(1, 0, 1) - 1/500 DATA(0, 1, 1) + 2000 + + 29 49 + + ---- DATA(1, 1, 1) - 3/2000 DATA(2, 2, -1) + ---- DATA(1, 2, -1) + 2000 2000 + + 49 + - 9/250 DATA(-1, 2, -1) + ---- DATA(2, 1, -1) + 2/125 DATA(2, 0, 0) + 2000 + + 27 43 + - ---- DATA(2, -1, 0) + ---- DATA(1, 2, 0) + 2/125 DATA(0, 2, 0) + 1000 2000 + + 27 43 21 + - ---- DATA(-1, 2, 0) + ---- DATA(2, 1, 0) - ---- DATA(2, 2, 0) + 1000 2000 2000 + + 19 + - 9/500 DATA(2, -1, 1) + ---- DATA(2, 0, 1) - 9/500 DATA(-1, 2, 1) + 1000 + + 37 37 19 + + ---- DATA(2, 1, 1) + ---- DATA(1, 2, 1) + ---- DATA(0, 2, 1) + 2000 2000 1000 + + 93 39 + + ---- DATA(-1, -1, 2) - ---- DATA(2, 2, 1) - 7/250 DATA(1, -1, 2) + 2000 2000 + + 11 23 19 + + --- DATA(2, 0, 2) - ---- DATA(0, 0, 2) - ---- DATA(-1, 0, 2) + 500 2000 2000 + + 27 + - 9/1000 DATA(2, -1, 2) + ---- DATA(1, 1, 2) - 1/1000 DATA(0, 1, 2) + 2000 + + 31 + - 7/250 DATA(-1, 1, 2) - 9/1000 DATA(-1, 2, 2) + ---- DATA(2, 1, 2) + 2000 + + 31 17 + + ---- DATA(1, 2, 2) - 7/2000 DATA(0, -1, 0) - --- DATA(1, -1, 0) + 2000 500 + + 17 111 + - 7/2000 DATA(-1, 0, 0) - --- DATA(-1, 1, 0) + ---- DATA(-1, -1, 1) + 500 2000 + + 13 31 13 + - ---- DATA(0, -1, 1) - ---- DATA(1, -1, 1) - ---- DATA(-1, 0, 1) + 2000 1000 2000 + + 31 17 + - ---- DATA(-1, 1, 1) - ---- DATA(0, 0, -1) - 1/250 DATA(1, 0, -1) + 1000 2000 + + 37 33 + - ---- DATA(-1, 1, -1) - 1/250 DATA(0, 1, -1) + ---- DATA(1, 1, -1) + 1000 2000 + + 129 147 + + ---- DATA(-1, -1, 0) + ---- DATA(-1, -1, -1) - 1/2000 DATA(0, -1, -1) + 2000 2000 + + 37 57 \ + - ---- DATA(1, -1, -1) - ---- DATA(2, 2, 2)| x y + (- 1/160 DATA(0, 2, -1) + 1000 2000 / + + - 3/160 DATA(2, 0, -1) - 1/160 DATA(0, -1, 2) - 1/160 DATA(0, 2, 2) + + - 1/160 DATA(1, 0, 2) + 3/160 DATA(-1, 0, -1) + 3/160 DATA(2, -1, -1) + + + 1/160 DATA(0, 0, 0) - 1/160 DATA(1, 0, 0) + 1/160 DATA(0, 1, 0) + + - 1/160 DATA(1, 1, 0) + 1/160 DATA(0, 0, 1) - 1/160 DATA(1, 0, 1) + + + 1/160 DATA(0, 1, 1) - 1/160 DATA(1, 1, 1) + 3/160 DATA(2, 2, -1) + + + 1/160 DATA(1, 2, -1) - 3/160 DATA(-1, 2, -1) - 3/160 DATA(2, 1, -1) + + - 3/160 DATA(2, 0, 0) + 3/160 DATA(2, -1, 0) + 1/160 DATA(1, 2, 0) + + - 1/160 DATA(0, 2, 0) - 3/160 DATA(-1, 2, 0) - 3/160 DATA(2, 1, 0) + + + 3/160 DATA(2, 2, 0) + 3/160 DATA(2, -1, 1) - 3/160 DATA(2, 0, 1) + + - 3/160 DATA(-1, 2, 1) - 3/160 DATA(2, 1, 1) + 1/160 DATA(1, 2, 1) + + - 1/160 DATA(0, 2, 1) - 3/160 DATA(-1, -1, 2) + 3/160 DATA(2, 2, 1) + + + 1/160 DATA(1, -1, 2) - 3/160 DATA(2, 0, 2) + 1/160 DATA(0, 0, 2) + + + 3/160 DATA(-1, 0, 2) + 3/160 DATA(2, -1, 2) - 1/160 DATA(1, 1, 2) + + + 1/160 DATA(0, 1, 2) + 3/160 DATA(-1, 1, 2) - 3/160 DATA(-1, 2, 2) + + - 3/160 DATA(2, 1, 2) + 1/160 DATA(1, 2, 2) - 1/160 DATA(0, -1, 0) + + + 1/160 DATA(1, -1, 0) + 3/160 DATA(-1, 0, 0) + 3/160 DATA(-1, 1, 0) + + - 3/160 DATA(-1, -1, 1) - 1/160 DATA(0, -1, 1) + 1/160 DATA(1, -1, 1) + + + 3/160 DATA(-1, 0, 1) + 3/160 DATA(-1, 1, 1) + 1/160 DATA(0, 0, -1) + + - 1/160 DATA(1, 0, -1) + 3/160 DATA(-1, 1, -1) + 1/160 DATA(0, 1, -1) + + - 1/160 DATA(1, 1, -1) - 3/160 DATA(-1, -1, 0) - 3/160 DATA(-1, -1, -1) + + - 1/160 DATA(0, -1, -1) + 1/160 DATA(1, -1, -1) + 3/160 DATA(2, 2, 2)) x + + 2 / 19 27 13 + y + |- ---- DATA(0, 2, -1) - ---- DATA(2, 0, -1) + ---- DATA(0, -1, 2) + \ 2000 1000 1000 + + 11 43 129 + + --- DATA(0, 2, 2) + ---- DATA(1, 0, 2) + ---- DATA(-1, 0, -1) + 500 2000 2000 + + 19 + - 9/250 DATA(2, -1, -1) - ---- DATA(0, 0, 0) - 3/1000 DATA(1, 0, 0) + 2000 + + 21 + - ---- DATA(0, 1, 0) - 1/500 DATA(1, 1, 0) - 3/1000 DATA(0, 0, 1) + 2000 + + 31 29 + + ---- DATA(1, 0, 1) - 1/500 DATA(0, 1, 1) + ---- DATA(1, 1, 1) + 2000 2000 + + 93 + - 9/1000 DATA(2, 2, -1) - 7/250 DATA(1, 2, -1) + ---- DATA(-1, 2, -1) + 2000 + + 13 + - 9/500 DATA(2, 1, -1) + 2/125 DATA(2, 0, 0) + ---- DATA(2, -1, 0) + 1000 + + 23 19 + - 1/1000 DATA(1, 2, 0) - ---- DATA(0, 2, 0) - ---- DATA(-1, 2, 0) + 2000 2000 + + 19 11 49 + + ---- DATA(2, 1, 0) + --- DATA(2, 2, 0) + ---- DATA(2, -1, 1) + 1000 500 2000 + + 43 37 + + ---- DATA(2, 0, 1) - 7/250 DATA(-1, 2, 1) + ---- DATA(2, 1, 1) + 2000 2000 + + 27 + + ---- DATA(1, 2, 1) - 1/1000 DATA(0, 2, 1) - 9/250 DATA(-1, -1, 2) + 2000 + + 31 49 21 + + ---- DATA(2, 2, 1) + ---- DATA(1, -1, 2) - ---- DATA(2, 0, 2) + 2000 2000 2000 + + 27 + + 2/125 DATA(0, 0, 2) - ---- DATA(-1, 0, 2) - 3/2000 DATA(2, -1, 2) + 1000 + + 37 19 + + ---- DATA(1, 1, 2) + ---- DATA(0, 1, 2) - 9/500 DATA(-1, 1, 2) + 2000 1000 + + 39 31 + - 9/1000 DATA(-1, 2, 2) - ---- DATA(2, 1, 2) + ---- DATA(1, 2, 2) + 2000 2000 + + 17 + - ---- DATA(0, -1, 0) - 1/250 DATA(1, -1, 0) - 7/2000 DATA(-1, 0, 0) + 2000 + + 13 37 + - ---- DATA(-1, 1, 0) - ---- DATA(-1, -1, 1) - 1/250 DATA(0, -1, 1) + 2000 1000 + + 33 17 31 + + ---- DATA(1, -1, 1) - --- DATA(-1, 0, 1) - ---- DATA(-1, 1, 1) + 2000 500 1000 + + 17 111 + - 7/2000 DATA(0, 0, -1) - --- DATA(1, 0, -1) + ---- DATA(-1, 1, -1) + 500 2000 + + 13 31 + - ---- DATA(0, 1, -1) - ---- DATA(1, 1, -1) - 1/2000 DATA(-1, -1, 0) + 2000 1000 + + 147 37 + + ---- DATA(-1, -1, -1) - 1/2000 DATA(0, -1, -1) - ---- DATA(1, -1, -1) + 2000 1000 + + 57 \ / 27 19 + - ---- DATA(2, 2, 2)| x z + |- ---- DATA(0, 2, -1) - ---- DATA(2, 0, -1) + 2000 / \ 1000 2000 + + 27 21 19 + - ---- DATA(0, -1, 2) - ---- DATA(0, 2, 2) + ---- DATA(1, 0, 2) + 1000 2000 1000 + + 93 19 + - 1/2000 DATA(-1, 0, -1) + ---- DATA(2, -1, -1) - ---- DATA(0, 0, 0) + 2000 2000 + + 21 + - ---- DATA(1, 0, 0) - 3/1000 DATA(0, 1, 0) - 1/500 DATA(1, 1, 0) + 2000 + + 31 + - 3/1000 DATA(0, 0, 1) - 1/500 DATA(1, 0, 1) + ---- DATA(0, 1, 1) + 2000 + + 29 + + ---- DATA(1, 1, 1) - 9/1000 DATA(2, 2, -1) - 9/500 DATA(1, 2, -1) + 2000 + + 23 + - 9/250 DATA(-1, 2, -1) - 7/250 DATA(2, 1, -1) - ---- DATA(2, 0, 0) + 2000 + + 19 19 + - ---- DATA(2, -1, 0) + ---- DATA(1, 2, 0) + 2/125 DATA(0, 2, 0) + 2000 1000 + + 13 11 + + ---- DATA(-1, 2, 0) - 1/1000 DATA(2, 1, 0) + --- DATA(2, 2, 0) + 1000 500 + + 49 + - 7/250 DATA(2, -1, 1) - 1/1000 DATA(2, 0, 1) + ---- DATA(-1, 2, 1) + 2000 + + 27 37 43 + + ---- DATA(2, 1, 1) + ---- DATA(1, 2, 1) + ---- DATA(0, 2, 1) + 2000 2000 2000 + + 31 + - 9/250 DATA(-1, -1, 2) + ---- DATA(2, 2, 1) - 9/500 DATA(1, -1, 2) + 2000 + + 11 13 + + --- DATA(2, 0, 2) + 2/125 DATA(0, 0, 2) + ---- DATA(-1, 0, 2) + 500 1000 + + 37 43 + - 9/1000 DATA(2, -1, 2) + ---- DATA(1, 1, 2) + ---- DATA(0, 1, 2) + 2000 2000 + + 49 31 + + ---- DATA(-1, 1, 2) - 3/2000 DATA(-1, 2, 2) + ---- DATA(2, 1, 2) + 2000 2000 + + 39 13 + - ---- DATA(1, 2, 2) - 7/2000 DATA(0, -1, 0) - ---- DATA(1, -1, 0) + 2000 2000 + + 17 37 + - ---- DATA(-1, 0, 0) - 1/250 DATA(-1, 1, 0) - ---- DATA(-1, -1, 1) + 2000 1000 + + 17 31 + - --- DATA(0, -1, 1) - ---- DATA(1, -1, 1) - 1/250 DATA(-1, 0, 1) + 500 1000 + + 33 13 + + ---- DATA(-1, 1, 1) - 7/2000 DATA(0, 0, -1) - ---- DATA(1, 0, -1) + 2000 2000 + + 37 17 31 + - ---- DATA(-1, 1, -1) - --- DATA(0, 1, -1) - ---- DATA(1, 1, -1) + 1000 500 1000 + + 147 129 + - 1/2000 DATA(-1, -1, 0) + ---- DATA(-1, -1, -1) + ---- DATA(0, -1, -1) + 2000 2000 + + 111 57 \ + + ---- DATA(1, -1, -1) - ---- DATA(2, 2, 2)| y z + (- 3/160 DATA(0, 2, -1) + 2000 2000 / + + + 3/160 DATA(2, 0, -1) + 3/160 DATA(0, -1, 2) + 3/160 DATA(0, 2, 2) + + - 3/160 DATA(1, 0, 2) + 3/160 DATA(-1, 0, -1) - 3/160 DATA(2, -1, -1) + + + 1/160 DATA(0, 0, 0) + 1/160 DATA(1, 0, 0) + 1/160 DATA(0, 1, 0) + + + 1/160 DATA(1, 1, 0) - 1/160 DATA(0, 0, 1) - 1/160 DATA(1, 0, 1) + + - 1/160 DATA(0, 1, 1) - 1/160 DATA(1, 1, 1) - 3/160 DATA(2, 2, -1) + + - 3/160 DATA(1, 2, -1) - 3/160 DATA(-1, 2, -1) + 3/160 DATA(2, 1, -1) + + + 1/160 DATA(2, 0, 0) - 1/160 DATA(2, -1, 0) - 1/160 DATA(1, 2, 0) + + - 1/160 DATA(0, 2, 0) - 1/160 DATA(-1, 2, 0) + 1/160 DATA(2, 1, 0) + + - 1/160 DATA(2, 2, 0) + 1/160 DATA(2, -1, 1) - 1/160 DATA(2, 0, 1) + + + 1/160 DATA(-1, 2, 1) - 1/160 DATA(2, 1, 1) + 1/160 DATA(1, 2, 1) + + + 1/160 DATA(0, 2, 1) + 3/160 DATA(-1, -1, 2) + 1/160 DATA(2, 2, 1) + + + 3/160 DATA(1, -1, 2) - 3/160 DATA(2, 0, 2) - 3/160 DATA(0, 0, 2) + + - 3/160 DATA(-1, 0, 2) + 3/160 DATA(2, -1, 2) - 3/160 DATA(1, 1, 2) + + - 3/160 DATA(0, 1, 2) - 3/160 DATA(-1, 1, 2) + 3/160 DATA(-1, 2, 2) + + - 3/160 DATA(2, 1, 2) + 3/160 DATA(1, 2, 2) - 1/160 DATA(0, -1, 0) + + - 1/160 DATA(1, -1, 0) + 1/160 DATA(-1, 0, 0) + 1/160 DATA(-1, 1, 0) + + + 1/160 DATA(-1, -1, 1) + 1/160 DATA(0, -1, 1) + 1/160 DATA(1, -1, 1) + + - 1/160 DATA(-1, 0, 1) - 1/160 DATA(-1, 1, 1) + 3/160 DATA(0, 0, -1) + + + 3/160 DATA(1, 0, -1) + 3/160 DATA(-1, 1, -1) + 3/160 DATA(0, 1, -1) + + + 3/160 DATA(1, 1, -1) - 1/160 DATA(-1, -1, 0) - 3/160 DATA(-1, -1, -1) + + 2 + - 3/160 DATA(0, -1, -1) - 3/160 DATA(1, -1, -1) + 3/160 DATA(2, 2, 2)) y + + 49 + z + ---- DATA(2, 0, 1) + (- 3/160 DATA(0, 2, -1) - 1/160 DATA(2, 0, -1) + 4000 + + + 3/160 DATA(0, -1, 2) - 3/160 DATA(0, 2, 2) + 1/160 DATA(1, 0, 2) + + - 1/160 DATA(-1, 0, -1) - 3/160 DATA(2, -1, -1) + 1/160 DATA(0, 0, 0) + + + 1/160 DATA(1, 0, 0) - 1/160 DATA(0, 1, 0) - 1/160 DATA(1, 1, 0) + + + 1/160 DATA(0, 0, 1) + 1/160 DATA(1, 0, 1) - 1/160 DATA(0, 1, 1) + + - 1/160 DATA(1, 1, 1) + 3/160 DATA(2, 2, -1) - 3/160 DATA(1, 2, -1) + + + 3/160 DATA(-1, 2, -1) + 1/160 DATA(2, 1, -1) - 1/160 DATA(2, 0, 0) + + - 3/160 DATA(2, -1, 0) - 3/160 DATA(1, 2, 0) - 3/160 DATA(0, 2, 0) + + + 3/160 DATA(-1, 2, 0) + 1/160 DATA(2, 1, 0) + 3/160 DATA(2, 2, 0) + + - 3/160 DATA(2, -1, 1) - 1/160 DATA(2, 0, 1) + 3/160 DATA(-1, 2, 1) + + + 1/160 DATA(2, 1, 1) - 3/160 DATA(1, 2, 1) - 3/160 DATA(0, 2, 1) + + - 3/160 DATA(-1, -1, 2) + 3/160 DATA(2, 2, 1) + 3/160 DATA(1, -1, 2) + + - 1/160 DATA(2, 0, 2) + 1/160 DATA(0, 0, 2) - 1/160 DATA(-1, 0, 2) + + - 3/160 DATA(2, -1, 2) - 1/160 DATA(1, 1, 2) - 1/160 DATA(0, 1, 2) + + + 1/160 DATA(-1, 1, 2) + 3/160 DATA(-1, 2, 2) + 1/160 DATA(2, 1, 2) + + - 3/160 DATA(1, 2, 2) + 3/160 DATA(0, -1, 0) + 3/160 DATA(1, -1, 0) + + - 1/160 DATA(-1, 0, 0) + 1/160 DATA(-1, 1, 0) - 3/160 DATA(-1, -1, 1) + + + 3/160 DATA(0, -1, 1) + 3/160 DATA(1, -1, 1) - 1/160 DATA(-1, 0, 1) + + + 1/160 DATA(-1, 1, 1) + 1/160 DATA(0, 0, -1) + 1/160 DATA(1, 0, -1) + + + 1/160 DATA(-1, 1, -1) - 1/160 DATA(0, 1, -1) - 1/160 DATA(1, 1, -1) + + - 3/160 DATA(-1, -1, 0) - 3/160 DATA(-1, -1, -1) + 3/160 DATA(0, -1, -1) + + 2 59 + + 3/160 DATA(1, -1, -1) + 3/160 DATA(2, 2, 2)) x y - ---- DATA(-1, 2, 1) + 2000 + + 23 23 49 + - --- DATA(2, 1, 1) - --- DATA(1, 2, 1) + ---- DATA(0, 2, 1) + 500 500 4000 + + 59 67 59 + - ---- DATA(-1, -1, 2) - ---- DATA(2, 2, 1) - ---- DATA(1, -1, 2) + 1000 4000 2000 + + 143 73 + + 7/250 DATA(2, 0, 2) + ---- DATA(0, 0, 2) + ---- DATA(-1, 0, 2) + 2000 4000 + + 59 23 49 + - ---- DATA(2, -1, 2) - --- DATA(1, 1, 2) + ---- DATA(0, 1, 2) + 4000 500 4000 + + 59 + - ---- DATA(-1, 1, 2) + (1/32 DATA(0, 2, -1) + 1/96 DATA(2, 0, -1) + 2000 + + + 1/32 DATA(0, -1, 2) + 1/32 DATA(0, 2, 2) - 1/32 DATA(1, 0, 2) + + - 1/96 DATA(-1, 0, -1) + 1/96 DATA(2, -1, -1) + 1/32 DATA(0, 0, 0) + + - 1/32 DATA(1, 0, 0) + 1/32 DATA(0, 1, 0) - 1/32 DATA(1, 1, 0) + + + 1/32 DATA(0, 0, 1) - 1/32 DATA(1, 0, 1) + 1/32 DATA(0, 1, 1) + + - 1/32 DATA(1, 1, 1) + 1/96 DATA(2, 2, -1) - 1/32 DATA(1, 2, -1) + + - 1/96 DATA(-1, 2, -1) + 1/96 DATA(2, 1, -1) + 1/96 DATA(2, 0, 0) + + + 1/96 DATA(2, -1, 0) - 1/32 DATA(1, 2, 0) + 1/32 DATA(0, 2, 0) + + - 1/96 DATA(-1, 2, 0) + 1/96 DATA(2, 1, 0) + 1/96 DATA(2, 2, 0) + + + 1/96 DATA(2, -1, 1) + 1/96 DATA(2, 0, 1) - 1/96 DATA(-1, 2, 1) + + + 1/96 DATA(2, 1, 1) - 1/32 DATA(1, 2, 1) + 1/32 DATA(0, 2, 1) + + - 1/96 DATA(-1, -1, 2) + 1/96 DATA(2, 2, 1) - 1/32 DATA(1, -1, 2) + + + 1/96 DATA(2, 0, 2) + 1/32 DATA(0, 0, 2) - 1/96 DATA(-1, 0, 2) + + + 1/96 DATA(2, -1, 2) - 1/32 DATA(1, 1, 2) + 1/32 DATA(0, 1, 2) + + - 1/96 DATA(-1, 1, 2) - 1/96 DATA(-1, 2, 2) + 1/96 DATA(2, 1, 2) + + - 1/32 DATA(1, 2, 2) + 1/32 DATA(0, -1, 0) - 1/32 DATA(1, -1, 0) + + - 1/96 DATA(-1, 0, 0) - 1/96 DATA(-1, 1, 0) - 1/96 DATA(-1, -1, 1) + + + 1/32 DATA(0, -1, 1) - 1/32 DATA(1, -1, 1) - 1/96 DATA(-1, 0, 1) + + - 1/96 DATA(-1, 1, 1) + 1/32 DATA(0, 0, -1) - 1/32 DATA(1, 0, -1) + + - 1/96 DATA(-1, 1, -1) + 1/32 DATA(0, 1, -1) - 1/32 DATA(1, 1, -1) + + - 1/96 DATA(-1, -1, 0) - 1/96 DATA(-1, -1, -1) + 1/32 DATA(0, -1, -1) + + 3 59 + - 1/32 DATA(1, -1, -1) + 1/96 DATA(2, 2, 2)) x - ---- DATA(-1, 2, 2) + 4000 + + 67 / + - ---- DATA(2, 1, 2) + |1/80 DATA(0, 2, -1) - 1/16 DATA(2, 0, -1) + 4000 \ + + + 1/40 DATA(0, -1, 2) - 1/160 DATA(0, 2, 2) - 1/20 DATA(1, 0, 2) + + 13 11 + - --- DATA(-1, 0, -1) + 1/32 DATA(2, -1, -1) - --- DATA(0, 0, 0) + 160 160 + + - 1/16 DATA(1, 0, 0) + 1/40 DATA(0, 1, 0) + 1/32 DATA(1, 1, 0) + + - 1/16 DATA(0, 0, 1) - 9/160 DATA(1, 0, 1) + 1/32 DATA(0, 1, 1) + + + 3/80 DATA(1, 1, 1) + 1/160 DATA(1, 2, -1) + 3/160 DATA(-1, 2, -1) + + + 1/32 DATA(2, 1, -1) - 9/160 DATA(2, 0, 0) + 1/40 DATA(2, -1, 0) + + + 1/160 DATA(0, 2, 0) + 1/80 DATA(-1, 2, 0) + 3/80 DATA(2, 1, 0) + + - 1/160 DATA(2, 2, 0) + 3/160 DATA(2, -1, 1) - 1/20 DATA(2, 0, 1) + + + 1/160 DATA(-1, 2, 1) + 7/160 DATA(2, 1, 1) - 1/160 DATA(1, 2, 1) + + + 1/32 DATA(-1, -1, 2) - 1/80 DATA(2, 2, 1) + 3/160 DATA(1, -1, 2) + + - 7/160 DATA(2, 0, 2) - 9/160 DATA(0, 0, 2) - 1/16 DATA(-1, 0, 2) + + + 1/80 DATA(2, -1, 2) + 7/160 DATA(1, 1, 2) + 3/80 DATA(0, 1, 2) + + + 1/32 DATA(-1, 1, 2) + 1/20 DATA(2, 1, 2) - 1/80 DATA(1, 2, 2) + + + 3/80 DATA(0, -1, 0) + 1/32 DATA(1, -1, 0) - 3/40 DATA(-1, 0, 0) + + + 3/160 DATA(-1, 1, 0) + 3/80 DATA(-1, -1, 1) + 1/32 DATA(0, -1, 1) + + 11 + + 1/40 DATA(1, -1, 1) - --- DATA(-1, 0, 1) + 1/40 DATA(-1, 1, 1) + 160 + + 11 + - 3/40 DATA(0, 0, -1) - --- DATA(1, 0, -1) + 1/80 DATA(-1, 1, -1) + 160 + + + 3/160 DATA(0, 1, -1) + 1/40 DATA(1, 1, -1) + 7/160 DATA(-1, -1, 0) + + + 1/20 DATA(-1, -1, -1) + 7/160 DATA(0, -1, -1) + 3/80 DATA(1, -1, -1) + + \ 2 67 469 + - 3/160 DATA(2, 2, 2)| y - ---- DATA(1, 2, 2) + ---- DATA(0, -1, 0) + / 4000 4000 + + 49 469 49 + + ---- DATA(1, -1, 0) + ---- DATA(-1, 0, 0) + ---- DATA(-1, 1, 0) + 1000 4000 1000 + + 97 49 61 + - ---- DATA(-1, -1, 1) + ---- DATA(0, -1, 1) - ---- DATA(1, -1, 1) + 4000 1000 4000 + + 49 61 469 + + ---- DATA(-1, 0, 1) - ---- DATA(-1, 1, 1) + ---- DATA(0, 0, -1) + 1000 4000 4000 + + 49 97 49 + + ---- DATA(1, 0, -1) - ---- DATA(-1, 1, -1) + ---- DATA(0, 1, -1) + 1000 4000 1000 + + 61 71 269 + - ---- DATA(1, 1, -1) + ---- DATA(-1, -1, 0) - ---- DATA(-1, -1, -1) + 4000 2000 4000 + + 71 97 77 / + + ---- DATA(0, -1, -1) - ---- DATA(1, -1, -1) + ---- DATA(2, 2, 2) + | + 2000 4000 2000 \ + + - 1/16 DATA(0, 2, -1) + 1/80 DATA(2, 0, -1) - 1/16 DATA(0, -1, 2) + + - 7/160 DATA(0, 2, 2) + 3/80 DATA(1, 0, 2) + 7/160 DATA(-1, 0, -1) + + 11 + + 3/160 DATA(2, -1, -1) - --- DATA(0, 0, 0) + 1/40 DATA(1, 0, 0) + 160 + + - 1/16 DATA(0, 1, 0) + 1/32 DATA(1, 1, 0) - 1/16 DATA(0, 0, 1) + + + 1/32 DATA(1, 0, 1) - 9/160 DATA(0, 1, 1) + 3/80 DATA(1, 1, 1) + + + 1/32 DATA(1, 2, -1) + 1/32 DATA(-1, 2, -1) + 1/160 DATA(2, 1, -1) + + + 1/160 DATA(2, 0, 0) + 1/80 DATA(2, -1, 0) + 3/80 DATA(1, 2, 0) + + - 9/160 DATA(0, 2, 0) + 1/40 DATA(-1, 2, 0) - 1/160 DATA(2, 2, 0) + + + 1/160 DATA(2, -1, 1) + 3/160 DATA(-1, 2, 1) - 1/160 DATA(2, 1, 1) + + + 7/160 DATA(1, 2, 1) - 1/20 DATA(0, 2, 1) + 1/32 DATA(-1, -1, 2) + + - 1/80 DATA(2, 2, 1) + 1/32 DATA(1, -1, 2) - 1/160 DATA(2, 0, 2) + + - 9/160 DATA(0, 0, 2) + 1/40 DATA(-1, 0, 2) + 7/160 DATA(1, 1, 2) + + - 1/20 DATA(0, 1, 2) + 3/160 DATA(-1, 1, 2) + 1/80 DATA(-1, 2, 2) + + - 1/80 DATA(2, 1, 2) + 1/20 DATA(1, 2, 2) - 3/40 DATA(0, -1, 0) + + + 3/160 DATA(1, -1, 0) + 3/80 DATA(-1, 0, 0) + 1/32 DATA(-1, 1, 0) + + 11 + + 3/80 DATA(-1, -1, 1) - --- DATA(0, -1, 1) + 1/40 DATA(1, -1, 1) + 160 + + + 1/32 DATA(-1, 0, 1) + 1/40 DATA(-1, 1, 1) - 3/40 DATA(0, 0, -1) + + 11 + + 3/160 DATA(1, 0, -1) + 3/80 DATA(-1, 1, -1) - --- DATA(0, 1, -1) + 160 + + + 1/40 DATA(1, 1, -1) + 7/160 DATA(-1, -1, 0) + 1/20 DATA(-1, -1, -1) + + 13 \ 2 / + - --- DATA(0, -1, -1) + 1/80 DATA(1, -1, -1) - 3/160 DATA(2, 2, 2)| x + | + 160 / \ + + 17 33 29 + - ---- DATA(0, 2, -1) - ---- DATA(2, 0, -1) - ---- DATA(0, -1, 2) + 3000 2000 6000 + + 167 79 39 + - ----- DATA(0, 2, 2) - ---- DATA(1, 0, 2) - ---- DATA(-1, 0, -1) + 12000 2000 4000 + + 281 161 87 + + ----- DATA(2, -1, -1) - ---- DATA(0, 0, 0) - ---- DATA(1, 0, 0) + 12000 4000 2000 + + 21 299 87 + + --- DATA(0, 1, 0) + ---- DATA(1, 1, 0) - ---- DATA(0, 0, 1) + 250 4000 2000 + + 191 299 133 + - ---- DATA(1, 0, 1) + ---- DATA(0, 1, 1) + ---- DATA(1, 1, 1) + 4000 4000 2000 + + 41 137 449 + - --- DATA(2, 2, -1) - ----- DATA(1, 2, -1) - ----- DATA(-1, 2, -1) + 750 12000 12000 + + 191 137 29 + + ---- DATA(2, 1, -1) - ---- DATA(2, 0, 0) - ---- DATA(2, -1, 0) + 4000 4000 6000 + + 79 349 17 + + ---- DATA(1, 2, 0) + ----- DATA(0, 2, 0) - ---- DATA(-1, 2, 0) + 3000 12000 3000 + + 53 167 53 + + ---- DATA(2, 1, 0) - ----- DATA(2, 2, 0) + ----- DATA(2, -1, 1) + 1000 12000 12000 + + 79 137 183 + - ---- DATA(2, 0, 1) - ----- DATA(-1, 2, 1) + ---- DATA(2, 1, 1) + 2000 12000 4000 + + 319 79 281 + + ----- DATA(1, 2, 1) + ---- DATA(0, 2, 1) + ----- DATA(-1, -1, 2) + 12000 3000 12000 + + 53 129 + - 4/375 DATA(2, 2, 1) + ----- DATA(1, -1, 2) - ---- DATA(2, 0, 2) + 12000 4000 + + 137 33 307 + - ---- DATA(0, 0, 2) - ---- DATA(-1, 0, 2) + ---- DATA(2, -1, 2) + 4000 2000 6000 + + 183 53 191 + + ---- DATA(1, 1, 2) + ---- DATA(0, 1, 2) + ---- DATA(-1, 1, 2) + 4000 1000 4000 + + 41 13 + - --- DATA(-1, 2, 2) + --- DATA(2, 1, 2) - 4/375 DATA(1, 2, 2) + 750 500 + + 437 691 49 + - ---- DATA(0, -1, 0) - ----- DATA(1, -1, 0) - ---- DATA(-1, 0, 0) + 6000 12000 2000 + + 323 97 691 + + ---- DATA(-1, 1, 0) - ---- DATA(-1, -1, 1) - ----- DATA(0, -1, 1) + 4000 3000 12000 + + 17 107 141 + - --- DATA(1, -1, 1) - ---- DATA(-1, 0, 1) + ---- DATA(-1, 1, 1) + 375 4000 2000 + + 49 107 157 + - ---- DATA(0, 0, -1) - ---- DATA(1, 0, -1) + ---- DATA(-1, 1, -1) + 2000 4000 2000 + + 323 141 607 + + ---- DATA(0, 1, -1) + ---- DATA(1, 1, -1) - ----- DATA(-1, -1, 0) + 4000 2000 12000 + + 47 607 97 + - ---- DATA(-1, -1, -1) - ----- DATA(0, -1, -1) - ---- DATA(1, -1, -1) + 1500 12000 3000 + + 539 \ / 33 17 + - ----- DATA(2, 2, 2)| y + |- ---- DATA(0, 2, -1) - ---- DATA(2, 0, -1) + 12000 / \ 2000 3000 + + 33 129 53 + - ---- DATA(0, -1, 2) - ---- DATA(0, 2, 2) + ---- DATA(1, 0, 2) + 2000 4000 1000 + + 607 449 161 + - ----- DATA(-1, 0, -1) - ----- DATA(2, -1, -1) - ---- DATA(0, 0, 0) + 12000 12000 4000 + + 21 87 299 + + --- DATA(1, 0, 0) - ---- DATA(0, 1, 0) + ---- DATA(1, 1, 0) + 250 2000 4000 + + 87 299 191 + - ---- DATA(0, 0, 1) + ---- DATA(1, 0, 1) - ---- DATA(0, 1, 1) + 2000 4000 4000 + + 133 41 191 + + ---- DATA(1, 1, 1) - --- DATA(2, 2, -1) + ---- DATA(1, 2, -1) + 2000 750 4000 + + 281 137 349 + + ----- DATA(-1, 2, -1) - ----- DATA(2, 1, -1) + ----- DATA(2, 0, 0) + 12000 12000 12000 + + 17 53 137 + - ---- DATA(2, -1, 0) + ---- DATA(1, 2, 0) - ---- DATA(0, 2, 0) + 3000 1000 4000 + + 29 79 167 + - ---- DATA(-1, 2, 0) + ---- DATA(2, 1, 0) - ----- DATA(2, 2, 0) + 6000 3000 12000 + + 137 79 53 + - ----- DATA(2, -1, 1) + ---- DATA(2, 0, 1) + ----- DATA(-1, 2, 1) + 12000 3000 12000 + + 319 183 79 + + ----- DATA(2, 1, 1) + ---- DATA(1, 2, 1) - ---- DATA(0, 2, 1) + 12000 4000 2000 + + 281 191 + + ----- DATA(-1, -1, 2) - 4/375 DATA(2, 2, 1) + ---- DATA(1, -1, 2) + 12000 4000 + + 167 137 29 + - ----- DATA(2, 0, 2) - ---- DATA(0, 0, 2) - ---- DATA(-1, 0, 2) + 12000 4000 6000 + + 41 183 79 + - --- DATA(2, -1, 2) + ---- DATA(1, 1, 2) - ---- DATA(0, 1, 2) + 750 4000 2000 + + 53 307 + + ----- DATA(-1, 1, 2) + ---- DATA(-1, 2, 2) - 4/375 DATA(2, 1, 2) + 12000 6000 + + 13 49 323 + + --- DATA(1, 2, 2) - ---- DATA(0, -1, 0) + ---- DATA(1, -1, 0) + 500 2000 4000 + + 437 691 97 + - ---- DATA(-1, 0, 0) - ----- DATA(-1, 1, 0) - ---- DATA(-1, -1, 1) + 6000 12000 3000 + + 107 141 691 + - ---- DATA(0, -1, 1) + ---- DATA(1, -1, 1) - ----- DATA(-1, 0, 1) + 4000 2000 12000 + + 17 49 323 + - --- DATA(-1, 1, 1) - ---- DATA(0, 0, -1) + ---- DATA(1, 0, -1) + 375 2000 4000 + + 97 107 141 + - ---- DATA(-1, 1, -1) - ---- DATA(0, 1, -1) + ---- DATA(1, 1, -1) + 3000 4000 2000 + + 607 47 39 + - ----- DATA(-1, -1, 0) - ---- DATA(-1, -1, -1) - ---- DATA(0, -1, -1) + 12000 1500 4000 + + 157 539 \ / + + ---- DATA(1, -1, -1) - ----- DATA(2, 2, 2)| x + |1/40 DATA(0, 2, -1) + 2000 12000 / \ + + + 1/40 DATA(2, 0, -1) + 1/80 DATA(0, -1, 2) - 1/160 DATA(0, 2, 2) + + 11 + + 7/160 DATA(-1, 0, -1) + 1/32 DATA(2, -1, -1) - --- DATA(0, 0, 0) + 160 + + - 1/16 DATA(1, 0, 0) - 1/16 DATA(0, 1, 0) - 9/160 DATA(1, 1, 0) + + + 1/40 DATA(0, 0, 1) + 1/32 DATA(1, 0, 1) + 1/32 DATA(0, 1, 1) + + + 3/80 DATA(1, 1, 1) + 1/80 DATA(2, 2, -1) + 3/160 DATA(1, 2, -1) + + + 1/32 DATA(-1, 2, -1) + 3/160 DATA(2, 1, -1) - 9/160 DATA(2, 0, 0) + + - 1/16 DATA(2, -1, 0) - 1/20 DATA(1, 2, 0) - 9/160 DATA(0, 2, 0) + + - 1/16 DATA(-1, 2, 0) - 1/20 DATA(2, 1, 0) - 7/160 DATA(2, 2, 0) + + + 1/32 DATA(2, -1, 1) + 3/80 DATA(2, 0, 1) + 1/32 DATA(-1, 2, 1) + + + 7/160 DATA(2, 1, 1) + 7/160 DATA(1, 2, 1) + 3/80 DATA(0, 2, 1) + + + 3/160 DATA(-1, -1, 2) + 1/20 DATA(2, 2, 1) + 1/160 DATA(1, -1, 2) + + - 1/160 DATA(2, 0, 2) + 1/160 DATA(0, 0, 2) + 1/80 DATA(-1, 0, 2) + + - 1/160 DATA(1, 1, 2) + 1/160 DATA(-1, 1, 2) - 1/80 DATA(2, 1, 2) + + 11 + - 1/80 DATA(1, 2, 2) - 3/40 DATA(0, -1, 0) - --- DATA(1, -1, 0) + 160 + + 11 + - 3/40 DATA(-1, 0, 0) - --- DATA(-1, 1, 0) + 1/80 DATA(-1, -1, 1) + 160 + + + 3/160 DATA(0, -1, 1) + 1/40 DATA(1, -1, 1) + 3/160 DATA(-1, 0, 1) + + + 1/40 DATA(-1, 1, 1) + 3/80 DATA(0, 0, -1) + 1/32 DATA(1, 0, -1) + + + 3/80 DATA(-1, 1, -1) + 1/32 DATA(0, 1, -1) + 1/40 DATA(1, 1, -1) + + 13 + - --- DATA(-1, -1, 0) + 1/20 DATA(-1, -1, -1) + 7/160 DATA(0, -1, -1) + 160 + + \ 2 + + 3/80 DATA(1, -1, -1) - 3/160 DATA(2, 2, 2)| z + (- 1/96 DATA(0, 2, -1) + / + + - 1/96 DATA(2, 0, -1) + 1/96 DATA(0, -1, 2) + 1/96 DATA(0, 2, 2) + + + 1/96 DATA(1, 0, 2) - 1/96 DATA(-1, 0, -1) - 1/96 DATA(2, -1, -1) + + + 1/32 DATA(0, 0, 0) + 1/32 DATA(1, 0, 0) + 1/32 DATA(0, 1, 0) + + + 1/32 DATA(1, 1, 0) - 1/32 DATA(0, 0, 1) - 1/32 DATA(1, 0, 1) + + - 1/32 DATA(0, 1, 1) - 1/32 DATA(1, 1, 1) - 1/96 DATA(2, 2, -1) + + - 1/96 DATA(1, 2, -1) - 1/96 DATA(-1, 2, -1) - 1/96 DATA(2, 1, -1) + + + 1/32 DATA(2, 0, 0) + 1/32 DATA(2, -1, 0) + 1/32 DATA(1, 2, 0) + + + 1/32 DATA(0, 2, 0) + 1/32 DATA(-1, 2, 0) + 1/32 DATA(2, 1, 0) + + + 1/32 DATA(2, 2, 0) - 1/32 DATA(2, -1, 1) - 1/32 DATA(2, 0, 1) + + - 1/32 DATA(-1, 2, 1) - 1/32 DATA(2, 1, 1) - 1/32 DATA(1, 2, 1) + + - 1/32 DATA(0, 2, 1) + 1/96 DATA(-1, -1, 2) - 1/32 DATA(2, 2, 1) + + + 1/96 DATA(1, -1, 2) + 1/96 DATA(2, 0, 2) + 1/96 DATA(0, 0, 2) + + + 1/96 DATA(-1, 0, 2) + 1/96 DATA(2, -1, 2) + 1/96 DATA(1, 1, 2) + + + 1/96 DATA(0, 1, 2) + 1/96 DATA(-1, 1, 2) + 1/96 DATA(-1, 2, 2) + + + 1/96 DATA(2, 1, 2) + 1/96 DATA(1, 2, 2) + 1/32 DATA(0, -1, 0) + + + 1/32 DATA(1, -1, 0) + 1/32 DATA(-1, 0, 0) + 1/32 DATA(-1, 1, 0) + + - 1/32 DATA(-1, -1, 1) - 1/32 DATA(0, -1, 1) - 1/32 DATA(1, -1, 1) + + - 1/32 DATA(-1, 0, 1) - 1/32 DATA(-1, 1, 1) - 1/96 DATA(0, 0, -1) + + - 1/96 DATA(1, 0, -1) - 1/96 DATA(-1, 1, -1) - 1/96 DATA(0, 1, -1) + + - 1/96 DATA(1, 1, -1) + 1/32 DATA(-1, -1, 0) - 1/96 DATA(-1, -1, -1) + + 3 + - 1/96 DATA(0, -1, -1) - 1/96 DATA(1, -1, -1) + 1/96 DATA(2, 2, 2)) z + ( + + 1/96 DATA(0, 2, -1) + 1/32 DATA(2, 0, -1) - 1/96 DATA(0, -1, 2) + + + 1/96 DATA(0, 2, 2) + 1/32 DATA(1, 0, 2) + 1/32 DATA(-1, 0, -1) + + - 1/96 DATA(2, -1, -1) + 1/32 DATA(0, 0, 0) + 1/32 DATA(1, 0, 0) + + - 1/32 DATA(0, 1, 0) - 1/32 DATA(1, 1, 0) + 1/32 DATA(0, 0, 1) + + + 1/32 DATA(1, 0, 1) - 1/32 DATA(0, 1, 1) - 1/32 DATA(1, 1, 1) + + + 1/96 DATA(2, 2, -1) + 1/96 DATA(1, 2, -1) + 1/96 DATA(-1, 2, -1) + + - 1/32 DATA(2, 1, -1) + 1/32 DATA(2, 0, 0) - 1/96 DATA(2, -1, 0) + + + 1/96 DATA(1, 2, 0) + 1/96 DATA(0, 2, 0) + 1/96 DATA(-1, 2, 0) + + - 1/32 DATA(2, 1, 0) + 1/96 DATA(2, 2, 0) - 1/96 DATA(2, -1, 1) + + + 1/32 DATA(2, 0, 1) + 1/96 DATA(-1, 2, 1) - 1/32 DATA(2, 1, 1) + + + 1/96 DATA(1, 2, 1) + 1/96 DATA(0, 2, 1) - 1/96 DATA(-1, -1, 2) + + + 1/96 DATA(2, 2, 1) - 1/96 DATA(1, -1, 2) + 1/32 DATA(2, 0, 2) + + + 1/32 DATA(0, 0, 2) + 1/32 DATA(-1, 0, 2) - 1/96 DATA(2, -1, 2) + + - 1/32 DATA(1, 1, 2) - 1/32 DATA(0, 1, 2) - 1/32 DATA(-1, 1, 2) + + + 1/96 DATA(-1, 2, 2) - 1/32 DATA(2, 1, 2) + 1/96 DATA(1, 2, 2) + + - 1/96 DATA(0, -1, 0) - 1/96 DATA(1, -1, 0) + 1/32 DATA(-1, 0, 0) + + - 1/32 DATA(-1, 1, 0) - 1/96 DATA(-1, -1, 1) - 1/96 DATA(0, -1, 1) + + - 1/96 DATA(1, -1, 1) + 1/32 DATA(-1, 0, 1) - 1/32 DATA(-1, 1, 1) + + + 1/32 DATA(0, 0, -1) + 1/32 DATA(1, 0, -1) - 1/32 DATA(-1, 1, -1) + + - 1/32 DATA(0, 1, -1) - 1/32 DATA(1, 1, -1) - 1/96 DATA(-1, -1, 0) + + - 1/96 DATA(-1, -1, -1) - 1/96 DATA(0, -1, -1) - 1/96 DATA(1, -1, -1) + + 3 / 29 29 + + 1/96 DATA(2, 2, 2)) y + |- ---- DATA(0, 2, -1) - ---- DATA(2, 0, -1) + \ 6000 6000 + + 17 167 79 + - ---- DATA(0, -1, 2) - ----- DATA(0, 2, 2) + ---- DATA(1, 0, 2) + 3000 12000 3000 + + 607 281 161 + - ----- DATA(-1, 0, -1) + ----- DATA(2, -1, -1) - ---- DATA(0, 0, 0) + 12000 12000 4000 + + 87 87 191 + - ---- DATA(1, 0, 0) - ---- DATA(0, 1, 0) - ---- DATA(1, 1, 0) + 2000 2000 4000 + + 21 299 299 + + --- DATA(0, 0, 1) + ---- DATA(1, 0, 1) + ---- DATA(0, 1, 1) + 250 4000 4000 + + 133 307 53 + + ---- DATA(1, 1, 1) + ---- DATA(2, 2, -1) + ----- DATA(1, 2, -1) + 2000 6000 12000 + + 281 53 137 + + ----- DATA(-1, 2, -1) + ----- DATA(2, 1, -1) - ---- DATA(2, 0, 0) + 12000 12000 4000 + + 33 79 137 + - ---- DATA(2, -1, 0) - ---- DATA(1, 2, 0) - ---- DATA(0, 2, 0) + 2000 2000 4000 + + 33 79 129 + - ---- DATA(-1, 2, 0) - ---- DATA(2, 1, 0) - ---- DATA(2, 2, 0) + 2000 2000 4000 + + 191 53 191 + + ---- DATA(2, -1, 1) + ---- DATA(2, 0, 1) + ---- DATA(-1, 2, 1) + 4000 1000 4000 + + 183 183 53 + + ---- DATA(2, 1, 1) + ---- DATA(1, 2, 1) + ---- DATA(0, 2, 1) + 4000 4000 1000 + + 449 13 137 + - ----- DATA(-1, -1, 2) + --- DATA(2, 2, 1) - ----- DATA(1, -1, 2) + 12000 500 12000 + + 167 349 17 + - ----- DATA(2, 0, 2) + ----- DATA(0, 0, 2) - ---- DATA(-1, 0, 2) + 12000 12000 3000 + + 41 319 79 + - --- DATA(2, -1, 2) + ----- DATA(1, 1, 2) + ---- DATA(0, 1, 2) + 750 12000 3000 + + 137 41 + - ----- DATA(-1, 1, 2) - --- DATA(-1, 2, 2) - 4/375 DATA(2, 1, 2) + 12000 750 + + 49 107 + - 4/375 DATA(1, 2, 2) - ---- DATA(0, -1, 0) - ---- DATA(1, -1, 0) + 2000 4000 + + 49 107 157 + - ---- DATA(-1, 0, 0) - ---- DATA(-1, 1, 0) + ---- DATA(-1, -1, 1) + 2000 4000 2000 + + 323 141 323 + + ---- DATA(0, -1, 1) + ---- DATA(1, -1, 1) + ---- DATA(-1, 0, 1) + 4000 2000 4000 + + 141 437 691 + + ---- DATA(-1, 1, 1) - ---- DATA(0, 0, -1) - ----- DATA(1, 0, -1) + 2000 6000 12000 + + 97 691 17 + - ---- DATA(-1, 1, -1) - ----- DATA(0, 1, -1) - --- DATA(1, 1, -1) + 3000 12000 375 + + 39 47 607 + - ---- DATA(-1, -1, 0) - ---- DATA(-1, -1, -1) - ----- DATA(0, -1, -1) + 4000 1500 12000 + + 97 539 \ / + - ---- DATA(1, -1, -1) - ----- DATA(2, 2, 2)| z + |9/1000 DATA(0, 2, -1) + 3000 12000 / \ + + + 9/1000 DATA(2, 0, -1) + 9/1000 DATA(0, -1, 2) - 9/1000 DATA(0, 2, 2) + + 27 + - 3/1000 DATA(1, 0, 2) - 9/1000 DATA(-1, 0, -1) + ---- DATA(2, -1, -1) + 1000 + + - 1/1000 DATA(0, 0, 0) + 1/1000 DATA(1, 0, 0) + 1/1000 DATA(0, 1, 0) + + - 1/1000 DATA(1, 1, 0) + 1/1000 DATA(0, 0, 1) - 1/1000 DATA(1, 0, 1) + + 27 + - 1/1000 DATA(0, 1, 1) + 1/1000 DATA(1, 1, 1) - ---- DATA(2, 2, -1) + 1000 + + 27 + - 9/1000 DATA(1, 2, -1) + ---- DATA(-1, 2, -1) - 9/1000 DATA(2, 1, -1) + 1000 + + + 3/1000 DATA(2, 0, 0) + 9/1000 DATA(2, -1, 0) - 3/1000 DATA(1, 2, 0) + + + 3/1000 DATA(0, 2, 0) + 9/1000 DATA(-1, 2, 0) - 3/1000 DATA(2, 1, 0) + + - 9/1000 DATA(2, 2, 0) - 9/1000 DATA(2, -1, 1) - 3/1000 DATA(2, 0, 1) + + - 9/1000 DATA(-1, 2, 1) + 3/1000 DATA(2, 1, 1) + 3/1000 DATA(1, 2, 1) + + 27 + - 3/1000 DATA(0, 2, 1) + ---- DATA(-1, -1, 2) + 9/1000 DATA(2, 2, 1) + 1000 + + - 9/1000 DATA(1, -1, 2) - 9/1000 DATA(2, 0, 2) + 3/1000 DATA(0, 0, 2) + + 27 + + 9/1000 DATA(-1, 0, 2) - ---- DATA(2, -1, 2) + 3/1000 DATA(1, 1, 2) + 1000 + + 27 + - 3/1000 DATA(0, 1, 2) - 9/1000 DATA(-1, 1, 2) - ---- DATA(-1, 2, 2) + 1000 + + + 9/1000 DATA(2, 1, 2) + 9/1000 DATA(1, 2, 2) - 3/1000 DATA(0, -1, 0) + + + 3/1000 DATA(1, -1, 0) - 3/1000 DATA(-1, 0, 0) + 3/1000 DATA(-1, 1, 0) + + + 9/1000 DATA(-1, -1, 1) + 3/1000 DATA(0, -1, 1) - 3/1000 DATA(1, -1, 1) + + + 3/1000 DATA(-1, 0, 1) - 3/1000 DATA(-1, 1, 1) - 3/1000 DATA(0, 0, -1) + + + 3/1000 DATA(1, 0, -1) + 9/1000 DATA(-1, 1, -1) + 3/1000 DATA(0, 1, -1) + + 27 + - 3/1000 DATA(1, 1, -1) - 9/1000 DATA(-1, -1, 0) - ---- DATA(-1, -1, -1) + 1000 + + 27 \ + - 9/1000 DATA(0, -1, -1) + 9/1000 DATA(1, -1, -1) + ---- DATA(2, 2, 2)| x + 1000 / + + y z + +> +# I +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=99223348, alloc=2424388, time=6.67 +bytes used=100293992, alloc=2424388, time=6.74 +bytes used=101294564, alloc=2424388, time=6.80 +bytes used=102360560, alloc=2424388, time=6.87 +bytes used=103375336, alloc=2424388, time=6.94 +bytes used=104447556, alloc=2555436, time=7.01 +bytes used=105482648, alloc=2555436, time=7.08 +bytes used=106482848, alloc=2620960, time=7.15 +bytes used=107532036, alloc=2883056, time=7.22 +bytes used=108565568, alloc=3079628, time=7.29 +bytes used=109574036, alloc=3276200, time=7.35 +bytes used=110586812, alloc=3276200, time=7.40 +bytes used=111598764, alloc=3276200, time=7.46 + 269 3 2 2 2 +[COEFF(-1, -1, -1) = - ---- - 1/96 x - 3/160 x y + 1/20 x - 3/160 y z + 4000 + + 27 147 2 3 147 2 + - ---- x y z + ---- y z - 3/160 y z - 1/96 z + ---- x z + 1/20 z + 1000 2000 2000 + + 2 2 47 147 47 2 47 + + 1/20 y - 3/160 x y - ---- x + ---- x y - ---- y - 3/160 x z - ---- z + 1500 2000 1500 1500 + + 2 3 71 129 2 + - 3/160 x z - 1/96 y , COEFF(0, -1, -1) = ---- + ---- y z + 7/160 y + 2000 2000 + + 2 2 2 + - 1/2000 x z - 9/1000 x y z - 3/160 y z + 3/160 x y + 3/160 x z + + 3 607 13 2 3 607 2 + - 1/96 z - ----- z - --- x - 1/96 y - 1/2000 x y - ----- y - 1/160 x y + 12000 160 12000 + + 2 2 39 3 2 + - 1/160 x z - 3/160 y z - ---- x + 1/32 x + 7/160 z , COEFF(1, -1, -1) + 4000 + + 97 3 37 2 2 + = - ---- - 1/96 z - ---- x y + 3/80 z + 1/160 x y + 9/1000 x y z + 4000 1000 + + 2 111 97 157 2 2 37 + + 3/80 y + ---- y z - ---- z + ---- x + 3/160 x z + 1/80 x - ---- x z + 2000 3000 2000 1000 + + 2 2 3 2 3 2 + - 3/160 y z + 1/160 x z - 1/32 x + 3/160 x y - 1/96 y - 3/160 y z + + 97 3 3 + - ---- y, COEFF(2, -1, -1) = 1/96 x - 9/250 x z - 9/250 x y - 1/96 y + 3000 + + 2 2 2 93 27 449 59 + + 3/160 x + 1/32 z + 3/160 x z + ---- y z + ---- x y z - ----- x - ---- + 2000 1000 12000 1000 + + 2 281 2 2 2 2 + - 3/160 x y + ----- z - 3/160 y z + 3/160 x y - 3/160 y z - 3/160 x z + 12000 + + 2 3 281 3 13 2 + + 1/32 y - 1/96 z + ----- y, COEFF(-1, 0, -1) = - 1/96 x - --- y + 12000 160 + + 39 2 3 2 607 + - ---- y + 7/160 z - 1/96 z - 1/160 x y - ----- z - 1/2000 y z + 4000 12000 + + 2 2 3 71 2 + - 9/1000 x y z + 7/160 x - 3/160 x z + 1/32 y + ---- + 3/160 y z + 2000 + + 607 2 129 2 2 + - ----- x + 3/160 x y + ---- x z - 1/160 y z - 3/160 x z - 1/2000 x y, + 12000 2000 + + 437 469 2 2 49 2 + COEFF(0, 0, -1) = - ---- z + ---- - 1/160 x z + 3/80 z - ---- x - 3/40 x + 6000 4000 2000 + + 3 2 2 3 2 2 + + 1/32 y - 1/160 y z + 1/160 x y + 1/32 x + 3/160 x z - 3/40 y + + 3 2 17 2 + - 1/96 z + 3/160 y z - 7/2000 x z - 7/2000 y z - ---- x y + 1/160 x y + 2000 + + 49 3 3 2 + - 3/1000 x y z - ---- y, COEFF(1, 0, -1) = - 1/96 z + 1/32 y + 3/160 x + 2000 + + 3 2 13 2 691 323 + - 1/250 x y - 1/32 x + 1/160 x y - ---- y z + 1/32 z - ----- z + ---- x + 2000 12000 4000 + + 2 2 2 11 2 107 + + 1/160 x z - 1/160 x y - 1/160 y z + 3/1000 x y z - --- y - ---- y + 160 4000 + + 49 17 2 2 73 + + ---- - --- x z + 3/160 y z + 3/160 x z, COEFF(2, 0, -1) = ---- + 1000 500 4000 + + 27 13 17 2 2 2 2 + - ---- x z + ---- x y - ---- x + 1/40 z - 1/160 x y - 1/16 y + 1/80 x + 1000 1000 3000 + + 3 2 3 2 2 29 + + 1/96 x - 3/160 x z + 1/32 y + 3/160 y z + 3/160 x z - ---- z + 6000 + + 33 19 2 3 2 + - ---- y - ---- y z - 3/160 x y - 1/96 z - 1/160 y z + 9/1000 x y z, + 2000 2000 + + 2 2 37 37 3 + COEFF(-1, 1, -1) = - 3/160 x z + 3/80 x - ---- x y - ---- y z - 1/32 y + 1000 1000 + + 2 2 2 111 2 97 + + 1/160 y z + 3/160 x y + 3/160 y z + ---- x z - 3/160 x z - ---- z + 2000 3000 + + 2 97 3 157 97 2 + + 9/1000 x y z + 1/160 x y - ---- x - 1/96 x + ---- y - ---- + 3/80 z + 3000 2000 4000 + + 3 2 49 3 17 13 + - 1/96 z + 1/80 y , COEFF(0, 1, -1) = ---- + 1/32 x - --- y z - ---- x z + 1000 500 2000 + + 11 2 2 3 2 107 + + 3/1000 x y z - --- x + 3/160 x z - 1/32 y - 1/160 x z - ---- x + 160 4000 + + 2 691 2 2 2 2 + + 1/160 x y - ----- z - 1/160 x y + 3/160 y + 3/160 y z + 1/160 y z + 12000 + + 2 3 323 2 + - 1/250 x y + 1/32 z - 1/96 z + ---- y, COEFF(1, 1, -1) = 1/160 y z + 4000 + + 141 2 2 33 3 2 17 + + ---- y + 3/160 y z + 1/40 y + ---- x y - 1/32 x + 1/40 z - --- z + 2000 2000 375 + + 31 2 2 31 61 + - 3/1000 x y z - ---- x z + 3/160 x z + 1/160 x z - ---- y z - ---- + 1000 1000 4000 + + 3 2 2 2 3 141 + - 1/96 z - 1/160 x y + 1/40 x - 1/160 x y - 1/32 y + ---- x, + 2000 + + 3 3 2 3 137 + COEFF(2, 1, -1) = - 1/96 z - 1/32 y + 1/160 y z + 1/96 x - ----- x + 12000 + + 53 59 2 2 49 2 2 + + ----- z - ---- + 1/32 y - 3/160 x y + ---- x y + 1/160 x + 3/160 y z + 12000 2000 2000 + + 2 191 2 2 2 + + 3/160 z + ---- y + 1/160 x y - 7/250 y z + 3/160 x z - 3/160 x z + 4000 + + 2 2 + - 9/1000 x y z - 9/500 x z, COEFF(-1, 2, -1) = 3/160 x y - 3/160 y z + + 93 59 2 2 2 2 + + ---- x z - ---- - 3/160 x y + 3/160 y z - 3/160 x z + 1/32 z + 2000 1000 + + 281 449 3 27 3 3 + + ----- z - ----- y - 1/96 z + ---- x y z + 1/96 y - 9/250 y z - 1/96 x + 12000 12000 1000 + + 2 281 2 2 + + 3/160 y + ----- x - 9/250 x y + 1/32 x - 3/160 x z , COEFF(0, 2, -1) + 12000 + + 27 2 73 2 13 2 + = - ---- y z + 3/160 y z + ---- - 3/160 x y + ---- x y + 1/80 y + 1000 4000 1000 + + 29 3 17 2 2 + - ---- z - 1/96 z - ---- y + 9/1000 x y z - 1/160 x z - 1/16 x + 6000 3000 + + 2 2 2 3 2 3 + - 3/160 y z + 1/40 z - 1/160 x y + 1/32 x + 3/160 x z + 1/96 y + + 19 33 2 2 2 + - ---- x z - ---- x, COEFF(1, 2, -1) = 1/160 x z + 3/160 z - 3/160 y z + 2000 2000 + + 2 2 2 3 3 191 + + 3/160 y z + 1/32 x - 7/250 x z + 1/160 y - 1/32 x + 1/96 y + ---- x + 4000 + + 2 59 2 49 137 + + 3/160 x z - ---- - 9/500 y z - 3/160 x y + ---- x y - ----- y + 2000 2000 12000 + + 2 3 53 59 + + 1/160 x y - 1/96 z - 9/1000 x y z + ----- z, COEFF(2, 2, -1) = - ---- + 12000 4000 + + 2 41 3 307 + - 9/1000 y z + 1/80 z - --- x + 1/96 x - 3/2000 x y + ---- z + 750 6000 + + 2 2 27 3 2 3 + + 3/160 x y - 3/160 y z - ---- x y z - 1/96 z - 3/160 x z + 1/96 y + 1000 + + 41 2 2 2 + - 9/1000 x z - --- y + 3/160 x z + 3/160 x y + 3/160 y z , + 750 + + 129 2 2 2 + COEFF(-1, -1, 0) = ---- x y - 1/160 x z - 1/160 y z + 3/160 x z + 2000 + + 2 2 39 2 3 + - 3/160 x y - 1/2000 y z - 3/160 x y - ---- z + 3/160 y z + 1/32 z + 4000 + + 71 3 2 607 2 607 + + ---- - 1/96 y + 7/160 y - ----- y + 7/160 x - 1/2000 x z - ----- x + 2000 12000 12000 + + 13 2 3 2 + - 9/1000 x y z - --- z - 1/96 x , COEFF(0, -1, 0) = - 1/160 y z + 160 + + 2 2 17 + - 3/1000 x y z - 1/160 x y + 1/160 x z - 7/2000 y z - ---- x z + 2000 + + 2 49 2 3 2 2 3 + + 1/160 x z - ---- x + 3/80 y - 1/96 y - 3/40 x - 3/40 z + 1/32 z + 2000 + + 469 49 2 437 2 3 + + ---- - ---- z + 3/160 x y - ---- y + 3/160 y z - 7/2000 x y + 1/32 x , + 4000 2000 6000 + + 3 2 323 2 691 + COEFF(1, -1, 0) = - 1/32 x + 3/160 y z + ---- x + 3/160 x y - ----- y + 4000 12000 + + 3 107 17 3 2 11 2 2 + - 1/96 y - ---- z - --- x y + 1/32 z - 1/160 x z - --- z - 1/160 y z + 4000 500 160 + + 2 13 49 2 + + 3/160 x + 3/1000 x y z - ---- y z + ---- - 1/250 x z + 1/160 x y + 2000 1000 + + 2 2 27 19 + + 1/160 x z + 1/32 y , COEFF(2, -1, 0) = - ---- x y - ---- y z + 1000 2000 + + 2 73 2 2 13 3 + - 1/160 x z + ---- + 3/160 y z - 1/160 y z + ---- x z + 1/96 x + 4000 1000 + + 2 33 2 2 2 + - 3/160 x y - ---- z + 9/1000 x y z - 1/16 z - 3/160 x z + 1/80 x + 2000 + + 17 3 2 29 2 3 + - ---- x - 1/96 y + 3/160 x y - ---- y + 1/40 y + 1/32 z , + 3000 6000 + + 2 2 17 + COEFF(-1, 0, 0) = 1/160 y z - 1/160 x y - ---- y z - 7/2000 x y + 2000 + + 3 2 49 2 3 + - 3/1000 x y z - 1/96 x - 1/160 x z - ---- z + 3/160 x z + 1/32 y + 2000 + + 2 49 2 3 437 + + 1/160 y z - ---- y + 3/160 x y + 1/32 z - ---- x - 7/2000 x z + 2000 6000 + + 2 2 469 2 177 + - 3/40 y - 3/40 z + ---- + 3/80 x , COEFF(0, 0, 0) = ---- - 1/1000 x y z + 4000 1000 + + 2 3 19 11 2 11 2 2 3 + + 1/160 y z + 1/32 x - ---- x z - --- z - --- x + 1/160 y z + 1/32 y + 2000 160 160 + + 19 161 2 2 19 2 + - ---- x y - ---- z + 1/160 x y + 1/160 x y - ---- y z + 1/160 x z + 2000 4000 2000 + + 3 11 2 161 161 2 + + 1/32 z - --- y - ---- y - ---- x + 1/160 x z , COEFF(1, 0, 0) = + 160 4000 4000 + + 2 21 21 3 2 87 + 1/1000 x y z + 1/160 x z - ---- y z + --- x - 1/32 x - 1/16 y - ---- z + 2000 250 2000 + + 2 2 2 3 3 + - 1/160 x y + 1/160 x y + 1/160 y z - 3/1000 x y + 1/32 z + 1/32 y + + 87 397 2 2 2 2 + - ---- y + ---- - 1/16 z + 1/160 y z - 3/1000 x z - 1/160 x z + 1/40 x + 2000 4000 + + 2 23 3 2 + , COEFF(2, 0, 0) = 2/125 x y + 1/160 y z - ---- y z + 1/32 z + 1/160 x + 2000 + + 2 2 2 3 2 + - 1/160 x y - 9/160 y - 3/160 x z + 1/96 x - 9/160 z + 3/1000 x y z + + 143 2 137 137 2 3 + + ---- + 1/160 y z - ---- z - ---- y - 3/160 x y + 2/125 x z + 1/32 y + 2000 4000 4000 + + 349 2 3 691 + + ----- x - 1/160 x z, COEFF(-1, 1, 0) = 3/1000 x y z - 1/32 y - ----- x + 12000 12000 + + 2 2 2 2 49 17 + - 1/160 y z + 1/32 x - 1/160 x z + 3/160 y + ---- - --- x y + 1000 500 + + 2 323 2 13 3 2 + + 1/160 y z + ---- y + 3/160 x z - ---- x z - 1/96 x + 3/160 x y + 4000 2000 + + 11 2 2 107 3 + - --- z + 1/160 x y - ---- z - 1/250 y z + 1/32 z , COEFF(0, 1, 0) = + 160 4000 + + 2 397 2 87 + - 3/1000 x y - 1/160 y z + ---- + 1/1000 x y z + 1/160 y z - ---- x + 4000 2000 + + 2 87 2 2 2 + + 1/160 x z - ---- z - 3/1000 y z + 1/160 x y - 1/160 x y - 1/16 z + 2000 + + 21 3 2 2 21 3 3 + - ---- x z + 1/32 z + 1/160 x z + 1/40 y + --- y - 1/32 y + 1/32 x + 2000 250 + + 2 2 3 2 2 + - 1/16 x , COEFF(1, 1, 0) = 1/160 y z - 1/32 y - 1/160 y z - 1/160 x y + + 31 299 299 191 2 3 + + ---- x y - 1/500 y z + ---- y + ---- x - ---- z + 1/32 y - 1/32 x + 2000 4000 4000 4000 + + 2 2 3 2 + - 1/160 x z - 1/500 x z - 1/1000 x y z + 1/32 x + 1/32 z - 1/160 x y + + 2 2 49 2 2 + - 9/160 z + 1/160 x z + ----, COEFF(2, 1, 0) = 1/160 x y - 3/160 x z + 2000 + + 2 79 53 43 2 + + 1/160 y z + ---- x + ---- y + ---- x y - 3/1000 x y z - 1/160 x z + 3000 1000 2000 + + 3 2 2 3 3 79 + - 1/32 y - 3/160 x y - 1/20 z + 1/96 x + 1/32 z - ---- z - 1/1000 y z + 2000 + + 49 2 19 2 2 + + ---- + 3/80 y + ---- x z - 1/160 y z , COEFF(-1, 2, 0) = - 1/160 y z + 4000 1000 + + 2 2 3 3 2 3 29 + + 1/80 y + 3/160 x y - 1/96 x + 1/96 y - 1/16 z + 1/32 z - ---- x + 6000 + + 73 2 19 33 13 + + ---- - 3/160 x y + 9/1000 x y z - ---- x z - ---- z + ---- y z + 4000 2000 2000 1000 + + 2 2 27 2 2 17 + + 1/40 x + 3/160 x z - ---- x y - 3/160 y z - 1/160 x z - ---- y, + 1000 3000 + + 2 349 143 2 23 + COEFF(0, 2, 0) = - 3/160 x y + ----- y + ---- - 9/160 z - ---- x z + 12000 2000 2000 + + 2 2 137 2 3 + - 3/160 y z + 1/160 x z - ---- z + 2/125 y z - 9/160 x + 1/32 x + 4000 + + 2 3 2 + + 3/1000 x y z - 1/160 y z + 1/96 y - 1/160 x y + 2/125 x y + + 2 2 137 3 3 + + 1/160 x z + 1/160 y - ---- x + 1/32 z , COEFF(1, 2, 0) = - 1/32 x + 4000 + + 3 49 3 43 + + 1/96 y - 1/1000 x z - 3/1000 x y z + ---- + 1/32 z + ---- x y + 4000 2000 + + 2 53 2 2 19 79 + - 1/160 x z + ---- x - 3/160 x y - 1/20 z + ---- y z + ---- y + 1000 1000 3000 + + 2 2 2 79 2 2 + + 1/160 x z + 3/80 x + 1/160 x y - ---- z - 1/160 y z - 3/160 y z , + 2000 + + 2 11 2 11 21 + COEFF(2, 2, 0) = 3/160 x y + --- x z - 1/160 x z + --- y z - ---- x y + 500 500 2000 + + 2 2 3 2 167 + - 1/160 y - 1/160 y z + 1/32 z - 3/160 y z - ----- x - 9/1000 x y z + 12000 + + 2 129 2 3 2 3 + - 7/160 z - ---- z - 1/160 x + 7/250 + 1/96 x + 3/160 x y + 1/96 y + 4000 + + 2 167 2 97 + - 3/160 x z - ----- y, COEFF(-1, -1, 1) = 9/1000 x y z + 1/80 z - ---- x + 12000 3000 + + 37 2 2 37 2 3 + - ---- y z + 1/160 y z + 3/80 x - ---- x z - 3/160 x y - 1/32 z + 1000 1000 + + 3 111 97 2 2 97 + - 1/96 x + ---- x y - ---- + 1/160 x z + 3/160 y z - ---- y + 2000 4000 3000 + + 2 157 3 2 2 + - 3/160 x y + ---- z - 1/96 y + 3/160 x z + 3/80 y , COEFF(0, -1, 1) = + 2000 + + 3 49 3 3 2 323 + - 1/96 y + ---- - 1/32 z + 1/32 x + 1/32 y + 3/1000 x y z + ---- z + 1000 4000 + + 17 107 2 2 2 691 + - --- y z - ---- x + 3/160 y z + 3/160 z + 1/160 y z - ----- y + 500 4000 12000 + + 2 11 2 2 2 13 + - 1/160 x y - --- x + 1/160 x z - 1/160 x z - ---- x y - 1/250 x z + 160 2000 + + 2 2 31 3 + + 3/160 x y, COEFF(1, -1, 1) = 1/160 y z - ---- x y - 1/32 x + 1000 + + 2 2 2 141 33 + - 3/1000 x y z + 1/160 x y + 3/160 x y - 1/160 x z + ---- x + ---- x z + 2000 2000 + + 2 61 17 2 2 31 2 + + 1/40 x - ---- - --- y + 3/160 y z + 1/40 y - ---- y z - 1/160 x z + 4000 375 1000 + + 3 3 2 141 2 + - 1/96 y - 1/32 z + 1/40 z + ---- z, COEFF(2, -1, 1) = 3/160 y z + 2000 + + 2 2 59 2 2 + + 3/160 x y - 7/250 y z - 3/160 x z - ---- - 3/160 x y + 1/160 y z + 2000 + + 3 49 2 137 2 + + 1/96 x + ---- x z + 1/32 z - 9/1000 x y z - ----- x + 3/160 y + 2000 12000 + + 3 3 2 53 2 191 + - 1/32 z - 1/96 y + 1/160 x z + ----- y - 9/500 x y + 1/160 x + ---- z + 12000 4000 + + 17 2 2 49 + , COEFF(-1, 0, 1) = - --- x z + 1/160 y z - 1/250 y z - 1/160 y z + ---- + 500 1000 + + 2 2 2 2 691 13 + + 3/160 x z - 1/160 x y + 3/160 z + 1/160 x z - ----- x - ---- x y + 12000 2000 + + 3 323 11 2 2 3 107 + - 1/32 z + 3/1000 x y z + ---- z - --- y + 3/160 x y + 1/32 y - ---- y + 4000 160 4000 + + 3 2 87 2 + - 1/96 x + 1/32 x , COEFF(0, 0, 1) = - ---- y - 3/1000 y z + 1/160 x y + 2000 + + 21 2 2 2 21 + + --- z + 1/1000 x y z + 1/160 x z + 1/160 y z - 1/160 y z - ---- x y + 250 2000 + + 2 2 3 2 3 397 2 + - 1/16 y - 1/160 x z + 1/32 y + 1/160 x y - 1/32 z + ---- + 1/40 z + 4000 + + 87 3 2 + - ---- x + 1/32 x - 3/1000 x z - 1/16 x , COEFF(1, 0, 1) = - 1/500 y z + 2000 + + 2 2 2 2 49 + - 1/160 y z - 1/160 x y - 1/160 x z + 1/160 y z + ---- - 1/500 x y + 2000 + + 299 2 2 2 3 31 + + ---- x + 1/160 x y - 9/160 y - 1/160 x z - 1/32 z + ---- x z + 4000 2000 + + 3 299 2 3 191 2 + + 1/32 y + ---- z + 1/32 z - 1/1000 x y z - 1/32 x - ---- y + 1/32 x , + 4000 4000 + + 43 2 2 + COEFF(2, 0, 1) = ---- x z - 3/160 x z - 1/160 x y - 3/1000 x y z + 2000 + + 2 53 79 2 2 + - 1/1000 y z - 3/160 x y + ---- z + ---- x - 1/160 y z - 1/20 y + 1000 3000 + + 19 3 2 3 49 2 2 + + ---- x y - 1/32 z + 1/160 x z + 1/32 y + ---- + 3/80 z + 1/160 y z + 1000 4000 + + 3 79 31 17 2 + + 1/96 x - ---- y, COEFF(-1, 1, 1) = - ---- x z - --- x + 1/160 x y + 2000 1000 375 + + 61 2 2 2 2 31 + - ---- + 3/160 x z - 1/160 y z + 3/160 x y + 1/160 x z - ---- x y + 4000 1000 + + 3 141 141 2 2 3 + - 1/96 x + ---- y - 3/1000 x y z + ---- z + 1/40 z + 1/40 y - 1/32 y + 2000 2000 + + 33 3 2 2 + + ---- y z - 1/32 z - 1/160 y z + 1/40 x , COEFF(0, 1, 1) = - 1/500 x z + 2000 + + 2 31 2 2 3 49 2 + - 1/160 y z + ---- y z + 1/32 z - 1/160 x z + 1/32 x + ---- + 1/32 y + 2000 2000 + + 299 2 299 3 + - 1/500 x y + ---- y + 1/160 x y + ---- z - 1/1000 x y z - 1/32 y + 4000 4000 + + 191 2 2 2 2 3 + - ---- x - 1/160 y z - 1/160 x y - 9/160 x + 1/160 x z - 1/32 z , + 4000 + + 29 2 29 2 193 + COEFF(1, 1, 1) = ---- y z - 1/160 x y + ---- x y - 1/160 x z - ---- + 2000 2000 4000 + + 2 29 133 2 2 + - 1/160 x y + ---- x z + ---- z + 1/1000 x y z - 1/160 y z - 1/160 x z + 2000 2000 + + 3 133 2 2 133 3 2 + - 1/32 z + ---- x + 3/80 x + 3/80 z + ---- y - 1/32 x - 1/160 y z + 2000 2000 + + 2 3 37 319 + + 3/80 y - 1/32 y , COEFF(2, 1, 1) = ---- x z + 3/1000 x y z + ----- x + 2000 12000 + + 23 2 2 2 3 183 2 + - --- + 7/160 z - 1/160 y z + 7/160 y + 1/96 x + ---- z - 1/160 y z + 500 4000 + + 3 2 183 37 3 2 + - 1/32 z - 3/160 x z + ---- y + ---- x y - 1/32 y + 1/160 x z + 4000 2000 + + 2 2 2 27 + + 1/160 x y - 3/160 x y - 1/160 x + ---- y z, COEFF(-1, 2, 1) = + 2000 + + 2 59 2 2 + - 9/1000 x y z - 3/160 y z - 9/500 x y - ---- + 1/160 x z + 3/160 x y + 2000 + + 2 2 2 49 191 2 + + 1/32 z - 3/160 x y + 1/160 y + ---- y z + ---- z + 3/160 x z + 2000 4000 + + 3 137 2 2 53 + - 1/32 z - 7/250 x z - ----- y + 1/160 y z + 3/160 x + ----- x + 12000 12000 + + 3 3 2 49 + - 1/96 x + 1/96 y , COEFF(0, 2, 1) = - 3/1000 x y z - 3/160 x y + ---- + 4000 + + 2 2 2 53 2 3 + - 3/160 y z - 1/160 x y - 1/160 x z + ---- z - 1/20 x - 1/32 z + 1000 + + 3 79 79 43 3 2 19 + + 1/32 x + ---- y - ---- x + ---- y z + 1/96 y + 1/160 x z + ---- x y + 3000 2000 2000 1000 + + 2 2 + - 1/1000 x z + 3/80 z + 1/160 y z, COEFF(1, 2, 1) = 3/1000 x y z + + 2 2 2 2 23 37 + - 1/160 x z + 1/160 x y - 3/160 y z - 1/160 y - --- + ---- x y + 500 2000 + + 3 2 2 27 183 2 + + 1/96 y - 1/160 x z + 7/160 z + ---- x z + ---- z + 1/160 y z + 2000 4000 + + 3 2 319 3 2 183 37 + - 1/32 z + 7/160 x + ----- y - 1/32 x - 3/160 x y + ---- x + ---- y z, + 12000 4000 2000 + + 2 2 2 67 39 + COEFF(2, 2, 1) = 3/160 x y - 3/160 y z + 1/160 x z - ---- - ---- x y + 4000 2000 + + 2 3 2 2 2 + + 9/1000 x y z + 1/160 y z + 1/96 y - 1/80 y + 1/20 z - 3/160 x z + + 13 3 3 31 2 2 + + --- z + 1/96 x - 1/32 z + ---- x z - 4/375 y - 1/80 x + 3/160 x y + 500 2000 + + 31 2 281 + - 4/375 x + ---- y z, COEFF(-1, -1, 2) = - 3/160 y z + ----- x + 2000 12000 + + 2 2 3 3 449 27 + - 3/160 x z + 3/160 y z - 1/96 y - 1/96 x - ----- z + ---- x y z + 12000 1000 + + 2 2 2 93 2 2 + + 1/32 y - 3/160 x y - 3/160 x y + ---- x y + 3/160 z + 3/160 x z + 2000 + + 3 281 2 59 + + 1/96 z - 9/250 x z + ----- y + 1/32 x - 9/250 y z - ----, + 12000 1000 + + 2 2 3 17 2 + COEFF(0, -1, 2) = 1/80 z - 1/16 x - 1/96 y - ---- z + 3/160 x y + 3000 + + 13 2 33 19 2 + + ---- x z + 9/1000 x y z + 1/40 y - ---- x - ---- x y - 3/160 y z + 1000 2000 2000 + + 2 3 2 73 2 3 + - 1/160 x y + 1/32 x - 3/160 x z + ---- - 1/160 x z + 1/96 z + 4000 + + 2 29 27 2 191 + + 3/160 y z - ---- y - ---- y z, COEFF(1, -1, 2) = 3/160 x y + ---- x + 6000 1000 4000 + + 59 3 2 3 2 49 53 + - ---- - 1/32 x + 1/32 x - 1/96 y + 3/160 y + ---- x z + ----- y + 2000 2000 12000 + + 2 3 137 2 + + 1/160 x y + 1/96 z - 7/250 x y - ----- z - 3/160 x z - 9/1000 x y z + 12000 + + 2 2 2 2 + - 9/500 y z - 3/160 y z + 3/160 y z + 1/160 z + 1/160 x z , + + 3 41 2 27 2 + COEFF(2, -1, 2) = 1/96 z - --- z + 1/80 y - ---- x y z - 3/160 x y + 750 1000 + + 41 2 307 2 + - 3/2000 x z - --- x + 3/160 x z + ---- y - 9/1000 y z - 3/160 y z + 750 6000 + + 2 3 2 59 2 3 + + 3/160 y z + 1/96 x + 3/160 x z - ---- + 3/160 x y - 1/96 y + 4000 + + 17 19 3 + - 9/1000 x y, COEFF(-1, 0, 2) = 9/1000 x y z - ---- z - ---- x y - 1/96 x + 3000 2000 + + 2 2 2 2 2 33 + - 1/160 y z - 3/160 x z - 1/160 x y - 1/16 y + 3/160 x z - ---- y + 2000 + + 13 29 2 3 73 27 2 + + ---- y z - ---- x - 3/160 y z + 1/96 z + ---- - ---- x z + 3/160 x y + 1000 6000 4000 1000 + + 2 3 2 23 2 + + 1/40 x + 1/32 y + 1/80 z , COEFF(0, 0, 2) = - ---- x y - 1/160 y z + 2000 + + 2 137 2 137 2 + + 1/160 x y - ---- x - 3/160 x z - ---- y + 2/125 y z + 1/160 z + 4000 4000 + + 349 3 3 2 3 143 + + ----- z + 1/32 y + 1/32 x - 9/160 y + 3/1000 x y z + 1/96 z + ---- + 12000 2000 + + 2 2 2 2 + - 1/160 x z + 2/125 x z - 3/160 y z - 9/160 x + 1/160 x y , + + 43 53 2 3 2 + COEFF(1, 0, 2) = ---- x z + ---- x - 1/160 y z - 1/32 x + 1/160 x y + 2000 1000 + + 2 2 3 2 2 + - 1/20 y - 3/160 x z + 1/32 y - 1/1000 x y - 3/160 y z + 1/160 x z + + 3 2 19 2 79 49 + + 1/96 z + 3/80 x + ---- y z - 1/160 x y - 3/1000 x y z + ---- z + ---- + 1000 3000 4000 + + 79 2 11 21 + - ---- y, COEFF(2, 0, 2) = 7/250 - 1/160 z + --- y z - ---- x z + 2000 500 2000 + + 2 2 2 3 2 167 + - 1/160 y z - 3/160 y z - 1/160 x y + 1/96 x + 3/160 x z - ----- x + 12000 + + 11 3 2 2 2 + + --- x y + 1/32 y + 3/160 x z - 7/160 y - 9/1000 x y z - 1/160 x + 500 + + 2 167 3 129 2 + - 3/160 x y - ----- z + 1/96 z - ---- y, COEFF(-1, 1, 2) = 3/160 x y + 12000 4000 + + 3 3 2 2 2 + + 1/96 z - 9/1000 x y z - 1/96 x - 3/160 y z - 3/160 x z + 3/160 x + + 2 2 49 2 + + 1/160 z + 1/32 y + ---- y z - 9/500 x z - 7/250 x y + 1/160 y z + 2000 + + 53 2 3 2 137 59 191 + + ----- x + 1/160 x y - 1/32 y + 3/160 x z - ----- z - ---- + ---- y, + 12000 12000 2000 4000 + + 53 2 49 + COEFF(0, 1, 2) = ---- y - 3/160 y z - 3/1000 x y z - 1/1000 x y + ---- + 1000 4000 + + 3 2 3 2 2 2 + + 1/32 x - 1/160 x y + 1/96 z - 3/160 x z + 3/80 y - 1/160 x z + + 2 79 2 3 19 79 2 + - 1/20 x - ---- x + 1/160 x y - 1/32 y + ---- x z + ---- z + 1/160 y z + 2000 1000 3000 + + 43 2 2 2 + + ---- y z, COEFF(1, 1, 2) = - 1/160 x y + 1/160 y z - 1/160 x y + 2000 + + 2 3 2 27 2 2 + - 3/160 x z - 1/32 x + 1/160 x z + ---- x y + 7/160 y - 3/160 y z + 2000 + + 183 2 3 183 319 3 + + ---- x - 1/160 z - 1/32 y + ---- y + ----- z + 1/96 z + 3/1000 x y z + 4000 4000 12000 + + 23 37 2 37 67 + - --- + ---- x z + 7/160 x + ---- y z, COEFF(2, 1, 2) = - ---- + 500 2000 2000 4000 + + 2 2 2 13 31 2 + - 3/160 x y - 1/80 z + 1/160 y z + --- y + ---- x y + 1/160 x y + 500 2000 + + 2 3 2 2 3 + + 1/20 y + 1/96 z - 3/160 y z + 3/160 x z - 4/375 x + 1/96 x + + 3 2 2 39 + - 1/32 y + 3/160 x z - 4/375 z - 1/80 x + 9/1000 x y z - ---- x z + 2000 + + 31 3 59 2 + + ---- y z, COEFF(-1, 2, 2) = - 3/2000 y z + 1/96 z - ---- - 3/160 x y + 2000 4000 + + 3 2 2 2 2 + - 1/96 x - 9/1000 x z - 3/160 x z + 3/160 y z + 3/160 y z + 3/160 x z + + 2 307 41 3 41 2 + + 1/80 x + ---- x - --- y + 1/96 y - 9/1000 x y - --- z + 3/160 x y + 6000 750 750 + + 27 2 2 21 + - ---- x y z, COEFF(0, 2, 2) = - 1/160 z - 1/160 x z - ---- y z + 1000 2000 + + 3 2 11 2 2 + + 1/96 z + 7/250 - 7/160 x + --- x z + 3/160 y z + 3/160 y z + 500 + + 2 2 2 11 129 3 + - 3/160 x y - 1/160 x y - 3/160 x z + --- x y - ---- x + 1/32 x + 500 4000 + + 3 167 167 2 + + 1/96 y - ----- y - ----- z - 1/160 y - 9/1000 x y z, COEFF(1, 2, 2) = + 12000 12000 + + 31 2 39 2 3 2 + ---- x z - 3/160 x y - ---- y z - 3/160 x z - 1/32 x + 1/160 x z + 2000 2000 + + 13 2 67 2 2 2 3 + + --- x + 3/160 y z - ---- + 3/160 y z - 1/80 z + 1/160 x y + 1/96 z + 500 4000 + + 3 31 2 2 + + 1/96 y - 4/375 z + ---- x y + 1/20 x - 1/80 y + 9/1000 x y z + 2000 + + 57 2 3 2 + - 4/375 y, COEFF(2, 2, 2) = - ---- x z + 3/160 x y + 1/96 x - 3/160 z + 2000 + + 77 2 3 57 57 539 2 + + ---- + 3/160 x z + 1/96 y - ---- y z - ---- x y - ----- x - 3/160 y + 2000 2000 2000 12000 + + 2 539 2 3 2 539 + + 3/160 x z - ----- y + 3/160 x y + 1/96 z + 3/160 y z - ----- z + 12000 12000 + + 2 27 2 + - 3/160 x + ---- x y z + 3/160 y z] + 1000 + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-I.compute.c"); +bytes used=112599024, alloc=3276200, time=7.52 +bytes used=113599216, alloc=3276200, time=7.58 +bytes used=114599368, alloc=3276200, time=7.65 +bytes used=115600012, alloc=3276200, time=7.72 +bytes used=116600420, alloc=3276200, time=7.80 +bytes used=117600596, alloc=3276200, time=7.93 +bytes used=118600792, alloc=3276200, time=8.00 +bytes used=119601080, alloc=3276200, time=8.09 +bytes used=120601296, alloc=3276200, time=8.17 +bytes used=121601456, alloc=3276200, time=8.24 +bytes used=122678980, alloc=3276200, time=8.31 +bytes used=123695576, alloc=3276200, time=8.37 +bytes used=124707888, alloc=3276200, time=8.43 +bytes used=125716244, alloc=3276200, time=8.49 +bytes used=126720556, alloc=3276200, time=8.56 +bytes used=127722684, alloc=3276200, time=8.61 +bytes used=128797096, alloc=3276200, time=8.67 +bytes used=129821484, alloc=3276200, time=8.73 +bytes used=130866004, alloc=3276200, time=8.80 +bytes used=131891576, 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time=22.16 +bytes used=255660312, alloc=3669344, time=22.22 +bytes used=256660724, alloc=3669344, time=22.29 +bytes used=257660900, alloc=3669344, time=22.35 +bytes used=258661176, alloc=3669344, time=22.42 +bytes used=259661404, alloc=3669344, time=22.58 +bytes used=260661664, alloc=3669344, time=22.90 +bytes used=261663204, alloc=3669344, time=23.01 +bytes used=262663356, alloc=3669344, time=23.10 +bytes used=263663516, alloc=3669344, time=23.19 +bytes used=264663672, alloc=3669344, time=23.28 +bytes used=265663888, alloc=3669344, time=23.38 +bytes used=266664140, alloc=3669344, time=23.47 +bytes used=267664368, alloc=3669344, time=23.94 +bytes used=268665232, alloc=3669344, time=24.32 +bytes used=269665904, alloc=3669344, time=24.48 +bytes used=270666408, alloc=3669344, time=24.53 +bytes used=271666608, alloc=3669344, time=24.65 +bytes used=272666992, alloc=3669344, time=24.77 +bytes used=273667180, alloc=3669344, time=24.90 +> +# d/dx +> simplify( diff(interp_3d_cube_order3_smooth0,x) ); +bytes used=274668316, alloc=3669344, time=24.98 +bytes used=275668480, alloc=3669344, time=25.05 +bytes used=276669456, alloc=3669344, time=25.12 +bytes used=277669672, alloc=3669344, time=25.19 +bytes used=278743076, alloc=3669344, time=25.26 +bytes used=279744244, alloc=3669344, time=25.33 +bytes used=280744584, alloc=3669344, time=25.41 +bytes used=281744824, alloc=3669344, time=25.48 +bytes used=282745060, alloc=3669344, time=25.55 +bytes used=283745348, alloc=3669344, time=25.62 + 33 17 33 +- ---- DATA(0, 2, -1) - ---- DATA(2, 0, -1) - ---- DATA(0, -1, 2) + 2000 3000 2000 + + 129 53 607 + - ---- DATA(0, 2, 2) + ---- DATA(1, 0, 2) - ----- DATA(-1, 0, -1) + 4000 1000 12000 + + 449 161 21 + - ----- DATA(2, -1, -1) - ---- DATA(0, 0, 0) + --- DATA(1, 0, 0) + 12000 4000 250 + + 87 299 87 + - ---- DATA(0, 1, 0) + ---- DATA(1, 1, 0) - ---- DATA(0, 0, 1) + 2000 4000 2000 + + 299 191 133 + + ---- DATA(1, 0, 1) - ---- DATA(0, 1, 1) + ---- DATA(1, 1, 1) + 4000 4000 2000 + + 41 191 281 + - --- DATA(2, 2, -1) + ---- DATA(1, 2, -1) + ----- DATA(-1, 2, -1) + 750 4000 12000 + + 137 349 17 + - ----- DATA(2, 1, -1) + ----- DATA(2, 0, 0) - ---- DATA(2, -1, 0) + 12000 12000 3000 + + 53 137 29 + + ---- DATA(1, 2, 0) - ---- DATA(0, 2, 0) - ---- DATA(-1, 2, 0) + 1000 4000 6000 + + 79 167 137 + + ---- DATA(2, 1, 0) - ----- DATA(2, 2, 0) - ----- DATA(2, -1, 1) + 3000 12000 12000 + + 79 53 319 + + ---- DATA(2, 0, 1) + ----- DATA(-1, 2, 1) + ----- DATA(2, 1, 1) + 3000 12000 12000 + + 183 79 281 + + ---- DATA(1, 2, 1) - ---- DATA(0, 2, 1) + ----- DATA(-1, -1, 2) + 4000 2000 12000 + + 191 167 + - 4/375 DATA(2, 2, 1) + ---- DATA(1, -1, 2) - ----- DATA(2, 0, 2) + 4000 12000 + + 137 29 41 + - ---- DATA(0, 0, 2) - ---- DATA(-1, 0, 2) - --- DATA(2, -1, 2) + 4000 6000 750 + + 183 79 53 + + ---- DATA(1, 1, 2) - ---- DATA(0, 1, 2) + ----- DATA(-1, 1, 2) + 4000 2000 12000 + + 307 13 + + ---- DATA(-1, 2, 2) - 4/375 DATA(2, 1, 2) + --- DATA(1, 2, 2) + 6000 500 + + 49 323 437 + - ---- DATA(0, -1, 0) + ---- DATA(1, -1, 0) - ---- DATA(-1, 0, 0) + 2000 4000 6000 + + 691 97 107 + - ----- DATA(-1, 1, 0) - ---- DATA(-1, -1, 1) - ---- DATA(0, -1, 1) + 12000 3000 4000 + + 141 691 17 + + ---- DATA(1, -1, 1) - ----- DATA(-1, 0, 1) - --- DATA(-1, 1, 1) + 2000 12000 375 + + 49 323 97 + - ---- DATA(0, 0, -1) + ---- DATA(1, 0, -1) - ---- DATA(-1, 1, -1) + 2000 4000 3000 + + 107 141 607 + - ---- DATA(0, 1, -1) + ---- DATA(1, 1, -1) - ----- DATA(-1, -1, 0) + 4000 2000 12000 + + 47 39 157 + - ---- DATA(-1, -1, -1) - ---- DATA(0, -1, -1) + ---- DATA(1, -1, -1) + 1500 4000 2000 + + 539 + - ----- DATA(2, 2, 2) - 1/80 x y DATA(1, 1, 0) + 1/1000 y z DATA(0, 0, 1) + 12000 + + + 3/80 x y DATA(2, 2, 1) - 3/1000 y z DATA(0, 2, 1) + + - 9/1000 y z DATA(0, 2, 2) - 1/80 x y DATA(-1, 0, 0) + + + 1/80 x y DATA(1, 0, 1) + 3/80 x y DATA(0, -1, 0) + + - 9/1000 y z DATA(-1, 0, -1) - 9/1000 y z DATA(2, 2, 0) + + 2 2 + - 3/80 x y DATA(1, 2, 2) - 1/32 x DATA(-1, 2, 2) + 1/32 x DATA(2, 1, 2) + + 2 2 2 + - 3/32 x DATA(1, 2, 2) + 3/32 x DATA(0, -1, 0) - 3/32 x DATA(1, -1, 0) + + 2 2 2 + - 1/32 x DATA(-1, 0, 0) - 1/32 x DATA(-1, 1, 0) + 1/32 x DATA(2, 1, 1) + + 2 2 2 + - 3/32 x DATA(1, 2, 1) + 3/32 x DATA(0, 2, 1) - 1/32 x DATA(-1, -1, 2) + + 2 2 2 + + 1/32 x DATA(2, 2, 1) - 3/32 x DATA(1, -1, 2) + 1/32 x DATA(2, 0, 2) + + 2 2 2 + + 3/32 x DATA(0, 0, 2) - 1/32 x DATA(-1, 0, 2) + 1/32 x DATA(2, -1, 2) + + 2 2 2 + - 3/32 x DATA(1, 1, 2) + 3/32 x DATA(0, 1, 2) - 1/32 x DATA(-1, 1, 2) + + 2 13 + + 3/32 x DATA(0, 2, -1) + 1/10 x DATA(-1, -1, -1) - -- x DATA(0, -1, -1) + 80 + + 11 + + 1/40 x DATA(1, -1, -1) - 3/80 x DATA(2, 2, 2) - -- x DATA(0, -1, 1) + 80 + + + 1/40 x DATA(-1, 2, 2) - 1/40 x DATA(2, 1, 2) + 1/10 x DATA(1, 2, 2) + + - 3/20 x DATA(0, -1, 0) + 1/80 x y DATA(1, 0, -1) + + 2 2 + - 3/160 z DATA(-1, 2, 2) + 3/160 z DATA(2, 1, 2) + + 2 2 + + 1/160 z DATA(1, 2, 2) + 1/160 z DATA(0, -1, 0) + + 2 2 + - 1/160 z DATA(1, -1, 0) + 3/160 z DATA(-1, 0, 0) + + 2 2 + + 3/160 z DATA(-1, 1, 0) + 3/160 z DATA(2, 2, -1) + + 2 2 + + 1/160 z DATA(1, 2, -1) - 3/160 z DATA(-1, 2, -1) + + 2 2 + + 3/160 z DATA(2, 1, -1) - 3/160 z DATA(2, 0, 0) + + 2 2 + - 3/160 z DATA(2, -1, 0) - 1/160 z DATA(1, 2, 0) + + 2 2 + + 1/160 z DATA(0, 2, 0) + 3/160 z DATA(-1, 2, 0) + + 2 2 + - 3/160 z DATA(2, 1, 0) - 3/160 z DATA(2, 2, 0) + + 2 2 + - 3/160 z DATA(2, -1, 1) - 3/160 z DATA(2, 0, 1) + + 2 2 + + 3/160 z DATA(-1, 2, 1) - 3/160 z DATA(2, 1, 1) + + 2 2 + - 1/32 x DATA(-1, -1, 1) - 3/32 x DATA(1, -1, 1) + + 2 2 2 + - 1/32 x DATA(-1, 0, 1) - 1/32 x DATA(-1, 1, 1) + 3/32 x DATA(0, 0, -1) + + 2 2 + - 3/32 x DATA(1, 0, -1) - 1/32 x DATA(-1, 1, -1) + + 2 2 + + 3/32 x DATA(0, 1, -1) - 3/32 x DATA(1, 1, -1) + + 2 2 + - 1/32 x DATA(-1, -1, 0) - 1/32 x DATA(-1, -1, -1) + + 2 2 + + 3/32 x DATA(0, -1, -1) - 3/32 x DATA(1, -1, -1) + + 2 2 + + 1/32 x DATA(2, 2, 2) + 3/32 x DATA(0, -1, 1) - 1/80 x y DATA(2, 0, -1) + + 2 2 + - 3/160 z DATA(2, 2, 1) + 1/160 z DATA(1, -1, 2) + + 2 2 + + 3/160 z DATA(2, 0, 2) - 1/160 z DATA(0, 0, 2) + + 2 2 + - 3/160 z DATA(-1, 0, 2) + 3/160 z DATA(2, -1, 2) + + 2 2 + + 1/160 z DATA(1, 1, 2) - 1/160 z DATA(0, 1, 2) + + 2 2 + - 3/160 z DATA(-1, 1, 2) - 1/160 z DATA(0, 2, -1) + + 2 2 + + 3/160 z DATA(-1, -1, 1) - 1/160 z DATA(1, -1, 1) + + 2 2 + + 3/160 z DATA(-1, 0, 1) + 3/160 z DATA(-1, 1, 1) + + 2 2 + - 1/160 z DATA(0, 0, -1) + 1/160 z DATA(1, 0, -1) + + 2 2 + - 3/160 z DATA(-1, 1, -1) - 1/160 z DATA(0, 1, -1) + + 2 2 + + 1/160 z DATA(1, 1, -1) + 3/160 z DATA(-1, -1, 0) + + 2 2 + - 3/160 z DATA(-1, -1, -1) - 1/160 z DATA(0, -1, -1) + + 2 2 + + 1/160 z DATA(1, -1, -1) + 3/160 z DATA(2, 2, 2) + + 2 27 + + 1/160 z DATA(0, -1, 1) + ---- z DATA(1, 2, 1) - 1/1000 z DATA(0, 2, 1) + 2000 + + 31 49 + - 9/250 z DATA(-1, -1, 2) + ---- z DATA(2, 2, 1) + ---- z DATA(1, -1, 2) + 2000 2000 + + 21 27 + - ---- z DATA(2, 0, 2) + 2/125 z DATA(0, 0, 2) - ---- z DATA(-1, 0, 2) + 2000 1000 + + 37 19 + - 3/2000 z DATA(2, -1, 2) + ---- z DATA(1, 1, 2) + ---- z DATA(0, 1, 2) + 2000 1000 + + 19 37 + - 9/500 z DATA(-1, 1, 2) - ---- z DATA(0, 2, -1) - ---- z DATA(-1, -1, 1) + 2000 1000 + + 33 23 + + ---- z DATA(1, -1, 1) - ---- z DATA(0, 2, 0) - 9/500 z DATA(2, 1, -1) + 2000 2000 + + 13 27 + + ---- z DATA(2, -1, 0) + 2/125 z DATA(2, 0, 0) - ---- z DATA(2, 0, -1) + 1000 1000 + + 13 11 43 + + ---- z DATA(0, -1, 2) + --- z DATA(0, 2, 2) + ---- z DATA(1, 0, 2) + 1000 500 2000 + + 129 19 + + ---- z DATA(-1, 0, -1) - 9/250 z DATA(2, -1, -1) - ---- z DATA(0, 0, 0) + 2000 2000 + + 21 + - 3/1000 z DATA(1, 0, 0) - ---- z DATA(0, 1, 0) - 1/500 z DATA(1, 1, 0) + 2000 + + 31 + - 3/1000 z DATA(0, 0, 1) + ---- z DATA(1, 0, 1) - 1/500 z DATA(0, 1, 1) + 2000 + + 29 + + ---- z DATA(1, 1, 1) - 9/1000 z DATA(2, 2, -1) - 7/250 z DATA(1, 2, -1) + 2000 + + 93 2 2 + + ---- z DATA(-1, 2, -1) - 1/160 z DATA(1, 2, 1) + 1/160 z DATA(0, 2, 1) + 2000 + + 2 + - 3/160 z DATA(-1, -1, 2) - 7/2000 z DATA(-1, 0, 0) + + 13 2 + - ---- z DATA(-1, 1, 0) - 3/160 y DATA(2, 0, -1) + 2000 + + 2 2 + - 1/160 y DATA(0, -1, 2) - 1/160 y DATA(0, 2, 2) + + 2 2 + - 1/160 y DATA(1, 0, 2) + 3/160 y DATA(-1, 0, -1) + + 2 2 + + 3/160 y DATA(2, -1, -1) + 1/160 y DATA(0, 0, 0) + + 2 2 2 + - 1/160 y DATA(1, 0, 0) + 1/160 y DATA(0, 1, 0) - 1/160 y DATA(1, 1, 0) + + 2 2 2 + + 1/160 y DATA(0, 0, 1) - 1/160 y DATA(1, 0, 1) + 1/160 y DATA(0, 1, 1) + + 2 2 + - 1/160 y DATA(1, 1, 1) + 3/160 y DATA(2, 2, -1) + + 2 2 + + 1/160 y DATA(1, 2, -1) - 3/160 y DATA(-1, 2, -1) + + 2 31 + - 3/160 y DATA(2, 1, -1) - ---- z DATA(-1, 1, 1) - 1/1000 z DATA(1, 2, 0) + 1000 + + 19 19 11 + - ---- z DATA(-1, 2, 0) + ---- z DATA(2, 1, 0) + --- z DATA(2, 2, 0) + 2000 1000 500 + + 49 43 + + ---- z DATA(2, -1, 1) + ---- z DATA(2, 0, 1) - 7/250 z DATA(-1, 2, 1) + 2000 2000 + + 37 2 + + ---- z DATA(2, 1, 1) + 1/1000 y z DATA(1, 1, 1) - 3/160 y DATA(2, 1, 2) + 2000 + + 2 2 + - 1/160 y DATA(0, -1, 0) + 1/160 y DATA(1, -1, 0) + + 2 2 + + 3/160 y DATA(-1, 0, 0) + 3/160 y DATA(-1, 1, 0) + + 2 2 + - 3/160 y DATA(2, 0, 0) + 3/160 y DATA(2, -1, 0) + + 2 2 + + 1/160 y DATA(1, 2, 0) - 1/160 y DATA(0, 2, 0) + + 2 2 17 + - 3/160 y DATA(-1, 2, 0) - 3/160 y DATA(2, 1, 0) - --- z DATA(-1, 0, 1) + 500 + + 17 111 + - 7/2000 z DATA(0, 0, -1) - --- z DATA(1, 0, -1) + ---- z DATA(-1, 1, -1) + 500 2000 + + 13 31 + - ---- z DATA(0, 1, -1) - ---- z DATA(1, 1, -1) - 1/2000 z DATA(-1, -1, 0) + 2000 1000 + + 147 + + ---- z DATA(-1, -1, -1) - 1/2000 z DATA(0, -1, -1) + 2000 + + 37 57 + - ---- z DATA(1, -1, -1) - ---- z DATA(2, 2, 2) - 1/250 z DATA(0, -1, 1) + 1000 2000 + + 39 31 + - 9/1000 z DATA(-1, 2, 2) - ---- z DATA(2, 1, 2) + ---- z DATA(1, 2, 2) + 2000 2000 + + 17 2 + - ---- z DATA(0, -1, 0) - 1/250 z DATA(1, -1, 0) + 1/160 y DATA(1, 2, 2) + 2000 + + 2 2 + - 3/160 y DATA(-1, 2, 1) - 3/160 y DATA(2, 1, 1) + + 2 2 + + 1/160 y DATA(1, 2, 1) - 1/160 y DATA(0, 2, 1) + + 2 2 + - 3/160 y DATA(-1, -1, 2) + 3/160 y DATA(2, 2, 1) + + 2 2 + + 1/160 y DATA(1, -1, 2) - 3/160 y DATA(2, 0, 2) + + 2 2 + + 1/160 y DATA(0, 0, 2) + 3/160 y DATA(-1, 0, 2) + + 2 2 + + 3/160 y DATA(2, -1, 2) - 1/160 y DATA(1, 1, 2) + + 2 2 + + 1/160 y DATA(0, 1, 2) + 3/160 y DATA(-1, 1, 2) + + 2 2 + - 1/160 y DATA(0, 2, -1) - 3/160 y DATA(-1, -1, 1) + + 2 2 + + 1/160 y DATA(1, -1, 1) + 3/160 y DATA(-1, 0, 1) + + 2 2 + + 3/160 y DATA(-1, 1, 1) + 1/160 y DATA(0, 0, -1) + + 2 2 + - 1/160 y DATA(1, 0, -1) + 3/160 y DATA(-1, 1, -1) + + 2 2 + + 1/160 y DATA(0, 1, -1) - 1/160 y DATA(1, 1, -1) + + 2 2 + - 3/160 y DATA(-1, -1, 0) - 3/160 y DATA(-1, -1, -1) + + 2 2 + - 1/160 y DATA(0, -1, -1) + 1/160 y DATA(1, -1, -1) + + 2 2 + + 3/160 y DATA(2, 2, 2) - 1/160 y DATA(0, -1, 1) + + 2 19 + - 3/160 y DATA(-1, 2, 2) - ---- y DATA(-1, 0, 2) + 2000 + + 27 + - 9/1000 y DATA(2, -1, 2) + ---- y DATA(1, 1, 2) - 1/1000 y DATA(0, 1, 2) + 2000 + + 13 111 + - 7/250 y DATA(-1, 1, 2) + ---- y DATA(0, 2, -1) + ---- y DATA(-1, -1, 1) + 1000 2000 + + 31 13 31 + - ---- y DATA(1, -1, 1) - ---- y DATA(-1, 0, 1) - ---- y DATA(-1, 1, 1) + 1000 2000 1000 + + 17 37 + - ---- y DATA(0, 0, -1) - 1/250 y DATA(1, 0, -1) - ---- y DATA(-1, 1, -1) + 2000 1000 + + 33 129 + - 1/250 y DATA(0, 1, -1) + ---- y DATA(1, 1, -1) + ---- y DATA(-1, -1, 0) + 2000 2000 + + 147 + + ---- y DATA(-1, -1, -1) - 1/2000 y DATA(0, -1, -1) + 2000 + + 37 57 49 + - ---- y DATA(1, -1, -1) - ---- y DATA(2, 2, 2) + ---- y DATA(2, 1, -1) + 1000 2000 2000 + + 19 + + 2/125 y DATA(2, 0, 0) - ---- y DATA(0, -1, 2) - 1/8 x DATA(0, -1, 2) + 2000 + + - 7/80 x DATA(0, 2, 2) + 3/40 x DATA(1, 0, 2) + 7/80 x DATA(-1, 0, -1) + + 11 + + 3/80 x DATA(2, -1, -1) - -- x DATA(0, 0, 0) + 1/20 x DATA(1, 0, 0) + 80 + + - 1/8 x DATA(0, 1, 0) + 1/16 x DATA(1, 1, 0) - 1/8 x DATA(0, 0, 1) + + 2 2 + + 1/40 x DATA(2, 0, -1) + 3/160 y DATA(2, 2, 0) + 3/160 y DATA(2, -1, 1) + + 2 + - 3/160 y DATA(2, 0, 1) + 1/80 x z DATA(1, -1, 0) + + + 1/80 x z DATA(0, -1, 0) - 3/80 x z DATA(1, 2, 2) + + + 3/80 x z DATA(2, 1, 2) - 3/80 x z DATA(2, 0, -1) + + 27 + + 1/1000 y z DATA(0, 1, 0) + ---- y z DATA(-1, 2, -1) + 1000 + + + 9/1000 y z DATA(2, 0, -1) - 3/80 x y DATA(-1, -1, 2) + + - 3/80 x y DATA(0, 2, 1) - 3/80 x y DATA(1, 2, 1) + + - 3/1000 y z DATA(1, 0, 2) + 1/80 x y DATA(2, 1, 0) + + - 3/80 x y DATA(-1, -1, -1) - 1/2000 y DATA(-1, 0, -1) + + 19 + - 9/250 y DATA(2, -1, -1) - ---- y DATA(0, 0, 0) - 3/1000 y DATA(1, 0, 0) + 2000 + + 31 21 + - 3/1000 y DATA(0, 1, 0) + ---- y DATA(1, 1, 0) - ---- y DATA(0, 0, 1) + 2000 2000 + + 29 + - 1/500 y DATA(1, 0, 1) - 1/500 y DATA(0, 1, 1) + ---- y DATA(1, 1, 1) + 2000 + + 49 + - 3/2000 y DATA(2, 2, -1) + ---- y DATA(1, 2, -1) + 2000 + + 27 43 + - 9/250 y DATA(-1, 2, -1) - ---- y DATA(2, -1, 0) + ---- y DATA(1, 2, 0) + 1000 2000 + + 27 43 + + 2/125 y DATA(0, 2, 0) - ---- y DATA(-1, 2, 0) + ---- y DATA(2, 1, 0) + 1000 2000 + + 21 19 + - ---- y DATA(2, 2, 0) - 9/500 y DATA(2, -1, 1) + ---- y DATA(2, 0, 1) + 2000 1000 + + 37 37 + - 9/500 y DATA(-1, 2, 1) + ---- y DATA(2, 1, 1) + ---- y DATA(1, 2, 1) + 2000 2000 + + 19 93 39 + + ---- y DATA(0, 2, 1) + ---- y DATA(-1, -1, 2) - ---- y DATA(2, 2, 1) + 1000 2000 2000 + + 11 23 + - 7/250 y DATA(1, -1, 2) + --- y DATA(2, 0, 2) - ---- y DATA(0, 0, 2) + 500 2000 + + + 1/80 x z DATA(2, 0, 1) + 1/80 x z DATA(2, -1, 1) + + + 3/80 x z DATA(-1, 2, 2) - 1/80 x z DATA(0, -1, 1) + + + 3/80 x z DATA(2, 2, 2) + 3/80 x z DATA(1, -1, -1) + + + 3/80 x z DATA(0, -1, -1) - 3/80 x z DATA(-1, -1, -1) + + - 1/80 x z DATA(-1, -1, 0) + 3/80 x z DATA(1, 1, -1) + + + 3/80 x y DATA(-1, 2, -1) + 3/80 x z DATA(0, 1, -1) + + - 3/80 x z DATA(-1, 1, -1) + 3/80 x z DATA(1, 0, -1) + + + 3/80 x z DATA(0, 0, -1) + 1/80 x z DATA(-1, 1, 1) + + + 1/80 x z DATA(-1, 0, 1) - 1/80 x z DATA(1, -1, 1) + + + 1/80 x z DATA(-1, -1, 1) + 3/80 x z DATA(0, 2, -1) + + - 1/80 x z DATA(-1, 1, 0) - 1/80 x z DATA(-1, 0, 0) + + - 3/1000 y z DATA(1, 2, 0) + 3/1000 y z DATA(1, 2, 1) + + + 3/80 x y DATA(-1, 2, 2) + 1/80 x y DATA(0, 0, -1) + + + 3/80 x y DATA(-1, 2, 0) - 1/80 x y DATA(2, 0, 0) + + 27 + + ---- y z DATA(2, -1, -1) - 3/80 x y DATA(2, -1, 2) + 1000 + + - 9/1000 y z DATA(2, -1, 1) + 9/1000 y z DATA(2, -1, 0) + + 27 + + ---- y z DATA(-1, -1, 2) - 1/80 x y DATA(2, 0, 1) + 1000 + + + 9/1000 y z DATA(0, -1, 2) - 3/80 x y DATA(-1, -1, 0) + + + 1/80 x y DATA(-1, 1, 1) + 3/1000 y z DATA(0, 1, -1) + + + 9/1000 y z DATA(-1, 1, -1) + 3/1000 y z DATA(1, 0, -1) + + - 3/1000 y z DATA(0, 0, -1) - 3/1000 y z DATA(-1, 1, 1) + + + 3/1000 y z DATA(-1, 0, 1) - 3/1000 y z DATA(1, -1, 1) + + + 9/1000 y z DATA(-1, -1, 1) + 9/1000 y z DATA(0, 2, -1) + + - 9/1000 y z DATA(-1, 1, 2) - 3/1000 y z DATA(0, 1, 2) + + + 3/1000 y z DATA(1, 1, 2) - 3/80 x y DATA(2, -1, 0) + + 27 + - ---- y z DATA(2, -1, 2) + 9/1000 y z DATA(-1, 0, 2) + 1000 + + + 3/1000 y z DATA(0, 0, 2) - 1/80 x y DATA(-1, 0, 2) + + 13 11 + + 1/80 x y DATA(2, 1, -1) + ---- y DATA(2, 0, -1) + --- y DATA(0, 2, 2) + 1000 500 + + - 1/1000 y DATA(1, 0, 2) - 3/80 x y DATA(-1, -1, 1) + + 2 2 2 + + 1/160 z DATA(0, 0, 0) - 1/160 z DATA(1, 0, 0) + 1/160 z DATA(0, 1, 0) + + 2 2 2 + - 1/160 z DATA(1, 1, 0) + 1/160 z DATA(0, 0, 1) - 1/160 z DATA(1, 0, 1) + + 2 2 + + 1/160 z DATA(0, 1, 1) - 1/160 z DATA(1, 1, 1) - 1/10 x DATA(0, 1, 2) + + + 3/80 x DATA(-1, 1, 2) - 1/8 x DATA(0, 2, -1) + 3/40 x DATA(-1, -1, 1) + + + 1/20 x DATA(1, -1, 1) + 1/16 x DATA(-1, 0, 1) + 1/20 x DATA(-1, 1, 1) + + - 3/20 x DATA(0, 0, -1) + 3/80 x DATA(1, 0, -1) + 3/40 x DATA(-1, 1, -1) + + 11 + - -- x DATA(0, 1, -1) + 1/20 x DATA(1, 1, -1) + 7/80 x DATA(-1, -1, 0) + 80 + + 13 31 + - ---- y DATA(0, -1, 1) - 9/1000 y DATA(-1, 2, 2) + ---- y DATA(2, 1, 2) + 2000 2000 + + 31 17 + + ---- y DATA(1, 2, 2) - 7/2000 y DATA(0, -1, 0) - --- y DATA(1, -1, 0) + 2000 500 + + 17 2 + - 7/2000 y DATA(-1, 0, 0) - --- y DATA(-1, 1, 0) + 3/160 z DATA(2, 0, -1) + 500 + + 2 2 + - 1/160 z DATA(0, -1, 2) - 1/160 z DATA(0, 2, 2) + + 2 2 + + 1/160 z DATA(1, 0, 2) - 3/160 z DATA(-1, 0, -1) + + 2 + + 3/160 z DATA(2, -1, -1) - 1/1000 y z DATA(0, 1, 1) + + 2 2 + + 3/80 x y DATA(1, -1, 0) + 1/32 x DATA(2, -1, 1) + 1/32 x DATA(2, 0, 1) + + 2 + - 1/32 x DATA(-1, 2, 1) + 1/16 x DATA(1, 0, 1) - 9/80 x DATA(0, 1, 1) + + + 3/40 x DATA(1, 1, 1) + 1/16 x DATA(1, 2, -1) + 1/16 x DATA(-1, 2, -1) + + + 1/80 x DATA(2, 1, -1) + 1/80 x DATA(2, 0, 0) + 1/40 x DATA(2, -1, 0) + + + 3/40 x DATA(1, 2, 0) - 9/80 x DATA(0, 2, 0) + 1/20 x DATA(-1, 2, 0) + + - 1/80 x DATA(2, 2, 0) + 1/80 x DATA(2, -1, 1) + 3/80 x DATA(-1, 2, 1) + + - 1/80 x DATA(2, 1, 1) + 7/80 x DATA(1, 2, 1) - 1/10 x DATA(0, 2, 1) + + + 1/16 x DATA(-1, -1, 2) - 1/40 x DATA(2, 2, 1) + 1/16 x DATA(1, -1, 2) + + - 1/80 x DATA(2, 0, 2) - 9/80 x DATA(0, 0, 2) + 1/20 x DATA(-1, 0, 2) + + + 7/80 x DATA(1, 1, 2) + 3/80 x DATA(1, -1, 0) + 3/40 x DATA(-1, 0, 0) + + 2 2 + + 1/16 x DATA(-1, 1, 0) + 1/32 x DATA(2, 0, -1) + 3/32 x DATA(0, -1, 2) + + 2 2 2 + + 3/32 x DATA(0, 2, 2) - 3/32 x DATA(1, 0, 2) - 1/32 x DATA(-1, 0, -1) + + 2 2 2 + + 1/32 x DATA(2, -1, -1) + 3/32 x DATA(0, 0, 0) - 3/32 x DATA(1, 0, 0) + + 2 2 2 + + 3/32 x DATA(0, 1, 0) - 3/32 x DATA(1, 1, 0) + 3/32 x DATA(0, 0, 1) + + 2 2 2 + - 3/32 x DATA(1, 0, 1) + 3/32 x DATA(0, 1, 1) - 3/32 x DATA(1, 1, 1) + + 2 2 + + 1/32 x DATA(2, 2, -1) - 3/32 x DATA(1, 2, -1) + + 2 2 2 + - 1/32 x DATA(-1, 2, -1) + 1/32 x DATA(2, 1, -1) + 1/32 x DATA(2, 0, 0) + + 2 2 2 + + 1/32 x DATA(2, -1, 0) - 3/32 x DATA(1, 2, 0) + 3/32 x DATA(0, 2, 0) + + 2 2 2 + - 1/32 x DATA(-1, 2, 0) + 1/32 x DATA(2, 1, 0) + 1/32 x DATA(2, 2, 0) + + - 1/80 x y DATA(0, 1, 2) + 9/1000 y z DATA(2, 2, 1) + + + 1/80 x y DATA(-1, 1, 0) + 1/80 x y DATA(1, 0, 0) + + - 3/80 x y DATA(1, 2, -1) - 9/1000 y z DATA(2, 0, 2) + + - 9/1000 y z DATA(1, -1, 2) - 3/80 x y DATA(0, 2, -1) + + 27 + + 1/80 x y DATA(2, 1, 2) - ---- y z DATA(2, 2, -1) + 1000 + + + 3/80 x y DATA(1, -1, -1) - 1/1000 y z DATA(1, 1, 0) + + + 3/80 x y DATA(1, -1, 2) - 3/80 x y DATA(0, 2, 0) + + + 3/80 x y DATA(2, 2, 0) + 3/80 x y DATA(0, -1, 2) + + - 3/1000 y z DATA(2, 1, 0) - 3/80 x z DATA(0, 2, 2) + + - 3/80 x z DATA(0, -1, 2) + 3/1000 y z DATA(-1, 1, 0) + + - 3/1000 y z DATA(-1, 0, 0) + 3/1000 y z DATA(1, -1, 0) + + - 3/1000 y z DATA(0, -1, 0) + 9/1000 y z DATA(1, 2, 2) + + + 1/80 x y DATA(-1, 1, 2) + 9/1000 y z DATA(2, 1, 2) + + 27 + - ---- y z DATA(-1, 2, 2) + 3/1000 y z DATA(0, -1, 1) + 1000 + + 27 + + ---- y z DATA(2, 2, 2) + 9/1000 y z DATA(1, -1, -1) + 1000 + + 27 + - 9/1000 y z DATA(0, -1, -1) - ---- y z DATA(-1, -1, -1) + 1000 + + - 3/80 x y DATA(1, 2, 0) - 9/1000 y z DATA(-1, -1, 0) + + - 3/1000 y z DATA(1, 1, -1) - 1/80 x z DATA(2, 2, 0) + + - 1/80 x z DATA(2, 1, 0) - 1/80 x z DATA(-1, 2, 0) + + + 1/80 x z DATA(0, 2, 0) + 1/80 x z DATA(1, 2, 0) + + - 1/80 x z DATA(2, -1, 0) - 1/80 x z DATA(2, 0, 0) + + - 3/80 x z DATA(2, 1, -1) - 3/80 x z DATA(-1, 2, -1) + + + 3/80 x z DATA(1, 2, -1) - 3/80 x z DATA(2, 2, -1) + + - 1/80 x z DATA(1, 1, 1) - 1/80 x z DATA(0, 1, 1) - 1/80 x z DATA(1, 0, 1) + + - 1/80 x z DATA(0, 0, 1) + 1/80 x z DATA(1, 1, 0) + 1/80 x z DATA(0, 1, 0) + + + 1/80 x z DATA(1, 0, 0) + 1/80 x z DATA(0, 0, 0) + + - 3/80 x z DATA(2, -1, -1) - 3/80 x z DATA(-1, 0, -1) + + - 3/80 x z DATA(1, 0, 2) + 3/80 x z DATA(-1, 1, 2) + + + 1/80 x y DATA(-1, 1, -1) - 1/80 x y DATA(1, 1, -1) + + - 3/80 x z DATA(0, 1, 2) - 3/80 x z DATA(1, 1, 2) + + + 3/80 x z DATA(2, -1, 2) + 3/80 x z DATA(-1, 0, 2) + + - 3/80 x z DATA(0, 0, 2) + 3/80 x y DATA(0, -1, -1) + + + 3/80 x z DATA(2, 0, 2) - 3/80 x z DATA(1, -1, 2) + + + 1/80 x z DATA(2, 2, 1) + 3/80 x z DATA(-1, -1, 2) + + - 1/80 x z DATA(0, 2, 1) - 1/80 x z DATA(1, 2, 1) + 1/80 x z DATA(2, 1, 1) + + + 1/80 x z DATA(-1, 2, 1) + 3/1000 y z DATA(2, 1, 1) + + - 1/80 x y DATA(-1, 0, 1) - 9/1000 y z DATA(-1, 2, 1) + + - 1/80 x y DATA(1, 1, 2) + 3/80 x y DATA(1, -1, 1) + + + 1/80 x y DATA(2, 1, 1) - 1/80 x y DATA(2, 0, 2) + 3/80 x y DATA(2, 2, 2) + + - 3/1000 y z DATA(2, 0, 1) + 9/1000 y z DATA(-1, 2, 0) + + + 3/80 x y DATA(0, -1, 1) - 9/1000 y z DATA(2, 1, -1) + + + 3/1000 y z DATA(0, 2, 0) + 1/80 x y DATA(0, 0, 1) + + - 1/1000 y z DATA(0, 0, 0) + 1/1000 y z DATA(1, 0, 0) + + - 1/80 x y DATA(0, 1, -1) + 3/80 x y DATA(-1, 2, 1) + + - 1/80 x y DATA(0, 1, 1) + 3/1000 y z DATA(2, 0, 0) + + - 3/80 x y DATA(2, -1, 1) - 9/1000 y z DATA(1, 2, -1) + + - 1/80 x y DATA(1, 1, 1) - 1/1000 y z DATA(1, 0, 1) + + - 3/80 x y DATA(0, 2, 2) + 1/80 x y DATA(1, 0, 2) - 1/80 x y DATA(0, 1, 0) + + - 3/80 x y DATA(2, -1, -1) - 1/80 x y DATA(-1, 0, -1) + + + 3/80 x y DATA(2, 2, -1) + 1/80 x y DATA(0, 0, 0) + + + 1/80 x y DATA(0, 0, 2) + +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=284745840, alloc=3669344, time=25.69 +bytes used=285767320, alloc=3669344, time=25.76 +bytes used=286767472, alloc=3669344, time=25.83 +bytes used=287775320, alloc=3669344, time=25.91 +bytes used=288801048, alloc=3734868, time=25.98 +bytes used=289805460, alloc=3865916, time=26.06 +bytes used=290805808, alloc=4259060, time=26.14 +bytes used=291810404, alloc=4652204, time=26.21 + 2 147 147 +[COEFF(-1, -1, -1) = - 1/32 x + ---- y - 3/80 x z + 1/10 x + ---- z - 3/80 x y + 2000 2000 + + 2 27 2 47 39 + - 3/160 z - ---- y z - 3/160 y - ----, COEFF(0, -1, -1) = - ---- + 1000 1500 4000 + + 2 2 13 + - 1/2000 y - 1/160 z - 9/1000 y z - 1/2000 z + 3/80 x z + 3/32 x - -- x + 80 + + 2 2 157 2 + + 3/80 x y - 1/160 y , COEFF(1, -1, -1) = - 3/32 x + ---- + 1/160 y + 2000 + + 37 2 37 + + 3/80 x z - ---- y + 3/80 x y + 1/160 z + 9/1000 y z + 1/40 x - ---- z, + 1000 1000 + + 2 27 + COEFF(2, -1, -1) = - 3/80 x z + 1/32 x + ---- y z - 9/250 y - 3/80 x y + 1000 + + 2 449 2 + + 3/160 y + 3/80 x - 9/250 z - ----- + 3/160 z , COEFF(-1, 0, -1) = + 12000 + + 2 607 129 + 7/80 x - 1/32 x - 9/1000 y z - 1/80 x y - ----- - 3/80 x z + ---- z + 12000 2000 + + 2 2 2 + + 3/160 y - 1/2000 y - 3/160 z , COEFF(0, 0, -1) = 3/80 x z + 1/160 y + + 2 17 2 49 + - 1/160 z - 3/20 x - ---- y + 3/32 x - 7/2000 z - ---- - 3/1000 y z + 2000 2000 + + 2 + + 1/80 x y, COEFF(1, 0, -1) = 3/80 x - 3/32 x + 3/1000 y z + 1/80 x y + + 17 2 2 323 + - --- z - 1/250 y - 1/160 y + 1/160 z + 3/80 x z + ----, COEFF(2, 0, -1) + 500 4000 + + 17 27 13 2 + = - ---- - ---- z + 1/40 x - 1/80 x y + ---- y + 9/1000 y z + 3/160 z + 3000 1000 1000 + + 2 2 97 + - 3/160 y - 3/80 x z + 1/32 x , COEFF(-1, 1, -1) = - ---- + 3/40 x + 3000 + + 111 37 2 2 2 + + ---- z + 9/1000 y z - ---- y + 3/160 y - 3/160 z - 1/32 x + 1/80 x y + 2000 1000 + + 107 13 11 + - 3/80 x z, COEFF(0, 1, -1) = - ---- - ---- z - -- x + 3/1000 y z + 4000 2000 80 + + 2 2 2 + + 3/80 x z - 1/160 z + 1/160 y - 1/250 y - 1/80 x y + 3/32 x , + + 141 31 33 2 + COEFF(1, 1, -1) = ---- + 3/80 x z - ---- z - 3/1000 y z + ---- y - 3/32 x + 2000 1000 2000 + + 2 2 + - 1/80 x y + 1/20 x + 1/160 z - 1/160 y , COEFF(2, 1, -1) = 1/80 x y + + 137 2 2 2 49 + - ----- - 3/160 y - 9/500 z + 3/160 z - 9/1000 y z + 1/32 x + ---- y + 12000 2000 + + - 3/80 x z + 1/80 x, COEFF(-1, 2, -1) = 1/16 x - 9/250 y - 3/80 x z + + 2 281 2 2 93 27 + - 3/160 z + ----- - 1/32 x + 3/80 x y - 3/160 y + ---- z + ---- y z, + 12000 2000 1000 + + 2 2 33 + COEFF(0, 2, -1) = - 1/160 z + 3/80 x z - 3/80 x y + 3/32 x - ---- - 1/8 x + 2000 + + 13 2 19 + + 9/1000 y z + ---- y - 1/160 y - ---- z, COEFF(1, 2, -1) = 3/80 x z + 1000 2000 + + 191 2 2 + - 9/1000 y z + ---- - 3/32 x + 1/16 x + 1/160 z - 3/80 x y - 7/250 z + 4000 + + 2 49 27 2 41 + + 1/160 y + ---- y, COEFF(2, 2, -1) = - ---- y z + 3/160 z - --- + 2000 1000 750 + + 2 2 + - 3/80 x z - 9/1000 z + 1/32 x - 3/2000 y + 3/160 y + 3/80 x y, + + 2 129 607 + COEFF(-1, -1, 0) = - 1/32 x - 1/80 x z - 9/1000 y z + ---- y - ----- + 2000 12000 + + 2 2 + - 1/2000 z + 3/160 z - 3/160 y + 7/80 x - 3/80 x y, COEFF(0, -1, 0) = + + 2 2 + 1/80 x z - 7/2000 y + 3/80 x y - 3/20 x - 3/1000 y z - 1/160 y + 1/160 z + + 17 2 49 2 2 + - ---- z + 3/32 x - ----, COEFF(1, -1, 0) = - 1/160 z + 1/160 y + 2000 2000 + + 17 323 + - 1/250 z + 3/1000 y z + 3/80 x + 3/80 x y - --- y + ---- + 1/80 x z + 500 4000 + + 2 2 + - 3/32 x , COEFF(2, -1, 0) = - 3/80 x y + 1/32 x + 1/40 x + 9/1000 y z + + 27 2 17 2 13 + - ---- y - 3/160 z - 1/80 x z - ---- + 3/160 y + ---- z, COEFF(-1, 0, 0) + 1000 3000 1000 + + 2 2 437 2 + = 3/160 y - 7/2000 z + 3/160 z - ---- - 1/80 x z + 3/40 x - 1/32 x + 6000 + + 2 161 11 + - 7/2000 y - 3/1000 y z - 1/80 x y, COEFF(0, 0, 0) = 3/32 x - ---- - -- x + 4000 80 + + 19 2 2 19 + + 1/80 x y - ---- z + 1/160 y + 1/160 z - ---- y - 1/1000 y z + 1/80 x z + 2000 2000 + + 2 2 21 + , COEFF(1, 0, 0) = 1/1000 y z - 3/32 x - 1/160 y + --- + 1/80 x y + 250 + + 2 + + 1/80 x z - 1/160 z - 3/1000 y + 1/20 x - 3/1000 z, COEFF(2, 0, 0) = + + 2 2 2 + - 1/80 x z + 1/80 x - 3/160 y - 3/160 z + 2/125 y - 1/80 x y + 1/32 x + + 349 + + ----- + 3/1000 y z + 2/125 z, COEFF(-1, 1, 0) = 1/16 x - 1/80 x z + 12000 + + 2 2 2 13 17 + + 3/1000 y z + 3/160 z - 1/32 x + 1/80 x y + 3/160 y - ---- z - --- y + 2000 500 + + 691 21 2 2 + - -----, COEFF(0, 1, 0) = - ---- z + 1/160 z + 3/32 x - 1/80 x y + 12000 2000 + + 2 87 + + 1/160 y - ---- - 1/8 x - 3/1000 y + 1/80 x z + 1/1000 y z, + 2000 + + 31 299 2 2 + COEFF(1, 1, 0) = ---- y - 1/1000 y z - 1/500 z + ---- - 3/32 x - 1/160 y + 2000 4000 + + 2 43 + - 1/160 z + 1/80 x z - 1/80 x y + 1/16 x, COEFF(2, 1, 0) = ---- y + 2000 + + 2 2 19 2 79 + + 1/32 x - 1/80 x z - 3/160 y + ---- z - 3/160 z + ---- - 3/1000 y z + 1000 3000 + + 2 2 + + 1/80 x y, COEFF(-1, 2, 0) = - 1/80 x z + 3/80 x y - 3/160 y + 3/160 z + + 2 27 19 29 + - 1/32 x + 9/1000 y z - ---- y + 1/20 x - ---- z - ----, COEFF(0, 2, 0) + 1000 2000 6000 + + 2 2 + = - 9/80 x + 3/1000 y z + 3/32 x - 1/160 y + 2/125 y - 3/80 x y + + 2 23 137 53 + + 1/160 z - ---- z - ---- + 1/80 x z, COEFF(1, 2, 0) = 3/40 x + ---- + 2000 4000 1000 + + 2 2 43 + - 1/160 z - 3/32 x - 3/1000 y z + ---- y - 3/80 x y + 1/80 x z + 2000 + + 2 2 167 + - 1/1000 z + 1/160 y , COEFF(2, 2, 0) = 1/32 x - 9/1000 y z - ----- + 12000 + + 11 2 21 2 + + --- z + 3/160 y - ---- y - 1/80 x z - 3/160 z - 1/80 x + 3/80 x y, + 500 2000 + + 2 2 97 + COEFF(-1, -1, 1) = - 3/160 y + 9/1000 y z + 3/40 x - 1/32 x - ---- + 3000 + + 2 111 37 + + 3/160 z - 3/80 x y + 1/80 x z + ---- y - ---- z, COEFF(0, -1, 1) = + 2000 1000 + + 107 2 2 13 11 + 3/1000 y z + 3/80 x y - ---- + 3/32 x + 1/160 z - ---- y - -- x + 4000 2000 80 + + 2 + - 1/160 y - 1/80 x z - 1/250 z, COEFF(1, -1, 1) = - 1/80 x z + 3/80 x y + + 2 33 2 31 2 + + 1/160 y + ---- z - 3/1000 y z - 1/160 z + 1/20 x - ---- y - 3/32 x + 2000 1000 + + 141 2 2 + + ----, COEFF(2, -1, 1) = - 3/160 z + 1/32 x + 1/80 x z - 9/500 y + 2000 + + 49 2 137 + - 3/80 x y + 1/80 x + ---- z + 3/160 y - 9/1000 y z - -----, + 2000 12000 + + 2 17 691 13 + COEFF(-1, 0, 1) = 3/160 z - --- z - 1/80 x y - ----- + 1/16 x - ---- y + 500 12000 2000 + + 2 2 87 + + 3/1000 y z + 3/160 y - 1/32 x + 1/80 x z, COEFF(0, 0, 1) = - ---- + 2000 + + 2 2 21 + + 1/160 y + 3/32 x + 1/1000 y z - ---- y - 3/1000 z + 1/80 x y - 1/8 x + 2000 + + 2 2 + + 1/160 z - 1/80 x z, COEFF(1, 0, 1) = 1/80 x y - 1/80 x z - 1/160 y + + 2 2 31 299 + - 1/1000 y z - 1/160 z - 3/32 x - 1/500 y + 1/16 x + ---- z + ----, + 2000 4000 + + 2 79 19 43 + COEFF(2, 0, 1) = - 3/160 y + ---- - 3/1000 y z + ---- y + ---- z + 3000 1000 2000 + + 2 2 17 + - 1/80 x y + 1/32 x - 3/160 z + 1/80 x z, COEFF(-1, 1, 1) = - --- + 375 + + 31 2 2 2 + - ---- z + 1/20 x - 1/32 x + 3/160 z + 1/80 x z + 3/160 y + 1/80 x y + 1000 + + 31 191 2 2 + - 3/1000 y z - ---- y, COEFF(0, 1, 1) = - ---- + 1/160 z + 3/32 x + 1000 4000 + + 2 + + 1/160 y - 1/80 x z - 9/80 x - 1/500 z - 1/500 y - 1/80 x y - 1/1000 y z + + 29 2 2 + , COEFF(1, 1, 1) = ---- z - 1/160 y + 1/1000 y z - 1/80 x z - 3/32 x + 2000 + + 133 2 29 319 + + ---- - 1/160 z + 3/40 x + ---- y - 1/80 x y, COEFF(2, 1, 1) = ----- + 2000 2000 12000 + + 2 37 37 2 + - 3/160 z - 1/80 x + ---- z + ---- y + 1/80 x y + 1/80 x z + 1/32 x + 2000 2000 + + 2 53 2 + + 3/1000 y z - 3/160 y , COEFF(-1, 2, 1) = ----- - 3/160 y - 9/500 y + 12000 + + 2 2 + + 3/80 x y - 9/1000 y z - 7/250 z + 3/80 x - 1/32 x + 3/160 z + 1/80 x z + + 2 79 19 + , COEFF(0, 2, 1) = - 1/160 y - ---- - 1/1000 z + ---- y - 1/80 x z + 2000 1000 + + 2 2 + + 1/160 z - 3/1000 y z + 3/32 x - 1/10 x - 3/80 x y, COEFF(1, 2, 1) = + + 183 2 27 + 7/80 x - 3/80 x y + ---- - 1/80 x z - 3/32 x + ---- z + 3/1000 y z + 4000 2000 + + 2 37 2 39 + + 1/160 y + ---- y - 1/160 z , COEFF(2, 2, 1) = 9/1000 y z - ---- y + 2000 2000 + + 2 31 2 + + 1/32 x + 3/80 x y - 4/375 + ---- z - 1/40 x - 3/160 z + 1/80 x z + 2000 + + 2 281 + + 3/160 y , COEFF(-1, -1, 2) = 1/16 x + ----- - 3/80 x y - 9/250 z + 12000 + + 2 27 93 2 2 + - 3/160 y + ---- y z + ---- y - 3/160 z - 1/32 x + 3/80 x z, + 1000 2000 + + 19 2 13 33 + COEFF(0, -1, 2) = - ---- y - 1/160 y + ---- z - ---- + 9/1000 y z + 2000 1000 2000 + + 2 2 + - 1/160 z + 3/80 x y - 1/8 x - 3/80 x z + 3/32 x , COEFF(1, -1, 2) = + + 2 2 2 191 + 1/160 y - 9/1000 y z - 3/80 x z + 1/160 z + 1/16 x - 3/32 x + ---- + 4000 + + 49 2 27 + + ---- z - 7/250 y + 3/80 x y, COEFF(2, -1, 2) = 3/160 y - ---- y z + 2000 1000 + + 2 2 41 + - 3/80 x y - 9/1000 y + 1/32 x - 3/2000 z + 3/160 z - --- + 3/80 x z, + 750 + + 19 2 29 27 + COEFF(-1, 0, 2) = - ---- y - 1/80 x y + 3/160 y - ---- - ---- z + 2000 6000 1000 + + 2 2 + + 9/1000 y z + 3/80 x z + 1/20 x - 3/160 z - 1/32 x , COEFF(0, 0, 2) = + + 2 2 23 2 + - 1/160 z + 3/32 x + 1/80 x y - ---- y - 3/80 x z + 1/160 y + 2/125 z + 2000 + + 137 + - 9/80 x - ---- + 3/1000 y z, COEFF(1, 0, 2) = - 3/80 x z - 1/1000 y + 4000 + + 2 43 2 2 53 + + 3/40 x - 1/160 y + 1/80 x y + ---- z - 3/32 x + 1/160 z + ---- + 2000 1000 + + 21 2 11 167 + - 3/1000 y z, COEFF(2, 0, 2) = - ---- z - 3/160 y + --- y - ----- + 2000 500 12000 + + 2 2 + + 3/160 z - 1/80 x y + 1/32 x - 9/1000 y z - 1/80 x + 3/80 x z, + + 2 53 + COEFF(-1, 1, 2) = - 1/32 x + 1/80 x y + ----- - 7/250 y - 9/1000 y z + 12000 + + 2 2 + + 3/80 x - 3/160 z + 3/160 y - 9/500 z + 3/80 x z, COEFF(0, 1, 2) = + + 2 19 2 2 + 3/32 x + ---- z - 3/80 x z - 1/160 z + 1/160 y - 3/1000 y z - 1/10 x + 1000 + + 79 27 2 + - 1/1000 y - 1/80 x y - ----, COEFF(1, 1, 2) = ---- y + 1/160 z + 2000 2000 + + 2 183 2 + - 1/80 x y - 1/160 y + ---- + 7/80 x - 3/80 x z + 3/1000 y z - 3/32 x + 4000 + + 37 2 + + ---- z, COEFF(2, 1, 2) = 1/80 x y - 3/160 y + 3/80 x z - 1/40 x + 2000 + + 2 39 2 31 + + 1/32 x + 9/1000 y z - 4/375 - ---- z + 3/160 z + ---- y, + 2000 2000 + + 307 27 2 + COEFF(-1, 2, 2) = 1/40 x - 9/1000 z + ---- - ---- y z - 3/160 y + 3/80 x z + 6000 1000 + + 2 2 11 11 + - 1/32 x - 3/160 z + 3/80 x y - 9/1000 y, COEFF(0, 2, 2) = --- z + --- y + 500 500 + + 129 2 2 + - 3/80 x y - 7/80 x - ---- - 1/160 y - 3/80 x z + 3/32 x - 9/1000 y z + 4000 + + 2 2 2 13 + - 1/160 z , COEFF(1, 2, 2) = 1/160 z + 1/160 y + --- + 1/10 x - 3/80 x y + 500 + + 31 2 31 + + ---- z - 3/32 x - 3/80 x z + ---- y + 9/1000 y z, COEFF(2, 2, 2) = + 2000 2000 + + 539 2 57 2 27 + - ----- - 3/80 x + 3/80 x z + 3/160 z - ---- y + 3/160 y + ---- y z + 12000 2000 1000 + + 57 2 + - ---- z + 3/80 x y + 1/32 x ] + 2000 + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dx.compute.c"); +bytes used=292810948, alloc=4652204, time=26.30 +bytes used=293811480, alloc=4652204, time=26.37 +bytes used=294811812, alloc=4652204, time=26.45 +bytes used=295812060, alloc=4652204, time=26.64 +bytes used=296812352, alloc=4652204, time=26.72 +bytes used=297815692, alloc=4652204, time=26.80 +bytes used=298832252, alloc=4652204, time=26.88 +bytes used=299864124, alloc=4652204, time=26.97 +bytes used=300882368, alloc=4652204, time=27.08 +bytes used=301889296, alloc=4652204, time=27.20 +bytes used=302889456, alloc=4652204, time=27.43 +bytes used=303889636, alloc=4652204, time=27.64 +bytes used=304890472, alloc=4652204, time=27.71 +bytes used=305890652, alloc=4652204, time=27.78 +bytes used=306891144, alloc=4652204, time=27.84 +bytes used=307891400, alloc=4652204, time=27.90 +bytes used=308893396, alloc=4652204, time=28.01 +bytes used=309898640, alloc=4652204, time=28.13 +bytes used=310898972, alloc=4652204, time=28.25 +bytes used=311910600, alloc=4652204, time=28.39 +bytes used=312913328, alloc=4652204, time=28.54 +bytes used=313924952, alloc=4652204, time=28.64 +bytes used=314925104, alloc=4652204, time=28.74 +bytes used=315930264, alloc=4652204, time=29.08 +bytes used=316930580, alloc=4652204, time=29.28 +bytes used=317930840, alloc=4652204, time=29.35 +bytes used=318931300, alloc=4652204, time=29.42 +bytes used=319931608, alloc=4652204, time=29.49 +bytes used=320931784, alloc=4652204, time=29.60 +bytes used=321941056, alloc=4652204, time=29.77 +bytes used=322941300, alloc=4652204, time=29.87 +bytes used=323943068, alloc=4652204, time=30.29 +bytes used=324943276, alloc=4652204, time=30.46 +bytes used=325943724, alloc=4652204, time=30.53 +bytes used=326943892, alloc=4652204, time=30.60 +bytes used=327944120, alloc=4652204, time=30.67 +bytes used=328944364, alloc=4652204, time=30.85 +bytes used=329944540, alloc=4652204, time=31.18 +bytes used=330944728, alloc=4652204, time=31.43 +bytes used=331945168, alloc=4652204, time=31.50 +bytes used=332945368, alloc=4652204, time=31.56 +bytes used=333945528, alloc=4652204, time=31.71 +bytes used=334945752, alloc=4652204, time=31.83 +bytes used=335946416, alloc=4652204, time=32.33 +bytes used=336947040, alloc=4652204, time=32.41 +bytes used=337947272, alloc=4652204, time=32.52 +> +# d/dy +> simplify( diff(interp_3d_cube_order3_smooth0,y) ); +bytes used=338947896, alloc=4652204, time=32.62 +bytes used=339949152, alloc=4652204, time=32.69 +bytes used=340950072, alloc=4652204, time=32.76 +bytes used=341950248, alloc=4652204, time=32.84 +bytes used=342951444, alloc=4652204, time=32.91 +bytes used=343952068, alloc=4652204, time=32.98 +bytes used=344952348, alloc=4652204, time=33.05 +bytes used=345952568, alloc=4652204, time=33.12 + 17 33 29 +- ---- DATA(0, 2, -1) - ---- DATA(2, 0, -1) - ---- DATA(0, -1, 2) + 3000 2000 6000 + + 167 79 39 + - ----- DATA(0, 2, 2) - ---- DATA(1, 0, 2) - ---- DATA(-1, 0, -1) + 12000 2000 4000 + + 281 161 87 + + ----- DATA(2, -1, -1) - ---- DATA(0, 0, 0) - ---- DATA(1, 0, 0) + 12000 4000 2000 + + 21 299 87 + + --- DATA(0, 1, 0) + ---- DATA(1, 1, 0) - ---- DATA(0, 0, 1) + 250 4000 2000 + + 191 299 133 + - ---- DATA(1, 0, 1) + ---- DATA(0, 1, 1) + ---- DATA(1, 1, 1) + 4000 4000 2000 + + 41 137 449 + - --- DATA(2, 2, -1) - ----- DATA(1, 2, -1) - ----- DATA(-1, 2, -1) + 750 12000 12000 + + 191 137 29 + + ---- DATA(2, 1, -1) - ---- DATA(2, 0, 0) - ---- DATA(2, -1, 0) + 4000 4000 6000 + + 79 349 17 + + ---- DATA(1, 2, 0) + ----- DATA(0, 2, 0) - ---- DATA(-1, 2, 0) + 3000 12000 3000 + + 53 167 53 + + ---- DATA(2, 1, 0) - ----- DATA(2, 2, 0) + ----- DATA(2, -1, 1) + 1000 12000 12000 + + 79 137 183 + - ---- DATA(2, 0, 1) - ----- DATA(-1, 2, 1) + ---- DATA(2, 1, 1) + 2000 12000 4000 + + 319 79 281 + + ----- DATA(1, 2, 1) + ---- DATA(0, 2, 1) + ----- DATA(-1, -1, 2) + 12000 3000 12000 + + 53 129 + - 4/375 DATA(2, 2, 1) + ----- DATA(1, -1, 2) - ---- DATA(2, 0, 2) + 12000 4000 + + 137 33 307 + - ---- DATA(0, 0, 2) - ---- DATA(-1, 0, 2) + ---- DATA(2, -1, 2) + 4000 2000 6000 + + 183 53 191 + + ---- DATA(1, 1, 2) + ---- DATA(0, 1, 2) + ---- DATA(-1, 1, 2) + 4000 1000 4000 + + 41 13 + - --- DATA(-1, 2, 2) + --- DATA(2, 1, 2) - 4/375 DATA(1, 2, 2) + 750 500 + + 437 691 49 + - ---- DATA(0, -1, 0) - ----- DATA(1, -1, 0) - ---- DATA(-1, 0, 0) + 6000 12000 2000 + + 323 97 691 + + ---- DATA(-1, 1, 0) - ---- DATA(-1, -1, 1) - ----- DATA(0, -1, 1) + 4000 3000 12000 + + 17 107 141 + - --- DATA(1, -1, 1) - ---- DATA(-1, 0, 1) + ---- DATA(-1, 1, 1) + 375 4000 2000 + + 49 107 157 + - ---- DATA(0, 0, -1) - ---- DATA(1, 0, -1) + ---- DATA(-1, 1, -1) + 2000 4000 2000 + + 323 141 607 + + ---- DATA(0, 1, -1) + ---- DATA(1, 1, -1) - ----- DATA(-1, -1, 0) + 4000 2000 12000 + + 47 607 97 + - ---- DATA(-1, -1, -1) - ----- DATA(0, -1, -1) - ---- DATA(1, -1, -1) + 1500 12000 3000 + + 539 + - ----- DATA(2, 2, 2) - 3/2000 x DATA(2, 2, -1) - 9/1000 x DATA(2, -1, 2) + 12000 + + 43 19 + + ---- x DATA(2, 1, 0) + ---- x DATA(2, 0, 1) - 1/80 x y DATA(1, 1, 0) + 2000 1000 + + - 1/80 y z DATA(0, 0, 1) + 3/80 x y DATA(2, 2, 1) + 1/80 y z DATA(0, 2, 1) + + + 3/80 y z DATA(0, 2, 2) + 3/80 x y DATA(-1, 0, 0) + + - 1/80 x y DATA(1, 0, 1) - 1/80 x y DATA(0, -1, 0) + + + 3/80 y z DATA(-1, 0, -1) - 1/80 y z DATA(2, 2, 0) + + 2 + + 1/80 x y DATA(1, 2, 2) + 3/160 x DATA(-1, 2, 2) + + 2 2 + + 1/160 x DATA(2, 1, 2) - 3/160 x DATA(1, 2, 2) + + 2 2 + + 3/160 x DATA(0, -1, 0) + 3/160 x DATA(1, -1, 0) + + 2 2 + - 1/160 x DATA(-1, 0, 0) + 1/160 x DATA(-1, 1, 0) + + 2 2 2 + + 1/160 x DATA(2, 1, 1) - 3/160 x DATA(1, 2, 1) - 3/160 x DATA(0, 2, 1) + + 2 2 + - 3/160 x DATA(-1, -1, 2) + 3/160 x DATA(2, 2, 1) + + 2 2 + + 3/160 x DATA(1, -1, 2) - 1/160 x DATA(2, 0, 2) + + 2 2 + + 1/160 x DATA(0, 0, 2) - 1/160 x DATA(-1, 0, 2) + + 2 2 + - 3/160 x DATA(2, -1, 2) - 1/160 x DATA(1, 1, 2) + + 2 2 + - 1/160 x DATA(0, 1, 2) + 1/160 x DATA(-1, 1, 2) + + 2 147 + - 3/160 x DATA(0, 2, -1) + ---- x DATA(-1, -1, -1) + 2000 + + 37 57 + - 1/2000 x DATA(0, -1, -1) - ---- x DATA(1, -1, -1) - ---- x DATA(2, 2, 2) + 1000 2000 + + 13 31 + - ---- x DATA(0, -1, 1) - 9/1000 x DATA(-1, 2, 2) + ---- x DATA(2, 1, 2) + 2000 2000 + + 31 + + ---- x DATA(1, 2, 2) - 7/2000 x DATA(0, -1, 0) - 1/80 x y DATA(1, 0, -1) + 2000 + + 2 2 + + 3/160 z DATA(-1, 2, 2) + 1/160 z DATA(2, 1, 2) + + 2 2 + + 3/160 z DATA(1, 2, 2) + 3/160 z DATA(0, -1, 0) + + 2 2 + + 3/160 z DATA(1, -1, 0) + 1/160 z DATA(-1, 0, 0) + + 2 2 + - 1/160 z DATA(-1, 1, 0) + 3/160 z DATA(2, 2, -1) + + 2 2 + + 3/160 z DATA(1, 2, -1) + 3/160 z DATA(-1, 2, -1) + + 2 2 + + 1/160 z DATA(2, 1, -1) + 1/160 z DATA(2, 0, 0) + + 2 2 + + 3/160 z DATA(2, -1, 0) - 3/160 z DATA(1, 2, 0) + + 2 2 + - 3/160 z DATA(0, 2, 0) - 3/160 z DATA(-1, 2, 0) + + 2 2 + - 1/160 z DATA(2, 1, 0) - 3/160 z DATA(2, 2, 0) + + 2 2 + + 3/160 z DATA(2, -1, 1) + 1/160 z DATA(2, 0, 1) + + 2 2 + - 3/160 z DATA(-1, 2, 1) - 1/160 z DATA(2, 1, 1) + + 2 2 + - 3/160 x DATA(-1, -1, 1) + 3/160 x DATA(1, -1, 1) + + 2 2 + - 1/160 x DATA(-1, 0, 1) + 1/160 x DATA(-1, 1, 1) + + 2 2 + + 1/160 x DATA(0, 0, -1) + 1/160 x DATA(1, 0, -1) + + 2 2 + + 1/160 x DATA(-1, 1, -1) - 1/160 x DATA(0, 1, -1) + + 2 2 + - 1/160 x DATA(1, 1, -1) - 3/160 x DATA(-1, -1, 0) + + 2 2 + - 3/160 x DATA(-1, -1, -1) + 3/160 x DATA(0, -1, -1) + + 2 2 + + 3/160 x DATA(1, -1, -1) + 3/160 x DATA(2, 2, 2) + + 2 + + 3/160 x DATA(0, -1, 1) - 3/80 x y DATA(2, 0, -1) + + 2 2 + - 3/160 z DATA(2, 2, 1) - 3/160 z DATA(1, -1, 2) + + 2 2 + - 1/160 z DATA(2, 0, 2) - 1/160 z DATA(0, 0, 2) + + 2 2 + - 1/160 z DATA(-1, 0, 2) - 3/160 z DATA(2, -1, 2) + + 2 2 + + 1/160 z DATA(1, 1, 2) + 1/160 z DATA(0, 1, 2) + + 2 2 + + 1/160 z DATA(-1, 1, 2) + 3/160 z DATA(0, 2, -1) + + 2 2 + + 3/160 z DATA(-1, -1, 1) + 3/160 z DATA(1, -1, 1) + + 2 2 + + 1/160 z DATA(-1, 0, 1) - 1/160 z DATA(-1, 1, 1) + + 2 2 + - 1/160 z DATA(0, 0, -1) - 1/160 z DATA(1, 0, -1) + + 2 2 + + 1/160 z DATA(-1, 1, -1) + 1/160 z DATA(0, 1, -1) + + 2 2 + + 1/160 z DATA(1, 1, -1) + 3/160 z DATA(-1, -1, 0) + + 2 2 + - 3/160 z DATA(-1, -1, -1) - 3/160 z DATA(0, -1, -1) + + 2 2 + - 3/160 z DATA(1, -1, -1) + 3/160 z DATA(2, 2, 2) + + 2 37 43 + + 3/160 z DATA(0, -1, 1) + ---- z DATA(1, 2, 1) + ---- z DATA(0, 2, 1) + 2000 2000 + + 31 + - 9/250 z DATA(-1, -1, 2) + ---- z DATA(2, 2, 1) - 9/500 z DATA(1, -1, 2) + 2000 + + 11 13 + + --- z DATA(2, 0, 2) + 2/125 z DATA(0, 0, 2) + ---- z DATA(-1, 0, 2) + 500 1000 + + 37 43 + - 9/1000 z DATA(2, -1, 2) + ---- z DATA(1, 1, 2) + ---- z DATA(0, 1, 2) + 2000 2000 + + 49 27 37 + + ---- z DATA(-1, 1, 2) - ---- z DATA(0, 2, -1) - ---- z DATA(-1, -1, 1) + 2000 1000 1000 + + 31 + - ---- z DATA(1, -1, 1) + 2/125 z DATA(0, 2, 0) - 7/250 z DATA(2, 1, -1) + 1000 + + 19 23 19 + - ---- z DATA(2, -1, 0) - ---- z DATA(2, 0, 0) - ---- z DATA(2, 0, -1) + 2000 2000 2000 + + 27 21 19 + - ---- z DATA(0, -1, 2) - ---- z DATA(0, 2, 2) + ---- z DATA(1, 0, 2) + 1000 2000 1000 + + 93 19 + - 1/2000 z DATA(-1, 0, -1) + ---- z DATA(2, -1, -1) - ---- z DATA(0, 0, 0) + 2000 2000 + + 21 + - ---- z DATA(1, 0, 0) - 3/1000 z DATA(0, 1, 0) - 1/500 z DATA(1, 1, 0) + 2000 + + 31 + - 3/1000 z DATA(0, 0, 1) - 1/500 z DATA(1, 0, 1) + ---- z DATA(0, 1, 1) + 2000 + + 29 + + ---- z DATA(1, 1, 1) - 9/1000 z DATA(2, 2, -1) - 9/500 z DATA(1, 2, -1) + 2000 + + 2 + - 9/250 z DATA(-1, 2, -1) - 3/160 z DATA(1, 2, 1) + + 2 2 + - 3/160 z DATA(0, 2, 1) - 3/160 z DATA(-1, -1, 2) + + 17 2 + - ---- z DATA(-1, 0, 0) - 1/250 z DATA(-1, 1, 0) + 3/32 y DATA(2, 0, -1) + 2000 + + 2 2 2 + - 1/32 y DATA(0, -1, 2) + 1/32 y DATA(0, 2, 2) + 3/32 y DATA(1, 0, 2) + + 2 2 + + 3/32 y DATA(-1, 0, -1) - 1/32 y DATA(2, -1, -1) + + 2 2 2 + + 3/32 y DATA(0, 0, 0) + 3/32 y DATA(1, 0, 0) - 3/32 y DATA(0, 1, 0) + + 2 2 2 + - 3/32 y DATA(1, 1, 0) + 3/32 y DATA(0, 0, 1) + 3/32 y DATA(1, 0, 1) + + 2 2 2 + - 3/32 y DATA(0, 1, 1) - 3/32 y DATA(1, 1, 1) + 1/32 y DATA(2, 2, -1) + + 2 2 + + 1/32 y DATA(1, 2, -1) + 1/32 y DATA(-1, 2, -1) + + 2 33 19 + - 3/32 y DATA(2, 1, -1) + ---- z DATA(-1, 1, 1) + ---- z DATA(1, 2, 0) + 2000 1000 + + 13 11 + + ---- z DATA(-1, 2, 0) - 1/1000 z DATA(2, 1, 0) + --- z DATA(2, 2, 0) + 1000 500 + + 49 + - 7/250 z DATA(2, -1, 1) - 1/1000 z DATA(2, 0, 1) + ---- z DATA(-1, 2, 1) + 2000 + + 27 2 + + ---- z DATA(2, 1, 1) - 1/80 y z DATA(1, 1, 1) - 3/32 y DATA(2, 1, 2) + 2000 + + 2 2 2 + - 1/32 y DATA(0, -1, 0) - 1/32 y DATA(1, -1, 0) + 3/32 y DATA(-1, 0, 0) + + 2 2 2 + - 3/32 y DATA(-1, 1, 0) + 3/32 y DATA(2, 0, 0) - 1/32 y DATA(2, -1, 0) + + 2 2 2 + + 1/32 y DATA(1, 2, 0) + 1/32 y DATA(0, 2, 0) + 1/32 y DATA(-1, 2, 0) + + 2 + - 3/32 y DATA(2, 1, 0) - 1/250 z DATA(-1, 0, 1) - 7/2000 z DATA(0, 0, -1) + + 13 37 17 + - ---- z DATA(1, 0, -1) - ---- z DATA(-1, 1, -1) - --- z DATA(0, 1, -1) + 2000 1000 500 + + 31 + - ---- z DATA(1, 1, -1) - 1/2000 z DATA(-1, -1, 0) + 1000 + + 147 129 + + ---- z DATA(-1, -1, -1) + ---- z DATA(0, -1, -1) + 2000 2000 + + 111 57 17 + + ---- z DATA(1, -1, -1) - ---- z DATA(2, 2, 2) - --- z DATA(0, -1, 1) + 2000 2000 500 + + 31 39 + - 3/2000 z DATA(-1, 2, 2) + ---- z DATA(2, 1, 2) - ---- z DATA(1, 2, 2) + 2000 2000 + + 13 2 + - 7/2000 z DATA(0, -1, 0) - ---- z DATA(1, -1, 0) + 1/32 y DATA(1, 2, 2) + 2000 + + 2 2 2 + + 1/32 y DATA(-1, 2, 1) - 3/32 y DATA(2, 1, 1) + 1/32 y DATA(1, 2, 1) + + 2 2 2 + + 1/32 y DATA(0, 2, 1) - 1/32 y DATA(-1, -1, 2) + 1/32 y DATA(2, 2, 1) + + 2 2 2 + - 1/32 y DATA(1, -1, 2) + 3/32 y DATA(2, 0, 2) + 3/32 y DATA(0, 0, 2) + + 2 2 2 + + 3/32 y DATA(-1, 0, 2) - 1/32 y DATA(2, -1, 2) - 3/32 y DATA(1, 1, 2) + + 2 2 2 + - 3/32 y DATA(0, 1, 2) - 3/32 y DATA(-1, 1, 2) + 1/32 y DATA(0, 2, -1) + + 2 2 + - 1/32 y DATA(-1, -1, 1) - 1/32 y DATA(1, -1, 1) + + 2 2 2 + + 3/32 y DATA(-1, 0, 1) - 3/32 y DATA(-1, 1, 1) + 3/32 y DATA(0, 0, -1) + + 2 2 + + 3/32 y DATA(1, 0, -1) - 3/32 y DATA(-1, 1, -1) + + 2 2 + - 3/32 y DATA(0, 1, -1) - 3/32 y DATA(1, 1, -1) + + 2 2 + - 1/32 y DATA(-1, -1, 0) - 1/32 y DATA(-1, -1, -1) + + 2 2 + - 1/32 y DATA(0, -1, -1) - 1/32 y DATA(1, -1, -1) + + 2 2 2 + + 1/32 y DATA(2, 2, 2) - 1/32 y DATA(0, -1, 1) + 1/32 y DATA(-1, 2, 2) + + - 1/8 y DATA(-1, 0, 2) + 1/40 y DATA(2, -1, 2) + 7/80 y DATA(1, 1, 2) + + + 3/40 y DATA(0, 1, 2) + 1/16 y DATA(-1, 1, 2) + 1/40 y DATA(0, 2, -1) + + 11 + + 3/40 y DATA(-1, -1, 1) + 1/20 y DATA(1, -1, 1) - -- y DATA(-1, 0, 1) + 80 + + 11 + + 1/20 y DATA(-1, 1, 1) - 3/20 y DATA(0, 0, -1) - -- y DATA(1, 0, -1) + 80 + + + 1/40 y DATA(-1, 1, -1) + 3/80 y DATA(0, 1, -1) + 1/20 y DATA(1, 1, -1) + + + 7/80 y DATA(-1, -1, 0) + 1/10 y DATA(-1, -1, -1) + + + 7/80 y DATA(0, -1, -1) + 3/40 y DATA(1, -1, -1) - 3/80 y DATA(2, 2, 2) + + + 1/16 y DATA(2, 1, -1) - 9/80 y DATA(2, 0, 0) + 1/20 y DATA(0, -1, 2) + + 19 11 + - ---- x DATA(0, -1, 2) + --- x DATA(0, 2, 2) - 1/1000 x DATA(1, 0, 2) + 2000 500 + + - 1/2000 x DATA(-1, 0, -1) - 9/250 x DATA(2, -1, -1) + + 19 + - ---- x DATA(0, 0, 0) - 3/1000 x DATA(1, 0, 0) - 3/1000 x DATA(0, 1, 0) + 2000 + + 31 21 13 + + ---- x DATA(1, 1, 0) - ---- x DATA(0, 0, 1) + ---- x DATA(2, 0, -1) + 2000 2000 1000 + + 2 2 2 + + 1/32 y DATA(2, 2, 0) - 1/32 y DATA(2, -1, 1) + 3/32 y DATA(2, 0, 1) + + + 3/1000 x z DATA(1, -1, 0) - 3/1000 x z DATA(0, -1, 0) + + + 9/1000 x z DATA(1, 2, 2) + 9/1000 x z DATA(2, 1, 2) + + + 9/1000 x z DATA(2, 0, -1) + 1/80 y z DATA(0, 1, 0) + + - 3/80 y z DATA(-1, 2, -1) + 3/80 y z DATA(2, 0, -1) + + - 3/80 x y DATA(-1, -1, 2) - 1/80 x y DATA(0, 2, 1) + + + 1/80 x y DATA(1, 2, 1) - 3/80 y z DATA(1, 0, 2) - 3/80 x y DATA(2, 1, 0) + + 13 + - 3/80 x y DATA(-1, -1, -1) - -- y DATA(-1, 0, -1) + 80 + + 11 + + 1/16 y DATA(2, -1, -1) - -- y DATA(0, 0, 0) - 1/8 y DATA(1, 0, 0) + 80 + + + 1/20 y DATA(0, 1, 0) + 1/16 y DATA(1, 1, 0) - 1/8 y DATA(0, 0, 1) + + - 9/80 y DATA(1, 0, 1) + 1/16 y DATA(0, 1, 1) + 3/40 y DATA(1, 1, 1) + + + 1/80 y DATA(1, 2, -1) + 3/80 y DATA(-1, 2, -1) + 1/20 y DATA(2, -1, 0) + + + 1/80 y DATA(0, 2, 0) + 1/40 y DATA(-1, 2, 0) + 3/40 y DATA(2, 1, 0) + + - 1/80 y DATA(2, 2, 0) + 3/80 y DATA(2, -1, 1) - 1/10 y DATA(2, 0, 1) + + + 1/80 y DATA(-1, 2, 1) + 7/80 y DATA(2, 1, 1) - 1/80 y DATA(1, 2, 1) + + + 1/16 y DATA(-1, -1, 2) - 1/40 y DATA(2, 2, 1) + 3/80 y DATA(1, -1, 2) + + - 7/80 y DATA(2, 0, 2) - 9/80 y DATA(0, 0, 2) - 3/1000 x z DATA(2, 0, 1) + + 27 + - 9/1000 x z DATA(2, -1, 1) - ---- x z DATA(-1, 2, 2) + 1000 + + 27 + + 3/1000 x z DATA(0, -1, 1) + ---- x z DATA(2, 2, 2) + 1000 + + + 9/1000 x z DATA(1, -1, -1) - 9/1000 x z DATA(0, -1, -1) + + 27 + - ---- x z DATA(-1, -1, -1) - 9/1000 x z DATA(-1, -1, 0) + 1000 + + - 3/1000 x z DATA(1, 1, -1) - 3/80 x y DATA(-1, 2, -1) + + + 3/1000 x z DATA(0, 1, -1) + 9/1000 x z DATA(-1, 1, -1) + + + 3/1000 x z DATA(1, 0, -1) - 3/1000 x z DATA(0, 0, -1) + + - 3/1000 x z DATA(-1, 1, 1) + 3/1000 x z DATA(-1, 0, 1) + + - 3/1000 x z DATA(1, -1, 1) + 9/1000 x z DATA(-1, -1, 1) + + + 9/1000 x z DATA(0, 2, -1) + 3/1000 x z DATA(-1, 1, 0) + + - 3/1000 x z DATA(-1, 0, 0) - 1/80 y z DATA(1, 2, 0) + + + 1/80 y z DATA(1, 2, 1) - 3/80 x y DATA(-1, 2, 2) + + + 1/80 x y DATA(0, 0, -1) - 3/80 x y DATA(-1, 2, 0) + + - 3/80 x y DATA(2, 0, 0) - 3/80 y z DATA(2, -1, -1) + + + 3/80 x y DATA(2, -1, 2) + 1/80 y z DATA(2, -1, 1) + + - 1/80 y z DATA(2, -1, 0) + 3/80 y z DATA(-1, -1, 2) + + - 3/80 x y DATA(2, 0, 1) + 3/80 y z DATA(0, -1, 2) + + - 3/80 x y DATA(-1, -1, 0) + 3/80 x y DATA(-1, 1, 1) + + + 3/80 y z DATA(0, 1, -1) + 3/80 y z DATA(-1, 1, -1) + + + 3/80 y z DATA(1, 0, -1) + 3/80 y z DATA(0, 0, -1) + + - 1/80 y z DATA(-1, 1, 1) - 1/80 y z DATA(-1, 0, 1) + + + 1/80 y z DATA(1, -1, 1) + 1/80 y z DATA(-1, -1, 1) + + - 3/80 y z DATA(0, 2, -1) - 3/80 y z DATA(-1, 1, 2) + + - 3/80 y z DATA(0, 1, 2) - 3/80 y z DATA(1, 1, 2) + + + 3/80 x y DATA(2, -1, 0) + 3/80 y z DATA(2, -1, 2) + + - 3/80 y z DATA(-1, 0, 2) - 3/80 y z DATA(0, 0, 2) + + + 3/80 x y DATA(-1, 0, 2) - 3/80 x y DATA(2, 1, -1) - 1/8 y DATA(2, 0, -1) + + - 1/80 y DATA(0, 2, 2) - 1/10 y DATA(1, 0, 2) - 3/80 x y DATA(-1, -1, 1) + + 2 2 2 + + 1/160 z DATA(0, 0, 0) + 1/160 z DATA(1, 0, 0) - 1/160 z DATA(0, 1, 0) + + 2 2 2 + - 1/160 z DATA(1, 1, 0) + 1/160 z DATA(0, 0, 1) + 1/160 z DATA(1, 0, 1) + + 2 2 + - 1/160 z DATA(0, 1, 1) - 1/160 z DATA(1, 1, 1) - 1/1000 x DATA(0, 1, 2) + + 13 111 + - 7/250 x DATA(-1, 1, 2) + ---- x DATA(0, 2, -1) + ---- x DATA(-1, -1, 1) + 1000 2000 + + 31 13 31 + - ---- x DATA(1, -1, 1) - ---- x DATA(-1, 0, 1) - ---- x DATA(-1, 1, 1) + 1000 2000 1000 + + 17 37 + - ---- x DATA(0, 0, -1) - 1/250 x DATA(1, 0, -1) - ---- x DATA(-1, 1, -1) + 2000 1000 + + 33 129 + - 1/250 x DATA(0, 1, -1) + ---- x DATA(1, 1, -1) + ---- x DATA(-1, -1, 0) + 2000 2000 + + + 1/16 y DATA(0, -1, 1) + 1/10 y DATA(2, 1, 2) - 1/40 y DATA(1, 2, 2) + + + 3/40 y DATA(0, -1, 0) + 1/16 y DATA(1, -1, 0) - 3/20 y DATA(-1, 0, 0) + + 2 + + 3/80 y DATA(-1, 1, 0) - 1/160 z DATA(2, 0, -1) + + 2 2 + - 3/160 z DATA(0, -1, 2) + 3/160 z DATA(0, 2, 2) + + 2 2 + - 1/160 z DATA(1, 0, 2) - 1/160 z DATA(-1, 0, -1) + + 2 + - 3/160 z DATA(2, -1, -1) - 1/80 y z DATA(0, 1, 1) + + 2 + + 1/80 x y DATA(1, -1, 0) - 3/160 x DATA(2, -1, 1) + + 2 2 + - 1/160 x DATA(2, 0, 1) + 3/160 x DATA(-1, 2, 1) - 1/500 x DATA(1, 0, 1) + + 29 49 + - 1/500 x DATA(0, 1, 1) + ---- x DATA(1, 1, 1) + ---- x DATA(1, 2, -1) + 2000 2000 + + 49 + - 9/250 x DATA(-1, 2, -1) + ---- x DATA(2, 1, -1) + 2/125 x DATA(2, 0, 0) + 2000 + + 27 43 + - ---- x DATA(2, -1, 0) + ---- x DATA(1, 2, 0) + 2/125 x DATA(0, 2, 0) + 1000 2000 + + 27 21 + - ---- x DATA(-1, 2, 0) - ---- x DATA(2, 2, 0) - 9/500 x DATA(2, -1, 1) + 1000 2000 + + 37 37 + - 9/500 x DATA(-1, 2, 1) + ---- x DATA(2, 1, 1) + ---- x DATA(1, 2, 1) + 2000 2000 + + 19 93 39 + + ---- x DATA(0, 2, 1) + ---- x DATA(-1, -1, 2) - ---- x DATA(2, 2, 1) + 1000 2000 2000 + + 11 23 + - 7/250 x DATA(1, -1, 2) + --- x DATA(2, 0, 2) - ---- x DATA(0, 0, 2) + 500 2000 + + 19 27 17 + - ---- x DATA(-1, 0, 2) + ---- x DATA(1, 1, 2) - --- x DATA(1, -1, 0) + 2000 2000 500 + + 17 2 + - 7/2000 x DATA(-1, 0, 0) - --- x DATA(-1, 1, 0) - 1/160 x DATA(2, 0, -1) + 500 + + 2 2 + + 3/160 x DATA(0, -1, 2) - 3/160 x DATA(0, 2, 2) + + 2 2 + + 1/160 x DATA(1, 0, 2) - 1/160 x DATA(-1, 0, -1) + + 2 2 + - 3/160 x DATA(2, -1, -1) + 1/160 x DATA(0, 0, 0) + + 2 2 2 + + 1/160 x DATA(1, 0, 0) - 1/160 x DATA(0, 1, 0) - 1/160 x DATA(1, 1, 0) + + 2 2 2 + + 1/160 x DATA(0, 0, 1) + 1/160 x DATA(1, 0, 1) - 1/160 x DATA(0, 1, 1) + + 2 2 + - 1/160 x DATA(1, 1, 1) + 3/160 x DATA(2, 2, -1) + + 2 2 + - 3/160 x DATA(1, 2, -1) + 3/160 x DATA(-1, 2, -1) + + 2 2 + + 1/160 x DATA(2, 1, -1) - 1/160 x DATA(2, 0, 0) + + 2 2 + - 3/160 x DATA(2, -1, 0) - 3/160 x DATA(1, 2, 0) + + 2 2 + - 3/160 x DATA(0, 2, 0) + 3/160 x DATA(-1, 2, 0) + + 2 2 + + 1/160 x DATA(2, 1, 0) + 3/160 x DATA(2, 2, 0) + 1/80 x y DATA(0, 1, 2) + + + 1/80 y z DATA(2, 2, 1) + 3/80 x y DATA(-1, 1, 0) + + - 1/80 x y DATA(1, 0, 0) + 1/80 x y DATA(1, 2, -1) + + - 3/80 y z DATA(2, 0, 2) + 3/80 y z DATA(1, -1, 2) + + - 1/80 x y DATA(0, 2, -1) - 3/80 x y DATA(2, 1, 2) + + - 3/80 y z DATA(2, 2, -1) + 1/80 x y DATA(1, -1, -1) + + + 1/80 y z DATA(1, 1, 0) + 1/80 x y DATA(1, -1, 2) + + - 1/80 x y DATA(0, 2, 0) + 3/80 x y DATA(2, 2, 0) + + - 1/80 x y DATA(0, -1, 2) + 1/80 y z DATA(2, 1, 0) + + - 9/1000 x z DATA(0, 2, 2) + 9/1000 x z DATA(0, -1, 2) + + + 1/80 y z DATA(-1, 1, 0) + 1/80 y z DATA(-1, 0, 0) + + - 1/80 y z DATA(1, -1, 0) - 1/80 y z DATA(0, -1, 0) + + + 3/80 y z DATA(1, 2, 2) + 3/80 x y DATA(-1, 1, 2) + + - 3/80 y z DATA(2, 1, 2) + 3/80 y z DATA(-1, 2, 2) + + + 1/80 y z DATA(0, -1, 1) + 3/80 y z DATA(2, 2, 2) + + - 3/80 y z DATA(1, -1, -1) - 3/80 y z DATA(0, -1, -1) + + - 3/80 y z DATA(-1, -1, -1) + 1/80 x y DATA(1, 2, 0) + + - 1/80 y z DATA(-1, -1, 0) + 3/80 y z DATA(1, 1, -1) + + - 9/1000 x z DATA(2, 2, 0) - 3/1000 x z DATA(2, 1, 0) + + + 9/1000 x z DATA(-1, 2, 0) + 3/1000 x z DATA(0, 2, 0) + + - 3/1000 x z DATA(1, 2, 0) + 9/1000 x z DATA(2, -1, 0) + + + 3/1000 x z DATA(2, 0, 0) - 9/1000 x z DATA(2, 1, -1) + + 27 + + ---- x z DATA(-1, 2, -1) - 9/1000 x z DATA(1, 2, -1) + 1000 + + 27 + - ---- x z DATA(2, 2, -1) + 1/1000 x z DATA(1, 1, 1) + 1000 + + - 1/1000 x z DATA(0, 1, 1) - 1/1000 x z DATA(1, 0, 1) + + + 1/1000 x z DATA(0, 0, 1) - 1/1000 x z DATA(1, 1, 0) + + + 1/1000 x z DATA(0, 1, 0) + 1/1000 x z DATA(1, 0, 0) + + 27 + - 1/1000 x z DATA(0, 0, 0) + ---- x z DATA(2, -1, -1) + 1000 + + - 9/1000 x z DATA(-1, 0, -1) - 3/1000 x z DATA(1, 0, 2) + + - 9/1000 x z DATA(-1, 1, 2) + 3/80 x y DATA(-1, 1, -1) + + - 1/80 x y DATA(1, 1, -1) - 3/1000 x z DATA(0, 1, 2) + + 27 + + 3/1000 x z DATA(1, 1, 2) - ---- x z DATA(2, -1, 2) + 1000 + + + 9/1000 x z DATA(-1, 0, 2) + 3/1000 x z DATA(0, 0, 2) + + - 1/80 x y DATA(0, -1, -1) - 9/1000 x z DATA(2, 0, 2) + + - 9/1000 x z DATA(1, -1, 2) + 9/1000 x z DATA(2, 2, 1) + + 27 + + ---- x z DATA(-1, -1, 2) - 3/1000 x z DATA(0, 2, 1) + 1000 + + + 3/1000 x z DATA(1, 2, 1) + 3/1000 x z DATA(2, 1, 1) + + - 9/1000 x z DATA(-1, 2, 1) - 1/80 y z DATA(2, 1, 1) + + + 3/80 x y DATA(-1, 0, 1) + 1/80 y z DATA(-1, 2, 1) + + - 1/80 x y DATA(1, 1, 2) + 1/80 x y DATA(1, -1, 1) + + - 3/80 x y DATA(2, 1, 1) - 3/80 x y DATA(2, 0, 2) + 3/80 x y DATA(2, 2, 2) + + - 1/80 y z DATA(2, 0, 1) - 1/80 y z DATA(-1, 2, 0) + + - 1/80 x y DATA(0, -1, 1) + 3/80 y z DATA(2, 1, -1) + + - 1/80 y z DATA(0, 2, 0) + 1/80 x y DATA(0, 0, 1) + 1/80 y z DATA(0, 0, 0) + + + 1/80 y z DATA(1, 0, 0) + 1/80 x y DATA(0, 1, -1) + + - 3/80 x y DATA(-1, 2, 1) + 1/80 x y DATA(0, 1, 1) + + + 1/80 y z DATA(2, 0, 0) + 3/80 x y DATA(2, -1, 1) + + - 3/80 y z DATA(1, 2, -1) - 1/80 x y DATA(1, 1, 1) + + - 1/80 y z DATA(1, 0, 1) - 1/80 x y DATA(0, 2, 2) - 1/80 x y DATA(1, 0, 2) + + + 1/80 x y DATA(0, 1, 0) + 3/80 x y DATA(2, -1, -1) + + + 3/80 x y DATA(-1, 0, -1) + 3/80 x y DATA(2, 2, -1) + + + 1/80 x y DATA(0, 0, 0) + 1/80 x y DATA(0, 0, 2) + +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=346974792, alloc=4652204, time=33.19 +bytes used=347974964, alloc=4652204, time=33.26 +bytes used=348975240, alloc=4652204, time=33.33 +bytes used=349979160, alloc=4652204, time=33.40 +bytes used=350979516, alloc=4652204, time=33.48 +bytes used=351998604, alloc=4652204, time=33.55 +bytes used=353000648, alloc=4652204, time=33.63 +bytes used=354000780, alloc=4652204, time=33.71 +bytes used=355015560, alloc=4914300, time=33.78 + 2 47 147 2 +[COEFF(-1, -1, -1) = - 3/160 x - ---- - 3/80 x y + ---- z - 3/160 z + 1/10 y + 1500 2000 + + 147 2 27 + + ---- x - 1/32 y - ---- x z - 3/80 y z, COEFF(0, -1, -1) = - 1/80 x y + 2000 1000 + + 2 2 2 607 129 + - 1/2000 x + 3/160 x - 3/160 z - 1/32 y - 9/1000 x z - ----- + ---- z + 12000 2000 + + 37 111 + + 7/80 y - 3/80 y z, COEFF(1, -1, -1) = - ---- x - 3/80 y z + ---- z + 1000 2000 + + 2 2 97 2 + + 1/80 x y - 3/160 z - 1/32 y + 9/1000 x z - ---- + 3/40 y + 3/160 x , + 3000 + + 281 27 2 93 + COEFF(2, -1, -1) = ----- - 3/80 y z + ---- x z - 1/32 y + 1/16 y + ---- z + 12000 1000 2000 + + 2 2 2 + - 3/160 z - 9/250 x - 3/160 x + 3/80 x y, COEFF(-1, 0, -1) = - 1/160 z + + 13 2 + - -- y - 1/2000 x - 9/1000 x z + 3/32 y - 1/2000 z + 3/80 y z + 3/80 x y + 80 + + 39 2 17 49 2 + - ---- - 1/160 x , COEFF(0, 0, -1) = 3/80 y z - ---- x - ---- + 3/32 y + 4000 2000 2000 + + 2 2 + - 7/2000 z + 1/160 x - 3/1000 x z + 1/80 x y - 3/20 y - 1/160 z , + + 11 107 2 2 + COEFF(1, 0, -1) = - 1/80 x y - -- y - ---- - 1/160 z - 1/250 x + 1/160 x + 80 4000 + + 13 2 + - ---- z + 3/1000 x z + 3/32 y + 3/80 y z, COEFF(2, 0, -1) = 3/80 y z + 2000 + + 19 33 2 2 2 13 + - ---- z - ---- - 1/160 z + 3/32 y + 9/1000 x z - 1/160 x + ---- x + 2000 2000 1000 + + 2 + - 3/80 x y - 1/8 y, COEFF(-1, 1, -1) = 3/80 y z + 1/160 x + 3/80 x y + + 37 37 2 157 2 + - ---- z - ---- x + 1/160 z + ---- - 3/32 y + 1/40 y + 9/1000 x z, + 1000 1000 2000 + + 17 2 2 2 + COEFF(0, 1, -1) = - --- z + 3/1000 x z + 1/160 z - 3/32 y - 1/160 x + 500 + + 323 + - 1/250 x + 3/80 y + 3/80 y z + ---- + 1/80 x y, COEFF(1, 1, -1) = + 4000 + + 2 141 2 31 + - 3/32 y - 1/80 x y + 3/80 y z + ---- - 1/160 x - 3/1000 x z - ---- z + 2000 1000 + + 2 33 2 + + 1/20 y + 1/160 z + ---- x, COEFF(2, 1, -1) = 1/160 z - 3/80 x y + 2000 + + 49 191 2 2 + + 1/16 y + ---- x + 3/80 y z + ---- - 3/32 y + 1/160 x - 7/250 z + 2000 4000 + + 27 + - 9/1000 x z, COEFF(-1, 2, -1) = ---- x z - 3/80 x y - 9/250 z - 9/250 x + 1000 + + 449 2 2 2 + - ----- + 1/32 y - 3/80 y z + 3/160 x + 3/160 z + 3/80 y, + 12000 + + 13 2 + COEFF(0, 2, -1) = ---- x - 3/80 y z - 1/80 x y + 9/1000 x z + 1/32 y + 1000 + + 27 2 17 2 + - ---- z + 3/160 z + 1/40 y - ---- - 3/160 x , COEFF(1, 2, -1) = + 1000 3000 + + 49 2 + - 9/1000 x z - 3/80 y z + 1/80 x y - 9/500 z + ---- x + 1/80 y + 3/160 z + 2000 + + 2 2 137 2 + - 3/160 x + 1/32 y - -----, COEFF(2, 2, -1) = - 3/80 y z + 3/160 z + 12000 + + 27 2 41 2 + - ---- x z + 3/160 x + 3/80 x y - --- - 9/1000 z + 1/32 y - 3/2000 x, + 1000 750 + + 2 129 607 + COEFF(-1, -1, 0) = - 1/32 y - 9/1000 x z - 1/2000 z + ---- x - ----- + 2000 12000 + + 2 2 + - 1/80 y z - 3/80 x y + 7/80 y - 3/160 x + 3/160 z , COEFF(0, -1, 0) = + + 2 2 437 2 + - 1/32 y - 7/2000 z + 3/160 x - ---- + 3/160 z - 1/80 x y + 3/40 y + 6000 + + 17 691 + - 1/80 y z - 7/2000 x - 3/1000 x z, COEFF(1, -1, 0) = - --- x - ----- + 500 12000 + + 13 2 2 + + 1/80 x y + 3/1000 x z - ---- z - 1/32 y + 3/160 z - 1/80 y z + 1/16 y + 2000 + + 2 2 + + 3/160 x , COEFF(2, -1, 0) = 1/20 y + 9/1000 x z - 1/32 y + 3/80 x y + + 29 27 19 2 2 + - ---- - ---- x - ---- z - 1/80 y z + 3/160 z - 3/160 x , COEFF(-1, 0, 0) + 6000 1000 2000 + + 17 2 + = - 3/20 y - 3/1000 x z - ---- z + 3/80 x y - 1/160 x - 7/2000 x + 2000 + + 2 49 2 19 11 + + 3/32 y + 1/80 y z - ---- + 1/160 z , COEFF(0, 0, 0) = - ---- x - -- y + 2000 2000 80 + + 2 19 2 161 + + 1/160 z - ---- z + 1/80 y z + 1/80 x y - 1/1000 x z + 1/160 x - ---- + 2000 4000 + + 2 2 + + 3/32 y , COEFF(1, 0, 0) = 1/1000 x z + 1/160 z + 1/80 y z - 3/1000 x + + 87 2 21 2 + - 1/8 y - ---- - 1/80 x y + 3/32 y - ---- z + 1/160 x , COEFF(2, 0, 0) = + 2000 2000 + + 2 23 + - 9/80 y + 1/80 y z - 1/160 x - ---- z - 3/80 x y + 3/1000 x z + 2/125 x + 2000 + + 2 137 2 17 323 + + 3/32 y - ---- + 1/160 z , COEFF(-1, 1, 0) = - --- x + ---- + 3/1000 x z + 4000 500 4000 + + 2 2 2 + - 1/160 z - 3/32 y + 1/160 x - 1/250 z + 1/80 y z + 3/80 x y + 3/80 y, + + 2 2 + COEFF(0, 1, 0) = - 1/160 x - 3/1000 x - 3/1000 z + 1/1000 x z - 3/32 y + + 21 2 + + 1/80 x y + --- + 1/20 y + 1/80 y z - 1/160 z , COEFF(1, 1, 0) = 1/80 y z + 250 + + 2 2 2 + - 1/160 x - 1/160 z - 1/500 z + 1/16 y - 3/32 y - 1/1000 x z - 1/80 x y + + 299 31 53 2 2 + + ---- + ---- x, COEFF(2, 1, 0) = ---- + 1/160 x + 1/80 y z - 3/32 y + 4000 2000 1000 + + 43 2 + + 3/40 y - 1/1000 z + ---- x - 3/1000 x z - 1/160 z - 3/80 x y, + 2000 + + 2 13 2 27 17 + COEFF(-1, 2, 0) = - 3/160 z + ---- z + 3/160 x - 3/80 x y - ---- x - ---- + 1000 1000 3000 + + 2 + + 1/32 y + 9/1000 x z - 1/80 y z + 1/40 y, COEFF(0, 2, 0) = 2/125 x + + 2 2 2 + - 1/80 x y - 3/160 x + 1/32 y + 1/80 y - 1/80 y z - 3/160 z + 2/125 z + + 349 19 2 + + ----- + 3/1000 x z, COEFF(1, 2, 0) = ---- z - 1/80 y z - 3/160 x + 12000 1000 + + 43 2 2 79 + + ---- x + 1/32 y - 3/160 z + ---- - 3/1000 x z + 1/80 x y, + 2000 3000 + + 167 2 2 21 11 + COEFF(2, 2, 0) = 3/80 x y - ----- + 1/32 y + 3/160 x - ---- x + --- z + 12000 2000 500 + + 2 + - 9/1000 x z - 1/80 y z - 1/80 y - 3/160 z , COEFF(-1, -1, 1) = 1/80 y z + + 2 2 37 111 + - 3/160 x + 3/40 y - 1/32 y - ---- z + ---- x + 9/1000 x z - 3/80 x y + 1000 2000 + + 97 2 2 691 + - ---- + 3/160 z , COEFF(0, -1, 1) = - 1/32 y + 3/1000 x z - ----- + 3000 12000 + + 17 2 13 2 + - --- z - 1/80 x y + 1/80 y z + 3/160 z - ---- x + 1/16 y + 3/160 x , + 500 2000 + + 2 17 2 31 + COEFF(1, -1, 1) = - 1/32 y - --- + 1/80 y z + 3/160 x - ---- z + 375 1000 + + 31 2 + - 3/1000 x z + 1/80 x y + 1/20 y - ---- x + 3/160 z , COEFF(2, -1, 1) = + 1000 + + 2 2 + 3/80 x y - 3/160 x - 9/1000 x z + 3/80 y - 7/250 z + 1/80 y z - 1/32 y + + 2 53 13 + + 3/160 z - 9/500 x + -----, COEFF(-1, 0, 1) = - 1/250 z - ---- x + 12000 2000 + + 2 2 11 107 + - 1/160 x + 3/80 x y + 1/160 z - -- y - 1/80 y z - ---- + 3/1000 x z + 80 4000 + + 2 21 + + 3/32 y , COEFF(0, 0, 1) = - ---- x - 3/1000 z - 1/80 y z + 1/80 x y + 2000 + + 2 2 2 87 + + 1/160 z + 1/160 x + 3/32 y + 1/1000 x z - ---- - 1/8 y, + 2000 + + 2 191 + COEFF(1, 0, 1) = - 1/500 z - 1/80 x y - 9/80 y + 1/160 x - 1/80 y z - ---- + 4000 + + 2 2 2 + - 1/1000 x z + 3/32 y - 1/500 x + 1/160 z , COEFF(2, 0, 1) = 1/160 z + + 79 2 2 + - ---- - 1/160 x - 1/80 y z - 1/1000 z - 3/1000 x z + 3/32 y - 3/80 x y + 2000 + + 19 31 2 + + ---- x - 1/10 y, COEFF(-1, 1, 1) = - ---- x - 1/80 y z - 1/160 z + 1000 1000 + + 2 141 33 2 + - 3/32 y + ---- + 3/80 x y + ---- z + 1/20 y - 3/1000 x z + 1/160 x , + 2000 2000 + + 2 299 31 + COEFF(0, 1, 1) = - 1/1000 x z - 1/160 z - 1/500 x + ---- + ---- z + 4000 2000 + + 2 2 + + 1/80 x y + 1/16 y - 1/80 y z - 3/32 y - 1/160 x , COEFF(1, 1, 1) = + + 29 133 29 2 2 + 3/40 y + ---- z + ---- + ---- x - 1/160 x - 1/80 x y - 1/160 z - 1/80 y z + 2000 2000 2000 + + 2 183 + + 1/1000 x z - 3/32 y , COEFF(2, 1, 1) = - 3/80 x y + ---- + 3/1000 x z + 4000 + + 2 27 37 2 2 + + 1/160 x + ---- z + ---- x + 7/80 y - 1/80 y z - 3/32 y - 1/160 z , + 2000 2000 + + 2 137 + COEFF(-1, 2, 1) = - 3/80 x y + 1/80 y z + 1/32 y - ----- - 9/1000 x z + 12000 + + 49 2 2 + + 1/80 y + ---- z - 3/160 z + 3/160 x - 9/500 x, COEFF(0, 2, 1) = + 2000 + + 2 19 79 43 2 + - 3/160 z + ---- x - 3/1000 x z + ---- + ---- z + 1/32 y + 1/80 y z + 1000 3000 2000 + + 2 37 319 2 + - 3/160 x - 1/80 x y, COEFF(1, 2, 1) = ---- x + ----- + 1/32 y + 2000 12000 + + 37 2 2 + + 3/1000 x z + ---- z + 1/80 x y - 3/160 z - 1/80 y - 3/160 x + 1/80 y z + 2000 + + 2 2 + , COEFF(2, 2, 1) = - 4/375 + 9/1000 x z + 3/160 x + 3/80 x y + 1/32 y + + 31 2 39 + + ---- z - 3/160 z + 1/80 y z - 1/40 y - ---- x, COEFF(-1, -1, 2) = + 2000 2000 + + 2 281 27 2 + 3/80 y z - 9/250 z - 3/160 z + ----- + ---- x z - 3/80 x y - 3/160 x + 12000 1000 + + 2 93 2 + + 1/16 y - 1/32 y + ---- x, COEFF(0, -1, 2) = 3/80 y z - 1/32 y + 2000 + + 2 29 19 27 2 + + 9/1000 x z + 3/160 x - ---- - ---- x - ---- z - 3/160 z + 1/20 y + 6000 2000 1000 + + 2 + - 1/80 x y, COEFF(1, -1, 2) = 1/80 x y + 3/80 y z - 3/160 z - 7/250 x + + 53 2 2 + + 3/80 y + ----- - 9/500 z - 9/1000 x z + 3/160 x - 1/32 y , + 12000 + + 27 2 + COEFF(2, -1, 2) = 3/80 x y - ---- x z + 1/40 y - 9/1000 z - 1/32 y + 1000 + + 2 2 307 + - 9/1000 x - 3/160 x + 3/80 y z - 3/160 z + ----, COEFF(-1, 0, 2) = + 6000 + + 2 2 2 33 19 + - 1/160 z - 1/160 x + 3/32 y + 3/80 x y - ---- - ---- x - 1/8 y + 2000 2000 + + 13 2 + + 9/1000 x z - 3/80 y z + ---- z, COEFF(0, 0, 2) = 3/32 y + 2/125 z + 1000 + + 2 137 23 + + 1/160 x - ---- + 1/80 x y - ---- x - 3/80 y z + 3/1000 x z - 9/80 y + 4000 2000 + + 2 19 + - 1/160 z , COEFF(1, 0, 2) = - 3/1000 x z + ---- z - 1/1000 x - 1/80 x y + 1000 + + 2 79 2 2 + - 1/160 z - 3/80 y z - ---- - 1/10 y + 1/160 x + 3/32 y , COEFF(2, 0, 2) + 2000 + + 2 2 11 11 + = - 1/160 x + 3/32 y + --- x - 3/80 y z - 9/1000 x z + --- z - 3/80 x y + 500 500 + + 129 2 + - ---- - 7/80 y - 1/160 z , COEFF(-1, 1, 2) = - 9/1000 x z + 1/16 y + 4000 + + 49 191 2 2 + + ---- z - 7/250 x - 3/80 y z + ---- + 3/80 x y + 1/160 z - 3/32 y + 2000 4000 + + 2 2 2 + + 1/160 x , COEFF(0, 1, 2) = 1/80 x y - 3/32 y - 1/160 x - 3/1000 x z + + 53 43 2 + - 1/1000 x + ---- + 3/40 y - 3/80 y z + ---- z + 1/160 z , COEFF(1, 1, 2) + 1000 2000 + + 2 37 2 27 183 + = - 1/80 x y - 1/160 x + ---- z - 3/32 y + 3/1000 x z + ---- x + ---- + 2000 2000 4000 + + 2 2 + + 7/80 y + 1/160 z - 3/80 y z, COEFF(2, 1, 2) = - 3/32 y + 9/1000 x z + + 31 2 31 2 13 + + ---- z + 1/160 z + ---- x + 1/160 x + 1/10 y - 3/80 y z + --- + 2000 2000 500 + + 41 27 + - 3/80 x y, COEFF(-1, 2, 2) = - --- - ---- x z - 3/80 x y - 3/2000 z + 750 1000 + + 2 2 2 + - 9/1000 x + 3/160 z + 1/32 y + 3/80 y z + 3/160 x , COEFF(0, 2, 2) = + + 2 167 21 2 + 1/32 y - ----- + 3/80 y z - 9/1000 x z - ---- z - 1/80 x y + 3/160 z + 12000 2000 + + 2 11 2 2 + - 3/160 x - 1/80 y + --- x, COEFF(1, 2, 2) = 1/32 y + 3/160 z + 500 + + 2 31 39 + - 3/160 x - 1/40 y + ---- x - 4/375 - ---- z + 9/1000 x z + 1/80 x y + 2000 2000 + + 2 2 539 + + 3/80 y z, COEFF(2, 2, 2) = 3/160 x + 1/32 y - 3/80 y - ----- + 12000 + + 57 27 57 2 + + 3/80 y z - ---- x + ---- x z - ---- z + 3/160 z + 3/80 x y] + 2000 1000 2000 + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dy.compute.c"); +bytes used=356015712, alloc=4914300, time=33.86 +bytes used=357015892, alloc=4914300, time=33.93 +bytes used=358016080, alloc=4914300, time=34.01 +bytes used=359016344, alloc=4914300, time=34.10 +bytes used=360016516, alloc=4914300, time=34.18 +bytes used=361025308, alloc=4914300, time=34.25 +bytes used=362027164, alloc=4914300, time=34.33 +bytes used=363032188, alloc=4914300, time=34.40 +bytes used=364035680, alloc=4914300, time=34.51 +bytes used=365035836, alloc=4914300, time=34.61 +bytes used=366036056, alloc=4914300, time=35.05 +bytes used=367037712, alloc=4914300, time=35.13 +bytes used=368037960, alloc=4914300, time=35.20 +bytes used=369039896, alloc=4914300, time=35.26 +bytes used=370040132, alloc=4914300, time=35.33 +bytes used=371041456, alloc=4914300, time=35.42 +bytes used=372044532, alloc=4914300, time=35.53 +bytes used=373052808, alloc=4914300, time=35.65 +bytes used=374058040, alloc=4914300, time=35.80 +bytes used=375059352, alloc=4914300, time=35.92 +bytes used=376059568, alloc=4914300, time=36.04 +bytes used=377067216, alloc=4914300, time=36.14 +bytes used=378067388, alloc=4914300, time=36.33 +bytes used=379067656, alloc=4914300, time=36.76 +bytes used=380067964, alloc=4914300, time=36.84 +bytes used=381068152, alloc=4914300, time=36.90 +bytes used=382068316, alloc=4914300, time=36.97 +bytes used=383068468, alloc=4914300, time=37.04 +bytes used=384068624, alloc=4914300, time=37.23 +bytes used=385068816, alloc=4914300, time=37.35 +bytes used=386068992, alloc=4914300, time=37.45 +bytes used=387069188, alloc=4914300, time=38.02 +bytes used=388069448, alloc=4914300, time=38.10 +bytes used=389069676, alloc=4914300, time=38.17 +bytes used=390069940, alloc=4914300, time=38.24 +bytes used=391070152, alloc=4914300, time=38.30 +bytes used=392070336, alloc=4914300, time=38.49 +bytes used=393070556, alloc=4914300, time=38.68 +bytes used=394070896, alloc=4914300, time=39.16 +bytes used=395071096, alloc=4914300, time=39.23 +bytes used=396071252, alloc=4914300, time=39.29 +bytes used=397071424, alloc=4914300, time=39.36 +bytes used=398071640, alloc=4914300, time=39.55 +bytes used=399071820, alloc=4914300, time=40.08 +bytes used=400072344, alloc=4914300, time=40.28 +bytes used=401072600, alloc=4914300, time=40.37 +bytes used=402072752, alloc=4914300, time=40.52 +> +# d/dz +> simplify( diff(interp_3d_cube_order3_smooth0,z) ); +bytes used=403072960, alloc=4914300, time=40.61 +bytes used=404073300, alloc=4914300, time=40.68 +bytes used=405073472, alloc=4914300, time=40.76 +bytes used=406073652, alloc=4914300, time=40.83 +bytes used=407073804, alloc=4914300, time=40.91 +bytes used=408074628, alloc=4914300, time=40.98 +bytes used=409074824, alloc=4914300, time=41.05 + 29 29 17 +- ---- DATA(0, 2, -1) - ---- DATA(2, 0, -1) - ---- DATA(0, -1, 2) + 6000 6000 3000 + + 167 79 607 + - ----- DATA(0, 2, 2) + ---- DATA(1, 0, 2) - ----- DATA(-1, 0, -1) + 12000 3000 12000 + + 281 161 87 + + ----- DATA(2, -1, -1) - ---- DATA(0, 0, 0) - ---- DATA(1, 0, 0) + 12000 4000 2000 + + 87 191 21 + - ---- DATA(0, 1, 0) - ---- DATA(1, 1, 0) + --- DATA(0, 0, 1) + 2000 4000 250 + + 299 299 133 + + ---- DATA(1, 0, 1) + ---- DATA(0, 1, 1) + ---- DATA(1, 1, 1) + 4000 4000 2000 + + 307 53 281 + + ---- DATA(2, 2, -1) + ----- DATA(1, 2, -1) + ----- DATA(-1, 2, -1) + 6000 12000 12000 + + 53 137 33 + + ----- DATA(2, 1, -1) - ---- DATA(2, 0, 0) - ---- DATA(2, -1, 0) + 12000 4000 2000 + + 79 137 33 + - ---- DATA(1, 2, 0) - ---- DATA(0, 2, 0) - ---- DATA(-1, 2, 0) + 2000 4000 2000 + + 79 129 191 + - ---- DATA(2, 1, 0) - ---- DATA(2, 2, 0) + ---- DATA(2, -1, 1) + 2000 4000 4000 + + 53 191 183 + + ---- DATA(2, 0, 1) + ---- DATA(-1, 2, 1) + ---- DATA(2, 1, 1) + 1000 4000 4000 + + 183 53 449 + + ---- DATA(1, 2, 1) + ---- DATA(0, 2, 1) - ----- DATA(-1, -1, 2) + 4000 1000 12000 + + 13 137 167 + + --- DATA(2, 2, 1) - ----- DATA(1, -1, 2) - ----- DATA(2, 0, 2) + 500 12000 12000 + + 349 17 41 + + ----- DATA(0, 0, 2) - ---- DATA(-1, 0, 2) - --- DATA(2, -1, 2) + 12000 3000 750 + + 319 79 137 + + ----- DATA(1, 1, 2) + ---- DATA(0, 1, 2) - ----- DATA(-1, 1, 2) + 12000 3000 12000 + + 41 + - --- DATA(-1, 2, 2) - 4/375 DATA(2, 1, 2) - 4/375 DATA(1, 2, 2) + 750 + + 49 107 49 + - ---- DATA(0, -1, 0) - ---- DATA(1, -1, 0) - ---- DATA(-1, 0, 0) + 2000 4000 2000 + + 107 157 323 + - ---- DATA(-1, 1, 0) + ---- DATA(-1, -1, 1) + ---- DATA(0, -1, 1) + 4000 2000 4000 + + 141 323 141 + + ---- DATA(1, -1, 1) + ---- DATA(-1, 0, 1) + ---- DATA(-1, 1, 1) + 2000 4000 2000 + + 437 691 97 + - ---- DATA(0, 0, -1) - ----- DATA(1, 0, -1) - ---- DATA(-1, 1, -1) + 6000 12000 3000 + + 691 17 39 + - ----- DATA(0, 1, -1) - --- DATA(1, 1, -1) - ---- DATA(-1, -1, 0) + 12000 375 4000 + + 47 607 97 + - ---- DATA(-1, -1, -1) - ----- DATA(0, -1, -1) - ---- DATA(1, -1, -1) + 1500 12000 3000 + + 539 43 + - ----- DATA(2, 2, 2) - 3/2000 y DATA(-1, 2, 2) + ---- y DATA(0, 2, 1) + 12000 2000 + + 19 + + ---- y DATA(1, 2, 0) - 9/1000 y DATA(2, 2, -1) - 9/1000 x DATA(2, 2, -1) + 1000 + + 19 43 + - 3/2000 x DATA(2, -1, 2) + ---- x DATA(2, 1, 0) + ---- x DATA(2, 0, 1) + 1000 2000 + + - 1/1000 x y DATA(1, 1, 0) + 1/80 y z DATA(0, 0, 1) + + + 9/1000 x y DATA(2, 2, 1) - 3/80 y z DATA(0, 2, 1) + + + 3/80 y z DATA(0, 2, 2) - 3/1000 x y DATA(-1, 0, 0) + + - 1/1000 x y DATA(1, 0, 1) - 3/1000 x y DATA(0, -1, 0) + + - 1/80 y z DATA(-1, 0, -1) - 3/80 y z DATA(2, 2, 0) + + 2 + + 9/1000 x y DATA(1, 2, 2) + 3/160 x DATA(-1, 2, 2) + + 2 2 + + 3/160 x DATA(2, 1, 2) - 3/160 x DATA(1, 2, 2) + + 2 2 + + 1/160 x DATA(0, -1, 0) + 1/160 x DATA(1, -1, 0) + + 2 2 + - 1/160 x DATA(-1, 0, 0) - 1/160 x DATA(-1, 1, 0) + + 2 2 2 + + 1/160 x DATA(2, 1, 1) - 1/160 x DATA(1, 2, 1) - 1/160 x DATA(0, 2, 1) + + 2 2 + + 3/160 x DATA(-1, -1, 2) + 1/160 x DATA(2, 2, 1) + + 2 2 + - 3/160 x DATA(1, -1, 2) + 3/160 x DATA(2, 0, 2) + + 2 2 + - 3/160 x DATA(0, 0, 2) + 3/160 x DATA(-1, 0, 2) + + 2 2 + + 3/160 x DATA(2, -1, 2) - 3/160 x DATA(1, 1, 2) + + 2 2 + - 3/160 x DATA(0, 1, 2) + 3/160 x DATA(-1, 1, 2) + + 2 147 + + 3/160 x DATA(0, 2, -1) + ---- x DATA(-1, -1, -1) + 2000 + + 37 57 + - 1/2000 x DATA(0, -1, -1) - ---- x DATA(1, -1, -1) - ---- x DATA(2, 2, 2) + 1000 2000 + + 39 + - 1/250 x DATA(0, -1, 1) - 9/1000 x DATA(-1, 2, 2) - ---- x DATA(2, 1, 2) + 2000 + + 31 17 + + ---- x DATA(1, 2, 2) - ---- x DATA(0, -1, 0) + 3/1000 x y DATA(1, 0, -1) + 2000 2000 + + 2 2 2 + + 1/32 z DATA(-1, 2, 2) + 1/32 z DATA(2, 1, 2) + 1/32 z DATA(1, 2, 2) + + 2 2 2 + + 3/32 z DATA(0, -1, 0) + 3/32 z DATA(1, -1, 0) + 3/32 z DATA(-1, 0, 0) + + 2 2 2 + + 3/32 z DATA(-1, 1, 0) - 1/32 z DATA(2, 2, -1) - 1/32 z DATA(1, 2, -1) + + 2 2 2 + - 1/32 z DATA(-1, 2, -1) - 1/32 z DATA(2, 1, -1) + 3/32 z DATA(2, 0, 0) + + 2 2 2 + + 3/32 z DATA(2, -1, 0) + 3/32 z DATA(1, 2, 0) + 3/32 z DATA(0, 2, 0) + + 2 2 2 + + 3/32 z DATA(-1, 2, 0) + 3/32 z DATA(2, 1, 0) + 3/32 z DATA(2, 2, 0) + + 2 2 2 + - 3/32 z DATA(2, -1, 1) - 3/32 z DATA(2, 0, 1) - 3/32 z DATA(-1, 2, 1) + + 2 2 + - 3/32 z DATA(2, 1, 1) + 1/160 x DATA(-1, -1, 1) + + 2 2 + - 1/160 x DATA(1, -1, 1) + 1/160 x DATA(-1, 0, 1) + + 2 2 + + 1/160 x DATA(-1, 1, 1) + 3/160 x DATA(0, 0, -1) + + 2 2 + + 3/160 x DATA(1, 0, -1) - 3/160 x DATA(-1, 1, -1) + + 2 2 + + 3/160 x DATA(0, 1, -1) + 3/160 x DATA(1, 1, -1) + + 2 2 + - 1/160 x DATA(-1, -1, 0) - 3/160 x DATA(-1, -1, -1) + + 2 2 + + 3/160 x DATA(0, -1, -1) + 3/160 x DATA(1, -1, -1) + + 2 2 + + 3/160 x DATA(2, 2, 2) - 1/160 x DATA(0, -1, 1) + + 2 + + 9/1000 x y DATA(2, 0, -1) - 3/32 z DATA(2, 2, 1) + + 2 2 2 + + 1/32 z DATA(1, -1, 2) + 1/32 z DATA(2, 0, 2) + 1/32 z DATA(0, 0, 2) + + 2 2 2 + + 1/32 z DATA(-1, 0, 2) + 1/32 z DATA(2, -1, 2) + 1/32 z DATA(1, 1, 2) + + 2 2 2 + + 1/32 z DATA(0, 1, 2) + 1/32 z DATA(-1, 1, 2) - 1/32 z DATA(0, 2, -1) + + 2 2 + - 3/32 z DATA(-1, -1, 1) - 3/32 z DATA(1, -1, 1) + + 2 2 2 + - 3/32 z DATA(-1, 0, 1) - 3/32 z DATA(-1, 1, 1) - 1/32 z DATA(0, 0, -1) + + 2 2 + - 1/32 z DATA(1, 0, -1) - 1/32 z DATA(-1, 1, -1) + + 2 2 + - 1/32 z DATA(0, 1, -1) - 1/32 z DATA(1, 1, -1) + + 2 2 + + 3/32 z DATA(-1, -1, 0) - 1/32 z DATA(-1, -1, -1) + + 2 2 + - 1/32 z DATA(0, -1, -1) - 1/32 z DATA(1, -1, -1) + + 2 2 + + 1/32 z DATA(2, 2, 2) - 3/32 z DATA(0, -1, 1) + 7/80 z DATA(1, 2, 1) + + + 3/40 z DATA(0, 2, 1) + 3/80 z DATA(-1, -1, 2) + 1/10 z DATA(2, 2, 1) + + + 1/80 z DATA(1, -1, 2) - 1/80 z DATA(2, 0, 2) + 1/80 z DATA(0, 0, 2) + + + 1/40 z DATA(-1, 0, 2) - 1/80 z DATA(1, 1, 2) + 1/80 z DATA(-1, 1, 2) + + + 1/20 z DATA(0, 2, -1) + 1/40 z DATA(-1, -1, 1) + 1/20 z DATA(1, -1, 1) + + - 9/80 z DATA(0, 2, 0) + 3/80 z DATA(2, 1, -1) - 1/8 z DATA(2, -1, 0) + + - 9/80 z DATA(2, 0, 0) + 1/20 z DATA(2, 0, -1) + 1/40 z DATA(0, -1, 2) + + - 1/80 z DATA(0, 2, 2) + 7/80 z DATA(-1, 0, -1) + 1/16 z DATA(2, -1, -1) + + 11 + - -- z DATA(0, 0, 0) - 1/8 z DATA(1, 0, 0) - 1/8 z DATA(0, 1, 0) + 80 + + - 9/80 z DATA(1, 1, 0) + 1/20 z DATA(0, 0, 1) + 1/16 z DATA(1, 0, 1) + + + 1/16 z DATA(0, 1, 1) + 3/40 z DATA(1, 1, 1) + 1/40 z DATA(2, 2, -1) + + 2 + + 3/80 z DATA(1, 2, -1) + 1/16 z DATA(-1, 2, -1) - 3/32 z DATA(1, 2, 1) + + 2 2 + - 3/32 z DATA(0, 2, 1) + 1/32 z DATA(-1, -1, 2) - 3/20 z DATA(-1, 0, 0) + + 11 2 2 + - -- z DATA(-1, 1, 0) + 3/160 y DATA(2, 0, -1) + 3/160 y DATA(0, -1, 2) + 80 + + 2 2 + + 3/160 y DATA(0, 2, 2) - 3/160 y DATA(1, 0, 2) + + 2 2 + + 3/160 y DATA(-1, 0, -1) - 3/160 y DATA(2, -1, -1) + + 2 2 2 + + 1/160 y DATA(0, 0, 0) + 1/160 y DATA(1, 0, 0) + 1/160 y DATA(0, 1, 0) + + 2 2 2 + + 1/160 y DATA(1, 1, 0) - 1/160 y DATA(0, 0, 1) - 1/160 y DATA(1, 0, 1) + + 2 2 + - 1/160 y DATA(0, 1, 1) - 1/160 y DATA(1, 1, 1) + + 2 2 + - 3/160 y DATA(2, 2, -1) - 3/160 y DATA(1, 2, -1) + + 2 2 + - 3/160 y DATA(-1, 2, -1) + 3/160 y DATA(2, 1, -1) + + + 1/20 z DATA(-1, 1, 1) - 1/10 z DATA(1, 2, 0) - 1/8 z DATA(-1, 2, 0) + + - 1/10 z DATA(2, 1, 0) - 7/80 z DATA(2, 2, 0) + 1/16 z DATA(2, -1, 1) + + + 3/40 z DATA(2, 0, 1) + 1/16 z DATA(-1, 2, 1) + 7/80 z DATA(2, 1, 1) + + 2 + - 1/80 y z DATA(1, 1, 1) - 3/160 y DATA(2, 1, 2) + + 2 2 + - 1/160 y DATA(0, -1, 0) - 1/160 y DATA(1, -1, 0) + + 2 2 + + 1/160 y DATA(-1, 0, 0) + 1/160 y DATA(-1, 1, 0) + + 2 2 + + 1/160 y DATA(2, 0, 0) - 1/160 y DATA(2, -1, 0) + + 2 2 + - 1/160 y DATA(1, 2, 0) - 1/160 y DATA(0, 2, 0) + + 2 2 + - 1/160 y DATA(-1, 2, 0) + 1/160 y DATA(2, 1, 0) + 3/80 z DATA(-1, 0, 1) + + + 3/40 z DATA(0, 0, -1) + 1/16 z DATA(1, 0, -1) + 3/40 z DATA(-1, 1, -1) + + 13 + + 1/16 z DATA(0, 1, -1) + 1/20 z DATA(1, 1, -1) - -- z DATA(-1, -1, 0) + 80 + + + 1/10 z DATA(-1, -1, -1) + 7/80 z DATA(0, -1, -1) + + + 3/40 z DATA(1, -1, -1) - 3/80 z DATA(2, 2, 2) + 3/80 z DATA(0, -1, 1) + + - 1/40 z DATA(2, 1, 2) - 1/40 z DATA(1, 2, 2) - 3/20 z DATA(0, -1, 0) + + 11 2 2 + - -- z DATA(1, -1, 0) + 3/160 y DATA(1, 2, 2) + 1/160 y DATA(-1, 2, 1) + 80 + + 2 2 2 + - 1/160 y DATA(2, 1, 1) + 1/160 y DATA(1, 2, 1) + 1/160 y DATA(0, 2, 1) + + 2 2 + + 3/160 y DATA(-1, -1, 2) + 1/160 y DATA(2, 2, 1) + + 2 2 + + 3/160 y DATA(1, -1, 2) - 3/160 y DATA(2, 0, 2) + + 2 2 + - 3/160 y DATA(0, 0, 2) - 3/160 y DATA(-1, 0, 2) + + 2 2 + + 3/160 y DATA(2, -1, 2) - 3/160 y DATA(1, 1, 2) + + 2 2 + - 3/160 y DATA(0, 1, 2) - 3/160 y DATA(-1, 1, 2) + + 2 2 + - 3/160 y DATA(0, 2, -1) + 1/160 y DATA(-1, -1, 1) + + 2 2 + + 1/160 y DATA(1, -1, 1) - 1/160 y DATA(-1, 0, 1) + + 2 2 + - 1/160 y DATA(-1, 1, 1) + 3/160 y DATA(0, 0, -1) + + 2 2 + + 3/160 y DATA(1, 0, -1) + 3/160 y DATA(-1, 1, -1) + + 2 2 + + 3/160 y DATA(0, 1, -1) + 3/160 y DATA(1, 1, -1) + + 2 2 + - 1/160 y DATA(-1, -1, 0) - 3/160 y DATA(-1, -1, -1) + + 2 2 + - 3/160 y DATA(0, -1, -1) - 3/160 y DATA(1, -1, -1) + + 2 2 + + 3/160 y DATA(2, 2, 2) + 1/160 y DATA(0, -1, 1) + + 2 13 + + 3/160 y DATA(-1, 2, 2) + ---- y DATA(-1, 0, 2) + 1000 + + 37 43 + - 9/1000 y DATA(2, -1, 2) + ---- y DATA(1, 1, 2) + ---- y DATA(0, 1, 2) + 2000 2000 + + 49 27 37 + + ---- y DATA(-1, 1, 2) - ---- y DATA(0, 2, -1) - ---- y DATA(-1, -1, 1) + 2000 1000 1000 + + 31 33 + - ---- y DATA(1, -1, 1) - 1/250 y DATA(-1, 0, 1) + ---- y DATA(-1, 1, 1) + 1000 2000 + + 13 37 + - 7/2000 y DATA(0, 0, -1) - ---- y DATA(1, 0, -1) - ---- y DATA(-1, 1, -1) + 2000 1000 + + 17 31 + - --- y DATA(0, 1, -1) - ---- y DATA(1, 1, -1) - 1/2000 y DATA(-1, -1, 0) + 500 1000 + + 147 129 + + ---- y DATA(-1, -1, -1) + ---- y DATA(0, -1, -1) + 2000 2000 + + 111 57 + + ---- y DATA(1, -1, -1) - ---- y DATA(2, 2, 2) - 7/250 y DATA(2, 1, -1) + 2000 2000 + + 23 27 13 + - ---- y DATA(2, 0, 0) - ---- y DATA(0, -1, 2) + ---- x DATA(0, -1, 2) + 2000 1000 1000 + + 11 43 129 + + --- x DATA(0, 2, 2) + ---- x DATA(1, 0, 2) + ---- x DATA(-1, 0, -1) + 500 2000 2000 + + 19 + - 9/250 x DATA(2, -1, -1) - ---- x DATA(0, 0, 0) - 3/1000 x DATA(1, 0, 0) + 2000 + + 21 + - ---- x DATA(0, 1, 0) - 1/500 x DATA(1, 1, 0) - 3/1000 x DATA(0, 0, 1) + 2000 + + 27 2 2 + - ---- x DATA(2, 0, -1) - 1/160 y DATA(2, 2, 0) + 1/160 y DATA(2, -1, 1) + 1000 + + 2 + - 1/160 y DATA(2, 0, 1) - 1/80 x z DATA(1, -1, 0) + + + 1/80 x z DATA(0, -1, 0) + 1/80 x z DATA(1, 2, 2) + + + 3/80 x z DATA(2, 1, 2) + 3/80 x z DATA(2, 0, -1) + + - 1/80 y z DATA(0, 1, 0) + 3/80 y z DATA(-1, 2, -1) + + 27 + - 1/80 y z DATA(2, 0, -1) + ---- x y DATA(-1, -1, 2) + 1000 + + - 3/1000 x y DATA(0, 2, 1) + 3/1000 x y DATA(1, 2, 1) + + - 1/80 y z DATA(1, 0, 2) - 3/1000 x y DATA(2, 1, 0) + + 27 + - ---- x y DATA(-1, -1, -1) - 1/2000 y DATA(-1, 0, -1) + 1000 + + 93 19 21 + + ---- y DATA(2, -1, -1) - ---- y DATA(0, 0, 0) - ---- y DATA(1, 0, 0) + 2000 2000 2000 + + - 3/1000 y DATA(0, 1, 0) - 1/500 y DATA(1, 1, 0) - 3/1000 y DATA(0, 0, 1) + + 31 29 + - 1/500 y DATA(1, 0, 1) + ---- y DATA(0, 1, 1) + ---- y DATA(1, 1, 1) + 2000 2000 + + 19 + - 9/500 y DATA(1, 2, -1) - 9/250 y DATA(-1, 2, -1) - ---- y DATA(2, -1, 0) + 2000 + + 13 + + 2/125 y DATA(0, 2, 0) + ---- y DATA(-1, 2, 0) - 1/1000 y DATA(2, 1, 0) + 1000 + + 11 + + --- y DATA(2, 2, 0) - 7/250 y DATA(2, -1, 1) - 1/1000 y DATA(2, 0, 1) + 500 + + 49 27 37 + + ---- y DATA(-1, 2, 1) + ---- y DATA(2, 1, 1) + ---- y DATA(1, 2, 1) + 2000 2000 2000 + + 31 + - 9/250 y DATA(-1, -1, 2) + ---- y DATA(2, 2, 1) - 9/500 y DATA(1, -1, 2) + 2000 + + 11 + + --- y DATA(2, 0, 2) + 2/125 y DATA(0, 0, 2) - 3/80 x z DATA(2, 0, 1) + 500 + + - 3/80 x z DATA(2, -1, 1) - 3/80 x z DATA(-1, 2, 2) + + + 1/80 x z DATA(0, -1, 1) + 3/80 x z DATA(2, 2, 2) + + + 1/80 x z DATA(1, -1, -1) - 1/80 x z DATA(0, -1, -1) + + - 3/80 x z DATA(-1, -1, -1) + 3/80 x z DATA(-1, -1, 0) + + 27 + + 1/80 x z DATA(1, 1, -1) + ---- x y DATA(-1, 2, -1) + 1000 + + - 1/80 x z DATA(0, 1, -1) - 3/80 x z DATA(-1, 1, -1) + + + 1/80 x z DATA(1, 0, -1) - 1/80 x z DATA(0, 0, -1) + + + 3/80 x z DATA(-1, 1, 1) + 3/80 x z DATA(-1, 0, 1) + + - 1/80 x z DATA(1, -1, 1) + 3/80 x z DATA(-1, -1, 1) + + - 1/80 x z DATA(0, 2, -1) + 3/80 x z DATA(-1, 1, 0) + + + 3/80 x z DATA(-1, 0, 0) - 3/80 y z DATA(1, 2, 0) + + 27 + - 3/80 y z DATA(1, 2, 1) - ---- x y DATA(-1, 2, 2) + 1000 + + - 3/1000 x y DATA(0, 0, -1) + 9/1000 x y DATA(-1, 2, 0) + + + 3/1000 x y DATA(2, 0, 0) - 3/80 y z DATA(2, -1, -1) + + 27 + - ---- x y DATA(2, -1, 2) + 3/80 y z DATA(2, -1, 1) + 1000 + + + 3/80 y z DATA(2, -1, 0) - 3/80 y z DATA(-1, -1, 2) + + - 3/1000 x y DATA(2, 0, 1) - 3/80 y z DATA(0, -1, 2) + + - 9/1000 x y DATA(-1, -1, 0) - 3/1000 x y DATA(-1, 1, 1) + + + 1/80 y z DATA(0, 1, -1) + 1/80 y z DATA(-1, 1, -1) + + - 1/80 y z DATA(1, 0, -1) - 1/80 y z DATA(0, 0, -1) + + - 1/80 y z DATA(-1, 1, 1) + 1/80 y z DATA(-1, 0, 1) + + + 3/80 y z DATA(1, -1, 1) + 3/80 y z DATA(-1, -1, 1) + + + 3/80 y z DATA(0, 2, -1) + 1/80 y z DATA(-1, 1, 2) + + + 1/80 y z DATA(0, 1, 2) + 1/80 y z DATA(1, 1, 2) + + + 9/1000 x y DATA(2, -1, 0) - 3/80 y z DATA(2, -1, 2) + + - 1/80 y z DATA(-1, 0, 2) - 1/80 y z DATA(0, 0, 2) + + + 9/1000 x y DATA(-1, 0, 2) - 9/1000 x y DATA(2, 1, -1) + + 19 21 19 + - ---- y DATA(2, 0, -1) - ---- y DATA(0, 2, 2) + ---- y DATA(1, 0, 2) + 2000 2000 1000 + + 2 + + 9/1000 x y DATA(-1, -1, 1) + 3/32 z DATA(0, 0, 0) + + 2 2 2 + + 3/32 z DATA(1, 0, 0) + 3/32 z DATA(0, 1, 0) + 3/32 z DATA(1, 1, 0) + + 2 2 2 + - 3/32 z DATA(0, 0, 1) - 3/32 z DATA(1, 0, 1) - 3/32 z DATA(0, 1, 1) + + 2 19 + - 3/32 z DATA(1, 1, 1) + ---- x DATA(0, 1, 2) - 9/500 x DATA(-1, 1, 2) + 1000 + + 19 37 33 + - ---- x DATA(0, 2, -1) - ---- x DATA(-1, -1, 1) + ---- x DATA(1, -1, 1) + 2000 1000 2000 + + 17 31 + - --- x DATA(-1, 0, 1) - ---- x DATA(-1, 1, 1) - 7/2000 x DATA(0, 0, -1) + 500 1000 + + 17 111 13 + - --- x DATA(1, 0, -1) + ---- x DATA(-1, 1, -1) - ---- x DATA(0, 1, -1) + 500 2000 2000 + + 31 17 + - ---- x DATA(1, 1, -1) - 1/2000 x DATA(-1, -1, 0) - --- y DATA(0, -1, 1) + 1000 500 + + 31 39 + + ---- y DATA(2, 1, 2) - ---- y DATA(1, 2, 2) - 7/2000 y DATA(0, -1, 0) + 2000 2000 + + 13 17 + - ---- y DATA(1, -1, 0) - ---- y DATA(-1, 0, 0) - 1/250 y DATA(-1, 1, 0) + 2000 2000 + + 2 2 2 + - 1/32 z DATA(2, 0, -1) + 1/32 z DATA(0, -1, 2) + 1/32 z DATA(0, 2, 2) + + 2 2 + + 1/32 z DATA(1, 0, 2) - 1/32 z DATA(-1, 0, -1) + + 2 + - 1/32 z DATA(2, -1, -1) - 1/80 y z DATA(0, 1, 1) + + 2 + + 3/1000 x y DATA(1, -1, 0) + 1/160 x DATA(2, -1, 1) + + 2 2 31 + + 1/160 x DATA(2, 0, 1) + 1/160 x DATA(-1, 2, 1) + ---- x DATA(1, 0, 1) + 2000 + + 29 + - 1/500 x DATA(0, 1, 1) + ---- x DATA(1, 1, 1) - 7/250 x DATA(1, 2, -1) + 2000 + + 93 + + ---- x DATA(-1, 2, -1) - 9/500 x DATA(2, 1, -1) + 2/125 x DATA(2, 0, 0) + 2000 + + 13 23 + + ---- x DATA(2, -1, 0) - 1/1000 x DATA(1, 2, 0) - ---- x DATA(0, 2, 0) + 1000 2000 + + 19 11 49 + - ---- x DATA(-1, 2, 0) + --- x DATA(2, 2, 0) + ---- x DATA(2, -1, 1) + 2000 500 2000 + + 37 27 + - 7/250 x DATA(-1, 2, 1) + ---- x DATA(2, 1, 1) + ---- x DATA(1, 2, 1) + 2000 2000 + + 31 + - 1/1000 x DATA(0, 2, 1) - 9/250 x DATA(-1, -1, 2) + ---- x DATA(2, 2, 1) + 2000 + + 49 21 + + ---- x DATA(1, -1, 2) - ---- x DATA(2, 0, 2) + 2/125 x DATA(0, 0, 2) + 2000 2000 + + 27 37 + - ---- x DATA(-1, 0, 2) + ---- x DATA(1, 1, 2) - 1/250 x DATA(1, -1, 0) + 1000 2000 + + 13 + - 7/2000 x DATA(-1, 0, 0) - ---- x DATA(-1, 1, 0) + 2000 + + 2 2 + - 3/160 x DATA(2, 0, -1) - 3/160 x DATA(0, -1, 2) + + 2 2 + - 3/160 x DATA(0, 2, 2) - 3/160 x DATA(1, 0, 2) + + 2 2 + - 3/160 x DATA(-1, 0, -1) - 3/160 x DATA(2, -1, -1) + + 2 2 2 + + 1/160 x DATA(0, 0, 0) + 1/160 x DATA(1, 0, 0) + 1/160 x DATA(0, 1, 0) + + 2 2 2 + + 1/160 x DATA(1, 1, 0) - 1/160 x DATA(0, 0, 1) - 1/160 x DATA(1, 0, 1) + + 2 2 + - 1/160 x DATA(0, 1, 1) - 1/160 x DATA(1, 1, 1) + + 2 2 + - 3/160 x DATA(2, 2, -1) + 3/160 x DATA(1, 2, -1) + + 2 2 + - 3/160 x DATA(-1, 2, -1) - 3/160 x DATA(2, 1, -1) + + 2 2 + - 1/160 x DATA(2, 0, 0) - 1/160 x DATA(2, -1, 0) + + 2 2 + + 1/160 x DATA(1, 2, 0) + 1/160 x DATA(0, 2, 0) + + 2 2 + - 1/160 x DATA(-1, 2, 0) - 1/160 x DATA(2, 1, 0) + + 2 + - 1/160 x DATA(2, 2, 0) - 3/1000 x y DATA(0, 1, 2) + + - 3/80 y z DATA(2, 2, 1) + 3/1000 x y DATA(-1, 1, 0) + + + 1/1000 x y DATA(1, 0, 0) - 9/1000 x y DATA(1, 2, -1) + + - 1/80 y z DATA(2, 0, 2) - 3/80 y z DATA(1, -1, 2) + + + 9/1000 x y DATA(0, 2, -1) + 9/1000 x y DATA(2, 1, 2) + + + 3/80 y z DATA(2, 2, -1) + 9/1000 x y DATA(1, -1, -1) + + - 1/80 y z DATA(1, 1, 0) - 9/1000 x y DATA(1, -1, 2) + + + 3/1000 x y DATA(0, 2, 0) - 9/1000 x y DATA(2, 2, 0) + + + 9/1000 x y DATA(0, -1, 2) - 1/80 y z DATA(2, 1, 0) + + - 1/80 x z DATA(0, 2, 2) - 1/80 x z DATA(0, -1, 2) + + - 1/80 y z DATA(-1, 1, 0) + 1/80 y z DATA(-1, 0, 0) + + + 3/80 y z DATA(1, -1, 0) + 3/80 y z DATA(0, -1, 0) + + + 3/80 y z DATA(1, 2, 2) - 9/1000 x y DATA(-1, 1, 2) + + + 1/80 y z DATA(2, 1, 2) + 3/80 y z DATA(-1, 2, 2) + + + 3/80 y z DATA(0, -1, 1) + 3/80 y z DATA(2, 2, 2) + + - 3/80 y z DATA(1, -1, -1) - 3/80 y z DATA(0, -1, -1) + + - 3/80 y z DATA(-1, -1, -1) - 3/1000 x y DATA(1, 2, 0) + + + 3/80 y z DATA(-1, -1, 0) + 1/80 y z DATA(1, 1, -1) + + - 3/80 x z DATA(2, 2, 0) - 3/80 x z DATA(2, 1, 0) + + + 3/80 x z DATA(-1, 2, 0) + 1/80 x z DATA(0, 2, 0) + + - 1/80 x z DATA(1, 2, 0) - 3/80 x z DATA(2, -1, 0) + + - 3/80 x z DATA(2, 0, 0) + 3/80 x z DATA(2, 1, -1) + + - 3/80 x z DATA(-1, 2, -1) + 1/80 x z DATA(1, 2, -1) + + + 3/80 x z DATA(2, 2, -1) - 1/80 x z DATA(1, 1, 1) + + + 1/80 x z DATA(0, 1, 1) - 1/80 x z DATA(1, 0, 1) + 1/80 x z DATA(0, 0, 1) + + - 1/80 x z DATA(1, 1, 0) + 1/80 x z DATA(0, 1, 0) - 1/80 x z DATA(1, 0, 0) + + + 1/80 x z DATA(0, 0, 0) + 3/80 x z DATA(2, -1, -1) + + - 3/80 x z DATA(-1, 0, -1) + 1/80 x z DATA(1, 0, 2) + + - 3/80 x z DATA(-1, 1, 2) + 9/1000 x y DATA(-1, 1, -1) + + - 3/1000 x y DATA(1, 1, -1) - 1/80 x z DATA(0, 1, 2) + + + 1/80 x z DATA(1, 1, 2) + 3/80 x z DATA(2, -1, 2) + + - 3/80 x z DATA(-1, 0, 2) - 1/80 x z DATA(0, 0, 2) + + - 9/1000 x y DATA(0, -1, -1) + 3/80 x z DATA(2, 0, 2) + + + 1/80 x z DATA(1, -1, 2) - 3/80 x z DATA(2, 2, 1) + + - 3/80 x z DATA(-1, -1, 2) + 1/80 x z DATA(0, 2, 1) + + - 1/80 x z DATA(1, 2, 1) - 3/80 x z DATA(2, 1, 1) + + + 3/80 x z DATA(-1, 2, 1) - 1/80 y z DATA(2, 1, 1) + + + 3/1000 x y DATA(-1, 0, 1) - 3/80 y z DATA(-1, 2, 1) + + + 3/1000 x y DATA(1, 1, 2) - 3/1000 x y DATA(1, -1, 1) + + + 3/1000 x y DATA(2, 1, 1) - 9/1000 x y DATA(2, 0, 2) + + 27 + + ---- x y DATA(2, 2, 2) + 1/80 y z DATA(2, 0, 1) + 1000 + + - 3/80 y z DATA(-1, 2, 0) + 3/1000 x y DATA(0, -1, 1) + + + 1/80 y z DATA(2, 1, -1) - 3/80 y z DATA(0, 2, 0) + + + 1/1000 x y DATA(0, 0, 1) + 1/80 y z DATA(0, 0, 0) + + + 1/80 y z DATA(1, 0, 0) + 3/1000 x y DATA(0, 1, -1) + + - 9/1000 x y DATA(-1, 2, 1) - 1/1000 x y DATA(0, 1, 1) + + + 1/80 y z DATA(2, 0, 0) - 9/1000 x y DATA(2, -1, 1) + + + 3/80 y z DATA(1, 2, -1) + 1/1000 x y DATA(1, 1, 1) + + + 1/80 y z DATA(1, 0, 1) - 9/1000 x y DATA(0, 2, 2) + + - 3/1000 x y DATA(1, 0, 2) + 1/1000 x y DATA(0, 1, 0) + + 27 + + ---- x y DATA(2, -1, -1) - 9/1000 x y DATA(-1, 0, -1) + 1000 + + 27 + - ---- x y DATA(2, 2, -1) - 1/1000 x y DATA(0, 0, 0) + 1000 + + + 3/1000 x y DATA(0, 0, 2) + +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=410110452, alloc=4914300, time=41.13 +bytes used=411142220, alloc=4914300, time=41.21 +bytes used=412142356, alloc=4914300, time=41.28 +bytes used=413190428, alloc=4914300, time=41.36 +bytes used=414192668, alloc=4914300, time=41.43 +bytes used=415192808, alloc=4914300, time=41.51 +bytes used=416193280, alloc=4914300, time=41.59 +bytes used=417204812, alloc=4914300, time=41.66 + 147 2 47 147 +[COEFF(-1, -1, -1) = ---- y - 1/32 z - ---- - 3/80 x z + ---- x + 1/10 z + 2000 1500 2000 + + 27 2 2 + - 3/80 y z - ---- x y - 3/160 x - 3/160 y , COEFF(0, -1, -1) = - 1/2000 x + 1000 + + 607 2 2 2 + - ----- - 3/160 y - 1/32 z + 3/160 x - 3/80 y z - 1/80 x z + 7/80 z + 12000 + + 129 111 97 + - 9/1000 x y + ---- y, COEFF(1, -1, -1) = ---- y - ---- + 3/40 z + 2000 2000 3000 + + 2 2 37 2 + + 9/1000 x y - 1/32 z - 3/160 y - ---- x + 3/160 x - 3/80 y z + 1000 + + 281 27 2 + + 1/80 x z, COEFF(2, -1, -1) = - 3/80 y z + ----- + ---- x y - 3/160 x + 12000 1000 + + 2 2 93 + - 1/32 z - 3/160 y + ---- y + 1/16 z - 9/250 x + 3/80 x z, + 2000 + + 2 2 + COEFF(-1, 0, -1) = - 1/32 z - 1/80 y z - 9/1000 x y + 3/160 y - 3/80 x z + + 2 607 129 + - 1/2000 y - 3/160 x - ----- + ---- x + 7/80 z, COEFF(0, 0, -1) = + 12000 2000 + + 2 + - 7/2000 x + 3/160 y - 1/80 y z - 1/80 x z - 7/2000 y - 3/1000 x y + + 2 2 437 + - 1/32 z + 3/160 x + 3/40 z - ----, COEFF(1, 0, -1) = 1/80 x z + 6000 + + 2 691 17 2 + + 3/160 y - 1/80 y z - ----- + 3/1000 x y + 1/16 z - --- x - 1/32 z + 12000 500 + + 2 13 2 27 + + 3/160 x - ---- y, COEFF(2, 0, -1) = - 1/32 z + 1/20 z - ---- x + 2000 1000 + + 2 19 29 2 + - 3/160 x - 1/80 y z - ---- y - ---- + 9/1000 x y + 3/80 x z + 3/160 y , + 2000 6000 + + 97 2 2 + COEFF(-1, 1, -1) = - ---- + 3/160 y + 3/40 z + 9/1000 x y - 3/160 x + 3000 + + 111 37 2 + + ---- x + 1/80 y z - ---- y - 3/80 x z - 1/32 z , COEFF(0, 1, -1) = + 2000 1000 + + 2 2 2 691 17 + 1/16 z + 3/160 x - 1/32 z + 3/160 y - ----- - --- y + 3/1000 x y + 12000 500 + + 13 17 + - ---- x - 1/80 x z + 1/80 y z, COEFF(1, 1, -1) = - --- + 1/80 x z + 2000 375 + + 31 31 2 2 + - ---- x - ---- y + 3/160 x + 1/80 y z - 1/32 z - 3/1000 x y + 1/20 z + 1000 1000 + + 2 53 + + 3/160 y , COEFF(2, 1, -1) = 1/80 y z + ----- - 9/500 x + 3/80 x z + 12000 + + 2 2 2 + - 9/1000 x y - 3/160 x - 7/250 y + 3/80 z - 1/32 z + 3/160 y , + + 281 27 2 2 + COEFF(-1, 2, -1) = - 9/250 y + ----- + ---- x y - 3/160 y - 3/160 x + 12000 1000 + + 2 93 + - 1/32 z - 3/80 x z + 1/16 z + ---- x + 3/80 y z, COEFF(0, 2, -1) = + 2000 + + 2 27 2 19 + - 3/160 y - ---- y + 9/1000 x y + 1/20 z - 1/32 z - 1/80 x z - ---- x + 1000 2000 + + 29 2 2 + - ---- + 3/160 x + 3/80 y z, COEFF(1, 2, -1) = - 7/250 x - 3/160 y + 6000 + + 2 2 53 + - 1/32 z + 3/160 x + 3/80 y z + ----- - 9/1000 x y - 9/500 y + 3/80 z + 12000 + + 2 27 2 + + 1/80 x z, COEFF(2, 2, -1) = 3/80 x z - 1/32 z - ---- x y - 3/160 y + 1000 + + 2 307 + - 9/1000 x + 1/40 z - 3/160 x + ---- - 9/1000 y + 3/80 y z, + 6000 + + 2 + COEFF(-1, -1, 0) = - 1/2000 x - 1/2000 y - 9/1000 x y + 3/80 x z - 1/160 x + + 39 2 2 13 2 + - ---- + 3/80 y z + 3/32 z - 1/160 y - -- z, COEFF(0, -1, 0) = 1/160 x + 4000 80 + + 17 2 + - 3/1000 x y - ---- x + 3/80 y z + 1/80 x z - 7/2000 y + 3/32 z + 2000 + + 2 49 2 107 + - 1/160 y - ---- - 3/20 z, COEFF(1, -1, 0) = 1/160 x - ---- - 1/250 x + 2000 4000 + + 11 2 2 13 + - -- z + 3/1000 x y - 1/160 y + 3/80 y z + 3/32 z - ---- y - 1/80 x z, + 80 2000 + + 2 19 33 + COEFF(2, -1, 0) = - 3/80 x z + 3/32 z + 3/80 y z - 1/8 z - ---- y - ---- + 2000 2000 + + 2 2 13 + - 1/160 y - 1/160 x + 9/1000 x y + ---- x, COEFF(-1, 0, 0) = 3/80 x z + 1000 + + 2 49 2 17 2 + - 1/160 x - ---- + 1/160 y - ---- y + 3/32 z - 3/20 z - 3/1000 x y + 2000 2000 + + 11 2 + + 1/80 y z - 7/2000 x, COEFF(0, 0, 0) = - -- z + 1/160 y - 1/1000 x y + 80 + + 19 2 161 2 19 + - ---- y + 1/80 y z + 3/32 z - ---- + 1/160 x + 1/80 x z - ---- x, + 2000 4000 2000 + + 2 + COEFF(1, 0, 0) = - 1/80 x z - 3/1000 x + 1/80 y z + 1/160 y + 1/1000 x y + + 87 2 2 21 137 + - 1/8 z - ---- + 1/160 x + 3/32 z - ---- y, COEFF(2, 0, 0) = - ---- + 2000 2000 4000 + + 2 2 2 23 + - 9/80 z + 1/160 y - 1/160 x - 3/80 x z + 3/32 z + 3/1000 x y - ---- y + 2000 + + 11 + + 1/80 y z + 2/125 x, COEFF(-1, 1, 0) = - 1/80 y z - -- z + 3/80 x z + 80 + + 2 2 13 107 2 + + 3/32 z - 1/160 x - 1/250 y - ---- x - ---- + 1/160 y + 3/1000 x y, + 2000 4000 + + 87 2 21 + COEFF(0, 1, 0) = - ---- + 1/1000 x y + 1/160 x - ---- x - 1/80 y z + 2000 2000 + + 2 2 + - 3/1000 y + 3/32 z - 1/8 z + 1/80 x z + 1/160 y , COEFF(1, 1, 0) = + + 2 191 + - 1/80 x z - 9/80 z + 1/160 y - ---- - 1/1000 x y - 1/500 y - 1/500 x + 4000 + + 2 2 2 19 + + 1/160 x - 1/80 y z + 3/32 z , COEFF(2, 1, 0) = 3/32 z + ---- x + 1000 + + 2 79 2 + - 1/10 z - 3/80 x z - 1/160 x - 3/1000 x y - 1/1000 y - ---- + 1/160 y + 2000 + + 2 19 13 + - 1/80 y z, COEFF(-1, 2, 0) = - 1/160 y - ---- x - 3/80 y z + ---- y + 2000 1000 + + 2 33 2 + + 3/32 z - ---- + 9/1000 x y + 3/80 x z - 1/160 x - 1/8 z, + 2000 + + 2 2 137 + COEFF(0, 2, 0) = 1/80 x z - 9/80 z + 3/32 z + 1/160 x - ---- + 3/1000 x y + 4000 + + 23 2 2 + - ---- x - 3/80 y z + 2/125 y - 1/160 y , COEFF(1, 2, 0) = - 1/160 y + 2000 + + 19 2 79 2 + + ---- y + 1/160 x - ---- - 1/80 x z - 3/1000 x y - 1/1000 x + 3/32 z + 1000 2000 + + 11 2 + - 3/80 y z - 1/10 z, COEFF(2, 2, 0) = --- x + 3/32 z - 7/80 z - 3/80 y z + 500 + + 2 11 129 2 + - 1/160 y - 3/80 x z - 9/1000 x y + --- y - ---- - 1/160 x , + 500 4000 + + 37 2 + COEFF(-1, -1, 1) = 3/80 y z + 1/40 z + 9/1000 x y - ---- x - 3/32 z + 1000 + + 37 2 157 2 + - ---- y + 1/160 x + 3/80 x z + ---- + 1/160 y , COEFF(0, -1, 1) = 3/80 z + 1000 2000 + + 323 17 2 2 + + ---- + 3/80 y z - --- y + 1/160 y + 3/1000 x y - 1/250 x - 3/32 z + 4000 500 + + 2 2 33 + - 1/160 x + 1/80 x z, COEFF(1, -1, 1) = 3/80 y z - 3/32 z + ---- x + 2000 + + 2 141 31 2 + + 1/20 z - 1/80 x z + 1/160 y - 3/1000 x y + ---- - ---- y - 1/160 x , + 2000 1000 + + 2 2 191 + COEFF(2, -1, 1) = 1/160 y - 3/80 x z + 1/160 x + 3/80 y z + ---- + 1/16 z + 4000 + + 49 2 + + ---- x - 3/32 z - 7/250 y - 9/1000 x y, COEFF(-1, 0, 1) = 1/80 y z + 2000 + + 2 2 323 + + 3/80 x z + 3/1000 x y - 1/160 y + 1/160 x + 3/80 z - 1/250 y + ---- + 4000 + + 2 17 2 2 21 + - 3/32 z - --- x, COEFF(0, 0, 1) = - 1/160 y + 1/20 z - 3/32 z + --- + 500 250 + + 2 + - 1/160 x + 1/80 x z + 1/1000 x y - 3/1000 x - 3/1000 y + 1/80 y z, + + 31 299 2 2 + COEFF(1, 0, 1) = - 1/500 y + ---- x + ---- + 1/16 z - 3/32 z - 1/160 x + 2000 4000 + + 2 + - 1/80 x z - 1/160 y + 1/80 y z - 1/1000 x y, COEFF(2, 0, 1) = 3/40 z + + 53 2 2 2 43 + + ---- - 3/1000 x y - 3/32 z - 1/160 y - 1/1000 y + 1/160 x + ---- x + 1000 2000 + + 33 + + 1/80 y z - 3/80 x z, COEFF(-1, 1, 1) = 1/20 z + ---- y - 1/80 y z + 2000 + + 31 141 2 2 2 + - ---- x + 3/80 x z + ---- - 3/32 z - 1/160 y + 1/160 x - 3/1000 x y, + 1000 2000 + + 2 31 299 + COEFF(0, 1, 1) = 1/16 z - 3/32 z + ---- y - 1/80 y z + ---- + 1/80 x z + 2000 4000 + + 2 2 + - 1/1000 x y - 1/500 x - 1/160 y - 1/160 x , COEFF(1, 1, 1) = - 1/80 y z + + 2 133 2 29 2 + - 1/160 x + ---- + 1/1000 x y - 3/32 z + ---- y - 1/160 y + 3/40 z + 2000 2000 + + 29 183 37 2 + + ---- x - 1/80 x z, COEFF(2, 1, 1) = ---- + ---- x + 1/160 x + 2000 4000 2000 + + 2 27 2 + + 3/1000 x y + 7/80 z - 1/80 y z - 3/32 z - 3/80 x z + ---- y - 1/160 y , + 2000 + + 191 2 49 + COEFF(-1, 2, 1) = 3/80 x z - 9/1000 x y + ---- + 1/16 z + 1/160 y + ---- y + 4000 2000 + + 2 2 53 + - 3/32 z - 3/80 y z + 1/160 x - 7/250 x, COEFF(0, 2, 1) = ---- + 1000 + + 2 2 43 + + 1/160 y + 1/80 x z + 3/40 z - 1/1000 x - 3/32 z + ---- y - 3/1000 x y + 2000 + + 2 27 2 + - 1/160 x - 3/80 y z, COEFF(1, 2, 1) = ---- x - 3/80 y z - 1/160 x + 2000 + + 2 183 37 2 + + 3/1000 x y - 1/80 x z + 1/160 y + ---- + ---- y + 7/80 z - 3/32 z , + 4000 2000 + + 31 13 2 31 2 + COEFF(2, 2, 1) = ---- x + --- + 9/1000 x y + 1/160 y + ---- y + 1/160 x + 2000 500 2000 + + 2 + - 3/32 z + 1/10 z - 3/80 x z - 3/80 y z, COEFF(-1, -1, 2) = 3/80 z + + 2 449 2 2 + + 1/32 z - 9/250 y - 9/250 x - 3/80 y z - ----- + 3/160 y + 3/160 x + 12000 + + 27 2 + - 3/80 x z + ---- x y, COEFF(0, -1, 2) = 1/32 z + 9/1000 x y - 1/80 x z + 1000 + + 13 17 2 27 2 + + ---- x - ---- + 3/160 y + 1/40 z - ---- y - 3/160 x - 3/80 y z, + 1000 3000 1000 + + 49 2 2 + COEFF(1, -1, 2) = - 9/1000 x y + ---- x + 1/32 z - 9/500 y - 3/160 x + 2000 + + 137 2 + + 1/80 x z - 3/80 y z - ----- + 1/80 z + 3/160 y , COEFF(2, -1, 2) = + 12000 + + 2 27 41 2 + 3/160 y - 3/80 y z - ---- x y - 3/2000 x - --- + 1/32 z - 9/1000 y + 1000 750 + + 2 2 13 + + 3/80 x z + 3/160 x , COEFF(-1, 0, 2) = 1/32 z + ---- y - 1/80 y z + 1000 + + 2 2 17 27 + + 3/160 x - 3/160 y - ---- - 3/80 x z + 1/40 z + 9/1000 x y - ---- x, + 3000 1000 + + 2 349 + COEFF(0, 0, 2) = 3/1000 x y - 3/160 y + ----- + 1/80 z - 1/80 x z + 12000 + + 2 2 + + 2/125 y + 2/125 x - 3/160 x - 1/80 y z + 1/32 z , COEFF(1, 0, 2) = + + 19 2 43 79 2 + ---- y - 3/160 x + ---- x + ---- - 3/1000 x y - 1/80 y z + 1/32 z + 1000 2000 3000 + + 2 21 + - 3/160 y + 1/80 x z, COEFF(2, 0, 2) = - 9/1000 x y - ---- x - 1/80 y z + 2000 + + 2 2 11 167 2 + + 1/32 z - 1/80 z + 3/160 x + 3/80 x z + --- y - ----- - 3/160 y , + 500 12000 + + 2 + COEFF(-1, 1, 2) = - 9/500 x + 1/80 y z - 9/1000 x y - 3/160 y + 1/80 z + + 49 2 2 137 43 + + ---- y + 1/32 z - 3/80 x z + 3/160 x - -----, COEFF(0, 1, 2) = ---- y + 2000 12000 2000 + + 2 2 19 + - 3/1000 x y + 1/80 y z - 3/160 x - 3/160 y + ---- x - 1/80 x z + 1000 + + 2 79 2 2 + + 1/32 z + ----, COEFF(1, 1, 2) = - 3/160 y + 1/80 x z - 3/160 x + 3000 + + 37 319 2 37 + + ---- y + ----- - 1/80 z + 1/80 y z + 1/32 z + 3/1000 x y + ---- x, + 2000 12000 2000 + + 2 39 31 2 + COEFF(2, 1, 2) = 1/32 z - ---- x + ---- y - 3/160 y - 4/375 + 1/80 y z + 2000 2000 + + 2 2 + + 3/160 x + 3/80 x z - 1/40 z + 9/1000 x y, COEFF(-1, 2, 2) = 3/160 y + + 41 27 2 + - --- + 3/80 y z - 9/1000 x - ---- x y + 3/160 x - 3/2000 y - 3/80 x z + 750 1000 + + 2 21 167 + + 1/32 z , COEFF(0, 2, 2) = - 1/80 x z - ---- y - ----- + 3/80 y z + 2000 12000 + + 2 2 11 2 + + 3/160 y - 3/160 x + --- x - 9/1000 x y + 1/32 z - 1/80 z, + 500 + + 2 + COEFF(1, 2, 2) = 3/160 y - 1/40 z + 3/80 y z + 9/1000 x y + 1/80 x z + + 2 39 2 31 + - 3/160 x - ---- y + 1/32 z - 4/375 + ---- x, COEFF(2, 2, 2) = 3/80 x z + 2000 2000 + + 57 27 539 2 2 + - ---- y + ---- x y + 3/80 y z - ----- - 3/80 z + 1/32 z + 3/160 x + 2000 1000 12000 + + 2 57 + + 3/160 y - ---- x] + 2000 + +> print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dz.compute.c"); +bytes used=418205100, alloc=4914300, time=41.74 +bytes used=419205616, alloc=4914300, time=41.82 +bytes used=420205780, alloc=4914300, time=41.89 +bytes used=421206144, alloc=4914300, time=42.03 +bytes used=422206316, alloc=4914300, time=42.12 +bytes used=423225048, alloc=4914300, time=42.19 +bytes used=424232576, alloc=4914300, time=42.27 +bytes used=425256628, alloc=4914300, time=42.35 +bytes used=426268612, alloc=4914300, time=42.46 +bytes used=427268792, alloc=4914300, time=42.57 +bytes used=428268980, alloc=4914300, time=43.10 +bytes used=429270148, alloc=4914300, time=43.25 +bytes used=430270332, alloc=4914300, time=43.31 +bytes used=431272084, alloc=4914300, time=43.37 +bytes used=432272284, alloc=4914300, time=43.44 +bytes used=433272452, alloc=4914300, time=43.51 +bytes used=434280840, alloc=4914300, time=43.62 +bytes used=435281092, alloc=4914300, time=43.74 +bytes used=436281244, alloc=4914300, time=43.89 +bytes used=437289104, alloc=4914300, time=44.01 +bytes used=438289320, alloc=4914300, time=44.14 +bytes used=439303432, alloc=4914300, time=44.24 +bytes used=440303940, alloc=4914300, time=44.33 +bytes used=441316200, alloc=4914300, time=44.89 +bytes used=442316540, alloc=4914300, time=45.10 +bytes used=443316804, alloc=4914300, time=45.17 +bytes used=444317120, alloc=4914300, time=45.24 +bytes used=445317508, alloc=4914300, time=45.31 +bytes used=446317700, alloc=4914300, time=45.37 +bytes used=447322516, alloc=4914300, time=45.58 +bytes used=448322784, alloc=4914300, time=45.69 +bytes used=449323564, alloc=4914300, time=46.29 +bytes used=450323776, alloc=4914300, time=46.55 +bytes used=451324284, alloc=4914300, time=46.63 +bytes used=452324592, alloc=4914300, time=46.70 +bytes used=453325024, alloc=4914300, time=46.76 +bytes used=454325180, alloc=4914300, time=46.84 +bytes used=455325364, alloc=4914300, time=47.01 +bytes used=456325536, alloc=4914300, time=47.63 +bytes used=457325924, alloc=4914300, time=47.81 +bytes used=458326112, alloc=4914300, time=47.88 +bytes used=459326504, alloc=4914300, time=47.95 +bytes used=460326708, alloc=4914300, time=48.01 +bytes used=461326944, alloc=4914300, time=48.19 +bytes used=462327156, alloc=4914300, time=48.65 +bytes used=463327336, alloc=4914300, time=49.00 +bytes used=464327500, alloc=4914300, time=49.07 +bytes used=465327720, alloc=4914300, time=49.18 +> +# d^2/dx^2 +> simplify( diff(interp_3d_cube_order3_smooth0,x,x) ); +- 1/8 DATA(0, 2, -1) + 1/40 DATA(2, 0, -1) - 1/8 DATA(0, -1, 2) + + - 7/80 DATA(0, 2, 2) + 3/40 DATA(1, 0, 2) + 7/80 DATA(-1, 0, -1) + + 11 + + 3/80 DATA(2, -1, -1) - -- DATA(0, 0, 0) + 1/20 DATA(1, 0, 0) + 80 + + - 1/8 DATA(0, 1, 0) + 1/16 DATA(1, 1, 0) - 1/8 DATA(0, 0, 1) + + + 1/16 DATA(1, 0, 1) - 9/80 DATA(0, 1, 1) + 3/40 DATA(1, 1, 1) + + + 1/16 DATA(1, 2, -1) + 1/16 DATA(-1, 2, -1) + 1/80 DATA(2, 1, -1) + + + 1/80 DATA(2, 0, 0) + 1/40 DATA(2, -1, 0) + 3/40 DATA(1, 2, 0) + + - 9/80 DATA(0, 2, 0) + 1/20 DATA(-1, 2, 0) - 1/80 DATA(2, 2, 0) + + + 1/80 DATA(2, -1, 1) + 3/80 DATA(-1, 2, 1) - 1/80 DATA(2, 1, 1) + + + 7/80 DATA(1, 2, 1) - 1/10 DATA(0, 2, 1) + 1/16 DATA(-1, -1, 2) + + - 1/40 DATA(2, 2, 1) + 1/16 DATA(1, -1, 2) - 1/80 DATA(2, 0, 2) + + - 9/80 DATA(0, 0, 2) + 1/20 DATA(-1, 0, 2) + 7/80 DATA(1, 1, 2) + + - 1/10 DATA(0, 1, 2) + 3/80 DATA(-1, 1, 2) + 1/40 DATA(-1, 2, 2) + + - 1/40 DATA(2, 1, 2) + 1/10 DATA(1, 2, 2) - 3/20 DATA(0, -1, 0) + + + 3/80 DATA(1, -1, 0) + 3/40 DATA(-1, 0, 0) + 1/16 DATA(-1, 1, 0) + + 11 + + 3/40 DATA(-1, -1, 1) - -- DATA(0, -1, 1) + 1/20 DATA(1, -1, 1) + 80 + + + 1/16 DATA(-1, 0, 1) + 1/20 DATA(-1, 1, 1) - 3/20 DATA(0, 0, -1) + + 11 + + 3/80 DATA(1, 0, -1) + 3/40 DATA(-1, 1, -1) - -- DATA(0, 1, -1) + 80 + + + 1/20 DATA(1, 1, -1) + 7/80 DATA(-1, -1, 0) + 1/10 DATA(-1, -1, -1) + + 13 + - -- DATA(0, -1, -1) + 1/40 DATA(1, -1, -1) - 3/80 DATA(2, 2, 2) + 80 + + - 3/80 z DATA(0, 1, 2) + 3/80 z DATA(-1, 2, 2) + 3/80 z DATA(2, -1, 2) + + - 3/80 z DATA(1, 0, 2) + 3/80 y DATA(-1, 2, 2) - 3/80 y DATA(0, 2, 1) + + - 3/80 y DATA(1, 2, 0) + 3/80 y DATA(2, 2, -1) + 1/16 x DATA(2, 2, -1) + + + 1/16 x DATA(2, -1, 2) + 1/16 x DATA(2, 1, 0) + 1/16 x DATA(2, 0, 1) + + - 1/16 x DATA(-1, -1, -1) + 3/16 x DATA(0, -1, -1) + + - 3/16 x DATA(1, -1, -1) + 1/16 x DATA(2, 2, 2) + 3/16 x DATA(0, -1, 1) + + - 1/16 x DATA(-1, 2, 2) + 1/16 x DATA(2, 1, 2) - 3/16 x DATA(1, 2, 2) + + + 3/16 x DATA(0, -1, 0) - 1/80 z DATA(1, 2, 1) - 1/80 z DATA(0, 2, 1) + + + 3/80 z DATA(-1, -1, 2) + 1/80 z DATA(2, 2, 1) - 3/80 z DATA(1, -1, 2) + + + 3/80 z DATA(2, 0, 2) - 3/80 z DATA(0, 0, 2) + 3/80 z DATA(-1, 0, 2) + + - 3/80 z DATA(1, 1, 2) + 3/80 z DATA(-1, 1, 2) + 3/80 z DATA(0, 2, -1) + + + 1/80 z DATA(-1, -1, 1) - 1/80 z DATA(1, -1, 1) + 1/80 z DATA(0, 2, 0) + + - 3/80 z DATA(2, 1, -1) - 1/80 z DATA(2, -1, 0) - 1/80 z DATA(2, 0, 0) + + - 3/80 z DATA(2, 0, -1) - 3/80 z DATA(0, -1, 2) - 3/80 z DATA(0, 2, 2) + + - 3/80 z DATA(-1, 0, -1) - 3/80 z DATA(2, -1, -1) + 1/80 z DATA(0, 0, 0) + + + 1/80 z DATA(1, 0, 0) + 1/80 z DATA(0, 1, 0) + 1/80 z DATA(1, 1, 0) + + - 1/80 z DATA(0, 0, 1) - 1/80 z DATA(1, 0, 1) - 1/80 z DATA(0, 1, 1) + + - 1/80 z DATA(1, 1, 1) - 3/80 z DATA(2, 2, -1) + 3/80 z DATA(1, 2, -1) + + - 3/80 z DATA(-1, 2, -1) - 1/80 z DATA(-1, 0, 0) - 1/80 z DATA(-1, 1, 0) + + + 1/80 z DATA(-1, 1, 1) + 1/80 z DATA(1, 2, 0) - 1/80 z DATA(-1, 2, 0) + + - 1/80 z DATA(2, 1, 0) - 1/80 z DATA(2, 2, 0) + 1/80 z DATA(2, -1, 1) + + + 1/80 z DATA(2, 0, 1) + 1/80 z DATA(-1, 2, 1) + 1/80 z DATA(2, 1, 1) + + + 1/80 z DATA(-1, 0, 1) + 3/80 z DATA(0, 0, -1) + 3/80 z DATA(1, 0, -1) + + - 3/80 z DATA(-1, 1, -1) + 3/80 z DATA(0, 1, -1) + 3/80 z DATA(1, 1, -1) + + - 1/80 z DATA(-1, -1, 0) - 3/80 z DATA(-1, -1, -1) + + + 3/80 z DATA(0, -1, -1) + 3/80 z DATA(1, -1, -1) + 3/80 z DATA(2, 2, 2) + + - 1/80 z DATA(0, -1, 1) + 3/80 z DATA(2, 1, 2) - 3/80 z DATA(1, 2, 2) + + + 1/80 z DATA(0, -1, 0) + 1/80 z DATA(1, -1, 0) - 1/80 y DATA(-1, 0, 2) + + - 3/80 y DATA(2, -1, 2) - 1/80 y DATA(1, 1, 2) - 1/80 y DATA(0, 1, 2) + + + 1/80 y DATA(-1, 1, 2) - 3/80 y DATA(0, 2, -1) - 3/80 y DATA(-1, -1, 1) + + + 3/80 y DATA(1, -1, 1) - 1/80 y DATA(-1, 0, 1) + 1/80 y DATA(-1, 1, 1) + + + 1/80 y DATA(0, 0, -1) + 1/80 y DATA(1, 0, -1) + 1/80 y DATA(-1, 1, -1) + + - 1/80 y DATA(0, 1, -1) - 1/80 y DATA(1, 1, -1) - 3/80 y DATA(-1, -1, 0) + + - 3/80 y DATA(-1, -1, -1) + 3/80 y DATA(0, -1, -1) + + + 3/80 y DATA(1, -1, -1) + 3/80 y DATA(2, 2, 2) + 1/80 y DATA(2, 1, -1) + + - 1/80 y DATA(2, 0, 0) + 3/80 y DATA(0, -1, 2) + 3/16 x DATA(0, -1, 2) + + + 3/16 x DATA(0, 2, 2) - 3/16 x DATA(1, 0, 2) - 1/16 x DATA(-1, 0, -1) + + + 1/16 x DATA(2, -1, -1) + 3/16 x DATA(0, 0, 0) - 3/16 x DATA(1, 0, 0) + + + 3/16 x DATA(0, 1, 0) - 3/16 x DATA(1, 1, 0) + 3/16 x DATA(0, 0, 1) + + + 1/16 x DATA(2, 0, -1) - 1/80 y DATA(-1, 0, -1) - 3/80 y DATA(2, -1, -1) + + + 1/80 y DATA(0, 0, 0) + 1/80 y DATA(1, 0, 0) - 1/80 y DATA(0, 1, 0) + + - 1/80 y DATA(1, 1, 0) + 1/80 y DATA(0, 0, 1) + 1/80 y DATA(1, 0, 1) + + - 1/80 y DATA(0, 1, 1) - 1/80 y DATA(1, 1, 1) - 3/80 y DATA(1, 2, -1) + + + 3/80 y DATA(-1, 2, -1) - 3/80 y DATA(2, -1, 0) - 3/80 y DATA(0, 2, 0) + + + 3/80 y DATA(-1, 2, 0) + 1/80 y DATA(2, 1, 0) + 3/80 y DATA(2, 2, 0) + + - 3/80 y DATA(2, -1, 1) - 1/80 y DATA(2, 0, 1) + 3/80 y DATA(-1, 2, 1) + + + 1/80 y DATA(2, 1, 1) - 3/80 y DATA(1, 2, 1) - 3/80 y DATA(-1, -1, 2) + + + 3/80 y DATA(2, 2, 1) + 3/80 y DATA(1, -1, 2) - 1/80 y DATA(2, 0, 2) + + + 1/80 y DATA(0, 0, 2) - 1/80 y DATA(2, 0, -1) - 3/80 y DATA(0, 2, 2) + + + 1/80 y DATA(1, 0, 2) + 3/16 x DATA(0, 1, 2) - 1/16 x DATA(-1, 1, 2) + + + 3/16 x DATA(0, 2, -1) - 1/16 x DATA(-1, -1, 1) - 3/16 x DATA(1, -1, 1) + + - 1/16 x DATA(-1, 0, 1) - 1/16 x DATA(-1, 1, 1) + 3/16 x DATA(0, 0, -1) + + - 3/16 x DATA(1, 0, -1) - 1/16 x DATA(-1, 1, -1) + 3/16 x DATA(0, 1, -1) + + - 3/16 x DATA(1, 1, -1) - 1/16 x DATA(-1, -1, 0) + 3/80 y DATA(0, -1, 1) + + + 1/80 y DATA(2, 1, 2) - 3/80 y DATA(1, 2, 2) + 3/80 y DATA(0, -1, 0) + + + 3/80 y DATA(1, -1, 0) - 1/80 y DATA(-1, 0, 0) + 1/80 y DATA(-1, 1, 0) + + - 3/16 x DATA(1, 0, 1) + 3/16 x DATA(0, 1, 1) - 3/16 x DATA(1, 1, 1) + + - 3/16 x DATA(1, 2, -1) - 1/16 x DATA(-1, 2, -1) + 1/16 x DATA(2, 1, -1) + + + 1/16 x DATA(2, 0, 0) + 1/16 x DATA(2, -1, 0) - 3/16 x DATA(1, 2, 0) + + + 3/16 x DATA(0, 2, 0) - 1/16 x DATA(-1, 2, 0) + 1/16 x DATA(2, 2, 0) + + + 1/16 x DATA(2, -1, 1) - 1/16 x DATA(-1, 2, 1) + 1/16 x DATA(2, 1, 1) + + - 3/16 x DATA(1, 2, 1) + 3/16 x DATA(0, 2, 1) - 1/16 x DATA(-1, -1, 2) + + + 1/16 x DATA(2, 2, 1) - 3/16 x DATA(1, -1, 2) + 1/16 x DATA(2, 0, 2) + + + 3/16 x DATA(0, 0, 2) - 1/16 x DATA(-1, 0, 2) - 3/16 x DATA(1, 1, 2) + + - 3/16 x DATA(1, -1, 0) - 1/16 x DATA(-1, 0, 0) - 1/16 x DATA(-1, 1, 0) + +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=466327912, alloc=4914300, time=49.31 +bytes used=467328084, alloc=4914300, time=49.38 +bytes used=468328536, alloc=4914300, time=49.45 +bytes used=469328704, alloc=4914300, time=49.52 +bytes used=470333744, alloc=4914300, time=49.60 +[COEFF(-1, -1, -1) = - 3/80 y - 1/16 x + 1/10 - 3/80 z, + + 13 + COEFF(0, -1, -1) = - -- + 3/16 x + 3/80 y + 3/80 z, + 80 + + COEFF(1, -1, -1) = - 3/16 x + 3/80 y + 1/40 + 3/80 z, + + COEFF(2, -1, -1) = 3/80 - 3/80 y - 3/80 z + 1/16 x, + + COEFF(-1, 0, -1) = - 1/80 y - 3/80 z + 7/80 - 1/16 x, + + COEFF(0, 0, -1) = - 3/20 + 1/80 y + 3/80 z + 3/16 x, + + COEFF(1, 0, -1) = 3/80 - 3/16 x + 3/80 z + 1/80 y, + + COEFF(2, 0, -1) = - 1/80 y + 1/16 x - 3/80 z + 1/40, + + COEFF(-1, 1, -1) = 1/80 y + 3/40 - 1/16 x - 3/80 z, + + 11 + COEFF(0, 1, -1) = 3/80 z - 1/80 y + 3/16 x - --, + 80 + + COEFF(1, 1, -1) = - 3/16 x + 3/80 z + 1/20 - 1/80 y, + + COEFF(2, 1, -1) = - 3/80 z + 1/16 x + 1/80 y + 1/80, + + COEFF(-1, 2, -1) = 1/16 - 1/16 x - 3/80 z + 3/80 y, + + COEFF(0, 2, -1) = 3/16 x - 1/8 - 3/80 y + 3/80 z, + + COEFF(1, 2, -1) = 1/16 + 3/80 z - 3/80 y - 3/16 x, + + COEFF(2, 2, -1) = 3/80 y - 3/80 z + 1/16 x, + + COEFF(-1, -1, 0) = - 1/80 z - 1/16 x - 3/80 y + 7/80, + + COEFF(0, -1, 0) = 3/16 x + 1/80 z - 3/20 + 3/80 y, + + COEFF(1, -1, 0) = 3/80 + 3/80 y - 3/16 x + 1/80 z, + + COEFF(2, -1, 0) = 1/40 - 3/80 y - 1/80 z + 1/16 x, + + COEFF(-1, 0, 0) = - 1/80 z - 1/80 y + 3/40 - 1/16 x, + + 11 + COEFF(0, 0, 0) = 3/16 x - -- + 1/80 y + 1/80 z, + 80 + + COEFF(1, 0, 0) = 1/20 + 1/80 y + 1/80 z - 3/16 x, + + COEFF(2, 0, 0) = 1/16 x - 1/80 z + 1/80 - 1/80 y, + + COEFF(-1, 1, 0) = 1/80 y + 1/16 - 1/80 z - 1/16 x, + + COEFF(0, 1, 0) = 1/80 z + 3/16 x - 1/80 y - 1/8, + + COEFF(1, 1, 0) = - 1/80 y - 3/16 x + 1/16 + 1/80 z, + + COEFF(2, 1, 0) = 1/80 y + 1/16 x - 1/80 z, + + COEFF(-1, 2, 0) = 3/80 y + 1/20 - 1/80 z - 1/16 x, + + COEFF(0, 2, 0) = 1/80 z - 9/80 - 3/80 y + 3/16 x, + + COEFF(1, 2, 0) = - 3/80 y + 1/80 z + 3/40 - 3/16 x, + + COEFF(2, 2, 0) = - 1/80 z + 1/16 x - 1/80 + 3/80 y, + + COEFF(-1, -1, 1) = - 3/80 y + 3/40 - 1/16 x + 1/80 z, + + 11 + COEFF(0, -1, 1) = - 1/80 z + 3/16 x + 3/80 y - --, + 80 + + COEFF(1, -1, 1) = - 1/80 z + 3/80 y - 3/16 x + 1/20, + + COEFF(2, -1, 1) = 1/80 z + 1/16 x + 1/80 - 3/80 y, + + COEFF(-1, 0, 1) = - 1/16 x + 1/80 z + 1/16 - 1/80 y, + + COEFF(0, 0, 1) = - 1/8 - 1/80 z + 3/16 x + 1/80 y, + + COEFF(1, 0, 1) = 1/16 + 1/80 y - 3/16 x - 1/80 z, + + COEFF(2, 0, 1) = 1/80 z - 1/80 y + 1/16 x, + + COEFF(-1, 1, 1) = 1/20 + 1/80 y + 1/80 z - 1/16 x, + + COEFF(0, 1, 1) = - 9/80 + 3/16 x - 1/80 z - 1/80 y, + + COEFF(1, 1, 1) = 3/40 - 1/80 z - 3/16 x - 1/80 y, + + COEFF(2, 1, 1) = 1/80 y + 1/80 z - 1/80 + 1/16 x, + + COEFF(-1, 2, 1) = 1/80 z + 3/80 + 3/80 y - 1/16 x, + + COEFF(0, 2, 1) = - 1/80 z + 3/16 x - 1/10 - 3/80 y, + + COEFF(1, 2, 1) = - 1/80 z + 7/80 - 3/80 y - 3/16 x, + + COEFF(2, 2, 1) = 3/80 y + 1/80 z - 1/40 + 1/16 x, + + COEFF(-1, -1, 2) = - 1/16 x + 1/16 + 3/80 z - 3/80 y, + + COEFF(0, -1, 2) = - 1/8 - 3/80 z + 3/16 x + 3/80 y, + + COEFF(1, -1, 2) = - 3/16 x - 3/80 z + 3/80 y + 1/16, + + COEFF(2, -1, 2) = 1/16 x + 3/80 z - 3/80 y, + + COEFF(-1, 0, 2) = 3/80 z + 1/20 - 1/16 x - 1/80 y, + + COEFF(0, 0, 2) = 3/16 x - 3/80 z - 9/80 + 1/80 y, + + COEFF(1, 0, 2) = - 3/80 z + 1/80 y - 3/16 x + 3/40, + + COEFF(2, 0, 2) = - 1/80 + 3/80 z + 1/16 x - 1/80 y, + + COEFF(-1, 1, 2) = 1/80 y + 3/80 z - 1/16 x + 3/80, + + COEFF(0, 1, 2) = - 1/10 + 3/16 x - 1/80 y - 3/80 z, + + COEFF(1, 1, 2) = 7/80 - 1/80 y - 3/80 z - 3/16 x, + + COEFF(2, 1, 2) = 3/80 z - 1/40 + 1/16 x + 1/80 y, + + COEFF(-1, 2, 2) = 1/40 + 3/80 z + 3/80 y - 1/16 x, + + COEFF(0, 2, 2) = - 7/80 - 3/80 z + 3/16 x - 3/80 y, + + COEFF(1, 2, 2) = - 3/80 y + 1/10 - 3/16 x - 3/80 z, + + COEFF(2, 2, 2) = - 3/80 + 3/80 z + 1/16 x + 3/80 y] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxx.compute.c"); +bytes used=471334096, alloc=4914300, time=49.68 +bytes used=472334324, alloc=4914300, time=49.74 +bytes used=473334528, alloc=4914300, time=49.89 +bytes used=474334756, alloc=4914300, time=49.98 +bytes used=475334916, alloc=4914300, time=50.24 +bytes used=476335148, alloc=4914300, time=50.30 +bytes used=477335324, alloc=4914300, time=50.38 +bytes used=478338460, alloc=4914300, time=50.46 +bytes used=479338740, alloc=4914300, time=50.73 +bytes used=480338972, alloc=4914300, time=50.86 +bytes used=481339228, alloc=4914300, time=51.17 +bytes used=482339540, alloc=4914300, time=51.35 +> +# d^2/dxdy +> simplify( diff(interp_3d_cube_order3_smooth0,x,y) ); + 13 13 19 +---- DATA(0, 2, -1) + ---- DATA(2, 0, -1) - ---- DATA(0, -1, 2) +1000 1000 2000 + + 11 + + --- DATA(0, 2, 2) - 1/1000 DATA(1, 0, 2) - 1/2000 DATA(-1, 0, -1) + 500 + + 19 + - 9/250 DATA(2, -1, -1) - ---- DATA(0, 0, 0) - 3/1000 DATA(1, 0, 0) + 2000 + + 31 21 + - 3/1000 DATA(0, 1, 0) + ---- DATA(1, 1, 0) - ---- DATA(0, 0, 1) + 2000 2000 + + 29 + - 1/500 DATA(1, 0, 1) - 1/500 DATA(0, 1, 1) + ---- DATA(1, 1, 1) + 2000 + + 49 + - 3/2000 DATA(2, 2, -1) + ---- DATA(1, 2, -1) - 9/250 DATA(-1, 2, -1) + 2000 + + 49 27 + + ---- DATA(2, 1, -1) + 2/125 DATA(2, 0, 0) - ---- DATA(2, -1, 0) + 2000 1000 + + 43 27 + + ---- DATA(1, 2, 0) + 2/125 DATA(0, 2, 0) - ---- DATA(-1, 2, 0) + 2000 1000 + + 43 21 + + ---- DATA(2, 1, 0) - ---- DATA(2, 2, 0) - 9/500 DATA(2, -1, 1) + 2000 2000 + + 19 37 + + ---- DATA(2, 0, 1) - 9/500 DATA(-1, 2, 1) + ---- DATA(2, 1, 1) + 1000 2000 + + 37 19 93 + + ---- DATA(1, 2, 1) + ---- DATA(0, 2, 1) + ---- DATA(-1, -1, 2) + 2000 1000 2000 + + 39 11 + - ---- DATA(2, 2, 1) - 7/250 DATA(1, -1, 2) + --- DATA(2, 0, 2) + 2000 500 + + 23 19 + - ---- DATA(0, 0, 2) - ---- DATA(-1, 0, 2) - 9/1000 DATA(2, -1, 2) + 2000 2000 + + 27 + + ---- DATA(1, 1, 2) - 1/1000 DATA(0, 1, 2) - 7/250 DATA(-1, 1, 2) + 2000 + + 31 31 + - 9/1000 DATA(-1, 2, 2) + ---- DATA(2, 1, 2) + ---- DATA(1, 2, 2) + 2000 2000 + + 17 + - 7/2000 DATA(0, -1, 0) - --- DATA(1, -1, 0) - 7/2000 DATA(-1, 0, 0) + 500 + + 17 111 13 + - --- DATA(-1, 1, 0) + ---- DATA(-1, -1, 1) - ---- DATA(0, -1, 1) + 500 2000 2000 + + 31 13 31 + - ---- DATA(1, -1, 1) - ---- DATA(-1, 0, 1) - ---- DATA(-1, 1, 1) + 1000 2000 1000 + + 17 37 + - ---- DATA(0, 0, -1) - 1/250 DATA(1, 0, -1) - ---- DATA(-1, 1, -1) + 2000 1000 + + 33 129 + - 1/250 DATA(0, 1, -1) + ---- DATA(1, 1, -1) + ---- DATA(-1, -1, 0) + 2000 2000 + + 147 37 + + ---- DATA(-1, -1, -1) - 1/2000 DATA(0, -1, -1) - ---- DATA(1, -1, -1) + 2000 1000 + + 57 27 + - ---- DATA(2, 2, 2) - 3/1000 z DATA(0, 1, 2) - ---- z DATA(-1, 2, 2) + 2000 1000 + + 27 + - ---- z DATA(2, -1, 2) - 3/1000 z DATA(1, 0, 2) - 3/80 y DATA(-1, 2, 2) + 1000 + + - 1/80 y DATA(0, 2, 1) + 1/80 y DATA(1, 2, 0) + 3/80 y DATA(2, 2, -1) + + + 3/80 x DATA(2, 2, -1) - 3/80 x DATA(2, -1, 2) + 1/80 x DATA(2, 1, 0) + + - 1/80 x DATA(2, 0, 1) - 3/80 x DATA(-1, -1, -1) + 3/80 x DATA(0, -1, -1) + + + 3/80 x DATA(1, -1, -1) + 3/80 x DATA(2, 2, 2) + 3/80 x DATA(0, -1, 1) + + + 3/80 x DATA(-1, 2, 2) + 1/80 x DATA(2, 1, 2) - 3/80 x DATA(1, 2, 2) + + + 3/80 x DATA(0, -1, 0) + 3/1000 z DATA(1, 2, 1) - 3/1000 z DATA(0, 2, 1) + + 27 + + ---- z DATA(-1, -1, 2) + 9/1000 z DATA(2, 2, 1) + 1000 + + - 9/1000 z DATA(1, -1, 2) - 9/1000 z DATA(2, 0, 2) + + + 3/1000 z DATA(0, 0, 2) + 9/1000 z DATA(-1, 0, 2) + + + 3/1000 z DATA(1, 1, 2) - 9/1000 z DATA(-1, 1, 2) + + + 9/1000 z DATA(0, 2, -1) + 9/1000 z DATA(-1, -1, 1) + + - 3/1000 z DATA(1, -1, 1) + 3/1000 z DATA(0, 2, 0) + + - 9/1000 z DATA(2, 1, -1) + 9/1000 z DATA(2, -1, 0) + + + 3/1000 z DATA(2, 0, 0) + 9/1000 z DATA(2, 0, -1) + + + 9/1000 z DATA(0, -1, 2) - 9/1000 z DATA(0, 2, 2) + + 27 + - 9/1000 z DATA(-1, 0, -1) + ---- z DATA(2, -1, -1) + 1000 + + - 1/1000 z DATA(0, 0, 0) + 1/1000 z DATA(1, 0, 0) + 1/1000 z DATA(0, 1, 0) + + - 1/1000 z DATA(1, 1, 0) + 1/1000 z DATA(0, 0, 1) - 1/1000 z DATA(1, 0, 1) + + 27 + - 1/1000 z DATA(0, 1, 1) + 1/1000 z DATA(1, 1, 1) - ---- z DATA(2, 2, -1) + 1000 + + 27 + - 9/1000 z DATA(1, 2, -1) + ---- z DATA(-1, 2, -1) + 1000 + + - 3/1000 z DATA(-1, 0, 0) + 3/1000 z DATA(-1, 1, 0) + + - 3/1000 z DATA(-1, 1, 1) - 3/1000 z DATA(1, 2, 0) + + + 9/1000 z DATA(-1, 2, 0) - 3/1000 z DATA(2, 1, 0) + + - 9/1000 z DATA(2, 2, 0) - 9/1000 z DATA(2, -1, 1) + + - 3/1000 z DATA(2, 0, 1) - 9/1000 z DATA(-1, 2, 1) + + + 3/1000 z DATA(2, 1, 1) + 3/1000 z DATA(-1, 0, 1) + + - 3/1000 z DATA(0, 0, -1) + 3/1000 z DATA(1, 0, -1) + + + 9/1000 z DATA(-1, 1, -1) + 3/1000 z DATA(0, 1, -1) + + - 3/1000 z DATA(1, 1, -1) - 9/1000 z DATA(-1, -1, 0) + + 27 + - ---- z DATA(-1, -1, -1) - 9/1000 z DATA(0, -1, -1) + 1000 + + 27 + + 9/1000 z DATA(1, -1, -1) + ---- z DATA(2, 2, 2) + 1000 + + + 3/1000 z DATA(0, -1, 1) + 9/1000 z DATA(2, 1, 2) + + + 9/1000 z DATA(1, 2, 2) - 3/1000 z DATA(0, -1, 0) + + + 3/1000 z DATA(1, -1, 0) + 3/80 y DATA(-1, 0, 2) + 3/80 y DATA(2, -1, 2) + + - 1/80 y DATA(1, 1, 2) + 1/80 y DATA(0, 1, 2) + 3/80 y DATA(-1, 1, 2) + + - 1/80 y DATA(0, 2, -1) - 3/80 y DATA(-1, -1, 1) + 1/80 y DATA(1, -1, 1) + + + 3/80 y DATA(-1, 0, 1) + 3/80 y DATA(-1, 1, 1) + 1/80 y DATA(0, 0, -1) + + - 1/80 y DATA(1, 0, -1) + 3/80 y DATA(-1, 1, -1) + 1/80 y DATA(0, 1, -1) + + - 1/80 y DATA(1, 1, -1) - 3/80 y DATA(-1, -1, 0) - 3/80 y DATA(-1, -1, -1) + + - 1/80 y DATA(0, -1, -1) + 1/80 y DATA(1, -1, -1) + 3/80 y DATA(2, 2, 2) + + - 3/80 y DATA(2, 1, -1) - 3/80 y DATA(2, 0, 0) - 1/80 y DATA(0, -1, 2) + + + 3/80 x DATA(0, -1, 2) - 3/80 x DATA(0, 2, 2) + 1/80 x DATA(1, 0, 2) + + - 1/80 x DATA(-1, 0, -1) - 3/80 x DATA(2, -1, -1) + 1/80 x DATA(0, 0, 0) + + + 1/80 x DATA(1, 0, 0) - 1/80 x DATA(0, 1, 0) - 1/80 x DATA(1, 1, 0) + + + 1/80 x DATA(0, 0, 1) - 1/80 x DATA(2, 0, -1) + 3/80 y DATA(-1, 0, -1) + + + 3/80 y DATA(2, -1, -1) + 1/80 y DATA(0, 0, 0) - 1/80 y DATA(1, 0, 0) + + + 1/80 y DATA(0, 1, 0) - 1/80 y DATA(1, 1, 0) + 1/80 y DATA(0, 0, 1) + + - 1/80 y DATA(1, 0, 1) + 1/80 y DATA(0, 1, 1) - 1/80 y DATA(1, 1, 1) + + + 1/80 y DATA(1, 2, -1) - 3/80 y DATA(-1, 2, -1) + 3/80 y DATA(2, -1, 0) + + - 1/80 y DATA(0, 2, 0) - 3/80 y DATA(-1, 2, 0) - 3/80 y DATA(2, 1, 0) + + + 3/80 y DATA(2, 2, 0) + 3/80 y DATA(2, -1, 1) - 3/80 y DATA(2, 0, 1) + + - 3/80 y DATA(-1, 2, 1) - 3/80 y DATA(2, 1, 1) + 1/80 y DATA(1, 2, 1) + + - 3/80 y DATA(-1, -1, 2) + 3/80 y DATA(2, 2, 1) + 1/80 y DATA(1, -1, 2) + + - 3/80 y DATA(2, 0, 2) + 1/80 y DATA(0, 0, 2) - 3/80 y DATA(2, 0, -1) + + - 1/80 y DATA(0, 2, 2) - 1/80 y DATA(1, 0, 2) - 1/80 x DATA(0, 1, 2) + + + 1/80 x DATA(-1, 1, 2) - 3/80 x DATA(0, 2, -1) - 3/80 x DATA(-1, -1, 1) + + + 3/80 x DATA(1, -1, 1) - 1/80 x DATA(-1, 0, 1) + 1/80 x DATA(-1, 1, 1) + + + 1/80 x DATA(0, 0, -1) + 1/80 x DATA(1, 0, -1) + 1/80 x DATA(-1, 1, -1) + + - 1/80 x DATA(0, 1, -1) - 1/80 x DATA(1, 1, -1) - 3/80 x DATA(-1, -1, 0) + + - 1/80 y DATA(0, -1, 1) - 3/80 y DATA(2, 1, 2) + 1/80 y DATA(1, 2, 2) + + - 1/80 y DATA(0, -1, 0) + 1/80 y DATA(1, -1, 0) + 3/80 y DATA(-1, 0, 0) + + + 3/80 y DATA(-1, 1, 0) + 1/80 x DATA(1, 0, 1) - 1/80 x DATA(0, 1, 1) + + - 1/80 x DATA(1, 1, 1) - 3/80 x DATA(1, 2, -1) + 3/80 x DATA(-1, 2, -1) + + + 1/80 x DATA(2, 1, -1) - 1/80 x DATA(2, 0, 0) - 3/80 x DATA(2, -1, 0) + + - 3/80 x DATA(1, 2, 0) - 3/80 x DATA(0, 2, 0) + 3/80 x DATA(-1, 2, 0) + + + 3/80 x DATA(2, 2, 0) - 3/80 x DATA(2, -1, 1) + 3/80 x DATA(-1, 2, 1) + + + 1/80 x DATA(2, 1, 1) - 3/80 x DATA(1, 2, 1) - 3/80 x DATA(0, 2, 1) + + - 3/80 x DATA(-1, -1, 2) + 3/80 x DATA(2, 2, 1) + 3/80 x DATA(1, -1, 2) + + - 1/80 x DATA(2, 0, 2) + 1/80 x DATA(0, 0, 2) - 1/80 x DATA(-1, 0, 2) + + - 1/80 x DATA(1, 1, 2) + 3/80 x DATA(1, -1, 0) - 1/80 x DATA(-1, 0, 0) + + + 1/80 x DATA(-1, 1, 0) + +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=483339844, alloc=4914300, time=51.43 +bytes used=484340016, alloc=4914300, time=51.50 +bytes used=485340380, alloc=4914300, time=51.57 +bytes used=486353448, alloc=4914300, time=51.64 +bytes used=487353608, alloc=4914300, time=51.72 + 27 147 +[COEFF(-1, -1, -1) = - ---- z + ---- - 3/80 x - 3/80 y, + 1000 2000 + + COEFF(0, -1, -1) = - 9/1000 z + 3/80 x - 1/80 y - 1/2000, + + 37 + COEFF(1, -1, -1) = 3/80 x + 9/1000 z + 1/80 y - ----, + 1000 + + 27 + COEFF(2, -1, -1) = ---- z + 3/80 y - 3/80 x - 9/250, + 1000 + + COEFF(-1, 0, -1) = - 1/80 x + 3/80 y - 9/1000 z - 1/2000, + + 17 + COEFF(0, 0, -1) = 1/80 x - 3/1000 z - ---- + 1/80 y, + 2000 + + COEFF(1, 0, -1) = - 1/80 y + 1/80 x - 1/250 + 3/1000 z, + + 13 + COEFF(2, 0, -1) = - 3/80 y - 1/80 x + ---- + 9/1000 z, + 1000 + + 37 + COEFF(-1, 1, -1) = 9/1000 z - ---- + 1/80 x + 3/80 y, + 1000 + + COEFF(0, 1, -1) = 3/1000 z + 1/80 y - 1/250 - 1/80 x, + + 33 + COEFF(1, 1, -1) = ---- - 3/1000 z - 1/80 y - 1/80 x, + 2000 + + 49 + COEFF(2, 1, -1) = - 3/80 y + ---- + 1/80 x - 9/1000 z, + 2000 + + 27 + COEFF(-1, 2, -1) = ---- z + 3/80 x - 3/80 y - 9/250, + 1000 + + 13 + COEFF(0, 2, -1) = 9/1000 z + ---- - 3/80 x - 1/80 y, + 1000 + + 49 + COEFF(1, 2, -1) = - 9/1000 z + 1/80 y - 3/80 x + ----, + 2000 + + 27 + COEFF(2, 2, -1) = 3/80 y + 3/80 x - 3/2000 - ---- z, + 1000 + + 129 + COEFF(-1, -1, 0) = ---- - 3/80 y - 9/1000 z - 3/80 x, + 2000 + + COEFF(0, -1, 0) = - 7/2000 - 3/1000 z - 1/80 y + 3/80 x, + + 17 + COEFF(1, -1, 0) = - --- + 3/80 x + 1/80 y + 3/1000 z, + 500 + + 27 + COEFF(2, -1, 0) = 3/80 y - 3/80 x + 9/1000 z - ----, + 1000 + + COEFF(-1, 0, 0) = - 7/2000 + 3/80 y - 1/80 x - 3/1000 z, + + 19 + COEFF(0, 0, 0) = - ---- + 1/80 x + 1/80 y - 1/1000 z, + 2000 + + COEFF(1, 0, 0) = 1/1000 z - 3/1000 + 1/80 x - 1/80 y, + + COEFF(2, 0, 0) = 3/1000 z - 3/80 y + 2/125 - 1/80 x, + + 17 + COEFF(-1, 1, 0) = - --- + 3/80 y + 1/80 x + 3/1000 z, + 500 + + COEFF(0, 1, 0) = 1/1000 z - 1/80 x - 3/1000 + 1/80 y, + + 31 + COEFF(1, 1, 0) = - 1/80 x - 1/80 y - 1/1000 z + ----, + 2000 + + 43 + COEFF(2, 1, 0) = - 3/80 y + ---- + 1/80 x - 3/1000 z, + 2000 + + 27 + COEFF(-1, 2, 0) = - ---- + 3/80 x - 3/80 y + 9/1000 z, + 1000 + + COEFF(0, 2, 0) = 2/125 - 1/80 y + 3/1000 z - 3/80 x, + + 43 + COEFF(1, 2, 0) = - 3/80 x - 3/1000 z + 1/80 y + ----, + 2000 + + 21 + COEFF(2, 2, 0) = - 9/1000 z + 3/80 x - ---- + 3/80 y, + 2000 + + 111 + COEFF(-1, -1, 1) = - 3/80 y - 3/80 x + ---- + 9/1000 z, + 2000 + + 13 + COEFF(0, -1, 1) = 3/80 x + 3/1000 z - 1/80 y - ----, + 2000 + + 31 + COEFF(1, -1, 1) = 3/80 x - ---- - 3/1000 z + 1/80 y, + 1000 + + COEFF(2, -1, 1) = - 9/500 - 9/1000 z - 3/80 x + 3/80 y, + + 13 + COEFF(-1, 0, 1) = - ---- - 1/80 x + 3/1000 z + 3/80 y, + 2000 + + 21 + COEFF(0, 0, 1) = 1/80 x + 1/1000 z - ---- + 1/80 y, + 2000 + + COEFF(1, 0, 1) = - 1/500 + 1/80 x - 1/80 y - 1/1000 z, + + 19 + COEFF(2, 0, 1) = - 3/1000 z - 3/80 y + ---- - 1/80 x, + 1000 + + 31 + COEFF(-1, 1, 1) = - 3/1000 z + 1/80 x + 3/80 y - ----, + 1000 + + COEFF(0, 1, 1) = - 1/1000 z - 1/80 x + 1/80 y - 1/500, + + 29 + COEFF(1, 1, 1) = - 1/80 x + 1/1000 z + ---- - 1/80 y, + 2000 + + 37 + COEFF(2, 1, 1) = 3/1000 z + 1/80 x - 3/80 y + ----, + 2000 + + COEFF(-1, 2, 1) = - 3/80 y + 3/80 x - 9/500 - 9/1000 z, + + 19 + COEFF(0, 2, 1) = ---- - 1/80 y - 3/1000 z - 3/80 x, + 1000 + + 37 + COEFF(1, 2, 1) = 1/80 y + 3/1000 z + ---- - 3/80 x, + 2000 + + 39 + COEFF(2, 2, 1) = 3/80 x + 9/1000 z - ---- + 3/80 y, + 2000 + + 93 27 + COEFF(-1, -1, 2) = - 3/80 x + ---- + ---- z - 3/80 y, + 2000 1000 + + 19 + COEFF(0, -1, 2) = - ---- + 9/1000 z - 1/80 y + 3/80 x, + 2000 + + COEFF(1, -1, 2) = - 9/1000 z - 7/250 + 3/80 x + 1/80 y, + + 27 + COEFF(2, -1, 2) = - ---- z - 3/80 x + 3/80 y - 9/1000, + 1000 + + 19 + COEFF(-1, 0, 2) = - 1/80 x + 3/80 y + 9/1000 z - ----, + 2000 + + 23 + COEFF(0, 0, 2) = 1/80 x - ---- + 1/80 y + 3/1000 z, + 2000 + + COEFF(1, 0, 2) = 1/80 x - 3/1000 z - 1/1000 - 1/80 y, + + 11 + COEFF(2, 0, 2) = - 9/1000 z - 1/80 x + --- - 3/80 y, + 500 + + COEFF(-1, 1, 2) = 3/80 y + 1/80 x - 7/250 - 9/1000 z, + + COEFF(0, 1, 2) = - 1/1000 - 1/80 x + 1/80 y - 3/1000 z, + + 27 + COEFF(1, 1, 2) = - 1/80 y + ---- + 3/1000 z - 1/80 x, + 2000 + + 31 + COEFF(2, 1, 2) = 1/80 x + ---- + 9/1000 z - 3/80 y, + 2000 + + 27 + COEFF(-1, 2, 2) = - ---- z - 3/80 y - 9/1000 + 3/80 x, + 1000 + + 11 + COEFF(0, 2, 2) = - 1/80 y + --- - 3/80 x - 9/1000 z, + 500 + + 31 + COEFF(1, 2, 2) = - 3/80 x + 9/1000 z + ---- + 1/80 y, + 2000 + + 27 57 + COEFF(2, 2, 2) = ---- z + 3/80 y - ---- + 3/80 x] + 1000 2000 + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxy.compute.c"); +bytes used=488353760, alloc=4914300, time=51.79 +bytes used=489354100, alloc=4914300, time=51.85 +bytes used=490354256, alloc=4914300, time=51.96 +bytes used=491354508, alloc=4914300, time=52.04 +bytes used=492354684, alloc=4914300, time=52.38 +bytes used=493354892, alloc=4914300, time=52.45 +bytes used=494355080, alloc=4914300, time=52.53 +bytes used=495355288, alloc=4914300, time=52.63 +bytes used=496355440, alloc=4914300, time=52.90 +bytes used=497355604, alloc=4914300, time=53.15 +bytes used=498355804, alloc=4914300, time=53.24 +bytes used=499355960, alloc=4914300, time=53.62 +bytes used=500356244, alloc=4914300, time=53.72 +> +# d^2/dxdz +> simplify( diff(interp_3d_cube_order3_smooth0,x,z) ); + 19 27 13 +- ---- DATA(0, 2, -1) - ---- DATA(2, 0, -1) + ---- DATA(0, -1, 2) + 2000 1000 1000 + + 11 43 129 + + --- DATA(0, 2, 2) + ---- DATA(1, 0, 2) + ---- DATA(-1, 0, -1) + 500 2000 2000 + + 19 + - 9/250 DATA(2, -1, -1) - ---- DATA(0, 0, 0) - 3/1000 DATA(1, 0, 0) + 2000 + + 21 + - ---- DATA(0, 1, 0) - 1/500 DATA(1, 1, 0) - 3/1000 DATA(0, 0, 1) + 2000 + + 31 29 + + ---- DATA(1, 0, 1) - 1/500 DATA(0, 1, 1) + ---- DATA(1, 1, 1) + 2000 2000 + + 93 + - 9/1000 DATA(2, 2, -1) - 7/250 DATA(1, 2, -1) + ---- DATA(-1, 2, -1) + 2000 + + 13 + - 9/500 DATA(2, 1, -1) + 2/125 DATA(2, 0, 0) + ---- DATA(2, -1, 0) + 1000 + + 23 19 + - 1/1000 DATA(1, 2, 0) - ---- DATA(0, 2, 0) - ---- DATA(-1, 2, 0) + 2000 2000 + + 19 11 49 + + ---- DATA(2, 1, 0) + --- DATA(2, 2, 0) + ---- DATA(2, -1, 1) + 1000 500 2000 + + 43 37 + + ---- DATA(2, 0, 1) - 7/250 DATA(-1, 2, 1) + ---- DATA(2, 1, 1) + 2000 2000 + + 27 + + ---- DATA(1, 2, 1) - 1/1000 DATA(0, 2, 1) - 9/250 DATA(-1, -1, 2) + 2000 + + 31 49 21 + + ---- DATA(2, 2, 1) + ---- DATA(1, -1, 2) - ---- DATA(2, 0, 2) + 2000 2000 2000 + + 27 + + 2/125 DATA(0, 0, 2) - ---- DATA(-1, 0, 2) - 3/2000 DATA(2, -1, 2) + 1000 + + 37 19 + + ---- DATA(1, 1, 2) + ---- DATA(0, 1, 2) - 9/500 DATA(-1, 1, 2) + 2000 1000 + + 39 31 + - 9/1000 DATA(-1, 2, 2) - ---- DATA(2, 1, 2) + ---- DATA(1, 2, 2) + 2000 2000 + + 17 + - ---- DATA(0, -1, 0) - 1/250 DATA(1, -1, 0) - 7/2000 DATA(-1, 0, 0) + 2000 + + 13 37 + - ---- DATA(-1, 1, 0) - ---- DATA(-1, -1, 1) - 1/250 DATA(0, -1, 1) + 2000 1000 + + 33 17 31 + + ---- DATA(1, -1, 1) - --- DATA(-1, 0, 1) - ---- DATA(-1, 1, 1) + 2000 500 1000 + + 17 111 + - 7/2000 DATA(0, 0, -1) - --- DATA(1, 0, -1) + ---- DATA(-1, 1, -1) + 500 2000 + + 13 31 + - ---- DATA(0, 1, -1) - ---- DATA(1, 1, -1) - 1/2000 DATA(-1, -1, 0) + 2000 1000 + + 147 37 + + ---- DATA(-1, -1, -1) - 1/2000 DATA(0, -1, -1) - ---- DATA(1, -1, -1) + 2000 1000 + + 57 + - ---- DATA(2, 2, 2) - 1/80 z DATA(0, 1, 2) - 3/80 z DATA(-1, 2, 2) + 2000 + + 27 + + 3/80 z DATA(2, -1, 2) + 1/80 z DATA(1, 0, 2) - ---- y DATA(-1, 2, 2) + 1000 + + 27 + - 3/1000 y DATA(0, 2, 1) - 3/1000 y DATA(1, 2, 0) - ---- y DATA(2, 2, -1) + 1000 + + - 3/80 x DATA(2, 2, -1) + 3/80 x DATA(2, -1, 2) - 1/80 x DATA(2, 1, 0) + + + 1/80 x DATA(2, 0, 1) - 3/80 x DATA(-1, -1, -1) + 3/80 x DATA(0, -1, -1) + + + 3/80 x DATA(1, -1, -1) + 3/80 x DATA(2, 2, 2) - 1/80 x DATA(0, -1, 1) + + + 3/80 x DATA(-1, 2, 2) + 3/80 x DATA(2, 1, 2) - 3/80 x DATA(1, 2, 2) + + + 1/80 x DATA(0, -1, 0) - 1/80 z DATA(1, 2, 1) + 1/80 z DATA(0, 2, 1) + + - 3/80 z DATA(-1, -1, 2) - 3/80 z DATA(2, 2, 1) + 1/80 z DATA(1, -1, 2) + + + 3/80 z DATA(2, 0, 2) - 1/80 z DATA(0, 0, 2) - 3/80 z DATA(-1, 0, 2) + + + 1/80 z DATA(1, 1, 2) - 3/80 z DATA(-1, 1, 2) - 1/80 z DATA(0, 2, -1) + + + 3/80 z DATA(-1, -1, 1) - 1/80 z DATA(1, -1, 1) + 1/80 z DATA(0, 2, 0) + + + 3/80 z DATA(2, 1, -1) - 3/80 z DATA(2, -1, 0) - 3/80 z DATA(2, 0, 0) + + + 3/80 z DATA(2, 0, -1) - 1/80 z DATA(0, -1, 2) - 1/80 z DATA(0, 2, 2) + + - 3/80 z DATA(-1, 0, -1) + 3/80 z DATA(2, -1, -1) + 1/80 z DATA(0, 0, 0) + + - 1/80 z DATA(1, 0, 0) + 1/80 z DATA(0, 1, 0) - 1/80 z DATA(1, 1, 0) + + + 1/80 z DATA(0, 0, 1) - 1/80 z DATA(1, 0, 1) + 1/80 z DATA(0, 1, 1) + + - 1/80 z DATA(1, 1, 1) + 3/80 z DATA(2, 2, -1) + 1/80 z DATA(1, 2, -1) + + - 3/80 z DATA(-1, 2, -1) + 3/80 z DATA(-1, 0, 0) + 3/80 z DATA(-1, 1, 0) + + + 3/80 z DATA(-1, 1, 1) - 1/80 z DATA(1, 2, 0) + 3/80 z DATA(-1, 2, 0) + + - 3/80 z DATA(2, 1, 0) - 3/80 z DATA(2, 2, 0) - 3/80 z DATA(2, -1, 1) + + - 3/80 z DATA(2, 0, 1) + 3/80 z DATA(-1, 2, 1) - 3/80 z DATA(2, 1, 1) + + + 3/80 z DATA(-1, 0, 1) - 1/80 z DATA(0, 0, -1) + 1/80 z DATA(1, 0, -1) + + - 3/80 z DATA(-1, 1, -1) - 1/80 z DATA(0, 1, -1) + 1/80 z DATA(1, 1, -1) + + + 3/80 z DATA(-1, -1, 0) - 3/80 z DATA(-1, -1, -1) + + - 1/80 z DATA(0, -1, -1) + 1/80 z DATA(1, -1, -1) + 3/80 z DATA(2, 2, 2) + + + 1/80 z DATA(0, -1, 1) + 3/80 z DATA(2, 1, 2) + 1/80 z DATA(1, 2, 2) + + + 1/80 z DATA(0, -1, 0) - 1/80 z DATA(1, -1, 0) + 9/1000 y DATA(-1, 0, 2) + + 27 + - ---- y DATA(2, -1, 2) + 3/1000 y DATA(1, 1, 2) - 3/1000 y DATA(0, 1, 2) + 1000 + + - 9/1000 y DATA(-1, 1, 2) + 9/1000 y DATA(0, 2, -1) + + + 9/1000 y DATA(-1, -1, 1) - 3/1000 y DATA(1, -1, 1) + + + 3/1000 y DATA(-1, 0, 1) - 3/1000 y DATA(-1, 1, 1) + + - 3/1000 y DATA(0, 0, -1) + 3/1000 y DATA(1, 0, -1) + + + 9/1000 y DATA(-1, 1, -1) + 3/1000 y DATA(0, 1, -1) + + - 3/1000 y DATA(1, 1, -1) - 9/1000 y DATA(-1, -1, 0) + + 27 + - ---- y DATA(-1, -1, -1) - 9/1000 y DATA(0, -1, -1) + 1000 + + 27 + + 9/1000 y DATA(1, -1, -1) + ---- y DATA(2, 2, 2) + 1000 + + - 9/1000 y DATA(2, 1, -1) + 3/1000 y DATA(2, 0, 0) + + + 9/1000 y DATA(0, -1, 2) - 3/80 x DATA(0, -1, 2) - 3/80 x DATA(0, 2, 2) + + - 3/80 x DATA(1, 0, 2) - 3/80 x DATA(-1, 0, -1) - 3/80 x DATA(2, -1, -1) + + + 1/80 x DATA(0, 0, 0) + 1/80 x DATA(1, 0, 0) + 1/80 x DATA(0, 1, 0) + + + 1/80 x DATA(1, 1, 0) - 1/80 x DATA(0, 0, 1) - 3/80 x DATA(2, 0, -1) + + 27 + - 9/1000 y DATA(-1, 0, -1) + ---- y DATA(2, -1, -1) + 1000 + + - 1/1000 y DATA(0, 0, 0) + 1/1000 y DATA(1, 0, 0) + 1/1000 y DATA(0, 1, 0) + + - 1/1000 y DATA(1, 1, 0) + 1/1000 y DATA(0, 0, 1) - 1/1000 y DATA(1, 0, 1) + + - 1/1000 y DATA(0, 1, 1) + 1/1000 y DATA(1, 1, 1) + + 27 + - 9/1000 y DATA(1, 2, -1) + ---- y DATA(-1, 2, -1) + 1000 + + + 9/1000 y DATA(2, -1, 0) + 3/1000 y DATA(0, 2, 0) + + + 9/1000 y DATA(-1, 2, 0) - 3/1000 y DATA(2, 1, 0) + + - 9/1000 y DATA(2, 2, 0) - 9/1000 y DATA(2, -1, 1) + + - 3/1000 y DATA(2, 0, 1) - 9/1000 y DATA(-1, 2, 1) + + 27 + + 3/1000 y DATA(2, 1, 1) + 3/1000 y DATA(1, 2, 1) + ---- y DATA(-1, -1, 2) + 1000 + + + 9/1000 y DATA(2, 2, 1) - 9/1000 y DATA(1, -1, 2) + + - 9/1000 y DATA(2, 0, 2) + 3/1000 y DATA(0, 0, 2) + + + 9/1000 y DATA(2, 0, -1) - 9/1000 y DATA(0, 2, 2) + + - 3/1000 y DATA(1, 0, 2) - 3/80 x DATA(0, 1, 2) + 3/80 x DATA(-1, 1, 2) + + + 3/80 x DATA(0, 2, -1) + 1/80 x DATA(-1, -1, 1) - 1/80 x DATA(1, -1, 1) + + + 1/80 x DATA(-1, 0, 1) + 1/80 x DATA(-1, 1, 1) + 3/80 x DATA(0, 0, -1) + + + 3/80 x DATA(1, 0, -1) - 3/80 x DATA(-1, 1, -1) + 3/80 x DATA(0, 1, -1) + + + 3/80 x DATA(1, 1, -1) - 1/80 x DATA(-1, -1, 0) + 3/1000 y DATA(0, -1, 1) + + + 9/1000 y DATA(2, 1, 2) + 9/1000 y DATA(1, 2, 2) + + - 3/1000 y DATA(0, -1, 0) + 3/1000 y DATA(1, -1, 0) + + - 3/1000 y DATA(-1, 0, 0) + 3/1000 y DATA(-1, 1, 0) - 1/80 x DATA(1, 0, 1) + + - 1/80 x DATA(0, 1, 1) - 1/80 x DATA(1, 1, 1) + 3/80 x DATA(1, 2, -1) + + - 3/80 x DATA(-1, 2, -1) - 3/80 x DATA(2, 1, -1) - 1/80 x DATA(2, 0, 0) + + - 1/80 x DATA(2, -1, 0) + 1/80 x DATA(1, 2, 0) + 1/80 x DATA(0, 2, 0) + + - 1/80 x DATA(-1, 2, 0) - 1/80 x DATA(2, 2, 0) + 1/80 x DATA(2, -1, 1) + + + 1/80 x DATA(-1, 2, 1) + 1/80 x DATA(2, 1, 1) - 1/80 x DATA(1, 2, 1) + + - 1/80 x DATA(0, 2, 1) + 3/80 x DATA(-1, -1, 2) + 1/80 x DATA(2, 2, 1) + + - 3/80 x DATA(1, -1, 2) + 3/80 x DATA(2, 0, 2) - 3/80 x DATA(0, 0, 2) + + + 3/80 x DATA(-1, 0, 2) - 3/80 x DATA(1, 1, 2) + 1/80 x DATA(1, -1, 0) + + - 1/80 x DATA(-1, 0, 0) - 1/80 x DATA(-1, 1, 0) + +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=501358788, alloc=4914300, time=53.80 +bytes used=502370528, alloc=4914300, time=53.87 +bytes used=503370696, alloc=4914300, time=53.95 +bytes used=504379756, alloc=4914300, time=54.02 +bytes used=505380016, alloc=4914300, time=54.09 + 147 27 +[COEFF(-1, -1, -1) = ---- - 3/80 x - 3/80 z - ---- y, + 2000 1000 + + COEFF(0, -1, -1) = - 1/2000 - 9/1000 y + 3/80 x - 1/80 z, + + 37 + COEFF(1, -1, -1) = 9/1000 y - ---- + 1/80 z + 3/80 x, + 1000 + + 27 + COEFF(2, -1, -1) = - 3/80 x - 9/250 + 3/80 z + ---- y, + 1000 + + 129 + COEFF(-1, 0, -1) = - 3/80 z - 3/80 x + ---- - 9/1000 y, + 2000 + + COEFF(0, 0, -1) = - 1/80 z - 3/1000 y - 7/2000 + 3/80 x, + + 17 + COEFF(1, 0, -1) = 1/80 z - --- + 3/80 x + 3/1000 y, + 500 + + 27 + COEFF(2, 0, -1) = 3/80 z - 3/80 x - ---- + 9/1000 y, + 1000 + + 111 + COEFF(-1, 1, -1) = ---- - 3/80 x + 9/1000 y - 3/80 z, + 2000 + + 13 + COEFF(0, 1, -1) = 3/80 x - 1/80 z + 3/1000 y - ----, + 2000 + + 31 + COEFF(1, 1, -1) = 1/80 z - ---- - 3/1000 y + 3/80 x, + 1000 + + COEFF(2, 1, -1) = 3/80 z - 9/1000 y - 3/80 x - 9/500, + + 93 27 + COEFF(-1, 2, -1) = - 3/80 x + ---- + ---- y - 3/80 z, + 2000 1000 + + 19 + COEFF(0, 2, -1) = - 1/80 z + 9/1000 y - ---- + 3/80 x, + 2000 + + COEFF(1, 2, -1) = 3/80 x - 7/250 - 9/1000 y + 1/80 z, + + 27 + COEFF(2, 2, -1) = 3/80 z - 9/1000 - 3/80 x - ---- y, + 1000 + + COEFF(-1, -1, 0) = - 1/80 x + 3/80 z - 9/1000 y - 1/2000, + + 17 + COEFF(0, -1, 0) = 1/80 x - 3/1000 y + 1/80 z - ----, + 2000 + + COEFF(1, -1, 0) = - 1/80 z + 3/1000 y - 1/250 + 1/80 x, + + 13 + COEFF(2, -1, 0) = - 3/80 z + 9/1000 y + ---- - 1/80 x, + 1000 + + COEFF(-1, 0, 0) = - 7/2000 - 1/80 x - 3/1000 y + 3/80 z, + + 19 + COEFF(0, 0, 0) = 1/80 x - 1/1000 y + 1/80 z - ----, + 2000 + + COEFF(1, 0, 0) = - 3/1000 + 1/80 x + 1/1000 y - 1/80 z, + + COEFF(2, 0, 0) = 3/1000 y - 3/80 z - 1/80 x + 2/125, + + 13 + COEFF(-1, 1, 0) = - ---- - 1/80 x + 3/80 z + 3/1000 y, + 2000 + + 21 + COEFF(0, 1, 0) = 1/80 z + 1/80 x + 1/1000 y - ----, + 2000 + + COEFF(1, 1, 0) = - 1/500 + 1/80 x - 1/1000 y - 1/80 z, + + 19 + COEFF(2, 1, 0) = - 1/80 x - 3/1000 y - 3/80 z + ----, + 1000 + + 19 + COEFF(-1, 2, 0) = 9/1000 y - ---- - 1/80 x + 3/80 z, + 2000 + + 23 + COEFF(0, 2, 0) = 1/80 z - ---- + 3/1000 y + 1/80 x, + 2000 + + COEFF(1, 2, 0) = - 3/1000 y - 1/1000 - 1/80 z + 1/80 x, + + 11 + COEFF(2, 2, 0) = - 3/80 z - 1/80 x + --- - 9/1000 y, + 500 + + 37 + COEFF(-1, -1, 1) = 1/80 x + 9/1000 y - ---- + 3/80 z, + 1000 + + COEFF(0, -1, 1) = 3/1000 y - 1/80 x + 1/80 z - 1/250, + + 33 + COEFF(1, -1, 1) = ---- - 3/1000 y - 1/80 z - 1/80 x, + 2000 + + 49 + COEFF(2, -1, 1) = - 3/80 z + 1/80 x + ---- - 9/1000 y, + 2000 + + 17 + COEFF(-1, 0, 1) = 1/80 x + 3/80 z + 3/1000 y - ---, + 500 + + COEFF(0, 0, 1) = - 1/80 x + 1/80 z - 3/1000 + 1/1000 y, + + 31 + COEFF(1, 0, 1) = - 1/80 x - 1/1000 y + ---- - 1/80 z, + 2000 + + 43 + COEFF(2, 0, 1) = - 3/80 z + ---- - 3/1000 y + 1/80 x, + 2000 + + 31 + COEFF(-1, 1, 1) = - 3/1000 y + 3/80 z - ---- + 1/80 x, + 1000 + + COEFF(0, 1, 1) = - 1/500 - 1/1000 y + 1/80 z - 1/80 x, + + 29 + COEFF(1, 1, 1) = ---- - 1/80 z + 1/1000 y - 1/80 x, + 2000 + + 37 + COEFF(2, 1, 1) = 1/80 x + 3/1000 y - 3/80 z + ----, + 2000 + + COEFF(-1, 2, 1) = 1/80 x - 7/250 - 9/1000 y + 3/80 z, + + COEFF(0, 2, 1) = - 1/80 x - 1/1000 - 3/1000 y + 1/80 z, + + 27 + COEFF(1, 2, 1) = ---- - 1/80 x + 3/1000 y - 1/80 z, + 2000 + + 31 + COEFF(2, 2, 1) = 9/1000 y + 1/80 x + ---- - 3/80 z, + 2000 + + 27 + COEFF(-1, -1, 2) = ---- y + 3/80 x - 3/80 z - 9/250, + 1000 + + 13 + COEFF(0, -1, 2) = 9/1000 y - 3/80 x + ---- - 1/80 z, + 1000 + + 49 + COEFF(1, -1, 2) = - 9/1000 y + 1/80 z - 3/80 x + ----, + 2000 + + 27 + COEFF(2, -1, 2) = 3/80 z - ---- y - 3/2000 + 3/80 x, + 1000 + + 27 + COEFF(-1, 0, 2) = 3/80 x + 9/1000 y - 3/80 z - ----, + 1000 + + COEFF(0, 0, 2) = - 3/80 x + 2/125 + 3/1000 y - 1/80 z, + + 43 + COEFF(1, 0, 2) = - 3/80 x - 3/1000 y + ---- + 1/80 z, + 2000 + + 21 + COEFF(2, 0, 2) = 3/80 x + 3/80 z - 9/1000 y - ----, + 2000 + + COEFF(-1, 1, 2) = - 3/80 z + 3/80 x - 9/1000 y - 9/500, + + 19 + COEFF(0, 1, 2) = ---- - 1/80 z - 3/80 x - 3/1000 y, + 1000 + + 37 + COEFF(1, 1, 2) = ---- - 3/80 x + 3/1000 y + 1/80 z, + 2000 + + 39 + COEFF(2, 1, 2) = - ---- + 9/1000 y + 3/80 z + 3/80 x, + 2000 + + 27 + COEFF(-1, 2, 2) = 3/80 x - 3/80 z - 9/1000 - ---- y, + 1000 + + 11 + COEFF(0, 2, 2) = - 9/1000 y - 3/80 x + --- - 1/80 z, + 500 + + 31 + COEFF(1, 2, 2) = ---- + 9/1000 y - 3/80 x + 1/80 z, + 2000 + + 57 27 + COEFF(2, 2, 2) = - ---- + 3/80 x + ---- y + 3/80 z] + 2000 1000 + +> print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxz.compute.c"); +bytes used=506380360, alloc=4914300, time=54.18 +bytes used=507380724, alloc=4914300, time=54.25 +bytes used=508380960, alloc=4914300, time=54.33 +bytes used=509381208, alloc=4914300, time=54.52 +bytes used=510381716, alloc=4914300, time=54.81 +bytes used=511381892, alloc=4914300, time=54.88 +bytes used=512382340, alloc=4914300, time=54.96 +bytes used=513382580, alloc=4914300, time=55.06 +bytes used=514382860, alloc=4914300, time=55.40 +bytes used=515383140, alloc=4914300, time=55.54 +bytes used=516383348, alloc=4914300, time=55.84 +bytes used=517383836, alloc=4914300, time=56.05 +> +# d^2/dy^2 +> simplify( diff(interp_3d_cube_order3_smooth0,y,y) ); +bytes used=518384240, alloc=4914300, time=56.19 +1/40 DATA(0, 2, -1) - 1/8 DATA(2, 0, -1) + 1/20 DATA(0, -1, 2) + + 13 + - 1/80 DATA(0, 2, 2) - 1/10 DATA(1, 0, 2) - -- DATA(-1, 0, -1) + 80 + + 11 + + 1/16 DATA(2, -1, -1) - -- DATA(0, 0, 0) - 1/8 DATA(1, 0, 0) + 80 + + + 1/20 DATA(0, 1, 0) + 1/16 DATA(1, 1, 0) - 1/8 DATA(0, 0, 1) + + - 9/80 DATA(1, 0, 1) + 1/16 DATA(0, 1, 1) + 3/40 DATA(1, 1, 1) + + + 1/80 DATA(1, 2, -1) + 3/80 DATA(-1, 2, -1) + 1/16 DATA(2, 1, -1) + + - 9/80 DATA(2, 0, 0) + 1/20 DATA(2, -1, 0) + 1/80 DATA(0, 2, 0) + + + 1/40 DATA(-1, 2, 0) + 3/40 DATA(2, 1, 0) - 1/80 DATA(2, 2, 0) + + + 3/80 DATA(2, -1, 1) - 1/10 DATA(2, 0, 1) + 1/80 DATA(-1, 2, 1) + + + 7/80 DATA(2, 1, 1) - 1/80 DATA(1, 2, 1) + 1/16 DATA(-1, -1, 2) + + - 1/40 DATA(2, 2, 1) + 3/80 DATA(1, -1, 2) - 7/80 DATA(2, 0, 2) + + - 9/80 DATA(0, 0, 2) - 1/8 DATA(-1, 0, 2) + 1/40 DATA(2, -1, 2) + + + 7/80 DATA(1, 1, 2) + 3/40 DATA(0, 1, 2) + 1/16 DATA(-1, 1, 2) + + + 1/10 DATA(2, 1, 2) - 1/40 DATA(1, 2, 2) + 3/40 DATA(0, -1, 0) + + + 1/16 DATA(1, -1, 0) - 3/20 DATA(-1, 0, 0) + 3/80 DATA(-1, 1, 0) + + + 3/40 DATA(-1, -1, 1) + 1/16 DATA(0, -1, 1) + 1/20 DATA(1, -1, 1) + + 11 + - -- DATA(-1, 0, 1) + 1/20 DATA(-1, 1, 1) - 3/20 DATA(0, 0, -1) + 80 + + 11 + - -- DATA(1, 0, -1) + 1/40 DATA(-1, 1, -1) + 3/80 DATA(0, 1, -1) + 80 + + + 1/20 DATA(1, 1, -1) + 7/80 DATA(-1, -1, 0) + 1/10 DATA(-1, -1, -1) + + + 7/80 DATA(0, -1, -1) + 3/40 DATA(1, -1, -1) - 3/80 DATA(2, 2, 2) + + - 3/80 z DATA(0, 1, 2) + 3/80 z DATA(-1, 2, 2) + 3/80 z DATA(2, -1, 2) + + - 3/80 z DATA(1, 0, 2) + 1/16 y DATA(-1, 2, 2) + 1/16 y DATA(0, 2, 1) + + + 1/16 y DATA(1, 2, 0) + 1/16 y DATA(2, 2, -1) + 3/80 x DATA(2, 2, -1) + + + 3/80 x DATA(2, -1, 2) - 3/80 x DATA(2, 1, 0) - 3/80 x DATA(2, 0, 1) + + - 3/80 x DATA(-1, -1, -1) - 1/80 x DATA(0, -1, -1) + + + 1/80 x DATA(1, -1, -1) + 3/80 x DATA(2, 2, 2) - 1/80 x DATA(0, -1, 1) + + - 3/80 x DATA(-1, 2, 2) - 3/80 x DATA(2, 1, 2) + 1/80 x DATA(1, 2, 2) + + - 1/80 x DATA(0, -1, 0) + 1/80 z DATA(1, 2, 1) + 1/80 z DATA(0, 2, 1) + + + 3/80 z DATA(-1, -1, 2) + 1/80 z DATA(2, 2, 1) + 3/80 z DATA(1, -1, 2) + + - 3/80 z DATA(2, 0, 2) - 3/80 z DATA(0, 0, 2) - 3/80 z DATA(-1, 0, 2) + + - 3/80 z DATA(1, 1, 2) - 3/80 z DATA(-1, 1, 2) - 3/80 z DATA(0, 2, -1) + + + 1/80 z DATA(-1, -1, 1) + 1/80 z DATA(1, -1, 1) - 1/80 z DATA(0, 2, 0) + + + 3/80 z DATA(2, 1, -1) - 1/80 z DATA(2, -1, 0) + 1/80 z DATA(2, 0, 0) + + + 3/80 z DATA(2, 0, -1) + 3/80 z DATA(0, -1, 2) + 3/80 z DATA(0, 2, 2) + + + 3/80 z DATA(-1, 0, -1) - 3/80 z DATA(2, -1, -1) + 1/80 z DATA(0, 0, 0) + + + 1/80 z DATA(1, 0, 0) + 1/80 z DATA(0, 1, 0) + 1/80 z DATA(1, 1, 0) + + - 1/80 z DATA(0, 0, 1) - 1/80 z DATA(1, 0, 1) - 1/80 z DATA(0, 1, 1) + + - 1/80 z DATA(1, 1, 1) - 3/80 z DATA(2, 2, -1) - 3/80 z DATA(1, 2, -1) + + - 3/80 z DATA(-1, 2, -1) + 1/80 z DATA(-1, 0, 0) + 1/80 z DATA(-1, 1, 0) + + - 1/80 z DATA(-1, 1, 1) - 1/80 z DATA(1, 2, 0) - 1/80 z DATA(-1, 2, 0) + + + 1/80 z DATA(2, 1, 0) - 1/80 z DATA(2, 2, 0) + 1/80 z DATA(2, -1, 1) + + - 1/80 z DATA(2, 0, 1) + 1/80 z DATA(-1, 2, 1) - 1/80 z DATA(2, 1, 1) + + - 1/80 z DATA(-1, 0, 1) + 3/80 z DATA(0, 0, -1) + 3/80 z DATA(1, 0, -1) + + + 3/80 z DATA(-1, 1, -1) + 3/80 z DATA(0, 1, -1) + 3/80 z DATA(1, 1, -1) + + - 1/80 z DATA(-1, -1, 0) - 3/80 z DATA(-1, -1, -1) + + - 3/80 z DATA(0, -1, -1) - 3/80 z DATA(1, -1, -1) + 3/80 z DATA(2, 2, 2) + + + 1/80 z DATA(0, -1, 1) - 3/80 z DATA(2, 1, 2) + 3/80 z DATA(1, 2, 2) + + - 1/80 z DATA(0, -1, 0) - 1/80 z DATA(1, -1, 0) + 3/16 y DATA(-1, 0, 2) + + - 1/16 y DATA(2, -1, 2) - 3/16 y DATA(1, 1, 2) - 3/16 y DATA(0, 1, 2) + + - 3/16 y DATA(-1, 1, 2) + 1/16 y DATA(0, 2, -1) - 1/16 y DATA(-1, -1, 1) + + - 1/16 y DATA(1, -1, 1) + 3/16 y DATA(-1, 0, 1) - 3/16 y DATA(-1, 1, 1) + + + 3/16 y DATA(0, 0, -1) + 3/16 y DATA(1, 0, -1) - 3/16 y DATA(-1, 1, -1) + + - 3/16 y DATA(0, 1, -1) - 3/16 y DATA(1, 1, -1) - 1/16 y DATA(-1, -1, 0) + + - 1/16 y DATA(-1, -1, -1) - 1/16 y DATA(0, -1, -1) + + - 1/16 y DATA(1, -1, -1) + 1/16 y DATA(2, 2, 2) - 3/16 y DATA(2, 1, -1) + + + 3/16 y DATA(2, 0, 0) - 1/16 y DATA(0, -1, 2) - 1/80 x DATA(0, -1, 2) + + - 1/80 x DATA(0, 2, 2) - 1/80 x DATA(1, 0, 2) + 3/80 x DATA(-1, 0, -1) + + + 3/80 x DATA(2, -1, -1) + 1/80 x DATA(0, 0, 0) - 1/80 x DATA(1, 0, 0) + + + 1/80 x DATA(0, 1, 0) - 1/80 x DATA(1, 1, 0) + 1/80 x DATA(0, 0, 1) + + - 3/80 x DATA(2, 0, -1) + 3/16 y DATA(-1, 0, -1) - 1/16 y DATA(2, -1, -1) + + + 3/16 y DATA(0, 0, 0) + 3/16 y DATA(1, 0, 0) - 3/16 y DATA(0, 1, 0) + + - 3/16 y DATA(1, 1, 0) + 3/16 y DATA(0, 0, 1) + 3/16 y DATA(1, 0, 1) + + - 3/16 y DATA(0, 1, 1) - 3/16 y DATA(1, 1, 1) + 1/16 y DATA(1, 2, -1) + + + 1/16 y DATA(-1, 2, -1) - 1/16 y DATA(2, -1, 0) + 1/16 y DATA(0, 2, 0) + + + 1/16 y DATA(-1, 2, 0) - 3/16 y DATA(2, 1, 0) + 1/16 y DATA(2, 2, 0) + + - 1/16 y DATA(2, -1, 1) + 3/16 y DATA(2, 0, 1) + 1/16 y DATA(-1, 2, 1) + + - 3/16 y DATA(2, 1, 1) + 1/16 y DATA(1, 2, 1) - 1/16 y DATA(-1, -1, 2) + + + 1/16 y DATA(2, 2, 1) - 1/16 y DATA(1, -1, 2) + 3/16 y DATA(2, 0, 2) + + + 3/16 y DATA(0, 0, 2) + 3/16 y DATA(2, 0, -1) + 1/16 y DATA(0, 2, 2) + + + 3/16 y DATA(1, 0, 2) + 1/80 x DATA(0, 1, 2) + 3/80 x DATA(-1, 1, 2) + + - 1/80 x DATA(0, 2, -1) - 3/80 x DATA(-1, -1, 1) + 1/80 x DATA(1, -1, 1) + + + 3/80 x DATA(-1, 0, 1) + 3/80 x DATA(-1, 1, 1) + 1/80 x DATA(0, 0, -1) + + - 1/80 x DATA(1, 0, -1) + 3/80 x DATA(-1, 1, -1) + 1/80 x DATA(0, 1, -1) + + - 1/80 x DATA(1, 1, -1) - 3/80 x DATA(-1, -1, 0) - 1/16 y DATA(0, -1, 1) + + - 3/16 y DATA(2, 1, 2) + 1/16 y DATA(1, 2, 2) - 1/16 y DATA(0, -1, 0) + + - 1/16 y DATA(1, -1, 0) + 3/16 y DATA(-1, 0, 0) - 3/16 y DATA(-1, 1, 0) + + - 1/80 x DATA(1, 0, 1) + 1/80 x DATA(0, 1, 1) - 1/80 x DATA(1, 1, 1) + + + 1/80 x DATA(1, 2, -1) - 3/80 x DATA(-1, 2, -1) - 3/80 x DATA(2, 1, -1) + + - 3/80 x DATA(2, 0, 0) + 3/80 x DATA(2, -1, 0) + 1/80 x DATA(1, 2, 0) + + - 1/80 x DATA(0, 2, 0) - 3/80 x DATA(-1, 2, 0) + 3/80 x DATA(2, 2, 0) + + + 3/80 x DATA(2, -1, 1) - 3/80 x DATA(-1, 2, 1) - 3/80 x DATA(2, 1, 1) + + + 1/80 x DATA(1, 2, 1) - 1/80 x DATA(0, 2, 1) - 3/80 x DATA(-1, -1, 2) + + + 3/80 x DATA(2, 2, 1) + 1/80 x DATA(1, -1, 2) - 3/80 x DATA(2, 0, 2) + + + 1/80 x DATA(0, 0, 2) + 3/80 x DATA(-1, 0, 2) - 1/80 x DATA(1, 1, 2) + + + 1/80 x DATA(1, -1, 0) + 3/80 x DATA(-1, 0, 0) + 3/80 x DATA(-1, 1, 0) + +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=519384512, alloc=4914300, time=56.26 +bytes used=520396020, alloc=4914300, time=56.33 +bytes used=521396360, alloc=4914300, time=56.41 +bytes used=522396492, alloc=4914300, time=56.48 +bytes used=523398116, alloc=4914300, time=56.55 +[COEFF(-1, -1, -1) = - 3/80 x - 1/16 y - 3/80 z + 1/10, + + COEFF(0, -1, -1) = - 1/80 x - 1/16 y + 7/80 - 3/80 z, + + COEFF(1, -1, -1) = - 1/16 y + 3/40 - 3/80 z + 1/80 x, + + COEFF(2, -1, -1) = - 3/80 z + 1/16 - 1/16 y + 3/80 x, + + 13 + COEFF(-1, 0, -1) = - -- + 3/80 x + 3/80 z + 3/16 y, + 80 + + COEFF(0, 0, -1) = 3/16 y - 3/20 + 3/80 z + 1/80 x, + + 11 + COEFF(1, 0, -1) = 3/16 y - -- - 1/80 x + 3/80 z, + 80 + + COEFF(2, 0, -1) = 3/16 y - 1/8 + 3/80 z - 3/80 x, + + COEFF(-1, 1, -1) = - 3/16 y + 3/80 z + 1/40 + 3/80 x, + + COEFF(0, 1, -1) = 1/80 x - 3/16 y + 3/80 + 3/80 z, + + COEFF(1, 1, -1) = 3/80 z + 1/20 - 1/80 x - 3/16 y, + + COEFF(2, 1, -1) = - 3/16 y + 3/80 z - 3/80 x + 1/16, + + COEFF(-1, 2, -1) = - 3/80 z - 3/80 x + 3/80 + 1/16 y, + + COEFF(0, 2, -1) = - 3/80 z + 1/16 y - 1/80 x + 1/40, + + COEFF(1, 2, -1) = - 3/80 z + 1/80 + 1/80 x + 1/16 y, + + COEFF(2, 2, -1) = - 3/80 z + 1/16 y + 3/80 x, + + COEFF(-1, -1, 0) = - 1/80 z + 7/80 - 3/80 x - 1/16 y, + + COEFF(0, -1, 0) = - 1/80 x - 1/80 z - 1/16 y + 3/40, + + COEFF(1, -1, 0) = 1/16 - 1/16 y - 1/80 z + 1/80 x, + + COEFF(2, -1, 0) = 1/20 + 3/80 x - 1/16 y - 1/80 z, + + COEFF(-1, 0, 0) = 3/80 x - 3/20 + 3/16 y + 1/80 z, + + 11 + COEFF(0, 0, 0) = 1/80 x - -- + 3/16 y + 1/80 z, + 80 + + COEFF(1, 0, 0) = 1/80 z - 1/80 x - 1/8 + 3/16 y, + + COEFF(2, 0, 0) = 3/16 y - 3/80 x + 1/80 z - 9/80, + + COEFF(-1, 1, 0) = 3/80 x + 1/80 z + 3/80 - 3/16 y, + + COEFF(0, 1, 0) = - 3/16 y + 1/80 x + 1/80 z + 1/20, + + COEFF(1, 1, 0) = - 3/16 y + 1/80 z + 1/16 - 1/80 x, + + COEFF(2, 1, 0) = 1/80 z - 3/16 y + 3/40 - 3/80 x, + + COEFF(-1, 2, 0) = - 1/80 z + 1/16 y + 1/40 - 3/80 x, + + COEFF(0, 2, 0) = 1/16 y + 1/80 - 1/80 x - 1/80 z, + + COEFF(1, 2, 0) = 1/80 x + 1/16 y - 1/80 z, + + COEFF(2, 2, 0) = - 1/80 z - 1/80 + 3/80 x + 1/16 y, + + COEFF(-1, -1, 1) = 1/80 z + 3/40 - 3/80 x - 1/16 y, + + COEFF(0, -1, 1) = 1/80 z - 1/16 y - 1/80 x + 1/16, + + COEFF(1, -1, 1) = - 1/16 y + 1/20 + 1/80 x + 1/80 z, + + COEFF(2, -1, 1) = - 1/16 y + 3/80 + 3/80 x + 1/80 z, + + 11 + COEFF(-1, 0, 1) = 3/16 y - 1/80 z - -- + 3/80 x, + 80 + + COEFF(0, 0, 1) = - 1/80 z - 1/8 + 3/16 y + 1/80 x, + + COEFF(1, 0, 1) = 3/16 y - 1/80 z - 1/80 x - 9/80, + + COEFF(2, 0, 1) = 3/16 y - 1/80 z - 3/80 x - 1/10, + + COEFF(-1, 1, 1) = 1/20 + 3/80 x - 3/16 y - 1/80 z, + + COEFF(0, 1, 1) = - 1/80 z + 1/80 x - 3/16 y + 1/16, + + COEFF(1, 1, 1) = - 3/16 y - 1/80 z + 3/40 - 1/80 x, + + COEFF(2, 1, 1) = 7/80 - 3/80 x - 1/80 z - 3/16 y, + + COEFF(-1, 2, 1) = 1/80 + 1/16 y + 1/80 z - 3/80 x, + + COEFF(0, 2, 1) = - 1/80 x + 1/16 y + 1/80 z, + + COEFF(1, 2, 1) = 1/80 x + 1/80 z - 1/80 + 1/16 y, + + COEFF(2, 2, 1) = - 1/40 + 1/16 y + 1/80 z + 3/80 x, + + COEFF(-1, -1, 2) = - 3/80 x + 1/16 - 1/16 y + 3/80 z, + + COEFF(0, -1, 2) = 3/80 z + 1/20 - 1/80 x - 1/16 y, + + COEFF(1, -1, 2) = 3/80 + 3/80 z + 1/80 x - 1/16 y, + + COEFF(2, -1, 2) = - 1/16 y + 3/80 x + 1/40 + 3/80 z, + + COEFF(-1, 0, 2) = 3/16 y - 1/8 + 3/80 x - 3/80 z, + + COEFF(0, 0, 2) = - 3/80 z + 1/80 x + 3/16 y - 9/80, + + COEFF(1, 0, 2) = 3/16 y - 3/80 z - 1/10 - 1/80 x, + + COEFF(2, 0, 2) = - 3/80 z - 3/80 x - 7/80 + 3/16 y, + + COEFF(-1, 1, 2) = - 3/80 z - 3/16 y + 3/80 x + 1/16, + + COEFF(0, 1, 2) = 1/80 x - 3/80 z - 3/16 y + 3/40, + + COEFF(1, 1, 2) = - 1/80 x - 3/80 z + 7/80 - 3/16 y, + + COEFF(2, 1, 2) = - 3/80 x - 3/80 z - 3/16 y + 1/10, + + COEFF(-1, 2, 2) = 3/80 z - 3/80 x + 1/16 y, + + COEFF(0, 2, 2) = - 1/80 + 3/80 z - 1/80 x + 1/16 y, + + COEFF(1, 2, 2) = 1/16 y + 1/80 x + 3/80 z - 1/40, + + COEFF(2, 2, 2) = - 3/80 + 3/80 z + 3/80 x + 1/16 y] + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dyy.compute.c"); +bytes used=524398336, alloc=4914300, time=56.62 +bytes used=525398564, alloc=4914300, time=56.79 +bytes used=526398736, alloc=4914300, time=56.87 +bytes used=527398932, alloc=4914300, time=57.16 +bytes used=528399196, alloc=4914300, time=57.24 +bytes used=529399372, alloc=4914300, time=57.31 +bytes used=530399600, alloc=4914300, time=57.40 +bytes used=531399824, alloc=4914300, time=57.54 +bytes used=532400012, alloc=4914300, time=57.89 +bytes used=533400172, alloc=4914300, time=58.10 +bytes used=534400428, alloc=4914300, time=58.37 +> +# d^2/dydz +> simplify( diff(interp_3d_cube_order3_smooth0,y,z) ); +bytes used=535400648, alloc=4914300, time=58.49 + 27 19 27 +- ---- DATA(0, 2, -1) - ---- DATA(2, 0, -1) - ---- DATA(0, -1, 2) + 1000 2000 1000 + + 21 19 + - ---- DATA(0, 2, 2) + ---- DATA(1, 0, 2) - 1/2000 DATA(-1, 0, -1) + 2000 1000 + + 93 19 21 + + ---- DATA(2, -1, -1) - ---- DATA(0, 0, 0) - ---- DATA(1, 0, 0) + 2000 2000 2000 + + - 3/1000 DATA(0, 1, 0) - 1/500 DATA(1, 1, 0) - 3/1000 DATA(0, 0, 1) + + 31 29 + - 1/500 DATA(1, 0, 1) + ---- DATA(0, 1, 1) + ---- DATA(1, 1, 1) + 2000 2000 + + - 9/1000 DATA(2, 2, -1) - 9/500 DATA(1, 2, -1) - 9/250 DATA(-1, 2, -1) + + 23 19 + - 7/250 DATA(2, 1, -1) - ---- DATA(2, 0, 0) - ---- DATA(2, -1, 0) + 2000 2000 + + 19 13 + + ---- DATA(1, 2, 0) + 2/125 DATA(0, 2, 0) + ---- DATA(-1, 2, 0) + 1000 1000 + + 11 + - 1/1000 DATA(2, 1, 0) + --- DATA(2, 2, 0) - 7/250 DATA(2, -1, 1) + 500 + + 49 27 + - 1/1000 DATA(2, 0, 1) + ---- DATA(-1, 2, 1) + ---- DATA(2, 1, 1) + 2000 2000 + + 37 43 + + ---- DATA(1, 2, 1) + ---- DATA(0, 2, 1) - 9/250 DATA(-1, -1, 2) + 2000 2000 + + 31 11 + + ---- DATA(2, 2, 1) - 9/500 DATA(1, -1, 2) + --- DATA(2, 0, 2) + 2000 500 + + 13 + + 2/125 DATA(0, 0, 2) + ---- DATA(-1, 0, 2) - 9/1000 DATA(2, -1, 2) + 1000 + + 37 43 49 + + ---- DATA(1, 1, 2) + ---- DATA(0, 1, 2) + ---- DATA(-1, 1, 2) + 2000 2000 2000 + + 31 39 + - 3/2000 DATA(-1, 2, 2) + ---- DATA(2, 1, 2) - ---- DATA(1, 2, 2) + 2000 2000 + + 13 17 + - 7/2000 DATA(0, -1, 0) - ---- DATA(1, -1, 0) - ---- DATA(-1, 0, 0) + 2000 2000 + + 37 17 + - 1/250 DATA(-1, 1, 0) - ---- DATA(-1, -1, 1) - --- DATA(0, -1, 1) + 1000 500 + + 31 33 + - ---- DATA(1, -1, 1) - 1/250 DATA(-1, 0, 1) + ---- DATA(-1, 1, 1) + 1000 2000 + + 13 37 + - 7/2000 DATA(0, 0, -1) - ---- DATA(1, 0, -1) - ---- DATA(-1, 1, -1) + 2000 1000 + + 17 31 + - --- DATA(0, 1, -1) - ---- DATA(1, 1, -1) - 1/2000 DATA(-1, -1, 0) + 500 1000 + + 147 129 111 + + ---- DATA(-1, -1, -1) + ---- DATA(0, -1, -1) + ---- DATA(1, -1, -1) + 2000 2000 2000 + + 57 + - ---- DATA(2, 2, 2) + 1/80 z DATA(0, 1, 2) + 3/80 z DATA(-1, 2, 2) + 2000 + + - 3/80 z DATA(2, -1, 2) - 1/80 z DATA(1, 0, 2) + 3/80 y DATA(-1, 2, 2) + + + 1/80 y DATA(0, 2, 1) - 1/80 y DATA(1, 2, 0) - 3/80 y DATA(2, 2, -1) + + 27 27 + - ---- x DATA(2, 2, -1) - ---- x DATA(2, -1, 2) - 3/1000 x DATA(2, 1, 0) + 1000 1000 + + 27 + - 3/1000 x DATA(2, 0, 1) - ---- x DATA(-1, -1, -1) + 1000 + + - 9/1000 x DATA(0, -1, -1) + 9/1000 x DATA(1, -1, -1) + + 27 27 + + ---- x DATA(2, 2, 2) + 3/1000 x DATA(0, -1, 1) - ---- x DATA(-1, 2, 2) + 1000 1000 + + + 9/1000 x DATA(2, 1, 2) + 9/1000 x DATA(1, 2, 2) + + - 3/1000 x DATA(0, -1, 0) - 3/80 z DATA(1, 2, 1) - 3/80 z DATA(0, 2, 1) + + - 3/80 z DATA(-1, -1, 2) - 3/80 z DATA(2, 2, 1) - 3/80 z DATA(1, -1, 2) + + - 1/80 z DATA(2, 0, 2) - 1/80 z DATA(0, 0, 2) - 1/80 z DATA(-1, 0, 2) + + + 1/80 z DATA(1, 1, 2) + 1/80 z DATA(-1, 1, 2) + 3/80 z DATA(0, 2, -1) + + + 3/80 z DATA(-1, -1, 1) + 3/80 z DATA(1, -1, 1) - 3/80 z DATA(0, 2, 0) + + + 1/80 z DATA(2, 1, -1) + 3/80 z DATA(2, -1, 0) + 1/80 z DATA(2, 0, 0) + + - 1/80 z DATA(2, 0, -1) - 3/80 z DATA(0, -1, 2) + 3/80 z DATA(0, 2, 2) + + - 1/80 z DATA(-1, 0, -1) - 3/80 z DATA(2, -1, -1) + 1/80 z DATA(0, 0, 0) + + + 1/80 z DATA(1, 0, 0) - 1/80 z DATA(0, 1, 0) - 1/80 z DATA(1, 1, 0) + + + 1/80 z DATA(0, 0, 1) + 1/80 z DATA(1, 0, 1) - 1/80 z DATA(0, 1, 1) + + - 1/80 z DATA(1, 1, 1) + 3/80 z DATA(2, 2, -1) + 3/80 z DATA(1, 2, -1) + + + 3/80 z DATA(-1, 2, -1) + 1/80 z DATA(-1, 0, 0) - 1/80 z DATA(-1, 1, 0) + + - 1/80 z DATA(-1, 1, 1) - 3/80 z DATA(1, 2, 0) - 3/80 z DATA(-1, 2, 0) + + - 1/80 z DATA(2, 1, 0) - 3/80 z DATA(2, 2, 0) + 3/80 z DATA(2, -1, 1) + + + 1/80 z DATA(2, 0, 1) - 3/80 z DATA(-1, 2, 1) - 1/80 z DATA(2, 1, 1) + + + 1/80 z DATA(-1, 0, 1) - 1/80 z DATA(0, 0, -1) - 1/80 z DATA(1, 0, -1) + + + 1/80 z DATA(-1, 1, -1) + 1/80 z DATA(0, 1, -1) + 1/80 z DATA(1, 1, -1) + + + 3/80 z DATA(-1, -1, 0) - 3/80 z DATA(-1, -1, -1) + + - 3/80 z DATA(0, -1, -1) - 3/80 z DATA(1, -1, -1) + 3/80 z DATA(2, 2, 2) + + + 3/80 z DATA(0, -1, 1) + 1/80 z DATA(2, 1, 2) + 3/80 z DATA(1, 2, 2) + + + 3/80 z DATA(0, -1, 0) + 3/80 z DATA(1, -1, 0) - 3/80 y DATA(-1, 0, 2) + + + 3/80 y DATA(2, -1, 2) - 3/80 y DATA(1, 1, 2) - 3/80 y DATA(0, 1, 2) + + - 3/80 y DATA(-1, 1, 2) - 3/80 y DATA(0, 2, -1) + 1/80 y DATA(-1, -1, 1) + + + 1/80 y DATA(1, -1, 1) - 1/80 y DATA(-1, 0, 1) - 1/80 y DATA(-1, 1, 1) + + + 3/80 y DATA(0, 0, -1) + 3/80 y DATA(1, 0, -1) + 3/80 y DATA(-1, 1, -1) + + + 3/80 y DATA(0, 1, -1) + 3/80 y DATA(1, 1, -1) - 1/80 y DATA(-1, -1, 0) + + - 3/80 y DATA(-1, -1, -1) - 3/80 y DATA(0, -1, -1) + + - 3/80 y DATA(1, -1, -1) + 3/80 y DATA(2, 2, 2) + 3/80 y DATA(2, 1, -1) + + + 1/80 y DATA(2, 0, 0) + 3/80 y DATA(0, -1, 2) + 9/1000 x DATA(0, -1, 2) + + - 9/1000 x DATA(0, 2, 2) - 3/1000 x DATA(1, 0, 2) + + 27 + - 9/1000 x DATA(-1, 0, -1) + ---- x DATA(2, -1, -1) + 1000 + + - 1/1000 x DATA(0, 0, 0) + 1/1000 x DATA(1, 0, 0) + 1/1000 x DATA(0, 1, 0) + + - 1/1000 x DATA(1, 1, 0) + 1/1000 x DATA(0, 0, 1) + + + 9/1000 x DATA(2, 0, -1) + 3/80 y DATA(-1, 0, -1) + + - 3/80 y DATA(2, -1, -1) + 1/80 y DATA(0, 0, 0) + 1/80 y DATA(1, 0, 0) + + + 1/80 y DATA(0, 1, 0) + 1/80 y DATA(1, 1, 0) - 1/80 y DATA(0, 0, 1) + + - 1/80 y DATA(1, 0, 1) - 1/80 y DATA(0, 1, 1) - 1/80 y DATA(1, 1, 1) + + - 3/80 y DATA(1, 2, -1) - 3/80 y DATA(-1, 2, -1) - 1/80 y DATA(2, -1, 0) + + - 1/80 y DATA(0, 2, 0) - 1/80 y DATA(-1, 2, 0) + 1/80 y DATA(2, 1, 0) + + - 1/80 y DATA(2, 2, 0) + 1/80 y DATA(2, -1, 1) - 1/80 y DATA(2, 0, 1) + + + 1/80 y DATA(-1, 2, 1) - 1/80 y DATA(2, 1, 1) + 1/80 y DATA(1, 2, 1) + + + 3/80 y DATA(-1, -1, 2) + 1/80 y DATA(2, 2, 1) + 3/80 y DATA(1, -1, 2) + + - 3/80 y DATA(2, 0, 2) - 3/80 y DATA(0, 0, 2) + 3/80 y DATA(2, 0, -1) + + + 3/80 y DATA(0, 2, 2) - 3/80 y DATA(1, 0, 2) - 3/1000 x DATA(0, 1, 2) + + - 9/1000 x DATA(-1, 1, 2) + 9/1000 x DATA(0, 2, -1) + + + 9/1000 x DATA(-1, -1, 1) - 3/1000 x DATA(1, -1, 1) + + + 3/1000 x DATA(-1, 0, 1) - 3/1000 x DATA(-1, 1, 1) + + - 3/1000 x DATA(0, 0, -1) + 3/1000 x DATA(1, 0, -1) + + + 9/1000 x DATA(-1, 1, -1) + 3/1000 x DATA(0, 1, -1) + + - 3/1000 x DATA(1, 1, -1) - 9/1000 x DATA(-1, -1, 0) + + + 1/80 y DATA(0, -1, 1) - 3/80 y DATA(2, 1, 2) + 3/80 y DATA(1, 2, 2) + + - 1/80 y DATA(0, -1, 0) - 1/80 y DATA(1, -1, 0) + 1/80 y DATA(-1, 0, 0) + + + 1/80 y DATA(-1, 1, 0) - 1/1000 x DATA(1, 0, 1) - 1/1000 x DATA(0, 1, 1) + + + 1/1000 x DATA(1, 1, 1) - 9/1000 x DATA(1, 2, -1) + + 27 + + ---- x DATA(-1, 2, -1) - 9/1000 x DATA(2, 1, -1) + 1000 + + + 3/1000 x DATA(2, 0, 0) + 9/1000 x DATA(2, -1, 0) + + - 3/1000 x DATA(1, 2, 0) + 3/1000 x DATA(0, 2, 0) + + + 9/1000 x DATA(-1, 2, 0) - 9/1000 x DATA(2, 2, 0) + + - 9/1000 x DATA(2, -1, 1) - 9/1000 x DATA(-1, 2, 1) + + + 3/1000 x DATA(2, 1, 1) + 3/1000 x DATA(1, 2, 1) - 3/1000 x DATA(0, 2, 1) + + 27 + + ---- x DATA(-1, -1, 2) + 9/1000 x DATA(2, 2, 1) + 1000 + + - 9/1000 x DATA(1, -1, 2) - 9/1000 x DATA(2, 0, 2) + + + 3/1000 x DATA(0, 0, 2) + 9/1000 x DATA(-1, 0, 2) + + + 3/1000 x DATA(1, 1, 2) + 3/1000 x DATA(1, -1, 0) + + - 3/1000 x DATA(-1, 0, 0) + 3/1000 x DATA(-1, 1, 0) + +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=536405436, alloc=4914300, time=58.56 +bytes used=537405652, alloc=4914300, time=58.63 +bytes used=538405804, alloc=4914300, time=58.70 +bytes used=539407024, alloc=4914300, time=58.78 +bytes used=540410872, alloc=4914300, time=58.85 + 27 147 +[COEFF(-1, -1, -1) = - 3/80 z - ---- x + ---- - 3/80 y, + 1000 2000 + + 129 + COEFF(0, -1, -1) = ---- - 3/80 z - 3/80 y - 9/1000 x, + 2000 + + 111 + COEFF(1, -1, -1) = - 3/80 z + 9/1000 x - 3/80 y + ----, + 2000 + + 27 93 + COEFF(2, -1, -1) = ---- x - 3/80 y - 3/80 z + ----, + 1000 2000 + + COEFF(-1, 0, -1) = 3/80 y - 1/2000 - 1/80 z - 9/1000 x, + + COEFF(0, 0, -1) = - 1/80 z - 7/2000 + 3/80 y - 3/1000 x, + + 13 + COEFF(1, 0, -1) = 3/80 y - 1/80 z - ---- + 3/1000 x, + 2000 + + 19 + COEFF(2, 0, -1) = - ---- - 1/80 z + 3/80 y + 9/1000 x, + 2000 + + 37 + COEFF(-1, 1, -1) = 9/1000 x - ---- + 1/80 z + 3/80 y, + 1000 + + 17 + COEFF(0, 1, -1) = 3/80 y + 3/1000 x + 1/80 z - ---, + 500 + + 31 + COEFF(1, 1, -1) = - 3/1000 x + 3/80 y - ---- + 1/80 z, + 1000 + + COEFF(2, 1, -1) = - 7/250 + 3/80 y + 1/80 z - 9/1000 x, + + 27 + COEFF(-1, 2, -1) = - 3/80 y + ---- x - 9/250 + 3/80 z, + 1000 + + 27 + COEFF(0, 2, -1) = 3/80 z - 3/80 y + 9/1000 x - ----, + 1000 + + COEFF(1, 2, -1) = - 9/500 + 3/80 z - 9/1000 x - 3/80 y, + + 27 + COEFF(2, 2, -1) = - ---- x + 3/80 z - 3/80 y - 9/1000, + 1000 + + COEFF(-1, -1, 0) = - 9/1000 x - 1/80 y + 3/80 z - 1/2000, + + COEFF(0, -1, 0) = 3/80 z - 7/2000 - 3/1000 x - 1/80 y, + + 13 + COEFF(1, -1, 0) = - ---- + 3/80 z + 3/1000 x - 1/80 y, + 2000 + + 19 + COEFF(2, -1, 0) = - ---- - 1/80 y + 9/1000 x + 3/80 z, + 2000 + + 17 + COEFF(-1, 0, 0) = 1/80 y + 1/80 z - ---- - 3/1000 x, + 2000 + + 19 + COEFF(0, 0, 0) = 1/80 z - ---- + 1/80 y - 1/1000 x, + 2000 + + 21 + COEFF(1, 0, 0) = - ---- + 1/80 z + 1/1000 x + 1/80 y, + 2000 + + 23 + COEFF(2, 0, 0) = 3/1000 x + 1/80 y - ---- + 1/80 z, + 2000 + + COEFF(-1, 1, 0) = 1/80 y + 3/1000 x - 1/80 z - 1/250, + + COEFF(0, 1, 0) = - 1/80 z + 1/80 y + 1/1000 x - 3/1000, + + COEFF(1, 1, 0) = - 1/500 - 1/80 z + 1/80 y - 1/1000 x, + + COEFF(2, 1, 0) = - 1/80 z - 3/1000 x + 1/80 y - 1/1000, + + 13 + COEFF(-1, 2, 0) = - 3/80 z + ---- + 9/1000 x - 1/80 y, + 1000 + + COEFF(0, 2, 0) = - 3/80 z + 3/1000 x - 1/80 y + 2/125, + + 19 + COEFF(1, 2, 0) = ---- - 1/80 y - 3/1000 x - 3/80 z, + 1000 + + 11 + COEFF(2, 2, 0) = - 9/1000 x - 3/80 z + --- - 1/80 y, + 500 + + 37 + COEFF(-1, -1, 1) = 3/80 z + 1/80 y - ---- + 9/1000 x, + 1000 + + 17 + COEFF(0, -1, 1) = 1/80 y - --- + 3/80 z + 3/1000 x, + 500 + + 31 + COEFF(1, -1, 1) = 1/80 y - 3/1000 x + 3/80 z - ----, + 1000 + + COEFF(2, -1, 1) = - 7/250 + 3/80 z + 1/80 y - 9/1000 x, + + COEFF(-1, 0, 1) = - 1/80 y + 1/80 z + 3/1000 x - 1/250, + + COEFF(0, 0, 1) = 1/1000 x - 3/1000 - 1/80 y + 1/80 z, + + COEFF(1, 0, 1) = - 1/1000 x + 1/80 z - 1/80 y - 1/500, + + COEFF(2, 0, 1) = - 1/1000 + 1/80 z - 3/1000 x - 1/80 y, + + 33 + COEFF(-1, 1, 1) = - 1/80 y - 1/80 z + ---- - 3/1000 x, + 2000 + + 31 + COEFF(0, 1, 1) = - 1/80 y + ---- - 1/80 z - 1/1000 x, + 2000 + + 29 + COEFF(1, 1, 1) = - 1/80 y + ---- + 1/1000 x - 1/80 z, + 2000 + + 27 + COEFF(2, 1, 1) = - 1/80 z + ---- - 1/80 y + 3/1000 x, + 2000 + + 49 + COEFF(-1, 2, 1) = - 9/1000 x + 1/80 y - 3/80 z + ----, + 2000 + + 43 + COEFF(0, 2, 1) = - 3/80 z - 3/1000 x + ---- + 1/80 y, + 2000 + + 37 + COEFF(1, 2, 1) = 3/1000 x - 3/80 z + 1/80 y + ----, + 2000 + + 31 + COEFF(2, 2, 1) = 1/80 y + 9/1000 x - 3/80 z + ----, + 2000 + + 27 + COEFF(-1, -1, 2) = - 3/80 z - 9/250 + 3/80 y + ---- x, + 1000 + + 27 + COEFF(0, -1, 2) = 9/1000 x - 3/80 z - ---- + 3/80 y, + 1000 + + COEFF(1, -1, 2) = 3/80 y - 9/500 - 9/1000 x - 3/80 z, + + 27 + COEFF(2, -1, 2) = - 3/80 z - 9/1000 - ---- x + 3/80 y, + 1000 + + 13 + COEFF(-1, 0, 2) = 9/1000 x - 1/80 z + ---- - 3/80 y, + 1000 + + COEFF(0, 0, 2) = - 3/80 y + 2/125 - 1/80 z + 3/1000 x, + + 19 + COEFF(1, 0, 2) = ---- - 1/80 z - 3/1000 x - 3/80 y, + 1000 + + 11 + COEFF(2, 0, 2) = - 9/1000 x - 3/80 y + --- - 1/80 z, + 500 + + 49 + COEFF(-1, 1, 2) = - 9/1000 x + 1/80 z - 3/80 y + ----, + 2000 + + 43 + COEFF(0, 1, 2) = ---- - 3/80 y - 3/1000 x + 1/80 z, + 2000 + + 37 + COEFF(1, 1, 2) = 1/80 z + 3/1000 x + ---- - 3/80 y, + 2000 + + 31 + COEFF(2, 1, 2) = 1/80 z + ---- - 3/80 y + 9/1000 x, + 2000 + + 27 + COEFF(-1, 2, 2) = - 3/2000 + 3/80 y + 3/80 z - ---- x, + 1000 + + 21 + COEFF(0, 2, 2) = 3/80 z - 9/1000 x - ---- + 3/80 y, + 2000 + + 39 + COEFF(1, 2, 2) = 9/1000 x - ---- + 3/80 y + 3/80 z, + 2000 + + 57 27 + COEFF(2, 2, 2) = 3/80 z + 3/80 y - ---- + ---- x] + 2000 1000 + +> print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dyz.compute.c"); +bytes used=541411112, alloc=4914300, time=58.94 +bytes used=542411340, alloc=4914300, time=59.11 +bytes used=543412560, alloc=4914300, time=59.19 +bytes used=544412780, alloc=4914300, time=59.51 +bytes used=545413112, alloc=4914300, time=59.69 +bytes used=546413320, alloc=4914300, time=59.75 +bytes used=547415428, alloc=4914300, time=59.84 +bytes used=548415576, alloc=4914300, time=59.95 +bytes used=549415756, alloc=4914300, time=60.32 +bytes used=550415900, alloc=4914300, time=60.42 +bytes used=551416040, alloc=4914300, time=60.82 +bytes used=552416820, alloc=4914300, time=61.03 +> +# d^2/dz^2 +> simplify( diff(interp_3d_cube_order3_smooth0,z,z) ); +bytes used=553417128, alloc=4914300, time=61.14 +1/20 DATA(0, 2, -1) + 1/20 DATA(2, 0, -1) + 1/40 DATA(0, -1, 2) + + - 1/80 DATA(0, 2, 2) + 7/80 DATA(-1, 0, -1) + 1/16 DATA(2, -1, -1) + + 11 + - -- DATA(0, 0, 0) - 1/8 DATA(1, 0, 0) - 1/8 DATA(0, 1, 0) + 80 + + - 9/80 DATA(1, 1, 0) + 1/20 DATA(0, 0, 1) + 1/16 DATA(1, 0, 1) + + + 1/16 DATA(0, 1, 1) + 3/40 DATA(1, 1, 1) + 1/40 DATA(2, 2, -1) + + + 3/80 DATA(1, 2, -1) + 1/16 DATA(-1, 2, -1) + 3/80 DATA(2, 1, -1) + + - 9/80 DATA(2, 0, 0) - 1/8 DATA(2, -1, 0) - 1/10 DATA(1, 2, 0) + + - 9/80 DATA(0, 2, 0) - 1/8 DATA(-1, 2, 0) - 1/10 DATA(2, 1, 0) + + - 7/80 DATA(2, 2, 0) + 1/16 DATA(2, -1, 1) + 3/40 DATA(2, 0, 1) + + + 1/16 DATA(-1, 2, 1) + 7/80 DATA(2, 1, 1) + 7/80 DATA(1, 2, 1) + + + 3/40 DATA(0, 2, 1) + 3/80 DATA(-1, -1, 2) + 1/10 DATA(2, 2, 1) + + + 1/80 DATA(1, -1, 2) - 1/80 DATA(2, 0, 2) + 1/80 DATA(0, 0, 2) + + + 1/40 DATA(-1, 0, 2) - 1/80 DATA(1, 1, 2) + 1/80 DATA(-1, 1, 2) + + - 1/40 DATA(2, 1, 2) - 1/40 DATA(1, 2, 2) - 3/20 DATA(0, -1, 0) + + 11 11 + - -- DATA(1, -1, 0) - 3/20 DATA(-1, 0, 0) - -- DATA(-1, 1, 0) + 80 80 + + + 1/40 DATA(-1, -1, 1) + 3/80 DATA(0, -1, 1) + 1/20 DATA(1, -1, 1) + + + 3/80 DATA(-1, 0, 1) + 1/20 DATA(-1, 1, 1) + 3/40 DATA(0, 0, -1) + + + 1/16 DATA(1, 0, -1) + 3/40 DATA(-1, 1, -1) + 1/16 DATA(0, 1, -1) + + 13 + + 1/20 DATA(1, 1, -1) - -- DATA(-1, -1, 0) + 1/10 DATA(-1, -1, -1) + 80 + + + 7/80 DATA(0, -1, -1) + 3/40 DATA(1, -1, -1) - 3/80 DATA(2, 2, 2) + + + 1/16 z DATA(0, 1, 2) + 1/16 z DATA(-1, 2, 2) + 1/16 z DATA(2, -1, 2) + + + 1/16 z DATA(1, 0, 2) + 3/80 y DATA(-1, 2, 2) - 3/80 y DATA(0, 2, 1) + + - 3/80 y DATA(1, 2, 0) + 3/80 y DATA(2, 2, -1) + 3/80 x DATA(2, 2, -1) + + + 3/80 x DATA(2, -1, 2) - 3/80 x DATA(2, 1, 0) - 3/80 x DATA(2, 0, 1) + + - 3/80 x DATA(-1, -1, -1) - 1/80 x DATA(0, -1, -1) + + + 1/80 x DATA(1, -1, -1) + 3/80 x DATA(2, 2, 2) + 1/80 x DATA(0, -1, 1) + + - 3/80 x DATA(-1, 2, 2) + 3/80 x DATA(2, 1, 2) + 1/80 x DATA(1, 2, 2) + + + 1/80 x DATA(0, -1, 0) - 3/16 z DATA(1, 2, 1) - 3/16 z DATA(0, 2, 1) + + + 1/16 z DATA(-1, -1, 2) - 3/16 z DATA(2, 2, 1) + 1/16 z DATA(1, -1, 2) + + + 1/16 z DATA(2, 0, 2) + 1/16 z DATA(0, 0, 2) + 1/16 z DATA(-1, 0, 2) + + + 1/16 z DATA(1, 1, 2) + 1/16 z DATA(-1, 1, 2) - 1/16 z DATA(0, 2, -1) + + - 3/16 z DATA(-1, -1, 1) - 3/16 z DATA(1, -1, 1) + 3/16 z DATA(0, 2, 0) + + - 1/16 z DATA(2, 1, -1) + 3/16 z DATA(2, -1, 0) + 3/16 z DATA(2, 0, 0) + + - 1/16 z DATA(2, 0, -1) + 1/16 z DATA(0, -1, 2) + 1/16 z DATA(0, 2, 2) + + - 1/16 z DATA(-1, 0, -1) - 1/16 z DATA(2, -1, -1) + 3/16 z DATA(0, 0, 0) + + + 3/16 z DATA(1, 0, 0) + 3/16 z DATA(0, 1, 0) + 3/16 z DATA(1, 1, 0) + + - 3/16 z DATA(0, 0, 1) - 3/16 z DATA(1, 0, 1) - 3/16 z DATA(0, 1, 1) + + - 3/16 z DATA(1, 1, 1) - 1/16 z DATA(2, 2, -1) - 1/16 z DATA(1, 2, -1) + + - 1/16 z DATA(-1, 2, -1) + 3/16 z DATA(-1, 0, 0) + 3/16 z DATA(-1, 1, 0) + + - 3/16 z DATA(-1, 1, 1) + 3/16 z DATA(1, 2, 0) + 3/16 z DATA(-1, 2, 0) + + + 3/16 z DATA(2, 1, 0) + 3/16 z DATA(2, 2, 0) - 3/16 z DATA(2, -1, 1) + + - 3/16 z DATA(2, 0, 1) - 3/16 z DATA(-1, 2, 1) - 3/16 z DATA(2, 1, 1) + + - 3/16 z DATA(-1, 0, 1) - 1/16 z DATA(0, 0, -1) - 1/16 z DATA(1, 0, -1) + + - 1/16 z DATA(-1, 1, -1) - 1/16 z DATA(0, 1, -1) - 1/16 z DATA(1, 1, -1) + + + 3/16 z DATA(-1, -1, 0) - 1/16 z DATA(-1, -1, -1) + + - 1/16 z DATA(0, -1, -1) - 1/16 z DATA(1, -1, -1) + 1/16 z DATA(2, 2, 2) + + - 3/16 z DATA(0, -1, 1) + 1/16 z DATA(2, 1, 2) + 1/16 z DATA(1, 2, 2) + + + 3/16 z DATA(0, -1, 0) + 3/16 z DATA(1, -1, 0) - 1/80 y DATA(-1, 0, 2) + + - 3/80 y DATA(2, -1, 2) + 1/80 y DATA(1, 1, 2) + 1/80 y DATA(0, 1, 2) + + + 1/80 y DATA(-1, 1, 2) + 3/80 y DATA(0, 2, -1) + 3/80 y DATA(-1, -1, 1) + + + 3/80 y DATA(1, -1, 1) + 1/80 y DATA(-1, 0, 1) - 1/80 y DATA(-1, 1, 1) + + - 1/80 y DATA(0, 0, -1) - 1/80 y DATA(1, 0, -1) + 1/80 y DATA(-1, 1, -1) + + + 1/80 y DATA(0, 1, -1) + 1/80 y DATA(1, 1, -1) + 3/80 y DATA(-1, -1, 0) + + - 3/80 y DATA(-1, -1, -1) - 3/80 y DATA(0, -1, -1) + + - 3/80 y DATA(1, -1, -1) + 3/80 y DATA(2, 2, 2) + 1/80 y DATA(2, 1, -1) + + + 1/80 y DATA(2, 0, 0) - 3/80 y DATA(0, -1, 2) - 1/80 x DATA(0, -1, 2) + + - 1/80 x DATA(0, 2, 2) + 1/80 x DATA(1, 0, 2) - 3/80 x DATA(-1, 0, -1) + + + 3/80 x DATA(2, -1, -1) + 1/80 x DATA(0, 0, 0) - 1/80 x DATA(1, 0, 0) + + + 1/80 x DATA(0, 1, 0) - 1/80 x DATA(1, 1, 0) + 1/80 x DATA(0, 0, 1) + + + 3/80 x DATA(2, 0, -1) - 1/80 y DATA(-1, 0, -1) - 3/80 y DATA(2, -1, -1) + + + 1/80 y DATA(0, 0, 0) + 1/80 y DATA(1, 0, 0) - 1/80 y DATA(0, 1, 0) + + - 1/80 y DATA(1, 1, 0) + 1/80 y DATA(0, 0, 1) + 1/80 y DATA(1, 0, 1) + + - 1/80 y DATA(0, 1, 1) - 1/80 y DATA(1, 1, 1) + 3/80 y DATA(1, 2, -1) + + + 3/80 y DATA(-1, 2, -1) + 3/80 y DATA(2, -1, 0) - 3/80 y DATA(0, 2, 0) + + - 3/80 y DATA(-1, 2, 0) - 1/80 y DATA(2, 1, 0) - 3/80 y DATA(2, 2, 0) + + + 3/80 y DATA(2, -1, 1) + 1/80 y DATA(2, 0, 1) - 3/80 y DATA(-1, 2, 1) + + - 1/80 y DATA(2, 1, 1) - 3/80 y DATA(1, 2, 1) - 3/80 y DATA(-1, -1, 2) + + - 3/80 y DATA(2, 2, 1) - 3/80 y DATA(1, -1, 2) - 1/80 y DATA(2, 0, 2) + + - 1/80 y DATA(0, 0, 2) - 1/80 y DATA(2, 0, -1) + 3/80 y DATA(0, 2, 2) + + - 1/80 y DATA(1, 0, 2) - 1/80 x DATA(0, 1, 2) - 3/80 x DATA(-1, 1, 2) + + - 1/80 x DATA(0, 2, -1) + 3/80 x DATA(-1, -1, 1) - 1/80 x DATA(1, -1, 1) + + + 3/80 x DATA(-1, 0, 1) + 3/80 x DATA(-1, 1, 1) - 1/80 x DATA(0, 0, -1) + + + 1/80 x DATA(1, 0, -1) - 3/80 x DATA(-1, 1, -1) - 1/80 x DATA(0, 1, -1) + + + 1/80 x DATA(1, 1, -1) + 3/80 x DATA(-1, -1, 0) + 3/80 y DATA(0, -1, 1) + + + 1/80 y DATA(2, 1, 2) + 3/80 y DATA(1, 2, 2) + 3/80 y DATA(0, -1, 0) + + + 3/80 y DATA(1, -1, 0) + 1/80 y DATA(-1, 0, 0) - 1/80 y DATA(-1, 1, 0) + + - 1/80 x DATA(1, 0, 1) + 1/80 x DATA(0, 1, 1) - 1/80 x DATA(1, 1, 1) + + + 1/80 x DATA(1, 2, -1) - 3/80 x DATA(-1, 2, -1) + 3/80 x DATA(2, 1, -1) + + - 3/80 x DATA(2, 0, 0) - 3/80 x DATA(2, -1, 0) - 1/80 x DATA(1, 2, 0) + + + 1/80 x DATA(0, 2, 0) + 3/80 x DATA(-1, 2, 0) - 3/80 x DATA(2, 2, 0) + + - 3/80 x DATA(2, -1, 1) + 3/80 x DATA(-1, 2, 1) - 3/80 x DATA(2, 1, 1) + + - 1/80 x DATA(1, 2, 1) + 1/80 x DATA(0, 2, 1) - 3/80 x DATA(-1, -1, 2) + + - 3/80 x DATA(2, 2, 1) + 1/80 x DATA(1, -1, 2) + 3/80 x DATA(2, 0, 2) + + - 1/80 x DATA(0, 0, 2) - 3/80 x DATA(-1, 0, 2) + 1/80 x DATA(1, 1, 2) + + - 1/80 x DATA(1, -1, 0) + 3/80 x DATA(-1, 0, 0) + 3/80 x DATA(-1, 1, 0) + +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=554417308, alloc=4914300, time=61.20 +bytes used=555417472, alloc=4914300, time=61.27 +bytes used=556418900, alloc=4914300, time=61.34 +bytes used=557419052, alloc=4914300, time=61.41 +bytes used=558420004, alloc=4914300, time=61.49 +[COEFF(-1, -1, -1) = - 1/16 z + 1/10 - 3/80 x - 3/80 y, + + COEFF(0, -1, -1) = - 3/80 y + 7/80 - 1/80 x - 1/16 z, + + COEFF(1, -1, -1) = - 3/80 y + 1/80 x - 1/16 z + 3/40, + + COEFF(2, -1, -1) = - 1/16 z - 3/80 y + 1/16 + 3/80 x, + + COEFF(-1, 0, -1) = 7/80 - 1/16 z - 1/80 y - 3/80 x, + + COEFF(0, 0, -1) = - 1/80 y - 1/16 z + 3/40 - 1/80 x, + + COEFF(1, 0, -1) = 1/16 + 1/80 x - 1/80 y - 1/16 z, + + COEFF(2, 0, -1) = - 1/16 z + 3/80 x + 1/20 - 1/80 y, + + COEFF(-1, 1, -1) = 3/40 - 3/80 x + 1/80 y - 1/16 z, + + COEFF(0, 1, -1) = - 1/16 z + 1/16 + 1/80 y - 1/80 x, + + COEFF(1, 1, -1) = 1/80 y - 1/16 z + 1/20 + 1/80 x, + + COEFF(2, 1, -1) = 3/80 + 3/80 x - 1/16 z + 1/80 y, + + COEFF(-1, 2, -1) = - 1/16 z - 3/80 x + 3/80 y + 1/16, + + COEFF(0, 2, -1) = - 1/16 z + 1/20 + 3/80 y - 1/80 x, + + COEFF(1, 2, -1) = 3/80 - 1/16 z + 1/80 x + 3/80 y, + + COEFF(2, 2, -1) = 3/80 x + 3/80 y - 1/16 z + 1/40, + + 13 + COEFF(-1, -1, 0) = - -- + 3/80 x + 3/16 z + 3/80 y, + 80 + + COEFF(0, -1, 0) = - 3/20 + 3/80 y + 1/80 x + 3/16 z, + + 11 + COEFF(1, -1, 0) = - 1/80 x - -- + 3/80 y + 3/16 z, + 80 + + COEFF(2, -1, 0) = 3/16 z - 1/8 + 3/80 y - 3/80 x, + + COEFF(-1, 0, 0) = 3/16 z + 1/80 y + 3/80 x - 3/20, + + 11 + COEFF(0, 0, 0) = 1/80 x + 1/80 y - -- + 3/16 z, + 80 + + COEFF(1, 0, 0) = - 1/80 x - 1/8 + 3/16 z + 1/80 y, + + COEFF(2, 0, 0) = - 3/80 x - 9/80 + 3/16 z + 1/80 y, + + 11 + COEFF(-1, 1, 0) = 3/80 x - 1/80 y - -- + 3/16 z, + 80 + + COEFF(0, 1, 0) = 3/16 z + 1/80 x - 1/8 - 1/80 y, + + COEFF(1, 1, 0) = 3/16 z - 1/80 y - 9/80 - 1/80 x, + + COEFF(2, 1, 0) = - 3/80 x - 1/10 + 3/16 z - 1/80 y, + + COEFF(-1, 2, 0) = 3/16 z + 3/80 x - 3/80 y - 1/8, + + COEFF(0, 2, 0) = 1/80 x + 3/16 z - 3/80 y - 9/80, + + COEFF(1, 2, 0) = - 1/80 x + 3/16 z - 3/80 y - 1/10, + + COEFF(2, 2, 0) = - 3/80 y + 3/16 z - 3/80 x - 7/80, + + COEFF(-1, -1, 1) = - 3/16 z + 3/80 y + 3/80 x + 1/40, + + COEFF(0, -1, 1) = 3/80 + 3/80 y + 1/80 x - 3/16 z, + + COEFF(1, -1, 1) = 1/20 - 3/16 z + 3/80 y - 1/80 x, + + COEFF(2, -1, 1) = - 3/80 x + 1/16 + 3/80 y - 3/16 z, + + COEFF(-1, 0, 1) = 3/80 - 3/16 z + 1/80 y + 3/80 x, + + COEFF(0, 0, 1) = 1/20 + 1/80 y - 3/16 z + 1/80 x, + + COEFF(1, 0, 1) = - 3/16 z + 1/16 - 1/80 x + 1/80 y, + + COEFF(2, 0, 1) = - 3/16 z + 1/80 y + 3/40 - 3/80 x, + + COEFF(-1, 1, 1) = 3/80 x - 3/16 z + 1/20 - 1/80 y, + + COEFF(0, 1, 1) = 1/16 - 3/16 z - 1/80 y + 1/80 x, + + COEFF(1, 1, 1) = - 1/80 x + 3/40 - 1/80 y - 3/16 z, + + COEFF(2, 1, 1) = - 3/80 x - 3/16 z - 1/80 y + 7/80, + + COEFF(-1, 2, 1) = 3/80 x - 3/16 z + 1/16 - 3/80 y, + + COEFF(0, 2, 1) = 1/80 x - 3/80 y - 3/16 z + 3/40, + + COEFF(1, 2, 1) = - 3/80 y + 7/80 - 1/80 x - 3/16 z, + + COEFF(2, 2, 1) = - 3/80 y + 1/10 - 3/80 x - 3/16 z, + + COEFF(-1, -1, 2) = - 3/80 x + 1/16 z + 3/80 - 3/80 y, + + COEFF(0, -1, 2) = 1/16 z + 1/40 - 3/80 y - 1/80 x, + + COEFF(1, -1, 2) = 1/16 z + 1/80 + 1/80 x - 3/80 y, + + COEFF(2, -1, 2) = 3/80 x + 1/16 z - 3/80 y, + + COEFF(-1, 0, 2) = - 3/80 x + 1/40 - 1/80 y + 1/16 z, + + COEFF(0, 0, 2) = 1/16 z - 1/80 y + 1/80 - 1/80 x, + + COEFF(1, 0, 2) = 1/16 z + 1/80 x - 1/80 y, + + COEFF(2, 0, 2) = 1/16 z - 1/80 + 3/80 x - 1/80 y, + + COEFF(-1, 1, 2) = 1/16 z + 1/80 + 1/80 y - 3/80 x, + + COEFF(0, 1, 2) = - 1/80 x + 1/80 y + 1/16 z, + + COEFF(1, 1, 2) = 1/80 y + 1/80 x + 1/16 z - 1/80, + + COEFF(2, 1, 2) = - 1/40 + 3/80 x + 1/80 y + 1/16 z, + + COEFF(-1, 2, 2) = - 3/80 x + 1/16 z + 3/80 y, + + COEFF(0, 2, 2) = 3/80 y - 1/80 + 1/16 z - 1/80 x, + + COEFF(1, 2, 2) = 3/80 y - 1/40 + 1/80 x + 1/16 z, + + COEFF(2, 2, 2) = - 3/80 + 1/16 z + 3/80 y + 3/80 x] + +> print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dzz.compute.c"); +bytes used=559420156, alloc=4914300, time=61.56 +bytes used=560420316, alloc=4914300, time=61.73 +bytes used=561420504, alloc=4914300, time=61.81 +bytes used=562420668, alloc=4914300, time=62.14 +bytes used=563420960, alloc=4914300, time=62.24 +bytes used=564421192, alloc=4914300, time=62.31 +bytes used=565421444, alloc=4914300, time=62.40 +bytes used=566421668, alloc=4914300, time=62.49 +bytes used=567421820, alloc=4914300, time=62.93 +bytes used=568422076, alloc=4914300, time=63.04 +bytes used=569422264, alloc=4914300, time=63.41 +> +################################################################################ +> +# +# 3d, cube, order=4, smoothing=0 (size=5) +# +> +# interpolating polynomial +> interp_3d_cube_order4_smooth0 +> := Lagrange_polynomial_interpolant(fn_3d_order4, coeffs_list_3d_order4, +> coords_list_3d, posn_list_3d_size5); +bytes used=570422516, alloc=4914300, time=63.53 +bytes used=571422828, alloc=4914300, time=63.60 +bytes used=572423056, alloc=4914300, time=63.68 +bytes used=573423260, alloc=4914300, time=63.75 +bytes used=574423572, alloc=4914300, time=63.83 +bytes used=575423796, alloc=4914300, time=63.90 +bytes used=576430880, alloc=4914300, time=63.96 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alloc=4914300, time=72.19 +bytes used=679692320, alloc=4914300, time=72.27 +bytes used=680712772, alloc=4914300, time=72.35 +bytes used=681718144, alloc=4914300, time=72.42 +bytes used=682718340, alloc=4914300, time=72.49 +bytes used=683726596, alloc=4914300, time=72.57 +bytes used=684732808, alloc=4914300, time=72.65 +bytes used=685746688, alloc=4914300, time=72.71 + 292 +interp_3d_cube_order4_smooth0 := ---- DATA(0, -2, 0) - 2/125 DATA(-2, -2, 1) + 6125 + + 173 + - ---- DATA(1, -2, 1) + (1/350 DATA(-2, -2, 1) - 1/700 DATA(1, -2, 1) + 6125 + + - 1/350 DATA(1, -2, 0) - 1/350 DATA(2, 0, -1) + 1/700 DATA(-1, -2, 1) + + + 1/350 DATA(-2, -1, 1) - 1/175 DATA(2, -2, 0) - 1/350 DATA(2, -2, 1) + + + 1/350 DATA(-2, 0, 1) + 1/175 DATA(-2, -1, 0) + 1/350 DATA(1, 0, 2) + + + 1/700 DATA(-1, 0, -1) - 1/350 DATA(2, -1, -1) - 1/350 DATA(1, 0, 0) + + - 1/350 DATA(1, 1, 0) - 1/700 DATA(1, 0, 1) - 1/700 DATA(1, 1, 1) + + - 1/350 DATA(2, 2, -1) - 1/700 DATA(1, 2, -1) - 1/175 DATA(-2, 1, -2) + + + 1/700 DATA(-1, 2, -1) - 1/350 DATA(2, 1, -1) - 1/175 DATA(2, 0, 0) + + + 1/350 DATA(-2, 1, 1) - 1/175 DATA(2, -1, 0) - 1/350 DATA(-1, 1, -2) + + - 1/350 DATA(1, 2, 0) + 1/175 DATA(2, 1, -2) + 1/350 DATA(-1, 2, 0) + + - 1/175 DATA(2, 1, 0) + 1/350 DATA(1, 1, -2) - 1/350 DATA(-1, 2, -2) + + - 1/175 DATA(-2, 2, -2) - 1/175 DATA(2, 2, 0) + 1/350 DATA(-2, 2, 1) + + - 1/350 DATA(2, -1, 1) + 1/175 DATA(2, 0, -2) + 1/175 DATA(-2, 0, 0) + + - 1/350 DATA(2, 0, 1) + 1/350 DATA(1, 2, -2) + 1/700 DATA(-1, -2, -1) + + + 1/700 DATA(-1, 2, 1) + 1/350 DATA(-2, -2, -1) + 1/175 DATA(2, 2, -2) + + - 1/350 DATA(2, 1, 1) - 1/700 DATA(1, 2, 1) - 1/350 DATA(-1, -1, 2) + + - 1/350 DATA(2, 2, 1) + 1/175 DATA(-2, 1, 0) - 1/175 DATA(-2, -2, 2) + + - 1/700 DATA(1, -2, -1) + 1/350 DATA(1, -1, 2) + 1/175 DATA(2, 0, 2) + + - 1/350 DATA(-1, 0, 2) + 1/350 DATA(-2, -1, -1) - 1/350 DATA(2, -2, -1) + + + 1/175 DATA(2, -1, 2) + 1/350 DATA(1, 1, 2) - 1/350 DATA(-1, 1, 2) + + - 1/350 DATA(-1, -2, 2) + 1/350 DATA(1, -2, 2) + 1/350 DATA(-2, 0, -1) + + - 1/350 DATA(-1, 2, 2) + 1/175 DATA(2, 1, 2) + 1/350 DATA(1, 2, 2) + + + 1/350 DATA(-2, 1, -1) - 1/350 DATA(1, -1, 0) + 1/350 DATA(-1, 0, 0) + + + 1/350 DATA(-1, 1, 0) + 1/700 DATA(-1, -1, 1) - 1/700 DATA(1, -1, 1) + + + 1/700 DATA(-1, 0, 1) + 1/700 DATA(-1, 1, 1) - 1/700 DATA(1, 0, -1) + + + 1/700 DATA(-1, 1, -1) - 1/700 DATA(1, 1, -1) + 1/350 DATA(-1, -1, 0) + + + 1/700 DATA(-1, -1, -1) - 1/700 DATA(1, -1, -1) + 1/175 DATA(2, -2, 2) + + + 1/350 DATA(-2, 2, -1) + 1/175 DATA(2, 2, 2) + 1/175 DATA(-2, -2, 0) + + + 1/350 DATA(-1, -2, 0) - 1/175 DATA(-2, -1, 2) + 1/175 DATA(-2, 2, 0) + + - 1/175 DATA(-2, 0, 2) - 1/175 DATA(-2, 1, 2) - 1/175 DATA(-2, -2, -2) + + - 1/175 DATA(-2, 2, 2) + 1/350 DATA(1, -2, -2) - 1/350 DATA(-1, -2, -2) + + - 1/175 DATA(-2, -1, -2) + 1/175 DATA(2, -2, -2) + 1/350 DATA(1, -1, -2) + + - 1/350 DATA(-1, -1, -2) - 1/175 DATA(-2, 0, -2) + 1/175 DATA(2, -1, -2) + + 2 + - 1/350 DATA(-1, 0, -2) + 1/350 DATA(1, 0, -2)) x z + ( + + 1/175 DATA(0, -2, 0) + 1/350 DATA(-2, -2, 1) + 1/350 DATA(1, -2, 1) + + + 1/350 DATA(0, -2, 1) + 1/175 DATA(1, -2, 0) - 1/350 DATA(0, 2, -1) + + + 1/350 DATA(-1, -2, 1) - 1/350 DATA(0, -1, 2) + 1/700 DATA(-2, -1, 1) + + + 1/175 DATA(2, -2, 0) + 1/350 DATA(2, -2, 1) + 1/350 DATA(-2, -1, 0) + + + 1/175 DATA(0, 2, 2) + 1/700 DATA(2, -1, -1) - 1/350 DATA(0, 1, 0) + + - 1/350 DATA(1, 1, 0) - 1/700 DATA(0, 1, 1) - 1/700 DATA(1, 1, 1) + + - 1/350 DATA(2, 2, -1) - 1/350 DATA(1, 2, -1) + 1/350 DATA(-2, 1, -2) + + - 1/350 DATA(-1, 2, -1) - 1/700 DATA(2, 1, -1) + 1/350 DATA(0, 1, -2) + + - 1/700 DATA(-2, 1, 1) + 1/350 DATA(2, -1, 0) + 1/350 DATA(-1, 1, -2) + + - 1/175 DATA(1, 2, 0) + 1/350 DATA(2, 1, -2) - 1/175 DATA(0, 2, 0) + + - 1/175 DATA(-1, 2, 0) - 1/350 DATA(2, 1, 0) + 1/350 DATA(1, 1, -2) + + + 1/175 DATA(-1, 2, -2) + 1/175 DATA(-2, 2, -2) - 1/175 DATA(2, 2, 0) + + + 1/175 DATA(0, 2, -2) - 1/350 DATA(-2, 2, 1) + 1/700 DATA(2, -1, 1) + + + 1/175 DATA(1, 2, -2) + 1/350 DATA(-1, -2, -1) - 1/350 DATA(-1, 2, 1) + + + 1/350 DATA(-2, -2, -1) + 1/175 DATA(2, 2, -2) - 1/700 DATA(2, 1, 1) + + - 1/350 DATA(1, 2, 1) - 1/350 DATA(0, 2, 1) + 1/350 DATA(0, -2, -1) + + - 1/350 DATA(-1, -1, 2) - 1/350 DATA(2, 2, 1) - 1/350 DATA(-2, 1, 0) + + - 1/175 DATA(-2, -2, 2) + 1/350 DATA(1, -2, -1) - 1/350 DATA(1, -1, 2) + + + 1/700 DATA(-2, -1, -1) + 1/350 DATA(2, -2, -1) - 1/350 DATA(2, -1, 2) + + - 1/175 DATA(0, -2, 2) + 1/350 DATA(1, 1, 2) + 1/350 DATA(0, 1, 2) + + + 1/350 DATA(-1, 1, 2) - 1/175 DATA(-1, -2, 2) - 1/175 DATA(1, -2, 2) + + + 1/175 DATA(-1, 2, 2) + 1/350 DATA(2, 1, 2) + 1/175 DATA(1, 2, 2) + + - 1/700 DATA(-2, 1, -1) + 1/350 DATA(0, -1, 0) + 1/350 DATA(1, -1, 0) + + - 1/350 DATA(-1, 1, 0) + 1/700 DATA(-1, -1, 1) + 1/700 DATA(0, -1, 1) + + + 1/700 DATA(1, -1, 1) - 1/700 DATA(-1, 1, 1) - 1/700 DATA(-1, 1, -1) + + - 1/700 DATA(0, 1, -1) - 1/700 DATA(1, 1, -1) + 1/350 DATA(-1, -1, 0) + + + 1/700 DATA(-1, -1, -1) + 1/700 DATA(0, -1, -1) + 1/700 DATA(1, -1, -1) + + - 1/175 DATA(2, -2, 2) - 1/350 DATA(-2, 2, -1) + 1/175 DATA(2, 2, 2) + + + 1/175 DATA(-2, -2, 0) + 1/175 DATA(-1, -2, 0) - 1/350 DATA(-2, -1, 2) + + - 1/175 DATA(-2, 2, 0) + 1/350 DATA(-2, 1, 2) - 1/175 DATA(-2, -2, -2) + + + 1/175 DATA(-2, 2, 2) - 1/175 DATA(1, -2, -2) - 1/175 DATA(0, -2, -2) + + - 1/175 DATA(-1, -2, -2) - 1/350 DATA(-2, -1, -2) - 1/175 DATA(2, -2, -2) + + - 1/350 DATA(1, -1, -2) - 1/350 DATA(0, -1, -2) - 1/350 DATA(-1, -1, -2) + + 2 / 47 + - 1/350 DATA(2, -1, -2)) y z + |- ---- DATA(-2, -2, 1) + \ 5250 + + 167 187 167 + - ---- DATA(1, -2, 1) - ---- DATA(1, -2, 0) + ---- DATA(-1, -2, 1) + 7000 7000 7000 + + 167 17 47 + + ---- DATA(-2, -1, 1) + ---- DATA(2, -2, 0) + ---- DATA(2, -2, 1) + 7000 5250 5250 + + 187 167 289 + + ---- DATA(-2, -1, 0) - ---- DATA(2, -1, -1) + ----- DATA(1, 1, 0) + 7000 7000 10500 + + 137 47 167 + + ---- DATA(1, 1, 1) - ---- DATA(2, 2, -1) + ---- DATA(1, 2, -1) + 5250 5250 7000 + + 107 167 167 + - ---- DATA(-2, 1, -2) - ---- DATA(-1, 2, -1) + ---- DATA(2, 1, -1) + 7000 7000 7000 + + 167 187 229 + - ---- DATA(-2, 1, 1) - ---- DATA(2, -1, 0) - ----- DATA(-1, 1, -2) + 7000 7000 10500 + + 187 107 187 + + ---- DATA(1, 2, 0) + ---- DATA(2, 1, -2) - ---- DATA(-1, 2, 0) + 7000 7000 7000 + + 187 229 107 + + ---- DATA(2, 1, 0) + ----- DATA(1, 1, -2) - ---- DATA(-1, 2, -2) + 7000 10500 7000 + + 137 17 47 + + ---- DATA(-2, 2, -2) - ---- DATA(2, 2, 0) + ---- DATA(-2, 2, 1) + 5250 5250 5250 + + 167 107 167 + - ---- DATA(2, -1, 1) + ---- DATA(1, 2, -2) + ---- DATA(-1, -2, -1) + 7000 7000 7000 + + 167 47 137 + - ---- DATA(-1, 2, 1) - ---- DATA(-2, -2, -1) - ---- DATA(2, 2, -2) + 7000 5250 5250 + + 167 167 229 + + ---- DATA(2, 1, 1) + ---- DATA(1, 2, 1) + ----- DATA(-1, -1, 2) + 7000 7000 10500 + + 47 187 137 + - ---- DATA(2, 2, 1) - ---- DATA(-2, 1, 0) - ---- DATA(-2, -2, 2) + 5250 7000 5250 + + 167 229 167 + - ---- DATA(1, -2, -1) - ----- DATA(1, -1, 2) + ---- DATA(-2, -1, -1) + 7000 10500 7000 + + 47 107 229 + + ---- DATA(2, -2, -1) - ---- DATA(2, -1, 2) + ----- DATA(1, 1, 2) + 5250 7000 10500 + + 229 107 107 + - ----- DATA(-1, 1, 2) + ---- DATA(-1, -2, 2) - ---- DATA(1, -2, 2) + 10500 7000 7000 + + 107 107 107 + - ---- DATA(-1, 2, 2) + ---- DATA(2, 1, 2) + ---- DATA(1, 2, 2) + 7000 7000 7000 + + 167 289 289 + - ---- DATA(-2, 1, -1) - ----- DATA(1, -1, 0) - ----- DATA(-1, 1, 0) + 7000 10500 10500 + + 137 137 137 + + ---- DATA(-1, -1, 1) - ---- DATA(1, -1, 1) - ---- DATA(-1, 1, 1) + 5250 5250 5250 + + 137 137 289 + - ---- DATA(-1, 1, -1) + ---- DATA(1, 1, -1) + ----- DATA(-1, -1, 0) + 5250 5250 10500 + + 137 137 137 + + ---- DATA(-1, -1, -1) - ---- DATA(1, -1, -1) + ---- DATA(2, -2, 2) + 5250 5250 5250 + + 47 137 17 + + ---- DATA(-2, 2, -1) - ---- DATA(2, 2, 2) - ---- DATA(-2, -2, 0) + 5250 5250 5250 + + 187 107 17 + + ---- DATA(-1, -2, 0) + ---- DATA(-2, -1, 2) + ---- DATA(-2, 2, 0) + 7000 7000 5250 + + 107 137 137 + - ---- DATA(-2, 1, 2) - ---- DATA(-2, -2, -2) + ---- DATA(-2, 2, 2) + 7000 5250 5250 + + 107 107 107 + - ---- DATA(1, -2, -2) + ---- DATA(-1, -2, -2) + ---- DATA(-2, -1, -2) + 7000 7000 7000 + + 137 229 229 + + ---- DATA(2, -2, -2) - ----- DATA(1, -1, -2) + ----- DATA(-1, -1, -2) + 5250 10500 10500 + + 107 \ / 107 + - ---- DATA(2, -1, -2)| x y + |- ---- DATA(-2, -2, 1) + 7000 / \ 7000 + + 167 187 187 + - ---- DATA(1, -2, 1) - ---- DATA(0, -2, 1) - ---- DATA(0, 2, -1) + 7000 7000 7000 + + 167 187 229 + - ---- DATA(-1, -2, 1) - ---- DATA(0, -1, 2) - ----- DATA(-2, -1, 1) + 7000 7000 10500 + + 107 17 229 + - ---- DATA(2, -2, 1) - ---- DATA(0, 2, 2) + ----- DATA(2, -1, -1) + 7000 5250 10500 + + 289 137 107 + + ----- DATA(0, 1, 1) + ---- DATA(1, 1, 1) - ---- DATA(2, 2, -1) + 10500 5250 7000 + + 167 107 167 + - ---- DATA(1, 2, -1) - ---- DATA(-2, 1, -2) - ---- DATA(-1, 2, -1) + 7000 7000 7000 + + 229 187 229 + - ----- DATA(2, 1, -1) - ---- DATA(0, 1, -2) + ----- DATA(-2, 1, 1) + 10500 7000 10500 + + 167 107 167 + - ---- DATA(-1, 1, -2) - ---- DATA(2, 1, -2) - ---- DATA(1, 1, -2) + 7000 7000 7000 + + 47 137 17 + + ---- DATA(-1, 2, -2) + ---- DATA(-2, 2, -2) + ---- DATA(0, 2, -2) + 5250 5250 5250 + + 107 229 47 + + ---- DATA(-2, 2, 1) - ----- DATA(2, -1, 1) + ---- DATA(1, 2, -2) + 7000 10500 5250 + + 167 167 107 + + ---- DATA(-1, -2, -1) + ---- DATA(-1, 2, 1) + ---- DATA(-2, -2, -1) + 7000 7000 7000 + + 137 229 167 + + ---- DATA(2, 2, -2) + ----- DATA(2, 1, 1) + ---- DATA(1, 2, 1) + 5250 10500 7000 + + 187 187 167 + + ---- DATA(0, 2, 1) + ---- DATA(0, -2, -1) - ---- DATA(-1, -1, 2) + 7000 7000 7000 + + 107 137 167 + + ---- DATA(2, 2, 1) + ---- DATA(-2, -2, 2) + ---- DATA(1, -2, -1) + 7000 5250 7000 + + 167 229 107 + - ---- DATA(1, -1, 2) + ----- DATA(-2, -1, -1) + ---- DATA(2, -2, -1) + 7000 10500 7000 + + 107 17 167 + - ---- DATA(2, -1, 2) + ---- DATA(0, -2, 2) + ---- DATA(1, 1, 2) + 7000 5250 7000 + + 187 167 47 + + ---- DATA(0, 1, 2) + ---- DATA(-1, 1, 2) + ---- DATA(-1, -2, 2) + 7000 7000 5250 + + 47 47 107 + + ---- DATA(1, -2, 2) - ---- DATA(-1, 2, 2) + ---- DATA(2, 1, 2) + 5250 5250 7000 + + 47 229 137 + - ---- DATA(1, 2, 2) - ----- DATA(-2, 1, -1) - ---- DATA(-1, -1, 1) + 5250 10500 5250 + + 289 137 137 + - ----- DATA(0, -1, 1) - ---- DATA(1, -1, 1) + ---- DATA(-1, 1, 1) + 10500 5250 5250 + + 137 289 137 + - ---- DATA(-1, 1, -1) - ----- DATA(0, 1, -1) - ---- DATA(1, 1, -1) + 5250 10500 5250 + + 137 289 137 + + ---- DATA(-1, -1, -1) + ----- DATA(0, -1, -1) + ---- DATA(1, -1, -1) + 5250 10500 5250 + + 137 107 137 + + ---- DATA(2, -2, 2) - ---- DATA(-2, 2, -1) - ---- DATA(2, 2, 2) + 5250 7000 5250 + + 107 107 137 + - ---- DATA(-2, -1, 2) + ---- DATA(-2, 1, 2) - ---- DATA(-2, -2, -2) + 7000 7000 5250 + + 137 47 17 + - ---- DATA(-2, 2, 2) - ---- DATA(1, -2, -2) - ---- DATA(0, -2, -2) + 5250 5250 5250 + + 47 107 137 + - ---- DATA(-1, -2, -2) + ---- DATA(-2, -1, -2) - ---- DATA(2, -2, -2) + 5250 7000 5250 + + 167 187 167 + + ---- DATA(1, -1, -2) + ---- DATA(0, -1, -2) + ---- DATA(-1, -1, -2) + 7000 7000 7000 + + 107 \ / 107 + + ---- DATA(2, -1, -2)| y z + |- ---- DATA(-2, -2, 1) + 7000 / \ 7000 + + 229 187 229 + + ----- DATA(1, -2, 1) - ---- DATA(2, 0, -1) - ----- DATA(-1, -2, 1) + 10500 7000 10500 + + 167 107 187 + - ---- DATA(-2, -1, 1) + ---- DATA(2, -2, 1) - ---- DATA(-2, 0, 1) + 7000 7000 7000 + + 187 289 167 + + ---- DATA(1, 0, 2) + ----- DATA(-1, 0, -1) - ---- DATA(2, -1, -1) + 7000 10500 7000 + + 289 137 107 + + ----- DATA(1, 0, 1) + ---- DATA(1, 1, 1) - ---- DATA(2, 2, -1) + 10500 5250 7000 + + 229 47 229 + - ----- DATA(1, 2, -1) - ---- DATA(-2, 1, -2) + ----- DATA(-1, 2, -1) + 10500 5250 10500 + + 167 167 167 + - ---- DATA(2, 1, -1) - ---- DATA(-2, 1, 1) + ---- DATA(-1, 1, -2) + 7000 7000 7000 + + 47 167 107 + + ---- DATA(2, 1, -2) - ---- DATA(1, 1, -2) + ---- DATA(-1, 2, -2) + 5250 7000 7000 + + 137 107 167 + - ---- DATA(-2, 2, -2) - ---- DATA(-2, 2, 1) + ---- DATA(2, -1, 1) + 5250 7000 7000 + + 17 187 107 + + ---- DATA(2, 0, -2) + ---- DATA(2, 0, 1) - ---- DATA(1, 2, -2) + 5250 7000 7000 + + 229 229 107 + + ----- DATA(-1, -2, -1) - ----- DATA(-1, 2, 1) + ---- DATA(-2, -2, -1) + 10500 10500 7000 + + 137 167 229 + + ---- DATA(2, 2, -2) + ---- DATA(2, 1, 1) + ----- DATA(1, 2, 1) + 5250 7000 10500 + + 167 107 137 + - ---- DATA(-1, -1, 2) + ---- DATA(2, 2, 1) + ---- DATA(-2, -2, 2) + 7000 7000 5250 + + 229 167 17 + - ----- DATA(1, -2, -1) + ---- DATA(1, -1, 2) - ---- DATA(2, 0, 2) + 10500 7000 5250 + + 187 167 107 + - ---- DATA(-1, 0, 2) + ---- DATA(-2, -1, -1) - ---- DATA(2, -2, -1) + 7000 7000 7000 + + 47 167 167 + - ---- DATA(2, -1, 2) + ---- DATA(1, 1, 2) - ---- DATA(-1, 1, 2) + 5250 7000 7000 + + 107 107 187 + - ---- DATA(-1, -2, 2) + ---- DATA(1, -2, 2) + ---- DATA(-2, 0, -1) + 7000 7000 7000 + + 107 47 107 + - ---- DATA(-1, 2, 2) - ---- DATA(2, 1, 2) + ---- DATA(1, 2, 2) + 7000 5250 7000 + + 167 137 137 + + ---- DATA(-2, 1, -1) - ---- DATA(-1, -1, 1) + ---- DATA(1, -1, 1) + 7000 5250 5250 + + 289 137 289 + - ----- DATA(-1, 0, 1) - ---- DATA(-1, 1, 1) - ----- DATA(1, 0, -1) + 10500 5250 10500 + + 137 137 137 + + ---- DATA(-1, 1, -1) - ---- DATA(1, 1, -1) + ---- DATA(-1, -1, -1) + 5250 5250 5250 + + 137 137 107 + - ---- DATA(1, -1, -1) - ---- DATA(2, -2, 2) + ---- DATA(-2, 2, -1) + 5250 5250 7000 + + 137 47 17 + - ---- DATA(2, 2, 2) + ---- DATA(-2, -1, 2) + ---- DATA(-2, 0, 2) + 5250 5250 5250 + + 47 137 137 + + ---- DATA(-2, 1, 2) - ---- DATA(-2, -2, -2) + ---- DATA(-2, 2, 2) + 5250 5250 5250 + + 107 107 47 + - ---- DATA(1, -2, -2) + ---- DATA(-1, -2, -2) - ---- DATA(-2, -1, -2) + 7000 7000 5250 + + 137 167 167 + + ---- DATA(2, -2, -2) - ---- DATA(1, -1, -2) + ---- DATA(-1, -1, -2) + 5250 7000 7000 + + 17 47 187 + - ---- DATA(-2, 0, -2) + ---- DATA(2, -1, -2) + ---- DATA(-1, 0, -2) + 5250 5250 7000 + + 187 \ + - ---- DATA(1, 0, -2)| x z + (- 1/175 DATA(-2, -2, 1) + 7000 / + + + 1/350 DATA(1, -2, 1) + 1/350 DATA(1, -2, 0) - 1/175 DATA(2, 0, -1) + + - 1/350 DATA(-1, -2, 1) + 1/350 DATA(-2, -1, 1) + 1/175 DATA(2, -2, 0) + + + 1/175 DATA(2, -2, 1) + 1/175 DATA(-2, 0, 1) + 1/350 DATA(-2, -1, 0) + + - 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DATA(-1, -1, 1) + 1/700 DATA(0, -1, 1) + 1/1400 DATA(1, -1, 1) + + - 1/1400 DATA(-1, 1, 1) + 1/1400 DATA(-1, 1, -1) + 1/700 DATA(0, 1, -1) + + + 1/1400 DATA(1, 1, -1) - 1/1400 DATA(-1, -1, -1) - 1/700 DATA(0, -1, -1) + + - 1/1400 DATA(1, -1, -1) - 1/175 DATA(2, -2, 2) - 1/350 DATA(-2, 2, -1) + + + 1/175 DATA(2, 2, 2) - 1/350 DATA(-2, -1, 2) + 1/350 DATA(-2, 1, 2) + + + 1/175 DATA(-2, -2, -2) + 1/175 DATA(-2, 2, 2) - 1/350 DATA(1, -2, -2) + + - 1/175 DATA(0, -2, -2) - 1/350 DATA(-1, -2, -2) + 1/350 DATA(-2, -1, -2) + + + 1/175 DATA(2, -2, -2) - 1/700 DATA(1, -1, -2) - 1/350 DATA(0, -1, -2) + + 2 + - 1/700 DATA(-1, -1, -2) + 1/350 DATA(2, -1, -2)) x y z + + 292 47 47 + + ---- DATA(0, 2, 0) + ---- DATA(-1, 2, 0) + ---- DATA(2, 1, 0) + 6125 6125 6125 + + 173 202 + - ---- DATA(1, 1, -2) - 2/125 DATA(-1, 2, -2) + ---- DATA(-2, 2, -2) + 6125 6125 + + 47 47 + + ---- DATA(2, 2, 0) + ---- DATA(0, 2, -2) - 2/125 DATA(-2, 2, 1) + 6125 6125 + + 173 47 292 + - ---- DATA(2, -1, 1) + ---- DATA(2, 0, -2) + ---- DATA(-2, 0, 0) + 6125 6125 6125 + + 47 173 + + ---- DATA(2, 0, 1) - 2/125 DATA(1, 2, -2) - ---- DATA(-1, -2, -1) + 6125 6125 + + 173 202 + - ---- DATA(-1, 2, 1) - 2/125 DATA(-2, -2, -1) + ---- DATA(2, 2, -2) + 6125 6125 + + 173 173 47 + - ---- DATA(2, 1, 1) - ---- DATA(1, 2, 1) + ---- DATA(0, 2, 1) + 6125 6125 6125 + + 47 173 + + ---- DATA(0, -2, -1) - ---- DATA(-1, -1, 2) - 2/125 DATA(2, 2, 1) + 6125 6125 + + 47 202 173 + + ---- DATA(-2, 1, 0) + ---- DATA(-2, -2, 2) - ---- DATA(1, -2, -1) + 6125 6125 6125 + + 173 47 292 + - ---- DATA(1, -1, 2) + ---- DATA(2, 0, 2) + ---- DATA(0, 0, 2) + 6125 6125 6125 + + 47 173 + + ---- DATA(-1, 0, 2) - ---- DATA(-2, -1, -1) - 2/125 DATA(2, -2, -1) + 6125 6125 + + 47 173 + - 2/125 DATA(2, -1, 2) + ---- DATA(0, -2, 2) - ---- DATA(1, 1, 2) + 6125 6125 + + 47 173 + + ---- DATA(0, 1, 2) - ---- DATA(-1, 1, 2) - 2/125 DATA(-1, -2, 2) + 6125 6125 + + 47 + - 2/125 DATA(1, -2, 2) + ---- DATA(-2, 0, -1) - 2/125 DATA(-1, 2, 2) + 6125 + + 173 + - 2/125 DATA(2, 1, 2) - 2/125 DATA(1, 2, 2) - ---- DATA(-2, 1, -1) + 6125 + + 592 272 592 + + ---- DATA(0, -1, 0) + ---- DATA(1, -1, 0) + ---- DATA(-1, 0, 0) + 6125 6125 6125 + + 272 23 272 + + ---- DATA(-1, 1, 0) - ---- DATA(-1, -1, 1) + ---- DATA(0, -1, 1) + 6125 6125 6125 + + 23 272 23 + - ---- DATA(1, -1, 1) + ---- DATA(-1, 0, 1) - ---- DATA(-1, 1, 1) + 6125 6125 6125 + + 592 272 23 + + ---- DATA(0, 0, -1) + ---- DATA(1, 0, -1) - ---- DATA(-1, 1, -1) + 6125 6125 6125 + + 272 23 272 + + ---- DATA(0, 1, -1) - ---- DATA(1, 1, -1) + ---- DATA(-1, -1, 0) + 6125 6125 6125 + + 23 272 23 + - ---- DATA(-1, -1, -1) + ---- DATA(0, -1, -1) - ---- DATA(1, -1, -1) + 6125 6125 6125 + + 202 202 / + + ---- DATA(2, -2, 2) - 2/125 DATA(-2, 2, -1) + ---- DATA(2, 2, 2) + | + 6125 6125 \ + + 128 211 + - 1/20 DATA(0, -2, 0) + ---- DATA(-2, -2, 1) + ---- DATA(1, -2, 1) + 3675 7350 + + + 2/75 DATA(0, -2, 1) - 9/196 DATA(1, -2, 0) + 2/75 DATA(0, 2, -1) + + 211 311 + + 2/75 DATA(2, 0, -1) + ---- DATA(-1, -2, 1) + ----- DATA(0, -1, 2) + 7350 29400 + + 211 33 128 + + ---- DATA(-2, -1, 1) - --- DATA(2, -2, 0) + ---- DATA(2, -2, 1) + 7350 980 3675 + + + 2/75 DATA(-2, 0, 1) - 9/196 DATA(-2, -1, 0) - 1/600 DATA(0, 2, 2) + + 311 151 211 + + ----- DATA(1, 0, 2) + ---- DATA(-1, 0, -1) + ---- DATA(2, -1, -1) + 29400 7350 7350 + + 13 61 61 + - --- DATA(0, 0, 0) - --- DATA(1, 0, 0) - --- DATA(0, 1, 0) + 196 980 980 + + 57 68 151 + - --- DATA(1, 1, 0) + ---- DATA(0, 0, 1) + ---- DATA(1, 0, 1) + 980 3675 7350 + + 151 83 128 + + ---- DATA(0, 1, 1) + ---- DATA(1, 1, 1) + ---- DATA(2, 2, -1) + 7350 3675 3675 + + 211 169 211 + + ---- DATA(1, 2, -1) - ----- DATA(-2, 1, -2) + ---- DATA(-1, 2, -1) + 7350 29400 7350 + + 211 311 + + ---- DATA(2, 1, -1) - 1/20 DATA(2, 0, 0) + ----- DATA(0, 1, -2) + 7350 29400 + + 211 191 + + ---- DATA(-2, 1, 1) - 9/196 DATA(2, -1, 0) + ----- DATA(-1, 1, -2) + 7350 29400 + + 169 + - 9/196 DATA(1, 2, 0) - ----- DATA(2, 1, -2) - 1/20 DATA(0, 2, 0) + 29400 + + 191 + - 9/196 DATA(-1, 2, 0) - 9/196 DATA(2, 1, 0) + ----- DATA(1, 1, -2) + 29400 + + 169 529 33 + - ----- DATA(-1, 2, -2) - ----- DATA(-2, 2, -2) - --- DATA(2, 2, 0) + 29400 29400 980 + + 128 211 + - 1/600 DATA(0, 2, -2) + ---- DATA(-2, 2, 1) + ---- DATA(2, -1, 1) + 3675 7350 + + - 1/600 DATA(2, 0, -2) - 1/20 DATA(-2, 0, 0) + 2/75 DATA(2, 0, 1) + + 169 211 211 + - ----- DATA(1, 2, -2) + ---- DATA(-1, -2, -1) + ---- DATA(-1, 2, 1) + 29400 7350 7350 + + 128 529 211 + + ---- DATA(-2, -2, -1) - ----- DATA(2, 2, -2) + ---- DATA(2, 1, 1) + 3675 29400 7350 + + 211 + + ---- DATA(1, 2, 1) + 2/75 DATA(0, 2, 1) + 2/75 DATA(0, -2, -1) + 7350 + + 191 128 + + ----- DATA(-1, -1, 2) + ---- DATA(2, 2, 1) - 9/196 DATA(-2, 1, 0) + 29400 3675 + + 529 211 191 + - ----- DATA(-2, -2, 2) + ---- DATA(1, -2, -1) + ----- DATA(1, -1, 2) + 29400 7350 29400 + + 431 311 + - 1/600 DATA(2, 0, 2) + ----- DATA(0, 0, 2) + ----- DATA(-1, 0, 2) + 29400 29400 + + 211 128 169 + + ---- DATA(-2, -1, -1) + ---- DATA(2, -2, -1) - ----- DATA(2, -1, 2) + 7350 3675 29400 + + 191 311 + - 1/600 DATA(0, -2, 2) + ----- DATA(1, 1, 2) + ----- DATA(0, 1, 2) + 29400 29400 + + 191 169 169 + + ----- DATA(-1, 1, 2) - ----- DATA(-1, -2, 2) - ----- DATA(1, -2, 2) + 29400 29400 29400 + + 169 169 + + 2/75 DATA(-2, 0, -1) - ----- DATA(-1, 2, 2) - ----- DATA(2, 1, 2) + 29400 29400 + + 169 211 61 + - ----- DATA(1, 2, 2) + ---- DATA(-2, 1, -1) - --- DATA(0, -1, 0) + 29400 7350 980 + + 57 61 57 + - --- DATA(1, -1, 0) - --- DATA(-1, 0, 0) - --- DATA(-1, 1, 0) + 980 980 980 + + 83 151 83 + + ---- DATA(-1, -1, 1) + ---- DATA(0, -1, 1) + ---- DATA(1, -1, 1) + 3675 7350 3675 + + 151 83 68 + + ---- DATA(-1, 0, 1) + ---- DATA(-1, 1, 1) + ---- DATA(0, 0, -1) + 7350 3675 3675 + + 151 83 151 + + ---- DATA(1, 0, -1) + ---- DATA(-1, 1, -1) + ---- DATA(0, 1, -1) + 7350 3675 7350 + + 83 57 83 + + ---- DATA(1, 1, -1) - --- DATA(-1, -1, 0) + ---- DATA(-1, -1, -1) + 3675 980 3675 + + 151 83 529 + + ---- DATA(0, -1, -1) + ---- DATA(1, -1, -1) - ----- DATA(2, -2, 2) + 7350 3675 29400 + + 128 529 33 + + ---- DATA(-2, 2, -1) - ----- DATA(2, 2, 2) - --- DATA(-2, -2, 0) + 3675 29400 980 + + 169 33 + - 9/196 DATA(-1, -2, 0) - ----- DATA(-2, -1, 2) - --- DATA(-2, 2, 0) + 29400 980 + + 169 529 + - 1/600 DATA(-2, 0, 2) - ----- DATA(-2, 1, 2) - ----- DATA(-2, -2, -2) + 29400 29400 + + 529 169 + - ----- DATA(-2, 2, 2) - ----- DATA(1, -2, -2) - 1/600 DATA(0, -2, -2) + 29400 29400 + + 169 169 529 + - ----- DATA(-1, -2, -2) - ----- DATA(-2, -1, -2) - ----- DATA(2, -2, -2) + 29400 29400 29400 + + 191 311 191 + + ----- DATA(1, -1, -2) + ----- DATA(0, -1, -2) + ----- DATA(-1, -1, -2) + 29400 29400 29400 + + 169 431 + - 1/600 DATA(-2, 0, -2) - ----- DATA(2, -1, -2) + ----- DATA(0, 0, -2) + 29400 29400 + + 311 311 \ 2 + + ----- DATA(-1, 0, -2) + ----- DATA(1, 0, -2)| z + ( + 29400 29400 / + + - 1/300 DATA(0, -2, 0) - 1/300 DATA(-2, -2, 1) - 1/300 DATA(1, -2, 1) + + - 1/300 DATA(0, -2, 1) - 1/300 DATA(1, -2, 0) + 1/300 DATA(0, 2, -1) + + - 1/300 DATA(-1, -2, 1) + 1/150 DATA(0, -1, 2) + 1/150 DATA(-2, -1, 1) + + - 1/300 DATA(2, -2, 0) - 1/300 DATA(2, -2, 1) + 1/150 DATA(-2, -1, 0) + + + 1/300 DATA(0, 2, 2) + 1/150 DATA(2, -1, -1) - 1/150 DATA(0, 1, 0) + + - 1/150 DATA(1, 1, 0) - 1/150 DATA(0, 1, 1) - 1/150 DATA(1, 1, 1) + + + 1/300 DATA(2, 2, -1) + 1/300 DATA(1, 2, -1) - 1/150 DATA(-2, 1, -2) + + + 1/300 DATA(-1, 2, -1) - 1/150 DATA(2, 1, -1) - 1/150 DATA(0, 1, -2) + + - 1/150 DATA(-2, 1, 1) + 1/150 DATA(2, -1, 0) - 1/150 DATA(-1, 1, -2) + + + 1/300 DATA(1, 2, 0) - 1/150 DATA(2, 1, -2) + 1/300 DATA(0, 2, 0) + + + 1/300 DATA(-1, 2, 0) - 1/150 DATA(2, 1, 0) - 1/150 DATA(1, 1, -2) + + + 1/300 DATA(-1, 2, -2) + 1/300 DATA(-2, 2, -2) + 1/300 DATA(2, 2, 0) + + + 1/300 DATA(0, 2, -2) + 1/300 DATA(-2, 2, 1) + 1/150 DATA(2, -1, 1) + + + 1/300 DATA(1, 2, -2) - 1/300 DATA(-1, -2, -1) + 1/300 DATA(-1, 2, 1) + + - 1/300 DATA(-2, -2, -1) + 1/300 DATA(2, 2, -2) - 1/150 DATA(2, 1, 1) + + + 1/300 DATA(1, 2, 1) + 1/300 DATA(0, 2, 1) - 1/300 DATA(0, -2, -1) + + + 1/150 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1) + + - 1/150 DATA(1, -1, 1) + 1/150 DATA(-1, 0, 1) + 1/150 DATA(-1, 1, 1) + + - 1/150 DATA(1, 0, -1) + 1/150 DATA(-1, 1, -1) - 1/150 DATA(1, 1, -1) + + + 1/150 DATA(-1, -1, 0) + 1/150 DATA(-1, -1, -1) - 1/150 DATA(1, -1, -1) + + + 1/300 DATA(2, -2, 2) - 1/300 DATA(-2, 2, -1) + 1/300 DATA(2, 2, 2) + + - 1/300 DATA(-2, -2, 0) + 1/150 DATA(-1, -2, 0) - 1/300 DATA(-2, -1, 2) + + - 1/300 DATA(-2, 2, 0) - 1/300 DATA(-2, 0, 2) - 1/300 DATA(-2, 1, 2) + + - 1/300 DATA(-2, -2, -2) - 1/300 DATA(-2, 2, 2) - 1/150 DATA(1, -2, -2) + + + 1/150 DATA(-1, -2, -2) - 1/300 DATA(-2, -1, -2) + 1/300 DATA(2, -2, -2) + + - 1/150 DATA(1, -1, -2) + 1/150 DATA(-1, -1, -2) - 1/300 DATA(-2, 0, -2) + + 3 + + 1/300 DATA(2, -1, -2) + 1/150 DATA(-1, 0, -2) - 1/150 DATA(1, 0, -2)) x + + + (- 1/150 DATA(-2, -2, 1) - 1/150 DATA(1, -2, 1) - 1/150 DATA(0, -2, 1) + + + 1/150 DATA(0, 2, -1) + 1/150 DATA(2, 0, -1) - 1/150 DATA(-1, -2, 1) + + + 1/300 DATA(0, -1, 2) - 1/150 DATA(-2, -1, 1) - 1/150 DATA(2, -2, 1) + + - 1/150 DATA(-2, 0, 1) + 1/300 DATA(0, 2, 2) + 1/300 DATA(1, 0, 2) + + + 1/150 DATA(-1, 0, -1) + 1/150 DATA(2, -1, -1) - 1/150 DATA(0, 0, 1) + + - 1/150 DATA(1, 0, 1) - 1/150 DATA(0, 1, 1) - 1/150 DATA(1, 1, 1) + + + 1/150 DATA(2, 2, -1) + 1/150 DATA(1, 2, -1) - 1/300 DATA(-2, 1, -2) + + + 1/150 DATA(-1, 2, -1) + 1/150 DATA(2, 1, -1) - 1/300 DATA(0, 1, -2) + + - 1/150 DATA(-2, 1, 1) - 1/300 DATA(-1, 1, -2) - 1/300 DATA(2, 1, -2) + + - 1/300 DATA(1, 1, -2) - 1/300 DATA(-1, 2, -2) - 1/300 DATA(-2, 2, -2) + + - 1/300 DATA(0, 2, -2) - 1/150 DATA(-2, 2, 1) - 1/150 DATA(2, -1, 1) + + - 1/300 DATA(2, 0, -2) - 1/150 DATA(2, 0, 1) - 1/300 DATA(1, 2, -2) + + + 1/150 DATA(-1, -2, -1) - 1/150 DATA(-1, 2, 1) + 1/150 DATA(-2, -2, -1) + + - 1/300 DATA(2, 2, -2) - 1/150 DATA(2, 1, 1) - 1/150 DATA(1, 2, 1) + + - 1/150 DATA(0, 2, 1) + 1/150 DATA(0, -2, -1) + 1/300 DATA(-1, -1, 2) + + - 1/150 DATA(2, 2, 1) + 1/300 DATA(-2, -2, 2) + 1/150 DATA(1, -2, -1) + + + 1/300 DATA(1, -1, 2) + 1/300 DATA(2, 0, 2) + 1/300 DATA(0, 0, 2) + + + 1/300 DATA(-1, 0, 2) + 1/150 DATA(-2, -1, -1) + 1/150 DATA(2, -2, -1) + + + 1/300 DATA(2, -1, 2) + 1/300 DATA(0, -2, 2) + 1/300 DATA(1, 1, 2) + + + 1/300 DATA(0, 1, 2) + 1/300 DATA(-1, 1, 2) + 1/300 DATA(-1, -2, 2) + + + 1/300 DATA(1, -2, 2) + 1/150 DATA(-2, 0, -1) + 1/300 DATA(-1, 2, 2) + + + 1/300 DATA(2, 1, 2) + 1/300 DATA(1, 2, 2) + 1/150 DATA(-2, 1, -1) + + - 1/150 DATA(-1, -1, 1) - 1/150 DATA(0, -1, 1) - 1/150 DATA(1, -1, 1) + + - 1/150 DATA(-1, 0, 1) - 1/150 DATA(-1, 1, 1) + 1/150 DATA(0, 0, -1) + + + 1/150 DATA(1, 0, -1) + 1/150 DATA(-1, 1, -1) + 1/150 DATA(0, 1, -1) + + + 1/150 DATA(1, 1, -1) + 1/150 DATA(-1, -1, -1) + 1/150 DATA(0, -1, -1) + + + 1/150 DATA(1, -1, -1) + 1/300 DATA(2, -2, 2) + 1/150 DATA(-2, 2, -1) + + + 1/300 DATA(2, 2, 2) + 1/300 DATA(-2, -1, 2) + 1/300 DATA(-2, 0, 2) + + + 1/300 DATA(-2, 1, 2) - 1/300 DATA(-2, -2, -2) + 1/300 DATA(-2, 2, 2) + + - 1/300 DATA(1, -2, -2) - 1/300 DATA(0, -2, -2) - 1/300 DATA(-1, -2, -2) + + - 1/300 DATA(-2, -1, -2) - 1/300 DATA(2, -2, -2) - 1/300 DATA(1, -1, -2) + + - 1/300 DATA(0, -1, -2) - 1/300 DATA(-1, -1, -2) - 1/300 DATA(-2, 0, -2) + + - 1/300 DATA(2, -1, -2) - 1/300 DATA(0, 0, -2) - 1/300 DATA(-1, 0, -2) + + 3 / 41 19 + - 1/300 DATA(1, 0, -2)) z + |- ---- DATA(0, -2, 0) + ---- DATA(-2, -2, 1) + \ 2100 2100 + + 17 29 29 + - ---- DATA(1, -2, 1) - ---- DATA(0, -2, 1) - ---- DATA(1, -2, 0) + 2100 2100 2100 + + 29 17 + + ---- DATA(0, 2, -1) - ---- DATA(-1, -2, 1) - 2/75 DATA(0, -1, 2) + 2100 2100 + + 19 + - 1/42 DATA(-2, -1, 1) + 1/300 DATA(2, -2, 0) + ---- DATA(2, -2, 1) + 2100 + + - 2/75 DATA(-2, -1, 0) - 1/300 DATA(0, 2, 2) - 1/42 DATA(2, -1, -1) + + 37 37 + + 4/105 DATA(0, 1, 0) + ---- DATA(1, 1, 0) + ---- DATA(0, 1, 1) + 1050 1050 + + 17 19 17 + + --- DATA(1, 1, 1) - ---- DATA(2, 2, -1) + ---- DATA(1, 2, -1) + 525 2100 2100 + + 17 + + 8/525 DATA(-2, 1, -2) + ---- DATA(-1, 2, -1) + 1/42 DATA(2, 1, -1) + 2100 + + + 2/75 DATA(0, 1, -2) + 1/42 DATA(-2, 1, 1) - 2/75 DATA(2, -1, 0) + + 29 + + 1/42 DATA(-1, 1, -2) + ---- DATA(1, 2, 0) + 8/525 DATA(2, 1, -2) + 2100 + + 41 29 + + ---- DATA(0, 2, 0) + ---- DATA(-1, 2, 0) + 2/75 DATA(2, 1, 0) + 2100 2100 + + 19 11 + + 1/42 DATA(1, 1, -2) - ---- DATA(-1, 2, -2) - --- DATA(-2, 2, -2) + 2100 420 + + 19 + - 1/300 DATA(2, 2, 0) - 1/300 DATA(0, 2, -2) - ---- DATA(-2, 2, 1) + 2100 + + 19 17 + - 1/42 DATA(2, -1, 1) - ---- DATA(1, 2, -2) - ---- DATA(-1, -2, -1) + 2100 2100 + + 17 19 11 + + ---- DATA(-1, 2, 1) + ---- DATA(-2, -2, -1) - --- DATA(2, 2, -2) + 2100 2100 420 + + 17 29 + + 1/42 DATA(2, 1, 1) + ---- DATA(1, 2, 1) + ---- DATA(0, 2, 1) + 2100 2100 + + 29 19 + - ---- DATA(0, -2, -1) - 1/42 DATA(-1, -1, 2) - ---- DATA(2, 2, 1) + 2100 2100 + + 11 17 + + 2/75 DATA(-2, 1, 0) + --- DATA(-2, -2, 2) - ---- DATA(1, -2, -1) + 420 2100 + + 19 + - 1/42 DATA(1, -1, 2) - 1/42 DATA(-2, -1, -1) + ---- DATA(2, -2, -1) + 2100 + + - 8/525 DATA(2, -1, 2) + 1/300 DATA(0, -2, 2) + 1/42 DATA(1, 1, 2) + + 19 + + 2/75 DATA(0, 1, 2) + 1/42 DATA(-1, 1, 2) + ---- DATA(-1, -2, 2) + 2100 + + 19 19 + + ---- DATA(1, -2, 2) - ---- DATA(-1, 2, 2) + 8/525 DATA(2, 1, 2) + 2100 2100 + + 19 + - ---- DATA(1, 2, 2) + 1/42 DATA(-2, 1, -1) - 4/105 DATA(0, -1, 0) + 2100 + + 37 37 17 + - ---- DATA(1, -1, 0) + ---- DATA(-1, 1, 0) - --- DATA(-1, -1, 1) + 1050 1050 525 + + 37 17 17 + - ---- DATA(0, -1, 1) - --- DATA(1, -1, 1) + --- DATA(-1, 1, 1) + 1050 525 525 + + 17 37 17 + + --- DATA(-1, 1, -1) + ---- DATA(0, 1, -1) + --- DATA(1, 1, -1) + 525 1050 525 + + 37 17 37 + - ---- DATA(-1, -1, 0) - --- DATA(-1, -1, -1) - ---- DATA(0, -1, -1) + 1050 525 1050 + + 17 11 19 + - --- DATA(1, -1, -1) + --- DATA(2, -2, 2) - ---- DATA(-2, 2, -1) + 525 420 2100 + + 11 29 + - --- DATA(2, 2, 2) + 1/300 DATA(-2, -2, 0) - ---- DATA(-1, -2, 0) + 420 2100 + + - 8/525 DATA(-2, -1, 2) - 1/300 DATA(-2, 2, 0) + 8/525 DATA(-2, 1, 2) + + 11 11 19 + + --- DATA(-2, -2, -2) - --- DATA(-2, 2, 2) + ---- DATA(1, -2, -2) + 420 420 2100 + + 19 + + 1/300 DATA(0, -2, -2) + ---- DATA(-1, -2, -2) - 8/525 DATA(-2, -1, -2) + 2100 + + 11 + + --- DATA(2, -2, -2) - 1/42 DATA(1, -1, -2) - 2/75 DATA(0, -1, -2) + 420 + + \ / 19 + - 1/42 DATA(-1, -1, -2) - 8/525 DATA(2, -1, -2)| y + |---- DATA(-2, -2, 1) + / \2100 + + 29 + + 1/42 DATA(1, -2, 1) + 2/75 DATA(1, -2, 0) + ---- DATA(2, 0, -1) + 2100 + + 17 + - 1/42 DATA(-1, -2, 1) - ---- DATA(-2, -1, 1) - 1/300 DATA(2, -2, 0) + 2100 + + 19 29 29 + - ---- DATA(2, -2, 1) - ---- DATA(-2, 0, 1) - ---- DATA(-2, -1, 0) + 2100 2100 2100 + + 37 17 + + 2/75 DATA(1, 0, 2) - ---- DATA(-1, 0, -1) + ---- DATA(2, -1, -1) + 1050 2100 + + 37 37 + + 4/105 DATA(1, 0, 0) + ---- DATA(1, 1, 0) + ---- DATA(1, 0, 1) + 1050 1050 + + 17 19 + + --- DATA(1, 1, 1) - ---- DATA(2, 2, -1) + 1/42 DATA(1, 2, -1) + 525 2100 + + 19 17 + + ---- DATA(-2, 1, -2) - 1/42 DATA(-1, 2, -1) + ---- DATA(2, 1, -1) + 2100 2100 + + 41 17 29 + + ---- DATA(2, 0, 0) - ---- DATA(-2, 1, 1) + ---- DATA(2, -1, 0) + 2100 2100 2100 + + 19 + - 1/42 DATA(-1, 1, -2) + 2/75 DATA(1, 2, 0) - ---- DATA(2, 1, -2) + 2100 + + 29 + - 2/75 DATA(-1, 2, 0) + ---- DATA(2, 1, 0) + 1/42 DATA(1, 1, -2) + 2100 + + 11 + - 8/525 DATA(-1, 2, -2) + --- DATA(-2, 2, -2) - 1/300 DATA(2, 2, 0) + 420 + + 19 17 + + ---- DATA(-2, 2, 1) + ---- DATA(2, -1, 1) - 1/300 DATA(2, 0, -2) + 2100 2100 + + 41 29 + - ---- DATA(-2, 0, 0) + ---- DATA(2, 0, 1) + 8/525 DATA(1, 2, -2) + 2100 2100 + + 19 + - 1/42 DATA(-1, -2, -1) - 1/42 DATA(-1, 2, 1) + ---- DATA(-2, -2, -1) + 2100 + + 11 17 + - --- DATA(2, 2, -2) + ---- DATA(2, 1, 1) + 1/42 DATA(1, 2, 1) + 420 2100 + + 19 29 + - 1/42 DATA(-1, -1, 2) - ---- DATA(2, 2, 1) - ---- DATA(-2, 1, 0) + 2100 2100 + + 11 + + --- DATA(-2, -2, 2) + 1/42 DATA(1, -2, -1) + 1/42 DATA(1, -1, 2) + 420 + + 17 + - 1/300 DATA(2, 0, 2) - 2/75 DATA(-1, 0, 2) - ---- DATA(-2, -1, -1) + 2100 + + 19 19 + - ---- DATA(2, -2, -1) - ---- DATA(2, -1, 2) + 1/42 DATA(1, 1, 2) + 2100 2100 + + - 1/42 DATA(-1, 1, 2) - 8/525 DATA(-1, -2, 2) + 8/525 DATA(1, -2, 2) + + 29 19 + - ---- DATA(-2, 0, -1) - 8/525 DATA(-1, 2, 2) - ---- DATA(2, 1, 2) + 2100 2100 + + 17 37 + + 8/525 DATA(1, 2, 2) - ---- DATA(-2, 1, -1) + ---- DATA(1, -1, 0) + 2100 1050 + + 37 17 + - 4/105 DATA(-1, 0, 0) - ---- DATA(-1, 1, 0) - --- DATA(-1, -1, 1) + 1050 525 + + 17 37 17 + + --- DATA(1, -1, 1) - ---- DATA(-1, 0, 1) - --- DATA(-1, 1, 1) + 525 1050 525 + + 37 17 17 + + ---- DATA(1, 0, -1) - --- DATA(-1, 1, -1) + --- DATA(1, 1, -1) + 1050 525 525 + + 37 17 17 + - ---- DATA(-1, -1, 0) - --- DATA(-1, -1, -1) + --- DATA(1, -1, -1) + 1050 525 525 + + 11 19 11 + - --- DATA(2, -2, 2) + ---- DATA(-2, 2, -1) - --- DATA(2, 2, 2) + 420 2100 420 + + 19 + + 1/300 DATA(-2, -2, 0) - 2/75 DATA(-1, -2, 0) + ---- DATA(-2, -1, 2) + 2100 + + 19 + + 1/300 DATA(-2, 2, 0) + 1/300 DATA(-2, 0, 2) + ---- DATA(-2, 1, 2) + 2100 + + 11 11 + + --- DATA(-2, -2, -2) + --- DATA(-2, 2, 2) + 8/525 DATA(1, -2, -2) + 420 420 + + 19 11 + - 8/525 DATA(-1, -2, -2) + ---- DATA(-2, -1, -2) - --- DATA(2, -2, -2) + 2100 420 + + + 1/42 DATA(1, -1, -2) - 1/42 DATA(-1, -1, -2) + 1/300 DATA(-2, 0, -2) + + 19 \ / + - ---- DATA(2, -1, -2) - 2/75 DATA(-1, 0, -2) + 2/75 DATA(1, 0, -2)| x + | + 2100 / \ + + 8/525 DATA(-2, -2, 1) + 1/42 DATA(1, -2, 1) + 2/75 DATA(0, -2, 1) + + - 2/75 DATA(0, 2, -1) - 2/75 DATA(2, 0, -1) + 1/42 DATA(-1, -2, 1) + + 29 + + ---- DATA(0, -1, 2) + 1/42 DATA(-2, -1, 1) + 8/525 DATA(2, -2, 1) + 2100 + + 29 + + 2/75 DATA(-2, 0, 1) - 1/300 DATA(0, 2, 2) + ---- DATA(1, 0, 2) + 2100 + + 37 + - ---- DATA(-1, 0, -1) - 1/42 DATA(2, -1, -1) + 4/105 DATA(0, 0, 1) + 1050 + + 37 37 17 + + ---- DATA(1, 0, 1) + ---- DATA(0, 1, 1) + --- DATA(1, 1, 1) + 1050 1050 525 + + 19 + - 8/525 DATA(2, 2, -1) - 1/42 DATA(1, 2, -1) + ---- DATA(-2, 1, -2) + 2100 + + 29 + - 1/42 DATA(-1, 2, -1) - 1/42 DATA(2, 1, -1) - ---- DATA(0, 1, -2) + 2100 + + 17 19 + + 1/42 DATA(-2, 1, 1) - ---- DATA(-1, 1, -2) + ---- DATA(2, 1, -2) + 2100 2100 + + 17 19 11 + - ---- DATA(1, 1, -2) + ---- DATA(-1, 2, -2) + --- DATA(-2, 2, -2) + 2100 2100 420 + + + 1/300 DATA(0, 2, -2) + 8/525 DATA(-2, 2, 1) + 1/42 DATA(2, -1, 1) + + 19 + + 1/300 DATA(2, 0, -2) + 2/75 DATA(2, 0, 1) + ---- DATA(1, 2, -2) + 2100 + + - 1/42 DATA(-1, -2, -1) + 1/42 DATA(-1, 2, 1) - 8/525 DATA(-2, -2, -1) + + 11 + + --- DATA(2, 2, -2) + 1/42 DATA(2, 1, 1) + 1/42 DATA(1, 2, 1) + 420 + + 17 + + 2/75 DATA(0, 2, 1) - 2/75 DATA(0, -2, -1) + ---- DATA(-1, -1, 2) + 2100 + + 11 + + 8/525 DATA(2, 2, 1) - --- DATA(-2, -2, 2) - 1/42 DATA(1, -2, -1) + 420 + + 17 41 + + ---- DATA(1, -1, 2) - 1/300 DATA(2, 0, 2) + ---- DATA(0, 0, 2) + 2100 2100 + + 29 + + ---- DATA(-1, 0, 2) - 1/42 DATA(-2, -1, -1) - 8/525 DATA(2, -2, -1) + 2100 + + 19 17 + - ---- DATA(2, -1, 2) - 1/300 DATA(0, -2, 2) + ---- DATA(1, 1, 2) + 2100 2100 + + 29 17 19 + + ---- DATA(0, 1, 2) + ---- DATA(-1, 1, 2) - ---- DATA(-1, -2, 2) + 2100 2100 2100 + + 19 19 + - ---- DATA(1, -2, 2) - 2/75 DATA(-2, 0, -1) - ---- DATA(-1, 2, 2) + 2100 2100 + + 19 19 + - ---- DATA(2, 1, 2) - ---- DATA(1, 2, 2) - 1/42 DATA(-2, 1, -1) + 2100 2100 + + 17 37 17 + + --- DATA(-1, -1, 1) + ---- DATA(0, -1, 1) + --- DATA(1, -1, 1) + 525 1050 525 + + 37 17 + + ---- DATA(-1, 0, 1) + --- DATA(-1, 1, 1) - 4/105 DATA(0, 0, -1) + 1050 525 + + 37 17 37 + - ---- DATA(1, 0, -1) - --- DATA(-1, 1, -1) - ---- DATA(0, 1, -1) + 1050 525 1050 + + 17 17 37 + - --- DATA(1, 1, -1) - --- DATA(-1, -1, -1) - ---- DATA(0, -1, -1) + 525 525 1050 + + 17 11 + - --- DATA(1, -1, -1) - --- DATA(2, -2, 2) - 8/525 DATA(-2, 2, -1) + 525 420 + + 11 19 + - --- DATA(2, 2, 2) - ---- DATA(-2, -1, 2) - 1/300 DATA(-2, 0, 2) + 420 2100 + + 19 11 11 + - ---- DATA(-2, 1, 2) + --- DATA(-2, -2, -2) - --- DATA(-2, 2, 2) + 2100 420 420 + + 19 19 + + ---- DATA(1, -2, -2) + 1/300 DATA(0, -2, -2) + ---- DATA(-1, -2, -2) + 2100 2100 + + 19 11 17 + + ---- DATA(-2, -1, -2) + --- DATA(2, -2, -2) - ---- DATA(1, -1, -2) + 2100 420 2100 + + 29 17 + - ---- DATA(0, -1, -2) - ---- DATA(-1, -1, -2) + 1/300 DATA(-2, 0, -2) + 2100 2100 + + 19 41 29 + + ---- DATA(2, -1, -2) - ---- DATA(0, 0, -2) - ---- DATA(-1, 0, -2) + 2100 2100 2100 + + 29 \ 47 47 / + - ---- DATA(1, 0, -2)| z + ---- DATA(-2, -2, 0) + ---- DATA(-1, -2, 0) + | + 2100 / 6125 6125 \ + + 431 169 191 + ----- DATA(0, -2, 0) - ----- DATA(-2, -2, 1) + ----- DATA(1, -2, 1) + 29400 29400 29400 + + 311 311 311 + + ----- DATA(0, -2, 1) + ----- DATA(1, -2, 0) + ----- DATA(0, 2, -1) + 29400 29400 29400 + + 191 + - 9/196 DATA(2, 0, -1) + ----- DATA(-1, -2, 1) + 2/75 DATA(0, -1, 2) + 29400 + + 211 169 + + ---- DATA(-2, -1, 1) - 1/600 DATA(2, -2, 0) - ----- DATA(2, -2, 1) + 7350 29400 + + - 9/196 DATA(-2, 0, 1) + 2/75 DATA(-2, -1, 0) - 1/600 DATA(0, 2, 2) + + 57 211 + - 9/196 DATA(1, 0, 2) - --- DATA(-1, 0, -1) + ---- DATA(2, -1, -1) + 980 7350 + + 13 61 68 + - --- DATA(0, 0, 0) - --- DATA(1, 0, 0) + ---- DATA(0, 1, 0) + 196 980 3675 + + 151 61 57 + + ---- DATA(1, 1, 0) - --- DATA(0, 0, 1) - --- DATA(1, 0, 1) + 7350 980 980 + + 151 83 169 + + ---- DATA(0, 1, 1) + ---- DATA(1, 1, 1) - ----- DATA(2, 2, -1) + 7350 3675 29400 + + 191 128 191 + + ----- DATA(1, 2, -1) + ---- DATA(-2, 1, -2) + ----- DATA(-1, 2, -1) + 29400 3675 29400 + + 211 + + ---- DATA(2, 1, -1) - 1/20 DATA(2, 0, 0) + 2/75 DATA(0, 1, -2) + 7350 + + 211 211 + + ---- DATA(-2, 1, 1) + 2/75 DATA(2, -1, 0) + ---- DATA(-1, 1, -2) + 7350 7350 + + 311 128 431 + + ----- DATA(1, 2, 0) + ---- DATA(2, 1, -2) + ----- DATA(0, 2, 0) + 29400 3675 29400 + + 311 211 + + ----- DATA(-1, 2, 0) + 2/75 DATA(2, 1, 0) + ---- DATA(1, 1, -2) + 29400 7350 + + 169 529 + - ----- DATA(-1, 2, -2) - ----- DATA(-2, 2, -2) - 1/600 DATA(2, 2, 0) + 29400 29400 + + 169 211 + - 1/600 DATA(0, 2, -2) - ----- DATA(-2, 2, 1) + ---- DATA(2, -1, 1) + 29400 7350 + + 33 + - --- DATA(2, 0, -2) - 1/20 DATA(-2, 0, 0) - 9/196 DATA(2, 0, 1) + 980 + + 169 191 191 + - ----- DATA(1, 2, -2) + ----- DATA(-1, -2, -1) + ----- DATA(-1, 2, 1) + 29400 29400 29400 + + 169 529 211 + - ----- DATA(-2, -2, -1) - ----- DATA(2, 2, -2) + ---- DATA(2, 1, 1) + 29400 29400 7350 + + 191 311 311 + + ----- DATA(1, 2, 1) + ----- DATA(0, 2, 1) + ----- DATA(0, -2, -1) + 29400 29400 29400 + + 211 169 + + ---- DATA(-1, -1, 2) - ----- DATA(2, 2, 1) + 2/75 DATA(-2, 1, 0) + 7350 29400 + + 529 191 211 + - ----- DATA(-2, -2, 2) + ----- DATA(1, -2, -1) + ---- DATA(1, -1, 2) + 29400 29400 7350 + + 33 + - --- DATA(2, 0, 2) - 1/20 DATA(0, 0, 2) - 9/196 DATA(-1, 0, 2) + 980 + + 211 169 128 + + ---- DATA(-2, -1, -1) - ----- DATA(2, -2, -1) + ---- DATA(2, -1, 2) + 7350 29400 3675 + + 211 + - 1/600 DATA(0, -2, 2) + ---- DATA(1, 1, 2) + 2/75 DATA(0, 1, 2) + 7350 + + 211 169 169 + + ---- DATA(-1, 1, 2) - ----- DATA(-1, -2, 2) - ----- DATA(1, -2, 2) + 7350 29400 29400 + + 169 128 + - 9/196 DATA(-2, 0, -1) - ----- DATA(-1, 2, 2) + ---- DATA(2, 1, 2) + 29400 3675 + + 169 211 68 + - ----- DATA(1, 2, 2) + ---- DATA(-2, 1, -1) + ---- DATA(0, -1, 0) + 29400 7350 3675 + + 151 61 151 + + ---- DATA(1, -1, 0) - --- DATA(-1, 0, 0) + ---- DATA(-1, 1, 0) + 7350 980 7350 + + 83 151 83 + + ---- DATA(-1, -1, 1) + ---- DATA(0, -1, 1) + ---- DATA(1, -1, 1) + 3675 7350 3675 + + 57 83 61 + - --- DATA(-1, 0, 1) + ---- DATA(-1, 1, 1) - --- DATA(0, 0, -1) + 980 3675 980 + + 57 83 151 + - --- DATA(1, 0, -1) + ---- DATA(-1, 1, -1) + ---- DATA(0, 1, -1) + 980 3675 7350 + + 83 151 83 + + ---- DATA(1, 1, -1) + ---- DATA(-1, -1, 0) + ---- DATA(-1, -1, -1) + 3675 7350 3675 + + 151 83 529 + + ---- DATA(0, -1, -1) + ---- DATA(1, -1, -1) - ----- DATA(2, -2, 2) + 7350 3675 29400 + + 169 529 + - ----- DATA(-2, 2, -1) - ----- DATA(2, 2, 2) - 1/600 DATA(-2, -2, 0) + 29400 29400 + + 311 128 + + ----- DATA(-1, -2, 0) + ---- DATA(-2, -1, 2) - 1/600 DATA(-2, 2, 0) + 29400 3675 + + 33 128 529 + - --- DATA(-2, 0, 2) + ---- DATA(-2, 1, 2) - ----- DATA(-2, -2, -2) + 980 3675 29400 + + 529 169 + - ----- DATA(-2, 2, 2) - ----- DATA(1, -2, -2) - 1/600 DATA(0, -2, -2) + 29400 29400 + + 169 128 529 + - ----- DATA(-1, -2, -2) + ---- DATA(-2, -1, -2) - ----- DATA(2, -2, -2) + 29400 3675 29400 + + 211 211 + + ---- DATA(1, -1, -2) + 2/75 DATA(0, -1, -2) + ---- DATA(-1, -1, -2) + 7350 7350 + + 33 128 + - --- DATA(-2, 0, -2) + ---- DATA(2, -1, -2) - 1/20 DATA(0, 0, -2) + 980 3675 + + \ 2 / + - 9/196 DATA(-1, 0, -2) - 9/196 DATA(1, 0, -2)| y + | + / \ + + 169 211 + - 1/20 DATA(0, -2, 0) - ----- DATA(-2, -2, 1) + ---- DATA(1, -2, 1) + 29400 7350 + + - 9/196 DATA(0, -2, 1) + 2/75 DATA(1, -2, 0) - 9/196 DATA(0, 2, -1) + + 311 211 + + ----- DATA(2, 0, -1) + ---- DATA(-1, -2, 1) - 9/196 DATA(0, -1, 2) + 29400 7350 + + 191 169 + + ----- DATA(-2, -1, 1) - 1/600 DATA(2, -2, 0) - ----- DATA(2, -2, 1) + 29400 29400 + + 311 311 33 + + ----- DATA(-2, 0, 1) + ----- DATA(-2, -1, 0) - --- DATA(0, 2, 2) + 29400 29400 980 + + 151 191 + + 2/75 DATA(1, 0, 2) + ---- DATA(-1, 0, -1) + ----- DATA(2, -1, -1) + 7350 29400 + + 13 68 61 + - --- DATA(0, 0, 0) + ---- DATA(1, 0, 0) - --- DATA(0, 1, 0) + 196 3675 980 + + 151 61 151 + + ---- DATA(1, 1, 0) - --- DATA(0, 0, 1) + ---- DATA(1, 0, 1) + 7350 980 7350 + + 57 83 169 + - --- DATA(0, 1, 1) + ---- DATA(1, 1, 1) - ----- DATA(2, 2, -1) + 980 3675 29400 + + 211 169 211 + + ---- DATA(1, 2, -1) - ----- DATA(-2, 1, -2) + ---- DATA(-1, 2, -1) + 7350 29400 7350 + + 191 431 + + ----- DATA(2, 1, -1) + ----- DATA(2, 0, 0) - 9/196 DATA(0, 1, -2) + 29400 29400 + + 191 311 211 + + ----- DATA(-2, 1, 1) + ----- DATA(2, -1, 0) + ---- DATA(-1, 1, -2) + 29400 29400 7350 + + 169 + + 2/75 DATA(1, 2, 0) - ----- DATA(2, 1, -2) - 1/20 DATA(0, 2, 0) + 29400 + + 311 211 + + 2/75 DATA(-1, 2, 0) + ----- DATA(2, 1, 0) + ---- DATA(1, 1, -2) + 29400 7350 + + 128 529 + + ---- DATA(-1, 2, -2) - ----- DATA(-2, 2, -2) - 1/600 DATA(2, 2, 0) + 3675 29400 + + 33 169 191 + - --- DATA(0, 2, -2) - ----- DATA(-2, 2, 1) + ----- DATA(2, -1, 1) + 980 29400 29400 + + 431 311 + - 1/600 DATA(2, 0, -2) + ----- DATA(-2, 0, 0) + ----- DATA(2, 0, 1) + 29400 29400 + + 128 211 211 + + ---- DATA(1, 2, -2) + ---- DATA(-1, -2, -1) + ---- DATA(-1, 2, 1) + 3675 7350 7350 + + 169 529 191 + - ----- DATA(-2, -2, -1) - ----- DATA(2, 2, -2) + ----- DATA(2, 1, 1) + 29400 29400 29400 + + 211 + + ---- DATA(1, 2, 1) - 9/196 DATA(0, 2, 1) - 9/196 DATA(0, -2, -1) + 7350 + + 211 169 311 + + ---- DATA(-1, -1, 2) - ----- DATA(2, 2, 1) + ----- DATA(-2, 1, 0) + 7350 29400 29400 + + 529 211 211 + - ----- DATA(-2, -2, 2) + ---- DATA(1, -2, -1) + ---- DATA(1, -1, 2) + 29400 7350 7350 + + - 1/600 DATA(2, 0, 2) - 1/20 DATA(0, 0, 2) + 2/75 DATA(-1, 0, 2) + + 191 169 169 + + ----- DATA(-2, -1, -1) - ----- DATA(2, -2, -1) - ----- DATA(2, -1, 2) + 29400 29400 29400 + + 33 211 + - --- DATA(0, -2, 2) + ---- DATA(1, 1, 2) - 9/196 DATA(0, 1, 2) + 980 7350 + + 211 128 128 + + ---- DATA(-1, 1, 2) + ---- DATA(-1, -2, 2) + ---- DATA(1, -2, 2) + 7350 3675 3675 + + 311 128 169 + + ----- DATA(-2, 0, -1) + ---- DATA(-1, 2, 2) - ----- DATA(2, 1, 2) + 29400 3675 29400 + + 128 191 61 + + ---- DATA(1, 2, 2) + ----- DATA(-2, 1, -1) - --- DATA(0, -1, 0) + 3675 29400 980 + + 151 68 151 + + ---- DATA(1, -1, 0) + ---- DATA(-1, 0, 0) + ---- DATA(-1, 1, 0) 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+ 1/600 DATA(2, 2, 2) + 1/100 DATA(-2, -2, 0) + 1/100 DATA(-1, -2, 0) + + + 1/600 DATA(-2, -1, 2) + 1/100 DATA(-2, 2, 0) + 1/600 DATA(-2, 0, 2) + + + 1/600 DATA(-2, 1, 2) + 1/600 DATA(-2, -2, -2) + 1/600 DATA(-2, 2, 2) + + + 1/600 DATA(1, -2, -2) + 1/600 DATA(0, -2, -2) + 1/600 DATA(-1, -2, -2) + + + 1/600 DATA(-2, -1, -2) + 1/600 DATA(2, -2, -2) + 1/600 DATA(1, -1, -2) + + + 1/600 DATA(0, -1, -2) + 1/600 DATA(-1, -1, -2) + 1/600 DATA(-2, 0, -2) + + + 1/600 DATA(2, -1, -2) + 1/600 DATA(0, 0, -2) + 1/600 DATA(-1, 0, -2) + + 4 47 + + 1/600 DATA(1, 0, -2)) z + ---- DATA(-2, 0, 2) - 2/125 DATA(-2, 1, 2) + 6125 + + 202 202 + + ---- DATA(-2, -2, -2) + ---- DATA(-2, 2, 2) - 2/125 DATA(1, -2, -2) + 6125 6125 + + 47 + + ---- DATA(0, -2, -2) - 2/125 DATA(-1, -2, -2) - 2/125 DATA(-2, -1, -2) + 6125 + + 202 173 47 + + ---- DATA(2, -2, -2) - ---- DATA(1, -1, -2) + ---- DATA(0, -1, -2) + 6125 6125 6125 + + 173 47 + - ---- DATA(-1, -1, -2) + ---- DATA(-2, 0, -2) - 2/125 DATA(2, -1, -2) + 6125 6125 + + 292 47 47 + + ---- DATA(0, 0, -2) + ---- DATA(-1, 0, -2) + ---- DATA(1, 0, -2) + 6125 6125 6125 + +> +# I +> coeffs_as_lc_of_data(%, posn_list_3d_size5); +bytes used=687026944, alloc=4914300, time=72.81 +bytes used=688127996, alloc=4914300, time=72.89 +bytes used=689366004, alloc=4914300, time=72.98 +bytes used=690441992, alloc=4914300, time=73.07 +bytes used=691442108, alloc=4914300, time=73.14 +bytes used=692490184, alloc=4914300, time=73.23 +bytes used=693490784, alloc=4914300, time=73.30 +bytes used=694657684, alloc=4914300, time=73.39 +bytes used=695658072, alloc=4914300, time=73.47 +bytes used=696729448, alloc=4914300, time=73.55 +bytes used=697835692, alloc=4914300, time=73.64 +bytes used=698835916, alloc=4914300, time=73.72 +bytes used=699868248, alloc=4914300, time=73.81 +bytes used=700868664, alloc=4914300, time=73.89 +bytes used=701909416, alloc=4914300, time=73.99 +bytes used=702909664, alloc=4914300, time=74.07 +bytes used=704041280, alloc=4914300, time=74.16 +bytes used=705096376, alloc=4914300, time=74.25 +bytes used=706284924, alloc=4914300, time=74.36 +bytes used=707285200, alloc=4914300, time=74.46 +bytes used=708324552, alloc=4914300, time=74.54 +bytes used=709427568, alloc=4914300, time=74.63 +bytes used=710504540, alloc=4914300, time=74.73 +bytes used=711504764, alloc=4914300, time=74.82 +bytes used=712505148, alloc=4914300, time=74.91 +bytes used=713524780, alloc=4914300, time=75.01 +bytes used=714525144, alloc=4914300, time=75.10 +bytes used=715525408, alloc=4914300, time=75.19 +bytes used=716525684, alloc=4914300, time=75.29 +bytes used=717526484, alloc=4914300, time=75.39 +bytes used=718599428, alloc=5045348, time=75.49 +bytes used=719687520, alloc=5504016, time=75.59 +bytes used=720817456, alloc=5569540, time=75.70 +bytes used=721888788, alloc=5635064, time=75.80 +bytes used=722914376, alloc=5700588, time=75.90 +bytes used=723914500, alloc=5766112, time=76.00 +bytes used=724914640, alloc=5831636, time=76.10 +bytes used=726025800, 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time=77.73 +bytes used=747409656, alloc=7076592, time=77.79 + 2 2 2 2 +[COEFF(-2, -2, -2) = 1/175 x y z + 1/175 x y z - 1/175 x y + 1/175 x y z + + 2 11 137 137 2 + - 1/175 x y - 1/125 x y z + --- x - ---- x y - ---- y z - 1/175 y z + 420 5250 5250 + + 2 11 11 3 3 3 + - 1/175 x z + --- y + --- z + 1/300 x y + 1/300 y z + 1/300 x z + 420 420 + + 3 137 2 2 2 2 3 + + 1/300 x z - ---- x z + 1/245 y z + 1/245 x z + 1/300 y z + 5250 + + 2 202 2 3 2 2 529 2 + - 1/175 y z + ---- - 1/175 x z + 1/300 x y + 1/245 x y - ----- y + 6125 29400 + + 529 2 529 2 3 3 3 4 + - ----- x - ----- z - 1/300 x - 1/300 y - 1/300 z + 1/600 z + 29400 29400 + + 4 4 2 2 + + 1/600 x + 1/600 y , COEFF(-1, -2, -2) = 1/350 x y z + 1/350 x y z + + 2 2 2 + + 1/350 x y - 1/350 x y z - 1/350 x y - 1/250 x y z - 8/525 x + + 107 47 2 2 19 19 + + ---- x y - ---- y z - 1/175 y z - 1/350 x z + ---- y + ---- z + 7000 5250 2100 2100 + + 3 3 3 3 107 + - 1/150 x y + 1/300 y z + 1/600 x z - 1/150 x z + ---- x z + 7000 + + 2 2 2 2 3 2 2 + + 1/245 y z - 1/490 x z + 1/300 y z - 1/175 y z + 1/350 x z + + 3 2 2 169 2 128 2 169 2 3 + + 1/600 x y - 1/490 x y - ----- y + ---- x - ----- z + 1/150 x + 29400 3675 29400 + + 3 3 4 4 4 + - 1/300 y - 1/300 z - 2/125 + 1/600 z - 1/150 x + 1/600 y , + + 17 3 2 4 33 2 + COEFF(0, -2, -2) = - ---- y z + 1/300 y z - 1/600 z + 1/100 x - --- x + 5250 980 + + 2 2 2 2 2 2 2 + + 1/245 y z - 1/175 x y z + 1/175 x y - 1/175 y z - 1/245 x z + + 2 2 2 2 2 4 + + 1/175 x z + 1/300 y - 1/245 x y - 1/175 y z - 1/600 y + 1/600 z + + 3 3 4 47 3 + + 1/300 z - 1/300 y - 1/300 z + 1/600 y + ---- + 1/300 y z , + 6125 + + 2 2 2 + COEFF(1, -2, -2) = - 1/350 x y z - 1/350 x y z + 1/350 x y + + 2 2 107 47 + - 1/350 x y z + 1/350 x y + 1/250 x y z + 8/525 x - ---- x y - ---- y z + 7000 5250 + + 2 2 19 19 3 3 + - 1/175 y z + 1/350 x z + ---- y + ---- z + 1/150 x y + 1/300 y z + 2100 2100 + + 3 3 107 2 2 2 2 + - 1/600 x z + 1/150 x z - ---- x z + 1/245 y z - 1/490 x z + 7000 + + 3 2 2 3 2 2 + + 1/300 y z - 1/175 y z + 1/350 x z - 1/600 x y - 1/490 x y + + 169 2 128 2 169 2 3 3 3 + - ----- y + ---- x - ----- z - 1/150 x - 1/300 y - 1/300 z - 2/125 + 29400 3675 29400 + + 4 4 4 2 + + 1/600 z - 1/150 x + 1/600 y , COEFF(2, -2, -2) = - 1/175 x y z + + 2 2 2 2 + - 1/175 x y z - 1/175 x y + 1/175 x y z + 1/175 x y + 1/125 x y z + + 11 137 137 2 2 11 11 + - --- x + ---- x y - ---- y z - 1/175 y z + 1/175 x z + --- y + --- z + 420 5250 5250 420 420 + + 3 3 3 3 137 + - 1/300 x y + 1/300 y z - 1/300 x z - 1/300 x z + ---- x z + 5250 + + 2 2 2 2 3 2 202 2 + + 1/245 y z + 1/245 x z + 1/300 y z - 1/175 y z + ---- - 1/175 x z + 6125 + + 3 2 2 529 2 529 2 529 2 3 + - 1/300 x y + 1/245 x y - ----- y - ----- x - ----- z + 1/300 x + 29400 29400 29400 + + 3 3 4 4 4 + - 1/300 y - 1/300 z + 1/600 z + 1/600 x + 1/600 y , COEFF(-2, -1, -2) + + 2 2 2 2 2 + = 1/350 x y z - 1/350 x y z - 1/350 x y + 1/350 x y z + 1/350 x y + + 19 107 107 2 2 + - 1/250 x y z + ---- x + ---- x y + ---- y z - 1/350 y z - 1/175 x z + 2100 7000 7000 + + 19 3 3 3 3 + - 8/525 y + ---- z + 1/600 x y - 1/150 y z + 1/300 x z + 1/300 x z + 2100 + + 47 2 2 2 2 3 2 + - ---- x z - 1/490 y z + 1/245 x z + 1/600 y z + 1/350 y z + 5250 + + 2 3 2 2 128 2 169 2 169 2 + - 1/175 x z - 1/150 x y - 1/490 x y + ---- y - ----- x - ----- z + 3675 29400 29400 + + 3 3 3 4 4 4 + - 1/300 x + 1/150 y - 1/300 z - 2/125 + 1/600 z + 1/600 x - 1/150 y , + + 2 2 2 2 + COEFF(-1, -1, -2) = 1/700 x y z - 1/700 x y z + 1/700 x y - 1/700 x y z + + 2 229 167 2 + + 1/700 x y - 1/500 x y z - 1/42 x + ----- x y + ---- y z - 1/350 y z + 10500 7000 + + 2 17 3 3 3 + - 1/350 x z - 1/42 y - ---- z - 1/300 x y - 1/150 y z + 1/600 x z + 2100 + + 3 167 2 2 2 2 3 173 + - 1/150 x z + ---- x z - 1/490 y z - 1/490 x z + 1/600 y z - ---- + 7000 6125 + + 2 2 3 2 2 211 2 211 2 + + 1/350 y z + 1/350 x z - 1/300 x y + 1/980 x y + ---- y + ---- x + 7350 7350 + + 191 2 3 3 3 4 4 + + ----- z + 1/150 x + 1/150 y - 1/300 z + 1/600 z - 1/150 x + 29400 + + 4 47 2 2 311 2 + - 1/150 y , COEFF(0, -1, -2) = ---- - 2/75 y - 1/245 x z + ----- z + 6125 29400 + + 4 29 2 3 2 2 2 + + 1/100 x - ---- z + 1/350 x y - 1/150 y z + 1/490 x y + 1/350 y z + 2100 + + 4 2 187 2 2 3 + + 1/600 z + 2/75 y + ---- y z - 9/196 x - 1/350 y z + 1/600 y z + 7000 + + 3 2 4 2 2 2 3 + + 1/150 y + 1/175 x z - 1/150 y - 1/490 y z - 1/350 x y z - 1/300 z + + 2 2 2 + , COEFF(1, -1, -2) = - 1/700 x y z + 1/700 x y z + 1/700 x y + + 2 2 229 167 + - 1/700 x y z - 1/700 x y + 1/500 x y z + 1/42 x - ----- x y + ---- y z + 10500 7000 + + 2 2 17 3 3 + - 1/350 y z + 1/350 x z - 1/42 y - ---- z + 1/300 x y - 1/150 y z + 2100 + + 3 3 167 2 2 2 2 + - 1/600 x z + 1/150 x z - ---- x z - 1/490 y z - 1/490 x z + 7000 + + 3 173 2 2 3 2 2 + + 1/600 y z - ---- + 1/350 y z + 1/350 x z + 1/300 x y + 1/980 x y + 6125 + + 211 2 211 2 191 2 3 3 3 4 + + ---- y + ---- x + ----- z - 1/150 x + 1/150 y - 1/300 z + 1/600 z + 7350 7350 29400 + + 4 4 2 2 + - 1/150 x - 1/150 y , COEFF(2, -1, -2) = - 1/350 x y z + 1/350 x y z + + 2 2 2 19 107 + - 1/350 x y + 1/350 x y z - 1/350 x y + 1/250 x y z - ---- x - ---- x y + 2100 7000 + + 107 2 2 19 3 + + ---- y z - 1/350 y z + 1/175 x z - 8/525 y + ---- z - 1/600 x y + 7000 2100 + + 3 3 3 47 2 2 + - 1/150 y z - 1/300 x z - 1/300 x z + ---- x z - 1/490 y z + 5250 + + 2 2 3 2 2 3 + + 1/245 x z + 1/600 y z + 1/350 y z - 1/175 x z + 1/150 x y + + 2 2 128 2 169 2 169 2 3 3 + - 1/490 x y + ---- y - ----- x - ----- z + 1/300 x + 1/150 y + 3675 29400 29400 + + 3 4 4 4 + - 1/300 z - 2/125 + 1/600 z + 1/600 x - 1/150 y , COEFF(-2, 0, -2) = + + 33 2 3 3 4 + - --- y + 1/300 x z + 1/300 x - 1/300 z + 1/300 z + 1/600 x + 980 + + 2 3 2 2 4 2 2 + - 1/175 x z - 1/300 x - 1/245 y z + 1/100 y - 1/600 z + 1/175 y z + + 2 2 3 47 2 2 2 + - 1/245 x y + 1/300 x z + ---- - 1/175 x z - 1/175 x y z - 1/600 x + 6125 + + 17 4 2 2 2 + - ---- x z + 1/600 z + 1/175 x y + 1/245 x z , COEFF(-1, 0, -2) = + 5250 + + 2 29 47 4 3 2 + 1/350 x y - ---- z + ---- + 1/100 y + 1/150 x - 1/350 x y z + 2100 6125 + + 2 2 2 2 2 4 2 + - 1/350 x z - 9/196 y + 2/75 x - 1/245 y z + 1/600 z + 1/175 y z + + 3 2 2 187 2 2 3 + - 1/150 x z + 1/490 x y + ---- x z - 1/490 x z - 1/300 z + 7000 + + 3 4 2 311 2 + + 1/600 x z - 1/150 x + 1/350 x z + ----- z - 2/75 x, COEFF(0, 0, -2) + 29400 + + 431 2 4 2 2 41 292 2 2 + = ----- z + 1/100 x + 1/245 x y - ---- z + ---- - 1/20 y - 1/20 x + 29400 2100 6125 + + 2 2 2 2 4 2 3 4 + - 1/245 y z - 1/245 x z + 1/600 z + 1/175 x z - 1/300 z + 1/100 y + + 2 3 47 3 + + 1/175 y z, COEFF(1, 0, -2) = - 1/300 z + ---- - 1/600 x z + 6125 + + 2 2 2 187 2 2 4 + - 1/245 y z - 9/196 y - ---- x z + 1/350 x z + 1/175 y z + 1/600 z + 7000 + + 2 2 2 29 2 4 + + 1/490 x y + 2/75 x - ---- z + 1/350 x y z + 2/75 x - 1/150 x + 2100 + + 2 2 2 311 2 4 2 3 + + 1/350 x z - 1/490 x z + ----- z + 1/100 y - 1/350 x y - 1/150 x + 29400 + + 3 47 33 2 2 2 2 + + 1/150 x z, COEFF(2, 0, -2) = ---- - --- y + 1/245 x z - 1/600 x + 6125 980 + + 3 2 2 17 2 2 + - 1/300 x z + 1/300 z - 1/175 x y + 1/175 x z + ---- x z - 1/245 y z + 5250 + + 3 2 2 4 2 3 2 + - 1/300 x z - 1/245 x y + 1/100 y + 1/175 y z - 1/300 z - 1/175 x z + + 4 4 2 2 3 + + 1/600 x + 1/600 z + 1/175 x y z - 1/600 z - 1/300 x + 1/300 x , + + 2 2 2 + COEFF(-2, 1, -2) = - 1/350 x y z - 1/350 x y z + 1/350 x y + + 2 2 19 107 107 + - 1/350 x y z + 1/350 x y + 1/250 x y z + ---- x - ---- x y - ---- y z + 2100 7000 7000 + + 2 2 19 3 3 + + 1/350 y z - 1/175 x z + 8/525 y + ---- z - 1/600 x y + 1/150 y z + 2100 + + 3 3 47 2 2 2 2 + + 1/300 x z + 1/300 x z - ---- x z - 1/490 y z + 1/245 x z + 5250 + + 3 2 2 3 2 2 + - 1/600 y z + 1/350 y z - 1/175 x z + 1/150 x y - 1/490 x y + + 128 2 169 2 169 2 3 3 3 + + ---- y - ----- x - ----- z - 1/300 x - 1/150 y - 1/300 z - 2/125 + 3675 29400 29400 + + 4 4 4 2 + + 1/600 z + 1/600 x - 1/150 y , COEFF(-1, 1, -2) = - 1/700 x y z + + 2 2 2 2 + - 1/700 x y z - 1/700 x y + 1/700 x y z + 1/700 x y + 1/500 x y z + + 229 167 2 2 + - 1/42 x - ----- x y - ---- y z + 1/350 y z - 1/350 x z + 1/42 y + 10500 7000 + + 17 3 3 3 3 167 + - ---- z + 1/300 x y + 1/150 y z + 1/600 x z - 1/150 x z + ---- x z + 2100 7000 + + 2 2 2 2 3 173 2 2 + - 1/490 y z - 1/490 x z - 1/600 y z - ---- + 1/350 y z + 1/350 x z + 6125 + + 3 2 2 211 2 211 2 191 2 3 + + 1/300 x y + 1/980 x y + ---- y + ---- x + ----- z + 1/150 x + 7350 7350 29400 + + 3 3 4 4 4 + - 1/150 y - 1/300 z + 1/600 z - 1/150 x - 1/150 y , COEFF(0, 1, -2) = + + 2 2 3 2 3 2 2 + - 1/245 x z - 1/300 z + 1/175 x z - 1/600 y z + 1/490 x y + + 2 2 3 311 2 4 + - 1/350 x y + 1/350 y z - 1/150 y + ----- z + 2/75 y + 1/100 x + 29400 + + 2 187 2 3 4 47 + - 9/196 x - ---- y z + 1/350 x y z + 1/150 y z - 1/150 y + ---- + 7000 6125 + + 2 29 2 2 4 2 + + 1/350 y z - ---- z - 1/490 y z + 1/600 z + 2/75 y , COEFF(1, 1, -2) + 2100 + + 2 2 2 2 2 + = 1/700 x y z + 1/700 x y z - 1/700 x y + 1/700 x y z - 1/700 x y + + 229 167 2 2 + - 1/500 x y z + 1/42 x + ----- x y - ---- y z + 1/350 y z + 1/350 x z + 10500 7000 + + 17 3 3 3 3 + + 1/42 y - ---- z - 1/300 x y + 1/150 y z - 1/600 x z + 1/150 x z + 2100 + + 167 2 2 2 2 3 173 2 + - ---- x z - 1/490 y z - 1/490 x z - 1/600 y z - ---- + 1/350 y z + 7000 6125 + + 2 3 2 2 211 2 211 2 191 2 + + 1/350 x z - 1/300 x y + 1/980 x y + ---- y + ---- x + ----- z + 7350 7350 29400 + + 3 3 3 4 4 4 + - 1/150 x - 1/150 y - 1/300 z + 1/600 z - 1/150 x - 1/150 y , + + 2 2 2 2 + COEFF(2, 1, -2) = 1/350 x y z + 1/350 x y z + 1/350 x y - 1/350 x y z + + 2 19 107 107 2 + - 1/350 x y - 1/250 x y z - ---- x + ---- x y - ---- y z + 1/350 y z + 2100 7000 7000 + + 2 19 3 3 3 + + 1/175 x z + 8/525 y + ---- z + 1/600 x y + 1/150 y z - 1/300 x z + 2100 + + 3 47 2 2 2 2 3 + - 1/300 x z + ---- x z - 1/490 y z + 1/245 x z - 1/600 y z + 5250 + + 2 2 3 2 2 128 2 169 2 + + 1/350 y z - 1/175 x z - 1/150 x y - 1/490 x y + ---- y - ----- x + 3675 29400 + + 169 2 3 3 3 4 4 + - ----- z + 1/300 x - 1/150 y - 1/300 z - 2/125 + 1/600 z + 1/600 x + 29400 + + 4 2 2 2 + - 1/150 y , COEFF(-2, 2, -2) = - 1/175 x y z + 1/175 x y z + 1/175 x y + + 2 2 11 137 137 + - 1/175 x y z - 1/175 x y + 1/125 x y z + --- x + ---- x y + ---- y z + 420 5250 5250 + + 2 2 11 11 3 3 + + 1/175 y z - 1/175 x z - --- y + --- z - 1/300 x y - 1/300 y z + 420 420 + + 3 3 137 2 2 2 2 + + 1/300 x z + 1/300 x z - ---- x z + 1/245 y z + 1/245 x z + 5250 + + 3 2 202 2 3 2 2 + - 1/300 y z - 1/175 y z + ---- - 1/175 x z - 1/300 x y + 1/245 x y + 6125 + + 529 2 529 2 529 2 3 3 3 + - ----- y - ----- x - ----- z - 1/300 x + 1/300 y - 1/300 z + 29400 29400 29400 + + 4 4 4 2 + + 1/600 z + 1/600 x + 1/600 y , COEFF(-1, 2, -2) = - 1/350 x y z + + 2 2 2 2 + + 1/350 x y z - 1/350 x y + 1/350 x y z - 1/350 x y + 1/250 x y z + + 107 47 2 2 19 + - 8/525 x - ---- x y + ---- y z + 1/175 y z - 1/350 x z - ---- y + 7000 5250 2100 + + 19 3 3 3 3 107 + + ---- z + 1/150 x y - 1/300 y z + 1/600 x z - 1/150 x z + ---- x z + 2100 7000 + + 2 2 2 2 3 2 2 + + 1/245 y z - 1/490 x z - 1/300 y z - 1/175 y z + 1/350 x z + + 3 2 2 169 2 128 2 169 2 3 + - 1/600 x y - 1/490 x y - ----- y + ---- x - ----- z + 1/150 x + 29400 3675 29400 + + 3 3 4 4 4 + + 1/300 y - 1/300 z - 2/125 + 1/600 z - 1/150 x + 1/600 y , + + 47 3 2 + COEFF(0, 2, -2) = ---- - 1/300 y + 1/300 z - 1/300 y z + 1/175 x z + 6125 + + 2 2 4 2 2 2 2 2 + - 1/600 z - 1/600 y + 1/600 z - 1/245 x z - 1/245 x y - 1/175 y z + + 3 3 4 2 2 33 2 + + 1/300 y - 1/300 y z + 1/600 y + 1/175 x y z + 1/175 y z - --- x + 980 + + 2 2 2 17 4 3 + - 1/175 x y + 1/245 y z + ---- y z + 1/100 x - 1/300 z , + 5250 + + 2 2 2 2 + COEFF(1, 2, -2) = 1/350 x y z - 1/350 x y z - 1/350 x y + 1/350 x y z + + 2 107 47 2 + + 1/350 x y - 1/250 x y z + 8/525 x + ---- x y + ---- y z + 1/175 y z + 7000 5250 + + 2 19 19 3 3 3 + + 1/350 x z - ---- y + ---- z - 1/150 x y - 1/300 y z - 1/600 x z + 2100 2100 + + 3 107 2 2 2 2 3 + + 1/150 x z - ---- x z + 1/245 y z - 1/490 x z - 1/300 y z + 7000 + + 2 2 3 2 2 169 2 128 2 + - 1/175 y z + 1/350 x z + 1/600 x y - 1/490 x y - ----- y + ---- x + 29400 3675 + + 169 2 3 3 3 4 4 + - ----- z - 1/150 x + 1/300 y - 1/300 z - 2/125 + 1/600 z - 1/150 x + 29400 + + 4 2 2 2 + + 1/600 y , COEFF(2, 2, -2) = 1/175 x y z - 1/175 x y z + 1/175 x y + + 2 2 11 137 137 + - 1/175 x y z + 1/175 x y - 1/125 x y z - --- x - ---- x y + ---- y z + 420 5250 5250 + + 2 2 11 11 3 3 + + 1/175 y z + 1/175 x z - --- y + --- z + 1/300 x y - 1/300 y z + 420 420 + + 3 3 137 2 2 2 2 + - 1/300 x z - 1/300 x z + ---- x z + 1/245 y z + 1/245 x z + 5250 + + 3 2 202 2 3 2 2 + - 1/300 y z - 1/175 y z + ---- - 1/175 x z + 1/300 x y + 1/245 x y + 6125 + + 529 2 529 2 529 2 3 3 3 + - ----- y - ----- x - ----- z + 1/300 x + 1/300 y - 1/300 z + 29400 29400 29400 + + 4 4 4 2 + + 1/600 z + 1/600 x + 1/600 y , COEFF(-2, -2, -1) = - 1/350 x y z + + 2 2 2 2 + + 1/350 x y z - 1/175 x y + 1/350 x y z - 1/175 x y - 1/250 x y z + + 19 47 107 2 2 19 + + ---- x - ---- x y + ---- y z + 1/350 y z + 1/350 x z + ---- y + 2100 5250 7000 2100 + + 3 3 3 3 107 + - 8/525 z + 1/300 x y + 1/600 y z - 1/150 x z + 1/600 x z + ---- x z + 7000 + + 2 2 2 2 3 2 2 + - 1/490 y z - 1/490 x z - 1/150 y z - 1/350 y z - 1/350 x z + + 3 2 2 169 2 169 2 128 2 3 + + 1/300 x y + 1/245 x y - ----- y - ----- x + ---- z - 1/300 x + 29400 29400 3675 + + 3 3 4 4 4 + - 1/300 y + 1/150 z - 2/125 - 1/150 z + 1/600 x + 1/600 y , + + 2 2 2 + COEFF(-1, -2, -1) = - 1/700 x y z + 1/700 x y z + 1/350 x y + + 2 2 167 167 + - 1/700 x y z - 1/350 x y - 1/500 x y z - 1/42 x + ---- x y + ---- y z + 7000 7000 + + 2 2 17 3 3 + + 1/350 y z + 1/700 x z - ---- y - 1/42 z - 1/150 x y + 1/600 y z + 2100 + + 3 3 229 2 2 2 2 + - 1/300 x z - 1/300 x z + ----- x z - 1/490 y z + 1/980 x z + 10500 + + 3 173 2 2 3 2 2 + - 1/150 y z - ---- - 1/350 y z + 1/700 x z + 1/600 x y - 1/490 x y + 6125 + + 191 2 211 2 211 2 3 3 3 4 + + ----- y + ---- x + ---- z + 1/150 x - 1/300 y + 1/150 z - 1/150 z + 29400 7350 7350 + + 4 4 3 3 187 + - 1/150 x + 1/600 y , COEFF(0, -2, -1) = 1/600 y z + 1/150 z + ---- y z + 7000 + + 2 2 311 2 2 2 47 3 2 + - 1/245 x y + ----- y + 1/490 x z + ---- - 1/150 y z - 1/350 y z + 29400 6125 + + 3 2 4 2 2 2 + - 1/300 y - 1/350 x y z + 1/600 y - 1/490 y z + 2/75 z - 2/75 z + + 2 2 4 2 2 4 + + 1/175 x y + 1/350 y z + 1/100 x + 1/350 x z - 9/196 x - 1/150 z + + 29 2 2 2 + - ---- y, COEFF(1, -2, -1) = 1/700 x y z - 1/700 x y z + 1/350 x y + 2100 + + 2 2 167 167 + - 1/700 x y z + 1/350 x y + 1/500 x y z + 1/42 x - ---- x y + ---- y z + 7000 7000 + + 2 2 17 3 3 + + 1/350 y z - 1/700 x z - ---- y - 1/42 z + 1/150 x y + 1/600 y z + 2100 + + 3 3 229 2 2 2 2 + + 1/300 x z + 1/300 x z - ----- x z - 1/490 y z + 1/980 x z + 10500 + + 3 173 2 2 3 2 2 + - 1/150 y z - ---- - 1/350 y z + 1/700 x z - 1/600 x y - 1/490 x y + 6125 + + 191 2 211 2 211 2 3 3 3 4 + + ----- y + ---- x + ---- z - 1/150 x - 1/300 y + 1/150 z - 1/150 z + 29400 7350 7350 + + 4 4 2 2 + - 1/150 x + 1/600 y , COEFF(2, -2, -1) = 1/350 x y z - 1/350 x y z + + 2 2 2 19 47 + - 1/175 x y + 1/350 x y z + 1/175 x y + 1/250 x y z - ---- x + ---- x y + 2100 5250 + + 107 2 2 19 3 + + ---- y z + 1/350 y z - 1/350 x z + ---- y - 8/525 z - 1/300 x y + 7000 2100 + + 3 3 3 107 2 2 + + 1/600 y z + 1/150 x z - 1/600 x z - ---- x z - 1/490 y z + 7000 + + 2 2 3 2 2 3 + - 1/490 x z - 1/150 y z - 1/350 y z - 1/350 x z - 1/300 x y + + 2 2 169 2 169 2 128 2 3 3 + + 1/245 x y - ----- y - ----- x + ---- z + 1/300 x - 1/300 y + 29400 29400 3675 + + 3 4 4 4 + + 1/150 z - 2/125 - 1/150 z + 1/600 x + 1/600 y , COEFF(-2, -1, -1) = + + 2 2 2 2 2 + - 1/700 x y z - 1/700 x y z - 1/350 x y + 1/700 x y z + 1/350 x y + + 17 167 229 2 2 + - 1/500 x y z - ---- x + ---- x y + ----- y z + 1/700 y z + 1/350 x z + 2100 7000 10500 + + 3 3 3 3 + - 1/42 y - 1/42 z + 1/600 x y - 1/300 y z - 1/150 x z + 1/600 x z + + 167 2 2 2 2 3 173 2 + + ---- x z + 1/980 y z - 1/490 x z - 1/300 y z - ---- + 1/700 y z + 7000 6125 + + 2 3 2 2 211 2 191 2 211 2 + - 1/350 x z - 1/150 x y - 1/490 x y + ---- y + ----- x + ---- z + 7350 29400 7350 + + 3 3 3 4 4 4 + - 1/300 x + 1/150 y + 1/150 z - 1/150 z + 1/600 x - 1/150 y , + + 2 2 2 + COEFF(-1, -1, -1) = - 1/1400 x y z - 1/1400 x y z + 1/700 x y + + 2 2 17 137 137 + - 1/1400 x y z + 1/700 x y - 1/1000 x y z - --- x + ---- x y + ---- y z + 525 5250 5250 + + 2 2 17 17 3 3 + + 1/700 y z + 1/700 x z - --- y - --- z - 1/300 x y - 1/300 y z + 525 525 + + 3 3 137 2 2 2 2 + - 1/300 x z - 1/300 x z + ---- x z + 1/980 y z + 1/980 x z + 5250 + + 3 2 23 2 3 2 2 + - 1/300 y z + 1/700 y z - ---- + 1/700 x z - 1/300 x y + 1/980 x y + 6125 + + 83 2 83 2 83 2 3 3 3 4 + + ---- y + ---- x + ---- z + 1/150 x + 1/150 y + 1/150 z - 1/150 z + 3675 3675 3675 + + 4 4 2 2 2 + - 1/150 x - 1/150 y , COEFF(0, -1, -1) = 1/980 y z - 1/700 x y z + + 3 2 2 3 2 4 272 + + 1/150 z + 1/490 x y + 1/150 y + 1/700 y z + 1/100 x + ---- + 6125 + + 4 2 37 3 151 2 289 + - 1/150 z + 1/350 x y - ---- z - 1/300 y z + ---- y + ----- y z + 1050 7350 10500 + + 2 37 3 57 2 2 4 + + 1/350 x z - ---- y - 1/300 y z - --- x + 1/700 y z - 1/150 y + 1050 980 + + 2 2 151 2 2 2 + + 1/490 x z + ---- z , COEFF(1, -1, -1) = 1/1400 x y z + 1/1400 x y z + 7350 + + 2 2 2 17 + + 1/700 x y - 1/1400 x y z - 1/700 x y + 1/1000 x y z + --- x + 525 + + 137 137 2 2 17 17 + - ---- x y + ---- y z + 1/700 y z - 1/700 x z - --- y - --- z + 5250 5250 525 525 + + 3 3 3 3 137 + + 1/300 x y - 1/300 y z + 1/300 x z + 1/300 x z - ---- x z + 5250 + + 2 2 2 2 3 2 23 2 + + 1/980 y z + 1/980 x z - 1/300 y z + 1/700 y z - ---- + 1/700 x z + 6125 + + 3 2 2 83 2 83 2 83 2 3 + + 1/300 x y + 1/980 x y + ---- y + ---- x + ---- z - 1/150 x + 3675 3675 3675 + + 3 3 4 4 4 + + 1/150 y + 1/150 z - 1/150 z - 1/150 x - 1/150 y , COEFF(2, -1, -1) + + 2 2 2 2 2 + = 1/700 x y z + 1/700 x y z - 1/350 x y + 1/700 x y z - 1/350 x y + + 17 167 229 2 2 + + 1/500 x y z + ---- x - ---- x y + ----- y z + 1/700 y z - 1/350 x z + 2100 7000 10500 + + 3 3 3 3 + - 1/42 y - 1/42 z - 1/600 x y - 1/300 y z + 1/150 x z - 1/600 x z + + 167 2 2 2 2 3 173 2 + - ---- x z + 1/980 y z - 1/490 x z - 1/300 y z - ---- + 1/700 y z + 7000 6125 + + 2 3 2 2 211 2 191 2 211 2 + - 1/350 x z + 1/150 x y - 1/490 x y + ---- y + ----- x + ---- z + 7350 29400 7350 + + 3 3 3 4 4 4 + + 1/300 x + 1/150 y + 1/150 z - 1/150 z + 1/600 x - 1/150 y , + + 2 29 2 4 4 + COEFF(-2, 0, -1) = 1/350 x z - ---- x + 1/350 y z + 1/600 x - 1/150 z + 2100 + + 187 311 2 3 2 2 3 47 + + ---- x z + ----- x - 1/150 x z - 1/245 x y + 1/150 z + ---- + 7000 29400 6125 + + 3 3 2 2 2 2 2 + - 1/300 x + 1/600 x z - 2/75 z - 1/490 x z + 1/490 y z + 2/75 z + + 2 4 2 2 2 + - 9/196 y + 1/100 y - 1/350 x y z + 1/175 x y - 1/350 x z, + + 3 2 3 272 + COEFF(-1, 0, -1) = - 1/300 x z - 1/700 x y z - 1/300 x z + ---- + 6125 + + 2 2 2 2 2 2 2 + + 1/700 x z + 1/350 y z + 1/490 x y + 1/980 x z + 1/700 x z + + 57 2 151 2 2 2 4 37 3 4 + - --- y + ---- x + 1/490 y z - 1/150 x - ---- x + 1/150 x - 1/150 z + 980 7350 1050 + + 37 3 2 151 2 289 4 + - ---- z + 1/150 z + 1/350 x y + ---- z + ----- x z + 1/100 y , + 1050 7350 10500 + + 592 2 2 61 2 68 2 2 2 + COEFF(0, 0, -1) = ---- + 1/245 x y - --- x + ---- z + 1/490 x z + 6125 980 3675 + + 4 2 2 4 2 3 2 + - 1/150 z + 1/490 y z + 1/100 x + 1/350 x z + 1/150 z + 1/350 y z + + 61 2 4 3 2 + - 4/105 z - --- y + 1/100 y , COEFF(1, 0, -1) = 1/300 x z + 1/350 y z + 980 + + 289 2 2 2 2 2 37 3 + - ----- x z + 1/490 y z - 1/700 x z + 1/980 x z - ---- z - 1/150 x + 10500 1050 + + 4 2 3 3 151 2 37 + - 1/150 z + 1/700 x z + 1/150 z + 1/300 x z + ---- z + ---- x + 7350 1050 + + 2 57 2 4 151 2 2 2 4 + + 1/700 x y z - --- y + 1/100 y + ---- x + 1/490 x y - 1/150 x + 980 7350 + + 272 2 29 47 187 + + ---- - 1/350 x y , COEFF(2, 0, -1) = ---- x + ---- - ---- x z - 2/75 z + 6125 2100 6125 7000 + + 3 2 4 2 2 2 + - 1/600 x z - 1/350 x z + 1/100 y - 1/245 x y - 9/196 y + + 2 2 4 3 311 2 2 + + 1/350 x y z - 1/350 x z - 1/150 z + 1/300 x + ----- x + 1/350 y z + 29400 + + 4 2 3 3 2 2 2 + + 1/600 x + 2/75 z + 1/150 x z + 1/150 z + 1/490 y z - 1/175 x y + + 2 2 2 2 2 + - 1/490 x z , COEFF(-2, 1, -1) = 1/700 x y z - 1/700 x y z + 1/350 x y + + 2 2 17 167 229 + - 1/700 x y z + 1/350 x y + 1/500 x y z - ---- x - ---- x y - ----- y z + 2100 7000 10500 + + 2 2 3 3 + - 1/700 y z + 1/350 x z + 1/42 y - 1/42 z - 1/600 x y + 1/300 y z + + 3 3 167 2 2 2 2 + - 1/150 x z + 1/600 x z + ---- x z + 1/980 y z - 1/490 x z + 7000 + + 3 173 2 2 3 2 2 + + 1/300 y z - ---- + 1/700 y z - 1/350 x z + 1/150 x y - 1/490 x y + 6125 + + 211 2 191 2 211 2 3 3 3 4 + + ---- y + ----- x + ---- z - 1/300 x - 1/150 y + 1/150 z - 1/150 z + 7350 29400 7350 + + 4 4 2 2 + + 1/600 x - 1/150 y , COEFF(-1, 1, -1) = 1/1400 x y z - 1/1400 x y z + + 2 2 2 17 + - 1/700 x y + 1/1400 x y z + 1/700 x y + 1/1000 x y z - --- x + 525 + + 137 137 2 2 17 17 + - ---- x y - ---- y z - 1/700 y z + 1/700 x z + --- y - --- z + 5250 5250 525 525 + + 3 3 3 3 137 + + 1/300 x y + 1/300 y z - 1/300 x z - 1/300 x z + ---- x z + 5250 + + 2 2 2 2 3 2 23 2 + + 1/980 y z + 1/980 x z + 1/300 y z + 1/700 y z - ---- + 1/700 x z + 6125 + + 3 2 2 83 2 83 2 83 2 3 + + 1/300 x y + 1/980 x y + ---- y + ---- x + ---- z + 1/150 x + 3675 3675 3675 + + 3 3 4 4 4 + - 1/150 y + 1/150 z - 1/150 z - 1/150 x - 1/150 y , COEFF(0, 1, -1) = + + 289 2 2 272 2 2 3 + - ----- y z + 1/700 y z + 1/350 x z + ---- + 1/490 x z - 1/150 y + 10500 6125 + + 2 2 2 3 3 2 4 + - 1/350 x y + 1/980 y z + 1/300 y z + 1/150 z - 1/700 y z - 1/150 z + + 57 2 37 4 2 2 151 2 4 + - --- x + ---- y - 1/150 y + 1/490 x y + ---- z + 1/100 x + 980 1050 7350 + + 3 151 2 2 37 + + 1/300 y z + ---- y + 1/700 x y z - ---- z, COEFF(1, 1, -1) = + 7350 1050 + + 2 2 2 2 2 + - 1/1400 x y z + 1/1400 x y z - 1/700 x y + 1/1400 x y z - 1/700 x y + + 17 137 137 2 2 + - 1/1000 x y z + --- x + ---- x y - ---- y z - 1/700 y z - 1/700 x z + 525 5250 5250 + + 17 17 3 3 3 3 + + --- y - --- z - 1/300 x y + 1/300 y z + 1/300 x z + 1/300 x z + 525 525 + + 137 2 2 2 2 3 2 23 + - ---- x z + 1/980 y z + 1/980 x z + 1/300 y z + 1/700 y z - ---- + 5250 6125 + + 2 3 2 2 83 2 83 2 83 2 + + 1/700 x z - 1/300 x y + 1/980 x y + ---- y + ---- x + ---- z + 3675 3675 3675 + + 3 3 3 4 4 4 + - 1/150 x - 1/150 y + 1/150 z - 1/150 z - 1/150 x - 1/150 y , + + 2 2 2 2 + COEFF(2, 1, -1) = - 1/700 x y z + 1/700 x y z + 1/350 x y - 1/700 x y z + + 2 17 167 229 2 + - 1/350 x y - 1/500 x y z + ---- x + ---- x y - ----- y z - 1/700 y z + 2100 7000 10500 + + 2 3 3 3 + - 1/350 x z + 1/42 y - 1/42 z + 1/600 x y + 1/300 y z + 1/150 x z + + 3 167 2 2 2 2 3 173 + - 1/600 x z - ---- x z + 1/980 y z - 1/490 x z + 1/300 y z - ---- + 7000 6125 + + 2 2 3 2 2 211 2 191 2 + + 1/700 y z - 1/350 x z - 1/150 x y - 1/490 x y + ---- y + ----- x + 7350 29400 + + 211 2 3 3 3 4 4 + + ---- z + 1/300 x - 1/150 y + 1/150 z - 1/150 z + 1/600 x + 7350 + + 4 2 2 2 + - 1/150 y , COEFF(-2, 2, -1) = 1/350 x y z + 1/350 x y z + 1/175 x y + + 2 2 19 47 107 + - 1/350 x y z - 1/175 x y + 1/250 x y z + ---- x + ---- x y - ---- y z + 2100 5250 7000 + + 2 2 19 3 3 + - 1/350 y z + 1/350 x z - ---- y - 8/525 z - 1/300 x y - 1/600 y z + 2100 + + 3 3 107 2 2 2 2 + - 1/150 x z + 1/600 x z + ---- x z - 1/490 y z - 1/490 x z + 7000 + + 3 2 2 3 2 2 + + 1/150 y z - 1/350 y z - 1/350 x z - 1/300 x y + 1/245 x y + + 169 2 169 2 128 2 3 3 3 + - ----- y - ----- x + ---- z - 1/300 x + 1/300 y + 1/150 z - 2/125 + 29400 29400 3675 + + 4 4 4 2 + - 1/150 z + 1/600 x + 1/600 y , COEFF(-1, 2, -1) = 1/700 x y z + + 2 2 2 2 + + 1/700 x y z - 1/350 x y + 1/700 x y z - 1/350 x y + 1/500 x y z + + 167 167 2 2 17 + - 1/42 x - ---- x y - ---- y z - 1/350 y z + 1/700 x z + ---- y - 1/42 z + 7000 7000 2100 + + 3 3 3 3 229 + + 1/150 x y - 1/600 y z - 1/300 x z - 1/300 x z + ----- x z + 10500 + + 2 2 2 2 3 173 2 2 + - 1/490 y z + 1/980 x z + 1/150 y z - ---- - 1/350 y z + 1/700 x z + 6125 + + 3 2 2 191 2 211 2 211 2 3 + - 1/600 x y - 1/490 x y + ----- y + ---- x + ---- z + 1/150 x + 29400 7350 7350 + + 3 3 4 4 4 + + 1/300 y + 1/150 z - 1/150 z - 1/150 x + 1/600 y , COEFF(0, 2, -1) = + + 3 2 2 2 2 2 2 2 + 1/150 z + 1/490 x z + 1/350 x z - 1/245 x y - 1/350 y z - 9/196 x + + 2 2 3 187 4 2 311 2 + - 1/490 y z + 1/150 y z - ---- y z + 1/600 y - 1/350 y z + ----- y + 7000 29400 + + 3 2 4 2 47 29 + - 1/600 y z + 1/350 x y z + 1/100 x - 1/175 x y + ---- + ---- y + 6125 2100 + + 4 2 3 2 + - 1/150 z - 2/75 z + 2/75 z + 1/300 y , COEFF(1, 2, -1) = - 1/700 x y z + + 2 2 2 2 + - 1/700 x y z - 1/350 x y + 1/700 x y z + 1/350 x y - 1/500 x y z + + 167 167 2 2 17 + + 1/42 x + ---- x y - ---- y z - 1/350 y z - 1/700 x z + ---- y - 1/42 z + 7000 7000 2100 + + 3 3 3 3 229 + - 1/150 x y - 1/600 y z + 1/300 x z + 1/300 x z - ----- x z + 10500 + + 2 2 2 2 3 173 2 2 + - 1/490 y z + 1/980 x z + 1/150 y z - ---- - 1/350 y z + 1/700 x z + 6125 + + 3 2 2 191 2 211 2 211 2 3 + + 1/600 x y - 1/490 x y + ----- y + ---- x + ---- z - 1/150 x + 29400 7350 7350 + + 3 3 4 4 4 + + 1/300 y + 1/150 z - 1/150 z - 1/150 x + 1/600 y , COEFF(2, 2, -1) = + + 2 2 2 2 2 + - 1/350 x y z - 1/350 x y z + 1/175 x y - 1/350 x y z + 1/175 x y + + 19 47 107 2 2 + - 1/250 x y z - ---- x - ---- x y - ---- y z - 1/350 y z - 1/350 x z + 2100 5250 7000 + + 19 3 3 3 3 + - ---- y - 8/525 z + 1/300 x y - 1/600 y z + 1/150 x z - 1/600 x z + 2100 + + 107 2 2 2 2 3 2 + - ---- x z - 1/490 y z - 1/490 x z + 1/150 y z - 1/350 y z + 7000 + + 2 3 2 2 169 2 169 2 128 2 + - 1/350 x z + 1/300 x y + 1/245 x y - ----- y - ----- x + ---- z + 29400 29400 3675 + + 3 3 3 4 4 4 + + 1/300 x + 1/300 y + 1/150 z - 2/125 - 1/150 z + 1/600 x + 1/600 y , + + 2 2 47 2 + COEFF(-2, -2, 0) = 1/300 y + 1/175 y z - 1/175 x y z + ---- - 1/600 y + 6125 + + 3 17 2 33 2 2 2 3 + + 1/300 x y - ---- x y + 1/175 x z - --- z + 1/245 x y + 1/300 x y + 5250 980 + + 4 2 2 3 2 2 + + 1/300 x + 1/600 y - 1/600 x - 1/175 x y - 1/300 x - 1/245 x z + + 4 2 4 2 2 3 + + 1/100 z - 1/175 x y + 1/600 x - 1/245 y z - 1/300 y , + + 187 2 3 29 2 + COEFF(-1, -2, 0) = ---- x y + 1/350 x y + 1/600 x y - ---- y - 9/196 z + 7000 2100 + + 4 2 311 2 3 4 2 2 + + 1/600 y + 1/175 y z + ----- y + 1/150 x + 1/100 z + 1/490 x z + 29400 + + 4 2 3 2 3 + - 2/75 x - 1/150 x + 2/75 x - 1/300 y - 1/350 x y - 1/150 x y + + 2 47 2 2 2 2 2 + - 1/350 x y z + ---- - 1/490 x y - 1/245 y z + 1/350 x z , + 6125 + + 2 431 2 2 2 2 2 + COEFF(0, -2, 0) = 1/175 y z + ----- y - 1/245 y z - 1/245 x y + 29400 + + 3 41 2 2 292 2 4 + - 1/300 y - ---- y - 1/20 x - 1/20 z + ---- + 1/175 x y + 1/100 x + 2100 6125 + + 2 2 4 4 2 + + 1/245 x z + 1/600 y + 1/100 z , COEFF(1, -2, 0) = 1/350 x y + + 2 2 2 47 3 3 + - 1/245 y z + 1/350 x y z + ---- - 1/150 x + 2/75 x + 1/150 x y + 6125 + + 29 2 4 2 3 187 + - ---- y + 1/175 y z + 1/100 z - 1/350 x z - 1/300 y - ---- x y + 2100 7000 + + 4 2 2 2 2 311 2 3 + + 1/600 y - 1/490 x y - 9/196 z + 1/350 x y + ----- y - 1/600 x y + 29400 + + 2 2 2 4 3 + + 2/75 x + 1/490 x z - 1/150 x , COEFF(2, -2, 0) = - 1/300 x - 1/300 y + + 3 47 33 2 4 3 3 + - 1/300 x y + ---- + 1/300 y - --- z + 1/100 z + 1/300 x - 1/300 x y + 6125 980 + + 2 2 4 2 2 2 2 + + 1/245 x y + 1/600 x - 1/175 x y - 1/600 x - 1/245 x z + + 2 2 2 17 2 2 + + 1/175 x y z - 1/245 y z + ---- x y + 1/175 y z + 1/175 x y + 5250 + + 2 2 4 187 + - 1/600 y - 1/175 x z + 1/600 y , COEFF(-2, -1, 0) = ---- x y + 7000 + + 2 2 2 2 2 2 2 + + 1/350 x y - 1/350 x y z + 1/350 y z + 1/490 y z - 1/245 x z + + 2 3 2 2 311 2 2 4 + - 1/350 x y + 1/600 x y - 1/490 x y + ----- x + 1/175 x z + 1/600 x + 29400 + + 3 2 47 4 4 29 3 + - 1/150 x y + 2/75 y + ---- - 1/150 y + 1/100 z - ---- x + 1/150 y + 6125 2100 + + 2 3 4 + - 2/75 y - 9/196 z - 1/300 x , COEFF(-1, -1, 0) = - 1/150 x + + 2 2 3 3 151 2 2 4 + + 1/490 x z - 1/300 x y - 1/300 x y + ---- y + 1/350 y z - 1/150 y + 7350 + + 57 2 2 2 2 2 2 272 + - --- z + 1/700 x y + 1/700 x y - 1/700 x y z + 1/980 x y + ---- + 980 6125 + + 4 3 151 2 2 2 37 3 + + 1/100 z + 1/150 y + ---- x + 1/490 y z - ---- x + 1/150 x + 7350 1050 + + 2 289 37 4 61 2 + + 1/350 x z + ----- x y - ---- y, COEFF(0, -1, 0) = - 1/150 y - --- z + 10500 1050 980 + + 68 2 4 2 4 61 2 + + ---- y + 1/100 z + 1/350 y z + 1/100 x - 4/105 y - --- x + 3675 980 + + 2 2 2 2 2 2 2 3 592 + + 1/490 x y + 1/490 y z + 1/245 x z + 1/350 x y + 1/150 y + ----, + 6125 + + 37 2 3 3 3 + COEFF(1, -1, 0) = ---- x - 1/700 x y + 1/300 x y - 1/150 x + 1/300 x y + 1050 + + 272 2 2 289 2 2 4 2 2 + + ---- + 1/490 y z - ----- x y + 1/980 x y - 1/150 x + 1/490 x z + 6125 10500 + + 4 2 4 2 2 + - 1/150 y + 1/350 y z + 1/100 z + 1/700 x y - 1/350 x z + + 2 151 2 151 2 37 57 2 3 + + 1/700 x y z + ---- x + ---- y - ---- y - --- z + 1/150 y , + 7350 7350 1050 980 + + 187 4 3 2 2 + COEFF(2, -1, 0) = - ---- x y + 1/100 z - 1/600 x y - 1/175 x z + 2/75 y + 7000 + + 2 2 3 3 47 2 2 + + 1/490 y z + 1/150 y + 1/150 x y - 2/75 y + ---- - 1/245 x z + 6125 + + 2 2 2 2 3 2 4 + - 1/490 x y + 1/350 y z - 1/350 x y + 1/300 x - 1/350 x y + 1/600 x + + 2 4 311 2 2 29 + + 1/350 x y z - 1/150 y + ----- x - 9/196 z + ---- x, COEFF(-2, 0, 0) + 29400 2100 + + 4 2 2 2 4 2 2 + = 1/600 x + 1/245 y z + 1/175 x y + 1/100 z - 1/20 y + 1/175 x z + + 2 2 292 2 2 2 41 4 + - 1/245 x y + ---- - 1/245 x z - 1/20 z - ---- x + 1/100 y + 6125 2100 + + 431 2 3 592 2 + + ----- x - 1/300 x , COEFF(-1, 0, 0) = ---- - 4/105 x + 1/350 x z + 29400 6125 + + 68 2 2 4 2 2 2 2 4 + + ---- x + 1/350 x y + 1/100 y + 1/490 x y + 1/245 y z + 1/100 z + 3675 + + 2 2 61 2 4 61 2 3 + + 1/490 x z - --- z - 1/150 x - --- y + 1/150 x , COEFF(0, 0, 0) = + 980 980 + + 937 13 2 13 2 2 2 13 2 4 2 2 + ---- - --- z - --- x + 1/245 x y - --- y + 1/100 x + 1/245 y z + 6125 196 196 196 + + 2 2 4 4 68 2 2 + + 1/245 x z + 1/100 z + 1/100 y , COEFF(1, 0, 0) = ---- x - 1/350 x y + 3675 + + 61 2 4 2 2 3 2 592 + - --- y + 4/105 x - 1/150 x + 1/490 x z - 1/150 x - 1/350 x z + ---- + 980 6125 + + 4 2 2 61 2 2 2 4 + + 1/100 z + 1/245 y z - --- z + 1/490 x y + 1/100 y , COEFF(2, 0, 0) + 980 + + 292 4 2 2 2 2 4 + = ---- + 1/100 z - 1/175 x z - 1/20 z + 1/245 y z + 1/100 y + 6125 + + 2 3 2 2 4 2 2 2 + - 1/175 x y + 1/300 x - 1/245 x z + 1/600 x - 1/245 x y - 1/20 y + + 41 431 2 47 2 + + ---- x + ----- x , COEFF(-2, 1, 0) = ---- + 2/75 y + 1/350 x y z + 2100 29400 6125 + + 187 3 2 3 4 2 + - ---- x y - 1/600 x y + 1/350 x y + 1/150 x y + 1/100 z + 1/350 x y + 7000 + + 4 2 2 2 2 29 3 + + 1/600 x + 1/175 x z + 2/75 y + 1/490 y z - ---- x - 1/150 y + 2100 + + 2 2 2 4 2 2 3 2 + - 9/196 z - 1/245 x z - 1/150 y - 1/490 x y - 1/300 x - 1/350 y z + + 311 2 272 3 2 151 2 + + ----- x , COEFF(-1, 1, 0) = ---- + 1/300 x y + 1/700 x y + ---- x + 29400 6125 7350 + + 2 2 151 2 3 37 2 4 + + 1/490 y z + ---- y + 1/300 x y + ---- y - 1/700 x y - 1/150 x + 7350 1050 + + 2 2 2 4 2 2 2 + + 1/350 x z + 1/490 x z - 1/150 y + 1/980 x y + 1/700 x y z + + 4 2 37 289 57 2 3 + + 1/100 z - 1/350 y z - ---- x - ----- x y - --- z - 1/150 y + 1050 10500 980 + + 3 2 2 61 2 + + 1/150 x , COEFF(0, 1, 0) = - 1/350 x y - 1/350 y z - --- z + 980 + + 2 2 592 61 2 4 3 + + 1/490 y z + ---- - --- x - 1/150 y - 1/150 y + 4/105 y + 6125 980 + + 2 2 68 2 2 2 4 4 + + 1/245 x z + ---- y + 1/490 x y + 1/100 x + 1/100 z , + 3675 + + 3 2 2 37 + COEFF(1, 1, 0) = - 1/300 x y - 1/700 x y z - 1/350 x z + ---- x + 1050 + + 3 2 3 272 289 151 2 + - 1/150 x - 1/700 x y - 1/300 x y + ---- + ----- x y + ---- x + 6125 10500 7350 + + 2 37 2 151 2 2 2 4 + - 1/700 x y + ---- y - 1/350 y z + ---- y + 1/490 y z - 1/150 x + 1050 7350 + + 2 2 57 2 2 2 4 3 4 + + 1/490 x z - --- z + 1/980 x y - 1/150 y - 1/150 y + 1/100 z , + 980 + + 4 2 2 2 2 29 + COEFF(2, 1, 0) = 1/100 z - 9/196 z - 1/490 x y - 1/350 x y z + ---- x + 2100 + + 4 187 2 47 2 + - 1/150 y + ---- x y + 2/75 y - 1/350 x y + ---- - 1/175 x z + 7000 6125 + + 3 2 3 2 2 2 2 + - 1/150 x y + 1/350 x y - 1/150 y + 1/490 y z - 1/245 x z + + 2 3 3 2 311 2 4 + - 1/350 y z + 1/600 x y + 1/300 x + 2/75 y + ----- x + 1/600 x , + 29400 + + 2 2 2 2 2 + COEFF(-2, 2, 0) = 1/175 x y + 1/175 x y z + 1/245 x y + 1/175 x z + + 2 2 2 47 4 3 + - 1/175 x y - 1/245 y z + ---- + 1/600 y - 1/300 x - 1/300 y + 6125 + + 4 33 2 3 2 3 + + 1/100 z - --- z + 1/300 y - 1/600 x - 1/300 x y + 1/300 x + 980 + + 2 17 4 3 2 2 2 + - 1/600 y + ---- x y + 1/600 x - 1/300 x y - 1/175 y z - 1/245 x z , + 5250 + + 2 2 2 2 2 2 + COEFF(-1, 2, 0) = - 1/245 y z - 1/175 y z - 1/490 x y + 1/350 x z + + 47 2 2 2 3 311 2 + + ---- - 1/350 x y - 1/350 x y + 1/350 x y z + 1/150 x y + ----- y + 6125 29400 + + 187 4 3 4 2 2 29 + - ---- x y - 1/150 x - 1/600 x y + 1/600 y + 1/490 x z + ---- y + 7000 2100 + + 3 2 4 3 2 + + 1/150 x + 2/75 x + 1/100 z - 2/75 x + 1/300 y - 9/196 z , + + 3 292 4 2 2 2 + COEFF(0, 2, 0) = 1/300 y + ---- + 1/100 z - 1/20 x - 1/245 y z + 6125 + + 41 4 431 2 2 2 4 2 2 + + ---- y + 1/600 y + ----- y - 1/245 x y + 1/100 x + 1/245 x z + 2100 29400 + + 2 2 2 187 47 + - 1/175 y z - 1/175 x y - 1/20 z , COEFF(1, 2, 0) = ---- x y + ---- + 7000 6125 + + 2 2 2 2 2 2 + - 1/175 y z + 2/75 x - 1/490 x y - 1/350 x y z + 1/490 x z + + 3 2 3 3 4 3 + + 1/600 x y - 1/350 x y + 1/300 y - 1/150 x + 1/100 z - 1/150 x y + + 311 2 2 2 2 4 2 2 + + ----- y + 1/350 x y - 9/196 z - 1/350 x z + 1/600 y - 1/245 y z + 29400 + + 29 4 2 2 2 + + ---- y - 1/150 x + 2/75 x , COEFF(2, 2, 0) = - 1/175 y z + 1/175 x y + 2100 + + 2 2 2 3 3 3 47 + - 1/175 x z - 1/245 y z + 1/300 x y + 1/300 y + 1/300 x + ---- + 6125 + + 4 3 2 17 4 2 2 + + 1/600 x + 1/300 x y - 1/175 x y z - ---- x y + 1/100 z + 1/245 x y + 5250 + + 2 2 2 4 2 + - 1/600 y - 1/245 x z + 1/600 y + 1/175 x y - 1/300 y - 1/300 x + + 2 33 2 2 2 + - 1/600 x - --- z , COEFF(-2, -2, 1) = - 1/350 x y z - 1/350 x y z + 980 + + 2 2 2 19 47 + - 1/175 x y - 1/350 x y z - 1/175 x y + 1/250 x y z + ---- x - ---- x y + 2100 5250 + + 107 2 2 19 3 + - ---- y z + 1/350 y z + 1/350 x z + ---- y + 8/525 z + 1/300 x y + 7000 2100 + + 3 3 3 107 2 2 + - 1/600 y z + 1/150 x z - 1/600 x z - ---- x z - 1/490 y z + 7000 + + 2 2 3 2 2 3 + - 1/490 x z + 1/150 y z + 1/350 y z + 1/350 x z + 1/300 x y + + 2 2 169 2 169 2 128 2 3 3 + + 1/245 x y - ----- y - ----- x + ---- z - 1/300 x - 1/300 y + 29400 29400 3675 + + 3 4 4 4 + - 1/150 z - 2/125 - 1/150 z + 1/600 x + 1/600 y , COEFF(-1, -2, 1) = + + 2 2 2 2 2 + - 1/700 x y z - 1/700 x y z + 1/350 x y + 1/700 x y z - 1/350 x y + + 167 167 2 2 + + 1/500 x y z - 1/42 x + ---- x y - ---- y z + 1/350 y z + 1/700 x z + 7000 7000 + + 17 3 3 3 3 + - ---- y + 1/42 z - 1/150 x y - 1/600 y z + 1/300 x z + 1/300 x z + 2100 + + 229 2 2 2 2 3 173 2 + - ----- x z - 1/490 y z + 1/980 x z + 1/150 y z - ---- + 1/350 y z + 10500 6125 + + 2 3 2 2 191 2 211 2 211 2 + - 1/700 x z + 1/600 x y - 1/490 x y + ----- y + ---- x + ---- z + 29400 7350 7350 + + 3 3 3 4 4 4 + + 1/150 x - 1/300 y - 1/150 z - 1/150 z - 1/150 x + 1/600 y , + + 2 2 2 2 + COEFF(0, -2, 1) = 1/350 y z - 1/350 x z + 1/175 x y + 1/350 x y z + + 4 29 3 2 2 3 2 + - 1/150 z - ---- y - 1/300 y + 1/490 x z + 1/150 y z - 9/196 x + 2100 + + 2 2 4 2 2 2 47 311 2 + - 1/245 x y + 1/600 y - 1/490 y z + 2/75 z + ---- + ----- y + 6125 29400 + + 3 187 3 2 4 + - 1/150 z - ---- y z + 2/75 z - 1/600 y z + 1/350 y z + 1/100 x , + 7000 + + 2 2 2 2 + COEFF(1, -2, 1) = 1/700 x y z + 1/700 x y z + 1/350 x y + 1/700 x y z + + 2 167 167 2 + + 1/350 x y - 1/500 x y z + 1/42 x - ---- x y - ---- y z + 1/350 y z + 7000 7000 + + 2 17 3 3 3 + - 1/700 x z - ---- y + 1/42 z + 1/150 x y - 1/600 y z - 1/300 x z + 2100 + + 3 229 2 2 2 2 3 173 + - 1/300 x z + ----- x z - 1/490 y z + 1/980 x z + 1/150 y z - ---- + 10500 6125 + + 2 2 3 2 2 191 2 211 2 + + 1/350 y z - 1/700 x z - 1/600 x y - 1/490 x y + ----- y + ---- x + 29400 7350 + + 211 2 3 3 3 4 4 + + ---- z - 1/150 x - 1/300 y - 1/150 z - 1/150 z - 1/150 x + 7350 + + 4 2 2 2 + + 1/600 y , COEFF(2, -2, 1) = 1/350 x y z + 1/350 x y z - 1/175 x y + + 2 2 19 47 107 + - 1/350 x y z + 1/175 x y - 1/250 x y z - ---- x + ---- x y - ---- y z + 2100 5250 7000 + + 2 2 19 3 3 + + 1/350 y z - 1/350 x z + ---- y + 8/525 z - 1/300 x y - 1/600 y z + 2100 + + 3 3 107 2 2 2 2 + - 1/150 x z + 1/600 x z + ---- x z - 1/490 y z - 1/490 x z + 7000 + + 3 2 2 3 2 2 + + 1/150 y z + 1/350 y z + 1/350 x z - 1/300 x y + 1/245 x y + + 169 2 169 2 128 2 3 3 3 + - ----- y - ----- x + ---- z + 1/300 x - 1/300 y - 1/150 z - 2/125 + 29400 29400 3675 + + 4 4 4 2 + - 1/150 z + 1/600 x + 1/600 y , COEFF(-2, -1, 1) = - 1/700 x y z + + 2 2 2 2 + + 1/700 x y z - 1/350 x y - 1/700 x y z + 1/350 x y + 1/500 x y z + + 17 167 229 2 2 + - ---- x + ---- x y - ----- y z + 1/700 y z + 1/350 x z - 1/42 y + 2100 7000 10500 + + 3 3 3 3 167 + + 1/42 z + 1/600 x y + 1/300 y z + 1/150 x z - 1/600 x z - ---- x z + 7000 + + 2 2 2 2 3 173 2 2 + + 1/980 y z - 1/490 x z + 1/300 y z - ---- - 1/700 y z + 1/350 x z + 6125 + + 3 2 2 211 2 191 2 211 2 3 + - 1/150 x y - 1/490 x y + ---- y + ----- x + ---- z - 1/300 x + 7350 29400 7350 + + 3 3 4 4 4 + + 1/150 y - 1/150 z - 1/150 z + 1/600 x - 1/150 y , COEFF(-1, -1, 1) + + 2 2 2 2 + = - 1/1400 x y z + 1/1400 x y z + 1/700 x y + 1/1400 x y z + + 2 17 137 137 2 + + 1/700 x y + 1/1000 x y z - --- x + ---- x y - ---- y z + 1/700 y z + 525 5250 5250 + + 2 17 17 3 3 3 + + 1/700 x z - --- y + --- z - 1/300 x y + 1/300 y z + 1/300 x z + 525 525 + + 3 137 2 2 2 2 3 + + 1/300 x z - ---- x z + 1/980 y z + 1/980 x z + 1/300 y z + 5250 + + 2 23 2 3 2 2 83 2 + - 1/700 y z - ---- - 1/700 x z - 1/300 x y + 1/980 x y + ---- y + 6125 3675 + + 83 2 83 2 3 3 3 4 4 + + ---- x + ---- z + 1/150 x + 1/150 y - 1/150 z - 1/150 z - 1/150 x + 3675 3675 + + 4 57 2 2 4 + - 1/150 y , COEFF(0, -1, 1) = - --- x + 1/700 y z - 1/150 y + 980 + + 2 2 289 2 2 2 2 + + 1/490 x z - ----- y z + 1/490 x y - 1/700 y z + 1/700 x y z + 10500 + + 2 37 2 2 151 2 3 4 + - 1/350 x z + ---- z + 1/980 y z + ---- y + 1/300 y z + 1/100 x + 1050 7350 + + 3 151 2 272 37 3 4 2 + + 1/300 y z + ---- z + ---- - ---- y + 1/150 y - 1/150 z + 1/350 x y + 7350 6125 1050 + + 3 2 2 2 + - 1/150 z , COEFF(1, -1, 1) = 1/1400 x y z - 1/1400 x y z + 1/700 x y + + 2 2 17 137 137 + + 1/1400 x y z - 1/700 x y - 1/1000 x y z + --- x - ---- x y - ---- y z + 525 5250 5250 + + 2 2 17 17 3 3 + + 1/700 y z - 1/700 x z - --- y + --- z + 1/300 x y + 1/300 y z + 525 525 + + 3 3 137 2 2 2 2 + - 1/300 x z - 1/300 x z + ---- x z + 1/980 y z + 1/980 x z + 5250 + + 3 2 23 2 3 2 2 + + 1/300 y z - 1/700 y z - ---- - 1/700 x z + 1/300 x y + 1/980 x y + 6125 + + 83 2 83 2 83 2 3 3 3 4 + + ---- y + ---- x + ---- z - 1/150 x + 1/150 y - 1/150 z - 1/150 z + 3675 3675 3675 + + 4 4 2 2 + - 1/150 x - 1/150 y , COEFF(2, -1, 1) = 1/700 x y z - 1/700 x y z + + 2 2 2 17 167 + - 1/350 x y - 1/700 x y z - 1/350 x y - 1/500 x y z + ---- x - ---- x y + 2100 7000 + + 229 2 2 3 + - ----- y z + 1/700 y z - 1/350 x z - 1/42 y + 1/42 z - 1/600 x y + 10500 + + 3 3 3 167 2 2 + + 1/300 y z - 1/150 x z + 1/600 x z + ---- x z + 1/980 y z + 7000 + + 2 2 3 173 2 2 3 + - 1/490 x z + 1/300 y z - ---- - 1/700 y z + 1/350 x z + 1/150 x y + 6125 + + 2 2 211 2 191 2 211 2 3 3 + - 1/490 x y + ---- y + ----- x + ---- z + 1/300 x + 1/150 y + 7350 29400 7350 + + 3 4 4 4 + - 1/150 z - 1/150 z + 1/600 x - 1/150 y , COEFF(-2, 0, 1) = + + 2 47 2 3 2 2 2 + - 1/350 y z + ---- + 1/350 x y z - 1/600 x z + 2/75 z + 1/490 y z + 6125 + + 3 2 2 4 4 2 3 + - 1/150 z - 1/245 x y + 1/600 x + 1/100 y - 9/196 y + 1/150 x z + + 2 2 2 2 187 3 + + 1/350 x z + 1/350 x z - 1/490 x z + 2/75 z - ---- x z - 1/300 x + 7000 + + 2 29 311 2 4 3 + + 1/175 x y - ---- x + ----- x - 1/150 z , COEFF(-1, 0, 1) = 1/300 x z + 2100 29400 + + 151 2 151 2 3 3 4 272 4 + + ---- x + ---- z - 1/150 z + 1/300 x z + 1/100 y + ---- - 1/150 x + 7350 7350 6125 + + 2 2 2 57 2 2 37 2 2 + + 1/350 x y + 1/980 x z - --- y - 1/350 y z + ---- z + 1/490 y z + 980 1050 + + 2 2 2 4 2 3 + - 1/700 x z + 1/490 x y - 1/150 z + 1/700 x y z + 1/150 x + + 289 37 2 4 2 2 + - ----- x z - ---- x + 1/700 x z , COEFF(0, 0, 1) = 1/100 x + 1/490 x z + 10500 1050 + + 61 2 592 4 68 2 61 2 2 2 3 + - --- x + ---- - 1/150 z + ---- z - --- y + 1/245 x y - 1/150 z + 980 6125 3675 980 + + 2 2 2 4 2 + + 1/490 y z - 1/350 y z + 1/100 y + 4/105 z - 1/350 x z, + + 2 2 151 2 4 2 57 2 + COEFF(1, 0, 1) = 1/490 y z + ---- x - 1/150 z - 1/700 x z - --- y + 7350 980 + + 3 37 3 2 4 3 + - 1/300 x z + ---- z - 1/150 x - 1/700 x y z + 1/100 y - 1/300 x z + 1050 + + 4 2 151 2 289 2 37 + - 1/150 x - 1/350 x y + ---- z + ----- x z - 1/350 y z + ---- x + 7350 10500 1050 + + 2 272 2 2 3 2 2 + - 1/700 x z + ---- + 1/980 x z - 1/150 z + 1/490 x y , COEFF(2, 0, 1) + 6125 + + 2 2 2 187 2 2 2 + = - 1/350 x z - 1/490 x z + ---- x z - 1/245 x y - 1/175 x y + 7000 + + 2 2 47 3 2 4 3 + + 1/490 y z + ---- - 1/150 x z - 1/350 x y z + 1/600 x + 1/600 x z + 6125 + + 2 2 29 3 2 + + 2/75 z + 1/350 x z + ---- x + 2/75 z + 1/300 x - 9/196 y + 2100 + + 2 3 4 4 311 2 + - 1/350 y z - 1/150 z - 1/150 z + 1/100 y + ----- x , COEFF(-2, 1, 1) + 29400 + + 2 2 2 2 2 + = 1/700 x y z + 1/700 x y z + 1/350 x y + 1/700 x y z + 1/350 x y + + 17 167 229 2 2 + - 1/500 x y z - ---- x - ---- x y + ----- y z - 1/700 y z + 1/350 x z + 2100 7000 10500 + + 3 3 3 3 + + 1/42 y + 1/42 z - 1/600 x y - 1/300 y z + 1/150 x z - 1/600 x z + + 167 2 2 2 2 3 173 2 + - ---- x z + 1/980 y z - 1/490 x z - 1/300 y z - ---- - 1/700 y z + 7000 6125 + + 2 3 2 2 211 2 191 2 211 2 + + 1/350 x z + 1/150 x y - 1/490 x y + ---- y + ----- x + ---- z + 7350 29400 7350 + + 3 3 3 4 4 4 + - 1/300 x - 1/150 y - 1/150 z - 1/150 z + 1/600 x - 1/150 y , + + 2 2 2 + COEFF(-1, 1, 1) = 1/1400 x y z + 1/1400 x y z - 1/700 x y + + 2 2 17 137 137 + - 1/1400 x y z + 1/700 x y - 1/1000 x y z - --- x - ---- x y + ---- y z + 525 5250 5250 + + 2 2 17 17 3 3 + - 1/700 y z + 1/700 x z + --- y + --- z + 1/300 x y - 1/300 y z + 525 525 + + 3 3 137 2 2 2 2 + + 1/300 x z + 1/300 x z - ---- x z + 1/980 y z + 1/980 x z + 5250 + + 3 2 23 2 3 2 2 + - 1/300 y z - 1/700 y z - ---- - 1/700 x z + 1/300 x y + 1/980 x y + 6125 + + 83 2 83 2 83 2 3 3 3 4 + + ---- y + ---- x + ---- z + 1/150 x - 1/150 y - 1/150 z - 1/150 z + 3675 3675 3675 + + 4 4 2 3 + - 1/150 x - 1/150 y , COEFF(0, 1, 1) = - 1/350 x y - 1/300 y z + + 2 2 2 2 2 2 + - 1/350 x z + 1/490 x y - 1/700 x y z - 1/700 y z - 1/700 y z + + 57 2 272 4 3 3 37 289 + - --- x + ---- - 1/150 y - 1/150 y - 1/300 y z + ---- y + ----- y z + 980 6125 1050 10500 + + 151 2 2 2 4 37 4 2 2 + + ---- z + 1/490 x z - 1/150 z + ---- z + 1/100 x + 1/980 y z + 7350 1050 + + 151 2 3 2 2 + + ---- y - 1/150 z , COEFF(1, 1, 1) = - 1/1400 x y z - 1/1400 x y z + 7350 + + 2 2 2 17 + - 1/700 x y - 1/1400 x y z - 1/700 x y + 1/1000 x y z + --- x + 525 + + 137 137 2 2 17 17 + + ---- x y + ---- y z - 1/700 y z - 1/700 x z + --- y + --- z + 5250 5250 525 525 + + 3 3 3 3 137 + - 1/300 x y - 1/300 y z - 1/300 x z - 1/300 x z + ---- x z + 5250 + + 2 2 2 2 3 2 23 2 + + 1/980 y z + 1/980 x z - 1/300 y z - 1/700 y z - ---- - 1/700 x z + 6125 + + 3 2 2 83 2 83 2 83 2 3 + - 1/300 x y + 1/980 x y + ---- y + ---- x + ---- z - 1/150 x + 3675 3675 3675 + + 3 3 4 4 4 + - 1/150 y - 1/150 z - 1/150 z - 1/150 x - 1/150 y , COEFF(2, 1, 1) = + + 2 2 2 2 2 + - 1/700 x y z - 1/700 x y z + 1/350 x y + 1/700 x y z - 1/350 x y + + 17 167 229 2 2 + + 1/500 x y z + ---- x + ---- x y + ----- y z - 1/700 y z - 1/350 x z + 2100 7000 10500 + + 3 3 3 3 + + 1/42 y + 1/42 z + 1/600 x y - 1/300 y z - 1/150 x z + 1/600 x z + + 167 2 2 2 2 3 173 2 + + ---- x z + 1/980 y z - 1/490 x z - 1/300 y z - ---- - 1/700 y z + 7000 6125 + + 2 3 2 2 211 2 191 2 211 2 + + 1/350 x z - 1/150 x y - 1/490 x y + ---- y + ----- x + ---- z + 7350 29400 7350 + + 3 3 3 4 4 4 + + 1/300 x - 1/150 y - 1/150 z - 1/150 z + 1/600 x - 1/150 y , + + 2 2 2 2 + COEFF(-2, 2, 1) = 1/350 x y z - 1/350 x y z + 1/175 x y + 1/350 x y z + + 2 19 47 107 2 + - 1/175 x y - 1/250 x y z + ---- x + ---- x y + ---- y z - 1/350 y z + 2100 5250 7000 + + 2 19 3 3 3 + + 1/350 x z - ---- y + 8/525 z - 1/300 x y + 1/600 y z + 1/150 x z + 2100 + + 3 107 2 2 2 2 3 + - 1/600 x z - ---- x z - 1/490 y z - 1/490 x z - 1/150 y z + 7000 + + 2 2 3 2 2 169 2 169 2 + + 1/350 y z + 1/350 x z - 1/300 x y + 1/245 x y - ----- y - ----- x + 29400 29400 + + 128 2 3 3 3 4 4 + + ---- z - 1/300 x + 1/300 y - 1/150 z - 2/125 - 1/150 z + 1/600 x + 3675 + + 4 2 2 2 + + 1/600 y , COEFF(-1, 2, 1) = 1/700 x y z - 1/700 x y z - 1/350 x y + + 2 2 167 167 + - 1/700 x y z - 1/350 x y - 1/500 x y z - 1/42 x - ---- x y + ---- y z + 7000 7000 + + 2 2 17 3 3 + - 1/350 y z + 1/700 x z + ---- y + 1/42 z + 1/150 x y + 1/600 y z + 2100 + + 3 3 229 2 2 2 2 + + 1/300 x z + 1/300 x z - ----- x z - 1/490 y z + 1/980 x z + 10500 + + 3 173 2 2 3 2 2 + - 1/150 y z - ---- + 1/350 y z - 1/700 x z - 1/600 x y - 1/490 x y + 6125 + + 191 2 211 2 211 2 3 3 3 4 + + ----- y + ---- x + ---- z + 1/150 x + 1/300 y - 1/150 z - 1/150 z + 29400 7350 7350 + + 4 4 2 2 + - 1/150 x + 1/600 y , COEFF(0, 2, 1) = - 1/350 x y z - 1/350 x z + + 187 2 2 2 47 4 3 + + ---- y z - 1/175 x y + 1/490 x z + ---- - 1/150 z + 1/300 y + 7000 6125 + + 2 2 29 3 2 + - 9/196 x - 1/350 y z + ---- y + 1/600 y z + 2/75 z + 2/75 z + 2100 + + 3 3 2 2 4 2 2 4 + - 1/150 y z - 1/150 z - 1/245 x y + 1/100 x - 1/490 y z + 1/600 y + + 2 311 2 2 2 + + 1/350 y z + ----- y , COEFF(1, 2, 1) = - 1/700 x y z + 1/700 x y z + 29400 + + 2 2 2 167 + - 1/350 x y - 1/700 x y z + 1/350 x y + 1/500 x y z + 1/42 x + ---- x y + 7000 + + 167 2 2 17 3 + + ---- y z - 1/350 y z - 1/700 x z + ---- y + 1/42 z - 1/150 x y + 7000 2100 + + 3 3 3 229 2 2 + + 1/600 y z - 1/300 x z - 1/300 x z + ----- x z - 1/490 y z + 10500 + + 2 2 3 173 2 2 3 + + 1/980 x z - 1/150 y z - ---- + 1/350 y z - 1/700 x z + 1/600 x y + 6125 + + 2 2 191 2 211 2 211 2 3 3 + - 1/490 x y + ----- y + ---- x + ---- z - 1/150 x + 1/300 y + 29400 7350 7350 + + 3 4 4 4 + - 1/150 z - 1/150 z - 1/150 x + 1/600 y , COEFF(2, 2, 1) = + + 2 2 2 2 2 + - 1/350 x y z + 1/350 x y z + 1/175 x y + 1/350 x y z + 1/175 x y + + 19 47 107 2 2 + + 1/250 x y z - ---- x - ---- x y + ---- y z - 1/350 y z - 1/350 x z + 2100 5250 7000 + + 19 3 3 3 3 + - ---- y + 8/525 z + 1/300 x y + 1/600 y z - 1/150 x z + 1/600 x z + 2100 + + 107 2 2 2 2 3 2 + + ---- x z - 1/490 y z - 1/490 x z - 1/150 y z + 1/350 y z + 7000 + + 2 3 2 2 169 2 169 2 128 2 + + 1/350 x z + 1/300 x y + 1/245 x y - ----- y - ----- x + ---- z + 29400 29400 3675 + + 3 3 3 4 4 4 + + 1/300 x + 1/300 y - 1/150 z - 2/125 - 1/150 z + 1/600 x + 1/600 y , + + 2 2 2 2 + COEFF(-2, -2, 2) = 1/175 x y z - 1/175 x y z - 1/175 x y - 1/175 x y z + + 2 11 137 137 2 + - 1/175 x y + 1/125 x y z + --- x - ---- x y + ---- y z - 1/175 y z + 420 5250 5250 + + 2 11 11 3 3 3 + - 1/175 x z + --- y - --- z + 1/300 x y - 1/300 y z - 1/300 x z + 420 420 + + 3 137 2 2 2 2 3 + - 1/300 x z + ---- x z + 1/245 y z + 1/245 x z - 1/300 y z + 5250 + + 2 202 2 3 2 2 529 2 + + 1/175 y z + ---- + 1/175 x z + 1/300 x y + 1/245 x y - ----- y + 6125 29400 + + 529 2 529 2 3 3 3 4 + - ----- x - ----- z - 1/300 x - 1/300 y + 1/300 z + 1/600 z + 29400 29400 + + 4 4 2 2 + + 1/600 x + 1/600 y , COEFF(-1, -2, 2) = 1/350 x y z - 1/350 x y z + + 2 2 2 + + 1/350 x y + 1/350 x y z - 1/350 x y + 1/250 x y z - 8/525 x + + 107 47 2 2 19 19 + + ---- x y + ---- y z - 1/175 y z - 1/350 x z + ---- y - ---- z + 7000 5250 2100 2100 + + 3 3 3 3 107 + - 1/150 x y - 1/300 y z - 1/600 x z + 1/150 x z - ---- x z + 7000 + + 2 2 2 2 3 2 2 + + 1/245 y z - 1/490 x z - 1/300 y z + 1/175 y z - 1/350 x z + + 3 2 2 169 2 128 2 169 2 3 + + 1/600 x y - 1/490 x y - ----- y + ---- x - ----- z + 1/150 x + 29400 3675 29400 + + 3 3 4 4 4 + - 1/300 y + 1/300 z - 2/125 + 1/600 z - 1/150 x + 1/600 y , + + 3 4 2 2 2 + COEFF(0, -2, 2) = 1/300 y + 1/300 z + 1/100 x - 1/600 y - 1/245 x z + + 3 2 3 47 4 2 2 + - 1/300 y z - 1/175 x z - 1/300 y z + ---- + 1/600 y + 1/245 y z + 6125 + + 2 2 33 2 17 4 2 + - 1/245 x y - --- x + ---- y z + 1/600 z - 1/300 z + 1/175 x y z + 980 5250 + + 2 2 3 2 2 + - 1/600 z + 1/175 y z - 1/300 y + 1/175 x y - 1/175 y z , + + 2 2 2 2 + COEFF(1, -2, 2) = - 1/350 x y z + 1/350 x y z + 1/350 x y + 1/350 x y z + + 2 107 47 2 + + 1/350 x y - 1/250 x y z + 8/525 x - ---- x y + ---- y z - 1/175 y z + 7000 5250 + + 2 19 19 3 3 3 + + 1/350 x z + ---- y - ---- z + 1/150 x y - 1/300 y z + 1/600 x z + 2100 2100 + + 3 107 2 2 2 2 3 + - 1/150 x z + ---- x z + 1/245 y z - 1/490 x z - 1/300 y z + 7000 + + 2 2 3 2 2 169 2 128 2 + + 1/175 y z - 1/350 x z - 1/600 x y - 1/490 x y - ----- y + ---- x + 29400 3675 + + 169 2 3 3 3 4 4 + - ----- z - 1/150 x - 1/300 y + 1/300 z - 2/125 + 1/600 z - 1/150 x + 29400 + + 4 2 2 2 + + 1/600 y , COEFF(2, -2, 2) = - 1/175 x y z + 1/175 x y z - 1/175 x y + + 2 2 11 137 137 + - 1/175 x y z + 1/175 x y - 1/125 x y z - --- x + ---- x y + ---- y z + 420 5250 5250 + + 2 2 11 11 3 3 + - 1/175 y z + 1/175 x z + --- y - --- z - 1/300 x y - 1/300 y z + 420 420 + + 3 3 137 2 2 2 2 + + 1/300 x z + 1/300 x z - ---- x z + 1/245 y z + 1/245 x z + 5250 + + 3 2 202 2 3 2 2 + - 1/300 y z + 1/175 y z + ---- + 1/175 x z - 1/300 x y + 1/245 x y + 6125 + + 529 2 529 2 529 2 3 3 3 + - ----- y - ----- x - ----- z + 1/300 x - 1/300 y + 1/300 z + 29400 29400 29400 + + 4 4 4 2 + + 1/600 z + 1/600 x + 1/600 y , COEFF(-2, -1, 2) = 1/350 x y z + + 2 2 2 2 + + 1/350 x y z - 1/350 x y - 1/350 x y z + 1/350 x y + 1/250 x y z + + 19 107 107 2 2 + + ---- x + ---- x y - ---- y z - 1/350 y z - 1/175 x z - 8/525 y + 2100 7000 7000 + + 19 3 3 3 3 47 + - ---- z + 1/600 x y + 1/150 y z - 1/300 x z - 1/300 x z + ---- x z + 2100 5250 + + 2 2 2 2 3 2 2 + - 1/490 y z + 1/245 x z - 1/600 y z - 1/350 y z + 1/175 x z + + 3 2 2 128 2 169 2 169 2 3 + - 1/150 x y - 1/490 x y + ---- y - ----- x - ----- z - 1/300 x + 3675 29400 29400 + + 3 3 4 4 4 + + 1/150 y + 1/300 z - 2/125 + 1/600 z + 1/600 x - 1/150 y , + + 2 2 2 2 + COEFF(-1, -1, 2) = 1/700 x y z + 1/700 x y z + 1/700 x y + 1/700 x y z + + 2 229 167 2 + + 1/700 x y + 1/500 x y z - 1/42 x + ----- x y - ---- y z - 1/350 y z + 10500 7000 + + 2 17 3 3 3 + - 1/350 x z - 1/42 y + ---- z - 1/300 x y + 1/150 y z - 1/600 x z + 2100 + + 3 167 2 2 2 2 3 173 + + 1/150 x z - ---- x z - 1/490 y z - 1/490 x z - 1/600 y z - ---- + 7000 6125 + + 2 2 3 2 2 211 2 211 2 + - 1/350 y z - 1/350 x z - 1/300 x y + 1/980 x y + ---- y + ---- x + 7350 7350 + + 191 2 3 3 3 4 4 + + ----- z + 1/150 x + 1/150 y + 1/300 z + 1/600 z - 1/150 x + 29400 + + 4 3 29 4 3 + - 1/150 y , COEFF(0, -1, 2) = 1/300 z + ---- z - 1/150 y + 1/150 y + 2100 + + 187 311 2 47 2 3 4 + - ---- y z + ----- z + ---- + 2/75 y - 1/600 y z + 1/100 x + 7000 29400 6125 + + 2 2 2 2 2 + - 1/350 y z + 1/350 x y z - 2/75 y + 1/350 x y + 1/490 x y + + 2 2 2 2 4 2 2 + - 1/175 x z - 1/350 y z - 1/490 y z + 1/600 z - 1/245 x z + + 2 3 2 2 + - 9/196 x + 1/150 y z, COEFF(1, -1, 2) = - 1/700 x y z - 1/700 x y z + + 2 2 2 + + 1/700 x y + 1/700 x y z - 1/700 x y - 1/500 x y z + 1/42 x + + 229 167 2 2 17 + - ----- x y - ---- y z - 1/350 y z + 1/350 x z - 1/42 y + ---- z + 10500 7000 2100 + + 3 3 3 3 167 + + 1/300 x y + 1/150 y z + 1/600 x z - 1/150 x z + ---- x z + 7000 + + 2 2 2 2 3 173 2 2 + - 1/490 y z - 1/490 x z - 1/600 y z - ---- - 1/350 y z - 1/350 x z + 6125 + + 3 2 2 211 2 211 2 191 2 3 + + 1/300 x y + 1/980 x y + ---- y + ---- x + ----- z - 1/150 x + 7350 7350 29400 + + 3 3 4 4 4 + + 1/150 y + 1/300 z + 1/600 z - 1/150 x - 1/150 y , COEFF(2, -1, 2) = + + 2 2 2 2 2 + - 1/350 x y z - 1/350 x y z - 1/350 x y - 1/350 x y z - 1/350 x y + + 19 107 107 2 2 + - 1/250 x y z - ---- x - ---- x y - ---- y z - 1/350 y z + 1/175 x z + 2100 7000 7000 + + 19 3 3 3 3 + - 8/525 y - ---- z - 1/600 x y + 1/150 y z + 1/300 x z + 1/300 x z + 2100 + + 47 2 2 2 2 3 2 + - ---- x z - 1/490 y z + 1/245 x z - 1/600 y z - 1/350 y z + 5250 + + 2 3 2 2 128 2 169 2 169 2 + + 1/175 x z + 1/150 x y - 1/490 x y + ---- y - ----- x - ----- z + 3675 29400 29400 + + 3 3 3 4 4 4 + + 1/300 x + 1/150 y + 1/300 z - 2/125 + 1/600 z + 1/600 x - 1/150 y , + + 2 17 2 2 33 2 + COEFF(-2, 0, 2) = - 1/175 x z + ---- x z - 1/245 x y - --- y + 5250 980 + + 3 3 2 3 4 + - 1/300 x z + 1/300 z + 1/175 x z - 1/300 x + 1/600 x + 1/300 x + + 3 2 47 2 2 2 + - 1/300 x z - 1/600 x + ---- + 1/175 x y + 1/175 x y z - 1/600 z + 6125 + + 2 2 2 2 4 2 4 + + 1/245 x z - 1/300 z - 1/245 y z + 1/100 y - 1/175 y z + 1/600 z , + + 2 3 2 2 2 311 2 + COEFF(-1, 0, 2) = 1/350 x y + 1/150 x + 2/75 x - 1/490 x z + ----- z + 29400 + + 29 47 4 4 2 2 + + ---- z + ---- + 1/100 y + 1/600 z - 1/350 x z + 1/350 x y z + 2100 6125 + + 2 2 2 2 2 2 4 + + 1/490 x y - 1/245 y z - 1/350 x z - 1/175 y z - 1/150 x + + 3 3 187 2 3 + + 1/150 x z + 1/300 z - ---- x z - 9/196 y - 1/600 x z - 2/75 x, + 7000 + + 292 2 2 2 2 2 3 + COEFF(0, 0, 2) = ---- - 1/245 x z - 1/245 y z - 1/175 y z + 1/300 z + 6125 + + 2 2 2 2 2 41 431 2 + - 1/20 y + 1/245 x y - 1/20 x - 1/175 x z + ---- z + ----- z + 2100 29400 + + 4 4 4 2 + + 1/100 y + 1/100 x + 1/600 z , COEFF(1, 0, 2) = - 1/350 x y + + 3 187 47 3 2 2 + - 1/150 x z + ---- x z + ---- + 1/600 x z + 1/350 x z - 1/350 x z + 7000 6125 + + 2 2 2 2 2 2 311 2 + - 1/245 y z + 1/490 x y - 1/175 y z - 1/350 x y z + ----- z + 29400 + + 4 3 3 4 2 4 + + 2/75 x - 1/150 x - 1/150 x + 1/300 z + 1/600 z - 9/196 y + 1/100 y + + 2 2 2 29 2 + + 2/75 x - 1/490 x z + ---- z, COEFF(2, 0, 2) = - 1/175 x y + 2100 + + 3 17 4 3 47 + + 1/300 x z - ---- x z + 1/100 y + 1/300 x z - 1/300 x + ---- + 5250 6125 + + 4 4 3 2 2 2 2 + + 1/600 x + 1/600 z + 1/300 x - 1/600 z - 1/245 y z - 1/175 x y z + + 2 2 3 2 33 2 2 2 + - 1/245 x y + 1/300 z + 1/175 x z - --- y + 1/175 x z - 1/600 x + 980 + + 2 2 2 2 + - 1/175 y z - 1/300 z + 1/245 x z , COEFF(-2, 1, 2) = - 1/350 x y z + + 2 2 2 2 + + 1/350 x y z + 1/350 x y + 1/350 x y z + 1/350 x y - 1/250 x y z + + 19 107 107 2 2 + + ---- x - ---- x y + ---- y z + 1/350 y z - 1/175 x z + 8/525 y + 2100 7000 7000 + + 19 3 3 3 3 47 + - ---- z - 1/600 x y - 1/150 y z - 1/300 x z - 1/300 x z + ---- x z + 2100 5250 + + 2 2 2 2 3 2 2 + - 1/490 y z + 1/245 x z + 1/600 y z - 1/350 y z + 1/175 x z + + 3 2 2 128 2 169 2 169 2 3 + + 1/150 x y - 1/490 x y + ---- y - ----- x - ----- z - 1/300 x + 3675 29400 29400 + + 3 3 4 4 4 + - 1/150 y + 1/300 z - 2/125 + 1/600 z + 1/600 x - 1/150 y , + + 2 2 2 2 + COEFF(-1, 1, 2) = - 1/700 x y z + 1/700 x y z - 1/700 x y - 1/700 x y z + + 2 229 167 2 + + 1/700 x y - 1/500 x y z - 1/42 x - ----- x y + ---- y z + 1/350 y z + 10500 7000 + + 2 17 3 3 3 + - 1/350 x z + 1/42 y + ---- z + 1/300 x y - 1/150 y z - 1/600 x z + 2100 + + 3 167 2 2 2 2 3 173 + + 1/150 x z - ---- x z - 1/490 y z - 1/490 x z + 1/600 y z - ---- + 7000 6125 + + 2 2 3 2 2 211 2 211 2 + - 1/350 y z - 1/350 x z + 1/300 x y + 1/980 x y + ---- y + ---- x + 7350 7350 + + 191 2 3 3 3 4 4 + + ----- z + 1/150 x - 1/150 y + 1/300 z + 1/600 z - 1/150 x + 29400 + + 4 3 2 187 + - 1/150 y , COEFF(0, 1, 2) = - 1/150 y + 2/75 y - 1/350 x y + ---- y z + 7000 + + 3 4 47 2 2 2 2 + + 1/300 z + 1/600 z + ---- - 1/350 x y z - 9/196 x + 1/490 x y + 6125 + + 2 2 29 4 311 2 4 3 + - 1/490 y z + ---- z - 1/150 y + ----- z + 1/100 x + 1/600 y z + 2100 29400 + + 2 2 2 2 2 2 + + 1/350 y z + 2/75 y - 1/245 x z - 1/350 y z - 1/175 x z + + 3 2 2 2 + - 1/150 y z, COEFF(1, 1, 2) = 1/700 x y z - 1/700 x y z - 1/700 x y + + 2 2 229 167 + - 1/700 x y z - 1/700 x y + 1/500 x y z + 1/42 x + ----- x y + ---- y z + 10500 7000 + + 2 2 17 3 3 + + 1/350 y z + 1/350 x z + 1/42 y + ---- z - 1/300 x y - 1/150 y z + 2100 + + 3 3 167 2 2 2 2 + + 1/600 x z - 1/150 x z + ---- x z - 1/490 y z - 1/490 x z + 7000 + + 3 173 2 2 3 2 2 + + 1/600 y z - ---- - 1/350 y z - 1/350 x z - 1/300 x y + 1/980 x y + 6125 + + 211 2 211 2 191 2 3 3 3 4 + + ---- y + ---- x + ----- z - 1/150 x - 1/150 y + 1/300 z + 1/600 z + 7350 7350 29400 + + 4 4 2 2 + - 1/150 x - 1/150 y , COEFF(2, 1, 2) = 1/350 x y z - 1/350 x y z + + 2 2 2 19 107 + + 1/350 x y + 1/350 x y z - 1/350 x y + 1/250 x y z - ---- x + ---- x y + 2100 7000 + + 107 2 2 19 3 + + ---- y z + 1/350 y z + 1/175 x z + 8/525 y - ---- z + 1/600 x y + 7000 2100 + + 3 3 3 47 2 2 + - 1/150 y z + 1/300 x z + 1/300 x z - ---- x z - 1/490 y z + 5250 + + 2 2 3 2 2 3 + + 1/245 x z + 1/600 y z - 1/350 y z + 1/175 x z - 1/150 x y + + 2 2 128 2 169 2 169 2 3 3 + - 1/490 x y + ---- y - ----- x - ----- z + 1/300 x - 1/150 y + 3675 29400 29400 + + 3 4 4 4 + + 1/300 z - 2/125 + 1/600 z + 1/600 x - 1/150 y , COEFF(-2, 2, 2) = + + 2 2 2 2 2 + - 1/175 x y z - 1/175 x y z + 1/175 x y + 1/175 x y z - 1/175 x y + + 11 137 137 2 2 + - 1/125 x y z + --- x + ---- x y - ---- y z + 1/175 y z - 1/175 x z + 420 5250 5250 + + 11 11 3 3 3 3 + - --- y - --- z - 1/300 x y + 1/300 y z - 1/300 x z - 1/300 x z + 420 420 + + 137 2 2 2 2 3 2 202 + + ---- x z + 1/245 y z + 1/245 x z + 1/300 y z + 1/175 y z + ---- + 5250 6125 + + 2 3 2 2 529 2 529 2 529 2 + + 1/175 x z - 1/300 x y + 1/245 x y - ----- y - ----- x - ----- z + 29400 29400 29400 + + 3 3 3 4 4 4 + - 1/300 x + 1/300 y + 1/300 z + 1/600 z + 1/600 x + 1/600 y , + + 2 2 2 2 + COEFF(-1, 2, 2) = - 1/350 x y z - 1/350 x y z - 1/350 x y - 1/350 x y z + + 2 107 47 2 + - 1/350 x y - 1/250 x y z - 8/525 x - ---- x y - ---- y z + 1/175 y z + 7000 5250 + + 2 19 19 3 3 3 + - 1/350 x z - ---- y - ---- z + 1/150 x y + 1/300 y z - 1/600 x z + 2100 2100 + + 3 107 2 2 2 2 3 + + 1/150 x z - ---- x z + 1/245 y z - 1/490 x z + 1/300 y z + 7000 + + 2 2 3 2 2 169 2 128 2 + + 1/175 y z - 1/350 x z - 1/600 x y - 1/490 x y - ----- y + ---- x + 29400 3675 + + 169 2 3 3 3 4 4 + - ----- z + 1/150 x + 1/300 y + 1/300 z - 2/125 + 1/600 z - 1/150 x + 29400 + + 4 2 2 3 + + 1/600 y , COEFF(0, 2, 2) = - 1/245 x y + 1/300 y z - 1/300 y + + 2 3 2 2 2 4 + - 1/175 x y + 1/300 y - 1/600 z - 1/300 z - 1/245 x z + 1/600 z + + 4 2 3 17 4 47 3 + + 1/100 x - 1/600 y + 1/300 z - ---- y z + 1/600 y + ---- + 1/300 y z + 5250 6125 + + 2 2 2 2 33 2 + - 1/175 x y z + 1/175 y z - 1/175 x z + 1/175 y z - --- x + 980 + + 2 2 2 2 2 + + 1/245 y z , COEFF(1, 2, 2) = 1/350 x y z + 1/350 x y z - 1/350 x y + + 2 2 107 47 + - 1/350 x y z + 1/350 x y + 1/250 x y z + 8/525 x + ---- x y - ---- y z + 7000 5250 + + 2 2 19 19 3 3 + + 1/175 y z + 1/350 x z - ---- y - ---- z - 1/150 x y + 1/300 y z + 2100 2100 + + 3 3 107 2 2 2 2 + + 1/600 x z - 1/150 x z + ---- x z + 1/245 y z - 1/490 x z + 7000 + + 3 2 2 3 2 2 + + 1/300 y z + 1/175 y z - 1/350 x z + 1/600 x y - 1/490 x y + + 169 2 128 2 169 2 3 3 3 + - ----- y + ---- x - ----- z - 1/150 x + 1/300 y + 1/300 z - 2/125 + 29400 3675 29400 + + 4 4 4 2 + + 1/600 z - 1/150 x + 1/600 y , COEFF(2, 2, 2) = 1/175 x y z + + 2 2 2 2 + + 1/175 x y z + 1/175 x y + 1/175 x y z + 1/175 x y + 1/125 x y z + + 11 137 137 2 2 11 11 + - --- x - ---- x y - ---- y z + 1/175 y z + 1/175 x z - --- y - --- z + 420 5250 5250 420 420 + + 3 3 3 3 137 + + 1/300 x y + 1/300 y z + 1/300 x z + 1/300 x z - ---- x z + 5250 + + 2 2 2 2 3 2 202 2 + + 1/245 y z + 1/245 x z + 1/300 y z + 1/175 y z + ---- + 1/175 x z + 6125 + + 3 2 2 529 2 529 2 529 2 3 + + 1/300 x y + 1/245 x y - ----- y - ----- x - ----- z + 1/300 x + 29400 29400 29400 + + 3 3 4 4 4 + + 1/300 y + 1/300 z + 1/600 z + 1/600 x + 1/600 y ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-I.compute.c"); +bytes used=748409820, alloc=7076592, time=77.87 +bytes used=749410248, alloc=7076592, time=77.95 +bytes used=750410436, alloc=7076592, time=78.01 +bytes used=751410816, alloc=7076592, time=78.08 +bytes used=752411484, alloc=7076592, time=78.15 +bytes 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DATA(-1, 2, -1) + + 19 + + 1/350 x y z DATA(1, 2, -1) + ---- DATA(-2, -2, 1) + 2100 + + - 1/175 x y z DATA(0, 1, 2) + 2/175 x y z DATA(0, -2, 2) + + - 1/175 x y z DATA(0, -2, -1) - 2/175 x y z DATA(2, 2, -2) + + + 1/1000 y z DATA(1, -1, -1) + 1/175 x y z DATA(1, 2, -2) + + - 1/350 x y z DATA(-1, -2, -1) + 1/42 DATA(1, -2, 1) + + - 1/175 x y z DATA(-2, -2, 1) - 1/1000 y z DATA(-1, -1, -1) + + - 2/175 x y z DATA(-2, 2, -2) + 1/350 x y z DATA(1, -2, 1) + + - 1/175 x y z DATA(0, 2, 1) + 1/175 x y z DATA(-2, 2, 1) + + + 1/350 x y z DATA(1, 1, -2) - 1/175 x y z DATA(2, 1, -2) + + + 2/75 DATA(1, -2, 0) + 1/350 x y z DATA(-1, 1, -2) + + + 1/350 x y z DATA(-2, 1, 1) + 1/350 x y z DATA(0, -1, 1) + + - 1/350 x y z DATA(-2, -1, 1) + 1/350 x y z DATA(-1, -2, 1) + + 29 + - 1/700 x y z DATA(1, 1, 1) + ---- DATA(2, 0, -1) - 1/42 DATA(-1, -2, 1) + 2100 + + + 1/350 x y z DATA(2, -1, -1) - 1/175 x y z DATA(2, -2, 1) + + + 1/350 x y z DATA(0, 1, -1) - 2/175 x y z DATA(-2, -2, 2) + + - 1/175 x y z DATA(2, 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z DATA(2, -2, 2) - 1/175 x y z DATA(-2, 2, -1) + + 29 + - ---- DATA(-2, -1, 0) + 2/175 x y z DATA(2, 2, 2) + 4/75 x DATA(1, 2, 0) + 2100 + + - 1/350 x y z DATA(1, -2, -1) - 1/350 x y z DATA(-2, 1, -1) + + + 1/175 x y z DATA(2, 1, 2) + 1/175 x y z DATA(2, -2, -1) + + 191 + + 1/350 x y z DATA(-2, -1, -1) + ----- x DATA(-2, 1, 1) + 14700 + + 166 211 + + ---- x DATA(1, 1, 1) + 2/75 DATA(1, 0, 2) + ---- x DATA(-1, 2, -1) + 3675 3675 + + 191 169 211 + + ----- x DATA(2, 1, -1) - ----- x DATA(2, 2, -1) + ---- x DATA(1, 2, -1) + 14700 14700 3675 + + 211 + + ---- x DATA(-1, -1, 2) - 1/700 x y z DATA(-1, -1, -1) + 3675 + + 211 37 529 + + ---- x DATA(1, 2, 1) - ---- DATA(-1, 0, -1) - ----- x DATA(2, 2, -2) + 3675 1050 14700 + + 191 211 + + ----- x DATA(2, -1, 1) + ---- x DATA(-1, 2, 1) + 14700 3675 + + 169 211 256 + - ----- x DATA(-2, -2, -1) + ---- x DATA(1, 1, -2) + ---- x DATA(1, 2, -2) + 14700 3675 3675 + + 311 529 + + ----- x DATA(2, -1, 0) - ----- x DATA(-2, 2, -2) + 14700 14700 + + 169 17 + - ----- x DATA(-2, 2, 1) + ---- DATA(2, -1, -1) + 4/105 DATA(1, 0, 0) + 14700 2100 + + 37 37 17 + + ---- DATA(1, 1, 0) + ---- DATA(1, 0, 1) + --- DATA(1, 1, 1) + 1050 1050 525 + + - 1/300 x DATA(2, 2, 0) + 1/175 x z DATA(-2, -1, 1) + + - 1/175 x z DATA(2, -1, -1) + 1/175 x z DATA(2, -2, 1) + + 2 + + 1/175 x z DATA(-2, -2, 1) - 1/350 y z DATA(-1, 2, 2) + + 2 + - 1/175 x z DATA(2, 0, -1) - 1/175 y z DATA(2, -2, 2) + + - 1/350 x z DATA(1, -2, 1) - 1/175 x z DATA(0, 2, 1) + + 2 + - 1/350 x z DATA(-1, -2, 1) + 1/700 y z DATA(-2, 1, -1) + + - 1/175 x z DATA(2, 2, -1) - 1/175 x z DATA(2, 1, -1) + + + 1/350 x z DATA(-1, 2, -1) - 1/350 x z DATA(1, 1, 1) + + 2 + + 1/175 x z DATA(-2, 1, 1) + 1/700 y z DATA(1, -1, 0) + + 2 + + 1/175 x z DATA(-1, 1, -2) + 1/350 y z DATA(2, 1, 2) + + - 2/175 x z DATA(2, 1, -2) + 1/175 x y z DATA(2, -1, -2) + + 2 + + 1/175 x z DATA(2, 2, 1) + 1/700 y z DATA(1, -2, -1) + + + 1/175 x z DATA(-1, 2, -2) + 1/175 x z DATA(1, 1, -2) + + + 1/175 x z DATA(-2, 2, 1) - 2/175 x 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DATA(0, 2, 1) + + + 1/175 x y DATA(1, -2, 1) + 1/175 x y DATA(1, -2, 0) + + 19 + + 1/300 DATA(-2, 0, -2) - ---- DATA(2, -1, -2) - 1/175 x z DATA(-2, 0, -1) + 2100 + + + 1/175 x z DATA(0, 1, -1) - 2/75 DATA(-1, 0, -2) + 2/75 DATA(1, 0, -2) + + + 2/175 x z DATA(2, 0, 2) - 1/175 x z DATA(-1, 0, 2) + + + 1/175 x z DATA(2, 0, 1) + 2/175 x z DATA(-2, 0, 2) + + + 2/175 x y DATA(0, -2, 1) + +bytes used=1233279872, alloc=7076592, time=157.39 +> coeffs_as_lc_of_data(%, posn_list_3d_size5); +bytes used=1234329228, alloc=7076592, time=157.47 +bytes used=1235452120, alloc=7076592, time=157.57 +bytes used=1236657932, alloc=7076592, time=157.66 +bytes used=1237840240, alloc=7076592, time=157.75 +bytes used=1239003288, alloc=7076592, time=157.85 +bytes used=1240144484, alloc=7076592, time=157.95 +bytes used=1241268368, alloc=7076592, time=158.04 +bytes used=1242374732, alloc=7207640, time=158.14 +bytes used=1243458624, alloc=7338688, time=158.24 +bytes used=1244523576, alloc=7469736, time=158.34 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alloc=11139080, time=160.67 +bytes used=1266313364, alloc=11532224, time=160.80 +bytes used=1267363516, alloc=11990892, time=160.95 +bytes used=1268366544, alloc=12318512, time=161.10 +bytes used=1269386424, alloc=12777180, time=161.25 +bytes used=1270418808, alloc=13235848, time=161.41 +bytes used=1271419096, alloc=13628992, time=161.56 +bytes used=1272460368, alloc=14218708, time=161.65 +bytes used=1273507928, alloc=14218708, time=161.72 +bytes used=1274555320, alloc=14218708, time=161.79 +bytes used=1275602968, alloc=14218708, time=161.86 +bytes used=1276650472, alloc=14218708, time=161.93 +bytes used=1277698032, alloc=14218708, time=162.00 + 2 3 2 +[COEFF(-2, -2, -2) = - 1/125 y z - 1/175 y + 1/300 y - 2/175 x y + 1/100 x y + + 2 3 2 137 529 + + 2/245 x z - 2/175 x z + 1/300 z - 1/175 z - ---- z - ----- x + 5250 14700 + + 2 2 2 2 + - 1/100 x + 2/245 x y + 1/175 y z + 2/175 x y z + 1/100 x z + + 2 11 3 137 + + 1/175 y z + --- + 1/150 x - ---- y, COEFF(-1, -2, -2) = - 1/250 y z + 420 5250 + + 3 2 3 2 256 + - 2/75 x + 1/175 x z - 1/245 x y + 1/600 z - 1/350 y + ---- x + 3675 + + 2 2 107 2 2 + - 1/245 x z - 1/50 x z + ---- z + 1/175 x y + 1/350 y z + 1/50 x + 7000 + + 3 107 2 2 + + 1/600 y + ---- y - 1/175 x y z - 8/525 + 1/350 y z - 1/50 x y + 7000 + + 2 2 + - 1/350 z , COEFF(0, -2, -2) = 2/175 x z - 2/245 x y + 2/175 x y + + 3 33 2 2 + + 1/25 x - --- x - 2/175 x y z - 2/245 x z , COEFF(1, -2, -2) = 1/50 x z + 490 + + 107 3 256 2 2 + - ---- z - 1/600 y + ---- x - 1/350 y z + 1/50 x y - 1/175 x y z + 7000 3675 + + 3 2 2 2 2 + - 1/600 z - 1/50 x + 1/175 x y + 1/350 z - 1/245 x z + 1/350 y + + 3 2 2 + + 8/525 - 2/75 x - 1/245 x y + 1/175 x z + 1/250 y z - 1/350 y z + + 107 2 2 2 + - ---- y, COEFF(2, -2, -2) = - 1/175 y z - 1/100 x z + 2/245 x y + 7000 + + 529 2 11 2 137 2 + - ----- x + 1/100 x - --- + 2/245 x z - 2/175 x y + ---- y - 1/175 y z + 14700 420 5250 + + 2 3 2 137 2 + + 2/175 x y z - 1/100 x y - 1/300 z + 1/175 z + ---- z + 1/175 y + 5250 + + 3 3 + + 1/150 x - 1/300 y + 1/125 y z - 2/175 x z, COEFF(-2, -1, -2) = + + 107 2 169 2 2 + - 2/175 x z + ---- y + 1/350 y z - ----- x + 1/350 y - 1/100 x + 7000 14700 + + 3 2 19 2 47 2 + - 1/150 y + 2/245 x z + ---- + 1/100 x z - ---- z - 1/350 y z + 2100 5250 + + 2 3 3 + - 1/175 x y - 1/245 x y + 1/175 x y z - 1/250 y z + 1/150 x + 1/300 z + + 2 2 2 + + 1/200 x y - 1/175 z , COEFF(-1, -1, -2) = 1/350 x y - 1/350 z + + 3 3 2 2 + - 1/500 y z + 1/600 z - 2/75 x + 1/700 y z + 1/490 x y + 1/175 x z + + 2 2 167 229 2 3 211 + - 1/50 x z + 1/700 y + ---- z + ----- y - 1/245 x z - 1/300 y + ---- x + 7000 10500 3675 + + 2 2 2 + - 1/42 - 1/350 x y z + 1/50 x - 1/700 y z - 1/100 x y, COEFF(0, -1, -2) + + 3 2 2 + = 1/25 x + 1/245 x y + 1/175 x y - 2/245 x z + 2/175 x z - 9/98 x + + 2 + - 1/175 x y z, COEFF(1, -1, -2) = 1/500 y z + 1/175 x z - 1/245 x z + + 2 3 2 2 211 + + 1/490 x y - 1/600 z - 1/700 y - 1/50 x + ---- x + 1/350 x y + 3675 + + 2 2 3 2 + - 1/700 y z - 1/350 x y z + 1/350 z + 1/300 y + 1/42 + 1/700 y z + + 2 229 167 3 2 + + 1/100 x y - ----- y - ---- z - 2/75 x + 1/50 x z, COEFF(2, -1, -2) = + 10500 7000 + + 2 2 3 3 + - 1/350 y z + 1/350 y z + 1/250 y z - 2/175 x z + 1/150 y - 1/300 z + + 2 47 3 107 2 2 + - 1/245 x y + ---- z + 1/150 x - ---- y - 1/100 x z - 1/200 x y + 5250 7000 + + 169 2 2 2 + - ----- x + 1/175 x y z - 1/350 y - 1/175 x y + 2/245 x z + 1/175 z + 14700 + + 2 19 17 2 + + 1/100 x - ----, COEFF(-2, 0, -2) = 1/300 - ---- z + 2/245 x z + 2100 5250 + + 3 2 2 2 + + 1/150 x - 1/300 x - 1/175 y z - 2/175 x z - 2/245 x y + 1/175 y + + 3 2 2 2 + + 1/300 z - 1/100 x + 1/100 x z - 1/175 z , COEFF(-1, 0, -2) = + + 2 3 2 3 187 2 + - 1/350 z - 2/75 x - 1/350 y z + 1/600 z - 2/75 + ---- z + 1/350 y + 7000 + + 2 2 2 2 + + 1/245 x y - 1/245 x z + 1/175 x z - 1/50 x z + 4/75 x + 1/50 x , + + 3 2 2 + COEFF(0, 0, -2) = - 1/10 x + 1/25 x + 2/175 x z - 2/245 x z + 2/245 x y , + + 2 2 2 + COEFF(1, 0, -2) = - 1/50 x + 1/175 x z + 1/50 x z + 2/75 + 1/350 y z + + 3 187 2 2 2 3 + - 1/600 z - ---- z + 4/75 x + 1/245 x y + 1/350 z - 1/350 y - 2/75 x + 7000 + + 2 2 3 2 + - 1/245 x z , COEFF(2, 0, -2) = - 1/100 x z - 1/300 z + 1/175 y z + + 2 2 17 2 2 + + 2/245 x z - 1/175 y - 1/300 - 2/175 x z + ---- z + 1/100 x + 1/175 z + 5250 + + 2 3 3 2 + - 1/300 x - 2/245 x y + 1/150 x , COEFF(-2, 1, -2) = 1/300 z - 1/175 z + + 2 2 107 2 + - 1/100 x + 1/250 y z + 1/175 x y - 1/200 x y - ---- y - 1/245 x y + 7000 + + 19 3 2 2 + + ---- - 1/175 x y z - 2/175 x z + 1/150 y + 1/350 y - 1/350 y z + 2100 + + 169 2 47 2 2 3 + - ----- x + 2/245 x z - ---- z + 1/100 x z - 1/350 y z + 1/150 x , + 14700 5250 + + 2 2 229 + COEFF(-1, 1, -2) = - 1/245 x z + 1/490 x y + 1/175 x z - ----- y + 10500 + + 2 2 2 3 3 + - 1/50 x z + 1/100 x y - 1/700 y z - 1/350 x y + 1/300 y - 2/75 x + + 3 167 2 2 + + 1/600 z + ---- z + 1/50 x - 1/42 + 1/700 y + 1/500 y z + 1/350 x y z + 7000 + + 2 2 211 2 + - 1/700 y z - 1/350 z + ---- x, COEFF(0, 1, -2) = 1/245 x y + 3675 + + 3 2 + + 1/175 x y z - 1/175 x y - 9/98 x + 1/25 x + 2/175 x z - 2/245 x z , + + 3 2 2 3 + COEFF(1, 1, -2) = - 1/600 z + 1/42 + 1/50 x z - 1/700 y - 1/300 y + + 229 2 2 2 + - 1/350 x y + 1/350 x y z + ----- y - 1/100 x y + 1/700 y z - 1/245 x z + 10500 + + 2 2 3 2 167 + + 1/490 x y + 1/175 x z + 1/350 z - 2/75 x - 1/50 x - ---- z + 7000 + + 2 211 19 2 + + 1/700 y z + ---- x - 1/500 y z, COEFF(2, 1, -2) = - ---- - 1/100 x z + 3675 2100 + + 2 3 2 2 2 + - 1/350 y + 1/150 x + 1/350 y z + 1/200 x y - 1/175 x y z + 1/175 z + + 107 3 47 2 3 + + ---- y + 1/175 x y - 1/300 z + ---- z - 2/175 x z + 1/100 x - 1/150 y + 7000 5250 + + 2 2 2 169 + + 1/350 y z + 2/245 x z - 1/245 x y - 1/250 y z - ----- x, + 14700 + + 3 2 3 2 + COEFF(-2, 2, -2) = 1/150 x - 1/175 y z - 1/300 y + 2/245 x y + + 2 3 137 2 2 + + 1/100 x z + 1/300 z - ---- z + 2/245 x z - 2/175 x y z - 1/175 y + 5250 + + 11 137 2 2 + + --- + 2/175 x y + ---- y - 1/175 z - 1/100 x y - 2/175 x z + 420 5250 + + 2 529 2 2 + + 1/175 y z - ----- x + 1/125 y z - 1/100 x , COEFF(-1, 2, -2) = 1/50 x + 14700 + + 3 2 2 2 3 + + 1/600 z - 1/350 z - 1/350 y - 1/175 x y - 1/50 x z - 2/75 x + + 2 107 2 2 + + 1/50 x y + 1/175 x z + ---- z + 1/250 y z - 1/245 x z - 1/245 x y + 7000 + + 256 3 2 2 + + ---- x - 1/600 y + 1/175 x y z + 1/350 y z - 1/350 y z - 8/525 + 3675 + + 107 2 + - ---- y, COEFF(0, 2, -2) = 2/175 x y z - 2/175 x y - 2/245 x y + 7000 + + 2 3 33 3 + - 2/245 x z + 2/175 x z + 1/25 x - --- x, COEFF(1, 2, -2) = - 1/600 z + 490 + + 2 107 2 3 256 2 + + 1/50 x z + 8/525 - ---- z + 1/350 y z - 2/75 x + ---- x + 1/350 z + 7000 3675 + + 2 2 2 + - 1/175 x y - 1/50 x + 1/175 x y z + 1/350 y - 1/245 x z - 1/250 y z + + 3 2 107 2 2 + + 1/175 x z + 1/600 y - 1/245 x y + ---- y - 1/50 x y - 1/350 y z, + 7000 + + 3 2 3 3 11 + COEFF(2, 2, -2) = 1/150 x + 2/245 x y + 1/300 y - 1/300 z - --- + 420 + + 2 137 2 2 + + 1/175 z - 2/175 x z + ---- z + 1/175 y + 1/100 x y - 2/175 x y z + 5250 + + 2 2 137 2 + - 1/125 y z + 2/245 x z + 1/175 y z - ---- y + 2/175 x y + 1/100 x + 5250 + + 529 2 2 47 + - ----- x - 1/175 y z - 1/100 x z, COEFF(-2, -2, -1) = - ---- y + 14700 5250 + + 2 2 169 2 + - 1/245 x z - 1/175 x z + 1/175 x y z + 1/350 y z - ----- x - 1/175 y + 14700 + + 2 3 2 2 2 2 + + 1/350 z + 1/150 x - 1/100 x + 1/100 x y + 2/245 x y + 1/200 x z + + 2 107 19 3 3 + - 1/350 y z - 2/175 x y + ---- z + ---- - 1/250 y z - 1/150 z + 1/300 y + 7000 2100 + + 211 2 229 2 2 + , COEFF(-1, -2, -1) = ---- x + 1/700 y z + ----- z + 1/50 x - 1/350 y + 3675 10500 + + 2 2 3 3 + - 1/50 x y + 1/490 x z - 1/42 + 1/350 x z - 1/300 z + 1/600 y + + 3 2 2 + - 2/75 x - 1/500 y z + 1/175 x y - 1/100 x z - 1/700 y z - 1/350 x y z + + 167 2 2 + + ---- y + 1/700 z - 1/245 x y , COEFF(0, -2, -1) = 2/175 x y + 7000 + + 2 2 3 + - 1/175 x y z - 2/245 x y + 1/245 x z + 1/175 x z - 9/98 x + 1/25 x , + + 2 2 + COEFF(1, -2, -1) = - 1/350 x y z - 1/700 z + 1/42 - 1/245 x y + + 2 229 2 2 + + 1/490 x z - ----- z - 1/50 x + 1/700 y z + 1/500 y z + 1/350 x z + 10500 + + 167 3 2 2 2 + - ---- y + 1/175 x y - 1/600 y + 1/100 x z - 1/700 y z + 1/50 x y + 7000 + + 2 3 3 211 2 + + 1/350 y + 1/300 z - 2/75 x + ---- x, COEFF(2, -2, -1) = 2/245 x y + 3675 + + 2 2 3 2 + - 1/245 x z + 1/175 x y z + 1/350 y z + 1/150 z + 1/100 x - 2/175 x y + + 47 2 169 3 107 + + ---- y - 1/350 y z - ----- x + 1/250 y z + 1/150 x - ---- z + 5250 14700 7000 + + 2 3 2 19 2 2 + - 1/100 x y - 1/300 y + 1/175 y - ---- - 1/350 z - 1/200 x z + 2100 + + 2 167 2 + - 1/175 x z, COEFF(-2, -1, -1) = - 1/100 x + ---- z + 1/200 x z + 7000 + + 2 2 167 3 + - 1/500 y z - 1/700 y z + 1/350 z - 1/175 x y + ---- y - 1/150 y + 7000 + + 2 191 3 17 2 + - 1/700 y z + 1/350 x y z + ----- x + 1/150 x - ---- + 1/200 x y + 14700 2100 + + 2 2 3 2 + - 1/175 x z + 1/350 y - 1/245 x z - 1/150 z - 1/245 x y , + + 2 17 137 3 + COEFF(-1, -1, -1) = - 1/1400 y z - --- - 1/1000 y z + ---- y - 1/300 z + 525 5250 + + 2 2 2 2 + - 1/700 x y z + 1/50 x + 1/700 z + 1/490 x y + 1/350 x y - 1/1400 y z + + 2 3 3 2 137 + - 1/100 x y - 1/300 y - 2/75 x - 1/100 x z + ---- z + 1/350 x z + 5250 + + 166 2 2 + + ---- x + 1/490 x z + 1/700 y , COEFF(0, -1, -1) = 1/175 x z + 1/175 x y + 3675 + + 57 3 2 2 + - --- x + 1/25 x + 1/245 x z + 1/245 x y - 1/350 x y z, + 490 + + 3 2 3 + COEFF(1, -1, -1) = 1/300 y + 1/350 x z - 1/700 z + 1/1000 y z + 1/300 z + + 2 2 2 2 2 + - 1/50 x + 1/490 x z + 1/490 x y + 1/100 x z + 1/1400 y z + 1/350 x y + + 3 166 2 2 17 137 137 + - 2/75 x + ---- x + 1/100 x y - 1/700 y + --- - ---- y - ---- z + 3675 525 5250 5250 + + 2 191 + - 1/700 x y z + 1/1400 y z, COEFF(2, -1, -1) = - 1/175 x z + ----- x + 14700 + + 2 2 2 2 + - 1/245 x y - 1/175 x y - 1/350 y - 1/200 x y + 1/500 y z + 1/100 x + + 167 3 3 2 2 + - ---- y + 1/150 z + 1/150 x - 1/350 z + 1/350 x y z + 1/700 y z + 7000 + + 2 167 2 2 17 3 + - 1/245 x z - ---- z + 1/700 y z - 1/200 x z + ---- + 1/150 y , + 7000 2100 + + 311 2 2 2 2 + COEFF(-2, 0, -1) = ----- x + 1/175 y + 1/200 x z - 1/245 x z + 1/350 z + 14700 + + 3 2 2 2 3 + + 1/150 x - 1/350 y z - 1/175 x z - 1/100 x - 2/245 x y - 1/150 z + + 187 29 2 2 + + ---- z - ----, COEFF(-1, 0, -1) = 1/350 x z - 1/100 x z + 1/700 z + 7000 2100 + + 2 37 2 151 2 289 2 + + 1/490 x z - ---- - 1/700 y z + ---- x + 1/245 x y + ----- z + 1/50 x + 1050 3675 10500 + + 3 3 2 + - 2/75 x - 1/300 z + 1/350 y , + + 2 3 2 61 + COEFF(0, 0, -1) = 2/245 x y + 1/25 x + 1/245 x z - --- x + 1/175 x z, + 490 + + 3 2 289 2 3 + COEFF(1, 0, -1) = 1/300 z - 1/50 x - ----- z + 1/490 x z - 2/75 x + 10500 + + 37 2 2 2 2 + + 1/350 x z + ---- + 1/245 x y - 1/350 y + 1/100 x z + 1/700 y z + 1050 + + 2 151 2 3 + - 1/700 z + ---- x, COEFF(2, 0, -1) = - 2/245 x y - 1/175 x z + 1/150 x + 3675 + + 2 2 2 187 29 2 + + 1/100 x - 1/175 y - 1/245 x z - ---- z + ---- - 1/200 x z + 7000 2100 + + 2 2 3 311 167 + + 1/350 y z - 1/350 z + 1/150 z + ----- x, COEFF(-2, 1, -1) = ---- z + 14700 7000 + + 2 3 2 2 + - 1/245 x z + 1/150 y - 1/175 x z + 1/700 y z - 1/700 y z + + 2 17 2 3 191 2 + - 1/350 x y z - 1/100 x - ---- + 1/350 y + 1/150 x + ----- x + 1/350 z + 2100 14700 + + 3 2 2 167 + + 1/500 y z - 1/150 z + 1/200 x z - 1/200 x y - ---- y + 1/175 x y + 7000 + + 2 2 2 + - 1/245 x y , COEFF(-1, 1, -1) = 1/490 x z + 1/700 z + 1/1000 y z + + 3 166 3 2 2 2 + - 2/75 x + ---- x - 1/300 z + 1/700 y - 1/100 x z + 1/490 x y + 3675 + + 3 137 2 2 + + 1/350 x z + 1/300 y + 1/700 x y z + ---- z - 1/1400 y z + 1/100 x y + 5250 + + 2 2 17 137 + + 1/50 x + 1/1400 y z - 1/350 x y - --- - ---- y, COEFF(0, 1, -1) = + 525 5250 + + 57 2 2 3 + - --- x + 1/245 x z + 1/245 x y + 1/25 x + 1/175 x z + 1/350 x y z + 490 + + 2 2 3 2 + - 1/175 x y, COEFF(1, 1, -1) = 1/1400 y z - 1/700 y - 1/300 y - 1/50 x + + 2 2 2 17 2 + + 1/700 x y z + 1/100 x z - 1/100 x y + 1/490 x z + --- - 1/700 z + 525 + + 2 3 166 137 + + 1/490 x y - 2/75 x + ---- x + ---- y - 1/1000 y z + 1/350 x z + 3675 5250 + + 3 2 137 + + 1/300 z - 1/350 x y - 1/1400 y z - ---- z, COEFF(2, 1, -1) = + 5250 + + 2 2 2 2 3 2 + 1/700 y z + 1/200 x y - 1/700 y z - 1/245 x y + 1/150 x - 1/200 x z + + 2 191 167 + - 1/350 x y z - 1/350 z + ----- x - ---- z - 1/175 x z - 1/500 y z + 14700 7000 + + 3 3 2 17 167 2 + - 1/150 y + 1/150 z + 1/100 x + ---- + ---- y + 1/175 x y - 1/350 y + 2100 7000 + + 2 169 2 2 + - 1/245 x z , COEFF(-2, 2, -1) = - ----- x - 1/175 y + 1/350 z + 14700 + + 2 2 2 107 2 + + 1/350 y z - 1/100 x - 1/100 x y + ---- z - 1/175 x y z + 1/200 x z + 7000 + + 47 3 2 2 19 + + ---- y - 1/300 y - 1/245 x z + 2/245 x y + ---- - 1/175 x z + 5250 2100 + + 3 2 3 + + 1/150 x + 1/250 y z + 2/175 x y + 1/350 y z - 1/150 z , + + 2 2 2 + COEFF(-1, 2, -1) = 1/50 x - 1/42 + 1/700 y z + 1/350 x z - 1/350 y + + 2 2 2 2 229 + - 1/245 x y + 1/490 x z - 1/100 x z + 1/50 x y + 1/500 y z + ----- z + 10500 + + 211 3 167 3 + + 1/350 x y z - 1/175 x y + ---- x - 1/600 y - ---- y - 2/75 x + 3675 7000 + + 3 2 2 3 + - 1/300 z + 1/700 y z + 1/700 z , COEFF(0, 2, -1) = 1/25 x - 9/98 x + + 2 2 + - 2/175 x y + 1/175 x z - 2/245 x y + 1/175 x y z + 1/245 x z , + + 2 167 + COEFF(1, 2, -1) = - 1/700 y z + 1/350 x y z + 1/350 x z + ---- y + 7000 + + 2 2 2 3 + - 1/175 x y + 1/42 - 1/700 z + 1/100 x z - 1/50 x - 2/75 x + + 2 2 2 211 229 2 + + 1/490 x z + 1/350 y - 1/700 y z + ---- x - ----- z - 1/50 x y + 3675 10500 + + 2 3 3 + - 1/245 x y + 1/600 y - 1/500 y z + 1/300 z , COEFF(2, 2, -1) = + + 2 2 3 2 19 2 + 1/100 x y + 1/175 y + 1/150 z - 1/200 x z - ---- - 1/350 y z + 2100 + + 3 47 2 2 + + 2/175 x y + 1/150 x - ---- y + 2/245 x y - 1/245 x z - 1/175 x y z + 5250 + + 2 2 169 3 2 + - 1/175 x z + 1/100 x - 1/350 z - ----- x + 1/300 y - 1/350 y z + 14700 + + 107 17 + - 1/250 y z - ---- z, COEFF(-2, -2, 0) = - 2/175 x y - ---- y - 1/300 x + 7000 5250 + + 2 2 2 3 2 2 + - 2/245 x z - 1/175 y z + 1/100 x y + 1/300 y + 1/175 z - 1/175 y + + 3 2 2 + + 1/300 + 1/150 x - 1/100 x + 2/245 x y , COEFF(-1, -2, 0) = + + 2 2 2 2 + - 1/245 x y - 1/350 y z + 1/245 x z + 4/75 x + 1/175 x y - 1/350 y + + 2 187 3 2 2 3 + - 1/50 x y + ---- y - 2/75 x + 1/350 z + 1/50 x - 2/75 + 1/600 y , + 7000 + + 2 2 3 + COEFF(0, -2, 0) = 2/245 x z - 1/10 x + 2/175 x y - 2/245 x y + 1/25 x , + + 2 2 2 2 3 + COEFF(1, -2, 0) = - 1/50 x - 1/350 z - 1/245 x y + 1/350 y z - 1/600 y + + 2 2 2 3 187 + + 1/245 x z + 4/75 x + 1/50 x y + 1/350 y + 2/75 - 2/75 x - ---- y + 7000 + + 2 2 3 + + 1/175 x y, COEFF(2, -2, 0) = 1/100 x - 1/175 z - 1/300 y - 2/175 x y + + 17 2 2 2 3 2 + + ---- y + 1/175 y z + 2/245 x y - 2/245 x z + 1/150 x + 1/175 y + 5250 + + 2 3 2 + - 1/300 x - 1/300 - 1/100 x y, COEFF(-2, -1, 0) = - 1/150 y + 1/175 z + + 2 2 2 311 2 29 + - 1/100 x + 1/200 x y - 1/245 x y + ----- x - 1/350 y z - ---- + 14700 2100 + + 187 2 2 3 + + ---- y + 1/350 y - 1/175 x y - 2/245 x z + 1/150 x , COEFF(-1, -1, 0) + 7000 + + 2 2 2 2 2 3 + = 1/245 x z - 1/100 x y + 1/50 x + 1/490 x y + 1/700 y - 2/75 x + + 37 3 2 2 151 289 + - ---- - 1/300 y + 1/350 z - 1/700 y z + ---- x + 1/350 x y + ----- y, + 1050 3675 10500 + + 3 2 61 2 + COEFF(0, -1, 0) = 1/175 x y + 1/25 x + 1/245 x y - --- x + 2/245 x z , + 490 + + 2 37 2 2 2 + COEFF(1, -1, 0) = - 1/700 y + ---- + 1/245 x z + 1/700 y z - 1/50 x + 1050 + + 3 2 289 2 3 151 + - 2/75 x + 1/490 x y - ----- y - 1/350 z + 1/300 y + ---- x + 10500 3675 + + 2 29 2 2 + + 1/350 x y + 1/100 x y, COEFF(2, -1, 0) = ---- - 1/350 y - 1/245 x y + 2100 + + 2 3 3 311 187 + - 1/200 x y + 1/150 y + 1/150 x - 1/175 x y + ----- x - ---- y + 14700 7000 + + 2 2 2 2 41 + + 1/100 x + 1/350 y z - 1/175 z - 2/245 x z , COEFF(-2, 0, 0) = - ---- + 2100 + + 2 3 2 2 2 2 + - 2/245 x y + 1/150 x - 2/245 x z + 1/175 y - 1/100 x + 1/175 z + + 431 2 2 136 2 + + ----- x, COEFF(-1, 0, 0) = 1/245 x z + 1/350 z + ---- x + 1/350 y + 14700 3675 + + 2 2 3 + - 4/105 + 1/50 x + 1/245 x y - 2/75 x , + + 2 13 3 2 + COEFF(0, 0, 0) = 2/245 x z - -- x + 1/25 x + 2/245 x y , COEFF(1, 0, 0) + 98 + + 2 3 2 2 136 + = - 1/50 x - 2/75 x - 1/350 z + 4/105 + 1/245 x y + ---- x + 3675 + + 2 2 41 2 2 + + 1/245 x z - 1/350 y , COEFF(2, 0, 0) = ---- - 2/245 x z + 1/100 x + 2100 + + 2 3 2 2 431 + - 1/175 z + 1/150 x - 2/245 x y - 1/175 y + ----- x, COEFF(-2, 1, 0) + 14700 + + 3 2 2 2 311 + = 1/150 x - 1/245 x y + 1/175 z + 1/175 x y - 1/200 x y + ----- x + 14700 + + 2 2 2 29 187 3 2 + + 1/350 y z - 1/100 x - 2/245 x z - ---- - ---- y + 1/150 y + 1/350 y + 2100 7000 + + 2 3 2 3 2 + , COEFF(-1, 1, 0) = 1/350 z - 2/75 x + 1/700 y z + 1/300 y + 1/100 x y + + 2 37 2 2 289 151 + + 1/490 x y - 1/350 x y - ---- + 1/245 x z + 1/700 y - ----- y + ---- x + 1050 10500 3675 + + 2 + + 1/50 x , + + 61 2 3 2 + COEFF(0, 1, 0) = - --- x + 1/245 x y - 1/175 x y + 1/25 x + 2/245 x z , + 490 + + 2 2 2 2 2 + COEFF(1, 1, 0) = - 1/350 z + 1/490 x y - 1/100 x y - 1/50 x - 1/700 y + + 2 2 37 3 151 289 + + 1/245 x z - 1/700 y z + ---- - 2/75 x + ---- x - 1/350 x y + ----- y + 1050 3675 10500 + + 3 187 2 3 + - 1/300 y , COEFF(2, 1, 0) = ---- y + 1/175 x y - 1/350 y + 1/150 x + 7000 + + 2 29 2 2 2 2 + - 1/350 y z + ---- - 2/245 x z - 1/245 x y + 1/100 x + 1/200 x y + 2100 + + 3 311 2 2 2 + - 1/150 y + ----- x - 1/175 z , COEFF(-2, 2, 0) = 1/175 z + 2/245 x y + 14700 + + 2 3 2 3 + + 2/175 x y - 2/245 x z - 1/300 y - 1/100 x y + 1/150 x - 1/300 x + + 2 2 2 17 + + 1/175 y z - 1/100 x + 1/300 - 1/175 y + ---- y, COEFF(-1, 2, 0) = + 5250 + + 187 2 2 2 2 + - ---- y + 1/50 x - 1/245 x y - 1/175 x y + 1/50 x y - 1/350 y + 7000 + + 3 2 2 3 2 + - 1/600 y + 1/350 y z + 1/350 z - 2/75 x - 2/75 + 4/75 x + 1/245 x z , + + 2 2 3 + COEFF(0, 2, 0) = - 1/10 x + 2/245 x z - 2/175 x y - 2/245 x y + 1/25 x , + + 3 2 2 2 2 + COEFF(1, 2, 0) = 1/600 y - 1/50 x - 1/350 z - 1/245 x y - 1/50 x y + + 2 2 2 3 187 + + 1/350 y - 1/350 y z - 1/175 x y + 2/75 + 1/245 x z - 2/75 x + ---- y + 7000 + + 2 2 + + 4/75 x, COEFF(2, 2, 0) = - 1/300 - 1/300 x + 2/245 x y + 1/100 x + + 3 2 2 2 2 17 + + 1/150 x + 1/175 y - 2/245 x z - 1/175 z - 1/175 y z - ---- y + 5250 + + 3 2 107 + + 2/175 x y + 1/300 y + 1/100 x y, COEFF(-2, -2, 1) = - ---- z + 7000 + + 2 2 3 2 19 + - 2/175 x y - 1/200 x z - 1/175 y + 1/300 y - 1/350 y z + ---- + 2100 + + 2 2 47 2 3 + + 1/350 z - 1/100 x - ---- y + 1/250 y z + 2/245 x y + 1/150 z + 5250 + + 2 169 3 2 2 + + 1/100 x y - ----- x - 1/175 x y z + 1/150 x - 1/245 x z - 1/350 y z + 14700 + + 2 167 3 3 + + 1/175 x z, COEFF(-1, -2, 1) = 1/490 x z + ---- y - 2/75 x + 1/300 z + 7000 + + 3 2 211 2 2 + + 1/600 y + 1/100 x z - 1/350 x z + ---- x - 1/700 y z - 1/700 y z + 3675 + + 2 2 229 + + 1/175 x y + 1/700 z - 1/245 x y - ----- z + 1/500 y z + 1/350 x y z + 10500 + + 2 2 2 + - 1/350 y - 1/42 + 1/50 x - 1/50 x y, COEFF(0, -2, 1) = - 1/175 x z + + 2 3 2 + - 2/245 x y + 1/25 x + 1/175 x y z + 2/175 x y + 1/245 x z - 9/98 x, + + 3 2 2 + COEFF(1, -2, 1) = - 2/75 x + 1/50 x y - 1/350 x z + 1/700 y z + + 2 2 2 2 211 229 + - 1/100 x z + 1/700 y z + 1/490 x z - 1/700 z + ---- x + ----- z + 3675 10500 + + 2 3 2 3 + - 1/50 x + 1/350 x y z - 1/300 z - 1/245 x y - 1/600 y - 1/500 y z + + 167 2 2 + + 1/175 x y + 1/42 - ---- y + 1/350 y , COEFF(2, -2, 1) = - 1/100 x y + 7000 + + 3 107 19 2 2 + + 1/150 x + ---- z - ---- - 1/245 x z + 1/350 y z - 1/175 x y z + 7000 2100 + + 2 2 47 2 + + 1/200 x z + 1/100 x - 2/175 x y - 1/250 y z + ---- y + 1/350 y z + 5250 + + 2 169 2 3 2 + + 2/245 x y - ----- x + 1/175 x z + 1/175 y - 1/150 z - 1/350 z + 14700 + + 3 3 3 + - 1/300 y , COEFF(-2, -1, 1) = - 1/350 x y z - 1/150 y + 1/150 x + + 167 2 2 167 2 3 + + ---- y + 1/200 x y + 1/350 z - ---- z - 1/700 y z + 1/150 z + 7000 7000 + + 191 17 2 2 + + ----- x - 1/175 x y - ---- - 1/245 x z + 1/500 y z - 1/200 x z + 14700 2100 + + 2 2 2 2 + + 1/175 x z - 1/100 x + 1/350 y - 1/245 x y + 1/700 y z, + + 2 2 17 + COEFF(-1, -1, 1) = 1/490 x z + 1/350 x y + 1/700 y - 1/350 x z - --- + 525 + + 2 166 3 3 2 + + 1/50 x + ---- x - 1/300 y + 1/700 x y z + 1/300 z + 1/490 x y + 3675 + + 2 2 3 137 137 2 + - 1/1400 y z + 1/100 x z - 2/75 x - ---- z + ---- y + 1/700 z + 5250 5250 + + 2 2 + + 1/1000 y z + 1/1400 y z - 1/100 x y, COEFF(0, -1, 1) = 1/350 x y z + + 3 2 57 2 + + 1/25 x + 1/175 x y - 1/175 x z + 1/245 x z - --- x + 1/245 x y , + 490 + + 2 17 3 2 + COEFF(1, -1, 1) = - 1/700 z + --- - 1/350 x z + 1/300 y + 1/1400 y z + 525 + + 137 2 3 3 + + 1/350 x y + ---- z + 1/490 x y + 1/700 x y z - 1/300 z - 2/75 x + 5250 + + 2 2 166 137 2 + - 1/1400 y z - 1/700 y + ---- x - ---- y - 1/50 x - 1/1000 y z + 3675 5250 + + 2 2 2 + + 1/490 x z - 1/100 x z + 1/100 x y, COEFF(2, -1, 1) = - 1/175 x y + + 3 2 2 191 2 + + 1/150 x - 1/350 y + 1/200 x z + 1/175 x z + ----- x - 1/700 y z + 14700 + + 2 3 2 17 2 2 + - 1/350 z - 1/150 z - 1/245 x z + ---- + 1/700 y z - 1/200 x y + 2100 + + 2 167 2 167 3 + + 1/100 x - ---- y - 1/245 x y - 1/350 x y z + ---- z + 1/150 y + 7000 7000 + + 2 3 3 + - 1/500 y z, COEFF(-2, 0, 1) = - 1/200 x z + 1/150 x + 1/150 z + + 2 2 2 2 187 + - 2/245 x y - 1/100 x + 1/175 y + 1/175 x z + 1/350 y z - ---- z + 7000 + + 2 2 311 29 2 + + 1/350 z - 1/245 x z + ----- x - ----, COEFF(-1, 0, 1) = 1/350 y + 14700 2100 + + 2 289 2 2 2 2 + + 1/700 z - ----- z + 1/490 x z + 1/100 x z + 1/50 x + 1/245 x y + 10500 + + 2 37 3 151 3 + + 1/700 y z - 1/350 x z - ---- + 1/300 z + ---- x - 2/75 x , + 1050 3675 + + 3 2 2 61 + COEFF(0, 0, 1) = 1/25 x + 2/245 x y + 1/245 x z - 1/175 x z - --- x, + 490 + + 3 2 289 3 + COEFF(1, 0, 1) = - 2/75 x - 1/350 x z - 1/700 z + ----- z - 1/300 z + 10500 + + 2 2 37 2 2 2 + - 1/350 y - 1/50 x + ---- - 1/100 x z + 1/245 x y + 1/490 x z + 1050 + + 2 151 2 2 + - 1/700 y z + ---- x, COEFF(2, 0, 1) = - 1/350 y z - 2/245 x y + 3675 + + 2 311 2 187 2 29 + + 1/100 x + ----- x - 1/350 z + 1/175 x z + ---- z + 1/200 x z + ---- + 14700 7000 2100 + + 2 3 2 3 167 + - 1/245 x z - 1/150 z - 1/175 y + 1/150 x , COEFF(-2, 1, 1) = - ---- z + 7000 + + 191 3 167 2 + + 1/350 x y z + ----- x + 1/150 y - ---- y - 1/100 x + 1/175 x z + 14700 7000 + + 3 2 2 2 2 + + 1/150 x - 1/200 x y - 1/245 x z + 1/175 x y + 1/350 y + 1/700 y z + + 2 2 2 17 2 + + 1/700 y z + 1/350 z - 1/500 y z - 1/245 x y - ---- - 1/200 x z + 2100 + + 3 3 3 166 + + 1/150 z , COEFF(-1, 1, 1) = 1/300 z + 1/300 y - 1/1000 y z + ---- x + 3675 + + 2 2 2 2 2 2 + + 1/1400 y z + 1/490 x y + 1/700 y + 1/100 x y + 1/100 x z + 1/50 x + + 17 2 3 137 2 + - --- + 1/700 z - 2/75 x - 1/700 x y z - ---- y + 1/1400 y z + 525 5250 + + 2 137 2 + + 1/490 x z - 1/350 x z - 1/350 x y - ---- z, COEFF(0, 1, 1) = 1/245 x y + 5250 + + 57 2 3 + - --- x + 1/245 x z - 1/175 x y - 1/175 x z + 1/25 x - 1/350 x y z, + 490 + + 166 2 137 3 + COEFF(1, 1, 1) = ---- x - 1/100 x z + ---- z - 1/350 x z - 1/300 z + 3675 5250 + + 2 2 2 2 17 + - 1/700 y - 1/350 x y + 1/490 x z - 1/100 x y - 1/1400 y z + --- + 525 + + 137 3 2 2 2 + + ---- y - 2/75 x - 1/50 x - 1/1400 y z + 1/1000 y z - 1/700 z + 5250 + + 2 3 + - 1/700 x y z + 1/490 x y - 1/300 y , COEFF(2, 1, 1) = 1/175 x y + + 2 2 167 2 + - 1/350 y + 1/500 y z + 1/200 x y + ---- y + 1/175 x z - 1/700 y z + 7000 + + 167 2 3 191 3 2 + + ---- z + 1/200 x z + 1/150 x + ----- x - 1/150 y - 1/350 z + 7000 14700 + + 2 2 17 3 2 + - 1/245 x y + 1/100 x + ---- - 1/150 z - 1/700 y z + 1/350 x y z + 2100 + + 2 19 2 2 + - 1/245 x z , COEFF(-2, 2, 1) = ---- - 1/100 x y + 1/350 z + 1/175 x y z + 2100 + + 2 169 2 107 + - 1/250 y z + 2/175 x y - 1/100 x - ----- x - 1/200 x z - ---- z + 14700 7000 + + 3 2 2 47 3 + + 1/150 x + 2/245 x y + 1/350 y z + 1/175 x z + ---- y - 1/300 y + 5250 + + 3 2 2 2 + + 1/150 z - 1/350 y z - 1/245 x z - 1/175 y , COEFF(-1, 2, 1) = + + 2 2 2 3 + - 1/245 x y + 1/700 z - 1/500 y z + 1/700 y z - 1/350 x y z - 1/600 y + + 2 2 2 211 229 2 + + 1/50 x - 1/700 y z + 1/50 x y + ---- x - ----- z - 1/350 y + 3675 10500 + + 2 167 2 3 3 + + 1/490 x z - ---- y - 1/42 + 1/100 x z + 1/300 z - 2/75 x - 1/350 x z + 7000 + + 3 2 + - 1/175 x y, COEFF(0, 2, 1) = 1/25 x - 2/245 x y - 1/175 x y z + + 2 + - 2/175 x y - 9/98 x + 1/245 x z - 1/175 x z, COEFF(1, 2, 1) = + + 2 2 3 + - 1/50 x y - 1/175 x y - 1/700 y z + 1/500 y z - 1/300 z - 1/350 x y z + + 2 2 167 2 + + 1/42 + 1/700 y z + 1/490 x z + ---- y - 1/350 x z - 1/700 z + 7000 + + 2 3 229 211 2 2 + + 1/350 y + 1/600 y + ----- z + ---- x - 1/245 x y - 1/100 x z + 10500 3675 + + 3 2 169 2 2 + - 2/75 x - 1/50 x , COEFF(2, 2, 1) = - ----- x + 2/245 x y + 1/200 x z + 14700 + + 3 2 2 3 107 47 3 + + 1/300 y - 1/350 y z + 1/175 y - 1/150 z + ---- z - ---- y + 1/150 x + 7000 5250 + + 2 2 19 2 + + 1/350 y z + 1/100 x y + 1/175 x z - ---- - 1/350 z + 2/175 x y + 2100 + + 2 2 + - 1/245 x z + 1/175 x y z + 1/100 x + 1/250 y z, COEFF(-2, -2, 2) = + + 2 2 3 3 2 + 2/175 x z + 2/245 x y - 1/175 y z - 1/300 z + 1/300 y - 1/175 y + + 2 529 137 2 137 2 + + 1/175 y z - ----- x + ---- z - 1/100 x - ---- y + 1/125 y z - 1/175 z + 14700 5250 5250 + + 2 11 3 2 2 + + 2/245 x z + --- - 2/175 x y + 1/150 x + 1/100 x y - 1/100 x z + 420 + + 2 3 2 + - 2/175 x y z, COEFF(-1, -2, 2) = - 1/350 z - 2/75 x - 8/525 - 1/50 x y + + 2 2 3 + - 1/175 x z + 1/50 x - 1/245 x y + 1/175 x y z + 1/250 y z - 1/600 z + + 2 3 2 107 2 + - 1/350 y z + 1/600 y + 1/50 x z + ---- y + 1/175 x y - 1/245 x z + 7000 + + 2 2 256 107 2 + + 1/350 y z - 1/350 y + ---- x - ---- z, COEFF(0, -2, 2) = - 2/245 x y + 3675 7000 + + 2 33 3 + - 2/245 x z + 2/175 x y - --- x + 2/175 x y z - 2/175 x z + 1/25 x , + 490 + + 3 2 256 2 2 + COEFF(1, -2, 2) = - 1/600 y - 1/245 x y + ---- x + 1/350 y - 1/350 y z + 3675 + + 3 107 2 + + 1/600 z + 8/525 + ---- z + 1/175 x y + 1/50 x y - 1/175 x z + 7000 + + 107 2 2 3 2 + - 1/250 y z - ---- y - 1/50 x + 1/350 y z - 2/75 x + 1/350 z + 7000 + + 2 2 3 + - 1/50 x z + 1/175 x y z - 1/245 x z , COEFF(2, -2, 2) = 1/150 x + + 3 3 529 + - 2/175 x y - 2/175 x y z - 1/300 y + 1/300 z - ----- x - 1/125 y z + 14700 + + 2 2 2 2 2 2 + + 2/245 x z + 1/175 y z + 1/175 z + 2/245 x y - 1/175 y z + 1/100 x + + 137 137 2 11 2 2 + + ---- y + 2/175 x z - ---- z - 1/100 x y - --- + 1/100 x z + 1/175 y , + 5250 5250 420 + + 2 2 3 + COEFF(-2, -1, 2) = 2/245 x z + 2/175 x z - 1/100 x z - 1/300 z + + 2 107 169 3 2 + + 1/350 y + ---- y - ----- x + 1/150 x + 1/250 y z - 1/245 x y + 7000 14700 + + 2 2 2 2 47 + - 1/175 z - 1/175 x y - 1/100 x + 1/200 x y + 1/350 y z + ---- z + 5250 + + 3 19 2 + - 1/150 y + ---- - 1/175 x y z + 1/350 y z , COEFF(-1, -1, 2) = + 2100 + + 2 211 2 3 2 167 + - 1/350 z + ---- x - 1/245 x z - 1/600 z + 1/50 x - ---- z + 1/350 x y + 3675 7000 + + 2 2 3 2 3 + - 1/100 x y + 1/490 x y - 2/75 x - 1/175 x z + 1/700 y z - 1/300 y + + 2 2 2 + + 1/500 y z + 1/50 x z + 1/700 y - 1/42 + 1/700 y z + 1/350 x y z + + 229 2 2 + + ----- y, COEFF(0, -1, 2) = 1/245 x y + 1/175 x y - 2/245 x z + 10500 + + 3 + + 1/175 x y z - 2/175 x z - 9/98 x + 1/25 x , COEFF(1, -1, 2) = + + 2 2 2 2 229 + 1/350 x y z - 1/50 x z - 1/700 y - 1/50 x + 1/490 x y - ----- y + 10500 + + 211 3 2 2 3 + + ---- x - 1/500 y z + 1/600 z - 1/245 x z + 1/350 z - 2/75 x + 3675 + + 3 167 2 2 + + 1/300 y - 1/175 x z + ---- z - 1/700 y z + 1/350 x y + 1/100 x y + 7000 + + 2 3 3 2 + + 1/42 - 1/700 y z , COEFF(2, -1, 2) = 1/150 x + 1/300 z + 1/175 z + + 2 2 19 169 + - 1/175 x y - 1/350 y - 1/350 y z - ---- + 2/175 x z - ----- x + 2100 14700 + + 2 3 2 2 2 + - 1/250 y z - 1/350 y z + 1/150 y + 1/100 x z + 2/245 x z + 1/100 x + + 2 107 47 2 + - 1/245 x y - ---- y - ---- z - 1/175 x y z - 1/200 x y, COEFF(-2, 0, 2) + 7000 5250 + + 3 2 17 2 + = - 1/300 z + 2/245 x z - 1/300 x + ---- z - 1/100 x z + 2/175 x z + 5250 + + 2 2 2 2 3 + - 2/245 x y - 1/100 x - 1/175 z + 1/175 y + 1/150 x + 1/300 + + 2 3 3 2 + + 1/175 y z, COEFF(-1, 0, 2) = - 1/600 z - 2/75 x + 1/245 x y + + 2 2 2 2 + - 1/175 x z + 4/75 x - 2/75 - 1/245 x z + 1/50 x z - 1/350 z + 1/350 y + + 187 2 2 + - ---- z + 1/50 x + 1/350 y z, + 7000 + + 3 2 2 + COEFF(0, 0, 2) = 1/25 x - 2/245 x z + 2/245 x y - 1/10 x - 2/175 x z, + + 187 2 2 2 2 + COEFF(1, 0, 2) = ---- z + 1/245 x y - 1/350 y + 2/75 + 1/350 z - 1/50 x + 7000 + + 2 3 2 2 3 + - 1/245 x z + 1/600 z - 1/350 y z + 4/75 x - 1/50 x z - 2/75 x + + 17 3 2 + - 1/175 x z, COEFF(2, 0, 2) = - 1/300 x - ---- z + 1/300 z + 1/100 x + 5250 + + 2 2 2 2 2 + + 2/175 x z - 1/175 y + 2/245 x z + 1/175 z - 2/245 x y + 1/100 x z + + 3 2 3 2 + - 1/300 + 1/150 x - 1/175 y z, COEFF(-2, 1, 2) = - 1/300 z + 1/350 y z + + 3 19 169 2 + + 1/175 x y + 1/150 x + 1/175 x y z + ---- - ----- x + 2/245 x z + 2100 14700 + + 2 2 2 2 + + 2/175 x z - 1/175 z + 1/350 y - 1/100 x - 1/250 y z - 1/245 x y + + 2 2 107 47 2 3 + - 1/100 x z - 1/200 x y - ---- y + ---- z - 1/350 y z + 1/150 y , + 7000 5250 + + 2 2 229 3 + COEFF(-1, 1, 2) = 1/50 x z + 1/700 y - ----- y + 1/300 y - 1/175 x z + 10500 + + 2 2 211 2 2 + + 1/490 x y - 1/245 x z + ---- x + 1/700 y z - 1/500 y z - 1/700 y z + 3675 + + 3 2 167 3 2 + - 1/600 z - 1/350 z - 1/350 x y - ---- z - 1/42 - 2/75 x + 1/100 x y + 7000 + + 2 2 + + 1/50 x - 1/350 x y z, COEFF(0, 1, 2) = - 2/245 x z - 1/175 x y z + + 3 2 + + 1/25 x + 1/245 x y - 2/175 x z - 1/175 x y - 9/98 x, COEFF(1, 1, 2) = + + 2 2 211 3 2 167 + - 1/350 x y - 1/50 x z + 1/350 z + ---- x + 1/600 z - 1/700 y + ---- z + 3675 7000 + + 3 229 2 3 + + 1/42 - 2/75 x - 1/350 x y z + ----- y + 1/500 y z - 1/50 x - 1/300 y + 10500 + + 2 2 2 2 + - 1/700 y z - 1/175 x z + 1/700 y z - 1/100 x y + 1/490 x y + + 2 19 2 3 + - 1/245 x z , COEFF(2, 1, 2) = 1/175 x y - ---- - 1/350 y + 1/300 z + 2100 + + 2 2 107 2 + + 1/100 x z + 1/175 x y z - 1/245 x y + 2/175 x z + ---- y + 1/100 x + 7000 + + 2 3 2 2 169 + + 2/245 x z - 1/150 y - 1/350 y z + 1/175 z + 1/250 y z - ----- x + 14700 + + 2 3 2 47 3 + + 1/350 y z + 1/150 x + 1/200 x y - ---- z, COEFF(-2, 2, 2) = 1/150 x + 5250 + + 2 137 11 137 3 2 + - 1/175 y z + ---- z + --- + ---- y - 1/300 z + 2/245 x z + 2/175 x z + 5250 420 5250 + + 2 2 2 529 + - 1/175 y - 1/175 y z + 2/175 x y z - 1/100 x z + 2/175 x y - ----- x + 14700 + + 3 2 2 2 2 + - 1/300 y - 1/175 z + 2/245 x y - 1/125 y z - 1/100 x y - 1/100 x , + + 2 107 3 + COEFF(-1, 2, 2) = - 1/350 z - 1/175 x y z - ---- z - 1/600 z - 1/175 x y + 7000 + + 2 3 2 2 + - 8/525 - 1/350 y z - 1/175 x z - 2/75 x - 1/350 y - 1/245 x y + + 2 107 3 256 2 2 + - 1/245 x z - ---- y - 1/600 y + ---- x + 1/50 x - 1/350 y z + 7000 3675 + + 2 2 3 2 + + 1/50 x z - 1/250 y z + 1/50 x y, COEFF(0, 2, 2) = 1/25 x - 2/245 x z + + 33 2 + - 2/175 x y z - --- x - 2/245 x y - 2/175 x y - 2/175 x z, COEFF(1, 2, 2) + 490 + + 256 2 107 + = 8/525 - 1/175 x y z + ---- x + 1/350 y + ---- z - 1/175 x y + 3675 7000 + + 2 3 2 2 2 2 + - 1/245 x y + 1/600 z + 1/350 z - 1/245 x z - 1/50 x z - 1/50 x y + + 3 2 2 107 + - 1/175 x z - 2/75 x + 1/350 y z - 1/50 x + 1/250 y z + ---- y + 7000 + + 2 3 2 11 3 + + 1/350 y z + 1/600 y , COEFF(2, 2, 2) = 2/245 x y - --- + 1/150 x + 420 + + 529 2 137 3 + - ----- x + 1/100 x y + 2/175 x y z - ---- y + 2/175 x y + 1/300 y + 14700 5250 + + 137 2 2 3 2 2 + - ---- z + 1/100 x + 1/175 y + 1/300 z + 1/175 z + 1/100 x z + 5250 + + 2 2 2 + + 2/175 x z + 1/175 y z + 1/175 y z + 2/245 x z + 1/125 y z] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dx.compute.c"); +bytes used=1278698152, alloc=14218708, time=162.07 +bytes used=1279698332, alloc=14218708, time=162.16 +bytes used=1280699032, alloc=14218708, 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used=1415866900, alloc=14218708, time=186.56 +bytes used=1416867096, alloc=14218708, time=186.89 +bytes used=1417889896, alloc=14218708, time=187.15 +bytes used=1418890048, alloc=14218708, time=187.28 +bytes used=1419890224, alloc=14218708, time=189.14 +bytes used=1420890452, alloc=14218708, time=190.53 +bytes used=1421890668, alloc=14218708, time=190.81 +bytes used=1422890988, alloc=14218708, time=190.89 +bytes used=1423891408, alloc=14218708, time=190.97 +bytes used=1424891652, alloc=14218708, time=191.04 +bytes used=1425891828, alloc=14218708, time=191.12 +bytes used=1426892200, alloc=14218708, time=191.20 +bytes used=1427892604, alloc=14218708, time=191.27 +bytes used=1428892904, alloc=14218708, time=191.36 +bytes used=1429893216, alloc=14218708, time=191.44 +bytes used=1430893484, alloc=14218708, time=191.52 +bytes used=1431893824, alloc=14218708, time=191.59 +bytes used=1432894112, alloc=14218708, time=191.67 +bytes used=1433894380, alloc=14218708, time=191.75 +bytes used=1434894836, alloc=14218708, time=191.82 +bytes used=1435895072, alloc=14218708, time=191.90 +bytes used=1436916320, alloc=14218708, time=191.98 +bytes used=1437919724, alloc=14218708, time=192.05 +bytes used=1438919888, alloc=14218708, time=192.39 +bytes used=1439920124, alloc=14218708, time=192.73 +bytes used=1440920304, alloc=14218708, time=193.04 +bytes used=1441920480, alloc=14218708, time=195.65 +bytes used=1442921820, alloc=14218708, time=196.22 +bytes used=1443922264, alloc=14218708, time=196.46 +bytes used=1444922856, alloc=14218708, time=196.54 +bytes used=1445923040, alloc=14218708, time=196.65 +bytes used=1446923204, alloc=14218708, time=196.83 +bytes used=1447923456, alloc=14218708, time=196.98 +> +# d/dy +> simplify( diff(interp_3d_cube_order4_smooth0,y) ); +bytes used=1448923620, alloc=14218708, time=197.09 +bytes used=1449924492, alloc=14218708, time=197.17 +bytes used=1450924676, alloc=14218708, time=197.25 +bytes used=1451925432, alloc=14218708, time=197.33 +bytes 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used=1472107636, alloc=14218708, time=199.07 +bytes used=1473108084, alloc=14218708, time=199.16 + 41 +- ---- DATA(0, -2, 0) - 1/175 x y z DATA(2, 2, -1) + 2100 + + - 1/175 x y z DATA(-2, 1, -2) + 1/350 x y z DATA(2, 1, -1) + + + 1/350 x y z DATA(-1, 2, -1) - 1/350 x y z DATA(1, 2, -1) + + 19 + + ---- DATA(-2, -2, 1) - 2/175 x y z DATA(2, 2, -2) + 2100 + + + 1/350 y z DATA(1, -1, -1) - 1/175 x y z DATA(1, 2, -2) + + 17 + + 1/350 x y z DATA(-1, -2, -1) - ---- DATA(1, -2, 1) + 2100 + + - 1/175 x y z DATA(-2, -2, 1) + 1/350 y z DATA(-1, -1, -1) + + + 2/175 x y z DATA(-2, 2, -2) + 1/350 x y z DATA(1, -2, 1) + + 29 + - ---- DATA(0, -2, 1) - 1/175 x y z DATA(-2, 2, 1) + 2100 + + + 1/350 x y z DATA(1, 1, -2) + 1/175 x y z DATA(2, 1, -2) + + 29 + - ---- DATA(1, -2, 0) - 1/350 x y z DATA(-1, 1, -2) + 2100 + + 29 + + 1/350 x y z DATA(-2, 1, 1) + ---- DATA(0, 2, -1) + 2100 + + + 1/350 x y z DATA(-2, -1, 1) - 1/350 x y z DATA(-1, -2, 1) + + 17 + - 1/700 x y z DATA(1, 1, 1) - ---- DATA(-1, -2, 1) + 2100 + + + 1/350 x y z DATA(2, -1, -1) + 1/175 x y z DATA(2, -2, 1) + + - 2/175 x y z DATA(-2, -2, 2) - 1/175 x y z DATA(2, -1, 2) + + - 2/75 DATA(0, -1, 2) + 1/350 y z DATA(1, 1, -1) + + - 1/350 x y z DATA(1, 1, 2) - 1/350 x y z DATA(-1, 2, 1) + + + 1/175 x y z DATA(-2, -2, -1) - 1/175 x y z DATA(-1, -2, 2) + + + 1/175 x y z DATA(1, -2, 2) + 1/350 y z DATA(-1, 1, -1) + + + 1/175 x y z DATA(-1, 2, -2) + 1/175 x y z DATA(2, 2, 1) + + - 1/350 y z DATA(-1, 1, 1) - 1/42 DATA(-2, -1, 1) + + - 1/350 x y z DATA(2, 1, 1) + 1/350 x y z DATA(1, 2, 1) + + 19 + + 1/300 DATA(2, -2, 0) + ---- DATA(2, -2, 1) - 1/350 x y z DATA(2, -1, 1) + 2100 + + 167 + + 1/175 x y z DATA(1, 2, 2) + ---- x DATA(-1, -2, -1) + 7000 + + + 1/700 x y z DATA(1, -1, -1) + 1/700 x y z DATA(-1, 1, 1) + + - 1/175 x y z DATA(-1, 2, 2) + 2/175 x y z DATA(2, -2, 2) + + + 1/175 x y z DATA(-2, 2, -1) - 2/75 DATA(-2, -1, 0) + + 187 + + 2/175 x y z DATA(2, 2, 2) + ---- x DATA(1, 2, 0) + 7000 + + - 1/350 x y z DATA(1, -2, -1) - 1/350 x y z DATA(-2, 1, -1) + + - 1/175 x y z DATA(2, 1, 2) - 1/175 x y z DATA(2, -2, -1) + + - 1/300 DATA(0, 2, 2) - 1/350 x y z DATA(-2, -1, -1) + + 167 137 167 + - ---- x DATA(-2, 1, 1) + ---- x DATA(1, 1, 1) - ---- x DATA(-1, 2, -1) + 7000 5250 7000 + + 167 47 167 + + ---- x DATA(2, 1, -1) - ---- x DATA(2, 2, -1) + ---- x DATA(1, 2, -1) + 7000 5250 7000 + + 229 + + ----- x DATA(-1, -1, 2) - 1/700 x y z DATA(-1, -1, -1) + 10500 + + 167 137 167 + + ---- x DATA(1, 2, 1) - ---- x DATA(2, 2, -2) - ---- x DATA(2, -1, 1) + 7000 5250 7000 + + 167 47 229 + - ---- x DATA(-1, 2, 1) - ---- x DATA(-2, -2, -1) + ----- x DATA(1, 1, -2) + 7000 5250 10500 + + 107 187 137 + + ---- x DATA(1, 2, -2) - ---- x DATA(2, -1, 0) + ---- x DATA(-2, 2, -2) + 7000 7000 5250 + + 47 + + ---- x DATA(-2, 2, 1) - 1/42 DATA(2, -1, -1) + 5250 + + 37 + + 1/175 x y z DATA(-2, 0, 1) + 4/105 DATA(0, 1, 0) + ---- DATA(1, 1, 0) + 1050 + + 37 17 17 + + ---- DATA(0, 1, 1) + --- DATA(1, 1, 1) - ---- x DATA(2, 2, 0) + 1050 525 5250 + + + 1/500 x z DATA(-2, -1, 1) + 1/500 x z DATA(2, -1, -1) + + - 1/250 x z DATA(2, -2, 1) + 1/250 x z DATA(-2, -2, 1) + + 2 2 + + 2/245 y z DATA(-1, 2, 2) + 2/245 y z DATA(2, -2, 2) + + - 1/500 x z DATA(1, -2, 1) + 1/500 x z DATA(-1, -2, 1) + + 2 + + 1/490 y z DATA(-2, 1, -1) - 1/250 x z DATA(2, 2, -1) + + - 1/500 x z DATA(2, 1, -1) + 1/500 x z DATA(-1, 2, -1) + + + 1/1000 x z DATA(1, 1, 1) - 1/500 x z DATA(-2, 1, 1) + + 2 + + 1/245 y z DATA(1, -1, 0) + 1/500 x z DATA(-1, 1, -2) + + 2 + - 1/245 y z DATA(2, 1, 2) - 1/250 x z DATA(2, 1, -2) + + + 1/175 x y z DATA(2, -1, -2) + 1/250 x z DATA(2, 2, 1) + + 2 + - 1/245 y z DATA(1, -2, -1) + 1/250 x z DATA(-1, 2, -2) + + - 1/500 x z DATA(1, 1, -2) - 1/250 x z DATA(-2, 2, 1) + + + 1/125 x z DATA(-2, 2, -2) - 1/500 x z DATA(-1, -2, -1) + + - 1/250 x z DATA(1, 2, -2) + 1/250 x z DATA(-2, 1, -2) + + 2 + - 1/500 x z DATA(1, 2, -1) + 2/245 y z DATA(-2, -2, 2) + + - 1/350 x y z DATA(-1, 0, -1) - 1/175 x y z DATA(1, 0, 2) + + 2 + - 1/500 x z DATA(-1, 2, 1) + 1/490 y z DATA(-2, -1, -1) + + - 1/125 x z DATA(2, 2, -2) + 1/500 x z DATA(1, 2, 1) + + + 1/500 x z DATA(-1, -1, 2) + 1/500 x z DATA(2, 1, 1) + + 19 + - 1/500 x z DATA(2, -1, 1) - ---- DATA(2, 2, -1) - 1/350 x y DATA(1, 1, 2) + 2100 + + 2 + - 1/175 x y DATA(2, -1, 2) - 1/245 y z DATA(1, -1, 2) + + 2 + - 1/245 y z DATA(2, -2, -1) - 1/250 x z DATA(-2, -2, -1) + + + 1/175 x y DATA(-2, -1, -1) - 1/350 x y DATA(1, -1, 2) + + 2 + + 1/490 y z DATA(-1, -1, 1) + 1/350 x y DATA(-1, 1, 2) + + 2 2 + + 2/245 y z DATA(-2, -2, -2) + 2/245 y z DATA(-2, 2, 2) + + 2 2 + - 2/245 y z DATA(-2, 2, 0) - 1/245 y z DATA(-2, 1, 2) + + + 2/175 x y DATA(2, -2, -1) - 1/175 x y DATA(2, 1, 2) + + - 1/350 x y DATA(1, -1, 0) + 1/175 x y DATA(-2, 1, -1) + + + 1/175 x y DATA(1, -2, -1) - 2/175 x y DATA(-2, -2, 2) + + 3 + - 1/300 z DATA(1, -1, -1) - 1/350 x y DATA(1, -1, -1) + + 2 2 + + 1/490 y z DATA(1, 1, -1) + 1/245 y z DATA(-1, 1, 0) + + + 1/350 x y DATA(-1, -1, -1) + 1/350 x y DATA(-1, -1, 0) + + + 1/175 x y DATA(1, 2, 2) + 2/175 x y DATA(2, 2, 2) + + 2 + - 2/175 x y DATA(-2, 2, -1) + 1/490 y z DATA(1, -1, 1) + + + 2/175 x y DATA(2, -2, 2) - 1/175 x y DATA(-1, 2, 2) + + + 1/350 x y DATA(-1, -1, 1) - 1/350 x y DATA(1, -1, 1) + + + 1/350 x y DATA(-1, 1, 0) - 1/350 x y DATA(1, 1, -1) + + 2 + + 1/490 y z DATA(-1, 1, -1) + 1/350 x y DATA(-1, 1, -1) + + + 1/350 x y DATA(-1, 1, 1) - 1/175 x y DATA(-1, -2, 0) + + 2 + - 2/175 x y DATA(-2, 2, 0) + 1/490 y z DATA(-1, 1, 1) + + - 2/175 x y DATA(-2, 2, 2) - 2/175 x y DATA(-2, -2, -2) + + + 1/175 x y DATA(-2, 1, 2) + 2/175 x y DATA(2, -2, -2) + + + 1/175 x y DATA(-2, -1, -2) - 2/175 x y DATA(-2, -2, 0) + + + 1/175 x y DATA(-2, -1, 2) - 1/350 x y DATA(1, -1, -2) + + - 1/175 x y DATA(2, -1, -2) + 1/350 x y DATA(-1, -1, -2) + + - 1/175 x y DATA(-1, -2, -2) + 1/175 x y DATA(1, -2, -2) + + 2 2 + + 1/175 x DATA(2, 2, 2) + 1/700 x DATA(-1, -1, 0) + + 3 3 + - 1/300 z DATA(-1, 1, 1) + 1/300 z DATA(-1, 1, -1) + + 3 3 + + 1/300 z DATA(1, 1, -1) + 1/300 z DATA(1, -1, 1) + + 3 3 + + 1/300 z DATA(-1, -1, 1) - 1/300 z DATA(-1, -2, 2) + + 3 3 + - 1/300 z DATA(1, -2, 2) - 1/600 z DATA(2, -1, 2) + + 3 3 + + 1/600 z DATA(1, 1, 2) + 1/600 z DATA(-1, 1, 2) + + 2 107 137 + - 1/350 x DATA(1, 2, 2) + ---- x DATA(2, 1, 2) + ---- x DATA(2, -2, 2) + 7000 5250 + + 47 2 + + ---- x DATA(-2, 2, -1) - 1/175 x DATA(2, -2, 2) + 5250 + + 2 107 + + 1/175 x DATA(-2, 2, -1) - ---- x DATA(-1, 2, 2) + 7000 + + 107 107 229 + + ---- x DATA(-1, -2, 2) - ---- x DATA(2, -1, 2) + ----- x DATA(1, 1, 2) + 7000 7000 10500 + + 229 229 47 + - ----- x DATA(-1, 1, 2) - ----- x DATA(1, -1, 2) + ---- x DATA(2, -2, -1) + 10500 10500 5250 + + 167 137 + + ---- x DATA(-2, -1, -1) - ---- x DATA(-2, -2, 2) + 7000 5250 + + 167 167 289 + - ---- x DATA(1, -2, -1) - ---- x DATA(-2, 1, -1) - ----- x DATA(1, -1, 0) + 7000 7000 10500 + + 107 17 107 + - ---- x DATA(1, -2, 2) + ---- DATA(1, 2, -1) - ---- x DATA(1, -2, -2) + 7000 2100 7000 + + 229 137 137 + + ----- x DATA(-1, -1, -2) - ---- x DATA(1, -1, 1) - ---- x DATA(2, 2, 2) + 10500 5250 5250 + + 107 289 137 + + ---- x DATA(1, 2, 2) + ----- x DATA(-1, -1, 0) + ---- x DATA(-1, -1, -1) + 7000 10500 5250 + + 137 137 137 + - ---- x DATA(1, -1, -1) - ---- x DATA(-1, 1, 1) - ---- x DATA(-1, 1, -1) + 5250 5250 5250 + + 137 107 + + ---- x DATA(1, 1, -1) + ---- x DATA(-1, -2, -2) + 5250 7000 + + 137 17 107 + - ---- x DATA(-2, -2, -2) + ---- x DATA(-2, 2, 0) - ---- x DATA(-2, 1, 2) + 5250 5250 7000 + + 187 107 17 + + ---- x DATA(-1, -2, 0) + ---- x DATA(-2, -1, 2) - ---- x DATA(-2, -2, 0) + 7000 7000 5250 + + 107 229 + + ---- x DATA(-2, -1, -2) - ----- x DATA(1, -1, -2) + 7000 10500 + + 137 137 + + ---- x DATA(2, -2, -2) + ---- x DATA(-2, 2, 2) + 8/525 DATA(-2, 1, -2) + 5250 5250 + + 107 289 137 + - ---- x DATA(2, -1, -2) - ----- x DATA(-1, 1, 0) + ---- x DATA(-1, -1, 1) + 7000 10500 5250 + + 3 3 + - 1/300 x DATA(2, -2, 1) + 1/150 x DATA(1, -2, 1) + + 3 3 + + 1/150 x DATA(1, -2, 0) + 1/300 x DATA(-2, -2, 1) + + 3 3 + + 1/600 x DATA(-2, -1, 0) + 1/300 x DATA(2, 2, -1) + + 3 3 + - 1/150 x DATA(1, 2, -1) - 1/600 x DATA(-2, 1, -2) + + 3 3 + - 1/150 x DATA(1, 2, -2) - 1/300 x DATA(2, -2, 0) + + 3 3 + - 1/600 x DATA(2, -1, -1) - 1/300 x DATA(1, 1, 0) + + 3 3 + - 1/150 x DATA(-1, -2, 1) + 1/600 x DATA(-2, -1, 1) + + 3 3 + + 1/600 x DATA(2, 1, -2) + 1/150 x DATA(-1, 2, 0) + + 3 3 + + 1/300 x DATA(-1, 1, -2) - 1/300 x DATA(-2, 2, -2) + + 3 3 + + 1/300 x DATA(2, 2, 0) + 1/600 x DATA(2, 1, 0) + + 3 3 + - 1/600 x DATA(2, -1, 0) - 1/150 x DATA(1, 2, 0) + + 3 3 + - 1/600 x DATA(-2, 1, 1) - 1/300 x DATA(1, 1, 1) + + 3 3 + + 1/150 x DATA(-1, 2, -1) + 1/600 x DATA(2, 1, -1) + + 3 3 + - 1/300 x DATA(-2, 2, 1) - 1/300 x DATA(1, 1, -2) + + 3 3 + + 1/150 x DATA(-1, 2, -2) + 1/300 x DATA(2, 2, 1) + + 3 3 + - 1/600 x DATA(-2, 1, 0) + 1/600 x DATA(2, 1, 1) + + 3 3 + - 1/150 x DATA(-1, -2, -1) + 1/150 x DATA(-1, 2, 2) + + 3 3 + - 1/300 x DATA(-2, 2, -1) + 1/150 x DATA(1, -2, 2) + + 3 3 + - 1/300 x DATA(1, 1, 2) + 1/300 x DATA(-1, 1, 2) + + 3 3 + + 1/300 x DATA(1, -1, 2) - 1/300 x DATA(2, -2, -1) + + 3 3 + + 1/600 x DATA(-2, -1, -1) - 1/600 x DATA(2, -1, 2) + + 3 3 + - 1/300 x DATA(-1, -1, 2) - 1/150 x DATA(1, 2, 1) + + 3 3 + + 1/300 x DATA(2, 2, -2) - 1/600 x DATA(2, -1, 1) + + 3 3 + + 1/150 x DATA(-1, 2, 1) + 1/300 x DATA(-2, -2, -1) + + 3 3 + - 1/150 x DATA(-1, -2, 2) - 1/300 x DATA(2, -2, 2) + + 3 3 + - 1/150 x DATA(1, 2, 2) + 1/300 x DATA(-2, -2, 2) + + 3 3 + + 1/150 x DATA(1, -2, -1) - 1/600 x DATA(-2, 1, -1) + + 3 3 + + 1/300 x DATA(1, -1, 0) + 1/600 x DATA(2, 1, 2) + + 3 3 + + 1/300 x DATA(1, -1, 1) + 1/300 x DATA(-2, -2, -2) + + 3 3 + - 1/300 x DATA(-2, 2, 2) - 1/300 x DATA(-2, 2, 0) + + 3 3 + - 1/600 x DATA(-2, 1, 2) - 1/150 x DATA(-1, -2, 0) + + 3 3 + - 1/300 x DATA(-1, -1, 1) - 1/300 x DATA(-1, -1, -1) + + 3 3 + + 1/300 x DATA(1, -1, -1) + 1/300 x DATA(-1, 1, 1) + + 3 3 + + 1/300 x DATA(-1, 1, -1) - 1/300 x DATA(1, 1, -1) + + 3 2 + + 1/300 x DATA(-1, 1, 0) + 1/200 x y DATA(1, 2, 1) + + 17 3 + + ---- DATA(-1, 2, -1) - 1/300 x DATA(-1, -1, -2) + 2100 + + 3 3 + - 1/600 x DATA(2, -1, -2) + 1/300 x DATA(2, 2, 2) + + 3 3 + - 1/300 x DATA(-1, -1, 0) + 1/600 x DATA(-2, -1, 2) + + 3 3 + + 1/300 x DATA(-2, -2, 0) + 1/600 x DATA(-2, -1, -2) + + 3 3 + + 1/300 x DATA(1, -1, -2) - 1/300 x DATA(2, -2, -2) + + 3 3 + + 1/150 x DATA(1, -2, -2) - 1/150 x DATA(-1, -2, -2) + + 2 2 + - 1/350 x DATA(-1, 2, 0) + 1/350 x DATA(1, -2, 0) + + 2 2 + - 1/175 x DATA(-2, -2, 1) - 1/350 x DATA(-2, -1, 0) + + 2 2 + - 1/175 x DATA(2, -2, 0) - 1/175 x DATA(2, -2, 1) + + 2 2 + + 1/350 x DATA(1, -2, 1) - 1/700 x DATA(1, 1, 1) + + 2 2 + - 1/350 x DATA(-1, 2, -1) + 1/350 x DATA(2, 1, -1) + + 2 2 + - 1/350 x DATA(2, -1, -1) - 1/700 x DATA(1, 1, 0) + + 2 2 + + 1/350 x DATA(-1, -2, 1) - 1/350 x DATA(-2, -1, 1) + + 2 2 + + 1/350 x DATA(2, 1, -2) - 1/700 x DATA(1, 1, -2) + + 2 2 + - 1/350 x DATA(-1, 2, -2) + 1/175 x DATA(2, 2, 1) + + 2 2 + + 1/175 x DATA(2, 2, 0) + 1/175 x DATA(2, 2, -1) + + 2 2 + + 1/350 x DATA(-2, 1, -2) - 1/350 x DATA(1, 2, -2) + + 2 2 + + 1/350 x DATA(-1, -2, -1) - 1/350 x DATA(2, -1, 0) + + 2 2 + + 1/175 x DATA(-2, 2, -2) - 1/350 x DATA(1, 2, -1) + + 2 2 + - 1/700 x DATA(-1, 1, -2) - 1/350 x DATA(1, 2, 0) + + 2 2 + + 1/350 x DATA(-2, 1, 1) - 1/245 x y DATA(2, 1, 0) + + 2 2 + - 1/700 x DATA(1, 1, 2) - 1/700 x DATA(-1, 1, 2) + + 2 2 + + 1/700 x DATA(1, -1, 2) - 1/175 x DATA(2, -2, -1) + + 2 2 + - 1/350 x DATA(-2, -1, -1) + 1/350 x DATA(-2, 1, 0) + + 2 2 + + 1/350 x DATA(2, 1, 1) + 1/700 x DATA(-1, -1, 2) + + 2 2 + - 1/350 x DATA(1, 2, 1) + 1/175 x DATA(2, 2, -2) + + 2 2 + - 1/350 x DATA(2, -1, 1) - 1/350 x DATA(-1, 2, 1) + + 2 2 + - 1/175 x DATA(-2, -2, -1) + 1/350 x DATA(-1, -2, 2) + + 2 2 + + 1/350 x DATA(1, -2, 2) + 1/175 x DATA(-2, 2, 1) + + 2 2 + + 1/350 x DATA(2, 1, 0) - 1/700 x DATA(-1, 1, 0) + + 2 2 + + 1/700 x DATA(-1, -1, 1) - 1/175 x DATA(-2, -2, -2) + + 2 2 + + 1/700 x DATA(1, -1, -1) - 1/175 x DATA(-2, -2, 2) + + 2 2 + + 1/350 x DATA(1, -2, -1) + 1/350 x DATA(-2, 1, -1) + + 2 2 + + 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0, 0) + 490 490 + + 33 136 61 + - --- y DATA(-2, 0, 2) + ---- y DATA(0, -1, 0) - --- y DATA(-1, 0, 0) + 490 3675 490 + + - 8/525 DATA(-2, -1, -2) + 2/175 x y DATA(2, -2, 1) + + 11 + - 1/175 x y DATA(2, -1, -1) + --- DATA(2, -2, -2) - 1/42 DATA(1, -1, -2) + 420 + + + 2/175 x y DATA(2, -2, 0) - 2/75 DATA(0, -1, -2) - 1/42 DATA(-1, -1, -2) + + - 2/175 x y DATA(-2, -2, 1) + 1/175 x y DATA(-2, -1, 0) + + + 1/175 x y DATA(1, -2, 1) + 1/175 x y DATA(1, -2, 0) + + 187 + - 8/525 DATA(2, -1, -2) + ---- z DATA(0, -1, -2) + 7000 + + 2 + - 1/350 x z DATA(0, -1, -2) + +> coeffs_as_lc_of_data(%, posn_list_3d_size5); +bytes used=1474194580, alloc=14218708, time=199.25 +bytes used=1475420244, alloc=14218708, time=199.35 +bytes used=1476623972, alloc=14218708, time=199.45 +bytes used=1477804196, alloc=14218708, time=199.54 +bytes used=1478963260, alloc=14218708, time=199.63 +bytes used=1480101092, alloc=14218708, time=199.72 +bytes used=1481224792, alloc=14218708, time=199.82 +bytes used=1482333932, 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529 137 2 + - 1/175 z + 1/300 x - ----- y - ---- x - 1/125 x z - 1/100 y + 14700 5250 + + 3 2 + + 2/175 x y z - 2/175 y z + 1/150 y , COEFF(-1, -2, -2) = 2/245 y z + + 2 47 2 3 3 19 + - 1/350 x z - ---- z - 1/175 z - 1/150 x + 1/300 z - 1/175 x y + ---- + 5250 2100 + + 2 169 2 2 3 + + 1/350 x - 2/175 y z - ----- y + 1/100 y z + 1/350 x z + 1/150 y + 14700 + + 2 107 2 2 + - 1/100 y + ---- x - 1/250 x z - 1/245 x y + 1/175 x y z + 1/200 x y , + 7000 + + 17 3 2 2 2 + COEFF(0, -2, -2) = - ---- z + 1/150 y + 1/100 y z - 1/175 x z + 1/175 x + 5250 + + 2 2 2 3 + - 2/175 y z + 1/300 - 2/245 x y + 2/245 y z - 1/175 z + 1/300 z + + 2 2 + - 1/300 y - 1/100 y , COEFF(1, -2, -2) = - 2/175 y z - 1/100 y + + 2 3 2 107 2 + - 1/200 x y + 1/150 y - 1/175 x y z + 1/100 y z - ---- x - 1/175 z + 7000 + + 169 3 2 2 47 + - ----- y + 1/300 z + 2/245 y z + 1/350 x + 1/175 x y - ---- z + 14700 5250 + + 3 2 2 2 19 + + 1/150 x - 1/350 x z - 1/245 x y - 1/350 x z + ---- + 1/250 x z, + 2100 + + 137 2 11 + COEFF(2, -2, -2) = 2/175 x y - ---- z + 1/100 y z + --- + 1/125 x z + 5250 420 + + 3 2 2 2 + - 2/175 x y z + 1/150 y + 2/245 y z - 2/175 y z - 1/100 y - 1/175 x z + + 529 3 2 137 3 2 + - ----- y - 1/300 x - 1/100 x y + ---- x + 1/300 z - 1/175 x + 14700 5250 + + 2 2 2 3 + + 2/245 x y - 1/175 z + 1/175 x z, COEFF(-2, -1, -2) = - 2/75 y + + 256 2 2 107 + + ---- y - 1/50 y z + 1/350 x z + ---- z - 1/175 x y z + 1/175 x y + 3675 7000 + + 107 2 2 2 + + ---- x - 8/525 - 1/350 z - 1/250 x z - 1/245 y z - 1/50 x y + 7000 + + 2 3 3 2 2 + + 1/175 y z - 1/350 x + 1/600 x + 1/600 z - 1/245 x y + 1/350 x z + + 2 2 211 3 + + 1/50 y , COEFF(-1, -1, -2) = 1/700 x + ---- y + 1/600 z + 1/350 x y + 3675 + + 2 2 3 + - 1/42 - 1/350 z - 1/245 y z - 2/75 y - 1/500 x z + 1/175 y z + + 2 2 3 2 + - 1/350 x y z - 1/700 x z - 1/50 y z - 1/300 x + 1/490 x y + + 2 167 2 229 2 + + 1/700 x z + ---- z - 1/100 x y + ----- x + 1/50 y , COEFF(0, -1, -2) + 7000 10500 + + 2 2 187 2 2 3 + = - 1/245 y z + 1/245 x y + ---- z - 1/350 x z - 1/350 z + 1/600 z + 7000 + + 3 2 2 2 + - 2/75 y + 1/50 y - 1/50 y z - 2/75 + 1/175 y z + 1/350 x + 4/75 y, + + 2 167 2 + COEFF(1, -1, -2) = 1/350 x y z - 1/50 y z + ---- z - 1/42 - 1/350 z + 7000 + + 2 229 3 2 + + 1/490 x y - ----- x + 1/300 x + 1/500 x z + 1/175 y z + 1/700 x + 10500 + + 2 211 2 2 2 + - 1/700 x z + ---- y - 1/700 x z - 1/350 x y + 1/100 x y - 1/245 y z + 3675 + + 2 3 3 2 2 + + 1/50 y + 1/600 z - 2/75 y , COEFF(2, -1, -2) = 1/350 x z + 1/50 x y + + 107 2 3 + - 8/525 + 1/250 x z - ---- x - 1/350 z - 1/600 x - 1/175 x y + 7000 + + 2 2 3 256 2 + + 1/175 x y z - 1/350 x - 1/350 x z + 1/600 z + ---- y - 1/50 y z + 3675 + + 3 2 107 2 2 + - 2/75 y + 1/50 y + ---- z + 1/175 y z - 1/245 y z - 1/245 x y, + 7000 + + 3 33 2 + COEFF(-2, 0, -2) = 2/175 x y + 2/175 y z + 1/25 y - --- y - 2/245 x y + 490 + + 2 + - 2/175 x y z - 2/245 y z , COEFF(-1, 0, -2) = 2/175 y z - 1/175 x y z + + 2 2 3 + + 1/175 x y + 1/245 x y - 9/98 y - 2/245 y z + 1/25 y , + + 3 2 2 + COEFF(0, 0, -2) = 1/25 y + 2/245 x y - 1/10 y + 2/175 y z - 2/245 y z , + + 2 2 + COEFF(1, 0, -2) = - 9/98 y - 2/245 y z + 1/175 x y z + 1/245 x y + + 3 + + 2/175 y z - 1/175 x y + 1/25 y , COEFF(2, 0, -2) = - 2/175 x y + + 2 2 33 3 + + 2/175 y z - 2/245 y z - 2/245 x y + 2/175 x y z - --- y + 1/25 y , + 490 + + 3 2 2 2 + COEFF(-2, 1, -2) = - 1/600 z + 8/525 + 1/350 x - 1/50 y + 1/50 y z + + 2 107 2 2 2 + + 1/50 x y - ---- z - 1/245 y z - 1/350 x z - 1/245 x y + 1/175 y z + 7000 + + 107 3 2 2 + - ---- x + 1/250 x z - 1/600 x + 1/350 z - 1/350 x z + 1/175 x y + 7000 + + 3 256 3 + - 2/75 y + ---- y - 1/175 x y z, COEFF(-1, 1, -2) = - 2/75 y + 3675 + + 2 2 211 2 2 + + 1/700 x z - 1/245 y z + ---- y + 1/490 x y + 1/350 x y - 1/700 x + 3675 + + 167 3 2 2 + - ---- z - 1/350 x y z + 1/300 x + 1/175 y z - 1/700 x z + 1/100 x y + 7000 + + 3 229 2 2 2 + + 1/500 x z - 1/600 z - ----- x + 1/42 - 1/50 y + 1/50 y z + 1/350 z , + 10500 + + 2 2 2 187 + COEFF(0, 1, -2) = 1/245 x y + 1/350 z - 1/350 x + 4/75 y - ---- z + 2/75 + 7000 + + 3 2 2 2 2 + - 1/600 z - 1/245 y z + 1/175 y z - 1/50 y + 1/50 y z + 1/350 x z + + 3 2 2 3 + - 2/75 y , COEFF(1, 1, -2) = - 1/100 x y - 1/50 y - 1/350 x y - 2/75 y + + 3 167 2 2 3 + - 1/300 x - ---- z + 1/700 x z + 1/490 x y - 1/600 z + 1/350 x y z + 7000 + + 2 229 2 2 2 + + 1/175 y z - 1/700 x + ----- x + 1/700 x z - 1/245 y z + 1/50 y z + 10500 + + 2 211 2 + + 1/350 z + ---- y - 1/500 x z + 1/42, COEFF(2, 1, -2) = 1/350 x z + 3675 + + 107 3 2 107 + + 1/175 y z + ---- x - 1/600 z + 1/175 x y z + 8/525 + 1/50 y z - ---- z + 7000 7000 + + 2 2 2 256 3 2 + + 1/350 z - 1/350 x z - 1/50 x y + ---- y - 2/75 y - 1/245 y z + 3675 + + 2 2 3 2 + + 1/350 x - 1/245 x y - 1/175 x y + 1/600 x - 1/250 x z - 1/50 y , + + 11 137 2 2 + COEFF(-2, 2, -2) = - --- + ---- z + 1/100 y + 1/175 z - 2/175 y z + 420 5250 + + 529 2 137 2 3 + - ----- y + 1/175 x + 2/175 x y z + ---- x + 2/245 x y + 1/150 y + 14700 5250 + + 2 2 2 2 + - 1/175 x z + 1/125 x z - 1/175 x z + 2/245 y z - 1/100 x y + + 2 3 3 + - 2/175 x y - 1/100 y z - 1/300 z - 1/300 x , COEFF(-1, 2, -2) = + + 2 47 3 2 2 + - 1/100 y z + 1/175 x y z + ---- z + 1/150 y + 1/100 y + 1/175 z + 5250 + + 2 169 2 2 3 2 + - 1/200 x y - ----- y - 1/245 x y + 2/245 y z + 1/150 x - 1/350 x + 14700 + + 19 107 3 + - 2/175 y z + 1/250 x z - ---- - ---- x - 1/300 z - 1/175 x y + 2100 7000 + + 2 2 + - 1/350 x z + 1/350 x z, COEFF(0, 2, -2) = - 1/300 - 1/300 y + + 2 2 2 2 3 17 + - 1/100 y z - 1/175 x - 2/245 x y + 1/100 y - 1/300 z + ---- z + 5250 + + 2 2 2 3 + + 1/175 z + 2/245 y z - 2/175 y z + 1/175 x z + 1/150 y , + + 2 2 107 3 + COEFF(1, 2, -2) = 1/350 x z - 1/245 x y + 1/175 x y + ---- x - 1/150 x + 7000 + + 2 2 19 3 + + 1/175 z - 1/175 x y z + 1/200 x y - 2/175 y z - ---- + 1/150 y + 2100 + + 2 169 47 2 3 + + 1/350 x z - ----- y + ---- z - 1/350 x - 1/300 z - 1/250 x z + 14700 5250 + + 2 2 2 137 + - 1/100 y z + 1/100 y + 2/245 y z , COEFF(2, 2, -2) = - ---- x + 5250 + + 2 3 11 2 + + 2/245 y z + 1/150 y - --- - 1/100 y z + 2/175 x y - 2/175 y z + 420 + + 2 3 2 2 + + 1/175 z - 1/125 x z - 1/300 z + 1/100 x y + 1/100 y - 2/175 x y z + + 2 2 3 2 137 2 + + 1/175 x z + 2/245 x y + 1/300 x - 1/175 x z + ---- z + 1/175 x + 5250 + + 529 2 169 3 + - ----- y, COEFF(-2, -2, -1) = 1/350 x z - 1/250 x z - ----- y - 1/150 z + 14700 14700 + + 2 2 3 2 + + 1/175 x y z + 1/100 x y - 1/100 y - 2/175 x y + 1/300 x - 1/245 y z + + 107 19 2 3 2 2 + + ---- z + ---- - 1/175 x + 1/150 y - 1/175 y z + 1/200 y z + 1/350 z + 7000 2100 + + 2 2 47 2 + + 2/245 x y - 1/350 x z - ---- x, COEFF(-1, -2, -1) = - 1/700 x z + 5250 + + 191 167 2 2 167 + - 1/175 y z + ----- y + ---- x + 1/200 y z + 1/200 x y + ---- z + 14700 7000 7000 + + 2 3 3 17 + - 1/245 x y + 1/350 x y z - 1/500 x z - 1/150 z - 1/150 x - ---- + 2100 + + 2 2 2 2 3 + + 1/350 z - 1/700 x z - 1/100 y + 1/350 x - 1/175 x y + 1/150 y + + 2 187 2 2 29 + - 1/245 y z , COEFF(0, -2, -1) = ---- z - 1/350 x z + 1/200 y z - ---- + 7000 2100 + + 2 2 3 3 2 + - 1/100 y + 1/350 z + 1/150 y - 1/150 z - 2/245 x y - 1/175 y z + + 311 2 2 2 + + ----- y - 1/245 y z + 1/175 x , COEFF(1, -2, -1) = - 1/245 x y + 14700 + + 2 167 2 2 2 + + 1/350 x - ---- x - 1/350 x y z - 1/100 y + 1/350 z + 1/200 y z + 7000 + + 191 2 3 167 17 + + 1/175 x y + ----- y - 1/245 y z - 1/175 y z - 1/150 z + ---- z - ---- + 14700 7000 2100 + + 2 3 3 2 2 + - 1/700 x z + 1/150 y + 1/150 x - 1/200 x y + 1/500 x z + 1/700 x z , + + 169 19 2 47 3 + COEFF(2, -2, -1) = - ----- y + ---- - 1/100 x y + ---- x - 1/150 z + 14700 2100 5250 + + 3 2 107 2 + - 1/300 x + 2/175 x y + 1/200 y z + ---- z + 1/250 x z + 1/350 z + 7000 + + 2 2 2 2 2 + - 1/100 y - 1/175 y z - 1/245 y z + 1/350 x z + 2/245 x y - 1/175 x + + 2 3 2 + + 1/350 x z - 1/175 x y z + 1/150 y , COEFF(-2, -1, -1) = 1/700 x z + + 3 2 211 3 2 167 + + 1/600 x - 1/700 x z + ---- y - 2/75 y + 1/700 z + ---- x + 3675 7000 + + 2 2 2 229 2 + - 1/245 x y - 1/350 x - 1/50 x y - 1/350 x y z + ----- z + 1/50 y + 10500 + + 2 2 + - 1/100 y z + 1/490 y z + 1/350 y z - 1/42 - 1/500 x z + 1/175 x y + + 3 3 + - 1/300 z , COEFF(-1, -1, -1) = - 1/700 x y z + 1/350 x y - 2/75 y + + 137 3 2 2 137 2 + + ---- x - 1/300 z + 1/50 y + 1/700 z + ---- z - 1/1400 x z + 5250 5250 + + 2 166 2 17 2 + - 1/1000 x z - 1/100 y z + ---- y + 1/700 x - --- + 1/490 x y + 3675 525 + + 2 2 3 2 + - 1/1400 x z - 1/100 x y - 1/300 x + 1/490 y z + 1/350 y z, + + 2 151 2 3 + COEFF(0, -1, -1) = 1/350 x + 1/350 y z + ---- y - 1/100 y z - 2/75 y + 3675 + + 2 3 2 37 289 2 2 + + 1/245 x y - 1/300 z + 1/700 z - ---- + ----- z + 1/50 y + 1/490 y z + 1050 10500 + + 2 2 2 2 3 + - 1/700 x z, COEFF(1, -1, -1) = 1/700 z + 1/50 y + 1/490 x y - 2/75 y + + 166 2 3 2 137 2 + + ---- y + 1/700 x + 1/300 x + 1/100 x y + ---- z - 1/1400 x z + 3675 5250 + + 2 2 2 137 + - 1/350 x y + 1/490 y z - 1/100 y z + 1/1400 x z + 1/1000 x z - ---- x + 5250 + + 17 3 3 + - --- + 1/350 y z + 1/700 x y z - 1/300 z , COEFF(2, -1, -1) = - 1/300 z + 525 + + 2 2 2 2 2 + - 1/350 x - 1/245 x y - 1/100 y z + 1/700 z + 1/350 y z + 1/700 x z + + 211 229 2 2 167 + + ---- y + ----- z + 1/50 y + 1/490 y z - 1/175 x y - ---- x + 1/500 x z + 3675 10500 7000 + + 2 3 2 3 + + 1/700 x z - 2/75 y + 1/50 x y + 1/350 x y z - 1/600 x - 1/42, + + 3 + COEFF(-2, 0, -1) = - 1/175 x y z + 1/175 y z - 9/98 y + 1/25 y + + 2 2 57 + + 1/245 y z - 2/245 x y + 2/175 x y, COEFF(-1, 0, -1) = - --- y + 490 + + 2 3 2 + + 1/245 y z + 1/25 y + 1/175 x y - 1/350 x y z + 1/175 y z + 1/245 x y, + + 2 3 61 2 + COEFF(0, 0, -1) = 2/245 x y + 1/25 y - --- y + 1/245 y z + 1/175 y z, + 490 + + 3 2 57 2 + COEFF(1, 0, -1) = 1/25 y + 1/245 x y + 1/350 x y z - --- y + 1/245 y z + 490 + + 2 + - 1/175 x y + 1/175 y z, COEFF(2, 0, -1) = 1/245 y z + 1/175 x y z + + 2 3 + - 2/175 x y - 2/245 x y + 1/175 y z - 9/98 y + 1/25 y , COEFF(-2, 1, -1) + + 3 2 2 2 + = 1/350 y z + 1/300 z + 1/490 y z + 1/500 x z + 1/100 y z + 1/350 x + + 2 167 229 2 2 3 + - 1/245 x y - ---- x - ----- z - 1/700 x z + 1/700 x z - 1/600 x + 7000 10500 + + 2 3 2 211 + + 1/50 x y - 1/350 x y z + 1/175 x y - 2/75 y - 1/50 y + ---- y + 3675 + + 2 17 2 2 + - 1/700 z + 1/42, COEFF(-1, 1, -1) = --- - 1/50 y + 1/490 y z + 525 + + 2 2 2 166 + + 1/100 y z + 1/100 x y + 1/490 x y + 1/1000 x z + 1/350 x y + ---- y + 3675 + + 3 3 137 2 137 + - 2/75 y - 1/700 x y z + 1/300 z - ---- z + 1/1400 x z - ---- x + 5250 5250 + + 2 2 2 3 + - 1/700 z + 1/350 y z - 1/700 x + 1/1400 x z + 1/300 x , + + 2 151 3 3 + COEFF(0, 1, -1) = 1/350 y z - 1/350 x + ---- y + 1/300 z - 2/75 y + 3675 + + 289 2 2 37 2 2 + - ----- z + 1/490 y z + 1/245 x y + ---- - 1/700 z - 1/50 y + 10500 1050 + + 2 2 2 + + 1/100 y z + 1/700 x z, COEFF(1, 1, -1) = 1/700 x y z + 1/100 y z + + 2 3 166 2 + - 1/100 x y + 1/350 y z - 1/350 x y - 1/300 x + ---- y - 1/700 x + 3675 + + 137 3 2 137 17 2 2 + + ---- x - 2/75 y - 1/1400 x z - ---- z + --- - 1/50 y + 1/490 y z + 5250 5250 525 + + 2 3 2 2 + + 1/1400 x z + 1/300 z - 1/1000 x z + 1/490 x y - 1/700 z , + + 2 2 3 + COEFF(2, 1, -1) = 1/100 y z + 1/350 x y z + 1/350 x + 1/600 x + + 2 211 229 3 2 + - 1/700 x z - 1/175 x y + ---- y - ----- z - 2/75 y - 1/700 z + 3675 10500 + + 2 2 2 167 + + 1/490 y z + 1/42 - 1/500 x z - 1/50 x y - 1/700 x z + ---- x + 7000 + + 2 2 3 + - 1/245 x y - 1/50 y + 1/350 y z + 1/300 z , COEFF(-2, 2, -1) = + + 2 3 2 3 2 + - 1/100 x y + 1/150 z + 1/350 x z + 1/150 y + 1/250 x z + 2/245 x y + + 2 169 107 + - 1/350 z - ----- y - ---- z + 1/175 x y z - 1/175 y z - 2/175 x y + 14700 7000 + + 47 2 2 2 2 2 + + ---- x - 1/200 y z + 1/175 x + 1/100 y - 1/350 x z - 1/245 y z + 5250 + + 3 19 3 2 + - 1/300 x - ----, COEFF(-1, 2, -1) = 1/150 z - 1/245 y z - 1/175 x y + 2100 + + 2 2 2 167 + - 1/350 x + 1/350 x y z - 1/175 y z + 1/700 x z + 1/100 y - ---- z + 7000 + + 2 3 167 3 17 2 + - 1/350 z + 1/150 x - ---- x + 1/500 x z + 1/150 y + ---- - 1/245 x y + 7000 2100 + + 191 2 2 2 + + ----- y + 1/700 x z - 1/200 y z - 1/200 x y , COEFF(0, 2, -1) = + 14700 + + 187 2 2 2 2 3 + - ---- z - 1/200 y z - 2/245 x y - 1/245 y z + 1/100 y + 1/150 y + 7000 + + 311 29 2 2 2 3 + + ----- y + ---- - 1/350 z - 1/175 y z - 1/175 x + 1/350 x z + 1/150 z + 14700 2100 + + 2 2 2 167 + , COEFF(1, 2, -1) = - 1/350 x + 1/700 x z - 1/350 z - ---- z - 1/500 x z + 7000 + + 2 2 191 2 167 2 + + 1/200 x y - 1/245 y z + ----- y - 1/700 x z + ---- x + 1/100 y + 14700 7000 + + 2 3 3 2 17 + - 1/245 x y - 1/150 x + 1/150 z - 1/200 y z - 1/175 y z + ---- + 2100 + + 3 2 + - 1/350 x y z + 1/175 x y + 1/150 y , COEFF(2, 2, -1) = 1/175 x + + 3 169 3 2 2 + + 1/300 x + 2/175 x y - ----- y + 1/150 y - 1/350 x z + 1/100 x y + 14700 + + 2 2 2 47 + - 1/175 y z - 1/175 x y z - 1/350 x z - 1/245 y z + 1/100 y - ---- x + 5250 + + 2 2 2 107 3 + - 1/250 x z - 1/200 y z - 1/350 z + 2/245 x y - ---- z + 1/150 z + 7000 + + 19 2 + - ----, COEFF(-2, -2, 0) = - 2/175 x y + 1/300 - 1/300 y + 2/245 x y + 2100 + + 2 2 17 3 3 2 + - 1/175 x + 1/175 z - ---- x + 1/300 x + 1/150 y - 1/175 x z + 5250 + + 2 2 2 3 + + 1/100 x y - 1/100 y - 2/245 y z , COEFF(-1, -2, 0) = - 1/150 x + + 2 311 2 187 2 + + 1/200 x y + ----- y - 1/100 y - 1/175 x y + ---- x + 1/175 z + 14700 7000 + + 2 2 3 2 2 29 + - 1/245 x y - 1/350 x z + 1/150 y - 2/245 y z + 1/350 x - ----, + 2100 + + 2 431 2 41 2 + COEFF(0, -2, 0) = - 2/245 x y + ----- y + 1/175 z - ---- + 1/175 x + 14700 2100 + + 2 3 2 2 + - 2/245 y z + 1/150 y - 1/100 y , COEFF(1, -2, 0) = - 1/100 y + + 2 29 2 2 2 + - 2/245 y z - ---- - 1/200 x y + 1/350 x z - 1/245 x y + 1/175 x y + 2100 + + 3 2 2 311 3 187 + + 1/150 y + 1/350 x + 1/175 z + ----- y + 1/150 x - ---- x, + 14700 7000 + + 2 2 17 2 + COEFF(2, -2, 0) = - 1/100 y - 1/100 x y + ---- x - 1/175 x + 1/300 + 5250 + + 2 2 2 2 3 + + 2/175 x y - 2/245 y z + 2/245 x y + 1/175 z + 1/175 x z - 1/300 x + + 3 2 2 + + 1/150 y - 1/300 y, COEFF(-2, -1, 0) = - 2/75 - 1/245 x y + 1/50 y + + 3 2 2 2 187 + - 2/75 y + 1/350 z - 1/50 x y - 1/350 x z + ---- x + 1/175 x y + 7000 + + 2 3 2 + - 1/350 x + 4/75 y + 1/600 x + 1/245 y z , COEFF(-1, -1, 0) = + + 2 289 3 37 2 151 + - 1/700 x z + ----- x - 2/75 y - ---- + 1/350 x y + 1/245 y z + ---- y + 10500 1050 3675 + + 3 2 2 2 2 2 + - 1/300 x + 1/50 y + 1/350 z + 1/490 x y + 1/700 x - 1/100 x y , + + 2 2 136 3 2 + COEFF(0, -1, 0) = 1/245 y z + 1/350 z + ---- y - 2/75 y + 1/350 x + 3675 + + 2 2 2 2 + - 4/105 + 1/50 y + 1/245 x y, COEFF(1, -1, 0) = 1/50 y + 1/700 x z + + 3 151 2 2 289 + + 1/300 x + ---- y + 1/100 x y - 1/350 x y + 1/245 y z - ----- x + 3675 10500 + + 2 2 3 37 2 + + 1/490 x y + 1/350 z - 2/75 y - ---- + 1/700 x , COEFF(2, -1, 0) = + 1050 + + 2 2 2 2 2 + 1/245 y z - 1/350 x + 1/350 z + 1/50 y - 1/175 x y - 1/245 x y - 2/75 + + 2 187 3 3 2 + + 1/50 x y + 4/75 y - ---- x - 2/75 y - 1/600 x + 1/350 x z , + 7000 + + 3 2 2 + COEFF(-2, 0, 0) = 1/25 y + 2/245 y z - 2/245 x y - 1/10 y + 2/175 x y, + + 61 2 3 2 + COEFF(-1, 0, 0) = - --- y + 2/245 y z + 1/25 y + 1/175 x y + 1/245 x y, + 490 + + 2 2 13 3 + COEFF(0, 0, 0) = 2/245 y z + 2/245 x y - -- y + 1/25 y , + 98 + + 61 2 2 3 + COEFF(1, 0, 0) = - 1/175 x y - --- y + 2/245 y z + 1/245 x y + 1/25 y , + 490 + + 3 2 2 + COEFF(2, 0, 0) = 1/25 y + 2/245 y z - 2/245 x y - 2/175 x y - 1/10 y, + + 187 2 2 3 2 + COEFF(-2, 1, 0) = - ---- x - 1/50 y + 1/350 x - 2/75 y + 1/50 x y + 7000 + + 2 2 2 2 + - 1/245 x y + 1/245 y z - 1/350 z + 2/75 + 1/350 x z + 4/75 y + + 3 151 289 2 + + 1/175 x y - 1/600 x , COEFF(-1, 1, 0) = ---- y - ----- x - 1/700 x + 3675 10500 + + 2 2 3 2 2 + + 1/350 x y + 1/700 x z + 1/490 x y + 1/300 x + 1/100 x y - 1/50 y + + 2 3 37 2 136 + + 1/245 y z - 2/75 y + ---- - 1/350 z , COEFF(0, 1, 0) = ---- y + 4/105 + 1050 3675 + + 3 2 2 2 2 2 + - 2/75 y - 1/50 y - 1/350 x - 1/350 z + 1/245 y z + 1/245 x y, + + 2 151 37 2 + COEFF(1, 1, 0) = - 1/700 x + ---- y - 1/350 x y + ---- - 1/50 y + 3675 1050 + + 2 2 3 289 2 2 + + 1/245 y z - 1/700 x z - 2/75 y + ----- x - 1/100 x y + 1/490 x y + 10500 + + 2 3 2 + - 1/350 z - 1/300 x , COEFF(2, 1, 0) = 1/245 y z - 1/175 x y + + 2 2 3 2 2 187 + - 1/245 x y + 1/350 x + 1/600 x - 1/50 y - 1/50 x y + 4/75 y + ---- x + 7000 + + 2 3 2 + - 1/350 x z + 2/75 - 2/75 y - 1/350 z , COEFF(-2, 2, 0) = - 1/300 + + 2 2 17 2 2 + - 1/175 z - 2/175 x y - 2/245 y z + ---- x + 1/100 y - 1/100 x y + 5250 + + 3 3 2 2 2 + - 1/300 x + 1/150 y - 1/300 y + 1/175 x z + 2/245 x y + 1/175 x , + + 2 311 2 + COEFF(-1, 2, 0) = - 1/245 x y + ----- y - 1/175 x y - 1/200 x y + 14700 + + 2 3 187 2 29 3 2 + + 1/100 y + 1/150 y - ---- x - 1/175 z + ---- + 1/150 x - 2/245 y z + 7000 2100 + + 2 2 2 431 41 + + 1/350 x z - 1/350 x , COEFF(0, 2, 0) = - 2/245 y z + ----- y + ---- + 14700 2100 + + 2 2 2 3 2 + - 2/245 x y - 1/175 x + 1/100 y + 1/150 y - 1/175 z , COEFF(1, 2, 0) + + 2 2 3 2 2 + = 1/200 x y - 1/175 z + 1/150 y - 1/245 x y + 1/175 x y - 1/350 x + + 2 2 311 3 2 187 29 + - 2/245 y z + 1/100 y + ----- y - 1/150 x - 1/350 x z + ---- x + ----, + 14700 7000 2100 + + 3 2 2 + COEFF(2, 2, 0) = 2/175 x y + 1/150 y - 1/300 + 1/175 x + 2/245 x y + + 2 2 2 2 2 3 + + 1/100 y - 1/175 x z + 1/100 x y - 2/245 y z - 1/175 z + 1/300 x + + 17 2 19 3 + - 1/300 y - ---- x, COEFF(-2, -2, 1) = - 1/350 x z + ---- + 1/150 z + 5250 2100 + + 2 2 2 3 + + 1/175 y z + 2/245 x y - 2/175 x y - 1/350 x z - 1/100 y + 1/300 x + + 2 3 107 2 169 + + 1/100 x y + 1/150 y - ---- z - 1/175 x - 1/175 x y z - ----- y + 7000 14700 + + 2 2 2 47 + - 1/245 y z + 1/250 x z - 1/200 y z + 1/350 z - ---- x, + 5250 + + 2 2 + COEFF(-1, -2, 1) = 1/350 z - 1/350 x y z - 1/245 x y + 1/500 x z + + 2 167 2 2 + + 1/700 x z - 1/175 x y + ---- x - 1/100 y - 1/700 x z + 1/175 y z + 7000 + + 2 2 3 3 2 3 + + 1/350 x + 1/200 x y - 1/150 x + 1/150 z - 1/245 y z + 1/150 y + + 167 2 17 191 3 + - ---- z - 1/200 y z - ---- + ----- y, COEFF(0, -2, 1) = 1/150 y + 7000 2100 14700 + + 2 311 29 3 2 + - 1/200 y z + ----- y + 1/175 y z - ---- + 1/150 z + 1/350 z + 14700 2100 + + 2 2 2 187 2 2 + + 1/350 x z + 1/175 x - 2/245 x y - ---- z - 1/100 y - 1/245 y z , + 7000 + + 167 191 2 3 + COEFF(1, -2, 1) = - ---- z + ----- y + 1/175 y z + 1/350 z + 1/150 z + 7000 14700 + + 2 17 2 167 2 + - 1/245 y z - ---- - 1/500 x z + 1/350 x - ---- x - 1/200 x y + 2100 7000 + + 3 2 2 2 3 2 + + 1/150 y - 1/200 y z - 1/100 y + 1/700 x z + 1/150 x - 1/245 x y + + 2 2 + + 1/175 x y + 1/700 x z + 1/350 x y z, COEFF(2, -2, 1) = 1/350 z + + 2 169 3 2 + + 1/175 y z - 1/100 y - ----- y - 1/300 x - 1/350 x z + 1/175 x y z + 14700 + + 47 2 3 2 2 + + ---- x - 1/100 x y + 1/150 z - 1/250 x z + 1/350 x z - 1/175 x + 5250 + + 3 2 2 107 19 2 + + 1/150 y + 2/245 x y - 1/245 y z - ---- z + ---- - 1/200 y z + 7000 2100 + + 2 2 229 + + 2/175 x y, COEFF(-2, -1, 1) = 1/50 y - 1/50 x y - 1/42 - ----- z + 10500 + + 2 2 211 2 2 3 + - 1/245 x y - 1/700 x z + ---- y - 1/700 x z + 1/490 y z + 1/600 x + 3675 + + 2 3 3 + + 1/350 x y z + 1/100 y z - 2/75 y + 1/500 x z + 1/175 x y + 1/300 z + + 2 167 2 2 + + 1/700 z + ---- x - 1/350 y z - 1/350 x , COEFF(-1, -1, 1) = 1/700 z + 7000 + + 2 137 137 2 2 17 + + 1/50 y - ---- z + ---- x + 1/490 y z - 1/1400 x z + 1/700 x y z - --- + 5250 5250 525 + + 2 166 2 3 3 + + 1/490 x y + 1/350 x y + ---- y + 1/1400 x z - 1/300 x + 1/300 z + 3675 + + 3 2 2 2 + - 2/75 y + 1/700 x - 1/100 x y - 1/350 y z + 1/100 y z + 1/1000 x z, + + 2 2 37 2 + COEFF(0, -1, 1) = 1/350 x + 1/50 y - 1/350 y z - ---- + 1/700 x z + 1050 + + 2 2 151 3 289 3 + + 1/245 x y + 1/700 z + ---- y + 1/300 z - ----- z - 2/75 y + 3675 10500 + + 2 2 2 + + 1/100 y z + 1/490 y z , COEFF(1, -1, 1) = 1/100 x y - 1/1000 x z + + 137 2 3 2 2 + - ---- z + 1/100 y z + 1/300 x + 1/490 x y - 1/700 x y z + 1/700 z + 5250 + + 137 2 2 17 3 + - ---- x + 1/1400 x z + 1/490 y z - --- + 1/300 z - 1/350 x y + 5250 525 + + 2 2 166 2 3 + + 1/1400 x z - 1/350 y z + 1/50 y + ---- y + 1/700 x - 2/75 y , + 3675 + + 3 2 2 + COEFF(2, -1, 1) = - 1/600 x + 1/490 y z - 1/350 x y z - 1/700 x z + + 3 2 3 2 + - 1/500 x z + 1/300 z + 1/700 z - 1/175 x y - 2/75 y + 1/50 x y + + 167 2 2 2 2 + - ---- x - 1/42 - 1/350 y z + 1/50 y + 1/100 y z - 1/350 x - 1/245 x y + 7000 + + 211 2 229 + + ---- y + 1/700 x z - ----- z, COEFF(-2, 0, 1) = 2/175 x y - 9/98 y + 3675 10500 + + 2 3 2 + - 1/175 y z + 1/175 x y z - 2/245 x y + 1/25 y + 1/245 y z , + + 57 2 3 2 + COEFF(-1, 0, 1) = 1/175 x y - --- y + 1/245 y z + 1/25 y + 1/245 x y + 490 + + - 1/175 y z + 1/350 x y z, + + 2 61 3 2 + COEFF(0, 0, 1) = 2/245 x y - --- y - 1/175 y z + 1/25 y + 1/245 y z , + 490 + + 57 2 2 + COEFF(1, 0, 1) = - --- y - 1/350 x y z + 1/245 x y + 1/245 y z + 490 + + 3 + - 1/175 y z + 1/25 y - 1/175 x y, COEFF(2, 0, 1) = - 1/175 y z - 9/98 y + + 2 2 3 + + 1/245 y z - 2/245 x y - 2/175 x y + 1/25 y - 1/175 x y z, + + 2 2 2 3 2 + COEFF(-2, 1, 1) = 1/700 x z - 1/100 y z - 1/700 z - 2/75 y - 1/50 y + + 211 229 2 3 + + ---- y + ----- z - 1/350 y z - 1/245 x y - 1/500 x z + 1/42 - 1/300 z + 3675 10500 + + 2 167 3 2 + + 1/175 x y + 1/700 x z - ---- x - 1/600 x + 1/350 x + 1/350 x y z + 7000 + + 2 2 3 2 + + 1/50 x y + 1/490 y z , COEFF(-1, 1, 1) = - 1/300 z - 1/100 y z + + 2 2 2 166 137 + - 1/350 y z - 1/700 z - 1/1400 x z - 1/700 x + ---- y + ---- z + 3675 5250 + + 2 2 2 3 17 3 + + 1/100 x y + 1/490 y z + 1/490 x y + 1/300 x + --- - 2/75 y + 525 + + 2 137 2 + + 1/1400 x z - ---- x - 1/50 y + 1/700 x y z + 1/350 x y - 1/1000 x z, + 5250 + + 289 3 2 2 + COEFF(0, 1, 1) = ----- z - 1/350 y z - 1/300 z - 1/350 x - 1/50 y + 10500 + + 2 2 2 37 151 3 + + 1/490 y z - 1/700 z + 1/245 x y + ---- + ---- y - 2/75 y + 1050 3675 + + 2 2 166 + - 1/700 x z - 1/100 y z, COEFF(1, 1, 1) = ---- y - 1/700 x y z + 3675 + + 2 2 2 2 + - 1/700 x - 1/100 x y - 1/350 y z - 1/1400 x z + 1/1000 x z - 1/50 y + + 2 3 17 3 2 2 + - 1/1400 x z - 1/300 x + --- - 1/300 z - 1/100 y z + 1/490 y z + 525 + + 137 2 2 137 3 + + ---- z + 1/490 x y - 1/350 x y - 1/700 z + ---- x - 2/75 y , + 5250 5250 + + 3 2 229 2 + COEFF(2, 1, 1) = 1/600 x - 1/175 x y - 1/50 x y + ----- z + 1/350 x + 10500 + + 2 2 3 2 + - 1/100 y z - 1/700 z - 1/350 x y z + 1/500 x z - 1/300 z + 1/700 x z + + 2 211 2 2 + + 1/42 + 1/490 y z + ---- y - 1/245 x y - 1/700 x z - 1/350 y z + 3675 + + 2 167 3 3 2 + - 1/50 y + ---- x - 2/75 y , COEFF(-2, 2, 1) = 1/150 y + 1/175 x + 7000 + + 169 3 2 2 + - ----- y - 1/150 z - 1/350 z - 2/175 x y - 1/250 x z - 1/100 x y + 14700 + + 3 19 2 107 2 + - 1/300 x - ---- - 1/245 y z + ---- z + 1/175 y z + 2/245 x y + 2100 7000 + + 2 47 2 2 2 + + 1/350 x z + ---- x + 1/200 y z - 1/175 x y z + 1/100 y + 1/350 x z , + 5250 + + 2 2 3 + COEFF(-1, 2, 1) = 1/700 x z + 1/100 y - 1/150 z - 1/500 x z + 1/175 y z + + 2 3 17 2 2 2 + - 1/350 x + 1/150 x + ---- + 1/200 y z - 1/245 y z - 1/700 x z + 2100 + + 2 167 3 2 + - 1/200 x y - 1/350 x y z + ---- z - 1/175 x y + 1/150 y - 1/350 z + 7000 + + 2 167 191 2 3 + - 1/245 x y - ---- x + ----- y, COEFF(0, 2, 1) = 1/100 y - 1/150 z + 7000 14700 + + 2 2 2 311 187 + + 1/200 y z + 1/175 y z - 1/350 z - 1/175 x + ----- y + ---- z + 14700 7000 + + 2 2 29 2 3 + - 1/245 y z - 1/350 x z + ---- - 2/245 x y + 1/150 y , COEFF(1, 2, 1) + 2100 + + 2 17 2 3 + = 1/350 x y z - 1/350 x + 1/175 y z + ---- + 1/200 y z + 1/150 y + 2100 + + 2 2 167 167 + + 1/500 x z - 1/700 x z - 1/350 z + 1/175 x y + ---- x + ---- z + 7000 7000 + + 2 2 2 191 3 2 + + 1/200 x y - 1/245 y z + 1/100 y + ----- y - 1/150 x - 1/245 x y + 14700 + + 3 2 47 2 + - 1/150 z - 1/700 x z, COEFF(2, 2, 1) = - ---- x + 1/100 y + 1/175 y z + 5250 + + 2 107 2 19 2 + - 1/245 y z + ---- z + 1/350 x z - ---- - 1/350 x z + 2/175 x y + 7000 2100 + + 2 3 2 3 3 169 + + 1/200 y z - 1/150 z + 1/175 x + 1/300 x + 1/150 y - ----- y + 14700 + + 2 2 2 + - 1/350 z + 2/245 x y + 1/100 x y + 1/250 x z + 1/175 x y z, + + 3 137 2 2 + COEFF(-2, -2, 2) = 1/300 x + ---- z + 1/175 x z - 1/175 x z + 1/125 x z + 5250 + + 2 3 2 2 + - 1/100 y + 2/175 y z + 1/150 y - 2/175 x y - 1/175 x - 1/100 y z + + 2 137 2 2 529 2 + + 2/245 x y - ---- x + 1/100 x y - 1/175 z - ----- y + 2/245 y z + 5250 14700 + + 3 11 2 3 + - 2/175 x y z - 1/300 z + ---, COEFF(-1, -2, 2) = 2/245 y z - 1/150 x + 420 + + 19 2 47 2 2 + + ---- + 1/350 x z + ---- z - 1/100 y + 1/350 x z + 2/175 y z + 2100 5250 + + 2 107 2 2 169 + - 1/175 z + ---- x - 1/175 x y z - 1/100 y z + 1/350 x - ----- y + 7000 14700 + + 2 3 3 2 + + 1/200 x y + 1/250 x z - 1/300 z + 1/150 y - 1/245 x y - 1/175 x y, + + 3 2 2 17 + COEFF(0, -2, 2) = - 1/300 z + 2/175 y z + 2/245 y z + 1/175 x + ---- z + 5250 + + 2 3 2 2 + - 1/300 y + 1/300 - 1/100 y z + 1/150 y - 2/245 x y - 1/100 y + + 2 2 2 2 + - 1/175 z + 1/175 x z, COEFF(1, -2, 2) = 1/350 x z - 1/100 y z + + 3 47 2 2 3 2 + + 1/150 x + ---- z - 1/200 x y - 1/175 z - 1/300 z + 2/245 y z + 5250 + + 169 19 2 3 + - 1/250 x z - ----- y + ---- + 1/175 x y + 2/175 y z + 1/350 x + 1/150 y + 14700 2100 + + 2 107 2 2 + - 1/100 y - ---- x - 1/350 x z + 1/175 x y z - 1/245 x y, + 7000 + + 2 137 2 3 3 + COEFF(2, -2, 2) = - 1/175 x + ---- z - 1/175 x z - 1/300 x + 1/150 y + 5250 + + 137 2 2 2 + + ---- x - 1/125 x z + 2/175 y z - 1/100 y z - 1/100 y + 2/245 y z + 5250 + + 529 3 11 2 + - ----- y - 1/300 z + 2/175 x y + 2/175 x y z + --- + 2/245 x y + 14700 420 + + 2 2 2 107 + - 1/175 x z - 1/175 z - 1/100 x y , COEFF(-2, -1, 2) = - ---- z + 7000 + + 2 107 2 2 2 + - 1/50 x y + ---- x + 1/350 x z - 1/175 y z + 1/50 y z - 1/350 z + 7000 + + 2 3 3 3 2 + + 1/50 y - 1/600 z + 1/175 x y - 8/525 + 1/600 x - 2/75 y - 1/350 x + + 256 2 2 2 + + ---- y + 1/175 x y z - 1/350 x z - 1/245 x y - 1/245 y z + 1/250 x z, + 3675 + + 167 2 + COEFF(-1, -1, 2) = 1/350 x y z + 1/500 x z - ---- z - 1/175 y z + 1/50 y + 7000 + + 211 3 3 2 2 + + ---- y - 2/75 y + 1/350 x y - 1/42 - 1/300 x - 1/100 x y + 1/700 x + 3675 + + 2 2 2 2 229 2 + + 1/700 x z - 1/245 y z + 1/50 y z + 1/700 x z + ----- x - 1/350 z + 10500 + + 3 2 2 2 + - 1/600 z + 1/490 x y, COEFF(0, -1, 2) = - 2/75 + 1/350 x z + 1/350 x + + 2 2 187 3 2 2 + + 4/75 y + 1/245 x y + 1/50 y - ---- z - 2/75 y + 1/50 y z - 1/350 z + 7000 + + 3 2 3 211 + - 1/600 z - 1/245 y z - 1/175 y z, COEFF(1, -1, 2) = 1/300 x + ---- y + 3675 + + 2 3 2 2 2 + + 1/700 x z - 1/600 z - 1/350 x y z + 1/50 y - 1/700 x z + 1/50 y z + + 2 2 229 3 167 + - 1/245 y z - 1/350 x y - 1/42 + 1/100 x y - ----- x - 2/75 y - ---- z + 10500 7000 + + 2 2 2 + + 1/490 x y + 1/700 x - 1/500 x z - 1/175 y z - 1/350 z , + + 3 2 107 2 + COEFF(2, -1, 2) = - 2/75 y + 1/50 y - ---- x - 1/350 z - 1/175 x y z + 7000 + + 2 256 2 2 + + 1/50 y z - 8/525 + ---- y - 1/175 y z - 1/350 x - 1/350 x z + 3675 + + 3 2 2 2 2 3 + - 1/600 x - 1/350 x z - 1/245 x y + 1/50 x y - 1/245 y z - 1/600 z + + 107 3 + - 1/175 x y - ---- z - 1/250 x z, COEFF(-2, 0, 2) = - 2/175 y z + 1/25 y + 7000 + + 33 2 2 + + 2/175 x y z - --- y + 2/175 x y - 2/245 y z - 2/245 x y, + 490 + + COEFF(-1, 0, 2) = - 9/98 y - 2/175 y z + 1/175 x y + 1/175 x y z + + 2 2 3 + - 2/245 y z + 1/245 x y + 1/25 y , + + 3 2 2 + COEFF(0, 0, 2) = 1/25 y - 2/175 y z - 2/245 y z - 1/10 y + 2/245 x y, + + 2 3 + COEFF(1, 0, 2) = - 1/175 x y - 9/98 y - 2/245 y z - 2/175 y z + 1/25 y + + 2 2 + - 1/175 x y z + 1/245 x y, COEFF(2, 0, 2) = - 2/175 x y z - 2/245 y z + + 3 2 33 + + 1/25 y - 2/245 x y - 2/175 y z - 2/175 x y - --- y, COEFF(-2, 1, 2) = + 490 + + 2 2 2 107 3 + 1/350 z - 1/245 x y + 8/525 + 1/50 x y + ---- z + 1/175 x y z - 1/600 x + 7000 + + 3 2 256 2 + + 1/600 z + 1/350 x z + ---- y - 1/250 x z - 1/50 y z + 1/175 x y + 3675 + + 2 2 2 3 2 + - 1/350 x z - 1/50 y - 1/175 y z - 1/245 y z - 2/75 y + 1/350 x + + 107 2 + - ---- x, COEFF(-1, 1, 2) = - 1/50 y z - 1/500 x z + 1/350 x y z + 7000 + + 2 2 2 167 2 + - 1/50 y - 1/700 x z - 1/700 x - 1/175 y z + 1/42 + ---- z - 1/245 y z + 7000 + + 229 3 211 2 3 2 + - ----- x - 2/75 y + ---- y + 1/100 x y + 1/600 z + 1/490 x y + 10500 3675 + + 2 2 3 + - 1/700 x z + 1/350 x y + 1/350 z + 1/300 x , COEFF(0, 1, 2) = 4/75 y + + 3 2 3 2 2 + + 1/600 z - 1/350 x z - 2/75 y - 1/175 y z + 1/245 x y - 1/245 y z + + 2 2 2 187 2 + - 1/350 x - 1/50 y z + 1/350 z + ---- z - 1/50 y + 2/75, + 7000 + + 3 2 2 2 + COEFF(1, 1, 2) = 1/600 z + 1/350 z + 1/500 x z - 1/700 x z + 1/700 x z + + 2 3 2 3 211 + - 1/245 y z - 2/75 y - 1/700 x + 1/42 - 1/300 x - 1/175 y z + ---- y + 3675 + + 167 2 2 229 2 + - 1/350 x y z + ---- z - 1/100 x y + 1/490 x y + ----- x - 1/50 y + 7000 10500 + + 2 2 2 2 + - 1/50 y z - 1/350 x y, COEFF(2, 1, 2) = 1/350 x - 1/50 y + 1/350 x z + + 3 3 2 3 2 + + 1/600 x - 1/175 x y + 8/525 - 2/75 y - 1/50 y z + 1/600 z + 1/350 z + + 107 2 2 2 256 + + ---- z - 1/245 y z + 1/350 x z - 1/50 x y - 1/175 y z + ---- y + 7000 3675 + + 2 107 + - 1/245 x y - 1/175 x y z + 1/250 x z + ---- x, COEFF(-2, 2, 2) = + 7000 + + 3 137 2 2 + 1/150 y - 2/175 x y + ---- x + 2/175 y z + 1/100 y + 2/245 x y + 5250 + + 3 3 2 529 2 + + 1/300 z - 1/300 x - 2/175 x y z + 1/175 x z - ----- y + 1/175 z + 14700 + + 2 137 11 2 2 + - 1/100 x y - ---- z - 1/125 x z - --- + 1/100 y z + 2/245 y z + 5250 420 + + 2 2 2 + + 1/175 x - 1/175 x z , COEFF(-1, 2, 2) = - 1/350 x z - 1/175 x y z + + 2 169 3 3 2 + + 2/245 y z - ----- y + 1/150 x - 1/175 x y + 1/300 z + 1/100 y z + 14700 + + 2 47 107 3 2 19 + - 1/250 x z - 1/350 x - ---- z - ---- x + 1/150 y - 1/200 x y - ---- + 5250 7000 2100 + + 2 2 2 2 + + 1/100 y + 2/175 y z - 1/245 x y + 1/175 z - 1/350 x z, + + 3 3 2 17 2 + COEFF(0, 2, 2) = 1/150 y - 1/300 + 1/300 z - 1/175 x - ---- z + 1/100 y + 5250 + + 2 2 2 2 + + 1/100 y z + 2/175 y z + 2/245 y z - 1/175 x z - 2/245 x y - 1/300 y + + 2 19 2 2 + + 1/175 z , COEFF(1, 2, 2) = - ---- + 1/175 x y + 1/100 y z - 1/350 x + 2100 + + 2 2 169 + + 1/250 x z + 1/100 y + 1/175 x y z + 2/175 y z - 1/350 x z - ----- y + 14700 + + 2 2 47 3 3 107 + + 1/350 x z + 1/175 z - ---- z + 1/150 y + 1/300 z + ---- x + 5250 7000 + + 2 2 3 2 + + 2/245 y z + 1/200 x y - 1/150 x - 1/245 x y, COEFF(2, 2, 2) = + + 137 11 2 2 3 + - ---- x - --- + 2/175 x y + 1/175 x + 1/100 y z + 1/300 z + 2/175 x y z + 5250 420 + + 529 2 2 2 3 + - ----- y + 1/100 y + 2/245 y z + 2/175 y z + 1/175 z + 1/150 y + 14700 + + 137 2 2 3 2 + + 1/125 x z - ---- z + 1/100 x y + 1/175 x z + 1/300 x + 1/175 x z + 5250 + + 2 + + 2/245 x y] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dy.compute.c"); 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used=1671780564, alloc=14284232, time=235.57 +bytes used=1672780908, alloc=14284232, time=235.64 +bytes used=1673781220, alloc=14284232, time=235.72 +bytes used=1674781420, alloc=14284232, time=235.80 +bytes used=1675781660, alloc=14284232, time=235.87 +bytes used=1676781924, alloc=14284232, time=235.95 +bytes used=1677782092, alloc=14284232, time=236.02 +bytes used=1678782300, alloc=14284232, time=236.20 +bytes used=1679783348, alloc=14284232, time=236.55 +bytes used=1680783504, alloc=14284232, time=236.78 +bytes used=1681783752, alloc=14284232, time=238.32 +bytes used=1682783944, alloc=14284232, time=240.34 +bytes used=1683784964, alloc=14284232, time=240.87 +bytes used=1684785116, alloc=14284232, time=241.09 +bytes used=1685785268, alloc=14284232, time=241.17 +bytes used=1686785428, alloc=14284232, time=241.26 +bytes used=1687785756, alloc=14284232, time=241.43 +bytes used=1688785908, alloc=14284232, time=241.56 +> +# d/dz +> simplify( diff(interp_3d_cube_order4_smooth0,z) ); +bytes 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2/175 x y z DATA(-2, -2, 2) + + 29 + - 1/175 x y z DATA(2, -1, 2) + ---- DATA(0, -1, 2) + 2100 + + - 1/350 y z DATA(1, 1, -1) + 1/350 x y z DATA(1, 1, 2) + + + 1/350 x y z DATA(-1, 2, 1) - 1/175 x y z DATA(-2, -2, -1) + + + 1/175 x y z DATA(-1, -2, 2) - 1/175 x y z DATA(1, -2, 2) + + - 1/350 y z DATA(-1, 1, -1) - 1/175 x y z DATA(-1, 2, -2) + + - 1/175 x y z DATA(2, 2, 1) - 1/350 y z DATA(-1, 1, 1) + + + 1/42 DATA(-2, -1, 1) - 1/350 x y z DATA(2, 1, 1) + + - 1/350 x y z DATA(1, 2, 1) + 8/525 DATA(2, -2, 1) + + + 1/350 x y z DATA(2, -1, 1) + 1/175 x y z DATA(1, 2, 2) + + 229 + + ----- x DATA(-1, -2, -1) + 2/75 DATA(-2, 0, 1) + 10500 + + + 1/700 x y z DATA(1, -1, -1) + 1/700 x y z DATA(-1, 1, 1) + + - 1/175 x y z DATA(-1, 2, 2) - 2/175 x y z DATA(2, -2, 2) + + + 1/175 x y z DATA(-2, 2, -1) + 2/175 x y z DATA(2, 2, 2) + + + 1/350 x y z DATA(1, -2, -1) + 1/350 x y z DATA(-2, 1, -1) + + + 1/175 x y z DATA(2, 1, 2) + 1/175 x y z DATA(2, -2, -1) + + - 1/300 DATA(0, 2, 2) - 1/350 x y z DATA(-2, -1, -1) + + 167 137 29 + - ---- x DATA(-2, 1, 1) + ---- x DATA(1, 1, 1) + ---- DATA(1, 0, 2) + 7000 5250 2100 + + 229 167 107 + + ----- x DATA(-1, 2, -1) - ---- x DATA(2, 1, -1) - ---- x DATA(2, 2, -1) + 10500 7000 7000 + + 229 167 + - ----- x DATA(1, 2, -1) - ---- x DATA(-1, -1, 2) + 10500 7000 + + 229 + - 1/700 x y z DATA(-1, -1, -1) + ----- x DATA(1, 2, 1) + 10500 + + 37 137 167 + - ---- DATA(-1, 0, -1) + ---- x DATA(2, 2, -2) + ---- x DATA(2, -1, 1) + 1050 5250 7000 + + 229 107 167 + - ----- x DATA(-1, 2, 1) + ---- x DATA(-2, -2, -1) - ---- x DATA(1, 1, -2) + 10500 7000 7000 + + 107 137 107 + - ---- x DATA(1, 2, -2) - ---- x DATA(-2, 2, -2) - ---- x DATA(-2, 2, 1) + 7000 5250 7000 + + 37 + - 1/42 DATA(2, -1, -1) + 4/105 DATA(0, 0, 1) + ---- DATA(1, 0, 1) + 1050 + + 37 17 + + ---- DATA(0, 1, 1) + --- DATA(1, 1, 1) + 1/175 x z DATA(-2, -1, 1) + 1050 525 + + - 1/175 x z DATA(2, -1, -1) - 1/175 x z DATA(2, -2, 1) + + 2 + + 1/175 x z DATA(-2, -2, 1) + 1/100 y z DATA(-1, 2, 2) + 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1) + + - 1/125 x y DATA(-2, 2, 2) - 1/125 x y DATA(-2, -2, -2) + + - 1/250 x y DATA(-2, 1, 2) + 1/125 x y DATA(2, -2, -2) + + - 1/250 x y DATA(-2, -1, -2) + 1/250 x y DATA(-2, -1, 2) + + + 1/500 x y DATA(1, -1, -2) + 1/250 x y DATA(2, -1, -2) + + - 1/500 x y DATA(-1, -1, -2) - 1/250 x y DATA(-1, -2, -2) + + 2 + + 1/250 x y DATA(1, -2, -2) + 1/175 x DATA(2, 2, 2) + + 3 3 + - 2/75 z DATA(-1, 1, 1) - 2/75 z DATA(-1, 1, -1) + + 3 3 + - 2/75 z DATA(1, 1, -1) - 2/75 z DATA(1, -1, 1) + + 3 3 + - 2/75 z DATA(-1, -1, 1) + 1/150 z DATA(-1, -2, 2) + + 3 3 + + 1/150 z DATA(1, -2, 2) + 1/150 z DATA(2, -1, 2) + + 3 3 + + 1/150 z DATA(1, 1, 2) + 1/150 z DATA(-1, 1, 2) + + 2 47 137 + - 1/350 x DATA(1, 2, 2) - ---- x DATA(2, 1, 2) - ---- x DATA(2, -2, 2) + 5250 5250 + + 107 2 + + ---- x DATA(-2, 2, -1) + 1/175 x DATA(2, -2, 2) + 7000 + + 2 107 + - 1/350 x DATA(-2, 2, -1) - ---- x DATA(-1, 2, 2) + 7000 + + 107 47 167 + - ---- x DATA(-1, -2, 2) - ---- x DATA(2, -1, 2) + ---- x DATA(1, 1, 2) + 7000 5250 7000 + + 167 167 107 + - ---- x DATA(-1, 1, 2) + ---- x DATA(1, -1, 2) - ---- x DATA(2, -2, -1) + 7000 7000 7000 + + 167 137 + + ---- x DATA(-2, -1, -1) + ---- x DATA(-2, -2, 2) + 7000 5250 + + 229 167 107 + - ----- x DATA(1, -2, -1) + ---- x DATA(-2, 1, -1) + ---- x DATA(1, -2, 2) + 10500 7000 7000 + + 107 167 + - 1/42 DATA(1, 2, -1) - ---- x DATA(1, -2, -2) + ---- x DATA(-1, -1, -2) + 7000 7000 + + 137 137 107 + + ---- x DATA(1, -1, 1) - ---- x DATA(2, 2, 2) + ---- x DATA(1, 2, 2) + 5250 5250 7000 + + 137 137 137 + + ---- x DATA(-1, -1, -1) - ---- x DATA(1, -1, -1) - ---- x DATA(-1, 1, 1) + 5250 5250 5250 + + 137 137 107 + + ---- x DATA(-1, 1, -1) - ---- x DATA(1, 1, -1) + ---- x DATA(-1, -2, -2) + 5250 5250 7000 + + 137 47 47 + - ---- x DATA(-2, -2, -2) + ---- x DATA(-2, 1, 2) + ---- x DATA(-2, -1, 2) + 5250 5250 5250 + + 47 167 + - ---- x DATA(-2, -1, -2) - ---- x DATA(1, -1, -2) + 5250 7000 + + 137 137 19 + + ---- x DATA(2, -2, -2) + ---- x DATA(-2, 2, 2) + ---- DATA(-2, 1, -2) + 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alloc=14284232, time=246.14 +bytes used=1740070476, alloc=14284232, time=246.26 +bytes used=1741070624, alloc=14284232, time=246.39 +bytes used=1742073320, alloc=14284232, time=246.52 +bytes used=1743090488, alloc=14284232, time=246.65 +bytes used=1744168184, alloc=14284232, time=246.79 +bytes used=1745171756, alloc=14284232, time=246.92 +bytes used=1746238992, alloc=14284232, time=247.06 +bytes used=1747257684, alloc=14284232, time=247.21 +bytes used=1748266056, alloc=14284232, time=247.35 +bytes used=1749298752, alloc=14677376, time=247.44 +bytes used=1750346404, alloc=14677376, time=247.51 +bytes used=1751394000, alloc=14677376, time=247.58 +bytes used=1752441428, alloc=14677376, time=247.65 +bytes used=1753489024, alloc=14677376, time=247.72 +bytes used=1754536564, alloc=14677376, time=247.79 + 137 3 2 2 529 +[COEFF(-2, -2, -2) = - ---- x + 1/300 x + 2/245 x z - 1/100 z - ----- z + 5250 14700 + + 2 2 2 3 + + 1/175 x y + 1/175 x y - 1/175 y + 1/150 z - 1/125 x y - 2/175 x z + + 2 2 2 137 3 + - 1/175 x + 2/175 x y z + 1/100 y z + 1/100 x z - ---- y + 1/300 y + 5250 + + 11 2 3 169 + - 2/175 y z + --- + 2/245 y z, COEFF(-1, -2, -2) = - 1/150 x - ----- z + 420 14700 + + 3 2 2 2 19 + + 1/300 y - 1/100 z + 1/350 x - 2/175 y z - 1/350 x y + ---- + 2100 + + 2 2 2 2 47 + + 1/100 y z - 1/175 x z + 2/245 y z + 1/350 x y - 1/175 y - ---- y + 5250 + + 2 3 107 2 + - 1/245 x z + 1/175 x y z + 1/150 z - 1/250 x y + ---- x + 1/200 x z , + 7000 + + 2 3 17 + COEFF(0, -2, -2) = - 1/300 z - 2/175 y z + 1/175 x + 1/150 z - ---- y + 5250 + + 2 2 2 2 2 + - 1/175 y - 1/175 x y + 1/100 y z - 2/245 x z - 1/100 z + 1/300 + + 3 2 2 2 + + 1/300 y + 2/245 y z, COEFF(1, -2, -2) = - 1/245 x z + 1/100 y z + + 3 2 2 169 3 + + 1/300 y - 1/350 x y - 1/100 z + 1/250 x y - ----- z + 1/150 z + 14700 + + 47 2 2 2 + + 1/175 x z - ---- y + 2/245 y z - 2/175 y z - 1/175 y - 1/350 x y + 5250 + + 19 2 3 107 2 + + ---- - 1/175 x y z + 1/350 x + 1/150 x - ---- x - 1/200 x z , + 2100 7000 + + 2 + COEFF(2, -2, -2) = 1/125 x y + 2/175 x z - 1/175 x - 2/175 x y z + + 11 2 2 529 2 137 + - 2/175 y z + --- + 2/245 x z - 1/175 y - ----- z - 1/175 x y + ---- x + 420 14700 5250 + + 137 3 2 3 2 2 + - ---- y + 1/150 z + 2/245 y z - 1/300 x + 1/175 x y - 1/100 z + 5250 + + 2 2 3 3 + + 1/100 y z - 1/100 x z + 1/300 y , COEFF(-2, -1, -2) = 1/150 z + + 107 2 2 2 3 + + ---- y - 1/350 x y + 1/100 x z + 1/350 y + 1/300 x - 2/175 x z + 7000 + + 169 19 2 2 3 47 + - ----- z - 1/175 y z + ---- + 1/200 y z - 1/245 y z - 1/150 y - ---- x + 14700 2100 5250 + + 2 2 2 2 + - 1/250 x y - 1/175 x + 1/350 x y - 1/100 z + 2/245 x z + 1/175 x y z, + + 2 3 17 + COEFF(-1, -1, -2) = 1/350 y - 1/150 x + 1/350 x y z - ---- - 1/175 x z + 2100 + + 2 2 191 2 + + 1/200 x z - 1/100 z - 1/175 y z - 1/500 x y + ----- z + 1/200 y z + 14700 + + 3 3 2 167 167 2 + - 1/150 y + 1/150 z - 1/245 y z + ---- x + ---- y - 1/700 x y + 7000 7000 + + 2 2 2 2 187 + + 1/350 x - 1/245 x z - 1/700 x y , COEFF(0, -1, -2) = 1/175 x + ---- y + 7000 + + 29 2 3 311 3 2 + - ---- - 1/245 y z - 1/150 y + ----- z + 1/150 z - 1/175 y z - 1/100 z + 2100 14700 + + 2 2 2 2 + + 1/350 y + 1/200 y z - 2/245 x z - 1/350 x y, COEFF(1, -1, -2) = + + 17 167 167 2 2 191 + - ---- + 1/500 x y - ---- x + ---- y + 1/700 x y - 1/700 x y + ----- z + 2100 7000 7000 14700 + + 2 3 2 3 + - 1/200 x z - 1/150 y - 1/245 y z - 1/175 y z + 1/175 x z + 1/150 z + + 2 2 3 2 2 + + 1/200 y z + 1/350 y - 1/350 x y z + 1/150 x - 1/245 x z - 1/100 z + + 2 169 107 2 3 + + 1/350 x , COEFF(2, -1, -2) = - ----- z + ---- y + 1/200 y z - 1/300 x + 14700 7000 + + 2 2 2 3 2 + - 1/100 z + 2/175 x z + 2/245 x z + 1/350 y + 1/150 z + 1/350 x y + + 2 47 2 2 + - 1/175 x + ---- x - 1/175 y z - 1/175 x y z - 1/245 y z + 1/350 x y + 5250 + + 3 2 19 + - 1/150 y - 1/100 x z + 1/250 x y + ----, COEFF(-2, 0, -2) = 1/300 + 2100 + + 2 3 17 3 2 + - 1/300 z - 1/100 z + 1/150 z - 2/175 x z - ---- x + 1/300 x + 1/175 y + 5250 + + 2 2 2 2 2 + + 2/245 x z - 1/175 x + 1/100 x z - 1/175 x y - 2/245 y z, + + 2 2 311 2 3 + COEFF(-1, 0, -2) = - 1/100 z + 1/350 x + ----- z - 1/245 x z - 1/150 x + 14700 + + 3 2 2 187 2 + + 1/150 z - 1/175 x z - 1/350 x y - 2/245 y z + ---- x + 1/175 y + 7000 + + 2 29 2 41 2 + + 1/200 x z - ----, COEFF(0, 0, -2) = - 1/100 z - ---- - 2/245 x z + 2100 2100 + + 2 3 2 431 2 + + 1/175 y + 1/150 z - 2/245 y z + ----- z + 1/175 x , COEFF(1, 0, -2) + 14700 + + 2 2 3 2 2 311 + = 1/175 y + 1/350 x y + 1/150 z - 1/245 x z - 1/200 x z + ----- z + 14700 + + 187 2 3 2 2 29 + - ---- x - 2/245 y z + 1/175 x z + 1/150 x - 1/100 z + 1/350 x - ----, + 7000 2100 + + 2 3 2 + COEFF(2, 0, -2) = 1/175 y + 1/300 - 1/300 x - 1/100 z - 1/300 z + + 2 2 2 3 2 + + 2/175 x z + 1/175 x y + 2/245 x z - 2/245 y z + 1/150 z - 1/175 x + + 2 17 47 2 + - 1/100 x z + ---- x, COEFF(-2, 1, -2) = - ---- x - 1/245 y z + 5250 5250 + + 3 19 2 2 + - 2/175 x z + 1/150 y + ---- - 1/175 x - 1/200 y z - 1/175 x y z + 2100 + + 2 2 3 3 2 + + 1/175 y z + 1/100 x z - 1/350 x y + 1/150 z + 1/300 x + 2/245 x z + + 2 2 169 2 107 + + 1/350 y - 1/100 z - ----- z + 1/250 x y - 1/350 x y - ---- y, + 14700 7000 + + 191 3 + COEFF(-1, 1, -2) = - 1/350 x y z + ----- z + 1/175 y z + 1/150 z + 14700 + + 2 2 2 167 + + 1/500 x y - 1/175 x z - 1/700 x y + 1/350 x + 1/700 x y + ---- x + 7000 + + 2 2 3 2 17 2 + + 1/200 x z - 1/200 y z - 1/150 x + 1/350 y - ---- - 1/245 x z + 2100 + + 2 167 2 3 29 + - 1/245 y z - ---- y - 1/100 z + 1/150 y , COEFF(0, 1, -2) = - ---- + 7000 2100 + + 2 2 2 2 2 2 + - 1/200 y z - 1/100 z - 1/245 y z + 1/350 x y + 1/175 x - 2/245 x z + + 311 187 3 3 2 + + ----- z + 1/175 y z - ---- y + 1/150 y + 1/150 z + 1/350 y , + 14700 7000 + + 167 2 2 3 2 + COEFF(1, 1, -2) = - ---- x + 1/700 x y - 1/245 y z + 1/150 y - 1/100 z + 7000 + + 2 3 17 2 191 + - 1/200 y z + 1/150 z - ---- + 1/350 y + 1/175 x z + ----- z + 2100 14700 + + 2 3 2 + + 1/175 y z + 1/350 x + 1/150 x + 1/350 x y z - 1/200 x z - 1/500 x y + + 2 2 167 2 + - 1/245 x z + 1/700 x y - ---- y, COEFF(2, 1, -2) = - 1/245 y z + 7000 + + 2 2 2 107 + - 1/350 x y + 2/175 x z - 1/100 x z - 1/250 x y - 1/100 z - ---- y + 7000 + + 3 2 19 169 + + 1/150 z + 1/175 x y z + 1/175 y z + 1/350 y + ---- - ----- z + 2100 14700 + + 3 2 2 2 3 47 + + 1/150 y + 1/350 x y - 1/200 y z - 1/175 x - 1/300 x + ---- x + 5250 + + 2 3 2 2 + + 2/245 x z, COEFF(-2, 2, -2) = 1/150 z - 1/175 x + 2/245 y z + + 2 2 3 2 2 + - 1/100 y z + 1/100 x z - 1/300 y + 1/175 x y - 1/175 x y - 2/175 x z + + 529 2 11 + + 2/175 y z - ----- z + 2/245 x z - 2/175 x y z + 1/125 x y + --- + 14700 420 + + 3 137 2 2 137 + + 1/300 x + ---- y - 1/100 z - 1/175 y - ---- x, COEFF(-1, 2, -2) = + 5250 5250 + + 3 47 3 3 2 2 + - 1/300 y + ---- y + 1/150 z - 1/150 x + 1/350 x y + 1/200 x z + 5250 + + 2 169 2 2 + + 1/350 x y - ----- z - 1/175 x z - 1/245 x z - 1/100 z + 1/250 x y + 14700 + + 2 107 19 2 2 + + 1/350 x + 2/175 y z + ---- x + ---- - 1/100 y z + 2/245 y z + 7000 2100 + + 2 2 + - 1/175 x y z - 1/175 y , COEFF(0, 2, -2) = 2/175 y z - 2/245 x z + + 2 3 2 17 2 + + 1/175 x y + 1/150 z - 1/100 z + 1/300 + ---- y - 1/100 y z + 5250 + + 2 2 3 2 + + 2/245 y z + 1/175 x - 1/300 z - 1/300 y - 1/175 y , COEFF(1, 2, -2) + + 3 2 169 107 + = 1/175 x y z - 1/300 y - 1/200 x z - ----- z - ---- x + 2/175 y z + 14700 7000 + + 2 2 2 19 2 + + 2/245 y z - 1/100 z - 1/250 x y - 1/245 x z + ---- - 1/350 x y + 2100 + + 47 2 3 3 2 2 + + ---- y - 1/175 y + 1/150 z + 1/150 x - 1/100 y z + 1/350 x y + 5250 + + 2 2 2 + + 1/350 x + 1/175 x z, COEFF(2, 2, -2) = - 1/100 x z - 1/175 x y + + 137 3 2 3 2 + + ---- x + 2/175 x y z - 1/300 y - 1/175 y + 1/150 z + 2/245 x z + 5250 + + 3 137 2 2 2 + - 1/300 x + ---- y - 1/125 x y - 1/175 x - 1/100 z + 2/245 y z + 5250 + + 529 11 2 2 + - ----- z + --- + 2/175 x z + 2/175 y z - 1/100 y z - 1/175 x y , + 14700 420 + + 2 107 2 3 + COEFF(-2, -2, -1) = - 1/245 x z + ---- y - 1/50 y z - 2/75 z + 1/175 y z + 7000 + + 2 2 2 3 + - 1/50 x z - 8/525 - 1/350 y - 1/250 x y + 1/350 x y + 1/600 x + + 3 2 107 2 2 + + 1/600 y - 1/175 x y z - 1/350 x + ---- x + 1/50 z + 1/350 x y + 7000 + + 2 256 229 3 + - 1/245 y z + 1/175 x z + ---- z, COEFF(-1, -2, -1) = ----- x - 2/75 z + 3675 10500 + + 2 211 2 2 3 + + 1/350 x z - 1/700 x y + ---- z + 1/490 x z + 1/700 x - 1/300 x + 3675 + + 3 2 2 2 + + 1/600 y + 1/175 y z - 1/350 x y z - 1/245 y z - 1/100 x z - 1/350 y + + 167 2 2 2 + - 1/42 - 1/500 x y + ---- y + 1/50 z + 1/700 x y - 1/50 y z , + 7000 + + 3 2 2 2 2 + COEFF(0, -2, -1) = 1/600 y - 1/350 y + 1/350 x - 1/245 y z + 1/50 z + + 3 2 187 2 + + 1/175 y z - 2/75 z - 1/350 x y + ---- y - 2/75 + 1/245 x z + 4/75 z + 7000 + + 2 229 211 3 + - 1/50 y z , COEFF(1, -2, -1) = - ----- x + 1/175 y z + ---- z + 1/600 y + 10500 3675 + + 2 2 167 + - 1/700 x y + 1/350 x y z + 1/490 x z - 1/42 - 1/350 x z + ---- y + 7000 + + 2 2 2 2 3 2 + - 1/245 y z + 1/50 z - 1/50 y z - 1/700 x y + 1/300 x + 1/700 x + + 2 2 3 + + 1/500 x y + 1/100 x z - 1/350 y - 2/75 z , COEFF(2, -2, -1) = + + 2 2 3 2 + - 1/175 x z - 8/525 + 1/50 z + 1/350 x y - 1/600 x - 1/350 x y + + 2 2 2 107 2 + + 1/175 x y z + 1/50 x z - 1/50 y z - 1/245 y z - ---- x - 1/245 x z + 7000 + + 2 3 256 2 3 107 + - 1/350 y + 1/600 y + ---- z - 1/350 x - 2/75 z + 1/175 y z + ---- y + 3675 7000 + + 2 2 3 + + 1/250 x y, COEFF(-2, -1, -1) = - 1/350 x + 1/700 x y - 1/300 y + + 211 2 2 2 + + 1/175 x z + ---- z + 1/50 z + 1/350 y z - 1/50 x z - 1/100 y z + 3675 + + 2 3 2 167 229 + - 1/700 x y + 1/600 x + 1/490 y z - 1/42 + ---- x + ----- y - 1/500 x y + 7000 10500 + + 2 3 2 + - 1/245 x z - 1/350 x y z - 2/75 z + 1/700 y , COEFF(-1, -1, -1) = + + 3 2 2 17 2 + - 1/300 y - 1/100 y z + 1/700 y - --- - 1/100 x z - 1/1000 x y + 525 + + 2 2 2 137 3 + - 1/1400 x y + 1/50 z + 1/700 x - 1/700 x y z + ---- y - 1/300 x + 5250 + + 2 2 137 166 + - 1/1400 x y + 1/350 y z + 1/490 y z + 1/350 x z + ---- x + ---- z + 5250 3675 + + 2 3 2 37 289 + + 1/490 x z - 2/75 z , COEFF(0, -1, -1) = 1/245 x z - ---- + ----- y + 1050 10500 + + 3 2 2 2 2 3 + - 2/75 z + 1/700 y - 1/100 y z + 1/50 z - 1/700 x y - 1/300 y + + 151 2 2 3 + + ---- z + 1/350 x + 1/490 y z + 1/350 y z, COEFF(1, -1, -1) = - 2/75 z + 3675 + + 2 2 2 2 + + 1/50 z + 1/1000 x y + 1/490 y z + 1/700 x + 1/1400 x y + 1/350 y z + + 2 2 137 2 + - 1/350 x z + 1/700 y + 1/700 x y z + 1/100 x z - ---- x - 1/100 y z + 5250 + + 166 3 3 2 17 2 137 + + ---- z - 1/300 y + 1/300 x - 1/1400 x y - --- + 1/490 x z + ---- y, + 3675 525 5250 + + 2 229 211 2 2 + COEFF(2, -1, -1) = 1/50 z + ----- y + ---- z - 1/100 y z + 1/50 x z + 10500 3675 + + 3 2 2 + + 1/350 x y z - 1/42 - 1/600 x - 1/245 x z - 1/350 x - 1/175 x z + + 2 167 2 3 2 + + 1/500 x y + 1/700 x y - ---- x + 1/490 y z - 2/75 z + 1/700 y + 7000 + + 3 2 187 + + 1/350 y z - 1/300 y + 1/700 x y , COEFF(-2, 0, -1) = ---- x + 7000 + + 2 3 3 2 2 + - 1/245 x z - 2/75 - 2/75 z + 1/600 x + 4/75 z - 1/50 x z + 1/50 z + + 2 2 2 2 + + 1/350 y - 1/350 x + 1/245 y z - 1/350 x y + 1/175 x z, + + 2 2 2 289 2 + COEFF(-1, 0, -1) = 1/50 z + 1/700 x + 1/245 y z + ----- x + 1/350 y + 10500 + + 2 2 151 3 2 + - 1/700 x y + 1/490 x z + ---- z - 1/300 x + 1/350 x z - 1/100 x z + 3675 + + 37 3 2 2 + - ---- - 2/75 z , COEFF(0, 0, -1) = 1/245 y z - 4/105 + 1/350 x + 1050 + + 3 2 136 2 2 + - 2/75 z + 1/245 x z + ---- z + 1/350 y + 1/50 z , COEFF(1, 0, -1) = + 3675 + + 2 151 2 2 2 + 1/490 x z + ---- z + 1/700 x y + 1/245 y z + 1/350 y - 1/350 x z + 3675 + + 289 2 3 2 37 2 3 + - ----- x + 1/700 x - 2/75 z + 1/100 x z - ---- + 1/50 z + 1/300 x , + 10500 1050 + + 2 3 187 2 2 + COEFF(2, 0, -1) = 1/350 y - 2/75 - 1/600 x - ---- x - 1/350 x + 1/50 z + 7000 + + 2 2 3 2 + - 1/175 x z + 1/350 x y + 1/245 y z + 4/75 z - 2/75 z + 1/50 x z + + 2 2 3 + - 1/245 x z, COEFF(-2, 1, -1) = 1/175 x z - 1/350 x + 1/300 y + + 3 2 2 2 + + 1/600 x - 1/245 x z + 1/500 x y - 1/350 y z + 1/50 z - 1/50 x z + + 2 2 2 3 167 + + 1/700 y - 1/700 x y + 1/100 y z - 2/75 z + 1/350 x y z + ---- x + 7000 + + 2 229 2 211 + + 1/490 y z - ----- y - 1/700 x y - 1/42 + ---- z, COEFF(-1, 1, -1) = + 10500 3675 + + 166 2 3 2 + ---- z - 1/100 x z + 1/350 x z - 1/350 y z - 2/75 z + 1/50 z + 3675 + + 2 2 2 137 + + 1/700 x y z + 1/100 y z + 1/1000 x y + 1/700 y + 1/490 x z - ---- y + 5250 + + 2 17 2 2 2 137 + + 1/700 x - --- - 1/1400 x y + 1/1400 x y + 1/490 y z + ---- x + 525 5250 + + 3 3 3 151 37 + - 1/300 x + 1/300 y , COEFF(0, 1, -1) = 1/300 y + ---- z - ---- + 3675 1050 + + 3 2 2 2 2 + - 2/75 z + 1/100 y z + 1/350 x + 1/490 y z + 1/245 x z - 1/350 y z + + 289 2 2 2 166 + - ----- y + 1/50 z + 1/700 y + 1/700 x y, COEFF(1, 1, -1) = ---- z + 10500 3675 + + 2 3 2 2 2 + + 1/700 x + 1/300 x - 1/1000 x y + 1/1400 x y + 1/490 y z + 1/100 x z + + 17 137 3 2 3 137 + - --- - ---- y - 1/700 x y z - 2/75 z + 1/700 y + 1/300 y - ---- x + 525 5250 5250 + + 2 2 2 2 + + 1/100 y z + 1/50 z + 1/1400 x y - 1/350 x z - 1/350 y z + 1/490 x z, + + 2 211 2 2 3 + COEFF(2, 1, -1) = 1/700 y + ---- z + 1/700 x y + 1/50 x z - 2/75 z + 3675 + + 2 3 167 + + 1/100 y z - 1/42 - 1/500 x y - 1/350 x y z - 1/600 x - ---- x + 7000 + + 3 2 2 2 2 + + 1/300 y + 1/50 z - 1/350 y z - 1/245 x z - 1/350 x + 1/490 y z + + 2 229 2 + - 1/700 x y - 1/175 x z - ----- y, COEFF(-2, 2, -1) = - 8/525 + 1/50 y z + 10500 + + 2 2 2 2 + + 1/175 x z - 1/245 y z - 1/350 y + 1/250 x y - 1/245 x z + 1/350 x y + + 3 2 256 3 3 + - 1/600 y - 1/50 x z + ---- z - 2/75 z + 1/175 x y z + 1/600 x + 3675 + + 107 2 2 107 2 + + ---- x + 1/50 z - 1/350 x - 1/175 y z - ---- y - 1/350 x y, + 7000 7000 + + 2 167 2 3 + COEFF(-1, 2, -1) = 1/700 x - ---- y + 1/700 x y - 1/42 - 2/75 z + 7000 + + 2 3 2 2 + + 1/350 x z - 1/100 x z + 1/350 x y z - 1/300 x + 1/50 z + 1/490 x z + + 2 211 229 3 + - 1/175 y z - 1/350 y + ---- z + ----- x - 1/600 y + 1/500 x y + 3675 10500 + + 2 2 2 + + 1/700 x y + 1/50 y z - 1/245 y z, COEFF(0, 2, -1) = - 1/175 y z + + 187 2 2 3 2 3 + - ---- y + 1/350 x y - 1/245 y z - 2/75 z + 1/350 x - 1/600 y + 7000 + + 2 2 2 2 + + 1/245 x z + 4/75 z - 1/350 y + 1/50 z + 1/50 y z - 2/75, + + 2 2 2 + COEFF(1, 2, -1) = 1/50 y z - 1/700 x y + 1/490 x z - 1/350 x z + + 2 3 229 2 2 3 + - 1/245 y z - 2/75 z - ----- x + 1/700 x + 1/700 x y - 1/600 y + 10500 + + 211 2 2 + - 1/500 x y - 1/42 - 1/350 x y z + ---- z + 1/100 x z + 1/50 z + 3675 + + 3 2 167 2 + + 1/300 x - 1/350 y - ---- y - 1/175 y z, COEFF(2, 2, -1) = - 1/350 x + 7000 + + 3 2 107 3 + - 1/600 y - 1/350 x y - 1/250 x y - ---- y - 1/600 x - 1/175 y z + 7000 + + 2 2 256 2 2 + - 1/350 y - 1/175 x z + 1/50 y z + ---- z - 8/525 + 1/50 z - 1/245 y z + 3675 + + 2 107 3 2 2 + + 1/50 x z - ---- x - 1/175 x y z - 2/75 z - 1/245 x z - 1/350 x y, + 7000 + + 33 3 + COEFF(-2, -2, 0) = 2/175 y z + 2/175 x z - 2/175 x y z - --- z + 1/25 z + 490 + + 2 2 2 + - 2/245 y z - 2/245 x z, COEFF(-1, -2, 0) = - 2/245 y z - 9/98 z + + 3 2 + + 1/175 x z + 1/25 z + 1/245 x z + 2/175 y z - 1/175 x y z, + + 2 2 3 + COEFF(0, -2, 0) = 2/175 y z - 1/10 z + 2/245 x z - 2/245 y z + 1/25 z , + + 2 2 + COEFF(1, -2, 0) = - 2/245 y z - 9/98 z + 1/175 x y z + 1/245 x z + + 3 2 + + 1/25 z - 1/175 x z + 2/175 y z, COEFF(2, -2, 0) = - 2/245 x z + + 3 33 2 + + 2/175 y z + 1/25 z - --- z + 2/175 x y z - 2/175 x z - 2/245 y z, + 490 + + 2 3 + COEFF(-2, -1, 0) = - 2/245 x z - 1/175 x y z - 9/98 z + 1/25 z + + 2 2 + + 1/175 y z + 1/245 y z + 2/175 x z, COEFF(-1, -1, 0) = 1/245 x z + + 3 2 57 + - 1/350 x y z + 1/25 z + 1/245 y z + 1/175 y z + 1/175 x z - --- z, + 490 + + 2 2 3 61 + COEFF(0, -1, 0) = 1/245 y z + 2/245 x z + 1/175 y z + 1/25 z - --- z, + 490 + + 2 3 57 2 + COEFF(1, -1, 0) = 1/245 y z + 1/25 z - --- z + 1/245 x z - 1/175 x z + 490 + + 3 + + 1/175 y z + 1/350 x y z, COEFF(2, -1, 0) = 1/25 z - 2/175 x z + + 2 2 + - 2/245 x z + 1/245 y z + 1/175 y z - 9/98 z + 1/175 x y z, + + 2 2 3 + COEFF(-2, 0, 0) = 2/245 y z - 2/245 x z + 2/175 x z + 1/25 z - 1/10 z, + + 61 2 2 3 + COEFF(-1, 0, 0) = 1/175 x z - --- z + 1/245 x z + 2/245 y z + 1/25 z , + 490 + + 3 2 13 2 + COEFF(0, 0, 0) = 1/25 z + 2/245 y z - -- z + 2/245 x z, + 98 + + 3 61 2 2 + COEFF(1, 0, 0) = 1/25 z - --- z + 2/245 y z + 1/245 x z - 1/175 x z, + 490 + + 2 3 2 + COEFF(2, 0, 0) = - 1/10 z - 2/245 x z - 2/175 x z + 1/25 z + 2/245 y z, + + 2 3 2 + COEFF(-2, 1, 0) = - 9/98 z - 2/245 x z + 1/25 z + 1/245 y z + + + 1/175 x y z + 2/175 x z - 1/175 y z, COEFF(-1, 1, 0) = - 1/175 y z + + 2 2 57 3 + + 1/175 x z + 1/245 x z + 1/245 y z + 1/350 x y z - --- z + 1/25 z , + 490 + + 2 2 61 3 + COEFF(0, 1, 0) = 2/245 x z - 1/175 y z + 1/245 y z - --- z + 1/25 z , + 490 + + 57 2 + COEFF(1, 1, 0) = - --- z + 1/245 y z - 1/350 x y z - 1/175 y z - 1/175 x z + 490 + + 3 2 2 + + 1/25 z + 1/245 x z, COEFF(2, 1, 0) = 1/245 y z - 2/175 x z - 9/98 z + + 2 3 + - 1/175 y z - 2/245 x z - 1/175 x y z + 1/25 z , COEFF(-2, 2, 0) = + + 2 3 2 + 2/175 x z - 2/245 y z + 2/175 x y z + 1/25 z - 2/175 y z - 2/245 x z + + 33 2 + - --- z, COEFF(-1, 2, 0) = - 2/175 y z + 1/175 x z + 1/245 x z + 490 + + 2 3 + - 2/245 y z + 1/175 x y z - 9/98 z + 1/25 z , + + 3 2 2 + COEFF(0, 2, 0) = - 2/175 y z + 1/25 z + 2/245 x z - 2/245 y z - 1/10 z, + + 2 3 + COEFF(1, 2, 0) = - 9/98 z - 2/245 y z - 1/175 x y z - 2/175 y z + 1/25 z + + 2 3 33 + + 1/245 x z - 1/175 x z, COEFF(2, 2, 0) = - 2/175 x y z + 1/25 z - --- z + 490 + + 2 2 + - 2/175 y z - 2/245 y z - 2/175 x z - 2/245 x z, COEFF(-2, -2, 1) = + + 2 2 107 3 3 + - 1/245 x z + 1/350 y - ---- y - 1/600 x + 1/175 y z - 2/75 z + 7000 + + 2 2 107 + + 1/50 x z - 1/350 x y - ---- x + 8/525 + 1/250 x y + 1/175 x z + 7000 + + 2 2 2 3 2 2 + - 1/245 y z - 1/350 x y - 1/50 z - 1/600 y + 1/50 y z + 1/350 x + + 256 3 3 2 + - 1/175 x y z + ---- z, COEFF(-1, -2, 1) = - 2/75 z - 1/600 y + 1/350 y + 3675 + + 2 2 3 2 2 + + 1/700 x y + 1/50 y z + 1/300 x - 1/50 z + 1/350 x z + 1/100 x z + + 229 2 167 2 + - ----- x + 1/490 x z + 1/500 x y - 1/350 x y z - ---- y - 1/700 x + 10500 7000 + + 2 211 2 + - 1/245 y z + 1/175 y z + ---- z - 1/700 x y + 1/42, COEFF(0, -2, 1) = + 3675 + + 187 2 2 2 2 + 4/75 z - ---- y + 1/350 y + 1/50 y z - 1/350 x + 1/350 x y + 2/75 + 7000 + + 3 3 2 2 2 + + 1/175 y z - 2/75 z - 1/600 y - 1/50 z - 1/245 y z + 1/245 x z, + + 2 3 2 + COEFF(1, -2, 1) = 1/490 x z - 2/75 z + 1/700 x y - 1/500 x y + 1/175 y z + + 211 2 2 2 2 + + ---- z + 1/42 - 1/700 x - 1/50 z + 1/350 y - 1/350 x z + 1/50 y z + 3675 + + 2 229 2 167 2 + + 1/700 x y + 1/350 x y z + ----- x - 1/100 x z - ---- y - 1/245 y z + 10500 7000 + + 3 3 107 2 107 + - 1/300 x - 1/600 y , COEFF(2, -2, 1) = ---- x - 1/50 z - ---- y + 7000 7000 + + 2 2 2 3 2 + + 1/350 x y + 1/50 y z + 1/350 y - 1/250 x y - 2/75 z - 1/350 x y + + 3 256 3 2 + + 1/600 x + ---- z - 1/600 y + 1/175 x y z - 1/175 x z - 1/245 x z + 3675 + + 2 2 2 + + 1/350 x + 1/175 y z + 8/525 - 1/50 x z - 1/245 y z, COEFF(-2, -1, 1) + + 2 2 229 211 + = 1/42 + 1/350 x - 1/350 x y z + 1/700 x y - ----- y + ---- z + 10500 3675 + + 2 3 2 167 + + 1/490 y z - 2/75 z - 1/50 z - ---- x + 1/500 x y + 1/350 y z + 7000 + + 2 2 3 2 3 2 + + 1/50 x z - 1/700 x y - 1/600 x - 1/245 x z + 1/300 y + 1/100 y z + + 2 2 2 + + 1/175 x z - 1/700 y , COEFF(-1, -1, 1) = - 1/50 z + 1/490 x z + + 2 2 137 166 137 2 + + 1/100 x z - 1/700 y - ---- y + ---- z - ---- x + 1/1400 x y + 5250 3675 5250 + + 3 2 17 2 + + 1/300 x + 1/350 x z + 1/1400 x y + --- - 1/700 x + 1/350 y z + 525 + + 2 3 2 3 + - 1/700 x y z + 1/490 y z + 1/1000 x y - 2/75 z + 1/100 y z + 1/300 y , + + 2 37 2 2 3 + COEFF(0, -1, 1) = 1/490 y z + ---- + 1/700 x y - 1/700 y + 1/300 y + 1050 + + 2 289 2 2 151 + - 1/350 x - ----- y + 1/100 y z + 1/245 x z + ---- z + 1/350 y z + 10500 3675 + + 2 3 166 137 + - 1/50 z - 2/75 z , COEFF(1, -1, 1) = ---- z + ---- x - 1/350 x z + 3675 5250 + + 2 3 2 3 3 2 + + 1/490 y z + 1/300 y - 1/100 x z - 2/75 z - 1/300 x + 1/490 x z + + 2 2 17 2 + - 1/1000 x y - 1/700 y - 1/50 z + --- + 1/1400 x y + 1/350 y z + 525 + + 2 2 137 2 + + 1/100 y z - 1/1400 x y + 1/700 x y z - ---- y - 1/700 x , + 5250 + + 3 2 167 2 2 + COEFF(2, -1, 1) = - 2/75 z - 1/245 x z + ---- x + 1/350 x - 1/50 z + 7000 + + 2 3 229 2 211 + - 1/175 x z + 1/100 y z + 1/300 y - ----- y + 1/490 y z + ---- z + 1/42 + 10500 3675 + + 2 2 2 2 3 + - 1/50 x z + 1/350 x y z - 1/700 x y - 1/700 y - 1/700 x y + 1/600 x + + 3 2 + + 1/350 y z - 1/500 x y, COEFF(-2, 0, 1) = - 1/600 x + 1/245 y z + + 2 187 2 2 + + 1/350 x y - ---- x + 4/75 z - 1/50 z + 2/75 + 1/350 x + 1/175 x z + 7000 + + 2 2 2 3 + - 1/245 x z + 1/50 x z - 1/350 y - 2/75 z , COEFF(-1, 0, 1) = 1/350 x z + + 2 3 289 2 2 2 37 + - 1/350 y - 2/75 z - ----- x + 1/490 x z - 1/50 z + 1/700 x y + ---- + 10500 1050 + + 3 2 2 2 151 + + 1/300 x + 1/100 x z - 1/700 x + 1/245 y z + ---- z, COEFF(0, 0, 1) + 3675 + + 2 2 3 136 2 2 + = - 1/50 z - 1/350 x - 2/75 z + ---- z - 1/350 y + 1/245 x z + 4/105 + 3675 + + 2 289 3 3 + + 1/245 y z, COEFF(1, 0, 1) = ----- x - 2/75 z - 1/350 x z - 1/300 x + 10500 + + 2 2 37 2 2 2 + + 1/245 y z - 1/50 z + ---- - 1/700 x y - 1/100 x z - 1/700 x + 1050 + + 151 2 2 187 3 + + ---- z + 1/490 x z - 1/350 y , COEFF(2, 0, 1) = ---- x + 2/75 - 2/75 z + 3675 7000 + + 2 2 2 2 + - 1/350 y - 1/175 x z + 4/75 z + 1/350 x - 1/245 x z - 1/50 z + + 2 2 2 3 + + 1/245 y z - 1/50 x z - 1/350 x y + 1/600 x , COEFF(-2, 1, 1) = + + 2 229 3 2 2 3 + 1/490 y z + ----- y - 1/600 x + 1/700 x y - 1/50 z - 2/75 z + 10500 + + 211 2 2 2 + - 1/500 x y + ---- z + 1/350 x + 1/350 x y z - 1/700 y - 1/100 y z + 3675 + + 2 3 2 2 + + 1/42 + 1/50 x z + 1/175 x z - 1/300 y + 1/700 x y - 1/245 x z + + 167 2 2 + - 1/350 y z - ---- x, COEFF(-1, 1, 1) = 1/1400 x y - 1/50 z - 1/1000 x y + 7000 + + 2 3 2 2 3 + - 1/700 x - 2/75 z - 1/1400 x y - 1/350 y z + 1/490 y z - 1/300 y + + 2 2 2 + + 1/700 x y z + 1/490 x z - 1/100 y z + 1/350 x z + 1/100 x z + + 2 137 166 3 17 137 + - 1/700 y - ---- x + ---- z + 1/300 x + --- + ---- y, COEFF(0, 1, 1) = + 5250 3675 525 5250 + + 2 2 3 37 289 2 + - 1/350 y z - 1/700 x y - 1/700 y - 2/75 z + ---- + ----- y - 1/50 z + 1050 10500 + + 2 2 2 2 3 151 + + 1/245 x z + 1/490 y z - 1/350 x - 1/100 y z - 1/300 y + ---- z, + 3675 + + 137 137 2 17 3 + COEFF(1, 1, 1) = ---- x - 1/350 y z + ---- y - 1/700 y + --- - 2/75 z + 5250 5250 525 + + 2 2 2 2 + - 1/350 x z + 1/490 y z - 1/100 y z - 1/700 x - 1/100 x z + + 2 3 2 + - 1/700 x y z + 1/1000 x y - 1/1400 x y - 1/300 x - 1/1400 x y + + 2 3 166 2 2 + + 1/490 x z - 1/300 y + ---- z - 1/50 z , COEFF(2, 1, 1) = - 1/50 z + 3675 + + 3 2 229 2 2 2 + + 1/600 x - 1/245 x z + ----- y - 1/50 x z - 1/700 y - 1/700 x y + 10500 + + 211 2 2 2 + + ---- z + 1/350 x - 1/350 y z - 1/100 y z - 1/350 x y z + 1/490 y z + 3675 + + 3 167 3 2 + - 2/75 z + 1/42 + 1/500 x y + ---- x - 1/300 y - 1/175 x z + 1/700 x y, + 7000 + + 2 2 3 2 + COEFF(-2, 2, 1) = 1/350 y + 8/525 - 1/50 y z - 1/600 x - 1/350 x y + + 2 2 2 + - 1/250 x y - 1/175 y z + 1/350 x y + 1/350 x - 1/50 z + 1/175 x y z + + 2 107 3 3 2 + - 1/245 x z + ---- y - 2/75 z + 1/175 x z + 1/600 y - 1/245 y z + 7000 + + 107 2 256 2 + - ---- x + 1/50 x z + ---- z, COEFF(-1, 2, 1) = 1/490 x z - 1/175 y z + 7000 3675 + + 2 2 167 2 211 3 + - 1/50 z + 1/350 y + ---- y - 1/50 y z + 1/42 + ---- z + 1/600 y + 7000 3675 + + 229 3 2 3 2 + - ----- x - 2/75 z + 1/350 x y z - 1/700 x y + 1/300 x - 1/700 x + 10500 + + 2 2 2 + + 1/100 x z - 1/245 y z - 1/500 x y + 1/350 x z - 1/700 x y , + + 187 2 2 + COEFF(0, 2, 1) = 2/75 + ---- y - 1/245 y z + 1/350 y - 1/175 y z + 7000 + + 2 3 2 2 2 2 + - 1/50 y z + 1/600 y - 1/350 x - 1/50 z - 1/350 x y + 1/245 x z + + 3 2 2 3 + - 2/75 z + 4/75 z, COEFF(1, 2, 1) = - 1/245 y z - 1/50 z - 2/75 z + + 3 2 + - 1/350 x y z + 1/42 + 1/500 x y - 1/300 x - 1/700 x - 1/350 x z + + 3 2 229 167 211 + + 1/600 y - 1/50 y z + ----- x - 1/175 y z + ---- y + ---- z + 10500 7000 3675 + + 2 2 2 2 2 + + 1/490 x z + 1/350 y + 1/700 x y - 1/100 x z - 1/700 x y, + + 2 2 + COEFF(2, 2, 1) = - 1/245 y z - 1/50 y z - 1/175 y z + 8/525 - 1/175 x y z + + 107 3 107 2 3 + - 1/175 x z + ---- x + 1/250 x y + 1/600 x + ---- y - 1/50 z + 1/600 y + 7000 7000 + + 2 3 256 2 2 2 + + 1/350 x - 2/75 z + ---- z - 1/50 x z - 1/245 x z + 1/350 x y + 3675 + + 2 2 137 2 + + 1/350 y + 1/350 x y, COEFF(-2, -2, 2) = ---- y - 1/175 x y + 5250 + + 2 2 529 2 2 2 + - 1/100 x z + 1/100 z - ----- z - 1/100 y z + 2/245 y z - 1/175 x y + 14700 + + 2 137 3 2 + + 2/175 x y z + 1/175 x - 2/175 x z + ---- x - 1/300 y + 1/175 y + 5250 + + 2 3 3 11 + + 2/245 x z - 1/300 x + 1/150 z + 1/125 x y - --- - 2/175 y z, + 420 + + 2 2 2 + COEFF(-1, -2, 2) = - 2/175 y z + 1/350 x y - 1/245 x z + 2/245 y z + + 2 47 2 3 107 2 + - 1/100 y z + ---- y - 1/350 x y + 1/150 x - ---- x - 1/350 x + 5250 7000 + + 2 2 169 19 + - 1/175 x z + 1/175 y + 1/175 x y z - 1/200 x z - ----- z - ---- + 14700 2100 + + 2 3 3 3 + + 1/100 z + 1/250 x y + 1/150 z - 1/300 y , COEFF(0, -2, 2) = 1/150 z + + 2 2 2 2 2 + + 1/100 z - 1/300 z + 1/175 y + 1/175 x y - 1/100 y z + 2/245 y z + + 2 17 2 3 + - 2/175 y z - 2/245 x z + ---- y - 1/300 - 1/175 x - 1/300 y , + 5250 + + 2 2 2 2 + COEFF(1, -2, 2) = 1/100 z + 1/200 x z + 1/175 y + 1/350 x y - 2/175 y z + + 169 2 2 2 3 3 + - ----- z - 1/350 x + 1/350 x y - 1/245 x z - 1/150 x - 1/300 y + 14700 + + 3 2 107 19 + + 1/150 z - 1/100 y z + 1/175 x z - 1/250 x y + ---- x - ---- + 7000 2100 + + 2 47 + + 2/245 y z - 1/175 x y z + ---- y, COEFF(2, -2, 2) = 2/175 x z + 5250 + + 2 2 2 2 3 2 + + 2/245 y z - 1/175 x y + 1/175 y + 1/175 x + 1/300 x - 1/100 y z + + 529 2 137 + - 2/175 x y z - ----- z + 1/100 z - 1/125 x y - ---- x - 2/175 y z + 14700 5250 + + 2 3 11 137 2 3 + + 1/175 x y - 1/300 y - --- + ---- y + 1/100 x z + 1/150 z + 420 5250 + + 2 2 107 2 19 + + 2/245 x z, COEFF(-2, -1, 2) = - 1/200 y z - ---- y - 1/245 y z - ---- + 7000 2100 + + 2 2 2 3 + - 1/175 y z + 1/250 x y + 1/350 x y + 2/245 x z - 1/100 x z - 1/300 x + + 2 2 3 2 + + 1/175 x - 1/350 x y + 1/175 x y z + 1/150 y + 1/100 z - 2/175 x z + + 2 47 169 3 + - 1/350 y + ---- x - ----- z + 1/150 z , COEFF(-1, -1, 2) = - 1/175 y z + 5250 14700 + + 17 2 167 3 167 + + 1/500 x y + ---- - 1/245 y z - ---- x + 1/150 x + 1/350 x y z - ---- y + 2100 7000 7000 + + 2 3 2 2 2 2 + + 1/700 x y + 1/150 y - 1/350 x - 1/200 y z - 1/350 y - 1/200 x z + + 191 2 3 2 2 + - 1/175 x z + ----- z - 1/245 x z + 1/150 z + 1/700 x y + 1/100 z , + 14700 + + 2 29 2 2 + COEFF(0, -1, 2) = - 1/175 y z - 1/175 x + ---- - 1/245 y z - 2/245 x z + 2100 + + 2 3 2 2 187 2 + - 1/200 y z + 1/150 y - 1/350 y + 1/350 x y - ---- y + 1/100 z + 7000 + + 3 311 2 + + 1/150 z + ----- z, COEFF(1, -1, 2) = - 1/500 x y + 1/175 x z - 1/350 x + 14700 + + 2 167 167 2 2 + - 1/200 y z - ---- y + ---- x + 1/700 x y + 1/200 x z - 1/350 x y z + 7000 7000 + + 3 2 191 2 2 + - 1/150 x + 1/100 z + ----- z - 1/245 x z - 1/175 y z - 1/700 x y + 14700 + + 3 17 2 2 3 + + 1/150 z + ---- - 1/350 y - 1/245 y z + 1/150 y , COEFF(2, -1, 2) = + 2100 + + 169 2 2 2 2 2 + - ----- z - 1/200 y z + 1/100 z - 1/350 x y - 1/350 x y + 1/100 x z + 14700 + + 47 2 19 3 + - ---- x + 2/175 x z + 1/175 x - 1/250 x y - ---- - 1/175 y z + 1/150 y + 5250 2100 + + 3 2 2 2 107 + + 1/150 z + 2/245 x z - 1/175 x y z - 1/350 y - 1/245 y z - ---- y + 7000 + + 3 2 3 + + 1/300 x , COEFF(-2, 0, 2) = - 1/300 - 1/175 y + 1/150 z - 1/300 z + + 2 2 17 2 2 2 + + 2/245 x z + 1/100 z + ---- x - 1/100 x z + 1/175 x - 2/245 y z + 5250 + + 3 2 2 29 + - 2/175 x z - 1/300 x + 1/175 x y , COEFF(-1, 0, 2) = - 1/350 x + ---- + 2100 + + 311 2 2 2 2 + + ----- z - 1/175 y + 1/100 z - 1/245 x z - 1/175 x z - 2/245 y z + 14700 + + 2 187 2 3 3 + + 1/350 x y - ---- x - 1/200 x z + 1/150 z + 1/150 x , COEFF(0, 0, 2) + 7000 + + 431 2 3 2 2 2 41 + = ----- z - 2/245 y z + 1/150 z - 1/175 y - 1/175 x + 1/100 z + ---- + 14700 2100 + + 2 2 2 3 + - 2/245 x z, COEFF(1, 0, 2) = - 2/245 y z - 1/350 x y + 1/150 z + + 3 187 2 311 29 2 + - 1/150 x + ---- x + 1/100 z + ----- z + ---- + 1/175 x z - 1/175 y + 7000 14700 2100 + + 2 2 2 2 + + 1/200 x z - 1/350 x - 1/245 x z, COEFF(2, 0, 2) = 2/245 x z + + 2 2 2 3 2 + - 1/175 x y - 2/245 y z + 1/175 x - 1/300 + 1/300 x - 1/175 y + + 2 17 3 2 + + 1/100 z - ---- x + 1/150 z - 1/300 z + 2/175 x z + 1/100 x z , + 5250 + + 2 3 2 47 + COEFF(-2, 1, 2) = - 1/245 y z - 1/150 y - 1/250 x y + 1/350 x y + ---- x + 5250 + + 2 169 107 2 2 2 + - 1/350 y - ----- z + ---- y + 2/245 x z + 1/100 z + 1/175 x + 14700 7000 + + 3 2 2 2 + + 1/175 y z - 1/300 x + 1/350 x y - 2/175 x z - 1/100 x z + 1/200 y z + + 3 19 2 + + 1/150 z - 1/175 x y z - ----, COEFF(-1, 1, 2) = - 1/200 x z + 2100 + + 2 2 3 3 2 191 + + 1/700 x y - 1/245 y z + 1/150 z - 1/150 y - 1/350 x + ----- z + 14700 + + 167 167 2 + - 1/500 x y + ---- y - 1/350 x y z - ---- x - 1/175 x z - 1/700 x y + 7000 7000 + + 17 2 3 2 2 + + ---- - 1/350 y + 1/150 x + 1/100 z + 1/175 y z - 1/245 x z + 2100 + + 2 2 2 3 + + 1/200 y z , COEFF(0, 1, 2) = - 2/245 x z - 1/350 x y + 1/150 z + + 3 311 29 2 2 187 2 + - 1/150 y + ----- z + ---- - 1/175 x - 1/350 y + ---- y + 1/100 z + 14700 2100 7000 + + 2 2 191 167 + - 1/245 y z + 1/175 y z + 1/200 y z , COEFF(1, 1, 2) = ----- z + ---- y + 14700 7000 + + 2 3 2 2 + - 1/245 x z - 1/150 y - 1/350 x + 1/350 x y z + 1/500 x y - 1/700 x y + + 2 17 2 3 2 + - 1/350 y + ---- - 1/700 x y + 1/150 z + 1/175 y z + 1/100 z + 2100 + + 2 167 2 3 2 + + 1/200 x z + ---- x - 1/245 y z - 1/150 x + 1/175 x z + 1/200 y z , + 7000 + + 3 47 2 3 169 + COEFF(2, 1, 2) = - 1/150 y - ---- x - 1/350 x y + 1/300 x - ----- z + 5250 14700 + + 2 2 2 107 + + 1/175 x y z + 1/350 x y - 1/245 y z + 2/175 x z + 1/100 x z + ---- y + 7000 + + 2 2 2 2 + + 1/175 y z + 1/200 y z - 1/350 y + 1/100 z + 1/250 x y + 2/245 x z + + 19 3 2 2 + - ---- + 1/150 z + 1/175 x , COEFF(-2, 2, 2) = 2/245 x z - 2/175 x y z + 2100 + + 2 2 2 137 + - 2/175 x z + 2/245 y z + 1/175 x y - 1/125 x y + 1/100 y z - ---- y + 5250 + + 2 2 2 11 3 3 137 + + 1/100 z + 1/175 y - 1/175 x y - --- + 1/150 z - 1/300 x + ---- x + 420 5250 + + 3 2 2 529 + + 1/300 y + 1/175 x - 1/100 x z + 2/175 y z - ----- z, COEFF(-1, 2, 2) + 14700 + + 2 3 2 2 + = - 1/245 x z + 1/150 x - 1/250 x y - 1/175 x z + 1/175 y - 1/350 x + + 2 3 169 107 2 + + 1/100 y z + 1/150 z - ----- z - 1/175 x y z - ---- x - 1/200 x z + 14700 7000 + + 2 2 3 47 19 + + 1/100 z + 2/175 y z + 2/245 y z + 1/300 y - ---- y - ---- + 5250 2100 + + 2 2 2 17 + - 1/350 x y - 1/350 x y, COEFF(0, 2, 2) = - 2/245 x z - ---- y + 5250 + + 2 2 2 3 + - 1/175 x y + 2/175 y z + 1/100 y z - 1/300 - 1/175 x + 1/300 y + + 3 2 2 2 + + 1/150 z - 1/300 z + 1/175 y + 2/245 y z + 1/100 z , COEFF(1, 2, 2) = + + 2 19 169 2 2 + - 1/350 x - ---- + 1/175 x z - ----- z - 1/245 x z + 1/175 y + 1/250 x y + 2100 14700 + + 2 107 3 2 47 + + 1/100 z + 1/175 x y z + ---- x + 1/300 y + 1/350 x y - ---- y + 7000 5250 + + 2 3 2 2 3 + - 1/350 x y + 2/175 y z - 1/150 x + 2/245 y z + 1/200 x z + 1/150 z + + 2 2 2 11 + + 1/100 y z , COEFF(2, 2, 2) = 1/175 x + 1/125 x y + 1/100 z - --- + 420 + + 529 137 2 137 2 3 + - ----- z - ---- y + 1/175 y - ---- x + 1/100 x z + 2/175 x z + 1/300 x + 14700 5250 5250 + + 2 3 3 2 2 + + 2/245 x z + 1/300 y + 1/150 z + 2/245 y z + 1/175 x y + 2/175 y z + + 2 2 + + 1/175 x y + 1/100 y z + 2/175 x y z] + +> print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dz.compute.c"); +bytes used=1755536768, 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alloc=14677376, time=282.07 +bytes used=1909603516, alloc=14677376, time=282.15 +bytes used=1910603764, alloc=14677376, time=282.23 +bytes used=1911604080, alloc=14677376, time=282.30 +bytes used=1912604252, alloc=14677376, time=282.38 +bytes used=1913604404, alloc=14677376, time=282.70 +bytes used=1914604644, alloc=14677376, time=283.07 +bytes used=1915604848, alloc=14677376, time=283.22 +bytes used=1916605080, alloc=14677376, time=286.71 +bytes used=1917605272, alloc=14677376, time=287.55 +bytes used=1918605556, alloc=14677376, time=287.81 +bytes used=1919605724, alloc=14677376, time=287.96 +bytes used=1920605944, alloc=14677376, time=288.02 +bytes used=1921606152, alloc=14677376, time=288.16 +bytes used=1922606352, alloc=14677376, time=288.29 +> +# d^2/dx^2 +> simplify( diff(interp_3d_cube_order4_smooth0,x,x) ); +bytes used=1923619420, alloc=14677376, time=288.45 +bytes used=1924619616, alloc=14677376, time=288.53 +bytes used=1925619916, alloc=14677376, time=288.62 +bytes used=1926620136, alloc=14677376, time=288.71 +bytes used=1927620292, alloc=14677376, time=288.79 +bytes used=1928620476, alloc=14677376, time=288.87 +bytes used=1929621504, alloc=14677376, time=288.95 +bytes used=1930621684, alloc=14677376, time=289.04 +bytes used=1931621808, alloc=14677376, time=289.12 +bytes used=1932622612, alloc=14677376, time=289.22 +bytes used=1933622820, alloc=14677376, time=289.30 + 169 +- 1/10 DATA(0, -2, 0) - ----- DATA(-2, -2, 1) - 1/700 y z DATA(1, -1, -1) + 14700 + + 211 + + ---- DATA(1, -2, 1) - 1/700 y z DATA(-1, -1, -1) - 9/98 DATA(0, -2, 1) + 3675 + + 311 + + 4/75 DATA(1, -2, 0) - 9/98 DATA(0, 2, -1) + ----- DATA(2, 0, -1) + 14700 + + 211 + + ---- DATA(-1, -2, 1) - 9/98 DATA(0, -1, 2) + 1/700 y z DATA(1, 1, -1) + 3675 + + + 1/700 y z DATA(-1, 1, -1) - 1/700 y z DATA(-1, 1, 1) + + 191 169 + + ----- DATA(-2, -1, 1) - 1/300 DATA(2, -2, 0) - ----- DATA(2, -2, 1) + 14700 14700 + + 311 311 + + 1/25 x DATA(-1, -2, -1) + ----- DATA(-2, 0, 1) + ----- DATA(-2, -1, 0) + 14700 14700 + + 33 + - --- DATA(0, 2, 2) - 1/50 x DATA(-2, 1, 1) - 1/25 x DATA(1, 1, 1) + 490 + + + 4/75 DATA(1, 0, 2) + 1/25 x DATA(-1, 2, -1) + 1/50 x DATA(2, 1, -1) + + 2 + + 1/50 x DATA(2, 2, -1) - 1/25 x DATA(1, 2, -1) - 1/245 y DATA(-1, -2, 0) + + 2 2 + + 2/245 y DATA(-2, -2, 0) + 1/490 y DATA(-1, 1, 0) + + 2 2 + + 1/490 y DATA(1, -1, 0) + 2/245 y DATA(2, -2, 0) + + 2 + + 1/25 x DATA(-1, -1, 2) - 1/245 y DATA(-2, 1, 0) + + 2 2 + + 1/245 y DATA(0, -1, 0) + 1/490 y DATA(1, 1, 0) + + 2 2 + + 2/245 y DATA(2, 2, 0) - 1/245 y DATA(-2, -1, 0) + + 2 2 + - 2/245 y DATA(0, 2, 0) - 1/245 y DATA(-1, 2, 0) + + 2 2 + - 1/245 y DATA(2, 1, 0) - 1/245 y DATA(2, -1, 0) + + 2 151 + + 1/245 y DATA(0, 1, 0) - 1/25 x DATA(1, 2, 1) + ---- DATA(-1, 0, -1) + 3675 + + 2 2 + - 2/245 y DATA(2, 0, 0) - 1/245 y DATA(1, -2, 0) + + 2 2 + + 1/245 y DATA(1, 0, 0) + 1/50 x DATA(2, 2, -2) - 2/245 y DATA(-2, 0, 0) + + 2 2 + + 1/245 y DATA(-1, 0, 0) + 2/245 y DATA(0, 0, 0) + 1/50 x DATA(2, -1, 1) + + 2 2 + + 1/245 z DATA(1, 2, 0) - 2/245 z DATA(2, -2, 0) + + 2 2 + - 2/245 z DATA(-2, 2, 0) + 1/490 y DATA(-1, -1, 0) + + 2 2 + + 1/245 z DATA(1, -1, 0) + 1/245 z DATA(-1, 1, 0) + + 2 2 + - 2/245 z DATA(-2, -2, 0) + 1/245 z DATA(-1, -2, 0) + + 2 + + 1/25 x DATA(-1, 2, 1) + 2/245 z DATA(0, -1, 0) + + 2 2 + - 2/245 z DATA(-2, 1, 0) + 2/245 z DATA(0, 1, 0) + + 2 + + 1/245 z DATA(1, 1, 0) - 1/50 x DATA(-2, -2, -1) + + 2 2 + - 2/245 z DATA(2, -1, 0) + 1/245 z DATA(-1, 2, 0) + + 2 2 2 + - 2/245 z DATA(2, 2, 0) + 2/245 z DATA(0, 2, 0) - 2/245 z DATA(2, 1, 0) + + 2 2 + - 1/25 x DATA(1, 1, -2) + 1/245 z DATA(-1, 0, 0) + 2/245 z DATA(0, 0, 0) + + 2 2 + + 1/245 z DATA(1, -2, 0) - 2/245 z DATA(-2, -1, 0) + + 2 2 + - 2/245 z DATA(-2, 0, 0) - 1/50 x DATA(-2, 2, 0) + 1/245 z DATA(1, 0, 0) + + 2 + - 2/245 z DATA(2, 0, 0) - 1/25 x DATA(1, 2, -2) - 1/25 x DATA(1, 2, 0) + + + 1/25 x DATA(-1, -2, 0) + 1/50 x DATA(2, -2, 0) - 1/25 x DATA(1, -1, 0) + + 2 + + 1/245 z DATA(-1, -1, 0) - 1/50 x DATA(-2, 1, 0) + 1/25 x 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1/175 y DATA(0, -1, -1) + + 2 2 + + 1/245 z DATA(0, 2, -1) - 2/245 z DATA(0, -1, 2) + + 169 + - ----- DATA(-2, -1, -2) - 1/50 x y DATA(2, -2, 1) + 14700 + + 529 211 + - 1/100 x y DATA(2, -1, -1) - ----- DATA(2, -2, -2) + ---- DATA(1, -1, -2) + 14700 3675 + + 211 + - 9/98 DATA(0, -1, -2) + ---- DATA(-1, -1, -2) + 1/50 x y DATA(-2, -2, 1) + 3675 + + 169 + + 1/25 x y DATA(1, -2, 1) - 1/300 DATA(-2, 0, -2) - ----- DATA(2, -1, -2) + 14700 + + - 1/10 DATA(0, 0, -2) + 4/75 DATA(-1, 0, -2) + 2/175 z DATA(0, -1, -2) + + + 4/75 DATA(1, 0, -2) - 1/25 x DATA(1, 0, -2) + +> coeffs_as_lc_of_data(%, posn_list_3d_size5); +bytes used=1934688616, alloc=14677376, time=289.39 +bytes used=1935688836, alloc=14677376, time=289.48 +bytes used=1936759636, alloc=14677376, time=289.57 +bytes used=1937759980, alloc=14677376, time=289.65 +bytes used=1938779044, alloc=14677376, time=289.73 +bytes used=1939863560, alloc=14677376, time=289.82 +bytes used=1940863700, alloc=14677376, time=289.91 +bytes used=1941863848, alloc=14677376, time=290.00 +bytes used=1942864264, alloc=14677376, time=290.08 +bytes used=1943864528, alloc=14677376, time=290.17 +bytes used=1944864900, alloc=14677376, time=290.26 +bytes used=1945865020, alloc=14677376, time=290.35 +bytes used=1946905692, alloc=14677376, time=290.44 +bytes used=1947905816, alloc=14677376, time=290.53 +bytes used=1948917232, alloc=14677376, time=290.63 +bytes used=1949934968, alloc=14677376, time=290.72 +bytes used=1950936392, alloc=14677376, time=290.82 +bytes used=1951936576, alloc=14677376, time=290.92 +bytes used=1952945852, alloc=14677376, time=291.02 +bytes used=1953957504, alloc=14677376, time=291.12 +bytes used=1954957664, alloc=14677376, time=291.22 +bytes used=1955957780, alloc=14677376, time=291.33 +bytes used=1956972780, alloc=14677376, time=291.44 +bytes used=1957973956, alloc=14677376, time=291.55 +bytes used=1958984176, alloc=14677376, time=291.66 +bytes used=1959992920, alloc=14677376, time=291.74 +bytes used=1961011124, alloc=14677376, time=291.82 +bytes used=1962029256, alloc=14677376, time=291.89 +bytes used=1963047124, alloc=14677376, time=291.97 + 529 2 +[COEFF(-2, -2, -2) = - ----- + 2/245 z - 1/50 x - 2/175 y + 2/175 y z + 14700 + + 2 2 + + 1/50 x z + 1/50 x + 2/245 y + 1/50 x y - 2/175 z, COEFF(-1, -2, -2) = + + 2 2 256 + - 1/25 x z - 1/245 y + 1/175 y - 2/25 x + ---- - 1/25 x y - 1/175 y z + 3675 + + 2 + + 1/25 x - 1/245 z + 1/175 z, COEFF(0, -2, -2) = + + 2 2 33 2 + - 2/245 z + 3/25 x - --- - 2/175 y z + 2/175 z + 2/175 y - 2/245 y , + 490 + + 2 2 + COEFF(1, -2, -2) = 1/175 y + 1/175 z + 1/25 x y - 2/25 x - 1/245 y + + 256 2 + - 1/25 x + 1/25 x z + ---- - 1/245 z - 1/175 y z, COEFF(2, -2, -2) = + 3675 + + 2 529 2 + - 2/175 y + 2/245 y - 1/50 x z - ----- - 2/175 z + 1/50 x + 1/50 x + 14700 + + 2 2 + + 2/175 y z - 1/50 x y + 2/245 z , COEFF(-2, -1, -2) = - 1/245 y + + 2 2 + + 1/100 x y - 1/175 y + 2/245 z - 1/50 x - 2/175 z + 1/50 x + 1/50 x z + + 169 2 2 + + 1/175 y z - -----, COEFF(-1, -1, -2) = - 2/25 x - 1/50 x y + 1/490 y + 14700 + + 211 2 + + ---- + 1/350 y + 1/175 z + 1/25 x - 1/245 z - 1/25 x z - 1/350 y z, + 3675 + + COEFF(0, -1, -2) = + + 2 2 2 + 1/245 y - 2/245 z - 9/98 - 1/175 y z + 1/175 y + 2/175 z + 3/25 x , + + 211 2 2 + COEFF(1, -1, -2) = ---- - 1/350 y z + 1/490 y - 2/25 x + 1/50 x y + 3675 + + 2 + + 1/25 x z - 1/25 x - 1/245 z + 1/175 z + 1/350 y, COEFF(2, -1, -2) = + + 2 2 + 1/175 y z - 1/175 y - 1/100 x y + 1/50 x + 2/245 z - 2/175 z + 1/50 x + + 169 2 + - ----- - 1/50 x z - 1/245 y , COEFF(-2, 0, -2) = + 14700 + + 2 2 2 + - 2/175 z + 1/50 x + 2/245 z + 1/50 x z - 2/245 y - 1/50 x - 1/300, + + COEFF(-1, 0, -2) = + + 2 2 2 + 4/75 + 1/25 x - 2/25 x - 1/245 z + 1/245 y - 1/25 x z + 1/175 z, + + 2 2 2 + COEFF(0, 0, -2) = - 2/245 z + 3/25 x - 1/10 + 2/245 y + 2/175 z, + + COEFF(1, 0, -2) = + + 2 2 2 + - 1/245 z + 4/75 + 1/245 y - 1/25 x + 1/25 x z + 1/175 z - 2/25 x , + + COEFF(2, 0, -2) = + + 2 2 2 + 2/245 z - 1/300 + 1/50 x - 2/245 y + 1/50 x - 2/175 z - 1/50 x z, + + 2 + COEFF(-2, 1, -2) = - 1/175 y z + 1/50 x z + 1/175 y - 1/245 y - 2/175 z + + 2 169 2 + + 1/50 x - 1/100 x y - ----- + 2/245 z - 1/50 x, COEFF(-1, 1, -2) = + 14700 + + 2 2 211 + - 1/245 z + 1/25 x + 1/175 z + 1/50 x y - 2/25 x + ---- + 1/350 y z + 3675 + + 2 + + 1/490 y - 1/350 y - 1/25 x z, COEFF(0, 1, -2) = + + 2 2 2 + - 2/245 z + 3/25 x + 2/175 z + 1/175 y z - 9/98 - 1/175 y + 1/245 y , + + 2 2 + COEFF(1, 1, -2) = 1/350 y z + 1/490 y + 1/175 z - 2/25 x - 1/25 x + + 211 2 + + 1/25 x z + ---- - 1/245 z - 1/50 x y - 1/350 y, COEFF(2, 1, -2) = + 3675 + + 2 2 169 + 2/245 z - 1/245 y + 1/175 y - ----- + 1/100 x y - 1/175 y z + 1/50 x + 14700 + + 2 529 + - 1/50 x z - 2/175 z + 1/50 x , COEFF(-2, 2, -2) = - ----- - 1/50 x + 14700 + + 2 2 2 + - 2/175 z + 2/245 z + 1/50 x - 1/50 x y + 2/245 y + 2/175 y + 1/50 x z + + 256 2 + - 2/175 y z, COEFF(-1, 2, -2) = ---- - 1/25 x z - 1/245 y + 1/175 z + 3675 + + 2 2 + - 1/175 y + 1/175 y z + 1/25 x - 1/245 z + 1/25 x y - 2/25 x , + + COEFF(0, 2, -2) = + + 2 2 33 2 + 2/175 z - 2/245 z - 2/245 y - --- + 3/25 x + 2/175 y z - 2/175 y, + 490 + + 2 256 2 + COEFF(1, 2, -2) = - 2/25 x + ---- - 1/245 y - 1/175 y + 1/25 x z + 3675 + + 2 + - 1/245 z + 1/175 z - 1/25 x y - 1/25 x + 1/175 y z, COEFF(2, 2, -2) = + + 529 2 + - 2/175 z - 1/50 x z - ----- + 2/175 y + 1/50 x y + 1/50 x + 1/50 x + 14700 + + 2 2 169 + - 2/175 y z + 2/245 z + 2/245 y , COEFF(-2, -2, -1) = - 1/50 x - ----- + 14700 + + 2 2 + + 2/245 y + 1/100 x z + 1/175 y z + 1/50 x - 2/175 y + 1/50 x y + + 2 211 + - 1/175 z - 1/245 z , COEFF(-1, -2, -1) = ---- - 1/350 y z - 1/25 x y + 3675 + + 2 2 2 + - 1/50 x z - 2/25 x + 1/25 x + 1/175 y + 1/350 z + 1/490 z - 1/245 y , + + COEFF(0, -2, -1) = + + 2 2 2 + 1/175 z - 9/98 + 3/25 x - 1/175 y z + 1/245 z - 2/245 y + 2/175 y, + + 2 2 2 + COEFF(1, -2, -1) = 1/490 z + 1/350 z - 1/245 y - 2/25 x - 1/25 x + + 211 + + 1/175 y + 1/50 x z - 1/350 y z + ---- + 1/25 x y, COEFF(2, -2, -1) = + 3675 + + 2 2 169 + - 1/100 x z - 1/245 z + 1/50 x + 1/50 x - 1/50 x y - ----- + 1/175 y z + 14700 + + 2 + + 2/245 y - 1/175 z - 2/175 y, COEFF(-2, -1, -1) = - 1/175 y - 1/175 z + + 2 2 191 + - 1/245 y + 1/350 y z + 1/50 x + 1/100 x z + 1/100 x y + ----- + 14700 + + 2 2 + - 1/245 z - 1/50 x, COEFF(-1, -1, -1) = - 1/50 x y - 2/25 x + 1/25 x + + 2 166 2 + + 1/490 y + ---- + 1/350 y + 1/490 z - 1/50 x z + 1/350 z - 1/700 y z, + 3675 + + COEFF(0, -1, -1) = + + 2 57 2 2 + 1/175 y - 1/350 y z + 3/25 x - --- + 1/175 z + 1/245 y + 1/245 z , + 490 + + 2 166 + COEFF(1, -1, -1) = - 1/700 y z + 1/350 z + 1/490 y + ---- + 1/350 y + 3675 + + 2 2 + + 1/490 z + 1/50 x z + 1/50 x y - 1/25 x - 2/25 x , COEFF(2, -1, -1) = + + 2 + 1/50 x - 1/100 x y - 1/175 z + 1/350 y z + 1/50 x - 1/175 y - 1/100 x z + + 2 191 2 + - 1/245 y + ----- - 1/245 z , COEFF(-2, 0, -1) = + 14700 + + 2 2 2 311 + - 2/245 y + 1/50 x + 1/100 x z - 1/245 z - 1/175 z + ----- - 1/50 x, + 14700 + + COEFF(-1, 0, -1) = + + 151 2 2 2 + ---- - 1/50 x z + 1/245 y - 2/25 x + 1/350 z + 1/490 z + 1/25 x, + 3675 + + 61 2 2 2 + COEFF(0, 0, -1) = - --- + 2/245 y + 1/175 z + 1/245 z + 3/25 x , + 490 + + COEFF(1, 0, -1) = + + 2 2 2 151 + 1/50 x z - 2/25 x + 1/490 z + 1/245 y + ---- + 1/350 z - 1/25 x, + 3675 + + COEFF(2, 0, -1) = + + 2 2 2 311 + - 1/100 x z - 1/245 z - 1/175 z + 1/50 x - 2/245 y + ----- + 1/50 x, + 14700 + + 2 + COEFF(-2, 1, -1) = - 1/350 y z + 1/175 y - 1/50 x + 1/50 x - 1/175 z + + 2 191 2 + - 1/245 y + ----- + 1/100 x z - 1/100 x y - 1/245 z , COEFF(-1, 1, -1) = + 14700 + + 166 2 2 + 1/700 y z + ---- + 1/350 z + 1/490 y + 1/50 x y - 2/25 x - 1/350 y + 3675 + + 2 + + 1/490 z + 1/25 x - 1/50 x z, COEFF(0, 1, -1) = + + 2 2 57 2 + 1/245 y + 1/350 y z + 1/245 z - --- + 3/25 x + 1/175 z - 1/175 y, + 490 + + 2 2 + COEFF(1, 1, -1) = 1/700 y z - 2/25 x + 1/50 x z - 1/350 y + 1/490 y + + 166 2 + + 1/350 z + ---- - 1/25 x + 1/490 z - 1/50 x y, COEFF(2, 1, -1) = + 3675 + + 2 2 2 + - 1/100 x z + 1/175 y + 1/50 x - 1/245 z - 1/175 z + 1/50 x - 1/245 y + + 191 169 + + ----- - 1/350 y z + 1/100 x y, COEFF(-2, 2, -1) = - ----- - 1/175 z + 14700 14700 + + 2 2 + + 1/100 x z + 2/245 y + 1/50 x + 2/175 y - 1/175 y z - 1/50 x y + + 2 211 2 + - 1/245 z - 1/50 x, COEFF(-1, 2, -1) = 1/350 z + ---- - 1/175 y - 2/25 x + 3675 + + 2 2 + - 1/50 x z + 1/350 y z + 1/490 z - 1/245 y + 1/25 x y + 1/25 x, + + COEFF(0, 2, -1) = + + 2 2 2 + - 9/98 + 1/175 z - 2/245 y - 2/175 y + 1/175 y z + 1/245 z + 3/25 x , + + 2 2 2 211 + COEFF(1, 2, -1) = 1/490 z - 1/25 x y - 1/245 y - 1/175 y - 2/25 x + ---- + 3675 + + 2 + - 1/25 x + 1/50 x z + 1/350 y z + 1/350 z, COEFF(2, 2, -1) = 2/245 y + + 169 2 2 + - ----- + 2/175 y - 1/245 z - 1/175 z + 1/50 x y + 1/50 x - 1/175 y z + 14700 + + - 1/100 x z + 1/50 x, COEFF(-2, -2, 0) = + + 2 2 2 + - 2/245 z - 1/300 + 1/50 x + 1/50 x y - 1/50 x - 2/175 y + 2/245 y , + + COEFF(-1, -2, 0) = + + 2 2 2 + 1/25 x - 1/25 x y + 1/175 y - 2/25 x + 4/75 + 1/245 z - 1/245 y , + + 2 2 2 + COEFF(0, -2, 0) = - 1/10 - 2/245 y + 2/245 z + 2/175 y + 3/25 x , + + COEFF(1, -2, 0) = + + 2 2 2 + 1/25 x y + 4/75 - 1/25 x - 1/245 y + 1/245 z - 2/25 x + 1/175 y, + + COEFF(2, -2, 0) = + + 2 2 2 + 1/50 x - 1/50 x y - 2/175 y - 1/300 + 2/245 y - 2/245 z + 1/50 x, + + COEFF(-2, -1, 0) = + + 311 2 2 2 + ----- + 1/50 x + 1/100 x y - 1/245 y - 1/50 x - 2/245 z - 1/175 y, + 14700 + + COEFF(-1, -1, 0) = + + 151 2 2 2 + 1/350 y + ---- + 1/490 y - 2/25 x + 1/245 z + 1/25 x - 1/50 x y, + 3675 + + 2 2 61 2 + COEFF(0, -1, 0) = 2/245 z + 1/175 y + 3/25 x - --- + 1/245 y , + 490 + + COEFF(1, -1, 0) = + + 151 2 2 2 + ---- + 1/350 y - 2/25 x + 1/245 z + 1/50 x y - 1/25 x + 1/490 y , + 3675 + + COEFF(2, -1, 0) = + + 311 2 2 2 + ----- + 1/50 x - 1/245 y - 2/245 z - 1/175 y - 1/100 x y + 1/50 x , + 14700 + + 431 2 2 2 + COEFF(-2, 0, 0) = ----- - 2/245 z + 1/50 x - 2/245 y - 1/50 x, + 14700 + + 2 2 2 136 + COEFF(-1, 0, 0) = - 2/25 x + 1/25 x + 1/245 z + 1/245 y + ----, + 3675 + + 13 2 2 2 + COEFF(0, 0, 0) = - -- + 3/25 x + 2/245 z + 2/245 y , + 98 + + 2 2 136 2 + COEFF(1, 0, 0) = 1/245 y - 2/25 x - 1/25 x + ---- + 1/245 z , + 3675 + + 2 2 2 431 + COEFF(2, 0, 0) = - 2/245 z - 2/245 y + 1/50 x + 1/50 x + -----, + 14700 + + COEFF(-2, 1, 0) = + + 2 2 2 311 + 1/50 x - 1/245 y - 1/100 x y - 2/245 z - 1/50 x + 1/175 y + -----, + 14700 + + COEFF(-1, 1, 0) = + + 151 2 2 2 + ---- + 1/50 x y + 1/490 y - 2/25 x - 1/350 y + 1/245 z + 1/25 x, + 3675 + + 2 2 61 2 + COEFF(0, 1, 0) = 1/245 y + 3/25 x - 1/175 y - --- + 2/245 z , + 490 + + COEFF(1, 1, 0) = + + 2 151 2 2 + 1/245 z + ---- - 1/350 y - 2/25 x + 1/490 y - 1/50 x y - 1/25 x, + 3675 + + COEFF(2, 1, 0) = + + 2 2 2 311 + 1/50 x + 1/175 y - 2/245 z + 1/100 x y - 1/245 y + 1/50 x + -----, + 14700 + + COEFF(-2, 2, 0) = + + 2 2 2 + - 2/245 z + 2/245 y - 1/50 x + 1/50 x - 1/300 - 1/50 x y + 2/175 y, + + COEFF(-1, 2, 0) = + + 2 2 2 + 1/25 x + 4/75 + 1/25 x y - 1/245 y - 2/25 x - 1/175 y + 1/245 z , + + 2 2 2 + COEFF(0, 2, 0) = - 2/175 y - 2/245 y + 3/25 x + 2/245 z - 1/10, + + COEFF(1, 2, 0) = + + 2 2 2 + - 1/175 y + 4/75 - 1/245 y + 1/245 z - 1/25 x y - 2/25 x - 1/25 x, + + COEFF(2, 2, 0) = + + 2 2 2 + 1/50 x y + 2/175 y - 2/245 z - 1/300 + 1/50 x + 2/245 y + 1/50 x , + + COEFF(-2, -2, 1) = 1/175 z - 2/175 y - 1/100 x z - 1/175 y z - 1/50 x + + 169 2 2 2 + - ----- + 1/50 x y - 1/245 z + 2/245 y + 1/50 x , COEFF(-1, -2, 1) = + 14700 + + 2 2 2 + 1/490 z + 1/350 y z - 1/350 z + 1/25 x - 1/245 y + 1/175 y - 2/25 x + + 211 + + ---- + 1/50 x z - 1/25 x y, COEFF(0, -2, 1) = + 3675 + + 2 2 2 + - 1/175 z - 9/98 + 1/175 y z + 1/245 z - 2/245 y + 2/175 y + 3/25 x , + + 2 2 + COEFF(1, -2, 1) = - 1/25 x - 1/245 y - 2/25 x + 1/25 x y + 1/350 y z + + 2 211 + - 1/350 z - 1/50 x z + 1/175 y + 1/490 z + ----, COEFF(2, -2, 1) = + 3675 + + 2 169 2 2 + 1/175 z + 1/50 x - 1/245 z - ----- + 1/50 x - 2/175 y + 2/245 y + 14700 + + 191 + + 1/100 x z - 1/50 x y - 1/175 y z, COEFF(-2, -1, 1) = ----- + 1/100 x y + 14700 + + 2 2 2 + - 1/245 y - 1/100 x z - 1/50 x - 1/350 y z - 1/175 y - 1/245 z + 1/50 x + + 2 2 2 + + 1/175 z, COEFF(-1, -1, 1) = 1/490 y + 1/700 y z - 2/25 x + 1/490 z + + 166 + + 1/350 y - 1/350 z - 1/50 x y + ---- + 1/25 x + 1/50 x z, COEFF(0, -1, 1) + 3675 + + 2 2 2 57 + = 3/25 x + 1/175 y - 1/175 z + 1/245 y + 1/245 z + 1/350 y z - ---, + 490 + + 166 2 + COEFF(1, -1, 1) = - 1/25 x + 1/700 y z + ---- + 1/490 y + 1/50 x y + 3675 + + 2 2 + - 1/350 z - 1/50 x z + 1/350 y - 2/25 x + 1/490 z , COEFF(2, -1, 1) = + + 2 2 2 + - 1/245 z - 1/245 y - 1/175 y - 1/350 y z + 1/50 x + 1/50 x + 1/100 x z + + 191 + + 1/175 z + ----- - 1/100 x y, COEFF(-2, 0, 1) = + 14700 + + 311 2 2 2 + ----- + 1/175 z + 1/50 x - 1/245 z - 1/50 x - 2/245 y - 1/100 x z, + 14700 + + COEFF(-1, 0, 1) = + + 2 151 2 2 + 1/245 y - 1/350 z + ---- - 2/25 x + 1/25 x + 1/490 z + 1/50 x z, + 3675 + + 2 61 2 2 + COEFF(0, 0, 1) = - 1/175 z + 2/245 y - --- + 3/25 x + 1/245 z , + 490 + + COEFF(1, 0, 1) = + + 2 2 2 151 + - 1/25 x + 1/245 y - 2/25 x + 1/490 z + ---- - 1/50 x z - 1/350 z, + 3675 + + COEFF(2, 0, 1) = + + 2 2 311 2 + - 1/245 z + 1/50 x + 1/50 x + ----- + 1/100 x z - 2/245 y + 1/175 z, + 14700 + + 191 + COEFF(-2, 1, 1) = - 1/100 x z + 1/350 y z - 1/100 x y + 1/175 y + ----- + 14700 + + 2 2 2 + - 1/50 x + 1/50 x - 1/245 y - 1/245 z + 1/175 z, COEFF(-1, 1, 1) = + + 2 166 + 1/50 x y - 2/25 x + 1/50 x z - 1/350 z + 1/25 x - 1/350 y + ---- + 3675 + + 2 2 + + 1/490 y - 1/700 y z + 1/490 z , COEFF(0, 1, 1) = + + 57 2 2 2 + - 1/350 y z - --- + 1/245 z - 1/175 y + 1/245 y - 1/175 z + 3/25 x , + 490 + + 2 + COEFF(1, 1, 1) = 1/490 y - 1/700 y z - 1/25 x - 1/350 z - 1/50 x z + + 2 2 166 + - 1/350 y - 1/50 x y + 1/490 z - 2/25 x + ----, COEFF(2, 1, 1) = + 3675 + + 2 2 2 + 1/350 y z - 1/245 y + 1/50 x + 1/175 y + 1/100 x z + 1/175 z - 1/245 z + + 191 2 + + 1/100 x y + 1/50 x + -----, COEFF(-2, 2, 1) = - 1/100 x z + 1/50 x + 14700 + + 2 2 + - 1/50 x + 2/245 y + 2/175 y - 1/245 z + 1/175 y z - 1/50 x y + 1/175 z + + 169 2 211 2 + - -----, COEFF(-1, 2, 1) = - 2/25 x + ---- + 1/490 z + 1/50 x z + 1/25 x + 14700 3675 + + 2 + + 1/25 x y - 1/350 y z - 1/350 z - 1/175 y - 1/245 y , COEFF(0, 2, 1) = + + 2 2 2 + - 9/98 - 1/175 z - 1/175 y z - 2/175 y - 2/245 y + 1/245 z + 3/25 x , + + 2 211 + COEFF(1, 2, 1) = 1/490 z + ---- - 1/175 y - 1/25 x - 1/50 x z - 1/350 y z + 3675 + + 2 2 + - 1/25 x y - 1/350 z - 1/245 y - 2/25 x , COEFF(2, 2, 1) = 1/50 x y + + 2 2 169 + + 1/100 x z + 1/175 y z - 1/245 z + 1/50 x - ----- + 1/175 z + 2/175 y + 14700 + + 2 2 + + 2/245 y + 1/50 x, COEFF(-2, -2, 2) = 1/50 x y + 2/245 y + 2/175 z + + 529 2 2 + - 2/175 y - 1/50 x - 2/175 y z - ----- + 1/50 x - 1/50 x z + 2/245 z , + 14700 + + 256 + COEFF(-1, -2, 2) = - 1/25 x y + 1/25 x z + 1/25 x + 1/175 y + ---- + 3675 + + 2 2 2 + - 1/245 z - 1/175 z + 1/175 y z - 2/25 x - 1/245 y , COEFF(0, -2, 2) = + + 2 2 33 2 + - 2/245 y - 2/245 z + 2/175 y z + 2/175 y - 2/175 z - --- + 3/25 x , + 490 + + 256 + COEFF(1, -2, 2) = 1/25 x y - 1/25 x z - 1/25 x - 1/175 z + 1/175 y + ---- + 3675 + + 2 2 2 + + 1/175 y z - 2/25 x - 1/245 y - 1/245 z , COEFF(2, -2, 2) = 1/50 x z + + 2 2 529 2 + + 2/175 z + 1/50 x + 2/245 y + 1/50 x - ----- - 2/175 y z + 2/245 z + 14700 + + - 2/175 y - 1/50 x y, COEFF(-2, -1, 2) = 1/100 x y + 2/175 z - 1/50 x + + 2 2 2 169 + - 1/245 y + 1/50 x + 2/245 z - 1/50 x z - 1/175 y z - ----- - 1/175 y, + 14700 + + 2 + COEFF(-1, -1, 2) = - 1/50 x y + 1/350 y + 1/25 x z - 2/25 x - 1/175 z + + 2 2 211 + + 1/350 y z + 1/25 x + 1/490 y - 1/245 z + ----, COEFF(0, -1, 2) = + 3675 + + 2 2 2 + - 2/245 z - 2/175 z + 1/245 y + 1/175 y z + 1/175 y - 9/98 + 3/25 x , + + 2 211 2 + COEFF(1, -1, 2) = 1/490 y - 1/25 x z - 1/175 z + ---- + 1/50 x y - 2/25 x + 3675 + + 2 2 + + 1/350 y - 1/245 z - 1/25 x + 1/350 y z, COEFF(2, -1, 2) = 1/50 x + + 2 169 + + 1/50 x - 1/100 x y + 2/175 z + 1/50 x z - 1/175 y + 2/245 z - ----- + 14700 + + 2 + - 1/245 y - 1/175 y z, COEFF(-2, 0, 2) = + + 2 2 2 + 2/175 z - 1/50 x - 2/245 y + 2/245 z - 1/50 x z - 1/300 + 1/50 x , + + COEFF(-1, 0, 2) = + + 2 2 2 + - 1/175 z + 4/75 - 2/25 x + 1/25 x - 1/245 z + 1/25 x z + 1/245 y , + + 2 2 2 + COEFF(0, 0, 2) = - 2/175 z + 3/25 x - 2/245 z - 1/10 + 2/245 y , + + COEFF(1, 0, 2) = + + 2 2 2 + - 1/245 z - 1/175 z - 1/25 x - 2/25 x + 1/245 y + 4/75 - 1/25 x z, + + COEFF(2, 0, 2) = + + 2 2 2 + - 1/300 + 2/245 z + 2/175 z + 1/50 x z + 1/50 x + 1/50 x - 2/245 y , + + 2 2 + COEFF(-2, 1, 2) = 1/175 y z - 1/50 x z + 1/50 x - 1/100 x y - 1/245 y + + 2 169 + + 2/175 z + 2/245 z - 1/50 x - ----- + 1/175 y, COEFF(-1, 1, 2) = + 14700 + + 2 2 211 2 + 1/50 x y + 1/25 x + 1/490 y - 2/25 x + ---- - 1/350 y z - 1/245 z + 3675 + + - 1/175 z + 1/25 x z - 1/350 y, COEFF(0, 1, 2) = + + 2 2 2 + 3/25 x - 1/175 y - 2/245 z - 1/175 y z - 9/98 + 1/245 y - 2/175 z, + + 2 2 211 2 + COEFF(1, 1, 2) = - 2/25 x + 1/490 y + ---- - 1/50 x y - 1/245 z + 3675 + + - 1/350 y z - 1/350 y - 1/175 z - 1/25 x - 1/25 x z, COEFF(2, 1, 2) = + + 2 169 2 + 2/245 z - ----- + 1/50 x + 1/100 x y + 1/50 x + 1/50 x z + 1/175 y + 14700 + + 2 2 + - 1/245 y + 1/175 y z + 2/175 z, COEFF(-2, 2, 2) = 2/175 y z + 2/245 z + + 2 529 2 + + 2/175 z - 1/50 x y + 1/50 x - ----- - 1/50 x z - 1/50 x + 2/245 y + 14700 + + 2 + + 2/175 y, COEFF(-1, 2, 2) = 1/25 x y - 1/175 y z - 1/245 z + 1/25 x + + 256 2 2 + + ---- + 1/25 x z - 2/25 x - 1/175 y - 1/175 z - 1/245 y , COEFF(0, 2, 2) + 3675 + + 2 2 2 33 + = - 2/175 y - 2/175 z - 2/245 y - 2/175 y z + 3/25 x - 2/245 z - ---, + 490 + + 2 2 + COEFF(1, 2, 2) = - 1/175 z - 1/245 y - 1/25 x z - 1/245 z - 1/25 x y + + 256 2 + + ---- - 2/25 x - 1/175 y - 1/175 y z - 1/25 x, COEFF(2, 2, 2) = 2/175 y + 3675 + + 529 2 2 + + 1/50 x y - ----- + 2/245 y + 2/175 y z + 2/175 z + 2/245 z + 1/50 x z + 14700 + + 2 + + 1/50 x + 1/50 x] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxx.compute.c"); +bytes used=1964047504, alloc=14677376, time=292.06 +bytes used=1965047664, alloc=14677376, time=292.14 +bytes used=1966047816, alloc=14677376, time=292.22 +bytes used=1967048152, alloc=14677376, time=292.31 +bytes used=1968048340, alloc=14677376, time=293.02 +bytes used=1969048728, alloc=14677376, time=293.73 +bytes used=1970049164, alloc=14677376, time=294.44 +bytes used=1971049552, alloc=14677376, time=295.14 +bytes used=1972050068, alloc=14677376, time=295.84 +bytes used=1973050400, alloc=14677376, time=296.13 +bytes used=1974050584, alloc=14677376, time=296.22 +bytes used=1975050740, alloc=14677376, time=296.31 +bytes used=1976086208, alloc=14677376, time=296.38 +bytes used=1977118624, alloc=14677376, time=296.46 +bytes used=1978127380, alloc=14677376, time=296.55 +bytes used=1979127568, alloc=14677376, time=296.65 +bytes used=1980127820, alloc=14677376, time=297.36 +bytes used=1981128036, alloc=14677376, time=298.18 +bytes used=1982128204, alloc=14677376, time=298.51 +bytes used=1983128448, alloc=14677376, time=298.59 +bytes used=1984128824, alloc=14677376, time=298.66 +bytes used=1985129300, alloc=14677376, time=298.73 +bytes used=1986129580, alloc=14677376, time=298.79 +bytes used=1987129824, alloc=14677376, time=298.85 +bytes used=1988130336, alloc=14677376, time=298.92 +bytes used=1989130528, alloc=14677376, time=298.99 +bytes used=1990130876, alloc=14677376, time=299.07 +bytes used=1991134116, alloc=14677376, time=299.14 +bytes used=1992134336, alloc=14677376, time=299.22 +bytes used=1993134800, alloc=14677376, time=299.32 +bytes used=1994135092, alloc=14677376, time=299.44 +bytes used=1995135284, alloc=14677376, time=299.55 +bytes used=1996135548, alloc=14677376, time=299.67 +bytes used=1997135812, alloc=14677376, time=299.78 +bytes used=1998135988, alloc=14677376, time=299.90 +bytes used=1999136156, alloc=14677376, time=300.01 +bytes used=2000146400, alloc=14677376, time=300.14 +bytes used=2001146952, alloc=14677376, time=300.26 +bytes used=2002151924, alloc=14677376, time=300.38 +bytes used=2003152240, alloc=14677376, time=300.48 +bytes used=2004152420, alloc=14677376, time=301.19 +bytes used=2005152628, alloc=14677376, time=302.55 +bytes used=2006152820, alloc=14677376, time=303.10 +bytes used=2007154220, alloc=14677376, time=303.19 +bytes used=2008154488, alloc=14677376, time=303.26 +bytes used=2009154652, alloc=14677376, time=303.34 +bytes used=2010155104, alloc=14677376, time=303.41 +bytes used=2011155312, alloc=14677376, time=303.49 +bytes used=2012155652, alloc=14677376, time=303.56 +bytes used=2013156012, alloc=14677376, time=303.63 +bytes used=2014156244, alloc=14677376, time=303.71 +bytes used=2015156696, alloc=14677376, time=303.78 +bytes used=2016157064, alloc=14677376, time=303.86 +bytes used=2017157240, alloc=14677376, time=303.93 +bytes used=2018157456, alloc=14677376, time=304.01 +bytes used=2019157692, alloc=14677376, time=304.20 +bytes used=2020157916, alloc=14677376, time=304.32 +bytes used=2021162332, alloc=14677376, time=304.45 +bytes used=2022162524, alloc=14677376, time=304.58 +bytes used=2023162760, alloc=14677376, time=304.94 +bytes used=2024164604, alloc=14677376, time=306.88 +bytes used=2025164812, alloc=14677376, time=307.50 +bytes used=2026165116, alloc=14677376, time=307.66 +bytes used=2027165308, alloc=14677376, time=307.74 +bytes used=2028165604, alloc=14677376, time=307.81 +bytes used=2029165772, alloc=14677376, time=307.89 +bytes used=2030166096, alloc=14677376, time=307.96 +bytes used=2031166252, alloc=14677376, time=308.04 +bytes used=2032166456, alloc=14677376, time=308.11 +bytes used=2033166656, alloc=14677376, time=308.26 +bytes used=2034166888, alloc=14677376, time=308.95 +bytes used=2035167124, alloc=14677376, time=310.69 +bytes used=2036167804, alloc=14677376, time=311.27 +bytes used=2037167996, alloc=14677376, time=311.42 +bytes used=2038168292, alloc=14677376, time=311.53 +bytes used=2039168556, alloc=14677376, time=311.70 +> +# d^2/dxdy +> simplify( diff(interp_3d_cube_order4_smooth0,x,y) ); +bytes used=2040168820, alloc=14677376, time=311.79 +bytes used=2041205784, alloc=14677376, time=311.88 +bytes used=2042206092, alloc=14677376, time=311.96 +bytes used=2043206244, alloc=14677376, time=312.04 +bytes used=2044207052, alloc=14677376, time=312.12 +bytes used=2045207192, alloc=14677376, time=312.21 +bytes used=2046207328, alloc=14677376, time=312.29 +bytes used=2047208468, alloc=14677376, time=312.37 + 47 +1/175 y z DATA(2, 0, -1) - 1/350 y z DATA(1, 0, 1) - ---- DATA(-2, -2, 1) + 5250 + + - 1/175 y z DATA(1, 0, 2) - 1/350 y z DATA(-1, 0, -1) + + 167 + + 1/700 y z DATA(1, -1, -1) - ---- DATA(1, -2, 1) + 7000 + + 187 167 + - 1/700 y z DATA(-1, -1, -1) - ---- DATA(1, -2, 0) + ---- DATA(-1, -2, 1) + 7000 7000 + + + 1/175 y DATA(-1, 0, -1) - 2/175 y DATA(2, 0, -1) - 1/175 y DATA(1, 0, 1) + + + 1/700 y z DATA(1, 1, -1) - 1/175 y DATA(1, 0, -2) + + - 1/175 y DATA(1, 0, 0) - 2/175 y DATA(2, 0, 1) + 2/175 y DATA(-2, 0, 1) + + - 1/175 y DATA(1, 0, 2) - 1/175 y DATA(1, 0, -1) + 1/175 y DATA(-1, 0, 1) + + - 2/175 y DATA(2, 0, 2) + 1/175 y DATA(-1, 0, 2) + 2/175 y DATA(-2, 0, -1) + + + 2/175 y DATA(-2, 0, 2) - 2/175 y DATA(2, 0, -2) + 1/175 y DATA(-1, 0, 0) + + - 2/175 y DATA(2, 0, 0) + 2/175 y DATA(-2, 0, 0) + 2/175 y DATA(-2, 0, -2) + + + 1/175 y DATA(-1, 0, -2) + 1/175 x DATA(0, -1, -2) + + - 1/700 y z DATA(-1, 1, -1) + 1/700 y z DATA(-1, 1, 1) + + 167 17 47 + + ---- DATA(-2, -1, 1) + ---- DATA(2, -2, 0) + ---- DATA(2, -2, 1) + 7000 5250 5250 + + 187 + + 1/175 x DATA(-1, -2, -1) + ---- DATA(-2, -1, 0) + 1/175 x DATA(-2, 1, 1) + 7000 + + + 1/175 x DATA(0, -1, 2) - 1/175 x DATA(0, 1, 0) - 1/175 x DATA(0, 1, 1) + + - 2/175 x DATA(0, 2, 0) - 2/175 x DATA(0, 2, -2) - 2/175 x DATA(0, 2, 2) + + - 1/175 x DATA(0, 1, -2) - 1/350 x DATA(1, 1, 1) + 2/175 x DATA(0, -2, 1) + + - 2/175 x DATA(0, 2, -1) - 1/175 x DATA(0, 1, 2) + 1/175 x DATA(0, -1, 1) + + - 1/175 x DATA(0, 1, -1) + 1/175 x DATA(0, -1, -1) + + + 2/175 x DATA(0, -2, -2) - 1/175 x DATA(-1, 2, -1) + + + 1/175 x DATA(2, 1, -1) + 2/175 x DATA(2, 2, -1) - 1/175 x DATA(1, 2, -1) + + + 2/175 x DATA(0, -2, -1) + 2/175 x DATA(0, -2, 2) + + + 1/175 x DATA(0, -1, 0) + 2/175 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1) + 1/200 y DATA(-1, -2, 1) + + 2 2 + - 1/50 y DATA(-2, -1, 1) - 1/50 y DATA(2, 1, -2) + + 2 2 + - 1/100 y DATA(-2, 2, 1) + 1/50 y DATA(2, -1, 1) + + 2 2 + + 1/100 y DATA(-2, -2, -1) + 1/100 y DATA(2, 2, 1) + + 2 2 + - 1/50 y DATA(2, 1, 1) - 1/100 y DATA(-1, -1, 2) + + 2 + - 1/200 y DATA(-1, 2, 1) + 1/175 y DATA(-2, -1, -2) + + + 1/175 y DATA(1, -2, -2) - 1/175 y DATA(-1, -2, -2) + + 2 + - 1/350 y DATA(1, -1, -2) + 1/200 y DATA(1, 2, 1) + + 2 + + 1/100 y DATA(2, 2, -2) + 2/175 y DATA(2, -2, -2) + + + 1/350 y DATA(-1, -1, -2) - 1/175 y DATA(2, -1, -2) + + 107 137 + - ---- DATA(-1, 2, -2) - 2/245 x y DATA(-2, 1, 0) + ---- DATA(-2, 2, -2) + 7000 5250 + + 17 + - ---- DATA(2, 2, 0) + 2/245 x y DATA(0, 1, 2) + 1/245 x y DATA(1, 1, 0) + 5250 + + 47 + + ---- DATA(-2, 2, 1) - 2/245 x y DATA(-2, -1, 0) + 5250 + + - 2/245 x y DATA(1, -2, 0) + 1/245 x y DATA(-1, -1, 0) + + 167 + - ---- DATA(2, -1, 1) - 4/245 x y DATA(2, 0, 2) + 2/245 x y DATA(-1, 0, 2) + 7000 + + - 4/245 x y DATA(-2, 0, -1) - 4/245 x y DATA(-2, 0, 2) + + 107 + - 4/245 x y DATA(0, -2, 1) + ---- DATA(1, 2, -2) + 7000 + + - 4/245 x y DATA(0, 2, -1) - 4/245 x y DATA(2, 0, 0) + + - 4/245 x y DATA(-2, 0, 0) + 4/245 x y DATA(0, 0, -1) + + 167 167 + + ---- DATA(-1, -2, -1) - ---- DATA(-1, 2, 1) - 4/245 x y DATA(-2, 0, -2) + 7000 7000 + + 47 + + 2/245 x y DATA(1, 0, -2) - ---- DATA(-2, -2, -1) + 5250 + + 137 + + 4/245 x y DATA(0, 0, 0) - ---- DATA(2, 2, -2) + 2/245 x y DATA(1, 0, 0) + 5250 + + 167 + + 2/245 x y DATA(-1, 0, -2) + ---- DATA(2, 1, 1) + 7000 + + + 2/245 x y DATA(1, 0, -1) + 2/245 x y DATA(-1, 0, 1) + + 167 + + 2/245 x y DATA(1, 0, 1) + ---- DATA(1, 2, 1) + 2/245 x y DATA(0, -1, -2) + 7000 + + + 2/245 x y DATA(0, -1, 1) + 2/245 x y DATA(0, 1, -1) + + + 2/245 x y DATA(0, -1, -1) - 4/245 x y DATA(0, -2, -2) + + - 4/245 x y DATA(2, 0, -1) + 4/245 x y DATA(0, 0, 1) + + 229 + + ----- DATA(-1, -1, 2) - 4/245 x y DATA(2, 0, 1) + 10500 + + - 4/245 x y DATA(-2, 0, 1) + 2/245 x y DATA(1, 0, 2) + + 47 187 + + 2/245 x y DATA(-1, 0, -1) - ---- DATA(2, 2, 1) - ---- DATA(-2, 1, 0) + 5250 7000 + + 137 167 229 + - ---- DATA(-2, -2, 2) - ---- DATA(1, -2, -1) - ----- DATA(1, -1, 2) + 5250 7000 10500 + + 167 47 + - 1/175 x z DATA(0, 1, 2) + ---- DATA(-2, -1, -1) + ---- DATA(2, -2, -1) + 7000 5250 + + 107 229 229 + - ---- DATA(2, -1, 2) + ----- DATA(1, 1, 2) - ----- DATA(-1, 1, 2) + 7000 10500 10500 + + 107 107 107 + + ---- DATA(-1, -2, 2) - ---- DATA(1, -2, 2) - ---- DATA(-1, 2, 2) + 7000 7000 7000 + + 107 107 167 + + ---- DATA(2, 1, 2) + ---- DATA(1, 2, 2) - ---- DATA(-2, 1, -1) + 7000 7000 7000 + + + 1/175 y z DATA(1, 2, 2) - 2/175 x z DATA(0, -2, -2) + + + 1/175 x z DATA(0, -2, 1) + 1/175 x z DATA(0, 2, -1) + + - 4/245 x y DATA(2, 0, -2) + 4/245 x y DATA(0, 0, -2) + + 289 289 137 + - ----- DATA(1, -1, 0) - ----- DATA(-1, 1, 0) + ---- DATA(-1, -1, 1) + 10500 10500 5250 + + 137 137 137 + - ---- DATA(1, -1, 1) - ---- DATA(-1, 1, 1) - ---- DATA(-1, 1, -1) + 5250 5250 5250 + + 137 289 + + ---- DATA(1, 1, -1) + ----- DATA(-1, -1, 0) + 2/245 x y DATA(-1, 0, 0) + 5250 10500 + + 137 137 + + ---- DATA(-1, -1, -1) - ---- DATA(1, -1, -1) + 4/245 x y DATA(0, 0, 2) + 5250 5250 + + 137 47 137 + + ---- DATA(2, -2, 2) + ---- DATA(-2, 2, -1) - ---- DATA(2, 2, 2) + 5250 5250 5250 + + 17 187 + + 1/350 y z DATA(1, 1, -2) - ---- DATA(-2, -2, 0) + ---- DATA(-1, -2, 0) + 5250 7000 + + + 1/175 y z DATA(-1, 2, -2) + 1/175 y z DATA(2, 2, 1) + + - 1/350 y z DATA(2, 1, 1) + 1/350 y z DATA(-1, -1, 2) + + + 1/350 y z DATA(1, 2, 1) - 2/175 y z DATA(2, 2, -2) + + - 1/350 y z DATA(2, -1, 1) - 1/350 y z DATA(-1, 2, 1) + + + 1/175 y z DATA(-2, -2, -1) - 1/175 y z DATA(-1, -2, 2) + + + 1/175 y z DATA(1, -2, 2) - 1/175 y z DATA(2, -1, 2) + + - 1/350 y z DATA(1, 1, 2) + 1/350 y z DATA(-1, 1, 2) + + - 1/350 y z DATA(1, -1, 2) - 1/175 y z DATA(2, -2, -1) + + - 1/350 y z DATA(-2, -1, -1) - 1/175 x z DATA(0, -1, -2) + + - 2/175 y z DATA(-2, -2, 2) - 1/350 y z DATA(1, -2, -1) + + - 1/350 y z DATA(-2, 1, -1) - 1/175 y z DATA(2, 1, 2) + + - 1/175 y z DATA(-1, 2, 2) + 1/350 x z DATA(0, -1, 1) + + + 2/175 y z DATA(2, -2, 2) + 1/175 y z DATA(-2, 2, -1) + + 107 + + ---- DATA(-2, -1, 2) + 2/175 y z DATA(2, 2, 2) + 7000 + + + 1/350 x z DATA(0, 1, -1) - 1/350 x z DATA(0, -1, -1) + + + 1/700 y z DATA(-1, -1, 1) + 2/175 y z DATA(-2, -2, -2) + + - 2/175 y z DATA(-2, 2, 2) + 1/175 y z DATA(-2, 1, 2) + + + 1/175 y z DATA(-2, -1, 2) - 1/175 y z DATA(-2, -1, -2) + + + 1/350 y z DATA(1, -1, -2) - 2/175 y z DATA(2, -2, -2) + + - 1/175 y z DATA(1, -2, -2) + 1/175 y z DATA(-1, -2, -2) + + - 1/350 y z DATA(-1, -1, -2) + 1/175 y z DATA(2, -1, -2) + + 17 + + ---- DATA(-2, 2, 0) + 2/175 y z DATA(-2, 2, -2) + 5250 + + + 1/350 y z DATA(-1, -2, -1) + 2/175 x z DATA(0, 2, -2) + + - 1/175 y z DATA(1, 2, -2) - 1/175 x z DATA(0, 2, 1) + + - 1/175 x z DATA(0, -2, -1) - 1/175 y z DATA(-2, 1, -2) + + + 2/175 x z DATA(0, -2, 2) - 1/700 y z DATA(1, -1, 1) + + - 1/175 y z DATA(-2, 2, 1) + 1/350 y z DATA(2, -1, -1) + + + 1/175 y z DATA(2, -2, 1) - 1/175 y z DATA(-2, -2, 1) + + 107 + - ---- DATA(-2, 1, 2) + 1/350 y z DATA(-2, 1, 1) + 7000 + + - 1/350 y z DATA(-1, 1, -2) + 1/175 y z DATA(2, 1, -2) + + + 1/350 y z DATA(-2, -1, 1) - 1/350 y z DATA(-1, -2, 1) + + + 1/350 y z DATA(2, 1, -1) + 1/350 y z DATA(-1, 2, -1) + + - 1/700 y z DATA(1, 1, 1) + 2/245 x y DATA(0, -1, 2) + + + 2/245 x y DATA(0, 1, 0) + 2/245 x y DATA(0, 1, 1) + + + 2/245 x y DATA(0, 1, -2) - 1/350 y z DATA(1, 2, -1) + + - 1/175 y z DATA(2, 2, -1) - 2/175 x z DATA(0, 2, 2) + + + 1/175 x z DATA(0, 1, -2) + 1/175 x z DATA(0, -1, 2) + + - 1/350 x z DATA(0, 1, 1) + 1/350 y z DATA(1, -2, 1) + + - 2/245 x y DATA(2, -1, 1) - 2/245 x y DATA(-1, 2, 1) + + + 4/245 x y DATA(-2, -2, -1) - 2/245 x y DATA(-1, -2, 2) + + - 2/245 x y DATA(1, -2, 2) + 1/245 x y DATA(1, 1, -2) + + - 2/245 x y DATA(-1, 2, -2) + 4/245 x y DATA(2, 2, 1) + + - 2/245 x y DATA(2, 1, 1) + 1/245 x y DATA(-1, -1, 2) + + - 2/245 x y DATA(1, 2, 1) + 4/245 x y DATA(2, 2, -2) + + + 4/245 x y DATA(-2, 2, 1) - 2/245 x y DATA(-1, -2, -1) + + + 4/245 x y DATA(-2, 2, -2) - 2/245 x y DATA(-2, 1, -2) + + - 2/245 x y DATA(1, 2, -2) - 2/245 x y DATA(2, 1, -1) + + + 4/245 x y DATA(2, 2, -1) - 2/245 x y DATA(1, 2, -1) + + 137 + - 2/245 x y DATA(-1, -2, 1) - ---- DATA(-2, -2, -2) + 5250 + + - 2/245 x y DATA(-2, -1, 1) - 2/245 x y DATA(2, 1, -2) + + 137 + + 1/245 x y DATA(-1, 1, -2) + ---- DATA(-2, 2, 2) + 5250 + + - 2/245 x y DATA(-2, 1, 1) + 1/245 x y DATA(1, 1, 1) + + 107 107 + - 2/245 x y DATA(-1, 2, -1) - ---- DATA(1, -2, -2) + ---- DATA(-1, -2, -2) + 7000 7000 + + 107 + + ---- DATA(-2, -1, -2) + 4/245 x y DATA(2, -2, 1) + 7000 + + 137 229 + - 2/245 x y DATA(2, -1, -1) + ---- DATA(2, -2, -2) - ----- DATA(1, -1, -2) + 5250 10500 + + 229 + + ----- DATA(-1, -1, -2) + 4/245 x y DATA(-2, -2, 1) + 10500 + + 107 + - 2/245 x y DATA(1, -2, 1) - ---- DATA(2, -1, -2) + 7000 + +> coeffs_as_lc_of_data(%, posn_list_3d_size5); +bytes used=2048208620, alloc=14677376, time=312.46 +bytes 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used=2068497544, alloc=14677376, time=314.26 +bytes used=2069497672, alloc=14677376, time=314.36 +bytes used=2070497872, alloc=14677376, time=314.46 +bytes used=2071498476, alloc=14677376, time=314.55 +bytes used=2072511432, alloc=14677376, time=314.62 +bytes used=2073516044, alloc=14677376, time=314.70 + 2 2 +[COEFF(-2, -2, -2) = 1/175 z + 4/245 x y + 2/175 y z + 2/175 x z + 1/100 y + + 2 137 + - 2/175 y + 1/100 x - ---- - 1/125 z - 2/175 x, COEFF(-1, -2, -2) = + 5250 + + 107 2 2 2 + 1/175 x + ---- - 1/50 x + 1/350 z + 1/200 y - 1/175 y - 2/245 x y + 7000 + + - 1/250 z + 1/175 y z - 1/175 x z, + + COEFF(0, -2, -2) = - 2/175 x z + 2/175 x - 4/245 x y, COEFF(1, -2, -2) = + + 2 2 107 2 + 1/175 y - 1/350 z + 1/50 x - 1/175 y z - ---- - 1/200 y + 1/250 z + 7000 + + 137 + + 1/175 x - 1/175 x z - 2/245 x y, COEFF(2, -2, -2) = ---- - 2/175 y z + 5250 + + 2 2 + + 1/125 z - 1/175 z + 2/175 y + 4/245 x y - 2/175 x - 1/100 x + + 2 2 107 + + 2/175 x z - 1/100 y , COEFF(-2, -1, -2) = - 1/175 x + 1/200 x + ---- + 7000 + + 2 2 + - 1/250 z + 1/175 x z - 1/50 y - 1/175 y z - 2/245 x y + 1/350 z + + 229 + + 1/175 y, COEFF(-1, -1, -2) = - 1/350 x z + 1/350 y - 1/350 y z + ----- + 10500 + + 2 2 2 + + 1/245 x y - 1/500 z + 1/350 x - 1/100 x + 1/700 z - 1/100 y , + + COEFF(0, -1, -2) = 1/175 x + 2/245 x y - 1/175 x z, COEFF(1, -1, -2) = + + 2 2 + 1/100 y + 1/245 x y - 1/700 z - 1/350 y + 1/350 y z - 1/350 x z + + 2 229 + + 1/100 x + 1/350 x - ----- + 1/500 z, COEFF(2, -1, -2) = - 2/245 x y + 10500 + + 2 2 2 107 + - 1/200 x + 1/175 x z + 1/50 y - 1/175 y - 1/350 z - 1/175 x - ---- + 7000 + + + 1/250 z + 1/175 y z, + + COEFF(-2, 0, -2) = - 2/175 y z + 2/175 y - 4/245 x y, + + COEFF(-1, 0, -2) = 2/245 x y + 1/175 y - 1/175 y z, + + COEFF(0, 0, -2) = 4/245 x y, + + COEFF(1, 0, -2) = 2/245 x y - 1/175 y + 1/175 y z, + + COEFF(2, 0, -2) = 2/175 y z - 4/245 x y - 2/175 y, COEFF(-2, 1, -2) = + + 2 2 2 107 + 1/50 y - 1/350 z + 1/250 z - 2/245 x y - 1/175 y z - 1/200 x - ---- + 7000 + + 2 + - 1/175 x z + 1/175 x + 1/175 y, COEFF(-1, 1, -2) = 1/350 x z + 1/100 y + + 2 2 229 + + 1/350 y - 1/700 z + 1/500 z + 1/100 x - ----- + 1/245 x y - 1/350 x + 10500 + + - 1/350 y z, COEFF(0, 1, -2) = 1/175 x z + 2/245 x y - 1/175 x, + + 229 + COEFF(1, 1, -2) = ----- - 1/350 y - 1/350 x + 1/350 x z + 1/245 x y + 10500 + + 2 2 2 + - 1/500 z + 1/350 y z + 1/700 z - 1/100 x - 1/100 y , COEFF(2, 1, -2) = + + 2 2 107 + 1/175 y z + 1/350 z + 1/175 x - 1/250 z + 1/200 x + ---- - 1/175 x z + 7000 + + 2 137 + - 2/245 x y - 1/175 y - 1/50 y , COEFF(-2, 2, -2) = 2/175 x + ---- + 5250 + + 2 2 + - 2/175 y - 1/175 z - 1/100 x + 4/245 x y + 2/175 y z + 1/125 z + + 2 2 2 + - 2/175 x z - 1/100 y , COEFF(-1, 2, -2) = 1/50 x - 2/245 x y - 1/200 y + + 2 107 + - 1/175 x - 1/350 z + 1/250 z + 1/175 x z - ---- + 1/175 y z - 1/175 y, + 7000 + + COEFF(0, 2, -2) = - 2/175 x + 2/175 x z - 4/245 x y, COEFF(1, 2, -2) = + + 107 2 2 2 + - 1/250 z - 1/175 x + ---- + 1/350 z - 2/245 x y - 1/50 x + 1/200 y + 7000 + + - 1/175 y z + 1/175 y + 1/175 x z, COEFF(2, 2, -2) = - 1/125 z + 4/245 x y + + 2 2 2 + + 1/100 x + 2/175 y + 1/175 z - 2/175 y z - 2/175 x z + 1/100 y + + 137 2 47 + + 2/175 x - ----, COEFF(-2, -2, -1) = 1/100 x - 2/175 y - 1/250 z - ---- + 5250 5250 + + 2 2 + + 1/100 y + 4/245 x y - 1/350 z + 1/175 y z + 1/175 x z - 2/175 x, + + 2 2 167 + COEFF(-1, -2, -1) = - 1/700 z - 1/500 z + 1/200 y + ---- + 1/350 y z + 7000 + + 2 + - 2/245 x y - 1/50 x + 1/175 x - 1/350 x z - 1/175 y, + + COEFF(0, -2, -1) = - 1/175 x z + 2/175 x - 4/245 x y, COEFF(1, -2, -1) = + + 167 2 2 2 + - 1/350 x z - ---- + 1/700 z - 1/200 y + 1/50 x - 1/350 y z + 1/500 z + 7000 + + 2 + - 2/245 x y + 1/175 y + 1/175 x, COEFF(2, -2, -1) = 1/350 z + 1/250 z + + 2 47 2 + - 1/100 x + 2/175 y - 2/175 x + 4/245 x y + ---- - 1/100 y - 1/175 y z + 5250 + + 167 2 + + 1/175 x z, COEFF(-2, -1, -1) = - 2/245 x y + ---- + 1/350 x z - 1/700 z + 7000 + + 2 2 + - 1/500 z - 1/175 x - 1/50 y + 1/200 x - 1/350 y z + 1/175 y, + + 2 2 + COEFF(-1, -1, -1) = - 1/100 y + 1/350 y - 1/1000 z - 1/1400 z - 1/700 x z + + 2 137 + + 1/245 x y + 1/350 x - 1/700 y z - 1/100 x + ----, + 5250 + + COEFF(0, -1, -1) = 1/175 x + 2/245 x y - 1/350 x z, COEFF(1, -1, -1) = + + 2 137 + 1/245 x y - 1/700 x z + 1/1400 z - ---- + 1/350 x - 1/350 y + 1/700 y z + 5250 + + 2 2 2 + + 1/100 y + 1/100 x + 1/1000 z, COEFF(2, -1, -1) = 1/50 y - 1/175 x + + 167 2 2 + + 1/500 z - ---- + 1/350 x z + 1/350 y z - 1/175 y - 1/200 x + 1/700 z + 7000 + + - 2/245 x y, COEFF(-2, 0, -1) = - 1/175 y z - 4/245 x y + 2/175 y, + + COEFF(-1, 0, -1) = 2/245 x y - 1/350 y z + 1/175 y, + + COEFF(0, 0, -1) = 4/245 x y, + + COEFF(1, 0, -1) = - 1/175 y + 1/350 y z + 2/245 x y, + + COEFF(2, 0, -1) = - 4/245 x y - 2/175 y + 1/175 y z, COEFF(-2, 1, -1) = + + 167 2 2 + - 2/245 x y - ---- + 1/700 z + 1/50 y - 1/350 x z - 1/350 y z + 1/175 x + 7000 + + 2 2 + + 1/500 z + 1/175 y - 1/200 x , COEFF(-1, 1, -1) = 1/1000 z + 1/100 x + + 2 137 2 + + 1/700 x z + 1/350 y + 1/100 y - 1/350 x - ---- + 1/1400 z + 1/245 x y + 5250 + + - 1/700 y z, COEFF(0, 1, -1) = - 1/175 x + 2/245 x y + 1/350 x z, + + 2 2 + COEFF(1, 1, -1) = - 1/350 y - 1/1000 z - 1/100 y + 1/700 x z - 1/100 x + + 2 137 + - 1/1400 z + 1/245 x y + 1/700 y z - 1/350 x + ----, COEFF(2, 1, -1) = + 5250 + + 2 2 167 + - 1/350 x z + 1/175 x - 1/700 z - 1/50 y + 1/350 y z + ---- - 1/175 y + 7000 + + 2 2 + - 1/500 z + 1/200 x - 2/245 x y, COEFF(-2, 2, -1) = 1/250 z - 1/100 x + + 2 47 + - 1/175 x z + 2/175 x + 1/350 z - 2/175 y + ---- + 4/245 x y + 1/175 y z + 5250 + + 2 2 + - 1/100 y , COEFF(-1, 2, -1) = - 1/200 y + 1/500 z + 1/350 x z + + 2 2 167 + + 1/350 y z - 1/175 y + 1/700 z - 1/175 x - 2/245 x y + 1/50 x - ----, + 7000 + + COEFF(0, 2, -1) = 1/175 x z - 2/175 x - 4/245 x y, COEFF(1, 2, -1) = + + 2 167 + - 1/500 z - 1/350 y z - 1/700 z + 1/175 y - 1/175 x - 2/245 x y + ---- + 7000 + + 2 2 2 + + 1/200 y - 1/50 x + 1/350 x z, COEFF(2, 2, -1) = 1/100 x - 1/250 z + + 47 2 2 + - 1/175 y z + 2/175 y - ---- + 4/245 x y + 1/100 y - 1/175 x z - 1/350 z + 5250 + + + 2/175 x, COEFF(-2, -2, 0) = + + 2 2 17 2 + 1/100 x - 1/175 z + 4/245 x y - 2/175 x - ---- + 1/100 y - 2/175 y, + 5250 + + COEFF(-1, -2, 0) = + + 2 187 2 2 + - 1/175 y + 1/200 y + 1/175 x + ---- - 1/50 x - 2/245 x y - 1/350 z , + 7000 + + COEFF(0, -2, 0) = 2/175 x - 4/245 x y, COEFF(1, -2, 0) = + + 2 187 2 2 + - 1/200 y - 2/245 x y - ---- + 1/50 x + 1/175 x + 1/350 z + 1/175 y, + 7000 + + COEFF(2, -2, 0) = + + 2 17 2 2 + - 1/100 x + ---- - 2/175 x - 1/100 y + 2/175 y + 1/175 z + 4/245 x y, + 5250 + + COEFF(-2, -1, 0) = + + 2 2 187 2 + - 2/245 x y - 1/350 z - 1/175 x + 1/175 y + 1/200 x + ---- - 1/50 y , + 7000 + + COEFF(-1, -1, 0) = + + 2 2 2 289 + 1/350 y + 1/245 x y - 1/100 x - 1/100 y - 1/700 z + ----- + 1/350 x, + 10500 + + COEFF(0, -1, 0) = 2/245 x y + 1/175 x, COEFF(1, -1, 0) = + + 2 2 2 289 + 1/350 x + 1/100 x + 1/100 y + 1/700 z - ----- - 1/350 y + 1/245 x y, + 10500 + + COEFF(2, -1, 0) = + + 2 187 2 2 + - 2/245 x y - 1/175 y + 1/50 y - ---- - 1/175 x - 1/200 x + 1/350 z , + 7000 + + COEFF(-2, 0, 0) = - 4/245 x y + 2/175 y, + + COEFF(-1, 0, 0) = 2/245 x y + 1/175 y, COEFF(0, 0, 0) = 4/245 x y, + + COEFF(1, 0, 0) = - 1/175 y + 2/245 x y, + + COEFF(2, 0, 0) = - 4/245 x y - 2/175 y, COEFF(-2, 1, 0) = + + 2 2 187 2 + - 1/200 x + 1/50 y - 2/245 x y - ---- + 1/175 y + 1/350 z + 1/175 x, + 7000 + + COEFF(-1, 1, 0) = + + 2 2 289 2 + 1/100 x + 1/700 z - ----- + 1/100 y + 1/350 y - 1/350 x + 1/245 x y, + 10500 + + COEFF(0, 1, 0) = 2/245 x y - 1/175 x, COEFF(1, 1, 0) = + + 2 2 289 2 + - 1/100 y - 1/100 x - 1/350 y + ----- + 1/245 x y - 1/700 z - 1/350 x, + 10500 + + COEFF(2, 1, 0) = + + 2 2 2 187 + - 1/350 z + 1/175 x - 1/50 y + 1/200 x - 2/245 x y + ---- - 1/175 y, + 7000 + + COEFF(-2, 2, 0) = + + 2 2 17 2 + - 1/100 x + 1/175 z + ---- - 1/100 y + 4/245 x y + 2/175 x - 2/175 y, + 5250 + + COEFF(-1, 2, 0) = + + 2 2 187 2 + - 1/175 y - 1/175 x - 2/245 x y + 1/50 x + 1/350 z - ---- - 1/200 y , + 7000 + + COEFF(0, 2, 0) = - 4/245 x y - 2/175 x, COEFF(1, 2, 0) = + + 2 187 2 2 + 1/200 y + 1/175 y + ---- - 1/175 x - 1/350 z - 1/50 x - 2/245 x y, + 7000 + + COEFF(2, 2, 0) = + + 2 2 17 2 + 1/100 y + 4/245 x y - 1/175 z - ---- + 2/175 y + 1/100 x + 2/175 x, + 5250 + + 2 2 + COEFF(-2, -2, 1) = 1/100 x - 1/175 x z - 1/175 y z + 1/250 z + 1/100 y + + 2 47 167 + + 4/245 x y - 1/350 z - 2/175 x - 2/175 y - ----, COEFF(-1, -2, 1) = ---- + 5250 7000 + + 2 2 2 + + 1/175 x + 1/200 y - 1/175 y + 1/500 z - 1/350 y z - 1/50 x - 1/700 z + + - 2/245 x y + 1/350 x z, + + COEFF(0, -2, 1) = - 4/245 x y + 2/175 x + 1/175 x z, COEFF(1, -2, 1) = + + 167 2 2 + - ---- + 1/700 z + 1/175 x + 1/350 y z - 1/500 z + 1/50 x - 2/245 x y + 7000 + + 2 + + 1/350 x z + 1/175 y - 1/200 y , COEFF(2, -2, 1) = - 1/250 z - 1/175 x z + + 47 2 2 2 + + 2/175 y + ---- + 1/175 y z - 1/100 x - 1/100 y - 2/175 x + 1/350 z + 5250 + + 2 + + 4/245 x y, COEFF(-2, -1, 1) = 1/350 y z + 1/175 y - 1/175 x + 1/200 x + + 2 2 167 + + 1/500 z - 1/350 x z - 1/50 y - 2/245 x y - 1/700 z + ----, + 7000 + + 2 2 2 + COEFF(-1, -1, 1) = 1/700 y z - 1/100 x - 1/1400 z - 1/100 y + 1/1000 z + + 137 + + 1/350 y + 1/700 x z + 1/245 x y + ---- + 1/350 x, + 5250 + + COEFF(0, -1, 1) = 1/175 x + 2/245 x y + 1/350 x z, COEFF(1, -1, 1) = + + 2 137 2 + 1/100 y - 1/1000 z + 1/700 x z - 1/700 y z - ---- + 1/245 x y + 1/100 x + 5250 + + 2 2 + + 1/350 x + 1/1400 z - 1/350 y, COEFF(2, -1, 1) = - 1/350 x z + 1/700 z + + 2 167 + + 1/50 y - 1/175 x - 1/350 y z - 1/175 y - 2/245 x y - ---- - 1/500 z + 7000 + + 2 + - 1/200 x , COEFF(-2, 0, 1) = 1/175 y z + 2/175 y - 4/245 x y, + + COEFF(-1, 0, 1) = 2/245 x y + 1/175 y + 1/350 y z, + + COEFF(0, 0, 1) = 4/245 x y, + + COEFF(1, 0, 1) = 2/245 x y - 1/175 y - 1/350 y z, + + COEFF(2, 0, 1) = - 2/175 y - 4/245 x y - 1/175 y z, COEFF(-2, 1, 1) = + + 2 2 167 2 + 1/700 z - 1/200 x - ---- + 1/350 x z + 1/50 y - 1/500 z + 1/175 x + 7000 + + 2 + + 1/175 y - 2/245 x y + 1/350 y z, COEFF(-1, 1, 1) = 1/245 x y + 1/1400 z + + 2 2 137 + + 1/700 y z - 1/1000 z + 1/350 y + 1/100 x + 1/100 y - 1/700 x z - ---- + 5250 + + - 1/350 x, COEFF(0, 1, 1) = - 1/350 x z + 2/245 x y - 1/175 x, + + 2 + COEFF(1, 1, 1) = - 1/700 x z - 1/350 x - 1/350 y + 1/1000 z - 1/100 y + + 2 2 137 + - 1/1400 z - 1/700 y z - 1/100 x + ---- + 1/245 x y, COEFF(2, 1, 1) = + 5250 + + 2 167 2 2 + - 1/700 z + ---- - 1/350 y z + 1/200 x + 1/175 x + 1/500 z - 1/50 y + 7000 + + + 1/350 x z - 2/245 x y - 1/175 y, COEFF(-2, 2, 1) = - 1/175 y z + + 2 47 2 + - 1/100 x + ---- + 1/175 x z + 1/350 z - 2/175 y + 4/245 x y + 2/175 x + 5250 + + 2 2 + - 1/250 z - 1/100 y , COEFF(-1, 2, 1) = - 1/200 y - 1/175 y - 1/500 z + + 2 167 2 + + 1/50 x - 1/350 y z - ---- - 1/175 x - 1/350 x z - 2/245 x y + 1/700 z , + 7000 + + COEFF(0, 2, 1) = - 1/175 x z - 4/245 x y - 2/175 x, COEFF(1, 2, 1) = + + 2 167 2 + 1/175 y - 1/50 x - 1/350 x z + ---- + 1/500 z + 1/350 y z + 1/200 y + 7000 + + 2 2 + - 2/245 x y - 1/175 x - 1/700 z , COEFF(2, 2, 1) = 1/175 y z + 1/100 y + + 2 47 + - 1/350 z - ---- + 2/175 x + 1/175 x z + 1/250 z + 2/175 y + 4/245 x y + 5250 + + 2 2 + + 1/100 x , COEFF(-2, -2, 2) = - 2/175 y z + 1/100 y - 2/175 x - 2/175 y + + 137 2 2 + - ---- + 1/125 z + 4/245 x y - 2/175 x z + 1/175 z + 1/100 x , + 5250 + + 2 2 + COEFF(-1, -2, 2) = 1/175 x z - 1/175 y z + 1/350 z - 1/50 x - 1/175 y + + 2 107 + + 1/175 x - 2/245 x y + 1/200 y + ---- + 1/250 z, + 7000 + + COEFF(0, -2, 2) = - 4/245 x y + 2/175 x + 2/175 x z, COEFF(1, -2, 2) = + + 2 2 2 + 1/175 x + 1/175 y z + 1/175 y + 1/50 x - 1/200 y - 1/350 z + 1/175 x z + + 107 2 2 + - ---- - 2/245 x y - 1/250 z, COEFF(2, -2, 2) = - 1/175 z - 1/100 y + 7000 + + 2 + - 1/100 x - 2/175 x z - 1/125 z + 2/175 y z + 2/175 y - 2/175 x + + 137 107 2 + + 4/245 x y + ----, COEFF(-2, -1, 2) = ---- - 2/245 x y + 1/350 z + 5250 7000 + + 2 2 + + 1/250 z - 1/175 x + 1/175 y z - 1/50 y + 1/175 y + 1/200 x - 1/175 x z + + , COEFF(-1, -1, 2) = 1/350 x z + 1/350 y z + 1/500 z + 1/350 x + 1/350 y + + 2 2 2 229 + - 1/100 x + 1/700 z - 1/100 y + ----- + 1/245 x y, + 10500 + + COEFF(0, -1, 2) = 1/175 x + 2/245 x y + 1/175 x z, COEFF(1, -1, 2) = + + 2 2 229 + 1/350 x + 1/100 x + 1/100 y + 1/245 x y - ----- - 1/500 z - 1/350 y z + 10500 + + 2 107 + - 1/700 z - 1/350 y + 1/350 x z, COEFF(2, -1, 2) = - 1/250 z - ---- + 7000 + + 2 2 + - 1/175 y - 1/175 y z + 1/50 y - 1/200 x - 2/245 x y - 1/175 x + + 2 + - 1/350 z - 1/175 x z, COEFF(-2, 0, 2) = 2/175 y - 4/245 x y + 2/175 y z, + + COEFF(-1, 0, 2) = 1/175 y + 2/245 x y + 1/175 y z, + + COEFF(0, 0, 2) = 4/245 x y, + + COEFF(1, 0, 2) = 2/245 x y - 1/175 y z - 1/175 y, + + COEFF(2, 0, 2) = - 2/175 y z - 2/175 y - 4/245 x y, COEFF(-2, 1, 2) = + + 2 2 2 + - 1/350 z + 1/175 x z - 2/245 x y + 1/175 y - 1/250 z + 1/50 y - 1/200 x + + 107 2 + + 1/175 x + 1/175 y z - ----, COEFF(-1, 1, 2) = 1/245 x y + 1/100 x + 7000 + + 229 2 2 + - 1/500 z - ----- + 1/350 y + 1/100 y - 1/700 z + 1/350 y z - 1/350 x + 10500 + + - 1/350 x z, COEFF(0, 1, 2) = 2/245 x y - 1/175 x - 1/175 x z, + + 2 229 2 + COEFF(1, 1, 2) = - 1/100 y - 1/350 y + ----- - 1/100 x - 1/350 x z + 10500 + + 2 + - 1/350 x - 1/350 y z + 1/700 z + 1/245 x y + 1/500 z, COEFF(2, 1, 2) = + + 2 2 107 + 1/175 x - 1/50 y + 1/250 z - 2/245 x y + 1/350 z + ---- - 1/175 y z + 7000 + + 2 + + 1/200 x + 1/175 x z - 1/175 y, COEFF(-2, 2, 2) = - 2/175 y - 1/125 z + + 2 2 2 + - 1/100 x + 2/175 x z - 1/175 z + 4/245 x y - 1/100 y - 2/175 y z + + 137 2 2 107 2 + + ---- + 2/175 x, COEFF(-1, 2, 2) = - 1/350 z - 1/200 y - ---- + 1/50 x + 5250 7000 + + - 1/250 z - 1/175 x - 1/175 x z - 1/175 y z - 1/175 y - 2/245 x y, + + 107 + COEFF(0, 2, 2) = - 2/175 x - 4/245 x y - 2/175 x z, COEFF(1, 2, 2) = ---- + 7000 + + 2 2 + - 1/50 x + 1/200 y - 1/175 x z + 1/250 z - 2/245 x y + 1/175 y - 1/175 x + + 2 2 137 + + 1/175 y z + 1/350 z , COEFF(2, 2, 2) = 1/100 y + 2/175 x - ---- + 5250 + + 2 2 + + 4/245 x y + 2/175 y + 1/100 x + 1/125 z + 2/175 x z + 1/175 z + + + 2/175 y z] + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxy.compute.c"); +bytes used=2074516392, alloc=14677376, time=314.78 +bytes used=2075516808, alloc=14677376, time=314.87 +bytes used=2076517336, alloc=14677376, time=314.93 +bytes used=2077517496, alloc=14677376, time=315.02 +bytes used=2078518140, alloc=14677376, time=315.65 +bytes used=2079518320, alloc=14677376, time=316.33 +bytes used=2080518860, alloc=14677376, time=317.00 +bytes used=2081519528, alloc=14677376, time=317.67 +bytes used=2082519692, alloc=14677376, time=318.33 +bytes used=2083519908, alloc=14677376, time=318.78 +bytes used=2084520108, alloc=14677376, time=318.87 +bytes used=2085520376, alloc=14677376, time=318.96 +bytes used=2086543844, alloc=14677376, time=319.04 +bytes used=2087574448, alloc=14677376, time=319.12 +bytes used=2088579428, alloc=14677376, time=319.21 +bytes used=2089579900, alloc=14677376, time=319.30 +bytes used=2090580168, alloc=14677376, time=320.23 +bytes used=2091580460, alloc=14677376, time=321.07 +bytes used=2092580772, alloc=14677376, time=321.40 +bytes used=2093580940, alloc=14677376, time=321.48 +bytes used=2094581108, alloc=14677376, time=321.54 +bytes used=2095581448, alloc=14677376, time=321.61 +bytes used=2096581676, alloc=14677376, time=321.68 +bytes used=2097582320, alloc=14677376, time=321.75 +bytes used=2098583068, alloc=14677376, time=321.82 +bytes used=2099583264, alloc=14677376, time=321.89 +bytes used=2100583472, alloc=14677376, time=321.97 +bytes used=2101583780, alloc=14677376, time=322.09 +bytes used=2102583932, alloc=14677376, time=322.21 +bytes used=2103584112, alloc=14677376, time=322.32 +bytes used=2104584280, alloc=14677376, time=322.44 +bytes used=2105584504, alloc=14677376, time=322.58 +bytes used=2106586816, alloc=14677376, time=322.70 +bytes used=2107587152, alloc=14677376, time=322.80 +bytes used=2108587304, alloc=14677376, time=323.48 +bytes used=2109587572, alloc=14677376, time=324.95 +bytes used=2110598988, alloc=14677376, time=325.47 +bytes used=2111599168, alloc=14677376, time=325.56 +bytes used=2112599372, alloc=14677376, time=325.63 +bytes used=2113599632, alloc=14677376, time=325.70 +bytes used=2114599952, alloc=14677376, time=325.78 +bytes used=2115600208, alloc=14677376, time=325.85 +bytes used=2116600416, alloc=14677376, time=325.92 +bytes used=2117600584, alloc=14677376, time=326.02 +bytes used=2118604176, alloc=14677376, time=326.18 +bytes used=2119616388, alloc=14677376, time=326.30 +bytes used=2120617124, alloc=14677376, time=326.42 +bytes used=2121617256, alloc=14677376, time=327.24 +bytes used=2122622952, alloc=14677376, time=328.49 +bytes used=2123623132, alloc=14677376, time=329.04 +bytes used=2124623436, alloc=14677376, time=329.34 +bytes used=2125623588, alloc=14677376, time=329.42 +bytes used=2126623748, alloc=14677376, time=329.51 +bytes used=2127623952, alloc=14677376, time=329.72 +bytes used=2128624188, alloc=14677376, time=331.30 +bytes used=2129624340, alloc=14677376, time=332.07 +bytes used=2130624700, alloc=14677376, time=332.36 +bytes used=2131624856, alloc=14677376, time=332.43 +bytes used=2132625020, alloc=14677376, time=332.60 +bytes used=2133625172, alloc=14677376, time=333.70 +bytes used=2134625464, alloc=14677376, time=334.94 +bytes used=2135626204, alloc=14677376, time=335.42 +bytes used=2136626416, alloc=14677376, time=335.53 +bytes used=2137626668, alloc=14677376, time=335.69 +> +# d^2/dxdz +> simplify( diff(interp_3d_cube_order4_smooth0,x,z) ); +bytes used=2138626836, alloc=14677376, time=335.83 +bytes used=2139627056, alloc=14677376, time=335.92 +bytes used=2140627992, alloc=14677376, time=336.00 +bytes used=2141628992, alloc=14677376, time=336.08 +bytes used=2142629232, alloc=14677376, time=336.16 +bytes used=2143629400, alloc=14677376, time=336.25 +bytes used=2144629560, alloc=14677376, time=336.33 +bytes used=2145630268, alloc=14677376, time=336.42 +bytes used=2146630556, alloc=14677376, time=336.50 + 107 229 +- ---- DATA(-2, -2, 1) + 1/700 y z DATA(1, -1, -1) + ----- DATA(1, -2, 1) + 7000 10500 + + 187 229 + - 1/700 y z DATA(-1, -1, -1) - ---- DATA(2, 0, -1) - ----- DATA(-1, -2, 1) + 7000 10500 + + - 1/700 y z DATA(1, 1, -1) + 2/175 x DATA(0, -1, -2) + + + 1/700 y z DATA(-1, 1, -1) + 1/700 y z DATA(-1, 1, 1) + + 167 107 + - ---- DATA(-2, -1, 1) + ---- DATA(2, -2, 1) + 1/350 x DATA(-1, -2, -1) + 7000 7000 + + 187 + - ---- DATA(-2, 0, 1) + 1/175 x DATA(-2, 1, 1) - 2/175 x DATA(0, -1, 2) + 7000 + + - 1/175 x DATA(0, 1, 1) + 2/175 x DATA(0, 2, -2) - 2/175 x DATA(0, 2, 2) + + + 2/175 x DATA(0, 1, -2) - 1/350 x DATA(1, 1, 1) - 1/175 x DATA(0, -2, 1) + + 187 + + 1/175 x DATA(0, 2, -1) - 2/175 x DATA(0, 1, 2) + ---- DATA(1, 0, 2) + 7000 + + - 1/175 x DATA(0, -1, 1) + 1/175 x DATA(0, 1, -1) + + + 1/175 x DATA(0, -1, -1) + 2/175 x DATA(0, -2, -2) + + + 1/350 x DATA(-1, 2, -1) - 1/175 x DATA(2, 1, -1) + + - 1/175 x DATA(2, 2, -1) + 1/350 x DATA(1, 2, -1) + + + 1/175 x DATA(0, -2, -1) - 2/175 x DATA(0, -2, 2) - 1/175 x DATA(0, 2, 1) + + 289 + - 1/175 x DATA(-1, -1, 2) - 1/350 x DATA(1, 2, 1) + ----- DATA(-1, 0, -1) + 10500 + + - 2/175 x DATA(2, 2, -2) + 1/175 x DATA(2, -1, 1) - 1/350 x DATA(-1, 2, 1) + + - 1/175 x DATA(-2, -2, -1) + 1/175 x DATA(1, 1, -2) + + + 1/175 x DATA(1, 2, -2) - 2/175 x DATA(-2, 2, -2) + + 167 289 + + 1/175 x DATA(-2, 2, 1) - ---- DATA(2, -1, -1) + ----- DATA(1, 0, 1) + 7000 10500 + + 137 + + ---- DATA(1, 1, 1) - 2/245 x z DATA(-2, -1, 1) + 5250 + + - 2/245 x z DATA(2, -1, -1) - 2/245 x z DATA(2, -2, 1) + + - 2/245 x z DATA(-2, -2, 1) + 1/245 x z DATA(1, -2, 1) + + + 1/245 x z DATA(-1, -2, 1) - 2/245 x z DATA(2, 2, -1) + + - 2/245 x z DATA(2, 1, -1) + 1/245 x z DATA(-1, 2, -1) + + + 1/245 x z DATA(1, 1, 1) - 2/245 x z DATA(-2, 1, 1) + + - 2/245 x z DATA(-1, 1, -2) + 4/245 x z DATA(2, 1, -2) + + - 2/245 x z DATA(2, 2, 1) - 2/245 x z DATA(-1, 2, -2) + + - 2/245 x z DATA(1, 1, -2) - 2/245 x z DATA(-2, 2, 1) + + + 4/245 x z DATA(-2, 2, -2) + 1/245 x z DATA(-1, -2, -1) + + - 2/245 x z DATA(1, 2, -2) 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DATA(2, 2, 1) + + 2 2 + - 1/700 y DATA(2, 1, 1) + 1/700 y DATA(-1, -1, 2) + + 2 + - 1/700 y DATA(-1, 2, 1) - 1/250 y DATA(-2, -1, -2) + + + 1/250 y DATA(1, -2, -2) - 1/250 y DATA(-1, -2, -2) + + 2 + + 1/500 y DATA(1, -1, -2) + 1/700 y DATA(1, 2, 1) + + 2 + - 1/175 y DATA(2, 2, -2) + 1/125 y DATA(2, -2, -2) + + - 1/500 y DATA(-1, -1, -2) + 1/250 y DATA(2, -1, -2) + + 107 137 + + ---- DATA(-1, 2, -2) - ---- DATA(-2, 2, -2) - 1/175 x y DATA(0, 1, 2) + 7000 5250 + + 107 167 17 + - ---- DATA(-2, 2, 1) + ---- DATA(2, -1, 1) + ---- DATA(2, 0, -2) + 7000 7000 5250 + + 187 107 + + 1/175 x y DATA(0, -2, 1) + ---- DATA(2, 0, 1) - ---- DATA(1, 2, -2) + 7000 7000 + + 229 229 + + 1/175 x y DATA(0, 2, -1) + ----- DATA(-1, -2, -1) - ----- DATA(-1, 2, 1) + 10500 10500 + + 107 137 167 + + ---- DATA(-2, -2, -1) + ---- DATA(2, 2, -2) + ---- DATA(2, 1, 1) + 7000 5250 7000 + + 229 + + ----- DATA(1, 2, 1) - 1/175 x y DATA(0, -1, -2) + 10500 + + + 1/350 x y DATA(0, -1, 1) + 1/350 x y DATA(0, 1, -1) + + - 1/350 x y DATA(0, -1, -1) - 2/175 x y DATA(0, -2, -2) + + - 4/245 x z DATA(-2, 0, 0) + 4/245 x z DATA(0, -1, 0) + + + 2/245 x z DATA(-1, 0, 0) + 4/245 x z DATA(0, 0, 0) + + + 4/245 x z DATA(0, 2, 0) + 2/245 x z DATA(-1, 1, 0) + + - 4/245 x z DATA(2, 2, 0) + 2/245 x z DATA(1, 2, 0) + + - 4/245 x z DATA(2, -1, 0) - 4/245 x z DATA(2, 1, 0) + + + 2/245 x z DATA(1, -1, 0) - 4/245 x z DATA(-2, 1, 0) + + 2 + - 1/100 x DATA(-1, 0, -1) - 4/245 x z DATA(0, 0, 2) + + + 2/245 x z DATA(0, 0, -1) + 2/245 x z DATA(-1, 2, 0) + + + 2/245 x z DATA(0, 0, 1) + 4/245 x z DATA(-2, 0, -2) + + - 2/245 x z DATA(-1, 0, -2) - 2/245 x z DATA(1, 0, -2) + + + 1/245 x z DATA(1, 0, -1) + 1/245 x z DATA(-1, 0, 1) + + - 2/245 x z DATA(2, 0, -1) - 2/245 x z DATA(-2, 0, 1) + + - 2/245 x z DATA(1, 0, 2) + 1/245 x z DATA(-1, 0, -1) + + 2 + + 4/245 x z DATA(-2, 0, 2) - 1/100 x DATA(1, 0, 1) + + 2 + - 1/200 x DATA(-2, 0, 1) + 1/245 x z DATA(1, 0, 1) + + 167 + - 4/245 x z DATA(2, -2, 0) - ---- DATA(-1, -1, 2) + 7000 + + 2 107 + + 1/175 z DATA(-2, 0, -1) - 1/50 z DATA(-2, 0, -1) + ---- DATA(2, 2, 1) + 7000 + + 137 + + ---- DATA(-2, -2, 2) - 1/350 y z DATA(-1, -1, 0) + 5250 + + - 2/175 y z DATA(-2, -2, 0) + 2/175 y z DATA(-2, 2, 0) + + - 1/175 y z DATA(-1, -2, 0) + 2/175 y z DATA(2, -2, 0) + + + 1/350 y z DATA(-1, 1, 0) + 1/175 y z DATA(1, -2, 0) + + - 1/175 y z DATA(-2, -1, 0) - 1/175 y z DATA(2, 1, 0) + + + 1/175 y z DATA(-1, 2, 0) - 1/350 y z DATA(1, 1, 0) + + + 1/175 y z DATA(-2, 1, 0) + 1/350 y z DATA(1, -1, 0) + + + 1/175 y z DATA(2, -1, 0) - 1/175 y z DATA(1, 2, 0) + + - 2/175 y z DATA(2, 2, 0) - 4/245 x z DATA(0, 0, -2) + + + 2/245 x z DATA(1, -2, 0) - 4/245 x z DATA(-2, -1, 0) + + + 2/245 x z DATA(1, 1, 0) - 4/245 x z DATA(2, 0, 0) + + + 2/245 x z DATA(-1, -2, 0) - 4/245 x z DATA(-2, 2, 0) + + + 4/245 x z DATA(0, -2, 0) + 2/245 x z DATA(1, 0, 0) + + + 4/245 x z DATA(0, 1, 0) + 2/245 x z DATA(-1, -1, 0) + + 229 + - 4/245 x z DATA(-2, -2, 0) - ----- DATA(1, -2, -1) + 10500 + + + 2/175 z DATA(2, 0, 2) + 2/175 z DATA(2, 0, -2) - 2/175 z DATA(2, -1, 0) + + - 1/175 z DATA(1, -2, 0) + 2/175 z DATA(-2, -1, 0) - 1/175 z DATA(1, 1, 0) + + + 1/175 z DATA(-1, 2, 0) - 2/175 z DATA(2, 1, 0) + 2/175 z DATA(-2, 0, 0) + + + 1/175 z DATA(-1, 0, 0) - 1/175 z DATA(1, -1, 0) - 1/175 z DATA(-1, 0, 2) + + - 1/175 z DATA(2, 0, 1) - 1/175 z DATA(-1, 0, -2) + 2/175 z DATA(-2, 1, 0) + + + 1/175 z DATA(-1, 1, 0) - 2/175 z DATA(2, 2, 0) - 1/175 z DATA(1, 2, 0) + + - 2/175 z DATA(-2, 0, -2) + 1/175 z DATA(1, 0, -2) + + 167 + - 1/350 z DATA(1, 0, -1) + ---- DATA(1, -1, 2) - 2/175 z DATA(2, -2, 0) + 7000 + + - 1/175 z DATA(2, 0, -1) + 1/175 z DATA(-2, 0, 1) + 1/175 z DATA(1, 0, 2) + + + 1/350 z DATA(-1, 0, -1) - 2/175 z DATA(-2, 0, 2) + + + 1/175 z DATA(-1, -1, 0) + 2/175 z DATA(-2, -2, 0) + + - 1/350 z DATA(1, 0, 1) + 1/350 z DATA(-1, 0, 1) + 1/175 z DATA(-1, -2, 0) + + + 2/175 z DATA(-2, 2, 0) - 1/175 z DATA(1, 0, 0) - 2/175 z DATA(2, 0, 0) + + 2 2 2 + + 1/100 z DATA(2, 0, 2) - 1/200 z DATA(-1, 0, 2) - 1/50 z DATA(2, 0, 1) + + 2 2 + - 1/100 z DATA(2, 0, -2) + 1/200 z DATA(-1, 0, -2) + + 2 2 + + 1/100 z DATA(-2, 0, -2) - 1/200 z DATA(1, 0, -2) + + 2 2 + + 1/100 z DATA(1, 0, -1) - 1/100 z DATA(-2, 0, 2) + + 2 2 + + 1/50 z DATA(-2, 0, 1) + 1/200 z DATA(1, 0, 2) + + 2 2 + - 1/100 z DATA(-1, 0, -1) - 1/100 z DATA(1, 0, 1) + + 2 2 + + 1/50 z DATA(2, 0, -1) + 1/100 z DATA(-1, 0, 1) + + 2 2 + - 1/350 y DATA(-2, 0, -1) + 1/175 y DATA(2, 0, -2) + + 2 2 + - 1/175 y DATA(2, 0, 2) + 1/350 y DATA(-1, 0, 2) + + 2 2 + - 1/350 y DATA(2, 0, 1) + 1/700 y DATA(1, 0, -1) + + 2 2 + - 1/175 y DATA(-2, 0, -2) - 1/350 y DATA(-1, 0, -2) + + 2 2 + + 1/350 y DATA(1, 0, -2) + 1/350 y DATA(2, 0, -1) + + 2 2 + + 1/175 y DATA(-2, 0, 2) + 1/700 y DATA(-1, 0, 1) + + 2 + - 4/245 x z DATA(0, 1, 2) + 1/350 y DATA(-2, 0, 1) + + 2 2 + - 1/350 y DATA(1, 0, 2) - 1/700 y DATA(-1, 0, -1) + + 2 + - 1/700 y DATA(1, 0, 1) - 1/175 x DATA(-2, 0, -1) + + - 1/175 x DATA(-1, 0, 2) + 1/175 x DATA(2, 0, 1) - 2/175 x DATA(2, 0, -2) + + + 2/175 x DATA(0, 0, -2) - 1/175 x DATA(0, 0, 1) + 2/175 x DATA(2, 0, 2) + + + 1/175 x DATA(1, 0, -2) - 2/175 x DATA(0, 0, 2) + 1/175 x DATA(0, 0, -1) + + + 2/175 x DATA(-2, 0, 2) - 2/175 x DATA(-2, 0, -2) + + + 1/175 x DATA(-1, 0, -2) - 1/175 x DATA(1, 0, 2) + + + 1/350 x DATA(-1, 0, -1) - 1/350 x DATA(1, 0, 1) - 1/350 x DATA(-1, 0, 1) + + + 1/350 x DATA(1, 0, -1) - 1/175 x DATA(2, 0, -1) + 1/175 x DATA(-2, 0, 1) + + 2 2 + + 1/200 x DATA(-2, 0, -1) + 1/100 x DATA(2, 0, 2) + + 2 2 + + 1/50 x DATA(-1, 0, 2) + 1/200 x DATA(2, 0, 1) + + 2 2 + - 1/100 x DATA(2, 0, -2) - 1/50 x DATA(-1, 0, -2) + + 2 2 + + 1/50 x DATA(1, 0, -2) + 1/100 x DATA(1, 0, -1) + + 2 2 + - 1/200 x DATA(2, 0, -1) - 1/100 x DATA(-2, 0, 2) + + 2 2 + + 1/100 x DATA(-2, 0, -2) + 1/100 x DATA(-1, 0, 1) + + 2 + - 2/245 x z DATA(-2, 0, -1) - 1/50 x DATA(1, 0, 2) + + + 4/245 x z DATA(2, 0, 2) - 2/245 x z DATA(-1, 0, 2) + + 17 + - 2/245 x z DATA(2, 0, 1) + 4/245 x z DATA(2, 0, -2) - ---- DATA(2, 0, 2) + 5250 + + 187 167 107 + - ---- DATA(-1, 0, 2) + ---- DATA(-2, -1, -1) - ---- DATA(2, -2, -1) + 7000 7000 7000 + + 47 167 167 + - ---- DATA(2, -1, 2) + ---- DATA(1, 1, 2) - ---- DATA(-1, 1, 2) + 5250 7000 7000 + + 107 107 187 + - ---- DATA(-1, -2, 2) + ---- DATA(1, -2, 2) + ---- DATA(-2, 0, -1) + 7000 7000 7000 + + 107 47 107 + - ---- DATA(-1, 2, 2) - ---- DATA(2, 1, 2) + ---- DATA(1, 2, 2) + 7000 5250 7000 + + 167 + + ---- DATA(-2, 1, -1) + 1/175 y z DATA(1, 2, 2) + 7000 + + - 4/245 x z DATA(0, -2, -2) + 2/245 x z DATA(0, -2, 1) + + 137 137 + + 2/245 x z DATA(0, 2, -1) - ---- DATA(-1, -1, 1) + ---- DATA(1, -1, 1) + 5250 5250 + + 289 137 289 + - ----- DATA(-1, 0, 1) - ---- DATA(-1, 1, 1) - ----- DATA(1, 0, -1) + 10500 5250 10500 + + 137 137 137 + + ---- DATA(-1, 1, -1) - ---- DATA(1, 1, -1) + ---- DATA(-1, -1, -1) + 5250 5250 5250 + + 137 137 107 + - ---- DATA(1, -1, -1) - ---- DATA(2, -2, 2) + ---- DATA(-2, 2, -1) + 5250 5250 7000 + + 137 + - ---- DATA(2, 2, 2) + 1/350 y z DATA(1, 1, -2) + 5250 + + - 1/175 y z DATA(-1, 2, -2) - 1/175 y z DATA(2, 2, 1) + + - 1/350 y z DATA(2, 1, 1) + 1/350 y z DATA(-1, -1, 2) + + - 1/350 y z DATA(1, 2, 1) + 2/175 y z DATA(2, 2, -2) + + + 1/350 y z DATA(2, -1, 1) + 1/350 y z DATA(-1, 2, 1) + + - 1/175 y z DATA(-2, -2, -1) + 1/175 y z DATA(-1, -2, 2) + + - 1/175 y z DATA(1, -2, 2) - 1/175 y z DATA(2, -1, 2) + + + 1/350 y z DATA(1, 1, 2) - 1/350 y z DATA(-1, 1, 2) + + - 1/350 y z DATA(1, -1, 2) + 1/175 y z DATA(2, -2, -1) + + - 1/350 y z DATA(-2, -1, -1) - 4/245 x z DATA(0, -1, -2) + + + 2/175 y z DATA(-2, -2, 2) + 1/350 y z DATA(1, -2, -1) + + + 1/350 y z DATA(-2, 1, -1) + 1/175 y z DATA(2, 1, 2) + + - 1/175 y z DATA(-1, 2, 2) + 2/245 x z DATA(0, -1, 1) + + - 2/175 y z DATA(2, -2, 2) + 1/175 y z DATA(-2, 2, -1) + + 47 + + ---- DATA(-2, -1, 2) + 2/175 y z DATA(2, 2, 2) + 5250 + + + 2/245 x z DATA(0, 1, -1) + 2/245 x z DATA(0, -1, -1) + + - 1/700 y z DATA(-1, -1, 1) + 2/175 y z DATA(-2, -2, -2) + + - 2/175 y z DATA(-2, 2, 2) - 1/175 y z DATA(-2, 1, 2) + + + 1/175 y z DATA(-2, -1, 2) + 1/175 y z DATA(-2, -1, -2) + + - 1/350 y z DATA(1, -1, -2) - 2/175 y z DATA(2, -2, -2) + + - 1/175 y z DATA(1, -2, -2) + 1/175 y z DATA(-1, -2, -2) + + + 1/350 y z DATA(-1, -1, -2) - 1/175 y z DATA(2, -1, -2) + + - 2/175 y z DATA(-2, 2, -2) - 1/350 y z DATA(-1, -2, -1) + + - 4/245 x z DATA(0, 2, -2) + 1/175 y z DATA(1, 2, -2) + + + 2/245 x z DATA(0, 2, 1) + 2/245 x z DATA(0, -2, -1) + + - 1/175 y z DATA(-2, 1, -2) - 4/245 x z DATA(0, -2, 2) + + + 1/700 y z DATA(1, -1, 1) + 1/175 y z DATA(-2, 2, 1) + + 17 + + ---- DATA(-2, 0, 2) + 1/350 y z DATA(2, -1, -1) + 5250 + + + 1/175 y z DATA(2, -2, 1) - 1/175 y z DATA(-2, -2, 1) + + 47 + + ---- DATA(-2, 1, 2) + 1/350 y z DATA(-2, 1, 1) + 5250 + + - 1/350 y z DATA(-1, 1, -2) + 1/175 y z DATA(2, 1, -2) + + - 1/350 y z DATA(-2, -1, 1) - 1/350 y z DATA(-1, -2, 1) + + - 1/350 y z DATA(2, 1, -1) + 1/350 y z DATA(-1, 2, -1) + + - 1/700 y z DATA(1, 1, 1) + 1/175 x y DATA(0, -1, 2) + + - 1/350 x y DATA(0, 1, 1) + 1/175 x y DATA(0, 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DATA(-2, 1, 1) - 1/700 x y DATA(1, 1, 1) + 5250 + + 107 107 + + 1/350 x y DATA(-1, 2, -1) - ---- DATA(1, -2, -2) + ---- DATA(-1, -2, -2) + 7000 7000 + + 47 + - ---- DATA(-2, -1, -2) - 1/175 x y DATA(2, -2, 1) + 5250 + + 137 167 + + 1/350 x y DATA(2, -1, -1) + ---- DATA(2, -2, -2) - ---- DATA(1, -1, -2) + 5250 7000 + + 167 + + ---- DATA(-1, -1, -2) - 1/175 x y DATA(-2, -2, 1) + 7000 + + 17 47 + + 1/350 x y DATA(1, -2, 1) - ---- DATA(-2, 0, -2) + ---- DATA(2, -1, -2) + 5250 5250 + + 187 187 + + ---- DATA(-1, 0, -2) - ---- DATA(1, 0, -2) + 7000 7000 + +> coeffs_as_lc_of_data(%, posn_list_3d_size5); +bytes used=2147630820, alloc=14677376, time=336.59 +bytes used=2148652936, alloc=14677376, time=336.67 +bytes used=2149732100, alloc=14677376, time=336.76 +bytes used=2150732228, alloc=14677376, time=336.84 +bytes used=2151732352, alloc=14677376, time=336.93 +bytes used=2152732708, alloc=14677376, time=337.01 +bytes used=2153733264, alloc=14677376, time=337.09 +bytes used=2154733568, alloc=14677376, time=337.18 +bytes used=2155784480, alloc=14677376, time=337.27 +bytes used=2156784780, alloc=14677376, time=337.35 +bytes used=2157799080, alloc=14677376, time=337.44 +bytes used=2158799376, alloc=14677376, time=337.53 +bytes used=2159799712, alloc=14677376, time=337.62 +bytes used=2160799872, alloc=14677376, time=337.72 +bytes used=2161804804, alloc=14677376, time=337.81 +bytes used=2162805384, alloc=14677376, time=337.91 +bytes used=2163806924, alloc=14677376, time=338.00 +bytes used=2164823788, alloc=14677376, time=338.10 +bytes used=2165823980, alloc=14677376, time=338.19 +bytes used=2166833724, alloc=14677376, time=338.29 +bytes used=2167845536, alloc=14677376, time=338.40 +bytes used=2168845656, alloc=14677376, time=338.51 +bytes used=2169854616, alloc=14677376, time=338.62 +bytes used=2170869252, alloc=14677376, time=338.70 +bytes used=2171873784, alloc=14677376, time=338.77 +bytes used=2172878644, alloc=14677376, time=338.84 + 2 2 +[COEFF(-2, -2, -2) = 1/100 x + 1/175 y + 4/245 x z - 2/175 z - 2/175 x + + 137 2 + - 1/125 y + 2/175 x y + 2/175 y z - ---- + 1/100 z , COEFF(-1, -2, -2) = + 5250 + + 107 2 2 + - 1/250 y + ---- - 1/175 x y - 2/245 x z - 1/50 x + 1/350 y - 1/175 z + 7000 + + 2 + + 1/200 z + 1/175 x + 1/175 y z, + + COEFF(0, -2, -2) = 2/175 x - 4/245 x z - 2/175 x y, COEFF(1, -2, -2) = + + 107 2 2 2 + - ---- + 1/50 x + 1/175 z - 1/175 x y - 1/350 y - 1/200 z - 2/245 x z + 7000 + + 137 + + 1/175 x + 1/250 y - 1/175 y z, COEFF(2, -2, -2) = 2/175 x y + ---- + 5250 + + 2 + - 2/175 y z + 2/175 z + 4/245 x z - 1/100 z - 2/175 x + 1/125 y + + 2 2 2 + - 1/175 y - 1/100 x , COEFF(-2, -1, -2) = 1/175 y z + 1/100 z - 1/250 y + + 2 47 2 + + 1/100 x - 2/175 z - ---- - 1/350 y + 4/245 x z - 2/175 x + 1/175 x y, + 5250 + + COEFF(-1, -1, -2) = - 1/350 x y - 1/500 y - 1/175 z + 1/175 x - 2/245 x z + + 2 2 2 167 + + 1/200 z - 1/50 x - 1/700 y + ---- + 1/350 y z, + 7000 + + COEFF(0, -1, -2) = - 1/175 x y - 4/245 x z + 2/175 x, COEFF(1, -1, -2) = + + 2 2 167 + 1/50 x - 1/350 y z + 1/700 y - 1/350 x y - ---- + 1/175 z + 1/500 y + 7000 + + 2 2 + - 1/200 z - 2/245 x z + 1/175 x, COEFF(2, -1, -2) = - 1/100 x + + 2 47 + - 1/175 y z + 1/250 y + 4/245 x z - 2/175 x + 1/350 y + 1/175 x y + ---- + 5250 + + 2 + + 2/175 z - 1/100 z , COEFF(-2, 0, -2) = + + 17 2 2 2 + - ---- - 2/175 x - 2/175 z - 1/175 y + 4/245 x z + 1/100 z + 1/100 x , + 5250 + + COEFF(-1, 0, -2) = + + 2 2 187 2 + - 1/50 x - 1/350 y + ---- + 1/200 z - 1/175 z + 1/175 x - 2/245 x z, + 7000 + + COEFF(0, 0, -2) = 2/175 x - 4/245 x z, COEFF(1, 0, -2) = + + 2 187 2 2 + - 1/200 z - ---- + 1/175 z + 1/350 y - 2/245 x z + 1/50 x + 1/175 x, + 7000 + + COEFF(2, 0, -2) = + + 2 2 17 2 + - 2/175 x - 1/100 x - 1/100 z + ---- + 2/175 z + 4/245 x z + 1/175 y , + 5250 + + 2 2 47 + COEFF(-2, 1, -2) = - 1/175 y z - 1/350 y + 1/100 z - 1/175 x y - ---- + 5250 + + 2 + + 4/245 x z - 2/175 x + 1/250 y + 1/100 x - 2/175 z, COEFF(-1, 1, -2) = + + 2 2 2 + - 2/245 x z - 1/50 x - 1/350 y z + 1/200 z - 1/700 y + 1/350 x y + + 167 + - 1/175 z + 1/175 x + ---- + 1/500 y, + 7000 + + COEFF(0, 1, -2) = 2/175 x + 1/175 x y - 4/245 x z, COEFF(1, 1, -2) = + + 2 2 167 + 1/700 y + 1/50 x - ---- - 1/500 y - 2/245 x z + 1/350 y z + 1/350 x y + 7000 + + 2 2 + + 1/175 x + 1/175 z - 1/200 z , COEFF(2, 1, -2) = - 1/100 x + 1/175 y z + + 2 47 + - 2/175 x + 2/175 z - 1/250 y - 1/175 x y + 4/245 x z + 1/350 y + ---- + 5250 + + 2 2 + - 1/100 z , COEFF(-2, 2, -2) = 1/175 y - 2/175 z - 2/175 x y + 1/125 y + + 2 137 2 + - 2/175 x + 4/245 x z + 1/100 z - ---- - 2/175 y z + 1/100 x , + 5250 + + 2 107 + COEFF(-1, 2, -2) = 1/350 y - 2/245 x z + ---- + 1/175 x - 1/175 y z + 7000 + + 2 2 + + 1/250 y - 1/50 x + 1/200 z - 1/175 z + 1/175 x y, + + COEFF(0, 2, -2) = 2/175 x y - 4/245 x z + 2/175 x, COEFF(1, 2, -2) = + + 2 2 + - 1/350 y - 1/250 y + 1/175 x y + 1/175 z - 2/245 x z + 1/50 x + + 2 107 + + 1/175 y z - 1/200 z - ---- + 1/175 x, COEFF(2, 2, -2) = - 1/125 y + 7000 + + 137 2 2 + + 4/245 x z + 2/175 y z - 2/175 x y + ---- - 1/175 y - 1/100 z + 5250 + + 2 + - 1/100 x - 2/175 x + 2/175 z, COEFF(-2, -2, -1) = 1/175 x y - 1/175 x + + 107 2 2 + + ---- - 1/250 y - 1/50 z + 1/175 z - 2/245 x z + 1/350 y - 1/175 y z + 7000 + + 2 2 2 + + 1/200 x , COEFF(-1, -2, -1) = 1/245 x z - 1/100 z - 1/100 x - 1/500 y + + 229 2 + - 1/350 x y + 1/350 x - 1/350 y z + ----- + 1/350 z + 1/700 y , + 10500 + + COEFF(0, -2, -1) = 1/175 x + 2/245 x z - 1/175 x y, COEFF(1, -2, -1) = + + 2 2 + 1/100 x - 1/350 x y + 1/500 y + 1/350 y z + 1/350 x + 1/245 x z - 1/700 y + + 2 229 107 + + 1/100 z - 1/350 z - -----, COEFF(2, -2, -1) = - ---- + 1/175 y z + 10500 7000 + + 2 2 2 + - 1/350 y - 1/175 x - 1/175 z + 1/250 y - 1/200 x + 1/50 z + 1/175 x y + + 2 + - 2/245 x z, COEFF(-2, -1, -1) = - 1/50 z + 1/350 x y + 1/175 z + + 2 2 167 + + 1/200 x - 1/700 y - 2/245 x z - 1/175 x - 1/350 y z - 1/500 y + ----, + 7000 + + 2 2 + COEFF(-1, -1, -1) = - 1/100 z - 1/700 x y + 1/350 z + 1/350 x - 1/100 x + + 2 137 + - 1/1400 y - 1/700 y z + 1/245 x z - 1/1000 y + ----, + 5250 + + COEFF(0, -1, -1) = - 1/350 x y + 1/175 x + 2/245 x z, COEFF(1, -1, -1) = + + 2 2 137 2 + - 1/350 z + 1/100 z + 1/700 y z + 1/1400 y - ---- + 1/350 x + 1/100 x + 5250 + + 167 + - 1/700 x y + 1/1000 y + 1/245 x z, COEFF(2, -1, -1) = - ---- - 2/245 x z + 7000 + + 2 2 2 + + 1/700 y - 1/175 x + 1/50 z - 1/175 z + 1/500 y + 1/350 x y - 1/200 x + + + 1/350 y z, COEFF(-2, 0, -1) = + + 2 187 2 2 + - 1/350 y + ---- - 1/175 x - 1/50 z - 2/245 x z + 1/175 z + 1/200 x , + 7000 + + COEFF(-1, 0, -1) = + + 2 289 2 2 + 1/245 x z + 1/350 z + 1/350 x - 1/700 y + ----- - 1/100 z - 1/100 x , + 10500 + + COEFF(0, 0, -1) = 1/175 x + 2/245 x z, COEFF(1, 0, -1) = + + 2 289 2 2 + 1/100 z + 1/245 x z - ----- - 1/350 z + 1/350 x + 1/100 x + 1/700 y , + 10500 + + COEFF(2, 0, -1) = + + 187 2 2 2 + - ---- - 1/200 x - 1/175 x - 2/245 x z - 1/175 z + 1/50 z + 1/350 y , + 7000 + + 2 167 2 + COEFF(-2, 1, -1) = - 1/700 y + 1/175 z + ---- - 1/350 x y + 1/200 x + 7000 + + 2 + + 1/500 y + 1/350 y z - 1/175 x - 1/50 z - 2/245 x z, COEFF(-1, 1, -1) = + + 2 2 + 1/1000 y - 1/100 z + 1/700 x y + 1/245 x z + 1/700 y z - 1/100 x + + 2 137 + - 1/1400 y + ---- + 1/350 z + 1/350 x, + 5250 + + COEFF(0, 1, -1) = 2/245 x z + 1/175 x + 1/350 x y, COEFF(1, 1, -1) = + + 2 2 2 + 1/1400 y + 1/100 z + 1/245 x z - 1/350 z + 1/350 x + 1/100 x + 1/700 x y + + 137 2 2 + - 1/1000 y - 1/700 y z - ----, COEFF(2, 1, -1) = 1/700 y - 1/200 x + 5250 + + 167 + - 1/350 y z - ---- - 1/175 x - 1/175 z - 1/350 x y - 2/245 x z - 1/500 y + 7000 + + 2 2 + + 1/50 z , COEFF(-2, 2, -1) = - 2/245 x z + 1/250 y - 1/175 x + 1/200 x + + 2 2 107 + + 1/175 y z + 1/175 z - 1/175 x y - 1/50 z + 1/350 y + ----, + 7000 + + 2 2 + COEFF(-1, 2, -1) = 1/350 x - 1/100 x - 1/100 z + 1/350 y z + 1/245 x z + + 229 2 + + 1/350 z + 1/500 y + ----- + 1/700 y + 1/350 x y, + 10500 + + COEFF(0, 2, -1) = 1/175 x + 2/245 x z + 1/175 x y, COEFF(1, 2, -1) = + + 2 2 + - 1/350 y z + 1/100 x - 1/350 z + 1/100 z + 1/245 x z + 1/350 x y + + 229 2 + + 1/350 x - 1/500 y - ----- - 1/700 y , COEFF(2, 2, -1) = - 1/175 y z + 10500 + + 2 2 107 + + 1/50 z - 2/245 x z - 1/250 y - 1/175 x y - 1/175 z - 1/200 x - ---- + 7000 + + 2 + - 1/175 x - 1/350 y , COEFF(-2, -2, 0) = - 4/245 x z - 2/175 y z + 2/175 z, + + COEFF(-1, -2, 0) = - 1/175 y z + 2/245 x z + 1/175 z, + + COEFF(0, -2, 0) = 4/245 x z, + + COEFF(1, -2, 0) = 2/245 x z + 1/175 y z - 1/175 z, + + COEFF(2, -2, 0) = - 4/245 x z + 2/175 y z - 2/175 z, + + COEFF(-2, -1, 0) = - 4/245 x z + 2/175 z - 1/175 y z, + + COEFF(-1, -1, 0) = 2/245 x z + 1/175 z - 1/350 y z, + + COEFF(0, -1, 0) = 4/245 x z, + + COEFF(1, -1, 0) = 2/245 x z + 1/350 y z - 1/175 z, + + COEFF(2, -1, 0) = - 2/175 z - 4/245 x z + 1/175 y z, + + COEFF(-2, 0, 0) = 2/175 z - 4/245 x z, + + COEFF(-1, 0, 0) = 2/245 x z + 1/175 z, COEFF(0, 0, 0) = 4/245 x z, + + COEFF(1, 0, 0) = 2/245 x z - 1/175 z, + + COEFF(2, 0, 0) = - 2/175 z - 4/245 x z, + + COEFF(-2, 1, 0) = - 4/245 x z + 2/175 z + 1/175 y z, + + COEFF(-1, 1, 0) = 1/175 z + 1/350 y z + 2/245 x z, + + COEFF(0, 1, 0) = 4/245 x z, + + COEFF(1, 1, 0) = - 1/175 z + 2/245 x z - 1/350 y z, + + COEFF(2, 1, 0) = - 2/175 z - 1/175 y z - 4/245 x z, + + COEFF(-2, 2, 0) = 2/175 z + 2/175 y z - 4/245 x z, + + COEFF(-1, 2, 0) = 1/175 z + 2/245 x z + 1/175 y z, + + COEFF(0, 2, 0) = 4/245 x z, + + COEFF(1, 2, 0) = - 1/175 y z - 1/175 z + 2/245 x z, + + COEFF(2, 2, 0) = - 2/175 y z - 4/245 x z - 2/175 z, COEFF(-2, -2, 1) = + + 2 107 2 + 1/175 x - 1/175 y z - 2/245 x z + 1/250 y - 1/350 y - ---- + 1/50 z + 7000 + + 2 2 + - 1/200 x - 1/175 x y + 1/175 z, COEFF(-1, -2, 1) = 1/245 x z + 1/100 x + + 2 2 229 + - 1/700 y + 1/100 z - 1/350 y z + 1/350 x y - ----- - 1/350 x + 1/500 y + 10500 + + + 1/350 z, COEFF(0, -2, 1) = - 1/175 x + 2/245 x z + 1/175 x y, + + 229 2 2 + COEFF(1, -2, 1) = ----- - 1/100 x + 1/350 y z + 1/700 y - 1/500 y + 10500 + + 2 + - 1/350 x + 1/245 x z + 1/350 x y - 1/350 z - 1/100 z , COEFF(2, -2, 1) = + + 2 2 107 2 + 1/350 y - 2/245 x z + 1/175 x - 1/50 z + 1/175 y z + ---- + 1/200 x + 7000 + + 2 + - 1/175 z - 1/175 x y - 1/250 y, COEFF(-2, -1, 1) = 1/175 z + 1/50 z + + 2 + + 1/175 x + 1/500 y - 2/245 x z - 1/350 y z - 1/200 x - 1/350 x y + + 2 167 2 + + 1/700 y - ----, COEFF(-1, -1, 1) = 1/350 z + 1/100 z + 1/245 x z + 7000 + + 137 2 2 + + 1/1000 y - ---- - 1/350 x - 1/700 y z + 1/1400 y + 1/100 x + 1/700 x y + 5250 + + , COEFF(0, -1, 1) = 1/350 x y - 1/175 x + 2/245 x z, COEFF(1, -1, 1) = + + 2 137 2 + 1/245 x z - 1/100 x + ---- - 1/350 z + 1/700 y z - 1/1400 y - 1/1000 y + 5250 + + 2 + - 1/350 x - 1/100 z + 1/700 x y, COEFF(2, -1, 1) = 1/350 y z - 1/500 y + + 167 2 2 2 + + ---- - 1/350 x y - 1/700 y - 2/245 x z + 1/200 x - 1/50 z - 1/175 z + 7000 + + + 1/175 x, COEFF(-2, 0, 1) = + + 2 187 2 2 + 1/50 z + 1/175 x + 1/175 z - ---- - 2/245 x z - 1/200 x + 1/350 y , + 7000 + + COEFF(-1, 0, 1) = + + 2 289 2 2 + - 1/350 x + 1/700 y - ----- + 1/245 x z + 1/100 x + 1/100 z + 1/350 z, + 10500 + + COEFF(0, 0, 1) = 2/245 x z - 1/175 x, COEFF(1, 0, 1) = + + 2 289 2 2 + - 1/100 z - 1/350 x + ----- - 1/100 x + 1/245 x z - 1/350 z - 1/700 y , + 10500 + + COEFF(2, 0, 1) = + + 2 187 2 2 + - 1/350 y + 1/175 x + ---- + 1/200 x - 1/175 z - 1/50 z - 2/245 x z, + 7000 + + 2 2 2 + COEFF(-2, 1, 1) = 1/700 y + 1/350 y z + 1/175 x + 1/50 z - 1/200 x + + 167 + + 1/175 z - ---- + 1/350 x y - 1/500 y - 2/245 x z, COEFF(-1, 1, 1) = + 7000 + + 2 137 2 + - 1/700 x y + 1/100 x - ---- + 1/350 z + 1/700 y z + 1/245 x z + 1/100 z + 5250 + + 2 + - 1/1000 y + 1/1400 y - 1/350 x, + + 137 + COEFF(0, 1, 1) = - 1/350 x y - 1/175 x + 2/245 x z, COEFF(1, 1, 1) = ---- + 5250 + + 2 2 + - 1/1400 y + 1/245 x z - 1/350 x + 1/1000 y - 1/100 z - 1/700 y z + + 2 167 + - 1/100 x - 1/350 z - 1/700 x y, COEFF(2, 1, 1) = ---- + 1/350 x y + 7000 + + 2 2 + - 1/175 z - 1/700 y - 2/245 x z - 1/350 y z + 1/175 x + 1/200 x + + 2 2 107 + + 1/500 y - 1/50 z , COEFF(-2, 2, 1) = - 1/350 y - 2/245 x z - ---- + 7000 + + 2 2 + - 1/200 x + 1/50 z + 1/175 x + 1/175 z - 1/250 y + 1/175 y z + 1/175 x y + + 2 2 + , COEFF(-1, 2, 1) = - 1/700 y + 1/245 x z + 1/350 z + 1/100 z - 1/500 y + + 2 229 + + 1/100 x + 1/350 y z - ----- - 1/350 x y - 1/350 x, + 10500 + + COEFF(0, 2, 1) = 2/245 x z - 1/175 x y - 1/175 x, COEFF(1, 2, 1) = + + 2 2 + - 1/350 y z - 1/350 z + 1/245 x z - 1/350 x - 1/100 z + 1/500 y - 1/100 x + + 2 229 2 107 + + 1/700 y + ----- - 1/350 x y, COEFF(2, 2, 1) = - 1/50 z + ---- + 10500 7000 + + 2 + - 2/245 x z - 1/175 y z + 1/175 x + 1/200 x + 1/175 x y - 1/175 z + + 2 2 137 2 + + 1/350 y + 1/250 y, COEFF(-2, -2, 2) = - 1/175 y + ---- - 1/100 x + 5250 + + 2 + + 4/245 x z - 2/175 x y - 2/175 z - 1/100 z + 2/175 y z + 2/175 x + + 2 + + 1/125 y, COEFF(-1, -2, 2) = - 1/350 y - 1/175 x + 1/250 y + 1/175 y z + + 2 107 2 + - 2/245 x z - 1/200 z - ---- + 1/175 x y + 1/50 x - 1/175 z, + 7000 + + COEFF(0, -2, 2) = - 2/175 x - 4/245 x z + 2/175 x y, COEFF(1, -2, 2) = + + 2 2 2 107 + 1/200 z + 1/175 z - 1/50 x + 1/350 y - 1/250 y - 2/245 x z + ---- + 7000 + + - 1/175 x + 1/175 x y - 1/175 y z, COEFF(2, -2, 2) = - 2/175 x y + + 2 137 2 + + 1/100 x + 4/245 x z - 2/175 y z + 2/175 z + 2/175 x - ---- + 1/175 y + 5250 + + 2 + + 1/100 z - 1/125 y, COEFF(-2, -1, 2) = 4/245 x z + 2/175 x - 1/175 x y + + 47 2 2 2 + + ---- + 1/250 y - 2/175 z + 1/175 y z - 1/100 z + 1/350 y - 1/100 x , + 5250 + + 167 2 2 + COEFF(-1, -1, 2) = - ---- + 1/350 y z + 1/700 y + 1/500 y - 1/200 z + 7000 + + 2 + - 1/175 x + 1/50 x - 2/245 x z + 1/350 x y - 1/175 z, + + COEFF(0, -1, 2) = - 2/175 x + 1/175 x y - 4/245 x z, COEFF(1, -1, 2) = + + 2 2 + - 2/245 x z - 1/50 x - 1/175 x - 1/500 y - 1/350 y z + 1/175 z - 1/700 y + + 2 167 2 + + 1/200 z + 1/350 x y + ----, COEFF(2, -1, 2) = - 1/350 y + 2/175 x + 7000 + + 47 2 2 + - 1/250 y - ---- + 4/245 x z + 1/100 x + 1/100 z - 1/175 y z - 1/175 x y + 5250 + + + 2/175 z, COEFF(-2, 0, 2) = + + 2 2 17 2 + 4/245 x z - 1/100 z - 1/100 x + ---- - 2/175 z + 1/175 y + 2/175 x, + 5250 + + COEFF(-1, 0, 2) = + + 187 2 2 2 + - 2/245 x z - ---- - 1/175 x + 1/50 x - 1/200 z - 1/175 z + 1/350 y , + 7000 + + COEFF(0, 0, 2) = - 2/175 x - 4/245 x z, COEFF(1, 0, 2) = + + 2 2 2 187 + 1/200 z + 1/175 z - 1/350 y - 1/50 x - 1/175 x + ---- - 2/245 x z, + 7000 + + COEFF(2, 0, 2) = + + 2 2 2 17 + 2/175 x + 2/175 z + 4/245 x z + 1/100 z + 1/100 x - 1/175 y - ----, + 5250 + + 47 2 2 + COEFF(-2, 1, 2) = ---- - 1/100 x - 2/175 z + 1/350 y + 2/175 x + 5250 + + 2 + + 4/245 x z - 1/250 y + 1/175 x y - 1/100 z - 1/175 y z, COEFF(-1, 1, 2) + + 167 2 + = - 1/350 x y - 1/175 z - ---- - 2/245 x z + 1/700 y - 1/350 y z + 7000 + + 2 2 + + 1/50 x - 1/500 y - 1/200 z - 1/175 x, + + COEFF(0, 1, 2) = - 4/245 x z - 2/175 x - 1/175 x y, COEFF(1, 1, 2) = + + 2 2 167 + - 1/50 x + 1/500 y + 1/200 z + ---- + 1/175 z - 1/175 x - 1/350 x y + 7000 + + 2 2 + - 1/700 y + 1/350 y z - 2/245 x z, COEFF(2, 1, 2) = - 1/350 y + + 47 2 2 + + 4/245 x z + 1/250 y + 2/175 x + 1/175 x y - ---- + 1/100 z + 1/100 x + 5250 + + 2 137 + + 1/175 y z + 2/175 z, COEFF(-2, 2, 2) = - 1/100 x + ---- + 2/175 x y + 5250 + + 2 2 + - 2/175 z - 1/175 y + 4/245 x z - 2/175 y z - 1/100 z - 1/125 y + + 2 2 107 + + 2/175 x, COEFF(-1, 2, 2) = 1/50 x - 1/175 z - 1/200 z - ---- + 7000 + + 2 + - 1/350 y - 2/245 x z - 1/175 x - 1/175 x y - 1/175 y z - 1/250 y, + + COEFF(0, 2, 2) = - 2/175 x - 4/245 x z - 2/175 x y, COEFF(1, 2, 2) = + + 2 2 107 + 1/250 y + 1/350 y + 1/200 z - 1/175 x + ---- - 1/175 x y + 1/175 y z + 7000 + + 2 + - 2/245 x z - 1/50 x + 1/175 z, COEFF(2, 2, 2) = 2/175 y z + 1/125 y + + 2 2 137 + + 2/175 z + 2/175 x + 1/100 z + 1/175 y + 4/245 x z - ---- + 2/175 x y + 5250 + + 2 + + 1/100 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxz.compute.c"); +bytes used=2173879132, alloc=14677376, time=338.93 +bytes used=2174879340, alloc=14677376, time=339.02 +bytes used=2175879540, alloc=14677376, time=339.10 +bytes used=2176879720, alloc=14677376, time=339.35 +bytes used=2177880300, alloc=14677376, time=340.02 +bytes used=2178880664, alloc=14677376, time=340.69 +bytes used=2179881340, alloc=14677376, time=341.37 +bytes used=2180881552, alloc=14677376, time=342.04 +bytes used=2181881812, alloc=14677376, time=342.68 +bytes used=2182881964, alloc=14677376, time=342.78 +bytes used=2183882304, alloc=14677376, time=342.87 +bytes used=2184922736, alloc=14677376, time=342.95 +bytes used=2185944208, alloc=14677376, time=343.03 +bytes used=2186970552, alloc=14677376, time=343.11 +bytes used=2187970784, alloc=14677376, time=343.21 +bytes used=2188970948, alloc=14677376, time=343.85 +bytes used=2189971160, alloc=14677376, time=344.96 +bytes used=2190971424, alloc=14677376, time=345.38 +bytes used=2191971636, alloc=14677376, time=345.46 +bytes used=2192973112, alloc=14677376, time=345.53 +bytes used=2193975160, alloc=14677376, time=345.60 +bytes used=2194975384, alloc=14677376, time=345.67 +bytes used=2195975556, alloc=14677376, time=345.74 +bytes used=2196975772, alloc=14677376, time=345.81 +bytes used=2197976004, alloc=14677376, time=345.89 +bytes used=2198976180, alloc=14677376, time=345.96 +bytes used=2199983556, alloc=14677376, time=346.07 +bytes used=2200983856, alloc=14677376, time=346.19 +bytes used=2201985960, alloc=14677376, time=346.30 +bytes used=2202986240, alloc=14677376, time=346.42 +bytes used=2203997972, alloc=14677376, time=346.56 +bytes used=2204998184, alloc=14677376, time=346.68 +bytes used=2206000532, alloc=14677376, time=346.80 +bytes used=2207000724, alloc=14677376, time=346.88 +bytes used=2208000972, alloc=14677376, time=348.25 +bytes used=2209001168, alloc=14677376, time=349.16 +bytes used=2210001340, alloc=14677376, time=349.59 +bytes used=2211001796, alloc=14677376, time=349.68 +bytes used=2212002164, alloc=14677376, time=349.75 +bytes used=2213002352, alloc=14677376, time=349.83 +bytes used=2214002624, alloc=14677376, time=349.90 +bytes used=2215002832, alloc=14677376, time=349.97 +bytes used=2216003172, alloc=14677376, time=350.05 +bytes used=2217003448, alloc=14677376, time=350.15 +bytes used=2218007788, alloc=14677376, time=350.30 +bytes used=2219020240, alloc=14677376, time=350.43 +bytes used=2220020412, alloc=14677376, time=350.56 +bytes used=2221020696, alloc=14677376, time=350.83 +bytes used=2222020848, alloc=14677376, time=352.61 +bytes used=2223021040, alloc=14677376, time=352.98 +bytes used=2224021316, alloc=14677376, time=353.47 +bytes used=2225021608, alloc=14677376, time=353.56 +bytes used=2226021984, alloc=14677376, time=353.64 +bytes used=2227022216, alloc=14677376, time=353.85 +bytes used=2228022436, alloc=14677376, time=355.20 +bytes used=2229022608, alloc=14677376, time=356.24 +bytes used=2230022776, alloc=14677376, time=356.74 +bytes used=2231022952, alloc=14677376, time=356.81 +bytes used=2232023200, alloc=14677376, time=357.04 +bytes used=2233023388, alloc=14677376, time=358.76 +bytes used=2234023552, alloc=14677376, time=359.51 +bytes used=2235024356, alloc=14677376, time=360.01 +bytes used=2236024752, alloc=14677376, time=360.09 +bytes used=2237024916, alloc=14677376, time=360.22 +> +# d^2/dy^2 +> simplify( diff(interp_3d_cube_order4_smooth0,y,y) ); +bytes used=2238025672, alloc=14677376, time=360.32 +bytes used=2239045912, alloc=14677376, time=360.41 +bytes used=2240046176, alloc=14677376, time=360.49 +bytes used=2241046520, alloc=14677376, time=360.57 +bytes used=2242046836, alloc=14677376, time=360.65 +bytes used=2243047088, alloc=14677376, time=360.74 +bytes used=2244047220, alloc=14677376, time=360.82 +bytes used=2245047392, alloc=14677376, time=360.90 +bytes used=2246047676, alloc=14677376, time=360.98 +bytes used=2247048084, alloc=14677376, time=361.06 + 431 169 +----- DATA(0, -2, 0) - ----- DATA(-2, -2, 1) - 1/50 y z DATA(1, -1, -1) +14700 14700 + + 191 311 + + ----- DATA(1, -2, 1) - 1/50 y z DATA(-1, -1, -1) + ----- DATA(0, -2, 1) + 14700 14700 + + 311 311 + + ----- DATA(1, -2, 0) + ----- DATA(0, 2, -1) - 9/98 DATA(2, 0, -1) + 14700 14700 + + 191 + + ----- DATA(-1, -2, 1) + 4/75 DATA(0, -1, 2) + 1/50 y z DATA(1, 1, -1) + 14700 + + + 1/50 y z DATA(-1, 1, -1) - 1/50 y z DATA(-1, 1, 1) + + 211 169 + + ---- DATA(-2, -1, 1) - 1/300 DATA(2, -2, 0) - ----- DATA(2, -2, 1) + 3675 14700 + + - 1/175 x DATA(-1, -2, -1) - 9/98 DATA(-2, 0, 1) + 4/75 DATA(-2, -1, 0) + + - 1/300 DATA(0, 2, 2) + 1/175 x DATA(-2, 1, 1) - 1/350 x DATA(1, 1, 1) + + - 9/98 DATA(1, 0, 2) - 1/175 x DATA(-1, 2, -1) - 1/175 x DATA(2, 1, -1) + + + 2/175 x DATA(2, 2, -1) + 1/175 x DATA(1, 2, -1) + + 57 + + 1/350 x DATA(-1, -1, 2) + 1/175 x DATA(1, 2, 1) - --- DATA(-1, 0, -1) + 490 + + + 2/175 x DATA(2, 2, -2) - 1/175 x DATA(2, -1, 1) - 1/175 x DATA(-1, 2, 1) + + - 2/175 x DATA(-2, -2, -1) - 1/350 x DATA(1, 1, -2) + + + 1/175 x DATA(1, 2, -2) - 2/175 x DATA(-2, 2, -2) + + 211 13 + - 2/175 x DATA(-2, 2, 1) + ---- DATA(2, -1, -1) - -- DATA(0, 0, 0) + 3675 98 + + 61 136 151 + - --- DATA(1, 0, 0) + ---- DATA(0, 1, 0) + ---- DATA(1, 1, 0) + 490 3675 3675 + + 61 57 151 + - --- DATA(0, 0, 1) - --- DATA(1, 0, 1) + ---- DATA(0, 1, 1) + 490 490 3675 + + 166 + + ---- DATA(1, 1, 1) + 1/350 x z DATA(-2, -1, 1) + 3675 + + + 1/350 x z DATA(2, -1, -1) + 1/175 x z DATA(2, -2, 1) + + - 1/175 x z DATA(-2, -2, 1) + 1/350 x z DATA(1, -2, 1) + + - 1/350 x z DATA(-1, -2, 1) - 1/175 x z DATA(2, 2, -1) + + + 1/350 x z DATA(2, 1, -1) + 1/350 x z DATA(-1, 2, -1) + + - 1/700 x z DATA(1, 1, 1) + 1/350 x z DATA(-2, 1, 1) + + - 1/350 x z DATA(-1, 1, -2) + 1/175 x z DATA(2, 1, -2) + + + 1/175 x z DATA(2, 2, 1) + 1/175 x z DATA(-1, 2, -2) + + + 1/350 x z DATA(1, 1, -2) - 1/175 x z DATA(-2, 2, 1) + + + 2/175 x z DATA(-2, 2, -2) + 1/350 x z DATA(-1, -2, -1) + + - 1/175 x z DATA(1, 2, -2) - 1/175 x z DATA(-2, 1, -2) + + - 1/350 x z DATA(1, 2, -1) - 1/350 x z DATA(-1, 2, 1) + + - 2/175 x z DATA(2, 2, -2) + 1/350 x z DATA(1, 2, 1) + + + 1/350 x z DATA(-1, -1, 2) - 1/350 x z DATA(2, 1, 1) + + 169 + - 1/350 x z DATA(2, -1, 1) - ----- DATA(2, 2, -1) - 1/50 x y DATA(1, 1, 2) + 14700 + + + 1/25 x y DATA(2, -1, 2) + 1/175 x z DATA(-2, -2, -1) + + - 1/25 x y DATA(-2, -1, -1) + 1/50 x y DATA(1, -1, 2) + + + 1/50 x y DATA(-1, 1, 2) - 1/50 x y DATA(2, -2, -1) + + - 1/25 x y DATA(2, 1, 2) + 1/25 x y DATA(-2, 1, -1) + + - 1/100 x y DATA(1, -2, -1) + 1/50 x y DATA(-2, -2, 2) + + + 1/50 x y DATA(1, -1, -1) - 1/50 x y DATA(-1, -1, -1) + + + 1/100 x y DATA(1, 2, 2) + 1/50 x y DATA(2, 2, 2) + + - 1/50 x y DATA(-2, 2, -1) - 1/50 x y DATA(2, -2, 2) + + - 1/100 x y DATA(-1, 2, 2) - 1/50 x y DATA(-1, -1, 1) + + + 1/50 x y DATA(1, -1, 1) - 1/50 x y DATA(1, 1, -1) + + + 1/50 x y DATA(-1, 1, -1) + 1/50 x y DATA(-1, 1, 1) + + - 1/50 x y DATA(-2, 2, 2) + 1/50 x y DATA(-2, -2, -2) + + + 1/25 x y DATA(-2, 1, 2) - 1/50 x y DATA(2, -2, -2) + + - 1/25 x y DATA(-2, -1, -2) - 1/25 x y DATA(-2, -1, 2) + + + 1/50 x y DATA(1, -1, -2) + 1/25 x y DATA(2, -1, -2) + + - 1/50 x y DATA(-1, -1, -2) + 1/100 x y DATA(-1, -2, -2) + + 2 + - 1/100 x y DATA(1, -2, -2) + 2/245 x DATA(2, 2, 2) + + 2 + - 1/245 x DATA(1, 2, 2) - 1/175 x DATA(2, 1, 2) + 2/175 x DATA(2, -2, 2) + + 2 + - 2/175 x DATA(-2, 2, -1) + 2/245 x DATA(2, -2, 2) + + 2 + + 2/245 x DATA(-2, 2, -1) - 1/175 x DATA(-1, 2, 2) + + - 1/175 x DATA(-1, -2, 2) - 1/175 x DATA(2, -1, 2) - 1/350 x DATA(1, 1, 2) + + + 1/350 x DATA(-1, 1, 2) - 1/350 x DATA(1, -1, 2) + + + 2/175 x DATA(2, -2, -1) + 1/175 x DATA(-2, -1, -1) + + - 2/175 x DATA(-2, -2, 2) + 1/175 x DATA(1, -2, -1) + + 191 + + 1/175 x DATA(-2, 1, -1) + 1/175 x DATA(1, -2, 2) + ----- DATA(1, 2, -1) + 14700 + + + 1/175 x DATA(1, -2, -2) + 1/350 x DATA(-1, -1, -2) + + - 1/350 x DATA(1, -1, 1) + 2/175 x DATA(2, 2, 2) + 1/175 x DATA(1, 2, 2) + + + 1/350 x DATA(-1, -1, -1) - 1/350 x DATA(1, -1, -1) + + + 1/350 x DATA(-1, 1, 1) + 1/350 x DATA(-1, 1, -1) + + - 1/350 x DATA(1, 1, -1) - 1/175 x DATA(-1, -2, -2) + + - 2/175 x DATA(-2, -2, -2) + 1/175 x DATA(-2, 1, 2) + + + 1/175 x DATA(-2, -1, 2) + 1/175 x DATA(-2, -1, -2) + + - 1/350 x DATA(1, -1, -2) + 2/175 x DATA(2, -2, -2) + + 256 + - 2/175 x DATA(-2, 2, 2) + ---- DATA(-2, 1, -2) - 1/175 x DATA(2, -1, -2) + 3675 + + 191 + + 1/350 x DATA(-1, -1, 1) + ----- DATA(-1, 2, -1) + 14700 + + 2 2 + + 2/245 x DATA(-2, -2, 1) + 2/245 x DATA(2, -2, 1) + + 2 2 + - 1/245 x DATA(1, -2, 1) + 1/490 x DATA(1, 1, 1) + + 2 2 + - 1/245 x DATA(-1, 2, -1) - 1/245 x DATA(2, 1, -1) + + 2 2 + - 1/245 x DATA(2, -1, -1) - 1/245 x DATA(-1, -2, 1) + + 2 2 + - 1/245 x DATA(-2, -1, 1) - 1/245 x DATA(2, 1, -2) + + 2 2 + + 1/490 x DATA(1, 1, -2) - 1/245 x DATA(-1, 2, -2) + + 2 2 + + 2/245 x DATA(2, 2, 1) + 2/245 x DATA(2, 2, -1) + + 2 2 + - 1/245 x DATA(-2, 1, -2) - 1/245 x DATA(1, 2, -2) + + 2 2 + - 1/245 x DATA(-1, -2, -1) + 2/245 x DATA(-2, 2, -2) + + 2 2 + - 1/245 x DATA(1, 2, -1) + 1/490 x DATA(-1, 1, -2) + + 2 2 + - 1/245 x DATA(-2, 1, 1) + 1/490 x DATA(1, 1, 2) + + 2 2 + + 1/490 x DATA(-1, 1, 2) + 1/490 x DATA(1, -1, 2) + + 2 2 + + 2/245 x DATA(2, -2, -1) - 1/245 x DATA(-2, -1, -1) + + 2 2 + - 1/245 x DATA(2, 1, 1) + 1/490 x DATA(-1, -1, 2) + + 2 2 + - 1/245 x DATA(1, 2, 1) + 2/245 x DATA(2, 2, -2) + + 2 2 + - 1/245 x DATA(2, -1, 1) - 1/245 x DATA(-1, 2, 1) + + 2 2 + + 2/245 x DATA(-2, -2, -1) - 1/245 x DATA(-1, -2, 2) + + 2 2 + - 1/245 x DATA(1, -2, 2) + 2/245 x DATA(-2, 2, 1) + + 2 2 + + 1/490 x DATA(-1, -1, 1) + 2/245 x DATA(-2, -2, -2) + + 2 2 + + 1/490 x DATA(1, -1, -1) + 2/245 x DATA(-2, -2, 2) + + 2 2 + - 1/245 x DATA(1, -2, -1) - 1/245 x DATA(-2, 1, -1) + + 2 2 + - 1/245 x DATA(2, 1, 2) - 1/245 x DATA(-1, 2, 2) + + 2 2 + - 1/245 x DATA(2, -1, 2) + 1/490 x DATA(1, -1, 1) + + 2 2 + + 2/245 x DATA(-2, 2, 2) - 1/245 x DATA(-2, 1, 2) + + 2 2 + - 1/245 x DATA(-2, -1, 2) - 1/245 x DATA(-2, -1, -2) + + 2 2 + + 1/490 x DATA(1, -1, -2) + 1/490 x DATA(-1, -1, -1) + + 2 2 + + 1/490 x DATA(-1, 1, 1) + 1/490 x DATA(-1, 1, -1) + + 2 2 + + 1/490 x DATA(1, 1, -1) + 2/245 x DATA(2, -2, -2) + + 2 2 + - 1/245 x DATA(1, -2, -2) - 1/245 x DATA(-1, -2, -2) + + 2 2 + + 1/490 x DATA(-1, -1, -2) - 1/245 x DATA(2, -1, -2) + + 211 + + ---- DATA(2, 1, -1) + 2/175 x DATA(2, -2, 1) - 1/175 x DATA(2, -1, -1) + 3675 + + + 1/175 x DATA(-2, 1, -2) + 1/175 x DATA(-2, -1, 1) + + - 1/175 x DATA(2, 1, -2) + 1/350 x DATA(-1, 1, -2) + + - 1/175 x DATA(-1, -2, 1) + 1/175 x DATA(1, -2, 1) + + - 2/175 x DATA(-2, -2, 1) - 1/175 x DATA(-1, 2, -2) + + + 2/175 x DATA(2, 2, 1) - 1/175 x DATA(2, 1, 1) - 1/50 y DATA(2, -2, 1) + + - 1/50 y DATA(1, -2, 1) - 1/25 y DATA(1, 1, 1) + 1/50 y DATA(-1, 2, -1) + + - 1/50 y DATA(-1, -2, 1) - 1/25 y DATA(2, 1, -2) - 1/25 y DATA(-1, 1, -2) + + + 1/25 y DATA(-2, -1, 1) + 1/25 y DATA(2, -1, -1) - 1/50 y DATA(-2, -2, 1) + + - 1/25 y DATA(-2, 1, 1) - 1/25 y DATA(2, 1, 1) + 1/25 y DATA(-1, -1, 2) + + + 1/50 y DATA(1, 2, 1) + 1/50 y DATA(-2, 2, 1) - 1/25 y DATA(1, 1, -2) + + + 1/50 y DATA(-1, 2, -2) + 1/50 y DATA(1, 2, -2) + 1/50 y DATA(-2, 2, -2) + + - 1/50 y DATA(-1, -2, -1) - 1/25 y DATA(2, 1, -1) + 1/50 y DATA(2, 2, -1) + + + 1/50 y DATA(1, 2, -1) - 1/25 y DATA(-2, 1, -2) - 1/25 y DATA(2, 1, 2) + + + 1/50 y DATA(-1, 2, 2) - 1/25 y DATA(-2, 1, -1) + 1/25 y DATA(1, -1, 2) + + + 1/25 y DATA(-2, -1, -1) - 1/50 y DATA(-2, -2, 2) + + - 1/50 y DATA(2, -2, -1) - 1/50 y DATA(1, -2, 2) - 1/25 y DATA(1, 1, 2) + + - 1/25 y DATA(-1, 1, 2) + 1/25 y DATA(2, -1, 2) + 1/50 y DATA(2, 2, -2) + + + 1/50 y DATA(-1, 2, 1) - 1/50 y DATA(-2, -2, -1) - 1/50 y DATA(-1, -2, 2) + + + 1/25 y DATA(2, -1, 1) + 1/50 y DATA(2, 2, 1) - 1/25 y DATA(-1, 1, -1) + + + 1/25 y DATA(-1, -1, -1) + 1/25 y DATA(1, -1, -1) - 1/25 y DATA(-1, 1, 1) + + - 1/50 y DATA(2, -2, 2) + 1/50 y DATA(-2, 2, -1) + 1/50 y DATA(2, 2, 2) + + + 1/50 y DATA(1, 2, 2) - 1/50 y DATA(1, -2, -1) - 1/25 y DATA(1, 1, -1) + + + 1/25 y DATA(-1, -1, 1) + 1/50 y DATA(-2, 2, 2) - 1/25 y DATA(-2, 1, 2) + + - 1/50 y DATA(-2, -2, -2) + 1/25 y DATA(1, -1, 1) + 1/25 y DATA(-2, -1, 2) + + 211 + - 1/10 DATA(2, 0, 0) + 4/75 DATA(0, 1, -2) + ---- DATA(-2, 1, 1) + 3675 + + 211 + + 4/75 DATA(2, -1, 0) + ---- DATA(-1, 1, -2) + 1/175 x z DATA(2, -1, -2) + 3675 + + - 1/350 x z DATA(-1, -1, -2) + 1/175 x z DATA(-1, -2, -2) + + + 1/175 x z DATA(1, -2, 2) - 1/175 x z DATA(-1, -2, 2) + + - 2/175 x z DATA(-2, -2, 2) - 1/350 x z DATA(-2, -1, -1) + + - 1/175 x z DATA(2, -2, -1) - 1/350 x z DATA(1, -1, 2) + + + 1/350 x z DATA(-1, 1, 2) - 1/700 x z DATA(-1, 1, -1) + + + 1/700 x z DATA(-1, 1, 1) + 1/700 x z DATA(1, -1, -1) + + - 1/700 x z DATA(-1, -1, -1) + 1/175 x z DATA(1, 2, 2) + + + 2/175 x z DATA(2, 2, 2) + 1/175 x z DATA(-2, 2, -1) + + + 2/175 x z DATA(2, -2, 2) - 1/175 x z DATA(-1, 2, 2) + + - 1/175 x z DATA(2, 1, 2) - 1/350 x z DATA(-2, 1, -1) + + - 1/350 x z DATA(1, -2, -1) - 2/175 x z DATA(-2, 2, 2) + + + 1/700 x z DATA(-1, -1, 1) - 1/700 x z DATA(1, -1, 1) + + + 1/700 x z DATA(1, 1, -1) + 2/175 x z DATA(-2, -2, -2) + + - 1/175 x z DATA(1, -2, -2) - 2/175 x z DATA(2, -2, -2) + + + 1/350 x z DATA(1, -1, -2) - 1/175 x z DATA(-2, -1, -2) + + + 1/175 x z DATA(-2, -1, 2) + 1/175 x z DATA(-2, 1, 2) + + 2 2 + + 1/490 z DATA(-1, 1, -1) + 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DATA(0, 1, 1) + + 2 + - 1/245 x DATA(-2, -1, 0) + 1/100 x y DATA(-1, -2, 1) + + 529 + - ----- DATA(-2, -2, -2) - 1/25 x y DATA(-2, -1, 1) + 14700 + + - 1/25 x y DATA(2, 1, -2) + 1/50 x y DATA(-1, 1, -2) + + 529 + - ----- DATA(-2, 2, 2) + 1/25 x y DATA(-2, 1, 1) - 1/50 x y DATA(1, 1, 1) + 14700 + + 169 + - 1/100 x y DATA(-1, 2, -1) - ----- DATA(1, -2, -2) + 14700 + + 169 256 + - 1/300 DATA(0, -2, -2) - ----- DATA(-1, -2, -2) + ---- DATA(-2, -1, -2) + 14700 3675 + + - 1/50 x y DATA(2, -2, 1) + 1/25 x y DATA(2, -1, -1) + + 529 211 + - ----- DATA(2, -2, -2) + ---- DATA(1, -1, -2) + 4/75 DATA(0, -1, -2) + 14700 3675 + + 211 + + ---- DATA(-1, -1, -2) + 1/50 x y DATA(-2, -2, 1) + 3675 + + 33 256 + - 1/100 x y DATA(1, -2, 1) - --- DATA(-2, 0, -2) + ---- DATA(2, -1, -2) + 490 3675 + + - 1/10 DATA(0, 0, -2) - 9/98 DATA(-1, 0, -2) - 9/98 DATA(1, 0, -2) + +> coeffs_as_lc_of_data(%, posn_list_3d_size5); +bytes used=2248100268, alloc=14677376, time=361.15 +bytes used=2249100616, alloc=14677376, 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+bytes used=2269598032, alloc=14677376, time=363.09 +bytes used=2270598244, alloc=14677376, time=363.19 +bytes used=2271598372, alloc=14677376, time=363.30 +bytes used=2272602892, alloc=14677376, time=363.42 +bytes used=2273606100, alloc=14677376, time=363.53 +bytes used=2274628016, alloc=14677376, time=363.61 +bytes used=2275646028, alloc=14677376, time=363.69 +bytes used=2276664160, alloc=14677376, time=363.76 + 529 2 +[COEFF(-2, -2, -2) = 1/50 y z - ----- + 2/175 x z + 2/245 x - 2/175 x + 14700 + + 2 2 + + 2/245 z - 2/175 z + 1/50 x y - 1/50 y + 1/50 y , COEFF(-1, -2, -2) = + + 2 169 2 + 1/175 x z + 1/50 y z - 1/245 x + 1/100 x y - 1/175 x - ----- + 1/50 y + 14700 + + 2 + - 1/50 y - 2/175 z + 2/245 z , COEFF(0, -2, -2) = + + 2 2 2 + 1/50 y - 2/175 z - 2/245 x + 1/50 y z + 2/245 z - 1/300 - 1/50 y, + + 169 + COEFF(1, -2, -2) = - 1/100 x y + 1/175 x - 1/175 x z - 2/175 z - ----- + 14700 + + 2 2 2 + + 1/50 y z + 2/245 z - 1/245 x - 1/50 y + 1/50 y , COEFF(2, -2, -2) = + + 529 2 2 2 + - ----- + 2/245 x + 2/245 z - 2/175 x z - 1/50 y + 1/50 y + 1/50 y z + 14700 + + 2 + - 1/50 x y - 2/175 z + 2/175 x, COEFF(-2, -1, -2) = - 1/245 z - 1/25 y z + + 256 2 + + 1/25 y + 1/175 z + ---- + 1/175 x - 1/245 x - 1/25 x y - 1/175 x z + 3675 + + 2 2 + - 2/25 y , COEFF(-1, -1, -2) = 1/350 x + 1/175 z - 1/350 x z - 2/25 y + + 211 2 2 + + ---- - 1/245 z + 1/25 y - 1/25 y z + 1/490 x - 1/50 x y, + 3675 + + COEFF(0, -1, -2) = + + 2 2 2 + 1/175 z + 4/75 + 1/25 y + 1/245 x - 1/245 z - 1/25 y z - 2/25 y , + + 2 211 + COEFF(1, -1, -2) = 1/490 x + 1/50 x y + 1/175 z + 1/25 y - 1/25 y z + ---- + 3675 + + 2 2 + - 2/25 y - 1/350 x + 1/350 x z - 1/245 z , COEFF(2, -1, -2) = 1/175 x z + + 256 2 2 2 + + ---- - 1/245 x - 2/25 y - 1/245 z - 1/25 y z - 1/175 x + 1/25 x y + 3675 + + + 1/25 y + 1/175 z, COEFF(-2, 0, -2) = + + 2 2 33 2 + - 2/245 x + 2/175 z + 3/25 y - --- - 2/245 z - 2/175 x z + 2/175 x, + 490 + + COEFF(-1, 0, -2) = + + 2 2 2 + 1/175 x - 2/245 z + 2/175 z - 1/175 x z + 3/25 y + 1/245 x - 9/98, + + 2 2 2 + COEFF(0, 0, -2) = - 1/10 + 2/175 z - 2/245 z + 2/245 x + 3/25 y , + + COEFF(1, 0, -2) = + + 2 2 2 + - 1/175 x - 2/245 z + 1/175 x z - 9/98 + 3/25 y + 2/175 z + 1/245 x , + + COEFF(2, 0, -2) = + + 33 2 2 2 + - 2/175 x - --- - 2/245 z + 2/175 x z + 2/175 z + 3/25 y - 2/245 x , + 490 + + 2 2 + COEFF(-2, 1, -2) = 1/175 z - 1/245 z - 2/25 y - 1/25 y + 1/25 y z + + 2 256 + - 1/175 x z - 1/245 x + 1/175 x + ---- + 1/25 x y, COEFF(-1, 1, -2) = + 3675 + + 2 2 + 1/490 x - 1/350 x z + 1/50 x y + 1/350 x - 2/25 y + 1/25 y z - 1/25 y + + 2 211 + - 1/245 z + 1/175 z + ----, COEFF(0, 1, -2) = + 3675 + + 2 2 2 + - 1/25 y - 2/25 y + 1/175 z + 1/25 y z + 1/245 x - 1/245 z + 4/75, + + 2 211 + COEFF(1, 1, -2) = 1/490 x + ---- - 1/350 x - 1/50 x y - 1/25 y + 1/350 x z + 3675 + + 2 2 + + 1/25 y z - 2/25 y - 1/245 z + 1/175 z, COEFF(2, 1, -2) = - 1/25 y + + 2 2 256 2 + - 1/245 x - 1/245 z + ---- + 1/175 z + 1/175 x z - 1/175 x - 2/25 y + 3675 + + 2 + + 1/25 y z - 1/25 x y, COEFF(-2, 2, -2) = 2/245 x - 2/175 x - 1/50 y z + + 2 529 2 + + 1/50 y - ----- - 1/50 x y - 2/175 z + 1/50 y + 2/245 z + 2/175 x z, + 14700 + + 2 2 2 + COEFF(-1, 2, -2) = - 1/100 x y - 1/50 y z + 1/50 y - 1/245 x + 2/245 z + + 169 + + 1/50 y - 1/175 x + 1/175 x z - ----- - 2/175 z, COEFF(0, 2, -2) = + 14700 + + 2 2 2 + - 2/175 z - 2/245 x - 1/300 + 1/50 y + 2/245 z + 1/50 y - 1/50 y z, + + 2 169 + COEFF(1, 2, -2) = 2/245 z - 1/175 x z - ----- + 1/175 x - 2/175 z + 14700 + + 2 2 + - 1/50 y z + 1/100 x y - 1/245 x + 1/50 y + 1/50 y , COEFF(2, 2, -2) = + + 2 2 + - 2/175 z - 1/50 y z - 2/175 x z + 2/175 x + 2/245 x + 1/50 x y + 1/50 y + + 2 529 + + 1/50 y + 2/245 z - -----, COEFF(-2, -2, -1) = 1/100 y z - 1/50 y + 14700 + + 2 2 169 + + 1/50 x y + 1/50 y - 1/245 z + 1/175 x z - 2/175 x - 1/175 z - ----- + 14700 + + 2 2 2 + + 2/245 x , COEFF(-1, -2, -1) = - 1/245 x - 1/245 z + 1/100 y z + + 2 191 + + 1/50 y - 1/175 x + 1/350 x z - 1/175 z + 1/100 x y + ----- - 1/50 y, + 14700 + + COEFF(0, -2, -1) = + + 2 2 311 2 + - 1/175 z - 1/245 z - 2/245 x + ----- - 1/50 y + 1/50 y + 1/100 y z, + 14700 + + 2 + COEFF(1, -2, -1) = - 1/245 x - 1/175 z - 1/100 x y - 1/50 y + 1/100 y z + + 2 2 191 + + 1/50 y - 1/350 x z - 1/245 z + ----- + 1/175 x, COEFF(2, -2, -1) = + 14700 + + 2 169 2 + - 1/50 y - 1/175 z - 1/175 x z + 2/245 x + 2/175 x - ----- - 1/245 z + 14700 + + 2 + + 1/100 y z - 1/50 x y + 1/50 y , COEFF(-2, -1, -1) = - 1/50 y z + + 2 2 211 2 + - 1/245 x + 1/490 z + ---- + 1/350 z - 2/25 y - 1/350 x z + 1/175 x + 3675 + + 2 + + 1/25 y - 1/25 x y, COEFF(-1, -1, -1) = - 1/50 y z + 1/350 x + 1/490 z + + 2 166 2 + + 1/350 z + 1/25 y - 1/700 x z - 2/25 y + ---- - 1/50 x y + 1/490 x , + 3675 + + COEFF(0, -1, -1) = + + 2 2 2 151 + - 1/50 y z + 1/245 x + 1/25 y + 1/490 z - 2/25 y + 1/350 z + ----, + 3675 + + 2 2 + COEFF(1, -1, -1) = - 1/50 y z + 1/490 x + 1/700 x z + 1/350 z - 2/25 y + + 166 2 + + 1/50 x y + 1/25 y + ---- + 1/490 z - 1/350 x, COEFF(2, -1, -1) = + 3675 + + 2 2 211 + - 2/25 y + 1/490 z + 1/25 y + 1/350 x z - 1/175 x + 1/350 z + ---- + 3675 + + 2 + + 1/25 x y - 1/245 x - 1/50 y z, COEFF(-2, 0, -1) = + + 2 2 2 + 3/25 y - 9/98 + 1/245 z - 1/175 x z - 2/245 x + 2/175 x + 1/175 z, + + COEFF(-1, 0, -1) = + + 2 2 57 2 + 1/175 z + 3/25 y + 1/245 z + 1/175 x - --- + 1/245 x - 1/350 x z, + 490 + + 61 2 2 2 + COEFF(0, 0, -1) = - --- + 2/245 x + 1/175 z + 3/25 y + 1/245 z , + 490 + + COEFF(1, 0, -1) = + + 2 57 2 2 + 1/175 z + 1/245 x - --- + 3/25 y - 1/175 x + 1/350 x z + 1/245 z , + 490 + + COEFF(2, 0, -1) = + + 2 2 2 + - 2/175 x - 2/245 x + 1/245 z + 1/175 z + 1/175 x z + 3/25 y - 9/98, + + 2 2 211 + COEFF(-2, 1, -1) = 1/490 z - 2/25 y + ---- + 1/50 y z - 1/350 x z + 3675 + + 2 + + 1/175 x + 1/25 x y - 1/25 y - 1/245 x + 1/350 z, COEFF(-1, 1, -1) = + + 2 166 + 1/490 z + ---- + 1/50 x y + 1/350 z + 1/350 x - 1/25 y - 1/700 x z + 3675 + + 2 2 + - 2/25 y + 1/50 y z + 1/490 x , COEFF(0, 1, -1) = + + 2 151 2 2 + - 1/25 y - 2/25 y + 1/50 y z + ---- + 1/350 z + 1/490 z + 1/245 x , + 3675 + + 2 2 2 + COEFF(1, 1, -1) = 1/490 z + 1/700 x z + 1/50 y z - 2/25 y + 1/490 x + + 166 + - 1/25 y + 1/350 z - 1/350 x + ---- - 1/50 x y, COEFF(2, 1, -1) = 1/350 z + 3675 + + 2 2 + + 1/50 y z - 1/25 x y - 1/25 y + 1/490 z - 1/175 x + 1/350 x z - 2/25 y + + 2 211 + - 1/245 x + ----, COEFF(-2, 2, -1) = - 2/175 x - 1/100 y z - 1/50 x y + 3675 + + 169 2 2 2 + + 1/175 x z - ----- - 1/175 z + 1/50 y + 1/50 y - 1/245 z + 2/245 x , + 14700 + + 191 2 + COEFF(-1, 2, -1) = ----- - 1/175 x - 1/175 z - 1/100 y z - 1/245 z + 14700 + + 2 2 + - 1/245 x + 1/50 y + 1/50 y + 1/350 x z - 1/100 x y, COEFF(0, 2, -1) = + + 2 2 2 311 + 1/50 y - 1/245 z - 1/100 y z - 2/245 x + 1/50 y - 1/175 z + -----, + 14700 + + 191 2 + COEFF(1, 2, -1) = 1/175 x + 1/100 x y + ----- - 1/350 x z + 1/50 y + 14700 + + 2 2 + - 1/245 x - 1/245 z - 1/175 z + 1/50 y - 1/100 y z, COEFF(2, 2, -1) = + + 2 2 2 + 2/245 x + 1/50 x y - 1/245 z + 1/50 y - 1/100 y z + 1/50 y - 1/175 x z + + 169 + + 2/175 x - ----- - 1/175 z, COEFF(-2, -2, 0) = + 14700 + + 2 2 2 + 1/50 y - 1/50 y - 2/175 x + 1/50 x y + 2/245 x - 1/300 - 2/245 z , + + COEFF(-1, -2, 0) = + + 2 311 2 2 + - 1/50 y - 1/245 x + ----- + 1/50 y - 1/175 x + 1/100 x y - 2/245 z , + 14700 + + 2 2 431 2 + COEFF(0, -2, 0) = - 2/245 z - 2/245 x + ----- - 1/50 y + 1/50 y , + 14700 + + COEFF(1, -2, 0) = + + 2 311 2 2 + - 1/245 x + ----- - 2/245 z - 1/100 x y - 1/50 y + 1/175 x + 1/50 y , + 14700 + + COEFF(2, -2, 0) = + + 2 2 2 + 1/50 y + 2/175 x - 1/50 x y - 1/50 y + 2/245 x - 2/245 z - 1/300, + + COEFF(-2, -1, 0) = + + 2 2 2 + - 1/25 x y + 1/245 z + 1/175 x - 2/25 y + 1/25 y - 1/245 x + 4/75, + + COEFF(-1, -1, 0) = + + 2 151 2 2 + 1/245 z + 1/25 y + ---- + 1/490 x + 1/350 x - 2/25 y - 1/50 x y, + 3675 + + 2 2 136 2 + COEFF(0, -1, 0) = 1/25 y + 1/245 x - 2/25 y + ---- + 1/245 z , + 3675 + + COEFF(1, -1, 0) = + + 2 2 151 2 + - 1/350 x + 1/245 z - 2/25 y + 1/50 x y + 1/25 y + ---- + 1/490 x , + 3675 + + COEFF(2, -1, 0) = + + 2 2 2 + 4/75 + 1/25 y + 1/25 x y + 1/245 z - 1/175 x - 2/25 y - 1/245 x , + + 2 2 2 + COEFF(-2, 0, 0) = 2/245 z + 3/25 y + 2/175 x - 1/10 - 2/245 x , + + 2 61 2 2 + COEFF(-1, 0, 0) = 1/245 x - --- + 1/175 x + 3/25 y + 2/245 z , + 490 + + 2 2 2 13 + COEFF(0, 0, 0) = 3/25 y + 2/245 z + 2/245 x - --, + 98 + + 2 61 2 2 + COEFF(1, 0, 0) = 1/245 x - --- - 1/175 x + 2/245 z + 3/25 y , + 490 + + 2 2 2 + COEFF(2, 0, 0) = - 1/10 + 3/25 y - 2/175 x + 2/245 z - 2/245 x , + + COEFF(-2, 1, 0) = + + 2 2 2 + 1/245 z + 1/175 x + 1/25 x y - 2/25 y - 1/25 y - 1/245 x + 4/75, + + COEFF(-1, 1, 0) = + + 2 2 2 151 + 1/350 x + 1/245 z - 1/25 y + 1/50 x y - 2/25 y + 1/490 x + ----, + 3675 + + 136 2 2 2 + COEFF(0, 1, 0) = ---- - 1/25 y + 1/245 x - 2/25 y + 1/245 z , + 3675 + + COEFF(1, 1, 0) = + + 2 151 2 2 + - 2/25 y - 1/25 y + ---- + 1/245 z - 1/50 x y - 1/350 x + 1/490 x , + 3675 + + COEFF(2, 1, 0) = + + 2 2 2 + 4/75 - 1/175 x + 1/245 z - 1/25 y - 2/25 y - 1/25 x y - 1/245 x , + + COEFF(-2, 2, 0) = + + 2 2 2 + - 1/300 - 1/50 x y - 2/175 x + 2/245 x + 1/50 y + 1/50 y - 2/245 z , + + COEFF(-1, 2, 0) = + + 311 2 2 2 + ----- - 1/100 x y + 1/50 y + 1/50 y - 1/175 x - 1/245 x - 2/245 z , + 14700 + + 2 431 2 2 + COEFF(0, 2, 0) = 1/50 y - 2/245 x + ----- + 1/50 y - 2/245 z , + 14700 + + COEFF(1, 2, 0) = + + 2 311 2 2 + - 2/245 z + 1/175 x + ----- + 1/100 x y + 1/50 y - 1/245 x + 1/50 y , + 14700 + + COEFF(2, 2, 0) = + + 2 2 2 + 1/50 y + 1/50 y - 2/245 z + 2/175 x + 2/245 x + 1/50 x y - 1/300, + + 169 2 2 + COEFF(-2, -2, 1) = - ----- - 1/50 y - 1/245 z - 1/100 y z + 1/50 y + 14700 + + 2 + - 1/175 x z - 2/175 x + 2/245 x + 1/50 x y + 1/175 z, COEFF(-1, -2, 1) = + + 2 2 2 + - 1/350 x z - 1/245 x - 1/245 z + 1/50 y - 1/175 x - 1/50 y - 1/100 y z + + 191 + + 1/175 z + 1/100 x y + -----, COEFF(0, -2, 1) = + 14700 + + 2 311 2 2 + 1/50 y + ----- + 1/175 z - 1/245 z - 1/100 y z - 2/245 x - 1/50 y, + 14700 + + 2 2 2 191 + COEFF(1, -2, 1) = 1/50 y + 1/175 z - 1/245 z - 1/245 x + 1/175 x + ----- + 14700 + + - 1/50 y + 1/350 x z - 1/100 y z - 1/100 x y, COEFF(2, -2, 1) = 1/175 z + + 2 2 + - 1/50 y - 1/100 y z + 1/50 y + 2/175 x - 1/245 z - 1/50 x y + 1/175 x z + + 169 2 211 + - ----- + 2/245 x , COEFF(-2, -1, 1) = ---- + 1/350 x z + 1/50 y z + 14700 3675 + + 2 2 2 + - 1/350 z - 1/245 x + 1/490 z - 1/25 x y - 2/25 y + 1/175 x + 1/25 y, + + 2 2 + COEFF(-1, -1, 1) = 1/25 y - 2/25 y + 1/350 x - 1/350 z + 1/490 x + + 166 2 + + 1/700 x z + ---- + 1/490 z - 1/50 x y + 1/50 y z, COEFF(0, -1, 1) = + 3675 + + 2 2 2 151 + 1/50 y z + 1/490 z + 1/245 x - 1/350 z - 2/25 y + 1/25 y + ----, + 3675 + + 2 2 + COEFF(1, -1, 1) = - 1/700 x z - 1/350 z - 2/25 y + 1/490 x + 1/50 y z + + 2 166 + + 1/490 z + 1/50 x y + ---- + 1/25 y - 1/350 x, COEFF(2, -1, 1) = + 3675 + + 2 2 2 + 1/25 x y - 1/245 x + 1/490 z - 1/350 x z - 2/25 y - 1/350 z + 1/25 y + + 211 + - 1/175 x + 1/50 y z + ----, COEFF(-2, 0, 1) = + 3675 + + 2 2 2 + - 1/175 z - 9/98 + 1/175 x z - 2/245 x + 1/245 z + 2/175 x + 3/25 y , + + COEFF(-1, 0, 1) = + + 2 2 2 57 + - 1/175 z + 1/245 x + 1/175 x + 3/25 y + 1/245 z - --- + 1/350 x z, + 490 + + 2 2 2 61 + COEFF(0, 0, 1) = 1/245 z + 2/245 x + 3/25 y - 1/175 z - ---, + 490 + + COEFF(1, 0, 1) = + + 57 2 2 2 + - --- - 1/350 x z + 1/245 z + 3/25 y - 1/175 z + 1/245 x - 1/175 x, + 490 + + COEFF(2, 0, 1) = + + 2 2 2 + - 1/175 x z + 3/25 y - 2/175 x - 9/98 - 2/245 x + 1/245 z - 1/175 z, + + 211 + COEFF(-2, 1, 1) = 1/350 x z - 1/25 y + ---- - 1/50 y z + 1/175 x + 1/25 x y + 3675 + + 2 2 2 + - 1/350 z - 2/25 y + 1/490 z - 1/245 x , COEFF(-1, 1, 1) = 1/700 x z + + 166 2 2 + + ---- + 1/490 x + 1/50 x y - 1/350 z + 1/350 x - 1/25 y + 1/490 z + 3675 + + 2 + - 1/50 y z - 2/25 y , COEFF(0, 1, 1) = + + 2 2 2 151 + - 1/350 z + 1/490 z - 1/25 y - 1/50 y z + 1/245 x - 2/25 y + ----, + 3675 + + 2 166 2 + COEFF(1, 1, 1) = - 2/25 y + ---- - 1/350 x - 1/350 z + 1/490 x - 1/50 y z + 3675 + + 2 + - 1/700 x z + 1/490 z - 1/25 y - 1/50 x y, COEFF(2, 1, 1) = - 1/25 x y + + 2 2 2 + - 1/245 x + 1/490 z - 1/350 z - 2/25 y - 1/25 y - 1/175 x - 1/350 x z + + 211 2 + - 1/50 y z + ----, COEFF(-2, 2, 1) = - 2/175 x - 1/50 x y + 2/245 x + 3675 + + 169 2 2 + - ----- + 1/175 z + 1/50 y + 1/50 y - 1/175 x z - 1/245 z + 1/100 y z, + 14700 + + 191 2 + COEFF(-1, 2, 1) = ----- + 1/175 z - 1/245 z - 1/100 x y + 1/100 y z + 14700 + + 2 2 + + 1/50 y - 1/175 x - 1/245 x - 1/350 x z + 1/50 y, COEFF(0, 2, 1) = + + 2 311 2 2 + 1/175 z - 2/245 x + ----- + 1/100 y z + 1/50 y + 1/50 y - 1/245 z , + 14700 + + 2 191 + COEFF(1, 2, 1) = - 1/245 z + 1/350 x z + 1/50 y + ----- + 1/175 x + 14700 + + 2 2 + + 1/100 x y - 1/245 x + 1/175 z + 1/50 y + 1/100 y z, COEFF(2, 2, 1) = + + 169 2 2 + 1/50 y - ----- + 2/245 x + 1/175 z + 1/100 y z - 1/245 z + 2/175 x + 14700 + + 2 2 + + 1/50 y + 1/175 x z + 1/50 x y, COEFF(-2, -2, 2) = 1/50 y + 2/175 z + + 2 529 2 + - 2/175 x z + 2/245 x - 2/175 x - 1/50 y - ----- - 1/50 y z + 2/245 z + 14700 + + 169 2 + + 1/50 x y, COEFF(-1, -2, 2) = - ----- - 1/175 x - 1/50 y + 2/245 z + 14700 + + 2 2 + - 1/50 y z + 1/50 y - 1/245 x + 2/175 z - 1/175 x z + 1/100 x y, + + COEFF(0, -2, 2) = + + 2 2 2 + 1/50 y - 1/50 y z - 1/50 y - 1/300 + 2/245 z + 2/175 z - 2/245 x , + + 2 + COEFF(1, -2, 2) = 1/175 x + 2/245 z - 1/100 x y - 1/50 y z + 1/175 x z + + 2 169 2 + + 1/50 y - 1/50 y - ----- + 2/175 z - 1/245 x , COEFF(2, -2, 2) = + 14700 + + 2 2 + - 1/50 x y + 2/175 x z - 1/50 y z + 2/175 x + 2/245 x + 2/175 z + 1/50 y + + 529 2 2 + - 1/50 y - ----- + 2/245 z , COEFF(-2, -1, 2) = - 2/25 y - 1/175 z + 14700 + + 2 2 256 + + 1/175 x + 1/25 y z + 1/175 x z - 1/245 z - 1/25 x y - 1/245 x + ---- + 3675 + + 2 2 211 + + 1/25 y, COEFF(-1, -1, 2) = 1/25 y - 1/245 z + 1/490 x + ---- + 1/350 x + 3675 + + 2 + + 1/25 y z - 1/50 x y - 1/175 z - 2/25 y + 1/350 x z, COEFF(0, -1, 2) = + + 2 2 2 + - 1/175 z + 4/75 - 1/245 z + 1/25 y + 1/245 x + 1/25 y z - 2/25 y , + + 2 211 2 + COEFF(1, -1, 2) = 1/490 x + ---- - 1/350 x - 1/175 z - 2/25 y + 1/25 y + 3675 + + 2 + - 1/245 z + 1/50 x y + 1/25 y z - 1/350 x z, COEFF(2, -1, 2) = - 1/175 x + + 2 2 + + 1/25 y - 1/175 z + 1/25 x y - 2/25 y - 1/245 z + 1/25 y z - 1/175 x z + + 2 256 + - 1/245 x + ----, COEFF(-2, 0, 2) = + 3675 + + 33 2 2 2 + - --- + 2/175 x z - 2/245 z - 2/175 z - 2/245 x + 3/25 y + 2/175 x, + 490 + + COEFF(-1, 0, 2) = + + 2 2 2 + 1/245 x - 9/98 + 1/175 x - 2/175 z + 3/25 y + 1/175 x z - 2/245 z , + + 2 2 2 + COEFF(0, 0, 2) = - 1/10 - 2/245 z + 2/245 x - 2/175 z + 3/25 y , + + COEFF(1, 0, 2) = + + 2 2 2 + - 1/175 x + 3/25 y - 2/245 z + 1/245 x - 2/175 z - 9/98 - 1/175 x z, + + COEFF(2, 0, 2) = + + 33 2 2 2 + - 2/175 x - --- - 2/245 x - 2/175 z - 2/175 x z + 3/25 y - 2/245 z , + 490 + + 2 2 2 + COEFF(-2, 1, 2) = 1/175 x - 1/175 z - 1/245 z - 2/25 y - 1/245 x + + 256 + + 1/175 x z - 1/25 y z + ---- - 1/25 y + 1/25 x y, COEFF(-1, 1, 2) = + 3675 + + 2 2 + - 1/25 y z - 1/25 y + 1/490 x + 1/350 x + 1/350 x z - 2/25 y + 1/50 x y + + 2 211 + - 1/245 z + ---- - 1/175 z, COEFF(0, 1, 2) = + 3675 + + 2 2 2 + 4/75 - 1/175 z - 2/25 y - 1/245 z - 1/25 y + 1/245 x - 1/25 y z, + + 2 2 + COEFF(1, 1, 2) = - 1/25 y - 2/25 y - 1/350 x z - 1/175 z - 1/245 z + + 211 2 + - 1/25 y z + ---- + 1/490 x - 1/350 x - 1/50 x y, COEFF(2, 1, 2) = + 3675 + + 2 2 2 + - 1/175 x z - 1/245 x - 2/25 y - 1/175 x - 1/25 x y - 1/25 y - 1/245 z + + 256 2 2 + - 1/25 y z + ---- - 1/175 z, COEFF(-2, 2, 2) = 2/245 x + 1/50 y + 3675 + + 2 529 + + 2/245 z - 2/175 x z - 2/175 x + 2/175 z - ----- + 1/50 y z + 1/50 y + 14700 + + 2 169 + - 1/50 x y, COEFF(-1, 2, 2) = - 1/175 x - 1/245 x + 2/175 z - ----- + 14700 + + 2 2 + + 1/50 y + 1/50 y - 1/100 x y + 2/245 z + 1/50 y z - 1/175 x z, + + COEFF(0, 2, 2) = + + 2 2 2 + - 1/300 + 2/175 z + 1/50 y z + 2/245 z - 2/245 x + 1/50 y + 1/50 y, + + 169 2 + COEFF(1, 2, 2) = - ----- + 1/175 x + 2/245 z + 1/175 x z + 2/175 z + 14700 + + 2 2 + + 1/50 y + 1/100 x y + 1/50 y z + 1/50 y - 1/245 x , COEFF(2, 2, 2) = + + 529 2 + 1/50 x y - ----- + 1/50 y z + 2/175 z + 2/245 x + 2/175 x z + 2/175 x + 14700 + + 2 2 + + 1/50 y + 1/50 y + 2/245 z ] + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dyy.compute.c"); +bytes used=2277664824, alloc=14677376, time=363.84 +bytes used=2278665472, alloc=14677376, time=363.91 +bytes used=2279665724, alloc=14677376, time=364.00 +bytes used=2280665892, alloc=14677376, time=364.09 +bytes used=2281666500, alloc=14677376, time=364.73 +bytes used=2282667048, alloc=14677376, time=365.37 +bytes used=2283667452, alloc=14677376, time=366.02 +bytes used=2284667680, alloc=14677376, time=366.67 +bytes used=2285667988, alloc=14677376, time=367.31 +bytes used=2286668148, alloc=14677376, time=367.71 +bytes used=2287668324, alloc=14677376, time=367.80 +bytes used=2288668636, alloc=14677376, time=367.88 +bytes used=2289718228, alloc=14677376, time=367.97 +bytes used=2290736504, alloc=14677376, time=368.05 +bytes used=2291743216, alloc=14677376, time=368.13 +bytes used=2292743412, alloc=14677376, time=368.23 +bytes used=2293743628, alloc=14677376, time=368.64 +bytes used=2294743868, alloc=14677376, time=369.93 +bytes used=2295744024, alloc=14677376, time=370.31 +bytes used=2296744280, alloc=14677376, time=370.48 +bytes used=2297744452, alloc=14677376, time=370.55 +bytes used=2298744792, alloc=14677376, time=370.61 +bytes used=2299744976, alloc=14677376, time=370.68 +bytes used=2300745236, alloc=14677376, time=370.75 +bytes used=2301745392, alloc=14677376, time=370.82 +bytes used=2302745968, alloc=14677376, time=370.89 +bytes used=2303746284, alloc=14677376, time=370.96 +bytes used=2304746684, alloc=14677376, time=371.03 +bytes used=2305746880, alloc=14677376, time=371.11 +bytes used=2306747144, alloc=14677376, time=371.18 +bytes used=2307757728, alloc=14677376, time=371.29 +bytes used=2308758812, alloc=14677376, time=371.40 +bytes used=2309764812, alloc=14677376, time=371.49 +bytes used=2310765036, alloc=14677376, time=371.60 +bytes used=2311767532, alloc=14677376, time=371.71 +bytes used=2312767724, alloc=14677376, time=371.82 +bytes used=2313767884, alloc=14677376, time=371.93 +bytes used=2314768488, alloc=14677376, time=372.04 +bytes used=2315768704, alloc=14677376, time=372.17 +bytes used=2316768904, alloc=14677376, time=372.29 +bytes used=2317769812, alloc=14677376, time=372.41 +bytes used=2318771472, alloc=14677376, time=372.52 +bytes used=2319771632, alloc=14677376, time=372.61 +bytes used=2320771824, alloc=14677376, time=374.40 +bytes used=2321772048, alloc=14677376, time=375.20 +bytes used=2322772228, alloc=14677376, time=375.66 +bytes used=2323772400, alloc=14677376, time=375.75 +bytes used=2324772688, alloc=14677376, time=375.82 +bytes used=2325773124, alloc=14677376, time=375.89 +bytes used=2326773380, alloc=14677376, time=375.97 +bytes used=2327773564, alloc=14677376, time=376.04 +bytes used=2328773824, alloc=14677376, time=376.11 +bytes used=2329774216, alloc=14677376, time=376.18 +bytes used=2330774368, alloc=14677376, time=376.25 +bytes used=2331774836, alloc=14677376, time=376.32 +bytes used=2332775132, alloc=14677376, time=376.39 +bytes used=2333775344, alloc=14677376, time=376.49 +bytes used=2334789156, alloc=14677376, time=376.66 +bytes used=2335803696, alloc=14677376, time=376.80 +bytes used=2336803852, alloc=14677376, time=376.92 +bytes used=2337804444, alloc=14677376, time=377.02 +bytes used=2338804636, alloc=14677376, time=378.91 +bytes used=2339804824, alloc=14677376, time=380.01 +bytes used=2340804984, alloc=14677376, time=380.56 +bytes used=2341805160, alloc=14677376, time=380.65 +bytes used=2342805368, alloc=14677376, time=380.73 +bytes used=2343805564, alloc=14677376, time=380.80 +bytes used=2344805980, alloc=14677376, time=380.87 +bytes used=2345806280, alloc=14677376, time=380.95 +bytes used=2346806712, alloc=14677376, time=381.02 +bytes used=2347807072, alloc=14677376, time=381.16 +bytes used=2348807320, alloc=14677376, time=381.61 +bytes used=2349807620, alloc=14677376, time=383.63 +bytes used=2350807796, alloc=14677376, time=384.39 +bytes used=2351808056, alloc=14677376, time=384.86 +bytes used=2352808220, alloc=14677376, time=384.93 +bytes used=2353808396, alloc=14677376, time=385.05 +> +# d^2/dydz +> simplify( diff(interp_3d_cube_order4_smooth0,y,z) ); +bytes used=2354808856, alloc=14677376, time=385.17 +bytes used=2355839772, alloc=14677376, time=385.25 +bytes used=2356839944, alloc=14677376, time=385.32 +bytes used=2357840360, alloc=14677376, time=385.40 +bytes used=2358840484, alloc=14677376, time=385.49 +bytes used=2359840748, alloc=14677376, time=385.57 +bytes used=2360840916, alloc=14677376, time=385.64 +bytes used=2361841124, alloc=14677376, time=385.73 +bytes used=2362841324, alloc=14677376, time=385.80 + 107 167 +- ---- DATA(-2, -2, 1) + 1/245 y z DATA(1, -1, -1) - ---- DATA(1, -2, 1) + 7000 7000 + + 187 187 + + 1/245 y z DATA(-1, -1, -1) - ---- DATA(0, -2, 1) - ---- DATA(0, 2, -1) + 7000 7000 + + 167 187 + - ---- DATA(-1, -2, 1) - ---- DATA(0, -1, 2) + 1/245 y z DATA(1, 1, -1) + 7000 7000 + + + 1/245 y z DATA(-1, 1, -1) + 1/245 y z DATA(-1, 1, 1) + + 229 107 + - ----- DATA(-2, -1, 1) - ---- DATA(2, -2, 1) - 1/500 x DATA(-1, -2, -1) + 10500 7000 + + 17 + - ---- DATA(0, 2, 2) - 1/500 x DATA(-2, 1, 1) + 1/1000 x DATA(1, 1, 1) + 5250 + + + 1/500 x DATA(-1, 2, -1) - 1/500 x DATA(2, 1, -1) + + - 1/250 x DATA(2, 2, -1) - 1/500 x DATA(1, 2, -1) + + + 1/500 x DATA(-1, -1, 2) + 1/500 x DATA(1, 2, 1) - 1/125 x DATA(2, 2, -2) + + - 1/500 x DATA(2, -1, 1) - 1/500 x DATA(-1, 2, 1) + + - 1/250 x DATA(-2, -2, -1) - 1/500 x DATA(1, 1, -2) + + - 1/250 x DATA(1, 2, -2) + 1/125 x DATA(-2, 2, -2) + + 229 289 + - 1/250 x DATA(-2, 2, 1) + ----- DATA(2, -1, -1) + ----- DATA(0, 1, 1) + 10500 10500 + + 137 + + ---- DATA(1, 1, 1) - 1/350 x z DATA(-2, -1, 1) + 5250 + + + 1/350 x z DATA(2, -1, -1) + 1/175 x z DATA(2, -2, 1) + + - 1/175 x z DATA(-2, -2, 1) + 1/350 x z DATA(1, -2, 1) + + - 1/350 x z DATA(-1, -2, 1) - 1/175 x z DATA(2, 2, -1) + + - 1/350 x z DATA(2, 1, -1) + 1/350 x z DATA(-1, 2, -1) + + - 1/700 x z DATA(1, 1, 1) + 1/350 x z DATA(-2, 1, 1) + + - 1/350 x z DATA(-1, 1, -2) + 1/175 x z DATA(2, 1, -2) + + - 1/175 x z DATA(2, 2, 1) - 1/175 x z DATA(-1, 2, -2) + + + 1/350 x z DATA(1, 1, -2) + 1/175 x z DATA(-2, 2, 1) + + - 2/175 x z DATA(-2, 2, -2) - 1/350 x z DATA(-1, -2, -1) + + + 1/175 x z DATA(1, 2, -2) - 1/175 x z DATA(-2, 1, -2) + + - 1/350 x z DATA(1, 2, -1) + 1/350 x z DATA(-1, 2, 1) + + + 2/175 x z DATA(2, 2, -2) - 1/350 x z DATA(1, 2, 1) + + + 1/350 x z DATA(-1, -1, 2) - 1/350 x z DATA(2, 1, 1) + + 107 + + 1/350 x z DATA(2, -1, 1) - ---- DATA(2, 2, -1) - 1/350 x y DATA(1, 1, 2) + 7000 + + - 1/175 x y DATA(2, -1, 2) - 1/175 x z DATA(-2, -2, -1) + + - 1/350 x y DATA(-2, -1, -1) - 1/350 x y DATA(1, -1, 2) + + + 1/350 x y DATA(-1, 1, 2) - 1/175 x y DATA(2, -2, -1) + + - 1/175 x y DATA(2, 1, 2) - 1/350 x y DATA(-2, 1, -1) + + - 1/350 x y DATA(1, -2, -1) - 2/175 x y DATA(-2, -2, 2) + + + 1/700 x y DATA(1, -1, -1) - 1/700 x y DATA(-1, -1, -1) + + + 1/175 x y DATA(1, 2, 2) + 2/175 x y DATA(2, 2, 2) + + + 1/175 x y DATA(-2, 2, -1) + 2/175 x y DATA(2, -2, 2) + + - 1/175 x y DATA(-1, 2, 2) + 1/700 x y DATA(-1, -1, 1) + + - 1/700 x y DATA(1, -1, 1) + 1/700 x y DATA(1, 1, -1) + + - 1/700 x y DATA(-1, 1, -1) + 1/700 x y DATA(-1, 1, 1) + + - 2/175 x y DATA(-2, 2, 2) + 2/175 x y DATA(-2, -2, -2) + + + 1/175 x y DATA(-2, 1, 2) - 2/175 x y DATA(2, -2, -2) + + - 1/175 x y DATA(-2, -1, -2) + 1/175 x y DATA(-2, -1, 2) + + + 1/350 x y DATA(1, -1, -2) + 1/175 x y DATA(2, -1, -2) + + - 1/350 x y DATA(-1, -1, -2) + 1/175 x y DATA(-1, -2, -2) + + 2 + - 1/175 x y DATA(1, -2, -2) + 1/175 x DATA(2, 2, 2) + + 2 + - 1/350 x DATA(1, 2, 2) + 1/250 x DATA(2, 1, 2) - 1/125 x DATA(2, -2, 2) + + 2 + + 1/250 x DATA(-2, 2, -1) - 1/175 x DATA(2, -2, 2) + + 2 + - 1/350 x DATA(-2, 2, -1) - 1/250 x DATA(-1, 2, 2) + + + 1/250 x DATA(-1, -2, 2) - 1/250 x DATA(2, -1, 2) + 1/500 x DATA(1, 1, 2) + + - 1/500 x DATA(-1, 1, 2) - 1/500 x DATA(1, -1, 2) + + + 1/250 x DATA(2, -2, -1) - 1/500 x DATA(-2, -1, -1) + + + 1/125 x DATA(-2, -2, 2) + 1/500 x DATA(1, -2, -1) + + 167 + + 1/500 x DATA(-2, 1, -1) - 1/250 x DATA(1, -2, 2) - ---- DATA(1, 2, -1) + 7000 + + + 1/250 x DATA(1, -2, -2) - 1/500 x DATA(-1, -1, -2) + + - 1/1000 x DATA(1, -1, 1) + 1/125 x DATA(2, 2, 2) + 1/250 x DATA(1, 2, 2) + + - 1/1000 x DATA(-1, -1, -1) + 1/1000 x DATA(1, -1, -1) + + - 1/1000 x DATA(-1, 1, 1) + 1/1000 x DATA(-1, 1, -1) + + - 1/1000 x DATA(1, 1, -1) - 1/250 x DATA(-1, -2, -2) + + - 1/125 x DATA(-2, -2, -2) - 1/250 x DATA(-2, 1, 2) + + + 1/250 x DATA(-2, -1, 2) - 1/250 x DATA(-2, -1, -2) + + + 1/500 x DATA(1, -1, -2) + 1/125 x DATA(2, -2, -2) + + 107 + - 1/125 x DATA(-2, 2, 2) - ---- DATA(-2, 1, -2) + 1/250 x DATA(2, -1, -2) + 7000 + + 167 + + 1/1000 x DATA(-1, -1, 1) - ---- DATA(-1, 2, -1) + 7000 + + 2 2 + - 1/350 x DATA(-2, -2, 1) - 1/350 x DATA(2, -2, 1) + + 2 2 + + 1/700 x DATA(1, -2, 1) - 1/1400 x DATA(1, 1, 1) + + 2 2 + + 1/700 x DATA(-1, 2, -1) - 1/700 x DATA(2, 1, -1) + + 2 2 + + 1/700 x DATA(2, -1, -1) + 1/700 x DATA(-1, -2, 1) + + 2 2 + - 1/700 x DATA(-2, -1, 1) - 1/350 x DATA(2, 1, -2) + + 2 2 + + 1/700 x DATA(1, 1, -2) + 1/350 x DATA(-1, 2, -2) + + 2 2 + + 1/350 x DATA(2, 2, 1) - 1/350 x DATA(2, 2, -1) + + 2 2 + - 1/350 x DATA(-2, 1, -2) + 1/350 x DATA(1, 2, -2) + + 2 2 + - 1/700 x DATA(-1, -2, -1) - 1/175 x DATA(-2, 2, -2) + + 2 2 + + 1/700 x DATA(1, 2, -1) + 1/700 x DATA(-1, 1, -2) + + 2 2 + + 1/700 x DATA(-2, 1, 1) - 1/700 x DATA(1, 1, 2) + + 2 2 + - 1/700 x DATA(-1, 1, 2) + 1/700 x DATA(1, -1, 2) + + 2 2 + + 1/350 x DATA(2, -2, -1) + 1/700 x DATA(-2, -1, -1) + + 2 2 + + 1/700 x DATA(2, 1, 1) + 1/700 x DATA(-1, -1, 2) + + 2 2 + - 1/700 x DATA(1, 2, 1) - 1/175 x DATA(2, 2, -2) + + 2 2 + - 1/700 x DATA(2, -1, 1) - 1/700 x DATA(-1, 2, 1) + + 2 2 + + 1/350 x DATA(-2, -2, -1) + 1/350 x DATA(-1, -2, 2) + + 2 2 + + 1/350 x DATA(1, -2, 2) + 1/350 x DATA(-2, 2, 1) + + 2 2 + + 1/1400 x DATA(-1, -1, 1) + 1/175 x DATA(-2, -2, -2) + + 2 2 + - 1/1400 x DATA(1, -1, -1) - 1/175 x DATA(-2, -2, 2) + + 2 2 + - 1/700 x DATA(1, -2, -1) - 1/700 x DATA(-2, 1, -1) + + 2 2 + + 1/350 x DATA(2, 1, 2) - 1/350 x DATA(-1, 2, 2) + + 2 2 + - 1/350 x DATA(2, -1, 2) + 1/1400 x DATA(1, -1, 1) + + 2 2 + + 1/175 x DATA(-2, 2, 2) + 1/350 x DATA(-2, 1, 2) + + 2 2 + - 1/350 x DATA(-2, -1, 2) + 1/350 x DATA(-2, -1, -2) + + 2 2 + - 1/700 x DATA(1, -1, -2) - 1/1400 x DATA(-1, -1, -1) + + 2 2 + - 1/1400 x DATA(-1, 1, 1) + 1/1400 x DATA(-1, 1, -1) + + 2 2 + + 1/1400 x DATA(1, 1, -1) + 1/175 x DATA(2, -2, -2) + + 2 2 + - 1/350 x DATA(1, -2, -2) - 1/350 x DATA(-1, -2, -2) + + 2 2 + - 1/700 x DATA(-1, -1, -2) + 1/350 x DATA(2, -1, -2) + + 229 + - ----- DATA(2, 1, -1) - 1/250 x DATA(2, -2, 1) + 1/500 x DATA(2, -1, -1) + 10500 + + + 1/250 x DATA(-2, 1, -2) + 1/500 x DATA(-2, -1, 1) + + - 1/250 x DATA(2, 1, -2) + 1/500 x DATA(-1, 1, -2) + + + 1/500 x DATA(-1, -2, 1) - 1/500 x DATA(1, -2, 1) + + + 1/250 x DATA(-2, -2, 1) + 1/250 x DATA(-1, 2, -2) + + + 1/250 x DATA(2, 2, 1) + 1/500 x DATA(2, 1, 1) + 1/175 y DATA(2, -2, 1) + + + 1/175 y DATA(1, -2, 1) - 1/350 y DATA(1, 1, 1) - 1/175 y DATA(-1, 2, -1) + + + 1/175 y DATA(-1, -2, 1) + 1/175 y DATA(2, 1, -2) + + + 1/175 y DATA(-1, 1, -2) - 1/350 y DATA(-2, -1, 1) + + + 1/350 y DATA(2, -1, -1) + 1/175 y DATA(-2, -2, 1) + + - 1/350 y DATA(-2, 1, 1) - 1/350 y DATA(2, 1, 1) - 1/175 y DATA(-1, -1, 2) + + + 1/175 y DATA(1, 2, 1) + 1/175 y DATA(-2, 2, 1) + 1/175 y DATA(1, 1, -2) + + - 2/175 y DATA(-1, 2, -2) - 2/175 y DATA(1, 2, -2) + + - 2/175 y DATA(-2, 2, -2) - 1/175 y DATA(-1, -2, -1) + + + 1/350 y DATA(2, 1, -1) - 1/175 y DATA(2, 2, -1) - 1/175 y DATA(1, 2, -1) + + + 1/175 y DATA(-2, 1, -2) - 1/175 y DATA(2, 1, 2) + 2/175 y DATA(-1, 2, 2) + + + 1/350 y DATA(-2, 1, -1) - 1/175 y DATA(1, -1, 2) + + + 1/350 y DATA(-2, -1, -1) + 2/175 y DATA(-2, -2, 2) + + - 1/175 y DATA(2, -2, -1) + 2/175 y DATA(1, -2, 2) - 1/175 y DATA(1, 1, 2) + + - 1/175 y DATA(-1, 1, 2) - 1/175 y DATA(2, -1, 2) - 2/175 y DATA(2, 2, -2) + + + 1/175 y DATA(-1, 2, 1) - 1/175 y DATA(-2, -2, -1) + + + 2/175 y DATA(-1, -2, 2) - 1/350 y DATA(2, -1, 1) + 1/175 y DATA(2, 2, 1) + + + 1/350 y DATA(-1, 1, -1) + 1/350 y DATA(-1, -1, -1) + + + 1/350 y DATA(1, -1, -1) - 1/350 y DATA(-1, 1, 1) + + + 2/175 y DATA(2, -2, 2) - 1/175 y DATA(-2, 2, -1) + 2/175 y DATA(2, 2, 2) + + + 2/175 y DATA(1, 2, 2) - 1/175 y DATA(1, -2, -1) + 1/350 y DATA(1, 1, -1) + + - 1/350 y DATA(-1, -1, 1) + 2/175 y DATA(-2, 2, 2) + + - 1/175 y DATA(-2, 1, 2) - 2/175 y DATA(-2, -2, -2) + + 187 + - 1/350 y DATA(1, -1, 1) - 1/175 y DATA(-2, -1, 2) - ---- DATA(0, 1, -2) + 7000 + + 229 167 + + ----- DATA(-2, 1, 1) - ---- DATA(-1, 1, -2) - 1/175 x z DATA(2, -1, -2) + 10500 7000 + + + 1/350 x z DATA(-1, -1, -2) + 1/175 x z DATA(-1, -2, -2) + + - 1/175 x z DATA(1, -2, 2) + 1/175 x z DATA(-1, -2, 2) + + + 2/175 x z DATA(-2, -2, 2) - 1/350 x z DATA(-2, -1, -1) + + + 1/175 x z DATA(2, -2, -1) - 1/350 x z DATA(1, -1, 2) + + - 1/350 x z DATA(-1, 1, 2) + 1/700 x z DATA(-1, 1, -1) + + + 1/700 x z DATA(-1, 1, 1) + 1/700 x z DATA(1, -1, -1) + + - 1/700 x z DATA(-1, -1, -1) + 1/175 x z DATA(1, 2, 2) + + + 2/175 x z DATA(2, 2, 2) + 1/175 x z DATA(-2, 2, -1) + + - 2/175 x z DATA(2, -2, 2) - 1/175 x z DATA(-1, 2, 2) + + + 1/175 x z DATA(2, 1, 2) + 1/350 x z DATA(-2, 1, -1) + + + 1/350 x z DATA(1, -2, -1) - 2/175 x z DATA(-2, 2, 2) + + - 1/700 x z DATA(-1, -1, 1) + 1/700 x z DATA(1, -1, 1) + + - 1/700 x z DATA(1, 1, -1) + 2/175 x z DATA(-2, -2, -2) + + - 1/175 x z DATA(1, -2, -2) - 2/175 x z DATA(2, -2, -2) + + - 1/350 x z DATA(1, -1, -2) + 1/175 x z DATA(-2, -1, -2) + + + 1/175 x z DATA(-2, -1, 2) - 1/175 x z DATA(-2, 1, 2) + + 2 2 + + 1/100 z DATA(-1, 1, -1) + 1/100 z DATA(1, 1, -1) + + 2 2 107 + + 1/100 z DATA(1, -1, 1) + 1/100 z DATA(-1, -1, 1) - ---- DATA(2, 1, -2) + 7000 + + 2 2 + + 1/100 z DATA(-2, -2, -2) + 1/100 z DATA(-2, 2, 2) + + 2 2 + + 1/200 z DATA(-2, 1, 2) - 1/200 z DATA(-2, -1, 2) + + 2 2 + + 1/200 z DATA(-2, -1, -2) + 1/200 z DATA(1, -1, -2) + + 2 2 + + 1/100 z DATA(2, -2, -2) + 1/100 z DATA(1, -2, -2) + + 2 2 + + 1/100 z DATA(-1, -2, -2) + 1/200 z DATA(-1, -1, -2) + + 2 + + 1/200 z DATA(2, -1, -2) - 1/175 z DATA(2, -1, -2) + + - 1/175 z DATA(-1, -1, -2) - 2/175 z DATA(2, -2, -2) + + 2 + - 2/175 z DATA(1, -2, -2) - 1/50 z DATA(2, -2, -1) + + 2 2 + - 1/100 z DATA(-2, -1, -1) - 1/100 z DATA(-2, -2, 2) + + 2 2 + - 1/200 z DATA(1, -1, 2) + 1/100 z DATA(1, 2, 2) + + 2 2 + - 1/100 z DATA(-1, -1, -1) - 1/100 z DATA(1, -1, -1) + + 2 2 + - 1/100 z DATA(-1, 1, 1) - 1/200 z DATA(-2, 1, -2) + + 2 2 + - 1/100 z DATA(1, 1, 1) + 1/50 z DATA(-1, 2, -1) + + 2 2 + + 1/100 z DATA(2, 1, -1) - 1/100 z DATA(-2, 1, 1) + + 2 2 + + 1/200 z DATA(2, 1, 2) - 1/100 z DATA(2, -2, 2) + + 2 2 + + 1/50 z DATA(-2, 2, -1) + 1/100 z DATA(2, 2, 2) + + 2 2 + + 1/100 z DATA(-1, 2, 2) - 1/50 z DATA(1, -2, -1) + + 2 2 + + 1/100 z DATA(-2, 1, -1) + 1/200 z DATA(-1, 1, 2) + + 2 2 + - 1/100 z DATA(-2, 2, -2) - 1/50 z DATA(-2, 2, 1) + + 2 2 + - 1/100 z DATA(1, 2, -2) - 1/50 z DATA(-1, -2, -1) + + 2 2 2 + + 1/50 z DATA(2, 2, -1) + 1/50 z DATA(1, 2, -1) - 1/100 z DATA(2, 1, 1) + + 2 2 + - 1/200 z DATA(1, 1, -2) - 1/100 z DATA(-1, 2, -2) + + 2 2 + - 1/100 z DATA(1, -2, 2) - 1/200 z DATA(2, -1, 2) + + 2 2 + + 1/200 z DATA(1, 1, 2) - 1/100 z DATA(2, 2, -2) + + 2 2 + + 1/100 z DATA(2, -1, 1) - 1/50 z DATA(-1, 2, 1) + + 2 2 2 + - 1/200 z DATA(-1, -1, 2) - 1/50 z DATA(1, 2, 1) - 1/50 z DATA(2, 2, 1) + + 2 2 + - 1/50 z DATA(-2, -2, -1) - 1/100 z DATA(-1, -2, 2) + + 2 + + 1/50 z DATA(-2, -2, 1) + 1/175 z DATA(-1, -2, 1) + + + 1/350 z DATA(-2, -1, 1) + 1/350 z DATA(2, -1, -1) + + + 1/175 z DATA(1, -2, 1) + 1/175 z DATA(-2, -2, 1) + + - 2/175 z DATA(2, -2, 2) - 1/175 z DATA(-2, 2, -1) + + 2 2 + + 1/50 z DATA(-1, -2, 1) + 1/100 z DATA(-2, -1, 1) + + 2 2 + - 1/200 z DATA(2, 1, -2) - 1/200 z DATA(-1, 1, -2) + + 2 2 + + 1/50 z DATA(2, -2, 1) - 1/100 z DATA(2, -1, -1) + + 2 + + 1/50 z DATA(1, -2, 1) - 1/175 z DATA(-1, 2, -1) + + - 1/175 z DATA(1, 2, -1) - 1/350 z DATA(2, 1, -1) + 1/175 z DATA(2, 1, -2) 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z DATA(-1, -1, -1) + + - 1/350 z DATA(-2, 1, -1) - 1/175 z DATA(-2, -1, -2) + + + 1/175 z DATA(-2, 1, 2) - 1/175 z DATA(-2, -1, 2) + + + 1/350 z DATA(1, -1, 1) - 2/175 z DATA(-2, -2, -2) + + + 2/175 z DATA(-2, 2, 2) + 1/350 z DATA(-1, -1, 1) + + + 1/350 z DATA(1, -1, -1) - 1/175 z DATA(1, -1, -2) + + + 1/350 x z DATA(1, 1, 2) - 1/175 x z DATA(2, -1, 2) + + 2 2 + + 1/50 y DATA(1, 1, -2) - 1/100 y DATA(-1, 2, -2) + + 2 + - 2/175 z DATA(-1, -2, -2) - 1/100 y DATA(-2, -1, -1) + + 2 2 + - 1/100 y DATA(-1, -2, 2) - 1/100 y DATA(1, -2, 2) + + 2 2 + + 1/50 y DATA(2, -1, 2) - 1/50 y DATA(1, 1, 2) + + 2 2 + - 1/200 y DATA(-2, 2, -1) - 1/100 y DATA(-2, -2, 2) + + 2 2 + + 1/200 y DATA(1, -2, -1) + 1/100 y DATA(-2, 1, -1) + + 2 2 + - 1/50 y DATA(-1, 1, 2) + 1/50 y DATA(1, -1, 2) + + 2 2 + + 1/200 y DATA(2, -2, -1) + 1/100 y DATA(-1, 1, -1) + + 2 2 + + 1/100 y DATA(1, 1, -1) + 1/100 y DATA(2, 2, 2) + + 2 2 + + 1/100 y DATA(1, 2, 2) - 1/100 y DATA(-1, -1, -1) + + 2 2 + - 1/50 y DATA(2, 1, 2) + 1/100 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- 1/100 y DATA(0, 1, 1) + + 2 + - 2/245 y z DATA(0, 1, 2) - 1/350 x DATA(0, 2, 1) + + 2 2 + - 1/350 x DATA(0, -2, -1) + 1/350 x DATA(0, 1, -2) + + 2 2 + + 1/175 x DATA(0, 2, -2) + 1/350 x DATA(0, -1, 2) + + 2 2 + + 1/350 x DATA(0, -2, 1) + 1/350 x DATA(0, 2, -1) + + 2 + - 1/350 x y DATA(1, 2, -1) - 1/175 x DATA(0, 2, 2) + + + 2/175 y DATA(0, -2, 2) - 1/175 y DATA(0, 1, 2) - 2/175 y DATA(0, -2, -2) + + + 1/350 y DATA(0, 1, -1) + 1/175 y DATA(0, -1, -2) + + + 1/350 y DATA(0, -1, -1) - 1/350 y DATA(0, -1, 1) + + 2 + - 1/700 x DATA(0, 1, 1) - 1/350 x y DATA(-1, -2, 1) + + 137 + - ---- DATA(-2, -2, -2) + 1/350 x y DATA(-2, -1, 1) + 5250 + + + 1/175 x y DATA(2, 1, -2) - 1/350 x y DATA(-1, 1, -2) + + 137 + - ---- DATA(-2, 2, 2) + 1/350 x y DATA(-2, 1, 1) - 1/700 x y DATA(1, 1, 1) + 5250 + + 47 17 + + 1/350 x y DATA(-1, 2, -1) - ---- DATA(1, -2, -2) - ---- DATA(0, -2, -2) + 5250 5250 + + 47 107 + - ---- DATA(-1, -2, -2) + ---- DATA(-2, -1, -2) + 1/175 x y DATA(2, -2, 1) + 5250 7000 + + 137 167 + + 1/350 x y DATA(2, -1, -1) - ---- DATA(2, -2, -2) + ---- DATA(1, -1, -2) + 5250 7000 + + 187 167 + + ---- DATA(0, -1, -2) + ---- DATA(-1, -1, -2) - 1/175 x y DATA(-2, -2, 1) + 7000 7000 + + 107 + + 1/350 x y DATA(1, -2, 1) + ---- DATA(2, -1, -2) + 7000 + +> coeffs_as_lc_of_data(%, posn_list_3d_size5); +bytes used=2363901008, alloc=14677376, time=385.88 +bytes used=2364901296, alloc=14677376, time=385.96 +bytes used=2365901528, alloc=14677376, time=386.03 +bytes used=2366924292, alloc=14677376, time=386.11 +bytes used=2367998724, alloc=14677376, time=386.19 +bytes used=2369048208, alloc=14677376, time=386.27 +bytes used=2370065768, alloc=14677376, time=386.36 +bytes used=2371072988, alloc=14677376, time=386.44 +bytes used=2372073244, alloc=14677376, time=386.52 +bytes used=2373073716, alloc=14677376, time=386.61 +bytes used=2374073884, alloc=14677376, time=386.69 +bytes used=2375083364, alloc=14677376, time=386.78 +bytes used=2376121972, alloc=14677376, time=386.86 +bytes used=2377150604, alloc=14677376, time=386.95 +bytes used=2378150808, alloc=14677376, time=387.04 +bytes used=2379151336, alloc=14677376, time=387.13 +bytes used=2380151500, alloc=14677376, time=387.22 +bytes used=2381171848, alloc=14677376, time=387.32 +bytes used=2382177612, alloc=14677376, time=387.41 +bytes used=2383177832, alloc=14677376, time=387.51 +bytes used=2384198240, alloc=14677376, time=387.61 +bytes used=2385202120, alloc=14677376, time=387.72 +bytes used=2386203148, alloc=14677376, time=387.82 +bytes used=2387215660, alloc=14677376, time=387.90 +bytes used=2388220296, alloc=14677376, time=387.98 +bytes used=2389225180, alloc=14677376, time=388.05 + 2 2 +[COEFF(-2, -2, -2) = 2/175 x z + 1/100 z - 2/175 z + 1/100 y + 4/245 y z + + 137 2 + - ---- - 1/125 x - 2/175 y + 1/175 x + 2/175 x y, COEFF(-1, -2, -2) = + 5250 + + 2 47 2 + 1/175 x z - 1/350 x - 2/175 y - ---- - 1/250 x - 2/175 z + 1/100 z + 5250 + + 2 + + 4/245 y z + 1/100 y + 1/175 x y, COEFF(0, -2, -2) = + + 2 17 2 2 + 1/100 y - ---- + 4/245 y z - 2/175 z + 1/100 z - 1/175 x - 2/175 y, + 5250 + + 2 2 47 + COEFF(1, -2, -2) = - 1/175 x y - 1/350 x + 1/100 z + 1/250 x - ---- + 5250 + + 2 + - 2/175 y - 2/175 z - 1/175 x z + 4/245 y z + 1/100 y , COEFF(2, -2, -2) + + 137 2 2 + = - 2/175 x y - 2/175 x z - ---- + 1/100 y - 2/175 y + 1/100 z + 1/125 x + 5250 + + 2 2 + + 1/175 x + 4/245 y z - 2/175 z, COEFF(-2, -1, -2) = 1/175 y + 1/350 x + + 2 107 + + 1/200 z - 2/245 y z + 1/175 x z - 1/250 x - 1/175 x y + ---- - 1/175 z + 7000 + + 2 2 + - 1/50 y , COEFF(-1, -1, -2) = - 1/700 x - 1/175 z - 1/500 x + 1/175 y + + 2 167 2 + - 1/350 x y + 1/350 x z - 1/50 y + ---- - 2/245 y z + 1/200 z , + 7000 + + COEFF(0, -1, -2) = + + 2 2 187 2 + - 1/50 y + 1/175 y - 1/175 z - 2/245 y z + 1/200 z + ---- - 1/350 x , + 7000 + + COEFF(1, -1, -2) = - 1/175 z + 1/500 x + 1/175 y - 2/245 y z + 1/350 x y + + 2 2 167 2 + + 1/200 z - 1/50 y - 1/350 x z + ---- - 1/700 x , COEFF(2, -1, -2) = + 7000 + + 2 107 2 2 + - 2/245 y z + 1/175 y + 1/350 x + 1/250 x + ---- - 1/50 y + 1/200 z + 7000 + + - 1/175 z - 1/175 x z + 1/175 x y, + + COEFF(-2, 0, -2) = - 4/245 y z - 2/175 x y + 2/175 y, + + COEFF(-1, 0, -2) = - 4/245 y z - 1/175 x y + 2/175 y, + + COEFF(0, 0, -2) = 2/175 y - 4/245 y z, + + COEFF(1, 0, -2) = - 4/245 y z + 2/175 y + 1/175 x y, + + COEFF(2, 0, -2) = 2/175 y - 4/245 y z + 2/175 x y, COEFF(-2, 1, -2) = + + 2 2 2 107 + - 1/200 z + 1/175 y + 1/50 y - 1/350 x - ---- + 1/250 x + 1/175 z + 7000 + + 2 + - 2/245 y z - 1/175 x z - 1/175 x y, COEFF(-1, 1, -2) = 1/700 x + 1/175 y + + 2 167 2 + - 1/350 x y - 1/200 z - 2/245 y z - ---- - 1/350 x z + 1/175 z + 1/50 y + 7000 + + + 1/500 x, COEFF(0, 1, -2) = + + 2 187 2 2 + 1/50 y - ---- + 1/175 y - 2/245 y z + 1/175 z + 1/350 x - 1/200 z , + 7000 + + 2 167 + COEFF(1, 1, -2) = 1/175 y + 1/350 x y + 1/50 y - 1/500 x - ---- + 7000 + + 2 2 + + 1/350 x z + 1/700 x - 2/245 y z + 1/175 z - 1/200 z , COEFF(2, 1, -2) + + 107 2 + = - 2/245 y z - ---- + 1/175 y + 1/50 y + 1/175 x z + 1/175 x y - 1/250 x + 7000 + + 2 2 + + 1/175 z - 1/350 x - 1/200 z , COEFF(-2, 2, -2) = 1/125 x + 2/175 z + + 2 2 137 + + 2/175 x y + 4/245 y z - 1/100 y - 1/100 z - 2/175 y + ---- - 2/175 x z + 5250 + + 2 2 + - 1/175 x , COEFF(-1, 2, -2) = 1/175 x y - 1/100 y - 1/175 x z + + 2 47 2 + + 4/245 y z - 1/100 z + ---- - 2/175 y + 2/175 z + 1/250 x + 1/350 x , + 5250 + + COEFF(0, 2, -2) = + + 2 17 2 2 + - 1/100 z + 2/175 z + ---- + 1/175 x - 2/175 y + 4/245 y z - 1/100 y , + 5250 + + 2 2 + COEFF(1, 2, -2) = 2/175 z + 1/350 x - 2/175 y - 1/100 y + 1/175 x z + + 2 47 + - 1/100 z - 1/250 x + 4/245 y z - 1/175 x y + ----, COEFF(2, 2, -2) = + 5250 + + 2 137 2 2 + - 1/175 x + ---- - 1/100 z - 1/100 y - 2/175 x y - 2/175 y + 2/175 x z + 5250 + + 2 + + 2/175 z + 4/245 y z - 1/125 x, COEFF(-2, -2, -1) = - 1/50 z - 1/175 x z + + 2 2 + + 1/175 x y + 1/175 z + 1/350 x - 1/250 x - 2/245 y z + 1/200 y + + 107 + - 1/175 y + ----, COEFF(-1, -2, -1) = - 1/350 x z - 1/500 x + 1/350 x y + 7000 + + 2 2 2 167 + + 1/200 y - 1/700 x - 1/50 z - 1/175 y - 2/245 y z + 1/175 z + ----, + 7000 + + COEFF(0, -2, -1) = + + 2 2 187 2 + 1/200 y - 1/175 y - 1/350 x + ---- - 2/245 y z + 1/175 z - 1/50 z , + 7000 + + 167 2 2 2 + COEFF(1, -2, -1) = ---- - 1/700 x - 2/245 y z + 1/200 y - 1/50 z + 7000 + + + 1/175 z + 1/350 x z + 1/500 x - 1/175 y - 1/350 x y, COEFF(2, -2, -1) = + + 2 107 2 + 1/350 x - 1/175 x y + ---- + 1/175 z - 1/50 z - 2/245 y z + 1/175 x z + 7000 + + 2 + + 1/200 y + 1/250 x - 1/175 y, COEFF(-2, -1, -1) = - 1/500 x - 1/350 x y + + 2 2 2 + - 1/350 x z + 1/350 z + 1/245 y z + 1/700 x - 1/100 y - 1/100 z + + 229 2 + + 1/350 y + -----, COEFF(-1, -1, -1) = 1/245 y z - 1/100 y - 1/700 x y + 10500 + + 2 137 2 + - 1/100 z - 1/700 x z + ---- - 1/1400 x - 1/1000 x + 1/350 y + 1/350 z, + 5250 + + COEFF(0, -1, -1) = + + 2 289 2 2 + - 1/100 z + 1/350 y + ----- - 1/100 y + 1/350 z + 1/245 y z - 1/700 x , + 10500 + + 137 2 + COEFF(1, -1, -1) = 1/700 x z + 1/1000 x + 1/350 y + ---- - 1/1400 x + 5250 + + 2 2 + + 1/700 x y + 1/245 y z - 1/100 z + 1/350 z - 1/100 y , COEFF(2, -1, -1) + + 229 2 2 + = ----- + 1/500 x - 1/100 z + 1/245 y z + 1/350 y - 1/100 y + 1/350 z + 10500 + + 2 + + 1/350 x z + 1/350 x y + 1/700 x , + + COEFF(-2, 0, -1) = - 1/175 x y + 1/175 y + 2/245 y z, + + COEFF(-1, 0, -1) = 1/175 y - 1/350 x y + 2/245 y z, + + COEFF(0, 0, -1) = 2/245 y z + 1/175 y, + + COEFF(1, 0, -1) = 2/245 y z + 1/175 y + 1/350 x y, + + COEFF(2, 0, -1) = 1/175 x y + 2/245 y z + 1/175 y, COEFF(-2, 1, -1) = + + 229 2 + - ----- + 1/245 y z - 1/350 z - 1/700 x + 1/500 x + 1/350 x z - 1/350 x y + 10500 + + 2 2 137 2 + + 1/100 y + 1/100 z + 1/350 y, COEFF(-1, 1, -1) = - ---- + 1/100 z + 5250 + + 2 2 + + 1/350 y + 1/100 y - 1/700 x y + 1/245 y z + 1/1400 x - 1/350 z + + + 1/1000 x + 1/700 x z, COEFF(0, 1, -1) = + + 2 2 289 2 + 1/100 y + 1/100 z - ----- + 1/350 y + 1/245 y z + 1/700 x - 1/350 z, + 10500 + + 2 2 + COEFF(1, 1, -1) = 1/245 y z - 1/350 z + 1/350 y + 1/100 z + 1/100 y + + 137 2 + - ---- - 1/700 x z + 1/700 x y + 1/1400 x - 1/1000 x, COEFF(2, 1, -1) = + 5250 + + 2 229 + 1/350 x y + 1/100 z - ----- + 1/245 y z - 1/350 z - 1/500 x - 1/350 x z + 10500 + + 2 2 + + 1/350 y + 1/100 y - 1/700 x , COEFF(-2, 2, -1) = 1/175 x y - 1/175 y + + 2 2 107 + - 1/200 y + 1/250 x - 1/350 x - 1/175 z - ---- - 2/245 y z + 1/175 x z + 7000 + + 2 2 2 + + 1/50 z , COEFF(-1, 2, -1) = - 2/245 y z + 1/50 z - 1/200 y + 1/350 x y + + 2 167 + - 1/175 z + 1/700 x - 1/175 y - ---- + 1/350 x z + 1/500 x, + 7000 + + COEFF(0, 2, -1) = + + 187 2 2 2 + - ---- - 1/200 y + 1/50 z - 2/245 y z - 1/175 y - 1/175 z + 1/350 x , + 7000 + + 2 2 + COEFF(1, 2, -1) = - 1/200 y - 1/350 x y + 1/50 z - 1/350 x z - 1/175 y + + 167 2 + - ---- - 2/245 y z + 1/700 x - 1/175 z - 1/500 x, COEFF(2, 2, -1) = + 7000 + + 2 107 2 + - 1/175 x z - 1/175 y - 1/175 x y - 1/350 x - ---- + 1/50 z - 1/250 x + 7000 + + 2 + - 1/175 z - 1/200 y - 2/245 y z, + + COEFF(-2, -2, 0) = - 4/245 y z + 2/175 z - 2/175 x z, + + COEFF(-1, -2, 0) = - 4/245 y z + 2/175 z - 1/175 x z, + + COEFF(0, -2, 0) = 2/175 z - 4/245 y z, + + COEFF(1, -2, 0) = - 4/245 y z + 2/175 z + 1/175 x z, + + COEFF(2, -2, 0) = - 4/245 y z + 2/175 z + 2/175 x z, + + COEFF(-2, -1, 0) = 1/175 z - 1/175 x z + 2/245 y z, + + COEFF(-1, -1, 0) = 1/175 z + 2/245 y z - 1/350 x z, + + COEFF(0, -1, 0) = 1/175 z + 2/245 y z, + + COEFF(1, -1, 0) = 2/245 y z + 1/175 z + 1/350 x z, + + COEFF(2, -1, 0) = 1/175 z + 1/175 x z + 2/245 y z, + + COEFF(-2, 0, 0) = 4/245 y z, COEFF(-1, 0, 0) = 4/245 y z, + + COEFF(0, 0, 0) = 4/245 y z, COEFF(1, 0, 0) = 4/245 y z, + + COEFF(2, 0, 0) = 4/245 y z, + + COEFF(-2, 1, 0) = 2/245 y z - 1/175 z + 1/175 x z, + + COEFF(-1, 1, 0) = - 1/175 z + 1/350 x z + 2/245 y z, + + COEFF(0, 1, 0) = 2/245 y z - 1/175 z, + + COEFF(1, 1, 0) = 2/245 y z - 1/175 z - 1/350 x z, + + COEFF(2, 1, 0) = - 1/175 z + 2/245 y z - 1/175 x z, + + COEFF(-2, 2, 0) = - 2/175 z - 4/245 y z + 2/175 x z, + + COEFF(-1, 2, 0) = - 2/175 z - 4/245 y z + 1/175 x z, + + COEFF(0, 2, 0) = - 2/175 z - 4/245 y z, + + COEFF(1, 2, 0) = - 2/175 z - 1/175 x z - 4/245 y z, + + COEFF(2, 2, 0) = - 4/245 y z - 2/175 x z - 2/175 z, COEFF(-2, -2, 1) = + + 107 2 2 + - 1/175 x y - ---- - 1/350 x + 1/175 y + 1/250 x - 1/175 x z - 1/200 y + 7000 + + 2 + + 1/175 z + 1/50 z - 2/245 y z, COEFF(-1, -2, 1) = 1/175 y + 1/500 x + + 2 2 167 2 + + 1/700 x + 1/175 z + 1/50 z - ---- - 1/350 x z - 1/200 y - 1/350 x y + 7000 + + - 2/245 y z, COEFF(0, -2, 1) = + + 2 187 2 2 + 1/350 x + 1/175 y - ---- - 2/245 y z + 1/175 z - 1/200 y + 1/50 z , + 7000 + + 2 + COEFF(1, -2, 1) = 1/175 y - 1/500 x + 1/700 x + 1/350 x y + 1/175 z + + 167 2 2 + + 1/350 x z - 2/245 y z - ---- + 1/50 z - 1/200 y , COEFF(2, -2, 1) = + 7000 + + 107 2 2 + 1/175 y + 1/175 x y - ---- + 1/175 x z - 1/350 x - 1/250 x - 1/200 y + 7000 + + 2 2 + + 1/175 z + 1/50 z - 2/245 y z, COEFF(-2, -1, 1) = 1/350 x y + 1/100 y + + 2 229 2 + + 1/100 z + 1/500 x + 1/350 z - 1/350 y - ----- - 1/700 x - 1/350 x z + 10500 + + 2 + + 1/245 y z, COEFF(-1, -1, 1) = - 1/350 y + 1/700 x y + 1/100 y + + 2 2 137 + + 1/1400 x + 1/245 y z + 1/1000 x + 1/100 z - 1/700 x z - ---- + 1/350 z + 5250 + + , COEFF(0, -1, 1) = + + 289 2 2 2 + - ----- + 1/700 x - 1/350 y + 1/100 y + 1/245 y z + 1/100 z + 1/350 z, + 10500 + + 2 2 137 + COEFF(1, -1, 1) = 1/100 z + 1/1400 x - ---- + 1/245 y z + 1/350 z + 5250 + + 2 + - 1/700 x y - 1/350 y + 1/700 x z + 1/100 y - 1/1000 x, COEFF(2, -1, 1) + + 2 229 + = - 1/700 x - 1/350 x y + 1/350 x z - ----- - 1/350 y + 1/350 z + 10500 + + 2 2 + + 1/100 z + 1/245 y z + 1/100 y - 1/500 x, + + COEFF(-2, 0, 1) = 2/245 y z + 1/175 x y - 1/175 y, + + COEFF(-1, 0, 1) = 1/350 x y - 1/175 y + 2/245 y z, + + COEFF(0, 0, 1) = 2/245 y z - 1/175 y, + + COEFF(1, 0, 1) = - 1/350 x y + 2/245 y z - 1/175 y, + + COEFF(2, 0, 1) = - 1/175 y - 1/175 x y + 2/245 y z, COEFF(-2, 1, 1) = + + 2 229 2 + - 1/100 y - 1/500 x + 1/350 x y + 1/350 x z + 1/245 y z + ----- - 1/100 z + 10500 + + 2 2 + - 1/350 z + 1/700 x - 1/350 y, COEFF(-1, 1, 1) = 1/700 x y - 1/1400 x + + 2 + - 1/1000 x + 1/700 x z + 1/245 y z - 1/350 z - 1/350 y - 1/100 z + + 2 137 + - 1/100 y + ----, COEFF(0, 1, 1) = + 5250 + + 289 2 2 2 + ----- - 1/350 z - 1/700 x + 1/245 y z - 1/100 z - 1/350 y - 1/100 y , + 10500 + + 2 2 2 + COEFF(1, 1, 1) = - 1/350 z - 1/1400 x - 1/100 z - 1/350 y - 1/100 y + + 137 + - 1/700 x z - 1/700 x y + 1/245 y z + 1/1000 x + ----, COEFF(2, 1, 1) = + 5250 + + 2 2 + 1/245 y z - 1/100 z - 1/350 x z - 1/350 x y - 1/350 z + 1/700 x - 1/350 y + + 2 229 2 + - 1/100 y + ----- + 1/500 x, COEFF(-2, 2, 1) = - 1/175 x y - 1/50 z + 10500 + + 2 2 107 + + 1/200 y - 2/245 y z - 1/175 z + 1/175 x z + 1/350 x + 1/175 y + ---- + 7000 + + 167 + - 1/250 x, COEFF(-1, 2, 1) = 1/350 x z + ---- - 1/500 x - 1/175 z + 7000 + + 2 2 2 + - 1/700 x - 2/245 y z - 1/350 x y - 1/50 z + 1/175 y + 1/200 y , + + COEFF(0, 2, 1) = + + 2 2 187 2 + 1/200 y + 1/175 y - 1/50 z + ---- - 1/175 z - 2/245 y z - 1/350 x , + 7000 + + 2 2 2 167 + COEFF(1, 2, 1) = - 1/700 x - 1/50 z + 1/200 y + ---- + 1/500 x + 7000 + + + 1/350 x y - 2/245 y z - 1/175 z + 1/175 y - 1/350 x z, COEFF(2, 2, 1) = + + 2 107 2 2 + - 1/50 z + ---- + 1/200 y + 1/350 x - 2/245 y z - 1/175 x z + 1/250 x + 7000 + + + 1/175 x y + 1/175 y - 1/175 z, COEFF(-2, -2, 2) = 4/245 y z + 2/175 y + + 137 2 2 + + ---- - 1/100 y + 1/125 x - 2/175 x y - 2/175 z + 2/175 x z - 1/175 x + 5250 + + 2 47 2 2 + - 1/100 z , COEFF(-1, -2, 2) = ---- + 1/250 x - 1/100 y + 1/350 x + 5250 + + 2 + + 4/245 y z + 1/175 x z - 1/100 z + 2/175 y - 1/175 x y - 2/175 z, + + COEFF(0, -2, 2) = + + 2 17 2 2 + 1/175 x + ---- - 1/100 y - 1/100 z - 2/175 z + 4/245 y z + 2/175 y, + 5250 + + 2 2 + COEFF(1, -2, 2) = - 2/175 z - 1/250 x + 1/175 x y + 1/350 x - 1/100 z + + 2 47 + - 1/100 y + ---- - 1/175 x z + 4/245 y z + 2/175 y, COEFF(2, -2, 2) = + 5250 + + 2 2 2 + 2/175 y - 1/125 x - 1/100 y - 1/100 z - 2/175 z - 1/175 x + 4/245 y z + + 137 107 + + 2/175 x y + ---- - 2/175 x z, COEFF(-2, -1, 2) = - ---- - 2/245 y z + 5250 7000 + + 2 2 2 + - 1/175 z - 1/350 x + 1/50 y - 1/200 z + 1/250 x + 1/175 x z - 1/175 y + + 2 2 + + 1/175 x y, COEFF(-1, -1, 2) = 1/500 x + 1/350 x z - 1/200 z + 1/50 y + + 2 167 + - 1/175 y + 1/700 x - 1/175 z + 1/350 x y - 2/245 y z - ----, + 7000 + + COEFF(0, -1, 2) = + + 2 2 2 187 + 1/350 x - 1/200 z - 1/175 y + 1/50 y - 1/175 z - ---- - 2/245 y z, + 7000 + + 2 + COEFF(1, -1, 2) = - 1/175 y - 1/350 x y - 1/500 x - 1/350 x z - 1/200 z + + 2 2 167 + + 1/700 x - 1/175 z - 2/245 y z + 1/50 y - ----, COEFF(2, -1, 2) = + 7000 + + 2 2 2 107 + - 1/200 z + 1/50 y - 1/350 x - 1/175 x z - 1/175 z - ---- - 2/245 y z + 7000 + + - 1/175 x y - 1/250 x - 1/175 y, + + COEFF(-2, 0, 2) = 2/175 x y - 4/245 y z - 2/175 y, + + COEFF(-1, 0, 2) = 1/175 x y - 4/245 y z - 2/175 y, + + COEFF(0, 0, 2) = - 2/175 y - 4/245 y z, + + COEFF(1, 0, 2) = - 4/245 y z - 2/175 y - 1/175 x y, + + COEFF(2, 0, 2) = - 4/245 y z - 2/175 x y - 2/175 y, COEFF(-2, 1, 2) = + + 2 107 + - 1/175 x z - 2/245 y z - 1/50 y - 1/250 x + ---- - 1/175 y + 1/175 z + 7000 + + 2 2 + + 1/200 z + 1/350 x + 1/175 x y, COEFF(-1, 1, 2) = - 1/500 x - 2/245 y z + + 167 2 2 2 + + ---- - 1/700 x + 1/350 x y + 1/200 z + 1/175 z - 1/350 x z - 1/50 y + 7000 + + - 1/175 y, COEFF(0, 1, 2) = + + 2 2 2 187 + - 1/175 y - 2/245 y z - 1/50 y + 1/175 z + 1/200 z - 1/350 x + ----, + 7000 + + 2 2 + COEFF(1, 1, 2) = - 2/245 y z + 1/500 x - 1/175 y + 1/200 z - 1/50 y + + 167 2 + + ---- - 1/700 x + 1/175 z - 1/350 x y + 1/350 x z, COEFF(2, 1, 2) = + 7000 + + 2 107 + - 2/245 y z + 1/175 z - 1/175 x y - 1/175 y + 1/200 z + 1/250 x + ---- + 7000 + + 2 2 + - 1/50 y + 1/175 x z + 1/350 x , COEFF(-2, 2, 2) = - 2/175 x y + + 2 137 + + 4/245 y z - 2/175 x z + 2/175 y + 1/100 y + 2/175 z - ---- - 1/125 x + 5250 + + 2 2 2 2 + + 1/100 z + 1/175 x , COEFF(-1, 2, 2) = - 1/175 x y - 1/350 x + 1/100 y + + 2 47 + + 2/175 y + 4/245 y z - 1/250 x - 1/175 x z + 2/175 z + 1/100 z - ----, + 5250 + + COEFF(0, 2, 2) = + + 17 2 2 2 + - ---- - 1/175 x + 1/100 y + 2/175 y + 1/100 z + 2/175 z + 4/245 y z, + 5250 + + 47 2 2 + COEFF(1, 2, 2) = 1/175 x y - ---- + 1/100 y + 1/175 x z - 1/350 x + 5250 + + 2 + + 1/100 z + 4/245 y z + 1/250 x + 2/175 z + 2/175 y, COEFF(2, 2, 2) = + + 137 2 2 + 2/175 z - ---- + 1/100 y + 1/125 x + 2/175 x z + 1/175 x + 2/175 y + 5250 + + 2 + + 2/175 x y + 4/245 y z + 1/100 z ] + +> print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dyz.compute.c"); +bytes used=2390225452, alloc=14677376, time=388.13 +bytes used=2391225608, alloc=14677376, time=388.21 +bytes used=2392225792, alloc=14677376, time=388.29 +bytes used=2393226252, alloc=14677376, time=388.42 +bytes used=2394226776, alloc=14677376, time=389.04 +bytes used=2395226948, alloc=14677376, time=389.66 +bytes used=2396227512, alloc=14677376, time=390.27 +bytes used=2397227804, alloc=14677376, time=390.88 +bytes used=2398228032, alloc=14677376, time=391.49 +bytes used=2399228384, alloc=14677376, time=391.65 +bytes used=2400228616, alloc=14677376, time=391.74 +bytes used=2401239544, alloc=14677376, time=391.82 +bytes used=2402285960, alloc=14677376, time=391.90 +bytes used=2403288548, alloc=14677376, time=391.98 +bytes used=2404288856, alloc=14677376, time=392.07 +bytes used=2405289028, alloc=14677376, time=392.40 +bytes used=2406289272, alloc=14677376, time=393.65 +bytes used=2407289472, alloc=14677376, time=394.07 +bytes used=2408289644, alloc=14677376, time=394.30 +bytes used=2409289924, alloc=14677376, time=394.37 +bytes used=2410290088, alloc=14677376, time=394.44 +bytes used=2411290336, alloc=14677376, time=394.50 +bytes used=2412290840, alloc=14677376, time=394.57 +bytes used=2413291344, alloc=14677376, time=394.64 +bytes used=2414291684, alloc=14677376, time=394.71 +bytes used=2415291904, alloc=14677376, time=394.79 +bytes used=2416292192, alloc=14677376, time=394.88 +bytes used=2417292416, alloc=14677376, time=394.98 +bytes used=2418292580, alloc=14677376, time=395.09 +bytes used=2419293268, alloc=14677376, time=395.21 +bytes used=2420303760, alloc=14677376, time=395.34 +bytes used=2421303968, alloc=14677376, time=395.47 +bytes used=2422307784, alloc=14677376, time=395.59 +bytes used=2423307968, alloc=14677376, time=395.70 +bytes used=2424308168, alloc=14677376, time=395.78 +bytes used=2425308452, alloc=14677376, time=397.29 +bytes used=2426308748, alloc=14677376, time=398.08 +bytes used=2427308924, alloc=14677376, time=398.56 +bytes used=2428309364, alloc=14677376, time=398.65 +bytes used=2429309648, alloc=14677376, time=398.72 +bytes used=2430310080, alloc=14677376, time=398.80 +bytes used=2431310344, alloc=14677376, time=398.87 +bytes used=2432310656, alloc=14677376, time=398.94 +bytes used=2433310884, alloc=14677376, time=399.01 +bytes used=2434311040, alloc=14677376, time=399.13 +bytes used=2435311228, alloc=14677376, time=399.26 +bytes used=2436315480, alloc=14677376, time=399.39 +bytes used=2437315656, alloc=14677376, time=399.51 +bytes used=2438315916, alloc=14677376, time=400.35 +bytes used=2439316500, alloc=14677376, time=401.71 +bytes used=2440316760, alloc=14677376, time=402.21 +bytes used=2441316988, alloc=14677376, time=402.59 +bytes used=2442317272, alloc=14677376, time=402.67 +bytes used=2443317448, alloc=14677376, time=402.74 +bytes used=2444318256, alloc=14677376, time=402.93 +bytes used=2445318416, alloc=14677376, time=403.96 +bytes used=2446318632, alloc=14677376, time=405.33 +bytes used=2447318812, alloc=14677376, time=405.90 +bytes used=2448319032, alloc=14677376, time=406.00 +bytes used=2449319276, alloc=14677376, time=406.07 +bytes used=2450319460, alloc=14677376, time=406.29 +bytes used=2451319696, alloc=14677376, time=407.94 +bytes used=2452319852, alloc=14677376, time=408.85 +bytes used=2453320096, alloc=14677376, time=409.39 +bytes used=2454320692, alloc=14677376, time=409.48 +bytes used=2455321056, alloc=14677376, time=409.62 +> +# d^2/dz^2 +> simplify( diff(interp_3d_cube_order4_smooth0,z,z) ); +bytes used=2456321320, alloc=14677376, time=409.75 +bytes used=2457439864, alloc=14677376, time=409.84 +bytes used=2458440080, alloc=14677376, time=409.92 +bytes used=2459440252, alloc=14677376, time=410.00 +bytes used=2460440724, alloc=14677376, time=410.08 +bytes used=2461440860, alloc=14677376, time=410.16 +bytes used=2462441164, alloc=14677376, time=410.24 +bytes used=2463441372, alloc=14677376, time=410.33 +bytes used=2464442072, alloc=14677376, time=410.41 +bytes used=2465442368, alloc=14677376, time=410.49 + 256 +- 1/10 DATA(0, -2, 0) + ---- DATA(-2, -2, 1) - 1/50 y z DATA(1, -1, -1) + 3675 + + 211 + + ---- DATA(1, -2, 1) - 1/50 y z DATA(-1, -1, -1) + 4/75 DATA(0, -2, 1) + 3675 + + - 9/98 DATA(1, -2, 0) + 4/75 DATA(0, 2, -1) + 4/75 DATA(2, 0, -1) + + 211 311 + + ---- DATA(-1, -2, 1) + ----- DATA(0, -1, 2) + 1/50 y z DATA(1, 1, -1) + 3675 14700 + + + 1/50 y z DATA(-1, 1, -1) - 1/50 y z DATA(-1, 1, 1) + + 211 33 256 + + ---- DATA(-2, -1, 1) - --- DATA(2, -2, 0) + ---- DATA(2, -2, 1) + 3675 490 3675 + + + 1/350 x DATA(-1, -2, -1) + 4/75 DATA(-2, 0, 1) - 9/98 DATA(-2, -1, 0) + + - 1/300 DATA(0, 2, 2) + 1/175 x DATA(-2, 1, 1) - 1/350 x DATA(1, 1, 1) + + 311 + + ----- DATA(1, 0, 2) + 1/350 x DATA(-1, 2, -1) - 1/175 x DATA(2, 1, -1) + 14700 + + - 1/175 x DATA(2, 2, -1) - 1/350 x DATA(1, 2, -1) + + 151 + - 1/175 x DATA(-1, -1, 2) - 1/350 x DATA(1, 2, 1) + ---- DATA(-1, 0, -1) + 3675 + + + 2/175 x DATA(2, 2, -2) - 1/175 x DATA(2, -1, 1) + 1/350 x DATA(-1, 2, 1) + + + 1/175 x DATA(-2, -2, -1) + 1/175 x DATA(1, 1, -2) + + + 1/175 x DATA(1, 2, -2) - 2/175 x DATA(-2, 2, -2) + + 211 13 + + 1/175 x DATA(-2, 2, 1) + ---- DATA(2, -1, -1) - -- DATA(0, 0, 0) + 3675 98 + + 61 61 57 + - --- DATA(1, 0, 0) - --- DATA(0, 1, 0) - --- DATA(1, 1, 0) + 490 490 490 + + 136 151 151 + + ---- DATA(0, 0, 1) + ---- DATA(1, 0, 1) + ---- DATA(0, 1, 1) + 3675 3675 3675 + + 166 + + ---- DATA(1, 1, 1) + 1/25 x z DATA(-2, -1, 1) + 1/25 x z DATA(2, -1, -1) + 3675 + + - 1/25 x z DATA(2, -2, 1) + 1/25 x z DATA(-2, -2, 1) + + - 1/50 x z DATA(1, -2, 1) + 1/50 x z DATA(-1, -2, 1) + + + 1/25 x z DATA(2, 2, -1) + 1/25 x z DATA(2, 1, -1) + + - 1/50 x z DATA(-1, 2, -1) - 1/50 x z DATA(1, 1, 1) + + + 1/25 x z DATA(-2, 1, 1) + 1/100 x z DATA(-1, 1, -2) + + - 1/50 x z DATA(2, 1, -2) - 1/25 x z DATA(2, 2, 1) + + + 1/100 x z DATA(-1, 2, -2) - 1/100 x z DATA(1, 1, -2) + + + 1/25 x z DATA(-2, 2, 1) + 1/50 x z DATA(-2, 2, -2) + + - 1/50 x z DATA(-1, -2, -1) - 1/100 x z DATA(1, 2, -2) + + + 1/50 x z DATA(-2, 1, -2) + 1/50 x z DATA(1, 2, -1) + + + 1/50 x z DATA(-1, 2, 1) - 1/50 x z DATA(2, 2, -2) + + - 1/50 x z DATA(1, 2, 1) - 1/100 x z DATA(-1, -1, 2) + + 256 + - 1/25 x z DATA(2, 1, 1) - 1/25 x z DATA(2, -1, 1) + ---- DATA(2, 2, -1) + 3675 + + + 1/350 x y DATA(1, 1, 2) - 1/175 x y DATA(2, -1, 2) + + - 1/25 x z DATA(-2, -2, -1) - 1/350 x y DATA(-2, -1, -1) + + - 1/350 x y DATA(1, -1, 2) - 1/350 x y DATA(-1, 1, 2) + + + 1/175 x y DATA(2, -2, -1) + 1/175 x y DATA(2, 1, 2) + + + 1/350 x y DATA(-2, 1, -1) + 1/350 x y DATA(1, -2, -1) + + + 2/175 x y DATA(-2, -2, 2) + 1/700 x y DATA(1, -1, -1) + + - 1/700 x y DATA(-1, -1, -1) + 1/175 x y DATA(1, 2, 2) + + + 2/175 x y DATA(2, 2, 2) + 1/175 x y DATA(-2, 2, -1) + + - 2/175 x y DATA(2, -2, 2) - 1/175 x y DATA(-1, 2, 2) + + - 1/700 x y DATA(-1, -1, 1) + 1/700 x y DATA(1, -1, 1) + + - 1/700 x y DATA(1, 1, -1) + 1/700 x y DATA(-1, 1, -1) + + + 1/700 x y DATA(-1, 1, 1) - 2/175 x y DATA(-2, 2, 2) + + + 2/175 x y DATA(-2, -2, -2) - 1/175 x y DATA(-2, 1, 2) + + - 2/175 x y DATA(2, -2, -2) + 1/175 x y DATA(-2, -1, -2) + + + 1/175 x y DATA(-2, -1, 2) - 1/350 x y DATA(1, -1, -2) + + - 1/175 x y DATA(2, -1, -2) + 1/350 x y DATA(-1, -1, -2) + + + 1/175 x y DATA(-1, -2, -2) - 1/175 x y DATA(1, -2, -2) + + 2 2 + + 2/245 x DATA(2, 2, 2) - 1/245 x DATA(1, 2, 2) + 2/175 x DATA(2, 1, 2) + + + 2/175 x DATA(2, -2, 2) + 1/175 x DATA(-2, 2, -1) + + 2 2 + + 2/245 x DATA(2, -2, 2) - 1/245 x DATA(-2, 2, -1) + + - 1/175 x DATA(-1, 2, 2) - 1/175 x DATA(-1, -2, 2) + + + 2/175 x DATA(2, -1, 2) + 1/175 x DATA(1, 1, 2) - 1/175 x DATA(-1, 1, 2) + + + 1/175 x DATA(1, -1, 2) - 1/175 x DATA(2, -2, -1) + + + 1/175 x DATA(-2, -1, -1) - 2/175 x DATA(-2, -2, 2) + + - 1/350 x DATA(1, -2, -1) + 1/175 x DATA(-2, 1, -1) + + 211 + + 1/175 x DATA(1, -2, 2) + ---- DATA(1, 2, -1) + 1/175 x DATA(1, -2, -2) + 3675 + + - 1/175 x DATA(-1, -1, -2) - 1/350 x DATA(1, -1, 1) + + + 2/175 x DATA(2, 2, 2) + 1/175 x DATA(1, 2, 2) + 1/350 x DATA(-1, -1, -1) + + - 1/350 x DATA(1, -1, -1) + 1/350 x DATA(-1, 1, 1) + + + 1/350 x DATA(-1, 1, -1) - 1/350 x DATA(1, 1, -1) + + - 1/175 x DATA(-1, -2, -2) - 2/175 x DATA(-2, -2, -2) + + - 2/175 x DATA(-2, 1, 2) - 2/175 x DATA(-2, -1, 2) + + - 2/175 x DATA(-2, -1, -2) + 1/175 x DATA(1, -1, -2) + + 169 + + 2/175 x DATA(2, -2, -2) - 2/175 x DATA(-2, 2, 2) - ----- DATA(-2, 1, -2) + 14700 + + 211 + + 2/175 x DATA(2, -1, -2) + 1/350 x DATA(-1, -1, 1) + ---- DATA(-1, 2, -1) + 3675 + + 2 2 + - 1/245 x DATA(-2, -2, 1) - 1/245 x DATA(2, -2, 1) + + 2 2 + + 1/490 x DATA(1, -2, 1) + 1/490 x DATA(1, 1, 1) + + 2 2 + + 1/490 x DATA(-1, 2, -1) - 1/245 x DATA(2, 1, -1) + + 2 2 + - 1/245 x DATA(2, -1, -1) + 1/490 x DATA(-1, -2, 1) + + 2 2 + - 1/245 x DATA(-2, -1, 1) + 2/245 x DATA(2, 1, -2) + + 2 2 + - 1/245 x DATA(1, 1, -2) - 1/245 x DATA(-1, 2, -2) + + 2 2 + - 1/245 x DATA(2, 2, 1) - 1/245 x DATA(2, 2, -1) + + 2 2 + + 2/245 x DATA(-2, 1, -2) - 1/245 x DATA(1, 2, -2) + + 2 2 + + 1/490 x DATA(-1, -2, -1) + 2/245 x DATA(-2, 2, -2) + + 2 2 + + 1/490 x DATA(1, 2, -1) - 1/245 x DATA(-1, 1, -2) + + 2 2 + - 1/245 x DATA(-2, 1, 1) - 1/245 x DATA(1, 1, 2) + + 2 2 + - 1/245 x DATA(-1, 1, 2) - 1/245 x DATA(1, -1, 2) + + 2 2 + - 1/245 x DATA(2, -2, -1) - 1/245 x DATA(-2, -1, -1) + + 2 2 + - 1/245 x DATA(2, 1, 1) - 1/245 x DATA(-1, -1, 2) + + 2 2 + + 1/490 x DATA(1, 2, 1) + 2/245 x DATA(2, 2, -2) + + 2 2 + - 1/245 x DATA(2, -1, 1) + 1/490 x DATA(-1, 2, 1) + + 2 2 + - 1/245 x DATA(-2, -2, -1) - 1/245 x DATA(-1, -2, 2) + + 2 2 + - 1/245 x DATA(1, -2, 2) - 1/245 x DATA(-2, 2, 1) + + 2 2 + + 1/490 x DATA(-1, -1, 1) + 2/245 x DATA(-2, -2, -2) + + 2 2 + + 1/490 x DATA(1, -1, -1) + 2/245 x DATA(-2, -2, 2) + + 2 2 + + 1/490 x DATA(1, -2, -1) - 1/245 x DATA(-2, 1, -1) + + 2 2 + + 2/245 x DATA(2, 1, 2) - 1/245 x DATA(-1, 2, 2) + + 2 2 + + 2/245 x DATA(2, -1, 2) + 1/490 x DATA(1, -1, 1) + + 2 2 + + 2/245 x DATA(-2, 2, 2) + 2/245 x DATA(-2, 1, 2) + + 2 2 + + 2/245 x DATA(-2, -1, 2) + 2/245 x DATA(-2, -1, -2) + + 2 2 + - 1/245 x DATA(1, -1, -2) + 1/490 x DATA(-1, -1, -1) + + 2 2 + + 1/490 x DATA(-1, 1, 1) + 1/490 x DATA(-1, 1, -1) + + 2 2 + + 1/490 x DATA(1, 1, -1) + 2/245 x DATA(2, -2, -2) + + 2 2 + - 1/245 x DATA(1, -2, -2) - 1/245 x DATA(-1, -2, -2) + + 2 2 + - 1/245 x DATA(-1, -1, -2) + 2/245 x DATA(2, -1, -2) + + 211 + + ---- DATA(2, 1, -1) - 1/175 x DATA(2, -2, 1) - 1/175 x DATA(2, -1, -1) + 3675 + + - 2/175 x DATA(-2, 1, -2) + 1/175 x DATA(-2, -1, 1) + + + 2/175 x DATA(2, 1, -2) - 1/175 x DATA(-1, 1, -2) + + + 1/350 x DATA(-1, -2, 1) - 1/350 x DATA(1, -2, 1) + + + 1/175 x DATA(-2, -2, 1) - 1/175 x DATA(-1, 2, -2) + + - 1/175 x DATA(2, 2, 1) - 1/175 x DATA(2, 1, 1) + 1/175 y DATA(2, -2, 1) + + + 1/175 y DATA(1, -2, 1) - 1/350 y DATA(1, 1, 1) - 1/175 y DATA(-1, 2, -1) + + + 1/175 y DATA(-1, -2, 1) + 1/175 y DATA(2, 1, -2) + + + 1/175 y DATA(-1, 1, -2) + 1/350 y DATA(-2, -1, 1) + + + 1/350 y DATA(2, -1, -1) + 1/175 y DATA(-2, -2, 1) + + - 1/350 y DATA(-2, 1, 1) - 1/350 y DATA(2, 1, 1) - 1/175 y DATA(-1, -1, 2) + + - 1/175 y DATA(1, 2, 1) - 1/175 y DATA(-2, 2, 1) + 1/175 y DATA(1, 1, -2) + + + 2/175 y DATA(-1, 2, -2) + 2/175 y DATA(1, 2, -2) + + + 2/175 y DATA(-2, 2, -2) + 1/175 y DATA(-1, -2, -1) + + - 1/350 y DATA(2, 1, -1) - 1/175 y DATA(2, 2, -1) - 1/175 y DATA(1, 2, -1) + + + 1/175 y DATA(-2, 1, -2) + 1/175 y DATA(2, 1, 2) + 2/175 y DATA(-1, 2, 2) + + - 1/350 y DATA(-2, 1, -1) - 1/175 y DATA(1, -1, 2) + + + 1/350 y DATA(-2, -1, -1) - 2/175 y DATA(-2, -2, 2) + + + 1/175 y DATA(2, -2, -1) - 2/175 y DATA(1, -2, 2) + 1/175 y DATA(1, 1, 2) + + + 1/175 y DATA(-1, 1, 2) - 1/175 y DATA(2, -1, 2) + 2/175 y DATA(2, 2, -2) + + - 1/175 y DATA(-1, 2, 1) + 1/175 y DATA(-2, -2, -1) + + - 2/175 y DATA(-1, -2, 2) + 1/350 y DATA(2, -1, 1) - 1/175 y DATA(2, 2, 1) + + - 1/350 y DATA(-1, 1, -1) + 1/350 y DATA(-1, -1, -1) + + + 1/350 y DATA(1, -1, -1) - 1/350 y DATA(-1, 1, 1) + + - 2/175 y DATA(2, -2, 2) - 1/175 y DATA(-2, 2, -1) + 2/175 y DATA(2, 2, 2) + + + 2/175 y DATA(1, 2, 2) + 1/175 y DATA(1, -2, -1) - 1/350 y DATA(1, 1, -1) + + + 1/350 y DATA(-1, -1, 1) + 2/175 y DATA(-2, 2, 2) + + + 1/175 y DATA(-2, 1, 2) - 2/175 y DATA(-2, -2, -2) + + + 1/350 y DATA(1, -1, 1) - 1/175 y DATA(-2, -1, 2) - 1/10 DATA(2, 0, 0) + + 311 211 + + ----- DATA(0, 1, -2) + ---- DATA(-2, 1, 1) - 9/98 DATA(2, -1, 0) + 14700 3675 + + 191 + + ----- DATA(-1, 1, -2) - 1/50 x z DATA(2, -1, -2) + 14700 + + + 1/100 x z DATA(-1, -1, -2) + 1/100 x z DATA(-1, -2, -2) + + + 1/100 x z DATA(1, -2, 2) - 1/100 x z DATA(-1, -2, 2) + + - 1/50 x z DATA(-2, 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DATA(0, -1, 1) + 1/245 x DATA(0, 1, 1) + + - 1/350 x y DATA(-1, -2, 1) + 1/50 z DATA(-2, 0, 2) + + 529 + - ----- DATA(-2, -2, -2) - 1/50 z DATA(-1, 0, -2) + 14700 + + - 1/350 x y DATA(-2, -1, 1) + 1/175 x y DATA(2, 1, -2) + + 529 + - 1/350 x y DATA(-1, 1, -2) - ----- DATA(-2, 2, 2) + 14700 + + + 1/25 z DATA(-2, 0, -1) + 1/350 x y DATA(-2, 1, 1) + + - 1/700 x y DATA(1, 1, 1) - 1/25 z DATA(-1, 0, 1) + 1/25 z DATA(0, 0, -1) + + 2 + + 1/350 x y DATA(-1, 2, -1) - 2/25 z DATA(-1, 0, -1) + + 2 2 2 + + 3/25 z DATA(0, 0, 0) + 3/25 z DATA(1, 0, 0) + 1/50 z DATA(1, 0, 2) + + 2 2 + + 3/25 z DATA(2, -2, 0) - 2/25 z DATA(-2, 0, 1) + + 2 2 2 + + 3/25 z DATA(-2, -1, 0) + 3/25 z DATA(-2, 1, 0) + 1/50 z DATA(2, 0, 2) + + 2 169 + + 1/50 z DATA(0, 0, 2) - ----- DATA(1, -2, -2) - 1/300 DATA(0, -2, -2) + 14700 + + - 1/25 z DATA(-2, 0, 1) + 1/50 z DATA(1, 0, 2) + 1/25 z DATA(-1, 0, -1) + + 169 169 2 + - ----- DATA(-1, -2, -2) - ----- DATA(-2, -1, -2) - 2/25 z DATA(0, 0, -1) + 14700 14700 + + 2 2 2 + - 2/25 z DATA(1, 0, -1) + 3/25 z DATA(2, 2, 0) - 2/25 z DATA(-1, 0, 1) + + 2 2 2 + + 3/25 z DATA(0, 2, 0) + 3/25 z DATA(-1, 2, 0) + 3/25 z DATA(0, 1, 0) + + 2 2 2 + + 3/25 z DATA(1, 1, 0) + 3/25 z DATA(2, 0, 0) + 3/25 z DATA(2, -1, 0) + + 2 2 2 + + 3/25 z DATA(1, 2, 0) + 1/50 z DATA(2, 0, -2) - 2/25 z DATA(2, 0, 1) + + 2 + + 3/25 z DATA(-2, 0, 0) + 1/175 x y DATA(2, -2, 1) + + 2 + + 1/350 x y DATA(2, -1, -1) + 3/25 z DATA(0, -2, 0) + + 2 2 2 + - 2/25 z DATA(0, 0, 1) - 2/25 z DATA(1, 0, 1) + 3/25 z DATA(1, -2, 0) + + 2 529 191 + - 2/25 z DATA(2, 0, -1) - ----- DATA(2, -2, -2) + ----- DATA(1, -1, -2) + 14700 14700 + + 311 191 + + ----- DATA(0, -1, -2) + ----- DATA(-1, -1, -2) + 14700 14700 + + 2 + - 1/175 x y DATA(-2, -2, 1) + 1/50 z DATA(-1, 0, 2) + + 2 + + 3/25 z DATA(2, 1, 0) + 1/175 x y DATA(1, -2, 0) + + - 1/350 x y DATA(1, 1, 0) + 2/175 x y DATA(2, -2, 0) + + 2 + - 1/175 x y DATA(-2, -1, 0) + 3/25 z DATA(-2, -2, 0) + + 2 2 + + 3/25 z DATA(-1, -2, 0) + 1/50 z DATA(0, 0, 2) + 3/25 z DATA(0, -1, 0) + + 2 2 + + 1/50 z DATA(-2, 0, 2) - 2/25 z DATA(-2, 0, -1) + + 2 + + 3/25 z DATA(-2, 2, 0) + 1/350 x y DATA(1, -2, 1) + + 169 + - 1/300 DATA(-2, 0, -2) - ----- DATA(2, -1, -2) + 14700 + + + 1/100 x z DATA(-1, 0, -2) - 2/175 x y DATA(2, 2, 0) + + + 1/350 x y DATA(1, -1, 0) + 1/350 x y DATA(-1, 1, 0) + + 431 + - 1/175 x y DATA(2, 1, 0) + ----- DATA(0, 0, -2) + 14700 + + + 1/175 x y DATA(-1, 2, 0) - 1/175 x y DATA(1, 2, 0) + + 311 311 + + 1/175 x y DATA(2, -1, 0) + ----- DATA(-1, 0, -2) + ----- DATA(1, 0, -2) + 14700 14700 + + - 1/100 x z DATA(1, 0, -2) - 1/50 z DATA(1, 0, -2) + + 2 2 2 + + 3/25 z DATA(1, -1, 0) + 3/25 z DATA(-1, 0, 0) + 3/25 z DATA(-1, 1, 0) + + - 1/50 x z DATA(-2, 0, 2) + +> coeffs_as_lc_of_data(%, posn_list_3d_size5); +bytes used=2466555596, alloc=14677376, time=410.58 +bytes used=2467555944, alloc=14677376, time=410.66 +bytes used=2468657096, alloc=14677376, time=410.75 +bytes used=2469657732, alloc=14677376, time=410.83 +bytes used=2470695080, alloc=14677376, 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+bytes used=2491058220, alloc=14677376, time=412.83 +bytes used=2492061428, alloc=14677376, time=412.95 +bytes used=2493083408, alloc=14677376, time=413.03 +bytes used=2494101524, alloc=14677376, time=413.10 +bytes used=2495119240, alloc=14677376, time=413.18 +[COEFF(-2, -2, -2) = - 2/175 x + 1/50 y z - 1/50 z + 2/175 x y + 1/50 x z + + 2 2 2 529 + - 2/175 y + 1/50 z + 2/245 x + 2/245 y - -----, COEFF(-1, -2, -2) = + 14700 + + 2 169 + 1/50 y z - 1/245 x - 1/175 x - 1/50 z - 2/175 y - ----- + 1/175 x y + 14700 + + 2 2 + + 2/245 y + 1/100 x z + 1/50 z , COEFF(0, -2, -2) = + + 2 2 2 + - 1/50 z - 2/175 y + 2/245 y - 2/245 x - 1/300 + 1/50 y z + 1/50 z , + + COEFF(1, -2, -2) = 1/50 y z - 1/50 z - 2/175 y + 1/175 x - 1/175 x y + + 2 2 169 2 + + 2/245 y + 1/50 z - ----- - 1/245 x - 1/100 x z, COEFF(2, -2, -2) = + 14700 + + 2 2 2 + - 2/175 y + 2/245 x + 2/245 y + 2/175 x - 1/50 x z + 1/50 z - 2/175 x y + + 529 + - 1/50 z + 1/50 y z - -----, COEFF(-2, -1, -2) = - 1/175 y - 1/50 z + 14700 + + 2 2 2 169 + + 1/50 z + 2/245 x - 2/175 x + 1/175 x y - 1/245 y + 1/100 y z - ----- + 14700 + + + 1/50 x z, COEFF(-1, -1, -2) = - 1/175 y + 1/350 x y + 1/100 x z - 1/50 z + + 2 2 191 2 + - 1/245 y + 1/100 y z - 1/245 x - 1/175 x + ----- + 1/50 z , + 14700 + + COEFF(0, -1, -2) = + + 2 311 2 2 + - 1/245 y + ----- - 2/245 x + 1/100 y z + 1/50 z - 1/50 z - 1/175 y, + 14700 + + 2 191 + COEFF(1, -1, -2) = 1/100 y z - 1/175 y - 1/245 x - 1/350 x y + ----- + 14700 + + 2 2 + + 1/175 x + 1/50 z - 1/50 z - 1/245 y - 1/100 x z, COEFF(2, -1, -2) = + + 2 2 169 + - 1/245 y - 1/175 y + 2/175 x + 1/50 z - 1/50 z - 1/50 x z - ----- + 14700 + + 2 + + 1/100 y z - 1/175 x y + 2/245 x , COEFF(-2, 0, -2) = + + 2 2 2 + - 2/245 y - 1/50 z + 1/50 z - 2/175 x + 1/50 x z - 1/300 + 2/245 x , + + COEFF(-1, 0, -2) = + + 311 2 2 2 + - 1/175 x + 1/100 x z + ----- - 1/245 x - 2/245 y - 1/50 z + 1/50 z , + 14700 + + 431 2 2 2 + COEFF(0, 0, -2) = ----- + 1/50 z - 1/50 z - 2/245 x - 2/245 y , + 14700 + + COEFF(1, 0, -2) = + + 311 2 2 2 + ----- - 2/245 y + 1/50 z - 1/50 z - 1/245 x - 1/100 x z + 1/175 x, + 14700 + + COEFF(2, 0, -2) = + + 2 2 2 + 2/245 x - 1/300 + 2/175 x - 2/245 y + 1/50 z - 1/50 z - 1/50 x z, + + 169 2 2 + COEFF(-2, 1, -2) = - 1/50 z - ----- - 1/100 y z - 1/245 y + 2/245 x + 14700 + + 2 + - 1/175 x y + 1/50 x z + 1/50 z + 1/175 y - 2/175 x, COEFF(-1, 1, -2) = + + 191 2 2 + - 1/50 z - 1/175 x + ----- + 1/175 y + 1/100 x z - 1/245 y - 1/245 x + 14700 + + 2 + - 1/100 y z + 1/50 z - 1/350 x y, COEFF(0, 1, -2) = + + 2 2 2 311 + 1/175 y - 1/50 z + 1/50 z - 1/245 y - 2/245 x - 1/100 y z + -----, + 14700 + + 191 + COEFF(1, 1, -2) = ----- - 1/100 x z - 1/50 z - 1/100 y z + 1/175 y + 14700 + + 2 2 2 + + 1/350 x y + 1/50 z - 1/245 y + 1/175 x - 1/245 x , COEFF(2, 1, -2) = + + 169 2 2 + 1/175 x y + 1/175 y - ----- - 1/100 y z + 1/50 z - 1/50 z + 2/245 x + 14700 + + 2 2 + - 1/245 y + 2/175 x - 1/50 x z, COEFF(-2, 2, -2) = 1/50 x z + 2/245 y + + 2 2 529 + - 1/50 y z + 1/50 z + 2/245 x + 2/175 y - 2/175 x - 2/175 x y - ----- + 14700 + + 169 + - 1/50 z, COEFF(-1, 2, -2) = - 1/50 y z + 1/100 x z - 1/175 x y - ----- + 14700 + + 2 2 2 + - 1/175 x + 2/245 y - 1/245 x + 1/50 z - 1/50 z + 2/175 y, + + COEFF(0, 2, -2) = + + 2 2 2 + 2/175 y + 1/50 z - 1/50 y z - 1/50 z - 1/300 - 2/245 x + 2/245 y , + + 2 169 2 + COEFF(1, 2, -2) = - 1/245 x - ----- - 1/100 x z + 1/50 z + 1/175 x + 14700 + + 2 + - 1/50 z + 2/245 y + 1/175 x y - 1/50 y z + 2/175 y, COEFF(2, 2, -2) = + + 529 2 2 + 2/175 x - 1/50 x z + 2/175 y - ----- + 1/50 z - 1/50 z + 2/245 y + 14700 + + 2 2 256 + + 2/245 x - 1/50 y z + 2/175 x y, COEFF(-2, -2, -1) = - 2/25 z + ---- + 3675 + + 2 2 + + 1/175 x - 1/175 x y + 1/175 y + 1/25 z - 1/245 y - 1/245 x - 1/25 y z + + 2 2 + - 1/25 x z, COEFF(-1, -2, -1) = - 1/25 y z - 2/25 z - 1/50 x z + 1/490 x + + 2 211 + + 1/25 z - 1/245 y + 1/175 y - 1/350 x y + 1/350 x + ----, + 3675 + + COEFF(0, -2, -1) = + + 2 2 2 + - 1/245 y + 1/175 y - 1/25 y z + 1/25 z + 1/245 x + 4/75 - 2/25 z , + + 2 2 + COEFF(1, -2, -1) = - 1/25 y z + 1/175 y + 1/490 x + 1/50 x z - 1/245 y + + 211 2 + + 1/350 x y - 1/350 x + 1/25 z + ---- - 2/25 z , COEFF(2, -2, -1) = + 3675 + + 2 2 + - 1/175 x - 2/25 z + 1/25 x z + 1/175 x y + 1/175 y - 1/245 x + 1/25 z + + 256 2 + + ---- - 1/25 y z - 1/245 y , COEFF(-2, -1, -1) = 1/25 z - 1/50 y z + 3675 + + 211 2 2 2 + - 1/350 x y - 1/25 x z + ---- + 1/490 y - 2/25 z + 1/175 x - 1/245 x + 3675 + + 2 + + 1/350 y, COEFF(-1, -1, -1) = - 1/50 y z + 1/350 y + 1/490 y - 1/700 x y + + 2 2 166 + - 2/25 z + 1/490 x + 1/25 z - 1/50 x z + 1/350 x + ----, + 3675 + + COEFF(0, -1, -1) = + + 2 151 2 2 + - 1/50 y z - 2/25 z + ---- + 1/245 x + 1/350 y + 1/490 y + 1/25 z, + 3675 + + 166 2 2 + COEFF(1, -1, -1) = ---- + 1/490 y + 1/700 x y + 1/350 y - 2/25 z + 3675 + + 2 + + 1/490 x + 1/25 z - 1/350 x - 1/50 y z + 1/50 x z, COEFF(2, -1, -1) = + + 211 2 2 + ---- + 1/350 x y - 1/175 x - 1/50 y z + 1/490 y - 2/25 z + 1/350 y + 3675 + + 2 + - 1/245 x + 1/25 x z + 1/25 z, COEFF(-2, 0, -1) = + + 2 2 2 + 1/175 x - 1/245 x + 4/75 + 1/25 z - 2/25 z - 1/25 x z + 1/245 y , + + COEFF(-1, 0, -1) = + + 151 2 2 2 + ---- + 1/350 x + 1/245 y - 2/25 z - 1/50 x z + 1/25 z + 1/490 x , + 3675 + + 2 2 136 2 + COEFF(0, 0, -1) = 1/245 y + 1/245 x + ---- + 1/25 z - 2/25 z , + 3675 + + COEFF(1, 0, -1) = + + 2 2 151 2 + 1/490 x - 2/25 z - 1/350 x + ---- + 1/50 x z + 1/245 y + 1/25 z, + 3675 + + COEFF(2, 0, -1) = + + 2 2 2 + - 1/175 x - 1/245 x + 4/75 - 2/25 z + 1/245 y + 1/25 z + 1/25 x z, + + 2 2 + COEFF(-2, 1, -1) = - 1/245 x - 1/350 y - 1/25 x z + 1/490 y + 1/350 x y + + 2 211 + + 1/50 y z - 2/25 z + ---- + 1/175 x + 1/25 z, COEFF(-1, 1, -1) = + 3675 + + 2 166 2 + - 2/25 z + ---- + 1/50 y z - 1/350 y + 1/490 y + 1/25 z + 1/700 x y + 3675 + + 2 + + 1/490 x - 1/50 x z + 1/350 x, COEFF(0, 1, -1) = + + 2 2 151 2 + 1/50 y z + 1/490 y + 1/245 x + ---- - 2/25 z + 1/25 z - 1/350 y, + 3675 + + 2 166 2 2 + COEFF(1, 1, -1) = 1/50 y z - 2/25 z - 1/350 x + ---- + 1/490 y + 1/490 x + 3675 + + - 1/700 x y - 1/350 y + 1/25 z + 1/50 x z, COEFF(2, 1, -1) = 1/50 y z + + 2 2 2 + - 2/25 z - 1/350 y - 1/245 x + 1/25 z + 1/25 x z - 1/175 x + 1/490 y + + 211 2 + - 1/350 x y + ----, COEFF(-2, 2, -1) = - 1/245 y - 1/25 x z + 1/175 x + 3675 + + 2 256 2 + - 1/245 x + 1/25 y z - 1/175 y + 1/175 x y + ---- - 2/25 z + 1/25 z, + 3675 + + 211 2 2 + COEFF(-1, 2, -1) = 1/25 y z + ---- + 1/490 x - 2/25 z - 1/50 x z + 3675 + + 2 + + 1/350 x y + 1/25 z - 1/245 y - 1/175 y + 1/350 x, COEFF(0, 2, -1) = + + 2 2 2 + 1/25 y z - 1/175 y - 1/245 y + 1/25 z + 4/75 - 2/25 z + 1/245 x , + + COEFF(1, 2, -1) = - 1/350 x y + 1/25 z + 1/25 y z + 1/50 x z - 1/175 y + + 211 2 2 2 + + ---- - 2/25 z - 1/350 x - 1/245 y + 1/490 x , COEFF(2, 2, -1) = + 3675 + + 256 2 2 + - 1/175 y - 1/175 x y + ---- - 1/245 y + 1/25 z + 1/25 x z - 1/245 x + 3675 + + 2 + - 1/175 x + 1/25 y z - 2/25 z , COEFF(-2, -2, 0) = + + 2 2 33 2 + 3/25 z - 2/245 x - --- + 2/175 y - 2/175 x y - 2/245 y + 2/175 x, + 490 + + COEFF(-1, -2, 0) = + + 2 2 2 + - 1/175 x y + 1/175 x + 3/25 z + 1/245 x - 2/245 y - 9/98 + 2/175 y, + + 2 2 2 + COEFF(0, -2, 0) = - 1/10 + 3/25 z - 2/245 y + 2/175 y + 2/245 x , + + COEFF(1, -2, 0) = + + 2 2 2 + 3/25 z + 1/245 x - 2/245 y - 1/175 x + 1/175 x y + 2/175 y - 9/98, + + COEFF(2, -2, 0) = + + 33 2 2 2 + - --- + 3/25 z - 2/245 y - 2/245 x + 2/175 y - 2/175 x + 2/175 x y, + 490 + + COEFF(-2, -1, 0) = + + 2 2 2 + 2/175 x + 3/25 z + 1/175 y - 1/175 x y + 1/245 y - 2/245 x - 9/98, + + COEFF(-1, -1, 0) = + + 57 2 2 2 + - 1/350 x y - --- + 1/175 x + 3/25 z + 1/245 x + 1/245 y + 1/175 y, + 490 + + 2 2 2 61 + COEFF(0, -1, 0) = 3/25 z + 1/245 y + 2/245 x + 1/175 y - ---, + 490 + + COEFF(1, -1, 0) = + + 2 57 2 2 + 1/350 x y + 1/245 y - 1/175 x - --- + 1/245 x + 3/25 z + 1/175 y, + 490 + + COEFF(2, -1, 0) = + + 2 2 2 + 3/25 z - 9/98 - 2/245 x - 2/175 x + 1/175 y + 1/175 x y + 1/245 y , + + 2 2 2 + COEFF(-2, 0, 0) = 3/25 z + 2/245 y - 1/10 - 2/245 x + 2/175 x, + + 2 2 2 61 + COEFF(-1, 0, 0) = 2/245 y + 1/245 x + 3/25 z - --- + 1/175 x, + 490 + + 2 2 13 2 + COEFF(0, 0, 0) = 2/245 x + 2/245 y - -- + 3/25 z , + 98 + + 61 2 2 2 + COEFF(1, 0, 0) = - --- + 1/245 x + 3/25 z + 2/245 y - 1/175 x, + 490 + + 2 2 2 + COEFF(2, 0, 0) = 2/245 y - 2/175 x + 3/25 z - 1/10 - 2/245 x , + + COEFF(-2, 1, 0) = + + 2 2 2 + 3/25 z + 1/245 y + 1/175 x y - 2/245 x - 9/98 - 1/175 y + 2/175 x, + + COEFF(-1, 1, 0) = + + 2 2 2 57 + 1/245 y + 1/245 x - 1/175 y + 1/175 x + 3/25 z - --- + 1/350 x y, + 490 + + 2 2 2 61 + COEFF(0, 1, 0) = - 1/175 y + 2/245 x + 1/245 y + 3/25 z - ---, + 490 + + COEFF(1, 1, 0) = + + 57 2 2 2 + - --- + 1/245 y + 1/245 x - 1/175 x - 1/175 y - 1/350 x y + 3/25 z , + 490 + + COEFF(2, 1, 0) = + + 2 2 2 + - 9/98 - 2/175 x + 3/25 z + 1/245 y - 1/175 x y - 1/175 y - 2/245 x , + + COEFF(-2, 2, 0) = + + 2 33 2 2 + - 2/245 x - 2/175 y + 2/175 x y - --- + 3/25 z + 2/175 x - 2/245 y , + 490 + + COEFF(-1, 2, 0) = + + 2 2 2 + 3/25 z - 9/98 - 2/175 y + 1/175 x - 2/245 y + 1/245 x + 1/175 x y, + + 2 2 2 + COEFF(0, 2, 0) = - 2/245 y - 1/10 - 2/175 y + 2/245 x + 3/25 z , + + COEFF(1, 2, 0) = + + 2 2 2 + - 2/175 y - 9/98 - 1/175 x + 1/245 x - 2/245 y - 1/175 x y + 3/25 z , + + COEFF(2, 2, 0) = + + 33 2 2 2 + - 2/175 y - --- - 2/175 x - 2/175 x y - 2/245 y - 2/245 x + 3/25 z , + 490 + + 256 2 + COEFF(-2, -2, 1) = 1/25 y z + 1/175 y + ---- - 1/245 x + 1/175 x + 3675 + + 2 2 + - 1/175 x y - 1/245 y + 1/25 x z - 1/25 z - 2/25 z , COEFF(-1, -2, 1) = + + 2 211 2 + - 1/25 z - 1/245 y + ---- + 1/490 x + 1/350 x + 1/25 y z + 1/175 y + 3675 + + 2 + - 1/350 x y - 2/25 z + 1/50 x z, COEFF(0, -2, 1) = + + 2 2 2 + - 1/25 z - 1/245 y + 1/25 y z + 1/175 y + 4/75 + 1/245 x - 2/25 z , + + COEFF(1, -2, 1) = - 1/350 x - 1/50 x z + 1/25 y z + 1/175 y - 1/25 z + + 2 2 211 2 + - 1/245 y + 1/350 x y - 2/25 z + ---- + 1/490 x , COEFF(2, -2, 1) = + 3675 + + 2 256 2 + - 1/245 x + ---- + 1/175 x y - 2/25 z - 1/25 z - 1/25 x z + 1/175 y + 3675 + + 2 + - 1/175 x - 1/245 y + 1/25 y z, COEFF(-2, -1, 1) = 1/50 y z + 1/25 x z + + 2 2 2 211 + - 1/245 x + 1/350 y + 1/490 y - 1/25 z - 2/25 z + ---- - 1/350 x y + 3675 + + 2 166 + + 1/175 x, COEFF(-1, -1, 1) = 1/490 y + 1/50 x z - 1/700 x y + ---- + 3675 + + 2 2 + + 1/350 x + 1/350 y + 1/490 x - 2/25 z - 1/25 z + 1/50 y z, + + COEFF(0, -1, 1) = + + 2 2 2 151 + - 2/25 z + 1/350 y + 1/245 x + 1/490 y + ---- - 1/25 z + 1/50 y z, + 3675 + + 166 2 2 + COEFF(1, -1, 1) = - 1/25 z + ---- + 1/350 y - 2/25 z - 1/350 x + 1/490 x + 3675 + + 2 2 + + 1/490 y - 1/50 x z + 1/50 y z + 1/700 x y, COEFF(2, -1, 1) = - 2/25 z + + 2 211 2 + + 1/490 y + 1/350 y + ---- - 1/25 x z - 1/245 x - 1/25 z - 1/175 x + 3675 + + + 1/350 x y + 1/50 y z, COEFF(-2, 0, 1) = + + 2 2 2 + - 1/25 z + 4/75 + 1/25 x z + 1/245 y + 1/175 x - 2/25 z - 1/245 x , + + COEFF(-1, 0, 1) = + + 151 2 2 2 + ---- + 1/245 y + 1/490 x - 2/25 z + 1/50 x z + 1/350 x - 1/25 z, + 3675 + + 2 2 2 136 + COEFF(0, 0, 1) = 1/245 y + 1/245 x - 1/25 z - 2/25 z + ----, + 3675 + + COEFF(1, 0, 1) = + + 151 2 2 2 + ---- + 1/490 x - 1/350 x + 1/245 y - 1/50 x z - 1/25 z - 2/25 z , + 3675 + + COEFF(2, 0, 1) = + + 2 2 2 + 1/245 y + 4/75 - 1/245 x - 2/25 z - 1/175 x - 1/25 x z - 1/25 z, + + 2 2 + COEFF(-2, 1, 1) = - 2/25 z + 1/175 x + 1/350 x y - 1/350 y - 1/245 x + + 2 211 + - 1/25 z + 1/490 y + ---- - 1/50 y z + 1/25 x z, COEFF(-1, 1, 1) = + 3675 + + 2 2 2 166 + - 2/25 z - 1/50 y z - 1/350 y + 1/490 x + 1/490 y + 1/700 x y + ---- + 3675 + + + 1/350 x - 1/25 z + 1/50 x z, COEFF(0, 1, 1) = + + 2 2 2 151 + 1/490 y - 2/25 z - 1/50 y z + 1/245 x + ---- - 1/350 y - 1/25 z, + 3675 + + 2 2 2 166 + COEFF(1, 1, 1) = 1/490 x - 2/25 z - 1/350 x - 1/350 y + 1/490 y + ---- + 3675 + + - 1/700 x y - 1/25 z - 1/50 y z - 1/50 x z, COEFF(2, 1, 1) = - 1/25 z + + 211 2 2 + - 1/350 x y + ---- - 2/25 z - 1/175 x - 1/25 x z - 1/245 x - 1/50 y z + 3675 + + 2 2 256 + - 1/350 y + 1/490 y , COEFF(-2, 2, 1) = - 2/25 z + ---- + 1/175 x y + 3675 + + 2 2 + - 1/25 y z - 1/245 y + 1/175 x + 1/25 x z - 1/25 z - 1/175 y - 1/245 x , + + 2 211 + COEFF(-1, 2, 1) = 1/350 x + 1/490 x - 1/25 z + 1/50 x z - 1/175 y + ---- + 3675 + + 2 2 + - 2/25 z + 1/350 x y - 1/245 y - 1/25 y z, COEFF(0, 2, 1) = + + 2 2 2 + - 1/25 y z - 1/245 y - 1/25 z + 4/75 + 1/245 x - 2/25 z - 1/175 y, + + 211 2 + COEFF(1, 2, 1) = - 1/350 x + ---- - 1/175 y + 1/490 x - 1/25 y z - 1/25 z + 3675 + + 2 2 + - 1/245 y - 1/350 x y - 1/50 x z - 2/25 z , COEFF(2, 2, 1) = - 1/25 z + + 2 2 256 + - 1/175 x y - 1/25 x z - 1/245 x - 1/25 y z - 1/175 y - 1/245 y + ---- + 3675 + + 2 2 + - 1/175 x - 2/25 z , COEFF(-2, -2, 2) = 2/245 x - 1/50 y z + 1/50 z + + 529 2 2 + - 2/175 x - 2/175 y - 1/50 x z - ----- + 1/50 z + 2/175 x y + 2/245 y , + 14700 + + 2 2 + COEFF(-1, -2, 2) = 2/245 y + 1/50 z - 1/175 x - 2/175 y + 1/50 z + + 2 169 + - 1/50 y z - 1/245 x + 1/175 x y - ----- - 1/100 x z, COEFF(0, -2, 2) = + 14700 + + 2 2 2 + - 2/245 x - 1/300 - 2/175 y + 1/50 z - 1/50 y z + 1/50 z + 2/245 y , + + 169 + COEFF(1, -2, 2) = 1/50 z + 1/100 x z - ----- - 1/50 y z - 2/175 y + 14700 + + 2 2 2 + - 1/175 x y + 1/50 z - 1/245 x + 1/175 x + 2/245 y , COEFF(2, -2, 2) = + + 2 529 + 2/175 x - 2/175 x y + 2/245 x + 1/50 z - ----- - 1/50 y z - 2/175 y + 14700 + + 2 2 2 + + 2/245 y + 1/50 z + 1/50 x z, COEFF(-2, -1, 2) = 1/50 z - 1/100 y z + + 169 2 2 + + 1/175 x y - 1/50 x z - ----- + 2/245 x + 1/50 z - 1/175 y - 1/245 y + 14700 + + 2 + - 2/175 x, COEFF(-1, -1, 2) = 1/50 z - 1/245 y - 1/100 y z - 1/175 x + + 2 2 191 + + 1/50 z - 1/175 y - 1/245 x + 1/350 x y + ----- - 1/100 x z, + 14700 + + COEFF(0, -1, 2) = + + 2 2 311 2 + 1/50 z - 1/245 y + 1/50 z + ----- - 1/175 y - 1/100 y z - 2/245 x , + 14700 + + 2 2 + COEFF(1, -1, 2) = 1/100 x z - 1/350 x y - 1/245 y - 1/175 y - 1/245 x + + 2 191 + + 1/50 z + 1/175 x + ----- + 1/50 z - 1/100 y z, COEFF(2, -1, 2) = + 14700 + + 2 2 2 + 1/50 z - 1/100 y z - 1/245 y + 2/175 x + 1/50 z + 1/50 x z + 2/245 x + + 169 + - 1/175 x y - ----- - 1/175 y, COEFF(-2, 0, 2) = + 14700 + + 2 2 2 + - 2/175 x - 1/300 + 1/50 z + 2/245 x - 2/245 y + 1/50 z - 1/50 x z, + + COEFF(-1, 0, 2) = + + 2 311 2 2 + - 2/245 y - 1/175 x + 1/50 z - 1/100 x z + ----- + 1/50 z - 1/245 x , + 14700 + + 2 431 2 2 + COEFF(0, 0, 2) = - 2/245 x + ----- + 1/50 z - 2/245 y + 1/50 z, + 14700 + + COEFF(1, 0, 2) = + + 2 2 311 2 + 1/175 x + 1/100 x z - 1/245 x + 1/50 z + ----- + 1/50 z - 2/245 y , + 14700 + + COEFF(2, 0, 2) = + + 2 2 2 + 1/50 x z + 2/245 x - 2/245 y - 1/300 + 2/175 x + 1/50 z + 1/50 z, + + 2 169 + COEFF(-2, 1, 2) = 2/245 x - 1/175 x y + 1/175 y - ----- - 1/50 x z + 14700 + + 2 2 + - 2/175 x - 1/245 y + 1/50 z + 1/100 y z + 1/50 z, COEFF(-1, 1, 2) = + + 2 191 2 2 + - 1/245 x - 1/350 x y + 1/50 z + ----- + 1/50 z + 1/100 y z - 1/245 y + 14700 + + + 1/175 y - 1/175 x - 1/100 x z, COEFF(0, 1, 2) = + + 2 311 2 2 + - 2/245 x + 1/50 z + ----- - 1/245 y + 1/50 z + 1/100 y z + 1/175 y, + 14700 + + 2 191 + COEFF(1, 1, 2) = 1/175 y + 1/50 z + 1/50 z + 1/350 x y + ----- + 1/175 x + 14700 + + 2 2 + - 1/245 x + 1/100 y z - 1/245 y + 1/100 x z, COEFF(2, 1, 2) = 1/50 x z + + 2 2 + + 1/175 y + 1/50 z + 2/175 x + 1/100 y z + 2/245 x + 1/175 x y + + 2 169 + - 1/245 y - ----- + 1/50 z, COEFF(-2, 2, 2) = - 2/175 x y + 2/175 y + 14700 + + 2 2 2 529 + + 1/50 z + 2/245 x + 2/245 y - 2/175 x + 1/50 z + 1/50 y z - ----- + 14700 + + 2 169 + - 1/50 x z, COEFF(-1, 2, 2) = - 1/245 x - ----- + 1/50 y z - 1/175 x + 14700 + + 2 2 + + 1/50 z - 1/100 x z + 1/50 z - 1/175 x y + 2/175 y + 2/245 y , + + COEFF(0, 2, 2) = + + 2 2 2 + - 1/300 + 1/50 z + 1/50 z + 1/50 y z + 2/175 y - 2/245 x + 2/245 y , + + 169 2 2 + COEFF(1, 2, 2) = 1/175 x - ----- - 1/245 x + 1/100 x z + 1/50 z + 14700 + + 2 + + 2/245 y + 2/175 y + 1/50 z + 1/50 y z + 1/175 x y, COEFF(2, 2, 2) = + + 2 529 2 + 1/50 z + 2/175 x y - ----- + 2/175 x + 2/245 y + 1/50 z + 1/50 y z + 14700 + + 2 + + 2/245 x + 1/50 x z + 2/175 y] + +> print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dzz.compute.c"); +bytes used=2496119468, alloc=14677376, time=413.26 +bytes used=2497119884, alloc=14677376, time=413.35 +bytes used=2498120056, alloc=14677376, time=413.44 +bytes used=2499120280, alloc=14677376, time=413.53 +bytes used=2500120820, alloc=14677376, time=414.14 +bytes used=2501121368, alloc=14677376, time=414.76 +bytes used=2502121772, alloc=14677376, time=415.37 +bytes used=2503122000, alloc=14677376, time=415.98 +bytes used=2504122308, alloc=14677376, time=416.58 +bytes used=2505122500, alloc=14677376, time=416.95 +bytes used=2506122728, alloc=14677376, time=417.04 +bytes used=2507122900, alloc=14677376, time=417.12 +bytes used=2508167828, alloc=14677376, time=417.20 +bytes used=2509187272, alloc=14677376, time=417.27 +bytes used=2510215088, alloc=14677376, time=417.35 +bytes used=2511215248, alloc=14677376, time=417.45 +bytes used=2512215448, alloc=14677376, time=417.92 +bytes used=2513215736, alloc=14677376, time=419.17 +bytes used=2514215940, alloc=14677376, time=419.63 +bytes used=2515216124, alloc=14677376, time=419.89 +bytes 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used=2573282052, alloc=14677376, time=434.79 +bytes used=2574282380, alloc=14677376, time=434.86 +bytes used=2575282532, alloc=14677376, time=434.94 +bytes used=2576282752, alloc=14677376, time=435.01 +bytes used=2577282968, alloc=14677376, time=435.15 +bytes used=2578283144, alloc=14677376, time=435.61 +bytes used=2579283360, alloc=14677376, time=437.62 +bytes used=2580283512, alloc=14677376, time=438.58 +bytes used=2581283852, alloc=14677376, time=439.28 +bytes used=2582284176, alloc=14677376, time=439.41 +bytes used=2583284328, alloc=14677376, time=439.51 +bytes used=2584284480, alloc=14677376, time=439.69 +> +################################################################################ +> quit +bytes used=2584297360, alloc=14677376, time=439.69 diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.maple b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.maple new file mode 100644 index 0000000..5d44fb2 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/3d.maple @@ -0,0 +1,248 @@ +# 3d.maple -- compute Lagrange interpolation coefficients in 3-D +# $Header$ + +################################################################################ + +# +# 3d, cube, order=1, smoothing=0 (size=2) +# + +# interpolating polynomial +interp_3d_cube_order1_smooth0 + := Lagrange_polynomial_interpolant(fn_3d_order1, coeffs_list_3d_order1, + coords_list_3d, posn_list_3d_size2); + +# I +coeffs_as_lc_of_data(%, posn_list_3d_size2); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "3d.coeffs/3d.cube.order1.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_3d_cube_order1_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_3d_size2); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "3d.coeffs/3d.cube.order1.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_3d_cube_order1_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size2); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "3d.coeffs/3d.cube.order1.smooth0/coeffs-dy.compute.c"); + +# d/dz +simplify( diff(interp_3d_cube_order1_smooth0,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size2); +print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", + "3d.coeffs/3d.cube.order1.smooth0/coeffs-dz.compute.c"); + +################################################################################ + +# +# 3d, cube, order=2, smoothing=0 (size=3) +# + +# interpolating polynomial +interp_3d_cube_order2_smooth0 + := Lagrange_polynomial_interpolant(fn_3d_order2, coeffs_list_3d_order2, + coords_list_3d, posn_list_3d_size3); + +# I +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_3d_cube_order2_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_3d_cube_order2_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dy.compute.c"); + +# d/dz +simplify( diff(interp_3d_cube_order2_smooth0,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dz.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_3d_cube_order2_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_3d_cube_order2_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxy.compute.c"); + +# d^2/dxdz +simplify( diff(interp_3d_cube_order2_smooth0,x,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxz.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_3d_cube_order2_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dyy.compute.c"); + +# d^2/dydz +simplify( diff(interp_3d_cube_order2_smooth0,y,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dyz.compute.c"); + +# d^2/dz^2 +simplify( diff(interp_3d_cube_order2_smooth0,z,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dzz.compute.c"); + +################################################################################ + +# +# 3d, cube, order=3, smoothing=0 (size=4) +# + +# interpolating polynomial +interp_3d_cube_order3_smooth0 + := Lagrange_polynomial_interpolant(fn_3d_order3, coeffs_list_3d_order3, + coords_list_3d, posn_list_3d_size4); + +# I +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_3d_cube_order3_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_3d_cube_order3_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dy.compute.c"); + +# d/dz +simplify( diff(interp_3d_cube_order3_smooth0,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dz.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_3d_cube_order3_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_3d_cube_order3_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxy.compute.c"); + +# d^2/dxdz +simplify( diff(interp_3d_cube_order3_smooth0,x,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxz.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_3d_cube_order3_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dyy.compute.c"); + +# d^2/dydz +simplify( diff(interp_3d_cube_order3_smooth0,y,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dyz.compute.c"); + +# d^2/dz^2 +simplify( diff(interp_3d_cube_order3_smooth0,z,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dzz.compute.c"); + +################################################################################ + +# +# 3d, cube, order=4, smoothing=0 (size=5) +# + +# interpolating polynomial +interp_3d_cube_order4_smooth0 + := Lagrange_polynomial_interpolant(fn_3d_order4, coeffs_list_3d_order4, + coords_list_3d, posn_list_3d_size5); + +# I +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_3d_cube_order4_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_3d_cube_order4_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dy.compute.c"); + +# d/dz +simplify( diff(interp_3d_cube_order4_smooth0,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dz.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_3d_cube_order4_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_3d_cube_order4_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxy.compute.c"); + +# d^2/dxdz +simplify( diff(interp_3d_cube_order4_smooth0,x,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxz.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_3d_cube_order4_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dyy.compute.c"); + +# d^2/dydz +simplify( diff(interp_3d_cube_order4_smooth0,y,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dyz.compute.c"); + +# d^2/dz^2 +simplify( diff(interp_3d_cube_order4_smooth0,z,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dzz.compute.c"); + +################################################################################ diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/README b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/README new file mode 100644 index 0000000..88f3af7 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/README @@ -0,0 +1,62 @@ +$Header$ + +This directory contains code for Lagrange polynomial interpolation, +using the maximum-degree definition for multiple dimensions. + +makefile + This has targets to create the subdirectories for the + Maple-generated coefficient files, and to run Maple to + generated those files. + +make.code.defn + This tells the Cactus build system which files to compile. + +[123]d.maple + These files contain the Maple code to generate the interpolation + coefficients. + +fns.maple + These files define the interpolation functions, coefficients, etc, + for the Maple code in [123]d.maple + +[123]d.cube.order?.smooth?.c + These files are the individual cases for the interpolation. + Each file defines a separate function. Each file just #defines + a bunch of macros, then #includes "../template.c" to get the + actual interpolation code. Unfortunately, the ISO C standard + only guarantees 31 characters for function names (in fact, it + doesn't even guarantee that for external names -- they may be + limited by a system linker -- but I quietly ignore that and + assume I can use 31), so the functions are named in a somewhat + cryptic manner: + 123456789 123456789 123456789 1 + LocalInterp_U_LagrMD_1dcube_10 + LocalInterp_U_LagrMD_1dcube_20 + LocalInterp_U_LagrMD_1dcube_30 + LocalInterp_U_LagrMD_1dcube_40 + LocalInterp_U_LagrMD_1dcube_50 + LocalInterp_U_LagrMD_1dcube_60 + LocalInterp_U_LagrMD_2dcube_10 + LocalInterp_U_LagrMD_2dcube_20 + LocalInterp_U_LagrMD_2dcube_30 + LocalInterp_U_LagrMD_2dcube_40 + LocalInterp_U_LagrMD_3dcube_10 + LocalInterp_U_LagrMD_3dcube_20 + LocalInterp_U_LagrMD_3dcube_30 + LocalInterp_U_LagrMD_3dcube_40 + The naming convention is as follows (eg for the last function) + LocalInterp name of this thorn + U these functions are all for the + CCTK_InterpLocalUniform() API + LagrMD these functions are all for the + "Lagrange polynomial interpolation (maximum degree)" + interpolation operator + 3d this function does 3-d interpolation + cube this function uses a cube-shaped + interpolation molecule + 4 this function does 4th order interpolation + 0 this function does smoothing=0 interpolation + +all_prototypes.h + This file contains C prototypes for each of the functions + in [123]d.cube.order?.smooth0.c. diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/all_prototypes.h b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/all_prototypes.h new file mode 100644 index 0000000..0a49904 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/all_prototypes.h @@ -0,0 +1,72 @@ +/* all-prototypes.h -- C prototypes for all template-generated functions */ +/* $Header$ */ + +/* + * 1D + */ + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrMD_1d_cube10 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrMD_1d_cube20 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrMD_1d_cube30 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrMD_1d_cube40 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrMD_1d_cube50 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrMD_1d_cube60 +#include "template.h" + + +/* + * 2D + */ + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrMD_2d_cube10 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrMD_2d_cube20 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrMD_2d_cube30 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrMD_2d_cube40 +#include "template.h" + + +/* + * 3D + */ + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrMD_3d_cube10 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrMD_3d_cube20 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrMD_3d_cube30 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrMD_3d_cube40 +#include "template.h" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/fns.maple b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/fns.maple new file mode 100644 index 0000000..6995524 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/fns.maple @@ -0,0 +1,266 @@ +# Maple code to define Lagrange interpolating functions/coords/coeffs +# $Header$ + +################################################################################ + +# +# 1-D interpolating functions +# + +fn_1d_order1 := +proc(x) ++ c0 + c1*x +end proc; + +fn_1d_order2 := +proc(x) ++ c0 + c1*x + c2*x^2 +end proc; + +fn_1d_order3 := +proc(x) ++ c0 + c1*x + c2*x^2 + c3*x^3 +end proc; + +fn_1d_order4 := +proc(x) ++ c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 +end; + +fn_1d_order5 := +proc(x) ++ c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 +end; + +fn_1d_order6 := +proc(x) ++ c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 +end; + +######################################## + +# coordinates for 1-D interpolating functions +coords_list_1d := [x]; + +######################################## + +# +# coefficients in 1-D interpolating functions +# + +coeffs_list_1d_order1 := [c0, c1]; +coeffs_list_1d_order2 := [c0, c1, c2]; +coeffs_list_1d_order3 := [c0, c1, c2, c3]; +coeffs_list_1d_order4 := [c0, c1, c2, c3, c4]; +coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5]; +coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6]; + +################################################################################ + +# +# 2-D interpolating functions (maximum degree) +# + +fn_2d_order1 := +proc(x,y) ++ c01*y ++ c00 + c10*x +end proc; + +fn_2d_order2 := +proc(x,y) ++ c02*y^2 ++ c01*y + c11*x*y ++ c00 + c10*x + c20*x^2 +end proc; + +fn_2d_order3 := +proc(x,y) ++ c03*y^3 ++ c02*y^2 + c12*x*y^2 ++ c01*y + c11*x*y + c21*x^2*y ++ c00 + c10*x + c20*x^2 + c30*x^3 +end proc; + +fn_2d_order4 := +proc(x,y) ++ c04*y^4 ++ c03*y^3 + c13*x*y^3 ++ c02*y^2 + c12*x*y^2 + c22*x^2*y^2 ++ c01*y + c11*x*y + c21*x^2*y + c31*x^3*y ++ c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 +end; + +######################################## + +# coordinates for 2-D interpolating functions +coords_list_2d := [x,y]; + +######################################## + +# +# coefficients in 2-D interpolating functions (maximum degree) +# + +coeffs_list_2d_order1 := [ + c01, + c00, c10 + ]; +coeffs_list_2d_order2 := [ + c02, + c01, c11, + c00, c10, c20 + ]; +coeffs_list_2d_order3 := [ + c03, + c02, c12, + c01, c11, c21, + c00, c10, c20, c30 + ]; +coeffs_list_2d_order4 := [ + c04, + c03, c13, + c02, c12, c22, + c01, c11, c21, c31, + c00, c10, c20, c30, c40 + ]; + +################################################################################ + +# +# 3-D interpolating functions (maximum degree) +# + +fn_3d_order1 := +proc(x,y,z) +# z^0 ----------- ++ c010*y ++ c000 + c100*x +# z^1 ----------- ++ c001*z +end proc; + +fn_3d_order2 := +proc(x,y,z) +# z^0 -------------------------- ++ c020*y^2 ++ c010*y + c110*x*y ++ c000 + c100*x + c200*x^2 +# z^1 -------------------------- ++ c011*y*z ++ c001*z + c101*x*z +# z^2 -------------------------- ++ c002*z^2 +end proc; + +fn_3d_order3 := +proc(x,y,z) +# z^0 ------------------------------------------- ++ c030*y^3 ++ c020*y^2 + c120*x*y^2 ++ c010*y + c110*x*y + c210*x^2*y ++ c000 + c100*x + c200*x^2 + c300*x^3 +# z^1 ------------------------------------------- ++ c021*y^2*z ++ c011*y *z + c111*x*y*z ++ c001 *z + c101*x *z + c201*x^2*z +# z^2 ------------------------------------------- ++ c012*y*z^2 ++ c002 *z^2 + c102*x*z^2 +# z^3 ------------------------------------------- ++ c003 *z^3 +end proc; + +fn_3d_order4 := +proc(x,y,z) +# z^0 -------------------------------------------------------- ++ c040*y^4 ++ c030*y^3 + c130*x*y^3 ++ c020*y^2 + c120*x*y^2 + c220*x^2*y^2 ++ c010*y + c110*x*y + c210*x^2*y + c310*x^3*y ++ c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 +# z^1 ------------------------------------------- ++ c031*y^3*z ++ c021*y^2*z + c121*x*y^2*z ++ c011*y *z + c111*x*y *z + c211*x^2*y*z ++ c001 *z + c101*x *z + c201*x^2 *z + c301*x^3*z +# z^2 ------------------------------------------- ++ c022*y^2*z^2 ++ c012*y *z^2 + c112*x*y*z^2 ++ c002 *z^2 + c102*x *z^2 + c202*x^2*z^2 +# z^3 ------------------------------------------- ++ c013*y *z^3 ++ c003 *z^3 + c103*x *z^3 +# z^4 ------------------------------------------- ++ c004 *z^4 +end; + +######################################## + +# coordinates for 3-D interpolating functions +coords_list_3d := [x,y,z]; + +######################################## + +# +# coefficients in 3-D interpolating functions (maximum degree) +# + +coeffs_list_3d_order1 := [ + # z^0 ----- + c010, + c000, c100, + # z^1 ----- + c001 + ]; +coeffs_list_3d_order2 := [ + # z^0 ----------- + c020, + c010, c110, + c000, c100, c200, + # z^1 ----------- + c011, + c001, c101, + # z^2 ----------- + c002 + ]; +coeffs_list_3d_order3 := [ + # z^0 ---------------- + c030, + c020, c120, + c010, c110, c210, + c000, c100, c200, c300, + # z^1 ---------------- + c021, + c011, c111, + c001, c101, c201, + # z^2 ---------------- + c012, + c002, c102, + # z^3 ---------------- + c003 + ]; +coeffs_list_3d_order4 := [ + # z^0 ----------------------- + c040, + c030, c130, + c020, c120, c220, + c010, c110, c210, c310, + c000, c100, c200, c300, c400, + # z^1 ----------------------- + c031, + c021, c121, + c011, c111, c211, + c001, c101, c201, c301, + # z^2 ----------------------- + c022, + c012, c112, + c002, c102, c202, + # z^3 ----------------------- + c013, + c003, c103, + # z^4 ----------------------- + c004 + ]; + +################################################################################ diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/make.code.defn b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/make.code.defn new file mode 100644 index 0000000..c656453 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/make.code.defn @@ -0,0 +1,22 @@ +# make.code.defn file for Lagrange polynomial interpolation +# $Header$ + +# Source files in this directory +SRCS = \ + 1d.cube.order1.smooth0.c \ + 1d.cube.order2.smooth0.c \ + 1d.cube.order3.smooth0.c \ + 1d.cube.order4.smooth0.c \ + 1d.cube.order5.smooth0.c \ + 1d.cube.order6.smooth0.c \ + \ + 2d.cube.order1.smooth0.c \ + 2d.cube.order2.smooth0.c \ + 2d.cube.order3.smooth0.c \ + 2d.cube.order4.smooth0.c \ + \ + 3d.cube.order1.smooth0.c \ + 3d.cube.order2.smooth0.c \ + 3d.cube.order3.smooth0.c \ + 3d.cube.order4.smooth0.c \ + # end of list diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/makefile b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/makefile new file mode 100644 index 0000000..c36a42f --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/makefile @@ -0,0 +1,72 @@ +# $Header: /mnt/data2/cvs2svn/cvs-repositories/arrangements/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/makefile,v 1.1 2003-04-15 17:12:54 jthorn Exp $ + +.PHONY : no-default-target +no-default-target: + @echo 'there is (deliberately) no default target in this makefile,' + @echo 'because (re)generating all the coefficients is quite slow :(' + @echo '==> see the makefile to find out about explicit targets' + +# +# main targets: rebuild machine-generated coefficient files +# + +.PHONY : 1d +1d : + -rm -f 1d.coeffs/*/*.c + cat ../util.maple ../interpolate.maple \ + ../common/cube_posns.maple fns.maple 1d.maple \ + | maple 2>&1 >1d.log + +# with Maple 7, this takes about 15 seconds on a 1.7GHz P4 +.PHONY : 2d +2d : + -rm -f 2d.coeffs/*/*.c + cat ../util.maple ../interpolate.maple \ + ../common/cube_posns.maple fns.maple 2d.maple \ + | maple 2>&1 >2d.log + +# with Maple 7, this takes about 8 to 9 minutes on a 1.7GHz P4 +.PHONY : 3d +3d : + -rm -f 3d.coeffs/*/*.c + cat ../util.maple ../interpolate.maple \ + ../common/cube_posns.maple fns.maple 3d.maple \ + | maple 2>&1 >3d.log + +################################################################################ + +# +# targets to initially create directories for machine-generated coefficients +# these only need to be run if you're setting up a new interpolator, +# i.e. if you don't already have the directories in cvs +# (you still have to add them to cvs by hand) +# + +.PHONY : 1d.dirs +1d.dirs: + -rm -rf 1d.coeffs + mkdir 1d.coeffs + cd 1d.coeffs && mkdir 1d.cube.order1.smooth0 + cd 1d.coeffs && mkdir 1d.cube.order2.smooth0 + cd 1d.coeffs && mkdir 1d.cube.order3.smooth0 + cd 1d.coeffs && mkdir 1d.cube.order4.smooth0 + cd 1d.coeffs && mkdir 1d.cube.order5.smooth0 + cd 1d.coeffs && mkdir 1d.cube.order6.smooth0 + +.PHONY : 2d.dirs +2d.dirs: + -rm -rf 2d.coeffs + mkdir 2d.coeffs + cd 2d.coeffs && mkdir 2d.cube.order1.smooth0 + cd 2d.coeffs && mkdir 2d.cube.order2.smooth0 + cd 2d.coeffs && mkdir 2d.cube.order3.smooth0 + cd 2d.coeffs && mkdir 2d.cube.order4.smooth0 + +.PHONY : 3d.dirs +3d.dirs: + -rm -rf 3d.coeffs + mkdir 3d.coeffs + cd 3d.coeffs && mkdir 3d.cube.order1.smooth0 + cd 3d.coeffs && mkdir 3d.cube.order2.smooth0 + cd 3d.coeffs && mkdir 3d.cube.order3.smooth0 + cd 3d.coeffs && mkdir 3d.cube.order4.smooth0 diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order1.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order1.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..c8a5114 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order1.smooth0/coeffs-I.compute.c @@ -0,0 +1,2 @@ + coeffs_I->coeff_0 = RATIONAL(1.0,1.0)-x; + coeffs_I->coeff_p1 = x; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order1.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order1.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..583278a --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order1.smooth0/coeffs-dx.compute.c @@ -0,0 +1,2 @@ + coeffs_dx->coeff_0 = RATIONAL(-1.0,1.0); + coeffs_dx->coeff_p1 = RATIONAL(1.0,1.0); diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order2.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order2.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..6e17264 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order2.smooth0/coeffs-I.compute.c @@ -0,0 +1,9 @@ +fp t3; +fp t2; +fp t1; + t3 = x*x; + t2 = RATIONAL(1.0,2.0); + t1 = t2*t3; + coeffs_I->coeff_m1 = RATIONAL(-1.0,2.0)*x+t1; + coeffs_I->coeff_0 = RATIONAL(1.0,1.0)-t3; + coeffs_I->coeff_p1 = t2*x+t1; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order2.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order2.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..5647f75 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order2.smooth0/coeffs-dx.compute.c @@ -0,0 +1,3 @@ + coeffs_dx->coeff_m1 = x+RATIONAL(-1.0,2.0); + coeffs_dx->coeff_0 = RATIONAL(-2.0,1.0)*x; + coeffs_dx->coeff_p1 = RATIONAL(1.0,2.0)+x; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order2.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order2.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..19689e7 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order2.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,5 @@ +fp t4; + t4 = RATIONAL(1.0,1.0); + coeffs_dxx->coeff_m1 = t4; + coeffs_dxx->coeff_0 = RATIONAL(-2.0,1.0); + coeffs_dxx->coeff_p1 = t4; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order3.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order3.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..6ee0b5a --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order3.smooth0/coeffs-I.compute.c @@ -0,0 +1,16 @@ +fp t10; +fp t9; +fp t8; +fp t7; +fp t6; +fp t5; + t10 = x*x; + t9 = x*t10; + t8 = RATIONAL(-1.0,2.0); + t7 = RATIONAL(1.0,2.0); + t6 = RATIONAL(-1.0,6.0); + t5 = t7*t10; + coeffs_I->coeff_m1 = RATIONAL(-1.0,3.0)*x+t5+t6*t9; + coeffs_I->coeff_0 = RATIONAL(1.0,1.0)+t8*x-t10+t7*t9; + coeffs_I->coeff_p1 = x+t5+t8*t9; + coeffs_I->coeff_p2 = t6*x+RATIONAL(1.0,6.0)*t9; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order3.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order3.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..1cf3fc6 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order3.smooth0/coeffs-dx.compute.c @@ -0,0 +1,8 @@ +fp t13; +fp t12; + t13 = x*x; + t12 = RATIONAL(-1.0,2.0); + coeffs_dx->coeff_m1 = x+t12*t13+RATIONAL(-1.0,3.0); + coeffs_dx->coeff_0 = t12+RATIONAL(-2.0,1.0)*x+RATIONAL(3.0,2.0)*t13; + coeffs_dx->coeff_p1 = x+RATIONAL(1.0,1.0)+RATIONAL(-3.0,2.0)*t13; + coeffs_dx->coeff_p2 = RATIONAL(1.0,2.0)*t13+RATIONAL(-1.0,6.0); diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order3.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order3.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..470882c --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order3.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,6 @@ +fp t14; + t14 = RATIONAL(1.0,1.0); + coeffs_dxx->coeff_m1 = t14-x; + coeffs_dxx->coeff_0 = RATIONAL(-2.0,1.0)+RATIONAL(3.0,1.0)*x; + coeffs_dxx->coeff_p1 = t14+RATIONAL(-3.0,1.0)*x; + coeffs_dxx->coeff_p2 = x; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order4.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order4.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..c30526f --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order4.smooth0/coeffs-I.compute.c @@ -0,0 +1,24 @@ +fp t25; +fp t23; +fp t29; +fp t21; +fp t22; +fp t28; +fp t24; +fp t20; +fp t19; + t25 = x*x; + t23 = t25*t25; + t29 = RATIONAL(1.0,24.0)*t23+RATIONAL(-1.0,24.0)*t25; + t21 = RATIONAL(-1.0,6.0); + t22 = RATIONAL(2.0,3.0); + t28 = t21*t23+t22*t25; + t24 = x*t25; + t20 = RATIONAL(1.0,12.0); + t19 = RATIONAL(-1.0,12.0); + coeffs_I->coeff_m2 = t20*x+t19*t24+t29; + coeffs_I->coeff_m1 = RATIONAL(-2.0,3.0)*x+RATIONAL(1.0,6.0)*t24+t28; + coeffs_I->coeff_0 = RATIONAL(-5.0,4.0)*t25+RATIONAL(1.0,1.0)+RATIONAL(1.0 +,4.0)*t23; + coeffs_I->coeff_p1 = t21*t24+t22*x+t28; + coeffs_I->coeff_p2 = t20*t24+t19*x+t29; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order4.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order4.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..14b1551 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order4.smooth0/coeffs-dx.compute.c @@ -0,0 +1,17 @@ +fp t34; +fp t37; +fp t36; +fp t40; +fp t35; +fp t39; + t34 = RATIONAL(-1.0,12.0); + t37 = x*x; + t36 = x*t37; + t40 = RATIONAL(1.0,6.0)*t36+t34*x; + t35 = RATIONAL(-2.0,3.0); + t39 = t35*t36+RATIONAL(4.0,3.0)*x; + coeffs_dx->coeff_m2 = RATIONAL(-1.0,4.0)*t37+RATIONAL(1.0,12.0)+t40; + coeffs_dx->coeff_m1 = t35+RATIONAL(1.0,2.0)*t37+t39; + coeffs_dx->coeff_0 = t36+RATIONAL(-5.0,2.0)*x; + coeffs_dx->coeff_p1 = RATIONAL(-1.0,2.0)*t37+RATIONAL(2.0,3.0)+t39; + coeffs_dx->coeff_p2 = t34+RATIONAL(1.0,4.0)*t37+t40; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order4.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order4.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..6f78a84 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order4.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,13 @@ +fp t46; +fp t48; +fp t44; +fp t47; + t46 = x*x; + t48 = RATIONAL(-2.0,1.0)*t46+RATIONAL(4.0,3.0); + t44 = RATIONAL(1.0,2.0); + t47 = t44*t46+RATIONAL(-1.0,12.0); + coeffs_dxx->coeff_m2 = RATIONAL(-1.0,2.0)*x+t47; + coeffs_dxx->coeff_m1 = x+t48; + coeffs_dxx->coeff_0 = RATIONAL(-5.0,2.0)+RATIONAL(3.0,1.0)*t46; + coeffs_dxx->coeff_p1 = -x+t48; + coeffs_dxx->coeff_p2 = t44*x+t47; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order5.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order5.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..2fe57b6 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order5.smooth0/coeffs-I.compute.c @@ -0,0 +1,28 @@ +fp t54; +fp t55; +fp t57; +fp t58; +fp t64; +fp t63; +fp t60; +fp t59; +fp t51; + t54 = RATIONAL(1.0,24.0); + t55 = RATIONAL(-1.0,24.0); + t57 = x*x; + t58 = t57*t57; + t64 = t54*t58+t55*t57; + t63 = RATIONAL(-1.0,6.0)*t58+RATIONAL(2.0,3.0)*t57; + t60 = x*t57; + t59 = t60*t57; + t51 = t55*t60; + coeffs_I->coeff_m2 = RATIONAL(1.0,20.0)*x+t51+RATIONAL(-1.0,120.0)*t59+ +t64; + coeffs_I->coeff_m1 = RATIONAL(-1.0,2.0)*x+t51+t54*t59+t63; + coeffs_I->coeff_0 = RATIONAL(1.0,1.0)+RATIONAL(-1.0,3.0)*x+RATIONAL(-5.0, +4.0)*t57+RATIONAL(5.0,12.0)*t60+RATIONAL(1.0,4.0)*t58+RATIONAL(-1.0,12.0)*t59; + coeffs_I->coeff_p1 = x+RATIONAL(-7.0,12.0)*t60+RATIONAL(1.0,12.0)*t59+t63 +; + coeffs_I->coeff_p2 = RATIONAL(-1.0,4.0)*x+RATIONAL(7.0,24.0)*t60+t55*t59+ +t64; + coeffs_I->coeff_p3 = RATIONAL(1.0,30.0)*x+RATIONAL(1.0,120.0)*t59+t51; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order5.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order5.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..0fc33a0 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order5.smooth0/coeffs-dx.compute.c @@ -0,0 +1,21 @@ +fp t71; +fp t70; +fp t76; +fp t75; +fp t72; +fp t67; + t71 = x*x; + t70 = t71*x; + t76 = RATIONAL(-2.0,3.0)*t70+RATIONAL(4.0,3.0)*x; + t75 = RATIONAL(-1.0,12.0)*x+RATIONAL(1.0,6.0)*t70; + t72 = t71*t71; + t67 = RATIONAL(-1.0,8.0)*t71; + coeffs_dx->coeff_m2 = RATIONAL(-1.0,24.0)*t72+RATIONAL(1.0,20.0)+t67+t75; + coeffs_dx->coeff_m1 = t67+RATIONAL(-1.0,2.0)+RATIONAL(5.0,24.0)*t72+t76; + coeffs_dx->coeff_0 = RATIONAL(-5.0,2.0)*x+t70+RATIONAL(-5.0,12.0)*t72+ +RATIONAL(-1.0,3.0)+RATIONAL(5.0,4.0)*t71; + coeffs_dx->coeff_p1 = RATIONAL(5.0,12.0)*t72+RATIONAL(-7.0,4.0)*t71+ +RATIONAL(1.0,1.0)+t76; + coeffs_dx->coeff_p2 = RATIONAL(7.0,8.0)*t71+RATIONAL(-1.0,4.0)+RATIONAL( +-5.0,24.0)*t72+t75; + coeffs_dx->coeff_p3 = RATIONAL(1.0,24.0)*t72+t67+RATIONAL(1.0,30.0); diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order5.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order5.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..2382d07 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order5.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,17 @@ +fp t83; +fp t86; +fp t85; +fp t82; +fp t78; + t83 = x*x; + t86 = RATIONAL(1.0,2.0)*t83+RATIONAL(-1.0,12.0); + t85 = RATIONAL(-2.0,1.0)*t83+RATIONAL(4.0,3.0); + t82 = x*t83; + t78 = RATIONAL(-1.0,4.0)*x; + coeffs_dxx->coeff_m2 = RATIONAL(-1.0,6.0)*t82+t78+t86; + coeffs_dxx->coeff_m1 = RATIONAL(5.0,6.0)*t82+t78+t85; + coeffs_dxx->coeff_0 = RATIONAL(-5.0,3.0)*t82+RATIONAL(5.0,2.0)*x+RATIONAL +(3.0,1.0)*t83+RATIONAL(-5.0,2.0); + coeffs_dxx->coeff_p1 = RATIONAL(5.0,3.0)*t82+RATIONAL(-7.0,2.0)*x+t85; + coeffs_dxx->coeff_p2 = RATIONAL(-5.0,6.0)*t82+RATIONAL(7.0,4.0)*x+t86; + coeffs_dxx->coeff_p3 = t78+RATIONAL(1.0,6.0)*t82; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order6.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order6.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..28b9679 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order6.smooth0/coeffs-I.compute.c @@ -0,0 +1,41 @@ +fp t103; +fp t106; +fp t107; +fp t105; +fp t113; +fp t112; +fp t100; +fp t96; +fp t101; +fp t111; +fp t104; +fp t99; +fp t98; +fp t97; + t103 = x*x; + t106 = t103*t103; + t107 = x*t103; + t105 = t107*t107; + t113 = RATIONAL(1.0,720.0)*t105+RATIONAL(1.0,180.0)*t103+RATIONAL(-1.0, +144.0)*t106; + t112 = RATIONAL(-1.0,120.0)*t105+RATIONAL(-3.0,40.0)*t103+RATIONAL(1.0, +12.0)*t106; + t100 = RATIONAL(1.0,48.0); + t96 = RATIONAL(-13.0,48.0); + t101 = RATIONAL(3.0,4.0); + t111 = t100*t105+t96*t106+t101*t103; + t104 = t107*t103; + t99 = RATIONAL(-1.0,60.0); + t98 = RATIONAL(1.0,60.0); + t97 = RATIONAL(-1.0,48.0); + coeffs_I->coeff_m3 = t99*x+t100*t107+RATIONAL(-1.0,240.0)*t104+t113; + coeffs_I->coeff_m2 = RATIONAL(3.0,20.0)*x+RATIONAL(-1.0,6.0)*t107+t98* +t104+t112; + coeffs_I->coeff_m1 = RATIONAL(-3.0,4.0)*x+RATIONAL(13.0,48.0)*t107+t97* +t104+t111; + coeffs_I->coeff_0 = RATIONAL(7.0,18.0)*t106+RATIONAL(-49.0,36.0)*t103+ +RATIONAL(1.0,1.0)+RATIONAL(-1.0,36.0)*t105; + coeffs_I->coeff_p1 = t96*t107+t101*x+t100*t104+t111; + coeffs_I->coeff_p2 = RATIONAL(1.0,6.0)*t107+RATIONAL(-3.0,20.0)*x+t99* +t104+t112; + coeffs_I->coeff_p3 = t97*t107+t98*x+RATIONAL(1.0,240.0)*t104+t113; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order6.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order6.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..d4d1004 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order6.smooth0/coeffs-dx.compute.c @@ -0,0 +1,32 @@ +fp t123; +fp t125; +fp t128; +fp t126; +fp t133; +fp t132; +fp t131; +fp t127; + t123 = RATIONAL(-3.0,20.0); + t125 = x*x; + t128 = x*t125; + t126 = t128*t125; + t133 = t123*x+RATIONAL(-1.0,20.0)*t126+RATIONAL(1.0,3.0)*t128; + t132 = RATIONAL(1.0,120.0)*t126+RATIONAL(1.0,90.0)*x+RATIONAL(-1.0,36.0)* +t128; + t131 = RATIONAL(3.0,2.0)*x+RATIONAL(-13.0,12.0)*t128+RATIONAL(1.0,8.0)* +t126; + t127 = t125*t125; + coeffs_dx->coeff_m3 = RATIONAL(-1.0,48.0)*t127+RATIONAL(-1.0,60.0)+ +RATIONAL(1.0,16.0)*t125+t132; + coeffs_dx->coeff_m2 = RATIONAL(-1.0,2.0)*t125+RATIONAL(3.0,20.0)+RATIONAL +(1.0,12.0)*t127+t133; + coeffs_dx->coeff_m1 = RATIONAL(-5.0,48.0)*t127+RATIONAL(13.0,16.0)*t125+ +RATIONAL(-3.0,4.0)+t131; + coeffs_dx->coeff_0 = RATIONAL(-1.0,6.0)*t126+RATIONAL(14.0,9.0)*t128+ +RATIONAL(-49.0,18.0)*x; + coeffs_dx->coeff_p1 = RATIONAL(5.0,48.0)*t127+RATIONAL(3.0,4.0)+RATIONAL( +-13.0,16.0)*t125+t131; + coeffs_dx->coeff_p2 = RATIONAL(1.0,2.0)*t125+RATIONAL(-1.0,12.0)*t127+ +t123+t133; + coeffs_dx->coeff_p3 = RATIONAL(-1.0,16.0)*t125+RATIONAL(1.0,60.0)+ +RATIONAL(1.0,48.0)*t127+t132; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order6.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order6.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..02aa677 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.coeffs/1d.cube.order6.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,24 @@ +fp t144; +fp t145; +fp t150; +fp t149; +fp t141; +fp t148; +fp t143; + t144 = x*x; + t145 = t144*t144; + t150 = RATIONAL(-13.0,4.0)*t144+RATIONAL(3.0,2.0)+RATIONAL(5.0,8.0)*t145; + t149 = t144+RATIONAL(-3.0,20.0)+RATIONAL(-1.0,4.0)*t145; + t141 = RATIONAL(-1.0,12.0); + t148 = RATIONAL(1.0,90.0)+RATIONAL(1.0,24.0)*t145+t141*t144; + t143 = x*t144; + coeffs_dxx->coeff_m3 = RATIONAL(1.0,8.0)*x+t141*t143+t148; + coeffs_dxx->coeff_m2 = -x+RATIONAL(1.0,3.0)*t143+t149; + coeffs_dxx->coeff_m1 = RATIONAL(-5.0,12.0)*t143+RATIONAL(13.0,8.0)*x+t150 +; + coeffs_dxx->coeff_0 = RATIONAL(14.0,3.0)*t144+RATIONAL(-5.0,6.0)*t145+ +RATIONAL(-49.0,18.0); + coeffs_dxx->coeff_p1 = RATIONAL(5.0,12.0)*t143+RATIONAL(-13.0,8.0)*x+t150 +; + coeffs_dxx->coeff_p2 = x+RATIONAL(-1.0,3.0)*t143+t149; + coeffs_dxx->coeff_p3 = RATIONAL(-1.0,8.0)*x+RATIONAL(1.0,12.0)*t143+t148; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order1.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order1.smooth0.c new file mode 100644 index 0000000..f919525 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order1.smooth0.c @@ -0,0 +1,57 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrTP_1d_cube10 +#include "../template.h" + +#define N_DIMS 1 +#define MOLECULE_MIN_M 0 +#define MOLECULE_MAX_M 1 +#define MOLECULE_SIZE 2 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +/* n.b. no 2nd derivatives for linear interpolation! */ + +#define XYZ x +#define FP_XYZ fp x +#define STRIDE_IJK stride_i +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride + +#define DATA_STRUCT data_struct_1d_cube_size2 +#define COEFFS_STRUCT coeffs_struct_1d_cube_size2 + +#define FETCH_DATA_REAL LocalInterp_fetch_1d_cube2_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_1d_cube2_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_1d_cube2_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_1d_cube2_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_1d_cube2_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_1d_cube2_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_1d_cube2_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_1d_cube2_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_1d_cube2 + +#define STORE_COEFFS LocalInterp_store_1d_cube2 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order1.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order1.smooth0/coeffs-dx.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order2.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order2.smooth0.c new file mode 100644 index 0000000..a435fa5 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order2.smooth0.c @@ -0,0 +1,58 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrTP_1d_cube20 +#include "../template.h" + +#define N_DIMS 1 +#define MOLECULE_MIN_M -1 +#define MOLECULE_MAX_M 1 +#define MOLECULE_SIZE 3 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DXX + +#define XYZ x +#define FP_XYZ fp x +#define STRIDE_IJK stride_i +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride + +#define DATA_STRUCT data_struct_1d_cube_size3 +#define COEFFS_STRUCT coeffs_struct_1d_cube_size3 + +#define FETCH_DATA_REAL LocalInterp_fetch_1d_cube3_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_1d_cube3_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_1d_cube3_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_1d_cube3_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_1d_cube3_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_1d_cube3_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_1d_cube3_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_1d_cube3_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_1d_cube3 + +#define STORE_COEFFS LocalInterp_store_1d_cube3 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order2.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order2.smooth0/coeffs-dx.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order2.smooth0/coeffs-dxx.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order3.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order3.smooth0.c new file mode 100644 index 0000000..f814878 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order3.smooth0.c @@ -0,0 +1,58 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrTP_1d_cube30 +#include "../template.h" + +#define N_DIMS 1 +#define MOLECULE_MIN_M -1 +#define MOLECULE_MAX_M 2 +#define MOLECULE_SIZE 4 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DXX + +#define XYZ x +#define FP_XYZ fp x +#define STRIDE_IJK stride_i +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride + +#define DATA_STRUCT data_struct_1d_cube_size4 +#define COEFFS_STRUCT coeffs_struct_1d_cube_size4 + +#define FETCH_DATA_REAL LocalInterp_fetch_1d_cube4_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_1d_cube4_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_1d_cube4_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_1d_cube4_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_1d_cube4_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_1d_cube4_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_1d_cube4_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_1d_cube4_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_1d_cube4 + +#define STORE_COEFFS LocalInterp_store_1d_cube4 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order3.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order3.smooth0/coeffs-dx.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order3.smooth0/coeffs-dxx.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order4.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order4.smooth0.c new file mode 100644 index 0000000..63a9f4d --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order4.smooth0.c @@ -0,0 +1,58 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrTP_1d_cube40 +#include "../template.h" + +#define N_DIMS 1 +#define MOLECULE_MIN_M -2 +#define MOLECULE_MAX_M 2 +#define MOLECULE_SIZE 5 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DXX + +#define XYZ x +#define FP_XYZ fp x +#define STRIDE_IJK stride_i +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride + +#define DATA_STRUCT data_struct_1d_cube_size5 +#define COEFFS_STRUCT coeffs_struct_1d_cube_size5 + +#define FETCH_DATA_REAL LocalInterp_fetch_1d_cube5_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_1d_cube5_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_1d_cube5_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_1d_cube5_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_1d_cube5_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_1d_cube5_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_1d_cube5_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_1d_cube5_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_1d_cube5 + +#define STORE_COEFFS LocalInterp_store_1d_cube5 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order4.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order4.smooth0/coeffs-dx.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order4.smooth0/coeffs-dxx.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order5.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order5.smooth0.c new file mode 100644 index 0000000..56471b9 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order5.smooth0.c @@ -0,0 +1,58 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrTP_1d_cube50 +#include "../template.h" + +#define N_DIMS 1 +#define MOLECULE_MIN_M -2 +#define MOLECULE_MAX_M 3 +#define MOLECULE_SIZE 6 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DXX + +#define XYZ x +#define FP_XYZ fp x +#define STRIDE_IJK stride_i +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride + +#define DATA_STRUCT data_struct_1d_cube_size6 +#define COEFFS_STRUCT coeffs_struct_1d_cube_size6 + +#define FETCH_DATA_REAL LocalInterp_fetch_1d_cube6_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_1d_cube6_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_1d_cube6_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_1d_cube6_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_1d_cube6_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_1d_cube6_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_1d_cube6_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_1d_cube6_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_1d_cube6 + +#define STORE_COEFFS LocalInterp_store_1d_cube6 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order5.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order5.smooth0/coeffs-dx.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order5.smooth0/coeffs-dxx.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order6.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order6.smooth0.c new file mode 100644 index 0000000..c3f0037 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.cube.order6.smooth0.c @@ -0,0 +1,58 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrTP_1d_cube60 +#include "../template.h" + +#define N_DIMS 1 +#define MOLECULE_MIN_M -3 +#define MOLECULE_MAX_M 3 +#define MOLECULE_SIZE 7 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DXX + +#define XYZ x +#define FP_XYZ fp x +#define STRIDE_IJK stride_i +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride + +#define DATA_STRUCT data_struct_1d_cube_size7 +#define COEFFS_STRUCT coeffs_struct_1d_cube_size7 + +#define FETCH_DATA_REAL LocalInterp_fetch_1d_cube7_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_1d_cube7_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_1d_cube7_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_1d_cube7_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_1d_cube7_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_1d_cube7_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_1d_cube7_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_1d_cube7_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_1d_cube7 + +#define STORE_COEFFS LocalInterp_store_1d_cube7 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order6.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order6.smooth0/coeffs-dx.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-tensor-product/1d.coeffs/1d.cube.order6.smooth0/coeffs-dxx.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.log b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.log new file mode 100644 index 0000000..4fbd840 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.log @@ -0,0 +1,2264 @@ + |\^/| Maple 7 (IBM INTEL LINUX) +._|\| |/|_. Copyright (c) 2001 by Waterloo Maple Inc. + \ MAPLE / All rights reserved. Maple is a registered trademark of + <____ ____> Waterloo Maple Inc. + | Type ? for help. +# util.maple -- misc utility routines +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/util.maple,v 1.4 2002/08/20 16:46:06 jthorn Exp $ +> +# +# fix_rationals - convert numbers to RATIONAL() calls +# nonmatching_names - find names in a list which *don't* have a specified prefix +# sprint_numeric_list - convert a numeric list to a valid C identifier suffix +# print_name_list_dcl - print C declarations for a list of names +# +# hypercube_points - compute all (integer) points in an N-dimensional hypercube +# +# ftruncate - truncate a file to zero length +# +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function converts all {integer, rational} subexpressions of its +# input except integer exponents and -1 factors in products, into function +# calls +# RATIONAL(num,den) +# This is useful in conjunction with the C() library function, since +# +# C( (1/3) * foo * bar ) +# t0 = foo*bar/3; +# +# generates a (slow) division (and runs the risk of mixed-mode-arithmetic +# problems), while +# +# C((1.0/3.0) * foo * bar); +# t0 = 0.3333333333*foo*bar; +# +# suffers from roundoff error. With this function, +# +# fix_rationals((1/3) * foo * bar); +# RATIONAL(1,3) foo bar +# C(%); +# t0 = RATIONAL(1.0,3.0)*foo*bar; +# +# which a C preprocessor macro can easily convert to the desired +# +# t0 = (1.0/3.0)*foo*bar; +# +# Additionally, this function can be told to leave certain types of +# subexpressions unconverged. For example, +# fix_rationals(expr, type, specfunc(integer, DATA)); +# will leave all subexpressions of the form DATA(integer arguments) +# unconverted. +# +# Arguments: +# expr = (in) The expression to be converted. +# inert_fn = (optional in) +# If specified, this argument should be a Boolean procedure +# or the name of a Boolean procedure. This procedure should +# take one or more argument, and return true if and only if +# the first argument should *not* be converted, i.e. if we +# should leave this expression unchanged. See the last +# example above. +# ... = (optional in) +# Any further arguments are passed as additional arguments to +# the inert_fn procedure. +# +> fix_rationals := +> proc( +> expr::{ +> algebraic, name = algebraic, +> list({algebraic, name = algebraic}), +> set ({algebraic, name = algebraic}) +> }, +> inert_fn::{name, procedure} +> ) +> local nn, k, +> base, power, fbase, fpower, +> fn, fn_args_list, +> num, den, mult; +> +# do we want to convert this expression? +> if ((nargs >= 2) and inert_fn(expr, args[3..nargs])) +> then return expr; +> end if; +> +# recurse over lists and sets +> if (type(expr, {list,set})) +> then return map(fix_rationals, expr, args[2..nargs]); +> end if; +> +# recurse over equation right hand sides +> if (type(expr, name = algebraic)) +> then return ( lhs(expr) = fix_rationals(rhs(expr), args[2..nargs]) ); +> end if; +> +# recurse over functions other than RATIONAL() +> if (type(expr, function)) +> then +> fn := op(0, expr); +> if (fn <> 'RATIONAL') +> then +> fn_args_list := [op(expr)]; +> fn_args_list := map(fix_rationals, fn_args_list, args[2..nargs]); +> fn; return '%'( op(fn_args_list) ); +> end if; +> end if; +> +> nn := nops(expr); +> +# recurse over sums +> if (type(expr, `+`)) +> then return sum('fix_rationals(op(k,expr), args[2..nargs])', 'k'=1..nn); +> end if; +> +# recurse over products +# ... leaving leading -1 factors intact, i.e. not converted to RATIONAL(-1,1) +> if (type(expr, `*`)) +> then +> if (op(1, expr) = -1) +> then return -1*fix_rationals(remove(type, expr, 'identical(-1)'), +> args[2..nargs]); +> else return product('fix_rationals(op(k,expr), args[2..nargs])', +> 'k'=1..nn); +> end if; +> end if; +> +# recurse over powers +# ... leaving integer exponents intact +> if (type(expr, `^`)) +> then +> base := op(1, expr); +> power := op(2, expr); +> +> fbase := fix_rationals(base, args[2..nargs]); +> if (type(power, integer)) +> then fpower := power; +> else fpower := fix_rationals(power, args[2..nargs]); +> end if; +> return fbase ^ fpower; +> end if; +> +# fix integers and fractions +> if (type(expr, integer)) +> then return 'RATIONAL'(expr, 1); +> end if; +> if (type(expr, fraction)) +> then +> num := op(1, expr); +> den := op(2, expr); +> +> return 'RATIONAL'(num, den); +> end if; +> +# turn Maple floating-point into integer fraction, then recursively fix that +> if (type(expr, float)) +> then +> mult := op(1, expr); +> power := op(2, expr); +> return fix_rationals(mult * 10^power, args[2..nargs]); +> end if; +> +# identity op on names +> if (type(expr, name)) +> then return expr; +> end if; +> +# unknown type +> error "%0", +> "unknown type for expr!", +> " whattype(expr) = ", whattype(expr), +> " expr = ", expr; +> end proc; +fix_rationals := proc(expr::{algebraic, name = algebraic, +list({algebraic, name = algebraic}), set({algebraic, name = algebraic})}, +inert_fn::{procedure, name}) +local nn, k, base, power, fbase, fpower, fn, fn_args_list, num, den, mult; + if 2 <= nargs and inert_fn(expr, args[3 .. nargs]) then return expr + end if; + if type(expr, {set, list}) then + return map(fix_rationals, expr, args[2 .. nargs]) + end if; + if type(expr, name = algebraic) then + return lhs(expr) = fix_rationals(rhs(expr), args[2 .. nargs]) + end if; + if type(expr, function) then + fn := op(0, expr); + if fn <> 'RATIONAL' then + fn_args_list := [op(expr)]; + fn_args_list := + map(fix_rationals, fn_args_list, args[2 .. nargs]); + fn; + return '%'(op(fn_args_list)) + end if + end if; + nn := nops(expr); + if type(expr, `+`) then return + sum('fix_rationals(op(k, expr), args[2 .. nargs])', 'k' = 1 .. nn) + end if; + if type(expr, `*`) then + if op(1, expr) = -1 then return -fix_rationals( + remove(type, expr, 'identical(-1)'), args[2 .. nargs]) + else return product('fix_rationals(op(k, expr), args[2 .. nargs])', + 'k' = 1 .. nn) + end if + end if; + if type(expr, `^`) then + base := op(1, expr); + power := op(2, expr); + fbase := fix_rationals(base, args[2 .. nargs]); + if type(power, integer) then fpower := power + else fpower := fix_rationals(power, args[2 .. nargs]) + end if; + return fbase^fpower + end if; + if type(expr, integer) then return 'RATIONAL'(expr, 1) end if; + if type(expr, fraction) then + num := op(1, expr); den := op(2, expr); return 'RATIONAL'(num, den) + end if; + if type(expr, float) then + mult := op(1, expr); + power := op(2, expr); + return fix_rationals(mult*10^power, args[2 .. nargs]) + end if; + if type(expr, name) then return expr end if; + error "%0", "unknown type for expr!", " whattype(expr) = ", + whattype(expr), " expr = ", expr +end proc + +> +################################################################################ +> +# +# This function finds names in a list which *don't* have a specified prefix. +# +# Arguments: +# name_list = A list of the names. +# prefix = The prefix we want to filter out. +# +# Results: +# This function returns the subset list of names which don't have the +# specified prefix. +# +> nonmatching_names := +> proc( name_list::list({name,string}), prefix::{name,string} ) +> +> select( proc(n) +> evalb(not StringTools[IsPrefix](prefix,n)); +> end proc +> , +> name_list +> ); +> end proc; +nonmatching_names := proc( +name_list::list({name, string}), prefix::{name, string}) + select(proc(n) evalb(not StringTools[IsPrefix](prefix, n)) end proc, + name_list) +end proc + +> +################################################################################ +> +# +# This function converts a numeric list to a string which is a valid +# C identifier suffix: elements are separated by "_", decimal points are +# replaced by "x", and all nonzero values have explicit +/- signs, which +# are replaced by "p"/"m". +# +# For example, [0,-3.5,+4] --> "0_m3x5_p4". +# +> sprint_numeric_list := +> proc(nlist::list(numeric)) +> +# generate preliminary string, eg "+0_-3.5_+4" +> map2(sprintf, "%+a", nlist); +> ListTools[Join](%, "_"); +> cat(op(%)); +> +# fixup bad characters +> StringTools[SubstituteAll](%, "+0", "0"); +> StringTools[CharacterMap](".+-", "xpm", %); +> +> return %; +> end proc; +sprint_numeric_list := proc(nlist::list(numeric)) + map2(sprintf, "%+a", nlist); + ListTools[Join](%, "_"); + cat(op(%)); + StringTools[SubstituteAll](%, "+0", "0"); + StringTools[CharacterMap](".+-", "xpm", %); + return % +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C declarations for a list of names. +# +# Argument: +# name_list = A list of the names. +# type_name = The C type of the names, eg. "double". +# file_name = The file name to write the declaration to. This is +# truncated before writing. +# +> print_name_list_dcl := +> proc( name_list::list({name,string}), +> type_name::string, +> file_name::string ) +> local blanks, separator_string; +> +> ftruncate(file_name); +> +> map( +> proc(var::{name,string}) +> fprintf(file_name, +> "%s %s;\n", +> type_name, var); +> end proc +> , +> name_list +> ); +> +> fclose(file_name); +> NULL; +> end proc; +print_name_list_dcl := proc( +name_list::list({name, string}), type_name::string, file_name::string) +local blanks, separator_string; + ftruncate(file_name); + map(proc(var::{name, string}) + fprintf(file_name, "%s %s;\n", type_name, var) + end proc, name_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes a list of all the (integer) points in an +# N-dimensional hypercube, in lexicographic order. The present +# implementation requires N <= 4. +# +# Arguments: +# cmin,cmax = N-element lists of cube minimum/maximum coordinates. +# +# Results: +# The function returns a set of d-element lists giving the coordinates. +# For example, +# hypercube([0,0], [2,1] +# returns +# { [0,0], [0,1], [1,0], [1,1], [2,0], [2,1] } +> hypercube_points := +> proc(cmin::list(integer), cmax::list(integer)) +> local N, i,j,k,l; +> +> N := nops(cmin); +> if (nops(cmax) <> N) +> then error +> "must have same number of dimensions for min and max coordinates!"; +> fi; +> +> if (N = 1) +> then return [seq([i], i=cmin[1]..cmax[1])]; +> elif (N = 2) +> then return [ +> seq( +> seq([i,j], j=cmin[2]..cmax[2]), +> i=cmin[1]..cmax[1]) +> ]; +> elif (N = 3) +> then return [ +> seq( +> seq( +> seq([i,j,k], k=cmin[3]..cmax[3]), +> j=cmin[2]..cmax[2] ), +> i=cmin[1]..cmax[1]) +> ]; +> elif (N = 4) +> then return [ +> seq( +> seq( +> seq( +> seq([i,j,k,l], l=cmin[4]..cmax[4]), +> k=cmin[3]..cmax[3] ), +> j=cmin[2]..cmax[2]), +> i=cmin[1]..cmax[1]) +> ]; +> else +> error "implementation restriction: must have N <= 4, got %1!", N; +> fi; +> end proc; +hypercube_points := proc(cmin::list(integer), cmax::list(integer)) +local N, i, j, k, l; + N := nops(cmin); + if nops(cmax) <> N then error + "must have same number of dimensions for min and max coordinates!" + end if; + if N = 1 then return [seq([i], i = cmin[1] .. cmax[1])] + elif N = 2 then return + [seq(seq([i, j], j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] + elif N = 3 then return [seq( + seq(seq([i, j, k], k = cmin[3] .. cmax[3]), j = cmin[2] .. cmax[2]) + , i = cmin[1] .. cmax[1])] + elif N = 4 then return [seq(seq(seq( + seq([i, j, k, l], l = cmin[4] .. cmax[4]), k = cmin[3] .. cmax[3]), + j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] + else error "implementation restriction: must have N <= 4, got %1!", N + end if +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function truncates a file to 0 length if it exists, or creates +# it at that length if it doesn't exist. +# +# Arguments: +# file_name = (in) The name of the file. +# +> ftruncate := +> proc(file_name::string) +> fopen(file_name, 'WRITE'); +> fclose(%); +> NULL; +> end proc; +ftruncate := + + proc(file_name::string) fopen(file_name, 'WRITE'); fclose(%); NULL end proc + +# interpolate.maple -- compute interpolation formulas/coefficients +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/interpolate.maple,v 1.10 2002/08/28 11:31:09 jthorn Exp $ +> +# +# <<>> +# Lagrange_polynomial_interpolant - compute Lagrange polynomial interpolant +# Hermite_polynomial_interpolant - compute Hermite polynomial interpolant +# coeffs_as_lc_of_data - coefficients of ... (linear combination of data) +# +# print_coeffs__lc_of_data - print C code to compute coefficients +# print_fetch_data - print C code to fetch input array chunk into struct data +# print_store_coeffs - print C code to store struct coeffs "somewhere" +# print_interp_cmpt__lc_of_data - print C code for computation of interpolant +# +# coeff_name - name of coefficient of data at a given [m] coordinate +# data_var_name - name of variable storing data value at a given [m] coordinate +# +> +################################################################################ +> +# +# ***** representation of numbers, data values, etc ***** +# +# We use RATIONAL(p.0,q.0) to denote the rational number p/q. +# +# We use DATA(...) to represent the data values being interpolated at a +# specified [m] coordinate, where the arguments are the [m] coordinates. +# +# We use COEFF(...) to represent the molecule coefficient at a specified +# [m] coordinate, where the arguments are the [m] coordinates. +# +# For example, the usual 1-D centered 2nd order 1st derivative molecule +# would be written +# RATIONAL(-1.0,2.0)*DATA(-1) + RATIONA(1.0,2.0)*DATA(1) +# and its coefficients as +# COEFF(-1) = RATIONAL(-1.0,2.0) +# COEFF(1) = RATIONAL(1.0,2.0) +# +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes a Lagrange polynomial interpolant in any +# number of dimensions. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) c00 + c10*x + c01*y end proc +# coeff_list = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example [c00, c10, c01]. +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# posn_list = A list of positions (each a list of numeric values) where the +# interpolant is to use data, for example hypercube([0,0], [1,1]). +# Any positions may be used; if they're redundant (as in the +# example) the least-squares interpolant is computed. +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Lagrange_polynomial_interpolant := +> proc( +> fn::procedure, coeff_list::list(name), +> coord_list::list(name), posn_list::list(list(numeric)) +> ) +> local posn, data_eqns, coeff_eqns; +> +# coefficients of interpolating polynomial +> data_eqns := { seq( fn(op(posn))='DATA'(op(posn)) , posn=posn_list ) }; +> coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); +> if (has(coeff_eqns, '_t')) +> then error "interpolation coefficients aren't uniquely determined!"; +> end if; +> +# interpolant as a polynomial in the coordinates +> return subs(coeff_eqns, eval(fn))(op(coord_list)); +> end proc; +Lagrange_polynomial_interpolant := proc(fn::procedure, coeff_list::list(name), +coord_list::list(name), posn_list::list(list(numeric))) +local posn, data_eqns, coeff_eqns; + data_eqns := {seq(fn(op(posn)) = 'DATA'(op(posn)), posn = posn_list)}; + coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); + if has(coeff_eqns, '_t') then + error "interpolation coefficients aren't uniquely determined!" + end if; + return subs(coeff_eqns, eval(fn))(op(coord_list)) +end proc + +> +################################################################################ +> +# +# This function computes a Hermite polynomial interpolant in any +# number of dimensions. This is a polynomial which +# * has values which match the given data DATA() at a specified set of +# points, and +# * has derivatives which match the specified finite-difference derivatives +# of the given data DATA() at a specified set of points +# +# For the derivative matching, we actually match all possible products +# of 1st derivatives, i.e. in 2-D we match dx, dy, and dxy, in 3-D we +# match dx, dy, dz, dxy, dxz, dyz, and dxyz, etc etc. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) +# + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 +# + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 +# + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +# + c00 + c10*x + c20*x^2 + c30*x^3 +# end proc; +# coeff_set = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example +# { +# c03, c13, c23, c33, +# c02, c12, c22, c32, +# c01, c11, c21, c31, +# c00, c10, c20, c30 +# } +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# deriv_set = A set of equations of the form +# {coords} = proc +# giving the derivatives which are to be matched, and the +# procedures to compute their finite-difference approximations. +# Each procedure should take N_dims integer arguments specifying +# an evaluation point, and return a suitable linear combination +# of the DATA() for the derivative at that point. For example +# { +# {x} = proc(i::integer, j::integer) +# - 1/2*DATA(i-1,j) + 1/2*DATA(i+1,j) +# end proc +# , +# {y} = proc(i::integer, j::integer) +# - 1/2*DATA(i,j-1) + 1/2*DATA(i,j+1) +# end proc +# , +# {x,y} = proc(i::integer, j::integer) +# - 1/4*DATA(i-1,j+1) + 1/4*DATA(i+1,j+1) +# + 1/4*DATA(i-1,j-1) - 1/4*DATA(i+1,j-1) +# end proc +# } +# fn_posn_set = A set of positions (each a list of numeric values) +# where the interpolant is to match the given data DATA(), +# for example +# {[0,0], [0,1], [1,0], [1,1]} +# deriv_posn_set = A list of positions (each a list of numeric values) +# where the interpolant is to match the derivatives +# specified by deriv_set , for example +# {[0,0], [0,1], [1,0], [1,1]} +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Hermite_polynomial_interpolant := +> proc( +> fn::procedure, +> coeff_set::set(name), +> coord_list::list(name), +> deriv_set::set(set(name) = procedure), +> fn_posn_set::set(list(numeric)), +> deriv_posn_set::set(list(numeric)) +> ) +> local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; +> +> +# +# compute a set of equations +# {fn(posn) = DATA(posn)} +# giving the function values to be matched +# +> fn_eqnset := map( +> # return equation that fn(posn) = DATA(posn) +> proc(posn::list(integer)) +> fn(op(posn)) = 'DATA'(op(posn)); +> end proc +> , +> fn_posn_set +> ); +> +> +# +# compute a set of equations +# { diff(fn,coords)(posn) = DERIV(coords)(posn) } +# giving the derivative values to be matched, where DERIV(coords) +# is a placeholder for the appropriate derivative +# +> map( +> # return set of equations for this particular derivative +> proc(deriv_coords::set(name)) +> local deriv_fn; +> fn(op(coord_list)); +> diff(%, op(deriv_coords)); +> deriv_fn := unapply(%, op(coord_list)); +> map( +> proc(posn::list(integer)) +> deriv_fn(op(posn)) = 'DERIV'(op(deriv_coords))(op(posn)); +> end proc +> , +> deriv_posn_set +> ); +> end proc +> , +> map(lhs, deriv_set) +> ); +> deriv_eqnset := `union`(op(%)); +> +> +# +# solve overall set of equations for coefficients +# in terms of DATA() and DERIV() values +# +> coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); +> if (indets(map(rhs,%)) <> {}) +> then error "no unique solution for coefficients -- %1 eqns for %2 coeffs", +> nops(fn_eqnset union deriv_eqnset), +> nops(coeff_set); +> fi; +> +> +# +# compute a set of substitution equations +# {'DERIV'(coords) = procedure} +# +> subs_eqnset := map( +> proc(eqn::set(name) = procedure) +> 'DERIV'(op(lhs(eqn))) = rhs(eqn); +> end proc +> , +> deriv_set +> ); +> +> +# +# compute the coefficients in terms of the DATA() values +# +> subs(subs_eqnset, coeff_eqns); +> eval(%); +> +# +# compute the interpolant as a polynomial in the coordinates +# +> subs(%, fn(op(coord_list))); +> end proc; +Hermite_polynomial_interpolant := proc(fn::procedure, coeff_set::set(name), +coord_list::list(name), deriv_set::set(set(name) = procedure), +fn_posn_set::set(list(numeric)), deriv_posn_set::set(list(numeric))) +local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; + fn_eqnset := map( + proc(posn::list(integer)) fn(op(posn)) = 'DATA'(op(posn)) end proc, + fn_posn_set); + map(proc(deriv_coords::set(name)) + local deriv_fn; + fn(op(coord_list)); + diff(%, op(deriv_coords)); + deriv_fn := unapply(%, op(coord_list)); + map(proc(posn::list(integer)) + deriv_fn(op(posn)) = + 'DERIV'(op(deriv_coords))(op(posn)) + end proc, deriv_posn_set) + end proc, map(lhs, deriv_set)); + deriv_eqnset := `union`(op(%)); + coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); + if indets(map(rhs, %)) <> {} then error + "no unique solution for coefficients -- %1 eqns for %2 coeffs", + nops(fn_eqnset union deriv_eqnset), nops(coeff_set) + end if; + subs_eqnset := map(proc(eqn::(set(name) = procedure)) + 'DERIV'(op(lhs(eqn))) = rhs(eqn) + end proc, deriv_set); + subs(subs_eqnset, coeff_eqns); + eval(%); + subs(%, fn(op(coord_list))) +end proc + +> +################################################################################ +> +# +# This function takes as input an interpolating polynomial, expresses +# it as a linear combination of the data values, and returns the coefficeints +# of that form. +# +# Arguments: +# interpolant = The interpolating polynomial (an algebraic expression +# in the coordinates and the data values). +# posn_list = The same list of data positions used in the interpolant. +# +# Results: +# This function returns the coefficients, as a list of equations of the +# form COEFF(...) = value , where each value is a polynomial in the +# coordinates. The order of the list matches that of posn_list. +# +> coeffs_as_lc_of_data := +> proc( +> interpolant::algebraic, +> posn_list::list(list(numeric)) +> ) +> local data_list, interpolant_as_lc_of_data; +> +# interpolant as a linear combination of the data values +> data_list := [ seq( 'DATA'(op(posn)) , posn=posn_list ) ]; +> interpolant_as_lc_of_data := collect(interpolant, data_list); +> +# coefficients of the data values in the linear combination +> return map( +> proc(posn::list(numeric)) +> coeff(interpolant_as_lc_of_data, DATA(op(posn))); +> 'COEFF'(op(posn)) = %; +> end proc +> , +> posn_list +> ); +> end proc; +coeffs_as_lc_of_data := proc( +interpolant::algebraic, posn_list::list(list(numeric))) +local data_list, interpolant_as_lc_of_data; + data_list := [seq('DATA'(op(posn)), posn = posn_list)]; + interpolant_as_lc_of_data := collect(interpolant, data_list); + return map(proc(posn::list(numeric)) + coeff(interpolant_as_lc_of_data, DATA(op(posn))); + 'COEFF'(op(posn)) = % + end proc, posn_list) +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function prints C expressions for the coefficients of an +# interpolating polynomial. (The polynomial is expressed as linear +# combinations of the data values with coefficients which are +# RATIONAL(p,q) calls.) +# +# Arguments: +# coeff_list = A list of the coefficients, as returned from +# coeffs_as_lc_of_data() . +# coeff_name_prefix = A prefix string for the coefficient names. +# temp_name_type = The C type to be used for Maple-introduced temporary +# names, eg. "double". +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_coeffs__lc_of_data := +> proc( coeff_list::list(specfunc(numeric,COEFF) = algebraic), +> coeff_name_prefix::string, +> temp_name_type::string, +> file_name::string ) +> global `codegen/C/function/informed`; +> local coeff_list2, cmpt_list, temp_name_list; +> +# convert LHS of each equation from a COEFF() call (eg COEFF(-1,+1)) +# to a Maple/C variable name (eg coeff_I_m1_p1) +> coeff_list2 := map( +> proc(coeff_eqn::specfunc(numeric,COEFF) = algebraic) +> local posn; +> posn := [op(lhs(coeff_eqn))]; +> coeff_name(posn,coeff_name_prefix); +> convert(%, name); # codegen[C] wants LHS +> # to be an actual Maple *name* +> % = fix_rationals(rhs(coeff_eqn)); +> end proc +> , +> coeff_list +> ); +> +# +# generate the C code +# +> +# tell codegen[C] not to warn about unknown RATIONAL() and DATA() "fn calls" +# via undocumented :( global table +> `codegen/C/function/informed`['RATIONAL'] := true; +> `codegen/C/function/informed`['DATA'] := true; +> +> ftruncate(file_name); +> +# optimized computation sequence for all the coefficients +# (may use local variables t0,t1,t2,...) +> cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; +> +# list of the t0,t1,t2,... local variables +> temp_name_list := nonmatching_names(map(lhs,cmpt_list), coeff_name_prefix); +> +# declare the t0,t1,t2,... local variables (if there are any) +> if (nops(temp_name_list) > 0) +> then print_name_list_dcl(%, temp_name_type, file_name); +> fi; +> +# now print the optimized computation sequence +> codegen[C](cmpt_list, filename=file_name); +> +> fclose(file_name); +> +> NULL; +> end proc; +print_coeffs__lc_of_data := proc( +coeff_list::list(specfunc(numeric, COEFF) = algebraic), +coeff_name_prefix::string, temp_name_type::string, file_name::string) +local coeff_list2, cmpt_list, temp_name_list; +global `codegen/C/function/informed`; + coeff_list2 := map(proc( + coeff_eqn::(specfunc(numeric, COEFF) = algebraic)) + local posn; + posn := [op(lhs(coeff_eqn))]; + coeff_name(posn, coeff_name_prefix); + convert(%, name); + % = fix_rationals(rhs(coeff_eqn)) + end proc, coeff_list); + `codegen/C/function/informed`['RATIONAL'] := true; + `codegen/C/function/informed`['DATA'] := true; + ftruncate(file_name); + cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; + temp_name_list := + nonmatching_names(map(lhs, cmpt_list), coeff_name_prefix); + if 0 < nops(temp_name_list) then + print_name_list_dcl(%, temp_name_type, file_name) + end if; + codegen[C](cmpt_list, filename = file_name); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C expression to assign the data-value +# variables, eg +# data->data_m1_p1 = DATA(-1,1); +# +# Arguments: +# posn_list = The same list of positions as was used to compute the +# interpolating polynomial. +# data_var_name_prefix = A prefix string for the data variable names. +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_fetch_data := +> proc( +> posn_list::list(list(numeric)), +> data_var_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> map( +> proc(posn::list(numeric)) +> fprintf(file_name, +> "%s = %a;\n", +> data_var_name(posn,data_var_name_prefix), +> DATA(op(posn))); +> end proc +> , +> posn_list +> ); +> fclose(file_name); +> +> NULL; +> end proc; +print_fetch_data := proc(posn_list::list(list(numeric)), +data_var_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + fprintf(file_name, "%s = %a;\n", + data_var_name(posn, data_var_name_prefix), DATA(op(posn))) + end proc, posn_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C expression to store the interpolation +# coefficients in COEFF(...) expressions, eg +# COEFF(1,-1) = factor * coeffs->coeff_p1_m1; +# +# Arguments: +# posn_list = The list of positions in the molecule. +# coeff_name_prefix = A prefix string for the coefficient names, +# eg "factor * coeffs->coeff_" +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_store_coeffs := +> proc( +> posn_list::list(list(numeric)), +> coeff_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> map( +> proc(posn::list(numeric)) +> fprintf(file_name, +> "%a = %s;\n", +> 'COEFF'(op(posn)), +> coeff_name(posn,coeff_name_prefix)); +> end proc +> , +> posn_list +> ); +> fclose(file_name); +> +> NULL; +> end proc; +print_store_coeffs := proc(posn_list::list(list(numeric)), +coeff_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + fprintf(file_name, "%a = %s;\n", 'COEFF'(op(posn)), + coeff_name(posn, coeff_name_prefix)) + end proc, posn_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a C expression to evaluate a molecule, i.e. +# to compute the molecule as a linear combination of the data values. +# +# Arguments: +# posn_list = The list of positions in the molecule. +# coeff_name_prefix = A prefix string for the coefficient names. +# data_var_name_prefix = A prefix string for the data variable names. +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_evaluate_molecule := +> proc( +> posn_list::list(list(numeric)), +> coeff_name_prefix::string, +> data_var_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> +# list of "coeff*data_var" terms +> map( +> proc(posn::list(numeric)) +> sprintf("%s*%s", +> coeff_name(posn,coeff_name_prefix), +> data_var_name(posn,data_var_name_prefix)); +> end proc +> , +> posn_list +> ); +> +> ListTools[Join](%, "\n + "); +> cat(op(%)); +> fprintf(file_name, " %s;\n", %); +> +> fclose(file_name); +> +> NULL; +> end proc; +print_evaluate_molecule := proc(posn_list::list(list(numeric)), +coeff_name_prefix::string, data_var_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + sprintf("%s*%s", coeff_name(posn, coeff_name_prefix), + data_var_name(posn, data_var_name_prefix)) + end proc, posn_list); + ListTools[Join](%, "\n + "); + cat(op(%)); + fprintf(file_name, " %s;\n", %); + fclose(file_name); + NULL +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes the name of the coefficient of the data at a +# given [m] position, i.e. it encapsulates our naming convention for this. +# +# Arguments: +# posn = (in) The [m] coordinates. +# name_prefix = A prefix string for the coefficient name. +# +# Results: +# The function returns the coefficient, as a Maple string. +# +> coeff_name := +> proc(posn::list(numeric), name_prefix::string) +> cat(name_prefix, sprint_numeric_list(posn)); +> end proc; +coeff_name := proc(posn::list(numeric), name_prefix::string) + cat(name_prefix, sprint_numeric_list(posn)) +end proc + +> +################################################################################ +> +# +# This function computes the name of the variable in which the C code +# will store the input data at a given [m] position, i.e. it encapsulates +# our naming convention for this. +# +# Arguments: +# posn = (in) The [m] coordinates. +# name_prefix = A prefix string for the variable name. +# +# Results: +# The function returns the variable name, as a Maple string. +# +> data_var_name := +> proc(posn::list(numeric), name_prefix::string) +> cat(name_prefix, sprint_numeric_list(posn)); +> end proc; +data_var_name := proc(posn::list(numeric), name_prefix::string) + cat(name_prefix, sprint_numeric_list(posn)) +end proc + +# Maple code to compute lists of point positions in hypercube-shaped molecules +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/common/cube_posns.maple,v 1.3 2002/08/20 16:56:41 jthorn Exp $ +> +################################################################################ +> +# +# 1D interpolation points +# +> posn_list_1d_size2 := hypercube_points([ 0], [+1]); + posn_list_1d_size2 := [[0], [1]] + +> posn_list_1d_size3 := hypercube_points([-1], [+1]); + posn_list_1d_size3 := [[-1], [0], [1]] + +> posn_list_1d_size4 := hypercube_points([-1], [+2]); + posn_list_1d_size4 := [[-1], [0], [1], [2]] + +> posn_list_1d_size5 := hypercube_points([-2], [+2]); + posn_list_1d_size5 := [[-2], [-1], [0], [1], [2]] + +> posn_list_1d_size6 := hypercube_points([-2], [+3]); + posn_list_1d_size6 := [[-2], [-1], [0], [1], [2], [3]] + +> posn_list_1d_size7 := hypercube_points([-3], [+3]); + posn_list_1d_size7 := [[-3], [-2], [-1], [0], [1], [2], [3]] + +> +################################################################################ +> +# +# 2D interpolation points (Fortran ordering) +# +> posn_list_2d_size2 := map(ListTools[Reverse], +> hypercube_points([ 0, 0], [+1,+1])); + posn_list_2d_size2 := [[0, 0], [1, 0], [0, 1], [1, 1]] + +> posn_list_2d_size3 := map(ListTools[Reverse], +> hypercube_points([-1,-1], [+1,+1])); +posn_list_2d_size3 := [[-1, -1], [0, -1], [1, -1], [-1, 0], [0, 0], [1, 0], + + [-1, 1], [0, 1], [1, 1]] + +> posn_list_2d_size4 := map(ListTools[Reverse], +> hypercube_points([-1,-1], [+2,+2])); +posn_list_2d_size4 := [[-1, -1], [0, -1], [1, -1], [2, -1], [-1, 0], [0, 0], + + [1, 0], [2, 0], [-1, 1], [0, 1], [1, 1], [2, 1], [-1, 2], [0, 2], [1, 2], + + [2, 2]] + +> posn_list_2d_size5 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+2,+2])); +posn_list_2d_size5 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [-2, -1], + + [-1, -1], [0, -1], [1, -1], [2, -1], [-2, 0], [-1, 0], [0, 0], [1, 0], + + [2, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], [-2, 2], [-1, 2], [0, 2], + + [1, 2], [2, 2]] + +> posn_list_2d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+3,+3])); +posn_list_2d_size6 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [3, -2], + + [-2, -1], [-1, -1], [0, -1], [1, -1], [2, -1], [3, -1], [-2, 0], [-1, 0], + + [0, 0], [1, 0], [2, 0], [3, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], + + [3, 1], [-2, 2], [-1, 2], [0, 2], [1, 2], [2, 2], [3, 2], [-2, 3], [-1, 3], + + [0, 3], [1, 3], [2, 3], [3, 3]] + +> +################################################################################ +> +# +# 3D interpolation points (Fortran ordering) +# +> posn_list_3d_size2 := map(ListTools[Reverse], +> hypercube_points([ 0, 0, 0], [+1,+1,+1])); +posn_list_3d_size2 := [[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], + + [1, 0, 1], [0, 1, 1], [1, 1, 1]] + +> posn_list_3d_size3 := map(ListTools[Reverse], +> hypercube_points([-1,-1,-1], [+1,+1,+1])); +posn_list_3d_size3 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [-1, 0, -1], + + [0, 0, -1], [1, 0, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], [-1, -1, 0], + + [0, -1, 0], [1, -1, 0], [-1, 0, 0], [0, 0, 0], [1, 0, 0], [-1, 1, 0], + + [0, 1, 0], [1, 1, 0], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [-1, 0, 1], + + [0, 0, 1], [1, 0, 1], [-1, 1, 1], [0, 1, 1], [1, 1, 1]] + +> posn_list_3d_size4 := map(ListTools[Reverse], +> hypercube_points([-1,-1,-1], [+2,+2,+2])); +posn_list_3d_size4 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [2, -1, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [-1, 1, -1], [0, 1, -1], + + [1, 1, -1], [2, 1, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-1, 0, 0], [0, 0, 0], + + [1, 0, 0], [2, 0, 0], [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [-1, -1, 1], [0, -1, 1], + + [1, -1, 1], [2, -1, 1], [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [-1, 2, 1], [0, 2, 1], + + [1, 2, 1], [2, 2, 1], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-1, 1, 2], [0, 1, 2], + + [1, 1, 2], [2, 1, 2], [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2]] + +> posn_list_3d_size5 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+2,+2,+2])); +posn_list_3d_size5 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], [1, -1, -2], + + [2, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], [1, 0, -2], [2, 0, -2], + + [-2, 1, -2], [-1, 1, -2], [0, 1, -2], [1, 1, -2], [2, 1, -2], [-2, 2, -2], + + [-1, 2, -2], [0, 2, -2], [1, 2, -2], [2, 2, -2], [-2, -2, -1], [-1, -2, -1], + + [0, -2, -1], [1, -2, -1], [2, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [-2, 0, -1], [-1, 0, -1], [0, 0, -1], + + [1, 0, -1], [2, 0, -1], [-2, 1, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], + + [2, 1, -1], [-2, 2, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], + + [-2, -2, 0], [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-2, 0, 0], [-1, 0, 0], + + [0, 0, 0], [1, 0, 0], [2, 0, 0], [-2, 1, 0], [-1, 1, 0], [0, 1, 0], + + [1, 1, 0], [2, 1, 0], [-2, 2, 0], [-1, 2, 0], [0, 2, 0], [1, 2, 0], + + [2, 2, 0], [-2, -2, 1], [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], + + [-2, -1, 1], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [-2, 1, 1], [-1, 1, 1], + + [0, 1, 1], [1, 1, 1], [2, 1, 1], [-2, 2, 1], [-1, 2, 1], [0, 2, 1], + + [1, 2, 1], [2, 2, 1], [-2, -2, 2], [-1, -2, 2], [0, -2, 2], [1, -2, 2], + + [2, -2, 2], [-2, -1, 2], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], + + [-2, 0, 2], [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [-2, 2, 2], [-1, 2, 2], + + [0, 2, 2], [1, 2, 2], [2, 2, 2]] + +> posn_list_3d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+3,+3,+3])); +posn_list_3d_size6 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [3, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], + + [1, -1, -2], [2, -1, -2], [3, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], + + [1, 0, -2], [2, 0, -2], [3, 0, -2], [-2, 1, -2], [-1, 1, -2], [0, 1, -2], + + [1, 1, -2], [2, 1, -2], [3, 1, -2], [-2, 2, -2], [-1, 2, -2], [0, 2, -2], + + [1, 2, -2], [2, 2, -2], [3, 2, -2], [-2, 3, -2], [-1, 3, -2], [0, 3, -2], + + [1, 3, -2], [2, 3, -2], [3, 3, -2], [-2, -2, -1], [-1, -2, -1], [0, -2, -1], + + [1, -2, -1], [2, -2, -1], [3, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [3, -1, -1], [-2, 0, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [3, 0, -1], [-2, 1, -1], + + [-1, 1, -1], [0, 1, -1], [1, 1, -1], [2, 1, -1], [3, 1, -1], [-2, 2, -1], + + [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], [3, 2, -1], [-2, 3, -1], + + [-1, 3, -1], [0, 3, -1], [1, 3, -1], [2, 3, -1], [3, 3, -1], [-2, -2, 0], + + [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [3, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [3, -1, 0], [-2, 0, 0], + + [-1, 0, 0], [0, 0, 0], [1, 0, 0], [2, 0, 0], [3, 0, 0], [-2, 1, 0], + + [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [3, 1, 0], [-2, 2, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [3, 2, 0], [-2, 3, 0], + + [-1, 3, 0], [0, 3, 0], [1, 3, 0], [2, 3, 0], [3, 3, 0], [-2, -2, 1], + + [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], [3, -2, 1], [-2, -1, 1], + + [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [3, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [3, 0, 1], [-2, 1, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [3, 1, 1], [-2, 2, 1], + + [-1, 2, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [3, 2, 1], [-2, 3, 1], + + [-1, 3, 1], [0, 3, 1], [1, 3, 1], [2, 3, 1], [3, 3, 1], [-2, -2, 2], + + [-1, -2, 2], [0, -2, 2], [1, -2, 2], [2, -2, 2], [3, -2, 2], [-2, -1, 2], + + [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], [3, -1, 2], [-2, 0, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [3, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [3, 1, 2], [-2, 2, 2], + + [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2], [3, 2, 2], [-2, 3, 2], + + [-1, 3, 2], [0, 3, 2], [1, 3, 2], [2, 3, 2], [3, 3, 2], [-2, -2, 3], + + [-1, -2, 3], [0, -2, 3], [1, -2, 3], [2, -2, 3], [3, -2, 3], [-2, -1, 3], + + [-1, -1, 3], [0, -1, 3], [1, -1, 3], [2, -1, 3], [3, -1, 3], [-2, 0, 3], + + [-1, 0, 3], [0, 0, 3], [1, 0, 3], [2, 0, 3], [3, 0, 3], [-2, 1, 3], + + [-1, 1, 3], [0, 1, 3], [1, 1, 3], [2, 1, 3], [3, 1, 3], [-2, 2, 3], + + [-1, 2, 3], [0, 2, 3], [1, 2, 3], [2, 2, 3], [3, 2, 3], [-2, 3, 3], + + [-1, 3, 3], [0, 3, 3], [1, 3, 3], [2, 3, 3], [3, 3, 3]] + +# Maple code to define Lagrange interpolating functions/coords/coeffs +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple,v 1.2 2002/08/20 16:31:24 jthorn Exp $ +> +################################################################################ +> +# +# 1-D interpolating functions +# +> +> fn_1d_order1 := +> proc(x) +> + c0 + c1*x +> end proc; + fn_1d_order1 := proc(x) c0 + c1*x end proc + +> +> fn_1d_order2 := +> proc(x) +> + c0 + c1*x + c2*x^2 +> end proc; + fn_1d_order2 := proc(x) c0 + c1*x + c2*x^2 end proc + +> +> fn_1d_order3 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 +> end proc; + fn_1d_order3 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 end proc + +> +> fn_1d_order4 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 +> end; + fn_1d_order4 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 end proc + +> +> fn_1d_order5 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 +> end; + fn_1d_order5 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 end proc + +> +> fn_1d_order6 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 +> end; +fn_1d_order6 := + + proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 end proc + +> +######################################## +> +# coordinates for 1-D interpolating functions +> coords_list_1d := [x]; + coords_list_1d := [x] + +> +######################################## +> +# +# coefficients in 1-D interpolating functions +# +> +> coeffs_list_1d_order1 := [c0, c1]; + coeffs_list_1d_order1 := [c0, c1] + +> coeffs_list_1d_order2 := [c0, c1, c2]; + coeffs_list_1d_order2 := [c0, c1, c2] + +> coeffs_list_1d_order3 := [c0, c1, c2, c3]; + coeffs_list_1d_order3 := [c0, c1, c2, c3] + +> coeffs_list_1d_order4 := [c0, c1, c2, c3, c4]; + coeffs_list_1d_order4 := [c0, c1, c2, c3, c4] + +> coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5]; + coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5] + +> coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6]; + coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6] + +> +################################################################################ +> +# +# 2-D interpolating functions +# +> +> fn_2d_order1 := +> proc(x,y) +> + c01*y +> + c00 + c10*x +> end proc; + fn_2d_order1 := proc(x, y) c01*y + c00 + c10*x end proc + +> +> fn_2d_order2 := +> proc(x,y) +> + c02*y^2 +> + c01*y + c11*x*y +> + c00 + c10*x + c20*x^2 +> end proc; +fn_2d_order2 := + + proc(x, y) c02*y^2 + c01*y + c11*x*y + c00 + c10*x + c20*x^2 end proc + +> +> fn_2d_order3 := +> proc(x,y) +> + c03*y^3 +> + c02*y^2 + c12*x*y^2 +> + c01*y + c11*x*y + c21*x^2*y +> + c00 + c10*x + c20*x^2 + c30*x^3 +> end proc; +fn_2d_order3 := proc(x, y) + c03*y^3 + c02*y^2 + c12*x*y^2 + c01*y + c11*x*y + c21*x^2*y + c00 + + c10*x + c20*x^2 + c30*x^3 +end proc + +> +> fn_2d_order4 := +> proc(x,y) +> + c04*y^4 +> + c03*y^3 + c13*x*y^3 +> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 +> + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +> + c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 +> end; +fn_2d_order4 := proc(x, y) + c04*y^4 + c03*y^3 + c13*x*y^3 + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + c00 + c10*x + c20*x^2 + + c30*x^3 + c40*x^4 +end proc + +> +######################################## +> +# coordinates for 2-D interpolating functions +> coords_list_2d := [x,y]; + coords_list_2d := [x, y] + +> +######################################## +> +# +# coefficients in 2-D interpolating functions +# +> +> coeffs_list_2d_order1 := [ +> c01, +> c00, c10 +> ]; + coeffs_list_2d_order1 := [c01, c00, c10] + +> coeffs_list_2d_order2 := [ +> c02, +> c01, c11, +> c00, c10, c20 +> ]; + coeffs_list_2d_order2 := [c02, c01, c11, c00, c10, c20] + +> coeffs_list_2d_order3 := [ +> c03, +> c02, c12, +> c01, c11, c21, +> c00, c10, c20, c30 +> ]; + coeffs_list_2d_order3 := [c03, c02, c12, c01, c11, c21, c00, c10, c20, c30] + +> coeffs_list_2d_order4 := [ +> c04, +> c03, c13, +> c02, c12, c22, +> c01, c11, c21, c31, +> c00, c10, c20, c30, c40 +> ]; +coeffs_list_2d_order4 := + + [c04, c03, c13, c02, c12, c22, c01, c11, c21, c31, c00, c10, c20, c30, c40] + +> +################################################################################ +> +# +# 3-D interpolating functions +# +> +> fn_3d_order1 := +> proc(x,y,z) +# z^0 ----------- +> + c010*y +> + c000 + c100*x +# z^1 ----------- +> + c001*z +> end proc; + fn_3d_order1 := proc(x, y, z) c010*y + c000 + c100*x + c001*z end proc + +> +> fn_3d_order2 := +> proc(x,y,z) +# z^0 -------------------------- +> + c020*y^2 +> + c010*y + c110*x*y +> + c000 + c100*x + c200*x^2 +# z^1 -------------------------- +> + c011*y*z +> + c001*z + c101*x*z +# z^2 -------------------------- +> + c002*z^2 +> end proc; +fn_3d_order2 := proc(x, y, z) + c020*y^2 + c010*y + c110*x*y + c000 + c100*x + c200*x^2 + c011*y*z + + c001*z + c101*x*z + c002*z^2 +end proc + +> +> fn_3d_order3 := +> proc(x,y,z) +# z^0 ------------------------------------------- +> + c030*y^3 +> + c020*y^2 + c120*x*y^2 +> + c010*y + c110*x*y + c210*x^2*y +> + c000 + c100*x + c200*x^2 + c300*x^3 +# z^1 ------------------------------------------- +> + c021*y^2*z +> + c011*y *z + c111*x*y*z +> + c001 *z + c101*x *z + c201*x^2*z +# z^2 ------------------------------------------- +> + c012*y*z^2 +> + c002 *z^2 + c102*x*z^2 +# z^3 ------------------------------------------- +> + c003 *z^3 +> end proc; +fn_3d_order3 := proc(x, y, z) + c030*y^3 + c020*y^2 + c120*x*y^2 + c010*y + c110*x*y + c210*x^2*y + + c000 + c100*x + c200*x^2 + c300*x^3 + c021*y^2*z + c011*y*z + + c111*x*y*z + c001*z + c101*x*z + c201*x^2*z + c012*y*z^2 + c002*z^2 + + c102*x*z^2 + c003*z^3 +end proc + +> +> fn_3d_order4 := +> proc(x,y,z) +# z^0 -------------------------------------------------------- +> + c040*y^4 +> + c030*y^3 + c130*x*y^3 +> + c020*y^2 + c120*x*y^2 + c220*x^2*y^2 +> + c010*y + c110*x*y + c210*x^2*y + c310*x^3*y +> + c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 +# z^1 ------------------------------------------- +> + c031*y^3*z +> + c021*y^2*z + c121*x*y^2*z +> + c011*y *z + c111*x*y *z + c211*x^2*y*z +> + c001 *z + c101*x *z + c201*x^2 *z + c301*x^3*z +# z^2 ------------------------------------------- +> + c022*y^2*z^2 +> + c012*y *z^2 + c112*x*y*z^2 +> + c002 *z^2 + c102*x *z^2 + c202*x^2*z^2 +# z^3 ------------------------------------------- +> + c013*y *z^3 +> + c003 *z^3 + c103*x *z^3 +# z^4 ------------------------------------------- +> + c004 *z^4 +> end; +fn_3d_order4 := proc(x, y, z) + c102*x*z^2 + c012*y*z^2 + c111*x*y*z + c121*x*y^2*z + c211*x^2*y*z + + c112*x*y*z^2 + c010*y + c110*x*y + c011*y*z + c101*x*z + c120*x*y^2 + + c210*x^2*y + c021*y^2*z + c201*x^2*z + c130*x*y^3 + c220*x^2*y^2 + + c310*x^3*y + c031*y^3*z + c301*x^3*z + c022*y^2*z^2 + c202*x^2*z^2 + + c013*y*z^3 + c103*x*z^3 + c000 + c100*x + c001*z + c020*y^2 + + c200*x^2 + c002*z^2 + c030*y^3 + c300*x^3 + c003*z^3 + c040*y^4 + + c400*x^4 + c004*z^4 +end proc + +> +######################################## +> +# coordinates for 3-D interpolating functions +> coords_list_3d := [x,y,z]; + coords_list_3d := [x, y, z] + +> +######################################## +> +# +# coefficients in 3-D interpolating functions +# +> +> coeffs_list_3d_order1 := [ +> # z^0 ----- +> c010, +> c000, c100, +> # z^1 ----- +> c001 +> ]; + coeffs_list_3d_order1 := [c010, c000, c100, c001] + +> coeffs_list_3d_order2 := [ +> # z^0 ----------- +> c020, +> c010, c110, +> c000, c100, c200, +> # z^1 ----------- +> c011, +> c001, c101, +> # z^2 ----------- +> c002 +> ]; +coeffs_list_3d_order2 := + + [c020, c010, c110, c000, c100, c200, c011, c001, c101, c002] + +> coeffs_list_3d_order3 := [ +> # z^0 ---------------- +> c030, +> c020, c120, +> c010, c110, c210, +> c000, c100, c200, c300, +> # z^1 ---------------- +> c021, +> c011, c111, +> c001, c101, c201, +> # z^2 ---------------- +> c012, +> c002, c102, +> # z^3 ---------------- +> c003 +> ]; +coeffs_list_3d_order3 := [c030, c020, c120, c010, c110, c210, c000, c100, c200, + + c300, c021, c011, c111, c001, c101, c201, c012, c002, c102, c003] + +> coeffs_list_3d_order4 := [ +> # z^0 ----------------------- +> c040, +> c030, c130, +> c020, c120, c220, +> c010, c110, c210, c310, +> c000, c100, c200, c300, c400, +> # z^1 ----------------------- +> c031, +> c021, c121, +> c011, c111, c211, +> c001, c101, c201, c301, +> # z^2 ----------------------- +> c022, +> c012, c112, +> c002, c102, c202, +> # z^3 ----------------------- +> c013, +> c003, c103, +> # z^4 ----------------------- +> c004 +> ]; +coeffs_list_3d_order4 := [c040, c030, c130, c020, c120, c220, c010, c110, c210, + + c310, c000, c100, c200, c300, c400, c031, c021, c121, c011, c111, c211, + + c001, c101, c201, c301, c022, c012, c112, c002, c102, c202, c013, c003, + + c103, c004] + +> +################################################################################ +# 1d.maple -- compute Lagrange interpolation coefficients in 1-D +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/1d.maple,v 1.2 2002/08/20 16:31:22 jthorn Exp $ +> +################################################################################ +> +# +# 1d, cube, order=1, smoothing=0 (size=2) +# +> +# interpolating polynomial +> interp_1d_cube_order1_smooth0 +> := Lagrange_polynomial_interpolant(fn_1d_order1, coeffs_list_1d_order1, +> coords_list_1d, posn_list_1d_size2); + interp_1d_cube_order1_smooth0 := DATA(0) + (DATA(1) - DATA(0)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_1d_size2); + [COEFF(0) = 1 - x, COEFF(1) = x] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "1d.coeffs/1d.cube.order1.smooth0/coeffs-I.compute.c"); +bytes used=1000428, alloc=917336, time=0.07 +> +# d/dx +> simplify( diff(interp_1d_cube_order1_smooth0,x) ); + DATA(1) - DATA(0) + +> coeffs_as_lc_of_data(%, posn_list_1d_size2); + [COEFF(0) = -1, COEFF(1) = 1] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "1d.coeffs/1d.cube.order1.smooth0/coeffs-dx.compute.c"); +> +################################################################################ +> +# +# 1d, cube, order=2, smoothing=0 (size=3) +# +> +# interpolating polynomial +> interp_1d_cube_order2_smooth0 +> := Lagrange_polynomial_interpolant(fn_1d_order2, coeffs_list_1d_order2, +> coords_list_1d, posn_list_1d_size3); +interp_1d_cube_order2_smooth0 := DATA(0) + (- 1/2 DATA(-1) + 1/2 DATA(1)) x + + 2 + + (1/2 DATA(-1) + 1/2 DATA(1) - DATA(0)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_1d_size3); + 2 2 2 + [COEFF(-1) = - 1/2 x + 1/2 x , COEFF(0) = 1 - x , COEFF(1) = 1/2 x + 1/2 x ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "1d.coeffs/1d.cube.order2.smooth0/coeffs-I.compute.c"); +> +# d/dx +> simplify( diff(interp_1d_cube_order2_smooth0,x) ); + - 1/2 DATA(-1) + 1/2 DATA(1) + x DATA(-1) + DATA(1) x - 2 x DATA(0) + +> coeffs_as_lc_of_data(%, posn_list_1d_size3); + [COEFF(-1) = x - 1/2, COEFF(0) = -2 x, COEFF(1) = 1/2 + x] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "1d.coeffs/1d.cube.order2.smooth0/coeffs-dx.compute.c"); +> +# d^2/dx^2 +> simplify( diff(interp_1d_cube_order2_smooth0,x,x) ); +bytes used=2000692, alloc=1441528, time=0.11 + DATA(-1) + DATA(1) - 2 DATA(0) + +> coeffs_as_lc_of_data(%, posn_list_1d_size3); + [COEFF(-1) = 1, COEFF(0) = -2, COEFF(1) = 1] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "1d.coeffs/1d.cube.order2.smooth0/coeffs-dxx.compute.c"); +> +################################################################################ +> +# +# 1d, cube, order=3, smoothing=0 (size=4) +# +> +# interpolating polynomial +> interp_1d_cube_order3_smooth0 +> := Lagrange_polynomial_interpolant(fn_1d_order3, coeffs_list_1d_order3, +> coords_list_1d, posn_list_1d_size4); +interp_1d_cube_order3_smooth0 := DATA(0) + + + (- 1/2 DATA(0) - 1/3 DATA(-1) + DATA(1) - 1/6 DATA(2)) x + + 2 + + (1/2 DATA(-1) + 1/2 DATA(1) - DATA(0)) x + + 3 + + (1/2 DATA(0) - 1/6 DATA(-1) - 1/2 DATA(1) + 1/6 DATA(2)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_1d_size4); + 2 3 2 3 +[COEFF(-1) = - 1/3 x + 1/2 x - 1/6 x , COEFF(0) = 1 - 1/2 x - x + 1/2 x , + + 2 3 3 + COEFF(1) = x + 1/2 x - 1/2 x , COEFF(2) = - 1/6 x + 1/6 x ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "1d.coeffs/1d.cube.order3.smooth0/coeffs-I.compute.c"); +> +# d/dx +> simplify( diff(interp_1d_cube_order3_smooth0,x) ); +bytes used=3001280, alloc=1769148, time=0.17 +- 1/2 DATA(0) - 1/3 DATA(-1) + DATA(1) - 1/6 DATA(2) + x DATA(-1) + x DATA(1) + + 2 2 2 + - 2 x DATA(0) + 3/2 x DATA(0) - 1/2 x DATA(-1) - 3/2 x DATA(1) + + 2 + + 1/2 x DATA(2) + +> coeffs_as_lc_of_data(%, posn_list_1d_size4); + 2 2 +[COEFF(-1) = x - 1/2 x - 1/3, COEFF(0) = - 1/2 - 2 x + 3/2 x , + + 2 2 + COEFF(1) = x + 1 - 3/2 x , COEFF(2) = 1/2 x - 1/6] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "1d.coeffs/1d.cube.order3.smooth0/coeffs-dx.compute.c"); +> +# d^2/dx^2 +> simplify( diff(interp_1d_cube_order3_smooth0,x,x) ); +DATA(-1) + DATA(1) - 2 DATA(0) + 3 x DATA(0) - x DATA(-1) - 3 x DATA(1) + + + x DATA(2) + +> coeffs_as_lc_of_data(%, posn_list_1d_size4); + [COEFF(-1) = 1 - x, COEFF(0) = -2 + 3 x, COEFF(1) = 1 - 3 x, COEFF(2) = x] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "1d.coeffs/1d.cube.order3.smooth0/coeffs-dxx.compute.c"); +> +################################################################################ +> +# +# 1d, cube, order=4, smoothing=0 (size=5) +# +> +# interpolating polynomial +> interp_1d_cube_order4_smooth0 +> := Lagrange_polynomial_interpolant(fn_1d_order4, coeffs_list_1d_order4, +> coords_list_1d, posn_list_1d_size5); +bytes used=4001452, alloc=1834672, time=0.27 +interp_1d_cube_order4_smooth0 := DATA(0) + + + (- 1/12 DATA(2) + 1/12 DATA(-2) - 2/3 DATA(-1) + 2/3 DATA(1)) x + + + (2/3 DATA(1) - 5/4 DATA(0) - 1/24 DATA(-2) + 2/3 DATA(-1) - 1/24 DATA(2)) + + 2 3 + x + (1/12 DATA(2) - 1/12 DATA(-2) + 1/6 DATA(-1) - 1/6 DATA(1)) x + + + (- 1/6 DATA(1) + 1/4 DATA(0) + 1/24 DATA(-2) - 1/6 DATA(-1) + 1/24 DATA(2)) + + 4 + x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_1d_size5); + 2 3 4 +[COEFF(-2) = 1/12 x - 1/24 x - 1/12 x + 1/24 x , + + 2 3 4 + COEFF(-1) = - 2/3 x + 2/3 x + 1/6 x - 1/6 x , + + 2 4 + COEFF(0) = - 5/4 x + 1 + 1/4 x , + + 3 2 4 + COEFF(1) = - 1/6 x + 2/3 x + 2/3 x - 1/6 x , + + 3 2 4 + COEFF(2) = 1/12 x - 1/12 x - 1/24 x + 1/24 x ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "1d.coeffs/1d.cube.order4.smooth0/coeffs-I.compute.c"); +bytes used=5001648, alloc=1900196, time=0.34 +> +# d/dx +> simplify( diff(interp_1d_cube_order4_smooth0,x) ); +- 1/12 DATA(2) + 1/12 DATA(-2) - 2/3 DATA(-1) + 2/3 DATA(1) + 4/3 x DATA(1) + + - 5/2 x DATA(0) - 1/12 x DATA(-2) + 4/3 x DATA(-1) - 1/12 x DATA(2) + + 2 2 2 2 + + 1/4 x DATA(2) - 1/4 x DATA(-2) + 1/2 x DATA(-1) - 1/2 x DATA(1) + + 3 3 3 3 + - 2/3 x DATA(1) + x DATA(0) + 1/6 x DATA(-2) - 2/3 x DATA(-1) + + 3 + + 1/6 x DATA(2) + +> coeffs_as_lc_of_data(%, posn_list_1d_size5); + 2 3 +[COEFF(-2) = - 1/12 x - 1/4 x + 1/12 + 1/6 x , + + 3 2 3 + COEFF(-1) = - 2/3 + 4/3 x - 2/3 x + 1/2 x , COEFF(0) = x - 5/2 x, + + 3 2 + COEFF(1) = 4/3 x - 2/3 x - 1/2 x + 2/3, + + 2 3 + COEFF(2) = - 1/12 - 1/12 x + 1/4 x + 1/6 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "1d.coeffs/1d.cube.order4.smooth0/coeffs-dx.compute.c"); +bytes used=6001824, alloc=1900196, time=0.42 +> +# d^2/dx^2 +> simplify( diff(interp_1d_cube_order4_smooth0,x,x) ); +4/3 DATA(1) - 5/2 DATA(0) - 1/12 DATA(-2) + 4/3 DATA(-1) - 1/12 DATA(2) + + 2 + + 1/2 x DATA(2) - 1/2 x DATA(-2) + x DATA(-1) - x DATA(1) - 2 x DATA(1) + + 2 2 2 2 + + 3 x DATA(0) + 1/2 x DATA(-2) - 2 x DATA(-1) + 1/2 x DATA(2) + +> coeffs_as_lc_of_data(%, posn_list_1d_size5); + 2 2 +[COEFF(-2) = - 1/12 - 1/2 x + 1/2 x , COEFF(-1) = 4/3 - 2 x + x, + + 2 2 + COEFF(0) = - 5/2 + 3 x , COEFF(1) = -x + 4/3 - 2 x , + + 2 + COEFF(2) = - 1/12 + 1/2 x + 1/2 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "1d.coeffs/1d.cube.order4.smooth0/coeffs-dxx.compute.c"); +bytes used=7002056, alloc=1900196, time=0.50 +> +################################################################################ +> +# +# 1d, cube, order=5, smoothing=0 (size=6) +# +> +# interpolating polynomial +> interp_1d_cube_order5_smooth0 +> := Lagrange_polynomial_interpolant(fn_1d_order5, coeffs_list_1d_order5, +> coords_list_1d, posn_list_1d_size6); +bytes used=8002252, alloc=1900196, time=0.55 +interp_1d_cube_order5_smooth0 := DATA(0) + (- 1/2 DATA(-1) - 1/4 DATA(2) + + - 1/3 DATA(0) + 1/20 DATA(-2) + DATA(1) + 1/30 DATA(3)) x + + + (2/3 DATA(1) - 5/4 DATA(0) - 1/24 DATA(-2) + 2/3 DATA(-1) - 1/24 DATA(2)) + + 2 + x + (- 1/24 DATA(-1) + 7/24 DATA(2) + 5/12 DATA(0) - 1/24 DATA(-2) + + 3 + - 7/12 DATA(1) - 1/24 DATA(3)) x + + + (- 1/6 DATA(1) + 1/4 DATA(0) + 1/24 DATA(-2) - 1/6 DATA(-1) + 1/24 DATA(2)) + + 4 + x + (1/24 DATA(-1) - 1/24 DATA(2) - 1/12 DATA(0) - 1/120 DATA(-2) + + 5 + + 1/12 DATA(1) + 1/120 DATA(3)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_1d_size6); + 2 3 4 5 +[COEFF(-2) = 1/20 x - 1/24 x - 1/24 x + 1/24 x - 1/120 x , + + 2 3 4 5 + COEFF(-1) = - 1/2 x + 2/3 x - 1/24 x - 1/6 x + 1/24 x , + + 2 3 4 5 + COEFF(0) = 1 - 1/3 x - 5/4 x + 5/12 x + 1/4 x - 1/12 x , + + 2 3 4 5 + COEFF(1) = x + 2/3 x - 7/12 x - 1/6 x + 1/12 x , + + 3 4 2 5 + COEFF(2) = - 1/4 x + 7/24 x + 1/24 x - 1/24 x - 1/24 x , + + 5 3 + COEFF(3) = 1/30 x + 1/120 x - 1/24 x ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "1d.coeffs/1d.cube.order5.smooth0/coeffs-I.compute.c"); +bytes used=9004240, alloc=1965720, time=0.63 +> +# d/dx +> simplify( diff(interp_1d_cube_order5_smooth0,x) ); +- 1/3 DATA(0) + DATA(1) - 1/4 DATA(2) - 1/2 DATA(-1) + 1/30 DATA(3) + + 4 4 4 4 + + 5/24 x DATA(-1) - 5/24 x DATA(2) - 5/12 x DATA(0) - 1/24 x DATA(-2) + + 4 4 + + 5/12 x DATA(1) + 1/24 x DATA(3) + 4/3 x DATA(1) - 5/2 x DATA(0) + + 2 + - 1/12 x DATA(-2) + 4/3 x DATA(-1) - 1/12 x DATA(2) - 1/8 x DATA(-1) + + 2 2 2 2 + + 7/8 x DATA(2) + 5/4 x DATA(0) - 1/8 x DATA(-2) - 7/4 x DATA(1) + + 2 3 3 3 + - 1/8 x DATA(3) - 2/3 x DATA(1) + x DATA(0) + 1/6 x DATA(-2) + + 3 3 + - 2/3 x DATA(-1) + 1/6 x DATA(2) + 1/20 DATA(-2) + +> coeffs_as_lc_of_data(%, posn_list_1d_size6); + 4 3 2 +[COEFF(-2) = - 1/12 x - 1/24 x + 1/6 x + 1/20 - 1/8 x , + + 3 2 4 + COEFF(-1) = - 2/3 x - 1/8 x - 1/2 + 5/24 x + 4/3 x, + + 3 4 2 + COEFF(0) = - 5/2 x + x - 5/12 x - 1/3 + 5/4 x , + + 4 3 2 + COEFF(1) = 5/12 x - 2/3 x + 4/3 x - 7/4 x + 1, + + 3 2 4 + COEFF(2) = 1/6 x - 1/12 x + 7/8 x - 1/4 - 5/24 x , + + 4 2 + COEFF(3) = 1/24 x - 1/8 x + 1/30] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "1d.coeffs/1d.cube.order5.smooth0/coeffs-dx.compute.c"); +bytes used=10004620, alloc=1965720, time=0.72 +bytes used=11005012, alloc=1965720, time=0.81 +> +# d^2/dx^2 +> simplify( diff(interp_1d_cube_order5_smooth0,x,x) ); +4/3 DATA(1) - 5/2 DATA(0) - 1/12 DATA(-2) + 4/3 DATA(-1) - 1/12 DATA(2) + + - 1/4 x DATA(-1) + 7/4 x DATA(2) + 5/2 x DATA(0) - 1/4 x DATA(-2) + + 2 2 + - 7/2 x DATA(1) - 1/4 x DATA(3) - 2 x DATA(1) + 3 x DATA(0) + + 2 2 2 3 + + 1/2 x DATA(-2) - 2 x DATA(-1) + 1/2 x DATA(2) + 5/6 x DATA(-1) + + 3 3 3 3 + - 5/6 x DATA(2) - 5/3 x DATA(0) - 1/6 x DATA(-2) + 5/3 x DATA(1) + + 3 + + 1/6 x DATA(3) + +> coeffs_as_lc_of_data(%, posn_list_1d_size6); + 2 3 +[COEFF(-2) = - 1/12 + 1/2 x - 1/6 x - 1/4 x, + + 2 3 + COEFF(-1) = -2 x + 5/6 x + 4/3 - 1/4 x, + + 3 2 + COEFF(0) = - 5/3 x + 5/2 x + 3 x - 5/2, + + 2 3 + COEFF(1) = 4/3 - 2 x + 5/3 x - 7/2 x, + + 3 2 3 + COEFF(2) = - 5/6 x + 1/2 x - 1/12 + 7/4 x, COEFF(3) = - 1/4 x + 1/6 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "1d.coeffs/1d.cube.order5.smooth0/coeffs-dxx.compute.c"); +bytes used=12005228, alloc=1965720, time=0.88 +> +################################################################################ +> +# +# 1d, cube, order=6, smoothing=0 (size=7) +# +> +# interpolating polynomial +> interp_1d_cube_order6_smooth0 +> := Lagrange_polynomial_interpolant(fn_1d_order6, coeffs_list_1d_order6, +> coords_list_1d, posn_list_1d_size7); +bytes used=13005380, alloc=1965720, time=0.95 +interp_1d_cube_order6_smooth0 := DATA(0) + (3/20 DATA(-2) + 3/4 DATA(1) + + / + + 1/60 DATA(3) - 1/60 DATA(-3) - 3/4 DATA(-1) - 3/20 DATA(2)) x + | + \ + + 1/180 DATA(-3) + 3/4 DATA(1) - 3/40 DATA(-2) + 1/180 DATA(3) + 3/4 DATA(-1) + + 49 \ 2 / 13 + - -- DATA(0) - 3/40 DATA(2)| x + |- 1/6 DATA(-2) - -- DATA(1) + 36 / \ 48 + + 13 \ 3 / + - 1/48 DATA(3) + 1/48 DATA(-3) + -- DATA(-1) + 1/6 DATA(2)| x + | + 48 / \ + + 13 13 + - 1/144 DATA(-3) - -- DATA(1) + 1/12 DATA(-2) - 1/144 DATA(3) - -- DATA(-1) + 48 48 + + \ 4 + + 7/18 DATA(0) + 1/12 DATA(2)| x + (1/60 DATA(-2) + 1/48 DATA(1) + / + + 5 + + 1/240 DATA(3) - 1/240 DATA(-3) - 1/48 DATA(-1) - 1/60 DATA(2)) x + ( + + 1/720 DATA(-3) + 1/48 DATA(1) - 1/120 DATA(-2) + 1/720 DATA(3) + + 6 + + 1/48 DATA(-1) - 1/36 DATA(0) - 1/120 DATA(2)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_1d_size7); + 2 3 4 5 6 +[COEFF(-3) = - 1/60 x + 1/180 x + 1/48 x - 1/144 x - 1/240 x + 1/720 x , + + 2 3 4 5 6 + COEFF(-2) = 3/20 x - 3/40 x - 1/6 x + 1/12 x + 1/60 x - 1/120 x , + + 2 13 3 13 4 5 6 + COEFF(-1) = - 3/4 x + 3/4 x + -- x - -- x - 1/48 x + 1/48 x , + 48 48 + + 4 49 2 6 + COEFF(0) = 7/18 x - -- x + 1 - 1/36 x , + 36 + + 13 3 2 5 6 13 4 + COEFF(1) = - -- x + 3/4 x + 3/4 x + 1/48 x + 1/48 x - -- x , + 48 48 + + 3 2 5 6 4 + COEFF(2) = 1/6 x - 3/20 x - 3/40 x - 1/60 x - 1/120 x + 1/12 x , + + 3 2 5 6 4 + COEFF(3) = - 1/48 x + 1/60 x + 1/180 x + 1/240 x + 1/720 x - 1/144 x ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "1d.coeffs/1d.cube.order6.smooth0/coeffs-I.compute.c"); +bytes used=14005568, alloc=1965720, time=1.03 +bytes used=15005724, alloc=1965720, time=1.12 +> +# d/dx +> simplify( diff(interp_1d_cube_order6_smooth0,x) ); +3/4 DATA(1) - 3/20 DATA(2) - 3/4 DATA(-1) - 1/60 DATA(-3) + 1/60 DATA(3) + + 13 3 3 3 3 + - -- x DATA(1) - 1/36 x DATA(-3) + 1/3 x DATA(-2) - 1/36 x DATA(3) + 12 + + 13 3 3 3 4 + - -- x DATA(-1) + 14/9 x DATA(0) + 1/3 x DATA(2) + 1/12 x DATA(-2) + 12 + + 4 4 4 4 + + 5/48 x DATA(1) + 1/48 x DATA(3) - 1/48 x DATA(-3) - 5/48 x DATA(-1) + + 4 5 5 5 + - 1/12 x DATA(2) + 1/120 x DATA(-3) + 1/8 x DATA(1) - 1/20 x DATA(-2) + + 5 5 5 5 + + 1/120 x DATA(3) + 1/8 x DATA(-1) - 1/6 x DATA(0) - 1/20 x DATA(2) + + + 1/90 x DATA(-3) + 3/2 x DATA(1) - 3/20 x DATA(-2) + 1/90 x DATA(3) + + 49 2 13 2 + + 3/2 x DATA(-1) - -- x DATA(0) - 1/2 x DATA(-2) - -- x DATA(1) + 18 16 + + 2 2 13 2 2 + - 1/16 x DATA(3) + 1/16 x DATA(-3) + -- x DATA(-1) + 1/2 x DATA(2) + 16 + + - 3/20 x DATA(2) + 3/20 DATA(-2) + +> coeffs_as_lc_of_data(%, posn_list_1d_size7); +bytes used=16005892, alloc=1965720, time=1.20 + 3 5 4 2 +[COEFF(-3) = - 1/36 x + 1/120 x - 1/48 x - 1/60 + 1/90 x + 1/16 x , + + 2 5 3 4 + COEFF(-2) = - 1/2 x - 1/20 x + 1/3 x + 3/20 - 3/20 x + 1/12 x , + + 4 13 2 13 3 5 + COEFF(-1) = 3/2 x - 5/48 x + -- x - -- x + 1/8 x - 3/4, + 16 12 + + 5 3 49 + COEFF(0) = - 1/6 x + 14/9 x - -- x, + 18 + + 4 5 13 2 13 3 + COEFF(1) = 5/48 x + 3/4 + 1/8 x + 3/2 x - -- x - -- x , + 16 12 + + 5 3 2 4 + COEFF(2) = - 1/20 x + 1/3 x + 1/2 x - 1/12 x - 3/20 - 3/20 x, + + 3 2 4 5 + COEFF(3) = - 1/36 x + 1/90 x - 1/16 x + 1/60 + 1/48 x + 1/120 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "1d.coeffs/1d.cube.order6.smooth0/coeffs-dx.compute.c"); +bytes used=17006200, alloc=1965720, time=1.29 +> +# d^2/dx^2 +> simplify( diff(interp_1d_cube_order6_smooth0,x,x) ); +bytes used=18007928, alloc=1965720, time=1.39 + 49 +- -- DATA(0) + 3/2 DATA(1) - 3/20 DATA(2) + 3/2 DATA(-1) + 1/90 DATA(-3) + 18 + + 3 3 3 + + 1/90 DATA(3) + 5/12 x DATA(1) - 1/12 x DATA(-3) + 1/3 x DATA(-2) + + 3 3 3 4 + + 1/12 x DATA(3) - 5/12 x DATA(-1) - 1/3 x DATA(2) - 1/4 x DATA(-2) + + 4 4 4 4 + + 5/8 x DATA(1) + 1/24 x DATA(3) + 1/24 x DATA(-3) + 5/8 x DATA(-1) + + 4 + - 1/4 x DATA(2) + 1/8 x DATA(-3) - 13/8 x DATA(1) - x DATA(-2) + + 2 2 + - 1/8 x DATA(3) + 13/8 x DATA(-1) + x DATA(-2) - 13/4 x DATA(1) + + 2 2 2 2 + - 1/12 x DATA(3) - 1/12 x DATA(-3) - 13/4 x DATA(-1) + x DATA(2) + + 2 4 + + x DATA(2) - 3/20 DATA(-2) + 14/3 x DATA(0) - 5/6 x DATA(0) + +> coeffs_as_lc_of_data(%, posn_list_1d_size7); + 2 4 3 +[COEFF(-3) = - 1/12 x + 1/24 x + 1/90 + 1/8 x - 1/12 x , + + 4 2 3 + COEFF(-2) = -x - 1/4 x - 3/20 + x + 1/3 x , + + 4 3 2 + COEFF(-1) = 5/8 x + 3/2 - 5/12 x + 13/8 x - 13/4 x , + + 2 4 49 + COEFF(0) = 14/3 x - 5/6 x - --, + 18 + + 2 3 4 + COEFF(1) = - 13/4 x + 5/12 x - 13/8 x + 5/8 x + 3/2, + + 2 4 3 + COEFF(2) = - 3/20 + x + x - 1/4 x - 1/3 x , + + 4 2 3 + COEFF(3) = 1/90 + 1/24 x - 1/8 x - 1/12 x + 1/12 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "1d.coeffs/1d.cube.order6.smooth0/coeffs-dxx.compute.c"); +bytes used=19008116, alloc=1965720, time=1.47 +> +################################################################################ +> quit +bytes used=19802260, alloc=1965720, time=1.53 diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.maple b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.maple new file mode 100644 index 0000000..cdf1494 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/1d.maple @@ -0,0 +1,166 @@ +# 1d.maple -- compute Lagrange interpolation coefficients in 1-D +# $Header$ + +################################################################################ + +# +# 1d, cube, order=1, smoothing=0 (size=2) +# + +# interpolating polynomial +interp_1d_cube_order1_smooth0 + := Lagrange_polynomial_interpolant(fn_1d_order1, coeffs_list_1d_order1, + coords_list_1d, posn_list_1d_size2); + +# I +coeffs_as_lc_of_data(%, posn_list_1d_size2); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "1d.coeffs/1d.cube.order1.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_1d_cube_order1_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size2); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "1d.coeffs/1d.cube.order1.smooth0/coeffs-dx.compute.c"); + +################################################################################ + +# +# 1d, cube, order=2, smoothing=0 (size=3) +# + +# interpolating polynomial +interp_1d_cube_order2_smooth0 + := Lagrange_polynomial_interpolant(fn_1d_order2, coeffs_list_1d_order2, + coords_list_1d, posn_list_1d_size3); + +# I +coeffs_as_lc_of_data(%, posn_list_1d_size3); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "1d.coeffs/1d.cube.order2.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_1d_cube_order2_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size3); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "1d.coeffs/1d.cube.order2.smooth0/coeffs-dx.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_1d_cube_order2_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size3); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "1d.coeffs/1d.cube.order2.smooth0/coeffs-dxx.compute.c"); + +################################################################################ + +# +# 1d, cube, order=3, smoothing=0 (size=4) +# + +# interpolating polynomial +interp_1d_cube_order3_smooth0 + := Lagrange_polynomial_interpolant(fn_1d_order3, coeffs_list_1d_order3, + coords_list_1d, posn_list_1d_size4); + +# I +coeffs_as_lc_of_data(%, posn_list_1d_size4); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "1d.coeffs/1d.cube.order3.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_1d_cube_order3_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size4); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "1d.coeffs/1d.cube.order3.smooth0/coeffs-dx.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_1d_cube_order3_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size4); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "1d.coeffs/1d.cube.order3.smooth0/coeffs-dxx.compute.c"); + +################################################################################ + +# +# 1d, cube, order=4, smoothing=0 (size=5) +# + +# interpolating polynomial +interp_1d_cube_order4_smooth0 + := Lagrange_polynomial_interpolant(fn_1d_order4, coeffs_list_1d_order4, + coords_list_1d, posn_list_1d_size5); + +# I +coeffs_as_lc_of_data(%, posn_list_1d_size5); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "1d.coeffs/1d.cube.order4.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_1d_cube_order4_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size5); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "1d.coeffs/1d.cube.order4.smooth0/coeffs-dx.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_1d_cube_order4_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size5); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "1d.coeffs/1d.cube.order4.smooth0/coeffs-dxx.compute.c"); + +################################################################################ + +# +# 1d, cube, order=5, smoothing=0 (size=6) +# + +# interpolating polynomial +interp_1d_cube_order5_smooth0 + := Lagrange_polynomial_interpolant(fn_1d_order5, coeffs_list_1d_order5, + coords_list_1d, posn_list_1d_size6); + +# I +coeffs_as_lc_of_data(%, posn_list_1d_size6); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "1d.coeffs/1d.cube.order5.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_1d_cube_order5_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size6); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "1d.coeffs/1d.cube.order5.smooth0/coeffs-dx.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_1d_cube_order5_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size6); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "1d.coeffs/1d.cube.order5.smooth0/coeffs-dxx.compute.c"); + +################################################################################ + +# +# 1d, cube, order=6, smoothing=0 (size=7) +# + +# interpolating polynomial +interp_1d_cube_order6_smooth0 + := Lagrange_polynomial_interpolant(fn_1d_order6, coeffs_list_1d_order6, + coords_list_1d, posn_list_1d_size7); + +# I +coeffs_as_lc_of_data(%, posn_list_1d_size7); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "1d.coeffs/1d.cube.order6.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_1d_cube_order6_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size7); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "1d.coeffs/1d.cube.order6.smooth0/coeffs-dx.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_1d_cube_order6_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_1d_size7); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "1d.coeffs/1d.cube.order6.smooth0/coeffs-dxx.compute.c"); + +################################################################################ diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..1680b1f --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c @@ -0,0 +1,8 @@ +fp t1; +fp t2; + t1 = x*y; + t2 = y-t1; + coeffs_I->coeff_0_0 = RATIONAL(1.0,1.0)-x-t2; + coeffs_I->coeff_p1_0 = x-t1; + coeffs_I->coeff_0_p1 = t2; + coeffs_I->coeff_p1_p1 = t1; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..13d4254 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c @@ -0,0 +1,4 @@ + coeffs_dx->coeff_0_0 = y+RATIONAL(-1.0,1.0); + coeffs_dx->coeff_p1_0 = -y+RATIONAL(1.0,1.0); + coeffs_dx->coeff_0_p1 = -y; + coeffs_dx->coeff_p1_p1 = y; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..ca7e73e --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c @@ -0,0 +1,4 @@ + coeffs_dy->coeff_0_0 = x+RATIONAL(-1.0,1.0); + coeffs_dy->coeff_p1_0 = -x; + coeffs_dy->coeff_0_p1 = RATIONAL(1.0,1.0)-x; + coeffs_dy->coeff_p1_p1 = x; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..a9bdd03 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c @@ -0,0 +1,53 @@ +fp t17; +fp t15; +fp t18; +fp t19; +fp t4; +fp t16; +fp t24; +fp t26; +fp t25; +fp t14; +fp t12; +fp t13; +fp t20; +fp t9; +fp t23; +fp t11; +fp t22; +fp t21; +fp t8; +fp t6; +fp t5; +fp t3; + t17 = x*x; + t15 = RATIONAL(1.0,4.0); + t18 = y*y; + t19 = t15*t18; + t4 = t17*t19; + t16 = RATIONAL(-1.0,4.0); + t24 = y*t16; + t26 = t4+t17*t24; + t25 = y*t15; + t14 = RATIONAL(1.0,2.0); + t12 = t14*t18; + t13 = RATIONAL(-1.0,2.0); + t20 = t13*t18; + t9 = t17*t20; + t23 = t12+t9; + t11 = t14*t17; + t22 = t11+t9; + t21 = t4+t17*t25; + t8 = x*t19; + t6 = x*t24; + t5 = x*t25; + t3 = t16*x*t18; + coeffs_I->coeff_m1_m1 = t3+t5+t26; + coeffs_I->coeff_0_m1 = (t13+t11)*y+t23; + coeffs_I->coeff_p1_m1 = t8+t6+t26; + coeffs_I->coeff_m1_0 = (t12+t13)*x+t22; + coeffs_I->coeff_0_0 = -t18+t17*t18+RATIONAL(1.0,1.0)-t17; + coeffs_I->coeff_p1_0 = (t20+t14)*x+t22; + coeffs_I->coeff_m1_p1 = t6+t3+t21; + coeffs_I->coeff_0_p1 = (t13*t17+t14)*y+t23; + coeffs_I->coeff_p1_p1 = t5+t8+t21; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..bc709b8 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c @@ -0,0 +1,35 @@ +fp t35; +fp t41; +fp t38; +fp t29; +fp t36; +fp t40; +fp t37; +fp t39; +fp t34; +fp t33; +fp t30; +fp t28; +fp t27; + t35 = RATIONAL(1.0,2.0); + t41 = x*t35; + t38 = y*y; + t29 = t38*t41; + t36 = RATIONAL(1.0,4.0); + t40 = t29+t36*t38; + t37 = RATIONAL(-1.0,4.0); + t39 = t29+t37*t38; + t34 = RATIONAL(-1.0,2.0); + t33 = t36*y; + t30 = t37*y; + t28 = t34*x*y; + t27 = y*t41; + coeffs_dx->coeff_m1_m1 = t33+t28+t39; + coeffs_dx->coeff_0_m1 = (y-t38)*x; + coeffs_dx->coeff_p1_m1 = t28+t30+t40; + coeffs_dx->coeff_m1_0 = x+t34+(t35-x)*t38; + coeffs_dx->coeff_0_0 = (RATIONAL(-2.0,1.0)+RATIONAL(2.0,1.0)*t38)*x; + coeffs_dx->coeff_p1_0 = x+t35+(t34-x)*t38; + coeffs_dx->coeff_m1_p1 = t30+t27+t39; + coeffs_dx->coeff_0_p1 = (-y-t38)*x; + coeffs_dx->coeff_p1_p1 = t27+t33+t40; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..d67f268 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,21 @@ +fp t62; +fp t61; +fp t60; +fp t59; +fp t58; +fp t57; + t62 = y*y; + t61 = RATIONAL(1.0,2.0); + t60 = t61*t62; + t59 = -t62+RATIONAL(1.0,1.0); + t58 = RATIONAL(-1.0,2.0)*y+t60; + t57 = t60+t61*y; + coeffs_dxx->coeff_m1_m1 = t58; + coeffs_dxx->coeff_0_m1 = y-t62; + coeffs_dxx->coeff_p1_m1 = t58; + coeffs_dxx->coeff_m1_0 = t59; + coeffs_dxx->coeff_0_0 = RATIONAL(2.0,1.0)*t62+RATIONAL(-2.0,1.0); + coeffs_dxx->coeff_p1_0 = t59; + coeffs_dxx->coeff_m1_p1 = t57; + coeffs_dxx->coeff_0_p1 = -t62-y; + coeffs_dxx->coeff_p1_p1 = t57; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c new file mode 100644 index 0000000..0fda87b --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c @@ -0,0 +1,29 @@ +fp t72; +fp t68; +fp t74; +fp t69; +fp t73; +fp t71; +fp t70; +fp t65; +fp t64; +fp t63; + t72 = x*y; + t68 = RATIONAL(-1.0,2.0); + t74 = t68*x+t72; + t69 = RATIONAL(1.0,2.0); + t73 = t69*x+t72; + t71 = RATIONAL(-1.0,4.0); + t70 = RATIONAL(1.0,4.0); + t65 = t68*y; + t64 = t69*y; + t63 = RATIONAL(-2.0,1.0)*t72; + coeffs_dxy->coeff_m1_m1 = t65+t70+t74; + coeffs_dxy->coeff_0_m1 = t63+x; + coeffs_dxy->coeff_p1_m1 = t71+t64+t74; + coeffs_dxy->coeff_m1_0 = t63+y; + coeffs_dxy->coeff_0_0 = RATIONAL(4.0,1.0)*t72; + coeffs_dxy->coeff_p1_0 = -y+t63; + coeffs_dxy->coeff_m1_p1 = t65+t71+t73; + coeffs_dxy->coeff_0_p1 = t63-x; + coeffs_dxy->coeff_p1_p1 = t70+t64+t73; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..e373f6b --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c @@ -0,0 +1,35 @@ +fp t50; +fp t56; +fp t53; +fp t43; +fp t51; +fp t55; +fp t52; +fp t54; +fp t49; +fp t47; +fp t45; +fp t44; +fp t42; + t50 = RATIONAL(1.0,2.0); + t56 = y*t50; + t53 = x*x; + t43 = t53*t56; + t51 = RATIONAL(1.0,4.0); + t55 = t43+t51*x; + t52 = RATIONAL(-1.0,4.0); + t54 = t43+t52*x; + t49 = RATIONAL(-1.0,2.0); + t47 = t52*t53; + t45 = t51*t53; + t44 = x*t56; + t42 = t49*x*y; + coeffs_dy->coeff_m1_m1 = t42+t47+t55; + coeffs_dy->coeff_0_m1 = t49+y+(-y+t50)*t53; + coeffs_dy->coeff_p1_m1 = t44+t47+t54; + coeffs_dy->coeff_m1_0 = (x-t53)*y; + coeffs_dy->coeff_0_0 = (RATIONAL(-2.0,1.0)+RATIONAL(2.0,1.0)*t53)*y; + coeffs_dy->coeff_p1_0 = (-x-t53)*y; + coeffs_dy->coeff_m1_p1 = t45+t42+t54; + coeffs_dy->coeff_0_p1 = t50+y+(t49-y)*t53; + coeffs_dy->coeff_p1_p1 = t44+t45+t55; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c new file mode 100644 index 0000000..9a941cd --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c @@ -0,0 +1,21 @@ +fp t80; +fp t79; +fp t78; +fp t77; +fp t76; +fp t75; + t80 = x*x; + t79 = RATIONAL(1.0,2.0); + t78 = t79*t80; + t77 = RATIONAL(1.0,1.0)-t80; + t76 = t78+RATIONAL(-1.0,2.0)*x; + t75 = t79*x+t78; + coeffs_dyy->coeff_m1_m1 = t76; + coeffs_dyy->coeff_0_m1 = t77; + coeffs_dyy->coeff_p1_m1 = t75; + coeffs_dyy->coeff_m1_0 = -t80+x; + coeffs_dyy->coeff_0_0 = RATIONAL(2.0,1.0)*t80+RATIONAL(-2.0,1.0); + coeffs_dyy->coeff_p1_0 = -x-t80; + coeffs_dyy->coeff_m1_p1 = t76; + coeffs_dyy->coeff_0_p1 = t77; + coeffs_dyy->coeff_p1_p1 = t75; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..cb6836d --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c @@ -0,0 +1,162 @@ +fp t128; +fp t116; +fp t105; +fp t120; +fp t152; +fp t127; +fp t151; +fp t150; +fp t118; +fp t149; +fp t148; +fp t121; +fp t147; +fp t146; +fp t137; +fp t138; +fp t145; +fp t139; +fp t141; +fp t144; +fp t129; +fp t130; +fp t142; +fp t143; +fp t115; +fp t104; +fp t96; +fp t119; +fp t136; +fp t110; +fp t135; +fp t101; +fp t114; +fp t134; +fp t133; +fp t113; +fp t112; +fp t111; +fp t109; +fp t108; +fp t100; +fp t98; +fp t91; +fp t88; +fp t87; +fp t86; +fp t85; +fp t84; +fp t83; +fp t82; + t128 = y*y; + t116 = RATIONAL(-3.0,40.0); + t105 = t116*y; + t120 = RATIONAL(-3.0,20.0); + t152 = t105+t120*t128; + t127 = x*x; + t151 = y*t127; + t150 = t128*x; + t118 = RATIONAL(-1.0,20.0); + t149 = t118*y; + t148 = RATIONAL(1.0,20.0)*y; + t121 = RATIONAL(3.0,20.0); + t147 = t121*y; + t146 = RATIONAL(-1.0,40.0)*y; + t137 = RATIONAL(1.0,8.0)*t127; + t138 = RATIONAL(1.0,4.0)*t127; + t145 = y*t137+t128*t138; + t139 = RATIONAL(-1.0,8.0)*t127; + t141 = RATIONAL(-1.0,4.0)*t127; + t144 = y*t139+t128*t141; + t129 = t127*x; + t130 = t128*y; + t142 = t129*t130; + t143 = RATIONAL(1.0,50.0)*t142+RATIONAL(-1.0,400.0)*t127; + t115 = RATIONAL(3.0,40.0); + t104 = t115*t128; + t96 = t128*t137; + t119 = RATIONAL(1.0,40.0); + t136 = t116*t128+t119*t150+t96; + t110 = RATIONAL(-11.0,40.0); + t135 = t110*t150+t104+t96; + t101 = t128*t139; + t114 = RATIONAL(11.0,40.0); + t134 = t114*t128+t101+x*t104; + t133 = RATIONAL(7.0,40.0)*t150+t101+RATIONAL(9.0,40.0)*t128; + t113 = RATIONAL(-1.0,300.0); + t112 = RATIONAL(11.0,20.0); + t111 = RATIONAL(-11.0,20.0); + t109 = RATIONAL(29.0,600.0); + t108 = t120*y; + t100 = y*t138; + t98 = y*t141; + t91 = x*t146; + t88 = RATIONAL(1.0,12.0)*t151; + t87 = RATIONAL(-1.0,12.0)*t151; + t86 = RATIONAL(-1.0,50.0)*t142; + t85 = RATIONAL(-1.0,24.0)*t151; + t84 = RATIONAL(1.0,24.0)*t151; + t83 = RATIONAL(1.0,100.0)*t142; + t82 = RATIONAL(-1.0,100.0)*t142; + coeffs_I->coeff_m1_m1 = RATIONAL(-111.0,2000.0)+RATIONAL(37.0,400.0)*t127 ++t87+RATIONAL(-37.0,600.0)*t129+t149+t83+(RATIONAL(-17.0,300.0)*t127+RATIONAL( +-2.0,125.0))*t130+(RATIONAL(481.0,6000.0)+RATIONAL(11.0,60.0)*y+RATIONAL(59.0, +750.0)*t130)*x+t135; + coeffs_I->coeff_0_m1 = t88+RATIONAL(-111.0,400.0)*t127+RATIONAL(333.0, +2000.0)+RATIONAL(-11.0,60.0)*y+RATIONAL(37.0,200.0)*t129+(RATIONAL(-481.0, +2000.0)+t149)*x+(RATIONAL(7.0,500.0)*x+RATIONAL(-3.0,100.0)*t129+RATIONAL(13.0, +150.0)*t127+RATIONAL(-89.0,750.0))*t130+t134; + coeffs_I->coeff_p1_m1 = t88+RATIONAL(-333.0,2000.0)+RATIONAL(-37.0,200.0) +*t129+RATIONAL(111.0,400.0)*t127+t108+(RATIONAL(-7.0,60.0)*y+RATIONAL(481.0, +2000.0))*x+(RATIONAL(3.0,100.0)*t129+t113*t127+RATIONAL(-73.0,750.0)*x+RATIONAL +(-6.0,125.0))*t130+t133; + coeffs_I->coeff_p2_m1 = t82+t87+t148+RATIONAL(-37.0,400.0)*t127+RATIONAL( +111.0,2000.0)+RATIONAL(37.0,600.0)*t129+(RATIONAL(2.0,125.0)+RATIONAL(-2.0,75.0 +)*t127)*t130+(RATIONAL(7.0,1500.0)*t130+RATIONAL(-481.0,6000.0)+RATIONAL(-1.0, +60.0)*y)*x+t136; + coeffs_I->coeff_m1_0 = RATIONAL(201.0,2000.0)+RATIONAL(133.0,400.0)*t127+ +RATIONAL(-11.0,200.0)*t129+(RATIONAL(23.0,200.0)*t127+RATIONAL(1.0,150.0)*t129+ +RATIONAL(81.0,1000.0))*t130+(t114*y+RATIONAL(-957.0,2000.0)+t112*t128+RATIONAL( +-851.0,3000.0)*t130)*x+t144+t152; + coeffs_I->coeff_0_0 = t86+RATIONAL(-199.0,400.0)*t127+t111*t128+t110*y+ +RATIONAL(33.0,200.0)*t129+RATIONAL(1397.0,2000.0)+(RATIONAL(-19.0,200.0)*t127+ +RATIONAL(257.0,1000.0))*t130+(RATIONAL(-129.0,2000.0)+RATIONAL(101.0,1000.0)* +t130+t152)*x+t145; + coeffs_I->coeff_p1_0 = RATIONAL(-9.0,40.0)*y+RATIONAL(-33.0,200.0)*t129+ +RATIONAL(603.0,2000.0)+RATIONAL(-9.0,20.0)*t128+(RATIONAL(243.0,1000.0)+ +RATIONAL(-31.0,200.0)*t127)*t130+(RATIONAL(149.0,1000.0)*t130+RATIONAL(-7.0, +40.0)*y+RATIONAL(-7.0,20.0)*t128+RATIONAL(1129.0,2000.0))*x+t143+t145; + coeffs_I->coeff_p2_0 = t115*y+RATIONAL(11.0,200.0)*t129+RATIONAL(67.0, +400.0)*t127+RATIONAL(-43.0,2000.0)*x+t91+RATIONAL(-201.0,2000.0)+(t118*x+t121)* +t128+(RATIONAL(-1.0,150.0)*t129+RATIONAL(101.0,3000.0)*x+RATIONAL(-81.0,1000.0) ++RATIONAL(27.0,200.0)*t127)*t130+t144; + coeffs_I->coeff_m1_p1 = RATIONAL(-29.0,600.0)*t129+RATIONAL(29.0,400.0)* +t127+RATIONAL(-87.0,2000.0)+t147+t100+(t111*y+RATIONAL(377.0,6000.0))*x+( +RATIONAL(-13.0,100.0)*t127+RATIONAL(1.0,300.0)*t129+RATIONAL(-9.0,125.0)+ +RATIONAL(203.0,750.0)*x)*t130+t135; + coeffs_I->coeff_0_p1 = RATIONAL(261.0,2000.0)+t98+RATIONAL(-87.0,400.0)* +t127+t112*y+t82+RATIONAL(29.0,200.0)*t129+(RATIONAL(-71.0,250.0)+RATIONAL(7.0, +50.0)*t127)*t130+(t147+RATIONAL(-31.0,500.0)*t130+RATIONAL(-377.0,2000.0))*x+ +t134; + coeffs_I->coeff_p1_p1 = RATIONAL(87.0,400.0)*t127+RATIONAL(9.0,20.0)*y+ +RATIONAL(-29.0,200.0)*t129+t98+t83+RATIONAL(-261.0,2000.0)+(RATIONAL(-27.0, +125.0)+RATIONAL(11.0,100.0)*t127)*t130+(RATIONAL(-47.0,250.0)*t130+RATIONAL(7.0 +,20.0)*y+RATIONAL(377.0,2000.0))*x+t133; + coeffs_I->coeff_p2_p1 = RATIONAL(87.0,2000.0)+RATIONAL(-29.0,400.0)*t127+ +t100+t109*t129+t108+(RATIONAL(-377.0,6000.0)+t148)*x+(RATIONAL(9.0,125.0)+ +RATIONAL(-31.0,1500.0)*x+t113*t129+RATIONAL(-3.0,25.0)*t127)*t130+t136; + coeffs_I->coeff_m1_p2 = RATIONAL(1.0,400.0)*t127+t146+t86+RATIONAL(-1.0, +600.0)*t129+t85+RATIONAL(-3.0,2000.0)+(RATIONAL(7.0,1000.0)+RATIONAL(43.0,600.0 +)*t127)*t130+(RATIONAL(11.0,120.0)*y+RATIONAL(-197.0,3000.0)*t130+RATIONAL(13.0 +,6000.0))*x; + coeffs_I->coeff_0_p2 = RATIONAL(-3.0,400.0)*t127+RATIONAL(-11.0,120.0)*y+ +t91+t84+RATIONAL(-13.0,2000.0)*x+RATIONAL(9.0,2000.0)+RATIONAL(1.0,200.0)*t129+ +(RATIONAL(-53.0,1000.0)*x+RATIONAL(3.0,50.0)*t129+RATIONAL(437.0,3000.0)+ +RATIONAL(-79.0,600.0)*t127)*t130; + coeffs_I->coeff_p1_p2 = RATIONAL(3.0,400.0)*t127+t105+t84+RATIONAL(-1.0, +200.0)*t129+RATIONAL(-9.0,2000.0)+(RATIONAL(13.0,2000.0)+RATIONAL(-7.0,120.0)*y +)*x+(RATIONAL(409.0,3000.0)*x+t109*t127+RATIONAL(21.0,1000.0)+RATIONAL(-3.0, +50.0)*t129)*t130; + coeffs_I->coeff_p2_p2 = RATIONAL(3.0,2000.0)+t119*y+t85+RATIONAL(1.0, +600.0)*t129+(RATIONAL(-7.0,1000.0)+RATIONAL(7.0,600.0)*t127)*t130+(RATIONAL( +-53.0,3000.0)*t130+RATIONAL(-1.0,120.0)*y+RATIONAL(-13.0,6000.0))*x+t143; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..a593111 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c @@ -0,0 +1,131 @@ +fp t207; +fp t193; +fp t206; +fp t205; +fp t204; +fp t188; +fp t168; +fp t203; +fp t167; +fp t202; +fp t201; +fp t191; +fp t200; +fp t199; +fp t192; +fp t194; +fp t198; +fp t197; +fp t183; +fp t196; +fp t187; +fp t186; +fp t185; +fp t184; +fp t182; +fp t181; +fp t180; +fp t179; +fp t178; +fp t177; +fp t176; +fp t175; +fp t174; +fp t173; +fp t172; +fp t171; +fp t169; +fp t158; +fp t156; +fp t155; +fp t154; +fp t153; + t207 = x*y; + t193 = y*y; + t206 = x*t193; + t205 = x*RATIONAL(-1.0,4.0); + t204 = x*RATIONAL(1.0,2.0); + t188 = RATIONAL(1.0,4.0); + t168 = t188*t206; + t203 = RATIONAL(-1.0,6.0)*t207+t168; + t167 = t193*t205; + t202 = RATIONAL(1.0,6.0)*t207+t167; + t201 = t188*t207+t193*t204; + t191 = RATIONAL(-1.0,2.0); + t200 = y*t205+t191*t206; + t199 = y*t204+t168; + t192 = x*x; + t194 = y*t193; + t198 = t192*t194; + t197 = t191*t207+t167; + t183 = RATIONAL(-1.0,200.0); + t196 = RATIONAL(3.0,50.0)*t198+t183*x; + t187 = RATIONAL(-1.0,20.0); + t186 = RATIONAL(3.0,200.0); + t185 = RATIONAL(-3.0,200.0); + t184 = RATIONAL(1.0,200.0); + t182 = RATIONAL(37.0,200.0); + t181 = RATIONAL(87.0,200.0); + t180 = RATIONAL(-37.0,200.0); + t179 = RATIONAL(-87.0,200.0); + t178 = RATIONAL(29.0,200.0); + t177 = RATIONAL(-29.0,200.0); + t176 = RATIONAL(111.0,200.0); + t175 = RATIONAL(-111.0,200.0); + t174 = RATIONAL(3.0,40.0)*t193; + t173 = RATIONAL(7.0,40.0)*t193; + t172 = RATIONAL(-1.0,40.0)*y; + t171 = RATIONAL(1.0,40.0)*t193; + t169 = RATIONAL(-11.0,40.0)*t193; + t158 = RATIONAL(-3.0,50.0)*t198; + t156 = RATIONAL(-1.0,12.0)*t207; + t155 = RATIONAL(1.0,12.0)*t207; + t154 = RATIONAL(3.0,100.0)*t198; + t153 = RATIONAL(-3.0,100.0)*t198; + coeffs_dx->coeff_m1_m1 = t180*t192+RATIONAL(481.0,6000.0)+t154+t169+ +RATIONAL(11.0,60.0)*y+RATIONAL(59.0,750.0)*t194+(RATIONAL(-17.0,150.0)*t194+ +t182)*x+t203; + coeffs_dx->coeff_0_m1 = t176*t192+t174+RATIONAL(-481.0,2000.0)+t175*x+ +t187*y+(RATIONAL(13.0,75.0)*x+RATIONAL(7.0,500.0)+RATIONAL(-9.0,100.0)*t192)* +t194+t202; + coeffs_dx->coeff_p1_m1 = t173+t176*x+RATIONAL(-7.0,60.0)*y+t175*t192+ +RATIONAL(481.0,2000.0)+(RATIONAL(-1.0,150.0)*x+RATIONAL(-73.0,750.0)+RATIONAL( +9.0,100.0)*t192)*t194+t202; + coeffs_dx->coeff_p2_m1 = RATIONAL(7.0,1500.0)*t194+t153+RATIONAL(-1.0, +60.0)*y+t171+t182*t192+RATIONAL(-481.0,6000.0)+(RATIONAL(-4.0,75.0)*t194+t180)* +x+t203; + coeffs_dx->coeff_m1_0 = RATIONAL(-33.0,200.0)*t192+RATIONAL(11.0,40.0)*y+ +RATIONAL(-957.0,2000.0)+RATIONAL(133.0,200.0)*x+RATIONAL(11.0,20.0)*t193+( +RATIONAL(-851.0,3000.0)+RATIONAL(23.0,100.0)*x+RATIONAL(1.0,50.0)*t192)*t194+ +t200; + coeffs_dx->coeff_0_0 = RATIONAL(-3.0,40.0)*y+RATIONAL(-129.0,2000.0)+t158 ++RATIONAL(101.0,1000.0)*t194+RATIONAL(-3.0,20.0)*t193+RATIONAL(99.0,200.0)*t192 ++(RATIONAL(-19.0,100.0)*t194+RATIONAL(-199.0,200.0))*x+t201; + coeffs_dx->coeff_p1_0 = RATIONAL(-7.0,40.0)*y+RATIONAL(1129.0,2000.0)+ +RATIONAL(-7.0,20.0)*t193+RATIONAL(-99.0,200.0)*t192+(RATIONAL(149.0,1000.0)+ +RATIONAL(-31.0,100.0)*x)*t194+t196+t201; + coeffs_dx->coeff_p2_0 = t172+t187*t193+RATIONAL(33.0,200.0)*t192+RATIONAL +(-43.0,2000.0)+RATIONAL(67.0,200.0)*x+(RATIONAL(-1.0,50.0)*t192+RATIONAL(27.0, +100.0)*x+RATIONAL(101.0,3000.0))*t194+t200; + coeffs_dx->coeff_m1_p1 = RATIONAL(-11.0,20.0)*y+t169+RATIONAL(377.0, +6000.0)+t178*x+t177*t192+(RATIONAL(-13.0,50.0)*x+RATIONAL(1.0,100.0)*t192+ +RATIONAL(203.0,750.0))*t194+t199; + coeffs_dx->coeff_0_p1 = t153+t181*t192+t174+RATIONAL(-31.0,500.0)*t194+ +RATIONAL(3.0,20.0)*y+RATIONAL(-377.0,2000.0)+(t179+RATIONAL(7.0,25.0)*t194)*x+ +t197; + coeffs_dx->coeff_p1_p1 = RATIONAL(7.0,20.0)*y+RATIONAL(-47.0,250.0)*t194+ +t179*t192+RATIONAL(377.0,2000.0)+t173+t154+(RATIONAL(11.0,50.0)*t194+t181)*x+ +t197; + coeffs_dx->coeff_p2_p1 = RATIONAL(1.0,20.0)*y+RATIONAL(-377.0,6000.0)+ +t178*t192+t171+t177*x+(RATIONAL(-31.0,1500.0)+RATIONAL(-6.0,25.0)*x+RATIONAL( +-1.0,100.0)*t192)*t194+t199; + coeffs_dx->coeff_m1_p2 = RATIONAL(11.0,120.0)*y+t183*t192+RATIONAL(13.0, +6000.0)+RATIONAL(-197.0,3000.0)*t194+t156+t158+(RATIONAL(43.0,300.0)*t194+t184) +*x; + coeffs_dx->coeff_0_p2 = t186*t192+t172+t155+RATIONAL(-13.0,2000.0)+t185*x ++(RATIONAL(-53.0,1000.0)+RATIONAL(-79.0,300.0)*x+RATIONAL(9.0,50.0)*t192)*t194; + coeffs_dx->coeff_p1_p2 = t155+t185*t192+RATIONAL(-7.0,120.0)*y+t186*x+ +RATIONAL(13.0,2000.0)+(RATIONAL(409.0,3000.0)+RATIONAL(-9.0,50.0)*t192+RATIONAL +(29.0,300.0)*x)*t194; + coeffs_dx->coeff_p2_p2 = RATIONAL(-1.0,120.0)*y+t184*t192+RATIONAL(-13.0, +6000.0)+t156+(RATIONAL(-53.0,3000.0)+RATIONAL(7.0,300.0)*x)*t194+t196; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..8c53891 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,74 @@ +fp t286; +fp t287; +fp t296; +fp t282; +fp t276; +fp t284; +fp t295; +fp t285; +fp t283; +fp t294; +fp t274; +fp t293; +fp t292; +fp t291; +fp t290; +fp t289; +fp t270; +fp t269; +fp t268; +fp t266; +fp t265; + t286 = y*y; + t287 = t286*y; + t296 = x*t287; + t282 = RATIONAL(1.0,4.0); + t276 = t282*t286; + t284 = RATIONAL(1.0,2.0); + t295 = t284*y+t276; + t285 = RATIONAL(-1.0,2.0); + t283 = RATIONAL(-1.0,4.0); + t294 = t283*y+t285*t286; + t274 = t283*t286; + t293 = t285*y+t274; + t292 = RATIONAL(3.0,25.0)*t296+RATIONAL(-1.0,200.0); + t291 = t284*t286+t282*y; + t290 = RATIONAL(-1.0,6.0)*y+t276; + t289 = RATIONAL(1.0,6.0)*y+t274; + t270 = RATIONAL(1.0,12.0)*y; + t269 = RATIONAL(-1.0,12.0)*y; + t268 = RATIONAL(-3.0,25.0)*t296; + t266 = RATIONAL(3.0,50.0)*t296; + t265 = RATIONAL(-3.0,50.0)*t296; + coeffs_dxx->coeff_m1_m1 = RATIONAL(-37.0,100.0)*x+RATIONAL(-17.0,150.0)* +t287+t266+RATIONAL(37.0,200.0)+t290; + coeffs_dxx->coeff_0_m1 = RATIONAL(-111.0,200.0)+RATIONAL(13.0,75.0)*t287+ +(RATIONAL(-9.0,50.0)*t287+RATIONAL(111.0,100.0))*x+t289; + coeffs_dxx->coeff_p1_m1 = RATIONAL(-1.0,150.0)*t287+RATIONAL(111.0,200.0) ++(RATIONAL(-111.0,100.0)+RATIONAL(9.0,50.0)*t287)*x+t289; + coeffs_dxx->coeff_p2_m1 = RATIONAL(-37.0,200.0)+RATIONAL(-4.0,75.0)*t287+ +t265+RATIONAL(37.0,100.0)*x+t290; + coeffs_dxx->coeff_m1_0 = RATIONAL(23.0,100.0)*t287+RATIONAL(133.0,200.0)+ +(RATIONAL(-33.0,100.0)+RATIONAL(1.0,25.0)*t287)*x+t294; + coeffs_dxx->coeff_0_0 = RATIONAL(-199.0,200.0)+RATIONAL(-19.0,100.0)*t287 ++RATIONAL(99.0,100.0)*x+t268+t291; + coeffs_dxx->coeff_p1_0 = RATIONAL(-99.0,100.0)*x+RATIONAL(-31.0,100.0)* +t287+t291+t292; + coeffs_dxx->coeff_p2_0 = RATIONAL(67.0,200.0)+RATIONAL(27.0,100.0)*t287+( +RATIONAL(-1.0,25.0)*t287+RATIONAL(33.0,100.0))*x+t294; + coeffs_dxx->coeff_m1_p1 = RATIONAL(-13.0,50.0)*t287+RATIONAL(29.0,200.0)+ +(RATIONAL(1.0,50.0)*t287+RATIONAL(-29.0,100.0))*x+t295; + coeffs_dxx->coeff_0_p1 = RATIONAL(-87.0,200.0)+t265+RATIONAL(87.0,100.0)* +x+RATIONAL(7.0,25.0)*t287+t293; + coeffs_dxx->coeff_p1_p1 = RATIONAL(-87.0,100.0)*x+t266+RATIONAL(87.0, +200.0)+RATIONAL(11.0,50.0)*t287+t293; + coeffs_dxx->coeff_p2_p1 = RATIONAL(-6.0,25.0)*t287+RATIONAL(-29.0,200.0)+ +(RATIONAL(-1.0,50.0)*t287+RATIONAL(29.0,100.0))*x+t295; + coeffs_dxx->coeff_m1_p2 = RATIONAL(43.0,300.0)*t287+RATIONAL(-1.0,100.0)* +x+t268+t269+RATIONAL(1.0,200.0); + coeffs_dxx->coeff_0_p2 = RATIONAL(-79.0,300.0)*t287+RATIONAL(-3.0,200.0)+ +t270+(RATIONAL(3.0,100.0)+RATIONAL(9.0,25.0)*t287)*x; + coeffs_dxx->coeff_p1_p2 = t270+RATIONAL(29.0,300.0)*t287+RATIONAL(3.0, +200.0)+(RATIONAL(-9.0,25.0)*t287+RATIONAL(-3.0,100.0))*x; + coeffs_dxx->coeff_p2_p2 = RATIONAL(1.0,100.0)*x+RATIONAL(7.0,300.0)*t287+ +t269+t292; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c new file mode 100644 index 0000000..ed83ce7 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c @@ -0,0 +1,87 @@ +fp t311; +fp t314; +fp t318; +fp t301; +fp t331; +fp t322; +fp t330; +fp t315; +fp t302; +fp t329; +fp t328; +fp t316; +fp t327; +fp t319; +fp t326; +fp t323; +fp t324; +fp t325; +fp t317; +fp t310; +fp t309; +fp t307; +fp t306; +fp t300; +fp t299; +fp t298; +fp t297; + t311 = RATIONAL(-1.0,2.0)*x; + t314 = RATIONAL(1.0,2.0)*x; + t318 = RATIONAL(7.0,20.0); + t301 = y*t311; + t331 = t318*y+t301; + t322 = x*y; + t330 = t322+RATIONAL(1.0,4.0)*x; + t315 = RATIONAL(-11.0,20.0); + t302 = y*t314; + t329 = t302+t315*y; + t328 = -t322+RATIONAL(-1.0,4.0)*x; + t316 = RATIONAL(1.0,20.0); + t327 = t302+t316*y; + t319 = RATIONAL(3.0,20.0); + t326 = t319*y+t301; + t323 = x*x; + t324 = y*y; + t325 = t323*t324; + t317 = RATIONAL(-1.0,40.0); + t310 = RATIONAL(-1.0,6.0)*x; + t309 = RATIONAL(1.0,6.0)*x; + t307 = RATIONAL(-1.0,12.0)*x; + t306 = RATIONAL(1.0,12.0)*x; + t300 = RATIONAL(-9.0,50.0)*t325; + t299 = RATIONAL(9.0,50.0)*t325; + t298 = RATIONAL(-9.0,100.0)*t325; + t297 = RATIONAL(9.0,100.0)*t325; + coeffs_dxy->coeff_m1_m1 = t310+RATIONAL(11.0,60.0)+t297+(RATIONAL(59.0, +250.0)+RATIONAL(-17.0,50.0)*x)*t324+t329; + coeffs_dxy->coeff_0_m1 = RATIONAL(-1.0,20.0)+t309+(RATIONAL(21.0,500.0)+ +RATIONAL(13.0,25.0)*x+RATIONAL(-27.0,100.0)*t323)*t324+t326; + coeffs_dxy->coeff_p1_m1 = t309+RATIONAL(-7.0,60.0)+(RATIONAL(-1.0,50.0)*x ++RATIONAL(-73.0,250.0)+RATIONAL(27.0,100.0)*t323)*t324+t331; + coeffs_dxy->coeff_p2_m1 = t298+t310+RATIONAL(-1.0,60.0)+(RATIONAL(-4.0, +25.0)*x+RATIONAL(7.0,500.0))*t324+t327; + coeffs_dxy->coeff_m1_0 = RATIONAL(11.0,10.0)*y+RATIONAL(11.0,40.0)+( +RATIONAL(3.0,50.0)*t323+RATIONAL(-851.0,1000.0)+RATIONAL(69.0,100.0)*x)*t324+ +t328; + coeffs_dxy->coeff_0_0 = t300+RATIONAL(-3.0,10.0)*y+RATIONAL(-3.0,40.0)+( +RATIONAL(303.0,1000.0)+RATIONAL(-57.0,100.0)*x)*t324+t330; + coeffs_dxy->coeff_p1_0 = RATIONAL(-7.0,10.0)*y+RATIONAL(-7.0,40.0)+t299+( +RATIONAL(447.0,1000.0)+RATIONAL(-93.0,100.0)*x)*t324+t330; + coeffs_dxy->coeff_p2_0 = t317+RATIONAL(-1.0,10.0)*y+(RATIONAL(101.0, +1000.0)+RATIONAL(-3.0,50.0)*t323+RATIONAL(81.0,100.0)*x)*t324+t328; + coeffs_dxy->coeff_m1_p1 = t315+t314+(RATIONAL(203.0,250.0)+RATIONAL(-39.0 +,50.0)*x+RATIONAL(3.0,100.0)*t323)*t324+t329; + coeffs_dxy->coeff_0_p1 = t319+t311+t298+(RATIONAL(-93.0,500.0)+RATIONAL( +21.0,25.0)*x)*t324+t326; + coeffs_dxy->coeff_p1_p1 = t311+t297+t318+(RATIONAL(33.0,50.0)*x+RATIONAL( +-141.0,250.0))*t324+t331; + coeffs_dxy->coeff_p2_p1 = t316+t314+(RATIONAL(-3.0,100.0)*t323+RATIONAL( +-31.0,500.0)+RATIONAL(-18.0,25.0)*x)*t324+t327; + coeffs_dxy->coeff_m1_p2 = t307+RATIONAL(11.0,120.0)+t300+(RATIONAL(-197.0 +,1000.0)+RATIONAL(43.0,100.0)*x)*t324; + coeffs_dxy->coeff_0_p2 = t317+t306+(RATIONAL(-159.0,1000.0)+RATIONAL(27.0 +,50.0)*t323+RATIONAL(-79.0,100.0)*x)*t324; + coeffs_dxy->coeff_p1_p2 = t306+RATIONAL(-7.0,120.0)+(RATIONAL(-27.0,50.0) +*t323+RATIONAL(29.0,100.0)*x+RATIONAL(409.0,1000.0))*t324; + coeffs_dxy->coeff_p2_p2 = t307+RATIONAL(-1.0,120.0)+t299+(RATIONAL(-53.0, +1000.0)+RATIONAL(7.0,100.0)*x)*t324; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..6c1ce7f --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c @@ -0,0 +1,114 @@ +fp t264; +fp t240; +fp t242; +fp t263; +fp t247; +fp t262; +fp t261; +fp t243; +fp t226; +fp t249; +fp t248; +fp t258; +fp t232; +fp t229; +fp t257; +fp t256; +fp t234; +fp t218; +fp t255; +fp t219; +fp t254; +fp t253; +fp t252; +fp t239; +fp t251; +fp t244; +fp t241; +fp t235; +fp t228; +fp t227; +fp t225; +fp t224; +fp t223; +fp t215; +fp t211; +fp t210; +fp t208; + t264 = RATIONAL(7.0,20.0)*x+RATIONAL(9.0,20.0); + t240 = RATIONAL(1.0,20.0); + t242 = RATIONAL(-3.0,20.0); + t263 = t240*x+t242; + t247 = x*x; + t262 = y*t247; + t261 = RATIONAL(-11.0,20.0)*x; + t243 = RATIONAL(3.0,20.0); + t226 = t243*y; + t249 = t247*x; + t248 = y*y; + t258 = t249*t248; + t232 = RATIONAL(1.0,4.0)*t247; + t229 = RATIONAL(-1.0,4.0)*t247; + t257 = RATIONAL(-1.0,8.0)*t247+RATIONAL(-1.0,2.0)*t262; + t256 = RATIONAL(1.0,8.0)*t247+RATIONAL(1.0,2.0)*t262; + t234 = RATIONAL(11.0,20.0); + t218 = y*t229; + t255 = x*t226+t234*y+t218; + t219 = y*t232; + t254 = t226+t219+y*t261; + t253 = t219+t263*y; + t252 = t218+t264*y; + t239 = RATIONAL(-3.0,40.0); + t251 = RATIONAL(-3.0,10.0)*y+t239; + t244 = RATIONAL(-1.0,40.0); + t241 = RATIONAL(-1.0,20.0); + t235 = RATIONAL(-1.0,100.0); + t228 = RATIONAL(-1.0,24.0)*t247; + t227 = t244*x; + t225 = RATIONAL(1.0,24.0)*t247; + t224 = RATIONAL(-1.0,12.0)*t247; + t223 = RATIONAL(1.0,12.0)*t247; + t215 = RATIONAL(3.0,50.0)*t258; + t211 = RATIONAL(-3.0,50.0)*t258; + t210 = RATIONAL(3.0,100.0)*t258; + t208 = RATIONAL(-3.0,100.0)*t258; + coeffs_dy->coeff_m1_m1 = t241+t210+RATIONAL(11.0,60.0)*x+t224+(RATIONAL( +-17.0,100.0)*t247+RATIONAL(-6.0,125.0)+RATIONAL(59.0,250.0)*x)*t248+t254; + coeffs_dy->coeff_0_m1 = t223+t241*x+RATIONAL(-11.0,60.0)+(RATIONAL(21.0, +500.0)*x+RATIONAL(13.0,50.0)*t247+RATIONAL(-9.0,100.0)*t249+RATIONAL(-89.0, +250.0))*t248+t255; + coeffs_dy->coeff_p1_m1 = t242+t223+RATIONAL(-7.0,60.0)*x+(RATIONAL(-18.0, +125.0)+t235*t247+RATIONAL(9.0,100.0)*t249+RATIONAL(-73.0,250.0)*x)*t248+t252; + coeffs_dy->coeff_p2_m1 = RATIONAL(-1.0,60.0)*x+t240+t208+t224+(RATIONAL( +-2.0,25.0)*t247+RATIONAL(6.0,125.0)+RATIONAL(7.0,500.0)*x)*t248+t253; + coeffs_dy->coeff_m1_0 = (RATIONAL(11.0,40.0)+RATIONAL(11.0,10.0)*y)*x+( +RATIONAL(-851.0,1000.0)*x+RATIONAL(69.0,200.0)*t247+RATIONAL(1.0,50.0)*t249+ +RATIONAL(243.0,1000.0))*t248+t251+t257; + coeffs_dy->coeff_0_0 = RATIONAL(-11.0,10.0)*y+t211+RATIONAL(-11.0,40.0)+( +RATIONAL(771.0,1000.0)+RATIONAL(-57.0,200.0)*t247)*t248+(RATIONAL(303.0,1000.0) +*t248+t251)*x+t256; + coeffs_dy->coeff_p1_0 = t215+RATIONAL(-9.0,10.0)*y+RATIONAL(-9.0,40.0)+( +RATIONAL(-93.0,200.0)*t247+RATIONAL(729.0,1000.0))*t248+(RATIONAL(-7.0,10.0)*y+ +RATIONAL(-7.0,40.0)+RATIONAL(447.0,1000.0)*t248)*x+t256; + coeffs_dy->coeff_p2_0 = RATIONAL(3.0,40.0)+t227+(RATIONAL(-1.0,10.0)*x+ +RATIONAL(3.0,10.0))*y+(RATIONAL(81.0,200.0)*t247+RATIONAL(101.0,1000.0)*x+ +RATIONAL(-243.0,1000.0)+RATIONAL(-1.0,50.0)*t249)*t248+t257; + coeffs_dy->coeff_m1_p1 = t243+t232+t261+(RATIONAL(-27.0,125.0)+RATIONAL( +-39.0,100.0)*t247+RATIONAL(203.0,250.0)*x+RATIONAL(1.0,100.0)*t249)*t248+t254; + coeffs_dy->coeff_0_p1 = t229+t234+t208+t243*x+(RATIONAL(-213.0,250.0)+ +RATIONAL(21.0,50.0)*t247+RATIONAL(-93.0,500.0)*x)*t248+t255; + coeffs_dy->coeff_p1_p1 = t229+t210+(RATIONAL(33.0,100.0)*t247+RATIONAL( +-141.0,250.0)*x+RATIONAL(-81.0,125.0))*t248+t252+t264; + coeffs_dy->coeff_p2_p1 = t232+(RATIONAL(-9.0,25.0)*t247+RATIONAL(-31.0, +500.0)*x+t235*t249+RATIONAL(27.0,125.0))*t248+t253+t263; + coeffs_dy->coeff_m1_p2 = t244+t228+RATIONAL(11.0,120.0)*x+t211+(RATIONAL( +-197.0,1000.0)*x+RATIONAL(43.0,200.0)*t247+RATIONAL(21.0,1000.0))*t248; + coeffs_dy->coeff_0_p2 = t225+t227+RATIONAL(-11.0,120.0)+(RATIONAL(-159.0, +1000.0)*x+RATIONAL(9.0,50.0)*t249+RATIONAL(-79.0,200.0)*t247+RATIONAL(437.0, +1000.0))*t248; + coeffs_dy->coeff_p1_p2 = t239+RATIONAL(-7.0,120.0)*x+t225+(RATIONAL(29.0, +200.0)*t247+RATIONAL(-9.0,50.0)*t249+RATIONAL(63.0,1000.0)+RATIONAL(409.0, +1000.0)*x)*t248; + coeffs_dy->coeff_p2_p2 = RATIONAL(1.0,40.0)+t215+t228+RATIONAL(-1.0,120.0 +)*x+(RATIONAL(7.0,200.0)*t247+RATIONAL(-21.0,1000.0)+RATIONAL(-53.0,1000.0)*x)* +t248; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c new file mode 100644 index 0000000..1b690c6 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c @@ -0,0 +1,71 @@ +fp t350; +fp t351; +fp t357; +fp t342; +fp t356; +fp t343; +fp t355; +fp t348; +fp t354; +fp t353; +fp t349; +fp t345; +fp t341; +fp t340; +fp t335; +fp t334; +fp t333; +fp t332; + t350 = x*x; + t351 = t350*x; + t357 = y*t351; + t342 = RATIONAL(-1.0,4.0)*t350; + t356 = RATIONAL(7.0,20.0)*x+t342+RATIONAL(9.0,20.0); + t343 = RATIONAL(1.0,4.0)*t350; + t355 = RATIONAL(1.0,20.0)*x+t343+RATIONAL(-3.0,20.0); + t348 = RATIONAL(3.0,20.0); + t354 = t348*x+t342+RATIONAL(11.0,20.0); + t353 = t343+t348+RATIONAL(-11.0,20.0)*x; + t349 = RATIONAL(-3.0,10.0); + t345 = RATIONAL(-1.0,50.0); + t341 = RATIONAL(-1.0,2.0)*t350; + t340 = RATIONAL(1.0,2.0)*t350; + t335 = RATIONAL(3.0,50.0)*t357; + t334 = RATIONAL(-3.0,50.0)*t357; + t333 = RATIONAL(-3.0,25.0)*t357; + t332 = RATIONAL(3.0,25.0)*t357; + coeffs_dyy->coeff_m1_m1 = t335+(RATIONAL(59.0,125.0)*x+RATIONAL(-12.0, +125.0)+RATIONAL(-17.0,50.0)*t350)*y+t353; + coeffs_dyy->coeff_0_m1 = (RATIONAL(-89.0,125.0)+RATIONAL(21.0,250.0)*x+ +RATIONAL(13.0,25.0)*t350+RATIONAL(-9.0,50.0)*t351)*y+t354; + coeffs_dyy->coeff_p1_m1 = (RATIONAL(-73.0,125.0)*x+RATIONAL(-36.0,125.0)+ +RATIONAL(9.0,50.0)*t351+t345*t350)*y+t356; + coeffs_dyy->coeff_p2_m1 = t334+(RATIONAL(12.0,125.0)+RATIONAL(-4.0,25.0)* +t350+RATIONAL(7.0,250.0)*x)*y+t355; + coeffs_dyy->coeff_m1_0 = RATIONAL(11.0,10.0)*x+t349+t341+(RATIONAL(243.0, +500.0)+RATIONAL(1.0,25.0)*t351+RATIONAL(69.0,100.0)*t350+RATIONAL(-851.0,500.0) +*x)*y; + coeffs_dyy->coeff_0_0 = t340+t349*x+t333+RATIONAL(-11.0,10.0)+(RATIONAL( +-57.0,100.0)*t350+RATIONAL(771.0,500.0)+RATIONAL(303.0,500.0)*x)*y; + coeffs_dyy->coeff_p1_0 = t332+t340+RATIONAL(-9.0,10.0)+RATIONAL(-7.0,10.0 +)*x+(RATIONAL(729.0,500.0)+RATIONAL(-93.0,100.0)*t350+RATIONAL(447.0,500.0)*x)* +y; + coeffs_dyy->coeff_p2_0 = t341+RATIONAL(3.0,10.0)+RATIONAL(-1.0,10.0)*x+( +RATIONAL(-243.0,500.0)+RATIONAL(101.0,500.0)*x+RATIONAL(81.0,100.0)*t350+ +RATIONAL(-1.0,25.0)*t351)*y; + coeffs_dyy->coeff_m1_p1 = (RATIONAL(1.0,50.0)*t351+RATIONAL(-54.0,125.0)+ +RATIONAL(203.0,125.0)*x+RATIONAL(-39.0,50.0)*t350)*y+t353; + coeffs_dyy->coeff_0_p1 = t334+(RATIONAL(-213.0,125.0)+RATIONAL(21.0,25.0) +*t350+RATIONAL(-93.0,250.0)*x)*y+t354; + coeffs_dyy->coeff_p1_p1 = t335+(RATIONAL(-141.0,125.0)*x+RATIONAL(33.0, +50.0)*t350+RATIONAL(-162.0,125.0))*y+t356; + coeffs_dyy->coeff_p2_p1 = (RATIONAL(54.0,125.0)+RATIONAL(-18.0,25.0)*t350 ++RATIONAL(-31.0,250.0)*x+t345*t351)*y+t355; + coeffs_dyy->coeff_m1_p2 = t333+(RATIONAL(21.0,500.0)+RATIONAL(-197.0, +500.0)*x+RATIONAL(43.0,100.0)*t350)*y; + coeffs_dyy->coeff_0_p2 = (RATIONAL(9.0,25.0)*t351+RATIONAL(-159.0,500.0)* +x+RATIONAL(-79.0,100.0)*t350+RATIONAL(437.0,500.0))*y; + coeffs_dyy->coeff_p1_p2 = (RATIONAL(29.0,100.0)*t350+RATIONAL(-9.0,25.0)* +t351+RATIONAL(63.0,500.0)+RATIONAL(409.0,500.0)*x)*y; + coeffs_dyy->coeff_p2_p2 = t332+(RATIONAL(7.0,100.0)*t350+RATIONAL(-53.0, +500.0)*x+RATIONAL(-21.0,500.0))*y; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..1c237bc --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c @@ -0,0 +1,287 @@ +fp t519; +fp t520; +fp t522; +fp t525; +fp t616; +fp t513; +fp t512; +fp t615; +fp t507; +fp t592; +fp t521; +fp t523; +fp t524; +fp t492; +fp t549; +fp t614; +fp t490; +fp t588; +fp t493; +fp t570; +fp t613; +fp t574; +fp t488; +fp t496; +fp t556; +fp t526; +fp t563; +fp t582; +fp t508; +fp t552; +fp t484; +fp t612; +fp t557; +fp t554; +fp t611; +fp t487; +fp t559; +fp t590; +fp t562; +fp t489; +fp t579; +fp t610; +fp t583; +fp t565; +fp t553; +fp t609; +fp t581; +fp t608; +fp t558; +fp t517; +fp t518; +fp t576; +fp t580; +fp t607; +fp t584; +fp t606; +fp t586; +fp t605; +fp t561; +fp t564; +fp t604; +fp t578; +fp t603; +fp t577; +fp t602; +fp t560; +fp t568; +fp t551; +fp t601; +fp t585; +fp t550; +fp t600; +fp t599; +fp t589; +fp t555; +fp t598; +fp t597; +fp t596; +fp t595; +fp t594; +fp t593; +fp t591; +fp t587; +fp t506; +fp t479; +fp t477; +fp t514; +fp t480; +fp t483; +fp t510; +fp t572; +fp t571; +fp t497; +fp t569; +fp t567; +fp t548; +fp t547; +fp t495; +fp t546; +fp t499; +fp t502; +fp t545; +fp t544; +fp t543; +fp t505; +fp t500; +fp t503; +fp t542; +fp t501; +fp t504; +fp t498; +fp t541; +fp t540; +fp t539; +fp t538; +fp t537; +fp t536; +fp t535; +fp t534; +fp t533; +fp t532; +fp t531; +fp t516; +fp t515; +fp t511; +fp t509; +fp t494; +fp t491; + t519 = RATIONAL(-1.0,9.0); + t520 = RATIONAL(4.0,9.0); + t522 = y*y; + t525 = t522*t522; + t616 = t520*t522+t519*t525; + t513 = RATIONAL(1.0,6.0); + t512 = RATIONAL(2.0,3.0); + t615 = t512+t513*t525; + t507 = RATIONAL(-1.0,18.0); + t592 = x*y; + t521 = x*x; + t523 = t521*x; + t524 = y*t522; + t492 = RATIONAL(-1.0,72.0); + t549 = t524*t492; + t614 = t507*t592+t523*t549; + t490 = RATIONAL(1.0,18.0); + t588 = x*t490; + t493 = RATIONAL(1.0,72.0); + t570 = t523*t493; + t613 = t524*t570+y*t588; + t574 = t521*t525; + t488 = RATIONAL(-1.0,144.0); + t496 = RATIONAL(-1.0,36.0); + t556 = t521*t496; + t526 = t521*t521; + t563 = t526*t525; + t582 = t488*t563+t522*t556; + t508 = RATIONAL(1.0,36.0); + t552 = t526*t508; + t484 = RATIONAL(1.0,144.0); + t612 = t484*t574+t582+t522*t552; + t557 = t522*t526; + t554 = t525*t508; + t611 = t484*t557+t582+t521*t554; + t487 = RATIONAL(-1.0,288.0); + t559 = t487*t521; + t590 = y*t526; + t562 = t526*t524; + t489 = RATIONAL(1.0,288.0); + t579 = t521*t489; + t610 = t487*t562+y*t559+t524*t579+t489*t590; + t583 = t523*t484; + t565 = t524*t484; + t553 = t523*t488; + t609 = t488*t592+x*t565+y*t583+t524*t553; + t581 = t522*t523; + t608 = t519*t581+t523*t554+t616*x; + t558 = t524*t496; + t517 = RATIONAL(-4.0,9.0); + t518 = RATIONAL(1.0,9.0); + t576 = t518*t523; + t580 = t518*t524; + t607 = y*t576+t523*t558+x*t580+t517*t592; + t584 = t521*t522; + t606 = (t574+t557)*RATIONAL(-1.0,576.0)+(t584+t563)*RATIONAL(1.0,576.0); + t586 = x*t524; + t605 = t490*t586+y*t570+t614; + t561 = t507*t521; + t564 = t521*t490; + t604 = t526*t549+t524*t564+y*t561+t493*t590; + t578 = t524*t488; + t603 = t484*t592+x*t578+y*t553+t523*t565; + t577 = t523*t490; + t602 = t493*t586+y*t577+t614; + t560 = t525*t493; + t568 = t507*t523; + t551 = t525*t492; + t601 = x*t551+t523*t560+(t568+t588)*t522; + t585 = y*t523; + t550 = t519*t524; + t600 = x*t550+t520*t592+t519*t585+t508*t523*t524; + t599 = t487*t590+t489*t562+y*t579+t524*t559; + t589 = x*t522; + t555 = t525*t496; + t598 = t522*t576+t517*t589+t523*t555+t518*x*t525; + t597 = x*t560+t523*t551+t522*t577+t507*t589; + t596 = x*t549+y*t568+t613; + t595 = t492*t590+t524*t561+y*t564+t493*t562; + t594 = t492*t585+t507*t586+t613; + t593 = t525*t552+t519*t557+t616*t521; + t591 = y*t521; + t587 = x*t487; + t506 = RATIONAL(1.0,24.0); + t479 = t506*t525; + t477 = t506*t526; + t514 = RATIONAL(-1.0,6.0); + t480 = t514*t526; + t483 = t514*t525; + t510 = RATIONAL(-5.0,6.0); + t572 = t510*t522; + t571 = RATIONAL(1.0,96.0)*t563+RATIONAL(5.0,96.0)*t584; + t497 = RATIONAL(-1.0,24.0); + t569 = t497*t563+t521*t572; + t567 = t525*t489; + t548 = t487*t523; + t547 = t522*t489; + t495 = RATIONAL(5.0,24.0); + t546 = t495*t557+t480+t569+t615*t521; + t499 = RATIONAL(-5.0,96.0); + t502 = RATIONAL(-1.0,96.0); + t545 = t499*t557+t497*t521+t477+t502*t574+t571; + t544 = t499*t574+t497*t522+t479+t502*t557+t571; + t543 = t513*t557+t512*t522+t495*t574+t483+t569; + t505 = RATIONAL(-1.0,12.0); + t500 = RATIONAL(-1.0,48.0); + t503 = RATIONAL(5.0,48.0); + t542 = t505+t503*t521+t500*t526; + t501 = RATIONAL(1.0,48.0); + t504 = RATIONAL(1.0,12.0); + t498 = RATIONAL(-5.0,48.0); + t541 = t504+t501*t526+t498*t521; + t540 = t500*t525+t503*t522+t505; + t539 = t501*t525+t498*t522+t504; + t538 = t612+t521*t565+t488*t562+(t552+t556)*y; + t537 = t496*t590+t508*t591+t484*t562+t521*t578+t612; + t536 = t525*t583+t508*t589+t522*t553+x*t555+t611; + t535 = t522*t587+t523*t547+x*t567+t525*t548+t606; + t534 = t525*t587+t522*t548+t523*t567+x*t547+t606; + t533 = t496*t589+x*t554+t525*t553+t484*t581+t611; + t532 = t517*t591+t526*t558+t518*t590+t521*t580+t593; + t531 = t521*t550+t520*t591+t519*t590+t524*t552+t593; + t516 = RATIONAL(-2.0,3.0); + t515 = RATIONAL(5.0,6.0); + t511 = RATIONAL(1.0,4.0); + t509 = RATIONAL(-5.0,4.0); + t494 = RATIONAL(-5.0,24.0); + t491 = RATIONAL(-5.0,16.0); + coeffs_I->coeff_m2_m2 = t535+t603+t610; + coeffs_I->coeff_m1_m2 = t536+t595+t605; + coeffs_I->coeff_0_m2 = t542*t524+t541*y+t544; + coeffs_I->coeff_p1_m2 = t533+t594+t595; + coeffs_I->coeff_p2_m2 = t534+t609+t610; + coeffs_I->coeff_m2_m1 = t537+t601+t602; + coeffs_I->coeff_m1_m1 = t532+t598+t600; + coeffs_I->coeff_0_m1 = (t513+t477+t494*t521)*t524+(t516+t515*t521+t480)*y ++t543; + coeffs_I->coeff_p1_m1 = t532+t607+t608; + coeffs_I->coeff_p2_m1 = t537+t596+t597; + coeffs_I->coeff_m2_0 = t540*t523+t539*x+t545; + coeffs_I->coeff_m1_0 = (t479+t494*t522+t513)*t523+(t483+t516+t515*t522)*x ++t546; + coeffs_I->coeff_0_0 = t511*t525+RATIONAL(1.0,1.0)+t509*t522+(t491*t522+ +t511+RATIONAL(1.0,16.0)*t525)*t526+(t491*t525+RATIONAL(25.0,16.0)*t522+t509)* +t521; + coeffs_I->coeff_p1_0 = (t497*t525+t495*t522+t514)*t523+(t572+t615)*x+t546 +; + coeffs_I->coeff_p2_0 = t539*t523+t540*x+t545; + coeffs_I->coeff_m2_p1 = t538+t596+t601; + coeffs_I->coeff_m1_p1 = t531+t598+t607; + coeffs_I->coeff_0_p1 = (t497*t526+t495*t521+t514)*t524+(t512+t510*t521+ +t513*t526)*y+t543; + coeffs_I->coeff_p1_p1 = t531+t600+t608; + coeffs_I->coeff_p2_p1 = t538+t597+t602; + coeffs_I->coeff_m2_p2 = t535+t599+t609; + coeffs_I->coeff_m1_p2 = t536+t594+t604; + coeffs_I->coeff_0_p2 = t541*t524+t542*y+t544; + coeffs_I->coeff_p1_p2 = t533+t604+t605; + coeffs_I->coeff_p2_p2 = t534+t599+t603; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..46af5f2 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c @@ -0,0 +1,261 @@ +fp t779; +fp t782; +fp t742; +fp t740; +fp t851; +fp t781; +fp t741; +fp t739; +fp t850; +fp t849; +fp t774; +fp t778; +fp t769; +fp t848; +fp t758; +fp t752; +fp t847; +fp t759; +fp t800; +fp t743; +fp t846; +fp t760; +fp t720; +fp t750; +fp t802; +fp t845; +fp t821; +fp t761; +fp t748; +fp t717; +fp t780; +fp t715; +fp t812; +fp t807; +fp t844; +fp t745; +fp t714; +fp t770; +fp t843; +fp t811; +fp t754; +fp t804; +fp t842; +fp t819; +fp t798; +fp t771; +fp t735; +fp t824; +fp t841; +fp t815; +fp t840; +fp t809; +fp t839; +fp t731; +fp t801; +fp t838; +fp t777; +fp t810; +fp t822; +fp t823; +fp t837; +fp t818; +fp t836; +fp t757; +fp t776; +fp t820; +fp t772; +fp t803; +fp t835; +fp t834; +fp t833; +fp t744; +fp t832; +fp t831; +fp t830; +fp t766; +fp t799; +fp t716; +fp t829; +fp t765; +fp t828; +fp t827; +fp t718; +fp t826; +fp t825; +fp t816; +fp t817; +fp t813; +fp t773; +fp t806; +fp t805; +fp t751; +fp t797; +fp t764; +fp t749; +fp t796; +fp t746; +fp t795; +fp t767; +fp t768; +fp t794; +fp t753; +fp t793; +fp t792; +fp t791; +fp t790; +fp t789; +fp t788; +fp t787; +fp t786; +fp t763; +fp t762; +fp t747; + t779 = y*y; + t782 = t779*t779; + t742 = RATIONAL(1.0,288.0); + t740 = RATIONAL(-1.0,288.0); + t851 = t740*t782+t742*t779; + t781 = t779*y; + t741 = RATIONAL(-1.0,144.0); + t739 = RATIONAL(1.0,144.0); + t850 = t741*t781+t739*y; + t849 = t741*y+t739*t781; + t774 = RATIONAL(1.0,3.0); + t778 = x*x; + t769 = RATIONAL(-4.0,9.0); + t848 = t769+t774*t778; + t758 = RATIONAL(-1.0,12.0); + t752 = RATIONAL(-1.0,48.0); + t847 = t752*t782+t758; + t759 = RATIONAL(1.0,24.0); + t800 = t759*t778; + t743 = RATIONAL(1.0,18.0); + t846 = t743*y+t781*t800; + t760 = RATIONAL(-1.0,18.0); + t720 = t760*y; + t750 = RATIONAL(-1.0,24.0); + t802 = t778*t750; + t845 = t720+t781*t802; + t821 = x*t743; + t761 = RATIONAL(1.0,36.0); + t748 = RATIONAL(-1.0,36.0); + t717 = t748*t782; + t780 = t778*x; + t715 = t760*t779; + t812 = t780*t717+x*t715; + t807 = t779*t780; + t844 = t761*t807+t812+t782*t821; + t745 = RATIONAL(1.0,72.0); + t714 = t745*t782; + t770 = RATIONAL(1.0,9.0); + t843 = x*t714+t812+t770*t807; + t811 = t778*t782; + t754 = RATIONAL(1.0,48.0); + t804 = t778*t754; + t842 = t761*t782+t752*t811+(t804+t748)*t779; + t819 = y*t780; + t798 = t780*t743; + t771 = RATIONAL(-1.0,9.0); + t735 = t771*t781; + t824 = x*y; + t841 = t760*t819+t770*t824+t781*t798+x*t735; + t815 = t780*t782; + t840 = t741*t807+t739*t815+t851*x; + t809 = t778*t779; + t839 = t717+t761*t779+t782*t804+t752*t809; + t731 = t770*t781; + t801 = t781*t780; + t838 = y*t798+t760*t801+t771*t824+x*t731; + t777 = RATIONAL(-2.0,9.0); + t810 = t780*t770; + t822 = x*RATIONAL(8.0,9.0); + t823 = x*t782; + t837 = t779*t822+t769*t807+t777*t823+t782*t810; + t818 = x*t781; + t836 = y*t822+t769*t819+t777*t818+t770*t801; + t757 = RATIONAL(1.0,12.0); + t776 = RATIONAL(-1.0,3.0); + t820 = y*t778; + t772 = RATIONAL(4.0,9.0); + t803 = t778*t781; + t835 = t757*t803+t776*t820+t735+t772*y; + t834 = t731+t758*t803+t848*y; + t833 = t772*t819+RATIONAL(2.0,9.0)*t818+t771*t801+RATIONAL(-8.0,9.0)*t824 +; + t744 = RATIONAL(-1.0,72.0); + t832 = t744*t819+t745*t801+t850*x; + t831 = t754*t803+t752*t820+t850; + t830 = t744*t801+t745*t819+t849*x; + t766 = RATIONAL(-1.0,6.0); + t799 = t778*t766; + t716 = t744*t781; + t829 = y*t799+t716+t846; + t765 = RATIONAL(1.0,6.0); + t828 = t765*t809+t714+t715+t782*t802; + t827 = (t800+t744)*t782+(t743+t799)*t779; + t718 = t745*t781; + t826 = t718+t765*t820+t845; + t825 = t752*t803+y*t804+t849; + t816 = RATIONAL(5.0,48.0)*t779; + t817 = t759*t815+x*t816; + t813 = t766*t782; + t773 = RATIONAL(-5.0,3.0); + t806 = t780*t813+t773*x*t779; + t805 = t778*RATIONAL(-1.0,96.0); + t751 = RATIONAL(-5.0,48.0); + t797 = t751*t823+t750*t807+t817; + t764 = RATIONAL(2.0,3.0); + t749 = RATIONAL(5.0,12.0); + t796 = t749*t823+t764*t807+t806; + t746 = RATIONAL(-5.0,24.0); + t795 = t817+t765*t780+t746*t807+t847*x; + t767 = RATIONAL(5.0,6.0); + t768 = RATIONAL(-2.0,3.0); + t794 = t774*t823+RATIONAL(4.0,3.0)*x+t768*t780+t767*t807+t806; + t753 = RATIONAL(1.0,96.0); + t793 = t753*t811+t779*t805+t840+t851; + t792 = t760*t781+y*t802+t844+t846; + t791 = y*t810+t748*t801+t843+(t718+t720)*x; + t790 = t776*t809+t771*t782+t772*t779+t757*t811+t837; + t789 = t761*t801+y*t821+x*t716+t771*t819+t843; + t788 = t753*t809+t740*t779+t840+(t742+t805)*t782; + t787 = t837+t758*t811+t770*t782+t848*t779; + t786 = t743*t781+y*t800+t844+t845; + t763 = RATIONAL(1.0,4.0); + t762 = RATIONAL(-5.0,8.0); + t747 = RATIONAL(5.0,24.0); + coeffs_dx->coeff_m2_m2 = t788+t830+t831; + coeffs_dx->coeff_m1_m2 = t786+t839+t841; + coeffs_dx->coeff_0_m2 = (t757*y+t758*t781)*t780+(t746*y+t747*t781)*x+t797 +; + coeffs_dx->coeff_p1_m2 = t792+t841+t842; + coeffs_dx->coeff_p2_m2 = t793+t825+t830; + coeffs_dx->coeff_m2_m1 = t789+t826+t827; + coeffs_dx->coeff_m1_m1 = t787+t833+t835; + coeffs_dx->coeff_0_m1 = (t765*t781+t768*y)*t780+(RATIONAL(5.0,3.0)*y+ +RATIONAL(-5.0,12.0)*t781)*x+t796; + coeffs_dx->coeff_p1_m1 = t790+t833+t834; + coeffs_dx->coeff_p2_m1 = t789+t828+t829; + coeffs_dx->coeff_m2_0 = t757+t754*t782+t751*t779+(RATIONAL(5.0,16.0)*t779 ++RATIONAL(-1.0,4.0)+RATIONAL(-1.0,16.0)*t782)*t778+t795; + coeffs_dx->coeff_m1_0 = t768+t813+t767*t779+(RATIONAL(1.0,2.0)+t762*t779+ +RATIONAL(1.0,8.0)*t782)*t778+t794; + coeffs_dx->coeff_0_0 = (1.0+t763*t782+RATIONAL(-5.0,4.0)*t779)*t780+( +RATIONAL(25.0,8.0)*t779+RATIONAL(-5.0,2.0)+t762*t782)*x; + coeffs_dx->coeff_p1_0 = RATIONAL(-5.0,6.0)*t779+t764+t765*t782+(RATIONAL( +5.0,8.0)*t779+RATIONAL(-1.0,2.0)+RATIONAL(-1.0,8.0)*t782)*t778+t794; + coeffs_dx->coeff_p2_0 = t816+(t763+RATIONAL(-5.0,16.0)*t779+RATIONAL(1.0, +16.0)*t782)*t778+t795+t847; + coeffs_dx->coeff_m2_p1 = t791+t827+t829; + coeffs_dx->coeff_m1_p1 = t787+t834+t836; + coeffs_dx->coeff_0_p1 = (t766*t781+t764*y)*t780+(t773*y+t749*t781)*x+t796 +; + coeffs_dx->coeff_p1_p1 = t790+t835+t836; + coeffs_dx->coeff_p2_p1 = t791+t826+t828; + coeffs_dx->coeff_m2_p2 = t788+t825+t832; + coeffs_dx->coeff_m1_p2 = t792+t838+t839; + coeffs_dx->coeff_0_p2 = (t757*t781+t758*y)*t780+(t747*y+t746*t781)*x+t797 +; + coeffs_dx->coeff_p1_p2 = t786+t838+t842; + coeffs_dx->coeff_p2_p2 = t793+t831+t832; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..15d553b --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,224 @@ +fp t1210; +fp t1181; +fp t1212; +fp t1182; +fp t1274; +fp t1185; +fp t1249; +fp t1180; +fp t1245; +fp t1273; +fp t1184; +fp t1244; +fp t1211; +fp t1248; +fp t1183; +fp t1106; +fp t1272; +fp t1271; +fp t1270; +fp t1250; +fp t1197; +fp t1252; +fp t1269; +fp t1268; +fp t1155; +fp t1267; +fp t1098; +fp t1253; +fp t1203; +fp t1266; +fp t1265; +fp t1264; +fp t1205; +fp t1246; +fp t1263; +fp t1262; +fp t1236; +fp t1240; +fp t1261; +fp t1247; +fp t1198; +fp t1260; +fp t1259; +fp t1258; +fp t1176; +fp t1186; +fp t1209; +fp t1242; +fp t1257; +fp t1175; +fp t1229; +fp t1256; +fp t1255; +fp t1237; +fp t1238; +fp t1193; +fp t1204; +fp t1206; +fp t1254; +fp t1251; +fp t1233; +fp t1243; +fp t1187; +fp t1232; +fp t1202; +fp t1239; +fp t1189; +fp t1235; +fp t1231; +fp t1230; +fp t1191; +fp t1171; +fp t1169; +fp t1194; +fp t1228; +fp t1196; +fp t1227; +fp t1188; +fp t1226; +fp t1179; +fp t1225; +fp t1190; +fp t1224; +fp t1223; +fp t1222; +fp t1200; +fp t1201; +fp t1221; +fp t1220; +fp t1219; +fp t1218; +fp t1217; +fp t1174; +fp t1173; +fp t1216; +fp t1215; + t1210 = y*y; + t1181 = RATIONAL(-1.0,48.0); + t1212 = t1210*t1210; + t1182 = RATIONAL(1.0,48.0); + t1274 = t1212*t1182+t1210*t1181; + t1185 = RATIONAL(1.0,24.0); + t1249 = x*t1185; + t1180 = RATIONAL(-1.0,24.0); + t1245 = x*t1180; + t1273 = t1212*t1249+t1210*t1245; + t1184 = RATIONAL(-1.0,12.0); + t1244 = x*t1184; + t1211 = y*t1210; + t1248 = x*t1211; + t1183 = RATIONAL(1.0,12.0); + t1106 = t1183*t1248; + t1272 = t1106+y*t1244; + t1271 = t1274*x; + t1270 = y*t1249+t1211*t1245; + t1250 = x*RATIONAL(-2.0,3.0); + t1197 = RATIONAL(1.0,6.0); + t1252 = x*t1212; + t1269 = t1210*t1250+t1197*t1252; + t1268 = y*t1250+t1197*t1248; + t1155 = t1181*t1212; + t1267 = (t1182*t1210+t1155)*x; + t1098 = t1211*t1244; + t1253 = x*y; + t1203 = RATIONAL(1.0,3.0); + t1266 = t1203*t1253+t1098; + t1265 = t1185*t1248+y*t1245; + t1264 = t1183*t1253+t1098; + t1205 = RATIONAL(-1.0,3.0); + t1246 = x*t1205; + t1263 = t1210*t1246+t1183*t1252; + t1262 = t1212*t1245+t1210*t1249; + t1236 = t1210*t1203; + t1240 = t1212*t1184; + t1261 = (t1236+t1240)*x; + t1247 = x*RATIONAL(2.0,3.0); + t1198 = RATIONAL(-1.0,6.0); + t1260 = t1210*t1247+t1198*t1252; + t1259 = y*t1247+t1198*t1248; + t1258 = y*t1246+t1106; + t1176 = RATIONAL(1.0,72.0); + t1186 = RATIONAL(-1.0,18.0); + t1209 = x*x; + t1242 = t1209*t1240+t1186*t1210; + t1257 = t1242+t1209*t1236+t1176*t1212; + t1175 = RATIONAL(1.0,18.0); + t1229 = t1183*t1209; + t1256 = t1242+t1175*t1212+t1210*t1229; + t1255 = RATIONAL(-1.0,288.0)*t1212+RATIONAL(1.0,288.0)*t1210+t1274*t1209; + t1237 = t1203*t1209; + t1238 = t1210*t1209; + t1193 = RATIONAL(-4.0,3.0); + t1204 = RATIONAL(8.0,9.0); + t1206 = RATIONAL(-2.0,9.0); + t1254 = t1193*t1238+t1204*t1210+(t1237+t1206)*t1212; + t1251 = y*t1209; + t1233 = RATIONAL(1.0,8.0)*t1212; + t1243 = RATIONAL(5.0,48.0)*t1210+t1209*t1233; + t1187 = RATIONAL(-1.0,2.0); + t1232 = t1187*t1209; + t1202 = RATIONAL(-5.0,3.0); + t1239 = t1202*t1210+t1212*t1232; + t1189 = RATIONAL(-5.0,8.0); + t1235 = t1189*t1210; + t1231 = t1211*t1209; + t1230 = RATIONAL(2.0,1.0)*t1209; + t1191 = RATIONAL(1.0,2.0); + t1171 = t1191*t1209; + t1169 = RATIONAL(-2.0,1.0)*t1209; + t1194 = RATIONAL(1.0,4.0); + t1228 = RATIONAL(-5.0,24.0)+t1194*t1209; + t1196 = RATIONAL(-1.0,4.0); + t1227 = t1196*t1209+RATIONAL(5.0,24.0); + t1188 = RATIONAL(-1.0,8.0); + t1226 = RATIONAL(-5.0,48.0)*t1212+t1188*t1238+t1243; + t1179 = RATIONAL(5.0,12.0); + t1225 = t1179*t1212+t1210*t1230+t1239; + t1190 = RATIONAL(4.0,3.0); + t1224 = t1169+t1203*t1212+RATIONAL(5.0,2.0)*t1238+t1190+t1239; + t1223 = t1171+t1209*t1235+t1184+t1155+t1243; + t1222 = t1204*y+t1206*t1211+t1193*t1251+t1203*t1231+t1254; + t1200 = RATIONAL(1.0,9.0); + t1201 = RATIONAL(-1.0,9.0); + t1221 = t1197*t1251+t1201*y+t1200*t1211+t1198*t1231+t1256; + t1220 = RATIONAL(2.0,9.0)*t1211+t1205*t1231+t1190*t1251+RATIONAL(-8.0,9.0 +)*y+t1254; + t1219 = t1201*t1211+t1198*t1251+t1197*t1231+t1200*y+t1256; + t1218 = t1205*t1251+t1175*y+t1257+(RATIONAL(-1.0,72.0)+t1229)*t1211; + t1217 = t1257+t1184*t1231+t1176*t1211+(t1186+t1237)*y; + t1174 = RATIONAL(-1.0,144.0); + t1173 = RATIONAL(1.0,144.0); + t1216 = t1174*y+t1185*t1251+t1180*t1231+t1173*t1211+t1255; + t1215 = t1185*t1231+t1180*t1251+t1173*y+t1174*t1211+t1255; + coeffs_dxx->coeff_m2_m2 = t1216+t1265+t1267; + coeffs_dxx->coeff_m1_m2 = t1219+t1264+t1273; + coeffs_dxx->coeff_0_m2 = t1227*t1211+t1228*y+t1226; + coeffs_dxx->coeff_p1_m2 = t1219+t1262+t1272; + coeffs_dxx->coeff_p2_m2 = t1216+t1270+t1271; + coeffs_dxx->coeff_m2_m1 = t1218+t1263+t1266; + coeffs_dxx->coeff_m1_m1 = t1220+t1260+t1268; + coeffs_dxx->coeff_0_m1 = (t1171+RATIONAL(-5.0,12.0))*t1211+(t1169+ +RATIONAL(5.0,3.0))*y+t1225; + coeffs_dxx->coeff_p1_m1 = t1220+t1259+t1269; + coeffs_dxx->coeff_p2_m1 = t1218+t1258+t1261; + coeffs_dxx->coeff_m2_0 = (RATIONAL(5.0,8.0)*t1210+t1187+t1188*t1212)*x+ +t1223; + coeffs_dxx->coeff_m1_0 = (t1194*t1212+1.0+RATIONAL(-5.0,4.0)*t1210)*x+ +t1224; + coeffs_dxx->coeff_0_0 = t1189*t1212+RATIONAL(-5.0,2.0)+RATIONAL(25.0,8.0) +*t1210+(RATIONAL(3.0,1.0)+RATIONAL(3.0,4.0)*t1212+RATIONAL(-15.0,4.0)*t1210)* +t1209; + coeffs_dxx->coeff_p1_0 = (t1196*t1212+RATIONAL(5.0,4.0)*t1210-1.0)*x+ +t1224; + coeffs_dxx->coeff_p2_0 = (t1191+t1233+t1235)*x+t1223; + coeffs_dxx->coeff_m2_p1 = t1217+t1258+t1263; + coeffs_dxx->coeff_m1_p1 = t1222+t1259+t1260; + coeffs_dxx->coeff_0_p1 = (t1179+t1232)*t1211+(t1202+t1230)*y+t1225; + coeffs_dxx->coeff_p1_p1 = t1222+t1268+t1269; + coeffs_dxx->coeff_p2_p1 = t1217+t1261+t1266; + coeffs_dxx->coeff_m2_p2 = t1215+t1267+t1270; + coeffs_dxx->coeff_m1_p2 = t1221+t1272+t1273; + coeffs_dxx->coeff_0_p2 = t1228*t1211+t1227*y+t1226; + coeffs_dxx->coeff_p1_p2 = t1221+t1262+t1264; + coeffs_dxx->coeff_p2_p2 = t1215+t1265+t1271; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c new file mode 100644 index 0000000..c0d0630 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c @@ -0,0 +1,256 @@ +fp t1387; +fp t1428; +fp t1430; +fp t1390; +fp t1485; +fp t1396; +fp t1484; +fp t1397; +fp t1388; +fp t1483; +fp t1426; +fp t1403; +fp t1482; +fp t1458; +fp t1427; +fp t1429; +fp t1389; +fp t1361; +fp t1425; +fp t1481; +fp t1343; +fp t1460; +fp t1480; +fp t1450; +fp t1418; +fp t1398; +fp t1395; +fp t1344; +fp t1479; +fp t1448; +fp t1414; +fp t1417; +fp t1423; +fp t1369; +fp t1401; +fp t1478; +fp t1459; +fp t1416; +fp t1422; +fp t1421; +fp t1402; +fp t1477; +fp t1366; +fp t1367; +fp t1413; +fp t1452; +fp t1476; +fp t1391; +fp t1475; +fp t1350; +fp t1474; +fp t1356; +fp t1400; +fp t1473; +fp t1373; +fp t1472; +fp t1362; +fp t1471; +fp t1351; +fp t1380; +fp t1470; +fp t1455; +fp t1469; +fp t1399; +fp t1355; +fp t1468; +fp t1386; +fp t1415; +fp t1467; +fp t1466; +fp t1449; +fp t1347; +fp t1465; +fp t1461; +fp t1464; +fp t1412; +fp t1463; +fp t1411; +fp t1447; +fp t1462; +fp t1457; +fp t1456; +fp t1454; +fp t1453; +fp t1393; +fp t1451; +fp t1446; +fp t1445; +fp t1409; +fp t1420; +fp t1444; +fp t1394; +fp t1443; +fp t1442; +fp t1441; +fp t1440; +fp t1439; +fp t1438; +fp t1437; +fp t1436; +fp t1435; +fp t1434; +fp t1433; +fp t1424; +fp t1419; +fp t1410; +fp t1408; +fp t1407; +fp t1406; +fp t1405; +fp t1404; +fp t1392; + t1387 = RATIONAL(1.0,144.0); + t1428 = y*y; + t1430 = y*t1428; + t1390 = RATIONAL(-1.0,72.0); + t1485 = t1387*y+t1390*t1430; + t1396 = RATIONAL(-1.0,48.0); + t1484 = t1396*t1428+t1387; + t1397 = RATIONAL(1.0,48.0); + t1388 = RATIONAL(-1.0,144.0); + t1483 = t1397*t1428+t1388; + t1426 = RATIONAL(-8.0,9.0); + t1403 = RATIONAL(4.0,9.0); + t1482 = t1426*y+t1403*t1430; + t1458 = x*t1430; + t1427 = x*x; + t1429 = t1427*x; + t1389 = RATIONAL(1.0,18.0); + t1361 = t1389*t1429; + t1425 = RATIONAL(2.0,9.0); + t1481 = y*t1361+t1425*t1458; + t1343 = t1389*t1430; + t1460 = y*t1429; + t1480 = x*t1343+t1425*t1460; + t1450 = t1428*t1429; + t1418 = RATIONAL(-1.0,9.0); + t1398 = RATIONAL(1.0,12.0); + t1395 = RATIONAL(-1.0,24.0); + t1344 = t1395*t1428; + t1479 = t1398*t1450+t1418*t1429+(t1389+t1344)*x; + t1448 = t1427*t1430; + t1414 = RATIONAL(1.0,6.0); + t1417 = RATIONAL(1.0,9.0); + t1423 = RATIONAL(-1.0,3.0); + t1369 = t1423*t1427; + t1401 = RATIONAL(-1.0,18.0); + t1478 = t1401*t1430+t1414*t1448+(t1369+t1417)*y; + t1459 = x*t1428; + t1416 = RATIONAL(-2.0,3.0); + t1422 = RATIONAL(8.0,9.0); + t1421 = RATIONAL(1.0,3.0); + t1402 = RATIONAL(-4.0,9.0); + t1477 = t1416*t1459+t1421*t1450+t1422*x+t1402*t1429; + t1366 = t1421*t1427; + t1367 = t1421*t1428; + t1413 = RATIONAL(-1.0,4.0); + t1452 = t1413*t1427; + t1476 = t1366+t1367+t1428*t1452+t1402; + t1391 = RATIONAL(1.0,72.0); + t1475 = t1391*t1429+t1395*t1450+t1483*x; + t1350 = t1397*t1427; + t1474 = t1391*t1430+t1395*t1448+(t1350+t1388)*y; + t1356 = t1396*t1427; + t1400 = RATIONAL(1.0,24.0); + t1473 = t1400*t1448+y*t1356+t1485; + t1373 = t1423*t1428; + t1472 = t1401*t1429+t1414*t1450+(t1373+t1417)*x; + t1362 = t1390*t1429; + t1471 = t1362+t1400*t1450+t1484*x; + t1351 = t1395*t1427; + t1380 = t1418*t1430; + t1470 = t1398*t1448+t1380+(t1351+t1389)*y; + t1455 = t1429*t1430; + t1469 = y*t1362+RATIONAL(1.0,36.0)*t1455+t1485*x; + t1399 = RATIONAL(-1.0,12.0); + t1355 = t1400*t1427; + t1468 = t1417*t1430+t1399*t1448+(t1355+t1401)*y; + t1386 = t1418*x; + t1415 = RATIONAL(-1.0,6.0); + t1467 = t1386+t1361+t1415*t1450+x*t1367; + t1466 = t1343+t1415*t1448+(t1366+t1418)*y; + t1449 = t1399*t1429; + t1347 = t1400*t1428; + t1465 = t1417*t1429+t1428*t1449+(t1401+t1347)*x; + t1461 = x*y; + t1464 = RATIONAL(16.0,9.0)*t1461+t1426*t1458+t1482*t1429; + t1412 = RATIONAL(2.0,3.0); + t1463 = t1412*t1459+t1423*t1450+t1426*x+t1403*t1429; + t1411 = RATIONAL(1.0,4.0); + t1447 = t1411*t1428; + t1462 = t1427*t1447+t1369+t1373+t1403; + t1457 = y*t1427; + t1456 = t1429*t1380+y*t1386; + t1454 = t1428*t1427; + t1453 = t1416*t1455+RATIONAL(-10.0,3.0)*t1461; + t1393 = RATIONAL(5.0,24.0); + t1451 = t1393*t1461+t1414*t1455; + t1446 = RATIONAL(1.0,8.0)*t1454+t1389+t1456; + t1445 = t1401+RATIONAL(-1.0,8.0)*t1454+t1456; + t1409 = RATIONAL(4.0,3.0); + t1420 = RATIONAL(5.0,3.0); + t1444 = t1420*t1458+t1409*t1460+t1453; + t1394 = RATIONAL(-5.0,12.0); + t1443 = t1394*t1458+y*t1449+t1451; + t1442 = t1420*t1460+t1409*t1458+t1453; + t1441 = t1399*t1458+t1394*t1460+t1451; + t1440 = t1350+RATIONAL(-1.0,16.0)*t1454+t1469+t1483; + t1439 = RATIONAL(1.0,16.0)*t1454+t1356+t1469+t1484; + t1438 = t1351+t1415*t1428+t1446+t1481; + t1437 = t1344+t1415*t1427+t1446+t1480; + t1436 = t1347+t1414*t1427+t1445+t1480; + t1435 = t1402*t1430+t1422*y+t1416*t1457+t1421*t1448+t1464; + t1434 = t1414*t1428+t1355+t1445+t1481; + t1433 = t1423*t1448+t1412*t1457+t1464+t1482; + t1424 = RATIONAL(5.0,4.0); + t1419 = RATIONAL(-5.0,3.0); + t1410 = RATIONAL(1.0,2.0); + t1408 = RATIONAL(-5.0,8.0); + t1407 = RATIONAL(-5.0,4.0); + t1406 = RATIONAL(-5.0,2.0); + t1405 = RATIONAL(-1.0,2.0); + t1404 = RATIONAL(5.0,8.0); + t1392 = RATIONAL(-5.0,24.0); + coeffs_dxy->coeff_m2_m2 = t1439+t1474+t1475; + coeffs_dxy->coeff_m1_m2 = t1434+t1470+t1472; + coeffs_dxy->coeff_0_m2 = (t1413*t1428+t1398)*t1429+(t1404*t1428+t1392)*x+ +t1443; + coeffs_dxy->coeff_p1_m2 = t1438+t1468+t1472; + coeffs_dxy->coeff_p2_m2 = t1440+t1473+t1475; + coeffs_dxy->coeff_m2_m1 = t1436+t1478+t1479; + coeffs_dxy->coeff_m1_m1 = t1433+t1462+t1463; + coeffs_dxy->coeff_0_m1 = (t1410*t1428+t1416)*t1429+(t1420+t1407*t1428)*x+ +t1444; + coeffs_dxy->coeff_p1_m1 = t1435+t1463+t1476; + coeffs_dxy->coeff_p2_m1 = t1437+t1466+t1479; + coeffs_dxy->coeff_m2_0 = (t1452+t1398)*t1430+(t1392+t1404*t1427)*y+t1441; + coeffs_dxy->coeff_m1_0 = (t1410*t1427+t1416)*t1430+(t1407*t1427+t1420)*y+ +t1442; + coeffs_dxy->coeff_0_0 = (t1406*y+t1430)*t1429+(RATIONAL(25.0,4.0)*y+t1406 +*t1430)*x; + coeffs_dxy->coeff_p1_0 = (t1405*t1427+t1412)*t1430+(t1424*t1427+t1419)*y+ +t1442; + coeffs_dxy->coeff_p2_0 = (t1399+t1411*t1427)*t1430+(t1393+t1408*t1427)*y+ +t1441; + coeffs_dxy->coeff_m2_p1 = t1437+t1465+t1478; + coeffs_dxy->coeff_m1_p1 = t1433+t1476+t1477; + coeffs_dxy->coeff_0_p1 = (t1405*t1428+t1412)*t1429+(t1419+t1424*t1428)*x+ +t1444; + coeffs_dxy->coeff_p1_p1 = t1435+t1462+t1477; + coeffs_dxy->coeff_p2_p1 = t1436+t1465+t1466; + coeffs_dxy->coeff_m2_p2 = t1440+t1471+t1474; + coeffs_dxy->coeff_m1_p2 = t1438+t1467+t1470; + coeffs_dxy->coeff_0_p2 = (t1447+t1399)*t1429+(t1393+t1408*t1428)*x+t1443; + coeffs_dxy->coeff_p1_p2 = t1434+t1467+t1468; + coeffs_dxy->coeff_p2_p2 = t1439+t1471+t1473; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..59006b6 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c @@ -0,0 +1,255 @@ +fp t1007; +fp t1006; +fp t1013; +fp t1015; +fp t964; +fp t1082; +fp t974; +fp t976; +fp t1081; +fp t1080; +fp t975; +fp t977; +fp t1017; +fp t1079; +fp t1004; +fp t1005; +fp t1078; +fp t987; +fp t993; +fp t1077; +fp t985; +fp t1014; +fp t1040; +fp t995; +fp t957; +fp t1076; +fp t994; +fp t978; +fp t952; +fp t1075; +fp t1052; +fp t996; +fp t1016; +fp t1039; +fp t983; +fp t1042; +fp t958; +fp t1048; +fp t1074; +fp t980; +fp t959; +fp t1038; +fp t1073; +fp t972; +fp t1054; +fp t1050; +fp t1043; +fp t1072; +fp t1071; +fp t1049; +fp t1010; +fp t1070; +fp t1053; +fp t1009; +fp t1069; +fp t992; +fp t1011; +fp t1068; +fp t1067; +fp t979; +fp t1066; +fp t989; +fp t1065; +fp t955; +fp t1064; +fp t1001; +fp t951; +fp t1063; +fp t1062; +fp t1061; +fp t1060; +fp t1059; +fp t1058; +fp t1000; +fp t1057; +fp t1056; +fp t1051; +fp t1055; +fp t1035; +fp t1008; +fp t1047; +fp t1045; +fp t1046; +fp t1041; +fp t1037; +fp t1036; +fp t1003; +fp t973; +fp t968; +fp t984; +fp t999; +fp t1034; +fp t986; +fp t1033; +fp t1032; +fp t981; +fp t1031; +fp t1030; +fp t1029; +fp t1028; +fp t988; +fp t990; +fp t1027; +fp t1026; +fp t1025; +fp t1024; +fp t1023; +fp t1022; +fp t1021; +fp t998; +fp t997; + t1007 = RATIONAL(4.0,9.0); + t1006 = RATIONAL(-1.0,9.0); + t1013 = x*x; + t1015 = t1013*x; + t964 = t1006*t1015; + t1082 = t964+t1007*x; + t974 = RATIONAL(1.0,144.0); + t976 = RATIONAL(-1.0,144.0); + t1081 = t974*x+t976*t1015; + t1080 = t974*t1015+t976*x; + t975 = RATIONAL(-1.0,288.0); + t977 = RATIONAL(1.0,288.0); + t1017 = t1013*t1013; + t1079 = t975*t1017+t977*t1013; + t1004 = RATIONAL(-4.0,9.0); + t1005 = RATIONAL(1.0,9.0); + t1078 = t1004*t1013+t1005*t1017; + t987 = RATIONAL(-1.0,48.0); + t993 = RATIONAL(-1.0,12.0); + t1077 = t987*t1017+t993; + t985 = RATIONAL(-1.0,24.0); + t1014 = y*y; + t1040 = t1014*t1015; + t995 = RATIONAL(-1.0,18.0); + t957 = t995*x; + t1076 = t985*t1040+t957; + t994 = RATIONAL(1.0,24.0); + t978 = RATIONAL(1.0,18.0); + t952 = t978*x; + t1075 = t994*t1040+t952; + t1052 = y*t1017; + t996 = RATIONAL(1.0,36.0); + t1016 = t1014*y; + t1039 = t1013*t1016; + t983 = RATIONAL(-1.0,36.0); + t1042 = t1017*t1016; + t958 = t995*t1013; + t1048 = t983*t1042+y*t958; + t1074 = t978*t1052+t1048+t996*t1039; + t980 = RATIONAL(1.0,72.0); + t959 = t980*t1017; + t1038 = t1005*t1016; + t1073 = y*t959+t1048+t1013*t1038; + t972 = t1005*t1015; + t1054 = x*y; + t1050 = x*t1016; + t1043 = t1016*t1015; + t1072 = t1006*t1054+y*t972+t978*t1050+t995*t1043; + t1071 = RATIONAL(2.0,9.0)*y*t1015+RATIONAL(-8.0,9.0)*t1054+t1082*t1016; + t1049 = y*RATIONAL(-2.0,9.0); + t1010 = RATIONAL(8.0,9.0); + t1070 = t1004*t1050+t1016*t972+t1010*t1054+t1015*t1049; + t1053 = x*t1014; + t1009 = RATIONAL(1.0,3.0); + t1069 = t972+t1004*x+t993*t1040+t1009*t1053; + t992 = RATIONAL(1.0,12.0); + t1011 = RATIONAL(-1.0,3.0); + t1068 = t1011*t1053+t992*t1040+t1082; + t1067 = t995*t1050+y*t964+t978*t1043+t1005*t1054; + t979 = RATIONAL(-1.0,72.0); + t1066 = t980*t1043+t979*t1050+t1081*y; + t989 = RATIONAL(1.0,48.0); + t1065 = t987*t1053+t989*t1040+t1081; + t955 = t980*t1015; + t1064 = t983*t1043+x*t1038+(t957+t955)*y; + t1001 = RATIONAL(-1.0,6.0); + t951 = t979*t1015; + t1063 = t1001*t1053+t951+t1075; + t1062 = t996*t1043+t1006*t1050+(t952+t951)*y; + t1061 = t979*t1043+t980*t1050+t1080*y; + t1060 = t989*t1053+t987*t1040+t1080; + t1059 = t978*t1015+t994*t1053+t1076; + t1058 = t995*t1015+t985*t1053+t1075; + t1000 = RATIONAL(1.0,6.0); + t1057 = t955+t1000*t1053+t1076; + t1056 = t974*t1042+t976*t1039+t1079*y; + t1051 = y*t1013; + t1055 = t1010*t1051+t1017*t1049+t1078*t1016; + t1035 = t1001*t1017; + t1008 = RATIONAL(-5.0,3.0); + t1047 = t1008*t1051+t1016*t1035; + t1045 = RATIONAL(5.0,48.0)*t1013; + t1046 = t994*t1042+y*t1045; + t1041 = t1017*t1014; + t1037 = t1013*t1014; + t1036 = RATIONAL(5.0,6.0)*t1013; + t1003 = RATIONAL(-2.0,3.0); + t973 = t1003*t1016; + t968 = t1000*t1016; + t984 = RATIONAL(5.0,12.0); + t999 = RATIONAL(2.0,3.0); + t1034 = t984*t1052+t999*t1039+t1047; + t986 = RATIONAL(-5.0,48.0); + t1033 = t986*t1052+t985*t1039+t1046; + t1032 = RATIONAL(5.0,24.0)*y+t993*t1016; + t981 = RATIONAL(-5.0,24.0); + t1031 = t992*t1016+t981*y; + t1030 = t973+t1009*t1052+t1016*t1036+RATIONAL(4.0,3.0)*y+t1047; + t1029 = t968+t981*t1039+t1046+t1077*y; + t1028 = t994*t1041+t1001*t1037+t978*t1013+t979*t1017+t1073; + t988 = RATIONAL(1.0,96.0); + t990 = RATIONAL(-1.0,96.0); + t1027 = t988*t1037+t977*t1017+t975*t1013+t990*t1041+t1056; + t1026 = t1007*t1013+t992*t1041+t1006*t1017+t1011*t1037+t1055; + t1025 = t987*t1041+t983*t1013+t996*t1017+t989*t1037+t1074; + t1024 = t993*t1041+t1009*t1037+t1055+t1078; + t1023 = t987*t1037+t983*t1017+t996*t1013+t989*t1041+t1074; + t1022 = t990*t1037+t988*t1041+t1056+t1079; + t1021 = t959+t985*t1041+t1000*t1037+t958+t1073; + t998 = RATIONAL(1.0,4.0); + t997 = RATIONAL(-5.0,8.0); + coeffs_dy->coeff_m2_m2 = t1027+t1061+t1065; + coeffs_dy->coeff_m1_m2 = t1028+t1057+t1062; + coeffs_dy->coeff_0_m2 = t986*t1013+t989*t1017+t992+(RATIONAL(5.0,16.0)* +t1013+RATIONAL(-1.0,4.0)+RATIONAL(-1.0,16.0)*t1017)*t1014+t1029; + coeffs_dy->coeff_p1_m2 = t1028+t1063+t1064; + coeffs_dy->coeff_p2_m2 = t1027+t1060+t1066; + coeffs_dy->coeff_m2_m1 = t1023+t1059+t1067; + coeffs_dy->coeff_m1_m1 = t1024+t1068+t1071; + coeffs_dy->coeff_0_m1 = t1036+t1003+t1035+(t997*t1013+RATIONAL(1.0,2.0)+ +RATIONAL(1.0,8.0)*t1017)*t1014+t1030; + coeffs_dy->coeff_p1_m1 = t1024+t1069+t1070; + coeffs_dy->coeff_p2_m1 = t1023+t1058+t1072; + coeffs_dy->coeff_m2_0 = t1032*t1015+t1031*x+t1033; + coeffs_dy->coeff_m1_0 = (RATIONAL(-5.0,12.0)*y+t968)*t1015+(RATIONAL(5.0, +3.0)*y+t973)*x+t1034; + coeffs_dy->coeff_0_0 = (RATIONAL(-5.0,4.0)*t1013+t998*t1017+1.0)*t1016+( +t997*t1017+RATIONAL(25.0,8.0)*t1013+RATIONAL(-5.0,2.0))*y; + coeffs_dy->coeff_p1_0 = (t1001*t1016+t984*y)*t1015+(t1008*y+t999*t1016)*x ++t1034; + coeffs_dy->coeff_p2_0 = t1031*t1015+t1032*x+t1033; + coeffs_dy->coeff_m2_p1 = t1025+t1058+t1067; + coeffs_dy->coeff_m1_p1 = t1026+t1069+t1071; + coeffs_dy->coeff_0_p1 = t1000*t1017+t999+RATIONAL(-5.0,6.0)*t1013+( +RATIONAL(5.0,8.0)*t1013+RATIONAL(-1.0,8.0)*t1017+RATIONAL(-1.0,2.0))*t1014+ +t1030; + coeffs_dy->coeff_p1_p1 = t1026+t1068+t1070; + coeffs_dy->coeff_p2_p1 = t1025+t1059+t1072; + coeffs_dy->coeff_m2_p2 = t1022+t1060+t1061; + coeffs_dy->coeff_m1_p2 = t1021+t1062+t1063; + coeffs_dy->coeff_0_p2 = t1045+(RATIONAL(1.0,16.0)*t1017+RATIONAL(-5.0, +16.0)*t1013+t998)*t1014+t1029+t1077; + coeffs_dy->coeff_p1_p2 = t1021+t1057+t1064; + coeffs_dy->coeff_p2_p2 = t1022+t1065+t1066; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c new file mode 100644 index 0000000..b1a740e --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c @@ -0,0 +1,223 @@ +fp t1613; +fp t1675; +fp t1611; +fp t1645; +fp t1612; +fp t1614; +fp t1586; +fp t1644; +fp t1504; +fp t1674; +fp t1585; +fp t1615; +fp t1649; +fp t1584; +fp t1635; +fp t1673; +fp t1583; +fp t1646; +fp t1648; +fp t1588; +fp t1672; +fp t1650; +fp t1671; +fp t1555; +fp t1654; +fp t1670; +fp t1651; +fp t1604; +fp t1647; +fp t1669; +fp t1603; +fp t1605; +fp t1668; +fp t1587; +fp t1643; +fp t1494; +fp t1667; +fp t1666; +fp t1633; +fp t1665; +fp t1664; +fp t1663; +fp t1609; +fp t1652; +fp t1662; +fp t1661; +fp t1660; +fp t1659; +fp t1589; +fp t1632; +fp t1636; +fp t1642; +fp t1579; +fp t1658; +fp t1580; +fp t1657; +fp t1601; +fp t1656; +fp t1655; +fp t1653; +fp t1641; +fp t1598; +fp t1640; +fp t1608; +fp t1591; +fp t1639; +fp t1568; +fp t1597; +fp t1573; +fp t1595; +fp t1637; +fp t1634; +fp t1599; +fp t1631; +fp t1602; +fp t1630; +fp t1592; +fp t1629; +fp t1578; +fp t1628; +fp t1596; +fp t1627; +fp t1626; +fp t1576; +fp t1577; +fp t1625; +fp t1624; +fp t1623; +fp t1622; +fp t1621; +fp t1620; +fp t1606; +fp t1607; +fp t1619; +fp t1618; + t1613 = y*y; + t1675 = RATIONAL(8.0,9.0)+t1613*RATIONAL(-4.0,3.0); + t1611 = RATIONAL(-1.0,3.0); + t1645 = t1611*x; + t1612 = x*x; + t1614 = t1612*x; + t1586 = RATIONAL(1.0,12.0); + t1644 = y*t1586; + t1504 = t1614*t1644; + t1674 = y*t1645+t1504; + t1585 = RATIONAL(1.0,48.0); + t1615 = t1612*t1612; + t1649 = y*t1615; + t1584 = RATIONAL(-1.0,48.0); + t1635 = t1612*t1584; + t1673 = t1585*t1649+y*t1635; + t1583 = RATIONAL(-1.0,24.0); + t1646 = x*t1583; + t1648 = y*t1614; + t1588 = RATIONAL(1.0,24.0); + t1672 = y*t1646+t1588*t1648; + t1650 = x*t1588; + t1671 = y*t1650+t1583*t1648; + t1555 = t1584*t1615; + t1654 = y*t1612; + t1670 = y*t1555+t1585*t1654; + t1651 = RATIONAL(2.0,3.0)*y; + t1604 = RATIONAL(-1.0,6.0); + t1647 = y*t1604; + t1669 = t1614*t1647+x*t1651; + t1603 = RATIONAL(1.0,6.0); + t1605 = RATIONAL(-2.0,3.0); + t1668 = t1605*t1654+t1603*t1649; + t1587 = RATIONAL(-1.0,12.0); + t1643 = y*t1587; + t1494 = t1614*t1643; + t1667 = x*t1644+t1494; + t1666 = t1583*t1654+t1588*t1649; + t1633 = t1603*t1614; + t1665 = (t1605*x+t1633)*y; + t1664 = t1615*t1647+t1612*t1651; + t1663 = t1615*t1644+t1611*t1654; + t1609 = RATIONAL(1.0,3.0); + t1652 = y*t1609; + t1662 = t1494+x*t1652; + t1661 = t1583*t1649+t1588*t1654; + t1660 = x*t1643+t1504; + t1659 = t1612*t1652+t1615*t1643; + t1589 = RATIONAL(-1.0,18.0); + t1632 = t1613*t1615; + t1636 = t1589*t1612+t1587*t1632; + t1642 = t1613*t1612; + t1579 = RATIONAL(1.0,18.0); + t1658 = t1636+t1579*t1615+t1586*t1642; + t1580 = RATIONAL(1.0,72.0); + t1657 = t1636+t1580*t1615+t1609*t1642; + t1601 = RATIONAL(-2.0,9.0); + t1656 = t1601*t1615+t1609*t1632+t1675*t1612; + t1655 = RATIONAL(-1.0,288.0)*t1615+t1613*t1635+RATIONAL(1.0,288.0)*t1612+ +t1585*t1632; + t1653 = x*t1613; + t1641 = RATIONAL(2.0,1.0)*t1613; + t1598 = RATIONAL(1.0,8.0); + t1640 = RATIONAL(5.0,48.0)*t1612+t1598*t1632; + t1608 = RATIONAL(-5.0,3.0); + t1591 = RATIONAL(-1.0,2.0); + t1639 = t1608*t1612+t1591*t1632; + t1568 = RATIONAL(-2.0,1.0)*t1613; + t1597 = RATIONAL(1.0,2.0); + t1573 = t1597*t1613; + t1595 = RATIONAL(-5.0,8.0); + t1637 = t1595*t1612; + t1634 = t1613*t1614; + t1599 = RATIONAL(1.0,4.0); + t1631 = t1599*t1613+RATIONAL(-5.0,24.0); + t1602 = RATIONAL(-1.0,4.0); + t1630 = t1602*t1613+RATIONAL(5.0,24.0); + t1592 = RATIONAL(-1.0,8.0); + t1629 = t1592*t1642+RATIONAL(-5.0,48.0)*t1615+t1640; + t1578 = RATIONAL(5.0,12.0); + t1628 = t1612*t1641+t1578*t1615+t1639; + t1596 = RATIONAL(4.0,3.0); + t1627 = t1609*t1615+RATIONAL(5.0,2.0)*t1642+t1568+t1596+t1639; + t1626 = t1555+t1587+t1573+t1613*t1637+t1640; + t1576 = RATIONAL(1.0,144.0); + t1577 = RATIONAL(-1.0,144.0); + t1625 = t1613*t1646+t1577*t1614+t1576*x+t1588*t1634+t1655; + t1624 = t1583*t1634+t1577*x+t1613*t1650+t1576*t1614+t1655; + t1623 = t1609*t1653+t1589*x+t1580*t1614+t1587*t1634+t1657; + t1622 = t1579*x+RATIONAL(-1.0,72.0)*t1614+t1586*t1634+t1613*t1645+t1657; + t1621 = t1601*t1614+t1609*t1634+t1656+t1675*x; + t1620 = RATIONAL(-8.0,9.0)*x+RATIONAL(2.0,9.0)*t1614+t1596*t1653+t1611* +t1634+t1656; + t1606 = RATIONAL(1.0,9.0); + t1607 = RATIONAL(-1.0,9.0); + t1619 = t1607*x+t1604*t1634+t1606*t1614+t1603*t1653+t1658; + t1618 = t1606*x+t1607*t1614+t1613*t1633+t1604*t1653+t1658; + coeffs_dyy->coeff_m2_m2 = t1624+t1670+t1672; + coeffs_dyy->coeff_m1_m2 = t1622+t1662+t1663; + coeffs_dyy->coeff_0_m2 = (RATIONAL(5.0,8.0)*t1612+t1592*t1615+t1591)*y+ +t1626; + coeffs_dyy->coeff_p1_m2 = t1623+t1663+t1674; + coeffs_dyy->coeff_p2_m2 = t1625+t1670+t1671; + coeffs_dyy->coeff_m2_m1 = t1618+t1666+t1667; + coeffs_dyy->coeff_m1_m1 = t1620+t1664+t1665; + coeffs_dyy->coeff_0_m1 = (1.0+t1599*t1615+RATIONAL(-5.0,4.0)*t1612)*y+ +t1627; + coeffs_dyy->coeff_p1_m1 = t1621+t1664+t1669; + coeffs_dyy->coeff_p2_m1 = t1619+t1660+t1666; + coeffs_dyy->coeff_m2_0 = t1630*t1614+t1631*x+t1629; + coeffs_dyy->coeff_m1_0 = (t1573+RATIONAL(-5.0,12.0))*t1614+(RATIONAL(5.0, +3.0)+t1568)*x+t1628; + coeffs_dyy->coeff_0_0 = RATIONAL(25.0,8.0)*t1612+RATIONAL(-5.0,2.0)+t1595 +*t1615+(RATIONAL(3.0,1.0)+RATIONAL(3.0,4.0)*t1615+RATIONAL(-15.0,4.0)*t1612)* +t1613; + coeffs_dyy->coeff_p1_0 = (t1591*t1613+t1578)*t1614+(t1641+t1608)*x+t1628; + coeffs_dyy->coeff_p2_0 = t1631*t1614+t1630*x+t1629; + coeffs_dyy->coeff_m2_p1 = t1618+t1660+t1661; + coeffs_dyy->coeff_m1_p1 = t1620+t1668+t1669; + coeffs_dyy->coeff_0_p1 = (t1602*t1615-1.0+RATIONAL(5.0,4.0)*t1612)*y+ +t1627; + coeffs_dyy->coeff_p1_p1 = t1621+t1665+t1668; + coeffs_dyy->coeff_p2_p1 = t1619+t1661+t1667; + coeffs_dyy->coeff_m2_p2 = t1624+t1671+t1673; + coeffs_dyy->coeff_m1_p2 = t1622+t1659+t1674; + coeffs_dyy->coeff_0_p2 = (t1637+t1597+t1598*t1615)*y+t1626; + coeffs_dyy->coeff_p1_p2 = t1623+t1659+t1662; + coeffs_dyy->coeff_p2_p2 = t1625+t1672+t1673; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.cube.order1.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.cube.order1.smooth0.c new file mode 100644 index 0000000..b45593e --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.cube.order1.smooth0.c @@ -0,0 +1,59 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrTP_2d_cube10 +#include "../template.h" + +#define N_DIMS 2 +#define MOLECULE_MIN_M 0 +#define MOLECULE_MAX_M 1 +#define MOLECULE_SIZE 2 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +/* n.b. no 2nd derivatives for linear interpolation! */ + +#define XYZ x, y +#define FP_XYZ fp x, fp y +#define STRIDE_IJK stride_i, stride_j +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride + +#define DATA_STRUCT data_struct_2d_cube_size2 +#define COEFFS_STRUCT coeffs_struct_2d_cube_size2 + +#define FETCH_DATA_REAL LocalInterp_fetch_2d_cube2_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_2d_cube2_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_2d_cube2_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_2d_cube2_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_2d_cube2_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_2d_cube2_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_2d_cube2_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_2d_cube2_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_2d_cube2 + +#define STORE_COEFFS LocalInterp_store_2d_cube2 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.cube.order2.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.cube.order2.smooth0.c new file mode 100644 index 0000000..35b758b --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.cube.order2.smooth0.c @@ -0,0 +1,64 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrTP_2d_cube20 +#include "../template.h" + +#define N_DIMS 2 +#define MOLECULE_MIN_M -1 +#define MOLECULE_MAX_M 1 +#define MOLECULE_SIZE 3 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +#define HAVE_OP_DXX +#define HAVE_OP_DXY +#define HAVE_OP_DYY + +#define XYZ x, y +#define FP_XYZ fp x, fp y +#define STRIDE_IJK stride_i, stride_j +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride + +#define DATA_STRUCT data_struct_2d_cube_size3 +#define COEFFS_STRUCT coeffs_struct_2d_cube_size3 + +#define FETCH_DATA_REAL LocalInterp_fetch_2d_cube3_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_2d_cube3_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_2d_cube3_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_2d_cube3_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_2d_cube3_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_2d_cube3_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_2d_cube3_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_2d_cube3_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_2d_cube3 + +#define STORE_COEFFS LocalInterp_store_2d_cube3 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c" +#define COEFFS_DXY_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c" +#define COEFFS_DYY_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.cube.order3.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.cube.order3.smooth0.c new file mode 100644 index 0000000..1942b50 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.cube.order3.smooth0.c @@ -0,0 +1,64 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrTP_2d_cube30 +#include "../template.h" + +#define N_DIMS 2 +#define MOLECULE_MIN_M -1 +#define MOLECULE_MAX_M 2 +#define MOLECULE_SIZE 4 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +#define HAVE_OP_DXX +#define HAVE_OP_DXY +#define HAVE_OP_DYY + +#define XYZ x, y +#define FP_XYZ fp x, fp y +#define STRIDE_IJK stride_i, stride_j +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride + +#define DATA_STRUCT data_struct_2d_cube_size4 +#define COEFFS_STRUCT coeffs_struct_2d_cube_size4 + +#define FETCH_DATA_REAL LocalInterp_fetch_2d_cube4_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_2d_cube4_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_2d_cube4_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_2d_cube4_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_2d_cube4_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_2d_cube4_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_2d_cube4_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_2d_cube4_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_2d_cube4 + +#define STORE_COEFFS LocalInterp_store_2d_cube4 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c" +#define COEFFS_DXY_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c" +#define COEFFS_DYY_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.cube.order4.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.cube.order4.smooth0.c new file mode 100644 index 0000000..50ff450 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.cube.order4.smooth0.c @@ -0,0 +1,64 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrTP_2d_cube40 +#include "../template.h" + +#define N_DIMS 2 +#define MOLECULE_MIN_M -2 +#define MOLECULE_MAX_M 2 +#define MOLECULE_SIZE 5 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +#define HAVE_OP_DXX +#define HAVE_OP_DXY +#define HAVE_OP_DYY + +#define XYZ x, y +#define FP_XYZ fp x, fp y +#define STRIDE_IJK stride_i, stride_j +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride + +#define DATA_STRUCT data_struct_2d_cube_size5 +#define COEFFS_STRUCT coeffs_struct_2d_cube_size5 + +#define FETCH_DATA_REAL LocalInterp_fetch_2d_cube5_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_2d_cube5_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_2d_cube5_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_2d_cube5_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_2d_cube5_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_2d_cube5_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_2d_cube5_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_2d_cube5_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_2d_cube5 + +#define STORE_COEFFS LocalInterp_store_2d_cube5 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c" +#define COEFFS_DXY_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c" +#define COEFFS_DYY_COMPUTE_FILE_NAME "Lagrange-tensor-product/2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.log b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.log new file mode 100644 index 0000000..20887a8 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.log @@ -0,0 +1,6898 @@ + |\^/| Maple 7 (IBM INTEL LINUX) +._|\| |/|_. Copyright (c) 2001 by Waterloo Maple Inc. + \ MAPLE / All rights reserved. Maple is a registered trademark of + <____ ____> Waterloo Maple Inc. + | Type ? for help. +# util.maple -- misc utility routines +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/util.maple,v 1.5 2002/09/02 10:21:03 jthorn Exp $ +> +# +# fix_rationals - convert numbers to RATIONAL() calls +# nonmatching_names - find names in a list which *don't* have a specified prefix +# sprint_numeric_list - convert a numeric list to a valid C identifier suffix +# print_name_list_dcl - print C declarations for a list of names +# +# hypercube_points - compute all (integer) points in an N-dimensional hypercube +# +# ftruncate - truncate a file to zero length +# +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function converts all {integer, rational} subexpressions of its +# input except integer exponents and -1 factors in products, into function +# calls +# RATIONAL(num,den) +# This is useful in conjunction with the C() library function, since +# +# C( (1/3) * foo * bar ) +# t0 = foo*bar/3; +# +# generates a (slow) division (and runs the risk of mixed-mode-arithmetic +# problems), while +# +# C((1.0/3.0) * foo * bar); +# t0 = 0.3333333333*foo*bar; +# +# suffers from roundoff error. With this function, +# +# fix_rationals((1/3) * foo * bar); +# RATIONAL(1,3) foo bar +# C(%); +# t0 = RATIONAL(1.0,3.0)*foo*bar; +# +# which a C preprocessor macro can easily convert to the desired +# +# t0 = (1.0/3.0)*foo*bar; +# +# Additionally, this function can be told to leave certain types of +# subexpressions unconverged. For example, +# fix_rationals(expr, type, specfunc(integer, DATA)); +# will leave all subexpressions of the form DATA(integer arguments) +# unconverted. +# +# Arguments: +# expr = (in) The expression to be converted. +# inert_fn = (optional in) +# If specified, this argument should be a Boolean procedure +# or the name of a Boolean procedure. This procedure should +# take one or more argument, and return true if and only if +# the first argument should *not* be converted, i.e. if we +# should leave this expression unchanged. See the last +# example above. +# ... = (optional in) +# Any further arguments are passed as additional arguments to +# the inert_fn procedure. +# +> fix_rationals := +> proc( +> expr::{ +> algebraic, name = algebraic, +> list({algebraic, name = algebraic}), +> set ({algebraic, name = algebraic}) +> }, +> inert_fn::{name, procedure} +> ) +> local nn, k, +> base, power, fbase, fpower, +> fn, fn_args_list, +> num, den, mult; +> +# do we want to convert this expression? +> if ((nargs >= 2) and inert_fn(expr, args[3..nargs])) +> then return expr; +> end if; +> +# recurse over lists and sets +> if (type(expr, {list,set})) +> then return map(fix_rationals, expr, args[2..nargs]); +> end if; +> +# recurse over equation right hand sides +> if (type(expr, name = algebraic)) +> then return ( lhs(expr) = fix_rationals(rhs(expr), args[2..nargs]) ); +> end if; +> +# recurse over functions other than RATIONAL() +> if (type(expr, function)) +> then +> fn := op(0, expr); +> if (fn <> 'RATIONAL') +> then +> fn_args_list := [op(expr)]; +> fn_args_list := map(fix_rationals, fn_args_list, args[2..nargs]); +> fn; return '%'( op(fn_args_list) ); +> end if; +> end if; +> +> nn := nops(expr); +> +# recurse over sums +> if (type(expr, `+`)) +> then return sum('fix_rationals(op(k,expr), args[2..nargs])', 'k'=1..nn); +> end if; +> +# recurse over products +# ... leaving leading -1 factors intact, i.e. not converted to RATIONAL(-1,1) +> if (type(expr, `*`)) +> then +> if (op(1, expr) = -1) +> then return -1*fix_rationals(remove(type, expr, 'identical(-1)'), +> args[2..nargs]); +> else return product('fix_rationals(op(k,expr), args[2..nargs])', +> 'k'=1..nn); +> end if; +> end if; +> +# recurse over powers +# ... leaving integer exponents intact +> if (type(expr, `^`)) +> then +> base := op(1, expr); +> power := op(2, expr); +> +> fbase := fix_rationals(base, args[2..nargs]); +> if (type(power, integer)) +> then fpower := power; +> else fpower := fix_rationals(power, args[2..nargs]); +> end if; +> return fbase ^ fpower; +> end if; +> +# fix integers and fractions +> if (type(expr, integer)) +> then return 'RATIONAL'(expr, 1); +> end if; +> if (type(expr, fraction)) +> then +> num := op(1, expr); +> den := op(2, expr); +> +> return 'RATIONAL'(num, den); +> end if; +> +# turn Maple floating-point into integer fraction, then recursively fix that +> if (type(expr, float)) +> then +> mult := op(1, expr); +> power := op(2, expr); +> return fix_rationals(mult * 10^power, args[2..nargs]); +> end if; +> +# identity op on names +> if (type(expr, name)) +> then return expr; +> end if; +> +# unknown type +> error "%0", +> "unknown type for expr!", +> " whattype(expr) = ", whattype(expr), +> " expr = ", expr; +> end proc; +fix_rationals := proc(expr::{algebraic, name = algebraic, +list({algebraic, name = algebraic}), set({algebraic, name = algebraic})}, +inert_fn::{procedure, name}) +local nn, k, base, power, fbase, fpower, fn, fn_args_list, num, den, mult; + if 2 <= nargs and inert_fn(expr, args[3 .. nargs]) then return expr + end if; + if type(expr, {set, list}) then + return map(fix_rationals, expr, args[2 .. nargs]) + end if; + if type(expr, name = algebraic) then + return lhs(expr) = fix_rationals(rhs(expr), args[2 .. nargs]) + end if; + if type(expr, function) then + fn := op(0, expr); + if fn <> 'RATIONAL' then + fn_args_list := [op(expr)]; + fn_args_list := + map(fix_rationals, fn_args_list, args[2 .. nargs]); + fn; + return '%'(op(fn_args_list)) + end if + end if; + nn := nops(expr); + if type(expr, `+`) then return + sum('fix_rationals(op(k, expr), args[2 .. nargs])', 'k' = 1 .. nn) + end if; + if type(expr, `*`) then + if op(1, expr) = -1 then return -fix_rationals( + remove(type, expr, 'identical(-1)'), args[2 .. nargs]) + else return product('fix_rationals(op(k, expr), args[2 .. nargs])', + 'k' = 1 .. nn) + end if + end if; + if type(expr, `^`) then + base := op(1, expr); + power := op(2, expr); + fbase := fix_rationals(base, args[2 .. nargs]); + if type(power, integer) then fpower := power + else fpower := fix_rationals(power, args[2 .. nargs]) + end if; + return fbase^fpower + end if; + if type(expr, integer) then return 'RATIONAL'(expr, 1) end if; + if type(expr, fraction) then + num := op(1, expr); den := op(2, expr); return 'RATIONAL'(num, den) + end if; + if type(expr, float) then + mult := op(1, expr); + power := op(2, expr); + return fix_rationals(mult*10^power, args[2 .. nargs]) + end if; + if type(expr, name) then return expr end if; + error "%0", "unknown type for expr!", " whattype(expr) = ", + whattype(expr), " expr = ", expr +end proc + +> +################################################################################ +> +# +# This function finds names in a list which *don't* have a specified prefix. +# +# Arguments: +# name_list = A list of the names. +# prefix = The prefix we want to filter out. +# +# Results: +# This function returns the subset list of names which don't have the +# specified prefix. +# +> nonmatching_names := +> proc( name_list::list({name,string}), prefix::{name,string} ) +> +> select( proc(n) +> evalb(not StringTools[IsPrefix](prefix,n)); +> end proc +> , +> name_list +> ); +> end proc; +nonmatching_names := proc( +name_list::list({name, string}), prefix::{name, string}) + select(proc(n) evalb(not StringTools[IsPrefix](prefix, n)) end proc, + name_list) +end proc + +> +################################################################################ +> +# +# This function converts a numeric list to a string which is a valid +# C identifier suffix: elements are separated by "_", decimal points are +# replaced by "x", and all nonzero values have explicit +/- signs, which +# are replaced by "p"/"m". +# +# For example, [0,-3.5,+4] --> "0_m3x5_p4". +# +> sprint_numeric_list := +> proc(nlist::list(numeric)) +> +# generate preliminary string, eg "+0_-3.5_+4" +> map2(sprintf, "%+a", nlist); +> ListTools[Join](%, "_"); +> cat(op(%)); +> +# fixup bad characters +> StringTools[SubstituteAll](%, "+0", "0"); +> StringTools[CharacterMap](".+-", "xpm", %); +> +> return %; +> end proc; +sprint_numeric_list := proc(nlist::list(numeric)) + map2(sprintf, "%+a", nlist); + ListTools[Join](%, "_"); + cat(op(%)); + StringTools[SubstituteAll](%, "+0", "0"); + StringTools[CharacterMap](".+-", "xpm", %); + return % +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C declarations for a list of names. +# +# Argument: +# name_list = A list of the names. +# type_name = The C type of the names, eg. "double". +# file_name = The file name to write the declaration to. This is +# truncated before writing. +# +> print_name_list_dcl := +> proc( name_list::list({name,string}), +> type_name::string, +> file_name::string ) +> local blanks, separator_string; +> +> ftruncate(file_name); +> +> map( +> proc(var::{name,string}) +> fprintf(file_name, +> "%s %s;\n", +> type_name, var); +> end proc +> , +> name_list +> ); +> +> fclose(file_name); +> NULL; +> end proc; +print_name_list_dcl := proc( +name_list::list({name, string}), type_name::string, file_name::string) +local blanks, separator_string; + ftruncate(file_name); + map(proc(var::{name, string}) + fprintf(file_name, "%s %s;\n", type_name, var) + end proc, name_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes a list of all the (integer) points in an +# N-dimensional hypercube, in lexicographic order. The present +# implementation requires N <= 4. +# +# Arguments: +# cmin,cmax = N-element lists of cube minimum/maximum coordinates. +# +# Results: +# The function returns a set of d-element lists giving the coordinates. +# For example, +# hypercube([0,0], [2,1] +# returns +# { [0,0], [0,1], [1,0], [1,1], [2,0], [2,1] } +> hypercube_points := +> proc(cmin::list(integer), cmax::list(integer)) +> local N, i,j,k,l; +> +> N := nops(cmin); +> if (nops(cmax) <> N) +> then error +> "must have same number of dimensions for min and max coordinates!"; +> fi; +> +> if (N = 1) +> then return [seq([i], i=cmin[1]..cmax[1])]; +> elif (N = 2) +> then return [ +> seq( +> seq([i,j], j=cmin[2]..cmax[2]), +> i=cmin[1]..cmax[1]) +> ]; +> elif (N = 3) +> then return [ +> seq( +> seq( +> seq([i,j,k], k=cmin[3]..cmax[3]), +> j=cmin[2]..cmax[2] ), +> i=cmin[1]..cmax[1]) +> ]; +> elif (N = 4) +> then return [ +> seq( +> seq( +> seq( +> seq([i,j,k,l], l=cmin[4]..cmax[4]), +> k=cmin[3]..cmax[3] ), +> j=cmin[2]..cmax[2]), +> i=cmin[1]..cmax[1]) +> ]; +> else +> error "implementation restriction: must have N <= 4, got %1!", N; +> fi; +> end proc; +hypercube_points := proc(cmin::list(integer), cmax::list(integer)) +local N, i, j, k, l; + N := nops(cmin); + if nops(cmax) <> N then error + "must have same number of dimensions for min and max coordinates!" + end if; + if N = 1 then return [seq([i], i = cmin[1] .. cmax[1])] + elif N = 2 then return + [seq(seq([i, j], j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] + elif N = 3 then return [seq( + seq(seq([i, j, k], k = cmin[3] .. cmax[3]), j = cmin[2] .. cmax[2]) + , i = cmin[1] .. cmax[1])] + elif N = 4 then return [seq(seq(seq( + seq([i, j, k, l], l = cmin[4] .. cmax[4]), k = cmin[3] .. cmax[3]), + j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] + else error "implementation restriction: must have N <= 4, got %1!", N + end if +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function truncates a file to 0 length if it exists, or creates +# it at that length if it doesn't exist. +# +# Arguments: +# file_name = (in) The name of the file. +# +> ftruncate := +> proc(file_name::string) +> fopen(file_name, 'WRITE'); +> fclose(%); +> NULL; +> end proc; +ftruncate := + + proc(file_name::string) fopen(file_name, 'WRITE'); fclose(%); NULL end proc + +# interpolate.maple -- compute interpolation formulas/coefficients +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/interpolate.maple,v 1.11 2002/09/02 10:21:02 jthorn Exp $ +> +# +# <<>> +# Lagrange_polynomial_interpolant - compute Lagrange polynomial interpolant +# Hermite_polynomial_interpolant - compute Hermite polynomial interpolant +# coeffs_as_lc_of_data - coefficients of ... (linear combination of data) +# +# print_coeffs__lc_of_data - print C code to compute coefficients +# print_fetch_data - print C code to fetch input array chunk into struct data +# print_store_coeffs - print C code to store struct coeffs "somewhere" +# print_interp_cmpt__lc_of_data - print C code for computation of interpolant +# +# coeff_name - name of coefficient of data at a given [m] coordinate +# data_var_name - name of variable storing data value at a given [m] coordinate +# +> +################################################################################ +> +# +# ***** representation of numbers, data values, etc ***** +# +# We use RATIONAL(p.0,q.0) to denote the rational number p/q. +# +# We use DATA(...) to represent the data values being interpolated at a +# specified [m] coordinate, where the arguments are the [m] coordinates. +# +# We use COEFF(...) to represent the molecule coefficient at a specified +# [m] coordinate, where the arguments are the [m] coordinates. +# +# For example, the usual 1-D centered 2nd order 1st derivative molecule +# would be written +# RATIONAL(-1.0,2.0)*DATA(-1) + RATIONA(1.0,2.0)*DATA(1) +# and its coefficients as +# COEFF(-1) = RATIONAL(-1.0,2.0) +# COEFF(1) = RATIONAL(1.0,2.0) +# +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes a Lagrange polynomial interpolant in any +# number of dimensions. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) c00 + c10*x + c01*y end proc +# coeff_list = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example [c00, c10, c01]. +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# posn_list = A list of positions (each a list of numeric values) where the +# interpolant is to use data, for example hypercube([0,0], [1,1]). +# Any positions may be used; if they're redundant (as in the +# example) the least-squares interpolant is computed. +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Lagrange_polynomial_interpolant := +> proc( +> fn::procedure, coeff_list::list(name), +> coord_list::list(name), posn_list::list(list(numeric)) +> ) +> local posn, data_eqns, coeff_eqns; +> +# coefficients of interpolating polynomial +> data_eqns := { seq( fn(op(posn))='DATA'(op(posn)) , posn=posn_list ) }; +> coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); +> if (has(coeff_eqns, '_t')) +> then error "interpolation coefficients aren't uniquely determined!"; +> end if; +> +# interpolant as a polynomial in the coordinates +> return subs(coeff_eqns, eval(fn))(op(coord_list)); +> end proc; +Lagrange_polynomial_interpolant := proc(fn::procedure, coeff_list::list(name), +coord_list::list(name), posn_list::list(list(numeric))) +local posn, data_eqns, coeff_eqns; + data_eqns := {seq(fn(op(posn)) = 'DATA'(op(posn)), posn = posn_list)}; + coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); + if has(coeff_eqns, '_t') then + error "interpolation coefficients aren't uniquely determined!" + end if; + return subs(coeff_eqns, eval(fn))(op(coord_list)) +end proc + +> +################################################################################ +> +# +# This function computes a Hermite polynomial interpolant in any +# number of dimensions. This is a polynomial which +# * has values which match the given data DATA() at a specified set of +# points, and +# * has derivatives which match the specified finite-difference derivatives +# of the given data DATA() at a specified set of points +# +# For the derivative matching, we actually match all possible products +# of 1st derivatives, i.e. in 2-D we match dx, dy, and dxy, in 3-D we +# match dx, dy, dz, dxy, dxz, dyz, and dxyz, etc etc. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) +# + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 +# + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 +# + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +# + c00 + c10*x + c20*x^2 + c30*x^3 +# end proc; +# coeff_set = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example +# { +# c03, c13, c23, c33, +# c02, c12, c22, c32, +# c01, c11, c21, c31, +# c00, c10, c20, c30 +# } +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# deriv_set = A set of equations of the form +# {coords} = proc +# giving the derivatives which are to be matched, and the +# procedures to compute their finite-difference approximations. +# Each procedure should take N_dims integer arguments specifying +# an evaluation point, and return a suitable linear combination +# of the DATA() for the derivative at that point. For example +# { +# {x} = proc(i::integer, j::integer) +# - 1/2*DATA(i-1,j) + 1/2*DATA(i+1,j) +# end proc +# , +# {y} = proc(i::integer, j::integer) +# - 1/2*DATA(i,j-1) + 1/2*DATA(i,j+1) +# end proc +# , +# {x,y} = proc(i::integer, j::integer) +# - 1/4*DATA(i-1,j+1) + 1/4*DATA(i+1,j+1) +# + 1/4*DATA(i-1,j-1) - 1/4*DATA(i+1,j-1) +# end proc +# } +# fn_posn_set = A set of positions (each a list of numeric values) +# where the interpolant is to match the given data DATA(), +# for example +# {[0,0], [0,1], [1,0], [1,1]} +# deriv_posn_set = A list of positions (each a list of numeric values) +# where the interpolant is to match the derivatives +# specified by deriv_set , for example +# {[0,0], [0,1], [1,0], [1,1]} +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Hermite_polynomial_interpolant := +> proc( +> fn::procedure, +> coeff_set::set(name), +> coord_list::list(name), +> deriv_set::set(set(name) = procedure), +> fn_posn_set::set(list(numeric)), +> deriv_posn_set::set(list(numeric)) +> ) +> local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; +> +> +# +# compute a set of equations +# {fn(posn) = DATA(posn)} +# giving the function values to be matched +# +> fn_eqnset := map( +> # return equation that fn(posn) = DATA(posn) +> proc(posn::list(integer)) +> fn(op(posn)) = 'DATA'(op(posn)); +> end proc +> , +> fn_posn_set +> ); +> +> +# +# compute a set of equations +# { diff(fn,coords)(posn) = DERIV(coords)(posn) } +# giving the derivative values to be matched, where DERIV(coords) +# is a placeholder for the appropriate derivative +# +> map( +> # return set of equations for this particular derivative +> proc(deriv_coords::set(name)) +> local deriv_fn; +> fn(op(coord_list)); +> diff(%, op(deriv_coords)); +> deriv_fn := unapply(%, op(coord_list)); +> map( +> proc(posn::list(integer)) +> deriv_fn(op(posn)) = 'DERIV'(op(deriv_coords))(op(posn)); +> end proc +> , +> deriv_posn_set +> ); +> end proc +> , +> map(lhs, deriv_set) +> ); +> deriv_eqnset := `union`(op(%)); +> +> +# +# solve overall set of equations for coefficients +# in terms of DATA() and DERIV() values +# +> coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); +> if (indets(map(rhs,%)) <> {}) +> then error "no unique solution for coefficients -- %1 eqns for %2 coeffs", +> nops(fn_eqnset union deriv_eqnset), +> nops(coeff_set); +> fi; +> +> +# +# compute a set of substitution equations +# {'DERIV'(coords) = procedure} +# +> subs_eqnset := map( +> proc(eqn::set(name) = procedure) +> 'DERIV'(op(lhs(eqn))) = rhs(eqn); +> end proc +> , +> deriv_set +> ); +> +> +# +# compute the coefficients in terms of the DATA() values +# +> subs(subs_eqnset, coeff_eqns); +> eval(%); +> +# +# compute the interpolant as a polynomial in the coordinates +# +> subs(%, fn(op(coord_list))); +> end proc; +Hermite_polynomial_interpolant := proc(fn::procedure, coeff_set::set(name), +coord_list::list(name), deriv_set::set(set(name) = procedure), +fn_posn_set::set(list(numeric)), deriv_posn_set::set(list(numeric))) +local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; + fn_eqnset := map( + proc(posn::list(integer)) fn(op(posn)) = 'DATA'(op(posn)) end proc, + fn_posn_set); + map(proc(deriv_coords::set(name)) + local deriv_fn; + fn(op(coord_list)); + diff(%, op(deriv_coords)); + deriv_fn := unapply(%, op(coord_list)); + map(proc(posn::list(integer)) + deriv_fn(op(posn)) = + 'DERIV'(op(deriv_coords))(op(posn)) + end proc, deriv_posn_set) + end proc, map(lhs, deriv_set)); + deriv_eqnset := `union`(op(%)); + coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); + if indets(map(rhs, %)) <> {} then error + "no unique solution for coefficients -- %1 eqns for %2 coeffs", + nops(fn_eqnset union deriv_eqnset), nops(coeff_set) + end if; + subs_eqnset := map(proc(eqn::(set(name) = procedure)) + 'DERIV'(op(lhs(eqn))) = rhs(eqn) + end proc, deriv_set); + subs(subs_eqnset, coeff_eqns); + eval(%); + subs(%, fn(op(coord_list))) +end proc + +> +################################################################################ +> +# +# This function takes as input an interpolating polynomial, expresses +# it as a linear combination of the data values, and returns the coefficeints +# of that form. +# +# Arguments: +# interpolant = The interpolating polynomial (an algebraic expression +# in the coordinates and the data values). +# posn_list = The same list of data positions used in the interpolant. +# +# Results: +# This function returns the coefficients, as a list of equations of the +# form COEFF(...) = value , where each value is a polynomial in the +# coordinates. The order of the list matches that of posn_list. +# +> coeffs_as_lc_of_data := +> proc( +> interpolant::algebraic, +> posn_list::list(list(numeric)) +> ) +> local data_list, interpolant_as_lc_of_data; +> +# interpolant as a linear combination of the data values +> data_list := [ seq( 'DATA'(op(posn)) , posn=posn_list ) ]; +> interpolant_as_lc_of_data := collect(interpolant, data_list); +> +# coefficients of the data values in the linear combination +> return map( +> proc(posn::list(numeric)) +> coeff(interpolant_as_lc_of_data, DATA(op(posn))); +> 'COEFF'(op(posn)) = %; +> end proc +> , +> posn_list +> ); +> end proc; +coeffs_as_lc_of_data := proc( +interpolant::algebraic, posn_list::list(list(numeric))) +local data_list, interpolant_as_lc_of_data; + data_list := [seq('DATA'(op(posn)), posn = posn_list)]; + interpolant_as_lc_of_data := collect(interpolant, data_list); + return map(proc(posn::list(numeric)) + coeff(interpolant_as_lc_of_data, DATA(op(posn))); + 'COEFF'(op(posn)) = % + end proc, posn_list) +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function prints C expressions for the coefficients of an +# interpolating polynomial. (The polynomial is expressed as linear +# combinations of the data values with coefficients which are +# RATIONAL(p,q) calls.) +# +# Arguments: +# coeff_list = A list of the coefficients, as returned from +# coeffs_as_lc_of_data() . +# coeff_name_prefix = A prefix string for the coefficient names. +# temp_name_type = The C type to be used for Maple-introduced temporary +# names, eg. "double". +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_coeffs__lc_of_data := +> proc( coeff_list::list(specfunc(numeric,COEFF) = algebraic), +> coeff_name_prefix::string, +> temp_name_type::string, +> file_name::string ) +> global `codegen/C/function/informed`; +> local coeff_list2, cmpt_list, temp_name_list; +> +# convert LHS of each equation from a COEFF() call (eg COEFF(-1,+1)) +# to a Maple/C variable name (eg coeff_I_m1_p1) +> coeff_list2 := map( +> proc(coeff_eqn::specfunc(numeric,COEFF) = algebraic) +> local posn; +> posn := [op(lhs(coeff_eqn))]; +> coeff_name(posn,coeff_name_prefix); +> convert(%, name); # codegen[C] wants LHS +> # to be an actual Maple *name* +> % = fix_rationals(rhs(coeff_eqn)); +> end proc +> , +> coeff_list +> ); +> +# +# generate the C code +# +> +# tell codegen[C] not to warn about unknown RATIONAL() and DATA() "fn calls" +# via undocumented :( global table +> `codegen/C/function/informed`['RATIONAL'] := true; +> `codegen/C/function/informed`['DATA'] := true; +> +> ftruncate(file_name); +> +# optimized computation sequence for all the coefficients +# (may use local variables t0,t1,t2,...) +> cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; +> +# list of the t0,t1,t2,... local variables +> temp_name_list := nonmatching_names(map(lhs,cmpt_list), coeff_name_prefix); +> +# declare the t0,t1,t2,... local variables (if there are any) +> if (nops(temp_name_list) > 0) +> then print_name_list_dcl(%, temp_name_type, file_name); +> fi; +> +# now print the optimized computation sequence +> codegen[C](cmpt_list, filename=file_name); +> +> fclose(file_name); +> +> NULL; +> end proc; +print_coeffs__lc_of_data := proc( +coeff_list::list(specfunc(numeric, COEFF) = algebraic), +coeff_name_prefix::string, temp_name_type::string, file_name::string) +local coeff_list2, cmpt_list, temp_name_list; +global `codegen/C/function/informed`; + coeff_list2 := map(proc( + coeff_eqn::(specfunc(numeric, COEFF) = algebraic)) + local posn; + posn := [op(lhs(coeff_eqn))]; + coeff_name(posn, coeff_name_prefix); + convert(%, name); + % = fix_rationals(rhs(coeff_eqn)) + end proc, coeff_list); + `codegen/C/function/informed`['RATIONAL'] := true; + `codegen/C/function/informed`['DATA'] := true; + ftruncate(file_name); + cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; + temp_name_list := + nonmatching_names(map(lhs, cmpt_list), coeff_name_prefix); + if 0 < nops(temp_name_list) then + print_name_list_dcl(%, temp_name_type, file_name) + end if; + codegen[C](cmpt_list, filename = file_name); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C expression to assign the data-value +# variables, eg +# data->data_m1_p1 = DATA(-1,1); +# +# Arguments: +# posn_list = The same list of positions as was used to compute the +# interpolating polynomial. +# data_var_name_prefix = A prefix string for the data variable names. +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_fetch_data := +> proc( +> posn_list::list(list(numeric)), +> data_var_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> map( +> proc(posn::list(numeric)) +> fprintf(file_name, +> "%s = %a;\n", +> data_var_name(posn,data_var_name_prefix), +> DATA(op(posn))); +> end proc +> , +> posn_list +> ); +> fclose(file_name); +> +> NULL; +> end proc; +print_fetch_data := proc(posn_list::list(list(numeric)), +data_var_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + fprintf(file_name, "%s = %a;\n", + data_var_name(posn, data_var_name_prefix), DATA(op(posn))) + end proc, posn_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C expression to store the interpolation +# coefficients in COEFF(...) expressions, eg +# COEFF(1,-1) = factor * coeffs->coeff_p1_m1; +# +# Arguments: +# posn_list = The list of positions in the molecule. +# coeff_name_prefix = A prefix string for the coefficient names, +# eg "factor * coeffs->coeff_" +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_store_coeffs := +> proc( +> posn_list::list(list(numeric)), +> coeff_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> map( +> proc(posn::list(numeric)) +> fprintf(file_name, +> "%a = %s;\n", +> 'COEFF'(op(posn)), +> coeff_name(posn,coeff_name_prefix)); +> end proc +> , +> posn_list +> ); +> fclose(file_name); +> +> NULL; +> end proc; +print_store_coeffs := proc(posn_list::list(list(numeric)), +coeff_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + fprintf(file_name, "%a = %s;\n", 'COEFF'(op(posn)), + coeff_name(posn, coeff_name_prefix)) + end proc, posn_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a C expression to evaluate a molecule, i.e. +# to compute the molecule as a linear combination of the data values. +# +# Arguments: +# posn_list = The list of positions in the molecule. +# coeff_name_prefix = A prefix string for the coefficient names. +# data_var_name_prefix = A prefix string for the data variable names. +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_evaluate_molecule := +> proc( +> posn_list::list(list(numeric)), +> coeff_name_prefix::string, +> data_var_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> +# list of "coeff*data_var" terms +> map( +> proc(posn::list(numeric)) +> sprintf("%s*%s", +> coeff_name(posn,coeff_name_prefix), +> data_var_name(posn,data_var_name_prefix)); +> end proc +> , +> posn_list +> ); +> +> ListTools[Join](%, "\n + "); +> cat(op(%)); +> fprintf(file_name, " %s;\n", %); +> +> fclose(file_name); +> +> NULL; +> end proc; +print_evaluate_molecule := proc(posn_list::list(list(numeric)), +coeff_name_prefix::string, data_var_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + sprintf("%s*%s", coeff_name(posn, coeff_name_prefix), + data_var_name(posn, data_var_name_prefix)) + end proc, posn_list); + ListTools[Join](%, "\n + "); + cat(op(%)); + fprintf(file_name, " %s;\n", %); + fclose(file_name); + NULL +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes the name of the coefficient of the data at a +# given [m] position, i.e. it encapsulates our naming convention for this. +# +# Arguments: +# posn = (in) The [m] coordinates. +# name_prefix = A prefix string for the coefficient name. +# +# Results: +# The function returns the coefficient, as a Maple string. +# +> coeff_name := +> proc(posn::list(numeric), name_prefix::string) +> cat(name_prefix, sprint_numeric_list(posn)); +> end proc; +coeff_name := proc(posn::list(numeric), name_prefix::string) + cat(name_prefix, sprint_numeric_list(posn)) +end proc + +> +################################################################################ +> +# +# This function computes the name of the variable in which the C code +# will store the input data at a given [m] position, i.e. it encapsulates +# our naming convention for this. +# +# Arguments: +# posn = (in) The [m] coordinates. +# name_prefix = A prefix string for the variable name. +# +# Results: +# The function returns the variable name, as a Maple string. +# +> data_var_name := +> proc(posn::list(numeric), name_prefix::string) +> cat(name_prefix, sprint_numeric_list(posn)); +> end proc; +data_var_name := proc(posn::list(numeric), name_prefix::string) + cat(name_prefix, sprint_numeric_list(posn)) +end proc + +# Maple code to compute lists of point positions in hypercube-shaped molecules +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/common/cube_posns.maple,v 1.3 2002/08/20 16:56:41 jthorn Exp $ +> +################################################################################ +> +# +# 1D interpolation points +# +> posn_list_1d_size2 := hypercube_points([ 0], [+1]); + posn_list_1d_size2 := [[0], [1]] + +> posn_list_1d_size3 := hypercube_points([-1], [+1]); + posn_list_1d_size3 := [[-1], [0], [1]] + +> posn_list_1d_size4 := hypercube_points([-1], [+2]); + posn_list_1d_size4 := [[-1], [0], [1], [2]] + +> posn_list_1d_size5 := hypercube_points([-2], [+2]); + posn_list_1d_size5 := [[-2], [-1], [0], [1], [2]] + +> posn_list_1d_size6 := hypercube_points([-2], [+3]); + posn_list_1d_size6 := [[-2], [-1], [0], [1], [2], [3]] + +> posn_list_1d_size7 := hypercube_points([-3], [+3]); + posn_list_1d_size7 := [[-3], [-2], [-1], [0], [1], [2], [3]] + +> +################################################################################ +> +# +# 2D interpolation points (Fortran ordering) +# +> posn_list_2d_size2 := map(ListTools[Reverse], +> hypercube_points([ 0, 0], [+1,+1])); + posn_list_2d_size2 := [[0, 0], [1, 0], [0, 1], [1, 1]] + +> posn_list_2d_size3 := map(ListTools[Reverse], +> hypercube_points([-1,-1], [+1,+1])); +posn_list_2d_size3 := [[-1, -1], [0, -1], [1, -1], [-1, 0], [0, 0], [1, 0], + + [-1, 1], [0, 1], [1, 1]] + +> posn_list_2d_size4 := map(ListTools[Reverse], +> hypercube_points([-1,-1], [+2,+2])); +posn_list_2d_size4 := [[-1, -1], [0, -1], [1, -1], [2, -1], [-1, 0], [0, 0], + + [1, 0], [2, 0], [-1, 1], [0, 1], [1, 1], [2, 1], [-1, 2], [0, 2], [1, 2], + + [2, 2]] + +> posn_list_2d_size5 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+2,+2])); +posn_list_2d_size5 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [-2, -1], + + [-1, -1], [0, -1], [1, -1], [2, -1], [-2, 0], [-1, 0], [0, 0], [1, 0], + + [2, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], [-2, 2], [-1, 2], [0, 2], + + [1, 2], [2, 2]] + +> posn_list_2d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+3,+3])); +posn_list_2d_size6 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [3, -2], + + [-2, -1], [-1, -1], [0, -1], [1, -1], [2, -1], [3, -1], [-2, 0], [-1, 0], + + [0, 0], [1, 0], [2, 0], [3, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], + + [3, 1], [-2, 2], [-1, 2], [0, 2], [1, 2], [2, 2], [3, 2], [-2, 3], [-1, 3], + + [0, 3], [1, 3], [2, 3], [3, 3]] + +> +################################################################################ +> +# +# 3D interpolation points (Fortran ordering) +# +> posn_list_3d_size2 := map(ListTools[Reverse], +> hypercube_points([ 0, 0, 0], [+1,+1,+1])); +posn_list_3d_size2 := [[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], + + [1, 0, 1], [0, 1, 1], [1, 1, 1]] + +> posn_list_3d_size3 := map(ListTools[Reverse], +> hypercube_points([-1,-1,-1], [+1,+1,+1])); +posn_list_3d_size3 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [-1, 0, -1], + + [0, 0, -1], [1, 0, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], [-1, -1, 0], + + [0, -1, 0], [1, -1, 0], [-1, 0, 0], [0, 0, 0], [1, 0, 0], [-1, 1, 0], + + [0, 1, 0], [1, 1, 0], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [-1, 0, 1], + + [0, 0, 1], [1, 0, 1], [-1, 1, 1], [0, 1, 1], [1, 1, 1]] + +> posn_list_3d_size4 := map(ListTools[Reverse], +> hypercube_points([-1,-1,-1], [+2,+2,+2])); +posn_list_3d_size4 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [2, -1, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [-1, 1, -1], [0, 1, -1], + + [1, 1, -1], [2, 1, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-1, 0, 0], [0, 0, 0], + + [1, 0, 0], [2, 0, 0], [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [-1, -1, 1], [0, -1, 1], + + [1, -1, 1], [2, -1, 1], [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [-1, 2, 1], [0, 2, 1], + + [1, 2, 1], [2, 2, 1], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-1, 1, 2], [0, 1, 2], + + [1, 1, 2], [2, 1, 2], [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2]] + +> posn_list_3d_size5 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+2,+2,+2])); +posn_list_3d_size5 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], [1, -1, -2], + + [2, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], [1, 0, -2], [2, 0, -2], + + [-2, 1, -2], [-1, 1, -2], [0, 1, -2], [1, 1, -2], [2, 1, -2], [-2, 2, -2], + + [-1, 2, -2], [0, 2, -2], [1, 2, -2], [2, 2, -2], [-2, -2, -1], [-1, -2, -1], + + [0, -2, -1], [1, -2, -1], [2, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [-2, 0, -1], [-1, 0, -1], [0, 0, -1], + + [1, 0, -1], [2, 0, -1], [-2, 1, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], + + [2, 1, -1], [-2, 2, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], + + [-2, -2, 0], [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-2, 0, 0], [-1, 0, 0], + + [0, 0, 0], [1, 0, 0], [2, 0, 0], [-2, 1, 0], [-1, 1, 0], [0, 1, 0], + + [1, 1, 0], [2, 1, 0], [-2, 2, 0], [-1, 2, 0], [0, 2, 0], [1, 2, 0], + + [2, 2, 0], [-2, -2, 1], [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], + + [-2, -1, 1], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [-2, 1, 1], [-1, 1, 1], + + [0, 1, 1], [1, 1, 1], [2, 1, 1], [-2, 2, 1], [-1, 2, 1], [0, 2, 1], + + [1, 2, 1], [2, 2, 1], [-2, -2, 2], [-1, -2, 2], [0, -2, 2], [1, -2, 2], + + [2, -2, 2], [-2, -1, 2], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], + + [-2, 0, 2], [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [-2, 2, 2], [-1, 2, 2], + + [0, 2, 2], [1, 2, 2], [2, 2, 2]] + +> posn_list_3d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+3,+3,+3])); +posn_list_3d_size6 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [3, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], + + [1, -1, -2], [2, -1, -2], [3, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], + + [1, 0, -2], [2, 0, -2], [3, 0, -2], [-2, 1, -2], [-1, 1, -2], [0, 1, -2], + + [1, 1, -2], [2, 1, -2], [3, 1, -2], [-2, 2, -2], [-1, 2, -2], [0, 2, -2], + + [1, 2, -2], [2, 2, -2], [3, 2, -2], [-2, 3, -2], [-1, 3, -2], [0, 3, -2], + + [1, 3, -2], [2, 3, -2], [3, 3, -2], [-2, -2, -1], [-1, -2, -1], [0, -2, -1], + + [1, -2, -1], [2, -2, -1], [3, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [3, -1, -1], [-2, 0, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [3, 0, -1], [-2, 1, -1], + + [-1, 1, -1], [0, 1, -1], [1, 1, -1], [2, 1, -1], [3, 1, -1], [-2, 2, -1], + + [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], [3, 2, -1], [-2, 3, -1], + + [-1, 3, -1], [0, 3, -1], [1, 3, -1], [2, 3, -1], [3, 3, -1], [-2, -2, 0], + + [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [3, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [3, -1, 0], [-2, 0, 0], + + [-1, 0, 0], [0, 0, 0], [1, 0, 0], [2, 0, 0], [3, 0, 0], [-2, 1, 0], + + [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [3, 1, 0], [-2, 2, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [3, 2, 0], [-2, 3, 0], + + [-1, 3, 0], [0, 3, 0], [1, 3, 0], [2, 3, 0], [3, 3, 0], [-2, -2, 1], + + [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], [3, -2, 1], [-2, -1, 1], + + [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [3, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [3, 0, 1], [-2, 1, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [3, 1, 1], [-2, 2, 1], + + [-1, 2, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [3, 2, 1], [-2, 3, 1], + + [-1, 3, 1], [0, 3, 1], [1, 3, 1], [2, 3, 1], [3, 3, 1], [-2, -2, 2], + + [-1, -2, 2], [0, -2, 2], [1, -2, 2], [2, -2, 2], [3, -2, 2], [-2, -1, 2], + + [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], [3, -1, 2], [-2, 0, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [3, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [3, 1, 2], [-2, 2, 2], + + [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2], [3, 2, 2], [-2, 3, 2], + + [-1, 3, 2], [0, 3, 2], [1, 3, 2], [2, 3, 2], [3, 3, 2], [-2, -2, 3], + + [-1, -2, 3], [0, -2, 3], [1, -2, 3], [2, -2, 3], [3, -2, 3], [-2, -1, 3], + + [-1, -1, 3], [0, -1, 3], [1, -1, 3], [2, -1, 3], [3, -1, 3], [-2, 0, 3], + + [-1, 0, 3], [0, 0, 3], [1, 0, 3], [2, 0, 3], [3, 0, 3], [-2, 1, 3], + + [-1, 1, 3], [0, 1, 3], [1, 1, 3], [2, 1, 3], [3, 1, 3], [-2, 2, 3], + + [-1, 2, 3], [0, 2, 3], [1, 2, 3], [2, 2, 3], [3, 2, 3], [-2, 3, 3], + + [-1, 3, 3], [0, 3, 3], [1, 3, 3], [2, 3, 3], [3, 3, 3]] + +# Maple code to define Lagrange interpolating functions/coords/coeffs +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple,v 1.3 2002/09/02 10:22:49 jthorn Exp $ +> +################################################################################ +> +# +# 1-D interpolating functions +# +> +> fn_1d_order1 := +> proc(x) +> + c0 + c1*x +> end proc; + fn_1d_order1 := proc(x) c0 + c1*x end proc + +> +> fn_1d_order2 := +> proc(x) +> + c0 + c1*x + c2*x^2 +> end proc; + fn_1d_order2 := proc(x) c0 + c1*x + c2*x^2 end proc + +> +> fn_1d_order3 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 +> end proc; + fn_1d_order3 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 end proc + +> +> fn_1d_order4 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 +> end; + fn_1d_order4 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 end proc + +> +> fn_1d_order5 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 +> end; + fn_1d_order5 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 end proc + +> +> fn_1d_order6 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 +> end; +fn_1d_order6 := + + proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 end proc + +> +######################################## +> +# coordinates for 1-D interpolating functions +> coords_list_1d := [x]; + coords_list_1d := [x] + +> +######################################## +> +# +# coefficients in 1-D interpolating functions +# +> +> coeffs_list_1d_order1 := [c0, c1]; + coeffs_list_1d_order1 := [c0, c1] + +> coeffs_list_1d_order2 := [c0, c1, c2]; + coeffs_list_1d_order2 := [c0, c1, c2] + +> coeffs_list_1d_order3 := [c0, c1, c2, c3]; + coeffs_list_1d_order3 := [c0, c1, c2, c3] + +> coeffs_list_1d_order4 := [c0, c1, c2, c3, c4]; + coeffs_list_1d_order4 := [c0, c1, c2, c3, c4] + +> coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5]; + coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5] + +> coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6]; + coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6] + +> +################################################################################ +> +# +# 2-D interpolating functions (tensor-product) +# +> +> fn_2d_order1 := +> proc(x,y) +> + c01*y + c11*x*y +> + c00 + c10*x +> end proc; + fn_2d_order1 := proc(x, y) c01*y + c11*x*y + c00 + c10*x end proc + +> +> fn_2d_order2 := +> proc(x,y) +> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 +> + c01*y + c11*x*y + c21*x^2*y +> + c00 + c10*x + c20*x^2 +> end proc; +fn_2d_order2 := proc(x, y) + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c01*y + c11*x*y + c21*x^2*y + c00 + + c10*x + c20*x^2 +end proc + +> +> fn_2d_order3 := +> proc(x,y) +> + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 +> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 +> + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +> + c00 + c10*x + c20*x^2 + c30*x^3 +> end proc; +fn_2d_order3 := proc(x, y) + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c02*y^2 + c12*x*y^2 + + c22*x^2*y^2 + c32*x^3*y^2 + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + + c00 + c10*x + c20*x^2 + c30*x^3 +end proc + +> +> fn_2d_order4 := +> proc(x,y) +> + c04*y^4 + c14*x*y^4 + c24*x^2*y^4 + c34*x^3*y^4 + c44*x^4*y^4 +> + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c43*x^4*y^3 +> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 + c42*x^4*y^2 +> + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + c41*x^4*y +> + c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 +> end; +fn_2d_order4 := proc(x, y) + c34*x^3*y^4 + c01*y + c10*x + c02*y^2 + c20*x^2 + c03*y^3 + c30*x^3 + + c04*y^4 + c40*x^4 + c11*x*y + c12*x*y^2 + c22*x^2*y^2 + c21*x^2*y + + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c32*x^3*y^2 + c31*x^3*y + + c14*x*y^4 + c24*x^2*y^4 + c44*x^4*y^4 + c00 + c43*x^4*y^3 + + c42*x^4*y^2 + c41*x^4*y +end proc + +> +######################################## +> +# coordinates for 2-D interpolating functions +> coords_list_2d := [x,y]; + coords_list_2d := [x, y] + +> +######################################## +> +# +# coefficients in 2-D interpolating functions (tensor-product) +# +> +> coeffs_list_2d_order1 := [ +> c01, c11, +> c00, c10 +> ]; + coeffs_list_2d_order1 := [c01, c11, c00, c10] + +> coeffs_list_2d_order2 := [ +> c02, c12, c22, +> c01, c11, c21, +> c00, c10, c20 +> ]; + coeffs_list_2d_order2 := [c02, c12, c22, c01, c11, c21, c00, c10, c20] + +> coeffs_list_2d_order3 := [ +> c03, c13, c23, c33, +> c02, c12, c22, c23, +> c01, c11, c21, c13, +> c00, c10, c20, c30 +> ]; +coeffs_list_2d_order3 := [c03, c13, c23, c33, c02, c12, c22, c23, c01, c11, c21, + + c13, c00, c10, c20, c30] + +> coeffs_list_2d_order4 := [ +> c04, c14, c24, c34, c44, +> c03, c13, c23, c33, c43, +> c02, c12, c22, c32, c42, +> c01, c11, c21, c31, c41, +> c00, c10, c20, c30, c40 +> ]; +coeffs_list_2d_order4 := [c04, c14, c24, c34, c44, c03, c13, c23, c33, c43, c02, + + c12, c22, c32, c42, c01, c11, c21, c31, c41, c00, c10, c20, c30, c40] + +> +################################################################################ +> +# +# 3-D interpolating functions (tensor-product) +# +> +> fn_3d_order1 := +> proc(x,y,z) +# z^1 ------------------- +> + c011 *y*z + c111*x*y*z +> + c001 *z + c101*x *z +# z^0 ------------------- +> + c010 *y + c110*x*y +> + c000 + c100*x +> end proc; +fn_3d_order1 := proc(x, y, z) + c011*y*z + c111*x*y*z + c001*z + c101*x*z + c010*y + c110*x*y + c000 + + c100*x +end proc + +> +> fn_3d_order2 := +> proc(x,y,z) +# z^2 -------------------------------------------------- +> + c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 +> + c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 +> + c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 +# z -------------------------------------------------- +> + c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z +> + c011 *y *z + c111*x *y *z + c211*x^2*y *z +> + c001 *z + c101*x *z + c201*x^2 *z +# z^0 ------------------------------------------------ +> + c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 +> + c010 *y + c110*x *y + c210*x^2*y +> + c000 + c100*x + c200*x^2 +> end proc; +fn_3d_order2 := proc(x, y, z) + c111*x*y*z + c122*x*y^2*z^2 + c222*x^2*y^2*z^2 + c112*x*y*z^2 + + c212*x^2*y*z^2 + c121*x*y^2*z + c221*x^2*y^2*z + c211*x^2*y*z + + c011*y*z + c101*x*z + c110*x*y + c022*y^2*z^2 + c012*y*z^2 + + c102*x*z^2 + c202*x^2*z^2 + c021*y^2*z + c201*x^2*z + c120*x*y^2 + + c220*x^2*y^2 + c210*x^2*y + c001*z + c010*y + c000 + c100*x + + c002*z^2 + c020*y^2 + c200*x^2 +end proc + +> +> fn_3d_order3 := +> proc(x,y,z) +# z^3 --------------------------------------------------------------------- +> + c033 *y^3*z^3 + c133*x *y^3*z^3 + c233*x^2*y^3*z^3 + c333*x^3*y^3*z^3 +> + c023 *y^2*z^3 + c123*x *y^2*z^3 + c223*x^2*y^2*z^3 + c323*x^3*y^2*z^3 +> + c013 *y *z^3 + c113*x *y *z^3 + c213*x^2*y *z^3 + c313*x^3*y *z^3 +> + c003 *z^3 + c103*x *z^3 + c203*x^2 *z^3 + c303*x^3 *z^3 +# z^2 --------------------------------------------------------------------- +> + c032 *y^3*z^2 + c132*x *y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 +> + c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 + c322*x^3*y^2*z^2 +> + c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 + c312*x^3*y *z^2 +> + c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 + c302*x^3 *z^2 +# z --------------------------------------------------------------------- +> + c031 *y^3*z + c131*x *y^3*z + c231*x^2*y^3*z + c331*x^3*y^3*z +> + c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z + c321*x^3*y^2*z +> + c011 *y *z + c111*x *y *z + c211*x^2*y *z + c311*x^3*y *z +> + c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z +# z^0 --------------------------------------------------------------------- +> + c030 *y^3 + c130*x *y^3 + c230*x^2*y^3 + c330*x^3*y^3 +> + c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 + c320*x^3*y^2 +> + c010 *y + c110*x *y + c210*x^2*y + c310*x^3*y +> + c000 + c100*x + c200*x^2 + c300*x^3 +> end proc; +fn_3d_order3 := proc(x, y, z) + c330*x^3*y^3 + c031*y^3*z + c103*x*z^3 + c111*x*y*z + c122*x*y^2*z^2 + + c222*x^2*y^2*z^2 + c112*x*y*z^2 + c212*x^2*y*z^2 + c121*x*y^2*z + + c221*x^2*y^2*z + c211*x^2*y*z + c133*x*y^3*z^3 + c233*x^2*y^3*z^3 + + c333*x^3*y^3*z^3 + c123*x*y^2*z^3 + c223*x^2*y^2*z^3 + + c323*x^3*y^2*z^3 + c113*x*y*z^3 + c213*x^2*y*z^3 + c313*x^3*y*z^3 + + c132*x*y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 + + c322*x^3*y^2*z^2 + c312*x^3*y*z^2 + c131*x*y^3*z + c231*x^2*y^3*z + + c331*x^3*y^3*z + c321*x^3*y^2*z + c311*x^3*y*z + c011*y*z + c101*x*z + + c110*x*y + c022*y^2*z^2 + c012*y*z^2 + c102*x*z^2 + c202*x^2*z^2 + + c021*y^2*z + c201*x^2*z + c120*x*y^2 + c220*x^2*y^2 + c210*x^2*y + + c033*y^3*z^3 + c023*y^2*z^3 + c013*y*z^3 + c203*x^2*z^3 + + c303*x^3*z^3 + c032*y^3*z^2 + c302*x^3*z^2 + c301*x^3*z + c130*x*y^3 + + c230*x^2*y^3 + c320*x^3*y^2 + c310*x^3*y + c001*z + c010*y + c000 + + c100*x + c002*z^2 + c020*y^2 + c200*x^2 + c003*z^3 + c030*y^3 + + c300*x^3 +end proc + +> +> fn_3d_order4 := +> proc(x,y,z) +# z^4 ---------------------------------------------------------------------------------------- +> + c044 *y^4*z^4 + c144*x *y^4*z^4 + c244*x^2*y^4*z^4 + c344*x^3*y^4*z^4 + c444*x^4*y^4*z^4 +> + c034 *y^3*z^4 + c134*x *y^3*z^4 + c234*x^2*y^3*z^4 + c334*x^3*y^3*z^4 + c434*x^4*y^3*z^4 +> + c024 *y^2*z^4 + c124*x *y^2*z^4 + c224*x^2*y^2*z^4 + c324*x^3*y^2*z^4 + c424*x^4*y^2*z^4 +> + c014 *y *z^4 + c114*x *y *z^4 + c214*x^2*y *z^4 + c314*x^3*y *z^4 + c414*x^4*y *z^4 +> + c004 *z^4 + c104*x *z^4 + c204*x^2 *z^4 + c304*x^3 *z^4 + c404*x^4 *z^4 +# z^3 ---------------------------------------------------------------------------------------- +> + c043 *y^4*z^3 + c143*x *y^4*z^3 + c243*x^2*y^4*z^3 + c343*x^3*y^4*z^3 + c443*x^4*y^4*z^3 +> + c033 *y^3*z^3 + c133*x *y^3*z^3 + c233*x^2*y^3*z^3 + c333*x^3*y^3*z^3 + c433*x^4*y^3*z^3 +> + c023 *y^2*z^3 + c123*x *y^2*z^3 + c223*x^2*y^2*z^3 + c323*x^3*y^2*z^3 + c423*x^4*y^2*z^3 +> + c013 *y *z^3 + c113*x *y *z^3 + c213*x^2*y *z^3 + c313*x^3*y *z^3 + c413*x^4*y *z^3 +> + c003 *z^3 + c103*x *z^3 + c203*x^2 *z^3 + c303*x^3 *z^3 + c403*x^4 *z^3 +# z^2 ---------------------------------------------------------------------------------------- +> + c042 *y^4*z^2 + c142*x *y^4*z^2 + c242*x^2*y^4*z^2 + c342*x^3*y^4*z^2 + c442*x^4*y^4*z^2 +> + c032 *y^3*z^2 + c132*x *y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 + c432*x^4*y^3*z^2 +> + c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 + c322*x^3*y^2*z^2 + c422*x^4*y^2*z^2 +> + c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 + c312*x^3*y *z^2 + c412*x^4*y *z^2 +> + c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 + c302*x^3 *z^2 + c402*x^4 *z^2 +# z ---------------------------------------------------------------------------------------- +> + c041 *y^4*z + c141*x *y^4*z + c241*x^2*y^4*z + c341*x^3*y^4*z + c441*x^4*y^4*z +> + c031 *y^3*z + c131*x *y^3*z + c231*x^2*y^3*z + c331*x^3*y^3*z + c431*x^4*y^3*z +> + c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z + c321*x^3*y^2*z + c421*x^4*y^2*z +> + c011 *y *z + c111*x *y *z + c211*x^2*y *z + c311*x^3*y *z + c411*x^4*y *z +> + c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z + c401*x^4 *z +# z^0 ---------------------------------------------------------------------------------------- +> + c040 *y^4 + c140*x *y^4 + c240*x^2*y^4 + c340*x^3*y^4 + c440*x^4*y^4 +> + c030 *y^3 + c130*x *y^3 + c230*x^2*y^3 + c330*x^3*y^3 + c430*x^4*y^3 +> + c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 + c320*x^3*y^2 + c420*x^4*y^2 +> + c010 *y + c110*x *y + c210*x^2*y + c310*x^3*y + c410*x^4*y +> + c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 +> end; +fn_3d_order4 := proc(x, y, z) + c104*x*z^4 + c330*x^3*y^3 + c042*y^4*z^2 + c031*y^3*z + c103*x*z^3 + + c304*x^3*z^4 + c024*y^2*z^4 + c111*x*y*z + c122*x*y^2*z^2 + + c222*x^2*y^2*z^2 + c112*x*y*z^2 + c212*x^2*y*z^2 + c121*x*y^2*z + + c221*x^2*y^2*z + c211*x^2*y*z + c133*x*y^3*z^3 + c233*x^2*y^3*z^3 + + c333*x^3*y^3*z^3 + c123*x*y^2*z^3 + c223*x^2*y^2*z^3 + + c323*x^3*y^2*z^3 + c113*x*y*z^3 + c213*x^2*y*z^3 + c313*x^3*y*z^3 + + c132*x*y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 + + c322*x^3*y^2*z^2 + c312*x^3*y*z^2 + c131*x*y^3*z + c231*x^2*y^3*z + + c331*x^3*y^3*z + c321*x^3*y^2*z + c311*x^3*y*z + c144*x*y^4*z^4 + + c244*x^2*y^4*z^4 + c344*x^3*y^4*z^4 + c444*x^4*y^4*z^4 + + c134*x*y^3*z^4 + c234*x^2*y^3*z^4 + c334*x^3*y^3*z^4 + + c434*x^4*y^3*z^4 + c124*x*y^2*z^4 + c224*x^2*y^2*z^4 + + c324*x^3*y^2*z^4 + c424*x^4*y^2*z^4 + c114*x*y*z^4 + c214*x^2*y*z^4 + + c314*x^3*y*z^4 + c414*x^4*y*z^4 + c143*x*y^4*z^3 + c243*x^2*y^4*z^3 + + c343*x^3*y^4*z^3 + c443*x^4*y^4*z^3 + c433*x^4*y^3*z^3 + + c423*x^4*y^2*z^3 + c413*x^4*y*z^3 + c142*x*y^4*z^2 + + c242*x^2*y^4*z^2 + c011*y*z + c101*x*z + c110*x*y + c022*y^2*z^2 + + c012*y*z^2 + c102*x*z^2 + c202*x^2*z^2 + c021*y^2*z + c201*x^2*z + + c120*x*y^2 + c220*x^2*y^2 + c210*x^2*y + c033*y^3*z^3 + c023*y^2*z^3 + + c013*y*z^3 + c203*x^2*z^3 + c303*x^3*z^3 + c032*y^3*z^2 + + c302*x^3*z^2 + c301*x^3*z + c130*x*y^3 + c230*x^2*y^3 + c320*x^3*y^2 + + c310*x^3*y + c001*z + c010*y + c000 + c100*x + c002*z^2 + c020*y^2 + + c200*x^2 + c003*z^3 + c030*y^3 + c300*x^3 + c004*z^4 + c044*y^4*z^4 + + c034*y^3*z^4 + c014*y*z^4 + c204*x^2*z^4 + c404*x^4*z^4 + + c043*y^4*z^3 + c403*x^4*z^3 + c402*x^4*z^2 + c041*y^4*z + c401*x^4*z + + c140*x*y^4 + c240*x^2*y^4 + c340*x^3*y^4 + c440*x^4*y^4 + + c430*x^4*y^3 + c420*x^4*y^2 + c410*x^4*y + c342*x^3*y^4*z^2 + + c442*x^4*y^4*z^2 + c432*x^4*y^3*z^2 + c422*x^4*y^2*z^2 + + c412*x^4*y*z^2 + c141*x*y^4*z + c241*x^2*y^4*z + c341*x^3*y^4*z + + c441*x^4*y^4*z + c431*x^4*y^3*z + c421*x^4*y^2*z + c411*x^4*y*z + + c040*y^4 + c400*x^4 +end proc + +> +######################################## +> +# coordinates for 3-D interpolating functions +> coords_list_3d := [x,y,z]; + coords_list_3d := [x, y, z] + +> +######################################## +> +# +# coefficients in 3-D interpolating functions +# +> +> coeffs_list_3d_order1 := [ +> # z^1 ----- +> c011, c111, +> c001, c101, +> # z^0 ----- +> c010, c110, +> c000, c100 +> ]; + coeffs_list_3d_order1 := [c011, c111, c001, c101, c010, c110, c000, c100] + +> coeffs_list_3d_order2 := [ +> # z^2 ----------- +> c022, c122, c222, +> c012, c112, c212, +> c002, c102, c202, +> # z^1 ----------- +> c021, c121, c221, +> c011, c111, c211, +> c001, c101, c201, +> # z^0 ----------- +> c020, c120, c220, +> c010, c110, c210, +> c000, c100, c200 +> ]; +coeffs_list_3d_order2 := [c022, c122, c222, c012, c112, c212, c002, c102, c202, + + c021, c121, c221, c011, c111, c211, c001, c101, c201, c020, c120, c220, + + c010, c110, c210, c000, c100, c200] + +> coeffs_list_3d_order3 := [ +> # z^3 ----------------- +> c033, c133, c233, c333, +> c023, c123, c223, c323, +> c013, c113, c213, c313, +> c003, c103, c203, c303, +> # z^2 ----------------- +> c032, c132, c232, c332, +> c022, c122, c222, c322, +> c012, c112, c212, c312, +> c002, c102, c202, c302, +> # z^1 ----------------- +> c031, c131, c231, c331, +> c021, c121, c221, c321, +> c011, c111, c211, c311, +> c001, c101, c201, c301, +> # z^0 ----------------- +> c030, c130, c230, c330, +> c020, c120, c220, c320, +> c010, c110, c210, c310, +> c000, c100, c200, c300 +> ]; +coeffs_list_3d_order3 := [c033, c133, c233, c333, c023, c123, c223, c323, c013, + + c113, c213, c313, c003, c103, c203, c303, c032, c132, c232, c332, c022, + + c122, c222, c322, c012, c112, c212, c312, c002, c102, c202, c302, c031, + + c131, c231, c331, c021, c121, c221, c321, c011, c111, c211, c311, c001, + + c101, c201, c301, c030, c130, c230, c330, c020, c120, c220, c320, c010, + + c110, c210, c310, c000, c100, c200, c300] + +> coeffs_list_3d_order4 := [ +> # z^4 ----------------------- +> c044, c144, c244, c344, c444, +> c034, c134, c234, c334, c434, +> c024, c124, c224, c324, c424, +> c014, c114, c214, c314, c414, +> c004, c104, c204, c304, c404, +> # z^3 ----------------------- +> c043, c143, c243, c343, c443, +> c033, c133, c233, c333, c433, +> c023, c123, c223, c323, c423, +> c013, c113, c213, c313, c413, +> c003, c103, c203, c303, c403, +> # z^2 ----------------------- +> c042, c142, c242, c342, c442, +> c032, c132, c232, c332, c432, +> c022, c122, c222, c322, c422, +> c012, c112, c212, c312, c412, +> c002, c102, c202, c302, c402, +> # z^1 ----------------------- +> c041, c141, c241, c341, c441, +> c031, c131, c231, c331, c431, +> c021, c121, c221, c321, c421, +> c011, c111, c211, c311, c411, +> c001, c101, c201, c301, c401, +> # z^0 ----------------------- +> c040, c140, c240, c340, c440, +> c030, c130, c230, c330, c430, +> c020, c120, c220, c320, c420, +> c010, c110, c210, c310, c410, +> c000, c100, c200, c300, c400 +> ]; +coeffs_list_3d_order4 := [c044, c144, c244, c344, c444, c034, c134, c234, c334, + + c434, c024, c124, c224, c324, c424, c014, c114, c214, c314, c414, c004, + + c104, c204, c304, c404, c043, c143, c243, c343, c443, c033, c133, c233, + + c333, c433, c023, c123, c223, c323, c423, c013, c113, c213, c313, c413, + + c003, c103, c203, c303, c403, c042, c142, c242, c342, c442, c032, c132, + + c232, c332, c432, c022, c122, c222, c322, c422, c012, c112, c212, c312, + + c412, c002, c102, c202, c302, c402, c041, c141, c241, c341, c441, c031, + + c131, c231, c331, c431, c021, c121, c221, c321, c421, c011, c111, c211, + + c311, c411, c001, c101, c201, c301, c401, c040, c140, c240, c340, c440, + + c030, c130, c230, c330, c430, c020, c120, c220, c320, c420, c010, c110, + + c210, c310, c410, c000, c100, c200, c300, c400] + +> +################################################################################ +# 2d.maple -- compute Lagrange interpolation coefficients in 2-D +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/2d.maple,v 1.3 2002/09/02 10:22:36 jthorn Exp $ +> +################################################################################ +> +# +# 2d, cube, order=1, smoothing=0 (size=2) +# +> +# interpolating polynomial +> interp_2d_cube_order1_smooth0 +> := Lagrange_polynomial_interpolant(fn_2d_order1, coeffs_list_2d_order1, +> coords_list_2d, posn_list_2d_size2); +interp_2d_cube_order1_smooth0 := (-DATA(0, 0) + DATA(0, 1)) y + + + (-DATA(1, 0) + DATA(0, 0) + DATA(1, 1) - DATA(0, 1)) x y + DATA(0, 0) + + + (DATA(1, 0) - DATA(0, 0)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_2d_size2); +[COEFF(0, 0) = x y + 1 - y - x, COEFF(1, 0) = x - x y, COEFF(0, 1) = y - x y, + + COEFF(1, 1) = x y] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c"); +bytes used=1009312, alloc=917336, time=0.09 +> +# d/dx +> simplify( diff(interp_2d_cube_order1_smooth0,x) ); +-y DATA(1, 0) + y DATA(0, 0) + y DATA(1, 1) - y DATA(0, 1) + DATA(1, 0) + + - DATA(0, 0) + +> coeffs_as_lc_of_data(%, posn_list_2d_size2); + [COEFF(0, 0) = y - 1, COEFF(1, 0) = -y + 1, COEFF(0, 1) = -y, COEFF(1, 1) = y] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c"); +> +# d/dy +> simplify( diff(interp_2d_cube_order1_smooth0,y) ); +-DATA(0, 0) + DATA(0, 1) - x DATA(1, 0) + x DATA(0, 0) + x DATA(1, 1) + + - x DATA(0, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size2); + [COEFF(0, 0) = x - 1, COEFF(1, 0) = -x, COEFF(0, 1) = 1 - x, COEFF(1, 1) = x] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c"); +> +################################################################################ +> +# +# 2d, cube, order=2, smoothing=0 (size=3) +# +> +# interpolating polynomial +> interp_2d_cube_order2_smooth0 +> := Lagrange_polynomial_interpolant(fn_2d_order2, coeffs_list_2d_order2, +> coords_list_2d, posn_list_2d_size3); +bytes used=2009852, alloc=1376004, time=0.15 +interp_2d_cube_order2_smooth0 := + + 2 + (-DATA(0, 0) + 1/2 DATA(0, -1) + 1/2 DATA(0, 1)) y + (1/4 DATA(1, 1) + + - 1/4 DATA(-1, -1) + 1/4 DATA(1, -1) - 1/4 DATA(-1, 1) + 1/2 DATA(-1, 0) + + 2 + - 1/2 DATA(1, 0)) x y + (1/4 DATA(-1, 1) - 1/2 DATA(-1, 0) + + - 1/2 DATA(1, 0) + DATA(0, 0) + 1/4 DATA(-1, -1) + 1/4 DATA(1, -1) + + 2 2 + + 1/4 DATA(1, 1) - 1/2 DATA(0, -1) - 1/2 DATA(0, 1)) x y + + + (- 1/2 DATA(0, -1) + 1/2 DATA(0, 1)) y + + + (1/4 DATA(1, 1) + 1/4 DATA(-1, -1) - 1/4 DATA(1, -1) - 1/4 DATA(-1, 1)) x y + + + (1/4 DATA(1, 1) - 1/4 DATA(-1, -1) - 1/4 DATA(1, -1) + 1/4 DATA(-1, 1) + + 2 + + 1/2 DATA(0, -1) - 1/2 DATA(0, 1)) x y + DATA(0, 0) + + + (- 1/2 DATA(-1, 0) + 1/2 DATA(1, 0)) x + + 2 + + (1/2 DATA(-1, 0) + 1/2 DATA(1, 0) - DATA(0, 0)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_2d_size3); + 2 2 2 2 +[COEFF(-1, -1) = - 1/4 x y - 1/4 x y + 1/4 x y + 1/4 x y , + + 2 2 2 2 + COEFF(0, -1) = 1/2 y - 1/2 x y - 1/2 y + 1/2 x y, + + 2 2 2 2 + COEFF(1, -1) = 1/4 x y - 1/4 x y + 1/4 x y - 1/4 x y, + + 2 2 2 2 + COEFF(-1, 0) = 1/2 x y + 1/2 x - 1/2 x - 1/2 x y , + + 2 2 2 2 + COEFF(0, 0) = -y + x y + 1 - x , + + 2 2 2 2 + COEFF(1, 0) = 1/2 x - 1/2 x y + 1/2 x - 1/2 x y , + + 2 2 2 2 + COEFF(-1, 1) = - 1/4 x y - 1/4 x y + 1/4 x y + 1/4 x y , + + 2 2 2 2 + COEFF(0, 1) = 1/2 y - 1/2 x y - 1/2 x y + 1/2 y, + + 2 2 2 2 + COEFF(1, 1) = 1/4 x y + 1/4 x y + 1/4 x y + 1/4 x y ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c"); +bytes used=3010044, alloc=1638100, time=0.21 +bytes used=4010200, alloc=1703624, time=0.29 +> +# d/dx +> simplify( diff(interp_2d_cube_order2_smooth0,x) ); +bytes used=5010460, alloc=1703624, time=0.36 + 2 +1/2 DATA(1, 0) + 1/2 x y DATA(-1, -1) + 1/2 x y DATA(1, 1) + + - 1/2 x y DATA(-1, -1) - 1/2 x y DATA(1, -1) + 1/2 x y DATA(-1, 1) + + 2 + + x y DATA(0, -1) - x y DATA(0, 1) + 1/2 x y DATA(-1, 1) + + 2 2 2 + - x y DATA(-1, 0) - x y DATA(1, 0) + 2 x y DATA(0, 0) + + 2 2 2 + + 1/2 x y DATA(1, -1) + 1/2 x y DATA(1, 1) - x y DATA(0, -1) + + 2 2 + - x y DATA(0, 1) - 1/2 DATA(-1, 0) - 1/2 y DATA(1, 0) + + + 1/4 y DATA(-1, -1) - 1/4 y DATA(1, -1) - 1/4 y DATA(-1, 1) + + 2 2 + + 1/4 y DATA(1, 1) + 1/4 y DATA(1, 1) - 1/4 y DATA(-1, -1) + + 2 2 2 + + 1/4 y DATA(1, -1) - 1/4 y DATA(-1, 1) + 1/2 y DATA(-1, 0) + + + x DATA(-1, 0) - 2 x DATA(0, 0) + x DATA(1, 0) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); + 2 2 2 +[COEFF(-1, -1) = 1/4 y + 1/2 x y - 1/2 x y - 1/4 y , COEFF(0, -1) = x y - x y , + + 2 2 + COEFF(1, -1) = 1/2 x y + 1/4 y - 1/2 x y - 1/4 y, + + 2 2 2 + COEFF(-1, 0) = x + 1/2 y - x y - 1/2, COEFF(0, 0) = -2 x + 2 x y , + + 2 2 + COEFF(1, 0) = - 1/2 y + x - x y + 1/2, + + 2 2 + COEFF(-1, 1) = - 1/4 y + 1/2 x y - 1/4 y + 1/2 x y , + + 2 + COEFF(0, 1) = -x y - x y , + + 2 2 + COEFF(1, 1) = 1/2 x y + 1/2 x y + 1/4 y + 1/4 y] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c"); +bytes used=6011072, alloc=1769148, time=0.42 +> +# d/dy +> simplify( diff(interp_2d_cube_order2_smooth0,y) ); +bytes used=7011376, alloc=1769148, time=0.49 +1/2 DATA(0, 1) + 1/2 x y DATA(1, 1) - 1/2 x y DATA(-1, -1) + + + 1/2 x y DATA(1, -1) - 1/2 x y DATA(-1, 1) - 1/2 DATA(0, -1) + + 2 2 2 + - x y DATA(1, 0) + 1/2 x y DATA(1, 1) - x y DATA(0, 1) + + 2 + - x y DATA(0, -1) - x y DATA(1, 0) + x y DATA(-1, 0) + 1/4 x DATA(1, 1) + + + 1/4 x DATA(-1, -1) - 1/4 x DATA(1, -1) - 1/4 x DATA(-1, 1) + + 2 2 2 + + 1/4 x DATA(1, 1) - 1/4 x DATA(-1, -1) - 1/4 x DATA(1, -1) + + 2 2 2 + + 1/4 x DATA(-1, 1) + 1/2 x DATA(0, -1) - 1/2 x DATA(0, 1) + + 2 + - 2 y DATA(0, 0) + y DATA(0, -1) + y DATA(0, 1) + 2 x y DATA(0, 0) + + 2 2 2 + + 1/2 x y DATA(-1, 1) + 1/2 x y DATA(1, -1) + 1/2 x y DATA(-1, -1) + + 2 + - x y DATA(-1, 0) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); + 2 2 +[COEFF(-1, -1) = - 1/2 x y + 1/2 x y - 1/4 x + 1/4 x, + + 2 2 + COEFF(0, -1) = -x y - 1/2 + 1/2 x + y, + + 2 2 + COEFF(1, -1) = 1/2 x y + 1/2 x y - 1/4 x - 1/4 x, + + 2 2 + COEFF(-1, 0) = x y - x y, COEFF(0, 0) = -2 y + 2 x y, + + 2 + COEFF(1, 0) = -x y - x y, + + 2 2 + COEFF(-1, 1) = 1/2 x y + 1/4 x - 1/2 x y - 1/4 x, + + 2 2 + COEFF(0, 1) = 1/2 - 1/2 x - x y + y, + + 2 2 + COEFF(1, 1) = 1/4 x + 1/2 x y + 1/2 x y + 1/4 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c"); +bytes used=8011672, alloc=1769148, time=0.57 +> +# d^2/dx^2 +> simplify( diff(interp_2d_cube_order2_smooth0,x,x) ); + 2 2 2 2 +1/2 y DATA(-1, 1) - y DATA(-1, 0) - y DATA(1, 0) + 2 y DATA(0, 0) + + 2 2 2 + + 1/2 y DATA(-1, -1) + 1/2 y DATA(1, -1) + 1/2 y DATA(1, 1) + + 2 2 + - y DATA(0, -1) - y DATA(0, 1) + 1/2 y DATA(1, 1) - 1/2 y DATA(-1, -1) + + - 1/2 y DATA(1, -1) + 1/2 y DATA(-1, 1) + y DATA(0, -1) - y DATA(0, 1) + + + DATA(-1, 0) + DATA(1, 0) - 2 DATA(0, 0) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); + 2 2 +[COEFF(-1, -1) = - 1/2 y + 1/2 y , COEFF(0, -1) = y - y , + + 2 2 + COEFF(1, -1) = - 1/2 y + 1/2 y , COEFF(-1, 0) = -y + 1, + + 2 2 + COEFF(0, 0) = 2 y - 2, COEFF(1, 0) = -y + 1, + + 2 2 + COEFF(-1, 1) = 1/2 y + 1/2 y, COEFF(0, 1) = -y - y, + + 2 + COEFF(1, 1) = 1/2 y + 1/2 y] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c"); +bytes used=9011872, alloc=1834672, time=0.66 +> +# d^2/dxdy +> simplify( diff(interp_2d_cube_order2_smooth0,x,y) ); +1/4 DATA(1, 1) - 2 x y DATA(0, -1) - 2 x y DATA(0, 1) + x y DATA(-1, 1) + + - 2 x y DATA(-1, 0) - 2 x y DATA(1, 0) + 4 x y DATA(0, 0) + + + x y DATA(-1, -1) + x y DATA(1, -1) + x y DATA(1, 1) + 1/2 y DATA(1, 1) + + - 1/2 y DATA(-1, -1) + 1/2 y DATA(1, -1) - 1/2 y DATA(-1, 1) + + + 1/4 DATA(-1, -1) - 1/4 DATA(1, -1) - 1/4 DATA(-1, 1) + x DATA(0, -1) + + - x DATA(0, 1) + 1/2 x DATA(1, 1) - 1/2 x DATA(-1, -1) - 1/2 x DATA(1, -1) + + + 1/2 x DATA(-1, 1) + y DATA(-1, 0) - y DATA(1, 0) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); +[COEFF(-1, -1) = - 1/2 y + x y - 1/2 x + 1/4, COEFF(0, -1) = -2 x y + x, + + COEFF(1, -1) = - 1/2 x - 1/4 + x y + 1/2 y, COEFF(-1, 0) = -2 x y + y, + + COEFF(0, 0) = 4 x y, COEFF(1, 0) = -y - 2 x y, + + COEFF(-1, 1) = x y - 1/2 y - 1/4 + 1/2 x, COEFF(0, 1) = -2 x y - x, + + COEFF(1, 1) = 1/4 + x y + 1/2 x + 1/2 y] + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c"); +bytes used=10012088, alloc=1834672, time=0.74 +> +# d^2/dy^2 +> simplify( diff(interp_2d_cube_order2_smooth0,y,y) ); +-2 DATA(0, 0) + DATA(0, -1) + DATA(0, 1) + 1/2 x DATA(1, 1) + + - 1/2 x DATA(-1, -1) + 1/2 x DATA(1, -1) - 1/2 x DATA(-1, 1) + + 2 2 + + x DATA(-1, 0) - x DATA(1, 0) + 1/2 x DATA(-1, 1) - x DATA(-1, 0) + + 2 2 2 + - x DATA(1, 0) + 2 x DATA(0, 0) + 1/2 x DATA(-1, -1) + + 2 2 2 2 + + 1/2 x DATA(1, -1) + 1/2 x DATA(1, 1) - x DATA(0, -1) - x DATA(0, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); + 2 2 +[COEFF(-1, -1) = 1/2 x - 1/2 x, COEFF(0, -1) = 1 - x , + + 2 2 + COEFF(1, -1) = 1/2 x + 1/2 x , COEFF(-1, 0) = -x + x, + + 2 2 + COEFF(0, 0) = 2 x - 2, COEFF(1, 0) = -x - x , + + 2 2 + COEFF(-1, 1) = 1/2 x - 1/2 x, COEFF(0, 1) = 1 - x , + + 2 + COEFF(1, 1) = 1/2 x + 1/2 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c"); +bytes used=11012264, alloc=1834672, time=0.82 +> +################################################################################ +> +# +# 2d, cube, order=3, smoothing=0 (size=4) +# +> +# interpolating polynomial +> interp_2d_cube_order3_smooth0 +> := Lagrange_polynomial_interpolant(fn_2d_order3, coeffs_list_2d_order3, +> coords_list_2d, posn_list_2d_size4); +bytes used=12012452, alloc=1834672, time=0.88 +bytes used=13012804, alloc=1900196, time=0.94 +bytes used=14014276, alloc=1900196, time=0.99 +bytes used=15014880, alloc=1965720, time=1.05 +bytes used=16015128, alloc=1965720, time=1.12 +bytes used=17015368, alloc=1965720, time=1.18 +bytes used=18015556, alloc=1965720, time=1.25 +bytes used=19016348, alloc=1965720, time=1.31 +bytes used=20016508, alloc=1965720, time=1.38 +bytes used=21016664, alloc=1965720, time=1.44 +bytes used=22016880, alloc=1965720, time=1.51 +bytes used=23019452, alloc=1965720, time=1.57 +bytes used=24021724, alloc=1965720, time=1.63 +bytes used=25022340, alloc=1965720, time=1.69 +interp_2d_cube_order3_smooth0 := (1/8 DATA(2, 1) - 1/4 DATA(2, 0) + + + 1/8 DATA(2, -1) - 3/2 c32 + 1/4 DATA(0, 0) + 1/4 DATA(1, 0) + + - 1/8 DATA(0, 1) - 1/8 DATA(1, 1) + 1/8 DATA(-1, -1) - 1/8 DATA(0, -1) + + 2 2 / + - 1/8 DATA(1, -1) - 1/4 DATA(-1, 0) + 1/8 DATA(-1, 1)) x y + | + \ + + 11 + - 1/120 DATA(2, 2) - 7/120 DATA(1, 2) + --- DATA(-1, 2) - 1/40 DATA(0, 2) + 120 + + 13 + + 1/20 DATA(2, 1) - 1/40 DATA(2, 0) - 1/60 DATA(2, -1) - -- c31 + 10 + + - 3/40 DATA(0, 0) - 7/40 DATA(1, 0) + 3/20 DATA(0, 1) + 7/20 DATA(1, 1) + + 11 11 + + -- DATA(-1, -1) - 1/20 DATA(0, -1) - 7/60 DATA(1, -1) + -- DATA(-1, 0) + 60 40 + + 11 \ + - -- DATA(-1, 1)| x y + (- 1/24 DATA(2, 2) + 1/24 DATA(1, 2) + 20 / + + - 1/24 DATA(-1, 2) + 1/24 DATA(0, 2) + 1/4 DATA(2, 1) - 1/8 DATA(2, 0) + + - 1/12 DATA(2, -1) - 3/2 c31 + 1/8 DATA(0, 0) + 1/8 DATA(1, 0) + + - 1/4 DATA(0, 1) - 1/4 DATA(1, 1) - 1/12 DATA(-1, -1) + 1/12 DATA(0, -1) + + 2 + + 1/12 DATA(1, -1) - 1/8 DATA(-1, 0) + 1/4 DATA(-1, 1)) x y + + + 3/2000 DATA(2, 2) - 9/2000 DATA(1, 2) - 3/2000 DATA(-1, 2) + + 87 201 111 + + 9/2000 DATA(0, 2) + ---- DATA(2, 1) - ---- DATA(2, 0) + ---- DATA(2, -1) + 2000 2000 2000 + + 3 3 2 / 53 409 + + c31 x y + c32 x y + |- ---- DATA(2, 2) + ---- DATA(1, 2) + \ 3000 3000 + + 197 53 31 101 + - ---- DATA(-1, 2) - ---- DATA(0, 2) - ---- DATA(2, 1) + ---- DATA(2, 0) + 3000 1000 1500 3000 + + 13 91 101 + + 7/1500 DATA(2, -1) + -- c32 + --- c31 + ---- DATA(0, 0) + 25 250 1000 + + 149 31 47 59 + + ---- DATA(1, 0) - --- DATA(0, 1) - --- DATA(1, 1) + --- DATA(-1, -1) + 1000 500 250 750 + + 73 851 203 + + 7/500 DATA(0, -1) - --- DATA(1, -1) - ---- DATA(-1, 0) + --- DATA(-1, 1) + 750 3000 750 + + \ 3 / 29 43 + | x y + |7/600 DATA(2, 2) + --- DATA(1, 2) + --- DATA(-1, 2) + / \ 600 600 + + 79 27 + - --- DATA(0, 2) - 3/25 DATA(2, 1) + --- DATA(2, 0) - 2/75 DATA(2, -1) + 600 200 + + 21 19 31 + + 3/5 c32 + -- c31 - --- DATA(0, 0) - --- DATA(1, 0) + 7/50 DATA(0, 1) + 50 200 200 + + 11 17 13 + + --- DATA(1, 1) - --- DATA(-1, -1) + --- DATA(0, -1) - 1/300 DATA(1, -1) + 100 300 150 + + 23 13 \ 2 3 + + --- DATA(-1, 0) - --- DATA(-1, 1)| x y + (1/50 DATA(2, 2) + 200 100 / + + - 3/50 DATA(1, 2) - 1/50 DATA(-1, 2) + 3/50 DATA(0, 2) - 1/300 DATA(2, 1) + + - 1/150 DATA(2, 0) - 1/100 DATA(2, -1) - 2/5 c32 - 7/25 c31 + + - 1/50 DATA(0, 0) + 1/50 DATA(1, 0) - 1/100 DATA(0, 1) + 1/100 DATA(1, 1) + + + 1/100 DATA(-1, -1) - 3/100 DATA(0, -1) + 3/100 DATA(1, -1) + + 3 3 / + + 1/150 DATA(-1, 0) + 1/300 DATA(-1, 1)) x y + |1/40 DATA(2, 1) + \ + + 13 + - 1/20 DATA(2, 0) + 1/40 DATA(2, -1) - -- c32 - 3/20 DATA(0, 0) + 10 + + 11 + - 7/20 DATA(1, 0) + 3/40 DATA(0, 1) + 7/40 DATA(1, 1) - -- DATA(-1, -1) + 40 + + 11 11 \ + + 3/40 DATA(0, -1) + 7/40 DATA(1, -1) + -- DATA(-1, 0) - -- DATA(-1, 1)| x + 20 40 / + + 2 63 27 1397 603 + y - --- c32 + --- c31 + ---- DATA(0, 0) + ---- DATA(1, 0) + 100 500 2000 2000 + + 261 261 / + + ---- DATA(0, 1) - ---- DATA(1, 1) + |- 1/400 DATA(2, 2) + 2000 2000 \ + + 29 + + 3/400 DATA(1, 2) + 1/400 DATA(-1, 2) - 3/400 DATA(0, 2) - --- DATA(2, 1) + 400 + + 67 37 21 199 + + --- DATA(2, 0) - --- DATA(2, -1) + -- c32 - 9/100 c31 - --- DATA(0, 0) + 400 400 20 400 + + 87 87 37 + - 1/400 DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1) + --- DATA(-1, -1) + 400 400 400 + + 111 111 133 29 \ + - --- DATA(0, -1) + --- DATA(1, -1) + --- DATA(-1, 0) + --- DATA(-1, 1)| + 400 400 400 400 / + + 2 / + x + |1/600 DATA(2, 2) - 1/200 DATA(1, 2) - 1/600 DATA(-1, 2) + \ + + 29 11 37 + + 1/200 DATA(0, 2) + --- DATA(2, 1) + --- DATA(2, 0) + --- DATA(2, -1) + 600 200 600 + + 33 33 29 + - 7/10 c32 + 3/50 c31 + --- DATA(0, 0) - --- DATA(1, 0) + --- DATA(0, 1) + 200 200 200 + + 29 37 37 37 + - --- DATA(1, 1) - --- DATA(-1, -1) + --- DATA(0, -1) - --- DATA(1, -1) + 200 600 200 200 + + 11 29 \ 3 / + - --- DATA(-1, 0) - --- DATA(-1, 1)| x + |- 3/40 DATA(2, 1) + 200 600 / \ + + 11 + + 3/20 DATA(2, 0) - 3/40 DATA(2, -1) + 9/10 c32 - -- DATA(0, 0) + 20 + + 11 + - 9/20 DATA(1, 0) + -- DATA(0, 1) + 9/40 DATA(1, 1) + 3/40 DATA(-1, -1) + 40 + + 11 \ + + -- DATA(0, -1) + 9/40 DATA(1, -1) - 3/20 DATA(-1, 0) + 3/40 DATA(-1, 1)| + 40 / + + 2 / 21 + y + |- 7/1000 DATA(2, 2) + ---- DATA(1, 2) + 7/1000 DATA(-1, 2) + \ 1000 + + 437 81 + + ---- DATA(0, 2) + 9/125 DATA(2, 1) - ---- DATA(2, 0) + 2/125 DATA(2, -1) + 3000 1000 + + 63 257 243 71 + - 9/25 c32 - --- c31 + ---- DATA(0, 0) + ---- DATA(1, 0) - --- DATA(0, 1) + 250 1000 1000 250 + + 27 89 + - --- DATA(1, 1) - 2/125 DATA(-1, -1) - --- DATA(0, -1) + 125 750 + + 81 \ 3 / + - 6/125 DATA(1, -1) + ---- DATA(-1, 0) - 9/125 DATA(-1, 1)| y + | + 1000 / \ + + 13 13 13 13 + - ---- DATA(2, 2) + ---- DATA(1, 2) + ---- DATA(-1, 2) - ---- DATA(0, 2) + 6000 2000 6000 2000 + + 377 43 481 91 39 + - ---- DATA(2, 1) - ---- DATA(2, 0) - ---- DATA(2, -1) + --- c32 - --- c31 + 6000 2000 6000 100 500 + + 129 1129 377 377 + - ---- DATA(0, 0) + ---- DATA(1, 0) - ---- DATA(0, 1) + ---- DATA(1, 1) + 2000 2000 2000 2000 + + 481 481 481 + + ---- DATA(-1, -1) - ---- DATA(0, -1) + ---- DATA(1, -1) + 6000 2000 2000 + + 957 377 \ / + - ---- DATA(-1, 0) + ---- DATA(-1, 1)| x + |1/40 DATA(2, 2) + 2000 6000 / \ + + 11 + - 3/40 DATA(1, 2) - 1/40 DATA(-1, 2) - --- DATA(0, 2) - 3/20 DATA(2, 1) + 120 + + 11 + + 3/40 DATA(2, 0) + 1/20 DATA(2, -1) + 9/10 c31 - -- DATA(0, 0) + 40 + + 11 + - 9/40 DATA(1, 0) + -- DATA(0, 1) + 9/20 DATA(1, 1) - 1/20 DATA(-1, -1) + 20 + + 11 \ + - -- DATA(0, -1) - 3/20 DATA(1, -1) - 3/40 DATA(-1, 0) + 3/20 DATA(-1, 1)| + 60 / + + 111 333 333 + y - ---- DATA(-1, -1) + ---- DATA(0, -1) - ---- DATA(1, -1) + 2000 2000 2000 + + 201 87 + + ---- DATA(-1, 0) - ---- DATA(-1, 1) + 2000 2000 + +> +# I +> coeffs_as_lc_of_data(%, posn_list_2d_size4); +bytes used=26023908, alloc=1965720, time=1.75 + 59 3 37 2 2 37 3 11 +[COEFF(-1, -1) = --- x y + --- x - 1/12 x y - --- x + -- x y - 1/20 y + 750 400 600 60 + + 481 3 3 3 2 2 2 11 2 111 + + ---- x + 1/100 x y - 2/125 y + 1/8 x y + 3/40 y - -- x y - ---- + 6000 40 2000 + + 17 2 3 13 2 3 2 3 333 + - --- x y , COEFF(0, -1) = --- x y + 1/12 x y + 7/500 x y + ---- + 300 150 2000 + + 2 2 2 481 111 2 11 37 3 3 3 + + 3/40 x y - 1/8 x y - ---- x - --- x - -- y + --- x - 3/100 x y + 2000 400 60 200 + + 11 2 89 3 2 2 2 333 + + -- y - 1/20 x y - --- y , COEFF(1, -1) = 1/12 x y - 1/8 x y - ---- + 40 750 2000 + + 2 3 2 3 3 111 2 73 3 + - 1/300 x y + 7/40 x y + 3/100 x y + --- x - 7/60 x y - --- x y + 400 750 + + 3 2 481 37 3 + - 6/125 y - 3/20 y + 9/40 y + ---- x - --- x , COEFF(2, -1) = - 1/60 x y + 2000 200 + + 3 3 2 481 3 37 2 + - 1/100 x y + 1/40 x y - ---- x + 1/20 y + 7/1500 x y - --- x + 6000 400 + + 2 3 2 3 2 111 37 3 2 2 + - 1/12 x y + 2/125 y - 2/75 x y - 3/40 y + ---- + --- x + 1/8 x y , + 2000 600 + + 201 23 2 3 133 2 11 2 2 + COEFF(-1, 0) = ---- + --- x y + --- x + -- x y - 3/40 y - 1/4 x y + 2000 200 400 40 + + 11 3 11 2 957 2 3 3 2 851 3 + - --- x + -- x y - ---- x - 1/8 x y + 1/150 x y - 3/20 y - ---- x y + 200 20 2000 3000 + + 81 3 19 2 3 3 3 11 2 + + ---- y , COEFF(0, 0) = - --- x y - 1/50 x y - 3/40 x y - -- y + 1000 200 20 + + 257 3 11 129 101 3 33 3 2 199 2 + + ---- y - -- y - ---- x + ---- x y + --- x + 1/8 x y - --- x + 1000 40 2000 1000 200 400 + + 2 2 2 1397 2 2 1129 + + 1/4 x y - 3/20 x y + ----, COEFF(1, 0) = 1/4 x y + ---- x + 2000 2000 + + 149 3 2 3 3 2 + - 7/40 x y + ---- x y - 1/400 x + 1/50 x y - 9/40 y - 7/20 x y + 1000 + + 2 603 243 3 33 3 2 31 2 3 + - 9/20 y + ---- + ---- y - --- x + 1/8 x y - --- x y , COEFF(2, 0) = + 2000 1000 200 200 + + 2 2 101 3 11 3 3 3 2 + - 1/4 x y + ---- x y + --- x - 1/150 x y - 1/8 x y + 3/40 y + 3000 200 + + 67 2 2 2 201 81 3 43 + - 1/40 x y + --- x - 1/20 x y + 3/20 y - ---- - ---- y - ---- x + 400 2000 1000 2000 + + 27 2 3 11 2 2 2 29 3 11 + + --- x y , COEFF(-1, 1) = - -- x y + 1/8 x y - --- x - -- x y + 200 40 600 20 + + 377 203 3 13 2 3 29 2 87 2 + + ---- x + --- x y + 3/20 y - --- x y + --- x - ---- + 1/4 x y + 6000 750 100 400 2000 + + 3 3 3 2 261 2 3 + + 1/300 x y - 9/125 y + 3/40 y , COEFF(0, 1) = ---- + 7/50 x y + 2000 + + 2 71 3 2 2 2 11 2 87 2 + - 1/4 x y - --- y + 3/40 x y - 1/8 x y + 3/20 x y + -- y - --- x + 250 40 400 + + 3 3 31 3 377 11 29 3 87 2 + - 1/100 x y - --- x y - ---- x + -- y + --- x , COEFF(1, 1) = --- x + 500 2000 20 200 400 + + 2 27 3 2 3 3 11 2 3 + + 9/40 y + 9/20 y - --- y - 1/4 x y + 1/100 x y + --- x y + 125 100 + + 47 3 2 377 261 29 3 2 2 + - --- x y + 7/40 x y + ---- x - ---- - --- x + 7/20 x y - 1/8 x y , + 250 2000 2000 200 + + 87 29 2 2 31 3 2 2 3 + COEFF(2, 1) = ---- - --- x + 1/4 x y - ---- x y - 3/40 y - 3/25 x y + 2000 400 1500 + + 377 3 29 3 2 3 3 + - 3/20 y - ---- x + 9/125 y + --- x + 1/40 x y + 1/20 x y - 1/300 x y + 6000 600 + + 2 2 2 3 3 3 + + 1/8 x y , COEFF(-1, 2) = 1/400 x - 1/40 y - 1/50 x y + 7/1000 y + + 11 13 2 197 3 3 43 2 3 + + --- x y + ---- x - 1/24 x y - 3/2000 - ---- x y - 1/600 x + --- x y + 120 6000 3000 600 + + 2 11 53 3 2 + , COEFF(0, 2) = - 3/400 x - --- y - 1/40 x y - ---- x y + 1/24 x y + 120 1000 + + 13 3 3 3 437 3 79 2 3 + - ---- x + 9/2000 + 3/50 x y + 1/200 x + ---- y - --- x y , + 2000 3000 600 + + 2 3 3 409 3 3 + COEFF(1, 2) = 3/400 x - 3/40 y - 3/50 x y + ---- x y - 1/200 x + 3000 + + 21 3 2 29 2 3 13 + + ---- y + 1/24 x y + --- x y - 7/120 x y - 9/2000 + ---- x, + 1000 600 2000 + + 2 53 3 3 + COEFF(2, 2) = - 1/400 x + 3/2000 + 1/40 y - ---- x y - 7/1000 y + 3000 + + 3 3 13 2 2 3 3 + + 1/50 x y - ---- x - 1/24 x y + 7/600 x y - 1/120 x y + 1/600 x ] + 6000 + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c"); +bytes used=27024116, alloc=2031244, time=1.82 +bytes used=28024396, alloc=2031244, time=1.90 +bytes used=29025884, alloc=2162292, time=1.99 +bytes used=30026144, alloc=2162292, time=2.06 +bytes used=31027088, alloc=2162292, time=2.12 +bytes used=32027348, alloc=2162292, time=2.18 +bytes used=33027500, alloc=2162292, time=2.24 +bytes used=34027920, alloc=2162292, time=2.30 +bytes used=35028400, alloc=2162292, time=2.38 +bytes used=36028584, alloc=2162292, time=2.46 +bytes used=37028772, alloc=2162292, time=2.56 +bytes used=38028952, alloc=2162292, time=2.67 +bytes used=39029156, alloc=2162292, time=2.73 +bytes used=40029332, alloc=2162292, time=2.80 +bytes used=41029504, alloc=2162292, time=2.92 +bytes used=42029680, alloc=2162292, time=2.99 +bytes used=43029840, alloc=2162292, time=3.09 +bytes used=44030180, alloc=2162292, time=3.20 +bytes used=45030460, alloc=2162292, time=3.31 +bytes used=46030800, alloc=2162292, time=3.38 +bytes used=47030988, alloc=2162292, time=3.48 +bytes used=48031208, alloc=2162292, time=3.62 +bytes used=49031368, alloc=2162292, time=3.76 +> +# d/dx +> simplify( diff(interp_2d_cube_order3_smooth0,x) ); +bytes used=50031616, alloc=2162292, time=3.86 +bytes used=51059256, alloc=2162292, time=3.92 +bytes used=52059500, alloc=2162292, time=3.99 + 3 13 13 13 +6/5 x y c32 - ---- DATA(2, 2) + ---- DATA(1, 2) + ---- DATA(-1, 2) + 6000 2000 6000 + + 13 377 43 481 + - ---- DATA(0, 2) - ---- DATA(2, 1) - ---- DATA(2, 0) - ---- DATA(2, -1) + 2000 6000 2000 6000 + + 2 2 2 91 39 + + 3 c32 x y + 3 c31 x y + 1/20 y DATA(2, 1) + --- c32 - --- c31 + 100 500 + + 129 1129 377 377 + - ---- DATA(0, 0) + ---- DATA(1, 0) - ---- DATA(0, 1) + ---- DATA(1, 1) + 2000 2000 2000 2000 + + 2 2 3 21 2 3 13 + - 3 x y c32 - 6/5 x y c32 - -- x y c31 - 3 x y c31 - -- y c31 + 25 10 + + 13 3 91 3 13 2 + + -- y c32 + --- y c31 - -- y c32 - 1/60 y DATA(2, -1) + 25 250 10 + + 21 2 2 + - 3/40 y DATA(0, 0) - 7/40 y DATA(1, 0) - -- x c32 + 9/50 x c31 + 10 + + 2 3 2 3 + + 9/100 x y DATA(1, -1) + 1/50 x y DATA(-1, 0) + + 2 3 + + 1/100 x y DATA(-1, 1) - 1/12 x y DATA(2, 2) + 1/12 x y DATA(1, 2) + + - 1/12 x y DATA(-1, 2) + 1/12 x y DATA(0, 2) + 1/2 x y DATA(2, 1) + + - 1/4 x y DATA(2, 0) - 1/6 x y DATA(2, -1) + 1/4 x y DATA(0, 0) + + 2 + + 1/4 x y DATA(1, 0) - 1/2 x y DATA(0, 1) + 1/4 x y DATA(2, 1) + + 3 + - 1/150 x y DATA(1, -1) - 1/2 x y DATA(1, 1) - 1/6 x y DATA(-1, -1) + + + 1/6 x y DATA(0, -1) + 1/6 x y DATA(1, -1) - 1/4 x y DATA(-1, 0) + + 11 + + 3/20 y DATA(0, 1) + 7/20 y DATA(1, 1) + -- y DATA(-1, -1) + 60 + + 11 + - 1/20 y DATA(0, -1) - 7/60 y DATA(1, -1) + -- y DATA(-1, 0) + 40 + + 11 53 3 + - -- y DATA(-1, 1) - 1/40 y DATA(2, 0) - ---- y DATA(2, 2) + 20 3000 + + 409 3 197 3 53 3 + + ---- y DATA(1, 2) - ---- y DATA(-1, 2) - ---- y DATA(0, 2) + 3000 3000 1000 + + 31 3 101 3 3 + - ---- y DATA(2, 1) + ---- y DATA(2, 0) + 7/1500 y DATA(2, -1) + 1500 3000 + + 101 3 149 3 31 3 + + ---- y DATA(0, 0) + ---- y DATA(1, 0) - --- y DATA(0, 1) + 1000 1000 500 + + 47 3 59 3 3 + - --- y DATA(1, 1) + --- y DATA(-1, -1) + 7/500 y DATA(0, -1) + 250 750 + + 73 3 851 3 203 3 + - --- y DATA(1, -1) - ---- y DATA(-1, 0) + --- y DATA(-1, 1) + 750 3000 750 + + 11 + - 1/120 y DATA(2, 2) - 7/120 y DATA(1, 2) + --- y DATA(-1, 2) + 120 + + 2 2 + - 1/40 y DATA(0, 2) + 1/40 y DATA(2, 1) - 1/20 y DATA(2, 0) + + 2 2 2 + + 1/40 y DATA(2, -1) - 3/20 y DATA(0, 0) - 7/20 y DATA(1, 0) + + 3 2 3 + + 7/300 x y DATA(2, 2) + 1/2 x y DATA(0, 0) - 4/75 x y DATA(2, -1) + + 79 3 2 3 2 + - --- x y DATA(0, 2) - 3/50 x y DATA(-1, 2) - 1/4 x y DATA(1, 1) + 300 + + 31 3 3 2 + - --- x y DATA(1, 0) + 7/25 x y DATA(0, 1) - 1/4 x y DATA(0, -1) + 100 + + 2 3 3 2 3 + - 3/100 x y DATA(2, -1) - 6/25 x y DATA(2, 1) - 9/50 x y DATA(1, 2) + + 2 2 3 11 3 + + 1/2 x y DATA(1, 0) - 1/100 x y DATA(2, 1) + -- x y DATA(1, 1) + 50 + + 19 3 21 2 + - --- x y DATA(0, 0) + -- x c32 - 9/50 x c31 + 1/4 x y DATA(-1, 1) + 100 10 + + 2 2 + - 1/2 x y DATA(2, 0) + 1/2 x y DATA(-1, 1) - 1/4 x y DATA(1, -1) + + 23 3 2 3 2 3 + + --- x y DATA(-1, 0) - 1/50 x y DATA(2, 0) - 3/100 x y DATA(0, 1) + 100 + + 2 3 2 3 13 3 + + 9/50 x y DATA(0, 2) - 3/50 x y DATA(0, 0) + -- x y DATA(0, -1) + 75 + + 2 2 29 3 + + 1/4 x y DATA(2, -1) + 1/4 x y DATA(-1, -1) + --- x y DATA(1, 2) + 300 + + 2 2 3 2 3 + - 1/4 x y DATA(0, 1) + 3/50 x y DATA(1, 0) + 3/50 x y DATA(2, 2) + + 17 3 13 3 43 3 + - --- x y DATA(-1, -1) - -- x y DATA(-1, 1) + --- x y DATA(-1, 2) + 150 50 300 + + 27 3 2 2 + + --- x y DATA(2, 0) - 1/2 x y DATA(-1, 0) + 3/40 y DATA(0, 1) + 100 + + 11 2 2 2 + - -- y DATA(-1, -1) + 3/40 y DATA(0, -1) + 7/40 y DATA(1, -1) + 40 + + 11 2 11 2 2 + + -- y DATA(-1, 0) - -- y DATA(-1, 1) + 1/200 x DATA(2, 2) + 20 40 + + 2 2 2 + - 3/200 x DATA(1, 2) - 1/200 x DATA(-1, 2) + 3/200 x DATA(0, 2) + + 29 2 33 2 37 2 + + --- x DATA(2, 1) + --- x DATA(2, 0) + --- x DATA(2, -1) + 200 200 200 + + 99 2 99 2 87 2 + + --- x DATA(0, 0) - --- x DATA(1, 0) + --- x DATA(0, 1) + 200 200 200 + + 87 2 37 2 111 2 + - --- x DATA(1, 1) - --- x DATA(-1, -1) + --- x DATA(0, -1) + 200 200 200 + + 111 2 33 2 29 2 + - --- x DATA(1, -1) - --- x DATA(-1, 0) - --- x DATA(-1, 1) + 200 200 200 + + 2 + - 1/200 x DATA(2, 2) + 3/200 x DATA(1, 2) + 7/40 y DATA(1, 1) + + 29 + + 1/200 x DATA(-1, 2) - 3/200 x DATA(0, 2) - --- x DATA(2, 1) + 200 + + 67 37 199 + + --- x DATA(2, 0) - --- x DATA(2, -1) - --- x DATA(0, 0) + 200 200 200 + + 87 87 + - 1/200 x DATA(1, 0) - --- x DATA(0, 1) + --- x DATA(1, 1) + 200 200 + + 37 111 111 + + --- x DATA(-1, -1) - --- x DATA(0, -1) + --- x DATA(1, -1) + 200 200 200 + + 133 29 21 3 481 + + --- x DATA(-1, 0) + --- x DATA(-1, 1) + -- x y c31 + ---- DATA(-1, -1) + 200 200 25 6000 + + 481 481 957 + - ---- DATA(0, -1) + ---- DATA(1, -1) - ---- DATA(-1, 0) + 2000 2000 2000 + + 377 2 3 2 3 + + ---- DATA(-1, 1) + 3/100 x y DATA(1, 1) + 3/100 x y DATA(-1, -1) + 6000 + + 2 3 + - 9/100 x y DATA(0, -1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); +bytes used=53061376, alloc=2162292, time=4.05 + 37 2 2 481 17 3 37 11 2 11 +[COEFF(-1, -1) = - --- x + 1/4 x y + ---- - --- x y + --- x - -- y + -- y + 200 6000 150 200 40 60 + + 2 3 59 3 3 2 + - 1/6 x y + 3/100 x y + --- y , COEFF(0, -1) = 7/500 y + 3/40 y + 750 + + 13 3 111 2 111 2 481 + + -- x y + 1/6 x y + --- x - --- x - 1/4 x y - 1/20 y - ---- + 75 200 200 2000 + + 2 3 73 3 2 3 3 + - 9/100 x y , COEFF(1, -1) = - --- y + 9/100 x y - 1/150 x y - 7/60 y + 750 + + 2 111 481 111 2 2 + + 1/6 x y + 7/40 y + --- x + ---- - --- x - 1/4 x y , COEFF(2, -1) = + 200 2000 200 + + 3 2 3 3 2 37 2 + - 4/75 x y - 1/6 x y - 3/100 x y - 1/60 y + 7/1500 y + 1/40 y + --- x + 200 + + 2 37 481 33 2 11 851 3 + + 1/4 x y - --- x - ----, COEFF(-1, 0) = - --- x + -- y - ---- y + 200 6000 200 40 3000 + + 2 3 11 2 957 23 3 133 2 + - 1/4 x y + 1/50 x y + -- y - ---- + --- x y + --- x - 1/2 x y , + 20 2000 100 200 + + 129 2 3 101 3 19 3 2 + COEFF(0, 0) = - 3/40 y - ---- - 3/50 x y + ---- y - --- x y + 1/2 x y + 2000 1000 100 + + 2 199 99 2 31 3 + - 3/20 y + 1/4 x y - --- x + --- x , COEFF(1, 0) = - --- x y + 200 200 100 + + 2 3 1129 2 2 99 2 149 3 + + 3/50 x y + ---- + 1/2 x y - 7/40 y - 7/20 y - --- x + ---- y + 2000 200 1000 + + 2 33 2 2 + - 1/200 x + 1/4 x y, COEFF(2, 0) = - 1/40 y - 1/20 y + --- x - 1/2 x y + 200 + + 27 3 101 3 2 3 43 67 + + --- x y + ---- y - 1/50 x y - 1/4 x y - ---- + --- x, COEFF(-1, 1) + 100 3000 2000 200 + + 13 3 11 2 2 377 2 3 203 3 29 + = - -- x y - -- y + 1/4 x y + ---- + 1/100 x y + --- y + --- x + 50 40 6000 750 200 + + 29 2 11 2 3 2 87 2 + - --- x - -- y + 1/2 x y, COEFF(0, 1) = - 3/100 x y - 1/4 x y + --- x + 200 20 200 + + 2 31 3 3 377 87 + + 3/40 y - --- y + 7/25 x y + 3/20 y - ---- - --- x - 1/2 x y, + 500 2000 200 + + 47 3 2 87 2 377 + COEFF(1, 1) = 7/20 y - --- y - 1/2 x y - 1/4 x y - --- x + ---- + 250 200 2000 + + 2 11 3 87 2 3 + + 7/40 y + -- x y + --- x + 3/100 x y , COEFF(2, 1) = 1/20 y + 50 200 + + 2 3 31 3 3 2 2 377 29 2 + - 1/100 x y - ---- y - 6/25 x y + 1/40 y + 1/4 x y - ---- + --- x + 1500 6000 200 + + 29 11 2 13 197 3 + + 1/2 x y - --- x, COEFF(-1, 2) = --- y - 1/200 x + ---- - ---- y + 200 120 6000 3000 + + 43 3 2 3 53 3 + + --- x y - 1/12 x y - 3/50 x y + 1/200 x, COEFF(0, 2) = - ---- y + 300 1000 + + 2 3 13 2 79 3 + - 1/40 y + 9/50 x y - ---- + 3/200 x - --- x y + 1/12 x y - 3/200 x, + 2000 300 + + 409 3 2 + COEFF(1, 2) = 1/12 x y + ---- y - 3/200 x - 7/120 y + 3/200 x + 3000 + + 2 3 13 29 3 53 3 + - 9/50 x y + ---- + --- x y , COEFF(2, 2) = - ---- y - 1/120 y + 2000 300 3000 + + 2 13 2 3 3 + + 1/200 x - ---- - 1/200 x + 3/50 x y + 7/300 x y - 1/12 x y] + 6000 + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c"); +bytes used=54061732, alloc=2162292, time=4.12 +bytes used=55062064, alloc=2162292, time=4.20 +bytes used=56062456, alloc=2162292, time=4.27 +bytes used=57062648, alloc=2162292, time=4.36 +bytes used=58062912, alloc=2162292, time=4.46 +bytes used=59063180, alloc=2162292, time=4.57 +bytes used=60063412, alloc=2162292, time=4.65 +bytes used=61063624, alloc=2162292, time=4.75 +bytes used=62064392, alloc=2162292, time=4.84 +bytes used=63064556, alloc=2162292, time=4.95 +> +# d/dy +> simplify( diff(interp_2d_cube_order3_smooth0,y) ); +bytes used=64064736, alloc=2162292, time=5.12 +bytes used=65064892, alloc=2162292, time=5.17 + 3 3 +2 c32 x y + c31 x + 1/40 DATA(2, 2) - 3/40 DATA(1, 2) - 1/40 DATA(-1, 2) + + 11 + - --- DATA(0, 2) - 3/20 DATA(2, 1) + 3/40 DATA(2, 0) + 1/20 DATA(2, -1) + 120 + + 2 2 3 2 + + 9/5 c32 x y - 3/20 y DATA(2, 1) - 6/5 c32 x y + 9/10 c31 + + 11 11 + - -- DATA(0, 0) - 9/40 DATA(1, 0) + -- DATA(0, 1) + 9/20 DATA(1, 1) + 40 20 + + 39 2 27 2 11 + + -- x y c32 - -- y c32 - 3/20 y DATA(2, -1) - -- y DATA(0, 0) + 25 25 10 + + 2 + - 9/10 y DATA(1, 0) - 3/2 x c31 + 1/20 x y DATA(2, 1) + + - 1/10 x y DATA(2, 0) + 1/20 x y DATA(2, -1) - 3/10 x y DATA(0, 0) + + 31 2 + - 7/10 x y DATA(1, 0) + 3/20 x y DATA(0, 1) - --- x y DATA(2, 1) + 500 + + 11 + + 7/20 x y DATA(1, 1) - -- x y DATA(-1, -1) + 3/20 x y DATA(0, -1) + 20 + + 11 2 + + 7/20 x y DATA(1, -1) + -- x y DATA(-1, 0) + 1/4 x y DATA(2, -1) + 10 + + 2 2 2 + + 1/2 x y DATA(0, 0) + 1/2 x y DATA(1, 0) - 1/4 x y DATA(0, 1) + + 2 2 2 + - 1/4 x y DATA(1, 1) + 1/4 x y DATA(-1, -1) - 1/4 x y DATA(0, -1) + + 2 2 2 + - 1/4 x y DATA(1, -1) - 1/2 x y DATA(-1, 0) + 1/4 x y DATA(-1, 1) + + 3 2 3 2 3 2 + - 9/50 x y DATA(1, 2) - 3/50 x y DATA(-1, 2) + 9/50 x y DATA(0, 2) + + 3 2 3 2 3 2 + - 1/100 x y DATA(2, 1) - 1/50 x y DATA(2, 0) + 3/50 x y DATA(2, 2) + + 3 2 3 2 + - 9/100 x y DATA(0, -1) - 3/100 x y DATA(2, -1) + + 3 2 3 2 93 2 2 + - 3/50 x y DATA(0, 0) + 3/50 x y DATA(1, 0) - --- x y DATA(1, 0) + 200 + + 21 2 2 3 2 3 2 + + -- x y DATA(0, 1) - 3/100 x y DATA(0, 1) + 3/100 x y DATA(1, 1) + 50 + + 3 2 2 2 81 2 2 + + 3/100 x y DATA(-1, -1) - 9/25 x y DATA(2, 1) + --- x y DATA(2, 0) + 200 + + 2 2 57 2 2 3 2 + - 2/25 x y DATA(2, -1) - --- x y DATA(0, 0) + 1/100 x y DATA(-1, 1) + 200 + + 29 2 2 43 2 2 79 2 2 + + --- x y DATA(1, 2) + --- x y DATA(-1, 2) - --- x y DATA(0, 2) + 200 200 200 + + 2 2 33 2 2 13 2 2 + + 7/200 x y DATA(2, 2) + --- x y DATA(1, 1) + -- x y DATA(0, -1) + 100 50 + + 2 2 69 2 2 17 2 2 + - 1/100 x y DATA(1, -1) + --- x y DATA(-1, 0) - --- x y DATA(-1, -1) + 200 100 + + 3 2 3 2 53 2 + + 9/100 x y DATA(1, -1) + 1/50 x y DATA(-1, 0) - ---- x y DATA(2, 2) + 1000 + + 39 2 2 409 2 197 2 + - --- x y DATA(-1, 1) + ---- x y DATA(1, 2) - ---- x y DATA(-1, 2) + 100 1000 1000 + + 159 2 11 + - ---- x y DATA(0, 2) + -- y DATA(0, 1) + 9/20 y DATA(1, 1) + 1000 20 + + 11 + + 3/20 y DATA(-1, -1) + -- y DATA(0, -1) + 9/20 y DATA(1, -1) + 20 + + - 3/10 y DATA(-1, 0) + 3/20 y DATA(-1, 1) + 3/10 y DATA(2, 0) + + 27 2 243 2 2 + + --- y DATA(2, 1) - ---- y DATA(2, 0) + 6/125 y DATA(2, -1) + 125 1000 + + 771 2 729 2 21 2 + + ---- y DATA(0, 0) + ---- y DATA(1, 0) - ---- y DATA(2, 2) + 1000 1000 1000 + + 63 2 21 2 437 2 + + ---- y DATA(1, 2) + ---- y DATA(-1, 2) + ---- y DATA(0, 2) + 1000 1000 1000 + + 2 2 189 2 273 2 + + 1/4 x y DATA(2, 1) - 1/2 x y DATA(2, 0) - --- y c31 + --- x y c31 + 250 250 + + 63 2 2 21 3 2 303 2 + + 9/5 y c32 + -- x y c31 - -- x y c31 + ---- x y DATA(0, 0) + 50 25 1000 + + 141 2 21 2 447 2 + - --- x y DATA(1, 1) + --- x y DATA(0, -1) + ---- x y DATA(1, 0) + 250 500 1000 + + 13 2 203 2 + - 13/5 x y c32 - -- x c31 - 3 x y c32 + --- x y DATA(-1, 1) + 10 250 + + 101 2 11 73 2 + + ---- x y DATA(2, 0) - -- x y DATA(-1, 1) - --- x y DATA(1, -1) + 1000 20 250 + + 2 59 2 93 2 + + 7/500 x y DATA(2, -1) + --- x y DATA(-1, -1) - --- x y DATA(0, 1) + 250 500 + + 851 2 213 2 2 + - ---- x y DATA(-1, 0) - --- y DATA(0, 1) - 6/125 y DATA(-1, -1) + 1000 250 + + 89 2 18 2 243 2 + - --- y DATA(0, -1) - --- y DATA(1, -1) + ---- y DATA(-1, 0) + 250 125 1000 + + 27 2 2 2 + - --- y DATA(-1, 1) - 1/24 x DATA(2, 2) + 1/24 x DATA(1, 2) + 125 + + 2 2 2 + - 1/24 x DATA(-1, 2) + 1/24 x DATA(0, 2) + 1/4 x DATA(2, 1) + + 2 2 2 + - 1/8 x DATA(2, 0) - 1/12 x DATA(2, -1) + 1/8 x DATA(0, 0) + + 2 2 2 + + 1/8 x DATA(1, 0) - 1/4 x DATA(0, 1) - 1/4 x DATA(1, 1) + + 2 2 2 + - 1/12 x DATA(-1, -1) + 1/12 x DATA(0, -1) + 1/12 x DATA(1, -1) + + 2 2 + - 1/8 x DATA(-1, 0) + 1/4 x DATA(-1, 1) - 1/120 x DATA(2, 2) + + 81 2 11 + - 7/120 x DATA(1, 2) - --- y DATA(1, 1) + --- x DATA(-1, 2) + 125 120 + + - 1/40 x DATA(0, 2) + 1/20 x DATA(2, 1) - 1/40 x DATA(2, 0) + + - 1/60 x DATA(2, -1) - 3/40 x DATA(0, 0) - 7/40 x DATA(1, 0) + + 11 + + 3/20 x DATA(0, 1) + 7/20 x DATA(1, 1) + -- x DATA(-1, -1) + 60 + + 11 + - 1/20 x DATA(0, -1) - 7/60 x DATA(1, -1) + -- x DATA(-1, 0) + 40 + + 11 11 + - -- x DATA(-1, 1) - 1/20 DATA(-1, -1) - -- DATA(0, -1) - 3/20 DATA(1, -1) + 20 60 + + - 3/40 DATA(-1, 0) + 3/20 DATA(-1, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); +bytes used=66073540, alloc=2162292, time=5.24 + 17 2 2 3 2 11 59 2 +[COEFF(-1, -1) = - --- x y - 1/20 + 3/100 x y + -- x + --- x y + 3/20 y + 100 60 250 + + 2 2 2 11 2 + - 6/125 y - 1/12 x + 1/4 x y - -- x y, COEFF(0, -1) = 1/12 x + 20 + + 2 13 2 2 11 21 2 11 + - 1/4 x y - 1/20 x + -- x y + 3/20 x y + -- y + --- x y - -- + 50 20 500 60 + + 3 2 89 2 2 2 2 + - 9/100 x y - --- y , COEFF(1, -1) = - 3/20 - 1/4 x y - 1/100 x y + 250 + + 18 2 2 3 2 73 2 + + 9/20 y + 7/20 x y - --- y + 1/12 x - 7/60 x + 9/100 x y - --- x y , + 125 250 + + 2 2 2 3 2 + COEFF(2, -1) = 1/4 x y - 1/60 x + 1/20 - 2/25 x y - 3/100 x y + + 2 2 2 + + 7/500 x y + 1/20 x y + 6/125 y - 1/12 x - 3/20 y, COEFF(-1, 0) = + + 11 851 2 2 69 2 2 3 2 + - 3/40 + -- x y - ---- x y - 1/2 x y - 3/10 y + --- x y + 1/50 x y + 10 1000 200 + + 11 2 243 2 2 303 2 11 + + -- x - 1/8 x + ---- y , COEFF(0, 0) = 1/8 x + ---- x y - -- y + 40 1000 1000 10 + + 3 2 11 2 771 2 57 2 2 + - 3/50 x y - -- + 1/2 x y - 3/40 x + ---- y - --- x y - 3/10 x y, + 40 1000 200 + + 93 2 2 3 2 2 + COEFF(1, 0) = - --- x y + 3/50 x y - 7/10 x y - 9/10 y + 1/2 x y + 200 + + 447 2 2 729 2 + + ---- x y + 1/8 x + ---- y - 7/40 x - 9/40, COEFF(2, 0) = 3/40 + 1000 1000 + + 2 81 2 2 2 101 2 243 2 + - 1/2 x y + --- x y - 1/40 x - 1/8 x + ---- x y - ---- y - 1/10 x y + 200 1000 1000 + + 3 2 39 2 2 2 27 2 + + 3/10 y - 1/50 x y , COEFF(-1, 1) = - --- x y + 3/20 + 1/4 x - --- y + 100 125 + + 3 2 11 203 2 11 2 + + 1/100 x y + 3/20 y - -- x + --- x y - -- x y + 1/4 x y, COEFF(0, 1) + 20 250 20 + + 213 2 11 11 21 2 2 93 2 3 2 + = - --- y + -- + -- y + -- x y - --- x y - 3/100 x y + 3/20 x + 250 20 20 50 500 + + 2 2 2 33 2 2 + - 1/4 x y - 1/4 x + 3/20 x y, COEFF(1, 1) = 9/20 y - 1/4 x + --- x y + 100 + + 81 2 2 141 2 3 2 + - --- y + 7/20 x - 1/4 x y - --- x y + 9/20 + 7/20 x y + 3/100 x y , + 125 250 + + 3 2 + COEFF(2, 1) = - 1/100 x y - 3/20 + 1/20 x + 1/20 x y - 3/20 y + + 2 2 31 2 2 2 27 2 + - 9/25 x y - --- x y + 1/4 x + 1/4 x y + --- y , COEFF(-1, 2) = + 500 125 + + 2 197 2 11 3 2 43 2 2 21 2 + - 1/40 - 1/24 x - ---- x y + --- x - 3/50 x y + --- x y + ---- y , + 1000 120 200 1000 + + COEFF(0, 2) = + + 79 2 2 159 2 3 2 2 11 437 2 + - --- x y - 1/40 x - ---- x y + 9/50 x y + 1/24 x - --- + ---- y , + 200 1000 120 1000 + + COEFF(1, 2) = + + 29 2 2 3 2 2 63 2 409 2 + - 3/40 + --- x y - 7/120 x - 9/50 x y + 1/24 x + ---- y + ---- x y , + 200 1000 1000 + + COEFF(2, 2) = + + 21 2 2 2 2 3 2 53 2 + 1/40 - ---- y - 1/24 x + 7/200 x y - 1/120 x + 3/50 x y - ---- x y ] + 1000 1000 + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c"); +bytes used=67073904, alloc=2162292, time=5.31 +bytes used=68074096, alloc=2162292, time=5.38 +bytes used=69074392, alloc=2162292, time=5.48 +bytes used=70074612, alloc=2162292, time=5.54 +bytes used=71074776, alloc=2162292, time=5.66 +bytes used=72075172, alloc=2162292, time=5.73 +bytes used=73075452, alloc=2162292, time=5.83 +bytes used=74076084, alloc=2162292, time=5.90 +bytes used=75076284, alloc=2162292, time=6.00 +bytes used=76076484, alloc=2162292, time=6.08 +bytes used=77083384, alloc=2162292, time=6.19 +bytes used=78083548, alloc=2162292, time=6.27 +bytes used=79083664, alloc=2162292, time=6.41 +bytes used=80083872, alloc=2162292, time=6.49 +bytes used=81084148, alloc=2162292, time=6.63 +bytes used=82084408, alloc=2162292, time=6.75 +> +# d^2/dx^2 +> simplify( diff(interp_2d_cube_order3_smooth0,x,x) ); +bytes used=83085440, alloc=2162292, time=6.83 +6 c31 x y - 1/200 DATA(2, 2) + 3/200 DATA(1, 2) + 1/200 DATA(-1, 2) + + 29 67 37 + - 3/200 DATA(0, 2) - --- DATA(2, 1) + --- DATA(2, 0) - --- DATA(2, -1) + 200 200 200 + + 29 3 3 + + 1/2 y DATA(2, 1) + --- y DATA(1, 2) + 7/300 y DATA(2, 2) + 300 + + 11 3 3 21 + + -- y DATA(1, 1) + 1/25 x y DATA(-1, 0) + -- c32 - 9/50 c31 + 50 10 + + 199 87 87 + - --- DATA(0, 0) - 1/200 DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1) + 200 200 200 + + 2 2 + + 6 x y c32 - 3 y c32 - 21/5 x c32 - 1/6 y DATA(2, -1) + + + 1/4 y DATA(0, 0) + 1/4 y DATA(1, 0) - 1/2 y DATA(0, 1) + + - 1/2 y DATA(1, 1) - 1/6 y DATA(-1, -1) + 1/6 y DATA(0, -1) + + + 1/6 y DATA(1, -1) - 1/4 y DATA(-1, 0) + 1/2 y DATA(-1, 1) + + 3 19 3 + - 1/4 y DATA(2, 0) + 7/25 y DATA(0, 1) - --- y DATA(0, 0) + 100 + + 3 27 3 3 + - 4/75 y DATA(2, -1) + --- y DATA(2, 0) - 6/25 y DATA(2, 1) + 100 + + 79 3 13 3 23 3 + - --- y DATA(0, 2) - -- y DATA(-1, 1) + --- y DATA(-1, 0) + 300 50 100 + + 3 13 3 17 3 + - 1/150 y DATA(1, -1) + -- y DATA(0, -1) - --- y DATA(-1, -1) + 75 150 + + 31 3 2 2 + - --- y DATA(1, 0) + 1/4 y DATA(2, 1) - 1/2 y DATA(2, 0) + 100 + + 2 2 2 + + 1/4 y DATA(2, -1) + 1/2 y DATA(0, 0) + 1/2 y DATA(1, 0) + 9/25 x c31 + + 2 2 2 + - 3 y c31 - 1/4 y DATA(0, 1) + 1/4 y DATA(-1, -1) - 1/4 y DATA(0, -1) + + 2 2 2 + - 1/4 y DATA(1, -1) - 1/2 y DATA(-1, 0) + 1/4 y DATA(-1, 1) + + 2 + + 1/100 x DATA(2, 2) - 3/100 x DATA(1, 2) - 1/4 y DATA(1, 1) + + 29 + - 1/100 x DATA(-1, 2) + 3/100 x DATA(0, 2) + --- x DATA(2, 1) + 100 + + 33 37 99 + + --- x DATA(2, 0) + --- x DATA(2, -1) + --- x DATA(0, 0) + 100 100 100 + + 99 87 87 + - --- x DATA(1, 0) + --- x DATA(0, 1) - --- x DATA(1, 1) + 100 100 100 + + 37 111 111 + - --- x DATA(-1, -1) + --- x DATA(0, -1) - --- x DATA(1, -1) + 100 100 100 + + 33 29 21 3 3 + - --- x DATA(-1, 0) - --- x DATA(-1, 1) + -- y c31 + 6/5 y c32 + 100 100 25 + + 37 111 111 133 + + --- DATA(-1, -1) - --- DATA(0, -1) + --- DATA(1, -1) + --- DATA(-1, 0) + 200 200 200 200 + + 29 42 3 3 3 + + --- DATA(-1, 1) - -- x y c31 - 12/5 x y c32 - 9/50 x y DATA(0, -1) + 200 25 + + 3 3 3 + + 9/50 x y DATA(1, -1) + 1/50 x y DATA(-1, 1) + 3/25 x y DATA(2, 2) + + 3 3 3 + - 9/25 x y DATA(1, 2) - 3/25 x y DATA(-1, 2) + 9/25 x y DATA(0, 2) + + 3 3 3 + - 1/50 x y DATA(2, 1) - 1/25 x y DATA(2, 0) - 3/50 x y DATA(2, -1) + + 3 3 3 + - 3/25 x y DATA(0, 0) + 3/25 x y DATA(1, 0) - 3/50 x y DATA(0, 1) + + 3 3 + + 3/50 x y DATA(1, 1) + 3/50 x y DATA(-1, -1) - 1/12 y DATA(2, 2) + + + 1/12 y DATA(1, 2) - 1/12 y DATA(-1, 2) + 1/12 y DATA(0, 2) + + 43 3 + + --- y DATA(-1, 2) + 300 + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); + 37 2 17 3 3 37 +[COEFF(-1, -1) = - --- x + 1/4 y - --- y + 3/50 x y - 1/6 y + ---, + 100 150 200 + + 111 2 13 3 3 111 + COEFF(0, -1) = - --- - 1/4 y + 1/6 y + -- y - 9/50 x y + --- x, + 200 75 100 + + 3 111 111 2 3 + COEFF(1, -1) = 9/50 x y + --- - --- x - 1/4 y - 1/150 y + 1/6 y, + 200 100 + + 37 2 3 3 37 + COEFF(2, -1) = - --- + 1/4 y - 1/6 y - 4/75 y - 3/50 x y + --- x, + 200 100 + + 23 3 133 2 33 3 + COEFF(-1, 0) = --- y + --- - 1/4 y - 1/2 y - --- x + 1/25 x y , + 100 200 100 + + 199 19 3 99 2 3 + COEFF(0, 0) = 1/4 y - --- - --- y + --- x + 1/2 y - 3/25 x y , + 200 100 100 + + 2 3 99 31 3 + COEFF(1, 0) = 1/4 y + 1/2 y + 3/25 x y - --- x - 1/200 - --- y , + 100 100 + + 33 67 3 2 27 3 + COEFF(2, 0) = --- x + --- - 1/25 x y - 1/2 y - 1/4 y + --- y , + 100 200 100 + + 29 13 3 3 29 2 + COEFF(-1, 1) = - --- x - -- y + 1/50 x y + --- + 1/4 y + 1/2 y, + 100 50 200 + + 2 87 3 87 3 + COEFF(0, 1) = - 1/4 y - --- - 1/2 y - 3/50 x y + --- x + 7/25 y , + 200 100 + + 87 3 2 87 11 3 + COEFF(1, 1) = - --- x + 3/50 x y - 1/4 y + --- - 1/2 y + -- y , + 100 200 50 + + 3 29 2 3 29 + COEFF(2, 1) = - 6/25 y + --- x + 1/4 y - 1/50 x y - --- + 1/2 y, + 100 200 + + 43 3 3 + COEFF(-1, 2) = --- y - 1/100 x - 3/25 x y - 1/12 y + 1/200, + 300 + + 79 3 3 + COEFF(0, 2) = 3/100 x - --- y - 3/200 + 1/12 y + 9/25 x y , + 300 + + 29 3 3 + COEFF(1, 2) = - 3/100 x + --- y + 3/200 - 9/25 x y + 1/12 y, + 300 + + 3 3 + COEFF(2, 2) = 1/100 x - 1/200 + 3/25 x y + 7/300 y - 1/12 y] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c"); +bytes used=84085660, alloc=2162292, time=6.91 +bytes used=85085812, alloc=2162292, time=6.99 +bytes used=86086048, alloc=2162292, time=7.09 +bytes used=87086364, alloc=2162292, time=7.18 +bytes used=88086596, alloc=2162292, time=7.29 +bytes used=89086816, alloc=2162292, time=7.43 +> +# d^2/dxdy +> simplify( diff(interp_2d_cube_order3_smooth0,x,y) ); +bytes used=90086976, alloc=2162292, time=7.50 + 2 2 11 +3 c31 x + 6 c32 x y - 1/120 DATA(2, 2) - 7/120 DATA(1, 2) + --- DATA(-1, 2) + 120 + + - 1/40 DATA(0, 2) + 1/20 DATA(2, 1) - 1/40 DATA(2, 0) - 1/60 DATA(2, -1) + + 13 + + 1/20 y DATA(2, 1) - -- c31 - 3/40 DATA(0, 0) - 7/40 DATA(1, 0) + 10 + + 2 39 2 + + 3/20 DATA(0, 1) + 7/20 DATA(1, 1) + 18/5 x y c32 + -- y c32 + 25 + + + 1/2 x y DATA(2, -1) + 1/20 y DATA(2, -1) - 3/10 y DATA(0, 0) + + - 7/10 y DATA(1, 0) + 3/20 y DATA(0, 1) + 7/20 y DATA(1, 1) + + 11 + - -- y DATA(-1, -1) + 3/20 y DATA(0, -1) + 7/20 y DATA(1, -1) + 20 + + 11 11 + + -- y DATA(-1, 0) - -- y DATA(-1, 1) - 1/10 y DATA(2, 0) + 10 20 + + 31 2 101 2 2 + - --- y DATA(2, 1) + ---- y DATA(2, 0) + 7/500 y DATA(2, -1) + 500 1000 + + 303 2 447 2 93 2 + + ---- y DATA(0, 0) + ---- y DATA(1, 0) - 3 x c31 - --- y DATA(0, 1) + 1000 1000 500 + + 59 2 21 2 73 2 + + --- y DATA(-1, -1) + --- y DATA(0, -1) - --- y DATA(1, -1) + 250 500 250 + + 851 2 203 2 + - ---- y DATA(-1, 0) + --- y DATA(-1, 1) - 1/12 x DATA(2, 2) + 1000 250 + + 141 2 + + 1/12 x DATA(1, 2) - --- y DATA(1, 1) - 1/12 x DATA(-1, 2) + 250 + + + 1/12 x DATA(0, 2) + 1/2 x DATA(2, 1) - 1/4 x DATA(2, 0) + + - 1/6 x DATA(2, -1) + 1/4 x DATA(0, 0) + 1/4 x DATA(1, 0) + + - 1/2 x DATA(0, 1) - 1/2 x DATA(1, 1) - 1/6 x DATA(-1, -1) + + + 1/6 x DATA(0, -1) + 1/6 x DATA(1, -1) - 1/4 x DATA(-1, 0) + + 2 2 2 2 + + 1/2 x DATA(-1, 1) + 3/100 x y DATA(-1, 1) + 3/50 x y DATA(-1, 0) + + 27 2 2 2 2 2 + + --- x y DATA(1, -1) + 7/100 x y DATA(2, 2) - 3/100 x y DATA(2, 1) + 100 + + 2 2 2 2 2 2 + - 9/50 x y DATA(0, 0) + 9/100 x y DATA(1, 1) - 9/100 x y DATA(0, 1) + + 27 2 2 2 2 2 2 + - --- x y DATA(0, -1) + 9/100 x y DATA(-1, -1) + 9/50 x y DATA(1, 0) + 100 + + 43 2 79 2 18 2 + + --- x y DATA(-1, 2) - --- x y DATA(0, 2) - -- x y DATA(2, 1) + 100 100 25 + + 2 2 27 2 2 2 2 + + 9/50 x y DATA(2, 2) + -- x y DATA(0, 2) - 9/50 x y DATA(-1, 2) + 50 + + 27 2 2 2 2 2 2 + - -- x y DATA(1, 2) - 9/100 x y DATA(2, -1) - 3/50 x y DATA(2, 0) + 50 + + 13 2 81 2 2 + + -- x y DATA(0, -1) + --- x y DATA(2, 0) - 4/25 x y DATA(2, -1) + 25 100 + + 57 2 29 2 2 + - --- x y DATA(0, 0) + --- x y DATA(1, 2) - 1/50 x y DATA(1, -1) + 100 100 + + 69 2 39 2 + + --- x y DATA(-1, 0) - -- x y DATA(-1, 1) + 1/2 x y DATA(2, 1) + 100 50 + + 93 2 21 2 + - x y DATA(2, 0) - --- x y DATA(1, 0) + -- x y DATA(0, 1) + 100 25 + + 33 2 17 2 + + -- x y DATA(1, 1) - -- x y DATA(-1, -1) + 1/2 x y DATA(-1, -1) + 50 50 + + - 1/2 x y DATA(1, -1) - x y DATA(-1, 0) + 1/2 x y DATA(-1, 1) + + - 1/2 x y DATA(0, -1) + x y DATA(0, 0) + x y DATA(1, 0) + + 159 2 + - 1/2 x y DATA(0, 1) - 1/2 x y DATA(1, 1) - ---- y DATA(0, 2) + 1000 + + 409 2 53 2 197 2 + + ---- y DATA(1, 2) - ---- y DATA(2, 2) - ---- y DATA(-1, 2) + 1000 1000 1000 + + 63 2 273 2 2 2 11 + - 6 x y c32 + -- x y c31 + --- y c31 - 18/5 c32 x y + -- DATA(-1, -1) + 25 250 60 + + 11 11 + - 1/20 DATA(0, -1) - 7/60 DATA(1, -1) + -- DATA(-1, 0) - -- DATA(-1, 1) + 40 20 + + 63 2 2 + - 13/5 y c32 - -- x y c31 + 25 + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); + 11 17 2 59 2 2 2 11 +[COEFF(-1, -1) = - -- y - 1/6 x - -- x y + 1/2 x y + --- y + 9/100 x y + -- + 20 50 250 60 + + , COEFF(0, -1) = + + 21 2 13 2 27 2 2 + - 1/20 + 1/6 x - 1/2 x y + --- y + -- x y + 3/20 y - --- x y , + 500 25 100 + + COEFF(1, -1) = + + 2 73 2 27 2 2 + - 1/2 x y - 1/50 x y + 1/6 x - 7/60 - --- y + --- x y + 7/20 y, + 250 100 + + COEFF(2, -1) = + + 2 2 2 2 + 1/2 x y + 1/20 y - 9/100 x y - 4/25 x y - 1/6 x - 1/60 + 7/500 y , + + 851 2 2 2 11 11 69 2 + COEFF(-1, 0) = -x y - ---- y + 3/50 x y - 1/4 x + -- + -- y + --- x y , + 1000 40 10 100 + + COEFF(0, 0) = + + 57 2 2 2 303 2 + - --- x y - 9/50 x y + x y + ---- y + 1/4 x - 3/10 y - 3/40, + 100 1000 + + 447 2 93 2 2 2 + COEFF(1, 0) = 1/4 x + ---- y - --- x y + 9/50 x y + x y - 7/10 y - 7/40 + 1000 100 + + , COEFF(2, 0) = + + 101 2 2 2 81 2 + -x y + ---- y - 1/4 x - 1/40 - 3/50 x y + --- x y - 1/10 y, + 1000 100 + + 203 2 11 11 39 2 2 2 + COEFF(-1, 1) = --- y - -- + 1/2 x - -- y - -- x y + 3/100 x y + 1/2 x y + 250 20 20 50 + + , COEFF(0, 1) = + + 93 2 21 2 2 2 + 3/20 + 3/20 y - 1/2 x y - --- y + -- x y - 1/2 x - 9/100 x y , + 500 25 + + COEFF(1, 1) = + + 33 2 141 2 2 2 + - 1/2 x + -- x y - --- y + 7/20 - 1/2 x y + 7/20 y + 9/100 x y , + 50 250 + + COEFF(2, 1) = + + 2 2 31 2 18 2 + - 3/100 x y + 1/2 x y + 1/20 + 1/2 x - --- y + 1/20 y - -- x y , + 500 25 + + 197 2 43 2 11 2 2 + COEFF(-1, 2) = - 1/12 x - ---- y + --- x y + --- - 9/50 x y , + 1000 100 120 + + 159 2 27 2 2 79 2 + COEFF(0, 2) = - 1/40 - ---- y + -- x y + 1/12 x - --- x y , + 1000 50 100 + + 27 2 2 29 2 409 2 + COEFF(1, 2) = 1/12 x - -- x y + --- x y + ---- y - 7/120, + 50 100 1000 + + 53 2 2 2 2 + COEFF(2, 2) = - ---- y - 1/12 x - 1/120 + 9/50 x y + 7/100 x y ] + 1000 + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c"); +bytes used=91087448, alloc=2162292, time=7.56 +bytes used=92087608, alloc=2162292, time=7.64 +bytes used=93087776, alloc=2162292, time=7.70 +bytes used=94088036, alloc=2162292, time=7.82 +bytes used=95088216, alloc=2162292, time=7.92 +bytes used=96088436, alloc=2162292, time=8.04 +bytes used=97088696, alloc=2162292, time=8.16 +> +# d^2/dy^2 +> simplify( diff(interp_2d_cube_order3_smooth0,y,y) ); +bytes used=98091880, alloc=2162292, time=8.28 + 2 +18/5 c32 x y - 3/20 DATA(2, 1) + 3/10 DATA(2, 0) - 3/20 DATA(2, -1) + + 3 54 42 3 3 + - 12/5 c32 x y + --- y DATA(2, 1) - -- c31 x y + 2 c32 x + 9/5 c32 + 125 25 + + 11 11 + - -- DATA(0, 0) - 9/10 DATA(1, 0) + -- DATA(0, 1) + 9/20 DATA(1, 1) + 10 20 + + 63 2 273 189 2 + - 13/5 x c32 + -- x y c31 + --- x y c31 - --- y c31 - 3 x c32 + 25 125 125 + + 81 2 2 57 2 + + --- x y DATA(2, 0) - 4/25 x y DATA(2, -1) - --- x y DATA(0, 0) + 100 100 + + 93 2 21 2 33 2 + - --- x y DATA(1, 0) + -- x y DATA(0, 1) + -- x y DATA(1, 1) + 100 25 50 + + 17 2 13 2 2 + - -- x y DATA(-1, -1) + -- x y DATA(0, -1) - 1/50 x y DATA(1, -1) + 50 25 + + 53 409 + + 7/250 x y DATA(2, -1) - --- x y DATA(2, 2) + --- x y DATA(1, 2) + 500 500 + + 197 159 3 + - --- x y DATA(-1, 2) - --- x y DATA(0, 2) + 3/25 x y DATA(2, 2) + 500 500 + + 3 3 3 + - 9/25 x y DATA(1, 2) - 3/25 x y DATA(-1, 2) + 9/25 x y DATA(0, 2) + + 3 3 3 + - 1/50 x y DATA(2, 1) - 1/25 x y DATA(2, 0) - 3/50 x y DATA(2, -1) + + 3 437 12 + - 3/25 x y DATA(0, 0) + --- y DATA(0, 2) + --- y DATA(2, -1) + 500 125 + + 771 729 213 + + --- y DATA(0, 0) + --- y DATA(1, 0) - --- y DATA(0, 1) + 500 500 125 + + 162 12 89 + - --- y DATA(1, 1) - --- y DATA(-1, -1) - --- y DATA(0, -1) + 125 125 125 + + 36 243 54 + - --- y DATA(1, -1) + --- y DATA(-1, 0) - --- y DATA(-1, 1) + 125 500 125 + + 243 3 3 + - --- y DATA(2, 0) + 3/25 x y DATA(1, 0) - 3/50 x y DATA(0, 1) + 500 + + 3 3 3 + + 3/50 x y DATA(1, 1) + 3/50 x y DATA(-1, -1) + 9/50 x y DATA(1, -1) + + 3 3 3 + + 1/25 x y DATA(-1, 0) + 1/50 x y DATA(-1, 1) - 9/50 x y DATA(0, -1) + + 29 2 2 79 2 + + --- x y DATA(1, 2) + 7/100 x y DATA(2, 2) - --- x y DATA(0, 2) + 100 100 + + 43 2 18 2 2 + + --- x y DATA(-1, 2) - -- x y DATA(2, 1) + 1/4 x DATA(2, 1) + 100 25 + + 2 2 2 + - 1/2 x DATA(2, 0) + 1/4 x DATA(2, -1) + 1/2 x DATA(0, 0) + + 2 2 2 + + 1/2 x DATA(1, 0) - 1/4 x DATA(0, 1) - 1/4 x DATA(1, 1) + + 2 21 63 + + 1/4 x DATA(-1, -1) - --- y DATA(2, 2) + --- y DATA(1, 2) + 500 500 + + 21 2 2 + + --- y DATA(-1, 2) + 1/4 x DATA(-1, 1) - 1/4 x DATA(0, -1) + 500 + + 2 2 69 2 + - 1/2 x DATA(-1, 0) - 1/4 x DATA(1, -1) + --- x y DATA(-1, 0) + 100 + + 39 2 + - -- x y DATA(-1, 1) + 1/20 x DATA(2, 1) - 1/10 x DATA(2, 0) + 50 + + + 1/20 x DATA(2, -1) - 3/10 x DATA(0, 0) - 7/10 x DATA(1, 0) + + 11 + + 3/20 x DATA(0, 1) + 7/20 x DATA(1, 1) - -- x DATA(-1, -1) + 20 + + 11 + + 3/20 x DATA(0, -1) + 7/20 x DATA(1, -1) + -- x DATA(-1, 0) + 10 + + 11 31 101 + - -- x DATA(-1, 1) - --- x y DATA(2, 1) + --- x y DATA(2, 0) + 20 250 500 + + 59 73 851 + + --- x y DATA(-1, -1) - --- x y DATA(1, -1) - --- x y DATA(-1, 0) + 125 125 500 + + 203 21 303 + + --- x y DATA(-1, 1) + --- x y DATA(0, -1) + --- x y DATA(0, 0) + 125 250 500 + + 447 93 141 + + --- x y DATA(1, 0) - --- x y DATA(0, 1) - --- x y DATA(1, 1) + 500 250 125 + + 78 11 + + -- x y c32 + 3/20 DATA(-1, -1) + -- DATA(0, -1) + 9/20 DATA(1, -1) + 25 20 + + 54 + - 3/10 DATA(-1, 0) + 3/20 DATA(-1, 1) - -- y c32 + 25 + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); +bytes used=99092352, alloc=2227816, time=8.34 + 2 12 3 59 11 17 2 +[COEFF(-1, -1) = 1/4 x - --- y + 3/50 y x + --- x y - -- x + 3/20 - -- y x , + 125 125 20 50 + + 21 13 2 3 89 11 2 + COEFF(0, -1) = --- x y + -- y x - 9/50 y x - --- y + -- + 3/20 x - 1/4 x + 250 25 125 20 + + , COEFF(1, -1) = + + 73 2 36 2 3 + 7/20 x - --- x y - 1/50 y x - --- y - 1/4 x + 9/50 y x + 9/20, + 125 125 + + COEFF(2, -1) = + + 12 2 2 3 + - 3/20 + --- y + 1/4 x - 4/25 y x - 3/50 y x + 7/250 x y + 1/20 x, + 125 + + COEFF(-1, 0) = + + 11 69 2 2 243 3 851 + -- x + --- y x - 1/2 x + --- y + 1/25 y x - 3/10 - --- x y, COEFF(0, 0) + 10 100 500 500 + + 57 2 771 3 11 2 303 + = - --- y x + --- y - 3/25 y x - -- + 1/2 x - 3/10 x + --- x y, + 100 500 10 500 + + COEFF(1, 0) = + + 3 729 2 93 2 447 + 3/25 y x + --- y + 1/2 x - 9/10 - --- y x + --- x y - 7/10 x, + 500 100 500 + + COEFF(2, 0) = + + 243 2 101 81 2 3 + - --- y - 1/2 x + 3/10 + --- x y + --- y x - 1/10 x - 1/25 y x , + 500 500 100 + + COEFF(-1, 1) = + + 11 203 3 54 2 39 2 + - -- x + --- x y + 1/50 y x - --- y + 1/4 x + 3/20 - -- y x , + 20 125 125 50 + + 11 3 213 21 2 2 93 + COEFF(0, 1) = -- - 3/50 y x - --- y + -- y x + 3/20 x - 1/4 x - --- x y, + 20 125 25 250 + + COEFF(1, 1) = + + 141 3 33 2 2 162 + 9/20 + 7/20 x - --- x y + 3/50 y x + -- y x - 1/4 x - --- y, COEFF(2, 1) + 125 50 125 + + 54 2 18 2 31 3 + = - 3/20 + --- y + 1/4 x - -- y x - --- x y - 1/50 y x + 1/20 x, + 125 25 250 + + 3 21 197 43 2 + COEFF(-1, 2) = - 3/25 y x + --- y - --- x y + --- y x , + 500 500 100 + + 3 159 79 2 437 + COEFF(0, 2) = 9/25 y x - --- x y - --- y x + --- y, + 500 100 500 + + 29 2 3 63 409 + COEFF(1, 2) = --- y x - 9/25 y x + --- y + --- x y, + 100 500 500 + + 2 53 3 21 + COEFF(2, 2) = 7/100 y x - --- x y + 3/25 y x - --- y] + 500 500 + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c"); +bytes used=100092548, alloc=2227816, time=8.41 +bytes used=101092996, alloc=2227816, time=8.49 +bytes used=102093148, alloc=2227816, time=8.61 +bytes used=103093312, alloc=2227816, time=8.69 +bytes used=104093644, alloc=2227816, time=8.84 +bytes used=105093832, alloc=2227816, time=8.92 +bytes used=106093996, alloc=2227816, time=9.05 +> +################################################################################ +> +# +# 2d, cube, order=4, smoothing=0 (size=5) +# +> +# interpolating polynomial +> interp_2d_cube_order4_smooth0 +> := Lagrange_polynomial_interpolant(fn_2d_order4, coeffs_list_2d_order4, +> coords_list_2d, posn_list_2d_size5); +bytes used=107094420, alloc=2227816, time=9.13 +bytes used=108095396, alloc=2227816, time=9.19 +bytes used=109095660, alloc=2227816, time=9.25 +bytes used=110095928, alloc=2227816, time=9.31 +bytes used=111096132, alloc=2227816, time=9.36 +bytes used=112096424, alloc=2227816, time=9.43 +bytes used=113096732, alloc=2227816, time=9.50 +bytes used=114097080, alloc=2227816, time=9.57 +bytes used=115097268, alloc=2227816, time=9.64 +bytes used=116097436, alloc=2227816, time=9.71 +bytes used=117097712, alloc=2227816, time=9.77 +bytes used=118100480, alloc=2227816, time=9.84 +bytes used=119101300, alloc=2227816, time=9.90 +bytes used=120101536, alloc=2227816, time=9.96 +bytes used=121102272, alloc=2227816, time=10.03 +bytes used=122103488, alloc=2227816, time=10.09 +bytes used=123103664, alloc=2227816, time=10.14 +bytes used=124103840, alloc=2227816, time=10.21 +bytes used=125104372, alloc=2227816, time=10.28 +interp_2d_cube_order4_smooth0 := (- 1/24 DATA(0, 2) - 5/4 DATA(0, 0) + + 2 + + 2/3 DATA(0, 1) - 1/24 DATA(0, -2) + 2/3 DATA(0, -1)) y + DATA(0, 0) + ( + + - 1/576 DATA(2, 2) + 1/144 DATA(1, 2) + 1/144 DATA(-1, 2) - 1/96 DATA(0, 2) + + + 1/36 DATA(2, 1) - 5/96 DATA(2, 0) + 1/36 DATA(2, -1) - 5/16 DATA(0, 0) + + + 5/24 DATA(1, 0) + 1/6 DATA(0, 1) - 1/9 DATA(1, 1) - 1/576 DATA(-2, 2) + + + 1/36 DATA(-2, 1) - 5/96 DATA(-2, 0) + 1/36 DATA(-2, -1) + + - 1/576 DATA(2, -2) + 1/144 DATA(1, -2) - 1/96 DATA(0, -2) + + + 1/144 DATA(-1, -2) - 1/576 DATA(-2, -2) - 1/9 DATA(-1, -1) + + + 1/6 DATA(0, -1) - 1/9 DATA(1, -1) + 5/24 DATA(-1, 0) - 1/9 DATA(-1, 1)) + + 4 2 + x y + (- 1/288 DATA(2, 2) + 1/72 DATA(1, 2) + 1/72 DATA(-1, 2) + + - 1/48 DATA(0, 2) + 1/36 DATA(2, 1) - 1/36 DATA(2, -1) + 1/6 DATA(0, 1) + + - 1/9 DATA(1, 1) - 1/288 DATA(-2, 2) + 1/36 DATA(-2, 1) + + - 1/36 DATA(-2, -1) + 1/288 DATA(2, -2) - 1/72 DATA(1, -2) + + + 1/48 DATA(0, -2) - 1/72 DATA(-1, -2) + 1/288 DATA(-2, -2) + + + 1/9 DATA(-1, -1) - 1/6 DATA(0, -1) + 1/9 DATA(1, -1) - 1/9 DATA(-1, 1)) + + 4 + x y + (1/144 DATA(2, 2) - 1/72 DATA(1, 2) + 1/72 DATA(-1, 2) + + - 1/72 DATA(2, 1) + 1/72 DATA(2, -1) - 1/72 DATA(-2, -1) + 1/36 DATA(1, 1) + + - 1/144 DATA(-2, 2) + 1/72 DATA(-2, 1) + 1/144 DATA(-2, -2) + + - 1/144 DATA(2, -2) + 1/72 DATA(1, -2) - 1/72 DATA(-1, -2) + + 3 3 + + 1/36 DATA(-1, -1) - 1/36 DATA(1, -1) - 1/36 DATA(-1, 1)) x y + ( + + - 1/288 DATA(2, 2) + 1/144 DATA(1, 2) - 1/144 DATA(-1, 2) + 1/18 DATA(2, 1) + + - 5/48 DATA(2, 0) + 1/18 DATA(2, -1) + 5/24 DATA(1, 0) - 1/9 DATA(1, 1) + + + 1/288 DATA(-2, 2) - 1/18 DATA(-2, 1) + 5/48 DATA(-2, 0) + + - 1/18 DATA(-2, -1) - 1/288 DATA(2, -2) + 1/144 DATA(1, -2) + + - 1/144 DATA(-1, -2) + 1/288 DATA(-2, -2) + 1/9 DATA(-1, -1) + + 3 2 + - 1/9 DATA(1, -1) - 5/24 DATA(-1, 0) + 1/9 DATA(-1, 1)) x y + ( + + - 1/144 DATA(2, 2) + 1/72 DATA(1, 2) - 1/72 DATA(-1, 2) + 1/18 DATA(2, 1) + + - 1/18 DATA(2, -1) - 1/9 DATA(1, 1) + 1/144 DATA(-2, 2) - 1/18 DATA(-2, 1) + + + 1/18 DATA(-2, -1) + 1/144 DATA(2, -2) - 1/72 DATA(1, -2) + + + 1/72 DATA(-1, -2) - 1/144 DATA(-2, -2) - 1/9 DATA(-1, -1) + + 3 + + 1/9 DATA(1, -1) + 1/9 DATA(-1, 1)) x y + (- 1/288 DATA(2, 2) + + + 1/36 DATA(1, 2) - 1/36 DATA(-1, 2) + 1/72 DATA(2, 1) - 1/48 DATA(2, 0) + + + 1/72 DATA(2, -1) + 1/6 DATA(1, 0) - 1/9 DATA(1, 1) + 1/288 DATA(-2, 2) + + - 1/72 DATA(-2, 1) + 1/48 DATA(-2, 0) - 1/72 DATA(-2, -1) + + - 1/288 DATA(2, -2) + 1/36 DATA(1, -2) - 1/36 DATA(-1, -2) + + + 1/288 DATA(-2, -2) + 1/9 DATA(-1, -1) - 1/9 DATA(1, -1) + + 4 + - 1/6 DATA(-1, 0) + 1/9 DATA(-1, 1)) x y + (- 1/576 DATA(2, 2) + + + 1/36 DATA(1, 2) + 1/36 DATA(-1, 2) - 5/96 DATA(0, 2) + 1/144 DATA(2, 1) + + - 1/96 DATA(2, 0) + 1/144 DATA(2, -1) - 5/16 DATA(0, 0) + 1/6 DATA(1, 0) + + + 5/24 DATA(0, 1) - 1/9 DATA(1, 1) - 1/576 DATA(-2, 2) + 1/144 DATA(-2, 1) + + - 1/96 DATA(-2, 0) + 1/144 DATA(-2, -1) - 1/576 DATA(2, -2) + + + 1/36 DATA(1, -2) - 5/96 DATA(0, -2) + 1/36 DATA(-1, -2) + + - 1/576 DATA(-2, -2) - 1/9 DATA(-1, -1) + 5/24 DATA(0, -1) + + 2 4 + - 1/9 DATA(1, -1) + 1/6 DATA(-1, 0) - 1/9 DATA(-1, 1)) x y + ( + + 1/576 DATA(2, 2) - 1/144 DATA(1, 2) - 1/144 DATA(-1, 2) + 1/96 DATA(0, 2) + + - 1/144 DATA(2, 1) + 1/96 DATA(2, 0) - 1/144 DATA(2, -1) + 1/16 DATA(0, 0) + + - 1/24 DATA(1, 0) - 1/24 DATA(0, 1) + 1/36 DATA(1, 1) + 1/576 DATA(-2, 2) + + - 1/144 DATA(-2, 1) + 1/96 DATA(-2, 0) - 1/144 DATA(-2, -1) + + + 1/576 DATA(2, -2) - 1/144 DATA(1, -2) + 1/96 DATA(0, -2) + + - 1/144 DATA(-1, -2) + 1/576 DATA(-2, -2) + 1/36 DATA(-1, -1) + + - 1/24 DATA(0, -1) + 1/36 DATA(1, -1) - 1/24 DATA(-1, 0) + + 4 4 + + 1/36 DATA(-1, 1)) x y + (1/288 DATA(2, 2) - 1/144 DATA(1, 2) + + + 1/144 DATA(-1, 2) - 1/72 DATA(2, 1) + 1/48 DATA(2, 0) - 1/72 DATA(2, -1) + + + 1/24 DATA(-1, 0) - 1/24 DATA(1, 0) + 1/36 DATA(1, 1) - 1/288 DATA(-2, 2) + + + 1/72 DATA(-2, 1) - 1/48 DATA(-2, 0) + 1/72 DATA(-2, -1) + + + 1/288 DATA(2, -2) - 1/144 DATA(1, -2) + 1/144 DATA(-1, -2) + + - 1/288 DATA(-2, -2) - 1/36 DATA(-1, -1) + 1/36 DATA(1, -1) + + 3 4 + - 1/36 DATA(-1, 1)) x y + (1/144 DATA(2, 2) - 1/18 DATA(1, 2) + + + 1/18 DATA(-1, 2) - 1/18 DATA(2, 1) + 1/18 DATA(2, -1) + 4/9 DATA(1, 1) + + - 1/144 DATA(-2, 2) + 1/18 DATA(-2, 1) - 1/18 DATA(-2, -1) + + - 1/144 DATA(2, -2) + 1/18 DATA(1, -2) - 1/18 DATA(-1, -2) + + + 1/144 DATA(-2, -2) + 4/9 DATA(-1, -1) - 4/9 DATA(1, -1) + + - 4/9 DATA(-1, 1)) x y + (1/288 DATA(2, 2) - 1/36 DATA(1, 2) + + + 1/36 DATA(-1, 2) - 1/18 DATA(2, 1) + 5/48 DATA(2, 0) - 1/18 DATA(2, -1) + + - 5/6 DATA(1, 0) + 4/9 DATA(1, 1) - 1/288 DATA(-2, 2) + 1/18 DATA(-2, 1) + + - 5/48 DATA(-2, 0) + 1/18 DATA(-2, -1) + 1/288 DATA(2, -2) + + - 1/36 DATA(1, -2) + 1/36 DATA(-1, -2) - 1/288 DATA(-2, -2) + + - 4/9 DATA(-1, -1) + 4/9 DATA(1, -1) + 5/6 DATA(-1, 0) - 4/9 DATA(-1, 1)) + + 2 / + x y + |1/576 DATA(2, 2) - 1/36 DATA(1, 2) - 1/36 DATA(-1, 2) + \ + + + 5/96 DATA(0, 2) - 1/36 DATA(2, 1) + 5/96 DATA(2, 0) - 1/36 DATA(2, -1) + + 25 + + -- DATA(0, 0) - 5/6 DATA(1, 0) - 5/6 DATA(0, 1) + 4/9 DATA(1, 1) + 16 + + + 1/576 DATA(-2, 2) - 1/36 DATA(-2, 1) + 5/96 DATA(-2, 0) + + - 1/36 DATA(-2, -1) + 1/576 DATA(2, -2) - 1/36 DATA(1, -2) + + + 5/96 DATA(0, -2) - 1/36 DATA(-1, -2) + 1/576 DATA(-2, -2) + + + 4/9 DATA(-1, -1) - 5/6 DATA(0, -1) + 4/9 DATA(1, -1) - 5/6 DATA(-1, 0) + + \ 2 2 + + 4/9 DATA(-1, 1)| x y + (1/288 DATA(2, 2) - 1/18 DATA(1, 2) + / + + - 1/18 DATA(-1, 2) + 5/48 DATA(0, 2) - 1/36 DATA(2, 1) + 1/36 DATA(2, -1) + + - 5/6 DATA(0, 1) + 4/9 DATA(1, 1) + 1/288 DATA(-2, 2) - 1/36 DATA(-2, 1) + + + 1/36 DATA(-2, -1) - 1/288 DATA(2, -2) + 1/18 DATA(1, -2) + + - 5/48 DATA(0, -2) + 1/18 DATA(-1, -2) - 1/288 DATA(-2, -2) + + - 4/9 DATA(-1, -1) + 5/6 DATA(0, -1) - 4/9 DATA(1, -1) + 4/9 DATA(-1, 1)) + + 2 + x y + (1/288 DATA(2, 2) - 1/72 DATA(1, 2) - 1/72 DATA(-1, 2) + + + 1/48 DATA(0, 2) - 1/144 DATA(2, 1) + 1/144 DATA(2, -1) + + - 1/36 DATA(1, -1) - 1/24 DATA(0, 1) + 1/36 DATA(1, 1) + 1/288 DATA(-2, 2) + + - 1/144 DATA(-2, 1) + 1/144 DATA(-2, -1) - 1/288 DATA(2, -2) + + + 1/72 DATA(1, -2) - 1/48 DATA(0, -2) + 1/72 DATA(-1, -2) + + - 1/288 DATA(-2, -2) - 1/36 DATA(-1, -1) + 1/24 DATA(0, -1) + + 4 3 + + 1/36 DATA(-1, 1)) x y + (1/24 DATA(0, 2) + 1/4 DATA(0, 0) + + 4 + - 1/6 DATA(0, 1) + 1/24 DATA(0, -2) - 1/6 DATA(0, -1)) y + ( + + 1/24 DATA(2, 0) + 1/4 DATA(0, 0) - 1/6 DATA(1, 0) + 1/24 DATA(-2, 0) + + 4 + - 1/6 DATA(-1, 0)) x + + + (- 1/12 DATA(2, 0) + 2/3 DATA(1, 0) + 1/12 DATA(-2, 0) - 2/3 DATA(-1, 0)) x + + + (- 1/24 DATA(2, 0) - 5/4 DATA(0, 0) + 2/3 DATA(1, 0) - 1/24 DATA(-2, 0) + + 2 + + 2/3 DATA(-1, 0)) x + + + 3 + (1/12 DATA(0, 2) - 1/6 DATA(0, 1) - 1/12 DATA(0, -2) + 1/6 DATA(0, -1)) y + + + + + (- 1/12 DATA(0, 2) + 2/3 DATA(0, 1) + 1/12 DATA(0, -2) - 2/3 DATA(0, -1)) y + + + (- 1/144 DATA(2, 2) + 1/18 DATA(1, 2) - 1/18 DATA(-1, 2) + + + 1/72 DATA(2, 1) - 1/72 DATA(2, -1) - 1/9 DATA(1, 1) + 1/144 DATA(-2, 2) + + - 1/72 DATA(-2, 1) + 1/72 DATA(-2, -1) + 1/144 DATA(2, -2) + + - 1/18 DATA(1, -2) + 1/18 DATA(-1, -2) - 1/144 DATA(-2, -2) + + 3 + - 1/9 DATA(-1, -1) + 1/9 DATA(1, -1) + 1/9 DATA(-1, 1)) x y + ( + + - 1/288 DATA(2, 2) + 1/18 DATA(1, 2) + 1/18 DATA(-1, 2) - 5/48 DATA(0, 2) + + + 1/144 DATA(2, 1) - 1/144 DATA(2, -1) + 5/24 DATA(0, 1) - 1/9 DATA(1, 1) + + - 1/288 DATA(-2, 2) + 1/144 DATA(-2, 1) - 1/144 DATA(-2, -1) + + + 1/288 DATA(2, -2) - 1/18 DATA(1, -2) + 5/48 DATA(0, -2) + + - 1/18 DATA(-1, -2) + 1/288 DATA(-2, -2) + 1/9 DATA(-1, -1) + + 2 3 + - 5/24 DATA(0, -1) + 1/9 DATA(1, -1) - 1/9 DATA(-1, 1)) x y + + + 3 + (1/12 DATA(2, 0) - 1/6 DATA(1, 0) - 1/12 DATA(-2, 0) + 1/6 DATA(-1, 0)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=126126424, alloc=2227816, time=10.34 +bytes used=127129732, alloc=2227816, time=10.40 + 4 2 3 3 2 +[COEFF(-2, -2) = 1/288 x y + 1/288 x y - 1/144 x y - 1/288 y x + + 2 4 4 3 4 2 2 3 + - 1/576 x y - 1/288 x y + 1/288 x y + 1/576 x y - 1/144 y x + + 2 3 2 3 3 3 4 + - 1/288 x y + 1/288 x y + 1/144 x y + 1/144 x y - 1/288 x y + + 4 2 4 4 2 2 4 3 + - 1/576 x y + 1/576 x y , COEFF(-1, -2) = - 1/36 x y + 1/72 x y + + 4 2 4 3 2 2 4 + - 1/72 x y + 1/18 y x - 1/36 x y - 1/144 x y + 1/36 x y + + 4 2 4 4 3 3 4 2 3 + + 1/144 x y - 1/144 x y + 1/18 x y + 1/144 x y - 1/18 x y + + 3 3 2 3 3 + - 1/18 x y - 1/72 x y + 1/36 x y + 1/72 y x , COEFF(0, -2) = - 1/12 y + + 4 4 4 2 2 3 2 + + 1/24 y + 1/48 x y - 1/96 x y + 5/48 x y + 1/12 y - 5/48 y x + + 2 4 4 3 4 4 2 2 2 + - 5/96 x y - 1/48 x y + 1/96 x y + 5/96 x y - 1/24 y , + + 4 3 3 2 2 4 + COEFF(1, -2) = 1/18 x y + 1/72 x y + 1/144 x y + 1/18 y x + 1/36 x y + + 4 2 3 4 3 3 4 4 + + 1/144 x y - 1/72 y x - 1/72 x y + 1/72 x y - 1/144 x y + + 3 2 3 2 2 4 3 4 + - 1/18 x y - 1/18 x y - 1/36 x y + 1/36 x y - 1/144 x y + + 2 2 2 4 2 2 3 + - 1/36 x y , COEFF(2, -2) = - 1/576 x y - 1/288 y x + 1/288 x y + + 4 4 3 3 4 4 2 + + 1/576 x y + 1/144 y x + 1/288 x y - 1/144 x y - 1/576 x y + + 4 3 2 3 2 3 4 + - 1/288 x y + 1/288 x y - 1/288 x y + 1/144 x y - 1/288 x y + + 3 3 2 2 4 4 + - 1/144 x y + 1/576 x y + 1/288 x y, COEFF(-2, -1) = - 1/36 x y + + 2 2 3 2 2 3 3 3 + + 1/36 y x - 1/144 x y - 1/36 x y + 1/18 y x - 1/72 x y + + 2 4 3 4 2 4 3 + + 1/144 x y + 1/72 x y - 1/18 x y + 1/36 x y + 1/144 x y + + 2 3 2 4 4 4 3 4 + + 1/18 x y - 1/18 x y - 1/144 x y - 1/72 x y + 1/72 x y , + + 2 4 3 3 3 4 + COEFF(-1, -1) = - 1/9 x y + 4/9 x y - 1/9 x y + 1/36 x y + 1/9 x y + + 2 2 4 2 3 2 2 2 4 4 + + 4/9 x y - 1/9 x y + 1/9 x y - 4/9 x y - 4/9 y x + 1/36 x y + + 4 3 4 3 4 3 2 3 + + 1/9 x y - 1/36 x y - 1/9 y x - 1/36 x y + 1/9 x y , COEFF(0, -1) + + 4 4 4 2 4 3 2 2 + = - 1/24 x y + 1/6 x y - 1/6 y + 1/6 y + 5/6 y x - 2/3 y + 2/3 y + + 2 3 2 4 4 4 3 2 2 + - 5/24 x y + 5/24 x y - 1/6 x y + 1/24 x y - 5/6 x y , + + 3 3 2 4 2 2 4 2 4 + COEFF(1, -1) = - 1/36 x y - 1/9 x y + 4/9 x y - 1/9 x y + 1/9 x y + + 2 3 3 2 2 3 4 3 + - 4/9 x y + 1/9 x y - 1/9 x y - 4/9 y x + 1/9 x y - 1/36 x y + + 2 4 4 3 4 4 3 + + 4/9 x y + 1/36 x y + 1/36 x y - 1/9 x y + 1/9 y x , COEFF(2, -1) + + 4 4 4 4 2 4 2 2 + = 1/18 x y - 1/144 x y - 1/36 x y + 1/36 x y + 1/72 x y - 1/36 x y + + 3 3 3 4 3 3 4 2 4 + + 1/72 x y - 1/18 y x + 1/144 x y - 1/72 x y + 1/144 x y + + 2 2 3 2 3 3 2 + - 1/18 x y + 1/36 y x - 1/72 x y - 1/144 x y + 1/18 x y , + + 4 2 3 3 4 2 2 4 + COEFF(-2, 0) = - 5/96 x y - 1/12 x - 1/48 x y + 5/96 x y + 1/24 x + + 4 2 4 4 4 2 2 3 2 + + 1/48 x y - 1/96 x y + 1/96 x y - 5/48 x y - 1/24 x + 5/48 x y + + 4 4 4 2 4 2 + + 1/12 x, COEFF(-1, 0) = - 1/24 x y - 1/6 x y + 5/6 x y + 5/24 x y + + 3 4 3 2 2 3 4 2 2 + + 1/24 x y - 5/24 x y + 2/3 x + 1/6 x - 1/6 x - 2/3 x - 5/6 x y + + 2 4 4 2 4 2 4 25 2 2 + + 1/6 x y , COEFF(0, 0) = - 5/16 x y + 1/4 x - 5/16 x y + -- x y + 16 + + 4 4 4 2 2 2 2 + + 1/16 x y + 1/4 y + 1 - 5/4 y - 5/4 x , COEFF(1, 0) = - 5/6 x y + + 2 4 2 4 4 4 4 3 4 + + 1/6 x y + 2/3 x - 1/24 x y + 1/6 x y - 1/6 x - 1/24 x y + 2/3 x + + 3 2 2 3 4 2 4 + + 5/24 x y - 5/6 x y - 1/6 x + 5/24 x y , COEFF(2, 0) = - 1/48 x y + + 4 2 4 4 2 4 4 2 + + 1/24 x + 5/48 x y - 1/12 x + 1/96 x y - 1/96 x y - 5/96 x y + + 3 2 3 4 3 2 2 2 + + 1/12 x - 1/24 x + 1/48 x y - 5/48 x y + 5/96 x y , COEFF(-2, 1) + + 3 4 2 3 2 3 2 + = - 1/72 x y + 1/36 x y + 1/144 x y - 1/36 y x - 1/18 x y + + 2 4 4 3 3 3 3 4 + + 1/18 x y + 1/144 x y - 1/144 x y + 1/72 x y + 1/72 x y + + 2 3 2 2 4 4 4 2 + + 1/18 x y - 1/18 y x - 1/36 x y - 1/144 x y + 1/36 x y + + 4 3 3 3 3 4 2 + - 1/72 x y , COEFF(-1, 1) = 1/9 x y - 1/36 x y + 1/9 y x - 1/9 x y + + 3 4 4 4 3 4 4 2 4 2 + - 1/36 x y - 1/9 x y + 1/36 x y + 1/36 x y - 1/9 x y - 4/9 x y + + 2 2 2 2 3 3 2 4 + + 4/9 y x + 4/9 x y - 1/9 x y + 1/9 x y - 4/9 x y + 1/9 x y , + + 4 2 2 3 2 4 4 4 + COEFF(0, 1) = 1/6 x y + 5/24 x y + 2/3 y + 2/3 y - 1/24 x y - 1/6 y + + 4 4 3 2 2 2 2 4 3 + + 1/6 x y - 1/24 x y - 5/6 x y - 5/6 y x + 5/24 x y - 1/6 y , + + 2 4 3 3 4 3 + COEFF(1, 1) = 4/9 x y + 1/36 x y - 1/9 x y - 1/9 x y - 1/9 y x + + 3 2 3 3 2 2 2 4 4 4 + - 1/9 x y + 1/36 x y + 4/9 x y - 1/9 x y + 1/36 x y + 4/9 x y + + 2 3 4 2 4 2 3 4 + - 1/9 x y - 1/9 x y - 1/9 x y + 4/9 y x + 1/36 x y , COEFF(2, 1) = + + 4 2 3 4 3 2 2 3 + 1/36 x y - 1/18 x y + 1/18 y x + 1/36 x y + 1/18 x y + 1/144 x y + + 2 4 3 2 4 4 2 4 + - 1/18 x y - 1/144 x y - 1/36 y x - 1/144 x y + 1/144 x y + + 3 4 3 2 2 3 3 4 + - 1/72 x y + 1/72 x y - 1/36 x y - 1/72 x y + 1/72 x y , + + 4 2 4 4 2 4 + COEFF(-2, 2) = - 1/288 x y + 1/288 y x + 1/576 x y - 1/576 x y + + 3 3 4 4 3 2 2 + + 1/144 x y - 1/288 x y - 1/144 x y + 1/288 x y + 1/576 x y + + 2 3 2 4 2 4 3 3 + - 1/288 x y - 1/288 x y - 1/576 x y + 1/288 x y - 1/144 x y + + 3 2 3 4 3 4 2 + + 1/288 x y + 1/144 y x , COEFF(-1, 2) = - 1/72 x y + 1/144 x y + + 4 4 4 3 3 3 2 4 + - 1/144 x y + 1/72 x y - 1/72 y x + 1/72 x y + 1/36 x y + + 2 2 2 3 2 3 2 2 + - 1/36 x y + 1/18 x y + 1/18 x y - 1/18 y x - 1/144 x y + 1/36 x y + + 3 4 3 4 4 2 + - 1/18 x y - 1/36 x y + 1/144 x y , COEFF(0, 2) = - 1/96 x y + + 2 4 3 2 4 4 2 + - 1/24 y + 1/48 x y - 5/96 x y + 1/24 y + 5/48 y x - 1/12 y + + 4 4 2 2 3 4 2 3 + + 1/96 x y + 5/96 x y + 1/12 y - 1/48 x y - 5/48 x y , COEFF(1, 2) + + 4 3 4 4 2 3 4 + = - 1/72 x y - 1/144 x y - 1/36 x y - 1/144 x y - 1/18 x y + + 3 2 3 2 4 3 3 + + 1/18 x y - 1/18 y x + 1/144 x y + 1/36 x y - 1/72 x y + + 2 4 2 3 4 2 2 2 4 + + 1/36 x y + 1/18 x y + 1/144 x y - 1/36 x y + 1/72 x y + + 3 4 3 4 2 4 4 + + 1/72 y x , COEFF(2, 2) = 1/288 x y - 1/576 x y + 1/576 x y + + 4 2 3 4 3 + - 1/288 x y + 1/288 x y + 1/288 x y + 1/144 x y - 1/144 x y + + 2 3 2 4 3 3 2 4 + + 1/288 y x - 1/288 x y - 1/288 x y + 1/144 x y - 1/576 x y + + 2 3 2 2 3 + - 1/288 x y + 1/576 x y - 1/144 y x ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c"); +bytes used=128130292, alloc=2227816, time=10.47 +bytes used=129130448, alloc=2227816, time=10.54 +bytes used=130130628, alloc=2227816, time=10.63 +bytes used=131157976, alloc=2227816, time=10.72 +bytes used=132170256, alloc=2227816, time=10.79 +bytes used=133182936, alloc=2227816, time=10.85 +bytes used=134184444, alloc=2227816, time=10.93 +bytes used=135184740, alloc=2227816, time=11.04 +bytes used=136185208, alloc=2227816, time=11.13 +bytes used=137185504, alloc=2227816, time=11.19 +bytes used=138185676, alloc=2227816, time=11.39 +bytes used=139186008, alloc=2227816, time=11.46 +bytes used=140186252, alloc=2227816, time=11.53 +bytes used=141186616, alloc=2227816, time=11.59 +bytes used=142186928, alloc=2227816, time=11.65 +bytes used=143187140, alloc=2227816, time=11.71 +bytes used=144187292, alloc=2227816, time=11.79 +bytes used=145187476, alloc=2424388, time=11.88 +bytes used=146187724, alloc=2424388, time=11.96 +bytes used=147188072, alloc=2424388, time=12.05 +bytes used=148188276, alloc=2424388, time=12.14 +bytes used=149188548, alloc=2424388, time=12.24 +bytes used=150189040, alloc=2424388, time=12.35 +bytes used=151189584, alloc=2424388, time=12.44 +bytes used=152189776, alloc=2424388, time=12.71 +bytes used=153190128, alloc=2424388, time=12.86 +bytes used=154190356, alloc=2424388, time=12.92 +bytes used=155198184, alloc=2424388, time=13.02 +bytes used=156199352, alloc=2424388, time=13.15 +bytes used=157206092, alloc=2424388, time=13.34 +bytes used=158206320, alloc=2424388, time=13.51 +bytes used=159206528, alloc=2424388, time=13.63 +bytes used=160206828, alloc=2424388, time=13.70 +bytes used=161207036, alloc=2424388, time=13.81 +bytes used=162207248, alloc=2424388, time=13.91 +bytes used=163207460, alloc=2424388, time=14.15 +bytes used=164207736, alloc=2424388, time=14.23 +bytes used=165207896, alloc=2424388, time=14.31 +bytes used=166208088, alloc=2424388, time=14.42 +bytes used=167208332, alloc=2424388, time=14.63 +bytes used=168208740, alloc=2424388, time=14.73 +bytes used=169208984, alloc=2424388, time=14.80 +bytes used=170209144, alloc=2424388, time=14.91 +bytes used=171209480, alloc=2424388, time=15.13 +bytes used=172209780, alloc=2424388, time=15.24 +> +# d/dx +> simplify( diff(interp_2d_cube_order4_smooth0,x) ); +bytes used=173210092, alloc=2424388, time=15.39 +bytes used=174210336, alloc=2424388, time=15.44 +bytes used=175210520, alloc=2424388, time=15.51 +bytes used=176210708, alloc=2424388, time=15.57 +bytes used=177210968, alloc=2489912, time=15.65 +bytes used=178211200, alloc=2620960, time=15.71 +- 1/12 DATA(2, 0) + 2/3 DATA(1, 0) + 1/12 DATA(-2, 0) - 2/3 DATA(-1, 0) + + 3 3 2 + - 1/18 y DATA(-1, 2) - 1/72 y DATA(2, -1) + 8/9 x y DATA(-1, -1) + + 2 2 2 2 2 2 + + 5/8 x y DATA(1, 0) - 1/3 x y DATA(1, 1) + 1/96 x y DATA(-2, 2) + + 3 3 3 + - 1/9 y DATA(1, 1) + 1/144 y DATA(-2, 2) - 1/72 y DATA(-2, 1) + + 3 3 + + 1/72 y DATA(2, 1) - 2/3 x DATA(-1, 0) - 1/12 x DATA(2, 0) + + - 5/2 x DATA(0, 0) + 4/3 x DATA(1, 0) - 1/12 x DATA(-2, 0) + + 3 3 + + 4/3 x DATA(-1, 0) - 1/144 y DATA(2, 2) + 1/18 y DATA(1, 2) + + 3 3 3 + + 1/72 y DATA(-2, -1) + 1/144 y DATA(2, -2) - 1/18 y DATA(1, -2) + + 2 2 2 2 + - 1/96 x y DATA(2, -2) + 1/48 x y DATA(1, -2) + + 2 2 2 2 + - 1/48 x y DATA(-1, -2) + 1/96 x y DATA(-2, -2) + + 2 2 2 2 2 2 + + 1/3 x y DATA(-1, -1) - 1/3 x y DATA(1, -1) - 5/8 x y DATA(-1, 0) + + 2 2 2 2 + + 1/3 x y DATA(-1, 1) + 1/24 y x DATA(1, 2) - 1/24 y x DATA(-1, 2) + + 2 2 2 2 2 + + 1/6 y x DATA(2, 1) + 5/16 x y DATA(-2, 0) - 1/6 x y DATA(-2, -1) + + 2 2 2 + - 1/24 y x DATA(1, -2) + 1/24 y x DATA(-1, -2) - 1/48 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4/9 y x DATA(-1, 1) + + 3 3 3 + - 4/9 y x DATA(1, 1) - 1/72 y x DATA(-2, 2) + 1/9 y x DATA(-2, 1) + + 3 3 3 + - 1/9 y x DATA(-2, -1) + 1/72 y x DATA(2, -2) + 1/18 y x DATA(1, 2) + + 3 3 3 + + 1/18 y x DATA(-1, 2) + 4/9 y x DATA(1, -1) - 1/18 y x DATA(1, -2) + + 3 3 3 + - 1/18 y x DATA(-1, -2) + 1/72 y x DATA(-2, -2) + 4/9 y x DATA(-1, -1) + + 3 2 3 2 3 + + 1/12 y x DATA(0, -2) + 1/24 x y DATA(-2, 1) + 1/48 x y DATA(-2, -2) + + 2 3 2 3 2 3 + - 1/48 x y DATA(2, -2) + 1/24 x y DATA(1, -2) + 1/24 x y DATA(2, -1) + + 2 3 2 3 2 3 + - 1/24 x y DATA(-2, -1) + 1/12 x y DATA(1, 1) - 1/48 x y DATA(-2, 2) + + 2 3 2 3 2 3 + + 1/48 x y DATA(2, 2) - 1/24 x y DATA(1, 2) + 1/24 x y DATA(-1, 2) + + 2 3 2 2 2 + - 1/24 x y DATA(2, 1) + 1/2 x DATA(-1, 0) - 1/6 x y DATA(-2, 1) + + 2 2 2 2 2 2 + + 1/48 x y DATA(1, 2) - 1/48 x y DATA(-1, 2) + 1/6 x y DATA(2, 1) + + 2 2 2 2 2 2 + - 5/16 x y DATA(2, 0) + 1/6 x y DATA(2, -1) - 1/96 x y DATA(2, 2) + + 2 3 2 3 + - 1/24 x y DATA(-1, -2) + 1/12 x y DATA(-1, -1) + + 2 3 2 3 + - 1/12 x y DATA(1, -1) - 1/12 x y DATA(-1, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=179213692, alloc=2620960, time=15.78 +bytes used=180223192, alloc=2620960, time=15.84 + 2 2 2 4 +[COEFF(-2, -2) = - 1/144 x y + 1/288 x y - 1/288 y + 1/144 y - 1/96 x y + + 3 2 2 3 4 3 3 + + 1/72 y x + 1/96 x y + 1/144 x y + 1/144 x y - 1/144 y + + 2 3 2 4 3 2 4 + + 1/48 x y - 1/48 y x - 1/288 x y - 1/144 x y + 1/288 y + + 3 3 2 4 3 4 3 2 + - 1/72 x y , COEFF(-1, -2) = 1/48 x y - 1/36 x y + 1/36 x y + + 2 2 2 3 3 3 3 + - 1/48 x y + 1/36 y + 1/18 x y - 1/9 x y + 1/18 y - 1/18 y + + 4 2 2 3 2 3 + - 1/36 y + 1/24 y x - 1/18 x y - 1/18 y x - 1/24 x y + 1/9 x y + + 4 3 3 3 3 2 + + 1/18 x y , COEFF(0, -2) = 1/12 y x - 1/12 x y - 1/24 x y + + 2 4 3 3 4 + + 5/48 x y - 5/24 x y - 5/48 x y + 5/24 x y + 1/24 x y , COEFF(1, -2) + + 2 3 2 2 3 3 4 + = - 1/18 x y - 1/18 y x - 1/24 y x + 1/24 x y - 1/36 x y + 1/18 y + + 3 2 2 3 3 2 4 3 2 2 + + 1/36 x y - 1/36 y + 1/18 x y - 1/48 x y - 1/18 y + 1/48 x y + + 3 4 4 4 + + 1/9 x y - 1/9 x y + 1/36 y + 1/18 x y , COEFF(2, -2) = - 1/288 y + + 2 3 3 2 3 4 + + 1/288 x y - 1/72 x y - 1/48 x y - 1/288 x y - 1/144 x y - 1/144 y + + 2 4 2 3 4 3 2 3 + + 1/96 x y + 1/48 y x + 1/144 x y - 1/144 x y + 1/144 x y + + 2 2 3 3 2 + - 1/96 x y + 1/144 y + 1/72 y x + 1/288 y , COEFF(-2, -1) = + + 3 4 4 2 3 2 2 + - 1/72 x y - 1/72 y + 1/72 x y - 1/24 x y + 1/18 y - 1/18 x y + + 3 4 2 4 2 3 3 + - 1/36 x y + 1/24 x y + 1/6 y x + 1/18 x y + 1/36 x y - 1/18 y + + 3 3 2 3 2 2 2 3 + - 1/9 y x + 1/9 x y + 1/72 y - 1/6 x y , COEFF(-1, -1) = 1/12 x y + + 2 2 4 3 3 3 4 + - 4/9 y - 8/9 x y - 1/12 x y - 1/9 y + 2/9 x y + 4/9 y x + 1/9 y + + 3 3 3 4 2 2 2 3 2 + - 1/9 x y + 4/9 y + 1/9 x y + 1/3 x y + 8/9 x y - 4/9 x y + + 2 4 3 3 3 3 4 + - 1/3 y x - 2/9 x y , COEFF(0, -1) = 1/6 x y - 2/3 y x - 1/6 x y + + 3 2 2 3 4 + + 2/3 x y - 5/3 x y + 5/3 x y - 5/12 x y + 5/12 x y , COEFF(1, -1) = + + 2 2 3 3 4 2 3 3 3 + - 1/3 x y + 4/9 y x + 1/9 x y + 4/9 y + 2/9 x y - 1/9 x y + + 2 2 4 4 2 3 2 + - 8/9 x y + 8/9 x y + 1/12 x y - 2/9 x y + 1/3 y x - 4/9 x y + + 3 4 2 3 2 2 + + 1/9 y - 4/9 y - 1/9 y - 1/12 x y , COEFF(2, -1) = 1/6 x y + + 2 3 2 4 4 4 2 3 + - 1/6 y x - 1/72 y - 1/24 x y + 1/72 y + 1/72 x y + 1/24 x y + + 3 2 2 3 4 2 3 3 + + 1/9 x y - 1/18 y - 1/36 x y + 1/18 x y - 1/18 x y + 1/36 x y + + 3 3 3 2 + + 1/18 y - 1/9 y x - 1/72 x y , COEFF(-2, 0) = 1/12 - 5/24 x y + + 4 2 4 2 2 3 4 3 + + 1/48 y - 1/16 x y + 5/48 x y - 1/4 x + 1/24 x y + 1/6 x + + 2 2 4 2 4 + + 5/16 x y - 1/48 x y - 5/48 y - 1/12 x, COEFF(-1, 0) = 1/3 x y - 2/3 + + 2 2 4 3 2 2 3 4 2 + - 5/3 x y + 1/8 x y + 5/6 x y + 1/2 x - 2/3 x - 1/6 y + 5/6 y + + 2 2 3 4 + - 5/8 x y + 4/3 x - 1/6 x y , + + 2 3 3 4 4 3 2 + COEFF(0, 0) = 25/8 x y + x + 1/4 x y - 5/2 x - 5/8 x y - 5/4 x y , + + 3 2 3 4 2 2 2 2 + COEFF(1, 0) = 5/6 x y - 1/6 x y - 5/3 x y - 5/6 y + 2/3 + 5/8 x y + + 2 2 4 3 4 4 + - 1/2 x - 1/8 x y - 2/3 x + 1/3 x y + 1/6 y + 4/3 x, COEFF(2, 0) = + + 2 2 3 2 3 4 + - 1/12 x + 1/4 x + 5/48 x y - 5/24 x y + 1/6 x - 1/12 - 1/48 y + + 4 2 2 2 2 4 3 4 + - 1/48 x y + 5/48 y - 5/16 x y + 1/16 x y + 1/24 x y , COEFF(-2, 1) + + 3 2 2 2 3 4 + = - 1/72 y - 1/18 x y + 1/18 y - 1/6 y x + 1/18 y - 1/36 x y + + 2 4 4 3 3 3 2 2 2 + + 1/24 x y - 1/72 y - 1/36 x y + 1/9 x y - 1/6 x y - 1/18 x y + + 3 4 2 3 3 4 + + 1/9 y x + 1/72 x y + 1/24 x y + 1/72 x y , COEFF(-1, 1) = - 2/9 x y + + 2 3 3 3 2 2 3 + + 8/9 x y - 4/9 y + 1/9 x y - 4/9 x y + 1/3 y x - 2/9 x y + + 3 2 4 4 3 4 2 2 2 + - 4/9 y x - 1/12 x y + 1/9 y + 1/9 x y + 8/9 x y + 1/3 x y + + 3 2 3 2 + + 1/9 y - 1/12 x y - 4/9 y, COEFF(0, 1) = - 5/3 x y - 5/3 x y + + 3 4 3 4 3 3 3 3 2 + - 1/6 x y + 5/12 x y + 5/12 x y - 1/6 x y + 2/3 y x + 2/3 x y , + + 2 2 3 3 3 4 3 + COEFF(1, 1) = - 1/3 y x + 1/12 x y + 1/9 x y - 2/9 x y - 2/9 x y + + 2 3 3 2 2 4 + + 4/9 y - 1/9 y + 8/9 x y + 4/9 y - 4/9 y x - 1/3 x y - 1/9 y + + 3 4 2 4 3 2 2 2 + + 1/9 x y + 1/12 x y - 4/9 x y + 8/9 x y , COEFF(2, 1) = 1/6 y x + + 4 3 2 3 2 4 2 + + 1/72 x y + 1/72 x y - 1/18 y + 1/9 y x - 1/24 x y - 1/18 x y + + 3 4 3 2 2 2 3 + - 1/36 x y + 1/9 x y + 1/6 x y + 1/72 y - 1/18 y - 1/18 x y + + 4 2 3 3 3 2 + + 1/72 y - 1/24 x y - 1/36 x y , COEFF(-2, 2) = 1/144 x y + 1/48 y x + + 3 3 3 2 3 2 4 2 3 + + 1/72 x y + 1/144 y + 1/288 x y - 1/144 x y + 1/288 y - 1/48 x y + + 2 2 2 3 4 3 4 + - 1/144 y + 1/96 x y - 1/288 y - 1/144 x y - 1/288 x y + 1/144 x y + + 2 4 3 2 4 2 + - 1/96 x y - 1/72 y x , COEFF(-1, 2) = 1/48 x y - 1/9 x y - 1/18 x y + + 3 3 2 2 2 3 4 2 3 + - 1/18 x y + 1/36 y - 1/48 x y + 1/18 y - 1/36 x y + 1/24 x y + + 3 2 3 2 3 4 4 + - 1/18 y - 1/24 y x + 1/36 x y + 1/18 y x + 1/18 x y - 1/36 y + + 3 2 3 3 3 2 + + 1/9 x y , COEFF(0, 2) = 5/48 x y + 1/12 x y - 1/24 x y + 5/24 x y + + 4 3 4 3 3 + - 5/48 x y + 1/24 x y - 1/12 y x - 5/24 x y , COEFF(1, 2) = + + 3 4 2 2 3 2 3 + - 1/36 x y - 1/9 x y + 1/48 x y + 1/18 y x + 1/24 y x + 1/9 x y + + 4 2 4 2 3 2 3 2 2 + + 1/18 x y - 1/48 x y - 1/24 x y - 1/36 y + 1/36 x y - 1/18 x y + + 3 3 4 3 3 + - 1/18 y - 1/18 x y + 1/36 y + 1/18 y , COEFF(2, 2) = - 1/144 y + + 2 2 2 3 4 3 3 2 + - 1/96 x y + 1/48 x y - 1/288 y + 1/72 x y + 1/288 x y + + 3 2 4 3 3 2 + - 1/144 x y - 1/48 y x - 1/288 x y - 1/72 y x - 1/144 x y + + 3 4 2 4 2 + + 1/144 x y + 1/96 x y + 1/144 y + 1/144 x y + 1/288 y ] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c"); +bytes used=181223344, alloc=2620960, time=15.90 +bytes used=182223500, alloc=2620960, time=15.97 +bytes used=183223664, alloc=2620960, time=16.07 +bytes used=184244420, alloc=2620960, time=16.17 +bytes used=185261976, alloc=2620960, time=16.24 +bytes used=186262132, alloc=2620960, time=16.32 +bytes used=187271400, alloc=2620960, time=16.41 +bytes used=188271672, alloc=2620960, time=16.50 +bytes used=189271940, alloc=2620960, time=16.57 +bytes used=190272092, alloc=2620960, time=16.84 +bytes used=191272872, alloc=2620960, time=16.90 +bytes used=192273040, alloc=2620960, time=16.96 +bytes used=193273564, alloc=2620960, time=17.03 +bytes used=194283560, alloc=2620960, time=17.13 +bytes used=195283924, alloc=2620960, time=17.24 +bytes used=196288796, alloc=2620960, time=17.34 +bytes used=197290992, alloc=2620960, time=17.43 +bytes used=198291176, alloc=2620960, time=17.52 +bytes used=199291660, alloc=2620960, time=17.61 +bytes used=200292092, alloc=2620960, time=17.89 +bytes used=201292244, alloc=2620960, time=18.05 +bytes used=202292640, alloc=2620960, time=18.12 +bytes used=203294780, alloc=2620960, time=18.22 +bytes used=204295016, alloc=2620960, time=18.34 +bytes used=205295216, alloc=2620960, time=18.44 +bytes used=206305080, alloc=2620960, time=18.68 +bytes used=207305332, alloc=2620960, time=18.84 +bytes used=208305696, alloc=2620960, time=18.90 +bytes used=209306900, alloc=2620960, time=19.00 +bytes used=210308068, alloc=2620960, time=19.12 +bytes used=211308248, alloc=2620960, time=19.34 +bytes used=212308496, alloc=2620960, time=19.47 +bytes used=213308676, alloc=2620960, time=19.54 +bytes used=214312144, alloc=2620960, time=19.67 +bytes used=215319752, alloc=2620960, time=19.92 +bytes used=216319980, alloc=2620960, time=20.07 +bytes used=217320236, alloc=2620960, time=20.15 +bytes used=218320488, alloc=2620960, time=20.29 +bytes used=219320656, alloc=2620960, time=20.59 +bytes used=220320808, alloc=2620960, time=20.75 +> +# d/dy +> simplify( diff(interp_2d_cube_order4_smooth0,y) ); +bytes used=221321332, alloc=2620960, time=20.87 +bytes used=222321548, alloc=2620960, time=20.93 +bytes used=223321736, alloc=2620960, time=21.00 +bytes used=224321912, alloc=2620960, time=21.06 + 4 2 4 2 +- 1/12 DATA(0, 2) - 1/12 x y DATA(-1, -1) + 1/8 x y DATA(0, -1) + + 4 2 4 2 + + 1/12 x y DATA(-1, 1) - 1/96 x y DATA(-2, -2) + + 4 2 3 3 + - 1/48 x y DATA(-2, 1) + 1/6 y DATA(0, 2) + y DATA(0, 0) + + 3 3 3 + - 2/3 y DATA(0, 1) + 1/6 y DATA(0, -2) - 2/3 y DATA(0, -1) + + 4 2 2 2 2 2 + + 1/24 x y DATA(-1, -2) - 5/16 x y DATA(0, 2) + 5/16 x y DATA(0, -2) + + 2 2 3 2 2 + + 5/8 x y DATA(0, 1) - 2/3 x y DATA(-1, 0) - 5/8 x y DATA(0, -1) + + 3 2 3 2 3 + + 1/12 x y DATA(-2, 0) + 2/3 x y DATA(-1, 0) + 2/3 x y DATA(1, 0) + + 2 3 2 3 2 3 + - 1/24 x y DATA(-2, 0) + 5/6 x y DATA(0, -1) - 1/24 x y DATA(2, 0) + + 2 3 4 3 4 3 + - 5/24 x y DATA(0, 2) - 1/6 x y DATA(-1, 0) - 1/36 x y DATA(-2, -1) + + 4 3 4 3 + + 1/144 x y DATA(2, -2) - 1/36 x y DATA(1, -2) + + 4 3 4 3 2 3 + - 1/36 x y DATA(-1, -2) + 1/24 x y DATA(2, 0) + 5/6 x y DATA(0, 1) + + 2 3 4 3 + - 5/24 x y DATA(0, -2) + 1/9 x y DATA(-1, 1) + + 4 3 4 3 2 3 + + 1/144 x y DATA(-2, -2) + 1/9 x y DATA(-1, -1) - 5/4 x y DATA(0, 0) + + 4 3 + + 1/9 x y DATA(1, -1) - 1/12 y DATA(0, 2) - 5/2 y DATA(0, 0) + + 4 3 + + 4/3 y DATA(0, 1) - 1/12 y DATA(0, -2) + 1/144 x y DATA(2, 2) + + 4 3 4 3 4 3 + - 1/36 x y DATA(-1, 2) - 1/6 x y DATA(0, 1) + 1/24 x y DATA(0, -2) + + 4 3 4 3 4 3 + - 1/6 x y DATA(0, -1) + 1/24 x y DATA(0, 2) - 1/36 x y DATA(1, 2) + + 4 3 4 3 4 3 + - 1/36 x y DATA(2, 1) - 1/6 x y DATA(1, 0) + 1/9 x y DATA(1, 1) + + 4 3 4 3 + - 1/36 x y DATA(-2, 1) + 1/24 x y DATA(-2, 0) + + 4 3 4 3 + + 1/144 x y DATA(-2, 2) - 1/36 x y DATA(2, -1) + 4/3 y DATA(0, -1) + + 2 2 2 + - 1/4 y DATA(0, -2) + 1/2 y DATA(0, -1) - 1/2 y DATA(0, 1) + + 2 3 3 + + 1/4 y DATA(0, 2) + 2/3 x y DATA(1, 0) - 1/12 x y DATA(2, 0) + + 3 3 3 + - 5/12 y x DATA(-1, 0) + 5/24 y x DATA(-2, 0) - 5/24 y x DATA(2, 0) + + 3 3 3 + + 5/12 y x DATA(1, 0) - 1/72 x DATA(-1, 2) + 1/72 x DATA(1, 2) + + 3 3 3 + - 1/144 x DATA(2, 2) + 1/144 x DATA(2, -2) + 1/18 x DATA(-2, -1) + + 3 3 3 + - 1/18 x DATA(-2, 1) + 1/144 x DATA(-2, 2) - 1/9 x DATA(1, 1) + + 3 3 4 + - 1/18 x DATA(2, -1) + 1/18 x DATA(2, 1) + 1/18 x y DATA(2, 1) + + 4 4 4 + + 1/72 x y DATA(-1, -2) + 1/72 x y DATA(1, -2) - 1/288 x y DATA(2, -2) + + 4 4 4 + - 5/48 x y DATA(2, 0) - 5/8 x y DATA(0, 0) + 1/3 x y DATA(0, -1) + + 4 4 4 + - 1/48 x y DATA(0, -2) + 1/3 x y DATA(0, 1) + 1/72 x y DATA(-1, 2) + + 4 4 4 + + 1/72 x y DATA(1, 2) - 1/288 x y DATA(2, 2) - 1/288 x y DATA(-2, 2) + + 4 4 4 + - 5/48 x y DATA(-2, 0) + 1/18 x y DATA(-2, 1) - 2/9 x y DATA(1, 1) + + 4 4 4 + + 5/12 x y DATA(1, 0) + 1/18 x y DATA(2, -1) - 1/48 x y DATA(0, 2) + + 4 4 4 + - 2/9 x y DATA(-1, 1) - 2/9 x y DATA(1, -1) - 2/9 x y DATA(-1, -1) + + 4 4 4 + - 1/288 x y DATA(-2, -2) + 5/12 x y DATA(-1, 0) - 1/288 x DATA(-2, 2) + + 3 3 3 + + 1/9 x DATA(-1, 1) + 1/9 x DATA(1, -1) - 1/9 x DATA(-1, -1) + + 3 3 3 + - 1/144 x DATA(-2, -2) + 1/72 x DATA(-1, -2) - 1/72 x DATA(1, -2) + + 4 4 4 + - 1/9 x DATA(1, 1) - 1/6 x DATA(0, -1) + 1/9 x DATA(-1, -1) + + 4 4 4 + + 1/288 x DATA(-2, -2) - 1/72 x DATA(-1, -2) + 1/48 x DATA(0, -2) + + 4 4 4 + - 1/72 x DATA(1, -2) + 1/288 x DATA(2, -2) - 1/36 x DATA(-2, -1) + + 4 4 + + 1/36 x DATA(-2, 1) + 1/18 x DATA(2, -1) + 1/6 x DATA(0, 1) + + 4 4 4 + - 1/36 x DATA(2, -1) + 1/36 x DATA(2, 1) - 1/48 x DATA(0, 2) + + 4 4 4 + + 1/72 x DATA(-1, 2) + 1/72 x DATA(1, 2) - 1/288 x DATA(2, 2) + + 4 4 + - 1/9 x DATA(-1, 1) + 1/9 x DATA(1, -1) + 5/24 x y DATA(2, 0) + + 4 3 3 3 + - 5/3 x y DATA(1, 0) + 1/4 x y DATA(0, 0) + 1/12 x y DATA(2, 0) + + 3 3 3 3 4 + + 1/6 x y DATA(-1, 0) - 1/6 x y DATA(1, 0) + 1/18 x y DATA(-2, -1) + + 3 3 2 2 + - 1/12 x y DATA(-2, 0) + 1/36 x DATA(-2, -1) + 1/18 x DATA(1, -2) + + 2 2 2 + - 5/48 x DATA(0, -2) + 1/18 x DATA(-1, -2) - 1/288 x DATA(-2, -2) + + - 4/9 x DATA(1, -1) - 4/9 x DATA(-1, 1) + 1/18 x DATA(-2, 1) + + - 1/144 x DATA(2, -2) + 1/18 x DATA(1, -2) - 1/18 x DATA(-1, -2) + + + 1/144 x DATA(-2, -2) + 4/9 x DATA(-1, -1) - 1/18 x DATA(-2, -1) + + + 4/9 x DATA(1, 1) - 1/144 x DATA(-2, 2) + 1/144 x DATA(2, 2) + + - 1/18 x DATA(1, 2) + 1/18 x DATA(-1, 2) - 1/18 x DATA(2, 1) + + 2 + - 1/288 x DATA(2, -2) + 5/3 x y DATA(-1, 0) - 5/24 x y DATA(-2, 0) + + 2 2 2 + + 5/48 y x DATA(-2, 0) - 5/3 y x DATA(-1, 0) - 5/3 y x DATA(0, 1) + + 2 2 2 + + 5/48 y x DATA(0, -2) - 5/3 y x DATA(0, -1) + 5/48 y x DATA(0, 2) + + 2 4 2 4 2 + + 25/8 y x DATA(0, 0) - 1/24 x y DATA(1, 2) - 1/24 x y DATA(-1, 2) + + 4 2 4 2 2 + + 1/16 x y DATA(0, 2) - 1/48 x y DATA(2, 1) + 5/48 y x DATA(2, 0) + + 2 2 2 + - 5/3 y x DATA(1, 0) + 5/6 x DATA(0, -1) - 4/9 x DATA(1, -1) + + 2 2 2 + + 4/9 x DATA(-1, 1) + 1/288 x DATA(2, 2) - 1/18 x DATA(1, 2) + + 2 2 2 + - 1/18 x DATA(-1, 2) + 5/48 x DATA(0, 2) - 1/36 x DATA(2, 1) + + 2 2 2 + + 1/36 x DATA(2, -1) - 5/6 x DATA(0, 1) + 4/9 x DATA(1, 1) + + 2 2 4 2 + + 1/288 x DATA(-2, 2) - 1/36 x DATA(-2, 1) + 1/12 x y DATA(1, 1) + + 4 2 4 2 4 2 + + 1/96 x y DATA(-2, 2) - 1/12 x y DATA(1, -1) + 1/96 x y DATA(2, 2) + + 4 2 4 2 4 2 + - 1/96 x y DATA(2, -2) + 1/24 x y DATA(1, -2) - 1/16 x y DATA(0, -2) + + 4 2 4 2 4 2 + + 1/48 x y DATA(-2, -1) + 1/48 x y DATA(2, -1) - 1/8 x y DATA(0, 1) + + 2 + - 4/9 x DATA(-1, -1) + 2/3 DATA(0, 1) + 1/12 DATA(0, -2) + + 2 2 2 + - 2/3 DATA(0, -1) - 1/3 x y DATA(-1, -1) - 1/3 x y DATA(1, 1) + + 2 2 2 2 2 2 + - 1/96 x y DATA(-2, 2) + 1/96 x y DATA(2, -2) - 1/6 x y DATA(1, -2) + + 2 2 2 2 + - 1/6 x y DATA(-1, -2) + 1/96 x y DATA(-2, -2) + + 2 2 2 2 2 2 + + 1/3 x y DATA(-1, -1) + 1/3 x y DATA(1, -1) - 1/3 x y DATA(-1, 1) + + 2 2 2 + - 1/18 y x DATA(1, 2) - 1/18 y x DATA(-1, 2) - 1/18 y x DATA(2, 1) + + 2 2 2 2 + - 1/48 x y DATA(-2, -1) - 1/18 y x DATA(1, -2) - 1/18 y x DATA(-1, -2) + + 2 2 2 + + 1/288 y x DATA(-2, -2) + 1/288 y x DATA(2, 2) + 8/9 y x DATA(1, 1) + + 2 2 2 + + 1/288 y x DATA(-2, 2) - 1/18 y x DATA(-2, 1) - 1/18 y x DATA(-2, -1) + + 2 2 2 + + 1/288 y x DATA(2, -2) + 8/9 y x DATA(-1, -1) + 8/9 y x DATA(1, -1) + + 2 2 2 + + 8/9 y x DATA(-1, 1) - 1/18 y x DATA(2, -1) + 1/3 x y DATA(1, -1) + + 2 2 2 + + 1/3 x y DATA(-1, 1) + 1/24 x y DATA(-2, -1) + 1/48 x y DATA(2, -2) + + 2 2 2 + - 1/6 x y DATA(1, -2) + 1/6 x y DATA(-1, -2) + 1/6 x y DATA(1, 2) + + 2 2 2 + - 1/6 x y DATA(-1, 2) + 1/24 x y DATA(2, 1) - 1/48 x y DATA(-2, -2) + + - 1/18 x y DATA(1, 2) + 1/18 x y DATA(-1, 2) - 1/9 x y DATA(2, 1) + + - 1/9 x y DATA(2, -1) + 8/9 x y DATA(1, 1) - 1/144 x y DATA(-2, 2) + + + 1/9 x y DATA(-2, 1) + 1/9 x y DATA(-2, -1) + 1/144 x y DATA(2, -2) + + 2 2 2 + - 1/3 x y DATA(1, 1) - 1/24 x y DATA(-2, 1) + 1/48 x y DATA(-2, 2) + + 2 2 + - 1/24 x y DATA(2, -1) - 1/48 x y DATA(2, 2) - 8/9 x y DATA(-1, 1) + + 3 3 3 3 3 3 + + 1/72 x y DATA(2, 2) - 1/36 x y DATA(1, 2) + 1/36 x y DATA(-1, 2) + + 3 3 3 3 3 3 + - 1/18 x y DATA(2, 1) - 1/18 x y DATA(2, -1) + 1/9 x y DATA(1, -1) + + 3 3 + + 1/144 x y DATA(2, 2) + 1/72 x y DATA(2, -2) - 1/18 x y DATA(1, -2) + + + 1/18 x y DATA(-1, -2) - 1/144 x y DATA(-2, -2) - 8/9 x y DATA(-1, -1) + + 3 3 3 3 + + 8/9 x y DATA(1, -1) + 1/36 x y DATA(-1, -2) - 1/72 x y DATA(-2, -2) + + 3 3 3 3 3 + - 1/9 x y DATA(-1, -1) - 1/9 x y DATA(-1, 1) - 1/72 x y DATA(2, 2) + + 3 3 3 3 3 3 + + 1/9 x y DATA(1, 1) - 1/72 x y DATA(-2, 2) + 1/18 x y DATA(-2, 1) + + 3 3 3 3 + + 1/18 x y DATA(-2, -1) + 1/18 x y DATA(2, -1) - 4/9 x y DATA(1, 1) + + 3 3 3 3 + + 1/72 x y DATA(-2, 2) - 1/18 x y DATA(-2, 1) - 1/36 x y DATA(1, -2) + + 3 3 3 + + 4/9 x y DATA(-1, 1) + 1/9 x y DATA(1, 2) - 1/9 x y DATA(-1, 2) + + 3 3 2 3 + + 1/18 x y DATA(2, 1) - 1/12 x y DATA(1, -1) - 1/18 x y DATA(-2, -1) + + 3 3 3 + - 1/72 x y DATA(2, -2) + 1/9 x y DATA(1, -2) - 1/9 x y DATA(-1, -2) + + 3 3 3 + + 1/72 x y DATA(-2, -2) + 4/9 x y DATA(-1, -1) - 4/9 x y DATA(1, -1) + + 3 2 3 3 2 + + 1/48 x y DATA(2, 2) - 1/144 y x DATA(2, 2) - 1/12 x y DATA(-1, 1) + + 3 2 3 2 + - 1/24 x y DATA(-2, -1) - 1/48 x y DATA(2, -2) + + 3 2 3 2 + + 1/24 x y DATA(1, -2) - 1/24 x y DATA(-1, -2) + + 3 2 3 2 + + 1/48 x y DATA(-2, -2) + 1/12 x y DATA(-1, -1) + + 3 2 3 2 3 + - 1/24 x y DATA(2, 1) + 1/24 x y DATA(2, -1) + 1/9 y x DATA(2, 1) + + 3 3 2 3 2 + + 1/9 y x DATA(2, -1) + 1/12 x y DATA(1, 1) + 1/24 x y DATA(-2, 1) + + 3 2 3 2 3 2 + - 1/48 x y DATA(-2, 2) - 1/24 x y DATA(1, 2) + 1/24 x y DATA(-1, 2) + + 3 3 3 + + 2/9 y x DATA(-1, 1) - 2/9 y x DATA(1, 1) + 1/144 y x DATA(-2, 2) + + 3 3 3 + - 1/9 y x DATA(-2, 1) - 1/9 y x DATA(-2, -1) - 1/144 y x DATA(2, -2) + + 3 3 3 + + 1/72 y x DATA(1, 2) - 1/72 y x DATA(-1, 2) - 2/9 y x DATA(1, -1) + + 3 3 3 + + 1/72 y x DATA(1, -2) - 1/72 y x DATA(-1, -2) + 1/144 y x DATA(-2, -2) + + 3 2 3 + + 2/9 y x DATA(-1, -1) + 1/36 x y DATA(-2, 1) + + 2 3 2 3 + - 1/144 x y DATA(-2, -2) - 1/144 x y DATA(2, -2) + + 2 3 2 3 2 3 + + 1/9 x y DATA(1, -2) + 1/36 x y DATA(2, -1) + 1/36 x y DATA(-2, -1) + + 2 3 2 3 2 3 + - 4/9 x y DATA(1, 1) - 1/144 x y DATA(-2, 2) - 1/144 x y DATA(2, 2) + + 2 3 2 3 2 3 + + 1/9 x y DATA(1, 2) + 1/9 x y DATA(-1, 2) + 1/36 x y DATA(2, 1) + + 2 2 2 2 2 2 + + 1/48 x y DATA(-2, 1) + 1/6 x y DATA(1, 2) + 1/6 x y DATA(-1, 2) + + 2 2 2 2 2 2 + + 1/48 x y DATA(2, 1) - 1/48 x y DATA(2, -1) - 1/96 x y DATA(2, 2) + + 2 3 2 3 2 3 + + 1/9 x y DATA(-1, -2) - 4/9 x y DATA(-1, -1) - 4/9 x y DATA(1, -1) + + 2 3 + - 4/9 x y DATA(-1, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=225340376, alloc=2752008, time=21.13 +bytes used=226340564, alloc=2752008, time=21.19 + 2 3 3 4 3 3 +[COEFF(-2, -2) = - 1/288 x - 1/72 x y + 1/144 x + 1/144 x y - 1/144 x + + 2 3 3 2 2 3 2 4 2 + - 1/144 x y + 1/72 x y + 1/96 x y + 1/48 x y - 1/96 x y + + 2 4 3 4 2 + + 1/288 y x - 1/288 x y + 1/144 y x + 1/288 x - 1/144 x y - 1/48 x y , + + 2 4 3 3 2 2 + COEFF(-1, -2) = 1/18 x - 1/36 x y - 1/72 y x - 1/18 y x + 1/6 x y + + 2 3 3 3 2 4 2 + + 1/9 x y + 1/72 x - 1/24 x y + 1/24 x y - 1/18 x + 1/18 x y + + 4 3 3 3 4 2 2 + - 1/72 x - 1/9 x y + 1/36 x y + 1/72 x y - 1/6 x y , COEFF(0, -2) = + + 4 2 2 4 2 3 + - 1/48 x y - 5/48 x + 5/48 y x + 1/48 x + 1/12 - 1/12 y - 5/24 x y + + 3 2 2 2 4 3 4 2 + + 1/6 y + 5/16 x y - 1/4 y + 1/24 x y - 1/16 x y , COEFF(1, -2) = + + 3 2 2 2 3 2 4 3 + - 1/18 x y + 1/24 x y - 1/6 x y - 1/72 x - 1/6 x y - 1/36 x y + + 4 3 3 2 4 2 3 3 + - 1/72 x + 1/9 x y + 1/72 y x + 1/18 x + 1/24 x y - 1/36 x y + + 2 3 2 4 3 + + 1/9 x y - 1/18 y x + 1/18 x + 1/72 x y, COEFF(2, -2) = - 1/144 y x + + 2 4 3 2 2 2 + + 1/288 y x + 1/144 x y + 1/96 x y + 1/144 x y - 1/144 x - 1/288 x + + 4 3 3 2 3 3 2 3 + - 1/288 x y + 1/144 x - 1/48 x y + 1/72 x y + 1/48 x y - 1/72 x y + + 4 2 3 4 2 2 + + 1/288 x - 1/144 x y - 1/96 x y , COEFF(-2, -1) = 1/24 x y + + 3 2 2 2 2 4 2 3 + - 1/24 x y + 1/9 x y - 1/48 x y - 1/18 y x + 1/48 x y - 1/18 x y + + 4 2 3 4 3 3 3 2 + + 1/18 x y + 1/36 x y - 1/36 x + 1/18 x y + 1/18 x + 1/36 x + + 3 4 3 3 2 + - 1/18 x - 1/9 y x - 1/36 x y , COEFF(-1, -1) = 1/12 x y - 8/9 x y + + 3 3 3 2 4 4 3 2 2 + + 4/9 x y - 1/9 x y - 4/9 x - 2/9 x y + 1/9 x y + 1/3 x y + + 4 2 3 2 3 2 4 2 + + 1/9 x - 4/9 x y + 8/9 y x + 2/9 y x + 4/9 x - 1/3 x y - 1/12 x y + + 3 4 2 2 2 2 + - 1/9 x , COEFF(0, -1) = 1/3 x y - 5/3 y x + 5/6 x - 2/3 - 5/8 x y + + 3 4 4 3 2 3 2 4 2 + + 4/3 y - 2/3 y - 1/6 x - 1/6 x y + 5/6 x y + 1/2 y + 1/8 x y , + + 3 2 2 3 4 3 + COEFF(1, -1) = 1/9 x + 8/9 x y + 1/3 x y - 4/9 x y + 1/9 x y + + 4 3 2 4 2 2 3 3 + - 2/9 x y - 1/12 x y - 1/12 x y + 8/9 y x - 4/9 x + 1/9 x y + + 2 2 3 4 2 3 + + 1/3 x y - 4/9 x - 2/9 y x + 1/9 x - 4/9 x y , COEFF(2, -1) = + + 4 3 2 3 3 2 2 4 2 + - 1/36 x + 1/9 y x + 1/36 x - 1/18 x y - 1/48 x y + 1/48 x y + + 2 4 3 2 3 2 3 + - 1/18 y x + 1/18 x - 1/36 x y - 1/24 x y + 1/24 x y + 1/18 x y + + 2 3 4 3 3 3 + + 1/36 x y + 1/18 x y - 1/18 x - 1/9 x y, COEFF(-2, 0) = - 1/12 x y + + 4 2 2 3 3 3 + - 5/48 x y + 5/48 y x - 1/24 x y + 5/24 y x + 1/12 x y - 5/24 x y + + 4 3 2 3 4 3 3 3 + + 1/24 x y , COEFF(-1, 0) = 2/3 x y - 1/6 x y + 1/6 x y + 5/3 x y + + 3 2 4 3 + - 5/12 y x - 5/3 y x + 5/12 x y - 2/3 x y , + + 2 3 4 2 3 4 3 + COEFF(0, 0) = 25/8 y x + y - 5/8 x y - 5/4 x y + 1/4 x y - 5/2 y, + + 2 3 4 4 3 3 3 + COEFF(1, 0) = 2/3 x y + 5/12 x y - 5/3 x y - 1/6 x y - 1/6 x y + + 2 3 3 3 3 + - 5/3 y x + 5/12 y x + 2/3 x y , COEFF(2, 0) = 5/24 x y + 1/12 x y + + 4 3 2 2 3 3 3 4 + + 1/24 x y + 5/48 y x - 1/24 x y - 1/12 x y - 5/24 y x - 5/48 x y, + + 3 3 2 4 3 4 2 + COEFF(-2, 1) = - 1/18 x + 1/24 x y + 1/18 x y - 1/9 y x - 1/48 x y + + 3 3 2 4 3 2 2 + + 1/9 x y + 1/18 x y - 1/24 x y + 1/36 x - 1/18 x y + 1/48 x y + + 2 3 4 3 2 2 + + 1/36 x y + 1/18 x - 1/36 x y - 1/36 x - 1/18 y x , COEFF(-1, 1) = + + 3 3 4 3 2 2 2 3 4 3 + - 1/9 x y - 1/9 x + 4/9 x y + 1/3 x y - 1/3 x y + 1/9 x + 1/9 x y + + 2 3 2 2 2 3 4 + + 8/9 y x - 1/12 x y + 4/9 x - 4/9 x y - 4/9 x - 2/9 x y - 8/9 x y + + 4 2 3 4 4 2 2 + + 1/12 x y + 2/9 y x , COEFF(0, 1) = 1/6 x - 1/8 x y - 1/2 y + 2/3 + + 2 3 4 3 2 2 2 2 4 + + 5/6 x y + 4/3 y - 1/6 x y - 5/6 x + 5/8 x y - 5/3 y x + 1/3 x y + + 3 2 3 4 2 4 + - 2/3 y , COEFF(1, 1) = - 1/3 x y - 4/9 x y + 1/12 x y - 1/9 x + + 3 2 3 3 2 2 2 3 4 + + 1/12 x y + 1/9 x y + 4/9 x - 1/3 x y - 2/9 y x - 2/9 x y + + 2 3 4 3 3 2 + + 4/9 x + 8/9 x y - 4/9 x y + 1/9 x y - 1/9 x + 8/9 y x , COEFF(2, 1) + + 3 2 2 2 2 2 2 3 + = 1/18 x y - 1/18 y x - 1/36 x + 1/48 x y + 1/24 x y + 1/36 x y + + 3 2 3 3 4 2 3 + - 1/24 x y - 1/18 x y - 1/9 x y - 1/48 x y - 1/18 x + 1/9 y x + + 3 4 3 4 4 + + 1/18 x - 1/36 x y + 1/36 x + 1/18 x y, COEFF(-2, 2) = - 1/144 x + + 2 2 4 2 4 2 2 3 + + 1/288 y x + 1/288 x + 1/96 x y - 1/288 x - 1/96 x y + 1/72 x y + + 2 3 3 4 3 2 2 + - 1/144 x y - 1/144 x y + 1/144 x - 1/288 x y - 1/48 x y + 1/48 x y + + 3 3 3 4 3 4 + - 1/72 x y + 1/144 y x + 1/144 x y , COEFF(-1, 2) = 1/72 x + + 3 3 3 4 2 3 2 + + 1/36 x y - 1/72 x - 1/24 x y + 1/18 x y - 1/72 y x - 1/18 x + + 3 2 2 3 2 2 2 2 3 + + 1/24 x y + 1/9 x y + 1/6 x y - 1/6 x y - 1/18 y x - 1/9 x y + + 4 3 4 2 + - 1/36 x y + 1/18 x + 1/72 x y, COEFF(0, 2) = - 1/12 - 1/12 y + 5/48 x + + 4 2 4 2 4 2 2 2 3 + + 1/16 x y - 1/48 x + 5/48 y x - 1/48 x y - 5/16 x y - 5/24 x y + + 3 4 3 2 + + 1/6 y + 1/24 x y + 1/4 y , COEFF(1, 2) = - 1/18 x - 1/18 x y + + 3 3 3 4 2 2 4 + - 1/36 x y + 1/72 x + 1/72 x y + 1/6 x y - 1/18 y x + 1/72 x + + 2 3 2 3 4 2 2 3 2 2 + - 1/18 x - 1/24 x y + 1/9 x y - 1/24 x y + 1/9 x y + 1/6 x y + + 3 4 3 3 4 2 + + 1/72 y x - 1/36 x y , COEFF(2, 2) = 1/144 x y - 1/144 x + 1/96 x y + + 4 4 2 2 2 3 + - 1/288 x + 1/144 x - 1/288 x y + 1/288 x - 1/96 x y - 1/72 x y + + 2 3 3 3 2 3 2 + - 1/48 x y + 1/72 x y - 1/144 y x - 1/144 x y + 1/288 y x + + 4 3 3 2 + + 1/144 x y + 1/48 x y ] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c"); +bytes used=227340944, alloc=2817532, time=21.27 +bytes used=228341108, alloc=2817532, time=21.34 +bytes used=229341284, alloc=2817532, time=21.43 +bytes used=230364276, alloc=2817532, time=21.51 +bytes used=231366896, alloc=2817532, time=21.59 +bytes used=232387828, alloc=2817532, time=21.65 +bytes used=233410164, alloc=2817532, time=21.73 +bytes used=234411164, alloc=2817532, time=21.82 +bytes used=235411816, alloc=2817532, time=21.89 +bytes used=236412028, alloc=2817532, time=22.25 +bytes used=237412372, alloc=2817532, time=22.32 +bytes used=238412628, alloc=2817532, time=22.39 +bytes used=239412864, alloc=2817532, time=22.45 +bytes used=240413072, alloc=2817532, time=22.53 +bytes used=241413260, alloc=2817532, time=22.64 +bytes used=242415104, alloc=2817532, time=22.74 +bytes used=243422528, alloc=2817532, time=22.84 +bytes used=244422796, alloc=2817532, time=22.92 +bytes used=245434308, alloc=2817532, time=23.25 +bytes used=246434640, alloc=2817532, time=23.47 +bytes used=247434804, alloc=2817532, time=23.55 +bytes used=248445404, alloc=2817532, time=23.66 +bytes used=249445736, alloc=2817532, time=23.79 +bytes used=250454324, alloc=2817532, time=24.11 +bytes used=251454648, alloc=2817532, time=24.31 +bytes used=252454820, alloc=2817532, time=24.38 +bytes used=253455412, alloc=2817532, time=24.47 +bytes used=254455864, alloc=2817532, time=24.59 +bytes used=255456212, alloc=2817532, time=24.96 +bytes used=256456488, alloc=2817532, time=25.03 +bytes used=257456656, alloc=2817532, time=25.12 +bytes used=258456848, alloc=2817532, time=25.35 +bytes used=259457064, alloc=2817532, time=25.61 +bytes used=260457280, alloc=2817532, time=25.69 +bytes used=261457952, alloc=2817532, time=25.80 +bytes used=262458396, alloc=2817532, time=26.10 +bytes used=263458644, alloc=2817532, time=26.17 +> +# d^2/dx^2 +> simplify( diff(interp_2d_cube_order4_smooth0,x,x) ); +bytes used=264458908, alloc=2817532, time=26.30 +bytes used=265459400, alloc=2817532, time=26.38 +bytes used=266459604, alloc=2817532, time=26.45 + 3 3 +- 1/12 DATA(2, 0) - 5/24 y DATA(0, 2) + 5/12 y DATA(0, 1) + + 3 3 2 2 + + 5/24 y DATA(0, -2) - 5/12 y DATA(0, -1) - 1/8 x y DATA(0, 2) + + 2 2 2 2 2 2 + - 1/8 x y DATA(0, -2) + 2 x y DATA(0, 1) + 2 x y DATA(0, -1) + + 2 3 2 3 2 3 + + 1/2 x y DATA(0, -1) + 1/4 x y DATA(0, 2) - 1/2 x y DATA(0, 1) + + 2 3 + - 1/4 x y DATA(0, -2) + 5/24 y DATA(0, 2) - 5/3 y DATA(0, 1) + + 2 + - 5/24 y DATA(0, -2) + 5/3 y DATA(0, -1) + 5/48 y DATA(0, -2) + + 2 2 2 + - 5/3 y DATA(0, -1) - 5/3 y DATA(0, 1) + 5/48 y DATA(0, 2) + + 2 2 2 + + 2 y x DATA(0, 1) + 1/4 y x DATA(0, -2) - 2 y x DATA(0, -1) + + 2 + - 1/4 y x DATA(0, 2) - 5/2 DATA(0, 0) + 4/3 DATA(1, 0) - 1/12 DATA(-2, 0) + + 2 2 2 + + 4/3 DATA(-1, 0) + 2/3 x y DATA(-1, -1) - 4/3 x y DATA(1, 1) + + 2 2 2 2 2 2 + - 1/48 x y DATA(-2, 2) - 1/48 x y DATA(2, -2) + 1/12 x y DATA(1, -2) + + 2 2 2 2 + + 1/12 x y DATA(-1, -2) - 1/48 x y DATA(-2, -2) + + 2 2 2 2 2 2 + - 4/3 x y DATA(-1, -1) - 4/3 x y DATA(1, -1) - 4/3 x y DATA(-1, 1) + + 2 2 2 + + 1/6 y x DATA(1, 2) + 1/6 y x DATA(-1, 2) + 1/3 y x DATA(2, 1) + + 2 2 2 2 + + 1/3 x y DATA(-2, -1) - 1/6 y x DATA(1, -2) - 1/6 y x DATA(-1, -2) + + 2 2 2 + + 1/24 y x DATA(-2, -2) - 1/24 y x DATA(2, 2) - 4/3 y x DATA(1, 1) + + 2 2 2 + - 1/24 y x DATA(-2, 2) + 1/3 y x DATA(-2, 1) - 1/3 y x DATA(-2, -1) + + 2 2 2 + + 1/24 y x DATA(2, -2) + 4/3 y x DATA(-1, -1) + 4/3 y x DATA(1, -1) + + 2 2 2 + - 4/3 y x DATA(-1, 1) - 1/3 y x DATA(2, -1) - 2/3 x y DATA(1, -1) + + 2 2 2 + + 2/3 x y DATA(-1, 1) - 1/3 x y DATA(-2, -1) - 1/48 x y DATA(2, -2) + + 2 2 2 + + 1/24 x y DATA(1, -2) - 1/24 x y DATA(-1, -2) + 1/24 x y DATA(1, 2) + + 2 2 2 + - 1/24 x y DATA(-1, 2) + 1/3 x y DATA(2, 1) + 1/48 x y DATA(-2, -2) + + + 1/12 x y DATA(1, 2) - 1/12 x y DATA(-1, 2) + 1/3 x y DATA(2, 1) + + - 1/3 x y DATA(2, -1) - 2/3 x y DATA(1, 1) + 1/24 x y DATA(-2, 2) + + - 1/3 x y DATA(-2, 1) + 1/3 x y DATA(-2, -1) + 1/24 x y DATA(2, -2) + + 2 2 2 + - 2/3 x y DATA(1, 1) - 1/3 x y DATA(-2, 1) + 1/48 x y DATA(-2, 2) + + 2 2 + + 1/3 x y DATA(2, -1) - 1/48 x y DATA(2, 2) + 2/3 x y DATA(-1, 1) + + - 1/24 x y DATA(2, 2) - 1/12 x y DATA(1, -2) + 1/12 x y DATA(-1, -2) + + - 1/24 x y DATA(-2, -2) - 2/3 x y DATA(-1, -1) + 2/3 x y DATA(1, -1) + + 3 3 3 + + 1/24 x y DATA(2, 2) + 1/12 x y DATA(2, -1) + 1/6 x y DATA(1, 1) + + 3 3 3 + - 1/24 x y DATA(-2, 2) + 1/12 x y DATA(-2, 1) - 1/6 x y DATA(-1, 1) + + 3 3 3 + - 1/12 x y DATA(1, 2) + 1/12 x y DATA(-1, 2) - 1/12 x y DATA(2, 1) + + 3 3 3 + - 1/12 x y DATA(-2, -1) - 1/24 x y DATA(2, -2) + 1/12 x y DATA(1, -2) + + 3 3 3 + - 1/12 x y DATA(-1, -2) + 1/24 x y DATA(-2, -2) + 1/6 x y DATA(-1, -1) + + 3 2 3 2 3 + - 1/6 x y DATA(1, -1) - 1/12 x y DATA(-2, 1) - 1/24 x y DATA(-2, -2) + + 2 3 2 3 2 3 + - 1/24 x y DATA(2, -2) + 1/6 x y DATA(1, -2) + 1/12 x y DATA(2, -1) + + 2 3 2 3 2 3 + + 1/12 x y DATA(-2, -1) + 1/3 x y DATA(1, 1) + 1/24 x y DATA(-2, 2) + + 2 3 2 3 2 3 + + 1/24 x y DATA(2, 2) - 1/6 x y DATA(1, 2) - 1/6 x y DATA(-1, 2) + + 2 3 2 2 2 2 + - 1/12 x y DATA(2, 1) + 1/3 x y DATA(-2, 1) + 1/12 x y DATA(1, 2) + + 2 2 2 2 2 2 + + 1/12 x y DATA(-1, 2) + 1/3 x y DATA(2, 1) + 1/3 x y DATA(2, -1) + + 2 2 2 3 2 3 + - 1/48 x y DATA(2, 2) + 1/6 x y DATA(-1, -2) - 1/3 x y DATA(-1, -1) + + 2 3 2 3 4 + - 1/3 x y DATA(1, -1) + 1/3 x y DATA(-1, 1) - 1/8 x y DATA(-2, 0) + + 4 4 4 + + 1/48 x y DATA(2, -2) - 1/24 x y DATA(1, -2) + 1/24 x y DATA(-1, -2) + + 4 4 4 + - 1/48 x y DATA(-2, -2) - 1/6 x y DATA(-1, -1) + 1/6 x y DATA(1, -1) + + 3 3 2 + - 1/9 y DATA(-1, -2) + 1/9 y DATA(-1, 2) + 1/2 x DATA(2, 0) + + 2 2 2 + + 3 x DATA(0, 0) - 2 x DATA(1, 0) + 1/2 x DATA(-2, 0) + + 2 3 + - 2 x DATA(-1, 0) - 1/144 y DATA(2, 2) - 1/18 y DATA(-2, 1) + + 2 2 + + 1/18 y DATA(-2, -1) - 1/144 y DATA(2, -2) + 5/2 x y DATA(1, 0) + + 2 2 2 2 2 2 + + 5/2 x y DATA(-1, 0) - 5/8 x y DATA(2, 0) - 15/4 x y DATA(0, 0) + + 2 2 2 3 + - 5/8 x y DATA(-2, 0) - 5/8 x y DATA(2, 0) + 2/9 y DATA(1, -1) + + 3 + - 2/9 y DATA(-1, 1) + 1/2 x DATA(2, 0) - x DATA(1, 0) - 1/2 x DATA(-2, 0) + + 3 3 3 + + 2/9 y DATA(-1, -1) + 1/9 y DATA(1, 2) + 1/72 y DATA(2, 1) + + 3 3 3 + - 1/72 y DATA(2, -1) - 2/9 y DATA(1, 1) - 1/144 y DATA(-2, 2) + + 3 3 3 + + 1/72 y DATA(-2, 1) - 1/72 y DATA(-2, -1) + 1/144 y DATA(2, -2) + + 3 2 4 4 + - 1/9 y DATA(1, -2) - 1/2 x y DATA(1, 0) + 1/18 y DATA(-1, 2) + + 4 4 4 + - 1/288 y DATA(-2, -2) + 5/12 y DATA(0, -1) - 2/9 y DATA(1, -1) + + 4 4 4 + + 1/3 y DATA(-1, 0) - 2/9 y DATA(-1, 1) - 2/9 y DATA(-1, -1) + + 4 4 4 + + 5/12 y DATA(0, 1) - 1/288 y DATA(-2, 2) + 1/72 y DATA(-2, 1) + + 4 4 4 + - 2/9 y DATA(1, 1) + 1/72 y DATA(-2, -1) - 1/288 y DATA(2, -2) + + 4 2 4 4 + + 1/18 y DATA(1, -2) - 1/12 x y DATA(1, 2) - 5/48 y DATA(0, -2) + + 4 4 4 + + 1/18 y DATA(-1, -2) - 1/48 y DATA(-2, 0) - 5/48 y DATA(0, 2) + + 4 4 4 + + 1/72 y DATA(2, 1) - 1/48 y DATA(2, 0) + 1/72 y DATA(2, -1) + + 4 4 4 + - 5/8 y DATA(0, 0) + 1/3 y DATA(1, 0) - 1/288 y DATA(2, 2) + + 4 2 4 2 4 + + 1/18 y DATA(1, 2) - 1/12 x y DATA(-1, 2) - 1/2 x y DATA(0, -1) + + 2 4 2 4 2 4 + + 1/3 x y DATA(1, -1) - 1/2 x y DATA(-1, 0) + 1/48 x y DATA(-2, -2) + + 2 4 2 4 2 4 + + 1/48 x y DATA(2, 2) + 1/8 x y DATA(0, 2) - 1/12 x y DATA(2, 1) + + 2 4 2 4 2 4 + + 1/8 x y DATA(2, 0) - 1/12 x y DATA(2, -1) - 1/12 x y DATA(-2, -1) + + 2 4 2 4 2 4 + + 1/48 x y DATA(2, -2) - 1/12 x y DATA(1, -2) + 1/8 x y DATA(0, -2) + + 2 4 2 4 4 + - 1/12 x y DATA(-1, -2) + 1/8 x y DATA(-2, 0) - 1/12 x y DATA(2, -1) + + 4 4 4 + + 1/4 x y DATA(-1, 0) - 1/4 x y DATA(1, 0) + 1/6 x y DATA(1, 1) + + 4 4 2 4 + - 1/48 x y DATA(-2, 2) + 1/12 x y DATA(-2, 1) + 3/4 x y DATA(0, 0) + + 2 4 2 4 4 + + 1/3 x y DATA(-1, 1) + 1/3 x y DATA(-1, -1) - 1/6 x y DATA(-1, 1) + + 4 4 4 + + 1/12 x y DATA(-2, -1) - 1/24 x y DATA(1, 2) + 1/48 x y DATA(2, 2) + + 4 4 4 + + 1/24 x y DATA(-1, 2) - 1/12 x y DATA(2, 1) + 1/8 x y DATA(2, 0) + + 2 2 2 + - 1/18 y DATA(1, 2) - 1/18 y DATA(-1, 2) + 1/288 y DATA(-2, -2) + + 2 2 2 + + 8/9 y DATA(1, -1) - 5/3 y DATA(-1, 0) + 8/9 y DATA(-1, 1) + + 2 2 2 + + 8/9 y DATA(-1, -1) + 1/288 y DATA(-2, 2) - 1/18 y DATA(-2, 1) + + 2 2 2 + + 8/9 y DATA(1, 1) - 1/18 y DATA(-2, -1) + 1/288 y DATA(2, -2) + + 2 2 + + 1/288 y DATA(2, 2) + 1/144 y DATA(2, 2) - 1/18 y DATA(2, 1) + + 2 2 2 + + 5/48 y DATA(2, 0) - 1/18 y DATA(2, -1) + 25/8 y DATA(0, 0) + + 2 + - 5/3 y DATA(1, 0) - 1/9 y DATA(1, 2) - 1/9 y DATA(-1, 2) + + - 1/18 y DATA(2, 1) + 1/18 y DATA(2, -1) + 8/9 y DATA(1, 1) + + 2 2 + + 1/144 y DATA(-2, 2) - 1/18 y DATA(1, -2) - 1/18 y DATA(-1, -2) + + 2 + + 5/48 y DATA(-2, 0) + 1/9 y DATA(1, -2) + 1/9 y DATA(-1, -2) + + - 1/144 y DATA(-2, -2) - 8/9 y DATA(-1, -1) - 8/9 y DATA(1, -1) + + 2 4 2 4 + + 8/9 y DATA(-1, 1) - 1/2 x y DATA(0, 1) + 1/48 x y DATA(-2, 2) + + 2 4 2 4 2 + - 1/12 x y DATA(-2, 1) + 1/3 x y DATA(1, 1) - 5/4 x y DATA(-1, 0) + + 2 2 3 + + 5/4 x y DATA(1, 0) + 5/8 x y DATA(-2, 0) + 1/144 y DATA(-2, -2) + + + x DATA(-1, 0) + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=267463800, alloc=2817532, time=26.51 + 2 4 2 2 4 2 2 +[COEFF(-2, -2) = 1/48 x y + 1/48 x y + 1/288 y - 1/288 y - 1/48 x y + + 2 3 4 3 2 3 + + 1/24 y x + 1/24 x y - 1/48 x y + 1/144 y - 1/144 y - 1/24 x y + + 4 2 2 2 + - 1/24 x y, COEFF(-1, -2) = 1/24 x y + 1/12 x y - 1/24 x y + 1/12 x y + + 3 2 4 3 2 4 2 + - 1/9 y + 1/9 y - 1/12 x y - 1/12 x y - 1/18 y + 1/18 y - 1/6 y x + + 2 3 2 2 3 + + 1/6 x y , COEFF(0, -2) = - 5/24 y + 5/48 y + 1/4 y x + 5/24 y + + 2 2 2 3 4 2 4 2 + - 1/8 x y - 1/4 x y - 5/48 y + 1/8 x y , COEFF(1, -2) = 1/24 x y + + 2 3 2 2 4 2 + - 1/12 x y - 1/6 y x - 1/9 y + 1/12 x y + 1/18 y - 1/18 y + + 3 2 3 4 2 4 + + 1/12 x y + 1/6 x y + 1/9 y - 1/24 x y - 1/12 x y , COEFF(2, -2) = + + 2 4 4 2 2 4 + - 1/48 x y - 1/288 y + 1/48 x y + 1/24 y x + 1/24 x y + 1/48 x y + + 3 2 2 2 2 3 3 + - 1/144 y + 1/144 y - 1/48 x y + 1/288 y - 1/24 x y - 1/24 x y , + + 2 2 3 2 2 3 + COEFF(-2, -1) = 1/3 x y + 1/3 x y - 1/72 y - 1/18 y + 1/12 x y + + 4 3 2 4 2 2 + + 1/18 y + 1/12 x y - 1/12 x y - 1/12 x y - 1/3 y x - 1/3 x y + + 4 4 2 2 4 + + 1/72 y , COEFF(-1, -1) = - 1/6 x y + 2/3 x y - 8/9 y + 1/3 x y + + 2 2 2 2 3 3 4 2 3 + + 8/9 y - 4/3 x y + 4/3 y x + 2/9 y + 1/6 x y - 2/9 y - 1/3 x y + + 2 3 2 2 4 2 + - 2/3 x y, COEFF(0, -1) = 1/2 x y + 2 x y + 5/12 y - 5/3 y + + 2 4 2 3 2 4 + - 1/2 x y - 2 y x - 5/12 y + 5/3 y, COEFF(1, -1) = 1/3 x y + 2/3 x y + + 4 3 2 2 2 4 2 3 + + 1/6 x y + 2/9 y - 4/3 x y - 8/9 y - 2/3 x y - 2/9 y - 1/3 x y + + 3 2 2 2 2 4 + - 1/6 x y + 8/9 y + 4/3 y x , COEFF(2, -1) = - 1/18 y - 1/12 x y + + 4 2 2 2 2 3 + - 1/12 x y + 1/3 x y + 1/3 x y + 1/18 y - 1/3 x y + 1/12 x y + + 3 3 4 2 2 + - 1/72 y + 1/12 x y + 1/72 y - 1/3 y x , COEFF(-2, 0) = 1/2 x + + 2 4 2 4 2 2 2 + + 1/8 x y + 5/8 x y - 1/48 y - 1/12 + 5/48 y - 5/8 x y - 1/2 x + + 4 2 2 2 4 4 + - 1/8 x y , COEFF(-1, 0) = 4/3 + 5/2 x y - 2 x + 1/4 x y + 1/3 y + x + + 2 4 2 2 + - 1/2 x y - 5/4 x y - 5/3 y , + + 2 4 2 4 2 2 2 + COEFF(0, 0) = 3 x - 5/8 y + 3/4 x y - 5/2 - 15/4 x y + 25/8 y , + + 4 2 2 2 2 2 4 + COEFF(1, 0) = - 1/4 x y + 5/2 x y + 5/4 x y - 5/3 y - 2 x + 1/3 y + + 2 4 2 2 2 4 + - 1/2 x y + 4/3 - x, COEFF(2, 0) = - 5/8 x y + 1/2 x + 1/8 x y + + 2 4 2 2 4 + + 1/8 x y - 5/8 x y + 1/2 x - 1/12 + 5/48 y - 1/48 y , COEFF(-2, 1) = + + 4 2 2 2 2 2 4 + - 1/18 y + 1/12 x y + 1/3 y x - 1/3 x y + 1/3 x y - 1/12 x y + + 3 3 2 4 2 3 + + 1/12 x y + 1/72 y - 1/18 y + 1/72 y - 1/3 x y - 1/12 x y , + + 3 2 4 2 4 + COEFF(-1, 1) = - 2/9 y - 4/3 y x - 1/6 x y + 2/3 x y + 1/3 x y + + 2 2 3 2 3 2 2 4 + + 2/3 x y + 1/3 x y + 8/9 y - 1/6 x y - 4/3 x y + 8/9 y - 2/9 y , + + 3 2 2 2 2 4 4 + COEFF(0, 1) = 5/12 y + 2 x y - 5/3 y - 1/2 x y - 5/3 y + 5/12 y + + 2 3 2 4 2 4 3 + - 1/2 x y + 2 y x , COEFF(1, 1) = - 2/9 y + 1/3 x y + 1/6 x y + + 3 4 2 2 2 2 3 2 + - 2/9 y + 8/9 y + 1/6 x y - 2/3 x y - 4/3 x y + 1/3 x y + 8/9 y + + 2 3 2 + - 4/3 y x - 2/3 x y, COEFF(2, 1) = 1/3 x y - 1/18 y + 1/72 y + 1/3 x y + + 2 3 2 4 2 2 2 2 4 + - 1/12 x y + 1/3 y x + 1/72 y + 1/3 x y - 1/18 y - 1/12 x y + + 4 3 2 2 3 + - 1/12 x y - 1/12 x y , COEFF(-2, 2) = 1/48 x y - 1/24 y x - 1/24 x y + + 2 2 2 2 3 2 4 3 + - 1/48 x y + 1/288 y + 1/144 y + 1/24 x y + 1/48 x y - 1/144 y + + 4 4 3 + + 1/24 x y - 1/288 y - 1/48 x y , COEFF(-1, 2) = - 1/12 x y + 1/9 y + + 4 2 4 2 2 2 4 2 + + 1/24 x y - 1/12 x y - 1/18 y + 1/12 x y + 1/18 y - 1/24 x y + + 2 2 3 3 2 + + 1/6 y x - 1/6 x y - 1/9 y + 1/12 x y , COEFF(0, 2) = 5/48 y + + 2 2 3 4 2 4 2 3 + - 1/8 x y - 5/24 y + 5/24 y - 5/48 y + 1/8 x y + 1/4 x y + + 2 4 2 + - 1/4 y x , COEFF(1, 2) = 1/12 x y + 1/18 y + 1/24 x y - 1/9 y + + 2 2 3 2 2 2 4 2 4 + + 1/6 y x - 1/6 x y + 1/12 x y - 1/18 y - 1/24 x y - 1/12 x y + + 3 3 4 4 2 2 + - 1/12 x y + 1/9 y , COEFF(2, 2) = - 1/288 y + 1/48 x y - 1/48 x y + + 2 2 3 2 4 + + 1/144 y + 1/288 y - 1/48 x y - 1/24 x y - 1/144 y + 1/48 x y + + 2 3 3 2 + + 1/24 x y + 1/24 x y - 1/24 y x ] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c"); +bytes used=268463952, alloc=2817532, time=26.58 +bytes used=269464108, alloc=2817532, time=26.64 +bytes used=270464264, alloc=2817532, time=26.72 +bytes used=271468824, alloc=2817532, time=26.79 +bytes used=272470884, alloc=2817532, time=26.86 +bytes used=273471272, alloc=2817532, time=26.94 +bytes used=274471420, alloc=2817532, time=27.14 +bytes used=275471752, alloc=2817532, time=27.42 +bytes used=276472040, alloc=2817532, time=27.49 +bytes used=277475512, alloc=2817532, time=27.55 +bytes used=278475700, alloc=2817532, time=27.65 +bytes used=279484180, alloc=2817532, time=27.75 +bytes used=280484464, alloc=2817532, time=27.86 +bytes used=281491584, alloc=2817532, time=28.19 +bytes used=282491764, alloc=2817532, time=28.39 +bytes used=283493688, alloc=2817532, time=28.47 +bytes used=284493880, alloc=2817532, time=28.62 +bytes used=285503016, alloc=2817532, time=28.93 +bytes used=286503156, alloc=2817532, time=29.13 +bytes used=287503572, alloc=2817532, time=29.21 +bytes used=288504456, alloc=2817532, time=29.36 +bytes used=289504572, alloc=2817532, time=29.68 +bytes used=290504728, alloc=2817532, time=29.75 +bytes used=291504932, alloc=2817532, time=30.12 +bytes used=292505132, alloc=2817532, time=30.26 +bytes used=293505260, alloc=2817532, time=30.36 +bytes used=294505412, alloc=2817532, time=30.69 +bytes used=295505644, alloc=2817532, time=30.79 +> +# d^2/dxdy +> simplify( diff(interp_2d_cube_order4_smooth0,x,y) ); +bytes used=296505980, alloc=2817532, time=30.89 +bytes used=297506132, alloc=2817532, time=30.96 +bytes used=298506352, alloc=2817532, time=31.03 +1/144 DATA(2, 2) - 1/18 DATA(1, 2) + 1/18 DATA(-1, 2) - 1/18 DATA(2, 1) + + + 1/18 DATA(2, -1) + 4/9 DATA(1, 1) - 1/144 DATA(-2, 2) + 1/18 DATA(-2, 1) + + - 1/18 DATA(-2, -1) - 1/144 DATA(2, -2) + 1/18 DATA(1, -2) + + - 1/18 DATA(-1, -2) + 1/144 DATA(-2, -2) + 4/9 DATA(-1, -1) + + 3 3 + - 4/9 DATA(1, -1) - 4/9 DATA(-1, 1) - 2/3 x y DATA(1, 0) + + 3 3 3 3 3 3 + + 1/6 x y DATA(-2, 0) - 2/3 x y DATA(-1, 0) + 4/9 x y DATA(-1, 1) + + 3 3 3 3 3 3 + + x y DATA(0, 0) - 1/9 x y DATA(2, 1) - 1/9 x y DATA(2, -1) + + + 8/9 x DATA(-1, 1) + 5/24 y DATA(2, 0) - 5/3 y DATA(1, 0) + + - 8/9 x DATA(-1, -1) + 5/3 x DATA(0, -1) - 8/9 x DATA(1, -1) + + 3 3 + + 5/3 y DATA(-1, 0) - 1/72 x DATA(2, 2) + 1/18 x DATA(1, 2) + + 3 3 3 + + 1/18 x DATA(-1, 2) - 1/12 x DATA(0, 2) + 1/72 x DATA(2, -2) + + 3 3 3 + - 1/18 x DATA(1, -2) + 1/12 x DATA(0, -2) - 1/18 x DATA(-1, -2) + + 3 3 3 + + 1/9 x DATA(2, 1) - 1/9 x DATA(2, -1) + 2/3 x DATA(0, 1) + + 3 3 + - 4/9 x DATA(1, 1) - 1/72 x DATA(-2, 2) - 5/24 y DATA(-2, 0) + + 3 3 3 3 3 3 + - 2/3 x y DATA(0, 1) + 1/36 x y DATA(-2, 2) - 1/9 x y DATA(-2, 1) + + 3 3 3 3 3 3 + + 4/9 x y DATA(1, 1) + 1/36 x y DATA(2, -2) - 1/9 x y DATA(1, -2) + + 3 3 3 3 3 3 + + 1/6 x y DATA(0, -2) - 1/9 x y DATA(-1, -2) + 1/36 x y DATA(-2, -2) + + 2 2 2 2 2 + + 2/3 x y DATA(-1, -1) + 1/4 x y DATA(1, 1) - 1/16 x y DATA(-2, 2) + + 3 3 3 3 3 3 + - 1/9 x y DATA(1, 2) - 1/9 x y DATA(-1, 2) + 1/36 x y DATA(2, 2) + + 3 3 3 + + 4/3 x y DATA(1, 0) - 1/12 x y DATA(-2, 0) + 4/3 x y DATA(-1, 0) + + 3 3 3 3 3 + - 5/2 x y DATA(0, 0) + 1/6 x y DATA(2, 0) - 1/9 x y DATA(-2, -1) + + 3 3 3 + + 1/72 x DATA(-2, -2) + 5/3 x y DATA(0, -1) - 5/12 x y DATA(0, 2) + + 3 3 3 3 + + 5/3 x y DATA(0, 1) - 1/12 x y DATA(2, 0) + 4/9 x y DATA(-1, -1) + + 3 3 3 3 + - 2/3 x y DATA(0, -1) - 5/12 x y DATA(0, -2) + 4/9 x DATA(-1, -1) + + 2 2 2 + + 5/4 y x DATA(1, 0) + 5/8 y x DATA(-2, 0) - 5/8 y x DATA(2, 0) + + 2 3 3 + - 5/4 y x DATA(-1, 0) - 5/2 y x DATA(0, 0) - 5/12 y x DATA(2, 0) + + 3 3 3 + + 2/9 y x DATA(-2, 1) + 2/9 y x DATA(-2, -1) - 1/72 y x DATA(2, -2) + + 3 3 3 + - 8/9 y x DATA(1, -1) + 5/3 y x DATA(1, 0) - 5/12 y x DATA(-2, 0) + + 3 3 3 + + 5/3 y x DATA(-1, 0) - 8/9 y x DATA(-1, 1) + 2/9 y x DATA(2, -1) + + 3 3 3 + - 1/12 y x DATA(0, 2) + 4/3 y x DATA(0, 1) - 8/9 y x DATA(1, 1) + + 3 3 3 + - 1/72 y x DATA(-2, 2) - 1/72 y x DATA(-2, -2) - 8/9 y x DATA(-1, -1) + + 3 3 3 + + 4/3 y x DATA(0, -1) + 1/18 y x DATA(1, 2) + 1/18 y x DATA(-1, 2) + + 3 3 2 + - 1/72 y x DATA(2, 2) + 2/9 y x DATA(2, 1) - 1/6 x DATA(2, -1) + + 2 2 2 + - 1/3 x DATA(1, 1) + 1/48 x DATA(-2, 2) - 1/6 x DATA(-2, 1) + + 2 2 2 + + 1/6 x DATA(-2, -1) + 1/48 x DATA(2, -2) - 1/24 x DATA(1, -2) + + 2 2 2 + + 1/24 x DATA(-1, -2) - 1/48 x DATA(-2, -2) - 1/3 x DATA(-1, -1) + + 2 2 2 + + 1/3 x DATA(1, -1) + 1/24 x DATA(1, 2) - 1/24 x DATA(-1, 2) + + 2 2 3 + + 1/6 x DATA(2, 1) - 1/48 x DATA(2, 2) - 2/3 x DATA(0, -1) + + 3 3 3 + + 4/9 x DATA(1, -1) - 4/9 x DATA(-1, 1) + 1/9 x DATA(-2, 1) + + 3 + - 1/9 x DATA(-2, -1) + 5/24 x DATA(0, 2) - 1/18 x DATA(2, 1) + + + 1/18 x DATA(2, -1) - 5/3 x DATA(0, 1) + 8/9 x DATA(1, 1) + + + 1/144 x DATA(-2, 2) - 1/18 x DATA(-2, 1) + 1/18 x DATA(-2, -1) + + - 1/144 x DATA(2, -2) + 1/9 x DATA(1, -2) - 5/24 x DATA(0, -2) + + 2 3 3 + + 5/4 x y DATA(0, 1) + 1/18 y x DATA(1, -2) - 1/12 y x DATA(0, -2) + + 3 2 + + 1/18 y x DATA(-1, -2) - 5/8 x y DATA(0, 2) + 1/9 x DATA(-1, -2) + + 3 2 3 2 3 2 + - 1/2 x y DATA(0, 1) + 1/3 x y DATA(1, 1) + 1/24 x y DATA(-2, 2) + + 3 2 3 2 + - 1/12 x y DATA(-2, 1) + 1/12 x y DATA(-2, -1) + + 3 2 2 2 + - 1/24 x y DATA(2, -2) + 5/8 x y DATA(0, -2) - 5/4 x y DATA(0, -1) + + 3 2 3 2 + - 1/144 x DATA(-2, -2) - 1/4 x y DATA(0, -2) + 1/24 x y DATA(2, 2) + + 3 2 3 2 3 2 + - 1/6 x y DATA(1, 2) - 1/6 x y DATA(-1, 2) + 1/4 x y DATA(0, 2) + + 3 2 3 2 3 2 + - 1/12 x y DATA(2, 1) + 1/12 x y DATA(2, -1) - 1/3 x y DATA(1, -1) + + 2 + + 1/3 x DATA(-1, 1) + 5/24 x y DATA(-2, 0) - 10/3 x y DATA(-1, 0) + + 3 2 3 2 3 2 + + 1/6 x y DATA(1, -2) + 1/6 x y DATA(-1, -2) - 1/24 x y DATA(-2, -2) + + 3 2 3 2 3 2 + - 1/3 x y DATA(-1, -1) + 1/2 x y DATA(0, -1) + 1/3 x y DATA(-1, 1) + + + 5/24 x y DATA(2, 0) - 10/3 x y DATA(1, 0) + 1/144 x DATA(2, 2) + + + 25/4 x y DATA(0, 0) + 5/24 x y DATA(0, 2) - 10/3 x y DATA(0, 1) + + 2 3 + + 5/24 x y DATA(0, -2) + 1/4 x y DATA(2, 0) - 10/3 x y DATA(0, -1) + + 2 3 2 3 3 + + 1/2 x y DATA(-1, 0) - 1/2 x y DATA(1, 0) - 2/3 y DATA(-1, 0) + + 3 3 + - 1/9 x DATA(1, 2) - 1/9 x DATA(-1, 2) + 1/6 x y DATA(0, 2) + + 2 3 3 3 + - 1/4 x y DATA(-2, 0) - 1/12 y DATA(2, 0) + 2/3 y DATA(1, 0) + + 3 3 3 2 2 + + 1/12 y DATA(-2, 0) + 4/9 x y DATA(1, -1) - 1/16 x y DATA(2, -2) + + 2 2 2 2 2 2 + + 1/8 x y DATA(1, -2) - 1/8 x y DATA(-1, -2) + 1/16 x y DATA(-2, -2) + + 2 2 2 2 2 2 + + 1/4 x y DATA(-1, -1) - 1/4 x y DATA(1, -1) - 1/4 x y DATA(-1, 1) + + 2 2 2 + + 1/24 y x DATA(1, 2) - 1/24 y x DATA(-1, 2) + 1/3 y x DATA(2, 1) + + 2 2 2 2 + - 1/8 x y DATA(-2, -1) + 1/24 y x DATA(1, -2) - 1/24 y x DATA(-1, -2) + + 2 2 2 + + 1/48 y x DATA(-2, -2) - 1/48 y x DATA(2, 2) - 2/3 y x DATA(1, 1) + + 2 2 2 + + 1/48 y x DATA(-2, 2) - 1/3 y x DATA(-2, 1) - 1/3 y x DATA(-2, -1) + + 2 2 2 + - 1/48 y x DATA(2, -2) + 2/3 y x DATA(-1, -1) - 2/3 y x DATA(1, -1) + + 2 2 2 + + 2/3 y x DATA(-1, 1) + 1/3 y x DATA(2, -1) + 2/3 x y DATA(1, -1) + + 2 2 2 + - 2/3 x y DATA(-1, 1) - 1/24 x y DATA(-2, -1) + 1/48 x y DATA(2, -2) + + 2 2 2 + - 1/3 x y DATA(1, -2) - 1/3 x y DATA(-1, -2) + 1/3 x y DATA(1, 2) + + 2 2 2 + + 1/3 x y DATA(-1, 2) + 1/24 x y DATA(2, 1) + 1/48 x y DATA(-2, -2) + + - 1/9 x y DATA(1, 2) - 1/9 x y DATA(-1, 2) - 1/9 x y DATA(2, 1) + + - 1/9 x y DATA(2, -1) + 16/9 x y DATA(1, 1) + 1/144 x y DATA(-2, 2) + + - 1/9 x y DATA(-2, 1) - 1/9 x y DATA(-2, -1) + 1/144 x y DATA(2, -2) + + 2 2 2 + - 2/3 x y DATA(1, 1) + 1/24 x y DATA(-2, 1) - 1/48 x y DATA(-2, 2) + + 2 2 + - 1/24 x y DATA(2, -1) - 1/48 x y DATA(2, 2) + 16/9 x y DATA(-1, 1) + + + 1/144 x y DATA(2, 2) - 1/9 x y DATA(1, -2) - 1/9 x y DATA(-1, -2) + + + 1/144 x y DATA(-2, -2) + 16/9 x y DATA(-1, -1) + 16/9 x y DATA(1, -1) + + 3 3 3 + - 1/72 x y DATA(2, 2) + 1/18 x y DATA(2, -1) - 8/9 x y DATA(1, 1) + + 3 3 3 + - 1/72 x y DATA(-2, 2) + 1/18 x y DATA(-2, 1) - 8/9 x y DATA(-1, 1) + + 3 3 3 + + 2/9 x y DATA(1, 2) + 2/9 x y DATA(-1, 2) + 1/18 x y DATA(2, 1) + + 3 3 3 + + 1/18 x y DATA(-2, -1) - 1/72 x y DATA(2, -2) + 2/9 x y DATA(1, -2) + + 3 3 3 + + 2/9 x y DATA(-1, -2) - 1/72 x y DATA(-2, -2) - 8/9 x y DATA(-1, -1) + + 3 2 3 2 3 + - 8/9 x y DATA(1, -1) + 1/6 x y DATA(-2, 1) - 1/24 x y DATA(-2, -2) + + 2 3 2 3 2 3 + + 1/24 x y DATA(2, -2) - 1/12 x y DATA(1, -2) - 1/6 x y DATA(2, -1) + + 2 3 2 3 2 3 + + 1/6 x y DATA(-2, -1) + 1/3 x y DATA(1, 1) - 1/24 x y DATA(-2, 2) + + 2 3 2 3 2 3 + + 1/24 x y DATA(2, 2) - 1/12 x y DATA(1, 2) + 1/12 x y DATA(-1, 2) + + 2 3 2 2 2 2 + - 1/6 x y DATA(2, 1) + 1/8 x y DATA(-2, 1) - 1/8 x y DATA(1, 2) + + 2 2 2 2 2 2 + + 1/8 x y DATA(-1, 2) - 1/8 x y DATA(2, 1) + 1/8 x y DATA(2, -1) + + 2 2 2 3 2 3 + + 1/16 x y DATA(2, 2) + 1/12 x y DATA(-1, -2) - 1/3 x y DATA(-1, -1) + + 2 3 2 3 3 + + 1/3 x y DATA(1, -1) - 1/3 x y DATA(-1, 1) - 1/9 y DATA(-1, -2) + + 3 3 + - 1/9 y DATA(-1, 2) - 1/72 y DATA(2, 2) + 1/9 y DATA(-2, 1) + + 3 + + 1/9 y DATA(-2, -1) + 1/144 y DATA(2, -2) - 4/9 y DATA(1, -1) + + 3 3 3 + + 4/9 y DATA(-1, 1) + 4/9 y DATA(-1, -1) + 1/9 y DATA(1, 2) + + 3 3 3 + + 1/18 y DATA(2, 1) + 1/18 y DATA(2, -1) - 4/9 y DATA(1, 1) + + 3 3 3 + + 1/72 y DATA(-2, 2) - 1/18 y DATA(-2, 1) - 1/18 y DATA(-2, -1) + + 3 3 2 + - 1/72 y DATA(2, -2) + 1/9 y DATA(1, -2) + 1/6 y DATA(1, 2) + + 2 2 2 + - 1/6 y DATA(-1, 2) - 1/48 y DATA(-2, -2) + 1/3 y DATA(1, -1) + + 2 2 2 + + 1/3 y DATA(-1, 1) - 1/3 y DATA(-1, -1) + 1/48 y DATA(-2, 2) + + 2 2 2 + - 1/24 y DATA(-2, 1) - 1/3 y DATA(1, 1) + 1/24 y DATA(-2, -1) + + 2 2 + + 1/48 y DATA(2, -2) - 1/48 y DATA(2, 2) + 1/144 y DATA(2, 2) + + 2 2 + + 1/24 y DATA(2, 1) - 1/24 y DATA(2, -1) - 1/18 y DATA(1, 2) + + + 1/18 y DATA(-1, 2) - 1/9 y DATA(2, 1) - 1/9 y DATA(2, -1) + + 2 + + 8/9 y DATA(1, 1) - 1/144 y DATA(-2, 2) - 1/6 y DATA(1, -2) + + 2 + + 1/6 y DATA(-1, -2) - 1/18 y DATA(1, -2) + 1/18 y DATA(-1, -2) + + - 1/144 y DATA(-2, -2) - 8/9 y DATA(-1, -1) + 8/9 y DATA(1, -1) + + 3 + - 8/9 y DATA(-1, 1) + 1/72 y DATA(-2, -2) + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=299534960, alloc=2817532, time=31.10 +bytes used=300538760, alloc=2817532, time=31.17 + 3 3 2 2 2 3 +[COEFF(-2, -2) = 1/36 x y - 1/144 y + 1/16 x y + 1/144 x y - 1/24 x y + + 2 2 3 2 3 3 + + 1/48 x y + 1/48 y x - 1/24 x y + 1/72 y + 1/72 x - 1/144 x + + 2 3 3 2 + - 1/48 y - 1/72 x y + 1/144 - 1/72 y x - 1/48 x , COEFF(-1, -2) = + + 2 3 2 2 3 3 + 1/24 x + 1/9 x + 1/6 x y + 1/18 y + 1/12 x y - 1/18 + 2/9 x y + + 2 2 2 2 3 3 3 + - 1/24 y x - 1/9 x y - 1/8 x y - 1/3 x y - 1/9 y - 1/9 x y + + 3 2 3 2 3 + - 1/18 x + 1/6 y + 1/18 y x , COEFF(0, -2) = 5/8 x y - 1/12 y x + + 3 3 3 3 2 3 + - 5/12 x y + 5/24 x y + 1/6 x y - 5/24 x - 1/4 x y + 1/12 x , + + 2 3 2 2 + COEFF(1, -2) = - 1/3 x y + 1/6 x y - 1/6 y - 1/18 y + 1/9 x + + 2 3 2 3 3 3 2 2 + - 1/12 x y + 1/24 y x + 1/18 + 1/18 y x + 1/9 y - 1/18 x + 1/8 x y + + 3 3 2 3 2 2 + - 1/9 x y - 1/24 x - 1/9 x y + 2/9 x y , COEFF(2, -2) = - 1/16 x y + + 3 2 3 2 2 + - 1/72 x y + 1/48 x y + 1/144 x y - 1/24 x y - 1/48 y x - 1/144 x + + 3 2 3 2 3 3 3 + - 1/72 y x + 1/24 x y + 1/48 y - 1/144 - 1/72 y + 1/36 x y + + 3 2 3 3 3 + + 1/72 x + 1/144 y + 1/48 x , COEFF(-2, -1) = - 1/18 - 1/9 x y - 1/9 x + + 3 2 3 2 3 2 3 + - 1/18 y + 1/6 x y + 1/6 x + 1/12 x y - 1/9 x y + 2/9 y x + 1/9 y + + 2 2 3 2 2 2 + - 1/8 x y + 1/18 x y + 1/24 y - 1/24 x y + 1/18 x - 1/3 y x , + + 3 3 3 2 3 + COEFF(-1, -1) = 4/9 x y - 8/9 y x + 16/9 x y + 4/9 - 1/3 x - 8/9 x y + + 3 2 2 3 2 2 + - 1/3 x y - 8/9 x + 2/3 x y + 4/9 x - 8/9 y + 2/3 y x - 1/3 y + + 2 3 3 2 2 3 3 3 + - 1/3 x y + 4/9 y + 1/4 x y , COEFF(0, -1) = - 2/3 x y + 4/3 y x + + 3 3 2 2 3 + + 5/3 x y + 1/2 x y + 5/3 x - 5/4 x y - 10/3 x y - 2/3 x , + + 3 3 3 3 3 3 + COEFF(1, -1) = - 4/9 y - 8/9 x y + 4/9 x - 8/9 x + 4/9 x y - 8/9 y x + + 2 3 2 2 3 2 2 2 + + 1/3 x y + 16/9 x y - 1/4 x y - 1/3 x y + 1/3 y + 1/3 x + 8/9 y + + 2 2 2 3 2 + - 2/3 y x - 4/9 + 2/3 x y , COEFF(2, -1) = 1/3 y x + 1/12 x y + + 3 3 2 2 3 3 + + 2/9 y x + 1/18 y - 1/6 x - 1/9 x y + 1/18 x - 1/24 y - 1/9 x y + + 2 2 2 3 2 3 3 + + 1/18 + 1/8 x y - 1/9 y - 1/6 x y - 1/24 x y + 1/18 x y - 1/9 x , + + 3 3 3 3 2 3 + COEFF(-2, 0) = 1/6 x y - 5/24 y - 5/12 y x - 1/12 x y - 1/4 x y + + 2 3 2 2 3 + + 5/24 x y + 5/8 y x + 1/12 y , COEFF(-1, 0) = - 5/4 y x + 1/2 x y + + 3 3 3 3 3 + + 4/3 x y + 5/3 y x - 10/3 x y - 2/3 y - 2/3 x y + 5/3 y, + + 3 3 3 3 + COEFF(0, 0) = 25/4 x y - 5/2 y x - 5/2 x y + x y , COEFF(1, 0) = + + 2 3 2 3 3 3 3 + - 1/2 x y + 5/4 y x - 5/3 y - 2/3 x y + 5/3 y x + 2/3 y - 10/3 x y + + 3 3 3 2 3 + + 4/3 x y , COEFF(2, 0) = 5/24 y + 1/6 x y + 5/24 x y + 1/4 x y + + 2 3 3 3 2 + - 5/8 y x - 5/12 y x - 1/12 y - 1/12 x y , COEFF(-2, 1) = 1/24 x y + + 2 3 2 2 3 2 3 3 + - 1/3 y x + 2/9 y x + 1/8 x y - 1/12 x y + 1/18 x y - 1/18 y + + 2 2 3 2 3 3 + - 1/9 x y - 1/6 x + 1/18 + 1/6 x y - 1/24 y - 1/9 x y + 1/9 y + + 3 2 2 + + 1/9 x - 1/18 x, COEFF(-1, 1) = 2/3 y x - 4/9 - 8/9 y - 2/3 x y + + 3 2 3 3 3 3 3 2 + - 8/9 x y + 1/3 x + 4/9 y + 16/9 x y - 4/9 x + 4/9 x y + 1/3 x y + + 3 2 2 3 2 2 + - 8/9 y x + 8/9 x + 1/3 y - 1/3 x y - 1/4 x y , COEFF(0, 1) = + + 3 3 2 3 3 3 3 + 4/3 y x - 1/2 x y + 5/3 x y - 2/3 x y - 10/3 x y - 5/3 x + 2/3 x + + 2 3 2 3 2 2 3 + + 5/4 x y , COEFF(1, 1) = - 4/9 x + 1/3 x y + 1/4 x y - 4/9 y + + 2 2 3 2 3 + - 1/3 y + 8/9 y - 1/3 x - 8/9 x y - 2/3 x y - 8/9 y x + 8/9 x + + 2 3 2 3 3 + - 2/3 y x + 1/3 x y + 4/9 x y + 16/9 x y + 4/9, COEFF(2, 1) = - 1/18 + + 3 2 3 2 3 2 2 + + 1/9 x - 1/18 x + 1/24 y - 1/12 x y + 2/9 y x + 1/6 x + 1/24 x y + + 2 3 3 2 2 3 3 3 + - 1/6 x y + 1/18 x y - 1/9 y - 1/8 x y - 1/9 x y + 1/18 y + + 2 2 2 2 + - 1/9 x y + 1/3 y x , COEFF(-2, 2) = - 1/48 x y + 1/48 x + 1/48 y x + + 2 2 2 2 3 + - 1/144 + 1/144 x y + 1/48 y - 1/16 x y - 1/24 x y + 1/144 x + + 3 3 3 3 3 3 2 + - 1/72 x y - 1/144 y - 1/72 x - 1/72 y x + 1/36 x y + 1/24 x y + + 3 2 3 3 2 + + 1/72 y , COEFF(-1, 2) = 1/3 x y - 1/9 y + 1/18 x - 1/24 y x + 1/18 + + 2 2 3 2 2 3 2 3 3 + - 1/24 x + 1/12 x y + 1/8 x y + 2/9 x y - 1/6 y - 1/9 x y + + 3 2 3 + - 1/6 x y - 1/9 x y + 1/18 y - 1/9 x + 1/18 y x , COEFF(0, 2) = 5/24 x + + 2 3 2 3 3 3 3 + - 5/8 x y + 5/24 x y + 1/4 x y + 1/6 x y - 5/12 x y - 1/12 y x + + 3 2 3 2 3 3 + - 1/12 x , COEFF(1, 2) = - 1/12 x y - 1/18 + 1/24 x + 1/18 x + 1/9 y + + 2 3 2 3 2 2 + + 1/6 y + 2/9 x y + 1/24 y x - 1/18 y + 1/18 y x - 1/8 x y - 1/9 x y + + 3 2 3 3 2 3 + - 1/6 x y - 1/9 x y + 1/3 x y - 1/9 x, COEFF(2, 2) = - 1/72 y x + + 3 2 2 2 3 + - 1/72 x - 1/48 x + 1/144 x y + 1/144 - 1/48 y + 1/144 x + 1/24 x y + + 2 3 2 2 2 3 2 3 + - 1/48 y x - 1/72 x y + 1/16 x y - 1/48 x y + 1/24 x y - 1/72 y + + 3 3 + + 1/36 x y + 1/144 y] + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c"); +bytes used=301539208, alloc=2817532, time=31.25 +bytes used=302539400, alloc=2817532, time=31.32 +bytes used=303539592, alloc=2817532, time=31.40 +bytes used=304557648, alloc=2817532, time=31.44 +bytes used=305571464, alloc=2817532, time=31.54 +bytes used=306581776, alloc=2817532, time=31.63 +bytes used=307582028, alloc=2817532, time=31.71 +bytes used=308582248, alloc=2817532, time=31.78 +bytes used=309582476, alloc=2817532, time=32.18 +bytes used=310582696, alloc=2817532, time=32.25 +bytes used=311582884, alloc=2817532, time=32.32 +bytes used=312583056, alloc=2817532, time=32.42 +bytes used=313583260, alloc=2817532, time=32.51 +bytes used=314583428, alloc=2817532, time=32.60 +bytes used=315583596, alloc=2817532, time=32.70 +bytes used=316593332, alloc=2817532, time=33.09 +bytes used=317593536, alloc=2817532, time=33.32 +bytes used=318593748, alloc=2817532, time=33.39 +bytes used=319593964, alloc=2817532, time=33.51 +bytes used=320594120, alloc=2817532, time=33.69 +bytes used=321594408, alloc=2817532, time=34.06 +bytes used=322594856, alloc=2817532, time=34.26 +bytes used=323595080, alloc=2817532, time=34.33 +bytes used=324595308, alloc=2817532, time=34.46 +bytes used=325595460, alloc=2817532, time=34.65 +bytes used=326595828, alloc=2817532, time=35.02 +bytes used=327596080, alloc=2817532, time=35.09 +bytes used=328596388, alloc=2817532, time=35.22 +bytes used=329596548, alloc=2817532, time=35.63 +bytes used=330596860, alloc=2817532, time=35.76 +bytes used=331597036, alloc=2817532, time=35.86 +bytes used=332597196, alloc=2817532, time=36.29 +bytes used=333597480, alloc=2817532, time=36.41 +> +# d^2/dy^2 +> simplify( diff(interp_2d_cube_order4_smooth0,y,y) ); +bytes used=334597656, alloc=2817532, time=36.56 +bytes used=335597820, alloc=2817532, time=36.64 +bytes used=336597976, alloc=2817532, time=36.70 +- 1/12 DATA(0, 2) - 5/2 DATA(0, 0) + 4/3 DATA(0, 1) - 1/12 DATA(0, -2) + + 3 4 4 + + 5/12 x DATA(1, 0) - 5/8 x DATA(0, 0) + 5/12 x DATA(-1, 0) + + 4 4 4 + - 5/48 x DATA(2, 0) + 5/12 x DATA(1, 0) + 1/72 x DATA(1, 2) + + 4 4 4 + + 1/72 x DATA(-1, 2) + 1/18 x DATA(2, 1) - 1/48 x DATA(0, 2) + + 3 3 + - 5/12 x DATA(-1, 0) + 5/24 x DATA(-2, 0) + 1/2 y DATA(0, 2) + + 4 4 4 + + 1/3 x DATA(0, -1) - 1/48 x DATA(0, -2) + 1/3 x DATA(0, 1) + + 4 4 4 + + 1/72 x DATA(1, -2) - 1/288 x DATA(2, -2) + 1/18 x DATA(-2, -1) + + 4 3 2 4 + - 5/48 x DATA(-2, 0) - 5/24 x DATA(2, 0) - 1/2 y x DATA(0, -1) + + 2 4 2 4 2 4 + - 1/2 y x DATA(0, 1) + 1/8 y x DATA(0, -2) + 1/48 y x DATA(2, -2) + + 2 4 2 4 2 4 + - 1/12 y x DATA(-2, -1) + 1/8 y x DATA(-2, 0) - 1/12 y x DATA(1, -2) + + 3 2 3 2 + + 1/4 x y DATA(2, 0) + 5/24 x DATA(2, 0) - 1/2 x y DATA(1, 0) + + 3 2 2 2 2 2 + + 1/2 x y DATA(-1, 0) - 5/8 x y DATA(0, 2) - 5/8 x y DATA(0, -2) + + 2 2 2 2 2 2 + - 15/4 x y DATA(0, 0) + 5/2 x y DATA(0, 1) - 1/8 x y DATA(-2, 0) + + 2 2 2 4 2 4 + + 5/2 x y DATA(0, -1) + 1/3 y x DATA(-1, -1) - 1/12 y x DATA(-1, -2) + + 2 4 2 4 2 4 + + 1/3 y x DATA(-1, 1) + 1/48 y x DATA(-2, -2) - 1/2 y x DATA(-1, 0) + + 2 4 2 4 2 4 + + 1/3 y x DATA(1, -1) + 1/3 y x DATA(1, 1) - 1/2 y x DATA(1, 0) + + 2 4 2 4 2 4 + + 1/8 y x DATA(2, 0) - 1/12 y x DATA(-2, 1) + 1/48 y x DATA(-2, 2) + + 2 2 4 2 4 + - 2 x y DATA(-1, 0) + 1/48 y x DATA(2, 2) - 1/12 y x DATA(2, -1) + + 2 2 2 2 2 2 + + 2 x y DATA(-1, 0) + 2 x y DATA(1, 0) - 1/8 x y DATA(2, 0) + + 2 + - 5/3 x DATA(1, 0) + 4/3 DATA(0, -1) + 2 x y DATA(1, 0) + + 2 2 4 + + 1/4 x y DATA(-2, 0) - 1/4 x y DATA(2, 0) - 2/9 x DATA(-1, -1) + + 2 4 4 + - 5/4 y x DATA(0, -1) - 1/288 x DATA(2, 2) + 1/72 x DATA(-1, -2) + + 4 4 4 + - 2/9 x DATA(1, -1) - 2/9 x DATA(-1, 1) - 2/9 x DATA(1, 1) + + 4 4 2 + - 1/288 x DATA(-2, 2) - 1/288 x DATA(-2, -2) + 5/8 y x DATA(0, -2) + + 2 + + 5/4 y x DATA(0, 1) - 1/2 y DATA(0, -2) - y DATA(0, 1) + + 2 2 + - 5/8 y x DATA(0, 2) + y DATA(0, -1) + 1/2 y DATA(0, 2) + + 2 2 2 + + 1/2 y DATA(0, -2) - 2 y DATA(0, 1) - 2 y DATA(0, -1) + + 4 4 4 + + 1/6 y x DATA(-1, 1) + 1/12 y x DATA(-1, -2) - 1/8 y x DATA(0, -2) + + 2 2 2 + + 3 y DATA(0, 0) - 5/3 x DATA(1, 0) + 5/48 x DATA(0, 2) + + 2 2 2 + - 5/3 x DATA(0, -1) + 5/48 x DATA(0, -2) - 5/3 x DATA(0, 1) + + 2 4 4 + + 25/8 x DATA(0, 0) - 1/6 y x DATA(-1, -1) - 1/48 y x DATA(-2, -2) + + 2 4 4 + + 5/48 x DATA(-2, 0) + 1/48 y x DATA(-2, 2) + 1/6 y x DATA(1, 1) + + 4 4 4 + + 1/4 y x DATA(0, -1) + 1/24 y x DATA(-2, -1) + 1/12 y x DATA(1, -2) + + 2 2 4 + - 5/3 x DATA(-1, 0) + 5/48 x DATA(2, 0) - 1/48 y x DATA(2, -2) + + 4 3 2 + - 1/24 y x DATA(-2, 1) - 1/4 x y DATA(-2, 0) - 5/24 x DATA(-2, 0) + + 4 4 4 + + 1/48 y x DATA(2, 2) + 1/18 x DATA(-2, 1) + 1/18 x DATA(2, -1) + + 4 4 4 + - 1/24 y x DATA(2, 1) + 1/8 y x DATA(0, 2) - 1/4 y x DATA(0, 1) + + 4 4 2 4 + + 1/24 y x DATA(2, -1) - 1/6 y x DATA(1, -1) - 1/12 y x DATA(-1, 2) + + 2 4 2 4 + - 1/12 y x DATA(1, 2) + 5/3 x DATA(-1, 0) + 3/4 y x DATA(0, 0) + + 2 4 2 4 4 + + 1/8 y x DATA(0, 2) - 1/12 y x DATA(2, 1) - 1/12 y x DATA(-1, 2) + + 4 + - 1/12 y x DATA(1, 2) - 8/9 x DATA(-1, 1) - 8/9 x DATA(-1, -1) + + 3 3 + + 8/9 x DATA(1, -1) - 1/144 x DATA(2, 2) + 1/72 x DATA(1, 2) + + 3 3 3 + - 1/72 x DATA(-1, 2) - 1/144 x DATA(2, -2) + 1/72 x DATA(1, -2) + + 3 3 3 + - 1/72 x DATA(-1, -2) + 1/9 x DATA(2, 1) + 1/9 x DATA(2, -1) + + 3 3 2 + - 2/9 x DATA(1, 1) + 1/144 x DATA(-2, 2) + 4/3 x y DATA(-1, -1) + + 2 2 2 2 3 + - 4/3 x y DATA(1, 1) - 1/48 x y DATA(-2, 2) + 1/144 x DATA(-2, -2) + + 3 3 3 + + 2/9 x DATA(-1, -1) + 1/12 y x DATA(-2, 1) - 1/12 y x DATA(-2, -1) + + 3 3 3 + - 1/24 y x DATA(2, -2) - 1/6 y x DATA(1, -1) - 1/6 y x DATA(-1, 1) + + 3 3 3 + + 1/12 y x DATA(2, -1) + 1/6 y x DATA(1, 1) - 1/24 y x DATA(-2, 2) + + 3 3 3 + + 1/24 y x DATA(-2, -2) + 1/6 y x DATA(-1, -1) - 1/12 y x DATA(1, 2) + + 3 3 3 + + 1/12 y x DATA(-1, 2) + 1/24 y x DATA(2, 2) - 1/12 y x DATA(2, 1) + + 2 2 2 + - 1/18 x DATA(2, -1) + 8/9 x DATA(1, 1) + 1/288 x DATA(-2, 2) + + 2 2 2 + - 1/18 x DATA(-2, 1) - 1/18 x DATA(-2, -1) + 1/288 x DATA(2, -2) + + 2 2 2 + - 1/18 x DATA(1, -2) - 1/18 x DATA(-1, -2) + 1/288 x DATA(-2, -2) + + 2 2 2 + + 8/9 x DATA(-1, -1) + 8/9 x DATA(1, -1) - 1/18 x DATA(1, 2) + + 2 2 2 + - 1/18 x DATA(-1, 2) - 1/18 x DATA(2, 1) + 1/288 x DATA(2, 2) + + 3 3 3 + - 2/9 x DATA(1, -1) + 2/9 x DATA(-1, 1) - 1/9 x DATA(-2, 1) + + 3 + - 1/9 x DATA(-2, -1) - 1/9 x DATA(2, 1) - 1/9 x DATA(2, -1) + + + 8/9 x DATA(1, 1) - 1/144 x DATA(-2, 2) + 1/9 x DATA(-2, 1) + + + 1/9 x DATA(-2, -1) + 1/144 x DATA(2, -2) - 1/18 x DATA(1, -2) + + 3 3 + + 1/12 y x DATA(1, -2) - 1/12 y x DATA(-1, -2) + 1/18 x DATA(-1, -2) + + 3 2 3 2 3 2 + + 1/3 x y DATA(1, 1) - 1/24 x y DATA(-2, 2) + 1/6 x y DATA(-2, 1) + + 3 2 3 2 + + 1/6 x y DATA(-2, -1) + 1/24 x y DATA(2, -2) - 1/144 x DATA(-2, -2) + + 3 2 3 2 3 2 + + 1/24 x y DATA(2, 2) - 1/12 x y DATA(1, 2) + 1/12 x y DATA(-1, 2) + + 3 2 3 2 3 2 + - 1/6 x y DATA(2, 1) - 1/6 x y DATA(2, -1) + 1/3 x y DATA(1, -1) + + 2 3 2 3 2 + + 8/9 x DATA(-1, 1) - 1/12 x y DATA(1, -2) + 1/12 x y DATA(-1, -2) + + 3 2 3 2 3 2 + - 1/24 x y DATA(-2, -2) - 1/3 x y DATA(-1, -1) - 1/3 x y DATA(-1, 1) + + + 1/144 x DATA(2, 2) - 1/18 x DATA(1, 2) + 1/18 x DATA(-1, 2) + + 2 2 2 2 2 2 + - 1/48 x y DATA(2, -2) + 1/3 x y DATA(1, -2) + 1/3 x y DATA(-1, -2) + + 2 2 2 2 2 2 + - 1/48 x y DATA(-2, -2) - 4/3 x y DATA(-1, -1) - 4/3 x y DATA(1, -1) + + 2 2 2 2 + - 4/3 x y DATA(-1, 1) + 1/3 y x DATA(1, 2) + 1/3 y x DATA(-1, 2) + + 2 2 2 2 + + 1/24 y x DATA(2, 1) + 1/12 x y DATA(-2, -1) - 1/3 y x DATA(1, -2) + + 2 2 2 + - 1/3 y x DATA(-1, -2) + 1/48 y x DATA(-2, -2) - 1/48 y x DATA(2, 2) + + 2 2 2 + - 2/3 y x DATA(1, 1) - 1/48 y x DATA(-2, 2) + 1/24 y x DATA(-2, 1) + + 2 2 2 + - 1/24 y x DATA(-2, -1) + 1/48 y x DATA(2, -2) + 2/3 y x DATA(-1, -1) + + 2 2 2 + + 2/3 y x DATA(1, -1) - 2/3 y x DATA(-1, 1) - 1/24 y x DATA(2, -1) + + 2 2 2 + - 4/3 x y DATA(1, -1) + 4/3 x y DATA(-1, 1) - 1/6 x y DATA(-2, -1) + + 2 2 2 + - 1/24 x y DATA(2, -2) + 1/3 x y DATA(1, -2) - 1/3 x y DATA(-1, -2) + + 2 2 2 + + 1/3 x y DATA(1, 2) - 1/3 x y DATA(-1, 2) + 1/6 x y DATA(2, 1) + + 2 + + 1/24 x y DATA(-2, -2) + 1/3 x y DATA(1, 2) - 1/3 x y DATA(-1, 2) + + + 1/12 x y DATA(2, 1) - 1/12 x y DATA(2, -1) - 2/3 x y DATA(1, 1) + + + 1/24 x y DATA(-2, 2) - 1/12 x y DATA(-2, 1) + 1/12 x y DATA(-2, -1) + + 2 2 + + 1/24 x y DATA(2, -2) - 4/3 x y DATA(1, 1) - 1/6 x y DATA(-2, 1) + + 2 2 2 + + 1/24 x y DATA(-2, 2) + 1/6 x y DATA(2, -1) - 1/24 x y DATA(2, 2) + + + 2/3 x y DATA(-1, 1) - 1/24 x y DATA(2, 2) - 1/3 x y DATA(1, -2) + + + 1/3 x y DATA(-1, -2) - 1/24 x y DATA(-2, -2) - 2/3 x y DATA(-1, -1) + + 2 2 2 2 + + 2/3 x y DATA(1, -1) + 1/12 x y DATA(-2, 1) + 1/3 x y DATA(1, 2) + + 2 2 2 2 2 2 + + 1/3 x y DATA(-1, 2) + 1/12 x y DATA(2, 1) + 1/12 x y DATA(2, -1) + + 2 2 + - 1/48 x y DATA(2, 2) + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=337598236, alloc=2817532, time=36.76 +bytes used=338598536, alloc=2817532, time=36.83 + 3 2 2 4 +[COEFF(-2, -2) = 1/144 x - 1/48 x y - 1/24 x y - 1/144 x - 1/48 y x + + 2 2 3 2 2 2 4 3 + + 1/48 y x + 1/288 x - 1/24 x y + 1/24 x y + 1/48 y x + 1/24 y x + + 4 3 2 4 2 2 + - 1/288 x , COEFF(-1, -2) = - 1/72 x - 1/3 y x + 1/72 x + 1/3 x y + + 3 2 2 3 2 2 4 + - 1/12 y x - 1/18 x + 1/3 x y - 1/3 x y + 1/12 x y - 1/12 y x + + 4 2 2 4 4 + + 1/18 x + 1/12 y x , COEFF(0, -2) = 5/8 y x + 1/8 y x - 1/8 y x + + 4 2 2 2 2 + - 1/48 x + 5/48 x + 1/2 y - 5/8 x y - 1/12 - 1/2 y, COEFF(1, -2) = + + 2 4 2 2 3 3 + - 1/18 x + 1/72 x + 1/3 x y - 1/3 x y + 1/12 y x - 1/18 x + 1/72 x + + 2 4 2 3 2 2 4 + - 1/12 y x - 1/3 y x - 1/12 x y + 1/3 x y + 1/12 y x , COEFF(2, -2) + + 2 4 2 2 2 + = - 1/24 x y - 1/48 y x + 1/288 x + 1/144 x - 1/48 x y + 1/24 x y + + 3 3 2 3 2 2 4 4 + - 1/144 x - 1/24 y x + 1/48 y x + 1/24 x y + 1/48 y x - 1/288 x , + + 4 3 2 2 2 + COEFF(-2, -1) = 1/12 x y + 1/18 x - 1/9 x + 1/12 x y - 1/24 y x + + 4 2 4 2 3 3 2 + + 1/24 y x - 1/12 y x - 1/18 x - 1/12 y x + 1/6 x y + 1/9 x + + 2 4 3 2 2 2 + - 1/6 x y , COEFF(-1, -1) = - 2/9 x - 1/3 x y + 8/9 x + 2/3 y x + + 4 2 4 3 3 2 2 2 + - 1/6 y x + 1/3 y x + 1/6 y x + 2/9 x - 4/3 x y - 8/9 x + 4/3 x y + + 2 4 2 2 2 + - 2/3 x y, COEFF(0, -1) = 4/3 - 1/2 y x + y - 5/3 x - 5/4 y x - 2 y + + 4 4 2 2 4 4 + + 1/4 y x + 1/3 x + 5/2 x y , COEFF(1, -1) = 8/9 x - 1/6 y x - 2/9 x + + 2 4 2 2 3 2 3 + + 1/3 y x - 4/3 x y + 2/3 y x + 1/3 x y - 2/9 x + 2/3 x y + + 2 2 2 3 3 2 + - 4/3 x y + 8/9 x - 1/6 y x , COEFF(2, -1) = 1/9 x + 1/6 x y - 1/9 x + + 2 3 4 2 2 3 2 + - 1/18 x + 1/12 y x + 1/24 y x + 1/12 x y - 1/6 x y - 1/12 x y + + 4 2 4 2 2 2 3 2 + + 1/18 x - 1/12 y x - 1/24 y x , COEFF(-2, 0) = - 1/8 x y - 1/4 x y + + 3 2 4 2 4 2 + + 5/24 x + 1/8 y x + 1/4 x y - 5/48 x - 5/24 x + 5/48 x , + + 3 2 2 2 2 4 2 4 + COEFF(-1, 0) = 1/2 x y + 2 x y + 5/3 x - 5/3 x + 5/12 x - 1/2 y x + + 3 2 + - 5/12 x - 2 x y , + + 2 2 4 2 4 2 2 + COEFF(0, 0) = 25/8 x - 5/2 + 3 y - 5/8 x + 3/4 y x - 15/4 x y , + + 2 4 2 2 2 2 3 2 3 + COEFF(1, 0) = - 1/2 y x + 2 x y + 2 x y - 5/3 x - 1/2 x y + 5/12 x + + 4 4 3 2 2 4 + + 5/12 x - 5/3 x, COEFF(2, 0) = - 5/48 x + 1/4 x y + 1/8 y x + + 2 2 2 2 3 + - 1/8 x y - 1/4 x y + 5/48 x - 5/24 x + 5/24 x, COEFF(-2, 1) = + + 3 2 2 4 3 + - 1/9 x + 1/12 x y - 1/12 x y + 1/9 x - 1/24 y x + 1/12 y x + + 2 2 2 4 2 4 3 2 + + 1/24 y x - 1/18 x - 1/12 y x - 1/6 x y + 1/18 x + 1/6 x y , + + 4 2 3 4 + COEFF(-1, 1) = 2/3 x y + 1/6 y x - 2/3 y x - 1/6 y x - 2/9 x + + 2 4 3 2 2 3 2 2 2 + + 1/3 y x + 2/9 x + 8/9 x - 8/9 x + 4/3 x y - 1/3 x y - 4/3 x y , + + 2 2 4 2 4 4 + COEFF(0, 1) = -2 y + 4/3 - 1/2 y x + 5/4 y x + 1/3 x - 1/4 y x - y + + 2 2 2 2 3 4 + + 5/2 x y - 5/3 x , COEFF(1, 1) = - 2/3 y x - 2/3 x y - 2/9 x - 2/9 x + + 4 2 2 2 3 2 4 + + 8/9 x + 1/6 y x - 4/3 x y - 4/3 x y + 1/6 y x + 1/3 y x + + 3 2 2 2 2 4 2 + + 1/3 x y + 8/9 x , COEFF(2, 1) = 1/12 x y + 1/18 x - 1/18 x + + 2 4 2 4 3 3 2 + - 1/12 y x + 1/6 x y - 1/24 y x + 1/12 x y + 1/9 x - 1/6 x y + + 3 2 2 2 + - 1/9 x - 1/12 y x + 1/24 y x , COEFF(-2, 2) = 1/24 x y + 1/288 x + + 3 2 4 4 3 + + 1/24 x y + 1/144 x + 1/48 y x - 1/144 x + 1/48 y x - 1/24 y x + + 4 2 2 2 3 2 + - 1/288 x - 1/48 y x - 1/48 x y - 1/24 x y , COEFF(-1, 2) = - 1/3 x y + + 2 2 2 3 2 2 2 4 3 + - 1/3 x y + 1/3 x y + 1/12 x y + 1/3 y x - 1/12 y x - 1/72 x + + 2 4 3 4 + + 1/18 x - 1/18 x + 1/72 x + 1/12 y x - 1/12 y x , COEFF(0, 2) = + + 4 2 4 2 2 4 2 2 + - 1/48 x - 5/8 y x + 1/2 y + 1/8 y x + 1/2 y + 1/8 y x - 5/8 x y + + 2 3 2 2 2 + + 5/48 x - 1/12, COEFF(1, 2) = - 1/12 x y + 1/3 x y + 1/3 x y + + 2 4 4 3 3 2 + + 1/3 x y + 1/72 x - 1/12 y x - 1/12 y x + 1/72 x - 1/18 x + + 2 2 4 3 + + 1/3 y x - 1/18 x - 1/12 y x , COEFF(2, 2) = - 1/24 x y - 1/144 x + + 2 2 3 2 4 2 3 2 + - 1/48 x y + 1/24 x y - 1/288 x - 1/48 y x + 1/24 y x + 1/288 x + + 4 2 2 4 + + 1/48 y x + 1/144 x - 1/24 x y + 1/48 y x ] + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c"); +bytes used=339598688, alloc=2817532, time=36.92 +bytes used=340598856, alloc=2817532, time=36.99 +bytes used=341599544, alloc=2817532, time=37.04 +bytes used=342609588, alloc=2817532, time=37.12 +bytes used=343617792, alloc=2817532, time=37.21 +bytes used=344618020, alloc=2817532, time=37.30 +bytes used=345618228, alloc=2817532, time=37.79 +bytes used=346618720, alloc=2817532, time=37.87 +bytes used=347618880, alloc=2817532, time=37.94 +bytes used=348623292, alloc=2817532, time=38.03 +bytes used=349623484, alloc=2817532, time=38.12 +bytes used=350623648, alloc=2817532, time=38.22 +bytes used=351625036, alloc=2817532, time=38.32 +bytes used=352625232, alloc=2817532, time=38.73 +bytes used=353625668, alloc=2817532, time=38.91 +bytes used=354625832, alloc=2817532, time=38.99 +bytes used=355626060, alloc=2817532, time=39.14 +bytes used=356630912, alloc=2817532, time=39.56 +bytes used=357631128, alloc=2817532, time=39.78 +bytes used=358631348, alloc=2817532, time=39.86 +bytes used=359632096, alloc=2817532, time=40.02 +bytes used=360632268, alloc=2817532, time=40.42 +bytes used=361632468, alloc=2817532, time=40.49 +bytes used=362632652, alloc=2817532, time=40.71 +bytes used=363633064, alloc=2817532, time=41.09 +bytes used=364633244, alloc=2817532, time=41.18 +bytes used=365633400, alloc=2817532, time=41.60 +bytes used=366633640, alloc=2817532, time=41.81 +> +################################################################################ +> quit +bytes used=367598444, alloc=2817532, time=41.95 diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.maple b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.maple new file mode 100644 index 0000000..a5b197c --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.maple @@ -0,0 +1,170 @@ +# 2d.maple -- compute Lagrange interpolation coefficients in 2-D +# $Header$ + +################################################################################ + +# +# 2d, cube, order=1, smoothing=0 (size=2) +# + +# interpolating polynomial +interp_2d_cube_order1_smooth0 + := Lagrange_polynomial_interpolant(fn_2d_order1, coeffs_list_2d_order1, + coords_list_2d, posn_list_2d_size2); + +# I +coeffs_as_lc_of_data(%, posn_list_2d_size2); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_2d_cube_order1_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size2); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_2d_cube_order1_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size2); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c"); + +################################################################################ + +# +# 2d, cube, order=2, smoothing=0 (size=3) +# + +# interpolating polynomial +interp_2d_cube_order2_smooth0 + := Lagrange_polynomial_interpolant(fn_2d_order2, coeffs_list_2d_order2, + coords_list_2d, posn_list_2d_size3); + +# I +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_2d_cube_order2_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_2d_cube_order2_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_2d_cube_order2_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_2d_cube_order2_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_2d_cube_order2_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size3); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c"); + +################################################################################ + +# +# 2d, cube, order=3, smoothing=0 (size=4) +# + +# interpolating polynomial +interp_2d_cube_order3_smooth0 + := Lagrange_polynomial_interpolant(fn_2d_order3, coeffs_list_2d_order3, + coords_list_2d, posn_list_2d_size4); + +# I +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_2d_cube_order3_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_2d_cube_order3_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_2d_cube_order3_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_2d_cube_order3_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_2d_cube_order3_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size4); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c"); + +################################################################################ + +# +# 2d, cube, order=4, smoothing=0 (size=5) +# + +# interpolating polynomial +interp_2d_cube_order4_smooth0 + := Lagrange_polynomial_interpolant(fn_2d_order4, coeffs_list_2d_order4, + coords_list_2d, posn_list_2d_size5); + +# I +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_2d_cube_order4_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_2d_cube_order4_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_2d_cube_order4_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_2d_cube_order4_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_2d_cube_order4_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_2d_size5); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c"); + +################################################################################ diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..c6a4b9c --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-I.compute.c @@ -0,0 +1,22 @@ +fp t2; +fp t8; +fp t1; +fp t3; +fp t7; +fp t6; +fp t5; + t2 = x*y; + t8 = -y+t2; + t1 = z*t2; + t3 = x*z; + t7 = t1-t3; + t6 = t1-y*z; + t5 = -t3+z+t6; + coeffs_I->coeff_0_0_0 = RATIONAL(1.0,1.0)-x-t5+t8; + coeffs_I->coeff_p1_0_0 = x-t2+t7; + coeffs_I->coeff_0_p1_0 = t6-t8; + coeffs_I->coeff_p1_p1_0 = -t1+t2; + coeffs_I->coeff_0_0_p1 = t5; + coeffs_I->coeff_p1_0_p1 = -t7; + coeffs_I->coeff_0_p1_p1 = -t6; + coeffs_I->coeff_p1_p1_p1 = t1; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..6ecb7d1 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-dx.compute.c @@ -0,0 +1,16 @@ +fp t11; +fp t9; +fp t12; +fp t10; + t11 = y*z; + t9 = -t11+z; + t12 = y+t9; + t10 = -t11+y; + coeffs_dx->coeff_0_0_0 = RATIONAL(-1.0,1.0)+t12; + coeffs_dx->coeff_p1_0_0 = RATIONAL(1.0,1.0)-t12; + coeffs_dx->coeff_0_p1_0 = -t10; + coeffs_dx->coeff_p1_p1_0 = t10; + coeffs_dx->coeff_0_0_p1 = -t9; + coeffs_dx->coeff_p1_0_p1 = t9; + coeffs_dx->coeff_0_p1_p1 = -t11; + coeffs_dx->coeff_p1_p1_p1 = t11; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..4830830 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-dy.compute.c @@ -0,0 +1,16 @@ +fp t15; +fp t14; +fp t16; +fp t13; + t15 = x*z; + t14 = -t15+x; + t16 = z+t14; + t13 = -t15+z; + coeffs_dy->coeff_0_0_0 = RATIONAL(-1.0,1.0)+t16; + coeffs_dy->coeff_p1_0_0 = -t14; + coeffs_dy->coeff_0_p1_0 = RATIONAL(1.0,1.0)-t16; + coeffs_dy->coeff_p1_p1_0 = t14; + coeffs_dy->coeff_0_0_p1 = -t13; + coeffs_dy->coeff_p1_0_p1 = -t15; + coeffs_dy->coeff_0_p1_p1 = t13; + coeffs_dy->coeff_p1_p1_p1 = t15; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-dz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-dz.compute.c new file mode 100644 index 0000000..6dc2843 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-dz.compute.c @@ -0,0 +1,16 @@ +fp t19; +fp t17; +fp t20; +fp t18; + t19 = y*x; + t17 = -t19+y; + t20 = x+t17; + t18 = x-t19; + coeffs_dz->coeff_0_0_0 = RATIONAL(-1.0,1.0)+t20; + coeffs_dz->coeff_p1_0_0 = -t18; + coeffs_dz->coeff_0_p1_0 = -t17; + coeffs_dz->coeff_p1_p1_0 = -t19; + coeffs_dz->coeff_0_0_p1 = RATIONAL(1.0,1.0)-t20; + coeffs_dz->coeff_p1_0_p1 = t18; + coeffs_dz->coeff_0_p1_p1 = t17; + coeffs_dz->coeff_p1_p1_p1 = t19; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..d629ea0 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-I.compute.c @@ -0,0 +1,245 @@ +fp t82; +fp t84; +fp t114; +fp t83; +fp t104; +fp t26; +fp t106; +fp t34; +fp t154; +fp t85; +fp t129; +fp t105; +fp t25; +fp t29; +fp t153; +fp t81; +fp t130; +fp t107; +fp t36; +fp t152; +fp t108; +fp t38; +fp t46; +fp t151; +fp t109; +fp t45; +fp t150; +fp t27; +fp t131; +fp t110; +fp t35; +fp t149; +fp t42; +fp t48; +fp t148; +fp t147; +fp t77; +fp t111; +fp t51; +fp t78; +fp t128; +fp t146; +fp t123; +fp t60; +fp t127; +fp t145; +fp t115; +fp t64; +fp t31; +fp t119; +fp t144; +fp t52; +fp t143; +fp t124; +fp t142; +fp t70; +fp t33; +fp t141; +fp t63; +fp t44; +fp t140; +fp t139; +fp t103; +fp t41; +fp t68; +fp t138; +fp t47; +fp t137; +fp t136; +fp t50; +fp t135; +fp t126; +fp t65; +fp t134; +fp t133; +fp t24; +fp t132; +fp t125; +fp t121; +fp t80; +fp t79; +fp t76; +fp t32; +fp t122; +fp t120; +fp t118; +fp t117; +fp t116; +fp t113; +fp t112; +fp t102; +fp t101; +fp t100; +fp t99; +fp t98; +fp t59; +fp t62; +fp t97; +fp t96; +fp t95; +fp t94; +fp t93; +fp t92; +fp t91; +fp t90; +fp t89; +fp t88; +fp t87; +fp t86; + t82 = RATIONAL(1.0,8.0); + t84 = z*z; + t114 = t82*t84; + t83 = x*x; + t104 = t83*t114; + t26 = y*t104; + t106 = x*t114; + t34 = y*t106; + t154 = t26+t34; + t85 = y*y; + t129 = z*t85; + t105 = t82*t129; + t25 = t83*t105; + t29 = x*t105; + t153 = t25+t29; + t81 = RATIONAL(-1.0,8.0); + t130 = x*t81; + t107 = t84*t130; + t36 = y*t107; + t152 = t26+t36; + t108 = t81*t129; + t38 = x*t108; + t46 = t83*t108; + t151 = t38+t46; + t109 = y*t81*t83; + t45 = t84*t109; + t150 = t34+t45; + t27 = z*t109; + t131 = y*z; + t110 = t82*t131; + t35 = x*t110; + t149 = t27+t35; + t42 = t130*t131; + t48 = t83*t110; + t148 = t42+t48; + t147 = t36+t45; + t77 = RATIONAL(1.0,4.0); + t111 = t77*t83; + t51 = z*t111; + t78 = RATIONAL(-1.0,4.0); + t128 = z*t78; + t146 = (t128+t51)*y; + t123 = t78*t84; + t60 = x*t123; + t127 = y*t77; + t145 = x*t127+y*t60; + t115 = t78*t85; + t64 = x*t115; + t31 = t84*t64; + t119 = t77*t85; + t144 = x*t119+t31; + t52 = z*t119; + t143 = (t128+t52)*x; + t124 = t77*t84; + t142 = x*t124+t31; + t70 = t84*t119; + t33 = x*t70; + t141 = t60+t33; + t63 = t85*t111; + t44 = z*t63; + t140 = z*t115+t44; + t139 = (t64+t77*x)*z; + t103 = t83*t115; + t41 = t84*t103; + t68 = t84*t111; + t138 = t41+t68; + t47 = t85*t104; + t137 = t85*t106+t47; + t136 = t85*t107+t47; + t50 = y*t124; + t135 = (t78*y+t50)*x; + t126 = t78*t83; + t65 = y*t126; + t134 = (t127+t65)*z; + t133 = t64+t33; + t24 = z*t103; + t132 = t24+t52; + t125 = t85+t84; + t121 = t83*t84; + t80 = RATIONAL(-1.0,2.0); + t79 = RATIONAL(1.0,2.0); + t76 = t79*t85; + t32 = t76*t121; + t122 = t80*t121+t32; + t120 = t85*t84; + t118 = y*t68+t41; + t117 = t84*t65+t41; + t116 = t84+t83; + t113 = t83+t85; + t112 = t80*t85; + t102 = 1.0+t120; + t101 = t121+1.0; + t100 = t83*t85+1.0; + t99 = t29+t46+t136; + t98 = z*t126+t44+t138; + t59 = t84*t112; + t62 = t83*t112; + t97 = t59+t32+t76+t62; + t96 = t79*t83+t62+t122; + t95 = t25+t38+t136; + t94 = y*t123+t70+t118; + t93 = t50+t70+t117; + t92 = t59+t79*t84+t122; + t91 = t63+t65+t118; + t90 = t63+y*t111+t117; + t89 = t35+t48+t137; + t88 = t27+t42+t137; + t87 = t51+t24+t138; + t86 = -t120+t125; + coeffs_I->coeff_m1_m1_m1 = t99+t148+t150; + coeffs_I->coeff_0_m1_m1 = t94+t134+t140; + coeffs_I->coeff_p1_m1_m1 = t89+t147+t151; + coeffs_I->coeff_m1_0_m1 = t98+t139+t141; + coeffs_I->coeff_0_0_m1 = (t100*t80+t113*t79)*z+t92; + coeffs_I->coeff_p1_0_m1 = t98+t142+t143; + coeffs_I->coeff_m1_p1_m1 = t99+t149+t152; + coeffs_I->coeff_0_p1_m1 = t93+t140+t146; + coeffs_I->coeff_p1_p1_m1 = t88+t151+t154; + coeffs_I->coeff_m1_m1_0 = t91+t133+t145; + coeffs_I->coeff_0_m1_0 = (t101*t80+t116*t79)*y+t97; + coeffs_I->coeff_p1_m1_0 = t91+t135+t144; + coeffs_I->coeff_m1_0_0 = (t102*t80+t125*t79)*x+t96; + coeffs_I->coeff_0_0_0 = RATIONAL(1.0,1.0)+(-1.0+t86)*t83-t86; + coeffs_I->coeff_p1_0_0 = (t102*t79+t125*t80)*x+t96; + coeffs_I->coeff_m1_p1_0 = t90+t133+t135; + coeffs_I->coeff_0_p1_0 = (t101*t79+t116*t80)*y+t97; + coeffs_I->coeff_p1_p1_0 = t90+t144+t145; + coeffs_I->coeff_m1_m1_p1 = t95+t149+t150; + coeffs_I->coeff_0_m1_p1 = t94+t132+t146; + coeffs_I->coeff_p1_m1_p1 = t88+t147+t153; + coeffs_I->coeff_m1_0_p1 = t87+t141+t143; + coeffs_I->coeff_0_0_p1 = (t100*t79+t113*t80)*z+t92; + coeffs_I->coeff_p1_0_p1 = t87+t139+t142; + coeffs_I->coeff_m1_p1_p1 = t95+t148+t152; + coeffs_I->coeff_0_p1_p1 = t93+t132+t134; + coeffs_I->coeff_p1_p1_p1 = t89+t153+t154; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..52dc6d6 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dx.compute.c @@ -0,0 +1,186 @@ +fp t202; +fp t206; +fp t207; +fp t223; +fp t205; +fp t160; +fp t201; +fp t231; +fp t174; +fp t242; +fp t218; +fp t179; +fp t241; +fp t198; +fp t194; +fp t178; +fp t197; +fp t240; +fp t228; +fp t180; +fp t156; +fp t239; +fp t165; +fp t238; +fp t196; +fp t175; +fp t237; +fp t172; +fp t161; +fp t236; +fp t193; +fp t188; +fp t235; +fp t166; +fp t182; +fp t234; +fp t189; +fp t177; +fp t233; +fp t232; +fp t230; +fp t229; +fp t227; +fp t226; +fp t225; +fp t224; +fp t222; +fp t203; +fp t221; +fp t220; +fp t204; +fp t219; +fp t171; +fp t187; +fp t217; +fp t216; +fp t167; +fp t168; +fp t158; +fp t162; +fp t215; +fp t214; +fp t213; +fp t212; +fp t211; +fp t181; +fp t170; +fp t159; +fp t210; +fp t163; +fp t184; +fp t186; +fp t209; +fp t173; +fp t185; +fp t155; +fp t208; +fp t183; +fp t176; + t202 = RATIONAL(-1.0,2.0); + t206 = z*z; + t207 = y*y; + t223 = t207*t206; + t205 = x*t223; + t160 = t202*t205; + t201 = RATIONAL(1.0,2.0); + t231 = x*t201; + t174 = t206*t231; + t242 = t160+t174; + t218 = t201*t207; + t179 = x*t218; + t241 = t179+t160; + t198 = RATIONAL(-1.0,4.0); + t194 = t198*t206; + t178 = y*t194; + t197 = RATIONAL(1.0,4.0); + t240 = t178+t197*y; + t228 = x*t202; + t180 = y*t228; + t156 = y*t174; + t239 = t180+t156; + t165 = t206*t180; + t238 = y*t231+t165; + t196 = t197*t206; + t175 = y*t196; + t237 = t198*y+t175; + t172 = z*t228; + t161 = z*t179; + t236 = t172+t161; + t193 = t198*t207; + t188 = t206*t193; + t235 = t188+t196; + t166 = t207*t172; + t182 = z*t231; + t234 = t166+t182; + t189 = t197*t207; + t177 = t206*t189; + t233 = t177+t194; + t232 = y*z; + t230 = t207*z; + t229 = t202-x; + t227 = y*t206; + t226 = t201-x; + t225 = x+t205; + t224 = x*t232; + t222 = z*t180+t160; + t203 = RATIONAL(-1.0,8.0); + t221 = t203*t207; + t220 = t160+y*t182; + t204 = RATIONAL(1.0,8.0); + t219 = t204*t206; + t171 = z*t193; + t187 = z*t189; + t217 = -y+t227; + t216 = -t230+z; + t167 = t198*t224; + t168 = x*t175; + t158 = x*t171; + t162 = x*t177; + t215 = t167+t168+t158+t162; + t214 = t171+t197*z+t242; + t213 = t187+t198*z+t242; + t212 = t188+t189+t241; + t211 = t177+t193+t241; + t181 = y*t219; + t170 = t204*t230; + t159 = t197*t224; + t210 = t181+t170+t159+t162; + t163 = x*t178; + t184 = t204*t232; + t186 = z*t221; + t209 = t163+t184+t186+t162; + t173 = t203*t232; + t185 = t203*t227; + t155 = x*t187; + t208 = t173+t185+t155+t162; + t183 = t207*t219; + t176 = t206*t221; + coeffs_dx->coeff_m1_m1_m1 = t163+t176+t158+t173+t210; + coeffs_dx->coeff_0_m1_m1 = t156+t161+t222; + coeffs_dx->coeff_p1_m1_m1 = t158+t159+t185+t183+t209; + coeffs_dx->coeff_m1_0_m1 = t214+t233+t236; + coeffs_dx->coeff_0_0_m1 = t205+(-t206+t216)*x; + coeffs_dx->coeff_p1_0_m1 = t213+t235+t236; + coeffs_dx->coeff_m1_p1_m1 = t184+t176+t185+t170+t215; + coeffs_dx->coeff_0_p1_m1 = t165+t161+t220; + coeffs_dx->coeff_p1_p1_m1 = t173+t183+t181+t186+t215; + coeffs_dx->coeff_m1_m1_0 = t211+t239+t240; + coeffs_dx->coeff_0_m1_0 = t205+(-t207-t217)*x; + coeffs_dx->coeff_p1_m1_0 = t212+t237+t239; + coeffs_dx->coeff_m1_0_0 = t202+t226*t207+(t202*t207+t226)*t206+t225; + coeffs_dx->coeff_0_0_0 = ((1.0+t223)*RATIONAL(-2.0,1.0)+(t207+t206)* +RATIONAL(2.0,1.0))*x; + coeffs_dx->coeff_p1_0_0 = t201+t229*t207+(t218+t229)*t206+t225; + coeffs_dx->coeff_m1_p1_0 = t211+t237+t238; + coeffs_dx->coeff_0_p1_0 = t205+(-t207+t217)*x; + coeffs_dx->coeff_p1_p1_0 = t212+t238+t240; + coeffs_dx->coeff_m1_m1_p1 = t167+t181+t155+t176+t209; + coeffs_dx->coeff_0_m1_p1 = t156+t166+t220; + coeffs_dx->coeff_p1_m1_p1 = t163+t183+t167+t170+t208; + coeffs_dx->coeff_m1_0_p1 = t213+t233+t234; + coeffs_dx->coeff_0_0_p1 = t205+(-t206-t216)*x; + coeffs_dx->coeff_p1_0_p1 = t214+t234+t235; + coeffs_dx->coeff_m1_p1_p1 = t168+t176+t159+t186+t208; + coeffs_dx->coeff_0_p1_p1 = t165+t166+t222; + coeffs_dx->coeff_p1_p1_p1 = t168+t155+t183+t184+t210; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..e8ab5c4 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,120 @@ +fp t465; +fp t485; +fp t464; +fp t484; +fp t467; +fp t483; +fp t468; +fp t482; +fp t460; +fp t481; +fp t461; +fp t480; +fp t466; +fp t479; +fp t478; +fp t477; +fp t473; +fp t448; +fp t476; +fp t459; +fp t458; +fp t452; +fp t453; +fp t475; +fp t474; +fp t444; +fp t472; +fp t471; +fp t470; +fp t469; +fp t455; +fp t454; +fp t451; +fp t450; +fp t447; +fp t446; +fp t445; +fp t443; +fp t442; +fp t441; +fp t440; +fp t439; +fp t438; +fp t437; +fp t436; +fp t435; + t465 = RATIONAL(-1.0,2.0); + t485 = t465*y; + t464 = RATIONAL(1.0,2.0); + t484 = t464*y; + t467 = z*z; + t483 = y*t467; + t468 = y*y; + t482 = t468*z; + t460 = RATIONAL(1.0,4.0); + t481 = y*t460; + t461 = RATIONAL(-1.0,4.0); + t480 = z*t461; + t466 = t467*t468; + t479 = -t468+t466; + t478 = t466-t467; + t477 = t468+t467; + t473 = t460*t468; + t448 = t467*t473; + t476 = z*t473+t448; + t459 = t464*t467; + t458 = t464*t468; + t452 = z*t458; + t453 = t465*t466; + t475 = t452+t453; + t474 = t448+t468*t480; + t444 = t465*t483; + t472 = t444+t453; + t471 = t453+t465*t482; + t470 = t482-z; + t469 = t483-y; + t455 = t461*t483; + t454 = y*t459; + t451 = z*t485; + t450 = y*t480; + t447 = t467*t481; + t446 = z*t484; + t445 = z*t481; + t443 = t466+RATIONAL(1.0,1.0)-t477; + t442 = t464*z+t459+t471; + t441 = t458+t484+t472; + t440 = t465*z+t459+t475; + t439 = t485+t454+t453+t458; + t438 = t447+t445+t476; + t437 = t455+t450+t476; + t436 = t455+t445+t474; + t435 = t450+t447+t474; + coeffs_dxx->coeff_m1_m1_m1 = t436; + coeffs_dxx->coeff_0_m1_m1 = t451+t454+t475; + coeffs_dxx->coeff_p1_m1_m1 = t436; + coeffs_dxx->coeff_m1_0_m1 = t440; + coeffs_dxx->coeff_0_0_m1 = -t470+t478; + coeffs_dxx->coeff_p1_0_m1 = t440; + coeffs_dxx->coeff_m1_p1_m1 = t435; + coeffs_dxx->coeff_0_p1_m1 = t452+t446+t472; + coeffs_dxx->coeff_p1_p1_m1 = t435; + coeffs_dxx->coeff_m1_m1_0 = t439; + coeffs_dxx->coeff_0_m1_0 = -t469+t479; + coeffs_dxx->coeff_p1_m1_0 = t439; + coeffs_dxx->coeff_m1_0_0 = t443; + coeffs_dxx->coeff_0_0_0 = (t466+1.0)*RATIONAL(-2.0,1.0)+t477*RATIONAL(2.0 +,1.0); + coeffs_dxx->coeff_p1_0_0 = t443; + coeffs_dxx->coeff_m1_p1_0 = t441; + coeffs_dxx->coeff_0_p1_0 = t469+t479; + coeffs_dxx->coeff_p1_p1_0 = t441; + coeffs_dxx->coeff_m1_m1_p1 = t437; + coeffs_dxx->coeff_0_m1_p1 = t446+t454+t471; + coeffs_dxx->coeff_p1_m1_p1 = t437; + coeffs_dxx->coeff_m1_0_p1 = t442; + coeffs_dxx->coeff_0_0_p1 = t470+t478; + coeffs_dxx->coeff_p1_0_p1 = t442; + coeffs_dxx->coeff_m1_p1_p1 = t438; + coeffs_dxx->coeff_0_p1_p1 = t444+t451+t471; + coeffs_dxx->coeff_p1_p1_p1 = t438; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxy.compute.c new file mode 100644 index 0000000..d5b8bd9 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxy.compute.c @@ -0,0 +1,170 @@ +fp t521; +fp t527; +fp t541; +fp t496; +fp t522; +fp t513; +fp t560; +fp t518; +fp t515; +fp t517; +fp t559; +fp t542; +fp t498; +fp t511; +fp t558; +fp t524; +fp t516; +fp t523; +fp t510; +fp t557; +fp t545; +fp t500; +fp t504; +fp t556; +fp t512; +fp t499; +fp t555; +fp t507; +fp t508; +fp t554; +fp t492; +fp t506; +fp t553; +fp t546; +fp t503; +fp t552; +fp t493; +fp t505; +fp t551; +fp t495; +fp t489; +fp t550; +fp t509; +fp t491; +fp t549; +fp t548; +fp t547; +fp t526; +fp t514; +fp t544; +fp t525; +fp t519; +fp t540; +fp t486; +fp t494; +fp t543; +fp t539; +fp t538; +fp t537; +fp t536; +fp t535; +fp t534; +fp t533; +fp t532; +fp t531; +fp t530; +fp t529; +fp t490; +fp t528; +fp t501; +fp t497; + t521 = RATIONAL(1.0,2.0); + t527 = z*z; + t541 = t521*t527; + t496 = y*t541; + t522 = RATIONAL(-1.0,2.0); + t513 = t522*y; + t560 = t496+t513; + t518 = RATIONAL(-1.0,4.0); + t515 = t518*t527; + t517 = RATIONAL(1.0,4.0); + t559 = t515+t517; + t542 = t522*t527; + t498 = y*t542; + t511 = t521*y; + t558 = t498+t511; + t524 = RATIONAL(-1.0,8.0); + t516 = t524*z; + t523 = RATIONAL(1.0,8.0); + t510 = t523*t527; + t557 = t516+t510; + t545 = z*t518; + t500 = y*t545; + t504 = y*t515; + t556 = t500+t504; + t512 = t517*t527; + t499 = y*t512; + t555 = t499+t500; + t507 = t523*z; + t508 = t524*t527; + t554 = t507+t508; + t492 = x*t545; + t506 = x*t515; + t553 = t492+t506; + t546 = z*t517; + t503 = y*t546; + t552 = t499+t503; + t493 = x*t512; + t505 = x*t546; + t551 = t493+t505; + t495 = z*t513; + t489 = x*t496; + t550 = x*t495+t489; + t509 = t521*x; + t491 = z*t509; + t549 = y*t491+t489; + t548 = t504+t503; + t547 = t518+t512; + t526 = y*x; + t514 = t522*x; + t544 = y*t527; + t525 = z*t526; + t519 = RATIONAL(2.0,1.0); + t540 = x*t544; + t486 = t519*t540; + t494 = RATIONAL(-2.0,1.0)*t526; + t543 = t494+t486; + t539 = (1.0-t527)*x; + t538 = y-t544; + t537 = -t525-t540; + t536 = t525-t540; + t535 = x*t541-t540; + t534 = t495-t540; + t533 = t516+t508+t549; + t532 = t505+t506+t550; + t531 = t507+t510+t549; + t530 = t492+t493+t550; + t529 = t514+t526+t535; + t490 = x*t542; + t528 = t490+t526-t540+t509; + t501 = z*t514; + t497 = z*t511; + coeffs_dxy->coeff_m1_m1_m1 = t532+t548+t557; + coeffs_dxy->coeff_0_m1_m1 = t501+t525+t535; + coeffs_dxy->coeff_p1_m1_m1 = t532+t554+t555; + coeffs_dxy->coeff_m1_0_m1 = t525+t496+t534; + coeffs_dxy->coeff_0_0_m1 = t486+z*t494; + coeffs_dxy->coeff_p1_0_m1 = t497+t498+t536; + coeffs_dxy->coeff_m1_p1_m1 = t530+t548+t554; + coeffs_dxy->coeff_0_p1_m1 = t491+t490+t536; + coeffs_dxy->coeff_p1_p1_m1 = t530+t555+t557; + coeffs_dxy->coeff_m1_m1_0 = t529+t559+t560; + coeffs_dxy->coeff_0_m1_0 = t539+t543; + coeffs_dxy->coeff_p1_m1_0 = t529+t547+t558; + coeffs_dxy->coeff_m1_0_0 = t538+t543; + coeffs_dxy->coeff_0_0_0 = (RATIONAL(-4.0,1.0)*t527+RATIONAL(4.0,1.0))* +t526; + coeffs_dxy->coeff_p1_0_0 = -t538+t543; + coeffs_dxy->coeff_m1_p1_0 = t528+t547+t560; + coeffs_dxy->coeff_0_p1_0 = -t539+t543; + coeffs_dxy->coeff_p1_p1_0 = t528+t558+t559; + coeffs_dxy->coeff_m1_m1_p1 = t531+t553+t556; + coeffs_dxy->coeff_0_m1_p1 = t491-t525+t535; + coeffs_dxy->coeff_p1_m1_p1 = t533+t552+t553; + coeffs_dxy->coeff_m1_0_p1 = t497+t496+t537; + coeffs_dxy->coeff_0_0_p1 = t486+t519*t525; + coeffs_dxy->coeff_p1_0_p1 = -t525+t498+t534; + coeffs_dxy->coeff_m1_p1_p1 = t533+t551+t556; + coeffs_dxy->coeff_0_p1_p1 = t490+t501+t537; + coeffs_dxy->coeff_p1_p1_p1 = t531+t551+t552; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxz.compute.c new file mode 100644 index 0000000..66fe899 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxz.compute.c @@ -0,0 +1,152 @@ +fp t596; +fp t602; +fp t597; +fp t618; +fp t565; +fp t629; +fp t593; +fp t587; +fp t592; +fp t628; +fp t617; +fp t576; +fp t627; +fp t583; +fp t626; +fp t624; +fp t616; +fp t601; +fp t625; +fp t623; +fp t622; +fp t621; +fp t620; +fp t571; +fp t615; +fp t562; +fp t619; +fp t581; +fp t567; +fp t614; +fp t613; +fp t600; +fp t612; +fp t611; +fp t610; +fp t609; +fp t598; +fp t589; +fp t590; +fp t564; +fp t561; +fp t608; +fp t599; +fp t591; +fp t573; +fp t569; +fp t607; +fp t588; +fp t577; +fp t566; +fp t606; +fp t578; +fp t580; +fp t563; +fp t605; +fp t572; +fp t604; +fp t570; +fp t603; +fp t579; +fp t575; +fp t574; + t596 = RATIONAL(1.0,2.0); + t602 = y*y; + t597 = RATIONAL(-1.0,2.0); + t618 = t602*t597; + t565 = x*t618; + t629 = t565+t596*x; + t593 = RATIONAL(-1.0,4.0); + t587 = t593*t602; + t592 = RATIONAL(1.0,4.0); + t628 = t587+t592; + t617 = t602*t596; + t576 = x*t617; + t627 = t576+t597*x; + t583 = t592*t602; + t626 = t593+t583; + t624 = t602*x; + t616 = z*t624; + t601 = x*z; + t625 = -t616+t601; + t623 = y*t593; + t622 = y*t592; + t621 = y*t597; + t620 = y*t596; + t571 = RATIONAL(-2.0,1.0)*t601; + t615 = RATIONAL(2.0,1.0)*t601; + t562 = t602*t615; + t619 = t571+t562; + t581 = z*t620; + t567 = z*t621; + t614 = (1.0-t602)*z; + t613 = x-t624; + t600 = y*t601; + t612 = -t600-t616; + t611 = t600-t616; + t610 = -t616+x*t620; + t609 = -t616+t567; + t598 = RATIONAL(1.0,8.0); + t589 = t598*y; + t590 = t598*t602; + t564 = z*t576; + t561 = x*t581; + t608 = t589+t590+t564+t561; + t599 = RATIONAL(-1.0,8.0); + t591 = t599*y; + t573 = z*t583; + t569 = x*t623; + t607 = t591+t573+t569+t564; + t588 = t599*t602; + t577 = z*t587; + t566 = x*t583; + t606 = t588+t577+t564+t566; + t578 = x*t622; + t580 = x*t587; + t563 = x*t567; + t605 = t564+t578+t580+t563; + t572 = z*t617; + t604 = t572+t597*z+t625; + t570 = z*t618; + t603 = t570+t596*z+t625; + t579 = z*t622; + t575 = x*t621; + t574 = z*t623; + coeffs_dxz->coeff_m1_m1_m1 = t579+t591+t590+t577+t605; + coeffs_dxz->coeff_0_m1_m1 = t575+t576+t611; + coeffs_dxz->coeff_p1_m1_m1 = t589+t574+t588+t573+t605; + coeffs_dxz->coeff_m1_0_m1 = t604+t627+t628; + coeffs_dxz->coeff_0_0_m1 = t613+t619; + coeffs_dxz->coeff_p1_0_m1 = t603+t626+t627; + coeffs_dxz->coeff_m1_p1_m1 = t580+t574+t569+t577+t608; + coeffs_dxz->coeff_0_p1_m1 = -t600+t576+t610; + coeffs_dxz->coeff_p1_p1_m1 = t588+t580+t561+t579+t607; + coeffs_dxz->coeff_m1_m1_0 = t572+t600+t609; + coeffs_dxz->coeff_0_m1_0 = t562+y*t571; + coeffs_dxz->coeff_p1_m1_0 = t581+t570+t611; + coeffs_dxz->coeff_m1_0_0 = t614+t619; + coeffs_dxz->coeff_0_0_0 = (RATIONAL(-4.0,1.0)*t602+RATIONAL(4.0,1.0))* +t601; + coeffs_dxz->coeff_p1_0_0 = -t614+t619; + coeffs_dxz->coeff_m1_p1_0 = t581+t572+t612; + coeffs_dxz->coeff_0_p1_0 = t562+y*t615; + coeffs_dxz->coeff_p1_p1_0 = t570-t600+t609; + coeffs_dxz->coeff_m1_m1_p1 = t579+t569+t563+t589+t606; + coeffs_dxz->coeff_0_m1_p1 = t565+t600+t610; + coeffs_dxz->coeff_p1_m1_p1 = t566+t574+t563+t590+t607; + coeffs_dxz->coeff_m1_0_p1 = t604+t626+t629; + coeffs_dxz->coeff_0_0_p1 = -t613+t619; + coeffs_dxz->coeff_p1_0_p1 = t603+t628+t629; + coeffs_dxz->coeff_m1_p1_p1 = t574+t591+t561+t578+t606; + coeffs_dxz->coeff_0_p1_p1 = t575+t565+t612; + coeffs_dxz->coeff_p1_p1_p1 = t579+t566+t578+t573+t608; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..9bc1495 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dy.compute.c @@ -0,0 +1,203 @@ +fp t285; +fp t295; +fp t286; +fp t282; +fp t262; +fp t339; +fp t294; +fp t284; +fp t307; +fp t265; +fp t338; +fp t289; +fp t313; +fp t263; +fp t244; +fp t290; +fp t319; +fp t273; +fp t337; +fp t272; +fp t254; +fp t336; +fp t270; +fp t278; +fp t335; +fp t280; +fp t257; +fp t334; +fp t333; +fp t332; +fp t291; +fp t306; +fp t246; +fp t331; +fp t292; +fp t316; +fp t268; +fp t320; +fp t311; +fp t251; +fp t330; +fp t259; +fp t256; +fp t329; +fp t258; +fp t243; +fp t328; +fp t252; +fp t317; +fp t269; +fp t327; +fp t326; +fp t314; +fp t260; +fp t264; +fp t255; +fp t325; +fp t324; +fp t293; +fp t253; +fp t310; +fp t274; +fp t323; +fp t271; +fp t245; +fp t266; +fp t322; +fp t321; +fp t318; +fp t315; +fp t312; +fp t261; +fp t309; +fp t308; +fp t305; +fp t304; +fp t303; +fp t302; +fp t301; +fp t300; +fp t299; +fp t298; +fp t297; +fp t296; +fp t288; +fp t287; +fp t249; +fp t248; + t285 = RATIONAL(1.0,4.0); + t295 = z*z; + t286 = RATIONAL(-1.0,4.0); + t282 = t286*t295; + t262 = x*t282; + t339 = t262+t285*x; + t294 = x*x; + t284 = t285*t294; + t307 = t294*t295; + t265 = t286*t307; + t338 = t284+t265; + t289 = RATIONAL(1.0,2.0); + t313 = y*t289; + t263 = t294*t313; + t244 = z*t263; + t290 = RATIONAL(-1.0,2.0); + t319 = y*t290; + t273 = z*t319; + t337 = t244+t273; + t272 = z*t313; + t254 = t294*t273; + t336 = t272+t254; + t270 = t285*t307; + t278 = t286*t294; + t335 = t270+t278; + t280 = t285*t295; + t257 = x*t280; + t334 = t286*x+t257; + t333 = t265+t280; + t332 = t282+t270; + t291 = RATIONAL(-1.0,8.0); + t306 = t294*t291; + t246 = y*t270; + t331 = t246+t295*t306; + t292 = RATIONAL(1.0,8.0); + t316 = x*t292; + t268 = z*t316; + t320 = x*z; + t311 = y*t320; + t251 = t286*t311; + t330 = t268+t251; + t259 = t295*t316; + t256 = y*t262; + t329 = t259+t256; + t258 = t291*t320; + t243 = t285*t311; + t328 = t258+t243; + t252 = y*t257; + t317 = x*t295; + t269 = t291*t317; + t327 = t252+t269; + t326 = t243+t268; + t314 = t294*z; + t260 = t292*t314; + t264 = z*t284; + t255 = y*t264; + t325 = t260+t255; + t324 = t258+t251; + t293 = y*t307; + t253 = t290*t293; + t310 = t289*t295; + t274 = y*t310; + t323 = t253+t274; + t271 = z*t278; + t245 = y*t271; + t266 = z*t306; + t322 = t245+t266; + t321 = t246+t292*t307; + t318 = -y+t290; + t315 = t293+y; + t312 = t289-y; + t261 = x*t319; + t309 = t295*t261+t253; + t308 = x*t274+t253; + t305 = -x+t317; + t304 = -z+t314; + t303 = t252+t259+t321; + t302 = t269+t256+t321; + t301 = t260+t245+t331; + t300 = t285*z+t271+t323; + t299 = t266+t255+t331; + t298 = t263+x*t313+t309; + t297 = t264+t286*z+t323; + t296 = t261+t263+t308; + t288 = RATIONAL(-2.0,1.0); + t287 = RATIONAL(2.0,1.0); + t249 = z*t261; + t248 = x*t272; + coeffs_dy->coeff_m1_m1_m1 = t301+t328+t329; + coeffs_dy->coeff_0_m1_m1 = t300+t332+t337; + coeffs_dy->coeff_p1_m1_m1 = t301+t327+t330; + coeffs_dy->coeff_m1_0_m1 = t249+t244+t308; + coeffs_dy->coeff_0_0_m1 = t293+(-t295-t304)*y; + coeffs_dy->coeff_p1_0_m1 = t248+t244+t309; + coeffs_dy->coeff_m1_p1_m1 = t302+t322+t326; + coeffs_dy->coeff_0_p1_m1 = t297+t333+t337; + coeffs_dy->coeff_p1_p1_m1 = t303+t322+t324; + coeffs_dy->coeff_m1_m1_0 = t296+t335+t339; + coeffs_dy->coeff_0_m1_0 = t290+t312*t295+(t290*t295+t312)*t294+t315; + coeffs_dy->coeff_p1_m1_0 = t298+t334+t335; + coeffs_dy->coeff_m1_0_0 = t293+(-t294-t305)*y; + coeffs_dy->coeff_0_0_0 = (t287*t295+t288+(t288*t295+t287)*t294)*y; + coeffs_dy->coeff_p1_0_0 = t293+(-t294+t305)*y; + coeffs_dy->coeff_m1_p1_0 = t296+t334+t338; + coeffs_dy->coeff_0_p1_0 = t289+t318*t295+(t310+t318)*t294+t315; + coeffs_dy->coeff_p1_p1_0 = t298+t338+t339; + coeffs_dy->coeff_m1_m1_p1 = t299+t329+t330; + coeffs_dy->coeff_0_m1_p1 = t297+t332+t336; + coeffs_dy->coeff_p1_m1_p1 = t299+t327+t328; + coeffs_dy->coeff_m1_0_p1 = t254+t248+t308; + coeffs_dy->coeff_0_0_p1 = t293+(-t295+t304)*y; + coeffs_dy->coeff_p1_0_p1 = t254+t249+t309; + coeffs_dy->coeff_m1_p1_p1 = t302+t324+t325; + coeffs_dy->coeff_0_p1_p1 = t300+t333+t336; + coeffs_dy->coeff_p1_p1_p1 = t303+t325+t326; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyy.compute.c new file mode 100644 index 0000000..5328b28 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyy.compute.c @@ -0,0 +1,116 @@ +fp t678; +fp t659; +fp t677; +fp t660; +fp t676; +fp t663; +fp t675; +fp t662; +fp t674; +fp t661; +fp t673; +fp t672; +fp t639; +fp t647; +fp t671; +fp t653; +fp t648; +fp t670; +fp t654; +fp t669; +fp t655; +fp t652; +fp t668; +fp t667; +fp t656; +fp t666; +fp t665; +fp t664; +fp t650; +fp t649; +fp t646; +fp t645; +fp t643; +fp t642; +fp t641; +fp t638; +fp t637; +fp t636; +fp t635; +fp t634; +fp t633; +fp t632; +fp t631; +fp t630; + t678 = x*z; + t659 = RATIONAL(1.0,2.0); + t677 = t659*x; + t660 = RATIONAL(-1.0,2.0); + t676 = t660*z; + t663 = z*z; + t675 = t663*x; + t662 = x*x; + t674 = z*t662; + t661 = t663*t662; + t673 = t661-t662; + t672 = t661-t663; + t639 = t660*t674; + t647 = t660*t661; + t671 = t639+t647; + t653 = t659*t662; + t648 = z*t653; + t670 = t647+t648; + t654 = t659*t663; + t669 = x*t654+t647; + t655 = RATIONAL(1.0,4.0); + t652 = t655*t661; + t668 = t655*t674+t652; + t667 = t663+t662; + t656 = RATIONAL(-1.0,4.0); + t666 = t652+t656*t674; + t665 = x-t675; + t664 = -z+t674; + t650 = t655*t678; + t649 = t656*t675; + t646 = t660*t675; + t645 = z*t677; + t643 = x*t676; + t642 = t656*t678; + t641 = t655*t675; + t638 = t661+RATIONAL(1.0,1.0)-t667; + t637 = t659*z+t654+t671; + t636 = t647+t653+t646+t677; + t635 = t653+t660*x+t669; + t634 = t654+t676+t670; + t633 = t649+t642+t668; + t632 = t650+t641+t668; + t631 = t641+t642+t666; + t630 = t649+t650+t666; + coeffs_dyy->coeff_m1_m1_m1 = t630; + coeffs_dyy->coeff_0_m1_m1 = t634; + coeffs_dyy->coeff_p1_m1_m1 = t631; + coeffs_dyy->coeff_m1_0_m1 = t643+t648+t669; + coeffs_dyy->coeff_0_0_m1 = -t664+t672; + coeffs_dyy->coeff_p1_0_m1 = t645+t646+t670; + coeffs_dyy->coeff_m1_p1_m1 = t630; + coeffs_dyy->coeff_0_p1_m1 = t634; + coeffs_dyy->coeff_p1_p1_m1 = t631; + coeffs_dyy->coeff_m1_m1_0 = t635; + coeffs_dyy->coeff_0_m1_0 = t638; + coeffs_dyy->coeff_p1_m1_0 = t636; + coeffs_dyy->coeff_m1_0_0 = t665+t673; + coeffs_dyy->coeff_0_0_0 = (1.0+t661)*RATIONAL(-2.0,1.0)+t667*RATIONAL(2.0 +,1.0); + coeffs_dyy->coeff_p1_0_0 = -t665+t673; + coeffs_dyy->coeff_m1_p1_0 = t635; + coeffs_dyy->coeff_0_p1_0 = t638; + coeffs_dyy->coeff_p1_p1_0 = t636; + coeffs_dyy->coeff_m1_m1_p1 = t633; + coeffs_dyy->coeff_0_m1_p1 = t637; + coeffs_dyy->coeff_p1_m1_p1 = t632; + coeffs_dyy->coeff_m1_0_p1 = t639+t645+t669; + coeffs_dyy->coeff_0_0_p1 = t664+t672; + coeffs_dyy->coeff_p1_0_p1 = t646+t643+t671; + coeffs_dyy->coeff_m1_p1_p1 = t633; + coeffs_dyy->coeff_0_p1_p1 = t637; + coeffs_dyy->coeff_p1_p1_p1 = t632; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyz.compute.c new file mode 100644 index 0000000..a17d581 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyz.compute.c @@ -0,0 +1,164 @@ +fp t716; +fp t720; +fp t714; +fp t737; +fp t694; +fp t682; +fp t756; +fp t711; +fp t740; +fp t693; +fp t710; +fp t742; +fp t696; +fp t755; +fp t715; +fp t754; +fp t705; +fp t753; +fp t691; +fp t752; +fp t717; +fp t738; +fp t692; +fp t681; +fp t708; +fp t751; +fp t699; +fp t750; +fp t704; +fp t739; +fp t684; +fp t680; +fp t749; +fp t697; +fp t701; +fp t688; +fp t748; +fp t695; +fp t747; +fp t746; +fp t698; +fp t686; +fp t745; +fp t735; +fp t687; +fp t744; +fp t743; +fp t719; +fp t741; +fp t733; +fp t679; +fp t690; +fp t736; +fp t734; +fp t732; +fp t731; +fp t730; +fp t729; +fp t728; +fp t727; +fp t726; +fp t725; +fp t724; +fp t723; +fp t722; +fp t721; +fp t718; +fp t689; + t716 = RATIONAL(1.0,8.0); + t720 = x*x; + t714 = RATIONAL(1.0,2.0); + t737 = t714*t720; + t694 = y*t737; + t682 = z*t694; + t756 = t682+t716*t720; + t711 = RATIONAL(-1.0,4.0); + t740 = x*t711; + t693 = y*t740; + t710 = RATIONAL(1.0,4.0); + t742 = x*t710; + t696 = z*t742; + t755 = t693+t696; + t715 = RATIONAL(-1.0,8.0); + t754 = t715*t720+t682; + t705 = t711*t720; + t753 = t705+t710; + t691 = z*t740; + t752 = t693+t691; + t717 = RATIONAL(-1.0,2.0); + t738 = x*t717; + t692 = y*t738; + t681 = z*t692; + t708 = t715*x; + t751 = t681+t708; + t699 = y*t742; + t750 = t696+t699; + t704 = t716*x; + t739 = x*t714; + t684 = z*t739; + t680 = y*t684; + t749 = t704+t680; + t697 = y*t705; + t701 = t710*t720; + t688 = z*t701; + t748 = t697+t688; + t695 = z*t737; + t747 = t717*z+t695; + t746 = t711+t701; + t698 = z*t705; + t686 = y*t701; + t745 = t698+t686; + t735 = t717*t720; + t687 = z*t735; + t744 = t714*z+t687; + t743 = t699+t691; + t719 = y*z; + t741 = y*t720; + t733 = RATIONAL(2.0,1.0)*t719; + t679 = t720*t733; + t690 = RATIONAL(-2.0,1.0)*t719; + t736 = t679+t690; + t734 = z*t741; + t732 = (t720-1.0)*z; + t731 = -y+t741; + t730 = -t734+z*t738; + t729 = -t734+t684; + t728 = t694-t734; + t727 = y*t735-t734; + t726 = t704+t681+t754; + t725 = t686+t688+t756; + t724 = t697+t698+t756; + t723 = t680+t708+t754; + t722 = t719+t714*y+t727; + t721 = t719+t717*y+t728; + t718 = x*t719; + t689 = y*t739; + coeffs_dyz->coeff_m1_m1_m1 = t724+t750+t751; + coeffs_dyz->coeff_0_m1_m1 = t721+t747+t753; + coeffs_dyz->coeff_p1_m1_m1 = t724+t749+t752; + coeffs_dyz->coeff_m1_0_m1 = t692+t718+t728; + coeffs_dyz->coeff_0_0_m1 = -t731+t736; + coeffs_dyz->coeff_p1_0_m1 = t689-t718+t728; + coeffs_dyz->coeff_m1_p1_m1 = t726+t743+t748; + coeffs_dyz->coeff_0_p1_m1 = t721+t744+t746; + coeffs_dyz->coeff_p1_p1_m1 = t723+t748+t755; + coeffs_dyz->coeff_m1_m1_0 = t695+t718+t730; + coeffs_dyz->coeff_0_m1_0 = -t732+t736; + coeffs_dyz->coeff_p1_m1_0 = t695-t718+t729; + coeffs_dyz->coeff_m1_0_0 = x*t690+t679; + coeffs_dyz->coeff_0_0_0 = (RATIONAL(4.0,1.0)+RATIONAL(-4.0,1.0)*t720)* +t719; + coeffs_dyz->coeff_p1_0_0 = x*t733+t679; + coeffs_dyz->coeff_m1_p1_0 = t687+t718+t729; + coeffs_dyz->coeff_0_p1_0 = t732+t736; + coeffs_dyz->coeff_p1_p1_0 = t687-t718+t730; + coeffs_dyz->coeff_m1_m1_p1 = t726+t745+t755; + coeffs_dyz->coeff_0_m1_p1 = t722+t746+t747; + coeffs_dyz->coeff_p1_m1_p1 = t723+t743+t745; + coeffs_dyz->coeff_m1_0_p1 = t689+t718+t727; + coeffs_dyz->coeff_0_0_p1 = t731+t736; + coeffs_dyz->coeff_p1_0_p1 = t692-t718+t727; + coeffs_dyz->coeff_m1_p1_p1 = t725+t751+t752; + coeffs_dyz->coeff_0_p1_p1 = t722+t744+t753; + coeffs_dyz->coeff_p1_p1_p1 = t725+t749+t750; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dz.compute.c new file mode 100644 index 0000000..19e7ca2 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dz.compute.c @@ -0,0 +1,196 @@ +fp t383; +fp t382; +fp t392; +fp t375; +fp t359; +fp t434; +fp t386; +fp t414; +fp t369; +fp t387; +fp t391; +fp t403; +fp t390; +fp t348; +fp t433; +fp t365; +fp t353; +fp t388; +fp t432; +fp t389; +fp t431; +fp t408; +fp t373; +fp t347; +fp t430; +fp t409; +fp t358; +fp t379; +fp t371; +fp t351; +fp t429; +fp t368; +fp t374; +fp t356; +fp t345; +fp t428; +fp t363; +fp t378; +fp t364; +fp t352; +fp t427; +fp t426; +fp t404; +fp t360; +fp t349; +fp t410; +fp t370; +fp t425; +fp t344; +fp t424; +fp t354; +fp t423; +fp t422; +fp t421; +fp t420; +fp t415; +fp t367; +fp t407; +fp t350; +fp t419; +fp t418; +fp t417; +fp t366; +fp t341; +fp t416; +fp t413; +fp t412; +fp t411; +fp t406; +fp t362; +fp t405; +fp t361; +fp t402; +fp t401; +fp t400; +fp t399; +fp t398; +fp t397; +fp t396; +fp t395; +fp t394; +fp t393; +fp t343; +fp t342; + t383 = RATIONAL(-1.0,4.0); + t382 = RATIONAL(1.0,4.0); + t392 = y*y; + t375 = t382*t392; + t359 = x*t375; + t434 = t383*x+t359; + t386 = RATIONAL(1.0,2.0); + t414 = z*t386; + t369 = t392*t414; + t387 = RATIONAL(-1.0,2.0); + t391 = x*x; + t403 = t392*t391; + t390 = z*t403; + t348 = t387*t390; + t433 = t369+t348; + t365 = t382*t403; + t353 = z*t365; + t388 = RATIONAL(-1.0,8.0); + t432 = t353+t388*t403; + t389 = RATIONAL(1.0,8.0); + t431 = t353+t389*t403; + t408 = x*t392; + t373 = t389*t408; + t347 = z*t359; + t430 = t373+t347; + t409 = t391*y; + t358 = t388*t409; + t379 = t383*t391; + t371 = y*t379; + t351 = z*t371; + t429 = t358+t351; + t368 = t389*t409; + t374 = t382*t391; + t356 = y*t374; + t345 = z*t356; + t428 = t368+t345; + t363 = t388*t408; + t378 = t383*t392; + t364 = x*t378; + t352 = z*t364; + t427 = t363+t352; + t426 = t378+t365; + t404 = t386*t391; + t360 = z*t404; + t349 = y*t360; + t410 = z*t387; + t370 = y*t410; + t425 = t349+t370; + t344 = t391*t370; + t424 = t344+y*t414; + t354 = t383*t403; + t423 = t354+t375; + t422 = t354+t374; + t421 = t382*x+t364; + t420 = t379+t365; + t415 = y*x; + t367 = t388*t415; + t407 = z*t415; + t350 = t382*t407; + t419 = t367+t350; + t418 = t345+t358; + t417 = t368+t351; + t366 = t389*t415; + t341 = t383*t407; + t416 = t366+t341; + t413 = z+t390; + t412 = t386-z; + t411 = -z+t387; + t406 = t348+x*t369; + t362 = x*t410; + t405 = t348+t392*t362; + t361 = x*t414; + t402 = t409-y; + t401 = -x+t408; + t400 = t373+t352+t432; + t399 = t360+t362+t406; + t398 = t371+t382*y+t433; + t397 = t363+t347+t432; + t396 = t360+t361+t405; + t395 = t366+t350+t431; + t394 = t356+t383*y+t433; + t393 = t367+t341+t431; + t343 = x*t370; + t342 = y*t361; + coeffs_dz->coeff_m1_m1_m1 = t400+t417+t419; + coeffs_dz->coeff_0_m1_m1 = t398+t425+t426; + coeffs_dz->coeff_p1_m1_m1 = t397+t416+t417; + coeffs_dz->coeff_m1_0_m1 = t399+t420+t421; + coeffs_dz->coeff_0_0_m1 = t387+t412*t391+(t387*t391+t412)*t392+t413; + coeffs_dz->coeff_p1_0_m1 = t396+t420+t434; + coeffs_dz->coeff_m1_p1_m1 = t400+t416+t418; + coeffs_dz->coeff_0_p1_m1 = t394+t424+t426; + coeffs_dz->coeff_p1_p1_m1 = t397+t418+t419; + coeffs_dz->coeff_m1_m1_0 = t343+t349+t406; + coeffs_dz->coeff_0_m1_0 = t390+(-t392-t402)*z; + coeffs_dz->coeff_p1_m1_0 = t342+t349+t405; + coeffs_dz->coeff_m1_0_0 = t390+(-t391-t401)*z; + coeffs_dz->coeff_0_0_0 = ((1.0+t403)*RATIONAL(-2.0,1.0)+(t392+t391)* +RATIONAL(2.0,1.0))*z; + coeffs_dz->coeff_p1_0_0 = t390+(-t391+t401)*z; + coeffs_dz->coeff_m1_p1_0 = t344+t342+t406; + coeffs_dz->coeff_0_p1_0 = t390+(-t392+t402)*z; + coeffs_dz->coeff_p1_p1_0 = t344+t343+t405; + coeffs_dz->coeff_m1_m1_p1 = t395+t427+t429; + coeffs_dz->coeff_0_m1_p1 = t394+t423+t425; + coeffs_dz->coeff_p1_m1_p1 = t393+t429+t430; + coeffs_dz->coeff_m1_0_p1 = t399+t422+t434; + coeffs_dz->coeff_0_0_p1 = t386+t411*t391+(t404+t411)*t392+t413; + coeffs_dz->coeff_p1_0_p1 = t396+t421+t422; + coeffs_dz->coeff_m1_p1_p1 = t393+t427+t428; + coeffs_dz->coeff_0_p1_p1 = t398+t423+t424; + coeffs_dz->coeff_p1_p1_p1 = t395+t428+t430; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dzz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dzz.compute.c new file mode 100644 index 0000000..c4ac417 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dzz.compute.c @@ -0,0 +1,120 @@ +fp t786; +fp t808; +fp t787; +fp t807; +fp t790; +fp t806; +fp t783; +fp t805; +fp t782; +fp t804; +fp t789; +fp t788; +fp t803; +fp t793; +fp t776; +fp t802; +fp t801; +fp t800; +fp t794; +fp t771; +fp t799; +fp t798; +fp t797; +fp t781; +fp t796; +fp t780; +fp t795; +fp t792; +fp t791; +fp t778; +fp t775; +fp t774; +fp t772; +fp t770; +fp t769; +fp t768; +fp t767; +fp t765; +fp t764; +fp t763; +fp t762; +fp t761; +fp t760; +fp t759; +fp t758; +fp t757; + t786 = RATIONAL(1.0,2.0); + t808 = t786*y; + t787 = RATIONAL(-1.0,2.0); + t807 = t787*x; + t790 = y*y; + t806 = t790*x; + t783 = RATIONAL(-1.0,4.0); + t805 = y*t783; + t782 = RATIONAL(1.0,4.0); + t804 = y*t782; + t789 = x*x; + t788 = t790*t789; + t803 = -t790+t788; + t793 = t787*t789; + t776 = t790*t793; + t802 = t776+y*t807; + t801 = -t789+t788; + t800 = t789+t790; + t794 = t782*t790; + t771 = t789*t794; + t799 = t783*t806+t771; + t798 = t771+x*t794; + t797 = t776+x*t808; + t781 = t786*t790; + t796 = t776+t781; + t780 = t786*t789; + t795 = t776+t780; + t792 = x-t806; + t791 = (1.0-t789)*y; + t778 = x*t805; + t775 = y*t780; + t774 = x*t804; + t772 = t789*t805; + t770 = x*t781; + t769 = t789*t804; + t768 = t787*t806; + t767 = y*t793; + t765 = RATIONAL(1.0,1.0)+t788-t800; + t764 = t775+t787*y+t796; + t763 = t770+t807+t795; + t762 = t786*x+t768+t795; + t761 = t808+t767+t796; + t760 = t772+t774+t799; + t759 = t772+t778+t798; + t758 = t769+t778+t799; + t757 = t769+t774+t798; + coeffs_dzz->coeff_m1_m1_m1 = t760; + coeffs_dzz->coeff_0_m1_m1 = t764; + coeffs_dzz->coeff_p1_m1_m1 = t759; + coeffs_dzz->coeff_m1_0_m1 = t763; + coeffs_dzz->coeff_0_0_m1 = t765; + coeffs_dzz->coeff_p1_0_m1 = t762; + coeffs_dzz->coeff_m1_p1_m1 = t758; + coeffs_dzz->coeff_0_p1_m1 = t761; + coeffs_dzz->coeff_p1_p1_m1 = t757; + coeffs_dzz->coeff_m1_m1_0 = t775+t770+t802; + coeffs_dzz->coeff_0_m1_0 = t791+t803; + coeffs_dzz->coeff_p1_m1_0 = t775+t768+t797; + coeffs_dzz->coeff_m1_0_0 = t792+t801; + coeffs_dzz->coeff_0_0_0 = (1.0+t788)*RATIONAL(-2.0,1.0)+t800*RATIONAL(2.0 +,1.0); + coeffs_dzz->coeff_p1_0_0 = -t792+t801; + coeffs_dzz->coeff_m1_p1_0 = t770+t767+t797; + coeffs_dzz->coeff_0_p1_0 = -t791+t803; + coeffs_dzz->coeff_p1_p1_0 = t768+t767+t802; + coeffs_dzz->coeff_m1_m1_p1 = t760; + coeffs_dzz->coeff_0_m1_p1 = t764; + coeffs_dzz->coeff_p1_m1_p1 = t759; + coeffs_dzz->coeff_m1_0_p1 = t763; + coeffs_dzz->coeff_0_0_p1 = t765; + coeffs_dzz->coeff_p1_0_p1 = t762; + coeffs_dzz->coeff_m1_p1_p1 = t758; + coeffs_dzz->coeff_0_p1_p1 = t761; + coeffs_dzz->coeff_p1_p1_p1 = t757; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..1e10970 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-I.compute.c @@ -0,0 +1,1421 @@ +fp t1283; +fp t1277; +fp t1252; +fp t1274; +fp t1282; +fp t1286; +fp t1488; +fp t1236; +fp t1692; +fp t1281; +fp t1250; +fp t1468; +fp t1691; +fp t1263; +fp t1456; +fp t1284; +fp t1258; +fp t1461; +fp t1393; +fp t867; +fp t1592; +fp t1285; +fp t1454; +fp t1369; +fp t874; +fp t1690; +fp t1259; +fp t1453; +fp t1264; +fp t1470; +fp t1138; +fp t934; +fp t1689; +fp t1688; +fp t1469; +fp t1182; +fp t1161; +fp t1651; +fp t1270; +fp t1568; +fp t1687; +fp t1686; +fp t1463; +fp t1214; +fp t1251; +fp t1685; +fp t1275; +fp t1450; +fp t1240; +fp t1684; +fp t1591; +fp t1506; +fp t1227; +fp t1466; +fp t1683; +fp t1444; +fp t1531; +fp t1175; +fp t1517; +fp t1153; +fp t1648; +fp t1215; +fp t1682; +fp t1249; +fp t1271; +fp t1449; +fp t1376; +fp t1681; +fp t1451; +fp t1191; +fp t1586; +fp t1680; +fp t1198; +fp t1276; +fp t1483; +fp t1400; +fp t1518; +fp t1381; +fp t1086; +fp t1243; +fp t1046; +fp t1679; +fp t1278; +fp t1588; +fp t1522; +fp t1422; +fp t1678; +fp t1204; +fp t1385; +fp t1579; +fp t1472; +fp t1590; +fp t1677; +fp t1585; +fp t1508; +fp t1582; +fp t1256; +fp t1425; +fp t1255; +fp t1676; +fp t1511; +fp t1411; +fp t1261; +fp t1497; +fp t1417; +fp t924; +fp t1262; +fp t1675; +fp t1266; +fp t1516; +fp t1428; +fp t882; +fp t1572; +fp t881; +fp t1674; +fp t1254; +fp t1457; +fp t1395; +fp t816; +fp t1253; +fp t1569; +fp t1418; +fp t1673; +fp t1500; +fp t1442; +fp t1384; +fp t1672; +fp t1486; +fp t1433; +fp t1414; +fp t1671; +fp t1477; +fp t1443; +fp t1471; +fp t1426; +fp t947; +fp t1670; +fp t1402; +fp t1496; +fp t1441; +fp t1669; +fp t1260; +fp t879; +fp t1257; +fp t1455; +fp t1375; +fp t843; +fp t1668; +fp t888; +fp t1513; +fp t1136; +fp t967; +fp t1667; +fp t1447; +fp t1377; +fp t1494; +fp t1440; +fp t1666; +fp t1410; +fp t1503; +fp t1391; +fp t1665; +fp t1664; +fp t1178; +fp t935; +fp t1663; +fp t844; +fp t1273; +fp t1662; +fp t1157; +fp t1661; +fp t1152; +fp t1660; +fp t1659; +fp t1491; +fp t1179; +fp t1183; +fp t1658; +fp t1388; +fp t1657; +fp t1162; +fp t1656; +fp t1485; +fp t1164; +fp t1174; +fp t1655; +fp t1509; +fp t1438; +fp t1654; +fp t1490; +fp t1370; +fp t851; +fp t1269; +fp t1498; +fp t1226; +fp t1078; +fp t1653; +fp t1280; +fp t1589; +fp t1199; +fp t1652; +fp t1474; +fp t1434; +fp t1004; +fp t1397; +fp t1650; +fp t1171; +fp t1143; +fp t1649; +fp t1154; +fp t1459; +fp t1177; +fp t939; +fp t1647; +fp t1372; +fp t1185; +fp t1075; +fp t1646; +fp t1479; +fp t1223; +fp t1481; +fp t1184; +fp t1645; +fp t1242; +fp t1129; +fp t1221; +fp t1065; +fp t1644; +fp t1478; +fp t1205; +fp t1475; +fp t1224; +fp t1643; +fp t1232; +fp t1642; +fp t1194; +fp t1109; +fp t1378; +fp t1641; +fp t921; +fp t1137; +fp t962; +fp t1504; +fp t1188; +fp t1033; +fp t1640; +fp t1234; +fp t1051; +fp t1639; +fp t1458; +fp t1241; +fp t1464; +fp t1247; +fp t1638; +fp t1208; +fp t1246; +fp t1072; +fp t1637; +fp t1202; +fp t1510; +fp t1427; +fp t1636; +fp t1217; +fp t1200; +fp t1635; +fp t1399; +fp t944; +fp t1150; +fp t957; +fp t1524; +fp t1233; +fp t1114; +fp t1634; +fp t1492; +fp t1387; +fp t910; +fp t1421; +fp t1558; +fp t1267; +fp t1575; +fp t1155; +fp t1633; +fp t908; +fp t1519; +fp t1435; +fp t1462; +fp t1380; +fp t1560; +fp t1448; +fp t1632; +fp t1562; +fp t946; +fp t1631; +fp t1412; +fp t1383; +fp t1577; +fp t1512; +fp t1525; +fp t1630; +fp t1159; +fp t850; +fp t1629; +fp t959; +fp t1628; +fp t1627; +fp t1482; +fp t1245; +fp t1027; +fp t1626; +fp t1543; +fp t1156; +fp t1625; +fp t1163; +fp t1574; +fp t1624; +fp t1394; +fp t1452; +fp t1220; +fp t1623; +fp t1430; +fp t1549; +fp t1622; +fp t1437; +fp t1559; +fp t1520; +fp t1172; +fp t1621; +fp t1501; +fp t1170; +fp t1620; +fp t1222; +fp t1052; +fp t1239; +fp t1209; +fp t1619; +fp t1460; +fp t1244; +fp t1248; +fp t1618; +fp t1617; +fp t1176; +fp t1616; +fp t833; +fp t1615; +fp t1473; +fp t1614; +fp t1578; +fp t1502; +fp t1165; +fp t1613; +fp t1576; +fp t1487; +fp t1382; +fp t1149; +fp t1612; +fp t1571; +fp t1611; +fp t1216; +fp t1610; +fp t1235; +fp t1609; +fp t1073; +fp t1374; +fp t1074; +fp t1608; +fp t1231; +fp t1108; +fp t1059; +fp t1607; +fp t1392; +fp t1068; +fp t1031; +fp t1135; +fp t1495; +fp t1230; +fp t1022; +fp t1606; +fp t1279; +fp t902; +fp t1032; +fp t831; +fp t1587; +fp t1514; +fp t1605; +fp t1467; +fp t1416; +fp t1565; +fp t1604; +fp t887; +fp t856; +fp t1603; +fp t950; +fp t1139; +fp t1602; +fp t1026; +fp t1213; +fp t1079; +fp t1580; +fp t1415; +fp t1601; +fp t1088; +fp t1331; +fp t1238; +fp t1600; +fp t1140; +fp t1413; +fp t987; +fp t1537; +fp t1339; +fp t1049; +fp t1599; +fp t1028; +fp t1373; +fp t900; +fp t1341; +fp t1598; +fp t1127; +fp t1597; +fp t956; +fp t1596; +fp t1389; +fp t952; +fp t1539; +fp t927; +fp t1595; +fp t1160; +fp t969; +fp t968; +fp t1548; +fp t1158; +fp t1570; +fp t1594; +fp t1567; +fp t1123; +fp t1593; +fp t1584; +fp t1583; +fp t1581; +fp t1573; +fp t1566; +fp t1564; +fp t926; +fp t1432; +fp t954; +fp t1563; +fp t1401; +fp t1561; +fp t1396; +fp t864; +fp t1557; +fp t1556; +fp t1141; +fp t982; +fp t1554; +fp t984; +fp t883; +fp t1553; +fp t853; +fp t1552; +fp t955; +fp t1551; +fp t889; +fp t1521; +fp t1181; +fp t885; +fp t1550; +fp t930; +fp t937; +fp t1547; +fp t821; +fp t1436; +fp t1546; +fp t845; +fp t1544; +fp t1542; +fp t892; +fp t832; +fp t1541; +fp t858; +fp t837; +fp t1540; +fp t994; +fp t1538; +fp t943; +fp t1536; +fp t1493; +fp t1431; +fp t993; +fp t1535; +fp t1534; +fp t1533; +fp t975; +fp t1532; +fp t1465; +fp t1386; +fp t1530; +fp t1409; +fp t1529; +fp t884; +fp t1003; +fp t1528; +fp t1527; +fp t1526; +fp t1523; +fp t1515; +fp t1507; +fp t1148; +fp t1505; +fp t1499; +fp t1489; +fp t1484; +fp t1480; +fp t1265; +fp t1476; +fp t1446; +fp t1445; +fp t1203; +fp t1439; +fp t1429; +fp t1424; +fp t1423; +fp t1420; +fp t1419; +fp t928; +fp t1408; +fp t931; +fp t1407; +fp t948; +fp t1406; +fp t1112; +fp t891; +fp t1405; +fp t1025; +fp t1404; +fp t1030; +fp t1403; +fp t1398; +fp t1193; +fp t1390; +fp t1210; +fp t1379; +fp t1371; +fp t1368; +fp t1367; +fp t1366; +fp t1365; +fp t1364; +fp t917; +fp t1363; +fp t1362; +fp t1361; +fp t830; +fp t1360; +fp t1359; +fp t1358; +fp t1357; +fp t972; +fp t1356; +fp t1355; +fp t1354; +fp t1353; +fp t1352; +fp t1351; +fp t863; +fp t1350; +fp t1349; +fp t1348; +fp t813; +fp t1347; +fp t1346; +fp t1345; +fp t1344; +fp t1342; +fp t992; +fp t973; +fp t1340; +fp t1338; +fp t1337; +fp t862; +fp t1335; +fp t1094; +fp t1334; +fp t1082; +fp t1330; +fp t1060; +fp t1021; +fp t1329; +fp t1328; +fp t1327; +fp t1326; +fp t1325; +fp t1324; +fp t951; +fp t936; +fp t1323; +fp t1322; +fp t997; +fp t1321; +fp t1092; +fp t1320; +fp t841; +fp t1319; +fp t1318; +fp t834; +fp t1317; +fp t1316; +fp t860; +fp t1315; +fp t1005; +fp t1314; +fp t1313; +fp t1089; +fp t1312; +fp t945; +fp t1311; +fp t1133; +fp t1310; +fp t1309; +fp t1096; +fp t1102; +fp t1308; +fp t1307; +fp t1306; +fp t1305; +fp t985; +fp t1304; +fp t1303; +fp t1302; +fp t1301; +fp t979; +fp t1300; +fp t1299; +fp t836; +fp t1298; +fp t1297; +fp t1085; +fp t1042; +fp t1296; +fp t1295; +fp t1294; +fp t1293; +fp t1121; +fp t1292; +fp t1291; +fp t1290; +fp t1272; +fp t1268; +fp t1169; +fp t1167; +fp t1062; +fp t1039; +fp t966; +fp t923; +fp t854; +fp t852; +fp t826; +fp t819; +fp t818; +fp t817; + t1283 = y*y; + t1277 = RATIONAL(1.0,2.0); + t1252 = t1277*t1283; + t1274 = RATIONAL(1.0,4.0); + t1282 = z*z; + t1286 = z*t1282; + t1488 = t1274*t1286; + t1236 = t1283*t1488; + t1692 = t1236+t1252; + t1281 = x*x; + t1250 = t1277*t1281; + t1468 = t1281*t1274; + t1691 = t1250+t1286*t1468; + t1263 = RATIONAL(-1.0,24.0); + t1456 = t1263*t1286; + t1284 = t1281*x; + t1258 = RATIONAL(1.0,24.0); + t1461 = t1284*t1258; + t1393 = t1286*t1461; + t867 = y*t1393; + t1592 = y*x; + t1285 = t1283*y; + t1454 = t1263*t1285; + t1369 = t1286*t1454; + t874 = t1284*t1369; + t1690 = t1456*t1592+t867+t874; + t1259 = RATIONAL(1.0,12.0); + t1453 = t1259*t1284; + t1264 = RATIONAL(-1.0,12.0); + t1470 = t1264*t1284; + t1138 = t1283*t1470; + t934 = z*t1138; + t1689 = z*t1453+t934; + t1688 = t1692*x; + t1469 = t1259*t1286; + t1182 = t1283*t1469; + t1161 = t1286*t1470; + t1651 = t1284*t1182+t1161; + t1270 = RATIONAL(1.0,6.0); + t1568 = z*t1270; + t1687 = t1651+x*t1568; + t1686 = t1691*y; + t1463 = t1282*t1274; + t1214 = t1285*t1463; + t1251 = t1277*t1282; + t1685 = t1214+t1251; + t1275 = RATIONAL(-1.0,4.0); + t1450 = t1275*t1284; + t1240 = t1285*t1450; + t1684 = z*t1240+t1488*t1592; + t1591 = y*z; + t1506 = t1275*t1285; + t1227 = t1286*t1506; + t1466 = t1274*t1284; + t1683 = t1466*t1591+x*t1227; + t1444 = z*t1461; + t1531 = t1285*t1444+t874; + t1175 = t1285*t1470; + t1517 = t1282*t1259; + t1153 = t1285*t1517; + t1648 = t1175+t1284*t1153; + t1215 = t1270*t1592; + t1682 = t1531+t1648+t1215; + t1249 = t1285*t1488; + t1271 = RATIONAL(-1.0,8.0); + t1449 = t1286*t1271; + t1376 = t1285*t1449; + t1681 = t1249+x*t1376+t1281*t1227; + t1451 = t1284*t1271; + t1191 = t1285*t1466; + t1586 = t1285*z; + t1680 = t1451*t1586+t1282*t1240+t1191; + t1198 = t1282*t1450; + t1276 = RATIONAL(1.0,8.0); + t1483 = t1276*t1284; + t1400 = t1282*t1483; + t1518 = t1285*t1282; + t1381 = t1271*t1518; + t1086 = t1284*t1381; + t1243 = t1283*t1466; + t1046 = t1282*t1243; + t1679 = t1198+t1086+y*t1400+t1046; + t1278 = RATIONAL(-1.0,2.0); + t1588 = t1278*y; + t1522 = t1276*t1286; + t1422 = x*t1522; + t1678 = z*t1588+t1285*t1422+t1227+t1281*t1249+t1450*t1591; + t1204 = t1286*t1450; + t1385 = t1286*t1483; + t1579 = x*t1285; + t1472 = z*t1579; + t1590 = x*z; + t1677 = t1275*t1472+t1204+y*t1385+t1278*t1590+t1284*t1236; + t1585 = x*t1286; + t1508 = y*t1585; + t1582 = z*t1284; + t1256 = RATIONAL(1.0,216.0); + t1425 = t1256*t1582; + t1255 = RATIONAL(1.0,108.0); + t1676 = t1285*t1425+t1255*t1508; + t1511 = t1281*t1285; + t1411 = z*t1511; + t1261 = RATIONAL(-1.0,36.0); + t1497 = t1261*t1286; + t1417 = y*t1497; + t924 = t1281*t1417; + t1262 = RATIONAL(1.0,72.0); + t1675 = t924+t1262*t1411; + t1266 = RATIONAL(1.0,36.0); + t1516 = t1266*t1285; + t1428 = x*t1516; + t882 = z*t1428; + t1572 = y*t1590; + t881 = t1261*t1572; + t1674 = t882+t881; + t1254 = RATIONAL(-1.0,216.0); + t1457 = t1284*t1254; + t1395 = t1286*t1457; + t816 = t1285*t1395; + t1253 = RATIONAL(-1.0,108.0); + t1569 = y*t1253; + t1418 = t1284*t1569; + t1673 = t816+t1286*t1418; + t1500 = t1281*t1282; + t1442 = y*t1500; + t1384 = t1285*t1500; + t1672 = t1263*t1384+t1264*t1442; + t1486 = t1284*t1286; + t1433 = y*t1486; + t1414 = t1253*t1586; + t1671 = x*t1414+t1255*t1433; + t1477 = t1282*t1262; + t1443 = y*t1477; + t1471 = t1261*t1285; + t1426 = x*t1471; + t947 = t1282*t1426; + t1670 = t1284*t1443+t947; + t1402 = t1281*t1456; + t1496 = t1283*t1281; + t1441 = z*t1496; + t1669 = t1283*t1402+t1264*t1441; + t1260 = RATIONAL(-1.0,18.0); + t879 = t1260*t1508; + t1257 = RATIONAL(-1.0,72.0); + t1455 = t1285*t1257; + t1375 = t1284*t1455; + t843 = z*t1375; + t1668 = t879+t843; + t888 = t1257*t1433; + t1513 = t1266*t1286; + t1136 = t1285*t1513; + t967 = x*t1136; + t1667 = t888+t967; + t1447 = t1263*t1284; + t1377 = t1282*t1447; + t1494 = t1283*t1282; + t1440 = x*t1494; + t1666 = t1283*t1377+t1264*t1440; + t1410 = t1255*t1582; + t1503 = t1285*t1256; + t1391 = t1286*t1503; + t1665 = x*t1391+y*t1410; + t1664 = t1447*t1591+t867; + t1178 = t1266*t1486; + t935 = y*t1178; + t1663 = t882+t935; + t844 = t1286*t1375; + t1273 = RATIONAL(1.0,9.0); + t1662 = t1273*t1572+t844; + t1157 = t1286*t1471; + t1661 = t1281*t1157+t1136; + t1152 = t1286*t1453; + t1660 = t1283*t1161+t1152; + t1659 = t1259*t1384+t1270*t1442; + t1491 = t1264*t1286; + t1179 = t1281*t1491; + t1183 = t1285*t1469; + t1658 = t1285*t1179+t1183; + t1388 = t1283*t1497; + t1657 = t1178+t1284*t1388; + t1162 = t1283*t1453; + t1656 = t1270*t1440+t1282*t1162; + t1485 = t1264*t1285; + t1164 = t1286*t1485; + t1174 = t1281*t1469; + t1655 = t1285*t1174+t1164; + t1509 = t1270*t1283; + t1438 = z*t1509; + t1654 = t1283*t1174+t1281*t1438; + t1490 = t1281*t1258; + t1370 = t1285*t1490; + t851 = t1286*t1370; + t1269 = RATIONAL(-1.0,6.0); + t1498 = t1281*t1269; + t1226 = z*t1498; + t1078 = y*t1226; + t1653 = t851+t1078; + t1280 = RATIONAL(-1.0,3.0); + t1589 = t1280*z; + t1199 = x*t1589; + t1652 = y*t1199+t874; + t1474 = t1261*t1284; + t1434 = y*t1474; + t1004 = t1282*t1434; + t1397 = t1285*t1477; + t1650 = t1004+x*t1397; + t1171 = t1284*t1471; + t1143 = t1284*t1516; + t1649 = t1282*t1171+t1143; + t1154 = y*t1453; + t1459 = t1282*t1264; + t1177 = t1284*t1459; + t939 = y*t1177; + t1647 = t1154+t939; + t1372 = t1283*t1449; + t1185 = t1283*t1468; + t1075 = z*t1185; + t1646 = t1075+t1281*t1372; + t1479 = t1269*t1284; + t1223 = y*t1479; + t1481 = t1270*t1284; + t1184 = y*t1481; + t1645 = t1184+t1282*t1223; + t1242 = z*t1252; + t1129 = x*t1242; + t1221 = t1283*t1450; + t1065 = z*t1221; + t1644 = t1129+t1065; + t1478 = t1270*t1285; + t1205 = x*t1478; + t1475 = t1269*t1285; + t1224 = x*t1475; + t1643 = t1282*t1224+t1205; + t1232 = z*t1478; + t1642 = t1232+t1269*t1411; + t1194 = t1283*t1463; + t1109 = x*t1194; + t1378 = t1283*t1451; + t1641 = t1109+t1282*t1378; + t921 = y*t1179; + t1137 = t1283*t1491; + t962 = x*t1137; + t1504 = t1269*t1283; + t1188 = z*t1504; + t1033 = x*t1188; + t1640 = t921+t962+t1033; + t1234 = t1281*t1463; + t1051 = y*t1234; + t1639 = t1281*t1381+t1051; + t1458 = t1269*t1286; + t1241 = y*t1458; + t1464 = t1270*t1286; + t1247 = y*t1464; + t1638 = t1281*t1241+t1247; + t1208 = t1281*t1506; + t1246 = z*t1250; + t1072 = y*t1246; + t1637 = z*t1208+t1072; + t1202 = z*t1481; + t1510 = t1284*t1283; + t1427 = z*t1510; + t1636 = t1202+t1269*t1427; + t1217 = x*t1464; + t1200 = x*t1458; + t1635 = t1283*t1200+t1217; + t1399 = t1282*t1461; + t944 = t1285*t1399; + t1150 = t1282*t1453; + t957 = y*t1150; + t1524 = t1269*t1282; + t1233 = x*t1524; + t1114 = y*t1233; + t1634 = t944+t957+t1114; + t1492 = t1262*t1286; + t1387 = t1281*t1492; + t910 = t1285*t1387; + t1421 = y*t1513; + t1558 = t1281*t1421+t1266*t1411; + t1267 = RATIONAL(1.0,18.0); + t1575 = y*t1267; + t1155 = z*t1575; + t1633 = t1281*t1155+t910+t1558; + t908 = t1284*t1397; + t1519 = t1266*t1284; + t1435 = y*t1519; + t1462 = t1266*t1282; + t1380 = t1285*t1462; + t1560 = x*t1380+t1282*t1435; + t1448 = t1267*t1282; + t1632 = t1448*t1592+t908+t1560; + t1562 = t1263*t1442+t1282*t1370; + t946 = t1261*t1411; + t1631 = t1562+y*t1387+t946; + t1412 = t1255*t1579; + t1383 = t1281*t1455; + t1577 = t1266*y; + t1512 = z*t1577; + t1525 = t1286*t1383+t1281*t1512; + t1630 = z*t1418+t1525+t1286*t1412; + t1159 = x*t1469; + t850 = y*t1159; + t1629 = t1283*t1217+t1200+t850; + t959 = z*t1154; + t1628 = z*t1479+t1270*t1427+t959; + t1627 = t1241+t1281*t1247+t850; + t1482 = t1283*t1275; + t1245 = x*t1482; + t1027 = z*t1245; + t1626 = z*t1243+t1242+t1027; + t1543 = t1259*t1442+t1264*t1384; + t1156 = y*t1459; + t1625 = t1543+t1153+t1156; + t1163 = z*t1470; + t1574 = z*t1259; + t1624 = t1163+(t1491+t1574)*x; + t1394 = t1282*t1482; + t1452 = t1278*t1282; + t1220 = t1283*t1452; + t1623 = t1109+t1284*t1394+t1220; + t1430 = x*t1517; + t1549 = (t1430+t1177)*t1283; + t1622 = x*t1459+t1150+t1549; + t1437 = t1281*t1574; + t1559 = (t1179+t1437)*t1283; + t1520 = t1281*t1264; + t1172 = z*t1520; + t1621 = t1559+t1172+t1174; + t1501 = t1283*t1264; + t1170 = x*t1501; + t1620 = t1549+t1162+t1170; + t1222 = t1281*t1452; + t1052 = y*t1222; + t1239 = y*t1251; + t1209 = t1284*t1463; + t1619 = t1052+y*t1209+t1239; + t1460 = t1278*t1283; + t1244 = t1281*t1460; + t1248 = t1286*t1482; + t1618 = t1281*t1248+t1244+t1075; + t1617 = t1559+t1182+z*t1501; + t1176 = t1259*t1511; + t1616 = t1543+y*t1520+t1176; + t833 = x*t1182; + t1615 = t833+t934+t1666; + t1473 = t1260*t1591; + t1614 = t1157+t1155+(t1136+t1473)*t1281; + t1578 = y*t1282; + t1502 = x*t1578; + t1165 = x*t1575; + t1613 = t1260*t1502+t1171+t1165+t1284*t1380; + t1576 = t1283*z; + t1487 = x*t1576; + t1382 = t1283*t1513; + t1149 = t1286*t1474; + t1612 = t1260*t1487+t1267*t1590+t1284*t1382+t1149; + t1571 = t1269*x; + t1611 = x*t1438+z*t1571+t1651; + t1216 = y*t1568; + t1610 = t1281*t1216+t1269*t1591+t1655; + t1235 = y*t1571; + t1609 = t1282*t1215+t1235+t1648; + t1073 = x*t1248; + t1374 = t1284*t1449; + t1074 = t1285*t1374; + t1608 = z*t1191+t1129+t1073+t1074; + t1231 = x*t1588; + t1108 = z*t1231; + t1059 = t1285*t1385; + t1607 = y*t1204+t1108+t1059+t1274*t1472; + t1392 = t1285*t1483; + t1068 = t1282*t1392; + t1031 = y*t1198; + t1135 = x*t1239; + t1495 = t1282*t1275; + t1230 = t1285*t1495; + t1022 = x*t1230; + t1606 = t1068+t1031+t1135+t1022; + t1279 = RATIONAL(1.0,3.0); + t902 = t1285*t1393; + t1032 = z*t1215; + t831 = x*t1369; + t1587 = t1281*z; + t1514 = y*t1587; + t1605 = t1279*t1514+t1032+y*t1589+t902+t831+t1658; + t1467 = t1286*t1258; + t1416 = x*t1467; + t1565 = x*t1263; + t1604 = t1565*t1591+t831+t1258*t1472+(t1416+t1444)*y; + t887 = t1264*t1572; + t856 = t1285*t1416; + t1603 = t1216+t887+t856+t1655; + t950 = y*t1430; + t1139 = t1285*t1459; + t1602 = t950+y*t1524+t1139+t1659; + t1026 = t1274*t1384; + t1213 = y*t1495; + t1079 = x*t1213; + t1580 = x*t1282; + t1415 = t1276*t1580; + t1601 = t1026+t1285*t1415+t1079+t1619+t1230+t1086; + t1088 = x*t1220; + t1331 = t1079+t1088+t1685*x; + t1238 = t1286*t1466; + t1600 = t1059+y*t1374+t1284*t1248+t1331+t1238; + t1140 = t1285*t1453; + t1413 = z*t1454; + t987 = t1284*t1413; + t1537 = t987+t902; + t1339 = t1140+t1282*t1175+t1537; + t1049 = x*t1241; + t1599 = t1280*t1592+t1032+t1339+t1279*t1502+t1049; + t1028 = z*t1224; + t1373 = t1286*t1447; + t900 = y*t1373; + t1341 = t902+t900+t1660; + t1598 = t1028+t1279*t1487+t1199+t1341+t1032; + t1127 = t1284*t1372; + t1597 = t1088+t1027+t1127+t1276*t1427+t1221+t1046+t1688; + t956 = x*t1139; + t1596 = t1177+t956+t950+t1233+t1656; + t1389 = t1283*t1461; + t952 = t1283*t1373; + t1539 = z*t1389+t952; + t927 = t1259*t1487; + t1595 = x*t1504+t1539+t1138+t927+t1656; + t1160 = y*t1491; + t969 = y*t1174; + t968 = y*t1172; + t1548 = t969+t968; + t1158 = z*t1485; + t1570 = y*t1259; + t1594 = t1160+t1548+z*t1570+t1158+t1658; + t1567 = t1274*y; + t1123 = t1567*t1590; + t1593 = t1231+t1240+t1123+t1135+t1284*t1214+t1275*t1508+t1074+z*t1392; + t1584 = t1254*z; + t1583 = y*t1284; + t1581 = t1274*z; + t1573 = 1.0-t1281; + t1566 = x*t1257; + t1564 = -1.0+t1283; + t926 = x*t1417; + t1432 = z*t1474; + t954 = y*t1432; + t1563 = t926+t954; + t1401 = t1283*t1467; + t1561 = t952+x*t1401; + t1396 = t1285*t1492; + t864 = t1284*t1396; + t1557 = t864+t843; + t1556 = t1266*t1427+x*t1382; + t1141 = t1281*t1485; + t982 = z*t1141; + t1554 = t956+t982; + t984 = x*t1156; + t883 = x*t1153; + t1553 = t984+t883; + t853 = z*t1170; + t1552 = t833+t853; + t955 = z*t1162; + t1551 = t955+t853; + t889 = x*t1164; + t1521 = t1259*t1285; + t1181 = z*t1521; + t885 = x*t1181; + t1550 = t889+t885; + t930 = y*t1399; + t937 = t1285*t1377; + t1547 = t930+t937; + t821 = t1284*t1391; + t1436 = t1285*t1584; + t1546 = t821+t1284*t1436; + t845 = z*t1176; + t1544 = t845+t955; + t1542 = t1262*t1433+t844; + t892 = z*t1140; + t832 = x*t1158; + t1541 = t892+t832; + t858 = z*t1435; + t837 = y*t1149; + t1540 = t858+t837; + t994 = x*t1183; + t1538 = t994+t832; + t943 = z*t1426; + t1536 = t943+t954; + t1493 = t1281*t1286; + t1431 = y*t1493; + t993 = t1281*t1369; + t1535 = t993+t1258*t1431; + t1534 = t993+z*t1370; + t1533 = t943+t967; + t975 = z*t1165; + t1532 = t864+t975; + t1465 = t1284*t1257; + t1386 = t1283*t1465; + t1530 = t1286*t1386+t1266*t1487; + t1409 = t1283*t1565; + t1529 = (t1409+t1389)*t1282; + t884 = y*t1163; + t1003 = y*t1152; + t1528 = t884+t1003; + t1527 = t1282*t1375+t1462*t1592; + t1526 = t1281*t1401+t1263*t1441; + t1523 = t1286+t1284; + t1515 = t1281*t1275; + t1507 = t1114+t1078; + t1148 = x*t1570; + t1505 = t1286+t1285; + t1499 = t1285+t1284; + t1489 = t1033+t1114; + t1484 = y*t1582; + t1480 = t1283*t1262; + t1265 = RATIONAL(-1.0,54.0); + t1476 = t1265*t1591; + t1446 = t1286*t1566; + t1445 = t1253*t1585; + t1203 = y*t1515; + t1439 = y*t1465; + t1429 = t1262*t1582; + t1424 = t1258*t1580; + t1423 = t1254*t1585; + t1420 = x*t1455; + t1419 = x*t1513; + t928 = t1267*t1484; + t1408 = t928+t935+t939; + t931 = z*t1143; + t1407 = t864+t937+t931; + t948 = t1286*t1165; + t1406 = t962+t967+t948; + t1112 = x*t1247; + t891 = y*t1161; + t1405 = t1112+t969+t891; + t1025 = x*t1232; + t1404 = t889+t883+t1025; + t1030 = z*t1223; + t1403 = t1030+t939+t1003; + t1398 = t1281*t1494; + t1193 = t1285*t1468; + t1390 = t1286*t1480; + t1210 = t1275*t1493; + t1379 = t1271*z+t1274; + t1371 = t1276*t1493; + t1368 = t1278+t1251; + t1367 = t1269+t1270*t1282; + t1366 = t1524+t1270; + t1365 = t1279+t1280*t1283; + t1364 = t1267*t1281+t1260; + t917 = t1284*t1390; + t1363 = t1283*t1446+z*t1386+t1480*t1590+t917; + t1362 = t1260*t1282+t1267; + t1361 = t1260*t1283+t1267; + t830 = t1286*t1389; + t1360 = t1258*t1487+t830+t1286*t1409+t1263*t1427; + t1359 = t1490*t1591+y*t1402+t851+t1263*t1411; + t1358 = t1260+t1267*t1283; + t1357 = t1260*t1281+t1267; + t972 = t1285*t1429; + t1356 = t972+z*t1439+t1542; + t1355 = t1250+t1278; + t1354 = t1270+t1504; + t1353 = t1509+t1269; + t1352 = t1278+t1252; + t1351 = x*t1443+t908+(t1439+t1420)*t1282; + t863 = x*t1396; + t1350 = t972+z*t1420+t863+t844; + t1349 = t863+y*t1446+t1542; + t1348 = t1460+t1277; + t813 = t1569*t1590; + t1347 = t816+t1256*t1433+t813+z*t1412; + t1346 = t944+t1454*t1580+(t1377+t1424)*y; + t1345 = t1279*t1283+t1280; + t1344 = t1448+t1260; + t1342 = t1262*t1514+t1257*t1431+t910+z*t1383; + t992 = z*t1148; + t973 = x*t1160; + t1340 = t992+t973+t1531; + t1338 = t1223+t1282*t1184+t959+t891; + t1337 = t1224+t1282*t1205+t1550; + t862 = z*t1175; + t1335 = t1270*t1411+z*t1475+t885+t862; + t1094 = t1281*t1394; + t1334 = t1271*t1440+t1194+t1283*t1400+t1094; + t1082 = t1277*t1398; + t1330 = t1222+t1275*t1384+t1051+t1082; + t1060 = z*t1203; + t1021 = z*t1244; + t1329 = t1060+t1021+z*t1193+t1246; + t1328 = t1234+t1271*t1442+t1276*t1384+t1094; + t1327 = t1283*t1371+t1271*t1441+t1185+t1094; + t1326 = t1494-t1282-t1283; + t1325 = t1518+t1283*t1286; + t1324 = -1.0-t1326; + t951 = t1286*t1420; + t936 = t1285*t1424; + t1323 = t951+t936+t943+t1407; + t1322 = t845+t968+t1535+t1562; + t997 = x*t1476; + t1321 = t1285*t1410+t997+t821+y*t1445+t1527; + t1092 = z*t1235; + t1320 = t1092+t984+t937+t902+t862+t850; + t841 = x*t1157; + t1319 = t841+t954+t1525+t1532; + t1318 = t1529+t1551+t1561; + t834 = z*t1171; + t1317 = t834+t926+t1527+t1532; + t1316 = t1526+t1539+t1552; + t860 = x*t1388; + t1315 = t1262*t1427+t860+t1526+t1530; + t1005 = t1261*t1427; + t1314 = t1005+x*t1390+t1529+t1530; + t1313 = t888+t1262*t1472+t951+t1492*t1592+y*t1429+t1566*t1591+t1557; + t1089 = t1276*t1398; + t1312 = t917+t1089+t1267*t1487+t1556+t1666+t1669; + t945 = t1267*t1472; + t1311 = t830+t945+t837+t1089+t1033+t1662+t1672; + t1133 = y*t1202; + t1310 = t1133+t994+t1089+t1641+t1652+t1653; + t1309 = t1354*t1282+t1353; + t1096 = t1285*t1371; + t1102 = y*t1210; + t1308 = t1096+t1089+t1102+t1637+t1639+t1646; + t1307 = t1354*t1281+t1353; + t1306 = t1366*t1281+t1367; + t1305 = t992+t884+t856+t1346+t1541+t1690; + t985 = y*t1419; + t1304 = t985+t881+t1350+t1360+t1540; + t1303 = t985+t841+t1356+t1359+t1674; + t1302 = t834+t858+t1346+t1349+t1674; + t1301 = t1340+t1359+t1538+t1664; + t979 = x*t1413; + t1300 = t979+t856+t1340+t1360+t1528; + t1299 = t1137+t1188+t927+t934+t1334+t1561+t1654; + t836 = y*t1437; + t1298 = t1141+t921+y*t1498+t836+t1327+t1534+t1659; + t1297 = t836+t1226+t1179+t982+t1328+t1535+t1654; + t1085 = t1281*t1376; + t1042 = t1281*t1236; + t1296 = y*t1371+t1085+t1042+t1210+t1328+t1329; + t1295 = t1021+t1042+t1127+t1248+t1283*t1422+t1334+t1626; + t1294 = t1052+t1060+t1085+t1026+t1208+t1276*t1411+t1327+t1686; + t1293 = y*t1470+t1148+t957+x*t1485+t900+t1339+t1553+t1604; + t1121 = t1283*t1385; + t1292 = t1243+x*t1372+t1082+t1245+t1276*t1487+t1121+t1618+t1623+(t1378+ +t1482)*z+t1692; + t1291 = t1193+z*t1515+t1276*t1514+t1203+t1096+t1330+t1618+(t1411+t1431)* +t1271+t1691; + t1290 = t1068+t1213+t1451*t1578+t1209+t1623+y*t1415+t1330+(t1381+t1495)*x ++t1685; + t1272 = RATIONAL(-1.0,9.0); + t1268 = RATIONAL(1.0,54.0); + t1169 = x*t1521; + t1167 = y*t1469; + t1062 = x*t1249; + t1039 = y*t1238; + t966 = t1284*t1473; + t923 = x*t1473; + t854 = x*t1512; + t852 = t1260*t1472; + t826 = t1285*t1423; + t819 = y*t1395; + t818 = t1284*t1414; + t817 = t1285*t1445; + coeffs_I->coeff_m1_m1_m1 = t818+(t1265*t1586+(RATIONAL(-1.0,27.0)*z+t1265 +*t1286)*y)*x+t1284*t1476+t1312+t817+t1632+t1633+t1672+t1673; + coeffs_I->coeff_0_m1_m1 = t1357*t1586+t923+t926+(t1357*t1286+(t1272*t1281 ++t1273)*z)*y+t1323+t1299+t1408+t1602+t1661; + coeffs_I->coeff_p1_m1_m1 = t956+t834+t966+t955+t1311+t1406+t1633+t1634+ +t1641+t1669; + coeffs_I->coeff_p2_m1_m1 = t1314+t1268*t1484+t826+t1321+t1650+t1671; + coeffs_I->coeff_m1_0_m1 = t1407+t1596+t930+t923+(t1361*t1286+(t1272*t1283 ++t1273)*z)*x+t1297+t945+t1361*t1582+t1563+t1657+t1667; + coeffs_I->coeff_0_0_m1 = t1159+t1290+t1603+t1307*t1286+(t1365*t1281+t1345 +)*z+t1167+t1335+t1078+t1628+t1640+t1687+t1690; + coeffs_I->coeff_p1_0_m1 = t884+t1331+t1297+t889+t1598+t892+t1629+t1636+ +t1679; + coeffs_I->coeff_p2_0_m1 = t1302+t1358*t1582+t860+t1419+t1612+t1622; + coeffs_I->coeff_m1_p1_m1 = t921+t834+t852+t944+t845+t883+t1312+t841+t948+ +t851+t1408+t1507+t1639+t1662; + coeffs_I->coeff_0_p1_m1 = t1030+t891+t1299+t1541+t1601+t1605+t1627+t1642; + coeffs_I->coeff_p1_p1_m1 = t830+t1310+t1025+t1049+t1003+t862+t1544+t1606+ +t1639+t1640+t1669; + coeffs_I->coeff_p2_p1_m1 = t984+t985+t957+t1314+t966+t837+t975+t1323; + coeffs_I->coeff_m1_p2_m1 = t1321+t1268*t1472+t819+t1630+t1631+t1670; + coeffs_I->coeff_0_p2_m1 = t1302+t1364*t1586+t924+t1421+t1614+t1625; + coeffs_I->coeff_p1_p2_m1 = t888+t852+t985+t931+t1319+t1547+t1553+t1631; + coeffs_I->coeff_p2_p2_m1 = t818+y*t1423+t1347+t1351+t1665; + coeffs_I->coeff_m1_m1_0 = t935+(t1362*t1285+(t1272*t1282+t1273)*y)*x+ +t1362*t1583+t923+t1406+t1298+t1536+t1557+t1595+t1649; + coeffs_I->coeff_0_m1_0 = t1169+t1306*t1285+t1292+t1603+(t1279*t1282+t1280 ++(t1279+t1280*t1282)*t1281)*y+t979+t1338+t1181+t1507+t1554+t1627+t1682; + coeffs_I->coeff_p1_m1_0 = t1337+t1298+t1528+t1597+t1599+t1645; + coeffs_I->coeff_p2_m1_0 = t1304+t1344*t1583+t1428+t947+t1613+t1620; + coeffs_I->coeff_m1_0_0 = t887+t1309*t1284+(t1365*t1282+t1345)*x+t1291+ +t1337+t1489+t1629+t1647+t1664+t1682+t1687+t1689; + coeffs_I->coeff_0_0_0 = t1326+t1600+t1324*t1281+RATIONAL(1.0,1.0)+t1680+( +t1505*t1275+(t1276*t1285+t1274)*z+(t1522+t1379)*y)*x+(t1286+t1284*t1494+t1325* +t1281+t1499)*t1277+t1619+t1499*t1275*z+t1626+(t1523*t1275+(t1483+t1274)*z)*y+(z ++y+x+t1523*t1283+t1499*t1282+t1505*t1281)*t1278+t1329+t1681+t1686+t1688; + coeffs_I->coeff_p1_0_0 = t1031+t1593+t1291+(t1505*t1277+t1325*t1278-t1324 +)*x+(t1581+t1348*t1282+t1379*y+t1352)*t1284+t1062+t1644+t1677; + coeffs_I->coeff_p2_0_0 = (t1353*t1282+t1354)*t1284+t1309*x+t833+t1293+ +t1551+t1624+t1660; + coeffs_I->coeff_m1_p1_0 = t1338+t962+t1294+t1538+t1595+t1599+t1643; + coeffs_I->coeff_0_p1_0 = t1292+t1039+t1593+(t1500-t1282+t1523*t1277+( +t1284*t1282+t1493)*t1278+t1573)*y+t1022+(t1581+(t1452+t1277)*t1281+t1379*x+ +t1368)*t1285+t1637+t1678; + coeffs_I->coeff_p1_p1_0 = (t1368*t1285+(1.0+t1277*t1286-t1282)*y)*x+t1368 +*t1583+t1294+t1597+t1607+t1680+t1683; + coeffs_I->coeff_p2_p1_0 = t1169+t956+t1300+t1609+t1620+t1645; + coeffs_I->coeff_m1_p2_0 = t1004+t1303+t1435+t1344*t1579+t1613+t1616; + coeffs_I->coeff_0_p2_0 = (t1367*t1281+t1366)*t1285+t1306*y+t845+t1293+ +t1594; + coeffs_I->coeff_p1_p2_0 = t1301+t1609+t1616+t1643+t1647; + coeffs_I->coeff_p2_p2_0 = t1434+(t1577+(t1578+t1285)*t1261)*x+t1313+t1560 ++t1649; + coeffs_I->coeff_m1_m1_p1 = t928+t931+t969+t841+t879+t1311+t982+t1615+ +t1632+t1646+t1653; + coeffs_I->coeff_0_m1_p1 = t937+t1295+t936+t973+t1335+t1403+t1602+t1605+ +t1638; + coeffs_I->coeff_p1_m1_p1 = t1028+t1310+t1121+t1073+t892+t1405+t1554+t1634 ++t1644+t1646+t1672; + coeffs_I->coeff_p2_m1_p1 = t951+t966+t1317+t1318+t1650+t1663; + coeffs_I->coeff_m1_0_p1 = t1296+t1596+t994+t973+t1547+t862+t1598+t1628+ +t1635; + coeffs_I->coeff_0_0_p1 = t1290+t1608+t1123+t1072+(t1496-t1281+t1499*t1277 ++(t1510+t1511)*t1278-t1564)*z+t1102+(t1567+t1348*t1281+(t1274+t1271*y)*x+t1352) +*t1286+t1677+t1678; + coeffs_I->coeff_p1_0_p1 = t1296+t1108+t1352*t1582+(t1352*t1286+(t1277* +t1285-t1564)*z)*x+t1600+t1679+t1683+t1684; + coeffs_I->coeff_p2_0_p1 = t1159+t1305+t962+t1611+t1622+t1636; + coeffs_I->coeff_m1_p1_p1 = t1308+t944+t830+t1112+t892+t1403+t1404+t1489+ +t1615+t1652; + coeffs_I->coeff_0_p1_p1 = t1355*t1586+t1295+(t1355*t1286+(t1277*t1284+ +t1573)*z)*y+t1601+t1607+t1681+t1684; + coeffs_I->coeff_p1_p1_p1 = t1308+(t1278*t1586+(t1278*t1286+z)*y)*x+t1039+ +t1278*t1484+t1121+t1065+t1062+t1606+t1608+t1641; + coeffs_I->coeff_p2_p1_p1 = t1133+t957+t936+t885+t891+t831+t1318+t1320; + coeffs_I->coeff_m1_p2_p1 = t852+t858+t1317+t1322+t1667+t1670; + coeffs_I->coeff_0_p2_p1 = t921+t1305+t1167+t1610+t1625+t1642; + coeffs_I->coeff_p1_p2_p1 = t930+t959+t1320+t900+t1322+t1404; + coeffs_I->coeff_p2_p2_p1 = t854+t931+t1349+t1351+t1536; + coeffs_I->coeff_m1_m1_p2 = t997+t1315+t1268*t1508+t1546+t1630+t1671+t1675 +; + coeffs_I->coeff_0_m1_p2 = t1304+t1364*t1286*y+z*t1516+t946+t1614+t1617; + coeffs_I->coeff_p1_m1_p2 = t1316+t1319+t1663+t1668+t1675; + coeffs_I->coeff_p2_m1_p2 = t813+x*t1436+t1363+t1665+t1673+t1676; + coeffs_I->coeff_m1_0_p2 = t1005+t1303+z*t1519+t1358*t1585+t1612+t1621; + coeffs_I->coeff_0_0_p2 = t1307*z+t987+t1544+t1341+t1594+t1552+(t1353* +t1281+t1354)*t1286+t1604+t1624; + coeffs_I->coeff_p1_0_p2 = t1301+t1611+t1621+t1635+t1689; + coeffs_I->coeff_p2_0_p2 = t1432+(t1266*z+(t1286+t1576)*t1261)*x+t1313+ +t1556+t1657; + coeffs_I->coeff_m1_p1_p2 = t1315+t1532+t1533+t1534+t1540+t1548+t1668; + coeffs_I->coeff_0_p1_p2 = t1181+t1300+t982+t1610+t1617+t1638; + coeffs_I->coeff_p1_p1_p2 = t1092+t959+t1316+t968+t1405+t1534+t1537+t1550; + coeffs_I->coeff_p2_p1_p2 = t935+t854+t1350+t1363+t1563; + coeffs_I->coeff_m1_p2_p2 = t817+t1457*t1591+t1342+t1347+t1676; + coeffs_I->coeff_0_p2_p2 = t1512+(t1586+(t1286+t1587)*y)*t1261+t1313+t1558 ++t1661; + coeffs_I->coeff_p1_p2_p2 = t854+t926+t1342+t1356+t1533; + coeffs_I->coeff_p2_p2_p2 = y*t1425+t826+t819+(z*t1503+(t1256*t1286+t1584) +*y)*x+t1546; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..ac35934 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dx.compute.c @@ -0,0 +1,1251 @@ +fp t2131; +fp t2104; +fp t2070; +fp t1999; +fp t2099; +fp t2132; +fp t2133; +fp t2248; +fp t1925; +fp t2448; +fp t2102; +fp t2095; +fp t2450; +fp t2096; +fp t2281; +fp t1947; +fp t2353; +fp t1953; +fp t2449; +fp t2110; +fp t2134; +fp t2292; +fp t1998; +fp t2130; +fp t2304; +fp t2117; +fp t2012; +fp t2447; +fp t1914; +fp t2090; +fp t2265; +fp t2446; +fp t2069; +fp t1906; +fp t2094; +fp t1952; +fp t2445; +fp t2347; +fp t2348; +fp t2444; +fp t1988; +fp t2111; +fp t2303; +fp t2443; +fp t2065; +fp t2106; +fp t2048; +fp t1792; +fp t2442; +fp t2277; +fp t2015; +fp t2036; +fp t2441; +fp t2279; +fp t2028; +fp t1769; +fp t2125; +fp t2080; +fp t1994; +fp t2440; +fp t2114; +fp t2239; +fp t2196; +fp t1888; +fp t2260; +fp t1990; +fp t2037; +fp t2387; +fp t2105; +fp t2439; +fp t2274; +fp t1940; +fp t2101; +fp t2345; +fp t1930; +fp t2438; +fp t2064; +fp t1934; +fp t1957; +fp t2437; +fp t2061; +fp t1923; +fp t2240; +fp t1933; +fp t2243; +fp t2081; +fp t1989; +fp t2116; +fp t2076; +fp t2436; +fp t2120; +fp t2263; +fp t2033; +fp t1798; +fp t2291; +fp t2017; +fp t1774; +fp t2018; +fp t1832; +fp t2128; +fp t2127; +fp t2295; +fp t2233; +fp t2416; +fp t2435; +fp t1924; +fp t1921; +fp t2326; +fp t2271; +fp t1922; +fp t1702; +fp t2108; +fp t2349; +fp t2283; +fp t2434; +fp t2235; +fp t1851; +fp t2433; +fp t2344; +fp t2280; +fp t2257; +fp t2230; +fp t2432; +fp t2307; +fp t1975; +fp t2427; +fp t2084; +fp t2044; +fp t1825; +fp t2275; +fp t2049; +fp t1776; +fp t2431; +fp t2112; +fp t2043; +fp t2119; +fp t2242; +fp t2211; +fp t2016; +fp t2430; +fp t2316; +fp t2232; +fp t2329; +fp t2429; +fp t2087; +fp t2078; +fp t1977; +fp t2428; +fp t2113; +fp t2217; +fp t2312; +fp t2006; +fp t2426; +fp t2305; +fp t2003; +fp t2425; +fp t2301; +fp t1959; +fp t2424; +fp t2121; +fp t2246; +fp t2067; +fp t1965; +fp t2423; +fp t2052; +fp t2346; +fp t2030; +fp t2422; +fp t1907; +fp t2093; +fp t2261; +fp t1966; +fp t1732; +fp t2068; +fp t1900; +fp t2247; +fp t2421; +fp t2098; +fp t2229; +fp t1751; +fp t2420; +fp t2026; +fp t2419; +fp t2418; +fp t2062; +fp t2063; +fp t1920; +fp t2417; +fp t2234; +fp t2088; +fp t2288; +fp t2415; +fp t2077; +fp t2056; +fp t1886; +fp t1986; +fp t2414; +fp t2413; +fp t2194; +fp t1841; +fp t2014; +fp t2412; +fp t2186; +fp t1932; +fp t1709; +fp t2411; +fp t2352; +fp t1991; +fp t1992; +fp t2410; +fp t2409; +fp t1981; +fp t2073; +fp t2408; +fp t2097; +fp t2407; +fp t2022; +fp t2406; +fp t2285; +fp t2199; +fp t2405; +fp t2236; +fp t2027; +fp t2404; +fp t1881; +fp t2403; +fp t2029; +fp t2293; +fp t2011; +fp t2402; +fp t2086; +fp t1995; +fp t2401; +fp t2203; +fp t1720; +fp t2308; +fp t2400; +fp t1983; +fp t1838; +fp t1847; +fp t2342; +fp t1987; +fp t1801; +fp t2399; +fp t2054; +fp t1802; +fp t1738; +fp t1968; +fp t1756; +fp t2290; +fp t2398; +fp t2092; +fp t2286; +fp t1912; +fp t2397; +fp t2041; +fp t1984; +fp t2396; +fp t2031; +fp t2395; +fp t1978; +fp t1788; +fp t2394; +fp t1973; +fp t2393; +fp t1889; +fp t2392; +fp t2107; +fp t2391; +fp t1797; +fp t2390; +fp t1931; +fp t2252; +fp t2231; +fp t2389; +fp t1943; +fp t1701; +fp t2388; +fp t2386; +fp t2000; +fp t2251; +fp t2002; +fp t2385; +fp t2200; +fp t1821; +fp t2384; +fp t1874; +fp t2383; +fp t2082; +fp t1997; +fp t2382; +fp t2381; +fp t2262; +fp t2040; +fp t2380; +fp t1944; +fp t2379; +fp t1980; +fp t2378; +fp t2287; +fp t1945; +fp t2278; +fp t2226; +fp t1749; +fp t1949; +fp t2335; +fp t2377; +fp t2325; +fp t2020; +fp t2255; +fp t2376; +fp t2375; +fp t2313; +fp t1982; +fp t2321; +fp t2374; +fp t1910; +fp t1733; +fp t1844; +fp t2373; +fp t2372; +fp t1950; +fp t1754; +fp t2371; +fp t2370; +fp t2205; +fp t2369; +fp t1909; +fp t2368; +fp t2197; +fp t2267; +fp t1901; +fp t2367; +fp t1876; +fp t2238; +fp t2225; +fp t1820; +fp t2174; +fp t2366; +fp t2072; +fp t2365; +fp t2331; +fp t2008; +fp t2364; +fp t2209; +fp t1829; +fp t1970; +fp t2363; +fp t1941; +fp t2362; +fp t2343; +fp t2058; +fp t1805; +fp t2361; +fp t2075; +fp t2360; +fp t2208; +fp t1736; +fp t2317; +fp t2314; +fp t2359; +fp t2039; +fp t1833; +fp t2216; +fp t1826; +fp t1795; +fp t2358; +fp t2289; +fp t2337; +fp t2323; +fp t1942; +fp t1695; +fp t2357; +fp t2227; +fp t2356; +fp t2035; +fp t1856; +fp t1787; +fp t2355; +fp t2354; +fp t2351; +fp t2350; +fp t2341; +fp t2100; +fp t2339; +fp t1937; +fp t2336; +fp t2334; +fp t1848; +fp t1938; +fp t2333; +fp t2330; +fp t2328; +fp t2009; +fp t1781; +fp t2327; +fp t2324; +fp t1870; +fp t2320; +fp t2319; +fp t2318; +fp t2074; +fp t2315; +fp t2228; +fp t1854; +fp t2311; +fp t1730; +fp t2237; +fp t1752; +fp t2310; +fp t2309; +fp t1712; +fp t2306; +fp t1823; +fp t1961; +fp t2302; +fp t2300; +fp t1704; +fp t1725; +fp t2299; +fp t2298; +fp t1877; +fp t2296; +fp t2294; +fp t2198; +fp t1834; +fp t2282; +fp t2276; +fp t2272; +fp t2034; +fp t2053; +fp t2270; +fp t2122; +fp t2269; +fp t2268; +fp t2024; +fp t2266; +fp t2264; +fp t2244; +fp t1905; +fp t2259; +fp t2258; +fp t2091; +fp t2256; +fp t2254; +fp t2013; +fp t1705; +fp t2253; +fp t2118; +fp t2250; +fp t2249; +fp t2245; +fp t2241; +fp t2045; +fp t2057; +fp t2032; +fp t1985; +fp t2224; +fp t1890; +fp t2223; +fp t1770; +fp t2222; +fp t1715; +fp t2221; +fp t1778; +fp t2220; +fp t1857; +fp t1799; +fp t2219; +fp t2218; +fp t2195; +fp t1786; +fp t2215; +fp t2038; +fp t2213; +fp t2126; +fp t2212; +fp t2210; +fp t1804; +fp t2204; +fp t2202; +fp t1767; +fp t2201; +fp t2115; +fp t2193; +fp t2192; +fp t2191; +fp t2190; +fp t2189; +fp t2188; +fp t2187; +fp t2185; +fp t2184; +fp t1882; +fp t1858; +fp t2183; +fp t2182; +fp t2181; +fp t2180; +fp t2179; +fp t2178; +fp t2177; +fp t2176; +fp t2175; +fp t2173; +fp t2172; +fp t2171; +fp t2170; +fp t1816; +fp t2169; +fp t1865; +fp t2167; +fp t1716; +fp t2166; +fp t1972; +fp t2165; +fp t1717; +fp t2164; +fp t2163; +fp t1719; +fp t2162; +fp t1913; +fp t2161; +fp t1811; +fp t2160; +fp t1908; +fp t1735; +fp t2159; +fp t2158; +fp t2157; +fp t2156; +fp t2155; +fp t1817; +fp t2124; +fp t2154; +fp t2153; +fp t2152; +fp t1887; +fp t2151; +fp t2150; +fp t2149; +fp t2148; +fp t2147; +fp t1819; +fp t2146; +fp t1946; +fp t2145; +fp t2144; +fp t2143; +fp t2142; +fp t1967; +fp t2141; +fp t2140; +fp t1862; +fp t2139; +fp t2138; +fp t2137; +fp t2123; +fp t2109; +fp t2103; +fp t2089; +fp t2042; +fp t1894; +fp t1891; +fp t1859; +fp t1855; +fp t1796; +fp t1784; +fp t1748; +fp t1742; +fp t1708; +fp t1707; + t2131 = z*z; + t2104 = RATIONAL(-1.0,6.0); + t2070 = t2104*t2131; + t1999 = y*t2070; + t2099 = RATIONAL(-1.0,12.0); + t2132 = y*y; + t2133 = t2132*y; + t2248 = t2133*t2131; + t1925 = t2099*t2248; + t2448 = t1999+t1925; + t2102 = RATIONAL(1.0,18.0); + t2095 = RATIONAL(-1.0,18.0); + t2450 = t2102+t2095*t2131; + t2096 = RATIONAL(-1.0,36.0); + t2281 = t2096*t2133; + t1947 = z*t2281; + t2353 = y*z; + t1953 = t2095*t2353; + t2449 = t1947+t1953; + t2110 = RATIONAL(1.0,4.0); + t2134 = z*t2131; + t2292 = t2110*t2134; + t1998 = y*t2292; + t2130 = x*x; + t2304 = t2130*t2133; + t2117 = RATIONAL(-3.0,4.0); + t2012 = t2117*t2304; + t2447 = z*t2012+t1998; + t1914 = t2096*t2353; + t2090 = RATIONAL(1.0,108.0); + t2265 = t2090*t2134; + t2446 = t2130*t1914+t2133*t2265; + t2069 = t2099*t2131; + t1906 = y*t2069; + t2094 = RATIONAL(1.0,12.0); + t1952 = t2094*t2248; + t2445 = t1906+t1952; + t2347 = t2133*z; + t2348 = y*t2134; + t2444 = t2347+t2348; + t1988 = t2110*t2353; + t2111 = RATIONAL(-1.0,4.0); + t2303 = t2111*t2133; + t2443 = z*t2303+t1988; + t2065 = t2094*y; + t2106 = RATIONAL(-1.0,8.0); + t2048 = t2106*t2248; + t1792 = t2130*t2048; + t2442 = t1792+t2131*t2065; + t2277 = t2130*t2134; + t2015 = t2117*t2277; + t2036 = t2110*t2347; + t2441 = t2036+y*t2015; + t2279 = t2134*t2106; + t2028 = t2133*t2279; + t1769 = t2130*t2028; + t2125 = RATIONAL(-1.0,3.0); + t2080 = t2125*z; + t1994 = y*t2080; + t2440 = t1769+t1994; + t2114 = RATIONAL(1.0,8.0); + t2239 = t2130*t2114; + t2196 = t2134*t2239; + t1888 = y*t2196; + t2260 = t1888+t1769; + t1990 = t2132*t2292; + t2037 = t2111*t2277; + t2387 = t2130*t1990+t2037; + t2105 = RATIONAL(1.0,6.0); + t2439 = t2260+t2387+t2105*z; + t2274 = t2096*t2134; + t1940 = y*t2274; + t2101 = RATIONAL(1.0,36.0); + t2345 = t2101*y; + t1930 = z*t2345; + t2438 = t1940+t1930; + t2064 = t2099*t2133; + t1934 = z*t2064; + t1957 = z*t2065; + t2437 = t1934+t1957; + t2061 = t2099*t2132; + t1923 = z*t2061; + t2240 = t2132*t2094; + t1933 = t2134*t2240; + t2243 = t1923+t1933; + t2081 = t2111*t2132; + t1989 = z*t2081; + t2116 = RATIONAL(1.0,2.0); + t2076 = t2116*t2132; + t2436 = t1990+t1989+t2076; + t2120 = RATIONAL(-1.0,2.0); + t2263 = t2120*t2134; + t2033 = x*t2263; + t1798 = y*t2033; + t2291 = t2133*t2134; + t2017 = t2110*t2291; + t1774 = x*t2017; + t2018 = z*t2076; + t1832 = x*t2018; + t2128 = x*z; + t2127 = y*t2128; + t2295 = t2120*t2133; + t2233 = z*t2295; + t2416 = t2127+x*t2233; + t2435 = t1798+t1774+t1832+t2416; + t1924 = t2102*t2347; + t1921 = t2102*t2348; + t2326 = (t1921+t1924)*x; + t2271 = t2101*t2134; + t1922 = t2133*t2271; + t1702 = x*t1922; + t2108 = RATIONAL(1.0,9.0); + t2349 = t2108*z; + t2283 = x*t2349; + t2434 = t2326+t1702+y*t2283; + t2235 = x*t2248; + t1851 = t2116*t2235; + t2433 = t1851+(t2295+t2036)*x; + t2344 = y*t2130; + t2280 = z*t2344; + t2257 = t2114*t2134; + t2230 = x*t2291; + t2432 = t2116*t2230+t2133*t2257+t2117*t2280; + t2307 = t2116*t2133; + t1975 = x*t2307; + t2427 = z*t1975+t2128; + t2084 = t2120*y; + t2044 = z*t2084; + t1825 = x*t2044; + t2275 = t2116*t2134; + t2049 = x*t2275; + t1776 = t2132*t2049; + t2431 = t1825+t2427+t2033+t1776+x*t1998; + t2112 = RATIONAL(3.0,4.0); + t2043 = t2112*t2304; + t2119 = RATIONAL(3.0,8.0); + t2242 = t2130*t2119; + t2211 = t2133*t2242; + t2016 = t2111*t2348; + t2430 = t2084+t2016+t2131*t2043+t2012+z*t2211; + t2316 = t2130*t2131; + t2232 = y*t2316; + t2329 = t2116*t2130; + t2429 = t2120*t2232+y*t2329; + t2087 = t2105*t2134; + t2078 = t2104*t2134; + t1977 = t2132*t2078; + t2428 = t2087+t1977; + t2113 = RATIONAL(-3.0,8.0); + t2217 = t2113*t2316; + t2312 = t2132*t2131; + t2006 = t2110*t2312; + t2426 = t2132*t2217+t2006; + t2305 = t2130*t2132; + t2003 = t2117*t2305; + t2425 = t2131*t2003+t2006; + t2301 = t2130*t2094; + t1959 = t2133*t2301; + t2424 = t1959+t2130*t1925; + t2121 = RATIONAL(1.0,3.0); + t2246 = t2121*t2128; + t2067 = t2094*t2133; + t1965 = z*t2067; + t2423 = t2133*t2246+t1965; + t2052 = t2132*t2087; + t2346 = t2132*z; + t2030 = t2121*t2346; + t2422 = (t2030+t2052)*x; + t1907 = y*t2271; + t2093 = RATIONAL(1.0,24.0); + t2261 = t2093*t2133; + t1966 = t2134*t2261; + t1732 = t2130*t1966; + t2068 = t2102*z; + t1900 = y*t2068; + t2247 = t1732+t1900; + t2421 = t1907+t2247; + t2098 = RATIONAL(-1.0,24.0); + t2229 = y*t2277; + t1751 = t2093*t2229; + t2420 = t1751+t2098*t2280; + t2026 = t2110*t2277; + t2419 = t2026+t2132*t2037; + t2418 = t2052+t2078; + t2062 = t2094*t2134; + t2063 = t2099*t2134; + t1920 = t2132*t2063; + t2417 = t2062+t1920; + t2234 = z*t2304; + t2088 = RATIONAL(-1.0,108.0); + t2288 = t2134*t2088; + t2415 = t2101*t2234+y*t2288; + t2077 = t2116*t2131; + t2056 = x*t2077; + t1886 = y*t2056; + t1986 = t2111*t2248; + t2414 = t1886+x*t1986; + t2413 = t2130*t2006+t2105*t2312; + t2194 = t2113*t2304; + t1841 = t2134*t2194; + t2014 = t2112*t2277; + t2412 = y*t2014+t1841; + t2186 = t2120+t2076; + t1932 = t2098*t2291; + t1709 = t2130*t1932; + t2411 = t1709+y*t2349; + t2352 = y*t2131; + t1991 = t2121*t2352; + t1992 = t2105*t2248; + t2410 = (t1992+t1991)*x; + t2409 = t2448*x; + t1981 = t2104*t2248; + t2073 = t2105*t2133; + t2408 = t1981+t2073; + t2097 = RATIONAL(1.0,72.0); + t2407 = t2097*t2229+t2090*t2347; + t2022 = t2106*t2312; + t2406 = t2130*t2022+t2099*t2312; + t2285 = t2097*t2130; + t2199 = t2133*t2285; + t2405 = y*t2265+z*t2199; + t2236 = z*t2305; + t2027 = z*t2329; + t2404 = t2120*t2236+t2027; + t1881 = x*t1994; + t2403 = t1881+t2448; + t2029 = t2130*t2303; + t2293 = t2110*t2130; + t2011 = t2133*t2293; + t2402 = t2131*t2029+t2011; + t2086 = t2104*t2132; + t1995 = z*t2086; + t2401 = (t1920+t1995)*x; + t2203 = t2099*t2305; + t1720 = z*t2203; + t2308 = t2097*t2132; + t2400 = t1720+t2134*t2308; + t1983 = z*t2073; + t1838 = x*t1983; + t1847 = t2104*t2230; + t2342 = x*t2104; + t1987 = y*t2342; + t1801 = z*t1987; + t2399 = t1847+t1838+t1801; + t2054 = x*t2087; + t1802 = y*t2054; + t1738 = x*t1965; + t1968 = t2133*t2063; + t1756 = x*t1968; + t2290 = t1738+t1756; + t2398 = t1801+t1802+t2290; + t2092 = RATIONAL(-1.0,72.0); + t2286 = t2133*t2092; + t1912 = t2097*t2291; + t2397 = t1912+z*t2286; + t2041 = t2117*t2316; + t1984 = y*t2077; + t2396 = t1984+y*t2041; + t2031 = t2110*t2248; + t2395 = t2130*t2031+t2029; + t1978 = t2111*t2316; + t1788 = y*t1978; + t2394 = t1999+t1788; + t1973 = t2130*t2062; + t2393 = t1973+t2134*t2203; + t1889 = t2105*t2230; + t2392 = y*t2246+t1889; + t2107 = RATIONAL(-1.0,9.0); + t2391 = t2107*t2127+t2102*t2230; + t1797 = t2132*t2196; + t2390 = t1995+t1797; + t1931 = t2132*t2274; + t2252 = t2093*t2130; + t2231 = z*t2252; + t2389 = t2132*t2231+t1931; + t1943 = t2134*t2286; + t1701 = t2130*t1943; + t2388 = t2088*t2353+t1701; + t2386 = t2132*t2033+t1832; + t2000 = t2111*t2305; + t2251 = (t2000+t2240)*t2131; + t2002 = t2131*t2293; + t2385 = t2069+t2251+t2002; + t2200 = t2113*t2277; + t1821 = t2132*t2200; + t2384 = t1776+t1821+t2132*t2257; + t1874 = t2131*t2194; + t2383 = t1874+t2114*t2248+t1851; + t2082 = t2105*y; + t1997 = z*t2082; + t2382 = t2080+t2030+t1997; + t2381 = t2132*t2015+y*t2200+t2014; + t2262 = t2120*t2132; + t2040 = t2131*t2262; + t2380 = t2031+t2040+t2077; + t1944 = z*t2240; + t2379 = t1944+t2422; + t1980 = t2132*t2293; + t2378 = t2061+t2251+t1980; + t2287 = t2101*t2133; + t1945 = z*t2287; + t2278 = t2134*t2095; + t2226 = x*t2278; + t1749 = y*t2226; + t1949 = t2133*t2274; + t2335 = (t1900+t1949)*x; + t2377 = x*t1945+t1749+t2335; + t2325 = t2105*t2131; + t2020 = y*t2325; + t2255 = (t2020+t1981)*x; + t2376 = t2255+x*t2073+t1987; + t2375 = t1920+t2401; + t2313 = t2105*t2132; + t1982 = z*t2313; + t2321 = (t1982+t1977)*x; + t2374 = t2054+z*t2342+t2321; + t1910 = t2133*t2062; + t1733 = x*t1910; + t1844 = y*t2027; + t2373 = t1733+t1910+t1844+t2440; + t2372 = t1733+t1949+t1881; + t1950 = t2095*t2347; + t1754 = x*t1950; + t2371 = t1754+x*t1907+t2335; + t2370 = t2104*z+t1982+t2387; + t2205 = t1825+(t2049+x)*y; + t2369 = t2043+t2131*t2012+z*t2194+t2205; + t1909 = t2099*t2304; + t2368 = t2131*t1959+t1909+t2450*y; + t2197 = t2130*t2240; + t2267 = t2095*t2132; + t1901 = t2130*t2063; + t2367 = t2134*t2197+t1901+t2068+z*t2267; + t1876 = t2133*t2196; + t2238 = t2130*t2106; + t2225 = z*t2238; + t1820 = t2133*t2225; + t2174 = t1876+t1820+t2402; + t2366 = t2125*y+t2174+t1991+t1997; + t2072 = t2104*y; + t2365 = t2072+t2020+t2395; + t2331 = t2130*t2111; + t2008 = y*t2331; + t2364 = t2008+t2064+t2065+t2445; + t2209 = t2133*t2239; + t1829 = z*t2209; + t1970 = t2099*t2353; + t2363 = t1829+t2082+t1970+t2395; + t1941 = t2093*t2248; + t2362 = t1941+t1788+t2410+t2442; + t2343 = x*t2125; + t2058 = z*t2343; + t1805 = x*t1997; + t2361 = t2058+x*t2078+t1805+t2422; + t2075 = t2104*t2133; + t2360 = x*t2075+t1805+y*t2343+t2410; + t2208 = t2131*t2252; + t1736 = t2133*t2208; + t2317 = t2102*t2131; + t2314 = t2101*t2248+t2094*t2232; + t2359 = t1736+t2314+y*t2317+t2406; + t2039 = t2134*t2081; + t1833 = z*t2003; + t2216 = t2134*t2242; + t1826 = t2132*t2216; + t1795 = x*t2039; + t2358 = t2039+t1833+t1826+t1795+t2018; + t2289 = z*t2197+t2132*t2271; + t2337 = t2102*t2132; + t2323 = t2093*t2134; + t1942 = t2132*t2323; + t1695 = t2130*t1942; + t2357 = z*t2337+t2289+t1695+t2401; + t2227 = y*t2239; + t2356 = t1932+y*t2323+t2098*t2353+(t2261+t2227)*z; + t2035 = t2111*t2291; + t1856 = t2134*t2211; + t1787 = x*t2035; + t2355 = t2044+t2035+t2112*t2280+t1856+t1787; + t2354 = t1841+y*t2216+t2132*t2014+t2120*z+t2015+t2018+t2443; + t2351 = z*t2130; + t2350 = x*t2131; + t2341 = 1.0-t2132; + t2100 = RATIONAL(-1.0,54.0); + t2339 = z*t2100; + t1937 = t2098*t2248; + t2336 = t2130*t1937+t2131*t2345; + t2334 = t2132*t2134; + t1848 = y*t2026; + t1938 = y*t2063; + t2333 = t1848+t1938; + t2330 = t1732+t1943; + t2328 = t1769+t1966; + t2009 = t2132*t2279; + t1781 = t2130*t2009; + t2327 = t1781+t1942; + t2324 = t2133*t2231+t1709; + t1870 = y*t2002; + t2320 = t1870+t1802; + t2319 = t1949+t1945; + t2318 = t2134-t2131; + t2074 = t2111*t2131; + t2315 = t2120*t2130; + t2228 = y*t2238; + t1854 = t2134*t2228; + t2311 = t1854+t1876; + t1730 = y*t1901; + t2237 = y*t2301; + t1752 = z*t2237; + t2310 = t1730+t1752; + t2309 = y*t2350; + t1712 = t2134*t2199; + t2306 = t1712+t2092*t2229; + t1823 = z*t2000; + t1961 = y*t2062; + t2302 = t1823+t1961; + t2300 = t2133+t2134; + t1704 = y*t1973; + t1725 = t2099*t2280; + t2299 = t1704+t1725; + t2298 = x*t2346; + t1877 = z*t2011; + t2296 = t1877+t1934; + t2294 = t2243*x; + t2198 = t2132*t2239; + t1834 = z*t2198; + t2282 = t1781+t1834; + t2276 = t1995+t1881; + t2272 = t1922+t1947; + t2034 = y*t2074; + t2053 = t2112*t2316; + t2270 = t2034+y*t2053; + t2122 = RATIONAL(-2.0,1.0); + t2269 = t2122-t2134; + t2268 = t2133-t2132; + t2024 = t2112*t2305; + t2266 = t1989+z*t2024; + t2264 = t2445*x; + t2244 = t2098*t2132; + t1905 = t2134*t2244; + t2259 = t2130*t1905+t2101*t2346; + t2258 = t1910+t1938; + t2091 = RATIONAL(1.0,216.0); + t2256 = t2091*t2133; + t2254 = x*t2348; + t2013 = z*t2072; + t1705 = z*t1959; + t2253 = t1705+t1725; + t2118 = RATIONAL(3.0,2.0); + t2250 = t2118*t2131; + t2249 = (t2244+t2198)*t2131; + t2245 = t2097*t2131; + t2241 = t1906+t1792; + t2045 = z*t2315; + t2057 = y*t2293; + t2032 = z*t2075; + t1985 = y*t2078; + t2224 = t1732+t1922+t1756; + t1890 = x*t1985; + t2223 = t1890+t1704+t1921; + t1770 = x*t2006; + t2222 = t1770+t2409; + t1715 = z*t1909; + t2221 = t1838+t1950+t1715; + t1778 = t2130*t1997; + t2220 = t1705+t1823+t1778; + t1857 = t2130*t2013; + t1799 = z*t1980; + t2219 = t1857+t1799+t1715; + t2218 = t2110+t2106*z; + t2195 = t2131*t2242; + t1786 = x*t2040; + t2215 = t1786+t2132*t2195+t2022; + t2038 = y*t2087; + t2213 = t2038+t1968+t1933; + t2126 = x*t2312; + t2212 = t2126+t1886+t2120*t2235; + t2210 = t1890+t1985+t1848; + t1804 = x*t2032; + t2204 = t1877+t2032+t1804; + t2202 = t1770+t2426; + t1767 = z*t2029; + t2201 = t1838+t1767+t1983; + t2115 = RATIONAL(-3.0,2.0); + t2193 = t2115*t2132+t2118; + t2192 = t2313+t2104; + t2191 = t2121+t2125*t2132; + t2190 = t2115+t2118*t2132; + t2189 = t2105+t2086; + t2188 = t2099*t2130+t2101; + t2187 = t2262+t2116; + t2185 = t1786+t2436*x; + t2184 = t1751+t1709+t2092*t2348+t1912; + t1882 = z*t2057; + t1858 = y*t2037; + t2183 = t2116*t2232+y*t2315+t1882+t1858; + t2182 = t1767+t1882+t2045+t2130*t2018; + t2181 = t2092*t2334+t2098*t2236+z*t2308+t1695; + t2180 = t1702+(t1947+t2438)*x; + t2179 = t1733+(t1938+t2437)*x; + t2178 = t1905+t2093*t2346+t2132*t2225+t1797; + t2177 = t2134*t2256+t2101*t2280+t2388; + t2176 = t1786+t2056+(t2031+t2034)*x; + t2175 = y*t2245+t2098*t2232+t1736+t2092*t2248; + t2173 = t1914+t1907+t2324; + t2172 = t2324+t2438; + t2171 = t1968+t2075+t1965+t1992; + t2170 = t2311+t2419; + t1816 = z*t2008; + t2169 = t1816+t1957+t2328; + t1865 = t2131*t2209; + t2167 = t1865+t2093*t2352+t1937+t2131*t2228; + t1716 = x*t1961; + t2166 = t1961+t1968+t1716+t1756+t2311; + t1972 = t2096*t2248; + t2165 = y*t2208+t1972+t2264+t2336; + t1717 = t2098*t2229; + t2164 = t1940+t1716+t1717+t2224; + t2163 = t1940+t1704+t2327+t2330; + t1719 = t2099*t2232; + t2162 = t1719+t2133*t2245+t2249+t2336; + t1913 = y*t2339; + t2161 = t1712+t1913+t2088*t2347+t2101*t2229+t2259; + t1811 = t2131*t2227; + t2160 = t1952+t1811+t2241+t2264; + t1908 = y*t2278; + t1735 = t2098*t2234; + t2159 = t1908+t1735+t2247+t2294; + t2158 = t1923+t1781+t2013+t1858+t1965+t1876; + t2157 = t1941+t1870+t2241+t2249; + t2156 = t2028+t2120*t2230+t1856+t2266+t2270; + t2155 = t2092*t2353+t1735+y*t2231+t1717+t2330+t2444*t2097; + t1817 = y*t2045; + t2124 = RATIONAL(2.0,3.0); + t2154 = t1932+t2124*t2127+t1847+t1817+t1876+t1997+t2215; + t2153 = t1865+t1952+t1770+t2394+t2406+t2414; + t2152 = t1924+t1730+t2222+t2390+t2411; + t1887 = t2133*t2195; + t2151 = t1887+t1986+t2202+t2396+t2414; + t2150 = t2113*t2236+t2009+t2126+t2081+t2024+t1826+t2114*t2346+t2386+t2425 +; + t2149 = t1887+t2048+t2074+t2114*t2352+y*t2217+t2053+t2212+t2425; + t2148 = t1914+t1945+t1715+t1752+t2167+t2184; + t2147 = t1925+t1978+t1811+t2070+t2176+t2413+t2442; + t1819 = t2131*t2024; + t2146 = t2041+t1874+t2034+t1819+y*t2195+t2176+t2380; + t1946 = t2098*t2347; + t2145 = t1829+t1946+t2169+t2178+t2333; + t2144 = t2173+t2179+t2319+t2420; + t2143 = t2003+t1821+t2040+t2119*t2236+t1819+t2185+t2436; + t2142 = t2173+t2178+t2310+t2397; + t1967 = t2098*t2348; + t2141 = t1888+t1967+t2167+t2169+t2296; + t2140 = t1920+t2086+t2000+t1944+t2185+t2282+t2413; + t1862 = y*t2225; + t2139 = t1862+t1829+t2179+t2258+t2260+t2437; + t2138 = t2212+t2049+t1774+t1975+t2386+((y+z)*t2120+1.0+t2016+t2443)*x; + t2137 = t1799+t2170+t2243+t1820+t2063+t2356+(t2094+t2331)*z; + t2123 = RATIONAL(-2.0,3.0); + t2109 = RATIONAL(2.0,1.0); + t2103 = RATIONAL(1.0,54.0); + t2089 = RATIONAL(-1.0,216.0); + t2042 = z*t2293; + t1894 = t2133*t2288; + t1891 = t2089*t2291; + t1859 = t2121*t2254; + t1855 = t2133*t2058; + t1796 = z*t2043; + t1784 = t2125*t2254; + t1748 = t2096*t2229; + t1742 = t2096*t2234; + t1708 = t2092*t2234; + t1707 = t2133*t2226; + coeffs_dx->coeff_m1_m1_m1 = t2357+t2222+(t2100*t2134+(RATIONAL(-1.0,27.0) ++t2095*t2130)*z)*y+t1748+t2133*t2339+t1701+t1894+t1742+t2359+t2434; + coeffs_dx->coeff_0_m1_m1 = t1707+(RATIONAL(-2.0,9.0)*t2353+t2444*t2107)*x ++t2163+t2215+t2220+t2362+t2379+t2449; + coeffs_dx->coeff_p1_m1_m1 = t1870+t1865+t1922+t2152+t1921+t2219+t2375+ +t2426+t2434+t2448; + coeffs_dx->coeff_p2_m1_m1 = t2161+t2130*t1900+t1891+t2162+t2400+t2415; + coeffs_dx->coeff_m1_0_m1 = t2164+t1924+(t2267+t2102)*t2134+t1953+(t2108+ +t2107*t2132+t2189*t2130)*z+t2147+t1804+t2253+t2361+t2393; + coeffs_dx->coeff_0_0_m1 = t1890+(-t2131+t2191*t2134+(t2123*t2132+t2124)*z +)*x+t1889+t1966+t1970+t2149+t1967+t2182+t2276+t2417+t2423+t2439; + coeffs_dx->coeff_p1_0_m1 = t2166+t1816+t2146+t2204+t2361+t2382+t2404+ +t2418+t2419; + coeffs_dx->coeff_p2_0_m1 = t2192*t2351+t2148+t1931+t2271+t2367+t2385; + coeffs_dx->coeff_m1_p1_m1 = t1778+t2153+t2221+t2223+t2357+t2372+t2411; + coeffs_dx->coeff_0_p1_m1 = t1855+t1858-t2309+t1859+t2154+t2270+t2296+ +t2302+t2327+t2379+t2383; + coeffs_dx->coeff_p1_p1_m1 = t2151+t1799+t1797+t2201+t2210+t2276+t2373+ +t2375; + coeffs_dx->coeff_p2_p1_m1 = t1705+t2157+t1857+t1943+t1730+t1947+t2259+ +t2400+t2421; + coeffs_dx->coeff_m1_p2_m1 = t1913+t2165+t2103*t2347+t2306+t2371+t2415+ +t2446; + coeffs_dx->coeff_0_p2_m1 = t2148+t2133*t2283+t1749+t2255+t2391; + coeffs_dx->coeff_p1_p2_m1 = t1950+t1949+t1717+t2160+t2253+t2371+t2421; + coeffs_dx->coeff_p2_p2_m1 = t1742+t2089*t2348+t2175+t2177+t2407; + coeffs_dx->coeff_m1_m1_0 = t2140+t2450*t2133+t2223+(t2108+t2107*t2131+( +t2105+t2070)*t2130)*y+t1725+t1738+t1735+t2224+t2360+t2424+t2449; + coeffs_dx->coeff_0_m1_0 = t2150+t1961+t2183+(-t2132+(t2125*t2131+t2121)* +t2133+(t2123*t2131+t2124)*y)*x+t1946+t1889+t1859+t2067+t1804+t2328+t2363+t2403; + coeffs_dx->coeff_p1_m1_0 = t2143+t2171+t1816+t2210+t2290+t2360+t2366+ +t2429; + coeffs_dx->coeff_p2_m1_0 = t2287+t2142+t1972+(t2104+t2325)*t2344+t2368+ +t2378; + coeffs_dx->coeff_m1_0_0 = t1862+t2125+(t2329-x+t2121)*t2132+t2315+t2302+ +t1995+(-x+t2187*t2130+t2191)*t2131+t2042+t2171+t2363+t2057+t2138+t2394+t2418+ +t2439; + coeffs_dx->coeff_0_0_0 = (t2257+t2218)*y+t2300*t2111+t2369+(-t2133+(t2134 +-z+t2109)*t2132+(t2109-y+t2122*t2132+t2133)*t2131+t2269)*x+(t2114*t2133+t2110)* +z+(t2118+t2117*z+t2132*t2250+(t2132+t2131)*t2115+(t2119*z+t2117)*y)*t2130+t2156 ++t1990+t2380+t2381+t2186+t2427; + coeffs_dx->coeff_p1_0_0 = (-1.0+t2263-x)*t2132+(-x+t2295-t2341)*t2131+ +t1833+t2300*t2116+t2354+RATIONAL(1.0,1.0)+t2138+t2017+(t2112*z+t2193*t2131+( +t2113*z+t2112)*y+t2190)*t2130+t2396+t2430; + coeffs_dx->coeff_p2_0_0 = t1870+t2189*t2131+t2137+(t2186*t2131+t2187)* +t2130+t2192+t2364+t2402; + coeffs_dx->coeff_m1_p1_0 = t2140+t2183-t2309+t1934+t1910+t1985+t1787+ +t2205+t2366+t2408+t2433; + coeffs_dx->coeff_0_p1_0 = t2150+t2218*t2133+t1988+t1984+(t2115*t2131+ +t2118)*t2344+(-t2248+(t2109*t2131+t2269)*y+t2268)*x+t1986+t2412+t2416+t2430+ +t2432; + coeffs_dx->coeff_p1_p1_0 = (t2120+t2077)*t2133+t2143+(1.0+t2275-t2131- +t2350+(t2115+t2250)*t2130)*y+t2355+t2369+t2433+t2441; + coeffs_dx->coeff_p2_p1_0 = t1925+t2145+t2067+t2365+t2378+t2429; + coeffs_dx->coeff_m1_p2_0 = t1719+(t2095+t2317)*t2133+t2237+t2144+t2368+ +t2376; + coeffs_dx->coeff_0_p2_0 = t1854+t2174+((y+t2248)*t2121+(t2133+t2352)* +t2125)*x+t2320+t2356+t2364+t2399; + coeffs_dx->coeff_p1_p2_0 = t2139+t2057+t1788+t2365+t2376+t2408; + coeffs_dx->coeff_p2_p2_0 = t2281+(t2096*t2131+t2188)*y+t2155+t2314+t2424; + coeffs_dx->coeff_m1_m1_p1 = t1802+t2152+t1832+t1795+t1908+t1933+t1804+ +t2220+t2359+t2372; + coeffs_dx->coeff_0_m1_p1 = t1767-t2298+t2154+t1784+t2266+t2333+t2362+ +t2384+t2423; + coeffs_dx->coeff_p1_m1_p1 = t2204+t2038+t1865+t2358+t2202+t1858+t2320+ +t1832+t2373+t2403+t2409; + coeffs_dx->coeff_p2_m1_p1 = t1923+t1945+t1900+t2162+t2163+t2219; + coeffs_dx->coeff_m1_0_p1 = t2170+t2182-t2298+t2032+t1787+t2147+t2258+ +t2382+t2428+t2431; + coeffs_dx->coeff_0_0_p1 = t1798+t2039+(t2106*y+t2110)*t2134+t2127+t2354+ +t2193*t2351+(-t2334+(t2109*t2132-t2133+t2122)*z+t2318)*x+t2149+t1796+t2432; + coeffs_dx->coeff_p1_0_p1 = t2186*t2134+(t2307-t2132*x+t2190*t2130+t2341)* +z+t2146+t2355+t2381+t2431+t2447; + coeffs_dx->coeff_p2_0_p1 = t2141+t2370+t2385+t2404+t2417; + coeffs_dx->coeff_m1_p1_p1 = t1877+t1823+t1983+t1817+t2153+t1848+t1795+ +t2213+t2390+t2435+t2440; + coeffs_dx->coeff_0_p1_p1 = t2118*t2280+t2044+(t2268*z+(t2122*z+t2318)*y)* +x+t2156+t2215+t2383+t2384+t2441+t2447; + coeffs_dx->coeff_p1_p1_p1 = t2151+(t2115*t2351+t2263+z)*y+t2233+t2017+ +t1796+t2358+t2412+t2435; + coeffs_dx->coeff_p2_p1_p1 = t1932+t2157+t1767+t1799+t1961+t1844+t1942+ +t2158; + coeffs_dx->coeff_m1_p2_p1 = t2164+t1801+t1900+t1752+t2165+t2221; + coeffs_dx->coeff_0_p2_p1 = t1890+t1855+t2141+t2255+t2392; + coeffs_dx->coeff_p1_p2_p1 = t2013+t1801+t1882+t2160+t2166+t2201; + coeffs_dx->coeff_p2_p2_p1 = t1947+t1930+t2175+t2184+t2253; + coeffs_dx->coeff_m1_m1_p2 = t2161+t1708+t2103*t2348+t2294+t2377+t2389+ +t2446; + coeffs_dx->coeff_0_m1_p2 = t1754+t2108*t2254+t2142+t2321+t2391; + coeffs_dx->coeff_p1_m1_p2 = t2159+t2243+t2282+t2299+t2319+t2377; + coeffs_dx->coeff_p2_m1_p2 = t2089*t2347+t1748+t2177+t2181+t2405; + coeffs_dx->coeff_m1_0_p2 = z*t2301+t1720+t2144+(t2095+t2337)*t2134+t2367+ +t2374; + coeffs_dx->coeff_0_0_p2 = ((t2334+z)*t2121+(t2346+t2134)*t2125)*x+t2137+ +t1802+t2399; + coeffs_dx->coeff_p1_0_p2 = t2139+t1823+t2042+t2370+t2374+t2428; + coeffs_dx->coeff_p2_0_p2 = t2274+(t2096*t2132+t2188)*z+t2155+t2289+t2393; + coeffs_dx->coeff_m1_p1_p2 = t2159+t2259+t2272+t2310+t2389+t2398; + coeffs_dx->coeff_0_p1_p2 = t2145+t1784+t1804+t2321+t2392; + coeffs_dx->coeff_p1_p1_p2 = t2158+t1882+t1834+t1820+t2213+t2294+t2398; + coeffs_dx->coeff_p2_p1_p2 = t2172+t2181+t2299+t2397; + coeffs_dx->coeff_m1_p2_p2 = t1894+t2092*t2280+t2180+t2388+t2405+t2407; + coeffs_dx->coeff_0_p2_p2 = x*t1953+t1707+t2155+t2326; + coeffs_dx->coeff_p1_p2_p2 = t2172+t2180+t2272+t2420; + coeffs_dx->coeff_p2_p2_p2 = t1891+t1708+z*t2256+(t2091*t2134+(t2285+t2089 +)*z)*y+t2306; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..70ed1db --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,891 @@ +fp t4232; +fp t4245; +fp t4248; +fp t4207; +fp t4229; +fp t4246; +fp t4201; +fp t4171; +fp t4434; +fp t4247; +fp t4198; +fp t4173; +fp t4206; +fp t4433; +fp t4368; +fp t4227; +fp t4313; +fp t4066; +fp t4231; +fp t4365; +fp t4242; +fp t4432; +fp t4230; +fp t4316; +fp t4070; +fp t4228; +fp t4375; +fp t4185; +fp t4063; +fp t4431; +fp t4373; +fp t4160; +fp t4314; +fp t4364; +fp t4134; +fp t4430; +fp t4168; +fp t4120; +fp t4429; +fp t4243; +fp t4360; +fp t4428; +fp t4233; +fp t4354; +fp t4219; +fp t4196; +fp t4147; +fp t4427; +fp t4317; +fp t4019; +fp t4136; +fp t4021; +fp t4426; +fp t4218; +fp t4199; +fp t4328; +fp t4155; +fp t4425; +fp t4226; +fp t4326; +fp t4144; +fp t4034; +fp t4141; +fp t4026; +fp t4424; +fp t4363; +fp t4163; +fp t4038; +fp t4223; +fp t4324; +fp t4162; +fp t4052; +fp t4423; +fp t4186; +fp t4057; +fp t4154; +fp t4422; +fp t4214; +fp t4330; +fp t4108; +fp t3992; +fp t4216; +fp t4337; +fp t4107; +fp t4421; +fp t4203; +fp t4420; +fp t4133; +fp t4419; +fp t4418; +fp t4183; +fp t4151; +fp t4058; +fp t4417; +fp t4119; +fp t4042; +fp t4149; +fp t4043; +fp t4416; +fp t4080; +fp t4415; +fp t4414; +fp t4413; +fp t4412; +fp t4159; +fp t4411; +fp t4195; +fp t4137; +fp t4410; +fp t4033; +fp t4409; +fp t4237; +fp t4200; +fp t4123; +fp t4211; +fp t4319; +fp t4104; +fp t4408; +fp t4350; +fp t4156; +fp t4407; +fp t4220; +fp t4383; +fp t4165; +fp t4406; +fp t4142; +fp t4205; +fp t4128; +fp t4405; +fp t4210; +fp t4121; +fp t4404; +fp t4140; +fp t4208; +fp t4403; +fp t4380; +fp t4174; +fp t4118; +fp t4402; +fp t4401; +fp t4177; +fp t4062; +fp t4400; +fp t4197; +fp t4127; +fp t4399; +fp t4039; +fp t4040; +fp t4398; +fp t4349; +fp t4397; +fp t4093; +fp t3988; +fp t4025; +fp t4370; +fp t4158; +fp t4028; +fp t4396; +fp t4395; +fp t4179; +fp t4394; +fp t4333; +fp t4393; +fp t4047; +fp t4122; +fp t4060; +fp t4392; +fp t4175; +fp t4176; +fp t4204; +fp t4191; +fp t4193; +fp t4327; +fp t4391; +fp t4369; +fp t4125; +fp t4046; +fp t4390; +fp t4367; +fp t4132; +fp t4389; +fp t4145; +fp t4344; +fp t4388; +fp t4030; +fp t4029; +fp t4387; +fp t4315; +fp t4087; +fp t4386; +fp t4238; +fp t4385; +fp t4384; +fp t4244; +fp t4241; +fp t4382; +fp t4221; +fp t4381; +fp t4379; +fp t4212; +fp t4378; +fp t4239; +fp t4213; +fp t4377; +fp t4376; +fp t4374; +fp t4372; +fp t4371; +fp t4215; +fp t4366; +fp t4202; +fp t4180; +fp t4094; +fp t4322; +fp t4095; +fp t4362; +fp t4361; +fp t4192; +fp t4325; +fp t4110; +fp t4359; +fp t4146; +fp t4055; +fp t4358; +fp t4357; +fp t4356; +fp t4355; +fp t4153; +fp t4077; +fp t4017; +fp t4353; +fp t4352; +fp t4167; +fp t4054; +fp t4157; +fp t4011; +fp t4351; +fp t4031; +fp t4348; +fp t4089; +fp t4092; +fp t4347; +fp t4338; +fp t4014; +fp t4045; +fp t4346; +fp t4345; +fp t4090; +fp t3980; +fp t3987; +fp t4343; +fp t4161; +fp t4098; +fp t4342; +fp t4099; +fp t4105; +fp t4341; +fp t4318; +fp t4106; +fp t3981; +fp t4112; +fp t4340; +fp t4096; +fp t3989; +fp t4339; +fp t4103; +fp t4336; +fp t4182; +fp t4036; +fp t4181; +fp t4015; +fp t4335; +fp t4091; +fp t4334; +fp t4240; +fp t4332; +fp t4234; +fp t4331; +fp t4329; +fp t4114; +fp t4217; +fp t4323; +fp t4321; +fp t4005; +fp t3994; +fp t4320; +fp t4130; +fp t4131; +fp t4135; +fp t4097; +fp t4101; +fp t4109; +fp t4113; +fp t4115; +fp t4184; +fp t4164; +fp t4126; +fp t4150; +fp t4312; +fp t4311; +fp t4129; +fp t4102; +fp t4310; +fp t4309; +fp t3996; +fp t4022; +fp t4308; +fp t4044; +fp t4307; +fp t4194; +fp t4306; +fp t4305; +fp t3985; +fp t4304; +fp t4041; +fp t4303; +fp t4302; +fp t4301; +fp t4300; +fp t4299; +fp t4012; +fp t4298; +fp t4297; +fp t4296; +fp t4224; +fp t4295; +fp t4294; +fp t4293; +fp t4292; +fp t4291; +fp t4290; +fp t4079; +fp t4289; +fp t4288; +fp t4287; +fp t4286; +fp t4008; +fp t4064; +fp t4285; +fp t4284; +fp t3997; +fp t4283; +fp t4282; +fp t4006; +fp t4281; +fp t4280; +fp t4279; +fp t4277; +fp t4276; +fp t4048; +fp t4275; +fp t4274; +fp t4273; +fp t4272; +fp t4271; +fp t4074; +fp t4078; +fp t4270; +fp t4082; +fp t4081; +fp t4269; +fp t4268; +fp t4267; +fp t4266; +fp t4236; +fp t4265; +fp t4010; +fp t4264; +fp t4076; +fp t4263; +fp t4088; +fp t4262; +fp t4061; +fp t4261; +fp t4260; +fp t4259; +fp t4258; +fp t4257; +fp t4256; +fp t4255; +fp t4254; +fp t4253; +fp t4252; +fp t4251; +fp t4235; +fp t4222; +fp t4189; +fp t4172; +fp t4170; +fp t4166; +fp t4100; +fp t4059; +fp t4049; +fp t4037; +fp t4035; +fp t4027; +fp t4023; +fp t4004; +fp t4003; +fp t4001; +fp t3998; +fp t3990; +fp t3986; +fp t3983; +fp t3982; + t4232 = RATIONAL(-1.0,2.0); + t4245 = z*z; + t4248 = z*t4245; + t4207 = t4232*t4248; + t4229 = RATIONAL(1.0,2.0); + t4246 = y*y; + t4201 = t4229*t4246; + t4171 = t4248*t4201; + t4434 = t4207+t4171; + t4247 = t4246*y; + t4198 = t4229*t4245; + t4173 = t4247*t4198; + t4206 = t4232*t4247; + t4433 = t4173+t4206; + t4368 = x*t4247; + t4227 = RATIONAL(3.0,4.0); + t4313 = t4227*t4368; + t4066 = t4248*t4313; + t4231 = RATIONAL(3.0,2.0); + t4365 = x*t4231; + t4242 = y*z; + t4432 = t4365*t4242+t4066; + t4230 = RATIONAL(-3.0,4.0); + t4316 = t4230*t4368; + t4070 = t4248*t4316; + t4228 = RATIONAL(-3.0,2.0); + t4375 = x*t4228; + t4185 = t4245*t4375; + t4063 = y*t4185; + t4431 = t4070+t4063; + t4373 = x*t4248; + t4160 = t4228*t4373; + t4314 = t4227*t4373; + t4364 = t4246*x; + t4134 = t4231*t4364; + t4430 = y*t4314+t4248*t4134+t4160; + t4168 = t4228*t4368; + t4120 = t4245*t4365; + t4429 = t4168+z*t4313+t4247*t4120; + t4243 = t4246*t4245; + t4360 = t4246+t4245; + t4428 = (-t4243-1.0+t4360)*x; + t4233 = RATIONAL(1.0,3.0); + t4354 = t4233*t4245; + t4219 = RATIONAL(1.0,6.0); + t4196 = t4219*t4247; + t4147 = t4245*t4196; + t4427 = y*t4354+t4147; + t4317 = t4230*t4364; + t4019 = t4245*t4317; + t4136 = z*t4201; + t4021 = x*t4136; + t4426 = t4019+t4021; + t4218 = RATIONAL(-1.0,6.0); + t4199 = t4218*t4248; + t4328 = t4219*t4246; + t4155 = t4248*t4328; + t4425 = (t4155+t4199)*x; + t4226 = RATIONAL(-1.0,4.0); + t4326 = t4247*t4226; + t4144 = t4245*t4326; + t4034 = x*t4144; + t4141 = x*t4196; + t4026 = z*t4141; + t4424 = t4034+t4026; + t4363 = t4246*z; + t4163 = t4218*t4363; + t4038 = x*t4163; + t4223 = RATIONAL(1.0,4.0); + t4324 = t4223*t4246; + t4162 = t4245*t4324; + t4052 = x*t4162; + t4423 = t4038+t4052; + t4186 = x*t4201; + t4057 = t4245*t4186; + t4154 = t4232*t4364; + t4422 = t4057+t4154; + t4214 = RATIONAL(-1.0,12.0); + t4330 = t4248*t4214; + t4108 = t4246*t4330; + t3992 = x*t4108; + t4216 = RATIONAL(1.0,18.0); + t4337 = t4248*t4216; + t4107 = y*t4337; + t4421 = x*t4107+t3992; + t4203 = t4218*t4247; + t4420 = (t4203+t4147)*x; + t4133 = t4232*x*t4245; + t4419 = t4057+t4133; + t4418 = t4108+t4163; + t4183 = x*t4198; + t4151 = t4232*t4243; + t4058 = x*t4151; + t4417 = t4183+t4058; + t4119 = y*t4199; + t4042 = x*t4119; + t4149 = t4248*t4324; + t4043 = x*t4149; + t4416 = t4042+t4043; + t4080 = t4245*t4316; + t4415 = t4080+t4173; + t4414 = t4433*x; + t4413 = t4058+t4186; + t4412 = t4434*x; + t4159 = t4245*t4203; + t4411 = x*t4159+t4141; + t4195 = t4232*z; + t4137 = x*t4195; + t4410 = t4137+t4021; + t4033 = t4248*t4317; + t4409 = t4171+t4033; + t4237 = RATIONAL(-1.0,3.0); + t4200 = t4237*z; + t4123 = y*t4200; + t4211 = RATIONAL(1.0,12.0); + t4319 = t4247*t4211; + t4104 = t4248*t4319; + t4408 = t4123+t4104; + t4350 = t4246*t4248; + t4156 = t4226*t4350; + t4407 = t4136+t4156; + t4220 = RATIONAL(-1.0,9.0); + t4383 = z*t4220; + t4165 = y*t4383; + t4406 = t4247*t4337+t4165; + t4142 = t4246*t4199; + t4205 = t4219*t4248; + t4128 = x*t4205; + t4405 = t4128+x*t4142; + t4210 = t4229*t4247; + t4121 = t4245*t4206; + t4404 = (t4210+t4121)*x; + t4140 = t4246*t4207; + t4208 = t4229*t4248; + t4403 = (t4140+t4208)*x; + t4380 = t4233*z; + t4174 = y*t4380; + t4118 = t4248*t4196; + t4402 = t4174+t4118; + t4401 = t4123+t4118; + t4177 = y*t4208; + t4062 = x*t4177; + t4400 = t4043+t4062; + t4197 = t4232*y; + t4127 = z*t4197; + t4399 = t4127+t4177; + t4039 = x*t4123; + t4040 = y*t4183; + t4398 = t4039+t4040; + t4349 = t4233*t4246; + t4397 = t4155+z*t4349; + t4093 = t4245*t4319; + t3988 = x*t4093; + t4025 = t4226*x*t4243; + t4370 = y*t4245; + t4158 = t4219*t4370; + t4028 = x*t4158; + t4396 = t3988+t4025+t4028; + t4395 = t4136+t4140-t4246; + t4179 = t4247*t4365; + t4394 = z*t4316+t4179+t4247*t4185; + t4333 = t4158+t4159; + t4393 = t4333+t4218*y+t4196; + t4047 = t4246*t4314; + t4122 = t4228*t4364; + t4060 = z*t4122; + t4392 = t4047+t4060+t4019; + t4175 = t4248*t4203; + t4176 = z*t4196; + t4204 = t4218*z; + t4191 = y*t4204; + t4193 = y*t4205; + t4327 = t4191+t4193; + t4391 = t4175+t4176+t4327; + t4369 = t4223*z; + t4125 = t4247*t4369; + t4046 = x*t4125; + t4390 = t4046+t4414; + t4367 = y*t4248; + t4132 = t4248*t4365; + t4389 = t4230*x*t4367+t4248*t4122+t4132; + t4145 = z*t4328; + t4344 = t4142+t4145; + t4388 = t4205+t4344+t4204; + t4030 = x*t4156; + t4029 = z*t4154; + t4387 = t4030+t4029+t4397; + t4315 = t4227*t4364; + t4087 = t4245*t4134; + t4386 = t4122+t4087+z*t4315+t4033; + t4238 = x*t4370; + t4385 = t4080+t4227*t4238+t4087+t4185; + t4384 = t4247*t4208+t4375*t4242+t4070+t4242; + t4244 = y*x; + t4241 = x*z; + t4382 = t4219*y; + t4221 = RATIONAL(1.0,9.0); + t4381 = z*t4221; + t4379 = x*t4218; + t4212 = RATIONAL(-1.0,18.0); + t4378 = z*t4212; + t4239 = y*t4241; + t4213 = RATIONAL(-1.0,36.0); + t4377 = z*t4213; + t4376 = y-t4247; + t4374 = z*t4214; + t4372 = z*t4216; + t4371 = x*t4229; + t4215 = RATIONAL(1.0,36.0); + t4366 = y*t4215; + t4202 = t4237*y; + t4180 = y*t4369; + t4094 = t4247*t4330; + t4322 = t4248*t4211; + t4095 = y*t4322; + t4362 = t4094+t4095; + t4361 = -t4244+t4238; + t4192 = y*t4371; + t4325 = t4245*t4214; + t4110 = y*t4325; + t4359 = t3988+x*t4110; + t4146 = z*t4206; + t4055 = x*t4146; + t4358 = t4055+t4247*t4380; + t4357 = t4093+t4110; + t4356 = t4247*t4245; + t4355 = t4223*t4248; + t4153 = y*t4207; + t4077 = x*t4153; + t4017 = z*t4192; + t4353 = t4077+t4017; + t4352 = t4248*t4213; + t4167 = y*t4355; + t4054 = x*t4167; + t4157 = t4248*t4326; + t4011 = x*t4157; + t4351 = t4054+t4011; + t4031 = y*t4133; + t4348 = t4029+t4031; + t4089 = y*t4372; + t4092 = t4247*t4352; + t4347 = t4089+t4092; + t4338 = z*t4379; + t4014 = y*t4338; + t4045 = y*t4128; + t4346 = t4014+t4045; + t4345 = t4245*t4315+t4151; + t4090 = t4247*t4374; + t3980 = x*t4090; + t3987 = x*t4104; + t4343 = t3980+t3987; + t4161 = y*t4381; + t4098 = z*t4319; + t4342 = t4094+t4098; + t4099 = t4246*t4322; + t4105 = t4214*t4363; + t4341 = t4099+t4105; + t4318 = t4247*t4215; + t4106 = t4248*t4318; + t3981 = x*t4106; + t4112 = t4247*t4377; + t4340 = x*t4112+t3981; + t4096 = t4248*t4366; + t3989 = x*t4092; + t4339 = x*t4096+t3989; + t4103 = t4247*t4372; + t4336 = t4103+t4107; + t4182 = z*t4326; + t4036 = x*t4182; + t4181 = t4247*t4355; + t4015 = x*t4181; + t4335 = t4036+t4015; + t4091 = t4211*t4242; + t4334 = t4030+t4324*t4241; + t4240 = x*t4363; + t4332 = t4240-t4241; + t4234 = RATIONAL(-2.0,1.0); + t4331 = t4234-t4248; + t4329 = y*t4378; + t4114 = z*t4366; + t4217 = RATIONAL(-3.0,1.0); + t4323 = t4217*t4245; + t4321 = t4248*t4212; + t4005 = x*t4098; + t3994 = x*t4094; + t4320 = t4005+t3994; + t4130 = z*t4382; + t4131 = z*t4203; + t4135 = z*t4210; + t4097 = t4247*t4378; + t4101 = z*t4318; + t4109 = y*t4321; + t4113 = y*t4352; + t4115 = y*t4330; + t4184 = t4226*t4367; + t4164 = t4218*t4370; + t4126 = t4226*t4370; + t4150 = t4226*t4363; + t4312 = t3987+t4424; + t4311 = t4055+t4034+t4015; + t4129 = t4223*t4356; + t4102 = t4247*t4325; + t4310 = t4042+t3987+t3992; + t4309 = t3994+t4416; + t3996 = x*t4102; + t4022 = x*t4131; + t4308 = t3996+t4022+t3987; + t4044 = x*t4174; + t4307 = t4044+t4031+t4045; + t4194 = y*t4198; + t4306 = t4144+t4162+t4194; + t4305 = t3996+t3981+x*t4103; + t3985 = x*t4099; + t4304 = t3985+t3989+x*t4109; + t4041 = x*t4129; + t4303 = t4041+t4022+t3994; + t4302 = t4030+t4021+t4052; + t4301 = t4102+t4162+t4164; + t4300 = t4011+t4400; + t4299 = t4239+t4077+t4040; + t4012 = x*t4135; + t4298 = t4041+t4011+t4012; + t4297 = t4354+t4237; + t4296 = t4233+t4237*t4245; + t4224 = RATIONAL(3.0,1.0); + t4295 = t4224+t4217*t4246; + t4294 = t4237*t4246+t4233; + t4293 = t4237+t4349; + t4292 = t4217+t4224*t4246; + t4291 = t4243+t4194+t4121-t4245; + t4290 = t4201+t4149+t4150+t4151; + t4079 = x*t4184; + t4289 = t4015+t4079+t4403; + t4288 = t4129+t4126+t4198+t4151; + t4287 = t4115+t4104+t4090+t4091; + t4286 = t4351+t4412; + t4008 = y*t4120; + t4064 = z*t4134; + t4285 = t4066+t4248*t4206+t4008+t4064; + t4284 = t4335+t4404; + t3997 = x*t4115; + t4283 = x*t4091+t3997+t4343; + t4282 = t4113+t4114+t4112+t4106; + t4006 = x*t4095; + t4281 = t4006+t4374*t4244+t4320; + t4280 = t4294*z; + t4279 = t4296*y; + t4277 = t4096+t4097+t4347+t4357; + t4276 = t4191+t4176+t4357+t4362; + t4048 = t4223*t4238; + t4275 = t4048+t4017+t4079+t4311; + t4274 = t4048+t4014+t3997+t4312; + t4273 = t4327+t4341+t4342; + t4272 = t4101+t4109+t4341+t4347; + t4271 = t4334+t4343+t4346; + t4074 = x*t4150; + t4078 = x*t4130; + t4270 = t4074+t4078+t4005+t4309; + t4082 = x*t4126; + t4081 = y*t4137; + t4269 = t4054+t4082+t4081+t4298; + t4268 = t4006+t4082+t4078+t4303; + t4267 = t4046+t4081+t4074+t4300; + t4266 = t4334+t4335+t4353; + t4236 = RATIONAL(2.0,3.0); + t4265 = -t4239+t4175+t4015+t4236*t4242+t4345; + t4010 = t4245*t4122; + t4264 = t4243+t4047+z*t4317+t4134+t4010+t4395; + t4076 = t4226*t4239; + t4263 = t4046+t4076+t4287+t4351; + t4088 = t4245*t4313; + t4262 = t4230*t4238+t4088+t4120+t4010+t4291; + t4061 = x*t4180; + t4261 = x*t4197+t4061+t4040+t4079+t4284; + t4260 = t4281+t4287; + t4259 = t4153+t4146+t4181+t4242+t4306+t4407; + t4258 = t4193+t4131+t4301+t4407+t4408; + t4257 = t4161+t4106+t4301+t4336+t4418; + t4256 = t4176+t4119+t4306+t4408+t4418; + t4255 = t4167+t4127+t4135+t4157+t4288+t4434; + t4254 = t4125+t4157+t4290+t4399+t4433; + t4253 = t4199+t4200+t4130+t4131+t4288+t4362+t4397; + t4252 = t4202+t4130+t4203+t4119+t4290+t4342+t4427; + t4251 = t4184+t4208+RATIONAL(1.0,1.0)+t4210+t4195+t4180+t4197+t4181+t4182 ++t4291+t4395; + t4235 = RATIONAL(-2.0,3.0); + t4222 = RATIONAL(2.0,1.0); + t4189 = t4233*t4367; + t4172 = t4247*t4200; + t4170 = z*t4371; + t4166 = t4248*t4202; + t4100 = t4247*t4321; + t4059 = y*t4132; + t4049 = y*t4160; + t4037 = x*t4164; + t4035 = x*t4145; + t4027 = z*t4179; + t4023 = z*t4168; + t4004 = x*t4329; + t4003 = t4211*t4238; + t4001 = x*t4113; + t3998 = x*t4089; + t3990 = x*t4097; + t3986 = t4211*t4240; + t3983 = x*t4101; + t3982 = x*t4105; + coeffs_dxx->coeff_m1_m1_m1 = t4035+x*t4165+t4257+t3990+t4304+t4396; + coeffs_dxx->coeff_0_m1_m1 = t4100+t4247*t4383+(t4220*t4248+RATIONAL(-2.0, +9.0)*z)*y+t4307+t4312+t4345+t4387+t4427; + coeffs_dxx->coeff_p1_m1_m1 = t4257+t4303+t4398+t4416+t4426; + coeffs_dxx->coeff_p2_m1_m1 = t4037+x*t4161+t4305+t4421+t4423; + coeffs_dxx->coeff_m1_0_m1 = x*t4280+t4253+t4274+t4405+t4419; + coeffs_dxx->coeff_0_0_m1 = t4262+(t4236+t4235*t4246)*z+t4294*t4248+t4119+ +t4017+t4286+t4332+t4358+t4401; + coeffs_dxx->coeff_p1_0_m1 = t4012+t4081+t4253+t4289-t4332+t4385; + coeffs_dxx->coeff_p2_0_m1 = t4293*t4241+t4268+t4417+t4425; + coeffs_dxx->coeff_m1_p1_m1 = t3985+t4256+t4035+t4025+t4303+t4307; + coeffs_dxx->coeff_0_p1_m1 = t4189+t4012+t4008+t4077-t4370+t4172+t4265+ +t4387+t4415; + coeffs_dxx->coeff_p1_p1_m1 = t4055+t4256+t4088+t4239+t4063+t4300+t4426; + coeffs_dxx->coeff_p2_p1_m1 = t4310+t4398+t4423+t4424; + coeffs_dxx->coeff_m1_p2_m1 = t4003+t4004+t4001+t4277+t4305; + coeffs_dxx->coeff_0_p2_m1 = t4109+t4247*t4381+t4268+t4333+t4406; + coeffs_dxx->coeff_p1_p2_m1 = t4274+t4277; + coeffs_dxx->coeff_p2_p2_m1 = t3998+t3990+t4339+t4359; + coeffs_dxx->coeff_m1_m1_0 = x*t4279+t4252+t4271+t4411+t4422; + coeffs_dxx->coeff_0_m1_0 = t4189+t4011+t4264+t4131+(t4236+t4235*t4245)*y+ +t4296*t4247+t4353+t4361+t4390+t4401; + coeffs_dxx->coeff_p1_m1_0 = t4252+t4081+t4062+t4284-t4361+t4386; + coeffs_dxx->coeff_p2_m1_0 = t4297*t4244+t4270+t4413+t4420; + coeffs_dxx->coeff_m1_0_0 = t4251+t4170+t4192+t4076+t4428+t4286+t4348+ +t4390; + coeffs_dxx->coeff_0_0_0 = z+t4285+(t4234*t4246+t4222-t4376)*t4245+(t4248+ +t4222-z)*t4246+(t4228*z+t4292*t4245+(t4228+t4227*z)*y+t4295)*x+t4135+t4331+ +t4376+t4389+t4394+t4399; + coeffs_dxx->coeff_p1_0_0 = (t4231*z+t4217+t4246*t4323+t4360*t4224+(t4230* +z+t4231)*y)*x+t4251+t4060+t4429+t4430+t4431; + coeffs_dxx->coeff_p2_0_0 = -t4428+t4261+t4403+t4410; + coeffs_dxx->coeff_m1_p1_0 = y+t4254-t4370+t4266+t4361+t4404+t4422; + coeffs_dxx->coeff_0_p1_0 = t4247+t4059-t4356+t4264+t4146+(t4222*t4245+( +t4323+t4224)*x+t4331)*y+t4384+t4429; + coeffs_dxx->coeff_p1_p1_0 = t4049+(-t4245+1.0+(t4217+t4224*t4245)*x)*y+ +t4254+t4386+t4394+t4432; + coeffs_dxx->coeff_p2_p1_0 = t4267-t4361+t4413+t4414; + coeffs_dxx->coeff_m1_p2_0 = x*t4382+t4037+t4260+t4393+t4420; + coeffs_dxx->coeff_0_p2_0 = t4297*t4247+t4279+t4261+t4391; + coeffs_dxx->coeff_p1_p2_0 = t4263+t4192+t4031+t4393+t4414; + coeffs_dxx->coeff_p2_p2_0 = y*t4379+t4028+t4283+t4411; + coeffs_dxx->coeff_m1_m1_p1 = t4044+t4029+t4026+t4258+t4309+t4396; + coeffs_dxx->coeff_0_m1_p1 = t4034+t4062+t4031+t4064+t4166+t4265-t4363+ +t4358+t4409+t4427; + coeffs_dxx->coeff_p1_m1_p1 = t4258+t4298+t4299+t4392; + coeffs_dxx->coeff_p2_m1_p1 = t4045+t4039+t4037+t4302+t4308; + coeffs_dxx->coeff_m1_0_p1 = z+t4255-t4363+t4275+t4332+t4403+t4419; + coeffs_dxx->coeff_0_0_p1 = t4262+(-t4247+t4234+t4222*t4246+t4295*x)*z+ +t4248+t4153-t4350+t4027+t4384+t4430; + coeffs_dxx->coeff_p1_0_p1 = t4023+(1.0-t4246+t4292*x)*z+t4255+t4385+t4389 ++t4432; + coeffs_dxx->coeff_p2_0_p1 = t4269-t4332+t4412+t4417; + coeffs_dxx->coeff_m1_p1_p1 = t4259+t4025-t4239+t4298+t4348+t4400; + coeffs_dxx->coeff_0_p1_p1 = t4049+t4023+(t4247-t4246)*z+(t4248-t4245+( +t4224*x+t4234)*z)*y+t4285+t4345+t4409+t4415; + coeffs_dxx->coeff_p1_p1_p1 = t4217*t4239+t4059+t4259+t4088+t4027+t4392+ +t4431; + coeffs_dxx->coeff_p2_p1_p1 = t4299+t4302+t4311; + coeffs_dxx->coeff_m1_p2_p1 = t3997+t4003+t4078+t4276+t4308; + coeffs_dxx->coeff_0_p2_p1 = t4119+t4172+t4269+t4333+t4402; + coeffs_dxx->coeff_p1_p2_p1 = t4275+t4276; + coeffs_dxx->coeff_p2_p2_p1 = t3994+t4014+t4026+t4006+t4359; + coeffs_dxx->coeff_m1_m1_p2 = t4004+t3986+t4272+t4340+t4421; + coeffs_dxx->coeff_0_m1_p2 = t4221*t4367+t4097+t4270+t4344+t4406; + coeffs_dxx->coeff_p1_m1_p2 = t4271+t4272; + coeffs_dxx->coeff_p2_m1_p2 = t3982+t3998+t3983+t4304; + coeffs_dxx->coeff_m1_0_p2 = t4219*t4241+t4038+t4260+t4388+t4425; + coeffs_dxx->coeff_0_0_p2 = t4036+t4061+t4293*t4248+t4280+t4289+t4391+ +t4410; + coeffs_dxx->coeff_p1_0_p2 = t4170+t4029+t4263+t4388+t4412; + coeffs_dxx->coeff_p2_0_p2 = t4035+t4338+t4283+t4405; + coeffs_dxx->coeff_m1_p1_p2 = t3980+t3986+t4078+t4273+t4310; + coeffs_dxx->coeff_0_p1_p2 = t4166+t4131+t4267+t4344+t4402; + coeffs_dxx->coeff_p1_p1_p2 = t4266+t4273; + coeffs_dxx->coeff_p2_p1_p2 = t3985+t3982+t4320+t4346; + coeffs_dxx->coeff_m1_p2_p2 = t4377*t4244+t3983+t4282+t4339; + coeffs_dxx->coeff_0_p2_p2 = t4329+t4100+t4283+t4336; + coeffs_dxx->coeff_p1_p2_p2 = t4281+t4282; + coeffs_dxx->coeff_p2_p2_p2 = t4001+x*t4114+t4340; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxy.compute.c new file mode 100644 index 0000000..fd76dbd --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxy.compute.c @@ -0,0 +1,1084 @@ +fp t4795; +fp t4830; +fp t4832; +fp t4756; +fp t4621; +fp t4820; +fp t4749; +fp t4613; +fp t5078; +fp t4831; +fp t4923; +fp t4829; +fp t4946; +fp t5071; +fp t4802; +fp t4777; +fp t4805; +fp t5077; +fp t4812; +fp t5076; +fp t4793; +fp t4810; +fp t4988; +fp t4684; +fp t4518; +fp t5075; +fp t4790; +fp t4731; +fp t4787; +fp t4922; +fp t4566; +fp t5074; +fp t4806; +fp t4960; +fp t4633; +fp t4963; +fp t4809; +fp t4647; +fp t5073; +fp t4742; +fp t4565; +fp t4789; +fp t4746; +fp t5072; +fp t4796; +fp t4917; +fp t4807; +fp t4909; +fp t5070; +fp t4593; +fp t5069; +fp t4783; +fp t4727; +fp t4726; +fp t5068; +fp t4936; +fp t4607; +fp t4506; +fp t4817; +fp t4992; +fp t4660; +fp t5067; +fp t4797; +fp t4764; +fp t4680; +fp t4760; +fp t4669; +fp t5066; +fp t4991; +fp t4631; +fp t4654; +fp t5065; +fp t4730; +fp t4616; +fp t4928; +fp t4759; +fp t4666; +fp t4808; +fp t4934; +fp t4682; +fp t5064; +fp t4893; +fp t4792; +fp t4482; +fp t4799; +fp t4753; +fp t5063; +fp t4775; +fp t4670; +fp t4919; +fp t4951; +fp t4956; +fp t4703; +fp t5062; +fp t4695; +fp t4939; +fp t4767; +fp t4755; +fp t4712; +fp t4504; +fp t4937; +fp t5061; +fp t4671; +fp t5060; +fp t5059; +fp t4641; +fp t4757; +fp t4702; +fp t4471; +fp t5058; +fp t4751; +fp t4885; +fp t4685; +fp t4659; +fp t5057; +fp t4677; +fp t4763; +fp t5056; +fp t4918; +fp t4804; +fp t4914; +fp t4704; +fp t5055; +fp t4984; +fp t4910; +fp t4798; +fp t4989; +fp t5054; +fp t4752; +fp t4901; +fp t4453; +fp t5053; +fp t4785; +fp t5052; +fp t4769; +fp t4664; +fp t4617; +fp t5051; +fp t5050; +fp t4791; +fp t4932; +fp t4587; +fp t5049; +fp t4768; +fp t4658; +fp t4479; +fp t5048; +fp t4788; +fp t5047; +fp t4559; +fp t5046; +fp t4653; +fp t4771; +fp t5045; +fp t4729; +fp t4990; +fp t5044; +fp t4761; +fp t4689; +fp t4548; +fp t4536; +fp t5043; +fp t4976; +fp t4889; +fp t4452; +fp t4750; +fp t4707; +fp t5042; +fp t4754; +fp t4640; +fp t5041; +fp t4642; +fp t4813; +fp t4762; +fp t4942; +fp t5040; +fp t4913; +fp t4507; +fp t5039; +fp t4618; +fp t4822; +fp t5038; +fp t4733; +fp t4782; +fp t4437; +fp t5037; +fp t4784; +fp t4734; +fp t4732; +fp t5036; +fp t4911; +fp t4460; +fp t5035; +fp t4644; +fp t4511; +fp t5034; +fp t4826; +fp t4823; +fp t5033; +fp t4994; +fp t4710; +fp t4451; +fp t5032; +fp t5031; +fp t4931; +fp t4698; +fp t5030; +fp t4597; +fp t5029; +fp t4679; +fp t4827; +fp t5028; +fp t4599; +fp t5027; +fp t4778; +fp t4745; +fp t4509; +fp t5026; +fp t5025; +fp t4629; +fp t4483; +fp t5024; +fp t4962; +fp t4610; +fp t4772; +fp t5023; +fp t4743; +fp t4601; +fp t4974; +fp t4953; +fp t4585; +fp t5022; +fp t4706; +fp t4672; +fp t4637; +fp t5021; +fp t4628; +fp t4481; +fp t4521; +fp t5020; +fp t4563; +fp t4440; +fp t4728; +fp t4609; +fp t4948; +fp t5019; +fp t4916; +fp t5018; +fp t5017; +fp t4738; +fp t5016; +fp t5015; +fp t4646; +fp t4486; +fp t5014; +fp t4696; +fp t4681; +fp t5013; +fp t4955; +fp t4912; +fp t4449; +fp t4662; +fp t5012; +fp t4776; +fp t4638; +fp t4484; +fp t5011; +fp t4957; +fp t4497; +fp t4907; +fp t4539; +fp t5010; +fp t4683; +fp t4505; +fp t4519; +fp t5009; +fp t4615; +fp t5008; +fp t4643; +fp t4514; +fp t5007; +fp t4676; +fp t4971; +fp t4709; +fp t5006; +fp t5005; +fp t4758; +fp t5004; +fp t4715; +fp t4461; +fp t4961; +fp t5003; +fp t4524; +fp t4673; +fp t4474; +fp t4938; +fp t5002; +fp t5001; +fp t5000; +fp t4529; +fp t4527; +fp t4993; +fp t4972; +fp t4800; +fp t4531; +fp t4999; +fp t4611; +fp t4998; +fp t4606; +fp t4491; +fp t4997; +fp t4828; +fp t4996; +fp t4995; +fp t4987; +fp t4562; +fp t4986; +fp t4985; +fp t4983; +fp t4700; +fp t4547; +fp t4982; +fp t4656; +fp t4981; +fp t4774; +fp t4572; +fp t4980; +fp t4979; +fp t4580; +fp t4978; +fp t4977; +fp t4975; +fp t4517; +fp t4973; +fp t4814; +fp t4651; +fp t4538; +fp t4825; +fp t4970; +fp t4675; +fp t4969; +fp t4968; +fp t4435; +fp t4966; +fp t4965; +fp t4634; +fp t4794; +fp t4964; +fp t4725; +fp t4781; +fp t4739; +fp t4959; +fp t4958; +fp t4954; +fp t4821; +fp t4898; +fp t4533; +fp t4952; +fp t4665; +fp t4950; +fp t4949; +fp t4947; +fp t4944; +fp t4570; +fp t4943; +fp t4941; +fp t4661; +fp t4940; +fp t4935; +fp t4705; +fp t4933; +fp t4455; +fp t4929; +fp t4927; +fp t4717; +fp t4512; +fp t4926; +fp t4925; +fp t4924; +fp t4639; +fp t4921; +fp t4920; +fp t4915; +fp t4608; +fp t4574; +fp t4908; +fp t4906; +fp t4714; +fp t4905; +fp t4904; +fp t4528; +fp t4468; +fp t4903; +fp t4902; +fp t4699; +fp t4652; +fp t4900; +fp t4627; +fp t4899; +fp t4678; +fp t4897; +fp t4477; +fp t4896; +fp t4895; +fp t4625; +fp t4894; +fp t4892; +fp t4891; +fp t4888; +fp t4890; +fp t4803; +fp t4887; +fp t4886; +fp t4884; +fp t4883; +fp t4882; +fp t4881; +fp t4880; +fp t4879; +fp t4878; +fp t4441; +fp t4877; +fp t4876; +fp t4875; +fp t4874; +fp t4873; +fp t4872; +fp t4871; +fp t4870; +fp t4779; +fp t4722; +fp t4869; +fp t4868; +fp t4740; +fp t4867; +fp t4450; +fp t4866; +fp t4786; +fp t4724; +fp t4865; +fp t4864; +fp t4546; +fp t4863; +fp t4571; +fp t4862; +fp t4765; +fp t4861; +fp t4860; +fp t4575; +fp t4859; +fp t4594; +fp t4858; +fp t4857; +fp t4573; +fp t4856; +fp t4855; +fp t4854; +fp t4515; +fp t4853; +fp t4852; +fp t4851; +fp t4719; +fp t4850; +fp t4454; +fp t4849; +fp t4848; +fp t4847; +fp t4846; +fp t4845; +fp t4844; +fp t4843; +fp t4842; +fp t4841; +fp t4840; +fp t4839; +fp t4838; +fp t4837; +fp t4836; +fp t4835; +fp t4834; +fp t4824; +fp t4819; +fp t4816; +fp t4811; +fp t4780; +fp t4701; +fp t4690; +fp t4583; +fp t4554; +fp t4550; +fp t4534; +fp t4469; +fp t4442; + t4795 = RATIONAL(-1.0,6.0); + t4830 = z*z; + t4832 = z*t4830; + t4756 = t4795*t4832; + t4621 = y*t4756; + t4820 = RATIONAL(-1.0,3.0); + t4749 = t4820*y; + t4613 = z*t4749; + t5078 = t4621+t4613; + t4831 = y*y; + t4923 = t4830*t4831; + t4829 = x*x; + t4946 = t4830*t4829; + t5071 = t4923+t4946; + t4802 = RATIONAL(1.0,4.0); + t4777 = t4802*z; + t4805 = RATIONAL(-1.0,4.0); + t5077 = t4777+t4805*t4832; + t4812 = RATIONAL(-1.0,2.0); + t5076 = t4812+t5077; + t4793 = RATIONAL(3.0,8.0); + t4810 = RATIONAL(3.0,2.0); + t4988 = t4810*t4829; + t4684 = y*t4988; + t4518 = t4830*t4684; + t5075 = t4518+t4793*t4946; + t4790 = RATIONAL(1.0,18.0); + t4731 = t4790*z; + t4787 = RATIONAL(-1.0,12.0); + t4922 = t4831*t4832; + t4566 = t4787*t4922; + t5074 = t4566+t4731; + t4806 = RATIONAL(3.0,4.0); + t4960 = t4806*t4831; + t4633 = z*t4960; + t4963 = t4829*t4832; + t4809 = RATIONAL(-3.0,4.0); + t4647 = t4809*t4963; + t5073 = t4633+t4647; + t4742 = t4787*z; + t4565 = t4831*t4742; + t4789 = RATIONAL(1.0,36.0); + t4746 = t4789*z; + t5072 = t4565+t4746; + t4796 = RATIONAL(-3.0,8.0); + t4917 = t4796*t4832; + t4807 = RATIONAL(-3.0,2.0); + t4909 = x*t4922; + t5070 = t4831*t4917+t4807*t4909; + t4593 = t4829*t4742; + t5069 = t4593+t4746; + t4783 = RATIONAL(1.0,12.0); + t4727 = t4783*z; + t4726 = t4787*t4832; + t5068 = t4727+t4726; + t4936 = t4812*t4832; + t4607 = x*t4936; + t4506 = t4831*t4607; + t4817 = RATIONAL(2.0,3.0); + t4992 = z*t4817; + t4660 = x*t4992; + t5067 = t4506+t4660; + t4797 = RATIONAL(1.0,6.0); + t4764 = t4797*t4832; + t4680 = y*t4764; + t4760 = t4795*y; + t4669 = z*t4760; + t5066 = t4669+t4680; + t4991 = t4829*z; + t4631 = t4806*t4991; + t4654 = t4809*t4922; + t5065 = t4631+t4654; + t4730 = t4787*t4830; + t4616 = t4802*t4946; + t4928 = t4730+t4616; + t4759 = t4812*z; + t4666 = y*t4759; + t4808 = RATIONAL(1.0,2.0); + t4934 = t4808*t4832; + t4682 = y*t4934; + t5064 = t4682+t4666; + t4893 = t4829*t4922; + t4792 = RATIONAL(-1.0,8.0); + t4482 = t4792*t4893; + t4799 = RATIONAL(1.0,9.0); + t4753 = t4799*z; + t5063 = t4482+t4753; + t4775 = t4805*t4830; + t4670 = t4806*t4946; + t4919 = t4775+t4670; + t4951 = t4829*t4793; + t4956 = t4809*t4831; + t4703 = z*t4956; + t5062 = t4703+(t4951+t4684)*t4832; + t4695 = t4806*t4923; + t4939 = (t4775+t4695)*x; + t4767 = t4802*t4832; + t4755 = t4812*x; + t4712 = z*t4755; + t4504 = x*t4654; + t4937 = t4712+t4504; + t5061 = t4939+t4937+x*t4767; + t4671 = t4809*t4991; + t5060 = t4793*t4922+t4810*t4909+t4671; + t5059 = t5078*x; + t4641 = t4809*t4946; + t4757 = t4808*t4830; + t4702 = x*t4757; + t4471 = y*t4702; + t5058 = y*t4641+t4471; + t4751 = t4797*t4830; + t4885 = t4751+t4795; + t4685 = t4829*t4956; + t4659 = t4829*t4960; + t5057 = t4830*t4659+t4685; + t4677 = t4812*t4946; + t4763 = t4808*t4829; + t5056 = t4677+t4763; + t4918 = t4831*t4792; + t4804 = RATIONAL(1.0,8.0); + t4914 = t4831*t4804; + t4704 = t4832*t4914; + t5055 = z*t4918+t4704; + t4984 = t4797*t4829; + t4910 = y*t4984; + t4798 = RATIONAL(-1.0,9.0); + t4989 = z*t4798; + t5054 = y*t4989+t4832*t4910; + t4752 = t4795*t4830; + t4901 = t4831*t4951; + t4453 = t4830*t4901; + t5053 = t4752+t4453; + t4785 = RATIONAL(-1.0,36.0); + t5052 = t4789*t4922+t4785*t4991; + t4769 = t4802*t4831; + t4664 = t4829*t4769; + t4617 = t4805*t4923; + t5051 = t4664+t4829*t4617; + t5050 = (t4617+t4752)*x; + t4791 = RATIONAL(1.0,24.0); + t4932 = t4829*t4791; + t4587 = z*t4932; + t5049 = t4831*t4587+RATIONAL(1.0,108.0)*t4832; + t4768 = t4812*t4829; + t4658 = z*t4768; + t4479 = y*t4658; + t5048 = t4613+t4479; + t4788 = RATIONAL(1.0,72.0); + t5047 = t4788*t4922+t4829*t4746; + t4559 = t4787*t4923; + t5046 = t4830*t4932+t4559; + t4653 = t4812*t4923; + t4771 = t4808*t4831; + t5045 = t4653+t4771; + t4729 = t4789*t4832; + t4990 = z*t4831; + t5044 = t4785*t4990+t4829*t4729; + t4761 = t4812*t4831; + t4689 = x*t4761; + t4548 = z*t4689; + t4536 = t4808*t4909; + t5043 = t4548+t4536; + t4976 = t4829*t4831; + t4889 = t4796*t4976; + t4452 = t4832*t4889; + t4750 = t4820*x; + t4707 = z*t4750; + t5042 = t4452+t4707; + t4754 = t4802*t4829; + t4640 = t4805*t4946; + t5041 = t4754+t4640; + t4642 = t4808*t4946; + t4813 = RATIONAL(1.0,3.0); + t4762 = t4813*t4830; + t4942 = (t4642+t4762)*y; + t5040 = t4942+t4617; + t4913 = x*t4923; + t4507 = t4810*t4913; + t5039 = t4507+t4793*t4923; + t4618 = z*t4754; + t4822 = y*t4991; + t5038 = t4618+t4822; + t4733 = t4785*t4832; + t4782 = RATIONAL(-1.0,24.0); + t4437 = t4782*t4893; + t5037 = t4829*t4733+t4437; + t4784 = RATIONAL(-1.0,18.0); + t4734 = t4784*z; + t4732 = t4783*t4830; + t5036 = t4734+t4732; + t4911 = z*t4976; + t4460 = t4804*t4911; + t5035 = t4460+t4782*t4990; + t4644 = t4802*t4922; + t4511 = x*t4644; + t5034 = t4707+t4511; + t4826 = x*z; + t4823 = y*t4826; + t5033 = t4823+y*t4607; + t4994 = z*t4813; + t4710 = y*t4994; + t4451 = t4829*t4682; + t5032 = t4710+t4451; + t5031 = t4769+t4617; + t4931 = t4804*t4832; + t4698 = t4829*t4931; + t5030 = t4792*t4991+t4698; + t4597 = t4787*t4946; + t5029 = t4791*t4923+t4597; + t4679 = y*t4936; + t4827 = y*z; + t5028 = t4679+t4827; + t4599 = t4782*t4991; + t5027 = t4460+t4599; + t4778 = t4797*z; + t4745 = t4783*t4832; + t4509 = t4793*t4893; + t5026 = t4745+t4778+t4509; + t5025 = t4797*t4909+x*t4989; + t4629 = t4807*t4831*x; + t4483 = z*t4629; + t5024 = t4826+t4483; + t4962 = (t4751+t4653)*x; + t4610 = x*t4771; + t4772 = t4795*x; + t5023 = t4962+t4610+t4772; + t4743 = t4784*t4832; + t4601 = x*t4743; + t4974 = t5074*x; + t4953 = t4783*t4831; + t4585 = z*t4953; + t5022 = t4601+t4974+x*t4585; + t4706 = z*t4769; + t4672 = t4832*t4918; + t4637 = t4830*t4914; + t5021 = t4706+t4672+t4637; + t4628 = z*t4763; + t4481 = y*t4628; + t4521 = t4829*t4679; + t5020 = t4481+t4521+t5066; + t4563 = t4783*t4922; + t4440 = x*t4563; + t4728 = t4790*t4832; + t4609 = t4831*t4778; + t4948 = (t4609+t4728)*x; + t5019 = t4440+x*t4753+t4948; + t4916 = (t4677+t4751)*y; + t5018 = t4916+y*t4763+t4760; + t5017 = t4507+x*t4633+t4629; + t4738 = t4782*t4832; + t5016 = t4698+t4704+t4738; + t5015 = t5057+t4885; + t4646 = t4802*t4963; + t4486 = y*t4646; + t5014 = t4481+t4486+t5059; + t4696 = t4792*t4963; + t4681 = z*t4761; + t5013 = t4696+t4521+y*t4992+t4681; + t4955 = t4810*t4831; + t4912 = z*t4955; + t4449 = x*t4912; + t4662 = t4807*y*t4829; + t5012 = t4449+t4695+t4832*t4662+t4829*t4917; + t4776 = t4805*t4831; + t4638 = t4829*t4776; + t4484 = z*t4638; + t5011 = t4728+t4484+t5063; + t4957 = t4919*y; + t4497 = y*t4647; + t4907 = z*t4988; + t4539 = y*t4907; + t5010 = t4957+t4666+t4497+y*t4767+t4539; + t4683 = t4806*t4963; + t4505 = y*t4683; + t4519 = z*t4662; + t5009 = t4505+t4519+t5033; + t4615 = t4802*t4923; + t5008 = t4829*t4615+t4784*t4830+t4638+t4790; + t4643 = t4809*t4923; + t4514 = x*t4643; + t5007 = t4702+t4514+t5053; + t4676 = t4808*t4923; + t4971 = (t4762+t4676)*x; + t4709 = x*t4778; + t5006 = t4689+t4971+t4709+t4750; + t5005 = t4662+t4497+t4518+y*t4631; + t4758 = t4820*z; + t5004 = t4758+t4511+t4628+t4644; + t4715 = t4804*t4946; + t4461 = t4831*t4715; + t4961 = t5071*t4783; + t5003 = t4461+t4961+t4790*t4830+t5050; + t4524 = y*t4618; + t4673 = t4805*t4963; + t4474 = y*t4673; + t4938 = t4474+y*t4778; + t5002 = y*t4768+t4524+t4942+t4938+t4749; + t5001 = t4672+t4696+t4804*t4991+t4791*t4832+(t4914+t4782)*z; + t5000 = t4641+t4643+t4757+t4514+t5058; + t4529 = t4830*t4662; + t4527 = t4807*t4913; + t4993 = x*t4830; + t4972 = y*t4993; + t4800 = RATIONAL(2.0,1.0); + t4531 = t4800*t4972; + t4999 = t4804*t4830+t4531+t4529+t4527+t5071*t4796; + t4611 = y*t4757; + t4998 = t4684+t4611+t4505+t4529+(t4671+t5076)*y; + t4606 = t4806*t4922; + t4491 = x*t4606; + t4997 = t4702+t4491+t4755+t4527+(t4703+t4955+t5077)*x; + t4828 = y*x; + t4996 = -1.0-x; + t4995 = y*t4830; + t4987 = t4783*t4829; + t4562 = t4829*t4726; + t4986 = (t4731+t4562)*y; + t4985 = (t4615+t4730)*x; + t4983 = t4831+t4829; + t4700 = t4805*t4922; + t4547 = x*t4700; + t4982 = t4547+x*t4706; + t4656 = t4830*t4918; + t4981 = t4789*t4830+t4829*t4656; + t4774 = t4805*t4829; + t4572 = t4832*t4932; + t4980 = t4482+t4572; + t4979 = t4673+t4618; + t4580 = t4791*t4922; + t4978 = t4482+t4580; + t4977 = t4928*y; + t4975 = t4729+t4562; + t4517 = z*t4659; + t4973 = t4673+t4517; + t4814 = RATIONAL(-2.0,1.0); + t4651 = t4814*t4828; + t4538 = z*t4651; + t4825 = t4832*t4828; + t4970 = t4538+t4825; + t4675 = z*t4774; + t4969 = t4675+t4517; + t4968 = t4832*t4820; + t4435 = t4791*t4893; + t4966 = t4435+t4831*t4599; + t4965 = t4813*t4832; + t4634 = x*t4994; + t4794 = RATIONAL(-3.0,1.0); + t4964 = t4794*t4831; + t4725 = t4788*t4832; + t4781 = RATIONAL(-1.0,72.0); + t4739 = t4781*t4832; + t4959 = t4795*t4831; + t4958 = t4799*t4832; + t4954 = t5066*x; + t4821 = RATIONAL(-9.0,8.0); + t4898 = t4821*t4976; + t4533 = t4830*t4898; + t4952 = t4533+t4775; + t4665 = x*t4965; + t4950 = (t4665+t4660)*y; + t4949 = t4452+z*t4901; + t4947 = z*t4910+y*t4728; + t4944 = t4733+t4563; + t4570 = t4783*t4963; + t4943 = t4593+t4570; + t4941 = t4547+x*t4745; + t4661 = z*t4776; + t4940 = t4661+t4644; + t4935 = t4509+z*t4889; + t4705 = x*t4756; + t4933 = t4621+t4705; + t4455 = t4804*t4893; + t4929 = t4792*t4911+t4455; + t4927 = t4675+t4646; + t4717 = z*t4772; + t4512 = z*t4610; + t4926 = t4717+t4512; + t4925 = t4706+t4700; + t4924 = t4798*t4832; + t4639 = y*t4968; + t4921 = x*t4639+y*t4634; + t4920 = t4474+t4669; + t4915 = t4794*t4829; + t4608 = t4795*t4991; + t4574 = z*t4987; + t4908 = x*t4959; + t4906 = y+t5064; + t4714 = x*t4764; + t4905 = t4743+t4562+t4714; + t4904 = t4828+t5064*x; + t4528 = z*t4685; + t4468 = t4830*t4889; + t4903 = t4528+t4468+t4509; + t4902 = t4640+t4646+t4658; + t4699 = RATIONAL(-9.0,4.0)*t4976; + t4652 = RATIONAL(9.0,4.0)*t4976; + t4900 = t4471+(t4640+t4752)*y; + t4627 = z*t4771; + t4899 = t4615+t4700+t4627; + t4678 = z*t4959; + t4897 = t4615+t4678+t4566; + t4477 = z*t4664; + t4896 = t4468+t4477+t4455; + t4895 = t4996*t4995; + t4625 = z*t4984; + t4894 = t4640+t4625+t4570; + t4892 = -t4995-t4830; + t4891 = t4796*z+t4806; + t4888 = RATIONAL(9.0,8.0)*t4976; + t4890 = t4611+t4830*t4888+t4702; + t4803 = RATIONAL(3.0,1.0); + t4887 = t4803*t4830+t4794; + t4886 = t4803*t4831+t4814; + t4884 = t4814+t4803*t4829; + t4883 = t4807*t4830+t4810; + t4882 = t4983*t4807; + t4881 = t4486+(t4675+t5068)*y; + t4880 = t4440+(t4733+t5072)*x; + t4879 = t4461+t4788*t4830+t5071*t4782; + t4878 = t4978+t5069; + t4441 = y*t4570; + t4877 = t4441+(t4733+t5069)*y; + t4876 = t4511+(t4661+t5068)*x; + t4875 = t4651-t4825+t4823+t4531; + t4874 = t4676+t4761+t4925; + t4873 = t4949+t5068; + t4872 = t4642+t4768+t4979; + t4871 = t4829*t4643+t4659+t4935; + t4870 = t4717+t4714+t4935; + t4779 = RATIONAL(-1.0,108.0); + t4722 = t4779*z; + t4869 = t4829*t4725+t4437+t4722+t4831*t4746; + t4868 = t4791*t4830+t4656+t4453+t4792*t4946; + t4740 = t4785*z; + t4867 = t4740+t4585+t4980; + t4450 = y*t4608; + t4866 = t4450+y*t4729+t4977+t4986; + t4786 = RATIONAL(-1.0,54.0); + t4724 = t4786*z; + t4865 = t4779*t4832+t4435+t4724+t4831*t4574+t4981; + t4864 = t4565+t4563+t4929+t4982; + t4546 = z*t4908; + t4863 = t4546+x*t4729+t4974+t4985; + t4571 = y*t4745; + t4862 = t4481+t4571+t4920+t4977; + t4765 = t4795*z; + t4861 = t4730+t4765+t4745+t4903; + t4860 = t4926+t4941+t4985; + t4575 = y*t4743; + t4859 = t4575+y*t4574+t4954+t4986; + t4594 = t4829*t4738; + t4858 = t4594+t4593+t4715+t4896; + t4857 = t4484+t4733+t4731+t4455+t4981; + t4573 = t4782*t4922; + t4856 = t4565+t4573+t4637+t4896; + t4855 = t4524+t4680+t4920+t4954; + t4854 = t4548+t4709+t4939+t4941+t4950; + t4515 = t4832*t4888; + t4853 = t4515+t4767+t4759+z*t4699+t4952+t4970; + t4852 = t4571+t4479+t4938+t4950+t4957; + t4851 = t4594+t4573+t4781*z+t4587+t4725+t4791*t4990+t4929; + t4719 = x*t4934; + t4850 = t4719+t4515+t4712+t4652+t4830*t4699+z*t4898+t4906; + t4454 = t4821*t4893; + t4849 = t4607+z*t4652+t4826+t4454+t4890+t5028; + t4848 = t4441+y*t4753+t4900+t4947+t5059; + t4847 = t4486+t4680+t4900+t5033+t5048; + t4846 = t4528+t4613+t4890+t4933+t5042; + t4845 = t4611+t4616+t4617+t5050+t5053+t5058; + t4844 = t4778-t4972+t4726+t4732+t4903+t4970; + t4843 = t4778+t4820+t4756+t4762+t4871+t4904; + t4842 = t4727+t4452+t4661+t4868+t4969+t5016; + t4841 = t4740+t4574+t4881+t4975+t4978+t5035; + t4840 = t4873+t4876+t4940+t5030; + t4839 = t4752+t4742+t4745+t4797+t4875+t4949+t5057; + t4838 = t4699+t4757+z*t4888+t4830*t4652+t4454+t4875+t5076; + t4837 = t4729+t4566+t4867+t4876+t5027; + t4836 = t4873+t4881+t4927+t5055; + t4835 = t4574+t4484+t4739+t4580+t4867+t4868; + t4834 = t4776+t4615+t4783+t4774+t4871+t4928+t5001; + t4824 = x*t4990; + t4819 = RATIONAL(4.0,1.0); + t4816 = RATIONAL(-2.0,3.0); + t4811 = RATIONAL(-2.0,9.0); + t4780 = RATIONAL(-1.0,216.0); + t4701 = y*t4965; + t4690 = x*t4968; + t4583 = t4785*t4922; + t4554 = t4829*t4739; + t4550 = t4781*t4922; + t4534 = t4829*t4621; + t4469 = t4832*t4908; + t4442 = t4831*t4593; + coeffs_dxy->coeff_m1_m1_m1 = t4848+(RATIONAL(-1.0,27.0)+t4983*t4784)*z+ +t4442+t4583+t4786*t4832+t5003+t5019+t5037; + coeffs_dxy->coeff_0_m1_m1 = t4852+t4733+(-t4995+t4924+(t4820*t4831+t4811) +*z)*x+t4469+t4856+t4894+t4971+t5036; + coeffs_dxy->coeff_p1_m1_m1 = t4845+t4563+t4562+t4608+t4609+t5011+t5014+ +t5019+t5078; + coeffs_dxy->coeff_p2_m1_m1 = t4829*t4731+t4865+t4550+t4866+t5029+t5044; + coeffs_dxy->coeff_m1_0_m1 = t4534+(-t4993+t4924+(t4811+t4820*t4829)*z)*y+ +t4854+t4609+t4858+t4944+t5036+t5040; + coeffs_dxy->coeff_0_0_m1 = t4706+t4742+t4846+t4999+t4824+(RATIONAL(-4.0, +3.0)*z+t4816*t4832)*t4828+t4536+t4451+t5016+t5038; + coeffs_dxy->coeff_p1_0_m1 = t4695+t4700+t4701+t4895+t4854-t4822+t4952+ +t4969+t5013+t5026+t5075; + coeffs_dxy->coeff_p2_0_m1 = t4829*t4710+t4575+t4835+t4916+t5054; + coeffs_dxy->coeff_m1_p1_m1 = t4848+t4705+t4512+t4894+t4897+t5007+t5011+ +t5034; + coeffs_dxy->coeff_0_p1_m1 = t4852+t4533+(-1.0-y)*t4993+t4672+t4661-t4824+ +t4658+t4665+t4919+t4973+t5026+t5039+t5067; + coeffs_dxy->coeff_p1_p1_m1 = t4846+t4646+t4627+t5000+t4512+t4756+t5004+ +t5014; + coeffs_dxy->coeff_p2_p1_m1 = t4731+t4608+t4856+t4866+t4928+t4975; + coeffs_dxy->coeff_m1_p2_m1 = t4863+t4831*t4731+t4554+t4865+t5046+t5052; + coeffs_dxy->coeff_0_p2_m1 = t4601+t4831*t4634+t4835+t4962+t5025; + coeffs_dxy->coeff_p1_p2_m1 = t4730+t4729+t4731+t4858+t4863+t4897; + coeffs_dxy->coeff_p2_p2_m1 = t4442+t4780*t4832+t4869+t4879+t5047; + coeffs_dxy->coeff_m1_m1_0 = t4728+t4933+t4904+t4799+t5002+t4734+t4864+ +t4983*t4797+t4943+(-t4828+t4798+t4983*t4795)*t4830+t5006+t5051; + coeffs_dxy->coeff_0_m1_0 = t4839+t4707+t4872+t4998+t4665+(t4831+t4817+(- +t4831+t4816)*t4830)*x+t5031+t5043+t5055; + coeffs_dxy->coeff_p1_m1_0 = t4874+t4705+t4906+t4843+t4895+t4927+t4982+ +t5005+t5006+t5056; + coeffs_dxy->coeff_p2_m1_0 = t4841+t4953+t4885*t4829+t4559+t5008+t5018; + coeffs_dxy->coeff_m1_0_0 = (t4829+t4817+(t4816-t4829)*t4830)*y+t4839+ +t4874+t4997+t4701+t4451+t5030+t5041+t5048; + coeffs_dxy->coeff_0_0_0 = -t4995+(t4793*t4831+t4792)*z+(t4793*z+t4809+ +t4887*y)*t4829+t4802+t4538+t4956+t4539+t4850+t4931+(-t4830+1.0+t4887*t4831+( +t4819+RATIONAL(-4.0,1.0)*t4830+t4800*t4832)*y)*x+t4919+t5012+t5070; + coeffs_dxy->coeff_p1_0_0 = t4641+(-t4832+(t4915+t4800)*t4830+t4884)*y+ +t4519+t4606+t4997+t4838+t4891*t4829+t4827+t4883*t4831+t5062; + coeffs_dxy->coeff_p2_0_0 = t4834+(-t4829+t4813+(t4829+t4820)*t4830)*y+ +t5020; + coeffs_dxy->coeff_m1_p1_0 = t4621+(1.0+t4892)*x+t4719+t4843+t4872+t4937+ +t4940+t5002+t5017+t5045; + coeffs_dxy->coeff_0_p1_0 = t4643+t4683+(-t4832+(t4800+t4964)*t4830+t4886) +*x+t4838+t4998+t4891*t4831+t4883*t4829+t5024+t5060; + coeffs_dxy->coeff_p1_p1_0 = x+t4904+t4882+RATIONAL(1.0,1.0)+t4759+t4850+ +t4934+t5005+(-t4828-y+t4983*t4810+t4996)*t4830+t4504+t5017+t5065+t5073; + coeffs_dxy->coeff_p2_p1_0 = t4836+t5015+t5018+t5031+t5056; + coeffs_dxy->coeff_m1_p2_0 = t4987+t4837+t4885*t4831+t4597+t5008+t5023; + coeffs_dxy->coeff_0_p2_0 = (t4813-t4831+(t4831+t4820)*t4830)*x+t4834+ +t4506+t4714+t4926; + coeffs_dxy->coeff_p1_p2_0 = t4840+t5015+t5023+t5041+t5045; + coeffs_dxy->coeff_p2_p2_0 = t4785*t4830+t4789+t4983*t4787+t4851+t4961+ +t5051; + coeffs_dxy->coeff_m1_m1_p1 = t4625+t4566+t4477+t4548+t4847+t4609+t4905+ +t5003+t5034+t5063; + coeffs_dxy->coeff_0_m1_p1 = t4824+t4690+t4844+t4902+t4971+t5010+t5021+ +t5067; + coeffs_dxy->coeff_p1_m1_p1 = t4764+t4845+t4548+t4714+t4681+t4973+t5004+ +t5009+t5028+t5042; + coeffs_dxy->coeff_p2_m1_p1 = t4857+t4585+t4570+t4573+t4608+t4862+t5029; + coeffs_dxy->coeff_m1_0_p1 = t4449+t4844+t4639+t4644+t4715+t5013+t5038+ +t5040+t5061; + coeffs_dxy->coeff_0_0_p1 = t4915*t4827+t4792*t4832+(z*t4964+(t4819*z+ +t4814*t4832)*y)*x+t4777+t4849+t4999+t5060+t5062; + coeffs_dxy->coeff_p1_0_p1 = t4853+t4912+(-t4830+t4832-t4993+t4884*z)*y+ +t5012+t5061+t5065+t5075; + coeffs_dxy->coeff_p2_0_p1 = t4621+t4842-t4822+t4916+t5032; + coeffs_dxy->coeff_m1_p1_p1 = t4764+t4452+t4758+t4607+t4491+t4847+t4517+ +t4899+t4902+t5007+t5024; + coeffs_dxy->coeff_0_p1_p1 = t4853+(t4832+t4886*z+t4892)*x+t4907+t4670+ +t5010+t5039+t5070+t5073; + coeffs_dxy->coeff_p1_p1_p1 = t4683+t4849+t4606+(1.0+t4882)*z+t4936+t4491+ +t4483+t5000+t5009; + coeffs_dxy->coeff_p2_p1_p1 = t4673+t4616+t4861+t4628+t4862+t5021; + coeffs_dxy->coeff_m1_p2_p1 = t4594+t4574+t4857+t4563+t4678+t4860+t5046; + coeffs_dxy->coeff_0_p2_p1 = t4705+t4842-t4824+t4536+t4634+t4962; + coeffs_dxy->coeff_p1_p2_p1 = t4696+t4860+t4618+t4715+t4861+t4899; + coeffs_dxy->coeff_p2_p2_p1 = t4739+t4565+t4477+t4572+t4878+t4879; + coeffs_dxy->coeff_m1_m1_p2 = RATIONAL(1.0,54.0)*t4832+t4724+t4859+t4966+ +t5022+t5044+t5052; + coeffs_dxy->coeff_0_m1_p2 = t4841+t4546+x*t4958+t4921+t5025; + coeffs_dxy->coeff_p1_m1_p2 = t4585+t4743+t4855+t4929+t4943+t5022+t5074; + coeffs_dxy->coeff_p2_m1_p2 = t4781*t4990+t4722+t4877+t5037+t5047+t5049; + coeffs_dxy->coeff_m1_0_p2 = t4837+t4450+y*t4958+t4921+t5054; + coeffs_dxy->coeff_0_0_p2 = t4512+t4506+(t4817*t4832+t4816*z)*t4828+t4870+ +t5001+t5020; + coeffs_dxy->coeff_p1_0_p2 = t4840+t4479+t4639+t4921+t5032; + coeffs_dxy->coeff_p2_0_p2 = t4534+y*t4734+t4851+t4947; + coeffs_dxy->coeff_m1_p1_p2 = t4717+t4574+t4731+t4859+t4864+t4905; + coeffs_dxy->coeff_0_p1_p2 = t4690+t4836+t4634+t4921+t5043; + coeffs_dxy->coeff_p1_p1_p2 = t4764+t4765+t4855+t4870+t4925+t4979+t4982; + coeffs_dxy->coeff_p2_p1_p2 = t4570+t4733+t4877+t4878+t5035; + coeffs_dxy->coeff_m1_p2_p2 = t4583+t4781*t4991+t4869+t4880+t5049; + coeffs_dxy->coeff_0_p2_p2 = t4469+x*t4734+t4851+t4948; + coeffs_dxy->coeff_p1_p2_p2 = t4880+t4944+t4980+t5027+t5072; + coeffs_dxy->coeff_p2_p2_p2 = RATIONAL(1.0,216.0)*t4832+t4550+t4554+(t4780 ++t4983*t4788)*z+t4966; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxz.compute.c new file mode 100644 index 0000000..e91b295 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxz.compute.c @@ -0,0 +1,1094 @@ +fp t5449; +fp t5446; +fp t5418; +fp t5475; +fp t5476; +fp t5718; +fp t5453; +fp t5474; +fp t5588; +fp t5356; +fp t5107; +fp t5456; +fp t5406; +fp t5289; +fp t5591; +fp t5412; +fp t5717; +fp t5454; +fp t5621; +fp t5310; +fp t5100; +fp t5437; +fp t5612; +fp t5716; +fp t5473; +fp t5452; +fp t5401; +fp t5258; +fp t5099; +fp t5448; +fp t5567; +fp t5256; +fp t5715; +fp t5574; +fp t5318; +fp t5431; +fp t5375; +fp t5609; +fp t5433; +fp t5371; +fp t5429; +fp t5387; +fp t5714; +fp t5636; +fp t5225; +fp t5690; +fp t5417; +fp t5267; +fp t5110; +fp t5411; +fp t5261; +fp t5095; +fp t5713; +fp t5450; +fp t5331; +fp t5169; +fp t5451; +fp t5633; +fp t5350; +fp t5129; +fp t5712; +fp t5264; +fp t5571; +fp t5279; +fp t5711; +fp t5427; +fp t5378; +fp t5384; +fp t5710; +fp t5572; +fp t5297; +fp t5161; +fp t5634; +fp t5274; +fp t5096; +fp t5709; +fp t5249; +fp t5708; +fp t5632; +fp t5317; +fp t5622; +fp t5302; +fp t5602; +fp t5322; +fp t5707; +fp t5415; +fp t5253; +fp t5620; +fp t5143; +fp t5413; +fp t5277; +fp t5706; +fp t5409; +fp t5269; +fp t5705; +fp t5439; +fp t5396; +fp t5532; +fp t5181; +fp t5704; +fp t5275; +fp t5466; +fp t5703; +fp t5333; +fp t5702; +fp t5402; +fp t5337; +fp t5464; +fp t5399; +fp t5319; +fp t5701; +fp t5457; +fp t5635; +fp t5349; +fp t5304; +fp t5136; +fp t5700; +fp t5470; +fp t5468; +fp t5606; +fp t5332; +fp t5699; +fp t5435; +fp t5564; +fp t5534; +fp t5698; +fp t5442; +fp t5640; +fp t5556; +fp t5441; +fp t5697; +fp t5696; +fp t5434; +fp t5391; +fp t5372; +fp t5695; +fp t5613; +fp t5201; +fp t5566; +fp t5694; +fp t5345; +fp t5397; +fp t5693; +fp t5270; +fp t5692; +fp t5691; +fp t5420; +fp t5529; +fp t5368; +fp t5689; +fp t5282; +fp t5688; +fp t5570; +fp t5208; +fp t5687; +fp t5285; +fp t5404; +fp t5686; +fp t5414; +fp t5321; +fp t5685; +fp t5432; +fp t5684; +fp t5326; +fp t5118; +fp t5683; +fp t5557; +fp t5682; +fp t5407; +fp t5263; +fp t5681; +fp t5311; +fp t5680; +fp t5294; +fp t5467; +fp t5679; +fp t5363; +fp t5678; +fp t5254; +fp t5278; +fp t5172; +fp t5677; +fp t5676; +fp t5315; +fp t5426; +fp t5675; +fp t5585; +fp t5207; +fp t5091; +fp t5674; +fp t5341; +fp t5673; +fp t5436; +fp t5582; +fp t5536; +fp t5171; +fp t5443; +fp t5400; +fp t5672; +fp t5428; +fp t5367; +fp t5388; +fp t5671; +fp t5600; +fp t5670; +fp t5562; +fp t5592; +fp t5094; +fp t5669; +fp t5134; +fp t5465; +fp t5605; +fp t5377; +fp t5668; +fp t5410; +fp t5628; +fp t5667; +fp t5403; +fp t5666; +fp t5665; +fp t5240; +fp t5086; +fp t5370; +fp t5328; +fp t5575; +fp t5664; +fp t5248; +fp t5595; +fp t5386; +fp t5203; +fp t5205; +fp t5663; +fp t5393; +fp t5362; +fp t5398; +fp t5295; +fp t5098; +fp t5584; +fp t5408; +fp t5327; +fp t5180; +fp t5662; +fp t5626; +fp t5661; +fp t5146; +fp t5352; +fp t5660; +fp t5461; +fp t5642; +fp t5344; +fp t5659; +fp t5268; +fp t5658; +fp t5440; +fp t5555; +fp t5148; +fp t5657; +fp t5559; +fp t5117; +fp t5354; +fp t5656; +fp t5175; +fp t5655; +fp t5607; +fp t5290; +fp t5546; +fp t5654; +fp t5625; +fp t5272; +fp t5653; +fp t5652; +fp t5627; +fp t5601; +fp t5353; +fp t5358; +fp t5651; +fp t5335; +fp t5177; +fp t5650; +fp t5251; +fp t5153; +fp t5649; +fp t5563; +fp t5312; +fp t5174; +fp t5276; +fp t5101; +fp t5648; +fp t5647; +fp t5638; +fp t5617; +fp t5444; +fp t5159; +fp t5151; +fp t5109; +fp t5646; +fp t5255; +fp t5645; +fp t5644; +fp t5643; +fp t5641; +fp t5639; +fp t5394; +fp t5637; +fp t5405; +fp t5425; +fp t5385; +fp t5458; +fp t5299; +fp t5631; +fp t5630; +fp t5629; +fp t5624; +fp t5623; +fp t5284; +fp t5619; +fp t5142; +fp t5618; +fp t5296; +fp t5616; +fp t5357; +fp t5615; +fp t5167; +fp t5158; +fp t5614; +fp t5213; +fp t5611; +fp t5610; +fp t5292; +fp t5608; +fp t5533; +fp t5131; +fp t5152; +fp t5604; +fp t5542; +fp t5603; +fp t5157; +fp t5173; +fp t5599; +fp t5598; +fp t5597; +fp t5087; +fp t5587; +fp t5193; +fp t5596; +fp t5309; +fp t5188; +fp t5594; +fp t5593; +fp t5235; +fp t5242; +fp t5590; +fp t5196; +fp t5589; +fp t5303; +fp t5586; +fp t5583; +fp t5581; +fp t5580; +fp t5469; +fp t5145; +fp t5579; +fp t5198; +fp t5578; +fp t5147; +fp t5577; +fp t5301; +fp t5576; +fp t5573; +fp t5568; +fp t5560; +fp t5360; +fp t5565; +fp t5438; +fp t5561; +fp t5558; +fp t5314; +fp t5343; +fp t5316; +fp t5472; +fp t5554; +fp t5553; +fp t5552; +fp t5187; +fp t5179; +fp t5551; +fp t5550; +fp t5093; +fp t5549; +fp t5548; +fp t5547; +fp t5545; +fp t5544; +fp t5543; +fp t5471; +fp t5541; +fp t5459; +fp t5540; +fp t5300; +fp t5539; +fp t5313; +fp t5538; +fp t5537; +fp t5150; +fp t5535; +fp t5462; +fp t5329; +fp t5445; +fp t5273; +fp t5447; +fp t5531; +fp t5530; +fp t5528; +fp t5527; +fp t5526; +fp t5525; +fp t5524; +fp t5230; +fp t5523; +fp t5522; +fp t5521; +fp t5520; +fp t5519; +fp t5199; +fp t5518; +fp t5517; +fp t5516; +fp t5423; +fp t5364; +fp t5515; +fp t5092; +fp t5514; +fp t5513; +fp t5512; +fp t5511; +fp t5120; +fp t5510; +fp t5509; +fp t5165; +fp t5508; +fp t5430; +fp t5390; +fp t5507; +fp t5243; +fp t5351; +fp t5506; +fp t5505; +fp t5504; +fp t5503; +fp t5502; +fp t5501; +fp t5202; +fp t5500; +fp t5271; +fp t5499; +fp t5334; +fp t5498; +fp t5122; +fp t5422; +fp t5497; +fp t5496; +fp t5288; +fp t5495; +fp t5108; +fp t5494; +fp t5493; +fp t5492; +fp t5491; +fp t5116; +fp t5490; +fp t5266; +fp t5489; +fp t5488; +fp t5487; +fp t5486; +fp t5379; +fp t5485; +fp t5484; +fp t5483; +fp t5482; +fp t5481; +fp t5480; +fp t5298; +fp t5479; +fp t5478; +fp t5463; +fp t5460; +fp t5455; +fp t5424; +fp t5348; +fp t5323; +fp t5283; +fp t5246; +fp t5226; +fp t5219; +fp t5184; +fp t5115; +fp t5090; + t5449 = RATIONAL(-1.0,4.0); + t5446 = RATIONAL(1.0,4.0); + t5418 = t5446*y; + t5475 = y*y; + t5476 = t5475*y; + t5718 = t5418+t5449*t5476; + t5453 = RATIONAL(-3.0,4.0); + t5474 = z*z; + t5588 = t5476*t5474; + t5356 = t5453*t5588; + t5107 = x*t5356; + t5456 = RATIONAL(-1.0,2.0); + t5406 = t5456*x; + t5289 = y*t5406; + t5591 = t5107+t5289; + t5412 = t5446*t5476; + t5717 = t5591+x*t5412; + t5454 = RATIONAL(3.0,2.0); + t5621 = t5454*t5474; + t5310 = x*t5621; + t5100 = t5475*t5310; + t5437 = RATIONAL(3.0,8.0); + t5612 = t5437*t5474; + t5716 = t5100+t5475*t5612; + t5473 = x*x; + t5452 = RATIONAL(1.0,2.0); + t5401 = t5452*t5473; + t5258 = z*t5401; + t5099 = t5476*t5258; + t5448 = RATIONAL(1.0,8.0); + t5567 = t5473*t5448; + t5256 = t5476*t5567; + t5715 = t5099+t5256; + t5574 = t5475*t5473; + t5318 = t5446*t5574; + t5431 = RATIONAL(-1.0,12.0); + t5375 = t5431*t5475; + t5609 = t5318+t5375; + t5433 = RATIONAL(1.0,36.0); + t5371 = t5433*y; + t5429 = RATIONAL(-1.0,36.0); + t5387 = t5429*t5476; + t5714 = t5371+t5387; + t5636 = y*t5474; + t5225 = t5431*t5636; + t5690 = t5225+t5371; + t5417 = t5452*t5474; + t5267 = y*t5417; + t5110 = x*t5267; + t5411 = t5446*t5474; + t5261 = t5476*t5411; + t5095 = x*t5261; + t5713 = t5110+t5095; + t5450 = RATIONAL(3.0,4.0); + t5331 = t5450*t5588; + t5169 = x*t5331; + t5451 = RATIONAL(-3.0,2.0); + t5633 = x*t5474; + t5350 = t5451*t5633; + t5129 = y*t5350; + t5712 = t5169+t5129; + t5264 = t5450*t5636; + t5571 = t5453*t5473; + t5279 = t5476*t5571; + t5711 = t5264+t5279; + t5427 = RATIONAL(1.0,12.0); + t5378 = t5427*y; + t5384 = t5431*t5476; + t5710 = t5378+t5384; + t5572 = t5450*t5473; + t5297 = t5476*t5572; + t5161 = z*t5297; + t5634 = t5473*z; + t5274 = t5451*t5634; + t5096 = y*t5274; + t5709 = t5161+t5096; + t5249 = y*t5571; + t5708 = t5476*t5310+t5437*t5588+t5249; + t5632 = t5453*t5474; + t5317 = y*t5632; + t5622 = t5454*t5473; + t5302 = z*t5622; + t5602 = t5473*t5476; + t5322 = t5437*t5602; + t5707 = t5317+t5476*t5302+t5322; + t5415 = t5449*t5475; + t5253 = t5475*t5572; + t5620 = (t5415+t5253)*z; + t5143 = z*t5279; + t5413 = t5456*z; + t5277 = y*t5413; + t5706 = t5620+z*t5412+t5143+t5277; + t5409 = t5449*t5473; + t5269 = y*t5409; + t5705 = t5269+t5710; + t5439 = RATIONAL(-1.0,6.0); + t5396 = t5439*t5475; + t5532 = t5474*t5574; + t5181 = t5437*t5532; + t5704 = t5396+t5181; + t5275 = y*t5411; + t5466 = y*t5633; + t5703 = t5275+t5466; + t5333 = t5473*t5411; + t5702 = t5333+t5449*t5532; + t5402 = t5439*t5476; + t5337 = z*t5402; + t5464 = RATIONAL(-1.0,3.0); + t5399 = t5464*y; + t5319 = x*t5399; + t5701 = x*t5337+z*t5319; + t5457 = RATIONAL(1.0,3.0); + t5635 = y*t5457; + t5349 = x*t5635; + t5304 = x*t5417; + t5136 = t5476*t5304; + t5700 = t5349+t5136; + t5470 = x*z; + t5468 = y*t5470; + t5606 = t5456*t5476; + t5332 = z*t5606; + t5699 = x*t5332+t5468; + t5435 = RATIONAL(1.0,24.0); + t5564 = t5435*t5474; + t5534 = t5473*t5564; + t5698 = y*t5534+RATIONAL(1.0,108.0)*t5476; + t5442 = RATIONAL(-1.0,9.0); + t5640 = y*t5442; + t5556 = x*t5588; + t5441 = RATIONAL(1.0,6.0); + t5697 = t5441*t5556+x*t5640; + t5696 = t5433*t5602+t5429*t5636; + t5434 = RATIONAL(1.0,18.0); + t5391 = t5434*y; + t5372 = t5433*t5476; + t5695 = t5391+t5372; + t5613 = t5475*t5474; + t5201 = t5431*t5613; + t5566 = t5435*t5473; + t5694 = t5201+t5475*t5566; + t5345 = t5449*t5574; + t5397 = t5446*t5473; + t5693 = t5345+t5397; + t5270 = t5456*t5574; + t5692 = t5270+t5401; + t5691 = (t5396+t5345)*z; + t5420 = t5441*t5475; + t5529 = t5420+t5439; + t5368 = t5429*y; + t5689 = t5368+t5372; + t5282 = t5474*t5572; + t5688 = t5453*t5532+t5282; + t5570 = t5431*t5473; + t5208 = t5475*t5570; + t5687 = t5475*t5564+t5208; + t5285 = t5475*t5417; + t5404 = t5456*t5474; + t5686 = t5285+t5404; + t5414 = t5452*t5475; + t5321 = z*t5414; + t5685 = t5337+t5321; + t5432 = RATIONAL(1.0,72.0); + t5684 = t5432*t5602+t5433*t5636; + t5326 = x*t5404; + t5118 = t5476*t5326; + t5683 = t5110+t5118; + t5557 = z*t5602; + t5682 = z*t5640+t5441*t5557; + t5407 = t5449*t5474; + t5263 = t5475*t5407; + t5681 = (t5263+t5396)*x; + t5311 = t5474*t5571; + t5680 = t5450*t5532+t5311; + t5294 = y*t5397; + t5467 = y*t5634; + t5679 = t5294+t5467; + t5363 = t5475*t5404; + t5678 = t5417+t5363; + t5254 = z*t5399; + t5278 = t5476*t5397; + t5172 = z*t5278; + t5677 = t5254+t5172; + t5676 = t5473*t5368+t5433*t5588; + t5315 = t5448*t5588; + t5426 = RATIONAL(-1.0,24.0); + t5675 = t5315+t5426*t5476; + t5585 = t5473*t5426; + t5207 = t5476*t5585; + t5091 = t5474*t5207; + t5674 = t5091+t5429*t5588; + t5341 = z*t5635; + t5673 = t5099+t5341; + t5436 = RATIONAL(-1.0,8.0); + t5582 = t5473*t5474; + t5536 = t5436*t5582; + t5171 = t5476*t5536; + t5443 = RATIONAL(1.0,9.0); + t5400 = t5443*y; + t5672 = t5171+t5400; + t5428 = RATIONAL(-1.0,18.0); + t5367 = t5428*y; + t5388 = t5427*t5475; + t5671 = t5367+t5388; + t5600 = t5436*t5474; + t5670 = t5315+y*t5600; + t5562 = t5427*t5474; + t5592 = t5475*t5562+t5427*t5574; + t5094 = t5448*t5532; + t5669 = t5592+t5094+t5434*t5475; + t5134 = y*t5282; + t5465 = RATIONAL(-9.0,8.0); + t5605 = t5415+t5465*t5532; + t5377 = t5427*t5476; + t5668 = t5134+t5605+t5377; + t5410 = t5439*x; + t5628 = (t5420+t5363)*x; + t5667 = t5304+t5410+t5628; + t5403 = t5457*t5475; + t5666 = t5403+t5402+t5464; + t5665 = t5100+x*t5264+t5350; + t5240 = t5476*t5562; + t5086 = x*t5240; + t5370 = t5434*t5476; + t5328 = t5441*t5636; + t5575 = (t5328+t5370)*x; + t5664 = t5086+x*t5400+t5575; + t5248 = t5431*t5588; + t5595 = (t5248+t5391)*x; + t5386 = t5428*t5476; + t5203 = x*t5386; + t5205 = y*t5562; + t5663 = t5595+t5203+x*t5205; + t5393 = t5441*t5476; + t5362 = z*t5393; + t5398 = t5439*z; + t5295 = y*t5398; + t5098 = y*t5258; + t5584 = t5295+t5098; + t5408 = t5456*t5473; + t5327 = z*t5408; + t5180 = t5476*t5327; + t5662 = t5362+t5584+t5180; + t5626 = (t5420+t5270)*z; + t5661 = t5626+t5398+t5258; + t5146 = t5475*t5302; + t5352 = y*t5572; + t5660 = t5356+t5146+t5352; + t5461 = RATIONAL(2.0,3.0); + t5642 = y*t5461; + t5344 = t5436*t5588; + t5659 = x*t5642+t5118+t5344; + t5268 = t5473*t5407; + t5658 = t5434+t5428*t5475+t5446*t5532+t5268; + t5440 = RATIONAL(-3.0,8.0); + t5555 = y*t5622; + t5148 = z*t5555; + t5657 = t5440*t5588+t5253+t5476*t5350+t5148; + t5559 = t5440*t5473; + t5117 = y*t5310; + t5354 = t5450*t5613; + t5656 = t5117+t5354+(t5274+t5559)*t5476; + t5175 = y*t5268; + t5655 = t5370+t5175+t5704; + t5607 = t5452*t5476; + t5290 = z*t5607; + t5546 = x*t5290+t5470+z*t5289; + t5654 = t5143+z*t5352+t5546+t5274; + t5625 = (t5285+t5403)*x; + t5272 = x*t5402; + t5653 = t5326+t5625+t5464*x+t5272; + t5652 = t5680+t5529; + t5627 = (t5415+t5354)*x; + t5601 = t5473*t5436; + t5353 = t5476*t5601; + t5358 = z*t5642; + t5651 = t5627+t5353+t5358+t5180; + t5335 = y*t5408; + t5177 = z*t5335; + t5650 = t5177+t5362+t5691; + t5251 = x*t5393; + t5153 = y*t5326; + t5649 = t5251+t5319+t5095+t5153; + t5563 = t5453*t5475; + t5312 = t5473*t5563; + t5174 = z*t5312; + t5276 = t5474*t5563; + t5101 = x*t5276; + t5648 = t5174+t5414+t5276+t5312+t5101; + t5647 = t5448*t5636+t5344+t5353+t5435*t5476+(t5567+t5426)*y; + t5638 = t5475*z; + t5617 = x*t5638; + t5444 = RATIONAL(2.0,1.0); + t5159 = t5444*t5617; + t5151 = t5475*t5274; + t5109 = t5475*t5350; + t5646 = t5159+t5151+t5109+t5440*t5613+(t5559+t5448)*t5475; + t5255 = x*t5414; + t5645 = t5255+t5169+t5406+t5109+t5310+(t5317+t5718)*x; + t5644 = t5302+t5151+t5413+t5161+t5321+(t5249+t5718)*z; + t5643 = -z-1.0; + t5641 = t5437*y; + t5639 = t5475*x; + t5394 = t5439*y; + t5637 = z*t5476; + t5405 = t5441*y; + t5425 = RATIONAL(-1.0,72.0); + t5385 = t5425*y; + t5458 = RATIONAL(-2.0,1.0); + t5299 = t5458*t5470; + t5631 = t5442*t5476; + t5630 = t5474+t5473; + t5629 = t5464*t5476; + t5624 = t5609*z; + t5623 = t5427*t5473; + t5284 = t5476*t5407; + t5619 = t5275+t5284; + t5142 = t5474*t5322; + t5618 = t5405+t5142; + t5296 = y*t5410; + t5616 = x*t5362+z*t5296; + t5357 = x*t5629; + t5615 = (t5349+t5357)*z; + t5167 = x*t5284; + t5158 = x*t5275; + t5614 = t5167+t5158; + t5213 = x*t5377; + t5611 = t5213+t5167; + t5610 = t5240+t5387; + t5292 = t5452*t5574; + t5608 = (t5292+t5403)*z; + t5533 = t5474*t5559; + t5131 = t5476*t5533; + t5152 = t5582*t5641; + t5604 = t5131+t5152; + t5542 = t5474*t5567; + t5603 = y*t5542+t5171; + t5157 = y*t5536; + t5173 = t5476*t5542; + t5599 = t5157+t5173; + t5598 = t5443*t5476; + t5597 = t5391+t5173; + t5087 = t5476*t5534; + t5587 = t5474*t5426; + t5193 = y*t5587; + t5596 = t5087+t5473*t5193; + t5309 = t5476*t5409; + t5188 = z*t5309; + t5594 = t5188+z*t5294; + t5593 = t5205+t5248; + t5235 = y*t5570; + t5242 = t5427*t5602; + t5590 = t5235+t5242; + t5196 = t5476*t5570; + t5589 = (t5391+t5196)*z; + t5303 = t5475*t5411; + t5586 = (t5303+t5375)*x; + t5583 = t5294+t5309; + t5581 = t5436*t5532+t5433*t5475; + t5580 = z*t5377+t5188; + t5469 = x*t5637; + t5145 = y*t5299; + t5579 = t5469+t5145; + t5198 = y*t5623; + t5578 = t5196+t5198; + t5147 = y*t5533; + t5577 = t5147+t5142; + t5301 = t5473*t5405; + t5576 = (t5370+t5301)*z; + t5573 = t5263+t5153; + t5568 = t5251+t5296; + t5560 = t5476*t5457; + t5360 = z*t5560; + t5565 = (t5360+t5358)*x; + t5438 = RATIONAL(-3.0,1.0); + t5561 = t5438*t5474; + t5558 = z+t5290+t5277; + t5314 = t5473*t5394; + t5343 = y*t5407; + t5316 = t5439*t5636; + t5472 = y*x; + t5554 = t5255+x*t5606+t5472; + t5553 = t5335+t5345+t5278; + t5552 = t5450+t5440*y; + t5187 = t5440*t5532; + t5179 = y*t5333; + t5551 = t5187+t5173+t5179; + t5550 = t5267+t5284+t5303; + t5093 = x*t5321; + t5549 = t5093+t5699; + t5548 = -t5475-t5638; + t5547 = t5255+t5319+t5272; + t5545 = t5093+t5701; + t5544 = t5316+t5303+t5248; + t5543 = t5345+t5301+t5242; + t5471 = y*z; + t5541 = t5471+t5332+t5321; + t5459 = RATIONAL(9.0,8.0); + t5540 = t5459*t5582; + t5300 = y*t5401; + t5539 = t5318+t5309+t5300; + t5313 = y*t5404; + t5538 = t5313+t5261+t5263; + t5537 = t5465*t5582; + t5150 = y*t5311; + t5535 = t5150+t5142+t5187; + t5462 = RATIONAL(-9.0,4.0); + t5329 = t5462*t5582; + t5445 = RATIONAL(9.0,4.0); + t5273 = t5445*t5582; + t5447 = RATIONAL(3.0,1.0); + t5531 = t5438+t5447*t5475; + t5530 = t5630*t5451; + t5528 = t5447*t5474+t5458; + t5527 = t5458+t5447*t5473; + t5526 = t5454+t5451*t5475; + t5525 = t5086+(t5387+t5690)*x; + t5524 = t5408+t5292+t5583; + t5230 = t5476*t5566; + t5523 = t5230+y*t5585+t5603; + t5522 = t5094+t5426*t5574+(t5432+t5587)*t5475; + t5521 = t5568+t5577; + t5520 = t5159-t5469+t5468+t5299; + t5519 = t5172+t5705*z; + t5199 = t5476*t5564; + t5518 = t5199+t5193+t5603; + t5517 = t5577+t5688; + t5516 = t5095+(t5343+t5710)*x; + t5423 = RATIONAL(-1.0,108.0); + t5364 = t5423*y; + t5515 = t5091+t5473*t5371+t5364+t5432*t5588; + t5092 = z*t5242; + t5514 = t5092+(t5235+t5714)*z; + t5513 = t5131+t5378+t5256+t5343; + t5512 = t5425*t5476+t5230+t5171+t5199; + t5511 = t5436*t5574+t5181+(t5600+t5435)*t5475; + t5120 = x*t5316; + t5510 = x*t5372+t5120+t5586+t5595; + t5509 = t5110+t5296+t5586+t5611; + t5165 = z*t5314; + t5508 = t5165+z*t5372+t5589+t5624; + t5430 = RATIONAL(-1.0,54.0); + t5390 = t5430*y; + t5507 = t5390+t5087+t5473*t5205+t5423*t5476+t5581; + t5243 = t5476*t5587; + t5351 = t5448*t5613; + t5506 = t5225+t5243+t5351+t5551; + t5505 = t5295+t5362+t5594+t5616; + t5504 = t5225+t5240+t5599+t5614; + t5503 = t5387+t5175+t5581+t5597; + t5502 = t5394+t5375+t5377+t5535; + t5501 = t5580+t5584+t5624; + t5202 = z*t5386; + t5500 = z*t5198+t5202+t5589+t5616; + t5271 = t5475*t5567; + t5499 = t5271+t5235+t5207+t5551; + t5334 = z*t5405; + t5498 = t5177+t5334+t5565+t5580+t5620; + t5122 = t5476*t5540; + t5422 = t5456*y; + t5497 = y*t5329+t5122+t5422+t5412+t5579+t5605; + t5496 = t5243+t5432*t5476+t5385+t5207+t5599+(t5566+t5564)*y; + t5288 = x*t5607; + t5495 = t5273+t5122+y*t5537+t5288+t5462*t5532+t5289+t5558; + t5108 = t5459*t5532; + t5494 = t5131+t5108+t5150+t5254+t5547+t5685; + t5493 = t5131+t5393+t5134+t5399+t5549+t5704; + t5492 = t5196+t5093+t5328+t5672+t5677+t5681; + t5491 = t5092+z*t5400+t5545+t5576+t5691; + t5116 = t5476*t5537; + t5490 = t5116+t5108+y*t5273+t5541+t5554; + t5266 = x*t5405; + t5489 = (-1.0-x)*t5638+t5146+t5266+t5167+t5284+t5269+t5618; + t5488 = t5405+t5384-t5617+t5388+t5535+t5579; + t5487 = t5337+t5334+t5464*z+t5327+t5546+t5594+t5608; + t5486 = t5516+t5523+t5593+t5689; + t5379 = t5431*y; + t5485 = t5379+t5396+t5441+t5377+t5520+t5604+t5680; + t5484 = t5134+t5269+t5511+t5513+t5675; + t5483 = t5518+t5519+t5578+t5689; + t5482 = t5116+t5414+t5329+t5445*t5532+t5456+y*t5540+t5520+t5718; + t5481 = t5278+t5519+t5604+t5670+t5705; + t5480 = t5368+t5205+t5198+t5175+t5511+t5512; + t5298 = y*t5601; + t5479 = t5261+t5384+t5152+t5298+t5513+t5516; + t5478 = t5409+t5407+t5303+t5427+t5517+t5609+t5647; + t5463 = RATIONAL(4.0,1.0); + t5460 = RATIONAL(-2.0,3.0); + t5455 = RATIONAL(-2.0,9.0); + t5424 = RATIONAL(-1.0,216.0); + t5348 = t5437*t5574; + t5323 = x*t5560; + t5283 = z*t5629; + t5246 = t5429*t5602; + t5226 = t5425*t5588; + t5219 = t5425*t5602; + t5184 = t5439*t5556; + t5115 = t5439*t5557; + t5090 = t5473*t5225; + coeffs_dxz->coeff_m1_m1_m1 = t5430*t5476+t5246+(RATIONAL(-1.0,27.0)+t5630 +*t5428)*y+t5090+t5491+t5664+t5669+t5674+t5681; + coeffs_dxz->coeff_0_m1_m1 = (t5631-t5638+(t5455+t5464*t5474)*y)*x+t5498+ +t5387+t5184+t5506+t5543+t5625+t5671; + coeffs_dxz->coeff_p1_m1_m1 = t5174+t5263+t5318+t5240+t5098+t5314+t5492+ +t5655+t5664+t5685+t5701; + coeffs_dxz->coeff_p2_m1_m1 = t5226+t5473*t5391+t5507+t5508+t5687+t5696; + coeffs_dxz->coeff_m1_0_m1 = t5367+t5370+t5487+t5266+t5504+t5443+(t5442- +t5470+t5630*t5439)*t5475+t5630*t5441+t5590+t5653+t5702; + coeffs_dxz->coeff_0_0_m1 = t5323+t5319+t5136+t5411+t5524+t5573+t5485+( +t5461+t5474+(-t5474+t5460)*t5475)*x+t5644+t5670; + coeffs_dxz->coeff_p1_0_m1 = t5147+t5275+t5489+t5653+t5654+t5158+t5558+ +t5278+t5666+t5686+t5688+t5692; + coeffs_dxz->coeff_p2_0_m1 = t5201+t5529*t5473+t5483+t5562+t5658+t5661; + coeffs_dxz->coeff_m1_p1_m1 = t5301+t5179+t5386+t5492+t5248+t5649+t5650+ +t5669+t5699; + coeffs_dxz->coeff_0_p1_m1 = t5357+t5351+t5148+t5488+t5553+t5625+t5659+ +t5703+t5706; + coeffs_dxz->coeff_p1_p1_m1 = t5174+t5493+t5538+t5539+t5541+t5649+t5681+ +t5709; + coeffs_dxz->coeff_p2_p1_m1 = t5243+t5205+t5501+t5314+t5242+t5503+t5687; + coeffs_dxz->coeff_m1_p2_m1 = t5500+RATIONAL(1.0,54.0)*t5476+t5390+t5596+ +t5663+t5676+t5696; + coeffs_dxz->coeff_0_p2_m1 = x*t5598+t5483+t5120+t5615+t5697; + coeffs_dxz->coeff_p1_p2_m1 = t5157+t5386+t5505+t5590+t5593+t5597+t5663; + coeffs_dxz->coeff_p2_p2_m1 = t5474*t5385+t5246+t5514+t5515+t5698; + coeffs_dxz->coeff_m1_m1_0 = t5115+t5499+(-t5639+t5631+(t5455+t5464*t5473) +*y)*z+t5266+t5328+t5565+t5573+t5608+t5610+t5611+t5627+t5671; + coeffs_dxz->coeff_0_m1_0 = t5379+t5494+t5646+t5136+(RATIONAL(-4.0,3.0)*y+ +t5460*t5476)*t5470+t5675+t5679+t5703+t5715; + coeffs_dxz->coeff_p1_m1_0 = t5313+t5348+t5489+t5213+t5360+t5354+t5153- +t5467+t5565+t5651+t5668; + coeffs_dxz->coeff_p2_m1_0 = t5480+t5473*t5341+t5202+t5626+t5682; + coeffs_dxz->coeff_m1_0_0 = t5177+t5360+t5298+t5254+t5619+t5485+t5645+( +t5473+t5461+(-t5473+t5460)*t5475)*z+t5686+t5693+t5715; + coeffs_dxz->coeff_0_0_0 = t5632+t5415+(t5641+t5453+t5531*z)*t5473-t5638+ +t5448*t5476+(1.0-t5475+t5531*t5474+(RATIONAL(-4.0,1.0)*t5475+t5444*t5476+t5463) +*z)*x+t5495+t5446+t5145+(t5436+t5612)*y+t5656+t5657; + coeffs_dxz->coeff_p1_0_0 = t5471+t5526*t5474+t5552*t5473+t5482+(-t5476+( +t5444+t5438*t5473)*t5475+t5527)*z+t5312+t5331+t5096+t5645+t5707; + coeffs_dxz->coeff_p2_0_0 = (t5457-t5473+(t5464+t5473)*t5475)*z+t5478+ +t5662; + coeffs_dxz->coeff_m1_p1_0 = t5271+t5283+t5117+t5488+t5538+t5608+t5651+ +t5679+t5717; + coeffs_dxz->coeff_0_p1_0 = (t5458*t5637+(t5561+t5463*z)*y)*x+t5436*t5476+ +t5418+t5490+t5438*t5467+t5646+t5707+t5708; + coeffs_dxz->coeff_p1_p1_0 = y*t5621+t5348+t5497+(-t5639-t5475+t5476+t5527 +*y)*z+t5627+t5656+t5660+t5717; + coeffs_dxz->coeff_p2_p1_0 = t5337+t5484-t5467+t5626+t5673; + coeffs_dxz->coeff_m1_p2_0 = t5165+z*t5598+t5486+t5615+t5682; + coeffs_dxz->coeff_0_p2_0 = (t5461*t5476+t5460*y)*t5470+t5521+t5647+t5662+ +t5683; + coeffs_dxz->coeff_p1_p2_0 = t5177+t5479+t5283+t5615+t5673; + coeffs_dxz->coeff_p2_p2_0 = z*t5367+t5115+t5496+t5576; + coeffs_dxz->coeff_m1_m1_p1 = t5491+t5101+t5543+t5544+t5547+t5655+t5672+ +t5713; + coeffs_dxz->coeff_0_m1_p1 = t5335+t5253+t5323+t5498+t5309+t5343-t5466+ +t5643*t5639+t5618+t5659+t5668+t5716; + coeffs_dxz->coeff_p1_m1_p1 = t5261+t5494+t5402+t5098+t5267+t5399+t5278+ +t5172+t5300+t5545+t5648+t5713; + coeffs_dxz->coeff_p2_m1_p1 = t5196+t5506+t5314+t5508+t5609+t5695; + coeffs_dxz->coeff_m1_0_p1 = t5405+t5261+t5487+t5517+t5288+t5524+t5343+( +1.0+t5548)*x+t5591+t5665+t5666+t5678; + coeffs_dxz->coeff_0_0_p1 = t5526*t5473+t5552*t5474+(-t5476+(t5561+t5444)* +t5475+t5528)*x+t5482+t5472+t5276+t5297+t5129+t5644+t5708; + coeffs_dxz->coeff_p1_0_p1 = t5107+x+t5607+t5654+(-t5470-x+t5630*t5454+ +t5643)*t5475+t5422+RATIONAL(1.0,1.0)+t5495+t5530+t5660+t5665+t5711; + coeffs_dxz->coeff_p2_0_p1 = t5263+t5411+t5481+t5652+t5661+t5692; + coeffs_dxz->coeff_m1_p1_p1 = t5101+t5493+t5550+t5553+t5554+t5650+t5677+ +t5712; + coeffs_dxz->coeff_0_p1_p1 = t5497+(t5476+t5528*y+t5548)*x+t5555+t5657+ +t5706+t5711+t5716; + coeffs_dxz->coeff_p1_p1_p1 = (1.0+t5530)*y+t5606+t5490+t5297+t5331+t5549+ +t5648+t5709+t5712; + coeffs_dxz->coeff_p2_p1_p1 = t5275+t5351+t5501+t5344+t5502+t5539; + coeffs_dxz->coeff_m1_p2_p1 = t5391+t5500+t5386+t5504+t5568+t5578; + coeffs_dxz->coeff_0_p2_p1 = t5357+t5153+t5481+t5615+t5700; + coeffs_dxz->coeff_p1_p2_p1 = t5393+t5394+t5505+t5521+t5583+t5614+t5619; + coeffs_dxz->coeff_p2_p2_p1 = t5514+t5518+t5590+t5714; + coeffs_dxz->coeff_m1_m1_p2 = t5474*t5391+t5507+t5219+t5510+t5676+t5694; + coeffs_dxz->coeff_0_m1_p2 = t5457*t5466+t5203+t5480+t5628+t5697; + coeffs_dxz->coeff_p1_m1_p2 = t5499+t5375+t5510+t5544+t5695; + coeffs_dxz->coeff_p2_m1_p2 = t5424*t5476+t5090+t5515+t5522+t5684; + coeffs_dxz->coeff_m1_0_p2 = t5623+t5529*t5474+t5486+t5208+t5658+t5667; + coeffs_dxz->coeff_0_0_p2 = t5478+(-t5474+t5457+(t5464+t5474)*t5475)*x+ +t5568+t5683; + coeffs_dxz->coeff_p1_0_p2 = t5479+t5652+t5667+t5678+t5693; + coeffs_dxz->coeff_p2_0_p2 = t5433+t5429*t5475+t5630*t5431+t5496+t5592+ +t5702; + coeffs_dxz->coeff_m1_p1_p2 = t5503+t5240+t5316+t5207+t5198+t5509+t5694; + coeffs_dxz->coeff_0_p1_p2 = t5484-t5466+t5272+t5628+t5700; + coeffs_dxz->coeff_p1_p1_p2 = t5271+t5353+t5294+t5502+t5509+t5550; + coeffs_dxz->coeff_p2_p1_p2 = t5235+t5179+t5512+t5522+t5690; + coeffs_dxz->coeff_m1_p2_p2 = t5364+t5473*t5385+t5525+t5674+t5684+t5698; + coeffs_dxz->coeff_0_p2_p2 = t5184+x*t5367+t5496+t5575; + coeffs_dxz->coeff_p1_p2_p2 = t5523+t5525+t5610+t5690; + coeffs_dxz->coeff_p2_p2_p2 = t5219+t5226+RATIONAL(1.0,216.0)*t5476+(t5424 ++t5630*t5432)*y+t5596; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..cfd0a58 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dy.compute.c @@ -0,0 +1,1268 @@ +fp t2888; +fp t2891; +fp t2868; +fp t3061; +fp t2874; +fp t2889; +fp t2841; +fp t3177; +fp t2869; +fp t2834; +fp t2816; +fp t3213; +fp t2890; +fp t3096; +fp t2871; +fp t2955; +fp t2606; +fp t2872; +fp t3089; +fp t3212; +fp t2747; +fp t2647; +fp t3067; +fp t2777; +fp t3211; +fp t2870; +fp t2892; +fp t3035; +fp t2765; +fp t3106; +fp t3014; +fp t3210; +fp t2853; +fp t2860; +fp t3209; +fp t2852; +fp t2824; +fp t2857; +fp t2818; +fp t2688; +fp t3208; +fp t2854; +fp t3060; +fp t2692; +fp t3116; +fp t2859; +fp t2685; +fp t3207; +fp t2821; +fp t2666; +fp t3003; +fp t2717; +fp t3070; +fp t3036; +fp t2864; +fp t2961; +fp t2621; +fp t2883; +fp t2845; +fp t2750; +fp t3206; +fp t2830; +fp t2803; +fp t2575; +fp t2835; +fp t2786; +fp t3205; +fp t2813; +fp t3055; +fp t3204; +fp t2862; +fp t2842; +fp t2751; +fp t2957; +fp t2571; +fp t3203; +fp t3107; +fp t2757; +fp t2875; +fp t3037; +fp t2797; +fp t3202; +fp t3033; +fp t2705; +fp t2819; +fp t2707; +fp t3201; +fp t2802; +fp t3200; +fp t2827; +fp t2659; +fp t2822; +fp t2658; +fp t3199; +fp t3101; +fp t2996; +fp t2616; +fp t3113; +fp t3198; +fp t3099; +fp t2994; +fp t3197; +fp t2991; +fp t2612; +fp t3042; +fp t2755; +fp t3148; +fp t2863; +fp t2836; +fp t3196; +fp t3047; +fp t2792; +fp t3163; +fp t2877; +fp t2967; +fp t2619; +fp t3195; +fp t3085; +fp t2762; +fp t3030; +fp t2878; +fp t3052; +fp t3194; +fp t2959; +fp t2974; +fp t2806; +fp t3193; +fp t2887; +fp t3044; +fp t2787; +fp t3183; +fp t2764; +fp t3064; +fp t2570; +fp t2838; +fp t2735; +fp t2558; +fp t3192; +fp t2524; +fp t3034; +fp t2766; +fp t3191; +fp t2977; +fp t2772; +fp t3190; +fp t2995; +fp t2846; +fp t3189; +fp t2832; +fp t2788; +fp t3075; +fp t2754; +fp t2648; +fp t3188; +fp t2783; +fp t3187; +fp t2837; +fp t2781; +fp t2879; +fp t3016; +fp t2782; +fp t3186; +fp t2671; +fp t3185; +fp t2851; +fp t2492; +fp t3066; +fp t2726; +fp t3184; +fp t2466; +fp t2856; +fp t2489; +fp t3182; +fp t3080; +fp t3069; +fp t2746; +fp t3181; +fp t2687; +fp t2632; +fp t3180; +fp t3059; +fp t2992; +fp t2865; +fp t3110; +fp t3179; +fp t3078; +fp t2980; +fp t3006; +fp t3103; +fp t3178; +fp t2850; +fp t2965; +fp t2502; +fp t3015; +fp t3176; +fp t2469; +fp t2855; +fp t3175; +fp t2722; +fp t3174; +fp t2761; +fp t3173; +fp t2886; +fp t3028; +fp t2676; +fp t3172; +fp t2839; +fp t2801; +fp t3087; +fp t2741; +fp t3171; +fp t2779; +fp t2618; +fp t2562; +fp t3081; +fp t3062; +fp t3170; +fp t2848; +fp t3076; +fp t2954; +fp t3169; +fp t2715; +fp t2972; +fp t3168; +fp t3008; +fp t2958; +fp t2508; +fp t2866; +fp t2790; +fp t3167; +fp t2829; +fp t2800; +fp t2564; +fp t2628; +fp t3166; +fp t2844; +fp t3165; +fp t3164; +fp t3072; +fp t2763; +fp t3162; +fp t3161; +fp t2774; +fp t3160; +fp t3159; +fp t3158; +fp t2523; +fp t2885; +fp t3157; +fp t2733; +fp t3156; +fp t3017; +fp t3054; +fp t2820; +fp t2662; +fp t3155; +fp t3154; +fp t2804; +fp t2635; +fp t3084; +fp t3153; +fp t3152; +fp t2753; +fp t2796; +fp t3151; +fp t2823; +fp t3150; +fp t2808; +fp t2633; +fp t3149; +fp t3005; +fp t2684; +fp t2811; +fp t2595; +fp t3147; +fp t3048; +fp t2675; +fp t2956; +fp t3146; +fp t2815; +fp t3145; +fp t2544; +fp t2736; +fp t2568; +fp t2831; +fp t2810; +fp t2541; +fp t3083; +fp t2776; +fp t2636; +fp t3144; +fp t3043; +fp t3143; +fp t3097; +fp t2817; +fp t3094; +fp t3111; +fp t3142; +fp t2704; +fp t3053; +fp t3051; +fp t2678; +fp t2496; +fp t3141; +fp t3100; +fp t2795; +fp t3077; +fp t3140; +fp t2759; +fp t3139; +fp t2703; +fp t2504; +fp t2572; +fp t3138; +fp t3137; +fp t2712; +fp t3032; +fp t3056; +fp t2990; +fp t2510; +fp t2663; +fp t3136; +fp t3135; +fp t2720; +fp t3134; +fp t2690; +fp t2973; +fp t3133; +fp t2840; +fp t2566; +fp t2969; +fp t2607; +fp t2932; +fp t3132; +fp t2625; +fp t3131; +fp t3130; +fp t2674; +fp t3026; +fp t3129; +fp t2664; +fp t2610; +fp t2882; +fp t3128; +fp t2634; +fp t2643; +fp t3127; +fp t3068; +fp t3022; +fp t2506; +fp t3126; +fp t2594; +fp t2789; +fp t3125; +fp t3065; +fp t2778; +fp t2952; +fp t2812; +fp t2535; +fp t3124; +fp t2997; +fp t2589; +fp t2587; +fp t3123; +fp t3108; +fp t3019; +fp t3114; +fp t3122; +fp t2740; +fp t2538; +fp t3121; +fp t2773; +fp t3120; +fp t2809; +fp t3119; +fp t2673; +fp t2592; +fp t2730; +fp t3118; +fp t2769; +fp t3117; +fp t3115; +fp t3112; +fp t2858; +fp t3109; +fp t3105; +fp t2604; +fp t2668; +fp t3102; +fp t3098; +fp t3095; +fp t3093; +fp t3092; +fp t2583; +fp t3091; +fp t3090; +fp t3088; +fp t2713; +fp t2486; +fp t2491; +fp t3086; +fp t3079; +fp t2723; +fp t3074; +fp t3073; +fp t3071; +fp t3058; +fp t3057; +fp t3050; +fp t3049; +fp t3018; +fp t2953; +fp t2452; +fp t3046; +fp t2500; +fp t3045; +fp t2516; +fp t3041; +fp t3040; +fp t3039; +fp t2849; +fp t3038; +fp t3031; +fp t3029; +fp t2718; +fp t2518; +fp t3027; +fp t3025; +fp t2677; +fp t3024; +fp t3023; +fp t2847; +fp t3021; +fp t2563; +fp t3020; +fp t3013; +fp t2472; +fp t3012; +fp t2876; +fp t3011; +fp t3010; +fp t3001; +fp t3009; +fp t2873; +fp t3007; +fp t3004; +fp t3002; +fp t2791; +fp t3000; +fp t2999; +fp t2998; +fp t2695; +fp t2993; +fp t2758; +fp t2989; +fp t2609; +fp t2988; +fp t2979; +fp t2987; +fp t2743; +fp t2985; +fp t2793; +fp t2798; +fp t2982; +fp t2748; +fp t2981; +fp t2767; +fp t2768; +fp t2978; +fp t2770; +fp t2976; +fp t2620; +fp t2975; +fp t2739; +fp t2711; +fp t2505; +fp t2971; +fp t2680; +fp t2970; +fp t2968; +fp t2966; +fp t2487; +fp t2599; +fp t2964; +fp t2884; +fp t2963; +fp t2951; +fp t2950; +fp t2949; +fp t2948; +fp t2947; +fp t2946; +fp t2945; +fp t2944; +fp t2943; +fp t2646; +fp t2623; +fp t2942; +fp t2480; +fp t2941; +fp t2940; +fp t2939; +fp t2937; +fp t2936; +fp t2728; +fp t2721; +fp t2493; +fp t2935; +fp t2934; +fp t2588; +fp t2933; +fp t2931; +fp t2930; +fp t2929; +fp t2649; +fp t2928; +fp t2927; +fp t2926; +fp t2925; +fp t2694; +fp t2924; +fp t2696; +fp t2923; +fp t2697; +fp t2922; +fp t2507; +fp t2921; +fp t2499; +fp t2503; +fp t2920; +fp t2919; +fp t2477; +fp t2918; +fp t2917; +fp t2916; +fp t2915; +fp t2547; +fp t2615; +fp t2914; +fp t2913; +fp t2553; +fp t2531; +fp t2912; +fp t2911; +fp t2910; +fp t2909; +fp t2908; +fp t2907; +fp t2906; +fp t2672; +fp t2905; +fp t2714; +fp t2904; +fp t2584; +fp t2903; +fp t2902; +fp t2724; +fp t2901; +fp t2465; +fp t2900; +fp t2686; +fp t2899; +fp t2593; +fp t2898; +fp t2585; +fp t2897; +fp t2559; +fp t2896; +fp t2895; +fp t2881; +fp t2880; +fp t2867; +fp t2861; +fp t2650; +fp t2608; +fp t2600; +fp t2555; +fp t2545; +fp t2528; +fp t2514; +fp t2485; +fp t2455; +fp t2451; + t2888 = x*x; + t2891 = t2888*x; + t2868 = RATIONAL(1.0,4.0); + t3061 = t2868*t2891; + t2874 = RATIONAL(1.0,2.0); + t2889 = z*z; + t2841 = t2874*t2889; + t3177 = t2889*t3061+t2841; + t2869 = RATIONAL(-1.0,4.0); + t2834 = t2869*t2889; + t2816 = x*t2834; + t3213 = t2816+t3177; + t2890 = y*y; + t3096 = t2890*t2889; + t2871 = RATIONAL(-3.0,8.0); + t2955 = t2871*t3096; + t2606 = t2891*t2955; + t2872 = RATIONAL(1.0,8.0); + t3089 = t2872*t2889; + t3212 = t2606+t2891*t3089; + t2747 = x*t2841; + t2647 = y*t2747; + t3067 = t2869*t2891; + t2777 = t2889*t3067; + t3211 = t2647+y*t2777; + t2870 = RATIONAL(3.0,4.0); + t2892 = t2889*z; + t3035 = t2892*t2869; + t2765 = t2891*t3035; + t3106 = x*t2890; + t3014 = z*t3106; + t3210 = t2870*t3014+t2765; + t2853 = RATIONAL(-1.0,18.0); + t2860 = RATIONAL(1.0,18.0); + t3209 = t2860+t2853*t2889; + t2852 = RATIONAL(1.0,12.0); + t2824 = t2852*t2891; + t2857 = RATIONAL(-1.0,12.0); + t2818 = t2857*t2891; + t2688 = t2889*t2818; + t3208 = t2824+t2688; + t2854 = RATIONAL(-1.0,36.0); + t3060 = t2854*t2891; + t2692 = z*t3060; + t3116 = x*z; + t2859 = RATIONAL(1.0,36.0); + t2685 = t2859*t3116; + t3207 = t2692+t2685; + t2821 = t2857*t2889; + t2666 = x*t2821; + t3003 = t2852*t2889; + t2717 = t2891*t3003; + t3070 = t2666+t2717; + t3036 = t2890*t2892; + t2864 = RATIONAL(-1.0,8.0); + t2961 = t2864*t3036; + t2621 = t2891*t2961; + t2883 = RATIONAL(-1.0,3.0); + t2845 = t2883*z; + t2750 = x*t2845; + t3206 = t2621+t2750; + t2830 = t2874*t2888; + t2803 = y*t2830; + t2575 = z*t2803; + t2835 = t2869*t2888; + t2786 = t2892*t2835; + t3205 = y*t2786+t2575; + t2813 = z*t2835; + t3055 = t2888*t2892; + t3204 = t2868*t3055+t2813; + t2862 = RATIONAL(-1.0,6.0); + t2842 = t2862*t2888; + t2751 = z*t2842; + t2957 = t2888*t3036; + t2571 = t2872*t2957; + t3203 = t2751+t2571; + t3107 = x*t2892; + t2757 = t2868*t3107; + t2875 = RATIONAL(-3.0,4.0); + t3037 = t2891*t2890; + t2797 = t2875*t3037; + t3202 = z*t2797+t2757; + t3033 = t2852*t2888; + t2705 = t2892*t3033; + t2819 = t2857*t2888; + t2707 = z*t2819; + t3201 = t2705+t2707; + t2802 = t2868*t3116; + t3200 = z*t3067+t2802; + t2827 = t2852*x; + t2659 = z*t2827; + t2822 = t2857*t2892; + t2658 = x*t2822; + t3199 = t2659+t2658; + t3101 = t2891*t2889; + t2996 = y*t3101; + t2616 = t2874*t2996; + t3113 = y*t2889; + t3198 = t2616-x*t3113; + t3099 = t2891*t2892; + t2994 = y*t3099; + t3197 = t2875*t3014+t2872*t3099+t2874*t2994; + t2991 = x*t3036; + t2612 = t2872*t2991; + t3042 = t2621+t2612; + t2755 = t2890*t3035; + t3148 = t2755+t2868*t2957; + t2863 = RATIONAL(1.0,6.0); + t2836 = t2863*z; + t3196 = t3042+t3148+t2751+t2836; + t3047 = t2875*t2890; + t2792 = t2889*t3047; + t3163 = x*t2792+t2747; + t2877 = RATIONAL(3.0,8.0); + t2967 = t2877*t3096; + t2619 = t2891*t2967; + t3195 = t3163+t2619+t3211; + t3085 = t2870*t2890; + t2762 = t2889*t3085; + t3030 = t2816+x*t2762; + t2878 = RATIONAL(-1.0,2.0); + t3052 = t2891*t2864; + t3194 = t3030+t2878*t2994+t2892*t3052; + t2959 = t2871*t3037; + t2974 = t2889*t3037; + t2806 = t2870*t3037; + t3193 = z*t2959+t2875*t2974+t2806; + t2887 = y*x; + t3044 = t2874*t2892; + t2787 = y*t3044; + t3183 = x*t2787+t2887; + t2764 = z*t3061; + t3064 = t2878*t2891; + t2570 = y*t2765; + t2838 = t2878*z; + t2735 = x*t2838; + t2558 = y*t2735; + t3192 = t2570+t2558+t3183+(t3064+t2764)*y; + t2524 = t2892*t2803; + t3034 = t2878*t2892; + t2766 = y*t3034; + t3191 = y*t2757+t2570+t2524+t2766; + t2977 = t2877*t3037; + t2772 = x*t3035; + t3190 = z*t2977+t2878*x+t2870*t2974+t2797+t2772; + t2995 = z*t3037; + t2846 = RATIONAL(-1.0,108.0); + t3189 = t2859*t2995+t2846*t3107; + t2832 = t2862*t2889; + t2788 = x*t2832; + t3075 = t2890*t2869; + t2754 = t2889*t3075; + t2648 = x*t2754; + t3188 = t2788+t2648; + t2783 = t2868*t3036; + t3187 = t2869*t2957+t2783; + t2837 = t2863*t2892; + t2781 = t2888*t2837; + t2879 = RATIONAL(1.0,3.0); + t3016 = t2879*t2888; + t2782 = z*t3016; + t3186 = (t2782+t2781)*y; + t2671 = t2892*t2819; + t3185 = (t2751+t2671)*y; + t2851 = RATIONAL(1.0,24.0); + t2492 = t2851*t2991; + t3066 = t2859*t2891; + t2726 = z*t3066; + t3184 = t2492+t2726; + t2466 = t2857*t3014; + t2856 = RATIONAL(-1.0,24.0); + t2489 = t2856*t2995; + t3182 = t2466+t2489; + t3080 = t2874*t2890; + t3069 = t2878*t2890; + t2746 = x*t3069; + t3181 = x*t3080+t2889*t2746; + t2687 = z*t3033; + t2632 = t2864*t2957; + t3180 = t2687+t2632; + t3059 = t2860*t2891; + t2992 = y*t3059; + t2865 = RATIONAL(-1.0,9.0); + t3110 = z*t2865; + t3179 = t2892*t2992+t3110*t2887; + t3078 = t2888*t2889; + t2980 = t2890*t3078; + t3006 = t2856*t2889; + t3103 = t2872*t2980+t2888*t3006; + t3178 = t2666+t3103; + t2850 = RATIONAL(-1.0,72.0); + t2965 = t2850*t3037; + t2502 = t2892*t2965; + t3015 = t2891*t2846; + t3176 = t2502+t2892*t3015; + t2469 = t2890*t2707; + t2855 = RATIONAL(1.0,72.0); + t3175 = t2469+t2855*t3055; + t2722 = t2852*t3036; + t3174 = t2857*t2957+t2722; + t2761 = t2892*t2842; + t3173 = t2761+t2837; + t2886 = y*z; + t3028 = t2879*t2886; + t2676 = z*t2824; + t3172 = t2891*t3028+t2676; + t2839 = t2863*t2891; + t2801 = t2889*t2839; + t3087 = t2879*t2889; + t2741 = x*t3087; + t3171 = (t2741+t2801)*y; + t2779 = t2869*t3037; + t2618 = z*t2779; + t2562 = t2864*t2974; + t3081 = t2851*t2889; + t3062 = t2891*t3081+t2562; + t3170 = t2618+t3062; + t2848 = RATIONAL(1.0,108.0); + t3076 = t2891*t2848; + t2954 = t2855*t3036; + t3169 = z*t3076+x*t2954; + t2715 = t2852*t3037; + t2972 = t2857*t3096; + t3168 = t2891*t2972+t2715; + t3008 = t2892*t2856; + t2958 = t2890*t3008; + t2508 = t2891*t2958; + t2866 = RATIONAL(1.0,9.0); + t2790 = t2866*t3116; + t3167 = t2508+t2790; + t2829 = t2862*t2891; + t2800 = y*t2829; + t2564 = z*t2800; + t2628 = t2863*t2994; + t3166 = t2564+t2628; + t2844 = t2862*t2892; + t3165 = t2844+t2781; + t3164 = t2892*t3076+t2854*t3014; + t3072 = t2868*t2889; + t2763 = t2888*t3072; + t3162 = t2763+t2875*t2980; + t3161 = t2848*t3107+t2855*t2995; + t2774 = t2889*t2829; + t3160 = t2774+t2839; + t3159 = t2779+t2868*t2974; + t3158 = (t2788+t2688)*y; + t2523 = x*t2766; + t2885 = y*t3116; + t3157 = t2523+t2885; + t2733 = t2868*t3037; + t3156 = t2733+t2869*t2974; + t3017 = t2859*t2888; + t3054 = z*t3017+t2856*t2957; + t2820 = t2860*z; + t2662 = x*t2820; + t3155 = t3054+t2662; + t3154 = t2878*t2996+t2647; + t2804 = t2890*t2835; + t2635 = z*t2804; + t3084 = t2890*t2868; + t3153 = z*t3084+t2635; + t3152 = t2868*t2980+t2863*t3078; + t2753 = z*t3069; + t2796 = z*t3080; + t3151 = t2888*t2753+t2796; + t2823 = t2852*t2892; + t3150 = t2823+t2671; + t2808 = y*t2844; + t2633 = x*t2808; + t3149 = t2633+t2628; + t3005 = t2851*t2888; + t2684 = t2892*t3005; + t2811 = t2888*t3084; + t2595 = z*t2811; + t3147 = t2684+t2595; + t3048 = t2854*t2892; + t2675 = t2888*t3048; + t2956 = t2890*t3005; + t3146 = z*t2956+t2675; + t2815 = x*t2836; + t3145 = t2815+t2845+t2782; + t2544 = t2862*t2994; + t2736 = y*t2837; + t2568 = x*t2736; + t2831 = t2862*z; + t2810 = x*t2831; + t2541 = y*t2810; + t3083 = t2568+t2541; + t2776 = y*t2839; + t2636 = z*t2776; + t3144 = t2544+t3083+t2636; + t3043 = t2888*t3003+t2869*t2980; + t3143 = t2811+t2819+t3043; + t3097 = t2863*t2889; + t2817 = x*t3097; + t3094 = (t2774+t2817)*y; + t3111 = y*t2862; + t3142 = x*t3111+t3094+t2776; + t2704 = t2860*t3107; + t3053 = z*t2992+y*t2704; + t3051 = t2859*t2892; + t2678 = t2891*t3051; + t2496 = y*t2678; + t3141 = t3053+y*t2790+t2496; + t3100 = t2863*t2888; + t2795 = z*t3100; + t3077 = (t2761+t2795)*y; + t3140 = t3077+z*t3111+t2736; + t2759 = t2890*t3072; + t3139 = t2821+t2759+t3043; + t2703 = t2891*t2823; + t2504 = y*t2703; + t2572 = x*t2796; + t3138 = t2572+t2504+t2703+t3206; + t3137 = t2635+t3203+t3205; + t2712 = t2891*t3048; + t3032 = (t2662+t2712)*y; + t3056 = t2853*t2891; + t2990 = y*t3056; + t2510 = z*t2990; + t2663 = x*t3051; + t3136 = t3032+y*t2663+t2510; + t3135 = t2862*x+t2817+t3159; + t2720 = x*t3003; + t3134 = t2720+t2648+t3171; + t2690 = t2857*t3037; + t2973 = t2890*t3003; + t3133 = t2891*t2973+t2690+t3209*x; + t2840 = t2883*x; + t2566 = t2864*t2995; + t2969 = t2872*t3037; + t2607 = t2892*t2969; + t2932 = t2566+t2607+t3156; + t3132 = t2840+t2815+t2741+t2932; + t2625 = t2889*t2969; + t3131 = t2625+t2688+t3158; + t3130 = t2831+t2795+t3148; + t2674 = t2857*t3036; + t3026 = t2853*t2888; + t3129 = t2674+t2820+t2852*t2957+z*t3026; + t2664 = t2891*t3008; + t2610 = x*t2753; + t2882 = RATIONAL(2.0,3.0); + t3128 = t2882*t2885+t2664+t2544+t2607+t2610+t2815; + t2634 = t2863*t3014; + t2643 = y*t2750; + t3127 = t2504+t2634+t2643+t3167; + t3068 = t2890*t2687+t2892*t3017; + t3022 = t2860*t2888; + t2506 = t2892*t2956; + t3126 = z*t3022+t3068+t2506+t3185; + t2594 = x*t2759; + t2789 = x*t3075; + t3125 = t2818+t2594+t3070+t2789+t2827; + t3065 = t2874*t2891; + t2778 = y*t3065; + t2952 = z*t2778+t2886+t2558; + t2812 = t2870*t3036; + t2535 = t2892*t2977; + t3124 = t2952+t2875*t2957+t2871*t2991+t2812+t2535; + t2997 = z*t3064; + t2589 = y*t2997; + t2587 = t2892*t2959; + t3123 = t2589+x*t2812+t2885+t2587+t2777; + t3108 = z*t2856; + t3019 = t2892*t2851; + t3114 = z*t2891; + t3122 = t2872*t3014+t2664+t2851*t3114+(t3108+t3019)*x; + t2740 = y*t2845; + t2538 = y*t2815; + t3121 = t2808+t2740+t2538+t3186; + t2773 = t2875*t3036; + t3120 = x*t2773+t2616+t2764+t2735+t2535; + t2809 = y*t2840; + t3119 = t2800+t2538+t2809+t3171; + t2673 = t2857*t3116; + t2592 = z*t2969; + t2730 = x*t2823; + t3118 = t2673+t2592+t2730+t2863*x+t3159; + t2769 = z*t2830; + t3117 = t2838+t2773+t2870*t2957+t2769+t2587+t2877*t2991+t3200; + t3115 = x*t2889; + t3112 = z*t2890; + t2858 = RATIONAL(-1.0,54.0); + t3109 = z*t2858; + t3105 = t2888*z; + t2604 = z*t2733; + t2668 = z*t2818; + t3102 = t2604+t2668; + t3098 = -t2888+t2891; + t3095 = t2850*t2891; + t3093 = t3201*y; + t3092 = t2788+t2643; + t2583 = x*t2961; + t3091 = t2607+t2583; + t3090 = t2712+t2663; + t3088 = t2707+t2632; + t2713 = t2891*t2822; + t2486 = y*t2713; + t2491 = y*t2676; + t3086 = t2486+t2491; + t3079 = t2888+t2889; + t2723 = t2853*t3116; + t3074 = t2890*t2864; + t3073 = t2850*t2892; + t3071 = t3070*y; + t3058 = x*t2973+t2889*t3066; + t3057 = t2891+t2892; + t3050 = t2872*t2888; + t3049 = t2852*t2890; + t3018 = t2890*t2851; + t2953 = t2891*t3018; + t2452 = t2892*t2953; + t3046 = t2452+t2662; + t2500 = z*t2715; + t3045 = t2466+t2500; + t2516 = t2891*t2954; + t3041 = t2850*t2991+t2516; + t3040 = t2856*t2974+t2859*t3115; + t3039 = t2692+t2452; + t2849 = RATIONAL(1.0,216.0); + t3038 = t2849*t2891; + t3031 = t2860*t2889; + t3029 = y*t3107; + t2718 = x*t3048; + t2518 = x*t2722; + t3027 = t2718+t2518; + t3025 = t2878*t2889; + t2677 = t2891*t3019; + t3024 = t2621+t2677; + t3023 = t2892-t2889; + t2847 = RATIONAL(-1.0,216.0); + t3021 = t2891*t2847; + t2563 = x*t2783; + t3020 = t2658+t2563; + t3013 = t2891*t2855; + t2472 = z*t2953; + t3012 = t2508+t2472; + t2876 = RATIONAL(3.0,2.0); + t3011 = t2876*t2888; + t3010 = y*t3105; + t3001 = x*t3096; + t3009 = t2872*t3001+t2562; + t2873 = RATIONAL(-3.0,2.0); + t3007 = t2873*t2888; + t3004 = t2668+t2703; + t3002 = t2890*t3105; + t2791 = x*t3084; + t3000 = t2890*t3108; + t2999 = z*t3074; + t2998 = z*t3049; + t2695 = t2853*t3107; + t2993 = x*t3018; + t2758 = z*t3050; + t2989 = t2859*t3106; + t2609 = y*t2763; + t2988 = t2888*t2955+t2609+t2763; + t2979 = t2889*t3074; + t2987 = t2609+t2889*t2819+t2888*t2979; + t2743 = x*t2837; + t2985 = t2713+t2743+t2705; + t2793 = t2888*t3025; + t2798 = z*t2829; + t2982 = t2798+t2604+t2564; + t2748 = x*t2844; + t2981 = t2748+t2633+t2563; + t2767 = t2888*t3085; + t2768 = t2888*t3047; + t2978 = t2868+t2864*z; + t2770 = z*t2839; + t2976 = t2770+t2618+t2636; + t2620 = y*t2793; + t2975 = t2888*t2967+t2864*t3078+t2620; + t2739 = t2892*t3061; + t2711 = z*t3056; + t2505 = z*t2690; + t2971 = t2711+t2505+t2636; + t2680 = z*t3059; + t2970 = t2564+t2680+t2500; + t2968 = t2695+t2705+t2712; + t2966 = t2452+t2486+t2678; + t2487 = x*t2674; + t2599 = t2862*t3014; + t2964 = t2487+t2594+t2599; + t2884 = y*t3078; + t2963 = t2884+t2888*t2766+t2575; + t2951 = t2704+t2518+t2633; + t2950 = t2857*t2890+t2859; + t2949 = t2879+t2883*t2888; + t2948 = t2879+t2883*t2889; + t2947 = t2874+t3025; + t2946 = z*t3005+t2571+(t2999+t3008)*t2888; + t2945 = t2803+t2620+t3204*y; + t2944 = t2504+(t2668+t3199)*y; + t2943 = t2855*t3105+t2888*t3000+t2506+t2850*t3055; + t2646 = x*t2755; + t2623 = z*t2791; + t2942 = t2646+t2890*t2747+t2623+t2746; + t2480 = t2889*t2953; + t2941 = t2480+t2856*t3001+t2855*t3115+t2889*t3095; + t2940 = t2713+t2801+t2829+t2676; + t2939 = t2830+t2793+t3204; + t2937 = t2891*t3006+t2625+(t2979+t3081)*x; + t2936 = t2890*t2769+t2753+t2618+t2623; + t2728 = t2854*t3116; + t2721 = t2892*t3013; + t2493 = x*t2998; + t2935 = t2508+t2728+t2721+t2493; + t2934 = t2620+t3213*y; + t2588 = z*t2789; + t2933 = t2588+t2659+t3024; + t2931 = t3091+t3187; + t2930 = t2496+(t2718+t3207)*y; + t2929 = t2508+t2492+t3207; + t2649 = t2846*t3116; + t2928 = z*t2989+t2502+t2892*t3038+t2649; + t2927 = -t3113+t3044-t2889; + t2926 = t2646+t2810+t2607+t2676+t3088; + t2925 = t2518+t2726+t3046+t3088; + t2694 = t2891*t3073; + t2924 = t2694+t2500+t3039+t3062; + t2696 = t2889*t3060; + t2923 = t2696+t2889*t2993+t3040+t3071; + t2697 = x*t3109; + t2922 = t2516+t2697+t2892*t2989+z*t3015+t3054; + t2507 = y*t2695; + t2921 = y*t2726+t2507+t3032+t3093; + t2499 = y*t2730; + t2503 = x*t2958; + t2920 = t2718+t2499+t2503+t2966; + t2919 = t2486+t2713+t2730+t2499+t3091; + t2477 = x*t2972; + t2918 = t2477+t2889*t3013+t3040+t3103; + t2917 = t3009+t3070+t3071; + t2916 = t3083+t3086+t3093; + t2915 = t2694+t2452+t2855*t3107+t2850*t3116+t2503+t2489+(t3013+t2993)*z; + t2547 = t2871*t2957; + t2615 = z*t2767; + t2914 = t2813+t2547+t2892*t3050+t2615+t2524+t2975; + t2913 = t2625+t2717+t2987+t3188+t3211; + t2553 = t2877*t2957; + t2531 = z*t2768; + t2912 = t2553+t2531+t2769+t2786+t2988+t3205; + t2911 = t2480+x*t3031+t2987+t3058+t3158; + t2910 = t2684+t2635+t2975+t3180+t3186; + t2909 = t2595+t2671+t2988+t3185+t3203; + t2908 = t2619+t2884+t2834+t2889*t3052+t3162+t2762+t3154+(t3089+t2955)*x; + t2907 = t2758+t2871*t3002+t2553+t2835+t2864*t3055+t2767+t2963+t3162; + t2906 = t2720+t2754+t2688+t2832+t2934+t3009+t3152; + t2672 = x*t3008; + t2905 = t2612+t2672+t2933+t2937+t3102; + t2714 = z*t3095; + t2904 = t2487+t2714+t2472+t2663+t2935+t2946; + t2584 = t2870*t2980; + t2903 = t2768+t2584+t2547+t2877*t3002+t2939+t2945; + t2902 = t2606+t2584+x*t2967+t2793+t2792+t2934+t3213; + t2724 = x*t3073; + t2901 = t2505+t2724+t2935+t2937+t3184; + t2465 = x*t3000; + t2900 = t2728+t2465+t2944+t3012+t3090+t3184; + t2686 = t2891*t3108; + t2899 = t2592+t2686+t2933+t2946+t3020; + t2593 = t2890*t2758; + t2898 = t2593+t2804+t2671+t2842+t2945+t3152+t3180; + t2585 = x*t2999; + t2897 = t2592+t2585+t2944+t3004+t3042+t3199; + t2559 = y*t2739; + t2896 = t2559+t2778+t2963+t2787+t3154+((z+x)*t2878+t2772+1.0+t3200)*y; + t2895 = t2566+t2595+t2931+t2822+t3122+(t3075+t2852)*z+t3201; + t2881 = RATIONAL(-2.0,3.0); + t2880 = RATIONAL(-2.0,1.0); + t2867 = RATIONAL(2.0,1.0); + t2861 = RATIONAL(1.0,54.0); + t2650 = t2892*t3021; + t2608 = t2891*t2740; + t2600 = t2879*t3029; + t2555 = t2892*t2809; + t2545 = z*t2806; + t2528 = x*t3028; + t2514 = t2892*t2990; + t2485 = t2854*t2995; + t2455 = t2854*t2991; + t2451 = z*t2965; + coeffs_dy->coeff_m1_m1_m1 = (t2858*t2892+(RATIONAL(-1.0,27.0)+t2853*t2890 +)*z)*x+t2911+t2455+t2891*t3109+t2485+t3126+t3141+t3176; + coeffs_dy->coeff_0_m1_m1 = t2466+t2723+t2920+t2906+(t3026+t2860)*t2892+( +t2866+t2865*t2888+(t2863+t2842)*t2890)*z+t2970+t3121+t3174; + coeffs_dy->coeff_p1_m1_m1 = t2913+t2712+t2951+t2971+t3126+t3127; + coeffs_dy->coeff_p2_m1_m1 = t2861*t3114+t2697+t2923+t3041+t3136+t3164+ +t3189; + coeffs_dy->coeff_m1_0_m1 = (t2891*t3110+(RATIONAL(-2.0,9.0)*z+t2865*t2892 +)*x)*y+t2723+t2634+t2910+t2514+t2924+t3027+t3134; + coeffs_dy->coeff_0_0_m1 = t2673+t2677+t2908+(-t2889+t2949*t2892+(t2881* +t2888+t2882)*z)*y+t2936+t2643+t2672+t3149+t3150+t3172+t3196; + coeffs_dy->coeff_p1_0_m1 = t2646+t2600+t2608+t2730+t2910+t3030+t3102+ +t3128+t3198+t3212; + coeffs_dy->coeff_p2_0_m1 = t2866*y*t3114+t2901+t2507+t3094+t3179; + coeffs_dy->coeff_m1_p1_m1 = t2788+t2909+t2704+t2678+t2505+t2680+t2964+ +t3131+t3141+t3167; + coeffs_dy->coeff_0_p1_m1 = t2588+t2919+t2902+t2982+t3121+t3145+t3151+ +t3165+t3187; + coeffs_dy->coeff_p1_p1_m1 = t2909+t2643+t2777+t2976+t2981+t3138+t3195; + coeffs_dy->coeff_p2_p1_m1 = t2711+t2503+t2917+t3045+t3046+t3090+t3136; + coeffs_dy->coeff_m1_p2_m1 = t2918+t2650+t2860*t3014+t2922+t3175+t3189; + coeffs_dy->coeff_0_p2_m1 = (t2862+t3100)*t3112+t2675+t3051+t2901+t3129+ +t3139; + coeffs_dy->coeff_p1_p2_m1 = t2924+t2663+t2964+t3155+t3175+t3178; + coeffs_dy->coeff_p2_p2_m1 = t2485+t2847*t3107+t2928+t2941+t3169; + coeffs_dy->coeff_m1_m1_0 = t2692+t2723+t3209*t2891+t2491+t2898+(t2866+ +t2865*t2889+(t2832+t2863)*t2890)*x+t2951+t2966+t3119+t3168+t3182; + coeffs_dy->coeff_0_m1_0 = (-y+t2947*t2890+t2948)*t2888+t2585+t2940+t3069+ +t2791+(t2879-y+t3080)*t2889+t3118+t2896+t2883+t3153+t3165+t3188+t3196; + coeffs_dy->coeff_p1_m1_0 = t2748+t2898+t2942+t3004+t3132+t3160+t3192+ +t3198; + coeffs_dy->coeff_p2_m1_0 = t2900+x*t3049+t2477+(t2853+t3031)*t2891+t3133+ +t3142; + coeffs_dy->coeff_m1_0_0 = t2600+t2907+t2686+(-t2888+t2948*t2891+(t2881* +t2889+t2882)*x)*y+t2942+t3024+t3092+t3118+t3166+t3208; + coeffs_dy->coeff_0_0_0 = t2939+t3124+(t2868+t2872*t2891)*z+t2878+t2615+( +t2872*t2892+t2978)*x+(t2880+(t2891-x+t2867)*t2889+(t2892-z+t2867+t2880*t2889)* +t2888-t3057)*y+t3057*t2869+(t2889*t3011+t2876+t2875*z+t3079*t2873+(t2875+t2877* +z)*x)*t2890+t3177+t3183+t3193+t3194; + coeffs_dy->coeff_p1_0_0 = t2747+(-t3101+(-t2892+t2880+t2867*t2889)*x+ +t3098)*y+(t2876+t2873*t2889)*t3106+t3123+t2907+t2978*t2891+t2802+t3190+t3197; + coeffs_dy->coeff_p2_0_0 = ((t3087+t2883)*t2891+t2948*x)*y+t2583+t2932+ +t3122+t3125+t3144; + coeffs_dy->coeff_m1_p1_0 = t2588+t2940+t2903+t2981+t3086+t3119+t3132+ +t3181; + coeffs_dy->coeff_0_p1_0 = t3117+t2947*t2891+RATIONAL(1.0,1.0)+t2531+t2927 ++(t3034-y+t2889-1.0)*t2888+t2739+t2896+(t2870*z+t2873+t2889*t3007+t3079*t2876+( +t2871*z+t2870)*x)*t2890+t3163+t3190; + coeffs_dy->coeff_p1_p1_0 = (1.0+(t2873+t2876*t2889)*t2890+t2927)*x+t2903+ +(t2878+t2841)*t2891+t3120+t3192+t3193+t3210; + coeffs_dy->coeff_p2_p1_0 = t2897+t2648+t2791+t3135+t3142+t3160; + coeffs_dy->coeff_m1_p2_0 = t3066+t2696+(t3097+t2862)*t3106+t2904+t3133+ +t3143; + coeffs_dy->coeff_0_p2_0 = t2889*t2842+t3079*t2863+t2895+t2862+((t3078+1.0 +)*t2874+t3079*t2878)*t2890+t3125+t3156; + coeffs_dy->coeff_p1_p2_0 = t2899+t3135+t3143+t3181+t3208; + coeffs_dy->coeff_p2_p2_0 = t3060+(t2854*t2889+t2950)*x+t2915+t3058+t3168; + coeffs_dy->coeff_m1_m1_p1 = t2487+t2911+t2568+t2968+t2970+t3127+t3137; + coeffs_dy->coeff_0_m1_p1 = t2798+t2906+t2936+t2931+t2703+t2658-t3010+ +t2952+t3145+t3173+t3191; + coeffs_dy->coeff_p1_m1_p1 = t2589+t2604+t2913+t2770+t2610+t2559+t2563+ +t2985+t3137+t3157+t3206; + coeffs_dy->coeff_p2_m1_p1 = t2920+t2541+t2662+t2493+t2923+t2971; + coeffs_dy->coeff_m1_0_p1 = t2914+t2555-t3010+t3020+t3128+t3134+t3170+ +t3172; + coeffs_dy->coeff_0_0_p1 = t3117+(-t3055+(-t2891+t2867*t2888+t2880)*z+ +t3023)*y+(t2876+t3007)*t3112+t2908+(t2864*x+t2868)*t2892+t2545+t2786+t3157+ +t3197; + coeffs_dy->coeff_p1_0_p1 = t2876*t3014+t2914+(t3098*z+(t2880*z+t3023)*x)* +y+t3120+t3194+t3202+t3212; + coeffs_dy->coeff_p2_0_p1 = t2905+t2608+t2528+t3094+t3149; + coeffs_dy->coeff_m1_p1_p1 = t2646+t2568+t2743+t2594+t2912+t2982+t3092+ +t3131+t3138; + coeffs_dy->coeff_0_p1_p1 = (t2878+t2830)*t2892+t2902+t2735+(t3065+1.0- +t2888-y*t2888+(t2873+t3011)*t2890)*z+t3124+t3191+t3202+t3210; + coeffs_dy->coeff_p1_p1_p1 = t2523+t2997+(t3034+t2873*t3112+z)*x+t2912+ +t2559+t2545+t2739+t3123+t3195; + coeffs_dy->coeff_p2_p1_p1 = t2810+t2623+t2541+t2917+t2919+t2976; + coeffs_dy->coeff_m1_p2_p1 = t2718+t2918+t2505+t2599+t2694+t2925+t3147; + coeffs_dy->coeff_0_p2_p1 = t2905+t3130+t3139+t3150+t3151; + coeffs_dy->coeff_p1_p2_p1 = t2664+t2730+t2572+t2594+t2926+t3147+t3170+ +t3178; + coeffs_dy->coeff_p2_p2_p1 = t2721+t2724+t2929+t2941+t3045; + coeffs_dy->coeff_m1_m1_p2 = t2861*t3107+t2921+t2451+t2922+t3146+t3164; + coeffs_dy->coeff_0_m1_p2 = t2900+t2469+t2998+(t3022+t2853)*t2892+t3129+ +t3140; + coeffs_dy->coeff_p1_m1_p2 = t2487+t2916+t2695+t2678+t2489+t2493+t3039+ +t3146+t3155; + coeffs_dy->coeff_p2_m1_p2 = t2649+t2850*t3014+t2930+t3161+t3169+t3176; + coeffs_dy->coeff_m1_0_p2 = t2866*t3029+t2510+t2904+t3077+t3179; + coeffs_dy->coeff_0_0_p2 = ((t3016+t2883)*t2892+t2949*z)*y+t2895+t3144; + coeffs_dy->coeff_p1_0_p2 = t2555+t2899+t2528+t3077+t3166; + coeffs_dy->coeff_p2_0_p2 = y*t2723+t2514+t2915+t3053; + coeffs_dy->coeff_m1_p1_p2 = t2593+t2921+t2925+t2968+t3182; + coeffs_dy->coeff_0_p1_p2 = t2897+t3130+t3140+t3153+t3173; + coeffs_dy->coeff_p1_p1_p2 = t2566+t2916+t2593+t2623+t2926+t2985; + coeffs_dy->coeff_p2_p1_p2 = t2472+t2718+t2678+t2465+t2929+t2930; + coeffs_dy->coeff_m1_p2_p2 = z*t3021+t2455+t2928+t2943+t3161; + coeffs_dy->coeff_0_p2_p2 = t3048+(t2854*t2888+t2950)*z+t2915+t3068+t3174; + coeffs_dy->coeff_p1_p2_p2 = t2685+t2714+t2466+t2721+t2943+t3012+t3027; + coeffs_dy->coeff_p2_p2_p2 = t2451+t2650+z*t3038+(t2849*t2892+(t2855*t2890 ++t2847)*z)*x+t3041; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyy.compute.c new file mode 100644 index 0000000..a3ca038 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyy.compute.c @@ -0,0 +1,889 @@ +fp t5986; +fp t5968; +fp t6113; +fp t5864; +fp t5784; +fp t5985; +fp t5987; +fp t5967; +fp t6118; +fp t6059; +fp t5816; +fp t6174; +fp t5988; +fp t5780; +fp t5896; +fp t6173; +fp t5969; +fp t5943; +fp t5981; +fp t6172; +fp t6103; +fp t6063; +fp t5971; +fp t6171; +fp t6120; +fp t5970; +fp t6060; +fp t5909; +fp t5887; +fp t6170; +fp t5983; +fp t6117; +fp t6169; +fp t5954; +fp t6068; +fp t5840; +fp t5742; +fp t5951; +fp t6116; +fp t6065; +fp t6168; +fp t5942; +fp t5919; +fp t5966; +fp t6094; +fp t5878; +fp t6167; +fp t5959; +fp t5935; +fp t5958; +fp t6081; +fp t5899; +fp t6166; +fp t5972; +fp t6080; +fp t5874; +fp t5763; +fp t6128; +fp t5932; +fp t6165; +fp t5772; +fp t6164; +fp t5950; +fp t6163; +fp t5930; +fp t5758; +fp t6087; +fp t5851; +fp t5729; +fp t6162; +fp t5910; +fp t5761; +fp t6071; +fp t5867; +fp t6161; +fp t5944; +fp t5865; +fp t5976; +fp t6160; +fp t5973; +fp t6091; +fp t6089; +fp t5922; +fp t6159; +fp t5946; +fp t5873; +fp t6158; +fp t5977; +fp t5938; +fp t5859; +fp t5829; +fp t6157; +fp t6086; +fp t5836; +fp t6109; +fp t5882; +fp t6156; +fp t5960; +fp t5893; +fp t5956; +fp t6072; +fp t6155; +fp t5915; +fp t5939; +fp t5917; +fp t6154; +fp t5926; +fp t5870; +fp t6153; +fp t5860; +fp t5753; +fp t5936; +fp t5885; +fp t6152; +fp t6093; +fp t6062; +fp t5755; +fp t5892; +fp t5754; +fp t6151; +fp t5947; +fp t5911; +fp t5886; +fp t6150; +fp t6149; +fp t5952; +fp t6124; +fp t5845; +fp t6099; +fp t5844; +fp t5726; +fp t6148; +fp t5821; +fp t6147; +fp t5949; +fp t5929; +fp t5905; +fp t6146; +fp t6104; +fp t6145; +fp t5802; +fp t5902; +fp t6144; +fp t6115; +fp t5931; +fp t5760; +fp t6143; +fp t5940; +fp t5907; +fp t6142; +fp t6141; +fp t5918; +fp t6140; +fp t5890; +fp t5863; +fp t6139; +fp t5908; +fp t5901; +fp t6138; +fp t5817; +fp t6137; +fp t5749; +fp t6064; +fp t5794; +fp t6058; +fp t5785; +fp t6136; +fp t5888; +fp t5945; +fp t5891; +fp t6077; +fp t6135; +fp t6134; +fp t5819; +fp t6125; +fp t5900; +fp t5810; +fp t6133; +fp t6114; +fp t5877; +fp t6132; +fp t5925; +fp t5796; +fp t6088; +fp t6131; +fp t5875; +fp t6130; +fp t6061; +fp t5766; +fp t6129; +fp t5984; +fp t5982; +fp t6127; +fp t6126; +fp t5937; +fp t6123; +fp t5955; +fp t6122; +fp t6121; +fp t6119; +fp t5980; +fp t5948; +fp t5963; +fp t6112; +fp t6111; +fp t5941; +fp t5961; +fp t6110; +fp t5837; +fp t5846; +fp t6108; +fp t5832; +fp t5833; +fp t6107; +fp t5811; +fp t6106; +fp t5831; +fp t6105; +fp t5978; +fp t5850; +fp t6102; +fp t5953; +fp t6092; +fp t5855; +fp t6101; +fp t6100; +fp t6098; +fp t5731; +fp t6097; +fp t5927; +fp t6096; +fp t5747; +fp t6074; +fp t5807; +fp t6095; +fp t5974; +fp t6090; +fp t6085; +fp t6066; +fp t5839; +fp t5744; +fp t5841; +fp t6084; +fp t5843; +fp t5724; +fp t6083; +fp t6082; +fp t5847; +fp t5725; +fp t5730; +fp t6079; +fp t5835; +fp t5834; +fp t6078; +fp t6076; +fp t6075; +fp t5979; +fp t6073; +fp t5853; +fp t6070; +fp t6069; +fp t5880; +fp t6067; +fp t5881; +fp t5830; +fp t5838; +fp t5854; +fp t5923; +fp t5916; +fp t5898; +fp t5924; +fp t5857; +fp t5852; +fp t5934; +fp t5858; +fp t5757; +fp t6057; +fp t5792; +fp t5791; +fp t5933; +fp t5800; +fp t6056; +fp t5801; +fp t5884; +fp t5777; +fp t6055; +fp t5856; +fp t6054; +fp t5738; +fp t5793; +fp t6053; +fp t6052; +fp t5868; +fp t6051; +fp t5928; +fp t5775; +fp t6050; +fp t6049; +fp t5803; +fp t6048; +fp t5748; +fp t6047; +fp t5805; +fp t5764; +fp t6046; +fp t5820; +fp t6045; +fp t6044; +fp t6043; +fp t5813; +fp t6042; +fp t5806; +fp t6041; +fp t6040; +fp t6039; +fp t5964; +fp t5957; +fp t6038; +fp t6037; +fp t6036; +fp t6035; +fp t6034; +fp t5824; +fp t6033; +fp t6032; +fp t5812; +fp t6031; +fp t6030; +fp t5765; +fp t6029; +fp t5719; +fp t6028; +fp t6027; +fp t6026; +fp t5736; +fp t6025; +fp t5789; +fp t6024; +fp t6023; +fp t6022; +fp t6021; +fp t5782; +fp t6020; +fp t5752; +fp t5827; +fp t6018; +fp t5750; +fp t6017; +fp t5804; +fp t6016; +fp t6015; +fp t6014; +fp t6013; +fp t6012; +fp t5798; +fp t5788; +fp t6011; +fp t6010; +fp t6009; +fp t6008; +fp t6007; +fp t6006; +fp t5795; +fp t6005; +fp t6004; +fp t6003; +fp t5759; +fp t6002; +fp t6001; +fp t5808; +fp t6000; +fp t5861; +fp t5999; +fp t5998; +fp t5997; +fp t5894; +fp t5996; +fp t5913; +fp t5995; +fp t5866; +fp t5994; +fp t5862; +fp t5993; +fp t5992; +fp t5991; +fp t5975; +fp t5962; +fp t5912; +fp t5903; +fp t5879; +fp t5869; +fp t5849; +fp t5825; +fp t5809; +fp t5776; +fp t5756; +fp t5751; +fp t5743; +fp t5741; +fp t5737; +fp t5735; +fp t5734; +fp t5723; +fp t5722; +fp t5721; + t5986 = z*z; + t5968 = RATIONAL(-3.0,2.0); + t6113 = y*t5968; + t5864 = t5986*t6113; + t5784 = x*t5864; + t5985 = x*x; + t5987 = t5985*x; + t5967 = RATIONAL(3.0,4.0); + t6118 = y*t5967; + t6059 = t5987*t6118; + t5816 = t5986*t6059; + t6174 = t5784+t5816; + t5988 = t5986*z; + t5780 = t5988*t6059; + t5896 = t5987*t6113; + t6173 = t5780+z*t5896; + t5969 = RATIONAL(1.0,2.0); + t5943 = t5969*t5988; + t5981 = x*z; + t6172 = t5987*t5943+t6113*t5981; + t6103 = t5986*t5987; + t6063 = y*t6103; + t5971 = RATIONAL(3.0,2.0); + t6171 = t5896+z*t6059+t5971*t6063; + t6120 = y*t5988; + t5970 = RATIONAL(-3.0,4.0); + t6060 = t5970*t6120; + t5909 = t5971*t6120; + t5887 = t5985*t6113; + t6170 = t5909+t5988*t5887+x*t6060; + t5983 = t5985*t5986; + t6117 = 1.0-t5986; + t6169 = (t5983-t5985+t6117)*y; + t5954 = RATIONAL(-1.0,12.0); + t6068 = t5986*t5954; + t5840 = t5987*t6068; + t5742 = y*t5840; + t5951 = RATIONAL(1.0,12.0); + t6116 = x*t5951; + t6065 = y*t6116; + t6168 = t5742+t5986*t6065; + t5942 = t5969*t5985; + t5919 = z*t5942; + t5966 = RATIONAL(-1.0,4.0); + t6094 = t5988*t5966; + t5878 = t5985*t6094; + t6167 = t5919+t5878; + t5959 = RATIONAL(1.0,6.0); + t5935 = t5959*t5987; + t5958 = RATIONAL(-1.0,6.0); + t6081 = t5986*t5958; + t5899 = t5987*t6081; + t6166 = (t5935+t5899)*y; + t5972 = RATIONAL(-1.0,2.0); + t6080 = t5986*t5972; + t5874 = y*t6080; + t5763 = x*t5874; + t6128 = y*t5969; + t5932 = x*t6128; + t6165 = t5763+t5932; + t5772 = t5987*t6060; + t6164 = t5772+x*t5909; + t5950 = t5972*t5988; + t6163 = x*t5950+t5981; + t5930 = z*t5935; + t5758 = y*t5930; + t6087 = t5951*t5987; + t5851 = t5986*t6087; + t5729 = y*t5851; + t6162 = t5758+t5729; + t5910 = y*t5942; + t5761 = t5986*t5910; + t6071 = t5972*t5985; + t5867 = y*t6071; + t6161 = t5761+t5867; + t5944 = t5958*t5988; + t5865 = t5987*t5944; + t5976 = RATIONAL(2.0,3.0); + t6160 = t5976*t5981+t5865; + t5973 = RATIONAL(1.0,3.0); + t6091 = t5973*t5986; + t6089 = t5986*t5959; + t5922 = t5987*t6089; + t6159 = t5922+x*t6091; + t5946 = t5959*t5988; + t5873 = t5985*t5946; + t6158 = (t5944+t5873)*y; + t5977 = RATIONAL(-1.0,3.0); + t5938 = t5977*z; + t5859 = x*t5938; + t5829 = t5988*t6087; + t6157 = t5859+t5829; + t6086 = t5988*t5954; + t5836 = t5985*t6086; + t6109 = t5985*z; + t5882 = t5958*t6109; + t6156 = t5836+t5882; + t5960 = RATIONAL(-1.0,9.0); + t5893 = t5960*t5981; + t5956 = RATIONAL(1.0,18.0); + t6072 = t5956*t5987; + t6155 = t5893+t5988*t6072; + t5915 = t5987*t6080; + t5939 = t5969*t5987; + t5917 = y*t5939; + t6154 = y*t5915+t5917; + t5926 = t5988*t6071; + t5870 = y*t5943; + t6153 = y*t5926+t5870; + t5860 = t5986*t6071; + t5753 = y*t5860; + t5936 = t5969*t5986; + t5885 = y*t5936; + t6152 = t5753+t5885; + t6093 = t5986*t5966; + t6062 = y*t6093; + t5755 = t5985*t6062; + t5892 = t5959*t6109; + t5754 = y*t5892; + t6151 = t5755+t5754; + t5947 = t5972*z; + t5911 = x*t5947; + t5886 = t5987*t6094; + t6150 = t5911+t5886; + t6149 = t5910+t5753; + t5952 = RATIONAL(-1.0,18.0); + t6124 = x*t5952; + t5845 = t5988*t6124; + t6099 = t5988*t5985; + t5844 = t5951*t6099; + t5726 = y*t5844; + t6148 = y*t5845+t5726; + t5821 = z*t5867; + t6147 = t5755+t5821; + t5949 = t5972*t5987; + t5929 = y*t5949; + t5905 = t5986*t5939; + t6146 = y*t5905+t5929; + t6104 = t5973*t5985; + t6145 = t5873+z*t6104; + t5802 = y*t5919; + t5902 = y*t5947; + t6144 = t5802+t5902; + t6115 = t5973*z; + t5931 = x*t6115; + t5760 = y*t5931; + t6143 = t5760+t5763; + t5940 = t5958*t5987; + t5907 = y*t5940; + t6142 = t5907+y*t5922; + t6141 = t5761+t5874; + t5918 = t5987*t5946; + t6140 = t5918+t5931; + t5890 = t5985*t5944; + t5863 = y*t5946; + t6139 = y*t5890+t5863; + t5908 = y*t5950; + t5901 = t5988*t5942; + t6138 = t5908+y*t5901; + t5817 = z*t5932; + t6137 = t5817+t5918+t5859; + t5749 = z*t5887; + t6064 = y*t5970*t5985; + t5794 = t5986*t6064; + t6058 = y*t6099; + t5785 = t5967*t6058; + t6136 = t5749+t5794+t5785; + t5888 = x*t5946; + t5945 = t5958*z; + t5891 = x*t5945; + t6077 = t5891+t5930; + t6135 = t5888+t5865+t6077; + t6134 = t5919-t5985+t5926; + t5819 = t5970*t6063; + t6125 = y*t5971; + t5900 = t5986*t6125; + t5810 = x*t5900; + t6133 = t5819+t5810+t5905; + t6114 = t5970*z; + t5877 = t5987*t6125; + t6132 = t5780+y*t5987*t6114+t5877+t5968*t6063; + t5925 = t5985*t6125; + t5796 = t5986*t5925; + t6088 = x*t6118; + t6131 = t5796+t5819+t5864+t5986*t6088; + t5875 = t5988*t6113; + t6130 = t5875+t5772+t5988*t6088+t5971*t6058; + t6061 = t5985*t6118; + t5766 = t5970*t6058; + t6129 = z*t6061+t5796+t5766+t5887; + t5984 = y*x; + t5982 = y*z; + t6127 = x*t5988; + t6126 = x*t5986; + t5937 = t5958*x; + t6123 = x-t5987; + t5955 = RATIONAL(1.0,36.0); + t6122 = x*t5955; + t6121 = z*t5987; + t6119 = z*t5959; + t5980 = y*t5981; + t5948 = t5972*x; + t5963 = RATIONAL(1.0,4.0); + t6112 = z*t5963; + t6111 = x*t5956; + t5941 = t5977*x; + t5961 = RATIONAL(1.0,9.0); + t6110 = z*t5961; + t5837 = z*t6122; + t5846 = t5954*t6109; + t6108 = t5844+t5846; + t5832 = t5988*t6116; + t5833 = t5987*t6086; + t6107 = t5832+t5833; + t5811 = x*t5908; + t6106 = t5973*t6127+t5811; + t5831 = z*t6087; + t6105 = t5833+t5831; + t5978 = y*t6126; + t5850 = z*t6111; + t6102 = t5986*t5963; + t5953 = RATIONAL(-1.0,36.0); + t6092 = t5988*t5953; + t5855 = t5987*t6092; + t6101 = t5850+t5855; + t6100 = z*t6124; + t6098 = t5963*t5984; + t5731 = y*t5833; + t6097 = y*t5832+t5731; + t5927 = x*t6089; + t6096 = t5927+t5899; + t5747 = z*t5907; + t6074 = y*t6119; + t5807 = x*t6074; + t6095 = t5747+t5807; + t5974 = RATIONAL(-2.0,1.0); + t6090 = -t5988+t5974; + t6085 = y*t5945; + t6066 = t5987*t5955; + t5839 = t5988*t6066; + t5744 = y*t5839; + t5841 = x*t6092; + t6084 = y*t5841+t5744; + t5843 = z*t6066; + t5724 = y*t5855; + t6083 = y*t5843+t5724; + t6082 = -t5984+t5978; + t5847 = x*t6086; + t5725 = y*t5847; + t5730 = y*t5829; + t6079 = t5725+t5730; + t5835 = t5988*t6111; + t5834 = z*t6072; + t6078 = t5835+t5834; + t6076 = t5892+t5890; + t6075 = t5986*t6061+t5860; + t5979 = y*t6109; + t6073 = t5982-t5979; + t5853 = x*t6068; + t6070 = t5851+t5853; + t6069 = t5952*t5987; + t5880 = x*t6110; + t6067 = t5963*t5988; + t5881 = x*t6081; + t5830 = t5954*t6121; + t5838 = t5953*t6121; + t5854 = z*t6069; + t5923 = t5966*t6121; + t5916 = t5987*t6112; + t5898 = x*t6067; + t5924 = x*t6094; + t5857 = x*t5944; + t5852 = t5988*t6122; + t5934 = t5966*t6109; + t5858 = t5987*t6093; + t5757 = y*t5858; + t6057 = t5758+t5730+t5757; + t5792 = x*t5870; + t5791 = y*t5886; + t5933 = t5985*t6067; + t5800 = y*t5933; + t6056 = t5792+t5791+t5800; + t5801 = x*t5885; + t5884 = t5985*t6102; + t5777 = y*t5884; + t6055 = t5801+t5757+t5777; + t5856 = x*t5936; + t6054 = t5858+t5884+t5856; + t5738 = y*t5836; + t5793 = y*t5857; + t6053 = t5738+t5793+t5730; + t6052 = t5800+t5793+t5731; + t5868 = t5987*t6102; + t6051 = -t5980+t5792+t5763; + t5928 = t5987*t6067; + t5775 = y*t5881; + t6050 = t5775+t5742+t5777; + t6049 = t5738+t5744+y*t5835; + t5803 = y*t5859; + t6048 = t5747+t5802+t5803; + t5748 = x*t5863; + t6047 = t5731+t5748+t5726; + t5805 = z*t5917; + t5764 = y*t5868; + t6046 = t5791+t5805+t5764; + t5820 = y*t5878; + t6045 = t5820+t5730+t5748; + t6044 = t5881+t5840+t5884; + t6043 = y*t5854+t5729+t5724; + t5813 = z*t5929; + t6042 = t5980+t5813+t5802; + t5806 = y*t5928; + t6041 = t5806+t5813+t5757; + t6040 = t5806+t5811+t5820; + t6039 = t6104+t5977; + t5964 = RATIONAL(3.0,1.0); + t5957 = RATIONAL(-3.0,1.0); + t6038 = t5964*t5985+t5957; + t6037 = t5977*t5986+t5973; + t6036 = t5977+t6091; + t6035 = t5977*t5985+t5973; + t6034 = t5957*t5985+t5964; + t5824 = y*t5916; + t6033 = t5824+t5791+t6146; + t6032 = t5830+t5847+z*t6116+t5829; + t5812 = y*t5898; + t6031 = t5791+t5812+t6138; + t6030 = t5983-t5986+t5915+t5856; + t5765 = y*t5923; + t6029 = t5806+t5765+t6154; + t5719 = y*t5831; + t6028 = t5954*t5980+t5719+t6097; + t6027 = t5837+t5838+t5839+t5841; + t6026 = t5936+t5868+x*t6093+t5860; + t5736 = y*t5830; + t6025 = t5736+z*t6065+t6079; + t5789 = y*t5924; + t6024 = t5806+t5789+t6153; + t6023 = t5942+t5933+t5934+t5860; + t6022 = t6035*z; + t6021 = t6037*x; + t5782 = z*t5925; + t6020 = t5782+t5901+t5766+t6075; + t5752 = x*t6085; + t5827 = t5963*t5979; + t6018 = t5736+t5752+t5827+t6045; + t5750 = t5986*t6098; + t6017 = t5750+t5725+t5752+t6057; + t5804 = x*t6062; + t6016 = t5804+t5764+t6095+t6097; + t6015 = t5852+t5854+t6070+t6101; + t6014 = t5888+t5891+t6105+t6108; + t6013 = t5843+t5845+t6101+t6108; + t6012 = t5817+t5827+t5765+t6040; + t5798 = x*t5902; + t5788 = y*t5934; + t6011 = t5798+t5824+t5788+t6056; + t6010 = t5804+t5798+t5812+t6046; + t6009 = t5807+t5719+t5788+t6052; + t6008 = t5820+t5821+t6075+t6145; + t6007 = t6070+t6077+t6107; + t6006 = t5817+t5750+t5789+t6041; + t5795 = t5986*t5887; + t6005 = t5925+t5785+t5983+z*t6064+t5795+t6134; + t6004 = t5935+t5937+t6032+t6096; + t6003 = t5816+t5795+t5900+t5970*t5978+t6030; + t5759 = z*t6098; + t6002 = y*t5948+t5801+t5789+t5759+t6029; + t6001 = t5945+t5946+t6032+t6076; + t5808 = t5966*t5980; + t6000 = z*t6128+t5824+t5821+t5808+t6031; + t5861 = z*t5940; + t5999 = t5888+t5861+t6044+t6157+t6167; + t5998 = t5930+t5857+t6054+t6156+t6157; + t5997 = t5880+t5839+t6044+t6078+t6156; + t5894 = z*t5949; + t5996 = t5894+t5928+t6054+t6163+t6167; + t5913 = x*t5943; + t5995 = t5913+t5916+t5949+t5905+t6023+t6150; + t5866 = z*t5939; + t5994 = t5866+t5898+t5901+t5950+t6026+t6150; + t5862 = x*t6119; + t5993 = t5938+t5861+t5944+t5862+t6026+t6107+t6145; + t5992 = t5862+t5940+t5941+t5857+t6023+t6105+t6159; + t5991 = RATIONAL(1.0,1.0)+t5939+t5943+t5928+t5923+x*t6112+t5947+t5948+ +t5924+t6030+t6134; + t5975 = RATIONAL(-2.0,3.0); + t5962 = RATIONAL(2.0,1.0); + t5912 = t5987*t6115; + t5903 = t5987*t5938; + t5879 = t5988*t5941; + t5869 = t5987*t5950; + t5849 = t5988*t6069; + t5825 = t5971*t5980; + t5809 = x*t5875; + t5776 = y*t5882; + t5756 = y*t5927; + t5751 = z*t5877; + t5743 = y*t6100; + t5741 = y*t5834; + t5737 = y*t5853; + t5735 = y*t5850; + t5734 = y*t5846; + t5723 = y*t5838; + t5722 = t5951*t5979; + t5721 = y*t5852; + coeffs_dyy->coeff_m1_m1_m1 = t5756+t5997+y*t5893+t6043+t6148+t6151; + coeffs_dyy->coeff_0_m1_m1 = y*t6022+t5993+t6017+t6139+t6141; + coeffs_dyy->coeff_p1_m1_m1 = t5998+t5747+t5764+t6047+t6143+t6151; + coeffs_dyy->coeff_p2_m1_m1 = t5741+t5743+t6015+t6084+t6168; + coeffs_dyy->coeff_m1_0_m1 = t5960*t6121+t5748+t5849+(t5960*t5988+RATIONAL +(-2.0,9.0)*z)*x+t6008+t6057+t6143+t6159; + coeffs_dyy->coeff_0_0_m1 = (t5976+t5975*t5985)*z+t6003+t5912+t5813+t6035* +t5988+t5857+t6031-t6073+t6137; + coeffs_dyy->coeff_p1_0_m1 = t5903-t6126+t5806-t5980+t6008+t5805+t6106+ +t6133+t6160; + coeffs_dyy->coeff_p2_0_m1 = t5987*t6110+t5845+t6016+t6096+t6155; + coeffs_dyy->coeff_m1_p1_m1 = t5997+t5794+t5764+t5801+t6048+t6052; + coeffs_dyy->coeff_0_p1_m1 = t5798+t5805+t5993+t6024+t6073+t6131; + coeffs_dyy->coeff_p1_p1_m1 = t5794+t5998+t6042+t6056+t6174; + coeffs_dyy->coeff_p2_p1_m1 = t6015+t6017; + coeffs_dyy->coeff_m1_p2_m1 = y*t5880+t5776+t5741+t6049+t6050; + coeffs_dyy->coeff_0_p2_m1 = t6039*t5982+t6016+t6152+t6158; + coeffs_dyy->coeff_p1_p2_m1 = t5803+t5776+t5758+t6053+t6055; + coeffs_dyy->coeff_p2_p2_m1 = t5721+t5737+t5735+t6043; + coeffs_dyy->coeff_m1_m1_0 = y*t6021+t5992+t6018+t6161+t6166; + coeffs_dyy->coeff_0_m1_0 = t5991-t6169+t6000+t6146+t6165; + coeffs_dyy->coeff_p1_m1_0 = x-t6126+t5995+t6012+t6082+t6154+t6161; + coeffs_dyy->coeff_p2_m1_0 = t6004+t5775+t5959*t5984+t6028+t6142; + coeffs_dyy->coeff_m1_0_0 = t5861+t6005+(t5975*t5986+t5976)*x+t6037*t5987+ +t6033+t6082+t6106+t6137; + coeffs_dyy->coeff_0_0_0 = t5911+z+t5913+t5782+t5869+t5810+t5866+(t5988+ +t5962-z)*t5985+(t5974*t5985+t5962-t6123)*t5986+(t5968*z+t6038*t5986+(t5968+ +t5967*z)*x+t6034)*y+t6090+t6123+t6132+t6170; + coeffs_dyy->coeff_p1_0_0 = t5894-t6103+t5987+t6005+t5981+(t5962*t5986+( +t5957*t5986+t5964)*y+t6090)*x+t6164+t6171+t6172; + coeffs_dyy->coeff_p2_0_0 = t6036*t5987+t6021+t6002+t6135; + coeffs_dyy->coeff_m1_p1_0 = t5792+t5798+t5992+t6029-t6082+t6129; + coeffs_dyy->coeff_0_p1_0 = t5784+t5749+t5991+(t5971*z+t6034*t5986+(t5971+ +t6114)*x+t6038)*y+t6130+t6171; + coeffs_dyy->coeff_p1_p1_0 = t5809+t5825+((t5957+t5964*t5986)*y+t6117)*x+ +t5995+t6129+t6132; + coeffs_dyy->coeff_p2_p1_0 = t6004+t5812+t5808+t6033+t6165; + coeffs_dyy->coeff_m1_p2_0 = t6036*t5984+t6009+t6142+t6149; + coeffs_dyy->coeff_0_p2_0 = t6169+t6002+t6144+t6153; + coeffs_dyy->coeff_p1_p2_0 = t6011-t6082+t6146+t6149; + coeffs_dyy->coeff_p2_p2_0 = t5756+y*t5937+t6025+t6166; + coeffs_dyy->coeff_m1_m1_p1 = t5756+t5760+t5999+t6052+t6147+t6162; + coeffs_dyy->coeff_0_m1_p1 = z+t5994-t6109+t6006-t6073+t6141+t6153; + coeffs_dyy->coeff_p1_m1_p1 = t5800+t5996+t6046+t6051+t6147; + coeffs_dyy->coeff_p2_m1_p1 = t6007+t6079+t6095+t6168; + coeffs_dyy->coeff_m1_0_p1 = -t6109+t5912+t5879+t6020+t6041+t6051+t6159+ +t6160; + coeffs_dyy->coeff_0_0_p1 = t6003+t5988-t6099+(-t5987+t5974+t5962*t5985+ +t6034*y)*z+t5751+t6130+t6163+t6172; + coeffs_dyy->coeff_p1_0_p1 = t5809+t5869+(t5987-t5985)*z+(t5988-t5986+( +t5964*y+t5974)*z)*x+t6020+t6133+t6173; + coeffs_dyy->coeff_p2_0_p1 = t5903+t5857+t6010+t6096+t6140; + coeffs_dyy->coeff_m1_p1_p1 = t5980+t5811+t5999+t5801+t6046+t6136; + coeffs_dyy->coeff_0_p1_p1 = (-t5985+1.0+t6038*y)*z+t5825+t5994+t6131+ +t6170+t6173; + coeffs_dyy->coeff_p1_p1_p1 = t5957*t5980+t5751+t5996+t6136+t6164+t6174; + coeffs_dyy->coeff_p2_p1_p1 = t6006+t6007; + coeffs_dyy->coeff_m1_p2_p1 = t6045+t6048+t6050; + coeffs_dyy->coeff_0_p2_p1 = t6010+t6073+t6138+t6152; + coeffs_dyy->coeff_p1_p2_p1 = t6040+t6042+t6055; + coeffs_dyy->coeff_p2_p2_p1 = t5737+t5752+t6097+t6162; + coeffs_dyy->coeff_m1_m1_p2 = t5723+t5743+t5722+t6013+t6049; + coeffs_dyy->coeff_0_m1_p2 = t5776+t6001+t6074+t6028+t6158; + coeffs_dyy->coeff_p1_m1_p2 = t5736+t5807+t5722+t6014+t6053; + coeffs_dyy->coeff_p2_m1_p2 = t5721+t5953*t5980+t6027+t6083; + coeffs_dyy->coeff_m1_0_p2 = t5854+t5961*t6127+t6009+t6076+t6155; + coeffs_dyy->coeff_0_0_p2 = t5765+t5759+t6039*t5988+t6022+t6024+t6135+ +t6144; + coeffs_dyy->coeff_p1_0_p2 = t5879+t5861+t6011+t6076+t6140; + coeffs_dyy->coeff_p2_0_p2 = t5849+t6100+t6025+t6078; + coeffs_dyy->coeff_m1_p1_p2 = t6013+t6018; + coeffs_dyy->coeff_0_p1_p2 = t6000+t6001; + coeffs_dyy->coeff_p1_p1_p2 = t6012+t6014; + coeffs_dyy->coeff_p2_p1_p2 = t6027+t6028; + coeffs_dyy->coeff_m1_p2_p2 = t5735+t5734+t6083+t6148; + coeffs_dyy->coeff_0_p2_p2 = t6085+t5754+t6025+t6139; + coeffs_dyy->coeff_p1_p2_p2 = t5752+t5734+t5719+t6047; + coeffs_dyy->coeff_p2_p2_p2 = t5723+y*t5837+t6084; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyz.compute.c new file mode 100644 index 0000000..71c01d8 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyz.compute.c @@ -0,0 +1,1098 @@ +fp t6539; +fp t6516; +fp t6569; +fp t6572; +fp t6541; +fp t6834; +fp t6570; +fp t6571; +fp t6667; +fp t6550; +fp t6833; +fp t6524; +fp t6467; +fp t6326; +fp t6523; +fp t6694; +fp t6300; +fp t6832; +fp t6545; +fp t6496; +fp t6401; +fp t6669; +fp t6631; +fp t6831; +fp t6554; +fp t6734; +fp t6389; +fp t6668; +fp t6647; +fp t6232; +fp t6830; +fp t6525; +fp t6483; +fp t6529; +fp t6472; +fp t6829; +fp t6491; +fp t6365; +fp t6828; +fp t6686; +fp t6353; +fp t6526; +fp t6464; +fp t6717; +fp t6560; +fp t6627; +fp t6283; +fp t6537; +fp t6504; +fp t6827; +fp t6546; +fp t6351; +fp t6733; +fp t6543; +fp t6455; +fp t6826; +fp t6707; +fp t6518; +fp t6713; +fp t6632; +fp t6220; +fp t6547; +fp t6652; +fp t6825; +fp t6703; +fp t6323; +fp t6335; +fp t6824; +fp t6710; +fp t6336; +fp t6823; +fp t6488; +fp t6471; +fp t6822; +fp t6492; +fp t6442; +fp t6821; +fp t6677; +fp t6420; +fp t6252; +fp t6493; +fp t6380; +fp t6362; +fp t6663; +fp t6820; +fp t6548; +fp t6692; +fp t6399; +fp t6704; +fp t6414; +fp t6819; +fp t6661; +fp t6418; +fp t6818; +fp t6210; +fp t6393; +fp t6498; +fp t6350; +fp t6681; +fp t6417; +fp t6544; +fp t6736; +fp t6386; +fp t6817; +fp t6531; +fp t6301; +fp t6521; +fp t6687; +fp t6816; +fp t6566; +fp t6563; +fp t6685; +fp t6429; +fp t6815; +fp t6622; +fp t6253; +fp t6474; +fp t6535; +fp t6505; +fp t6814; +fp t6702; +fp t6532; +fp t6413; +fp t6813; +fp t6506; +fp t6364; +fp t6231; +fp t6812; +fp t6534; +fp t6490; +fp t6619; +fp t6309; +fp t6811; +fp t6419; +fp t6432; +fp t6810; +fp t6440; +fp t6400; +fp t6809; +fp t6509; +fp t6433; +fp t6502; +fp t6808; +fp t6501; +fp t6398; +fp t6807; +fp t6451; +fp t6212; +fp t6551; +fp t6732; +fp t6448; +fp t6806; +fp t6469; +fp t6708; +fp t6644; +fp t6207; +fp t6805; +fp t6512; +fp t6239; +fp t6804; +fp t6510; +fp t6415; +fp t6803; +fp t6646; +fp t6802; +fp t6657; +fp t6340; +fp t6801; +fp t6559; +fp t6515; +fp t6556; +fp t6666; +fp t6623; +fp t6233; +fp t6800; +fp t6714; +fp t6645; +fp t6536; +fp t6735; +fp t6799; +fp t6387; +fp t6282; +fp t6428; +fp t6237; +fp t6798; +fp t6527; +fp t6797; +fp t6267; +fp t6796; +fp t6507; +fp t6447; +fp t6425; +fp t6795; +fp t6454; +fp t6794; +fp t6357; +fp t6306; +fp t6793; +fp t6366; +fp t6670; +fp t6792; +fp t6307; +fp t6176; +fp t6520; +fp t6791; +fp t6564; +fp t6494; +fp t6405; +fp t6790; +fp t6371; +fp t6676; +fp t6373; +fp t6789; +fp t6388; +fp t6259; +fp t6788; +fp t6787; +fp t6424; +fp t6281; +fp t6786; +fp t6269; +fp t6193; +fp t6785; +fp t6343; +fp t6427; +fp t6784; +fp t6705; +fp t6650; +fp t6783; +fp t6435; +fp t6272; +fp t6508; +fp t6378; +fp t6782; +fp t6352; +fp t6781; +fp t6409; +fp t6780; +fp t6779; +fp t6778; +fp t6341; +fp t6777; +fp t6699; +fp t6643; +fp t6776; +fp t6444; +fp t6247; +fp t6434; +fp t6256; +fp t6775; +fp t6774; +fp t6530; +fp t6630; +fp t6194; +fp t6696; +fp t6773; +fp t6679; +fp t6441; +fp t6202; +fp t6199; +fp t6372; +fp t6217; +fp t6772; +fp t6226; +fp t6674; +fp t6771; +fp t6517; +fp t6697; +fp t6770; +fp t6377; +fp t6715; +fp t6381; +fp t6390; +fp t6769; +fp t6487; +fp t6334; +fp t6731; +fp t6768; +fp t6213; +fp t6767; +fp t6513; +fp t6684; +fp t6766; +fp t6500; +fp t6395; +fp t6675; +fp t6765; +fp t6648; +fp t6248; +fp t6764; +fp t6654; +fp t6763; +fp t6725; +fp t6475; +fp t6298; +fp t6762; +fp t6761; +fp t6369; +fp t6760; +fp t6503; +fp t6437; +fp t6416; +fp t6673; +fp t6268; +fp t6759; +fp t6758; +fp t6191; +fp t6481; +fp t6482; +fp t6757; +fp t6756; +fp t6438; +fp t6280; +fp t6755; +fp t6754; +fp t6459; +fp t6426; +fp t6753; +fp t6649; +fp t6255; +fp t6752; +fp t6751; +fp t6360; +fp t6243; +fp t6750; +fp t6242; +fp t6465; +fp t6749; +fp t6728; +fp t6175; +fp t6748; +fp t6721; +fp t6606; +fp t6747; +fp t6224; +fp t6651; +fp t6200; +fp t6746; +fp t6452; +fp t6450; +fp t6716; +fp t6745; +fp t6177; +fp t6690; +fp t6744; +fp t6743; +fp t6737; +fp t6718; +fp t6538; +fp t6262; +fp t6198; +fp t6258; +fp t6742; +fp t6741; +fp t6356; +fp t6740; +fp t6567; +fp t6739; +fp t6738; +fp t6468; +fp t6477; +fp t6730; +fp t6552; +fp t6406; +fp t6333; +fp t6729; +fp t6218; +fp t6565; +fp t6727; +fp t6410; +fp t6726; +fp t6431; +fp t6724; +fp t6693; +fp t6367; +fp t6723; +fp t6489; +fp t6443; +fp t6722; +fp t6279; +fp t6449; +fp t6287; +fp t6720; +fp t6533; +fp t6712; +fp t6204; +fp t6709; +fp t6338; +fp t6706; +fp t6700; +fp t6275; +fp t6271; +fp t6698; +fp t6664; +fp t6391; +fp t6695; +fp t6691; +fp t6689; +fp t6688; +fp t6683; +fp t6682; +fp t6680; +fp t6528; +fp t6183; +fp t6672; +fp t6671; +fp t6662; +fp t6404; +fp t6659; +fp t6658; +fp t6656; +fp t6655; +fp t6653; +fp t6368; +fp t6642; +fp t6641; +fp t6640; +fp t6639; +fp t6383; +fp t6638; +fp t6637; +fp t6636; +fp t6196; +fp t6634; +fp t6633; +fp t6355; +fp t6629; +fp t6628; +fp t6568; +fp t6625; +fp t6624; +fp t6621; +fp t6620; +fp t6540; +fp t6618; +fp t6617; +fp t6616; +fp t6615; +fp t6614; +fp t6613; +fp t6612; +fp t6611; +fp t6610; +fp t6609; +fp t6608; +fp t6607; +fp t6605; +fp t6604; +fp t6603; +fp t6602; +fp t6601; +fp t6304; +fp t6600; +fp t6599; +fp t6598; +fp t6597; +fp t6495; +fp t6596; +fp t6327; +fp t6595; +fp t6522; +fp t6486; +fp t6594; +fp t6593; +fp t6592; +fp t6591; +fp t6590; +fp t6589; +fp t6588; +fp t6587; +fp t6214; +fp t6586; +fp t6585; +fp t6584; +fp t6583; +fp t6582; +fp t6581; +fp t6580; +fp t6579; +fp t6578; +fp t6577; +fp t6576; +fp t6575; +fp t6574; +fp t6562; +fp t6558; +fp t6553; +fp t6549; +fp t6519; +fp t6457; +fp t6349; +fp t6296; +fp t6292; +fp t6290; +fp t6266; +fp t6219; +fp t6185; +fp t6178; + t6539 = RATIONAL(1.0,4.0); + t6516 = t6539*x; + t6569 = x*x; + t6572 = t6569*x; + t6541 = RATIONAL(-1.0,4.0); + t6834 = t6516+t6541*t6572; + t6570 = z*z; + t6571 = y*y; + t6667 = t6570+t6571; + t6550 = RATIONAL(-1.0,2.0); + t6833 = t6550+t6834; + t6524 = RATIONAL(-1.0,18.0); + t6467 = t6524*t6572; + t6326 = z*t6467; + t6523 = RATIONAL(1.0,12.0); + t6694 = t6523*t6571; + t6300 = x*t6694; + t6832 = z*t6300+t6326; + t6545 = RATIONAL(1.0,2.0); + t6496 = t6545*t6569; + t6401 = z*t6496; + t6669 = t6570*t6571; + t6631 = RATIONAL(9.0,8.0)*t6669; + t6831 = t6569*t6631+t6401; + t6554 = RATIONAL(2.0,3.0); + t6734 = x*t6554; + t6389 = y*t6734; + t6668 = t6570*t6572; + t6647 = y*t6668; + t6232 = t6550*t6647; + t6830 = t6389+t6232; + t6525 = RATIONAL(-1.0,36.0); + t6483 = t6525*t6572; + t6529 = RATIONAL(1.0,36.0); + t6472 = t6529*x; + t6829 = t6483+t6472; + t6491 = t6539*t6572; + t6365 = RATIONAL(-9.0,4.0)*t6669; + t6828 = t6491+x*t6365; + t6686 = t6569*t6571; + t6353 = t6539*t6686; + t6526 = RATIONAL(-1.0,12.0); + t6464 = t6526*t6569; + t6717 = t6353+t6464; + t6560 = RATIONAL(-1.0,8.0); + t6627 = t6560*t6669; + t6283 = t6572*t6627; + t6537 = RATIONAL(1.0,9.0); + t6504 = t6537*x; + t6827 = t6283+t6504; + t6546 = RATIONAL(-3.0,4.0); + t6351 = t6546*t6668; + t6733 = x*t6571; + t6543 = RATIONAL(3.0,4.0); + t6455 = t6543*t6733; + t6826 = t6351+t6455; + t6707 = t6543*t6570; + t6518 = t6541*t6569; + t6713 = t6569*t6707+t6518; + t6632 = RATIONAL(-9.0,8.0)*t6669; + t6220 = t6569*t6632; + t6547 = RATIONAL(3.0,8.0); + t6652 = t6569*t6547; + t6825 = t6220+t6518+t6570*t6652; + t6703 = t6523*t6570; + t6323 = x*t6703; + t6335 = y*t6467; + t6824 = y*t6323+t6335; + t6710 = t6526*t6570; + t6336 = x*t6710; + t6823 = t6336+t6472; + t6488 = t6523*x; + t6471 = t6526*t6572; + t6822 = t6488+t6471; + t6492 = t6541*t6570; + t6442 = x*t6492; + t6821 = t6488+t6442; + t6677 = t6571*t6572; + t6420 = t6546*t6677; + t6252 = z*t6420; + t6493 = t6550*x; + t6380 = z*t6493; + t6362 = t6543*t6686; + t6663 = (t6518+t6362)*z; + t6820 = z*t6491+t6252+t6380+t6663; + t6548 = RATIONAL(3.0,2.0); + t6692 = t6548*t6571; + t6399 = z*t6692; + t6704 = t6546*t6570; + t6414 = x*t6704; + t6819 = t6547*t6677+t6572*t6399+t6414; + t6661 = t6547*t6570; + t6418 = t6546*t6733; + t6818 = t6548*t6647+t6418+t6572*t6661; + t6210 = y*t6351; + t6393 = x*t6707; + t6498 = t6550*y; + t6350 = x*t6498; + t6681 = t6545*t6572; + t6417 = y*t6681; + t6544 = RATIONAL(-3.0,2.0); + t6736 = y*t6570; + t6386 = t6544*t6736; + t6817 = t6210+t6350+t6417+y*t6393+t6386; + t6531 = RATIONAL(1.0,24.0); + t6301 = t6531*t6668; + t6521 = RATIONAL(-1.0,24.0); + t6687 = t6570*t6521; + t6816 = t6301+x*t6687; + t6566 = x*z; + t6563 = y*t6566; + t6685 = t6550*t6572; + t6429 = z*t6685; + t6815 = t6563+y*t6429; + t6622 = t6571*t6661; + t6253 = t6572*t6622; + t6474 = t6523*t6572; + t6535 = RATIONAL(1.0,6.0); + t6505 = t6535*x; + t6814 = t6505+t6253+t6474; + t6702 = t6570*t6560; + t6532 = RATIONAL(1.0,8.0); + t6413 = t6532*t6668; + t6813 = t6413+x*t6702; + t6506 = t6545*t6570; + t6364 = y*t6506; + t6231 = x*t6364; + t6812 = t6231+t6232; + t6534 = RATIONAL(-1.0,6.0); + t6490 = t6535*t6569; + t6619 = t6534+t6490; + t6309 = y*t6474; + t6811 = t6309+t6231; + t6419 = t6541*t6669; + t6432 = t6539*t6669; + t6810 = t6432+t6569*t6419; + t6440 = t6543*t6669; + t6400 = t6546*t6669; + t6809 = t6569*t6440+t6400; + t6509 = t6550*t6571; + t6433 = t6569*t6509; + t6502 = t6545*t6571; + t6808 = t6433+t6502; + t6501 = t6550*t6570; + t6398 = t6569*t6501; + t6807 = t6398+t6506; + t6451 = z*t6681; + t6212 = t6571*t6451; + t6551 = RATIONAL(1.0,3.0); + t6732 = x*t6551; + t6448 = z*t6732; + t6806 = t6212+t6448; + t6469 = t6529*t6572; + t6708 = t6534*t6570; + t6644 = y*t6708; + t6207 = x*t6644; + t6805 = y*t6469+t6207; + t6512 = t6534*t6569; + t6239 = t6569*t6622; + t6804 = t6512+t6239; + t6510 = t6539*t6570; + t6415 = t6569*t6492; + t6803 = t6510+t6415; + t6646 = x*t6669; + t6802 = t6531*t6646+RATIONAL(1.0,108.0)*t6572; + t6657 = t6571*t6521; + t6340 = t6531*t6677; + t6801 = x*t6657+t6340; + t6559 = RATIONAL(-1.0,3.0); + t6515 = t6559*x; + t6556 = RATIONAL(-3.0,8.0); + t6666 = t6571*t6556; + t6623 = t6570*t6666; + t6233 = t6572*t6623; + t6800 = t6515+t6233; + t6714 = t6535*t6570; + t6645 = y*t6714; + t6536 = RATIONAL(-1.0,9.0); + t6735 = x*t6536; + t6799 = y*t6735+t6572*t6645; + t6387 = t6539*t6677; + t6282 = z*t6387; + t6428 = x*t6502; + t6237 = z*t6428; + t6798 = t6282+t6237; + t6527 = RATIONAL(1.0,72.0); + t6797 = t6570*t6472+t6527*t6677; + t6267 = t6571*t6429; + t6796 = t6237+t6267; + t6507 = t6534*t6572; + t6447 = z*t6507; + t6425 = z*t6515; + t6795 = t6447+t6425; + t6454 = y*t6507; + t6794 = z*t6454+y*t6425; + t6357 = t6534*t6733; + t6306 = t6521*t6668; + t6793 = t6357+t6306; + t6366 = t6532*t6677; + t6670 = t6571*t6560; + t6792 = t6366+x*t6670; + t6307 = t6572*t6657; + t6176 = t6570*t6307; + t6520 = RATIONAL(-1.0,108.0); + t6791 = t6176+t6520*x; + t6564 = z*t6733; + t6494 = t6539*t6571; + t6405 = x*t6494; + t6790 = t6564+t6405; + t6371 = t6569*t6510; + t6676 = (t6464+t6371)*y; + t6373 = t6532*t6686; + t6789 = t6676+t6373; + t6388 = y*t6732; + t6259 = t6545*t6647; + t6788 = t6388+t6259; + t6787 = t6523*t6646+t6520*t6572; + t6424 = z*t6509; + t6281 = x*t6424; + t6786 = t6281+t6425; + t6269 = t6569*t6623; + t6193 = x*t6432; + t6785 = t6269+t6193; + t6343 = t6523*t6668; + t6427 = x*t6714; + t6784 = t6343+t6427; + t6705 = t6548*t6570; + t6650 = x*t6705; + t6783 = y*t6650+t6350; + t6435 = y*t6501; + t6272 = x*t6435; + t6508 = t6559*y; + t6378 = x*t6508; + t6782 = t6272+t6378; + t6352 = t6541*t6686; + t6781 = t6352+t6494; + t6409 = x*t6708; + t6780 = t6371+t6409; + t6779 = (t6415+t6512)*y; + t6778 = t6566+t6429; + t6341 = t6523*t6677; + t6777 = t6341+t6323; + t6699 = t6535*t6571; + t6643 = z*t6699; + t6776 = z*t6735+t6572*t6643; + t6444 = t6544*t6571*z; + t6247 = x*t6444; + t6434 = t6543*t6677; + t6256 = z*t6434; + t6775 = t6247+t6256; + t6774 = (t6512+t6352)*z; + t6530 = RATIONAL(1.0,18.0); + t6630 = t6532*t6669; + t6194 = t6569*t6630; + t6696 = t6569*t6703+t6523*t6686; + t6773 = t6530*t6569+t6194+t6696; + t6679 = t6569*t6546; + t6441 = t6570*t6679; + t6202 = y*t6441; + t6199 = x*t6386; + t6372 = t6543*t6668; + t6217 = y*t6372; + t6772 = t6202+t6199+t6217; + t6226 = z*t6357; + t6674 = t6717*z; + t6771 = z*t6469+t6226+t6674; + t6517 = t6534*y; + t6697 = (t6398+t6490)*y; + t6770 = t6517+t6697+t6364; + t6377 = x*t6510; + t6715 = t6532*t6570; + t6381 = t6569*t6715; + t6390 = t6560*t6668; + t6769 = t6377+t6381+t6390; + t6487 = t6530*x; + t6334 = t6526*t6668; + t6731 = (t6334+t6487)*y; + t6768 = t6525*t6733+t6731+t6529*t6668; + t6213 = x*t6400; + t6767 = t6795+t6213+t6831; + t6513 = t6534*z; + t6684 = (t6490+t6433)*z; + t6766 = t6513+t6684+z*t6502; + t6500 = t6551*t6569; + t6395 = t6545*t6686; + t6675 = (t6500+t6395)*z; + t6765 = t6675+t6373+t6415; + t6648 = z*t6686; + t6248 = t6548*t6648; + t6764 = t6220+t6571*t6652+t6248; + t6654 = t6713*y; + t6763 = t6654+t6210+y*t6491; + t6725 = (t6627+t6529)*t6569; + t6475 = t6531*t6569; + t6298 = t6526*t6686; + t6762 = t6725+t6298+t6570*t6475; + t6761 = t6413+t6366+t6233+t6521*t6572; + t6369 = RATIONAL(9.0,4.0)*t6669; + t6760 = t6569*t6365+t6369+x*t6632; + t6503 = t6535*t6572; + t6437 = y*t6503; + t6416 = x*t6513; + t6673 = y*t6416+z*t6437; + t6268 = x*t6627; + t6759 = t6673+t6268+t6467; + t6758 = t6469+t6785; + t6191 = t6572*t6630; + t6481 = t6523*t6569; + t6482 = t6524*x; + t6757 = t6191+t6785+t6481+t6482+t6483; + t6756 = t6419+t6530+(t6432+t6524)*t6569; + t6438 = t6539*t6668; + t6280 = y*t6438; + t6755 = t6437+t6280+t6782; + t6754 = t6809+t6619; + t6459 = t6572*t6670; + t6426 = x*t6501; + t6753 = z*t6734+t6459+t6426+t6267; + t6649 = x*t6692; + t6255 = z*t6649; + t6752 = t6544*t6647+t6556*t6668+t6255+t6362; + t6751 = t6438+t6428+t6800; + t6360 = t6571*t6679; + t6243 = z*t6360; + t6750 = t6243+t6441+t6360+t6496; + t6242 = x*t6419; + t6465 = t6530*t6572; + t6749 = t6242+t6465+t6827; + t6728 = y*t6465+x*t6645; + t6175 = y*t6343; + t6748 = y*t6504+t6728+t6175+t6794; + t6721 = t6253+x*t6623; + t6606 = t6569*t6400+t6440+t6721; + t6747 = t6500+t6505+t6559+t6507+t6606; + t6224 = t6572*t6631; + t6651 = t6569*t6736; + t6200 = t6548*t6651; + t6746 = t6493+t6393+t6224+t6200+t6420; + t6452 = y*t6505; + t6450 = t6569*t6506; + t6716 = (t6450+t6500)*y; + t6745 = t6452+t6454+t6435+t6508+t6716; + t6177 = z*t6341; + t6690 = x*t6643+z*t6465; + t6744 = t6177+t6690+z*t6504+t6774; + t6743 = t6531*t6572+t6532*t6733+t6459+t6390+(t6715+t6521)*x; + t6737 = t6569*z; + t6718 = y*t6737; + t6538 = RATIONAL(2.0,1.0); + t6262 = t6538*t6718; + t6198 = t6544*t6651; + t6258 = t6544*t6648; + t6742 = t6262+t6258+t6198+(t6532+t6667*t6556)*t6569; + t6741 = t6256+t6399+t6401+t6258+(t6418+t6833)*z; + t6356 = y*t6496; + t6740 = t6498+t6356+t6198+t6217+(t6705+t6414+t6834)*y; + t6567 = y*z; + t6739 = -y-z; + t6738 = y*t6569; + t6468 = t6525*x; + t6477 = t6526*x; + t6730 = x*t6622+t6233; + t6552 = RATIONAL(-2.0,1.0); + t6406 = t6552*t6567; + t6333 = t6526*t6677; + t6729 = (t6333+t6487)*z; + t6218 = x*t6406; + t6565 = t6572*t6567; + t6727 = t6218+t6565; + t6410 = t6541*t6677; + t6726 = t6410+t6405; + t6431 = z*t6503; + t6724 = t6431+t6416; + t6693 = t6572*t6551; + t6367 = z*t6693; + t6723 = y*t6367+z*t6389; + t6489 = t6541*t6571; + t6443 = x*t6489; + t6722 = t6387+t6443; + t6279 = y*t6377; + t6449 = t6541*t6668; + t6287 = y*t6449; + t6720 = t6279+t6287; + t6533 = RATIONAL(-3.0,1.0); + t6712 = t6533*t6570; + t6204 = x*t6440; + t6709 = t6204+t6443; + t6338 = t6571*t6477; + t6706 = t6341+t6338; + t6700 = t6442+t6438; + t6275 = z*t6405; + t6271 = z*t6410; + t6698 = t6275+t6271; + t6664 = t6572*t6559; + t6391 = y*t6664; + t6695 = (t6391+t6388)*z; + t6691 = t6451+t6380; + t6689 = t6204+t6410; + t6688 = z*t6505+t6271; + t6683 = t6533*t6571; + t6682 = t6377+t6449; + t6680 = t6572*t6537; + t6528 = RATIONAL(-1.0,72.0); + t6183 = t6570*t6340; + t6672 = t6183+t6528*t6677; + t6671 = t6283+x*t6630; + t6662 = t6191+t6487; + t6404 = x*t6517; + t6659 = t6437+t6404; + t6658 = t6528*t6570; + t6656 = t6287+t6404; + t6655 = t6242+t6300; + t6653 = t6536*t6572; + t6368 = x*t6506; + t6642 = t6371+t6449+t6368; + t6641 = -t6738-t6569; + t6640 = t6253+t6269+t6213; + t6639 = t6543+t6556*x; + t6383 = x*t6509; + t6638 = t6387+t6352+t6383; + t6637 = t6454+t6356+t6378; + t6636 = y*t6380+t6567+z*t6417; + t6196 = z*t6356; + t6634 = t6196+t6815; + t6633 = -t6737-t6569; + t6355 = x*t6699; + t6629 = t6341+t6352+t6355; + t6628 = t6287+t6191+t6343; + t6568 = y*x; + t6625 = t6356+y*t6685+t6568; + t6624 = t6196+t6779; + t6621 = t6548+t6544*t6569; + t6620 = t6667*t6544; + t6540 = RATIONAL(3.0,1.0); + t6618 = t6540*t6569+t6533; + t6617 = t6540*t6570+t6552; + t6616 = t6540*t6571+t6552; + t6615 = t6262+t6563-t6565+t6406; + t6614 = t6301+t6283+t6528*t6572+t6340; + t6613 = t6177+(t6338+t6829)*z; + t6612 = t6194+(t6657+t6687+t6527)*t6569; + t6611 = t6501+t6450+t6682; + t6610 = t6509+t6395+t6726; + t6609 = t6280+(t6471+t6821)*y; + t6608 = t6239+t6475+(t6702+t6670)*t6569; + t6607 = t6175+(t6483+t6823)*y; + t6605 = t6730+t6822; + t6604 = t6282+(t6443+t6822)*z; + t6603 = t6468+t6469+t6671; + t6602 = t6527*t6668+t6529*t6733+t6791; + t6601 = t6671+t6829; + t6304 = z*t6474; + t6600 = t6237+t6416+t6304+t6271+t6674; + t6599 = t6659+t6721+t6724; + t6598 = t6334+t6338+t6662+t6731; + t6597 = t6336+t6333+t6662+t6729; + t6495 = t6534*x; + t6596 = t6474+t6464+t6495+t6640; + t6327 = t6569*t6710; + t6595 = t6327+t6531*t6686+t6676+t6725; + t6522 = RATIONAL(-1.0,54.0); + t6486 = t6522*x; + t6594 = t6486+t6529*t6677+t6570*t6468+t6183+t6729; + t6593 = t6281+t6304+t6663+t6688+t6723; + t6592 = t6307+t6527*t6572+t6191+t6306+t6531*t6733+t6268+(t6531*t6570+ +t6528)*x; + t6591 = t6452+t6287+t6309+t6272+t6654+t6723; + t6590 = t6218+t6783+t6224+t6713+(t6444+t6666)*t6572; + t6589 = t6252+z*t6455+t6248+t6444+t6636+t6691; + t6588 = t6243+t6401+t6353+t6415+t6624+t6804; + t6587 = t6282+t6431+t6634+t6774+t6786; + t6214 = t6572*t6632; + t6586 = t6214+x*t6369+t6625+t6778+t6831; + t6585 = t6196+t6202+t6231+t6280+t6637+t6794; + t6584 = t6481+t6505-t6718+t6471+t6640+t6727; + t6583 = t6424+t6447+t6275+t6559*z+t6636+t6675+t6688; + t6582 = t6474+t6512+t6535+t6477+t6615+t6730+t6809; + t6581 = t6605+t6609+t6700+t6792; + t6580 = t6323+t6334+t6603+t6609+t6801; + t6579 = t6608+t6709+t6761+t6821; + t6578 = t6604+t6605+t6722+t6813; + t6577 = t6468+t6323+t6608+t6614+t6655; + t6576 = t6333+t6300+t6603+t6604+t6816; + t6575 = x*t6631+t6214+t6569*t6369+t6365+t6496+t6615+t6833; + t6574 = t6371+t6492+t6489+t6523+t6606+t6717+t6743; + t6562 = x*t6736; + t6558 = RATIONAL(4.0,1.0); + t6553 = RATIONAL(-2.0,3.0); + t6549 = RATIONAL(-2.0,9.0); + t6519 = RATIONAL(-1.0,216.0); + t6457 = z*t6664; + t6349 = y*t6693; + t6296 = t6572*t6658; + t6292 = t6525*t6668; + t6290 = t6525*t6677; + t6266 = t6572*t6644; + t6219 = t6571*t6447; + t6185 = t6521*t6646; + t6178 = t6526*t6646; + coeffs_dyz->coeff_m1_m1_m1 = t6624+t6292+t6744+(RATIONAL(-1.0,27.0)+t6667 +*t6524)*x+t6290+t6522*t6572+t6178+t6176+t6748+t6773; + coeffs_dyz->coeff_0_m1_m1 = t6279+t6667*t6535+t6465+(-t6567+t6536+t6667* +t6534)*t6569+t6336+t6537+t6583+t6482+t6628+t6268+t6706+t6745+t6810; + coeffs_dyz->coeff_p1_m1_m1 = t6333+t6587+t6334+t6427+t6355+t6193+t6467+ +t6755+t6773+t6779+t6827; + coeffs_dyz->coeff_p2_m1_m1 = t6594+RATIONAL(1.0,54.0)*t6572+t6185+t6673+ +t6768+t6824+t6832; + coeffs_dyz->coeff_m1_0_m1 = t6381+(-t6737+t6653+(t6549+t6559*t6570)*x)*y+ +t6306+t6336+t6266+t6593+t6629+t6716+t6757; + coeffs_dyz->coeff_0_0_m1 = t6741+(t6570+t6554+(t6553-t6570)*t6569)*y+ +t6349+t6582+t6610+t6259+t6782+t6803+t6813; + coeffs_dyz->coeff_p1_0_m1 = t6255+t6391+t6584+t6562+t6638+t6716+t6769+ +t6820+t6830; + coeffs_dyz->coeff_p2_0_m1 = t6207+y*t6680+t6576+t6695+t6799; + coeffs_dyz->coeff_m1_p1_m1 = t6357+t6588+t6333+t6748+t6749+t6784+t6795+ +t6798; + coeffs_dyz->coeff_0_p1_m1 = (1.0+t6641)*z+t6589+t6611+t6720+t6722+t6745+ +t6747+t6808; + coeffs_dyz->coeff_p1_p1_m1 = t6503+t6588+t6426+t6689+t6751+t6755+t6775+ +t6778+t6815; + coeffs_dyz->coeff_p2_p1_m1 = t6598+t6698+t6724+t6759+t6777+t6824; + coeffs_dyz->coeff_m1_p2_m1 = t6571*t6487+t6594+t6296+t6762+t6771+t6787; + coeffs_dyz->coeff_0_p2_m1 = t6327+t6703+t6619*t6571+t6576+t6756+t6766; + coeffs_dyz->coeff_p1_p2_m1 = t6242+t6600+t6483+t6662+t6762+t6777+t6793; + coeffs_dyz->coeff_p2_p2_m1 = t6290+x*t6658+t6602+t6613+t6802; + coeffs_dyz->coeff_m1_m1_0 = t6307+t6219+(t6653-t6738+(t6549+t6559*t6571)* +x)*z+t6591+t6338+t6757+t6765+t6784; + coeffs_dyz->coeff_0_m1_0 = t6367+t6212+t6740+t6582+t6611+(t6554+t6571+( +t6553-t6571)*t6569)*z+t6781+t6786+t6792; + coeffs_dyz->coeff_p1_m1_0 = t6457+t6584+t6438+t6753+t6763+t6765+t6783+ +t6790; + coeffs_dyz->coeff_p2_m1_0 = t6226+t6580+z*t6680+t6695+t6776; + coeffs_dyz->coeff_m1_0_0 = t6377+t6212+(t6553*t6572+RATIONAL(-4.0,3.0)*x) +*t6567+t6477+t6637+t6742+t6562+t6259+t6761+t6767+t6790; + coeffs_dyz->coeff_0_0_0 = z-t6737+t6590+(t6560+t6661)*x+t6704+t6532*t6572 ++(t6546+t6547*x+t6618*z)*t6571+t6539+(-t6569+1.0+t6618*t6570+(t6538*t6572+ +RATIONAL(-4.0,1.0)*t6569+t6558)*z)*y+t6417+t6691+t6752+t6760; + coeffs_dyz->coeff_p1_0_0 = (t6560+t6406)*t6572+(z*t6683+(t6712+t6558*z)*y +)*x+t6516+t6586+t6742+t6818+t6819; + coeffs_dyz->coeff_p2_0_0 = (t6553*x+t6554*t6572)*t6567+t6599+t6743+t6796+ +t6812; + coeffs_dyz->coeff_m1_p1_0 = -t6564+(-1.0-y)*t6737+t6367+t6591+t6449+t6709 ++t6713+t6753+t6764+t6814; + coeffs_dyz->coeff_0_p1_0 = t6566+(-t6572+(t6683+t6538)*t6569+t6616)*z+ +t6740+t6372+t6247+t6639*t6571+t6575+t6360+t6621*t6570+t6819; + coeffs_dyz->coeff_p1_p1_0 = t6590+t6650+t6493+t6565+(t6572+t6616*x+t6641) +*z+t6763+t6764+t6826+t6828; + coeffs_dyz->coeff_p2_p1_0 = t6581+t6457+t6281+t6695+t6806; + coeffs_dyz->coeff_m1_p2_0 = t6571*t6448+t6326+t6577+t6684+t6776; + coeffs_dyz->coeff_0_p2_0 = t6574+(t6551-t6571+(t6571+t6559)*t6569)*z+ +t6724+t6796; + coeffs_dyz->coeff_p1_p2_0 = -t6564+t6579+t6447+t6684+t6806; + coeffs_dyz->coeff_p2_p2_0 = t6219+z*t6482+t6592+t6690; + coeffs_dyz->coeff_m1_m1_p1 = t6585+t6334+t6629+t6744+t6749+t6780+t6804; + coeffs_dyz->coeff_0_m1_p1 = (1.0+t6633)*y+t6583+t6610+t6200+t6700+t6747+ +t6807+t6817; + coeffs_dyz->coeff_p1_m1_p1 = t6204+t6503+t6587+t6625+t6638+t6642+t6772+ +t6800+t6804; + coeffs_dyz->coeff_p2_m1_p1 = t6279+t6597+t6343+t6437+t6300+t6656+t6759+ +t6832; + coeffs_dyz->coeff_m1_0_p1 = (-z-1.0)*t6738+t6349+t6362+t6383+t6442+t6390+ +t6200+t6593-t6562+t6689+t6814+t6825+t6830; + coeffs_dyz->coeff_0_0_p1 = t6621*t6571+t6441+t6741+t6639*t6570+t6434+(- +t6572+(t6712+t6538)*t6569+t6617)*y+t6199+t6575+t6568+t6818; + coeffs_dyz->coeff_p1_0_p1 = t6727+t6649+(t6572+t6617*x+t6633)*y+t6746+ +t6752+t6820+t6825+t6828; + coeffs_dyz->coeff_p2_0_p1 = t6391+t6272+t6578+t6695+t6788; + coeffs_dyz->coeff_m1_p1_p1 = t6387+t6585+t6507+t6368+t6750+t6751+t6767+ +t6798; + coeffs_dyz->coeff_0_p1_p1 = t6681-t6739+t6620+(-t6567-1.0+t6667*t6548+ +t6739)*t6569+RATIONAL(1.0,1.0)+t6589+t6746+t6760+t6817+t6826; + coeffs_dyz->coeff_p1_p1_p1 = t6434+(1.0+t6620)*x+t6372+t6586+t6685+t6634+ +t6750+t6772+t6775; + coeffs_dyz->coeff_p2_p1_p1 = t6503+t6495+t6599+t6673+t6682+t6698+t6720+ +t6726; + coeffs_dyz->coeff_m1_p2_p1 = t6381+t6597+t6717+t6758+t6771+t6793; + coeffs_dyz->coeff_0_p2_p1 = t6578+t6754+t6766+t6803+t6808; + coeffs_dyz->coeff_p1_p2_p1 = t6596+t6410+t6353+t6428+t6600+t6769; + coeffs_dyz->coeff_p2_p2_p1 = t6601+t6613+t6706+t6816; + coeffs_dyz->coeff_m1_m1_p2 = t6486+t6595+t6570*t6487+t6672+t6768+t6787+ +t6805; + coeffs_dyz->coeff_0_m1_p2 = t6580+t6694+t6619*t6570+t6298+t6756+t6770; + coeffs_dyz->coeff_p1_m1_p2 = t6307+t6595+t6487+t6404+t6409+t6483+t6628+ +t6655+t6811; + coeffs_dyz->coeff_p2_m1_p2 = t6292+t6528*t6733+t6607+t6791+t6797+t6802; + coeffs_dyz->coeff_m1_0_p2 = t6570*t6388+t6577+t6335+t6697+t6799; + coeffs_dyz->coeff_0_0_p2 = t6574+(t6551-t6570+(t6570+t6559)*t6569)*y+ +t6659+t6812; + coeffs_dyz->coeff_p1_0_p2 = t6454+t6579-t6562+t6697+t6788; + coeffs_dyz->coeff_p2_0_p2 = t6266+y*t6482+t6592+t6728; + coeffs_dyz->coeff_m1_p1_p2 = t6307+t6464+t6598+t6758+t6780+t6789+t6805; + coeffs_dyz->coeff_0_p1_p2 = t6581+t6754+t6770+t6781+t6807; + coeffs_dyz->coeff_p1_p1_p2 = t6596+t6459+t6405+t6642+t6656+t6789+t6811; + coeffs_dyz->coeff_p2_p1_p2 = t6336+t6343+t6601+t6607+t6801; + coeffs_dyz->coeff_m1_p2_p2 = t6178+t6519*t6572+t6602+t6612+t6797; + coeffs_dyz->coeff_0_p2_p2 = t6529+t6525*t6569+t6667*t6526+t6592+t6696+ +t6810; + coeffs_dyz->coeff_p1_p2_p2 = t6193+t6338+t6612+t6614+t6823; + coeffs_dyz->coeff_p2_p2_p2 = RATIONAL(1.0,216.0)*t6572+t6296+t6185+(t6519 ++t6667*t6527)*x+t6672; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dz.compute.c new file mode 100644 index 0000000..005a57a --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dz.compute.c @@ -0,0 +1,1264 @@ +fp t3620; +fp t3653; +fp t3651; +fp t3654; +fp t3780; +fp t3463; +fp t3625; +fp t3603; +fp t3523; +fp t3978; +fp t3623; +fp t3616; +fp t3977; +fp t3655; +fp t3631; +fp t3781; +fp t3637; +fp t3593; +fp t3927; +fp t3632; +fp t3601; +fp t3505; +fp t3976; +fp t3614; +fp t3768; +fp t3462; +fp t3652; +fp t3627; +fp t3772; +fp t3731; +fp t3409; +fp t3619; +fp t3801; +fp t3488; +fp t3975; +fp t3617; +fp t3793; +fp t3494; +fp t3622; +fp t3867; +fp t3422; +fp t3974; +fp t3615; +fp t3453; +fp t3584; +fp t3424; +fp t3854; +fp t3449; +fp t3825; +fp t3635; +fp t3535; +fp t3389; +fp t3838; +fp t3649; +fp t3648; +fp t3607; +fp t3548; +fp t3336; +fp t3645; +fp t3973; +fp t3581; +fp t3445; +fp t3785; +fp t3428; +fp t3853; +fp t3600; +fp t3517; +fp t3972; +fp t3594; +fp t3539; +fp t3332; +fp t3971; +fp t3764; +fp t3876; +fp t3536; +fp t3970; +fp t3880; +fp t3641; +fp t3969; +fp t3874; +fp t3471; +fp t3968; +fp t3634; +fp t3778; +fp t3725; +fp t3283; +fp t3784; +fp t3633; +fp t3567; +fp t3967; +fp t3502; +fp t3866; +fp t3765; +fp t3966; +fp t3501; +fp t3638; +fp t3543; +fp t3965; +fp t3583; +fp t3489; +fp t3588; +fp t3467; +fp t3964; +fp t3804; +fp t3545; +fp t3384; +fp t3963; +fp t3732; +fp t3569; +fp t3932; +fp t3812; +fp t3761; +fp t3864; +fp t3626; +fp t3595; +fp t3592; +fp t3566; +fp t3962; +fp t3646; +fp t3504; +fp t3558; +fp t3763; +fp t3390; +fp t3707; +fp t3642; +fp t3814; +fp t3549; +fp t3961; +fp t3773; +fp t3755; +fp t3589; +fp t3464; +fp t3850; +fp t3797; +fp t3470; +fp t3219; +fp t3629; +fp t3875; +fp t3807; +fp t3960; +fp t3836; +fp t3541; +fp t3311; +fp t3724; +fp t3307; +fp t3959; +fp t3794; +fp t3573; +fp t3958; +fp t3640; +fp t3806; +fp t3737; +fp t3319; +fp t3520; +fp t3834; +fp t3525; +fp t3284; +fp t3957; +fp t3605; +fp t3529; +fp t3394; +fp t3322; +fp t3813; +fp t3577; +fp t3914; +fp t3798; +fp t3956; +fp t3828; +fp t3511; +fp t3734; +fp t3955; +fp t3721; +fp t3532; +fp t3954; +fp t3563; +fp t3953; +fp t3628; +fp t3952; +fp t3458; +fp t3454; +fp t3273; +fp t3951; +fp t3609; +fp t3791; +fp t3800; +fp t3476; +fp t3950; +fp t3618; +fp t3869; +fp t3758; +fp t3216; +fp t3949; +fp t3437; +fp t3230; +fp t3948; +fp t3597; +fp t3571; +fp t3329; +fp t3865; +fp t3782; +fp t3947; +fp t3760; +fp t3946; +fp t3945; +fp t3527; +fp t3944; +fp t3499; +fp t3400; +fp t3559; +fp t3943; +fp t3574; +fp t3942; +fp t3612; +fp t3756; +fp t3941; +fp t3510; +fp t3399; +fp t3753; +fp t3940; +fp t3811; +fp t3939; +fp t3546; +fp t3608; +fp t3938; +fp t3774; +fp t3430; +fp t3232; +fp t3937; +fp t3512; +fp t3337; +fp t3936; +fp t3460; +fp t3935; +fp t3531; +fp t3934; +fp t3613; +fp t3766; +fp t3726; +fp t3221; +fp t3868; +fp t3933; +fp t3611; +fp t3879; +fp t3736; +fp t3931; +fp t3585; +fp t3433; +fp t3930; +fp t3821; +fp t3757; +fp t3718; +fp t3268; +fp t3929; +fp t3515; +fp t3928; +fp t3926; +fp t3873; +fp t3496; +fp t3382; +fp t3852; +fp t3606; +fp t3516; +fp t3315; +fp t3925; +fp t3924; +fp t3722; +fp t3923; +fp t3469; +fp t3922; +fp t3820; +fp t3560; +fp t3754; +fp t3921; +fp t3572; +fp t3522; +fp t3920; +fp t3256; +fp t3919; +fp t3482; +fp t3918; +fp t3917; +fp t3374; +fp t3916; +fp t3257; +fp t3473; +fp t3845; +fp t3276; +fp t3799; +fp t3472; +fp t3851; +fp t3915; +fp t3790; +fp t3528; +fp t3913; +fp t3604; +fp t3565; +fp t3338; +fp t3376; +fp t3912; +fp t3833; +fp t3514; +fp t3859; +fp t3911; +fp t3910; +fp t3537; +fp t3805; +fp t3602; +fp t3909; +fp t3787; +fp t3822; +fp t3519; +fp t3908; +fp t3586; +fp t3487; +fp t3907; +fp t3318; +fp t3906; +fp t3580; +fp t3905; +fp t3751; +fp t3842; +fp t3493; +fp t3904; +fp t3727; +fp t3835; +fp t3903; +fp t3863; +fp t3728; +fp t3582; +fp t3483; +fp t3902; +fp t3901; +fp t3551; +fp t3759; +fp t3293; +fp t3871; +fp t3900; +fp t3796; +fp t3723; +fp t3899; +fp t3898; +fp t3288; +fp t3897; +fp t3361; +fp t3896; +fp t3530; +fp t3309; +fp t3858; +fp t3466; +fp t3895; +fp t3524; +fp t3339; +fp t3474; +fp t3280; +fp t3455; +fp t3894; +fp t3285; +fp t3599; +fp t3506; +fp t3893; +fp t3554; +fp t3408; +fp t3334; +fp t3348; +fp t3892; +fp t3819; +fp t3370; +fp t3882; +fp t3891; +fp t3830; +fp t3840; +fp t3224; +fp t3890; +fp t3387; +fp t3889; +fp t3490; +fp t3402; +fp t3888; +fp t3368; +fp t3497; +fp t3887; +fp t3843; +fp t3552; +fp t3886; +fp t3223; +fp t3885; +fp t3716; +fp t3817; +fp t3884; +fp t3883; +fp t3881; +fp t3621; +fp t3878; +fp t3877; +fp t3872; +fp t3870; +fp t3314; +fp t3860; +fp t3360; +fp t3856; +fp t3423; +fp t3855; +fp t3849; +fp t3492; +fp t3302; +fp t3848; +fp t3769; +fp t3440; +fp t3847; +fp t3610; +fp t3275; +fp t3846; +fp t3844; +fp t3841; +fp t3578; +fp t3839; +fp t3837; +fp t3434; +fp t3233; +fp t3832; +fp t3831; +fp t3829; +fp t3827; +fp t3826; +fp t3824; +fp t3636; +fp t3823; +fp t3818; +fp t3720; +fp t3270; +fp t3239; +fp t3815; +fp t3242; +fp t3810; +fp t3809; +fp t3808; +fp t3456; +fp t3803; +fp t3439; +fp t3802; +fp t3775; +fp t3396; +fp t3795; +fp t3792; +fp t3352; +fp t3347; +fp t3788; +fp t3643; +fp t3786; +fp t3783; +fp t3779; +fp t3777; +fp t3776; +fp t3771; +fp t3767; +fp t3544; +fp t3762; +fp t3576; +fp t3436; +fp t3556; +fp t3752; +fp t3509; +fp t3750; +fp t3335; +fp t3457; +fp t3749; +fp t3748; +fp t3346; +fp t3747; +fp t3746; +fp t3344; +fp t3745; +fp t3744; +fp t3300; +fp t3743; +fp t3555; +fp t3350; +fp t3735; +fp t3741; +fp t3570; +fp t3740; +fp t3333; +fp t3739; +fp t3500; +fp t3738; +fp t3564; +fp t3733; +fp t3729; +fp t3647; +fp t3717; +fp t3639; +fp t3715; +fp t3714; +fp t3713; +fp t3712; +fp t3711; +fp t3710; +fp t3709; +fp t3708; +fp t3706; +fp t3218; +fp t3705; +fp t3385; +fp t3704; +fp t3703; +fp t3702; +fp t3701; +fp t3700; +fp t3699; +fp t3698; +fp t3465; +fp t3245; +fp t3697; +fp t3696; +fp t3695; +fp t3694; +fp t3693; +fp t3692; +fp t3690; +fp t3689; +fp t3451; +fp t3688; +fp t3229; +fp t3231; +fp t3687; +fp t3686; +fp t3259; +fp t3685; +fp t3262; +fp t3684; +fp t3683; +fp t3446; +fp t3682; +fp t3568; +fp t3681; +fp t3240; +fp t3680; +fp t3679; +fp t3678; +fp t3316; +fp t3677; +fp t3676; +fp t3395; +fp t3298; +fp t3675; +fp t3674; +fp t3426; +fp t3673; +fp t3672; +fp t3671; +fp t3670; +fp t3669; +fp t3401; +fp t3668; +fp t3667; +fp t3666; +fp t3665; +fp t3664; +fp t3663; +fp t3442; +fp t3662; +fp t3661; +fp t3660; +fp t3659; +fp t3658; +fp t3644; +fp t3630; +fp t3624; +fp t3419; +fp t3342; +fp t3320; +fp t3308; +fp t3306; +fp t3305; +fp t3291; +fp t3274; +fp t3248; +fp t3237; +fp t3217; +fp t3214; + t3620 = RATIONAL(-1.0,12.0); + t3653 = y*y; + t3651 = x*x; + t3654 = t3651*x; + t3780 = t3654*t3653; + t3463 = t3620*t3780; + t3625 = RATIONAL(-1.0,6.0); + t3603 = t3625*t3653; + t3523 = x*t3603; + t3978 = t3523+t3463; + t3623 = RATIONAL(1.0,18.0); + t3616 = RATIONAL(-1.0,18.0); + t3977 = t3616*t3653+t3623; + t3655 = t3653*y; + t3631 = RATIONAL(1.0,4.0); + t3781 = t3651*t3631; + t3637 = RATIONAL(1.0,2.0); + t3593 = t3637*t3651; + t3927 = t3655*t3781+t3593; + t3632 = RATIONAL(-1.0,4.0); + t3601 = t3632*t3651; + t3505 = y*t3601; + t3976 = t3505+t3927; + t3614 = RATIONAL(1.0,24.0); + t3768 = t3614*t3654; + t3462 = t3655*t3768; + t3652 = z*z; + t3627 = RATIONAL(-1.0,8.0); + t3772 = t3652*t3627; + t3731 = t3655*t3772; + t3409 = t3654*t3731; + t3619 = RATIONAL(-1.0,24.0); + t3801 = t3619*t3654; + t3488 = y*t3801; + t3975 = t3462+t3409+t3488; + t3617 = RATIONAL(-1.0,36.0); + t3793 = t3617*t3654; + t3494 = y*t3793; + t3622 = RATIONAL(1.0,36.0); + t3867 = t3622*y; + t3422 = x*t3867; + t3974 = t3494+t3422; + t3615 = RATIONAL(1.0,12.0); + t3453 = t3615*t3780; + t3584 = t3620*t3653; + t3424 = x*t3584; + t3854 = t3453+t3424; + t3449 = t3655*t3801; + t3825 = t3654*t3655; + t3635 = RATIONAL(1.0,8.0); + t3535 = t3635*t3825; + t3389 = t3652*t3535; + t3838 = t3449+t3389; + t3649 = x*z; + t3648 = y*t3649; + t3607 = t3625*t3655; + t3548 = z*t3607; + t3336 = t3654*t3548; + t3645 = RATIONAL(2.0,3.0); + t3973 = t3336+t3838+t3645*t3648; + t3581 = t3620*t3651; + t3445 = y*t3581; + t3785 = t3651*t3655; + t3428 = t3615*t3785; + t3853 = t3445+t3428; + t3600 = t3632*t3653; + t3517 = x*t3600; + t3972 = t3631*t3780+t3517; + t3594 = t3637*t3653; + t3539 = z*t3594; + t3332 = x*t3539; + t3971 = t3453+t3332; + t3764 = t3632*t3655; + t3876 = t3631*x; + t3536 = y*t3876; + t3970 = x*t3764+t3536; + t3880 = y*t3654; + t3641 = RATIONAL(-1.0,2.0); + t3969 = t3641*y+t3632*t3880; + t3874 = y*t3616; + t3471 = x*t3874; + t3968 = t3471+t3494; + t3634 = RATIONAL(-3.0,8.0); + t3778 = t3652*t3634; + t3725 = t3654*t3778; + t3283 = t3655*t3725; + t3784 = t3652*t3654; + t3633 = RATIONAL(3.0,4.0); + t3567 = t3633*t3784; + t3967 = t3283+y*t3567; + t3502 = t3654*t3764; + t3866 = x*t3652; + t3765 = y*t3866; + t3966 = t3502+t3633*t3765; + t3501 = t3655*t3876; + t3638 = RATIONAL(-3.0,4.0); + t3543 = t3638*t3784; + t3965 = t3501+y*t3543; + t3583 = t3615*y; + t3489 = x*t3583; + t3588 = t3620*t3654; + t3467 = y*t3588; + t3964 = t3489+t3467; + t3804 = t3631*t3652; + t3545 = t3652*t3600; + t3384 = x*t3545; + t3963 = t3384+x*t3804; + t3732 = t3652*t3785; + t3569 = t3652*t3764; + t3932 = t3631*t3732+t3569; + t3812 = t3635*t3652; + t3761 = x*t3812; + t3864 = t3655*t3761+t3409; + t3626 = RATIONAL(1.0,6.0); + t3595 = t3626*y; + t3592 = t3625*t3651; + t3566 = y*t3592; + t3962 = t3595+t3864+t3932+t3566; + t3646 = RATIONAL(-1.0,3.0); + t3504 = t3632*t3780; + t3558 = t3631*t3784; + t3763 = y*t3784; + t3390 = t3627*t3763; + t3707 = t3389+t3558+t3390+t3652*t3504; + t3642 = RATIONAL(1.0,3.0); + t3814 = t3642*t3653; + t3549 = x*t3814; + t3961 = t3707+t3646*x+t3549; + t3773 = t3655*t3623; + t3755 = z*t3773; + t3589 = t3623*y; + t3464 = t3654*t3589; + t3850 = x*t3755+z*t3464; + t3797 = t3622*t3655; + t3470 = t3654*t3797; + t3219 = z*t3470; + t3629 = RATIONAL(1.0,9.0); + t3875 = t3629*x; + t3807 = z*t3875; + t3960 = t3850+y*t3807+t3219; + t3836 = t3652*t3633; + t3541 = t3653*t3836; + t3311 = x*t3541; + t3724 = t3653*t3778; + t3307 = t3654*t3724; + t3959 = t3307+t3311+t3517+t3635*t3780; + t3794 = t3637*t3655; + t3573 = z*t3794; + t3958 = t3535+t3654*t3573+t3638*t3765; + t3640 = RATIONAL(3.0,8.0); + t3806 = t3652*t3640; + t3737 = t3653*t3806; + t3319 = t3654*t3737; + t3520 = x*t3594; + t3834 = t3652*t3638; + t3525 = t3653*t3834; + t3284 = x*t3525; + t3957 = t3319+t3504+t3520+t3284+t3332; + t3605 = t3641*x; + t3529 = z*t3605; + t3394 = y*t3529; + t3322 = z*t3502; + t3813 = t3631*t3654; + t3577 = y*t3813; + t3914 = x*t3573+t3649; + t3798 = t3641*t3654; + t3956 = t3394+t3914+t3322+(t3798+t3577)*z; + t3828 = t3652*t3655; + t3511 = t3638*t3828; + t3734 = t3655*t3806; + t3955 = t3511+t3633*t3732+x*t3734+t3969; + t3721 = t3651*t3778; + t3532 = t3653*t3781; + t3954 = t3653*t3721+t3532; + t3563 = t3626*t3780; + t3953 = (t3549+t3563)*z; + t3628 = RATIONAL(-1.0,9.0); + t3952 = t3654*t3755+t3628*t3648; + t3458 = x*t3797; + t3454 = t3654*t3874; + t3273 = z*t3454; + t3951 = t3273+z*t3458; + t3609 = RATIONAL(-1.0,108.0); + t3791 = t3655*t3609; + t3800 = t3622*t3654; + t3476 = y*t3800; + t3950 = t3652*t3476+x*t3791; + t3618 = RATIONAL(1.0,72.0); + t3869 = y*t3652; + t3758 = t3651*t3869; + t3216 = t3620*t3758; + t3949 = t3216+t3618*t3785; + t3437 = t3615*t3784; + t3230 = y*t3437; + t3948 = t3230+t3458; + t3597 = t3626*t3655; + t3571 = z*t3597; + t3329 = t3654*t3571; + t3865 = y*t3642; + t3782 = z*t3865; + t3947 = t3329+x*t3782; + t3760 = y*t3798; + t3946 = z*t3760+t3648; + t3945 = t3532+t3651*t3525; + t3527 = t3655*t3804; + t3944 = t3527+t3632*t3732; + t3499 = t3652*t3601; + t3400 = y*t3499; + t3559 = y*t3804; + t3943 = t3400+t3559; + t3574 = t3632*t3784; + t3942 = t3574+t3653*t3558; + t3612 = RATIONAL(1.0,216.0); + t3756 = t3622*t3866; + t3941 = y*t3756+t3612*t3825; + t3510 = y*t3593; + t3399 = z*t3510; + t3753 = z*t3785; + t3940 = t3399+t3641*t3753; + t3811 = t3626*t3653; + t3939 = t3651*t3811+t3652*t3532; + t3546 = t3625*t3780; + t3608 = t3626*t3654; + t3938 = t3546+t3608; + t3774 = t3655*t3616; + t3430 = x*t3774; + t3232 = t3652*t3488; + t3937 = t3430+t3232; + t3512 = z*t3608; + t3337 = y*t3512; + t3936 = t3454+t3337; + t3460 = t3620*t3784; + t3935 = t3437+t3653*t3460; + t3531 = t3625*t3785; + t3934 = t3531+t3597; + t3613 = RATIONAL(-1.0,72.0); + t3766 = t3613*t3655; + t3726 = t3652*t3766; + t3221 = t3654*t3726; + t3868 = y*t3609; + t3933 = x*t3868+t3221; + t3611 = RATIONAL(1.0,108.0); + t3879 = x*t3655; + t3736 = t3618*t3784; + t3931 = t3611*t3879+y*t3736; + t3585 = t3615*t3655; + t3433 = t3620*t3785; + t3930 = t3585+t3433; + t3821 = t3619*t3652; + t3757 = x*t3821; + t3718 = t3652*t3768; + t3268 = y*t3718; + t3929 = y*t3757+t3268; + t3515 = t3651*t3764; + t3928 = t3510+t3515; + t3926 = t3462+t3619*t3879; + t3873 = t3646*z; + t3496 = x*t3873; + t3382 = y*t3496; + t3852 = t3382+t3523; + t3606 = t3625*t3654; + t3516 = y*t3606; + t3315 = z*t3516; + t3925 = t3852+t3463+t3315; + t3924 = t3978*z; + t3722 = t3651*t3772; + t3923 = t3651*t3584+t3653*t3722; + t3469 = t3652*t3585; + t3922 = t3620*t3732+t3469; + t3820 = t3637*t3652; + t3560 = x*t3820; + t3754 = t3653*t3866; + t3921 = t3560+t3641*t3754; + t3572 = t3626*t3785; + t3522 = t3651*t3865; + t3920 = (t3522+t3572)*z; + t3256 = z*t3430; + t3919 = z*t3476+t3256; + t3482 = t3613*t3880; + t3918 = t3482+t3268; + t3917 = y*t3820+t3641*t3758; + t3374 = t3635*t3732; + t3916 = t3566+t3374; + t3257 = t3655*t3718; + t3473 = t3654*t3766; + t3845 = t3257+t3473; + t3276 = x*t3469; + t3799 = t3617*t3655; + t3472 = x*t3799; + t3851 = t3276+t3472; + t3915 = t3845+t3851; + t3790 = t3641*t3655; + t3528 = z*t3790; + t3913 = t3627*t3825+t3654*t3528; + t3604 = t3625*y; + t3565 = z*t3604; + t3338 = x*t3565; + t3376 = x*t3571; + t3912 = t3336+t3338+t3376+t3337; + t3833 = t3626*t3651; + t3514 = y*t3833; + t3859 = (t3531+t3514)*z; + t3911 = t3859+t3565+t3571; + t3910 = y*t3725+t3567+t3653*t3543; + t3537 = x*t3811; + t3805 = (t3537+t3546)*z; + t3602 = t3625*x; + t3909 = t3805+t3512+z*t3602; + t3787 = t3651*t3615; + t3822 = t3651*t3545+t3653*t3787; + t3519 = t3653*t3804; + t3908 = t3822+t3584+t3519; + t3586 = t3615*t3654; + t3487 = y*t3586; + t3907 = t3606+t3487+t3563; + t3318 = x*t3519; + t3906 = t3318+t3924; + t3580 = t3652*t3781; + t3905 = t3580+t3581+t3822; + t3751 = t3614*t3869; + t3842 = t3853*z; + t3493 = t3617*t3785; + t3904 = t3651*t3751+t3842+t3493; + t3727 = t3651*t3821; + t3835 = t3651*t3867+t3655*t3727; + t3903 = t3835+t3655*t3756+t3654*t3868; + t3863 = t3616*t3651; + t3728 = t3652*t3787; + t3582 = t3620*t3655; + t3483 = t3652*t3582; + t3902 = t3655*t3728+y*t3863+t3589+t3483; + t3901 = t3602+t3537+t3942; + t3551 = x*t3595; + t3759 = z*t3780; + t3293 = t3637*t3759; + t3871 = t3653*x; + t3900 = t3551+t3293-z*t3871+t3467; + t3796 = t3653*t3615; + t3723 = t3652*t3796; + t3899 = t3654*t3723+t3460+t3977*x; + t3898 = t3604+t3514+t3932; + t3288 = t3651*t3541; + t3897 = t3307+t3525+x*t3737+t3288; + t3361 = t3637*t3753; + t3896 = z*t3501+t3322+t3528+t3361; + t3530 = t3627*t3780; + t3309 = t3652*t3530; + t3858 = t3653*t3768+t3309; + t3466 = x*t3796; + t3895 = t3858+t3466+t3953; + t3524 = y*t3875; + t3339 = t3626*t3765; + t3474 = t3654*t3585; + t3280 = z*t3474; + t3455 = t3655*t3793; + t3894 = t3524+t3339+t3280+t3455; + t3285 = y*t3560; + t3599 = t3646*y; + t3506 = x*t3599; + t3893 = t3474+t3285+t3506+t3280; + t3554 = t3655*t3813; + t3408 = z*t3554; + t3334 = z*t3504; + t3348 = x*t3528; + t3892 = t3408+t3334+t3348+t3946; + t3819 = t3614*t3655; + t3370 = x*t3731; + t3882 = y*x; + t3891 = x*t3819+t3370+t3619*t3882+(t3768+t3761)*y; + t3830 = t3623*t3653; + t3840 = x*t3723+t3622*t3780; + t3224 = t3653*t3718; + t3890 = t3840+t3224+x*t3830+t3924; + t3387 = z*t3551; + t3889 = t3387+y*t3873+t3548+t3920; + t3490 = t3620*t3882; + t3402 = t3635*t3763; + t3888 = t3490+t3402+t3626*x+t3942; + t3368 = t3654*t3734; + t3497 = y*t3605; + t3887 = t3293+t3368+t3577+x*t3511+t3497; + t3843 = t3652*t3632; + t3552 = y*t3843; + t3886 = t3582+t3552+t3583+t3944; + t3223 = z*t3487; + t3885 = t3223+t3387+t3496+z*t3606+t3953; + t3716 = t3653*t3812; + t3817 = x*t3716+t3309; + t3884 = t3817+t3463+t3466+t3545+t3603+t3939; + t3883 = t3283+t3640*t3763+t3520+t3605+t3653*t3567+t3543+t3970; + t3881 = -1.0-z; + t3621 = RATIONAL(-1.0,54.0); + t3878 = y*t3621; + t3877 = y*t3651; + t3872 = 1.0-t3653; + t3870 = t3654*z; + t3314 = y*t3580; + t3860 = t3445+t3314; + t3360 = y*t3574; + t3856 = t3360+t3487; + t3423 = x*t3589; + t3855 = t3257+t3423; + t3849 = t3652*t3615; + t3492 = x*t3585; + t3302 = x*t3569; + t3848 = t3492+t3302; + t3769 = t3619*t3653; + t3440 = t3654*t3769; + t3847 = t3652*t3440+t3622*t3871; + t3610 = RATIONAL(-1.0,216.0); + t3275 = t3655*t3736; + t3846 = t3610*t3825+t3275; + t3844 = t3655+t3654; + t3841 = t3654-t3651; + t3578 = t3651*t3836; + t3839 = y*t3578+t3505; + t3837 = z*t3877; + t3434 = t3654*t3582; + t3233 = z*t3434; + t3832 = t3233+t3338; + t3831 = -t3653+t3655; + t3829 = (t3716+t3769)*t3651; + t3827 = y*t3728+t3622*t3785; + t3826 = t3641*t3652; + t3824 = t3623*t3651; + t3636 = RATIONAL(-3.0,2.0); + t3823 = t3636*t3652; + t3818 = t3653*t3651; + t3720 = t3652*t3819; + t3270 = x*t3720; + t3239 = t3652*t3449; + t3815 = t3270+t3239; + t3242 = y*t3460; + t3810 = t3476+t3242; + t3809 = t3637*t3654; + t3808 = y*t3870; + t3456 = x*t3582; + t3803 = t3474+t3456; + t3439 = t3618*t3825; + t3802 = t3439+t3239; + t3775 = t3651*t3614; + t3396 = t3655*t3722; + t3795 = t3396+t3655*t3775; + t3792 = t3641*t3653; + t3352 = x*t3552; + t3347 = y*t3558; + t3788 = t3352+t3347; + t3643 = RATIONAL(-2.0,1.0); + t3786 = -t3654+t3643; + t3783 = t3635*t3758+t3396; + t3779 = t3618*t3653; + t3777 = t3854*z; + t3776 = t3651*t3627; + t3771 = (t3423+t3455)*z; + t3767 = t3611*t3654; + t3544 = x*t3826; + t3762 = y*t3849; + t3576 = z*t3809; + t3436 = t3618*t3879; + t3556 = x*t3607; + t3752 = x*t3772; + t3509 = x*t3597; + t3750 = t3376+t3302+t3509; + t3335 = z*t3556; + t3457 = x*t3773; + t3749 = t3335+t3276+t3457; + t3748 = t3233+t3257+t3470; + t3346 = x*t3527; + t3747 = t3335+t3346+t3556; + t3746 = t3230+t3315+t3464; + t3344 = y*t3544; + t3745 = t3346+t3384+t3344; + t3744 = t3631+t3627*y; + t3300 = z*t3532; + t3743 = t3399+z*t3515+t3300; + t3555 = t3651*t3792; + t3350 = z*t3555; + t3735 = t3651*t3806; + t3741 = t3350+(t3735+t3776)*t3653; + t3570 = t3651*t3834; + t3740 = t3300+(t3566+t3433)*z; + t3333 = t3654*t3716; + t3739 = t3242+t3239+t3333; + t3500 = y*t3608; + t3738 = t3500+t3360+t3337; + t3564 = t3633*t3828; + t3733 = t3394+(t3576+z)*y; + t3729 = t3409+t3347+t3333; + t3647 = z*t3818; + t3717 = t3647+t3641*t3759+t3332; + t3639 = RATIONAL(3.0,2.0); + t3715 = t3639*t3653+t3636; + t3714 = t3603+t3626; + t3713 = t3636*t3653+t3639; + t3712 = t3642+t3646*t3653; + t3711 = t3594+t3641; + t3710 = t3625+t3811; + t3709 = t3620*t3652+t3622; + t3708 = t3613*t3780+t3619*t3754+x*t3779+t3224; + t3706 = t3350+t3976*z; + t3218 = t3651*t3720; + t3705 = y*t3727+t3651*t3766+t3618*t3877+t3218; + t3385 = x*t3559; + t3704 = t3544+t3302+t3637*t3754+t3385; + t3703 = t3594+t3555+t3972; + t3702 = t3572+t3492+t3607+t3434; + t3701 = t3350+t3539+t3972*z; + t3700 = t3614*t3871+t3440+t3333+t3653*t3752; + t3699 = t3219+(t3472+t3974)*z; + t3698 = t3864+t3964; + t3465 = t3617*t3882; + t3245 = x*t3762; + t3697 = t3465+t3245+t3802; + t3696 = t3619*t3785+t3374+(t3722+t3775)*y; + t3695 = t3838+t3860; + t3694 = t3280+(t3456+t3964)*z; + t3693 = t3815+t3974; + t3692 = t3652*t3436+y*t3767+t3933; + t3690 = y*t3826+t3360+t3385+t3637*t3758; + t3689 = (t3637+t3792)*t3652; + t3451 = t3617*t3780; + t3688 = t3614*t3754+t3451+t3777+t3847; + t3229 = z*t3492; + t3231 = t3655*t3757; + t3687 = t3229+t3472+t3231+t3748; + t3686 = t3783+t3842+t3853; + t3259 = x*t3483; + t3685 = t3494+t3259+t3835+t3855; + t3262 = t3620*t3754; + t3684 = t3262+t3654*t3779+t3829+t3847; + t3683 = t3318+t3424+t3829+t3858; + t3446 = x*t3878; + t3682 = t3617*t3765+t3655*t3767+t3446+t3275+t3771; + t3568 = x*t3604; + t3681 = t3389+t3568+t3385+t3434+t3832; + t3240 = t3620*t3765; + t3680 = t3240+t3455+t3771+t3855; + t3679 = t3777+t3817+t3854; + t3678 = x*t3751+t3436+t3618*t3880+t3231+t3613*t3882+t3232+t3845; + t3316 = t3655*t3721; + t3677 = t3316+t3635*t3785+t3361+t3741+t3839; + t3676 = t3218+y*t3824+t3740+t3827+t3923; + t3395 = y*t3570; + t3298 = t3640*t3732; + t3675 = t3395+t3298+t3743+t3928+t3954; + t3674 = t3314+t3433+t3740+t3916+t3954; + t3426 = y*t3787; + t3673 = t3426+t3400+t3741+t3795+t3920; + t3672 = t3400+t3428+t3743+t3916+t3923; + t3671 = t3319+t3530+t3600+x*t3724+t3541+t3635*t3871+t3717+t3945; + t3670 = t3647+t3635*t3877+t3298+y*t3721+t3601+t3578+t3655*t3776+t3940+ +t3945; + t3669 = t3564+t3368+t3778*t3879+t3638*t3732+t3703+t3733; + t3401 = y*t3752; + t3668 = t3402+t3401+t3694+t3698+t3803; + t3667 = t3458+t3259+t3696+t3697+t3918; + t3666 = t3465+t3476+t3458+t3455+t3694+t3815+t3929; + t3665 = t3570+t3555+t3316+t3288+y*t3735+t3706+t3976; + t3664 = t3489+t3456+t3402+t3346+t3352+t3696+t3975; + t3663 = t3698+t3700+t3788+t3926; + t3442 = x*t3766; + t3662 = t3270+t3442+t3697+t3700+t3810; + t3661 = t3551+t3370+t3516+t3522+t3389+t3599+t3701+t3944; + t3660 = t3426+t3499+t3592+t3433+t3706+t3783+t3939; + t3659 = t3408+t3573+t3940+t3576+t3529+t3717+(1.0+t3969+t3970)*z; + t3658 = t3318+t3449+t3854+t3588+t3707+t3891+(t3843+t3615)*x; + t3644 = RATIONAL(-2.0,3.0); + t3630 = RATIONAL(2.0,1.0); + t3624 = RATIONAL(1.0,54.0); + t3419 = t3654*t3791; + t3342 = x*t3564; + t3320 = t3654*t3782; + t3308 = t3646*t3808; + t3306 = t3655*t3496; + t3305 = t3642*z*t3879; + t3291 = t3625*t3765; + t3274 = t3652*t3482; + t3248 = t3774*t3870; + t3237 = x*t3726; + t3217 = t3652*t3472; + t3214 = t3652*t3494; + coeffs_dz->coeff_m1_m1_m1 = (t3621*t3655+(RATIONAL(-1.0,27.0)+t3616*t3652 +)*y)*x+t3654*t3878+t3221+t3217+t3676+t3419+t3214+t3890+t3960; + coeffs_dz->coeff_0_m1_m1 = t3471+t3240+t3884+(t3623+t3863)*t3655+(t3626* +t3652+t3629+(t3628+t3625*t3652)*t3651)*y+t3746+t3687+t3701+t3889+t3922; + coeffs_dz->coeff_p1_m1_m1 = t3334+t3384+t3676+t3739+t3749+t3852+t3894+ +t3936+t3971; + coeffs_dz->coeff_p2_m1_m1 = t3682+t3237+t3624*t3880+t3688+t3950+t3951; + coeffs_dz->coeff_m1_0_m1 = t3977*t3654+t3240+t3660+t3748+(t3629+t3628* +t3653+t3714*t3652)*x+t3232+t3749+t3885+t3935+t3968; + coeffs_dz->coeff_0_0_m1 = t3646+t3826+t3702+t3888+(-z+t3689+t3712)*t3651+ +(t3820-z+t3642)*t3653+t3401+t3659+t3523+t3907+t3943+t3962+t3963; + coeffs_dz->coeff_p1_0_m1 = t3660+t3474+t3556+t3704+t3900+t3938+t3956+ +t3961; + coeffs_dz->coeff_p2_0_m1 = t3262+t3666+(t3616+t3830)*t3654+x*t3849+t3899+ +t3909; + coeffs_dz->coeff_m1_p1_m1 = t3672+t3376+t3430+t3259+t3239+t3382+t3746+ +t3890+t3894; + coeffs_dz->coeff_0_p1_m1 = t3690+t3884-t3837+t3661+t3803+t3733+t3896+ +t3934; + coeffs_dz->coeff_p1_p1_m1 = t3672+t3500+t3506+t3523+t3434+t3509+t3729+ +t3745+t3892+t3971; + coeffs_dz->coeff_p2_p1_m1 = t3338+t3242+t3245+t3687+t3423+t3688+t3936; + coeffs_dz->coeff_m1_p2_m1 = t3682+t3624*t3879+t3274+t3903+t3904+t3919; + coeffs_dz->coeff_0_p2_m1 = t3666+(t3616+t3824)*t3655+t3762+t3216+t3902+ +t3911; + coeffs_dz->coeff_p1_p2_m1 = t3685+t3376+t3223+t3245+t3470+t3832+t3904+ +t3937; + coeffs_dz->coeff_p2_p2_m1 = t3419+t3613*t3765+t3692+t3699+t3931; + coeffs_dz->coeff_m1_m1_0 = t3248+(t3628*t3880+(t3628*t3655+RATIONAL(-2.0, +9.0)*y)*x)*z+t3673+t3384+t3230+t3339+t3895+t3915+t3968; + coeffs_dz->coeff_0_m1_0 = t3490+t3335+t3329+t3690+t3320+(-t3653+(t3646* +t3651+t3642)*t3655+(t3645+t3644*t3651)*y)*z+t3487+t3671+t3382+t3926+t3930+t3962 +; + coeffs_dz->coeff_p1_m1_0 = t3673+t3344+t3347+t3305+t3308+t3848+t3900+ +t3959+t3973; + coeffs_dz->coeff_p2_m1_0 = t3662+t3256+t3629*t3808+t3805+t3952; + coeffs_dz->coeff_m1_0_0 = t3329+(-t3651+t3712*t3654+(t3644*t3653+t3645)*x +)*z+t3305+t3586+t3492+t3670+t3704+t3888+t3925+t3975; + coeffs_dz->coeff_0_0_0 = t3311+(t3635*t3655+t3744)*x+(t3635*t3654+t3631)* +y+t3844*t3632+(t3639*t3818+t3639+t3638*y+(t3651+t3653)*t3636+(t3638+t3640*y)*x) +*t3652+t3669+t3641+(-t3655+(t3630-x+t3654)*t3653+(t3643*t3653+t3630+t3655-y)* +t3651+t3786)*z+t3839+t3910+t3913+t3914+t3927; + coeffs_dz->coeff_p1_0_0 = t3342+t3744*t3654+t3504+t3670+(-t3780+(t3630* +t3653+t3643-t3655)*x+t3841)*z+t3883+t3713*t3866+t3946+t3958; + coeffs_dz->coeff_p2_0_0 = t3658+((t3646+t3814)*t3654+t3712*x)*z+t3912; + coeffs_dz->coeff_m1_p1_0 = t3306+t3456+t3551-t3837+t3677+t3320+t3745+ +t3856+t3895+t3973; + coeffs_dz->coeff_0_p1_0 = (t3627*x+t3631)*t3655+t3648+(t3639+t3636*t3651) +*t3869+(-t3785+(t3630*t3651+t3786)*y+t3831)*z+t3536+t3348+t3671+t3928+t3955+ +t3958+t3967; + coeffs_dz->coeff_p1_p1_0 = t3677+(t3841*y+(t3643*y+t3831)*x)*z+t3639* +t3765+t3887+t3913+t3959+t3965; + coeffs_dz->coeff_p2_p1_0 = t3335+t3308+t3663+t3805+t3947; + coeffs_dz->coeff_m1_p2_0 = t3273+t3655*t3807+t3667+t3859+t3952; + coeffs_dz->coeff_0_p2_0 = ((t3785+y)*t3642+(t3655+t3877)*t3646)*z+t3428+ +t3390+t3695+t3886+t3891+t3912; + coeffs_dz->coeff_p1_p2_0 = t3306+t3315+t3664+t3859+t3947; + coeffs_dz->coeff_p2_p2_0 = t3248+z*t3471+t3678+t3850; + coeffs_dz->coeff_m1_m1_p1 = t3674+t3524+t3457+t3291+t3259+t3464+t3470+ +t3739+t3906+t3960+t3978; + coeffs_dz->coeff_0_m1_p1 = t3233+t3229+t3703+t3702+t3661+t3315+t3788+ +t3889+t3897+t3917; + coeffs_dz->coeff_p1_m1_p1 = t3674+t3334+t3409+t3382+t3738+t3747+t3893+ +t3957; + coeffs_dz->coeff_p2_m1_p1 = t3454+t3679+t3231+t3680+t3948+t3951; + coeffs_dz->coeff_m1_0_p1 = t3233+t3551+t3352+t3747+t3885+t3665+t3434+ +t3907+t3921+t3961; + coeffs_dz->coeff_0_0_p1 = t3510+t3554+(t3790-z-t3872)*t3651+t3844*t3637+ +t3395+t3284+RATIONAL(1.0,1.0)+(t3798+t3881)*t3653+t3659+t3883+(t3633*y+t3713* +t3651+(t3633+t3634*y)*x+t3715)*t3652+t3955; + coeffs_dz->coeff_p1_0_p1 = t3711*t3654+(t3794-t3653*z+t3715*t3652+t3872)* +x+t3665+t3887+t3910+t3956+t3966; + coeffs_dz->coeff_p2_0_p1 = t3668+t3901+t3909+t3938+t3963; + coeffs_dz->coeff_m1_p1_p1 = t3675+t3516+t3729+t3750+t3893+t3906+t3925; + coeffs_dz->coeff_0_p1_p1 = (t3593+t3641)*t3655+t3669+(t3809+1.0+t3823+( +t3639*t3652+t3881)*t3651)*y+t3701+t3497+t3896+t3897+t3965+t3966; + coeffs_dz->coeff_p1_p1_p1 = t3342+(y+t3790+y*t3823)*x+t3554+t3675+t3760+ +t3892+t3957+t3967; + coeffs_dz->coeff_p2_p1_p1 = t3229+t3370+t3679+t3492+t3681+t3738; + coeffs_dz->coeff_m1_p2_p1 = t3276+t3476+t3680+t3686+t3919+t3937; + coeffs_dz->coeff_0_p2_p1 = t3668+t3898+t3911+t3934+t3943; + coeffs_dz->coeff_p1_p2_p1 = t3223+t3487+t3681+t3390+t3686+t3750; + coeffs_dz->coeff_p2_p2_p1 = t3472+t3470+t3693+t3699+t3929; + coeffs_dz->coeff_m1_m1_p2 = t3623*t3765+t3684+t3446+t3846+t3903+t3949+ +t3950; + coeffs_dz->coeff_0_m1_p2 = t3662+t3797+(t3625+t3833)*t3869+t3493+t3902+ +t3908; + coeffs_dz->coeff_p1_m1_p2 = t3291+t3683+t3473+t3685+t3948+t3949; + coeffs_dz->coeff_p2_m1_p2 = t3214+t3610*t3879+t3692+t3708+t3941; + coeffs_dz->coeff_m1_0_p2 = t3800+t3667+t3710*t3866+t3451+t3899+t3905; + coeffs_dz->coeff_0_0_p2 = t3658+t3314+t3689+(t3711*t3652+t3714)*t3651+ +t3710+t3853+t3886; + coeffs_dz->coeff_p1_0_p2 = t3463+t3586+t3664+t3901+t3905+t3921; + coeffs_dz->coeff_p2_0_p2 = t3793+(t3617*t3653+t3709)*x+t3678+t3840+t3935; + coeffs_dz->coeff_m1_p1_p2 = t3291+t3684+t3423+t3795+t3810+t3860+t3915; + coeffs_dz->coeff_0_p1_p2 = t3663+t3898+t3908+t3917+t3930; + coeffs_dz->coeff_p1_p1_p2 = t3285+t3683+t3568+t3695+t3795+t3848+t3856; + coeffs_dz->coeff_p2_p1_p2 = t3230+t3240+t3442+t3439+t3693+t3708; + coeffs_dz->coeff_m1_p2_p2 = t3217+t3610*t3880+t3705+t3931+t3933+t3941; + coeffs_dz->coeff_0_p2_p2 = t3799+(t3617*t3651+t3709)*y+t3678+t3827+t3922; + coeffs_dz->coeff_p1_p2_p2 = t3422+t3240+t3705+t3802+t3851+t3918; + coeffs_dz->coeff_p2_p2_p2 = t3237+t3274+t3612*t3880+(t3612*t3655+(t3618* +t3652+t3610)*y)*x+t3846; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dzz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dzz.compute.c new file mode 100644 index 0000000..3a21eaf --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dzz.compute.c @@ -0,0 +1,869 @@ +fp t7102; +fp t7084; +fp t7023; +fp t6907; +fp t7083; +fp t7101; +fp t7103; +fp t7200; +fp t7176; +fp t6924; +fp t7283; +fp t7104; +fp t7231; +fp t6980; +fp t7179; +fp t6914; +fp t7282; +fp t7098; +fp t7095; +fp t7085; +fp t7061; +fp t7281; +fp t7087; +fp t7225; +fp t6972; +fp t7228; +fp t7214; +fp t7086; +fp t7280; +fp t7215; +fp t7177; +fp t7279; +fp t7097; +fp t7272; +fp t7233; +fp t7278; +fp t7067; +fp t7070; +fp t6961; +fp t6849; +fp t7234; +fp t7096; +fp t7277; +fp t7194; +fp t6945; +fp t7093; +fp t7054; +fp t6976; +fp t7276; +fp t7075; +fp t7052; +fp t6987; +fp t7074; +fp t7056; +fp t6985; +fp t7275; +fp t7060; +fp t6997; +fp t7274; +fp t6988; +fp t7195; +fp t6995; +fp t7273; +fp t7088; +fp t7184; +fp t6981; +fp t6874; +fp t7053; +fp t7008; +fp t7271; +fp t7051; +fp t7002; +fp t6910; +fp t7063; +fp t7032; +fp t7270; +fp t6992; +fp t6886; +fp t7269; +fp t7050; +fp t7058; +fp t6996; +fp t7268; +fp t7089; +fp t7221; +fp t7267; +fp t7204; +fp t6950; +fp t7232; +fp t7266; +fp t7039; +fp t7227; +fp t7047; +fp t7265; +fp t7100; +fp t7076; +fp t7015; +fp t7072; +fp t7189; +fp t7264; +fp t6925; +fp t6957; +fp t6853; +fp t7263; +fp t7262; +fp t7236; +fp t7041; +fp t7261; +fp t7011; +fp t7064; +fp t7046; +fp t7260; +fp t6867; +fp t7237; +fp t7030; +fp t7259; +fp t7219; +fp t7258; +fp t7066; +fp t7035; +fp t7029; +fp t7257; +fp t7059; +fp t7038; +fp t7256; +fp t7226; +fp t7175; +fp t6905; +fp t7255; +fp t7082; +fp t6974; +fp t6977; +fp t7254; +fp t7253; +fp t7216; +fp t7028; +fp t7024; +fp t7252; +fp t6999; +fp t7092; +fp t7251; +fp t7037; +fp t7062; +fp t7022; +fp t7250; +fp t7021; +fp t7026; +fp t7249; +fp t7079; +fp t6986; +fp t6894; +fp t7207; +fp t7174; +fp t6891; +fp t7248; +fp t6975; +fp t6983; +fp t7055; +fp t7005; +fp t7247; +fp t7246; +fp t6881; +fp t7245; +fp t7048; +fp t6904; +fp t7173; +fp t6892; +fp t7244; +fp t7006; +fp t6872; +fp t6909; +fp t6930; +fp t7243; +fp t7013; +fp t6883; +fp t6964; +fp t6842; +fp t7242; +fp t6878; +fp t7042; +fp t6890; +fp t7241; +fp t7025; +fp t7240; +fp t7178; +fp t7239; +fp t7009; +fp t7238; +fp t7099; +fp t7235; +fp t7230; +fp t7065; +fp t7229; +fp t7224; +fp t7223; +fp t7222; +fp t6965; +fp t7220; +fp t6952; +fp t6958; +fp t7218; +fp t7077; +fp t6998; +fp t7071; +fp t6969; +fp t7069; +fp t7183; +fp t6963; +fp t6841; +fp t6970; +fp t7217; +fp t6971; +fp t6962; +fp t7213; +fp t7212; +fp t7211; +fp t7210; +fp t6919; +fp t7209; +fp t7208; +fp t6838; +fp t6956; +fp t6835; +fp t7206; +fp t6949; +fp t6847; +fp t7205; +fp t6863; +fp t7185; +fp t6906; +fp t7202; +fp t7201; +fp t7199; +fp t7068; +fp t7198; +fp t7197; +fp t7196; +fp t7193; +fp t7192; +fp t7191; +fp t7190; +fp t6959; +fp t6850; +fp t6947; +fp t7188; +fp t6960; +fp t6953; +fp t7187; +fp t7186; +fp t7182; +fp t6993; +fp t7181; +fp t7090; +fp t7180; +fp t7001; +fp t7049; +fp t6946; +fp t6955; +fp t6954; +fp t6968; +fp t6967; +fp t7019; +fp t7043; +fp t7017; +fp t7036; +fp t6951; +fp t6979; +fp t7040; +fp t6928; +fp t6880; +fp t7172; +fp t6973; +fp t6938; +fp t6875; +fp t7171; +fp t6865; +fp t6935; +fp t6870; +fp t7170; +fp t6900; +fp t6941; +fp t7169; +fp t6845; +fp t7168; +fp t6889; +fp t7167; +fp t7003; +fp t6864; +fp t7166; +fp t7044; +fp t7165; +fp t6885; +fp t7164; +fp t7163; +fp t6877; +fp t6931; +fp t7162; +fp t7161; +fp t7160; +fp t6916; +fp t6923; +fp t7159; +fp t7158; +fp t7157; +fp t7156; +fp t7155; +fp t7154; +fp t7080; +fp t7073; +fp t7153; +fp t7152; +fp t7151; +fp t7150; +fp t6933; +fp t7149; +fp t6920; +fp t7148; +fp t7147; +fp t7146; +fp t6858; +fp t7145; +fp t6927; +fp t7144; +fp t7143; +fp t6917; +fp t7142; +fp t7141; +fp t7140; +fp t6856; +fp t7139; +fp t7138; +fp t7137; +fp t6918; +fp t7136; +fp t6871; +fp t7134; +fp t6934; +fp t6929; +fp t7133; +fp t7132; +fp t6939; +fp t6868; +fp t7131; +fp t7130; +fp t6869; +fp t7129; +fp t7128; +fp t7127; +fp t7126; +fp t7125; +fp t7124; +fp t7123; +fp t7122; +fp t6922; +fp t7121; +fp t7120; +fp t6895; +fp t7119; +fp t7118; +fp t6866; +fp t7117; +fp t7116; +fp t6982; +fp t7115; +fp t6978; +fp t7114; +fp t7007; +fp t7113; +fp t7112; +fp t7018; +fp t7111; +fp t7110; +fp t7109; +fp t7108; +fp t7107; +fp t7091; +fp t7078; +fp t7031; +fp t7020; +fp t7000; +fp t6994; +fp t6966; +fp t6940; +fp t6937; +fp t6901; +fp t6893; +fp t6882; +fp t6862; +fp t6859; +fp t6854; +fp t6851; +fp t6846; +fp t6844; +fp t6840; +fp t6837; + t7102 = y*y; + t7084 = RATIONAL(-3.0,2.0); + t7023 = t7084*t7102*z; + t6907 = x*t7023; + t7083 = RATIONAL(3.0,4.0); + t7101 = x*x; + t7103 = t7101*x; + t7200 = t7102*t7103; + t7176 = z*t7200; + t6924 = t7083*t7176; + t7283 = t6907+t6924; + t7104 = t7102*y; + t7231 = z*t7104; + t6980 = t7084*t7231; + t7179 = t7083*t7231; + t6914 = t7103*t7179; + t7282 = t6914+x*t6980; + t7098 = x*z; + t7095 = y*t7098; + t7085 = RATIONAL(1.0,2.0); + t7061 = t7085*t7104; + t7281 = t7084*t7095+t7103*t7061; + t7087 = RATIONAL(3.0,2.0); + t7225 = z*t7087; + t6972 = t7103*t7225; + t7228 = z*t7103; + t7214 = y*t7228; + t7086 = RATIONAL(-3.0,4.0); + t7280 = t7084*t7176+t6972+t7086*t7214; + t7215 = t7104*t7101; + t7177 = z*t7215; + t7279 = t6980+x*t7179+t7087*t7177; + t7097 = t7102*t7101; + t7272 = t7097-t7101; + t7233 = 1.0-t7102; + t7278 = (t7233+t7272)*z; + t7067 = RATIONAL(1.0,12.0); + t7070 = RATIONAL(-1.0,12.0); + t6961 = t7070*t7200; + t6849 = z*t6961; + t7234 = t7102*x; + t7096 = z*t7234; + t7277 = t7067*t7096+t6849; + t7194 = t7067*t7103; + t6945 = t7104*t7194; + t7093 = RATIONAL(-1.0,3.0); + t7054 = t7093*y; + t6976 = x*t7054; + t7276 = t6945+t6976; + t7075 = RATIONAL(1.0,6.0); + t7052 = t7075*t7104; + t6987 = t7101*t7052; + t7074 = RATIONAL(-1.0,6.0); + t7056 = t7074*t7104; + t6985 = z*t7056; + t7275 = z*t6987+t6985; + t7060 = t7074*x; + t6997 = t7102*t7060; + t7274 = t6961+t6997; + t6988 = z*t7052; + t7195 = t7101*t7074; + t6995 = t7104*t7195; + t7273 = t6988+z*t6995; + t7088 = RATIONAL(-1.0,2.0); + t7184 = t7102*t7088; + t6981 = t7101*t7184; + t6874 = z*t6981; + t7053 = t7085*t7102; + t7008 = z*t7053; + t7271 = t6874+t7008; + t7051 = t7085*t7101; + t7002 = y*t7051; + t6910 = z*t7002; + t7063 = t7088*y; + t7032 = z*t7063; + t7270 = t6910+t7032; + t6992 = z*t7184; + t6886 = t7101*t7008; + t7269 = t6992+t6886; + t7050 = t7075*t7200; + t7058 = t7074*t7103; + t6996 = z*t7058; + t7268 = z*t7050+t6996; + t7089 = RATIONAL(1.0,3.0); + t7221 = t7089*t7101; + t7267 = t6987+y*t7221; + t7204 = t7070*t7104; + t6950 = t7103*t7204; + t7232 = y*t7075; + t7266 = t6950+x*t7232; + t7039 = t7103*t7052; + t7227 = t7089*y; + t7047 = x*t7227; + t7265 = t7039+t7047; + t7100 = y*x; + t7076 = RATIONAL(-1.0,9.0); + t7015 = t7076*t7100; + t7072 = RATIONAL(1.0,18.0); + t7189 = t7072*t7103; + t7264 = t7104*t7189+t7015; + t6925 = x*t6985; + t6957 = t7101*t7204; + t6853 = z*t6957; + t7263 = t6925+t6853; + t7262 = t6874+z*t7051; + t7236 = t7101*z; + t7041 = t7088*t7236; + t7261 = t7041+t6886; + t7011 = t7074*t7200; + t7064 = t7075*t7103; + t7046 = z*t7064; + t7260 = z*t7011+t7046; + t6867 = x*t6992; + t7237 = z*t7085; + t7030 = x*t7237; + t7259 = t6867+t7030; + t7219 = t7089*t7102; + t7258 = t7050+x*t7219; + t7066 = t7088*t7103; + t7035 = z*t7066; + t7029 = t7085*t7200; + t7257 = t7035+z*t7029; + t7059 = t7088*t7104; + t7038 = t7101*t7059; + t7256 = (t7038+t7061)*z; + t7226 = z*t7086; + t7175 = t7104*t7226; + t6905 = t7103*t7175; + t7255 = y*t6972+t6905; + t7082 = RATIONAL(-1.0,4.0); + t6974 = t7082*t7200; + t6977 = x*t7053; + t7254 = t6974+t6977; + t7253 = x*t7059+t7100; + t7216 = t7103*t7082; + t7028 = t7104*t7216; + t7024 = x*t7063; + t7252 = t7028+t7024; + t6999 = t7103*t7056; + t7092 = RATIONAL(2.0,3.0); + t7251 = t7092*t7100+t6999; + t7037 = t7103*t7184; + t7062 = t7085*t7103; + t7022 = z*t7062; + t7250 = t7022+z*t7037; + t7021 = t7101*t7061; + t7026 = z*t7059; + t7249 = z*t7021+t7026; + t7079 = RATIONAL(1.0,4.0); + t6986 = t7079*t7200; + t6894 = z*t6986; + t7207 = t7102*t7082; + t7174 = z*t7207; + t6891 = t7101*t7174; + t7248 = t6867+t6894+t6891; + t6975 = y*t7064; + t6983 = x*t7052; + t7055 = t7074*y; + t7005 = x*t7055; + t7247 = t6975+t6983+t7005+t6999; + t7246 = t7037-t7102+t6977; + t6881 = y*t7030; + t7245 = t6976+t7039+t6881; + t7048 = t7101*t7225; + t6904 = y*t7048; + t7173 = t7101*t7226; + t6892 = t7104*t7173; + t7244 = t7021+t6904+t6892; + t7006 = t7084*t7236; + t6872 = y*t7006; + t6909 = t7083*t7177; + t6930 = t7102*t7173; + t7243 = t6872+t6909+t6930; + t7013 = t7075*t7234; + t6883 = z*t7013; + t6964 = t7102*t7194; + t6842 = z*t6964; + t7242 = t6883+t6891+t6842; + t6878 = t7086*t7176; + t7042 = t7102*t7225; + t6890 = t7101*t7042; + t7241 = t7083*t7096+t6878+t6890+t7023; + t7025 = t7104*t7225; + t7240 = t7084*t7177+t7025+x*t7175+t6914; + t7178 = t7083*t7236; + t7239 = t7006+t6890+y*t7178+t6892; + t7009 = t7084*t7228; + t7238 = t7009+t7087*t7176+t7083*t7214+t6905; + t7099 = y*z; + t7235 = y*t7101; + t7230 = y*t7103; + t7065 = t7088*x; + t7229 = y*t7079; + t7224 = x*t7104; + t7223 = t7087*y; + t7222 = y-t7104; + t6965 = t7070*t7234; + t7220 = t6964+t6965; + t6952 = y*t7189; + t6958 = t7072*t7224; + t7218 = t6952+t6958; + t7077 = RATIONAL(1.0,9.0); + t6998 = t7077*t7100; + t7071 = RATIONAL(1.0,36.0); + t6969 = t7071*t7100; + t7069 = RATIONAL(-1.0,36.0); + t7183 = t7104*t7069; + t6963 = t7103*t7183; + t6841 = z*t6963; + t6970 = t7071*t7224; + t7217 = t6841+z*t6970; + t6971 = t7072*t7100; + t6962 = t7067*t7100; + t7213 = z*t6965+t6842; + t7212 = t6981+t7102*t7178; + t7211 = t7079*t7103; + t7210 = t7101*t7082; + t6919 = y*t7035; + t7209 = t6919+t7103*t7227; + t7208 = t7071*t7103; + t6838 = z*t6945; + t6956 = x*t7204; + t6835 = z*t6956; + t7206 = t6838+t6835; + t6949 = t7067*t7224; + t6847 = z*t6950; + t7205 = z*t6949+t6847; + t6863 = y*t6996; + t7185 = z*t7232; + t6906 = x*t7185; + t7202 = t6863+t6906; + t7201 = t7098-t7096; + t7199 = t6963+t6971; + t7068 = RATIONAL(-1.0,18.0); + t7198 = t7103*t7068; + t7197 = t7101*t7067; + t7196 = t6950+t7005; + t7193 = t7068*t7100; + t7192 = t7101*t7079; + t7191 = z*t7235-t7099; + t7190 = z*t7060; + t6959 = t7104*t7208; + t6850 = z*t6959; + t6947 = x*t7183; + t7188 = t6850+z*t6947; + t6960 = t7104*t7197; + t6953 = t7070*t7235; + t7187 = t6960+t6953; + t7186 = z*t7229; + t7182 = t7011+t7013; + t6993 = t7101*t7232; + t7181 = t6995+t6993; + t7090 = RATIONAL(-2.0,1.0); + t7180 = -t7103+t7090; + t7001 = y*t7195; + t7049 = y*t7210; + t6946 = t7069*t7230; + t6955 = y*t7208; + t6954 = t7070*t7230; + t6968 = y*t7198; + t6967 = y*t7194; + t7019 = y*t7211; + t7043 = y*t7216; + t7017 = t7079*t7224; + t7036 = t7082*t7224; + t6951 = t7068*t7224; + t6979 = x*t7061; + t7040 = t7104*t7211; + t6928 = z*t7040; + t6880 = z*t6974; + t7172 = t6919+t6928+t6880; + t6973 = t7104*t7210; + t6938 = z*t6973; + t6875 = x*t7026; + t7171 = t6938+t6928+t6875; + t6865 = z*t7047; + t6935 = y*t7041; + t6870 = y*t7046; + t7170 = t6865+t6935+t6870; + t6900 = y*t7022; + t6941 = z*t7028; + t7169 = t6900+t6894+t6941; + t6845 = z*t6960; + t7168 = z*t6951+t6841+t6845; + t6889 = x*t7008; + t7167 = t7095+t6889+t6875; + t7003 = t7102*t7192; + t6864 = z*t6976; + t7166 = t6863+t6910+t6864; + t7044 = t7104*t7192; + t7165 = t6900+t6935-t7095; + t6885 = x*t6988; + t7164 = t6838+t6885+t6938; + t7163 = t7003+t7001+t6957; + t6877 = z*t7003; + t6931 = z*t6997; + t7162 = t6877+t6931+t6849; + t7161 = t6885+t6845+t6847; + t7160 = t6850+z*t6958+t6853; + t6916 = z*t6979; + t6923 = z*t7044; + t7159 = t6941+t6916+t6923; + t7158 = t7003+t6973+t7002; + t7157 = t6925+t6847+t6923; + t7156 = t6838+t6880+t6870; + t7155 = t7093*t7101+t7089; + t7154 = t7219+t7093; + t7080 = RATIONAL(3.0,1.0); + t7073 = RATIONAL(-3.0,1.0); + t7153 = t7080*t7102+t7073; + t7152 = t7093+t7221; + t7151 = t7073*t7102+t7080; + t7150 = t7093*t7102+t7089; + t6933 = z*t7019; + t7149 = t6933+t6941+t7257; + t6920 = z*t7036; + t7148 = t6920+t6928+t7256; + t7147 = t7053+x*t7207+t6981+t6986; + t7146 = t6959+t6947+t6946+t6969; + t6858 = z*t6954; + t7145 = z*t6962+t6858+t7206; + t6927 = z*t7043; + t7144 = t6927+t6928+t7250; + t7143 = t7002+t7038+t7272; + t6917 = z*t7017; + t7142 = t6941+t6917+t7249; + t7141 = t6945+t6962+t6954+t6956; + t7140 = t7051+t7049+t6981+t7044; + t6856 = z*t6967; + t7139 = t7070*t7095+t6856+t7205; + t7138 = t7155*y; + t7137 = t7150*x; + t6918 = x*t7042; + t7136 = t6918+t6878+t7029+t7212; + t6871 = t7079*t7096; + t7134 = t6871+t6920+t6881+t7172; + t6934 = x*t7032; + t6929 = z*t7049; + t7133 = t6934+t6933+t6929+t7159; + t7132 = t6906+t6856+t6929+t7157; + t6939 = t7101*t7186; + t6868 = y*t7190; + t7131 = t6939+t6868+t6858+t7164; + t7130 = t6871+t6835+t6868+t7156; + t6869 = x*t7174; + t7129 = t6934+t6869+t6917+t7169; + t7128 = t6894+t6869+t7202+t7205; + t7127 = t6951+t6955+t7187+t7199; + t7126 = t6967+t6983+t7187+t7196; + t7125 = t6939+t6927+t6881+t7171; + t7124 = t6867+t6880+t7212+t7258; + t7123 = t6975+t6949+t7196+t7220; + t7122 = t6968+t6970+t7199+t7220; + t6922 = t7101*t7023; + t7121 = t6909+t6922+y*t7173+t7048+t7143; + t7120 = t7097+t7086*t7096+t6924+t7042+t6922+t7246; + t6895 = x*t7186; + t7119 = t6895+z*t7065+t6889+t6920+t7144; + t7118 = t7055+t7052+t7141+t7181; + t6866 = t7082*t7095; + t7117 = y*t7237+t6866+t6935+t6933+t7142; + t7116 = t7060+t7064+t7141+t7182; + t6982 = y*t7058; + t7115 = t6982+t6983+t7158+t7274+t7276; + t6978 = x*t7056; + t7114 = t6975+t6978+t7163+t7254+t7276; + t7007 = y*t7066; + t7113 = t7007+t7040+t7158+t7253+t7254; + t7112 = t6959+t6998+t7163+t7218+t7274; + t7018 = y*t7062; + t7111 = t7018+t7017+t7021+t7059+t7147+t7252; + t7110 = t7066+t7019+t6979+t7029+t7140+t7252; + t7109 = t7054+t6982+t6949+t7056+t7147+t7266+t7267; + t7108 = t7093*x+t7058+t6967+t6978+t7140+t7258+t7266; + t7107 = x*t7229+RATIONAL(1.0,1.0)+t7043+t7065+t7061+t7062+t7063+t7036+ +t7040+t7143+t7246; + t7091 = RATIONAL(-2.0,3.0); + t7078 = RATIONAL(2.0,1.0); + t7031 = t7093*t7230; + t7020 = t7103*t7059; + t7000 = t7093*t7224; + t6994 = t7089*t7224; + t6966 = t7104*t7198; + t6940 = y*t7009; + t6937 = t7223*t7098; + t6901 = z*t7001; + t6893 = x*t7025; + t6882 = z*t6993; + t6862 = z*t6952; + t6859 = z*t6955; + t6854 = t7197*t7099; + t6851 = z*t6946; + t6846 = z*t7193; + t6844 = z*t6968; + t6840 = z*t6953; + t6837 = z*t6971; + coeffs_dzz->coeff_m1_m1_m1 = z*t7015+t6882+t6844+t7112+t7168+t7242; + coeffs_dzz->coeff_0_m1_m1 = z*t7138+t7109+t7130+t7269+t7273; + coeffs_dzz->coeff_p1_m1_m1 = t6865+t6863+t6882+t7114+t7161+t7248; + coeffs_dzz->coeff_p2_m1_m1 = t6846+t6862+t7122+t7188+t7277; + coeffs_dzz->coeff_m1_0_m1 = t7108+z*t7137+t7131+t7260+t7261; + coeffs_dzz->coeff_0_0_m1 = -t7278+t7107+t7117+t7257+t7259; + coeffs_dzz->coeff_p1_0_m1 = x+t7110-t7234+t7125-t7201+t7250+t7261; + coeffs_dzz->coeff_p2_0_m1 = t6931+t7075*t7098+t7116+t7139+t7268; + coeffs_dzz->coeff_m1_p1_m1 = t7115+t7157+t7170+t7242; + coeffs_dzz->coeff_0_p1_m1 = y-t7235+t7111+t7134+t7191+t7256+t7269; + coeffs_dzz->coeff_p1_p1_m1 = t7113+t7159+t7165+t7248; + coeffs_dzz->coeff_p2_p1_m1 = t7123+t7202+t7206+t7277; + coeffs_dzz->coeff_m1_p2_m1 = t6854+t6846+t6851+t7127+t7160; + coeffs_dzz->coeff_0_p2_m1 = t7118+t6901+t7185+t7139+t7275; + coeffs_dzz->coeff_p1_p2_m1 = t6906+t6838+t6854+t6858+t7126+t7263; + coeffs_dzz->coeff_p2_p2_m1 = t7069*t7095+t6859+t7146+t7217; + coeffs_dzz->coeff_m1_m1_0 = t6966+t7076*t7230+(t7076*t7104+RATIONAL(-2.0, +9.0)*y)*x+t7124+t7164+t7170+t7267; + coeffs_dzz->coeff_0_m1_0 = t7120+(t7091*t7101+t7092)*y+t6978+t7155*t7104+ +t7142+t7191+t7209+t7245; + coeffs_dzz->coeff_p1_m1_0 = t7031-t7234+t6994+t7136+t7165+t7171+t7251+ +t7267; + coeffs_dzz->coeff_p2_m1_0 = t6951+t7077*t7230+t7128+t7182+t7264; + coeffs_dzz->coeff_m1_0_0 = (t7091*t7102+t7092)*x+t6994+t7121+t7150*t7103+ +t6982+t6875+t7149-t7201+t7245; + coeffs_dzz->coeff_0_0_0 = t7018+x+t6979+t6904+t6918+t7024+t7020+(-x+t7078 ++t7103)*t7102+(t7078+t7090*t7102-t7222)*t7101+(t7084*y+t7153*t7101+(t7083*y+ +t7084)*x+t7151)*z+t7180+t7222+t7240+t7280; + coeffs_dzz->coeff_p1_0_0 = t6893+(-t7104+t7078*t7102+t7090+t7151*z)*x+ +t7103+t7121+t7007-t7200+t7100+t7238+t7281; + coeffs_dzz->coeff_p2_0_0 = t7154*t7103+t7137+t7119+t7247; + coeffs_dzz->coeff_m1_p1_0 = -t7095-t7235+t7124+t6928+t6916+t7000+t7209+ +t7244+t7251; + coeffs_dzz->coeff_0_p1_0 = -t7215+t7104+(t7078*t7101+(t7080+t7073*t7101)* +z+t7180)*y+t7120+t7253+t7255+t7279+t7281; + coeffs_dzz->coeff_p1_p1_0 = t7020+t6940+(t7103-t7101)*y+(-t7102+t7104+( +t7080*z+t7090)*y)*x+t7136+t7244+t7282; + coeffs_dzz->coeff_p2_p1_0 = t6978+t7031+t7129+t7182+t7265; + coeffs_dzz->coeff_m1_p2_0 = t7077*t7224+t6968+t7132+t7181+t7264; + coeffs_dzz->coeff_0_p2_0 = t6895+t6927+t7152*t7104+t7138+t7148+t7247+ +t7270; + coeffs_dzz->coeff_p1_p2_0 = t7000+t6982+t7133+t7181+t7265; + coeffs_dzz->coeff_p2_p2_0 = t7193+t6966+t7145+t7218; + coeffs_dzz->coeff_m1_m1_p1 = t6889+t6894+t7112+t6930+t7157+t7166; + coeffs_dzz->coeff_0_m1_p1 = t6934+t6900+t7109+t7148-t7191+t7241; + coeffs_dzz->coeff_p1_m1_p1 = t6919+t7095+t6910+t7114+t6930+t7159+t7283; + coeffs_dzz->coeff_p2_m1_p1 = t7122+t7130; + coeffs_dzz->coeff_m1_0_p1 = t6934+t7108+t6916+t7144+t7201+t7239; + coeffs_dzz->coeff_0_0_p1 = t6907+t6872+(t7223+t7151*t7101+(t7086*y+t7087) +*x+t7153)*z+t7107+t7238+t7279; + coeffs_dzz->coeff_p1_0_p1 = (t7153*z+t7233)*x+t6937+t7110+t7239+t7280+ +t7282; + coeffs_dzz->coeff_p2_0_p1 = t6866+t6917+t7116+t7149+t7259; + coeffs_dzz->coeff_m1_p1_p1 = t7115+t7167+t7169+t7243; + coeffs_dzz->coeff_0_p1_p1 = (-t7101+1.0+(t7080*t7101+t7073)*z)*y+t6937+ +t7111+t6940+t7240+t7241; + coeffs_dzz->coeff_p1_p1_p1 = t6893+t7113+t7073*t7095+t7243+t7255+t7283; + coeffs_dzz->coeff_p2_p1_p1 = t7123+t7134; + coeffs_dzz->coeff_m1_p2_p1 = t7127+t7131; + coeffs_dzz->coeff_0_p2_p1 = t7117+t7118; + coeffs_dzz->coeff_p1_p2_p1 = t7125+t7126; + coeffs_dzz->coeff_p2_p2_p1 = t7139+t7146; + coeffs_dzz->coeff_m1_m1_p2 = t6862+z*t6998+t6901+t7160+t7162; + coeffs_dzz->coeff_0_m1_p2 = t7152*t7099+t7128+t7271+t7275; + coeffs_dzz->coeff_p1_m1_p2 = t6864+t6901+t6889+t6877+t7156+t7263; + coeffs_dzz->coeff_p2_m1_p2 = t6844+t6837+t7213+t7217; + coeffs_dzz->coeff_m1_0_p2 = t7154*t7098+t7132+t7262+t7268; + coeffs_dzz->coeff_0_0_p2 = t7278+t7119+t7256+t7270; + coeffs_dzz->coeff_p1_0_p2 = t7133+t7201+t7257+t7262; + coeffs_dzz->coeff_p2_0_p2 = t7190+t6883+t7145+t7260; + coeffs_dzz->coeff_m1_p1_p2 = t7162+t7164+t7166; + coeffs_dzz->coeff_0_p1_p2 = t7129-t7191+t7249+t7271; + coeffs_dzz->coeff_p1_p1_p2 = t6910+t6877+t6938+t7167+t7172; + coeffs_dzz->coeff_p2_p1_p2 = t6870+t6868+t7205+t7213; + coeffs_dzz->coeff_m1_p2_p2 = t6837+t6840+t6859+t7168; + coeffs_dzz->coeff_0_p2_p2 = t6882+z*t7055+t7145+t7273; + coeffs_dzz->coeff_p1_p2_p2 = t6840+t6868+t6856+t7161; + coeffs_dzz->coeff_p2_p2_p2 = z*t6969+t6851+t7188; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-I.compute.c new file mode 100644 index 0000000..64d1223 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-I.compute.c @@ -0,0 +1,2724 @@ +fp t9058; +fp t9057; +fp t9060; +fp t9696; +fp t8960; +fp t9307; +fp t9063; +fp t8964; +fp t9563; +fp t9262; +fp t10201; +fp t9021; +fp t9025; +fp t9767; +fp t9759; +fp t10200; +fp t9059; +fp t9061; +fp t9065; +fp t9571; +fp t8975; +fp t9774; +fp t9510; +fp t10199; +fp t9046; +fp t9681; +fp t9016; +fp t9616; +fp t9064; +fp t8809; +fp t10198; +fp t9598; +fp t9062; +fp t9372; +fp t9733; +fp t9251; +fp t10197; +fp t9649; +fp t9037; +fp t10196; +fp t9662; +fp t9434; +fp t9583; +fp t10195; +fp t8997; +fp t9622; +fp t8972; +fp t9569; +fp t10194; +fp t9719; +fp t9764; +fp t9449; +fp t10193; +fp t8995; +fp t9699; +fp t9723; +fp t10192; +fp t9000; +fp t9639; +fp t9005; +fp t9674; +fp t9326; +fp t10191; +fp t9782; +fp t9023; +fp t9019; +fp t9769; +fp t10190; +fp t9742; +fp t9457; +fp t9675; +fp t9554; +fp t10189; +fp t9600; +fp t9508; +fp t9690; +fp t9549; +fp t10188; +fp t9673; +fp t9589; +fp t10187; +fp t9702; +fp t9788; +fp t9011; +fp t10186; +fp t9601; +fp t9047; +fp t9652; +fp t10185; +fp t9461; +fp t9724; +fp t9289; +fp t10184; +fp t9608; +fp t9440; +fp t9380; +fp t10183; +fp t10182; +fp t8963; +fp t9772; +fp t9615; +fp t9243; +fp t10181; +fp t9017; +fp t8983; +fp t9590; +fp t10180; +fp t8962; +fp t9297; +fp t10179; +fp t9003; +fp t9635; +fp t9225; +fp t9001; +fp t9657; +fp t10178; +fp t9646; +fp t9629; +fp t9235; +fp t10177; +fp t9779; +fp t9018; +fp t9503; +fp t9777; +fp t8982; +fp t10176; +fp t9008; +fp t9015; +fp t9645; +fp t10175; +fp t9052; +fp t10174; +fp t9738; +fp t9685; +fp t10173; +fp t9698; +fp t8634; +fp t9042; +fp t9587; +fp t10172; +fp t8977; +fp t10171; +fp t9627; +fp t8998; +fp t10170; +fp t9614; +fp t8641; +fp t10169; +fp t9642; +fp t8723; +fp t9566; +fp t8832; +fp t10168; +fp t9605; +fp t10167; +fp t10166; +fp t9632; +fp t9558; +fp t10165; +fp t9752; +fp t10164; +fp t9040; +fp t9055; +fp t9786; +fp t10163; +fp t9594; +fp t9732; +fp t10162; +fp t9004; +fp t9597; +fp t10161; +fp t8968; +fp t9596; +fp t10160; +fp t9741; +fp t9500; +fp t9462; +fp t10159; +fp t9056; +fp t9634; +fp t9640; +fp t10158; +fp t9705; +fp t10157; +fp t9041; +fp t9577; +fp t10156; +fp t9570; +fp t9002; +fp t9581; +fp t10155; +fp t10154; +fp t9526; +fp t10153; +fp t9751; +fp t10152; +fp t8970; +fp t8973; +fp t10151; +fp t9661; +fp t8815; +fp t10150; +fp t9726; +fp t10149; +fp t8981; +fp t9038; +fp t9636; +fp t10148; +fp t9531; +fp t9745; +fp t10147; +fp t8716; +fp t8713; +fp t10146; +fp t9682; +fp t10145; +fp t9770; +fp t9760; +fp t10144; +fp t8958; +fp t10143; +fp t10142; +fp t8959; +fp t9643; +fp t9753; +fp t10141; +fp t9754; +fp t10140; +fp t9660; +fp t10139; +fp t9565; +fp t10138; +fp t9013; +fp t9707; +fp t9787; +fp t10137; +fp t10136; +fp t9035; +fp t9027; +fp t9585; +fp t10135; +fp t8976; +fp t9708; +fp t9410; +fp t9562; +fp t10134; +fp t9617; +fp t9196; +fp t10133; +fp t9762; +fp t9735; +fp t9007; +fp t9666; +fp t9241; +fp t10132; +fp t9790; +fp t9543; +fp t9655; +fp t9207; +fp t9584; +fp t9253; +fp t10029; +fp t9700; +fp t9430; +fp t9381; +fp t7750; +fp t10131; +fp t8979; +fp t9775; +fp t9504; +fp t8986; +fp t9619; +fp t9489; +fp t10130; +fp t9781; +fp t9547; +fp t9778; +fp t9497; +fp t10129; +fp t9766; +fp t9572; +fp t9582; +fp t9310; +fp t10128; +fp t8829; +fp t10127; +fp t9722; +fp t10126; +fp t9039; +fp t9574; +fp t9044; +fp t10125; +fp t9656; +fp t9505; +fp t7739; +fp t9443; +fp t9339; +fp t9268; +fp t10015; +fp t9518; +fp t10124; +fp t9654; +fp t10123; +fp t9665; +fp t10122; +fp t9612; +fp t10121; +fp t9595; +fp t10120; +fp t9687; +fp t10119; +fp t9591; +fp t9453; +fp t10118; +fp t9743; +fp t9513; +fp t10117; +fp t9784; +fp t9468; +fp t9704; +fp t9507; +fp t10116; +fp t10115; +fp t9206; +fp t10114; +fp t9715; +fp t9613; +fp t10113; +fp t9501; +fp t10112; +fp t9647; +fp t9467; +fp t9433; +fp t10111; +fp t9620; +fp t9276; +fp t9299; +fp t9470; +fp t10110; +fp t9306; +fp t10109; +fp t9680; +fp t9485; +fp t9431; +fp t9737; +fp t9541; +fp t10079; +fp t10108; +fp t9400; +fp t9285; +fp t10107; +fp t9229; +fp t9261; +fp t10106; +fp t9298; +fp t10105; +fp t9791; +fp t9417; +fp t10104; +fp t9528; +fp t10103; +fp t9325; +fp t9272; +fp t10102; +fp t8967; +fp t9283; +fp t8969; +fp t10101; +fp t9221; +fp t10100; +fp t9329; +fp t8980; +fp t9248; +fp t10099; +fp t9219; +fp t10098; +fp t9267; +fp t9367; +fp t10097; +fp t9376; +fp t9313; +fp t8974; +fp t8971; +fp t10096; +fp t9588; +fp t9256; +fp t9269; +fp t10095; +fp t10094; +fp t9694; +fp t9264; +fp t9308; +fp t10093; +fp t10092; +fp t9050; +fp t9670; +fp t9373; +fp t10091; +fp t9378; +fp t10090; +fp t8999; +fp t9028; +fp t10089; +fp t9033; +fp t9302; +fp t10088; +fp t10087; +fp t9201; +fp t10086; +fp t10085; +fp t9604; +fp t9362; +fp t10084; +fp t10083; +fp t10082; +fp t9424; +fp t10081; +fp t9281; +fp t9575; +fp t9414; +fp t10080; +fp t9303; +fp t9343; +fp t9631; +fp t9312; +fp t10078; +fp t9198; +fp t9483; +fp t10077; +fp t9757; +fp t9498; +fp t9209; +fp t10076; +fp t9346; +fp t9559; +fp t9200; +fp t10075; +fp t9678; +fp t9442; +fp t10074; +fp t9347; +fp t10073; +fp t9481; +fp t9290; +fp t10072; +fp t9428; +fp t9556; +fp t9713; +fp t9493; +fp t10071; +fp t10070; +fp t9542; +fp t10069; +fp t9333; +fp t10068; +fp t10067; +fp t8990; +fp t9437; +fp t9517; +fp t9291; +fp t9419; +fp t10066; +fp t9749; +fp t9469; +fp t9514; +fp t10065; +fp t9024; +fp t9049; +fp t9034; +fp t9036; +fp t10064; +fp t9464; +fp t9651; +fp t9353; +fp t10063; +fp t9650; +fp t9368; +fp t9720; +fp t9478; +fp t9288; +fp t10062; +fp t9511; +fp t9521; +fp t10061; +fp t9369; +fp t8608; +fp t10060; +fp t10059; +fp t9477; +fp t9475; +fp t10058; +fp t9389; +fp t9279; +fp t10057; +fp t9195; +fp t9271; +fp t10056; +fp t9697; +fp t9340; +fp t10055; +fp t8834; +fp t9548; +fp t8629; +fp t10054; +fp t9216; +fp t10053; +fp t9592; +fp t9361; +fp t10052; +fp t10051; +fp t9533; +fp t9427; +fp t10050; +fp t10049; +fp t9456; +fp t9618; +fp t9226; +fp t9287; +fp t10048; +fp t10047; +fp t8994; +fp t9026; +fp t9573; +fp t9593; +fp t8989; +fp t10046; +fp t8748; +fp t9676; +fp t8616; +fp t10045; +fp t9667; +fp t9332; +fp t9716; +fp t9413; +fp t10044; +fp t10043; +fp t9448; +fp t10042; +fp t9022; +fp t9568; +fp t9473; +fp t10041; +fp t10040; +fp t9659; +fp t9370; +fp t9644; +fp t9357; +fp t8668; +fp t10039; +fp t9730; +fp t9502; +fp t9395; +fp t9211; +fp t10038; +fp t9217; +fp t10037; +fp t9454; +fp t9249; +fp t10036; +fp t10035; +fp t9399; +fp t10034; +fp t9405; +fp t9671; +fp t8649; +fp t9296; +fp t10033; +fp t10032; +fp t9274; +fp t9204; +fp t8686; +fp t10031; +fp t8673; +fp t9280; +fp t10030; +fp t10028; +fp t10027; +fp t9761; +fp t9534; +fp t9292; +fp t10026; +fp t9776; +fp t9551; +fp t9250; +fp t10025; +fp t10024; +fp t10023; +fp t9197; +fp t9331; +fp t10022; +fp t9265; +fp t9491; +fp t10021; +fp t9535; +fp t9527; +fp t9205; +fp t9630; +fp t9282; +fp t10020; +fp t9321; +fp t10019; +fp t10018; +fp t9599; +fp t9295; +fp t9354; +fp t9553; +fp t10017; +fp t9536; +fp t9387; +fp t9270; +fp t9409; +fp t10016; +fp t9611; +fp t10014; +fp t9771; +fp t9460; +fp t10013; +fp t10012; +fp t9383; +fp t9247; +fp t10011; +fp t10010; +fp t10009; +fp t9232; +fp t10008; +fp t9792; +fp t9610; +fp t9277; +fp t9218; +fp t10007; +fp t9363; +fp t9451; +fp t10006; +fp t9429; +fp t10005; +fp t9746; +fp t9684; +fp t10004; +fp t9411; +fp t10003; +fp t10002; +fp t9736; +fp t8597; +fp t10001; +fp t8670; +fp t9496; +fp t10000; +fp t9624; +fp t8644; +fp t9275; +fp t9999; +fp t9546; +fp t9445; +fp t9663; +fp t9998; +fp t9335; +fp t9532; +fp t9997; +fp t9486; +fp t9552; +fp t9499; +fp t9996; +fp t9484; +fp t9995; +fp t9537; +fp t9479; +fp t9482; +fp t9994; +fp t9773; +fp t9471; +fp t9993; +fp t9356; +fp t9314; +fp t9992; +fp t9452; +fp t9991; +fp t9322; +fp t9990; +fp t9579; +fp t9224; +fp t9989; +fp t9260; +fp t9988; +fp t9606; +fp t9444; +fp t9609; +fp t9520; +fp t9987; +fp t9692; +fp t8756; +fp t9785; +fp t9986; +fp t9524; +fp t9985; +fp t9984; +fp t9783; +fp t9637; +fp t9672; +fp t8721; +fp t9744; +fp t9983; +fp t9982; +fp t8598; +fp t9981; +fp t9980; +fp t9576; +fp t8606; +fp t9979; +fp t9561; +fp t9231; +fp t9978; +fp t8701; +fp t9305; +fp t9212; +fp t9623; +fp t9174; +fp t9977; +fp t9976; +fp t9446; +fp t9975; +fp t9459; +fp t9974; +fp t9401; +fp t9973; +fp t9972; +fp t8603; +fp t9240; +fp t9227; +fp t9159; +fp t8725; +fp t9971; +fp t9970; +fp t9968; +fp t9633; +fp t9641; +fp t8620; +fp t9967; +fp t9966; +fp t9509; +fp t9965; +fp t9964; +fp t8677; +fp t9963; +fp t9273; +fp t9962; +fp t9961; +fp t9960; +fp t9958; +fp t7925; +fp t9957; +fp t9544; +fp t9530; +fp t9956; +fp t9350; +fp t9955; +fp t9954; +fp t9953; +fp t9341; +fp t9328; +fp t9952; +fp t9348; +fp t9951; +fp t9950; +fp t9949; +fp t9948; +fp t9242; +fp t9379; +fp t9947; +fp t9342; +fp t9679; +fp t9516; +fp t9398; +fp t9946; +fp t9945; +fp t9220; +fp t9944; +fp t9943; +fp t9942; +fp t9941; +fp t9940; +fp t9352; +fp t9939; +fp t9344; +fp t9364; +fp t9938; +fp t9371; +fp t9937; +fp t9625; +fp t9626; +fp t9653; +fp t8689; +fp t9936; +fp t9664; +fp t9257; +fp t9412; +fp t9396; +fp t9935; +fp t7687; +fp t9934; +fp t9933; +fp t9402; +fp t9450; +fp t9580; +fp t9932; +fp t9931; +fp t9930; +fp t9390; +fp t9929; +fp t9375; +fp t9366; +fp t9330; +fp t9432; +fp t9320; +fp t9928; +fp t9927; +fp t9259; +fp t9926; +fp t9925; +fp t9924; +fp t9683; +fp t9923; +fp t9922; +fp t9921; +fp t9920; +fp t9919; +fp t9729; +fp t9441; +fp t9918; +fp t9917; +fp t8139; +fp t9916; +fp t9915; +fp t9914; +fp t8595; +fp t9913; +fp t9912; +fp t9789; +fp t9564; +fp t9266; +fp t9557; +fp t9658; +fp t9911; +fp t9293; +fp t9910; +fp t9909; +fp t9908; +fp t9907; +fp t9238; +fp t9906; +fp t9435; +fp t8071; +fp t9905; +fp t9711; +fp t9263; +fp t9904; +fp t9391; +fp t9540; +fp t9436; +fp t9213; +fp t9903; +fp t9902; +fp t9718; +fp t9515; +fp t9901; +fp t9900; +fp t9899; +fp t9337; +fp t9525; +fp t9418; +fp t9898; +fp t9578; +fp t8931; +fp t9319; +fp t8929; +fp t9897; +fp t9309; +fp t9896; +fp t9480; +fp t9895; +fp t9317; +fp t9894; +fp t9358; +fp t9893; +fp t9892; +fp t9891; +fp t9890; +fp t9286; +fp t9889; +fp t9385; +fp t9210; +fp t9888; +fp t9887; +fp t7990; +fp t9886; +fp t9885; +fp t8148; +fp t9884; +fp t9883; +fp t9882; +fp t8895; +fp t8890; +fp t9881; +fp t9203; +fp t9880; +fp t9879; +fp t9878; +fp t9408; +fp t9877; +fp t9876; +fp t9875; +fp t9874; +fp t9873; +fp t9872; +fp t9871; +fp t8714; +fp t8927; +fp t9388; +fp t8923; +fp t9870; +fp t9143; +fp t9869; +fp t9868; +fp t9147; +fp t9867; +fp t9458; +fp t9490; +fp t9866; +fp t9439; +fp t9865; +fp t8684; +fp t9712; +fp t9864; +fp t9316; +fp t9404; +fp t9863; +fp t9862; +fp t9425; +fp t8662; +fp t9740; +fp t9861; +fp t9860; +fp t9426; +fp t9355; +fp t9545; +fp t9529; +fp t9859; +fp t8738; +fp t9202; +fp t9734; +fp t9858; +fp t9351; +fp t9602; +fp t9857; +fp t8754; +fp t9686; +fp t9555; +fp t9415; +fp t9856; +fp t9855; +fp t9438; +fp t9854; +fp t9689; +fp t8751; +fp t8661; +fp t9853; +fp t9701; +fp t9607; +fp t8752; +fp t8683; +fp t9852; +fp t9474; +fp t9851; +fp t9717; +fp t9669; +fp t8770; +fp t8659; +fp t9850; +fp t9849; +fp t9728; +fp t9848; +fp t9847; +fp t9739; +fp t9233; +fp t9846; +fp t9386; +fp t9294; +fp t9688; +fp t8710; +fp t9845; +fp t9710; +fp t9709; +fp t9394; +fp t9844; +fp t9843; +fp t9721; +fp t9311; +fp t9842; +fp t9841; +fp t9768; +fp t9495; +fp t9840; +fp t9714; +fp t9839; +fp t9382; +fp t8744; +fp t9731; +fp t9838; +fp t9567; +fp t9638; +fp t9837; +fp t8746; +fp t9300; +fp t9836; +fp t8839; +fp t9835; +fp t9834; +fp t9833; +fp t9392; +fp t9832; +fp t9214; +fp t9831; +fp t8794; +fp t9830; +fp t9756; +fp t9403; +fp t8827; +fp t9829; +fp t8625; +fp t9828; +fp t8687; +fp t9827; +fp t8763; +fp t8753; +fp t9826; +fp t9825; +fp t9824; +fp t9750; +fp t9823; +fp t9822; +fp t9677; +fp t9821; +fp t8775; +fp t9706; +fp t8776; +fp t9725; +fp t9820; +fp t9727; +fp t8592; +fp t9819; +fp t8602; +fp t9818; +fp t9817; +fp t9816; +fp t9815; +fp t9814; +fp t9813; +fp t9812; +fp t9811; +fp t9810; +fp t9809; +fp t9808; +fp t9807; +fp t9806; +fp t9805; +fp t9804; +fp t7923; +fp t9803; +fp t9802; +fp t9801; +fp t9800; +fp t9799; +fp t9798; +fp t9797; +fp t9796; +fp t9795; +fp t9794; +fp t9793; +fp t8952; +fp t9703; +fp t8950; +fp t9693; +fp t7904; +fp t9691; +fp t9668; +fp t8949; +fp t9628; +fp t7817; +fp t9621; +fp t8945; +fp t9603; +fp t7706; +fp t9560; +fp t8845; +fp t9487; +fp t8833; +fp t8853; +fp t9422; +fp t9416; +fp t9397; +fp t9374; +fp t9194; +fp t9193; +fp t9192; +fp t9191; +fp t9188; +fp t9187; +fp t9186; +fp t9185; +fp t9184; +fp t9183; +fp t9030; +fp t8966; +fp t8987; +fp t9180; +fp t9010; +fp t9009; +fp t9048; +fp t9179; +fp t9178; +fp t9006; +fp t9043; +fp t9177; +fp t9029; +fp t8993; +fp t8991; +fp t9176; +fp t9045; +fp t9054; +fp t9175; +fp t9014; +fp t9032; +fp t9173; +fp t8984; +fp t9172; +fp t9012; +fp t8978; +fp t9171; +fp t9170; +fp t9169; +fp t9051; +fp t8992; +fp t9168; +fp t8965; +fp t9167; +fp t9166; +fp t9165; +fp t8996; +fp t9164; +fp t9053; +fp t9163; +fp t9162; +fp t9020; +fp t9031; +fp t9161; +fp t9160; +fp t9158; +fp t8985; +fp t9157; +fp t9156; +fp t9155; +fp t9154; +fp t9153; +fp t9152; +fp t9151; +fp t9150; +fp t9148; +fp t9146; +fp t9145; +fp t9144; +fp t9142; +fp t9141; +fp t9140; +fp t8988; +fp t8961; +fp t9139; +fp t9138; +fp t9137; +fp t9136; +fp t9135; +fp t9134; +fp t9133; +fp t9132; +fp t9131; +fp t9130; +fp t9129; +fp t9128; +fp t9127; +fp t9126; +fp t9125; +fp t9124; +fp t9123; +fp t9122; +fp t9121; +fp t9120; +fp t9119; +fp t9118; +fp t9117; +fp t9116; +fp t9115; +fp t9114; +fp t9113; +fp t9112; +fp t9111; +fp t9110; +fp t9109; +fp t9108; +fp t9107; +fp t9106; +fp t9105; +fp t9104; +fp t9103; +fp t9102; +fp t9101; +fp t9100; +fp t9099; +fp t9098; +fp t9097; +fp t9096; +fp t9095; +fp t9094; +fp t9093; +fp t9092; +fp t9091; +fp t9090; +fp t9089; +fp t9088; +fp t9087; +fp t9086; +fp t9085; +fp t9084; +fp t9083; +fp t9082; +fp t9081; +fp t9080; +fp t9079; +fp t9078; +fp t9077; +fp t9076; +fp t9075; +fp t9074; +fp t9073; +fp t9072; + t9058 = z*z; + t9057 = x*x; + t9060 = t9057*x; + t9696 = t9058*t9060; + t8960 = RATIONAL(1.0,1728.0); + t9307 = t8960*t9696; + t9063 = t9058*t9058; + t8964 = RATIONAL(-1.0,1728.0); + t9563 = t9063*t8964; + t9262 = t9060*t9563; + t10201 = t9262+t9307; + t9021 = RATIONAL(-1.0,54.0); + t9025 = RATIONAL(2.0,27.0); + t9767 = x*t9025; + t9759 = z*t9060; + t10200 = t9021*t9759+z*t9767; + t9059 = y*y; + t9061 = t9059*y; + t9065 = t9057*t9057; + t9571 = t9061*t9065; + t8975 = RATIONAL(1.0,216.0); + t9774 = y*t9065; + t9510 = t9021*t9774; + t10199 = t8975*t9571+t9510; + t9046 = RATIONAL(-1.0,9.0); + t9681 = t9046*t9060; + t9016 = RATIONAL(-1.0,36.0); + t9616 = t9016*t9060; + t9064 = t9059*t9059; + t8809 = t9064*t9616; + t10198 = t9681+t8809; + t9598 = t9064*t9057; + t9062 = t9058*z; + t9372 = t9062*t9598; + t9733 = t9062*t9065; + t9251 = t9059*t9733; + t10197 = t9251+t9372; + t9649 = t9065*t9046; + t9037 = RATIONAL(1.0,36.0); + t10196 = t9037*t9733+z*t9649; + t9662 = t9021*t9063; + t9434 = y*t9662; + t9583 = t9061*t8975; + t10195 = t9434+t9063*t9583; + t8997 = RATIONAL(-1.0,288.0); + t9622 = t8997*t9058; + t8972 = RATIONAL(-5.0,1152.0); + t9569 = t9063*t8972; + t10194 = t9057*t9569+t9622; + t9719 = t9061*t8964; + t9764 = z*t8960; + t9449 = t9061*t9764; + t10193 = t9062*t9719+t9449; + t8995 = RATIONAL(1.0,288.0); + t9699 = t8995*t9058; + t9723 = t9063*t8997; + t10192 = t9699+t9723; + t9000 = RATIONAL(1.0,144.0); + t9639 = t9062*t9000; + t9005 = RATIONAL(1.0,576.0); + t9674 = t9065*t9005; + t9326 = t9062*t9674; + t10191 = t9326+t9639; + t9782 = z*t9065; + t9023 = RATIONAL(-2.0,27.0); + t9019 = RATIONAL(8.0,27.0); + t9769 = z*t9019; + t10190 = t9023*t9782+t9057*t9769; + t9742 = t9062*t9059; + t9457 = x*t9742; + t9675 = t9060*t9059; + t9554 = z*t9675; + t10189 = t9554+t9457; + t9600 = t9058*t9059; + t9508 = x*t9600; + t9690 = t9063*t9064; + t9549 = x*t9690; + t10188 = t9549+t9508; + t9673 = t9061*t9063; + t9589 = t9063*t9046; + t10187 = y*t9589+t9037*t9673; + t9702 = t9063*t9060; + t9788 = x*t9063; + t9011 = RATIONAL(1.0,54.0); + t10186 = t9023*t9788+t9011*t9702; + t9601 = t9065*t9016; + t9047 = RATIONAL(1.0,9.0); + t9652 = t9047*t9065; + t10185 = t9062*t9601+z*t9652; + t9461 = z*t9719; + t9724 = t9062*t8960; + t9289 = t9061*t9724; + t10184 = t9461+t9289; + t9608 = t9058*t9064; + t9440 = x*t9608; + t9380 = t9060*t9600; + t10183 = t9380+t9440; + t10182 = t9065*t9639+z*t9601; + t8963 = RATIONAL(-1.0,3456.0); + t9772 = y*t9058; + t9615 = t9063*t8963; + t9243 = t9061*t9615; + t10181 = t9243+t8963*t9772; + t9017 = RATIONAL(1.0,27.0); + t8983 = RATIONAL(-1.0,108.0); + t9590 = t9063*t9059; + t10180 = t8983*t9590+t9017*t9600; + t8962 = RATIONAL(1.0,3456.0); + t9297 = t8962*t9696; + t10179 = t9060*t9615+t9297; + t9003 = RATIONAL(5.0,576.0); + t9635 = t9003*t9058; + t9225 = t9061*t9635; + t9001 = RATIONAL(-1.0,144.0); + t9657 = t9061*t9001; + t10178 = t9657+t9225; + t9646 = t9062*t9064; + t9629 = t8962*t9059; + t9235 = t9062*t9629; + t10177 = t8963*t9646+t9235; + t9779 = z*t9059; + t9018 = RATIONAL(-1.0,27.0); + t9503 = t9018*t9779; + t9777 = z*t9064; + t8982 = RATIONAL(1.0,108.0); + t10176 = t9503+t8982*t9777; + t9008 = RATIONAL(-1.0,72.0); + t9015 = RATIONAL(-1.0,18.0); + t9645 = t9015*t9057; + t10175 = t9645+t9008*t9598; + t9052 = RATIONAL(-4.0,9.0); + t10174 = x*t9052+t9047*t9060; + t9738 = t9064*t9046; + t9685 = t9064*t9060; + t10173 = t9037*t9685+x*t9738; + t9698 = t8995*t9065; + t8634 = t9062*t9698; + t9042 = RATIONAL(1.0,72.0); + t9587 = t9042*t9062; + t10172 = t8634+t9587; + t8977 = RATIONAL(-1.0,432.0); + t10171 = t9064*t9563+t8977*t9600; + t9627 = t9015*t9059; + t8998 = RATIONAL(-5.0,288.0); + t10170 = t9627+t8998*t9608; + t9614 = t9061*t9008; + t8641 = t8997*t9571; + t10169 = t9614+t8641; + t9642 = t9042*t9065; + t8723 = y*t9642; + t9566 = t9008*t9065; + t8832 = t9061*t9566; + t10168 = t8723+t8832; + t9605 = t9061*t9057; + t10167 = t9657+t9003*t9605; + t10166 = t9019*t9772+t9011*t9673; + t9632 = t9011*t9064; + t9558 = t9062*t9023; + t10165 = t9059*t9558+t9062*t9632; + t9752 = t9065*t9037; + t10164 = t9016*t9057+t9752; + t9040 = RATIONAL(-5.0,36.0); + t9055 = RATIONAL(5.0,9.0); + t9786 = y*t9057; + t10163 = t9055*t9786+t9040*t9605; + t9594 = t9061*t9016; + t9732 = t9063*t9047; + t10162 = y*t9732+t9063*t9594; + t9004 = RATIONAL(-1.0,576.0); + t9597 = t9064*t9004; + t10161 = z*t9597+t9639; + t8968 = RATIONAL(-1.0,6912.0); + t9596 = t8968*t9058; + t10160 = t9064*t9596+t8968*t9590; + t9741 = t9065*t9059; + t9500 = z*t9741; + t9462 = z*t9598; + t10159 = t9462+t9500; + t9056 = RATIONAL(4.0,9.0); + t9634 = t9056*t9057; + t9640 = t9063*t9057; + t10158 = t9047*t9640+t9634; + t9705 = t9021*t9059; + t10157 = t9062*t9705+t9025*t9779; + t9041 = RATIONAL(-5.0,72.0); + t9577 = t9058*t9041; + t10156 = t9057*t9577+t9065*t9723; + t9570 = t9062*t9001; + t9002 = RATIONAL(-5.0,576.0); + t9581 = t9002*t9057; + t10155 = z*t9581+t9570; + t10154 = t8964*t9608+t8977*t9590; + t9526 = z*t9571; + t10153 = t9526+y*t9733; + t9751 = t9047*t9064; + t10152 = t9016*t9646+z*t9751; + t8970 = RATIONAL(5.0,1152.0); + t8973 = RATIONAL(1.0,1152.0); + t10151 = t8973*t9608+t8970*t9590; + t9661 = t9061*t9047; + t8815 = t9037*t9571; + t10150 = t9661+t8815; + t9726 = t9062*t9046; + t10149 = t9726+z*t9056; + t8981 = RATIONAL(5.0,288.0); + t9038 = RATIONAL(1.0,18.0); + t9636 = t9038*t9058; + t10148 = t8981*t9640+t9636; + t9531 = z*t9605; + t9745 = z*t9774; + t10147 = t9531+t9745; + t8716 = y*t9566; + t8713 = t9042*t9571; + t10146 = t8713+t8716; + t9682 = t9001*t9060; + t10145 = x*t9000+t9682; + t9770 = y*t8982; + t9760 = y*t9018; + t10144 = t9057*t9760+t9065*t9770; + t8958 = RATIONAL(-1.0,1152.0); + t10143 = t8958*t9590+t8972*t9608; + t10142 = t8963*t9786+t8962*t9774; + t8959 = RATIONAL(1.0,6912.0); + t9643 = t8959*t9065; + t9753 = t9059*t9057; + t10141 = t9064*t9643+t8959*t9753; + t9754 = t9064*t9065; + t10140 = t9059*t9643+t8968*t9754; + t9660 = t9016*t9059; + t10139 = t9064*t9037+t9660; + t9565 = t8958*t9064; + t10138 = t9059*t9569+t9622+t9058*t9565; + t9013 = RATIONAL(-8.0,27.0); + t9707 = t9061*t9058; + t9787 = y*t9063; + t10137 = t9013*t9772+(t9707+t9787)*t9025; + t10136 = t9590+t9741; + t9035 = RATIONAL(1.0,24.0); + t9027 = RATIONAL(-5.0,96.0); + t9585 = t9027*t9057; + t10135 = t9035+t9585; + t8976 = RATIONAL(1.0,432.0); + t9708 = t9061*t9060; + t9410 = t8976*t9708; + t9562 = z*t9760; + t10134 = x*t9562+t9062*t9410; + t9617 = t8981*t9058; + t9196 = t9061*t9617; + t10133 = t9196+t9614; + t9762 = y*t8975; + t9735 = z*t9762; + t9007 = RATIONAL(-1.0,864.0); + t9666 = t9007*t9060; + t9241 = t9061*t9666; + t10132 = t9062*t9241+x*t9735; + t9790 = x*z; + t9543 = t9017*t9779; + t9655 = t8982*t9059; + t9207 = t9060*t9655; + t9584 = t9064*t8983; + t9253 = t9060*t9646; + t10029 = t9062*t9207+x*t9543+t9584*t9790+t8977*t9253; + t9700 = t9062*t8983; + t9430 = x*t9700; + t9381 = t8976*t9646; + t7750 = x*t9381; + t10131 = t9059*t9430+t10029+t10176*t9060+t7750; + t8979 = RATIONAL(1.0,864.0); + t9775 = t9061*z; + t9504 = t8979*t9775; + t8986 = RATIONAL(-1.0,216.0); + t9619 = t8986*t9060; + t9489 = y*t9619; + t10130 = x*t9504+t9062*t9489; + t9781 = x*t8986; + t9547 = t9061*t9781; + t9778 = y*t9060; + t9497 = t8979*t9778; + t10129 = z*t9547+t9062*t9497; + t9766 = y*t9017; + t9572 = x*t9766; + t9582 = t9061*t8977; + t9310 = t9062*t9582; + t10128 = t9060*t9310+z*t9572; + t8829 = t9016*t9571; + t10127 = t8829+y*t9652; + t9722 = t8997*t9059; + t10126 = t8972*t9598+t9722; + t9039 = RATIONAL(5.0,24.0); + t9574 = t9039*t9059; + t9044 = RATIONAL(-1.0,6.0); + t10125 = t9044+t9574; + t9656 = t9064*t8977; + t9505 = x*t9656; + t7739 = t9062*t9505; + t9443 = x*t9655; + t9339 = t9060*t9584; + t9268 = t9062*t9675; + t10015 = t8976*t9253+t8983*t9268+t10176*x; + t9518 = t9017*t9759; + t10124 = t7739+z*t9339+t9062*t9443+t9059*t9518+t10015; + t9654 = t9058*t9065; + t10123 = t9608+t9654; + t9665 = t8997*t9057; + t10122 = t9057*t9565+t9665; + t9612 = t9058*t9037; + t10121 = t9612+t9063*t9016; + t9595 = t9063*t8973; + t10120 = t8970*t9654+t9057*t9595; + t9687 = t8995*t9057; + t10119 = t8997*t9065+t9687; + t9591 = t9062*t9007; + t9453 = x*t9591; + t10118 = t9061*t9453+t9060*t9735; + t9743 = x*t9775; + t9513 = t9060*t9770; + t10117 = t9062*t9513+t8983*t9743; + t9784 = x*t8982; + t9468 = t9062*t9784; + t9704 = t8983*t9060; + t9507 = y*t9704; + t10116 = z*t9507+t9061*t9468; + t10115 = t9636+t8981*t9590; + t9206 = t9061*t9700; + t10114 = x*t9206+z*t9513; + t9715 = t9063*t9037; + t9613 = t9058*t9016; + t10113 = t9613+t9715; + t9501 = t9061*x*t9062; + t10112 = t8979*t9501+z*t9489; + t9647 = t9061*t8982; + t9467 = z*t9647; + t9433 = y*t9700; + t10111 = x*t9467+t9060*t9433; + t9620 = t8976*t9058; + t9276 = t9060*t9620; + t9299 = t9061*t9563; + t9470 = x*t9707; + t10110 = y*t9276+x*t9299+t8960*t9470; + t9306 = t9061*t9620; + t10109 = x*t9306+t10201*y; + t9680 = t9062*t8986; + t9485 = x*t9680; + t9431 = z*t9583; + t9737 = t9062*t9060; + t9541 = y*t9737; + t10079 = x*t9431+t9007*t9541; + t10108 = z*t9497+t9061*t9485+t10079; + t9400 = t9063*t9598; + t9285 = t9065*t9600; + t10107 = t8962*t9400+t9007*t9285; + t9229 = t9064*t9615; + t9261 = t8979*t9600; + t10106 = t9057*t9261+t9065*t9229; + t9298 = t8979*t9640; + t10105 = t9064*t9298+t8963*t9285; + t9791 = y*z; + t9417 = t8979*t9708; + t10104 = t9062*t9417+t9781*t9791; + t9528 = t9062*t9762; + t10103 = z*t9241+x*t9528; + t9325 = t9065*t9590; + t9272 = t9007*t9598; + t10102 = t9058*t9272+t8962*t9325; + t8967 = RATIONAL(5.0,2304.0); + t9283 = t9058*t9598; + t8969 = RATIONAL(-1.0,2304.0); + t10101 = t8967*t9283+t8969*t9325; + t9221 = t8979*t9590; + t10100 = t9065*t9221+t8963*t9283; + t9329 = t9065*t9608; + t8980 = RATIONAL(-5.0,144.0); + t9248 = t8980*t9590; + t10099 = t9005*t9329+t9057*t9248; + t9219 = t9064*t9581; + t10098 = t9058*t9219+t9000*t9325; + t9267 = t8980*t9600; + t9367 = t9005*t9598; + t10097 = t9065*t9267+t9063*t9367; + t9376 = t9057*t9600; + t9313 = t9065*t9690; + t8974 = RATIONAL(1.0,2304.0); + t8971 = RATIONAL(-5.0,2304.0); + t10096 = t8971*t9376+t8974*t9313; + t9588 = t8986*t9059; + t9256 = t9063*t9588; + t9269 = t8975*t9608; + t10095 = t9057*t9269+t9065*t9256; + t10094 = t8969*t9400+t8967*t9285; + t9694 = t8979*t9065; + t9264 = t9063*t9694; + t9308 = t9057*t9705; + t10093 = t9064*t9264+t9058*t9308; + t10092 = t9005*t9325+t8980*t9283; + t9050 = RATIONAL(-5.0,9.0); + t9670 = t9050*t9057; + t9373 = t9058*t9670; + t10091 = t9000*t9313+t9059*t9373; + t9378 = t9000*t9690; + t10090 = t9057*t9378+t9002*t9285; + t8999 = RATIONAL(25.0,24.0); + t9028 = RATIONAL(-1.0,96.0); + t10089 = t8999*t9376+t9028*t9313; + t9033 = RATIONAL(5.0,36.0); + t9302 = t9033*t9640; + t10088 = t9059*t9302+t9016*t9329; + t10087 = t8986*t9400+t8975*t9285; + t9201 = t9063*t9581; + t10086 = t9059*t9201+t9000*t9329; + t10085 = RATIONAL(1.0,384.0)*t9313+RATIONAL(-25.0,384.0)*t9376; + t9604 = t9063*t9007; + t9362 = t9057*t9604; + t10084 = t9059*t9362+t8962*t9329; + t10083 = t9011*t9283+t9007*t9325; + t10082 = t9016*t9325+t9033*t9283; + t9424 = t9057*t9590; + t10081 = t8979*t9329+t8963*t9424; + t9281 = t8986*t9608; + t9575 = t8975*t9057; + t9414 = t9063*t9575; + t10080 = t9065*t9281+t9059*t9414; + t9303 = t9058*t9583; + t9343 = t9060*t9673; + t9631 = t8975*t9058; + t9312 = t9060*t9631; + t10078 = t8979*t9343+x*t9303+y*t9312; + t9198 = t8982*t9605; + t9483 = t9057*t9766; + t10077 = t9065*t9433+t9062*t9483+z*t9198; + t9757 = t9062*t9057; + t9498 = y*t9757; + t9209 = t8982*t9733; + t10076 = y*t9209+t8983*t9531+t9018*t9498; + t9346 = t9065*t9591; + t9559 = t8986*t9057; + t9200 = t9061*t9559; + t10075 = z*t9200+t8986*t9498+t9061*t9346; + t9678 = t9065*t8983; + t9442 = z*t9678; + t10074 = t9061*t9442+t9017*t9531+t8982*t9498; + t9347 = t9058*t9619; + t10073 = y*t9347+t8986*t9470+t9063*t9241; + t9481 = y*t9575; + t9290 = t9062*t9694; + t10072 = t9062*t9481+t9061*t9290+t9057*t9431; + t9428 = x*t9724; + t9556 = x*t9646; + t9713 = t8976*t9059; + t9493 = z*t9713; + t10071 = t9060*t9493+t9059*t9428+t8964*t9556; + t10070 = t8979*t9253+t10189*t8975; + t9542 = t9063*t9784; + t10069 = t9058*t9507+t9018*t9470+t9061*t9542; + t9333 = t9018*t9605; + t10068 = t9057*t9433+z*t9333+t9065*t9467; + t10067 = t9007*t9253+t10189*t8986; + t8990 = RATIONAL(5.0,144.0); + t9437 = t8990*t9779; + t9517 = z*t9754; + t9291 = t9057*t9742; + t9419 = t9062*t9597; + t10066 = t9002*t9291+t9057*t9437+t9065*t9419+t9000*t9517; + t9749 = t9063*t9065; + t9469 = y*t9749; + t9514 = t9021*t9786; + t10065 = t8986*t9469+t9058*t9514+t9061*t9264+t9057*t9303; + t9024 = RATIONAL(5.0,96.0); + t9049 = RATIONAL(-5.0,6.0); + t9034 = RATIONAL(-1.0,24.0); + t9036 = RATIONAL(-5.0,24.0); + t10064 = t9034*t9690+t9036*t9285+t9024*t9400+t9049*t9600; + t9464 = x*t9021*t9058; + t9651 = t8979*t9064; + t9353 = t9063*t9651; + t10063 = t8986*t9549+t9060*t9353+(t9312+t9464)*t9059; + t9650 = t8976*t9057; + t9368 = t8964*t9733; + t9720 = t9065*t8977; + t9478 = z*t9720; + t9288 = t9062*t9605; + t10062 = y*t9478+t8960*t9288+t9650*t9791+t9061*t9368; + t9511 = t8964*t9777; + t9521 = t8960*t9759; + t10061 = t8976*t9457+t7739+t9060*t9511+t9059*t9521; + t9369 = t9033*t9605; + t8608 = t9000*t9571; + t10060 = t9063*t8608+y*t9373+t9016*t9469+t9058*t9369; + t10059 = t10106+t10107; + t9477 = x*t9713; + t9475 = t8960*t9788; + t10058 = t9058*t9477+t9064*t9475+t10171*t9060; + t9389 = t9063*t9565; + t9279 = t8970*t9600; + t10057 = t9060*t9389+t8973*t9549+x*t9279+t8972*t9380; + t9195 = t9011*t9600; + t9271 = t9064*t9604; + t10056 = t9065*t9195+t9057*t9271+t10095; + t9697 = t9063*t8976; + t9340 = t9060*t9697; + t10055 = t9059*t9340+t9064*t9307+t10154*x; + t8834 = t9064*t9752; + t9548 = z*t9753; + t8629 = t9065*t9570; + t10054 = t9040*t9291+z*t8834+t9055*t9548+t9064*t8629; + t9216 = t9060*t9595; + t10053 = t9060*t9279+t9064*t9216+x*t9389+t8972*t9508; + t9592 = t9064*t8960; + t9361 = t9060*t9592; + t10052 = t9063*t9361+t9059*t9276+t10171*x; + t10051 = t10100+t10107; + t9533 = y*t9620; + t9427 = t8977*t9788; + t10050 = x*t9533+y*t9427+t10201*t9061; + t10049 = t10084+t10100; + t9456 = t8976*t9782; + t9618 = t8977*t9059; + t9226 = t9062*t9618; + t9287 = t8964*t9757; + t10048 = t9064*t9287+t8960*t9462+t9065*t9226+t9059*t9456; + t10047 = t10080+t10083; + t8994 = RATIONAL(-5.0,384.0); + t9026 = RATIONAL(1.0,96.0); + t9573 = t9026*t9065; + t9593 = t9024*t9058; + t8989 = RATIONAL(5.0,384.0); + t10046 = t8989*t9283+t9057*t9593+t9063*t9573+t8994*t9325; + t8748 = t9065*t9715; + t9676 = t9063*t9001; + t8616 = t9065*t9676; + t10045 = y*t8748+t9061*t8616+t10163*t9058; + t9667 = t9064*t9007; + t9332 = t9065*t9667; + t9716 = t8975*t9064; + t9413 = t9065*t9716; + t10044 = t9062*t9332+z*t9413+t9011*t9548+t8986*t9291; + t10043 = t9065*t9310+t9062*t9198+z*t9483+y*t9442; + t9448 = x*t9716; + t10042 = t9059*t9347+t9063*t9448+x*t9195+t9060*t9271; + t9022 = RATIONAL(5.0,72.0); + t9568 = t9022*t9057; + t9473 = y*t9568; + t10041 = t8995*t9469+t9058*t9473+t10156*t9061; + t10040 = t10103+t10104; + t9659 = t9003*t9059; + t9370 = t9060*t9659; + t9644 = t9064*t9005; + t9357 = t9060*t9644; + t8668 = t9064*t9676; + t10039 = t9058*t9370+t9063*t9357+(t9267+t8668)*x; + t9730 = t8977*t9057; + t9502 = z*t9730; + t9395 = t9062*t9592; + t9211 = t9062*t9650; + t10038 = (t9211+t9502)*t9059+(t9395+t9511)*t9065; + t9217 = t9058*t9582; + t10037 = t9065*t9299+t8960*t9469+(t9217+t9533)*t9057; + t9454 = z*t9670; + t9249 = t9033*t9742; + t10036 = t9059*t9454+t9057*t9249+t10182*t9064; + t10035 = y*t9485+z*t9417+t10132; + t9399 = t9062*t9571; + t10034 = t8976*t9399+t9057*t9206+t10144*z; + t9405 = t9063*t9685; + t9671 = t8997*t9064; + t8649 = x*t9671; + t9296 = t9022*t9675; + t10033 = t9063*t8649+t8995*t9405+t9041*t9508+t9058*t9296; + t10032 = t8964*t9462+t9059*t9478+t8960*t9372+t8976*t9251; + t9274 = t9065*t9671; + t9204 = t9059*t9568; + t8686 = z*t9698; + t10031 = t9064*t8686+t9041*t9291+z*t9204+t9062*t9274; + t8673 = t8995*t9571; + t9280 = t9061*t9568; + t10030 = t9063*t8673+t9058*t9280+t10156*y; + t10028 = t10104+t10118; + t10027 = t8960*t9517+t9064*t9368+(t9226+t9493)*t9057; + t9761 = x*t8979; + t9534 = t9062*t9761; + t9292 = t9061*t9619; + t10026 = y*t9534+z*t9292+t10079; + t9776 = y*t9011; + t9551 = t9057*t9776; + t9250 = t9061*t9604; + t10025 = t9065*t9250+t8975*t9469+(t9200+t9551)*t9058; + t10024 = t9060*t9467+y*t9430+t10128; + t10023 = t10080+t10093; + t9197 = t9063*t9597; + t9331 = t8990*t9600; + t10022 = t9060*t9197+t9002*t9380+(t9378+t9331)*x; + t9265 = t8960*t9673; + t9491 = t8977*t9772; + t10021 = t9065*t9265+t8964*t9469+(t9491+t9306)*t9057; + t9535 = t8983*t9787; + t9527 = t9058*t9766; + t9205 = t9058*t9647; + t9630 = t8977*t9060; + t9282 = t9063*t9630; + t10020 = t9060*t9205+t9061*t9282+(t9535+t9527)*x; + t9321 = t8986*t9754; + t10019 = t9064*t9290+t8975*t9291+(t9308+t9321)*z; + t10018 = t9061*t9287+t9065*t9289+(t9456+t9502)*y; + t9599 = t9058*t9002; + t9295 = t9061*t9599; + t9354 = t9063*t9571; + t9553 = t9057*t9772; + t10017 = t9004*t9354+t9000*t9469+t8990*t9553+t9057*t9295; + t9536 = x*t9590; + t9387 = t8977*t9608; + t9270 = t8976*t9608; + t9409 = t9060*t9590; + t10016 = t8960*t9409+t9060*t9270+t8964*t9536+x*t9387; + t9611 = t9026*t9064; + t10014 = t9063*t9611+t9059*t9593+t8989*t9285+t8994*t9400; + t9771 = z*t9041; + t9460 = t9059*t9771; + t10013 = t9064*t8634+t9057*t9460+t9062*t9204+z*t9274; + t10012 = t10103+t10130; + t9383 = t9058*t9605; + t9247 = t8958*t9749; + t10011 = t8970*t9553+t8972*t9383+t8973*t9469+t9061*t9247; + t10010 = t10087+t10093; + t10009 = t8960*t9268+t8964*t9253+(t9477+t9505)*z; + t9232 = t8970*t9605; + t10008 = t8973*t9354+t8972*t9553+t9058*t9232+y*t9247; + t9792 = y*x; + t9610 = t9058*t9018; + t9277 = t8976*t9673; + t9218 = t9061*t9704; + t10007 = t9610*t9792+y*t9542+t9058*t9218+t9060*t9277; + t9363 = t8964*t9696; + t9451 = x*t9697; + t10006 = x*t9491+t9060*t9265+t9061*t9363+y*t9451; + t9429 = x*t8976*t9064; + t10005 = t8964*t9268+z*t9429+t9618*t9790+t8960*t9253; + t9746 = t9034*t9065; + t9684 = t9049*t9057; + t10004 = t9063*t9746+t9058*t9684+t9024*t9325+t9036*t9283; + t9411 = t9011*t9640; + t10003 = t9059*t9411+t9007*t9329+t10095; + t10002 = z*t9218+y*t9468+t10134; + t9736 = t9065*t9001; + t8597 = t9064*t9736; + t10001 = t8980*t9548+t9064*t9326+t9003*t9291+z*t8597; + t8670 = t9063*t9674; + t9496 = t8980*t9786; + t10000 = t9057*t9225+y*t8616+t9058*t9496+t9061*t8670; + t9624 = t8995*t9064; + t8644 = x*t9624; + t9275 = t9060*t9577; + t9999 = t9022*t9508+t9063*t8644+t9059*t9275+t8997*t9405; + t9546 = y*t9666; + t9445 = t9063*t9761; + t9663 = x*t9772; + t9998 = t8986*t9663+t9063*t9546+y*t9445+x*t9250+t9058*t9292; + t9335 = t9064*t9666; + t9532 = z*t9651; + t9997 = t8986*t9268+t9588*t9790+x*t9532+z*t9335+t9064*t9453; + t9486 = z*t9705; + t9552 = z*t9685; + t9499 = x*t9632; + t9996 = z*t9499+x*t9486+t9007*t9268+t9064*t9485+t8986*t9552; + t9484 = t9065*t9762; + t9995 = t8979*t9288+t9062*t9484+(t9551+t10199)*z; + t9537 = y*t9559; + t9479 = t9007*t9775; + t9482 = y*t9694; + t9994 = t9065*t9479+t9062*t9200+y*t9346+(t9482+t9537)*z; + t9773 = x*t9059; + t9471 = t8975*t9773; + t9993 = t9064*t9534+t9060*t9532+t8975*t9268+z*t9471+t9667*t9790; + t9356 = t8975*t9702; + t9314 = t8979*t9707; + t9992 = t9060*t9314+t9011*t9663+y*t9356+t10195*x; + t9452 = t9007*t9774; + t9991 = t8975*t9288+y*t9290+t9065*t9504+(t9452+t9481)*z; + t9322 = t9065*t9680; + t9990 = t9007*t9288+y*t9322+t9011*t9745+z*t9514+t8986*t9526; + t9579 = x*t9787; + t9224 = t9060*t9583; + t9989 = t9007*t9579+t9631*t9792+t9058*t9224+t9061*t9445+t9063*t9497; + t9260 = t9063*t9619; + t9988 = t9011*t9579+t9063*t9547+t9058*t9241+(t9464+t9260)*y; + t9606 = t9021*t9064; + t9444 = z*t9716; + t9609 = t9011*t9059; + t9520 = x*t9609; + t9987 = t9062*t9448+t8979*t9268+t9606*t9790+z*t9520+t9060*t9444; + t9692 = t9042*t9064; + t8756 = z*t9692; + t9785 = z*t9038; + t9986 = t8998*t9268+t8995*t9253+t9060*t9587+(t8756+t9460+t9785)*x; + t9524 = t9057*t9771; + t9985 = t8998*t9288+z*t8723+(t9785+t9524)*y+t10172*t9061; + t9984 = t10027+t10084; + t9783 = x*t9015; + t9637 = t9008*t9060; + t9672 = t9008*t9064; + t8721 = x*t9672; + t9744 = z*t9773; + t9983 = t8981*t9268+t9062*t9637+t9022*t9744+t8997*t9253+(t8721+t9783)*z; + t9982 = t9015*t9791+t8981*t9288+t10169*t9062+(t8716+t9473)*z; + t8598 = t9000*t9741; + t9981 = t9037*t9598+t8598+t10090+t10092; + t9980 = t8977*t9462+t8964*t9500+t8960*t9251+t9064*t9211+t10105; + t9576 = t9037*t9059; + t8606 = t9000*t9598; + t9979 = t8606+t9065*t9576+t10097+t10098; + t9561 = t9062*t9018; + t9231 = t9059*t9561; + t9978 = t9064*t9468+x*t9231+t8983*t9554+t10029; + t8701 = t9000*t9640; + t9305 = t9003*t9590; + t9212 = t9001*t9598; + t9623 = t9057*t9331+t9065*t9197; + t9174 = t9057*t9613+t8616+t9058*t9212+t9065*t9305+t9623; + t9977 = t9065*t9612+t8701+t9174+t10086+t10097; + t9976 = t9057*t9449+t9065*t9461+y*t9211+t10018; + t9446 = y*t9630; + t9975 = t8964*t9470+x*t9265+t9058*t9446+t10050; + t9459 = y*t9724; + t9974 = t8976*t9531+y*t9368+t9057*t9459+t10018; + t9401 = t8983*t9673; + t9973 = t9017*t9470+t9058*t9513+x*t9401+t10007; + t9972 = t10034+t10077; + t8603 = t9000*t9590; + t9240 = t9003*t9598; + t9227 = t9059*t9736; + t9159 = t9058*t9227+t9063*t9240+t9016*t9600+t8668+t9623; + t8725 = t9037*t9608; + t9971 = t8603+t9159+t8725+t10086+t10092; + t9970 = t10006+t10110; + t9968 = t10034+t10074; + t9633 = t9037*t9057; + t9641 = t9058*t9000; + t8620 = t9065*t9641; + t9967 = t9063*t9633+t8620+t9174+t10090+t10099; + t9966 = t10020+t10069; + t9509 = z*t9630; + t9965 = t9059*t9509+t8964*t9457+x*t9395+t10009; + t9964 = t9064*t9430+t9017*t9457+z*t9207+t10015; + t8677 = t9000*t9608; + t9963 = t9159+t9063*t9576+t8677+t10098+t10099; + t9273 = t9062*t9730; + t9962 = t9065*t9449+t9057*t9461+y*t9273+t10062; + t9961 = t9061*t9502+y*t9287+t9065*t9459+t10062; + t9960 = t10043+t10076; + t9958 = t10043+t10068; + t7925 = t9064*t9509; + t9957 = t7925+t9964; + t9544 = y*t9640; + t9530 = y*t9654; + t9956 = t9065*t9217+t8976*t9530+t9057*t9299+t8960*t9544+t10021; + t9350 = t8986*t9654; + t9955 = t9057*t9250+y*t9414+t9061*t9350+t9011*t9530+t10065; + t9954 = t10055+t10058; + t9953 = x*t9310+y*t9518+t10002+t10111; + t9341 = t9060*t9610; + t9328 = t8982*t9608; + t9952 = t9060*t9328+t9064*t9282+t9059*t9341+t8983*t9440+(t9207+t9429)* +t9063+t10180*x; + t9348 = t8979*t9598; + t9951 = t9065*t9486+t8975*t9251+t9062*t9348+t8986*t9462+t10044; + t9950 = z*t9224+y*t9453+t10112+t10129+t10132; + t9949 = t9060*t9256+t9063*t9520+x*t9269+t9058*t9335+t10063; + t9948 = z*t9361+t8964*t9554+x*t9226+t7750+t10009; + t9242 = t9059*t9678; + t9379 = t9065*t9656; + t9947 = t9059*t9209+z*t9242+t9062*t9379+t8983*t9462+t9064*t9456+t8982* +t9372+(t9231+t9543)*t9057; + t9342 = t8963*t9707; + t9679 = t8962*t9063; + t9516 = x*t9679; + t9398 = t9060*t9679; + t9946 = y*t9398+t8963*t9579+t8962*t9663+x*t9342+t10181*t9060+(t9297+t9516 +)*t9061; + t9945 = t8959*t9462+t10141*t9062+t10140*z+(t9548+t10197)*t8968; + t9220 = t8959*t9685; + t9944 = t9063*t9220+t10160*t9060+t10188*t8968+(t9536+t10183)*t8959; + t9943 = (t9325+t9376+t9400+t9329)*RATIONAL(-1.0,13824.0)+(t9285+t9313+ +t9283+t9424)*RATIONAL(1.0,13824.0); + t9942 = t10038+t10048; + t9941 = x*t9270+t9060*t9387+t10052+(t9475+t9262)*t9059; + t9940 = t8975*t9500+t8986*t9372+t9011*t9462+t9007*t9251+t10019; + t9352 = t8983*t9707; + t9939 = t9017*t9383+t8977*t9469+t9057*t9401+t8982*t9544+(t9277+t9352)* +t9065+t10144*t9058; + t9344 = t8962*t9605; + t9364 = t8962*t9571; + t9938 = t9063*t9344+t9057*t9342+t8979*t9553+t9065*t9243+(t9364+t9452)* +t9058+(t9362+t9264)*y; + t9371 = t9058*t9571; + t9937 = t8977*t9544+t9057*t9277+t8964*t9530+t8960*t9371+t10037; + t9625 = t9005*t9057; + t9626 = t9063*t9004; + t9653 = t9065*t9004; + t8689 = t9058*t9653; + t9936 = t8971*t9325+t9057*t9626+t8670+t8974*t9283+t8689+t9058*t9625+ +t10094; + t9664 = t8962*t9064; + t9257 = t9060*t9664; + t9412 = t8979*t9608; + t9396 = t8963*t9685; + t9935 = t9063*t9257+t9007*t9508+t9058*t9396+t10179*t9059+(t9412+t9221+ +t9271)*x; + t7687 = t8976*t9552; + t9934 = t7687+t9978; + t9933 = y*t9350+t9065*t9314+t10025+t10195*t9057; + t9402 = t9011*t9708; + t9450 = t9062*t9776; + t9580 = x*t9769; + t9932 = t9060*t9450+t9062*t9292+z*t9402+t9558*t9792+t9011*t9501+t9023* +t9743+(t9580+t9023*t9759)*y; + t9931 = z*t9410+t9561*t9792+t10116+t10117+t10128; + t9930 = t9996+t10070; + t9390 = t9007*t9590; + t9929 = t8963*t9380+t9058*t9257+t9007*t9440+t9059*t9398+t9060*t9229+( +t9390+t9261+t9353)*x; + t9375 = t8968*t9640; + t9366 = t9061*t9596; + t9330 = t8959*t9605; + t9432 = t8959*t9787; + t9320 = t9058*t9643; + t9928 = t9057*t9432+t9058*t9330+t8959*t9354+y*t9320+t9061*t9375+t9065* +t9366+(t9469+t9553)*t8968; + t9927 = t9060*t9528+x*t9479+t10035+t10112; + t9259 = t9021*t9598; + t9926 = t8979*t9251+t8986*t9500+t8975*t9372+z*t9259+t10044; + t9925 = t9062*t9572+t9061*t9509+t10111+t10114+t10134; + t9924 = t9065*t9205+t8976*t9469+t9057*t9535+t8983*t9530+t8977*t9354+t9063 +*t9198+(t9483+t9333)*t9058; + t9683 = z*t9786; + t9923 = z*t9364+t10142*t9062+(t9288+t9683)*t8962+(t9399+t10147)*t8963; + t9922 = t9060*t9342+(t9343+t9470)*t8962+t10181*x+(t9516+t10179)*y; + t9921 = t9062*t9364+t8962*t9498+(t9288+t10153)*t8963+(t9344+t10142)*z; + t9920 = t8959*t9553+t9063*t9330+t9061*t9320+t9057*t9366+t9065*t9432+y* +t9375+(t9530+t9354)*t8968; + t9919 = t10006+t10040; + t9729 = t8964*t9792; + t9441 = t8964*t9778; + t9918 = t9062*t9441+z*t9729+t10184*t9060+(t9428+t9521)*y+t10193*x; + t9917 = t10063+t9063*t9471+t9011*t9440+(t9281+t9390)*t9060; + t8139 = x*t9277; + t9916 = t8139+x*t9217+t10050+(t8960*t9702+t9363)*y; + t9915 = t9997+t10070; + t9914 = t9992+t10073; + t8595 = t9058*t9597; + t9913 = t8974*t9285+t9005*t9600+t8595+t9063*t9644+t9004*t9590+t8971*t9400 ++t10101; + t9912 = t9058*t9220+(t9405+t9380)*t8968+t10160*x+(t9409+t10188)*t8959; + t9789 = y*t9062; + t9564 = t9061*t9021; + t9266 = t9062*t9564; + t9557 = t9025*t9060; + t9658 = t9013*t9790; + t9911 = t9062*t9224+x*t9266+t9557*t9791+y*t9658+t9021*t9541+t9767*t9789+ +t10200*t9061; + t9293 = t9021*t9590; + t9910 = t9060*t9412+t9059*t9356+t10042+(t9293+t9281)*x; + t9909 = t9060*t9562+t8976*t9501+t10024+t10117; + t9908 = t10052+t8960*t9440+t9059*t9451+t10154*t9060; + t9907 = t9063*t9507+t10007+t10023+t9060*t9527+x*t9205+t10056; + t9238 = t9065*t9609; + t9906 = t8986*t9251+t9062*t9272+z*t9238+t9057*t9444+t10019; + t9435 = t8976*t9789; + t8071 = t9065*t9435; + t9905 = t8071+t9962; + t9711 = x*t9777; + t9263 = t9060*t9632; + t9904 = t9011*t9268+t8986*t9253+t9059*t9580+z*t9263+(t9711+t9554)*t9023+ +t10165*x; + t9391 = t8962*t9646; + t9540 = z*t9629; + t9436 = t8963*t9779; + t9213 = t8962*t9737; + t9903 = z*t9257+t9059*t9213+t9060*t9436+(t9540+t9391)*x+(t9457+t9711+ +t9253)*t8963; + t9902 = t10027+t10032; + t9718 = t9058*t9023; + t9515 = y*t9718; + t9901 = t9058*t9402+t9061*t9260+t9023*t9470+t9060*t9515+t10186*y+t10166*x +; + t9900 = t9060*t9540+z*t9396+t8963*t9268+t9064*t9213+t9664*t9790+(t9436+ +t10177)*x; + t9899 = t8983*t9372+t9062*t9242+t9057*t9503+t9017*t9291+t9065*t9381+z* +t9379+t10159*t8982; + t9337 = t9058*t9557; + t9525 = x*t9662; + t9418 = t9061*t9696; + t9898 = y*t9337+t9021*t9418+t9060*t9434+t9063*t9224+t9061*t9525+t10137*x; + t9578 = t9046*t9059; + t8931 = t9065*t9578; + t9319 = t8980*t9654; + t8929 = t9046*t9598; + t9897 = t8931+t8834+t10082+t9064*t9319+t8929+t10158*t9059; + t9309 = t9058*t9606; + t9896 = t9013*t9508+t9059*t9337+(t9293+t9309)*t9060+(t9536+t9440)*t9025+( +t9356+t9525)*t9064; + t9480 = y*t9720; + t9895 = t9065*t9306+t9058*t9480+t8964*t9544+t9057*t9265+t10037; + t9317 = t9011*t9571; + t9894 = t9065*t9450+z*t9317+t9011*t9288+t9061*t9322+(t9498+t9531)*t9023+ +t10190*y; + t9358 = t9065*t9564; + t9893 = z*t9358+t9013*t9683+t9057*t9266+t10199*t9062+(t9498+t10147)*t9025 +; + t9892 = t10042+(t9221+t9269)*t9060+(t9309+t9256)*x; + t9891 = t10003+t10010; + t9890 = t8975*t9253+t9021*t9556+t9025*t9457+t9059*t9658+t10157*t9060+ +t10200*t9064; + t9286 = t9019*t9600; + t9889 = t9058*t9263+t9064*t9260+x*t9286+t9063*t9499+t10183*t9023+t10186* +t9059; + t9385 = t9023*t9640; + t9210 = t9057*t9718; + t9888 = t9058*t9317+y*t9385+t9061*t9210+t9065*t9515+t8986*t9354+t9011* +t9469+t10166*t9057; + t9887 = t9018*t9743+t9060*t9435+t10024+t10116; + t7990 = y*t9340; + t9886 = t7990+t9975; + t9885 = z*t9441+t9764*t9792+t9062*t9729+t10184*x+(t9459+t10193)*t9060; + t8148 = t9062*t9480; + t9884 = t8148+t9976; + t9883 = t8962*t9354+t9063*t9452+t9007*t9553+t9065*t9342+t9057*t9243+y* +t9298+(t9344+t9482)*t9058; + t9882 = t8959*t9372+t10140*t9062+t10141*z+(t9291+t10159)*t8968; + t8895 = t9057*t9589; + t8890 = t9058*t9649; + t9881 = t9065*t9248+t9058*t9634+t8748+t9047*t9283+t8895+t8890+t10088; + t9203 = t9065*t9632; + t9880 = t9023*t9462+z*t9203+t10165*t9057+t10190*t9059+(t9238+t9321)*t9062 +; + t9879 = t9018*t9508+t9058*t9339+t9063*t9443+x*t9328+t10180*t9060+(t9427+ +t9340)*t9064; + t9878 = t9063*t9200+y*t9411+t9007*t9371+t9058*t9484+t10065; + t9408 = t9063*t9605; + t9877 = t9058*t9358+t9025*t9530+t9021*t9408+t10195*t9065+t10137*t9057; + t9876 = z*t9546+t8975*t9501+t10035+t10129; + t9875 = t9065*t9303+t9058*t9510+t9063*t9537+t9061*t9298+t10025; + t9874 = t9013*t9548+t9021*t9517+t10157*t9065+(t9462+t9291)*t9025+(t9259+ +t9413)*t9062; + t9873 = t9017*t9743+t9062*t9446+t10002+t10114; + t9872 = t9063*t9238+t9064*t9210+t9057*t9286+t9058*t9203+t9023*t9285+t9011 +*t9400+t9059*t9385+t8986*t9313; + t9871 = t8960*t9530+t8976*t9544+t8977*t9408+t8964*t9371+t10021; + t8714 = t9037*t9690; + t8927 = t9046*t9608; + t9388 = t8980*t9598; + t8923 = t9063*t9578; + t9870 = t9056*t9600+t10088+t10091+t8714+t8927+t9047*t9285+t8923+t9063* +t9388+t10082; + t9143 = t10020+t10023; + t9869 = t8139+y*t9341+t9143+x*t9352+t9063*t9513+t10056; + t9868 = t10096+t10101+t9065*t9644+t9057*t9597+t10094+t8974*t9424+t8971* +t9329+(t9625+t9653)*t9059; + t9147 = t10038+t10084+t10106; + t9867 = t9064*t9273+t8976*t9462+t9147+t8960*t9500+t8964*t9251+t10102+ +t10105; + t9458 = t8979*t9779; + t9490 = t9007*t9779; + t9866 = z*t9272+t8979*t9517+t9057*t9458+t8962*t9372+t10081+t8963*t9291+( +t9490+t10177)*t9065; + t9439 = x*t9644; + t9865 = t9003*t9457+t9005*t9253+t10161*t9060+(t9744+t9268)*t9002+(t9419+ +t9570)*x+(t9370+t9439+t10145)*z; + t8684 = t8997*t9702; + t9712 = t9063*t8995; + t9864 = t8684+t8995*t9696+t10057+t10151*t9060+(t9712+t10138)*x; + t9316 = t9008*t9640; + t9404 = t9042*t9640; + t9863 = t8998*t9530+t9065*t9196+t9038*t9605+t9061*t9404+t10041+(t9645+ +t9316)*y+t10168; + t9862 = t10081+t10102+(t9490+t9235)*t9057+(t9391+t9458)*t9065+t10197* +t8963+(t9348+t9332)*z; + t9425 = t8970*t9608; + t8662 = t9060*t9624; + t9740 = t8995*t9059; + t9861 = t10053+t8997*t9675+t8649+t8662+t8973*t9536+t10143*t9060+(t9740+ +t9425)*x; + t9860 = t9057*t9639+t8980*t9500+t9062*t9367+t8629+t9003*t9251+t10066+( +t9212+t10164)*z; + t9426 = t9060*t9635; + t9355 = t9060*t9626; + t9545 = t9005*t9788; + t9529 = x*t9626; + t9859 = t9000*t9708+t9599*t9792+t9005*t9343+t9060*t9295+t9061*t9529+ +t10178*x+(t9355+t9426+t9545+t10145)*y; + t8738 = t9037*t9646; + t9202 = t8990*t9675; + t9734 = t9047*t9062; + t9858 = t9055*t9744+t9001*t9253+t10189*t9040+(t9202+t9616)*t9062+(t9734+ +t8738)*x+(t10173+t10174)*z; + t9351 = t9016*t9640; + t9602 = t9061*t9046; + t9857 = t8815+t9057*t9602+t9033*t9530+t10060+(t9351+t9319)*t9061+(t9649+ +t10158)*y; + t8754 = t9063*t9616; + t9686 = t9061*t9037; + t9555 = y*t9696; + t9415 = t8980*t9696; + t9856 = t9000*t9343+t9061*t9415+t9060*t9686+t9056*t9792+t9050*t9663+( +t9470+t9555)*t9033+(t8754+t9681)*y+(t9602+t10162)*x; + t9855 = t9004*t9372+t9065*t9437+t9002*t9251+t9057*t9570+t10001+(t9633+ +t8606)*z+t10182; + t9438 = t9040*t9786; + t9854 = t8990*t9288+t9061*t8629+t9052*t9791+(t9594+t9438)*t9062+(t9734+ +t10196)*y+(t10150+t10163)*z; + t9689 = t9015*t9062; + t8751 = t9008*t9646; + t8661 = t9060*t9671; + t9853 = t8981*t9554+t9022*t9457+t9986+(t9637+t8661)*z+(t9689+t8751)*x; + t9701 = t9038*t9060; + t9607 = t9042*t9060; + t8752 = t9064*t9607; + t8683 = t9062*t9624; + t9852 = t9060*t9460+t8998*t9457+t9983+(t8752+t9701)*z+(t9587+t8683)*x; + t9474 = t9033*t9779; + t9851 = t8980*t9268+t9037*t9737+t9000*t9253+t9050*t9744+t9060*t9474+ +t10198*z+(t9249+t10149+t10152)*x; + t9717 = t9015*t9060; + t9669 = t9008*t9062; + t8770 = t9064*t9637; + t8659 = t8997*t9646; + t9850 = t8981*t9457+t9986+(t8659+t9669)*x+(t9296+t9717+t8770)*z; + t9849 = t8980*t9251+t9065*t9474+t9047*t9462+t9016*t9372+t9057*t9726+z* +t9634+t10036+t10196; + t9728 = t9052*t9057; + t9848 = t9037*t9372+t9057*t9734+t9040*t9500+t8990*t9251+t10054+(t8929+ +t9728)*z+t10185; + t9847 = t8980*t9288+t9033*t9498+(t8608+t9686)*t9062+(t9369+t8829+t9602)*z ++(t9454+t10149+t10185)*y; + t9739 = t9038*t9057; + t9233 = t8998*t9707; + t9846 = t9015*t9605+t8981*t9530+t9061*t9316+t9065*t9233+t10030+(t9404+ +t9739)*y+t10146; + t9386 = t9060*t9599; + t9294 = t8990*t9608; + t9688 = t9064*t9016; + t8710 = x*t9688; + t9845 = t9000*t9685+t9001*t9675+t8710+t9059*t9355+t9064*t9386+t10039+( +t9576+t8603+t9294)*x; + t9710 = t9061*t9000; + t9709 = t9000*t9060; + t9394 = t9005*t9702; + t9844 = t9061*t9545+t9004*t9343+t10178*t9060+(t9001+t9635)*t9792+(t9710+ +t9295)*x+(t9386+t9529+t9709+t9394)*y; + t9843 = t9060*t9425+t8995*t9675+t8661+t10057+t9059*t9216+t8644+(t9722+ +t10143)*x; + t9721 = t9038*t9059; + t9311 = t9042*t9590; + t9842 = t9008*t9409+t8721+t8752+t8981*t9440+t10033+t10170*t9060+(t9311+ +t9721)*x; + t9841 = t10017+t9065*t9225+t9000*t9605+t9005*t9408+(t9544+t9571)*t9001+( +t9319+t10164)*y; + t9768 = z*t9001; + t9495 = t9003*t9786; + t9840 = t9004*t9399+t9653*t9791+t9005*t9526+t9002*t9498+t9003*t9288+( +t9710+t9495)*z+t10155*t9061+(t9768+t10191)*y; + t9714 = t9056*t9059; + t9839 = t9047*t9500+t8738+t9062*t9578+t8980*t9372+t9033*t9462+t9016*t9251 ++t10036+(t9738+t9714)*z; + t9382 = t8998*t9605; + t8744 = t9042*t9673; + t9731 = t9063*t9008; + t9838 = t8744+t9015*t9707+t9063*t9382+t10030+t10168*t9058+(t9731+t10148)* +y; + t9567 = t9047*t9059; + t9638 = t9052*t9059; + t9837 = t9040*t9462+t9062*t9567+t9037*t9251+t8990*t9372+t10054+(t8931+ +t9638)*z+t10152; + t8746 = t9037*t9702; + t9300 = t9040*t9696; + t9836 = t9001*t9343+t8990*t9418+t9060*t9594+t9040*t9470+t9055*t9663+( +t9661+t10187)*x+(t8746+t9300+t10174)*y; + t8839 = t9062*t9566; + t9835 = t9062*t9473+t9985+t8981*t9531+t10169*z+(t8839+t9689)*y; + t9834 = t9004*t9408+t8990*t9530+t9065*t9295+t9001*t9605+t8608+t10000+( +t8701+t9601+t9633)*y; + t9833 = t9037*t9408+t9047*t9605+t9040*t9530+t10127+t8990*t9371+t10045+( +t9728+t8895)*y; + t9392 = t9060*t9617; + t9832 = t9064*t9392+t9038*t9675+t9060*t9311+t9008*t9536+t8770+t9999+( +t9692+t10170)*x; + t9214 = t9001*t9590; + t9831 = t10022+t9059*t9394+t9000*t9675+t8980*t9440+(t9426+t9682)*t9064+( +t9214+t10139)*x; + t8794 = z*t9642; + t9830 = t8998*t9500+t8981*t9251+t8794+t8839+t9062*t9739+t9042*t9372+ +t10031+t10175*z; + t9756 = t9062*t9038; + t9403 = t8998*t9675; + t8827 = t9064*t9587; + t9829 = t9041*t9457+t9983+(t9756+t8827)*x+(t8662+t9403+t9607)*z; + t8625 = t8995*t9673; + t9828 = t8970*t9544+t8973*t9530+t8625+t8958*t9371+t10008+t10192*y+t10194* +t9061; + t8687 = t8995*t9702; + t9827 = t10053+t8687+t10138*t9060+(t10151+t10192)*x; + t8763 = t9065*t9587; + t8753 = z*t9566; + t9826 = t8998*t9251+t9042*t9462+t8763+t8753+z*t9739+t8981*t9500+t10013+ +t10175*t9062; + t9825 = t9002*t9288+t9062*t9495+t10153*t9004+t10167*z+t10155*y+(t9674+ +t9000)*t9791+t10191*t9061; + t9824 = t8998*t9372+t9059*t8794+t9062*t9627+t9008*t9251+t8981*t9462+t8827 ++t10013+(t9721+t9672)*z; + t9750 = t9061*t9042; + t9823 = t9041*t9498+t9982+(t9756+t8763)*y+(t8673+t9382+t9750)*z; + t9822 = t9062*t9439+t9003*t9268+t9659*t9790+t9004*t9253+t9060*t9570+ +t10189*t9002+(t9357+t9709)*z+(t9768+t10161)*x; + t9677 = t9061*t9038; + t9821 = t8998*t9498+t9061*t9524+t9982+(t9677+t8713)*z+t10172*y; + t8775 = t9063*t9614; + t9706 = t9042*t9063; + t8776 = y*t9706; + t9725 = t9015*t9058; + t9820 = t10041+t8776+y*t9725+t8775+t8998*t9544+t10146*t9058+t10148*t9061; + t9727 = t9061*t9015; + t8592 = t8997*t9733; + t9819 = t8981*t9498+t9985+(t8592+t9669)*y+(t9280+t8832+t9727)*z; + t8602 = t8997*t9673; + t9818 = t9061*t9699+t9063*t9232+t8958*t9530+t8602+t8973*t9371+t10011+( +t9712+t10194)*y; + t9817 = t8998*t9462+t9059*t8753+t8751+z*t9627+t8756+t9042*t9251+t9062* +t9721+t8981*t9372+t10031; + t9816 = t10072+t9990+t10131; + t9815 = t9950+t9989; + t9814 = t10075+t9995+t10124; + t9813 = t9937+t9991; + t9812 = t9998+t10026+t10028; + t9811 = t9871+t9994; + t9810 = t9956+t9961; + t9809 = t9919+t10108+t10109; + t9808 = t9895+t9974; + t9807 = t9941+t9965; + t9806 = t9895+t9961; + t9805 = t9956+t9974; + t9804 = t10005+t10016+t10058+t10071; + t7923 = t9061*t9427; + t9803 = t7923+t9876+t10006+t10109; + t9802 = t9875+t9952; + t9801 = t9909+t9951; + t9800 = t9916+t10040+t10108; + t9799 = t9906+t9909; + t9798 = t9879+t9955; + t9797 = t9876+t9916; + t9796 = t9906+t9953; + t9795 = t9929+t10005+t10061; + t9794 = t9951+t9953; + t9793 = t9935+t9948; + t8952 = t9044*t9064; + t9703 = t8071+t7990; + t8950 = t9044*t9065; + t9693 = t9024*t9059; + t7904 = t9061*t9456; + t9691 = t7925+t7904; + t9668 = t9056*t9058; + t8949 = t9035*t9064; + t9628 = t9058*t9052; + t7817 = t9061*t9478; + t9621 = t7817+t7687; + t8945 = t9035*t9065; + t9603 = t9027*t9059; + t7706 = y*t9282; + t9560 = t8148+t7706; + t8845 = x*t9731; + t9487 = t9022*t9772; + t8833 = t9063*t9607; + t8853 = t9063*t9637; + t9422 = t8973*t9754; + t9416 = t9065*t9565; + t9397 = t8990*t9640; + t9374 = t8958*t9640; + t9194 = t7706+t10067; + t9193 = t7904+t10078; + t9192 = t7923+t10075; + t9191 = t7817+t10078; + t9188 = t9064*t9351+t9033*t9285+t10091; + t9187 = t8969*t9329+t8967*t9424+t10096; + t9186 = t7923+t10072; + t9185 = t7706+t10070; + t9184 = t7817+t10073; + t9183 = t7990+t10067; + t9030 = RATIONAL(5.0,48.0); + t8966 = RATIONAL(-25.0,192.0); + t8987 = RATIONAL(5.0,192.0); + t9180 = t8966*t9057+t8987*t9065+t9030; + t9010 = RATIONAL(-5.0,16.0); + t9009 = RATIONAL(1.0,16.0); + t9048 = RATIONAL(1.0,4.0); + t9179 = t9048+t9010*t9057+t9009*t9065; + t9178 = t9573+t10135; + t9006 = RATIONAL(25.0,16.0); + t9043 = RATIONAL(-5.0,4.0); + t9177 = t9006*t9057+t9010*t9065+t9043; + t9029 = RATIONAL(1.0,48.0); + t8993 = RATIONAL(1.0,192.0); + t8991 = RATIONAL(-5.0,192.0); + t9176 = t9029+t8993*t9065+t8991*t9057; + t9045 = RATIONAL(1.0,6.0); + t9054 = RATIONAL(2.0,3.0); + t9175 = t9045*t9065+t9684+t9054; + t9014 = RATIONAL(1.0,12.0); + t9032 = RATIONAL(-5.0,48.0); + t9173 = t9032*t9057+t9029*t9065+t9014; + t8984 = RATIONAL(-25.0,96.0); + t9172 = t8984*t9057+t9039+t9024*t9065; + t9012 = RATIONAL(-5.0,64.0); + t8978 = RATIONAL(25.0,64.0); + t9171 = t9012*t9065+t8978*t9057+t9010; + t9170 = t9045+t9036*t9057+t8945; + t9169 = t9034*t9064+t10125; + t9051 = RATIONAL(5.0,6.0); + t8992 = RATIONAL(-25.0,24.0); + t9168 = t8992*t9057+t9051+t9039*t9065; + t8965 = RATIONAL(25.0,192.0); + t9167 = t8965*t9057+t9032+t8991*t9065; + t9166 = t8949+t9036*t9059+t9045; + t9165 = t9024*t9329+t9064*t9746+t9036*t9424+t9059*t9684+t10089; + t8996 = RATIONAL(25.0,96.0); + t9164 = t9027*t9065+t9036+t8996*t9057; + t9053 = RATIONAL(-2.0,3.0); + t9163 = t9053+t9051*t9057+t8950; + t9162 = t9044+t9746+t9039*t9057; + t9020 = RATIONAL(-1.0,12.0); + t9031 = RATIONAL(-1.0,48.0); + t9161 = t9020+t9031*t9065+t9030*t9057; + t9160 = t9064*t9573+t8989*t9424+t8994*t9329+t9057*t9693+t10085; + t9158 = t8597+t9003*t9329+t9623+(t9214+t9660)*t9057; + t8985 = RATIONAL(-1.0,192.0); + t9157 = t8987*t9057+t9031+t8985*t9065; + t9156 = t8999*t9057+t9049+t9036*t9065; + t9155 = t9028*t9065+t9034+t9024*t9057; + t9154 = t10058+t10059; + t9153 = t9984+t10106; + t9152 = t10005+t10102+t10106; + t9151 = t10010+t10034; + t9150 = t10028+t10059; + t9148 = t8972*t9291+t9062*t9416+t8970*t9548+z*t9422+t9187; + t9146 = t9001*t9405+x*t8714+t9059*t9300+t9055*t9508+t9188; + t9145 = t10010+t10043; + t9144 = t8972*t9548+t9062*t9422+t8970*t9291+z*t9416+t9187; + t9142 = t9063*t8710+t9033*t9380+t9060*t9378+t9050*t9508+t9188; + t9141 = t9158+t8997*t9343+x*t9487+t10133*t9060+(t9783+t8845)*y; + t9140 = t9060*t9233+t9061*t9607+t9158+x*t8776+t8995*t9343+(t9577+t9038)* +t9792; + t8988 = RATIONAL(-1.0,384.0); + t8961 = RATIONAL(25.0,384.0); + t9139 = t10014+t9027*t9590+t8988*t9329+t9034*t9058+t10085+t8961*t9424+ +t10046+t10123*t9028+t10135*t9063; + t9138 = t9034*t9059+t8949+t9064*t9585+t9027*t9608+t8961*t9283+t9160+t8988 +*t9325+t10014+t10136*t9028; + t9137 = t9065*t9574+t9165+t8984*t9285+t10004+t9035*t9400+t8950+t9039* +t9654+(t9054+(t9064+t9063)*t9045)*t9057; + t9136 = t9034*t9057+t9065*t9603+t8945+t8961*t9285+t8988*t9400+t9160+t9027 +*t9654+t10046+(t9640+t9598)*t9028; + t9135 = t8984*t9283+t10064+t9054*t9059+t8952+t9165+t9035*t9325+(t9608+ +t9598)*t9039+t10136*t9045; + t9134 = t9035*t9329+t10064+t9054*t9058+t9039*t9640+t10089+t8984*t9424+ +t10004+t10123*t9045+t10125*t9063; + t9133 = t9180*t9058+t9157*t9063+t9161; + t9132 = t9167*t9059+t9176*t9064+t9173; + t9131 = t9020+t9031*t9064+t9030*t9059+(t8987*t9064+t9030+t8966*t9059)* +t9058+(t9031+t8985*t9064+t8987*t9059)*t9063; + t9130 = t9167*t9058+t9176*t9063+t9173; + t9129 = t9180*t9059+t9157*t9064+t9161; + t9128 = t9029*t9064+t9014+t9032*t9059+(t8991*t9064+t9032+t8965*t9059)* +t9058+(t8991*t9059+t9029+t8993*t9064)*t9063; + t9127 = t9060*t9578+t9064*t9415+t9142+t9047*t9536+t9033*t9440+x*t9714+ +t9016*t9409+t9897+t10173; + t9126 = t8998*t9555+t9141+t9041*t9470+t9981+(t9607+t8687)*y+(t8744+t9677) +*x; + t9125 = t8973*t9251+t9148+t9913+t8958*t9500+t9062*t9740+t8659+t8970*t9372 ++(t9624+t10126)*z; + t9124 = t9141+t9979+(t8833+t9275+t9701)*y+(t9233+t8625+t9750)*x; + t9123 = t9870+t8980*t9408+t10060+(t9302+t9668)*y+(t9602+t10127)*t9058+ +t10187; + t9122 = t9059*t9570+t9971+t9062*t9219+t8990*t9462+t9064*t9639+t10001+ +t9004*t9251+(t9688+t9576+t8598)*z; + t9121 = t9061*t9641+t10017+t9005*t9371+t9001*t9530+t9963+t10113*y+(t9496+ +t10167)*t9063; + t9120 = t8972*t9530+t9868+t8995*t9605+t8641+t10011+t10120*t9061+(t9665+ +t9698+t9374)*y; + t9119 = t9000*t9702+t9967+t9060*t8595+t9058*t9682+t8990*t9536+t9002*t9409 ++t10039+(t8677+t10121)*x; + t9118 = t9058*t8770+t9042*t9440+t9015*t9696+t9063*t9403+t8833+t8845+t9977 ++t10033+t10115*x; + t9117 = t9063*t9202+t8754+t9881+t9040*t9536+t9060*t8725+t9146+t9047*t9696 ++(t9732+t9628+t8927)*x; + t9116 = t9060*t9248+t9881+t9047*t9440+t9142+t8746+t9033*t9536+t10198* +t9058+(t9589+t9668)*x; + t9115 = t9060*t9487+t9140+t9979+(t9717+t8853)*y+(t8602+t10133)*x; + t9114 = t8970*t9462+t8683+t8958*t9251+t9144+t9913+t8973*t9500+t10126* +t9062+(t9671+t9740)*z; + t9113 = t8972*t9371+t8673+t9868+t8997*t9605+t9061*t9374+t10008+(t10119+ +t10120)*y; + t9112 = t9005*t9251+t9062*t9240+t9971+t9059*t9639+t10066+t9064*t9570+( +t9388+t9227+t10139)*z; + t9111 = t8973*t9372+t8970*t9251+t9062*t9687+t8592+t9148+t8686+t8972*t9500 ++t9936+t10122*z; + t9110 = t8998*t9536+t9977+t8853+t9058*t8752+t9999+t9008*t9440+t10115* +t9060+(t9725+t9706)*x; + t9109 = t9963+t9058*t9657+t9000*t9673+t10000+(t9201+t8689)*t9061+(t9397+ +t8620+t10121)*y; + t9108 = t9140+t9022*t9470+t9981+(t8775+t9727)*x+(t9392+t9637+t8684)*y; + t9107 = t8634+t9144+t8970*t9500+t8973*t9462+t8972*t9251+t9936+t10122* +t9062+t10119*z; + t9106 = t9061*t9397+t9870+t10045+t9063*t9438+t10150*t9058+(t8890+t9628)*y ++t10162; + t9105 = t9967+t10022+t9058*t9357+t9001*t9440+(t9676+t9305+t9641)*t9060+( +t9248+t10113)*x; + t9104 = t9040*t9440+t9897+t9146+t8809+t9037*t9409+(t9294+t9567)*t9060+( +t9751+t8923+t9638)*x; + t9103 = t9957+t9191+t9151+t9988+t10003+t10077; + t9102 = t9877+t9874+t9872+t9894; + t9101 = t9150+t9883+t9993+t10012+t10049+t10067; + t9100 = t8071+t9194+t9973+t9145+t9987+t10047+t10068; + t9099 = t9900+t9920+t9885+t9943; + t9098 = t9950+t9862+t9998+t10059+t10078; + t9097 = t9150+t9862+t9989+t10026+t10073; + t9096 = t9869+t9952+t9955; + t9095 = t9151+t9940+t9939+t8148+t10047+t10074; + t9094 = t9893+t9889+t9872+t9911; + t9093 = t9905+t9927+t9154+t10049+t10055; + t9092 = t9878+t9145+t9947+t7904+t10003+t10076; + t9091 = t9186+t9907+t9990+t10124; + t9090 = t9867+t9937+t9994+t10072; + t9089 = t9928+t9882+t9923+t9943; + t9088 = t7687+t9154+t9866+t9965+t10016+t10102; + t9087 = t9143+t9917+t9924+t7990+t10069+t10083+t10087; + t9086 = t9192+t9907+t9995+t10131; + t9085 = t9884+t9147+t9938+t10048+t10051; + t9084 = t9929+t9153+t9948+t9980+t10102; + t9083 = t9880+t9890+t9872+t9896; + t9082 = t9918+t9943+t9921+t9944; + t9081 = t9926+t9930+t9892+t10010+t10047; + t9080 = t9152+t9935+t9980+t9984+t10061; + t9079 = t9914+t9891+t9899+t9931; + t9078 = t9912+t9903+t9943+t9945; + t9077 = t9891+t9925+t9933+t9934; + t9076 = t9888+t9904+t9872+t9932; + t9075 = t9908+t9153+t9915+t10032+t10051; + t9074 = t9871+t9867+t9991+t10075; + t9073 = t9869+t9875+t9879; + t9072 = t9152+t7925+t9941+t9866+t10071+t10107; + coeffs_I->coeff_m2_m2_m2 = t9912+t9882+t9099+t9921+t9922; + coeffs_I->coeff_m1_m2_m2 = t9800+t9074+t9793; + coeffs_I->coeff_0_m2_m2 = t9125+t9818+t9825; + coeffs_I->coeff_p1_m2_m2 = t9795+t9074+t9803; + coeffs_I->coeff_p2_m2_m2 = t9082+t9903+t9882+t9920+t9946; + coeffs_I->coeff_m2_m1_m2 = t9942+t9908+t9962+t9101+t9703+t9975; + coeffs_I->coeff_m1_m1_m2 = t9931+t9103+t9910+t9933+t9947; + coeffs_I->coeff_0_m1_m2 = t9109+t9823+t9824; + coeffs_I->coeff_p1_m1_m2 = t9077+t9949+t9947+t9184+t9972+t9992; + coeffs_I->coeff_p2_m1_m2 = t9942+t9185+t9883+t9093+t9970+t9997; + coeffs_I->coeff_m2_0_m2 = t9865+t9111+t9864; + coeffs_I->coeff_m1_0_m2 = t9826+t9119+t9829; + coeffs_I->coeff_0_0_m2 = t9129*t9062+t9139+t9132*z; + coeffs_I->coeff_p1_0_m2 = t9826+t9853+t9105; + coeffs_I->coeff_p2_0_m2 = t9822+t9827+t9111; + coeffs_I->coeff_m2_p1_m2 = t9194+t9085+t9908+t9927+t9970+t9993; + coeffs_I->coeff_m1_p1_m2 = t9092+t9914+t9910+t9925+t9957; + coeffs_I->coeff_0_p1_m2 = t9835+t9121+t9824; + coeffs_I->coeff_p1_p1_m2 = t9949+t9931+t9092+t9934+t9988+t10078; + coeffs_I->coeff_p2_p1_m2 = t9085+t9954+t9915+t9886+t10012+t10028; + coeffs_I->coeff_m2_p2_m2 = t9900+t9089+t9918+t9912+t9946; + coeffs_I->coeff_m1_p2_m2 = t9803+t9090+t9793; + coeffs_I->coeff_0_p2_m2 = t9828+t9840+t9125; + coeffs_I->coeff_p1_p2_m2 = t9795+t9800+t9090; + coeffs_I->coeff_p2_p2_m2 = t9089+t9903+t9922+t9885+t9944; + coeffs_I->coeff_m2_m2_m1 = t7687+t9097+t9810+t9807+t7904; + coeffs_I->coeff_m1_m2_m1 = t9887+t9924+t9560+t9081+t9968+t9973; + coeffs_I->coeff_0_m2_m1 = t9821+t9122+t9838; + coeffs_I->coeff_p1_m2_m1 = t9926+t9087+t9873+t8148+t9968+t9987+t10067; + coeffs_I->coeff_p2_m2_m1 = t9098+t9810+t9804+t9691; + coeffs_I->coeff_m2_m1_m1 = t9802+t9091+t9801; + coeffs_I->coeff_m1_m1_m1 = t9102+t9901+t9896+t9904+t9911; + coeffs_I->coeff_0_m1_m1 = t9106+t9847+t9837; + coeffs_I->coeff_p1_m1_m1 = t9890+t9898+t9102+t9889+t9932; + coeffs_I->coeff_p2_m1_m1 = t9073+t9816+t9794; + coeffs_I->coeff_m2_0_m1 = t9118+t9855+t9852; + coeffs_I->coeff_m1_0_m1 = t9851+t9848+t9117; + coeffs_I->coeff_0_0_m1 = (t9168*t9059+t9162*t9064+t9163)*z+(t9164*t9059+ +t9178*t9064+t9170)*t9062+t9134; + coeffs_I->coeff_p1_0_m1 = t9858+t9116+t9848; + coeffs_I->coeff_p2_0_m1 = t9110+t9850+t9855; + coeffs_I->coeff_m2_p1_m1 = t9814+t9794+t9096; + coeffs_I->coeff_m1_p1_m1 = t9076+t9893+t9896+t9874+t9898; + coeffs_I->coeff_0_p1_m1 = t9854+t9837+t9123; + coeffs_I->coeff_p1_p1_m1 = t9890+t9094+t9888+t9874+t9901; + coeffs_I->coeff_p2_p1_m1 = t9086+t9801+t9798; + coeffs_I->coeff_m2_p2_m1 = t9808+t9098+t9807+t9621; + coeffs_I->coeff_m1_p2_m1 = t9958+t9939+t9081+t9873+t9703+t9966; + coeffs_I->coeff_0_p2_m1 = t9122+t9819+t9820; + coeffs_I->coeff_p1_p2_m1 = t9100+t9887+t9917+t9926+t9939; + coeffs_I->coeff_p2_p2_m1 = t7817+t9808+t9097+t7925+t9804; + coeffs_I->coeff_m2_m2_0 = t9843+t9120+t9859; + coeffs_I->coeff_m1_m2_0 = t9846+t9126+t9845; + coeffs_I->coeff_0_m2_0 = t9138+t9130*y+t9133*t9061; + coeffs_I->coeff_p1_m2_0 = t9846+t9108+t9831; + coeffs_I->coeff_p2_m2_0 = t9861+t9844+t9120; + coeffs_I->coeff_m2_m1_0 = t9842+t9124+t9834; + coeffs_I->coeff_m1_m1_0 = t9856+t9104+t9833; + coeffs_I->coeff_0_m1_0 = t9135+(t9164*t9058+t9178*t9063+t9170)*t9061+( +t9168*t9058+t9162*t9063+t9163)*y; + coeffs_I->coeff_p1_m1_0 = t9127+t9836+t9833; + coeffs_I->coeff_p2_m1_0 = t9115+t9834+t9832; + coeffs_I->coeff_m2_0_0 = t9131*t9060+t9136+t9128*x; + coeffs_I->coeff_m1_0_0 = (t9051*t9059+t8952+t9053+(t8992*t9059+t9039* +t9064+t9051)*t9058+t9169*t9063)*x+((t8996*t9059+t9027*t9064+t9036)*t9058+(t9611 ++t9035+t9603)*t9063+t9166)*t9060+t9137; + coeffs_I->coeff_0_0_0 = t9043*t9057+RATIONAL(1.0,1.0)+t9048*t9065+t9177* +t9059+t9179*t9064+((RATIONAL(-125.0,64.0)*t9057+t9006+t8978*t9065)*t9059+t9171* +t9064+t9177)*t9058+(t9171*t9059+(RATIONAL(1.0,64.0)*t9065+t9009+t9012*t9057)* +t9064+t9179)*t9063; + coeffs_I->coeff_p1_0_0 = ((t9024*t9064+t9039+t8984*t9059)*t9058+(t9693+ +t9028*t9064+t9034)*t9063+t9169)*t9060+t9137+(t9054+t9049*t9059+t9045*t9064+( +t8999*t9059+t9049+t9036*t9064)*t9058+t9166*t9063)*x; + coeffs_I->coeff_p2_0_0 = t9136+t9131*x+t9128*t9060; + coeffs_I->coeff_m2_p1_0 = t9842+t9115+t9841; + coeffs_I->coeff_m1_p1_0 = t9104+t9836+t9857; + coeffs_I->coeff_0_p1_0 = t9135+(t9156*t9058+t9170*t9063+t9175)*y+(t9172* +t9058+t9155*t9063+t9162)*t9061; + coeffs_I->coeff_p1_p1_0 = t9856+t9127+t9857; + coeffs_I->coeff_p2_p1_0 = t9124+t9841+t9832; + coeffs_I->coeff_m2_p2_0 = t9113+t9844+t9843; + coeffs_I->coeff_m1_p2_0 = t9863+t9108+t9845; + coeffs_I->coeff_0_p2_0 = t9138+t9130*t9061+t9133*y; + coeffs_I->coeff_p1_p2_0 = t9863+t9126+t9831; + coeffs_I->coeff_p2_p2_0 = t9113+t9861+t9859; + coeffs_I->coeff_m2_m2_p1 = t9815+t9072+t9805+t9184; + coeffs_I->coeff_m1_m2_p1 = t9100+t9924+t9873+t9892+t9940; + coeffs_I->coeff_0_m2_p1 = t9819+t9112+t9838; + coeffs_I->coeff_p1_m2_p1 = t8071+t9887+t9940+t9087+t9930+t9958; + coeffs_I->coeff_p2_m2_p1 = t9088+t9191+t9805+t9812; + coeffs_I->coeff_m2_m1_p1 = t9802+t9086+t9796; + coeffs_I->coeff_m1_m1_p1 = t9893+t9901+t9083+t9877+t9932; + coeffs_I->coeff_0_m1_p1 = t9106+t9854+t9839; + coeffs_I->coeff_p1_m1_p1 = t9880+t9898+t9094+t9877+t9904; + coeffs_I->coeff_p2_m1_p1 = t9814+t9073+t9799; + coeffs_I->coeff_m2_0_p1 = t9118+t9850+t9860; + coeffs_I->coeff_m1_0_p1 = t9849+t9858+t9117; + coeffs_I->coeff_0_0_p1 = (t9156*t9059+t9170*t9064+t9175)*z+t9134+(t9172* +t9059+t9155*t9064+t9162)*t9062; + coeffs_I->coeff_p1_0_p1 = t9849+t9851+t9116; + coeffs_I->coeff_p2_0_p1 = t9110+t9860+t9852; + coeffs_I->coeff_m2_p1_p1 = t9816+t9799+t9096; + coeffs_I->coeff_m1_p1_p1 = t9898+t9083+t9888+t9894+t9911; + coeffs_I->coeff_0_p1_p1 = t9847+t9839+t9123; + coeffs_I->coeff_p1_p1_p1 = t9880+t9076+t9889+t9894+t9901; + coeffs_I->coeff_p2_p1_p1 = t9091+t9796+t9798; + coeffs_I->coeff_m2_p2_p1 = t9806+t9193+t9072+t9812; + coeffs_I->coeff_m1_p2_p1 = t9095+t9887+t9183+t9892+t9966+t9987; + coeffs_I->coeff_0_p2_p1 = t9821+t9112+t9820; + coeffs_I->coeff_p1_p2_p1 = t9095+t9185+t9917+t9873+t9973+t9996; + coeffs_I->coeff_p2_p2_p1 = t9806+t9088+t9815+t7904+t10073; + coeffs_I->coeff_m2_m2_p2 = t9078+t9918+t9922+t9920+t9923; + coeffs_I->coeff_m1_m2_p2 = t9080+t9811+t9797+t10072; + coeffs_I->coeff_0_m2_p2 = t9840+t9818+t9114; + coeffs_I->coeff_p1_m2_p2 = t9811+t9809+t9084+t9186; + coeffs_I->coeff_p2_m2_p2 = t9945+t9099+t9923+t9944+t9946; + coeffs_I->coeff_m2_m1_p2 = t9884+t9886+t9883+t9075+t9927; + coeffs_I->coeff_m1_m1_p2 = t9077+t9193+t9899+t9910+t9960+t9988; + coeffs_I->coeff_0_m1_p2 = t9835+t9109+t9817; + coeffs_I->coeff_p1_m1_p2 = t9079+t9949+t9691+t9960+t9933+t9964; + coeffs_I->coeff_p2_m1_p2 = t9902+t9970+t9101+t9954+t9560+t9976; + coeffs_I->coeff_m2_0_p2 = t9107+t9822+t9864; + coeffs_I->coeff_m1_0_p2 = t9119+t9853+t9830; + coeffs_I->coeff_0_0_p2 = t9129*z+t9139+t9132*t9062; + coeffs_I->coeff_p1_0_p2 = t9830+t9829+t9105; + coeffs_I->coeff_p2_0_p2 = t9107+t9865+t9827; + coeffs_I->coeff_m2_p1_p2 = t9905+t9919+t7706+t9075+t9938+t10110+t10118+ +t10130; + coeffs_I->coeff_m1_p1_p2 = t9079+t9878+t9910+t9972+t9621+t9978; + coeffs_I->coeff_0_p1_p2 = t9121+t9817+t9823; + coeffs_I->coeff_p1_p1_p2 = t9103+t9878+t9899+t9925+t9949; + coeffs_I->coeff_p2_p1_p2 = t9902+t9183+t9093+t9938+t9975+t9993; + coeffs_I->coeff_m2_p2_p2 = t9928+t9078+t9885+t9921+t9946; + coeffs_I->coeff_m1_p2_p2 = t9080+t9192+t9809+t9813; + coeffs_I->coeff_0_p2_p2 = t9828+t9825+t9114; + coeffs_I->coeff_p1_p2_p2 = t9813+t9084+t9797+t10075; + coeffs_I->coeff_p2_p2_p2 = t9900+t9928+t9082+t9922+t9945; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dx.compute.c new file mode 100644 index 0000000..4044656 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dx.compute.c @@ -0,0 +1,2720 @@ +fp t11752; +fp t11751; +fp t11876; +fp t11880; +fp t12847; +fp t11877; +fp t11882; +fp t11756; +fp t11749; +fp t12846; +fp t11816; +fp t11875; +fp t11878; +fp t12197; +fp t12367; +fp t11823; +fp t12124; +fp t12845; +fp t11799; +fp t11766; +fp t12231; +fp t12199; +fp t12844; +fp t11839; +fp t11854; +fp t12843; +fp t11840; +fp t12378; +fp t11853; +fp t12842; +fp t11753; +fp t11879; +fp t11881; +fp t12210; +fp t11750; +fp t12285; +fp t12841; +fp t11796; +fp t11795; +fp t12325; +fp t12400; +fp t12840; +fp t11806; +fp t11873; +fp t12392; +fp t12839; +fp t11748; +fp t12206; +fp t12092; +fp t11760; +fp t12280; +fp t12040; +fp t12838; +fp t11808; +fp t12384; +fp t12318; +fp t12837; +fp t11847; +fp t12255; +fp t11794; +fp t12836; +fp t12256; +fp t12032; +fp t11821; +fp t12382; +fp t12835; +fp t11763; +fp t12221; +fp t11791; +fp t12281; +fp t12057; +fp t12834; +fp t12322; +fp t11664; +fp t11874; +fp t12302; +fp t12833; +fp t12207; +fp t12061; +fp t12270; +fp t12832; +fp t11820; +fp t12211; +fp t11803; +fp t12831; +fp t11846; +fp t12234; +fp t12830; +fp t12238; +fp t12829; +fp t11213; +fp t12250; +fp t12828; +fp t12375; +fp t12827; +fp t11809; +fp t12826; +fp t11513; +fp t12825; +fp t11462; +fp t12212; +fp t12824; +fp t11736; +fp t12823; +fp t12822; +fp t11764; +fp t12398; +fp t11765; +fp t12399; +fp t12821; +fp t11861; +fp t11869; +fp t12820; +fp t11811; +fp t12333; +fp t12819; +fp t12818; +fp t12317; +fp t12817; +fp t12816; +fp t12815; +fp t12814; +fp t11835; +fp t12330; +fp t11822; +fp t12304; +fp t12014; +fp t12813; +fp t12812; +fp t11828; +fp t12346; +fp t12811; +fp t12328; +fp t11814; +fp t12810; +fp t12289; +fp t11439; +fp t12809; +fp t12808; +fp t11837; +fp t12348; +fp t11825; +fp t12058; +fp t12807; +fp t12390; +fp t12376; +fp t12806; +fp t12239; +fp t12237; +fp t12805; +fp t11844; +fp t11440; +fp t11872; +fp t12300; +fp t12804; +fp t12279; +fp t11588; +fp t11779; +fp t11391; +fp t12803; +fp t12205; +fp t11331; +fp t12802; +fp t12241; +fp t12225; +fp t12801; +fp t12307; +fp t11815; +fp t12800; +fp t12193; +fp t12799; +fp t11834; +fp t11414; +fp t11866; +fp t12798; +fp t11831; +fp t12262; +fp t11780; +fp t12016; +fp t12797; +fp t11812; +fp t12374; +fp t12796; +fp t12795; +fp t11762; +fp t12405; +fp t12794; +fp t11789; +fp t11354; +fp t12793; +fp t12792; +fp t12753; +fp t11807; +fp t12272; +fp t12791; +fp t12790; +fp t11295; +fp t11800; +fp t12789; +fp t11200; +fp t12788; +fp t11785; +fp t11787; +fp t12005; +fp t12787; +fp t12397; +fp t12786; +fp t11827; +fp t11473; +fp t12785; +fp t11863; +fp t12784; +fp t11841; +fp t11848; +fp t12385; +fp t12783; +fp t11792; +fp t12162; +fp t11768; +fp t12267; +fp t12782; +fp t12200; +fp t11688; +fp t12781; +fp t11797; +fp t12273; +fp t11798; +fp t11793; +fp t11685; +fp t12780; +fp t11684; +fp t12320; +fp t12779; +fp t12309; +fp t12778; +fp t12380; +fp t12777; +fp t12776; +fp t12371; +fp t12287; +fp t12404; +fp t12775; +fp t12344; +fp t12209; +fp t12774; +fp t12773; +fp t12394; +fp t12772; +fp t12771; +fp t11767; +fp t12220; +fp t11725; +fp t12770; +fp t11330; +fp t12769; +fp t11774; +fp t12338; +fp t11387; +fp t12265; +fp t12156; +fp t12768; +fp t12298; +fp t11285; +fp t12090; +fp t12767; +fp t12766; +fp t11852; +fp t11838; +fp t12765; +fp t12349; +fp t12172; +fp t11775; +fp t12201; +fp t11336; +fp t12764; +fp t12204; +fp t11712; +fp t11497; +fp t12763; +fp t12387; +fp t11260; +fp t12245; +fp t12145; +fp t12762; +fp t12236; +fp t12761; +fp t12760; +fp t11744; +fp t12242; +fp t12759; +fp t11705; +fp t12758; +fp t12342; +fp t11416; +fp t11505; +fp t12757; +fp t11813; +fp t12321; +fp t12756; +fp t11604; +fp t11694; +fp t12003; +fp t12755; +fp t12314; +fp t12754; +fp t12752; +fp t12037; +fp t11275; +fp t12751; +fp t12181; +fp t11819; +fp t12284; +fp t11559; +fp t12263; +fp t12062; +fp t12337; +fp t12019; +fp t12750; +fp t11867; +fp t11870; +fp t12749; +fp t12748; +fp t12213; +fp t12327; +fp t12120; +fp t12054; +fp t12747; +fp t12301; +fp t11342; +fp t12222; +fp t11343; +fp t12335; +fp t12126; +fp t12746; +fp t11276; +fp t11726; +fp t12184; +fp t12187; +fp t12745; +fp t12323; +fp t12141; +fp t12744; +fp t12080; +fp t11329; +fp t12743; +fp t11995; +fp t12111; +fp t12742; +fp t12269; +fp t12047; +fp t12741; +fp t12383; +fp t11300; +fp t11267; +fp t12031; +fp t12740; +fp t11393; +fp t12244; +fp t12130; +fp t12739; +fp t11355; +fp t11226; +fp t12044; +fp t12738; +fp t12737; +fp t11361; +fp t12319; +fp t11485; +fp t12171; +fp t12259; +fp t12046; +fp t12736; +fp t10549; +fp t12735; +fp t12246; +fp t11290; +fp t12373; +fp t12180; +fp t12734; +fp t12326; +fp t12123; +fp t12056; +fp t12227; +fp t12050; +fp t11296; +fp t12733; +fp t11315; +fp t12403; +fp t12053; +fp t12074; +fp t12732; +fp t11999; +fp t12076; +fp t12731; +fp t12045; +fp t12730; +fp t12729; +fp t11204; +fp t12069; +fp t11407; +fp t12728; +fp t12059; +fp t12268; +fp t12727; +fp t11364; +fp t12070; +fp t12177; +fp t12224; +fp t12029; +fp t12726; +fp t11366; +fp t12202; +fp t11385; +fp t12725; +fp t12306; +fp t12113; +fp t12196; +fp t12020; +fp t12724; +fp t12146; +fp t11269; +fp t12723; +fp t11363; +fp t12248; +fp t11586; +fp t12722; +fp t12257; +fp t11282; +fp t12065; +fp t12721; +fp t12030; +fp t11410; +fp t12720; +fp t12240; +fp t11488; +fp t12208; +fp t11308; +fp t12719; +fp t12253; +fp t12004; +fp t11317; +fp t12718; +fp t12366; +fp t11337; +fp t12088; +fp t12717; +fp t11758; +fp t12249; +fp t11254; +fp t12716; +fp t12264; +fp t11205; +fp t12715; +fp t12401; +fp t12108; +fp t12104; +fp t12714; +fp t12105; +fp t12713; +fp t11397; +fp t12712; +fp t12711; +fp t12114; +fp t12710; +fp t12709; +fp t12188; +fp t12708; +fp t11408; +fp t12707; +fp t11771; +fp t12706; +fp t12228; +fp t11383; +fp t12704; +fp t11824; +fp t11755; +fp t12703; +fp t12015; +fp t12702; +fp t11268; +fp t12701; +fp t12700; +fp t12369; +fp t12140; +fp t11284; +fp t12699; +fp t12216; +fp t11571; +fp t12698; +fp t11372; +fp t12697; +fp t12296; +fp t11322; +fp t12329; +fp t12161; +fp t12696; +fp t12365; +fp t12695; +fp t11220; +fp t12694; +fp t12125; +fp t11368; +fp t12693; +fp t12157; +fp t12048; +fp t12692; +fp t11370; +fp t12691; +fp t11829; +fp t11864; +fp t12690; +fp t11722; +fp t11527; +fp t12689; +fp t12203; +fp t12035; +fp t12688; +fp t11759; +fp t12288; +fp t11255; +fp t12687; +fp t11297; +fp t12082; +fp t12686; +fp t11262; +fp t12012; +fp t12064; +fp t12685; +fp t11367; +fp t12006; +fp t12684; +fp t12683; +fp t12311; +fp t11447; +fp t12121; +fp t12356; +fp t12682; +fp t11435; +fp t12251; +fp t12110; +fp t11467; +fp t12681; +fp t11351; +fp t11706; +fp t12143; +fp t12680; +fp t12010; +fp t11335; +fp t12679; +fp t12271; +fp t11577; +fp t12055; +fp t12678; +fp t12388; +fp t12115; +fp t12677; +fp t12166; +fp t11400; +fp t12676; +fp t12324; +fp t11316; +fp t12350; +fp t12183; +fp t12675; +fp t12674; +fp t12232; +fp t11535; +fp t12389; +fp t12361; +fp t12235; +fp t12085; +fp t12673; +fp t11324; +fp t12672; +fp t12363; +fp t12063; +fp t12671; +fp t11601; +fp t12670; +fp t11541; +fp t11489; +fp t12021; +fp t12669; +fp t11845; +fp t12173; +fp t11650; +fp t11843; +fp t11511; +fp t12395; +fp t12354; +fp t12668; +fp t12381; +fp t12159; +fp t11563; +fp t12667; +fp t12666; +fp t11476; +fp t12357; +fp t12665; +fp t12664; +fp t11998; +fp t12112; +fp t12663; +fp t12662; +fp t12661; +fp t11842; +fp t11836; +fp t11850; +fp t12229; +fp t12191; +fp t11860; +fp t12660; +fp t11283; +fp t12659; +fp t12658; +fp t12219; +fp t11442; +fp t12657; +fp t12656; +fp t12072; +fp t12655; +fp t12654; +fp t11291; +fp t12653; +fp t11328; +fp t12018; +fp t12652; +fp t11782; +fp t11256; +fp t11784; +fp t11997; +fp t12103; +fp t12651; +fp t12292; +fp t11340; +fp t12650; +fp t11302; +fp t12649; +fp t12386; +fp t11259; +fp t12095; +fp t12648; +fp t12647; +fp t12186; +fp t12646; +fp t11346; +fp t12645; +fp t11600; +fp t12079; +fp t12644; +fp t12027; +fp t12643; +fp t11281; +fp t12642; +fp t11833; +fp t12086; +fp t12218; +fp t11514; +fp t12226; +fp t12641; +fp t12013; +fp t12640; +fp t12142; +fp t12639; +fp t11477; +fp t12066; +fp t12638; +fp t11338; +fp t12637; +fp t11603; +fp t12160; +fp t12359; +fp t12636; +fp t12635; +fp t11731; +fp t11673; +fp t12634; +fp t11531; +fp t11353; +fp t12633; +fp t12051; +fp t12000; +fp t12632; +fp t12039; +fp t11521; +fp t12631; +fp t12630; +fp t12261; +fp t12067; +fp t11783; +fp t12313; +fp t11777; +fp t12075; +fp t12629; +fp t12628; +fp t12089; +fp t12043; +fp t12627; +fp t12626; +fp t12138; +fp t12625; +fp t11386; +fp t12355; +fp t12624; +fp t11636; +fp t12167; +fp t12362; +fp t12623; +fp t12278; +fp t12178; +fp t12622; +fp t12621; +fp t12620; +fp t12243; +fp t11288; +fp t12033; +fp t12619; +fp t12254; +fp t12192; +fp t12618; +fp t11591; +fp t11576; +fp t12274; +fp t11561; +fp t12144; +fp t12617; +fp t12283; +fp t11484; +fp t12291; +fp t11457; +fp t11472; +fp t12616; +fp t12615; +fp t12614; +fp t12230; +fp t11381; +fp t12022; +fp t12613; +fp t12612; +fp t12611; +fp t12402; +fp t12148; +fp t12610; +fp t12339; +fp t12609; +fp t11710; +fp t12147; +fp t11356; +fp t12084; +fp t11463; +fp t12608; +fp t12607; +fp t12372; +fp t12128; +fp t12606; +fp t12605; +fp t12604; +fp t11357; +fp t12603; +fp t12602; +fp t11781; +fp t11788; +fp t12601; +fp t12600; +fp t12215; +fp t11348; +fp t11538; +fp t12599; +fp t12598; +fp t12597; +fp t12011; +fp t12596; +fp t12595; +fp t12594; +fp t12593; +fp t12118; +fp t12592; +fp t12591; +fp t12590; +fp t12119; +fp t12083; +fp t12589; +fp t12028; +fp t12135; +fp t12588; +fp t12155; +fp t12169; +fp t11620; +fp t11979; +fp t12587; +fp t12586; +fp t12358; +fp t12585; +fp t12370; +fp t11560; +fp t11359; +fp t12584; +fp t11487; +fp t11517; +fp t12583; +fp t12071; +fp t12582; +fp t12581; +fp t12580; +fp t11265; +fp t12579; +fp t12578; +fp t12577; +fp t11719; +fp t11507; +fp t12576; +fp t11700; +fp t11465; +fp t12297; +fp t11417; +fp t12106; +fp t12575; +fp t12574; +fp t12573; +fp t12572; +fp t12571; +fp t12570; +fp t12569; +fp t12568; +fp t12260; +fp t11309; +fp t11960; +fp t12293; +fp t12567; +fp t11371; +fp t11962; +fp t11506; +fp t12566; +fp t12565; +fp t12564; +fp t12185; +fp t12563; +fp t12562; +fp t12561; +fp t11640; +fp t12560; +fp t11512; +fp t11509; +fp t12559; +fp t12558; +fp t12557; +fp t12152; +fp t11596; +fp t12556; +fp t12555; +fp t12554; +fp t12102; +fp t12553; +fp t12552; +fp t12551; +fp t12550; +fp t12098; +fp t12549; +fp t12174; +fp t12179; +fp t12548; +fp t12547; +fp t11519; +fp t11425; +fp t12546; +fp t12545; +fp t12100; +fp t12093; +fp t12165; +fp t12544; +fp t12189; +fp t12543; +fp t12364; +fp t12542; +fp t12117; +fp t12541; +fp t12007; +fp t12540; +fp t12539; +fp t12538; +fp t12537; +fp t12290; +fp t11557; +fp t11778; +fp t12134; +fp t12536; +fp t12535; +fp t12534; +fp t12533; +fp t12532; +fp t12531; +fp t12530; +fp t12529; +fp t12528; +fp t11455; +fp t12527; +fp t12312; +fp t12526; +fp t12525; +fp t12524; +fp t12175; +fp t12523; +fp t12522; +fp t12266; +fp t11495; +fp t12038; +fp t12521; +fp t12520; +fp t12233; +fp t12034; +fp t12519; +fp t12518; +fp t12517; +fp t12516; +fp t12107; +fp t11478; +fp t12515; +fp t11859; +fp t12163; +fp t12514; +fp t12513; +fp t12026; +fp t12122; +fp t12512; +fp t12511; +fp t12510; +fp t12509; +fp t12508; +fp t12507; +fp t12506; +fp t12505; +fp t12504; +fp t12503; +fp t12502; +fp t12501; +fp t12151; +fp t12002; +fp t12500; +fp t12017; +fp t12499; +fp t11580; +fp t12498; +fp t12497; +fp t12347; +fp t12049; +fp t12190; +fp t12496; +fp t12001; +fp t12495; +fp t11264; +fp t12494; +fp t12493; +fp t12492; +fp t11994; +fp t12491; +fp t12336; +fp t12041; +fp t12009; +fp t12490; +fp t11558; +fp t12489; +fp t12488; +fp t12094; +fp t12487; +fp t11325; +fp t12168; +fp t12137; +fp t12486; +fp t12485; +fp t11757; +fp t11761; +fp t12073; +fp t12484; +fp t12483; +fp t12482; +fp t12481; +fp t12480; +fp t12277; +fp t12133; +fp t11613; +fp t12479; +fp t12478; +fp t12477; +fp t12476; +fp t12158; +fp t12475; +fp t11735; +fp t11630; +fp t12474; +fp t12473; +fp t12472; +fp t12471; +fp t11402; +fp t12470; +fp t12469; +fp t12468; +fp t12467; +fp t12466; +fp t12465; +fp t12464; +fp t12463; +fp t12462; +fp t12461; +fp t12460; +fp t12077; +fp t12459; +fp t12458; +fp t12457; +fp t12456; +fp t12455; +fp t12334; +fp t11483; +fp t11583; +fp t12454; +fp t12453; +fp t12452; +fp t10451; +fp t12451; +fp t12450; +fp t12449; +fp t12448; +fp t12447; +fp t12446; +fp t11369; +fp t12445; +fp t12444; +fp t12443; +fp t12442; +fp t11654; +fp t11660; +fp t11536; +fp t12441; +fp t11981; +fp t12440; +fp t12439; +fp t11626; +fp t11458; +fp t12438; +fp t12396; +fp t12437; +fp t11832; +fp t12194; +fp t12060; +fp t12436; +fp t11523; +fp t12435; +fp t12315; +fp t11490; +fp t12434; +fp t12096; +fp t12433; +fp t12276; +fp t11547; +fp t12432; +fp t11582; +fp t12431; +fp t12430; +fp t12429; +fp t12025; +fp t12068; +fp t11713; +fp t12428; +fp t12427; +fp t12252; +fp t12426; +fp t11598; +fp t12425; +fp t12424; +fp t11723; +fp t12391; +fp t12423; +fp t12422; +fp t12421; +fp t12420; +fp t12419; +fp t12097; +fp t12418; +fp t11572; +fp t12417; +fp t12416; +fp t12415; +fp t12414; +fp t12413; +fp t12412; +fp t12411; +fp t12410; +fp t12299; +fp t11569; +fp t12409; +fp t12408; +fp t12407; +fp t12406; +fp t12345; +fp t10342; +fp t10375; +fp t12341; +fp t10419; +fp t10357; +fp t12332; +fp t12331; +fp t12310; +fp t12305; +fp t12295; +fp t12294; +fp t10556; +fp t12286; +fp t12258; +fp t12247; +fp t10416; +fp t12217; +fp t12170; +fp t12164; +fp t12078; +fp t11433; +fp t11993; +fp t11992; +fp t11991; +fp t11988; +fp t11987; +fp t11985; +fp t11984; +fp t11983; +fp t11980; +fp t11978; +fp t11977; +fp t11976; +fp t11975; +fp t11790; +fp t11974; +fp t11973; +fp t11802; +fp t11857; +fp t11801; +fp t11972; +fp t11971; +fp t11776; +fp t11970; +fp t11969; +fp t11968; +fp t11871; +fp t11967; +fp t11966; +fp t11965; +fp t11964; +fp t11770; +fp t11810; +fp t11855; +fp t11963; +fp t11961; +fp t11959; +fp t11958; +fp t11957; +fp t11956; +fp t11955; +fp t11954; +fp t11953; +fp t11952; +fp t11951; +fp t11950; +fp t11754; +fp t11949; +fp t11772; +fp t11948; +fp t11947; +fp t11946; +fp t11945; +fp t11944; +fp t11943; +fp t11942; +fp t11941; +fp t11940; +fp t11939; +fp t11938; +fp t11937; +fp t11786; +fp t11936; +fp t11935; +fp t11934; +fp t11933; +fp t11932; +fp t11931; +fp t11930; +fp t11929; +fp t11928; +fp t11927; +fp t11926; +fp t11925; +fp t11924; +fp t11923; +fp t11922; +fp t11921; +fp t11920; +fp t11919; +fp t11918; +fp t11917; +fp t11916; +fp t11915; +fp t11914; +fp t11913; +fp t11912; +fp t11911; +fp t11910; +fp t11909; +fp t11908; +fp t11907; +fp t11906; +fp t11905; +fp t11904; +fp t11903; +fp t11902; +fp t11901; +fp t11900; +fp t11899; +fp t11898; +fp t11897; +fp t11896; +fp t11895; +fp t11894; +fp t11893; +fp t11892; +fp t11891; +fp t11890; +fp t11889; +fp t11888; +fp t11868; +fp t11858; +fp t11856; +fp t11851; +fp t11849; +fp t11830; +fp t11826; +fp t11818; +fp t11817; +fp t11805; +fp t11804; +fp t11773; +fp t11769; + t11752 = RATIONAL(-1.0,3456.0); + t11751 = RATIONAL(1.0,3456.0); + t11876 = z*z; + t11880 = z*t11876; + t12847 = t11751*t11880+z*t11752; + t11877 = y*y; + t11882 = t11877*t11877; + t11756 = RATIONAL(-1.0,6912.0); + t11749 = RATIONAL(1.0,6912.0); + t12846 = t11882*t11756+t11877*t11749; + t11816 = RATIONAL(-1.0,54.0); + t11875 = x*x; + t11878 = t11875*x; + t12197 = t11816*t11878; + t12367 = z*t11878; + t11823 = RATIONAL(2.0,27.0); + t12124 = t11823*t12367; + t12845 = t11880*t12197+t12124; + t11799 = RATIONAL(-1.0,864.0); + t11766 = RATIONAL(1.0,864.0); + t12231 = t11882*t11766; + t12199 = t11882*t11880; + t12844 = t11799*t12199+z*t12231; + t11839 = RATIONAL(1.0,36.0); + t11854 = RATIONAL(1.0,9.0); + t12843 = t11854*t11880+t11839*t12199; + t11840 = RATIONAL(1.0,18.0); + t12378 = x*t11840; + t11853 = RATIONAL(-1.0,9.0); + t12842 = t12378+t11878*t11853; + t11753 = RATIONAL(-1.0,1728.0); + t11879 = y*t11877; + t11881 = t11876*t11876; + t12210 = t11879*t11881; + t11750 = RATIONAL(1.0,1728.0); + t12285 = t11876*t11750; + t12841 = t11753*t12210+t11879*t12285; + t11796 = RATIONAL(5.0,576.0); + t11795 = RATIONAL(-5.0,576.0); + t12325 = t11876*t11879; + t12400 = y*t11876; + t12840 = t11795*t12400+t11796*t12325; + t11806 = RATIONAL(-8.0,27.0); + t11873 = RATIONAL(2.0,9.0); + t12392 = y*t11875; + t12839 = t11873*t12392+y*t11806; + t11748 = RATIONAL(-1.0,1152.0); + t12206 = t11877*t11748; + t12092 = t11875*t12206; + t11760 = RATIONAL(1.0,1152.0); + t12280 = t11760*t11875; + t12040 = t11882*t12280; + t12838 = t12092+t12040; + t11808 = RATIONAL(-1.0,18.0); + t12384 = x*t11808; + t12318 = t11854*t11878; + t12837 = t12318+t12384; + t11847 = RATIONAL(1.0,72.0); + t12255 = t11847*t11878; + t11794 = RATIONAL(-1.0,144.0); + t12836 = t12255+x*t11794; + t12256 = t11876*t11878; + t12032 = t11823*t12256; + t11821 = RATIONAL(-4.0,27.0); + t12382 = x*t11821; + t12835 = t12032+t11876*t12382; + t11763 = RATIONAL(1.0,216.0); + t12221 = t11882*t11763; + t11791 = RATIONAL(-1.0,288.0); + t12281 = t11791*t11875; + t12057 = t11882*t12281; + t12834 = t12057+t12221; + t12322 = t11878*t11880; + t11664 = t11853*t12322; + t11874 = RATIONAL(4.0,9.0); + t12302 = t11874*t11878; + t12833 = t11664+z*t12302; + t12207 = t11882*t11748; + t12061 = t11875*t12207; + t12270 = t11877*t11875; + t12832 = t11760*t12270+t12061; + t11820 = RATIONAL(-2.0,27.0); + t12211 = t11880*t11820; + t11803 = RATIONAL(1.0,54.0); + t12831 = t11803*t12199+t11877*t12211; + t11846 = RATIONAL(-5.0,72.0); + t12234 = t11876*t11846; + t12830 = t12234+t11840; + t12238 = t11877*t11880; + t12829 = t11753*t12238+t11750*t12199; + t11213 = t11750*t12210; + t12250 = t11753*t11879; + t12828 = t11213+t11876*t12250; + t12375 = y*t11881; + t12827 = t11799*t12210+t11766*t12375; + t11809 = RATIONAL(-1.0,36.0); + t12826 = t11853*t11880+t11809*t12199; + t11513 = t11839*t12210; + t12825 = t11513+t11854*t11879; + t11462 = t11816*t12210; + t12212 = t11879*t11823; + t12824 = t11462+t11876*t12212; + t11736 = t11853*t11879; + t12823 = t11809*t12210+t11736; + t12822 = t11877*t11799+t12061; + t11764 = RATIONAL(1.0,432.0); + t12398 = z*t11882; + t11765 = RATIONAL(-1.0,432.0); + t12399 = z*t11877; + t12821 = t11764*t12398+t11765*t12399; + t11861 = RATIONAL(1.0,3.0); + t11869 = RATIONAL(-4.0,9.0); + t12820 = t11869+t11861*t11875; + t11811 = RATIONAL(1.0,27.0); + t12333 = t11811*t11879; + t12819 = y*t12382+x*t12333; + t12818 = t11765*t12375+t11764*t12400; + t12317 = t11869*t11878; + t12817 = y*t12317+t11879*t12318; + t12816 = t11796*t12399+t11795*t12238; + t12815 = t11879*t12280+t11748*t12392; + t12814 = t11882*t11823+t11873*t12270; + t11835 = RATIONAL(-1.0,24.0); + t12330 = t11835*t11875; + t11822 = RATIONAL(5.0,96.0); + t12304 = t11876*t11875; + t12014 = t11822*t12304; + t12813 = t12330+t12014; + t12812 = t11766*t12199+t11799*t12398; + t11828 = RATIONAL(1.0,48.0); + t12346 = t11828*t11875; + t12811 = t11794+t12346; + t12328 = t11880*t11875; + t11814 = RATIONAL(8.0,27.0); + t12810 = t11840*t12328+z*t11814; + t12289 = t11820*t11881; + t11439 = t11803*t12210; + t12809 = y*t12289+t11439; + t12808 = t11823*t12238+t11816*t12199; + t11837 = RATIONAL(1.0,24.0); + t12348 = t11837*t11875; + t11825 = RATIONAL(-5.0,96.0); + t12058 = t11825*t12304; + t12807 = t12058+t12348; + t12390 = x*RATIONAL(8.0,9.0); + t12376 = x*t11881; + t12806 = t11873*t12376+t12390; + t12239 = t11876*t11765; + t12237 = t11764*t11881; + t12805 = (t12239+t12237)*y; + t11844 = RATIONAL(-5.0,36.0); + t11440 = t11844*t12238; + t11872 = RATIONAL(5.0,9.0); + t12300 = t11877*t11872; + t12804 = t11440+z*t12300; + t12279 = t11803*t11881; + t11588 = y*t12279; + t11779 = RATIONAL(-1.0,216.0); + t11391 = t11779*t12210; + t12803 = t11588+t11391; + t12205 = t11766*t11879; + t11331 = t11881*t12205; + t12802 = t11799*t12375+t11331; + t12241 = t11882*t11765; + t12225 = t11877*t11764; + t12801 = (t12225+t12241)*z; + t12307 = t11882*t11875; + t11815 = RATIONAL(-1.0,12.0); + t12800 = t11854*t11882+t11815*t12307; + t12193 = t11839*t11875; + t12799 = t11882*t12193+t11853*t12270; + t11834 = RATIONAL(5.0,36.0); + t11414 = t11834*t12238; + t11866 = RATIONAL(-5.0,9.0); + t12798 = t11866*t12399+t11414; + t11831 = RATIONAL(-1.0,48.0); + t12262 = t11831*t11875; + t11780 = RATIONAL(5.0,192.0); + t12016 = t11780*t12304; + t12797 = t12016+t12262; + t11812 = RATIONAL(4.0,27.0); + t12374 = x*t11812; + t12796 = t11814*t12367+t11880*t12374; + t12795 = t12262+t11839; + t11762 = RATIONAL(-16.0,27.0); + t12405 = y*x; + t12794 = t11879*t12374+t11762*t12405; + t11789 = RATIONAL(1.0,288.0); + t11354 = t11789*t12210; + t12793 = t11354+t11847*t11879; + t12792 = t11795*t12399+t11796*t12238; + t12753 = y*t12302+t11878*t11736; + t11807 = RATIONAL(1.0,12.0); + t12272 = t11807*t11875; + t12791 = (t11853+t12272)*t11882; + t12790 = t11796*t12400+t11795*t12325; + t11295 = t11791*t12210; + t11800 = RATIONAL(-1.0,72.0); + t12789 = t11295+t11800*t11879; + t11200 = t11750*t12238; + t12788 = t11753*t12199+t11200; + t11785 = RATIONAL(-5.0,192.0); + t11787 = RATIONAL(1.0,192.0); + t12005 = t11787*t12307; + t12787 = t12005+t11785*t12270; + t12397 = x*t11882; + t12786 = t12390+t11873*t12397; + t11827 = RATIONAL(-1.0,96.0); + t11473 = t11827*t12307; + t12785 = t11473+t11822*t12270; + t11863 = RATIONAL(-1.0,3.0); + t12784 = t11874+t11863*t11875; + t11841 = RATIONAL(-10.0,9.0); + t11848 = RATIONAL(5.0,18.0); + t12385 = x*t11879; + t12783 = t11841*t12405+t11848*t12385; + t11792 = RATIONAL(-5.0,288.0); + t12162 = t11792*t12385; + t11768 = RATIONAL(5.0,288.0); + t12267 = t11794*t11878; + t12782 = t11768*t12405+y*t12267+t12162; + t12200 = t11876*t11760; + t11688 = t11791*t11881; + t12781 = t11789*t11876+t11882*t12200+t11688; + t11797 = RATIONAL(-1.0,576.0); + t12273 = t11882*t11797; + t11798 = RATIONAL(1.0,576.0); + t11793 = RATIONAL(1.0,144.0); + t11685 = t11793*t11880; + t12780 = t11798*t12199+t11685+z*t12273; + t11684 = t11789*t11877; + t12320 = t11877*t11881; + t12779 = t11791*t11882+t11760*t12320+t11684; + t12309 = t11752*t11876; + t12778 = t11879*t12309+t11752*t12375+(t12400+t12210)*t11751; + t12380 = z*t11751; + t12777 = t11752*t12199+t11882*t12380+t12847*t11877; + t12776 = t11752*t12238+t11877*t12380+t12847*t11882; + t12371 = z*t11879; + t12287 = t11880*t11750; + t12404 = y*z; + t12775 = t11750*t12371+y*t12287+t11753*t12404+t11880*t12250; + t12344 = t11877*t11876; + t12209 = t11882*t11749; + t12774 = t11756*t12344+t11876*t12209+t12846*t11881; + t12773 = t11752*t12210+y*t12309+(t12375+t12325)*t11751; + t12394 = y*t11880; + t12772 = t11750*t12404+t11753*t12394+t11879*t12287+z*t12250; + t12771 = t11794*t11880+t11793*z+t11797*t12199+t11798*t12398; + t11767 = RATIONAL(-5.0,144.0); + t12220 = t11882*t11767; + t11725 = t11808*t11877; + t12770 = x*t12220+t11878*t11725; + t11330 = t11789*t12199; + t12769 = t11330+t11847*t11880; + t11774 = RATIONAL(1.0,108.0); + t12338 = t11774*t11880; + t11387 = t11879*t12338; + t12265 = t11809*t11875; + t12156 = z*t12265; + t12768 = y*t12156+t11387; + t12298 = t11879*t11779; + t11285 = z*t12298; + t12090 = t11789*t12328; + t12767 = t11285+y*t12090; + t12766 = t11800*t11880+t11791*t12199; + t11852 = RATIONAL(1.0,6.0); + t11838 = RATIONAL(-5.0,24.0); + t12765 = t11852+t11838*t11877; + t12349 = t11879*t11875; + t12172 = z*t12349; + t11775 = RATIONAL(-1.0,108.0); + t12201 = t11775*t11880; + t11336 = y*t12201; + t12764 = t11336+t11839*t12172; + t12204 = t11878*t11840; + t11712 = t11808*t11879; + t11497 = t11878*t11712; + t12763 = y*t12204+t11497; + t12387 = y*t11799; + t11260 = t11880*t12387; + t12245 = t11847*t11875; + t12145 = z*t12245; + t12762 = t11260+t11879*t12145; + t12236 = t11791*t11878; + t12761 = t11795*t12397+t11877*t12236; + t12760 = t11878*t11684+t11796*t12397; + t11744 = t11854*t11881; + t12242 = t11875*t11881; + t12759 = t11744+t11815*t12242; + t11705 = t11800*t11881; + t12758 = t11877*t11705+t11725; + t12342 = t11808*t11878; + t11416 = y*t12342; + t11505 = t11879*t12204; + t12757 = t11416+t11505; + t11813 = RATIONAL(-1.0,27.0); + t12321 = t11813*t11880; + t12756 = y*t12321+t11793*t12172; + t11604 = t11811*t12404; + t11694 = t11794*t11879; + t12003 = t11880*t11694; + t12755 = t11875*t12003+t11604; + t12314 = t11882*t11876; + t12754 = t11808*t11876+t11800*t12314; + t12752 = t11831*t11882+t11815; + t12037 = t11880*t12193; + t11275 = t11775*t12371; + t12751 = y*t12037+t11275; + t12181 = t11768*t12397; + t11819 = RATIONAL(5.0,72.0); + t12284 = t11877*t11819; + t11559 = t11876*t12284; + t12263 = t11882*t11878; + t12062 = t11881*t12263; + t12337 = t11794*t12062+x*t11559; + t12019 = t11877*t12256; + t12750 = t12337+t11809*t12019+t11881*t12181; + t11867 = RATIONAL(5.0,6.0); + t11870 = RATIONAL(-2.0,3.0); + t12749 = t11867*t11876+t11870; + t12748 = t11798*t12210+t11793*t11879+t11797*t12375; + t12213 = t11879*t11765; + t12327 = t11797*t11875; + t12120 = y*t12327; + t12054 = t11798*t12242; + t12747 = y*t12054+(t12213+t12120)*t11876; + t12301 = t11879*t11763; + t11342 = z*t12301; + t12222 = t11766*t11880; + t11343 = y*t12222; + t12335 = t11878*t11765; + t12126 = y*t12335; + t12746 = t11880*t12126+(t11343+t11342)*x; + t11276 = t11774*t12325; + t11726 = t11809*t11881; + t12184 = y*t11726; + t12187 = y*t12304; + t12745 = t11875*t12184+t11854*t12187+t11276; + t12323 = t11794*t11875; + t12141 = y*t12323; + t12744 = t11876*t12141+t12828; + t12080 = t11876*t12193; + t11329 = t11775*t12210; + t12743 = y*t12080+t11811*t12325+t11329; + t11995 = t11798*t12270; + t12111 = z*t12307; + t12742 = t11797*t12111+t11880*t12225+z*t11995; + t12269 = t11877*t11793; + t12047 = t11875*t12269; + t12741 = z*t12047+t12788; + t12383 = y*t11763; + t11300 = t11880*t12383; + t11267 = z*t12205; + t12031 = t11878*t12213; + t12740 = z*t12031+(t11300+t11267)*x; + t11393 = t11877*t12201; + t12244 = t11774*t11878; + t12130 = z*t12244; + t12739 = t11878*t11393+t11877*t12130+t12844*x; + t11355 = t11882*t12239; + t11226 = t11753*t12320; + t12044 = t11793*t12307; + t12738 = t11355+t11226+t11881*t11995+t11876*t12044; + t12737 = t12751+t12756; + t11361 = t11775*t12199; + t12319 = t11877*t11803; + t11485 = z*t12319; + t12171 = t11811*t12397; + t12259 = t11779*t11880; + t12046 = t11878*t12259; + t12736 = z*t12171+t11878*t11485+t11877*t12046+x*t11361; + t10549 = t11878*t11275; + t12735 = t10549+t12746; + t12246 = t11764*t11879; + t11290 = t11880*t12246; + t12373 = y*t11853; + t12180 = t11875*t12373; + t12734 = z*t12180+t11290+t12764; + t12326 = t11775*t11881; + t12123 = x*t12326; + t12056 = t11803*t12256; + t12227 = t11878*t11820; + t12050 = t11876*t12227; + t11296 = t11764*t12210; + t12733 = t11879*t12056+x*t11296+(t12050+t12123)*y; + t11315 = t11779*t12199; + t12403 = x*z; + t12053 = t11877*t12335; + t12074 = t11878*t12225; + t12732 = t12221*t12403+z*t12074+t11880*t12053+x*t11315; + t11999 = t11877*t12242; + t12076 = t11882*t12304; + t12731 = t11764*t12314+t11794*t12076+t11797*t11999+t11750*t12320; + t12045 = t11876*t12273; + t12730 = t11881*t12225+t11882*t12285+t11875*t12045+t11794*t11999; + t12729 = t11793*y+t11797*t12210+t11694+t11798*t12375; + t11204 = t11753*t12314; + t12069 = t11798*t12304; + t11407 = t11765*t12320; + t12728 = t11204+t11793*t11999+t11407+t11882*t12069; + t12059 = t11875*t11685; + t12268 = t11879*t11813; + t12727 = z*t12268+y*t12059+t12764; + t11364 = t11774*t12210; + t12070 = t11876*t12197; + t12177 = t11813*t12376; + t12224 = t11878*t11763; + t12029 = t11876*t12224; + t12726 = x*t11364+t11879*t12029+(t12177+t12070)*y; + t11366 = t11765*t12199; + t12202 = t11882*t11774; + t11385 = z*t12202; + t12725 = t12845*t11877+(t11366+t11385)*x; + t12306 = t11877*t11846; + t12113 = x*t12306; + t12196 = t11793*t11878; + t12020 = t11876*t12196; + t12724 = t11882*t12020+t11881*t12113; + t12146 = y*t12193; + t11269 = t11879*t12201; + t12723 = z*t12146+t11269; + t11363 = t11876*t12202; + t12248 = t11816*t11881; + t11586 = t11877*t12248; + t12722 = x*t11363+t11878*t11586; + t12257 = t11792*t11876; + t11282 = t11882*t12257; + t12065 = t11878*t12320; + t12721 = t11839*t12065+x*t11282; + t12030 = t11879*t12281; + t11410 = z*t12383; + t12720 = t11880*t12030+t11410; + t12240 = t11839*t11878; + t11488 = t11876*t12240; + t12208 = t11792*t11877; + t11308 = t11881*t12208; + t12719 = x*t11308+t11882*t11488; + t12253 = t11809*t11880; + t12004 = t11875*t12253; + t11317 = t11774*t12371; + t12718 = y*t12004+t11317; + t12366 = z*t11779; + t11337 = y*t12366; + t12088 = t11879*t12328; + t12717 = t11337+t11789*t12088; + t11758 = RATIONAL(5.0,1152.0); + t12249 = t11877*t11758; + t11254 = t11881*t12249; + t12716 = t11878*t12045+x*t11254; + t12264 = t11882*t11881; + t11205 = t11750*t12264; + t12715 = t11779*t12019+x*t11205; + t12401 = x*t11877; + t12108 = t11848*t12401; + t12104 = t11882*t12256; + t12714 = t11853*t12104+t11881*t12108; + t12105 = t11880*t12281; + t12713 = t11342+y*t12105; + t11397 = y*t12259; + t12712 = t11789*t12172+t11397; + t12711 = t11300+z*t12030; + t12114 = x*t12344; + t12710 = t11841*t12114+t11839*t12062; + t12709 = t11803*t12019+t11882*t12123; + t12188 = x*t12264; + t12708 = t11785*t12188+t11822*t12019; + t11408 = t11876*t12225; + t12707 = t11799*t12062+x*t11408; + t11771 = RATIONAL(25.0,12.0); + t12706 = t11835*t12062+t11771*t12114; + t12228 = t11774*t11881; + t11383 = t11877*t12228; + t12704 = t11882*t12070+x*t11383; + t11824 = RATIONAL(1.0,96.0); + t11755 = RATIONAL(-25.0,192.0); + t12703 = t11824*t12062+t11755*t12114; + t12015 = t11878*t12221; + t12702 = t11876*t12015+x*t11226; + t11268 = t11766*t12320; + t12701 = t11878*t11268+x*t11355; + t12700 = t11808*t12188+t11872*t12019; + t12369 = z*t11875; + t12140 = t11800*t12369; + t11284 = t11880*t12205; + t12699 = y*t12140+t11284; + t12216 = t11877*t11813; + t11571 = t11876*t12216; + t12698 = x*t11571+t11881*t12015; + t11372 = t11789*t12264; + t12697 = t11844*t12019+x*t11372; + t12296 = t11779*t11881; + t11322 = t11877*t12296; + t12329 = t11876*t11811; + t12161 = x*t12329; + t12696 = t11882*t12161+t11878*t11322; + t12365 = y*t11813; + t12695 = z*t12365+t11879*t12059; + t11220 = t11758*t12314; + t12694 = x*t11220+t11797*t12065; + t12125 = x*t12234; + t11368 = t11881*t12196; + t12693 = t11882*t12125+t11877*t11368; + t12157 = t11811*t12376; + t12048 = t11779*t12263; + t12692 = t11876*t12048+t11877*t12157; + t11370 = t11881*t12241; + t12691 = t11823*t12019+x*t11370; + t11829 = RATIONAL(5.0,48.0); + t11864 = RATIONAL(-5.0,6.0); + t12690 = t11864*t12019+t11829*t12188; + t11722 = t11847*t11881; + t11527 = x*t11722; + t12689 = t11882*t11527+t11767*t12019; + t12203 = t11766*t11876; + t12035 = t11878*t12203; + t12688 = x*t11407+t11882*t12035; + t11759 = RATIONAL(-5.0,1152.0); + t12288 = t11876*t11759; + t11255 = t11877*t12288; + t12687 = t11798*t12062+x*t11255; + t11297 = t11763*t12238; + t12082 = t11877*t12245; + t12686 = t11297+z*t12082+t11875*t11330; + t11262 = t11876*t12298; + t12012 = t11875*t12210; + t12064 = t11800*t12304; + t12685 = t11262+y*t12064+t11791*t12012; + t11367 = y*t12338; + t12006 = t11879*t12322; + t12684 = t11763*t12006+(t11367+t11317)*x; + t12683 = t11779*t12006+(t11336+t11275)*x; + t12311 = t11823*t11880; + t11447 = y*t12311; + t12121 = t11878*t12365; + t12356 = x*t12371; + t12682 = x*t11447+t11880*t12121+t11803*t12356; + t11435 = t11811*t12394; + t12251 = t11816*t11879; + t12110 = z*t12251; + t11467 = y*t12211; + t12681 = t11878*t11435+(t11467+t12110)*x; + t11351 = t11774*t12199; + t11706 = t11809*t11877; + t12143 = z*t11706; + t12680 = t11351+t11880*t12216+t11875*t12143; + t12010 = t11800*t12270; + t11335 = t11779*t12238; + t12679 = z*t12010+t11880*t12057+t11335; + t12271 = t11803*t11880; + t11577 = z*t12212; + t12055 = t11878*t12268; + t12678 = t12271*t12405+x*t11577+z*t12055; + t12388 = y*t11878; + t12115 = t11764*t12388; + t12677 = t11880*t12115+(t11260+t11285)*x; + t12166 = y*t12245; + t11400 = t11876*t12301; + t12676 = t11876*t12166+t11789*t12012+t11400; + t12324 = t11879*t11799; + t11316 = z*t12324; + t12350 = t11879*t11878; + t12183 = z*t12350; + t12675 = t11764*t12183+(t11397+t11316)*x; + t12674 = t11393+t12799*z; + t12232 = t11879*t11820; + t11535 = z*t12232; + t12389 = x*t11880; + t12361 = y*t12389; + t12235 = t11811*t11878; + t12085 = t11879*t12235; + t12673 = z*t12085+t11816*t12361+x*t11535; + t11324 = t11876*t12383; + t12672 = (t12115+t12031)*t11881+(t11262+t11324)*x; + t12363 = x*t12375; + t12063 = t11764*t12256; + t12671 = x*t11391+t11876*t12031+t11763*t12363+y*t12063; + t11601 = z*t12216; + t12670 = t11877*t12004+t11880*t12044+t11601+t11385; + t11541 = y*t12248; + t11489 = t11876*t12365; + t12021 = t11881*t12224; + t12669 = t11878*t11541+t11879*t12021+(t11489+t11276)*x; + t11845 = RATIONAL(-5.0,18.0); + t12173 = t11845*t12385; + t11650 = t11878*t11744; + t11843 = RATIONAL(10.0,9.0); + t11511 = t11878*t11726; + t12395 = x*t11876; + t12354 = y*t12395; + t12668 = t11843*t12354+y*t11650+t11876*t12173+t11879*t11511; + t12381 = z*t11820; + t12159 = y*t12235; + t11563 = t11880*t12251; + t12667 = z*t12159+t12381*t12405+t11774*t12006+x*t11563; + t12666 = t12834*t11881+(t12010+t12319)*t11876; + t11476 = t11879*t12271; + t12357 = t11823*t12403; + t12665 = y*t12357+x*t11476+z*t12121+t11775*t12006; + t12664 = t12692+t12722; + t11998 = t11878*t12199; + t12112 = z*t12263; + t12663 = t11791*t12112+t11789*t11998+t12792*x; + t12662 = t12702+t12715; + t12661 = t12751+t12755; + t11842 = RATIONAL(5.0,24.0); + t11836 = RATIONAL(-5.0,12.0); + t11850 = RATIONAL(-1.0,6.0); + t12229 = t11850*t11881; + t12191 = x*t12314; + t11860 = RATIONAL(-5.0,3.0); + t12660 = t11842*t12065+t11836*t12191+t11860*t12395+t11878*t12229; + t11283 = t11882*t12237; + t12659 = x*t11283+t11799*t12019+t12688; + t12658 = t11880*t12301+t12281*t12404+t12712; + t12219 = t11877*t11811; + t11442 = z*t12219; + t12657 = t11803*t12112+t11779*t11998+(t11442+t11393)*x; + t12656 = t11847*t11999+t11789*t12076+t11586+t11779*t12314; + t12072 = t11800*t12328; + t12655 = t11267+y*t12072+t12711; + t12654 = t10549+t12682; + t11291 = t11774*t12238; + t12653 = t11816*t12112+t11763*t11998+(t11601+t11291)*x; + t11328 = y*t12228; + t12018 = t11876*t12265; + t12652 = t11328+t11489+t11879*t12018+t11793*t12012; + t11782 = RATIONAL(5.0,384.0); + t11256 = t11881*t12207; + t11784 = RATIONAL(1.0,384.0); + t11997 = t11784*t12307; + t12103 = t11876*t12270; + t12651 = t11255+t11256+t11782*t12103+t11881*t11997; + t12292 = t11877*t11763; + t11340 = z*t12292; + t12650 = t11764*t12112+t11765*t11998+(t11335+t11340)*x; + t11302 = t11877*t12366; + t12649 = t11764*t11998+t11765*t12112+(t11302+t11297)*x; + t12386 = z*t11775; + t11259 = t11882*t12386; + t12095 = t11880*t12323; + t12648 = t11877*t12037+t11259+t11442+t11882*t12095; + t12647 = t11789*t12112+t11791*t11998+t12816*x; + t12186 = t11844*t12399; + t12646 = t11800*t12112+t11847*t11998+(t12186+t11414)*x; + t11346 = t11794*t12264; + t12645 = t11346+t11877*t12016+t11767*t12344+t11881*t12005; + t11600 = t11824*t12242; + t12079 = t11842*t12304; + t12644 = t11791*t12264+t11882*t11600+(t12079+t12234)*t11877; + t12027 = t11882*t12245; + t12643 = t11322+t11816*t12314+t11876*t12027+t11789*t11999; + t11281 = y*t12326; + t12642 = y*t12329+t11879*t12080+t11794*t12012+t11281; + t11833 = RATIONAL(5.0,12.0); + t12086 = t11833*t12270; + t12218 = t11828*t11881; + t11514 = t11875*t12218; + t12226 = t11866*t11876; + t12641 = t11809*t12264+t11876*t12086+t11877*t12226+t11882*t11514; + t12013 = t11879*t12327; + t12640 = t11876*t12013+t11798*t12012+t12805; + t12142 = y*t11688; + t12639 = (t11354+t12142)*t11878+t12840*x; + t11477 = t11831*t12242; + t12066 = t11836*t12270; + t12638 = t11839*t12264+t11882*t11477+(t12300+t12066)*t11876; + t11338 = t11880*t12324; + t12637 = t11338+y*t12145+t12717; + t11603 = z*t12204; + t12160 = t11767*t12385; + t12359 = t11844*t12405; + t12636 = t11847*t12006+z*t12359+y*t11603+t11880*t12160; + t12635 = t11879*t12156+t11367+t12695; + t11731 = t11853*t11881; + t11673 = y*t11731; + t12634 = (t11673+t11513)*t11878+t12783*t11876; + t11531 = z*t12284; + t11353 = t11880*t12208; + t12633 = t11794*t11998+t11839*t12112+(t11531+t11353)*x; + t12051 = t11798*t12328; + t12000 = t11797*t12270; + t12632 = t11882*t12051+t11880*t12000+t12821; + t12039 = t11838*t12270; + t11521 = t11827*t12242; + t12631 = t11372+t11876*t12039+t11882*t11521+t11559; + t12630 = t11343+t11879*t12140+t12713; + t12261 = t11785*t11876; + t12067 = t11875*t12261; + t11783 = RATIONAL(5.0,144.0); + t12313 = t11877*t11783; + t11777 = RATIONAL(-1.0,192.0); + t12075 = t11777*t12307; + t12629 = t11876*t12313+t11793*t12264+t11877*t12067+t11881*t12075; + t12628 = t12691+t12722; + t12089 = t11882*t12242; + t12043 = t11794*t12270; + t12627 = t11408+t11205+t11797*t12089+t11876*t12043; + t12626 = t11877*t12021+x*t11204+t12688; + t12138 = t11775*t12388; + t12625 = z*t12138+t11765*t12006+(t11410+t11284)*x; + t11386 = t11880*t12213; + t12355 = y*t12369; + t12624 = t11854*t12355+t11386+t12718; + t11636 = t11854*t12263; + t12167 = t11845*t12389; + t12362 = x*t12399; + t12623 = z*t11636+t11877*t12167+t11843*t12362+t11809*t11998; + t12278 = t11877*t11834; + t12178 = z*t12278; + t12622 = t11847*t12112+t11800*t11998+(t11440+t12178)*x; + t12621 = t12720+t12767; + t12620 = t12755+t12768; + t12243 = t11876*t11768; + t11288 = t11879*t12243; + t12033 = t11879*t12196; + t12619 = x*t11288+t11881*t12033+(t11511+t12125)*y; + t12254 = t11837*t11878; + t12192 = t11829*t11876; + t12618 = t11881*t12254+x*t12192+t11825*t12065+t11780*t12191; + t11591 = t11800*t12210; + t11576 = y*t11722; + t12274 = t11844*t11879; + t11561 = t11876*t12274; + t12144 = t11834*t12400; + t12617 = (t11591+t11576)*t11878+(t11561+t12144)*x; + t12283 = t11844*t11876; + t11484 = y*t11705; + t12291 = t11834*t11879; + t11457 = t11876*t12291; + t11472 = t11847*t12210; + t12616 = x*t11457+t12283*t12405+(t11472+t11484)*t11878; + t12615 = t12698+t12704; + t12614 = t12699+t12762; + t12230 = t11876*t11775; + t11381 = t11879*t12230; + t12022 = t11876*t12244; + t12613 = t11878*t11381+y*t12022+t12827*x; + t12612 = z*t12333+y*t12095+t12723; + t12611 = t11876*t12047+t11877*t12239+t11882*t12054+t11753*t12264; + t12402 = y*t12403; + t12148 = t11783*t12389; + t12610 = z*t11416+t11800*t12006+t11879*t12148+t11834*t12402; + t12339 = t11816*t11876; + t12609 = t11877*t12339+t11876*t12082+t11789*t12089+t11779*t12264; + t11710 = t11839*t11881; + t12147 = y*t11710; + t11356 = t11879*t12257; + t12084 = t11879*t12267; + t11463 = t11819*t12400; + t12608 = t11878*t12147+t11881*t12084+(t11463+t11356)*x; + t12607 = t11797*t12012+t11879*t12069+t12818; + t12372 = y*t11789; + t12128 = t11878*t12372; + t12606 = t11881*t12128+t11878*t11295+t12790*x; + t12605 = t12701+t12702; + t12604 = t12696+t12704; + t11357 = t11779*t12400; + t12603 = t11881*t12126+t11878*t11296+(t11400+t11357)*x; + t12602 = y*t12130+t11764*t12006+(t11338+t11337)*x; + t11781 = RATIONAL(-1.0,384.0); + t11788 = RATIONAL(-5.0,384.0); + t12601 = t11760*t12264+t11876*t12249+t11781*t12089+t11788*t12103; + t12600 = t12699+t12720; + t12215 = t11877*t11768; + t11348 = t11880*t12215; + t11538 = t11809*t12263; + t12599 = x*t11348+t11793*t11998+(t12113+t11538)*z; + t12598 = t12707+t12715; + t12597 = t11853*t12112+t11880*t12108+t11841*t12362+t11839*t11998; + t12011 = t11880*t12327; + t12596 = t11880*t11995+t11882*t12011+t12801; + t12595 = y*t12161+x*t11381+t12803*t11878; + t12594 = t12698+t12709; + t12593 = t12701+t12707; + t12118 = z*t12224; + t12592 = t11879*t12118+t11774*t12402+x*t11387+(t11300+t11337)*t11878; + t12591 = t11878*t11285+x*t11269+t12386*t12405+(t12118+t12046)*y; + t12590 = t11357+t11879*t12064+t11875*t12142+t12827; + t12119 = t11875*t12372; + t12083 = t11879*t12304; + t12589 = t11324+t11881*t12119+t11847*t12083+t12802; + t12028 = t11878*t12271; + t12135 = z*t12227; + t12588 = t11803*t12183+(t12028+t12135)*y+(t11290+t11604)*x; + t12155 = t11846*t12397; + t12169 = t11848*t12397; + t11620 = t11877*t11731; + t11979 = t11878*t11620+t11876*t12169+t12710; + t12587 = t11874*t12019+t11881*t12155+t11979+t12714; + t12586 = t12724+t12721+t12750; + t12358 = t11813*t12403; + t12585 = t11878*t12110+x*t11386+(t12358+t12845)*y; + t12370 = z*t11816; + t11560 = t11882*t12370; + t11359 = t11763*t12199; + t12584 = z*t12027+t11560+t11485+t11877*t12090+t11359; + t11487 = t11803*t12398; + t11517 = t11877*t12370; + t12583 = t11315+t11800*t12111+t11877*t12105+t11487+t11517; + t12071 = t11800*t12242; + t12582 = t11876*t12030+(t12339+t12071)*y+t12803; + t12581 = t11880*t12010+t11302+z*t12057+t12844; + t12580 = t12719+t12693+t12750; + t11265 = t11763*t12210; + t12579 = t11541+t11265+t11875*t11576+t11789*t12083+t11803*t12400; + t12578 = t12687+t12694+t11759*t12188+t11798*t12019+t12716; + t12577 = t11880*t12082+t11340+t11789*t12111+t12812; + t11719 = t11800*t11882; + t11507 = z*t11719; + t12576 = t11835*t12328+t11808*z+t11531+t11507+t12785*t11880; + t11700 = t11847*t11882; + t11465 = z*t11700; + t12297 = t11824*t11875; + t11417 = t11882*t12297; + t12106 = t11875*t12238; + t12575 = t11825*t12106+t11465+t11880*t11417+t11837*t12328+(t11840+t12306) +*z; + t12574 = t11808*y+t11463+t11827*t12012+t11484+t12813*t11879; + t12573 = t11576+t11824*t12012+t12807*t11879+t12830*y; + t12572 = z*t12043+t12596+t12829; + t12571 = t12607+t12744; + t12570 = t11381+t11881*t12146+t11876*t12180+t12642; + t12569 = t11765*t12238+t11798*t12111+z*t12000+t12596; + t12568 = t12665+t12681; + t12260 = t11882*t11783; + t11309 = t11876*t12260; + t11960 = t11538+t11878*t11309+t12337+t12758*x; + t12293 = t11877*t11854; + t12567 = t11960+t11878*t12293+x*t11700+t12697+t12721; + t11371 = t11881*t12313; + t11962 = t12337+t11878*t11371+t11511+t12754*x; + t11506 = t11840*t12376; + t12566 = t11962+t11506+t11488+t12689+t12724; + t12565 = t12625+t12677; + t12564 = t12625+t12675; + t12185 = t11793*t12392; + t12563 = t11876*t12185+t12640+t12841; + t12562 = t12648+t12674; + t12561 = t12652+t12743; + t11640 = t11854*t12256; + t12560 = t11962+t11640+t11527+t12697+t12719; + t11512 = t11877*t12240; + t11509 = t11882*t12378; + t12559 = t11960+t11512+t11509+t12689+t12693; + t12558 = t11364+y*t12018+t11876*t12268+t12642; + t12557 = t12652+t12745; + t12152 = z*t12270; + t11596 = t11880*t12219; + t12556 = t11839*t12152+t11361+t11596+t12670; + t12555 = y*t12069+t11881*t12120+t11876*t12246+t12640; + t12554 = t12665+t12673; + t12102 = t11854*t12270; + t12553 = t11291+z*t12102+t11809*t12111+t12670; + t12552 = t12632+t12741; + t12551 = t12648+t12680; + t12550 = t11798*t12355+y*t12011+t11879*t12051+z*t12013+t12775; + t12098 = t11878*t12238; + t12549 = t11766*t11998+z*t12048+t11799*t12098+t11877*t12118+(t12788+ +t12821)*x; + t12174 = y*t12256; + t12179 = x*t12210; + t12548 = t11846*t12363+t11768*t12179+t11879*t12020+t11809*t12174+t12608; + t12547 = t12595+t12726; + t11519 = t11880*t12204; + t11425 = t11879*t12255; + t12546 = t12610+t11880*t12359+y*t11519+(t12160+t11425)*z; + t12545 = z*t12119+t11879*t12259+t12711+t12713+t12717; + t12100 = t11879*t12256; + t12093 = t11876*t12236; + t12165 = t11796*t12376; + t12544 = y*t12093+t11795*t12363+t11789*t12100+t11879*t12165+t12606; + t12189 = y*t12242; + t12543 = t11748*t12012+t11760*t12189+t12815*t11876+t12778; + t12364 = z*t12397; + t12542 = z*t12053+t11779*t12364+x*t11359+t11880*t12074+t12650; + t12117 = x*t12321; + t12541 = t11803*t12006+t11878*t11467+(t12117+t12135)*t11879+t12794*z+ +t12796*y; + t12007 = t11880*t12196; + t12540 = t11878*t12143+z*t12155+t11877*t12007+t11880*t12181+t12633; + t12539 = z*t12084+t12196*t12404+t11793*t12006+t11768*t12356+t11792*t12402 ++t12782*t11880; + t12538 = t12598+t12626; + t12537 = t12627+t12728; + t12290 = t11823*t11881; + t11557 = t11877*t12290; + t11778 = RATIONAL(16.0,27.0); + t12134 = t11877*t12382; + t12536 = t11881*t12134+t11878*t11557+t11778*t12114+t11816*t12062+t11806* +t12019+(t12157+t12835)*t11882; + t12535 = t12649+t12732; + t12534 = t12669+x*t11329+t11878*t11262+(t12056+t12157)*y; + t12533 = t12582+t12676; + t12532 = t12630+t12637; + t12531 = (t12062+t12019)*t11751+(t12104+t12065)*t11752+t12774*x; + t12530 = t12649+t12739; + t12529 = t12661+t12734; + t12528 = t12653+t12725; + t11455 = t11880*t12255; + t12527 = t12274*t12403+y*t11455+z*t11505+t11767*t12361+t12610; + t12312 = t11876*t11820; + t12526 = t12312*t12405+(t11364+t11281)*t11878+(t12159+t12055)*t11876+( +t11588+t12824)*x; + t12525 = t12611+t12731; + t12524 = t11366+t12553; + t12175 = t11880*t12385; + t12523 = y*t11664+t11839*t12006+t11846*t12175+t11848*t12361+(t12783+ +t12753)*z; + t12522 = t12637+t12655; + t12266 = t11877*t11806; + t11495 = z*t12266; + t12038 = t11878*t12311; + t12521 = t11823*t12112+t11821*t12364+t11878*t11495+t11816*t11998+t11778* +t12362+t11877*t12038+(t12134+t12171)*t11880; + t12520 = t12603+t12671; + t12233 = t11808*t11875; + t12034 = t11880*t12233; + t12519 = t11495+t11880*t12027+t11808*t12111+t11877*t12034+t12814*z+t12808 +; + t12518 = t12607+t12649; + t12517 = t12653+t12736; + t12516 = t12603+t12613; + t12107 = t11806*t12388; + t11478 = y*t12290; + t12515 = t11876*t12107+t11778*t12354+t12819*t11881+(t11478+t11462)*t11878 ++t12835*t11879; + t11859 = RATIONAL(-2.0,9.0); + t12163 = t11859*t12392; + t12514 = t11535+t11879*t12072+t11840*t12172+z*t12163+t11467+t11476+t12810 +*y; + t12513 = t11879*t12011+y*t12051+t11798*t12172+z*t12120+t12772; + t12026 = t11878*t12324; + t12122 = y*t12296; + t12512 = y*t12029+t11876*t12026+(t11331+t12122)*t11878+(t12805+t12841)*x; + t12511 = t12627+t12738; + t12510 = y*t12038+t11879*t12124+t11821*t12356+t11778*t12402+z*t12107+ +t11816*t12006+t12819*t11880; + t12509 = t11366+t12632+t12742; + t12508 = t12672+t11876*t12126+t11879*t12063+(t11265+t12122)*x; + t12507 = t12595+t12733; + t12506 = t12588+t12683; + t12505 = t12590+t12676; + t12504 = t12593+t12659; + t12503 = t11878*t11357+t11881*t12026+y*t12021+t11879*t12035+(t12818+ +t12828)*x; + t12502 = t12615+t12628; + t12501 = t11775*t12320+t11882*t12230+t11283+t11839*t11999+t11875*t11346+( +t12219+t12799)*t11876; + t12151 = t11878*t12375; + t12002 = t11753*t12256; + t12500 = t11878*t11213+t11750*t12174+t11879*t12002+t11753*t12151+t12773*x +; + t12017 = t11875*t12200; + t12499 = t11760*t11999+t11799*t12314+t11882*t12017+t11876*t12092+t11877* +t12203+(t12231+t12822)*t11881; + t11580 = t11800*t12322; + t12498 = z*t11497+t12291*t12403+t12636+(t11580+t12148)*y; + t12497 = t11876*t12138+t11879*t12022+t12672+t12802*x; + t12347 = t11877*t11878; + t12049 = t11753*t12347; + t12190 = z*t12347; + t12496 = t11880*t12049+t11753*t12112+(t11998+t12190)*t11750+t12777*x; + t12001 = t11878*t12216; + t12495 = t11820*t12362+t11880*t12001+t11774*t11998+t11775*t12112+t11878* +t11442+(t11487+t12808)*x; + t11264 = t11764*t12199; + t12494 = t11264+t12569; + t12493 = t12621+t12632; + t12492 = t11268+t11882*t12203+t11877*t12017+t11799*t12264+t11881*t12040+ +t11748*t11999+t12822*t11876; + t11994 = t11876*t12233; + t12491 = t11808*t12189+t11847*t12012+t11879*t11994+t11478+t12839*t11876+ +t12824; + t12336 = t11876*t11814; + t12041 = t11859*t12270; + t12009 = t11840*t12304; + t12490 = t11803*t12264+t11876*t12041+t11840*t11999+(t12336+t12289)*t11877 ++(t12009+t12312+t12071)*t11882; + t11558 = t11876*t12232; + t12489 = t11800*t12012+t11558+t11840*t12189+t11879*t12009+y*t12336+t11876 +*t12163+t12809; + t12488 = t11363+t11882*t12018+t11809*t11999+t11383+t11571+t11876*t12102+ +t11881*t12044+t11370; + t12094 = t11878*t12222; + t12487 = z*t12015+t11878*t11302+t11799*t11998+t11877*t12094+(t12801+ +t12829)*x; + t11325 = t11877*t12267; + t12168 = t11792*t12389; + t12137 = t11819*t12397; + t12486 = t12599+t11882*t12168+t11880*t11325+(t12137+t11512)*z; + t12485 = t12609+t11800*t11999+t11877*t12279+t12834*t11876; + t11757 = RATIONAL(-1.0,2304.0); + t11761 = RATIONAL(1.0,2304.0); + t12073 = t11757*t12304; + t12484 = t11882*t12073+t11757*t11999+(t12089+t12103)*t11761+t12774; + t12483 = t11823*t12354+(t11328+t11329)*t11878+(t12121+t12085)*t11876+( +t11541+t11558+t11439)*x; + t12482 = t12635+t12653; + t12481 = t12611+t12730; + t12480 = t12652+t12653; + t12277 = t11879*t11819; + t12133 = x*t12277; + t11613 = t11880*t12318; + t12479 = t11880*t12133+t11809*t12006+t11843*t12402+(t12167+t11613)*y+( +t12173+t12817)*z; + t12478 = t11878*t11596+t11877*t12357+t11775*t11998+z*t12001+t11774*t12112 ++(t11560+t12831)*x; + t12477 = z*t12041+t11840*t12111+t12810*t11877+(t12381+t12072)*t11882+ +t12831; + t12476 = y*t12002+t11750*t12151+t12841*t11878+t12778*x; + t12158 = t11766*t12367; + t12475 = y*t12158+z*t12026+t11766*t12006+t11878*t11260+t12775*x; + t11735 = t11869*t11877; + t11630 = t11878*t11735; + t12474 = t11880*t12137+z*t11630+t11877*t11613+t11845*t12364+t12623; + t12473 = t12602+t12627; + t12472 = t11447+t11577+t11808*t12172+y*t12034+t11563+t11847*t12088+t12839 +*z; + t12471 = t12650+t11878*t11291+t11775*t12190+t12812*x; + t11402 = t11765*t12210; + t12470 = t11402+t12555; + t12469 = t11756*t12320+t11877*t12073+t11881*t12209+t11757*t12089+(t12076+ +t11999)*t11761+t12846*t11876; + t12468 = t11296+t12607+t12747; + t12467 = t12367*t12387+y*t12094+t11799*t12006+t11879*t12158+t12772*x; + t12466 = t12832*t11880+t12838*z+t12776; + t12465 = t11881*t12292+t11791*t11999+t11882*t12064+t11803*t12314+t12609; + t12464 = t11812*t12363+t11814*t12174+t12809*t11878+(t12177+t12050)*t11879 ++t12794*t11876; + t12463 = t11768*t12175+t11878*t12003+(t12168+t12007)*y+(t12033+t12782)*z; + t12462 = t12595+t12661; + t12461 = t11316+t11880*t12166+t12600+t12712; + t12460 = t12838*t11880+t12832*z+t12777; + t12077 = t11877*t12227; + t12459 = t11877*t12028+z*t12077+t12657+(t11264+t11259)*x; + t12458 = y*t12017+t11748*t12083+t12815*t11881+t12773; + t12457 = t11753*t11998+z*t12049+t11750*t12112+t11878*t11200+t12776*x; + t12456 = y*t12032+t11879*t12070+t12669+(t11328+t11402)*x; + t12455 = t11435+t11794*t12172+t12695+t12718+t12723; + t12334 = t11800*t11878; + t11483 = t11879*t12334; + t11583 = t11808*t12322; + t12454 = y*t11583+t11834*t12361+z*t11483+t11783*t12356+t12636; + t12453 = t12657+x*t11351+t11882*t12358+(t11297+t11517)*t11878; + t12452 = t12602+t12611; + t10451 = z*t12044; + t12451 = t10451+t12572; + t12450 = t12592+t12683; + t12449 = t12597+t11880*t12155+z*t12169+t12833*t11877; + t12448 = t11876*t12128+t11795*t12179+y*t12165+t11879*t12093+t12639; + t12447 = t11812*t12364+t11880*t12077+t11803*t11998+t11820*t12112+t11762* +t12362+t11882*t12117+t12796*t11877; + t12446 = t12620+t12666; + t11369 = t11794*t12256; + t12445 = y*t11488+t11881*t12162+t11879*t11369+t11819*t12363+t12619; + t12444 = t11296+t12570; + t12443 = t12620+t12667; + t12442 = t11557+t11808*t11999+t11881*t12027+(t12248+t11994)*t11882+( +t12266+t12814)*t11876; + t11654 = t11869*t12256; + t11660 = t11859*t12376; + t11536 = t11844*t12320; + t12441 = t11650+t11654+t11660+t11878*t11536+t12714+t12700+t12710+t12786* +t11876; + t11981 = t11796*t12019+x*t11256+t12687; + t12440 = t11325+t11795*t12104+t12694+t11882*t12196+t11981+t12779*x; + t12439 = t11369+t11981+t11368+t11795*t12065+t12716+t12781*x; + t11626 = t11859*t12397; + t11458 = t11882*t12283; + t12438 = t11636+t11630+t11626+t12700+t11878*t11458+t11979+t12806*t11877; + t12396 = x*RATIONAL(-8.0,9.0); + t12437 = t11879*t11506+t11866*t12174+t11873*t12385+t12753+t11878*t11457+ +t12668+(t11660+t12396)*y; + t11832 = RATIONAL(-5.0,48.0); + t12194 = t11832*t11876; + t12060 = t11875*t12194; + t12436 = t11815*t11999+t11881*t12293+t11882*t12060+t11874*t11877+t11834* +t12314+t11863*t12270+t12641+t12791; + t11523 = t11837*t12242; + t12435 = t11881*t12215+t11825*t11999+t11705+t11840*t11876+t11835*t12076+ +t11850*t12304+t11847*t12314+t11523+t12644; + t12315 = t11875*t11850; + t11490 = t11835*t12307; + t12434 = t11348+t12766+t11842*t12152+t12575+(t12315+t11490)*z; + t12096 = t11844*t12256; + t12433 = t12608+t11809*t12350+t11783*t12100+(t12096+t12837)*y+(t11484+ +t12793)*x; + t12276 = t11837*t11882; + t11547 = t11875*t12276; + t12432 = t11835*t11999+t11850*t12270+t11719+t11547+t12644+(t11722+t11840) +*t11877+(t12058+t12243)*t11882; + t11582 = t11828*t12328; + t12431 = t11582+t11780*t12152+t12787*t11880+(t12075+t12262)*z+t12771+ +t12792; + t12430 = t11861*t12270+t11735+t11807*t11999+t11620+t11458+t11829*t12076+ +t12638+t12800; + t12429 = t12663+t11455+t11878*t11353+z*t12334+t11768*t12190+t12771*x; + t12025 = t11878*t12306; + t12068 = t11878*t12284; + t11713 = t11809*t11882; + t12428 = t11880*t12068+t11603+t11583+t12622+z*t12025+(t11853+t11713)* +t12403+t12843*x; + t12427 = t11873*t12389+t11880*t11509+t12623+t12798*t11878+(t12396+t11626) +*z+t12833; + t12252 = t11767*t11881; + t12426 = t11477+t11877*t12252+t11794*t12314+t11710+t11780*t11999+t11828* +t12304+t12629+(t11809+t12005)*t11876; + t11598 = t11880*t12262; + t12425 = t11815*t12328+t11829*t12106+t11882*t11598+(t12066+t12791+t12820) +*z+t12804+t12843; + t12424 = t11882*t11582+t11880*t12272+t11832*t12106+(t12086+t12784+t12800) +*z+t12798+t12826; + t11723 = t11839*t11882; + t12391 = x*t11854; + t12423 = t11519+t12646+t11723*t12403+t11880*t12025+t12826*x+(t12068+ +t12391+t12342)*z; + t12422 = t11859*t12389+t12597+t11613+t12199*t12384+t12804*t11878+(t12317+ +t12786)*z; + t12421 = t11598+t11880*t12075+t11780*t12106+(t12787+t12811)*z+t12780+ +t12816; + t12420 = t11878*t12144+t11767*t12100+t12619+t11879*t12240+t12842*y+( +t11576+t12789)*x; + t12419 = t11282+t11837*t11999+t11882*t12014+t11700+t11852*t12270+t11490+ +t12631+t12758; + t12097 = t11878*t12234; + t12418 = y*t12391+t11819*t12174+t12616+t12757+t11879*t12097+(t12147+ +t12823)*x; + t11572 = t11876*t12277; + t12417 = t11712+t11591+t11572+t12573+(t11521+t12813)*y; + t12416 = t11787*t12189+t11777*t12012+t12748+t12797*t11879+(t12067+t12811) +*y+t12790; + t12415 = t11472+t12574+t12830*t11879+(t11600+t12807)*y; + t12414 = t11879*t12096+t11859*t12385+t12634+t11872*t12174+t11808*t12179+ +t12806*y+t12817; + t12413 = t11878*t11572+t12617+y*t12097+t12763+(t12373+t12184+t12825)*x; + t12412 = t11881*t12206+t11791*t11877+t11784*t11999+t11782*t12076+t11473+ +t11824*t12270+t12601+(t11789+t12288)*t11882; + t12411 = t11417+t11827*t12270+t11220+t11781*t11999+t11788*t12076+t12651+ +t12779; + t12410 = t12729+t11777*t12189+t11787*t12012+(t12067+t12346)*t11879+t12797 +*y+t12840; + t12299 = t11852*t11875; + t11569 = t11835*t12242; + t12409 = t11822*t11999+t11837*t12076+t11876*t12299+t11722+t11569+t11308+ +t12631+t12754; + t12408 = t11726+t11514+t11785*t11999+t11793*t12314+t11371+t12645+(t12075+ +t12795)*t11876; + t12407 = t12576+t12769+t11353+(t12039+t11547+t12299)*z; + t12406 = t11580+t11878*t11348+t11792*t12190+t12647+t12836*z+t12780*x; + t12345 = t11867*t11877; + t10342 = t11880*t12138; + t10375 = t11881*t12141; + t12341 = t10342+t10375; + t10419 = t11878*t11367; + t10357 = t11881*t12185; + t12332 = t10419+t10357; + t12331 = t11829*t11877; + t12310 = t11832*t11882; + t12305 = t11828*t11882; + t12295 = t11833*t11881; + t12294 = t11832*t11881; + t10556 = t11879*t12130; + t12286 = t10451+t10556; + t12258 = t11831*t11881; + t12247 = t11833*t11882; + t10416 = t11794*t12111; + t12217 = t10549+t10416; + t12170 = x*t12320; + t12164 = t11783*t12376; + t12078 = t11878*t12243; + t11433 = t11807*t12242; + t11993 = t11296+t12684; + t11992 = t10357+t12686; + t11991 = t10375+t12679; + t11988 = t10342+t12686; + t11987 = t10416+t12676; + t11985 = t10419+t12679; + t11984 = t10416+t12685; + t11983 = t10451+t12685; + t11980 = t11366+t12684; + t11978 = t11402+t12684; + t11977 = t11264+t12683; + t11976 = t11807+t11832*t11877+t12305; + t11975 = t12331+t12752; + t11790 = RATIONAL(25.0,96.0); + t11974 = t11838+t11825*t11882+t11790*t11877; + t11973 = t11852+t11838*t11876+t11837*t11881; + t11802 = RATIONAL(-5.0,16.0); + t11857 = RATIONAL(1.0,4.0); + t11801 = RATIONAL(1.0,16.0); + t11972 = t11857+t11801*t11881+t11802*t11876; + t11971 = t11838+t11825*t11881+t11790*t11876; + t11776 = RATIONAL(-25.0,96.0); + t11970 = t11776*t11876+t11842+t11822*t11881; + t11969 = t11842*t11876+t11850+t11835*t11881; + t11968 = t11842+t11822*t11882+t11776*t11877; + t11871 = RATIONAL(2.0,3.0); + t11967 = t11852*t11881+t11864*t11876+t11871; + t11966 = t12229+t12749; + t11965 = t12192+t11815+t12258; + t11964 = t11807+t12218+t12194; + t11770 = RATIONAL(25.0,32.0); + t11810 = RATIONAL(-5.0,32.0); + t11855 = RATIONAL(-5.0,8.0); + t11963 = t11855+t11810*t11881+t11770*t11876; + t11961 = t11836*t12170+t11842*t12104+t11850*t12263+t11860*t12401+t12706; + t11959 = t11825*t12104+x*t12331+t11780*t12170+t11882*t12254+t12703; + t11958 = t12615+t12635; + t11957 = t12593+t12603; + t11956 = t12594+t12667; + t11955 = t12594+t12666; + t11954 = t12594+t12665; + t11953 = t12593+t12621; + t11952 = t12598+t12637; + t11951 = t12648+t12698+t12722; + t11950 = t12598+t12625; + t11754 = RATIONAL(25.0,192.0); + t11949 = t11835*t12256+t11827*t12104+x*t12294+t11754*t12170+t12618+t12703 ++t12708; + t11772 = RATIONAL(-25.0,48.0); + t11948 = t11852*t12065+t11772*t12191+t11871*t12347+x*t12247+t11961+t12690 +; + t11947 = x*t12295+t11852*t12104+t11871*t12256+t11772*t12170+t12660+t12690 ++t12706; + t11946 = t11835*t12347+t11827*t12065+x*t12310+t11754*t12191+t11959+t12708 +; + t11945 = t12647+t12578+t12760*t11880+t12761*z; + t11944 = t11877*t11603+t12260*t12403+t12586+t12646+t12770*t11880; + t11943 = t11848*t12363+t11846*t12179+t12587+t12634+t12753*t11876; + t11942 = t12586+t11877*t11519+t11882*t12148+t12622+t12770*z; + t11941 = t12578+t12663+t12761*t11880+t12760*z; + t11940 = t12580+t12616+t11881*t12160+y*t12164+t12763*t11876; + t11939 = t12580+t12252*t12405+t11879*t12164+t12617+t12757*t11876; + t11938 = t11881*t12133+y*t11654+t11845*t12363+t11879*t11640+t12587+t12668 +; + t11937 = t12618+t11777*t12188+t11838*t12256+t11790*t12019+t11959+t12765* +t11878+(t12258+t12752)*x; + t11786 = RATIONAL(-25.0,24.0); + t11936 = t11807*t12188+t12660+t11961+RATIONAL(4.0,3.0)*x+t11786*t12019+( +t12376+t12397)*t11861+(t12345+t12749)*t11878; + t11935 = t11828*t12270+t11723+t12559+t11706+t11787*t11999+t11876*t12220+ +t11794*t12320+t12629+t12797*t11882; + t11934 = t12439+t11759*t12320+t11521+t11789*t11881+t12601+t11782*t11999+( +t11997+t12207+t12297+t11791)*t11876; + t11933 = t11869*t11876+t11829*t11999+t11853*t12314+t12441+t11536+t11861* +t12304+t11807*t12076+t12638+t12759; + t11932 = t12566+t11825*t12152+t11846*t12238+t11840*t11880+t11847*t12199+ +t12576+(t11417+t12348)*z; + t11931 = t11288+t12573+t12567+(t12315+t11569+t12079)*y+t12789; + t11930 = t12438+t11833*t12187+t11828*t12012+t11457+(t12060+t12272)*t11879 ++(t12226+t12759+t12784)*y+t12823; + t11929 = t11483+t12440+t11792*t12174+t11879*t12078+t12606+t12836*y+t12748 +*x; + t11928 = t12439+t11600+t11827*t12304+t11781*t12076+t11788*t11999+t11254+ +t12651+t12781; + t11927 = t12566+t11808*t11880+t11800*t12199+t11819*t12238+t12575+(t12330+ +t12785)*z; + t11926 = t11878*t12178+t11880*t12240+t11767*t12098+t12560+t12599+t12842*z ++(t11465+t12766)*x; + t11925 = t11874*t11876+t11815*t12076+t12441+t11731+t11854*t12314+t11881* +t12278+t11863*t12304+t11433+t11832*t11999+t12641; + t11924 = t11356+t12574+t11838*t12187+t12567+(t11523+t12299)*y+t12793; + t11923 = t11309+t11881*t12269+t11882*t12067+t12559+t11875*t12305+t11713+ +t11777*t11999+t12645+t12795*t11877; + t11922 = t12639+t12440+t11425+t11878*t11356+(t12334+t12078)*y+t12729*x; + t11921 = t11783*t12098+t12560+t12633+(t12253+t12186)*t11878+t12837*z+( +t11507+t12769)*x; + t11920 = t11673+t11561+t12438+t11831*t12012+t11829*t12083+t11815*t12349+ +t11872*t12400+t11836*t12187+(t11433+t12820)*y+t12825; + t11919 = t11954+t12465+t10419+t12604+t12620+t12673+t12727; + t11918 = t11264+t12570+t11993+t11951+t12585+t12674+t12691+t12704; + t11917 = t12509+t12504+t12508+t12545; + t11916 = t11954+t12556+t10556+t11984+t12579+t12664+t12681; + t11915 = t12476+t12496+t12467+t12531; + t11914 = t12518+t11952+t10357+t12626+t12655+t12739+t12744; + t11913 = t12584+t10342+t10357+t11956+t12558+t12604+t12678+t12679; + t11912 = t11957+t12468+t12492+t12659+t12671; + t11911 = t12483+t11955+t10375+t12561+t12604+t12643; + t11910 = t12452+t11953+t12614+t12662+t12731+t12735; + t11909 = t12497+t12487+t10556+t11950+t12605+t12677; + t11908 = t12538+t12503+t12461+t12577+t12679; + t11907 = t12521+t12477+t12490+t12536; + t11906 = t12495+t12534+t11956+t12654+t12664; + t11905 = t12506+t11958+t12501+t12624+t12628; + t11904 = t11955+t12547+t12533+t12656+t12664; + t11903 = t12489+t12464+t12442+t12536; + t11902 = t12485+t10451+t12478+t11951+t12680+t12692+t12709; + t11901 = t12460+t12531+t12500+t12550; + t11900 = t12581+t12563+t10419+t10375+t11950+t12626+t12675+t12686; + t11899 = t12524+t12502+t12462+t12733+t12734; + t11898 = t12475+t12466+t12531+t12543; + t11897 = t12513+t12458+t12457+t12531; + t11896 = t12538+t12512+t12471+t10342+t12602+t12740; + t11895 = t12494+t12504+t11978+t12555+t12591; + t11894 = t12491+t12510+t12519+t12536; + t11893 = t12505+t11957+t12511+t12613+t12662; + t11892 = t11952+t12549+t12589+t12605+t12630+t12685; + t11891 = t12499+t12450+t11953+t12658+t12659; + t11890 = t12536+t12515+t12447+t12541; + t11889 = t11958+t12526+t12583+t12612+t12686+t12696+t12709; + t11888 = t11402+t12502+t12488+t12456+t12557; + t11868 = RATIONAL(-1.0,8.0); + t11858 = RATIONAL(1.0,8.0); + t11856 = RATIONAL(5.0,3.0); + t11851 = RATIONAL(5.0,8.0); + t11849 = RATIONAL(-5.0,4.0); + t11830 = RATIONAL(-1.0,16.0); + t11826 = RATIONAL(5.0,64.0); + t11818 = RATIONAL(5.0,32.0); + t11817 = RATIONAL(5.0,16.0); + t11805 = RATIONAL(-5.0,64.0); + t11804 = RATIONAL(25.0,8.0); + t11773 = RATIONAL(25.0,48.0); + t11769 = RATIONAL(-25.0,12.0); + coeffs_dx->coeff_m2_m2_m2 = t11897+t12460+t12475+t12469+t12476; + coeffs_dx->coeff_m1_m2_m2 = t11912+t12535+t11977+t12545+t12569+t12592; + coeffs_dx->coeff_0_m2_m2 = t11945+t12539+t12544; + coeffs_dx->coeff_p1_m2_m2 = t12509+t11891+t12470+t12520+t12535; + coeffs_dx->coeff_p2_m2_m2 = t12476+t12457+t12484+t11898+t12550; + coeffs_dx->coeff_m2_m1_m2 = t11914+t12512+t12481+t11985+t12564+t12577; + coeffs_dx->coeff_m1_m1_m2 = t12217+t12556+t11904+t12443+t12478+t12682+ +t12737; + coeffs_dx->coeff_0_m1_m2 = t12445+t11944+t12546; + coeffs_dx->coeff_p1_m1_m2 = t12455+t11902+t12579+t12547+t12654+t12667+ +t12685; + coeffs_dx->coeff_p2_m1_m2 = t11900+t12512+t12530+t12461+t12537; + coeffs_dx->coeff_m2_0_m2 = t12406+t12431+t11934; + coeffs_dx->coeff_m1_0_m2 = t11932+t12423+t12408; + coeffs_dx->coeff_0_0_m2 = t11949+(t11968*t11880+t11974*z)*x+(t11975* +t11880+t11976*z)*t11878; + coeffs_dx->coeff_p1_0_m2 = t12426+t12423+t11927; + coeffs_dx->coeff_p2_0_m2 = t11928+t12421+t12406; + coeffs_dx->coeff_m2_p1_m2 = t11908+t12452+t12563+t12530+t12341+t12730+ +t12740; + coeffs_dx->coeff_m1_p1_m2 = t11916+t12455+t12478+t12534+t12656+t12666; + coeffs_dx->coeff_0_p1_m2 = t12454+t11944+t12548; + coeffs_dx->coeff_p1_p1_m2 = t11902+t12568+t10556+t12534+t12533+t12620+ +t12737; + coeffs_dx->coeff_p2_p1_m2 = t11914+t11988+t12503+t12473+t12581+t12728+ +t12740; + coeffs_dx->coeff_m2_p2_m2 = t12457+t11901+t12467+t12469+t12543; + coeffs_dx->coeff_m1_p2_m2 = t12535+t11895+t12492+t12508+t12621+t12658; + coeffs_dx->coeff_0_p2_m2 = t11945+t12448+t12463; + coeffs_dx->coeff_p1_p2_m2 = t12499+t11917+t12518+t11993+t12591+t12732+ +t12747; + coeffs_dx->coeff_p2_p2_m2 = t11897+t12484+t12466+t12467+t12500; + coeffs_dx->coeff_m2_m2_m1 = t12516+t12286+t11892+t12525+t12565+t12572; + coeffs_dx->coeff_m1_m2_m1 = t12453+t11911+t11988+t12443+t12583+t12678+ +t12727; + coeffs_dx->coeff_0_m2_m1 = t12486+t11940+t12527; + coeffs_dx->coeff_p1_m2_m1 = t12465+t12453+t12483+t11913+t12612+t12635; + coeffs_dx->coeff_p2_m2_m1 = t12493+t11893+t10416+t10556+t12549+t12565+ +t12614+t12741; + coeffs_dx->coeff_m2_m1_m1 = t11899+t11978+t12501+t12459+t12557+t12585; + coeffs_dx->coeff_m1_m1_m1 = t11903+t12472+t12477+t12447+t12510; + coeffs_dx->coeff_0_m1_m1 = t12474+t11938+t12523; + coeffs_dx->coeff_p1_m1_m1 = t12464+t11894+t12447+t12490+t12514; + coeffs_dx->coeff_p2_m1_m1 = t12507+t12488+t11918+t12459+t12624+t12635; + coeffs_dx->coeff_m2_0_m1 = t12435+t12407+t11926; + coeffs_dx->coeff_m1_0_m1 = t12424+t12427+t11933; + coeffs_dx->coeff_0_0_m1 = t11947+((t12276+t12765)*t11880+(t11870+t12345+ +t11850*t11882)*z)*t11878+((t11773*t11877+t12310+t11836)*t11880+(t11769*t11877+ +t12247+t11856)*z)*x; + coeffs_dx->coeff_p1_0_m1 = t12425+t11925+t12427; + coeffs_dx->coeff_p2_0_m1 = t12434+t12409+t11926; + coeffs_dx->coeff_m2_p1_m1 = t12444+t11905+t12456+t12459+t12524; + coeffs_dx->coeff_m1_p1_m1 = t12491+t11890+t12477+t12442+t12514; + coeffs_dx->coeff_0_p1_m1 = t12474+t11943+t12479; + coeffs_dx->coeff_p1_p1_m1 = t12472+t12489+t11890+t12490+t12519; + coeffs_dx->coeff_p2_p1_m1 = t12529+t11888+t11977+t12459+t12562+t12588; + coeffs_dx->coeff_m2_p2_m1 = t12451+t12505+t12497+t11910+t12549; + coeffs_dx->coeff_m1_p2_m1 = t11889+t12453+t12554+t12332+t12558+t12643+ +t12666; + coeffs_dx->coeff_0_p2_m1 = t11939+t12486+t12498; + coeffs_dx->coeff_p1_p2_m1 = t11919+t12453+t11991+t12526+t12561+t12584; + coeffs_dx->coeff_p2_p2_m1 = t12217+t12552+t12497+t11892+t12473+t12738+ +t12746; + coeffs_dx->coeff_m2_m2_0 = t12410+t11929+t12412; + coeffs_dx->coeff_m1_m2_0 = t12418+t12415+t11923; + coeffs_dx->coeff_0_m2_0 = (t11965*t11879+t11964*y)*t11878+t11946+(t11970* +t11879+t11971*y)*x; + coeffs_dx->coeff_p1_m2_0 = t12417+t11935+t12418; + coeffs_dx->coeff_p2_m2_0 = t12411+t12416+t11929; + coeffs_dx->coeff_m2_m1_0 = t11924+t12432+t12420; + coeffs_dx->coeff_m1_m1_0 = t11930+t12430+t12437; + coeffs_dx->coeff_0_m1_0 = t11948+(t11973*t11879+t11966*y)*t11878+((t11836 ++t12294+t11773*t11876)*t11879+(t12295+t11769*t11876+t11856)*y)*x; + coeffs_dx->coeff_p1_m1_0 = t12436+t11920+t12437; + coeffs_dx->coeff_p2_m1_0 = t11931+t12420+t12419; + coeffs_dx->coeff_m2_0_0 = t11937+(t11787*t11881+t11828+t12261)*t11882+( +t11754*t11876+t11785*t11881+t11832)*t11877+(RATIONAL(-1.0,4.0)+t11830*t11881+ +t11817*t11876+(t11817+t11826*t11881+RATIONAL(-25.0,64.0)*t11876)*t11877+(t11830 ++t11826*t11876+RATIONAL(-1.0,64.0)*t11881)*t11882)*t11875+t11964; + coeffs_dx->coeff_m1_0_0 = (t11867+t11786*t11876+t11842*t11881)*t11877+ +t11936+(RATIONAL(1.0,2.0)+t11858*t11881+t11855*t11876+t11963*t11877+(t11810* +t11876+t11858+RATIONAL(1.0,32.0)*t11881)*t11882)*t11875+t11969*t11882+t11966; + coeffs_dx->coeff_0_0_0 = (1.0+t11849*t11876+t11857*t11881+(t11802*t11881+ +RATIONAL(25.0,16.0)*t11876+t11849)*t11877+t11972*t11882)*t11878+(t11804*t11876+ +t11855*t11881+RATIONAL(-5.0,2.0)+(t11804+RATIONAL(-125.0,32.0)*t11876+t11770* +t11881)*t11877+t11963*t11882)*x; + coeffs_dx->coeff_p1_0_0 = t11973*t11882+(RATIONAL(25.0,24.0)*t11876+ +t11838*t11881+t11864)*t11877+t11936+(t11868*t11881+RATIONAL(-1.0,2.0)+t11851* +t11876+(RATIONAL(-25.0,32.0)*t11876+t11818*t11881+t11851)*t11877+(RATIONAL(-1.0 +,32.0)*t11881+t11818*t11876+t11868)*t11882)*t11875+t11967; + coeffs_dx->coeff_p2_0_0 = t11937+((RATIONAL(25.0,64.0)*t11876+t11802+ +t11805*t11881)*t11877+(t11805*t11876+t11801+RATIONAL(1.0,64.0)*t11881)*t11882+ +t11972)*t11875+(t11831+t11780*t11876+t11777*t11881)*t11882+(t11755*t11876+ +t11780*t11881+t11829)*t11877+t11965; + coeffs_dx->coeff_m2_p1_0 = t11931+t12433+t12432; + coeffs_dx->coeff_m1_p1_0 = t12414+t11920+t12430; + coeffs_dx->coeff_0_p1_0 = t11948+((t11833+t11829*t11881+t11772*t11876)* +t11879+(t11836*t11881+t11860+t11771*t11876)*y)*x+(t11969*t11879+t11967*y)* +t11878; + coeffs_dx->coeff_p1_p1_0 = t12436+t11930+t12414; + coeffs_dx->coeff_p2_p1_0 = t11924+t12433+t12419; + coeffs_dx->coeff_m2_p2_0 = t12416+t12412+t11922; + coeffs_dx->coeff_m1_p2_0 = t12417+t12413+t11923; + coeffs_dx->coeff_0_p2_0 = t11946+(t11971*t11879+t11970*y)*x+(t11964* +t11879+t11965*y)*t11878; + coeffs_dx->coeff_p1_p2_0 = t11935+t12415+t12413; + coeffs_dx->coeff_p2_p2_0 = t12410+t12411+t11922; + coeffs_dx->coeff_m2_m2_p1 = t12516+t12487+t11910+t11984+t12552+t12589; + coeffs_dx->coeff_m1_m2_p1 = t12482+t11911+t12554+t11985+t12584+t12612+ +t12736; + coeffs_dx->coeff_0_m2_p1 = t11940+t12498+t12540; + coeffs_dx->coeff_p1_m2_p1 = t11919+t12517+t12483+t11992+t12558+t12583; + coeffs_dx->coeff_p2_m2_p1 = t12451+t11893+t12487+t12532+t12602+t12735; + coeffs_dx->coeff_m2_m1_p1 = t11264+t11402+t12562+t11905+t12507+t12480+ +t12725+t12745; + coeffs_dx->coeff_m1_m1_p1 = t12521+t11903+t12519+t12514+t12541; + coeffs_dx->coeff_0_m1_p1 = t12449+t11938+t12479; + coeffs_dx->coeff_p1_m1_p1 = t12491+t12472+t11907+t12464+t12541; + coeffs_dx->coeff_p2_m1_p1 = t12444+t12506+t11899+t12488+t12528; + coeffs_dx->coeff_m2_0_p1 = t12435+t11921+t12434; + coeffs_dx->coeff_m1_0_p1 = t12425+t12422+t11933; + coeffs_dx->coeff_0_0_p1 = ((t11772*t11877+t11833+t11829*t11882)*t11880+( +t11836*t11882+t11771*t11877+t11860)*z)*x+t11947+((t11850+t11835*t11882+t11842* +t11877)*t11880+(t11864*t11877+t11852*t11882+t11871)*z)*t11878; + coeffs_dx->coeff_p1_0_p1 = t12424+t11925+t12422; + coeffs_dx->coeff_p2_0_p1 = t11921+t12407+t12409; + coeffs_dx->coeff_m2_p1_p1 = t12528+t12456+t12501+t11918+t12529; + coeffs_dx->coeff_m1_p1_p1 = t12472+t12442+t12515+t11894+t12521; + coeffs_dx->coeff_0_p1_p1 = t11943+t12449+t12523; + coeffs_dx->coeff_p1_p1_p1 = t12489+t12510+t11907+t12514+t12515; + coeffs_dx->coeff_p2_p1_p1 = t12482+t12553+t11980+t11888+t12585+t12624+ +t12725; + coeffs_dx->coeff_m2_p2_p1 = t11909+t11987+t12532+t12525+t12552+t12590; + coeffs_dx->coeff_m1_p2_p1 = t12517+t12446+t11913+t12526+t12643+t12727; + coeffs_dx->coeff_0_p2_p1 = t11939+t12527+t12540; + coeffs_dx->coeff_p1_p2_p1 = t11889+t12465+t12480+t12341+t12667+t12678+ +t12736+t12743; + coeffs_dx->coeff_p2_p2_p1 = t11909+t12572+t11983+t12511+t12589+t12600+ +t12762+t12767; + coeffs_dx->coeff_m2_m2_p2 = t12458+t11915+t12466+t12469+t12550; + coeffs_dx->coeff_m1_m2_p2 = t12493+t11912+t12542+t11980+t12591+t12658+ +t12742; + coeffs_dx->coeff_0_m2_p2 = t11941+t12463+t12544; + coeffs_dx->coeff_p1_m2_p2 = t12499+t12542+t11895+t12520+t12545; + coeffs_dx->coeff_p2_m2_p2 = t12513+t12460+t12484+t11915+t12543; + coeffs_dx->coeff_m2_m1_p2 = t11896+t12481+t12461+t11992+t12571+t12581; + coeffs_dx->coeff_m1_m1_p2 = t12455+t12495+t11904+t12286+t12551+t12568; + coeffs_dx->coeff_0_m1_p2 = t11942+t12445+t12454; + coeffs_dx->coeff_p1_m1_p2 = t11916+t12495+t12462+t12485+t12726+t12756+ +t12768; + coeffs_dx->coeff_p2_m1_p2 = t11896+t12522+t11991+t12537+t12563+t12577; + coeffs_dx->coeff_m2_0_p2 = t12429+t12421+t11934; + coeffs_dx->coeff_m1_0_p2 = t12428+t12408+t11927; + coeffs_dx->coeff_0_0_p2 = t11949+(t11974*t11880+t11968*z)*x+(t11976* +t11880+t11975*z)*t11878; + coeffs_dx->coeff_p1_0_p2 = t12428+t11932+t12426; + coeffs_dx->coeff_p2_0_p2 = t11928+t12429+t12431; + coeffs_dx->coeff_m2_p1_p2 = t11900+t12481+t12471+t12503+t12522; + coeffs_dx->coeff_m1_p1_p2 = t11906+t12446+t11983+t12551+t12579+t12656+ +t12737; + coeffs_dx->coeff_0_p1_p2 = t11942+t12546+t12548; + coeffs_dx->coeff_p1_p1_p2 = t11906+t11987+t12455+t12485+t12556+t12582; + coeffs_dx->coeff_p2_p1_p2 = t11908+t12564+t12537+t12471+t12332+t12571; + coeffs_dx->coeff_m2_p2_p2 = t12496+t11898+t12469+t12500+t12513; + coeffs_dx->coeff_m1_p2_p2 = t11917+t12492+t12450+t12470+t12542; + coeffs_dx->coeff_0_p2_p2 = t12448+t11941+t12539; + coeffs_dx->coeff_p1_p2_p2 = t12494+t11891+t12468+t12508+t12542; + coeffs_dx->coeff_p2_p2_p2 = t12458+t12475+t12484+t11901+t12496; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxx.compute.c new file mode 100644 index 0000000..f89b946 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxx.compute.c @@ -0,0 +1,2321 @@ +fp t19297; +fp t19389; +fp t19725; +fp t19263; +fp t20254; +fp t19327; +fp t19387; +fp t19690; +fp t20253; +fp t19390; +fp t19394; +fp t20252; +fp t19345; +fp t19671; +fp t19601; +fp t19306; +fp t19662; +fp t19391; +fp t19392; +fp t19497; +fp t20251; +fp t20250; +fp t19303; +fp t19757; +fp t19304; +fp t19729; +fp t20249; +fp t19289; +fp t19395; +fp t20248; +fp t19393; +fp t19713; +fp t19507; +fp t19778; +fp t19618; +fp t20234; +fp t19743; +fp t19790; +fp t18792; +fp t20247; +fp t20246; +fp t19322; +fp t19329; +fp t20245; +fp t19309; +fp t19315; +fp t19714; +fp t20244; +fp t19300; +fp t19205; +fp t19542; +fp t19276; +fp t19724; +fp t20243; +fp t19861; +fp t19631; +fp t20242; +fp t19839; +fp t19374; +fp t19318; +fp t20241; +fp t19529; +fp t19367; +fp t19585; +fp t20240; +fp t19320; +fp t20239; +fp t19264; +fp t19265; +fp t20238; +fp t19770; +fp t20237; +fp t19295; +fp t19750; +fp t20236; +fp t19372; +fp t19777; +fp t19764; +fp t19373; +fp t20235; +fp t19853; +fp t19356; +fp t19841; +fp t19177; +fp t20233; +fp t19293; +fp t19767; +fp t19336; +fp t20232; +fp t19384; +fp t19863; +fp t19358; +fp t19868; +fp t19137; +fp t20231; +fp t19852; +fp t19313; +fp t19870; +fp t19077; +fp t20230; +fp t19292; +fp t19340; +fp t19669; +fp t19028; +fp t20229; +fp t20228; +fp t19342; +fp t19858; +fp t19331; +fp t19850; +fp t20227; +fp t19278; +fp t19298; +fp t20226; +fp t19330; +fp t19673; +fp t20225; +fp t19376; +fp t19371; +fp t19819; +fp t20224; +fp t20223; +fp t19321; +fp t19866; +fp t19334; +fp t19221; +fp t19636; +fp t20222; +fp t19842; +fp t19731; +fp t18973; +fp t20221; +fp t19678; +fp t19573; +fp t19833; +fp t19658; +fp t20220; +fp t19860; +fp t19632; +fp t19705; +fp t19112; +fp t20219; +fp t19706; +fp t19352; +fp t19522; +fp t19266; +fp t19786; +fp t20218; +fp t19299; +fp t19854; +fp t19830; +fp t19344; +fp t19762; +fp t19565; +fp t20217; +fp t19547; +fp t19317; +fp t19721; +fp t20216; +fp t19650; +fp t19642; +fp t20215; +fp t19879; +fp t19202; +fp t19604; +fp t18235; +fp t19695; +fp t20214; +fp t19775; +fp t18997; +fp t19602; +fp t20213; +fp t19530; +fp t19274; +fp t19682; +fp t20212; +fp t19206; +fp t18130; +fp t19702; +fp t19571; +fp t20211; +fp t19223; +fp t19581; +fp t19881; +fp t19758; +fp t18571; +fp t20210; +fp t19672; +fp t19734; +fp t19527; +fp t19505; +fp t19325; +fp t19760; +fp t19679; +fp t20209; +fp t19208; +fp t18227; +fp t20208; +fp t19851; +fp t19113; +fp t20207; +fp t19233; +fp t19603; +fp t19203; +fp t19610; +fp t20206; +fp t19234; +fp t19580; +fp t19845; +fp t19593; +fp t20088; +fp t19314; +fp t19226; +fp t19645; +fp t20205; +fp t19824; +fp t19231; +fp t19635; +fp t20087; +fp t20204; +fp t19739; +fp t19634; +fp t20203; +fp t19370; +fp t19375; +fp t20202; +fp t19878; +fp t19619; +fp t19867; +fp t19584; +fp t20201; +fp t19747; +fp t19640; +fp t18364; +fp t19228; +fp t20200; +fp t19569; +fp t19820; +fp t19592; +fp t20199; +fp t19772; +fp t19576; +fp t19201; +fp t18883; +fp t19783; +fp t19588; +fp t20103; +fp t20198; +fp t20197; +fp t19612; +fp t20196; +fp t19549; +fp t19275; +fp t19753; +fp t20195; +fp t19754; +fp t19277; +fp t20194; +fp t20193; +fp t19831; +fp t19822; +fp t18501; +fp t19217; +fp t20192; +fp t19211; +fp t18793; +fp t19209; +fp t19590; +fp t20102; +fp t19835; +fp t19829; +fp t20191; +fp t18140; +fp t20190; +fp t19864; +fp t19607; +fp t18339; +fp t20189; +fp t19089; +fp t20188; +fp t20187; +fp t18799; +fp t19577; +fp t20110; +fp t19614; +fp t20186; +fp t20185; +fp t19712; +fp t18875; +fp t20094; +fp t20184; +fp t19524; +fp t20183; +fp t19518; +fp t20082; +fp t20182; +fp t19806; +fp t19656; +fp t20181; +fp t19606; +fp t20099; +fp t19600; +fp t20180; +fp t20179; +fp t19807; +fp t19836; +fp t19821; +fp t20178; +fp t20177; +fp t19637; +fp t20176; +fp t20175; +fp t19827; +fp t20174; +fp t19813; +fp t19586; +fp t18229; +fp t19210; +fp t20173; +fp t19856; +fp t19823; +fp t19227; +fp t19621; +fp t20172; +fp t19766; +fp t19589; +fp t20171; +fp t18494; +fp t20170; +fp t19880; +fp t19514; +fp t18253; +fp t20169; +fp t19625; +fp t19232; +fp t20168; +fp t18562; +fp t20167; +fp t19273; +fp t19663; +fp t19567; +fp t19290; +fp t19689; +fp t20166; +fp t19271; +fp t19816; +fp t19653; +fp t19815; +fp t19639; +fp t19261; +fp t19622; +fp t19795; +fp t19661; +fp t20165; +fp t19115; +fp t19361; +fp t19857; +fp t19616; +fp t19626; +fp t19382; +fp t20164; +fp t19305; +fp t19735; +fp t19704; +fp t19498; +fp t20163; +fp t19844; +fp t19596; +fp t19659; +fp t20162; +fp t19641; +fp t20161; +fp t19703; +fp t19696; +fp t19556; +fp t20160; +fp t19219; +fp t19097; +fp t20159; +fp t19241; +fp t19552; +fp t19874; +fp t19244; +fp t19655; +fp t20158; +fp t19843; +fp t20157; +fp t19629; +fp t18451; +fp t20156; +fp t20155; +fp t20154; +fp t20153; +fp t19360; +fp t19246; +fp t19597; +fp t19258; +fp t19599; +fp t19388; +fp t19865; +fp t19544; +fp t20152; +fp t19726; +fp t19876; +fp t19575; +fp t18569; +fp t20151; +fp t19587; +fp t20150; +fp t19630; +fp t20149; +fp t19840; +fp t19825; +fp t20148; +fp t19872; +fp t19828; +fp t19617; +fp t19046; +fp t20147; +fp t18735; +fp t18762; +fp t18742; +fp t20146; +fp t20145; +fp t19285; +fp t20144; +fp t20143; +fp t19566; +fp t20142; +fp t19091; +fp t20141; +fp t18969; +fp t20140; +fp t20139; +fp t18935; +fp t20138; +fp t19710; +fp t19698; +fp t19535; +fp t20100; +fp t19838; +fp t19286; +fp t19761; +fp t19496; +fp t20097; +fp t19993; +fp t19471; +fp t19765; +fp t19495; +fp t19871; +fp t20137; +fp t19504; +fp t20089; +fp t19862; +fp t19742; +fp t19536; +fp t20069; +fp t19466; +fp t19811; +fp t19613; +fp t18466; +fp t19751; +fp t20136; +fp t19532; +fp t19805; +fp t20061; +fp t19973; +fp t19475; +fp t19763; +fp t19717; +fp t19543; +fp t20135; +fp t19541; +fp t19533; +fp t19468; +fp t20134; +fp t19665; +fp t20010; +fp t20133; +fp t19817; +fp t19736; +fp t20132; +fp t19555; +fp t18544; +fp t19728; +fp t20131; +fp t19579; +fp t19508; +fp t19513; +fp t20130; +fp t19582; +fp t19812; +fp t20129; +fp t19720; +fp t19564; +fp t20128; +fp t19572; +fp t20127; +fp t19326; +fp t19686; +fp t20126; +fp t19272; +fp t20125; +fp t19875; +fp t19537; +fp t20124; +fp t19849; +fp t20123; +fp t19748; +fp t19545; +fp t20122; +fp t19379; +fp t20121; +fp t19722; +fp t19620; +fp t19627; +fp t19676; +fp t19801; +fp t19526; +fp t20120; +fp t19553; +fp t20119; +fp t19550; +fp t20118; +fp t19803; +fp t19638; +fp t20117; +fp t20116; +fp t19738; +fp t19502; +fp t20115; +fp t19649; +fp t19709; +fp t19594; +fp t19519; +fp t20114; +fp t19694; +fp t19826; +fp t20113; +fp t19818; +fp t20112; +fp t20111; +fp t19814; +fp t20109; +fp t19568; +fp t19332; +fp t19802; +fp t19624; +fp t20107; +fp t19288; +fp t19269; +fp t20106; +fp t19346; +fp t19779; +fp t20105; +fp t19341; +fp t19746; +fp t19633; +fp t20104; +fp t19338; +fp t19646; +fp t19333; +fp t20101; +fp t19809; +fp t19605; +fp t19328; +fp t19859; +fp t19628; +fp t20098; +fp t20096; +fp t20095; +fp t19609; +fp t20093; +fp t20092; +fp t19351; +fp t19737; +fp t20090; +fp t19499; +fp t20086; +fp t19363; +fp t20084; +fp t20083; +fp t19378; +fp t19591; +fp t20081; +fp t18878; +fp t20080; +fp t19652; +fp t20079; +fp t20078; +fp t19319; +fp t20077; +fp t20076; +fp t20075; +fp t20074; +fp t18918; +fp t20073; +fp t19282; +fp t19727; +fp t19381; +fp t20072; +fp t19380; +fp t19611; +fp t20071; +fp t19324; +fp t20070; +fp t19224; +fp t20068; +fp t20066; +fp t19699; +fp t20065; +fp t19291; +fp t20064; +fp t20063; +fp t19789; +fp t19359; +fp t20062; +fp t19337; +fp t20060; +fp t19525; +fp t20058; +fp t19353; +fp t19687; +fp t20057; +fp t19294; +fp t19523; +fp t20056; +fp t19270; +fp t20055; +fp t19796; +fp t19510; +fp t19643; +fp t20054; +fp t19681; +fp t19837; +fp t19598; +fp t20053; +fp t20052; +fp t19873; +fp t19752; +fp t19517; +fp t20051; +fp t19349; +fp t19787; +fp t19546; +fp t19339; +fp t19664; +fp t19693; +fp t19506; +fp t20050; +fp t20049; +fp t19141; +fp t19846; +fp t20048; +fp t19302; +fp t19503; +fp t19301; +fp t19719; +fp t20047; +fp t19027; +fp t18961; +fp t20046; +fp t20045; +fp t19528; +fp t19745; +fp t20044; +fp t20043; +fp t19348; +fp t19165; +fp t19350; +fp t20042; +fp t19797; +fp t19691; +fp t19647; +fp t20041; +fp t19574; +fp t20040; +fp t19215; +fp t18900; +fp t19316; +fp t19366; +fp t19741; +fp t20039; +fp t20038; +fp t20037; +fp t19793; +fp t19184; +fp t20036; +fp t19804; +fp t19187; +fp t19718; +fp t19744; +fp t18990; +fp t19855; +fp t20035; +fp t19755; +fp t19118; +fp t20034; +fp t20033; +fp t20032; +fp t19810; +fp t19129; +fp t20031; +fp t20030; +fp t19386; +fp t19733; +fp t19368; +fp t19357; +fp t20029; +fp t20028; +fp t20027; +fp t20026; +fp t20025; +fp t20024; +fp t18535; +fp t19557; +fp t20023; +fp t19071; +fp t18528; +fp t19563; +fp t20022; +fp t20021; +fp t19218; +fp t19040; +fp t20020; +fp t19869; +fp t19031; +fp t19657; +fp t20019; +fp t19685; +fp t20018; +fp t20017; +fp t19521; +fp t20016; +fp t18482; +fp t19560; +fp t20015; +fp t19877; +fp t20014; +fp t19107; +fp t20013; +fp t19509; +fp t20012; +fp t19347; +fp t20011; +fp t19848; +fp t20009; +fp t20008; +fp t20007; +fp t20006; +fp t19102; +fp t20005; +fp t20004; +fp t19214; +fp t18941; +fp t19644; +fp t20003; +fp t19074; +fp t20002; +fp t20001; +fp t19030; +fp t20000; +fp t19677; +fp t19136; +fp t19999; +fp t19651; +fp t19998; +fp t19997; +fp t19996; +fp t18960; +fp t19995; +fp t19994; +fp t19343; +fp t19847; +fp t19654; +fp t19992; +fp t19578; +fp t19991; +fp t19723; +fp t19595; +fp t19990; +fp t19989; +fp t18966; +fp t18518; +fp t19561; +fp t19988; +fp t19558; +fp t19987; +fp t19986; +fp t19985; +fp t19562; +fp t19984; +fp t18861; +fp t19983; +fp t19539; +fp t19982; +fp t19551; +fp t19711; +fp t19981; +fp t19980; +fp t19570; +fp t19979; +fp t19978; +fp t19977; +fp t19976; +fp t19799; +fp t19173; +fp t19975; +fp t19974; +fp t19972; +fp t19971; +fp t19970; +fp t19969; +fp t19968; +fp t19967; +fp t19966; +fp t19540; +fp t19965; +fp t19964; +fp t19480; +fp t19715; +fp t19094; +fp t19963; +fp t19962; +fp t19961; +fp t19960; +fp t19144; +fp t19096; +fp t19959; +fp t18947; +fp t19958; +fp t19957; +fp t19956; +fp t19955; +fp t19954; +fp t19953; +fp t19952; +fp t19951; +fp t19950; +fp t19159; +fp t19769; +fp t19949; +fp t19948; +fp t19947; +fp t19135; +fp t19131; +fp t19946; +fp t19781; +fp t19945; +fp t18944; +fp t19692; +fp t19792; +fp t19157; +fp t19944; +fp t19943; +fp t19559; +fp t19660; +fp t19554; +fp t19942; +fp t19785; +fp t19941; +fp t19940; +fp t19675; +fp t19939; +fp t19938; +fp t19937; +fp t19936; +fp t19935; +fp t19260; +fp t19934; +fp t19933; +fp t19932; +fp t19931; +fp t19930; +fp t19929; +fp t19928; +fp t19927; +fp t19926; +fp t19925; +fp t19924; +fp t19923; +fp t19922; +fp t19921; +fp t19784; +fp t19920; +fp t19740; +fp t19919; +fp t19834; +fp t19918; +fp t19917; +fp t19916; +fp t19915; +fp t19914; +fp t19913; +fp t19912; +fp t19911; +fp t19910; +fp t19909; +fp t18948; +fp t19193; +fp t19688; +fp t19908; +fp t19907; +fp t19906; +fp t19905; +fp t19904; +fp t19903; +fp t19902; +fp t19901; +fp t19900; +fp t19899; +fp t19898; +fp t19467; +fp t19749; +fp t19897; +fp t19175; +fp t19255; +fp t19154; +fp t19896; +fp t19895; +fp t19788; +fp t19894; +fp t19893; +fp t19892; +fp t19891; +fp t19890; +fp t19889; +fp t19888; +fp t19887; +fp t19886; +fp t19701; +fp t19666; +fp t19667; +fp t19885; +fp t19884; +fp t19883; +fp t19882; +fp t19216; +fp t19225; +fp t19794; +fp t19791; +fp t19230; +fp t19222; +fp t19771; +fp t19369; +fp t19730; +fp t19716; +fp t19674; +fp t19161; +fp t19186; +fp t19004; +fp t18975; +fp t19188; +fp t19198; +fp t19538; +fp t19493; +fp t19491; +fp t19490; +fp t19323; +fp t19377; +fp t19335; +fp t19488; +fp t19308; +fp t19307; +fp t19364; +fp t19487; +fp t19486; +fp t19362; +fp t19365; +fp t19485; +fp t19281; +fp t19484; +fp t19483; +fp t19482; +fp t19479; +fp t19478; +fp t19476; +fp t19474; +fp t19473; +fp t19472; +fp t19470; +fp t19469; +fp t19267; +fp t19311; +fp t19465; +fp t19464; +fp t19283; +fp t19463; +fp t19462; +fp t19287; +fp t19461; +fp t19296; +fp t19460; +fp t19459; +fp t19458; +fp t19457; +fp t19456; +fp t19455; +fp t19454; +fp t19453; +fp t19452; +fp t19451; +fp t19450; +fp t19449; +fp t19448; +fp t19447; +fp t19446; +fp t19445; +fp t19444; +fp t19443; +fp t19442; +fp t19441; +fp t19440; +fp t19439; +fp t19438; +fp t19437; +fp t19436; +fp t19435; +fp t19434; +fp t19433; +fp t19432; +fp t19431; +fp t19430; +fp t19429; +fp t19428; +fp t19427; +fp t19426; +fp t19425; +fp t19424; +fp t19423; +fp t19422; +fp t19421; +fp t19420; +fp t19419; +fp t19418; +fp t19417; +fp t19416; +fp t19415; +fp t19414; +fp t19413; +fp t19412; +fp t19411; +fp t19410; +fp t19409; +fp t19408; +fp t19407; +fp t19406; +fp t19405; +fp t19404; +fp t19403; +fp t19402; +fp t19401; +fp t19400; +fp t19385; +fp t19355; +fp t19354; +fp t19312; +fp t19310; +fp t19284; +fp t19280; +fp t19279; + t19297 = RATIONAL(-1.0,288.0); + t19389 = x*x; + t19725 = t19297*t19389; + t19263 = RATIONAL(1.0,1728.0); + t20254 = t19725+t19263; + t19327 = RATIONAL(-4.0,27.0); + t19387 = RATIONAL(2.0,9.0); + t19690 = t19387*t19389; + t20253 = t19327+t19690; + t19390 = z*z; + t19394 = t19390*t19390; + t20252 = t20253*t19394; + t19345 = RATIONAL(1.0,18.0); + t19671 = t19345*t19389; + t19601 = y*t19671; + t19306 = RATIONAL(-1.0,72.0); + t19662 = t19306*t19389; + t19391 = y*y; + t19392 = t19391*y; + t19497 = t19392*t19662; + t20251 = t19601+t19497; + t20250 = t20253*t19392; + t19303 = RATIONAL(-1.0,576.0); + t19757 = t19394*t19303; + t19304 = RATIONAL(1.0,576.0); + t19729 = t19394*t19304; + t20249 = t19392*t19757+y*t19729; + t19289 = RATIONAL(16.0,27.0); + t19395 = t19391*t19391; + t20248 = t19391*t19289+t19327*t19395; + t19393 = t19390*z; + t19713 = t19391*t19393; + t19507 = t19389*t19713; + t19778 = t19395*t19389; + t19618 = z*t19778; + t20234 = t19618+t19507; + t19743 = t19395*t19303; + t19790 = t19395*t19304; + t18792 = t19393*t19790; + t20247 = t18792+z*t19743; + t20246 = t19392*t19729+y*t19757; + t19322 = RATIONAL(-1.0,54.0); + t19329 = RATIONAL(2.0,27.0); + t20245 = t19390*t19329+t19394*t19322; + t19309 = RATIONAL(1.0,54.0); + t19315 = RATIONAL(-1.0,36.0); + t19714 = t19395*t19315; + t20244 = t19389*t19714+t19309*t19395; + t19300 = RATIONAL(-1.0,144.0); + t19205 = t19300*t19393; + t19542 = t19389*t19205; + t19276 = RATIONAL(1.0,864.0); + t19724 = t19276*t19393; + t20243 = t19724+t19542; + t19861 = x*t19391; + t19631 = t19303*t19861; + t20242 = x*t19790+t19631; + t19839 = y*t19389; + t19374 = RATIONAL(8.0,9.0); + t19318 = RATIONAL(4.0,27.0); + t20241 = t19392*t19318+t19374*t19839; + t19529 = t19392*t19671; + t19367 = RATIONAL(-2.0,9.0); + t19585 = t19367*t19839; + t20240 = t19585+t19529; + t19320 = RATIONAL(-1.0,27.0); + t20239 = t19585+t19320*t19392; + t19264 = RATIONAL(1.0,3456.0); + t19265 = RATIONAL(-1.0,3456.0); + t20238 = t19389*t19757+t19264*t19394+t19390*t19265; + t19770 = t19390*t19389; + t20237 = t19389*t19729+t19264*t19390+t19303*t19770; + t19295 = RATIONAL(1.0,288.0); + t19750 = t19295*t19389; + t20236 = y*t19750+t20254*t19392; + t19372 = RATIONAL(-4.0,3.0); + t19777 = t19372*t19389; + t19764 = t19389*t19393; + t19373 = RATIONAL(1.0,3.0); + t20235 = z*t19777+t19373*t19764; + t19853 = x*RATIONAL(-2.0,3.0); + t19356 = RATIONAL(-1.0,6.0); + t19841 = x*t19356; + t19177 = t19395*t19841; + t20233 = t19853+t19177; + t19293 = RATIONAL(-5.0,192.0); + t19767 = t19394*t19293; + t19336 = RATIONAL(-1.0,48.0); + t20232 = t19391*t19767+t19390*t19336; + t19384 = RATIONAL(2.0,3.0); + t19863 = x*t19384; + t19358 = RATIONAL(1.0,6.0); + t19868 = x*t19358; + t19137 = t19395*t19868; + t20231 = t19137+t19863; + t19852 = x*t19373; + t19313 = RATIONAL(1.0,12.0); + t19870 = x*t19395; + t19077 = t19313*t19870; + t20230 = t19852+t19077; + t19292 = RATIONAL(5.0,144.0); + t19340 = RATIONAL(-1.0,24.0); + t19669 = t19392*t19340; + t19028 = t19389*t19669; + t20229 = t19028+t19292*t19392; + t20228 = t19394*t19387+t19374; + t19342 = RATIONAL(1.0,24.0); + t19858 = x*t19342; + t19331 = RATIONAL(-5.0,96.0); + t19850 = x*t19331; + t20227 = t19391*t19850+t19858; + t19278 = RATIONAL(5.0,288.0); + t19298 = RATIONAL(-5.0,288.0); + t20226 = z*t19278+t19298*t19393; + t19330 = RATIONAL(1.0,96.0); + t19673 = t19330*t19394; + t20225 = x*t19673+t19858; + t19376 = RATIONAL(-1.0,3.0); + t19371 = RATIONAL(4.0,3.0); + t19819 = t19371*t19389; + t20224 = t19376*t19764+z*t19819; + t20223 = t19387*t19395+t19374; + t19321 = RATIONAL(-1.0,12.0); + t19866 = x*t19321; + t19334 = RATIONAL(5.0,48.0); + t19221 = t19334*t19391; + t19636 = x*t19221; + t20222 = t19866+t19636; + t19842 = x*t19376; + t19731 = t19321*t19395; + t18973 = x*t19731; + t20221 = t19842+t18973; + t19678 = t19394*t19300; + t19573 = x*t19678; + t19833 = x*t19315; + t19658 = t19390*t19833; + t20220 = t19395*t19658+t19391*t19573; + t19860 = x*t19297; + t19632 = t19391*t19860; + t19705 = t19306*t19395; + t19112 = t19390*t19705; + t20219 = t19394*t19632+x*t19112; + t19706 = t19390*t19395; + t19352 = RATIONAL(1.0,72.0); + t19522 = t19352*t19706; + t19266 = RATIONAL(-1.0,1728.0); + t19786 = t19394*t19266; + t20218 = t19391*t19786+t19389*t19522; + t19299 = RATIONAL(1.0,144.0); + t19854 = z*t19395; + t19830 = x*t19854; + t19344 = RATIONAL(1.0,36.0); + t19762 = t19344*t19393; + t19565 = x*t19762; + t20217 = t19391*t19565+t19299*t19830; + t19547 = t19389*t19706; + t19317 = RATIONAL(1.0,27.0); + t19721 = t19394*t19317; + t20216 = t19391*t19721+t19306*t19547; + t19650 = x*t19713; + t19642 = t19300*t19870; + t20215 = z*t19642+t19315*t19650; + t19879 = x*z; + t19202 = t19299*t19393; + t19604 = y*t19202; + t18235 = x*t19604; + t19695 = t19344*t19392; + t20214 = t18235+t19695*t19879; + t19775 = t19306*t19394; + t18997 = t19391*t19775; + t19602 = t19390*t19860; + t20213 = x*t18997+t19395*t19602; + t19530 = t19390*t19725; + t19274 = RATIONAL(1.0,432.0); + t19682 = t19274*t19395; + t20212 = t19391*t19530+t19394*t19682; + t19206 = t19300*t19392; + t18130 = t19206*t19879; + t19702 = t19315*t19393; + t19571 = y*t19702; + t20211 = t18130+x*t19571; + t19223 = t19352*t19392; + t19581 = x*t19223; + t19881 = y*x; + t19758 = t19345*t19393; + t18571 = t19758*t19881; + t20210 = z*t19581+t18571; + t19672 = t19395*t19298; + t19734 = t19391*t19389; + t19527 = t19394*t19734; + t19505 = t19336*t19778; + t19325 = RATIONAL(5.0,72.0); + t19760 = t19390*t19325; + t19679 = t19394*t19505+t19391*t19760; + t20209 = t19679+t19390*t19672+t19313*t19527; + t19208 = t19299*t19392; + t18227 = t19208*t19879; + t20208 = y*t19565+t18227; + t19851 = z*t19344; + t19113 = t19395*t19851; + t20207 = t19299*t19650+x*t19113; + t19233 = t19352*t19394; + t19603 = x*t19233; + t19203 = t19295*t19390; + t19610 = x*t19203; + t20206 = t19391*t19603+t19395*t19610; + t19234 = t19306*t19393; + t19580 = x*t19234; + t19845 = x*t19345; + t19593 = t19391*t19845; + t20088 = t19395*t19580+t19393*t19593; + t19314 = RATIONAL(-1.0,18.0); + t19226 = t19314*t19391; + t19645 = x*t19226; + t20205 = t20088+z*t19645; + t19824 = y*t19845; + t19231 = t19314*t19390; + t19635 = x*t19231; + t20087 = t19394*t19581+t19392*t19635; + t20204 = t19390*t19824+t20087; + t19739 = t19394*t19315; + t19634 = x*t19739; + t20203 = t19391*t19634+t19390*t19642; + t19370 = RATIONAL(-2.0,1.0); + t19375 = RATIONAL(5.0,2.0); + t20202 = t19370+t19375*t19390; + t19878 = x*t19390; + t19619 = t19344*t19878; + t19867 = x*t19299; + t19584 = t19394*t19867; + t20201 = t19392*t19619+y*t19584; + t19747 = t19392*t19345; + t19640 = x*t19747; + t18364 = z*t19640; + t19228 = t19352*t19393; + t20200 = t18364+t19228*t19881; + t19569 = t19390*t19867; + t19820 = t19344*t19394; + t19592 = x*t19820; + t20199 = t19395*t19569+t19391*t19592; + t19772 = t19390*t19306; + t19576 = y*t19772; + t19201 = t19297*t19394; + t18883 = t19392*t19201; + t19783 = t19295*t19392; + t19588 = x*t19783; + t20103 = x*t18883+t19390*t19588; + t20198 = x*t19576+t20103; + t20197 = t19266*t19706+t19352*t19527; + t19612 = t19392*t19833; + t20196 = t19390*t19612+y*t19573; + t19549 = t19390*t19734; + t19275 = RATIONAL(-1.0,432.0); + t19753 = t19275*t19395; + t20195 = t19387*t19549+t19394*t19753; + t19754 = t19356*t19389; + t19277 = RATIONAL(-5.0,144.0); + t20194 = t19394*t19277+t19390*t19754; + t20193 = t19358*t19770+t19292*t19394; + t19831 = y*t19393; + t19822 = x*t19831; + t18501 = t19314*t19822; + t19217 = t19306*t19392; + t20192 = t18501+t19217*t19879; + t19211 = t19297*t19395; + t18793 = t19393*t19211; + t19209 = t19295*t19391; + t19590 = x*t19209; + t20102 = t19393*t19590+x*t18793; + t19835 = z*t19391; + t19829 = x*t19835; + t20191 = t20102+t19306*t19829; + t18140 = t19205*t19881; + t20190 = t18140+z*t19612; + t19864 = z*t19392; + t19607 = t19314*t19864; + t18339 = x*t19607; + t20189 = t18339+y*t19580; + t19089 = z*t19714; + t20188 = x*t19089+t19300*t19650; + t20187 = t19394*t19590+x*t19522; + t18799 = t19394*t19783; + t19577 = t19392*t19860; + t20110 = t19390*t19577+x*t18799; + t19614 = t19352*t19878; + t20186 = t20110+y*t19614; + t20185 = t19392*t19569+y*t19592; + t19712 = t19295*t19395; + t18875 = t19393*t19712; + t20094 = x*t18875+t19393*t19632; + t20184 = t20094+t19352*t19829; + t19524 = t19394*t19662; + t20183 = t19317*t19706+t19391*t19524; + t19518 = t19395*t19228; + t20082 = t19393*t19645+x*t19518; + t20182 = t20082+z*t19593; + t19806 = t19390*t19392; + t19656 = x*t19806; + t20181 = y*t19634+t19300*t19656; + t19606 = x*t19775; + t20099 = t19390*t19640+t19392*t19606; + t19600 = y*t19231; + t20180 = t20099+x*t19600; + t20179 = t19391*t19584+t19395*t19619; + t19807 = t19395*t19314; + t19836 = x*t19387; + t19821 = z*t19836; + t20178 = t20082+t19391*t19821+t19807*t19879; + t20177 = z*t19632+t20102+t19712*t19879; + t19637 = x*t19201; + t20176 = t20110+(t19637+t19610)*y; + t20175 = t20094+z*t19590+t19211*t19879; + t19827 = t19295*t19881; + t20174 = y*t19602+t20103+t19394*t19827; + t19813 = t19392*t19393; + t19586 = x*t19813; + t18229 = t19300*t19586; + t19210 = t19300*y; + t20173 = t19210*t19879+t18229+t18235+t18227; + t19856 = x*t19367; + t19823 = z*t19856; + t19227 = t19345*t19395; + t19621 = x*t19227; + t20172 = z*t19621+t20088+t19391*t19823; + t19766 = t19394*t19314; + t19589 = t19390*t19836; + t20171 = y*t19589+t19766*t19881+t20087; + t18494 = t19393*t19581; + t20170 = y*t19821+t18501+t18494+t18339; + t19880 = y*z; + t19514 = t19393*t19208; + t18253 = x*t19514; + t20169 = t18140+t18130+t18253+t19867*t19880; + t19625 = t19390*t19856; + t19232 = t19345*t19394; + t20168 = t20099+t19232*t19881+y*t19625; + t18562 = t19392*t19580; + t20167 = y*t19823+t18364+t18562+t18571; + t19273 = RATIONAL(1.0,216.0); + t19663 = t19395*t19273; + t19567 = z*t19734; + t19290 = RATIONAL(-1.0,216.0); + t19689 = t19395*t19290; + t20166 = z*t19689+t19393*t19663+t19299*t19507+t19300*t19567; + t19271 = RATIONAL(1.0,1152.0); + t19816 = t19391*t19394; + t19653 = x*t19816; + t19815 = t19394*t19395; + t19639 = x*t19815; + t19261 = RATIONAL(-1.0,1152.0); + t19622 = t19261*t19878; + t19795 = t19390*t19391; + t19661 = x*t19795; + t20165 = t19261*t19653+t19395*t19622+(t19639+t19661)*t19271; + t19115 = t19395*t19702; + t19361 = RATIONAL(1.0,9.0); + t19857 = x*t19361; + t19616 = t19395*t19857; + t19626 = t19391*t19857; + t19382 = RATIONAL(-4.0,9.0); + t20164 = z*t19616+t19393*t19626+x*t19115+t19382*t19829; + t19305 = RATIONAL(-1.0,864.0); + t19735 = t19395*t19305; + t19704 = t19344*t19391; + t19498 = t19389*t19704; + t20163 = t19315*t19567+t19395*t19724+z*t19735+t19393*t19498; + t19844 = x*t19304; + t19596 = t19391*t19844; + t19659 = x*t19706; + t20162 = t19390*t19596+t19303*t19659+t20242*t19394; + t19641 = t19390*t19844; + t20161 = y*t19641+t19303*t19656+t20246*x; + t19703 = t19391*t19290; + t19696 = t19391*t19273; + t19556 = t19395*t19764; + t20160 = t19299*t19556+t19300*t19618+t19393*t19696+z*t19703; + t19219 = t19352*t19395; + t19097 = t19394*t19219; + t20159 = t19395*t19635+t19391*t19589+t19394*t19645+x*t19097; + t19241 = t19361*t19393; + t19552 = t19392*t19702; + t19874 = x*t19382; + t19244 = t19361*t19392; + t19655 = x*t19244; + t20158 = t19874*t19880+t19241*t19881+x*t19552+z*t19655; + t19843 = z*t19276; + t20157 = t19393*t19735+t19395*t19843+t19315*t19507+z*t19498; + t19629 = t19389*t19864; + t18451 = t19389*t19571; + t20156 = t18451+t19273*t19831+t19300*t19629+t19392*t19843; + t20155 = t19297*t19822+t19295*t19586+(t19577+t19827)*z; + t20154 = z*t19663+t19300*t19507+t19299*t19567+t19393*t19689; + t20153 = t19394*t19596+t19303*t19639+t20242*t19390; + t19360 = RATIONAL(-1.0,9.0); + t19246 = t19360*t19392; + t19597 = x*t19246; + t19258 = t19360*t19393; + t19599 = y*t19258; + t19388 = RATIONAL(4.0,9.0); + t19865 = x*t19388; + t19544 = t19393*t19695; + t20152 = z*t19597+t19865*t19880+(t19599+t19544)*x; + t19726 = t19392*t19273; + t19876 = z*t19389; + t19575 = t19315*t19876; + t18569 = t19392*t19575; + t20151 = z*t19726+t18569+t20243*y; + t19587 = t19299*t19876; + t20150 = z*t19696+t19393*t19703+(t19542+t19587)*t19395; + t19630 = t19390*t19874; + t20149 = t19390*t19616+t19391*t19630+t19394*t19626+t19395*t19634; + t19840 = y*t19390; + t19825 = x*t19840; + t20148 = t19392*t19641+t19303*t19825+t20249*x; + t19872 = x*t19394; + t19828 = y*t19872; + t19617 = t19390*t19865; + t19046 = t19394*t19695; + t20147 = t19390*t19597+y*t19617+t19360*t19828+x*t19046; + t18735 = t19271*t19706; + t18762 = t19271*t19816; + t18742 = t19261*t19815; + t20146 = t19391*t19622+(t18735+t18762+t18742)*x; + t20145 = t19295*t19822+t19860*t19880+z*t19588+t19393*t19577; + t19285 = RATIONAL(1.0,108.0); + t20144 = t19314*t19507+t19285*t19854+t19393*t19753+t19387*t19567; + t20143 = t19391*t19625+t19394*t19593+t19390*t19621+t19395*t19606; + t19566 = t19360*t19861; + t20142 = t19360*t19659+t19391*t19617+t19394*t19566+t19395*t19592; + t19091 = t19395*t19762; + t20141 = t19388*t19829+x*t19091+t19393*t19566+t19360*t19830; + t18969 = t19392*t19739; + t20140 = t19390*t19655+y*t19630+t19361*t19828+x*t18969; + t20139 = t19393*t19631+z*t19596+t20247*x; + t18935 = t19393*t19743; + t20138 = x*t18935+t19393*t19596+t20242*z; + t19710 = t19320*t19391; + t19698 = t19352*t19389; + t19535 = t19394*t19698; + t20100 = t19395*t19535+t19390*t19710; + t19838 = y*t19317; + t19286 = RATIONAL(-1.0,108.0); + t19761 = t19314*t19389; + t19496 = t19394*t19761; + t20097 = t19285*t19706+t19391*t19496; + t19993 = t20097+t19390*t19838+t19286*t19806+t20251*t19394; + t19471 = t19993+t20100; + t19765 = t19285*t19392; + t19495 = t19392*t19698; + t19871 = y*t19320; + t20137 = t19390*t19495+t19471+t19389*t19600+(t19765+t19871)*t19394; + t19504 = t19394*t19725; + t20089 = t19395*t19504+t19274*t19795; + t19862 = y*t19273; + t19742 = t19394*t19263; + t19536 = t19391*t19772; + t20069 = t19395*t19742+t19389*t19536; + t19466 = z*t19862+t20089+y*t19575+t20069+t20243*t19392; + t19811 = t19344*t19389; + t19613 = z*t19811; + t18466 = t19392*t19613; + t19751 = t19392*t19290; + t20136 = t19466+t18466+t19389*t19604+t19305*t19831+z*t19751; + t19532 = t19395*t19761; + t19805 = t19285*t19394; + t20061 = t19391*t19805+t19390*t19532; + t19973 = t19285*t19713+t19389*t19518+t20061+(t19532+t19710)*z; + t19475 = t19973+t20100; + t19763 = t19317*t19395; + t19717 = t19395*t19286; + t19543 = t19391*t19671; + t20135 = t19475+t19306*t19507+t19393*t19717+(t19763+t19543)*z; + t19541 = t19395*t19671; + t19533 = t19393*t19662; + t19468 = t19286*t19713+t19395*t19533+t19317*t19835+z*t19541+t20061+t20100 +; + t20134 = z*t19717+t19468+t19345*t19507+t19393*t19682+t19367*t19567; + t19665 = t19394*t19286; + t20010 = t19390*t19765+t19320*t19840+t19394*t19495+y*t19496+t20097; + t20133 = t19392*t19665+y*t19721+t20010+t20100+t20251*t19390; + t19817 = t19320*t19395; + t19736 = t19285*t19393; + t20132 = t19468+t19395*t19736+t19352*t19507+z*t19817+t19314*t19567; + t19555 = t19389*t19762; + t18544 = y*t19555; + t19728 = t19392*t19305; + t20131 = z*t19728+t19290*t19831+t19466+t18544+t19392*t19587; + t19579 = y*t19690; + t19508 = z*t19765+y*t19736+t19393*t19495; + t19513 = t19393*t19761; + t20130 = t19275*t19813+t19508+y*t19513+t19389*t19607+(t19871+t19579)*z; + t19582 = y*t19698; + t19812 = t19286*t19393; + t20129 = t19286*t19880+t19508+t19392*t19812+y*t19533+(t19497+t19582)*z; + t19720 = t19274*t19392; + t19564 = t19393*t19497+t19286*t19864+y*t19812; + t20128 = t19564+(t19720+t19601)*t19393+(t19838+t20240)*z; + t19572 = z*t19662; + t20127 = t19285*t19880+z*t19495+t19392*t19736+t19393*t19582+t19564+y* +t19572; + t19326 = RATIONAL(-2.0,27.0); + t19686 = t19322*t19393; + t20126 = t19361*t19567+t19360*t19507+t19329*t19713+t19326*t19835+(t19555+ +t19686)*t19395+t20244*z; + t19272 = RATIONAL(-16.0,27.0); + t20125 = t19374*t19567+t19272*t19835+(t19541+t19817)*t19393+(t19713+ +t19854)*t19318+t20234*t19367; + t19875 = y*t19394; + t19537 = t19392*t19770; + t20124 = t19265*t19875+t19304*t19537+t20238*t19392+t20237*y; + t19849 = z*t19322; + t20123 = t19326*t19713+t19360*t19567+t19329*t19835+t19361*t19507+t20244* +t19393+(t19613+t19849)*t19395; + t19748 = t19266*t19393; + t19545 = t19392*t19750; + t20122 = z*t19545+t19266*t19864+y*t19748+t20254*t19880+t20236*t19393; + t19379 = RATIONAL(-8.0,9.0); + t20121 = t19395*t19513+t19379*t19567+t19327*t19713+t19393*t19763+t20234* +t19387+t20248*z; + t19722 = t19309*t19392; + t19620 = t19360*t19839; + t19627 = y*t19811; + t19676 = t19326*t19390; + t19801 = t19394*t19389; + t19526 = t19392*t19801; + t20120 = t19315*t19526+t19392*t19676+t19361*t19537+t19390*t19620+(t19627+ +t19722)*t19394+t20245*y; + t19553 = t19393*t19725; + t20119 = t19263*t19831+t19266*t19880+t19392*t19748+y*t19553+t19393*t19545 ++t20236*z; + t19550 = t19394*t19778; + t20118 = (t19816+t19706)*RATIONAL(1.0,6912.0)+(t19815+t19795)*RATIONAL( +-1.0,6912.0)+(t19527+t19547)*t19261+(t19550+t19549)*t19271; + t19803 = t19394*t19392; + t19638 = y*t19770; + t20117 = t19265*t19803+t19304*t19638+t20237*t19392+t20238*y; + t20116 = t19387*t19547+t19379*t19549+(t19721+t19496)*t19395+t20252*t19391 ++t20248*t19390; + t19738 = t19391*t19275; + t19502 = t19389*t19712; + t20115 = t19263*t19713+t19297*t19507+t19393*t19502+t19352*t19567+(t19748+ +t19572)*t19395+(t19738+t19682)*z; + t19649 = y*t19801; + t19709 = t19361*t19389; + t19594 = y*t19709; + t19519 = t19389*t19246; + t20114 = t19309*t19875+t19344*t19526+y*t19676+t19315*t19649+t20245*t19392 ++(t19519+t19594)*t19390; + t19694 = t19317*t19392; + t19826 = z*t19839; + t20113 = t19289*t19880+t19379*t19826+t19392*t19513+t19327*t19831+(t19579+ +t19694)*t19393+t20250*z; + t19818 = t19395*t19393; + t20112 = t19306*t19567+t19274*t19835+t19266*t19713+z*t19753+t19263*t19818 ++t19352*t19618+t19395*t19553+t19295*t19507; + t20111 = t19367*t19629+t19272*t19880+t19318*t19831+t20241*z+(t19529+ +t20239)*t19393; + t19814 = t19278*t19395; + t20109 = t19394*t19814+t19321*t19549; + t19568 = t19390*t19850; + t19332 = RATIONAL(-1.0,96.0); + t19802 = t19394*t19332; + t19624 = x*t19802; + t20107 = t19395*t19624+t19391*t19568; + t19288 = RATIONAL(-1.0,192.0); + t19269 = RATIONAL(5.0,1152.0); + t20106 = t19269*t19706+t19288*t19527; + t19346 = RATIONAL(-10.0,9.0); + t19779 = t19391*t19346; + t20105 = t19390*t19779+t19313*t19550; + t19341 = RATIONAL(-5.0,12.0); + t19746 = t19341*t19391; + t19633 = x*t19746; + t20104 = t19336*t19639+t19390*t19633; + t19338 = RATIONAL(5.0,12.0); + t19646 = t19338*t19861; + t19333 = RATIONAL(1.0,48.0); + t20101 = t19333*t19639+t19390*t19646; + t19809 = t19330*t19395; + t19605 = x*t19809; + t19328 = RATIONAL(5.0,96.0); + t19859 = x*t19328; + t19628 = t19390*t19859; + t20098 = t19391*t19628+t19394*t19605; + t20096 = t19395*t19584+t19391*t19619; + t20095 = t19390*t19543+t19395*t19665; + t19609 = x*t19818; + t20093 = t19704*t19879+t19299*t19609; + t20092 = t19275*t19706+t19295*t19527; + t19351 = RATIONAL(-5.0,72.0); + t19737 = t19351*t19391; + t20090 = t19333*t19547+t19394*t19737; + t19499 = t19394*t19208; + t20086 = x*t19499+y*t19619; + t19363 = RATIONAL(5.0,3.0); + t20084 = t19363*t19549+t19395*t19766; + t20083 = t19851*t19881+t18253; + t19378 = RATIONAL(-5.0,6.0); + t19591 = t19378*t19878; + t20081 = t19391*t19591+t19340*t19639; + t18878 = t19394*t19712; + t20080 = t19391*t19614+x*t18878; + t19652 = t19391*t19833; + t20079 = t19395*t19573+t19390*t19652; + t20078 = t19395*t19637+x*t19536; + t19319 = RATIONAL(1.0,32.0); + t20077 = RATIONAL(-25.0,192.0)*t19795+t19319*t19550; + t20076 = z*t19824+t18494; + t20075 = t19394*t19738+t19390*t19502; + t20074 = t18229+t19833*t19880; + t18918 = t19288*t19815; + t20073 = x*t18918+t19293*t19661; + t19282 = RATIONAL(25.0,12.0); + t19727 = t19282*t19391; + t19381 = RATIONAL(-1.0,8.0); + t20072 = t19390*t19727+t19381*t19550; + t19380 = RATIONAL(5.0,6.0); + t19611 = t19380*t19878; + t20071 = t19391*t19611+t19342*t19639; + t19324 = RATIONAL(5.0,32.0); + t20070 = t19324*t19549+t19395*t19767; + t19224 = t19314*y; + t20068 = t18562+t19224*t19879; + t20066 = t19300*t19609+z*t19652; + t19699 = t19394*t19298; + t20065 = t19391*t19699+t19313*t19547; + t19291 = RATIONAL(5.0,192.0); + t20064 = t19291*t19549+t18742; + t20063 = y*t19658+t19392*t19573; + t19789 = t19334*t19395; + t19359 = RATIONAL(-5.0,2.0); + t20062 = t19394*t19789+t19359*t19549; + t19337 = RATIONAL(-5.0,48.0); + t20060 = t19337*t19549+t19097; + t19525 = t19341*t19734; + t20058 = t18878+t19390*t19525; + t19353 = RATIONAL(5.0,18.0); + t19687 = t19391*t19353; + t20057 = t19394*t19687+t19376*t19547; + t19294 = RATIONAL(1.0,192.0); + t19523 = t19294*t19815; + t20056 = x*t19523+t19291*t19661; + t19270 = RATIONAL(-5.0,1152.0); + t20055 = t19270*t19795+t19389*t19523; + t19796 = t19321*t19392; + t19510 = t19334*t19806; + t19643 = x*t19803; + t20054 = t19336*t19643+(t19796+t19510)*x; + t19681 = t19313*t19393; + t19837 = x*t19337; + t19598 = t19391*t19837; + t20053 = t19393*t19598+t19333*t19609+x*t19681; + t20052 = t19336*t19609+t20222*t19393; + t19873 = x*t19313; + t19752 = t19392*t19333; + t19517 = t19394*t19752; + t20051 = x*t19517+t19392*t19873+t19337*t19656; + t19349 = RATIONAL(-5.0,36.0); + t19787 = t19342*t19395; + t19546 = t19393*t19787; + t19339 = RATIONAL(5.0,36.0); + t19664 = t19339*t19393; + t19693 = t19340*t19389; + t19506 = t19395*t19693; + t20050 = t19349*t19835+t19391*t19664+z*t19506+t19389*t19546; + t20049 = t20065+t20109; + t19141 = y*t19754; + t19846 = z*t19339; + t20048 = y*t19846+z*t19141+t20229*t19393; + t19302 = RATIONAL(5.0,576.0); + t19503 = t19389*t19673; + t19301 = RATIONAL(-5.0,576.0); + t19719 = t19392*t19301; + t20047 = y*t19503+t19390*t19719+t19302*t19840+t19332*t19526; + t19027 = t19333*t19778; + t18961 = t19389*t19731; + t20046 = t19393*t19027+t19278*t19713+(t19737+t18961)*z; + t20045 = t19298*t19713+t19325*t19835+t19393*t19505+t19313*t19618; + t19528 = t19371*t19734; + t19745 = t19351*t19394; + t20044 = t19395*t19745+t19390*t19528+t20057; + t20043 = t20076+t20079; + t19348 = RATIONAL(10.0,9.0); + t19165 = t19373*t19778; + t19350 = RATIONAL(-5.0,18.0); + t20042 = t19348*t19835+t19350*t19713+z*t19165+t19321*t19556; + t19797 = t19392*t19298; + t19691 = t19313*t19394; + t19647 = y*t19691; + t20041 = t19336*t19526+y*t19760+t19390*t19797+t19389*t19647; + t19574 = y*t19802; + t20040 = t19301*t19840+t19392*t19503+t19389*t19574+t19302*t19806; + t19215 = t19334*t19390; + t18900 = t19291*t19706; + t19316 = RATIONAL(-5.0,32.0); + t19366 = RATIONAL(1.0,8.0); + t19741 = t19366*t19389; + t20039 = t19394*t19741+t19215+t18900+t19316*t19527; + t20038 = t20068+t20096; + t20037 = t20074+t20078; + t19793 = t19376*t19389; + t19184 = z*t19793; + t20036 = t19313*t19556+t19395*t19184+t19393*t19687+z*t19779; + t19804 = t19358*t19389; + t19187 = z*t19804; + t19718 = t19277*t19393; + t19744 = t19342*t19392; + t18990 = t19389*t19744; + t19855 = z*t19349; + t20035 = t19392*t19718+t19393*t18990+(t19187+t19855)*y; + t19755 = t19394*t19321; + t19118 = t19389*t19755; + t20034 = t19278*t19806+y*t19118+t19351*t19840+t19389*t19517; + t20033 = t20076+t20096; + t20032 = t20068+t20079; + t19810 = t19342*t19389; + t19129 = z*t19810; + t20031 = t19349*t19713+t19393*t19506+t19395*t19129+t19339*t19835; + t20030 = t20080+t20083; + t19386 = RATIONAL(-1.0,2.0); + t19733 = t19386*t19389; + t19368 = RATIONAL(-5.0,3.0); + t19357 = RATIONAL(5.0,8.0); + t20029 = t19395*t19733+t19368*t19391+t19394*t19746+t19357*t19547; + t20028 = t18997+t18961+t19334*t19547+t19226; + t20027 = t20074+t20080; + t20026 = t19270*t19815+t19294*t19549+t20106; + t20025 = t20078+t20083; + t20024 = t20090+t20109+t20209; + t18535 = y*t19603; + t19557 = t18535+t20093; + t20023 = t19557+t20198+t20215; + t19071 = z*t19219; + t18528 = x*t19071; + t19563 = t18528+t20086; + t20022 = t19563+t20181+t20205; + t20021 = t20075+t20150; + t19218 = t19336*t19395; + t19040 = x*t19218; + t20020 = t19040+t19294*t19653+x*t18900+t19333*t19861+t20073; + t19869 = x*t19333; + t19031 = t19394*t19869; + t19657 = t19390*t19837; + t20019 = t20054+(t19031+t19873+t19657)*y; + t19685 = t19394*t19276; + t20018 = t19392*t19685+t19305*t19875+t19344*t19537+t19315*t19638+t20218; + t20017 = t20107+t19395*t19628+t19340*t19870+t20225*t19391; + t19521 = t19389*t19678; + t20016 = t19390*t19751+t19273*t19840+t19392*t19521+t19299*t19649+t20092; + t18482 = y*t19606; + t19560 = t18482+t20066; + t20015 = t19560+t20186+t20217; + t19877 = x*t19340; + t20014 = t19332*t19659+t19390*t19877+t20098+t20227*t19394; + t19107 = x*t19669; + t20013 = t19107+(t19624+t19628)*t19392+(t19568+t20225)*y; + t19509 = t18535+t20066; + t20012 = t19509+t20180+t20207; + t19347 = RATIONAL(5.0,24.0); + t20011 = t19378*t19829+t19347*t19650+t19340*t19609+t19393*t19841+t20231*z +; + t19848 = z*t19329; + t20009 = t19389*t19552+y*t19848+z*t19620+t19393*t19722+t20095; + t20008 = t20053+(t19040+t20222)*z; + t20007 = t19321*t19653+t19077+t19391*t19842+t19395*t19657+t20101; + t20006 = t20052+(t19633+t20230)*z; + t19102 = t19395*t19869; + t20005 = t20052+(t19598+t19873+t19102)*z; + t20004 = x*t19647+y*t19852+t19341*t19825+t20054; + t19214 = t19336*t19394; + t18941 = x*t19214; + t19644 = x*t19215; + t20003 = t20051+(t19644+t19866+t18941)*y; + t19074 = x*t19691; + t20002 = t20101+t19074+t19394*t19598+t20221*t19390; + t20001 = t19560+t20204+t20207; + t19030 = x*t19744; + t20000 = t19330*t19643+x*t19574+t19392*t19568+t19030+(t19877+t19628)*y; + t19677 = t19356*t19392; + t19136 = t19394*t19868; + t19999 = x*t19677+t19347*t19656+t19394*t19107+(t19863+t19591+t19136)*y; + t19651 = t19391*t19859; + t19998 = t20107+t19340*t19872+t19394*t19651+(t19605+t19858)*t19390; + t19997 = t19177+t19347*t19659+t19358*t19653+t19384*t19861+t20081; + t19996 = t19509+t20198+t20217; + t18960 = x*t19755; + t19995 = t18960+t19394*t19636+t20104+t20230*t19390; + t19994 = t19393*t19728+y*t19613+t19389*t19514+t19290*t19880+t20069; + t19343 = RATIONAL(-5.0,24.0); + t19847 = x*t19343; + t19654 = t19390*t19847; + t19992 = t19356*t19653+t19137+t19395*t19654+t19391*t19853+t20071; + t19578 = z*t19709; + t19991 = t19389*t19544+t19326*t19880+y*t19578+t19392*t19686+t20095; + t19723 = t19358*t19393; + t19595 = t19391*t19847; + t19990 = t19380*t19829+t19393*t19595+t20233*z+(t19723+t19546)*x; + t19989 = t20071+t19136+t19394*t19595+t20233*t19390; + t18966 = z*t19705; + t18518 = x*t18966; + t19561 = t18518+t20086; + t19988 = t19561+t20184+t20196; + t19558 = t18482+t20093; + t19987 = t19558+t20186+t20215; + t19986 = t19338*t19825+t20051+(t19842+t18960)*y; + t19985 = t20104+t18973+t19395*t19644+(t19074+t19852)*t19391; + t19562 = t18518+t20063; + t19984 = t19562+t20184+t20201; + t18861 = t19291*t19816; + t19983 = x*t18861+t19294*t19659+t18941+t19390*t19869+t20073; + t19539 = t18528+t20063; + t19982 = t19539+t20185+t20205; + t19551 = t19393*t19809; + t19711 = t19395*t19332; + t19981 = x*t19551+t19711*t19879+t20227*t19393+(t19651+t19877)*z; + t19980 = t19557+t20180+t20188; + t19570 = z*t19809; + t19979 = t19332*t19609+t19328*t19650+t19393*t19877+x*t19570+t20227*z; + t19978 = t19561+t20181+t20182; + t19977 = t19562+t20182+t20185; + t19976 = t20056+t19031+t19288*t19659+t20232*x; + t19799 = t19358*t19392; + t19173 = t19394*t19841; + t19975 = t19392*t19654+t19394*t19030+x*t19799+(t19173+t19853+t19611)*y; + t19974 = t20053+(t19646+t20221)*z; + t19972 = t19558+t20188+t20204; + t19971 = t19390*t19726+t19290*t19840+t19389*t19499+y*t19521+t20092; + t19970 = y*t19665+t19394*t19720+t20195+t20240*t19390; + t19969 = t19539+t20191+t20201; + t19968 = t19563+t20191+t20196; + t19967 = t19395*t19568+x*t19787+t19340*t19861+t19391*t19624+t20098; + t19966 = t20081+t19173+t19347*t19653+t20231*t19390; + t19540 = t19293*t19706; + t19965 = x*t19540+t19288*t19653+t19102+t19336*t19861+t20056; + t19964 = t20028+t19219+t19373*t19734+t20058+t20209; + t19480 = t19231+t19334*t19527+t19118+t19112+t19679; + t19715 = t19313*t19389; + t19094 = t19390*t19715; + t19963 = t19480+t19094+t19232+t20060+t20090; + t19962 = t19233+t19480+t19373*t19770+t20058+t20065; + t19961 = t20153+t20175; + t19960 = t20173+t20176; + t19144 = t19389*t19799; + t19096 = t19342*t19764; + t19959 = t20048+z*t19144+t19392*t19855+(t19718+t19096)*y; + t18947 = t19391*t19715; + t19958 = t18947+t19227+t20028+t20060; + t19957 = t20155+t20161; + t19956 = t20169+t20176; + t19955 = t20025+t20206+t20211; + t19954 = t20169+t20174; + t19953 = t20038+t20200+t20220; + t19952 = t20038+t20203+t20210; + t19951 = t20147+t20152; + t19950 = t20173+t20174; + t19159 = t19372*t19734; + t19769 = t19325*t19393; + t19949 = z*t19159+t19350*t19854+t19373*t19507+t19395*t19769+t20042; + t19948 = t20043+t20192+t20199; + t19947 = t20027+t20208+t20213; + t19135 = t19389*t19677; + t19131 = t19393*t19693; + t19946 = z*t19135+t19292*t19831+y*t19131+t19392*t19846+t20035; + t19781 = t19389*t19333; + t19945 = t19201+t18735+t19203+t19394*t19781+t20064+t20232*t19389; + t18944 = t19389*t19796; + t19692 = t19392*t19350; + t19792 = t19373*t19389; + t19157 = t19392*t19792; + t19944 = t19393*t18944+t19350*t19831+t19392*t19769+t19348*t19880+(t19692+ +t19157)*z+t20235*y; + t19943 = t20037+t20187+t20214; + t19559 = t19336*t19764; + t19660 = y*t19781; + t19554 = t19389*t19752; + t19942 = z*t19660+t19278*t19831+t19393*t19554+y*t19559+t19298*t19880+ +t19336*t19629+t20226*t19392; + t19785 = t19351*t19395; + t19941 = t19353*t19854+t19393*t19785+t19376*t19507+z*t19528+t20036; + t19940 = t20141+t20149; + t19675 = t19302*t19394; + t19939 = t19301*t19875+t19330*t19537+t19332*t19638+t19392*t19675+t20047; + t19938 = t19394*t19719+t19330*t19638+t19332*t19537+y*t19675+t20040; + t19937 = t20032+t20179+t20200; + t19936 = t20037+t20206+t20208; + t19935 = t19278*t19813+t19336*t19826+t19392*t19559+t19393*t19660+(t19797+ +t19554)*z+t20226*y; + t19260 = t19367*t19395; + t19934 = t19165+t19159+t20084+t19341*t19547+t19260+t20228*t19391; + t19933 = t19393*t19814+t19321*t19567+t19333*t19507+z*t19785+t20045; + t19932 = t20030+t20190+t20219; + t19931 = t20143+t20172; + t19930 = t20032+t20199+t20210; + t19929 = t20170+t20171; + t19928 = t20167+t20168; + t19927 = t20167+t20171; + t19926 = t20145+t20161; + t19925 = t20159+t20172; + t19924 = t20030+t20211+t20213; + t19923 = t20141+t20142; + t19922 = t20139+t20146; + t19921 = t20043+t20179+t20189; + t19784 = t19394*t19325; + t19920 = t20034+t19392*t19699+t19336*t19537+(t19094+t19784)*y; + t19740 = t19292*t19395; + t19919 = t19356*t19507+z*t19740+t19358*t19567+t19395*t19718+t20050; + t19834 = z*t19277; + t19918 = t19393*t19740+t19395*t19834+t19358*t19507+t19356*t19567+t20031; + t19917 = t19393*t19672+t19336*t19507+t19325*t19854+z*t18947+t20046; + t19916 = t20027+t20214+t20219; + t19915 = t20138+t20165; + t19914 = t20162+t20177; + t19913 = t19278*t19803+t19333*t19537+y*t19745+t19321*t19638+t20041; + t19912 = t20025+t20187+t20190; + t19911 = t20140+t20164; + t19910 = t20143+t20178; + t19909 = t20147+t20158; + t18948 = t19392*t19715; + t19193 = t19392*t19793; + t19688 = t19351*t19392; + t19908 = t19346*t19880+z*t19193+(t19688+t18948)*t19393+(t19831+t19864)* +t19353+t20224*y; + t19907 = t20168+t20170; + t19906 = t20033+t20189+t20220; + t19905 = t20033+t20192+t20203; + t19904 = t20153+t20177; + t19903 = t20138+t20146; + t19902 = t20148+t20155; + t19901 = t20159+t20178; + t19900 = t20145+t20148; + t19899 = t20162+t20175; + t19898 = t20139+t20165; + t19467 = t20016+t20089; + t19749 = t19394*t19290; + t19897 = y*t19749+t19467+t19299*t19537+t19394*t19726+t19300*t19638+t20075 ++t20212; + t19175 = t19394*t19792; + t19255 = t19367*t19394; + t19154 = t19372*t19770; + t19896 = t19175+t19255+t20057+t20105+t20084+t19154+t19394*t19525+t20223* +t19390; + t19895 = t19389*t19540+t18762+t19336*t19734+t19027+t19211+t19209+t20055+ +t20106+t20064; + t19788 = t19394*t19275; + t19894 = t20197+t19274*t19840+t19295*t19537+t19266*t19806+t19389*t19576+( +t19504+t19742)*t19392+(t19788+t19535)*y; + t19893 = t19389*t19599+z*t19722+t18569+t19329*t19831+t19991+t20216; + t19892 = t19309*t19831+t19392*t19848+t18451+z*t19519+t19991+t20183; + t19891 = y*t19686+t19392*t19578+t19326*t19864+t18544+t20009+t20183; + t19890 = t19314*t19537+y*t19805+t19390*t19579+t19392*t19788+t20010+t20195 +; + t19889 = t19393*t19594+t18466+t19392*t19849+t19326*t19831+t20009+t20216; + t19888 = t19394*t19728+t19315*t19537+t19390*t19627+y*t19685+t19971+t20218 +; + t19887 = t19300*t19537+t19392*t19749+t19394*t19862+t19299*t19638+t19971+ +t20212; + t19886 = t19295*t19526+t20197+t19274*t19875+t19275*t19840+t19263*t19806+ +t19390*t19582+y*t19524+t20075+(t19530+t19786)*t19392; + t19701 = t19264*t19391; + t19666 = t19264*t19395; + t19667 = t19265*t19393; + t19885 = t19391*t19667+t19303*t19567+t20118+t19265*t19854+t19393*t19666+ +t19389*t18935+z*t19701+t20234*t19304; + t19884 = t19304*t19567+t20118+t19389*t18792+t19265*t19835+t19393*t19701+z +*t19666+t19395*t19667+t20234*t19303; + t19883 = t20116+t19345*t19526+t19272*t19840+t19318*t19875+t19367*t19537+ +t20239*t19394+t20241*t19390; + t19882 = t20116+t19394*t19694+t19379*t19638+t19392*t19496+t19289*t19840+ +t20250*t19390+t20252*y; + t19216 = t19337*t19394; + t19225 = t19338*t19394; + t19794 = t19390*t19339; + t19791 = t19395*t19301; + t19230 = t19338*t19395; + t19222 = t19337*t19395; + t19771 = t19302*t19395; + t19369 = RATIONAL(2.0,1.0); + t19730 = t19369*t19389; + t19716 = t19390*t19349; + t19674 = t19390*t19353; + t19161 = y*t19819; + t19186 = y*t19793; + t19004 = y*t19810; + t18975 = y*t19693; + t19188 = t19393*t19754; + t19198 = t19389*t19723; + t19538 = t19389*t19711; + t19493 = t19376*t19527+t19395*t19674+t20105; + t19491 = t19351*t19706+t19333*t19527+t19679; + t19490 = t19269*t19816+t19288*t19547+t20055; + t19323 = RATIONAL(5.0,16.0); + t19377 = RATIONAL(-1.0,4.0); + t19335 = RATIONAL(-1.0,16.0); + t19488 = t19377+t19335*t19395+t19323*t19391; + t19308 = RATIONAL(-5.0,16.0); + t19307 = RATIONAL(1.0,16.0); + t19364 = RATIONAL(1.0,4.0); + t19487 = t19364+t19308*t19391+t19307*t19395; + t19486 = t19357*t19391+t19381*t19395+t19386; + t19362 = RATIONAL(-5.0,8.0); + t19365 = RATIONAL(1.0,2.0); + t19485 = t19362*t19391+t19366*t19395+t19365; + t19281 = RATIONAL(25.0,32.0); + t19484 = t19281*t19391+t19316*t19395+t19362; + t19483 = t19221+t19316*t19547+t18861+t19395*t19741+t20077; + t19482 = t19341*t19706+t19394*t19733+t19357*t19527+t19368*t19390+t20072; + t19479 = y*t19794+t19392*t19716+t19394*t19004+t19340*t19526+t19491; + t19478 = t19302*t19835+t19389*t19570+t19301*t19713+t19393*t19538+t19490; + t19476 = t19301*t19835+t19302*t19713+t19389*t19551+z*t19538+t19490; + t19474 = t19994+t20089; + t19473 = t19392*t19794+t19342*t19526+y*t19716+t19394*t18975+t19491; + t19472 = t20075+t20089+t20160; + t19470 = y*t19175+t19348*t19840+t19390*t19692+t19321*t19526+t19493; + t19469 = t19394*t19186+t19346*t19840+t19392*t19674+t19313*t19526+t19493; + t19267 = RATIONAL(25.0,192.0); + t19311 = RATIONAL(-1.0,32.0); + t19465 = t19267*t19816+t19381*t19770+t19311*t19547+t19216+t20039+t20070+ +t20077; + t19464 = t19267*t19706+t19381*t19734+t19222+t19311*t19527+t19483+t20070; + t19283 = RATIONAL(-25.0,48.0); + t19463 = t19391*t19730+t19365*t19527+t19230+t19283*t19706+t20029+t20062+ +t20072; + t19462 = t19283*t19816+t19225+t19390*t19730+t19365*t19547+t19482+t20062; + t19287 = RATIONAL(-25.0,96.0); + t19461 = t19347+t19287*t19391+t19328*t19395+t19488*t19389; + t19296 = RATIONAL(25.0,96.0); + t19460 = t19331*t19395+t19296*t19391+t19343+t19487*t19389; + t19459 = t19296*t19390+t19331*t19394+t19343+(t19307*t19394+t19308*t19390+ +t19364)*t19389; + t19458 = t19287*t19390+t19347+t19328*t19394+(t19377+t19323*t19390+t19335* +t19394)*t19389; + t19457 = z*t19771+t19330*t19567+t19332*t19507+t19393*t19791+t19476+t20026 +; + t19456 = y*t19198+t19349*t19831+z*t18990+t19392*t19834+t20024+t20048; + t19455 = t19376*t19537+t19390*t19161+t19394*t19688+t19353*t19875+t19469+ +t20044; + t19454 = t19473+t20049+t20194*t19392+t20193*y; + t19453 = t19373*t19537+y*t19154+t19392*t19784+t19350*t19875+t19470+t20044 +; + t19452 = t20035+t20024+t20229*z+(t19664+t19188)*y; + t19451 = t19479+t20049+t20193*t19392+t20194*y; + t19450 = t19393*t19771+t19330*t19507+z*t19791+t19478+t19332*t19567+t20026 +; + t19449 = RATIONAL(-25.0,8.0)*t19549+t19375*t19734+t19373*t19394+t20029+ +t19482+t19371+t20202*t19389+(t19691+t19373)*t19395; + t19448 = t19321+t19281*t19549+t19483+t19214+t19218+t20039+t19365*t19389+ +t18918+(t19770+t19734)*t19362; + t19447 = t19387*t19393+t19896+t19395*t19758+t20042+t19338*t19507+t19368* +t19567+(t19379+t19260)*z+t20224; + t19446 = t19299*y+t18975+t19895+t19331*t19537+t19206+t19328*t19638+t18990 ++t20040+t20249; + t19445 = t19091+t19347*t19507+t19187+t19963+t19241+t19360*z+t19089+t19188 ++t19343*t19567+t20031; + t19444 = t18883+t18948+t19186+t19217+t19337*t19537+t20034+t19338*t19638+ +t19964+(t19233+t19345)*y; + t19443 = t19004+t19895+t19028+t19331*t19638+t19210+t19328*t19537+t19208+ +t20047+t20246; + t19442 = t18944+t19389*t19510+t19223+t19341*t19638+t18799+t20041+t19224+ +t19964+(t19792+t19775)*y; + t19441 = t19934+t19161+t19193+t19394*t19747+t19368*t19638+t19338*t19537+ +t19387*t19392+t19470+(t19379+t19255)*y; + t19440 = t20036+t19896+t19341*t19507+t19363*t19567+(t19807+t19367)*t19393 ++t20223*z+t20235; + t19439 = t19945+t19131+t19331*t19567+t19300*z+t19328*t19507+t19129+t19478 ++t19202+t20247; + t19438 = t19334*t19507+t19321*t19764+t19962+t18966+t19228+t18875+t20045+( +t19525+t19792+t19314)*z; + t19437 = t18935+t19945+t19331*t19507+t19328*t19567+t19205+t19476+t19096+( +t19299+t19693+t19790)*z; + t19436 = t19479+t19135+t19343*t19638+t19347*t19537+t19958+t19046+t19244+( +t19739+t19804+t19360)*y; + t19435 = t19347*t19638+t19343*t19537+t19473+t18969+t19141+t19958+t19246+ +t19144+(t19361+t19820)*y; + t19434 = t19363*t19638+t19934+t19157+t19341*t19537+t19469+(t19766+t19367) +*t19392+(t19777+t20228)*y; + t19433 = t19071+t18793+t19389*t19681+t19962+t19337*t19507+t19345*z+t19234 ++t19338*t19567+t19184+t20046; + t19432 = t19115+t19347*t19567+t19963+t19258+t19113+t19343*t19507+t19198+ +t20050+(t19754+t19361)*z; + t19431 = t20021+t19887+t20089+t20129+t20166; + t19430 = t19887+t19472+t20127+t20154; + t19429 = t19889+t20123+t20133; + t19428 = t19893+t20126+t20133; + t19427 = t19475+t19890+t20130+t20144; + t19426 = t19890+t20128+t20134; + t19425 = t19891+t20114+t20132; + t19424 = t19472+t19894+t19994+t20156+t20157; + t19423 = t20117+t19885+t20122; + t19422 = t20119+t19885+t20124; + t19421 = t19471+t19973+t19970+t20128+t20144; + t19420 = t20117+t19884+t20119; + t19419 = t20111+t19883+t20121; + t19418 = t19892+t20120+t20132; + t19417 = t19891+t20120+t20135; + t19416 = t20113+t19883+t20125; + t19415 = t19882+t20111+t20125; + t19414 = t20122+t19884+t20124; + t19413 = t19893+t20123+t20137; + t19412 = t20113+t19882+t20121; + t19411 = t19889+t20126+t20137; + t19410 = t19886+t19474+t20150+t20156+t20163; + t19409 = t20018+t20016+t20112+t20136; + t19408 = t19894+t20021+t20131+t20163; + t19407 = t19897+t20127+t20150+t20166; + t19406 = t19897+t20129+t20154+t20160; + t19405 = t19886+t20131+t20157+t20160; + t19404 = t19467+t19994+t20018+t20115+t20151; + t19403 = t19970+t19993+t20130+t20134; + t19402 = t19888+t19474+t20112+t20151; + t19401 = t19888+t20115+t20136; + t19400 = t19892+t20114+t20135; + t19385 = RATIONAL(5.0,4.0); + t19355 = RATIONAL(-5.0,4.0); + t19354 = RATIONAL(3.0,4.0); + t19312 = RATIONAL(25.0,8.0); + t19310 = RATIONAL(-15.0,4.0); + t19284 = RATIONAL(25.0,48.0); + t19280 = RATIONAL(-25.0,12.0); + t19279 = RATIONAL(-15.0,16.0); + coeffs_dxx->coeff_m2_m2_m2 = t19422+t19922+t19926; + coeffs_dxx->coeff_m1_m2_m2 = t19914+t19430+t19954; + coeffs_dxx->coeff_0_m2_m2 = t19939+t19450+t19942; + coeffs_dxx->coeff_p1_m2_m2 = t19430+t19960+t19961; + coeffs_dxx->coeff_p2_m2_m2 = t19422+t19902+t19915; + coeffs_dxx->coeff_m2_m1_m2 = t19405+t19924+t19996; + coeffs_dxx->coeff_m1_m1_m2 = t19413+t19930+t19978; + coeffs_dxx->coeff_0_m1_m2 = t19456+t19919+t19920; + coeffs_dxx->coeff_p1_m1_m2 = t19413+t19905+t19982; + coeffs_dxx->coeff_p2_m1_m2 = t19405+t19936+t19987; + coeffs_dxx->coeff_m2_0_m2 = t19439+t19981+t19983; + coeffs_dxx->coeff_m1_0_m2 = t19432+t20005+t20014; + coeffs_dxx->coeff_0_0_m2 = t19465+t19460*z+t19461*t19393; + coeffs_dxx->coeff_p1_0_m2 = t19432+t19998+t20008; + coeffs_dxx->coeff_p2_0_m2 = t19439+t19976+t19979; + coeffs_dxx->coeff_m2_p1_m2 = t19424+t19947+t20015; + coeffs_dxx->coeff_m1_p1_m2 = t19429+t19948+t19977; + coeffs_dxx->coeff_0_p1_m2 = t19452+t19913+t19919; + coeffs_dxx->coeff_p1_p1_m2 = t19429+t19952+t20022; + coeffs_dxx->coeff_p2_p1_m2 = t19424+t19955+t20023; + coeffs_dxx->coeff_m2_p2_m2 = t19423+t19902+t19922; + coeffs_dxx->coeff_m1_p2_m2 = t19914+t19406+t19960; + coeffs_dxx->coeff_0_p2_m2 = t19935+t19450+t19938; + coeffs_dxx->coeff_p1_p2_m2 = t19406+t19954+t19961; + coeffs_dxx->coeff_p2_p2_m2 = t19423+t19915+t19926; + coeffs_dxx->coeff_m2_m2_m1 = t19401+t19932+t19969; + coeffs_dxx->coeff_m1_m2_m1 = t19418+t19937+t19972; + coeffs_dxx->coeff_0_m2_m1 = t19454+t19917+t19959; + coeffs_dxx->coeff_p1_m2_m1 = t19418+t19906+t20012; + coeffs_dxx->coeff_p2_m2_m1 = t19401+t19943+t19988; + coeffs_dxx->coeff_m2_m1_m1 = t19403+t19910+t19927; + coeffs_dxx->coeff_m1_m1_m1 = t19911+t19416+t20142+t20152; + coeffs_dxx->coeff_0_m1_m1 = t19453+t19908+t19949; + coeffs_dxx->coeff_p1_m1_m1 = t19909+t19416+t19940; + coeffs_dxx->coeff_p2_m1_m1 = t19403+t19907+t19925; + coeffs_dxx->coeff_m2_0_m1 = t19433+t20002+t20006; + coeffs_dxx->coeff_m1_0_m1 = t19447+t19966+t19990; + coeffs_dxx->coeff_0_0_m1 = t19462+(t19341+t19284*t19391+t19222+t19485* +t19389)*t19393+(t19280*t19391+t19230+t19363+(t19375*t19391+t19370+t19386*t19395 +)*t19389)*z; + coeffs_dxx->coeff_p1_0_m1 = t19447+t19989+t20011; + coeffs_dxx->coeff_p2_0_m1 = t19433+t19974+t19995; + coeffs_dxx->coeff_m2_p1_m1 = t19426+t19907+t19910; + coeffs_dxx->coeff_m1_p1_m1 = t19909+t19415+t20142+t20164; + coeffs_dxx->coeff_0_p1_m1 = t19455+t19944+t19949; + coeffs_dxx->coeff_p1_p1_m1 = t19415+t19940+t20140+t20152; + coeffs_dxx->coeff_p2_p1_m1 = t19426+t19925+t19927; + coeffs_dxx->coeff_m2_p2_m1 = t19404+t19916+t19968; + coeffs_dxx->coeff_m1_p2_m1 = t19425+t19921+t19980; + coeffs_dxx->coeff_0_p2_m1 = t19451+t19917+t19946; + coeffs_dxx->coeff_p1_p2_m1 = t19425+t19953+t20001; + coeffs_dxx->coeff_p2_p2_m1 = t19404+t19912+t19984; + coeffs_dxx->coeff_m2_m2_0 = t19443+t20000+t20020; + coeffs_dxx->coeff_m1_m2_0 = t19435+t19967+t20019; + coeffs_dxx->coeff_0_m2_0 = t19464+t19458*t19392+t19459*y; + coeffs_dxx->coeff_p1_m2_0 = t19435+t20003+t20017; + coeffs_dxx->coeff_p2_m2_0 = t19443+t19965+t20013; + coeffs_dxx->coeff_m2_m1_0 = t19444+t20004+t20007; + coeffs_dxx->coeff_m1_m1_0 = t19441+t19975+t19997; + coeffs_dxx->coeff_0_m1_0 = (t19363+t19280*t19390+t19225+(t19386*t19394+ +t20202)*t19389)*y+t19463+(t19341+t19216+t19284*t19390+(t19362*t19390+t19365+ +t19366*t19394)*t19389)*t19392; + coeffs_dxx->coeff_p1_m1_0 = t19441+t19992+t19999; + coeffs_dxx->coeff_p2_m1_0 = t19444+t19985+t19986; + coeffs_dxx->coeff_m2_0_0 = ((t19381+t19324*t19391+t19311*t19395)*t19394+( +RATIONAL(-25.0,32.0)*t19391+t19324*t19395+t19357)*t19390+t19486)*x+t19448; + coeffs_dxx->coeff_m1_0_0 = (1.0+t19355*t19391+t19364*t19395+t19487*t19394 ++(t19355+t19308*t19395+RATIONAL(25.0,16.0)*t19391)*t19390)*x+t19449; + coeffs_dxx->coeff_0_0_0 = t19359+t19312*t19391+t19362*t19395+t19484* +t19394+(t19281*t19395+RATIONAL(-125.0,32.0)*t19391+t19312)*t19390+(t19310* +t19391+t19354*t19395+RATIONAL(3.0,1.0)+(t19279*t19391+RATIONAL(3.0,16.0)*t19395 ++t19354)*t19394+(t19310+RATIONAL(75.0,16.0)*t19391+t19279*t19395)*t19390)* +t19389; + coeffs_dxx->coeff_p1_0_0 = (t19377*t19395+t19385*t19391-1.0+t19488*t19394 ++(RATIONAL(-25.0,16.0)*t19391+t19323*t19395+t19385)*t19390)*x+t19449; + coeffs_dxx->coeff_p2_0_0 = t19448+((t19366+t19316*t19391+t19319*t19395)* +t19394+t19484*t19390+t19485)*x; + coeffs_dxx->coeff_m2_p1_0 = t19442+t19986+t20007; + coeffs_dxx->coeff_m1_p1_0 = t19434+t19997+t19999; + coeffs_dxx->coeff_0_p1_0 = (t19338+t19334*t19394+t19283*t19390+(t19381* +t19394+t19357*t19390+t19386)*t19389)*t19392+(t19282*t19390+t19368+t19341*t19394 ++(t19359*t19390+t19365*t19394+t19369)*t19389)*y+t19463; + coeffs_dxx->coeff_p1_p1_0 = t19434+t19975+t19992; + coeffs_dxx->coeff_p2_p1_0 = t19442+t19985+t20004; + coeffs_dxx->coeff_m2_p2_0 = t19446+t20013+t20020; + coeffs_dxx->coeff_m1_p2_0 = t19436+t19967+t20003; + coeffs_dxx->coeff_0_p2_0 = t19464+t19458*y+t19459*t19392; + coeffs_dxx->coeff_p1_p2_0 = t19436+t20017+t20019; + coeffs_dxx->coeff_p2_p2_0 = t19446+t19965+t20000; + coeffs_dxx->coeff_m2_m2_p1 = t19402+t19916+t19984; + coeffs_dxx->coeff_m1_m2_p1 = t19417+t19921+t20001; + coeffs_dxx->coeff_0_m2_p1 = t19454+t19933+t19946; + coeffs_dxx->coeff_p1_m2_p1 = t19417+t19953+t19980; + coeffs_dxx->coeff_p2_m2_p1 = t19402+t19912+t19968; + coeffs_dxx->coeff_m2_m1_p1 = t19929+t19421+t19931; + coeffs_dxx->coeff_m1_m1_p1 = t19923+t19419+t20140+t20158; + coeffs_dxx->coeff_0_m1_p1 = t19453+t19941+t19944; + coeffs_dxx->coeff_p1_m1_p1 = t19419+t19951+t20149+t20164; + coeffs_dxx->coeff_p2_m1_p1 = t19901+t19421+t19928; + coeffs_dxx->coeff_m2_0_p1 = t19438+t19974+t20002; + coeffs_dxx->coeff_m1_0_p1 = t19440+t19966+t20011; + coeffs_dxx->coeff_0_0_p1 = t19462+(t19283*t19391+t19789+t19338+t19486* +t19389)*t19393+(t19341*t19395+t19727+t19368+(t19359*t19391+t19369+t19365*t19395 +)*t19389)*z; + coeffs_dxx->coeff_p1_0_p1 = t19440+t19989+t19990; + coeffs_dxx->coeff_p2_0_p1 = t19438+t19995+t20006; + coeffs_dxx->coeff_m2_p1_p1 = t19928+t19427+t19931; + coeffs_dxx->coeff_m1_p1_p1 = t19923+t19412+t19951; + coeffs_dxx->coeff_0_p1_p1 = t19455+t19908+t19941; + coeffs_dxx->coeff_p1_p1_p1 = t19911+t19412+t20149+t20158; + coeffs_dxx->coeff_p2_p1_p1 = t19901+t19427+t19929; + coeffs_dxx->coeff_m2_p2_p1 = t19409+t19932+t19988; + coeffs_dxx->coeff_m1_p2_p1 = t19400+t19937+t20012; + coeffs_dxx->coeff_0_p2_p1 = t19451+t19933+t19959; + coeffs_dxx->coeff_p1_p2_p1 = t19400+t19906+t19972; + coeffs_dxx->coeff_p2_p2_p1 = t19409+t19943+t19969; + coeffs_dxx->coeff_m2_m2_p2 = t19414+t19903+t19957; + coeffs_dxx->coeff_m1_m2_p2 = t19431+t19899+t19950; + coeffs_dxx->coeff_0_m2_p2 = t19457+t19935+t19939; + coeffs_dxx->coeff_p1_m2_p2 = t19431+t19904+t19956; + coeffs_dxx->coeff_p2_m2_p2 = t19898+t19414+t19900; + coeffs_dxx->coeff_m2_m1_p2 = t19410+t19947+t20023; + coeffs_dxx->coeff_m1_m1_p2 = t19411+t19948+t20022; + coeffs_dxx->coeff_0_m1_p2 = t19918+t19452+t19920; + coeffs_dxx->coeff_p1_m1_p2 = t19411+t19952+t19977; + coeffs_dxx->coeff_p2_m1_p2 = t19410+t19955+t20015; + coeffs_dxx->coeff_m2_0_p2 = t19437+t19979+t19983; + coeffs_dxx->coeff_m1_0_p2 = t19445+t20008+t20014; + coeffs_dxx->coeff_0_0_p2 = t19461*z+t19465+t19460*t19393; + coeffs_dxx->coeff_p1_0_p2 = t19445+t19998+t20005; + coeffs_dxx->coeff_p2_0_p2 = t19437+t19976+t19981; + coeffs_dxx->coeff_m2_p1_p2 = t19408+t19924+t19987; + coeffs_dxx->coeff_m1_p1_p2 = t19428+t19930+t19982; + coeffs_dxx->coeff_0_p1_p2 = t19456+t19913+t19918; + coeffs_dxx->coeff_p1_p1_p2 = t19428+t19905+t19978; + coeffs_dxx->coeff_p2_p1_p2 = t19408+t19936+t19996; + coeffs_dxx->coeff_m2_p2_p2 = t19900+t19420+t19903; + coeffs_dxx->coeff_m1_p2_p2 = t19407+t19899+t19956; + coeffs_dxx->coeff_0_p2_p2 = t19938+t19457+t19942; + coeffs_dxx->coeff_p1_p2_p2 = t19407+t19904+t19950; + coeffs_dxx->coeff_p2_p2_p2 = t19898+t19420+t19957; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxy.compute.c new file mode 100644 index 0000000..5a340c9 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxy.compute.c @@ -0,0 +1,2557 @@ +fp t21716; +fp t21801; +fp t21806; +fp t21710; +fp t22624; +fp t21674; +fp t21805; +fp t21677; +fp t22623; +fp t21675; +fp t21676; +fp t22622; +fp t21773; +fp t21726; +fp t22098; +fp t22621; +fp t21709; +fp t21686; +fp t22620; +fp t21800; +fp t21673; +fp t21678; +fp t22033; +fp t22157; +fp t22619; +fp t21729; +fp t21802; +fp t21804; +fp t22182; +fp t22001; +fp t21736; +fp t21803; +fp t22072; +fp t21946; +fp t22618; +fp t21783; +fp t21659; +fp t21792; +fp t22617; +fp t21715; +fp t21712; +fp t22616; +fp t21695; +fp t22071; +fp t21681; +fp t21588; +fp t22615; +fp t21706; +fp t21718; +fp t21596; +fp t22110; +fp t22614; +fp t21757; +fp t22084; +fp t21774; +fp t22613; +fp t22117; +fp t22172; +fp t22612; +fp t21750; +fp t21636; +fp t21742; +fp t22056; +fp t21293; +fp t22611; +fp t22114; +fp t21701; +fp t22042; +fp t21054; +fp t22610; +fp t22109; +fp t21202; +fp t22609; +fp t21724; +fp t22608; +fp t22607; +fp t21700; +fp t21737; +fp t22606; +fp t22111; +fp t21522; +fp t22605; +fp t22604; +fp t21780; +fp t22059; +fp t21758; +fp t22108; +fp t22603; +fp t22082; +fp t22602; +fp t21713; +fp t21579; +fp t21702; +fp t22601; +fp t21683; +fp t21682; +fp t21599; +fp t22600; +fp t21755; +fp t21632; +fp t21384; +fp t21719; +fp t21629; +fp t22599; +fp t22598; +fp t21046; +fp t22597; +fp t21798; +fp t22062; +fp t21725; +fp t22106; +fp t22596; +fp t22026; +fp t21532; +fp t22595; +fp t22031; +fp t21593; +fp t22594; +fp t22143; +fp t21542; +fp t21759; +fp t21621; +fp t22593; +fp t21766; +fp t22592; +fp t22591; +fp t21684; +fp t21597; +fp t22036; +fp t22590; +fp t21602; +fp t21694; +fp t22102; +fp t22589; +fp t21784; +fp t22588; +fp t22057; +fp t22066; +fp t22587; +fp t21799; +fp t21785; +fp t21651; +fp t22586; +fp t22185; +fp t22585; +fp t21544; +fp t22584; +fp t22037; +fp t22116; +fp t22583; +fp t22138; +fp t22061; +fp t22582; +fp t21680; +fp t22581; +fp t22580; +fp t21739; +fp t22090; +fp t21732; +fp t21606; +fp t22579; +fp t21708; +fp t22088; +fp t21592; +fp t22578; +fp t21625; +fp t22041; +fp t21344; +fp t22577; +fp t22576; +fp t21705; +fp t21743; +fp t21622; +fp t22575; +fp t22127; +fp t22574; +fp t21052; +fp t22573; +fp t22572; +fp t22571; +fp t22570; +fp t21731; +fp t22569; +fp t22568; +fp t21041; +fp t22567; +fp t21740; +fp t22566; +fp t22103; +fp t22101; +fp t22565; +fp t21434; +fp t22564; +fp t22563; +fp t22139; +fp t21667; +fp t22562; +fp t21574; +fp t22561; +fp t22560; +fp t21628; +fp t22559; +fp t21576; +fp t22122; +fp t22170; +fp t22558; +fp t22557; +fp t22048; +fp t22093; +fp t22556; +fp t22555; +fp t22554; +fp t22147; +fp t22553; +fp t22091; +fp t22105; +fp t22552; +fp t21699; +fp t21746; +fp t21644; +fp t22551; +fp t22550; +fp t22097; +fp t21391; +fp t22187; +fp t21397; +fp t22549; +fp t22047; +fp t22548; +fp t22145; +fp t22069; +fp t22547; +fp t22546; +fp t22094; +fp t21297; +fp t21301; +fp t22545; +fp t21748; +fp t22077; +fp t21405; +fp t21789; +fp t21654; +fp t22544; +fp t21728; +fp t21620; +fp t22060; +fp t21963; +fp t22543; +fp t22121; +fp t21205; +fp t22067; +fp t22542; +fp t21753; +fp t22080; +fp t21251; +fp t21796; +fp t21658; +fp t22541; +fp t21763; +fp t21486; +fp t21749; +fp t22155; +fp t21437; +fp t22160; +fp t22092; +fp t21458; +fp t22183; +fp t22168; +fp t22540; +fp t22136; +fp t21160; +fp t22539; +fp t22131; +fp t21278; +fp t21319; +fp t22538; +fp t22180; +fp t22537; +fp t22058; +fp t22536; +fp t21704; +fp t22046; +fp t21714; +fp t21589; +fp t22535; +fp t21605; +fp t22534; +fp t21609; +fp t21342; +fp t21764; +fp t22018; +fp t22533; +fp t22076; +fp t21426; +fp t21472; +fp t22086; +fp t21549; +fp t22532; +fp t21325; +fp t22531; +fp t21730; +fp t21252; +fp t21614; +fp t22193; +fp t22530; +fp t22194; +fp t22104; +fp t22124; +fp t21277; +fp t22529; +fp t21943; +fp t21577; +fp t22482; +fp t22528; +fp t22000; +fp t21722; +fp t22054; +fp t22527; +fp t21347; +fp t22039; +fp t21517; +fp t21421; +fp t22526; +fp t21182; +fp t21126; +fp t21087; +fp t22115; +fp t21941; +fp t22525; +fp t21587; +fp t21059; +fp t21185; +fp t22052; +fp t21971; +fp t22524; +fp t22523; +fp t22045; +fp t21330; +fp t22075; +fp t21051; +fp t22087; +fp t21933; +fp t22107; +fp t21091; +fp t22522; +fp t22095; +fp t21102; +fp t21266; +fp t21545; +fp t21984; +fp t22521; +fp t21940; +fp t21685; +fp t22150; +fp t21150; +fp t22520; +fp t22030; +fp t21488; +fp t21949; +fp t22519; +fp t21969; +fp t21616; +fp t22518; +fp t22195; +fp t21630; +fp t21617; +fp t21283; +fp t22517; +fp t21381; +fp t21401; +fp t22516; +fp t21134; +fp t22515; +fp t21089; +fp t21073; +fp t22514; +fp t21735; +fp t22153; +fp t21495; +fp t22064; +fp t21315; +fp t22513; +fp t21769; +fp t21752; +fp t22162; +fp t22512; +fp t21744; +fp t21968; +fp t21747; +fp t22006; +fp t22511; +fp t21604; +fp t21428; +fp t22008; +fp t22510; +fp t21595; +fp t21158; +fp t22509; +fp t21618; +fp t21490; +fp t22508; +fp t22507; +fp t22149; +fp t22506; +fp t22007; +fp t22505; +fp t22014; +fp t22504; +fp t21945; +fp t21043; +fp t22503; +fp t21601; +fp t22502; +fp t21063; +fp t21226; +fp t22501; +fp t21765; +fp t21634; +fp t21355; +fp t22500; +fp t21627; +fp t21275; +fp t21398; +fp t22499; +fp t21192; +fp t22498; +fp t21446; +fp t22021; +fp t22497; +fp t21074; +fp t21177; +fp t22496; +fp t22494; +fp t21751; +fp t21668; +fp t21509; +fp t22493; +fp t21781; +fp t22492; +fp t21338; +fp t22159; +fp t21247; +fp t22491; +fp t22119; +fp t21057; +fp t21936; +fp t22490; +fp t22085; +fp t21254; +fp t22130; +fp t21055; +fp t22489; +fp t21312; +fp t21112; +fp t22488; +fp t21048; +fp t22487; +fp t22140; +fp t21558; +fp t21762; +fp t22486; +fp t21101; +fp t22485; +fp t22484; +fp t21504; +fp t22481; +fp t21934; +fp t22480; +fp t21056; +fp t21950; +fp t22479; +fp t21583; +fp t22478; +fp t22035; +fp t21271; +fp t21274; +fp t21938; +fp t22477; +fp t21109; +fp t22476; +fp t21365; +fp t21373; +fp t22475; +fp t21578; +fp t21957; +fp t22474; +fp t22473; +fp t22123; +fp t21180; +fp t21960; +fp t22191; +fp t21491; +fp t22472; +fp t21970; +fp t22471; +fp t22470; +fp t22469; +fp t22027; +fp t21975; +fp t22177; +fp t21295; +fp t22468; +fp t22096; +fp t21305; +fp t22164; +fp t22467; +fp t21375; +fp t21339; +fp t22466; +fp t22161; +fp t21374; +fp t21485; +fp t22465; +fp t22129; +fp t21116; +fp t22464; +fp t21546; +fp t21516; +fp t22192; +fp t22163; +fp t22463; +fp t22462; +fp t21455; +fp t22461; +fp t21386; +fp t22460; +fp t21269; +fp t21961; +fp t21613; +fp t22050; +fp t22459; +fp t21760; +fp t22125; +fp t21790; +fp t22176; +fp t21985; +fp t22458; +fp t22457; +fp t21246; +fp t22456; +fp t21276; +fp t22455; +fp t21584; +fp t21097; +fp t22454; +fp t21633; +fp t21741; +fp t22065; +fp t21412; +fp t21976; +fp t22453; +fp t22011; +fp t21611; +fp t21487; +fp t22452; +fp t22451; +fp t21346; +fp t22181; +fp t22450; +fp t22449; +fp t22043; +fp t21379; +fp t22120; +fp t21166; +fp t22448; +fp t22189; +fp t21110; +fp t21986; +fp t22447; +fp t21400; +fp t22025; +fp t21931; +fp t22446; +fp t22445; +fp t21352; +fp t22444; +fp t22443; +fp t22442; +fp t21165; +fp t22081; +fp t22441; +fp t21594; +fp t22440; +fp t21336; +fp t21243; +fp t21409; +fp t22439; +fp t21623; +fp t21279; +fp t22169; +fp t21306; +fp t22020; +fp t22438; +fp t21956; +fp t22437; +fp t22436; +fp t22137; +fp t21366; +fp t21767; +fp t21958; +fp t22435; +fp t22038; +fp t21478; +fp t21935; +fp t22434; +fp t22175; +fp t21183; +fp t21108; +fp t22433; +fp t21037; +fp t22432; +fp t22174; +fp t21998; +fp t22178; +fp t21990; +fp t22431; +fp t22430; +fp t21738; +fp t22034; +fp t21348; +fp t22429; +fp t22113; +fp t21408; +fp t22074; +fp t22428; +fp t21974; +fp t21270; +fp t21435; +fp t22427; +fp t22426; +fp t22425; +fp t21105; +fp t22424; +fp t21479; +fp t21703; +fp t22156; +fp t21106; +fp t22423; +fp t21326; +fp t21164; +fp t22005; +fp t22422; +fp t21098; +fp t22421; +fp t22420; +fp t21155; +fp t22419; +fp t22418; +fp t22083; +fp t21377; +fp t22417; +fp t22416; +fp t21947; +fp t22415; +fp t21638; +fp t21456; +fp t22016; +fp t22414; +fp t22413; +fp t21260; +fp t21955; +fp t22412; +fp t22029; +fp t21235; +fp t22411; +fp t21953; +fp t22410; +fp t22409; +fp t22408; +fp t21443; +fp t22407; +fp t22406; +fp t22118; +fp t21284; +fp t21457; +fp t22405; +fp t21061; +fp t22404; +fp t22063; +fp t21146; +fp t22173; +fp t21045; +fp t21942; +fp t21959; +fp t22403; +fp t22402; +fp t22401; +fp t22400; +fp t22073; +fp t21060; +fp t22399; +fp t22398; +fp t21291; +fp t22397; +fp t21171; +fp t22051; +fp t22396; +fp t22078; +fp t21273; +fp t22151; +fp t21787; +fp t22004; +fp t22395; +fp t21258; +fp t21494; +fp t22394; +fp t21142; +fp t22393; +fp t21413; +fp t21220; +fp t21951; +fp t22392; +fp t21445; +fp t22391; +fp t22390; +fp t21404; +fp t21070; +fp t21952; +fp t22389; +fp t21308; +fp t21997; +fp t22388; +fp t22387; +fp t21436; +fp t22386; +fp t22385; +fp t22384; +fp t22383; +fp t21263; +fp t22382; +fp t22381; +fp t21072; +fp t22380; +fp t22379; +fp t21972; +fp t22378; +fp t22377; +fp t21734; +fp t21791; +fp t22376; +fp t21779; +fp t21727; +fp t22375; +fp t22374; +fp t22373; +fp t22372; +fp t21176; +fp t22371; +fp t22040; +fp t22370; +fp t22369; +fp t22368; +fp t21562; +fp t22367; +fp t22366; +fp t22365; +fp t22364; +fp t21068; +fp t22363; +fp t21983; +fp t21523; +fp t22362; +fp t22361; +fp t21514; +fp t22360; +fp t22359; +fp t22358; +fp t22357; +fp t22356; +fp t22355; +fp t21552; +fp t21788; +fp t21560; +fp t21550; +fp t22354; +fp t22353; +fp t22352; +fp t22351; +fp t22350; +fp t22349; +fp t21396; +fp t21932; +fp t22348; +fp t21771; +fp t21568; +fp t21367; +fp t22165; +fp t22347; +fp t21309; +fp t22024; +fp t22015; +fp t22346; +fp t22345; +fp t22344; +fp t22343; +fp t21754; +fp t22167; +fp t22013; +fp t22342; +fp t22341; +fp t21994; +fp t21995; +fp t22049; +fp t21385; +fp t22340; +fp t21965; +fp t22339; +fp t21978; +fp t22338; +fp t21973; +fp t22337; +fp t22336; +fp t21991; +fp t22335; +fp t21954; +fp t22089; +fp t22334; +fp t22333; +fp t22002; +fp t21996; +fp t22332; +fp t22331; +fp t22330; +fp t22152; +fp t22329; +fp t21610; +fp t21944; +fp t22328; +fp t22327; +fp t22053; +fp t22326; +fp t22325; +fp t21448; +fp t21520; +fp t22324; +fp t22323; +fp t22322; +fp t22321; +fp t21962; +fp t22320; +fp t22019; +fp t22319; +fp t21463; +fp t22318; +fp t22317; +fp t22112; +fp t22316; +fp t21536; +fp t22184; +fp t21392; +fp t21761; +fp t22179; +fp t22003; +fp t22023; +fp t22315; +fp t22314; +fp t22313; +fp t22312; +fp t21966; +fp t22311; +fp t21127; +fp t22310; +fp t22309; +fp t22308; +fp t22307; +fp t21512; +fp t22068; +fp t21988; +fp t21662; +fp t22306; +fp t22305; +fp t21528; +fp t22304; +fp t22303; +fp t22302; +fp t22301; +fp t22300; +fp t22299; +fp t22298; +fp t22297; +fp t21989; +fp t22188; +fp t22296; +fp t22295; +fp t22294; +fp t21647; +fp t21531; +fp t22293; +fp t21170; +fp t22292; +fp t22291; +fp t22290; +fp t22289; +fp t22055; +fp t21519; +fp t22166; +fp t22288; +fp t22012; +fp t22186; +fp t21756; +fp t22287; +fp t22286; +fp t22285; +fp t22284; +fp t21982; +fp t21508; +fp t22283; +fp t21964; +fp t22282; +fp t21525; +fp t22281; +fp t22280; +fp t22017; +fp t22279; +fp t21679; +fp t21999; +fp t22278; +fp t22277; +fp t22142; +fp t22276; +fp t22275; +fp t21981; +fp t21987; +fp t22274; +fp t22273; +fp t21979; +fp t22010; +fp t22126; +fp t22272; +fp t22271; +fp t22270; +fp t22269; +fp t22268; +fp t22171; +fp t21174; +fp t22267; +fp t21360; +fp t22266; +fp t21977; +fp t22265; +fp t22264; +fp t22044; +fp t21244; +fp t22263; +fp t22262; +fp t22261; +fp t22260; +fp t22259; +fp t22258; +fp t22257; +fp t22256; +fp t21203; +fp t22255; +fp t22022; +fp t22254; +fp t22253; +fp t22252; +fp t21645; +fp t22251; +fp t22250; +fp t22249; +fp t22248; +fp t22247; +fp t22246; +fp t22245; +fp t22244; +fp t22243; +fp t22242; +fp t21872; +fp t22241; +fp t21873; +fp t22240; +fp t21745; +fp t22239; +fp t22238; +fp t21733; +fp t21786; +fp t22237; +fp t22079; +fp t22236; +fp t21793; +fp t22235; +fp t21230; +fp t21720; +fp t22234; +fp t22233; +fp t22232; +fp t21175; +fp t22231; +fp t21259; +fp t22230; +fp t22229; +fp t22228; +fp t21470; +fp t22227; +fp t21980; +fp t22226; +fp t22225; +fp t22224; +fp t21721; +fp t21777; +fp t22223; +fp t21794; +fp t22222; +fp t22221; +fp t22220; +fp t22219; +fp t22218; +fp t22217; +fp t22216; +fp t22215; +fp t22214; +fp t22213; +fp t22212; +fp t22211; +fp t22210; +fp t22209; +fp t22208; +fp t22207; +fp t22206; +fp t22205; +fp t21687; +fp t21688; +fp t22204; +fp t22203; +fp t22202; +fp t22201; +fp t22200; +fp t22199; +fp t22198; +fp t22197; +fp t22196; +fp t20583; +fp t20513; +fp t22154; +fp t22148; +fp t22144; +fp t22141; +fp t22135; +fp t22134; +fp t22133; +fp t20722; +fp t22132; +fp t20750; +fp t22128; +fp t22099; +fp t21993; +fp t21406; +fp t21476; +fp t21236; +fp t21058; +fp t21939; +fp t21937; +fp t21930; +fp t21929; +fp t21927; +fp t21926; +fp t21925; +fp t21924; +fp t21923; +fp t21922; +fp t21921; +fp t21917; +fp t21916; +fp t21914; +fp t21913; +fp t21912; +fp t21911; +fp t21910; +fp t21909; +fp t21776; +fp t21908; +fp t21907; +fp t21906; +fp t21775; +fp t21905; +fp t21717; +fp t21768; +fp t21904; +fp t21903; +fp t21902; +fp t21901; +fp t21900; +fp t21899; +fp t21689; +fp t21898; +fp t21897; +fp t21770; +fp t21896; +fp t21895; +fp t21894; +fp t21893; +fp t21707; +fp t21892; +fp t21891; +fp t21890; +fp t21888; +fp t21887; +fp t21886; +fp t21885; +fp t21884; +fp t21698; +fp t21883; +fp t21882; +fp t21881; +fp t21880; +fp t21879; +fp t21878; +fp t21877; +fp t21876; +fp t21875; +fp t21874; +fp t21871; +fp t21693; +fp t21870; +fp t21782; +fp t21869; +fp t21868; +fp t21867; +fp t21866; +fp t21865; +fp t21864; +fp t21863; +fp t21862; +fp t21861; +fp t21860; +fp t21859; +fp t21858; +fp t21857; +fp t21856; +fp t21855; +fp t21854; +fp t21853; +fp t21852; +fp t21851; +fp t21850; +fp t21849; +fp t21848; +fp t21847; +fp t21846; +fp t21845; +fp t21844; +fp t21843; +fp t21842; +fp t21841; +fp t21840; +fp t21839; +fp t21838; +fp t21837; +fp t21836; +fp t21835; +fp t21834; +fp t21833; +fp t21832; +fp t21831; +fp t21830; +fp t21829; +fp t21828; +fp t21827; +fp t21826; +fp t21825; +fp t21824; +fp t21823; +fp t21822; +fp t21821; +fp t21820; +fp t21819; +fp t21818; +fp t21817; +fp t21816; +fp t21815; +fp t21814; +fp t21813; +fp t21812; +fp t21811; +fp t21692; + t21716 = RATIONAL(1.0,576.0); + t21801 = z*z; + t21806 = t21801*t21801; + t21710 = RATIONAL(1.0,144.0); + t22624 = t21716*t21806+t21710; + t21674 = RATIONAL(1.0,1728.0); + t21805 = t21801*z; + t21677 = RATIONAL(-1.0,1728.0); + t22623 = t21674*z+t21677*t21805; + t21675 = RATIONAL(1.0,3456.0); + t21676 = RATIONAL(-1.0,3456.0); + t22622 = t21675*t21806+t21676*t21801; + t21773 = RATIONAL(-1.0,9.0); + t21726 = RATIONAL(-1.0,36.0); + t22098 = t21806*t21726; + t22621 = t22098+t21773; + t21709 = RATIONAL(-5.0,288.0); + t21686 = RATIONAL(5.0,288.0); + t22620 = t21709*z+t21805*t21686; + t21800 = x*x; + t21673 = RATIONAL(-1.0,1152.0); + t21678 = RATIONAL(1.0,1152.0); + t22033 = t21806*t21678; + t22157 = t21800*t21801; + t22619 = t21800*t22033+t21673*t22157; + t21729 = RATIONAL(4.0,27.0); + t21802 = y*y; + t21804 = t21802*y; + t22182 = x*t21804; + t22001 = t21729*t22182; + t21736 = RATIONAL(-2.0,27.0); + t21803 = x*t21800; + t22072 = t21804*t21803; + t21946 = t21736*t22072; + t22618 = t21946+t22001; + t21783 = RATIONAL(1.0,3.0); + t21659 = t21783*t21800; + t21792 = RATIONAL(-4.0,9.0); + t22617 = (t21792+t21659)*t21804; + t21715 = RATIONAL(-1.0,576.0); + t21712 = RATIONAL(-1.0,144.0); + t22616 = t21715*t21806+t21712; + t21695 = RATIONAL(-1.0,108.0); + t22071 = t21695*t21804; + t21681 = RATIONAL(1.0,216.0); + t21588 = t21681*z; + t22615 = y*t21588+z*t22071; + t21706 = RATIONAL(1.0,288.0); + t21718 = RATIONAL(-1.0,864.0); + t21596 = t21718*t21806; + t22110 = t21802*t21806; + t22614 = t21706*t22110+t21596; + t21757 = RATIONAL(1.0,36.0); + t22084 = t21757*t21806; + t21774 = RATIONAL(1.0,9.0); + t22613 = t22084+t21774; + t22117 = t21805*t21803; + t22172 = z*t21803; + t22612 = t21710*t22172+t21712*t22117; + t21750 = RATIONAL(-1.0,24.0); + t21636 = t21750*t21800; + t21742 = RATIONAL(-1.0,96.0); + t22056 = t21800*t21806; + t21293 = t21742*t22056; + t22611 = t21636+t21293; + t22114 = t21681*t21804; + t21701 = RATIONAL(-1.0,216.0); + t22042 = t21701*t21804; + t21054 = t21805*t22042; + t22610 = z*t22114+t21054; + t22109 = t21715*t21800; + t21202 = t21716*t22056; + t22609 = t21801*t22109+t21202; + t21724 = RATIONAL(1.0,12.0); + t22608 = t21724*t22056+t21659; + t22607 = t21675*t21801+t21676*t21806; + t21700 = RATIONAL(16.0,27.0); + t21737 = RATIONAL(-4.0,27.0); + t22606 = t21737*t21806+t21700*t21801; + t22111 = t21802*t21803; + t21522 = t21783*t22111; + t22605 = t21522+t21792*t21803; + t22604 = t21710*t22117+t21712*t22172; + t21780 = RATIONAL(-2.0,9.0); + t22059 = t21802*t21780; + t21758 = RATIONAL(1.0,18.0); + t22108 = t21758*t21802; + t22603 = t21801*t22059+t21806*t22108; + t22082 = t21802*t21801; + t22602 = t21716*t22110+t21715*t22082; + t21713 = RATIONAL(-5.0,576.0); + t21579 = t21713*t21801; + t21702 = RATIONAL(5.0,192.0); + t22601 = t21579+t21702*t22157; + t21683 = RATIONAL(-1.0,432.0); + t21682 = RATIONAL(1.0,432.0); + t21599 = t21682*t21801; + t22600 = t21683*t21806+t21599; + t21755 = RATIONAL(1.0,24.0); + t21632 = t21755*t21800; + t21384 = t21804*t21632; + t21719 = RATIONAL(-1.0,72.0); + t21629 = t21719*t21804; + t22599 = t21629+t21384; + t22598 = z*t22042+t21805*t22114; + t21046 = t21716*t22082; + t22597 = t21715*t22110+t21046; + t21798 = RATIONAL(2.0,9.0); + t22062 = t21802*t21798; + t21725 = RATIONAL(-1.0,18.0); + t22106 = t21802*t21725; + t22596 = t21801*t22062+t21806*t22106; + t22026 = t21800*t21780; + t21532 = t21801*t22026; + t22595 = t21758*t22056+t21532; + t22031 = t21805*t21682; + t21593 = t21718*t21805; + t22594 = x*t21593+t21803*t22031; + t22143 = t21800*t21798; + t21542 = z*t22143; + t21759 = RATIONAL(-8.0,27.0); + t21621 = t21759*z; + t22593 = t21621+t21542; + t21766 = RATIONAL(1.0,72.0); + t22592 = t21758+t21766*t21806; + t22591 = t21725*t22056+t21801*t22143; + t21684 = RATIONAL(1.0,864.0); + t21597 = t21684*t21805; + t22036 = t21803*t21683; + t22590 = x*t21597+t21805*t22036; + t21602 = t21701*z; + t21694 = RATIONAL(1.0,108.0); + t22102 = t21694*t21803; + t22589 = x*t21602+z*t22102; + t21784 = RATIONAL(8.0,9.0); + t22588 = t21806*t21798+t21784; + t22057 = t21673*t21802; + t22066 = t21678*t21801; + t22587 = t21806*t22057+t21802*t22066; + t21799 = RATIONAL(4.0,9.0); + t21785 = RATIONAL(-1.0,3.0); + t21651 = t21785*t21800; + t22586 = (t21799+t21651)*t21804; + t22185 = x*t21802; + t22585 = t21803*t22062+t21792*t22185; + t21544 = t21785*t22111; + t22584 = t21544+t21799*t21803; + t22037 = t21803*t21701; + t22116 = t21681*t21803; + t22583 = z*t22116+t21805*t22037; + t22138 = t21806*t21804; + t22061 = t21674*t21804; + t22582 = t21801*t22061+t21677*t22138; + t21680 = RATIONAL(-16.0,27.0); + t22581 = t21729*t21806+t21680*t21801; + t22580 = t21750*t21802+t21742*t22110; + t21739 = RATIONAL(2.0,27.0); + t22090 = t21739*t21801; + t21732 = RATIONAL(-1.0,54.0); + t21606 = t21732*t21806; + t22579 = t22090+t21606; + t21708 = RATIONAL(-1.0,288.0); + t22088 = t21802*t21708; + t21592 = t21684*t21806; + t22578 = t21806*t22088+t21592; + t21625 = t21736*t21805; + t22041 = t21729*t21805; + t21344 = y*t22041; + t22577 = t21344+t21804*t21625; + t22576 = t21803*t22059+t21799*t22185; + t21705 = RATIONAL(1.0,192.0); + t21743 = RATIONAL(1.0,48.0); + t21622 = t21743*t21800; + t22575 = t21622+t21705*t22056; + t22127 = t21800*t21716; + t22574 = z*t22109+t21805*t22127; + t21052 = t21715*t22056; + t22573 = t21801*t22127+t21052; + t22572 = t21684*t22117+t21718*t22172; + t22571 = t21682*t21806+t21683*t21801; + t22570 = t22620*x; + t21731 = RATIONAL(-1.0,12.0); + t22569 = t21651+t21731*t22056; + t22568 = t22621*y; + t21041 = t21805*t22116; + t22567 = t21041+z*t22037; + t21740 = RATIONAL(1.0,96.0); + t22566 = t21755*t21802+t21740*t22110; + t22103 = t21805*t21737; + t22101 = t21739*t21804; + t22565 = t21805*t22101+y*t22103; + t21434 = t21740*t22056; + t22564 = t21632+t21434; + t22563 = t21725+t21719*t21806; + t22139 = t21800*t21804; + t21667 = t21773*t21804; + t22562 = t21724*t22139+t21667; + t21574 = t21674*t21805; + t22561 = t21805*t22109+z*t22127+t21574; + t22560 = t21719*t21803+t22624*x; + t21628 = t21759*t21801; + t22559 = t21628+t22591; + t21576 = t21677*z; + t22122 = t21715*t21802; + t22170 = z*t21802; + t22558 = t21576+t21805*t22122+t21716*t22170; + t22557 = t21684*t22172+x*t21574+t21718*t22117; + t22048 = t21718*t21804; + t22093 = t21804*t21684; + t22556 = z*t22093+y*t21576+t21805*t22048; + t22555 = t21802*t22033+t21801*t22057+t22607; + t22554 = z*t22048+t21805*t22093+t22623*y; + t22147 = t21805*t21802; + t22553 = t21716*t22147+z*t22122+t22623; + t22091 = t21803*t21801; + t22105 = t21803*t21806; + t22552 = t21674*t22091+t21677*t22105+t22622*x; + t21699 = RATIONAL(-1.0,192.0); + t21746 = RATIONAL(-1.0,48.0); + t21644 = t21746*t21800; + t22551 = t21699*t22056+t21644+t22624; + t22550 = t21673*t22056+t21800*t22066+t22622; + t22097 = t21802*t21726; + t21391 = t21805*t22097; + t22187 = z*t21800; + t21397 = t21757*t22187; + t22549 = t21391+t21397; + t22047 = t21802*t21731; + t22548 = t21806*t22047+t21785*t21802; + t22145 = t21805*t21804; + t22069 = t21712*t21804; + t22547 = t21710*t22145+z*t22069; + t22546 = t21746*t21802+t21699*t22110; + t22094 = t21800*t21726; + t21297 = z*t22094; + t21301 = t21757*t22147; + t22545 = t21297+t21301; + t21748 = RATIONAL(5.0,12.0); + t22077 = t21802*t21748; + t21405 = t21801*t22077; + t21789 = RATIONAL(-5.0,9.0); + t21654 = t21789*t21801; + t22544 = t21405+t21654; + t21728 = RATIONAL(1.0,27.0); + t21620 = t21728*z; + t22060 = t21800*t21802; + t21963 = t21746*t22060; + t22543 = t21805*t21963+t21620; + t22121 = t21805*t21712; + t21205 = t21802*t22121; + t22067 = t21800*t21774; + t22542 = z*t22067+t21205; + t21753 = RATIONAL(-5.0,12.0); + t22080 = t21753*t21801; + t21251 = t21802*t22080; + t21796 = RATIONAL(5.0,9.0); + t21658 = t21796*t21801; + t22541 = t21658+t21251; + t21763 = RATIONAL(-5.0,36.0); + t21486 = t21804*t22098; + t21749 = RATIONAL(5.0,36.0); + t22155 = t21749*t21801; + t21437 = x*t22155; + t22160 = t21803*t21486+y*t21437; + t22092 = t21757*t21801; + t21458 = t21804*t22092; + t22183 = x*t21806; + t22168 = y*t22183; + t22540 = t22160+t21763*t22168+t21803*t21458; + t22136 = t21802*t21774; + t21160 = t21800*t22121; + t22539 = z*t22136+t21160; + t22131 = t21805*t21800; + t21278 = t21757*t22131; + t21319 = z*t22097; + t22538 = t21278+t21319; + t22180 = z*t21804; + t22537 = t21710*t22180+t21805*t22069; + t22058 = t21802*t21724; + t22536 = t21783*t21802+t21806*t22058; + t21704 = RATIONAL(-5.0,192.0); + t22046 = t21704*t21801; + t21714 = RATIONAL(5.0,576.0); + t21589 = t21714*t21801; + t22535 = t21589+t21802*t22046; + t21605 = t21728*t21805; + t22534 = t21605+z*t21963; + t21609 = t21766*t21804; + t21342 = t21806*t21609; + t21764 = RATIONAL(-5.0,18.0); + t22018 = y*t22091; + t22533 = t22160+t21764*t22018+x*t21342; + t22076 = t21726*t21801; + t21426 = t21802*t22076; + t21472 = t21757*t22056; + t22086 = t21800*t21773; + t21549 = t21801*t22086; + t22532 = t21426+t21472+t21549; + t21325 = t21719*t22170; + t22531 = x*t21325+t22594; + t21730 = RATIONAL(-1.0,27.0); + t21252 = t21730*t22117; + t21614 = t21739*t21805; + t22193 = x*z; + t22530 = t21252+x*t21614+t22108*t22193; + t22194 = y*z; + t22104 = t21800*t21758; + t22124 = t21730*t21804; + t21277 = t21805*t22124; + t22529 = t22104*t22194+y*t21614+t21277; + t21943 = t21800*t22047; + t21577 = t21694*t21805; + t22482 = z*t21943+t21577; + t22528 = t22482+t22542; + t22000 = z*t21667; + t21722 = RATIONAL(1.0,54.0); + t22054 = t21805*t21722; + t22527 = t21800*t22000+(t22054+t21542)*y; + t21347 = t21800*t22076; + t22039 = t21802*t21773; + t21517 = t21801*t22039; + t21421 = t21802*t22084; + t22526 = t21347+t21517+t21421; + t21182 = t21801*t22071; + t21126 = t21706*t22056; + t21087 = y*t21596; + t22115 = t21804*t21801; + t21941 = t21800*t22115; + t22525 = t21182+t21087+t21757*t21941+y*t21126; + t21587 = t21701*t21805; + t21059 = z*t22088; + t21185 = t21805*t22102; + t22052 = t21802*t21710; + t21971 = t21803*t22052; + t22524 = t21185+z*t21971+(t21059+t21587)*x; + t22523 = t21743*t21802+t21705*t22110+t22616; + t22045 = t21800*t21766; + t21330 = t21806*t22045; + t22075 = t21683*t21804; + t21051 = t21801*t22075; + t22087 = t21800*t21710; + t21933 = t21804*t22087; + t22107 = t21806*t21701; + t21091 = y*t22107; + t22522 = y*t21330+t21051+t21801*t21933+t21091; + t22095 = t21803*t21695; + t21102 = t21805*t22095; + t21266 = x*t22054; + t21545 = z*t22062; + t21984 = z*t22111; + t22521 = x*t21545+t21102+t21266+t21773*t21984; + t21940 = t21774*t22091; + t21685 = RATIONAL(-5.0,144.0); + t22150 = t21685*t21806; + t21150 = y*t22150; + t22520 = x*t21150+t21804*t21940; + t22030 = t21736*t21801; + t21488 = x*t22030; + t21949 = t21806*t22072; + t22519 = t21722*t21949+y*t21488; + t21969 = t21805*t22060; + t21616 = t21730*z; + t22518 = t21743*t21969+t21616; + t22195 = y*x; + t21630 = t21739*t21806; + t21617 = t21732*t21801; + t21283 = t21804*t21617; + t22517 = t21803*t21283+t21630*t22195; + t21381 = t21805*t22094; + t21401 = t21757*t22170; + t22516 = t21381+t21401; + t21134 = t21806*t22095; + t22515 = t21801*t22001+y*t21134; + t21089 = t21695*t22091; + t21073 = t21682*t22138; + t22514 = x*t21073+y*t21089; + t21735 = RATIONAL(5.0,72.0); + t22153 = t21735*t21806; + t21495 = y*t22153; + t22064 = t21725*t21801; + t21315 = t21804*t22064; + t22513 = t21803*t21495+x*t21315; + t21769 = RATIONAL(-1.0,6.0); + t21752 = RATIONAL(25.0,6.0); + t22162 = t21801*t22195; + t22512 = t21769*t21949+t21752*t22162; + t21744 = RATIONAL(5.0,48.0); + t21968 = t21744*t22091; + t21747 = RATIONAL(-5.0,48.0); + t22006 = t21747*t22183; + t22511 = t21804*t22006+y*t21968; + t21604 = t21728*t21801; + t21428 = t21804*t21604; + t22008 = y*t22105; + t22510 = t21730*t22008+x*t21428; + t21595 = t21681*t21801; + t21158 = t21804*t21595; + t22509 = x*t21091+t21803*t21158; + t21618 = t21722*t21806; + t21490 = y*t21618; + t22508 = x*t21490+t21801*t21946; + t22507 = t21742*t21969+t21588; + t22149 = RATIONAL(-25.0,96.0)*t21801; + t22506 = t21755*t21949+t22149*t22195; + t22007 = x*t22115; + t22505 = t21744*t22007+t21747*t22008; + t22014 = z*t22060; + t22504 = t21587+t21740*t22014; + t21945 = t21710*t22105; + t21043 = x*t21579; + t22503 = y*t21043+t21804*t21945; + t21601 = t21681*t21805; + t22502 = t21601+t21742*t22014; + t21063 = t21694*t22138; + t21226 = t21801*t22036; + t22501 = y*t21226+x*t21063; + t21765 = RATIONAL(-5.0,72.0); + t21634 = t21765*t21801; + t21355 = t21804*t21634; + t22500 = x*t21355+t21758*t22008; + t21627 = t21758*t21804; + t21275 = x*t21627; + t21398 = t21803*t21634; + t22499 = t21806*t21275+y*t21398; + t21192 = t21682*t22105; + t22498 = y*t21192+x*t21182; + t21446 = t21803*t22064; + t22021 = x*t22138; + t22497 = t21735*t22021+y*t21446; + t21074 = t21686*t22091; + t21177 = t21708*t22138; + t22496 = y*t21074+x*t21177; + t22494 = t21740*t21969+t21602; + t21751 = RATIONAL(-20.0,9.0); + t21668 = t21774*t21804; + t21509 = t21806*t21668; + t22493 = t21803*t21509+t21751*t22162; + t21781 = RATIONAL(-5.0,3.0); + t22492 = t21781*t22018+t21748*t22021; + t21338 = t21728*t22091; + t22159 = t21730*t21806; + t21247 = x*t22159; + t22491 = y*t21338+t21804*t21247; + t22119 = t21806*t21714; + t21057 = x*t22119; + t21936 = t21712*t22091; + t22490 = t21804*t21936+y*t21057; + t22085 = t21800*t21719; + t21254 = z*t22085; + t22130 = t21802*t21706; + t21055 = t21805*t22130; + t22489 = t21254+t21055; + t21312 = z*t22045; + t21112 = t21805*t22088; + t22488 = t21312+t21112; + t21048 = t21806*t22071; + t22487 = t21729*t22018+x*t21048; + t22140 = t21806*t21780; + t21558 = x*t22140; + t21762 = RATIONAL(10.0,9.0); + t22486 = t21804*t21558+t21762*t22018; + t21101 = x*t21595; + t22485 = y*t21101+t21701*t21949; + t22484 = t21748*t22008+t21781*t22007; + t21504 = t21792*t22115; + t22481 = t21803*t21504+t21796*t22168; + t21934 = t21805*t22111; + t22480 = t21766*t21934+(t21401+t21577)*x; + t21056 = y*t21577; + t21950 = t21804*t22131; + t22479 = y*t21397+t21766*t21950+t21056; + t21583 = t21695*t21805; + t22478 = t21719*t21934+(t21583+t21319)*x; + t22035 = t21766*t21801; + t21271 = t21800*t22035; + t21274 = t21802*t22035; + t21938 = t21802*t22056; + t22477 = t21740*t21938+t21271+t21274; + t21109 = y*t21583; + t22476 = t21719*t21950+y*t21297+t21109; + t21365 = t21719*t22082; + t21373 = t21801*t22085; + t22475 = t21365+t21373+t21742*t21938; + t21578 = t21695*t21806; + t21957 = t21801*t22060; + t22474 = t21724*t21957+t21604+t21746*t21938+t21578; + t22473 = t21699*t21938+t21705*t21957+t22600; + t22123 = t21805*t21685; + t21180 = y*t22123; + t21960 = t21774*t22072; + t22191 = z*t21749; + t21491 = y*t22191; + t22472 = t21726*t21805*t22072+z*t21960+(t21491+t21180)*x; + t21970 = t21802*t22105; + t22471 = x*t21365+t21101+t21192+t21712*t21970; + t22470 = t22497+t22520; + t22469 = t22518+t22549; + t22027 = t21722*t21804; + t21975 = t21803*t22027; + t22177 = z*t21736; + t21295 = x*t22177; + t22468 = t21805*t21975+z*t21946+(t21295+t21266)*y; + t22096 = t21805*t21732; + t21305 = t21803*t22096; + t22164 = y*t22172; + t22467 = y*t21305+t21722*t22164+t22610*x; + t21375 = t21725*t22131; + t21339 = t21804*t21620; + t22466 = t21339+t21757*t21950+(t22177+t21375)*y; + t22161 = t21737*t22193; + t21374 = t21804*t21605; + t21485 = t21730*t22172; + t22465 = t21804*t22161+x*t21374+(t21485+t21185)*y; + t22129 = t21800*t21706; + t21116 = t21805*t22129; + t22464 = y*t21116+t21712*t21950+t22615; + t21546 = t21799*t22072; + t21516 = t21773*t22072; + t22192 = y*t22193; + t22163 = t21805*t22195; + t22463 = t21789*t22163+t21805*t21516+z*t21546+RATIONAL(20.0,9.0)*t22192; + t22462 = t22516+t22518; + t21455 = t21803*t22054; + t22461 = t21732*t22164+y*t21455+t22598*x; + t21386 = t21801*t22027; + t22460 = t21803*t21386+x*t21087+t22514; + t21269 = t21800*t22092; + t21961 = t21804*t22045; + t21613 = t21730*t21801; + t22050 = t21804*t21732; + t22459 = (t21961+t22050)*t21806+(t21613+t21269)*y; + t21760 = RATIONAL(-10.0,9.0); + t22125 = t21760*t21801; + t21790 = RATIONAL(5.0,6.0); + t22176 = y*t21800; + t21985 = t21790*t22176; + t22458 = t21801*t21985+y*t22125+t22562*t21806; + t22457 = t22482+t22539; + t21246 = t21719*t22056; + t22456 = t21806*t22027+t21804*t21246+(t21604+t21347)*y; + t21276 = t21728*t22172; + t22455 = z*t22001+x*t21277+(t21102+t21276)*y; + t21584 = t21694*t21806; + t21097 = t21712*t22056; + t22454 = t21725*t21941+t21804*t22090+(t21584+t21097)*y; + t21633 = t21735*t21801; + t21741 = RATIONAL(-5.0,96.0); + t22065 = t21741*t21800; + t21412 = t21801*t22065; + t21976 = t21804*t21644; + t22453 = t21804*t22084+t21806*t21976+(t21412+t21633)*y; + t22011 = y*t22131; + t21611 = t21725*t21804; + t21487 = z*t21611; + t22452 = t21491+t21487+t21744*t22011+t21750*t21950; + t22451 = t22485+t22498; + t21346 = t21805*t22108; + t22181 = t21739*z; + t22450 = t21726*t21934+t21485+(t22181+t21346)*x; + t22449 = t22491+t22515; + t22043 = t21802*t21766; + t21379 = z*t22043; + t22120 = t21800*t21708; + t21166 = t21805*t22120; + t22448 = t21379+t21166+t22494; + t22189 = z*t21695; + t21110 = x*t22189; + t21986 = z*t22072; + t22447 = t21804*t21185+x*t21056+y*t21110+t21695*t21986; + t21400 = t21805*t22106; + t22025 = t21757*t21803; + t21931 = t21802*t22025; + t22446 = t21805*t21931+x*t21400+t21276+t21295; + t22445 = t22516+t22534; + t21352 = t21805*t22027; + t22444 = x*t21352+t22050*t22193+t22567*y; + t22443 = t21801*t21943+t21584+t21743*t21938+t21613; + t22442 = t22508+t22515; + t21165 = t21800*t22046; + t22081 = t21706*t21804; + t22441 = t21806*t22081+t21804*t21293+(t21165+t21589)*y; + t21594 = t21701*t21801; + t22440 = t21802*t21945+t21806*t22036+(t21274+t21594)*x; + t21336 = t21805*t22104; + t21243 = z*t22124; + t21409 = y*t22181; + t22439 = t21243+y*t21336+t21409+t21726*t21950; + t21623 = t21758*t21803; + t21279 = z*t21623; + t22169 = t21763*z; + t21306 = x*t22169; + t22020 = x*t22147; + t22438 = t21747*t22020+t21279+t21306+t21755*t21934; + t21956 = t21719*t22111; + t22437 = t21806*t21956+t21722*t22105+(t21426+t21604)*x; + t22436 = t22510+t22517; + t22137 = t21805*t21764; + t21366 = y*t22137; + t21767 = RATIONAL(5.0,18.0); + t21958 = t21725*t22072; + t22435 = x*t21366+t21767*t22192+t21805*t21958+t21758*t21986; + t22038 = t21741*t21802; + t21478 = t21801*t22038; + t21935 = t21746*t22105; + t22434 = t21806*t22025+t21802*t21935+(t21478+t21633)*x; + t22175 = z*t21694; + t21183 = x*t22175; + t21108 = t21805*t22071; + t22433 = t21694*t21986+y*t21183+t21803*t21108+x*t21109; + t21037 = t21804*t22175; + t22432 = t21805*t21933+t21037+(t21166+t21602)*y; + t22174 = y*t21803; + t21998 = t21784*t22174; + t22178 = x*t21764; + t21990 = t21804*t22178; + t22431 = t21801*t21998+t21806*t21990+t22481; + t22430 = (t22075+t21933)*t21806+(t21594+t21271)*y; + t21738 = RATIONAL(5.0,96.0); + t22034 = t21738*t21801; + t21348 = t21802*t22034; + t22429 = t21803*t22098+t21743*t21970+(t21348+t21634)*x; + t22113 = t21800*t21748; + t21408 = t21801*t22113; + t22074 = t21763*t21801; + t22428 = t22599*t21806+(t22074+t21408)*y; + t21974 = t21739*t22072; + t21270 = t21805*t22050; + t21435 = y*t22096; + t22427 = z*t21974+t21803*t21270+(t21409+t21435)*x; + t22426 = t21699*t21957+t21705*t21938+t22571; + t22425 = t22027*t22193+x*t21270+t22583*y; + t21105 = z*t22120; + t22424 = t21105+t21805*t22043+t22504; + t21479 = t21804*t22025; + t21703 = RATIONAL(5.0,144.0); + t22156 = t21805*t21703; + t21106 = y*t22156; + t22423 = y*t21306+z*t21516+t21805*t21479+x*t21106; + t21326 = t21728*t22117; + t21164 = t21804*t21577; + t22005 = t21737*t22174; + t22422 = y*t21326+z*t22005+(t21243+t21164)*x; + t21098 = z*t22095; + t22421 = t21098+t21712*t21934+(t21588+t21055)*x; + t22420 = x*t21112+t21710*t21934+t22589; + t21155 = t21806*t22102; + t22419 = x*t21051+y*t21155+t22514; + t22418 = t22485+t22509; + t22083 = t21749*t21804; + t21377 = t21801*t22083; + t22417 = t21516+t21803*t21377+t22568*x; + t22416 = t21583+t21724*t22014+t22543; + t21947 = t21805*t21632; + t22415 = z*t21627+t21747*t22011+y*t22169+t21804*t21947; + t21638 = t21725*t21803; + t21456 = z*t21638; + t22016 = t21744*t22185; + t22414 = t21456+x*t22191+t21750*t21934+t21805*t22016; + t22413 = t21116+t21325+t22507; + t21260 = t21800*t22034; + t21955 = t21804*t21622; + t22412 = t21806*t21955+t21486+(t21260+t21634)*y; + t22029 = t21728*t21806; + t21235 = t21806*t22097; + t22411 = t21801*t21956+t21722*t22091+(t21235+t22029)*x; + t21953 = t21800*t22069; + t22410 = t21806*t21953+t21073+(t21373+t21595)*y; + t22409 = t21804*t21434+t21177+t22601*y; + t22408 = t21729*t22164+y*t21252+(t21339+t21108)*x; + t21443 = t21757*t22082; + t22407 = t21732*t22105+t21766*t21970+(t21613+t21443)*x; + t22406 = t22508+t22519; + t22118 = t21805*t21767; + t21284 = x*t22118; + t21457 = t21805*t21627; + t22405 = y*t21284+t22178*t22194+z*t21958+t21803*t21457; + t21061 = t21712*t22110; + t22404 = t21803*t22090+t21802*t21446+(t21061+t21584)*x; + t22063 = t21709*t21805; + t21146 = y*t22063; + t22173 = z*t21686; + t21045 = x*t22173; + t21942 = t21719*t22072; + t21959 = t21766*t22072; + t22403 = t21805*t21942+x*t21146+y*t21045+z*t21959; + t22402 = t22487+t22510; + t22401 = z*t21942+t21805*t21959+t22570*y; + t22400 = t21751*t22192+t21805*t21960+t21792*t21986+t21796*t22163; + t22073 = t21706*t21803; + t21060 = t21801*t22073; + t22399 = t21709*t22021+y*t21060+t22490; + t22398 = t22491+t22519; + t21291 = t21726*t22056; + t22397 = t21386+t21719*t21941+(t21291+t22029)*y; + t21171 = z*t22129; + t22051 = t21805*t21719; + t22396 = t21802*t22051+t21171+t22502; + t22078 = t21731*t21804; + t21273 = t21800*t22078; + t22151 = t21762*t21801; + t21787 = RATIONAL(-5.0,6.0); + t22004 = y*t22157; + t22395 = t21787*t22004+y*t22151+t21806*t21273+t21509; + t21258 = t21800*t22080; + t21494 = t21804*t21636; + t22394 = t21342+t21806*t21494+(t22155+t21258)*y; + t21142 = t21801*t22081; + t22393 = t22490+t22503+t21709*t22008+x*t21142+t22496; + t21413 = t21736*t22172; + t21220 = t21805*t22052; + t21951 = t21803*t22108; + t22392 = t21413+t21455+z*t21951+(t21620+t21220)*x; + t21445 = t21739*t22172; + t22391 = t21305+t21445+t21725*t21984+(t21205+t21616)*x; + t22390 = t22520+t22513+t22533; + t21404 = t21804*t22177; + t21070 = t21805*t22087; + t21952 = t21804*t22104; + t22389 = z*t21952+t21404+t21352+(t21620+t21070)*y; + t21308 = z*t22101; + t21997 = t21725*t22187; + t22388 = t21270+t21308+t21804*t21997+(t21160+t21616)*y; + t22387 = t21110+z*t21956+x*t21391+t22583; + t21436 = t21806*t22043; + t22386 = t21330+t21722*t21801+t21436+t21606+t21740*t21957; + t22385 = t21804*t21254+(t22189+t21381)*y+t22610; + t22384 = t22486+t22493+t21764*t22008+t21784*t22007+t22481; + t22383 = t22499+t22513+t22540; + t21263 = t21719*t22110; + t22382 = t21246+t21263+t21618+t21742*t21957+t21617; + t22381 = t22497+t22500+t22540; + t21072 = t21708*t22056; + t22380 = t21594+t21072+t21750*t21957+t22578; + t22379 = t21126+t21595+t21755*t21957+t22614; + t21972 = t21803*t22043; + t22378 = x*t21301+z*t21972+t21183+t22567; + t22377 = z*t21961+(t22175+t21278)*y+t22598; + t21734 = RATIONAL(5.0,32.0); + t21791 = RATIONAL(-1.0,8.0); + t22376 = t21734*t21957+RATIONAL(-1.0,32.0)*t21938+t21633+t21791*t22060+ +t22563; + t21779 = RATIONAL(1.0,8.0); + t21727 = RATIONAL(-5.0,32.0); + t22375 = RATIONAL(1.0,32.0)*t21938+t21779*t22060+t21634+t21727*t21957+ +t22592; + t22374 = t22474+t22526; + t22373 = t21712*t22157+t22473+t22602; + t22372 = t22466+t22527; + t21176 = t21805*t22075; + t22371 = t21176+t22432+(t21597+t21312)*y; + t22040 = t21710*t21801; + t22370 = t21802*t22040+t22426+t22573; + t22369 = t21800*t22040+t22426+t22597; + t22368 = z*t21953+t22432+(t21601+t21171)*y; + t21562 = t21801*t22067; + t22367 = t21291+t21443+t21562+t22443; + t22366 = t22474+t22532; + t22365 = t21326+x*t21625+t22106*t22193+t22450; + t22364 = t22446+t22530; + t21068 = t21804*t22031; + t22363 = t21068+t22464+(t21254+t21593)*y; + t21983 = z*t21668; + t21523 = z*t22026; + t22362 = t21800*t21983+t21435+y*t21523+t22439; + t22361 = z*t21933+t22464+(t21587+t21105)*y; + t21514 = t21798*t22174; + t22360 = t21275+t21514+t22417+t22500+t22533; + t22359 = t21712*t22082+t22473+t22609; + t22358 = t22466+t22529; + t22357 = t21374+t22439+(t21997+t21625)*y; + t22356 = t21269+t21774*t22082+t21235+t22443; + t22355 = x*t21379+t22420+t22590; + t21552 = t21804*t21654; + t21788 = RATIONAL(-8.0,9.0); + t21560 = t21788*t22174; + t21550 = t21788*t22182; + t22354 = t21546+RATIONAL(16.0,9.0)*t22195+t21560+t21550+t21803*t21552+ +t21799*t22168+t22486; + t22353 = t22404+t22407; + t22352 = t21802*t21947+t21375+t21769*t22014+t21545+t21614+t21400+t22593; + t22351 = t22392+t22478; + t22350 = t21705*t22014+t21699*t21969+t22553+t22574; + t22349 = y*t21623+t21798*t22182+t22417+t22499; + t21396 = t21739*t22117; + t21932 = t21728*t22072; + t22348 = z*t21932+t21804*t21252+t21729*t22192+(t21396+t21413)*y+(t21404+ +t22565)*x; + t21771 = RATIONAL(1.0,6.0); + t21568 = t21771*t22139; + t21367 = t21805*t21609; + t22165 = z*t22176; + t22347 = t21180+z*t21568+t21753*t22165+t21367+t22452; + t21309 = t21804*t22051; + t22024 = y*t22117; + t22015 = t21767*t22174; + t22346 = t21765*t22024+x*t21309+t22423+(t22015+t21275)*z; + t22345 = t22408+t22468; + t22344 = t22462+t22528; + t22343 = t22447+t22467; + t21754 = RATIONAL(8.0,27.0); + t22167 = x*t22180; + t22013 = x*t22145; + t22342 = RATIONAL(-32.0,27.0)*t22192+t21759*t21986+t21737*t22013+t21754* +t22163+(t22167+t22164)*t21700+(t22005+t21974)*t21805; + t22341 = t21743*t22014+t21730*t21805+t22538+t22543+t22545; + t21994 = t21799*t22176; + t21995 = y*t22056; + t22049 = t21754*t21804; + t21385 = t21801*t22049; + t22340 = t21806*t21952+t21385+t21736*t22138+t21804*t21532+t21773*t21995+ +t21801*t21994+t22581*y; + t21965 = t21804*t22036; + t22339 = t21682*t21986+t21805*t21965+t22572*y+t22554*x; + t21978 = t21801*t22072; + t22338 = t21684*t21949+t21718*t21978+t22582*x+t22552*y; + t21973 = t21803*t22088; + t22337 = t21681*t22091+t21806*t22037+t21801*t21973+t21706*t21970+(t22571+ +t22597)*x; + t22336 = t22433+t22461; + t21991 = t21767*t22182; + t22335 = t21760*t22167+z*t21560+t22463+(t21991+t21514)*t21805; + t21954 = t21803*t22097; + t22089 = t21694*t21801; + t22334 = t21803*t22089+t21801*t21954+t22440+t22578*x; + t22333 = t21704*t21995+y*t22119+t21142+t21742*t21941+t22409; + t22002 = y*t22065; + t21996 = t21738*t22176; + t22332 = t21805*t22002+t21743*t21950+t22537+(t21996+t21976)*z+t22620*y; + t22331 = t21708*t21934+t21706*t21984+t22553*x+t22572; + t22330 = z*t21975+t21803*t21054+(t21098+t22594)*y+(t21068+t22615)*x; + t22152 = t21763*t21805; + t22329 = z*t21384+y*t22152+t21457+t21747*t22165+t22452; + t21610 = t21754*t21801; + t21944 = t21771*t22060; + t22328 = t21750*t21938+t21736*t21806+t21801*t21944+t21610+t22595+t22603; + t22327 = t22427+t22465; + t22053 = t21677*t21801; + t22326 = t21806*t22061+t21716*t21941+(t22053+t21052)*t21804+(t22607+ +t22619)*y; + t22325 = t21804*t21202+t21715*t21941+t22550*y+t22582; + t21448 = t21803*t22051; + t21520 = t21769*t22111; + t22324 = t22077*t22193+x*t22156+t21448+z*t21520+t22438; + t22323 = t22472+t21764*t22164+t21735*t22024+(t21367+t21487)*x; + t22322 = z*t21965+t21803*t21068+t22557*y+t22556*x; + t22321 = t21805*t21996+t21146+y*t22173+t21746*t21950+t22547+(t21955+ +t22002)*z; + t21962 = t21715*t22111; + t22320 = t21716*t21970+t21801*t21962+t22587*x+t22552; + t22019 = x*t22039; + t22319 = t21736*t22105+t21803*t21610+t22576*t21801+(t22019+t21951)*t21806 ++t22581*x; + t21463 = t21766*t22117; + t22318 = t22472+z*t21990+t21735*t22013+(t21463+t21456)*y; + t22317 = t22446+t22521; + t22112 = t21806*t21713; + t22316 = y*t22112+t21708*t22115+t21702*t21995+t21740*t21941+t22441; + t21536 = t21774*t22117; + t22184 = z*t21762; + t21392 = x*t22184; + t21761 = RATIONAL(5.0,24.0); + t22179 = t21761*x; + t22003 = t21802*t22179; + t22023 = t21787*t22185; + t22315 = t21536+x*t22137+t21392+t21805*t22003+t21731*t21934+(t22023+ +t22605)*z; + t22314 = t21059+t21805*t22045+t22489+t22504+t22507; + t22313 = t22410+t22522; + t22312 = z*t22086+t21220+t22416+t22538; + t21966 = t21757*t22139; + t22311 = t21804*t21549+t21806*t21966+t21048+t21428+t21490+(t22030+t22591) +*y; + t21127 = z*t22130; + t22310 = t21800*t22051+t21127+t22488+t22494+t22502; + t22309 = t21089+t21801*t21931+t22471+t22614*x; + t22308 = t22474+t22482+t22518; + t22307 = t21762*t22164+t21780*t22013+t21784*t22167+t21803*t21366+t22400; + t21512 = t21773*t22117; + t22068 = t21763*t21804; + t21988 = x*t22068; + t21662 = t21774*t21803; + t22306 = t21805*t21988+y*t21512+t22083*t22193+t21662*t22194+t22405; + t22305 = t22385+t22479; + t21528 = t21805*t21668; + t22304 = t21528+t21731*t21950+t21366+y*t22184+t21761*t22011+t21787*t22165 ++t22617*z; + t22303 = t21792*t22004+t21774*t21995+t21806*t22101+t22606*y+t22559*t21804 +; + t22302 = t21705*t21969+t21699*t22014+t22558+t22561; + t22301 = t21155+t21803*t21613+t21802*t21940+t21806*t21954+(t22579+t22603) +*x; + t22300 = t22422+t22427; + t22299 = t22421+t22524; + t22298 = t22423+t21765*t22013+z*t21991+(t21279+t21448)*y; + t22297 = t22455+t22468; + t21989 = x*t22136; + t22188 = z*t21700; + t22296 = t21396+t21805*t21989+t21803*t21621+t21725*t21934+t22585*z+( +t22103+t22188)*x; + t22295 = t22430+t21726*t21941+t21804*t22089+(t21072+t21592)*y; + t22294 = t21760*t22164+t21805*t22015+z*t21550+t21798*t22013+t22463; + t21647 = t21769*t21800; + t21531 = t21804*t21647; + t22293 = t21309+z*t21531+t22113*t22194+t21106+t22415; + t21170 = t21710*t22056; + t22292 = t21758*t21941+t21804*t22030+t22456+(t21170+t21578)*y; + t22291 = t22462+t22466; + t22290 = t21706*t21934+z*t21973+t22558*x+t22557; + t22289 = t21804*t21041+t21732*t21986+(t21037+t21176)*x+(t22589+t22590)*y; + t22055 = t21771*t21803; + t21519 = t21802*t22055; + t22166 = x*t22170; + t22288 = x*t22123+z*t21519+t21463+t21753*t22166+t22414; + t22012 = t21790*t22185; + t22186 = z*t21760; + t21756 = RATIONAL(-5.0,24.0); + t22287 = x*t22186+t21284+t21756*t22020+t21512+t21724*t21934+(t22012+ +t22584)*z; + t22286 = t22446+t22459; + t22285 = t21170+t22374; + t22284 = z*t22039+t21070+t22416+t22545; + t21982 = t21756*t22176; + t21508 = t21805*t21667; + t22283 = t21805*t21982+t21508+t21724*t21950+(t22118+t22186)*y+(t21985+ +t22586)*z; + t21964 = t21804*t22120; + t22282 = z*t21964+t21706*t21950+t22561*y+t22556; + t21525 = z*t22059; + t22281 = t21525+t21336+t21750*t21969+t21625+t21346+t21523+(t21944+t21754) +*z; + t22280 = t21766*t21941+t21283+t22456+(t22159+t21472)*y; + t22017 = t21763*t22174; + t22279 = t21749*t22164+t21805*t22017+t22405+(t21983+t21508)*x; + t21679 = RATIONAL(32.0,27.0); + t21999 = t21680*t22182; + t22278 = t21759*t22168+t21729*t22008+t21803*t21385+t21801*t21999+t21680* +t22018+t21679*t22162+t22618*t21806; + t22277 = t21708*t21950+t21804*t21171+t22574*y+t22554; + t22142 = t21681*t21806; + t22276 = t21804*t21599+t21712*t21941+t22430+(t21246+t22142)*y; + t22275 = t21102+t21712*t21984+t22420+(t21127+t21601)*x; + t21981 = t21685*t22182; + t21987 = t21703*t22182; + t22274 = t22403+t21805*t21987+z*t21981+t22604*y; + t22273 = t21774*t22011+t21725*t21950+y*t22188+t21792*t22165+t22593*t21804 ++t22565; + t21979 = t21743*t22111; + t22010 = t21738*t22185; + t22126 = t21765*t21806; + t22272 = t21806*t22010+t21803*t22076+x*t22126+t21801*t21979+t22434; + t22271 = t22440+t21682*t22091+t21802*t21936+(t22142+t21263)*x; + t22270 = t22407+t22411; + t22269 = t22377+t22476; + t22268 = t22418+t22419; + t22171 = z*t21680; + t21174 = y*t22171; + t22267 = z*t21999+t21679*t22192+t21754*t21986+t21759*t22163+(t21344+ +t21174)*t21803+t22618*t21805; + t21360 = t21736*t22117; + t22266 = t21730*t21986+t21805*t21932+(t21445+t21360+t22161)*y+(t21308+ +t22577)*x; + t21977 = t21746*t22111; + t22265 = t21741*t22020+t21743*t21934+(t21977+t22010)*z+t22570+t22612; + t22264 = t21806*t21931+t21338+t21803*t21517+t21134+t21488+(t21618+t22596) +*x; + t22044 = t21805*t21749; + t21244 = y*t22044; + t22263 = z*t21494+t21744*t22165+t21805*t21611+t21244+t22415; + t22262 = t21360+t21758*t21934+t21754*t22172+t21805*t22019+t22576*z+( +t22041+t22171)*x; + t22261 = z*t21998+t21804*t21392+t21805*t21990+t21780*t22024+t22400; + t22260 = t21063+t21800*t21486+(t21613+t21562)*t21804+(t22579+t22595)*y; + t22259 = t21801*t22037+t21708*t21970+t21802*t21060+t21681*t22105+(t22600+ +t22602)*x; + t22258 = t21630+t21755*t21938+t21769*t21957+t22559+t22596; + t22257 = t21674*t22105+t21806*t21962+(t21046+t22053)*t21803+t22555*x; + t22256 = t21746*t21934+t22038*t22193+t21045+t21805*t22010+z*t21979+x* +t22063+t22604; + t21203 = t21806*t22052; + t22255 = t22437+t21801*t21951+t21803*t22030+(t21203+t21578)*x; + t22022 = x*t22110; + t22254 = t22429+x*t22153+t21741*t22022+(t22025+t21977)*t21801; + t22253 = t21773*t22011+t21174+t21758*t21950+t21804*t21523+(t22049+t21994) +*z+t22577; + t22252 = t21803*t21628+t21725*t21970+t21739*t22105+t21806*t21989+t22585* +t21801+t22606*x; + t21645 = t21773*t21803; + t22251 = t21645*t22194+t21749*t22013+y*t21536+z*t21988+t22435; + t22250 = t22410+t22421; + t22249 = x*t21421+t21803*t21617+t21801*t21972+t21247+t22437; + t22248 = t21097+t22356; + t22247 = t21164+t22362; + t22246 = t21801*t21971+t21226+t22471+(t22107+t21436)*x; + t22245 = t22450+t21185+t21774*t21984+(t22096+t21525)*x; + t22244 = x*t21629+t21479+t21685*t21978+t22496+t22560*y; + t22243 = t22435+t21803*t21244+z*t22017+(t22000+t21528)*x; + t22242 = z*t21987+t21805*t21981+t22401+t22612*y; + t21872 = t22448+t22451; + t22241 = t21597+t21750*t22014+t21872+t22460+t22488; + t21873 = t22413+t22451; + t22240 = t21755*t22014+t21593+t21873+t22460+t22489; + t21745 = RATIONAL(-1.0,16.0); + t22239 = RATIONAL(5.0,64.0)*t21957+t21745*t22060+t21165+RATIONAL(-1.0, +64.0)*t21938+t22523+t22535+t22575; + t22238 = t21801*t22068+t21273+t21668+t21744*t21941+t22453+(t22563+t22564) +*y; + t21733 = RATIONAL(5.0,16.0); + t21786 = RATIONAL(-1.0,4.0); + t22237 = t21258+t21733*t21957+t21745*t21938+t21786*t22060+t21773*t21806+ +t21792+t22536+t22541+t22608; + t22079 = t21756*t21801; + t22236 = t21755*t22110+t22376+t21412+(t22079+t21771)*t21802+t22564; + t21793 = RATIONAL(-2.0,3.0); + t22235 = t21769*t21995+t21804*t21658+t21753*t21941+t22458+t21793*t22176+ +t22588*y+t22617; + t21230 = t21702*t22082; + t21720 = RATIONAL(1.0,16.0); + t22234 = RATIONAL(1.0,64.0)*t21938+t21720*t22060+t21230+RATIONAL(-5.0, +64.0)*t21957+t22546+t22551+t22601; + t22233 = t21531+t21627+t21761*t21941+t21355+t22394+t22608*y+t22568; + t22232 = t21802*t21968+t21662+t22434+(t22074+t22047)*t21803+(t22563+ +t22566)*x; + t21175 = t21686*t22115; + t22231 = t21741*t21941+t22409+t21175+t22551*y+t22599; + t21259 = t21761*t22082; + t22230 = t21769*t21802+t21260+t21750*t22110+t21259+t22375+t22611; + t22229 = t21747*t21941+t21377+t22412+(t22592+t22611)*y+t22562; + t22228 = t21804*t21126+t22509+t21806*t22042+t21158+t22501+t21708*t21941+( +t22571+t22573)*y; + t21470 = t21800*t22079; + t22227 = t22428+t21611+t21568+(t21470+t21633)*t21804+(t22569+t22613)*y; + t21980 = t21803*t22082; + t22226 = t21747*t21980+t21645+t21749*t22091+t22429+t21803*t22058+(t22580+ +t22592)*x; + t22225 = t21609+t21709*t22115+t21494+t22441+t21738*t21941+(t22575+t22616) +*y; + t22224 = t22498+t21706*t21941+t21801*t22042+t22501+(t21964+t22114)*t21806 ++(t22600+t22609)*y; + t21721 = RATIONAL(-5.0,16.0); + t21777 = RATIONAL(1.0,4.0); + t22223 = t21408+t21721*t21957+t21799+t21720*t21938+t21774*t21806+t21777* +t22060+t22544+t22548+t22569; + t21794 = RATIONAL(2.0,3.0); + t22222 = t21552+t21771*t21995+t21794*t22176+t21748*t21941+t22395+(t21788+ +t22140)*y+t22586; + t22221 = t22330+t22380; + t22220 = t22387+t22396+t22448; + t22219 = t22378+t22413+t22424; + t22218 = t22289+t22379; + t22217 = t22334+t22371; + t22216 = t22246+t22370; + t22215 = t22246+t22359; + t22214 = t22271+t22359; + t22213 = t22295+t22355; + t22212 = t22309+t22363; + t22211 = t22271+t22370; + t22210 = t22355+t22410+t22525; + t22209 = t22295+t22421+t22531; + t22208 = t22250+t22525+t22531; + t22207 = t22361+t22425+t22447; + t22206 = t22368+t22433+t22444; + t22205 = t22339+t22350; + t21687 = RATIONAL(1.0,384.0); + t21688 = RATIONAL(-1.0,384.0); + t22204 = t21688*t21957+t21687*t21938+t22338+t22550+t22587; + t22203 = t21687*t21957+t21688*t21938+t22338+t22555+t22619; + t22202 = t22282+t22331; + t22201 = t22320+t22326; + t22200 = t22277+t22290; + t22199 = t22257+t22325; + t22198 = t22302+t22322; + t22197 = t22320+t22325; + t22196 = t22257+t22326; + t20583 = z*t21931; + t20513 = z*t21966; + t22154 = t20583+t20513; + t22148 = t21738*t21806; + t22144 = t21164+t21061; + t22141 = t21767*t21806; + t22135 = t21703*t21806; + t22134 = t21764*t21806; + t22133 = t21203+t21108; + t20722 = t21804*t21297; + t22132 = t20722+t20583; + t20750 = z*t21954; + t22128 = t20750+t20513; + t22099 = t20722+t20750; + t21993 = t21703*t22174; + t21406 = t21755*t22111; + t21476 = t21750*t22111; + t21236 = t21766*t22105; + t21058 = t21708*t22105; + t21939 = t21740*t22111; + t21937 = t21803*t22079; + t21930 = t21170+t22479; + t21929 = t21780*t22008+t21762*t22007+t22493; + t21927 = x*t21175+y*t21058+t22503; + t21926 = t21170+t22476; + t21925 = t21203+t22480; + t21924 = t20750+t22475; + t21923 = t21061+t22480; + t21922 = t20750+t22477; + t21921 = t21097+t22479; + t21917 = t20583+t22477; + t21916 = t20583+t22475; + t21914 = t21801*t21990+y*t21236+t22160; + t21913 = t21203+t22478; + t21912 = t21097+t22476; + t21911 = t21781*z+t21748*t21805; + t21910 = t21756*z+t21761*t21805; + t21909 = t21756*t21805+t21761*z; + t21776 = RATIONAL(5.0,3.0); + t21908 = t21776*z+t21753*t21805; + t21907 = t21794+t21787*t21801+t21771*t21806; + t21906 = RATIONAL(5.0,4.0)+RATIONAL(-25.0,16.0)*t21801+t21733*t21806; + t21775 = RATIONAL(-5.0,8.0); + t21905 = RATIONAL(25.0,8.0)*t21801+RATIONAL(-5.0,2.0)+t21775*t21806; + t21717 = RATIONAL(25.0,16.0); + t21768 = RATIONAL(-5.0,4.0); + t21904 = t21768+t21721*t21806+t21717*t21801; + t21903 = t21744*t21801+t21746*t21806+t21731; + t21902 = t21743*t21806+t21747*t21801+t21724; + t21901 = t21769*t21806+t21790*t21801+t21793; + t21900 = t21781+t21753*t21806+RATIONAL(25.0,12.0)*t21801; + t21899 = t21775+t21727*t21806+RATIONAL(25.0,32.0)*t21801; + t21689 = RATIONAL(-25.0,12.0); + t21898 = t21776+t21748*t21806+t21689*t21801; + t21897 = t21720*t21806+t21777+t21721*t21801; + t21770 = RATIONAL(5.0,8.0); + t21896 = t21734*t21806+RATIONAL(-25.0,32.0)*t21801+t21770; + t21895 = t21779*t21806+RATIONAL(1.0,2.0)+t21775*t21801; + t21894 = t21786+t21745*t21806+t21733*t21801; + t21893 = RATIONAL(-1.0,2.0)+t21770*t21801+t21791*t21806; + t21707 = RATIONAL(25.0,96.0); + t21892 = t21756+t21741*t21806+t21707*t21801; + t21891 = t22149+t22148+t21761; + t21890 = t22506+y*t22179+t22148*t22195+(t22055+t21937)*t21804; + t21888 = t21787*t22168+t21793*t22072+RATIONAL(-10.0,3.0)*t22195+t21790* +t21978+t22512; + t21887 = t21750*t21978+t21707*t22168+t22505+t22506+t22511; + t21886 = x*t21251+t21236+t21750*t21970+t21437+t21914; + t21885 = t22418+t22447; + t21884 = t21801*t22012+t21773*t22105+x*t22125+t21724*t21970+t21929; + t21698 = RATIONAL(-25.0,24.0); + t21883 = t21698*t22168+t21794*t21978+t22484+t22492+t22512; + t21882 = t21801*t22023+x*t22151+t21774*t22105+t21731*t21970+t21929; + t21881 = t22418+t22433; + t21880 = t21806*t22073+t21742*t21970+t21927+t22535*x; + t21879 = t22398+t22469; + t21878 = x*t21230+t21058+t21806*t21939+t21043+t21927; + t21877 = t22407+t22510+t22519; + t21876 = t22406+t22468; + t21875 = t21914+t21719*t22105+t21755*t21970+(t21405+t22074)*x; + t21874 = t22398+t22459; + t21871 = t22406+t22427; + t21693 = RATIONAL(25.0,48.0); + t21870 = t21731*t22174+t21753*t22182+t21693*t22007+y*t21935+t21890+t22511 +; + t21782 = RATIONAL(4.0,3.0); + t21869 = t21782*t22174+t21783*t22008+t21776*t22182+t21689*t22007+t21888+ +t22492; + t21868 = x*t22078+t21753*t22174+t21746*t22021+t21693*t22018+t21890+t22505 +; + t21867 = t21783*t22021+t21782*t22182+t21776*t22174+t21689*t22018+t21888+ +t22484; + t21866 = t21738*t21995+y*t22126+t21804*t22076+t21743*t21941+t22383+t22453 +; + t21865 = t21886+t21806*t22016+t21446+x*t22150+t21801*t21519+t22470; + t21864 = t21882+x*t22134+t21792*t22091+t21806*t22003+t21801*t21522+t22431 +; + t21863 = t22393+t22403+t21805*t21993+t21685*t22164+t22547*x; + t21862 = t21057+t21060+t21704*t22022+t21742*t21980+t21878+t22399; + t21861 = t22381+t21725*t22117+x*t22044+t22438+(t22016+t21476)*z; + t21860 = t21771*t21941+t21315+t21744*t21995+t21150+t22390+t22394; + t21859 = x*t22141+t21799*t22091+t21801*t21544+t21884+t21756*t22022+t22431 +; + t21858 = y*t22141+t21785*t21941+t21806*t21982+t21799*t22115+t22384+t22458 +; + t21857 = t21801*t21520+x*t22135+t21802*t22006+t21758*t22091+t21875+t22470 +; + t21856 = t21769*t21941+t21758*t22115+t21747*t21995+y*t22135+t22390+t22428 +; + t21855 = t21783*t21941+y*t22134+t21504+t21761*t21995+t22384+t22395; + t21854 = z*t21406+t21747*t22166+t21758*t22117+x*t22152+t22381+t22414; + t21853 = t21746*t21941+t21495+t21741*t21995+t21458+t22383+t22412; + t21852 = t22393+t21803*t21180+z*t21993+t22401+t22537*x; + t21851 = t21801*t21939+t21702*t22022+t21708*t22091+x*t22112+t21880+t22399 +; + t21850 = t21771*t21800+t21470+t21478+t21755*t22056+t22360+t22376+t22566; + t21849 = t21880+t21476+t21709*t22091+t22244+(t21766+t21348)*t21803+t22523 +*x; + t21848 = t21348+t21647+t21750*t22056+t22360+t21761*t22157+t22375+t22580; + t21847 = t21558+t21788*x+t21882+t22354+t21794*t22185+t21771*t22022+t22544 +*t21803+t22584; + t21846 = t21074+t21803*t21478+t21406+t21878+t22244+t22546*x+t22560; + t21845 = t21793*t22185+t21884+t21769*t22022+t22354+t22541*t21803+t22588*x ++t22605; + t21844 = t21519+t21638+t21802*t21937+t21803*t21633+t22349+t21875+(t22548+ +t22613)*x; + t21843 = t21623+t21886+t21398+t22349+t21803*t21259+t21520+(t22536+t22621) +*x; + t21842 = t22311+t22367+t21061+t21877+t22404+t22487+t22508; + t21841 = t22302+t22203+t22339; + t21840 = t21108+t22224+t21885+t22368+t22425; + t21839 = t22267+t22281+t22278+t22328; + t21838 = t22277+t22204+t22331; + t21837 = t22268+t22276+t22299+t22310; + t21836 = t22245+t22284+t21874+t22442+t22454; + t21835 = t22252+t22262+t22278+t22342; + t21834 = t22348+t22341+t22382+t22398+t22436+t22477; + t21833 = t22366+t21925+t22247+t22391+t22402+t22406; + t21832 = t22292+t21876+t22389+t22449+t22455+t22476; + t21831 = t22228+t21873+t22387+t22424+t22480; + t21830 = t21881+t22275+t22337+t22419+t22461; + t21829 = t21108+t22372+t21871+t22260+t22402+t22422; + t21828 = t22228+t21872+t22378+t22396+t22478; + t21827 = t22334+t20513+t22241+t22363; + t21826 = t20722+t22266+t21874+t22358+t22397+t22436; + t21825 = t20722+t22309+t22241+t22371; + t21824 = t22282+t22204+t22290; + t21823 = t21879+t22357+t20513+t22249+t22436+t22445; + t21822 = t22289+t22240+t22380+t22477; + t21821 = t22280+t21877+t22386+t22411+t22475+t22491+t22517; + t21820 = t21879+t22264+t22388+t22442+t22457+t22479; + t21819 = t22255+t21876+t22351+t22402+t22408; + t21818 = t22314+t21885+t21097+t22369+t22419+t22467; + t21817 = t22268+t21170+t22259+t22313+t22373; + t21816 = t22322+t22203+t22350; + t21815 = t22253+t22278+t22258+t22296; + t21814 = t22240+t22330+t22379+t22475; + t21813 = t21871+t22301+t22317+t22449+t22465; + t21812 = t21164+t22224+t21881+t22361+t22444; + t21811 = t22273+t22278+t22319+t22352; + t21692 = RATIONAL(-25.0,48.0); + coeffs_dxy->coeff_m2_m2_m2 = t21824+t22205+t22196; + coeffs_dxy->coeff_m1_m2_m2 = t21828+t21203+t21164+t22214+t22207; + coeffs_dxy->coeff_0_m2_m2 = t22265+t21851+t22274; + coeffs_dxy->coeff_p1_m2_m2 = t22219+t21840+t21061+t22211+t22478; + coeffs_dxy->coeff_p2_m2_m2 = t22200+t21841+t22199; + coeffs_dxy->coeff_m2_m1_m2 = t21837+t21926+t22337+t22343+t22373+t22377; + coeffs_dxy->coeff_m1_m1_m2 = t21834+t22280+t22249+t22358+t22099+t22364; + coeffs_dxy->coeff_0_m1_m2 = t22254+t21854+t22306; + coeffs_dxy->coeff_p1_m1_m2 = t22348+t22286+t21823+t21924+t22386+t22397+ +t22530; + coeffs_dxy->coeff_p2_m1_m2 = t22305+t22337+t22250+t21818+t22522+t22524; + coeffs_dxy->coeff_m2_0_m2 = t21863+t22316+t22332; + coeffs_dxy->coeff_m1_0_m2 = t21853+t22279+t22329; + coeffs_dxy->coeff_0_0_m2 = ((t21731*t21805+t21724*z)*t21804+t21910*y)* +t21803+(t21910*t21804+(t21692*t21805+t21693*z)*y)*x+t21887; + coeffs_dxy->coeff_p1_0_m2 = t22263+t21866+t22279; + coeffs_dxy->coeff_p2_0_m2 = t21863+t22321+t22333; + coeffs_dxy->coeff_m2_p1_m2 = t22259+t22269+t22275+t21818+t22276; + coeffs_dxy->coeff_m1_p1_m2 = t22348+t22291+t22365+t21821+t22132+t22529+ +t22534+t22549; + coeffs_dxy->coeff_0_p1_m2 = t22272+t21861+t22306; + coeffs_dxy->coeff_p1_p1_m2 = t21834+t22357+t22365+t22270+t22154+t22397+ +t22459; + coeffs_dxy->coeff_p2_p1_m2 = t22305+t21817+t22310+t22275+t22343; + coeffs_dxy->coeff_m2_p2_m2 = t21841+t22202+t22201; + coeffs_dxy->coeff_m1_p2_m2 = t21831+t22144+t22216+t22207; + coeffs_dxy->coeff_0_p2_m2 = t21862+t22256+t22274; + coeffs_dxy->coeff_p1_p2_m2 = t21925+t22220+t21840+t22215; + coeffs_dxy->coeff_p2_p2_m2 = t21838+t22205+t22197; + coeffs_dxy->coeff_m2_m2_m1 = t22218+t21916+t22209+t21827; + coeffs_dxy->coeff_m1_m2_m1 = t21813+t22284+t21921+t22292+t22356+t22388; + coeffs_dxy->coeff_0_m2_m1 = t21857+t22288+t22298; + coeffs_dxy->coeff_p1_m2_m1 = t21813+t22308+t22389+t21926+t22454+t22459+ +t22526+t22539+t22549; + coeffs_dxy->coeff_p2_m2_m1 = t21822+t22208+t22217+t22132; + coeffs_dxy->coeff_m2_m1_m1 = t22255+t21829+t21923+t22312+t22367+t22391; + coeffs_dxy->coeff_m1_m1_m1 = t22328+t21811+t22340+t22296+t22342; + coeffs_dxy->coeff_0_m1_m1 = t21864+t22287+t22335; + coeffs_dxy->coeff_p1_m1_m1 = t21815+t22281+t22303+t22319+t22342; + coeffs_dxy->coeff_p2_m1_m1 = t22300+t22255+t22311+t21833+t22344; + coeffs_dxy->coeff_m2_0_m1 = t21856+t22346+t22347; + coeffs_dxy->coeff_m1_0_m1 = t21855+t22283+t22294; + coeffs_dxy->coeff_0_0_m1 = ((t21771*t21805+t21793*z)*t21804+t21908*y)* +t21803+(t21908*t21804+(RATIONAL(25.0,24.0)*t21805+RATIONAL(-25.0,6.0)*z)*y)*x+ +t21883; + coeffs_dxy->coeff_p1_0_m1 = t21858+t22294+t22304; + coeffs_dxy->coeff_p2_0_m1 = t21860+t22293+t22346; + coeffs_dxy->coeff_m2_p1_m1 = t22308+t21829+t21913+t22353+t22392+t22516+ +t22532+t22542; + coeffs_dxy->coeff_m1_p1_m1 = t22273+t21835+t22281+t22258+t22340; + coeffs_dxy->coeff_0_p1_m1 = t21859+t22315+t22335; + coeffs_dxy->coeff_p1_p1_m1 = t21835+t22253+t22328+t22303+t22352; + coeffs_dxy->coeff_p2_p1_m1 = t22300+t22247+t21842+t22312+t22351; + coeffs_dxy->coeff_m2_p2_m1 = t21822+t22212+t22128+t22213; + coeffs_dxy->coeff_m1_p2_m1 = t22285+t22245+t22292+t21820+t22327; + coeffs_dxy->coeff_0_p2_m1 = t22298+t21865+t22324; + coeffs_dxy->coeff_p1_p2_m1 = t21836+t22264+t22327+t21912+t22356+t22389; + coeffs_dxy->coeff_p2_p2_m1 = t21825+t22210+t22218+t21924; + coeffs_dxy->coeff_m2_m2_0 = t22225+t22234+t21849; + coeffs_dxy->coeff_m1_m2_0 = t22236+t22229+t21844; + coeffs_dxy->coeff_0_m2_0 = t21870+(t21894*t21802+t21902)*t21803+(t21896* +t21802+t21892)*x; + coeffs_dxy->coeff_p1_m2_0 = t21844+t22238+t22230; + coeffs_dxy->coeff_p2_m2_0 = t22231+t22239+t21849; + coeffs_dxy->coeff_m2_m1_0 = t22227+t21850+t22226; + coeffs_dxy->coeff_m1_m1_0 = t22223+t21847+t22222; + coeffs_dxy->coeff_0_m1_0 = (t21895*t21802+t21901)*t21803+(t21904*t21802+ +t21898)*x+t21869; + coeffs_dxy->coeff_p1_m1_0 = t22235+t22237+t21847; + coeffs_dxy->coeff_p2_m1_0 = t21848+t22233+t22226; + coeffs_dxy->coeff_m2_0_0 = t21868+(t21896*t21800+t21892)*y+(t21894*t21800 ++t21902)*t21804; + coeffs_dxy->coeff_m1_0_0 = t21867+(t21895*t21800+t21901)*t21804+(t21904* +t21800+t21898)*y; + coeffs_dxy->coeff_0_0_0 = ((t21777*t21806+t21768*t21801+1.0)*t21804+ +t21905*y)*t21803+(t21905*t21804+(RATIONAL(25.0,4.0)+RATIONAL(-125.0,16.0)* +t21801+t21717*t21806)*y)*x; + coeffs_dxy->coeff_p1_0_0 = (t21893*t21800+t21907)*t21804+t21867+(t21906* +t21800+t21900)*y; + coeffs_dxy->coeff_p2_0_0 = (t21897*t21800+t21903)*t21804+t21868+(t21899* +t21800+t21891)*y; + coeffs_dxy->coeff_m2_p1_0 = t22227+t22232+t21848; + coeffs_dxy->coeff_m1_p1_0 = t22237+t21845+t22222; + coeffs_dxy->coeff_0_p1_0 = (t21893*t21802+t21907)*t21803+(t21906*t21802+ +t21900)*x+t21869; + coeffs_dxy->coeff_p1_p1_0 = t22223+t22235+t21845; + coeffs_dxy->coeff_p2_p1_0 = t21850+t22232+t22233; + coeffs_dxy->coeff_m2_p2_0 = t22239+t21846+t22225; + coeffs_dxy->coeff_m1_p2_0 = t21843+t22229+t22230; + coeffs_dxy->coeff_0_p2_0 = t21870+(t21897*t21802+t21903)*t21803+(t21899* +t21802+t21891)*x; + coeffs_dxy->coeff_p1_p2_0 = t21843+t22236+t22238; + coeffs_dxy->coeff_p2_p2_0 = t22231+t21846+t22234; + coeffs_dxy->coeff_m2_m2_p1 = t21814+t22213+t22217+t22099; + coeffs_dxy->coeff_m1_m2_p1 = t22248+t21832+t22301+t22245+t22457+t22469; + coeffs_dxy->coeff_0_m2_p1 = t22318+t21857+t22324; + coeffs_dxy->coeff_p1_m2_p1 = t21930+t22297+t22301+t21836+t22374+t22388; + coeffs_dxy->coeff_p2_m2_p1 = t21922+t22221+t22210+t21827; + coeffs_dxy->coeff_m2_m1_p1 = t21819+t22144+t22260+t22344+t22362+t22367; + coeffs_dxy->coeff_m1_m1_p1 = t22253+t22262+t21839+t22319+t22340; + coeffs_dxy->coeff_0_m1_p1 = t21864+t22261+t22315; + coeffs_dxy->coeff_p1_m1_p1 = t22267+t22262+t21811+t22258+t22303; + coeffs_dxy->coeff_p2_m1_p1 = t21819+t22311+t22366+t22133+t22312+t22372; + coeffs_dxy->coeff_m2_0_p1 = t21856+t22293+t22323; + coeffs_dxy->coeff_m1_0_p1 = t22304+t21855+t22307; + coeffs_dxy->coeff_0_0_p1 = ((t21769*t21805+t21794*z)*t21804+t21911*y)* +t21803+(t21911*t21804+(t21698*t21805+t21752*z)*y)*x+t21883; + coeffs_dxy->coeff_p1_0_p1 = t21858+t22283+t22307; + coeffs_dxy->coeff_p2_0_p1 = t22323+t21860+t22347; + coeffs_dxy->coeff_m2_p1_p1 = t21833+t22260+t22312+t22345+t22353; + coeffs_dxy->coeff_m1_p1_p1 = t21815+t22267+t22252+t22340+t22352; + coeffs_dxy->coeff_0_p1_p1 = t21859+t22261+t22287; + coeffs_dxy->coeff_p1_p1_p1 = t22273+t22252+t22296+t21839+t22303; + coeffs_dxy->coeff_p2_p1_p1 = t21108+t22291+t22391+t21842+t22345+t22480+ +t22527+t22528; + coeffs_dxy->coeff_m2_p2_p1 = t21825+t22221+t22209+t21917; + coeffs_dxy->coeff_m1_p2_p1 = t22285+t21832+t22284+t22264+t22317; + coeffs_dxy->coeff_0_p2_p1 = t21865+t22288+t22318; + coeffs_dxy->coeff_p1_p2_p1 = t22248+t22286+t22297+t21820+t22454+t22521; + coeffs_dxy->coeff_p2_p2_p1 = t22212+t22208+t21814+t22154; + coeffs_dxy->coeff_m2_m2_p2 = t21838+t22198+t22196; + coeffs_dxy->coeff_m1_m2_p2 = t21831+t22133+t22214+t22206; + coeffs_dxy->coeff_0_m2_p2 = t21851+t22242+t22256; + coeffs_dxy->coeff_p1_m2_p2 = t22220+t21812+t21923+t22211; + coeffs_dxy->coeff_p2_m2_p2 = t21816+t22202+t22199; + coeffs_dxy->coeff_m2_m1_p2 = t22314+t22276+t21930+t21830+t22373+t22385; + coeffs_dxy->coeff_m1_m1_p2 = t22266+t22280+t21823+t21917+t22365+t22382; + coeffs_dxy->coeff_0_m1_p2 = t21861+t22251+t22254; + coeffs_dxy->coeff_p1_m1_p2 = t21826+t22341+t21916+t22249+t22365+t22386; + coeffs_dxy->coeff_p2_m1_p2 = t21830+t22310+t22313+t21912+t22369+t22377; + coeffs_dxy->coeff_m2_0_p2 = t22316+t21852+t22321; + coeffs_dxy->coeff_m1_0_p2 = t21853+t22243+t22263; + coeffs_dxy->coeff_0_0_p2 = ((t21731*z+t21724*t21805)*t21804+t21909*y)* +t21803+(t21909*t21804+(t21692*z+t21693*t21805)*y)*x+t21887; + coeffs_dxy->coeff_p1_0_p2 = t21866+t22243+t22329; + coeffs_dxy->coeff_p2_0_p2 = t22332+t21852+t22333; + coeffs_dxy->coeff_m2_p1_p2 = t21837+t22259+t21921+t22336+t22369+t22385; + coeffs_dxy->coeff_m1_p1_p2 = t22266+t22357+t22341+t22128+t21821+t22364; + coeffs_dxy->coeff_0_p1_p2 = t21854+t22251+t22272; + coeffs_dxy->coeff_p1_p1_p2 = t22364+t21826+t21922+t22270+t22382+t22445+ +t22469; + coeffs_dxy->coeff_p2_p1_p2 = t22314+t22269+t21817+t22299+t22336; + coeffs_dxy->coeff_m2_p2_p2 = t22200+t21816+t22201; + coeffs_dxy->coeff_m1_p2_p2 = t21828+t21108+t22216+t22206+t21061; + coeffs_dxy->coeff_0_p2_p2 = t21862+t22242+t22265; + coeffs_dxy->coeff_p1_p2_p2 = t22219+t21812+t21913+t22215; + coeffs_dxy->coeff_p2_p2_p2 = t21824+t22198+t22197; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxz.compute.c new file mode 100644 index 0000000..ad552c3 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxz.compute.c @@ -0,0 +1,2488 @@ +fp t24172; +fp t24176; +fp t24086; +fp t24080; +fp t24974; +fp t24047; +fp t24174; +fp t24044; +fp t24973; +fp t24972; +fp t24079; +fp t24056; +fp t24971; +fp t24970; +fp t24043; +fp t24170; +fp t24463; +fp t24048; +fp t24389; +fp t24969; +fp t24143; +fp t24096; +fp t24398; +fp t24968; +fp t24155; +fp t24033; +fp t24169; +fp t24967; +fp t24136; +fp t24128; +fp t24903; +fp t24085; +fp t24454; +fp t23448; +fp t24405; +fp t24966; +fp t24144; +fp t24171; +fp t24175; +fp t24411; +fp t23905; +fp t24162; +fp t24017; +fp t24965; +fp t24416; +fp t24433; +fp t24964; +fp t24052; +fp t24088; +fp t23970; +fp t24963; +fp t24106; +fp t24450; +fp t23830; +fp t24092; +fp t23833; +fp t24962; +fp t24111; +fp t24431; +fp t24113; +fp t24173; +fp t24495; +fp t24319; +fp t24961; +fp t24072; +fp t24083; +fp t23956; +fp t24435; +fp t24960; +fp t24125; +fp t24110; +fp t24385; +fp t24959; +fp t24099; +fp t24448; +fp t24482; +fp t24958; +fp t24054; +fp t23950; +fp t24053; +fp t23511; +fp t24957; +fp t24412; +fp t23421; +fp t24453; +fp t24956; +fp t24109; +fp t24443; +fp t24102; +fp t23975; +fp t24955; +fp t24107; +fp t24500; +fp t24954; +fp t24095; +fp t24455; +fp t24168; +fp t24953; +fp t24473; +fp t24952; +fp t23998; +fp t24312; +fp t24471; +fp t24951; +fp t24154; +fp t24950; +fp t24418; +fp t24949; +fp t24153; +fp t24094; +fp t24948; +fp t24947; +fp t24150; +fp t24403; +fp t24124; +fp t24946; +fp t24522; +fp t24336; +fp t24543; +fp t24129; +fp t24945; +fp t24425; +fp t23747; +fp t24944; +fp t24390; +fp t24943; +fp t24479; +fp t23748; +fp t24942; +fp t24127; +fp t24476; +fp t24941; +fp t24082; +fp t24940; +fp t24076; +fp t23952; +fp t24486; +fp t24939; +fp t24051; +fp t24447; +fp t24071; +fp t24460; +fp t24938; +fp t24391; +fp t23424; +fp t24388; +fp t24937; +fp t23971; +fp t24936; +fp t24935; +fp t24120; +fp t24112; +fp t24934; +fp t24065; +fp t24519; +fp t23961; +fp t24933; +fp t24089; +fp t23985; +fp t24875; +fp t23958; +fp t24932; +fp t24526; +fp t23702; +fp t24931; +fp t24064; +fp t24493; +fp t23947; +fp t24930; +fp t24929; +fp t24928; +fp t24070; +fp t24927; +fp t24101; +fp t23621; +fp t24926; +fp t23972; +fp t24078; +fp t24925; +fp t24075; +fp t24924; +fp t24525; +fp t23773; +fp t23657; +fp t24923; +fp t23498; +fp t24922; +fp t24032; +fp t24921; +fp t24084; +fp t23966; +fp t24074; +fp t24920; +fp t24919; +fp t24020; +fp t23852; +fp t24918; +fp t24045; +fp t24046; +fp t24917; +fp t24406; +fp t24299; +fp t24916; +fp t23503; +fp t24915; +fp t24914; +fp t23943; +fp t24913; +fp t23945; +fp t24386; +fp t24912; +fp t24440; +fp t24402; +fp t24911; +fp t24451; +fp t24910; +fp t24909; +fp t24908; +fp t24457; +fp t24907; +fp t24520; +fp t24906; +fp t24116; +fp t23994; +fp t24069; +fp t24905; +fp t24904; +fp t24902; +fp t23658; +fp t24464; +fp t23647; +fp t24901; +fp t24367; +fp t24098; +fp t24900; +fp t23964; +fp t23461; +fp t24468; +fp t23603; +fp t24899; +fp t24512; +fp t24119; +fp t24459; +fp t23625; +fp t24462; +fp t24324; +fp t24490; +fp t24133; +fp t24313; +fp t24898; +fp t24897; +fp t23788; +fp t23547; +fp t24896; +fp t23695; +fp t23984; +fp t24895; +fp t24118; +fp t23613; +fp t24159; +fp t24894; +fp t24893; +fp t23987; +fp t23801; +fp t24892; +fp t23954; +fp t24441; +fp t24373; +fp t24891; +fp t24445; +fp t24484; +fp t24890; +fp t24889; +fp t24888; +fp t24384; +fp t23643; +fp t24414; +fp t23583; +fp t24887; +fp t24002; +fp t24294; +fp t24886; +fp t24885; +fp t24884; +fp t24317; +fp t24883; +fp t24882; +fp t24881; +fp t24533; +fp t23819; +fp t24392; +fp t23834; +fp t24880; +fp t24879; +fp t23667; +fp t23851; +fp t24878; +fp t24030; +fp t24877; +fp t24876; +fp t23467; +fp t23651; +fp t24874; +fp t23965; +fp t24873; +fp t24055; +fp t24417; +fp t23434; +fp t24872; +fp t24871; +fp t23639; +fp t24485; +fp t24296; +fp t24470; +fp t24870; +fp t23532; +fp t24393; +fp t24869; +fp t24300; +fp t23516; +fp t24868; +fp t24413; +fp t23491; +fp t24867; +fp t24432; +fp t23771; +fp t23732; +fp t24866; +fp t24346; +fp t24151; +fp t24478; +fp t24347; +fp t24865; +fp t24461; +fp t23670; +fp t24100; +fp t24474; +fp t24348; +fp t24864; +fp t24121; +fp t24508; +fp t24863; +fp t23509; +fp t24862; +fp t23479; +fp t23510; +fp t24861; +fp t24487; +fp t24380; +fp t24114; +fp t24496; +fp t24378; +fp t24117; +fp t24860; +fp t24135; +fp t23770; +fp t24328; +fp t24859; +fp t23981; +fp t23823; +fp t24858; +fp t24166; +fp t24511; +fp t24857; +fp t24502; +fp t24856; +fp t24401; +fp t23493; +fp t23576; +fp t24855; +fp t23635; +fp t24105; +fp t24854; +fp t24494; +fp t23757; +fp t24853; +fp t24852; +fp t23832; +fp t24134; +fp t24524; +fp t24359; +fp t24851; +fp t24132; +fp t24850; +fp t23536; +fp t23456; +fp t24849; +fp t23951; +fp t24848; +fp t23805; +fp t24847; +fp t24139; +fp t24122; +fp t24846; +fp t24005; +fp t24844; +fp t23815; +fp t24506; +fp t24337; +fp t24843; +fp t23420; +fp t24841; +fp t23949; +fp t23426; +fp t24840; +fp t23508; +fp t23499; +fp t24839; +fp t23997; +fp t23640; +fp t24838; +fp t24837; +fp t23570; +fp t23558; +fp t24836; +fp t24444; +fp t23472; +fp t24835; +fp t24437; +fp t23604; +fp t23982; +fp t23622; +fp t24834; +fp t24427; +fp t23782; +fp t23785; +fp t24309; +fp t24833; +fp t23960; +fp t24330; +fp t24832; +fp t24420; +fp t24831; +fp t23739; +fp t23730; +fp t24830; +fp t23990; +fp t23776; +fp t24545; +fp t24829; +fp t23561; +fp t24828; +fp t23592; +fp t24303; +fp t24827; +fp t23515; +fp t24826; +fp t24825; +fp t24824; +fp t24823; +fp t23497; +fp t24822; +fp t23419; +fp t24821; +fp t24820; +fp t24424; +fp t24028; +fp t24365; +fp t24157; +fp t24323; +fp t24819; +fp t23865; +fp t23780; +fp t24523; +fp t23660; +fp t24818; +fp t23962; +fp t23599; +fp t24531; +fp t24375; +fp t24817; +fp t24421; +fp t23594; +fp t24816; +fp t23565; +fp t24815; +fp t23969; +fp t23571; +fp t24814; +fp t23862; +fp t23701; +fp t24297; +fp t24813; +fp t23743; +fp t23736; +fp t24419; +fp t24315; +fp t24812; +fp t24541; +fp t23587; +fp t23450; +fp t24318; +fp t24811; +fp t24810; +fp t24809; +fp t24308; +fp t24808; +fp t23514; +fp t23733; +fp t24807; +fp t23543; +fp t24316; +fp t24806; +fp t24805; +fp t23646; +fp t24001; +fp t24804; +fp t24452; +fp t23682; +fp t24803; +fp t24542; +fp t24802; +fp t24123; +fp t24394; +fp t23843; +fp t24801; +fp t24800; +fp t24456; +fp t23769; +fp t24004; +fp t23610; +fp t24137; +fp t24507; +fp t23606; +fp t24799; +fp t23973; +fp t24798; +fp t24011; +fp t24475; +fp t24797; +fp t24796; +fp t23991; +fp t24795; +fp t24794; +fp t24513; +fp t23741; +fp t23573; +fp t24793; +fp t23786; +fp t23778; +fp t24792; +fp t24535; +fp t24349; +fp t23811; +fp t24529; +fp t24791; +fp t24790; +fp t23483; +fp t24789; +fp t24788; +fp t24073; +fp t24428; +fp t23559; +fp t23868; +fp t24527; +fp t23618; +fp t24787; +fp t24481; +fp t23858; +fp t24786; +fp t24785; +fp t23706; +fp t24409; +fp t23821; +fp t24010; +fp t23721; +fp t24784; +fp t24407; +fp t23803; +fp t24439; +fp t23845; +fp t24783; +fp t23717; +fp t23612; +fp t24782; +fp t24538; +fp t23608; +fp t23626; +fp t24381; +fp t24781; +fp t23835; +fp t24780; +fp t24515; +fp t24408; +fp t23930; +fp t23883; +fp t24779; +fp t23520; +fp t23439; +fp t24778; +fp t23983; +fp t24423; +fp t23690; +fp t24304; +fp t24777; +fp t24130; +fp t24395; +fp t24539; +fp t24160; +fp t24340; +fp t24776; +fp t24775; +fp t24108; +fp t23798; +fp t23989; +fp t24332; +fp t24774; +fp t24426; +fp t24325; +fp t24773; +fp t23728; +fp t24466; +fp t24772; +fp t24771; +fp t23863; +fp t23438; +fp t24770; +fp t23473; +fp t24769; +fp t24768; +fp t24767; +fp t24766; +fp t24765; +fp t24341; +fp t24764; +fp t24345; +fp t23891; +fp t24763; +fp t24344; +fp t23624; +fp t24762; +fp t24438; +fp t23449; +fp t24761; +fp t24760; +fp t23700; +fp t24310; +fp t24759; +fp t24343; +fp t24758; +fp t23800; +fp t24757; +fp t24756; +fp t23729; +fp t23750; +fp t24755; +fp t24754; +fp t24753; +fp t24752; +fp t24751; +fp t23553; +fp t24750; +fp t24400; +fp t23664; +fp t24749; +fp t24530; +fp t24360; +fp t24283; +fp t24748; +fp t24747; +fp t23765; +fp t24306; +fp t24746; +fp t24745; +fp t23996; +fp t24339; +fp t24744; +fp t23468; +fp t24358; +fp t24743; +fp t24301; +fp t24742; +fp t24741; +fp t24740; +fp t23772; +fp t23584; +fp t23652; +fp t24739; +fp t23645; +fp t24738; +fp t24161; +fp t24104; +fp t24737; +fp t24149; +fp t24097; +fp t24736; +fp t23909; +fp t24022; +fp t24305; +fp t24735; +fp t24734; +fp t23429; +fp t24733; +fp t24514; +fp t23976; +fp t23857; +fp t24732; +fp t23839; +fp t24446; +fp t24731; +fp t23705; +fp t24254; +fp t24730; +fp t24729; +fp t24728; +fp t23535; +fp t24727; +fp t24726; +fp t24725; +fp t23661; +fp t24724; +fp t24516; +fp t24723; +fp t23812; +fp t24383; +fp t24722; +fp t24721; +fp t24720; +fp t24326; +fp t23892; +fp t24719; +fp t23826; +fp t24718; +fp t24717; +fp t24544; +fp t24716; +fp t24311; +fp t24715; +fp t24058; +fp t24298; +fp t24714; +fp t24141; +fp t24713; +fp t24370; +fp t24712; +fp t24327; +fp t24711; +fp t24353; +fp t24449; +fp t24331; +fp t24710; +fp t24709; +fp t24050; +fp t24458; +fp t23524; +fp t24369; +fp t24465; +fp t24342; +fp t24708; +fp t23638; +fp t24429; +fp t24352; +fp t24707; +fp t24706; +fp t24705; +fp t24540; +fp t24377; +fp t24704; +fp t24302; +fp t24703; +fp t24702; +fp t24314; +fp t24701; +fp t24700; +fp t24374; +fp t24699; +fp t23977; +fp t24698; +fp t24131; +fp t24387; +fp t24368; +fp t24697; +fp t24696; +fp t24372; +fp t24695; +fp t23123; +fp t24694; +fp t24376; +fp t24693; +fp t24469; +fp t24692; +fp t24691; +fp t24690; +fp t24689; +fp t23633; +fp t24410; +fp t23928; +fp t24688; +fp t24517; +fp t24510; +fp t24687; +fp t24686; +fp t24321; +fp t24685; +fp t24534; +fp t24338; +fp t24684; +fp t24038; +fp t24295; +fp t24683; +fp t23915; +fp t24682; +fp t24681; +fp t24680; +fp t24351; +fp t24364; +fp t24679; +fp t23719; +fp t24354; +fp t24499; +fp t24678; +fp t24677; +fp t24329; +fp t24676; +fp t24675; +fp t24674; +fp t24673; +fp t24672; +fp t24671; +fp t23073; +fp t24670; +fp t24669; +fp t24039; +fp t23902; +fp t23849; +fp t24668; +fp t24667; +fp t24472; +fp t24666; +fp t24382; +fp t23459; +fp t24665; +fp t23234; +fp t24664; +fp t24663; +fp t24322; +fp t24662; +fp t24363; +fp t24661; +fp t23575; +fp t24660; +fp t24659; +fp t23557; +fp t23672; +fp t23850; +fp t24658; +fp t24657; +fp t24656; +fp t24503; +fp t24655; +fp t24528; +fp t23855; +fp t24362; +fp t24654; +fp t24307; +fp t24653; +fp t23501; +fp t24652; +fp t24651; +fp t24650; +fp t24505; +fp t24649; +fp t23676; +fp t24648; +fp t23577; +fp t24371; +fp t24647; +fp t24646; +fp t24645; +fp t24644; +fp t24537; +fp t23523; +fp t24643; +fp t23225; +fp t24642; +fp t24356; +fp t24641; +fp t24640; +fp t24639; +fp t24638; +fp t24637; +fp t23767; +fp t24636; +fp t24635; +fp t24634; +fp t24489; +fp t24396; +fp t24633; +fp t24632; +fp t24631; +fp t23683; +fp t24630; +fp t24629; +fp t24628; +fp t24627; +fp t23794; +fp t24626; +fp t24504; +fp t24126; +fp t24625; +fp t24041; +fp t23934; +fp t24415; +fp t24333; +fp t24361; +fp t24624; +fp t24049; +fp t24623; +fp t24622; +fp t24621; +fp t24620; +fp t24619; +fp t24618; +fp t24366; +fp t24617; +fp t23877; +fp t24616; +fp t24615; +fp t24158; +fp t24037; +fp t23871; +fp t24614; +fp t24613; +fp t24422; +fp t24612; +fp t24611; +fp t24610; +fp t24609; +fp t24608; +fp t24607; +fp t24034; +fp t23867; +fp t24536; +fp t23654; +fp t24606; +fp t24605; +fp t24604; +fp t24603; +fp t24602; +fp t24241; +fp t24601; +fp t24600; +fp t23433; +fp t24243; +fp t24599; +fp t24242; +fp t24598; +fp t24115; +fp t24597; +fp t24090; +fp t24596; +fp t23462; +fp t24595; +fp t24404; +fp t24164; +fp t24594; +fp t24434; +fp t24593; +fp t24091; +fp t24147; +fp t24592; +fp t24436; +fp t23869; +fp t23687; +fp t24591; +fp t23796; +fp t24026; +fp t23876; +fp t24590; +fp t24589; +fp t24588; +fp t24587; +fp t24016; +fp t23936; +fp t24163; +fp t24586; +fp t24585; +fp t24584; +fp t24018; +fp t24156; +fp t24103; +fp t24583; +fp t24582; +fp t24581; +fp t24483; +fp t24580; +fp t24579; +fp t24284; +fp t24578; +fp t24577; +fp t24279; +fp t24576; +fp t24575; +fp t24574; +fp t24573; +fp t24399; +fp t24572; +fp t24571; +fp t24570; +fp t24569; +fp t24498; +fp t24568; +fp t24567; +fp t24566; +fp t24565; +fp t24564; +fp t24563; +fp t24562; +fp t24561; +fp t24560; +fp t24559; +fp t24558; +fp t24557; +fp t24556; +fp t24555; +fp t24554; +fp t24553; +fp t24552; +fp t24551; +fp t24550; +fp t24549; +fp t24548; +fp t24547; +fp t24546; +fp t24146; +fp t24518; +fp t24497; +fp t24492; +fp t24491; +fp t24027; +fp t24480; +fp t24467; +fp t24357; +fp t24355; +fp t24350; +fp t24334; +fp t24293; +fp t24292; +fp t24289; +fp t24288; +fp t24285; +fp t24282; +fp t24278; +fp t24277; +fp t24276; +fp t24275; +fp t24274; +fp t24273; +fp t24063; +fp t24272; +fp t24271; +fp t24059; +fp t24270; +fp t24140; +fp t24269; +fp t24145; +fp t24268; +fp t24077; +fp t24267; +fp t24266; +fp t24265; +fp t24264; +fp t24263; +fp t24262; +fp t24261; +fp t24260; +fp t24259; +fp t24258; +fp t24087; +fp t24138; +fp t24257; +fp t24256; +fp t24255; +fp t24253; +fp t24252; +fp t24251; +fp t24068; +fp t24250; +fp t24249; +fp t24248; +fp t24247; +fp t24246; +fp t24245; +fp t24244; +fp t24152; +fp t24240; +fp t24239; +fp t24238; +fp t24237; +fp t24236; +fp t24235; +fp t24234; +fp t24233; +fp t24232; +fp t24231; +fp t24230; +fp t24229; +fp t24228; +fp t24227; +fp t24226; +fp t24225; +fp t24224; +fp t24223; +fp t24222; +fp t24221; +fp t24220; +fp t24219; +fp t24218; +fp t24217; +fp t24216; +fp t24215; +fp t24214; +fp t24213; +fp t24212; +fp t24211; +fp t24210; +fp t24209; +fp t24208; +fp t24207; +fp t24206; +fp t24205; +fp t24204; +fp t24203; +fp t24202; +fp t24201; +fp t24200; +fp t24199; +fp t24198; +fp t24197; +fp t24196; +fp t24195; +fp t24194; +fp t24193; +fp t24192; +fp t24191; +fp t24190; +fp t24189; +fp t24188; +fp t24187; +fp t24186; +fp t24185; +fp t24184; +fp t24183; +fp t24182; +fp t24181; + t24172 = y*y; + t24176 = t24172*t24172; + t24086 = RATIONAL(1.0,576.0); + t24080 = RATIONAL(1.0,144.0); + t24974 = t24086*t24176+t24080; + t24047 = RATIONAL(-1.0,1728.0); + t24174 = t24172*y; + t24044 = RATIONAL(1.0,1728.0); + t24973 = t24047*t24174+t24044*y; + t24972 = t24047*y+t24044*t24174; + t24079 = RATIONAL(-5.0,288.0); + t24056 = RATIONAL(5.0,288.0); + t24971 = y*t24056+t24174*t24079; + t24970 = t24174*t24056+y*t24079; + t24043 = RATIONAL(-1.0,1152.0); + t24170 = x*x; + t24463 = t24172*t24170; + t24048 = RATIONAL(1.0,1152.0); + t24389 = t24048*t24170; + t24969 = t24043*t24463+t24176*t24389; + t24143 = RATIONAL(-1.0,9.0); + t24096 = RATIONAL(-1.0,36.0); + t24398 = t24096*t24176; + t24968 = t24398+t24143; + t24155 = RATIONAL(-1.0,3.0); + t24033 = t24155*t24170; + t24169 = RATIONAL(4.0,9.0); + t24967 = t24033+t24169; + t24136 = RATIONAL(1.0,72.0); + t24128 = RATIONAL(1.0,18.0); + t24903 = t24136*t24176+t24128; + t24085 = RATIONAL(-1.0,576.0); + t24454 = t24085*t24170; + t23448 = t24176*t24454; + t24405 = t24172*t24086; + t24966 = t24170*t24405+t23448; + t24144 = RATIONAL(1.0,9.0); + t24171 = z*z; + t24175 = t24171*z; + t24411 = t24174*t24175; + t23905 = t24144*t24411; + t24162 = RATIONAL(-4.0,9.0); + t24017 = t24162*t24175; + t24965 = t23905+y*t24017; + t24416 = t24170*t24086; + t24433 = t24174*t24170; + t24964 = t24085*t24433+y*t24416; + t24052 = RATIONAL(1.0,432.0); + t24088 = RATIONAL(-1.0,864.0); + t23970 = t24088*t24174; + t24963 = t24052*t24411+z*t23970; + t24106 = RATIONAL(-2.0,27.0); + t24450 = t24175*t24106; + t23830 = y*t24450; + t24092 = RATIONAL(1.0,54.0); + t23833 = t24092*t24411; + t24962 = t23830+t23833; + t24111 = RATIONAL(-5.0,96.0); + t24431 = t24171*t24111; + t24113 = RATIONAL(1.0,48.0); + t24173 = x*t24170; + t24495 = t24173*t24171; + t24319 = t24113*t24495; + t24961 = x*t24431+t24319; + t24072 = RATIONAL(5.0,192.0); + t24083 = RATIONAL(-5.0,576.0); + t23956 = t24083*t24172; + t24435 = t24172*t24171; + t24960 = t23956+t24072*t24435; + t24125 = RATIONAL(1.0,24.0); + t24110 = RATIONAL(1.0,96.0); + t24385 = t24171*t24110; + t24959 = t24176*t24385+t24125*t24171; + t24099 = RATIONAL(4.0,27.0); + t24448 = t24174*t24099; + t24482 = t24173*t24174; + t24958 = x*t24448+t24106*t24482; + t24054 = RATIONAL(1.0,864.0); + t23950 = t24054*t24174; + t24053 = RATIONAL(-1.0,432.0); + t23511 = t24053*t24411; + t24957 = t23511+z*t23950; + t24412 = t24085*t24171; + t23421 = t24172*t24412; + t24453 = t24176*t24171; + t24956 = t23421+t24086*t24453; + t24109 = RATIONAL(2.0,27.0); + t24443 = t24109*t24172; + t24102 = RATIONAL(-1.0,54.0); + t23975 = t24102*t24176; + t24955 = t24443+t23975; + t24107 = RATIONAL(-4.0,27.0); + t24500 = t24107*t24174; + t24954 = x*t24500+t24109*t24482; + t24095 = RATIONAL(-1.0,18.0); + t24455 = t24095*t24170; + t24168 = RATIONAL(2.0,9.0); + t24953 = t24168*t24463+t24176*t24455; + t24473 = t24173*t24054; + t24952 = t24088*t24482+y*t24473; + t23998 = t24128*t24173; + t24312 = t24171*t23998; + t24471 = t24143*t24171; + t24951 = t24312+x*t24471; + t24154 = RATIONAL(8.0,9.0); + t24950 = t24168*t24176+t24154; + t24418 = t24095*t24171; + t24949 = t24176*t24418+t24168*t24435; + t24153 = RATIONAL(1.0,3.0); + t24094 = RATIONAL(1.0,12.0); + t24948 = t24153*t24171+t24094*t24453; + t24947 = t24174*t24416+y*t24454; + t24150 = RATIONAL(-2.0,9.0); + t24403 = t24150*t24171; + t24124 = RATIONAL(8.0,27.0); + t24946 = (t24124+t24403)*t24173; + t24522 = x*t24099; + t24336 = t24175*t24522; + t24543 = x*z; + t24129 = RATIONAL(-8.0,27.0); + t24945 = t24129*t24543+t24336; + t24425 = t24175*t24129; + t23747 = t24109*t24411; + t24944 = y*t24425+t23747; + t24390 = t24176*t24128; + t24943 = t24171*t24390+t24172*t24403; + t24479 = t24136*t24170; + t23748 = t24176*t24479; + t24942 = t23748+t23975; + t24127 = RATIONAL(1.0,36.0); + t24476 = t24127*t24176; + t24941 = t24144+t24476; + t24082 = RATIONAL(-1.0,144.0); + t24940 = t24085*t24176+t24082; + t24076 = RATIONAL(1.0,288.0); + t23952 = t24088*t24176; + t24486 = t24176*t24170; + t24939 = t23952+t24076*t24486; + t24051 = RATIONAL(1.0,216.0); + t24447 = t24173*t24051; + t24071 = RATIONAL(-1.0,216.0); + t24460 = t24173*t24071; + t24938 = t24174*t24460+y*t24447; + t24391 = t24175*t24051; + t23424 = t24174*t24391; + t24388 = t24071*t24175; + t24937 = t23424+y*t24388; + t23971 = t24053*t24176; + t24936 = t23971+t24052*t24172; + t24935 = t24150*t24463+t24170*t24390; + t24120 = RATIONAL(-1.0,24.0); + t24112 = RATIONAL(-1.0,96.0); + t24934 = t24112*t24453+t24120*t24171; + t24065 = RATIONAL(-1.0,108.0); + t24519 = y*t24065; + t23961 = t24051*y; + t24933 = z*t23961+t24175*t24519; + t24089 = RATIONAL(-1.0,72.0); + t23985 = t24089*t24176; + t24875 = t23985+t24095; + t23958 = t24052*t24176; + t24932 = t23958+t24053*t24172; + t24526 = y*t24175; + t23702 = t24106*t24411; + t24931 = t23702+t24124*t24526; + t24064 = RATIONAL(1.0,108.0); + t24493 = t24173*t24064; + t23947 = t24071*y; + t24930 = x*t23947+y*t24493; + t24929 = t24174*t24447+y*t24460; + t24928 = t24172*t24454+t24176*t24416; + t24070 = RATIONAL(16.0,27.0); + t24927 = t24070*t24172+t24107*t24176; + t24101 = RATIONAL(-1.0,12.0); + t23621 = t24101*t24486; + t24926 = t24144*t24176+t23621; + t23972 = t24054*t24176; + t24078 = RATIONAL(-1.0,288.0); + t24925 = t24078*t24453+t23972; + t24075 = RATIONAL(1.0,192.0); + t24924 = t24113*t24171+t24075*t24453; + t24525 = y*t24109; + t23773 = t24175*t24525; + t23657 = t24102*t24411; + t24923 = t23657+t23773; + t23498 = t24174*t24388; + t24922 = y*t24391+t23498; + t24032 = t24155*t24171; + t24921 = t24032+t24101*t24453; + t24084 = RATIONAL(5.0,576.0); + t23966 = t24084*t24172; + t24074 = RATIONAL(-5.0,192.0); + t24920 = t23966+t24074*t24435; + t24919 = t24088*y*t24173+t24174*t24473; + t24020 = t24143*t24176; + t23852 = t24094*t24486; + t24918 = t24020+t23852; + t24045 = RATIONAL(1.0,3456.0); + t24046 = RATIONAL(-1.0,3456.0); + t24917 = t24046*t24176+t24045*t24172; + t24406 = t24173*t24078; + t24299 = t24171*t24406; + t24916 = t24447+t24299; + t23503 = t24171*t24405; + t24915 = t23503+t24176*t24412; + t24914 = t24089*t24175+t24974*z; + t23943 = t24046*t24172; + t24913 = t23943+t24172*t24389+t24043*t24486; + t23945 = t24045*t24176; + t24386 = t24043*t24171; + t24912 = t24048*t24435+t23945+t24176*t24386; + t24440 = t24175*t24172; + t24402 = t24047*t24176; + t24911 = t24175*t24402+t24044*t24440+z*t23945; + t24451 = t24173*t24044; + t24910 = x*t23943+t24172*t24451+t24173*t24402; + t24909 = t24048*t24453+t24172*t24386+t24917; + t24908 = t24054*t24526+t24088*t24411+t24972*z; + t24457 = t24174*t24171; + t24907 = t24086*t24457+y*t24412+t24973; + t24520 = y*t24171; + t24906 = t24174*t24412+t24086*t24520+t24972; + t24116 = RATIONAL(-1.0,48.0); + t23994 = t24116*t24171; + t24069 = RATIONAL(-1.0,192.0); + t24905 = t24069*t24453+t23994+t24974; + t24904 = t24088*t24526+t24054*t24411+t24973*z; + t24902 = t24967*t24175; + t23658 = t24127*t24457; + t24464 = t24096*t24170; + t23647 = y*t24464; + t24901 = t23658+t23647; + t24367 = y*t23994; + t24098 = RATIONAL(1.0,27.0); + t24900 = t24170*t24367+t24098*t24174; + t23964 = t24064*t24176; + t23461 = t24175*t23964; + t24468 = t24173*t24053; + t23603 = t24172*t24468; + t24899 = z*t23603+x*t23461; + t24512 = t24176*t24543; + t24119 = RATIONAL(5.0,36.0); + t24459 = t24119*t24172; + t23625 = x*t24459; + t24462 = t24173*t24175; + t24324 = t24176*t24462; + t24490 = t24096*t24324+z*t23625; + t24133 = RATIONAL(-5.0,36.0); + t24313 = t24173*t24440; + t24898 = t24490+t24127*t24313+t24133*t24512; + t24897 = t24082*t24526+t24080*t24411; + t23788 = y*t24479; + t23547 = t24078*t24457; + t24896 = t23788+t23547; + t23695 = t24110*t24486; + t23984 = t24125*t24170; + t24895 = t23695+t23984; + t24118 = RATIONAL(5.0,12.0); + t23613 = t24118*t24435; + t24159 = RATIONAL(-5.0,9.0); + t24894 = t23613+t24159*t24172; + t24893 = t24970*x; + t23987 = t24120*t24170; + t23801 = t24112*t24486; + t24892 = t23987+t23801; + t23954 = t24071*t24174; + t24441 = t24171*t24170; + t24373 = y*t24441; + t24891 = t23954+t24110*t24373; + t24445 = t24173*t24080; + t24484 = t24173*t24082; + t24890 = y*t24484+t24174*t24445; + t24889 = t24968*x; + t24888 = t24971*x; + t24384 = t24171*t24136; + t23643 = y*t24384; + t24414 = t24078*t24170; + t23583 = t24174*t24414; + t24887 = t23643+t23583; + t24002 = t24098*y; + t24294 = t24116*t24457; + t24886 = t24002+t24170*t24294; + t24885 = t24082*t24482+y*t24445; + t24884 = t24153*t24495+t24162*t24173; + t24317 = t24171*t24433; + t24883 = t23961+t24112*t24317; + t24882 = t23950+t24120*t24373; + t24881 = t24082*t24411+t24080*t24526; + t24533 = y*t24170; + t23819 = t24127*t24533; + t24392 = t24096*t24171; + t23834 = t24174*t24392; + t24880 = t23819+t23834; + t24879 = t24116*t24170+t24069*t24486; + t23667 = t24127*t24433; + t23851 = y*t24392; + t24878 = t23667+t23851; + t24030 = t24169*t24173; + t24877 = t24173*t24032+t24030; + t24876 = t23947+t24110*t24317; + t23467 = t24076*t24433; + t23651 = t24089*t24520; + t24874 = t23467+t23651; + t23965 = t24051*t24174; + t24873 = t23965+t24112*t24373; + t24055 = RATIONAL(-5.0,144.0); + t24417 = t24176*t24055; + t23434 = z*t24417; + t24872 = x*t23434+t24144*t24313+t24490; + t24871 = t24113*t24170+t24075*t24486+t24940; + t23639 = t24170*t23985; + t24485 = t24175*t24170; + t24296 = t24082*t24485; + t24470 = t24176*t24051; + t24870 = t24052*t24440+t24172*t24296+(t24470+t23639)*z; + t23532 = t24076*t24520; + t24393 = t24089*t24174; + t24869 = t23532+t24170*t24393+t24873; + t24300 = t24175*t24464; + t23516 = t24176*t24414; + t24868 = t24172*t24300+t24064*t24440+(t23972+t23516)*z; + t24413 = t24173*t24065; + t23491 = t24176*t24413; + t24867 = t24172*t24336+z*t23491; + t24432 = t24174*t24096; + t23771 = t24170*t24432; + t23732 = t24127*t24520; + t24866 = t23771+t23732; + t24346 = x*t24440; + t24151 = RATIONAL(-5.0,3.0); + t24478 = t24173*t24176; + t24347 = z*t24478; + t24865 = t24118*t24347+t24151*t24346; + t24461 = t24173*t24098; + t23670 = t24172*t24461; + t24100 = RATIONAL(-1.0,27.0); + t24474 = t24175*t24100; + t24348 = x*t24474; + t24864 = z*t23670+t24176*t24348; + t24121 = RATIONAL(-20.0,9.0); + t24508 = t24172*t24543; + t24863 = t24121*t24508+t24144*t24324; + t23509 = z*t23956; + t24862 = t24080*t24324+x*t23509; + t23479 = t24173*t23958; + t23510 = t24065*t24440; + t24861 = z*t23479+x*t23510; + t24487 = t24176*t24175; + t24380 = x*t24487; + t24114 = RATIONAL(5.0,48.0); + t24496 = t24173*t24172; + t24378 = z*t24496; + t24117 = RATIONAL(-5.0,48.0); + t24860 = t24117*t24380+t24114*t24378; + t24135 = RATIONAL(-5.0,72.0); + t23770 = t24135*t24496; + t24328 = t24175*t24390; + t24859 = x*t24328+z*t23770; + t23981 = t24092*t24176; + t23823 = z*t23981; + t24858 = x*t23823+t24106*t24313; + t24166 = RATIONAL(5.0,9.0); + t24511 = t24166*t24543; + t24857 = t24162*t24313+t24176*t24511; + t24502 = RATIONAL(-25.0,96.0)*t24172; + t24856 = t24125*t24324+t24502*t24543; + t24401 = t24172*t24056; + t23493 = t24175*t24401; + t23576 = t24176*t24406; + t24855 = x*t23493+z*t23576; + t23635 = t24095*t24440; + t24105 = RATIONAL(5.0,72.0); + t24854 = t24105*t24347+x*t23635; + t24494 = t24172*t24106; + t23757 = x*t24494; + t24853 = t24092*t24324+z*t23757; + t24852 = t24151*t24378+t24118*t24380; + t23832 = t24136*t24487; + t24134 = RATIONAL(-5.0,18.0); + t24524 = z*t24134; + t24359 = t24173*t24524; + t24851 = t24172*t24359+x*t23832; + t24132 = RATIONAL(10.0,9.0); + t24850 = t24132*t24346+t24150*t24347; + t23536 = t24078*t24487; + t23456 = t24173*t24401; + t24849 = x*t23536+z*t23456; + t23951 = t24064*t24174; + t24848 = t23951+t24101*t24373; + t23805 = t24135*t24440; + t24847 = x*t23805+t24128*t24347; + t24139 = RATIONAL(-1.0,6.0); + t24122 = RATIONAL(25.0,6.0); + t24846 = t24122*t24508+t24139*t24324; + t24005 = t24100*y; + t24844 = t24005+t24113*t24317; + t23815 = t24098*t24440; + t24506 = t24173*t24100; + t24337 = z*t24506; + t24843 = t24176*t24337+x*t23815; + t23420 = x*t23952; + t24841 = t24092*t24313+z*t23420; + t23949 = t24051*t24172; + t23426 = x*t23949; + t24840 = t24071*t24324+z*t23426; + t23508 = t24053*t24440; + t23499 = t24173*t23964; + t24839 = z*t23499+x*t23508; + t23997 = t24136*t24173; + t23640 = t24176*t23997; + t24838 = t24134*t24346+z*t23640; + t24837 = t24114*t24346+t24117*t24347; + t23570 = t24172*t24413; + t23558 = t24175*t23958; + t24836 = x*t23558+z*t23570; + t24444 = t24071*t24176; + t23472 = x*t24444; + t24835 = z*t23472+t24051*t24313; + t24437 = t24176*t24105; + t23604 = x*t24437; + t23982 = t24095*t24173; + t23622 = t24172*t23982; + t24834 = z*t23622+t24175*t23604; + t24427 = t24089*t24172; + t23782 = t24171*t24427; + t23785 = t24170*t24427; + t24309 = t24176*t24441; + t24833 = t23782+t23785+t24112*t24309; + t23960 = t24065*t24174; + t24330 = t24173*t24457; + t24832 = t24089*t24330+(t23851+t23960)*x; + t24420 = t24172*t24082; + t24831 = t24170*t24420+t24956; + t23739 = t24172*t24384; + t23730 = t24136*t24463; + t24830 = t23739+t24110*t24309+t23730; + t23990 = t24106*t24174; + t23776 = t24174*t24461; + t24545 = y*x; + t24829 = t23776+t24418*t24545+x*t23990; + t23561 = t24076*t24533; + t24828 = y*t24296+(t23561+t23965)*z; + t23592 = z*t23960; + t24303 = t24170*t24411; + t24827 = t23592+t24089*t24303+z*t23647; + t23515 = x*t23951; + t24826 = t23515+t24136*t24330+x*t23732; + t24825 = t24171*t24420+t24928; + t24824 = z*t23788+t24957; + t24823 = t24136*t24303+(t23951+t23819)*z; + t23497 = t24174*t24468; + t24822 = t23497+(t23643+t23950)*x; + t23419 = t24072*t24463; + t24821 = t24175*t23695+t23509+t23536+z*t23419; + t24820 = t24176*t24296+t23558+(t23949+t23785)*z; + t24424 = t24132*t24172; + t24028 = t24144*t24173; + t24365 = x*t24435; + t24157 = RATIONAL(-5.0,6.0); + t24323 = t24173*t24453; + t24819 = x*t24424+t24157*t24365+t24101*t24323+t24176*t24028; + t23865 = t24098*t24526; + t23780 = t24095*t24433; + t24523 = y*t24106; + t23660 = z*t24523; + t24818 = t23865+z*t23780+t24127*t24303+t23660; + t23962 = t24065*t24176; + t23599 = t24175*t23962; + t24531 = t24173*z; + t24375 = t24099*t24531; + t24817 = t24172*t24375+x*t23599+t24843; + t24421 = t24144*t24171; + t23594 = t24082*t24433; + t24816 = y*t24421+t23594+t24848; + t23565 = t24076*t24496; + t24815 = t24079*t24380+z*t23565+t24855; + t23969 = t24071*t24172; + t23571 = t24080*t24486; + t24814 = (t23971+t23571)*t24175+(t23969+t23730)*z; + t23862 = x*t24525; + t23701 = t24128*t24457; + t24297 = t24173*t24432; + t24813 = x*t23701+y*t24506+t23862+t24171*t24297; + t23743 = y*t24461; + t23736 = t24174*t24418; + t24419 = t24173*t24127; + t24315 = t24174*t24419; + t24812 = t23743+t24171*t24315+(t23736+t24523)*x; + t24541 = y*t24064; + t23587 = x*t24541; + t23450 = t24064*t24526; + t24318 = t24175*t24413; + t24811 = t24174*t24318+z*t23587+t24173*t23450+x*t23592; + t24810 = t24876+t24896; + t24809 = t24841+t24861; + t24308 = t24170*t24435; + t24808 = t24075*t24308+t24069*t24309+t24936; + t23514 = t24076*t24457; + t23733 = t24089*t24533; + t24807 = t23514+t23733+t24883; + t23543 = y*t24413; + t24316 = t24171*t24484; + t24806 = t23543+t24174*t24316+(t23514+t23961)*x; + t24805 = t24176*t24468+t24080*t24323+(t23969+t23739)*x; + t23646 = t24127*t24463; + t24001 = t24100*t24172; + t24804 = t24942*t24175+(t24001+t23646)*z; + t24452 = t24174*t24092; + t23682 = x*t24452; + t24803 = x*t23660+z*t23682+t24962*t24173; + t24542 = y*t24543; + t24802 = t24121*t24542+t24174*t24511+t24965*t24173; + t24123 = RATIONAL(-5.0,12.0); + t24394 = t24171*t24123; + t23843 = t24172*t24394; + t24801 = t24120*t24323+x*t23843+t23640+t23625; + t24800 = t24174*t24296+z*t23467+t24933; + t24456 = t24174*t24134; + t23769 = z*t24456; + t24004 = t24128*t24175; + t23610 = y*t24004; + t24137 = RATIONAL(5.0,18.0); + t24507 = t24137*t24545; + t23606 = t24095*t24411; + t24799 = x*t23769+z*t24507+(t23606+t23610)*t24173; + t23973 = t24098*t24172; + t24798 = t24116*t24309+t23962+t24094*t24308+t23973; + t24011 = t24089*t24173; + t24475 = t24172*t24133; + t24797 = t24176*t24011+t24125*t24323+(t24475+t23613)*x; + t24796 = t24853+t24864; + t23991 = t24109*t24176; + t24795 = t24102*t24313+t23991*t24543+t24843; + t24794 = t24075*t24309+t24069*t24308+t24932; + t24513 = t24107*t24545; + t23741 = t24098*t24411; + t23573 = t24064*t24482; + t24793 = y*t24337+t24175*t24513+z*t23573+x*t23741; + t23786 = t24175*t23985; + t23778 = t24096*t24463; + t24792 = t24170*t23786+t24175*t23981+(t23778+t23973)*z; + t24535 = x*t24171; + t24349 = t24117*t24535; + t23811 = y*t23998; + t24529 = x*t24133; + t24791 = t23811+t24174*t24349+t24125*t24330+y*t24529; + t24790 = t23479+x*t23782+t23426+t24176*t24316; + t23483 = t24076*t24440; + t24789 = x*t23483+t24079*t24347+t24849; + t24788 = t24076*t24478+t24112*t24323+t24920*x; + t24073 = RATIONAL(5.0,144.0); + t24428 = t24174*t24073; + t23559 = x*t24428; + t23868 = t24143*t24462; + t24527 = z*t24133; + t23618 = y*t24527; + t24787 = x*t23618+y*t23868+z*t23559+t24175*t24315; + t24481 = t24174*t24102; + t23858 = x*t24481; + t24786 = (t23858+t23862)*z+t24923*t24173; + t24785 = t23450+t24080*t24303+(t23947+t23583)*z; + t23706 = t24128*t24411; + t24409 = t24137*t24174; + t23821 = z*t24409; + t24010 = t24095*t24175; + t23721 = y*t24010; + t24784 = t24524*t24545+x*t23821+(t23706+t23721)*t24173; + t24407 = t24120*t24176; + t23803 = t24170*t24407; + t24439 = t24170*t24123; + t23845 = t24172*t24439; + t24783 = t23832+t24175*t23803+(t23845+t24459)*z; + t23717 = t24176*t23984; + t23612 = t24118*t24463; + t24782 = t24175*t23717+t23786+(t23612+t24475)*z; + t24538 = y*t24119; + t23608 = x*t24538; + t23626 = y*t23982; + t24381 = t24114*t24535; + t24781 = t23608+t23626+t24174*t24381+t24120*t24330; + t23835 = t24127*t24435; + t24780 = t24173*t23975+t24136*t24323+(t24001+t23835)*x; + t24515 = t24174*t24543; + t24408 = t24143*t24174; + t23930 = t24175*t24408; + t23883 = t24175*t24030; + t24779 = y*t23883+t24173*t23930+RATIONAL(20.0,9.0)*t24542+t24159*t24515; + t23520 = x*t24519; + t23439 = t24064*t24411; + t24778 = y*t24318+t24173*t23439+(t23520+t23515)*z; + t23983 = t24105*t24172; + t24423 = t24170*t24111; + t23690 = t24172*t24423; + t24304 = t24116*t24485; + t24777 = t24175*t24476+t24176*t24304+(t23983+t23690)*z; + t24130 = RATIONAL(-10.0,9.0); + t24395 = t24172*t24130; + t24539 = z*t24170; + t24160 = RATIONAL(5.0,6.0); + t24340 = t24160*t24539; + t24776 = z*t24395+t24172*t24340+t24918*t24175; + t24775 = t24876+t24887; + t24108 = RATIONAL(5.0,96.0); + t23798 = t24108*t24463; + t23989 = t24135*t24172; + t24332 = t24113*t24485; + t24774 = t24175*t24398+t24176*t24332+(t23989+t23798)*z; + t24426 = t24171*t24080; + t24325 = t24173*t24426; + t24773 = x*t23547+t24174*t24325+t24930; + t23728 = t24172*t24392; + t24466 = t24173*t24092; + t24772 = t24089*t24323+t24176*t24466+(t23728+t23973)*x; + t24771 = t23964+t24001+t24113*t24309+t24101*t24308; + t23863 = t24100*t24411; + t23438 = t24174*t24413; + t24770 = x*t23863+y*t24336+(t23743+t23438)*z; + t23473 = t24074*t24463; + t24769 = t24175*t23801+t24076*t24487+(t23473+t23966)*z; + t24768 = t24853+t24858; + t24767 = t24835+t24840; + t24766 = t24844+t24880; + t24765 = t24844+t24866; + t24341 = z*t24433; + t24764 = t23610+t24117*t24341+t23618+t24125*t24303; + t24345 = y*t24028; + t23891 = y*t24403; + t24763 = t24171*t24345+x*t23891+t23858+t23573; + t24344 = t24157*t24539; + t23624 = z*t24424; + t24762 = t24172*t24344+t23624+t24926*t24175; + t24438 = t24174*t24055; + t23449 = z*t24438; + t24761 = z*t23608+x*t23449+(t24297+t24345)*t24175; + t24760 = t24836+t24840; + t23700 = t24172*t24431; + t24310 = t24116*t24478; + t24759 = t24171*t24310+t24176*t24419+(t23700+t23983)*x; + t24343 = t24160*t24535; + t24758 = t24094*t24323+x*t24395+t24172*t24343+t24173*t24020; + t23800 = t24108*t24435; + t24757 = t24173*t24398+t24176*t24319+(t23989+t23800)*x; + t24756 = t24094*t24373+t23960+t24886; + t23729 = t24128*t24433; + t23750 = y*t24474; + t24755 = t23750+t24174*t24300+(t24525+t23729)*z; + t24754 = t24114*t24341+t23721+z*t24538+t24120*t24303; + t24753 = t24110*t24323+t23576+t24960*x; + t24752 = t24851+t24854+t24872; + t24751 = t24175*t23733+(t24519+t23771)*z+t24922; + t23553 = t24076*t24453; + t24750 = t23553+t23949+t24125*t24308+t24939; + t24400 = t24176*t24134; + t23664 = x*t24400; + t24749 = t24154*t24378+t24175*t23664+t24850+t24863+t24857; + t24530 = x*t24175; + t24360 = t24150*t24530; + t24283 = t24173*t23624+t24176*t24360+t24863; + t24748 = t24134*t24347+t24283+t24154*t24346+t24857; + t24747 = t24854+t24859+t24898; + t23765 = t24176*t24384; + t24306 = t24172*t24385; + t24746 = t24170*t24306+t24092*t24172+t23765+t24942; + t24745 = t23969+t24120*t24308+t23516+t24925; + t23996 = t24136*t24175; + t24339 = y*t23996; + t24744 = t24170*t24339+(t24541+t23667)*z+t24937; + t23468 = t24080*t24433; + t24358 = y*t24485; + t24743 = t24128*t24358+(t23468+t24002)*z+t24962; + t24301 = t24175*t24455; + t24742 = y*t24301+(t24005+t23594)*z+t24923; + t24741 = t24847+t24834+t24898; + t24740 = t24834+t24838+t24872; + t23772 = t24173*t24523; + t23584 = t24174*t24426; + t23652 = t24173*t24452; + t24739 = t23772+t23652+y*t24312+(t24002+t23584)*x; + t23645 = t24089*t24453; + t24738 = t24102*t24172+t23639+t23645+t24112*t24308+t23981; + t24161 = RATIONAL(-1.0,8.0); + t24104 = RATIONAL(5.0,32.0); + t24737 = RATIONAL(-1.0,32.0)*t24309+t23983+t24104*t24308+t24161*t24441+ +t24875; + t24149 = RATIONAL(1.0,8.0); + t24097 = RATIONAL(-5.0,32.0); + t24736 = t24149*t24441+t23989+t24097*t24308+RATIONAL(1.0,32.0)*t24309+ +t24903; + t23909 = t24168*t24533; + t24022 = t24143*t24175; + t24305 = t24170*t24022; + t24735 = y*t24305+t24818+(t24452+t23909)*z; + t24734 = t23587+t24173*t23643+x*t23658+t24899+t24929; + t23429 = y*t24414; + t24733 = t24080*t24358+t24800+(t23954+t23429)*z; + t24514 = x*t24520; + t23976 = t24109*t24174; + t23857 = t24100*t24482; + t24732 = t23857+x*t23976+t24128*t24514+t24812; + t23839 = t24170*t24398; + t24446 = t24144*t24170; + t24731 = t23835+t23839+t24172*t24446+t24771; + t23705 = x*t24004; + t24254 = t24119*t24313+t23868+t24490+t24889*z; + t24730 = t24168*t24531+t23705+t24254+t24847+t24851; + t24729 = z*t23733+t24800+t24963; + t24728 = t24813+t24829; + t23535 = t24052*t24482; + t24727 = t23535+t24806+(t23970+t23651)*x; + t24726 = t24773+t24822; + t24725 = t24785+t24824; + t23661 = t24176*t24392; + t24724 = t23661+t24172*t24421+t23646+t24771; + t24516 = z*t24533; + t24723 = t23863+t24128*t24516+z*t23976+t24818; + t23812 = t24170*t24476; + t24383 = t24143*t24172; + t24722 = t23812+t23728+t24170*t24383+t24798; + t24721 = t24080*t24463+t24794+t24915; + t24720 = t24172*t24426+t24794+t24966; + t24326 = t24175*t24446; + t23892 = t24150*t24533; + t24719 = y*t24326+t24755+(t24481+t23892)*z; + t23826 = t24127*t24453; + t24718 = t23826+t24171*t24383+t23778+t24798; + t24717 = z*t23998+t24254+t24168*t24530+t24838+t24859; + t24544 = y*z; + t24716 = t24455*t24544+z*t23990+t23741+t24755; + t24311 = t24069*t24441; + t24715 = t24075*t24373+t24174*t24311+t24907+t24947; + t24058 = RATIONAL(-1.0,384.0); + t24298 = RATIONAL(1.0,384.0)*t24441; + t24714 = t24176*t24298+t24058*t24308+t24912+t24913; + t24141 = RATIONAL(1.0,6.0); + t24713 = t24124*y+t23990+t23701+t24120*t24317+t23891+t23729+t23892+t24141 +*t24373; + t24370 = t24102*t24526; + t24712 = (t24370+t23424)*t24173+(t23497+t24930)*z+(t23450+t24957)*x; + t24327 = t24170*t24440; + t24711 = t23508+t24080*t24327+t24820+(t24444+t23748)*z; + t24353 = x*t24421; + t24449 = t24173*t24129; + t24331 = t24173*t24435; + t24710 = t24168*t24331+t24109*t24478+t24172*t24449+t24162*t24365+t24095* +t24323+t24176*t24353+t24927*x; + t24709 = t24127*t24327+t23510+t24820+t24939*z; + t24050 = RATIONAL(-16.0,27.0); + t24458 = t24172*t24050; + t23524 = z*t24458; + t24369 = z*t24486; + t24465 = t24176*t24099; + t24342 = t24169*t24539; + t24708 = z*t24465+t24176*t24450+t23524+t24143*t24369+t24172*t24342+t24170 +*t24328+t24150*t24327+t24124*t24440; + t23638 = t24175*t23987; + t24429 = t24119*t24174; + t24352 = t24114*t24539; + t24707 = z*t24429+t23606+t24764+(t24352+t23638)*y; + t24706 = t24108*t24516+t24113*t24303+t24111*t24341+y*t24304+t24881+t24970 +*z; + t24705 = t24750+t24833; + t24540 = y*t24070; + t24377 = y*t24495; + t24704 = t24168*t24377+x*t24540+y*t24449+t24174*t24353+t24095*t24330+ +t24162*t24514+t24954; + t24302 = t24173*t24392; + t24703 = t24805+(t24493+t24302)*t24172+t24925*x; + t24702 = t24775+t24882+t24896; + t24314 = t24052*t24462; + t24701 = t24173*t23511+y*t24314+t24919*z+t24904*x; + t24700 = y*t24471+t23468+t24756+t24901; + t24374 = y*t24462; + t24699 = t24174*t24314+t24053*t24374+t24952*z+t24908*x; + t23977 = t24106*t24176; + t24698 = t24141*t24308+t23977+t24120*t24309+t24124*t24172+t24935+t24943; + t24131 = RATIONAL(5.0,24.0); + t24387 = t24131*t24171; + t24368 = x*t24387; + t24697 = t24176*t24368+t23664+t24162*t24496+t24153*t24331+t24819; + t24696 = t24175*t23429+t24076*t24303+t24964*z+t24908; + t24372 = t24092*t24526; + t24695 = (t23543+t23535)*z+(t24372+t23498)*t24173+(t24933+t24963)*x; + t23123 = y*t24300; + t24694 = t23123+t24723; + t24376 = t24162*t24539; + t24693 = t24144*t24341+y*t24376+t24174*t24301+t24175*t23909+(t24500+ +t24540)*z+t24944; + t24469 = t24176*t24098; + t24692 = t24092*t24440+t24089*t24327+t24804+(t23839+t24469)*z; + t24691 = t24176*t24451+t24085*t24323+t24047*t24496+t24173*t23503+t24909*x +; + t24690 = t24172*t24298+t24058*t24309+t24909+t24969; + t24689 = t24054*t24324+t24088*t24313+t24910*z+t24911*x; + t23633 = t24175*t24393; + t24410 = t24139*t24175; + t23928 = t24170*t24410; + t24688 = y*t23928+t23633+t24118*t24516+z*t24428+t24764; + t24517 = x*t24526; + t24510 = y*t24531; + t24687 = t24154*t24517+t24132*t24510+t24802+(t24360+t24359)*t24174; + t24686 = t24176*t24301+t24109*t24487+t24168*t24327+t24144*t24369+(t24376+ +t24425)*t24172+t24927*z; + t24321 = t24175*t24416; + t24685 = t24044*t24487+t24172*t24321+t24047*t24440+t24175*t23448+(t24917+ +t24969)*z; + t24534 = t24131*z; + t24338 = t24170*t24534; + t24684 = t24162*t24440+z*t24400+t24153*t24327+t24176*t24338+t24762; + t24038 = t24139*t24170; + t24295 = t24172*t24038; + t24683 = t24125*t24309+t24171*t24295+t23991+t24129*t24172+t24949+t24953; + t23915 = t24168*t24520; + t24682 = t23976+t24129*y+t24139*t24373+t23736+t23915+t23909+t24125*t24317 ++t23780; + t24681 = t23429+t24174*t24384+t24874+t24883+t24891; + t24680 = t24143*t24533+t23584+t24756+t24878; + t24351 = t24107*t24531; + t24364 = x*t24411; + t24679 = t24107*t24364+t24124*t24515+t24174*t24351+RATIONAL(-32.0,27.0)* +t24542+(t24510+t24517)*t24070+t24944*t24173; + t23719 = t24175*t23984; + t24354 = t24117*t24539; + t24499 = t24174*t24133; + t24678 = t23706+z*t24499+t24754+(t23719+t24354)*y; + t24677 = t24795+t24796; + t24329 = t24076*t24485; + t24676 = t24172*t24391+t24078*t24327+(t24329+t24388)*t24176+(t24932+ +t24966)*z; + t24675 = t24765+t24880+t24900; + t24674 = t23472+t23603+x*t23765+t24172*t24325+t24790; + t24673 = t24780+t24172*t24466+t24173*t23782+(t24469+t23661)*x; + t24672 = t23970+t24125*t24373+t24807+t24874; + t24671 = t24778+t24938*z+(t24372+t23657)*x; + t23073 = y*t24302; + t24670 = t23073+t24732; + t24669 = t24814+t24868; + t24039 = t24141*t24170; + t23902 = t24175*t24039; + t23849 = t24136*t24411; + t24668 = t24439*t24544+y*t23902+t23449+t23849+t24754; + t24667 = t24086*t24323+t24173*t23421+t24912*x+t24910; + t24472 = t24176*t24073; + t24666 = z*t24472+t24128*t24440+t24175*t24295+t24176*t24354+t24782; + t24382 = t24176*t24082; + t23459 = t24171*t24382; + t24665 = t24780+t24095*t24331+t24173*t24443+(t23459+t23964)*x; + t23234 = t24173*t23732; + t24664 = t23234+t24727; + t24663 = t24811+t24929*z+(t24370+t23833)*x; + t24322 = t24173*t24471; + t24662 = y*t24322+x*t23915+t23438+t23682+t24812; + t24363 = t24108*t24535; + t24661 = t24888+t24174*t24363+t24173*t24294+t24890+t24961*y; + t23575 = t24176*t24426; + t24660 = t24173*t24494+t24172*t24312+t24772+(t23962+t23575)*x; + t24659 = t24171*t24393+t23561+t24775+t24873; + t23557 = t24082*t24457; + t23672 = t24173*t24525; + t23850 = t24173*t24481; + t24658 = t23850+t24095*t24377+t23672+t24826+(t23557+t24005)*x; + t24657 = t23815+t23599+t23823+t24172*t24305+t24175*t23812+(t24494+t24953) +*z; + t24656 = t24173*t23977+t24169*t24365+t24946*t24172+t24951*t24176+(t24458+ +t24465)*x; + t24503 = t24176*t24100; + t24655 = t24173*t23739+t24102*t24496+t24772+(t23826+t24503)*x; + t24528 = y*t24132; + t23855 = x*t24528; + t24362 = z*t24482; + t24654 = t24150*t24362+t24134*t24364+t24154*t24510+t24175*t23855+t24802; + t24307 = t24175*t24461; + t24653 = t24173*t23863+y*t24307+t24522*t24544+(t23830+t23747)*x+(t23772+ +t24954)*z; + t23501 = t24078*t24520; + t24652 = t24136*t24433+t23501+t24807+t24891; + t24651 = t24127*t24331+t23570+t23420+x*t23553+t24790; + t24650 = t24136*t24327+t24102*t24440+t24792+(t24503+t23812)*z; + t24505 = t24084*t24176; + t24649 = t24074*t24369+t24112*t24327+z*t24505+t23483+t24821; + t23676 = t24120*t24495; + t24648 = x*t24429+t24174*t23982+t24791+(t23676+t24381)*y; + t23577 = x*t24505; + t24371 = x*t24453; + t24647 = t24112*t24331+t23577+t23565+t24074*t24371+t24753; + t24646 = t24174*t24299+t24173*t23532+t24907*x+t24919; + t24645 = t24078*t24303+y*t24329+t24947*z+t24904; + t24644 = t24760+t24809; + t24537 = y*t24050; + t23523 = x*t24537; + t24643 = t23523+t24169*t24514+t24951*t24174+t24946*y+t24958; + t23225 = t24175*t23819; + t24642 = t23225+t24729; + t24356 = z*t24423; + t24641 = z*t24437+t24127*t24440+t24172*t24304+t24176*t24356+t24774; + t24640 = t24805+t24172*t24316+t24052*t24496+(t23645+t24470)*x; + t24639 = t24173*t24444+t24076*t24323+t24916*t24172+(t24915+t24932)*x; + t24638 = y*t24311+t24075*t24317+t24906+t24964; + t24637 = y*t24446+t23557+t24765+t24848; + t23767 = t24125*t24495; + t24636 = t24781+t24174*t23998+x*t24499+(t23767+t24349)*y; + t24635 = t24127*t24323+t23670+t23491+t24172*t24322+t23757+(t23981+t24949) +*x; + t24634 = x*t24417+t24141*t24331+t24114*t24371+t23622+t24801; + t24489 = t24083*t24176; + t24396 = t24078*t24172; + t24633 = t24175*t24396+t24110*t24327+z*t24489+t24072*t24369+t24769; + t24632 = t24085*t24327+t24176*t24321+t24913*z+t24911; + t24631 = z*t23850+t24466*t24544+t24778+t24922*x; + t23683 = t24174*t23997; + t24630 = t24761+t24105*t24364+t24134*t24517+(t23683+t23626)*z; + t24629 = t23499+t24144*t24331+t24173*t24001+t24176*t24302+(t24943+t24955) +*x; + t24628 = t24113*t24373+t24100*t24174+t24878+t24886+t24901; + t24627 = t23225+t24716; + t23794 = t24173*t24393; + t24626 = t24175*t24507+t24135*t24364+t24787+(t23811+t23794)*z; + t24504 = t24137*t24176; + t24126 = RATIONAL(-5.0,24.0); + t24625 = z*t24504+t24155*t24327+t24126*t24369+t24169*t24440+t24776; + t24041 = t24143*t24173; + t23934 = t24174*t24028; + t24415 = t24119*t24175; + t24333 = x*t24415; + t24361 = t24175*t24529; + t24624 = t24041*t24544+t24174*t24333+y*t24361+z*t23934+t24799; + t24049 = RATIONAL(32.0,27.0); + t24623 = t24099*t24347+t24106*t24324+t24050*t24346+t24173*t23524+t24124* +t24313+t24049*t24508+t24945*t24176; + t24622 = t24175*t23523+t24050*t24510+t24049*t24542+t24099*t24362+t24945* +t24174+t24931*t24173; + t24621 = t24143*t24341+y*t24342+t24128*t24303+t24175*t23892+(t24537+ +t24448)*z+t24931; + t24620 = t24746+t24833; + t24619 = t24897+t24116*t24303+t24108*t24341+t24971*z+(t24332+t24356)*y; + t24618 = t24176*t24300+t24175*t24001+t23461+t24172*t24326+(t24935+t24955) +*z; + t24366 = t24126*t24535; + t24617 = t24155*t24331+t24176*t24366+x*t24504+t24172*t24030+t24758; + t23877 = t24173*t24408; + t24616 = t24784+t24174*t24361+y*t24333+(t23877+t24345)*z; + t24615 = t24141*t24327+t23635+t23434+t24176*t24352+t24783; + t24158 = RATIONAL(-8.0,9.0); + t24037 = t24158*x; + t23871 = t24175*t24037; + t24614 = t24168*t24364+t24137*t24362+t24130*t24510+y*t23871+t24779; + t24613 = t24139*t24331+x*t24472+t24176*t24349+t24172*t23998+t24797; + t24422 = t24176*t24135; + t24612 = z*t24422+t24096*t24440+t24108*t24369+t24113*t24327+t24777; + t24611 = t24173*t23750+t24174*t24307+(t23702+t23773)*x+(t24513+t23672+ +t24958)*z; + t24610 = t24788+t24072*t24371+x*t24489+(t24396+t24306)*t24173; + t24609 = t24173*t24367+t24893+y*t24363+t24885+t24961*t24174; + t24608 = y*t24299+t24076*t24330+t24906*x+t24952; + t24607 = t24810+t24814; + t24034 = t24158*z; + t23867 = t24173*t24034; + t24536 = y*t24130; + t23654 = x*t24536; + t24606 = t24137*t24364+t24168*t24362+t24175*t23654+y*t23867+t24779; + t24605 = t24176*t24391+t24172*t24388+t24170*t23536+t24076*t24327+(t24928+ +t24936)*z; + t24604 = t24811+t24102*t24510+z*t23652+t24937*x; + t24603 = t24173*t23969+t24076*t24331+t24916*t24176+(t24936+t24956)*x; + t24602 = RATIONAL(16.0,9.0)*t24543+t24159*t24313+t23867+t24283+t23871+ +t24169*t24512+t23883+t24850; + t24241 = t24768+t24786; + t24601 = t24241+t24817+z*t23776+x*t23439+(t24348+t24351)*y; + t24600 = t24862+t24175*t24419+t24855+t24849+z*t24011+t24055*t24313+t24914 +*x; + t23433 = t24065*t24411; + t24243 = t24768+t24803; + t24599 = z*t23857+y*t24375+t24243+t24817+(t23865+t23433)*x; + t24242 = t24760+t24773; + t24598 = t23438+t24242+y*t24316+t24835+t24839+(t23532+t23965)*x; + t24115 = RATIONAL(-1.0,16.0); + t24597 = RATIONAL(5.0,64.0)*t24308+t24115*t24441+t23473+RATIONAL(-1.0, +64.0)*t24309+t24871+t24920+t24924; + t24090 = RATIONAL(1.0,16.0); + t24596 = t23419+t24090*t24441+RATIONAL(1.0,64.0)*t24309+RATIONAL(-5.0, +64.0)*t24308+t24879+t24905+t24960; + t23462 = t24170*t24382; + t24595 = t24172*t24301+t24109*t24440+t24867+t24804+t24858+(t23964+t23462) +*z; + t24404 = t24150*t24176; + t24164 = RATIONAL(2.0,3.0); + t24594 = t24034+t24164*t24539+z*t24404+t24141*t24369+t24159*t24440+t24118 +*t24327+t24762+t24902; + t24434 = t24172*t24079; + t24593 = t23676+t23997+t24788+(t23800+t24434)*t24173+(t24924+t24940)*x; + t24091 = RATIONAL(-5.0,16.0); + t24147 = RATIONAL(1.0,4.0); + t24592 = t24147*t24441+t24091*t24308+t24090*t24309+t23612+t24894+t24921+ +t24926+t24967; + t24436 = t24173*t24141; + t23869 = t24171*t24436; + t23687 = t24126*t24435; + t24591 = t24173*t23687+t23869+t24105*t24496+t24797+t23982+(t24921+t24941) +*x; + t23796 = t24172*t24387; + t24026 = t24139*t24171; + t23876 = t24173*t24026; + t24590 = t23770+t24173*t23796+t24801+t23998+t23876+t24889+t24948*x; + t24589 = t24806+t23573+y*t24325+t24836+t24839+(t23501+t23954)*x; + t24588 = t23796+t24026+t24171*t24407+t23798+t24736+t24892; + t24587 = t24117*t24331+t24173*t24459+t24041+t24757+t24094*t24495+(t24934+ +t24903)*x; + t24016 = t24153*t24170; + t23936 = t24175*t24016; + t24163 = RATIONAL(-2.0,3.0); + t24586 = t24166*t24440+t24163*t24539+t24123*t24327+t24139*t24369+t24776+ +t23936+t24017+t24950*z; + t24585 = t24106*t24440+t24864+t24128*t24327+t24792+t24867+(t23571+t23962) +*z; + t24584 = t24125*t24453+t23687+t24141*t24171+t23690+t24737+t24895; + t24018 = t24166*t24172; + t24156 = RATIONAL(-1.0,4.0); + t24103 = RATIONAL(5.0,16.0); + t24583 = t24018+t23845+t24162+t23843+t24016+t24103*t24308+t24115*t24309+ +t24156*t24441+t24918+t24948; + t24582 = t24753+t24173*t23700+t24011+t23767+t23456+t24905*x; + t24581 = t24782+t23902+t24010+t24126*t24327+t24105*t24440+(t24033+t23621+ +t24941)*z; + t24483 = t24101*t24173; + t24580 = t24759+t24028+t24171*t24483+t24173*t24475+t24114*t24331+(t24875+ +t24959)*x; + t24579 = t24131*t24327+t23805+t24004+t23928+t24783+(t24016+t23852+t24968) +*z; + t24284 = t23571+t24823; + t24578 = t24284+t24751+t24808+t24831; + t24577 = t24742+t24770+t24803; + t24279 = t23462+t24827; + t24576 = t24279+t24721+t24744; + t24575 = t24743+t24786+t24793; + t24574 = t24660+t24739; + t24573 = t24629+t24718; + t24399 = t23439+t23459; + t24572 = t24399+t24720+t24733; + t24571 = t24680+t24731; + t24570 = t24657+t24719; + t24569 = t24680+t24722; + t24498 = t23433+t23575; + t24568 = t24498+t24785+t24808+t24825+t24828; + t24567 = t24635+t24724; + t24566 = t24618+t24735; + t24565 = t24637+t24722; + t24564 = t24637+t24731; + t24563 = t24662+t24700; + t24562 = t24629+t23462+t24724; + t24561 = t24652+t24814+t24870; + t24560 = t24711+t24810+t24869; + t24559 = t24676+t24681; + t24558 = t24652+t24711; + t24557 = t24605+t24681; + t24556 = t24603+t24604; + t24555 = t24663+t24674; + t24554 = t24635+t23571+t24718; + t24553 = t24659+t24676; + t24552 = t24640+t24671; + t24551 = t24658+t24665; + t24550 = t24631+t24639; + t24549 = t24605+t24659; + t24548 = t24763+t24766+t24813+t24816; + t24547 = t23520+t24173*t23651+x*t23834+t24767+t24826+t24861+t24899+t24938 +; + t24546 = t24607+t24869+t24870; + t24146 = RATIONAL(5.0,3.0); + t24518 = t24146*z; + t24497 = t24108*t24176; + t24492 = t24146*t24175; + t24491 = t24123*t24175; + t24027 = t24144*t24175; + t24480 = t24094*t24175; + t24467 = t24101*t24175; + t24357 = t24055*t24531; + t24355 = t24173*t24527; + t24350 = t24119*t24531; + t24334 = t24073*t24531; + t24293 = t23571+t24827; + t24292 = t23123+t24833; + t24289 = t23234+t24830; + t24288 = t23575+t24832; + t24285 = t23462+t24823; + t24282 = z*t23577+t24082*t24313+t24862; + t24278 = t23459+t24832; + t24277 = t23225+t24830; + t24276 = t23073+t24830; + t24275 = t24131*t24175+RATIONAL(-25.0,48.0)*z; + t24274 = t24126*z+t24480; + t24273 = t24534+t24467; + t24063 = RATIONAL(25.0,48.0); + t24272 = t24063*z+t24126*t24175; + t24271 = t24157*t24172+t24141*t24176+t24164; + t24059 = RATIONAL(-25.0,12.0); + t24270 = t24146+t24118*t24176+t24059*t24172; + t24140 = RATIONAL(5.0,8.0); + t24269 = t24140+t24104*t24176+RATIONAL(-25.0,32.0)*t24172; + t24145 = RATIONAL(-5.0,8.0); + t24268 = RATIONAL(25.0,8.0)*t24172+t24145*t24176+RATIONAL(-5.0,2.0); + t24077 = RATIONAL(25.0,96.0); + t24267 = t24126+t24111*t24176+t24077*t24172; + t24266 = t24131+t24502+t24497; + t24265 = t24113*t24176+t24117*t24172+t24094; + t24264 = t24163+t24160*t24172+t24139*t24176; + t24263 = t24101+t24114*t24172+t24116*t24176; + t24262 = t24097*t24176+t24145+RATIONAL(25.0,32.0)*t24172; + t24261 = t24103*t24176+RATIONAL(5.0,4.0)+RATIONAL(-25.0,16.0)*t24172; + t24260 = t24147+t24091*t24172+t24090*t24176; + t24259 = RATIONAL(1.0,2.0)+t24149*t24176+t24145*t24172; + t24258 = RATIONAL(-1.0,2.0)+t24140*t24172+t24161*t24176; + t24087 = RATIONAL(25.0,16.0); + t24138 = RATIONAL(-5.0,4.0); + t24257 = t24138+t24087*t24172+t24091*t24176; + t24256 = t24115*t24176+t24156+t24103*t24172; + t24255 = RATIONAL(25.0,12.0)*t24172+t24123*t24176+t24151; + t24253 = t24497*t24543+t24175*t24436+t24126*t24313+x*t24534+t24856; + t24252 = RATIONAL(-10.0,3.0)*t24543+t24160*t24313+t24157*t24512+t24163* +t24462+t24846; + t24251 = t24077*t24512+t24120*t24313+t24837+t24856+t24860; + t24068 = RATIONAL(-25.0,24.0); + t24250 = t24164*t24313+t24068*t24512+t24846+t24852+t24865; + t24249 = t24282+t24888*z+(t24339+t23633)*t24173; + t24248 = t24173*t23849+t24089*t24374+t24282+t24893*z; + t24247 = t24785+t24840+t24861; + t24246 = t24766+t24796; + t24245 = t24767+t24808; + t24244 = t24796+t24813; + t24152 = RATIONAL(4.0,3.0); + t24240 = t24152*t24531+x*t24492+t24153*t24347+t24059*t24346+t24252+t24852 +; + t24239 = t24253+x*t24491+t24063*t24346+t24860+(t24483+t24310)*z; + t24238 = t24152*t24530+t24153*t24380+t24173*t24518+t24059*t24378+t24252+ +t24865; + t24237 = t24116*t24380+t24123*t24531+x*t24467+t24063*t24378+t24253+t24837 +; + t24236 = t24248+t24073*t24517+t24055*t24364+t24815+t24885*z; + t24235 = x*t23930+t24027*t24545+y*t24350+t24174*t24355+t24747+t24784; + t24234 = t23559+t23794+y*t23876+t24118*t24514+t24740+t24791; + t24233 = t23877+x*t24409+t24094*t24330+t23654+t24174*t24366+t24749+( +t24343+t24877)*y; + t24232 = t24135*t24362+t24137*t24510+y*t23705+x*t23633+t24752+t24787; + t24231 = y*t24357+t24249+t24174*t24334+t24789+t24897*x; + t24230 = t24174*t24368+t23934+t24157*t24514+x*t24456+t23855+t24101*t24330 ++t24749+t24884*y; + t24229 = t24174*t24357+t24248+y*t24334+t24789+t24881*x; + t24228 = t24172*t24319+x*t24422+t24176*t24363+t24096*t24496+t24741+t24759 +; + t24227 = t24748+z*t24536+t23821+t24126*t24341+t23930+t24094*t24303+( +t24340+t24902)*y; + t24226 = x*t23905+t24174*t24350+y*t24355+t24022*t24545+t24747+t24799; + t24225 = x*t24438+t23683+y*t23869+t24394*t24545+t24740+t24781; + t24224 = t24249+t24055*t24517+t24073*t24364+t24815+t24890*z; + t24223 = t24752+t24105*t24362+y*t24359+t24761+(t23721+t23849)*x; + t24222 = t23769+t24174*t24338+t24101*t24303+z*t24528+t24748+(t24344+ +t23936)*y+t24965; + t24221 = t23604+t24111*t24371+t24172*t24419+t24116*t24331+t24741+t24757; + t24220 = t24039+t24126*t24463+t24730+t23717+t23700+t24737+t24959; + t24219 = t24123*t24331+t24602+t24163*t24535+t24139*t24371+t24173*t24018+ +t24758+t24950*x+t24884; + t24218 = t24027+t24717+t24133*t24440+t24170*t24467+t24777+t24114*t24327+( +t24875+t24895)*z; + t24217 = t24117*t24327+t24170*t24480+t24022+t24172*t24415+t24774+t24717+( +t24892+t24903)*z; + t24216 = t24038+t23800+t23803+t24730+t24131*t24463+t24736+t24934; + t24215 = t23996+t23638+t24108*t24327+t24175*t24434+t24600+t24769+t24871*z +; + t24214 = t24141*t24371+x*t24404+t24037+t24164*t24535+t24602+t24819+t24894 +*t24173+t24877; + t24213 = t23493+t23719+t24600+t24111*t24327+t24821+t24879*z+t24914; + t24212 = t24547+t24671+t24674; + t24211 = t24727+t24247+t24289+t23123+t24745+t24824+t24836+t24841; + t24210 = t24246+t24595+t24662+t24816; + t24209 = t24285+t24721+t24589+t24751+t24767; + t24208 = t24623+t24622+t24621+t24708; + t24207 = t24601+t24665+t24739+t24832; + t24206 = t24623+t24679+t24656+t24704; + t24205 = t24655+t24627+t24246+t24795+t24866+t24900; + t24204 = t24677+t24276+t24694+t24732+t24738; + t24203 = t24241+t24585+t24742+t24793+t24823; + t24202 = t24638+t24689+t24690+t24701; + t24201 = t24242+t24669+t24672+t23073+t24809+t24822; + t24200 = t24691+t24685+t24689+t24714; + t24199 = t24245+t24589+t24293+t24744+t24831; + t24198 = t24603+t24598+t24631; + t24197 = t24623+t24643+t24683+t24693; + t24196 = t23433+t24720+t24247+t24278+t24734+t24828+t24835; + t24195 = t24620+t24611+t24628+t24677; + t24194 = t24585+t24243+t24743+t24770+t24827; + t24193 = t24618+t23439+t24599+t24719; + t24192 = t24667+t24608+t24689+t24699; + t24191 = t24644+t24702+t24705+t24712; + t24190 = t24632+t24689+t24646+t24715; + t24189 = t24244+t24595+t24700+t24763; + t24188 = t24245+t24733+t23439+t24288+t24734+t24825+t24861; + t24187 = t24547+t24640+t24663; + t24186 = t24642+t24695+t24644+t24709; + t24185 = t24623+t24698+t24686+t24710; + t24184 = t24604+t24598+t24639; + t24183 = t24653+t24244+t24673+t23234+t24795+t24829; + t24182 = t24601+t24658+t24660; + t24181 = t23433+t24657+t24599+t24735; + coeffs_dxz->coeff_m2_m2_m2 = t24200+t24608+t24701+t24696+t24715; + coeffs_dxz->coeff_m1_m2_m2 = t24553+t24188+t24552; + coeffs_dxz->coeff_0_m2_m2 = t24609+t24224+t24610; + coeffs_dxz->coeff_p1_m2_m2 = t24196+t24557+t24552; + coeffs_dxz->coeff_p2_m2_m2 = t24202+t24632+t24608+t24645+t24691; + coeffs_dxz->coeff_m2_m1_m2 = t24191+t24642+t24669+t24664+t24703; + coeffs_dxz->coeff_m1_m1_m2 = t24563+t24203+t24562; + coeffs_dxz->coeff_0_m1_m2 = t24225+t24613+t24626; + coeffs_dxz->coeff_p1_m1_m2 = t24573+t24210+t24575+t24293; + coeffs_dxz->coeff_p2_m1_m2 = t24703+t24211+t24672+t24709+t24712; + coeffs_dxz->coeff_m2_0_m2 = t24215+t24596+t24593; + coeffs_dxz->coeff_m1_0_m2 = t24217+t24584+t24591; + coeffs_dxz->coeff_0_0_m2 = (t24256*t24171+t24265)*t24173+t24239+(t24269* +t24171+t24267)*x; + coeffs_dxz->coeff_p1_0_m2 = t24218+t24588+t24591; + coeffs_dxz->coeff_p2_0_m2 = t24597+t24593+t24213; + coeffs_dxz->coeff_m2_p1_m2 = t24695+t24703+t24201+t24292+t24725+t24750; + coeffs_dxz->coeff_m1_p1_m2 = t24194+t24548+t24562; + coeffs_dxz->coeff_0_p1_m2 = t24234+t24613+t24630; + coeffs_dxz->coeff_p1_p1_m2 = t24573+t24577+t24189+t24284; + coeffs_dxz->coeff_p2_p1_m2 = t24703+t24186+t24702+t24276+t24726+t24745; + coeffs_dxz->coeff_m2_p2_m2 = t24200+t24638+t24645+t24646+t24699; + coeffs_dxz->coeff_m1_p2_m2 = t24187+t24559+t24568; + coeffs_dxz->coeff_0_p2_m2 = t24610+t24236+t24661; + coeffs_dxz->coeff_p1_p2_m2 = t24187+t24572+t24549; + coeffs_dxz->coeff_p2_p2_m2 = t24691+t24190+t24690+t24696+t24699; + coeffs_dxz->coeff_m2_m2_m1 = t24550+t24546+t24199; + coeffs_dxz->coeff_m1_m2_m1 = t24204+t24653+t24628+t24650+t24655; + coeffs_dxz->coeff_0_m2_m1 = t24616+t24221+t24636; + coeffs_dxz->coeff_p1_m2_m1 = t24620+t24653+t24205+t24670+t24692; + coeffs_dxz->coeff_p2_m2_m1 = t24209+t24550+t24558; + coeffs_dxz->coeff_m2_m1_m1 = t23433+t24571+t24182+t23459+t24566; + coeffs_dxz->coeff_m1_m1_m1 = t24698+t24693+t24206+t24682+t24708; + coeffs_dxz->coeff_0_m1_m1 = t24233+t24606+t24697; + coeffs_dxz->coeff_p1_m1_m1 = t24206+t24621+t24686+t24683+t24713; + coeffs_dxz->coeff_p2_m1_m1 = t23575+t24565+t23439+t24182+t24570; + coeffs_dxz->coeff_m2_0_m1 = t24220+t24581+t24587; + coeffs_dxz->coeff_m1_0_m1 = t24594+t24592+t24214; + coeffs_dxz->coeff_0_0_m1 = (t24259*t24171+t24264)*t24173+t24240+(t24257* +t24171+t24270)*x; + coeffs_dxz->coeff_p1_0_m1 = t24586+t24214+t24583; + coeffs_dxz->coeff_p2_0_m1 = t24216+t24587+t24579; + coeffs_dxz->coeff_m2_p1_m1 = t24564+t24193+t24574+t24278; + coeffs_dxz->coeff_m1_p1_m1 = t24698+t24643+t24208+t24656+t24713; + coeffs_dxz->coeff_0_p1_m1 = t24230+t24654+t24697; + coeffs_dxz->coeff_p1_p1_m1 = t24197+t24622+t24682+t24656+t24686; + coeffs_dxz->coeff_p2_p1_m1 = t24569+t24181+t24574+t24288; + coeffs_dxz->coeff_m2_p2_m1 = t24184+t24561+t24578; + coeffs_dxz->coeff_m1_p2_m1 = t24205+t24289+t24611+t24650+t24728+t24738; + coeffs_dxz->coeff_0_p2_m1 = t24624+t24221+t24648; + coeffs_dxz->coeff_p1_p2_m1 = t24195+t24655+t24692+t23234+t24694+t24728; + coeffs_dxz->coeff_p2_p2_m1 = t24184+t24560+t24576; + coeffs_dxz->coeff_m2_m2_0 = t24231+t24633+t24706; + coeffs_dxz->coeff_m1_m2_0 = t24235+t24641+t24678; + coeffs_dxz->coeff_0_m2_0 = (t24273*t24174+t24274*y)*t24173+(t24275*t24174 ++t24272*y)*x+t24251; + coeffs_dxz->coeff_p1_m2_0 = t24612+t24235+t24707; + coeffs_dxz->coeff_p2_m2_0 = t24231+t24619+t24649; + coeffs_dxz->coeff_m2_m1_0 = t24232+t24666+t24668; + coeffs_dxz->coeff_m1_m1_0 = t24614+t24227+t24684; + coeffs_dxz->coeff_0_m1_0 = ((t24141*t24175+t24123*z)*t24174+(t24163* +t24175+t24518)*y)*t24173+((t24491+RATIONAL(25.0,24.0)*z)*t24174+(t24492+ +RATIONAL(-25.0,6.0)*z)*y)*x+t24250; + coeffs_dxz->coeff_p1_m1_0 = t24614+t24222+t24625; + coeffs_dxz->coeff_p2_m1_0 = t24232+t24615+t24688; + coeffs_dxz->coeff_m2_0_0 = t24237+(t24256*t24170+t24265)*t24175+(t24269* +t24170+t24267)*z; + coeffs_dxz->coeff_m1_0_0 = (t24259*t24170+t24264)*t24175+(t24257*t24170+ +t24270)*z+t24238; + coeffs_dxz->coeff_0_0_0 = ((t24138*t24172+1.0+t24147*t24176)*t24175+ +t24268*z)*t24173+(t24268*t24175+(RATIONAL(-125.0,16.0)*t24172+t24087*t24176+ +RATIONAL(25.0,4.0))*z)*x; + coeffs_dxz->coeff_p1_0_0 = t24238+(t24258*t24170+t24271)*t24175+(t24261* +t24170+t24255)*z; + coeffs_dxz->coeff_p2_0_0 = (t24260*t24170+t24263)*t24175+(t24262*t24170+ +t24266)*z+t24237; + coeffs_dxz->coeff_m2_p1_0 = t24223+t24666+t24688; + coeffs_dxz->coeff_m1_p1_0 = t24684+t24222+t24687; + coeffs_dxz->coeff_0_p1_0 = ((t24410+t24118*z)*t24174+(t24151*z+t24164* +t24175)*y)*t24173+((t24068*z+t24118*t24175)*t24174+(t24151*t24175+t24122*z)*y)* +x+t24250; + coeffs_dxz->coeff_p1_p1_0 = t24227+t24625+t24687; + coeffs_dxz->coeff_p2_p1_0 = t24223+t24615+t24668; + coeffs_dxz->coeff_m2_p2_0 = t24229+t24619+t24633; + coeffs_dxz->coeff_m1_p2_0 = t24641+t24226+t24707; + coeffs_dxz->coeff_0_p2_0 = (t24274*t24174+t24273*y)*t24173+(t24272*t24174 ++t24275*y)*x+t24251; + coeffs_dxz->coeff_p1_p2_0 = t24612+t24226+t24678; + coeffs_dxz->coeff_p2_p2_0 = t24229+t24649+t24706; + coeffs_dxz->coeff_m2_m2_p1 = t24198+t24561+t24576; + coeffs_dxz->coeff_m1_m2_p1 = t24183+t24675+t24292+t24650+t24723+t24746; + coeffs_dxz->coeff_0_m2_p1 = t24228+t24616+t24648; + coeffs_dxz->coeff_p1_m2_p1 = t24183+t24692+t24277+t24628+t24716+t24738; + coeffs_dxz->coeff_p2_m2_p1 = t24198+t24560+t24578; + coeffs_dxz->coeff_m2_m1_p1 = t24207+t24565+t24498+t24566; + coeffs_dxz->coeff_m1_m1_p1 = t24197+t24679+t24710+t24708+t24713; + coeffs_dxz->coeff_0_m1_p1 = t24230+t24606+t24617; + coeffs_dxz->coeff_p1_m1_p1 = t24679+t24643+t24185+t24621+t24682; + coeffs_dxz->coeff_p2_m1_p1 = t24571+t24207+t24570+t24399; + coeffs_dxz->coeff_m2_0_p1 = t24580+t24581+t24216; + coeffs_dxz->coeff_m1_0_p1 = t24594+t24219+t24583; + coeffs_dxz->coeff_0_0_p1 = t24240+(t24258*t24171+t24271)*t24173+(t24261* +t24171+t24255)*x; + coeffs_dxz->coeff_p1_0_p1 = t24219+t24592+t24586; + coeffs_dxz->coeff_p2_0_p1 = t24220+t24580+t24579; + coeffs_dxz->coeff_m2_p1_p1 = t24551+t23575+t24569+t24193; + coeffs_dxz->coeff_m1_p1_p1 = t24208+t24683+t24682+t24704+t24710; + coeffs_dxz->coeff_0_p1_p1 = t24233+t24617+t24654; + coeffs_dxz->coeff_p1_p1_p1 = t24693+t24622+t24185+t24704+t24713; + coeffs_dxz->coeff_p2_p1_p1 = t24551+t24564+t24181+t23459; + coeffs_dxz->coeff_m2_p2_p1 = t24209+t24556+t24546; + coeffs_dxz->coeff_m1_p2_p1 = t24195+t24627+t24670+t24650+t24673; + coeffs_dxz->coeff_0_p2_p1 = t24228+t24624+t24636; + coeffs_dxz->coeff_p1_p2_p1 = t24204+t24673+t24675+t24611+t24692; + coeffs_dxz->coeff_p2_p2_p1 = t24556+t24558+t24199; + coeffs_dxz->coeff_m2_m2_p2 = t24667+t24202+t24685+t24646+t24696; + coeffs_dxz->coeff_m1_m2_p2 = t24212+t24559+t24572; + coeffs_dxz->coeff_0_m2_p2 = t24647+t24224+t24661; + coeffs_dxz->coeff_p1_m2_p2 = t24212+t24568+t24549; + coeffs_dxz->coeff_p2_m2_p2 = t24667+t24190+t24645+t24701+t24714; + coeffs_dxz->coeff_m2_m1_p2 = t24277+t24201+t24712+t24651+t24729+t24745; + coeffs_dxz->coeff_m1_m1_p2 = t24203+t24548+t24554; + coeffs_dxz->coeff_0_m1_p2 = t24234+t24626+t24634; + coeffs_dxz->coeff_p1_m1_p2 = t24567+t24279+t24575+t24189; + coeffs_dxz->coeff_p2_m1_p2 = t24191+t24709+t24651+t24725+t23123+t23073+ +t24726; + coeffs_dxz->coeff_m2_0_p2 = t24215+t24582+t24597; + coeffs_dxz->coeff_m1_0_p2 = t24217+t24588+t24590; + coeffs_dxz->coeff_0_0_p2 = t24239+(t24260*t24171+t24263)*t24173+(t24262* +t24171+t24266)*x; + coeffs_dxz->coeff_p1_0_p2 = t24218+t24584+t24590; + coeffs_dxz->coeff_p2_0_p2 = t24596+t24582+t24213; + coeffs_dxz->coeff_m2_p1_p2 = t24695+t24607+t24211+t24651+t24868+t24882+ +t24887; + coeffs_dxz->coeff_m1_p1_p2 = t24563+t24194+t24554; + coeffs_dxz->coeff_0_p1_p2 = t24630+t24225+t24634; + coeffs_dxz->coeff_p1_p1_p2 = t24567+t24285+t24210+t24577; + coeffs_dxz->coeff_p2_p1_p2 = t24186+t24672+t24651+t24664+t24705; + coeffs_dxz->coeff_m2_p2_p2 = t24192+t24685+t24645+t24690+t24715; + coeffs_dxz->coeff_m1_p2_p2 = t24555+t24196+t24553; + coeffs_dxz->coeff_0_p2_p2 = t24236+t24609+t24647; + coeffs_dxz->coeff_p1_p2_p2 = t24555+t24557+t24188; + coeffs_dxz->coeff_p2_p2_p2 = t24638+t24632+t24192+t24696+t24714; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dy.compute.c new file mode 100644 index 0000000..aede0f2 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dy.compute.c @@ -0,0 +1,2721 @@ +fp t14452; +fp t14523; +fp t14525; +fp t14424; +fp t15465; +fp t14469; +fp t14913; +fp t14462; +fp t14522; +fp t14526; +fp t14949; +fp t15464; +fp t14521; +fp t14528; +fp t15028; +fp t14410; +fp t14054; +fp t14411; +fp t15017; +fp t14029; +fp t15463; +fp t14396; +fp t14870; +fp t13886; +fp t14399; +fp t14882; +fp t15462; +fp t14460; +fp t15018; +fp t14449; +fp t14524; +fp t14907; +fp t14527; +fp t14187; +fp t15461; +fp t15006; +fp t14204; +fp t14915; +fp t14222; +fp t15460; +fp t14916; +fp t14712; +fp t14466; +fp t14997; +fp t14784; +fp t15459; +fp t14901; +fp t14848; +fp t15429; +fp t14911; +fp t13963; +fp t15458; +fp t15012; +fp t14090; +fp t15457; +fp t14420; +fp t14929; +fp t13920; +fp t14459; +fp t14914; +fp t15456; +fp t14899; +fp t14937; +fp t14454; +fp t14519; +fp t15455; +fp t14873; +fp t13853; +fp t15454; +fp t14646; +fp t14457; +fp t14989; +fp t14790; +fp t15453; +fp t14723; +fp t14749; +fp t15452; +fp t14983; +fp t15004; +fp t14984; +fp t15451; +fp t14947; +fp t15450; +fp t14467; +fp t15010; +fp t15449; +fp t14458; +fp t15032; +fp t14408; +fp t14878; +fp t15008; +fp t15448; +fp t14515; +fp t14507; +fp t15447; +fp t14446; +fp t14928; +fp t14439; +fp t15446; +fp t14442; +fp t14441; +fp t15025; +fp t14918; +fp t15445; +fp t14888; +fp t14426; +fp t14665; +fp t14423; +fp t14932; +fp t15444; +fp t14437; +fp t14345; +fp t14010; +fp t15443; +fp t14499; +fp t14382; +fp t14520; +fp t14845; +fp t15442; +fp t14425; +fp t14857; +fp t13923; +fp t14891; +fp t14136; +fp t15441; +fp t14097; +fp t15440; +fp t14461; +fp t14096; +fp t14500; +fp t15439; +fp t14351; +fp t14147; +fp t15438; +fp t14509; +fp t15437; +fp t14440; +fp t14493; +fp t15436; +fp t14936; +fp t15435; +fp t14924; +fp t14954; +fp t14031; +fp t15434; +fp t14360; +fp t14435; +fp t14333; +fp t13959; +fp t15433; +fp t14474; +fp t15432; +fp t14455; +fp t14389; +fp t14883; +fp t15431; +fp t14964; +fp t15015; +fp t15430; +fp t14421; +fp t14930; +fp t14688; +fp t14990; +fp t14782; +fp t15428; +fp t14412; +fp t14876; +fp t14445; +fp t15427; +fp t13895; +fp t15426; +fp t13988; +fp t15425; +fp t14923; +fp t14902; +fp t15424; +fp t15423; +fp t14363; +fp t15422; +fp t14468; +fp t14481; +fp t14963; +fp t15421; +fp t13986; +fp t15420; +fp t14854; +fp t14922; +fp t15419; +fp t15418; +fp t14477; +fp t14898; +fp t14122; +fp t14485; +fp t14355; +fp t15417; +fp t14453; +fp t15416; +fp t15415; +fp t13922; +fp t14350; +fp t15414; +fp t13919; +fp t15413; +fp t14394; +fp t14406; +fp t14645; +fp t15412; +fp t14855; +fp t15411; +fp t14863; +fp t13904; +fp t15410; +fp t15409; +fp t15408; +fp t14342; +fp t14443; +fp t15013; +fp t14444; +fp t15407; +fp t14919; +fp t13984; +fp t15406; +fp t13917; +fp t15405; +fp t14880; +fp t13857; +fp t14340; +fp t15404; +fp t13949; +fp t15403; +fp t15402; +fp t14868; +fp t15024; +fp t15401; +fp t14397; +fp t14398; +fp t15026; +fp t14896; +fp t15400; +fp t14402; +fp t14395; +fp t14973; +fp t14841; +fp t14910; +fp t15399; +fp t15398; +fp t14912; +fp t15005; +fp t15397; +fp t15396; +fp t15030; +fp t15395; +fp t14388; +fp t14070; +fp t15394; +fp t14934; +fp t15393; +fp t15392; +fp t15001; +fp t14192; +fp t14655; +fp t15391; +fp t14931; +fp t14797; +fp t15002; +fp t13976; +fp t15390; +fp t13952; +fp t14102; +fp t14667; +fp t14948; +fp t14008; +fp t14697; +fp t15260; +fp t14652; +fp t13048; +fp t14877; +fp t14809; +fp t15389; +fp t14038; +fp t15388; +fp t15021; +fp t14157; +fp t14747; +fp t15387; +fp t14967; +fp t14957; +fp t15386; +fp t14240; +fp t15385; +fp t15384; +fp t14904; +fp t14117; +fp t15383; +fp t14414; +fp t14792; +fp t14858; +fp t13910; +fp t14465; +fp t14925; +fp t14059; +fp t14900; +fp t14354; +fp t14748; +fp t15382; +fp t13931; +fp t14691; +fp t15381; +fp t13902; +fp t14409; +fp t13975; +fp t15380; +fp t14041; +fp t13129; +fp t14057; +fp t14962; +fp t14232; +fp t15217; +fp t15379; +fp t14020; +fp t15378; +fp t14498; +fp t14484; +fp t15377; +fp t14037; +fp t15019; +fp t14802; +fp t15376; +fp t14513; +fp t14516; +fp t15375; +fp t14052; +fp t14966; +fp t14791; +fp t15374; +fp t14367; +fp t14243; +fp t14413; +fp t14842; +fp t13993; +fp t15373; +fp t14960; +fp t14668; +fp t15372; +fp t14996; +fp t13916; +fp t14759; +fp t15318; +fp t13990; +fp t15371; +fp t14998; +fp t14778; +fp t14940; +fp t13925; +fp t14941; +fp t14745; +fp t15306; +fp t15370; +fp t14105; +fp t13998; +fp t15289; +fp t14647; +fp t15369; +fp t14016; +fp t15368; +fp t14906; +fp t14789; +fp t14210; +fp t14718; +fp t14851; +fp t14769; +fp t15220; +fp t15367; +fp t15366; +fp t13908; +fp t14862; +fp t14757; +fp t13855; +fp t15309; +fp t14043; +fp t15302; +fp t14036; +fp t13933; +fp t15291; +fp t14601; +fp t15365; +fp t13974; +fp t14368; +fp t14804; +fp t14892; +fp t14225; +fp t14024; +fp t15311; +fp t13926; +fp t14170; +fp t15299; +fp t15252; +fp t14738; +fp t15364; +fp t14875; +fp t14681; +fp t14946; +fp t14053; +fp t13983; +fp t14704; +fp t14720; +fp t14145; +fp t15277; +fp t15363; +fp t14015; +fp t14943; +fp t14206; +fp t14709; +fp t15250; +fp t15362; +fp t14837; +fp t15361; +fp t14971; +fp t14822; +fp t14887; +fp t14708; +fp t14828; +fp t15243; +fp t15360; +fp t14093; +fp t15003; +fp t15235; +fp t14119; +fp t14727; +fp t15359; +fp t14730; +fp t13978; +fp t14807; +fp t15358; +fp t14781; +fp t13909; +fp t15213; +fp t15357; +fp t14056; +fp t14945; +fp t14743; +fp t15356; +fp t14866; +fp t13991; +fp t15355; +fp t13970; +fp t14806; +fp t15354; +fp t14092; +fp t14908; +fp t14230; +fp t14677; +fp t13930; +fp t15272; +fp t14773; +fp t15214; +fp t14605; +fp t15353; +fp t13905; +fp t14005; +fp t14353; +fp t14795; +fp t14827; +fp t15352; +fp t14814; +fp t14042; +fp t13979; +fp t14921; +fp t14780; +fp t13972; +fp t15225; +fp t15351; +fp t14044; +fp t13239; +fp t15000; +fp t14007; +fp t14011; +fp t14706; +fp t15273; +fp t15350; +fp t14707; +fp t15254; +fp t15349; +fp t14872; +fp t14680; +fp t14740; +fp t14871; +fp t14649; +fp t15227; +fp t13927; +fp t15348; +fp t14986; +fp t15347; +fp t13950; +fp t14009; +fp t14657; +fp t15248; +fp t14869; +fp t14831; +fp t14763; +fp t15346; +fp t15345; +fp t14755; +fp t14717; +fp t15251; +fp t15344; +fp t13937; +fp t14909; +fp t14673; +fp t15241; +fp t14608; +fp t15343; +fp t14654; +fp t15226; +fp t14682; +fp t15342; +fp t15231; +fp t15341; +fp t14035; +fp t14905; +fp t14751; +fp t14045; +fp t15265; +fp t15340; +fp t14249; +fp t14032; +fp t15287; +fp t15339; +fp t14776; +fp t14221; +fp t14191; +fp t13946; +fp t15284; +fp t15338; +fp t13934; +fp t14700; +fp t14689; +fp t15337; +fp t14959; +fp t14788; +fp t14683; +fp t15336; +fp t15014; +fp t14151; +fp t14172; +fp t15335; +fp t14803; +fp t14808; +fp t15334; +fp t14838; +fp t14897; +fp t14735; +fp t15333; +fp t14999; +fp t14229; +fp t15332; +fp t14812; +fp t15331; +fp t14977; +fp t14799; +fp t15330; +fp t14884; +fp t14829; +fp t14669; +fp t14656; +fp t15329; +fp t14662; +fp t15328; +fp t14505; +fp t14771; +fp t14933; +fp t14216; +fp t14486; +fp t14658; +fp t14767; +fp t14725; +fp t15327; +fp t14648; +fp t15326; +fp t14073; +fp t15325; +fp t14356; +fp t14698; +fp t14956; +fp t14152; +fp t15324; +fp t14752; +fp t14787; +fp t15323; +fp t15322; +fp t15016; +fp t14976; +fp t14813; +fp t14981; +fp t14794; +fp t15321; +fp t15320; +fp t15319; +fp t13997; +fp t14716; +fp t15317; +fp t14492; +fp t14801; +fp t13948; +fp t15316; +fp t14783; +fp t14518; +fp t14968; +fp t14256; +fp t15315; +fp t14826; +fp t14431; +fp t14765; +fp t15314; +fp t13929; +fp t14768; +fp t15313; +fp t14475; +fp t14510; +fp t15312; +fp t14860; +fp t13967; +fp t15310; +fp t14696; +fp t14993; +fp t14815; +fp t15307; +fp t14438; +fp t13992; +fp t15305; +fp t13955; +fp t15303; +fp t13911; +fp t15301; +fp t15300; +fp t13914; +fp t14033; +fp t15298; +fp t14404; +fp t13877; +fp t14674; +fp t15297; +fp t14405; +fp t13872; +fp t14762; +fp t15296; +fp t13953; +fp t15295; +fp t14417; +fp t14836; +fp t15294; +fp t13866; +fp t14758; +fp t15293; +fp t14401; +fp t14470; +fp t14894; +fp t14670; +fp t15292; +fp t13899; +fp t15290; +fp t14281; +fp t14494; +fp t14834; +fp t15288; +fp t13968; +fp t15286; +fp t14034; +fp t15285; +fp t15283; +fp t15282; +fp t15281; +fp t14785; +fp t15280; +fp t14679; +fp t15279; +fp t14991; +fp t14770; +fp t14687; +fp t15278; +fp t14650; +fp t14733; +fp t14490; +fp t14886; +fp t14480; +fp t14082; +fp t15031; +fp t15275; +fp t14491; +fp t14489; +fp t14988; +fp t14262; +fp t15274; +fp t13889; +fp t14428; +fp t14692; +fp t14430; +fp t14715; +fp t15271; +fp t14980; +fp t14644; +fp t14429; +fp t14850; +fp t14238; +fp t15270; +fp t15269; +fp t14433; +fp t14849; +fp t14737; +fp t15268; +fp t13973; +fp t14659; +fp t15267; +fp t14793; +fp t14672; +fp t15266; +fp t14741; +fp t15264; +fp t14482; +fp t14661; +fp t15263; +fp t14950; +fp t14246; +fp t14811; +fp t14978; +fp t15262; +fp t14874; +fp t14110; +fp t14927; +fp t14651; +fp t15261; +fp t14987; +fp t15259; +fp t15258; +fp t14137; +fp t14935; +fp t14744; +fp t14885; +fp t13945; +fp t15257; +fp t15256; +fp t14483; +fp t14903; +fp t14471; +fp t14844; +fp t15255; +fp t13999; +fp t15253; +fp t14512; +fp t14939; +fp t14861; +fp t14174; +fp t14479; +fp t14695; +fp t15249; +fp t14000; +fp t15247; +fp t15246; +fp t15245; +fp t14893; +fp t14211; +fp t15244; +fp t15242; +fp t14427; +fp t14702; +fp t14434; +fp t15240; +fp t15239; +fp t14244; +fp t15238; +fp t14711; +fp t15237; +fp t15236; +fp t15234; +fp t14879; +fp t13913; +fp t14113; +fp t14942; +fp t14133; +fp t15233; +fp t15232; +fp t14488; +fp t14496; +fp t14852; +fp t14840; +fp t14506; +fp t15011; +fp t15230; +fp t14719; +fp t15229; +fp t14047; +fp t14830; +fp t15228; +fp t15224; +fp t14663; +fp t14185; +fp t15222; +fp t14856; +fp t13996; +fp t14223; +fp t15221; +fp t13918; +fp t15219; +fp t15218; +fp t14722; +fp t15216; +fp t14881; +fp t14048; +fp t14212; +fp t14684; +fp t15215; +fp t15212; +fp t15211; +fp t15210; +fp t13957; +fp t15209; +fp t15208; +fp t15207; +fp t14796; +fp t14779; +fp t15206; +fp t14140; +fp t14671; +fp t15205; +fp t15204; +fp t15203; +fp t14731; +fp t14364; +fp t15202; +fp t14160; +fp t15201; +fp t15200; +fp t14473; +fp t14118; +fp t15199; +fp t15198; +fp t15197; +fp t15196; +fp t15195; +fp t15194; +fp t15193; +fp t14224; +fp t14995; +fp t14199; +fp t15192; +fp t14171; +fp t14068; +fp t15191; +fp t13938; +fp t15190; +fp t15188; +fp t15186; +fp t14764; +fp t15185; +fp t14675; +fp t15184; +fp t14195; +fp t14186; +fp t15183; +fp t14165; +fp t14226; +fp t15182; +fp t14994; +fp t14261; +fp t14074; +fp t14508; +fp t15023; +fp t14259; +fp t15181; +fp t14678; +fp t14969; +fp t14833; +fp t15180; +fp t15179; +fp t14742; +fp t15178; +fp t14772; +fp t14750; +fp t15177; +fp t15176; +fp t14101; +fp t14134; +fp t15175; +fp t15174; +fp t15173; +fp t14336; +fp t14982; +fp t14805; +fp t15172; +fp t14326; +fp t14786; +fp t15171; +fp t14756; +fp t14775; +fp t15170; +fp t13343; +fp t15169; +fp t14760; +fp t14766; +fp t15168; +fp t13262; +fp t15167; +fp t14690; +fp t15166; +fp t14754; +fp t14685; +fp t15165; +fp t15164; +fp t15163; +fp t14798; +fp t15162; +fp t15161; +fp t14003; +fp t15160; +fp t14821; +fp t15159; +fp t15158; +fp t15157; +fp t14703; +fp t15156; +fp t14264; +fp t15155; +fp t14666; +fp t15154; +fp t15153; +fp t15152; +fp t14729; +fp t14824; +fp t15151; +fp t15150; +fp t13865; +fp t13846; +fp t14736; +fp t15149; +fp t14126; +fp t15148; +fp t14267; +fp t15020; +fp t14774; +fp t14979; +fp t15147; +fp t15146; +fp t15145; +fp t15144; +fp t15143; +fp t15142; +fp t15141; +fp t14818; +fp t14084; +fp t14065; +fp t15140; +fp t15139; +fp t14407; +fp t14403; +fp t14714; +fp t15138; +fp t15137; +fp t15136; +fp t14701; +fp t15135; +fp t15134; +fp t15133; +fp t15132; +fp t15131; +fp t15130; +fp t15129; +fp t15128; +fp t15127; +fp t14636; +fp t15126; +fp t15125; +fp t14132; +fp t14777; +fp t14270; +fp t14287; +fp t14271; +fp t15124; +fp t14710; +fp t15123; +fp t15122; +fp t15121; +fp t14664; +fp t14705; +fp t15120; +fp t15119; +fp t15022; +fp t15118; +fp t14066; +fp t14972; +fp t15117; +fp t14839; +fp t15116; +fp t14182; +fp t14938; +fp t15115; +fp t15114; +fp t15113; +fp t14846; +fp t14724; +fp t15112; +fp t14131; +fp t15111; +fp t15110; +fp t14189; +fp t15109; +fp t15108; +fp t15107; +fp t14325; +fp t15106; +fp t15105; +fp t15104; +fp t14859; +fp t15103; +fp t14067; +fp t15102; +fp t15029; +fp t15101; +fp t14478; +fp t15100; +fp t15099; +fp t15098; +fp t15097; +fp t14176; +fp t15096; +fp t14761; +fp t15095; +fp t14952; +fp t14236; +fp t14739; +fp t15094; +fp t14676; +fp t15093; +fp t14992; +fp t15092; +fp t14106; +fp t15091; +fp t14304; +fp t15090; +fp t15089; +fp t15088; +fp t14694; +fp t15087; +fp t14890; +fp t14114; +fp t15086; +fp t15085; +fp t15084; +fp t15083; +fp t15082; +fp t13101; +fp t14643; +fp t15081; +fp t14631; +fp t15080; +fp t15079; +fp t13276; +fp t14847; +fp t15078; +fp t15077; +fp t13309; +fp t14944; +fp t15076; +fp t14953; +fp t15075; +fp t15074; +fp t15073; +fp t15072; +fp t15071; +fp t15070; +fp t15069; +fp t15068; +fp t15067; +fp t15066; +fp t15065; +fp t15064; +fp t15063; +fp t15062; +fp t15061; +fp t15060; +fp t15059; +fp t15058; +fp t15057; +fp t15056; +fp t15055; +fp t15054; +fp t15053; +fp t15052; +fp t15051; +fp t15050; +fp t15049; +fp t15048; +fp t15047; +fp t15046; +fp t15045; +fp t15044; +fp t15043; +fp t15042; +fp t15041; +fp t15040; +fp t14819; +fp t15039; +fp t15038; +fp t15037; +fp t15036; +fp t15035; +fp t15034; +fp t15033; +fp t14975; +fp t14970; +fp t14958; +fp t14955; +fp t14373; +fp t14926; +fp t14920; +fp t14889; +fp t14865; +fp t14864; +fp t14843; +fp t14835; +fp t14283; +fp t14825; +fp t14820; +fp t14810; +fp t14746; +fp t14699; +fp t14653; +fp t14642; +fp t14641; +fp t14635; +fp t14629; +fp t14628; +fp t14627; +fp t14626; +fp t14625; +fp t14456; +fp t14416; +fp t14501; +fp t14624; +fp t14623; +fp t14447; +fp t14448; +fp t14503; +fp t14622; +fp t14621; +fp t14436; +fp t14620; +fp t14517; +fp t14619; +fp t14422; +fp t14618; +fp t14617; +fp t14616; +fp t14614; +fp t14613; +fp t14610; +fp t14609; +fp t14607; +fp t14606; +fp t14604; +fp t14603; +fp t14599; +fp t14598; +fp t14400; +fp t14597; +fp t14596; +fp t14418; +fp t14595; +fp t14594; +fp t14593; +fp t14592; +fp t14591; +fp t14590; +fp t14589; +fp t14588; +fp t14587; +fp t14586; +fp t14585; +fp t14584; +fp t14432; +fp t14583; +fp t14582; +fp t14581; +fp t14580; +fp t14579; +fp t14578; +fp t14577; +fp t14576; +fp t14575; +fp t14574; +fp t14573; +fp t14572; +fp t14571; +fp t14570; +fp t14569; +fp t14568; +fp t14567; +fp t14566; +fp t14565; +fp t14564; +fp t14563; +fp t14562; +fp t14561; +fp t14560; +fp t14559; +fp t14558; +fp t14557; +fp t14556; +fp t14555; +fp t14554; +fp t14553; +fp t14552; +fp t14551; +fp t14550; +fp t14549; +fp t14548; +fp t14547; +fp t14546; +fp t14545; +fp t14544; +fp t14543; +fp t14542; +fp t14541; +fp t14540; +fp t14539; +fp t14538; +fp t14537; +fp t14536; +fp t14535; +fp t14534; +fp t14514; +fp t14504; +fp t14502; +fp t14497; +fp t14495; +fp t14476; +fp t14472; +fp t14464; +fp t14463; +fp t14451; +fp t14450; +fp t14419; +fp t14415; + t14452 = RATIONAL(-8.0,27.0); + t14523 = y*y; + t14525 = t14523*y; + t14424 = RATIONAL(16.0,27.0); + t15465 = t14452*t14525+y*t14424; + t14469 = RATIONAL(2.0,27.0); + t14913 = t14525*t14469; + t14462 = RATIONAL(-1.0,54.0); + t14522 = z*z; + t14526 = t14522*z; + t14949 = t14462*t14526; + t15464 = z*t14913+t14525*t14949; + t14521 = x*x; + t14528 = t14521*t14521; + t15028 = z*t14528; + t14410 = RATIONAL(1.0,432.0); + t14054 = t14410*t15028; + t14411 = RATIONAL(-1.0,432.0); + t15017 = z*t14411; + t14029 = t14521*t15017; + t15463 = t14054+t14029; + t14396 = RATIONAL(1.0,1728.0); + t14870 = t14526*t14396; + t13886 = t14528*t14870; + t14399 = RATIONAL(-1.0,1728.0); + t14882 = t14526*t14399; + t15462 = t13886+t14521*t14882; + t14460 = RATIONAL(8.0,27.0); + t15018 = x*t14460; + t14449 = RATIONAL(1.0,54.0); + t14524 = x*t14521; + t14907 = t14449*t14524; + t14527 = t14522*t14522; + t14187 = t14527*t14907; + t15461 = t14187+t14522*t15018; + t15006 = x*t14469; + t14204 = t14526*t15006; + t14915 = t14469*t14524; + t14222 = z*t14915; + t15460 = t14204+t14222; + t14916 = t14526*t14449; + t14712 = t14525*t14916; + t14466 = RATIONAL(-2.0,27.0); + t14997 = z*t14466; + t14784 = t14525*t14997; + t15459 = t14712+t14784; + t14901 = t14527*t14521; + t14848 = t14528*t14522; + t15429 = t14848+t14901; + t14911 = t14410*t14521; + t13963 = z*t14911; + t15458 = t14528*t15017+t13963; + t15012 = x*t14526; + t14090 = t14466*t15012; + t15457 = t14090+z*t15018; + t14420 = RATIONAL(1.0,108.0); + t14929 = t14420*t14524; + t13920 = t14527*t14929; + t14459 = RATIONAL(-1.0,27.0); + t14914 = t14459*t14524; + t15456 = t14522*t14914+t13920; + t14899 = t14523*t14521; + t14937 = t14528*t14523; + t14454 = RATIONAL(-1.0,18.0); + t14519 = RATIONAL(2.0,9.0); + t15455 = t14519*t14899+t14454*t14937; + t14873 = t14528*t14399; + t13853 = t14526*t14873; + t15454 = t13853+t14521*t14870; + t14646 = t14521*t14913; + t14457 = RATIONAL(1.0,27.0); + t14989 = y*t14528; + t14790 = t14457*t14989; + t15453 = t14790+t14646; + t14723 = t14527*t14899; + t14749 = t14523*t14848; + t15452 = t14749+t14723; + t14983 = y*t15012; + t15004 = z*t14524; + t14984 = y*t15004; + t15451 = t14984+t14983; + t14947 = t14524*t14527; + t15450 = t14522*t14915+t14462*t14947; + t14467 = RATIONAL(-4.0,27.0); + t15010 = y*t14527; + t15449 = t14467*t15010+t15465*t14522; + t14458 = RATIONAL(4.0,27.0); + t15032 = y*x; + t14408 = RATIONAL(-16.0,27.0); + t14878 = t14466*t14524; + t15008 = y*t14524; + t15448 = t14525*t14878+t14408*t15032+t14458*t15008; + t14515 = RATIONAL(-4.0,9.0); + t14507 = RATIONAL(1.0,3.0); + t15447 = t14523*t14507+t14515; + t14446 = RATIONAL(-1.0,72.0); + t14928 = t14525*t14446; + t14439 = RATIONAL(1.0,144.0); + t15446 = y*t14439+t14928; + t14442 = RATIONAL(5.0,576.0); + t14441 = RATIONAL(-5.0,576.0); + t15025 = z*t14521; + t14918 = t14526*t14521; + t15445 = t14441*t14918+t14442*t15025; + t14888 = t14523*t14522; + t14426 = RATIONAL(5.0,192.0); + t14665 = t14426*t14888; + t14423 = RATIONAL(-1.0,192.0); + t14932 = t14523*t14527; + t15444 = t14423*t14932+t14665; + t14437 = RATIONAL(-1.0,288.0); + t14345 = t14437*t14527; + t14010 = t14524*t14345; + t15443 = t14010+t14446*t14524; + t14499 = RATIONAL(-1.0,9.0); + t14382 = t14499*t14524; + t14520 = RATIONAL(4.0,9.0); + t14845 = t14525*t14520; + t15442 = x*t14845+t14525*t14382; + t14425 = RATIONAL(-1.0,216.0); + t14857 = t14425*t14526; + t13923 = t14528*t14857; + t14891 = t14528*t14449; + t14136 = z*t14891; + t15441 = t13923+t14136; + t14097 = t14446*t14848; + t15440 = t14454*t14522+t14097; + t14461 = RATIONAL(-1.0,12.0); + t14096 = t14461*t14937; + t14500 = RATIONAL(1.0,9.0); + t15439 = t14096+t14500*t14528; + t14351 = t14446*t14527; + t14147 = x*t14351; + t15438 = t14147+t14454*x; + t14509 = RATIONAL(-1.0,3.0); + t15437 = t14520+t14523*t14509; + t14440 = RATIONAL(-1.0,144.0); + t14493 = RATIONAL(1.0,72.0); + t15436 = y*t14440+t14525*t14493; + t14936 = t14522*t14524; + t15435 = t14396*t14947+t14399*t14936; + t14924 = t14410*t14527; + t14954 = t14522*t14411; + t14031 = x*t14954; + t15434 = x*t14924+t14031; + t14360 = t14493*t14524; + t14435 = RATIONAL(1.0,288.0); + t14333 = t14435*t14527; + t13959 = t14524*t14333; + t15433 = t14360+t13959; + t14474 = RATIONAL(1.0,48.0); + t15432 = t14440+t14523*t14474; + t14455 = RATIONAL(-1.0,36.0); + t14389 = t14499*t14526; + t14883 = t14528*t14526; + t15431 = t14389+t14455*t14883; + t14964 = t14410*t14522; + t15015 = x*t14527; + t15430 = x*t14964+t14411*t15015; + t14421 = RATIONAL(-1.0,108.0); + t14930 = t14525*t14421; + t14688 = t14526*t14930; + t14990 = z*t14420; + t14782 = t14525*t14990; + t15428 = t14782+t14688; + t14412 = RATIONAL(1.0,864.0); + t14876 = t14412*t14528; + t14445 = RATIONAL(-1.0,864.0); + t15427 = z*t14876+t14445*t14883; + t13895 = t14396*t14936; + t15426 = t13895+t14399*t14947; + t13988 = t14526*t14876; + t15425 = t14445*t15028+t13988; + t14923 = t14522*t14441; + t14902 = t14442*t14522; + t15424 = t14524*t14923+x*t14902; + t15423 = t14462*t14883+t14469*t14918; + t14363 = t14446*t14528; + t15422 = (t14363+t14454)*z; + t14468 = RATIONAL(5.0,96.0); + t14481 = RATIONAL(-1.0,24.0); + t14963 = t14523*t14481; + t15421 = t14963+t14468*t14899; + t13986 = t14412*t14947; + t15420 = t13986+t14445*t15015; + t14854 = t14525*t14515; + t14922 = t14525*t14500; + t15419 = x*t14854+t14524*t14922; + t15418 = (t14454+t14351)*t14521; + t14477 = RATIONAL(-1.0,48.0); + t14898 = t14477*t14527; + t14122 = t14523*t14898; + t14485 = RATIONAL(1.0,36.0); + t14355 = t14485*t14527; + t15417 = t14355+t14122; + t14453 = RATIONAL(1.0,12.0); + t15416 = t14499*t14528+t14453*t14937; + t15415 = x*t14923+t14524*t14902; + t13922 = t14435*t14883; + t14350 = t14493*t14526; + t15414 = t13922+t14350; + t13919 = t14437*t14883; + t15413 = t14446*t14526+t13919; + t14394 = RATIONAL(-1.0,1152.0); + t14406 = RATIONAL(1.0,1152.0); + t14645 = t14406*t14937; + t15412 = t14394*t14899+t14645; + t14855 = t14466*t14521; + t15411 = t14526*t14855+t14449*t14883; + t14863 = t14445*t14524; + t13904 = t14527*t14863; + t15410 = t14412*t15015+t13904; + t15409 = t14485*t14883+t14500*t14526; + t15408 = t14442*t14918+t14441*t15025; + t14342 = t14439*t14526; + t14443 = RATIONAL(-1.0,576.0); + t15013 = z*t14443; + t14444 = RATIONAL(1.0,576.0); + t15407 = t14444*t14883+t14528*t15013+t14342; + t14919 = t14444*t14527; + t13984 = t14443*t15015; + t15406 = t13984+(t14439+t14919)*t14524; + t13917 = t14444*t15028; + t15405 = t14443*t14883+t13917+t14440*t14526; + t14880 = t14406*t14527; + t13857 = t14521*t14880; + t14340 = t14437*t14528; + t15404 = t14435*t14521+t13857+t14340; + t13949 = t14443*t14947; + t15403 = t13949+t14440*t14524+x*t14919; + t15402 = t14345+t14435*t14522+t14406*t14848; + t14868 = t14526*t14524; + t15024 = z*t14396; + t15401 = t14396*t14868+t14399*t15004+(t15024+t14882)*x; + t14397 = RATIONAL(1.0,3456.0); + t14398 = RATIONAL(-1.0,3456.0); + t15026 = x*t14522; + t14896 = t14397*t14524; + t15400 = t14527*t14896+t14397*t15026+(t15015+t14936)*t14398; + t14402 = RATIONAL(-1.0,6912.0); + t14395 = RATIONAL(1.0,6912.0); + t14973 = t14522*t14521; + t14841 = t14395*t14527; + t14910 = t14528*t14527; + t15399 = t14395*t14848+t14521*t14841+(t14910+t14973)*t14402; + t15398 = t14397*t15015+t14522*t14896+(t15026+t14947)*t14398; + t14912 = t14398*t14521; + t15005 = z*t14397; + t15397 = t14398*t15028+t14397*t14883+t14521*t15005+t14526*t14912; + t15396 = t14528*t15005+z*t14912+t14398*t14883+t14397*t14918; + t15030 = x*z; + t15395 = x*t14870+t14396*t15004+(t14868+t15030)*t14399; + t14388 = t14500*t14527; + t14070 = t14461*t14932; + t15394 = t14388+t14070; + t14934 = t14525*t14521; + t15393 = t14435*t14934+t14442*t14989; + t15392 = (t14500+t14355)*t14524; + t15001 = z*t14457; + t14192 = x*t15001; + t14655 = t14440*t14868; + t15391 = t14192+t14523*t14655; + t14931 = t14523*t14524; + t14797 = z*t14931; + t15002 = x*t14421; + t13976 = t14526*t15002; + t15390 = t13976+t14485*t14797; + t13952 = t14420*t14883; + t14102 = t14521*t15001; + t14667 = t14440*t14937; + t14948 = t14528*t14421; + t14008 = z*t14948; + t14697 = t14485*t14899; + t15260 = t14102+t14008+(t14697+t14667)*t14526; + t14652 = t14439*t14937; + t13048 = z*t14652; + t14877 = t14523*t14455; + t14809 = z*t14877; + t15389 = t13048+t14521*t14809+t13952+t14459*t14918+t15260; + t14038 = t14420*t14868; + t15388 = x*t14809+t14038; + t15021 = x*t14459; + t14157 = z*t15021; + t14747 = t14523*t14342; + t15387 = t14524*t14747+t14157; + t14967 = t14525*t14485; + t14957 = t14525*t14499; + t15386 = t14526*t14967+z*t14957; + t14240 = t14453*t14932; + t15385 = t14240+t14499*t14527; + t15384 = t14461+t14898; + t14904 = t14455*t14524; + t14117 = t14527*t14904; + t15383 = t14117+t14382; + t14414 = RATIONAL(5.0,288.0); + t14792 = t14414*t14989; + t14858 = t14440*t14527; + t13910 = t14528*t14858; + t14465 = RATIONAL(5.0,72.0); + t14925 = t14465*t14521; + t14059 = t14522*t14925; + t14900 = y*t14059+t14525*t13910; + t14354 = t14455*t14522; + t14748 = t14525*t14354; + t15382 = t14900+t14527*t14792+t14521*t14748; + t13931 = z*t14929; + t14691 = t14526*t14877; + t15381 = x*t14691+t13931; + t13902 = t14399*t14901; + t14409 = RATIONAL(1.0,216.0); + t13975 = t14409*t14848; + t15380 = y*t13902+t14525*t13975; + t14041 = t14421*t14883; + t13129 = z*t14667; + t14057 = t14528*t14990; + t14962 = t14459*t14521; + t14232 = z*t14962; + t15217 = t14057+t14521*t14691+t14526*t14652+t14232; + t15379 = t14041+t14457*t14918+z*t14697+t15217+t13129; + t14020 = t14420*t15012; + t15378 = t14455*t14797+t14020; + t14498 = RATIONAL(1.0,6.0); + t14484 = RATIONAL(-5.0,24.0); + t15377 = t14484*t14522+t14498; + t14037 = t14412*t14868; + t15019 = z*t14523; + t14802 = t14446*t15019; + t15376 = t14037+x*t14802; + t14513 = RATIONAL(5.0,6.0); + t14516 = RATIONAL(-2.0,3.0); + t15375 = t14513*t14521+t14516; + t14052 = z*t14863; + t14966 = t14523*t14526; + t14791 = x*t14966; + t15374 = t14493*t14791+t14052; + t14367 = t14493*t14527; + t14243 = y*t14367; + t14413 = RATIONAL(-5.0,144.0); + t14842 = t14413*t14521; + t13993 = t14522*t14842; + t15373 = t14900+t14528*t14243+t14525*t13993; + t14960 = t14477*t14523; + t14668 = t14423*t14937; + t15372 = t14668+t14426*t14899+t14960; + t14996 = z*t14409; + t13916 = t14524*t14996; + t14759 = t14437*t14966; + t15318 = t13916+x*t14759; + t13990 = t14412*t15012; + t15371 = t15318+t14446*t14797+t13990; + t14998 = x*t14523; + t14778 = t14437*t14998; + t14940 = t14425*t14524; + t13925 = z*t14940; + t14941 = t14523*t14435; + t14745 = t14526*t14941; + t15306 = t13925+x*t14745; + t15370 = t14409*t14868+z*t14778+t15306; + t14105 = t14462*t14848; + t13998 = t14420*t14901; + t15289 = t14525*t14105+y*t13998; + t14647 = t14425*t14934; + t15369 = t14522*t14790+t15289+t14527*t14647; + t14016 = t14411*t14910; + t15368 = t14522*t14646+y*t14016+t15289; + t14906 = t14525*t14459; + t14789 = z*t14906; + t14210 = t14462*t14868; + t14718 = t14525*t14868; + t14851 = t14457*t14525; + t14769 = x*t14851; + t15220 = t14420*t14718+z*t14769+y*t14210+t14997*t15032; + t15367 = t14524*t14789+y*t14222+t14916*t15032+t15220; + t15366 = t15374+t15376; + t13908 = t14445*t15012; + t14862 = t14523*t14493; + t14757 = t14524*t14862; + t13855 = t14396*t14910; + t15309 = t14522*t14647+y*t13855; + t14043 = x*t14996; + t15302 = t14524*t14759+t14043; + t14036 = t14522*t14911; + t13933 = t14445*t14910; + t15291 = t14525*t13933+y*t14036; + t14601 = t15291+t15302+t15309+t15376; + t15365 = t13908+z*t14757+t14601+t15306; + t13974 = t14420*t14918; + t14368 = t14455*t14528; + t14804 = z*t14368; + t14892 = t14462*t14521; + t14225 = t14527*t14892; + t14024 = t14420*t14848; + t15311 = y*t14024+t14525*t14225; + t13926 = t14409*t14910; + t14170 = t14522*t14962; + t15299 = y*t14170+t14525*t13926; + t15252 = t15299+t15311; + t14738 = t14500*t14899; + t15364 = t15217+t15252+t13974+t14523*t14804+z*t14738; + t14875 = t14457*t14524; + t14681 = t14485*t14888; + t14946 = t14421*t14527; + t14053 = t14524*t14946; + t13983 = t14420*t15015; + t14704 = t14439*t14932; + t14720 = t14522*t14877; + t14145 = t14522*t15021; + t15277 = t13983+t14145+(t14720+t14704)*t14524; + t15363 = t14522*t14875+x*t14681+t14053+t15277; + t14015 = x*t14946; + t14943 = t14457*t14522; + t14206 = x*t14943; + t14709 = t14523*t14858; + t15250 = t14015+t14206+(t14709+t14681)*t14524; + t15362 = t15250+x*t14720+t15456; + t14837 = z*t14899; + t15361 = t14439*t14837+t13129+t15454; + t14971 = t14525*t14526; + t14822 = x*t14971; + t14887 = t14525*t14411; + t14708 = t14526*t14887; + t14828 = z*t14930; + t15243 = x*t14828+t14524*t14708+(t14037+t14043)*y; + t15360 = t14410*t14822+t15243+(t13908+t13925)*y; + t14093 = t14449*t14868; + t15003 = z*t14469; + t15235 = x*t14789+t15003*t15032+t14524*t14688+y*t14093; + t14119 = z*t14878; + t14727 = t14524*t14851; + t15359 = z*t14727+t15235+y*t14119+t14949*t15032; + t14730 = t14524*t14888; + t13978 = t14409*t15026; + t14807 = x*t14932; + t15358 = t14493*t14730+t14435*t14807+t13978+t15420; + t14781 = t14485*t14998; + t13909 = t14421*t14868; + t15213 = z*t14781+t13909+t15387; + t15357 = t14440*t14791+z*t14875+t15213+t15378; + t14056 = t14411*t14868; + t14945 = t14525*t14524; + t14743 = t14462*t14945; + t15356 = z*t14743+(t14056+t14157)*y+t15464*x; + t14866 = t14425*t14522; + t13991 = x*t14866; + t15355 = t14446*t14730+t13991+t14527*t14778+t15410; + t13970 = t14410*t14868; + t14806 = z*t14907; + t15354 = t14525*t14806+(t14192+t13970)*y+t15459*x; + t14092 = t14493*t14848; + t14908 = t14449*t14521; + t14230 = t14522*t14908; + t14677 = t14446*t14899; + t13930 = t14528*t14345; + t15272 = t13926+t14522*t14677+t14523*t13930+t14230; + t14773 = y*t14948; + t15214 = t14527*t14773+t14525*t14230+t15299; + t14605 = t15214+t15272; + t15353 = t14105+t14425*t14901+t14523*t14092+t14435*t14723+t14605; + t13905 = t14410*t14883; + t14005 = t14421*t14918; + t14353 = t14485*t14528; + t14795 = z*t14353; + t14827 = t14499*t15019; + t15352 = t15252+t15260+t13905+t14521*t14827+t14523*t14795+t14005; + t14814 = t14522*t15006; + t14042 = t14411*t14947; + t13979 = t14409*t14947; + t14921 = t14525*t14527; + t14780 = x*t14921; + t13972 = t14522*t14929; + t15225 = t14525*t13979+t14462*t14780+(t14145+t13972)*y; + t15351 = t15225+t14522*t14743+t14525*t14814+(t13983+t14042)*y; + t14044 = t14421*t15004; + t13239 = t14525*t14044; + t15000 = x*t14425; + t14007 = z*t15000; + t14011 = t14526*t14863; + t14706 = t14410*t14945; + t15273 = t14526*t14706+x*t14782+(t14011+t14007)*y; + t15350 = t15273+t13239+x*t14708+(t13990+t13916)*y; + t14707 = t14525*t14918; + t15254 = t15441*t14525+(t14102+t14005)*y; + t15349 = y*t13905+t14521*t14784+t14449*t14707+z*t14773+t15254; + t14872 = t14523*t14444; + t14680 = t14527*t14872; + t14740 = t14523*t14910; + t14871 = t14440*t14522; + t14649 = t14523*t14871; + t15227 = t14036+t13855+t14521*t14649+t14443*t14740; + t13927 = t14411*t14848; + t15348 = t13902+t15227+t14521*t14680+t13927+t14522*t14652; + t14986 = z*t14998; + t15347 = t14056+t14500*t14986+t15381+t15387+t15378; + t13950 = t14524*t14924; + t14009 = t14421*t14936; + t14657 = t14525*t14940; + t15248 = t14527*t14657+t14449*t14780+(t14206+t14009)*y; + t14869 = t14522*t14466; + t14831 = x*t14869; + t14763 = t14525*t14936; + t15346 = t15248+t14449*t14763+t14525*t14831+(t13950+t14015)*y; + t15345 = x*t14747+t15388+t15391+z*t14914+t15390; + t14755 = t14526*t14899; + t14717 = t14443*t14966; + t15251 = t14444*t14755+t14528*t14717+t15458; + t15344 = t14440*t14837+t15251+t13048+t15462; + t13937 = t14528*t14333; + t14909 = t14528*t14425; + t14673 = t14521*t14862; + t15241 = t14527*t14909+t14523*t13937+(t14673+t14892)*t14522; + t14608 = t15214+t15241; + t15343 = t14523*t14097+t14409*t14901+t14437*t14723+t14608+t14449*t14848; + t14654 = t14439*t14888; + t15226 = t14528*t14680+t14527*t14873+(t14954+t14654)*t14521; + t14682 = t14443*t14899; + t15342 = t14527*t14682+t14410*t14848+t14396*t14901+t15226+t14528*t14649; + t15231 = t14526*t14781+t14044+t15391; + t15341 = t13970+x*t14827+t15231+t15390; + t14035 = t14411*t14883; + t14905 = t14528*t14525; + t14751 = t14462*t14905; + t14045 = t14409*t14883; + t15265 = t14525*t14045+z*t14751+(t14232+t13974)*y; + t15340 = t14462*t14707+z*t14646+t15265+(t14035+t14057)*y; + t14249 = z*t14892; + t14032 = t14409*t14918; + t15287 = t14523*t13922+z*t14673+t14032; + t15339 = t14437*t14755+t14249+t15287+t14528*t14802+t15441; + t14776 = z*t14862; + t14221 = t14462*t15028; + t14191 = z*t14908; + t13946 = t14521*t14857; + t15284 = t14523*t13919+t13946+z*t14677; + t15338 = t14528*t14776+t14045+t14221+t14191+t14521*t14745+t15284; + t13934 = t14410*t14910; + t14700 = t14499*t14888; + t14689 = t14521*t14355; + t15337 = t14528*t14681+t14523*t14689+t13934+t14527*t14667+(t14700+t14943) +*t14521+t15429*t14421; + t14959 = t14525*t14425; + t14788 = z*t14959; + t14683 = t14409*t14934; + t15336 = t14445*t14707+t14525*t13988+t14528*t14788+z*t14683+(t15454+ +t15463)*y; + t15014 = x*t14462; + t14151 = t14527*t15014; + t14172 = t14524*t14869; + t15335 = t14420*t14780+t14522*t14727+(t14145+t14053)*t14525+(t14814+ +t14172+t14187+t14151)*y; + t14803 = y*t14936; + t14808 = y*t14947; + t15334 = t14469*t14780+t14467*t14803+t14457*t14808+t15450*t14525+t15449*x +; + t14838 = t14528*t14996; + t14897 = t14525*t14445; + t14735 = t14526*t14897; + t15333 = z*t14647+t14525*t14838+t14528*t14735+t14412*t14707+(t15458+ +t15462)*y; + t14999 = x*t14449; + t14229 = t14527*t14999; + t15332 = t14522*t14769+t14421*t14780+t15456*t14525+(t14831+t14229+t15450) +*y; + t14812 = y*t14868; + t15331 = t14458*t14983+t14459*t14812+t14524*t14712+t15457*t14525+t15448*z +; + t14977 = x*t15010; + t14799 = t14459*t15010; + t15330 = t14524*t14799+t14458*t14977+t14466*t14780+t15461*t14525+t15448* +t14522; + t14884 = t14469*t14527; + t14829 = x*t14888; + t14669 = t14454*t14936; + t14656 = t14527*t14862; + t15329 = t14454*t14807+t14524*t14656+t14523*t14669+t14452*t15026+t14519* +t14829+x*t14884+t15450; + t14662 = t14527*t14877; + t15328 = t14521*t14662+t14016+t14528*t14720+t13998+t14522*t14738+t14024+ +t14170+t14527*t14652; + t14505 = RATIONAL(-2.0,9.0); + t14771 = t14505*t15019; + t14933 = t14460*t14521; + t14216 = z*t14933; + t14486 = RATIONAL(1.0,18.0); + t14658 = t14486*t14918; + t14767 = t14486*t15019; + t14725 = t14523*t14883; + t15327 = t14446*t14725+t14521*t14771+t14216+t14523*t14658+t15411+(t14767+ +t14997)*t14528; + t14648 = t14505*t14888; + t15326 = t14446*t14740+t14466*t14848+t14521*t14648+t14522*t14933+(t14891+ +t14855)*t14527+t15452*t14486; + t14073 = t14524*t14351; + t15325 = x*t14648+t14523*t14073+t14466*t15015+t14172+(t14730+t14807)* +t14486+t15461; + t14356 = t14454*t14526; + t14698 = t14523*t14356; + t14956 = t14452*t14521; + t14152 = z*t14956; + t15324 = t14521*t14698+t14528*t15003+t14152+t14493*t14725+t15423+t15455*z +; + t14752 = t14525*t14848; + t14787 = t14467*t14989; + t15323 = t14522*t14787+t14469*t14752+t15449*t14521+(t14751+t15453)*t14527 +; + t15322 = t14457*t14812+t14462*t14718+t15460*t14525+t15465*t15030+t15451* +t14467; + t15016 = y*t14521; + t14976 = z*t15016; + t14813 = y*t14918; + t14981 = z*t14989; + t14794 = t14459*t14989; + t15321 = t14466*t14707+t14526*t14794+t14408*t14976+t14525*t14216+(t14813+ +t14981)*t14458+t15459*t14528; + t15320 = t14462*t14910+t14469*t14848+t14521*t14884+t14454*t14723+t14528* +t14656+(t14956+t15455)*t14522; + t15319 = z*t14787+t14525*t14152+t14424*t14976+t14467*t14813+t15453*t14526 ++t15464*t14528; + t13997 = x*t14857; + t14716 = t14435*t14931; + t15317 = t13997+z*t14716; + t14492 = RATIONAL(-5.0,72.0); + t14801 = t14492*t14989; + t13948 = t14439*t14921; + t15316 = t14521*t13948+t14522*t14801; + t14783 = t14454*t15010; + t14518 = RATIONAL(5.0,9.0); + t14968 = t14518*t14522; + t14256 = t14521*t14968; + t15315 = t14528*t14783+t14525*t14256; + t14826 = y*t14910; + t14431 = RATIONAL(-5.0,192.0); + t14765 = t14522*t14934; + t15314 = t14468*t14765+t14431*t14826; + t13929 = t14439*t14905; + t14768 = t14492*t15010; + t15313 = t14521*t14768+t14522*t13929; + t14475 = RATIONAL(5.0,48.0); + t14510 = RATIONAL(-5.0,6.0); + t15312 = t14510*t14765+t14475*t14826; + t14860 = t14412*t14521; + t13967 = t14527*t14860; + t15310 = y*t13927+t14525*t13967; + t14696 = t14525*t14355; + t14993 = y*RATIONAL(-10.0,9.0); + t14815 = t14521*t14993; + t15307 = t14522*t14815+t14528*t14696; + t14438 = RATIONAL(-5.0,288.0); + t13992 = t14438*t14848; + t15305 = t14525*t14689+y*t13992; + t13955 = t14445*t14973; + t15303 = y*t13934+t14525*t13955; + t13911 = t14438*t14901; + t15301 = y*t13911+t14485*t14752; + t15300 = t14007+t14526*t14716; + t13914 = t14412*t14848; + t14033 = t14411*t14901; + t15298 = y*t14033+t14525*t13914; + t14404 = RATIONAL(5.0,1152.0); + t13877 = t14404*t14901; + t14674 = t14443*t14848; + t15297 = t14525*t14674+y*t13877; + t14405 = RATIONAL(-5.0,1152.0); + t13872 = t14405*t14973; + t14762 = t14527*t14905; + t15296 = y*t13872+t14444*t14762; + t13953 = t14409*t15012; + t15295 = t14437*t14797+t13953; + t14417 = RATIONAL(25.0,12.0); + t14836 = y*t14973; + t15294 = t14417*t14836+t14481*t14762; + t13866 = t14404*t14848; + t14758 = t14525*t14901; + t15293 = y*t13866+t14443*t14758; + t14401 = RATIONAL(-25.0,192.0); + t14470 = RATIONAL(1.0,96.0); + t14894 = t14528*t14470; + t14670 = t14527*t14894; + t15292 = t14401*t14836+t14525*t14670; + t13899 = t14399*t14848; + t15290 = t14527*t14683+y*t13899; + t14281 = t14499*t14901; + t14494 = RATIONAL(5.0,18.0); + t14834 = y*t14848; + t15288 = t14525*t14281+t14494*t14834; + t13968 = t14524*t14866; + t15286 = t13968+t14446*t14829+t14523*t14010; + t14034 = t14409*t14936; + t15285 = t14523*t13959+t14034+t14493*t14829; + t15283 = t14526*t14657+(t13976+t14044)*y; + t15282 = t14409*t14718+(t14020+t13931)*y; + t15281 = x*t14654+t15426; + t14785 = t14523*t15013; + t15280 = t14528*t14785+t14444*t14837+t14526*t14911; + t14679 = t14522*t14872; + t15279 = t14410*t14936+x*t14679+t14523*t13984; + t14991 = x*t14525; + t14770 = t14435*t14991; + t14687 = t14525*t14345; + t15278 = t14527*t14770+t14524*t14687+t15424*y; + t14650 = t14493*t14905; + t14733 = t14446*t14905; + t14490 = RATIONAL(-5.0,36.0); + t14886 = t14490*t14521; + t14480 = RATIONAL(5.0,36.0); + t14082 = t14480*t14918; + t15031 = y*z; + t15275 = y*t14082+t14886*t15031+z*t14733+t14526*t14650; + t14491 = RATIONAL(-5.0,18.0); + t14489 = RATIONAL(10.0,9.0); + t14988 = t14489*t15032; + t14262 = t14525*t14388; + t15274 = x*t14262+t14525*t14117+t14491*t14803+t14522*t14988; + t13889 = t14394*t14910; + t14428 = RATIONAL(5.0,384.0); + t14692 = t14428*t14899; + t14430 = RATIONAL(1.0,384.0); + t14715 = t14430*t14937; + t15271 = t13889+t13872+t14527*t14715+t14522*t14692; + t14980 = t14480*t15031; + t14644 = t14446*t14868; + t14429 = RATIONAL(5.0,144.0); + t14850 = t14525*t14454; + t14238 = z*t14850; + t15270 = t14525*t14644+t14429*t14812+(t14238+t14980)*x; + t15269 = t15291+t15298; + t14433 = RATIONAL(1.0,192.0); + t14849 = t14523*t14433; + t14737 = t14527*t14849; + t15268 = t13910+t14528*t14737+t14521*t14665+t13993; + t13973 = t14521*t14996; + t14659 = t14528*t14887; + t15267 = t14525*t14054+t14526*t14659+(t13946+t13973)*y; + t14793 = z*t14340; + t14672 = t14435*t14905; + t15266 = t14525*t14793+t14526*t14672+t15408*y; + t14741 = t14521*t14888; + t15264 = t14431*t14741+t14429*t14973+t14439*t14910+t14527*t14668; + t14482 = RATIONAL(-5.0,12.0); + t14661 = t14482*t14899; + t15263 = t14522*t14661+t14256+t15417*t14528; + t14950 = t14525*t14486; + t14246 = z*t14950; + t14811 = t14413*t15008; + t14978 = t14490*t15032; + t15262 = t14493*t14718+z*t14978+x*t14246+t14526*t14811; + t14874 = t14480*t14522; + t14110 = t14524*t14874; + t14927 = t14490*t14522; + t14651 = t14493*t14921; + t15261 = y*t14110+t14927*t15032+t14524*t14651+t14446*t14780; + t14987 = x*t14993; + t15259 = t14494*t14803+t14499*t14780+t14522*t14987+t14524*t14696; + t15258 = x*t14776+t14011+t15300; + t14137 = t14465*t15026; + t14935 = t14525*t14440; + t14744 = t14524*t14935; + t14885 = t14438*t14522; + t13945 = t14524*t14885; + t15257 = x*t14696+t14527*t14744+(t14137+t13945)*y; + t15256 = t14525*t14042+t14410*t14780+(t13978+t13968)*y; + t14483 = RATIONAL(1.0,24.0); + t14903 = t14483*t14527; + t14471 = RATIONAL(-5.0,96.0); + t14844 = t14475*t14522; + t15255 = t14471*t14758+y*t14844+t14426*t14834+t14525*t14903; + t13999 = t14425*t15025; + t15253 = t14525*t13905+z*t14659+(t14032+t13999)*y; + t14512 = RATIONAL(-5.0,9.0); + t14939 = t14512*t14521; + t14861 = t14474*t14527; + t14174 = t14523*t14861; + t14479 = RATIONAL(5.0,12.0); + t14695 = t14479*t14899; + t15249 = t14528*t14174+t14455*t14910+(t14939+t14695)*t14522; + t14000 = t14412*t15004; + t15247 = t14000+t14446*t14791+t15295; + t15246 = z*t14672+t14525*t13919+t15445*y; + t15245 = x*t14687+t14525*t13959+t15415*y; + t14893 = t14490*t14524; + t14211 = t14522*t14893; + t15244 = y*t14211+x*t14651+t14874*t15032+t14525*t14073; + t15242 = t14523*t13949+t14524*t14679+t15430; + t14427 = RATIONAL(-1.0,384.0); + t14702 = t14427*t14932; + t14434 = RATIONAL(-5.0,384.0); + t15240 = t14404*t14973+t14434*t14741+(t14702+t14880)*t14528; + t15239 = t15290+t15309; + t14244 = t14526*t14886; + t15238 = y*t14244+t14526*t14733+z*t14650+t14480*t14976; + t14711 = t14522*t14845; + t15237 = t14528*t14768+t14521*t14711+t15288; + t15236 = t15290+t15298; + t15234 = t14411*t14780+t14527*t14706+(t14034+t13991)*y; + t14879 = t14526*t14414; + t13913 = t14521*t14879; + t14113 = t14455*t14905; + t14942 = t14492*t14521; + t14133 = z*t14942; + t15233 = t14526*t13929+z*t14113+(t14133+t13913)*y; + t15232 = t14526*t14682+t14444*t14725+t15463; + t14488 = RATIONAL(5.0,24.0); + t14496 = RATIONAL(-1.0,6.0); + t14852 = t14496*t14528; + t14840 = y*t14901; + t14506 = RATIONAL(-5.0,3.0); + t15011 = y*t14506; + t15230 = t14525*t14852+t14482*t14840+t14521*t15011+t14488*t14752; + t14719 = t14437*t14888; + t15229 = t14527*t14677+t14449*t14901+t14528*t14719+t13975; + t14047 = t14425*t14848; + t14830 = t14457*t15010; + t15228 = t14525*t14047+t14521*t14830+t15311; + t15224 = t14225+t14521*t14656+t14047+t14435*t14749; + t14663 = t14429*t14934; + t14185 = t14455*t14921; + t15222 = t14527*t14663+t14185+t15440*y; + t14856 = t14522*t14414; + t13996 = t14524*t14856; + t14223 = t14492*t15026; + t15221 = x*t14185+t14524*t13948+(t13996+t14223)*y; + t13918 = t14429*t14848; + t15219 = t14113+t14525*t13918+t15418*y; + t15218 = t15302+t15317; + t14722 = t14443*t14931; + t15216 = t14522*t14722+t14524*t14680+t15434; + t14881 = t14438*t14526; + t14048 = t14521*t14881; + t14212 = z*t14925; + t14684 = t14526*t14935; + t15215 = t14525*t14795+t14528*t14684+(t14212+t14048)*y; + t15212 = t14525*t13963+t14411*t14707+(t13923+t14838)*y; + t15211 = t15303+t15310; + t15210 = t15428*t14521+t15427*y; + t13957 = t14527*t14940; + t15209 = t14524*t14719+t14523*t14147+t14522*t15014+t13957+t14229; + t15208 = t15293+t15296+t14405*t14826+t14444*t14765+t15297; + t15207 = t15301+t15316+t15382; + t14796 = x*t14959; + t14779 = t14409*t14991; + t15206 = t15002*t15031+y*t13909+t14526*t14796+(t14779+t14657)*z; + t14140 = t14522*t14999; + t14671 = t14435*t14936; + t15205 = t13979+t14140+x*t14656+t14523*t14671+t14151; + t15204 = x*t14788+y*t14038+t14990*t15032+t14526*t14779+t14525*t13916; + t15203 = t15313+t15305+t15382; + t14731 = t14471*t14899; + t14364 = t14493*t14528; + t15202 = t14470*t14725+t14526*t14731+t14483*t14966+t14133+(t14486+t14364) +*z; + t14160 = t14470*t14932; + t15201 = t14471*t14730+t14524*t14160+t14483*t14931+t14223+(t14486+t14367) +*x; + t15200 = t15258+t15309; + t14473 = RATIONAL(-1.0,96.0); + t14118 = t14473*t14932; + t15199 = t14481*t14931+t14468*t14730+t14524*t14118+t14137+t15438; + t15198 = t14212+t14473*t14725+t15421*t14526+t15422; + t15197 = t15216+t15279; + t15196 = t15232+t15280; + t15195 = z*t14706+t15243+(t14052+t13997)*y; + t15194 = x*t14649+t15242+t15435; + t15193 = t14887*t15004+t15273+(t14000+t13953)*y; + t14224 = t14522*t14967; + t14995 = y*t14486; + t14199 = t14527*t14995; + t15192 = t15222+t14224+t14199+t15313+t15373; + t14171 = t14486*t14989; + t14068 = t14485*t14934; + t15191 = t14171+t15219+t14068+t15316+t15373; + t13938 = t14411*t14936; + t15190 = t13938+x*t14680+t14443*t14829+t15242; + t15188 = t15216+t15281; + t15186 = t14526*t14769+t14462*t14984+t15214+t15235+y*t14090+t15228; + t14764 = t14524*t14872; + t15185 = x*t14785+t14524*t14717+z*t14764+t14444*t14791+t15401; + t14675 = t14521*t14851; + t15184 = t14469*t14976+t14525*t14232+t14526*t14675+t15428*t14528+(t14221+ +t15411)*y; + t14195 = t14526*t14950; + t14186 = t14493*t14945; + t15183 = t15270+t14526*t14978+x*t14195+(t14811+t14186)*z; + t14165 = t14524*t14928; + t14226 = t14526*t14850; + t15182 = x*t14226+z*t14165+t14480*t14983+t14429*t14984+t15262; + t14994 = y*t14505; + t14261 = t14527*t14994; + t14074 = t14527*t14886; + t14508 = RATIONAL(8.0,9.0); + t15023 = y*t14508; + t14259 = t14522*t14854; + t15181 = t14261+t14525*t14074+t14522*t15023+t14519*t14834+t14262+t14259+ +t15315; + t14678 = t14522*t14950; + t14969 = t14525*t14522; + t14833 = x*t14969; + t15180 = t14454*t14833+t14524*t14678+t14413*t14977+t14429*t14808+t15244; + t15179 = t14872*t15030+x*t14717+t14526*t14764+z*t14722+t15395; + t14742 = t14439*t14945; + t15178 = t15257+t14522*t14742+t14414*t14808+(t14748+t14768)*x; + t14772 = t14409*t15015; + t14750 = t14412*t14945; + t15177 = (t14796+t14750)*t14522+(t13904+t14772)*t14525+(t15430+t15435)*y; + t15176 = t14521*t14828+t14420*t14707+t15267+t15425*y; + t14101 = t14524*t14850; + t14134 = t14526*t14928; + t15175 = t14429*t14983+z*t14101+t14524*t14980+x*t14134+t15262; + t15174 = t15247+t15258; + t15173 = t14525*t14140+x*t14830+y*t14053+t14522*t14657+t15225; + t14336 = t14439*z; + t14982 = t14414*t15031; + t14805 = y*t14879; + t15172 = t14524*t14982+z*t14744+t14439*t14718+t14991*t14336+(y*t15030+ +t14812)*t14438+(t14805+t14684)*x; + t14326 = t14522*t14922; + t14786 = t14465*t15008; + t15171 = t14527*t14786+t14491*t14977+t14524*t14326+x*t14259+t15274; + t14756 = t14525*t14863; + t14775 = t14527*t15000; + t15170 = (t14779+t14756)*t14522+(t13986+t14775)*t14525+(t15426+t15434)*y; + t13343 = x*t14704; + t15169 = t13343+t15194; + t14760 = t14437*t14969; + t14766 = t14442*t15010; + t15168 = x*t14760+t14441*t14977+t14524*t14766+t14525*t14671+t15278; + t13262 = x*t14688; + t15167 = t13262+t15193; + t14690 = t14525*t14964; + t15166 = t15256+t14524*t14690+t14525*t14031+(t13979+t14775)*y; + t14754 = t14523*t14880; + t14685 = t14394*t14931; + t15165 = t14527*t14685+t14394*t14829+x*t14754+t14406*t14730+t15400; + t15164 = t14243+t14326+t15222+t15301; + t15163 = t14528*t14679+t13899+t14033+t14521*t14704+t15227; + t14798 = t14412*t14991; + t15162 = t14445*t14718+t14526*t14798+t14897*t15030+z*t14750+t15401*y; + t15161 = t14439*t14797+t14459*t15012+t15231+t15388; + t14003 = t14521*t14858; + t15160 = t15226+t14410*t14901+t14396*t14848+(t14003+t14674)*t14523; + t14821 = z*t14941; + t15159 = t14524*t14857+x*t14821+t15295+t15300+t15318; + t15158 = t14440*t14797+t14457*t15012+t15213+t15381; + t15157 = t14526*t14673+t13973+t14528*t14821+t15284+t15425; + t14703 = t14394*t14937; + t15156 = t14406*t14837+z*t14703+t15412*t14526+t15396; + t14264 = t14525*t14389; + t15155 = x*t14264+t14485*t14718+t14492*t14812+t15451*t14494+(t14987+ +t15442)*z; + t14666 = t14399*t14921; + t15154 = t14524*t14666+t14396*t14780+t14525*t13895+t14399*t14833+t15400*y +; + t15153 = t15218+t15370; + t15152 = t15218+t15253; + t14729 = t14522*t14957; + t14824 = t14494*t15010; + t15151 = t15259+(t14729+t14768)*t14524+(t14711+t14824)*x; + t15150 = t14525*t13938+x*t14690+t15234+(t13957+t14772)*y; + t13865 = t14394*t14901; + t13846 = t14394*t14848; + t14736 = t14406*t14888; + t15149 = t14527*t14645+t13914+t13933+t14521*t14736+t13955+t13967+(t13846+ +t13865)*t14523; + t14126 = y*t14364; + t15148 = t14126+t14521*t14922+t15219+t15305; + t14267 = t14526*t14922; + t15020 = y*t14526; + t14774 = t14491*t15020; + t14979 = t14491*t15031; + t15147 = t14455*t14718+t14524*t14979+t14526*t14786+(t14774+t14267)*x+( +t14988+t15419)*z; + t15146 = t14412*t14718+x*t14735+(t14756+t14798)*z+t15395*y; + t15145 = x*t14736+t14522*t14685+t14524*t14754+t14394*t14807+t15398; + t15144 = (t14752+t14758)*t14398+(t14762+t14765)*t14397+t15399*y; + t15143 = x*t14666+t14396*t14833+t15435*t14525+t15398*y; + t15142 = t13950+t15190; + t15141 = t14438*t14808+t14522*t14744+x*t14224+t14465*t14977+t15221; + t14818 = t14413*t15020; + t14084 = t14525*t14350; + t14065 = t14486*t14945; + t15140 = z*t14065+t14893*t15031+t15270+(t14084+t14818)*x; + t15139 = t14525*t14029+t14410*t14707+t14909*t15031+y*t14045+t15267; + t14407 = RATIONAL(1.0,2304.0); + t14403 = RATIONAL(-1.0,2304.0); + t14714 = t14407*t14888; + t15138 = t14407*t14723+t14395*t14973+(t14741+t14740)*t14403+(t14841+ +t14714)*t14528+t15429*t14402; + t15137 = t14413*t14808+x*t14678+t14525*t14669+t14429*t14977+t15261; + t15136 = t14407*t14740+t14521*t14714+t15452*t14403+t15399; + t14701 = t14526*t14906; + t15135 = t14521*t14701+t14855*t15031+z*t14675+(t13952+t14008)*t14525+( +t14136+t15423)*y; + t15134 = t14523*t13857+(t14876+t14703)*t14527+t15429*t14445+(t14860+ +t15412)*t14522; + t15133 = t15206+t15282; + t15132 = t14438*t14984+t14881*t15032+t14935*t15030+t14525*t14655+z*t14742 ++x*t14982+t14439*t14822+t14524*t14805; + t15131 = t14406*t14755+t14526*t14703+t15412*z+t15397; + t15130 = t14526*t14677+t13999+t14523*t14793+t15287+t15427; + t15129 = t14462*t14833+t14525*t14034+y*t13920+x*t14799+t15248; + t15128 = t14524*t14760+t14522*t14770+x*t14766+t14441*t14808+t15245; + t15127 = t14411*t14918+t13905+t14523*t13917+z*t14682+t15251; + t14636 = y*t13889+t14442*t14765+t15296; + t15126 = t14440*t14934+t13929+t15293+t14636+t14441*t14752+t15404*y; + t15125 = t14441*t14758+t14525*t14871+t13948+t14636+t15297+t15402*y; + t14132 = t14490*t14848; + t14777 = t14519*t15010; + t14270 = t14505*t14989; + t14287 = t14521*t14854; + t14271 = t14500*t14905; + t15124 = t15288+t15307+t14525*t14132+t14270+t14287+t14508*t15016+t14521* +t14777+t14271+t15315; + t14710 = t14522*t14930; + t15123 = x*t14710+t14525*t13972+t15256+t15380+t15420*y; + t15122 = x*t14700+t14009+t14527*t14781+t15250+t15368; + t15121 = t14500*t14829+x*t14662+t13972+t15277+t15368; + t14664 = t14525*t14856; + t14705 = t14525*t14885; + t15120 = t15245+t14524*t14705+t14186+t15403*y+(t14664+t15446)*x; + t15119 = t14477*t14931+t14431*t14829+t15444*t14524+(t14737+t15432)*x+ +t15406+t15424; + t15022 = y*t14500; + t15118 = t14525*t14212+t14195+t14492*t14707+t14238+t15275+z*t15022+( +t14795+t15431)*y; + t14066 = t14523*t14894; + t14972 = t14483*t14523; + t15117 = t14492*t14918+t14486*t14526+t14493*t14883+t15198+(t14972+t14731+ +t14066)*z; + t14839 = z*t14934; + t15116 = t15266+t14414*t14839+t14084+t14438*t14707+t15446*z+t15405*y; + t14182 = t14481*t14932; + t14938 = t14523*t14496; + t15115 = t13996+t14488*t14829+t15201+(t14938+t14182)*x+t15443; + t15114 = t14470*t14888+t14333+t14405*t14901+t14118+t13846+t14527*t14692+ +t15240+(t14437+t14715)*t14522; + t15113 = t13877+t14434*t14723+t14473*t14888+t14427*t14749+t14160+t15271+ +t15402; + t14846 = t14525*t14480; + t14724 = t14522*t14846; + t15112 = t14413*t14763+t14485*t14945+t15221+t15443*y+(t14995+t14957+ +t14243+t14724)*x; + t14131 = t14481*t14937; + t15111 = t13913+t15202+t14488*t14837+(t14131+t14938)*z+t15413; + t15110 = t15246+t14438*t14839+t14414*t14707+t14134+t15436*z+t15407*y; + t14189 = t14455*t14971; + t15109 = t14490*t14839+t14526*t14663+z*t14922+t14189+t15215+(t15414+ +t15422)*y; + t15108 = t14475*t14749+t14132+t15263+t14281+(t14240+t15447)*t14521+t15439 +; + t15107 = t14518*t14833+t14525*t14211+t15259+(t14994+t14783)*t14524+( +t14777+t15023)*x+t15419; + t14325 = t14518*t15025; + t15106 = t14475*t14755+t14461*t14966+t14477*t14725+t14244+t14325+(t14661+ +t15416+t15447)*z+t15409; + t15105 = z*t14794+t14526*t14683+y*t13952+t14525*t14249+t15254+t15369; + t15104 = t14524*t14664+t15278+t14165+t15406*y+(t14705+t15436)*x; + t14859 = t14474*t14528; + t15103 = t14439*t14901+t14423*t14723+t14485*t14521+t14368+t13918+t14431* +t14749+t14477*t14899+t14523*t14859+t15268; + t14067 = t14465*t14936; + t15102 = t14067+t14073+t14468*t14829+t14454*t14524+t15201+(t14118+t14963) +*x; + t15029 = y*RATIONAL(-8.0,9.0); + t15101 = t14512*t14833+t14519*t15008+t15274+(t14724+t14199)*t14524+( +t15029+t14261)*x+t15442; + t14478 = RATIONAL(-5.0,48.0); + t15100 = t14480*t14848+t14509*t14899+t14500*t14901+t14478*t14749+t15249+( +t14070+t14520)*t14521+t15416; + t15099 = t15234+t14420*t14833+t15380+t14524*t14710+t15310+t15410*y; + t15098 = x*t14701+t13239+t15220+t15228+(t14204+t14806)*y; + t15097 = t14433*t14723+t14003+t14413*t14848+t14353+t14528*t14665+t14455* +t14521+t14474*t14899+t14477*t14937+t15264; + t14176 = t14492*t14936; + t15096 = t14176+t14486*t14524+t14471*t14829+t14527*t14360+t15199+(t14160+ +t14972)*x; + t14761 = t14525*t14927; + t15095 = t15257+t14525*t14904+t14429*t14763+(t14922+t14761)*x+(t15433+ +t15438)*y; + t14952 = t14523*t14498; + t14236 = t14523*t14903; + t14739 = t14484*t14888; + t15094 = t15199+t13945+(t14952+t14236+t14739)*x+t15433; + t14676 = t14478*t14899; + t15093 = t14480*t14901+t14500*t14848+t15249+t14509*t14888+t14527*t14676+ +t15385+(t14096+t14520)*t14522; + t14992 = y*t14499; + t15092 = t14246+z*t14992+t14465*t14707+t14525*t14133+t14226+t15238+( +t14804+t15409)*y; + t14106 = t14473*t14937; + t15091 = t14356+t14446*t14883+t14465*t14918+t15202+(t14106+t15421)*z; + t14304 = z*t14939; + t15090 = t14304+t14453*t14966+t14526*t14676+t14474*t14725+t14082+(t14695+ +t15437+t15439)*z+t15431; + t15089 = t14524*t14737+t14474*t14931+t14431*t14730+(t14960+t14439+t15444) +*x+t15403+t15415; + t15088 = t14453*t14749+t14475*t14723+t15263+t15394+t14499*t14848+t14074+ +t15447*t14522; + t14694 = t14521*t14846; + t15087 = t14413*t14707+t15386+t15233+t15413*y+(t14126+t14995+t14694)*z; + t14890 = t14483*t14528; + t14114 = t14523*t14890; + t15086 = t14484*t14837+t14048+t15198+(t14114+t14952)*z+t15414; + t15085 = t14525*t14191+t14526*t14647+z*t14790+y*t14041+t15265+t15369; + t15084 = t15285+t15209+t15379; + t15083 = t15286+t15350+t15358; + t15082 = t15286+t15205+t15389; + t13101 = t14524*t14782; + t14643 = t13101+t15286; + t15081 = t14643+t15358+t15360; + t14631 = t13101+t15285; + t15080 = t14631+t15355+t15360; + t15079 = t15285+t15350+t15355; + t13276 = x*t14709; + t14847 = t13276+t13262; + t15078 = t14847+t15363+t15367; + t15077 = t13343+t13262+t15362+t15367; + t13309 = t14525*t14020; + t14944 = t13276+t13309; + t15076 = t14944+t15359+t15363; + t14953 = t13343+t13309; + t15075 = t14953+t15359+t15362; + t15074 = t15165+t15185; + t15073 = t15341+t15349; + t15072 = t15333+t15342; + t15071 = t15336+t15348; + t15070 = t15158+t15224+t15272; + t15069 = t15173+t15184; + t15068 = t15347+t15349; + t15067 = t15335+t15357; + t15066 = t15332+t15345; + t15065 = t15154+t15162; + t15064 = t15319+t15334; + t15063 = t15336+t15342; + t15062 = t14093+t14523*t14644+t14119+t14524*t14767+x*t14771+t14486*t14791 ++t15323+t15457; + t15061 = t15319+t15330; + t15060 = t15337+t15351; + t15059 = t15143+t15162; + t15058 = t15138+t15156; + t15057 = t15161+t15229+t15241; + t15056 = t15129+t15135; + t15055 = t15327+t15329; + t15054 = t15135+t15173; + t15053 = t15340+t15347; + t15052 = t15324+t15329; + t15051 = t15328+t15351; + t15050 = t15146+t15154; + t15049 = t14210+t14519*t14986+t14526*t14757+x*t14698+t14452*t15030+t15323 ++t14454*t14797+t15460; + t15048 = t15131+t15136; + t15047 = t15332+t15357; + t15046 = t15337+t15346; + t15045 = t15324+t15325; + t15044 = t15333+t15348; + t15043 = t15328+t15346; + t15042 = t15129+t15184; + t15041 = t15321+t15334; + t15040 = t15325+t15327; + t14819 = t14525*t15024; + t15039 = t15144+t14396*t14707+t14525*t13853+t14399*t14839+t14528*t14819+ +t15397*y; + t15038 = t15144+t14399*t14707+t14521*t14819+(z*t14873+t13886)*t14525+ +t15396*y; + t15037 = t15143+t15146; + t15036 = t15145+t15179; + t15035 = t15335+t15345; + t15034 = t15321+t15330; + t15033 = t15340+t15341; + t14975 = t14478*t14528; + t14970 = t14478*t14527; + t14958 = t14479*t14527; + t14955 = t14477*t14528; + t14373 = t14455*t14527; + t14926 = t14525*t14481; + t14920 = t14479*t14528; + t14889 = t14484*t14521; + t14865 = t14496*t14527; + t14864 = t14475*t14521; + t14843 = t14513*t14522; + t14835 = y*t14883; + t14283 = z*t14845; + t14825 = t14465*t14989; + t14820 = t14441*t14989; + t14810 = t14429*t14989; + t14746 = t14431*t14899; + t14699 = t14471*t14848; + t14653 = t14426*t14901; + t14642 = t14521*t14761+y*t13937+t14900; + t14641 = t14035+t15283; + t14635 = t13950+t15282; + t14629 = t14042+t15283; + t14628 = t14521*t14824+t14528*t14729+t15307; + t14627 = t14453+t14859+t14478*t14521; + t14626 = t14461+t14955+t14864; + t14625 = t14481*t14527+t14496+t14488*t14522; + t14456 = RATIONAL(-5.0,32.0); + t14416 = RATIONAL(25.0,32.0); + t14501 = RATIONAL(-5.0,8.0); + t14624 = t14501+t14416*t14522+t14456*t14527; + t14623 = t14844+t15384; + t14447 = RATIONAL(1.0,16.0); + t14448 = RATIONAL(-5.0,16.0); + t14503 = RATIONAL(1.0,4.0); + t14622 = t14448*t14522+t14447*t14527+t14503; + t14621 = t14861+t14453+t14478*t14522; + t14436 = RATIONAL(25.0,96.0); + t14620 = t14484+t14436*t14521+t14471*t14528; + t14517 = RATIONAL(2.0,3.0); + t14619 = t14510*t14522+t14517+t14498*t14527; + t14422 = RATIONAL(-25.0,96.0); + t14618 = t14468*t14528+t14422*t14521+t14488; + t14617 = t14903+t15377; + t14616 = t14865+t14843+t14516; + t14614 = t14482*t14834+t14525*t14865+t14522*t15011+t14488*t14758+t15294; + t14613 = t15292+(t14890+t14699)*t14525+(t14864+t14653)*y; + t14610 = t14521*t14739+t13937+t14528*t14118+t14059+t14642; + t14609 = t15216+t15269; + t14607 = t15200+t15291; + t14606 = t14521*t14774+z*t14271+t14489*t14976+t14528*t14189+t14628; + t14604 = z*t14815+t14494*t14813+t14628+t15386*t14528; + t14603 = t15232+t15291+t15310; + t14599 = t14488*t14741+t13930+t14522*t14942+t14523*t14670+t14642; + t14598 = t15253+t15269; + t14400 = RATIONAL(25.0,192.0); + t14597 = y*t14975+t14400*t14834+t14473*t14758+t14521*t14926+t14613+t15314 +; + t14596 = t14473*t14752+t14522*t14926+t14400*t14840+y*t14970+t15255+t15292 ++t15314; + t14418 = RATIONAL(-25.0,48.0); + t14595 = y*t14920+t14498*t14758+t14418*t14834+t14517*t14934+t15230+t15294 ++t15312; + t14594 = t14517*t14969+t14498*t14752+t14418*t14840+y*t14958+t14614+t15312 +; + t14593 = t14623*t14525+(t14422*t14522+t14468*t14527+t14488)*y; + t14592 = t14621*t14525+(t14471*t14527+t14484+t14436*t14522)*y; + t14591 = t14525*t14658+t14526*t14810+t14413*t14981+t14521*t14238+t15203+ +t15238; + t14590 = t14454*t14707+t14521*t14246+t14528*t14818+z*t14810+t15203+t15275 +; + t14589 = t14526*t14792+t14455*t14839+t14439*t14707+z*t14801+t15207+t15215 +; + t14588 = t15208+t14437*t14839+z*t14820+t15246+t15393*t14526; + t14587 = t14521*t14283+t14604+t14494*t14981+t14499*t14707+t14526*t14801+ +t15237; + t14586 = t14438*t14835+t15233+t14521*t14684+t15207+(t14825+t14068)*z; + t14585 = t14526*t14820+t15266+t14437*t14707+t15208+t15393*z; + t14584 = t14500*t14707+t14526*t14825+z*t14287+t14528*t14979+t14606+t15237 +; + t14432 = RATIONAL(-25.0,24.0); + t14583 = RATIONAL(4.0,3.0)*y+t14614+t14432*t14765+t14453*t14826+t15230+( +t15010+t14989)*t14507+(t14843+t15375)*t14525; + t14582 = t14613+t14423*t14826+t14436*t14765+t15255+(t14889+t15377)*t14525 ++(t14955+t15384)*y; + t14581 = t13865+t14405*t14848+t14437*t14521+t14106+t14435*t14528+t15126+ +t14430*t14723+t14470*t14899+t14428*t14749+t15240; + t14580 = t15124+t14211+t14524*t14122+t14475*t14730+t14461*t14931+t14482* +t14829+(t14968+t15385+t15447)*x+t15392; + t14579 = t14468*t14723+t13911+t15164+t14610+t14182+t14367+t14522*t14114+ +t14498*t14888+t15440; + t14578 = t14336+t14433*t14725+t14526*t14746+t14474*t14966+t15125+t15372*z ++t15405+t15408; + t14577 = t14477*t14888+t14429*t14901+t14174+t14439*t14848+t14373+t15268+ +t14431*t14723+t15192+(t14668+t14485)*t14522; + t14576 = t14599+t15148+t14114+t14363+t14493*t14901+t14496*t14899+t14523* +t14699+t14414*t14848+(t14486+t14182)*t14521; + t14575 = t15181+t14264+t14283+t14525*t14304+t14606+t14519*t15020+(t14694+ +t14171)*t14526+(t14270+t15029)*z; + t14574 = t14492*t14833+t15244+t15191+t14101+t14373*t15032+t14525*t14067+ +t15392*y+(t14992+t14950)*x; + t14573 = t14066+t14434*t14749+t13866+t15126+t14521*t14702+t14473*t14899+ +t15271+t15404; + t14572 = t14355*t15032+t15191+t14065+t15261+(t14137+t14176)*t14525+t15383 +*y+(t14850+t15022)*x; + t14571 = t15148+t13992+t14131+t14610+t14521*t14236+t14364+t14468*t14749+ +t14498*t14899+t15418; + t14570 = t14849*t15028+t15125+t15372*t14526+(t14746+t15432)*z+t15407+ +t15445; + t14569 = t14354+t14527*t14842+t14433*t14749+t14523*t14653+t14474*t14888+ +t15192+t14440*t14848+t15264+t15417; + t14568 = t14599+t14414*t14901+t14351+t14092+t14236+t14496*t14888+t15164+ +t14471*t14723+(t14486+t14131)*t14522; + t14567 = t15124+t14524*t14174+t14512*t15026+t14479*t14829+t14110+t14478* +t14730+t14453*t14931+(t15394+t15437)*x+t15383; + t14566 = t15181+t14267+t14519*t14981+t14604+t14526*t14994+t14525*t14325+ +t14490*t14707+t14454*t14835+(t14854+t15023)*z; + t14565 = t14603+t15123+t15200+t15361+t15371; + t14564 = t15105+t15339+t15353; + t14563 = t15133+t14598+t15166+t15211+t15212; + t14562 = t14042+t15121+t14035+t15282+t15356+t15364; + t14561 = t14643+t15186+t15205+t15379; + t14560 = t13950+t14641+t15122+t15354+t15364; + t14559 = t15049+t15320+t15322; + t14558 = t15098+t14608+t15158+t15229; + t14557 = t15062+t15322+t15326; + t14556 = t14598+t15167+t15177+t15210+t15239; + t14555 = t15145+t15039+t15185; + t14554 = t14607+t15099+t15344+t15371; + t14553 = t15099+t15232+t15361+t15365; + t14552 = t15122+t14635+t15352+t15356; + t14551 = t15176+t15169+t14601+t15236+t15317+t15374; + t14550 = t15136+t15038+t15156; + t14549 = t15326+t15049+t15331; + t14548 = t14603+t15149+t15139+t14035+t15280+t15298+t15303; + t14547 = t15062+t15320+t15331; + t14546 = t15121+t14629+t15352+t15354; + t14545 = t15105+t15338+t15343; + t14544 = t14607+t15157+t15170+t15236+t15247; + t14543 = t15098+t14605+t15161+t15224; + t14542 = t15131+t15038+t15138; + t14541 = t15123+t15310+t15344+t15365; + t14540 = t15130+t14944+t15195+t14609+t15239+t15281; + t14539 = t15085+t15339+t15343; + t14538 = t15186+t14631+t15209+t15389; + t14537 = t15085+t15338+t15353; + t14536 = t15127+t15142+t15204+t15211+t15269+t15283; + t14535 = t14042+t15134+t14609+t15150+t15211+t15279; + t14534 = t15165+t15039+t15179; + t14514 = RATIONAL(-1.0,8.0); + t14504 = RATIONAL(1.0,8.0); + t14502 = RATIONAL(5.0,3.0); + t14497 = RATIONAL(5.0,8.0); + t14495 = RATIONAL(-5.0,4.0); + t14476 = RATIONAL(-1.0,16.0); + t14472 = RATIONAL(5.0,64.0); + t14464 = RATIONAL(5.0,32.0); + t14463 = RATIONAL(5.0,16.0); + t14451 = RATIONAL(-5.0,64.0); + t14450 = RATIONAL(25.0,8.0); + t14419 = RATIONAL(25.0,48.0); + t14415 = RATIONAL(-25.0,12.0); + coeffs_dy->coeff_m2_m2_m2 = t14555+t15058+t15050; + coeffs_dy->coeff_m1_m2_m2 = t14544+t15195+t15160+t15194+t14953+t15210+ +t15253; + coeffs_dy->coeff_0_m2_m2 = t15114+t15110+t14578; + coeffs_dy->coeff_p1_m2_m2 = t13276+t15188+t15160+t14556+t15157+t15218+ +t15366; + coeffs_dy->coeff_p2_m2_m2 = t15058+t15059+t14534; + coeffs_dy->coeff_m2_m1_m2 = t14536+t15159+t15149+t15150+t15212+t15253; + coeffs_dy->coeff_m1_m1_m2 = t14543+t15084+t15042; + coeffs_dy->coeff_0_m1_m2 = t15117+t14577+t15118; + coeffs_dy->coeff_p1_m1_m2 = t14561+t15069+t15070; + coeffs_dy->coeff_p2_m1_m2 = t14042+t15127+t15149+t14563+t15153+t15197; + coeffs_dy->coeff_m2_0_m2 = t14588+t15168+t15172; + coeffs_dy->coeff_m1_0_m2 = t14590+t15141+t15183; + coeffs_dy->coeff_0_0_m2 = (t14626*t14526+t14627*z)*t14525+(t14618*t14526+ +t14620*z)*y+t14596; + coeffs_dy->coeff_p1_0_m2 = t14590+t15178+t15182; + coeffs_dy->coeff_p2_0_m2 = t15128+t14588+t15132; + coeffs_dy->coeff_m2_p1_m2 = t15196+t15152+t14641+t14535+t15204+t15212+ +t15370; + coeffs_dy->coeff_m1_p1_m2 = t14558+t15042+t15082; + coeffs_dy->coeff_0_p1_m2 = t15091+t15118+t14569; + coeffs_dy->coeff_p1_p1_m2 = t14538+t15069+t15057; + coeffs_dy->coeff_p2_p1_m2 = t15134+t15159+t14563+t14035+t15142+t15196; + coeffs_dy->coeff_m2_p2_m2 = t15048+t14534+t15050; + coeffs_dy->coeff_m1_p2_m2 = t15152+t15163+t14540+t15170+t15210+t15366; + coeffs_dy->coeff_0_p2_m2 = t15113+t14570+t15110; + coeffs_dy->coeff_p1_p2_m2 = t15130+t15169+t14556+t15163+t15174; + coeffs_dy->coeff_p2_p2_m2 = t14555+t15048+t15059; + coeffs_dy->coeff_m2_m2_m1 = t14554+t15063+t15081; + coeffs_dy->coeff_m1_m2_m1 = t14562+t15073+t15046; + coeffs_dy->coeff_0_m2_m1 = t14568+t15087+t15086; + coeffs_dy->coeff_p1_m2_m1 = t15060+t14560+t15068; + coeffs_dy->coeff_p2_m2_m1 = t15079+t14541+t15063; + coeffs_dy->coeff_m2_m1_m1 = t14564+t15035+t15078; + coeffs_dy->coeff_m1_m1_m1 = t14559+t15040+t15034; + coeffs_dy->coeff_0_m1_m1 = t14575+t15088+t15090; + coeffs_dy->coeff_p1_m1_m1 = t14547+t15055+t15041; + coeffs_dy->coeff_p2_m1_m1 = t15047+t15075+t14564; + coeffs_dy->coeff_m2_0_m1 = t15137+t14586+t15140; + coeffs_dy->coeff_m1_0_m1 = t14584+t15155+t15171; + coeffs_dy->coeff_0_0_m1 = t14594+((t14419*t14521+t14975+t14482)*t14526+( +t14920+t14415*t14521+t14502)*z)*y+((t14498+t14889+t14890)*t14526+(t14852+t15375 +)*z)*t14525; + coeffs_dy->coeff_p1_0_m1 = t14584+t15147+t15151; + coeffs_dy->coeff_p2_0_m1 = t15175+t14586+t15180; + coeffs_dy->coeff_m2_p1_m1 = t14545+t15067+t15077; + coeffs_dy->coeff_m1_p1_m1 = t14557+t15034+t15052; + coeffs_dy->coeff_0_p1_m1 = t15093+t15106+t14575; + coeffs_dy->coeff_p1_p1_m1 = t15045+t14549+t15041; + coeffs_dy->coeff_p2_p1_m1 = t14545+t15066+t15076; + coeffs_dy->coeff_m2_p2_m1 = t15071+t15080+t14553; + coeffs_dy->coeff_m1_p2_m1 = t15043+t14552+t15068; + coeffs_dy->coeff_0_p2_m1 = t14579+t15087+t15111; + coeffs_dy->coeff_p1_p2_m1 = t14546+t15073+t15051; + coeffs_dy->coeff_p2_p2_m1 = t14565+t15083+t15071; + coeffs_dy->coeff_m2_m2_0 = t15089+t14581+t15104; + coeffs_dy->coeff_m1_m2_0 = t14576+t15094+t15112; + coeffs_dy->coeff_0_m2_0 = (t14476*t14527+RATIONAL(-1.0,4.0)+t14463*t14522 ++(t14463+t14472*t14527+RATIONAL(-25.0,64.0)*t14522)*t14521+(RATIONAL(-1.0,64.0) +*t14527+t14476+t14472*t14522)*t14528)*t14523+(t14400*t14522+t14478+t14431* +t14527)*t14521+(t14433*t14527+t14431*t14522+t14474)*t14528+t14582+t14621; + coeffs_dy->coeff_p1_m2_0 = t15115+t14576+t15095; + coeffs_dy->coeff_p2_m2_0 = t15119+t14581+t15120; + coeffs_dy->coeff_m2_m1_0 = t15103+t14572+t15096; + coeffs_dy->coeff_m1_m1_0 = t15101+t14567+t15108; + coeffs_dy->coeff_0_m1_0 = t14625*t14528+t14583+(t14488*t14527+t14513+ +t14432*t14522)*t14521+(RATIONAL(1.0,2.0)+t14501*t14522+t14504*t14527+t14624* +t14521+(t14456*t14522+RATIONAL(1.0,32.0)*t14527+t14504)*t14528)*t14523+t14616; + coeffs_dy->coeff_p1_m1_0 = t14580+t15108+t15107; + coeffs_dy->coeff_p2_m1_0 = t14574+t15103+t15102; + coeffs_dy->coeff_m2_0_0 = t14592*x+t14597+t14593*t14524; + coeffs_dy->coeff_m1_0_0 = (t14617*t14525+(t14970+t14482+t14419*t14522)*y) +*t14524+(t14616*t14525+(t14502+t14958+t14415*t14522)*y)*x+t14595; + coeffs_dy->coeff_0_0_0 = (t14503*t14527+t14495*t14522+1.0+(t14448*t14527+ +t14495+RATIONAL(25.0,16.0)*t14522)*t14521+t14622*t14528)*t14525+(t14501*t14527+ +RATIONAL(-5.0,2.0)+t14450*t14522+(t14416*t14527+RATIONAL(-125.0,32.0)*t14522+ +t14450)*t14521+t14624*t14528)*y; + coeffs_dy->coeff_p1_0_0 = (t14625*t14525+(t14418*t14522+t14479+t14475* +t14527)*y)*t14524+t14595+(t14619*t14525+(t14417*t14522+t14506+t14482*t14527)*y) +*x; + coeffs_dy->coeff_p2_0_0 = t14592*t14524+t14597+t14593*x; + coeffs_dy->coeff_m2_p1_0 = t15097+t15102+t14572; + coeffs_dy->coeff_m1_p1_0 = t15101+t14580+t15100; + coeffs_dy->coeff_0_p1_0 = t14583+t14617*t14528+(t14514*t14527+t14497* +t14522+RATIONAL(-1.0,2.0)+(RATIONAL(-25.0,32.0)*t14522+t14497+t14464*t14527)* +t14521+(t14464*t14522+RATIONAL(-1.0,32.0)*t14527+t14514)*t14528)*t14523+( +RATIONAL(25.0,24.0)*t14522+t14484*t14527+t14510)*t14521+t14619; + coeffs_dy->coeff_p1_p1_0 = t14567+t15100+t15107; + coeffs_dy->coeff_p2_p1_0 = t15097+t14574+t15096; + coeffs_dy->coeff_m2_p2_0 = t15119+t15104+t14573; + coeffs_dy->coeff_m1_p2_0 = t14571+t15115+t15112; + coeffs_dy->coeff_0_p2_0 = (t14475+t14401*t14522+t14426*t14527)*t14521+(( +RATIONAL(25.0,64.0)*t14522+t14451*t14527+t14448)*t14521+(t14447+t14451*t14522+ +RATIONAL(1.0,64.0)*t14527)*t14528+t14622)*t14523+(t14423*t14527+t14426*t14522+ +t14477)*t14528+t14582+t14623; + coeffs_dy->coeff_p1_p2_0 = t14571+t15095+t15094; + coeffs_dy->coeff_p2_p2_0 = t15089+t15120+t14573; + coeffs_dy->coeff_m2_m2_p1 = t15072+t15083+t14553; + coeffs_dy->coeff_m1_m2_p1 = t14546+t15046+t15053; + coeffs_dy->coeff_0_m2_p1 = t15109+t14568+t15111; + coeffs_dy->coeff_p1_m2_p1 = t14552+t15060+t15033; + coeffs_dy->coeff_p2_m2_p1 = t15072+t14565+t15080; + coeffs_dy->coeff_m2_m1_p1 = t14537+t15067+t15076; + coeffs_dy->coeff_m1_m1_p1 = t14547+t15045+t15061; + coeffs_dy->coeff_0_m1_p1 = t15106+t15088+t14566; + coeffs_dy->coeff_p1_m1_p1 = t14559+t15052+t15064; + coeffs_dy->coeff_p2_m1_p1 = t14537+t15077+t15066; + coeffs_dy->coeff_m2_0_p1 = t14589+t15137+t15175; + coeffs_dy->coeff_m1_0_p1 = t14587+t15147+t15171; + coeffs_dy->coeff_0_0_p1 = t14594+((t14475*t14528+t14418*t14521+t14479)* +t14526+(t14506+t14482*t14528+t14417*t14521)*z)*y+((t14481*t14528+t14496+t14488* +t14521)*t14526+(t14510*t14521+t14498*t14528+t14517)*z)*t14525; + coeffs_dy->coeff_p1_0_p1 = t15151+t14587+t15155; + coeffs_dy->coeff_p2_0_p1 = t15140+t14589+t15180; + coeffs_dy->coeff_m2_p1_p1 = t14539+t15075+t15035; + coeffs_dy->coeff_m1_p1_p1 = t15055+t14549+t15061; + coeffs_dy->coeff_0_p1_p1 = t15093+t15090+t14566; + coeffs_dy->coeff_p1_p1_p1 = t14557+t15040+t15064; + coeffs_dy->coeff_p2_p1_p1 = t15047+t14539+t15078; + coeffs_dy->coeff_m2_p2_p1 = t15079+t14554+t15044; + coeffs_dy->coeff_m1_p2_p1 = t15043+t14560+t15033; + coeffs_dy->coeff_0_p2_p1 = t15109+t14579+t15086; + coeffs_dy->coeff_p1_p2_p1 = t14562+t15051+t15053; + coeffs_dy->coeff_p2_p2_p1 = t14541+t15044+t15081; + coeffs_dy->coeff_m2_m2_p2 = t15036+t14542+t15065; + coeffs_dy->coeff_m1_m2_p2 = t15130+t14551+t15160+t15167+t15170; + coeffs_dy->coeff_0_m2_p2 = t14570+t15114+t15116; + coeffs_dy->coeff_p1_m2_p2 = t15174+t15176+t15160+t14540+t15177; + coeffs_dy->coeff_p2_m2_p2 = t14542+t15037+t15074; + coeffs_dy->coeff_m2_m1_p2 = t14548+t15150+t14635+t15153+t15190+t15206; + coeffs_dy->coeff_m1_m1_p2 = t14538+t15056+t15070; + coeffs_dy->coeff_0_m1_p2 = t14577+t15091+t15092; + coeffs_dy->coeff_p1_m1_p2 = t15054+t14543+t15082; + coeffs_dy->coeff_p2_m1_p2 = t14629+t14548+t15159+t15166+t15197+t15204; + coeffs_dy->coeff_m2_0_p2 = t15132+t14585+t15168; + coeffs_dy->coeff_m1_0_p2 = t15141+t14591+t15182; + coeffs_dy->coeff_0_0_p2 = (t14627*t14526+t14626*z)*t14525+(t14620*t14526+ +t14618*z)*y+t14596; + coeffs_dy->coeff_p1_0_p2 = t14591+t15178+t15183; + coeffs_dy->coeff_p2_0_p2 = t15128+t14585+t15172; + coeffs_dy->coeff_m2_p1_p2 = t15133+t15127+t15139+t14535+t15159; + coeffs_dy->coeff_m1_p1_p2 = t14561+t15056+t15057; + coeffs_dy->coeff_0_p1_p2 = t15117+t14569+t15092; + coeffs_dy->coeff_p1_p1_p2 = t15054+t15084+t14558; + coeffs_dy->coeff_p2_p1_p2 = t14536+t15134+t15139+t15153+t15166; + coeffs_dy->coeff_m2_p2_p2 = t15065+t14550+t15074; + coeffs_dy->coeff_m1_p2_p2 = t15176+t14544+t14847+t15188+t15163+t15193; + coeffs_dy->coeff_0_p2_p2 = t15113+t14578+t15116; + coeffs_dy->coeff_p1_p2_p2 = t14551+t15163+t15157+t13309+t15177+t15195; + coeffs_dy->coeff_p2_p2_p2 = t15036+t15037+t14550; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyy.compute.c new file mode 100644 index 0000000..e0a8845 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyy.compute.c @@ -0,0 +1,2265 @@ +fp t26280; +fp t26283; +fp t26257; +fp t26263; +fp t27110; +fp t26194; +fp t26157; +fp t26281; +fp t27109; +fp t26279; +fp t26285; +fp t26242; +fp t26120; +fp t25852; +fp t26187; +fp t26637; +fp t25677; +fp t27108; +fp t26282; +fp t26612; +fp t26522; +fp t26661; +fp t26500; +fp t27084; +fp t26284; +fp t26584; +fp t26623; +fp t26193; +fp t25777; +fp t27107; +fp t26156; +fp t27106; +fp t26694; +fp t26665; +fp t27105; +fp t27104; +fp t27103; +fp t26668; +fp t25713; +fp t27102; +fp t26723; +fp t26686; +fp t26675; +fp t26527; +fp t27101; +fp t26235; +fp t26629; +fp t26575; +fp t26497; +fp t27100; +fp t25699; +fp t26728; +fp t27099; +fp t27098; +fp t26208; +fp t26162; +fp t27097; +fp t26216; +fp t26199; +fp t27096; +fp t26621; +fp t26507; +fp t26678; +fp t26479; +fp t27095; +fp t26632; +fp t26400; +fp t26552; +fp t26394; +fp t27094; +fp t26234; +fp t25859; +fp t26205; +fp t26704; +fp t25889; +fp t27093; +fp t26196; +fp t26677; +fp t25871; +fp t26185; +fp t25815; +fp t27092; +fp t26269; +fp t26150; +fp t26217; +fp t27091; +fp t26155; +fp t26636; +fp t27090; +fp t26158; +fp t26585; +fp t26647; +fp t27089; +fp t26714; +fp t25896; +fp t26559; +fp t25715; +fp t27088; +fp t26108; +fp t26149; +fp t27087; +fp t27086; +fp t26179; +fp t27085; +fp t26245; +fp t26602; +fp t26167; +fp t27083; +fp t26203; +fp t26711; +fp t26705; +fp t26223; +fp t25959; +fp t27082; +fp t26220; +fp t26622; +fp t26222; +fp t27081; +fp t26260; +fp t26596; +fp t26266; +fp t26560; +fp t27080; +fp t26218; +fp t26699; +fp t26504; +fp t26230; +fp t26724; +fp t27079; +fp t26166; +fp t26606; +fp t27078; +fp t26219; +fp t26249; +fp t26131; +fp t27077; +fp t26232; +fp t26578; +fp t26229; +fp t27076; +fp t26259; +fp t26633; +fp t26261; +fp t26570; +fp t27075; +fp t27074; +fp t26241; +fp t26168; +fp t26550; +fp t27073; +fp t26240; +fp t26238; +fp t27072; +fp t26227; +fp t27071; +fp t26258; +fp t26231; +fp t27070; +fp t26190; +fp t26180; +fp t27069; +fp t25957; +fp t26100; +fp t26473; +fp t27068; +fp t26700; +fp t25954; +fp t26189; +fp t26095; +fp t26517; +fp t27067; +fp t27066; +fp t27065; +fp t26514; +fp t25447; +fp t26106; +fp t26739; +fp t27064; +fp t26123; +fp t26508; +fp t26900; +fp t26204; +fp t26117; +fp t27063; +fp t26696; +fp t26687; +fp t25203; +fp t27062; +fp t25948; +fp t26098; +fp t26476; +fp t27061; +fp t26101; +fp t26478; +fp t25043; +fp t26737; +fp t26519; +fp t27060; +fp t26119; +fp t26539; +fp t26515; +fp t26910; +fp t27059; +fp t26124; +fp t26679; +fp t26109; +fp t26444; +fp t26554; +fp t26405; +fp t26952; +fp t27058; +fp t26646; +fp t26536; +fp t27057; +fp t26645; +fp t26467; +fp t27056; +fp t26740; +fp t26555; +fp t26102; +fp t26513; +fp t25118; +fp t27055; +fp t26481; +fp t26942; +fp t26471; +fp t27054; +fp t26191; +fp t27053; +fp t26468; +fp t27052; +fp t26093; +fp t25065; +fp t26484; +fp t27051; +fp t26385; +fp t26610; +fp t26491; +fp t27050; +fp t26535; +fp t26923; +fp t26693; +fp t26683; +fp t27049; +fp t26489; +fp t27048; +fp t27047; +fp t27046; +fp t26605; +fp t26470; +fp t25243; +fp t27045; +fp t26207; +fp t26663; +fp t27044; +fp t26597; +fp t27043; +fp t26615; +fp t26122; +fp t26387; +fp t27042; +fp t27041; +fp t26697; +fp t25749; +fp t26692; +fp t26523; +fp t26948; +fp t27040; +fp t26094; +fp t26524; +fp t26722; +fp t26474; +fp t27039; +fp t25381; +fp t26116; +fp t26501; +fp t27038; +fp t27037; +fp t26505; +fp t26949; +fp t26475; +fp t27036; +fp t26097; +fp t26531; +fp t27035; +fp t25134; +fp t27034; +fp t26164; +fp t26576; +fp t26451; +fp t27033; +fp t27032; +fp t26104; +fp t26525; +fp t26934; +fp t27031; +fp t25978; +fp t26416; +fp t27030; +fp t26680; +fp t27029; +fp t26738; +fp t26543; +fp t26490; +fp t25242; +fp t27028; +fp t26175; +fp t26592; +fp t26917; +fp t26165; +fp t26549; +fp t26277; +fp t26649; +fp t26390; +fp t27027; +fp t26099; +fp t27026; +fp t26391; +fp t25114; +fp t27025; +fp t27024; +fp t26096; +fp t27023; +fp t26493; +fp t27022; +fp t26410; +fp t25140; +fp t27021; +fp t26420; +fp t25403; +fp t26690; +fp t27020; +fp t26532; +fp t26107; +fp t26520; +fp t27019; +fp t27018; +fp t26599; +fp t27017; +fp t26486; +fp t26105; +fp t27016; +fp t26091; +fp t26538; +fp t26415; +fp t26659; +fp t26163; +fp t26568; +fp t27015; +fp t26482; +fp t27014; +fp t26684; +fp t27013; +fp t26409; +fp t25462; +fp t26641; +fp t27012; +fp t26710; +fp t26384; +fp t26542; +fp t26620; +fp t27011; +fp t26480; +fp t27010; +fp t26133; +fp t26487; +fp t26127; +fp t26494; +fp t26278; +fp t26688; +fp t27009; +fp t26638; +fp t26503; +fp t26195; +fp t26574; +fp t27008; +fp t26210; +fp t26706; +fp t27007; +fp t26685; +fp t26250; +fp t25960; +fp t26272; +fp t26682; +fp t26125; +fp t26436; +fp t27006; +fp t26389; +fp t26488; +fp t26129; +fp t27005; +fp t25445; +fp t27004; +fp t26492; +fp t26689; +fp t27003; +fp t26664; +fp t26540; +fp t26176; +fp t26630; +fp t26558; +fp t26398; +fp t27002; +fp t25963; +fp t27001; +fp t26561; +fp t26472; +fp t26676; +fp t26528; +fp t27000; +fp t26999; +fp t26998; +fp t26152; +fp t26161; +fp t26546; +fp t26447; +fp t26997; +fp t25639; +fp t25660; +fp t25661; +fp t26996; +fp t26995; +fp t26516; +fp t25849; +fp t26994; +fp t25693; +fp t26993; +fp t26992; +fp t26670; +fp t26399; +fp t26616; +fp t26991; +fp t26423; +fp t26990; +fp t26020; +fp t26989; +fp t26988; +fp t26987; +fp t26650; +fp t26986; +fp t26424; +fp t26673; +fp t26388; +fp t26701; +fp t26985; +fp t26573; +fp t26984; +fp t26983; +fp t26982; +fp t26448; +fp t26981; +fp t26980; +fp t26919; +fp t26936; +fp t26870; +fp t26359; +fp t26979; +fp t26361; +fp t26499; +fp t26618; +fp t26978; +fp t26593; +fp t26212; +fp t26938; +fp t26604; +fp t26496; +fp t26432; +fp t26735; +fp t26842; +fp t26736; +fp t26977; +fp t26498; +fp t26586; +fp t26674; +fp t26356; +fp t26976; +fp t26708; +fp t26624; +fp t26450; +fp t26731; +fp t26681; +fp t26412; +fp t26428; +fp t26975; +fp t26462; +fp t26974; +fp t26973; +fp t26541; +fp t26972; +fp t26395; +fp t26426; +fp t26639; +fp t26971; +fp t26970; +fp t26716; +fp t26969; +fp t26452; +fp t26643; +fp t26968; +fp t26402; +fp t26967; +fp t26966; +fp t26965; +fp t26483; +fp t26964; +fp t26963; +fp t26590; +fp t26962; +fp t26564; +fp t26510; +fp t26961; +fp t26960; +fp t26408; +fp t26959; +fp t26958; +fp t26720; +fp t26548; +fp t26053; +fp t26957; +fp t26956; +fp t26406; +fp t26614; +fp t26090; +fp t26955; +fp t26583; +fp t26954; +fp t26953; +fp t26228; +fp t26521; +fp t26951; +fp t26253; +fp t26431; +fp t26950; +fp t26611; +fp t26947; +fp t26236; +fp t26608; +fp t26946; +fp t25680; +fp t26419; +fp t26945; +fp t26178; +fp t25737; +fp t26183; +fp t26944; +fp t26943; +fp t26941; +fp t26443; +fp t26940; +fp t26939; +fp t26181; +fp t26658; +fp t26392; +fp t26933; +fp t26932; +fp t26268; +fp t26509; +fp t26931; +fp t26243; +fp t26557; +fp t26930; +fp t26929; +fp t26248; +fp t26224; +fp t26928; +fp t26927; +fp t26214; +fp t26926; +fp t26925; +fp t26188; +fp t26594; +fp t25965; +fp t26924; +fp t26922; +fp t26209; +fp t26920; +fp t26727; +fp t26221; +fp t26506; +fp t26918; +fp t26916; +fp t26184; +fp t26915; +fp t26270; +fp t26526; +fp t26914; +fp t26913; +fp t26912; +fp t26151; +fp t26911; +fp t26909; +fp t26226; +fp t26495; +fp t26907; +fp t26906; +fp t26905; +fp t26172; +fp t26581; +fp t26271; +fp t26904; +fp t26903; +fp t26902; +fp t26901; +fp t25857; +fp t26899; +fp t26160; +fp t26898; +fp t26211; +fp t26598; +fp t26897; +fp t26111; +fp t26456; +fp t26114; +fp t26422; +fp t26896; +fp t26631; +fp t26455; +fp t26895; +fp t26894; +fp t25974; +fp t26589; +fp t26004; +fp t26893; +fp t26892; +fp t26239; +fp t26707; +fp t26654; +fp t26413; +fp t26891; +fp t26215; +fp t26567; +fp t26512; +fp t26656; +fp t26401; +fp t26890; +fp t26437; +fp t26547; +fp t25913; +fp t26579; +fp t26889; +fp t26888; +fp t25990; +fp t26887; +fp t26886; +fp t26655; +fp t26192; +fp t26642; +fp t26885; +fp t26884; +fp t26883; +fp t26882; +fp t26881; +fp t26880; +fp t26562; +fp t26551; +fp t26660; +fp t26438; +fp t26879; +fp t26028; +fp t26878; +fp t26877; +fp t26617; +fp t26876; +fp t26875; +fp t26026; +fp t26580; +fp t25928; +fp t26635; +fp t26874; +fp t26873; +fp t26404; +fp t26872; +fp t26871; +fp t25848; +fp t26869; +fp t26246; +fp t26276; +fp t26868; +fp t26867; +fp t25741; +fp t26206; +fp t26256; +fp t26648; +fp t26866; +fp t26733; +fp t25906; +fp t25927; +fp t26865; +fp t26734; +fp t26864; +fp t25260; +fp t26453; +fp t26863; +fp t25475; +fp t26463; +fp t26862; +fp t25778; +fp t25850; +fp t26861; +fp t26732; +fp t26530; +fp t26534; +fp t26556; +fp t26652; +fp t26860; +fp t26403; +fp t26859; +fp t26112; +fp t26005; +fp t26858; +fp t25486; +fp t26465; +fp t26857; +fp t25938; +fp t25350; +fp t26430; +fp t26856; +fp t26440; +fp t26855; +fp t26729; +fp t26066; +fp t26233; +fp t26485; +fp t26247; +fp t26703; +fp t26273; +fp t26715; +fp t26854; +fp t25922; +fp t26853; +fp t26110; +fp t26852; +fp t26851; +fp t26237; +fp t26274; +fp t26725; +fp t26029; +fp t26850; +fp t25920; +fp t26041; +fp t26849; +fp t26848; +fp t26565; +fp t26847; +fp t26846; +fp t26449; +fp t26845; +fp t26718; +fp t26844; +fp t26843; +fp t26841; +fp t26840; +fp t26628; +fp t26839; +fp t26077; +fp t26838; +fp t26407; +fp t26837; +fp t26836; +fp t26835; +fp t26834; +fp t26442; +fp t26833; +fp t26832; +fp t26625; +fp t26425; +fp t25925; +fp t26831; +fp t26830; +fp t26021; +fp t26829; +fp t26828; +fp t26827; +fp t26826; +fp t26825; +fp t26824; +fp t26823; +fp t26822; +fp t26821; +fp t26466; +fp t26820; +fp t26819; +fp t26533; +fp t26818; +fp t26817; +fp t26816; +fp t26815; +fp t26672; +fp t26372; +fp t26814; +fp t26068; +fp t26373; +fp t26813; +fp t26812; +fp t26811; +fp t26032; +fp t26810; +fp t26809; +fp t26808; +fp t26807; +fp t26806; +fp t26805; +fp t26804; +fp t26803; +fp t26802; +fp t26801; +fp t26800; +fp t26799; +fp t26798; +fp t26797; +fp t26439; +fp t26796; +fp t26795; +fp t26794; +fp t26793; +fp t26792; +fp t26791; +fp t26790; +fp t26789; +fp t26788; +fp t26459; +fp t26182; +fp t26713; +fp t26787; +fp t26786; +fp t26087; +fp t26785; +fp t26572; +fp t26784; +fp t26588; +fp t26783; +fp t26782; +fp t26709; +fp t26601; +fp t26081; +fp t26781; +fp t26780; +fp t26779; +fp t26778; +fp t26777; +fp t26698; +fp t26712; +fp t26776; +fp t26775; +fp t26056; +fp t26464; +fp t26774; +fp t25863; +fp t26773; +fp t26640; +fp t26033; +fp t26772; +fp t26771; +fp t26695; +fp t26653; +fp t26057; +fp t26770; +fp t26769; +fp t26768; +fp t26767; +fp t26626; +fp t26766; +fp t26765; +fp t26764; +fp t26763; +fp t26762; +fp t26761; +fp t26760; +fp t26759; +fp t25410; +fp t26758; +fp t26757; +fp t26357; +fp t26756; +fp t26644; +fp t26755; +fp t26052; +fp t26139; +fp t26067; +fp t26754; +fp t26363; +fp t26753; +fp t25471; +fp t26752; +fp t26751; +fp t26544; +fp t26386; +fp t26750; +fp t26749; +fp t26748; +fp t26747; +fp t26746; +fp t25867; +fp t26745; +fp t26744; +fp t26730; +fp t26726; +fp t26743; +fp t26742; +fp t26741; +fp t26702; +fp t26118; +fp t26121; +fp t26671; +fp t26103; +fp t26115; +fp t26607; +fp t26173; +fp t26587; +fp t26582; +fp t26545; +fp t26027; +fp t26089; +fp t26063; +fp t26082; +fp t26037; +fp t25993; +fp t25981; +fp t26446; +fp t26441; +fp t25931; +fp t26435; +fp t25846; +fp t26418; +fp t26397; +fp t26381; +fp t26380; +fp t26379; +fp t26254; +fp t26198; +fp t26197; +fp t26378; +fp t26255; +fp t26252; +fp t26377; +fp t26225; +fp t26213; +fp t26267; +fp t26376; +fp t26375; +fp t26171; +fp t26374; +fp t26371; +fp t26370; +fp t26369; +fp t26368; +fp t26367; +fp t26366; +fp t26365; +fp t26364; +fp t26360; +fp t26358; +fp t26154; +fp t26200; +fp t26355; +fp t26262; +fp t26354; +fp t26353; +fp t26352; +fp t26186; +fp t26351; +fp t26177; +fp t26350; +fp t26349; +fp t26348; +fp t26347; +fp t26346; +fp t26345; +fp t26344; +fp t26343; +fp t26342; +fp t26341; +fp t26340; +fp t26264; +fp t26265; +fp t26339; +fp t26338; +fp t26337; +fp t26336; +fp t26335; +fp t26334; +fp t26333; +fp t26332; +fp t26331; +fp t26330; +fp t26329; +fp t26328; +fp t26327; +fp t26326; +fp t26325; +fp t26324; +fp t26323; +fp t26322; +fp t26321; +fp t26320; +fp t26319; +fp t26318; +fp t26317; +fp t26316; +fp t26315; +fp t26314; +fp t26313; +fp t26312; +fp t26311; +fp t26310; +fp t26309; +fp t26308; +fp t26307; +fp t26306; +fp t26305; +fp t26304; +fp t26303; +fp t26302; +fp t26301; +fp t26300; +fp t26299; +fp t26298; +fp t26297; +fp t26296; +fp t26295; +fp t26294; +fp t26293; +fp t26292; +fp t26291; +fp t26290; +fp t26275; +fp t26251; +fp t26244; +fp t26202; +fp t26201; +fp t26174; +fp t26170; +fp t26169; + t26280 = z*z; + t26283 = z*t26280; + t26257 = RATIONAL(-2.0,9.0); + t26263 = RATIONAL(8.0,9.0); + t27110 = t26257*t26283+t26263*z; + t26194 = RATIONAL(1.0,576.0); + t26157 = RATIONAL(-1.0,3456.0); + t26281 = y*y; + t27109 = t26157+t26194*t26281; + t26279 = x*x; + t26285 = t26279*t26279; + t26242 = RATIONAL(1.0,72.0); + t26120 = t26242*t26285; + t25852 = z*t26120; + t26187 = RATIONAL(-1.0,288.0); + t26637 = t26283*t26187; + t25677 = t26285*t26637; + t27108 = t25852+t25677; + t26282 = t26279*x; + t26612 = t26282*t26281; + t26522 = z*t26612; + t26661 = t26283*t26281; + t26500 = x*t26661; + t27084 = t26500+t26522; + t26284 = t26280*t26280; + t26584 = t26194*t26284; + t26623 = t26282*t26284; + t26193 = RATIONAL(-1.0,576.0); + t25777 = t26193*t26623; + t27107 = x*t26584+t25777; + t26156 = RATIONAL(1.0,3456.0); + t27106 = t26156*t26280+t26281*t26584; + t26694 = z*t26193; + t26665 = t26194*t26285; + t27105 = t26285*t26694+t26283*t26665; + t27104 = t26157*t26280+t26156*t26284; + t27103 = t27109*t26285; + t26668 = t26283*t26285; + t25713 = t26193*t26668; + t27102 = t25713+z*t26665; + t26723 = x*t26284; + t26686 = y*t26723; + t26675 = t26282*t26280; + t26527 = y*t26675; + t27101 = t26527+t26686; + t26235 = RATIONAL(1.0,18.0); + t26629 = t26283*t26235; + t26575 = t26257*t26281; + t26497 = z*t26575; + t27100 = t26281*t26629+t26497; + t25699 = t26193*t26723; + t26728 = x*t26280; + t27099 = t25699+t26194*t26728; + t27098 = t27110*t26281; + t26208 = RATIONAL(4.0,27.0); + t26162 = RATIONAL(-16.0,27.0); + t27097 = t26282*t26208+x*t26162; + t26216 = RATIONAL(-2.0,27.0); + t26199 = RATIONAL(1.0,54.0); + t27096 = t26199*t26285+t26216*t26279; + t26621 = t26280*t26285; + t26507 = y*t26621; + t26678 = t26279*t26284; + t26479 = y*t26678; + t27095 = t26507+t26479; + t26632 = t26279*t26281; + t26400 = t26284*t26632; + t26552 = t26280*t26281; + t26394 = t26285*t26552; + t27094 = t26400+t26394; + t26234 = RATIONAL(1.0,36.0); + t25859 = t26234*t26668; + t26205 = RATIONAL(-1.0,36.0); + t26704 = z*t26205; + t25889 = t26285*t26704; + t27093 = t25889+t25859; + t26196 = RATIONAL(-1.0,72.0); + t26677 = t26284*t26196; + t25871 = x*t26677; + t26185 = RATIONAL(1.0,288.0); + t25815 = t26185*t26623; + t27092 = t25815+t25871; + t26269 = RATIONAL(-8.0,9.0); + t26150 = t26269*x; + t26217 = RATIONAL(-4.0,27.0); + t27091 = t26282*t26217+t26281*t26150; + t26155 = RATIONAL(1.0,1728.0); + t26636 = t26283*t26155; + t27090 = t26636+t26281*t26637; + t26158 = RATIONAL(-1.0,1728.0); + t26585 = t26283*t26158; + t26647 = t26185*t26281; + t27089 = t26585+t26283*t26647; + t26714 = z*t26285; + t25896 = t26196*t26714; + t26559 = t26185*t26285; + t25715 = t26283*t26559; + t27088 = t25896+t25715; + t26108 = t26235*t26285; + t26149 = t26257*t26285; + t27087 = z*t26149+t26283*t26108; + t27086 = t26156*t26285+t27109*t26279; + t26179 = RATIONAL(16.0,27.0); + t27085 = t26279*t26179+t26269*t26632+t26217*t26285; + t26245 = RATIONAL(-1.0,6.0); + t26602 = t26245*t26281; + t26167 = RATIONAL(-5.0,144.0); + t27083 = t26167*t26285+t26279*t26602; + t26203 = RATIONAL(1.0,12.0); + t26711 = y*t26203; + t26705 = y*t26285; + t26223 = RATIONAL(1.0,48.0); + t25959 = t26223*t26705; + t27082 = t26711+t25959; + t26220 = RATIONAL(1.0,96.0); + t26622 = t26220*t26284; + t26222 = RATIONAL(-1.0,96.0); + t27081 = x*t26622+t26222*t26623; + t26260 = RATIONAL(4.0,3.0); + t26596 = t26281*t26260; + t26266 = RATIONAL(-1.0,3.0); + t26560 = t26266*t26281; + t27080 = x*t26596+t26282*t26560; + t26218 = RATIONAL(5.0,96.0); + t26699 = y*t26280; + t26504 = t26218*t26699; + t26230 = RATIONAL(-1.0,24.0); + t26724 = y*t26230; + t27079 = t26504+t26724; + t26166 = RATIONAL(1.0,864.0); + t26606 = t26234*t26279; + t27078 = t26281*t26606+t26166*t26285; + t26219 = RATIONAL(2.0,27.0); + t26249 = RATIONAL(-1.0,9.0); + t26131 = t26249*x; + t27077 = t26281*t26131+x*t26219; + t26232 = RATIONAL(1.0,24.0); + t26578 = t26232*t26281; + t26229 = RATIONAL(5.0,36.0); + t27076 = t26229*t26280+t26284*t26578; + t26259 = RATIONAL(-4.0,3.0); + t26633 = t26259*t26281; + t26261 = RATIONAL(1.0,3.0); + t26570 = t26261*t26281; + t27075 = x*t26633+t26282*t26570; + t27074 = t26282*t26622+t26222*t26723; + t26241 = RATIONAL(-5.0,72.0); + t26168 = RATIONAL(5.0,288.0); + t26550 = t26282*t26168; + t27073 = x*t26241+t26550; + t26240 = RATIONAL(-5.0,18.0); + t26238 = RATIONAL(10.0,9.0); + t27072 = t26240*t26282+x*t26238; + t26227 = RATIONAL(-5.0,48.0); + t27071 = t26711+t26227*t26699; + t26258 = RATIONAL(-5.0,3.0); + t26231 = RATIONAL(-5.0,12.0); + t27070 = t26258+t26231*t26284; + t26190 = RATIONAL(-1.0,144.0); + t26180 = RATIONAL(-1.0,216.0); + t27069 = t26180*t26285+t26190*t26632; + t25957 = t26196*t26621; + t26100 = t26187*t26284; + t26473 = y*t26100; + t27068 = y*t25957+t26279*t26473; + t26700 = x*t26234; + t25954 = t26284*t26700; + t26189 = RATIONAL(1.0,144.0); + t26095 = t26189*t26282; + t26517 = y*t26095; + t27067 = y*t25954+t26280*t26517; + t27066 = t26632+t26552; + t27065 = t26158*t26678+t26242*t26394; + t26514 = y*t26629; + t25447 = x*t26514; + t26106 = t26242*t26282; + t26739 = y*z; + t27064 = t25447+t26106*t26739; + t26123 = t26196*t26283; + t26508 = y*t26123; + t26900 = t26285*t26508+t26279*t26514; + t26204 = RATIONAL(-1.0,18.0); + t26117 = t26204*t26279; + t27063 = t26117*t26739+t26900; + t26696 = y*t26204; + t26687 = z*t26696; + t25203 = t26282*t26687; + t27062 = t25203+x*t26508; + t25948 = t26279*t26677; + t26098 = t26187*t26285; + t26476 = y*t26098; + t27061 = t26280*t26476+y*t25948; + t26101 = t26189*t26283; + t26478 = x*t26101; + t25043 = y*t26478; + t26737 = z*t26282; + t26519 = t26234*t26737; + t27060 = t25043+y*t26519; + t26119 = t26235*x; + t26539 = t26280*t26119; + t26515 = y*t26623; + t26910 = t26242*t26515+t26204*t26527; + t27059 = y*t26539+t26910; + t26124 = t26235*z; + t26679 = y*t26124; + t26109 = t26242*t26283; + t26444 = t26285*t26109; + t26554 = t26283*t26204; + t26405 = t26279*t26554; + t26952 = (t26444+t26405)*y; + t27058 = t26279*t26679+t26952; + t26646 = t26283*t26279; + t26536 = y*t26646; + t27057 = t26190*t26536+y*t25889; + t26645 = t26205*t26284; + t26467 = y*t26645; + t27056 = t26190*t26527+x*t26467; + t26740 = y*x; + t26555 = t26283*t26205; + t26102 = t26190*t26282; + t26513 = z*t26102; + t25118 = y*t26513; + t27055 = t26555*t26740+t25118; + t26481 = t26187*t26699; + t26942 = t26282*t26481+y*t25815; + t26471 = t26242*t26699; + t27054 = x*t26471+t26942; + t26191 = RATIONAL(-5.0,576.0); + t27053 = t26191*t26285+t26222*t26632; + t26468 = t26234*t26699; + t27052 = t26282*t26468+t26189*t26686; + t26093 = t26190*t26283; + t25065 = t26093*t26740; + t26484 = t26282*t26704; + t27051 = t25065+y*t26484; + t26385 = t26279*t26555; + t26610 = t26190*t26285; + t26491 = y*t26610; + t27050 = z*t26491+y*t26385; + t26535 = y*t26637; + t26923 = y*t25715+t26279*t26535; + t26693 = z*t26279; + t26683 = y*t26693; + t27049 = t26242*t26683+t26923; + t26489 = t26205*t26699; + t27048 = t26190*t26479+t26285*t26489; + t27047 = t26234*t26479+t26189*t26507; + t27046 = t26185*t26479+t26285*t26471; + t26605 = t26282*t26235; + t26470 = z*t26605; + t25243 = y*t26470; + t27045 = t26109*t26740+t25243; + t26207 = RATIONAL(1.0,27.0); + t26663 = t26284*t26207; + t27044 = t26279*t26663+t26196*t26394; + t26597 = t26222*t26285; + t27043 = t26191*t26279+t26281*t26597; + t26615 = t26158*t26280; + t26122 = t26242*t26284; + t26387 = t26279*t26122; + t27042 = t26281*t26387+t26285*t26615; + t27041 = t26189*t26479+t26285*t26468; + t26697 = y*t26196; + t25749 = t26282*t26100; + t26692 = y*t26185; + t26523 = t26282*t26692; + t26948 = t26280*t26523+y*t25749; + t27040 = t26697*t26728+t26948; + t26094 = t26189*z; + t26524 = t26285*t26094; + t26722 = t26283*y; + t26474 = t26234*t26722; + t27039 = y*t26524+t26279*t26474; + t25381 = t26554*t26740; + t26116 = t26196*t26282; + t26501 = y*t26116; + t27038 = t25381+z*t26501; + t27037 = t26279*t26467+t26280*t26491; + t26505 = t26283*t26692; + t26949 = t26279*t26505+y*t25677; + t26475 = t26279*t26697; + t27036 = t26949+z*t26475; + t26097 = t26190*x; + t26531 = t26284*t26097; + t27035 = y*t26531+t26282*t26489; + t25134 = z*t26517; + t27034 = x*t26474+t25134; + t26164 = RATIONAL(1.0,432.0); + t26576 = t26284*t26285; + t26451 = t26279*t26552; + t27033 = t26187*t26451+t26164*t26576; + t27032 = t26185*t26507+y*t26387; + t26104 = t26204*t26280; + t26525 = x*t26104; + t26934 = t26235*t26527+t26284*t26501; + t27031 = y*t26525+t26934; + t25978 = t26234*t26714; + t26416 = t26279*t26101; + t27030 = (t26416+t25978)*y; + t26680 = x*t26692; + t27029 = x*t26481+t26284*t26680+t26948; + t26738 = x*z; + t26543 = t26283*t26282; + t26490 = y*t26543; + t25242 = t26196*t26490; + t27028 = t26257*y*t26738+t25447+t25243+t25242; + t26175 = RATIONAL(1.0,108.0); + t26592 = t26279*t26175; + t26917 = t26284*t26592+t26204*t26394; + t26165 = RATIONAL(-1.0,432.0); + t26549 = t26284*t26165; + t26277 = RATIONAL(2.0,9.0); + t26649 = t26279*t26277; + t26390 = t26280*t26649; + t27027 = t26917+t26285*t26549+t26281*t26390; + t26099 = t26185*t26280; + t27026 = t26942+t26099*t26740+x*t26473; + t26391 = t26189*t26543; + t25114 = y*t26391; + t27025 = t25065+t26094*t26740+t25118+t25114; + t27024 = t26187*t26683+t26559*t26739+t26949; + t26096 = t26185*t26279; + t27023 = t26096*t26739+t26923+z*t26476; + t26493 = t26285*t26696; + t27022 = z*t26493+t26649*t26739+t26952; + t26410 = t26190*t26543; + t25140 = y*t26410; + t27021 = t25134+t26097*t26739+t25043+t25140; + t26420 = t26242*t26543; + t25403 = y*t26420; + t26690 = x*t26277; + t27020 = t25203+t25403+t25381+t26690*t26739; + t26532 = t26280*t26690; + t26107 = t26204*x; + t26520 = t26284*t26107; + t27019 = t26910+(t26532+t26520)*y; + t27018 = t26108*t26739+t26257*t26683+t26900; + t26599 = t26285*t26207; + t27017 = t26917+t26196*t26400+t26280*t26599; + t26486 = t26257*t26699; + t26105 = t26235*t26284; + t27016 = x*t26486+t26934+t26105*t26740; + t26091 = t26189*x; + t26538 = t26281*t26091; + t26415 = t26190*t26623; + t26659 = t26180*t26280; + t26163 = RATIONAL(1.0,216.0); + t26568 = t26163*t26280; + t27015 = t26282*t26659+x*t26568+t26284*t26538+t26281*t26415; + t26482 = y*t26576; + t27014 = t26279*t26486+t26196*t26482+t27095*t26235; + t26684 = t26187*t26739; + t27013 = t26185*t26490+x*t26535+t26282*t26684+z*t26680; + t26409 = t26281*t26555; + t25462 = x*t26409; + t26641 = t26283*t26163; + t27012 = t25462+x*t26641+t26281*t26513+t26166*t26737; + t26710 = x*t26180; + t26384 = t26282*t26552; + t26542 = x*t26552; + t26620 = t26163*t26282; + t27011 = t26190*t26542+t26189*t26384+(t26710+t26620)*t26284; + t26480 = t26193*t26699; + t27010 = t26279*t26480+t26193*t26482+t27095*t26194; + t26133 = t26249*t26282; + t26487 = z*t26133; + t26127 = t26249*t26283; + t26494 = x*t26127; + t26278 = RATIONAL(4.0,9.0); + t26688 = t26278*t26740; + t27009 = z*t26688+t26282*t26474+(t26494+t26487)*y; + t26638 = t26234*t26281; + t26503 = x*t26638; + t26195 = RATIONAL(-1.0,864.0); + t26574 = t26282*t26195; + t27008 = t26284*t26574+t26205*t26384+t26166*t26723+t26280*t26503; + t26210 = RATIONAL(-1.0,27.0); + t26706 = x*t26210; + t27007 = t26175*t26623+t26284*t26706+t26242*t26384+t26281*t26525; + t26685 = z*t26705; + t26250 = RATIONAL(1.0,9.0); + t25960 = t26285*t26555; + t26272 = RATIONAL(-4.0,9.0); + t26682 = t26272*t26739; + t26125 = t26250*t26283; + t26436 = t26279*t26125; + t27006 = t26279*t26682+t26250*t26685+(t26436+t25960)*y; + t26389 = t26205*t26543; + t26488 = x*t26125; + t26129 = t26250*t26282; + t27005 = x*t26682+t26129*t26739+(t26389+t26488)*y; + t25445 = t26234*t26500; + t27004 = t25445+z*t26574+t26189*t26522+t26283*t26710; + t26492 = t26281*t26704; + t26689 = x*t26163; + t27003 = x*t26492+t26281*t26410+z*t26689+t26166*t26543; + t26664 = t26281*t26285; + t26540 = z*t26664; + t26176 = RATIONAL(-1.0,108.0); + t26630 = t26283*t26176; + t26558 = t26196*t26281; + t26398 = t26283*t26558; + t27002 = t26235*t26540+t26279*t26630+t26207*t26693+t26285*t26398; + t25963 = t26242*t26576; + t27001 = t26280*t26493+t26204*t26479+(t26390+t25963)*y; + t26561 = t26279*t26249; + t26472 = y*t26561; + t26676 = t26279*t26280; + t26528 = y*t26676; + t27000 = t26284*t26472+t26278*t26528+t26234*t26482+t26249*t26507; + t26999 = t26195*t26543+t26281*t26391+(t26710+t26503)*z; + t26998 = t26234*t26384+t26166*t26623+t26195*t26723+t26205*t26542; + t26152 = RATIONAL(-1.0,1152.0); + t26161 = RATIONAL(1.0,1152.0); + t26546 = t26279*t26161; + t26447 = t26280*t26546; + t26997 = y*t26447+t26161*t26482+t27095*t26152; + t25639 = t26284*t26546; + t25660 = t26161*t26621; + t25661 = t26152*t26576; + t26996 = t26152*t26528+(t25639+t25660+t25661)*y; + t26995 = x*t26480+t26194*t26527+t27107*y; + t26516 = t26272*t26699; + t25849 = t26205*t26623; + t26994 = y*t25849+x*t26516+t27101*t26250; + t25693 = t26282*t26584; + t26993 = t26282*t26480+(t25693+t27099)*y; + t26992 = z*t26523+t26187*t26490+(t26684+t26505)*x; + t26670 = t26284*t26281; + t26399 = t26242*t26670; + t26616 = t26280*t26175; + t26991 = t26280*t26706+t26281*t26520+(t26616+t26399)*t26282; + t26423 = t26189*t26623; + t26990 = t26282*t26568+x*t26659+(t26423+t26531)*t26281; + t26020 = t26234*t26623; + t26989 = t26280*t26688+y*t26020+t27101*t26249; + t26988 = t26194*t26536+t26193*t26683+t27102*y; + t26987 = t26279*t26516+t26285*t26467+t27095*t26250; + t26650 = t26279*t26210; + t26986 = t26204*t26540+z*t26650+t26283*t26592+t26281*t26444; + t26424 = t26235*t26670; + t26673 = t26176*t26282; + t26388 = t26282*t26558; + t26701 = x*t26207; + t26985 = t26284*t26388+x*t26424+(t26673+t26701)*t26280; + t26573 = t26176*t26284; + t26984 = t26196*t26384+t26282*t26573+x*t26663+t26281*t26539; + t26983 = t26285*t26480+t26193*t26479+(t26482+t26528)*t26194; + t26982 = t26284*t26689+t26180*t26623+t26190*t26384+t26280*t26538; + t26448 = t26193*t26646; + t26981 = t26194*t26683+(t26448+t27105)*y; + t26980 = t26283*t26472+t26249*t26685+y*t25859+t26278*t26683; + t26919 = t26285*t26399+t26280*t26650; + t26936 = t26204*t26400+t26285*t26616; + t26870 = t26919+t26936; + t26359 = t26870+t26991; + t26979 = t26175*t26723+t26281*t26532+t26204*t26384+t26282*t26549+t26359; + t26361 = t26870+t26985; + t26499 = x*t26575; + t26618 = t26164*t26284; + t26978 = t26361+x*t26573+t26282*t26618+t26280*t26499+t26235*t26384; + t26593 = t26282*t26219; + t26212 = RATIONAL(-1.0,54.0); + t26938 = t26285*t26573+t26235*t26451; + t26604 = t26250*t26281; + t26496 = x*t26604; + t26432 = t26281*t26543; + t26735 = x*t26216; + t26842 = t26212*t26543+t26234*t26432+t26938+(t26735+t26496)*z; + t26736 = x*t26283; + t26977 = t25462+z*t26593+t26842+t26919+t26281*t26487+t26199*t26736; + t26498 = z*t26604; + t26586 = t26283*t26212; + t26674 = t26282*t26216; + t26356 = t26199*t26543+t26938+t26281*t26389+t26919+t27077*z; + t26976 = t26282*t26498+t25445+t26356+x*t26586+z*t26674; + t26708 = z*t26175; + t26624 = t26283*t26175; + t26450 = t26282*t26708+x*t26624+t26281*t26420; + t26731 = x*t26281; + t26681 = z*t26731; + t26412 = t26281*t26554; + t26428 = t26204*t26612; + t26975 = t26165*t26543+t26450+t26277*t26681+x*t26412+(t26428+t26706)*z; + t26462 = t26283*t26388+z*t26673+x*t26630; + t26974 = t26175*t26543+t26558*t26738+x*t26708+t26462+t27084*t26242; + t26973 = t26164*t26543+t26281*t26470+t26462+z*t26701+t27100*x; + t26541 = t26242*t26731; + t26972 = t26450+x*t26398+(t26738+t26543)*t26176+(t26541+t26388)*z; + t26395 = t26196*t26552; + t26426 = t26187*t26612; + t26639 = t26164*t26280; + t26971 = t26185*t26384+t26282*t26615+t26284*t26426+t26155*t26623+(t26399+ +t26395+t26549+t26639)*x; + t26970 = t26210*t26668+t26162*t26693+t27087*t26281+t27098*t26279+(t26646+ +t26714)*t26208; + t26716 = x*t26208; + t26969 = t26210*t26623+t26257*t26384+t26263*t26542+t26282*t26424+t27097* +t26280+(t26716+t26499)*t26284; + t26452 = t26281*t26561; + t26643 = t26283*t26219; + t26968 = t26285*t26586+t26283*t26452+t27093*t26281+(t26643+t26498)*t26279 ++t27096*z; + t26402 = t26281*t26576; + t26967 = t26161*t26402+t26281*t26447+(t26576+t26676)*RATIONAL(-1.0,6912.0 +)+(t26621+t26678)*RATIONAL(1.0,6912.0)+t27094*t26152; + t26966 = t26193*t26384+t26157*t26623+t27099*t26281+t27106*t26282+t27104*x +; + t26965 = t26285*t26409+t26219*t26693+t26212*t26714+z*t26452+(t26436+ +t25978)*t26281+t27096*t26283; + t26483 = t26281*t26694; + t26964 = t26281*t25713+t26279*t26483+t26156*t26693+t27103*z+t27086*t26283 +; + t26963 = x*t26618+t26155*t26675+t26165*t26728+t26158*t26623+t26187*t26384 ++t26280*t26541+t27092*t26281; + t26590 = t26279*t26217; + t26962 = t26207*t26576+t26284*t26590+t26204*t26402+t27094*t26277+t27085* +t26280; + t26564 = t26285*t26165; + t26510 = z*t26632; + t26961 = t26196*t26510+z*t26564+t26164*t26693+t26285*t26636+t27108*t26281 ++t27089*t26279; + t26960 = t26285*t26483+t26156*t26646+t26281*t26448+t27103*t26283+t27086*z +; + t26408 = t26242*t26632; + t26959 = z*t26408+t26165*t26693+t26285*t26585+t26164*t26714+t27088*t26281 ++t27090*t26279; + t26958 = t26194*t26384+t26157*t26723+t26281*t25777+t26193*t26542+t27104* +t26282+t27106*x; + t26720 = x*t26217; + t26548 = t26284*t26277; + t26053 = x*t26548; + t26957 = t26207*t26623+t26277*t26384+t26281*t26053+t26179*t26728+t27091* +t26280+(t26720+t26428)*t26284; + t26956 = t26210*t26714+t26285*t26624+t26283*t26408+t26204*t26510+t27002; + t26406 = t26277*t26632; + t26614 = t26285*t26277; + t26090 = z*t26614; + t26955 = t26285*t26412+t26281*t26090+t27085*z+(t26590+t26599+t26406)* +t26283; + t26583 = t26176*t26285; + t26954 = t26279*t26398+t26283*t26583+z*t26599+t26235*t26510+t26986; + t26953 = t26700*t26739+t25114; + t26228 = RATIONAL(5.0,12.0); + t26521 = t26228*t26699; + t26951 = t26223*t26482+t26279*t26521; + t26253 = RATIONAL(5.0,3.0); + t26431 = t26253*t26632; + t26950 = t26280*t26431+t26204*t26576; + t26611 = t26241*t26279; + t26947 = t26223*t26394+t26284*t26611; + t26236 = RATIONAL(-10.0,9.0); + t26608 = t26236*t26280; + t26946 = t26279*t26608+t26203*t26402; + t25680 = t26284*t26559; + t26419 = t26231*t26632; + t26945 = t26280*t26419+t25680; + t26178 = RATIONAL(-1.0,192.0); + t25737 = t26178*t26576; + t26183 = RATIONAL(-5.0,192.0); + t26944 = t26183*t26528+y*t25737; + t26943 = y*t26423+x*t26468; + t26941 = t26189*t26482+t26279*t26468; + t26443 = t26285*t26101; + t26940 = t26606*t26739+y*t26443; + t26939 = t26279*t26549+t26185*t26394; + t26181 = RATIONAL(5.0,192.0); + t26658 = t26279*t26181; + t26392 = t26280*t26658; + t26933 = t25661+t26281*t26392; + t26932 = t26220*t26482+t26279*t26504; + t26268 = RATIONAL(-5.0,6.0); + t26509 = t26268*t26699; + t26931 = t26230*t26482+t26279*t26509; + t26243 = RATIONAL(5.0,18.0); + t26557 = t26243*t26279; + t26930 = t26266*t26394+t26284*t26557; + t26929 = t26227*t26451+t25963; + t26248 = RATIONAL(-5.0,2.0); + t26224 = RATIONAL(5.0,48.0); + t26928 = t26224*t26576+t26248*t26451; + t26927 = t26280*t26564+t26185*t26400; + t26214 = RATIONAL(5.0,32.0); + t26926 = t26183*t26576+t26214*t26451; + t26925 = y*t26415+x*t26489; + t26188 = RATIONAL(-5.0,288.0); + t26594 = t26284*t26188; + t25965 = t26203*t26552; + t26924 = t26279*t26594+t26285*t25965; + t26922 = t26241*t26621+t26223*t26400; + t26209 = RATIONAL(1.0,32.0); + t26920 = t26209*t26402+RATIONAL(-25.0,192.0)*t26676; + t26727 = y*t26279; + t26221 = RATIONAL(-5.0,96.0); + t26506 = t26221*t26727; + t26918 = t26222*t26482+t26280*t26506; + t26916 = t25403+x*t26679; + t26184 = RATIONAL(1.0,192.0); + t26915 = t26184*t26482+y*t26392; + t26270 = RATIONAL(5.0,6.0); + t26526 = t26270*t26699; + t26914 = t26279*t26526+t26232*t26482; + t26913 = t26279*t26471+y*t25680; + t26912 = t26283*t26491+t26205*t26683; + t26151 = RATIONAL(5.0,1152.0); + t26911 = t26178*t26400+t26151*t26621; + t26909 = t25140+t26704*t26740; + t26226 = RATIONAL(-1.0,48.0); + t26495 = t26231*t26699; + t26907 = t26226*t26482+t26279*t26495; + t26906 = t26285*t26473+t26280*t26475; + t26905 = t26187*t26402+t26279*t26639; + t26172 = RATIONAL(25.0,12.0); + t26581 = t26172*t26280; + t26271 = RATIONAL(-1.0,8.0); + t26904 = t26271*t26402+t26279*t26581; + t26903 = x*t26687+t25242; + t26902 = t26155*t26576+t26279*t26395; + t26901 = t26279*t26489+t26190*t26482; + t25857 = t26203*t26632; + t26899 = t26284*t25857+t26188*t26621; + t26160 = RATIONAL(-5.0,1152.0); + t26898 = t26184*t26402+t26160*t26676; + t26211 = RATIONAL(-1.0,12.0); + t26598 = t26211*t26282; + t26897 = t26226*t26515+t26224*t26527+y*t26598; + t26111 = t26224*t26279; + t26456 = t26283*t26111; + t26114 = t26226*t26285; + t26422 = t26283*t26114; + t26896 = t26211*t26722+(t26422+t26456)*y; + t26631 = t26227*t26279; + t26455 = t26283*t26631; + t26895 = y*t26455+t27082*t26283; + t26894 = t26223*t26515+t27071*t26282; + t25974 = t26211*t26670; + t26589 = t26223*t26284; + t26004 = t26281*t26589; + t26893 = t26282*t26004+x*t25974+t27073*t26280; + t26892 = t26903+t26941; + t26239 = RATIONAL(-5.0,36.0); + t26707 = x*t26239; + t26654 = t26230*t26284; + t26413 = t26281*t26654; + t26891 = x*t26413+t26280*t26707+t27076*t26282; + t26215 = RATIONAL(5.0,72.0); + t26567 = t26284*t26203; + t26512 = x*t26567; + t26656 = t26226*t26281; + t26401 = t26284*t26656; + t26890 = t26281*t26512+t26215*t26728+t26188*t26675+t26282*t26401; + t26437 = t26230*t26664; + t26547 = t26232*t26283; + t25913 = t26281*t26547; + t26579 = t26229*t26279; + t26889 = z*t26437+t26283*t26579+t26239*t26693+t26285*t25913; + t26888 = t26160*t26576+t26184*t26451+t26911; + t25990 = z*t26578; + t26887 = t26283*t26437+t26285*t25990+t26239*t26646+z*t26579; + t26886 = t26899+t26947; + t26655 = t26191*t26280; + t26192 = RATIONAL(5.0,576.0); + t26642 = t26192*t26280; + t26885 = x*t26642+t26282*t26655+t27081*t26281; + t26884 = t26913+t26953; + t26883 = t26906+t26909; + t26882 = t26901+t26903; + t26881 = t26901+t26916; + t26880 = t26916+t26941; + t26562 = t26283*t26188; + t26551 = t26215*t26279; + t26660 = t26203*t26281; + t26438 = t26285*t26660; + t26879 = t26281*t26422+t26279*t26562+(t26438+t26551)*z; + t26028 = z*t26560; + t26878 = t26285*t26028+t26236*t26693+(t26557+t26438)*t26283; + t26877 = t26282*t26642+x*t26655+t27074*t26281; + t26617 = t26282*t26239; + t26876 = t26282*t26413+t26280*t26617+t27076*x; + t26875 = t26906+t26953; + t26026 = t26285*t26570; + t26580 = t26211*t26285; + t25928 = t26281*t26580; + t26635 = t26283*t26240; + t26874 = t26238*t26693+t26283*t25928+z*t26026+t26279*t26635; + t26873 = t26909+t26913; + t26404 = t26260*t26552; + t26872 = t26241*t26576+t26279*t26404+t26930; + t26871 = t26922+t26924; + t25848 = t26223*t26664; + t26869 = t26283*t25848+t26168*t26646+(t26611+t25928)*z; + t26246 = RATIONAL(5.0,8.0); + t26276 = RATIONAL(-1.0,2.0); + t26868 = t26246*t26394+t26276*t26664+t27070*t26279; + t26867 = t26905+t26927; + t25741 = t26284*t26658; + t26206 = RATIONAL(-5.0,32.0); + t26256 = RATIONAL(1.0,8.0); + t26648 = t26256*t26285; + t26866 = t25741+t26281*t26648+t26111+t26206*t26394; + t26733 = t26211*y; + t25906 = t26284*t26733; + t25927 = t26203*t26705; + t26865 = t25906+t26280*t25927+t26261*t26699+t26224*t26479+t26907; + t26734 = y*t26261; + t26864 = t26231*t26683+t26896+(t26734+t25927)*z; + t25260 = y*t25852; + t26453 = t25260+t26925; + t26863 = t26453+t27036+t27052; + t25475 = y*t25871; + t26463 = t25475+t26912; + t26862 = t26463+t27039+t27054; + t25778 = t26181*t26621; + t25850 = y*t26114; + t26861 = t25850+y*t25778+t26184*t26479+t26223*t26727+t26944; + t26732 = t26232*y; + t26530 = t26218*t26727; + t26534 = y*t26668; + t26556 = t26220*t26285; + t26652 = t26283*t26230; + t26860 = y*t26652+t26556*t26739+t26222*t26534+t26283*t26530+(t26732+ +t26506)*z; + t26403 = t25475+t26940; + t26859 = t26403+t27050+t27054; + t26112 = t26226*t26284; + t26005 = y*t26112; + t26858 = t26223*t26699+t26184*t26507+t26005+y*t25741+t26944; + t25486 = y*t25896; + t26465 = t25486+t26943; + t26857 = t26465+t27035+t27049; + t25938 = x*t26122; + t25350 = y*t25938; + t26430 = t25350+t26940; + t26856 = t26430+t27031+t27057; + t26440 = t26281*t26610; + t26855 = t26180*t26646+t26163*t26693+t26281*t26524+t26283*t26440+t26939; + t26729 = y*t26245; + t26066 = t26284*t26729; + t26233 = RATIONAL(-5.0,24.0); + t26485 = t26233*t26699; + t26247 = RATIONAL(1.0,6.0); + t26703 = t26247*y; + t26273 = RATIONAL(-2.0,3.0); + t26715 = y*t26273; + t26854 = t26232*t26515+(t26485+t26703)*t26282+(t26066+t26526+t26715)*x; + t25922 = y*t26580; + t26853 = y*t26567+t26280*t25922+t26266*t26699+t26227*t26479+t26951; + t26110 = t26224*t26280; + t26852 = t26110*t26740+t26894+(t26733+t26005)*x; + t26851 = t26463+t27030+t27059; + t26237 = RATIONAL(5.0,24.0); + t26274 = RATIONAL(2.0,3.0); + t26725 = y*t26274; + t26029 = t26245*t26705; + t26850 = t26247*t26479+t26237*t26507+t26029+t26279*t26725+t26931; + t25920 = t26230*t26705; + t26041 = t26285*t26703; + t26849 = t26237*t26536+t26283*t25920+t26245*t26722+t26268*t26683+(t26041+ +t26725)*z; + t26848 = t26220*t26479+t25920+t26232*t26727+t26285*t26504+t26918; + t26565 = t26261*t26279; + t26847 = t25922+t26203*t26479+y*t26565+t26224*t26507+t26907; + t26846 = t26280*t26041+t26066+t26237*t26479+t26274*t26699+t26931; + t26449 = t25350+t26912; + t26845 = t26449+t27039+t27040; + t26718 = y*t26266; + t26844 = t26894+(t25906+t26718+t26521)*x; + t26843 = t26403+t27057+t27059; + t26841 = t26245*t26479+t26285*t26485+t26041+t26279*t26715+t26914; + t26840 = t26284*t26732+t26230*t26699+t26221*t26479+t26222*t26507+t26932; + t26628 = t26226*t26279; + t26839 = t26178*t26479+y*t26628+t26183*t26507+t25959+t26915; + t26077 = t26284*t26703; + t26838 = t26233*t26479+t26273*t26699+t26077+t26280*t26029+t26914; + t26407 = t25486+t26925; + t26837 = t26407+t27058+t27067; + t26836 = t26230*t26515+t26237*t26527+t26282*t26729+(t26725+t26509+t26077) +*x; + t26835 = t26111*t26739+t26895+(t26733+t25850)*z; + t26834 = t26465+t27056+t27058; + t26442 = t26221*t26646; + t26833 = t26220*t26534+t26597*t26739+(t26724+t26530)*z+(t26547+t26442)*y; + t26832 = t26282*t26732+t26221*t26527+t27074*y+t27079*x; + t26625 = t26247*t26283; + t26425 = t26233*t26646; + t25925 = t26232*t26705; + t26831 = t26270*t26683+t26283*t25925+(t26029+t26715)*z+(t26425+t26625)*y; + t26830 = t26407+t27049+t27052; + t26021 = y*t26589; + t26829 = t26178*t26507+t26183*t26479+t26021+t26226*t26699+t26915; + t26828 = t26220*t26507+t26218*t26479+y*t26654+t26232*t26699+t26918; + t26827 = t26453+t27063+t27067; + t26826 = t26902+t26999; + t26825 = t26222*t26479+t26279*t26724+t25925+t26221*t26507+t26932; + t26824 = y*t26512+t26897+(t26495+t26734)*x; + t26823 = t26430+t27040+t27050; + t26822 = t26228*t26683+t26895+(t26718+t25922)*z; + t26821 = t26897+(t26021+t27071)*x; + t26466 = t25260+t26943; + t26820 = t26466+t27035+t27036; + t26819 = t26211*t26479+t26227*t26507+t26279*t26718+t25927+t26951; + t26533 = t26221*t26728; + t26818 = x*t26732+t27079*t26282+(t26533+t27081)*y; + t26817 = t26631*t26739+t26896+t27082*z; + t26816 = t26449+t27030+t27031; + t26815 = t26466+t27056+t27063; + t26672 = t26280*t26551+t26285*t26401; + t26372 = t25974+t26104+t25957+t26224*t26400+t26672; + t26814 = t26372+t26105+t25965+t26929+t26947; + t26068 = t26281*t26565; + t26373 = t26224*t26394+t25948+t25928+t26117+t26672; + t26813 = t26068+t26373+t26120+t26899+t26945; + t26812 = t26122+t26372+t26261*t26552+t26924+t26945; + t26811 = t26108+t26373+t25857+t26922+t26929; + t26032 = t26259*t26632; + t26810 = t26026+t26231*t26394+t26032+t26149+t26950+(t26263+t26548)*t26279 +; + t26809 = t26995+t27013; + t26808 = t26993+t26997; + t26807 = t26892+t27037+t27064; + t26806 = t26988+t26992; + t26805 = t26883+t27032+t27034; + t26804 = t26880+t27037+t27038; + t26803 = t26875+t27046+t27051; + t26802 = t26882+t27041+t27045; + t26801 = t27000+t27005; + t26800 = t26881+t27038+t27047; + t26799 = t26882+t27047+t27064; + t26798 = t27024+t27025; + t26797 = t26993+t26996; + t26439 = t26211*t26552; + t26796 = t26223*t26384+x*t26439+t26890+t27073*t26284; + t26795 = t25660+t26100+t26004+t26183*t26400+t26099+t26226*t26552+t26933; + t26794 = t26987+t27005; + t26793 = t26980+t26989; + t26792 = t26873+t27060+t27068; + t26791 = t27001+t27020; + t26790 = t26884+t27055+t27061; + t26789 = t27014+t27016; + t26788 = t27006+t27009; + t26459 = t26247*t26632; + t26182 = RATIONAL(5.0,144.0); + t26713 = z*t26182; + t26787 = t26889+z*t26459+t26285*t26713+t27083*t26283; + t26786 = t27019+t27022; + t26087 = t26283*t26570; + t26785 = t26215*t26543+t26211*t26432+(t26635+t26087)*x+(t27072+t27075)*z; + t26572 = t26215*t26285; + t26784 = t26874+z*t26032+t26240*t26714+(t26572+t26068)*t26283; + t26588 = t26192*t26284; + t26783 = t26191*t26623+x*t26588+t26222*t26384+t26220*t26542+t26877; + t26782 = t26880+t27048+t27062; + t26709 = x*t26167; + t26601 = t26284*t26182; + t26081 = x*t26602; + t26781 = t26247*t26384+t26282*t26601+t26280*t26081+t26284*t26709+t26876; + t26780 = t26873+t27034+t27061; + t26779 = t27018+t27028; + t26778 = t26881+t27041+t27062; + t26777 = t26226*t26384+x*t25965+t26282*t26594+t26215*t26723+t26893; + t26698 = z*t26188; + t26712 = x*t26168; + t26776 = z*t26550+x*t26698+t26283*t26712+t26188*t26543+(t26432+t26681)* +t26223+t27084*t26226; + t26775 = t26883+t27046+t27060; + t26056 = z*t26596; + t26464 = t26283*t26632; + t26774 = t26279*t26056+t26243*t26714+t26241*t26668+t26266*t26464+t26878; + t25863 = t26281*t26628; + t26773 = t26285*t26562+t26283*t25863+t26869+(t26572+t25857)*z; + t26640 = t26247*t26281; + t26033 = x*t26640; + t26772 = t26280*t26033+x*t26601+t26245*t26384+t26167*t26623+t26891; + t26771 = t26875+t27032+t27055; + t26695 = x*t26243; + t26653 = t26282*t26243; + t26057 = t26283*t26560; + t26770 = x*t26057+t26283*t26695+t26241*t26543+t26236*t26738+t26203*t26432 ++(t26653+t27080)*z; + t26769 = t26223*t26464+t26168*t26668+t26241*t26714+t26211*t26510+t26879; + t26768 = t26892+t27045+t27048; + t26767 = t27023+t27026; + t26626 = t26283*t26182; + t26766 = t26283*t26459+t26285*t26626+t26887+t27083*z; + t26765 = t27010+t27021; + t26764 = x*t26562+t26282*t26698+t26656*t26738+t26226*t26432+t26168*t26543 ++z*t26712+t27084*t26223; + t26763 = t26884+t27051+t27068; + t26762 = t26980+t26994; + t26761 = t26220*t26384+t26282*t26588+t26191*t26723+t26222*t26542+t26885; + t26760 = t26983+t27029; + t26759 = t26981+t26992; + t25410 = t26281*t26519; + t26758 = t26212*t26737+t26283*t26735+t26356+t26281*t26488+t25410+t26936+ +t27044; + t26757 = t25863+t25639+t26098+t26898+t26933+t26183*t26394+t25848+t26096+ +t26911; + t26357 = z*t26440+t26180*t26693+t26279*t26641+t26281*t26443+t26905+t26939 +; + t26756 = t26357+t26189*t26510+t26163*t26714+t26927+t27033+t27069*t26283; + t26644 = t26283*t26195; + t26755 = t26281*t26385+t26902+t26285*t26644+t26357+t27042+t27078*z; + t26052 = t26259*t26552; + t26139 = t26257*t26284; + t26067 = t26284*t26570; + t26754 = t26946+t26052+t26231*t26400+t26930+t26950+t26139+t26067+(t26614+ +t26263)*t26280; + t26363 = t26902+t26905+t27003; + t26753 = t26363+x*t26644+t26281*t26478+t26180*t26737+t25410+t26927+t27065 +; + t25471 = t26281*t26484; + t26752 = t26190*t26500+t25471+t26166*t26736+z*t26620+t26826+t27065; + t26751 = z*t26406+t26285*t26708+t26281*t26405+t26283*t26564+t26986+t27027 +; + t26544 = t26199*t26284; + t26386 = t26284*t26638; + t26750 = t26250*t26384+t26282*t26544+t26281*t25849+x*t26386+t26212*t26723 ++t27017+(t26674+t27077)*t26280; + t26749 = t26855+t26279*t26492+t26195*t26714+t27042+t27078*t26283; + t26748 = t25471+t26281*t26494+x*t26643+t26199*t26737+t26842+t27044; + t26747 = z*t26583+t27027+t26164*t26668+t27002+t27100*t26279; + t26746 = t26285*t26641+t26281*t26416+t26855+t27033+t27069*z; + t25867 = x*t26645; + t26745 = t26281*t25867+t26212*t26623+x*t26544+t26216*t26728+t26249*t26384 ++t26282*t26386+t27017+(t26496+t26593)*t26280; + t26744 = t26283*t26720+t26282*t26412+t26962+t26179*t26738+t26207*t26543+ +t27084*t26277+t27091*z; + t26730 = z*t26155; + t26726 = z*t26158; + t26743 = t26158*t26543+t26282*t26730+t26185*t26432+t26647*t26738+t26967+z +*t26426+(t26726+t27090)*x; + t26742 = t26282*t26497+t26962+t26235*t26432+t26283*t26716+t26210*t26543+ +t27097*z+t27098*x; + t26741 = t26185*t26522+t26283*t26426+t26155*t26543+t26282*t26726+t26967+ +t26187*t26681+(t26730+t27089)*x; + t26702 = x*t26229; + t26118 = t26228*t26284; + t26121 = t26227*t26284; + t26671 = t26230*t26281; + t26103 = t26227*t26285; + t26115 = t26228*t26285; + t26607 = t26256*t26284; + t26173 = RATIONAL(-25.0,48.0); + t26587 = t26173*t26280; + t26582 = t26276*t26284; + t26545 = t26283*t26192; + t26027 = z*t26602; + t26089 = t26282*t26602; + t26063 = t26247*t26612; + t26082 = t26281*t26625; + t26037 = t26283*t26602; + t25993 = t26281*t26652; + t25981 = t26282*t26578; + t26446 = t26228*t26632; + t26441 = t26218*t26632; + t25931 = t26203*t26612; + t26435 = t26281*t26556; + t25846 = t26230*t26612; + t26418 = t26237*t26632; + t26397 = t26284*t26560; + t26381 = t26151*t26678+t26178*t26394+t26898; + t26380 = t26279*t26439+t26168*t26576+t26672; + t26379 = t26243*t26621+t26279*t26397+t26946; + t26254 = RATIONAL(1.0,4.0); + t26198 = RATIONAL(-5.0,16.0); + t26197 = RATIONAL(1.0,16.0); + t26378 = t26254+t26197*t26284+t26198*t26280; + t26255 = RATIONAL(1.0,2.0); + t26252 = RATIONAL(-5.0,8.0); + t26377 = t26252*t26280+t26607+t26255; + t26225 = RATIONAL(-1.0,16.0); + t26213 = RATIONAL(5.0,16.0); + t26267 = RATIONAL(-1.0,4.0); + t26376 = t26267+t26225*t26284+t26213*t26280; + t26375 = t26271*t26284+t26276+t26246*t26280; + t26171 = RATIONAL(25.0,32.0); + t26374 = t26171*t26280+t26252+t26206*t26284; + t26371 = t26246*t26400+t26281*t26582+t26258*t26280+t26231*t26621+t26904; + t26370 = t25778+t26110+t26206*t26400+t26281*t26607+t26920; + t26369 = t26279*t26545+t26283*t26435+t26381+t27043*z; + t26368 = t26192*t26693+z*t26435+t26381+t27043*t26283; + t26367 = t26867+t26990; + t26366 = t26167*t26543+t26232*t26432+t26380+(t26033+t26707)*z; + t26365 = t26182*t26543+x*t26027+t26283*t25846+z*t26702+t26380; + t26364 = t26867+t27015; + t26360 = t26379+t26282*t25974+x*t26067+t27072*t26280; + t26358 = t26284*t25931+t26280*t26653+t26379+(t26608+t26397)*x; + t26154 = RATIONAL(25.0,192.0); + t26200 = RATIONAL(-1.0,32.0); + t26355 = t26154*t26621+t26271*t26632+t26200*t26400+t26103+t26866+t26920+ +t26926; + t26262 = RATIONAL(2.0,1.0); + t26354 = t26118+t26173*t26678+t26255*t26394+t26262*t26552+t26371+t26928; + t26353 = t26154*t26678+t26200*t26394+t26271*t26552+t26121+t26370+t26926; + t26352 = t26285*t26587+t26255*t26400+t26115+t26262*t26632+t26868+t26904+ +t26928; + t26186 = RATIONAL(25.0,96.0); + t26351 = t26186*t26279+t26221*t26285+t26233+(t26198*t26279+t26197*t26285+ +t26254)*t26281; + t26177 = RATIONAL(-25.0,96.0); + t26350 = t26237+t26218*t26285+t26177*t26279+(t26225*t26285+t26267+t26213* +t26279)*t26281; + t26349 = t26237+t26177*t26280+t26218*t26284+t26376*t26281; + t26348 = t26221*t26284+t26186*t26280+t26233+t26378*t26281; + t26347 = t26241*t26623+x*t26404+t26266*t26384+t26284*t26695+t26358+t26872 +; + t26346 = x*t26037+z*t25846+t26282*t26713+t26283*t26702+t26366+t26886; + t26345 = t26365+t26283*t26709+x*t25913+t26871+(t26617+t26063)*z; + t26344 = t26366+z*t26089+t26229*t26737+t26871+(t26626+t25993)*x; + t26343 = t26285*t26545+t26220*t26464+t26368+t26888+t27053*z; + t26342 = x*t26052+t26360+t26240*t26723+t26215*t26623+t26261*t26384+t26872 +; + t26341 = t26220*t26510+t26369+t26192*t26714+t26888+t27053*t26283; + t26340 = t26167*t26737+z*t25981+t26283*t26707+t26365+x*t26082+t26886; + t26264 = RATIONAL(-2.0,1.0); + t26265 = RATIONAL(5.0,2.0); + t26339 = RATIONAL(-25.0,8.0)*t26451+t26285*t26567+t26371+t26260+t26868+ +t26264*t26281+t27066*t26265+(t26285+t26284)*t26261; + t26338 = t26211+t25737+t26114+t26255*t26281+t26171*t26451+t26370+t26112+ +t26866+t27066*t26252; + t26337 = t26090+t26283*t26419+t26285*t26554+t26087+t26878+t26754+(t26431+ +t26633)*z+t27110; + t26336 = t25938+t25749+t26228*t26542+t26116+t26227*t26384+t26813+x*t26560 ++t26119+t25931+t26893; + t26335 = t25954+t26250*x+t26237*t26542+t26811+t26233*t26384+t26133+t26081 ++t25849+t26063+t26891; + t26334 = t26795+t25990+t25993+t26283*t26441+t26368+t26221*t26510+t26101+ +t26190*z+t27105; + t26333 = t26257*t26282+t26204*t26623+t26253*t26542+t26231*t26384+t26358+ +t26053+t26263*x+t26810+t27075; + t26332 = t26211*t26661+t26812+t26109+t26879+t26281*t26456+(t26204+t26570+ +t26419)*z+t27088; + t26331 = t26281*t26455+z*t26446+t26812+t26283*t26660+t26028+t26124+t26123 ++t26869+t27108; + t26330 = t26221*t26384+x*t26671+t26102+t26757+t26218*t26542+t25981+t26091 ++t26877+t27107; + t26329 = t26150+t26284*t26605+t26277*t26282+x*t26139+t26360+t26228*t26384 ++t26258*t26542+t26810+t27080; + t26328 = t25867+t26237*t26384+t26811+t26020+t26233*t26542+t26129+t26089+ +t26033+t26131+t26876; + t26327 = t25699+t25693+t25846+t26757+t26281*t26533+t26097+t26218*t26384+ +t26095+x*t26578+t26885; + t26326 = t26754+t26269*z+t26056+t26057+t26258*t26510+t26874+(t26277+ +t26446)*t26283+t27087; + t26325 = t26795+t26094+t26369+t26281*t26442+t26093+t25913+(t26441+t26671) +*z+t27102; + t26324 = t26082+t25978+t26127+t26814+t26281*t26425+t25960+t26027+t26889+( +t26250+t26418)*z; + t26323 = t26106+t26224*t26384+t26281*t26598+t26231*t26542+t26813+t26107+x +*t26570+t26890+t27092; + t26322 = t26814+t26233*t26510+t26125+t26283*t26418+t26037+t26887+(t26249+ +t26640)*z+t27093; + t26321 = t26748+t26361+t26965+t27007; + t26320 = t26756+t26974+t26982+t26990; + t26319 = t26751+t26973+t26978; + t26318 = t26364+t26752+t26959+t26998; + t26317 = t26750+t26956+t26977; + t26316 = t26756+t26972+t27011+t27015; + t26315 = t26746+t26367+t26972+t26982; + t26314 = t26747+t26973+t26979; + t26313 = t26751+t26975+t26979; + t26312 = t26958+t26743+t26964; + t26311 = t26959+t26753+t26990+t27008; + t26310 = t26963+t26755+t27003+t27004; + t26309 = t26747+t26975+t26978; + t26308 = t26750+t26954+t26976; + t26307 = t26961+t26753+t26998+t27015; + t26306 = t26744+t26955+t26957; + t26305 = t26960+t26743+t26966; + t26304 = t26742+t26955+t26969; + t26303 = t26744+t26969+t26970; + t26302 = t26363+t26749+t26971+t27004; + t26301 = t26745+t26956+t26976; + t26300 = t26964+t26741+t26966; + t26299 = t26742+t26957+t26970; + t26298 = t26958+t26741+t26960; + t26297 = t26965+t26758+t26984+t26991; + t26296 = t26968+t26758+t26985+t27007; + t26295 = t26755+t26971+t26999+t27012; + t26294 = t26748+t26359+t26968+t26984; + t26293 = t26745+t26954+t26977; + t26292 = t26367+t26752+t26961+t27008; + t26291 = t26826+t26749+t26905+t26963+t27012; + t26290 = t26746+t26364+t26974+t27011; + t26275 = RATIONAL(5.0,4.0); + t26251 = RATIONAL(3.0,4.0); + t26244 = RATIONAL(-5.0,4.0); + t26202 = RATIONAL(25.0,8.0); + t26201 = RATIONAL(-15.0,4.0); + t26174 = RATIONAL(25.0,48.0); + t26170 = RATIONAL(-15.0,16.0); + t26169 = RATIONAL(-25.0,12.0); + coeffs_dyy->coeff_m2_m2_m2 = t26312+t26759+t26797; + coeffs_dyy->coeff_m1_m2_m2 = t26310+t26790+t26845; + coeffs_dyy->coeff_0_m2_m2 = t26334+t26833+t26858; + coeffs_dyy->coeff_p1_m2_m2 = t26295+t26780+t26862; + coeffs_dyy->coeff_p2_m2_m2 = t26300+t26809+t26981+t26996; + coeffs_dyy->coeff_m2_m1_m2 = t26320+t26760+t26798; + coeffs_dyy->coeff_m1_m1_m2 = t26321+t26799+t26834; + coeffs_dyy->coeff_0_m1_m2 = t26324+t26817+t26840; + coeffs_dyy->coeff_p1_m1_m2 = t26297+t26800+t26837; + coeffs_dyy->coeff_p2_m1_m2 = t26316+t26983+t27021+t27024+t27026; + coeffs_dyy->coeff_m2_0_m2 = t26343+t26761+t26776; + coeffs_dyy->coeff_m1_0_m2 = t26777+t26340+t26787; + coeffs_dyy->coeff_0_0_m2 = t26351*z+t26350*t26283+t26353; + coeffs_dyy->coeff_p1_0_m2 = t26346+t26787+t26796; + coeffs_dyy->coeff_p2_0_m2 = t26343+t26764+t26783; + coeffs_dyy->coeff_m2_p1_m2 = t26320+t26765+t26767; + coeffs_dyy->coeff_m1_p1_m2 = t26321+t26804+t26827; + coeffs_dyy->coeff_0_p1_m2 = t26324+t26828+t26835; + coeffs_dyy->coeff_p1_p1_m2 = t26297+t26807+t26815; + coeffs_dyy->coeff_p2_p1_m2 = t26316+t27010+t27023+t27025+t27029; + coeffs_dyy->coeff_m2_p2_m2 = t26312+t26809+t26988+t26997; + coeffs_dyy->coeff_m1_p2_m2 = t26310+t26805+t26859; + coeffs_dyy->coeff_0_p2_m2 = t26334+t26829+t26860; + coeffs_dyy->coeff_p1_p2_m2 = t26295+t26771+t26823; + coeffs_dyy->coeff_p2_p2_m2 = t26300+t26806+t26808; + coeffs_dyy->coeff_m2_m2_m1 = t26311+t26763+t26863; + coeffs_dyy->coeff_m1_m2_m1 = t26786+t26309+t27014+t27028; + coeffs_dyy->coeff_0_m2_m1 = t26331+t26853+t26864; + coeffs_dyy->coeff_p1_m2_m1 = t26789+t26314+t27020+t27022; + coeffs_dyy->coeff_p2_m2_m1 = t26318+t26792+t26820; + coeffs_dyy->coeff_m2_m1_m1 = t26317+t26802+t26843; + coeffs_dyy->coeff_m1_m1_m1 = t26303+t26788+t26994+t27000; + coeffs_dyy->coeff_0_m1_m1 = t26326+t26831+t26846; + coeffs_dyy->coeff_p1_m1_m1 = t26299+t26801+t26989+t27006; + coeffs_dyy->coeff_p2_m1_m1 = t26301+t26778+t26856; + coeffs_dyy->coeff_m2_0_m1 = t26772+t26345+t26773; + coeffs_dyy->coeff_m1_0_m1 = t26342+t26770+t26784; + coeffs_dyy->coeff_0_0_m1 = t26354+(t26169*t26279+t26115+t26253+(t26264+ +t26265*t26279+t26276*t26285)*t26281)*z+(t26231+t26174*t26279+t26103+(t26648+ +t26255+t26252*t26279)*t26281)*t26283; + coeffs_dyy->coeff_p1_0_m1 = t26784+t26347+t26785; + coeffs_dyy->coeff_p2_0_m1 = t26773+t26344+t26781; + coeffs_dyy->coeff_m2_p1_m1 = t26317+t26782+t26816; + coeffs_dyy->coeff_m1_p1_m1 = t26303+t26793+t26794; + coeffs_dyy->coeff_0_p1_m1 = t26326+t26838+t26849; + coeffs_dyy->coeff_p1_p1_m1 = t26299+t26762+t26987+t27009; + coeffs_dyy->coeff_p2_p1_m1 = t26301+t26768+t26851; + coeffs_dyy->coeff_m2_p2_m1 = t26311+t26775+t26857; + coeffs_dyy->coeff_m1_p2_m1 = t26309+t26791+t27016+t27018; + coeffs_dyy->coeff_0_p2_m1 = t26331+t26822+t26865; + coeffs_dyy->coeff_p1_p2_m1 = t26779+t26314+t27001+t27019; + coeffs_dyy->coeff_p2_p2_m1 = t26318+t26803+t26830; + coeffs_dyy->coeff_m2_m2_0 = t26327+t26832+t26861; + coeffs_dyy->coeff_m1_m2_0 = t26336+t26819+t26824; + coeffs_dyy->coeff_0_m2_0 = ((t26200*t26284+t26214*t26280+t26271)*t26285+( +t26214*t26284+RATIONAL(-25.0,32.0)*t26280+t26246)*t26279+t26375)*y+t26338; + coeffs_dyy->coeff_p1_m2_0 = t26323+t26819+t26844; + coeffs_dyy->coeff_p2_m2_0 = t26330+t26818+t26861; + coeffs_dyy->coeff_m2_m1_0 = t26335+t26821+t26825; + coeffs_dyy->coeff_m1_m1_0 = t26329+t26850+t26854; + coeffs_dyy->coeff_0_m1_0 = (t26254*t26284+t26244*t26280+1.0+t26378*t26285 ++(RATIONAL(25.0,16.0)*t26280+t26198*t26284+t26244)*t26279)*y+t26339; + coeffs_dyy->coeff_p1_m1_0 = t26333+t26836+t26850; + coeffs_dyy->coeff_p2_m1_0 = t26328+t26825+t26852; + coeffs_dyy->coeff_m2_0_0 = t26355+t26348*x+t26349*t26282; + coeffs_dyy->coeff_m1_0_0 = t26352+(t26174*t26280+t26231+t26121+t26377* +t26281)*t26282+(t26118+t26169*t26280+t26253+(t26265*t26280+t26582+t26264)* +t26281)*x; + coeffs_dyy->coeff_0_0_0 = t26248+t26202*t26280+t26252*t26284+t26374* +t26285+(t26171*t26284+RATIONAL(-125.0,32.0)*t26280+t26202)*t26279+(RATIONAL(3.0 +,1.0)+t26201*t26280+t26251*t26284+(t26251+RATIONAL(3.0,16.0)*t26284+t26170* +t26280)*t26285+(RATIONAL(75.0,16.0)*t26280+t26201+t26170*t26284)*t26279)*t26281 +; + coeffs_dyy->coeff_p1_0_0 = (t26581+(t26248*t26280+t26255*t26284+t26262)* +t26281+t27070)*x+t26352+(t26224*t26284+t26587+t26228+t26375*t26281)*t26282; + coeffs_dyy->coeff_p2_0_0 = t26348*t26282+t26355+t26349*x; + coeffs_dyy->coeff_m2_p1_0 = t26335+t26848+t26852; + coeffs_dyy->coeff_m1_p1_0 = t26329+t26836+t26841; + coeffs_dyy->coeff_0_p1_0 = t26339+(-1.0+t26275*t26280+t26267*t26284+ +t26376*t26285+(RATIONAL(-25.0,16.0)*t26280+t26275+t26213*t26284)*t26279)*y; + coeffs_dyy->coeff_p1_p1_0 = t26333+t26841+t26854; + coeffs_dyy->coeff_p2_p1_0 = t26328+t26821+t26848; + coeffs_dyy->coeff_m2_p2_0 = t26327+t26818+t26839; + coeffs_dyy->coeff_m1_p2_0 = t26336+t26844+t26847; + coeffs_dyy->coeff_0_p2_0 = ((t26209*t26284+t26206*t26280+t26256)*t26285+ +t26374*t26279+t26377)*y+t26338; + coeffs_dyy->coeff_p1_p2_0 = t26323+t26824+t26847; + coeffs_dyy->coeff_p2_p2_0 = t26330+t26832+t26839; + coeffs_dyy->coeff_m2_m2_p1 = t26292+t26792+t26830; + coeffs_dyy->coeff_m1_m2_p1 = t26319+t27014+t27018+t27019+t27020; + coeffs_dyy->coeff_0_m2_p1 = t26332+t26822+t26853; + coeffs_dyy->coeff_p1_m2_p1 = t26313+t26779+t26789; + coeffs_dyy->coeff_p2_m2_p1 = t26307+t26763+t26857; + coeffs_dyy->coeff_m2_m1_p1 = t26308+t26778+t26851; + coeffs_dyy->coeff_m1_m1_p1 = t26304+t26762+t26801; + coeffs_dyy->coeff_0_m1_p1 = t26337+t26846+t26849; + coeffs_dyy->coeff_p1_m1_p1 = t26793+t26306+t27000+t27009; + coeffs_dyy->coeff_p2_m1_p1 = t26293+t26802+t26816; + coeffs_dyy->coeff_m2_0_p1 = t26769+t26344+t26772; + coeffs_dyy->coeff_m1_0_p1 = t26342+t26774+t26785; + coeffs_dyy->coeff_0_0_p1 = t26354+(t26172*t26279+t26258+t26231*t26285+( +t26255*t26285+t26248*t26279+t26262)*t26281)*z+(t26228+t26173*t26279+t26224* +t26285+(t26276+t26246*t26279+t26271*t26285)*t26281)*t26283; + coeffs_dyy->coeff_p1_0_p1 = t26770+t26347+t26774; + coeffs_dyy->coeff_p2_0_p1 = t26345+t26769+t26781; + coeffs_dyy->coeff_m2_p1_p1 = t26308+t26768+t26856; + coeffs_dyy->coeff_m1_p1_p1 = t26788+t26304+t26987+t26989; + coeffs_dyy->coeff_0_p1_p1 = t26337+t26831+t26838; + coeffs_dyy->coeff_p1_p1_p1 = t26794+t26306+t26994+t27006; + coeffs_dyy->coeff_p2_p1_p1 = t26293+t26782+t26843; + coeffs_dyy->coeff_m2_p2_p1 = t26292+t26803+t26820; + coeffs_dyy->coeff_m1_p2_p1 = t26319+t27001+t27016+t27022+t27028; + coeffs_dyy->coeff_0_p2_p1 = t26332+t26864+t26865; + coeffs_dyy->coeff_p1_p2_p1 = t26786+t26313+t26791; + coeffs_dyy->coeff_p2_p2_p1 = t26307+t26775+t26863; + coeffs_dyy->coeff_m2_m2_p2 = t26797+t26298+t26988+t27013; + coeffs_dyy->coeff_m1_m2_p2 = t26291+t26780+t26823; + coeffs_dyy->coeff_0_m2_p2 = t26325+t26858+t26860; + coeffs_dyy->coeff_p1_m2_p2 = t26302+t26790+t26859; + coeffs_dyy->coeff_p2_m2_p2 = t26806+t26305+t26995+t26996; + coeffs_dyy->coeff_m2_m1_p2 = t26315+t26760+t27021+t27023; + coeffs_dyy->coeff_m1_m1_p2 = t26296+t26800+t26815; + coeffs_dyy->coeff_0_m1_p2 = t26322+t26835+t26840; + coeffs_dyy->coeff_p1_m1_p2 = t26294+t26799+t26827; + coeffs_dyy->coeff_p2_m1_p2 = t26290+t26767+t26983+t27025; + coeffs_dyy->coeff_m2_0_p2 = t26341+t26761+t26764; + coeffs_dyy->coeff_m1_0_p2 = t26346+t26766+t26777; + coeffs_dyy->coeff_0_0_p2 = t26350*z+t26351*t26283+t26353; + coeffs_dyy->coeff_p1_0_p2 = t26766+t26340+t26796; + coeffs_dyy->coeff_p2_0_p2 = t26341+t26776+t26783; + coeffs_dyy->coeff_m2_p1_p2 = t26315+t26798+t27010+t27026; + coeffs_dyy->coeff_m1_p1_p2 = t26296+t26807+t26837; + coeffs_dyy->coeff_0_p1_p2 = t26322+t26817+t26828; + coeffs_dyy->coeff_p1_p1_p2 = t26294+t26804+t26834; + coeffs_dyy->coeff_p2_p1_p2 = t26765+t26290+t27024+t27029; + coeffs_dyy->coeff_m2_p2_p2 = t26759+t26298+t26995+t26997; + coeffs_dyy->coeff_m1_p2_p2 = t26291+t26771+t26862; + coeffs_dyy->coeff_0_p2_p2 = t26325+t26829+t26833; + coeffs_dyy->coeff_p1_p2_p2 = t26302+t26805+t26845; + coeffs_dyy->coeff_p2_p2_p2 = t26305+t26808+t26981+t27013; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyz.compute.c new file mode 100644 index 0000000..ffe18fc --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyz.compute.c @@ -0,0 +1,2550 @@ +fp t28586; +fp t28656; +fp t28662; +fp t28535; +fp t29473; +fp t28533; +fp t28659; +fp t28530; +fp t29472; +fp t28531; +fp t28532; +fp t29471; +fp t28565; +fp t28572; +fp t29470; +fp t28564; +fp t28541; +fp t29469; +fp t29468; +fp t28534; +fp t28658; +fp t28946; +fp t28529; +fp t28961; +fp t29467; +fp t28654; +fp t28642; +fp t28527; +fp t29466; +fp t28660; +fp t29018; +fp t28554; +fp t28914; +fp t28075; +fp t28536; +fp t29465; +fp t28657; +fp t28661; +fp t28952; +fp t28917; +fp t29464; +fp t28645; +fp t28637; +fp t29463; +fp t29016; +fp t28619; +fp t29462; +fp t28538; +fp t28915; +fp t27997; +fp t28539; +fp t28441; +fp t29461; +fp t28977; +fp t28571; +fp t28919; +fp t29460; +fp t28537; +fp t28440; +fp t29459; +fp t28574; +fp t28948; +fp t29458; +fp t28648; +fp t29020; +fp t28653; +fp t28930; +fp t29457; +fp t29456; +fp t28601; +fp t28846; +fp t28607; +fp t28466; +fp t28293; +fp t29455; +fp t28641; +fp t29454; +fp t28594; +fp t28553; +fp t29453; +fp t28561; +fp t28445; +fp t29452; +fp t28581; +fp t28884; +fp t28910; +fp t29451; +fp t28613; +fp t28954; +fp t29450; +fp t28575; +fp t28481; +fp t29394; +fp t28600; +fp t28497; +fp t28559; +fp t29449; +fp t28101; +fp t29448; +fp t29447; +fp t28945; +fp t28407; +fp t29446; +fp t29445; +fp t28612; +fp t28902; +fp t28631; +fp t29444; +fp t28622; +fp t28882; +fp t28275; +fp t28589; +fp t28491; +fp t29443; +fp t28593; +fp t28476; +fp t28958; +fp t29442; +fp t28588; +fp t28891; +fp t28104; +fp t29441; +fp t29440; +fp t28953; +fp t29033; +fp t29439; +fp t28567; +fp t29438; +fp t28457; +fp t28548; +fp t28947; +fp t29437; +fp t28444; +fp t28547; +fp t29436; +fp t29435; +fp t28552; +fp t28603; +fp t28485; +fp t29434; +fp t28580; +fp t28900; +fp t28640; +fp t29433; +fp t28609; +fp t28479; +fp t28597; +fp t28883; +fp t28188; +fp t29432; +fp t28514; +fp t28192; +fp t29431; +fp t29430; +fp t28628; +fp t28509; +fp t29429; +fp t28949; +fp t28122; +fp t28604; +fp t28856; +fp t29428; +fp t28368; +fp t28526; +fp t29427; +fp t28906; +fp t29031; +fp t29426; +fp t28471; +fp t29385; +fp t28114; +fp t28596; +fp t29015; +fp t28225; +fp t29425; +fp t28940; +fp t29424; +fp t28450; +fp t29423; +fp t28578; +fp t28310; +fp t29014; +fp t28267; +fp t29422; +fp t29421; +fp t28967; +fp t29420; +fp t28095; +fp t29419; +fp t28555; +fp t28568; +fp t28448; +fp t29418; +fp t29417; +fp t28894; +fp t29416; +fp t29415; +fp t27889; +fp t29414; +fp t28899; +fp t29413; +fp t28898; +fp t29412; +fp t28911; +fp t29411; +fp t28599; +fp t28937; +fp t28319; +fp t29410; +fp t29409; +fp t28938; +fp t28916; +fp t29408; +fp t28437; +fp t28563; +fp t29407; +fp t28487; +fp t28334; +fp t29027; +fp t28583; +fp t29406; +fp t29405; +fp t29404; +fp t29403; +fp t28987; +fp t29402; +fp t29401; +fp t29400; +fp t29399; +fp t29398; +fp t28986; +fp t28905; +fp t29397; +fp t28585; +fp t28921; +fp t28340; +fp t28587; +fp t28976; +fp t28153; +fp t29353; +fp t28785; +fp t28951; +fp t28350; +fp t29344; +fp t29282; +fp t29396; +fp t29395; +fp t29040; +fp t28461; +fp t28145; +fp t28886; +fp t28266; +fp t28125; +fp t29356; +fp t29393; +fp t28582; +fp t28997; +fp t28630; +fp t28505; +fp t29392; +fp t28171; +fp t28912; +fp t28321; +fp t29391; +fp t28472; +fp t28801; +fp t29390; +fp t27908; +fp t28982; +fp t28279; +fp t29389; +fp t28158; +fp t28002; +fp t29388; +fp t28232; +fp t28974; +fp t28256; +fp t29387; +fp t28055; +fp t29386; +fp t28823; +fp t29384; +fp t28325; +fp t29383; +fp t28970; +fp t28209; +fp t28896; +fp t28185; +fp t29382; +fp t28522; +fp t28810; +fp t28540; +fp t28904; +fp t27921; +fp t28606; +fp t28994; +fp t28097; +fp t28998; +fp t29381; +fp t28558; +fp t28956; +fp t28569; +fp t28453; +fp t29380; +fp t28451; +fp t28942; +fp t28783; +fp t29379; +fp t28265; +fp t29378; +fp t28827; +fp t28455; +fp t29377; +fp t28459; +fp t28814; +fp t29376; +fp t27987; +fp t29375; +fp t28033; +fp t29374; +fp t27920; +fp t29373; +fp t29000; +fp t29372; +fp t28852; +fp t28096; +fp t29371; +fp t27931; +fp t28885; +fp t29370; +fp t28373; +fp t29008; +fp t28625; +fp t29369; +fp t28013; +fp t27996; +fp t29368; +fp t28893; +fp t28060; +fp t28920; +fp t28335; +fp t29367; +fp t28822; +fp t29366; +fp t28874; +fp t28824; +fp t29365; +fp t28880; +fp t28879; +fp t29364; +fp t28782; +fp t28932; +fp t29363; +fp t28182; +fp t28620; +fp t29009; +fp t28869; +fp t29362; +fp t29028; +fp t28626; +fp t29361; +fp t28959; +fp t27913; +fp t28806; +fp t29360; +fp t28259; +fp t29026; +fp t28849; +fp t29359; +fp t28442; +fp t27973; +fp t29358; +fp t27917; +fp t27915; +fp t29357; +fp t28605; +fp t28638; +fp t28872; +fp t29355; +fp t28010; +fp t27986; +fp t29354; +fp t28016; +fp t27891; +fp t29352; +fp t28475; +fp t28201; +fp t28224; +fp t29351; +fp t28289; +fp t27966; +fp t29350; +fp t27929; +fp t28897; +fp t27975; +fp t29349; +fp t28616; +fp t28837; +fp t29024; +fp t28841; +fp t29348; +fp t28818; +fp t28936; +fp t27963; +fp t29347; +fp t28089; +fp t29345; +fp t29343; +fp t28307; +fp t28592; +fp t28881; +fp t28131; +fp t29342; +fp t28871; +fp t28962; +fp t28071; +fp t29341; +fp t28621; +fp t28272; +fp t28802; +fp t29339; +fp t29003; +fp t29338; +fp t28177; +fp t28130; +fp t29337; +fp t28784; +fp t28115; +fp t29336; +fp t27959; +fp t28148; +fp t29335; +fp t28889; +fp t28789; +fp t29334; +fp t29333; +fp t28452; +fp t27912; +fp t28305; +fp t29332; +fp t29011; +fp t27890; +fp t28439; +fp t28803; +fp t29331; +fp t28102; +fp t29330; +fp t28166; +fp t28981; +fp t28804; +fp t29329; +fp t28338; +fp t28332; +fp t29328; +fp t28268; +fp t28280; +fp t29327; +fp t27960; +fp t29326; +fp t28004; +fp t28834; +fp t29325; +fp t28149; +fp t28088; +fp t29324; +fp t28477; +fp t28787; +fp t28446; +fp t29323; +fp t28205; +fp t28492; +fp t29322; +fp t29034; +fp t28270; +fp t28470; +fp t28287; +fp t29321; +fp t28828; +fp t29320; +fp t29319; +fp t28618; +fp t28992; +fp t28944; +fp t28112; +fp t29318; +fp t28557; +fp t28903; +fp t27926; +fp t28792; +fp t28508; +fp t28406; +fp t29041; +fp t28137; +fp t29317; +fp t29316; +fp t28291; +fp t28608; +fp t28928; +fp t28197; +fp t29315; +fp t28339; +fp t28110; +fp t29314; +fp t28807; +fp t28434; +fp t28829; +fp t29313; +fp t27968; +fp t28447; +fp t29312; +fp t29311; +fp t28901; +fp t28798; +fp t28121; +fp t29310; +fp t27940; +fp t27924; +fp t29309; +fp t28276; +fp t28868; +fp t28644; +fp t28925; +fp t29308; +fp t28465; +fp t28786; +fp t28595; +fp t28331; +fp t28922; +fp t29307; +fp t28036; +fp t28218; +fp t29306; +fp t28848; +fp t28478; +fp t28217; +fp t28797; +fp t29305; +fp t29304; +fp t28180; +fp t28263; +fp t28793; +fp t28269; +fp t29303; +fp t28228; +fp t28199; +fp t28143; +fp t29302; +fp t28165; +fp t28085; +fp t29301; +fp t28990; +fp t28191; +fp t29300; +fp t29299; +fp t27972; +fp t29298; +fp t28984; +fp t27897; +fp t29297; +fp t28045; +fp t28892; +fp t28233; +fp t29296; +fp t28264; +fp t29295; +fp t28480; +fp t28598; +fp t28229; +fp t29294; +fp t29030; +fp t27950; +fp t29293; +fp t29292; +fp t28878; +fp t29291; +fp t29290; +fp t29289; +fp t28963; +fp t28875; +fp t29288; +fp t27918; +fp t29287; +fp t29013; +fp t27895; +fp t28816; +fp t28817; +fp t29286; +fp t29285; +fp t28348; +fp t28800; +fp t29284; +fp t28260; +fp t29283; +fp t29039; +fp t29038; +fp t28384; +fp t28400; +fp t28655; +fp t29005; +fp t29281; +fp t28084; +fp t29280; +fp t28500; +fp t29279; +fp t29278; +fp t28512; +fp t28395; +fp t29277; +fp t28183; +fp t28813; +fp t29276; +fp t28068; +fp t29019; +fp t28864; +fp t29275; +fp t29274; +fp t28993; +fp t28179; +fp t29273; +fp t28311; +fp t28151; +fp t28808; +fp t29272; +fp t28794; +fp t28254; +fp t28337; +fp t29271; +fp t28194; +fp t29270; +fp t28323; +fp t29269; +fp t28623; +fp t28988; +fp t28330; +fp t28791; +fp t29268; +fp t29267; +fp t29037; +fp t28070; +fp t29266; +fp t28646; +fp t28836; +fp t28518; +fp t28614; +fp t28973; +fp t29265; +fp t28821; +fp t28929; +fp t28251; +fp t29264; +fp t29263; +fp t29262; +fp t29032; +fp t28061; +fp t28918; +fp t27946; +fp t29261; +fp t28124; +fp t29260; +fp t29259; +fp t28069; +fp t28249; +fp t29258; +fp t29257; +fp t28496; +fp t28854; +fp t28160; +fp t29021; +fp t29256; +fp t28207; +fp t28250; +fp t29255; +fp t28141; +fp t29254; +fp t29022; +fp t28190; +fp t28995; +fp t28257; +fp t29253; +fp t29252; +fp t28774; +fp t29251; +fp t28839; +fp t29250; +fp t29249; +fp t29248; +fp t28126; +fp t28128; +fp t29247; +fp t28831; +fp t28833; +fp t28767; +fp t28842; +fp t28943; +fp t28302; +fp t29246; +fp t29245; +fp t27902; +fp t29244; +fp t29243; +fp t28811; +fp t28163; +fp t27909; +fp t28971; +fp t28317; +fp t29242; +fp t27958; +fp t29241; +fp t29240; +fp t29239; +fp t28054; +fp t29238; +fp t28825; +fp t27927; +fp t29237; +fp t29236; +fp t28845; +fp t29235; +fp t29234; +fp t28058; +fp t28931; +fp t28136; +fp t29233; +fp t28636; +fp t28983; +fp t28830; +fp t28584; +fp t29232; +fp t28591; +fp t28647; +fp t29231; +fp t29230; +fp t27444; +fp t29229; +fp t29228; +fp t28923; +fp t29227; +fp t28888; +fp t29226; +fp t28421; +fp t28146; +fp t28150; +fp t28743; +fp t29225; +fp t28484; +fp t28152; +fp t29224; +fp t29029; +fp t28391; +fp t29223; +fp t28972; +fp t28796; +fp t28413; +fp t29222; +fp t29221; +fp t28469; +fp t28196; +fp t29220; +fp t28377; +fp t29219; +fp t29218; +fp t29217; +fp t29216; +fp t29215; +fp t28211; +fp t29214; +fp t28378; +fp t29213; +fp t28858; +fp t28957; +fp t29212; +fp t28556; +fp t28799; +fp t29211; +fp t28866; +fp t28907; +fp t28862; +fp t29210; +fp t29209; +fp t29208; +fp t29207; +fp t28865; +fp t28857; +fp t29206; +fp t29205; +fp t28524; +fp t28805; +fp t28978; +fp t28859; +fp t29204; +fp t27899; +fp t28838; +fp t29203; +fp t29202; +fp t29201; +fp t28844; +fp t29200; +fp t29199; +fp t28360; +fp t29035; +fp t28092; +fp t28863; +fp t29198; +fp t28850; +fp t28877; +fp t29197; +fp t28996; +fp t28195; +fp t29196; +fp t29195; +fp t27954; +fp t29194; +fp t28861; +fp t29193; +fp t28316; +fp t29192; +fp t29191; +fp t29190; +fp t28965; +fp t28867; +fp t29189; +fp t28870; +fp t29188; +fp t28826; +fp t29187; +fp t28873; +fp t28611; +fp t28960; +fp t29186; +fp t28939; +fp t28405; +fp t28387; +fp t29036; +fp t29006; +fp t28615; +fp t29010; +fp t28843; +fp t29185; +fp t28950; +fp t29184; +fp t29183; +fp t29182; +fp t28320; +fp t29181; +fp t29002; +fp t29180; +fp t29179; +fp t28820; +fp t29178; +fp t29177; +fp t28366; +fp t28347; +fp t29176; +fp t28851; +fp t29175; +fp t28855; +fp t29174; +fp t28860; +fp t29173; +fp t29172; +fp t29171; +fp t28463; +fp t29170; +fp t29169; +fp t29168; +fp t29167; +fp t28790; +fp t28788; +fp t28909; +fp t29166; +fp t29165; +fp t28934; +fp t28832; +fp t29164; +fp t29163; +fp t29162; +fp t29161; +fp t29160; +fp t29159; +fp t28835; +fp t29158; +fp t29157; +fp t28401; +fp t29156; +fp t29155; +fp t29154; +fp t29153; +fp t29012; +fp t29152; +fp t29151; +fp t29150; +fp t29149; +fp t29148; +fp t28969; +fp t28318; +fp t29147; +fp t29146; +fp t27911; +fp t29145; +fp t29144; +fp t29001; +fp t29004; +fp t29143; +fp t29142; +fp t28840; +fp t29141; +fp t29140; +fp t29139; +fp t28184; +fp t29138; +fp t28795; +fp t29137; +fp t29136; +fp t29135; +fp t29134; +fp t29133; +fp t28386; +fp t29132; +fp t29131; +fp t28941; +fp t28980; +fp t29130; +fp t29129; +fp t29128; +fp t29127; +fp t28306; +fp t28464; +fp t29126; +fp t29125; +fp t29124; +fp t29123; +fp t29122; +fp t29121; +fp t29120; +fp t29119; +fp t29118; +fp t29117; +fp t29116; +fp t28927; +fp t29115; +fp t28203; +fp t29114; +fp t29113; +fp t29112; +fp t29111; +fp t29110; +fp t28819; +fp t29109; +fp t28363; +fp t29108; +fp t28371; +fp t29107; +fp t29106; +fp t28023; +fp t28729; +fp t29105; +fp t27961; +fp t28742; +fp t29104; +fp t28342; +fp t28507; +fp t29103; +fp t29102; +fp t28026; +fp t28576; +fp t28175; +fp t29101; +fp t29100; +fp t28517; +fp t28220; +fp t29099; +fp t28343; +fp t28913; +fp t28374; +fp t29098; +fp t28895; +fp t28243; +fp t29097; +fp t28412; +fp t29096; +fp t28602; +fp t28144; +fp t29095; +fp t29094; +fp t27718; +fp t29093; +fp t28650; +fp t29092; +fp t29091; +fp t29090; +fp t29089; +fp t29088; +fp t28809; +fp t29087; +fp t27932; +fp t29086; +fp t28649; +fp t29085; +fp t29084; +fp t29083; +fp t27721; +fp t28770; +fp t29082; +fp t28763; +fp t29081; +fp t27559; +fp t28768; +fp t29080; +fp t28765; +fp t29079; +fp t29078; +fp t29077; +fp t28780; +fp t29076; +fp t29075; +fp t29074; +fp t29073; +fp t29072; +fp t29071; +fp t29070; +fp t29069; +fp t29068; +fp t29067; +fp t29066; +fp t29065; +fp t29064; +fp t29063; +fp t29062; +fp t29061; +fp t29060; +fp t29059; +fp t29058; +fp t29057; +fp t29056; +fp t29055; +fp t29054; +fp t29053; +fp t29052; +fp t29051; +fp t29050; +fp t29049; +fp t29048; +fp t29047; +fp t29046; +fp t29045; +fp t29044; +fp t29043; +fp t29042; +fp t28633; +fp t29025; +fp t29017; +fp t29007; +fp t28989; +fp t28979; +fp t28964; +fp t28955; +fp t28935; +fp t28933; +fp t28926; +fp t28908; +fp t28887; +fp t28853; +fp t28415; +fp t28376; +fp t28781; +fp t28776; +fp t28772; +fp t28771; +fp t28769; +fp t28766; +fp t28764; +fp t28562; +fp t28762; +fp t28627; +fp t28761; +fp t28542; +fp t28760; +fp t28590; +fp t28759; +fp t28632; +fp t28758; +fp t28757; +fp t28756; +fp t28577; +fp t28634; +fp t28755; +fp t28754; +fp t28753; +fp t28643; +fp t28752; +fp t28751; +fp t28750; +fp t28749; +fp t28624; +fp t28573; +fp t28748; +fp t28747; +fp t28746; +fp t28745; +fp t28744; +fp t28740; +fp t28739; +fp t28738; +fp t28737; +fp t28736; +fp t28735; +fp t28734; +fp t28733; +fp t28551; +fp t28732; +fp t28731; +fp t28730; +fp t28728; +fp t28546; +fp t28727; +fp t28639; +fp t28726; +fp t28725; +fp t28724; +fp t28723; +fp t28722; +fp t28721; +fp t28720; +fp t28719; +fp t28718; +fp t28717; +fp t28716; +fp t28715; +fp t28714; +fp t28713; +fp t28712; +fp t28711; +fp t28710; +fp t28709; +fp t28708; +fp t28707; +fp t28706; +fp t28705; +fp t28704; +fp t28703; +fp t28702; +fp t28701; +fp t28700; +fp t28699; +fp t28698; +fp t28697; +fp t28696; +fp t28695; +fp t28694; +fp t28693; +fp t28692; +fp t28691; +fp t28690; +fp t28689; +fp t28688; +fp t28687; +fp t28686; +fp t28685; +fp t28684; +fp t28683; +fp t28682; +fp t28681; +fp t28680; +fp t28679; +fp t28678; +fp t28677; +fp t28676; +fp t28675; +fp t28674; +fp t28673; +fp t28672; +fp t28671; +fp t28670; +fp t28669; +fp t28668; +fp t28667; + t28586 = RATIONAL(4.0,27.0); + t28656 = x*x; + t28662 = t28656*t28656; + t28535 = RATIONAL(-16.0,27.0); + t29473 = t28586*t28662+t28535*t28656; + t28533 = RATIONAL(-1.0,1728.0); + t28659 = t28656*x; + t28530 = RATIONAL(1.0,1728.0); + t29472 = t28530*x+t28533*t28659; + t28531 = RATIONAL(1.0,3456.0); + t28532 = RATIONAL(-1.0,3456.0); + t29471 = t28531*t28662+t28532*t28656; + t28565 = RATIONAL(1.0,144.0); + t28572 = RATIONAL(1.0,576.0); + t29470 = t28565+t28572*t28662; + t28564 = RATIONAL(-5.0,288.0); + t28541 = RATIONAL(5.0,288.0); + t29469 = x*t28541+t28564*t28659; + t29468 = t28530*t28659+t28533*x; + t28534 = RATIONAL(1.0,1152.0); + t28658 = y*y; + t28946 = t28662*t28658; + t28529 = RATIONAL(-1.0,1152.0); + t28961 = t28656*t28658; + t29467 = t28529*t28961+t28534*t28946; + t28654 = RATIONAL(4.0,9.0); + t28642 = RATIONAL(-1.0,3.0); + t28527 = t28642*t28658; + t29466 = t28527+t28654; + t28660 = t28658*y; + t29018 = x*t28660; + t28554 = RATIONAL(-1.0,216.0); + t28914 = t28660*t28554; + t28075 = t28659*t28914; + t28536 = RATIONAL(1.0,216.0); + t29465 = t28075+t28536*t29018; + t28657 = z*z; + t28661 = t28657*z; + t28952 = t28661*t28554; + t28917 = t28661*t28536; + t29464 = t28659*t28952+x*t28917; + t28645 = RATIONAL(-8.0,9.0); + t28637 = RATIONAL(-2.0,9.0); + t29463 = t28645+t28662*t28637; + t29016 = z*t28658; + t28619 = RATIONAL(8.0,27.0); + t29462 = t28661*t28619+t28654*t29016; + t28538 = RATIONAL(-1.0,432.0); + t28915 = t28538*t28659; + t27997 = t28661*t28915; + t28539 = RATIONAL(1.0,864.0); + t28441 = t28539*t28659; + t29461 = z*t28441+t27997; + t28977 = t28657*t28572; + t28571 = RATIONAL(-1.0,576.0); + t28919 = t28657*t28662; + t29460 = t28656*t28977+t28571*t28919; + t28537 = RATIONAL(1.0,432.0); + t28440 = t28537*t28662; + t29459 = t28538*t28656+t28440; + t28574 = RATIONAL(-1.0,864.0); + t28948 = t28659*t28660; + t29458 = t28539*t28948+t28574*t29018; + t28648 = RATIONAL(-4.0,9.0); + t29020 = y*t28657; + t28653 = RATIONAL(2.0,9.0); + t28930 = t28657*t28653; + t29457 = t28660*t28930+t28648*t29020; + t29456 = t28538*t28662+t28537*t28656; + t28601 = RATIONAL(5.0,48.0); + t28846 = t28601*t29016; + t28607 = RATIONAL(-1.0,24.0); + t28466 = t28607*t28658; + t28293 = t28661*t28466; + t29455 = t28293+t28846; + t28641 = RATIONAL(8.0,9.0); + t29454 = t28641+t28653*t28662; + t28594 = RATIONAL(-4.0,27.0); + t28553 = RATIONAL(16.0,27.0); + t29453 = t28553*t28656+t28594*t28662; + t28561 = RATIONAL(1.0,288.0); + t28445 = t28574*t28662; + t29452 = t28561*t28946+t28445; + t28581 = RATIONAL(-1.0,18.0); + t28884 = t28581*t28658; + t28910 = t28653*t28658; + t29451 = t28662*t28884+t28656*t28910; + t28613 = RATIONAL(1.0,18.0); + t28954 = t28637*t28656; + t29450 = t28613*t28919+t28657*t28954; + t28575 = RATIONAL(-1.0,72.0); + t28481 = t28575*t28662; + t29394 = t28581+t28481; + t28600 = RATIONAL(1.0,48.0); + t28497 = t28600*t28658; + t28559 = RATIONAL(1.0,192.0); + t29449 = t28559*t28946+t28497; + t28101 = t28581*t28919; + t29448 = t28656*t28930+t28101; + t29447 = t29469*y; + t28945 = t28613*t28658; + t28407 = t28658*t28954; + t29446 = t28407+t28662*t28945; + t29445 = t29473*z; + t28612 = RATIONAL(1.0,36.0); + t28902 = t28662*t28612; + t28631 = RATIONAL(1.0,9.0); + t29444 = t28902+t28631; + t28622 = RATIONAL(1.0,72.0); + t28882 = t28658*t28622; + t28275 = t28662*t28882; + t28589 = RATIONAL(-1.0,54.0); + t28491 = t28589*t28662; + t29443 = t28275+t28491; + t28593 = RATIONAL(-2.0,27.0); + t28476 = t28593*t28659; + t28958 = t28586*t28659; + t29442 = t28661*t28476+z*t28958; + t28588 = RATIONAL(-1.0,12.0); + t28891 = t28588*t28658; + t28104 = t28662*t28891; + t29441 = t28631*t28662+t28104; + t29440 = x*t28914+t28536*t28948; + t28953 = t28659*t28661; + t29033 = x*t28661; + t29439 = t28574*t28953+t28539*t29033; + t28567 = RATIONAL(-1.0,144.0); + t29438 = t28571*t28662+t28567; + t28457 = t28536*x; + t28548 = RATIONAL(-1.0,108.0); + t28947 = t28548*t28660; + t29437 = y*t28457+x*t28947; + t28444 = t28554*x; + t28547 = RATIONAL(1.0,108.0); + t29436 = y*t28444+t28547*t29018; + t29435 = t28567*t28948+t28565*t29018; + t28552 = RATIONAL(-1.0,192.0); + t28603 = RATIONAL(-1.0,48.0); + t28485 = t28603*t28658; + t29434 = t28552*t28946+t28485; + t28580 = RATIONAL(1.0,12.0); + t28900 = t28580*t28662; + t28640 = RATIONAL(1.0,3.0); + t29433 = (t28900+t28640)*t28657; + t28609 = RATIONAL(1.0,24.0); + t28479 = t28609*t28658; + t28597 = RATIONAL(1.0,96.0); + t28883 = t28597*t28658; + t28188 = t28662*t28883; + t29432 = t28479+t28188; + t28514 = t28640*t28658; + t28192 = t28658*t28900; + t29431 = t28514+t28192; + t29430 = t28534*t28961+t28529*t28946; + t28628 = RATIONAL(1.0,6.0); + t28509 = t28628*t28658; + t29429 = t28657*t28509+t28619; + t28949 = t28657*t28660; + t28122 = t28609*t28949; + t28604 = RATIONAL(-5.0,48.0); + t28856 = t28604*t29020; + t29428 = t28122+t28856; + t28368 = t28642*t28949; + t28526 = t28654*t28660; + t29427 = t28368+t28526; + t28906 = t28659*t28658; + t29031 = x*t28658; + t29426 = t28572*t28906+t28571*t29031; + t28471 = t28622*t28662; + t29385 = t28471+t28613; + t28114 = t28589*t28948; + t28596 = RATIONAL(2.0,27.0); + t29015 = x*t28596; + t28225 = t28660*t29015; + t29425 = t28225+t28114; + t28940 = t28572*t28658; + t29424 = t28571*t28961+t28662*t28940; + t28450 = t28574*t28659; + t29423 = t28537*t28948+y*t28450; + t28578 = RATIONAL(1.0,54.0); + t28310 = t28578*t28948; + t29014 = x*t28593; + t28267 = t28660*t29014; + t29422 = t28267+t28310; + t29421 = t28659*t28917+x*t28952; + t28967 = t28657*t28571; + t29420 = t28656*t28967+t28572*t28919; + t28095 = t28660*t28476; + t29419 = t28095+t28619*t29018; + t28555 = RATIONAL(5.0,192.0); + t28568 = RATIONAL(-5.0,576.0); + t28448 = t28568*t28656; + t29418 = t28448+t28555*t28961; + t29417 = t28567*t29018+t28565*t28948; + t28894 = t28661*t28565; + t29416 = x*t28894+t28567*t28953; + t29415 = t28532*t28662+t28531*t28656; + t27889 = t28659*t28894; + t29414 = t28567*t29033+t27889; + t28899 = t28656*t28596; + t29413 = t28899+t28491; + t28898 = t28657*t28588; + t29412 = t28642*t28657+t28662*t28898; + t28911 = t28657*t28659; + t29411 = x*t28977+t28571*t28911; + t28599 = RATIONAL(-1.0,96.0); + t28937 = t28599*t28658; + t28319 = t28662*t28937; + t29410 = t28466+t28319; + t29409 = t28656*t28940+t28571*t28946; + t28938 = t28662*t28660; + t28916 = t28656*t28660; + t29408 = t28533*t28938+t28530*t28916; + t28437 = t28539*t28662; + t28563 = RATIONAL(-1.0,288.0); + t29407 = t28437+t28563*t28919; + t28487 = t28596*t28659; + t28334 = t28660*t28487; + t29027 = x*t28553; + t28583 = RATIONAL(-8.0,27.0); + t29406 = t28334+t28583*t29018+y*t29027; + t29405 = t28619*t28916+t29473*y; + t29404 = t28575*t28661+t29470*z; + t29403 = t28539*t28953+t28574*t29033+t29472*z; + t28987 = t28657*t28656; + t29402 = t28529*t28987+t28534*t28919+t29415; + t29401 = x*t28940+t28571*t28906+t29468; + t29400 = t28572*t28911+x*t28967+t29472; + t29399 = t28574*t28948+t28539*t29018+t29468*y; + t29398 = t28534*t28987+t28529*t28919+t29471; + t28986 = t28661*t28662; + t28905 = t28661*t28530; + t29397 = t28656*t28905+t28533*t28986+t29471*z; + t28585 = RATIONAL(1.0,27.0); + t28921 = t28661*t28656; + t28340 = t28585*t28921; + t28587 = RATIONAL(-1.0,27.0); + t28976 = t28587*t28662; + t28153 = z*t28976; + t29353 = y*t28340+t28660*t28153; + t28785 = t28661*t28938; + t28951 = t28593*t28656; + t28350 = z*t28951; + t29344 = t28578*t28785+y*t28350; + t29282 = t29344+t29353; + t29396 = (t28648+t28514)*t28661; + t29395 = t29466*t28661; + t29040 = y*z; + t28461 = t28596*t28662; + t28145 = t28589*t28916; + t28886 = t28585*t28660; + t28266 = t28656*t28886; + t28125 = y*t28976; + t29356 = z*t28266+t28661*t28125; + t29393 = t28461*t29040+t28661*t28145+t29356; + t28582 = RATIONAL(-1.0,36.0); + t28997 = t28582*t28662; + t28630 = RATIONAL(-1.0,9.0); + t28505 = t28630*y; + t29392 = y*t28997+t28505; + t28171 = t28582*t28911; + t28912 = t28612*t28658; + t28321 = x*t28912; + t29391 = t28171+t28321; + t28472 = t28587*x; + t28801 = t28600*t28911; + t29390 = t28658*t28801+t28472; + t27908 = t28561*t28906; + t28982 = t28657*t28575; + t28279 = x*t28982; + t29389 = t27908+t28279; + t28158 = t28575*t29031; + t28002 = t28561*t28911; + t29388 = t28158+t28002; + t28232 = t28582*t28906; + t28974 = t28657*t28612; + t28256 = x*t28974; + t29387 = t28232+t28256; + t28055 = t28561*t29031; + t29386 = t28055+t28575*t28911; + t28823 = t28657*t28906; + t29384 = t28457+t28599*t28823; + t28325 = t28597*t28919; + t29383 = t28609*t28657+t28325; + t28970 = t28657*t28582; + t28209 = x*t28970; + t28896 = t28659*t28612; + t28185 = t28658*t28896; + t29382 = t28209+t28185; + t28522 = t28631*t28660; + t28810 = t28661*t28522; + t28540 = RATIONAL(-5.0,144.0); + t28904 = t28662*t28540; + t27921 = z*t28904; + t28606 = RATIONAL(5.0,36.0); + t28994 = t28606*t28656; + t28097 = y*t28994; + t28998 = t28582*t28785+z*t28097; + t29381 = t28656*t28810+y*t27921+t28998; + t28558 = RATIONAL(-5.0,192.0); + t28956 = t28558*t28656; + t28569 = RATIONAL(5.0,576.0); + t28453 = t28569*t28656; + t29380 = t28453+t28657*t28956; + t28451 = t28548*t28659; + t28942 = t28580*t28658; + t28783 = t28657*t28942; + t29379 = t28451+x*t28783; + t28265 = t28599*t28919; + t29378 = t28607*t28657+t28265; + t28827 = t28657*t28937; + t28455 = t28536*t28659; + t29377 = x*t28827+t28455; + t28459 = t28585*x; + t28814 = t28603*t28906; + t29376 = t28459+t28657*t28814; + t27987 = t28565*t28961; + t29375 = t27987+t29460; + t28033 = t28552*t28919; + t29374 = t28033+t28603*t28657+t29470; + t27920 = t28559*t28919; + t29373 = t27920+t28600*t28657+t29438; + t29000 = z*t29018; + t29372 = z*t28114+t28578*t29000+t29464*y; + t28852 = t28578*t29033; + t28096 = t28589*t28953; + t29371 = t29465*z+(t28096+t28852)*y; + t27931 = t28567*t28919; + t28885 = t28657*t28565; + t29370 = t28656*t28885+t27931+t29409; + t28373 = t28648*t28916; + t29008 = t28662*t29040; + t28625 = RATIONAL(5.0,9.0); + t29369 = t28661*t28373+t28625*t29008; + t28013 = t28547*t28938; + t27996 = t28538*t28921; + t29368 = z*t28013+y*t27996; + t28893 = t28659*t28563; + t28060 = t28658*t28893; + t28920 = t28657*t28622; + t28335 = x*t28920; + t29367 = t28060+t28335; + t28822 = t28657*t28883; + t29366 = t28444+t28659*t28822; + t28874 = z*t28938; + t28824 = t28601*t28921; + t29365 = y*t28824+t28604*t28874; + t28880 = y*t28986; + t28879 = z*t28916; + t29364 = t28604*t28880+t28601*t28879; + t28782 = t28609*t28938; + t28932 = RATIONAL(-25.0,96.0)*t28656; + t29363 = t28932*t29040+t28661*t28782; + t28182 = t28622*t28938; + t28620 = RATIONAL(-5.0,18.0); + t29009 = y*t28620; + t28869 = t28661*t29009; + t29362 = t28656*t28869+z*t28182; + t29028 = RATIONAL(25.0,6.0)*z; + t28626 = RATIONAL(-1.0,6.0); + t29361 = t28626*t28785+y*t28656*t29028; + t28959 = t28662*t28554; + t27913 = y*t28959; + t28806 = t28660*t28917; + t29360 = z*t27913+t28656*t28806; + t28259 = t28661*t28471; + t29026 = z*t28660; + t28849 = t28620*t29026; + t29359 = t28656*t28849+y*t28259; + t28442 = t28536*t28656; + t27973 = z*t28442; + t29358 = y*t27973+t28554*t28785; + t27917 = t28563*t28986; + t27915 = t28541*t28916; + t29357 = z*t27915+y*t27917; + t28605 = RATIONAL(5.0,12.0); + t28638 = RATIONAL(-5.0,3.0); + t28872 = y*t28921; + t29355 = t28638*t28872+t28605*t28874; + t28010 = t28661*t28440; + t27986 = t28548*t28916; + t29354 = y*t28010+z*t27986; + t28016 = t28548*t28921; + t27891 = t28537*t28938; + t29352 = y*t28016+z*t27891; + t28475 = t28578*t28662; + t28201 = y*t28475; + t28224 = t28593*t28916; + t29351 = t28661*t28224+z*t28201; + t28289 = t28578*t28916; + t27966 = y*t28445; + t29350 = t28661*t28289+z*t27966; + t27929 = t28538*t28916; + t28897 = t28661*t28547; + t27975 = t28662*t28897; + t29349 = y*t27975+z*t27929; + t28616 = RATIONAL(10.0,9.0); + t28837 = t28616*t29026; + t29024 = y*t28661; + t28841 = t28637*t29024; + t29348 = t28662*t28841+t28656*t28837; + t28818 = t28661*t28916; + t28936 = t28662*t28569; + t27963 = z*t28936; + t29347 = y*t27963+t28567*t28818; + t28089 = y*t28448; + t29345 = z*t28089+t28565*t28785; + t29343 = t28638*t28879+t28605*t28880; + t28307 = t28581*t28916; + t28592 = RATIONAL(5.0,72.0); + t28881 = t28662*t28592; + t28131 = y*t28881; + t29342 = t28661*t28131+z*t28307; + t28871 = t28586*t29026; + t28962 = t28661*t28548; + t28071 = t28662*t28962; + t29341 = y*t28071+t28656*t28871; + t28621 = RATIONAL(-5.0,72.0); + t28272 = t28621*t28921; + t28802 = t28613*t28938; + t29339 = z*t28802+y*t28272; + t29003 = RATIONAL(-20.0,9.0)*t29040; + t29338 = t28631*t28785+t28656*t29003; + t28177 = z*t28881; + t28130 = t28581*t28921; + t29337 = t28660*t28177+y*t28130; + t28784 = t28613*t28986; + t28115 = t28621*t28916; + t29336 = z*t28115+y*t28784; + t27959 = t28657*t28893; + t28148 = x*t28882; + t29335 = t27959+t28148; + t28889 = t28567*t28658; + t28789 = t28661*t28889; + t29334 = x*t28789+(t28455+t28055)*z; + t29333 = z*t28148+t29461; + t28452 = t28547*t28659; + t27912 = z*t28452; + t28305 = t28622*t28953; + t29332 = t27912+z*t28321+t28658*t28305; + t29011 = x*t28563; + t27890 = t28657*t29011; + t28439 = t28554*t28659; + t28803 = t28660*t28885; + t29331 = x*t28803+(t28439+t27890)*y; + t28102 = t28622*t28948; + t29330 = t28657*t28102+(t28452+t28256)*y; + t28166 = t28582*t29031; + t28981 = t28661*t28658; + t28804 = t28575*t28981; + t29329 = t28659*t28804+(t28451+t28166)*z; + t28338 = t28575*t28961; + t28332 = t28656*t28982; + t29328 = t28657*t28319+t28338+t28332; + t28268 = t28656*t28882; + t28280 = t28656*t28920; + t29327 = t28658*t28325+t28268+t28280; + t27960 = t28537*t28953; + t29326 = t27960+(t28158+t28450)*z; + t28004 = t28658*t29011; + t28834 = x*t28981; + t29325 = t28565*t28834+(t28439+t28004)*z; + t28149 = t28575*t28948; + t28088 = y*t28451; + t29324 = t28657*t28149+y*t28209+t28088; + t28477 = t28585*t28656; + t28787 = t28662*t28485; + t28446 = t28548*t28662; + t29323 = t28656*t28783+t28477+t28657*t28787+t28446; + t28205 = t28656*t28974; + t28492 = t28587*t28656; + t29322 = t28589*t28938+t28657*t28182+(t28205+t28492)*y; + t29034 = x*t28606; + t28270 = z*t29034; + t28470 = t28581*t28661; + t28287 = x*t28470; + t29321 = t28270+t28287+t29455*t28659; + t28828 = t28657*t28961; + t29320 = t28658*t27920+t28552*t28828+t29459; + t29319 = t27917+t28661*t28188+t29418*z; + t28618 = RATIONAL(-5.0,36.0); + t28992 = t28618*t28656; + t28944 = t28605*t28656; + t28112 = t28657*t28944; + t29318 = t28657*t28782+t28575*t28938+(t28112+t28992)*y; + t28557 = RATIONAL(5.0,144.0); + t28903 = t28659*t28557; + t27926 = y*t28903; + t28792 = t28661*t28896; + t28508 = t28630*t28660; + t28406 = t28661*t28508; + t29041 = y*x; + t28137 = t28618*t29041; + t29317 = t28660*t28792+x*t28406+(t28137+t27926)*z; + t29316 = t29354+t29368; + t28291 = t28607*t28949; + t28608 = RATIONAL(-5.0,12.0); + t28928 = t28608*t28656; + t28197 = t28657*t28928; + t29315 = t28182+y*t28197+t28097+t28662*t28291; + t28339 = t28662*t28479; + t28110 = t28658*t28944; + t29314 = (t28481+t28339)*t28661+(t28110+t28992)*z; + t28807 = t28657*t28891; + t28434 = t28547*t28662; + t28829 = t28657*t28497; + t29313 = t28656*t28807+t28434+t28662*t28829+t28492; + t27968 = t28565*t28946; + t28447 = t28554*t28656; + t29312 = t28538*t28986+t28661*t27968+(t28268+t28447)*z; + t29311 = t28538*t28938+t28662*t28803+(t28447+t28280)*y; + t28901 = t28585*t28662; + t28798 = t28575*t28949; + t28121 = t28582*t28919; + t29310 = t28289+t28656*t28798+(t28121+t28901)*y; + t27940 = t28561*t28986; + t27924 = t28658*t28956; + t29309 = t27940+t28661*t28319+(t27924+t28453)*z; + t28276 = t28660*t28898; + t28868 = y*t28987; + t28644 = RATIONAL(-5.0,6.0); + t28925 = t28656*t28616; + t29308 = t28644*t28868+y*t28925+t28631*t28938+t28662*t28276; + t28465 = t28621*t28656; + t28786 = t28661*t28497; + t28595 = RATIONAL(5.0,96.0); + t28331 = t28595*t28961; + t28922 = t28582*t28661; + t29307 = (t28922+t28786)*t28662+(t28331+t28465)*z; + t28036 = t28662*t28885; + t28218 = t28613*t28916; + t29306 = t28657*t28218+t28224+(t28446+t28036)*y; + t28848 = t28601*t29020; + t28478 = t28581*t28660; + t28217 = x*t28478; + t28797 = t28607*t28911; + t29305 = t28660*t28797+y*t29034+t28659*t28848+t28217; + t29304 = t29349+t29360; + t28180 = t28613*t28906; + t28263 = t28587*t29033; + t28793 = t28658*t28922; + t28269 = z*t29015; + t29303 = z*t28180+t28659*t28793+t28263+t28269; + t28228 = z*t29014; + t28199 = t28661*t28459; + t28143 = t28659*t28884; + t29302 = t28228+z*t28143+t28199+t28658*t28792; + t28165 = t28659*t28886; + t28085 = t28659*t28897; + t29301 = t28594*t29000+z*t28165+(t28085+t28263)*y; + t28990 = t28659*t28578; + t28191 = z*t28990; + t29300 = t29422*t28661+(t28228+t28191)*y; + t29299 = t29366+t29377; + t27972 = t28561*t28916; + t29298 = z*t27972+t28564*t28880+t29347; + t28984 = t28659*t28540; + t27897 = y*t28984; + t29297 = y*t28270+t28922*t28948+z*t27897+x*t28810; + t28045 = t28548*t28953; + t28892 = t28587*t28660; + t28233 = t28659*t28892; + t29296 = x*t28871+z*t28233+(t28199+t28045)*y; + t28264 = t28657*t28896; + t29295 = t28264+t28166+t29376; + t28480 = t28592*t28656; + t28598 = RATIONAL(-5.0,96.0); + t28229 = t28598*t28961; + t29294 = (t28787+t28902)*t28661+(t28229+t28480)*z; + t29030 = x*t28657; + t27950 = t28561*t29030; + t29293 = t27950+t28575*t28906+t29335; + t29292 = t29352+t29358; + t28878 = t28644*t29016; + t29291 = z*t28925+t28656*t28878+t29441*t28661; + t29290 = t29366+t29367; + t29289 = t28657*t28307+t28660*t28899+(t27931+t28434)*y; + t28963 = t28660*t28661; + t28875 = x*t28963; + t29288 = t28622*t28875+t28661*t28149+t29447*z; + t27918 = x*t28897; + t29287 = t28658*t27889+t27918+(t28444+t28060)*z; + t29013 = x*t28548; + t27895 = z*t29013; + t28816 = t28661*t28947; + t28817 = t28660*t28897; + t29286 = x*t28816+t28659*t28817+(t27895+t27912)*y; + t29285 = t28659*t28803+y*t27959+t29436; + t28348 = t28598*t28987; + t28800 = t28603*t28938; + t29284 = t28657*t28800+t28660*t28902+(t28480+t28348)*y; + t28260 = t28622*t28919; + t29283 = y*t28260+t27913+t27929+t28656*t28803; + t29039 = x*z; + t29038 = y*t29039; + t28384 = t28661*t28526; + t28400 = t28630*t28948; + t28655 = RATIONAL(-5.0,9.0); + t29005 = t28659*t29040; + t29281 = t28655*t29005+RATIONAL(20.0,9.0)*t29038+x*t28384+t28661*t28400; + t28084 = x*t28962; + t29280 = t28084+t28659*t28789+(t28457+t27908)*z; + t28500 = t28613*t28660; + t29279 = x*t28500+t28137+t29428*t28659; + t29278 = x*t28807+t28452+t29390; + t28512 = t28648*t28660; + t28395 = x*t28512; + t29277 = t28659*t28810+t28625*t29005+x*t29003+t28661*t28395; + t28183 = t28657*t28902; + t28813 = t28657*t28916; + t29276 = t28622*t28813+y*t28183+t28125+t28145; + t28068 = t28548*t28938; + t29019 = y*t28586; + t28864 = t28661*t29019; + t29275 = t28656*t28864+z*t28068+t29356; + t29274 = t29344+t29351; + t28993 = t28659*t28589; + t28179 = y*t28993; + t29273 = y*t28269+z*t28179+t29425*t28661; + t28311 = t28581*t28911; + t28151 = x*t28886; + t28808 = t28660*t28911; + t29272 = t28612*t28808+t28151+(t28311+t29014)*y; + t28794 = t28582*t28949; + t28254 = t28613*t28911; + t28337 = x*t28892; + t29271 = t28659*t28794+t28337+(t28254+t29015)*y; + t28194 = t28582*t28961; + t29270 = t28662*t28804+t28661*t28475+(t28194+t28477)*z; + t28323 = t28656*t28970; + t29269 = t28578*t28938+t28662*t28798+(t28323+t28477)*y; + t28623 = RATIONAL(5.0,18.0); + t28988 = t28659*t28623; + t28330 = z*t28988; + t28791 = t28661*t28500; + t29268 = y*t28330+t28661*t28217+t28659*t28791+t29009*t29039; + t29267 = t29358+t29360; + t29037 = x*t28547; + t28070 = y*t29037; + t29266 = t28659*t28816+x*t28817+(t28088+t28070)*z; + t28646 = RATIONAL(5.0,6.0); + t28836 = t28646*t29016; + t28518 = t28630*t28662; + t28614 = RATIONAL(-10.0,9.0); + t28973 = t28656*t28614; + t29265 = t28656*t28836+z*t28973+(t28518+t28192)*t28661; + t28821 = t28600*t28949; + t28929 = t28657*t28595; + t28251 = t28656*t28929; + t29264 = t28662*t28821+t28582*t28938+(t28465+t28251)*y; + t29263 = x*t28822+t28439+t29384; + t29262 = t28660*t27931+t27891+(t28442+t28332)*y; + t29032 = x*t28564; + t28061 = z*t29032; + t28918 = t28659*t28541; + t27946 = y*t28918; + t29261 = t28575*t28875+z*t27946+t28661*t28102+y*t28061; + t28124 = t28656*t28912; + t29260 = t29443*t28661+(t28124+t28492)*z; + t29259 = t28010+t27973+z*t28338+t28662*t28789; + t28069 = t28561*t28919; + t28249 = t28612*t28916; + t29258 = t28657*t28249+t27986+y*t28069+t27966; + t29257 = y*t28002+t28567*t28808+t29437; + t28496 = t28613*t28661; + t28854 = z*t28906; + t28160 = t28661*t28479; + t29021 = z*t28618; + t29256 = t28659*t28160+t28604*t28854+(t29021+t28496)*x; + t28207 = t28658*t28928; + t28250 = t28607*t28946; + t29255 = t28661*t28250+t28259+(t28994+t28207)*z; + t28141 = t28580*t28949; + t29254 = t28662*t28141+y*t28973+t28630*t28938+t28646*t28868; + t29022 = y*t28623; + t28190 = t28581*t28948; + t28995 = t28659*t28620; + t28257 = y*t28995; + t29253 = z*t28257+x*t28791+t28661*t28190+t29022*t29039; + t29252 = t28559*t28828+t28658*t28033+t29456; + t28774 = t28618*t29008+t28661*t28249+t28998; + t29251 = t28774+t29336+t29337; + t28839 = x*t28949; + t29250 = t28622*t28839+y*t28264+t28070+t29440; + t29249 = t29362+t29342+t29381; + t29248 = t28260+(t28578+t28822)*t28656+t29443; + t28126 = t28575*t28946; + t28128 = t28575*t28919; + t29247 = t28126+t28475+t28128+(t28827+t28589)*t28656; + t28831 = t28637*t29026; + t28833 = t28616*t29024; + t28767 = t28656*t28833+t28662*t28831+t29338; + t28842 = t28641*t29026; + t28943 = t28662*t28620; + t28302 = y*t28943; + t29246 = t28767+t28656*t28842+t28661*t28302+t29369; + t29245 = t28661*t28148+(t28185+t29037)*z+t29421; + t27902 = t28659*t28885; + t29244 = t28613*t28839+(t28459+t27902)*y+t29422; + t29243 = t29359+t29337+t29381; + t28811 = t28661*t28945; + t28163 = t28578*t28953; + t27909 = t28565*t28906; + t28971 = t28661*t28593; + t28317 = x*t28971; + t29242 = x*t28811+t28163+t28317+(t27909+t28459)*z; + t27958 = t28561*t28921; + t29241 = y*t27958+t29345+t29357+t28564*t28874+t29347; + t29240 = t28069+t28442+t28609*t28828+t29452; + t29239 = t28774+t29339+t29342; + t28054 = t28567*t28911; + t29238 = t28581*t28839+(t28054+t28472)*y+t29425; + t28825 = t28657*t28466; + t27927 = t28563*t28946; + t29237 = t28656*t28825+t28447+t27927+t29407; + t29236 = x*t28798+(t28171+t29013)*y+t29465; + t28845 = t28641*t29024; + t29235 = t28656*t28845+t28662*t28849+t29338+t29348+t29369; + t29234 = z*t28232+t27895+x*t28804+t29464; + t28058 = t28659*t28889; + t28931 = t28661*t28596; + t28136 = x*t28931; + t29233 = t28096+t28581*t28834+t28136+(t28058+t28472)*z; + t28636 = RATIONAL(1.0,8.0); + t28983 = t28657*t28658; + t28830 = t28658*t28919; + t28584 = RATIONAL(-5.0,32.0); + t29232 = RATIONAL(1.0,32.0)*t28830+t28465+t28636*t28983+t28584*t28828+ +t29385; + t28591 = RATIONAL(5.0,32.0); + t28647 = RATIONAL(-1.0,8.0); + t29231 = t28591*t28828+t28480+t28647*t28983+RATIONAL(-1.0,32.0)*t28830+ +t29394; + t29230 = t29257+t29354; + t27444 = t28612*t28839; + t29229 = t27444+y*t28279+t29350+t29423; + t29228 = t29320+t29375; + t28923 = t28631*t28656; + t29227 = t28657*t28923+t28121+t28124+t29313; + t28888 = t28630*t28656; + t29226 = t28183+t28657*t28888+t28194+t29323; + t28421 = t28653*t29026; + t28146 = y*t28496; + t28150 = t28606*t28916; + t28743 = t28406+t28661*t28150+t28998+t29392*z; + t29225 = t28421+t28146+t28743+t29339+t29359; + t28484 = t28585*t28659; + t28152 = t28661*t28484; + t29224 = t28884*t29039+z*t28476+t28152+t29303; + t29029 = x*t28637; + t28391 = t28658*t29029; + t29223 = t28631*t28834+t29303+(t28391+t28993)*z; + t28972 = t28630*t28658; + t28796 = t28661*t28972; + t28413 = x*t28910; + t29222 = z*t28413+x*t28796+t28191+t29302; + t29221 = t29257+t29331; + t28469 = t28587*t28659; + t28196 = t28661*t28469; + t29220 = z*t28487+t28196+t28945*t29039+t29302; + t28377 = x*t28930; + t29219 = t28630*t28839+t29272+(t28990+t28377)*y; + t29218 = t29280+t29325; + t29217 = t28567*t28839+t29285+(t28455+t27950)*y; + t29216 = t29287+t29334; + t29215 = t28656*t28889+t29252+t29420; + t28211 = z*t28500; + t29214 = t28653*t29024+t28211+t28743+t29336+t29362; + t28378 = t28657*t29029; + t29213 = y*t28378+t28631*t28839+t28179+t29271; + t28858 = t28595*t29016; + t28957 = t28621*t28662; + t29212 = t28656*t28786+z*t28957+t28662*t28858+t28582*t28921+t29294; + t28556 = RATIONAL(-1.0,384.0); + t28799 = RATIONAL(1.0,384.0)*t28983; + t29211 = t28662*t28799+t28556*t28828+t29398+t29430; + t28866 = y*t28953; + t28907 = t28661*t28606; + t28862 = y*t28907; + t29210 = x*t28862+t28618*t28866+t28522*t29039+z*t28400+t29268; + t29209 = t28630*t29030+t27909+t29295+t29379; + t29208 = t28016+t28661*t28124+t29259+t29452*z; + t29207 = t28661*t27987+t27996+t29259+(t28275+t28959)*z; + t28865 = t28594*t29024; + t28857 = z*t28948; + t29206 = t28594*t28857+RATIONAL(-32.0,27.0)*t29038+t28553*t29000+t28619* +t29005+t28659*t28865+t29406*t28661; + t29205 = t29286+t29372; + t28524 = t28626*t28658; + t28805 = t28656*t28524; + t28978 = t28662*t28557; + t28859 = t28604*t29016; + t29204 = t28661*t28805+t28662*t28859+z*t28978+t28613*t28921+t29314; + t27899 = t28660*t28915; + t28838 = t28589*t29018; + t29203 = t28661*t28838+t28659*t28806+(t27899+t29436)*z+(t27918+t29461)*y; + t29202 = t28661*t28194+t28656*t28897+t29312+(t27927+t28437)*z; + t29201 = t28556*t28830+t28656*t28799+t29402+t29467; + t28844 = t28557*t29026; + t29200 = t29288+t28659*t28844+t28540*t29000+t29414*y; + t29199 = x*t28825+t28441+t29290+t29335; + t28360 = t28645*t29026; + t29035 = x*t28614; + t28092 = y*t29035; + t28863 = t28661*t29022; + t29198 = t29281+x*t28360+t28661*t28092+(t28421+t28863)*t28659; + t28850 = t28654*t29020; + t28877 = y*t28919; + t29197 = t28630*t28877+t28637*t28813+t28657*t28802+t28593*t28938+t28656* +t28850+t29405; + t28996 = t28659*t28606; + t28195 = t28659*t28470; + t29196 = t29256+z*t28996+t28195+t29455*x; + t29195 = t28561*t28808+t28563*t28839+t29411*y+t29399; + t27954 = t28563*t28938; + t29194 = t28657*t27954+t28561*t28813+t28536*t28938+t28656*t28914+(t29420+ +t29456)*y; + t28861 = t28598*t29020; + t29193 = t28603*t28813+t28249+t28662*t28861+t28131+t29264; + t28316 = t28575*t28953; + t29192 = y*t28316+t28623*t29000+t28621*t28857+x*t28146+t29317; + t29191 = t29286+t29371; + t29190 = t27890+t28659*t28882+t29263+t29388; + t28965 = t28657*t28631; + t28867 = y*t28965; + t29189 = t28583*t28916+t28662*t28867+t28660*t28101+t28596*t28938+t29457* +t28656+t29453*y; + t28870 = x*t28983; + t29188 = t28484+t28603*t28870+t29387+t29390+t29391; + t28826 = t28658*t28921; + t29187 = t28662*t28846+t28130+t27921+t28628*t28826+t29255; + t28873 = z*t28946; + t28611 = RATIONAL(-5.0,24.0); + t28960 = t28623*t28662; + t29186 = t28611*t28873+t28642*t28826+t28654*t28921+z*t28960+t29265; + t28939 = t28659*t28631; + t28405 = t28660*t28939; + t28387 = t28640*t28949; + t29036 = x*t28616; + t29006 = x*t29020; + t28615 = RATIONAL(5.0,24.0); + t29010 = t28615*y; + t28843 = t28657*t29010; + t29185 = y*t29036+t28644*t29006+x*t28387+t28405+t28257+t28395+(t28276+ +t28843)*t28659; + t28950 = t28662*t28536; + t29184 = t28537*t28916+t28567*t28813+t29311+(t28950+t28128)*y; + t29183 = t29277+(t28841+t28849)*t28659+(t28845+t28837)*x; + t29182 = t28662*t28952+t28563*t28826+t28658*t27940+t28656*t28917+(t29409+ +t29459)*z; + t28320 = t28658*t28902; + t29181 = z*t28320+t28153+t28589*t28921+t28661*t28268+t29270; + t29002 = x*t29024; + t29180 = y*t28163+t28589*t29002+t29266+t29440*z; + t29179 = t28469+x*t28829+t29295+t29382; + t28820 = t28561*t28949; + t29178 = t28536*t28916+t28563*t28813+(t28914+t28820)*t28662+(t29459+ +t29460)*y; + t29177 = t27902+x*t28972+t29376+t29379+t29382; + t28366 = t28645*t29024; + t28347 = z*t29035; + t29176 = t28660*t28347+t28653*t28866+x*t28366+t28623*t28857+t29281; + t28851 = t28615*t29016; + t29175 = t28662*t28851+z*t28943+t28648*t28921+t28640*t28826+t29291; + t28855 = t28648*t29016; + t29174 = t28656*t28855+t28583*t28921+t28662*t28931+t28631*t28873+t29451* +t28661+t29453*z; + t28860 = y*t28929; + t29173 = t28600*t28813+t28662*t28860+y*t28957+t28582*t28916+t29284; + t29172 = t28657*t28250+t28593*t28662+t29429*t28656+t29446+t29450; + t29171 = t28058+x*t28965+t29278+t29391; + t28463 = t28575*t28660; + t29170 = z*t28463+t28540*t28818+t28612*t28963+t29357+t29404*y; + t29169 = t29290+t29377+t29386; + t29168 = t28559*t28823+t28552*t28870+t29401+t29411; + t29167 = t29236+t29330; + t28790 = t28571*t28949; + t28788 = t28572*t28949; + t28909 = t28533*t28656; + t29166 = t28662*t28790+t28660*t28909+t28530*t28938+t28656*t28788+t29402*y +; + t29165 = t29320+t29370; + t28934 = t28657*t28611; + t28832 = y*t28934; + t29164 = t28646*t29006+y*t28988+t28400+t28092+(t28832+t28141)*t28659+ +t29427*x; + t29163 = t28660*t27997+t28537*t28875+t29458*z+t29403*y; + t29162 = t29267+t29316; + t29161 = t28036+t28567*t28987+t29252+t29424; + t29160 = t28656*t28811+t28593*t28921+t29270+(t27968+t28446)*z; + t29159 = t29262+t29283; + t28835 = z*t28972; + t29158 = t28658*t28784+t28661*t28407+t29462*t28656+(t28835+t28971)*t28662 ++t29445; + t29157 = t28656*t28796+t28340+t28661*t28320+t28071+t28350+(t28475+t29451) +*z; + t28401 = t28628*t28949; + t29156 = x*t28401+t28608*t29006+t28102+t27897+t29305; + t29155 = t29297+t28592*t28866+x*t28869+(t28102+t28217)*z; + t29154 = t28659*t28860+t28603*t28808+(t28861+t28821)*x+t29417+t29447; + t29153 = t28054+t28631*t29031+t29278+t29387; + t29012 = x*t28535; + t29152 = t28637*t28834+z*t29012+(t28835+t28811)*t28659+t29462*x+t29442; + t29151 = t29424*t28661+t29430*z+t29397; + t29150 = t29286+t29320; + t29149 = t28563*t28808+x*t28820+t29400*y+t29458; + t29148 = t28662*t28917+t28561*t28826+t28661*t27927+t28554*t28921+(t29424+ +t29456)*z; + t28969 = t28594*t28659; + t28318 = y*t28969; + t29147 = t28657*t28190+t28318+t28659*t28867+t29457*x+t29406; + t29146 = t28659*t28831+t28620*t28866+t29277+(t28833+t28842)*x; + t27911 = t28662*t28889; + t29145 = t28581*t28826+t28661*t28899+t29260+(t28434+t27911)*z; + t29144 = t28538*t28875+t28660*t27960+t29439*y+t29399*z; + t29001 = RATIONAL(32.0,27.0)*t29040; + t29004 = t28583*t29040; + t29143 = t28662*t29004+t28656*t29001+t28593*t28785+t29445*t28660+t29405* +t28661; + t29142 = t28004+t28622*t28911+t29263+t29389; + t28840 = t28557*t29024; + t29141 = t29288+t28540*t29002+t28659*t28840+t29417*z; + t29140 = x*t29001+t28586*t28857+(t29000+t29002)*t28535+t29419*t28661+( +t28864+t29004)*t28659; + t29139 = t28613*t28808+t28637*t28839+t28911*t28505+x*t28850+(t28958+ +t29012)*y+t29419; + t28184 = t28582*t28946; + t29138 = t29260+t28578*t28921+t28661*t28338+(t28184+t28901)*z; + t28795 = t28661*t28892; + t29137 = x*t28795+t28661*t28165+t28594*t29038+(t28225+t28095)*z+(t28136+ +t29442)*y; + t29136 = t28660*t28183+t28630*t28813+t28201+t28266+t28068+(t28951+t29448) +*y; + t29135 = t28618*t29002+z*t28405+t28659*t28862+t28508*t29039+t29253; + t29134 = x*t28849+t28592*t28857+t29297+(t28305+t28287)*y; + t29133 = t28661*t28075+t28660*t28852+(t28084+t27960)*y+(t29423+t29437)*z; + t28386 = t28658*t28923; + t29132 = t28661*t28386+t28587*t28921+t27975+t28662*t28793+(t29413+t29446) +*z; + t29131 = t28450+t28609*t28870+t29384+t29388+t29389; + t28941 = t28659*t28613; + t28980 = t28618*t28659; + t29130 = t29321+t28661*t28941+z*t28980+(t28160+t28859)*x; + t29129 = t28378+t28658*t28797+t28391+t28180+t28254+t28476+t29429*x; + t29128 = t28547*t28916+t28656*t28794+t29311+t29407*y; + t29127 = t28540*t28866+x*t28840+t29261+t29435*z; + t28306 = t28661*t28487; + t28464 = t28583*x; + t29126 = t28658*t28195+t28653*t28834+t28631*t28854+x*t28855+t28306+t28661 +*t28464+(t29027+t28969)*z; + t29125 = t28013+t28631*t28813+t28656*t28892+t28662*t28794+(t29413+t29450) +*y; + t29124 = t27958+t28599*t28826+t28558*t28873+t27963+t29319; + t29123 = t28659*t28795+t29019*t29039+t28661*t28151+(t28306+t28317)*y+( +t28267+t28318+t28334)*z; + t29122 = t28539*t28785+t28574*t28818+t29408*z+t29397*y; + t29121 = t28626*t28870+t28487+t28377+t28311+t28464+t28143+t28413+t28609* +t28823; + t29120 = t28662*t28788+t28656*t28790+t29398*y+t29408; + t29119 = t28659*t28861+t27946+x*t28860+t28603*t28839+t28660*t28801+y* +t29032+t29435; + t29118 = t28540*t28857+x*t28844+t29261+t29416*y; + t29117 = t29317+t28621*t28866+z*t28149+(t28863+t28211)*x; + t29116 = t28537*t28921+t28656*t28789+t29312+(t28126+t28950)*z; + t28927 = t28568*t28662; + t29115 = t28555*t28873+t28597*t28826+z*t28927+t28563*t28921+t29309; + t28203 = t28609*t28919; + t29114 = t28657*t28805+t28658*t28203+t28583*t28656+t28461+t29448+t29451; + t29113 = t28552*t28823+t28559*t28870+t29400+t29426; + t29112 = t28662*t28905+(t28909+t29409)*t28661+(t29415+t29467)*z; + t29111 = t29266+(t28838+t28310)*z+t29421*y; + t29110 = t29293+t29299; + t28819 = t28661*t28485; + t29109 = t28598*t28873+t28177+t28656*t28819+t28612*t28921+t29307; + t28363 = t28626*t28949; + t29108 = t28605*t29006+t27926+x*t28363+t28149+t29279; + t28371 = t28655*t28916; + t29107 = t28366+t28767+t28360+t28384+RATIONAL(16.0,9.0)*t29040+t28654* +t29008+t28661*t28371+t29348; + t29106 = t28165+y*t28476+t28581*t29006+t27444+t29271+t29393+t29282; + t28023 = t28659*t28947; + t28729 = t29274+t29300; + t29105 = t28729+x*t28864+y*t28196+t29275+(t28023+t28151)*z; + t27961 = t28547*t28948; + t28742 = t29273+t29274; + t29104 = t28742+y*t28152+x*t28865+t29275+(t27961+t28337)*z; + t28342 = t28661*t28891; + t28507 = t28631*t28661; + t29103 = t28658*t28824+t28342+t28618*t28921+t29294+t28507+(t29432+t29394) +*z; + t29102 = t28564*t28921+t28293+t29309+(t28331+t28622)*t28661+(t29438+ +t29449)*z; + t28026 = t28555*t28987; + t28576 = RATIONAL(1.0,16.0); + t28175 = t28576*t28983; + t29101 = RATIONAL(1.0,64.0)*t28830+t28026+t28175+RATIONAL(-5.0,64.0)* +t28828+t29374+t29418+t29434; + t29100 = t28500+t28363+t29315+t29392+t28615*t28813+t28115+t29433*y; + t28517 = t28630*t28661; + t28220 = t28661*t28942; + t29099 = t28604*t28826+t28517+t28656*t28907+t29307+t28220+(t29410+t29385) +*z; + t28343 = t28611*t28961; + t28913 = t28628*t28661; + t28374 = t28658*t28913; + t29098 = t28661*t28343+t28592*t28921+t28470+t28374+t29314+(t28527+t28104+ +t29444)*z; + t28895 = t28615*t28656; + t28243 = t28658*t28895; + t29097 = t28243+t28524+t28250+t28251+t29232+t29378; + t28412 = t28661*t28524; + t29096 = t28661*t28243+t28496+t28412+t28272+t29255+(t28997+t28630+t29431) +*z; + t28602 = RATIONAL(-1.0,16.0); + t28144 = t28602*t28983; + t29095 = RATIONAL(-1.0,64.0)*t28830+t28144+RATIONAL(5.0,64.0)*t28828+ +t27924+t29373+t29380+t29449; + t29094 = t28343+t28348+t28339+t28509+t29231+t29383; + t27718 = x*t28794; + t29093 = t27718+t27899+t29354+t29285+t29350+(t28335+t28441)*y; + t28650 = RATIONAL(2.0,3.0); + t29092 = t28628*t28877+t28650*t29020+t28371+t28605*t28813+t29308+t29463*y ++t29427; + t29091 = t28628*t28873+t28650*t29016+t29291+t28661*t28110+t28655*t28921+ +t29395+t29463*z; + t29090 = t27718+t28613*t29006+t28233+y*t28487+t29272+t29393; + t29089 = t27931+t28386+t28205+t28184+t29313+t29341+t29351; + t29088 = t28036+t28658*t28888+t28320+t28323+t29323+t29341+t29353; + t28809 = t28611*t28916; + t29087 = t28657*t28809+t28592*t28916+t28401+t28478+t29318+(t29412+t29444) +*y; + t27932 = t28541*t28921; + t29086 = t28661*t28229+t27932+t29319+t28160+t29434*z+t29404; + t28649 = RATIONAL(-2.0,3.0); + t29085 = t28608*t28813+t28626*t28877+t28387+t28649*t29020+t28625*t28916+ +t28512+t29254+t29454*y; + t29084 = t28661*t28207+t28625*t28921+t28649*t29016+t29396+t28626*t28873+ +t29265+t29454*z; + t29083 = t29160+t29242; + t27721 = x*t28793; + t28770 = t27721+t29327; + t29082 = t28770+t29220+t29247; + t28763 = t28045+t29324; + t29081 = t28763+t29222+t29244; + t27559 = t28612*t28834; + t28768 = t27559+t29328; + t29080 = t28768+t29240+t29280+t29326; + t28765 = t28085+t29330; + t29079 = t28765+t29223+t29238; + t29078 = t28770+t29237+t29287+t29333; + t29077 = t28045+t29330+t29222+t29238; + t28780 = t28085+t29324; + t29076 = t28780+t29223+t29244; + t29075 = t29145+t29233; + t29074 = t28768+t29224+t29248; + t29073 = t29136+t29213; + t29072 = t29209+t29226; + t29071 = t29171+t29227; + t29070 = t29209+t29227; + t29069 = t29125+t29219; + t29068 = t29171+t29226; + t29067 = t29123+t29310+t29322; + t29066 = t29203+t29258+t29262; + t29065 = t29132+t29289+t29322; + t29064 = t29122+(t28060+t28055)*t28661+t29426*z+t29403; + t29063 = t29181+t29188; + t29062 = t29149+t29201; + t29061 = t29128+t29133; + t29060 = t29112+t29144; + t29059 = t29199+t29202; + t29058 = t29166+t29168; + t29057 = t29157+t29269+t29306; + t29056 = t29112+t29163; + t29055 = t29179+t29181; + t29054 = t29153+t29296+t29300; + t29053 = t29199+t29208; + t29052 = t29138+t29179; + t29051 = t29137+t29269+t29276; + t29050 = t29195+t29211; + t29049 = t29177+t29273+t29301; + t29048 = t29144+t29151; + t29047 = t29131+t29202; + t29046 = t29131+t29208; + t29045 = t29122+(t27908+t28004)*t28661+t29401*z+t29439; + t29044 = t29113+t29120; + t29043 = t29138+t29188; + t29042 = t29151+t29163; + t28633 = RATIONAL(5.0,3.0); + t29025 = t28633*z; + t29017 = t28608*z; + t29007 = x*t29016; + t28989 = t28633*t28661; + t28979 = t27968+t27961; + t28964 = t28588*t28661; + t28955 = t28649*t28661; + t28935 = t27911+t27961; + t28933 = t28595*t28662; + t28926 = t28608*t28661; + t28908 = t27911+t28023; + t28887 = t27968+t28023; + t28853 = t28660*t29021; + t28415 = t28661*t28939; + t28376 = t28630*t28953; + t28781 = z*t27954+y*t27932+t29345; + t28776 = t27559+t29327; + t28772 = t27968+t29329; + t28771 = t27968+t29332; + t28769 = t27911+t29329; + t28766 = t27911+t29332; + t28764 = t27721+t29328; + t28562 = RATIONAL(25.0,96.0); + t28762 = t28598*t28662+t28562*t28656+t28611; + t28627 = RATIONAL(5.0,8.0); + t28761 = RATIONAL(-1.0,2.0)+t28627*t28656+t28647*t28662; + t28542 = RATIONAL(-25.0,12.0); + t28760 = t28633+t28605*t28662+t28542*t28656; + t28590 = RATIONAL(5.0,16.0); + t28759 = t28590*t28662+RATIONAL(5.0,4.0)+RATIONAL(-25.0,16.0)*t28656; + t28632 = RATIONAL(-5.0,8.0); + t28758 = RATIONAL(25.0,32.0)*t28656+t28584*t28662+t28632; + t28757 = t28649+t28646*t28656+t28626*t28662; + t28756 = RATIONAL(1.0,2.0)+t28636*t28662+t28632*t28656; + t28577 = RATIONAL(-5.0,16.0); + t28634 = RATIONAL(1.0,4.0); + t28755 = t28577*t28656+t28634+t28576*t28662; + t28754 = t28608*t28662+RATIONAL(25.0,12.0)*t28656+t28638; + t28753 = t28615+t28933+t28932; + t28643 = RATIONAL(-1.0,4.0); + t28752 = t28643+t28602*t28662+t28590*t28656; + t28751 = t28628*t28662+t28644*t28656+t28650; + t28750 = t28591*t28662+RATIONAL(-25.0,32.0)*t28656+t28627; + t28749 = t28632*t28662+RATIONAL(-5.0,2.0)+RATIONAL(25.0,8.0)*t28656; + t28624 = RATIONAL(-5.0,4.0); + t28573 = RATIONAL(25.0,16.0); + t28748 = t28624+t28573*t28656+t28577*t28662; + t28747 = t28603*t28662+t28601*t28656+t28588; + t28746 = t28580+t28604*t28656+t28600*t28662; + t28745 = t28660*t28955+t28644*t29008+t28646*t28818+RATIONAL(-10.0,3.0)* +t29040+t29361; + t28744 = t28660*t28913+t28933*t29040+t28661*t28809+z*t29010+t29363; + t28740 = t29267+t29299; + t28739 = t28561*t28938+t28660*t28265+t28781+t29380*y; + t28738 = t29280+t29292; + t28737 = t29230+t29358; + t28736 = t29262+t29292; + t28735 = t29287+t29292; + t28734 = t29282+t29322; + t28733 = t28660*t28325+y*t28026+t28089+t27954+t28781; + t28551 = RATIONAL(-25.0,24.0); + t28732 = t28650*t28818+t28551*t29008+t29343+t29355+t29361; + t28731 = t28562*t29008+t28607*t28818+t29363+t29364+t29365; + t28730 = t29269+t29282; + t28728 = (t28964+t28615*z)*t28660+(RATIONAL(-25.0,48.0)*z+t28615*t28661)* +y; + t28546 = RATIONAL(25.0,48.0); + t28727 = (t28580*t28661+t28611*z)*t28660+(t28611*t28661+t28546*z)*y; + t28639 = RATIONAL(4.0,3.0); + t28726 = t28640*t28874+t28639*t29026+y*t28989+t28542*t28872+t28745+t29343 +; + t28725 = t28546*t28879+t28603*t28880+y*t28964+t28660*t29017+t28744+t29365 +; + t28724 = t28640*t28880+t28542*t28879+t28660*t29025+t28639*t29024+t28745+ +t29355; + t28723 = t28546*t28872+z*t28800+t28588*t29026+y*t28926+t28744+t29364; + t28722 = t28599*t28813+y*t28936+t28733+t28558*t28877+t27972+t29298; + t28721 = t28517*t29041+y*t28415+x*t28853+t28606*t28857+t29251+t29253; + t28720 = t28373+t28662*t28843+t28302+t28656*t28387+t29246+t29308; + t28719 = y*t28978+t28662*t28856+t28218+t28656*t28363+t29249+t29318; + t28718 = t29239+y*t28980+t28660*t28941+t29305+t29428*x; + t28717 = t29235+t28415+(t28342+t28851)*t28659+(t29036+t28995)*z+(t28878+ +t29396)*x; + t28716 = z*t28903+x*t28412+t28605*t29007+t28316+t29243+t29256; + t28715 = t28662*t28848+t28307+y*t28904+t28628*t28813+t29249+t29315; + t28714 = t28563*t28916+t28739+y*t28927+t28597*t28813+t28555*t28877+t29298 +; + t28713 = t28662*t28832+t28656*t28368+t28654*t28916+y*t28960+t29246+t29254 +; + t28712 = t28606*t29000+y*t28376+t28507*t29041+t28659*t28853+t29251+t29268 +; + t28711 = x*t28786+t28661*t28814+t28595*t28854+t29241+t28598*t29007+t29469 +*z+t29414; + t28710 = z*t28918+t28061+t29241+t28598*t28854+t28659*t28786+(t28819+ +t28858)*x+t29416; + t28709 = t29239+t28190+y*t28996+t29279+(t28291+t28848)*x; + t28708 = z*t28984+x*t28374+t28608*t29007+t28305+t29243+t29321; + t28707 = t28659*t28220+t28347+t28330+t28611*t28854+t29235+t28376+(t28836+ +t29395)*x; + t28706 = t28739+t28564*t28916+t29170+t28291+t28622*t28660+t28595*t28813+ +t29373*y; + t28705 = t29214+t28229+t28203+t28628*t28657+t28656*t28934+t29231+t29432; + t28704 = t28648+t28207+t28197+t28518+t28590*t28828+t28625*t28656+t29107+ +t28662*t28144+t28643*t28983+t29431+t29433; + t28703 = t28508+t28150+t28141+t29264+t29225+t28604*t28813+(t29378+t29385) +*y; + t28702 = t28634*t28983+t28662*t28175+t28655*t28656+t29107+t28110+t28112+ +t28577*t28828+t29412+t29441+t29466; + t28701 = t28733+t28463+t29170+t27915+t28598*t28813+t28122+t29374*y; + t28700 = t29214+t28607*t28919+t28331+t29232+(t28895+t28626)*t28657+t29410 +; + t28699 = t28601*t28813+t28522+t28276+t29225+t28618*t28916+t29284+(t29383+ +t29394)*y; + t28698 = t27961+t29178+t29205+t28737+t29331+t29360+t29368; + t28697 = t29088+t28742+t29153+t29301; + t28696 = t29093+t28738+t28776+t29237+t29326; + t28695 = t28023+t29207+t29217+t28740+t29293+t29316; + t28694 = t29114+t29139+t29126+t29143; + t28693 = t29045+t29120+t29168; + t28692 = t29160+t29104+t29233+t29332; + t28691 = t29113+t29045+t29166; + t28690 = t29143+t29140+t29147+t29189; + t28689 = t29165+t28736+t29182+t29283+t29304; + t28688 = t29152+t29174+t29143+t29206; + t28687 = t28764+t29106+t29220+t29248; + t28686 = t29088+t28729+t29177+t29296; + t28685 = t29194+t29162+t29190+t29245+t29329; + t28684 = t29089+t28734+t29157+t29289; + t28683 = t29149+t29064+t29211; + t28682 = t29089+t28730+t29132+t29306; + t28681 = t29229+t28736+t29133+t29230+t29258; + t28680 = t27961+t29105+t29125+t29213; + t28679 = t29093+t28764+t28735+t29240+t29333; + t28678 = t28045+t29184+t28735+t29142+t29304+t29334; + t28677 = t29064+t29195+t29201; + t28676 = t29116+t29162+t29111+t29234+t29332; + t28675 = t29161+t28738+t28780+t29250+t29304+t29325; + t28674 = t29105+t29136+t28023+t29219; + t28673 = t28776+t29106+t29224+t29247; + t28672 = t28734+t29090+t29137+t29310; + t28671 = t28730+t29090+t29123+t29276; + t28670 = t29203+t29128+t28737+t29229+t29352; + t28669 = t29148+t29167+t28740+t29349+t29352+t29367+t29386; + t28668 = t29172+t29143+t29158+t29197; + t28667 = t29104+t29145+t29242+t29329; + coeffs_dyz->coeff_m2_m2_m2 = t28691+t29050+t29056; + coeffs_dyz->coeff_m1_m2_m2 = t29059+t28670+t29080; + coeffs_dyz->coeff_0_m2_m2 = t29101+t28706+t29102; + coeffs_dyz->coeff_p1_m2_m2 = t28679+t29047+t29061; + coeffs_dyz->coeff_p2_m2_m2 = t29058+t29060+t28683; + coeffs_dyz->coeff_m2_m1_m2 = t28675+t29169+t29184+t29182+t29191; + coeffs_dyz->coeff_m1_m1_m2 = t29070+t28692+t28908+t29069; + coeffs_dyz->coeff_0_m1_m2 = t28705+t29087+t29099; + coeffs_dyz->coeff_p1_m1_m2 = t29071+t28680+t28769+t29083; + coeffs_dyz->coeff_p2_m1_m2 = t29161+t29180+t29167+t28678+t29182; + coeffs_dyz->coeff_m2_0_m2 = t28714+t29119+t29141; + coeffs_dyz->coeff_m1_0_m2 = t28719+t29117+t29156; + coeffs_dyz->coeff_0_0_m2 = (t28750*t28657+t28762)*y+t28723+(t28752*t28657 ++t28746)*t28660; + coeffs_dyz->coeff_p1_0_m2 = t28719+t29108+t29155; + coeffs_dyz->coeff_p2_0_m2 = t28714+t29127+t29154; + coeffs_dyz->coeff_m2_p1_m2 = t29148+t29250+t28678+t29150+t29324+t29370+ +t29371; + coeffs_dyz->coeff_m1_p1_m2 = t29068+t28667+t28887+t29069; + coeffs_dyz->coeff_0_p1_m2 = t28700+t29087+t29103; + coeffs_dyz->coeff_p1_p1_m2 = t28771+t28680+t29072+t29075; + coeffs_dyz->coeff_p2_p1_m2 = t29180+t29165+t29184+t28669+t28085+t29218; + coeffs_dyz->coeff_m2_p2_m2 = t29058+t28677+t29042; + coeffs_dyz->coeff_m1_p2_m2 = t29078+t29046+t28670; + coeffs_dyz->coeff_0_p2_m2 = t28706+t29086+t29095; + coeffs_dyz->coeff_p1_p2_m2 = t28696+t29061+t29053; + coeffs_dyz->coeff_p2_p2_m2 = t28691+t29062+t29048; + coeffs_dyz->coeff_m2_m2_m1 = t29116+t28698+t29110+t28772+t29215+t29245; + coeffs_dyz->coeff_m1_m2_m1 = t29077+t28682+t29049; + coeffs_dyz->coeff_0_m2_m1 = t28703+t29094+t29098; + coeffs_dyz->coeff_p1_m2_m1 = t28682+t29054+t29076; + coeffs_dyz->coeff_p2_m2_m1 = t29215+t29178+t28676+t28887+t29190+t29217; + coeffs_dyz->coeff_m2_m1_m1 = t29055+t28671+t29082; + coeffs_dyz->coeff_m1_m1_m1 = t28668+t29121+t29147+t29126+t29206; + coeffs_dyz->coeff_0_m1_m1 = t28702+t29092+t29091; + coeffs_dyz->coeff_p1_m1_m1 = t28668+t29139+t29129+t29140+t29152; + coeffs_dyz->coeff_p2_m1_m1 = t28673+t29051+t29063; + coeffs_dyz->coeff_m2_0_m1 = t28718+t29193+t29210; + coeffs_dyz->coeff_m1_0_m1 = t28720+t29164+t29198; + coeffs_dyz->coeff_0_0_m1 = t28726+(t28756*t28657+t28757)*t28660+(t28748* +t28657+t28760)*y; + coeffs_dyz->coeff_p1_0_m1 = t29146+t28720+t29185; + coeffs_dyz->coeff_p2_0_m1 = t28709+t29135+t29193; + coeffs_dyz->coeff_m2_p1_m1 = t29074+t29043+t28671; + coeffs_dyz->coeff_m1_p1_m1 = t28688+t29114+t29129+t29147+t29197; + coeffs_dyz->coeff_0_p1_m1 = t29084+t29092+t28704; + coeffs_dyz->coeff_p1_p1_m1 = t28694+t29174+t29121+t29140+t29197; + coeffs_dyz->coeff_p2_p1_m1 = t28687+t29051+t29052; + coeffs_dyz->coeff_m2_p2_m1 = t29207+t28698+t29190+t28766+t29228+t29234; + coeffs_dyz->coeff_m1_p2_m1 = t28697+t29079+t29057; + coeffs_dyz->coeff_0_p2_m1 = t28703+t29096+t29097; + coeffs_dyz->coeff_p1_p2_m1 = t29081+t28686+t29057; + coeffs_dyz->coeff_p2_p2_m1 = t28695+t29178+t28769+t29111+t29228+t29245; + coeffs_dyz->coeff_m2_m2_0 = t28710+t29115+t29200; + coeffs_dyz->coeff_m1_m2_0 = t29192+t28708+t29204; + coeffs_dyz->coeff_0_m2_0 = t28725+(t28752*t28658+t28746)*t28661+(t28750* +t28658+t28762)*z; + coeffs_dyz->coeff_p1_m2_0 = t28716+t29134+t29204; + coeffs_dyz->coeff_p2_m2_0 = t28711+t29115+t29118; + coeffs_dyz->coeff_m2_m1_0 = t28712+t29109+t29130; + coeffs_dyz->coeff_m1_m1_0 = t29175+t28707+t29176; + coeffs_dyz->coeff_0_m1_0 = (t28756*t28658+t28757)*t28661+(t28748*t28658+ +t28760)*z+t28724; + coeffs_dyz->coeff_p1_m1_0 = t28717+t29175+t29183; + coeffs_dyz->coeff_p2_m1_0 = t28721+t29109+t29196; + coeffs_dyz->coeff_m2_0_0 = t28728*t28659+t28727*x+t28731; + coeffs_dyz->coeff_m1_0_0 = ((t29017+t28913)*t28660+(t28926+RATIONAL(25.0, +24.0)*z)*y)*t28659+((t29025+t28955)*t28660+(RATIONAL(-25.0,6.0)*z+t28989)*y)*x+ +t28732; + coeffs_dyz->coeff_0_0_0 = ((t28634*t28662+1.0+t28624*t28656)*t28661+ +t28749*z)*t28660+(t28749*t28661+(RATIONAL(-125.0,16.0)*t28656+t28573*t28662+ +RATIONAL(25.0,4.0))*z)*y; + coeffs_dyz->coeff_p1_0_0 = ((t28605*z+t28626*t28661)*t28660+(t28551*z+ +t28605*t28661)*y)*t28659+((t28638*z+t28650*t28661)*t28660+(t28638*t28661+t29028 +)*y)*x+t28732; + coeffs_dyz->coeff_p2_0_0 = t28727*t28659+t28728*x+t28731; + coeffs_dyz->coeff_m2_p1_0 = t28712+t29196+t29212; + coeffs_dyz->coeff_m1_p1_0 = t28717+t29176+t29186; + coeffs_dyz->coeff_0_p1_0 = (t28759*t28658+t28754)*z+(t28761*t28658+t28751 +)*t28661+t28724; + coeffs_dyz->coeff_p1_p1_0 = t29183+t28707+t29186; + coeffs_dyz->coeff_p2_p1_0 = t28721+t29130+t29212; + coeffs_dyz->coeff_m2_p2_0 = t29124+t28711+t29200; + coeffs_dyz->coeff_m1_p2_0 = t28716+t29187+t29192; + coeffs_dyz->coeff_0_p2_0 = t28725+(t28755*t28658+t28747)*t28661+(t28758* +t28658+t28753)*z; + coeffs_dyz->coeff_p1_p2_0 = t29134+t28708+t29187; + coeffs_dyz->coeff_p2_p2_0 = t28710+t29118+t29124; + coeffs_dyz->coeff_m2_m2_p1 = t29116+t28908+t28685+t29217+t29150+t29372+ +t29375; + coeffs_dyz->coeff_m1_m2_p1 = t29081+t28697+t29065; + coeffs_dyz->coeff_0_m2_p1 = t28699+t29097+t29098; + coeffs_dyz->coeff_p1_m2_p1 = t29079+t28686+t29065; + coeffs_dyz->coeff_p2_m2_p1 = t29194+t28935+t28676+t29221+t29110+t29228; + coeffs_dyz->coeff_m2_m1_p1 = t28687+t29067+t29063; + coeffs_dyz->coeff_m1_m1_p1 = t29189+t28694+t29129+t29158+t29206; + coeffs_dyz->coeff_0_m1_p1 = t29085+t29091+t28704; + coeffs_dyz->coeff_p1_m1_p1 = t29152+t29121+t29114+t28690+t29158; + coeffs_dyz->coeff_p2_m1_p1 = t29074+t28672+t29055; + coeffs_dyz->coeff_m2_0_p1 = t28709+t29173+t29210; + coeffs_dyz->coeff_m1_0_p1 = t28713+t29185+t29198; + coeffs_dyz->coeff_0_0_p1 = t28726+(t28761*t28657+t28751)*t28660+(t28759* +t28657+t28754)*y; + coeffs_dyz->coeff_p1_0_p1 = t28713+t29146+t29164; + coeffs_dyz->coeff_p2_0_p1 = t29135+t28718+t29173; + coeffs_dyz->coeff_m2_p1_p1 = t28673+t29067+t29052; + coeffs_dyz->coeff_m1_p1_p1 = t29172+t28688+t29121+t29139+t29189; + coeffs_dyz->coeff_0_p1_p1 = t29085+t28702+t29084; + coeffs_dyz->coeff_p1_p1_p1 = t29172+t29129+t29126+t28690+t29174; + coeffs_dyz->coeff_p2_p1_p1 = t28672+t29043+t29082; + coeffs_dyz->coeff_m2_p2_p1 = t29194+t28695+t28771+t29205+t29215+t29234; + coeffs_dyz->coeff_m1_p2_p1 = t29076+t28684+t29049; + coeffs_dyz->coeff_0_p2_p1 = t28699+t29096+t29094; + coeffs_dyz->coeff_p1_p2_p1 = t29077+t29054+t28684; + coeffs_dyz->coeff_p2_p2_p1 = t29215+t29207+t29111+t28685+t28979+t29221; + coeffs_dyz->coeff_m2_m2_p2 = t29062+t28693+t29056; + coeffs_dyz->coeff_m1_m2_p2 = t29047+t28696+t29066; + coeffs_dyz->coeff_0_m2_p2 = t29095+t29102+t28701; + coeffs_dyz->coeff_p1_m2_p2 = t29078+t29059+t28681; + coeffs_dyz->coeff_p2_m2_p2 = t29060+t29044+t28677; + coeffs_dyz->coeff_m2_m1_p2 = t29191+t28689+t28765+t29142+t29218+t29236; + coeffs_dyz->coeff_m1_m1_p2 = t28692+t29068+t29073+t28979; + coeffs_dyz->coeff_0_m1_p2 = t28700+t29100+t29099; + coeffs_dyz->coeff_p1_m1_p2 = t28674+t29072+t29083+t28772; + coeffs_dyz->coeff_p2_m1_p2 = t29180+t28763+t28689+t29169+t29216+t29250; + coeffs_dyz->coeff_m2_0_p2 = t28722+t29141+t29154; + coeffs_dyz->coeff_m1_0_p2 = t29108+t28715+t29117; + coeffs_dyz->coeff_0_0_p2 = (t28755*t28657+t28747)*t28660+(t28758*t28657+ +t28753)*y+t28723; + coeffs_dyz->coeff_p1_0_p2 = t29155+t28715+t29156; + coeffs_dyz->coeff_p2_0_p2 = t28722+t29119+t29127; + coeffs_dyz->coeff_m2_p1_p2 = t29161+t29191+t28045+t28669+t29159+t29216; + coeffs_dyz->coeff_m1_p1_p2 = t29070+t28935+t28667+t29073; + coeffs_dyz->coeff_0_p1_p2 = t29100+t28705+t29103; + coeffs_dyz->coeff_p1_p1_p2 = t28674+t29071+t29075+t28766; + coeffs_dyz->coeff_p2_p1_p2 = t29148+t28675+t29159+t29142+t29180; + coeffs_dyz->coeff_m2_p2_p2 = t29044+t28683+t29042; + coeffs_dyz->coeff_m1_p2_p2 = t28679+t29053+t29066; + coeffs_dyz->coeff_0_p2_p2 = t29101+t29086+t28701; + coeffs_dyz->coeff_p1_p2_p2 = t29046+t29080+t28681; + coeffs_dyz->coeff_p2_p2_p2 = t29050+t28693+t29048; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dz.compute.c new file mode 100644 index 0000000..6bb660c --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dz.compute.c @@ -0,0 +1,2737 @@ +fp t17016; +fp t17015; +fp t17141; +fp t17145; +fp t18084; +fp t18083; +fp t17139; +fp t17146; +fp t17551; +fp t17605; +fp t18082; +fp t17579; +fp t17568; +fp t18081; +fp t17140; +fp t17144; +fp t17582; +fp t17295; +fp t17457; +fp t17266; +fp t18080; +fp t17080; +fp t17493; +fp t17529; +fp t17111; +fp t17278; +fp t18079; +fp t17062; +fp t17631; +fp t17143; +fp t17580; +fp t17061; +fp t17270; +fp t18078; +fp t17550; +fp t17413; +fp t17142; +fp t17524; +fp t17320; +fp t18033; +fp t17020; +fp t17013; +fp t18077; +fp t17014; +fp t17548; +fp t17483; +fp t17017; +fp t17635; +fp t17448; +fp t18076; +fp t17464; +fp t17627; +fp t17540; +fp t17478; +fp t18075; +fp t17617; +fp t17646; +fp t17482; +fp t18074; +fp t17648; +fp t18073; +fp t18072; +fp t18071; +fp t17117; +fp t17009; +fp t17071; +fp t17531; +fp t18013; +fp t17645; +fp t17053; +fp t16949; +fp t17060; +fp t18070; +fp t17492; +fp t17447; +fp t16503; +fp t18069; +fp t17133; +fp t17125; +fp t17497; +fp t18068; +fp t17059; +fp t17474; +fp t17538; +fp t18067; +fp t17284; +fp t17505; +fp t17351; +fp t18066; +fp t17055; +fp t17088; +fp t17444; +fp t18065; +fp t17070; +fp t17636; +fp t17087; +fp t17527; +fp t18064; +fp t18063; +fp t17084; +fp t17067; +fp t17473; +fp t18062; +fp t17072; +fp t17589; +fp t16709; +fp t17104; +fp t17556; +fp t16714; +fp t18061; +fp t16493; +fp t18060; +fp t16960; +fp t16610; +fp t18059; +fp t17127; +fp t17138; +fp t18058; +fp t17028; +fp t17534; +fp t16646; +fp t17029; +fp t17504; +fp t18057; +fp t16993; +fp t17073; +fp t17459; +fp t18056; +fp t17103; +fp t16991; +fp t17118; +fp t18055; +fp t17519; +fp t16804; +fp t18054; +fp t17075; +fp t16832; +fp t17039; +fp t17541; +fp t16639; +fp t18053; +fp t16970; +fp t17095; +fp t17535; +fp t18052; +fp t17123; +fp t17566; +fp t18051; +fp t17077; +fp t17570; +fp t17465; +fp t17302; +fp t18050; +fp t17100; +fp t17136; +fp t17552; +fp t18049; +fp t16963; +fp t17064; +fp t18048; +fp t18047; +fp t17637; +fp t18046; +fp t17615; +fp t17078; +fp t17555; +fp t18045; +fp t17099; +fp t17567; +fp t17091; +fp t16739; +fp t18044; +fp t18043; +fp t16488; +fp t18042; +fp t16996; +fp t17079; +fp t17495; +fp t17998; +fp t17051; +fp t17453; +fp t17049; +fp t17307; +fp t18041; +fp t17449; +fp t17076; +fp t17629; +fp t18040; +fp t17409; +fp t17626; +fp t17613; +fp t18039; +fp t16987; +fp t17092; +fp t17487; +fp t18038; +fp t17559; +fp t17600; +fp t18037; +fp t18036; +fp t17137; +fp t18035; +fp t17030; +fp t17553; +fp t17063; +fp t17494; +fp t16589; +fp t18034; +fp t17641; +fp t18032; +fp t17581; +fp t18031; +fp t18030; +fp t17643; +fp t17561; +fp t18029; +fp t17041; +fp t17360; +fp t18028; +fp t17446; +fp t16582; +fp t18027; +fp t16509; +fp t18026; +fp t17573; +fp t16938; +fp t18025; +fp t16981; +fp t16831; +fp t18024; +fp t17466; +fp t17633; +fp t18023; +fp t17458; +fp t18022; +fp t17558; +fp t17539; +fp t18021; +fp t17442; +fp t16738; +fp t17031; +fp t17622; +fp t17379; +fp t18020; +fp t17472; +fp t17578; +fp t18019; +fp t16735; +fp t17101; +fp t17445; +fp t17089; +fp t17343; +fp t18018; +fp t17024; +fp t16479; +fp t18017; +fp t17549; +fp t18016; +fp t17058; +fp t16560; +fp t17590; +fp t18015; +fp t17057; +fp t16598; +fp t18014; +fp t18012; +fp t16636; +fp t17475; +fp t17418; +fp t18011; +fp t17364; +fp t16608; +fp t18010; +fp t17043; +fp t17575; +fp t16633; +fp t17507; +fp t17408; +fp t18009; +fp t17271; +fp t17027; +fp t17634; +fp t16526; +fp t18008; +fp t17517; +fp t17263; +fp t17056; +fp t17523; +fp t16627; +fp t17083; +fp t17533; +fp t16836; +fp t17490; +fp t17314; +fp t17604; +fp t18007; +fp t16623; +fp t17592; +fp t17318; +fp t18006; +fp t16597; +fp t17638; +fp t17422; +fp t18005; +fp t16571; +fp t17419; +fp t18004; +fp t16532; +fp t18003; +fp t17516; +fp t18002; +fp t16570; +fp t18001; +fp t17632; +fp t16824; +fp t18000; +fp t17999; +fp t17131; +fp t17134; +fp t17997; +fp t16628; +fp t17476; +fp t17427; +fp t17996; +fp t17995; +fp t17616; +fp t16613; +fp t17994; +fp t17485; +fp t17993; +fp t16957; +fp t16523; +fp t17992; +fp t17102; +fp t17116; +fp t17991; +fp t17397; +fp t17038; +fp t16632; +fp t17990; +fp t16951; +fp t17376; +fp t17500; +fp t17989; +fp t17583; +fp t16642; +fp t17988; +fp t17609; +fp t16826; +fp t17628; +fp t16777; +fp t17987; +fp t17644; +fp t16759; +fp t17331; +fp t17986; +fp t16790; +fp t17611; +fp t17366; +fp t17985; +fp t17515; +fp t17456; +fp t17984; +fp t17546; +fp t17279; +fp t17983; +fp t16818; +fp t17652; +fp t17496; +fp t17982; +fp t17440; +fp t17981; +fp t17324; +fp t17489; +fp t17980; +fp t17509; +fp t16573; +fp t17557; +fp t16563; +fp t17290; +fp t17394; +fp t17979; +fp t17455; +fp t17375; +fp t17978; +fp t16586; +fp t17436; +fp t16593; +fp t17521; +fp t17258; +fp t17977; +fp t17976; +fp t17569; +fp t16554; +fp t17940; +fp t16674; +fp t17435; +fp t17649; +fp t16756; +fp t17939; +fp t17536; +fp t16574; +fp t17935; +fp t17853; +fp t17975; +fp t17451; +fp t16781; +fp t17514; +fp t17283; +fp t17974; +fp t16556; +fp t17378; +fp t16858; +fp t17296; +fp t17866; +fp t17498; +fp t17431; +fp t17973; +fp t17393; +fp t17330; +fp t17565; +fp t16780; +fp t16948; +fp t17342; +fp t17869; +fp t16620; +fp t17972; +fp t17461; +fp t16798; +fp t17587; +fp t16631; +fp t17310; +fp t17861; +fp t16629; +fp t17411; +fp t17971; +fp t17513; +fp t17970; +fp t17404; +fp t17506; +fp t16649; +fp t17289; +fp t17264; +fp t17335; +fp t17854; +fp t17969; +fp t17968; +fp t16652; +fp t17522; +fp t16625; +fp t17434; +fp t17879; +fp t17967; +fp t16640; +fp t17433; +fp t17334; +fp t17370; +fp t17851; +fp t17966; +fp t16525; +fp t17326; +fp t17406; +fp t16577; +fp t17926; +fp t16775; +fp t16551; +fp t17943; +fp t17868; +fp t16592; +fp t17374; +fp t17880; +fp t17221; +fp t17965; +fp t17357; +fp t17349; +fp t17428; +fp t17964; +fp t17012; +fp t17963; +fp t17396; +fp t17510; +fp t17341; +fp t17322; +fp t17962; +fp t17361; +fp t16603; +fp t17333; +fp t17961; +fp t17960; +fp t17654; +fp t17959; +fp t17260; +fp t16557; +fp t17958; +fp t17614; +fp t17957; +fp t17308; +fp t17439; +fp t17956; +fp t17955; +fp t17025; +fp t17316; +fp t17365; +fp t17021; +fp t17317; +fp t17954; +fp t17953; +fp t17348; +fp t17952; +fp t17484; +fp t17344; +fp t17951; +fp t17950; +fp t17259; +fp t17110; +fp t17403; +fp t17949; +fp t16638; +fp t17948; +fp t17438; +fp t17947; +fp t17410; +fp t17945; +fp t17105; +fp t17625; +fp t17395; +fp t17944; +fp t17023; +fp t17450; +fp t16470; +fp t17265; +fp t17942; +fp t17416; +fp t17941; +fp t17938; +fp t17093; +fp t17128; +fp t17937; +fp t17285; +fp t16527; +fp t17936; +fp t16504; +fp t17363; +fp t17934; +fp t17022; +fp t17544; +fp t16477; +fp t17933; +fp t16495; +fp t17932; +fp t16672; +fp t17108; +fp t17362; +fp t17931; +fp t17086; +fp t17930; +fp t17400; +fp t17297; +fp t17019; +fp t17929; +fp t17032; +fp t16968; +fp t17303; +fp t17928; +fp t16481; +fp t17927; +fp t17112; +fp t17261; +fp t17925; +fp t16669; +fp t17924; +fp t17327; +fp t17381; +fp t17923; +fp t16579; +fp t16562; +fp t17922; +fp t17035; +fp t17921; +fp t16478; +fp t17920; +fp t16966; +fp t16727; +fp t16529; +fp t17919; +fp t17354; +fp t17918; +fp t17269; +fp t17917; +fp t16622; +fp t17352; +fp t17916; +fp t16538; +fp t17915; +fp t17914; +fp t16671; +fp t17603; +fp t17424; +fp t17913; +fp t17486; +fp t17346; +fp t17912; +fp t16616; +fp t16602; +fp t17911; +fp t16659; +fp t17910; +fp t16635; +fp t17909; +fp t17273; +fp t17908; +fp t17305; +fp t16605; +fp t17907; +fp t17618; +fp t17373; +fp t17906; +fp t17607; +fp t17905; +fp t17325; +fp t17904; +fp t16803; +fp t17903; +fp t16575; +fp t17328; +fp t17902; +fp t17106; +fp t17124; +fp t17114; +fp t17901; +fp t17003; +fp t17268; +fp t17900; +fp t17899; +fp t16641; +fp t17898; +fp t17642; +fp t17405; +fp t17897; +fp t17047; +fp t17470; +fp t16715; +fp t16711; +fp t17651; +fp t17098; +fp t17399; +fp t17896; +fp t17895; +fp t17414; +fp t16764; +fp t17894; +fp t17332; +fp t17044; +fp t17893; +fp t17337; +fp t17892; +fp t17503; +fp t17891; +fp t17890; +fp t17889; +fp t17291; +fp t17888; +fp t16568; +fp t17887; +fp t16600; +fp t17377; +fp t17886; +fp t17520; +fp t17885; +fp t16752; +fp t17653; +fp t17884; +fp t16626; +fp t17883; +fp t17882; +fp t16606; +fp t17429; +fp t17881; +fp t17562; +fp t17359; +fp t17878; +fp t16591; +fp t17560; +fp t16774; +fp t17877; +fp t17275; +fp t17368; +fp t17876; +fp t16787; +fp t16772; +fp t16619; +fp t16545; +fp t17875; +fp t17045; +fp t16521; +fp t17052; +fp t17306; +fp t17874; +fp t16653; +fp t17873; +fp t17281; +fp t17872; +fp t16624; +fp t17586; +fp t17437; +fp t17871; +fp t17870; +fp t17867; +fp t16588; +fp t16730; +fp t17571; +fp t16673; +fp t17380; +fp t17865; +fp t17864; +fp t17863; +fp t16612; +fp t16681; +fp t17372; +fp t17319; +fp t17862; +fp t17286; +fp t17860; +fp t17859; +fp t17858; +fp t17857; +fp t16852; +fp t17301; +fp t17856; +fp t17855; +fp t17852; +fp t17452; +fp t17491; +fp t17850; +fp t17598; +fp t17525; +fp t17545; +fp t17256; +fp t17849; +fp t17630; +fp t17608; +fp t17383; +fp t17848; +fp t17048; +fp t17046; +fp t17847; +fp t17846; +fp t17845; +fp t17844; +fp t16867; +fp t17255; +fp t17528; +fp t16851; +fp t17585; +fp t17421; +fp t17843; +fp t16685; +fp t17511; +fp t17292; +fp t17537; +fp t16533; +fp t17288; +fp t17842; +fp t17841; +fp t17840; +fp t17839; +fp t17107; +fp t16944; +fp t17109; +fp t17838; +fp t17130; +fp t17462; +fp t17097; +fp t17358; +fp t17837; +fp t17836; +fp t16768; +fp t17576; +fp t17835; +fp t17834; +fp t17833; +fp t16736; +fp t16783; +fp t17832; +fp t16766; +fp t16833; +fp t17831; +fp t17312; +fp t17830; +fp t17298; +fp t17336; +fp t16677; +fp t17829; +fp t17828; +fp t16518; +fp t17246; +fp t17827; +fp t17826; +fp t17825; +fp t17824; +fp t16607; +fp t17355; +fp t17823; +fp t17822; +fp t16975; +fp t16684; +fp t17821; +fp t17820; +fp t16965; +fp t16779; +fp t17819; +fp t17818; +fp t17817; +fp t17386; +fp t17816; +fp t17621; +fp t16753; +fp t16704; +fp t17276; +fp t17232; +fp t17815; +fp t17814; +fp t16630; +fp t17813; +fp t17812; +fp t17811; +fp t17810; +fp t17809; +fp t17808; +fp t17807; +fp t17806; +fp t17805; +fp t17804; +fp t17803; +fp t17802; +fp t17801; +fp t17800; +fp t17799; +fp t17299; +fp t17798; +fp t17367; +fp t17797; +fp t17796; +fp t17795; +fp t15875; +fp t17794; +fp t17793; +fp t16969; +fp t16865; +fp t16679; +fp t17480; +fp t17792; +fp t16973; +fp t17282; +fp t17391; +fp t17398; +fp t17791; +fp t17790; +fp t17789; +fp t17085; +fp t17042; +fp t17407; +fp t17788; +fp t16840; +fp t17423; +fp t17415; +fp t17787; +fp t17392; +fp t17786; +fp t17606; +fp t17612; +fp t17026; +fp t17785; +fp t16802; +fp t17294; +fp t17784; +fp t17783; +fp t17441; +fp t17426; +fp t17782; +fp t17781; +fp t17338; +fp t17350; +fp t17780; +fp t17471; +fp t17779; +fp t16656; +fp t17778; +fp t17777; +fp t17776; +fp t17775; +fp t17774; +fp t17463; +fp t17300; +fp t17387; +fp t17773; +fp t17772; +fp t17432; +fp t17771; +fp t17304; +fp t17547; +fp t17477; +fp t17770; +fp t16918; +fp t17769; +fp t17768; +fp t15940; +fp t17767; +fp t16534; +fp t17766; +fp t17382; +fp t17430; +fp t17765; +fp t17764; +fp t17267; +fp t17763; +fp t17762; +fp t17761; +fp t17760; +fp t17759; +fp t17758; +fp t16916; +fp t16767; +fp t17369; +fp t17757; +fp t17756; +fp t17755; +fp t16751; +fp t17754; +fp t16702; +fp t17753; +fp t17311; +fp t17752; +fp t17751; +fp t17750; +fp t17610; +fp t17749; +fp t17748; +fp t17747; +fp t17746; +fp t17745; +fp t16892; +fp t16797; +fp t17402; +fp t17744; +fp t17743; +fp t17742; +fp t17741; +fp t17740; +fp t17739; +fp t17738; +fp t17737; +fp t17736; +fp t17735; +fp t17384; +fp t17011; +fp t16937; +fp t17734; +fp t17733; +fp t17732; +fp t17731; +fp t17730; +fp t17729; +fp t17728; +fp t17727; +fp t17726; +fp t15971; +fp t17725; +fp t17624; +fp t16943; +fp t17126; +fp t17724; +fp t16813; +fp t17723; +fp t17722; +fp t17347; +fp t17420; +fp t17721; +fp t16838; +fp t16854; +fp t17720; +fp t17719; +fp t17718; +fp t16864; +fp t17717; +fp t17716; +fp t17715; +fp t17481; +fp t17714; +fp t17713; +fp t16897; +fp t16924; +fp t16994; +fp t16917; +fp t17712; +fp t17711; +fp t17639; +fp t17293; +fp t17710; +fp t17709; +fp t16873; +fp t17650; +fp t17620; +fp t17708; +fp t17096; +fp t17468; +fp t17329; +fp t17707; +fp t16718; +fp t16884; +fp t17313; +fp t17706; +fp t17543; +fp t17467; +fp t17339; +fp t17705; +fp t17704; +fp t17508; +fp t17703; +fp t16988; +fp t17443; +fp t17702; +fp t17701; +fp t17640; +fp t17700; +fp t17574; +fp t17699; +fp t17698; +fp t17647; +fp t17697; +fp t16845; +fp t16932; +fp t17696; +fp t17695; +fp t17694; +fp t16724; +fp t17577; +fp t17693; +fp t17601; +fp t16848; +fp t17692; +fp t17412; +fp t17599; +fp t17691; +fp t16786; +fp t17499; +fp t16719; +fp t17690; +fp t17588; +fp t17689; +fp t17688; +fp t17687; +fp t17686; +fp t17623; +fp t17685; +fp t17684; +fp t16771; +fp t17683; +fp t17682; +fp t17681; +fp t17680; +fp t17679; +fp t16853; +fp t17678; +fp t17677; +fp t17676; +fp t17675; +fp t17674; +fp t17673; +fp t17593; +fp t17672; +fp t17671; +fp t17670; +fp t17460; +fp t17669; +fp t17596; +fp t17668; +fp t17667; +fp t17666; +fp t17665; +fp t17664; +fp t17356; +fp t17321; +fp t17663; +fp t17662; +fp t17661; +fp t17660; +fp t17659; +fp t17658; +fp t17657; +fp t17656; +fp t17655; +fp t16956; +fp t17619; +fp t15847; +fp t15741; +fp t17597; +fp t17595; +fp t17584; +fp t17563; +fp t17554; +fp t15685; +fp t15966; +fp t17532; +fp t17530; +fp t15849; +fp t17518; +fp t17488; +fp t17479; +fp t17469; +fp t17454; +fp t17425; +fp t16868; +fp t16877; +fp t17390; +fp t17388; +fp t16808; +fp t16822; +fp t17340; +fp t17323; +fp t17309; +fp t17274; +fp t17262; +fp t17257; +fp t17254; +fp t17253; +fp t17252; +fp t17250; +fp t17248; +fp t17245; +fp t17244; +fp t17243; +fp t17242; +fp t17135; +fp t17241; +fp t17240; +fp t17074; +fp t17034; +fp t17119; +fp t17239; +fp t17238; +fp t17237; +fp t17236; +fp t17065; +fp t17066; +fp t17121; +fp t17235; +fp t17233; +fp t17231; +fp t17230; +fp t17229; +fp t17228; +fp t17227; +fp t17226; +fp t17225; +fp t17224; +fp t17223; +fp t17222; +fp t17219; +fp t17218; +fp t17018; +fp t17217; +fp t17036; +fp t17216; +fp t17215; +fp t17214; +fp t17040; +fp t17213; +fp t17054; +fp t17212; +fp t17211; +fp t17210; +fp t17209; +fp t17208; +fp t17207; +fp t17206; +fp t17205; +fp t17204; +fp t17203; +fp t17202; +fp t17050; +fp t17201; +fp t17200; +fp t17199; +fp t17198; +fp t17197; +fp t17196; +fp t17195; +fp t17194; +fp t17193; +fp t17192; +fp t17191; +fp t17190; +fp t17189; +fp t17188; +fp t17187; +fp t17186; +fp t17185; +fp t17184; +fp t17183; +fp t17182; +fp t17181; +fp t17180; +fp t17179; +fp t17178; +fp t17177; +fp t17176; +fp t17175; +fp t17174; +fp t17173; +fp t17172; +fp t17171; +fp t17170; +fp t17169; +fp t17168; +fp t17167; +fp t17166; +fp t17165; +fp t17164; +fp t17163; +fp t17162; +fp t17161; +fp t17160; +fp t17159; +fp t17158; +fp t17157; +fp t17156; +fp t17155; +fp t17154; +fp t17153; +fp t17152; +fp t17132; +fp t17122; +fp t17120; +fp t17115; +fp t17113; +fp t17094; +fp t17090; +fp t17082; +fp t17081; +fp t17069; +fp t17068; +fp t17037; +fp t17033; + t17016 = RATIONAL(-1.0,3456.0); + t17015 = RATIONAL(1.0,3456.0); + t17141 = y*y; + t17145 = t17141*t17141; + t18084 = t17016*t17141+t17015*t17145; + t18083 = t17015*t17141+t17016*t17145; + t17139 = x*x; + t17146 = t17139*t17139; + t17551 = t17146*t17141; + t17605 = t17145*t17139; + t18082 = t17551+t17605; + t17579 = t17146*t17145; + t17568 = t17141*t17139; + t18081 = t17579+t17568; + t17140 = z*z; + t17144 = z*t17140; + t17582 = t17144*t17139; + t17295 = t17145*t17582; + t17457 = t17146*t17144; + t17266 = t17141*t17457; + t18080 = t17295+t17266; + t17080 = RATIONAL(-1.0,54.0); + t17493 = t17146*t17080; + t17529 = t17140*t17146; + t17111 = RATIONAL(1.0,72.0); + t17278 = t17111*t17529; + t18079 = t17493+t17278; + t17062 = RATIONAL(1.0,576.0); + t17631 = y*t17140; + t17143 = t17141*y; + t17580 = t17140*t17143; + t17061 = RATIONAL(-1.0,576.0); + t17270 = t17061*t17580; + t18078 = t17270+t17062*t17631; + t17550 = t17140*t17145; + t17413 = x*t17550; + t17142 = x*t17139; + t17524 = t17142*t17141; + t17320 = t17140*t17524; + t18033 = t17320+t17413; + t17020 = RATIONAL(-1.0,6912.0); + t17013 = RATIONAL(1.0,6912.0); + t18077 = t18082*t17013+t18081*t17020; + t17014 = RATIONAL(1.0,1728.0); + t17548 = t17142*t17014; + t17483 = t17143*t17014; + t17017 = RATIONAL(-1.0,1728.0); + t17635 = y*t17017; + t17448 = t17017*t17143; + t18076 = t17142*t17448+y*t17548+(t17635+t17483)*x; + t17464 = t17016*t17139; + t17627 = y*t17146; + t17540 = t17146*t17016; + t17478 = t17015*t17143; + t18075 = t17015*t17627+t17143*t17540+t17139*t17478+y*t17464; + t17617 = y*t17142; + t17646 = y*t17014; + t17482 = t17142*t17143; + t18074 = t17014*t17482+t17017*t17617+(t17646+t17448)*x; + t17648 = y*t17139; + t18073 = t17146*t17478+t17015*t17648+t17143*t17464+y*t17540; + t18072 = t18083*t17142+t18084*x; + t18071 = t18084*t17142+t18083*x; + t17117 = RATIONAL(-1.0,9.0); + t17009 = t17117*t17145; + t17071 = RATIONAL(1.0,12.0); + t17531 = t17140*t17071; + t18013 = t17009+t17145*t17531; + t17645 = z*t17146; + t17053 = RATIONAL(1.0,288.0); + t16949 = t17053*t17139; + t17060 = RATIONAL(5.0,576.0); + t18070 = t17144*t16949+t17060*t17645; + t17492 = t17141*t17014; + t17447 = t17017*t17145; + t16503 = t17142*t17447; + t18069 = t17142*t17492+t16503; + t17133 = RATIONAL(-4.0,9.0); + t17125 = RATIONAL(1.0,3.0); + t17497 = t17140*t17125; + t18068 = t17133+t17497; + t17059 = RATIONAL(-5.0,576.0); + t17474 = t17059*t17139; + t17538 = t17143*t17139; + t18067 = y*t17474+t17060*t17538; + t17284 = t17141*t17529; + t17505 = t17140*t17139; + t17351 = t17145*t17505; + t18066 = t17284+t17351; + t17055 = RATIONAL(-1.0,288.0); + t17088 = RATIONAL(1.0,96.0); + t17444 = t17140*t17088; + t18065 = t17444+t17055; + t17070 = RATIONAL(-8.0,27.0); + t17636 = x*t17070; + t17087 = RATIONAL(2.0,27.0); + t17527 = t17087*t17144; + t18064 = t17142*t17527+t17144*t17636; + t18063 = t17071*t17529+t17117*t17146; + t17084 = RATIONAL(-2.0,27.0); + t17067 = RATIONAL(1.0,54.0); + t17473 = t17067*t17145; + t18062 = t17084*t17524+t17142*t17473; + t17072 = RATIONAL(-1.0,18.0); + t17589 = t17072*t17144; + t16709 = t17143*t17589; + t17104 = RATIONAL(1.0,18.0); + t17556 = t17144*t17104; + t16714 = y*t17556; + t18061 = t16714+t16709; + t16493 = t17145*t17548; + t18060 = t16493+t17017*t17524; + t16960 = t17053*t17145; + t16610 = t17142*t16960; + t18059 = t16610+t17111*t17142; + t17127 = RATIONAL(-1.0,3.0); + t17138 = RATIONAL(4.0,9.0); + t18058 = t17138+t17140*t17127; + t17028 = RATIONAL(1.0,432.0); + t17534 = t17028*t17139; + t16646 = y*t17534; + t17029 = RATIONAL(-1.0,432.0); + t17504 = t17146*t17029; + t18057 = t16646+y*t17504; + t16993 = t17117*t17143; + t17073 = RATIONAL(-1.0,36.0); + t17459 = t17073*t17143; + t18056 = t16993+t17146*t17459; + t17103 = RATIONAL(1.0,36.0); + t16991 = t17103*t17146; + t17118 = RATIONAL(1.0,9.0); + t18055 = (t17118+t16991)*t17143; + t17519 = t17080*t17145; + t16804 = t17142*t17519; + t18054 = t16804+t17087*t17524; + t17075 = RATIONAL(1.0,27.0); + t16832 = t17075*t17648; + t17039 = RATIONAL(-1.0,108.0); + t17541 = t17146*t17039; + t16639 = y*t17541; + t18053 = t16639+t16832; + t16970 = t17103*t17145; + t17095 = RATIONAL(-1.0,48.0); + t17535 = t17140*t17095; + t18052 = t16970+t17145*t17535; + t17123 = RATIONAL(-2.0,9.0); + t17566 = t17140*t17141; + t18051 = t17084*t17145+t17123*t17566; + t17077 = RATIONAL(-1.0,27.0); + t17570 = t17077*t17143; + t17465 = t17067*t17144; + t17302 = t17143*t17465; + t18050 = t17302+z*t17570; + t17100 = RATIONAL(-5.0,12.0); + t17136 = RATIONAL(5.0,9.0); + t17552 = t17141*t17136; + t18049 = t17552+t17100*t17566; + t16963 = t17055*t17145; + t17064 = RATIONAL(-1.0,72.0); + t18048 = (t16963+t17064)*t17142; + t18047 = t17087*t17538+t17143*t17493; + t17637 = x*t17141; + t18046 = t17059*t17524+t17060*t17637; + t17615 = y*t17084; + t17078 = RATIONAL(8.0,27.0); + t17555 = t17078*t17139; + t18045 = t17146*t17615+y*t17555; + t17099 = RATIONAL(-1.0,24.0); + t17567 = t17140*t17099; + t17091 = RATIONAL(-1.0,96.0); + t16739 = t17091*t17529; + t18044 = t16739+t17567; + t18043 = t17059*t17637+t17060*t17524; + t16488 = t17146*t17448; + t18042 = t17139*t17483+t16488; + t16996 = t17118*t17145; + t17079 = RATIONAL(-1.0,12.0); + t17495 = t17140*t17079; + t17998 = t17145*t17495+t16996; + t17051 = RATIONAL(1.0,192.0); + t17453 = t17140*t17051; + t17049 = RATIONAL(-5.0,192.0); + t17307 = t17049*t17505; + t18041 = t17307+t17146*t17453; + t17449 = t17084*t17144; + t17076 = RATIONAL(4.0,27.0); + t17629 = z*t17143; + t18040 = t17076*t17629+t17143*t17449; + t17409 = z*t17524; + t17626 = z*t17145; + t17613 = x*t17626; + t18039 = t17613+t17409; + t16987 = t17073*t17145; + t17092 = RATIONAL(1.0,48.0); + t17487 = t17092*t17145; + t18038 = t17140*t17487+t16987; + t17559 = t17142*t17144; + t17600 = t17133*t17144; + t18037 = x*t17600+t17118*t17559; + t18036 = t17060*t17648+t17143*t17474; + t17137 = RATIONAL(2.0,9.0); + t18035 = t17137*t17566+t17087*t17145; + t17030 = RATIONAL(1.0,864.0); + t17553 = t17030*t17145; + t17063 = RATIONAL(-1.0,864.0); + t17494 = t17142*t17063; + t16589 = t17145*t17494; + t18034 = t16589+x*t17553; + t17641 = x*t17145; + t18032 = t17029*t17637+t17028*t17641; + t17581 = t17146*t17067; + t18031 = t17084*t17538+t17143*t17581; + t18030 = (t17495+t17118)*t17146; + t17643 = z*t17072; + t17561 = t17118*t17144; + t18029 = t17643+t17561; + t17041 = RATIONAL(-1.0,192.0); + t17360 = t17041*t17529; + t18028 = t17535+t17360; + t17446 = t17141*t17028; + t16582 = x*t17446; + t18027 = t16582+t17029*t17641; + t16509 = t17146*t17483; + t18026 = t17139*t17448+t16509; + t17573 = t17138*t17144; + t16938 = t17144*t16993; + t18025 = t16938+y*t17573; + t16981 = t17064*t17145; + t16831 = t17139*t16981; + t18024 = t16831+t17072*t17139; + t17466 = t17142*t17030; + t17633 = x*t17063; + t18023 = (t17466+t17633)*t17145; + t17458 = t17063*t17143; + t18022 = t17030*t17627+t17146*t17458; + t17558 = t17029*t17139; + t17539 = t17146*t17028; + t18021 = (t17539+t17558)*y; + t17442 = t17111*t17144; + t16738 = t17142*t17442; + t17031 = RATIONAL(-5.0,144.0); + t17622 = z*t17031; + t17379 = t17142*t17622; + t18020 = t16738+t17379; + t17472 = t17146*t17063; + t17578 = t17030*t17143; + t18019 = t17146*t17578+y*t17472; + t16735 = t17146*t17444; + t17101 = RATIONAL(1.0,24.0); + t17445 = t17140*t17101; + t17089 = RATIONAL(-5.0,96.0); + t17343 = t17089*t17505; + t18018 = t16735+t17343+t17445; + t17024 = RATIONAL(1.0,1152.0); + t16479 = t17024*t17605; + t18017 = t16949+t16479+t17055*t17146; + t17549 = t17146*t17024; + t18016 = t16963+(t17549+t17053)*t17141; + t17058 = RATIONAL(-1.0,144.0); + t16560 = t17062*t17641; + t17590 = t17142*t17145; + t18015 = t17058*t17142+t17061*t17590+t16560; + t17057 = RATIONAL(1.0,144.0); + t16598 = t17061*t17641; + t18014 = t17058*x+t16598+t17062*t17590+t17057*t17142; + t18012 = t17072*t17141+t17064*t17551; + t16636 = t17039*t17617; + t17475 = t17140*t17103; + t17418 = x*t17475; + t18011 = t16636+t17143*t17418; + t17364 = t17144*t17568; + t16608 = t17145*t17504; + t18010 = z*t16608+t17087*t17364; + t17043 = RATIONAL(-1.0,216.0); + t17575 = t17043*t17143; + t16633 = x*t17575; + t17507 = t17140*t17053; + t17408 = y*t17507; + t18009 = t16633+t17142*t17408; + t17271 = t17140*t17482; + t17027 = RATIONAL(1.0,216.0); + t17634 = y*t17027; + t16526 = x*t17634; + t18008 = t16526+t17055*t17271; + t17517 = t17103*t17144; + t17263 = t17145*t17517; + t17056 = RATIONAL(-5.0,288.0); + t17523 = t17141*t17056; + t16627 = t17146*t17523; + t17083 = RATIONAL(5.0,72.0); + t17533 = t17083*t17139; + t16836 = t17141*t17533; + t17490 = t17058*t17145; + t17314 = t17144*t17490; + t17604 = z*t16836+t17146*t17314; + t18007 = t17604+z*t16627+t17139*t17263; + t16623 = t17145*t17539; + t17592 = t17141*t17144; + t17318 = t17063*t17592; + t18006 = t17139*t17318+z*t16623; + t16597 = t17142*t17458; + t17638 = x*t17140; + t17422 = t17111*t17638; + t18005 = t16597+y*t17422; + t16571 = t17027*t17617; + t17419 = x*t17580; + t18004 = t16571+t17055*t17419; + t16532 = y*t17494; + t18003 = t17111*t17419+t16532; + t17516 = t17055*t17143; + t18002 = t17064*t17143+t17146*t17516; + t16570 = t17039*t17482; + t18001 = t16570+y*t17418; + t17632 = x*t17075; + t16824 = y*t17632; + t18000 = t17058*t17271+t16824; + t17999 = (t16987+t17117)*t17142; + t17131 = RATIONAL(5.0,6.0); + t17134 = RATIONAL(-2.0,3.0); + t17997 = t17131*t17141+t17134; + t16628 = t17143*t17466; + t17476 = t17140*t17064; + t17427 = y*t17476; + t17996 = t16628+x*t17427; + t17995 = (t16970+t17118)*t17142; + t17616 = y*t17043; + t16613 = x*t17616; + t17994 = t17053*t17271+t16613; + t17485 = t17095*t17146; + t17993 = t17079+t17485; + t16957 = t17053*t17146; + t16523 = t17143*t16957; + t17992 = t16523+t17111*t17143; + t17102 = RATIONAL(-5.0,24.0); + t17116 = RATIONAL(1.0,6.0); + t17991 = t17116+t17102*t17141; + t17397 = t17073*t17631; + t17038 = RATIONAL(1.0,108.0); + t16632 = t17038*t17482; + t17990 = x*t17397+t16632; + t16951 = t17058*y; + t17376 = t17140*t16951; + t17500 = t17075*t17143; + t17989 = x*t17500+t17142*t17376; + t17583 = t17142*t17043; + t16642 = y*t17583; + t17988 = t16642+t17053*t17419; + t17609 = z*t17617; + t16826 = x*t17570; + t17628 = x*t17087; + t16777 = t17143*t17628; + t17987 = t17144*t16826+z*t16777+t17067*t17609; + t17644 = x*t17143; + t16759 = t17084*t17644; + t17331 = t17144*t17500; + t17986 = z*t16759+t17080*t17609+x*t17331; + t16790 = t17087*t17617; + t17611 = x*t17629; + t17366 = y*t17559; + t17985 = z*t16790+t17067*t17611+t17077*t17366; + t17515 = t17146*t17061; + t17456 = t17146*t17062; + t17984 = y*t17456+(t17515+t17058)*t17143; + t17546 = t17140*t17057; + t17279 = t17141*t17546; + t17983 = x*t17279+t18069; + t16818 = t17142*t17615; + t17652 = x*z; + t17496 = t17080*t17143; + t17982 = t17496*t17652+z*t16818+t17075*t17366; + t17440 = x*t17566; + t17981 = t17140*t16598+t17142*t17446+t17062*t17440; + t17324 = t17145*t17507; + t17489 = t17043*t17139; + t17980 = t17145*t17489+t17139*t17324+t18079*t17141; + t17509 = t17142*t17028; + t16573 = t17145*t17509; + t17557 = t17039*t17145; + t16563 = x*t17557; + t17290 = t17141*t17465; + t17394 = x*t17449; + t17979 = t17142*t17290+t17141*t17394+(t16573+t16563)*z; + t17455 = t17140*t17055; + t17375 = y*t17455; + t17978 = t17027*t17482+x*t17375+t17988; + t16586 = t17143*t17504; + t17436 = y*t17527; + t16593 = t17038*t17627; + t17521 = t17080*t17139; + t17258 = t17144*t17521; + t17977 = t17139*t17436+t17143*t17258+(t16593+t16586)*z; + t17976 = t17140*t16831+t17027*t17551+t17055*t17284+t17139*t17473; + t17569 = t17143*t17038; + t16554 = x*t17569; + t17940 = t17142*t17397+t16554; + t16674 = t17029*t17482; + t17435 = t17118*t17638; + t17649 = y*t17077; + t16756 = x*t17649; + t17939 = t16756+t17057*t17271; + t17536 = t17142*t17038; + t16574 = y*t17536; + t17935 = t17073*t17419+t16574; + t17853 = t17935+t17939; + t17975 = y*t17435+t17940+t16674+t17853; + t17451 = t17111*t17139; + t16781 = t17145*t17451; + t17514 = t17043*t17141; + t17283 = t17141*t17507; + t17974 = t17139*t17519+t17140*t16781+(t17283+t17514)*t17146; + t16556 = t17039*t17524; + t17378 = x*t16970; + t16858 = t17141*t17632; + t17296 = t17142*t17550; + t17866 = t16858+t17103*t17320+t16563+t17058*t17296; + t17498 = t17140*t17117; + t17431 = x*t17498; + t17973 = t17141*t17431+t16556+t17140*t17378+t17866; + t17393 = y*t17505; + t17330 = t17073*t17505; + t17565 = t17077*t17139; + t16780 = y*t17565; + t16948 = t17057*t17143; + t17342 = t17140*t16948; + t17869 = t16780+t17146*t17342+t16593+t17143*t17330; + t16620 = t17038*t17538; + t17972 = t17118*t17393+t17146*t17397+t17869+t16620; + t17461 = t17077*t17141; + t16798 = x*t17461; + t17587 = t17038*t17145; + t16631 = x*t17587; + t17310 = t17073*t17566; + t17861 = t17057*t17296+t16798+t16631+t17142*t17310; + t16629 = t17038*t17524; + t17411 = x*t16987; + t17971 = t17141*t17435+t17140*t17411+t17861+t16629; + t17513 = t17027*t17145; + t17970 = t17067*t17551+t17064*t17284+t17139*t17513+t17055*t17351; + t17404 = y*t17529; + t17506 = t17039*t17139; + t16649 = t17143*t17506; + t17289 = t17139*t17498; + t17264 = t17139*t17475; + t17335 = t17058*t17529; + t17854 = (t17264+t17335)*t17143+t18053; + t17969 = y*t17289+t17103*t17404+t16649+t17854; + t17968 = t16951+y*t17515+t16948+t17143*t17456; + t16652 = t17028*t17482; + t17522 = t17143*t17039; + t16625 = x*t17522; + t17434 = t17140*t17617; + t17879 = t16625+t17103*t17434+t18000; + t17967 = t16652+y*t17431+t17879+t18011; + t16640 = t17143*t17539; + t17433 = t17139*t17615; + t17334 = t17143*t17457; + t17370 = y*t17465; + t17851 = t17146*t17370+t17043*t17334+(t16649+t16832)*z; + t17966 = t17139*t17302+t17144*t17433+t17851+(t16639+t16640)*z; + t16525 = t17029*t17590; + t17326 = t17144*t17524; + t17406 = t17141*t17628; + t16577 = t17038*t17551; + t17926 = z*t16577+t17145*t17258; + t16775 = t17139*t17461; + t16551 = t17146*t17513; + t17943 = z*t16775+t17144*t16551; + t17868 = t17926+t17943; + t16592 = t17142*t17513; + t17374 = t17144*t17641; + t17880 = t17080*t17374+t17144*t16592+(t16798+t16629)*z; + t17221 = t17868+t17880; + t17965 = t17144*t17406+t17080*t17326+t17221+(t16525+t16631)*z; + t17357 = t17144*t17538; + t17349 = t17017*t17582; + t17428 = t17144*t17646; + t17964 = t17146*t17428+t17144*t16488+t17014*t17357+y*t17349+t18073*z; + t17012 = RATIONAL(-1.0,1152.0); + t17963 = t18033*t17024+(t17440+t17296)*t17012+t18071; + t17396 = t17144*t17633; + t17510 = t17030*t17144; + t17341 = t17143*t17510; + t17322 = t17144*t17494; + t17962 = y*t17396+t17143*t17322+t17030*t17366+x*t17341+t18074*z; + t17361 = t17141*t17505; + t16603 = t17139*t17587; + t17333 = t17145*t17546; + t17961 = t17145*t17330+t16603+t16775+t16577+t17073*t17284+t17146*t17333+ +t16608+t17118*t17361; + t17960 = t17143*t17349+t17457*t17635+t17139*t17428+t17144*t16509+t18075*z +; + t17654 = y*x; + t17959 = y*t17322+t17143*t17396+t17510*t17654+t17142*t17341+t18076*z; + t17260 = t17103*t17551; + t16557 = t17146*t17490; + t17958 = t16623+t17075*t17568+(t17506+t17264)*t17145+(t17289+t17541)* +t17141+(t16557+t17260)*t17140; + t17614 = x*t17631; + t17957 = t17062*t17419+t17061*t17614+t18078*t17142+t18074; + t17308 = t17144*t17492; + t17439 = x*t17592; + t17956 = t17014*t17374+t17017*t17439+t17144*t16503+t17142*t17308+t18071*z +; + t17955 = t17061*t17434+t17062*t17271+t18078*x+t18076; + t17025 = RATIONAL(1.0,2304.0); + t17316 = t17025*t17505; + t17365 = t17145*t17529; + t17021 = RATIONAL(-1.0,2304.0); + t17317 = t17021*t17550; + t17954 = t17139*t17317+t17025*t17365+t17021*t17284+t17141*t17316+t18077; + t17953 = x*t17308+t17144*t16493+(t17326+t17374)*t17017+t18072*z; + t17348 = t17145*t17457; + t17952 = (t17348+t17364)*t17015+t18080*t17016+t18077*z; + t17484 = t17140*t17024; + t17344 = t17141*t17484; + t17951 = t17024*t17296+x*t17344+t18033*t17012+t18072; + t17950 = t17146*t17317+t17145*t17316+t17025*t17284+t17021*t17361+t18081* +t17013+t18082*t17020; + t17259 = t17057*t17592; + t17110 = RATIONAL(-5.0,72.0); + t17403 = t17110*t17626; + t17949 = t17146*t17259+t17139*t17403; + t16638 = t17145*t17558; + t17948 = t17030*t17266+z*t16638; + t17438 = z*t17579; + t17947 = t17039*t17438+t17139*t17290; + t17410 = z*t17605; + t17945 = t17075*t17410+t17043*t17266; + t17105 = RATIONAL(-10.0,9.0); + t17625 = z*t17139; + t17395 = t17105*t17625; + t17944 = t17141*t17395+t17146*t17263; + t17023 = RATIONAL(-5.0,1152.0); + t17450 = t17141*t17023; + t16470 = t17139*t17450; + t17265 = t17145*t17456; + t17942 = t17144*t17265+z*t16470; + t17416 = z*t17551; + t17941 = t17043*t17295+t17075*t17416; + t17938 = t17080*t17266+z*t16603; + t17093 = RATIONAL(5.0,48.0); + t17128 = RATIONAL(-5.0,6.0); + t17937 = t17128*t17364+t17093*t17438; + t17285 = t17145*t17510; + t16527 = t17141*t17504; + t17936 = t17139*t17285+z*t16527; + t16504 = t17014*t17579; + t17363 = t17144*t17514; + t17934 = t17139*t17363+z*t16504; + t17022 = RATIONAL(5.0,1152.0); + t17544 = t17022*t17139; + t16477 = t17145*t17544; + t17933 = z*t16477+t17061*t17266; + t16495 = t17017*t17551; + t17932 = t17027*t17295+z*t16495; + t16672 = t17146*t16960; + t17108 = RATIONAL(-5.0,36.0); + t17362 = t17108*t17592; + t17931 = z*t16672+t17139*t17362; + t17086 = RATIONAL(5.0,96.0); + t17930 = t17049*t17438+t17086*t17364; + t17400 = z*t17568; + t17297 = t17088*t17579; + t17019 = RATIONAL(-25.0,192.0); + t17929 = t17144*t17297+t17019*t17400; + t17032 = RATIONAL(5.0,288.0); + t16968 = t17073*t17141; + t17303 = t17144*t16968; + t17928 = t17032*t17438+t17139*t17303; + t16481 = t17012*t17579; + t17927 = t17060*t17364+z*t16481; + t17112 = RATIONAL(5.0,18.0); + t17261 = t17144*t17009; + t17925 = t17112*t17416+t17139*t17261; + t16669 = t17056*t17605; + t17924 = t17144*t17260+z*t16669; + t17327 = t17144*t17552; + t17381 = t17146*t17643; + t17923 = t17139*t17327+t17145*t17381; + t16579 = t17139*t17446; + t16562 = t17145*t17472; + t17922 = t17144*t16562+z*t16579; + t17035 = RATIONAL(25.0,12.0); + t17921 = t17035*t17400+t17099*t17348; + t16478 = t17139*t17447; + t17920 = t17027*t17266+z*t16478; + t16966 = t17111*t17145; + t16727 = z*t16966; + t16529 = t17031*t17568; + t17919 = t17146*t16727+t17144*t16529; + t17354 = t17144*t17482; + t17918 = t17043*t17354+(t16625+t16636)*z; + t17269 = t17144*t17509; + t17917 = y*t17269+(t16633+t16532)*z; + t16622 = t17027*t17538; + t17352 = t17140*t17451; + t17916 = t16622+y*t17352+t17140*t16523; + t16538 = x*t17458; + t17915 = t17028*t17144*t17644+(t16538+t16642)*z; + t17914 = t17058*t17440+t18060; + t16671 = x*t17578; + t17603 = t17029*t17144; + t17424 = x*t17603; + t17913 = t17143*t17424+(t16571+t16671)*z; + t17486 = t17027*t17144; + t17346 = t17143*t17486; + t17912 = t17142*t17346+(t16574+t16554)*z; + t16616 = y*t17466; + t16602 = t17027*t17644; + t17911 = t17029*t17366+(t16616+t16602)*z; + t16659 = t17142*t17514; + t17910 = t16659+t17055*t17296+t17064*t17440; + t16635 = t17027*t17524; + t17909 = t17141*t17422+t17053*t17296+t16635; + t17273 = t17061*t17566; + t17908 = t17029*t17524+x*t17273+t17140*t16560; + t17305 = t17146*t17455; + t16605 = t17143*t17489; + t17907 = t17143*t17305+t17064*t17393+t16605; + t17618 = x*t17039; + t17373 = t17144*t17618; + t17906 = y*t17373+t17029*t17354+(t16628+t16526)*z; + t17607 = t17108*t17652; + t17905 = x*t16714+y*t17607+t18020*t17143; + t17325 = t17140*t17456; + t17904 = t17143*t17325+t17139*t17270+t18021; + t16803 = y*t17493; + t17903 = t17144*t16803+t17027*t17334+(t16780+t16620)*z; + t16575 = t17139*t17634; + t17328 = t17028*t17457; + t17902 = t17029*t17334+y*t17328+(t16605+t16575)*z; + t17106 = RATIONAL(5.0,24.0); + t17124 = RATIONAL(-5.0,3.0); + t17114 = RATIONAL(-1.0,6.0); + t17901 = t17114*t17457+t17124*t17625+t17106*t17266+t17100*t17410; + t17003 = t17138*t17139; + t17268 = t17144*t17003; + t17900 = t17141*t17268+t17146*t17403+t17925; + t17899 = t18049*t17139+t18052*t17146; + t16641 = t17145*t17583; + t17898 = t17067*t17374+t17144*t16641+(t16858+t16556)*z; + t17642 = y*t17038; + t17405 = t17144*t17642; + t17897 = x*t17405+t17143*t17269+(t16597+t16613)*z; + t17047 = RATIONAL(5.0,144.0); + t17470 = t17144*t17064; + t16715 = t17142*t17470; + t16711 = y*t17589; + t17651 = y*t17652; + t17098 = RATIONAL(5.0,36.0); + t17399 = z*t17482; + t17896 = t17047*t17399+t17098*t17651+x*t16711+t17143*t16715; + t17895 = t17936+t18006; + t17414 = t17144*t17632; + t16764 = t17080*t17482; + t17894 = y*t17414+z*t16764+t17615*t17652+t17038*t17354; + t17332 = t17145*t17453; + t17044 = RATIONAL(5.0,192.0); + t17893 = t17044*t17361+t16529+t17146*t17332+t16557; + t17337 = t17140*t17515; + t17892 = t16579+t16504+t17058*t17361+t17145*t17337; + t17503 = t17067*t17139; + t17891 = t17064*t17361+t17145*t17305+t17141*t17503+t16551; + t17890 = t17932+t17948; + t17889 = t18008+t18009; + t17291 = t17144*t17506; + t17888 = t17139*t17405+t17143*t17291+t18022*z; + t16568 = t17142*t17557; + t17887 = x*t17290+z*t16568+t17075*t17613+t17043*t17326; + t16600 = y*t17489; + t17377 = y*t17603; + t17886 = t17146*t17377+t17143*t17328+(t16600+t16622)*z; + t17520 = t17142*t17075; + t17885 = y*t17520+t17058*t17419+t17940; + t16752 = t17067*t17482; + t17653 = y*z; + t17884 = t17628*t17653+t17144*t16756+t17039*t17354+z*t16752; + t16626 = x*t17514; + t17883 = t17145*t17269+t17029*t17374+(t16635+t16626)*z; + t17882 = t17945+t17947; + t16606 = t17146*t17522; + t17429 = t17075*t17645; + t17881 = t17139*t17370+y*t17429+z*t16606+t17043*t17357; + t17562 = t17110*t17141; + t17359 = t17106*t17505; + t17878 = t17141*t17359+t17139*t17562+t17140*t17297+t17146*t16963; + t16591 = t17142*t17523; + t17560 = t17083*t17141; + t16774 = x*t17560; + t17877 = t17142*t17314+x*t17263+(t16591+t16774)*z; + t17275 = t17055*t17457; + t17368 = y*t16957; + t17876 = t17144*t17368+t17143*t17275+t18036*z; + t16787 = t17110*t17648; + t16772 = t17073*t17457; + t16619 = t17032*t17538; + t16545 = t17057*t17457; + t17875 = y*t16772+t17143*t16545+(t16619+t16787)*z; + t17045 = RATIONAL(-1.0,384.0); + t16521 = t17145*t17549; + t17052 = RATIONAL(-5.0,384.0); + t17306 = t17052*t17505; + t17874 = t16521+t17045*t17365+(t17306+t17544)*t17141; + t16653 = t17027*t17637; + t17873 = t17028*t17374+t17144*t16525+(t16659+t16653)*z; + t17281 = t17055*t17559; + t17872 = t17145*t17281+t17053*t17374+t18046*z; + t16624 = t17146*t17575; + t17586 = t17146*t17027; + t17437 = y*t17586; + t17871 = t17144*t16646+t17029*t17357+(t17437+t16624)*z; + t17870 = t17922+t17934; + t17867 = t17932+t17934; + t16588 = t17032*t17524; + t16730 = t17144*t16987; + t17571 = t17057*t17145; + t16673 = t17144*t17571; + t17380 = z*t17562; + t17865 = t17142*t16673+z*t16588+(t16730+t17380)*x; + t17864 = t17062*t17320+t17061*t17296+t18027; + t17863 = t17139*t17279+t17141*t17558+t17146*t17447+t17140*t17265; + t16612 = t17145*t17536; + t16681 = t17080*t17637; + t17372 = t17077*t17626; + t17319 = t17141*t17486; + t17862 = t17142*t17319+z*t16612+x*t17372+t17144*t16681; + t17286 = t17062*t17505; + t17860 = t17143*t17286+t17146*t17270+t18057; + t17859 = t17935+t17989; + t17858 = t17055*t17374+t17144*t16610+t18043*z; + t17857 = t17144*t16523+y*t17275+t18067*z; + t16852 = t17091*t17550; + t17301 = t17102*t17505; + t17856 = t17141*t17301+t16672+t17146*t16852+t16836; + t17855 = t17939+t18001; + t17852 = t17941+t17947; + t17452 = t17047*t17141; + t17491 = t17146*t17057; + t17850 = t17141*t17307+t17139*t17452+(t17360+t17491)*t17145; + t17598 = t17093*t17141; + t17525 = t17101*t17145; + t17545 = t17044*t17141; + t17256 = t17146*t17545; + t17849 = t17089*t17295+t17144*t17525+(t17256+t17598)*z; + t17630 = z*t17141; + t17608 = x*t17630; + t17383 = z*t17142*t17112; + t17848 = t17141*t17383+t17105*t17608+t17142*t17263+x*t17261; + t17048 = RATIONAL(1.0,384.0); + t17046 = RATIONAL(5.0,384.0); + t17847 = t17046*t17361+t16481+t16470+t17048*t17365; + t17846 = t17924+t17928; + t17845 = t17142*t17375+t16602+t17994; + t17844 = t17996+t18008; + t16867 = y*t17470; + t17255 = t17146*t17442; + t17528 = t17098*t17143; + t16851 = t17139*t17528; + t17585 = t17108*t17139; + t17421 = y*t17585; + t17843 = t17146*t16867+t17143*t17255+(t16851+t17421)*z; + t16685 = y*t17533; + t17511 = t17058*t17144; + t17292 = t17143*t17511; + t17537 = t17143*t17056; + t16533 = t17139*t17537; + t17288 = t17103*t17457; + t17842 = y*t17288+t17146*t17292+(t16685+t16533)*z; + t17841 = t17142*t17273+t17062*t17296+t18032; + t17840 = t17043*t17579+t17146*t17324+(t17352+t17521)*t17141; + t17839 = t17938+t17943; + t17107 = RATIONAL(10.0,9.0); + t16944 = t17144*t16996; + t17109 = RATIONAL(-5.0,18.0); + t17838 = t17109*t17409+t17142*t16730+x*t16944+t17107*t17608; + t17130 = RATIONAL(-5.0,9.0); + t17462 = t17130*t17139; + t17097 = RATIONAL(5.0,12.0); + t17358 = t17097*t17505; + t17837 = (t17462+t17358)*t17141+t18038*t17146; + t17836 = t17922+t17948; + t16768 = t17108*t17538; + t17576 = t17098*t17139; + t17835 = y*t17255+t17576*t17653+z*t16768+t17064*t17334; + t17834 = t17922+t17936; + t17833 = t16772+t17047*t17266+t18024*z; + t16736 = x*t17473; + t16783 = x*t16981; + t17832 = t16736+t16681+t17140*t16783+t17055*t17320+t16641; + t16766 = x*t17519; + t16833 = x*t16966; + t17831 = t17140*t16833+t16766+t16592+t17067*t17637+t17142*t17283; + t17312 = t17143*t17476; + t17830 = y*t17305+t16600+t17139*t17312+t18022; + t17298 = t17146*t17476; + t17336 = t17139*t17516; + t16677 = y*t17581; + t17829 = t16624+t17140*t17336+t16677+(t17521+t17298)*y; + t17828 = t17928+t17949+t18007; + t16518 = t17022*t17551; + t17246 = t17061*t17295+z*t16518+t17942; + t17827 = t17062*t17364+t17246+t17023*t17438+t17933; + t17826 = x*t17324+t17111*t17320+t16653+t18023; + t17825 = t17064*t17320+t16626+t17055*t17413+t18034; + t17824 = t17140*t17368+t17143*t17352+t16575+t18019; + t16607 = t17143*t17586; + t17355 = t17143*t17505; + t17823 = t16803+t16607+t17053*t17355+(t17278+t17503)*y; + t17822 = t17898+t17926; + t16975 = t17064*t17146; + t16684 = y*t16975; + t17821 = t17086*t17355+t16684+t16685+t17072*y+t18044*t17143; + t17820 = t17142*t17445+t17088*t17296+t16833+t17089*t17320+(t17562+t17104) +*x; + t16965 = t17111*t17146; + t16779 = y*t16965; + t17819 = t16779+t17104*y+t16787+t18018*t17143; + t17818 = t17086*t17320+t17072*x+t16783+t16774+t17142*t17567+t17091*t17296 +; + t17817 = t17894+t17987; + t17386 = y*t17546; + t17816 = t17139*t17386+t17904+t18042; + t17621 = z*t17104; + t16753 = t17145*t17621; + t16704 = t17141*t17517; + t17276 = t17047*t17582; + t17232 = t16730+t17145*t17276+t17604+t18012*z; + t17815 = t16753+t16704+t17232+t17919+t17949; + t17814 = t16568+t17861+(t17418+t17520)*t17141; + t16630 = t17146*t17569; + t17813 = t17077*t17538+t16630+y*t17330+t17854; + t17812 = t17884+t17986; + t17811 = t17841+t17983; + t17810 = t17864+t17914; + t17809 = t16612+t17142*t17461+x*t17310+t17866; + t17808 = t17139*t17376+t17860+t18026; + t17807 = t17906+t17917; + t17806 = t17864+t17908; + t17805 = t17143*t17534+t17904+(t17337+t17286)*y; + t17804 = t17897+t17911; + t17803 = t17029*t17538+y*t17325+t17061*t17393+t17860; + t17802 = t17841+t17981; + t17801 = t16606+t17139*t17500+y*t17264+t17869; + t17800 = t16727+t17141*t17561+t17232+t17924+t17931; + t17799 = t17139*t17561+z*t16965+t17833+t17931+t18007; + t17299 = t17144*t17557; + t17798 = t17075*t17326+t17144*t16798+t17038*t17374+t17142*t17299+(t16766+ +t17406+t18062)*z; + t17367 = t17144*t17616; + t17797 = t17146*t17367+t17063*t17357+t17144*t16575+t17030*t17334+(t18021+ +t18042)*z; + t17796 = x*t17319+t17043*t17374+(t17285+t17318)*t17142+(t18032+t18069)*z; + t17795 = t17891+t17980; + t15875 = x*t17333; + t17794 = t15875+t17809; + t17793 = t17886+t17888; + t16969 = t17072*t17142; + t16865 = t17144*t16969; + t16679 = t17143*t17470; + t17480 = t17142*t17098; + t17792 = x*t16679+y*t16865+t17047*t17611+t17480*t17653+t17905; + t16973 = t17104*t17139; + t17282 = t17143*t16973; + t17391 = t17123*t17631; + t17398 = t17104*t17631; + t17791 = t17143*t17298+t17146*t17398+t17139*t17391+t17140*t17282+t18031+ +t18045; + t17790 = t17844+t18003+t18009; + t17789 = t17839+t17852; + t17085 = RATIONAL(-4.0,27.0); + t17042 = RATIONAL(16.0,27.0); + t17407 = z*t17590; + t17788 = t17075*t17407+t17042*t17608+t17144*t16804+t17087*t17374+t18064* +t17141+t18039*t17085; + t16840 = t17139*t17517; + t17423 = t17083*t17645; + t17415 = z*t17537; + t17787 = t17875+t17146*t17415+t17139*t17292+(t17423+t16840)*y; + t17392 = t17059*t17626; + t17786 = t17060*t17613+t17053*t17439+t17141*t17281+t17142*t17392+t17858; + t17606 = y*t17625; + t17612 = z*t17627; + t17026 = RATIONAL(-16.0,27.0); + t17785 = t17076*t17612+t17026*t17606+t18040*t17139+t18045*t17144+t18050* +t17146; + t16802 = t17078*t17654; + t17294 = t17142*t17449; + t17784 = y*t17294+t17076*t17609+t17144*t16802+t17026*t17651+t18050*t17142 ++t18040*x; + t17783 = t17064*t17271+t17104*t17419+t17142*t17398+t16802+t16759+t16818+ +t16752+x*t17391; + t17441 = y*t17582; + t17426 = t17032*t17629; + t17782 = t17057*t17357+t17110*t17612+t17073*t17441+t17146*t17426+t17842; + t17781 = t17111*t17296+t17141*t17636+t18033*t17072+t18035*x+t18054; + t17338 = t17143*t17527; + t17350 = t17144*t17496; + t17780 = t17042*t17651+x*t17338+t17075*t17399+t17142*t17350+(t17609+ +t17611)*t17085+t18064*y; + t17471 = t17070*t17139; + t17779 = t17087*t17551+t17141*t17471+t18035*t17139+t18079*t17145+t18066* +t17072; + t16656 = t17139*t17571; + t17778 = t16495+t17062*t17284+t16638+t17140*t16656+t17892; + t17777 = t17513*t17652+z*t16641+t17029*t17326+t17144*t16582+t17883; + t17776 = t16586+t17805; + t17775 = x*t17392+t17055*t17439+t17053*t17326+t17060*t17407+t17872; + t17774 = t17618*t17653+t17043*t17366+z*t16570+t17486*t17654+t17144*t16633 ++t17912; + t17463 = t17140*t17072; + t17300 = t17143*t17463; + t17387 = y*t17463; + t17773 = t17111*t17271+t16790+y*t17636+t16777+x*t17300+t17142*t17387+ +t16764+t17137*t17614; + t17772 = t17862+t17898; + t17432 = t17059*t17645; + t17771 = t17144*t17336+t17143*t17432+t17857+t18070*y; + t17304 = t17012*t17505; + t17547 = t17030*t17141; + t17477 = t17063*t17139; + t17770 = t17139*t17547+t17146*t17553+t17145*t17477+t17024*t17284+(t17472+ +t17304)*t17141+(t16481+t16479)*t17140; + t16918 = x*t17573; + t17769 = t17117*t17326+t17141*t16918+t17112*t17613+t17142*t17403+t17848; + t17768 = t17891+t17974; + t15940 = t17143*t17373; + t17767 = t15940+t17894+t17985; + t16534 = t17139*t17490; + t17766 = t17863+t17140*t16534+t17145*t17534+(t17492+t17273)*t17146; + t17382 = t17143*t17622; + t17430 = t17047*t17645; + t17765 = y*t17430+t17146*t17382+t17843+t18061*t17139; + t17764 = t17876+y*t17432+t17055*t17441+t18070*t17143; + t17267 = t17144*t17565; + t17763 = t17039*t17334+t17146*t17405+t17139*t17331+t17087*t17606+y*t17267 ++(t16803+t18031)*z; + t17762 = t17891+t17894; + t17761 = t17871+t17886; + t17760 = t17058*t17284+t17146*t17446+t17014*t17605+t17061*t17351+t17863; + t17759 = t17146*t17547+t17141*t17477+t16562+t17145*t17304+t17140*t16521+ +t17012*t17284+(t17344+t17553)*t17139; + t17758 = t17142*t17427+t16671+t17994+t18004+t18005; + t16916 = t17117*t17559; + t16767 = t17142*t17517; + t17369 = t17110*t17629; + t17757 = t17112*t17611+t17142*t17369+t17105*t17651+t17143*t16767+(t17383+ +t16916)*y+t18025*x; + t17756 = t17889+t17978; + t17755 = x*t17408+t17043*t17482+t17845+t18004; + t16751 = t17078*t17637; + t17754 = t17064*t17296+t16751+t18033*t17104+t18051*x+t18062; + t16702 = t17143*t17556; + t17753 = x*t16702+t17143*t17607+t17896+t18020*y; + t17311 = t17142*t17465; + t17752 = t17144*t16751+t17142*t17372+t17145*t17311+t17084*t17374+t17026* +t17608+t17141*t17294+t18039*t17076; + t17751 = t17143*t17430+t17139*t16711+t17031*t17612+t17144*t17282+t17835; + t17750 = t17528*t17652+y*t16715+t17047*t17609+x*t16709+t17905; + t17610 = z*t17649; + t17749 = z*t16630+t17146*t17610+t17139*t17346+y*t17258+t17851; + t17748 = t17841+t17889; + t17747 = t17834+t17948+t18006; + t17746 = t17881+t17903; + t17745 = t17030*t17326+t17144*t16589+t17027*t17374+x*t17363+(t18027+ +t18060)*z; + t16892 = t17143*t17561; + t16797 = t17144*t17459; + t17402 = t17109*t17629; + t17744 = t17083*t17399+t17109*t17609+t17142*t16797+t17107*t17651+t18037*y ++(t16892+t17402)*x; + t17743 = t17840+t17976; + t17742 = t17824+t17907; + t17741 = t17043*t17613+z*t16592+t17873+(t17424+t17269)*t17141; + t17740 = t17840+t17884; + t17739 = t17823+t17907; + t17738 = t16478+t17145*t17286+t16527+t17146*t17279+t17892; + t17737 = t17880+t17887; + t17736 = x*t17312+t16616+t17845+t18005; + t17735 = t17111*t17434+t16538+t17844+t17988; + t17384 = t17083*t17626; + t17011 = t17133*t17141; + t16937 = t17144*t17011; + t17734 = t17109*t17613+t17142*t17384+x*t16937+t17118*t17326+t17838; + t17733 = t17027*t17366+t17642*t17652+z*t16632+t17918+(t17367+t17346)*x; + t17732 = t17139*t17377+z*t16607+t17028*t17357+t17043*t17612+t17902; + t17731 = t16826+t17142*t17386+t17990+t18000+t18011; + t17730 = t17840+t17855; + t17729 = t17143*t17267+t17038*t17334+t18053*t17144+(t16677+t17433+t18047) +*z; + t17728 = t17831+t17910; + t17727 = t17084*t17608+x*t17299+t17141*t17414+t17144*t16612+t17077*t17326 ++(t16736+t18054)*z; + t17726 = t17077*t17617+x*t17342+t17879+t17990; + t15971 = t17144*t16554; + t17725 = t15971+t17884+t17982; + t17624 = z*t17123; + t16943 = t17145*t17624; + t17126 = RATIONAL(8.0,9.0); + t17724 = t17108*t17295+t17137*t17416+t16937+t16943+t16944+t17126*t17630+ +t17923; + t16813 = t17087*t17627; + t17723 = t17146*t17387+t16813+t17137*t17393+t17139*t17300+y*t17471+t17143 +*t17278+t18047; + t17722 = t17084*t17551+t17146*t17473+t17141*t17555+t17145*t17298+t18051* +t17139+t18066*t17104; + t17347 = t17144*t17471; + t17420 = z*t17538; + t17721 = t17139*t17338+y*t17347+t17042*t17606+t17143*t17429+t17080*t17334 ++t17144*t16813+(t17612+t17420)*t17085; + t16838 = t17142*t17556; + t16854 = t17143*t17442; + t17720 = y*t16838+t17108*t17609+t17896+(t16854+t17382)*x; + t17719 = t17144*t17437+t17063*t17334+(t17367+t17341)*t17139+(t18026+ +t18057)*z; + t17718 = t17145*t17429+t17042*t17400+t17080*t17348+t17141*t17347+t18080* +t17087+(t17416+t17410)*t17085; + t16864 = t17146*t17621; + t17717 = t16840+t16864+t17833+t17919; + t17716 = t17902+y*t17291+t17038*t17357+t18019*z; + t17715 = t17059*t17266+t17139*t17511+t17246+t17927+t16545+t18017*z; + t17481 = t17058*t17141; + t17714 = t17059*t17295+t16673+t17927+t17942+t17144*t17481+t17933+t18016*z +; + t17713 = t17883+t17039*t17326+t17920+t17834+t17038*t17439+t17934+t18034*z +; + t16897 = t17146*t17624; + t16924 = t17118*t17457; + t16994 = t17133*t17139; + t16917 = t17144*t16994; + t17712 = t16897+t17108*t17266+t16924+t17137*t17410+t17126*t17625+t16917+ +t17925+t17944+t17923; + t17711 = x*t17302+t17918+t18010+(t16652+t16824)*z+(t17311+t17394)*y; + t17639 = z*t17118; + t17293 = t17144*t17533; + t17710 = t17843+t16991*t17653+t16711+t16702+t17110*t17357+t18056*z+( +t17293+t17639)*y; + t17709 = t16994+t17108*t17551+t17899+t17093*t17284+(t17497+t18013)*t17139 ++t18030; + t16873 = t17130*t17637; + t17650 = z*RATIONAL(-8.0,9.0); + t17620 = z*t17137; + t17708 = t17098*t17326+t17144*t16873+t16916+t16918+t17838+(t17620+t16753) +*t17142+(t17650+t16943)*x; + t17096 = RATIONAL(-5.0,48.0); + t17468 = t17096*t17139; + t17329 = t17140*t17468; + t17707 = t17138*t17141+t17118*t17551+t17127*t17566+t18013+t17079*t17284+ +t17837+(t17576+t17329)*t17145; + t16718 = t17140*t17485; + t16884 = t17136*t17648; + t17313 = t17093*t17505; + t17706 = t16768+t17100*t17393+t16884+(t17495+t16718+t17313)*t17143+( +t18063+t18068)*y+t18055; + t17543 = t17031*t17145; + t17467 = t17044*t17145; + t17339 = t17139*t17467; + t17705 = t17139*t17543+t17146*t17481+t16968+t17051*t17284+t17140*t17339+ +t17092*t17566+t17850+t18052; + t17704 = t17086*t17440+t17083*t17524+t17142*t16981+t16969+t17820+(t17567+ +t16852)*x; + t17508 = t17047*t17145; + t17703 = t17139*t17508+t17041*t17284+t17145*t17307+t17893+(t17491+t17535+ +t17103)*t17141+t18038; + t16988 = t17073*t17146; + t17443 = t17092*t17146; + t17702 = t16988+t17140*t17443+t17095*t17505+t17103*t17139+t17041*t17351+ +t17146*t17452+t16656+t17049*t17284+t17893; + t17701 = t17048*t17351+t16739+t17146*t17450+t16957+t17874+t17046*t17284+ +t17012*t17605+t18065*t17139; + t17640 = z*t17117; + t17700 = t17143*t17293+t16988*t17653+t17835+y*t17640+t17144*t16787+t18055 +*z+t18061; + t17574 = t17140*t17092; + t17699 = t17044*t17355+t17968+t18028*t17143+(t17574+t18041)*y+t18036; + t17698 = t17048*t17284+t17023*t17605+t16852+t17046*t17351+t17012*t17551+ +t16960+t17874+t18065*t17141; + t17647 = z*t17126; + t17697 = t17142*t17624+t17137*t17613+t17072*t17407+t17108*t17326+t17848+( +t17647+t17327)*x+t18037; + t16845 = t17143*t17574; + t16932 = y*t17462; + t17696 = t17146*t16845+t16851+t16932+(t17329+t17531)*t17143+(t17358+ +t18030+t18058)*y+t18056; + t17695 = t17117*t17551+t17011+t17071*t17284+t17141*t17497+t17899+t17998+( +t17313+t17585)*t17145; + t17694 = t17056*t17439+t17032*t17326+t16715+x*t17442+t17872+t18014*z; + t16724 = t17145*t17445; + t17577 = t17032*t17139; + t17693 = t17099*t17284+t17111*t17551+t17104*t17141+t17114*t17566+t16724+ +t16981+t17878+(t17343+t17577)*t17145; + t17601 = t17140*t17114; + t16848 = t17099*t17529; + t17692 = t16619+t18002+t17819+(t16848+t17359+t17601)*y; + t17412 = t17098*t17637; + t17599 = t17117*t17144; + t17691 = t17144*t17412+t16767+t17031*t17326+t17865+t18048*z+(t17621+ +t17599+t16727)*x; + t16786 = t17146*t17445; + t17499 = t17099*t17145; + t16719 = t17140*t17499; + t17690 = t17139*t16719+t16973+t17032*t17551+t16781+t16786+t16975+t17114* +t17505+t17089*t17284+t17878; + t17588 = t17140*t17116; + t17689 = t17821+t16533+t17992+(t16786+t17301+t17588)*y; + t17688 = t16669+t17116*t17566+t16966+t17101*t17284+t16719+t17086*t17351+ +t17856+t18012; + t17687 = t17877+t17047*t17326+t17073*t17559+(t16783+t18059)*z+(t17362+ +t18029)*x; + t17686 = t17080*t17366+t17912+t17938+z*t16674+t18010+(t17350+t17610+ +t17436)*x; + t17623 = z*t17057; + t17685 = t16738+t17858+t17056*t17326+t17032*t17439+(t17623+t17470)*x+ +t18015*z; + t17684 = t16735+t17052*t17284+t17091*t17505+t17045*t17351+t16518+t17847+ +t18017; + t16771 = t17145*t17444; + t17683 = t16477+t16771+t17145*t17306+t17091*t17566+t17045*t17284+t17847+ +t18016; + t17682 = t17044*t17393+t16845+t17984+t18041*t17143+(t17057+t18028)*y+ +t18067; + t17681 = t17873+t17038*t17326+t17141*t17373+t17920+t17936+t18023*z; + t17680 = t17116*t17505+t16627+t17139*t16724+t17086*t17284+t16848+t16965+ +t17856+t18024; + t17679 = t17140*t17256+t16991+t16534+t17031*t17551+t16718+t17092*t17505+ +t17850+(t17073+t17332)*t17139; + t16853 = t17142*t16966; + t17678 = t17104*t17142+t17110*t17524+t16853+t17089*t17440+t17818+(t17445+ +t16771)*x; + t17677 = t17003+t17127*t17505+t17096*t17284+t17098*t17551+t17837+t17998* +t17139+t18063; + t17676 = t17760+t17825; + t17675 = t17738+t17826; + t17674 = t17735+t17816; + t17673 = t16525+t16586+t17971+t17972; + t17593 = t16573+t16586; + t17672 = t17593+t17972+t17973; + t17671 = t17797+t17906+t17915; + t17670 = t17735+t17808; + t17460 = t16573+t16640; + t17669 = t17460+t17969+t17973; + t17596 = t16525+t16640; + t17668 = t17596+t17969+t17971; + t17667 = t17758+t17816; + t17666 = t17719+t17897+t17913; + t17665 = t17758+t17808; + t17664 = t17958+t17967; + t17356 = t17012*t17529; + t17321 = t17143*t17484; + t17663 = t17143*t17304+t17952+y*t17356+t17146*t17321+t17024*t17393+t18075 +; + t17662 = t17139*t17321+t17143*t17356+t17952+y*t17304+t17024*t17404+t18073 +; + t17661 = t17960+t17962; + t17660 = t17961+t17967; + t17659 = t17961+t17975; + t17658 = t17950+t17959; + t17657 = t17958+t17975; + t17656 = t17951+t17964; + t17655 = t17954+t17963; + t16956 = t17057*x; + t17619 = z*t17056; + t15847 = t17146*t17386; + t15741 = t17039*t17366; + t17597 = t15847+t15741; + t17595 = t15971+t15875; + t17584 = t17093*t17139; + t17563 = t17096*t17146; + t17554 = t17095*t17145; + t15685 = y*t17335; + t15966 = t17038*t17366; + t17532 = t15685+t15966; + t17530 = t17097*t17146; + t15849 = t17058*t17413; + t17518 = t15849+t15940; + t17488 = t17096*t17145; + t17479 = t17097*t17145; + t17469 = t17131*t17139; + t17454 = t17114*t17145; + t17425 = t17144*t16956; + t16868 = x*t17556; + t16877 = y*t17599; + t17390 = z*t17508; + t17388 = t17142*t17619; + t16808 = t17108*t17524; + t16822 = t17141*t17480; + t17340 = t17144*t17576; + t17323 = t17144*t17560; + t17309 = t17144*t17562; + t17274 = t17144*t17577; + t17262 = t17145*t17470; + t17257 = t17141*t17589; + t17254 = t17146*t17380+t17057*t17295+t17604; + t17253 = t15847+t17910; + t17252 = t15849+t17916; + t17250 = t15875+t17916; + t17248 = t17117*t17266+t17112*t17410+t17944; + t17245 = t15849+t17907; + t17244 = t15685+t17909; + t17243 = t15847+t17909; + t17242 = t17454+t17997; + t17135 = RATIONAL(2.0,3.0); + t17241 = t17116*t17145+t17128*t17141+t17135; + t17240 = t17071+t17487+t17096*t17141; + t17074 = RATIONAL(-5.0,32.0); + t17034 = RATIONAL(25.0,32.0); + t17119 = RATIONAL(-5.0,8.0); + t17239 = t17119+t17074*t17145+t17034*t17141; + t17238 = t17499+t17106*t17141+t17114; + t17237 = t17525+t17991; + t17236 = t17554+t17598+t17079; + t17065 = RATIONAL(1.0,16.0); + t17066 = RATIONAL(-5.0,16.0); + t17121 = RATIONAL(1.0,4.0); + t17235 = t17065*t17145+t17066*t17141+t17121; + t17233 = t17929+t17089*t17266+t17101*t17457+(t17584+t17339)*z; + t17231 = t17144*t17454+t17124*t17630+t17106*t17295+t17100*t17416+t17921; + t17230 = t17139*t17402+t17107*t17606+t17073*t17334+y*t16924+t17248; + t17229 = t17144*t16853+x*t17262+t17141*t17607+z*t16822+t17254; + t17228 = t17855+t17943+t17947; + t17227 = t17836+t17864; + t17226 = t17111*t17374+t17142*t17262+t17254+(t17412+t16808)*z; + t17225 = t17822+t17943; + t17224 = t17839+t17903; + t17223 = t17112*t17420+t17143*t17288+y*t17395+t17146*t16877+t17248; + t17222 = t17836+t17886; + t17219 = t17870+t17906; + t17218 = t17870+t17897; + t17018 = RATIONAL(25.0,192.0); + t17217 = t17099*t17582+z*t17563+t17091*t17295+t17018*t17416+t17233+t17930 +; + t17036 = RATIONAL(-25.0,48.0); + t17216 = t17135*t17582+z*t17530+t17116*t17295+t17036*t17416+t17901+t17921 ++t17937; + t17215 = z*t17488+t17099*t17592+t17018*t17410+t17091*t17266+t17849+t17929 ++t17930; + t17214 = t17135*t17592+t17036*t17410+z*t17479+t17116*t17266+t17231+t17937 +; + t17040 = RATIONAL(-25.0,96.0); + t17213 = t17236*t17144+(t17086*t17145+t17106+t17040*t17141)*z; + t17054 = RATIONAL(25.0,96.0); + t17212 = t17240*t17144+(t17102+t17054*t17141+t17089*t17145)*z; + t17211 = (t17468+t17443+t17071)*t17144+(t17089*t17146+t17054*t17139+ +t17102)*z; + t17210 = (t17584+t17993)*t17144+(t17040*t17139+t17106+t17086*t17146)*z; + t17209 = t17141*t16868+x*t17390+t17142*t17257+t17229+t17145*t17379+t17846 +; + t17208 = t17109*t17612+y*t16917+t17143*t17423+t17230+t17139*t16892+t17900 +; + t17207 = t17057*t17354+t17619*t17654+y*t17425+t17032*t17609+t17058*t17366 ++t17143*t17388+t17827+(t17292+t17426)*x; + t17206 = t17828+t17142*t17259+t17032*t17407+t17877+(t17303+t17403)*x; + t17205 = t17145*t17388+t17865+t17058*t17326+t17828+(t17384+t16704)*x; + t17204 = t17112*t17612+y*t17268+t17139*t16938+t17146*t17369+t17223+t17900 +; + t17203 = t17142*t17390+t17104*t17326+t17543*t17652+t17226+x*t17257+t17846 +; + t17202 = t17511*t17654+t17143*t17425+t17142*t17292+x*t17415+t17827+y* +t17388+t17057*t17366+(t17399+t17651)*t17032; + t17050 = RATIONAL(-25.0,24.0); + t17201 = t17050*t17364+t17071*t17438+t17231+t17901+RATIONAL(4.0,3.0)*z+( +t17626+t17645)*t17125+(t17469+t17997)*t17144; + t17200 = t17054*t17364+t17102*t17582+t17233+t17041*t17438+t17849+t17991* +t17144+(t17554+t17993)*z; + t17199 = t17110*t17538+t17815+t17821+(t17104+t16965)*t17143+t18018*y; + t17198 = t17230+t17144*t16932+t17724+(t16897+t17650)*y+(t16864+t17620+ +t17340)*t17143+t18025; + t17197 = t16591+t17799+t17102*t17440+t17818+(t17588+t16724)*x+t18059; + t17196 = t17717+t17229+t17142*t17309+t16838+(t17378+t17999)*z+(t17589+ +t17323+t17639)*x; + t17195 = t17142*t17531+t17097*t17440+t16822+t17096*t17320+t16873+t17712+ +t17092*t17296+(t17998+t18058)*x+t17999; + t17194 = t17800+t17144*t17421+t17143*t17276+t16797+t17842+t18029*y+( +t16684+t17992)*z; + t17193 = t17144*t16884+t16892+t17724+t17108*t17357+t17137*t17612+t17223+( +t17381+t17624)*t17143+(t17647+t17600)*y; + t17192 = t17031*t17357+t16877+t17800+t17143*t17517+t17875+(t17621+t17340) +*y+(t16779+t18002)*z; + t17191 = t17715+t17049*t17440+t17041*t17296+t17044*t17320+t17142*t17535+( +t17574+t17332)*x+t18014+t18046; + t17190 = t17056*t17357+t16867+t16854+t17714+t17857+(t17623+t17274)*y+ +t17984*z; + t17189 = t16588+t17799+t17106*t17440+t17820+(t16719+t17601)*x+t18048; + t17188 = t17717+t16865+t16868+t17142*t17323+t17226+(t17309+t17640)*x+( +t17411+t17995)*z; + t17187 = t17715+t17044*t17440+t17049*t17320+t16956+t17051*t17296+t17041* +t17413+x*t17535+t17142*t17574+t18015+t18043; + t17186 = t16679+t17056*t17441+t17714+y*t17442+t17143*t17274+t17876+t17968 +*z; + t17185 = t17142*t17495+t16808+t17712+t17095*t17296+t17093*t17320+(t18013+ +t18049+t18068)*x+t17995; + t17184 = t17815+t17086*t17393+t17819+t18044*y+(t17072+t16975+t17533)* +t17143; + t17183 = t17224+t17767+t17727+t17852+t17881; + t17182 = t17760+t17713+t17826+t17910; + t17181 = t17953+t17663+t17955; + t17180 = t15971+t17811+t17219+t17252+t17830+t17890+t17917; + t17179 = t17225+t17686+t17966+t17979; + t17178 = t17763+t17228+t17728+t17859+t17926+t17945; + t17177 = t17681+t15741+t17218+t17797+t17913; + t17176 = t17752+t17718+t17722+t17781; + t17175 = t17711+t17938+t17965+t17966; + t17174 = t17770+t17222+t17776+t17871+t17895; + t17173 = t17716+t15940+t17796+t17218+t17890+t17911; + t17172 = t17756+t17747+t17759+t17774; + t17171 = t17813+t17243+t15966+t17812+t17832+t17868+t17882; + t17170 = t17789+t17749+t17739+t17840+t17970; + t17169 = t17228+t17725+t17795+t17885+t17938+t17941; + t17168 = t17718+t17754+t17773+t17785; + t17167 = t17686+t17903+t17965+t17977; + t17166 = t17721+t17718+t17780+t17788; + t17165 = t15875+t17745+t17227+t17778+t17867+t17914; + t17164 = t17738+t17713+t17825+t17909; + t17163 = t17732+t17755+t16525+t17747+t17802; + t17162 = t17225+t17801+t15685+t17731+t17862+t17882; + t17161 = t17953+t17662+t17957; + t17160 = t17956+t17663+t17957; + t17159 = t17729+t17817+t17221+t15741+t17882+t17887; + t17158 = t17766+t17222+t17742+t17867+t17888; + t17157 = t17779+t17718+t17783+t17784; + t17156 = t17224+t17711+t17822+t17977+t17979; + t17155 = t17955+t17662+t17956; + t17154 = t17227+t17460+t17733+t17803+t17895+t17908; + t17153 = t17726+t17798+t17789+t17829+t17916; + t17152 = t17681+t17219+t15966+t17719+t17915; + t17132 = RATIONAL(-1.0,8.0); + t17122 = RATIONAL(1.0,8.0); + t17120 = RATIONAL(5.0,3.0); + t17115 = RATIONAL(5.0,8.0); + t17113 = RATIONAL(-5.0,4.0); + t17094 = RATIONAL(-1.0,16.0); + t17090 = RATIONAL(5.0,64.0); + t17082 = RATIONAL(5.0,32.0); + t17081 = RATIONAL(5.0,16.0); + t17069 = RATIONAL(-5.0,64.0); + t17068 = RATIONAL(25.0,8.0); + t17037 = RATIONAL(25.0,48.0); + t17033 = RATIONAL(-25.0,12.0); + coeffs_dz->coeff_m2_m2_m2 = t17658+t17656+t17160; + coeffs_dz->coeff_m1_m2_m2 = t17158+t17736+t17595+t17796+t17807+t17810; + coeffs_dz->coeff_0_m2_m2 = t17698+t17682+t17186; + coeffs_dz->coeff_p1_m2_m2 = t17745+t17158+t17804+t17518+t17748+t17983+ +t17996+t18003; + coeffs_dz->coeff_p2_m2_m2 = t17181+t17963+t17950+t17962+t17964; + coeffs_dz->coeff_m2_m1_m2 = t17182+t15847+t15966+t17671+t17665; + coeffs_dz->coeff_m1_m1_m2 = t17664+t17179+t17673; + coeffs_dz->coeff_0_m1_m2 = t17693+t17689+t17192; + coeffs_dz->coeff_p1_m1_m2 = t17657+t17175+t17672; + coeffs_dz->coeff_p2_m1_m2 = t17243+t17676+t17177+t17670; + coeffs_dz->coeff_m2_0_m2 = t17701+t17694+t17187; + coeffs_dz->coeff_m1_0_m2 = t17691+t17690+t17197; + coeffs_dz->coeff_0_0_m2 = (t17049*t17145+t17018*t17141+t17096)*t17139+( +RATIONAL(-1.0,4.0)+t17094*t17145+t17081*t17141+(RATIONAL(-25.0,64.0)*t17141+ +t17081+t17090*t17145)*t17139+(t17094+t17090*t17141+RATIONAL(-1.0,64.0)*t17145)* +t17146)*t17140+(t17049*t17141+t17051*t17145+t17092)*t17146+t17200+t17240; + coeffs_dz->coeff_p1_0_m2 = t17189+t17687+t17690; + coeffs_dz->coeff_p2_0_m2 = t17701+t17685+t17191; + coeffs_dz->coeff_m2_p1_m2 = t17674+t17182+t15685+t17666+t15741; + coeffs_dz->coeff_m1_p1_m2 = t17657+t17156+t17668; + coeffs_dz->coeff_0_p1_m2 = t17693+t17194+t17692; + coeffs_dz->coeff_p1_p1_m2 = t17664+t17167+t17669; + coeffs_dz->coeff_p2_p1_m2 = t17667+t17244+t17676+t17152; + coeffs_dz->coeff_m2_p2_m2 = t17661+t17155+t17950+t17951; + coeffs_dz->coeff_m1_p2_m2 = t17790+t17766+t17173+t17250+t17810+t17830; + coeffs_dz->coeff_0_p2_m2 = t17699+t17698+t17190; + coeffs_dz->coeff_p1_p2_m2 = t17745+t17716+t17736+t17180+t17766; + coeffs_dz->coeff_p2_p2_m2 = t17161+t17658+t17960+t17963; + coeffs_dz->coeff_m2_m2_m1 = t17755+t17154+t17759+t17761+t17777; + coeffs_dz->coeff_m1_m2_m1 = t17762+t17763+t17162+t17832+t15741+t17909+ +t17974+t17987; + coeffs_dz->coeff_0_m2_m1 = t17710+t17703+t17199; + coeffs_dz->coeff_p1_m2_m1 = t17178+t17801+t17532+t17768+t17737+t17812; + coeffs_dz->coeff_p2_m2_m1 = t17802+t17596+t17761+t17741+t17172+t17803; + coeffs_dz->coeff_m2_m1_m1 = t17762+t17814+t17153+t17518+t17749+t17980+ +t17985; + coeffs_dz->coeff_m1_m1_m1 = t17779+t17752+t17168+t17780+t17791; + coeffs_dz->coeff_0_m1_m1 = t17198+t17695+t17696; + coeffs_dz->coeff_p1_m1_m1 = t17788+t17785+t17157+t17781+t17791; + coeffs_dz->coeff_p2_m1_m1 = t17250+t17749+t17169+t17727+t17809+t17829; + coeffs_dz->coeff_m2_0_m1 = t17196+t17702+t17678; + coeffs_dz->coeff_m1_0_m1 = t17709+t17195+t17708; + coeffs_dz->coeff_0_0_m1 = t17201+t17238*t17146+(t17122*t17145+RATIONAL( +1.0,2.0)+t17119*t17141+t17239*t17139+(t17074*t17141+RATIONAL(1.0,32.0)*t17145+ +t17122)*t17146)*t17140+(t17131+t17106*t17145+t17050*t17141)*t17139+t17242; + coeffs_dz->coeff_p1_0_m1 = t17697+t17709+t17185; + coeffs_dz->coeff_p2_0_m1 = t17188+t17702+t17704; + coeffs_dz->coeff_m2_p1_m1 = t17798+t17245+t17169+t17746+t17814+t17823; + coeffs_dz->coeff_m1_p1_m1 = t17723+t17752+t17157+t17721+t17754; + coeffs_dz->coeff_0_p1_m1 = t17695+t17706+t17193; + coeffs_dz->coeff_p1_p1_m1 = t17723+t17779+t17166+t17773+t17781; + coeffs_dz->coeff_p2_p1_m1 = t17726+t17794+t17183+t17739+t17795; + coeffs_dz->coeff_m2_p2_m1 = t17732+t17593+t17777+t17172+t17805+t17806; + coeffs_dz->coeff_m1_p2_m1 = t17729+t17772+t17171+t17768+t17853+t17989+ +t18001; + coeffs_dz->coeff_0_p2_m1 = t17184+t17703+t17700; + coeffs_dz->coeff_p1_p2_m1 = t17253+t17159+t17731+t17768+t17813+t17831; + coeffs_dz->coeff_p2_p2_m1 = t17733+t17163+t17759+t17741+t17776; + coeffs_dz->coeff_m2_m2_0 = t17207+t17764+t17775; + coeffs_dz->coeff_m1_m2_0 = t17753+t17205+t17765; + coeffs_dz->coeff_0_m2_0 = t17215+t17211*y+t17210*t17143; + coeffs_dz->coeff_p1_m2_0 = t17750+t17206+t17765; + coeffs_dz->coeff_p2_m2_0 = t17202+t17764+t17786; + coeffs_dz->coeff_m2_m1_0 = t17720+t17209+t17787; + coeffs_dz->coeff_m1_m1_0 = t17208+t17734+t17757; + coeffs_dz->coeff_0_m1_0 = t17214+((t17116+t17101*t17146+t17102*t17139)* +t17144+(t17563+t17037*t17139+t17100)*z)*t17143+((t17134+t17469+t17114*t17146)* +t17144+(t17120+t17033*t17139+t17530)*z)*y; + coeffs_dz->coeff_p1_m1_0 = t17208+t17744+t17769; + coeffs_dz->coeff_p2_m1_0 = t17203+t17787+t17792; + coeffs_dz->coeff_m2_0_0 = t17213*t17142+t17212*x+t17217; + coeffs_dz->coeff_m1_0_0 = t17216+(t17242*t17144+(t17479+t17120+t17033* +t17141)*z)*x+(t17237*t17144+(t17488+t17100+t17037*t17141)*z)*t17142; + coeffs_dz->coeff_0_0_0 = (t17113*t17141+1.0+t17121*t17145+(t17113+t17066* +t17145+RATIONAL(25.0,16.0)*t17141)*t17139+t17235*t17146)*t17144+(t17119*t17145+ +t17068*t17141+RATIONAL(-5.0,2.0)+(t17034*t17145+t17068+RATIONAL(-125.0,32.0)* +t17141)*t17139+t17239*t17146)*z; + coeffs_dz->coeff_p1_0_0 = t17216+(t17238*t17144+(t17093*t17145+t17036* +t17141+t17097)*z)*t17142+(t17241*t17144+(t17035*t17141+t17124+t17100*t17145)*z) +*x; + coeffs_dz->coeff_p2_0_0 = t17212*t17142+t17217+t17213*x; + coeffs_dz->coeff_m2_p1_0 = t17782+t17209+t17792; + coeffs_dz->coeff_m1_p1_0 = t17204+t17734+t17744; + coeffs_dz->coeff_0_p1_0 = t17214+((t17116*t17146+t17128*t17139+t17135)* +t17144+(t17124+t17035*t17139+t17100*t17146)*z)*y+((t17114+t17099*t17146+t17106* +t17139)*t17144+(t17097+t17036*t17139+t17093*t17146)*z)*t17143; + coeffs_dz->coeff_p1_p1_0 = t17204+t17757+t17769; + coeffs_dz->coeff_p2_p1_0 = t17720+t17203+t17782; + coeffs_dz->coeff_m2_p2_0 = t17202+t17771+t17775; + coeffs_dz->coeff_m1_p2_0 = t17750+t17205+t17751; + coeffs_dz->coeff_0_p2_0 = t17211*t17143+t17215+t17210*y; + coeffs_dz->coeff_p1_p2_0 = t17206+t17751+t17753; + coeffs_dz->coeff_p2_p2_0 = t17207+t17771+t17786; + coeffs_dz->coeff_m2_m2_p1 = t16525+t17733+t17174+t17777+t17748+t17978+ +t17981; + coeffs_dz->coeff_m1_m2_p1 = t17178+t17772+t17813+t17743+t17597+t17817; + coeffs_dz->coeff_0_m2_p1 = t17184+t17705+t17710; + coeffs_dz->coeff_p1_m2_p1 = t17171+t17731+t17737+t17743+t17763; + coeffs_dz->coeff_p2_m2_p1 = t17755+t16573+t17174+t17774+t17741+t17806; + coeffs_dz->coeff_m2_m1_p1 = t17170+t17794+t17767+t17798+t17855+t17885; + coeffs_dz->coeff_m1_m1_p1 = t17723+t17176+t17783+t17780+t17785; + coeffs_dz->coeff_0_m1_p1 = t17198+t17707+t17706; + coeffs_dz->coeff_p1_m1_p1 = t17723+t17168+t17722+t17784+t17788; + coeffs_dz->coeff_p2_m1_p1 = t17726+t17170+t15849+t17725+t17727+t17814; + coeffs_dz->coeff_m2_0_p1 = t17196+t17679+t17704; + coeffs_dz->coeff_m1_0_p1 = t17677+t17185+t17708; + coeffs_dz->coeff_0_0_p1 = (t17115*t17141+t17132*t17145+RATIONAL(-1.0,2.0) ++(t17082*t17145+RATIONAL(-25.0,32.0)*t17141+t17115)*t17139+(t17082*t17141+ +RATIONAL(-1.0,32.0)*t17145+t17132)*t17146)*t17140+t17201+t17237*t17146+(t17102* +t17145+RATIONAL(25.0,24.0)*t17141+t17128)*t17139+t17241; + coeffs_dz->coeff_p1_0_p1 = t17697+t17677+t17195; + coeffs_dz->coeff_p2_0_p1 = t17188+t17679+t17678; + coeffs_dz->coeff_m2_p1_p1 = t17740+t17153+t17595+t17809+t17746+t17970+ +t17982; + coeffs_dz->coeff_m1_p1_p1 = t17176+t17721+t17784+t17773+t17791; + coeffs_dz->coeff_0_p1_p1 = t17707+t17696+t17193; + coeffs_dz->coeff_p1_p1_p1 = t17166+t17722+t17754+t17783+t17791; + coeffs_dz->coeff_p2_p1_p1 = t17814+t17252+t17183+t17730+t17829+t17885+ +t17970; + coeffs_dz->coeff_m2_p2_p1 = t17770+t17163+t16640+t17777+t17774+t17803; + coeffs_dz->coeff_m1_p2_p1 = t17729+t17740+t15966+t17162+t17728+t17976+ +t17986; + coeffs_dz->coeff_0_p2_p1 = t17705+t17199+t17700; + coeffs_dz->coeff_p1_p2_p1 = t17159+t17244+t17801+t17730+t17832+t17859+ +t17976; + coeffs_dz->coeff_p2_p2_p1 = t17732+t17756+t17154+t17741+t17770; + coeffs_dz->coeff_m2_m2_p2 = t17155+t17959+t17655+t17964; + coeffs_dz->coeff_m1_m2_p2 = t17778+t17790+t17793+t17180+t17796; + coeffs_dz->coeff_0_m2_p2 = t17699+t17683+t17186; + coeffs_dz->coeff_p1_m2_p2 = t17165+t17736+t15940+t17793+t17804+t17830+ +t17916; + coeffs_dz->coeff_p2_m2_p2 = t17161+t17656+t17954+t17962; + coeffs_dz->coeff_m2_m1_p2 = t17674+t17164+t17532+t17671; + coeffs_dz->coeff_m1_m1_p2 = t17179+t17659+t17669; + coeffs_dz->coeff_0_m1_p2 = t17192+t17688+t17692; + coeffs_dz->coeff_p1_m1_p2 = t17175+t17668+t17660; + coeffs_dz->coeff_p2_m1_p2 = t17667+t17675+t15685+t17177+t17910; + coeffs_dz->coeff_m2_0_p2 = t17191+t17694+t17684; + coeffs_dz->coeff_m1_0_p2 = t17189+t17691+t17680; + coeffs_dz->coeff_0_0_p2 = (t17041*t17145+t17545+t17095)*t17146+(t17019* +t17141+t17093+t17467)*t17139+((t17066+t17069*t17145+RATIONAL(25.0,64.0)*t17141) +*t17139+(t17065+t17069*t17141+RATIONAL(1.0,64.0)*t17145)*t17146+t17235)*t17140+ +t17200+t17236; + coeffs_dz->coeff_p1_0_p2 = t17687+t17680+t17197; + coeffs_dz->coeff_p2_0_p2 = t17685+t17187+t17684; + coeffs_dz->coeff_m2_p1_p2 = t17164+t17666+t17665+t17597; + coeffs_dz->coeff_m1_p1_p2 = t17156+t17672+t17660; + coeffs_dz->coeff_0_p1_p2 = t17689+t17194+t17688; + coeffs_dz->coeff_p1_p1_p2 = t17167+t17659+t17673; + coeffs_dz->coeff_p2_p1_p2 = t17253+t17675+t17152+t17670; + coeffs_dz->coeff_m2_p2_p2 = t17661+t17160+t17655; + coeffs_dz->coeff_m1_p2_p2 = t17778+t17173+t17736+t17245+t17811+t17824; + coeffs_dz->coeff_0_p2_p2 = t17683+t17682+t17190; + coeffs_dz->coeff_p1_p2_p2 = t15971+t17790+t17716+t17165+t17742+t17807; + coeffs_dz->coeff_p2_p2_p2 = t17181+t17951+t17954+t17959+t17960; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dzz.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dzz.compute.c new file mode 100644 index 0000000..d9422aa --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dzz.compute.c @@ -0,0 +1,2341 @@ +fp t30715; +fp t30750; +fp t30779; +fp t31096; +fp t31648; +fp t30693; +fp t30692; +fp t31208; +fp t30778; +fp t30780; +fp t30782; +fp t31072; +fp t31647; +fp t30781; +fp t30783; +fp t31094; +fp t31259; +fp t30321; +fp t31646; +fp t30706; +fp t30675; +fp t31056; +fp t31645; +fp t31172; +fp t31147; +fp t31644; +fp t30684; +fp t31065; +fp t30899; +fp t30663; +fp t31643; +fp t30657; +fp t31642; +fp t30734; +fp t30602; +fp t30695; +fp t31095; +fp t30907; +fp t31641; +fp t31246; +fp t31197; +fp t31144; +fp t30890; +fp t31640; +fp t30223; +fp t31639; +fp t31021; +fp t30658; +fp t31064; +fp t31638; +fp t30784; +fp t30245; +fp t31086; +fp t31637; +fp t31164; +fp t31008; +fp t31043; +fp t31636; +fp t30711; +fp t30718; +fp t31635; +fp t30689; +fp t30688; +fp t30592; +fp t30968; +fp t31634; +fp t31139; +fp t31059; +fp t31633; +fp t30698; +fp t31632; +fp t30768; +fp t30637; +fp t30776; +fp t31066; +fp t31631; +fp t30758; +fp t30639; +fp t31630; +fp t30703; +fp t31225; +fp t31629; +fp t30704; +fp t31146; +fp t31628; +fp t30707; +fp t30661; +fp t31082; +fp t31627; +fp t30660; +fp t31128; +fp t31083; +fp t30650; +fp t31626; +fp t30678; +fp t30716; +fp t31625; +fp t31102; +fp t31624; +fp t30747; +fp t31060; +fp t30543; +fp t30745; +fp t31191; +fp t30544; +fp t31623; +fp t31216; +fp t31206; +fp t30552; +fp t31622; +fp t31222; +fp t31209; +fp t30541; +fp t31621; +fp t31097; +fp t30547; +fp t31192; +fp t30546; +fp t31620; +fp t30759; +fp t30730; +fp t31619; +fp t30710; +fp t31145; +fp t30457; +fp t30765; +fp t31214; +fp t31618; +fp t31167; +fp t30762; +fp t30553; +fp t31617; +fp t30667; +fp t30687; +fp t31616; +fp t30729; +fp t31177; +fp t30731; +fp t31160; +fp t30406; +fp t31615; +fp t31614; +fp t30690; +fp t30721; +fp t31125; +fp t31613; +fp t31105; +fp t30527; +fp t30761; +fp t31188; +fp t31612; +fp t31093; +fp t31611; +fp t31260; +fp t31610; +fp t31254; +fp t30719; +fp t30998; +fp t31219; +fp t31609; +fp t31263; +fp t31608; +fp t30739; +fp t30737; +fp t31607; +fp t30720; +fp t31264; +fp t31606; +fp t31223; +fp t30991; +fp t31217; +fp t31045; +fp t31605; +fp t30702; +fp t31604; +fp t30924; +fp t31077; +fp t31024; +fp t31603; +fp t30741; +fp t31114; +fp t30915; +fp t31602; +fp t31002; +fp t30733; +fp t31111; +fp t31031; +fp t31601; +fp t30913; +fp t30958; +fp t31600; +fp t31266; +fp t29631; +fp t31109; +fp t31003; +fp t31599; +fp t31181; +fp t30686; +fp t31100; +fp t31027; +fp t30239; +fp t31458; +fp t31598; +fp t30619; +fp t31041; +fp t31050; +fp t30604; +fp t31036; +fp t31442; +fp t31597; +fp t30571; +fp t31596; +fp t31595; +fp t31148; +fp t29895; +fp t31594; +fp t31123; +fp t30598; +fp t31014; +fp t29588; +fp t31593; +fp t31238; +fp t30348; +fp t30972; +fp t31592; +fp t30894; +fp t31591; +fp t30618; +fp t31049; +fp t30953; +fp t31461; +fp t31252; +fp t31199; +fp t31590; +fp t30471; +fp t30590; +fp t31012; +fp t31589; +fp t30593; +fp t31023; +fp t30222; +fp t31476; +fp t31235; +fp t31200; +fp t31588; +fp t31190; +fp t31040; +fp t30502; +fp t31587; +fp t30255; +fp t31486; +fp t31265; +fp t31586; +fp t31016; +fp t30904; +fp t31585; +fp t31202; +fp t30600; +fp t31005; +fp t29552; +fp t31584; +fp t30664; +fp t31101; +fp t30986; +fp t31583; +fp t31149; +fp t31038; +fp t29956; +fp t30606; +fp t31006; +fp t31582; +fp t30601; +fp t31044; +fp t31581; +fp t31124; +fp t31011; +fp t31580; +fp t31015; +fp t31579; +fp t30621; +fp t31052; +fp t31099; +fp t29886; +fp t31578; +fp t30603; +fp t31462; +fp t31577; +fp t30596; +fp t29510; +fp t31203; +fp t31576; +fp t30495; +fp t31575; +fp t30911; +fp t31574; +fp t30287; +fp t30599; +fp t31009; +fp t31441; +fp t31573; +fp t31091; +fp t31071; +fp t30954; +fp t31572; +fp t30922; +fp t31463; +fp t31112; +fp t31571; +fp t31570; +fp t30754; +fp t30751; +fp t31569; +fp t30757; +fp t30760; +fp t31568; +fp t31162; +fp t29658; +fp t31567; +fp t31033; +fp t31566; +fp t31565; +fp t30981; +fp t30714; +fp t30725; +fp t30610; +fp t30888; +fp t31156; +fp t30740; +fp t31119; +fp t30722; +fp t31564; +fp t31563; +fp t31230; +fp t31010; +fp t30616; +fp t31022; +fp t31562; +fp t31079; +fp t30622; +fp t31001; +fp t31561; +fp t31113; +fp t31560; +fp t31211; +fp t31201; +fp t31559; +fp t31204; +fp t31558; +fp t31557; +fp t29887; +fp t31556; +fp t31267; +fp t29628; +fp t31555; +fp t30595; +fp t31554; +fp t29621; +fp t31553; +fp t31140; +fp t31034; +fp t31552; +fp t29946; +fp t31551; +fp t31017; +fp t30608; +fp t30385; +fp t30971; +fp t31550; +fp t31549; +fp t30993; +fp t31168; +fp t31032; +fp t31548; +fp t31547; +fp t30163; +fp t30164; +fp t30170; +fp t31546; +fp t31545; +fp t31187; +fp t31048; +fp t31205; +fp t31544; +fp t30674; +fp t31179; +fp t30892; +fp t30709; +fp t31244; +fp t30931; +fp t31543; +fp t31542; +fp t31039; +fp t31541; +fp t30679; +fp t30662; +fp t31058; +fp t30928; +fp t31540; +fp t30994; +fp t30665; +fp t31258; +fp t30694; +fp t31169; +fp t31539; +fp t30951; +fp t31142; +fp t30896; +fp t31538; +fp t30440; +fp t30771; +fp t31026; +fp t31537; +fp t31262; +fp t31536; +fp t30999; +fp t31535; +fp t30777; +fp t30749; +fp t31019; +fp t30506; +fp t30996; +fp t31534; +fp t30258; +fp t31030; +fp t31533; +fp t31532; +fp t30388; +fp t31531; +fp t31530; +fp t31198; +fp t30626; +fp t30625; +fp t31529; +fp t31092; +fp t31037; +fp t31528; +fp t30919; +fp t31070; +fp t31251; +fp t31018; +fp t31527; +fp t30933; +fp t31526; +fp t30937; +fp t31249; +fp t31184; +fp t31053; +fp t31525; +fp t31524; +fp t31523; +fp t30397; +fp t31522; +fp t30648; +fp t30646; +fp t31521; +fp t31218; +fp t31120; +fp t30939; +fp t31482; +fp t31256; +fp t30985; +fp t31468; +fp t31242; +fp t30629; +fp t31054; +fp t31165; +fp t31349; +fp t29943; +fp t31520; +fp t31474; +fp t30982; +fp t31448; +fp t31122; +fp t30857; +fp t31250; +fp t31519; +fp t31232; +fp t30955; +fp t31439; +fp t31410; +fp t30861; +fp t31518; +fp t30859; +fp t31517; +fp t31152; +fp t30855; +fp t30944; +fp t31224; +fp t29958; +fp t31516; +fp t31515; +fp t31143; +fp t30973; +fp t31514; +fp t31080; +fp t30921; +fp t31513; +fp t30967; +fp t31233; +fp t31078; +fp t30950; +fp t31171; +fp t31512; +fp t31511; +fp t30952; +fp t31510; +fp t31158; +fp t30362; +fp t30942; +fp t31509; +fp t30654; +fp t31196; +fp t31257; +fp t31508; +fp t31157; +fp t30979; +fp t30925; +fp t31076; +fp t31507; +fp t30656; +fp t31234; +fp t31506; +fp t31505; +fp t31241; +fp t30977; +fp t31504; +fp t30539; +fp t31129; +fp t30887; +fp t30959; +fp t31503; +fp t30623; +fp t30469; +fp t30964; +fp t31502; +fp t31501; +fp t30763; +fp t31243; +fp t31500; +fp t31108; +fp t31499; +fp t31047; +fp t31498; +fp t30437; +fp t31497; +fp t31496; +fp t31495; +fp t31494; +fp t31493; +fp t30708; +fp t31492; +fp t30752; +fp t30897; +fp t31491; +fp t30717; +fp t31490; +fp t31067; +fp t30938; +fp t31488; +fp t31110; +fp t30918; +fp t31487; +fp t30284; +fp t31485; +fp t30726; +fp t31175; +fp t30949; +fp t31484; +fp t31483; +fp t31253; +fp t30485; +fp t30727; +fp t31084; +fp t30995; +fp t31481; +fp t30331; +fp t30735; +fp t31090; +fp t31480; +fp t31479; +fp t31478; +fp t30683; +fp t30975; +fp t30680; +fp t30980; +fp t31477; +fp t31475; +fp t31473; +fp t30390; +fp t30769; +fp t31472; +fp t30742; +fp t30932; +fp t31471; +fp t31470; +fp t30609; +fp t31469; +fp t30677; +fp t30275; +fp t30682; +fp t30997; +fp t31467; +fp t31004; +fp t31466; +fp t31464; +fp t31180; +fp t30914; +fp t31460; +fp t31459; +fp t31457; +fp t31456; +fp t30614; +fp t31455; +fp t31261; +fp t30427; +fp t30767; +fp t31454; +fp t31453; +fp t30659; +fp t31452; +fp t30770; +fp t30671; +fp t31126; +fp t31451; +fp t31450; +fp t30988; +fp t30748; +fp t30723; +fp t31449; +fp t30992; +fp t31446; +fp t30655; +fp t30884; +fp t31445; +fp t31443; +fp t30713; +fp t31440; +fp t31073; +fp t30499; +fp t31438; +fp t31227; +fp t31155; +fp t30936; +fp t31436; +fp t30613; +fp t30379; +fp t31221; +fp t30965; +fp t31435; +fp t30519; +fp t31434; +fp t30893; +fp t30934; +fp t31433; +fp t31432; +fp t31431; +fp t31154; +fp t30901; +fp t30691; +fp t31430; +fp t30738; +fp t31141; +fp t30728; +fp t31183; +fp t31429; +fp t31428; +fp t30926; +fp t31427; +fp t31426; +fp t30487; +fp t31161; +fp t31425; +fp t30423; +fp t31178; +fp t30930; +fp t31248; +fp t31424; +fp t31231; +fp t31423; +fp t31422; +fp t31421; +fp t30666; +fp t31063; +fp t31240; +fp t31420; +fp t31419; +fp t30517; +fp t30895; +fp t31418; +fp t31417; +fp t30681; +fp t31115; +fp t31226; +fp t31416; +fp t31415; +fp t31414; +fp t30746; +fp t30775; +fp t31106; +fp t31413; +fp t30176; +fp t30756; +fp t31121; +fp t30605; +fp t30705; +fp t31412; +fp t31411; +fp t30491; +fp t31130; +fp t30912; +fp t31409; +fp t31408; +fp t30566; +fp t31407; +fp t31406; +fp t31405; +fp t30442; +fp t29927; +fp t30987; +fp t31404; +fp t30905; +fp t31403; +fp t30467; +fp t29810; +fp t30970; +fp t31402; +fp t30736; +fp t31401; +fp t31400; +fp t29806; +fp t31399; +fp t30990; +fp t31398; +fp t29931; +fp t30957; +fp t31397; +fp t31020; +fp t30886; +fp t31396; +fp t31395; +fp t31104; +fp t31394; +fp t30493; +fp t29911; +fp t30962; +fp t31393; +fp t31392; +fp t30267; +fp t31391; +fp t31193; +fp t31228; +fp t30482; +fp t31390; +fp t31207; +fp t31098; +fp t31195; +fp t31055; +fp t31389; +fp t31388; +fp t30507; +fp t30607; +fp t31387; +fp t30989; +fp t31386; +fp t31170; +fp t31385; +fp t31384; +fp t31229; +fp t31383; +fp t30351; +fp t31382; +fp t31173; +fp t30488; +fp t31255; +fp t31381; +fp t31380; +fp t31379; +fp t31378; +fp t31189; +fp t30927; +fp t31377; +fp t31376; +fp t31057; +fp t30732; +fp t30961; +fp t31375; +fp t30563; +fp t31374; +fp t31373; +fp t31134; +fp t31372; +fp t31151; +fp t31371; +fp t31370; +fp t31369; +fp t31150; +fp t30945; +fp t31368; +fp t31367; +fp t30542; +fp t31366; +fp t31365; +fp t30984; +fp t31364; +fp t31363; +fp t31132; +fp t31362; +fp t31035; +fp t31361; +fp t31360; +fp t31359; +fp t31358; +fp t31357; +fp t31356; +fp t30908; +fp t31355; +fp t31354; +fp t31353; +fp t31352; +fp t31351; +fp t31350; +fp t31348; +fp t31347; +fp t30416; +fp t30496; +fp t30872; +fp t31346; +fp t31194; +fp t30574; +fp t31345; +fp t30354; +fp t31344; +fp t31343; +fp t31342; +fp t31341; +fp t31340; +fp t31339; +fp t30929; +fp t31338; +fp t31337; +fp t31336; +fp t31335; +fp t31136; +fp t31334; +fp t30946; +fp t30943; +fp t31333; +fp t31332; +fp t31153; +fp t30438; +fp t30572; +fp t31331; +fp t31330; +fp t31329; +fp t31215; +fp t31328; +fp t30940; +fp t31327; +fp t30916; +fp t31326; +fp t31325; +fp t31068; +fp t30492; +fp t31324; +fp t31323; +fp t31322; +fp t31321; +fp t31320; +fp t31319; +fp t31318; +fp t31317; +fp t31316; +fp t30456; +fp t30589; +fp t31315; +fp t31314; +fp t31061; +fp t31182; +fp t31313; +fp t31312; +fp t31311; +fp t31310; +fp t31127; +fp t31309; +fp t31308; +fp t31307; +fp t31306; +fp t31305; +fp t31304; +fp t31303; +fp t30537; +fp t31116; +fp t31302; +fp t31301; +fp t31300; +fp t31212; +fp t30560; +fp t31299; +fp t31298; +fp t30966; +fp t30645; +fp t31297; +fp t31296; +fp t31295; +fp t31294; +fp t31293; +fp t31292; +fp t31291; +fp t31290; +fp t31289; +fp t31288; +fp t31287; +fp t31286; +fp t31285; +fp t31284; +fp t30525; +fp t30638; +fp t30534; +fp t31283; +fp t29870; +fp t31282; +fp t30516; +fp t31281; +fp t30858; +fp t31280; +fp t31279; +fp t31075; +fp t31278; +fp t31277; +fp t31276; +fp t31275; +fp t31117; +fp t31274; +fp t30956; +fp t31273; +fp t31272; +fp t31176; +fp t31138; +fp t31271; +fp t30522; +fp t31270; +fp t31269; +fp t31268; +fp t31239; +fp t30612; +fp t30617; +fp t30764; +fp t31159; +fp t30611; +fp t30615; +fp t31137; +fp t31135; +fp t31133; +fp t31103; +fp t31081; +fp t31069; +fp t31046; +fp t30983; +fp t30976; +fp t30974; +fp t30383; +fp t30969; +fp t30947; +fp t30910; +fp t30900; +fp t30889; +fp t30883; +fp t30881; +fp t30880; +fp t30696; +fp t30753; +fp t30697; +fp t30877; +fp t30724; +fp t30766; +fp t30712; +fp t30876; +fp t30875; +fp t30874; +fp t30670; +fp t30873; +fp t30871; +fp t30869; +fp t30868; +fp t30867; +fp t30866; +fp t30864; +fp t30863; +fp t30862; +fp t30860; +fp t30856; +fp t30672; +fp t30854; +fp t30651; +fp t30699; +fp t30853; +fp t30852; +fp t30851; +fp t30676; +fp t30850; +fp t30849; +fp t30685; +fp t30848; +fp t30847; +fp t30846; +fp t30845; +fp t30844; +fp t30843; +fp t30842; +fp t30841; +fp t30840; +fp t30839; +fp t30838; +fp t30837; +fp t30836; +fp t30835; +fp t30834; +fp t30833; +fp t30832; +fp t30831; +fp t30830; +fp t30829; +fp t30828; +fp t30827; +fp t30826; +fp t30825; +fp t30824; +fp t30823; +fp t30822; +fp t30821; +fp t30820; +fp t30819; +fp t30818; +fp t30817; +fp t30816; +fp t30815; +fp t30814; +fp t30813; +fp t30812; +fp t30811; +fp t30810; +fp t30809; +fp t30808; +fp t30807; +fp t30806; +fp t30805; +fp t30804; +fp t30803; +fp t30802; +fp t30801; +fp t30800; +fp t30799; +fp t30798; +fp t30797; +fp t30796; +fp t30795; +fp t30794; +fp t30793; +fp t30792; +fp t30791; +fp t30790; +fp t30789; +fp t30774; +fp t30744; +fp t30743; +fp t30701; +fp t30700; +fp t30673; +fp t30669; +fp t30668; + t30715 = RATIONAL(-2.0,27.0); + t30750 = RATIONAL(1.0,9.0); + t30779 = z*z; + t31096 = t30750*t30779; + t31648 = t30715+t31096; + t30693 = RATIONAL(1.0,576.0); + t30692 = RATIONAL(-1.0,576.0); + t31208 = y*t30692; + t30778 = x*x; + t30780 = y*y; + t30782 = t30780*y; + t31072 = t30778*t30782; + t31647 = t30778*t31208+t30693*t31072; + t30781 = x*t30778; + t30783 = t30780*t30780; + t31094 = t30781*t30783; + t31259 = x*t30783; + t30321 = t30692*t31259; + t31646 = t30693*t31094+t30321; + t30706 = RATIONAL(1.0,27.0); + t30675 = RATIONAL(-1.0,108.0); + t31056 = t30675*t30781; + t31645 = x*t30706+t31056; + t31172 = t30780*t30779; + t31147 = t30693*t30779; + t31644 = t30692*t31172+t30783*t31147; + t30684 = RATIONAL(1.0,288.0); + t31065 = t30782*t30684; + t30899 = t30779*t31065; + t30663 = RATIONAL(1.0,432.0); + t31643 = t30899+y*t30663; + t30657 = RATIONAL(-1.0,3456.0); + t31642 = (t31147+t30657)*t30780; + t30734 = RATIONAL(1.0,18.0); + t30602 = t30734*x; + t30695 = RATIONAL(-1.0,72.0); + t31095 = t30695*t30779; + t30907 = t30781*t31095; + t31641 = t30907+t30779*t30602; + t31246 = x*t30779; + t31197 = y*t31246; + t31144 = t30782*t30779; + t30890 = t30781*t31144; + t31640 = t30890+t31197; + t30223 = t30692*t31094; + t31639 = t30223+t30693*t31259; + t31021 = x*t31095; + t30658 = RATIONAL(-1.0,1728.0); + t31064 = t30658*t30781; + t31638 = t31064+t31021; + t30784 = t30778*t30778; + t30245 = t30784*t31208; + t31086 = t30784*t30693; + t31637 = t30782*t31086+t30245; + t31164 = t30781*t30779; + t31008 = y*t31164; + t31043 = x*t31144; + t31636 = t31043+t31008; + t30711 = RATIONAL(-1.0,54.0); + t30718 = RATIONAL(2.0,27.0); + t31635 = t30711*t30783+t30780*t30718; + t30689 = RATIONAL(-1.0,144.0); + t30688 = RATIONAL(1.0,144.0); + t30592 = t30688*t30781; + t30968 = t30779*t30592; + t31634 = t30689*t31246+t30968; + t31139 = t30778*t30783; + t31059 = t30784*t30780; + t31633 = t31139+t31059; + t30698 = RATIONAL(1.0,54.0); + t31632 = t30784*t30698+t30778*t31096; + t30768 = RATIONAL(-8.0,9.0); + t30637 = t30768*y; + t30776 = RATIONAL(2.0,9.0); + t31066 = t30779*t30776; + t31631 = t30782*t31066+t30779*t30637; + t30758 = RATIONAL(-2.0,9.0); + t30639 = t30758*t30783; + t31630 = t30734*t31094+x*t30639; + t30703 = RATIONAL(-1.0,18.0); + t31225 = x*t30776; + t31629 = t30703*t31094+t30783*t31225; + t30704 = RATIONAL(-1.0,36.0); + t31146 = t30704*t30779; + t31628 = t30783*t31146+t31648*t30780; + t30707 = RATIONAL(4.0,27.0); + t30661 = RATIONAL(-16.0,27.0); + t31082 = t30779*t30758; + t31627 = x*t30661+(t31082+t30707)*t30781; + t30660 = RATIONAL(1.0,1152.0); + t31128 = t30780*t30778; + t31083 = t30660*t30783; + t30650 = RATIONAL(-1.0,1152.0); + t31626 = t30650*t31059+t30660*t31128+t30784*t31083; + t30678 = RATIONAL(16.0,27.0); + t30716 = RATIONAL(-4.0,27.0); + t31625 = x*t30678+(t31066+t30716)*t30781; + t31102 = t30692*t30782; + t31624 = y*t31147+t30779*t31102; + t30747 = RATIONAL(1.0,6.0); + t31060 = t30782*t30747; + t30543 = t30779*t31060; + t30745 = RATIONAL(-1.0,6.0); + t31191 = t30745*t30779; + t30544 = y*t31191; + t31623 = t30544+t30543; + t31216 = z*RATIONAL(2.0,3.0); + t31206 = z*t30747; + t30552 = t30783*t31206; + t31622 = t30552+t31216; + t31222 = z*RATIONAL(-2.0,3.0); + t31209 = z*t30745; + t30541 = t30783*t31209; + t31621 = t30541+t31222; + t31097 = t30745*t30782; + t30547 = t30779*t31097; + t31192 = t30747*t30779; + t30546 = y*t31192; + t31620 = t30547+t30546; + t30759 = RATIONAL(-5.0,3.0); + t30730 = RATIONAL(-5.0,12.0); + t31619 = t30730*t30783+t30759; + t30710 = RATIONAL(-1.0,12.0); + t31145 = t30710*t30783; + t30457 = z*t31145; + t30765 = RATIONAL(-1.0,3.0); + t31214 = z*t30765; + t31618 = t31214+t30457; + t31167 = t30779*RATIONAL(-4.0,3.0); + t30762 = RATIONAL(1.0,3.0); + t30553 = t30762*t31164; + t31617 = t30553+x*t31167; + t30667 = RATIONAL(5.0,288.0); + t30687 = RATIONAL(-5.0,288.0); + t31616 = y*t30687+t30667*t30782; + t30729 = RATIONAL(-1.0,24.0); + t31177 = t30729*t30779; + t30731 = RATIONAL(1.0,24.0); + t31160 = t30731*t30779; + t30406 = t30781*t31160; + t31615 = x*t31177+t30406; + t31614 = t31648*x; + t30690 = RATIONAL(-5.0,576.0); + t30721 = RATIONAL(-1.0,96.0); + t31125 = t30721*t30779; + t31613 = t30690*t30783+t30780*t31125; + t31105 = t30779*t30765; + t30527 = t30782*t31105; + t30761 = RATIONAL(4.0,3.0); + t31188 = t30761*t30779; + t31612 = t30527+y*t31188; + t31093 = t30721*t30783; + t31611 = t30780*t30690+t30779*t31093; + t31260 = t30784*y; + t31610 = t31072+t31260; + t31254 = t30784*z; + t30719 = RATIONAL(1.0,96.0); + t30998 = t30719*t31254; + t31219 = z*t30731; + t31609 = t30998+t31219; + t31263 = z*t30783; + t31608 = t30719*t31263+t31219; + t30739 = RATIONAL(-5.0,18.0); + t30737 = RATIONAL(10.0,9.0); + t31607 = t30781*t30739+x*t30737; + t30720 = RATIONAL(-5.0,96.0); + t31264 = z*t30780; + t31606 = t30720*t31264+t31608; + t31223 = z*t30704; + t30991 = t30780*t31223; + t31217 = z*t30689; + t31045 = t30783*t31217; + t31605 = t30781*t30991+x*t31045; + t30702 = RATIONAL(1.0,12.0); + t31604 = x*t31105+t30702*t31164; + t30924 = t30689*t31072; + t31077 = t30784*t30704; + t31024 = z*t31077; + t31603 = y*t31024+z*t30924; + t30741 = RATIONAL(1.0,72.0); + t31114 = t30780*t30741; + t30915 = t30779*t31114; + t31602 = t30658*t31139+t30784*t30915; + t31002 = z*t31059; + t30733 = RATIONAL(1.0,36.0); + t31111 = t30688*t30783; + t31031 = z*t31111; + t31601 = t30778*t31031+t30733*t31002; + t30913 = t30741*t31139; + t30958 = t30684*t31059; + t31600 = (t30958+t30913)*z; + t31266 = y*z; + t29631 = t30592*t31266; + t31109 = t30782*t30733; + t31003 = z*t31109; + t31599 = x*t31003+t29631; + t31181 = t30778*t30741; + t30686 = RATIONAL(-1.0,288.0); + t31100 = t30686*t30782; + t31027 = z*t31100; + t30239 = t30784*t31065; + t31458 = t30778*t31027+z*t30239; + t31598 = t31181*t31266+t31458; + t30619 = t30703*t30778; + t31041 = z*t30619; + t31050 = z*t31072; + t30604 = t30695*t30782; + t31036 = z*t30604; + t31442 = t30734*t31050+t30784*t31036; + t31597 = y*t31041+t31442; + t30571 = t30781*t31105; + t31596 = t30571+x*t31188; + t31595 = t30779*t30913+t30658*t31059; + t31148 = t30703*t30781; + t29895 = t31148*t31266; + t31594 = x*t31036+t29895; + t31123 = t30781*t30704; + t30598 = t30689*t30782; + t31014 = z*t30598; + t29588 = x*t31014; + t31593 = t31123*t31266+t29588; + t31238 = y*t30733; + t30348 = t30784*t31238; + t30972 = t30688*t31072; + t31592 = (t30972+t30348)*z; + t30894 = t30784*t31095; + t31591 = t30706*t31139+t30780*t30894; + t30618 = t30741*t30781; + t31049 = z*t30618; + t30953 = t30780*t31148; + t31461 = z*t30953+t30783*t31049; + t31252 = x*t30780; + t31199 = z*t31252; + t31590 = t31461+t30734*t31199; + t30471 = t30695*t31059; + t30590 = t30686*t30783; + t31012 = z*t30590; + t31589 = z*t30471+t30778*t31012; + t30593 = t30684*t30778; + t31023 = z*t30593; + t30222 = t30784*t31100; + t31476 = z*t30222+t30782*t31023; + t31235 = z*t30778; + t31200 = y*t31235; + t31588 = t31476+t30695*t31200; + t31190 = t30780*t30781; + t31040 = z*t31190; + t30502 = t30704*t31259; + t31587 = t30689*t31040+z*t30502; + t30255 = t30684*t31094; + t31486 = z*t30255+t30686*t31040; + t31265 = x*z; + t31586 = t31486+t31114*t31265; + t31016 = t30784*t31217; + t30904 = t30704*t31072; + t31585 = y*t31016+z*t30904; + t31202 = z*t31238; + t30600 = t30688*t30782; + t31005 = z*t30600; + t29552 = x*t31005; + t31584 = t30781*t31202+t29552; + t30664 = RATIONAL(-1.0,432.0); + t31101 = t30784*t30664; + t30986 = t30778*t31066; + t31583 = t30780*t30986+t30783*t31101; + t31149 = t30781*t30734; + t31038 = z*t31149; + t29956 = y*t31038; + t30606 = t30741*t30782; + t31006 = z*t30606; + t31582 = t29956+x*t31006; + t30601 = t30688*y; + t31044 = t30784*t30601; + t31581 = z*t31044+t30778*t31003; + t31124 = t30733*t30783; + t31011 = z*t31124; + t31580 = x*t31011+t30688*t31040; + t31015 = x*t31111; + t31579 = t30733*t31040+z*t31015; + t30621 = t30695*t30781; + t31052 = z*t30621; + t31099 = t30703*t30782; + t29886 = t31099*t31265; + t31578 = y*t31052+t29886; + t30603 = t30703*t30780; + t31462 = t30780*t31038+t30783*t31052; + t31577 = t30603*t31265+t31462; + t30596 = t30689*t30781; + t29510 = t30596*t31266; + t31203 = x*t31223; + t31576 = t29510+t30782*t31203; + t30495 = t30695*t31139; + t31575 = t30686*t31002+z*t30495; + t30911 = t30783*t30593; + t31574 = z*t30911+t30741*t31002; + t30287 = t30686*t31094; + t30599 = t30684*t30780; + t31009 = z*t30599; + t31441 = z*t30287+t30781*t31009; + t31573 = t31441+t30695*t31199; + t31091 = t30663*t30783; + t31071 = t30686*t30780; + t30954 = t30779*t31071; + t31572 = t30778*t30954+t30784*t31091; + t30922 = t30784*t30606; + t31463 = t30782*t31041+z*t30922; + t31112 = t30778*t30734; + t31571 = t31463+t31112*t31266; + t31570 = t30706*t31059+t30779*t30495; + t30754 = RATIONAL(1.0,2.0); + t30751 = RATIONAL(-5.0,8.0); + t31569 = t30751*t30778+t30754; + t30757 = RATIONAL(5.0,2.0); + t30760 = RATIONAL(-2.0,1.0); + t31568 = t30757*t30778+t30760; + t31162 = t30782*t30734; + t29658 = t31162*t31265; + t31567 = y*t31049+t29658; + t31033 = z*t31139; + t31566 = t30784*t30991+t30689*t31033; + t31565 = t30704*t31033+t30689*t31002; + t30981 = t30779*t31059; + t30714 = RATIONAL(5.0,72.0); + t30725 = RATIONAL(-1.0,48.0); + t30610 = t30725*t30783; + t30888 = t30784*t30610; + t31156 = t30714*t31128+t30779*t30888; + t30740 = RATIONAL(-5.0,72.0); + t31119 = t30740*t30783; + t30722 = RATIONAL(1.0,48.0); + t31564 = t31156+t30722*t30981+t30778*t31119; + t31563 = t30688*t31002+t30778*t31011; + t31230 = x*t30758; + t31010 = t30780*t31230; + t30616 = t30734*t30783; + t31022 = z*t30616; + t31562 = x*t31022+t31462+z*t31010; + t31079 = t30778*t30758; + t30622 = t30734*t30784; + t31001 = y*t30622; + t31561 = t31079*t31266+z*t31001+t31442; + t31113 = t30784*t30684; + t31560 = t31476+t30686*t31200+t31113*t31266; + t31211 = z*t30684; + t31201 = x*t31211; + t31559 = t31441+t31071*t31265+t30783*t31201; + t31204 = y*t31254; + t31558 = t31463+t30703*t31204+t30776*t31200; + t31557 = t31486+(t31009+t31012)*x; + t29887 = t30781*t31006; + t31556 = t31225*t31266+t29887+t29895+t29886; + t31267 = y*x; + t29628 = t30781*t31014; + t31555 = t29631+t29628+t29552+t31217*t31267; + t30595 = t30686*t30784; + t31554 = t31458+t30595*t31266+y*t31023; + t29621 = t30781*t31005; + t31553 = t29588+t29510+t29621+t30601*t31265; + t31140 = t30703*t30783; + t31034 = t30780*t31225; + t31552 = z*t31034+t31461+t31140*t31265; + t29946 = t30781*t31036; + t31551 = t29956+t29946+t29658+t31230*t31266; + t31017 = z*t31128; + t30608 = t30741*t30783; + t30385 = t30784*t30608; + t30971 = t30703*t31059; + t31550 = t30703*t31033+t30776*t31017+(t30971+t30385)*z; + t31549 = t31641*t30783+t31645*t30780; + t30993 = t30693*t31235; + t31168 = t30784*t30783; + t31032 = z*t31168; + t31548 = t30783*t30993+t30693*t31002+(t31032+t31017)*t30692; + t31547 = t30758*t31017+t30695*t31032+t30734*t31002+t30778*t31022; + t30163 = t30650*t31168; + t30164 = t30660*t31059; + t30170 = t30778*t31083; + t31546 = t30650*t31017+(t30163+t30164+t30170)*z; + t31545 = t31645*t30783+t31641*t30780; + t31187 = t30781*t30782; + t31048 = z*t31187; + t31205 = t30686*t31266; + t31544 = x*t31027+y*t31201+t30684*t31048+t30781*t31205; + t30674 = RATIONAL(1.0,108.0); + t31179 = t30674*t30781; + t30892 = t30741*t31164; + t30709 = RATIONAL(-1.0,27.0); + t31244 = x*t30709; + t30931 = t30779*t31140; + t31543 = t30783*t30892+x*t30931+(t31179+t31244)*t30780; + t31542 = y*t30993+t30692*t31050+t31637*z; + t31039 = t30692*t31264; + t31541 = t30781*t31039+t30693*t31199+t31646*z; + t30679 = RATIONAL(-1.0,216.0); + t30662 = RATIONAL(1.0,216.0); + t31058 = t30778*t30662; + t30928 = t30689*t31144; + t31540 = t30679*t31072+t30784*t30928+y*t31058+t30779*t31044; + t30994 = t30778*t31238; + t30665 = RATIONAL(1.0,864.0); + t31258 = y*t30665; + t30694 = RATIONAL(-1.0,864.0); + t31169 = t30694*t30782; + t31539 = (t30994+t30904)*t30779+(t31169+t31258)*t30784; + t30951 = t30779*t31123; + t31142 = t30780*t30733; + t30896 = t30779*t31142; + t31538 = t30665*t31259+t30694*t31094+t30780*t30951+x*t30896; + t30440 = t30704*t31094; + t30771 = RATIONAL(-4.0,9.0); + t31026 = t30750*t31263; + t31537 = x*t31026+t30771*t31199+t30750*t31040+z*t30440; + t31262 = y*t30781; + t31536 = t30781*t31027+t31211*t31262+t31065*t31265+x*t31205; + t30999 = t30750*t31254; + t31535 = t30778*t31026+t30771*t31017+t30780*t30999+t30783*t31024; + t30777 = RATIONAL(4.0,9.0); + t30749 = RATIONAL(-1.0,9.0); + t31019 = t30749*t31263; + t30506 = t30733*t31094; + t30996 = t30749*t31264; + t31534 = t30781*t30996+x*t31019+z*t30506+t30777*t31199; + t30258 = t30784*t31102; + t31030 = z*t31086; + t31533 = y*t31030+(t30258+t31647)*z; + t31532 = t30780*t30993+t30783*t31030+(t31033+t31002)*t30692; + t30388 = t30784*t31109; + t31531 = t30777*t31200+z*t30388+(t31204+t31050)*t30749; + t31530 = x*t31039+t30693*t31040+t31639*z; + t31198 = t30771*t31266; + t30626 = t30750*t30782; + t30625 = t30750*t30781; + t31529 = x*t31198+t30704*t31048+t30626*t31265+t30625*t31266; + t31092 = t30674*t30783; + t31037 = x*t31172; + t31528 = t30781*t31092+t30783*t31244+t30703*t31037+t30780*t30892; + t30919 = t30779*t31109; + t31070 = t30665*t30782; + t31251 = y*t30778; + t31018 = t30704*t31251; + t31527 = t30694*t31260+t30779*t31018+t30784*t31070+t30778*t30919; + t30933 = t30779*t30596; + t31526 = t30688*t31037+t30662*t31259+t30679*t31094+t30780*t30933; + t30937 = t30784*t31144; + t31249 = t30679*y; + t31184 = t30784*t30779; + t31053 = y*t31184; + t31525 = t30782*t31058+t30688*t30937+t30778*t31249+t30689*t31053; + t31524 = t30778*t31019+t30777*t31017+(t30996+t31011)*t30784; + t31523 = t30650*t31033+t31626*z; + t30397 = t30782*t31077; + t31522 = t30750*t31050+t30778*t31198+y*t30999+z*t30397; + t30648 = t30749*t30781; + t30646 = t30749*t30782; + t31521 = t30648*t31266+t30781*t31003+(t30646+t30777*y)*t31265; + t31218 = y*t30715; + t31120 = t30778*t30709; + t30939 = t30779*t30608; + t31482 = t30784*t30939+t30780*t31120; + t31256 = x*t30782; + t30985 = t30779*t31112; + t31468 = t30675*t31168+t30780*t30985; + t31242 = x*t30718; + t30629 = t30749*y; + t31054 = t30779*t30629; + t31165 = t30781*t30698; + t31349 = x*t31054+t30782*t31165+y*t31242+t30704*t30890+t31468; + t29943 = x*t30919; + t31520 = t30750*t31008+t31349+t31482+t30781*t31218+t29943+t30711*t31256; + t31474 = t30664*t31059+t30779*t30911; + t30982 = t30779*t31168; + t31448 = t30663*t31128+t30686*t30982; + t31122 = t30679*t30781; + t30857 = t30783*t30933+t30662*t31252+t30780*t31122+t30779*t31015+t31448+ +t31474; + t31250 = x*t30679; + t31519 = t30662*t31094+t30783*t31250+t30857+t31634*t30780; + t31232 = x*t30675; + t30955 = t30779*t31149; + t31439 = t30674*t31059+t30778*t30931; + t31410 = t31439+t31482; + t30861 = t31410+t31549; + t31518 = t30779*t31010+t30781*t31091+t30780*t30955+t30861+t30783*t31232; + t30859 = t31410+t31543; + t31517 = x*t31092+t30859+t30664*t31094+(t30953+t31034)*t30779; + t31152 = t30781*t30711; + t30855 = t31468+t30782*t31152+t30733*t30890+t31482+t31614*y; + t30944 = t30779*t30648; + t31224 = x*t30698; + t29958 = t30704*t31043; + t31516 = t30782*t31224+y*t30944+t30855+t29958+t30718*t31262; + t31515 = t30781*t30896+t30857+t30665*t31094+t30704*t31037+t30694*t31259; + t31143 = t30674*t30782; + t30973 = t30741*t30890+y*t31179+x*t31143; + t31514 = t30973+t30741*t31197+(t31021+t31056)*t30782+(t31232+t30907)*y; + t31080 = t30664*t30782; + t30921 = t30779*t31099; + t31513 = t31066*t31267+t30781*t31080+t30703*t31008+t30973+y*t31244+x* +t30921; + t30967 = t30734*t31144; + t31233 = y*t30706; + t31078 = t30675*t30782; + t30950 = y*t31056+x*t31078+t30695*t30890; + t31171 = t30782*t30663; + t31512 = t30950+t31082*t31267+y*t30955+t30781*t31171+(t30967+t31233)*x; + t31511 = t30950+t30781*t31143+t30741*t31043+t30674*t31267+(t30892+t31021) +*y; + t30952 = t30779*t31139; + t31510 = t30650*t30952+(t31128+t31168)*RATIONAL(-1.0,6912.0)+t31633* +RATIONAL(1.0,6912.0)+t31626*t30779; + t31158 = t30784*t30711; + t30362 = y*t31077; + t30942 = t30749*t31144; + t31509 = t30718*t31072+t30784*t30919+t30782*t31158+t30779*t30362+(t31218+ +t30942)*t30778+t31632*y; + t30654 = RATIONAL(1.0,1728.0); + t31196 = t30654*t30782; + t31257 = y*t30654; + t31508 = t30782*t31064+t30658*t31267+x*t31196+t30781*t31257+t31640*t30684 ++t31636*t30686; + t31157 = t30658*t30782; + t30979 = t30779*t31072; + t30925 = t30779*t31181; + t31076 = t30664*t30778; + t31507 = t30686*t30979+t30654*t31072+(t31076+t30925+t30894)*y+(t31157+ +t31643)*t30784; + t30656 = RATIONAL(1.0,3456.0); + t31234 = x*t30656; + t31506 = t30656*t31190+t30779*t30321+t30657*t31094+t30783*t31234+t31644* +t30781+t31642*x; + t31505 = t30780*t30944+t30783*t31224+t30779*t30506+t31635*t30781+t31628*x +; + t31241 = x*t30664; + t30977 = t30684*t31164; + t31504 = t30779*t30287+t30663*t31252+t30654*t31094+t30783*t31241+x*t30939 ++(t30977+t31638)*t30780; + t30539 = t30776*t31139; + t31129 = t30784*t30706; + t30887 = t30784*t31066; + t30959 = t30768*t31172; + t31503 = t30779*t30539+t30778*t30959+t30783*t31129+t30678*t31128+t30780* +t30887+t30784*t30931+t31633*t30716; + t30623 = t30741*t30784; + t30469 = y*t30623; + t30964 = t30778*t31095; + t31502 = t30784*t31196+t30686*t30937+t30658*t31072+t30779*t30469+t31643* +t30778+(t31101+t30964)*y; + t31501 = t30654*t31190+t30780*t31241+t30781*t30954+t30779*t30255+t31638* +t30783+(t30915+t31091)*x; + t30763 = RATIONAL(8.0,9.0); + t31243 = x*t30707; + t31500 = t30763*t31037+t30783*t31243+t30709*t31094+t31630*t30779+t31627* +t30780; + t31108 = t30706*t30782; + t31499 = t30716*t31256+t30781*t31108+t30703*t30890+t31631*x+t31625*y; + t31047 = t30779*t31238; + t31498 = t30715*t31072+t30784*t31047+t30704*t30937+t30718*t31251+t30778* +t31054+y*t31158+t31632*t30782; + t30437 = x*t31124; + t31497 = t30698*t31094+t30749*t31037+t30779*t30437+t31635*x+t31628*t30781 +; + t31496 = t30656*t31094+t30780*t31234+t30779*t30223+t30657*t31259+t31642* +t30781+t31644*x; + t31495 = x*t30959+t30716*t31259+t30706*t31094+t31629*t30779+t31625*t30780 +; + t31494 = t30758*t31043+t30763*t31197+t30709*t31187+t30734*t30890+t30782* +t31243+t31627*y; + t31493 = t30654*t31187+t31640*t30686+(t31064+t30977)*y+(t31157+t31257+ +t30899)*x; + t30708 = RATIONAL(1.0,32.0); + t31492 = t30708*t30982+RATIONAL(-25.0,192.0)*t31128; + t30752 = RATIONAL(5.0,3.0); + t30897 = t30752*t31172; + t31491 = t30784*t31140+t30778*t30897; + t30717 = RATIONAL(5.0,96.0); + t31490 = t30783*t30998+t30717*t31017; + t31067 = t30784*t30667; + t30938 = t30710*t31172; + t31488 = t30783*t31067+t30778*t30938; + t31110 = t30702*t30783; + t30918 = t30778*t31110; + t31487 = t30687*t31059+t30779*t30918; + t30284 = t30783*t31113; + t31485 = t30741*t31017+z*t30284; + t30726 = RATIONAL(-5.0,48.0); + t31175 = t30778*t30726; + t30949 = t30779*t31175; + t31484 = t30780*t30949+t30385; + t31483 = t30783*t31076+t30779*t30958; + t31253 = z*t30722; + t30485 = t30783*t31253; + t30727 = RATIONAL(5.0,12.0); + t31084 = t30780*t30727; + t30995 = z*t31084; + t31481 = t30784*t30485+t30778*t30995; + t30331 = t30784*t31110; + t30735 = RATIONAL(-10.0,9.0); + t31090 = t30735*t30780; + t31480 = t30778*t31090+t30779*t30331; + t31479 = x*t30991+t30781*t31045; + t31478 = t30695*t31017+t30784*t31012; + t30683 = RATIONAL(1.0,192.0); + t30975 = t30683*t31168; + t30680 = RATIONAL(5.0,192.0); + t30980 = t30680*t31128; + t31477 = (t30975+t30980)*z; + t31475 = t30784*t31031+t30733*t31017; + t31473 = t30654*t31168+t30780*t30964; + t30390 = t30783*t31219; + t30769 = RATIONAL(5.0,6.0); + t31472 = t30769*t31017+t30784*t30390; + t30742 = RATIONAL(5.0,18.0); + t30932 = t30784*t31105; + t31471 = t30780*t30932+t30742*t31139; + t31470 = t29621+x*t31202; + t30609 = t30734*y; + t31469 = t30609*t31265+t29887; + t30677 = RATIONAL(-1.0,192.0); + t30275 = t30677*t31168; + t30682 = RATIONAL(-5.0,192.0); + t30997 = t30682*t31235; + t31467 = z*t30275+t30780*t30997; + t31004 = t30721*t31254; + t31466 = t30720*t31017+t30783*t31004; + t31464 = t30778*t30991+t30783*t31016; + t31180 = t30778*t30730; + t30914 = t30779*t31180; + t31460 = t30284+t30780*t30914; + t31459 = y*t31203+t29628; + t31457 = t30784*t31005+z*t30994; + t31456 = t30781*t31031+t31142*t31265; + t30614 = t30703*y; + t31455 = t30614*t31265+t29946; + t31261 = z*t30729; + t30427 = t30783*t31261; + t30767 = RATIONAL(-5.0,6.0); + t31454 = t30784*t30427+t30767*t31017; + t31453 = t30163+t30779*t30980; + t30659 = RATIONAL(-5.0,1152.0); + t31452 = t30779*t30975+t30659*t31128; + t30770 = RATIONAL(-1.0,8.0); + t30671 = RATIONAL(25.0,12.0); + t31126 = t30671*t30778; + t31451 = t30780*t31126+t30770*t30982; + t31450 = t30784*t31014+z*t31018; + t30988 = t30779*t31128; + t30748 = RATIONAL(-5.0,2.0); + t30723 = RATIONAL(5.0,48.0); + t31449 = t30748*t30988+t30723*t31168; + t30992 = t30730*t31264; + t31446 = z*t30888+t30778*t30992; + t30655 = RATIONAL(5.0,1152.0); + t30884 = t30677*t31139; + t31445 = t30655*t31059+t30779*t30884; + t31443 = t30779*t30971+t30778*t31092; + t30713 = RATIONAL(5.0,32.0); + t31440 = t30713*t30988+t30682*t31168; + t31073 = t30722*t30779; + t30499 = t30783*t31073; + t31438 = t30740*t31059+t30778*t30499; + t31227 = z*t30781; + t31155 = t30780*t30726; + t30936 = t30781*t31155; + t31436 = t30702*t31227+t30781*t30485+z*t30936; + t30613 = t30725*t30784; + t30379 = z*t30613; + t31221 = z*t30782; + t30965 = t30723*t31072; + t31435 = t30710*t31221+t30782*t30379+z*t30965; + t30519 = t30784*t31253; + t31434 = t30782*t30519+t30702*t31221+t30726*t31050; + t30893 = t30725*t31094; + t30934 = t30723*t31190; + t31433 = t30710*t31227+(t30934+t30893)*z; + t31432 = t31455+t31475; + t31431 = t31470+t31478; + t31154 = t30719*t30779; + t30901 = t30783*t31154; + t30691 = RATIONAL(5.0,576.0); + t31430 = t30691*t31252+x*t30901+t31611*t30781; + t30738 = RATIONAL(-5.0,36.0); + t31141 = t30780*t30738; + t30728 = RATIONAL(5.0,36.0); + t31183 = t30728*t30780; + t31429 = t30781*t31183+x*t31141+t31615*t30783; + t31428 = t31470+t31485; + t30926 = t30778*t31188; + t31427 = t30780*t30926+t30784*t31119+t31471; + t31426 = t31438+t31488; + t30487 = t30779*t31145; + t31161 = t30667*t30781; + t31425 = t30740*t31252+x*t30487+t30780*t31161+t30781*t30499; + t30423 = y*t31177; + t31178 = t30731*t30782; + t30930 = t30784*t31178; + t31248 = y*t30738; + t31424 = t30728*t31072+t30778*t31248+t30779*t30930+t30784*t30423; + t31231 = y*t30735; + t31423 = y*t30932+t30778*t31231+t30702*t30937+t30742*t31072; + t31422 = t31110*t31246+t30687*t31190+t30714*t31252+t30779*t30893; + t31421 = t31464+t31469; + t30666 = RATIONAL(-5.0,144.0); + t31063 = t30781*t30666; + t31240 = x*t30738; + t31420 = x*t30546+t30782*t31063+t30731*t30890+y*t31240; + t31419 = t31469+t31475; + t30517 = x*t31160; + t30895 = t30729*t31094; + t31418 = t30783*t30517+x*t31183+t30781*t31141+t30779*t30895; + t31417 = t31455+t31464; + t30681 = RATIONAL(5.0,144.0); + t31115 = t30681*t30782; + t31226 = y*t30728; + t31416 = t30781*t31115+t30729*t30890+(t31226+t30544)*x; + t31415 = t30659*t31168+t30683*t30988+t31445; + t31414 = t31459+t31478; + t30746 = RATIONAL(5.0,8.0); + t30775 = RATIONAL(-1.0,2.0); + t31106 = t30775*t30784; + t31413 = t30746*t30981+t30779*t31106+t31619*t30778; + t30176 = t30680*t31139; + t30756 = RATIONAL(1.0,8.0); + t31121 = t30756*t30779; + t30605 = t30723*t30778; + t30705 = RATIONAL(-5.0,32.0); + t31412 = t30784*t31121+t30176+t30605+t30705*t30981; + t31411 = t30781*t30901+t30691*t31190+t31611*x; + t30491 = y*t31160; + t31130 = t30729*t30782; + t30912 = t30784*t31130; + t31409 = t30778*t31226+t30784*t30491+t30738*t31072+t30779*t30912; + t31408 = t30471+t30603+t30487+t30723*t30952; + t30566 = t30762*t31184; + t31407 = t30737*t31251+t30739*t31072+y*t30566+t30710*t30937; + t31406 = t31459+t31485; + t31405 = t31487+t31488+t31564; + t30442 = t30695*t31259; + t29927 = z*t30442; + t30987 = t29927+t31450; + t31404 = t30987+t31581+t31586; + t30905 = t29927+t31457; + t31403 = t30905+t31585+t31586; + t30467 = t30695*t31260; + t29810 = z*t30467; + t30970 = t29810+t31456; + t31402 = t30970+t31571+t31587; + t30736 = RATIONAL(5.0,24.0); + t31401 = t30736*t31033+t30747*t31002+t30780*t31216+t30541+t31454; + t31400 = t30970+t31598+t31605; + t29806 = t30733*t31008; + t31399 = y*t31122+x*t31169+t29806+t30688*t31043+t31602; + t30990 = t29810+t31479; + t31398 = t30990+t31579+t31598; + t29931 = z*t30469; + t30957 = t29931+t31479; + t31397 = t30957+t31579+t31588; + t31020 = z*t31093; + t30886 = t30717*t31190; + t31396 = z*t30886+t30729*t31227+t30781*t31020+t31606*x; + t31395 = t30721*t31002+t30390+t30780*t31261+t30720*t31033+t31490; + t31104 = t30781*t30662; + t31394 = t31474+t31634*t30783+(t31104+t31250)*t30780; + t30493 = x*t30608; + t29911 = z*t30493; + t30962 = t29911+t31450; + t31393 = t30962+t31573+t31581; + t31392 = t30782*t30998+t30720*t31050+t30717*t31200+z*t31178+(t31004+ +t31261)*y; + t30267 = t30680*t31059; + t31391 = t30722*t31235+t30379+t30683*t31033+z*t30267+t31467; + t31193 = t30778*t30727; + t31228 = z*t30710; + t30482 = t30784*t31228; + t31390 = t31193*t31266+t31434+(t31214+t30482)*y; + t31207 = y*t30662; + t31098 = t30784*t30679; + t31195 = t30778*t30779; + t31055 = y*t31195; + t31389 = t30779*t30924+t30688*t31055+t30782*t31098+t30784*t31207+t31572; + t31388 = t31483+t31540; + t30507 = z*t30610; + t30607 = t30723*t30780; + t31387 = t30607*t31265+t31436+(t31228+t30507)*x; + t30989 = t29931+t31456; + t31386 = t30989+t31587+t31597; + t31170 = t30780*t30725; + t31385 = z*t31170+t30677*t31002+t30485+t30783*t30997+t31477; + t31384 = t31436+(t30995+t31618)*x; + t31229 = z*t30702; + t31383 = t31175*t31266+t31435+(t31229+t30519)*y; + t30351 = z*t31110; + t31382 = t30351+t30780*t31214+t30710*t31002+t30726*t31033+t31481; + t31173 = t30784*t30702; + t30488 = z*t31173; + t31255 = z*t30762; + t31381 = t31180*t31266+t31435+(t30488+t31255)*y; + t31380 = t30488+t30726*t31002+t31481+t31618*t30778; + t31379 = t30778*t31233+t30675*t31072+t30779*t31001+t30782*t30894+t31443; + t31378 = t30962+t31577+t31592; + t31189 = t30720*t30778; + t30927 = t30717*t31072; + t31377 = t30782*t31004+t31189*t31266+(t31130+t30927)*z+t31609*y; + t31376 = t30729*t31235+t30720*t31002+t30784*t31219+t30778*t31020+t31490; + t31057 = t30781*t30747; + t30732 = RATIONAL(-5.0,24.0); + t30961 = t30732*t31190; + t31375 = t30769*t31199+t30781*t30390+(t30961+t31057)*z+t31621*x; + t30563 = t30784*t31206; + t31374 = t31472+t30563+t30732*t31002+t31621*t30778; + t31373 = t30507+t30780*t31253+z*t30176+t30683*t31002+t31467; + t31134 = t30781*t30694; + t31372 = t30782*t31134+t30688*t30890+t31473+(t31047+t31249)*x; + t31151 = t30778*t30725; + t31371 = t30519+t30682*t31002+t31477+(t31151+t30884)*z; + t31370 = t30717*t31199+(t31020+t31261)*x+t31606*t30781; + t31369 = t31483+t31525; + t31150 = t30745*t30781; + t30945 = t30736*t31190; + t31368 = t30767*t31199+t31622*x+(t31150+t30945+t30895)*z; + t31367 = t31466+t30427+t30717*t31033+t31609*t30780; + t30542 = t30784*t31209; + t31366 = t30542+t30736*t31002+t31454+t31622*t30778; + t31365 = t30905+t31590+t31603; + t30984 = t29911+t31457; + t31364 = t30984+t31577+t31603; + t31363 = t31146*t31267+t30689*t30890+x*t31207+t30781*t31070+t31473; + t31132 = t30780*t30762; + t31362 = z*t31132+t30702*t31002+t30457+t30723*t31033+t31446; + t31035 = t30779*t30614; + t31361 = t30779*t30922+y*t31120+t30674*t31072+t30784*t31035+t31443; + t31360 = t31466+t30729*t31254+t30717*t31002+t31608*t30778; + t31359 = t30987+t31590+t31592; + t31358 = t30605*t31266+t31434+(t31228+t30379)*y; + t31357 = t30957+t31580+t31597; + t31356 = t30984+t31573+t31585; + t30908 = t30723*t31059; + t31355 = t30762*t31235+t30482+t31446+(t30918+t30908)*z; + t31354 = t30745*t31002+t30732*t31033+t30552+t30780*t31222+t31472; + t31353 = t31155*t31265+t31433+(t30485+t31229)*x; + t31352 = t31433+(t30992+t31255+t30351)*x; + t31351 = t30990+t31571+t31580; + t31350 = t30769*t31200+t30732*t31050+(t30930+t31060)*z+(t30542+t31222)*y; + t31348 = t30767*t31200+t30736*t31050+(t30912+t31097)*z+(t30563+t31216)*y; + t31347 = t30989+t31588+t31605; + t30416 = t30702*t31195; + t30496 = t30710*t31184; + t30872 = t30495+t30619+t30779*t30908+t30496+t31156; + t31346 = t30416+t30872+t30622+t31438+t31484; + t31194 = t30779*t30762; + t30574 = t30778*t31194; + t31345 = t30623+t30872+t30574+t31460+t31487; + t30354 = t30702*t31172; + t31344 = t31408+t30354+t30616+t31484+t31564; + t31343 = t31431+t31574+t31593; + t31342 = t31428+t31575+t31576; + t31341 = t31548+t31553; + t31340 = t31548+t31555; + t31339 = t31522+t31524; + t30929 = t30780*t31154; + t31338 = t30691*t31094+t30781*t30929+t31430+t31613*x; + t31337 = t31431+t31576+t31600; + t31336 = t31554+t31559; + t31335 = t31521+t31537; + t31136 = t30687*t30782; + t31334 = t30781*t31136+t31073*t31267+y*t31161+t30722*t30890+t31636*t30725 ++t31616*x; + t30946 = t30745*t31172; + t30943 = t30747*t31172; + t31333 = t30781*t30946+x*t30943+t30783*t31063+t30681*t31259+t31429; + t31332 = t31414+t31599+t31600; + t31153 = t30666*t30782; + t30438 = t30731*t31144; + t30572 = t30779*t31057; + t31331 = t31416+t30781*t31248+y*t30572+(t30438+t31153)*x; + t31330 = t31406+t31575+t31599; + t31329 = t31432+t31566+t31582; + t31215 = y*t30681; + t31328 = t31424+t31620*t30778+(t31215+t31153)*t30784; + t30940 = t30781*t31073; + t31327 = t30780*t30940+t30667*t31094+t31422+(t30938+t31119)*x; + t30916 = t30782*t31073; + t31326 = t30667*t31267+y*t30940+t31640*t30725+t31616*t30781+(t31136+ +t30916)*x; + t31325 = t30691*t31259+x*t30929+t31411+t31613*t30781; + t31068 = t30714*t30783; + t30492 = t30779*t31170; + t31324 = t30781*t30492+t30687*t31094+t31425+(t30354+t31068)*x; + t31323 = t30784*t31115+t30666*t31260+t31409+t31623*t30778; + t31322 = t31521+t31534; + t31321 = t31428+t31589+t31593; + t31320 = t31532+t31555; + t31319 = t31557+t31560; + t31318 = t31524+t31531; + t31317 = t31421+t31594+t31601; + t31316 = t31558+t31562; + t30456 = t30779*t31130; + t30589 = t30779*t31150; + t31315 = t30781*t31226+y*t30589+t31420+(t30456+t31115)*x; + t31314 = t30599+t30499+t30164+t30492+t30682*t30952+t30590+t31453; + t31061 = t30781*t30740; + t31182 = t30742*t30781; + t31313 = t30782*t31061+t30742*t31256+t30702*t30890+(t30571+t31182)*y+( +t31231+t31612)*x; + t31312 = t31421+t31563+t31578; + t31311 = t31417+t31563+t31567; + t31310 = t31419+t31565+t31578; + t31127 = t30784*t30740; + t31309 = t30778*t30527+t30782*t31127+y*t30926+t30742*t31260+t31423; + t31308 = t31559+t31560; + t31307 = t31417+t31582+t31601; + t31306 = t30681*t31094+x*t30946+t30666*t31259+t30781*t30943+t31418; + t31305 = t31414+t31574+t31584; + t31304 = t31406+t31584+t31589; + t31303 = t31522+t31535; + t30537 = t30778*t31167; + t31116 = t30714*t30782; + t31302 = y*t30537+t30784*t31116+t30739*t31260+t30782*t30574+t31407; + t31301 = t31529+t31537; + t31300 = t31550+t31556; + t31212 = x*t30739; + t30560 = t30762*t31144; + t31299 = t30781*t31116+x*t30560+t30710*t30890+t30782*t31212+(t31607+ +t31617)*y; + t31298 = t31544+t31546; + t30966 = t30730*t31172; + t30645 = t30758*t30784; + t31297 = t30539+t30645+t30537+t30763*t30778+t30566+t30784*t30966+t31491; + t31296 = t31547+t31556; + t31295 = t31533+t31536; + t31294 = t31551+t31552; + t31293 = t31523+t31541; + t31292 = t30608+t30779*t31132+t31408+t31460; + t31291 = t31529+t31534; + t31290 = t31554+t31557; + t31289 = t31530+t31542; + t31288 = t31532+t31553; + t31287 = t31531+t31535; + t31286 = t31432+t31565+t31567; + t31285 = t31561+t31562; + t31284 = t31419+t31566+t31594; + t30525 = t30780*t31167; + t30638 = t30762*t30783; + t30534 = t30779*t30638; + t31283 = t30639+t30763*t30780+t30525+t30783*t30914+t30776*t31059+t31480+ +t31491+t30534+t31471; + t29870 = y*t30951; + t31282 = t30782*t31242+t29870+x*t30942+t30855+y*t31165+t31439+t31591; + t30516 = t30779*t31151; + t31281 = t30682*t30981+t30595+t30170+t30593+t30516+t30784*t31073+t31445+ +t31452+t31453; + t30858 = t31363+t31448; + t31280 = t30858+t30782*t31250+t31595+t29943+t31483+(t31134+t30968)*y; + t31279 = t31361+t31570+t30784*t31078+t30782*t30964+(t31129+t30985)*y; + t31075 = t30662*t30782; + t31278 = t30689*t31055+t30784*t31075+t30779*t30972+y*t31098+t31388+t31572 +; + t31277 = t30784*t31080+t30778*t30921+t30674*t31260+y*t30986+t31361+t31583 +; + t31276 = t31372+y*t31104+t29870+t31602+(t30928+t31070)*x; + t31275 = t30781*t31258+x*t31075+y*t30933+t29958+t31372+t31595; + t31117 = t30784*t30709; + t31274 = t30778*t31035+t30784*t31143+t30782*t30925+y*t31117+t31379+t31570 +; + t30956 = t30779*t31079; + t31273 = t30675*t31260+t30784*t31171+t30778*t30967+y*t30956+t31379+t31583 +; + t31272 = y*t31152+t29806+t31349+t31591+t31614*t30782; + t31176 = t30784*t30657; + t31138 = t30784*t30656; + t31271 = y*t31176+t30656*t31251+t31510+t30782*t31138+t30657*t31072+t31647 +*t30779+t31624*t30784; + t30522 = y*t30645; + t31270 = t30763*t31055+t30734*t30937+t30779*t30522+t30661*t31251+t31503+( +t30956+t31117)*t30782+t31610*t30707; + t31269 = y*t30887+t31503+t30678*t31251+t31610*t30716+t31631*t30778+( +t31108+t30921)*t30784; + t31268 = t30656*t31072+t30693*t30937+t30779*t30245+t31510+t30782*t31176+y +*t31138+t30657*t31251+t31624*t30778; + t31239 = y*t30690; + t30612 = t30726*t30784; + t30617 = t30727*t30784; + t30764 = RATIONAL(2.0,1.0); + t31159 = t30764*t30779; + t30611 = t30726*t30783; + t30615 = t30727*t30783; + t31137 = t30775*t30783; + t31135 = t30751*t30780; + t31133 = t30757*t30780; + t31103 = t30784*t30691; + t31081 = t30770*t30779; + t31069 = t30690*t30782; + t31046 = y*t31154; + t30983 = t30779*t31084; + t30976 = t30732*t31195; + t30974 = t30779*t31173; + t30383 = t30729*t31164; + t30969 = t30720*t31172; + t30947 = t30779*t31189; + t30910 = t30778*t31125; + t30900 = t30779*t31193; + t30889 = t30719*t31144; + t30883 = t30742*t31059+t30765*t30952+t31480; + t30881 = t30655*t31139+t30677*t30981+t31452; + t30880 = t30687*t31139+t30780*t30974+t31156; + t30696 = RATIONAL(1.0,16.0); + t30753 = RATIONAL(1.0,4.0); + t30697 = RATIONAL(-5.0,16.0); + t30877 = t30753+t30697*t30780+t30696*t30783; + t30724 = RATIONAL(-1.0,16.0); + t30766 = RATIONAL(-1.0,4.0); + t30712 = RATIONAL(5.0,16.0); + t30876 = t30724*t30783+t30766+t30712*t30780; + t30875 = t30754+t31135+t30756*t30783; + t30874 = t30775+t30746*t30780+t30770*t30783; + t30670 = RATIONAL(25.0,32.0); + t30873 = t30670*t30780+t30705*t30783+t30751; + t30871 = t30607+t30267+t30783*t31121+t30705*t30952+t31492; + t30869 = t30730*t31059+t30779*t31137+t30746*t30952+t30759*t30780+t31451; + t30868 = t30691*t31251+t30721*t30937+t30778*t31069+t30784*t31046+t30881; + t30867 = x*t30534+t30781*t30487+t30883+t31607*t30780; + t30866 = t30778*t31239+t30691*t31072+t30721*t31053+t30784*t30889+t30881; + t30864 = t31394+t31448; + t30863 = t31369+t31448; + t30862 = t30714*t31251+t30687*t31072+y*t30974+t30725*t30937+t30880; + t30860 = y*t30496+t30740*t31251+t30667*t31072+t30784*t30916+t30880; + t30856 = x*t31090+t30780*t31182+t30883+t31604*t30783; + t30672 = RATIONAL(-25.0,48.0); + t30854 = t30754*t30981+t30615+t30672*t31139+t30780*t31159+t30869+t31449; + t30651 = RATIONAL(25.0,192.0); + t30699 = RATIONAL(-1.0,32.0); + t30853 = t30651*t31059+t30699*t30952+t30612+t30778*t31081+t31412+t31440+ +t31492; + t30852 = t30754*t30952+t30617+t30672*t31059+t30778*t31159+t31413+t31449+ +t31451; + t30851 = t30651*t31139+t30611+t30780*t31081+t30699*t30981+t30871+t31440; + t30676 = RATIONAL(-25.0,96.0); + t30850 = t30676*t30780+t30736+t30717*t30783+t30876*t30779; + t30849 = t30736+t30717*t30784+t30676*t30778+(t30712*t30778+t30724*t30784+ +t30766)*t30779; + t30685 = RATIONAL(25.0,96.0); + t30848 = t30720*t30784+t30732+t30685*t30778+(t30696*t30784+t30697*t30778+ +t30753)*t30779; + t30847 = t30685*t30780+t30732+t30720*t30783+t30877*t30779; + t30846 = x*t30547+y*t30383+t30781*t31215+t30728*t31256+t31405+t31420; + t30845 = x*t30525+t30783*t31212+t30781*t31068+t30780*t30553+t30867+t31427 +; + t30844 = t30782*t31103+y*t30910+t30784*t31239+t30868+t30778*t30889+t31415 +; + t30843 = t30782*t31067+t30862+t30778*t30916+t30710*t31055+y*t31127+t31426 +; + t30842 = t30784*t31136+t30714*t31260+t30860+t30782*t30516+y*t30416+t31426 +; + t30841 = t30778*t31046+t30784*t31069+t30866+t30782*t30910+y*t31103+t31415 +; + t30840 = t31405+t30782*t31240+x*t30543+t31416+(t30406+t31063)*y; + t30839 = t30742*t31259+t31427+t30856+t30783*t31061+t31596*t30780; + t30838 = t30275+t30710+t30610+t30613+t30871+t30670*t30988+t31412+(t31135+ +t31569)*t30779; + t30837 = t30331+t31413+RATIONAL(-25.0,8.0)*t30988+t30869+t30761+t30762* +t30784+t30638+(t31133+t31568)*t30779; + t30836 = t30440+t30736*t31037+t30779*t30961+t30648+t31346+t30437+t30572+ +t31429+(t31191+t30750)*x; + t30835 = t30388+t30736*t30979+y*t30976+t31344+t30629+t30626+t30362+t31409 ++t31620; + t30834 = t30258+t30866+t30423+y*t31086+t30601+t30782*t30947+t30598+t31314 ++t30438+t30717*t31055; + t30833 = t30784*t31099+t30776*t31260+t30560+t31283+t30752*t31055+t31423+( +t30758+t30914)*t30782+(t31167+t30763)*y; + t30832 = t30862+t30467+t31292+t30614+t30239+t30606+t30710*t31144+t30779* +t30965+(t31194+t30914)*y; + t30831 = t30348+t30750*y+t31344+t30397+t30782*t30976+t30736*t31055+t30646 ++t31424+t31623; + t30830 = t30625+t31346+t30589+t30779*t30945+t30502+t31418+t30732*t31037+ +t30506+(t30749+t31192)*x; + t30829 = t30287+t31345+x*t30983+t30621+t30779*t30936+t30493+t30602+t31425 ++t31604; + t30828 = t30781*t30969+t30717*t31037+t31281+t30688*x+t30596+t31411+t31615 ++t31639; + t30827 = t30456+t30491+t30779*t30927+t30868+t31314+t30600+(t30689+t30947) +*y+t31637; + t30826 = t30637+t30759*t31055+t31283+t30784*t31162+t30522+t31407+(t30776+ +t30900)*t30782+t31612; + t30825 = t30255+t31345+t30710*t31164+t30442+t30779*t30934+t30618+t31422+( +t30703+t31194+t30966)*x; + t30824 = t31297+t30856+(t30758+t30966)*t30781+(t30897+t30763)*x+t31617+ +t31629; + t30823 = t30702*t31144+t30609+t30782*t30949+t30469+t30860+t31292+t30604+ +t30222+(t30900+t31105)*y; + t30822 = t31281+t30383+t30517+t30779*t30886+t30592+t31430+(t30969+t30689) +*x+t31646; + t30821 = t31297+t30759*t31037+t30867+t30768*x+(t30983+t30776)*t30781+ +t31596+t31630; + t30820 = t31276+t31507+t31515; + t30819 = t31389+t31369+t31514+t31519; + t30818 = t31278+t30864+t31514+t31526; + t30817 = t31506+t31268+t31508; + t30816 = t31363+t31399+t31502+t31515; + t30815 = t31493+t31271+t31506; + t30814 = t31494+t31269+t31500; + t30813 = t31399+t31394+t30858+t31507+t31538; + t30812 = t31279+t31505+t31516; + t30811 = t31277+t31513+t31517; + t30810 = t31272+t30859+t31498+t31545; + t30809 = t31389+t30863+t31394+t31511+t31526; + t30808 = t31494+t31270+t31495; + t30807 = t31499+t31270+t31500; + t30806 = t31504+t31280+t31527+t31540; + t30805 = t31501+t31280+t31525+t31539; + t30804 = t31273+t31513+t31518; + t30803 = t31282+t31498+t31528+t31549; + t30802 = t31273+t31512+t31517; + t30801 = t31496+t31271+t31508; + t30800 = t31272+t30861+t31509+t31528; + t30799 = t31388+t31275+t31448+t31501+t31527; + t30798 = t31282+t31509+t31543+t31545; + t30797 = t31277+t31512+t31518; + t30796 = t31493+t31268+t31496; + t30795 = t31269+t31495+t31499; + t30794 = t31275+t30863+t31504+t31539; + t30793 = t31279+t31497+t31520; + t30792 = t31276+t30864+t31502+t31538; + t30791 = t31274+t31497+t31516; + t30790 = t31278+t31511+t31519; + t30789 = t31274+t31505+t31520; + t30774 = RATIONAL(5.0,4.0); + t30744 = RATIONAL(3.0,4.0); + t30743 = RATIONAL(-5.0,4.0); + t30701 = RATIONAL(-15.0,4.0); + t30700 = RATIONAL(25.0,8.0); + t30673 = RATIONAL(25.0,48.0); + t30669 = RATIONAL(-25.0,12.0); + t30668 = RATIONAL(-15.0,16.0); + coeffs_dzz->coeff_m2_m2_m2 = t30801+t31536+t31541+t31542+t31546; + coeffs_dzz->coeff_m1_m2_m2 = t30805+t31342+t31393; + coeffs_dzz->coeff_0_m2_m2 = t30827+t31373+t31392; + coeffs_dzz->coeff_p1_m2_m2 = t30794+t31330+t31404; + coeffs_dzz->coeff_p2_m2_m2 = t31289+t30815+t31298; + coeffs_dzz->coeff_m2_m1_m2 = t30813+t31321+t31397; + coeffs_dzz->coeff_m1_m1_m2 = t30804+t31294+t31547+t31558; + coeffs_dzz->coeff_0_m1_m2 = t30823+t31381+t31382; + coeffs_dzz->coeff_p1_m1_m2 = t31296+t30802+t31316; + coeffs_dzz->coeff_p2_m1_m2 = t30820+t31304+t31347; + coeffs_dzz->coeff_m2_0_m2 = t30822+t31370+t31391; + coeffs_dzz->coeff_m1_0_m2 = t30829+t31352+t31380; + coeffs_dzz->coeff_0_0_m2 = ((RATIONAL(-25.0,32.0)*t30780+t30746+t30713* +t30783)*t30778+(t30770+t30699*t30783+t30713*t30780)*t30784+t30874)*z+t30838; + coeffs_dzz->coeff_p1_0_m2 = t30825+t31380+t31384; + coeffs_dzz->coeff_p2_0_m2 = t30828+t31391+t31396; + coeffs_dzz->coeff_m2_p1_m2 = t30792+t31304+t31398; + coeffs_dzz->coeff_m1_p1_m2 = t30797+t31296+t31552+t31561; + coeffs_dzz->coeff_0_p1_m2 = t30832+t31382+t31390; + coeffs_dzz->coeff_p1_p1_m2 = t30811+t31285+t31547+t31551; + coeffs_dzz->coeff_p2_p1_m2 = t30816+t31321+t31400; + coeffs_dzz->coeff_m2_p2_m2 = t30796+t31298+t31533+t31541; + coeffs_dzz->coeff_m1_p2_m2 = t30799+t31330+t31356; + coeffs_dzz->coeff_0_p2_m2 = t30834+t31373+t31377; + coeffs_dzz->coeff_p1_p2_m2 = t30806+t31342+t31403; + coeffs_dzz->coeff_p2_p2_m2 = t30817+t31295+t31530+t31546; + coeffs_dzz->coeff_m2_m2_m1 = t30809+t31288+t31308; + coeffs_dzz->coeff_m1_m2_m1 = t30803+t31311+t31402; + coeffs_dzz->coeff_0_m2_m1 = t30831+t31383+t31395; + coeffs_dzz->coeff_p1_m2_m1 = t30810+t31312+t31351; + coeffs_dzz->coeff_p2_m2_m1 = t31319+t30819+t31320; + coeffs_dzz->coeff_m2_m1_m1 = t30791+t31307+t31365; + coeffs_dzz->coeff_m1_m1_m1 = t30807+t31335+t31339; + coeffs_dzz->coeff_0_m1_m1 = t30826+t31350+t31401; + coeffs_dzz->coeff_p1_m1_m1 = t30808+t31291+t31339; + coeffs_dzz->coeff_p2_m1_m1 = t30789+t31317+t31364; + coeffs_dzz->coeff_m2_0_m1 = t30836+t31353+t31376; + coeffs_dzz->coeff_m1_0_m1 = t30821+t31366+t31375; + coeffs_dzz->coeff_0_0_m1 = (t30753*t30783+1.0+t30743*t30780+(RATIONAL( +25.0,16.0)*t30780+t30743+t30697*t30783)*t30778+t30877*t30784)*z+t30837; + coeffs_dzz->coeff_p1_0_m1 = t30824+t31366+t31368; + coeffs_dzz->coeff_p2_0_m1 = t30830+t31376+t31387; + coeffs_dzz->coeff_m2_p1_m1 = t30793+t31317+t31359; + coeffs_dzz->coeff_m1_p1_m1 = t31301+t30814+t31318; + coeffs_dzz->coeff_0_p1_m1 = t30833+t31348+t31401; + coeffs_dzz->coeff_p1_p1_m1 = t30795+t31318+t31322; + coeffs_dzz->coeff_p2_p1_m1 = t30812+t31307+t31378; + coeffs_dzz->coeff_m2_p2_m1 = t30818+t31320+t31336; + coeffs_dzz->coeff_m1_p2_m1 = t30800+t31312+t31386; + coeffs_dzz->coeff_0_p2_m1 = t30835+t31358+t31395; + coeffs_dzz->coeff_p1_p2_m1 = t30798+t31311+t31357; + coeffs_dzz->coeff_p2_p2_m1 = t31288+t30790+t31290; + coeffs_dzz->coeff_m2_m2_0 = t31334+t30844+t31338; + coeffs_dzz->coeff_m1_m2_0 = t31324+t30840+t31328; + coeffs_dzz->coeff_0_m2_0 = t30849*t30782+t30851+t30848*y; + coeffs_dzz->coeff_p1_m2_0 = t31327+t30846+t31328; + coeffs_dzz->coeff_p2_m2_0 = t31325+t30844+t31326; + coeffs_dzz->coeff_m2_m1_0 = t31331+t30842+t31333; + coeffs_dzz->coeff_m1_m1_0 = t30845+t31302+t31313; + coeffs_dzz->coeff_0_m1_0 = t30854+(t30730+t30612+t30673*t30778+(t30756* +t30784+t31569)*t30779)*t30782+(t30617+t30752+t30669*t30778+(t31106+t31568)* +t30779)*y; + coeffs_dzz->coeff_p1_m1_0 = t31299+t30839+t31302; + coeffs_dzz->coeff_p2_m1_0 = t31306+t30842+t31315; + coeffs_dzz->coeff_m2_0_0 = t30853+t30847*x+t30850*t30781; + coeffs_dzz->coeff_m1_0_0 = (t30730+t30611+t30673*t30780+t30875*t30779)* +t30781+(t30615+t30752+t30669*t30780+(t31133+t31137+t30760)*t30779)*x+t30852; + coeffs_dzz->coeff_0_0_0 = t30751*t30783+t30748+t30700*t30780+(t30700+ +RATIONAL(-125.0,32.0)*t30780+t30670*t30783)*t30778+t30873*t30784+(t30701*t30780 ++t30744*t30783+RATIONAL(3.0,1.0)+(t30701+t30668*t30783+RATIONAL(75.0,16.0)* +t30780)*t30778+(t30668*t30780+RATIONAL(3.0,16.0)*t30783+t30744)*t30784)*t30779; + coeffs_dzz->coeff_p1_0_0 = (t30672*t30780+t30727+t30723*t30783+t30874* +t30779)*t30781+(t30671*t30780+(t30764+t30754*t30783+t30748*t30780)*t30779+ +t31619)*x+t30852; + coeffs_dzz->coeff_p2_0_0 = t30853+t30847*t30781+t30850*x; + coeffs_dzz->coeff_m2_p1_0 = t30843+t31315+t31333; + coeffs_dzz->coeff_m1_p1_0 = t31299+t30845+t31309; + coeffs_dzz->coeff_0_p1_0 = (t30672*t30778+t30723*t30784+t30727+(t30770* +t30784+t30775+t30746*t30778)*t30779)*t30782+(t31126+t30759+t30730*t30784+( +t30754*t30784+t30748*t30778+t30764)*t30779)*y+t30854; + coeffs_dzz->coeff_p1_p1_0 = t30839+t31309+t31313; + coeffs_dzz->coeff_p2_p1_0 = t30843+t31306+t31331; + coeffs_dzz->coeff_m2_p2_0 = t31326+t30841+t31338; + coeffs_dzz->coeff_m1_p2_0 = t31323+t30846+t31324; + coeffs_dzz->coeff_0_p2_0 = t30851+t30848*t30782+t30849*y; + coeffs_dzz->coeff_p1_p2_0 = t31323+t30840+t31327; + coeffs_dzz->coeff_p2_p2_0 = t30841+t31325+t31334; + coeffs_dzz->coeff_m2_m2_p1 = t31290+t30809+t31340; + coeffs_dzz->coeff_m1_m2_p1 = t30803+t31310+t31357; + coeffs_dzz->coeff_0_m2_p1 = t30831+t31358+t31367; + coeffs_dzz->coeff_p1_m2_p1 = t30810+t31286+t31386; + coeffs_dzz->coeff_p2_m2_p1 = t31336+t30819+t31341; + coeffs_dzz->coeff_m2_m1_p1 = t30791+t31284+t31378; + coeffs_dzz->coeff_m1_m1_p1 = t30807+t31287+t31291; + coeffs_dzz->coeff_0_m1_p1 = t30826+t31348+t31354; + coeffs_dzz->coeff_p1_m1_p1 = t30808+t31287+t31335; + coeffs_dzz->coeff_p2_m1_p1 = t30789+t31329+t31359; + coeffs_dzz->coeff_m2_0_p1 = t30836+t31360+t31387; + coeffs_dzz->coeff_m1_0_p1 = t30821+t31368+t31374; + coeffs_dzz->coeff_0_0_p1 = t30837+(-1.0+t30766*t30783+t30774*t30780+( +RATIONAL(-25.0,16.0)*t30780+t30712*t30783+t30774)*t30778+t30876*t30784)*z; + coeffs_dzz->coeff_p1_0_p1 = t30824+t31374+t31375; + coeffs_dzz->coeff_p2_0_p1 = t30830+t31353+t31360; + coeffs_dzz->coeff_m2_p1_p1 = t30793+t31329+t31364; + coeffs_dzz->coeff_m1_p1_p1 = t30814+t31303+t31322; + coeffs_dzz->coeff_0_p1_p1 = t30833+t31350+t31354; + coeffs_dzz->coeff_p1_p1_p1 = t30795+t31301+t31303; + coeffs_dzz->coeff_p2_p1_p1 = t30812+t31284+t31365; + coeffs_dzz->coeff_m2_p2_p1 = t30818+t31319+t31341; + coeffs_dzz->coeff_m1_p2_p1 = t30800+t31286+t31351; + coeffs_dzz->coeff_0_p2_p1 = t30835+t31367+t31383; + coeffs_dzz->coeff_p1_p2_p1 = t30798+t31310+t31402; + coeffs_dzz->coeff_p2_p2_p1 = t31308+t30790+t31340; + coeffs_dzz->coeff_m2_m2_p2 = t30801+t31523+t31530+t31533+t31544; + coeffs_dzz->coeff_m1_m2_p2 = t30805+t31332+t31403; + coeffs_dzz->coeff_0_m2_p2 = t30827+t31377+t31385; + coeffs_dzz->coeff_p1_m2_p2 = t30794+t31337+t31356; + coeffs_dzz->coeff_p2_m2_p2 = t31293+t30815+t31295; + coeffs_dzz->coeff_m2_m1_p2 = t30813+t31305+t31400; + coeffs_dzz->coeff_m1_m1_p2 = t30804+t31285+t31300; + coeffs_dzz->coeff_0_m1_p2 = t30823+t31362+t31390; + coeffs_dzz->coeff_p1_m1_p2 = t31294+t30802+t31550+t31561; + coeffs_dzz->coeff_p2_m1_p2 = t30820+t31343+t31398; + coeffs_dzz->coeff_m2_0_p2 = t30822+t31371+t31396; + coeffs_dzz->coeff_m1_0_p2 = t30829+t31355+t31384; + coeffs_dzz->coeff_0_0_p2 = (t30873*t30778+(t30705*t30780+t30756+t30708* +t30783)*t30784+t30875)*z+t30838; + coeffs_dzz->coeff_p1_0_p2 = t30825+t31352+t31355; + coeffs_dzz->coeff_p2_0_p2 = t30828+t31370+t31371; + coeffs_dzz->coeff_m2_p1_p2 = t30792+t31343+t31347; + coeffs_dzz->coeff_m1_p1_p2 = t31316+t30797+t31550+t31551; + coeffs_dzz->coeff_0_p1_p2 = t30832+t31362+t31381; + coeffs_dzz->coeff_p1_p1_p2 = t30811+t31300+t31552+t31558; + coeffs_dzz->coeff_p2_p1_p2 = t30816+t31305+t31397; + coeffs_dzz->coeff_m2_p2_p2 = t30796+t31289+t31523+t31536; + coeffs_dzz->coeff_m1_p2_p2 = t30799+t31337+t31404; + coeffs_dzz->coeff_0_p2_p2 = t30834+t31385+t31392; + coeffs_dzz->coeff_p1_p2_p2 = t30806+t31332+t31393; + coeffs_dzz->coeff_p2_p2_p2 = t30817+t31293+t31542+t31544; diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.cube.order1.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.cube.order1.smooth0.c new file mode 100644 index 0000000..a31a491 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.cube.order1.smooth0.c @@ -0,0 +1,61 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrTP_3d_cube10 +#include "../template.h" + +#define N_DIMS 3 +#define MOLECULE_MIN_M 0 +#define MOLECULE_MAX_M 1 +#define MOLECULE_SIZE 2 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +#define HAVE_OP_DZ +/* n.b. no 2nd derivatives for linear interpolation! */ + +#define XYZ x, y, z +#define FP_XYZ fp x, fp y, fp z +#define STRIDE_IJK stride_i, stride_j, stride_k +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride, Jacobian_mk_stride + +#define DATA_STRUCT data_struct_3d_cube_size2 +#define COEFFS_STRUCT coeffs_struct_3d_cube_size2 + +#define FETCH_DATA_REAL LocalInterp_fetch_3d_cube2_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_3d_cube2_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_3d_cube2_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_3d_cube2_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_3d_cube2_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_3d_cube2_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_3d_cube2_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_3d_cube2_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_3d_cube2 + +#define STORE_COEFFS LocalInterp_store_3d_cube2 + +/* note pathnames are all relative to "../template.c" */ +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-dy.compute.c" +#define COEFFS_DZ_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order1.smooth0/coeffs-dz.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.cube.order2.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.cube.order2.smooth0.c new file mode 100644 index 0000000..6a703d5 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.cube.order2.smooth0.c @@ -0,0 +1,71 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrTP_3d_cube20 +#include "../template.h" + +#define N_DIMS 3 +#define MOLECULE_MIN_M -1 +#define MOLECULE_MAX_M 1 +#define MOLECULE_SIZE 3 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +#define HAVE_OP_DZ +#define HAVE_OP_DXX +#define HAVE_OP_DXY +#define HAVE_OP_DXZ +#define HAVE_OP_DYY +#define HAVE_OP_DYZ +#define HAVE_OP_DZZ + +#define XYZ x, y, z +#define FP_XYZ fp x, fp y, fp z +#define STRIDE_IJK stride_i, stride_j, stride_k +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride, Jacobian_mk_stride + +#define DATA_STRUCT data_struct_3d_cube_size3 +#define COEFFS_STRUCT coeffs_struct_3d_cube_size3 + +#define FETCH_DATA_REAL LocalInterp_fetch_3d_cube3_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_3d_cube3_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_3d_cube3_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_3d_cube3_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_3d_cube3_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_3d_cube3_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_3d_cube3_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_3d_cube3_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_3d_cube3 + +#define STORE_COEFFS LocalInterp_store_3d_cube3 + +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dy.compute.c" +#define COEFFS_DZ_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dz.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxx.compute.c" +#define COEFFS_DXY_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxy.compute.c" +#define COEFFS_DXZ_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dxz.compute.c" +#define COEFFS_DYY_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyy.compute.c" +#define COEFFS_DYZ_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dyz.compute.c" +#define COEFFS_DZZ_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order2.smooth0/coeffs-dzz.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.cube.order3.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.cube.order3.smooth0.c new file mode 100644 index 0000000..922876f --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.cube.order3.smooth0.c @@ -0,0 +1,71 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrTP_3d_cube30 +#include "../template.h" + +#define N_DIMS 3 +#define MOLECULE_MIN_M -1 +#define MOLECULE_MAX_M 2 +#define MOLECULE_SIZE 4 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +#define HAVE_OP_DZ +#define HAVE_OP_DXX +#define HAVE_OP_DXY +#define HAVE_OP_DXZ +#define HAVE_OP_DYY +#define HAVE_OP_DYZ +#define HAVE_OP_DZZ + +#define XYZ x, y, z +#define FP_XYZ fp x, fp y, fp z +#define STRIDE_IJK stride_i, stride_j, stride_k +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride, Jacobian_mk_stride + +#define DATA_STRUCT data_struct_3d_cube_size4 +#define COEFFS_STRUCT coeffs_struct_3d_cube_size4 + +#define FETCH_DATA_REAL LocalInterp_fetch_3d_cube4_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_3d_cube4_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_3d_cube4_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_3d_cube4_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_3d_cube4_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_3d_cube4_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_3d_cube4_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_3d_cube4_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_3d_cube4 + +#define STORE_COEFFS LocalInterp_store_3d_cube4 + +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dy.compute.c" +#define COEFFS_DZ_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dz.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxx.compute.c" +#define COEFFS_DXY_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxy.compute.c" +#define COEFFS_DXZ_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dxz.compute.c" +#define COEFFS_DYY_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyy.compute.c" +#define COEFFS_DYZ_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dyz.compute.c" +#define COEFFS_DZZ_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order3.smooth0/coeffs-dzz.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.cube.order4.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.cube.order4.smooth0.c new file mode 100644 index 0000000..4842b2f --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.cube.order4.smooth0.c @@ -0,0 +1,71 @@ +/* $Header$ */ + +#include +#include +#include +#include +#include + +#include "util_ErrorCodes.h" +#include "cctk.h" +#include "../InterpLocalUniform.h" +#include "../common/structs.h" +#include "../common/fetch.h" +#include "../common/evaluate.h" +#include "../common/store.h" + +/* function prototype */ +#define FUNCTION_NAME LocalInterp_U_LagrTP_3d_cube40 +#include "../template.h" + +#define N_DIMS 3 +#define MOLECULE_MIN_M -2 +#define MOLECULE_MAX_M 2 +#define MOLECULE_SIZE 5 + +/* which derivative ops do we support? */ +#define HAVE_OP_I +#define HAVE_OP_DX +#define HAVE_OP_DY +#define HAVE_OP_DZ +#define HAVE_OP_DXX +#define HAVE_OP_DXY +#define HAVE_OP_DXZ +#define HAVE_OP_DYY +#define HAVE_OP_DYZ +#define HAVE_OP_DZZ + +#define XYZ x, y, z +#define FP_XYZ fp x, fp y, fp z +#define STRIDE_IJK stride_i, stride_j, stride_k +#define JACOBIAN_MIJK_STRIDE Jacobian_mi_stride, Jacobian_mj_stride, Jacobian_mk_stride + +#define DATA_STRUCT data_struct_3d_cube_size5 +#define COEFFS_STRUCT coeffs_struct_3d_cube_size5 + +#define FETCH_DATA_REAL LocalInterp_fetch_3d_cube5_r +#define FETCH_DATA_REAL4 LocalInterp_fetch_3d_cube5_r4 +#define FETCH_DATA_REAL8 LocalInterp_fetch_3d_cube5_r8 +#define FETCH_DATA_REAL16 LocalInterp_fetch_3d_cube5_r16 +#define FETCH_DATA_COMPLEX LocalInterp_fetch_3d_cube5_c +#define FETCH_DATA_COMPLEX8 LocalInterp_fetch_3d_cube5_c8 +#define FETCH_DATA_COMPLEX16 LocalInterp_fetch_3d_cube5_c16 +#define FETCH_DATA_COMPLEX32 LocalInterp_fetch_3d_cube5_c32 + +#define EVALUATE_MOLECULE LocalInterp_eval_3d_cube5 + +#define STORE_COEFFS LocalInterp_store_3d_cube5 + +#define COEFFS_I_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-I.compute.c" +#define COEFFS_DX_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dx.compute.c" +#define COEFFS_DY_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dy.compute.c" +#define COEFFS_DZ_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dz.compute.c" +#define COEFFS_DXX_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxx.compute.c" +#define COEFFS_DXY_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxy.compute.c" +#define COEFFS_DXZ_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dxz.compute.c" +#define COEFFS_DYY_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyy.compute.c" +#define COEFFS_DYZ_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dyz.compute.c" +#define COEFFS_DZZ_COMPUTE_FILE_NAME "Lagrange-tensor-product/3d.coeffs/3d.cube.order4.smooth0/coeffs-dzz.compute.c" + +/* actual code */ +#include "../template.c" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.log b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.log new file mode 100644 index 0000000..98b4ae0 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.log @@ -0,0 +1,200156 @@ + |\^/| Maple 7 (IBM INTEL LINUX) +._|\| |/|_. Copyright (c) 2001 by Waterloo Maple Inc. + \ MAPLE / All rights reserved. Maple is a registered trademark of + <____ ____> Waterloo Maple Inc. + | Type ? for help. +# util.maple -- misc utility routines +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/util.maple,v 1.5 2002/09/02 10:21:03 jthorn Exp $ +> +# +# fix_rationals - convert numbers to RATIONAL() calls +# nonmatching_names - find names in a list which *don't* have a specified prefix +# sprint_numeric_list - convert a numeric list to a valid C identifier suffix +# print_name_list_dcl - print C declarations for a list of names +# +# hypercube_points - compute all (integer) points in an N-dimensional hypercube +# +# ftruncate - truncate a file to zero length +# +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function converts all {integer, rational} subexpressions of its +# input except integer exponents and -1 factors in products, into function +# calls +# RATIONAL(num,den) +# This is useful in conjunction with the C() library function, since +# +# C( (1/3) * foo * bar ) +# t0 = foo*bar/3; +# +# generates a (slow) division (and runs the risk of mixed-mode-arithmetic +# problems), while +# +# C((1.0/3.0) * foo * bar); +# t0 = 0.3333333333*foo*bar; +# +# suffers from roundoff error. With this function, +# +# fix_rationals((1/3) * foo * bar); +# RATIONAL(1,3) foo bar +# C(%); +# t0 = RATIONAL(1.0,3.0)*foo*bar; +# +# which a C preprocessor macro can easily convert to the desired +# +# t0 = (1.0/3.0)*foo*bar; +# +# Additionally, this function can be told to leave certain types of +# subexpressions unconverged. For example, +# fix_rationals(expr, type, specfunc(integer, DATA)); +# will leave all subexpressions of the form DATA(integer arguments) +# unconverted. +# +# Arguments: +# expr = (in) The expression to be converted. +# inert_fn = (optional in) +# If specified, this argument should be a Boolean procedure +# or the name of a Boolean procedure. This procedure should +# take one or more argument, and return true if and only if +# the first argument should *not* be converted, i.e. if we +# should leave this expression unchanged. See the last +# example above. +# ... = (optional in) +# Any further arguments are passed as additional arguments to +# the inert_fn procedure. +# +> fix_rationals := +> proc( +> expr::{ +> algebraic, name = algebraic, +> list({algebraic, name = algebraic}), +> set ({algebraic, name = algebraic}) +> }, +> inert_fn::{name, procedure} +> ) +> local nn, k, +> base, power, fbase, fpower, +> fn, fn_args_list, +> num, den, mult; +> +# do we want to convert this expression? +> if ((nargs >= 2) and inert_fn(expr, args[3..nargs])) +> then return expr; +> end if; +> +# recurse over lists and sets +> if (type(expr, {list,set})) +> then return map(fix_rationals, expr, args[2..nargs]); +> end if; +> +# recurse over equation right hand sides +> if (type(expr, name = algebraic)) +> then return ( lhs(expr) = fix_rationals(rhs(expr), args[2..nargs]) ); +> end if; +> +# recurse over functions other than RATIONAL() +> if (type(expr, function)) +> then +> fn := op(0, expr); +> if (fn <> 'RATIONAL') +> then +> fn_args_list := [op(expr)]; +> fn_args_list := map(fix_rationals, fn_args_list, args[2..nargs]); +> fn; return '%'( op(fn_args_list) ); +> end if; +> end if; +> +> nn := nops(expr); +> +# recurse over sums +> if (type(expr, `+`)) +> then return sum('fix_rationals(op(k,expr), args[2..nargs])', 'k'=1..nn); +> end if; +> +# recurse over products +# ... leaving leading -1 factors intact, i.e. not converted to RATIONAL(-1,1) +> if (type(expr, `*`)) +> then +> if (op(1, expr) = -1) +> then return -1*fix_rationals(remove(type, expr, 'identical(-1)'), +> args[2..nargs]); +> else return product('fix_rationals(op(k,expr), args[2..nargs])', +> 'k'=1..nn); +> end if; +> end if; +> +# recurse over powers +# ... leaving integer exponents intact +> if (type(expr, `^`)) +> then +> base := op(1, expr); +> power := op(2, expr); +> +> fbase := fix_rationals(base, args[2..nargs]); +> if (type(power, integer)) +> then fpower := power; +> else fpower := fix_rationals(power, args[2..nargs]); +> end if; +> return fbase ^ fpower; +> end if; +> +# fix integers and fractions +> if (type(expr, integer)) +> then return 'RATIONAL'(expr, 1); +> end if; +> if (type(expr, fraction)) +> then +> num := op(1, expr); +> den := op(2, expr); +> +> return 'RATIONAL'(num, den); +> end if; +> +# turn Maple floating-point into integer fraction, then recursively fix that +> if (type(expr, float)) +> then +> mult := op(1, expr); +> power := op(2, expr); +> return fix_rationals(mult * 10^power, args[2..nargs]); +> end if; +> +# identity op on names +> if (type(expr, name)) +> then return expr; +> end if; +> +# unknown type +> error "%0", +> "unknown type for expr!", +> " whattype(expr) = ", whattype(expr), +> " expr = ", expr; +> end proc; +fix_rationals := proc(expr::{algebraic, name = algebraic, +list({algebraic, name = algebraic}), set({algebraic, name = algebraic})}, +inert_fn::{procedure, name}) +local nn, k, base, power, fbase, fpower, fn, fn_args_list, num, den, mult; + if 2 <= nargs and inert_fn(expr, args[3 .. nargs]) then return expr + end if; + if type(expr, {set, list}) then + return map(fix_rationals, expr, args[2 .. nargs]) + end if; + if type(expr, name = algebraic) then + return lhs(expr) = fix_rationals(rhs(expr), args[2 .. nargs]) + end if; + if type(expr, function) then + fn := op(0, expr); + if fn <> 'RATIONAL' then + fn_args_list := [op(expr)]; + fn_args_list := + map(fix_rationals, fn_args_list, args[2 .. nargs]); + fn; + return '%'(op(fn_args_list)) + end if + end if; + nn := nops(expr); + if type(expr, `+`) then return + sum('fix_rationals(op(k, expr), args[2 .. nargs])', 'k' = 1 .. nn) + end if; + if type(expr, `*`) then + if op(1, expr) = -1 then return -fix_rationals( + remove(type, expr, 'identical(-1)'), args[2 .. nargs]) + else return product('fix_rationals(op(k, expr), args[2 .. nargs])', + 'k' = 1 .. nn) + end if + end if; + if type(expr, `^`) then + base := op(1, expr); + power := op(2, expr); + fbase := fix_rationals(base, args[2 .. nargs]); + if type(power, integer) then fpower := power + else fpower := fix_rationals(power, args[2 .. nargs]) + end if; + return fbase^fpower + end if; + if type(expr, integer) then return 'RATIONAL'(expr, 1) end if; + if type(expr, fraction) then + num := op(1, expr); den := op(2, expr); return 'RATIONAL'(num, den) + end if; + if type(expr, float) then + mult := op(1, expr); + power := op(2, expr); + return fix_rationals(mult*10^power, args[2 .. nargs]) + end if; + if type(expr, name) then return expr end if; + error "%0", "unknown type for expr!", " whattype(expr) = ", + whattype(expr), " expr = ", expr +end proc + +> +################################################################################ +> +# +# This function finds names in a list which *don't* have a specified prefix. +# +# Arguments: +# name_list = A list of the names. +# prefix = The prefix we want to filter out. +# +# Results: +# This function returns the subset list of names which don't have the +# specified prefix. +# +> nonmatching_names := +> proc( name_list::list({name,string}), prefix::{name,string} ) +> +> select( proc(n) +> evalb(not StringTools[IsPrefix](prefix,n)); +> end proc +> , +> name_list +> ); +> end proc; +nonmatching_names := proc( +name_list::list({name, string}), prefix::{name, string}) + select(proc(n) evalb(not StringTools[IsPrefix](prefix, n)) end proc, + name_list) +end proc + +> +################################################################################ +> +# +# This function converts a numeric list to a string which is a valid +# C identifier suffix: elements are separated by "_", decimal points are +# replaced by "x", and all nonzero values have explicit +/- signs, which +# are replaced by "p"/"m". +# +# For example, [0,-3.5,+4] --> "0_m3x5_p4". +# +> sprint_numeric_list := +> proc(nlist::list(numeric)) +> +# generate preliminary string, eg "+0_-3.5_+4" +> map2(sprintf, "%+a", nlist); +> ListTools[Join](%, "_"); +> cat(op(%)); +> +# fixup bad characters +> StringTools[SubstituteAll](%, "+0", "0"); +> StringTools[CharacterMap](".+-", "xpm", %); +> +> return %; +> end proc; +sprint_numeric_list := proc(nlist::list(numeric)) + map2(sprintf, "%+a", nlist); + ListTools[Join](%, "_"); + cat(op(%)); + StringTools[SubstituteAll](%, "+0", "0"); + StringTools[CharacterMap](".+-", "xpm", %); + return % +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C declarations for a list of names. +# +# Argument: +# name_list = A list of the names. +# type_name = The C type of the names, eg. "double". +# file_name = The file name to write the declaration to. This is +# truncated before writing. +# +> print_name_list_dcl := +> proc( name_list::list({name,string}), +> type_name::string, +> file_name::string ) +> local blanks, separator_string; +> +> ftruncate(file_name); +> +> map( +> proc(var::{name,string}) +> fprintf(file_name, +> "%s %s;\n", +> type_name, var); +> end proc +> , +> name_list +> ); +> +> fclose(file_name); +> NULL; +> end proc; +print_name_list_dcl := proc( +name_list::list({name, string}), type_name::string, file_name::string) +local blanks, separator_string; + ftruncate(file_name); + map(proc(var::{name, string}) + fprintf(file_name, "%s %s;\n", type_name, var) + end proc, name_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes a list of all the (integer) points in an +# N-dimensional hypercube, in lexicographic order. The present +# implementation requires N <= 4. +# +# Arguments: +# cmin,cmax = N-element lists of cube minimum/maximum coordinates. +# +# Results: +# The function returns a set of d-element lists giving the coordinates. +# For example, +# hypercube([0,0], [2,1] +# returns +# { [0,0], [0,1], [1,0], [1,1], [2,0], [2,1] } +> hypercube_points := +> proc(cmin::list(integer), cmax::list(integer)) +> local N, i,j,k,l; +> +> N := nops(cmin); +> if (nops(cmax) <> N) +> then error +> "must have same number of dimensions for min and max coordinates!"; +> fi; +> +> if (N = 1) +> then return [seq([i], i=cmin[1]..cmax[1])]; +> elif (N = 2) +> then return [ +> seq( +> seq([i,j], j=cmin[2]..cmax[2]), +> i=cmin[1]..cmax[1]) +> ]; +> elif (N = 3) +> then return [ +> seq( +> seq( +> seq([i,j,k], k=cmin[3]..cmax[3]), +> j=cmin[2]..cmax[2] ), +> i=cmin[1]..cmax[1]) +> ]; +> elif (N = 4) +> then return [ +> seq( +> seq( +> seq( +> seq([i,j,k,l], l=cmin[4]..cmax[4]), +> k=cmin[3]..cmax[3] ), +> j=cmin[2]..cmax[2]), +> i=cmin[1]..cmax[1]) +> ]; +> else +> error "implementation restriction: must have N <= 4, got %1!", N; +> fi; +> end proc; +hypercube_points := proc(cmin::list(integer), cmax::list(integer)) +local N, i, j, k, l; + N := nops(cmin); + if nops(cmax) <> N then error + "must have same number of dimensions for min and max coordinates!" + end if; + if N = 1 then return [seq([i], i = cmin[1] .. cmax[1])] + elif N = 2 then return + [seq(seq([i, j], j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] + elif N = 3 then return [seq( + seq(seq([i, j, k], k = cmin[3] .. cmax[3]), j = cmin[2] .. cmax[2]) + , i = cmin[1] .. cmax[1])] + elif N = 4 then return [seq(seq(seq( + seq([i, j, k, l], l = cmin[4] .. cmax[4]), k = cmin[3] .. cmax[3]), + j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] + else error "implementation restriction: must have N <= 4, got %1!", N + end if +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function truncates a file to 0 length if it exists, or creates +# it at that length if it doesn't exist. +# +# Arguments: +# file_name = (in) The name of the file. +# +> ftruncate := +> proc(file_name::string) +> fopen(file_name, 'WRITE'); +> fclose(%); +> NULL; +> end proc; +ftruncate := + + proc(file_name::string) fopen(file_name, 'WRITE'); fclose(%); NULL end proc + +# interpolate.maple -- compute interpolation formulas/coefficients +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/interpolate.maple,v 1.11 2002/09/02 10:21:02 jthorn Exp $ +> +# +# <<>> +# Lagrange_polynomial_interpolant - compute Lagrange polynomial interpolant +# Hermite_polynomial_interpolant - compute Hermite polynomial interpolant +# coeffs_as_lc_of_data - coefficients of ... (linear combination of data) +# +# print_coeffs__lc_of_data - print C code to compute coefficients +# print_fetch_data - print C code to fetch input array chunk into struct data +# print_store_coeffs - print C code to store struct coeffs "somewhere" +# print_interp_cmpt__lc_of_data - print C code for computation of interpolant +# +# coeff_name - name of coefficient of data at a given [m] coordinate +# data_var_name - name of variable storing data value at a given [m] coordinate +# +> +################################################################################ +> +# +# ***** representation of numbers, data values, etc ***** +# +# We use RATIONAL(p.0,q.0) to denote the rational number p/q. +# +# We use DATA(...) to represent the data values being interpolated at a +# specified [m] coordinate, where the arguments are the [m] coordinates. +# +# We use COEFF(...) to represent the molecule coefficient at a specified +# [m] coordinate, where the arguments are the [m] coordinates. +# +# For example, the usual 1-D centered 2nd order 1st derivative molecule +# would be written +# RATIONAL(-1.0,2.0)*DATA(-1) + RATIONA(1.0,2.0)*DATA(1) +# and its coefficients as +# COEFF(-1) = RATIONAL(-1.0,2.0) +# COEFF(1) = RATIONAL(1.0,2.0) +# +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes a Lagrange polynomial interpolant in any +# number of dimensions. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) c00 + c10*x + c01*y end proc +# coeff_list = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example [c00, c10, c01]. +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# posn_list = A list of positions (each a list of numeric values) where the +# interpolant is to use data, for example hypercube([0,0], [1,1]). +# Any positions may be used; if they're redundant (as in the +# example) the least-squares interpolant is computed. +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Lagrange_polynomial_interpolant := +> proc( +> fn::procedure, coeff_list::list(name), +> coord_list::list(name), posn_list::list(list(numeric)) +> ) +> local posn, data_eqns, coeff_eqns; +> +# coefficients of interpolating polynomial +> data_eqns := { seq( fn(op(posn))='DATA'(op(posn)) , posn=posn_list ) }; +> coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); +> if (has(coeff_eqns, '_t')) +> then error "interpolation coefficients aren't uniquely determined!"; +> end if; +> +# interpolant as a polynomial in the coordinates +> return subs(coeff_eqns, eval(fn))(op(coord_list)); +> end proc; +Lagrange_polynomial_interpolant := proc(fn::procedure, coeff_list::list(name), +coord_list::list(name), posn_list::list(list(numeric))) +local posn, data_eqns, coeff_eqns; + data_eqns := {seq(fn(op(posn)) = 'DATA'(op(posn)), posn = posn_list)}; + coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); + if has(coeff_eqns, '_t') then + error "interpolation coefficients aren't uniquely determined!" + end if; + return subs(coeff_eqns, eval(fn))(op(coord_list)) +end proc + +> +################################################################################ +> +# +# This function computes a Hermite polynomial interpolant in any +# number of dimensions. This is a polynomial which +# * has values which match the given data DATA() at a specified set of +# points, and +# * has derivatives which match the specified finite-difference derivatives +# of the given data DATA() at a specified set of points +# +# For the derivative matching, we actually match all possible products +# of 1st derivatives, i.e. in 2-D we match dx, dy, and dxy, in 3-D we +# match dx, dy, dz, dxy, dxz, dyz, and dxyz, etc etc. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) +# + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 +# + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 +# + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +# + c00 + c10*x + c20*x^2 + c30*x^3 +# end proc; +# coeff_set = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example +# { +# c03, c13, c23, c33, +# c02, c12, c22, c32, +# c01, c11, c21, c31, +# c00, c10, c20, c30 +# } +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# deriv_set = A set of equations of the form +# {coords} = proc +# giving the derivatives which are to be matched, and the +# procedures to compute their finite-difference approximations. +# Each procedure should take N_dims integer arguments specifying +# an evaluation point, and return a suitable linear combination +# of the DATA() for the derivative at that point. For example +# { +# {x} = proc(i::integer, j::integer) +# - 1/2*DATA(i-1,j) + 1/2*DATA(i+1,j) +# end proc +# , +# {y} = proc(i::integer, j::integer) +# - 1/2*DATA(i,j-1) + 1/2*DATA(i,j+1) +# end proc +# , +# {x,y} = proc(i::integer, j::integer) +# - 1/4*DATA(i-1,j+1) + 1/4*DATA(i+1,j+1) +# + 1/4*DATA(i-1,j-1) - 1/4*DATA(i+1,j-1) +# end proc +# } +# fn_posn_set = A set of positions (each a list of numeric values) +# where the interpolant is to match the given data DATA(), +# for example +# {[0,0], [0,1], [1,0], [1,1]} +# deriv_posn_set = A list of positions (each a list of numeric values) +# where the interpolant is to match the derivatives +# specified by deriv_set , for example +# {[0,0], [0,1], [1,0], [1,1]} +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Hermite_polynomial_interpolant := +> proc( +> fn::procedure, +> coeff_set::set(name), +> coord_list::list(name), +> deriv_set::set(set(name) = procedure), +> fn_posn_set::set(list(numeric)), +> deriv_posn_set::set(list(numeric)) +> ) +> local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; +> +> +# +# compute a set of equations +# {fn(posn) = DATA(posn)} +# giving the function values to be matched +# +> fn_eqnset := map( +> # return equation that fn(posn) = DATA(posn) +> proc(posn::list(integer)) +> fn(op(posn)) = 'DATA'(op(posn)); +> end proc +> , +> fn_posn_set +> ); +> +> +# +# compute a set of equations +# { diff(fn,coords)(posn) = DERIV(coords)(posn) } +# giving the derivative values to be matched, where DERIV(coords) +# is a placeholder for the appropriate derivative +# +> map( +> # return set of equations for this particular derivative +> proc(deriv_coords::set(name)) +> local deriv_fn; +> fn(op(coord_list)); +> diff(%, op(deriv_coords)); +> deriv_fn := unapply(%, op(coord_list)); +> map( +> proc(posn::list(integer)) +> deriv_fn(op(posn)) = 'DERIV'(op(deriv_coords))(op(posn)); +> end proc +> , +> deriv_posn_set +> ); +> end proc +> , +> map(lhs, deriv_set) +> ); +> deriv_eqnset := `union`(op(%)); +> +> +# +# solve overall set of equations for coefficients +# in terms of DATA() and DERIV() values +# +> coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); +> if (indets(map(rhs,%)) <> {}) +> then error "no unique solution for coefficients -- %1 eqns for %2 coeffs", +> nops(fn_eqnset union deriv_eqnset), +> nops(coeff_set); +> fi; +> +> +# +# compute a set of substitution equations +# {'DERIV'(coords) = procedure} +# +> subs_eqnset := map( +> proc(eqn::set(name) = procedure) +> 'DERIV'(op(lhs(eqn))) = rhs(eqn); +> end proc +> , +> deriv_set +> ); +> +> +# +# compute the coefficients in terms of the DATA() values +# +> subs(subs_eqnset, coeff_eqns); +> eval(%); +> +# +# compute the interpolant as a polynomial in the coordinates +# +> subs(%, fn(op(coord_list))); +> end proc; +Hermite_polynomial_interpolant := proc(fn::procedure, coeff_set::set(name), +coord_list::list(name), deriv_set::set(set(name) = procedure), +fn_posn_set::set(list(numeric)), deriv_posn_set::set(list(numeric))) +local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; + fn_eqnset := map( + proc(posn::list(integer)) fn(op(posn)) = 'DATA'(op(posn)) end proc, + fn_posn_set); + map(proc(deriv_coords::set(name)) + local deriv_fn; + fn(op(coord_list)); + diff(%, op(deriv_coords)); + deriv_fn := unapply(%, op(coord_list)); + map(proc(posn::list(integer)) + deriv_fn(op(posn)) = + 'DERIV'(op(deriv_coords))(op(posn)) + end proc, deriv_posn_set) + end proc, map(lhs, deriv_set)); + deriv_eqnset := `union`(op(%)); + coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); + if indets(map(rhs, %)) <> {} then error + "no unique solution for coefficients -- %1 eqns for %2 coeffs", + nops(fn_eqnset union deriv_eqnset), nops(coeff_set) + end if; + subs_eqnset := map(proc(eqn::(set(name) = procedure)) + 'DERIV'(op(lhs(eqn))) = rhs(eqn) + end proc, deriv_set); + subs(subs_eqnset, coeff_eqns); + eval(%); + subs(%, fn(op(coord_list))) +end proc + +> +################################################################################ +> +# +# This function takes as input an interpolating polynomial, expresses +# it as a linear combination of the data values, and returns the coefficeints +# of that form. +# +# Arguments: +# interpolant = The interpolating polynomial (an algebraic expression +# in the coordinates and the data values). +# posn_list = The same list of data positions used in the interpolant. +# +# Results: +# This function returns the coefficients, as a list of equations of the +# form COEFF(...) = value , where each value is a polynomial in the +# coordinates. The order of the list matches that of posn_list. +# +> coeffs_as_lc_of_data := +> proc( +> interpolant::algebraic, +> posn_list::list(list(numeric)) +> ) +> local data_list, interpolant_as_lc_of_data; +> +# interpolant as a linear combination of the data values +> data_list := [ seq( 'DATA'(op(posn)) , posn=posn_list ) ]; +> interpolant_as_lc_of_data := collect(interpolant, data_list); +> +# coefficients of the data values in the linear combination +> return map( +> proc(posn::list(numeric)) +> coeff(interpolant_as_lc_of_data, DATA(op(posn))); +> 'COEFF'(op(posn)) = %; +> end proc +> , +> posn_list +> ); +> end proc; +coeffs_as_lc_of_data := proc( +interpolant::algebraic, posn_list::list(list(numeric))) +local data_list, interpolant_as_lc_of_data; + data_list := [seq('DATA'(op(posn)), posn = posn_list)]; + interpolant_as_lc_of_data := collect(interpolant, data_list); + return map(proc(posn::list(numeric)) + coeff(interpolant_as_lc_of_data, DATA(op(posn))); + 'COEFF'(op(posn)) = % + end proc, posn_list) +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function prints C expressions for the coefficients of an +# interpolating polynomial. (The polynomial is expressed as linear +# combinations of the data values with coefficients which are +# RATIONAL(p,q) calls.) +# +# Arguments: +# coeff_list = A list of the coefficients, as returned from +# coeffs_as_lc_of_data() . +# coeff_name_prefix = A prefix string for the coefficient names. +# temp_name_type = The C type to be used for Maple-introduced temporary +# names, eg. "double". +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_coeffs__lc_of_data := +> proc( coeff_list::list(specfunc(numeric,COEFF) = algebraic), +> coeff_name_prefix::string, +> temp_name_type::string, +> file_name::string ) +> global `codegen/C/function/informed`; +> local coeff_list2, cmpt_list, temp_name_list; +> +# convert LHS of each equation from a COEFF() call (eg COEFF(-1,+1)) +# to a Maple/C variable name (eg coeff_I_m1_p1) +> coeff_list2 := map( +> proc(coeff_eqn::specfunc(numeric,COEFF) = algebraic) +> local posn; +> posn := [op(lhs(coeff_eqn))]; +> coeff_name(posn,coeff_name_prefix); +> convert(%, name); # codegen[C] wants LHS +> # to be an actual Maple *name* +> % = fix_rationals(rhs(coeff_eqn)); +> end proc +> , +> coeff_list +> ); +> +# +# generate the C code +# +> +# tell codegen[C] not to warn about unknown RATIONAL() and DATA() "fn calls" +# via undocumented :( global table +> `codegen/C/function/informed`['RATIONAL'] := true; +> `codegen/C/function/informed`['DATA'] := true; +> +> ftruncate(file_name); +> +# optimized computation sequence for all the coefficients +# (may use local variables t0,t1,t2,...) +> cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; +> +# list of the t0,t1,t2,... local variables +> temp_name_list := nonmatching_names(map(lhs,cmpt_list), coeff_name_prefix); +> +# declare the t0,t1,t2,... local variables (if there are any) +> if (nops(temp_name_list) > 0) +> then print_name_list_dcl(%, temp_name_type, file_name); +> fi; +> +# now print the optimized computation sequence +> codegen[C](cmpt_list, filename=file_name); +> +> fclose(file_name); +> +> NULL; +> end proc; +print_coeffs__lc_of_data := proc( +coeff_list::list(specfunc(numeric, COEFF) = algebraic), +coeff_name_prefix::string, temp_name_type::string, file_name::string) +local coeff_list2, cmpt_list, temp_name_list; +global `codegen/C/function/informed`; + coeff_list2 := map(proc( + coeff_eqn::(specfunc(numeric, COEFF) = algebraic)) + local posn; + posn := [op(lhs(coeff_eqn))]; + coeff_name(posn, coeff_name_prefix); + convert(%, name); + % = fix_rationals(rhs(coeff_eqn)) + end proc, coeff_list); + `codegen/C/function/informed`['RATIONAL'] := true; + `codegen/C/function/informed`['DATA'] := true; + ftruncate(file_name); + cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; + temp_name_list := + nonmatching_names(map(lhs, cmpt_list), coeff_name_prefix); + if 0 < nops(temp_name_list) then + print_name_list_dcl(%, temp_name_type, file_name) + end if; + codegen[C](cmpt_list, filename = file_name); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C expression to assign the data-value +# variables, eg +# data->data_m1_p1 = DATA(-1,1); +# +# Arguments: +# posn_list = The same list of positions as was used to compute the +# interpolating polynomial. +# data_var_name_prefix = A prefix string for the data variable names. +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_fetch_data := +> proc( +> posn_list::list(list(numeric)), +> data_var_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> map( +> proc(posn::list(numeric)) +> fprintf(file_name, +> "%s = %a;\n", +> data_var_name(posn,data_var_name_prefix), +> DATA(op(posn))); +> end proc +> , +> posn_list +> ); +> fclose(file_name); +> +> NULL; +> end proc; +print_fetch_data := proc(posn_list::list(list(numeric)), +data_var_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + fprintf(file_name, "%s = %a;\n", + data_var_name(posn, data_var_name_prefix), DATA(op(posn))) + end proc, posn_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C expression to store the interpolation +# coefficients in COEFF(...) expressions, eg +# COEFF(1,-1) = factor * coeffs->coeff_p1_m1; +# +# Arguments: +# posn_list = The list of positions in the molecule. +# coeff_name_prefix = A prefix string for the coefficient names, +# eg "factor * coeffs->coeff_" +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_store_coeffs := +> proc( +> posn_list::list(list(numeric)), +> coeff_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> map( +> proc(posn::list(numeric)) +> fprintf(file_name, +> "%a = %s;\n", +> 'COEFF'(op(posn)), +> coeff_name(posn,coeff_name_prefix)); +> end proc +> , +> posn_list +> ); +> fclose(file_name); +> +> NULL; +> end proc; +print_store_coeffs := proc(posn_list::list(list(numeric)), +coeff_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + fprintf(file_name, "%a = %s;\n", 'COEFF'(op(posn)), + coeff_name(posn, coeff_name_prefix)) + end proc, posn_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a C expression to evaluate a molecule, i.e. +# to compute the molecule as a linear combination of the data values. +# +# Arguments: +# posn_list = The list of positions in the molecule. +# coeff_name_prefix = A prefix string for the coefficient names. +# data_var_name_prefix = A prefix string for the data variable names. +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_evaluate_molecule := +> proc( +> posn_list::list(list(numeric)), +> coeff_name_prefix::string, +> data_var_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> +# list of "coeff*data_var" terms +> map( +> proc(posn::list(numeric)) +> sprintf("%s*%s", +> coeff_name(posn,coeff_name_prefix), +> data_var_name(posn,data_var_name_prefix)); +> end proc +> , +> posn_list +> ); +> +> ListTools[Join](%, "\n + "); +> cat(op(%)); +> fprintf(file_name, " %s;\n", %); +> +> fclose(file_name); +> +> NULL; +> end proc; +print_evaluate_molecule := proc(posn_list::list(list(numeric)), +coeff_name_prefix::string, data_var_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + sprintf("%s*%s", coeff_name(posn, coeff_name_prefix), + data_var_name(posn, data_var_name_prefix)) + end proc, posn_list); + ListTools[Join](%, "\n + "); + cat(op(%)); + fprintf(file_name, " %s;\n", %); + fclose(file_name); + NULL +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes the name of the coefficient of the data at a +# given [m] position, i.e. it encapsulates our naming convention for this. +# +# Arguments: +# posn = (in) The [m] coordinates. +# name_prefix = A prefix string for the coefficient name. +# +# Results: +# The function returns the coefficient, as a Maple string. +# +> coeff_name := +> proc(posn::list(numeric), name_prefix::string) +> cat(name_prefix, sprint_numeric_list(posn)); +> end proc; +coeff_name := proc(posn::list(numeric), name_prefix::string) + cat(name_prefix, sprint_numeric_list(posn)) +end proc + +> +################################################################################ +> +# +# This function computes the name of the variable in which the C code +# will store the input data at a given [m] position, i.e. it encapsulates +# our naming convention for this. +# +# Arguments: +# posn = (in) The [m] coordinates. +# name_prefix = A prefix string for the variable name. +# +# Results: +# The function returns the variable name, as a Maple string. +# +> data_var_name := +> proc(posn::list(numeric), name_prefix::string) +> cat(name_prefix, sprint_numeric_list(posn)); +> end proc; +data_var_name := proc(posn::list(numeric), name_prefix::string) + cat(name_prefix, sprint_numeric_list(posn)) +end proc + +# Maple code to compute lists of point positions in hypercube-shaped molecules +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/common/cube_posns.maple,v 1.3 2002/08/20 16:56:41 jthorn Exp $ +> +################################################################################ +> +# +# 1D interpolation points +# +> posn_list_1d_size2 := hypercube_points([ 0], [+1]); + posn_list_1d_size2 := [[0], [1]] + +> posn_list_1d_size3 := hypercube_points([-1], [+1]); + posn_list_1d_size3 := [[-1], [0], [1]] + +> posn_list_1d_size4 := hypercube_points([-1], [+2]); + posn_list_1d_size4 := [[-1], [0], [1], [2]] + +> posn_list_1d_size5 := hypercube_points([-2], [+2]); + posn_list_1d_size5 := [[-2], [-1], [0], [1], [2]] + +> posn_list_1d_size6 := hypercube_points([-2], [+3]); + posn_list_1d_size6 := [[-2], [-1], [0], [1], [2], [3]] + +> posn_list_1d_size7 := hypercube_points([-3], [+3]); + posn_list_1d_size7 := [[-3], [-2], [-1], [0], [1], [2], [3]] + +> +################################################################################ +> +# +# 2D interpolation points (Fortran ordering) +# +> posn_list_2d_size2 := map(ListTools[Reverse], +> hypercube_points([ 0, 0], [+1,+1])); + posn_list_2d_size2 := [[0, 0], [1, 0], [0, 1], [1, 1]] + +> posn_list_2d_size3 := map(ListTools[Reverse], +> hypercube_points([-1,-1], [+1,+1])); +posn_list_2d_size3 := [[-1, -1], [0, -1], [1, -1], [-1, 0], [0, 0], [1, 0], + + [-1, 1], [0, 1], [1, 1]] + +> posn_list_2d_size4 := map(ListTools[Reverse], +> hypercube_points([-1,-1], [+2,+2])); +posn_list_2d_size4 := [[-1, -1], [0, -1], [1, -1], [2, -1], [-1, 0], [0, 0], + + [1, 0], [2, 0], [-1, 1], [0, 1], [1, 1], [2, 1], [-1, 2], [0, 2], [1, 2], + + [2, 2]] + +> posn_list_2d_size5 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+2,+2])); +posn_list_2d_size5 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [-2, -1], + + [-1, -1], [0, -1], [1, -1], [2, -1], [-2, 0], [-1, 0], [0, 0], [1, 0], + + [2, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], [-2, 2], [-1, 2], [0, 2], + + [1, 2], [2, 2]] + +> posn_list_2d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+3,+3])); +posn_list_2d_size6 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [3, -2], + + [-2, -1], [-1, -1], [0, -1], [1, -1], [2, -1], [3, -1], [-2, 0], [-1, 0], + + [0, 0], [1, 0], [2, 0], [3, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], + + [3, 1], [-2, 2], [-1, 2], [0, 2], [1, 2], [2, 2], [3, 2], [-2, 3], [-1, 3], + + [0, 3], [1, 3], [2, 3], [3, 3]] + +> +################################################################################ +> +# +# 3D interpolation points (Fortran ordering) +# +> posn_list_3d_size2 := map(ListTools[Reverse], +> hypercube_points([ 0, 0, 0], [+1,+1,+1])); +posn_list_3d_size2 := [[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], + + [1, 0, 1], [0, 1, 1], [1, 1, 1]] + +> posn_list_3d_size3 := map(ListTools[Reverse], +> hypercube_points([-1,-1,-1], [+1,+1,+1])); +posn_list_3d_size3 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [-1, 0, -1], + + [0, 0, -1], [1, 0, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], [-1, -1, 0], + + [0, -1, 0], [1, -1, 0], [-1, 0, 0], [0, 0, 0], [1, 0, 0], [-1, 1, 0], + + [0, 1, 0], [1, 1, 0], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [-1, 0, 1], + + [0, 0, 1], [1, 0, 1], [-1, 1, 1], [0, 1, 1], [1, 1, 1]] + +> posn_list_3d_size4 := map(ListTools[Reverse], +> hypercube_points([-1,-1,-1], [+2,+2,+2])); +posn_list_3d_size4 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [2, -1, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [-1, 1, -1], [0, 1, -1], + + [1, 1, -1], [2, 1, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-1, 0, 0], [0, 0, 0], + + [1, 0, 0], [2, 0, 0], [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [-1, -1, 1], [0, -1, 1], + + [1, -1, 1], [2, -1, 1], [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [-1, 2, 1], [0, 2, 1], + + [1, 2, 1], [2, 2, 1], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-1, 1, 2], [0, 1, 2], + + [1, 1, 2], [2, 1, 2], [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2]] + +> posn_list_3d_size5 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+2,+2,+2])); +posn_list_3d_size5 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], [1, -1, -2], + + [2, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], [1, 0, -2], [2, 0, -2], + + [-2, 1, -2], [-1, 1, -2], [0, 1, -2], [1, 1, -2], [2, 1, -2], [-2, 2, -2], + + [-1, 2, -2], [0, 2, -2], [1, 2, -2], [2, 2, -2], [-2, -2, -1], [-1, -2, -1], + + [0, -2, -1], [1, -2, -1], [2, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [-2, 0, -1], [-1, 0, -1], [0, 0, -1], + + [1, 0, -1], [2, 0, -1], [-2, 1, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], + + [2, 1, -1], [-2, 2, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], + + [-2, -2, 0], [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-2, 0, 0], [-1, 0, 0], + + [0, 0, 0], [1, 0, 0], [2, 0, 0], [-2, 1, 0], [-1, 1, 0], [0, 1, 0], + + [1, 1, 0], [2, 1, 0], [-2, 2, 0], [-1, 2, 0], [0, 2, 0], [1, 2, 0], + + [2, 2, 0], [-2, -2, 1], [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], + + [-2, -1, 1], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [-2, 1, 1], [-1, 1, 1], + + [0, 1, 1], [1, 1, 1], [2, 1, 1], [-2, 2, 1], [-1, 2, 1], [0, 2, 1], + + [1, 2, 1], [2, 2, 1], [-2, -2, 2], [-1, -2, 2], [0, -2, 2], [1, -2, 2], + + [2, -2, 2], [-2, -1, 2], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], + + [-2, 0, 2], [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [-2, 2, 2], [-1, 2, 2], + + [0, 2, 2], [1, 2, 2], [2, 2, 2]] + +> posn_list_3d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+3,+3,+3])); +posn_list_3d_size6 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [3, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], + + [1, -1, -2], [2, -1, -2], [3, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], + + [1, 0, -2], [2, 0, -2], [3, 0, -2], [-2, 1, -2], [-1, 1, -2], [0, 1, -2], + + [1, 1, -2], [2, 1, -2], [3, 1, -2], [-2, 2, -2], [-1, 2, -2], [0, 2, -2], + + [1, 2, -2], [2, 2, -2], [3, 2, -2], [-2, 3, -2], [-1, 3, -2], [0, 3, -2], + + [1, 3, -2], [2, 3, -2], [3, 3, -2], [-2, -2, -1], [-1, -2, -1], [0, -2, -1], + + [1, -2, -1], [2, -2, -1], [3, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [3, -1, -1], [-2, 0, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [3, 0, -1], [-2, 1, -1], + + [-1, 1, -1], [0, 1, -1], [1, 1, -1], [2, 1, -1], [3, 1, -1], [-2, 2, -1], + + [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], [3, 2, -1], [-2, 3, -1], + + [-1, 3, -1], [0, 3, -1], [1, 3, -1], [2, 3, -1], [3, 3, -1], [-2, -2, 0], + + [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [3, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [3, -1, 0], [-2, 0, 0], + + [-1, 0, 0], [0, 0, 0], [1, 0, 0], [2, 0, 0], [3, 0, 0], [-2, 1, 0], + + [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [3, 1, 0], [-2, 2, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [3, 2, 0], [-2, 3, 0], + + [-1, 3, 0], [0, 3, 0], [1, 3, 0], [2, 3, 0], [3, 3, 0], [-2, -2, 1], + + [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], [3, -2, 1], [-2, -1, 1], + + [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [3, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [3, 0, 1], [-2, 1, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [3, 1, 1], [-2, 2, 1], + + [-1, 2, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [3, 2, 1], [-2, 3, 1], + + [-1, 3, 1], [0, 3, 1], [1, 3, 1], [2, 3, 1], [3, 3, 1], [-2, -2, 2], + + [-1, -2, 2], [0, -2, 2], [1, -2, 2], [2, -2, 2], [3, -2, 2], [-2, -1, 2], + + [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], [3, -1, 2], [-2, 0, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [3, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [3, 1, 2], [-2, 2, 2], + + [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2], [3, 2, 2], [-2, 3, 2], + + [-1, 3, 2], [0, 3, 2], [1, 3, 2], [2, 3, 2], [3, 3, 2], [-2, -2, 3], + + [-1, -2, 3], [0, -2, 3], [1, -2, 3], [2, -2, 3], [3, -2, 3], [-2, -1, 3], + + [-1, -1, 3], [0, -1, 3], [1, -1, 3], [2, -1, 3], [3, -1, 3], [-2, 0, 3], + + [-1, 0, 3], [0, 0, 3], [1, 0, 3], [2, 0, 3], [3, 0, 3], [-2, 1, 3], + + [-1, 1, 3], [0, 1, 3], [1, 1, 3], [2, 1, 3], [3, 1, 3], [-2, 2, 3], + + [-1, 2, 3], [0, 2, 3], [1, 2, 3], [2, 2, 3], [3, 2, 3], [-2, 3, 3], + + [-1, 3, 3], [0, 3, 3], [1, 3, 3], [2, 3, 3], [3, 3, 3]] + +# Maple code to define Lagrange interpolating functions/coords/coeffs +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple,v 1.3 2002/09/02 10:22:49 jthorn Exp $ +> +################################################################################ +> +# +# 1-D interpolating functions +# +> +> fn_1d_order1 := +> proc(x) +> + c0 + c1*x +> end proc; + fn_1d_order1 := proc(x) c0 + c1*x end proc + +> +> fn_1d_order2 := +> proc(x) +> + c0 + c1*x + c2*x^2 +> end proc; + fn_1d_order2 := proc(x) c0 + c1*x + c2*x^2 end proc + +> +> fn_1d_order3 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 +> end proc; + fn_1d_order3 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 end proc + +> +> fn_1d_order4 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 +> end; + fn_1d_order4 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 end proc + +> +> fn_1d_order5 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 +> end; + fn_1d_order5 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 end proc + +> +> fn_1d_order6 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 +> end; +fn_1d_order6 := + + proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 end proc + +> +######################################## +> +# coordinates for 1-D interpolating functions +> coords_list_1d := [x]; + coords_list_1d := [x] + +> +######################################## +> +# +# coefficients in 1-D interpolating functions +# +> +> coeffs_list_1d_order1 := [c0, c1]; + coeffs_list_1d_order1 := [c0, c1] + +> coeffs_list_1d_order2 := [c0, c1, c2]; + coeffs_list_1d_order2 := [c0, c1, c2] + +> coeffs_list_1d_order3 := [c0, c1, c2, c3]; + coeffs_list_1d_order3 := [c0, c1, c2, c3] + +> coeffs_list_1d_order4 := [c0, c1, c2, c3, c4]; + coeffs_list_1d_order4 := [c0, c1, c2, c3, c4] + +> coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5]; + coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5] + +> coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6]; + coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6] + +> +################################################################################ +> +# +# 2-D interpolating functions (tensor-product) +# +> +> fn_2d_order1 := +> proc(x,y) +> + c01*y + c11*x*y +> + c00 + c10*x +> end proc; + fn_2d_order1 := proc(x, y) c01*y + c11*x*y + c00 + c10*x end proc + +> +> fn_2d_order2 := +> proc(x,y) +> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 +> + c01*y + c11*x*y + c21*x^2*y +> + c00 + c10*x + c20*x^2 +> end proc; +fn_2d_order2 := proc(x, y) + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c01*y + c11*x*y + c21*x^2*y + c00 + + c10*x + c20*x^2 +end proc + +> +> fn_2d_order3 := +> proc(x,y) +> + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 +> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 +> + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +> + c00 + c10*x + c20*x^2 + c30*x^3 +> end proc; +fn_2d_order3 := proc(x, y) + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c02*y^2 + c12*x*y^2 + + c22*x^2*y^2 + c32*x^3*y^2 + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + + c00 + c10*x + c20*x^2 + c30*x^3 +end proc + +> +> fn_2d_order4 := +> proc(x,y) +> + c04*y^4 + c14*x*y^4 + c24*x^2*y^4 + c34*x^3*y^4 + c44*x^4*y^4 +> + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c43*x^4*y^3 +> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 + c42*x^4*y^2 +> + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + c41*x^4*y +> + c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 +> end; +fn_2d_order4 := proc(x, y) + c34*x^3*y^4 + c01*y + c10*x + c02*y^2 + c20*x^2 + c03*y^3 + c30*x^3 + + c04*y^4 + c40*x^4 + c11*x*y + c12*x*y^2 + c22*x^2*y^2 + c21*x^2*y + + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c32*x^3*y^2 + c31*x^3*y + + c14*x*y^4 + c24*x^2*y^4 + c44*x^4*y^4 + c00 + c43*x^4*y^3 + + c42*x^4*y^2 + c41*x^4*y +end proc + +> +######################################## +> +# coordinates for 2-D interpolating functions +> coords_list_2d := [x,y]; + coords_list_2d := [x, y] + +> +######################################## +> +# +# coefficients in 2-D interpolating functions (tensor-product) +# +> +> coeffs_list_2d_order1 := [ +> c01, c11, +> c00, c10 +> ]; + coeffs_list_2d_order1 := [c01, c11, c00, c10] + +> coeffs_list_2d_order2 := [ +> c02, c12, c22, +> c01, c11, c21, +> c00, c10, c20 +> ]; + coeffs_list_2d_order2 := [c02, c12, c22, c01, c11, c21, c00, c10, c20] + +> coeffs_list_2d_order3 := [ +> c03, c13, c23, c33, +> c02, c12, c22, c23, +> c01, c11, c21, c13, +> c00, c10, c20, c30 +> ]; +coeffs_list_2d_order3 := [c03, c13, c23, c33, c02, c12, c22, c23, c01, c11, c21, + + c13, c00, c10, c20, c30] + +> coeffs_list_2d_order4 := [ +> c04, c14, c24, c34, c44, +> c03, c13, c23, c33, c43, +> c02, c12, c22, c32, c42, +> c01, c11, c21, c31, c41, +> c00, c10, c20, c30, c40 +> ]; +coeffs_list_2d_order4 := [c04, c14, c24, c34, c44, c03, c13, c23, c33, c43, c02, + + c12, c22, c32, c42, c01, c11, c21, c31, c41, c00, c10, c20, c30, c40] + +> +################################################################################ +> +# +# 3-D interpolating functions (tensor-product) +# +> +> fn_3d_order1 := +> proc(x,y,z) +# z^1 ------------------- +> + c011 *y*z + c111*x*y*z +> + c001 *z + c101*x *z +# z^0 ------------------- +> + c010 *y + c110*x*y +> + c000 + c100*x +> end proc; +fn_3d_order1 := proc(x, y, z) + c011*y*z + c111*x*y*z + c001*z + c101*x*z + c010*y + c110*x*y + c000 + + c100*x +end proc + +> +> fn_3d_order2 := +> proc(x,y,z) +# z^2 -------------------------------------------------- +> + c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 +> + c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 +> + c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 +# z -------------------------------------------------- +> + c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z +> + c011 *y *z + c111*x *y *z + c211*x^2*y *z +> + c001 *z + c101*x *z + c201*x^2 *z +# z^0 ------------------------------------------------ +> + c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 +> + c010 *y + c110*x *y + c210*x^2*y +> + c000 + c100*x + c200*x^2 +> end proc; +fn_3d_order2 := proc(x, y, z) + c111*x*y*z + c122*x*y^2*z^2 + c222*x^2*y^2*z^2 + c112*x*y*z^2 + + c212*x^2*y*z^2 + c121*x*y^2*z + c221*x^2*y^2*z + c211*x^2*y*z + + c011*y*z + c101*x*z + c110*x*y + c022*y^2*z^2 + c012*y*z^2 + + c102*x*z^2 + c202*x^2*z^2 + c021*y^2*z + c201*x^2*z + c120*x*y^2 + + c220*x^2*y^2 + c210*x^2*y + c001*z + c010*y + c000 + c100*x + + c002*z^2 + c020*y^2 + c200*x^2 +end proc + +> +> fn_3d_order3 := +> proc(x,y,z) +# z^3 --------------------------------------------------------------------- +> + c033 *y^3*z^3 + c133*x *y^3*z^3 + c233*x^2*y^3*z^3 + c333*x^3*y^3*z^3 +> + c023 *y^2*z^3 + c123*x *y^2*z^3 + c223*x^2*y^2*z^3 + c323*x^3*y^2*z^3 +> + c013 *y *z^3 + c113*x *y *z^3 + c213*x^2*y *z^3 + c313*x^3*y *z^3 +> + c003 *z^3 + c103*x *z^3 + c203*x^2 *z^3 + c303*x^3 *z^3 +# z^2 --------------------------------------------------------------------- +> + c032 *y^3*z^2 + c132*x *y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 +> + c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 + c322*x^3*y^2*z^2 +> + c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 + c312*x^3*y *z^2 +> + c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 + c302*x^3 *z^2 +# z --------------------------------------------------------------------- +> + c031 *y^3*z + c131*x *y^3*z + c231*x^2*y^3*z + c331*x^3*y^3*z +> + c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z + c321*x^3*y^2*z +> + c011 *y *z + c111*x *y *z + c211*x^2*y *z + c311*x^3*y *z +> + c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z +# z^0 --------------------------------------------------------------------- +> + c030 *y^3 + c130*x *y^3 + c230*x^2*y^3 + c330*x^3*y^3 +> + c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 + c320*x^3*y^2 +> + c010 *y + c110*x *y + c210*x^2*y + c310*x^3*y +> + c000 + c100*x + c200*x^2 + c300*x^3 +> end proc; +fn_3d_order3 := proc(x, y, z) + c330*x^3*y^3 + c031*y^3*z + c103*x*z^3 + c111*x*y*z + c122*x*y^2*z^2 + + c222*x^2*y^2*z^2 + c112*x*y*z^2 + c212*x^2*y*z^2 + c121*x*y^2*z + + c221*x^2*y^2*z + c211*x^2*y*z + c133*x*y^3*z^3 + c233*x^2*y^3*z^3 + + c333*x^3*y^3*z^3 + c123*x*y^2*z^3 + c223*x^2*y^2*z^3 + + c323*x^3*y^2*z^3 + c113*x*y*z^3 + c213*x^2*y*z^3 + c313*x^3*y*z^3 + + c132*x*y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 + + c322*x^3*y^2*z^2 + c312*x^3*y*z^2 + c131*x*y^3*z + c231*x^2*y^3*z + + c331*x^3*y^3*z + c321*x^3*y^2*z + c311*x^3*y*z + c011*y*z + c101*x*z + + c110*x*y + c022*y^2*z^2 + c012*y*z^2 + c102*x*z^2 + c202*x^2*z^2 + + c021*y^2*z + c201*x^2*z + c120*x*y^2 + c220*x^2*y^2 + c210*x^2*y + + c033*y^3*z^3 + c023*y^2*z^3 + c013*y*z^3 + c203*x^2*z^3 + + c303*x^3*z^3 + c032*y^3*z^2 + c302*x^3*z^2 + c301*x^3*z + c130*x*y^3 + + c230*x^2*y^3 + c320*x^3*y^2 + c310*x^3*y + c001*z + c010*y + c000 + + c100*x + c002*z^2 + c020*y^2 + c200*x^2 + c003*z^3 + c030*y^3 + + c300*x^3 +end proc + +> +> fn_3d_order4 := +> proc(x,y,z) +# z^4 ---------------------------------------------------------------------------------------- +> + c044 *y^4*z^4 + c144*x *y^4*z^4 + c244*x^2*y^4*z^4 + c344*x^3*y^4*z^4 + c444*x^4*y^4*z^4 +> + c034 *y^3*z^4 + c134*x *y^3*z^4 + c234*x^2*y^3*z^4 + c334*x^3*y^3*z^4 + c434*x^4*y^3*z^4 +> + c024 *y^2*z^4 + c124*x *y^2*z^4 + c224*x^2*y^2*z^4 + c324*x^3*y^2*z^4 + c424*x^4*y^2*z^4 +> + c014 *y *z^4 + c114*x *y *z^4 + c214*x^2*y *z^4 + c314*x^3*y *z^4 + c414*x^4*y *z^4 +> + c004 *z^4 + c104*x *z^4 + c204*x^2 *z^4 + c304*x^3 *z^4 + c404*x^4 *z^4 +# z^3 ---------------------------------------------------------------------------------------- +> + c043 *y^4*z^3 + c143*x *y^4*z^3 + c243*x^2*y^4*z^3 + c343*x^3*y^4*z^3 + c443*x^4*y^4*z^3 +> + c033 *y^3*z^3 + c133*x *y^3*z^3 + c233*x^2*y^3*z^3 + c333*x^3*y^3*z^3 + c433*x^4*y^3*z^3 +> + c023 *y^2*z^3 + c123*x *y^2*z^3 + c223*x^2*y^2*z^3 + c323*x^3*y^2*z^3 + c423*x^4*y^2*z^3 +> + c013 *y *z^3 + c113*x *y *z^3 + c213*x^2*y *z^3 + c313*x^3*y *z^3 + c413*x^4*y *z^3 +> + c003 *z^3 + c103*x *z^3 + c203*x^2 *z^3 + c303*x^3 *z^3 + c403*x^4 *z^3 +# z^2 ---------------------------------------------------------------------------------------- +> + c042 *y^4*z^2 + c142*x *y^4*z^2 + c242*x^2*y^4*z^2 + c342*x^3*y^4*z^2 + c442*x^4*y^4*z^2 +> + c032 *y^3*z^2 + c132*x *y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 + c432*x^4*y^3*z^2 +> + c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 + c322*x^3*y^2*z^2 + c422*x^4*y^2*z^2 +> + c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 + c312*x^3*y *z^2 + c412*x^4*y *z^2 +> + c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 + c302*x^3 *z^2 + c402*x^4 *z^2 +# z ---------------------------------------------------------------------------------------- +> + c041 *y^4*z + c141*x *y^4*z + c241*x^2*y^4*z + c341*x^3*y^4*z + c441*x^4*y^4*z +> + c031 *y^3*z + c131*x *y^3*z + c231*x^2*y^3*z + c331*x^3*y^3*z + c431*x^4*y^3*z +> + c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z + c321*x^3*y^2*z + c421*x^4*y^2*z +> + c011 *y *z + c111*x *y *z + c211*x^2*y *z + c311*x^3*y *z + c411*x^4*y *z +> + c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z + c401*x^4 *z +# z^0 ---------------------------------------------------------------------------------------- +> + c040 *y^4 + c140*x *y^4 + c240*x^2*y^4 + c340*x^3*y^4 + c440*x^4*y^4 +> + c030 *y^3 + c130*x *y^3 + c230*x^2*y^3 + c330*x^3*y^3 + c430*x^4*y^3 +> + c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 + c320*x^3*y^2 + c420*x^4*y^2 +> + c010 *y + c110*x *y + c210*x^2*y + c310*x^3*y + c410*x^4*y +> + c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 +> end; +fn_3d_order4 := proc(x, y, z) + c104*x*z^4 + c330*x^3*y^3 + c042*y^4*z^2 + c031*y^3*z + c103*x*z^3 + + c304*x^3*z^4 + c024*y^2*z^4 + c111*x*y*z + c122*x*y^2*z^2 + + c222*x^2*y^2*z^2 + c112*x*y*z^2 + c212*x^2*y*z^2 + c121*x*y^2*z + + c221*x^2*y^2*z + c211*x^2*y*z + c133*x*y^3*z^3 + c233*x^2*y^3*z^3 + + c333*x^3*y^3*z^3 + c123*x*y^2*z^3 + c223*x^2*y^2*z^3 + + c323*x^3*y^2*z^3 + c113*x*y*z^3 + c213*x^2*y*z^3 + c313*x^3*y*z^3 + + c132*x*y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 + + c322*x^3*y^2*z^2 + c312*x^3*y*z^2 + c131*x*y^3*z + c231*x^2*y^3*z + + c331*x^3*y^3*z + c321*x^3*y^2*z + c311*x^3*y*z + c144*x*y^4*z^4 + + c244*x^2*y^4*z^4 + c344*x^3*y^4*z^4 + c444*x^4*y^4*z^4 + + c134*x*y^3*z^4 + c234*x^2*y^3*z^4 + c334*x^3*y^3*z^4 + + c434*x^4*y^3*z^4 + c124*x*y^2*z^4 + c224*x^2*y^2*z^4 + + c324*x^3*y^2*z^4 + c424*x^4*y^2*z^4 + c114*x*y*z^4 + c214*x^2*y*z^4 + + c314*x^3*y*z^4 + c414*x^4*y*z^4 + c143*x*y^4*z^3 + c243*x^2*y^4*z^3 + + c343*x^3*y^4*z^3 + c443*x^4*y^4*z^3 + c433*x^4*y^3*z^3 + + c423*x^4*y^2*z^3 + c413*x^4*y*z^3 + c142*x*y^4*z^2 + + c242*x^2*y^4*z^2 + c011*y*z + c101*x*z + c110*x*y + c022*y^2*z^2 + + c012*y*z^2 + c102*x*z^2 + c202*x^2*z^2 + c021*y^2*z + c201*x^2*z + + c120*x*y^2 + c220*x^2*y^2 + c210*x^2*y + c033*y^3*z^3 + c023*y^2*z^3 + + c013*y*z^3 + c203*x^2*z^3 + c303*x^3*z^3 + c032*y^3*z^2 + + c302*x^3*z^2 + c301*x^3*z + c130*x*y^3 + c230*x^2*y^3 + c320*x^3*y^2 + + c310*x^3*y + c001*z + c010*y + c000 + c100*x + c002*z^2 + c020*y^2 + + c200*x^2 + c003*z^3 + c030*y^3 + c300*x^3 + c004*z^4 + c044*y^4*z^4 + + c034*y^3*z^4 + c014*y*z^4 + c204*x^2*z^4 + c404*x^4*z^4 + + c043*y^4*z^3 + c403*x^4*z^3 + c402*x^4*z^2 + c041*y^4*z + c401*x^4*z + + c140*x*y^4 + c240*x^2*y^4 + c340*x^3*y^4 + c440*x^4*y^4 + + c430*x^4*y^3 + c420*x^4*y^2 + c410*x^4*y + c342*x^3*y^4*z^2 + + c442*x^4*y^4*z^2 + c432*x^4*y^3*z^2 + c422*x^4*y^2*z^2 + + c412*x^4*y*z^2 + c141*x*y^4*z + c241*x^2*y^4*z + c341*x^3*y^4*z + + c441*x^4*y^4*z + c431*x^4*y^3*z + c421*x^4*y^2*z + c411*x^4*y*z + + c040*y^4 + c400*x^4 +end proc + +> +######################################## +> +# coordinates for 3-D interpolating functions +> coords_list_3d := [x,y,z]; + coords_list_3d := [x, y, z] + +> +######################################## +> +# +# coefficients in 3-D interpolating functions +# +> +> coeffs_list_3d_order1 := [ +> # z^1 ----- +> c011, c111, +> c001, c101, +> # z^0 ----- +> c010, c110, +> c000, c100 +> ]; + coeffs_list_3d_order1 := [c011, c111, c001, c101, c010, c110, c000, c100] + +> coeffs_list_3d_order2 := [ +> # z^2 ----------- +> c022, c122, c222, +> c012, c112, c212, +> c002, c102, c202, +> # z^1 ----------- +> c021, c121, c221, +> c011, c111, c211, +> c001, c101, c201, +> # z^0 ----------- +> c020, c120, c220, +> c010, c110, c210, +> c000, c100, c200 +> ]; +coeffs_list_3d_order2 := [c022, c122, c222, c012, c112, c212, c002, c102, c202, + + c021, c121, c221, c011, c111, c211, c001, c101, c201, c020, c120, c220, + + c010, c110, c210, c000, c100, c200] + +> coeffs_list_3d_order3 := [ +> # z^3 ----------------- +> c033, c133, c233, c333, +> c023, c123, c223, c323, +> c013, c113, c213, c313, +> c003, c103, c203, c303, +> # z^2 ----------------- +> c032, c132, c232, c332, +> c022, c122, c222, c322, +> c012, c112, c212, c312, +> c002, c102, c202, c302, +> # z^1 ----------------- +> c031, c131, c231, c331, +> c021, c121, c221, c321, +> c011, c111, c211, c311, +> c001, c101, c201, c301, +> # z^0 ----------------- +> c030, c130, c230, c330, +> c020, c120, c220, c320, +> c010, c110, c210, c310, +> c000, c100, c200, c300 +> ]; +coeffs_list_3d_order3 := [c033, c133, c233, c333, c023, c123, c223, c323, c013, + + c113, c213, c313, c003, c103, c203, c303, c032, c132, c232, c332, c022, + + c122, c222, c322, c012, c112, c212, c312, c002, c102, c202, c302, c031, + + c131, c231, c331, c021, c121, c221, c321, c011, c111, c211, c311, c001, + + c101, c201, c301, c030, c130, c230, c330, c020, c120, c220, c320, c010, + + c110, c210, c310, c000, c100, c200, c300] + +> coeffs_list_3d_order4 := [ +> # z^4 ----------------------- +> c044, c144, c244, c344, c444, +> c034, c134, c234, c334, c434, +> c024, c124, c224, c324, c424, +> c014, c114, c214, c314, c414, +> c004, c104, c204, c304, c404, +> # z^3 ----------------------- +> c043, c143, c243, c343, c443, +> c033, c133, c233, c333, c433, +> c023, c123, c223, c323, c423, +> c013, c113, c213, c313, c413, +> c003, c103, c203, c303, c403, +> # z^2 ----------------------- +> c042, c142, c242, c342, c442, +> c032, c132, c232, c332, c432, +> c022, c122, c222, c322, c422, +> c012, c112, c212, c312, c412, +> c002, c102, c202, c302, c402, +> # z^1 ----------------------- +> c041, c141, c241, c341, c441, +> c031, c131, c231, c331, c431, +> c021, c121, c221, c321, c421, +> c011, c111, c211, c311, c411, +> c001, c101, c201, c301, c401, +> # z^0 ----------------------- +> c040, c140, c240, c340, c440, +> c030, c130, c230, c330, c430, +> c020, c120, c220, c320, c420, +> c010, c110, c210, c310, c410, +> c000, c100, c200, c300, c400 +> ]; +coeffs_list_3d_order4 := [c044, c144, c244, c344, c444, c034, c134, c234, c334, + + c434, c024, c124, c224, c324, c424, c014, c114, c214, c314, c414, c004, + + c104, c204, c304, c404, c043, c143, c243, c343, c443, c033, c133, c233, + + c333, c433, c023, c123, c223, c323, c423, c013, c113, c213, c313, c413, + + c003, c103, c203, c303, c403, c042, c142, c242, c342, c442, c032, c132, + + c232, c332, c432, c022, c122, c222, c322, c422, c012, c112, c212, c312, + + c412, c002, c102, c202, c302, c402, c041, c141, c241, c341, c441, c031, + + c131, c231, c331, c431, c021, c121, c221, c321, c421, c011, c111, c211, + + c311, c411, c001, c101, c201, c301, c401, c040, c140, c240, c340, c440, + + c030, c130, c230, c330, c430, c020, c120, c220, c320, c420, c010, c110, + + c210, c310, c410, c000, c100, c200, c300, c400] + +> +################################################################################ +# 3d.maple -- compute Lagrange interpolation coefficients in 3-D +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/3d.maple,v 1.3 2002/09/02 10:22:48 jthorn Exp $ +> +################################################################################ +> +# +# 3d, cube, order=1, smoothing=0 (size=2) +# +> +# interpolating polynomial +> interp_3d_cube_order1_smooth0 +> := Lagrange_polynomial_interpolant(fn_3d_order1, coeffs_list_3d_order1, +> coords_list_3d, posn_list_3d_size2); +bytes used=1000044, alloc=917336, time=0.04 +bytes used=2000348, alloc=1376004, time=0.09 +interp_3d_cube_order1_smooth0 := + + (DATA(0, 0, 0) - DATA(0, 0, 1) - DATA(0, 1, 0) + DATA(0, 1, 1)) y z + ( + + DATA(1, 1, 1) + DATA(1, 0, 0) - DATA(0, 0, 0) - DATA(1, 0, 1) + + + DATA(0, 0, 1) - DATA(1, 1, 0) + DATA(0, 1, 0) - DATA(0, 1, 1)) x y z + + + (-DATA(0, 0, 0) + DATA(0, 0, 1)) z + + + (-DATA(1, 0, 0) + DATA(0, 0, 0) + DATA(1, 0, 1) - DATA(0, 0, 1)) x z + + + (-DATA(0, 0, 0) + DATA(0, 1, 0)) y + + + (-DATA(1, 0, 0) + DATA(0, 0, 0) + DATA(1, 1, 0) - DATA(0, 1, 0)) x y + + + DATA(0, 0, 0) + (DATA(1, 0, 0) - DATA(0, 0, 0)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_3d_size2); +[COEFF(0, 0, 0) = -x y z + y z + x z - z + x y + 1 - y - x, + + COEFF(1, 0, 0) = x - x z + x y z - x y, + + COEFF(0, 1, 0) = -y z + x y z + y - x y, COEFF(1, 1, 0) = -x y z + x y, + + COEFF(0, 0, 1) = -y z - x z + x y z + z, COEFF(1, 0, 1) = x z - x y z, + + COEFF(0, 1, 1) = y z - x y z, COEFF(1, 1, 1) = x y z] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "3d.coeffs/3d.cube.order1.smooth0/coeffs-I.compute.c"); +bytes used=3003344, alloc=1441528, time=0.17 +> +# d/dx +> simplify( diff(interp_3d_cube_order1_smooth0,x) ); +y z DATA(1, 1, 1) + y z DATA(1, 0, 0) - y z DATA(0, 0, 0) - y z DATA(1, 0, 1) + + + y z DATA(0, 0, 1) - y z DATA(1, 1, 0) + y z DATA(0, 1, 0) + + - y z DATA(0, 1, 1) - z DATA(1, 0, 0) + z DATA(0, 0, 0) + z DATA(1, 0, 1) + + - z DATA(0, 0, 1) - y DATA(1, 0, 0) + y DATA(0, 0, 0) + y DATA(1, 1, 0) + + - y DATA(0, 1, 0) + DATA(1, 0, 0) - DATA(0, 0, 0) + +> coeffs_as_lc_of_data(%, posn_list_3d_size2); +[COEFF(0, 0, 0) = z + y - y z - 1, COEFF(1, 0, 0) = y z - y - z + 1, + + COEFF(0, 1, 0) = -y + y z, COEFF(1, 1, 0) = -y z + y, + + COEFF(0, 0, 1) = y z - z, COEFF(1, 0, 1) = -y z + z, COEFF(0, 1, 1) = -y z, + + COEFF(1, 1, 1) = y z] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "3d.coeffs/3d.cube.order1.smooth0/coeffs-dx.compute.c"); +> +# d/dy +> simplify( diff(interp_3d_cube_order1_smooth0,y) ); +z DATA(0, 0, 0) - z DATA(0, 0, 1) - z DATA(0, 1, 0) + z DATA(0, 1, 1) + + + x z DATA(1, 1, 1) + x z DATA(1, 0, 0) - x z DATA(0, 0, 0) + + - x z DATA(1, 0, 1) + x z DATA(0, 0, 1) - x z DATA(1, 1, 0) + + + x z DATA(0, 1, 0) - x z DATA(0, 1, 1) - DATA(0, 0, 0) + DATA(0, 1, 0) + + - x DATA(1, 0, 0) + x DATA(0, 0, 0) + x DATA(1, 1, 0) - x DATA(0, 1, 0) + +> coeffs_as_lc_of_data(%, posn_list_3d_size2); +[COEFF(0, 0, 0) = -x z + x - 1 + z, COEFF(1, 0, 0) = -x + x z, + + COEFF(0, 1, 0) = -z + 1 - x + x z, COEFF(1, 1, 0) = -x z + x, + + COEFF(0, 0, 1) = x z - z, COEFF(1, 0, 1) = -x z, COEFF(0, 1, 1) = -x z + z, + + COEFF(1, 1, 1) = x z] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "3d.coeffs/3d.cube.order1.smooth0/coeffs-dy.compute.c"); +bytes used=4003500, alloc=1572576, time=0.23 +> +# d/dz +> simplify( diff(interp_3d_cube_order1_smooth0,z) ); +y DATA(0, 0, 0) - y DATA(0, 0, 1) - y DATA(0, 1, 0) + y DATA(0, 1, 1) + + + y x DATA(1, 1, 1) + y x DATA(1, 0, 0) - y x DATA(0, 0, 0) + + - y x DATA(1, 0, 1) + y x DATA(0, 0, 1) - y x DATA(1, 1, 0) + + + y x DATA(0, 1, 0) - y x DATA(0, 1, 1) - DATA(0, 0, 0) + DATA(0, 0, 1) + + - x DATA(1, 0, 0) + x DATA(0, 0, 0) + x DATA(1, 0, 1) - x DATA(0, 0, 1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size2); +[COEFF(0, 0, 0) = -y x + x - 1 + y, COEFF(1, 0, 0) = -x + y x, + + COEFF(0, 1, 0) = -y + y x, COEFF(1, 1, 0) = -y x, + + COEFF(0, 0, 1) = 1 - y + y x - x, COEFF(1, 0, 1) = x - y x, + + COEFF(0, 1, 1) = -y x + y, COEFF(1, 1, 1) = y x] + +> print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", +> "3d.coeffs/3d.cube.order1.smooth0/coeffs-dz.compute.c"); +bytes used=5003684, alloc=1703624, time=0.30 +> +################################################################################ +> +# +# 3d, cube, order=2, smoothing=0 (size=3) +# +> +# interpolating polynomial +> interp_3d_cube_order2_smooth0 +> := Lagrange_polynomial_interpolant(fn_3d_order2, coeffs_list_3d_order2, +> coords_list_3d, posn_list_3d_size3); +bytes used=6004156, alloc=1769148, time=0.36 +bytes used=7004640, alloc=1834672, time=0.40 +bytes used=8004840, alloc=1834672, time=0.46 +bytes used=9005040, alloc=1900196, time=0.52 +bytes used=10005280, alloc=1900196, time=0.57 +bytes used=11005444, alloc=1965720, time=0.63 +bytes used=12007864, alloc=1965720, time=0.69 +bytes used=13008076, alloc=1965720, time=0.75 +bytes used=14008892, alloc=1965720, time=0.82 +bytes used=15010120, alloc=1965720, time=0.88 +bytes used=16010724, alloc=1965720, time=0.95 +bytes used=17011012, alloc=1965720, time=1.01 +interp_3d_cube_order2_smooth0 := DATA(0, 0, 0) + (1/4 DATA(-1, 0, -1) + + - 1/4 DATA(1, 0, -1) - 1/4 DATA(-1, 0, 1) + 1/4 DATA(1, 0, 1)) x z + ( + + - 1/4 DATA(-1, 1, 0) - 1/4 DATA(1, -1, 0) + 1/4 DATA(-1, -1, 0) + + + 1/4 DATA(1, 1, 0)) x y + (- 1/2 DATA(0, 0, -1) + 1/4 DATA(0, 1, -1) + + - 1/2 DATA(0, -1, 0) + 1/4 DATA(0, -1, 1) + DATA(0, 0, 0) + + - 1/2 DATA(0, 1, 0) - 1/2 DATA(0, 0, 1) + 1/4 DATA(0, 1, 1) + + 2 2 + + 1/4 DATA(0, -1, -1)) y z + (1/4 DATA(0, 1, -1) - 1/4 DATA(0, -1, 1) + + + 1/4 DATA(0, 1, 1) + 1/2 DATA(0, -1, 0) - 1/2 DATA(0, 1, 0) + + 2 + - 1/4 DATA(0, -1, -1)) y z + (- 1/4 DATA(-1, 0, -1) + 1/4 DATA(1, 0, -1) + + - 1/4 DATA(-1, 0, 1) + 1/4 DATA(1, 0, 1) + 1/2 DATA(-1, 0, 0) + + 2 + - 1/2 DATA(1, 0, 0)) x z + (- 1/4 DATA(0, 1, -1) - 1/4 DATA(0, -1, 1) + + + 1/4 DATA(0, 1, 1) + 1/4 DATA(0, -1, -1)) y z + (1/4 DATA(-1, 1, 0) + + + 1/4 DATA(1, -1, 0) - 1/2 DATA(0, -1, 0) + 1/4 DATA(-1, -1, 0) + + - 1/2 DATA(0, 1, 0) + 1/4 DATA(1, 1, 0) - 1/2 DATA(-1, 0, 0) + + 2 2 + + DATA(0, 0, 0) - 1/2 DATA(1, 0, 0)) x y + (1/4 DATA(-1, 1, 0) + + - 1/4 DATA(1, -1, 0) + 1/2 DATA(0, -1, 0) - 1/4 DATA(-1, -1, 0) + + 2 + - 1/2 DATA(0, 1, 0) + 1/4 DATA(1, 1, 0)) x y + (- 1/2 DATA(0, 0, -1) + + + 1/4 DATA(-1, 0, -1) + 1/4 DATA(1, 0, -1) + 1/4 DATA(-1, 0, 1) + + - 1/2 DATA(0, 0, 1) + 1/4 DATA(1, 0, 1) - 1/2 DATA(-1, 0, 0) + + 2 2 + + DATA(0, 0, 0) - 1/2 DATA(1, 0, 0)) x z + + + (- 1/2 DATA(-1, 0, 0) + 1/2 DATA(1, 0, 0)) x + + 2 + + (1/2 DATA(0, 0, -1) - DATA(0, 0, 0) + 1/2 DATA(0, 0, 1)) z + + 2 + + (1/2 DATA(0, -1, 0) + 1/2 DATA(0, 1, 0) - DATA(0, 0, 0)) y + + 2 + + (1/2 DATA(-1, 0, 0) - DATA(0, 0, 0) + 1/2 DATA(1, 0, 0)) x + ( + + - 1/4 DATA(0, 1, -1) + 1/4 DATA(0, -1, 1) + 1/4 DATA(0, 1, 1) + + 2 + + 1/2 DATA(0, 0, -1) - 1/2 DATA(0, 0, 1) - 1/4 DATA(0, -1, -1)) y z + ( + + 1/2 DATA(0, 0, -1) - 1/4 DATA(-1, 0, -1) - 1/4 DATA(1, 0, -1) + + 2 + + 1/4 DATA(-1, 0, 1) - 1/2 DATA(0, 0, 1) + 1/4 DATA(1, 0, 1)) x z + ( + + - 1/4 DATA(-1, 1, 0) + 1/2 DATA(-1, 0, 0) + 1/4 DATA(1, -1, 0) + + 2 + - 1/4 DATA(-1, -1, 0) - 1/2 DATA(1, 0, 0) + 1/4 DATA(1, 1, 0)) x y + ( + + - 1/8 DATA(-1, 1, 1) + 1/8 DATA(1, -1, -1) + 1/8 DATA(-1, 1, -1) + + - 1/8 DATA(1, 1, -1) - 1/8 DATA(-1, -1, -1) - 1/8 DATA(1, -1, 1) + + + 1/8 DATA(-1, -1, 1) + 1/8 DATA(1, 1, 1)) x y z + (1/8 DATA(1, -1, -1) + + - 1/8 DATA(-1, 1, -1) + 1/8 DATA(1, 1, -1) + 1/4 DATA(-1, 1, 0) + + - 1/4 DATA(1, -1, 0) + 1/4 DATA(-1, -1, 0) - 1/8 DATA(-1, 1, 1) + + + 1/8 DATA(1, -1, 1) - 1/8 DATA(-1, -1, 1) - 1/4 DATA(1, 1, 0) + + + 1/8 DATA(1, 1, 1) + 1/4 DATA(-1, 0, -1) - 1/4 DATA(1, 0, -1) + + + 1/4 DATA(-1, 0, 1) - 1/4 DATA(1, 0, 1) - 1/2 DATA(-1, 0, 0) + + 2 2 + + 1/2 DATA(1, 0, 0) - 1/8 DATA(-1, -1, -1)) x y z + (1/8 DATA(1, -1, -1) + + + 1/2 DATA(0, 0, -1) - 1/4 DATA(-1, 0, -1) + 1/8 DATA(-1, 1, -1) + + + 1/8 DATA(1, 1, -1) - 1/4 DATA(0, 1, -1) - 1/4 DATA(1, 0, -1) + + - 1/4 DATA(-1, 1, 0) + 1/2 DATA(-1, 0, 0) - 1/4 DATA(1, -1, 0) + + + 1/2 DATA(0, -1, 0) - 1/4 DATA(-1, -1, 0) + 1/8 DATA(-1, 1, 1) + + - 1/4 DATA(-1, 0, 1) + 1/8 DATA(1, -1, 1) - 1/4 DATA(0, -1, 1) + + + 1/8 DATA(-1, -1, 1) - DATA(0, 0, 0) + 1/2 DATA(1, 0, 0) + + + 1/2 DATA(0, 1, 0) - 1/4 DATA(1, 1, 0) + 1/2 DATA(0, 0, 1) + + - 1/4 DATA(1, 0, 1) - 1/4 DATA(0, 1, 1) + 1/8 DATA(1, 1, 1) + + 2 2 2 + + 1/8 DATA(-1, -1, -1) - 1/4 DATA(0, -1, -1)) x y z + ( + + 1/8 DATA(1, -1, -1) - 1/8 DATA(-1, 1, -1) - 1/8 DATA(1, 1, -1) + + + 1/8 DATA(-1, 1, 1) - 1/8 DATA(1, -1, 1) - 1/8 DATA(-1, -1, 1) + + + 1/8 DATA(1, 1, 1) + 1/8 DATA(-1, -1, -1) + 1/4 DATA(0, 1, -1) + + 2 + + 1/4 DATA(0, -1, 1) - 1/4 DATA(0, 1, 1) - 1/4 DATA(0, -1, -1)) x y z + ( + + - 1/8 DATA(1, -1, -1) - 1/8 DATA(-1, 1, -1) - 1/8 DATA(1, 1, -1) + + + 1/4 DATA(0, 1, -1) + 1/8 DATA(-1, 1, 1) + 1/8 DATA(1, -1, 1) + + - 1/4 DATA(0, -1, 1) + 1/8 DATA(-1, -1, 1) - 1/4 DATA(0, 1, 1) + + + 1/8 DATA(1, 1, 1) - 1/2 DATA(0, 0, -1) + 1/4 DATA(-1, 0, -1) + + + 1/4 DATA(1, 0, -1) - 1/4 DATA(-1, 0, 1) + 1/2 DATA(0, 0, 1) + + 2 2 + - 1/4 DATA(1, 0, 1) - 1/8 DATA(-1, -1, -1) + 1/4 DATA(0, -1, -1)) x y z + + + (- 1/8 DATA(1, -1, -1) + 1/8 DATA(-1, 1, -1) - 1/8 DATA(1, 1, -1) + + - 1/8 DATA(-1, 1, 1) + 1/8 DATA(1, -1, 1) - 1/8 DATA(-1, -1, 1) + + + 1/8 DATA(1, 1, 1) + 1/8 DATA(-1, -1, -1) - 1/4 DATA(-1, 0, -1) + + 2 + + 1/4 DATA(1, 0, -1) + 1/4 DATA(-1, 0, 1) - 1/4 DATA(1, 0, 1)) x y z + ( + + - 1/8 DATA(1, -1, -1) + 1/8 DATA(-1, 1, -1) + 1/8 DATA(1, 1, -1) + + - 1/4 DATA(0, 1, -1) + 1/8 DATA(-1, 1, 1) - 1/8 DATA(1, -1, 1) + + + 1/4 DATA(0, -1, 1) - 1/8 DATA(-1, -1, 1) - 1/4 DATA(0, 1, 1) + + + 1/8 DATA(1, 1, 1) - 1/4 DATA(-1, 1, 0) + 1/4 DATA(1, -1, 0) + + - 1/2 DATA(0, -1, 0) + 1/4 DATA(-1, -1, 0) + 1/2 DATA(0, 1, 0) + + 2 2 + - 1/4 DATA(1, 1, 0) - 1/8 DATA(-1, -1, -1) + 1/4 DATA(0, -1, -1)) x y z + + + (- 1/8 DATA(1, -1, -1) - 1/8 DATA(-1, 1, -1) + 1/8 DATA(1, 1, -1) + + - 1/8 DATA(-1, 1, 1) - 1/8 DATA(1, -1, 1) + 1/8 DATA(-1, -1, 1) + + + 1/8 DATA(1, 1, 1) + 1/8 DATA(-1, -1, -1) + 1/4 DATA(-1, 1, 0) + + 2 + + 1/4 DATA(1, -1, 0) - 1/4 DATA(-1, -1, 0) - 1/4 DATA(1, 1, 0)) x y z + + + (- 1/2 DATA(0, 0, -1) + 1/2 DATA(0, 0, 1)) z + + + (- 1/2 DATA(0, -1, 0) + 1/2 DATA(0, 1, 0)) y + +> +# I +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +bytes used=18011188, alloc=1965720, time=1.06 +bytes used=19013292, alloc=1965720, time=1.12 + 2 2 2 2 2 2 +[COEFF(-1, -1, -1) = 1/8 x y z - 1/8 y x z + 1/8 x y z - 1/8 x y z + + 2 2 2 2 2 2 + - 1/8 x y z - 1/8 x y z + 1/8 y x z + 1/8 x y z, COEFF(0, -1, -1) = + + 2 2 2 2 2 2 2 2 2 + - 1/4 y z + 1/4 x y z + 1/4 y z - 1/4 x y z - 1/4 x y z + 1/4 y z + + 2 2 2 2 2 2 + + 1/4 x y z - 1/4 y z, COEFF(1, -1, -1) = 1/8 x y z - 1/8 x y z + + 2 2 2 2 2 2 2 2 2 + - 1/8 y x z + 1/8 x y z - 1/8 x y z + 1/8 x y z - 1/8 x y z + + 2 2 2 + + 1/8 y x z, COEFF(-1, 0, -1) = - 1/4 x z + 1/4 x z + 1/4 x z + + 2 2 2 2 2 2 2 2 2 + + 1/4 x y z - 1/4 x y z - 1/4 x y z + 1/4 x y z - 1/4 x z , + + 2 2 2 2 2 2 2 2 + COEFF(0, 0, -1) = - 1/2 z - 1/2 x z - 1/2 y z + 1/2 x y z + 1/2 y z + + 2 2 2 2 2 2 + + 1/2 x z + 1/2 z - 1/2 x y z, COEFF(1, 0, -1) = - 1/4 x y z + + 2 2 2 2 2 2 2 2 2 + + 1/4 x z + 1/4 x y z - 1/4 x z - 1/4 x y z + 1/4 x z + 1/4 x y z + + 2 2 2 2 2 + - 1/4 x z, COEFF(-1, 1, -1) = 1/8 y x z + 1/8 x y z - 1/8 x y z + + 2 2 2 2 2 2 2 2 + + 1/8 x y z + 1/8 x y z - 1/8 x y z - 1/8 y x z - 1/8 x y z, + + 2 2 2 2 2 2 + COEFF(0, 1, -1) = 1/4 y z + 1/4 y z + 1/4 x y z + 1/4 x y z + + 2 2 2 2 2 2 + - 1/4 x y z - 1/4 y z - 1/4 y z - 1/4 x y z , COEFF(1, 1, -1) = + + 2 2 2 2 2 2 2 2 + - 1/8 x y z + 1/8 x y z - 1/8 x y z + 1/8 y x z + 1/8 x y z + + 2 2 2 2 2 2 + - 1/8 y x z - 1/8 x y z + 1/8 x y z , COEFF(-1, -1, 0) = 1/4 x y z + + 2 2 2 2 2 2 2 2 + - 1/4 x y - 1/4 y x z + 1/4 y x - 1/4 x y z - 1/4 x y + 1/4 x y z + + 2 2 2 2 2 + + 1/4 x y , COEFF(0, -1, 0) = - 1/2 x y - 1/2 y + 1/2 y z + + 2 2 2 2 2 2 2 2 2 + - 1/2 x y z + 1/2 y - 1/2 y z + 1/2 x y + 1/2 x y z , + + 2 2 2 2 2 2 + COEFF(1, -1, 0) = - 1/4 y x + 1/4 y x z + 1/4 x y z - 1/4 x y z + + 2 2 2 2 2 2 + - 1/4 x y + 1/4 x y + 1/4 x y - 1/4 x y z , COEFF(-1, 0, 0) = + + 2 2 2 2 2 2 2 2 2 2 2 + 1/2 x z + 1/2 x y z - 1/2 x y + 1/2 x - 1/2 x z - 1/2 x y z + + 2 + - 1/2 x + 1/2 x y , + + 2 2 2 2 2 2 2 2 2 2 2 2 + COEFF(0, 0, 0) = -x - x y z + x y - y + x z + y z - z + 1, + + 2 2 2 2 2 2 2 + COEFF(1, 0, 0) = 1/2 x - 1/2 x y + 1/2 x y z - 1/2 x z - 1/2 x y + + 2 2 2 2 2 2 + + 1/2 x y z + 1/2 x - 1/2 x z , COEFF(-1, 1, 0) = 1/4 x y + + 2 2 2 2 2 2 2 2 2 2 + - 1/4 x y z - 1/4 x y + 1/4 x y z - 1/4 x y z + 1/4 x y + + 2 2 2 2 2 + - 1/4 y x + 1/4 y x z , COEFF(0, 1, 0) = 1/2 x y z - 1/2 y z + + 2 2 2 2 2 2 2 2 + + 1/2 x y z - 1/2 y z - 1/2 x y + 1/2 y - 1/2 x y + 1/2 y, + + 2 2 2 2 2 2 2 + COEFF(1, 1, 0) = - 1/4 x y z - 1/4 y x z - 1/4 x y z + 1/4 x y + + 2 2 2 2 2 + + 1/4 x y + 1/4 y x + 1/4 x y - 1/4 x y z , COEFF(-1, -1, 1) = + + 2 2 2 2 2 2 2 2 2 2 + 1/8 x y z - 1/8 x y z - 1/8 x y z - 1/8 x y z + 1/8 x y z + + 2 2 + + 1/8 y x z - 1/8 x y z + 1/8 y x z, COEFF(0, -1, 1) = - 1/4 y z + + 2 2 2 2 2 2 2 2 2 + + 1/4 y z - 1/4 y z + 1/4 x y z - 1/4 x y z + 1/4 x y z + 1/4 y z + + 2 2 2 2 2 2 2 2 + - 1/4 x y z , COEFF(1, -1, 1) = 1/8 x y z - 1/8 x y z + 1/8 x y z + + 2 2 2 2 2 2 2 + - 1/8 x y z - 1/8 y x z + 1/8 x y z - 1/8 y x z + 1/8 x y z, + + 2 2 2 2 + COEFF(-1, 0, 1) = - 1/4 x z + 1/4 x y z + 1/4 x y z - 1/4 x z + + 2 2 2 2 2 2 2 2 + - 1/4 x y z - 1/4 x y z + 1/4 x z + 1/4 x z , COEFF(0, 0, 1) = + + 2 2 2 2 2 2 2 2 2 2 2 + 1/2 x y z + 1/2 x y z - 1/2 y z - 1/2 x z + 1/2 z - 1/2 x z + + 2 2 2 2 + + 1/2 z - 1/2 y z, COEFF(1, 0, 1) = - 1/4 x y z + 1/4 x z - 1/4 x y z + + 2 2 2 2 2 2 2 2 2 + + 1/4 x z - 1/4 x y z - 1/4 x y z + 1/4 x z + 1/4 x z , + + 2 2 2 2 2 2 + COEFF(-1, 1, 1) = 1/8 x y z - 1/8 y x z + 1/8 x y z + 1/8 x y z + + 2 2 2 2 2 2 + - 1/8 x y z + 1/8 x y z - 1/8 y x z - 1/8 x y z , COEFF(0, 1, 1) = + + 2 2 2 2 2 2 2 2 2 + 1/4 y z + 1/4 y z - 1/4 x y z - 1/4 x y z - 1/4 x y z + 1/4 y z + + 2 2 2 2 2 2 2 + - 1/4 x y z + 1/4 y z, COEFF(1, 1, 1) = 1/8 x y z + 1/8 x y z + + 2 2 2 2 2 2 + + 1/8 y x z + 1/8 x y z + 1/8 x y z + 1/8 y x z + 1/8 x y z + + 2 2 + + 1/8 x y z] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-I.compute.c"); +bytes used=20014052, alloc=1965720, time=1.17 +bytes used=21014204, alloc=1965720, time=1.25 +bytes used=22026492, alloc=1965720, time=1.31 +bytes used=23026644, alloc=1965720, time=1.38 +bytes used=24027108, alloc=1965720, time=1.45 +bytes used=25027360, alloc=1965720, time=1.53 +bytes used=26028312, alloc=1965720, time=1.59 +bytes used=27032484, alloc=1965720, time=1.68 +bytes used=28032700, alloc=1965720, time=1.76 +bytes used=29032836, alloc=1965720, time=1.84 +bytes used=30032956, alloc=1965720, time=1.94 +bytes used=31033144, alloc=1965720, time=2.02 +bytes used=32033480, alloc=1965720, time=2.10 +bytes used=33033872, alloc=1965720, time=2.19 +bytes used=34034148, alloc=1965720, time=2.28 +bytes used=35034336, alloc=1965720, time=2.37 +bytes used=36034540, alloc=1965720, time=2.49 +bytes used=37034732, alloc=1965720, time=2.60 +> +# d/dx +> simplify( diff(interp_3d_cube_order2_smooth0,x) ); +bytes used=38034920, alloc=1965720, time=2.66 +bytes used=39035636, alloc=2096768, time=2.72 + 2 +- 1/2 DATA(-1, 0, 0) + 1/2 DATA(1, 0, 0) + 1/2 x y DATA(-1, 1, 0) + + 2 2 2 + + 1/4 x y z DATA(-1, 1, -1) - 1/2 y x z DATA(0, 1, -1) + + 2 2 2 2 2 2 + + x y z DATA(-1, 0, 0) + x y z DATA(1, 0, 0) + x y z DATA(0, -1, 0) + + 2 2 2 2 + + x y z DATA(0, 1, 0) + x y z DATA(0, 0, 1) + + 2 2 2 2 + + 1/4 x y z DATA(-1, 1, 1) + 1/4 x y z DATA(1, -1, -1) + + 2 2 2 2 + - 1/2 x y z DATA(-1, 0, -1) + 1/4 x y z DATA(-1, -1, -1) + + 2 2 2 2 + + 1/4 x y z DATA(1, -1, 1) + 1/4 x y z DATA(-1, -1, 1) + + 2 2 2 2 + + 1/4 x y z DATA(1, 1, 1) - 1/2 x y z DATA(0, 1, -1) + + 2 2 2 2 + - 1/2 x y z DATA(0, -1, 1) - 1/2 x y z DATA(0, 1, 1) + + 2 2 2 2 + - 1/2 x y z DATA(0, -1, -1) - 2 x y z DATA(0, 0, 0) + + 2 2 2 2 + + x y z DATA(0, 0, -1) - 1/2 x y z DATA(1, 0, -1) + + 2 2 2 2 + - 1/2 x y z DATA(-1, 0, 1) - 1/2 x y z DATA(1, 0, 1) + + 2 2 2 2 + - 1/2 x y z DATA(-1, 1, 0) - 1/2 x y z DATA(1, -1, 0) + + 2 2 2 2 + - 1/2 x y z DATA(-1, -1, 0) - 1/2 x y z DATA(1, 1, 0) + + 2 + + 1/4 y x z DATA(1, 1, -1) - 1/4 y x z DATA(-1, 1, -1) + + - 1/4 y x z DATA(1, 1, -1) + 1/4 y x z DATA(-1, 1, 1) + + - 1/4 y x z DATA(1, -1, 1) - 1/4 y x z DATA(-1, -1, 1) + + + 1/4 y x z DATA(1, 1, 1) + 1/4 y x z DATA(-1, -1, -1) + + + 1/2 y x z DATA(0, 1, -1) + 1/2 y x z DATA(0, -1, 1) + + - 1/2 y x z DATA(0, 1, 1) - 1/2 y x z DATA(0, -1, -1) + + 2 + - 1/4 x y z DATA(1, -1, -1) + 1/4 y x z DATA(1, -1, -1) + + 2 2 2 + + 1/4 x y z DATA(1, 1, -1) + 1/8 y z DATA(1, 1, -1) + + 2 2 + + 1/2 x y z DATA(0, 1, -1) + 1/4 x y z DATA(-1, 1, 1) + + 2 2 + + 1/4 x y z DATA(1, -1, 1) - 1/2 x y z DATA(0, -1, 1) + + 2 2 + + 1/4 x y z DATA(-1, -1, 1) - 1/2 x y z DATA(0, 1, 1) + + 2 2 + + 1/4 x y z DATA(1, 1, 1) - x y z DATA(0, 0, -1) + + 2 2 + + 1/2 x y z DATA(-1, 0, -1) + 1/2 x y z DATA(1, 0, -1) + + 2 2 + - 1/2 x y z DATA(-1, 0, 1) + x y z DATA(0, 0, 1) + + 2 2 + - 1/2 x y z DATA(1, 0, 1) - 1/4 x y z DATA(-1, -1, -1) + + 2 2 + + 1/2 x y z DATA(0, -1, -1) - 1/4 y x z DATA(1, -1, -1) + + 2 2 + + 1/4 y x z DATA(-1, 1, -1) - 1/8 y z DATA(-1, 1, -1) + + 2 2 + - 1/8 y z DATA(1, -1, 1) + 1/8 y z DATA(-1, -1, 1) + + 2 2 + + 1/8 y z DATA(1, 1, 1) + 1/8 y z DATA(-1, -1, -1) + + 2 2 + + 1/4 y z DATA(-1, 1, 0) + 1/4 y z DATA(1, -1, 0) + + 2 2 + - 1/4 y z DATA(-1, -1, 0) - 1/4 y z DATA(1, 1, 0) + + 2 2 + - 1/8 y z DATA(-1, 1, 1) + 1/4 y x z DATA(-1, 1, 1) + + 2 2 + - 1/4 y x z DATA(1, -1, 1) + 1/2 y x z DATA(0, -1, 1) + + 2 2 + - 1/4 y x z DATA(-1, -1, 1) - 1/2 y x z DATA(0, 1, 1) + + 2 2 + + 1/4 y x z DATA(1, 1, 1) - 1/2 y x z DATA(-1, 1, 0) + + 2 2 + + 1/2 y x z DATA(1, -1, 0) - y x z DATA(0, -1, 0) + + 2 2 + + 1/2 y x z DATA(-1, -1, 0) + y x z DATA(0, 1, 0) + + 2 2 + - 1/2 y x z DATA(1, 1, 0) - 1/4 y x z DATA(-1, -1, -1) + + 2 2 + + 1/2 y x z DATA(0, -1, -1) - 1/4 x y z DATA(-1, 1, -1) + + 2 + - 1/4 x y z DATA(1, 1, -1) + x DATA(-1, 0, 0) - 2 x DATA(0, 0, 0) + + 2 2 + + x DATA(1, 0, 0) - 1/4 y DATA(-1, 1, 0) + 1/2 y DATA(-1, 0, 0) + + 2 2 + + 1/4 y DATA(1, 1, 0) - 1/4 z DATA(-1, 0, -1) + 1/4 z DATA(1, 0, -1) + + 2 2 2 + - 1/4 z DATA(-1, 0, 1) + 1/4 z DATA(1, 0, 1) + 1/2 z DATA(-1, 0, 0) + + 2 2 2 + - 1/2 z DATA(1, 0, 0) - 1/8 y z DATA(-1, 1, 1) + + 2 2 2 2 + + 1/8 y z DATA(1, -1, 1) - 1/8 y z DATA(-1, -1, 1) + + 2 2 2 2 + - 1/4 y z DATA(1, 1, 0) + 1/8 y z DATA(1, 1, 1) + + 2 2 2 2 + + 1/4 y z DATA(-1, 0, -1) - 1/4 y z DATA(1, 0, -1) + + 2 2 2 2 2 + + 1/4 y z DATA(-1, 0, 1) - 1/4 y z DATA(1, 0, 1) - x z DATA(0, 0, 1) + + 2 2 2 + + 1/2 x z DATA(1, 0, 1) - x z DATA(-1, 0, 0) + 2 x z DATA(0, 0, 0) + + 2 + - x z DATA(1, 0, 0) + x z DATA(0, 0, -1) - 1/2 x z DATA(-1, 0, -1) + + - 1/2 x z DATA(1, 0, -1) + 1/2 x z DATA(-1, 0, 1) - x z DATA(0, 0, 1) + + + 1/2 x z DATA(1, 0, 1) - 1/8 y z DATA(-1, 1, 1) + 1/8 y z DATA(1, -1, -1) + + + 1/8 y z DATA(-1, 1, -1) - 1/8 y z DATA(1, 1, -1) + + - 1/8 y z DATA(-1, -1, -1) - 1/8 y z DATA(1, -1, 1) + + 2 + + 1/8 y z DATA(-1, -1, 1) + 1/2 x z DATA(1, 0, -1) + + 2 2 2 + + 1/2 x z DATA(-1, 0, 1) - 1/2 y z DATA(-1, 0, 0) + + 2 2 2 + - 1/8 y z DATA(-1, -1, -1) - 1/8 y z DATA(1, -1, -1) + + 2 2 + + 1/8 y z DATA(-1, 1, -1) - 1/8 y z DATA(1, 1, -1) + + 2 2 + - 1/8 y z DATA(-1, 1, 1) + 1/8 y z DATA(1, -1, 1) + + 2 2 + - 1/8 y z DATA(-1, -1, 1) + 1/8 y z DATA(1, 1, 1) + + 2 2 + + 1/8 y z DATA(-1, -1, -1) - 1/4 y z DATA(-1, 0, -1) + + 2 2 + + 1/4 y z DATA(1, 0, -1) + 1/4 y z DATA(-1, 0, 1) + + 2 2 + - 1/4 y z DATA(1, 0, 1) - 1/8 y z DATA(1, -1, -1) + + 2 2 + + 1/2 y z DATA(1, 0, 0) + 1/8 y z DATA(1, 1, 1) + + 2 2 2 2 + + 1/8 y z DATA(1, -1, -1) - 1/8 y z DATA(-1, 1, -1) + + 2 2 2 2 + + 1/8 y z DATA(1, 1, -1) + 1/4 y z DATA(-1, 1, 0) + + 2 2 2 2 + - 1/4 y z DATA(1, -1, 0) + 1/4 y z DATA(-1, -1, 0) + + 2 2 2 + + 1/2 x y DATA(1, -1, 0) - x y DATA(0, -1, 0) + 1/2 x y DATA(-1, -1, 0) + + 2 2 2 + - x y DATA(0, 1, 0) + 1/2 x y DATA(1, 1, 0) - x y DATA(-1, 0, 0) + + 2 + + 2 x y DATA(0, 0, 0) + 1/4 z DATA(-1, 0, -1) - 1/4 z DATA(-1, 0, 1) + + + 1/4 z DATA(1, 0, 1) - 1/4 y DATA(-1, 1, 0) - 1/4 y DATA(1, -1, 0) + + 2 2 + + 1/4 y DATA(-1, -1, 0) + 1/4 y DATA(1, -1, 0) - 1/4 y DATA(-1, -1, 0) + + 2 2 2 + - 1/2 y DATA(1, 0, 0) + 1/4 y DATA(1, 1, 0) - x y DATA(1, 0, 0) + + - 1/2 y x DATA(1, -1, 0) + y x DATA(0, -1, 0) - 1/2 y x DATA(-1, -1, 0) + + 2 + - y x DATA(0, 1, 0) + 1/2 y x DATA(1, 1, 0) - x z DATA(0, 0, -1) + + 2 + + 1/2 x z DATA(-1, 0, -1) + 1/2 y x DATA(-1, 1, 0) - 1/4 z DATA(1, 0, -1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +bytes used=40036144, alloc=2162292, time=2.78 +bytes used=41040352, alloc=2162292, time=2.85 + 2 2 2 2 +[COEFF(-1, -1, -1) = - 1/4 y x z + 1/4 x y z + 1/8 y z + 1/4 y x z + + 2 2 2 2 + - 1/8 y z - 1/4 x y z - 1/8 y z + 1/8 y z, + + 2 2 2 2 + COEFF(0, -1, -1) = 1/2 y x z - 1/2 y x z + 1/2 x y z - 1/2 x y z , + + 2 2 2 + COEFF(1, -1, -1) = - 1/4 x y z + 1/4 y x z - 1/8 y z - 1/4 y x z + + 2 2 2 2 2 + + 1/4 x y z - 1/8 y z + 1/8 y z + 1/8 y z , COEFF(-1, 0, -1) = + + 2 2 2 2 2 2 + - 1/4 z + 1/4 z + 1/4 y z + 1/2 x z + 1/2 x y z - 1/4 y z - 1/2 x z + + 2 2 2 2 2 2 + - 1/2 x y z , COEFF(0, 0, -1) = -x z + x z + x y z - x y z, + + 2 2 2 2 2 2 + COEFF(1, 0, -1) = - 1/2 x y z + 1/2 x z + 1/4 y z - 1/2 x z - 1/4 y z + + 2 2 2 2 + + 1/2 x y z + 1/4 z - 1/4 z, COEFF(-1, 1, -1) = 1/8 y z + 1/4 x y z + + 2 2 2 2 2 2 + - 1/8 y z - 1/8 y z + 1/4 y x z - 1/4 y x z + 1/8 y z - 1/4 x y z, + + 2 2 2 2 + COEFF(0, 1, -1) = 1/2 y x z - 1/2 y x z - 1/2 x y z + 1/2 x y z, + + 2 2 2 + COEFF(1, 1, -1) = - 1/4 y x z - 1/8 y z + 1/4 y x z + 1/4 x y z + + 2 2 2 2 2 + + 1/8 y z + 1/8 y z - 1/4 x y z - 1/8 y z, COEFF(-1, -1, 0) = + + 2 2 2 2 2 2 2 + 1/2 x y - 1/4 y - 1/4 y z - 1/2 y x + 1/4 y z + 1/4 y - 1/2 x y z + + 2 2 2 2 2 + + 1/2 y x z , COEFF(0, -1, 0) = y x - y x z + x y z - x y , + + 2 2 2 2 2 2 + COEFF(1, -1, 0) = 1/2 x y - 1/2 y x - 1/4 y z + 1/2 y x z - 1/2 x y z + + 2 2 + + 1/4 y - 1/4 y + 1/4 y z , COEFF(-1, 0, 0) = + + 2 2 2 2 2 2 2 2 + x y z + 1/2 y - x y - 1/2 y z - 1/2 + 1/2 z - x z + x, + + 2 2 2 2 + COEFF(0, 0, 0) = 2 x z - 2 x y z + 2 x y - 2 x, COEFF(1, 0, 0) = + + 2 2 2 2 2 2 2 2 + - 1/2 z - x z + x - 1/2 y + 1/2 + x y z + 1/2 y z - x y , + + 2 2 2 + COEFF(-1, 1, 0) = - 1/4 y - 1/4 y + 1/2 y x + 1/2 x y - 1/2 y x z + + 2 2 2 2 2 + - 1/2 x y z + 1/4 y z + 1/4 y z , + + 2 2 2 2 + COEFF(0, 1, 0) = x y z + y x z - y x - x y , COEFF(1, 1, 0) = + + 2 2 2 2 2 + - 1/2 y x z - 1/2 x y z + 1/4 y - 1/4 y z + 1/2 x y + 1/2 y x + + 2 2 2 2 2 + - 1/4 y z + 1/4 y , COEFF(-1, -1, 1) = 1/4 x y z - 1/4 y x z + 1/8 y z + + 2 2 2 2 2 2 + + 1/8 y z + 1/4 x y z - 1/4 y x z - 1/8 y z - 1/8 y z , + + 2 2 2 2 + COEFF(0, -1, 1) = 1/2 y x z + 1/2 y x z - 1/2 x y z - 1/2 x y z, + + 2 2 2 2 + COEFF(1, -1, 1) = - 1/8 y z - 1/4 y x z + 1/8 y z - 1/4 y x z - 1/8 y z + + 2 2 2 2 2 + + 1/4 x y z + 1/8 y z + 1/4 x y z , COEFF(-1, 0, 1) = - 1/4 z + + 2 2 2 2 2 + + 1/4 y z + 1/4 y z + 1/2 x z - 1/4 z - 1/2 x y z + 1/2 x z + + 2 2 2 2 2 2 + - 1/2 x y z , COEFF(0, 0, 1) = x y z + x y z - x z - x z, + + 2 2 2 2 2 2 + COEFF(1, 0, 1) = - 1/4 y z - 1/4 y z - 1/2 x y z + 1/2 x z + 1/2 x z + + 2 2 2 2 2 + - 1/2 x y z + 1/4 z + 1/4 z, COEFF(-1, 1, 1) = 1/4 y x z - 1/8 y z + + 2 2 2 2 2 + - 1/8 y z - 1/8 y z + 1/4 y x z - 1/8 y z + 1/4 x y z + 1/4 x y z , + + 2 2 2 2 + COEFF(0, 1, 1) = - 1/2 x y z - 1/2 y x z - 1/2 y x z - 1/2 x y z, + + 2 2 2 2 2 + COEFF(1, 1, 1) = 1/8 y z + 1/8 y z + 1/4 y x z + 1/4 x y z + + 2 2 2 + + 1/4 x y z + 1/8 y z + 1/4 y x z + 1/8 y z] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dx.compute.c"); +bytes used=42040556, alloc=2162292, time=2.92 +bytes used=43053988, alloc=2162292, time=3.00 +bytes used=44054148, alloc=2162292, time=3.05 +bytes used=45054348, alloc=2162292, time=3.15 +bytes used=46054556, alloc=2162292, time=3.22 +bytes used=47054764, alloc=2162292, time=3.31 +bytes used=48054964, alloc=2162292, time=3.40 +bytes used=49055592, alloc=2162292, time=3.49 +bytes used=50055804, alloc=2162292, time=3.60 +bytes used=51055996, alloc=2162292, time=3.69 +bytes used=52056160, alloc=2162292, time=3.81 +> +# d/dy +> simplify( diff(interp_3d_cube_order2_smooth0,y) ); +bytes used=53056316, alloc=2162292, time=3.89 +bytes used=54056572, alloc=2162292, time=3.94 + 2 +- 1/2 DATA(0, -1, 0) + 1/2 DATA(0, 1, 0) - y z DATA(0, 0, 1) + + 2 2 + + 1/2 y z DATA(0, 1, 1) + 1/2 x y DATA(-1, 1, 0) + + 2 2 2 + + 1/2 x y DATA(1, -1, 0) - x y DATA(0, -1, 0) + 1/2 x y DATA(-1, -1, 0) + + 2 2 2 + - x y DATA(0, 1, 0) + 1/2 x y DATA(1, 1, 0) - x y DATA(-1, 0, 0) + + 2 2 2 + + 2 x y DATA(0, 0, 0) - x y DATA(1, 0, 0) + 1/2 y z DATA(0, -1, -1) + + 2 2 2 + + 1/2 y z DATA(0, -1, 1) + 2 y z DATA(0, 0, 0) - y z DATA(0, 1, 0) + + + 1/8 x z DATA(1, -1, -1) + 1/8 x z DATA(-1, 1, -1) + + - 1/8 x z DATA(1, 1, -1) - 1/8 x z DATA(-1, -1, -1) + + - 1/8 x z DATA(1, -1, 1) + 1/8 x z DATA(-1, -1, 1) + 1/8 x z DATA(1, 1, 1) + + 2 + - 1/8 x z DATA(-1, 1, -1) + 1/2 y z DATA(0, -1, 1) + + + 1/2 y z DATA(0, 1, 1) + y z DATA(0, 0, -1) - y z DATA(0, 0, 1) + + - 1/2 y z DATA(0, -1, -1) - 1/2 y z DATA(0, 1, -1) + + 2 + - 1/8 x z DATA(-1, 1, 1) - 1/2 y x z DATA(1, 0, -1) + + 2 2 + + 1/2 y x z DATA(-1, 0, 1) - 1/2 y x z DATA(1, 0, 1) + + 2 2 2 + - y x z DATA(-1, 0, 0) + y x z DATA(1, 0, 0) + 1/8 x z DATA(1, -1, -1) + + 2 2 2 2 + + x y z DATA(0, 1, 0) + x y z DATA(0, 0, 1) + + 2 2 2 2 + - 1/2 x y z DATA(0, 1, 1) + 1/4 x y z DATA(1, -1, -1) + + 2 2 2 2 + + 1/4 x y z DATA(1, 1, -1) + 1/4 x y z DATA(-1, -1, -1) + + 2 2 2 2 + + 1/4 x y z DATA(1, -1, 1) + 1/4 x y z DATA(-1, -1, 1) + + 2 2 2 + + 1/4 x y z DATA(1, 1, 1) + 1/2 y x z DATA(-1, 0, -1) + + 2 2 2 + + 1/4 x DATA(-1, 1, 0) - 1/2 x y z DATA(-1, 1, 0) + + 2 2 2 2 + - 1/2 x y z DATA(-1, -1, 0) - 1/2 x y z DATA(1, 1, 0) + + 2 2 2 2 + - 1/2 x y z DATA(-1, 0, -1) - 1/2 x y z DATA(1, 0, -1) + + 2 2 2 2 + - 1/2 x y z DATA(-1, 0, 1) - 1/2 x y z DATA(1, 0, 1) + + 2 2 2 2 + - 1/2 x y z DATA(0, -1, 1) - 2 x y z DATA(0, 0, 0) + + 2 + + 1/4 y x z DATA(1, 1, -1) + 1/4 y x z DATA(-1, 1, -1) + + - 1/4 y x z DATA(1, 1, -1) - 1/4 y x z DATA(-1, 1, 1) + + + 1/4 y x z DATA(1, -1, 1) - 1/4 y x z DATA(-1, -1, 1) + + + 1/4 y x z DATA(1, 1, 1) + 1/4 y x z DATA(-1, -1, -1) + + 2 2 + - 1/4 y x z DATA(1, -1, -1) + x y z DATA(-1, 0, 0) + + 2 2 + - 1/4 x y z DATA(1, -1, -1) - 1/4 x y z DATA(-1, 1, -1) + + 2 2 2 2 + - 2 y DATA(0, 0, 0) + x y z DATA(0, -1, 0) - 1/2 x y z DATA(1, -1, 0) + + 2 2 2 2 + - 1/2 x y z DATA(0, -1, -1) + x y z DATA(1, 0, 0) + + 2 2 2 2 + + 1/4 x y z DATA(-1, 1, 1) + 1/4 x y z DATA(-1, 1, -1) + + 2 2 + + 1/4 x z DATA(0, 1, -1) + 1/4 x z DATA(0, -1, 1) + + 2 2 + - 1/4 x z DATA(0, 1, 1) - 1/4 x z DATA(0, -1, -1) + + 2 2 2 2 + - 1/8 x z DATA(1, -1, -1) + 1/8 x z DATA(-1, 1, -1) + + 2 2 + + 1/8 x z DATA(1, 1, -1) + y x DATA(-1, 0, 0) - y x DATA(1, 0, 0) + + 2 2 + + 1/4 x y z DATA(-1, 1, 1) + 1/4 x y z DATA(1, -1, 1) + + 2 2 + - 1/2 x y z DATA(0, -1, 1) + 1/4 x y z DATA(-1, -1, 1) + + 2 2 2 + - 1/2 x y z DATA(0, 1, 1) + x y z DATA(0, 0, -1) + + 2 2 2 + - 1/2 x y z DATA(0, 1, -1) + 1/8 x z DATA(1, 1, 1) + + 2 2 + - 1/4 x y z DATA(-1, -1, -1) + 1/2 x y z DATA(0, -1, -1) + + 2 2 + + 1/4 x y z DATA(1, 1, 1) + 1/2 x y z DATA(-1, 0, -1) + + 2 2 + + 1/2 x y z DATA(1, 0, -1) - 1/2 x y z DATA(-1, 0, 1) + + 2 2 + - x y z DATA(0, 0, -1) - 1/4 x y z DATA(1, 1, -1) + + 2 2 + + 1/2 x y z DATA(0, 1, -1) - 1/8 x z DATA(1, 1, -1) + + 2 + + 1/2 y x z DATA(-1, 0, 1) + x y z DATA(0, 0, 1) + + 2 2 + - 1/2 x y z DATA(1, 0, 1) + 1/8 x z DATA(-1, -1, -1) + + 2 2 + + 1/4 y x z DATA(1, -1, -1) - 1/4 y x z DATA(-1, 1, -1) + + 2 2 2 + + 1/2 x z DATA(0, 1, 0) + 1/8 x z DATA(-1, 1, 1) + + 2 2 + - 1/8 x z DATA(1, -1, 1) - 1/8 x z DATA(-1, -1, 1) + y DATA(0, 1, 0) + + 2 2 2 2 + + 1/4 x z DATA(0, -1, 1) - 1/8 x z DATA(-1, -1, 1) + + 2 2 2 2 + - 1/4 x z DATA(0, 1, 1) + 1/8 x z DATA(1, 1, 1) + + 2 2 2 2 + - 1/4 x z DATA(-1, 1, 0) + 1/4 x z DATA(1, -1, 0) + + 2 2 2 2 + - 1/2 x z DATA(0, -1, 0) + 1/4 x z DATA(-1, -1, 0) + + 2 2 2 + - 1/4 x z DATA(1, 1, 0) - 1/4 x z DATA(1, 1, 0) + + 2 2 2 2 + - 1/8 x z DATA(-1, -1, -1) + 1/4 x z DATA(0, -1, -1) + + 2 2 + - 1/8 x z DATA(1, -1, -1) - 1/8 x z DATA(-1, 1, -1) + + 2 2 + + 1/8 x z DATA(1, 1, -1) - 1/8 x z DATA(-1, 1, 1) + + 2 2 2 2 + - 1/4 x z DATA(0, 1, -1) + 1/8 x z DATA(-1, 1, 1) + + 2 2 + - 1/8 x z DATA(1, -1, 1) - 1/4 z DATA(0, -1, 1) - 1/4 z DATA(0, 1, -1) + + 2 2 + - 1/4 z DATA(0, -1, -1) - 1/2 z DATA(0, 1, 0) + y DATA(0, -1, 0) + + 2 2 2 + + 1/4 x DATA(1, 1, 0) - 1/2 x DATA(0, 1, 0) - 1/4 x DATA(-1, -1, 0) + + 2 2 2 + + 1/2 x DATA(0, -1, 0) - 1/4 x DATA(1, -1, 0) + 1/2 y z DATA(0, 1, -1) + + 2 2 + - 1/8 x z DATA(1, -1, 1) + 1/8 x z DATA(-1, -1, 1) + + 2 2 + + 1/8 x z DATA(1, 1, 1) + 1/8 x z DATA(-1, -1, -1) + + 2 2 + + 1/4 x z DATA(-1, 1, 0) + 1/4 x z DATA(1, -1, 0) + + 2 2 2 + - 1/4 x z DATA(-1, -1, 0) - y z DATA(0, -1, 0) + 1/2 z DATA(0, -1, 0) + + 2 2 2 + + 1/4 z DATA(0, 1, 1) - y z DATA(0, 0, -1) + 1/4 z DATA(0, 1, -1) + + - 1/4 x DATA(1, -1, 0) + 1/4 x DATA(-1, -1, 0) + 1/4 x DATA(1, 1, 0) + + + 1/4 z DATA(0, -1, -1) + 1/4 z DATA(0, 1, 1) - 1/4 x DATA(-1, 1, 0) + + - 1/2 y x z DATA(-1, 0, -1) + 1/2 y x z DATA(1, 0, -1) + + 2 2 + - 1/4 y x z DATA(-1, 1, 1) + 1/4 y x z DATA(1, -1, 1) + + 2 2 + - 1/4 y x z DATA(-1, -1, 1) + 1/4 y x z DATA(1, 1, 1) + + 2 2 + + 1/2 y x z DATA(-1, 1, 0) - 1/2 y x z DATA(1, -1, 0) + + 2 2 + + 1/2 y x z DATA(-1, -1, 0) - 1/2 y x z DATA(1, 1, 0) + + 2 + - 1/4 y x z DATA(-1, -1, -1) - 1/2 y x z DATA(1, 0, 1) + + 2 + - 1/4 z DATA(0, -1, 1) + 1/2 y x DATA(1, -1, 0) - 1/2 y x DATA(-1, -1, 0) + + + 1/2 y x DATA(1, 1, 0) - 1/2 y x DATA(-1, 1, 0) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +bytes used=55061328, alloc=2227816, time=4.01 + 2 2 2 2 +[COEFF(-1, -1, -1) = 1/8 x z + 1/8 x z - 1/8 x z + 1/4 y x z + 1/4 x y z + + 2 2 2 2 2 + - 1/4 y x z - 1/8 x z - 1/4 x y z, COEFF(0, -1, -1) = - 1/4 z + 1/4 z + + 2 2 2 2 2 2 2 + + 1/2 y z - 1/2 y z + 1/2 x y z - 1/4 x z + 1/4 x z - 1/2 x y z , + + 2 2 2 2 + COEFF(1, -1, -1) = 1/4 y x z - 1/4 y x z - 1/8 x z - 1/8 x z + + 2 2 2 2 + + 1/4 x y z + 1/8 x z + 1/8 x z - 1/4 x y z, + + 2 2 2 2 + COEFF(-1, 0, -1) = 1/2 y x z - 1/2 y x z + 1/2 x y z - 1/2 x y z , + + 2 2 2 2 + COEFF(0, 0, -1) = x y z + y z - x y z - y z , + + 2 2 2 2 + COEFF(1, 0, -1) = - 1/2 x y z + 1/2 y x z - 1/2 y x z + 1/2 x y z, + + 2 2 2 2 2 2 + COEFF(-1, 1, -1) = - 1/8 x z + 1/8 x z + 1/4 x y z - 1/4 y x z + + 2 2 2 + - 1/4 x y z + 1/4 y x z - 1/8 x z + 1/8 x z, COEFF(0, 1, -1) = 1/4 z + + 2 2 2 2 2 2 + + 1/4 x z - 1/2 x y z - 1/4 z - 1/4 x z + 1/2 y z - 1/2 y z + + 2 2 2 + + 1/2 x y z, COEFF(1, 1, -1) = - 1/4 y x z - 1/4 x y z + 1/8 x z + + 2 2 2 2 2 2 + - 1/8 x z + 1/8 x z + 1/4 y x z + 1/4 x y z - 1/8 x z, + + 2 2 2 2 2 + COEFF(-1, -1, 0) = 1/4 x + 1/2 x y + 1/2 y x z - 1/4 x + 1/4 x z + + 2 2 2 + - 1/2 x y z - 1/4 x z - 1/2 y x, COEFF(0, -1, 0) = + + 2 2 2 2 2 2 2 2 + - 1/2 - 1/2 x z + 1/2 z - x y + y + 1/2 x - y z + x y z , + + 2 2 2 2 2 2 + COEFF(1, -1, 0) = 1/4 x z - 1/2 x y z - 1/4 x + 1/2 x y + 1/4 x z + + 2 2 + - 1/2 y x z + 1/2 y x - 1/4 x , + + 2 2 2 2 + COEFF(-1, 0, 0) = -x y + y x - y x z + x y z , + + 2 2 2 2 + COEFF(0, 0, 0) = -2 x y z + 2 y z - 2 y + 2 x y, + + 2 2 2 2 2 + COEFF(1, 0, 0) = y x z - y x + x y z - x y, COEFF(-1, 1, 0) = 1/2 x y + + 2 2 2 2 2 + + 1/2 y x z + 1/4 x z - 1/2 y x + 1/4 x - 1/4 x - 1/4 x z + + 2 2 + - 1/2 x y z , COEFF(0, 1, 0) = + + 2 2 2 2 2 2 2 2 + x y z - y z - 1/2 z - x y + 1/2 x z + 1/2 + y - 1/2 x , + + 2 2 2 2 2 + COEFF(1, 1, 0) = 1/4 x + 1/4 x - 1/2 y x z - 1/4 x z - 1/2 x y z + + 2 2 2 2 2 + + 1/2 x y - 1/4 x z + 1/2 y x, COEFF(-1, -1, 1) = - 1/8 x z + 1/8 x z + + 2 2 2 2 2 2 + - 1/4 y x z - 1/8 x z + 1/8 x z + 1/4 x y z + 1/4 x y z - 1/4 y x z , + + 2 2 2 2 2 2 + COEFF(0, -1, 1) = 1/4 x z - 1/4 z - 1/2 x y z - 1/2 x y z + 1/2 y z + + 2 2 2 2 + - 1/4 z + 1/2 y z + 1/4 x z, COEFF(1, -1, 1) = 1/4 x y z - 1/8 x z + + 2 2 2 2 2 2 + + 1/4 y x z - 1/8 x z + 1/4 y x z + 1/4 x y z - 1/8 x z - 1/8 x z, + + 2 2 2 2 + COEFF(-1, 0, 1) = - 1/2 x y z - 1/2 x y z + 1/2 y x z + 1/2 y x z , + + 2 2 2 2 + COEFF(0, 0, 1) = x y z + x y z - y z - y z, + + 2 2 2 2 + COEFF(1, 0, 1) = - 1/2 x y z - 1/2 x y z - 1/2 y x z - 1/2 y x z, + + 2 2 2 2 2 + COEFF(-1, 1, 1) = 1/4 x y z - 1/4 y x z - 1/8 x z + 1/8 x z + 1/8 x z + + 2 2 2 2 + - 1/8 x z - 1/4 y x z + 1/4 x y z , COEFF(0, 1, 1) = 1/2 y z - 1/4 x z + + 2 2 2 2 2 2 2 + + 1/2 y z - 1/2 x y z + 1/4 z + 1/4 z - 1/4 x z - 1/2 x y z , + + 2 2 2 2 + COEFF(1, 1, 1) = 1/8 x z + 1/8 x z + 1/4 x y z + 1/8 x z + 1/4 y x z + + 2 2 2 2 + + 1/8 x z + 1/4 x y z + 1/4 y x z ] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dy.compute.c"); +bytes used=56061492, alloc=2227816, time=4.08 +bytes used=57061808, alloc=2227816, time=4.17 +bytes used=58072892, alloc=2227816, time=4.24 +bytes used=59073132, alloc=2227816, time=4.31 +bytes used=60073296, alloc=2227816, time=4.40 +bytes used=61073508, alloc=2227816, time=4.46 +bytes used=62073768, alloc=2227816, time=4.54 +bytes used=63073928, alloc=2227816, time=4.66 +bytes used=64077852, alloc=2227816, time=4.76 +bytes used=65078036, alloc=2227816, time=4.89 +bytes used=66078276, alloc=2227816, time=4.97 +bytes used=67078448, alloc=2227816, time=5.12 +> +# d/dz +> simplify( diff(interp_3d_cube_order2_smooth0,z) ); +bytes used=68078608, alloc=2227816, time=5.25 +bytes used=69078852, alloc=2227816, time=5.32 +- 1/2 DATA(0, 0, -1) + 1/2 DATA(0, 0, 1) + 1/4 y DATA(0, -1, -1) + + + z DATA(0, 0, -1) - 2 z DATA(0, 0, 0) + z DATA(0, 0, 1) + + 2 2 2 + - 1/4 y DATA(0, 1, -1) + 1/4 y DATA(0, -1, 1) + 1/4 y DATA(0, 1, 1) + + 2 2 2 + + 1/2 y DATA(0, 0, -1) - 1/2 y DATA(0, 0, 1) - 1/4 y DATA(0, -1, -1) + + 2 2 2 + + 1/2 x DATA(0, 0, -1) - 1/4 x DATA(-1, 0, -1) - 1/4 x DATA(1, 0, -1) + + 2 2 2 + + 1/4 x DATA(-1, 0, 1) - 1/2 x DATA(0, 0, 1) + 1/4 x DATA(1, 0, 1) + + + 1/4 y DATA(0, 1, 1) + 1/8 y x DATA(-1, 1, -1) - 1/8 y x DATA(1, 1, -1) + + - 1/8 y x DATA(-1, -1, -1) - 1/8 y x DATA(1, -1, 1) + + + 1/8 y x DATA(-1, -1, 1) + 1/8 y x DATA(1, 1, 1) + + 2 2 + + 1/8 x y DATA(1, -1, -1) - 1/8 x y DATA(-1, 1, -1) + + 2 2 + - 1/8 x y DATA(1, 1, -1) + 1/8 x y DATA(-1, 1, 1) + + 2 2 + + 1/4 x y z DATA(1, -1, -1) - 1/4 x y z DATA(-1, 1, -1) + + 2 2 + + 1/4 x y z DATA(1, 1, -1) + 1/2 x y z DATA(-1, 1, 0) + + 2 2 + - 1/2 x y z DATA(1, -1, 0) + 1/2 x y z DATA(-1, -1, 0) + + 2 2 + - 1/4 x y z DATA(-1, 1, 1) + 1/4 x y z DATA(1, -1, 1) + + 2 2 + - 1/4 x y z DATA(-1, -1, 1) - 1/2 x y z DATA(1, 1, 0) + + 2 2 + + 1/4 x y z DATA(1, 1, 1) + 1/2 x y z DATA(-1, 0, -1) + + 2 + - 1/4 y DATA(0, -1, 1) - 1/8 x y DATA(1, -1, 1) + + 2 2 + - 1/8 x y DATA(-1, -1, 1) + 1/8 x y DATA(1, 1, 1) + + 2 2 + + 1/8 x y DATA(-1, -1, -1) + 1/4 x y DATA(0, 1, -1) + + 2 2 + + 1/4 x y DATA(0, -1, 1) - 1/4 x y DATA(0, 1, 1) + + 2 2 2 + - 1/4 x y DATA(0, -1, -1) - 1/8 y x DATA(1, -1, -1) + + + 1/2 x z DATA(1, 0, -1) - 1/2 x z DATA(-1, 0, 1) + 1/2 x z DATA(1, 0, 1) + + 2 + + x z DATA(-1, 0, 0) - x z DATA(1, 0, 0) - x z DATA(0, 0, -1) + + 2 2 + + 1/2 x z DATA(-1, 0, -1) + 1/2 x z DATA(1, 0, -1) + + 2 2 + + 1/2 x z DATA(-1, 0, 1) - x z DATA(0, 0, 1) + + 2 2 2 2 + - 1/2 z y x DATA(-1, 1, 0) - 1/2 z y x DATA(1, -1, 0) + + 2 2 2 2 + - 1/2 z y x DATA(-1, -1, 0) - 1/2 z y x DATA(1, 1, 0) + + 2 2 2 2 + + 1/4 z y x DATA(1, 1, 1) + z y x DATA(-1, 0, 0) + + 2 2 2 2 + + z y x DATA(1, 0, 0) + 1/4 z y x DATA(-1, 1, 1) + + 2 2 2 2 + + 1/4 z y x DATA(1, -1, -1) + 1/4 z y x DATA(-1, 1, -1) + + 2 2 2 + + 1/4 z y x DATA(1, 1, -1) - 1/2 x y z DATA(-1, 1, 0) + + 2 2 + + 1/2 x y z DATA(1, -1, 0) - x y z DATA(0, -1, 0) + + 2 2 + + 1/2 x y z DATA(-1, -1, 0) + x y z DATA(0, 1, 0) + + 2 2 + - 1/2 x y z DATA(1, 1, 0) - 1/2 x y z DATA(1, 0, -1) + + 2 2 2 2 + + 1/4 z y x DATA(-1, -1, -1) + 1/4 z y x DATA(1, -1, 1) + + 2 2 2 2 + - 1/2 z y x DATA(-1, 0, -1) - 1/2 z y x DATA(1, 0, -1) + + 2 2 2 2 + - 1/2 z y x DATA(-1, 0, 1) - 1/2 z y x DATA(1, 0, 1) + + 2 2 2 2 + + z y x DATA(0, 0, -1) - 1/2 z y x DATA(0, 1, -1) + + 2 2 2 2 + + z y x DATA(0, -1, 0) - 1/2 z y x DATA(0, -1, 1) + + 2 2 2 2 2 2 + - 2 z y x DATA(0, 0, 0) + z y x DATA(0, 1, 0) + z y x DATA(0, 0, 1) + + 2 2 2 2 + - 1/2 z y x DATA(0, 1, 1) - 1/2 z y x DATA(0, -1, -1) + + 2 2 2 + - 1/2 x y z DATA(1, 0, 1) - x y z DATA(-1, 0, 0) + x y z DATA(1, 0, 0) + + 2 2 2 + - 1/4 x y z DATA(-1, -1, -1) + 1/4 z y x DATA(-1, -1, 1) + + 2 + + 1/2 x y z DATA(-1, 0, 1) - 1/4 x DATA(1, 0, -1) - 1/4 x DATA(-1, 0, 1) + + 2 2 2 + + 1/4 x DATA(1, 0, 1) - y z DATA(0, 0, -1) - 1/4 y x DATA(0, 1, 1) + + 2 2 2 2 + + 1/8 y x DATA(1, 1, 1) - 1/2 y x DATA(0, 0, -1) + + 2 2 2 2 + + 1/4 y x DATA(-1, 0, -1) + 1/4 y x DATA(1, 0, -1) + + 2 2 2 2 + - 1/4 y x DATA(-1, 0, 1) + 1/2 y x DATA(0, 0, 1) + + 2 2 + + 1/8 x y DATA(-1, 1, -1) - 1/8 x y DATA(1, 1, -1) + + 2 2 + - 1/8 x y DATA(-1, 1, 1) + 1/8 x y DATA(1, -1, 1) + + 2 2 + - 1/8 x y DATA(-1, -1, 1) + 1/8 x y DATA(1, 1, 1) + + 2 2 + + 1/8 x y DATA(-1, -1, -1) - 1/4 x y DATA(-1, 0, -1) + + 2 2 + + 1/4 x y DATA(1, 0, -1) + 1/4 x y DATA(-1, 0, 1) + + 2 2 2 + - 1/4 x y DATA(1, 0, 1) - 1/8 y x DATA(-1, 1, -1) + + 2 2 2 2 + - 1/8 y x DATA(1, 1, -1) + 1/4 y x DATA(0, 1, -1) + + 2 2 2 2 + + 1/8 y x DATA(-1, 1, 1) + 1/8 y x DATA(1, -1, 1) + + 2 2 2 2 + - 1/4 y x DATA(0, -1, 1) + 1/8 y x DATA(-1, -1, 1) + + + 1/2 y x z DATA(-1, 1, 0) + 1/2 y x z DATA(1, -1, 0) + + - 1/2 y x z DATA(-1, -1, 0) - 1/2 y x z DATA(1, 1, 0) + + 2 2 + + 1/4 x DATA(-1, 0, -1) + 1/2 x z DATA(1, 0, 1) - x z DATA(-1, 0, 0) + + 2 2 2 + + 2 x z DATA(0, 0, 0) - x z DATA(1, 0, 0) + 1/2 y z DATA(0, 1, -1) + + 2 2 2 + - y z DATA(0, -1, 0) + 1/2 y z DATA(0, -1, 1) + 2 y z DATA(0, 0, 0) + + 2 2 2 + - y z DATA(0, 1, 0) - y z DATA(0, 0, 1) + 1/2 y z DATA(0, 1, 1) + + 2 + + 1/2 y z DATA(0, -1, -1) + y z DATA(0, -1, 0) - y z DATA(0, 1, 0) + + 2 2 + - 1/2 x z DATA(-1, 0, -1) - 1/4 y x DATA(1, 0, 1) + + 2 2 2 2 + - 1/8 y x DATA(-1, -1, -1) + 1/4 y x DATA(0, -1, -1) + + 2 + - 1/8 x y DATA(1, -1, -1) + 1/8 y x DATA(1, -1, -1) + + - 1/2 y z DATA(0, -1, 1) + 1/2 y z DATA(0, 1, 1) - 1/2 y z DATA(0, -1, -1) + + + 1/2 y z DATA(0, 1, -1) - 1/4 y x z DATA(-1, 1, -1) + + + 1/4 y x z DATA(1, 1, -1) - 1/4 y x z DATA(-1, 1, 1) + + - 1/4 y x z DATA(1, -1, 1) + 1/4 y x z DATA(-1, -1, 1) + + + 1/4 y x z DATA(1, 1, 1) + 1/4 y x z DATA(-1, -1, -1) + + 2 + - 1/4 y x z DATA(1, -1, -1) - 1/4 x y z DATA(1, -1, -1) + + 2 2 + + 1/4 x y z DATA(-1, 1, -1) + 1/4 x y z DATA(-1, 1, 1) + + 2 2 + - 1/4 x y z DATA(1, -1, 1) + 1/2 x y z DATA(0, -1, 1) + + 2 2 + - 1/4 x y z DATA(-1, -1, 1) - 1/2 x y z DATA(0, 1, 1) + + 2 2 + - 1/4 x y z DATA(-1, -1, -1) + 1/2 x y z DATA(0, -1, -1) + + 2 2 + + 1/4 x y z DATA(1, 1, 1) + 1/4 x y z DATA(1, 1, -1) + + 2 + - 1/2 x y z DATA(0, 1, -1) - 1/8 y x DATA(-1, 1, 1) + + - 1/4 y DATA(0, 1, -1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +bytes used=70082388, alloc=2227816, time=5.40 + 2 2 2 2 2 +[COEFF(-1, -1, -1) = 1/4 z y x - 1/8 y x + 1/8 x y + 1/4 y x z - 1/8 y x + + 2 2 2 2 + - 1/4 x y z + 1/8 x y - 1/4 x y z, COEFF(0, -1, -1) = 1/2 y z + + 2 2 2 2 2 2 + - 1/2 y z - 1/2 z y x - 1/4 y - 1/4 x y + 1/4 y + 1/4 y x + + 2 2 2 + + 1/2 x y z, COEFF(1, -1, -1) = 1/8 y x + 1/4 x y z + 1/8 x y + + 2 2 2 2 2 2 + - 1/8 x y - 1/4 x y z + 1/4 z y x - 1/8 y x - 1/4 y x z, + + 2 2 2 2 + COEFF(-1, 0, -1) = 1/2 x y z - 1/2 z y x - 1/4 x y - 1/2 x z + + 2 2 2 2 + + 1/4 y x + 1/4 x - 1/4 x + 1/2 x z, COEFF(0, 0, -1) = + + 2 2 2 2 2 2 2 2 + - 1/2 - 1/2 y x + 1/2 x - y z + z y x + 1/2 y + z - x z, + + 2 2 2 2 + COEFF(1, 0, -1) = - 1/2 z y x + 1/2 x z + 1/2 x z - 1/4 x + 1/4 x y + + 2 2 2 2 2 2 + - 1/4 x - 1/2 x y z + 1/4 y x , COEFF(-1, 1, -1) = 1/4 z y x + + 2 2 2 2 + - 1/8 x y - 1/4 x y z + 1/8 x y - 1/4 y x z + 1/8 y x + 1/4 x y z + + 2 2 2 2 + - 1/8 y x , COEFF(0, 1, -1) = 1/2 y z + 1/4 x y - 1/4 y + 1/2 y z + + 2 2 2 2 2 2 + + 1/4 y x - 1/2 x y z - 1/2 z y x - 1/4 y , COEFF(1, 1, -1) = + + 2 2 2 2 2 + 1/4 x y z - 1/8 y x + 1/4 z y x - 1/8 x y - 1/8 x y + 1/4 y x z + + 2 2 2 + + 1/4 x y z - 1/8 y x , + + 2 2 2 2 + COEFF(-1, -1, 0) = - 1/2 y x z + 1/2 x y z - 1/2 z y x + 1/2 x y z, + + 2 2 2 2 + COEFF(0, -1, 0) = z y x - y z - x y z + y z, + + 2 2 2 2 + COEFF(1, -1, 0) = 1/2 y x z - 1/2 z y x + 1/2 x y z - 1/2 x y z, + + 2 2 2 2 + COEFF(-1, 0, 0) = -x z + x z - x y z + z y x , + + 2 2 2 2 + COEFF(0, 0, 0) = -2 z - 2 z y x + 2 y z + 2 x z, + + 2 2 2 2 + COEFF(1, 0, 0) = z y x - x z - x z + x y z, + + 2 2 2 2 + COEFF(-1, 1, 0) = - 1/2 x y z + 1/2 x y z - 1/2 z y x + 1/2 y x z, + + 2 2 2 2 + COEFF(0, 1, 0) = z y x - y z + x y z - y z, + + 2 2 2 2 + COEFF(1, 1, 0) = - 1/2 x y z - 1/2 z y x - 1/2 y x z - 1/2 x y z, + + 2 2 2 2 + COEFF(-1, -1, 1) = - 1/4 x y z - 1/4 x y z + 1/8 y x + 1/8 y x + + 2 2 2 2 + - 1/8 x y + 1/4 y x z + 1/4 z y x - 1/8 x y, COEFF(0, -1, 1) = + + 2 2 2 2 2 2 2 + - 1/2 z y x - 1/4 y + 1/4 x y + 1/4 y - 1/4 y x - 1/2 y z + 1/2 y z + + 2 2 2 2 2 2 + + 1/2 x y z, COEFF(1, -1, 1) = 1/4 z y x + 1/8 y x - 1/4 x y z + + 2 2 2 + - 1/4 y x z + 1/8 x y + 1/4 x y z - 1/8 x y - 1/8 y x, COEFF(-1, 0, 1) + + 2 2 2 2 2 2 + = - 1/2 z y x - 1/2 x z - 1/4 y x + 1/2 x y z - 1/4 x + 1/4 x + + 2 2 + + 1/4 x y + 1/2 x z, COEFF(0, 0, 1) = + + 2 2 2 2 2 2 2 2 + z + 1/2 - x z - 1/2 y + 1/2 y x + z y x - y z - 1/2 x , + + 2 2 2 2 2 + COEFF(1, 0, 1) = 1/2 x z - 1/2 z y x - 1/2 x y z + 1/2 x z + 1/4 x + + 2 2 2 2 2 + - 1/4 y x + 1/4 x - 1/4 x y , COEFF(-1, 1, 1) = 1/8 x y - 1/4 x y z + + 2 2 2 2 2 2 + - 1/4 y x z + 1/4 z y x - 1/8 y x - 1/8 x y + 1/8 y x + 1/4 x y z, + + 2 2 2 + COEFF(0, 1, 1) = - 1/2 x y z + 1/4 y - 1/4 x y + 1/2 y z + 1/2 y z + + 2 2 2 2 2 2 2 + - 1/2 z y x - 1/4 y x + 1/4 y , COEFF(1, 1, 1) = 1/4 x y z + 1/8 x y + + 2 2 2 2 2 2 + + 1/8 x y + 1/8 y x + 1/4 x y z + 1/4 y x z + 1/4 z y x + 1/8 y x ] + +> print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dz.compute.c"); +bytes used=71082972, alloc=2227816, time=5.45 +bytes used=72083168, alloc=2227816, time=5.53 +bytes used=73083352, alloc=2227816, time=5.60 +bytes used=74085748, alloc=2227816, time=5.68 +bytes used=75085980, alloc=2227816, time=5.82 +bytes used=76086188, alloc=2227816, time=5.88 +bytes used=77086440, alloc=2227816, time=5.98 +bytes used=78086768, alloc=2227816, time=6.06 +bytes used=79086928, alloc=2227816, time=6.19 +bytes used=80087176, alloc=2227816, time=6.29 +bytes used=81087364, alloc=2227816, time=6.41 +bytes used=82087784, alloc=2227816, time=6.55 +> +# d^2/dx^2 +> simplify( diff(interp_3d_cube_order2_smooth0,x,x) ); +bytes used=83087956, alloc=2227816, time=6.67 +- 1/2 z DATA(1, 0, -1) + 1/2 z DATA(-1, 0, 1) + 1/2 y DATA(1, 1, 0) + + 2 2 2 + - z DATA(0, 0, -1) + 1/2 z DATA(-1, 0, -1) + 1/2 z DATA(1, 0, -1) + + 2 2 2 + + 1/2 z DATA(-1, 0, 1) - z DATA(0, 0, 1) + 1/2 z DATA(1, 0, 1) + + 2 2 + - y DATA(0, 1, 0) + 1/2 y DATA(-1, 1, 0) + 1/2 y DATA(1, -1, 0) + + 2 2 2 + - y DATA(0, -1, 0) + 1/2 y DATA(-1, -1, 0) - y DATA(0, 1, 0) + + 2 2 2 + + 1/2 y DATA(1, 1, 0) - y DATA(-1, 0, 0) + 2 y DATA(0, 0, 0) + + 2 + - y DATA(1, 0, 0) + 1/2 y DATA(-1, 1, 0) - 1/2 y DATA(1, -1, 0) + + + y DATA(0, -1, 0) - 1/2 y DATA(-1, -1, 0) - 1/2 z DATA(-1, 0, -1) + + 2 2 2 2 + - 1/2 z y DATA(0, -1, 1) + 1/4 z y DATA(-1, -1, 1) + + 2 2 2 2 2 2 + - 2 z y DATA(0, 0, 0) + z y DATA(1, 0, 0) + z y DATA(0, 0, -1) + + 2 2 2 2 + - 1/2 z y DATA(-1, 0, -1) - 1/2 z y DATA(-1, 1, 0) + + 2 2 2 2 + - 1/2 z y DATA(0, 1, 1) + 1/4 z y DATA(1, 1, 1) + + 2 2 2 2 + + 1/4 z y DATA(-1, -1, -1) - 1/2 z y DATA(0, -1, -1) + + 2 2 2 2 + - 1/2 z y DATA(1, 0, -1) - 1/2 z y DATA(1, -1, 0) + + 2 2 2 2 2 2 + + z y DATA(0, -1, 0) - 1/2 z y DATA(-1, -1, 0) + z y DATA(0, 1, 0) + + 2 2 2 + - 1/2 z y DATA(1, 1, 0) - 1/2 y z DATA(1, 0, 1) + + 2 2 + - 1/4 y z DATA(-1, -1, -1) + 2 z DATA(0, 0, 0) + DATA(-1, 0, 0) + + 2 2 + + 1/4 y z DATA(-1, 1, 1) - 1/4 y z DATA(1, -1, 1) + + 2 2 + + 1/2 y z DATA(0, -1, 1) - 1/4 y z DATA(-1, -1, 1) + + 2 2 + - 1/2 y z DATA(0, 1, 1) + 1/4 y z DATA(1, 1, 1) + + 2 2 2 + - 1/2 y z DATA(-1, 1, 0) + 1/2 y z DATA(1, -1, 0) - y z DATA(0, -1, 0) + + 2 2 2 + + 1/2 y z DATA(-1, -1, 0) + y z DATA(0, 1, 0) - 1/2 y z DATA(1, 1, 0) + + 2 2 + - 1/4 y z DATA(-1, -1, -1) + 1/2 y z DATA(0, -1, -1) + + 2 + - 1/4 y z DATA(1, -1, -1) - 2 DATA(0, 0, 0) + DATA(1, 0, 0) + + 2 + + z DATA(0, 0, -1) - z DATA(0, 0, 1) - y z DATA(0, 0, -1) + + 2 2 2 + + 1/2 y z DATA(0, 1, -1) - 1/2 y z DATA(0, -1, 1) + y z DATA(0, 0, 1) + + 2 2 + - 1/2 y z DATA(0, 1, 1) + 1/2 y z DATA(0, -1, -1) + + + 1/4 y z DATA(1, -1, -1) - 1/4 y z DATA(-1, 1, -1) + + - 1/4 y z DATA(1, 1, -1) + 1/4 y z DATA(-1, 1, 1) - 1/4 y z DATA(1, -1, 1) + + - 1/4 y z DATA(-1, -1, 1) + 1/4 y z DATA(1, 1, 1) + + 2 2 + + 1/4 y z DATA(-1, -1, -1) - 1/2 z y DATA(-1, 0, 1) + + 2 2 2 2 + + z y DATA(0, 0, 1) - 1/2 z y DATA(1, 0, 1) + + 2 2 2 2 + + 1/4 z y DATA(1, -1, -1) + 1/4 z y DATA(-1, 1, -1) + + 2 2 2 2 + + 1/4 z y DATA(1, 1, -1) - 1/2 z y DATA(0, 1, -1) + + 2 2 2 2 + + 1/4 z y DATA(-1, 1, 1) + 1/4 z y DATA(1, -1, 1) + + 2 2 + + 1/4 y z DATA(1, 1, 1) + 1/2 y z DATA(-1, 0, -1) + + 2 2 + + 1/2 y z DATA(1, 0, -1) - 1/2 y z DATA(-1, 0, 1) + + 2 2 + - 1/4 y z DATA(-1, 1, -1) - 1/4 y z DATA(1, 1, -1) + + 2 2 + + 1/4 y z DATA(-1, 1, 1) + 1/4 y z DATA(1, -1, 1) + + 2 2 + + 1/4 y z DATA(-1, -1, 1) - 1/4 y z DATA(1, -1, -1) + + 2 2 + + 1/4 y z DATA(-1, 1, -1) + 1/4 y z DATA(1, 1, -1) + + 2 + - 1/2 y z DATA(0, 1, -1) + 1/2 y z DATA(0, -1, 1) - 1/2 y z DATA(0, 1, 1) + + 2 + - 1/2 y z DATA(0, -1, -1) + 1/2 y z DATA(0, 1, -1) - z DATA(-1, 0, 0) + + 2 2 2 + + z y DATA(-1, 0, 0) - z DATA(1, 0, 0) + 1/2 z DATA(1, 0, 1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +bytes used=84088124, alloc=2227816, time=6.73 + 2 2 2 2 +[COEFF(-1, -1, -1) = - 1/4 y z + 1/4 z y + 1/4 y z - 1/4 y z, + + 2 2 2 2 + COEFF(0, -1, -1) = 1/2 y z - 1/2 y z - 1/2 z y + 1/2 y z , + + 2 2 2 2 + COEFF(1, -1, -1) = - 1/4 y z + 1/4 z y + 1/4 y z - 1/4 y z, + + 2 2 2 2 + COEFF(-1, 0, -1) = - 1/2 z + 1/2 y z + 1/2 z - 1/2 z y , + + 2 2 2 2 + COEFF(0, 0, -1) = -z - y z + z y + z, + + 2 2 2 2 + COEFF(1, 0, -1) = - 1/2 z + 1/2 y z + 1/2 z - 1/2 z y , + + 2 2 2 2 + COEFF(-1, 1, -1) = 1/4 z y - 1/4 y z - 1/4 y z + 1/4 y z , + + 2 2 2 2 + COEFF(0, 1, -1) = - 1/2 z y + 1/2 y z + 1/2 y z - 1/2 y z , + + 2 2 2 2 + COEFF(1, 1, -1) = 1/4 z y - 1/4 y z - 1/4 y z + 1/4 y z , + + 2 2 2 2 + COEFF(-1, -1, 0) = - 1/2 y + 1/2 y z - 1/2 z y + 1/2 y , + + 2 2 2 2 + COEFF(0, -1, 0) = -y z + y - y + z y , + + 2 2 2 2 + COEFF(1, -1, 0) = - 1/2 y + 1/2 y z - 1/2 z y + 1/2 y , + + 2 2 2 2 + COEFF(-1, 0, 0) = -z + z y - y + 1, + + 2 2 2 2 + COEFF(0, 0, 0) = -2 z y - 2 + 2 y + 2 z , + + 2 2 2 2 + COEFF(1, 0, 0) = -z + z y - y + 1, + + 2 2 2 2 + COEFF(-1, 1, 0) = - 1/2 y z + 1/2 y + 1/2 y - 1/2 z y , + + 2 2 2 2 + COEFF(0, 1, 0) = y z - y - y + z y , + + 2 2 2 2 + COEFF(1, 1, 0) = - 1/2 y z + 1/2 y + 1/2 y - 1/2 z y , + + 2 2 2 2 + COEFF(-1, -1, 1) = - 1/4 y z + 1/4 y z + 1/4 z y - 1/4 y z, + + 2 2 2 2 + COEFF(0, -1, 1) = 1/2 y z - 1/2 z y + 1/2 y z - 1/2 y z, + + 2 2 2 2 + COEFF(1, -1, 1) = - 1/4 y z + 1/4 y z + 1/4 z y - 1/4 y z, + + 2 2 2 2 + COEFF(-1, 0, 1) = 1/2 z + 1/2 z - 1/2 z y - 1/2 y z, + + 2 2 2 2 + COEFF(0, 0, 1) = y z + z y - z - z, + + 2 2 2 2 + COEFF(1, 0, 1) = 1/2 z + 1/2 z - 1/2 z y - 1/2 y z, + + 2 2 2 2 + COEFF(-1, 1, 1) = 1/4 y z + 1/4 z y + 1/4 y z + 1/4 y z, + + 2 2 2 2 + COEFF(0, 1, 1) = - 1/2 y z - 1/2 y z - 1/2 y z - 1/2 z y , + + 2 2 2 2 + COEFF(1, 1, 1) = 1/4 y z + 1/4 z y + 1/4 y z + 1/4 y z] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxx.compute.c"); +bytes used=85088688, alloc=2227816, time=6.80 +bytes used=86088860, alloc=2227816, time=6.87 +bytes used=87089184, alloc=2227816, time=6.98 +bytes used=88089340, alloc=2227816, time=7.10 +bytes used=89089724, alloc=2227816, time=7.22 +> +# d^2/dxdy +> simplify( diff(interp_3d_cube_order2_smooth0,x,y) ); +bytes used=90089884, alloc=2227816, time=7.29 +1/2 y DATA(1, 1, 0) - 1/2 y DATA(-1, 1, 0) + 1/2 y DATA(1, -1, 0) + + - 1/2 y DATA(-1, -1, 0) - 1/4 DATA(-1, 1, 0) - 1/4 DATA(1, -1, 0) + + 2 2 + - 1/4 y z DATA(-1, 1, 1) + 1/4 y z DATA(1, -1, 1) + + 2 2 + - 1/4 y z DATA(-1, -1, 1) + 1/4 y z DATA(1, 1, 1) + + 2 2 + + 1/2 y z DATA(-1, 1, 0) - 1/2 y z DATA(1, -1, 0) + + 2 2 + + 1/2 y z DATA(-1, -1, 0) - 1/2 y z DATA(1, 1, 0) + + 2 + - 1/4 y z DATA(-1, -1, -1) + 1/4 DATA(-1, -1, 0) + 1/4 DATA(1, 1, 0) + + - 1/4 y z DATA(1, -1, -1) + 1/4 y z DATA(-1, 1, -1) + + - 1/4 y z DATA(1, 1, -1) - 1/4 y z DATA(-1, 1, 1) + 1/4 y z DATA(1, -1, 1) + + - 1/4 y z DATA(-1, -1, 1) + 1/4 y z DATA(1, 1, 1) + + 2 + + 1/4 y z DATA(-1, -1, -1) + 1/4 y z DATA(1, -1, -1) + + 2 2 + - 1/4 y z DATA(-1, 1, -1) + 1/4 y z DATA(1, 1, -1) + + 2 2 + - 1/4 z x DATA(1, -1, -1) + 1/2 z x DATA(0, -1, 1) + + 2 2 + - 1/2 z x DATA(-1, 1, 0) + 1/4 z x DATA(1, 1, 1) + + 2 2 2 + - 1/2 z x DATA(0, 1, 1) - 1/4 z x DATA(-1, -1, 1) + z x DATA(0, 1, 0) + + 2 2 2 + + 1/2 z x DATA(-1, -1, 0) - z x DATA(0, -1, 0) + 1/2 z x DATA(1, -1, 0) + + 2 2 + + 1/2 z x DATA(0, -1, -1) - 1/4 z x DATA(-1, -1, -1) + + 2 2 + - 1/2 z x DATA(1, 1, 0) - 1/4 z x DATA(1, -1, 1) + + 2 2 + + 1/4 z x DATA(-1, 1, 1) - 1/2 z x DATA(0, 1, -1) + + 2 2 + + 1/4 z x DATA(1, 1, -1) + 1/4 z x DATA(-1, 1, -1) + + 2 2 + - z y x DATA(-1, 0, -1) + 1/2 z y x DATA(-1, 1, -1) + + 2 2 + + 1/2 z y x DATA(1, 1, -1) + 1/2 z y x DATA(-1, -1, -1) + + 2 2 + + 1/2 z y x DATA(1, -1, 1) + 1/2 z y x DATA(-1, -1, 1) + + 2 2 2 + + 1/2 z y x DATA(1, 1, 1) - z y x DATA(1, 0, -1) - z y x DATA(1, 0, 1) + + 2 2 2 + + 2 z y x DATA(0, 0, -1) - z y x DATA(-1, 0, 1) - z y x DATA(1, 1, 0) + + 2 2 2 + + 2 z y x DATA(0, -1, 0) + 2 z y x DATA(0, 1, 0) - z y x DATA(0, 1, -1) + + 2 2 2 + + 2 z y x DATA(0, 0, 1) - z y x DATA(0, 1, 1) - z y x DATA(0, -1, -1) + + 2 2 2 + - z y x DATA(-1, 1, 0) - z y x DATA(1, -1, 0) - z y x DATA(-1, -1, 0) + + 2 + - 1/8 z DATA(-1, 1, -1) + 1/2 y x z DATA(-1, 1, 1) + + 2 + + 1/2 y x z DATA(1, -1, 1) + 2 z y x DATA(-1, 0, 0) + + 2 2 + - 4 z y x DATA(0, 0, 0) + 2 z y x DATA(1, 0, 0) + + - 1/2 y x z DATA(-1, 1, -1) - 1/2 y x z DATA(1, 1, -1) + + + y x z DATA(0, 1, -1) - y x z DATA(0, 1, 1) + 1/2 y x z DATA(1, 1, 1) + + - 1/2 y x z DATA(1, -1, -1) - 1/2 y x z DATA(-1, -1, -1) + + 2 + - y x z DATA(0, -1, 1) + 1/2 y x z DATA(-1, -1, 1) - 1/4 z DATA(1, 1, 0) + + 2 + - 1/8 z DATA(-1, -1, -1) + 1/8 z DATA(-1, 1, -1) + 1/8 z DATA(1, 1, -1) + + 2 2 2 + - 1/8 z DATA(-1, 1, 1) - 1/8 z DATA(1, -1, 1) + 1/8 z DATA(-1, -1, 1) + + 2 2 2 + + 1/8 z DATA(1, 1, 1) - 1/8 z DATA(1, -1, -1) + 1/8 z DATA(-1, -1, -1) + + 2 2 2 + + 1/4 z DATA(-1, 1, 0) + 1/4 z DATA(1, -1, 0) - 1/4 z DATA(-1, -1, 0) + + - 1/8 z DATA(1, 1, -1) + 1/2 x DATA(1, 1, 0) - 1/8 z DATA(-1, 1, 1) + + - y DATA(1, 0, 0) + 1/8 z DATA(1, 1, 1) + 1/8 z DATA(-1, -1, 1) + + - 1/8 z DATA(1, -1, 1) + 1/8 z DATA(1, -1, -1) - 1/2 x z DATA(0, 1, 1) + + + 1/2 y z DATA(1, 0, -1) - 1/2 y z DATA(1, 0, 1) + 1/2 y z DATA(-1, 0, 1) + + 2 + - z y x DATA(0, -1, 1) - x DATA(0, 1, 0) - 1/2 x DATA(-1, -1, 0) + + + x DATA(0, -1, 0) + 1/2 x DATA(-1, 1, 0) + y DATA(-1, 0, 0) + + 2 + + y x DATA(-1, 1, 0) + 1/2 z y x DATA(-1, 1, 1) + + 2 + + 1/2 z y x DATA(1, -1, -1) + y x z DATA(0, -1, -1) + + - 2 y x z DATA(0, 0, -1) + y x z DATA(-1, 0, -1) + y x z DATA(1, 0, -1) + + - y x z DATA(-1, 0, 1) + 2 y x z DATA(0, 0, 1) - y x z DATA(1, 0, 1) + + + y x DATA(-1, -1, 0) - 2 y x DATA(0, 1, 0) + y x DATA(1, 1, 0) + + - 2 y x DATA(-1, 0, 0) + 4 y x DATA(0, 0, 0) - 2 y x DATA(1, 0, 0) + + 2 2 + - 1/2 y z DATA(1, 0, 1) - y z DATA(-1, 0, 0) + y x DATA(1, -1, 0) + + 2 + - 2 y x DATA(0, -1, 0) + 1/2 y z DATA(-1, 0, -1) + + 2 2 + - 1/2 y z DATA(1, 0, -1) + 1/2 y z DATA(-1, 0, 1) + + + 1/2 x z DATA(0, -1, 1) - 1/2 x DATA(1, -1, 0) - 1/4 x z DATA(1, -1, 1) + + - 1/4 x z DATA(-1, -1, 1) + 1/4 x z DATA(1, 1, 1) + + + 1/4 x z DATA(-1, -1, -1) - 1/2 x z DATA(0, -1, -1) + + + 1/2 x z DATA(0, 1, -1) - 1/4 x z DATA(1, 1, -1) + 1/4 x z DATA(-1, 1, 1) + + 2 + + y z DATA(1, 0, 0) + 1/4 x z DATA(1, -1, -1) - 1/4 x z DATA(-1, 1, -1) + + - 1/2 y z DATA(-1, 0, -1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +bytes used=91090076, alloc=2227816, time=7.35 +bytes used=92090532, alloc=2227816, time=7.42 + 2 +[COEFF(-1, -1, -1) = - 1/8 z + 1/4 y z - 1/4 y z - 1/2 y x z + 1/4 x z + + 2 2 2 + - 1/4 z x + 1/8 z + 1/2 z y x, + + 2 2 + COEFF(0, -1, -1) = - 1/2 x z + 1/2 z x - z y x + y x z, COEFF(1, -1, -1) + + 2 2 2 2 + = - 1/8 z - 1/4 z x - 1/4 y z - 1/2 y x z + 1/2 z y x + 1/4 y z + + + 1/8 z + 1/4 x z, + + 2 2 + COEFF(-1, 0, -1) = - 1/2 y z + y x z - z y x + 1/2 y z , + + 2 + COEFF(0, 0, -1) = 2 z y x - 2 y x z, + + 2 2 + COEFF(1, 0, -1) = 1/2 y z - 1/2 y z - z y x + y x z, COEFF(-1, 1, -1) = + + 2 2 2 + 1/4 y z - 1/4 y z - 1/8 z + 1/8 z + 1/4 z x - 1/4 x z - 1/2 y x z + + 2 2 2 + + 1/2 z y x, COEFF(0, 1, -1) = 1/2 x z + y x z - 1/2 z x - z y x, + + 2 2 2 + COEFF(1, 1, -1) = 1/8 z - 1/8 z - 1/4 x z + 1/4 z x + 1/4 y z + + 2 + + 1/2 z y x - 1/4 y z - 1/2 y x z, COEFF(-1, -1, 0) = + + 2 2 2 2 + 1/4 - 1/2 y + 1/2 y z - 1/2 x - 1/4 z - z y x + y x + 1/2 z x, + + 2 2 + COEFF(0, -1, 0) = 2 z y x - 2 y x + x - z x, COEFF(1, -1, 0) = + + 2 2 2 2 + 1/2 z x + 1/2 y - z y x - 1/2 x - 1/4 - 1/2 y z + 1/4 z + y x, + + 2 2 + COEFF(-1, 0, 0) = -2 y x - y z + 2 z y x + y, + + 2 + COEFF(0, 0, 0) = -4 z y x + 4 y x, + + 2 2 + COEFF(1, 0, 0) = -y + y z - 2 y x + 2 z y x, COEFF(-1, 1, 0) = + + 2 2 2 2 + 1/4 z + 1/2 x + 1/2 y z - z y x - 1/2 z x - 1/4 + y x - 1/2 y, + + 2 2 + COEFF(0, 1, 0) = 2 z y x + z x - x - 2 y x, COEFF(1, 1, 0) = + + 2 2 2 2 + - 1/4 z - 1/2 y z + y x + 1/4 + 1/2 y - 1/2 z x + 1/2 x - z y x, + + 2 + COEFF(-1, -1, 1) = 1/2 y x z - 1/4 y z - 1/4 x z + 1/2 z y x + 1/8 z + + 2 2 2 + - 1/4 z x + 1/8 z - 1/4 y z , + + 2 2 + COEFF(0, -1, 1) = 1/2 z x - z y x + 1/2 x z - y x z, COEFF(1, -1, 1) = + + 2 2 2 2 + 1/4 y z - 1/8 z + 1/4 y z - 1/8 z + 1/2 z y x - 1/4 x z - 1/4 z x + + 2 2 + + 1/2 y x z, COEFF(-1, 0, 1) = -z y x - y x z + 1/2 y z + 1/2 y z , + + 2 + COEFF(0, 0, 1) = 2 z y x + 2 y x z, + + 2 2 + COEFF(1, 0, 1) = - 1/2 y z - y x z - z y x - 1/2 y z , COEFF(-1, 1, 1) = + + 2 2 2 2 + 1/4 z x + 1/2 y x z - 1/8 z + 1/2 z y x - 1/8 z - 1/4 y z - 1/4 y z + + 2 2 + + 1/4 x z, COEFF(0, 1, 1) = -y x z - 1/2 z x - 1/2 x z - z y x, + + 2 2 2 + COEFF(1, 1, 1) = 1/2 z y x + 1/8 z + 1/8 z + 1/4 z x + 1/4 x z + 1/4 y z + + 2 + + 1/4 y z + 1/2 y x z] + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxy.compute.c"); +bytes used=93090716, alloc=2227816, time=7.50 +bytes used=94090920, alloc=2227816, time=7.57 +bytes used=95091564, alloc=2227816, time=7.68 +bytes used=96094492, alloc=2227816, time=7.77 +bytes used=97094652, alloc=2227816, time=7.91 +bytes used=98094828, alloc=2227816, time=8.00 +bytes used=99094980, alloc=2227816, time=8.17 +bytes used=100095136, alloc=2227816, time=8.31 +> +# d^2/dxdz +> simplify( diff(interp_3d_cube_order2_smooth0,x,z) ); +bytes used=101095296, alloc=2227816, time=8.38 +bytes used=102095644, alloc=2227816, time=8.45 +1/4 DATA(-1, 0, -1) - 1/4 DATA(1, 0, -1) - 1/4 DATA(-1, 0, 1) + + + 1/4 DATA(1, 0, 1) - 1/4 y z DATA(1, -1, -1) - 1/4 y z DATA(-1, 1, -1) + + + 1/4 y z DATA(1, 1, -1) - 1/4 y z DATA(-1, 1, 1) - 1/4 y z DATA(1, -1, 1) + + + 1/4 y z DATA(-1, -1, 1) + 1/4 y z DATA(1, 1, 1) + + + 1/4 y z DATA(-1, -1, -1) + 1/2 y x z DATA(-1, 1, 1) + + - 1/2 y x z DATA(1, -1, 1) + 1/2 y x z DATA(-1, 1, -1) + + + 1/2 y x z DATA(1, 1, -1) - y x z DATA(0, 1, -1) - y x z DATA(0, 1, 1) + + + 1/2 y x z DATA(1, 1, 1) - 1/2 y x z DATA(1, -1, -1) + + - 1/2 y x z DATA(-1, -1, -1) + y x z DATA(0, -1, 1) + + - 1/2 y x z DATA(-1, -1, 1) + y x z DATA(0, -1, -1) + + 2 2 + + 1/4 y z DATA(1, -1, 1) - 1/4 y z DATA(-1, -1, 1) + + 2 2 + - 1/2 y z DATA(1, 1, 0) + 1/4 y z DATA(1, 1, 1) + + 2 2 2 + + 1/2 y z DATA(-1, 0, -1) - z y x DATA(-1, 0, -1) - z y x DATA(1, 1, 0) + + 2 2 2 + - z y x DATA(0, 1, -1) + 2 z y x DATA(0, -1, 0) - z y x DATA(-1, -1, 0) + + 2 2 + + 2 z y x DATA(0, 1, 0) + 1/2 z y x DATA(-1, 1, -1) + + 2 2 + + 1/2 z y x DATA(1, 1, -1) + 1/2 z y x DATA(-1, -1, -1) + + 2 2 + + 1/2 z y x DATA(1, -1, 1) + 1/2 z y x DATA(-1, -1, 1) + + 2 2 + + 1/2 z y x DATA(1, 1, 1) - z y x DATA(-1, 1, 0) + + 2 2 + + 1/2 z y x DATA(-1, 1, 1) + 2 z y x DATA(-1, 0, 0) + + 2 2 + - y x z DATA(-1, 1, 0) + 2 z y x DATA(0, 0, -1) + 2 z y x DATA(0, 0, 1) + + 2 2 2 + - 4 z y x DATA(0, 0, 0) - z y x DATA(1, 0, -1) - z y x DATA(1, 0, 1) + + 2 2 2 + + 2 z y x DATA(1, 0, 0) - z y x DATA(-1, 0, 1) - z y x DATA(0, -1, 1) + + 2 + - 1/4 y z DATA(-1, 1, 1) - 1/2 y x DATA(0, 1, 1) + + 2 + + 1/4 y x DATA(1, -1, -1) - 1/4 y z DATA(-1, -1, -1) + + - 1/4 y x DATA(-1, 1, -1) - 1/4 y x DATA(1, 1, -1) + + 2 + + 1/4 y x DATA(-1, 1, 1) - 1/2 y z DATA(1, 0, -1) + + 2 2 2 + + 1/2 y z DATA(-1, 0, 1) - 1/2 y z DATA(1, 0, 1) - y z DATA(-1, 0, 0) + + + 1/4 y x DATA(1, 1, 1) + 1/4 y x DATA(-1, -1, -1) + + + 1/2 y x DATA(0, 1, -1) + 1/2 y x DATA(0, -1, 1) + + 2 2 + + 1/2 z y x DATA(1, -1, -1) - 1/4 y x DATA(1, 1, -1) + + 2 + + 1/2 y x DATA(0, 1, -1) - 1/4 y x DATA(1, -1, 1) + + 2 + - 1/4 y x DATA(-1, -1, 1) + 1/4 y x DATA(-1, 1, 1) + + 2 2 + + 1/4 y x DATA(1, -1, 1) - 1/2 y x DATA(0, -1, 1) + + 2 2 + + 1/4 y x DATA(-1, -1, 1) - 1/2 y x DATA(0, 1, 1) + + 2 2 + + 1/4 y x DATA(1, 1, 1) - 1/4 y x DATA(1, -1, -1) + + 2 + - 1/2 y x DATA(0, -1, -1) - 1/4 y x DATA(-1, 1, -1) + + 2 2 2 + + 1/8 y DATA(1, 1, 1) + 1/8 y DATA(-1, -1, -1) - 1/4 y DATA(-1, 0, -1) + + 2 2 2 + + 1/4 y DATA(1, 0, -1) + 1/4 y DATA(-1, 0, 1) - 1/4 y DATA(1, 0, 1) + + 2 2 2 + - 1/8 y DATA(1, -1, -1) + 1/8 y DATA(-1, 1, -1) - 1/8 y DATA(1, 1, -1) + + 2 + - 1/8 y DATA(-1, 1, 1) + 1/8 y DATA(-1, -1, 1) + 1/8 y DATA(1, 1, 1) + + + y x z DATA(1, -1, 0) + y x z DATA(-1, -1, 0) + 2 y x z DATA(0, 1, 0) + + - y x z DATA(1, 1, 0) - 2 y x z DATA(0, -1, 0) - 1/2 y z DATA(-1, -1, 0) + + 2 2 2 + - y x DATA(0, 0, -1) + 1/2 y x DATA(-1, 0, -1) + 1/2 y x DATA(1, 0, -1) + + 2 2 2 + - 1/2 y x DATA(-1, 0, 1) + y x DATA(0, 0, 1) - 1/2 y x DATA(1, 0, 1) + + 2 2 + - 1/4 y x DATA(-1, -1, -1) + 1/2 y x DATA(0, -1, -1) - z DATA(1, 0, 0) + + - 1/2 x DATA(-1, 0, -1) - 1/2 x DATA(1, 0, -1) + 1/2 x DATA(-1, 0, 1) + + 2 2 + + 1/2 z DATA(1, 0, 1) + 1/8 y DATA(1, -1, 1) - 1/8 y DATA(-1, -1, 1) + + 2 2 + + x DATA(0, 0, -1) - 1/2 y z DATA(1, -1, 0) + 1/2 y z DATA(-1, -1, 0) + + - 2 x z DATA(0, 0, -1) + x z DATA(-1, 0, -1) - 1/2 y z DATA(1, 1, 0) + + + 1/2 y z DATA(-1, 1, 0) + 1/2 y z DATA(1, -1, 0) + 1/8 y DATA(1, -1, -1) + + 2 + + 1/8 y DATA(-1, 1, -1) - 1/8 y DATA(1, 1, -1) + y z DATA(1, 0, 0) + + + x z DATA(1, 0, -1) + x z DATA(-1, 0, 1) - 2 x z DATA(0, 0, 1) + + + x z DATA(1, 0, 1) - 2 x z DATA(-1, 0, 0) + 4 x z DATA(0, 0, 0) + + 2 + - 2 x z DATA(1, 0, 0) + 1/4 y z DATA(1, -1, -1) + + 2 + - 1/4 y z DATA(-1, 1, -1) - 1/8 y DATA(1, -1, 1) - x DATA(0, 0, 1) + + + 1/2 x DATA(1, 0, 1) - 1/8 y DATA(-1, 1, 1) - 1/2 z DATA(-1, 0, -1) + + + 1/2 z DATA(1, 0, -1) - 1/2 z DATA(-1, 0, 1) + z DATA(-1, 0, 0) + + 2 2 2 + - z y x DATA(0, -1, -1) - z y x DATA(0, 1, 1) - z y x DATA(1, -1, 0) + + 2 + - 1/8 y DATA(-1, -1, -1) + 1/4 y z DATA(1, 1, -1) + + 2 + + 1/2 y z DATA(-1, 1, 0) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +bytes used=103095980, alloc=2227816, time=8.52 + 2 2 2 +[COEFF(-1, -1, -1) = 1/2 z y x + 1/4 y z + 1/4 y x - 1/8 y - 1/4 y x + 1/8 y + + 2 + - 1/2 y x z - 1/4 y z, + + 2 2 + COEFF(0, -1, -1) = - 1/2 y x + 1/2 y x + y x z - z y x, COEFF(1, -1, -1) + + 2 2 2 2 + = 1/8 y - 1/4 y z + 1/2 z y x - 1/2 y x z - 1/8 y + 1/4 y z - 1/4 y x + + + 1/4 y x, COEFF(-1, 0, -1) = + + 2 2 2 2 + x z + 1/2 y z - z y x - 1/2 z - 1/2 x - 1/4 y + 1/4 + 1/2 y x, + + 2 2 + COEFF(0, 0, -1) = -y x + x + 2 z y x - 2 x z, COEFF(1, 0, -1) = + + 2 2 2 2 + 1/2 y x - z y x - 1/2 x + x z - 1/2 y z + 1/4 y + 1/2 z - 1/4, + + 2 + COEFF(-1, 1, -1) = - 1/4 y x - 1/4 y z + 1/8 y + 1/2 y x z - 1/4 y x + + 2 2 2 + + 1/8 y - 1/4 y z + 1/2 z y x, + + 2 2 + COEFF(0, 1, -1) = -y x z + 1/2 y x + 1/2 y x - z y x, COEFF(1, 1, -1) = + + 2 2 2 2 + 1/4 y z - 1/8 y - 1/4 y x - 1/8 y + 1/2 z y x - 1/4 y x + 1/2 y x z + + 2 2 + + 1/4 y z, COEFF(-1, -1, 0) = -z y x + 1/2 y z - 1/2 y z + y x z, + + 2 + COEFF(0, -1, 0) = 2 z y x - 2 y x z, + + 2 2 + COEFF(1, -1, 0) = y x z - z y x + 1/2 y z - 1/2 y z, + + 2 2 + COEFF(-1, 0, 0) = z + 2 z y x - y z - 2 x z, + + 2 + COEFF(0, 0, 0) = -4 z y x + 4 x z, + + 2 2 + COEFF(1, 0, 0) = y z - 2 x z + 2 z y x - z, + + 2 2 + COEFF(-1, 1, 0) = -z y x + 1/2 y z + 1/2 y z - y x z, + + 2 + COEFF(0, 1, 0) = 2 z y x + 2 y x z, + + 2 2 + COEFF(1, 1, 0) = - 1/2 y z - 1/2 y z - y x z - z y x, COEFF(-1, -1, 1) = + + 2 2 2 2 + - 1/8 y + 1/4 y z + 1/4 y x - 1/4 y x - 1/4 y z - 1/2 y x z + 1/2 z y x + + 2 2 + + 1/8 y, COEFF(0, -1, 1) = -z y x + 1/2 y x - 1/2 y x + y x z, + + 2 2 + COEFF(1, -1, 1) = 1/4 y x - 1/4 y z - 1/2 y x z - 1/8 y + 1/8 y - 1/4 y x + + 2 2 + + 1/2 z y x + 1/4 y z, COEFF(-1, 0, 1) = + + 2 2 2 2 + - 1/2 z + x z - z y x + 1/4 y + 1/2 y z - 1/4 + 1/2 x - 1/2 y x, + + 2 2 + COEFF(0, 0, 1) = -x - 2 x z + y x + 2 z y x, COEFF(1, 0, 1) = + + 2 2 2 2 + 1/4 - 1/4 y + x z - z y x - 1/2 y z + 1/2 x - 1/2 y x + 1/2 z, + + 2 2 2 + COEFF(-1, 1, 1) = - 1/4 y z - 1/8 y - 1/8 y + 1/4 y x + 1/2 z y x + + 2 + + 1/2 y x z + 1/4 y x - 1/4 y z, + + 2 2 + COEFF(0, 1, 1) = -y x z - z y x - 1/2 y x - 1/2 y x, COEFF(1, 1, 1) = + + 2 2 2 2 + 1/4 y z + 1/2 z y x + 1/4 y x + 1/4 y x + 1/8 y + 1/8 y + 1/4 y z + + + 1/2 y x z] + +> print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxz.compute.c"); +bytes used=104096192, alloc=2293340, time=8.59 +bytes used=105100008, alloc=2293340, time=8.68 +bytes used=106100284, alloc=2293340, time=8.86 +bytes used=107100532, alloc=2293340, time=8.93 +bytes used=108100740, alloc=2293340, time=9.01 +bytes used=109100968, alloc=2293340, time=9.19 +bytes used=110101164, alloc=2293340, time=9.36 +bytes used=111101332, alloc=2293340, time=9.52 +> +# d^2/dy^2 +> simplify( diff(interp_3d_cube_order2_smooth0,y,y) ); +bytes used=112134600, alloc=2293340, time=9.63 +bytes used=113134924, alloc=2293340, time=9.69 + 2 +DATA(0, -1, 0) - 2 DATA(0, 0, 0) + DATA(0, 1, 0) - z DATA(0, 0, -1) + + - 1/2 x z DATA(-1, 0, -1) + 1/2 x z DATA(1, 0, -1) + + + 1/2 x z DATA(-1, 0, 1) - 1/2 x z DATA(1, 0, 1) + + 2 2 2 2 + + 1/4 z x DATA(-1, -1, -1) + 1/4 z x DATA(-1, -1, 1) + + 2 2 2 2 + + z x DATA(1, 0, 0) + 1/4 z x DATA(1, -1, -1) + + 2 2 2 2 + + 1/4 z x DATA(-1, 1, -1) + 1/4 z x DATA(1, 1, -1) + + 2 2 2 + + 1/4 z x DATA(-1, 1, 1) - 1/4 z x DATA(1, -1, -1) + + 2 2 + - 1/4 z x DATA(-1, 1, -1) - 1/4 z x DATA(1, 1, -1) + + 2 2 + + 1/2 z x DATA(0, 1, -1) + 1/4 z x DATA(-1, 1, 1) + + 2 2 + + 1/4 z x DATA(1, -1, 1) - 1/2 z x DATA(0, -1, 1) + + 2 2 + + 1/4 z x DATA(-1, -1, 1) - 1/2 z x DATA(0, 1, 1) + + 2 2 2 + + 1/4 z x DATA(1, 1, 1) - z x DATA(0, 0, -1) + 1/2 z x DATA(-1, 0, -1) + + 2 2 2 + + 1/2 z x DATA(1, 0, -1) - 1/2 z x DATA(-1, 0, 1) + z x DATA(0, 0, 1) + + 2 2 + - 1/2 z x DATA(1, 0, 1) - 1/4 z x DATA(-1, -1, -1) + + 2 + + 1/2 z x DATA(0, -1, -1) - 1/4 x z DATA(1, -1, -1) + + + 1/4 x z DATA(-1, 1, -1) - 1/4 x z DATA(1, 1, -1) + + - 1/4 x z DATA(-1, 1, 1) + 1/4 x z DATA(1, -1, 1) + + 2 + - 1/4 x z DATA(-1, -1, 1) - 1/2 z x DATA(1, 0, 1) + z DATA(0, 0, -1) + + - z DATA(0, 0, 1) - 1/2 z DATA(0, -1, -1) - 1/2 x DATA(-1, 1, 0) + + + x DATA(-1, 0, 0) + 1/2 x DATA(1, -1, 0) - 1/2 x DATA(-1, -1, 0) + + 2 + - x DATA(1, 0, 0) + 1/2 x DATA(1, 1, 0) + 2 x DATA(0, 0, 0) + + 2 2 2 + + 1/2 z DATA(0, 1, -1) - z DATA(0, -1, 0) + 1/2 z DATA(0, -1, 1) + + 2 2 2 + + 2 z DATA(0, 0, 0) - z DATA(0, 1, 0) - z DATA(0, 0, 1) + + 2 2 2 + + 1/2 z DATA(0, 1, 1) + 1/2 z DATA(0, -1, -1) + 1/2 x DATA(-1, 1, 0) + + 2 2 2 + + 1/2 x DATA(1, -1, 0) - x DATA(0, -1, 0) + 1/2 x DATA(-1, -1, 0) + + 2 2 2 + - x DATA(0, 1, 0) + 1/2 x DATA(1, 1, 0) + 1/4 z x DATA(1, 1, 1) + + 2 + + 1/4 x z DATA(-1, -1, -1) + 1/2 z x DATA(-1, 0, -1) + + 2 + - 1/2 z x DATA(1, 0, -1) + 1/4 x z DATA(1, 1, 1) + + 2 2 + + 1/4 z x DATA(1, -1, -1) - 1/4 z x DATA(-1, 1, -1) + + 2 2 + + 1/4 z x DATA(1, 1, -1) + 1/2 z x DATA(-1, 1, 0) + + 2 2 + - 1/2 z x DATA(1, -1, 0) + 1/2 z x DATA(-1, -1, 0) + + 2 2 + - 1/4 z x DATA(-1, 1, 1) + 1/4 z x DATA(1, -1, 1) + + 2 2 2 + - 1/4 z x DATA(-1, -1, 1) - 1/2 z x DATA(1, 1, 0) - x DATA(-1, 0, 0) + + 2 + - x DATA(1, 0, 0) - 1/2 z DATA(0, 1, -1) + 1/2 z DATA(0, -1, 1) + + 2 2 + + 1/2 z DATA(0, 1, 1) + 1/2 z x DATA(-1, 0, 1) - z x DATA(-1, 0, 0) + + 2 2 2 2 + + z x DATA(1, 0, 0) - 1/4 z x DATA(-1, -1, -1) + z x DATA(0, 0, -1) + + 2 2 2 2 + - 1/2 z x DATA(0, 1, -1) + z x DATA(0, -1, 0) + + 2 2 2 2 2 2 + - 1/2 z x DATA(0, -1, 1) - 2 z x DATA(0, 0, 0) + z x DATA(0, 1, 0) + + 2 2 2 2 + + z x DATA(0, 0, 1) - 1/2 z x DATA(0, 1, 1) + + 2 2 2 2 + - 1/2 z x DATA(0, -1, -1) - 1/2 z x DATA(-1, 1, 0) + + 2 2 2 2 + - 1/2 z x DATA(1, -1, 0) - 1/2 z x DATA(-1, -1, 0) + + 2 2 2 2 + - 1/2 z x DATA(1, 1, 0) + z x DATA(-1, 0, 0) + + 2 2 2 2 + + 1/4 z x DATA(1, -1, 1) + 1/4 z x DATA(1, 1, 1) + + 2 2 2 2 + - 1/2 z x DATA(-1, 0, -1) - 1/2 z x DATA(1, 0, -1) + + 2 2 2 2 + - 1/2 z x DATA(-1, 0, 1) - 1/2 z x DATA(1, 0, 1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +bytes used=114137392, alloc=2293340, time=9.75 + 2 2 2 2 +[COEFF(-1, -1, -1) = - 1/4 z x + 1/4 x z - 1/4 z x + 1/4 z x , + + 2 2 2 2 + COEFF(0, -1, -1) = - 1/2 z x + 1/2 z - 1/2 z + 1/2 z x , + + 2 2 2 2 + COEFF(1, -1, -1) = - 1/4 z x + 1/4 z x - 1/4 x z + 1/4 z x , + + 2 2 2 2 + COEFF(-1, 0, -1) = - 1/2 z x - 1/2 x z + 1/2 z x + 1/2 z x , + + 2 2 2 2 + COEFF(0, 0, -1) = z + z x - z - z x , + + 2 2 2 2 + COEFF(1, 0, -1) = 1/2 z x + 1/2 x z - 1/2 z x - 1/2 z x , + + 2 2 2 2 + COEFF(-1, 1, -1) = - 1/4 z x + 1/4 x z - 1/4 z x + 1/4 z x , + + 2 2 2 2 + COEFF(0, 1, -1) = - 1/2 z x + 1/2 z - 1/2 z + 1/2 z x , + + 2 2 2 2 + COEFF(1, 1, -1) = - 1/4 z x + 1/4 z x - 1/4 x z + 1/4 z x , + + 2 2 2 2 + COEFF(-1, -1, 0) = 1/2 z x + 1/2 x - 1/2 z x - 1/2 x, + + 2 2 2 2 + COEFF(0, -1, 0) = -x - z + z x + 1, + + 2 2 2 2 + COEFF(1, -1, 0) = - 1/2 z x + 1/2 x - 1/2 z x + 1/2 x, + + 2 2 2 2 + COEFF(-1, 0, 0) = z x - z x - x + x, + + 2 2 2 2 + COEFF(0, 0, 0) = 2 z - 2 + 2 x - 2 z x , + + 2 2 2 2 + COEFF(1, 0, 0) = z x + z x - x - x , + + 2 2 2 2 + COEFF(-1, 1, 0) = 1/2 z x + 1/2 x - 1/2 z x - 1/2 x, + + 2 2 2 2 + COEFF(0, 1, 0) = -x - z + z x + 1, + + 2 2 2 2 + COEFF(1, 1, 0) = - 1/2 z x + 1/2 x - 1/2 z x + 1/2 x, + + 2 2 2 2 + COEFF(-1, -1, 1) = - 1/4 z x - 1/4 x z + 1/4 z x + 1/4 z x , + + 2 2 2 2 + COEFF(0, -1, 1) = - 1/2 z x + 1/2 z - 1/2 z x + 1/2 z , + + 2 2 2 2 + COEFF(1, -1, 1) = 1/4 x z + 1/4 z x + 1/4 z x + 1/4 z x, + + 2 2 2 2 + COEFF(-1, 0, 1) = - 1/2 z x - 1/2 z x + 1/2 z x + 1/2 x z, + + 2 2 2 2 + COEFF(0, 0, 1) = z x + z x - z - z , + + 2 2 2 2 + COEFF(1, 0, 1) = - 1/2 z x - 1/2 z x - 1/2 x z - 1/2 z x , + + 2 2 2 2 + COEFF(-1, 1, 1) = - 1/4 z x - 1/4 x z + 1/4 z x + 1/4 z x , + + 2 2 2 2 + COEFF(0, 1, 1) = - 1/2 z x + 1/2 z - 1/2 z x + 1/2 z , + + 2 2 2 2 + COEFF(1, 1, 1) = 1/4 x z + 1/4 z x + 1/4 z x + 1/4 z x] + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dyy.compute.c"); +bytes used=115137736, alloc=2293340, time=9.81 +bytes used=116137936, alloc=2293340, time=9.95 +bytes used=117138368, alloc=2293340, time=10.03 +bytes used=118138588, alloc=2293340, time=10.24 +> +# d^2/dydz +> simplify( diff(interp_3d_cube_order2_smooth0,y,z) ); +bytes used=119139236, alloc=2293340, time=10.39 +bytes used=120139448, alloc=2293340, time=10.45 + 2 +- 1/4 DATA(0, 1, -1) - 1/4 DATA(0, -1, 1) + 1/2 z y x DATA(1, -1, 1) + + 2 2 + + 1/2 z y x DATA(-1, -1, 1) + 1/2 z y x DATA(1, 1, 1) + + 2 2 2 + - z y x DATA(-1, 1, 0) - z y x DATA(1, -1, 0) - z y x DATA(-1, -1, 0) + + 2 2 2 + - z y x DATA(1, 1, 0) - z y x DATA(0, 1, -1) + 2 z y x DATA(0, -1, 0) + + 2 2 2 + - z y x DATA(0, -1, 1) - 4 z y x DATA(0, 0, 0) - z y x DATA(-1, 0, -1) + + 2 + - z y x DATA(-1, 0, 1) + 1/4 DATA(0, 1, 1) - 2 y z DATA(0, 0, -1) + + + y z DATA(0, 1, -1) - 2 y z DATA(0, -1, 0) + y z DATA(0, -1, 1) + + + 4 y z DATA(0, 0, 0) - 2 y z DATA(0, 1, 0) - 2 y z DATA(0, 0, 1) + + 2 + + y z DATA(0, 1, 1) + y z DATA(0, -1, -1) - 1/4 y x DATA(1, -1, -1) + + 2 2 + - 1/4 y x DATA(-1, 1, -1) - 1/4 y x DATA(1, 1, -1) + + 2 2 + + 1/2 y x DATA(0, 1, -1) + 1/4 y x DATA(-1, 1, 1) + + 2 2 + + 1/4 y x DATA(1, -1, 1) - 1/2 y x DATA(0, -1, 1) + + 2 + + 1/4 y x DATA(-1, -1, 1) + z DATA(0, -1, 0) - z DATA(0, 1, 0) + + - 1/2 y DATA(0, 1, -1) + 1/2 y DATA(0, -1, 1) + 1/2 y DATA(0, 1, 1) + + + y DATA(0, 0, -1) - y DATA(0, 0, 1) - 1/2 y DATA(0, -1, -1) + + 2 2 2 + - 1/2 y x DATA(0, 1, 1) + 1/4 y x DATA(1, 1, 1) - y x DATA(0, 0, -1) + + 2 2 + + 1/2 y x DATA(-1, 0, -1) + 1/2 y x DATA(1, 0, -1) + + 2 2 2 + - 1/2 y x DATA(-1, 0, 1) + y x DATA(0, 0, 1) - 1/2 y x DATA(1, 0, 1) + + 2 2 + - 1/4 y x DATA(-1, -1, -1) + 1/2 y x DATA(0, -1, -1) + + - 1/4 y x DATA(1, -1, -1) + 1/4 y x DATA(-1, 1, -1) + + - 1/4 y x DATA(1, 1, -1) - 1/4 y x DATA(-1, 1, 1) + 1/4 y x DATA(1, -1, 1) + + - 1/4 y x DATA(-1, -1, 1) + 1/4 y x DATA(1, 1, 1) + + + 1/4 y x DATA(-1, -1, -1) - 1/2 y x DATA(-1, 0, -1) + + + 1/2 y x DATA(1, 0, -1) + 1/2 x z DATA(-1, 1, 0) - 1/8 x DATA(1, 1, -1) + + - 1/8 x DATA(-1, -1, -1) - 1/8 x DATA(1, -1, 1) + 1/8 x DATA(-1, -1, 1) + + 2 2 + + 1/8 x DATA(1, 1, 1) + 1/8 x DATA(1, -1, -1) - 1/8 x DATA(-1, 1, -1) + + 2 2 2 + - 1/8 x DATA(1, 1, -1) + 1/8 x DATA(-1, 1, 1) - 1/8 x DATA(1, -1, 1) + + 2 2 2 + - 1/8 x DATA(-1, -1, 1) + 1/8 x DATA(1, 1, 1) + 1/8 x DATA(-1, -1, -1) + + 2 2 2 + + 1/4 x DATA(0, 1, -1) + 1/4 x DATA(0, -1, 1) - 1/4 x DATA(0, 1, 1) + + 2 + - 1/4 x DATA(0, -1, -1) + 1/2 y x z DATA(1, 1, -1) + y x z DATA(-1, 1, 0) + + 2 + + 1/2 y x DATA(-1, 0, 1) - 1/2 z x DATA(-1, 1, 0) + + 2 2 2 + + 1/2 z x DATA(1, -1, 0) - z x DATA(0, -1, 0) + 1/2 z x DATA(-1, -1, 0) + + 2 2 + + z x DATA(0, 1, 0) - 1/2 z x DATA(1, 1, 0) - 1/2 y x DATA(1, 0, 1) + + + 1/2 x z DATA(1, -1, 0) - 1/2 x z DATA(-1, -1, 0) - 1/2 x z DATA(1, 1, 0) + + + 1/2 y x z DATA(1, -1, 1) - 1/2 y x z DATA(-1, -1, 1) + + - y x z DATA(1, 1, 0) + 1/2 y x z DATA(1, 1, 1) + y x z DATA(-1, 0, -1) + + - y x z DATA(1, 0, -1) + y x z DATA(-1, 0, 1) - y x z DATA(1, 0, 1) + + - 2 y x z DATA(-1, 0, 0) + 2 y x z DATA(1, 0, 0) + + 2 + - 1/2 y x z DATA(-1, -1, -1) + 2 z y x DATA(0, 0, -1) + + + 1/2 y x z DATA(1, -1, -1) - 1/2 y x z DATA(-1, 1, -1) + + 2 2 2 + - z y x DATA(1, 0, 1) + 2 z y x DATA(1, 0, 0) - z y x DATA(1, 0, -1) + + 2 2 + + 1/2 z y x DATA(-1, 1, 1) + 2 z y x DATA(0, 1, 0) + + 2 2 2 + + 2 z y x DATA(0, 0, 1) - z y x DATA(0, 1, 1) - z y x DATA(0, -1, -1) + + 2 2 + + 1/2 z y x DATA(1, -1, -1) + 1/2 z y x DATA(-1, 1, -1) + + 2 2 + + 1/2 z y x DATA(1, 1, -1) + 1/2 z y x DATA(-1, -1, -1) + + - y x z DATA(1, -1, 0) + y x z DATA(-1, -1, 0) - 1/2 y x z DATA(-1, 1, 1) + + 2 + + 2 z y x DATA(-1, 0, 0) + 1/4 DATA(0, -1, -1) - 1/8 x DATA(-1, 1, 1) + + 2 + + 1/8 x DATA(1, -1, -1) + 1/8 x DATA(-1, 1, -1) - 1/4 z x DATA(1, -1, -1) + + 2 2 + + 1/4 z x DATA(-1, 1, -1) + 1/4 z x DATA(1, 1, -1) + + 2 2 + - 1/2 z x DATA(0, 1, -1) + 1/4 z x DATA(-1, 1, 1) + + 2 2 + - 1/4 z x DATA(1, -1, 1) + 1/2 z x DATA(0, -1, 1) + + 2 2 + - 1/4 z x DATA(-1, -1, 1) - 1/2 z x DATA(0, 1, 1) + + 2 2 + + 1/4 z x DATA(1, 1, 1) - 1/4 z x DATA(-1, -1, -1) + + 2 + + 1/2 z x DATA(0, -1, -1) - 1/4 x z DATA(1, -1, -1) + + - 1/4 x z DATA(-1, 1, -1) + 1/4 x z DATA(1, 1, -1) + + - 1/4 x z DATA(-1, 1, 1) - 1/4 x z DATA(1, -1, 1) + + + 1/4 x z DATA(-1, -1, 1) - 1/2 z DATA(0, -1, -1) + + + 1/4 x z DATA(-1, -1, -1) + 1/4 x z DATA(1, 1, 1) + 1/2 z DATA(0, 1, -1) + + - 1/2 z DATA(0, -1, 1) + 1/2 z DATA(0, 1, 1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +bytes used=121139696, alloc=2293340, time=10.53 + 2 2 2 +[COEFF(-1, -1, -1) = 1/8 x - 1/4 y x + 1/4 y x - 1/4 z x - 1/8 x + 1/4 x z + + 2 + - 1/2 y x z + 1/2 z y x , COEFF(0, -1, -1) = + + 2 2 2 2 + -z y x - 1/2 y + 1/2 z x + y z - 1/4 x - 1/2 z + 1/2 y x + 1/4, + + 2 2 + COEFF(1, -1, -1) = - 1/4 z x + 1/8 x + 1/2 y x z - 1/4 y x - 1/4 y x + + 2 2 + + 1/2 z y x - 1/4 x z + 1/8 x , + + 2 2 + COEFF(-1, 0, -1) = - 1/2 y x - z y x + 1/2 y x + y x z, + + 2 2 + COEFF(0, 0, -1) = -2 y z - y x + y + 2 z y x , + + 2 2 + COEFF(1, 0, -1) = 1/2 y x - y x z + 1/2 y x - z y x , COEFF(-1, 1, -1) = + + 2 2 2 2 + - 1/8 x + 1/4 y x + 1/8 x + 1/2 z y x + 1/4 z x - 1/4 x z - 1/4 y x + + - 1/2 y x z, COEFF(0, 1, -1) = + + 2 2 2 2 + 1/2 z - 1/2 z x - z y x + 1/2 y x + y z + 1/4 x - 1/4 - 1/2 y, + + 2 2 2 + COEFF(1, 1, -1) = 1/2 y x z - 1/8 x - 1/8 x + 1/2 z y x - 1/4 y x + + 2 + - 1/4 y x + 1/4 z x + 1/4 x z, + + 2 2 + COEFF(-1, -1, 0) = 1/2 z x + y x z - 1/2 x z - z y x , + + 2 2 + COEFF(0, -1, 0) = -z x + 2 z y x - 2 y z + z, + + 2 2 + COEFF(1, -1, 0) = 1/2 x z + 1/2 z x - y x z - z y x , + + 2 2 + COEFF(-1, 0, 0) = -2 y x z + 2 z y x , COEFF(0, 0, 0) = 4 y z - 4 z y x , + + 2 + COEFF(1, 0, 0) = 2 y x z + 2 z y x , + + 2 2 + COEFF(-1, 1, 0) = -z y x - 1/2 z x + y x z + 1/2 x z, + + 2 2 + COEFF(0, 1, 0) = -2 y z + 2 z y x - z + z x , + + 2 2 + COEFF(1, 1, 0) = - 1/2 x z - 1/2 z x - y x z - z y x , COEFF(-1, -1, 1) = + + 2 2 2 + 1/2 z y x - 1/4 y x - 1/8 x + 1/4 x z + 1/8 x - 1/2 y x z + 1/4 y x + + 2 + - 1/4 z x , COEFF(0, -1, 1) = + + 2 2 2 2 + 1/2 z x - 1/2 z + 1/4 x + y z + 1/2 y - z y x - 1/2 y x - 1/4, + + 2 2 2 + COEFF(1, -1, 1) = 1/2 y x z + 1/2 z y x - 1/8 x + 1/4 y x - 1/4 x z + + 2 + - 1/4 z x + 1/4 y x - 1/8 x, + + 2 2 + COEFF(-1, 0, 1) = 1/2 y x + y x z - z y x - 1/2 y x , + + 2 2 + COEFF(0, 0, 1) = y x - 2 y z + 2 z y x - y, + + 2 2 + COEFF(1, 0, 1) = - 1/2 y x - 1/2 y x - z y x - y x z, COEFF(-1, 1, 1) = + + 2 2 2 + - 1/4 x z - 1/2 y x z + 1/2 z y x - 1/8 x + 1/8 x + 1/4 z x - 1/4 y x + + 2 + + 1/4 y x , COEFF(0, 1, 1) = + + 2 2 2 2 + 1/2 z + 1/2 y + 1/4 - 1/2 y x - 1/2 z x + y z - 1/4 x - z y x , + + 2 2 2 + COEFF(1, 1, 1) = 1/4 y x + 1/2 y x z + 1/8 x + 1/8 x + 1/4 z x + 1/4 y x + + 2 + + 1/4 x z + 1/2 z y x ] + +> print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dyz.compute.c"); +bytes used=122139992, alloc=2293340, time=10.59 +bytes used=123145132, alloc=2293340, time=10.65 +bytes used=124145328, alloc=2293340, time=10.82 +bytes used=125147412, alloc=2293340, time=10.89 +bytes used=126147620, alloc=2293340, time=10.99 +bytes used=127147824, alloc=2293340, time=11.17 +bytes used=128147992, alloc=2293340, time=11.36 +bytes used=129148172, alloc=2293340, time=11.52 +bytes used=130148380, alloc=2293340, time=11.72 +> +# d^2/dz^2 +> simplify( diff(interp_3d_cube_order2_smooth0,z,z) ); +bytes used=131148540, alloc=2293340, time=11.82 + 2 +DATA(0, 0, -1) - 2 DATA(0, 0, 0) + DATA(0, 0, 1) - 1/4 y x DATA(1, -1, -1) + + 2 2 + + 1/4 y x DATA(-1, 1, -1) + 1/4 y x DATA(1, 1, -1) + + 2 2 + - 1/2 y x DATA(0, 1, -1) + 1/4 y x DATA(-1, 1, 1) + + 2 2 + - 1/4 y x DATA(1, -1, 1) + 1/2 y x DATA(0, -1, 1) + + 2 + - 1/4 y x DATA(-1, -1, 1) + 1/2 y DATA(0, 1, -1) - 1/2 y DATA(0, -1, 1) + + + 1/2 y DATA(0, 1, 1) - 1/2 y DATA(0, -1, -1) + 1/2 y x DATA(-1, 1, 0) + + + 1/2 y x DATA(1, -1, 0) - 1/2 y x DATA(-1, -1, 0) - 1/2 y x DATA(1, 1, 0) + + 2 2 + - 1/2 y x DATA(0, 1, 1) + 1/4 y x DATA(1, 1, 1) + + 2 2 + - 1/4 y x DATA(-1, -1, -1) + 1/2 y x DATA(0, -1, -1) + + - 1/4 y x DATA(1, -1, -1) - 1/4 y x DATA(-1, 1, -1) + + + 1/4 y x DATA(1, 1, -1) - 1/4 y x DATA(-1, 1, 1) - 1/4 y x DATA(1, -1, 1) + + + 1/4 y x DATA(-1, -1, 1) + 1/4 y x DATA(1, 1, 1) + + 2 2 + + 1/4 y x DATA(-1, -1, -1) - 1/4 y x DATA(-1, -1, 1) + y x DATA(1, 0, 0) + + 2 2 + - y x DATA(-1, 0, 0) - 1/4 y x DATA(-1, -1, -1) + + 2 2 2 2 + + 1/4 y x DATA(-1, 1, -1) + 1/4 y x DATA(-1, -1, -1) + + 2 2 2 2 + + 1/4 y x DATA(1, 1, 1) - 1/2 y x DATA(1, 1, 0) + + 2 2 2 2 + - 1/2 y x DATA(-1, 1, 0) + 1/4 y x DATA(1, 1, -1) + + 2 2 2 + - 1/2 y x DATA(1, -1, 0) - 1/2 y x DATA(1, 0, -1) + + 2 2 + + 1/2 y x DATA(-1, 0, -1) + 1/4 y x DATA(1, 1, 1) + + 2 2 + - 1/2 y x DATA(1, 1, 0) - 1/2 y x DATA(1, -1, 0) + + 2 2 + + 1/2 y x DATA(-1, 1, 0) - 1/2 y x DATA(1, 0, 1) + + 2 2 + + 1/2 y x DATA(-1, 0, 1) + 1/4 y x DATA(1, 1, -1) + + 2 2 + + 1/4 y x DATA(1, -1, -1) + 1/4 y x DATA(1, -1, 1) + + 2 2 + - 1/4 y x DATA(-1, 1, 1) + 1/2 y x DATA(-1, -1, 0) + + 2 2 2 + - 1/4 y x DATA(-1, 1, -1) + 1/4 y x DATA(1, -1, 1) + + 2 2 2 2 + + 1/4 y x DATA(-1, -1, 1) - 1/2 y x DATA(-1, 0, 1) + + 2 2 2 2 2 2 + - 1/2 y x DATA(1, 0, 1) + y x DATA(-1, 0, 0) + y x DATA(1, 0, 0) + + 2 2 2 2 2 2 + - 1/2 y x DATA(0, -1, 1) - 2 y x DATA(0, 0, 0) + y x DATA(0, 1, 0) + + 2 2 2 2 + + y x DATA(0, 0, 1) - 1/2 y x DATA(-1, -1, 0) + + 2 2 2 2 + + 1/4 y x DATA(-1, 1, 1) - 1/2 y x DATA(0, 1, 1) + + 2 2 2 2 + - 1/2 y x DATA(-1, 0, -1) - 1/2 y x DATA(1, 0, -1) + + 2 2 2 2 + - 1/2 y x DATA(0, -1, -1) + 1/4 y x DATA(1, -1, -1) + + 2 2 2 2 2 2 + + y x DATA(0, 0, -1) - 1/2 y x DATA(0, 1, -1) + y x DATA(0, -1, 0) + + 2 2 2 + - 1/2 y x DATA(-1, 1, 0) + 1/2 y x DATA(1, -1, 0) - y x DATA(0, -1, 0) + + 2 2 2 + + 1/2 y x DATA(-1, -1, 0) + y x DATA(0, 1, 0) - 1/2 y x DATA(1, 1, 0) + + 2 2 2 + - y DATA(0, -1, 0) + 1/2 y DATA(0, 1, -1) - y DATA(0, 0, -1) + + 2 2 2 + + 2 y DATA(0, 0, 0) - y DATA(0, 1, 0) - y DATA(0, 0, 1) + + 2 2 2 + + 1/2 y DATA(0, 1, 1) + 1/2 y DATA(0, -1, -1) + 1/2 y DATA(0, -1, 1) + + + 1/2 x DATA(1, 0, 1) + x DATA(-1, 0, 0) - x DATA(1, 0, 0) + + + y DATA(0, -1, 0) - y DATA(0, 1, 0) - 1/2 x DATA(-1, 0, -1) + + 2 + + 1/2 x DATA(1, 0, -1) - 1/2 x DATA(-1, 0, 1) - x DATA(-1, 0, 0) + + 2 2 2 + + 2 x DATA(0, 0, 0) - x DATA(1, 0, 0) + 1/2 x DATA(-1, 0, 1) + + 2 2 2 + - x DATA(0, 0, 1) + 1/2 x DATA(1, 0, 1) - x DATA(0, 0, -1) + + 2 2 + + 1/2 x DATA(-1, 0, -1) + 1/2 x DATA(1, 0, -1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size3); +bytes used=132152392, alloc=2293340, time=11.89 + 2 2 2 2 +[COEFF(-1, -1, -1) = 1/4 y x - 1/4 y x - 1/4 y x + 1/4 y x, + + 2 2 2 2 + COEFF(0, -1, -1) = 1/2 y x - 1/2 y - 1/2 y x + 1/2 y , + + 2 2 2 2 + COEFF(1, -1, -1) = - 1/4 y x + 1/4 y x + 1/4 y x - 1/4 y x, + + 2 2 2 2 + COEFF(-1, 0, -1) = 1/2 x + 1/2 y x - 1/2 y x - 1/2 x, + + 2 2 2 2 + COEFF(0, 0, -1) = 1 - x - y + y x , + + 2 2 2 2 + COEFF(1, 0, -1) = 1/2 x + 1/2 x - 1/2 y x - 1/2 y x , + + 2 2 2 2 + COEFF(-1, 1, -1) = 1/4 y x - 1/4 y x - 1/4 y x + 1/4 y x , + + 2 2 2 2 + COEFF(0, 1, -1) = 1/2 y + 1/2 y - 1/2 y x - 1/2 y x , + + 2 2 2 2 + COEFF(1, 1, -1) = 1/4 y x + 1/4 y x + 1/4 y x + 1/4 y x, + + 2 2 2 2 + COEFF(-1, -1, 0) = - 1/2 y x - 1/2 y x + 1/2 y x + 1/2 y x, + + 2 2 2 2 + COEFF(0, -1, 0) = -y + y x + y - y x , + + 2 2 2 2 + COEFF(1, -1, 0) = - 1/2 y x + 1/2 y x + 1/2 y x - 1/2 y x, + + 2 2 2 2 + COEFF(-1, 0, 0) = -x - y x + x + y x , + + 2 2 2 2 + COEFF(0, 0, 0) = -2 + 2 x - 2 y x + 2 y , + + 2 2 2 2 + COEFF(1, 0, 0) = y x + y x - x - x , + + 2 2 2 2 + COEFF(-1, 1, 0) = 1/2 y x - 1/2 y x - 1/2 y x + 1/2 y x, + + 2 2 2 2 + COEFF(0, 1, 0) = y x - y + y x - y , + + 2 2 2 2 + COEFF(1, 1, 0) = - 1/2 y x - 1/2 y x - 1/2 y x - 1/2 y x , + + 2 2 2 2 + COEFF(-1, -1, 1) = 1/4 y x - 1/4 y x - 1/4 y x + 1/4 y x, + + 2 2 2 2 + COEFF(0, -1, 1) = 1/2 y x - 1/2 y - 1/2 y x + 1/2 y , + + 2 2 2 2 + COEFF(1, -1, 1) = - 1/4 y x + 1/4 y x + 1/4 y x - 1/4 y x, + + 2 2 2 2 + COEFF(-1, 0, 1) = 1/2 x + 1/2 y x - 1/2 y x - 1/2 x, + + 2 2 2 2 + COEFF(0, 0, 1) = 1 - x - y + y x , + + 2 2 2 2 + COEFF(1, 0, 1) = 1/2 x + 1/2 x - 1/2 y x - 1/2 y x , + + 2 2 2 2 + COEFF(-1, 1, 1) = 1/4 y x - 1/4 y x - 1/4 y x + 1/4 y x , + + 2 2 2 2 + COEFF(0, 1, 1) = 1/2 y + 1/2 y - 1/2 y x - 1/2 y x , + + 2 2 2 2 + COEFF(1, 1, 1) = 1/4 y x + 1/4 y x + 1/4 y x + 1/4 y x] + +> print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp", +> "3d.coeffs/3d.cube.order2.smooth0/coeffs-dzz.compute.c"); +bytes used=133152732, alloc=2293340, time=11.97 +bytes used=134153236, alloc=2293340, time=12.04 +bytes used=135153524, alloc=2293340, time=12.19 +bytes used=136153736, alloc=2293340, time=12.38 +bytes used=137153964, alloc=2293340, time=12.55 +> +################################################################################ +> +# +# 3d, cube, order=3, smoothing=0 (size=4) +# +> +# interpolating polynomial +> interp_3d_cube_order3_smooth0 +> := Lagrange_polynomial_interpolant(fn_3d_order3, coeffs_list_3d_order3, +> coords_list_3d, posn_list_3d_size4); +bytes used=138154184, alloc=2293340, time=12.63 +bytes used=139154372, alloc=2293340, time=12.70 +bytes used=140154632, alloc=2293340, time=12.77 +bytes used=141154864, alloc=2293340, time=12.83 +bytes used=142155052, alloc=2293340, time=12.90 +bytes used=143155388, alloc=2555436, time=12.96 +bytes used=144159028, alloc=2555436, time=13.02 +bytes used=145161676, alloc=2555436, time=13.09 +bytes used=146164564, alloc=2555436, time=13.16 +bytes used=147167176, alloc=2555436, time=13.23 +bytes used=148169788, alloc=2555436, time=13.29 +bytes used=149172676, alloc=2620960, time=13.36 +bytes used=150175288, alloc=2620960, time=13.43 +bytes used=151177900, alloc=2620960, time=13.50 +bytes used=152180788, alloc=2686484, time=13.56 +bytes used=153183400, alloc=2686484, time=13.62 +bytes used=154186288, alloc=2686484, time=13.69 +bytes used=155188900, alloc=2686484, time=13.76 +bytes used=156191512, alloc=2752008, time=13.82 +bytes used=157194400, 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DATA(0, 1, 0) - 1/4 DATA(0, 0, 1) + + + 1/4 DATA(0, 1, 1) - 1/36 DATA(0, 2, -1) + 1/12 DATA(0, 2, 0) + + - 1/12 DATA(0, 2, 1) + 1/12 DATA(0, 0, 2) - 1/36 DATA(0, -1, 2) + + 3 3 + - 1/12 DATA(0, 1, 2) + 1/36 DATA(0, 2, 2) + 1/36 DATA(0, -1, -1)) y z + + + DATA(0, 0, 0) + (1/6 DATA(0, 0, -1) - 1/12 DATA(0, 1, -1) + + + 1/4 DATA(0, -1, 0) - 1/4 DATA(0, -1, 1) - 1/2 DATA(0, 0, 0) + + + 1/4 DATA(0, 1, 0) + 1/2 DATA(0, 0, 1) - 1/4 DATA(0, 1, 1) + + - 1/6 DATA(0, 0, 2) + 1/12 DATA(0, -1, 2) + 1/12 DATA(0, 1, 2) + + 2 3 + - 1/12 DATA(0, -1, -1)) y z + (1/12 DATA(0, 0, -1) - 1/6 DATA(0, 1, -1) + + - 1/6 DATA(0, -1, 0) + 1/6 DATA(0, -1, 1) - 1/4 DATA(0, 0, 0) + + + 1/2 DATA(0, 1, 0) + 1/4 DATA(0, 0, 1) - 1/2 DATA(0, 1, 1) + + + 1/36 DATA(0, 2, -1) - 1/12 DATA(0, 2, 0) + 1/12 DATA(0, 2, 1) + + - 1/12 DATA(0, 0, 2) - 1/18 DATA(0, -1, 2) + 1/6 DATA(0, 1, 2) + + 3 + - 1/36 DATA(0, 2, 2) + 1/18 DATA(0, -1, -1)) y z + (1/6 DATA(0, 0, -1) + + - 1/12 DATA(-1, 0, -1) - 1/12 DATA(1, 0, -1) + 1/4 DATA(-1, 0, 0) + + - 1/4 DATA(-1, 0, 1) - 1/2 DATA(0, 0, 0) + 1/4 DATA(1, 0, 0) + + + 1/2 DATA(0, 0, 1) - 1/4 DATA(1, 0, 1) + 1/12 DATA(-1, 0, 2) + + 2 3 + - 1/6 DATA(0, 0, 2) + 1/12 DATA(1, 0, 2)) x z + (- 1/12 DATA(0, 0, -1) + + + 1/36 DATA(-1, 0, -1) + 1/12 DATA(1, 0, -1) - 1/12 DATA(-1, 0, 0) + + + 1/12 DATA(-1, 0, 1) + 1/4 DATA(0, 0, 0) - 1/4 DATA(1, 0, 0) + + - 1/4 DATA(0, 0, 1) + 1/4 DATA(1, 0, 1) - 1/36 DATA(2, 0, -1) + + + 1/12 DATA(2, 0, 0) - 1/12 DATA(2, 0, 1) - 1/36 DATA(-1, 0, 2) + + 3 3 + + 1/12 DATA(0, 0, 2) + 1/36 DATA(2, 0, 2) - 1/12 DATA(1, 0, 2)) x z + ( + + 1/4 DATA(0, 0, -1) - 1/4 DATA(0, 1, -1) + 1/6 DATA(0, -1, 0) + + - 1/12 DATA(0, -1, 1) - 1/2 DATA(0, 0, 0) + 1/2 DATA(0, 1, 0) + + + 1/4 DATA(0, 0, 1) - 1/4 DATA(0, 1, 1) + 1/12 DATA(0, 2, -1) + + 3 2 + - 1/6 DATA(0, 2, 0) + 1/12 DATA(0, 2, 1) - 1/12 DATA(0, -1, -1)) y z + ( + + 1/4 DATA(0, 0, -1) - 1/12 DATA(-1, 0, -1) - 1/4 DATA(1, 0, -1) + + + 1/6 DATA(-1, 0, 0) - 1/12 DATA(-1, 0, 1) - 1/2 DATA(0, 0, 0) + + + 1/2 DATA(1, 0, 0) + 1/4 DATA(0, 0, 1) - 1/4 DATA(1, 0, 1) + + 3 2 + + 1/12 DATA(2, 0, -1) - 1/6 DATA(2, 0, 0) + 1/12 DATA(2, 0, 1)) x z + ( + + - 1/6 DATA(0, 0, -1) + 1/18 DATA(-1, 0, -1) + 1/6 DATA(1, 0, -1) + + + 1/12 DATA(-1, 0, 0) - 1/6 DATA(-1, 0, 1) - 1/4 DATA(0, 0, 0) + + + 1/4 DATA(1, 0, 0) + 1/2 DATA(0, 0, 1) - 1/2 DATA(1, 0, 1) + + - 1/18 DATA(2, 0, -1) - 1/12 DATA(2, 0, 0) + 1/6 DATA(2, 0, 1) + + + 1/36 DATA(-1, 0, 2) - 1/12 DATA(0, 0, 2) - 1/36 DATA(2, 0, 2) + + 3 + + 1/12 DATA(1, 0, 2)) x z + (1/6 DATA(-1, 1, 0) - 1/6 DATA(-1, 0, 0) + + - 1/6 DATA(1, -1, 0) + 1/12 DATA(0, -1, 0) + 1/18 DATA(-1, -1, 0) + + - 1/4 DATA(0, 0, 0) + 1/2 DATA(1, 0, 0) + 1/4 DATA(0, 1, 0) + + - 1/2 DATA(1, 1, 0) - 1/12 DATA(2, 0, 0) + 1/36 DATA(2, -1, 0) + + - 1/36 DATA(2, 2, 0) + 1/6 DATA(1, 2, 0) - 1/12 DATA(0, 2, 0) + + 3 + - 1/18 DATA(-1, 2, 0) + 1/12 DATA(2, 1, 0)) x y + (- 1/4 DATA(-1, 1, 0) + + + 1/4 DATA(-1, 0, 0) - 1/12 DATA(1, -1, 0) + 1/6 DATA(0, -1, 0) + + - 1/12 DATA(-1, -1, 0) - 1/2 DATA(0, 0, 0) + 1/4 DATA(1, 0, 0) + + + 1/2 DATA(0, 1, 0) - 1/4 DATA(1, 1, 0) + 1/12 DATA(1, 2, 0) + + 2 3 + - 1/6 DATA(0, 2, 0) + 1/12 DATA(-1, 2, 0)) x y + (- 1/12 DATA(-1, 1, 0) + + + 1/6 DATA(-1, 0, 0) - 1/4 DATA(1, -1, 0) + 1/4 DATA(0, -1, 0) + + - 1/12 DATA(-1, -1, 0) - 1/2 DATA(0, 0, 0) + 1/2 DATA(1, 0, 0) + + + 1/4 DATA(0, 1, 0) - 1/4 DATA(1, 1, 0) - 1/6 DATA(2, 0, 0) + + 3 2 + + 1/12 DATA(2, -1, 0) + 1/12 DATA(2, 1, 0)) x y + (- 1/6 DATA(1, -1, -1) + + - 1/6 DATA(0, 0, -1) - 1/9 DATA(-1, 0, -1) + 1/18 DATA(-1, 1, -1) + + - 1/6 DATA(1, 1, -1) + 1/12 DATA(0, 1, -1) + 1/3 DATA(1, 0, -1) + + + 1/12 DATA(-1, 1, 0) - 1/6 DATA(-1, 0, 0) - 1/4 DATA(1, -1, 0) + + + 1/8 DATA(0, -1, 0) + 1/12 DATA(-1, -1, 0) - 1/6 DATA(-1, 1, 1) + + + 1/3 DATA(-1, 0, 1) + 1/2 DATA(1, -1, 1) - 1/4 DATA(0, -1, 1) + + - 1/6 DATA(-1, -1, 1) - 1/4 DATA(0, 0, 0) + 1/2 DATA(1, 0, 0) + + + 1/8 DATA(0, 1, 0) - 1/4 DATA(1, 1, 0) + 1/2 DATA(0, 0, 1) + + - DATA(1, 0, 1) - 1/4 DATA(0, 1, 1) + 1/2 DATA(1, 1, 1) + + + 1/36 DATA(2, -1, -1) + 1/36 DATA(2, 1, -1) - 1/18 DATA(2, 0, -1) + + - 1/12 DATA(2, 0, 0) + 1/24 DATA(2, -1, 0) + 1/24 DATA(2, 1, 0) + + + 1/6 DATA(2, 0, 1) - 1/12 DATA(2, -1, 1) - 1/12 DATA(2, 1, 1) + + - 1/18 DATA(-1, 0, 2) - 1/12 DATA(0, 0, 2) + 1/72 DATA(2, -1, 2) + + - 1/12 DATA(1, -1, 2) + 1/24 DATA(0, -1, 2) + 1/36 DATA(-1, -1, 2) + + + 1/72 DATA(2, 1, 2) - 1/12 DATA(1, 1, 2) + 1/24 DATA(0, 1, 2) + + + 1/36 DATA(-1, 1, 2) + 1/18 DATA(-1, -1, -1) - 1/36 DATA(2, 0, 2) + + 2 + + 1/6 DATA(1, 0, 2) + 1/12 DATA(0, -1, -1)) x y z + ( + + - 1/12 DATA(1, -1, -1) - 1/3 DATA(0, 0, -1) + 1/6 DATA(-1, 0, -1) + + - 1/12 DATA(-1, 1, -1) - 1/12 DATA(1, 1, -1) + 1/6 DATA(0, 1, -1) + + + 1/6 DATA(1, 0, -1) - 1/8 DATA(-1, 1, 0) + 1/4 DATA(-1, 0, 0) + + - 1/8 DATA(1, -1, 0) + 1/4 DATA(0, -1, 0) - 1/8 DATA(-1, -1, 0) + + + 1/4 DATA(-1, 1, 1) - 1/2 DATA(-1, 0, 1) + 1/4 DATA(1, -1, 1) + + - 1/2 DATA(0, -1, 1) + 1/4 DATA(-1, -1, 1) - 1/2 DATA(0, 0, 0) + + + 1/4 DATA(1, 0, 0) + 1/4 DATA(0, 1, 0) - 1/8 DATA(1, 1, 0) + + + DATA(0, 0, 1) - 1/2 DATA(1, 0, 1) - 1/2 DATA(0, 1, 1) + + + 1/4 DATA(1, 1, 1) + 1/12 DATA(-1, 0, 2) - 1/6 DATA(0, 0, 2) + + - 1/24 DATA(1, -1, 2) + 1/12 DATA(0, -1, 2) - 1/24 DATA(-1, -1, 2) + + - 1/24 DATA(1, 1, 2) + 1/12 DATA(0, 1, 2) - 1/24 DATA(-1, 1, 2) + + 2 2 + - 1/12 DATA(-1, -1, -1) + 1/12 DATA(1, 0, 2) + 1/6 DATA(0, -1, -1)) x y + + z + (- 1/6 DATA(1, -1, -1) + 1/8 DATA(0, 0, -1) + 1/12 DATA(-1, 0, -1) + + - 1/6 DATA(-1, 1, -1) + 1/2 DATA(1, 1, -1) - 1/4 DATA(0, 1, -1) + + - 1/4 DATA(1, 0, -1) + 1/3 DATA(-1, 1, 0) - 1/6 DATA(-1, 0, 0) + + + 1/3 DATA(1, -1, 0) - 1/6 DATA(0, -1, 0) - 1/9 DATA(-1, -1, 0) + + - 1/6 DATA(-1, 1, 1) + 1/12 DATA(-1, 0, 1) - 1/6 DATA(1, -1, 1) + + + 1/12 DATA(0, -1, 1) + 1/18 DATA(-1, -1, 1) - 1/4 DATA(0, 0, 0) + + + 1/2 DATA(1, 0, 0) + 1/2 DATA(0, 1, 0) - DATA(1, 1, 0) + + + 1/8 DATA(0, 0, 1) - 1/4 DATA(1, 0, 1) - 1/4 DATA(0, 1, 1) + + + 1/2 DATA(1, 1, 1) + 1/36 DATA(2, -1, -1) - 1/12 DATA(1, 2, -1) + + + 1/24 DATA(0, 2, -1) + 1/36 DATA(-1, 2, -1) - 1/12 DATA(2, 1, -1) + + + 1/24 DATA(2, 0, -1) - 1/12 DATA(2, 0, 0) - 1/18 DATA(2, -1, 0) + + + 1/72 DATA(2, 2, -1) - 1/36 DATA(2, 2, 0) + 1/6 DATA(1, 2, 0) + + - 1/12 DATA(0, 2, 0) - 1/18 DATA(-1, 2, 0) + 1/6 DATA(2, 1, 0) + + + 1/24 DATA(2, 0, 1) + 1/36 DATA(2, -1, 1) + 1/72 DATA(2, 2, 1) + + - 1/12 DATA(1, 2, 1) + 1/24 DATA(0, 2, 1) + 1/36 DATA(-1, 2, 1) + + - 1/12 DATA(2, 1, 1) + 1/18 DATA(-1, -1, -1) + 1/12 DATA(0, -1, -1)) x y + + 2 + z + (- 1/12 DATA(1, -1, -1) + 1/4 DATA(0, 0, -1) - 1/8 DATA(-1, 0, -1) + + + 1/4 DATA(-1, 1, -1) + 1/4 DATA(1, 1, -1) - 1/2 DATA(0, 1, -1) + + - 1/8 DATA(1, 0, -1) - 1/2 DATA(-1, 1, 0) + 1/4 DATA(-1, 0, 0) + + + 1/6 DATA(1, -1, 0) - 1/3 DATA(0, -1, 0) + 1/6 DATA(-1, -1, 0) + + + 1/4 DATA(-1, 1, 1) - 1/8 DATA(-1, 0, 1) - 1/12 DATA(1, -1, 1) + + + 1/6 DATA(0, -1, 1) - 1/12 DATA(-1, -1, 1) - 1/2 DATA(0, 0, 0) + + + 1/4 DATA(1, 0, 0) + DATA(0, 1, 0) - 1/2 DATA(1, 1, 0) + + + 1/4 DATA(0, 0, 1) - 1/8 DATA(1, 0, 1) - 1/2 DATA(0, 1, 1) 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0) + 1/12 DATA(2, 0, 1) - 1/24 DATA(2, -1, 1) + + - 1/24 DATA(2, 1, 1) + 1/36 DATA(-1, 0, 2) - 1/12 DATA(0, 0, 2) + + + 1/72 DATA(2, -1, 2) - 1/24 DATA(1, -1, 2) + 1/24 DATA(0, -1, 2) + + - 1/72 DATA(-1, -1, 2) + 1/72 DATA(2, 1, 2) - 1/24 DATA(1, 1, 2) + + + 1/24 DATA(0, 1, 2) - 1/72 DATA(-1, 1, 2) + 1/72 DATA(-1, -1, -1) + + 3 2 3 + - 1/36 DATA(2, 0, 2) + 1/12 DATA(1, 0, 2) - 1/24 DATA(0, -1, -1)) x y z + + + (- 1/6 DATA(0, 0, -1) + 1/2 DATA(0, 0, 0) - 1/2 DATA(0, 0, 1) + + 3 + + 1/6 DATA(0, 0, 2)) z + (- 1/6 DATA(0, -1, 0) + 1/2 DATA(0, 0, 0) + + 3 + - 1/2 DATA(0, 1, 0) + 1/6 DATA(0, 2, 0)) y + (- 1/6 DATA(-1, 0, 0) + + 3 + + 1/2 DATA(0, 0, 0) - 1/2 DATA(1, 0, 0) + 1/6 DATA(2, 0, 0)) x + ( + + - 1/3 DATA(0, 0, -1) - 1/2 DATA(0, 0, 0) + DATA(0, 0, 1) + + - 1/6 DATA(0, 0, 2)) z + (1/4 DATA(1, -1, -1) + 1/4 DATA(0, 0, -1) + + + 1/6 DATA(-1, 0, -1) - 1/12 DATA(-1, 1, -1) + 1/4 DATA(1, 1, -1) + + - 1/8 DATA(0, 1, -1) - 1/2 DATA(1, 0, -1) + 1/6 DATA(-1, 1, 0) + + - 1/3 DATA(-1, 0, 0) - 1/2 DATA(1, -1, 0) + 1/4 DATA(0, -1, 0) + + + 1/6 DATA(-1, -1, 0) - 1/12 DATA(-1, 1, 1) + 1/6 DATA(-1, 0, 1) + + + 1/4 DATA(1, -1, 1) - 1/8 DATA(0, -1, 1) - 1/12 DATA(-1, -1, 1) + + - 1/2 DATA(0, 0, 0) + DATA(1, 0, 0) + 1/4 DATA(0, 1, 0) + + - 1/2 DATA(1, 1, 0) + 1/4 DATA(0, 0, 1) - 1/2 DATA(1, 0, 1) + + - 1/8 DATA(0, 1, 1) + 1/4 DATA(1, 1, 1) - 1/24 DATA(2, -1, -1) + + - 1/24 DATA(2, 1, -1) + 1/12 DATA(2, 0, -1) - 1/6 DATA(2, 0, 0) + + + 1/12 DATA(2, -1, 0) + 1/12 DATA(2, 1, 0) + 1/12 DATA(2, 0, 1) + + - 1/24 DATA(2, -1, 1) - 1/24 DATA(2, 1, 1) - 1/12 DATA(-1, -1, -1) + + 2 2 + - 1/8 DATA(0, -1, -1)) x y z + (- 1/12 DATA(1, -1, -1) + + - 1/12 DATA(0, 0, -1) - 1/18 DATA(-1, 0, -1) + 1/36 DATA(-1, 1, -1) + + - 1/12 DATA(1, 1, -1) + 1/24 DATA(0, 1, -1) + 1/6 DATA(1, 0, -1) + + - 1/12 DATA(-1, 1, 0) + 1/6 DATA(-1, 0, 0) + 1/4 DATA(1, -1, 0) + + - 1/8 DATA(0, -1, 0) - 1/12 DATA(-1, -1, 0) + 1/12 DATA(-1, 1, 1) + + - 1/6 DATA(-1, 0, 1) - 1/4 DATA(1, -1, 1) + 1/8 DATA(0, -1, 1) + + + 1/12 DATA(-1, -1, 1) + 1/4 DATA(0, 0, 0) - 1/2 DATA(1, 0, 0) + + - 1/8 DATA(0, 1, 0) + 1/4 DATA(1, 1, 0) - 1/4 DATA(0, 0, 1) + + + 1/2 DATA(1, 0, 1) + 1/8 DATA(0, 1, 1) - 1/4 DATA(1, 1, 1) + + + 1/72 DATA(2, -1, -1) + 1/72 DATA(2, 1, -1) - 1/36 DATA(2, 0, -1) + + + 1/12 DATA(2, 0, 0) - 1/24 DATA(2, -1, 0) - 1/24 DATA(2, 1, 0) + + - 1/12 DATA(2, 0, 1) + 1/24 DATA(2, -1, 1) + 1/24 DATA(2, 1, 1) + + + 1/18 DATA(-1, 0, 2) + 1/12 DATA(0, 0, 2) - 1/72 DATA(2, -1, 2) + + + 1/12 DATA(1, -1, 2) - 1/24 DATA(0, -1, 2) - 1/36 DATA(-1, -1, 2) + + - 1/72 DATA(2, 1, 2) + 1/12 DATA(1, 1, 2) - 1/24 DATA(0, 1, 2) + + - 1/36 DATA(-1, 1, 2) + 1/36 DATA(-1, -1, -1) + 1/36 DATA(2, 0, 2) + + 2 3 + - 1/6 DATA(1, 0, 2) + 1/24 DATA(0, -1, -1)) x y z + ( + + - 1/3 DATA(0, -1, 0) - 1/2 DATA(0, 0, 0) + DATA(0, 1, 0) + + - 1/6 DATA(0, 2, 0)) y + (- 1/24 DATA(1, -1, -1) - 1/6 DATA(0, 0, -1) + + + 1/12 DATA(-1, 0, -1) - 1/24 DATA(-1, 1, -1) - 1/24 DATA(1, 1, -1) + + + 1/12 DATA(0, 1, -1) + 1/12 DATA(1, 0, -1) + 1/8 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DATA(0, 2, 2) + 1/72 DATA(-1, 2, 2) - 1/9 DATA(0, -1, -1)) x y z + + + (1/36 DATA(1, -1, -1) + 1/24 DATA(0, 0, -1) + 1/36 DATA(-1, 0, -1) + + - 1/36 DATA(-1, 1, -1) + 1/12 DATA(1, 1, -1) - 1/24 DATA(0, 1, -1) + + - 1/12 DATA(1, 0, -1) + 1/12 DATA(-1, 1, 0) - 1/12 DATA(-1, 0, 0) + + - 1/12 DATA(1, -1, 0) + 1/24 DATA(0, -1, 0) + 1/36 DATA(-1, -1, 0) + + - 1/12 DATA(-1, 1, 1) + 1/12 DATA(-1, 0, 1) + 1/12 DATA(1, -1, 1) + + - 1/24 DATA(0, -1, 1) - 1/36 DATA(-1, -1, 1) - 1/8 DATA(0, 0, 0) + + + 1/4 DATA(1, 0, 0) + 1/8 DATA(0, 1, 0) - 1/4 DATA(1, 1, 0) + + + 1/8 DATA(0, 0, 1) - 1/4 DATA(1, 0, 1) - 1/8 DATA(0, 1, 1) + + + 1/4 DATA(1, 1, 1) - 1/216 DATA(2, -1, -1) - 1/36 DATA(1, 2, -1) + + + 1/72 DATA(0, 2, -1) + 1/108 DATA(-1, 2, -1) - 1/72 DATA(2, 1, -1) + + + 1/72 DATA(2, 0, -1) - 1/24 DATA(2, 0, 0) + 1/72 DATA(2, -1, 0) + + + 1/216 DATA(2, 2, -1) - 1/72 DATA(2, 2, 0) + 1/12 DATA(1, 2, 0) + + - 1/24 DATA(0, 2, 0) - 1/36 DATA(-1, 2, 0) + 1/24 DATA(2, 1, 0) + + + 1/24 DATA(2, 0, 1) - 1/72 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1/12 DATA(0, 1, 2) - 1/18 DATA(-1, 1, 2) - 1/54 DATA(-1, -1, -1) + + + 1/72 DATA(2, 0, 2) - 1/12 DATA(1, 0, 2) + 1/216 DATA(2, 2, 2) + + - 1/36 DATA(1, 2, 2) + 1/72 DATA(0, 2, 2) + 1/108 DATA(-1, 2, 2) + + 3 + - 1/36 DATA(0, -1, -1)) x y z + (- 1/2 DATA(0, 0, -1) + + + 1/4 DATA(0, 1, -1) - 1/2 DATA(0, -1, 0) + 1/4 DATA(0, -1, 1) + + + DATA(0, 0, 0) - 1/2 DATA(0, 1, 0) - 1/2 DATA(0, 0, 1) + + 2 2 + + 1/4 DATA(0, 1, 1) + 1/4 DATA(0, -1, -1)) y z + (1/4 DATA(-1, 1, 0) + + + 1/4 DATA(1, -1, 0) - 1/2 DATA(0, -1, 0) + 1/4 DATA(-1, -1, 0) + + - 1/2 DATA(0, 1, 0) + 1/4 DATA(1, 1, 0) - 1/2 DATA(-1, 0, 0) + + 2 2 + + DATA(0, 0, 0) - 1/2 DATA(1, 0, 0)) x y + (- 1/2 DATA(0, 0, -1) + + + 1/4 DATA(-1, 0, -1) + 1/4 DATA(1, 0, -1) + 1/4 DATA(-1, 0, 1) + + - 1/2 DATA(0, 0, 1) + 1/4 DATA(1, 0, 1) - 1/2 DATA(-1, 0, 0) + + 2 2 + + DATA(0, 0, 0) - 1/2 DATA(1, 0, 0)) x z + + 2 + + (1/2 DATA(0, 0, -1) - DATA(0, 0, 0) + 1/2 DATA(0, 0, 1)) z + + 2 + + (1/2 DATA(0, -1, 0) + 1/2 DATA(0, 1, 0) - DATA(0, 0, 0)) y + + 2 + + (1/2 DATA(-1, 0, 0) - DATA(0, 0, 0) + 1/2 DATA(1, 0, 0)) x + ( + + 1/8 DATA(1, -1, -1) + 1/2 DATA(0, 0, -1) - 1/4 DATA(-1, 0, -1) + + + 1/8 DATA(-1, 1, -1) + 1/8 DATA(1, 1, -1) - 1/4 DATA(0, 1, -1) + + - 1/4 DATA(1, 0, -1) - 1/4 DATA(-1, 1, 0) + 1/2 DATA(-1, 0, 0) + + - 1/4 DATA(1, -1, 0) + 1/2 DATA(0, -1, 0) - 1/4 DATA(-1, -1, 0) + + + 1/8 DATA(-1, 1, 1) - 1/4 DATA(-1, 0, 1) + 1/8 DATA(1, -1, 1) + + - 1/4 DATA(0, -1, 1) + 1/8 DATA(-1, -1, 1) - DATA(0, 0, 0) + + + 1/2 DATA(1, 0, 0) + 1/2 DATA(0, 1, 0) - 1/4 DATA(1, 1, 0) + + + 1/2 DATA(0, 0, 1) - 1/4 DATA(1, 0, 1) - 1/4 DATA(0, 1, 1) + + 2 2 2 + + 1/8 DATA(1, 1, 1) + 1/8 DATA(-1, -1, -1) - 1/4 DATA(0, -1, -1)) x y z + +> +# I +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=4818544732, alloc=3669344, time=380.05 +bytes used=4819596104, alloc=3669344, time=380.12 +bytes used=4820662420, alloc=3669344, time=380.19 +bytes used=4821672228, alloc=3669344, time=380.26 +bytes used=4822754604, alloc=3669344, time=380.34 +bytes used=4823755032, alloc=3669344, time=380.41 +bytes used=4824849792, alloc=3669344, time=380.48 +bytes used=4825852112, alloc=3669344, time=380.56 +bytes used=4826862920, alloc=3669344, time=380.63 +bytes used=4827904260, alloc=3669344, time=380.70 +bytes used=4828904628, alloc=3669344, time=380.78 +bytes used=4829904852, alloc=3669344, time=380.85 +bytes used=4830924480, alloc=3669344, time=380.91 +bytes used=4831950868, alloc=3669344, time=380.96 +bytes used=4832976736, alloc=3669344, time=381.01 +bytes used=4834002604, alloc=3669344, time=381.06 + 2 2 3 3 2 2 2 +[COEFF(-1, -1, -1) = 1/18 y x z + 1/36 y x z - 1/54 y x z + 1/8 y x z + + 2 3 2 2 3 2 3 + - 1/27 y x z + 1/18 z y x - 1/54 x y z - 1/24 y x z + 1/36 y x z + + 2 2 3 3 3 2 3 3 3 2 + - 1/12 y x z - 1/216 x y z + 1/72 x y z + 1/36 x y z + + 3 3 2 3 2 3 3 3 2 + + 1/72 x y z + 1/36 x y z - 1/108 x y z + 1/36 x y z + + 3 3 2 3 2 2 3 2 3 + - 1/108 x y z + 1/36 x y z - 1/12 y x z + 1/72 x y z + + 2 2 2 3 3 2 3 2 + - 1/12 y x z + 1/18 y x z - 1/108 x y z - 1/24 x y z + + 3 2 2 3 2 + - 1/24 x y z - 1/54 x y z, COEFF(0, -1, -1) = 1/12 y x z + + 2 3 3 2 2 2 2 2 + - 1/18 y x z - 1/36 y x z - 1/4 y x z + 1/4 y z - 1/18 y x z + + 2 3 2 2 3 2 3 + - 1/9 z y x + 1/9 y z - 1/36 x y z + 1/12 y x z + 1/24 y x z + + 2 2 3 3 3 2 3 3 3 2 + - 1/8 y x z + 1/72 x y z - 1/36 x y z - 1/12 x y z + + 3 3 2 3 2 3 3 3 2 + - 1/24 x y z + 1/24 x y z + 1/36 x y z - 1/12 x y z + + 3 3 2 3 2 2 3 2 3 2 2 + + 1/36 x y z - 1/18 x y z + 1/6 y x z - 1/24 x y z + 1/6 y x z + + 2 3 3 2 3 2 3 2 + + 1/12 y x z - 1/72 x y z + 1/12 x y z + 1/18 y z - 1/6 y z + + 3 2 3 2 3 3 3 2 + - 1/12 y z + 1/18 y z - 1/12 y z + 1/36 y z - 1/6 y z + + 3 2 2 3 2 + + 1/8 x y z + 1/18 x y z, COEFF(1, -1, -1) = - 1/6 y x z + + 2 3 3 2 2 2 2 + + 1/36 y x z + 1/18 y x z + 1/8 y x z + 1/9 y x z + 1/18 z y x + + 3 2 2 3 2 3 2 2 3 3 3 + + 1/18 x y z - 1/24 y x z - 1/12 y x z + 1/4 y x z - 1/72 x y z + + 2 3 3 3 2 3 3 2 3 2 + + 1/72 x y z + 1/12 x y z + 1/24 x y z - 1/12 x y z + + 3 3 3 2 3 3 2 3 2 2 + - 1/36 x y z + 1/12 x y z - 1/36 x y z + 1/36 x y z - 1/12 y x z + + 3 2 3 2 2 2 3 3 2 3 2 + + 1/24 x y z - 1/12 y x z - 1/6 y x z + 1/36 x y z - 1/24 x y z + + 3 2 2 3 3 2 3 + - 1/8 x y z - 1/18 x y z, COEFF(2, -1, -1) = - 1/72 x y z + + 3 3 2 3 3 3 2 2 3 2 2 + - 1/72 x y z + 1/216 x y z - 1/24 y x z + 1/24 x y z + + 2 3 3 2 3 2 2 3 + + 1/36 y x z + 1/54 x y z - 1/36 x y z - 1/36 x y z + 1/72 y x z + + 3 2 3 2 3 3 + - 1/108 x y z + 1/36 y x z + 1/72 x y z - 1/54 y x z - 1/216 x y z + + 3 3 3 3 3 + - 1/108 y x z + 1/108 x y z + 1/108 x y z , COEFF(-1, 0, -1) = + + 2 2 3 3 2 2 2 2 2 + - 1/9 y x z + 1/24 y x z - 1/36 y x z - 1/4 y x z + 1/4 x z + + 2 3 2 2 3 2 3 + - 1/18 y x z + 1/12 z y x + 1/18 x y z + 1/12 y x z - 1/18 y x z + + 2 2 3 3 3 2 3 3 3 2 + + 1/6 y x z + 1/72 x y z - 1/24 x y z + 1/24 x y z + + 3 3 2 3 2 3 3 3 2 + - 1/24 x y z - 1/12 x y z - 1/72 x y z - 1/18 x y z + + 3 3 2 3 2 2 3 2 3 2 2 + + 1/36 x y z - 1/12 x y z + 1/6 y x z - 1/36 x y z - 1/8 y x z + + 2 3 3 2 3 2 3 2 2 + + 1/12 y x z + 1/36 x y z + 1/8 x y z + 1/9 x z + 1/12 x y z + + 3 2 2 3 3 2 3 3 + + 1/18 x z - 1/6 x z - 1/6 x z + 1/18 x z - 1/12 x z + 1/36 x z + + 2 3 3 2 + - 1/12 x z - 1/36 x y z, COEFF(0, 0, -1) = - 1/3 z - 1/6 y x z + + 2 3 3 2 2 2 2 2 2 2 + - 1/12 y x z - 1/24 y x z + 1/2 y x z - 1/2 y z - 1/2 x z + + 3 2 2 3 + - 1/6 z + 1/2 z - 1/12 y x z - 1/6 z y x + 1/6 y z + 1/12 x y z + + 2 2 3 2 3 2 2 3 3 3 + - 1/6 y x z - 1/12 y x z + 1/4 y x z - 1/24 x y z + + 2 3 3 3 2 3 3 2 3 2 3 3 + + 1/12 x y z - 1/8 x y z + 1/8 x y z - 1/8 x y z + 1/24 x y z + + 3 2 3 3 2 3 2 2 3 2 3 + + 1/6 x y z - 1/12 x y z + 1/6 x y z - 1/3 y x z + 1/12 x y z + + 2 2 2 3 3 2 3 2 3 + + 1/4 y x z + 1/8 y x z + 1/24 x y z - 1/4 x y z - 1/6 y z + + 2 3 2 3 2 3 3 3 2 + - 1/4 y z + 1/4 y z + 1/12 y z + 1/6 y z - 1/12 y z + 1/3 y z + + 3 2 2 3 2 2 3 + + 1/6 x z - 1/4 x y z + 1/12 x z + 1/3 x z - 1/4 x z - 1/6 x z + + 3 2 3 3 2 3 3 + + 1/4 x z - 1/12 x z + 1/6 x z + 1/12 x y z, COEFF(1, 0, -1) = + + 2 2 3 3 2 2 2 2 2 + 1/3 y x z + 1/24 y x z + 1/12 y x z - 1/4 y x z + 1/4 x z + + 2 3 2 2 3 2 3 + + 1/6 y x z + 1/12 z y x - 1/6 x y z + 1/12 y x z + 1/6 y x z + + 2 2 3 3 3 2 3 3 3 2 3 3 2 + - 1/2 y x z + 1/24 x y z - 1/24 x y z + 1/8 x y z - 1/8 x y z + + 3 2 3 3 3 2 3 3 2 3 + + 1/4 x y z - 1/24 x y z - 1/6 x y z + 1/12 x y z - 1/12 x y z + + 2 2 3 2 3 2 2 2 3 3 + + 1/6 y x z - 1/12 x y z - 1/8 y x z - 1/4 y x z - 1/12 x y z + + 2 3 2 3 2 2 3 2 2 + + 1/8 x y z - 1/3 x z + 1/4 x y z - 1/6 x z - 1/6 x z + 1/2 x z + + 3 3 2 3 3 2 3 3 + + 1/6 x z - 1/4 x z + 1/12 x z - 1/12 x z - 1/12 x y z, + + 3 3 3 3 3 2 + COEFF(2, 0, -1) = - 1/72 x y z + 1/36 x y z - 1/36 y x z + 1/18 x y z + + 3 2 2 3 3 3 + + 1/12 x z - 1/18 y x z + 1/18 x z - 1/72 y x z - 1/36 x y z + + 3 3 3 3 3 2 3 2 3 3 2 + - 1/36 x z + 1/72 x y z + 1/36 x y z + 1/24 y x z + 1/24 x y z + + 3 3 3 3 3 2 2 2 + + 1/36 x z + 1/72 x y z - 1/18 x z - 1/24 x y z + 1/12 y x z + + 2 2 3 3 2 2 3 2 3 + - 1/12 x z - 1/36 y x z - 1/12 x y z - 1/24 x y z + 1/36 x y z, + + 2 2 3 3 2 2 2 + COEFF(-1, 1, -1) = 1/18 y x z - 1/12 y x z + 1/18 y x z + 1/8 y x z + + 2 3 2 2 3 2 3 + + 1/9 y x z - 1/6 z y x - 1/18 x y z - 1/24 y x z + 1/36 y x z + + 2 2 3 3 3 2 3 3 3 2 + - 1/12 y x z - 1/72 x y z + 1/24 x y z - 1/12 x y z + + 3 3 2 3 2 3 3 3 2 + + 1/24 x y z + 1/12 x y z + 1/36 x y z + 1/36 x y z + + 3 3 2 3 2 2 3 2 3 2 2 + - 1/36 x y z + 1/12 x y z - 1/12 y x z + 1/72 x y z + 1/4 y x z + + 2 3 3 2 3 2 3 2 2 3 + - 1/6 y x z - 1/36 x y z - 1/8 x y z - 1/24 x y z + 1/18 x y z, + + 2 2 3 3 2 2 2 + COEFF(0, 1, -1) = 1/12 y x z + 1/6 y x z + 1/12 y x z - 1/4 y x z + + 2 2 2 3 + + 1/4 y z + 1/6 y x z + 1/3 z y x - 1/3 y z - 1/12 x y z + + 2 2 3 2 3 2 2 3 3 3 + + 1/12 y x z + 1/24 y x z - 1/8 y x z + 1/24 x y z + + 2 3 3 3 2 3 3 2 3 2 3 3 + - 1/12 x y z + 1/4 x y z - 1/8 x y z + 1/8 x y z - 1/12 x y z + + 3 2 3 3 2 3 2 2 3 2 3 + - 1/12 x y z + 1/12 x y z - 1/6 x y z + 1/6 y x z - 1/24 x y z + + 2 2 2 3 3 2 3 2 3 + - 1/2 y x z - 1/4 y x z - 1/24 x y z + 1/4 x y z + 1/6 y z + + 2 3 2 3 2 3 3 3 2 + + 1/2 y z - 1/4 y z - 1/6 y z - 1/12 y z + 1/12 y z - 1/6 y z + + 3 2 2 3 2 2 3 + + 1/8 x y z - 1/6 x y z, COEFF(1, 1, -1) = - 1/6 y x z - 1/12 y x z + + 3 2 2 2 2 3 + - 1/6 y x z + 1/8 y x z - 1/3 y x z - 1/6 z y x + 1/6 x y z + + 2 2 3 2 3 2 2 3 3 3 + - 1/24 y x z - 1/12 y x z + 1/4 y x z - 1/24 x y z + + 2 3 3 3 2 3 3 2 3 2 3 3 + + 1/24 x y z - 1/4 x y z + 1/8 x y z - 1/4 x y z + 1/12 x y z + + 3 2 3 3 2 3 2 2 + + 1/12 x y z - 1/12 x y z + 1/12 x y z - 1/12 y x z + + 3 2 3 2 2 2 3 3 2 3 2 + + 1/24 x y z + 1/4 y x z + 1/2 y x z + 1/12 x y z - 1/8 x y z + + 3 2 2 3 3 3 + - 1/8 x y z + 1/6 x y z, COEFF(2, 1, -1) = - 1/72 x y z + + 2 3 3 2 2 3 + - 1/12 y x z + 1/36 y x z - 1/18 x y z + 1/36 y x z + 1/72 y x z + + 3 2 3 2 3 3 3 3 3 3 + + 1/12 x y z - 1/72 x y z - 1/36 x y z + 1/72 x y z + + 3 3 2 3 2 2 3 3 2 + - 1/36 x y z - 1/36 x y z + 1/18 y x z + 1/24 x y z - 1/24 x y z + + 3 2 3 3 2 2 + + 1/24 x y z + 1/36 x y z - 1/24 y x z , COEFF(-1, 2, -1) = + + 2 3 2 2 3 3 3 3 3 2 + 1/24 x y z + 1/72 y x z + 1/54 x y z - 1/108 x y z - 1/72 x y z + + 3 2 2 2 2 3 3 2 + + 1/72 x y z + 1/36 y x z + 1/36 z y x - 1/36 x y z - 1/36 x y z + + 3 3 2 3 3 3 3 2 2 + + 1/108 x y z - 1/72 x y z - 1/216 x y z - 1/24 y x z + + 3 3 3 3 3 3 + - 1/108 y x z - 1/54 y x z + 1/216 x y z + 1/108 x y z, + + 2 3 2 3 2 2 3 + COEFF(0, 2, -1) = - 1/12 x y z + 1/36 x y z - 1/12 y z - 1/36 y x z + + 3 3 3 3 2 3 3 3 + - 1/18 y z - 1/36 y z + 1/36 x y z + 1/18 x y z + 1/72 x y z + + 3 2 2 2 2 + + 1/18 y z - 1/72 y x z + 1/12 y x z + 1/24 y x z - 1/18 z y x + + 3 3 2 3 2 3 3 3 + + 1/24 x y z - 1/24 x y z + 1/72 x y z - 1/36 y x z + 1/36 y z + + 3 2 3 2 3 3 3 2 3 3 3 3 + - 1/24 x y z + 1/12 y z - 1/72 x y z + 1/36 x y z - 1/36 x y z + + 2 3 3 3 3 + , COEFF(1, 2, -1) = 1/36 z y x + 1/36 y x z + 1/72 x y z + + 3 2 3 2 3 3 3 3 2 + + 1/24 x y z - 1/18 x y z - 1/12 y x z - 1/72 x y z - 1/24 x y z + + 3 2 3 3 3 3 3 2 3 2 + + 1/12 x y z - 1/36 x y z + 1/36 x y z - 1/36 x y z + 1/24 x y z + + 2 3 2 3 3 2 3 2 2 + - 1/36 x y z + 1/18 y x z - 1/72 x y z + 1/72 y x z - 1/24 y x z , + + 3 3 3 3 + COEFF(2, 2, -1) = 1/108 x y z - 1/216 x y z - 1/108 y x z + + 3 3 3 2 2 3 2 + + 1/216 x y z - 1/72 x y z + 1/72 y x z - 1/72 x y z + + 3 3 3 3 3 3 3 2 + - 1/108 x y z + 1/108 x y z + 1/216 x y z + 1/72 x y z + + 3 3 3 2 3 3 + - 1/216 y x z , COEFF(-1, -1, 0) = 1/36 x y - 1/12 x y + 1/18 x y + + 2 2 3 3 3 + + 1/12 y x z - 1/12 y x z + 1/18 x y + 1/9 y x + 1/18 y x z + + 2 2 2 2 2 3 2 + - 1/4 y x z - 1/18 y x z + 1/12 z y x - 1/6 y x - 1/12 x y + + 2 2 2 3 2 2 3 2 3 + + 1/4 y x - 1/6 y x - 1/36 x y z + 1/8 y x z - 1/12 y x z + + 2 2 3 3 3 2 3 3 3 2 + + 1/6 y x z + 1/72 x y z - 1/24 x y z - 1/18 x y z + + 3 3 2 3 2 3 3 3 2 + - 1/36 x y z - 1/18 x y z + 1/36 x y z + 1/24 x y z + + 3 3 2 3 2 2 3 2 3 2 2 + - 1/72 x y z + 1/24 x y z - 1/8 y x z - 1/24 x y z + 1/6 y x z + + 2 3 3 2 3 2 3 2 2 3 + - 1/9 y x z + 1/36 x y z + 1/12 x y z + 1/12 x y z - 1/36 x y z, + + 3 3 2 3 3 2 + COEFF(0, -1, 0) = - 1/12 x y + 1/6 x y - 1/6 x y - 1/3 y + 1/8 y x z + + 2 3 3 3 2 2 2 + + 1/6 y x z + 1/12 x y + 1/6 y x + 1/12 y x z + 1/2 y x z + + 2 2 3 2 2 + - 1/2 y z - 1/6 y + 1/2 y - 1/12 y x z - 1/6 z y x + 1/6 y z + + 2 3 2 2 2 2 3 2 2 3 + + 1/3 y x + 1/4 x y - 1/2 y x - 1/4 y x - 1/24 x y z - 1/4 y x z + + 2 3 2 2 3 3 3 2 3 3 3 2 + - 1/8 y x z + 1/4 y x z - 1/24 x y z + 1/12 x y z + 1/6 x y z + + 3 3 2 3 2 3 3 3 2 3 3 + + 1/12 x y z - 1/12 x y z - 1/12 x y z - 1/8 x y z + 1/24 x y z + + 2 3 2 2 3 2 3 2 2 2 + - 1/12 x y z + 1/4 y x z + 1/8 x y z - 1/3 y x z - 1/6 y x z + + 3 3 2 3 2 3 2 3 2 + + 1/24 x y z - 1/6 x y z + 1/12 y z + 1/3 y z + 1/6 y z + + 3 2 3 3 3 2 3 2 2 + - 1/6 y z + 1/4 y z - 1/12 y z - 1/4 y z - 1/4 x y z + + 3 3 3 2 3 3 + + 1/12 x y z, COEFF(1, -1, 0) = 1/12 x y - 1/12 x y + 1/6 x y + + 2 2 3 3 3 + - 1/4 y x z - 1/12 y x z - 1/6 x y - 1/3 y x - 1/6 y x z + + 2 2 2 2 2 3 2 + - 1/4 y x z + 1/6 y x z + 1/12 z y x - 1/6 y x - 1/4 x y + + 2 2 2 3 2 2 3 2 3 + + 1/4 y x + 1/2 y x + 1/12 x y z + 1/8 y x z + 1/4 y x z + + 2 2 3 3 3 2 3 3 3 2 + - 1/2 y x z + 1/24 x y z - 1/24 x y z - 1/6 x y z + + 3 3 2 3 2 3 3 3 2 3 3 + - 1/12 x y z + 1/6 x y z + 1/12 x y z + 1/8 x y z - 1/24 x y z + + 2 3 2 2 3 2 3 2 2 2 + + 1/24 x y z - 1/8 y x z - 1/8 x y z + 1/6 y x z + 1/3 y x z + + 3 3 2 3 2 3 2 2 3 + - 1/12 x y z + 1/12 x y z + 1/4 x y z - 1/12 x y z, + + 3 3 3 3 + COEFF(2, -1, 0) = - 1/18 x y - 1/36 y x z + 1/72 x y z - 1/72 x y z + + 3 3 2 2 2 2 3 2 + - 1/36 x y - 1/12 y x - 1/18 y x z + 1/12 y x z - 1/36 x y z + + 3 2 3 3 2 3 2 3 3 3 + + 1/36 x y + 1/24 y x z + 1/36 x y z + 1/18 x y z - 1/72 x y z + + 3 3 3 2 3 3 2 2 3 2 + + 1/72 x y z + 1/18 y x + 1/24 x y z - 1/12 x y z - 1/24 x y z + + 3 2 2 3 3 3 3 3 + + 1/12 x y - 1/24 y x z + 1/36 y x z + 1/36 x y z - 1/36 x y z , + + 3 3 2 3 3 2 + COEFF(-1, 0, 0) = - 1/12 x y - 1/3 x + 1/4 x y + 1/12 x y - 1/6 y x z + + 2 3 3 3 2 2 2 + - 1/8 y x z - 1/6 x y + 1/6 y x + 1/12 y x z + 1/2 y x z + + 2 2 3 2 2 2 + - 1/2 x z - 1/6 x + 1/2 x - 1/12 y x z + 1/8 z y x - 1/4 y x + + 3 2 2 2 2 3 2 2 3 + + 1/6 x y - 1/2 y x + 1/3 y x + 1/12 x y z - 1/4 y x z + + 2 3 2 2 3 3 3 2 3 3 3 2 + + 1/6 y x z - 1/3 y x z - 1/24 x y z + 1/8 x y z - 1/12 x y z + + 3 3 2 3 2 3 3 3 2 3 3 + + 1/12 x y z + 1/6 x y z + 1/24 x y z - 1/12 x y z + 1/24 x y z + + 2 3 2 2 3 2 3 2 2 2 + - 1/8 x y z + 1/4 y x z + 1/12 x y z + 1/4 y x z - 1/6 y x z + + 3 3 2 3 2 3 2 2 3 + - 1/12 x y z - 1/4 x y z + 1/6 x z - 1/6 x y z - 1/6 x z + + 2 2 3 3 2 3 3 2 3 + - 1/4 x z + 1/3 x z + 1/12 x z + 1/6 x z - 1/12 x z + 1/4 x z + + 3 3 3 2 3 + - 1/24 x y z, COEFF(0, 0, 0) = 1 + 1/4 x y - 1/2 x - 1/2 x y + + 3 2 2 3 3 + - 1/4 x y - 1/2 y - 1/2 z - 1/4 y x z + 1/4 y x z - 1/4 x y + 1/4 y x + + 3 2 2 2 2 2 2 2 3 3 3 2 + + 1/8 y x z - y x z + y z + x z + 1/2 z + 1/2 y + 1/2 x - y + + 2 2 2 2 3 2 + - z - x - 1/8 y x z - 1/4 z y x + 1/4 y z + 1/2 y x - 1/2 x y + + 2 2 2 3 2 2 3 2 3 2 2 + + y x + 1/2 y x + 1/8 x y z + 1/2 y x z + 1/4 y x z - 1/2 y x z + + 3 3 3 2 3 3 3 2 3 3 2 3 2 + + 1/8 x y z - 1/4 x y z + 1/4 x y z - 1/4 x y z + 1/4 x y z + + 3 3 3 2 3 3 2 3 2 2 + - 1/8 x y z + 1/4 x y z - 1/8 x y z + 1/4 x y z - 1/2 y x z + + 3 2 3 2 2 2 3 3 2 3 2 + - 1/4 x y z - 1/2 y x z - 1/4 y x z - 1/8 x y z + 1/2 x y z + + 3 2 3 2 3 2 3 3 3 + - 1/4 y z + 1/2 y z - 1/2 y z - 1/4 y z - 1/2 y z + 1/4 y z + + 2 3 2 2 3 2 2 + + 1/2 y z + 1/4 x z + 1/2 x y z - 1/4 x z + 1/2 x z + 1/2 x z + + 3 3 2 3 3 2 3 3 + - 1/4 x z - 1/2 x z + 1/4 x z - 1/2 x z + 1/8 x y z, + + 3 3 2 3 3 2 + COEFF(1, 0, 0) = - 1/4 x y + x + 1/4 x y + 1/4 x y + 1/2 y x z + + 2 3 3 3 2 2 2 2 2 + - 1/8 y x z + 1/2 x y - 1/2 y x - 1/4 y x z + 1/2 y x z - 1/2 x z + + 3 2 2 2 3 2 + - 1/2 x + 1/2 x + 1/4 y x z + 1/8 z y x - 1/4 y x + 1/2 x y + + 2 2 2 3 2 2 3 2 3 2 2 + - 1/2 y x - y x - 1/4 x y z - 1/4 y x z - 1/2 y x z + y x z + + 3 3 3 2 3 3 3 2 3 3 2 3 2 + - 1/8 x y z + 1/8 x y z - 1/4 x y z + 1/4 x y z - 1/2 x y z + + 3 3 3 2 3 3 2 3 2 2 + + 1/8 x y z - 1/4 x y z + 1/8 x y z - 1/8 x y z + 1/4 y x z + + 3 2 3 2 2 2 3 3 2 3 2 + + 1/4 x y z + 1/4 y x z + 1/2 y x z + 1/4 x y z - 1/4 x y z + + 3 2 2 3 2 2 3 + - 1/2 x z - 1/2 x y z + 1/2 x z - 1/4 x z - x z + 1/4 x z + + 3 2 3 3 2 3 3 + + 1/2 x z - 1/4 x z + 1/4 x z - 1/8 x y z, COEFF(2, 0, 0) = + + 3 3 3 2 3 + 1/12 x y - 1/6 x - 1/12 x y - 1/12 y x z - 1/12 x y + 1/12 y x + + 3 3 3 2 2 3 + + 1/24 y x z + 1/6 x - 1/24 y x z - 1/6 x y + 1/6 y x + 1/24 x y z + + 2 3 2 2 3 3 3 3 2 + + 1/12 y x z - 1/6 y x z + 1/24 x y z + 1/12 x y z + + 3 3 2 3 2 3 3 3 2 + - 1/12 x y z + 1/12 x y z - 1/24 x y z + 1/12 x y z + + 3 3 3 2 3 2 3 3 + - 1/24 x y z - 1/12 x y z - 1/12 y x z - 1/24 x y z + 1/12 x z + + 3 2 2 3 2 3 3 2 3 3 + + 1/6 x y z - 1/12 x z + 1/6 x z - 1/12 x z - 1/6 x z + 1/12 x z + + 3 3 3 2 3 3 + + 1/24 x y z, COEFF(-1, 1, 0) = 1/12 x y - 1/4 x y - 1/6 x y + + 2 2 3 3 3 + + 1/12 y x z + 1/4 y x z + 1/6 x y - 1/3 y x - 1/6 y x z + + 2 2 2 2 2 3 2 + - 1/4 y x z + 1/6 y x z - 1/4 z y x + 1/2 y x - 1/12 x y + + 2 2 2 3 2 2 3 2 3 + + 1/4 y x - 1/6 y x - 1/12 x y z + 1/8 y x z - 1/12 y x z + + 2 2 3 3 3 2 3 3 3 2 3 3 2 + + 1/6 y x z + 1/24 x y z - 1/8 x y z + 1/6 x y z - 1/12 x y z + + 3 2 3 3 3 2 3 3 2 3 + - 1/6 x y z - 1/12 x y z + 1/24 x y z - 1/24 x y z + 1/8 x y z + + 2 2 3 2 3 2 2 2 3 3 + - 1/8 y x z - 1/24 x y z - 1/2 y x z + 1/3 y x z + 1/12 x y z + + 2 3 2 3 2 2 3 3 3 + + 1/4 x y z + 1/12 x y z + 1/12 x y z, COEFF(0, 1, 0) = - 1/4 x y + + 2 3 3 2 2 3 3 + + 1/2 x y + 1/2 x y + y + 1/8 y x z - 1/2 y x z + 1/4 x y - 1/2 y x + + 3 2 2 2 2 2 3 2 + - 1/4 y x z + 1/2 y x z - 1/2 y z - 1/2 y + 1/2 y + 1/4 y x z + + 2 2 3 2 2 2 2 + + 1/2 z y x - 1/2 y z - y x + 1/4 x y - 1/2 y x - 1/4 y x + + 3 2 2 3 2 3 2 2 3 3 3 + - 1/8 x y z - 1/4 y x z - 1/8 y x z + 1/4 y x z - 1/8 x y z + + 2 3 3 3 2 3 3 2 3 2 3 3 + + 1/4 x y z - 1/2 x y z + 1/4 x y z - 1/4 x y z + 1/4 x y z + + 3 2 3 3 2 3 2 2 3 2 3 + - 1/8 x y z + 1/8 x y z - 1/4 x y z + 1/4 y x z + 1/8 x y z + + 2 2 2 3 3 2 3 2 3 2 + + y x z + 1/2 y x z + 1/8 x y z - 1/2 x y z + 1/4 y z - y z + + 3 2 3 2 3 3 3 2 3 2 2 + + 1/2 y z + 1/2 y z + 1/4 y z - 1/4 y z - 1/4 y z - 1/4 x y z + + 3 3 3 2 3 3 + - 1/4 x y z, COEFF(1, 1, 0) = 1/4 x y - 1/4 x y - 1/2 x y + + 2 2 3 3 3 2 2 2 + - 1/4 y x z + 1/4 y x z - 1/2 x y + y x + 1/2 y x z - 1/4 y x z + + 2 2 3 2 2 2 2 + - 1/2 y x z - 1/4 z y x + 1/2 y x - 1/4 x y + 1/4 y x + 1/2 y x + + 3 2 2 3 2 3 2 2 3 3 3 + + 1/4 x y z + 1/8 y x z + 1/4 y x z - 1/2 y x z + 1/8 x y z + + 2 3 3 3 2 3 3 2 3 2 3 3 + - 1/8 x y z + 1/2 x y z - 1/4 x y z + 1/2 x y z - 1/4 x y z + + 3 2 3 3 2 3 2 2 3 2 3 + + 1/8 x y z - 1/8 x y z + 1/8 x y z - 1/8 y x z - 1/8 x y z + + 2 2 2 3 3 2 3 2 3 2 2 + - 1/2 y x z - y x z - 1/4 x y z + 1/4 x y z + 1/4 x y z + + 3 3 2 3 3 3 + + 1/4 x y z, COEFF(2, 1, 0) = 1/12 x y - 1/24 y x z + 1/12 x y z + + 3 2 3 2 2 3 3 2 + + 1/12 x y + 1/12 y x z - 1/12 x y z + 1/24 y x z + 1/12 x y z + + 3 3 3 2 3 3 + - 1/12 y x z - 1/12 x y - 1/12 y x + 1/24 x y z - 1/6 y x + + 3 2 3 3 3 3 3 3 3 2 + + 1/24 x y z + 1/24 x y z - 1/24 x y z - 1/6 x y z + + 3 2 2 3 3 2 3 2 + - 1/12 x y z - 1/12 x y z - 1/24 x y z + 1/6 x y + 1/6 y x z + + 2 2 3 3 3 + + 1/12 y x z - 1/24 x y z, COEFF(-1, 2, 0) = - 1/36 x y z + + 2 3 3 2 3 2 3 2 2 3 + + 1/24 x y z - 1/12 y x + 1/36 x y z - 1/12 x y z + 1/12 x y + + 3 3 3 3 3 2 3 3 + + 1/72 x y z + 1/36 x y + 1/36 x y z - 1/72 x y z - 1/18 x y + + 2 3 2 3 2 2 2 + - 1/24 y x z + 1/24 z y x + 1/18 x y z + 1/12 y x z - 1/36 y x z + + 2 3 3 3 3 3 3 3 2 2 + - 1/24 x y z + 1/72 x y z - 1/72 x y z - 1/36 x y z - 1/18 y x z + + 3 3 3 3 3 + - 1/36 x y + 1/36 y x z + 1/18 y x, COEFF(0, 2, 0) = 1/12 x y + + 2 3 3 2 3 3 + - 1/6 x y - 1/12 x y - 1/6 y + 1/12 y x z - 1/12 x y + 1/12 y x + + 3 3 2 2 + + 1/24 y x z + 1/6 y - 1/24 y x z - 1/12 z y x + 1/12 y z + 1/6 y x + + 3 3 3 3 2 3 3 3 2 + + 1/24 x y z + 1/24 x y z - 1/12 x y z + 1/12 x y z + + 3 3 2 3 2 3 3 3 3 + - 1/12 x y z + 1/12 x y z - 1/24 x y z - 1/24 x y z + + 2 3 2 2 2 3 3 2 3 2 + + 1/12 x y z - 1/6 y x z - 1/12 y x z - 1/24 x y z + 1/6 x y z + + 3 2 3 2 3 3 3 3 + - 1/12 y z + 1/6 y z - 1/6 y z - 1/12 y z + 1/12 y z + 1/24 x y z, + + 2 3 3 2 2 3 3 + COEFF(1, 2, 0) = - 1/24 y x z - 1/12 x y z - 1/24 x y z - 1/12 x y z + + 3 3 3 2 3 3 2 + + 1/24 x y z - 1/6 x y z + 1/12 x y z + 1/12 y x z - 1/12 y x + + 3 3 3 3 2 3 3 + - 1/24 x y z - 1/24 x y z + 1/6 y x z + 1/12 x y - 1/12 y x z + + 3 3 3 2 3 2 3 3 + + 1/6 x y - 1/12 x y - 1/12 x y z - 1/6 y x + 1/24 x y z + + 2 3 3 2 3 2 3 3 2 2 2 + + 1/24 x y z + 1/12 x y + 1/24 z y x + 1/12 x y z + 1/12 y x z , + + 3 3 3 3 3 3 + COEFF(2, 2, 0) = - 1/72 x y z + 1/72 x y z + 1/72 x y z + + 3 3 2 3 3 3 2 3 2 3 + - 1/36 x y z - 1/72 x y z + 1/36 x y z + 1/36 x y z + 1/72 y x z + + 3 2 3 3 + + 1/72 x y z - 1/36 y x z + 1/36 x y + 1/36 y x - 1/72 y x z + + 3 3 3 3 2 + - 1/72 x y z - 1/36 x y - 1/36 x y, COEFF(-1, -1, 1) = - 1/6 y x z + + 2 3 3 2 2 2 2 + + 1/12 y x z - 1/18 y x z + 1/8 y x z + 1/9 y x z - 1/6 z y x + + 3 2 2 3 2 3 2 2 3 3 3 + + 1/18 x y z - 1/8 y x z + 1/12 y x z - 1/12 y x z - 1/72 x y z + + 2 3 3 3 2 3 3 2 3 2 + + 1/24 x y z + 1/36 x y z + 1/72 x y z + 1/36 x y z + + 3 3 3 2 3 3 2 3 2 2 + - 1/36 x y z - 1/12 x y z + 1/36 x y z - 1/12 x y z + 1/4 y x z + + 3 2 3 2 2 2 3 3 + + 1/24 x y z - 1/12 y x z + 1/18 y x z - 1/36 x y z + + 2 3 2 3 2 2 3 + - 1/24 x y z - 1/24 x y z + 1/18 x y z, COEFF(0, -1, 1) = + + 2 2 3 3 2 2 2 2 2 + - 1/4 y x z - 1/6 y x z - 1/12 y x z - 1/4 y x z + 1/4 y z + + 2 3 2 2 3 + + 1/6 y x z + 1/3 z y x - 1/3 y z + 1/12 x y z + 1/4 y x z + + 2 3 2 2 3 3 3 2 3 3 3 2 + + 1/8 y x z - 1/8 y x z + 1/24 x y z - 1/12 x y z - 1/12 x y z + + 3 3 2 3 2 3 3 3 2 3 3 + - 1/24 x y z + 1/24 x y z + 1/12 x y z + 1/4 x y z - 1/12 x y z + + 2 3 2 2 3 2 3 2 2 2 + + 1/6 x y z - 1/2 y x z - 1/8 x y z + 1/6 y x z + 1/12 y x z + + 3 3 2 3 2 3 2 3 2 + - 1/24 x y z + 1/12 x y z - 1/6 y z - 1/6 y z - 1/12 y z + + 3 2 3 3 3 2 3 2 2 3 + + 1/6 y z - 1/4 y z + 1/12 y z + 1/2 y z + 1/8 x y z - 1/6 x y z + + 2 2 3 3 2 2 2 + , COEFF(1, -1, 1) = 1/2 y x z + 1/12 y x z + 1/6 y x z + 1/8 y x z + + 2 3 2 2 3 2 3 + - 1/3 y x z - 1/6 z y x - 1/6 x y z - 1/8 y x z - 1/4 y x z + + 2 2 3 3 3 2 3 3 3 2 + + 1/4 y x z - 1/24 x y z + 1/24 x y z + 1/12 x y z + + 3 3 2 3 2 3 3 3 2 3 3 + + 1/24 x y z - 1/12 x y z - 1/12 x y z - 1/4 x y z + 1/12 x y z + + 2 3 2 2 3 2 3 2 2 2 + - 1/12 x y z + 1/4 y x z + 1/8 x y z - 1/12 y x z - 1/6 y x z + + 3 3 2 3 2 3 2 2 3 + + 1/12 x y z - 1/24 x y z - 1/8 x y z + 1/6 x y z, + + 3 3 2 2 3 2 2 + COEFF(2, -1, 1) = 1/36 x y z + 1/24 x y z + 1/72 x y z + 1/36 y x z + + 3 3 2 3 3 3 3 3 2 + - 1/36 y x z + 1/12 x y z - 1/36 x y z + 1/72 x y z - 1/12 y x z + + 2 2 3 3 3 3 2 + - 1/24 y x z + 1/18 y x z - 1/18 x y z - 1/72 x y z - 1/36 x y z + + 3 2 3 3 3 2 2 3 3 3 + - 1/24 x y z - 1/72 x y z + 1/24 y x z + 1/36 x y z , + + 2 2 3 3 2 2 2 + COEFF(-1, 0, 1) = 1/3 y x z + 1/8 y x z - 1/12 y x z - 1/4 y x z + + 2 2 2 3 2 2 3 + + 1/4 x z + 1/6 y x z - 1/4 z y x - 1/6 x y z + 1/4 y x z + + 2 3 2 2 3 3 3 2 3 3 3 2 + - 1/6 y x z + 1/6 y x z + 1/24 x y z - 1/8 x y z + 1/24 x y z + + 3 3 2 3 2 3 3 3 2 3 3 + - 1/24 x y z - 1/12 x y z - 1/24 x y z + 1/6 x y z - 1/12 x y z + + 2 3 2 2 3 2 3 2 2 2 + + 1/4 x y z - 1/2 y x z - 1/12 x y z - 1/8 y x z + 1/12 y x z + + 3 3 2 3 2 3 2 2 3 + + 1/12 x y z + 1/8 x y z - 1/3 x z + 1/12 x y z + 1/6 x z + + 2 2 3 3 2 3 3 2 3 + + 1/2 x z - 1/6 x z - 1/6 x z - 1/12 x z + 1/12 x z - 1/4 x z + + 3 2 2 3 3 + + 1/12 x y z, COEFF(0, 0, 1) = z + 1/2 y x z - 1/4 y x z - 1/8 y x z + + 2 2 2 2 2 2 2 3 2 + + 1/2 y x z - 1/2 y z - 1/2 x z - 1/2 z + 1/2 z + 1/4 y x z + + 2 3 2 2 3 2 3 + + 1/2 z y x - 1/2 y z - 1/4 x y z - 1/2 y x z - 1/4 y x z + + 2 2 3 3 3 2 3 3 3 2 3 3 2 + + 1/4 y x z - 1/8 x y z + 1/4 x y z - 1/8 x y z + 1/8 x y z + + 3 2 3 3 3 2 3 3 2 3 + - 1/8 x y z + 1/8 x y z - 1/2 x y z + 1/4 x y z - 1/2 x y z + + 2 2 3 2 3 2 2 2 3 3 + + y x z + 1/4 x y z + 1/4 y x z + 1/8 y x z + 1/8 x y z + + 2 3 2 3 2 3 2 3 2 3 + - 1/4 x y z + 1/2 y z - 1/4 y z + 1/4 y z + 1/4 y z + 1/2 y z + + 3 3 2 3 2 2 3 2 2 + - 1/4 y z - y z - 1/2 x z - 1/4 x y z + 1/4 x z - x z - 1/4 x z + + 3 3 2 3 3 2 3 3 + + 1/2 x z + 1/4 x z - 1/4 x z + 1/2 x z - 1/4 x y z, + + 2 2 3 3 2 2 2 + COEFF(1, 0, 1) = -y x z + 1/8 y x z + 1/4 y x z - 1/4 y x z + + 2 2 2 3 2 2 3 + + 1/4 x z - 1/2 y x z - 1/4 z y x + 1/2 x y z + 1/4 y x z + + 2 3 2 2 3 3 3 2 3 3 3 2 + + 1/2 y x z - 1/2 y x z + 1/8 x y z - 1/8 x y z + 1/8 x y z + + 3 3 2 3 2 3 3 3 2 3 3 + - 1/8 x y z + 1/4 x y z - 1/8 x y z + 1/2 x y z - 1/4 x y z + + 2 3 2 2 3 2 3 2 2 2 + + 1/4 x y z - 1/2 y x z - 1/4 x y z - 1/8 y x z - 1/4 y x z + + 3 3 2 3 2 3 2 2 3 2 + - 1/4 x y z + 1/8 x y z + x z + 1/4 x y z - 1/2 x z + 1/2 x z + + 2 3 3 2 3 3 2 3 3 + + 1/2 x z - 1/2 x z - 1/4 x z + 1/4 x z - 1/4 x z + 1/4 x y z, + + 3 2 2 3 3 2 2 + COEFF(2, 0, 1) = - 1/12 x y z + 1/24 x y z + 1/12 y x z + + 3 3 3 2 3 2 3 3 3 + + 1/24 x y z - 1/24 x y z - 1/6 x y z - 1/24 x y z - 1/6 x z + + 2 3 2 3 3 2 3 3 + + 1/24 y x z + 1/12 x z - 1/12 x z + 1/24 x y z - 1/12 x z + + 3 3 3 3 2 3 3 2 + + 1/12 x y z + 1/6 x z + 1/12 x y z - 1/24 x y z + 1/12 y x z + + 2 2 3 3 3 2 3 + + 1/6 y x z - 1/12 y x z - 1/12 x y z + 1/12 x z - 1/24 y x z + + 3 2 2 3 3 + - 1/12 x y z, COEFF(-1, 1, 1) = - 1/6 y x z - 1/4 y x z + 1/6 y x z + + 2 2 2 2 3 2 2 3 + + 1/8 y x z - 1/3 y x z + 1/2 z y x + 1/6 x y z - 1/8 y x z + + 2 3 2 2 3 3 3 2 3 3 + + 1/12 y x z - 1/12 y x z - 1/24 x y z + 1/8 x y z + + 3 2 3 3 2 3 2 3 3 + - 1/12 x y z + 1/24 x y z + 1/12 x y z + 1/12 x y z + + 3 2 3 3 2 3 2 2 3 2 3 + - 1/12 x y z + 1/12 x y z - 1/4 x y z + 1/4 y x z + 1/24 x y z + + 2 2 2 3 3 2 3 2 3 2 2 + + 1/4 y x z - 1/6 y x z - 1/12 x y z - 1/8 x y z - 1/24 x y z + + 3 2 2 3 3 + - 1/6 x y z, COEFF(0, 1, 1) = - 1/4 y x z + 1/2 y x z + 1/4 y x z + + 2 2 2 2 2 2 3 + - 1/4 y x z + 1/4 y z - 1/2 y x z - z y x + y z + 1/4 x y z + + 2 2 3 2 3 2 2 3 3 3 2 3 3 + + 1/4 y x z + 1/8 y x z - 1/8 y x z + 1/8 x y z - 1/4 x y z + + 3 2 3 3 2 3 2 3 3 3 2 + + 1/4 x y z - 1/8 x y z + 1/8 x y z - 1/4 x y z + 1/4 x y z + + 3 3 2 3 2 2 3 2 3 2 2 + - 1/4 x y z + 1/2 x y z - 1/2 y x z - 1/8 x y z - 1/2 y x z + + 2 3 3 2 3 2 3 2 + - 1/4 y x z - 1/8 x y z + 1/4 x y z - 1/2 y z + 1/2 y z + + 3 2 3 2 3 3 3 2 3 2 2 + - 1/4 y z - 1/2 y z - 1/4 y z + 1/4 y z + 1/2 y z + 1/8 x y z + + 3 2 2 3 3 + + 1/2 x y z, COEFF(1, 1, 1) = 1/2 y x z - 1/4 y x z - 1/2 y x z + + 2 2 2 2 3 2 2 3 + + 1/8 y x z + y x z + 1/2 z y x - 1/2 x y z - 1/8 y x z + + 2 3 2 2 3 3 3 2 3 3 3 2 + - 1/4 y x z + 1/4 y x z - 1/8 x y z + 1/8 x y z - 1/4 x y z + + 3 3 2 3 2 3 3 3 2 3 3 + + 1/8 x y z - 1/4 x y z + 1/4 x y z - 1/4 x y z + 1/4 x y z + + 2 3 2 2 3 2 3 2 2 2 + - 1/4 x y z + 1/4 y x z + 1/8 x y z + 1/4 y x z + 1/2 y x z + + 3 3 2 3 2 3 2 2 3 + + 1/4 x y z - 1/8 x y z - 1/8 x y z - 1/2 x y z, COEFF(2, 1, 1) + + 3 3 3 2 2 3 2 3 3 2 + = 1/24 x y z - 1/24 y x z + 1/12 y x z + 1/24 y x z + 1/12 x y z + + 3 2 2 3 3 3 3 2 + + 1/24 x y z - 1/12 x y z - 1/6 y x z + 1/6 x y z + 1/12 x y z + + 2 3 3 2 3 3 3 3 2 3 + - 1/12 y x z - 1/24 x y z + 1/12 x y z - 1/24 x y z - 1/24 x y z + + 2 3 2 3 3 + - 1/12 y x z + 1/24 x y z - 1/12 x y z , COEFF(-1, 2, 1) = + + 2 2 3 3 2 3 3 + - 1/12 z y x + 1/24 y x z + 1/36 x y z - 1/24 x y z + 1/18 y x z + + 3 3 3 3 2 3 3 3 2 + - 1/72 x y z - 1/18 x y z - 1/36 x y z - 1/36 x y z + 1/72 x y z + + 3 3 3 2 2 3 2 3 3 + - 1/36 y x z - 1/72 x y z + 1/24 x y z + 1/36 x y z + + 2 2 2 3 3 3 2 3 + - 1/24 y x z + 1/36 y x z + 1/72 x y z + 1/12 x y z, + + 2 3 3 3 2 + COEFF(0, 2, 1) = 1/6 z y x - 1/12 x y z - 1/12 x y z - 1/24 x y z + + 3 3 2 3 2 3 2 2 3 + + 1/12 x y z - 1/12 x y z - 1/24 x y z - 1/12 y x z - 1/6 y z + + 2 3 3 3 3 3 3 3 2 2 2 + - 1/6 x y z + 1/24 x y z - 1/12 y z + 1/24 x y z + 1/12 y x z + + 3 2 2 3 2 + + 1/12 y z + 1/12 y x z + 1/24 y x z - 1/24 y x z - 1/12 y z + + 3 3 3 3 2 3 3 3 3 3 + - 1/24 x y z + 1/6 y z + 1/12 x y z + 1/12 y z + 1/24 x y z , + + 3 3 3 3 2 3 + COEFF(1, 2, 1) = - 1/12 x y z - 1/12 x y z - 1/12 z y x + 1/6 x y z + + 2 3 2 3 2 3 3 2 + + 1/24 x y z + 1/12 x y z - 1/24 x y z - 1/12 y x z + + 3 3 3 3 3 3 2 3 2 + + 1/24 x y z + 1/12 y x z - 1/24 x y z - 1/6 y x z + 1/24 x y z + + 2 2 3 3 2 3 3 2 2 3 + - 1/24 y x z - 1/24 x y z + 1/12 x y z + 1/12 x y z + 1/24 y x z + + 3 2 2 3 + , COEFF(2, 2, 1) = 1/36 y x z - 1/72 x y z + 1/72 y x z - 1/36 x y z + + 3 3 2 3 3 2 3 3 3 + + 1/72 x y z - 1/36 x y z - 1/72 x y z - 1/72 x y z + + 3 3 3 3 3 3 3 + + 1/72 x y z + 1/72 x y z + 1/36 x y z - 1/72 y x z , + + 3 3 3 3 3 3 3 + COEFF(-1, -1, 2) = 1/216 x y z + 1/108 x y z + 1/108 x y z + + 3 2 2 3 3 3 2 2 + - 1/54 y x z + 1/54 y x z + 1/24 y x z - 1/216 x y z - 1/24 y x z + + 3 2 2 3 2 3 3 3 2 + - 1/108 x y z + 1/36 z y x - 1/36 y x z - 1/72 x y z + 1/72 x y z + + 2 3 2 2 3 3 2 3 3 + - 1/36 y x z + 1/36 y x z + 1/72 x y z - 1/72 x y z - 1/108 x y z + + 2 3 2 2 3 3 3 + , COEFF(0, -1, 2) = 1/12 y z - 1/18 z y x + 1/36 x y z - 1/18 y z + + 2 3 3 3 3 3 3 3 + + 1/18 y x z + 1/36 y z - 1/72 x y z - 1/36 y z - 1/36 x y z + + 2 2 3 2 2 2 3 + + 1/18 y z - 1/12 y x z - 1/36 y x z + 1/12 y x z - 1/36 x y z + + 3 3 2 3 3 2 3 3 3 + + 1/36 x y z - 1/24 x y z + 1/72 x y z + 1/24 y x z - 1/72 x y z + + 3 2 3 3 3 2 3 3 2 + + 1/24 x y z + 1/72 x y z - 1/24 y x z + 1/36 y x z - 1/12 y z, + + 2 2 3 2 3 + COEFF(1, -1, 2) = - 1/12 y x z + 1/18 y x z + 1/72 x y z + 1/12 y x z + + 3 3 3 3 3 3 2 3 3 + - 1/36 x y z + 1/72 x y z - 1/24 x y z - 1/18 y x z + + 3 2 3 3 2 3 3 2 2 3 + + 1/24 x y z + 1/36 x y z - 1/72 x y z + 1/24 y x z + + 2 2 2 3 3 2 3 + + 1/36 z y x - 1/24 y x z + 1/36 x y z - 1/36 x y z - 1/36 y x z + + 3 3 3 2 3 2 3 + - 1/72 x y z, COEFF(2, -1, 2) = - 1/72 x y z + 1/72 x y z + + 3 2 3 3 3 3 + + 1/108 x y z - 1/72 y x z + 1/216 x y z + 1/108 y x z + + 3 3 3 3 3 3 + - 1/216 x y z - 1/108 y x z - 1/216 x y z + 1/216 x y z + + 2 3 3 3 3 + + 1/72 y x z - 1/108 x y z , COEFF(-1, 0, 2) = 1/72 x y z + + 3 3 3 2 3 3 3 2 3 + - 1/72 x y z + 1/72 x y z - 1/12 x z - 1/72 x y z + 1/12 x z + + 3 2 3 2 3 3 + + 1/36 y x z - 1/24 x y z - 1/36 y x z + 1/24 z y x - 1/36 x y z + + 3 2 3 3 2 3 3 + + 1/18 x z - 1/36 x y z - 1/18 x z + 1/36 x y z + 1/36 x y z + + 2 3 2 3 3 2 2 3 3 + + 1/18 y x z + 1/24 x y z - 1/18 y x z - 1/24 y x z + 1/36 x z + + 2 2 3 3 2 2 3 + + 1/12 y x z - 1/36 x z - 1/12 y x z , COEFF(0, 0, 2) = - 1/6 z + + 2 2 3 3 3 + - 1/12 y x z + 1/12 y x z + 1/24 y x z + 1/6 z - 1/24 y x z + + 2 3 2 2 3 2 3 + - 1/12 z y x + 1/12 y z + 1/24 x y z + 1/6 y x z + 1/12 y x z + + 3 3 3 2 3 3 3 3 3 2 + + 1/24 x y z - 1/12 x y z - 1/24 x y z + 1/12 x y z + + 3 3 2 3 2 2 3 2 3 3 3 + - 1/24 x y z + 1/12 x y z - 1/6 y x z - 1/12 x y z - 1/24 x y z + + 3 3 2 3 3 3 2 + - 1/12 y z - 1/12 y z - 1/6 y z + 1/12 y z + 1/6 y z + 1/12 x z + + 3 2 3 3 3 2 3 3 + - 1/12 x z + 1/6 x z - 1/12 x z + 1/12 x z - 1/6 x z + 1/24 x y z, + + 3 3 2 2 3 3 + COEFF(1, 0, 2) = 1/24 x y z - 1/12 y x z + 1/12 y x z + 1/12 x z + + 3 3 3 3 + - 1/12 x y z - 1/6 x z - 1/24 x y z + 1/6 x z - 1/12 y x z + + 3 3 3 2 3 3 3 2 3 3 + - 1/24 x y z + 1/12 x z + 1/24 x y z - 1/12 x z - 1/12 x z + + 2 3 3 3 2 3 2 3 + - 1/24 x y z + 1/12 x y z + 1/24 z y x + 1/12 x y z + + 2 3 3 2 3 2 3 2 2 2 + + 1/24 x y z - 1/6 y x z - 1/24 y x z + 1/6 y x z + 1/12 y x z + + 3 2 3 2 3 3 3 + - 1/12 x y z, COEFF(2, 0, 2) = - 1/36 x y z - 1/72 x y z + + 2 3 3 3 3 3 3 3 3 + + 1/36 y x z + 1/72 x y z - 1/72 x y z + 1/72 y x z + 1/72 x y z + + 3 3 3 3 3 3 + + 1/72 x y z - 1/72 x y z + 1/36 x z - 1/36 x z + 1/36 x z + + 3 2 3 2 + - 1/36 x z - 1/36 y x z - 1/72 y x z + 1/36 x y z, COEFF(-1, 1, 2) = + + 2 3 3 2 2 3 2 2 2 2 3 + - 1/24 x y z - 1/12 z y x + 1/24 x y z - 1/24 y x z + 1/24 y x z + + 3 3 3 3 3 3 2 3 2 3 + + 1/36 x y z - 1/36 x y z - 1/72 x y z + 1/72 x y z - 1/72 x y z + + 3 3 3 2 3 3 + - 1/36 x y z + 1/18 y x z + 1/36 x y z - 1/36 y x z - 1/18 y x z + + 2 3 3 3 3 2 2 3 + + 1/12 y x z + 1/72 x y z + 1/36 y x z, COEFF(0, 1, 2) = 1/12 y z + + 3 2 3 3 3 3 + + 1/6 y z + 1/12 x y z + 1/12 y z - 1/24 x y z - 1/6 y z + + 2 3 3 3 3 3 3 2 3 + + 1/6 z y x - 1/12 y z + 1/24 x y z + 1/12 x y z - 1/12 x y z + + 3 3 3 3 2 2 2 3 2 3 + + 1/24 x y z - 1/12 y x z - 1/24 x y z + 1/12 y x z + 1/24 x y z + + 3 3 3 2 2 3 2 3 3 + - 1/24 x y z + 1/12 y x z - 1/12 y x z - 1/24 y x z - 1/12 x y z + + 2 3 2 2 2 + - 1/6 y x z - 1/12 y z + 1/24 y x z, COEFF(1, 1, 2) = - 1/12 y x z + + 3 3 2 2 3 3 2 3 3 3 + - 1/12 x y z - 1/24 y x z - 1/24 x y z - 1/24 x y z + 1/12 x y z + + 3 3 3 2 3 3 3 3 3 2 + + 1/24 x y z + 1/12 y x z + 1/12 x y z - 1/12 x y z + 1/24 x y z + + 2 3 2 3 2 3 2 2 3 3 + + 1/24 x y z - 1/12 z y x - 1/24 x y z + 1/24 y x z + 1/6 y x z + + 2 3 3 3 2 + + 1/12 y x z - 1/6 y x z, COEFF(2, 1, 2) = 1/36 x y z + 1/72 y x z + + 3 3 2 3 3 2 3 3 3 3 + + 1/72 x y z - 1/72 y x z - 1/72 x y z - 1/72 x y z - 1/72 x y z + + 3 3 3 3 3 2 3 + - 1/36 x y z + 1/72 x y z - 1/36 y x z + 1/36 y x z + 1/72 x y z , + + 2 3 2 3 3 2 3 + COEFF(-1, 2, 2) = 1/72 z y x + 1/108 x y z + 1/72 x y z - 1/72 y x z + + 2 3 3 3 3 3 3 3 + - 1/72 x y z + 1/108 y x z + 1/216 x y z - 1/216 x y z + + 3 3 3 3 3 + - 1/108 x y z + 1/216 x y z - 1/108 y x z - 1/216 x y z, + + 2 3 2 3 3 + COEFF(0, 2, 2) = 1/36 x y z + 1/36 y z - 1/36 z y x - 1/72 x y z + + 3 3 2 3 2 3 3 3 3 + + 1/36 y z + 1/36 y x z - 1/36 x y z + 1/72 x y z + 1/72 y x z + + 3 3 3 3 3 3 3 3 + - 1/72 x y z - 1/72 x y z - 1/72 y x z - 1/36 y z + 1/72 x y z + + 3 3 2 2 3 3 + - 1/36 y z + 1/72 x y z, COEFF(1, 2, 2) = 1/72 z y x + 1/72 x y z + + 3 2 3 3 3 3 3 3 3 + - 1/36 x y z - 1/72 y x z + 1/72 x y z - 1/72 x y z - 1/72 x y z + + 3 3 3 3 2 3 3 + + 1/36 x y z + 1/72 x y z + 1/36 y x z - 1/72 x y z - 1/36 y x z , + + 3 3 3 3 3 + COEFF(2, 2, 2) = 1/216 x y z - 1/216 x y z - 1/216 x y z + + 3 3 3 3 3 3 3 + - 1/216 x y z + 1/216 x y z + 1/216 y x z + 1/216 x y z + + - 1/216 y x z] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-I.compute.c"); +bytes used=4835003040, alloc=3669344, time=381.12 +bytes used=4836003668, alloc=3669344, time=381.20 +bytes 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time=449.62 +bytes used=5369826736, alloc=4259060, time=449.68 +bytes used=5370827060, alloc=4259060, time=449.88 +bytes used=5371827232, alloc=4259060, time=450.03 +bytes used=5372827444, alloc=4259060, time=450.23 +bytes used=5373827652, alloc=4259060, time=450.41 +> +# d/dx +> simplify( diff(interp_3d_cube_order3_smooth0,x) ); +bytes used=5374828728, alloc=4259060, time=450.52 +bytes used=5375828916, alloc=4259060, time=450.59 +bytes used=5376829480, alloc=4259060, time=450.67 +bytes used=5377829708, alloc=4259060, time=450.75 +bytes used=5378829912, alloc=4259060, time=450.82 +bytes used=5379830124, alloc=4259060, time=450.90 +bytes used=5381021784, alloc=4259060, time=450.99 +bytes used=5382022240, alloc=4259060, time=451.07 +bytes used=5383022388, alloc=4259060, time=451.15 +bytes used=5384023116, alloc=4259060, time=451.23 +bytes used=5385023260, alloc=4259060, time=451.30 +bytes used=5386024008, alloc=4259060, time=451.39 +bytes used=5387025088, alloc=4259060, time=451.47 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- 1/8 x y z DATA(-1, 1, 1) + + 2 3 3 2 3 3 + + 1/24 x y z DATA(1, 2, -1) - 1/24 x y z DATA(0, 2, -1) + + 3 2 3 3 + + 1/18 x y z DATA(0, 2, 2) + 1/8 x y z DATA(2, 0, 0) + + 2 3 3 3 3 + - 1/8 x y z DATA(2, 1, 0) - 1/36 y z DATA(-1, -1, 1) + + 3 3 3 3 + - 1/8 y z DATA(0, 1, 1) + 1/4 y z DATA(1, 1, 1) + + 3 3 3 3 + - 1/36 y z DATA(1, 2, -1) + 1/72 y z DATA(0, 2, -1) + + 3 3 3 3 + + 1/108 y z DATA(-1, 2, -1) - 1/24 y z DATA(0, -1, 1) + + 3 3 3 3 + - 1/24 y z DATA(2, 0, 0) + 1/24 y z DATA(2, 1, 0) + + 3 3 3 3 + + 1/36 y z DATA(1, -1, -1) - 1/36 y z DATA(-1, 1, -1) + + 3 3 3 3 + + 1/72 y z DATA(0, -1, 2) + 1/12 y z DATA(1, -1, 1) + + 2 3 3 + - 1/36 y z DATA(2, 2, 0) + 1/24 y z DATA(0, 2, 1) + + 3 3 3 3 + + 1/36 y z DATA(-1, 2, 1) - 1/36 y z DATA(-1, 0, 2) + + 3 3 3 3 + - 1/24 y z DATA(0, 0, 2) - 1/36 y z DATA(1, -1, 2) + + 3 3 3 + - 1/216 y z DATA(2, -1, 2) - 1/12 y z DATA(1, 2, 1) + + 3 3 + - 1/36 y z DATA(2, 1, -1) + 1/36 y z DATA(2, -1, 1) + + 3 + + 1/12 y z DATA(2, 1, 1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=5398028488, alloc=5110872, time=452.42 +bytes used=5399028932, alloc=5110872, time=452.50 +bytes used=5400029116, alloc=5176396, time=452.59 +bytes used=5401029340, alloc=5307444, time=452.67 +bytes used=5402205184, alloc=5504016, time=452.77 +bytes used=5403205400, alloc=5766112, time=452.87 +bytes used=5404306948, alloc=6093732, time=452.97 +bytes used=5405492072, alloc=6486876, time=453.10 +bytes used=5406605012, alloc=7207640, time=453.22 +bytes used=5407618720, alloc=7469736, time=453.32 +bytes used=5408619032, alloc=7928404, time=453.43 +bytes used=5409636580, alloc=8190500, time=453.55 +bytes used=5410684120, alloc=8780216, time=453.68 +bytes used=5411752508, alloc=9369932, time=453.80 +bytes used=5412783724, alloc=9959648, time=453.93 +bytes used=5413807564, alloc=10549364, time=454.01 +bytes used=5414810512, alloc=10549364, time=454.07 +bytes used=5415813068, alloc=10549364, time=454.13 +bytes used=5416815624, alloc=10549364, time=454.18 + 2 2 3 3 2 2 2 +[COEFF(-1, -1, -1) = - 1/6 y x z - 1/36 y x z + 1/18 y x z - 1/8 y x z + + 2 2 2 3 + - 1/12 y z + 1/9 y x z - 1/18 z y x - 1/27 y z + 1/18 x y z + + 2 2 3 2 3 2 2 2 3 3 + + 1/24 y x z - 1/12 y x z + 1/4 y x z - 1/72 x y z + + 3 2 2 3 2 2 2 2 2 + - 1/12 x y z - 1/36 x y z + 1/12 y x z + 1/12 y x z - 1/6 y x z + + 3 3 2 3 2 3 2 3 2 + + 1/36 x y z + 1/24 x y z - 1/54 y z + 1/18 y z + 1/36 y z + + 3 2 3 3 3 2 + - 1/54 y z + 1/36 y z - 1/108 y z + 1/18 y z, COEFF(0, -1, -1) = + + 2 2 3 3 2 2 2 2 2 + 1/3 y x z + 1/12 y x z - 1/9 y x z + 3/8 y x z - 1/8 y z + + 2 3 2 2 3 + - 2/9 y x z + 1/6 z y x - 1/18 y z - 1/9 x y z - 1/8 y x z + + 2 3 2 2 2 3 3 3 2 2 3 + + 1/6 y x z - 1/2 y x z + 1/24 x y z + 1/6 x y z + 1/12 x y z + + 2 2 2 2 2 3 3 2 3 2 + - 1/4 y x z - 1/4 y x z + 1/3 y x z - 1/18 x y z - 1/8 x y z + + 3 2 3 2 3 2 3 3 3 + - 1/36 y z + 1/12 y z + 1/24 y z - 1/36 y z + 1/24 y z - 1/72 y z + + 2 2 2 3 3 + + 1/12 y z, COEFF(1, -1, -1) = - 1/6 y x z - 1/12 y x z + 1/18 y x z + + 2 2 2 2 2 2 + - 3/8 y x z + 1/4 y z + 1/9 y x z - 1/6 z y x + 1/9 y z + + 3 2 2 3 2 3 2 2 2 3 3 + + 1/18 x y z + 1/8 y x z - 1/12 y x z + 1/4 y x z - 1/24 x y z + + 3 2 2 3 2 2 2 2 2 + - 1/12 x y z - 1/12 x y z + 1/4 y x z + 1/4 y x z - 1/6 y x z + + 3 3 2 3 2 3 2 3 2 + + 1/36 x y z + 1/8 x y z + 1/18 y z - 1/6 y z - 1/12 y z + + 3 2 3 3 3 2 + + 1/18 y z - 1/12 y z + 1/36 y z - 1/6 y z, COEFF(2, -1, -1) = + + 2 3 2 3 2 2 3 2 2 2 2 3 3 + - 1/24 x y z + 1/72 y z + 1/36 x y z + 1/8 y x z + 1/72 x y z + + 2 2 2 2 2 3 + + 1/36 y z + 1/36 y z + 1/18 z y x - 1/54 y z - 1/24 y z - 1/108 y z + + 2 2 3 2 3 3 2 3 2 2 + - 1/24 y x z + 1/72 y z - 1/108 y z + 1/36 y x z - 1/12 y x z + + 3 3 2 2 2 + - 1/216 y z - 1/12 y x z , COEFF(-1, 0, -1) = 1/9 z + 1/3 y x z + + 2 3 3 2 2 2 2 2 2 2 + - 1/24 y x z + 1/12 y x z + 1/4 y x z + 1/6 y z - 1/4 x z + + 3 2 2 3 + + 1/18 z - 1/6 z + 1/6 y x z - 1/12 z y x - 1/18 y z - 1/6 x y z + + 2 2 3 2 3 2 2 2 3 3 3 2 + - 1/12 y x z + 1/6 y x z - 1/2 y x z + 1/24 x y z + 1/4 x y z + + 2 3 2 2 2 2 2 3 3 + + 1/12 x y z - 1/6 y x z + 1/8 y x z - 1/4 y x z - 1/12 x y z + + 2 3 2 3 2 3 2 3 + - 1/8 x y z + 1/18 y z + 1/12 y z - 1/12 y z - 1/36 y z + + 2 3 3 3 2 3 2 + - 1/18 y z + 1/36 y z - 1/9 y z - 1/3 x z - 1/6 x z + 1/6 x z + + 2 2 3 2 + + 1/2 x z + 1/12 x z , COEFF(0, 0, -1) = 1/6 z - 2/3 y x z + + 2 3 3 2 2 2 2 2 2 2 + + 1/8 y x z - 1/6 y x z - 3/4 y x z + 1/4 y z + 3/4 x z + + 3 2 2 3 + + 1/12 z - 1/4 z - 1/3 y x z + 1/4 z y x - 1/12 y z + 1/3 x y z + + 2 2 3 2 3 2 2 2 3 3 3 2 + + 1/4 y x z - 1/3 y x z + y x z - 1/8 x y z - 1/2 x y z + + 2 3 2 2 2 2 2 3 3 + - 1/4 x y z + 1/2 y x z - 3/8 y x z + 1/2 y x z + 1/6 x y z + + 2 3 2 3 2 3 2 3 2 3 + + 3/8 x y z + 1/12 y z + 1/8 y z - 1/8 y z - 1/24 y z - 1/12 y z + + 3 3 2 3 2 2 2 3 + + 1/24 y z - 1/6 y z + 2/3 x z + 1/3 x z - 1/2 x z - x z - 1/4 x z + + 2 2 3 3 + , COEFF(1, 0, -1) = - 1/3 z + 1/3 y x z - 1/8 y x z + 1/12 y x z + + 2 2 2 2 2 2 2 3 2 + + 3/4 y x z - 1/2 y z - 3/4 x z - 1/6 z + 1/2 z + 1/6 y x z + + 2 3 2 2 3 2 3 + - 1/4 z y x + 1/6 y z - 1/6 x y z - 1/4 y x z + 1/6 y x z + + 2 2 2 3 3 3 2 2 3 2 2 + - 1/2 y x z + 1/8 x y z + 1/4 x y z + 1/4 x y z - 1/2 y x z + + 2 2 2 3 3 2 3 2 3 + + 3/8 y x z - 1/4 y x z - 1/12 x y z - 3/8 x y z - 1/6 y z + + 2 3 2 3 2 3 3 3 2 + - 1/4 y z + 1/4 y z + 1/12 y z + 1/6 y z - 1/12 y z + 1/3 y z + + 3 2 2 2 3 + - 1/3 x z - 1/6 x z + 1/2 x z + 1/2 x z + 1/4 x z , COEFF(2, 0, -1) = + + 2 2 2 2 3 2 3 2 3 2 + 1/12 y z - 1/12 z + 1/8 x y z + 1/36 y z - 1/12 x y z - 1/6 x z + + 3 2 2 2 3 2 2 2 2 2 2 2 + - 1/24 y z + 1/12 y x z + 1/6 y x z - 1/4 y x z + 1/4 x z + + 2 3 2 3 3 2 3 2 3 + - 1/36 y z - 1/24 x y z + 1/24 y x z - 1/18 y z + 1/36 z + + 2 2 2 3 3 2 + + 1/12 z y x - 1/8 y x z + 1/18 z - 1/36 y z + 1/72 y z + 1/24 y z + + 2 3 3 2 2 3 + - 1/12 x z - 1/72 y z , COEFF(-1, 1, -1) = - 1/6 y x z + 1/12 y x z + + 3 2 2 2 2 2 2 + - 1/6 y x z - 1/8 y x z - 1/12 y z - 1/3 y x z + 1/6 z y x + + 3 2 2 3 2 3 2 2 + + 1/9 y z + 1/6 x y z + 1/24 y x z - 1/12 y x z + 1/4 y x z + + 2 3 3 3 2 2 3 2 2 2 2 + - 1/24 x y z - 1/4 x y z - 1/12 x y z + 1/12 y x z - 1/4 y x z + + 2 3 3 2 3 2 3 2 + + 1/2 y x z + 1/12 x y z + 1/8 x y z - 1/18 y z - 1/6 y z + + 3 2 3 2 3 3 3 2 + + 1/12 y z + 1/18 y z + 1/36 y z - 1/36 y z + 1/18 y z, + + 2 2 3 3 2 2 2 + COEFF(0, 1, -1) = 1/3 y x z - 1/4 y x z + 1/3 y x z + 3/8 y x z + + 2 2 2 3 2 2 3 + - 1/8 y z + 2/3 y x z - 1/2 z y x + 1/6 y z - 1/3 x y z - 1/8 y x z + + 2 3 2 2 2 3 3 3 2 2 3 + + 1/6 y x z - 1/2 y x z + 1/8 x y z + 1/2 x y z + 1/4 x y z + + 2 2 2 2 2 3 3 2 3 2 + - 1/4 y x z + 3/4 y x z - y x z - 1/6 x y z - 3/8 x y z + + 3 2 3 2 3 2 3 3 3 + - 1/12 y z - 1/4 y z + 1/8 y z + 1/12 y z + 1/24 y z - 1/24 y z + + 2 2 2 3 3 + + 1/12 y z, COEFF(1, 1, -1) = - 1/6 y x z + 1/4 y x z - 1/6 y x z + + 2 2 2 2 2 2 3 + - 3/8 y x z + 1/4 y z - 1/3 y x z + 1/2 z y x - 1/3 y z + 1/6 x y z + + 2 2 3 2 3 2 2 2 3 3 3 2 + + 1/8 y x z - 1/12 y x z + 1/4 y x z - 1/8 x y z - 1/4 x y z + + 2 3 2 2 2 2 2 3 3 + - 1/4 x y z + 1/4 y x z - 3/4 y x z + 1/2 y x z + 1/12 x y z + + 2 3 2 3 2 3 2 3 2 3 + + 3/8 x y z + 1/6 y z + 1/2 y z - 1/4 y z - 1/6 y z - 1/12 y z + + 3 3 2 3 3 + + 1/12 y z - 1/6 y z, COEFF(2, 1, -1) = - 1/36 y z + 1/36 y z + + 2 2 2 3 2 2 3 2 3 + - 1/12 y z - 1/6 z y x + 1/72 y z - 1/24 y x z - 1/12 y x z + + 2 3 3 2 3 3 2 2 2 2 + + 1/24 x y z + 1/12 x y z + 1/24 y z + 1/8 y x z + 1/18 y z + + 2 3 2 2 2 2 2 2 2 2 + - 1/8 x y z + 1/36 y z + 1/4 y x z - 1/12 y x z - 1/24 y z + + 3 3 2 3 + - 1/72 y z , COEFF(-1, 2, -1) = 1/18 y x z - 1/72 y x z - 1/54 y z + + 2 3 2 3 2 3 + - 1/36 z y x + 1/12 x y z + 1/36 y x z + 1/36 y z - 1/18 x y z + + 3 3 3 2 3 3 2 2 3 + - 1/108 y z + 1/108 y z + 1/72 x y z + 1/24 y x z + 1/54 y z + + 2 2 3 2 3 3 2 3 3 2 + - 1/12 y x z - 1/24 x y z - 1/36 x y z + 1/36 x y z - 1/36 y z , + + 2 2 3 2 3 3 3 2 + COEFF(0, 2, -1) = - 1/8 y x z - 1/24 y z + 1/18 x y z - 1/6 x y z + + 2 2 3 2 3 3 2 + + 1/24 y z - 1/9 y x z + 1/24 y x z - 1/24 x y z + 1/6 y x z + + 3 3 3 3 2 + - 1/18 y x z - 1/72 y z - 1/36 y z + 1/72 y z + 1/12 z y x + + 3 2 3 2 3 2 3 + + 1/9 x y z + 1/8 x y z + 1/36 y z - 1/12 x y z, COEFF(1, 2, -1) = + + 3 2 2 3 3 2 + - 1/18 x y z - 1/12 y z - 1/24 y x z + 1/18 y x z + 1/12 x y z + + 2 3 3 3 2 3 3 3 2 + + 1/24 x y z + 1/36 y x z - 1/12 y x z - 1/36 y z + 1/12 y z + + 3 2 3 2 2 3 3 3 + + 1/18 y z + 1/36 y z - 1/8 x y z + 1/12 x y z - 1/36 x y z + + 3 2 2 2 2 3 + - 1/18 y z + 1/8 y x z - 1/12 z y x , COEFF(2, 2, -1) = 1/72 y x z + + 2 3 2 2 3 2 2 2 + + 1/24 x y z - 1/36 x y z - 1/108 y z - 1/24 y x z + 1/72 y z + + 3 2 3 3 3 3 2 3 2 + - 1/216 y z - 1/72 x y z + 1/216 y z + 1/36 z y x - 1/72 y z + + 3 2 3 2 + + 1/108 y z, COEFF(-1, -1, 0) = 1/12 x y + 1/9 y - 1/4 y x z + + 2 3 3 3 2 2 2 + + 1/12 y x z - 1/6 x y - 1/3 y x - 1/6 y x z + 1/4 y x z + + 2 2 3 2 2 + + 1/6 y z + 1/18 y - 1/6 y + 1/6 y x z - 1/12 z y x - 1/18 y z + + 2 2 2 2 3 2 2 3 + + 1/6 y x - 1/4 y x + 1/2 y x + 1/12 x y z - 1/8 y x z + + 2 3 2 2 2 3 3 3 2 2 3 + + 1/4 y x z - 1/2 y x z + 1/24 x y z + 1/6 x y z - 1/24 x y z + + 2 2 2 2 2 3 3 2 3 2 + + 1/8 y x z - 1/6 y x z + 1/3 y x z - 1/12 x y z - 1/12 x y z + + 3 2 3 2 3 2 3 3 3 + - 1/36 y z - 1/9 y z - 1/18 y z + 1/18 y z - 1/12 y z + 1/36 y z + + 2 2 3 2 + + 1/12 y z, COEFF(0, -1, 0) = - 1/4 x y + 1/6 y + 1/2 y x z + + 2 3 3 3 2 2 2 2 2 + - 1/4 y x z + 1/3 x y + 2/3 y x + 1/3 y x z - 3/4 y x z + 1/4 y z + + 3 2 2 2 + + 1/12 y - 1/4 y - 1/3 y x z + 1/4 z y x - 1/12 y z - 1/2 y x + + 2 2 2 3 2 2 3 2 3 2 2 + + 3/4 y x - y x - 1/6 x y z + 3/8 y x z - 1/2 y x z + y x z + + 2 3 3 3 2 2 3 2 2 2 2 + - 1/8 x y z - 1/3 x y z + 1/8 x y z - 3/8 y x z + 1/2 y x z + + 2 3 3 2 3 2 3 2 + - 2/3 y x z + 1/6 x y z + 1/4 x y z - 1/24 y z - 1/6 y z + + 3 2 3 2 3 3 3 2 + - 1/12 y z + 1/12 y z - 1/8 y z + 1/24 y z + 1/8 y z, + + 2 3 2 2 3 3 + COEFF(1, -1, 0) = 1/4 x y - 1/3 y - 1/4 y x z + 1/4 y x z - 1/6 x y + + 3 2 2 2 2 2 3 2 + - 1/3 y x - 1/6 y x z + 3/4 y x z - 1/2 y z - 1/6 y + 1/2 y + + 2 2 2 2 2 + + 1/6 y x z - 1/4 z y x + 1/6 y z + 1/2 y x - 3/4 y x + 1/2 y x + + 3 2 2 3 2 3 2 2 2 3 3 + + 1/12 x y z - 3/8 y x z + 1/4 y x z - 1/2 y x z + 1/8 x y z + + 3 2 2 3 2 2 2 2 2 + + 1/6 x y z - 1/8 x y z + 3/8 y x z - 1/2 y x z + 1/3 y x z + + 3 3 2 3 2 3 2 3 2 + - 1/12 x y z - 1/4 x y z + 1/12 y z + 1/3 y z + 1/6 y z + + 3 2 3 3 3 2 3 + - 1/6 y z + 1/4 y z - 1/12 y z - 1/4 y z, COEFF(2, -1, 0) = 1/36 y + + 3 3 2 2 2 2 3 2 + + 1/72 y z - 1/18 y z - 1/12 y - 1/6 y x + 1/12 x y z + + 2 2 2 2 3 2 2 3 2 3 + - 1/4 y x z + 1/24 x y z + 1/8 y x z - 1/36 y z - 1/12 x y + + 2 2 2 2 2 3 3 3 2 2 3 + - 1/8 y x z + 1/12 y z - 1/24 x y z - 1/36 y z - 1/12 y x z + + 2 2 2 3 3 3 2 2 + + 1/4 y x - 1/24 y z + 1/36 y z - 1/72 y z + 1/12 z y x + 1/24 y z + + 2 2 2 3 + + 1/18 y + 1/6 y x z , COEFF(-1, 0, 0) = x - 1/4 x y + 1/6 y + 1/6 z + + 2 2 3 3 3 + + 1/2 y x z + 1/8 y x z + 1/2 x y - 1/2 y x - 1/4 y x z + + 2 2 2 2 2 2 2 3 3 2 + - 1/2 y x z - 1/3 y z + 1/2 x z - 1/6 z - 1/6 y - 1/3 + 1/3 y + + 2 2 2 2 + + 1/3 z - 1/2 x + 1/4 y x z - 1/8 z y x - 1/12 y z + 1/4 y x + + 2 2 2 3 2 2 3 2 3 2 2 + + 1/2 y x - y x - 1/4 x y z + 1/4 y x z - 1/2 y x z + y x z + + 2 3 3 3 2 2 3 2 2 2 2 + - 1/8 x y z - 1/2 x y z + 1/8 x y z - 1/4 y x z - 1/4 y x z + + 2 3 3 2 3 2 3 2 + + 1/2 y x z + 1/4 x y z + 1/4 x y z + 1/12 y z - 1/6 y z + + 3 2 3 2 3 3 3 2 + + 1/6 y z + 1/12 y z + 1/6 y z - 1/12 y z - 1/6 y z - 1/2 x z + + 3 2 2 2 3 + + 1/2 x z + 1/4 x z - x z - 1/4 x z , COEFF(0, 0, 0) = -2 x + + 2 3 2 2 3 3 + + 3/4 x y - 1/2 + 1/4 y + 1/4 z - y x z - 3/8 y x z - x y + y x + + 3 2 2 2 2 2 2 2 3 3 + + 1/2 y x z + 3/2 y x z - 1/2 y z - 3/2 x z - 1/4 z - 1/4 y + + 2 2 2 2 2 + + 1/2 y + 1/2 z + 3/2 x - 1/2 y x z + 3/8 z y x - 1/8 y z - 3/4 y x + + 2 2 2 3 2 2 3 2 3 2 2 + - 3/2 y x + 2 y x + 1/2 x y z - 3/4 y x z + y x z - 2 y x z + + 2 3 3 3 2 2 3 2 2 2 2 + + 3/8 x y z + x y z - 3/8 x y z + 3/4 y x z + 3/4 y x z + + 2 3 3 2 3 2 3 2 3 2 + - y x z - 1/2 x y z - 3/4 x y z + 1/8 y z - 1/4 y z + 1/4 y z + + 3 2 3 3 3 2 3 2 + + 1/8 y z + 1/4 y z - 1/8 y z - 1/4 y z + x z - x z - 3/4 x z + + 2 2 3 2 3 + + 2 x z + 3/4 x z , COEFF(1, 0, 0) = 1 + x - 3/4 x y - 1/2 y - 1/2 z + + 2 2 3 3 3 + + 1/2 y x z + 3/8 y x z + 1/2 x y - 1/2 y x - 1/4 y x z + + 2 2 2 2 2 2 2 3 3 2 2 2 + - 3/2 y x z + y z + 3/2 x z + 1/2 z + 1/2 y - y - z - 3/2 x + + 2 2 2 2 2 + + 1/4 y x z - 3/8 z y x + 1/4 y z + 3/4 y x + 3/2 y x - y x + + 3 2 2 3 2 3 2 2 2 3 3 + - 1/4 x y z + 3/4 y x z - 1/2 y x z + y x z - 3/8 x y z + + 3 2 2 3 2 2 2 2 2 + - 1/2 x y z + 3/8 x y z - 3/4 y x z - 3/4 y x z + 1/2 y x z + + 3 3 2 3 2 3 2 3 2 3 + + 1/4 x y z + 3/4 x y z - 1/4 y z + 1/2 y z - 1/2 y z - 1/4 y z + + 2 3 3 3 2 3 2 2 + - 1/2 y z + 1/4 y z + 1/2 y z - 1/2 x z + 1/2 x z + 3/4 x z - x z + + 2 3 2 3 2 3 + - 3/4 x z , COEFF(2, 0, 0) = 1/4 x y + 1/12 y + 1/12 z - 1/8 y x z + + 2 2 2 2 2 2 2 3 3 2 + + 1/2 y x z - 1/6 y z - 1/2 x z - 1/12 z - 1/12 y - 1/6 + 1/6 y + + 2 2 2 2 2 2 + + 1/6 z + 1/2 x + 1/8 z y x - 1/24 y z - 1/4 y x - 1/2 y x + + 2 2 3 2 3 3 2 3 2 2 2 2 + - 1/4 y x z + 1/8 x y z - 1/8 x y z + 1/4 y x z + 1/4 y x z + + 2 3 2 3 2 3 2 3 + - 1/4 x y z + 1/24 y z - 1/12 y z + 1/12 y z + 1/24 y z + + 2 3 3 3 2 2 2 3 + + 1/12 y z - 1/24 y z - 1/12 y z - 1/4 x z + 1/4 x z , + + 2 3 2 2 3 3 + COEFF(-1, 1, 0) = 1/4 x y - 1/3 y - 1/4 y x z - 1/4 y x z - 1/2 x y + + 3 2 2 2 2 2 3 2 + + y x + 1/2 y x z + 1/4 y x z + 1/6 y z + 1/6 y - 1/6 y + + 2 2 2 2 2 + - 1/2 y x z + 1/4 z y x + 1/6 y z - 1/2 y x - 1/4 y x + 1/2 y x + + 3 2 2 3 2 3 2 2 2 3 3 + + 1/4 x y z - 1/8 y x z + 1/4 y x z - 1/2 y x z + 1/8 x y z + + 3 2 2 3 2 2 2 2 2 + + 1/2 x y z - 1/8 x y z + 1/8 y x z + 1/2 y x z - y x z + + 3 3 2 3 2 3 2 3 2 3 + - 1/4 x y z - 1/4 x y z - 1/12 y z + 1/3 y z - 1/6 y z - 1/6 y z + + 2 3 3 3 2 2 3 + - 1/12 y z + 1/12 y z + 1/12 y z, COEFF(0, 1, 0) = - 3/4 x y + + 2 2 3 3 3 2 2 2 + - 1/2 y + 1/2 y x z + 3/4 y x z + x y - 2 y x - y x z - 3/4 y x z + + 2 2 3 2 2 2 + + 1/4 y z + 1/4 y - 1/4 y + y x z - 3/4 z y x + 1/4 y z + 3/2 y x + + 2 2 2 3 2 2 3 2 3 2 2 + + 3/4 y x - y x - 1/2 x y z + 3/8 y x z - 1/2 y x z + y x z + + 2 3 3 3 2 2 3 2 2 2 2 + - 3/8 x y z - x y z + 3/8 x y z - 3/8 y x z - 3/2 y x z + + 2 3 3 2 3 2 3 2 3 2 + + 2 y x z + 1/2 x y z + 3/4 x y z - 1/8 y z + 1/2 y z - 1/4 y z + + 3 2 3 3 3 2 2 3 + - 1/4 y z - 1/8 y z + 1/8 y z + 1/8 y z, COEFF(1, 1, 0) = 3/4 x y + + 2 2 3 3 3 + + y - 1/4 y x z - 3/4 y x z - 1/2 x y + y x + 1/2 y x z + + 2 2 2 2 2 3 2 2 + + 3/4 y x z - 1/2 y z - 1/2 y + 1/2 y - 1/2 y x z + 3/4 z y x + + 2 2 2 2 3 2 2 3 + - 1/2 y z - 3/2 y x - 3/4 y x + 1/2 y x + 1/4 x y z - 3/8 y x z + + 2 3 2 2 2 3 3 3 2 2 3 + + 1/4 y x z - 1/2 y x z + 3/8 x y z + 1/2 x y z - 3/8 x y z + + 2 2 2 2 2 3 3 2 3 2 + + 3/8 y x z + 3/2 y x z - y x z - 1/4 x y z - 3/4 x y z + + 3 2 3 2 3 2 3 3 3 + + 1/4 y z - y z + 1/2 y z + 1/2 y z + 1/4 y z - 1/4 y z + + 2 2 2 3 3 2 3 + - 1/4 y z, COEFF(2, 1, 0) = 1/8 y x z + 1/12 y - 1/24 y z - 1/6 y + + 2 2 2 2 3 3 2 2 3 3 2 + - 1/4 y x z + 1/8 x y z - 1/12 y z - 1/8 x y z - 1/12 y + + 2 2 3 2 2 2 2 + + 1/2 y x - 1/4 x y - 1/4 z y x + 1/12 y z + 1/4 y x + 1/6 y z + + 2 2 2 2 2 2 3 2 2 3 + - 1/2 y x z + 1/24 y z - 1/8 y x z + 1/4 x y z + 1/4 y x z + + 3 2 2 3 3 3 + - 1/12 y z + 1/12 y z + 1/24 y z - 1/24 y z, COEFF(-1, 2, 0) = + + 2 3 2 3 2 2 3 3 2 + 1/24 y x z + 1/12 x y z + 1/24 x y z - 1/18 y - 1/24 z y x + + 2 3 3 2 3 3 2 2 + - 1/18 y z - 1/36 y z - 1/12 x y + 1/18 y z - 1/6 y x + 1/6 y x z + + 3 3 2 3 2 2 3 3 + + 1/18 y + 1/6 x y - 1/6 x y z + 1/36 y z + 1/12 y x - 1/24 x y z + + 3 3 3 2 2 + + 1/12 y x z - 1/36 y z + 1/12 x y z - 1/12 x y z - 1/12 y x z + + 3 3 3 + - 1/12 y x z + 1/36 y z, COEFF(0, 2, 0) = 1/12 y + 1/24 y z + + 3 2 3 2 3 + + 1/3 x y z + 1/3 y x - 1/6 y x z + 1/24 y z - 1/24 y z + 1/4 x y + + 2 3 2 3 3 2 3 2 + - 1/8 y x z + 1/8 x y z + 1/8 z y x - 1/3 x y - 1/3 y x z + + 2 3 2 3 2 3 3 2 2 2 + - 1/8 x y z - 1/4 x y z - 1/6 x y z + 1/4 y x z - 1/4 y x + + 3 3 3 3 3 2 2 3 + + 1/6 y x z - 1/24 y z + 1/6 x y z + 1/12 y z - 1/12 y z - 1/12 y , + + 2 3 3 3 + COEFF(1, 2, 0) = 1/8 y x z + 1/12 y z - 1/6 y x + 1/6 y - 1/12 y z + + 3 3 2 3 2 2 3 2 + + 1/12 x y z - 1/8 z y x - 1/6 x y z - 1/6 y + 1/4 x y z + + 2 3 2 2 3 3 2 3 + + 1/4 y x - 1/6 y z - 1/4 x y - 1/12 x y z + 1/6 y z + 1/6 x y + + 3 3 2 3 3 + - 1/12 y z + 1/12 y x z - 1/12 y x z + 1/6 y x z + 1/12 y z + + 2 3 3 2 3 2 2 2 + - 1/8 x y z + 1/8 x y z - 1/4 y x z , COEFF(2, 2, 0) = - 1/12 y x + + 3 3 3 3 2 3 2 + - 1/72 y z + 1/72 y z + 1/72 y z - 1/72 y z + 1/24 z y x + 1/36 y z + + 2 3 2 2 3 2 3 3 2 3 + - 1/24 y x z + 1/12 y x z - 1/36 y + 1/24 x y z - 1/24 x y z + + 2 2 3 2 3 2 + + 1/36 y - 1/36 y z + 1/12 x y - 1/12 x y z , COEFF(-1, -1, 1) = + + 2 2 3 3 2 2 2 2 2 + 1/2 y x z - 1/12 y x z + 1/6 y x z - 1/8 y x z - 1/12 y z + + 2 3 2 2 3 + - 1/3 y x z + 1/6 z y x + 1/9 y z - 1/6 x y z + 1/8 y x z + + 2 3 2 2 2 3 3 3 2 2 3 + - 1/4 y x z + 1/4 y x z - 1/24 x y z - 1/12 x y z + 1/12 x y z + + 2 2 2 2 2 3 3 2 3 2 + - 1/4 y x z + 1/12 y x z - 1/6 y x z + 1/12 x y z + 1/24 x y z + + 3 2 3 2 3 2 3 3 3 + + 1/18 y z + 1/18 y z + 1/36 y z - 1/18 y z + 1/12 y z - 1/36 y z + + 2 2 2 3 3 + - 1/6 y z, COEFF(0, -1, 1) = -y x z + 1/4 y x z - 1/3 y x z + + 2 2 2 2 2 2 3 + + 3/8 y x z - 1/8 y z + 2/3 y x z - 1/2 z y x + 1/6 y z + 1/3 x y z + + 2 2 3 2 3 2 2 2 3 3 3 2 + - 3/8 y x z + 1/2 y x z - 1/2 y x z + 1/8 x y z + 1/6 x y z + + 2 3 2 2 2 2 2 3 3 + - 1/4 x y z + 3/4 y x z - 1/4 y x z + 1/3 y x z - 1/6 x y z + + 2 3 2 3 2 3 2 3 + - 1/8 x y z + 1/12 y z + 1/12 y z + 1/24 y z - 1/12 y z + + 2 3 3 3 2 2 + + 1/8 y z - 1/24 y z - 1/4 y z, COEFF(1, -1, 1) = 1/2 y x z + + 2 3 3 2 2 2 2 2 + - 1/4 y x z + 1/6 y x z - 3/8 y x z + 1/4 y z - 1/3 y x z + + 2 3 2 2 3 2 3 + + 1/2 z y x - 1/3 y z - 1/6 x y z + 3/8 y x z - 1/4 y x z + + 2 2 2 3 3 3 2 2 3 2 2 + + 1/4 y x z - 1/8 x y z - 1/12 x y z + 1/4 x y z - 3/4 y x z + + 2 2 2 3 3 2 3 2 3 + + 1/4 y x z - 1/6 y x z + 1/12 x y z + 1/8 x y z - 1/6 y z + + 2 3 2 3 2 3 3 3 2 + - 1/6 y z - 1/12 y z + 1/6 y z - 1/4 y z + 1/12 y z + 1/2 y z, + + 2 2 3 2 3 2 3 3 + COEFF(2, -1, 1) = - 1/8 y x z + 1/12 y x z + 1/24 x y z + + 2 2 3 3 2 2 2 + - 1/12 y x z - 1/36 y z + 1/72 y z + 1/18 y z + 1/4 y x z + + 2 2 3 2 2 2 2 2 2 + + 1/36 y z + 1/24 y z - 1/6 z y x - 1/24 y z + 1/8 y x z + + 3 3 2 3 2 2 2 3 3 + - 1/72 y z - 1/24 x y z - 1/12 y z - 1/12 x y z + 1/36 y z, + + 2 2 3 3 + COEFF(-1, 0, 1) = - 1/3 z - y x z - 1/8 y x z + 1/4 y x z + + 2 2 2 2 2 2 2 3 2 + + 1/4 y x z + 1/6 y z - 1/4 x z + 1/6 z - 1/6 z - 1/2 y x z + + 2 3 2 2 3 2 3 + + 1/4 z y x + 1/6 y z + 1/2 x y z - 1/4 y x z + 1/2 y x z + + 2 2 2 3 3 3 2 2 3 2 2 + - 1/2 y x z + 1/8 x y z + 1/4 x y z - 1/4 x y z + 1/2 y x z + + 2 2 2 3 3 2 3 2 3 + + 1/8 y x z - 1/4 y x z - 1/4 x y z - 1/8 x y z - 1/6 y z + + 2 3 2 3 2 3 3 3 2 + + 1/12 y z - 1/12 y z - 1/12 y z - 1/6 y z + 1/12 y z + 1/3 y z + + 3 2 2 2 3 + + x z - 1/2 x z - 1/2 x z + 1/2 x z + 1/4 x z , COEFF(0, 0, 1) = + + 2 2 3 3 2 2 2 2 2 + - 1/2 z + 2 y x z + 3/8 y x z - 1/2 y x z - 3/4 y x z + 1/4 y z + + 2 2 3 2 2 3 + + 3/4 x z + 1/4 z - 1/4 z + y x z - 3/4 z y x + 1/4 y z - x y z + + 2 2 3 2 3 2 2 2 3 3 3 2 + + 3/4 y x z - y x z + y x z - 3/8 x y z - 1/2 x y z + + 2 3 2 2 2 2 2 3 3 + + 3/4 x y z - 3/2 y x z - 3/8 y x z + 1/2 y x z + 1/2 x y z + + 2 3 2 3 2 3 2 3 2 3 + + 3/8 x y z - 1/4 y z + 1/8 y z - 1/8 y z - 1/8 y z - 1/4 y z + + 3 3 2 3 2 2 2 3 + + 1/8 y z + 1/2 y z - 2 x z + x z + 3/2 x z - x z - 3/4 x z , + + 2 2 3 3 2 2 2 + COEFF(1, 0, 1) = z - y x z - 3/8 y x z + 1/4 y x z + 3/4 y x z + + 2 2 2 2 3 2 2 + - 1/2 y z - 3/4 x z - 1/2 z + 1/2 z - 1/2 y x z + 3/4 z y x + + 3 2 2 3 2 3 2 2 + - 1/2 y z + 1/2 x y z - 3/4 y x z + 1/2 y x z - 1/2 y x z + + 2 3 3 3 2 2 3 2 2 2 2 + + 3/8 x y z + 1/4 x y z - 3/4 x y z + 3/2 y x z + 3/8 y x z + + 2 3 3 2 3 2 3 2 + - 1/4 y x z - 1/4 x y z - 3/8 x y z + 1/2 y z - 1/4 y z + + 3 2 3 2 3 3 3 2 3 + + 1/4 y z + 1/4 y z + 1/2 y z - 1/4 y z - y z + x z - 1/2 x z + + 2 2 2 3 2 2 + - 3/2 x z + 1/2 x z + 3/4 x z , COEFF(2, 0, 1) = 1/12 y z + + 2 3 2 2 2 3 3 2 2 3 2 2 + + 1/4 x y z - 1/8 y x z - 1/8 x y z + 1/4 y x z - 1/2 y x z + + 3 2 2 3 2 2 2 2 3 2 + - 1/24 y z + 1/2 x z - 1/24 y z - 1/6 z - 1/4 y x z + 1/8 x y z + + 3 3 3 2 2 3 + + 1/12 z + 1/24 y z + 1/24 y z + 1/12 y z - 1/4 z y x - 1/12 y z + + 2 3 2 2 2 3 2 2 2 3 + - 1/12 y z + 1/4 x z - 1/4 x z + 1/6 y z - 1/12 z + 1/8 y x z , + + 2 2 3 3 2 2 2 + COEFF(-1, 1, 1) = 1/2 y x z + 1/4 y x z - 1/2 y x z - 1/8 y x z + + 2 2 2 3 2 2 3 + - 1/12 y z + y x z - 1/2 z y x - 1/3 y z - 1/2 x y z + 1/8 y x z + + 2 3 2 2 2 3 3 3 2 2 3 + - 1/4 y x z + 1/4 y x z - 1/8 x y z - 1/4 x y z + 1/4 x y z + + 2 2 2 2 2 3 3 2 3 2 + - 1/4 y x z - 1/4 y x z + 1/2 y x z + 1/4 x y z + 1/8 x y z + + 3 2 3 2 3 2 3 3 3 + + 1/6 y z - 1/6 y z + 1/12 y z + 1/6 y z + 1/12 y z - 1/12 y z + + 2 2 2 3 3 2 2 2 + - 1/6 y z, COEFF(0, 1, 1) = -y x z - 3/4 y x z + y x z + 3/8 y x z + + 2 2 2 3 2 2 3 + - 1/8 y z - 2 y x z + 3/2 z y x - 1/2 y z + x y z - 3/8 y x z + + 2 3 2 2 2 3 3 3 2 2 3 + + 1/2 y x z - 1/2 y x z + 3/8 x y z + 1/2 x y z - 3/4 x y z + + 2 2 2 2 2 3 3 2 3 2 + + 3/4 y x z + 3/4 y x z - y x z - 1/2 x y z - 3/8 x y z + + 3 2 3 2 3 2 3 3 3 + + 1/4 y z - 1/4 y z + 1/8 y z + 1/4 y z + 1/8 y z - 1/8 y z + + 2 2 2 3 3 + - 1/4 y z, COEFF(1, 1, 1) = 1/2 y x z + 3/4 y x z - 1/2 y x z + + 2 2 2 2 2 2 3 + - 3/8 y x z + 1/4 y z + y x z - 3/2 z y x + y z - 1/2 x y z + + 2 2 3 2 3 2 2 2 3 3 3 2 + + 3/8 y x z - 1/4 y x z + 1/4 y x z - 3/8 x y z - 1/4 x y z + + 2 3 2 2 2 2 2 3 3 + + 3/4 x y z - 3/4 y x z - 3/4 y x z + 1/2 y x z + 1/4 x y z + + 2 3 2 3 2 3 2 3 2 3 + + 3/8 x y z - 1/2 y z + 1/2 y z - 1/4 y z - 1/2 y z - 1/4 y z + + 3 3 2 3 2 + + 1/4 y z + 1/2 y z, COEFF(2, 1, 1) = 1/12 y z - 1/12 y z - 1/6 y z + + 2 3 2 2 3 2 2 2 2 3 2 2 2 + - 1/4 y x z - 1/8 y x z + 1/8 y x z - 1/8 x y z - 1/24 y z + + 2 3 3 2 3 3 2 3 3 2 + + 1/2 z y x - 1/24 y z + 1/8 x y z - 1/4 x y z + 1/24 y z + + 2 2 2 2 3 2 2 3 + + 1/4 y x z + 1/4 y x z + 1/12 y z - 1/12 y z + 1/24 y z , + + 3 2 3 2 + COEFF(-1, 2, 1) = - 1/6 y x z + 1/6 x y z - 1/12 x y z - 1/12 y x z + + 3 3 2 3 3 2 2 2 2 + - 1/12 x y z - 1/24 y x z + 1/12 x y z + 1/24 y x z + 1/12 z y x + + 3 3 2 3 2 2 3 3 2 + + 1/36 y z - 1/24 x y z + 1/24 x y z + 1/18 y z + 1/36 y z + + 3 3 2 3 3 + + 1/12 y x z - 1/36 y z - 1/36 y z - 1/18 y z, COEFF(0, 2, 1) = + + 3 3 2 2 2 3 + 1/24 y z + 1/12 y z + 1/24 y z - 1/8 y x z + 1/3 y x z - 1/24 y z + + 2 3 2 3 3 2 3 2 + + 1/8 y x z + 1/6 y x z + 1/6 x y z - 1/4 z y x - 1/24 y z + + 2 3 2 3 2 2 3 2 3 3 3 + + 1/8 x y z - 1/6 x y z + 1/4 x y z - 1/8 x y z - 1/3 x y z + + 3 3 2 3 2 + - 1/6 y x z - 1/12 y z, COEFF(1, 2, 1) = - 1/12 y x z + 1/12 y z + + 3 2 2 3 2 2 3 3 3 + + 1/12 x y z - 1/8 x y z + 1/8 x y z + 1/12 y z - 1/6 y z + + 2 3 3 3 2 2 2 + - 1/12 y z + 1/6 y z - 1/12 x y z + 1/8 y x z + 1/4 z y x + + 2 3 3 2 3 3 + - 1/4 x y z + 1/6 x y z - 1/6 y x z - 1/8 y x z + 1/12 y x z + + 3 3 2 3 2 3 3 3 + - 1/12 y z , COEFF(2, 2, 1) = 1/24 x y z + 1/72 y z - 1/36 y z + + 2 3 3 3 2 2 2 3 + + 1/24 y x z - 1/72 y z - 1/72 y z + 1/72 y z + 1/12 x y z + + 2 2 2 2 3 3 + + 1/36 y z - 1/24 y x z - 1/12 z y x - 1/24 x y z , COEFF(-1, -1, 2) + + 2 3 2 2 3 3 3 2 + = 1/12 y x z + 1/24 y x z + 1/36 x y z - 1/36 x y z - 1/12 y x z + + 3 3 2 3 3 2 3 + - 1/108 y z + 1/54 y z + 1/36 y z + 1/108 y z - 1/36 y z + + 2 3 2 2 3 2 + + 1/36 y x z - 1/24 y x z - 1/36 z y x - 1/54 y z + 1/18 y x z + + 3 2 3 2 3 3 + - 1/18 y x z - 1/72 x y z + 1/72 x y z , COEFF(0, -1, 2) = + + 3 3 2 3 3 3 2 + 1/18 x y z - 1/9 y x z - 1/6 y x z + 1/72 y z + 1/24 y z + + 2 3 3 3 2 + - 1/24 y z + 1/36 y z - 1/36 y z - 1/72 y z + 1/6 y x z + + 2 3 2 3 3 2 2 2 2 3 + + 1/24 x y z - 1/24 x y z - 1/8 y x z + 1/12 z y x - 1/12 y x z + + 2 2 3 3 3 2 3 + + 1/8 y x z - 1/18 x y z + 1/9 y x z , COEFF(1, -1, 2) = 1/12 y z + + 3 2 3 3 3 + - 1/18 y z - 1/12 y z - 1/36 x y z + 1/18 y z + 1/36 x y z + + 2 3 2 2 2 2 3 + + 1/12 y x z + 1/8 y x z + 1/18 y x z - 1/12 y x z - 1/24 x y z + + 3 3 3 2 3 3 2 2 3 + - 1/36 y z + 1/36 y z + 1/24 x y z - 1/12 z y x + 1/12 y x z + + 3 2 2 3 2 3 3 + - 1/18 y x z - 1/8 y x z , COEFF(2, -1, 2) = - 1/72 x y z + + 2 2 2 2 3 2 3 2 + - 1/108 y z - 1/24 y x z + 1/24 y x z + 1/72 x y z + 1/36 z y x + + 3 3 2 3 2 3 3 + + 1/216 y z - 1/72 y z + 1/72 y z - 1/216 y z + 1/108 y z + + 2 3 3 2 3 + - 1/36 y x z , COEFF(-1, 0, 2) = - 1/6 x z + 1/36 y z + 1/24 x y z + + 2 2 3 2 3 2 2 3 3 + + 1/6 y x z - 1/6 y x z + 1/24 y x z + 1/12 y x z + 1/6 x z + + 2 3 3 3 2 3 + + 1/12 y x z + 1/12 x z - 1/12 x y z + 1/12 x y z - 1/12 x z + + 2 2 3 2 2 3 3 3 3 + - 1/18 y z + 1/18 y z - 1/12 y x z - 1/18 z - 1/36 y z + 1/36 y z + + 2 3 3 2 3 + - 1/24 x y z - 1/24 z y x + 1/18 z - 1/36 y z - 1/12 y x z , + + 2 3 2 3 2 3 2 3 + COEFF(0, 0, 2) = 1/3 y x z - 1/8 y x z + 1/12 y z - 1/8 x y z + + 3 3 2 3 2 3 + - 1/6 y x z - 1/24 y z + 1/12 z + 1/4 x z - 1/3 y x z + 1/6 x y z + + 2 2 3 2 3 3 3 + - 1/4 y x z - 1/4 x z + 1/24 y z - 1/6 x y z - 1/24 y z + + 2 2 2 3 3 3 + + 1/4 y x z - 1/12 y z - 1/12 z - 1/3 x z + 1/3 x z + 1/24 y z + + 2 3 3 2 3 2 2 + + 1/8 x y z + 1/8 z y x + 1/6 y x z , COEFF(1, 0, 2) = - 1/4 y x z + + 2 3 2 3 3 3 2 + + 1/8 y x z + 1/12 y x z - 1/6 y z - 1/6 z + 1/12 y z - 1/8 z y x + + 2 3 3 2 3 3 3 2 + - 1/8 x y z - 1/4 x z + 1/12 y z + 1/12 x y z + 1/6 y x z + + 3 3 3 2 3 2 + - 1/12 y z - 1/12 y x z + 1/6 x z - 1/6 x z - 1/6 y x z + 1/6 y z + + 2 3 2 2 3 3 3 2 3 + + 1/8 x y z + 1/4 y x z - 1/12 y z - 1/12 x y z + 1/4 x z + 1/6 z + + 2 3 3 3 3 + , COEFF(2, 0, 2) = - 1/24 y x z - 1/72 y z - 1/72 y z - 1/36 z + + 2 2 3 3 2 3 2 + - 1/36 y z + 1/24 x y z - 1/24 x y z + 1/36 z - 1/12 x z + + 3 2 2 2 3 2 3 + + 1/72 y z + 1/12 y x z + 1/24 z y x + 1/72 y z + 1/36 y z + + 2 2 3 2 3 3 2 2 + - 1/12 y x z + 1/12 x z , COEFF(-1, 1, 2) = - 1/36 y z + 1/24 y x z + + 2 3 2 3 2 3 3 + + 1/12 y x z - 1/12 y x z - 1/18 y z - 1/24 x y z + 1/12 x y z + + 2 3 3 3 3 3 + - 1/36 y z - 1/6 y x z - 1/12 x y z + 1/36 y z + 1/18 y z + + 2 2 3 2 2 3 2 2 3 3 + + 1/36 y z - 1/12 y x z - 1/24 y x z + 1/12 z y x + 1/24 x y z + + 3 2 3 2 2 3 + + 1/6 y x z , COEFF(0, 1, 2) = - 1/24 y z + 1/6 y x z + 1/8 x y z + + 3 2 3 2 2 2 3 + + 1/12 y z - 1/12 y z - 1/6 y x z - 1/8 y x z + 1/4 y x z + + 3 2 3 3 3 3 2 3 + - 1/3 y x z - 1/8 x y z + 1/6 x y z - 1/4 z y x - 1/24 y z + + 3 3 2 3 2 2 3 + + 1/24 y z + 1/24 y z - 1/6 x y z + 1/8 y x z + 1/3 y x z, + + 2 3 3 2 2 + COEFF(1, 1, 2) = 1/12 y x z + 1/12 y z - 1/12 y x z + 1/4 z y x + + 2 2 3 2 3 3 3 + - 1/6 y x z - 1/12 y z + 1/12 y z + 1/8 x y z + 1/12 x y z + + 3 3 2 3 2 3 3 + - 1/12 y z - 1/8 x y z - 1/4 y x z - 1/6 y z + 1/6 y x z + + 3 3 3 2 2 3 2 2 + - 1/12 x y z + 1/6 y z - 1/8 y x z + 1/8 y x z, COEFF(2, 1, 2) = + + 2 2 2 3 2 2 2 3 3 + - 1/24 y x z + 1/12 y x z - 1/12 z y x + 1/72 y z - 1/24 x y z + + 2 2 3 3 3 3 2 3 + + 1/24 y x z - 1/36 y z + 1/72 y z + 1/36 y z + 1/24 x y z + + 2 3 3 3 3 + - 1/72 y z - 1/72 y z, COEFF(-1, 2, 2) = - 1/108 y z + 1/36 y x z + + 3 3 3 2 3 3 + + 1/108 y z + 1/108 y z - 1/36 y x z + 1/72 y x z - 1/36 x y z + + 2 2 3 3 3 3 2 3 + - 1/108 y z - 1/72 z y x - 1/72 x y z + 1/36 x y z + 1/72 x y z, + + 3 2 3 + COEFF(0, 2, 2) = - 1/18 y x z + 1/72 y z - 1/24 y x z - 1/72 y z + + 3 2 3 2 3 3 3 3 2 + + 1/18 y x z - 1/24 x y z + 1/24 x y z - 1/72 y z + 1/24 z y x + + 3 3 3 3 3 + - 1/18 x y z + 1/72 y z + 1/18 x y z, COEFF(1, 2, 2) = - 1/36 y z + + 2 3 3 3 3 2 3 3 3 3 + + 1/24 x y z + 1/36 y z - 1/36 x y z - 1/24 x y z + 1/36 x y z + + 3 2 3 2 3 + - 1/36 y z + 1/36 y x z - 1/24 z y x - 1/36 y x z + 1/24 y x z + + 2 3 3 2 3 + + 1/36 y z, COEFF(2, 2, 2) = 1/72 z y x - 1/216 y z - 1/72 y x z + + 3 2 3 3 2 3 3 + + 1/216 y z - 1/216 y z - 1/72 x y z + 1/216 y z + 1/72 x y z ] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dx.compute.c"); +bytes used=5417815848, alloc=10549364, time=454.26 +bytes used=5418816132, alloc=10549364, time=454.34 +bytes used=5419816352, alloc=10549364, time=454.42 +bytes used=5420816780, alloc=10549364, time=454.50 +bytes used=5421817180, alloc=10549364, time=454.58 +bytes 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-1) = 1/36 x y z - 1/12 x y z + 1/36 x z - 1/36 x y z + + 3 2 2 3 2 3 3 3 3 3 + + 1/24 x y z - 1/72 x y z + 1/18 x y z - 1/54 x z - 1/108 x z + + 2 2 3 3 2 2 2 2 2 + - 1/18 y x z - 1/12 y x z + 1/18 y x z - 1/8 y x z - 1/12 x z + + 2 2 2 3 2 3 2 2 + + 1/9 y x z - 1/6 z y x + 1/24 y x z - 1/36 y x z + 1/12 y x z + + 2 2 2 2 2 3 + + 1/12 y x z + 1/4 y x z - 1/6 y x z - 1/27 x z - 1/54 x z + + 2 2 2 3 3 3 + + 1/18 x z + 1/18 x z + 1/36 x z , COEFF(0, -1, -1) = - 1/12 x y z + + 3 2 3 2 3 2 3 2 2 3 2 3 + + 1/4 x y z - 1/12 x z + 1/12 x y z - 1/8 x y z + 1/24 x y z + + 3 3 3 3 2 2 3 + - 1/6 x y z + 1/18 x z + 1/9 z + 1/36 x z - 1/12 y x z + 1/6 y x z + + 3 2 2 2 2 2 2 2 3 2 + + 1/12 y x z + 1/4 y x z - 1/4 y z + 1/6 x z + 1/18 z - 1/6 z + + 2 2 2 3 2 3 + + 1/6 y x z + 1/3 z y x - 1/3 y z - 1/12 y x z - 1/24 y x z + + 2 2 2 2 2 2 2 2 + + 1/8 y x z - 1/6 y x z - 1/2 y x z - 1/4 y x z + 1/2 y z + + 3 2 3 2 3 2 + - 1/6 y z + 1/12 y z + 1/6 y z - 1/18 x z - 1/36 x z - 1/9 x z + + 2 2 3 3 3 3 2 + + 1/12 x z - 1/18 x z , COEFF(1, -1, -1) = 1/12 x y z - 1/4 x y z + + 3 2 3 2 3 2 2 3 2 3 3 + + 1/12 x z - 1/12 x y z + 1/8 x y z - 1/24 x y z + 1/6 x y z + + 3 3 3 2 2 3 3 + - 1/18 x z - 1/36 x z + 1/6 y x z - 1/12 y x z - 1/6 y x z + + 2 2 2 2 2 2 2 2 3 + - 1/8 y x z - 1/12 x z - 1/3 y x z - 1/6 z y x + 1/24 y x z + + 2 3 2 2 2 2 2 2 2 + + 1/12 y x z - 1/4 y x z + 1/12 y x z + 1/4 y x z + 1/2 y x z + + 3 2 2 2 3 + + 1/9 x z + 1/18 x z + 1/18 x z - 1/6 x z + 1/36 x z , + + 2 3 2 3 2 3 + COEFF(2, -1, -1) = - 1/72 y x z + 1/36 x z + 1/72 x y z + 1/18 y x z + + 3 3 2 3 2 3 + + 1/36 y x z - 1/18 x y z - 1/12 y x z + 1/12 x y z - 1/108 x z + + 3 2 3 3 3 2 2 2 + + 1/36 x y z + 1/108 x z - 1/36 x z + 1/24 y x z - 1/54 x z + + 3 3 3 2 3 2 2 + - 1/36 x y z + 1/54 x z - 1/36 y x z - 1/24 x y z , COEFF(-1, 0, -1) + + 3 3 3 2 3 2 3 2 3 2 2 + = - 1/18 x y z + 1/6 x y z + 1/24 x z + 1/12 x y z - 1/8 x y z + + 3 2 3 3 3 3 3 2 + + 1/24 x y z - 1/9 x y z - 1/36 x z - 1/72 x z + 1/6 y x z + + 2 3 3 2 2 2 2 2 + + 1/6 y x z - 1/9 y x z + 3/8 y x z - 1/8 x z - 2/9 y x z + + 2 2 2 3 2 3 2 2 2 2 + + 1/3 z y x - 1/8 y x z + 1/12 y x z - 1/4 y x z - 1/4 y x z + + 2 2 2 3 2 2 + - 1/2 y x z + 1/3 y x z - 1/18 x z - 1/36 x z + 1/12 x z + 1/12 x z + + 2 3 3 3 3 2 3 2 + + 1/24 x z , COEFF(0, 0, -1) = 1/6 x y z - 1/2 x y z - 1/8 x z + + 3 2 3 2 2 3 2 3 3 3 + - 1/4 x y z + 3/8 x y z - 1/8 x y z + 1/3 x y z + 1/12 x z + + 3 3 2 2 3 3 + + 1/6 z + 1/24 x z + 1/4 y x z - 1/3 y x z - 1/6 y x z + + 2 2 2 2 2 2 2 3 2 + - 3/4 y x z + 3/4 y z + 1/4 x z + 1/12 z - 1/4 z - 1/3 y x z + + 2 2 2 3 2 3 2 2 + - 2/3 z y x + 2/3 y z + 1/4 y x z + 1/8 y x z - 3/8 y x z + + 2 2 2 2 2 2 3 2 3 + + 1/2 y x z + y x z + 1/2 y x z - y z + 1/3 y z - 1/4 y z + + 2 3 2 2 2 3 + - 1/2 y z - 1/12 x z - 1/24 x z - 1/6 x z + 1/8 x z - 1/12 x z , + + 3 3 3 2 3 2 3 2 + COEFF(1, 0, -1) = - 1/6 x y z + 1/2 x y z + 1/8 x z + 1/4 x y z + + 3 2 2 3 2 3 3 3 3 3 + - 3/8 x y z + 1/8 x y z - 1/3 x y z - 1/12 x z - 1/24 x z + + 2 2 3 3 2 2 2 2 2 + - 1/2 y x z + 1/6 y x z + 1/3 y x z + 3/8 y x z - 1/8 x z + + 2 2 2 3 2 3 2 2 + + 2/3 y x z + 1/3 z y x - 1/8 y x z - 1/4 y x z + 3/4 y x z + + 2 2 2 2 2 3 2 + - 1/4 y x z - 1/2 y x z - y x z + 1/6 x z + 1/12 x z + 1/12 x z + + 2 2 3 3 3 + - 1/4 x z + 1/24 x z , COEFF(2, 0, -1) = 1/36 x z - 1/18 y x z + + 3 2 2 3 2 2 2 2 + - 1/24 x z + 1/6 y x z + 1/8 x y z - 1/36 x z - 1/8 y x z + + 2 3 3 3 2 3 3 3 2 + + 1/24 x z + 1/72 x z - 1/24 x y z + 1/9 x y z - 1/12 x y z + + 2 3 3 2 3 3 + - 1/9 y x z + 1/24 y x z - 1/72 x z + 1/12 y x z + 1/18 x y z + + 3 2 3 3 3 2 3 2 + - 1/6 x y z , COEFF(-1, 1, -1) = 1/36 x y z - 1/12 x y z - 1/12 x z + + 3 2 3 2 2 3 2 3 3 3 + - 1/12 x y z + 1/8 x y z - 1/24 x y z + 1/18 x y z + 1/18 x z + + 3 3 2 2 3 3 2 2 2 + + 1/36 x z - 1/6 y x z - 1/12 y x z + 1/18 y x z - 3/8 y x z + + 2 2 2 2 2 3 2 3 + + 1/4 x z + 1/9 y x z - 1/6 z y x + 1/8 y x z - 1/12 y x z + + 2 2 2 2 2 2 2 + + 1/4 y x z + 1/4 y x z + 1/4 y x z - 1/6 y x z + 1/9 x z + + 3 2 2 2 3 + + 1/18 x z - 1/6 x z - 1/6 x z - 1/12 x z , COEFF(0, 1, -1) = + + 3 3 3 2 3 2 3 2 3 2 2 + - 1/12 x y z + 1/4 x y z + 1/4 x z + 1/4 x y z - 3/8 x y z + + 3 2 3 3 3 3 3 2 + + 1/8 x y z - 1/6 x y z - 1/6 x z - 1/3 z - 1/12 x z - 1/4 y x z + + 2 3 3 2 2 2 2 2 2 2 + + 1/6 y x z + 1/12 y x z + 3/4 y x z - 3/4 y z - 1/2 x z + + 3 2 2 2 2 3 + - 1/6 z + 1/2 z + 1/6 y x z + 1/3 z y x - 1/3 y z - 1/4 y x z + + 2 3 2 2 2 2 2 2 2 + - 1/8 y x z + 3/8 y x z - 1/2 y x z - 1/2 y x z - 1/4 y x z + + 2 3 2 3 2 3 + + 1/2 y z - 1/6 y z + 1/4 y z + 1/2 y z + 1/6 x z + 1/12 x z + + 2 2 2 3 3 3 + + 1/3 x z - 1/4 x z + 1/6 x z , COEFF(1, 1, -1) = 1/12 x y z + + 3 2 3 2 3 2 3 2 2 3 2 3 + - 1/4 x y z - 1/4 x z - 1/4 x y z + 3/8 x y z - 1/8 x y z + + 3 3 3 3 2 2 3 + + 1/6 x y z + 1/6 x z + 1/12 x z + 1/2 y x z - 1/12 y x z + + 3 2 2 2 2 2 2 + - 1/6 y x z - 3/8 y x z + 1/4 x z - 1/3 y x z - 1/6 z y x + + 2 2 3 2 3 2 2 2 2 2 2 + + 1/8 y x z + 1/4 y x z - 3/4 y x z + 1/4 y x z + 1/4 y x z + + 2 3 2 2 2 3 + + 1/2 y x z - 1/3 x z - 1/6 x z - 1/6 x z + 1/2 x z - 1/12 x z , + + 3 2 2 3 3 3 3 3 + COEFF(2, 1, -1) = - 1/8 x y z - 1/36 x y z - 1/36 x z + 1/36 y x z + + 2 2 2 3 2 + - 1/12 y x z + 1/18 y x z + 1/8 y x z - 1/18 x y z - 1/12 x z + + 3 2 3 2 3 2 3 3 3 2 + + 1/12 x z + 1/12 x y z + 1/24 x y z + 1/36 x z + 1/12 x y z + + 2 3 3 2 + - 1/24 y x z - 1/18 x z - 1/12 y x z + 1/18 x z, COEFF(-1, 2, -1) = + + 2 3 3 3 2 2 2 3 + 1/72 x z - 1/216 x z + 1/36 x z - 1/12 y x z - 1/108 x z + + 3 2 3 2 3 2 2 2 2 3 + + 1/72 x z + 1/72 x y z + 1/18 y x z + 1/8 y x z - 1/108 x z + + 2 2 3 2 2 2 3 2 2 + - 1/24 y x z - 1/12 y x z - 1/54 x z + 1/36 x z - 1/24 x y z + + 3 2 2 2 2 3 2 2 + + 1/36 x y z - 1/24 x z + 1/36 y x z , COEFF(0, 2, -1) = 1/12 x z + + 2 3 2 3 2 2 2 + - 1/18 x z - 1/12 x y z - 1/72 x z + 1/24 x z - 1/8 y x z + + 3 2 2 3 3 2 2 2 + - 1/24 x z + 1/12 y x z + 1/36 x z + 1/8 x y z - 1/36 x z - 1/12 z + + 3 2 3 2 2 3 2 3 2 + - 1/24 x y z + 1/12 y x z - 1/36 x z - 1/6 y z + 1/18 z + + 2 2 2 3 3 2 2 2 3 3 + - 1/4 y x z + 1/72 x z + 1/4 y z - 1/12 y z + 1/36 z + + 2 3 2 2 2 + + 1/24 y x z + 1/6 y x z, COEFF(1, 2, -1) = - 1/6 y x z + + 2 2 2 3 2 2 3 2 2 2 3 2 + + 1/8 y x z - 1/8 x y z + 1/24 x z - 1/24 y x z + 1/36 x z + + 3 3 2 2 3 2 2 2 2 3 + - 1/72 x z - 1/12 y x z + 1/12 x y z + 1/4 y x z - 1/12 y x z + + 2 3 3 2 3 2 3 + + 1/72 x z + 1/24 x y z - 1/12 x z + 1/18 x z + 1/36 x z + + 3 2 2 2 2 2 + - 1/36 x z - 1/24 x z , COEFF(2, 2, -1) = - 1/24 y x z + 1/72 x z + + 3 2 3 2 2 3 3 3 + - 1/36 x y z + 1/24 x y z - 1/108 x z + 1/108 x z + 1/216 x z + + 3 2 3 2 3 2 3 2 3 + - 1/72 x z - 1/216 x z + 1/36 y x z - 1/72 x y z + 1/72 y x z , + + 3 3 3 2 3 2 3 2 + COEFF(-1, -1, 0) = - 1/12 x y z + 1/6 x y z - 1/18 x z - 1/24 x y z + + 3 2 2 3 2 3 3 3 + - 1/12 x y z + 1/24 x y z + 1/12 x y z + 1/9 x - 1/36 x z + + 3 3 2 2 3 3 + + 1/36 x z - 1/12 y x z + 1/4 y x z - 1/3 y x - 1/6 y x z + + 2 2 2 2 2 3 2 2 + + 1/4 y x z + 1/6 x z + 1/18 x - 1/6 x + 1/6 y x z - 1/4 z y x + + 2 2 2 2 2 2 3 2 3 + + 1/2 y x - 1/4 y x + 1/6 y x - 1/8 y x z + 1/12 y x z + + 2 2 2 2 2 2 2 + - 1/6 y x z + 1/8 y x z - 1/2 y x z + 1/3 y x z - 1/18 x z + + 3 2 2 2 3 3 2 3 + + 1/18 x z + 1/12 x z - 1/9 x z - 1/12 x z + 1/12 x y - 1/6 x y, + + 3 3 3 2 3 2 3 2 + COEFF(0, -1, 0) = 1/4 x y z - 1/2 x y z + 1/6 x z + 1/8 x y z + + 3 2 2 3 2 3 3 3 + + 1/4 x y z - 1/8 x y z - 1/4 x y z + 1/6 x + 1/12 x z + y + 1/6 z + + 3 3 2 2 3 3 + - 1/12 x z - 1/8 y x z - 1/2 y x z - 1/2 y x - 1/4 y x z + + 2 2 2 2 2 2 2 3 3 2 + - 1/2 y x z + 1/2 y z - 1/3 x z - 1/6 z - 1/6 x - 1/3 - 1/2 y + + 2 2 2 2 2 2 + + 1/3 z + 1/3 x + 1/4 y x z + 1/2 z y x - 1/2 y z - y x + 1/2 y x + + 2 2 2 3 2 3 2 2 2 2 + + 1/4 y x + 1/4 y x z + 1/8 y x z - 1/4 y x z - 1/4 y x z + + 2 2 2 2 3 2 3 2 + + y x z + 1/2 y x z - y z + 1/2 y z - 1/4 y z + 1/4 y z - 1/12 x z + + 3 2 2 2 3 3 2 3 + + 1/12 x z - 1/6 x z - 1/6 x z + 1/6 x z - 1/4 x y + 1/2 x y, + + 3 3 3 2 3 2 3 2 + COEFF(1, -1, 0) = - 1/4 x y z + 1/2 x y z - 1/6 x z - 1/8 x y z + + 3 2 2 3 2 3 3 3 + - 1/4 x y z + 1/8 x y z + 1/4 x y z - 1/3 x - 1/12 x z + + 3 3 2 2 3 3 2 2 2 + + 1/12 x z + 1/4 y x z + 1/4 y x z + y x + 1/2 y x z + 1/4 y x z + + 2 2 3 2 2 2 + + 1/6 x z + 1/6 x - 1/6 x - 1/2 y x z - 1/4 z y x + 1/2 y x + + 2 2 2 2 2 3 2 3 2 2 + - 1/4 y x - 1/2 y x - 1/8 y x z - 1/4 y x z + 1/2 y x z + + 2 2 2 2 2 3 2 + + 1/8 y x z - 1/2 y x z - y x z + 1/6 x z - 1/6 x z + 1/12 x z + + 2 2 3 3 2 3 + + 1/3 x z - 1/12 x z + 1/4 x y - 1/2 x y, COEFF(2, -1, 0) = + + 3 3 3 3 2 3 2 2 + 1/12 x y z - 1/18 x - 1/12 x y z + 1/6 y x z + 1/12 x y z + + 3 2 3 3 2 3 2 + + 1/18 x z + 1/36 x z - 1/24 x y z + 1/12 y x z + 1/12 y x + + 3 3 2 2 2 3 2 + - 1/6 y x - 1/36 x z - 1/12 y x z - 1/18 x z + 1/24 x y z + + 3 3 2 3 2 2 2 3 + - 1/12 y x z - 1/12 x y - 1/6 x y z - 1/24 y x z + 1/24 y x z + + 3 3 3 3 + + 1/6 x y + 1/18 x + 1/36 x z - 1/36 x z, COEFF(-1, 0, 0) = 1/6 x y z + + 3 2 3 2 3 2 3 2 2 3 2 3 + - 1/3 x y z - 1/12 x z + 1/8 x y z + 1/4 x y z - 1/8 x y z + + 3 3 3 3 2 2 3 + - 1/6 x y z + 1/6 x - 1/24 x z + 1/24 x z + 1/4 y x z - 1/2 y x z + + 3 2 2 2 2 2 3 2 + + 2/3 y x + 1/3 y x z - 3/4 y x z + 1/4 x z + 1/12 x - 1/4 x + + 2 2 2 2 2 2 2 3 + - 1/3 y x z + 1/2 z y x - y x + 3/4 y x - 1/2 y x + 3/8 y x z + + 2 3 2 2 2 2 2 2 2 + - 1/4 y x z + 1/2 y x z - 3/8 y x z + y x z - 2/3 y x z + + 3 2 2 2 3 3 2 + - 1/12 x z + 1/12 x z + 1/8 x z - 1/6 x z - 1/8 x z - 1/4 x y + + 3 3 3 3 2 3 2 + + 1/3 x y, COEFF(0, 0, 0) = - 1/2 x y z + x y z + 1/4 x z + + 3 2 3 2 2 3 2 3 3 + - 3/8 x y z - 3/4 x y z + 3/8 x y z + 1/2 x y z + 1/4 x + + 3 3 3 2 2 3 + + 1/8 x z - 1/2 - 2 y + 1/4 z - 1/8 x z + 3/8 y x z + y x z + y x + + 3 2 2 2 2 2 2 2 3 3 + + 1/2 y x z + 3/2 y x z - 3/2 y z - 1/2 x z - 1/4 z - 1/4 x + + 2 2 2 2 2 2 2 + + 3/2 y + 1/2 z + 1/2 x - 1/2 y x z - z y x + y z + 2 y x - 3/2 y x + + 2 2 2 3 2 3 2 2 2 2 + - 3/4 y x - 3/4 y x z - 3/8 y x z + 3/4 y x z + 3/4 y x z + + 2 2 2 2 3 2 3 2 + - 2 y x z - y x z + 2 y z - y z + 3/4 y z - 3/4 y z - 1/8 x z + + 3 2 2 2 3 3 2 3 + + 1/8 x z - 1/4 x z - 1/4 x z + 1/4 x z + 3/4 x y - x y, + + 3 3 3 2 3 2 3 2 + COEFF(1, 0, 0) = 1/2 x y z - x y z - 1/4 x z + 3/8 x y z + + 3 2 2 3 2 3 3 3 3 3 + + 3/4 x y z - 3/8 x y z - 1/2 x y z - 1/2 x - 1/8 x z + 1/8 x z + + 2 2 3 3 2 2 2 2 2 + - 3/4 y x z - 1/2 y x z - 2 y x - y x z - 3/4 y x z + 1/4 x z + + 3 2 2 2 2 2 2 + + 1/4 x - 1/4 x + y x z + 1/2 z y x - y x + 3/4 y x + 3/2 y x + + 2 2 3 2 3 2 2 2 2 2 2 + + 3/8 y x z + 3/4 y x z - 3/2 y x z - 3/8 y x z + y x z + + 2 3 2 2 2 3 + + 2 y x z + 1/4 x z - 1/4 x z + 1/8 x z + 1/2 x z - 1/8 x z + + 3 2 3 2 3 + - 3/4 x y + x y, COEFF(2, 0, 0) = - 1/3 y x z + 1/3 y x + 1/6 y x z + + 3 2 3 2 3 2 3 2 2 + - 1/6 y x z + 1/3 x y z + 1/12 x z + 1/8 x y z + 1/4 y x z + + 3 3 3 2 3 3 + - 1/3 x y + 1/24 x z - 1/8 x y z - 1/24 x z - 1/12 x + 1/24 x z + + 3 3 2 3 3 3 2 2 + - 1/24 x z - 1/12 x z - 1/6 x y z + 1/4 x y + 1/8 y x z + + 3 3 2 2 2 3 2 + + 1/6 x y z - 1/4 x y z + 1/12 x - 1/8 y x z - 1/4 y x, + + 3 3 3 2 3 2 3 2 + COEFF(-1, 1, 0) = - 1/12 x y z + 1/6 x y z + 1/6 x z - 1/8 x y z + + 3 2 2 3 2 3 3 3 + - 1/4 x y z + 1/8 x y z + 1/12 x y z - 1/3 x + 1/12 x z + + 3 3 2 2 3 3 + - 1/12 x z - 1/4 y x z + 1/4 y x z - 1/3 y x - 1/6 y x z + + 2 2 2 2 2 3 2 2 + + 3/4 y x z - 1/2 x z - 1/6 x + 1/2 x + 1/6 y x z - 1/4 z y x + + 2 2 2 2 2 2 3 2 3 + + 1/2 y x - 3/4 y x + 1/2 y x - 3/8 y x z + 1/4 y x z + + 2 2 2 2 2 2 2 + - 1/2 y x z + 3/8 y x z - 1/2 y x z + 1/3 y x z + 1/6 x z + + 3 2 2 2 3 3 2 3 + - 1/6 x z - 1/4 x z + 1/3 x z + 1/4 x z + 1/4 x y - 1/6 x y, + + 3 3 3 2 3 2 3 2 + COEFF(0, 1, 0) = 1 + 1/4 x y z - 1/2 x y z - 1/2 x z + 3/8 x y z + + 3 2 2 3 2 3 3 3 + + 3/4 x y z - 3/8 x y z - 1/4 x y z - 1/2 x - 1/4 x z + y - 1/2 z + + 3 3 2 2 3 3 + + 1/4 x z - 3/8 y x z - 1/2 y x z - 1/2 y x - 1/4 y x z + + 2 2 2 2 2 2 2 3 3 2 2 2 + - 3/2 y x z + 3/2 y z + x z + 1/2 z + 1/2 x - 3/2 y - z - x + + 2 2 2 2 2 + + 1/4 y x z + 1/2 z y x - 1/2 y z - y x + 3/2 y x + 3/4 y x + + 2 2 3 2 3 2 2 2 2 2 2 + + 3/4 y x z + 3/8 y x z - 3/4 y x z - 3/4 y x z + y x z + + 2 2 3 2 3 2 3 + + 1/2 y x z - y z + 1/2 y z - 3/4 y z + 3/4 y z + 1/4 x z - 1/4 x z + + 2 2 2 3 3 2 3 + + 1/2 x z + 1/2 x z - 1/2 x z - 3/4 x y + 1/2 x y, COEFF(1, 1, 0) + + 3 3 3 2 3 2 3 2 3 2 2 + = - 1/4 x y z + 1/2 x y z + 1/2 x z - 3/8 x y z - 3/4 x y z + + 3 2 3 3 3 3 3 2 + + 3/8 x y z + 1/4 x y z + x + 1/4 x z - 1/4 x z + 3/4 y x z + + 2 3 3 2 2 2 2 2 3 + + 1/4 y x z + y x + 1/2 y x z + 3/4 y x z - 1/2 x z - 1/2 x + + 2 2 2 2 2 2 + + 1/2 x - 1/2 y x z - 1/4 z y x + 1/2 y x - 3/4 y x - 3/2 y x + + 2 2 3 2 3 2 2 2 2 2 2 + - 3/8 y x z - 3/4 y x z + 3/2 y x z + 3/8 y x z - 1/2 y x z + + 2 3 2 2 2 3 3 2 + - y x z - 1/2 x z + 1/2 x z - 1/4 x z - x z + 1/4 x z + 3/4 x y + + 3 3 3 + - 1/2 x y, COEFF(2, 1, 0) = 1/12 x z - 1/12 y x z + 1/6 x + 1/12 y x z + + 3 3 2 2 2 2 3 3 2 + - 1/12 x z + 1/4 x y z - 1/8 y x z + 1/8 y x z + 1/8 x y z + + 3 2 3 2 2 3 + - 1/8 x y z - 1/6 x + 1/6 x z + 1/6 y x z - 1/6 y x - 1/12 x y z + + 3 3 3 3 2 3 2 2 2 + + 1/12 x y z - 1/12 x z - 1/6 x z - 1/6 x y z - 1/4 y x z + + 3 3 3 3 2 2 3 + + 1/6 x y + 1/12 x z - 1/4 x y + 1/4 y x, COEFF(-1, 2, 0) = 1/36 x + + 3 2 2 2 2 2 2 3 3 + + 1/24 x y z - 1/8 y x z - 1/12 x + 1/18 x + 1/4 y x + 1/72 x z + + 2 2 2 2 2 3 2 2 + + 1/6 y x z - 1/18 x z + 1/12 x z - 1/12 x y + 1/24 x z + + 3 2 3 2 3 2 2 3 + - 1/36 x z - 1/24 x y z + 1/12 y x z - 1/36 x z - 1/12 y x z + + 3 2 2 2 2 2 3 2 3 3 + + 1/12 x y z - 1/6 y x + 1/8 y x z - 1/24 x z + 1/36 x z + + 2 2 2 3 3 2 3 2 + - 1/4 y x z - 1/72 x z, COEFF(0, 2, 0) = 1/12 x z - 1/8 x y z + + 3 2 2 3 2 3 3 3 3 + - 1/4 x y z + 1/8 x y z + 1/12 x + 1/24 x z + 1/12 z - 1/24 x z + + 2 2 2 2 2 2 2 2 3 3 + + 1/8 y x z + 1/2 y x z - 1/2 y z - 1/6 x z - 1/12 z - 1/12 x + + 2 2 2 2 2 2 2 2 3 + - 1/6 + 1/2 y + 1/6 z + 1/6 x - 1/2 y x - 1/4 y x - 1/4 y x z + + 2 3 2 2 2 2 2 3 2 + - 1/8 y x z + 1/4 y x z + 1/4 y x z + 1/4 y z - 1/4 y z + + 3 2 2 2 3 3 2 + - 1/24 x z + 1/24 x z - 1/12 x z - 1/12 x z + 1/12 x z + 1/4 x y , + + 2 2 2 3 2 + COEFF(1, 2, 0) = - 1/8 y x z - 1/4 y x z - 1/24 x z + 1/24 x z + + 3 2 2 2 3 2 3 2 2 3 + + 1/4 x y z - 1/12 x - 1/12 x z + 1/12 x + 1/2 y x - 1/24 x z + + 3 3 2 2 3 2 3 + - 1/6 x + 1/24 x z + 1/12 x z - 1/4 x y + 1/12 x z - 1/12 x z + + 2 2 2 3 2 3 2 2 2 2 + + 1/6 x z + 1/8 y x z + 1/4 y x z + 1/4 y x - 1/2 y x z + + 3 2 2 2 2 3 2 3 2 2 + + 1/8 x y z - 1/4 y x z - 1/8 x y z , COEFF(2, 2, 0) = 1/12 y x z + + 3 2 3 2 3 2 3 3 3 + + 1/24 x y z + 1/24 y x z - 1/24 x y z + 1/72 x z - 1/72 x z + + 3 3 2 2 3 2 2 + - 1/36 x + 1/12 x y - 1/24 y x z - 1/12 y x - 1/36 x z + + 3 2 2 3 3 2 + - 1/12 x y z - 1/72 x z + 1/36 x + 1/72 x z + 1/36 x z , + + 3 3 3 2 3 2 3 2 + COEFF(-1, -1, 1) = 1/12 x y z - 1/12 x y z + 1/36 x z + 1/12 x y z + + 3 2 2 3 2 3 3 3 3 3 + + 1/24 x y z - 1/24 x y z - 1/6 x y z + 1/18 x z - 1/36 x z + + 2 2 3 3 2 2 2 2 2 + + 1/6 y x z - 1/4 y x z + 1/6 y x z - 1/8 y x z - 1/12 x z + + 2 2 2 3 2 3 2 2 + - 1/3 y x z + 1/2 z y x + 1/8 y x z - 1/12 y x z + 1/12 y x z + + 2 2 2 2 2 3 2 + - 1/4 y x z + 1/4 y x z - 1/6 y x z + 1/9 x z - 1/18 x z - 1/6 x z + + 2 2 3 3 3 3 2 + + 1/18 x z + 1/12 x z , COEFF(0, -1, 1) = - 1/4 x y z + 1/4 x y z + + 3 2 3 2 3 2 2 3 2 3 3 + - 1/12 x z - 1/4 x y z - 1/8 x y z + 1/8 x y z + 1/2 x y z + + 3 3 3 2 2 3 3 + - 1/6 x z - 1/3 z + 1/12 x z + 1/4 y x z + 1/2 y x z + 1/4 y x z + + 2 2 2 2 2 2 2 3 2 + + 1/4 y x z - 1/4 y z + 1/6 x z + 1/6 z - 1/6 z - 1/2 y x z + + 2 2 2 3 2 3 2 2 2 2 + - z y x + y z - 1/4 y x z - 1/8 y x z + 1/8 y x z + 1/2 y x z + + 2 2 2 2 3 2 3 2 + - 1/2 y x z - 1/4 y x z + 1/2 y z - 1/2 y z + 1/4 y z - 1/2 y z + + 3 2 2 2 3 + + 1/6 x z - 1/12 x z + 1/3 x z + 1/12 x z - 1/6 x z , COEFF(1, -1, 1) + + 3 3 3 2 3 2 3 2 3 2 2 + = 1/4 x y z - 1/4 x y z + 1/12 x z + 1/4 x y z + 1/8 x y z + + 3 2 3 3 3 3 3 2 + - 1/8 x y z - 1/2 x y z + 1/6 x z - 1/12 x z - 1/2 y x z + + 2 3 3 2 2 2 2 2 + - 1/4 y x z - 1/2 y x z - 1/8 y x z - 1/12 x z + y x z + + 2 2 2 3 2 3 2 2 2 2 + + 1/2 z y x + 1/8 y x z + 1/4 y x z - 1/4 y x z - 1/4 y x z + + 2 2 2 3 2 2 + + 1/4 y x z + 1/2 y x z - 1/3 x z + 1/6 x z - 1/6 x z - 1/6 x z + + 2 3 3 2 3 3 2 2 + + 1/12 x z , COEFF(2, -1, 1) = 1/24 x y z + 1/6 x y z + 1/24 y x z + + 3 2 2 3 3 3 2 3 3 + - 1/24 x y z - 1/36 x z - 1/18 x z - 1/12 x y z - 1/12 x y z + + 2 2 3 2 3 + + 1/36 x z - 1/12 y x z + 1/18 x z + 1/12 x y z + 1/12 y x z + + 2 3 3 3 3 2 2 + - 1/24 y x z + 1/36 x z - 1/36 x z - 1/6 y x z + 1/12 y x z, + + 3 3 3 2 3 2 3 2 + COEFF(-1, 0, 1) = - 1/6 x y z + 1/6 x y z + 1/24 x z - 1/4 x y z + + 3 2 2 3 2 3 3 3 3 3 + - 1/8 x y z + 1/8 x y z + 1/3 x y z + 1/12 x z - 1/24 x z + + 2 2 3 3 2 2 2 2 2 + - 1/2 y x z + 1/2 y x z - 1/3 y x z + 3/8 y x z - 1/8 x z + + 2 2 2 3 2 3 2 2 + + 2/3 y x z - z y x - 3/8 y x z + 1/4 y x z - 1/4 y x z + + 2 2 2 2 2 3 2 + + 3/4 y x z - 1/2 y x z + 1/3 y x z + 1/6 x z - 1/12 x z - 1/4 x z + + 2 2 3 3 3 3 2 + + 1/12 x z + 1/8 x z , COEFF(0, 0, 1) = 1/2 x y z - 1/2 x y z + + 3 2 3 2 3 2 2 3 2 3 3 + - 1/8 x z + 3/4 x y z + 3/8 x y z - 3/8 x y z - x y z + + 3 3 3 2 2 3 3 + - 1/4 x z - 1/2 z + 1/8 x z - 3/4 y x z - y x z - 1/2 y x z + + 2 2 2 2 2 2 2 3 2 + - 3/4 y x z + 3/4 y z + 1/4 x z + 1/4 z - 1/4 z + y x z + + 2 2 2 3 2 3 2 2 + + 2 z y x - 2 y z + 3/4 y x z + 3/8 y x z - 3/8 y x z + + 2 2 2 2 2 2 3 2 3 2 + - 3/2 y x z + y x z + 1/2 y x z - y z + y z - 3/4 y z + 3/2 y z + + 3 2 2 2 3 + + 1/4 x z - 1/8 x z + 1/2 x z + 1/8 x z - 1/4 x z , COEFF(1, 0, 1) = + + 3 3 3 2 3 2 3 2 3 2 2 + - 1/2 x y z + 1/2 x y z + 1/8 x z - 3/4 x y z - 3/8 x y z + + 3 2 3 3 3 3 3 2 2 3 + + 3/8 x y z + x y z + 1/4 x z - 1/8 x z + 3/2 y x z + 1/2 y x z + + 3 2 2 2 2 2 2 2 2 3 + + y x z + 3/8 y x z - 1/8 x z - 2 y x z - z y x - 3/8 y x z + + 2 3 2 2 2 2 2 2 2 + - 3/4 y x z + 3/4 y x z + 3/4 y x z - 1/2 y x z - y x z - 1/2 x z + + 3 2 2 2 3 + + 1/4 x z - 1/4 x z - 1/4 x z + 1/8 x z , COEFF(2, 0, 1) = + + 3 3 3 3 3 2 3 3 2 3 + - 1/3 x y z + 1/6 x y z + 1/24 x z + 1/8 y x z - 1/8 x y z + + 3 3 3 3 2 2 + - 1/24 x z + 1/12 x z - 1/6 y x z - 1/12 x z - 1/6 x y z - 1/4 y x z + + 3 2 2 2 2 3 2 2 + - 1/24 x z + 1/3 y x z + 1/6 y x z - 1/8 y x z + 1/8 x y z + + 3 2 2 3 3 3 2 + + 1/4 x y z + 1/24 x z , COEFF(-1, 1, 1) = 1/12 x y z - 1/12 x y z + + 3 2 3 2 3 2 2 3 2 3 3 + - 1/12 x z + 1/4 x y z + 1/8 x y z - 1/8 x y z - 1/6 x y z + + 3 3 3 2 2 3 3 + - 1/6 x z + 1/12 x z + 1/2 y x z - 1/4 y x z + 1/6 y x z + + 2 2 2 2 2 2 2 2 3 + - 3/8 y x z + 1/4 x z - 1/3 y x z + 1/2 z y x + 3/8 y x z + + 2 3 2 2 2 2 2 2 2 + - 1/4 y x z + 1/4 y x z - 3/4 y x z + 1/4 y x z - 1/6 y x z + + 3 2 2 2 3 + - 1/3 x z + 1/6 x z + 1/2 x z - 1/6 x z - 1/4 x z , COEFF(0, 1, 1) = + + 3 3 3 2 3 2 3 2 3 2 2 + - 1/4 x y z + 1/4 x y z + 1/4 x z - 3/4 x y z - 3/8 x y z + + 3 2 3 3 3 3 3 2 + + 3/8 x y z + 1/2 x y z + 1/2 x z + z - 1/4 x z + 3/4 y x z + + 2 3 3 2 2 2 2 2 2 2 3 + + 1/2 y x z + 1/4 y x z + 3/4 y x z - 3/4 y z - 1/2 x z - 1/2 z + + 2 2 2 2 3 2 3 + + 1/2 z - 1/2 y x z - z y x + y z - 3/4 y x z - 3/8 y x z + + 2 2 2 2 2 2 2 2 + + 3/8 y x z + 3/2 y x z - 1/2 y x z - 1/4 y x z + 1/2 y z + + 3 2 3 2 3 2 2 + - 1/2 y z + 3/4 y z - 3/2 y z - 1/2 x z + 1/4 x z - x z - 1/4 x z + + 2 3 3 3 3 2 3 2 + + 1/2 x z , COEFF(1, 1, 1) = 1/4 x y z - 1/4 x y z - 1/4 x z + + 3 2 3 2 2 3 2 3 3 3 + + 3/4 x y z + 3/8 x y z - 3/8 x y z - 1/2 x y z - 1/2 x z + + 3 3 2 2 3 3 2 2 2 + + 1/4 x z - 3/2 y x z - 1/4 y x z - 1/2 y x z - 3/8 y x z + + 2 2 2 2 2 3 2 3 + + 1/4 x z + y x z + 1/2 z y x + 3/8 y x z + 3/4 y x z + + 2 2 2 2 2 2 2 3 + - 3/4 y x z - 3/4 y x z + 1/4 y x z + 1/2 y x z + x z - 1/2 x z + + 2 2 2 3 2 + + 1/2 x z + 1/2 x z - 1/4 x z , COEFF(2, 1, 1) = - 1/12 x z + + 2 2 3 3 2 2 3 + + 1/8 y x z + 1/12 y x z - 1/4 x y z + 1/4 y x z + 1/12 x z + + 2 3 2 2 3 2 3 3 3 + - 1/12 y x z - 1/8 x y z + 1/12 x z + 1/6 x z - 1/12 x y z + + 2 3 3 2 3 3 3 + - 1/6 y x z - 1/8 y x z + 1/8 x y z - 1/6 x z - 1/12 x z + + 3 2 3 3 2 3 2 + + 1/12 x y z + 1/6 x y z, COEFF(-1, 2, 1) = 1/24 x y z - 1/12 x z + + 2 3 2 2 2 2 2 3 3 2 + - 1/6 y x z - 1/24 x y z + 1/4 y x z + 1/24 x z - 1/12 x y z + + 2 2 2 2 2 3 3 2 2 + + 1/8 y x z + 1/18 x z - 1/8 y x z + 1/36 x z - 1/12 y x z + + 2 2 3 2 2 3 3 3 + - 1/24 x z + 1/72 x z + 1/36 x z - 1/36 x z - 1/72 x z + + 2 3 2 3 2 2 3 + + 1/12 y x z , COEFF(0, 2, 1) = - 1/4 y z + 1/4 y z - 1/24 x z + + 3 2 3 2 2 2 3 2 + + 1/12 z - 1/12 x z + 1/24 x z + 1/4 y x z - 1/4 y x z + + 2 3 2 2 2 2 2 + + 1/8 y x z + 1/12 x z + 1/2 y z - 1/2 y x z + 1/12 x z + + 2 2 2 3 2 2 2 2 2 2 + - 1/4 y x z + 1/8 x y z + 1/6 x z - 1/8 y x z - 1/12 z - 1/6 z + + 3 2 3 2 3 2 3 3 3 3 + + 1/4 x y z - 1/24 x z - 1/8 x y z - 1/12 x z + 1/24 x z , + + 3 2 3 2 2 + COEFF(1, 2, 1) = - 1/4 x y z + 1/12 x z - 1/6 x z + 1/4 y x z + + 2 2 2 2 2 2 2 3 3 3 + + 1/8 y x z + 1/2 y x z - 1/12 x z - 1/8 y x z - 1/24 x z + + 2 3 3 2 2 3 2 3 2 3 + + 1/24 x z + 1/12 x z + 1/4 y x z + 1/24 x z + 1/8 x y z + + 2 2 2 2 3 3 2 2 + - 1/12 x z - 1/24 x z - 1/4 y x z - 1/8 x y z , COEFF(2, 2, 1) = + + 2 2 2 3 3 2 2 3 2 + - 1/24 y x z + 1/24 y x z + 1/24 x y z + 1/36 x z - 1/72 x z + + 3 2 2 3 3 3 2 3 3 + + 1/12 x y z - 1/12 y x z + 1/72 x z - 1/24 x y z - 1/72 x z + + 2 3 3 2 2 3 + + 1/72 x z - 1/36 x z, COEFF(-1, -1, 2) = - 1/72 x y z - 1/36 x z + + 2 2 3 2 2 3 3 3 2 3 + - 1/24 y x z - 1/36 y x z + 1/36 y x z - 1/18 y x z + 1/72 x y z + + 3 3 3 2 3 + - 1/36 x y z + 1/54 x z + 1/18 y x z - 1/12 z y x - 1/108 x z + + 2 3 3 2 2 3 + + 1/36 x z + 1/108 x z + 1/24 y x z - 1/54 x z + 1/36 x y z + + 2 3 2 3 3 2 + + 1/12 y x z , COEFF(0, -1, 2) = - 1/12 y z + 1/12 y x z + 1/24 x y z + + 3 3 3 3 2 2 2 3 + + 1/36 x z + 1/12 x y z + 1/6 y z - 1/24 y x z + 1/12 y x z + + 2 3 3 3 2 3 + + 1/18 x z - 1/18 z - 1/12 x y z - 1/6 y z - 1/6 y x z + + 2 3 2 2 3 3 + + 1/24 y x z - 1/12 y x z - 1/12 y x z + 1/18 z + 1/36 x z + + 3 2 3 2 3 3 2 + - 1/24 x y z + 1/6 z y x - 1/36 x z - 1/36 x z - 1/18 x z + + 2 2 2 + + 1/12 y z, COEFF(1, -1, 2) = - 1/6 y x z + 1/18 x z + 1/24 y x z + + 2 3 3 3 3 2 3 + - 1/36 x z + 1/12 x y z - 1/18 x z - 1/36 x z + 1/12 y x z + + 3 3 3 3 3 2 2 2 3 + + 1/36 x z - 1/12 x y z - 1/24 x y z + 1/36 x z - 1/12 y x z + + 3 2 2 2 2 3 3 2 3 + + 1/6 y x z + 1/12 y x z - 1/12 z y x - 1/24 y x z + 1/24 x y z , + + 3 3 3 2 + COEFF(2, -1, 2) = - 1/36 x y z - 1/36 y x z + 1/72 x y z - 1/108 x z + + 3 3 3 3 3 3 + + 1/108 x z - 1/108 x z + 1/36 y x z + 1/108 x z + 1/36 x y z + + 2 3 3 2 3 2 + + 1/72 y x z - 1/72 x y z - 1/72 y x z, COEFF(-1, 0, 2) = + + 2 2 2 3 2 + - 1/8 y x z + 1/24 x z - 1/9 y x z - 1/36 x z + 1/24 x y z + + 3 3 2 3 2 3 2 2 3 3 + + 1/72 x z - 1/6 y x z - 1/12 y x z + 1/8 y x z - 1/72 x z + + 3 3 3 2 3 3 2 + + 1/18 x y z - 1/18 x y z - 1/24 x z + 1/9 y x z + 1/12 y x z + + 2 3 2 3 3 3 + + 1/6 z y x - 1/24 x y z + 1/36 x z , COEFF(0, 0, 2) = 1/24 x z + + 2 3 3 3 3 + - 1/6 y x z - 1/8 y x z + 1/3 y z + 1/12 z - 1/6 x y z - 1/3 y z + + 3 3 2 3 2 2 2 3 2 + - 1/12 z + 1/8 x y z - 1/12 x z + 1/4 y x z - 1/8 x y z + + 3 2 3 3 3 2 3 2 + - 1/24 x z + 1/24 x z + 1/3 y x z - 1/24 x z + 1/12 x z - 1/4 y z + + 2 2 3 3 3 2 + + 1/8 y x z + 1/4 y z + 1/6 x y z + 1/6 y x z - 1/3 z y x + + 2 2 3 3 2 3 2 3 + - 1/4 y x z , COEFF(1, 0, 2) = - 1/8 x y z + 1/6 z y x - 1/12 x z + + 3 3 2 3 3 3 2 + - 1/24 x z + 1/8 x y z + 1/24 x z - 1/3 y x z - 1/4 y x z + + 3 3 3 2 3 + - 1/6 x y z + 1/6 x y z + 1/12 x z + 1/3 y x z - 1/6 y x z + + 2 2 2 3 2 3 2 3 2 2 + + 1/24 x z + 1/8 y x z + 1/4 y x z - 1/24 x z - 1/8 y x z, + + 2 3 2 3 3 + COEFF(2, 0, 2) = - 1/18 y x z + 1/24 y x z + 1/24 x y z + 1/18 x y z + + 2 3 3 3 3 3 + - 1/24 y x z + 1/18 y x z - 1/72 x z + 1/72 x z - 1/72 x z + + 3 2 3 3 3 3 + - 1/24 x y z - 1/18 x y z + 1/72 x z, COEFF(-1, 1, 2) = 1/36 x y z + + 2 3 3 3 2 2 2 + + 1/18 x z + 1/12 x z - 1/36 x y z + 1/8 y x z - 1/12 z y x + + 3 2 3 2 3 3 2 + - 1/18 y x z - 1/12 x z + 1/24 x y z + 1/18 y x z - 1/24 x y z + + 3 3 2 2 3 2 2 3 3 + - 1/36 x z - 1/8 y x z - 1/12 y x z + 1/12 y x z - 1/18 x z + + 3 2 3 3 2 3 + + 1/36 x z + 1/12 y x z , COEFF(0, 1, 2) = - 1/12 x y z - 1/4 y z + + 2 3 3 2 2 + + 1/8 y x z + 1/12 y x z - 1/6 y z + 1/8 x y z + 1/12 x z + 1/6 x z + + 3 2 3 2 3 3 3 2 + + 1/6 z - 1/6 y x z - 1/6 x z + 1/12 x y z + 1/6 z y x + + 2 2 3 3 3 2 2 2 3 + - 1/4 y x z + 1/12 x z - 1/12 x z - 1/8 y x z + 1/4 y x z + + 3 3 3 2 3 2 3 + - 1/12 y x z - 1/12 x z - 1/6 z + 1/6 y z + 1/4 y z - 1/8 x y z , + + 3 3 3 2 3 2 + COEFF(1, 1, 2) = - 1/12 x y z + 1/12 x z - 1/12 x z - 1/8 x y z + + 2 3 2 3 + - 1/6 x z + 1/4 y x z + 1/6 y x z - 1/6 y x z + 1/12 y x z + + 2 3 2 2 3 2 2 3 3 3 + - 1/4 y x z - 1/12 z y x + 1/12 x z - 1/8 y x z - 1/12 x z + + 3 2 3 3 3 2 2 + + 1/8 x y z + 1/6 x z + 1/12 x y z + 1/8 y x z, COEFF(2, 1, 2) = + + 3 3 3 2 2 3 3 3 + 1/36 x y z + 1/24 x y z + 1/24 y x z - 1/36 y x z - 1/36 x z + + 3 3 3 3 + - 1/36 x y z + 1/36 x z + 1/36 y x z + 1/36 x z - 1/36 x z + + 3 2 3 2 3 2 3 + - 1/24 x y z - 1/24 y x z, COEFF(-1, 2, 2) = - 1/72 x y z + + 3 3 2 2 3 2 + + 1/108 x z + 1/72 x y z - 1/72 x z - 1/108 x z + 1/36 y x z + + 2 2 3 3 2 3 2 3 + - 1/24 y x z + 1/216 x z + 1/72 x z - 1/216 x z - 1/36 y x z + + 2 2 3 2 3 2 3 + + 1/24 y x z , COEFF(0, 2, 2) = - 1/36 x z - 1/36 z - 1/24 y x z + + 2 2 3 2 3 2 + + 1/12 y x z + 1/72 x z - 1/72 x z + 1/24 y x z - 1/24 x y z + + 3 2 3 3 3 2 3 2 + + 1/72 x z + 1/36 x z - 1/72 x z + 1/12 y z + 1/36 z - 1/12 y z + + 3 2 3 2 2 3 2 + + 1/24 x y z - 1/12 y x z , COEFF(1, 2, 2) = 1/36 x z + 1/72 x z + + 2 2 3 2 3 2 3 3 2 3 + - 1/24 y x z - 1/24 x y z + 1/12 y x z + 1/24 x y z - 1/72 x z + + 2 3 3 2 2 3 3 2 3 + - 1/12 y x z + 1/72 x z + 1/24 y x z - 1/36 x z - 1/72 x z , + + 3 2 3 2 3 + COEFF(2, 2, 2) = 1/216 x z + 1/72 y x z - 1/216 x z + 1/72 x y z + + 3 2 3 3 2 3 3 + - 1/72 x y z - 1/216 x z - 1/72 y x z + 1/216 x z] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dy.compute.c"); +bytes used=5852433560, alloc=10549364, time=515.67 +bytes used=5853433892, alloc=10549364, time=515.75 +bytes used=5854434184, alloc=10549364, time=515.83 +bytes used=5855434364, alloc=10549364, time=515.91 +bytes used=5856434660, alloc=10549364, time=515.99 +bytes used=5857434844, 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alloc=10549364, time=573.16 +bytes used=6222928728, alloc=10549364, time=573.23 +bytes used=6223928920, alloc=10549364, time=573.30 +bytes used=6224929116, alloc=10549364, time=573.37 +bytes used=6225929464, alloc=10549364, time=573.44 +bytes used=6226929912, alloc=10549364, time=573.51 +bytes used=6227930140, alloc=10549364, time=573.60 +bytes used=6228930412, alloc=10549364, time=573.68 +bytes used=6229930656, alloc=10549364, time=573.84 +bytes used=6230930876, alloc=10549364, time=574.09 +bytes used=6231931088, alloc=10549364, time=574.33 +bytes used=6232933232, alloc=10549364, time=574.55 +bytes used=6233933424, alloc=10549364, time=574.76 +bytes used=6234933740, alloc=10549364, time=574.94 +bytes used=6235934012, alloc=10549364, time=575.18 +bytes used=6236934228, alloc=10549364, time=575.29 +bytes used=6237934444, alloc=10549364, time=575.41 +bytes used=6238934616, alloc=10549364, time=575.53 +bytes used=6239935216, alloc=10549364, time=575.64 +bytes used=6240935440, alloc=10549364, time=575.76 +bytes used=6241935724, alloc=10549364, time=575.88 +bytes used=6242935936, alloc=10549364, time=578.64 +bytes used=6243936336, alloc=10549364, time=580.46 +bytes used=6244938196, alloc=10549364, time=580.75 +bytes used=6245939596, alloc=10549364, time=581.02 +bytes used=6246940860, alloc=10549364, time=581.17 +bytes used=6247941192, alloc=10549364, time=581.23 +bytes used=6248941384, alloc=10549364, time=581.37 +bytes used=6249941616, alloc=10549364, time=581.53 +bytes used=6250941884, alloc=10549364, time=581.74 +bytes used=6251942192, alloc=10549364, time=581.90 +> +# d/dz +> simplify( diff(interp_3d_cube_order3_smooth0,z) ); +bytes used=6253573680, alloc=10549364, time=582.03 +bytes used=6254574108, alloc=10549364, time=582.11 +bytes used=6255574372, alloc=10549364, time=582.19 +bytes used=6256574580, alloc=10549364, time=582.27 +bytes used=6257574912, alloc=10549364, time=582.35 +bytes used=6258575784, alloc=10549364, time=582.43 +bytes used=6259576376, 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+> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=6270608444, alloc=10549364, time=583.52 +bytes used=6271641788, alloc=10549364, time=583.60 +bytes used=6272734248, alloc=10549364, time=583.69 +bytes used=6273739652, alloc=10549364, time=583.77 +bytes used=6274925688, alloc=10549364, time=583.87 +bytes used=6275925824, alloc=10549364, time=583.96 +bytes used=6276965528, alloc=10549364, time=584.06 +bytes used=6278113468, alloc=10549364, time=584.16 +bytes used=6279189336, alloc=10549364, time=584.28 +bytes used=6280211996, alloc=10549364, time=584.37 +bytes used=6281313660, alloc=10549364, time=584.47 +bytes used=6282352080, alloc=10549364, time=584.58 +bytes used=6283352220, alloc=10549364, time=584.68 +bytes used=6284354500, alloc=10549364, time=584.78 +bytes used=6285366028, alloc=10549364, time=584.89 +bytes used=6286401212, alloc=10549364, time=584.97 +bytes used=6287403768, alloc=10549364, time=585.03 +bytes used=6288406716, alloc=10549364, time=585.09 +bytes used=6289409272, alloc=10549364, time=585.15 + 3 3 2 3 3 2 3 2 +[COEFF(-1, -1, -1) = 1/36 z y x - 1/72 z y x + 1/24 x y z + + 3 2 3 2 2 3 3 3 2 + - 1/36 x y z - 1/36 x y z - 1/12 x y z + 1/18 x y z - 1/12 x y z + + 3 2 2 3 3 2 2 3 + + 1/24 x y z + 1/18 x y z - 1/54 x y - 1/6 y x z + 1/36 x y + + 3 3 2 2 2 2 + - 1/108 y x - 1/27 y x - 1/8 y x z + 1/9 y x z - 1/6 z y x + + 2 2 2 2 2 2 2 2 + + 1/18 y x - 1/12 y x + 1/18 y x + 1/12 y x z + 1/4 y x z + + 2 2 2 3 2 3 + + 1/12 y x z - 1/18 y x z + 1/36 x y - 1/54 x y, COEFF(0, -1, -1) = + + 3 3 2 3 3 2 3 2 3 2 + - 1/12 z y x + 1/24 z y x - 1/12 x y z - 1/24 x y z + + 3 2 2 3 3 3 2 3 2 2 + + 1/12 x y z + 1/6 x y z + 1/12 x y z + 1/4 x y z - 1/8 x y z + + 3 3 2 2 3 3 3 + - 1/6 x y z - 1/36 x y + 1/9 y - 1/4 y x z - 1/18 x y + 1/36 y x + + 2 2 2 3 3 2 2 2 3 + - 1/18 y x + 1/4 y x z - 1/6 y z + 1/12 y z - 1/4 y z + 1/18 y + + 2 2 2 2 2 + - 1/6 y + 1/6 y x z + 1/3 z y x - 1/3 y z - 1/9 y x + 1/6 y x + + 2 2 2 2 2 2 2 2 + + 1/12 y x + 1/8 y x z - 1/2 y x z - 1/6 y x z - 1/12 y x z + + 2 2 3 2 3 + + 1/6 y z + 1/2 y z - 1/12 x y + 1/18 x y, COEFF(1, -1, -1) = + + 3 3 2 3 3 2 3 2 3 2 3 2 + 1/12 z y x - 1/24 z y x + 1/24 x y z + 1/12 x y z - 1/12 x y z + + 2 3 3 3 2 3 2 2 3 + - 1/12 x y z - 1/6 x y z - 1/4 x y z + 1/8 x y z + 1/6 x y z + + 3 2 2 3 3 3 + + 1/18 x y + 1/2 y x z + 1/36 x y - 1/36 y x + 1/9 y x + + 2 2 2 2 2 2 2 + - 1/8 y x z - 1/3 y x z - 1/6 z y x + 1/18 y x - 1/12 y x + + 2 2 2 2 2 2 2 2 + - 1/6 y x - 1/4 y x z + 1/4 y x z + 1/12 y x z + 1/6 y x z + + 3 2 3 3 3 3 + + 1/12 x y - 1/18 x y, COEFF(2, -1, -1) = 1/36 x y z + 1/108 y x + + 3 2 2 3 2 3 2 3 3 3 2 + - 1/24 x y z - 1/36 x y - 1/72 x y z - 1/36 z y x + 1/36 x y z + + 2 3 3 2 2 3 2 3 + + 1/72 z y x + 1/24 y x z + 1/12 x y z + 1/18 y x z - 1/18 x y z + + 3 2 2 2 + + 1/54 x y + 1/36 y x - 1/12 y x z - 1/36 y x z - 1/54 y x + + 3 3 3 2 3 3 + - 1/108 x y , COEFF(-1, 0, -1) = - 1/12 z y x + 1/24 z y x + + 2 3 2 3 2 3 2 2 3 3 + - 1/8 x y z + 1/12 x y z - 1/24 x y z + 1/4 x y z - 1/6 x y z + + 3 2 3 2 3 2 2 3 + + 1/12 x z + 1/6 x y z - 1/12 x y z + 1/12 x y z + 1/9 x + + 3 3 2 2 3 3 3 + + 1/18 x y - 1/6 x z + 1/3 y x z - 1/12 x y + 1/36 y x - 1/18 y x + + 2 2 2 2 2 3 2 2 + + 1/4 y x z - 1/4 x z + 1/18 x - 1/6 x + 1/6 y x z - 1/4 z y x + + 2 2 2 2 2 2 2 2 + + 1/12 y x + 1/6 y x - 1/9 y x - 1/6 y x z - 1/2 y x z + + 2 2 2 2 2 3 2 + + 1/8 y x z - 1/12 y x z - 1/3 x z + 1/2 x z + 1/6 x z - 1/18 x y + + 3 3 3 2 3 3 2 3 2 + - 1/36 x y, COEFF(0, 0, -1) = 1/4 z y x - 1/8 z y x + 1/4 x y z + + 3 2 3 2 2 3 3 3 2 + + 1/8 x y z + 1/8 x y z - 1/2 x y z - 1/4 x y z - 1/4 x z + + 3 2 3 2 2 3 3 3 + - 1/2 x y z + 1/4 x y z - 1/4 x y z + 1/6 x + 1/12 x y + 1/2 x z + + 2 2 3 3 3 + + 1/6 y + z + 1/2 y x z + 1/6 x y - 1/12 y x - 1/12 y x + + 2 2 2 3 3 2 2 2 2 2 3 + - 1/2 y x z + 1/2 y z - 1/4 y z + 1/2 y z + 1/2 x z - 1/6 y + + 3 2 2 2 2 + - 1/6 x - 1/3 + 1/3 y - 1/2 z + 1/3 x + 1/4 y x z + 1/2 z y x + + 2 2 2 2 2 2 2 2 + - 1/2 y z - 1/6 y x - 1/3 y x - 1/6 y x - 1/4 y x z + y x z + + 2 2 2 2 2 2 2 + - 1/4 y x z - 1/8 y x z + 1/4 y z - y z - 1/2 x z - x z + 1/4 x z + + 3 2 3 3 3 2 3 3 + + 1/6 x y + 1/12 x y, COEFF(1, 0, -1) = - 1/4 z y x + 1/8 z y x + + 2 3 2 3 2 3 2 2 3 3 + - 1/8 x y z - 1/4 x y z - 1/8 x y z + 1/4 x y z + 1/2 x y z + + 3 2 3 2 3 2 2 3 3 + + 1/4 x z + 1/2 x y z - 1/4 x y z + 1/4 x y z - 1/3 x - 1/6 x y + + 3 2 2 3 3 3 2 2 2 + - 1/2 x z - y x z - 1/12 x y + 1/12 y x + 1/6 y x + 1/4 y x z + + 2 2 3 2 2 2 + - 1/4 x z + 1/6 x - 1/6 x - 1/2 y x z - 1/4 z y x + 1/12 y x + + 2 2 2 2 2 2 2 2 2 + + 1/6 y x + 1/3 y x + 1/2 y x z - 1/2 y x z + 1/8 y x z + + 2 2 2 3 2 3 + + 1/4 y x z + x z + 1/2 x z - 1/2 x z - 1/6 x y - 1/12 x y, + + 3 2 3 2 2 + COEFF(2, 0, -1) = 1/24 x y z + 1/12 y x z + 1/18 x y + 1/6 y x z + + 3 2 3 2 3 + - 1/18 x - 1/36 y x - 1/24 y x z - 1/12 x z - 1/6 x z + 1/36 x y + + 2 3 3 3 3 3 3 + - 1/24 z y x - 1/12 x y z + 1/18 x - 1/12 x y z - 1/36 y x + + 2 3 2 2 3 3 2 3 2 + + 1/12 x z + 1/12 x y z + 1/36 x y - 1/6 x y z + 1/24 x y z + + 3 3 3 2 2 2 + + 1/12 z y x + 1/6 x z - 1/18 y x - 1/12 y x z , COEFF(-1, 1, -1) = + + 3 3 2 3 3 2 3 2 3 2 3 2 + 1/12 z y x - 1/24 z y x + 1/8 x y z - 1/12 x y z + 1/12 x y z + + 2 3 3 3 2 3 2 2 3 + - 1/4 x y z + 1/6 x y z - 1/12 x y z + 1/24 x y z - 1/6 x y z + + 3 2 2 3 3 3 + - 1/18 x y - 1/6 y x z + 1/12 x y - 1/36 y x + 1/9 y x + + 2 2 2 2 2 2 2 + - 1/8 y x z - 1/3 y x z + 1/2 z y x - 1/6 y x - 1/12 y x + + 2 2 2 2 2 2 2 2 + + 1/18 y x + 1/12 y x z + 1/4 y x z - 1/4 y x z + 1/6 y x z + + 3 2 3 3 3 2 3 3 + + 1/36 x y + 1/18 x y, COEFF(0, 1, -1) = - 1/4 z y x + 1/8 z y x + + 2 3 2 3 2 3 2 2 3 3 + - 1/4 x y z - 1/8 x y z - 1/4 x y z + 1/2 x y z + 1/4 x y z + + 3 2 3 2 2 3 3 2 + + 1/4 x y z - 1/8 x y z + 1/2 x y z - 1/12 x y - 1/3 y - 1/4 y x z + + 2 3 3 3 2 2 2 3 3 2 + - 1/6 x y + 1/12 y x + 1/6 y x + 1/4 y x z - 1/2 y z + 1/4 y z + + 2 2 3 2 2 2 + - 1/4 y z + 1/6 y - 1/6 y - 1/2 y x z - z y x + y z + 1/3 y x + + 2 2 2 2 2 2 2 2 2 + + 1/6 y x + 1/12 y x + 1/8 y x z - 1/2 y x z + 1/2 y x z + + 2 2 2 3 2 3 + + 1/4 y x z - 1/2 y z + 1/2 y z - 1/12 x y - 1/6 x y, + + 3 3 2 3 3 2 3 2 3 2 + COEFF(1, 1, -1) = 1/4 z y x - 1/8 z y x + 1/8 x y z + 1/4 x y z + + 3 2 2 3 3 3 2 3 2 2 + + 1/4 x y z - 1/4 x y z - 1/2 x y z - 1/4 x y z + 1/8 x y z + + 3 3 2 2 3 3 3 + - 1/2 x y z + 1/6 x y + 1/2 y x z + 1/12 x y - 1/12 y x - 1/3 y x + + 2 2 2 2 2 2 2 2 + - 1/8 y x z + y x z + 1/2 z y x - 1/6 y x - 1/12 y x - 1/6 y x + + 2 2 2 2 2 2 2 3 2 + - 1/4 y x z + 1/4 y x z - 1/4 y x z - 1/2 y x z + 1/12 x y + + 3 2 2 2 3 2 + + 1/6 x y, COEFF(2, 1, -1) = 1/24 y x z - 1/12 y x z - 1/12 x y z + + 3 3 3 3 2 2 3 3 3 2 + + 1/36 y x - 1/12 z y x + 1/12 y x z + 1/24 z y x + 1/12 x y z + + 3 2 3 2 3 + - 1/6 y x z + 1/18 y x - 1/36 x y - 1/24 x y z + 1/6 x y z + + 3 2 2 3 2 3 3 + - 1/24 x y z - 1/18 x y + 1/36 y x - 1/36 x y + 1/12 x y z, + + 3 2 2 3 2 3 2 + COEFF(-1, 2, -1) = - 1/72 x y z - 1/24 x y z + 1/36 x y z + + 3 3 3 2 3 2 3 2 2 + + 1/108 y x - 1/108 x y + 1/12 x y z - 1/36 x y + 1/24 y x z + + 3 2 2 3 + + 1/54 x y - 1/36 y x z - 1/12 z y x - 1/54 y x + 1/36 x y z + + 2 3 3 3 2 3 3 + + 1/36 y x + 1/18 y x z - 1/18 x y z - 1/36 z y x + 1/72 z y x , + + 2 2 3 2 3 3 3 + COEFF(0, 2, -1) = - 1/12 y x z + 1/24 x y z + 1/6 y z + 1/12 z y x + + 3 3 2 3 2 + + 1/18 y - 1/12 x y z - 1/12 x y z + 1/12 y z - 1/18 y + 1/6 z y x + + 2 3 2 3 2 3 2 3 2 2 + + 1/18 x y - 1/6 x y z + 1/12 x y z - 1/12 y z - 1/24 y x z + + 2 3 3 2 3 3 + + 1/12 y x z - 1/18 y x + 1/36 x y + 1/24 x y z - 1/36 y x + + 3 2 3 3 + + 1/36 x y - 1/36 y x - 1/24 z y x - 1/6 y z, COEFF(1, 2, -1) = + + 3 2 3 3 3 3 3 + 1/12 x y z + 1/24 z y x - 1/6 y x z - 1/18 x y + 1/36 y x + + 3 2 3 2 2 3 2 2 3 3 + - 1/36 x y - 1/24 x y z - 1/36 x y + 1/24 y x z - 1/12 z y x + + 3 2 2 3 2 3 + - 1/12 x y z + 1/18 y x + 1/12 y x z - 1/24 x y z + 1/6 x y z + + 2 2 3 2 + - 1/12 z y x + 1/12 x y z + 1/36 y x , COEFF(2, 2, -1) = 1/36 y x z + + 3 2 3 3 3 2 3 3 3 + + 1/72 x y z + 1/36 z y x + 1/72 x y z - 1/108 y x + 1/108 x y + + 3 3 2 3 + - 1/36 x y z + 1/108 x y - 1/108 y x - 1/72 y x z - 1/36 x y z + + 2 3 3 3 3 2 3 3 + - 1/72 z y x , COEFF(-1, -1, 0) = - 1/18 z y x + 1/24 z y x + + 2 3 2 3 2 3 2 2 3 3 + - 1/8 x y z + 1/12 x y z + 1/12 x y z + 1/6 x y z - 1/9 x y z + + 3 2 3 2 2 3 3 2 + + 1/6 x y z - 1/8 x y z - 1/9 x y z - 1/36 x y + 1/3 y x z + + 2 3 3 3 2 2 2 + + 1/24 x y - 1/72 y x - 1/18 y x + 3/8 y x z - 2/9 y x z + + 2 2 2 2 2 2 2 + + 1/3 z y x + 1/12 y x - 1/8 y x + 1/12 y x - 1/4 y x z + + 2 2 2 2 2 3 2 3 + - 1/2 y x z - 1/4 y x z + 1/6 y x z + 1/24 x y - 1/36 x y, + + 3 3 2 3 3 2 3 2 3 2 + COEFF(0, -1, 0) = 1/6 z y x - 1/8 z y x + 1/4 x y z + 1/8 x y z + + 3 2 2 3 3 3 2 3 2 2 + - 1/4 x y z - 1/3 x y z - 1/6 x y z - 1/2 x y z + 3/8 x y z + + 3 3 2 2 3 3 3 + + 1/3 x y z - 1/24 x y + 1/6 y + 1/2 y x z - 1/12 x y + 1/24 y x + + 2 2 2 3 3 2 2 2 3 + - 1/12 y x - 3/4 y x z + 1/3 y z - 1/4 y z + 3/4 y z + 1/12 y + + 2 2 2 2 2 + - 1/4 y - 1/3 y x z - 2/3 z y x + 2/3 y z - 1/6 y x + 1/4 y x + + 2 2 2 2 2 2 2 2 2 + + 1/8 y x - 3/8 y x z + y x z + 1/2 y x z + 1/4 y x z - 1/2 y z + + 2 3 2 3 3 3 + - y z - 1/8 x y + 1/12 x y, COEFF(1, -1, 0) = - 1/6 z y x + + 2 3 3 2 3 2 3 2 3 2 2 3 + + 1/8 z y x - 1/8 x y z - 1/4 x y z + 1/4 x y z + 1/6 x y z + + 3 3 2 3 2 2 3 3 + + 1/3 x y z + 1/2 x y z - 3/8 x y z - 1/3 x y z + 1/12 x y + + 2 2 3 3 3 2 2 2 + - y x z + 1/24 x y - 1/24 y x + 1/6 y x + 3/8 y x z + 2/3 y x z + + 2 2 2 2 2 2 2 + + 1/3 z y x + 1/12 y x - 1/8 y x - 1/4 y x + 3/4 y x z + + 2 2 2 2 2 3 2 3 + - 1/2 y x z - 1/4 y x z - 1/2 y x z + 1/8 x y - 1/12 x y, + + 3 3 3 2 3 2 + COEFF(2, -1, 0) = 1/36 x y + 1/9 x y z - 1/24 x y + 1/24 x y z + + 3 2 2 3 2 3 3 2 3 + + 1/8 x y z - 1/72 x y - 1/24 z y x + 1/24 y x - 1/18 x y z + + 2 2 3 3 2 + - 1/8 y x z + 1/72 y x + 1/6 y x z - 1/9 y x z - 1/36 y x + + 2 3 2 3 3 3 2 + + 1/12 y x z - 1/6 x y z + 1/18 z y x - 1/12 x y z , COEFF(-1, 0, 0) + + 3 3 2 3 3 2 3 2 3 2 3 2 + = 1/6 z y x - 1/8 z y x + 3/8 x y z - 1/4 x y z + 1/8 x y z + + 2 3 3 3 2 3 2 3 2 2 + - 1/2 x y z + 1/3 x y z - 1/4 x z - 1/3 x y z + 1/4 x y z + + 3 3 3 2 2 3 + - 1/6 x y z + 1/6 x + 1/12 x y + 1/3 x z - 2/3 y x z - 1/8 x y + + 3 3 2 2 2 2 2 3 2 + + 1/24 y x - 1/12 y x - 3/4 y x z + 3/4 x z + 1/12 x - 1/4 x + + 2 2 2 2 2 2 2 + - 1/3 y x z + 1/2 z y x + 1/8 y x + 1/4 y x - 1/6 y x + 1/2 y x z + + 2 2 2 2 2 2 2 + + y x z - 3/8 y x z + 1/4 y x z + 2/3 x z - x z - 1/2 x z + + 3 2 3 3 3 2 3 3 + - 1/12 x y - 1/24 x y, COEFF(0, 0, 0) = - 1/2 z y x + 3/8 z y x + + 2 3 2 3 2 3 2 2 3 3 + - 3/4 x y z - 3/8 x y z - 3/8 x y z + x y z + 1/2 x y z + + 3 2 3 2 3 2 2 3 3 + + 3/4 x z + x y z - 3/4 x y z + 1/2 x y z + 1/4 x + 1/8 x y + + 3 2 2 3 3 3 + - x z - 1/2 + 1/4 y - 2 z - y x z + 1/4 x y - 1/8 y x - 1/8 y x + + 2 2 2 3 3 2 2 2 2 2 3 + + 3/2 y x z - y z + 3/4 y z - 3/2 y z - 3/2 x z - 1/4 y + + 3 2 2 2 2 2 + - 1/4 x + 1/2 y + 3/2 z + 1/2 x - 1/2 y x z - z y x + y z - 1/4 y x + + 2 2 2 2 2 2 2 2 2 + - 1/2 y x - 1/4 y x + 3/4 y x z - 2 y x z + 3/4 y x z + + 2 2 2 2 2 3 2 + + 3/8 y x z - 3/4 y z + 2 y z + x z + 2 x z - 3/4 x z + 1/4 x y + + 3 3 3 2 3 3 2 3 2 + + 1/8 x y, COEFF(1, 0, 0) = 1/2 z y x - 3/8 z y x + 3/8 x y z + + 3 2 3 2 2 3 3 3 2 3 2 + + 3/4 x y z + 3/8 x y z - 1/2 x y z - x y z - 3/4 x z - x y z + + 3 2 2 3 3 3 2 + + 3/4 x y z - 1/2 x y z - 1/2 x - 1/4 x y + x z + 2 y x z + + 2 3 3 3 2 2 2 2 2 3 + - 1/8 x y + 1/8 y x + 1/4 y x - 3/4 y x z + 3/4 x z + 1/4 x + + 2 2 2 2 2 2 + - 1/4 x + y x z + 1/2 z y x + 1/8 y x + 1/4 y x + 1/2 y x + + 2 2 2 2 2 2 2 2 + - 3/2 y x z + y x z - 3/8 y x z - 3/4 y x z - 2 x z - x z + + 2 3 2 3 3 3 + + 3/2 x z - 1/4 x y - 1/8 x y, COEFF(2, 0, 0) = 1/24 x y + 1/6 x y z + + 3 3 2 3 2 3 3 2 + - 1/12 x + 1/12 x y - 1/8 x y z - 1/24 y x - 1/24 y x - 1/4 x z + + 3 2 3 3 2 3 + + 1/24 x y + 1/12 x - 1/6 y x z + 1/8 z y x - 1/12 y x - 1/3 x z + + 3 2 3 2 3 2 + + 1/3 x z + 1/6 x y z - 1/3 y x z + 1/4 x z + 1/3 x y z + + 3 2 3 2 2 2 2 2 3 3 + - 1/8 x y z - 1/4 x y z + 1/8 y x z + 1/4 y x z - 1/6 z y x , + + 3 3 2 3 3 2 3 2 3 2 + COEFF(-1, 1, 0) = - 1/6 z y x + 1/8 z y x - 3/8 x y z + 1/4 x y z + + 3 2 2 3 3 3 2 3 2 2 + - 1/4 x y z + 1/2 x y z - 1/3 x y z + 1/6 x y z - 1/8 x y z + + 3 3 2 2 3 3 3 + + 1/3 x y z - 1/12 x y + 1/3 y x z + 1/8 x y - 1/24 y x + 1/6 y x + + 2 2 2 2 2 2 2 2 + + 3/8 y x z + 2/3 y x z - z y x - 1/4 y x - 1/8 y x + 1/12 y x + + 2 2 2 2 2 2 2 3 2 + - 1/4 y x z - 1/2 y x z + 3/4 y x z - 1/2 y x z + 1/24 x y + + 3 3 3 2 3 3 2 3 2 + + 1/12 x y, COEFF(0, 1, 0) = 1/2 z y x - 3/8 z y x + 3/4 x y z + + 3 2 3 2 2 3 3 3 2 + + 3/8 x y z + 3/4 x y z - x y z - 1/2 x y z - 1/2 x y z + + 3 2 2 3 3 2 2 3 + + 3/8 x y z - x y z - 1/8 x y - 1/2 y + 1/2 y x z - 1/4 x y + + 3 3 2 2 2 3 3 2 2 2 + + 1/8 y x + 1/4 y x - 3/4 y x z + y z - 3/4 y z + 3/4 y z + + 3 2 2 2 2 2 + + 1/4 y - 1/4 y + y x z + 2 z y x - 2 y z + 1/2 y x + 1/4 y x + + 2 2 2 2 2 2 2 2 2 + + 1/8 y x - 3/8 y x z + y x z - 3/2 y x z - 3/4 y x z + 3/2 y z + + 2 3 2 3 3 3 + - y z - 1/8 x y - 1/4 x y, COEFF(1, 1, 0) = - 1/2 z y x + + 2 3 3 2 3 2 3 2 3 2 2 3 + + 3/8 z y x - 3/8 x y z - 3/4 x y z - 3/4 x y z + 1/2 x y z + + 3 3 2 3 2 2 3 3 2 + + x y z + 1/2 x y z - 3/8 x y z + x y z + 1/4 x y - y x z + + 2 3 3 3 2 2 2 2 + + 1/8 x y - 1/8 y x - 1/2 y x + 3/8 y x z - 2 y x z - z y x + + 2 2 2 2 2 2 2 2 + - 1/4 y x - 1/8 y x - 1/4 y x + 3/4 y x z - 1/2 y x z + + 2 2 2 3 2 3 + + 3/4 y x z + 3/2 y x z + 1/8 x y + 1/4 x y, COEFF(2, 1, 0) = + + 2 3 3 2 3 3 2 + - 1/8 z y x + 1/3 y x z + 1/6 y x z - 1/12 x y + 1/8 x y z + + 3 3 3 3 3 3 2 2 2 + + 1/6 z y x + 1/24 y x - 1/24 x y - 1/24 x y - 1/8 y x z + + 2 2 3 2 2 3 + + 1/12 y x + 1/24 y x - 1/4 y x z + 1/8 x y z - 1/6 x y z + + 3 2 3 3 2 3 2 + - 1/6 x y z - 1/3 x y z + 1/4 x y z , COEFF(-1, 2, 0) = - 1/12 x y z + + 3 3 3 2 3 3 + - 1/36 y x - 1/18 x y z + 1/72 y x + 1/12 y x z + 1/18 z y x + + 2 3 3 2 2 3 2 + + 1/6 z y x - 1/72 x y + 1/24 x y z - 1/6 x y z + 1/24 y x + + 2 2 2 3 2 3 3 3 + - 1/8 y x z - 1/24 x y - 1/24 z y x + 1/9 x y z - 1/9 y x z + + 2 3 2 3 3 2 2 + + 1/8 x y z + 1/36 x y , COEFF(0, 2, 0) = 1/24 x y + 1/4 y x z + + 3 2 2 3 3 3 + - 1/8 x y z - 1/24 y x - 1/12 y x - 1/24 y x - 1/3 y z + 1/12 y + + 3 3 2 2 2 3 2 + + 1/24 x y + 1/6 x y z - 1/3 z y x - 1/4 y z - 1/4 x y z + + 3 2 3 3 3 2 + - 1/6 y x z + 1/3 y z + 1/4 y z - 1/12 y + 1/6 x y z - 1/8 x y z + + 2 3 3 2 3 2 3 3 2 3 + + 1/8 z y x + 1/3 x y z + 1/8 y x z - 1/6 z y x + 1/12 x y , + + 3 3 2 2 2 3 2 + COEFF(1, 2, 0) = - 1/24 x y - 1/12 x y - 1/8 y x z + 1/8 x y z + + 3 3 2 3 2 2 + + 1/12 y x + 1/24 y x - 1/6 x y z + 1/24 y x - 1/4 y x z + + 2 2 3 3 2 3 3 3 + + 1/6 z y x - 1/8 z y x - 1/24 x y + 1/6 z y x + 1/3 y x z + + 3 2 3 3 2 3 + + 1/4 x y z - 1/3 x y z + 1/8 x y z - 1/6 x y z, COEFF(2, 2, 0) = + + 3 3 2 3 3 3 3 + 1/72 x y - 1/24 x y z - 1/72 y x - 1/18 z y x - 1/72 y x + + 3 2 3 2 3 + - 1/24 x y z - 1/18 y x z + 1/18 x y z + 1/24 y x z + 1/72 x y + + 3 2 3 3 3 3 + + 1/18 x y z + 1/24 z y x , COEFF(-1, -1, 1) = 1/36 z y x + + 2 3 3 2 3 2 3 2 3 2 + - 1/24 z y x + 1/8 x y z - 1/12 x y z - 1/12 x y z + + 2 3 3 3 2 3 2 2 3 + - 1/12 x y z + 1/18 x y z - 1/12 x y z + 1/8 x y z + 1/18 x y z + + 3 2 2 3 3 3 + + 1/18 x y - 1/6 y x z - 1/12 x y + 1/36 y x + 1/9 y x + + 2 2 2 2 2 2 2 2 + - 3/8 y x z + 1/9 y x z - 1/6 z y x - 1/6 y x + 1/4 y x - 1/6 y x + + 2 2 2 2 2 2 2 3 2 + + 1/4 y x z + 1/4 y x z + 1/4 y x z - 1/6 y x z - 1/12 x y + + 3 3 3 2 3 3 + + 1/18 x y, COEFF(0, -1, 1) = - 1/12 z y x + 1/8 z y x + + 2 3 2 3 2 3 2 2 3 3 + - 1/4 x y z - 1/8 x y z + 1/4 x y z + 1/6 x y z + 1/12 x y z + + 3 2 3 2 2 3 3 2 + + 1/4 x y z - 3/8 x y z - 1/6 x y z + 1/12 x y - 1/3 y - 1/4 y x z + + 2 3 3 3 2 2 2 3 3 2 + + 1/6 x y - 1/12 y x + 1/6 y x + 3/4 y x z - 1/6 y z + 1/4 y z + + 2 2 3 2 2 + - 3/4 y z - 1/6 y + 1/2 y + 1/6 y x z + 1/3 z y x - 1/3 y z + + 2 2 2 2 2 2 2 2 + + 1/3 y x - 1/2 y x - 1/4 y x + 3/8 y x z - 1/2 y x z + + 2 2 2 2 2 3 2 3 + - 1/2 y x z - 1/4 y x z + 1/2 y z + 1/2 y z + 1/4 x y - 1/6 x y, + + 3 3 2 3 3 2 3 2 3 2 + COEFF(1, -1, 1) = 1/12 z y x - 1/8 z y x + 1/8 x y z + 1/4 x y z + + 3 2 2 3 3 3 2 3 2 2 + - 1/4 x y z - 1/12 x y z - 1/6 x y z - 1/4 x y z + 3/8 x y z + + 3 3 2 2 3 3 3 + + 1/6 x y z - 1/6 x y + 1/2 y x z - 1/12 x y + 1/12 y x - 1/3 y x + + 2 2 2 2 2 2 2 2 + - 3/8 y x z - 1/3 y x z - 1/6 z y x - 1/6 y x + 1/4 y x + 1/2 y x + + 2 2 2 2 2 2 2 3 2 + - 3/4 y x z + 1/4 y x z + 1/4 y x z + 1/2 y x z - 1/4 x y + + 3 3 3 3 3 + + 1/6 x y, COEFF(2, -1, 1) = - 1/36 y x + 1/36 x y z - 1/18 x y z + + 3 2 3 3 2 2 + + 1/18 y x z + 1/12 x y z - 1/18 x y + 1/12 x y - 1/12 y x + + 3 2 3 2 2 2 3 3 2 + + 1/18 y x - 1/24 x y z - 1/8 x y z + 1/24 z y x - 1/12 y x z + + 3 3 3 3 2 2 2 2 + + 1/36 x y - 1/36 z y x + 1/12 x y z + 1/8 y x z - 1/12 y x z, + + 3 3 2 3 3 2 3 2 + COEFF(-1, 0, 1) = - 1/12 z y x + 1/8 z y x - 3/8 x y z + + 3 2 3 2 2 3 3 3 2 + + 1/4 x y z - 1/8 x y z + 1/4 x y z - 1/6 x y z + 1/4 x z + + 3 2 3 2 2 3 3 3 + + 1/6 x y z - 1/4 x y z + 1/12 x y z - 1/3 x - 1/6 x y - 1/6 x z + + 2 2 3 3 3 2 2 2 2 2 + + 1/3 y x z + 1/4 x y - 1/12 y x + 1/6 y x + 3/4 y x z - 3/4 x z + + 3 2 2 2 2 2 + - 1/6 x + 1/2 x + 1/6 y x z - 1/4 z y x - 1/4 y x - 1/2 y x + + 2 2 2 2 2 2 2 2 + + 1/3 y x - 1/2 y x z - 1/2 y x z + 3/8 y x z - 1/4 y x z + + 2 2 3 2 3 + - 1/3 x z + 1/2 x z + 1/2 x z + 1/6 x y + 1/12 x y, COEFF(0, 0, 1) = + + 3 3 2 3 3 2 3 2 3 2 3 2 + 1 + 1/4 z y x - 3/8 z y x + 3/4 x y z + 3/8 x y z + 3/8 x y z + + 2 3 3 3 2 3 2 3 2 2 + - 1/2 x y z - 1/4 x y z - 3/4 x z - 1/2 x y z + 3/4 x y z + + 3 3 3 2 + - 1/4 x y z - 1/2 x - 1/4 x y + 1/2 x z - 1/2 y + z + 1/2 y x z + + 2 3 3 3 2 2 2 3 3 2 + - 1/2 x y + 1/4 y x + 1/4 y x - 3/2 y x z + 1/2 y z - 3/4 y z + + 2 2 2 2 3 3 2 2 2 + + 3/2 y z + 3/2 x z + 1/2 y + 1/2 x - y - 3/2 z - x + 1/4 y x z + + 2 2 2 2 2 2 2 + + 1/2 z y x - 1/2 y z + 1/2 y x + y x + 1/2 y x - 3/4 y x z + + 2 2 2 2 2 2 2 2 + + y x z - 3/4 y x z - 3/8 y x z + 3/4 y z - y z - 1/2 x z - x z + + 2 3 2 3 3 3 + + 3/4 x z - 1/2 x y - 1/4 x y, COEFF(1, 0, 1) = - 1/4 z y x + + 2 3 3 2 3 2 3 2 3 2 2 3 + + 3/8 z y x - 3/8 x y z - 3/4 x y z - 3/8 x y z + 1/4 x y z + + 3 3 2 3 2 3 2 2 3 + + 1/2 x y z + 3/4 x z + 1/2 x y z - 3/4 x y z + 1/4 x y z + x + + 3 3 2 2 3 3 3 + + 1/2 x y - 1/2 x z - y x z + 1/4 x y - 1/4 y x - 1/2 y x + + 2 2 2 2 2 3 2 2 + + 3/4 y x z - 3/4 x z - 1/2 x + 1/2 x - 1/2 y x z - 1/4 z y x + + 2 2 2 2 2 2 2 2 2 2 + - 1/4 y x - 1/2 y x - y x + 3/2 y x z - 1/2 y x z + 3/8 y x z + + 2 2 2 3 2 3 + + 3/4 y x z + x z + 1/2 x z - 3/2 x z + 1/2 x y + 1/4 x y, + + 3 2 3 3 2 2 + COEFF(2, 0, 1) = - 1/6 x + 1/8 x y z - 1/12 x y z + 1/4 x y z + + 3 3 2 3 3 3 2 2 + - 1/12 x y + 1/6 x - 1/8 z y x + 1/8 x y z + 1/12 y x z + 1/6 y x + + 3 2 3 3 3 2 3 + - 1/6 x y - 1/12 x y - 1/6 x z + 1/12 z y x + 1/6 y x z + 1/6 x z + + 2 3 2 3 3 2 2 + - 1/8 y x z - 1/6 x y z + 1/12 y x - 1/4 y x z + 1/12 y x + + 3 2 3 2 3 3 + - 1/12 x y z + 1/4 x z - 1/4 x z , COEFF(-1, 1, 1) = 1/12 z y x + + 2 3 3 2 3 2 3 2 3 2 2 3 + - 1/8 z y x + 3/8 x y z - 1/4 x y z + 1/4 x y z - 1/4 x y z + + 3 3 2 3 2 2 3 3 + + 1/6 x y z - 1/12 x y z + 1/8 x y z - 1/6 x y z + 1/6 x y + + 2 2 3 3 3 2 2 2 + - 1/6 y x z - 1/4 x y + 1/12 y x - 1/3 y x - 3/8 y x z - 1/3 y x z + + 2 2 2 2 2 2 2 2 2 + + 1/2 z y x + 1/2 y x + 1/4 y x - 1/6 y x + 1/4 y x z + 1/4 y x z + + 2 2 2 3 2 3 + - 3/4 y x z + 1/2 y x z - 1/12 x y - 1/6 x y, COEFF(0, 1, 1) = + + 3 3 2 3 3 2 3 2 3 2 3 2 + - 1/4 z y x + 3/8 z y x - 3/4 x y z - 3/8 x y z - 3/4 x y z + + 2 3 3 3 2 3 2 2 3 + + 1/2 x y z + 1/4 x y z + 1/4 x y z - 3/8 x y z + 1/2 x y z + + 3 2 2 3 3 3 + + 1/4 x y + y - 1/4 y x z + 1/2 x y - 1/4 y x - 1/2 y x + + 2 2 2 3 3 2 2 2 3 2 + + 3/4 y x z - 1/2 y z + 3/4 y z - 3/4 y z - 1/2 y + 1/2 y + + 2 2 2 2 2 2 2 + - 1/2 y x z - z y x + y z - y x - 1/2 y x - 1/4 y x + 3/8 y x z + + 2 2 2 2 2 2 2 3 2 + - 1/2 y x z + 3/2 y x z + 3/4 y x z - 3/2 y z + 1/2 y z + 1/4 x y + + 3 3 3 2 3 3 2 3 2 + + 1/2 x y, COEFF(1, 1, 1) = 1/4 z y x - 3/8 z y x + 3/8 x y z + + 3 2 3 2 2 3 3 3 2 + + 3/4 x y z + 3/4 x y z - 1/4 x y z - 1/2 x y z - 1/4 x y z + + 3 2 2 3 3 2 2 3 + + 3/8 x y z - 1/2 x y z - 1/2 x y + 1/2 y x z - 1/4 x y + + 3 3 2 2 2 2 2 + + 1/4 y x + y x - 3/8 y x z + y x z + 1/2 z y x + 1/2 y x + + 2 2 2 2 2 2 2 2 2 + + 1/4 y x + 1/2 y x - 3/4 y x z + 1/4 y x z - 3/4 y x z + + 2 3 2 3 3 2 2 + - 3/2 y x z - 1/4 x y - 1/2 x y, COEFF(2, 1, 1) = - 1/8 x y z + + 3 3 3 2 3 3 + - 1/6 y x - 1/12 z y x - 1/8 x y z + 1/12 x y z + 1/6 x y z + + 2 3 3 2 2 2 2 2 + + 1/8 z y x - 1/12 y x + 1/8 y x z - 1/12 y x z + 1/4 y x z + + 3 2 3 3 3 2 3 3 2 + - 1/4 x y z - 1/12 y x + 1/12 x y + 1/12 x y + 1/12 x y z + + 3 3 2 + - 1/6 y x z + 1/6 x y, COEFF(-1, 2, 1) = - 1/24 x y z + 1/18 y x + + 3 3 3 3 3 2 + + 1/36 x y z + 1/36 x y - 1/18 x y - 1/36 z y x - 1/12 y x z + + 3 3 2 3 3 3 2 3 + - 1/36 y x + 1/24 z y x - 1/18 x y z + 1/18 y x z + 1/12 x y z + + 3 2 2 2 2 2 3 2 3 2 + + 1/12 x y z - 1/12 y x + 1/8 y x z + 1/12 x y - 1/8 x y z + + 2 2 3 3 2 3 2 + - 1/12 z y x , COEFF(0, 2, 1) = - 1/6 x y z - 1/12 x y + 1/4 x y z + + 2 2 2 3 3 3 3 3 + - 1/4 y x z - 1/6 x y + 1/12 z y x - 1/12 x y z - 1/12 x y + + 3 3 2 3 2 2 + + 1/6 y + 1/8 x y z - 1/6 y z - 1/12 x y z - 1/8 y x z + 1/6 z y x + + 2 3 3 3 3 3 2 2 + - 1/8 z y x + 1/12 y x + 1/12 y x z - 1/6 y + 1/8 x y z + 1/4 y z + + 3 2 3 2 + + 1/12 y x + 1/6 y z + 1/6 y x - 1/4 y z , COEFF(1, 2, 1) = + + 2 3 2 3 2 2 3 3 + - 1/8 x y z + 1/6 x y - 1/6 y x + 1/4 y x z + 1/8 z y x + + 3 3 3 2 3 2 3 3 + + 1/6 x y z - 1/12 z y x + 1/12 x y z - 1/12 z y x - 1/12 y x + + 2 2 3 3 2 3 3 2 + + 1/8 y x z + 1/12 x y z + 1/12 x y + 1/12 x y - 1/4 x y z + + 2 3 2 + - 1/12 y x - 1/6 y x z - 1/8 x y z , COEFF(2, 2, 1) = 1/36 y x z + + 3 2 3 3 3 2 3 3 + - 1/36 x y - 1/24 z y x + 1/36 y x + 1/24 x y z + 1/36 y x + + 3 3 3 3 3 2 3 + + 1/36 z y x - 1/36 x y z - 1/36 x y + 1/24 x y z - 1/36 x y z + + 2 3 2 2 2 2 + - 1/24 y x z , COEFF(-1, -1, 2) = 1/36 x y z + 1/36 y x - 1/24 y x + + 3 2 3 2 2 2 3 + - 1/108 x y + 1/36 y x - 1/24 x y z + 1/18 y x z - 1/108 x y + + 2 2 2 2 3 3 3 3 3 2 + + 1/8 y x z + 1/72 z y x - 1/216 y x + 1/72 x y - 1/54 y x + + 2 2 3 2 2 2 2 3 2 2 3 + - 1/12 y x z + 1/36 x y z - 1/12 y x z - 1/24 x y z + 1/72 x y , + + 3 2 2 2 2 3 + COEFF(0, -1, 2) = 1/36 x y - 1/18 y x + 1/6 y x z - 1/36 x y + + 3 3 3 3 2 3 2 3 2 + + 1/72 y x + 1/36 y - 1/12 x y z - 1/12 y z - 1/24 x y + + 2 3 3 2 2 2 3 2 + - 1/24 z y x + 1/18 y - 1/12 y - 1/36 y x + 1/24 y x + 1/12 x y z + + 3 2 2 3 2 2 2 + - 1/72 x y + 1/12 y x + 1/24 x y z - 1/6 y z + 1/12 y x z + + 2 2 2 2 2 2 2 3 2 2 + + 1/4 y z - 1/4 y x z - 1/8 y x z + 1/8 x y z , COEFF(1, -1, 2) + + 2 3 2 3 2 2 2 3 2 + = - 1/24 x y z + 1/24 x y + 1/4 y x z + 1/12 x y z + 1/18 y x + + 3 2 2 2 2 2 2 2 3 2 2 + - 1/12 x y z + 1/8 y x z - 1/12 y x z - 1/12 y x - 1/8 x y z + + 3 3 3 3 2 2 + - 1/36 x y - 1/72 y x + 1/36 x y - 1/6 y x z + 1/36 y x + + 2 3 3 2 3 2 2 3 2 2 + + 1/24 z y x + 1/72 x y - 1/24 y x , COEFF(2, -1, 2) = 1/24 x y z + + 3 2 3 2 2 3 + - 1/36 x y z - 1/216 x y - 1/24 y x z + 1/108 x y - 1/108 y x + + 3 2 2 3 3 2 3 3 2 + + 1/72 x y z - 1/72 z y x + 1/72 y x + 1/216 y x + 1/36 y x z + + 3 2 2 3 3 2 2 + - 1/72 x y , COEFF(-1, 0, 2) = 1/12 y x z + 1/36 x + 1/12 x y z + + 2 2 3 3 2 2 2 3 2 + - 1/8 y x z - 1/72 x y - 1/36 x y - 1/12 x - 1/6 x z + 1/24 x y z + + 2 3 2 3 2 2 2 3 3 + + 1/8 x y z - 1/12 x y z + 1/4 x z - 1/36 y x + 1/72 y x + 1/18 x + + 3 2 2 3 2 2 2 2 2 2 + - 1/12 x z - 1/24 x y + 1/12 y x - 1/18 y x - 1/4 y x z + + 3 2 2 3 3 2 2 + + 1/36 x y + 1/24 y x - 1/24 z y x + 1/6 y x z , COEFF(0, 0, 2) = + + 2 3 3 2 3 2 3 2 3 2 3 2 + 1/8 z y x - 1/4 x y z - 1/8 x y z - 1/8 x y z + 1/4 x z + + 3 2 2 3 2 3 3 3 + - 1/4 x y z + 1/12 x + 1/24 x y + 1/12 y + 1/12 x y - 1/24 y x + + 2 2 2 3 2 2 2 2 2 3 + - 1/24 y x + 1/2 y x z + 1/4 y z - 1/2 y z - 1/2 x z - 1/12 y + + 3 2 2 2 2 2 2 + - 1/12 x - 1/6 + 1/6 y + 1/2 z + 1/6 x - 1/12 y x - 1/6 y x + + 2 2 2 2 2 2 2 2 + - 1/12 y x + 1/4 y x z + 1/4 y x z + 1/8 y x z - 1/4 y z - 1/4 x z + + 3 2 3 2 3 2 2 + + 1/12 x y + 1/24 x y, COEFF(1, 0, 2) = 1/2 x z + 1/4 x y z + + 2 3 2 2 3 2 2 2 2 3 + + 1/8 x y z - 1/24 x y + 1/12 y x + 1/24 y x - 1/12 x - 1/24 x y + + 3 2 3 3 3 2 2 2 2 3 2 + - 1/12 x y - 1/8 z y x - 1/4 x z - 1/4 y x z - 1/12 x y + + 2 2 3 2 3 3 2 2 + - 1/8 y x z + 1/12 y x + 1/4 x y z + 1/24 y x - 1/2 y x z + + 2 3 2 2 3 2 2 + - 1/4 y x z - 1/6 x + 1/8 x y z + 1/6 y x + 1/12 x + 1/4 x z , + + 3 3 2 3 3 2 2 + COEFF(2, 0, 2) = 1/36 x - 1/72 y x + 1/24 z y x + 1/12 y x z + + 3 2 2 3 2 3 2 3 2 + - 1/12 x y z + 1/12 x z + 1/36 x y - 1/72 y x - 1/24 x y z + + 3 2 3 2 3 2 3 + - 1/24 x y z - 1/36 x - 1/12 x z + 1/72 x y - 1/36 y x + 1/72 x y + + 2 2 2 2 2 3 3 3 + + 1/24 y x z , COEFF(-1, 1, 2) = 1/8 y x z + 1/24 z y x + 1/36 x y + + 3 2 2 2 3 3 2 2 3 2 + - 1/24 x y z + 1/36 y x - 1/36 x y + 1/12 x y z - 1/8 x y z + + 3 2 2 2 3 3 2 2 + + 1/18 y x - 1/12 x y z + 1/4 y x z - 1/72 y x - 1/24 y x + + 2 2 2 2 2 3 3 2 + - 1/12 y x - 1/12 y x z - 1/6 y x z + 1/24 x y + 1/72 x y , + + 2 2 2 3 2 2 2 + COEFF(0, 1, 2) = - 1/6 y - 1/4 y x z - 1/24 x y - 1/2 y x z + + 3 2 3 2 2 2 3 3 2 + + 1/12 y + 1/24 y x - 1/4 y z + 1/6 y x - 1/8 z y x + 1/2 y z + + 2 2 2 2 3 2 3 2 2 + - 1/12 y - 1/4 y x z + 1/4 y z + 1/8 x y z + 1/8 x y z + + 2 3 2 3 2 3 3 2 2 + + 1/4 x y z + 1/12 y x + 1/4 x y z + 1/24 y x + 1/12 y x + + 2 3 2 2 3 3 + - 1/12 x y - 1/8 y x z - 1/12 x y - 1/24 x y , COEFF(1, 1, 2) = + + 3 2 2 3 2 2 2 3 2 + - 1/4 x y z - 1/12 y x - 1/8 x y z - 1/12 y x + 1/24 x y + + 2 2 2 2 2 3 2 3 2 2 + + 1/4 y x z + 1/8 y x z - 1/4 x y z + 1/12 x y - 1/24 y x + + 2 2 2 3 2 3 3 2 + + 1/4 y x z - 1/6 y x - 1/8 x y z - 1/24 y x + 1/2 y x z + + 3 2 3 3 2 3 2 + + 1/12 x y + 1/8 z y x + 1/24 x y , COEFF(2, 1, 2) = 1/72 y x + + 2 3 3 3 2 2 2 3 2 3 + - 1/24 z y x + 1/12 x y z - 1/24 y x z + 1/24 x y z - 1/36 x y + + 2 3 2 2 3 3 2 + - 1/12 y x z + 1/24 x y z + 1/36 y x - 1/72 x y - 1/72 x y + + 3 3 3 2 2 3 2 + + 1/72 y x , COEFF(-1, 2, 2) = - 1/36 x y z + 1/24 x y z + + 2 3 3 3 3 2 2 + - 1/72 z y x - 1/216 x y + 1/108 x y + 1/72 y x + 1/36 y x z + + 3 2 2 3 3 3 2 2 + - 1/108 y x + 1/72 x y z - 1/72 x y + 1/216 y x - 1/24 y x z , + + 3 2 3 2 3 + COEFF(0, 2, 2) = 1/36 y - 1/24 x y z - 1/24 x y z + 1/72 x y + + 2 2 2 3 2 3 3 3 2 + + 1/12 y x z + 1/36 x y + 1/24 z y x - 1/72 y x + 1/12 y z + + 2 2 3 2 3 2 3 3 + - 1/36 y x + 1/24 y x z - 1/36 y - 1/12 x y z - 1/72 y x + + 2 3 3 3 2 3 + - 1/12 y z + 1/72 x y, COEFF(1, 2, 2) = 1/72 y x - 1/72 x y + + 3 2 2 3 2 2 3 3 3 + + 1/12 x y z + 1/24 x y z + 1/36 y x - 1/24 z y x - 1/36 x y + + 2 3 2 2 2 3 2 + + 1/72 y x - 1/72 x y - 1/12 y x z - 1/24 y x z + 1/24 x y z , + + 2 3 2 3 3 2 + COEFF(2, 2, 2) = 1/72 y x z - 1/72 x y z + 1/216 x y - 1/72 x y z + + 3 3 3 2 3 3 + - 1/216 y x + 1/216 x y + 1/72 z y x - 1/216 y x] + +> print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dz.compute.c"); +bytes used=6290409452, alloc=10549364, time=585.24 +bytes used=6291409856, alloc=10549364, time=585.34 +bytes used=6292410192, alloc=10549364, time=585.43 +bytes used=6293410580, alloc=10549364, time=585.52 +bytes used=6294410920, 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DATA(0, 0, 0) - 1/2 y z DATA(-1, 1, 0) + 1/2 x y DATA(2, 0, 0) + + 3 3 + - 1/2 x y DATA(-1, 0, 0) + 3/2 x y DATA(0, 0, 0) + + 3 3 + - 3/2 x y DATA(1, 0, 0) - 1/2 x y DATA(0, -1, 0) + + 3 + - 3/2 x y DATA(0, 1, 0) + +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=6705955472, alloc=10549364, time=661.57 +bytes used=6706975228, alloc=10549364, time=661.66 +bytes used=6707995840, alloc=10549364, time=661.75 +bytes used=6708996020, alloc=10549364, time=661.84 +bytes used=6709997576, alloc=10549364, time=661.93 +bytes used=6711067388, alloc=10549364, time=662.02 +bytes used=6712075184, alloc=10549364, time=662.12 +bytes used=6713083388, alloc=10549364, time=662.21 +bytes used=6714083792, alloc=10549364, time=662.31 +bytes used=6715088284, alloc=10549364, time=662.41 +bytes used=6716091252, alloc=10549364, time=662.51 +bytes used=6717126688, alloc=10549364, time=662.59 +bytes used=6718151884, alloc=10549364, time=662.66 + 2 2 3 3 3 2 3 +[COEFF(-1, -1, -1) = 1/4 y z + 1/36 z y + 1/9 y z + 1/18 y z - 1/12 y z + + 2 2 3 2 3 3 + - 1/6 y z - 1/6 y z + 1/12 x y z - 1/18 y x z - 1/18 x y z + + 2 3 2 2 3 2 + + 1/12 y x z + 1/6 y x z - 1/9 y x z + 1/6 y x z - 1/12 y z + + 2 2 3 3 3 3 3 + - 1/4 y x z + 1/18 y z - 1/36 z y x, COEFF(0, -1, -1) = 1/12 z y x + + 3 2 2 3 3 2 2 2 + - 1/4 x y z + 1/6 y z - 1/9 y z + 3/4 y x z - 1/2 y x z + + 3 3 3 2 3 2 2 2 + + 1/6 x y z - 1/18 z y - 1/4 y x z - 1/2 y x z - 1/2 y z + + 2 3 3 2 2 + + 1/3 y z + 1/6 y x z - 2/9 y z + 1/3 y x z + 1/6 y z + 1/3 y z + + 3 2 3 3 + - 1/9 y z, COEFF(1, -1, -1) = 1/4 y x z - 1/6 x y z + 1/9 y z + + 3 2 3 3 2 3 2 + - 1/6 y x z + 1/2 y x z + 1/36 z y - 1/12 y z - 1/6 y z + + 3 2 2 2 3 2 + + 1/4 x y z - 3/4 y x z - 1/3 y x z + 1/18 y z + 1/2 y x z + + 2 2 3 3 2 3 3 2 + + 1/4 y z - 1/12 z y x - 1/6 y z + 1/18 y z - 1/12 y z , + + 3 2 2 3 2 + COEFF(2, -1, -1) = 1/18 x y z - 1/6 y x z - 1/12 y x z - 1/6 y x z + + 2 2 3 2 3 3 3 + + 1/4 y x z - 1/12 x y z + 1/18 y x z + 1/9 y x z + 1/36 z y x, + + 3 3 3 2 2 3 + COEFF(-1, 0, -1) = - 1/3 z + 1/12 z y x - 1/4 x y z - 1/6 y x z + + 3 2 2 2 2 2 2 + + 1/6 x y z - 1/2 y z - 1/2 x z + 1/2 y x z - 1/3 y x z + + 3 2 3 3 2 2 + - 1/12 y x z - 1/6 y x z + 1/6 y z + 1/4 y z + 1/6 y z + 1/3 y z + + 3 3 3 2 2 3 3 + - 1/6 y z - 1/12 z y - 1/4 y z + 1/4 y x z + 1/6 x z + 1/12 y z + + 2 3 3 2 + + 1/2 z - 1/6 z + 1/3 x z, COEFF(0, 0, -1) = - 1/3 y z - 1/2 y z + + 2 2 2 3 2 + - 3/2 y x z + 3/2 x z + 1/2 y x z + 1/4 y x z + y x z + 2/3 z + + 3 2 2 3 3 3 3 3 + - 1/6 y z - 2/3 y z - 1/3 y z + 1/6 z y - x z - 1/4 z y x + + 3 2 3 3 3 2 + - 1/2 x z - 3/4 y x z + 1/3 y z - 1/2 x y z + 1/3 z - z + + 3 2 2 2 2 2 3 + + 3/4 x y z + 1/2 y z + y z + 1/2 y x z , COEFF(1, 0, -1) = + + 3 3 2 3 2 2 2 2 + - 1/12 z y - 1/2 y x z + 3/4 y x z + x z + 3/2 y x z - y x z + + 3 2 2 2 3 2 3 3 2 + + 1/2 x z - 1/2 y z - 1/4 y z + 1/12 y z + 1/6 y z + 1/4 y z + + 2 3 3 2 + - 3/2 x z - 1/3 z - 1/4 y x z + 1/6 y z - 3/4 x y z - 1/2 y x z + + 3 2 3 3 3 3 2 + - 1/6 y z + 1/2 z + 1/4 z y x + 1/2 x y z - 1/6 z + 1/3 y z, + + 3 3 2 3 2 + COEFF(2, 0, -1) = 1/12 y x z - 1/6 x z + 1/2 x z + 1/4 x y z + + 2 3 2 2 3 3 + + 1/6 y x z - 1/4 y x z - 1/3 x z + 1/3 y x z - 1/12 z y x + + 3 2 2 + + 1/6 y x z - 1/6 x y z - 1/2 y x z , COEFF(-1, 1, -1) = 1/3 y x z + + 2 3 2 2 2 2 3 3 + + 1/12 y x z + 1/6 y x z + 1/4 y z - 1/2 y x z + 1/12 z y + + 3 3 2 2 3 3 2 2 + - 1/6 x y z + 1/4 x y z - 1/3 y z - 1/12 y z - 1/4 y z - 1/6 y z + + 3 3 3 2 2 2 3 3 + - 1/6 y z + 1/6 y x z + 1/6 y z + 1/2 y z - 1/4 y x z - 1/12 z y x + + 3 3 3 2 2 + , COEFF(0, 1, -1) = 1/2 x y z - 1/6 z y + 1/3 y z - 1/2 y x z + + 2 3 2 2 2 3 2 2 3 2 + - 1/4 y x z - y z - 1/2 y z + 1/2 y z + 3/2 y x z - 3/4 x y z + + 2 2 3 2 3 3 + + 3/4 y x z + 1/3 y z + 1/6 y z - 1/3 y z - y x z + 2/3 y z + + 3 3 3 2 2 3 + + 1/4 z y x - 1/2 y x z , COEFF(1, 1, -1) = - 3/4 y x z + 1/6 y z + + 3 2 3 2 3 3 2 + + 3/4 x y z + 1/2 y x z - 3/2 y x z - 1/4 z y x + y x z - 1/6 y z + + 2 2 2 2 3 3 2 3 3 + + 1/2 y x z - 1/3 y z + 1/4 y z - 1/12 y z - 1/4 y z + 1/12 z y + + 2 3 3 2 3 + + 1/4 y x z - 1/2 x y z + 1/2 y z - 1/6 y z , COEFF(2, 1, -1) = + + 3 2 2 3 3 3 3 + 1/6 x y z - 1/6 y x z - 1/12 y x z - 1/6 y x z + 1/12 z y x + + 2 2 2 3 2 + + 1/4 y x z + 1/2 y x z - 1/4 x y z - 1/3 y x z, COEFF(-1, 2, -1) = + + 3 3 3 2 3 2 + - 1/18 y z + 1/36 y z + 1/18 x y z + 1/12 y x z - 1/12 x y z + + 3 2 3 3 3 3 + + 1/12 y z + 1/36 z y x - 1/18 y x z - 1/36 z y + 1/18 y z + + 3 2 3 2 3 3 + - 1/36 y x z - 1/12 y z , COEFF(0, 2, -1) = 1/4 x y z + 1/18 z y + + 2 3 3 3 + - 1/4 y x z + 1/6 y x z - 1/18 y z + 1/12 y x z - 1/6 x y z + + 3 3 3 2 3 2 + - 1/12 z y x - 1/9 y z + 1/9 y z + 1/6 y z - 1/6 y z , + + 2 3 2 3 3 + COEFF(1, 2, -1) = - 1/12 y z + 1/18 y z - 1/4 x y z - 1/36 z y + + 2 3 3 3 3 + + 1/4 y x z - 1/18 y z - 1/6 y x z + 1/6 x y z + 1/12 z y x + + 3 3 2 3 + + 1/36 y z + 1/12 y z - 1/12 y x z , COEFF(2, 2, -1) = 1/18 y x z + + 2 3 3 3 2 3 3 + - 1/12 y x z + 1/36 y x z - 1/18 x y z + 1/12 x y z - 1/36 z y x, + + 2 2 2 2 3 2 + COEFF(-1, -1, 0) = 1/2 y x z - 1/2 y x + 1/4 y z + 1/3 y x - 1/4 y z + + 2 3 3 3 2 3 2 2 + - 1/3 y x z - 1/6 y z + 1/12 z y x - 1/4 y x z - 1/2 y z + 1/6 y z + + 2 3 3 2 3 2 3 + + 1/4 y x z + 1/6 y x z + 1/6 y z - 1/6 x y z + 1/12 y z + + 3 3 3 3 2 2 3 + - 1/12 z y - 1/6 y + 1/6 x y + 1/3 y z + 1/2 y - 1/12 x y z - 1/3 y + + 3 3 2 3 + - 1/6 y x z, COEFF(0, -1, 0) = - 1/2 x y + 1/4 x y z - 1/2 y z + + 2 3 2 2 2 2 2 + - 1/3 y z + 3/4 y x z - y + y z + 2/3 y - 2/3 y z + 1/2 y z + + 2 3 3 3 2 3 + + y x z + 1/3 y + 1/6 z y + 3/2 y x - y x + 1/2 y x z - 1/6 y z + + 3 3 3 2 2 2 3 3 + - 1/4 z y x - 1/3 y z - 3/2 y x z - 1/2 y x z + 1/3 y z + + 3 2 2 3 2 + + 1/2 x y z - 3/4 y x z, COEFF(1, -1, 0) = 1/2 y x z - y x z + y x + + 2 3 3 2 2 3 3 3 + + 1/3 y z - 1/4 x y z - 1/6 y + 3/2 y x z + 1/4 z y x - 1/6 y z + + 3 2 3 2 2 3 2 + - 1/2 x y z + 1/2 x y - 1/4 y z + 1/4 y z + 1/6 y z - 3/2 y x + + 2 3 2 3 2 2 3 2 + - 3/4 y x z + 1/2 y - 1/3 y + 1/12 y z - 1/2 y z + 1/6 y z + + 3 3 2 2 3 + - 1/12 z y + 3/4 y x z - 1/2 y x z, COEFF(2, -1, 0) = 1/4 y x z + + 3 2 2 3 + + 1/6 y x z + 1/12 x y z - 1/4 y x z + 1/2 y x - 1/6 y x z - 1/3 y x + + 3 2 3 3 2 3 2 2 + + 1/6 x y z - 1/12 z y x + 1/3 y x z - 1/6 x y - 1/2 y x z , + + 3 3 2 3 3 3 + COEFF(-1, 0, 0) = 1 - 1/4 y z + 1/2 x y z - 1/4 z y x + 1/4 y x z + + 2 3 3 2 3 3 3 3 + + 1/2 y x z + 1/4 x y z - x - 1/2 y z + 1/4 z y - 1/2 x y - 1/2 y + + 2 3 3 2 2 2 3 + - 1/2 z - 1/2 y x z + 1/2 y x - 1/4 y z - 1/2 y z + y z + 1/2 z + + 3 2 2 3 2 2 2 + + 1/2 y - y - z - 1/2 x z - 1/4 y x z + 1/4 y z + y x - y x z + + 2 2 2 2 + - 1/2 y x z + 1/2 y z + 1/2 y z + 1/2 x z + x z , COEFF(0, 0, 0) = -2 + + 3 3 2 3 3 3 2 3 + + 1/2 y z - 3/2 x y z + 3/4 z y x - 3/4 y x z - 3/2 y x z + + 3 2 3 3 3 3 2 + - 3/4 x y z + 3 x + y z - 1/2 z y + 3/2 x y + y + z + 3/2 y x z + + 3 3 2 2 2 3 3 2 2 3 + - 3/2 y x + 1/2 y z + y z - 2 y z - z - y + 2 y + 2 z + 3/2 x z + + 2 2 2 2 2 2 + + 3/4 y x z - 1/2 y z - 3 y x + 3 y x z + 3/2 y x z - y z - y z + + 2 3 3 2 + - 3/2 x z - 3 x z , COEFF(1, 0, 0) = 1 - 1/4 y z + 3/2 x y z + + 3 3 3 2 3 3 2 3 + - 3/4 z y x + 3/4 y x z + 3/2 y x z + 3/4 x y z - 3 x - 1/2 y z + + 3 3 3 2 3 + + 1/4 z y - 3/2 x y - 1/2 y - 1/2 z - 3/2 y x z + 3/2 y x - 1/4 y z + + 3 2 2 2 3 3 2 2 3 + - 1/2 y z + y z + 1/2 z + 1/2 y - y - z - 3/2 x z - 3/4 y x z + + 2 2 2 2 2 2 + + 1/4 y z + 3 y x - 3 y x z - 3/2 y x z + 1/2 y z + 1/2 y z + + 2 2 2 3 3 + + 3/2 x z + 3 x z , COEFF(2, 0, 0) = y x z + 1/2 x z + 1/2 x y + + 2 2 3 2 3 3 2 + + 1/2 y x z - 1/2 y x z + 1/4 y x z - x z + 1/4 z y x + 1/2 y x z + + 2 3 2 3 3 + - y x - 1/2 y x - 1/2 x y z - 1/2 x z - 1/4 x y z + x - 1/4 y x z , + + 2 3 2 3 + COEFF(-1, 1, 0) = y x z + 1/2 y x z - 1/2 y - 1/2 y x + 1/4 y z + + 3 2 2 3 2 2 2 3 3 + + 1/2 y z - y z - 1/4 x y z - 1/2 y z + 1/4 y z + 1/2 y z - y x + + 2 2 2 3 2 3 3 3 3 + + 1/2 y + 1/2 y x z - 1/2 x y z + 1/4 z y x - 1/2 y z - 1/4 z y + + 3 2 2 3 2 3 + - 1/2 y x z - 1/4 y z + 1/4 y x z + y + 1/2 x y - 1/4 y x z , + + 3 3 3 3 2 2 2 3 + COEFF(0, 1, 0) = -y z - 3/4 z y x - y z + 2 y z - y + y - 3/2 y x z + + 2 2 3 2 3 3 + - 3/2 y x z + 3/2 y x z - 2 y + 3 y x - 1/2 y z - 1/2 y z + + 3 3 2 2 3 3 3 2 2 + + 3/4 x y z + 3/2 x y z + 3/4 y x z + 1/2 z y + y z + y z + + 2 2 2 2 3 + + 3/2 y x + 1/2 y z - 3 y x z - 3/4 y x z - 3/2 x y , COEFF(1, 1, 0) + + 3 3 3 3 2 3 3 3 2 2 + = - 1/4 z y + 1/2 y z - 1/2 y + 1/4 y z + 3/4 z y x - 1/2 y z + + 2 3 2 2 3 2 2 + - 3/4 y x z - 1/4 y z - 3/2 y x + 1/2 y z + 3/2 y x z - y z + + 3 2 2 2 3 3 2 + - 3/2 x y z + 3/2 y x z - 3 y x - 3/4 x y z - 3/2 y x z + 1/2 y + + 3 2 2 3 + + 1/4 y z + 3/4 y x z + y - 1/2 y z + 3 y x z + 3/2 x y , + + 3 2 3 2 2 + COEFF(2, 1, 0) = 1/4 x y z + 1/4 y x z + 1/2 y x - 1/4 y x z + + 3 3 3 2 2 3 2 3 2 + - 1/4 z y x + 1/2 y x z - 1/2 y x z - 1/2 x y - y x z + 1/2 x y z + + 3 3 3 + + y x - 1/2 y x z, COEFF(-1, 2, 0) = - 1/12 z y x + 1/12 x y z + + 3 3 3 2 + + 1/12 z y + 1/12 y x z + 1/6 y x - 1/12 y x z - 1/6 y x z + + 3 2 3 2 3 3 2 + + 1/6 x y z - 1/6 y z + 1/6 y + 1/12 y z - 1/12 y z + 1/6 y z + + 3 3 3 3 + - 1/6 y - 1/6 x y - 1/12 y z , COEFF(0, 2, 0) = 1/3 y - 1/3 y + 1/6 y z + + 3 3 3 2 2 3 + - 1/4 x y z - 1/2 y x - 1/4 y x z - 1/2 x y z - 1/3 y z + 1/6 y z + + 3 3 3 3 3 3 2 + - 1/6 z y + 1/4 y x z - 1/6 y z + 1/2 x y + 1/4 z y x + 1/3 y z + + 2 3 2 3 2 + + 1/2 y x z , COEFF(1, 2, 0) = 1/4 x y z + 1/6 y z - 1/6 y z + + 3 2 3 3 + + 1/12 y z + 1/2 x y z + 1/4 y x z + 1/2 y x - 1/4 y x z - 1/12 y z + + 2 3 3 3 3 3 + - 1/2 y x z - 1/6 y - 1/12 y z - 1/2 x y + 1/6 y + 1/12 z y + + 3 3 3 3 3 3 + - 1/4 z y x, COEFF(2, 2, 0) = 1/12 z y x - 1/12 x y z - 1/12 y x z + + 3 2 3 2 + + 1/12 y x z - 1/6 x y z - 1/6 y x + 1/6 x y + 1/6 y x z , + + 2 2 2 2 3 3 2 + COEFF(-1, -1, 1) = 1/4 y z + 1/2 y z - 1/3 y z - 1/4 y z - 1/12 y z + + 3 3 3 3 3 2 + + 1/12 z y + 1/3 y x z - 1/6 y x z + 1/6 x y z + 1/12 x y z + + 2 3 2 2 2 3 3 2 + + 1/4 y x z - 1/2 y x z - 1/4 y x z - 1/12 z y x + 1/6 y x z + + 3 3 2 2 2 + - 1/6 y z + 1/6 y z - 1/6 y z , COEFF(0, -1, 1) = - 1/2 y z + + 2 3 2 2 3 3 2 3 + - 1/2 y x z - 1/4 x y z - y z - 1/2 x y z + 1/2 y x z + 1/2 y z + + 2 3 3 3 3 3 2 2 + + 3/2 y x z + 1/4 z y x - y x z - 1/3 y z - 1/6 z y + 3/4 y x z + + 3 2 2 3 2 3 + + 1/6 y z + 1/3 y z + 1/3 y z + 2/3 y z - 3/4 y x z , COEFF(1, -1, 1) + + 3 3 2 2 3 3 2 3 + = 1/12 z y + 1/4 y z + 1/2 x y z - 1/2 y x z - 3/2 y x z - 1/6 y z + + 3 2 3 3 3 2 + - 1/3 y z + 1/6 y z + y x z - 1/4 y z - 1/4 z y x + 1/2 y z + + 2 2 2 3 2 3 2 2 3 + + 1/2 y x z - 3/4 y x z + 1/4 x y z - 1/12 y z + 3/4 y x z + + 2 3 3 3 2 + - 1/6 y z , COEFF(2, -1, 1) = 1/12 z y x + 1/6 y x z + 1/2 y x z + + 2 3 3 2 2 2 3 + - 1/4 y x z - 1/12 x y z - 1/3 y x z + 1/4 y x z - 1/6 x y z + + 2 3 2 2 + - 1/6 y x z , COEFF(-1, 0, 1) = - 1/4 x y z - 1/2 y z - x z - 1/4 y z + + 3 2 3 2 3 3 2 2 + + 1/4 y z + 1/4 y x z - 1/2 z + 1/2 y z + z + 1/4 y z - 1/2 x z + + 3 3 3 2 2 2 3 + + 1/4 z y x + 1/2 x z - y z + 1/2 y x z - 1/2 x y z + 1/2 y x z + + 2 2 2 3 2 3 2 3 + - 1/2 y z + y x z + 1/2 y z + 1/2 z - 1/4 y x z - 1/2 y x z + + 3 3 3 2 3 2 2 2 2 + - 1/4 z y , COEFF(0, 0, 1) = z + 3/2 x z - 1/2 y z - 3/2 y x z - z + + 3 2 3 2 3 3 3 + + 3/4 x y z + 3/4 y x z - 3/2 y x z + 1/2 y z + 1/2 z y - y z + + 3 2 2 3 2 2 2 3 2 + + 3 x z + 3/2 x y z - 3 y x z + 3/2 y x z + y z - y z + 2 y z + + 3 3 2 3 3 + - 3/2 x z + y z - 2 z - 1/2 y z - 3/4 y x z - 3/4 z y x, + + 3 3 3 2 2 2 + COEFF(1, 0, 1) = 3/4 z y x + 1/4 y z - 1/4 y z - 3/2 x z + 3/2 y x z + + 2 2 2 2 3 2 2 3 2 + + 3/4 y x z + 3/2 y x z + 1/2 y z - 1/2 y z - 3/4 y x z + 1/2 z + + 3 3 3 3 2 2 3 2 + + 1/4 y z - 1/2 z - 1/4 z y - y z + 3 y x z - 3/4 x y z - 3 x z + + 2 3 3 3 3 + - 3/2 y x z - 3/2 x y z + 3/2 x z + z + 1/2 y z - 1/2 y z, + + 2 3 3 2 3 + COEFF(2, 0, 1) = 1/2 x z + 1/4 y x z - 1/2 x z - 1/4 y x z + 1/2 x y z + + 2 3 2 2 2 3 3 + - y x z + 1/4 x y z - 1/2 y x z - 1/2 y x z - 1/4 z y x + x z + + 2 3 3 3 3 2 + + 1/2 y x z , COEFF(-1, 1, 1) = - 1/4 z y x + 1/2 x y z + 1/2 y z + + 3 3 2 3 3 3 3 + - y x z + 1/4 z y + 1/4 y x z + 1/2 y x z - 1/2 y z - 1/2 y z + + 2 3 2 2 2 3 2 + - 1/4 y z + 1/2 y z - 1/2 y x z - 1/2 y x z + 1/4 x y z + y z + + 3 2 2 2 2 2 + - 1/4 y z + 1/4 y z - 1/4 y x z , COEFF(0, 1, 1) = 3 y x z + + 3 3 2 2 3 3 3 3 3 + - 3/2 y x z + y z - 1/2 y z - 1/2 z y + 3/4 z y x - 3/2 x y z + + 2 2 2 2 3 2 3 2 + + 3/4 y x z - 2 y z + 3/2 y x z - y z - 3/4 x y z + y z - y z + + 3 2 2 2 3 2 3 + + 1/2 y z + 3/2 y x z + 1/2 y z - 3/4 y x z , COEFF(1, 1, 1) = y z + + 3 3 2 3 3 2 2 3 2 + + 3/2 x y z - 1/2 y z + 1/2 y z + 1/4 z y - 3/4 y x z - 1/4 y z + + 2 2 2 3 3 2 3 + + 1/4 y z - 3/2 y x z - 3 y x z - 3/4 z y x + 3/4 y x z + + 2 3 2 3 2 2 3 3 + - 3/2 y x z + 3/4 x y z + 3/2 y x z + 1/2 y z - 1/4 y z - 1/2 y z , + + 3 3 3 2 3 2 3 + COEFF(2, 1, 1) = 1/4 z y x - 1/4 x y z - 1/2 x y z - 1/4 y x z + + 3 2 2 2 2 + - 1/2 y x z + 1/2 y x z + 1/2 y x z + 1/4 y x z + y x z, + + 2 3 3 3 3 + COEFF(-1, 2, 1) = - 1/12 y z - 1/6 x y z + 1/12 y z - 1/12 z y + + 3 2 3 3 3 2 3 + - 1/12 x y z - 1/12 y x z + 1/12 z y x + 1/12 y x z + 1/6 y z + + 3 2 3 + + 1/6 y x z + 1/12 y z - 1/6 y z, COEFF(0, 2, 1) = - 1/6 y z + + 3 3 2 3 2 2 3 3 + + 1/2 x y z + 1/4 x y z - 1/6 y z - 1/4 y x z + 1/3 y z + 1/6 z y + + 2 3 3 3 3 + - 1/2 y x z + 1/6 y z - 1/3 y z + 1/4 y x z - 1/4 z y x, + + 2 3 3 3 3 + COEFF(1, 2, 1) = 1/4 y x z + 1/4 z y x - 1/6 y z - 1/12 z y + + 3 3 2 3 3 3 + - 1/2 x y z + 1/12 y z - 1/4 y x z + 1/6 y z + 1/12 y z + + 3 2 2 3 3 + - 1/4 x y z - 1/12 y z + 1/2 y x z, COEFF(2, 2, 1) = - 1/12 z y x + + 3 3 2 2 3 + - 1/6 y x z + 1/6 x y z + 1/12 x y z - 1/12 y x z + 1/12 y x z , + + 3 3 3 2 3 3 + COEFF(-1, -1, 2) = 1/36 z y x + 1/18 y x z - 1/12 y z - 1/36 z y + + 3 2 3 2 3 + + 1/36 y z + 1/12 y z - 1/18 y x z + 1/12 y x z - 1/18 y z + + 3 2 3 2 3 + - 1/36 x y z - 1/12 y x z + 1/18 y z, COEFF(0, -1, 2) = - 1/6 y z + + 2 3 3 3 3 2 + + 1/6 y z - 1/12 z y x + 1/9 y z - 1/6 y x z - 1/9 y z - 1/4 y x z + + 2 3 3 3 3 3 + + 1/4 y x z + 1/12 x y z + 1/6 y x z + 1/18 z y - 1/18 y z, + + 2 3 3 3 + COEFF(1, -1, 2) = - 1/4 y x z + 1/12 z y x - 1/6 y x z + 1/18 y z + + 2 2 3 3 3 3 + + 1/4 y x z + 1/12 y z + 1/36 y z - 1/12 x y z + 1/6 y x z + + 3 2 3 3 2 + - 1/18 y z - 1/12 y z - 1/36 z y , COEFF(2, -1, 2) = - 1/12 y x z + + 3 3 3 2 3 3 + + 1/18 y x z - 1/36 z y x + 1/36 x y z + 1/12 y x z - 1/18 y x z , + + 3 3 2 3 + COEFF(-1, 0, 2) = - 1/12 y x z + 1/6 x z + 1/12 z y - 1/6 y z + + 2 3 3 3 3 + - 1/6 y x z + 1/12 y x z + 1/12 y z + 1/6 z - 1/12 y z - 1/6 x z + + 2 3 3 2 3 3 3 + + 1/6 y x z + 1/12 x y z + 1/6 y z - 1/12 z y x - 1/6 z - 1/12 y z, + + 3 3 3 3 3 3 + COEFF(0, 0, 2) = 1/4 z y x - 1/4 x y z + 1/6 y z - 1/6 z y - 1/2 x z + + 2 2 3 3 3 + + 1/4 y x z - 1/6 y z + 1/2 y x z - 1/2 y x z + 1/2 x z - 1/4 y x z + + 2 3 3 2 3 + + 1/3 z - 1/3 y z - 1/3 z + 1/6 y z + 1/3 y z , COEFF(1, 0, 2) = + + 2 3 3 3 3 2 + 1/2 x z - 1/2 y x z - 1/2 x z + 1/6 z - 1/4 z y x + 1/6 y z + + 3 2 3 2 3 3 + + 1/4 x y z - 1/6 y z + 1/12 y z + 1/2 y x z - 1/12 y z - 1/6 z + + 3 3 3 3 + + 1/12 z y + 1/4 y x z - 1/4 y x z - 1/12 y z, COEFF(2, 0, 2) = + + 3 3 3 2 3 + 1/6 x z + 1/12 z y x + 1/6 y x z - 1/6 x z + 1/12 y x z - 1/12 y x z + + 3 2 3 3 + - 1/12 x y z - 1/6 y x z , COEFF(-1, 1, 2) = - 1/12 x y z + + 2 3 3 3 3 2 + - 1/12 y x z - 1/12 z y - 1/6 y x z + 1/12 y x z - 1/6 y z + + 3 2 3 2 3 3 3 + + 1/6 y z + 1/12 y z - 1/12 y z + 1/12 z y x + 1/12 y z + 1/6 y x z + + 3 3 2 3 3 3 + , COEFF(0, 1, 2) = 1/6 z y + 1/4 y x z + 1/4 x y z + 1/2 y x z + + 3 3 3 2 3 2 + - 1/4 z y x - 1/3 y z - 1/2 y x z + 1/6 y z - 1/6 y z - 1/4 y x z + + 2 3 3 3 3 + + 1/3 y z - 1/6 y z , COEFF(1, 1, 2) = - 1/12 z y - 1/2 y x z + + 3 3 3 3 2 + - 1/4 x y z + 1/6 y z - 1/6 y z + 1/4 z y x - 1/12 y z + 1/2 y x z + + 3 2 3 2 2 3 + + 1/12 y z + 1/12 y z + 1/4 y x z - 1/4 y x z , COEFF(2, 1, 2) = + + 3 2 3 2 3 + 1/6 y x z - 1/6 y x z + 1/12 y x z - 1/12 y x z + 1/12 x y z + + 3 3 3 3 + - 1/12 z y x, COEFF(-1, 2, 2) = - 1/36 y x z + 1/36 x y z - 1/36 y z + + 3 3 3 3 3 3 + + 1/36 y z + 1/36 y x z - 1/36 y z - 1/36 z y x + 1/36 z y , + + 3 3 3 + COEFF(0, 2, 2) = - 1/18 y z - 1/12 x y z + 1/12 y x z - 1/18 z y + + 3 3 3 3 3 + + 1/18 y z + 1/18 y z - 1/12 y x z + 1/12 z y x, COEFF(1, 2, 2) = + + 3 3 3 3 3 + 1/36 z y + 1/12 x y z - 1/36 y z + 1/36 y z + 1/12 y x z - 1/12 y x z + + 3 3 3 + - 1/36 y z - 1/12 z y x, + + 3 3 3 3 + COEFF(2, 2, 2) = 1/36 z y x - 1/36 y x z - 1/36 x y z + 1/36 y x z] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxx.compute.c"); +bytes used=6719152144, alloc=10549364, time=662.74 +bytes used=6720152796, alloc=10549364, time=662.81 +bytes used=6721153304, alloc=10549364, time=662.90 +bytes used=6722153476, alloc=10549364, time=662.99 +bytes used=6723153992, alloc=10549364, time=663.06 +bytes used=6724154200, alloc=10549364, time=663.17 +bytes used=6725154492, alloc=10549364, time=663.26 +bytes used=6726154664, alloc=10549364, time=663.37 +bytes used=6727154964, alloc=10549364, time=663.46 +bytes used=6728155144, alloc=10549364, time=663.55 +bytes used=6729170236, 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alloc=10549364, time=692.21 +bytes used=6883034404, alloc=10549364, time=692.41 +bytes used=6884034624, alloc=10549364, time=692.52 +bytes used=6885034892, alloc=10549364, time=692.63 +bytes used=6886035180, alloc=10549364, time=692.74 +bytes used=6887035384, alloc=10549364, time=692.84 +bytes used=6888035632, alloc=10549364, time=695.58 +bytes used=6889035816, alloc=10549364, time=696.66 +bytes used=6890036252, alloc=10549364, time=696.87 +bytes used=6891036440, alloc=10549364, time=696.95 +bytes used=6892036616, alloc=10549364, time=697.03 +bytes used=6893036988, alloc=10549364, time=697.11 +bytes used=6894037392, alloc=10549364, time=697.18 +bytes used=6895037628, alloc=10549364, time=697.26 +bytes used=6896037820, alloc=10549364, time=697.34 +bytes used=6897038052, alloc=10549364, time=697.47 +bytes used=6898039372, alloc=10549364, time=697.67 +bytes used=6899039560, alloc=10549364, time=697.88 +bytes used=6900039844, alloc=10549364, time=697.99 +bytes used=6901040068, alloc=10549364, time=698.10 +bytes used=6902040240, alloc=10549364, time=698.21 +bytes used=6903040520, alloc=10549364, time=698.32 +bytes used=6904040748, alloc=10549364, time=701.16 +bytes used=6905040976, alloc=10549364, time=702.21 +bytes used=6906041184, alloc=10549364, time=702.54 +bytes used=6907041908, alloc=10549364, time=702.69 +bytes used=6908042184, alloc=10549364, time=702.75 +bytes used=6909042520, alloc=10549364, time=702.93 +bytes used=6910042740, alloc=10549364, time=703.13 +> +# d^2/dxdy +> simplify( diff(interp_3d_cube_order3_smooth0,x,y) ); +bytes used=6911043220, alloc=10549364, time=703.23 +bytes used=6912043528, alloc=10549364, time=703.31 +bytes used=6913043764, alloc=10549364, time=703.38 +bytes used=6914044252, alloc=10549364, time=703.46 +bytes used=6915044432, alloc=10549364, time=703.55 +bytes used=6916044956, alloc=10549364, time=703.63 +bytes used=6917045124, alloc=10549364, time=703.71 +bytes used=6918045532, alloc=10549364, time=703.80 +bytes 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DATA(0, -1, 2) + + 2 2 + - 1/6 y DATA(-1, 2, 0) - 1/2 z y x DATA(0, 1, -1) + + 2 + - z y x DATA(1, 0, -1) - 1/3 x z DATA(1, 1, -1) + + 2 2 + - 1/6 y z DATA(-1, 1, -1) + 1/4 z y x DATA(1, 1, 2) + + 2 + + 1/6 z y x DATA(2, 0, 2) - 1/2 x z DATA(-1, 1, 0) + + 2 + + 1/2 y z DATA(1, -1, -1) - 1/3 x z DATA(-1, 1, -1) + x z DATA(-1, 1, 1) + + 2 + - 1/3 x z DATA(1, -1, 1) + 1/2 y z DATA(1, 1, -1) + + 2 2 + + 1/2 y z DATA(1, -1, 1) - 1/6 y z DATA(-1, 1, 1) + + - 1/3 x z DATA(-1, -1, 1) - 1/6 y z DATA(0, 0, 2) + 1/3 y z DATA(1, 0, 2) + + - 1/9 y z DATA(-1, 0, 2) + 1/6 y z DATA(-1, 1, 0) - 1/2 x z DATA(1, 1, 0) + + + x z DATA(0, 1, 0) + 2/3 x z DATA(0, -1, 1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=6927072480, alloc=10549364, time=704.59 +bytes used=6928253132, alloc=10549364, time=704.69 +bytes used=6929253320, alloc=10549364, time=704.77 +bytes used=6930300056, alloc=10549364, time=704.86 +bytes used=6931438456, alloc=10549364, time=704.96 +bytes used=6932521968, alloc=10549364, time=705.06 +bytes used=6933548588, alloc=10549364, time=705.16 +bytes used=6934552708, alloc=10549364, time=705.26 +bytes used=6935561000, alloc=10549364, time=705.36 +bytes used=6936571944, alloc=10549364, time=705.47 +bytes used=6937572872, alloc=10549364, time=705.58 +bytes used=6938606752, alloc=10549364, time=705.69 +bytes used=6939618396, alloc=10549364, time=705.80 +bytes used=6940627312, alloc=10549364, time=705.87 +bytes used=6941628656, alloc=10549364, time=705.93 +bytes used=6942629704, alloc=10549364, time=705.99 + 3 3 2 3 2 3 +[COEFF(-1, -1, -1) = 1/18 y z - 1/6 y x z + 1/12 y x z - 1/36 y z + + 2 3 2 2 2 2 2 2 + - 1/27 z + 1/6 y x z - 1/36 z x + 1/8 y x z + 1/12 y z + + 2 2 3 2 3 2 + + 1/12 x z - 1/54 z + 1/18 z + 1/18 x z - 1/3 y x z + 1/6 z y x + + 2 2 2 2 2 2 2 + + 1/9 y z - 1/4 y x z - 1/12 y x z - 1/4 y x z + 1/2 y x z + + 2 2 2 2 3 2 2 + - 1/6 y z - 1/18 y z + 1/9 x z - 1/18 x z - 1/6 x z - 1/24 z y x + + 3 2 3 3 2 3 + + 1/12 z y x , COEFF(0, -1, -1) = 1/12 y z + 1/3 y x z - 1/6 y x z + + 2 3 2 3 2 2 2 2 2 2 + - 1/24 y z - 1/18 z - 1/3 y x z + 1/12 z x - 3/8 y x z + 1/8 y z + + 2 2 3 2 3 2 + - 1/4 x z - 1/36 z + 1/12 z - 1/9 x z + 2/3 y x z - 1/2 z y x + + 2 2 2 2 2 2 2 2 + + 1/6 y z + 1/2 y x z + 1/4 y x z + 3/4 y x z - y x z - 1/4 y z + + 2 2 2 3 2 2 3 2 + - 1/12 y z - 2/9 x z + 1/6 x z + 1/3 x z + 1/8 z y x - 1/4 z y x , + + 3 3 2 3 2 3 + COEFF(1, -1, -1) = - 1/6 y z - 1/6 y x z + 1/12 y x z + 1/12 y z + + 2 3 2 2 2 2 2 2 2 2 + + 1/9 z + 1/6 y x z - 1/12 z x + 3/8 y x z - 1/4 y z + 1/4 x z + + 3 2 3 2 + + 1/18 z - 1/6 z + 1/18 x z - 1/3 y x z + 1/2 z y x - 1/3 y z + + 2 2 2 2 2 2 2 2 + - 1/4 y x z - 1/4 y x z - 3/4 y x z + 1/2 y x z + 1/2 y z + + 2 2 2 3 2 2 3 2 + + 1/6 y z + 1/9 x z - 1/6 x z - 1/6 x z - 1/8 z y x + 1/4 z y x , + + 2 2 2 + COEFF(2, -1, -1) = - 1/54 z - 1/6 z y x + 1/18 y z + 1/36 z - 1/36 y z + + 3 2 2 3 2 2 3 2 2 + - 1/108 z + 1/12 y x z + 1/36 z x - 1/72 y z - 1/12 x z + + 2 2 2 3 2 2 2 2 2 + + 1/18 x z + 1/24 y z + 1/24 z y x + 1/4 y x z - 1/12 y z + + 3 3 2 2 2 2 3 + + 1/36 y z - 1/12 z y x - 1/8 y x z , COEFF(-1, 0, -1) = - 1/9 y z + + 3 2 3 2 3 2 3 2 + + 1/3 y x z - 1/4 y x z + 1/12 y z - 1/18 z - 1/2 y x z - 1/24 z x + + 2 2 2 2 2 2 2 3 2 3 + - 3/8 y x z - 1/4 y z + 1/8 x z - 1/36 z + 1/12 z + 1/12 x z + + 2 2 2 2 2 + + 2/3 y x z - 1/3 z y x - 2/9 y z + 3/4 y x z + 1/4 y x z + + 2 2 2 2 2 2 + + 1/2 y x z - y x z + 1/3 y z + 1/6 y z + 1/6 x z - 1/12 x z + + 2 3 2 2 3 2 3 + - 1/4 x z + 1/8 z y x - 1/6 z y x , COEFF(0, 0, -1) = - 1/6 y z + + 3 2 3 2 3 2 3 2 + - 2/3 y x z + 1/2 y x z + 1/8 y z - 1/12 z + y x z + 1/8 z x + + 2 2 2 2 2 2 2 3 2 3 + + 9/8 y x z - 3/8 y z - 3/8 x z - 1/24 z + 1/8 z - 1/6 x z + + 2 2 2 2 2 2 2 + - 4/3 y x z + z y x - 1/3 y z - 3/2 y x z - 3/4 y x z - 3/2 y x z + + 2 2 2 2 2 + + 2 y x z + 1/2 y z + 1/4 y z - 1/3 x z + 1/4 x z + 1/2 x z + + 3 2 2 3 2 3 3 + - 3/8 z y x + 1/2 z y x , COEFF(1, 0, -1) = 1/3 y z + 1/3 y x z + + 2 3 2 3 2 3 2 2 2 2 + - 1/4 y x z - 1/4 y z + 1/6 z - 1/2 y x z - 1/8 z x - 9/8 y x z + + 2 2 2 2 3 2 3 + + 3/4 y z + 3/8 x z + 1/12 z - 1/4 z + 1/12 x z + 2/3 y x z + + 2 2 2 2 2 2 2 2 + - z y x + 2/3 y z + 3/4 y x z + 3/4 y x z + 3/2 y x z - y x z + + 2 2 2 2 3 2 2 + - y z - 1/2 y z + 1/6 x z - 1/4 x z - 1/4 x z + 3/8 z y x + + 3 2 3 2 2 2 + - 1/2 z y x , COEFF(2, 0, -1) = - 1/9 y z - 1/8 z y x + 1/3 z y x + + 2 2 2 3 2 2 3 2 2 2 + + 1/12 y z - 1/8 y z + 1/6 z y x + 1/24 y z - 1/4 y x z + 1/24 z + + 3 2 2 2 2 2 2 2 2 + - 1/18 y z - 1/8 x z + 3/8 y x z - 1/2 y x z + 1/6 y z + + 2 3 3 2 3 + + 1/12 x z - 1/72 z - 1/36 z + 1/24 z x , COEFF(-1, 1, -1) = 1/18 y z + + 3 2 3 2 3 2 3 2 + - 1/6 y x z + 1/4 y x z - 1/12 y z + 1/9 z + 1/2 y x z + 1/12 z x + + 2 2 2 2 2 2 2 3 2 3 + + 3/8 y x z + 1/4 y z - 1/4 x z + 1/18 z - 1/6 z - 1/6 x z + + 2 2 2 2 2 + - 1/3 y x z + 1/6 z y x + 1/9 y z - 3/4 y x z - 1/4 y x z + + 2 2 2 2 2 2 + - 1/4 y x z + 1/2 y x z - 1/6 y z - 1/6 y z - 1/3 x z + 1/6 x z + + 2 3 2 2 3 2 3 + + 1/2 x z - 1/8 z y x + 1/12 z y x , COEFF(0, 1, -1) = 1/12 y z + + 3 2 3 2 3 2 3 2 + + 1/3 y x z - 1/2 y x z - 1/8 y z + 1/6 z - y x z - 1/4 z x + + 2 2 2 2 2 2 2 3 2 3 + - 9/8 y x z + 3/8 y z + 3/4 x z + 1/12 z - 1/4 z + 1/3 x z + + 2 2 2 2 2 + + 2/3 y x z - 1/2 z y x + 1/6 y z + 3/2 y x z + 3/4 y x z + + 2 2 2 2 2 2 2 + + 3/4 y x z - y x z - 1/4 y z - 1/4 y z + 2/3 x z - 1/2 x z - x z + + 3 2 2 3 2 3 3 + + 3/8 z y x - 1/4 z y x , COEFF(1, 1, -1) = - 1/6 y z - 1/6 y x z + + 2 3 2 3 2 3 2 2 2 2 + + 1/4 y x z + 1/4 y z - 1/3 z + 1/2 y x z + 1/4 z x + 9/8 y x z + + 2 2 2 2 3 2 3 + - 3/4 y z - 3/4 x z - 1/6 z + 1/2 z - 1/6 x z - 1/3 y x z + + 2 2 2 2 2 2 2 + + 1/2 z y x - 1/3 y z - 3/4 y x z - 3/4 y x z - 3/4 y x z + + 2 2 2 2 2 + + 1/2 y x z + 1/2 y z + 1/2 y z - 1/3 x z + 1/2 x z + 1/2 x z + + 3 2 2 3 2 2 2 2 2 + - 3/8 z y x + 1/4 z y x , COEFF(2, 1, -1) = 1/4 y x z + 1/4 y x z + + 2 2 2 2 2 + - 1/12 y z - 1/12 z + 1/18 z + 1/4 x z + 1/18 y z - 1/6 z y x + + 2 3 2 2 2 3 3 3 2 + - 1/12 y z - 1/12 z y x + 1/8 y z + 1/36 y z + 1/36 z - 1/12 z x + + 3 2 2 2 3 2 2 2 2 + + 1/8 z y x - 1/24 y z - 1/6 x z - 3/8 y x z , COEFF(-1, 2, -1) = + + 2 2 2 2 2 2 3 2 3 + - 1/8 y x z - 1/12 y z + 1/18 x z + 1/36 y z - 1/12 y x z - 1/54 z + + 2 2 2 3 2 2 2 2 2 + - 1/12 x z + 1/24 x z + 1/24 z y x + 1/12 y x z + 1/18 y z + + 3 2 2 2 2 2 3 3 + - 1/72 z x + 1/36 z + 1/4 y x z - 1/6 y x z - 1/108 z + 1/36 x z + + 2 2 2 2 3 2 2 + - 1/36 x z, COEFF(0, 2, -1) = 1/12 x z - 1/4 y x z - 1/8 z y x + + 3 2 2 2 2 2 2 3 + - 1/18 x z - 1/36 z - 1/2 y x z - 1/8 x z + 1/24 z + 1/24 y z + + 2 2 2 3 2 2 2 + + 1/6 x z + 1/12 y z + 1/6 y x z - 1/9 x z + 1/3 y x z - 1/8 y z + + 3 3 2 2 2 2 3 2 + - 1/72 z + 1/24 z x + 3/8 y x z , COEFF(1, 2, -1) = - 1/24 z x + + 3 2 2 2 3 2 2 2 2 3 + + 1/36 z + 1/4 y z - 1/12 z + 1/8 z y x - 1/12 x z - 1/12 y x z + + 2 2 2 2 2 2 3 2 + - 1/12 x z - 1/6 y x z - 3/8 y x z - 1/12 y z + 1/18 z - 1/6 y z + + 2 2 3 2 2 2 2 + + 1/4 y x z + 1/36 x z + 1/8 x z + 1/4 y x z + 1/18 x z, + + 2 2 3 2 2 2 2 + COEFF(2, 2, -1) = - 1/12 y x z + 1/72 z x + 1/8 y x z - 1/108 z + + 3 2 2 2 2 2 3 2 2 + - 1/24 z y x - 1/24 y z + 1/72 y z + 1/72 z + 1/36 y z + + 2 3 2 2 3 + + 1/36 x z - 1/216 z - 1/24 x z , COEFF(-1, -1, 0) = - 1/6 y z + + 3 2 3 2 3 + + 1/2 y x z - 1/4 y x z - 1/3 x + 1/12 y z - 1/3 y - 1/18 z + + 2 3 2 2 2 2 2 2 2 2 + + 1/4 y x z + y x + 1/12 z x - 1/4 y x z - 1/6 y z - 1/6 x z + + 3 2 2 2 3 2 + + 1/18 z + 1/6 y - 1/9 z + 1/6 x - 1/6 x z - 1/2 y x z + 1/4 z y x + + 2 2 2 2 2 2 2 + + 1/9 + 1/6 y z - 1/2 y x + 1/2 y x z - 1/8 y x z + 1/2 y x z + + 2 2 2 2 2 + - y x z + 1/3 y z - 1/12 y z + 1/6 x z - 1/12 x z + 1/3 x z + + 3 2 2 3 2 2 2 2 + + 1/8 z y x - 1/4 z y x + 1/4 y x - 1/2 y x , COEFF(0, -1, 0) = + + 3 3 2 3 2 3 + - 1/4 y z - y x z + 1/2 y x z + 2/3 x + 1/8 y z - 1/2 y - 1/12 z + + 2 3 2 2 2 2 2 2 2 2 + - 1/2 y x z - 2 y x - 1/4 z x + 3/4 y x z - 1/4 y z + 1/2 x z + + 3 2 2 2 3 2 + + 1/12 z + 1/6 + 1/4 y - 1/6 z - 1/2 x + 1/3 x z + y x z - 3/4 z y x + + 2 2 2 2 2 2 2 2 + + 1/4 y z + y x - y x z + 3/8 y x z - 3/2 y x z + 2 y x z + + 2 2 2 2 3 2 2 + + 1/2 y z - 1/8 y z - 1/3 x z + 1/4 x z - 2/3 x z - 3/8 z y x + + 3 2 2 2 2 3 + + 3/4 z y x - 3/4 y x + 3/2 y x , COEFF(1, -1, 0) = 1/2 y z + + 3 2 3 2 3 2 + + 1/2 y x z - 1/4 y x z - 1/3 x - 1/4 y z + y + 1/6 z + 1/4 y x z + + 3 2 2 2 2 2 2 2 2 3 + + y x + 1/4 z x - 3/4 y x z + 1/2 y z - 1/2 x z - 1/6 z - 1/3 + + 2 2 2 3 2 + - 1/2 y + 1/3 z + 1/2 x - 1/6 x z - 1/2 y x z + 3/4 z y x - 1/2 y z + + 2 2 2 2 2 2 2 2 2 + - 1/2 y x + 1/2 y x z - 3/8 y x z + 3/2 y x z - y x z - y z + + 2 2 2 3 2 2 3 2 + + 1/4 y z + 1/6 x z - 1/4 x z + 1/3 x z + 3/8 z y x - 3/4 z y x + + 2 2 2 3 + + 3/4 y x - 3/2 y x , COEFF(2, -1, 0) = - 1/36 z - 1/6 y - 1/12 y z + + 2 2 3 2 2 2 2 + - 1/24 y z - 1/4 z y x - 1/12 z x - 1/12 y z + 1/18 + 1/6 y z + + 3 2 2 2 2 2 2 2 3 2 2 + - 1/8 z y x - 1/2 y x z - 1/18 z + 1/8 y x z + 1/36 z + 1/6 x z + + 3 2 2 2 2 2 2 + + 1/4 z y x + 1/12 y z + 1/12 x z - 1/6 x + 1/2 y x - 1/4 y x + + 2 3 2 2 2 2 3 3 + + 1/24 y z + 1/4 y x z + 1/12 y , COEFF(-1, 0, 0) = 1/3 y z - y x z + + 2 3 2 3 2 + + 3/4 y x z - 1/2 x - 1/4 y z + 2/3 y - 1/12 z - 3/4 y x z - 2 y x + + 3 2 2 2 2 2 2 2 2 3 + + 1/8 z x + 3/4 y x z + 1/2 y z - 1/4 x z + 1/12 z + 1/6 + + 2 2 2 3 2 + - 1/2 y - 1/6 z + 1/4 x - 1/4 x z + y x z - 1/2 z y x - 1/3 y z + + 2 2 2 2 2 2 2 2 2 + + 3/2 y x - 3/2 y x z + 3/8 y x z - y x z + 2 y x z - 2/3 y z + + 2 2 2 3 2 2 3 2 + + 1/4 y z + 1/4 x z - 1/8 x z + 1/2 x z - 3/8 z y x + 1/2 z y x + + 2 2 2 3 3 2 3 + - 3/4 y x + y x , COEFF(0, 0, 0) = 1/2 y z + 2 y x z - 3/2 y x z + x + + 2 3 2 3 2 + - 3/8 y z + 1/4 + y - 1/8 z + 3/2 y x z + 4 y x - 3/8 z x + + 2 2 2 2 2 2 2 3 2 2 2 + - 9/4 y x z + 3/4 y z + 3/4 x z + 1/8 z - 3/4 y - 1/4 z - 3/4 x + + 3 2 2 2 2 + + 1/2 x z - 2 y x z + 3/2 z y x - 1/2 y z - 3 y x + 3 y x z + + 2 2 2 2 2 2 2 + - 9/8 y x z + 3 y x z - 4 y x z - y z + 3/8 y z - 1/2 x z + + 2 2 3 2 2 3 2 2 2 2 + + 3/8 x z - x z + 9/8 z y x - 3/2 z y x + 9/4 y x - 3 y x , + + 3 3 2 3 2 3 + COEFF(1, 0, 0) = -y z - y x z + 3/4 y x z - 1/2 x + 3/4 y z - 1/2 + + 2 3 2 2 2 2 2 2 + - 2 y + 1/4 z - 3/4 y x z - 2 y x + 3/8 z x + 9/4 y x z - 3/2 y z + + 2 2 3 2 2 2 3 + - 3/4 x z - 1/4 z + 3/2 y + 1/2 z + 3/4 x - 1/4 x z + y x z + + 2 2 2 2 2 2 2 2 + - 3/2 z y x + y z + 3/2 y x - 3/2 y x z + 9/8 y x z - 3 y x z + + 2 2 2 2 2 + + 2 y x z + 2 y z - 3/4 y z + 1/4 x z - 3/8 x z + 1/2 x z + + 3 2 2 3 2 2 2 2 + - 9/8 z y x + 3/2 z y x - 9/4 y x + 3 y x , COEFF(2, 0, 0) = + + 2 3 2 2 3 3 2 2 2 + - 1/8 y z + y x z + 1/24 z - 1/2 z y x + 1/12 + 3/4 y x + 1/3 y + + 2 2 3 2 2 3 2 2 2 + - 1/4 y + 1/2 z y x + 3/8 z y x - 1/8 z x + 1/8 x z - 1/4 x + + 2 2 2 2 3 2 2 2 + - 1/24 z - 3/8 y x z - 1/12 z - y x + 1/6 y z + 1/4 x z + 1/8 y z + + 2 2 2 2 2 2 + + 1/4 y z - 3/4 y x z - 1/3 y z - 1/6 y z, COEFF(-1, 1, 0) = + + 3 3 2 3 2 3 + - 1/6 y z + 1/2 y x z - 3/4 y x z + x + 1/4 y z - 1/3 y + 1/6 z + + 2 3 2 2 2 2 2 2 2 2 + + 3/4 y x z + y x - 1/4 z x - 3/4 y x z - 1/2 y z + 1/2 x z + + 3 2 2 2 3 + - 1/6 z - 1/3 + 1/2 y + 1/3 z - 1/2 x + 1/2 x z - 1/2 y x z + + 2 2 2 2 2 2 + + 1/4 z y x + 1/6 y z - 3/2 y x + 3/2 y x z - 3/8 y x z + + 2 2 2 2 2 2 2 + + 1/2 y x z - y x z + 1/3 y z - 1/4 y z - 1/2 x z + 1/4 x z - x z + + 3 2 2 3 2 2 2 2 + + 3/8 z y x - 1/4 z y x + 3/4 y x - 1/2 y x , COEFF(0, 1, 0) = + + 3 3 2 3 2 3 + - 1/4 y z - y x z + 3/2 y x z - 2 x + 3/8 y z - 1/2 - 1/2 y + 1/4 z + + 2 3 2 2 2 2 2 2 2 2 + - 3/2 y x z - 2 y x + 3/4 z x + 9/4 y x z - 3/4 y z - 3/2 x z + + 3 2 2 2 3 2 + - 1/4 z + 3/4 y + 1/2 z + 3/2 x - x z + y x z - 3/4 z y x + 1/4 y z + + 2 2 2 2 2 2 2 2 2 + + 3 y x - 3 y x z + 9/8 y x z - 3/2 y x z + 2 y x z + 1/2 y z + + 2 2 2 3 2 2 3 2 + - 3/8 y z + x z - 3/4 x z + 2 x z - 9/8 z y x + 3/4 z y x + + 2 2 2 3 3 + - 9/4 y x + 3/2 y x , COEFF(1, 1, 0) = 1 + 1/2 y z + 1/2 y x z + + 2 3 2 3 2 3 2 + - 3/4 y x z + x - 3/4 y z + y - 1/2 z + 3/4 y x z + y x - 3/4 z x + + 2 2 2 2 2 2 2 3 2 2 2 + - 9/4 y x z + 3/2 y z + 3/2 x z + 1/2 z - 3/2 y - z - 3/2 x + + 3 2 2 2 2 + + 1/2 x z - 1/2 y x z + 3/4 z y x - 1/2 y z - 3/2 y x + 3/2 y x z + + 2 2 2 2 2 2 2 + - 9/8 y x z + 3/2 y x z - y x z - y z + 3/4 y z - 1/2 x z + + 2 2 3 2 2 3 2 2 2 2 + + 3/4 x z - x z + 9/8 z y x - 3/4 z y x + 9/4 y x - 3/2 y x , + + 2 3 2 2 2 + COEFF(2, 1, 0) = 1/4 y - 1/12 y z + 1/12 y z + 1/2 y x - 1/2 x z + + 2 2 2 2 3 2 2 2 + - 1/8 y z + 1/2 x + 1/6 y z + 1/8 y z - 1/4 z y x - 1/4 y z + + 2 2 2 2 2 2 2 3 2 3 2 + + 3/8 y x z - 1/2 y x z + 3/4 y x z + 1/4 z x + 1/4 z y x + + 2 3 2 2 2 2 3 + - 1/4 x z - 1/6 y + 1/12 z - 3/8 z y x - 3/4 y x - 1/6 - 1/12 z + + 2 2 2 2 2 2 + + 1/6 z , COEFF(-1, 2, 0) = 1/6 x z + 1/12 x - 1/4 y x + 1/2 y x + + 2 2 3 2 2 3 2 2 2 3 + + 1/6 y z - 1/8 z y x + 1/36 z + 1/8 y x z - 1/12 y z + + 2 3 3 2 2 2 + + 1/12 y z + 1/18 - 1/12 x z + 1/24 z x - 1/18 z - 1/4 y x z + + 2 2 2 2 2 + - 1/2 y x z - 1/12 x z - 1/6 x - 1/36 z - 1/24 x z + 1/12 x z + + 2 2 2 2 3 2 2 2 + + 1/4 y x z + 1/4 y x z - 1/6 y , COEFF(0, 2, 0) = 1/4 x z + + 2 3 3 2 3 2 2 2 3 + - 1/8 y z + 1/6 x z + 1/8 x z - 1/6 x z + 3/8 z y x - 1/2 y x z + + 3 2 2 3 2 2 2 2 2 + + 1/24 z + 3/4 y x - 1/8 z x - 1/4 x + 1/8 y z + 1/2 y x z - y x + + 2 2 2 2 2 2 2 2 + - 1/24 z + 1/3 x - 1/4 y - 3/4 y x z - 3/8 y x z + 1/4 y z + 1/12 + + 2 2 2 2 2 2 + - 1/12 z + y x z - 1/3 x z , COEFF(1, 2, 0) = - 1/6 x - 3/4 y x + + 2 3 2 2 2 2 2 2 2 2 + + 1/4 y z + 1/2 y + 1/6 x z + 3/4 y x z - 1/2 y x z + 1/2 y x + + 2 3 2 2 2 3 + + 1/4 x - 1/12 z - 1/8 x z + 1/12 x z - 1/4 x z - 1/12 x z - 1/6 + + 2 3 2 2 2 2 + + 1/4 y x z - 1/4 y z + 3/8 y x z - 1/4 y x z + 1/12 z + + 3 2 2 3 2 2 2 2 + - 3/8 z y x + 1/8 z x - 1/2 y z + 1/6 z , COEFF(2, 2, 0) = + + 2 2 3 2 2 3 2 3 2 2 2 + 1/4 y x + 1/8 z y x + 1/72 z - 1/24 y z - 1/36 z + 1/12 y z + + 2 2 2 3 2 2 2 2 + - 1/8 y x z + 1/24 y z - 1/24 z x + 1/24 x z - 1/12 y - 1/12 x + + 2 2 2 2 2 3 + + 1/12 x z - 1/72 z - 1/4 y x z + 1/36, COEFF(-1, -1, 1) = 1/6 y z + + 3 2 3 2 3 2 3 2 + - 1/2 y x z + 1/4 y x z - 1/12 y z + 1/9 z - 1/2 y x z - 1/12 z x + + 2 2 2 2 2 2 2 3 2 3 + + 1/8 y x z + 1/12 y z + 1/12 x z - 1/18 z + 1/18 z + 1/6 x z + + 2 2 2 2 2 2 2 + + y x z - 1/2 z y x - 1/3 y z - 1/4 y x z + 1/4 y x z - 1/4 y x z + + 2 2 2 2 2 + + 1/2 y x z - 1/6 y z + 1/6 y z - 1/3 x z + 1/6 x z - 1/6 x z + + 3 2 2 3 2 3 3 + - 1/8 z y x + 1/4 z y x , COEFF(0, -1, 1) = 1/4 y z + y x z + + 2 3 2 3 2 3 2 2 2 2 + - 1/2 y x z - 1/8 y z + 1/6 z + y x z + 1/4 z x - 3/8 y x z + + 2 2 2 2 3 2 3 + + 1/8 y z - 1/4 x z - 1/12 z + 1/12 z - 1/3 x z - 2 y x z + + 2 2 2 2 2 2 2 2 + + 3/2 z y x - 1/2 y z + 1/2 y x z - 3/4 y x z + 3/4 y x z - y x z + + 2 2 2 2 3 2 2 + - 1/4 y z + 1/4 y z + 2/3 x z - 1/2 x z + 1/3 x z + 3/8 z y x + + 3 2 3 3 2 3 + - 3/4 z y x , COEFF(1, -1, 1) = - 1/2 y z - 1/2 y x z + 1/4 y x z + + 2 3 2 3 2 2 2 2 2 2 + + 1/4 y z - 1/3 z - 1/2 y x z - 1/4 z x + 3/8 y x z - 1/4 y z + + 2 2 3 2 3 2 + + 1/4 x z + 1/6 z - 1/6 z + 1/6 x z + y x z - 3/2 z y x + y z + + 2 2 2 2 2 2 2 2 + - 1/4 y x z + 3/4 y x z - 3/4 y x z + 1/2 y x z + 1/2 y z + + 2 2 2 3 2 2 3 2 + - 1/2 y z - 1/3 x z + 1/2 x z - 1/6 x z - 3/8 z y x + 3/4 z y x , + + 3 2 2 3 2 2 + COEFF(2, -1, 1) = - 1/4 z y x + 1/36 z + 1/12 z x + 1/12 y z + + 2 2 2 2 2 2 2 2 2 2 + + 1/4 y x z - 1/4 y x z + 1/2 z y x - 1/8 y x z + 1/24 y z + + 2 3 2 3 2 2 3 + - 1/24 y z - 1/12 y z - 1/6 y z + 1/8 z y x + 1/12 y z + 1/18 z + + 3 2 2 2 3 3 + - 1/36 z - 1/12 x z - 1/6 x z, COEFF(-1, 0, 1) = - 1/3 y z + y x z + + 2 3 2 3 2 3 2 2 2 2 + - 3/4 y x z + 1/4 y z + 1/6 z + 3/2 y x z - 1/8 z x - 3/8 y x z + + 2 2 2 2 3 2 3 2 + - 1/4 y z + 1/8 x z - 1/12 z + 1/12 z + 1/4 x z - 2 y x z + z y x + + 2 2 2 2 2 2 2 2 + + 2/3 y z + 3/4 y x z - 3/4 y x z + 1/2 y x z - y x z + 1/3 y z + + 2 2 2 3 2 2 3 2 + - 1/2 y z - 1/2 x z + 1/4 x z - 1/4 x z + 3/8 z y x - 1/2 z y x , + + 3 3 2 3 2 3 + COEFF(0, 0, 1) = - 1/2 y z - 2 y x z + 3/2 y x z + 3/8 y z + 1/4 z + + 2 3 2 2 2 2 2 2 2 2 3 + - 3 y x z + 3/8 z x + 9/8 y x z - 3/8 y z - 3/8 x z - 1/8 z + + 2 3 2 2 2 2 2 + + 1/8 z - 1/2 x z + 4 y x z - 3 z y x + y z - 3/2 y x z + 9/4 y x z + + 2 2 2 2 2 2 2 + - 3/2 y x z + 2 y x z + 1/2 y z - 3/4 y z + x z - 3/4 x z + 1/2 x z + + 3 2 2 3 2 3 3 2 3 + - 9/8 z y x + 3/2 z y x , COEFF(1, 0, 1) = y z + y x z - 3/4 y x z + + 2 3 2 3 2 2 2 2 2 2 + - 3/4 y z - 1/2 z + 3/2 y x z - 3/8 z x - 9/8 y x z + 3/4 y z + + 2 2 3 2 3 2 + + 3/8 x z + 1/4 z - 1/4 z + 1/4 x z - 2 y x z + 3 z y x - 2 y z + + 2 2 2 2 2 2 2 2 2 + + 3/4 y x z - 9/4 y x z + 3/2 y x z - y x z - y z + 3/2 y z + + 2 2 3 2 2 3 2 + - 1/2 x z + 3/4 x z - 1/4 x z + 9/8 z y x - 3/2 z y x , + + 3 2 2 2 2 2 2 + COEFF(2, 0, 1) = 1/2 z y x - 1/4 x z + 1/3 y z + 1/6 y z + 3/8 y x z + + 2 3 3 2 2 2 3 2 + + 1/24 z - 1/6 y z - 1/24 z - z y x + 1/12 z + 3/4 y x z + 1/8 z x + + 2 2 2 3 3 2 2 2 2 2 2 + - 1/8 x z + 1/8 y z - 3/8 z y x - 1/8 y z - 1/2 y x z + + 2 3 3 2 3 + - 1/4 y z, COEFF(-1, 1, 1) = 1/6 y z - 1/2 y x z + 3/4 y x z + + 2 3 2 3 2 2 2 2 2 2 + - 1/4 y z - 1/3 z - 3/2 y x z + 1/4 z x + 3/8 y x z + 1/4 y z + + 2 2 3 2 3 2 + - 1/4 x z + 1/6 z - 1/6 z - 1/2 x z + y x z - 1/2 z y x - 1/3 y z + + 2 2 2 2 2 2 2 2 + - 3/4 y x z + 3/4 y x z - 1/4 y x z + 1/2 y x z - 1/6 y z + + 2 2 2 3 2 2 3 2 + + 1/2 y z + x z - 1/2 x z + 1/2 x z - 3/8 z y x + 1/4 z y x , + + 3 3 2 3 2 3 + COEFF(0, 1, 1) = 1/4 y z + y x z - 3/2 y x z - 3/8 y z - 1/2 z + + 2 3 2 2 2 2 2 2 2 2 3 + + 3 y x z - 3/4 z x - 9/8 y x z + 3/8 y z + 3/4 x z + 1/4 z + + 2 3 2 2 2 + - 1/4 z + x z - 2 y x z + 3/2 z y x - 1/2 y z + 3/2 y x z + + 2 2 2 2 2 2 2 + - 9/4 y x z + 3/4 y x z - y x z - 1/4 y z + 3/4 y z - 2 x z + + 2 2 3 2 2 3 2 + + 3/2 x z - x z + 9/8 z y x - 3/4 z y x , COEFF(1, 1, 1) = + + 3 3 2 3 2 3 2 + - 1/2 y z - 1/2 y x z + 3/4 y x z + 3/4 y z + z - 3/2 y x z + + 3 2 2 2 2 2 2 2 2 3 2 + + 3/4 z x + 9/8 y x z - 3/4 y z - 3/4 x z - 1/2 z + 1/2 z + + 3 2 2 2 2 2 + - 1/2 x z + y x z - 3/2 z y x + y z - 3/4 y x z + 9/4 y x z + + 2 2 2 2 2 2 + - 3/4 y x z + 1/2 y x z + 1/2 y z - 3/2 y z + x z - 3/2 x z + + 2 3 2 2 3 2 2 3 + + 1/2 x z - 9/8 z y x + 3/4 z y x , COEFF(2, 1, 1) = - 1/8 y z + + 2 2 2 2 2 2 + - 1/12 z - 3/4 y x z - 1/6 y z + 1/4 x z + 1/2 z y x - 1/6 z + + 2 2 2 2 2 2 2 3 2 + + 1/4 y x z - 3/8 y x z + 1/2 x z + 1/4 y z - 1/4 z x + + 3 2 2 3 3 3 2 2 2 2 + - 1/4 z y x - 1/12 y z + 1/12 y z + 1/12 z + 3/8 z y x + 1/8 y z + + 2 2 2 3 2 2 3 + , COEFF(-1, 2, 1) = 1/36 z - 1/4 y x z + 1/8 z y x + 1/18 z - 1/36 z + + 3 3 2 2 2 2 2 2 + + 1/12 x z - 1/24 z x + 1/2 y x z - 1/12 x z - 1/6 y z + 1/4 y x z + + 2 3 2 2 2 2 2 2 3 2 2 + - 1/4 y x z - 1/8 y x z + 1/24 x z + 1/12 y z - 1/12 y z + + 2 2 2 2 3 2 + - 1/6 x z + 1/12 x z, COEFF(0, 2, 1) = - 1/8 x z + 1/8 y z - 1/4 x z + + 3 3 2 3 2 2 + - 1/24 z + 1/12 z - 1/6 x z - 1/4 y z + 1/3 x z - 3/8 z y x + + 2 3 2 2 2 2 2 2 2 2 + + 1/24 z + 1/8 z x - 1/2 y x z + 3/8 y x z + 3/4 y x z + + 2 2 2 2 2 3 + - 1/8 y z + 1/6 x z - y x z + 1/2 y x z , COEFF(1, 2, 1) = + + 3 2 2 3 2 2 2 2 2 2 + - 1/8 z x - 1/4 y z - 1/12 z + 1/4 x z - 1/12 x z - 3/8 y x z + + 2 2 2 2 3 2 2 + + 1/2 y x z - 3/4 y x z - 1/4 y x z - 1/6 z - 1/6 x z + 1/4 y x z + + 2 2 2 2 3 2 2 2 3 3 + + 1/8 x z + 1/4 y z + 3/8 z y x + 1/2 y z + 1/12 x z + 1/12 z , + + 2 2 2 2 3 2 2 2 + COEFF(2, 2, 1) = 1/72 z + 1/8 y x z - 1/72 z - 1/12 x z - 1/24 x z + + 2 2 3 2 2 3 2 + - 1/12 y z + 1/24 y z + 1/4 y x z + 1/36 z + 1/24 z x + + 3 2 2 2 2 2 + - 1/8 z y x - 1/24 y z , COEFF(-1, -1, 2) = - 1/36 y z + 1/18 x z + + 3 3 2 2 3 3 2 2 + + 1/6 y x z - 1/18 x z + 1/12 y x z - 1/12 y x z + 1/24 z y x + + 2 3 3 2 2 2 2 3 + + 1/36 y z - 1/54 z + 1/36 z x - 1/36 x z - 1/24 y x z - 1/18 y z + + 3 2 2 3 + - 1/12 z y x + 1/18 y z - 1/6 y x z + 1/12 z y x + 1/54 z , + + 2 2 + COEFF(0, -1, 2) = - 1/36 z - 1/4 z y x - 1/6 y x z + 1/12 y z + 1/3 y x z + + 3 2 2 3 3 3 2 + + 1/36 z + 1/12 x z - 1/9 x z + 1/24 y z + 1/9 x z + 1/4 z y x + + 2 2 2 3 2 3 2 2 2 3 + - 1/24 y z + 1/8 y x z - 1/12 z x - 1/8 z y x + 1/6 y x z + + 3 3 2 3 2 + - 1/12 y z - 1/3 y x z , COEFF(1, -1, 2) = - 1/12 y x z + 1/4 z y x + + 2 3 3 2 2 3 + - 1/12 x z + 1/18 x z + 1/18 z + 1/6 y z + 1/8 z y x - 1/18 x z + + 2 3 3 2 3 + - 1/12 y z - 1/6 y z - 1/18 z + 1/12 y x z - 1/6 y x z + 1/6 y x z + + 3 2 3 2 2 2 2 + - 1/4 z y x + 1/12 z x + 1/12 y z - 1/8 y x z, COEFF(2, -1, 2) = + + 2 2 2 2 2 + 1/24 y x z - 1/12 z y x + 1/36 x z - 1/72 y z + 1/36 y z - 1/108 z + + 3 2 3 3 2 2 3 3 + - 1/36 z x + 1/108 z + 1/12 z y x + 1/72 y z - 1/36 y z + + 3 2 2 3 2 2 2 + - 1/24 z y x , COEFF(-1, 0, 2) = 1/24 z x - 1/24 x z - 1/6 z y x + + 2 2 3 3 3 + - 1/4 y x z + 1/12 x z - 1/12 y z - 1/12 x z + 1/9 y z + 1/3 y x z + + 3 3 2 2 2 3 2 3 + - 1/3 y x z - 1/36 z + 1/6 z y x + 1/8 y x z + 1/36 z + 1/4 y x z + + 3 2 2 2 2 + - 1/8 z y x - 1/9 y z + 1/12 y z, COEFF(0, 0, 2) = 1/8 x z + + 2 3 2 3 2 3 + + 1/2 y x z + 2/3 y x z - 2/3 y x z + 1/2 z y x + 1/6 y z - 1/8 y z + + 3 2 3 3 2 2 2 + - 1/2 z y x - 1/6 x z + 1/6 x z - 1/8 z x - 3/8 y x z - 1/6 y z + + 3 2 3 3 2 2 2 + - 1/24 z + 1/24 z - 1/2 y x z + 3/8 z y x + 1/8 y z, COEFF(1, 0, 2) + + 3 2 3 2 2 2 2 3 2 2 + = 1/8 z x - 3/8 z y x + 3/8 y x z + 1/2 z y x - 1/2 z y x + + 3 3 2 3 2 3 + + 1/12 x z - 1/3 y x z - 1/12 x z + 1/4 y x z - 1/8 x z - 1/3 y z + + 2 2 2 3 3 + + 1/3 y z - 1/4 y x z - 1/4 y z + 1/4 y z + 1/12 z - 1/12 z + + 2 2 2 3 2 + + 1/3 y x z, COEFF(2, 0, 2) = 1/24 y z - 1/8 y x z - 1/6 z y x + + 3 2 3 3 2 2 2 + - 1/24 z x + 1/18 y z + 1/8 z y x + 1/6 z y x - 1/72 z - 1/18 y z + + 3 2 2 3 + + 1/72 z + 1/24 x z - 1/24 y z , COEFF(-1, 1, 2) = 1/18 y z + + 2 3 2 3 3 2 + - 1/4 y x z - 1/6 x z - 1/6 y x z + 1/12 y z - 1/12 z y x + + 3 2 3 2 3 3 2 + - 1/12 z x + 1/6 x z - 1/12 y z - 1/18 y z + 1/6 y x z + 1/12 z y x + + 3 2 3 2 2 2 2 2 + - 1/18 z + 1/4 y x z + 1/8 z y x - 1/8 y x z + 1/18 z + 1/12 x z, + + 3 2 2 2 3 2 3 2 + COEFF(0, 1, 2) = - 3/8 z y x - 1/4 x z + 1/4 z x + 1/4 z y x + + 2 2 2 2 3 3 2 3 + + 3/8 y x z - 1/4 z y x + 1/8 y z - 1/3 y x z + 1/2 y x z + 1/12 z + + 2 3 2 3 3 + + 1/12 y z - 1/8 y z - 1/12 y z - 1/2 y x z - 1/3 x z - 1/12 z + + 2 3 3 2 2 + + 1/3 y x z + 1/3 x z, COEFF(1, 1, 2) = - 1/4 y x z + 3/8 z y x + + 2 3 2 3 + + 1/4 y x z - 1/6 y x z + 1/6 y x z + 1/4 z y x + 1/6 x z - 1/6 y z + + 2 2 2 3 3 2 + - 3/8 y x z - 1/6 z + 1/4 y z + 1/6 y z - 1/4 z y x - 1/6 x z + + 3 3 2 2 2 3 2 3 + + 1/6 z - 1/4 z x + 1/4 x z - 1/4 y z , COEFF(2, 1, 2) = 1/24 y z + + 3 2 3 2 3 2 2 + - 1/36 y z - 1/24 y z + 1/12 z y x + 1/12 z x - 1/12 z y x + 1/36 z + + 2 3 2 2 3 2 2 + - 1/12 x z - 1/8 z y x - 1/36 z + 1/8 y x z + 1/36 y z, + + 3 2 3 3 2 2 + COEFF(-1, 2, 2) = - 1/36 x z - 1/36 y z - 1/24 z y x + 1/36 x z + + 2 2 2 3 2 2 + + 1/24 y x z + 1/12 y x z - 1/72 x z - 1/108 z + 1/36 y z + + 3 2 2 3 2 2 + + 1/72 z x - 1/12 y x z + 1/108 z , COEFF(0, 2, 2) = - 1/8 y x z + + 2 3 2 3 2 2 3 3 2 2 + - 1/24 y z + 1/6 y x z - 1/24 z x - 1/6 y x z + 1/8 z y x + + 2 2 3 3 + + 1/24 x z - 1/72 z - 1/18 x z + 1/24 y z + 1/18 x z + 1/72 z , + + 2 3 2 3 2 2 + COEFF(1, 2, 2) = 1/12 y z + 1/36 z + 1/12 y x z + 1/8 y x z + + 3 3 2 3 2 2 2 3 + - 1/36 x z + 1/24 z x - 1/8 z y x - 1/12 y x z - 1/36 z + 1/36 x z + + 2 2 3 2 + - 1/24 x z - 1/12 y z, COEFF(2, 2, 2) = 1/216 z + 1/72 x z + + 2 3 3 2 3 2 2 2 2 + - 1/72 y z - 1/72 z x + 1/24 z y x - 1/24 y x z - 1/216 z + + 2 + + 1/72 y z] + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxy.compute.c"); +bytes used=6943629980, alloc=10549364, time=706.06 +bytes used=6944630276, alloc=10549364, time=706.15 +bytes used=6945630540, alloc=10549364, time=706.23 +bytes used=6946630840, alloc=10549364, time=706.31 +bytes used=6947631232, alloc=10549364, time=706.40 +bytes used=6948631792, alloc=10549364, time=706.48 +bytes used=6949632048, alloc=10549364, time=706.56 +bytes used=6950632452, alloc=10549364, time=706.68 +bytes used=6951632648, alloc=10549364, time=706.78 +bytes used=6952633052, alloc=10549364, time=706.86 +bytes used=6953633256, alloc=10549364, time=706.95 +bytes used=6954633548, alloc=10549364, time=707.04 +bytes used=6955633844, alloc=10549364, time=707.13 +bytes used=6956634068, alloc=10549364, 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alloc=10549364, time=772.60 +bytes used=7259372168, alloc=10549364, time=772.69 +bytes used=7260372644, alloc=10549364, time=772.77 +bytes used=7261442396, alloc=10549364, time=772.85 +bytes used=7262585984, alloc=10549364, time=772.95 +bytes used=7263670972, alloc=10549364, time=773.04 +bytes used=7264705920, alloc=10549364, time=773.13 +bytes used=7265707712, alloc=10549364, time=773.21 +bytes used=7266791044, alloc=10549364, time=773.31 +bytes used=7267802952, alloc=10549364, time=773.40 +bytes used=7268893568, alloc=10549364, time=773.50 +bytes used=7269893712, alloc=10549364, time=773.60 +bytes used=7270927276, alloc=10549364, time=773.71 +bytes used=7271946632, alloc=10549364, time=773.78 +bytes used=7272947680, alloc=10549364, time=773.84 +bytes used=7273949024, alloc=10549364, time=773.90 + 3 2 3 3 +[COEFF(-1, -1, -1) = 1/12 x y z - 1/6 x y z + 1/18 x y - 1/27 y + + 2 2 2 2 3 3 2 + + 1/2 y x z + 1/9 y x + 1/8 y x z + 1/18 y z - 1/36 y z + + 2 2 2 3 2 3 2 3 2 + + 1/12 y z - 1/24 z y x + 1/12 z y x - 1/54 y + 1/18 y + + 2 3 2 2 2 2 + - 1/3 y x z + 1/6 z y x + 1/9 y z - 1/36 y x - 1/6 y x - 1/4 y x z + + 2 2 2 2 2 2 2 + - 1/4 y x z - 1/12 y x z + 1/6 y x z - 1/18 y z - 1/6 y z + + 2 2 2 3 2 3 + + 1/12 y x - 1/18 y x , COEFF(0, -1, -1) = - 1/6 x y z + 1/3 x y z + + 3 2 2 2 2 3 + - 1/9 x y - 1/18 y - y x z - 2/9 y x - 3/8 y x z + 1/12 y z + + 3 2 2 2 2 3 2 3 2 3 2 + - 1/24 y z + 1/8 y z + 1/8 z y x - 1/4 z y x - 1/36 y + 1/12 y + + 2 3 2 2 2 2 + + 2/3 y x z - 1/2 z y x + 1/6 y z + 1/12 y x + 1/3 y x + 1/2 y x z + + 2 2 2 2 2 2 2 + + 3/4 y x z + 1/4 y x z - 1/3 y x z - 1/12 y z - 1/4 y z + + 2 2 2 3 2 3 + - 1/4 y x + 1/6 y x , COEFF(1, -1, -1) = 1/12 x y z - 1/6 x y z + + 3 2 2 2 2 3 + + 1/18 x y + 1/9 y + 1/2 y x z + 1/9 y x + 3/8 y x z - 1/6 y z + + 3 2 2 2 2 3 2 3 2 3 2 + + 1/12 y z - 1/4 y z - 1/8 z y x + 1/4 z y x + 1/18 y - 1/6 y + + 2 3 2 2 2 2 + - 1/3 y x z + 1/2 z y x - 1/3 y z - 1/12 y x - 1/6 y x - 1/4 y x z + + 2 2 2 2 2 2 2 2 2 + - 3/4 y x z - 1/4 y x z + 1/6 y x z + 1/6 y z + 1/2 y z + 1/4 y x + + 2 2 2 2 3 2 3 + - 1/6 y x , COEFF(2, -1, -1) = - 1/8 y x z - 1/72 y z + 1/36 y z + + 2 2 2 2 3 2 2 + - 1/54 y + 1/24 y z + 1/12 y x z - 1/12 z y x - 1/12 y z + + 2 2 2 3 3 2 + - 1/6 z y x + 1/36 y + 1/18 y z - 1/36 y z - 1/108 y + 1/36 y x + + 2 2 3 2 2 2 2 2 + + 1/18 y x + 1/24 z y x - 1/12 y x + 1/4 y x z, COEFF(-1, 0, -1) + + 3 2 3 3 2 + = - 1/4 x y z + 1/2 x y z - 1/3 x - 1/6 x y - 1/18 y - 1/3 z - y x z + + 2 2 2 3 3 2 2 2 + + 1/6 y x - 1/4 y x z - 1/6 y z + 1/12 y z - 1/6 y z + + 2 3 2 3 2 2 2 3 2 2 + + 1/8 z y x - 1/4 z y x + 1/4 x z + 1/18 y - 1/9 y + 1/6 z + + 2 2 3 2 2 + + 1/6 x - 1/2 y x z + 1/4 z y x + 1/9 + 1/6 y z + 1/12 y x + 1/3 y x + + 2 2 2 2 2 2 2 2 + + 1/2 y x z + 1/2 y x z - 1/8 y x z + 1/4 y x z - 1/12 y z + + 2 2 2 2 2 2 + + 1/3 y z + x z - 1/2 x z - 1/2 x z - 1/6 y x - 1/12 y x , + + 3 2 3 3 + COEFF(0, 0, -1) = 1/2 x y z - x y z + 2/3 x + 1/3 x y - 1/12 y - 1/2 z + + 2 2 2 2 3 3 2 2 2 + + 2 y x z - 1/3 y x + 3/4 y x z - 1/4 y z + 1/8 y z - 1/4 y z + + 2 3 2 3 2 2 2 3 2 2 + - 3/8 z y x + 3/4 z y x - 3/4 x z + 1/12 y + 1/6 - 1/6 y + 1/4 z + + 2 2 3 2 2 2 2 + - 1/2 x + y x z - 3/4 z y x + 1/4 y z - 1/4 y x - 2/3 y x - y x z + + 2 2 2 2 2 2 2 + - 3/2 y x z + 3/8 y x z - 1/2 y x z - 1/8 y z + 1/2 y z - 2 x z + + 2 2 2 2 2 3 2 + + 3/2 x z + x z + 1/2 y x + 1/4 y x , COEFF(1, 0, -1) = - 1/4 x y z + + 3 3 2 + + 1/2 x y z - 1/3 x - 1/6 x y + 1/6 y + z - y x z + 1/6 y x + + 2 2 2 3 3 2 2 2 2 3 2 + - 3/4 y x z + 1/2 y z - 1/4 y z + 1/2 y z + 3/8 z y x + + 3 2 2 2 3 2 2 2 + - 3/4 z y x + 3/4 x z - 1/6 y - 1/3 + 1/3 y - 1/2 z + 1/2 x + + 2 3 2 2 2 2 + - 1/2 y x z + 3/4 z y x - 1/2 y z + 1/4 y x + 1/3 y x + 1/2 y x z + + 2 2 2 2 2 2 2 + + 3/2 y x z - 3/8 y x z + 1/4 y x z + 1/4 y z - y z + x z + + 2 2 2 2 2 + - 3/2 x z - 1/2 x z - 1/2 y x - 1/4 y x , COEFF(2, 0, -1) = + + 2 2 2 2 2 3 2 + - 1/4 x z + 1/4 y x z + 1/36 y - 1/18 y + 1/12 y z - 1/6 z + + 3 2 2 3 2 2 2 3 2 2 + + 1/4 z y x - 1/8 z y x - 1/12 y z - 1/12 y x + 1/12 z + + 2 3 2 2 2 2 2 2 + + 1/2 x z + 1/24 y z + 1/8 y x z + 1/12 y x + 1/6 y x + + 2 2 2 2 2 3 + - 1/2 y x z - 1/36 y - 1/4 z y x + 1/6 y z - 1/24 y z - 1/12 y z + + 2 3 2 3 3 + + 1/18 - 1/6 x , COEFF(-1, 1, -1) = 1/4 x y z - 1/2 x y z + 1/6 x y + + 2 2 2 2 3 3 2 + + 1/9 y + 1/2 y x z - 1/3 y x + 1/8 y x z + 1/6 y z - 1/12 y z + + 2 2 2 3 2 3 2 3 2 + + 1/12 y z - 1/8 z y x + 1/4 z y x - 1/18 y + 1/18 y + y x z + + 2 3 2 2 2 2 2 2 + - 1/2 z y x - 1/3 y z - 1/12 y x - 1/6 y x - 1/4 y x z - 1/4 y x z + + 2 2 2 2 2 2 2 2 + + 1/4 y x z - 1/2 y x z + 1/6 y z - 1/6 y z + 1/12 y x + 1/6 y x , + + 3 2 3 3 2 + COEFF(0, 1, -1) = - 1/2 x y z + x y z - 1/3 x y + 1/6 y - y x z + + 2 2 2 3 3 2 2 2 2 3 2 + + 2/3 y x - 3/8 y x z + 1/4 y z - 1/8 y z + 1/8 y z + 3/8 z y x + + 3 2 3 2 2 + - 3/4 z y x - 1/12 y + 1/12 y - 2 y x z + 3/2 z y x - 1/2 y z + + 3 2 2 2 2 2 2 2 2 2 + + 1/4 y x + 1/3 y x + 1/2 y x z + 3/4 y x z - 3/4 y x z + y x z + + 2 2 2 2 2 + + 1/4 y z - 1/4 y z - 1/4 y x - 1/2 y x , COEFF(1, 1, -1) = + + 3 2 3 3 2 + 1/4 x y z - 1/2 x y z + 1/6 x y - 1/3 y + 1/2 y x z - 1/3 y x + + 2 2 2 3 3 2 2 2 2 3 2 + + 3/8 y x z - 1/2 y z + 1/4 y z - 1/4 y z - 3/8 z y x + + 3 2 3 2 2 3 2 + + 3/4 z y x + 1/6 y - 1/6 y + y x z - 3/2 z y x + y z - 1/4 y x + + 2 2 2 2 2 2 2 2 + - 1/6 y x - 1/4 y x z - 3/4 y x z + 3/4 y x z - 1/2 y x z + + 2 2 2 2 2 + - 1/2 y z + 1/2 y z + 1/4 y x + 1/2 y x , COEFF(2, 1, -1) = + + 2 2 2 2 2 3 + - 1/8 y x z - 1/6 y z - 1/6 y x + 1/36 y + 1/18 y - 1/36 y + + 2 3 2 2 2 2 2 3 2 3 + + 1/8 z y x + 1/4 y x z + 1/24 y z + 1/12 y x + 1/12 y z + + 2 2 2 3 2 2 2 2 + + 1/2 z y x - 1/4 y x z - 1/4 z y x - 1/12 y x + 1/12 y z + + 2 3 2 3 2 3 2 + - 1/12 y z - 1/24 y z , COEFF(-1, 2, -1) = 1/54 y + 1/24 z y x + + 3 2 3 3 2 2 + - 1/12 z y x - 1/18 x y - 1/18 y z - 1/36 y x - 1/36 y z + + 2 2 3 3 2 + - 1/24 y x z + 1/6 x y z + 1/36 y z - 1/6 y x z - 1/54 y + 1/18 y x + + 3 2 3 2 2 2 + + 1/36 y x + 1/18 y z - 1/12 x y z + 1/12 z y x + 1/12 y x z , + + 2 3 2 3 2 + COEFF(0, 2, -1) = - 1/6 y x z - 1/12 y x + 1/9 x y + 1/12 y x + + 2 3 2 2 2 3 2 + - 1/4 z y x - 1/3 x y z + 1/8 y x z - 1/8 z y x - 1/9 y x + + 3 2 3 3 2 3 2 + + 1/24 y z + 1/3 y x z - 1/36 y - 1/12 y z + 1/6 x y z + 1/4 z y x + + 2 3 2 3 2 + - 1/24 y z + 1/12 y z + 1/36 y , COEFF(1, 2, -1) = 1/8 z y x + + 2 2 3 3 2 2 + - 1/8 y x z - 1/6 y x z - 1/18 x y + 1/12 y x + 1/12 y x z + + 3 3 2 2 3 2 3 + + 1/6 y z - 1/18 y + 1/4 z y x + 1/12 y z - 1/12 y z + 1/6 x y z + + 3 2 2 3 2 + - 1/4 z y x - 1/12 y x + 1/18 y + 1/18 y x - 1/12 x y z - 1/6 y z, + + 3 2 2 3 2 2 2 + COEFF(2, 2, -1) = 1/72 y z - 1/24 z y x - 1/72 y z - 1/12 z y x + + 3 2 3 2 2 2 3 2 + - 1/36 y x + 1/108 y + 1/36 y x + 1/24 y x z + 1/12 z y x + + 3 3 2 + - 1/36 y z + 1/36 y z - 1/108 y, COEFF(-1, -1, 0) = - 1/4 x y z + + 3 3 2 2 2 2 + + 1/3 x y z + 1/12 x y - 1/18 y - y x z + 1/6 y x - 3/8 y x z + + 3 3 2 2 2 2 3 2 3 2 3 + - 1/9 y z + 1/12 y z - 1/4 y z + 1/8 z y x - 1/6 z y x - 1/36 y + + 2 2 3 2 2 + + 1/12 y + 2/3 y x z - 1/3 z y x - 2/9 y z - 1/24 y x - 1/4 y x + + 2 2 2 2 2 2 2 2 + + 3/4 y x z + 1/2 y x z + 1/4 y x z - 1/2 y x z + 1/6 y z + + 2 2 2 2 3 2 + + 1/3 y z + 1/8 y x - 1/12 y x , COEFF(0, -1, 0) = 1/2 x y z + + 3 3 2 2 2 2 + - 2/3 x y z - 1/6 x y - 1/12 y + 2 y x z - 1/3 y x + 9/8 y x z + + 3 3 2 2 2 2 3 2 3 2 3 + - 1/6 y z + 1/8 y z - 3/8 y z - 3/8 z y x + 1/2 z y x - 1/24 y + + 2 2 3 2 2 + + 1/8 y - 4/3 y x z + z y x - 1/3 y z + 1/8 y x + 1/2 y x + + 2 2 2 2 2 2 2 2 2 + - 3/2 y x z - 3/2 y x z - 3/4 y x z + y x z + 1/4 y z + 1/2 y z + + 2 2 2 3 2 3 + - 3/8 y x + 1/4 y x , COEFF(1, -1, 0) = - 1/4 x y z + 1/3 x y z + + 3 2 2 2 2 3 + + 1/12 x y + 1/6 y - y x z + 1/6 y x - 9/8 y x z + 1/3 y z + + 3 2 2 2 2 3 2 3 2 3 2 + - 1/4 y z + 3/4 y z + 3/8 z y x - 1/2 z y x + 1/12 y - 1/4 y + + 2 3 2 2 2 2 + + 2/3 y x z - z y x + 2/3 y z - 1/8 y x - 1/4 y x + 3/4 y x z + + 2 2 2 2 2 2 2 2 2 + + 3/2 y x z + 3/4 y x z - 1/2 y x z - 1/2 y z - y z + 3/8 y x + + 2 3 2 2 2 2 + - 1/4 y x , COEFF(2, -1, 0) = 1/24 y z - 1/2 y x z + 1/3 z y x + + 2 3 2 3 2 2 2 2 2 2 2 + - 1/8 z y x + 1/6 z y x - 1/8 y x - 1/4 y x z - 1/8 y z + + 2 2 3 3 2 + + 1/12 y z + 1/24 y - 1/9 y z - 1/18 y z - 1/72 y + 1/12 y x - 1/36 y + + 2 3 2 2 2 2 3 2 + + 1/6 y z + 1/24 y x + 3/8 y x z , COEFF(-1, 0, 0) = 3/4 x y z + + 3 3 2 + - x y z - 1/2 x - 1/4 x y - 1/12 y + 2/3 z + 2 y x z + 1/4 y x + + 2 2 2 3 3 2 2 2 2 3 2 + + 3/4 y x z + 1/3 y z - 1/4 y z + 1/2 y z - 3/8 z y x + + 3 2 2 2 3 2 2 2 + + 1/2 z y x - 3/4 x z + 1/12 y + 1/6 - 1/6 y - 1/2 z + 1/4 x + + 2 3 2 2 2 2 + + y x z - 1/2 z y x - 1/3 y z + 1/8 y x + 1/2 y x - 3/2 y x z + + 2 2 2 2 2 2 2 2 + - y x z + 3/8 y x z - 3/4 y x z + 1/4 y z - 2/3 y z - 2 x z + x z + + 2 2 2 2 3 2 + + 3/2 x z - 1/4 y x - 1/8 y x , COEFF(0, 0, 0) = - 3/2 x y z + + 3 3 2 + + 2 x y z + x + 1/2 x y + 1/4 - 1/8 y + z - 4 y x z - 1/2 y x + + 2 2 2 3 3 2 2 2 2 3 2 + - 9/4 y x z + 1/2 y z - 3/8 y z + 3/4 y z + 9/8 z y x + + 3 2 2 2 3 2 2 2 + - 3/2 z y x + 9/4 x z + 1/8 y - 1/4 y - 3/4 z - 3/4 x - 2 y x z + + 2 3 2 2 2 2 2 2 + + 3/2 z y x - 1/2 y z - 3/8 y x - y x + 3 y x z + 3 y x z + + 2 2 2 2 2 2 2 + - 9/8 y x z + 3/2 y x z + 3/8 y z - y z + 4 x z - 3 x z - 3 x z + + 2 2 2 3 2 3 + + 3/4 y x + 3/8 y x , COEFF(1, 0, 0) = 3/4 x y z - x y z - 1/2 x + + 3 2 2 2 2 3 + - 1/4 x y - 1/2 + 1/4 y - 2 z + 2 y x z + 1/4 y x + 9/4 y x z - y z + + 3 2 2 2 2 3 2 3 2 2 2 3 + + 3/4 y z - 3/2 y z - 9/8 z y x + 3/2 z y x - 9/4 x z - 1/4 y + + 2 2 2 2 3 2 + + 1/2 y + 3/2 z + 3/4 x + y x z - 3/2 z y x + y z + 3/8 y x + + 2 2 2 2 2 2 2 2 2 + + 1/2 y x - 3/2 y x z - 3 y x z + 9/8 y x z - 3/4 y x z - 3/4 y z + + 2 2 2 2 2 2 + + 2 y z - 2 x z + 3 x z + 3/2 x z - 3/4 y x - 3/8 y x , + + 3 2 3 2 2 3 2 2 2 + COEFF(2, 0, 0) = - 1/8 y z - 1/2 z y x + 3/8 z y x - 1/4 x - x z + + 2 2 2 2 3 2 2 + + y x z + 1/4 y x + 1/3 z - 1/6 y z + 1/24 y + 1/2 z y x - 1/4 z + + 2 2 2 2 2 2 2 2 + + 1/12 - 1/3 y z + 1/4 y z - 3/4 y x z + 1/8 y z - 1/12 y + + 3 3 2 2 2 2 2 2 + + 1/6 y z - 1/8 y x - 3/8 y x z + 1/8 y x + 3/4 x z - 1/24 y, + + 3 2 3 3 2 + COEFF(-1, 1, 0) = - 3/4 x y z + x y z + 1/4 x y + 1/6 y - y x z + + 2 2 2 3 3 2 2 2 2 3 2 + - 1/2 y x - 3/8 y x z - 1/3 y z + 1/4 y z - 1/4 y z + 3/8 z y x + + 3 2 3 2 2 3 2 + - 1/2 z y x - 1/12 y + 1/12 y - 2 y x z + z y x + 2/3 y z - 1/8 y x + + 2 2 2 2 2 2 2 2 + - 1/4 y x + 3/4 y x z + 1/2 y x z - 3/4 y x z + 3/2 y x z + + 2 2 2 2 2 3 2 + - 1/2 y z + 1/3 y z + 1/8 y x + 1/4 y x , COEFF(0, 1, 0) = 3/2 x y z + + 3 3 2 2 2 2 3 + - 2 x y z - 1/2 x y + 1/4 y + 2 y x z + y x + 9/8 y x z - 1/2 y z + + 3 2 2 2 2 3 2 3 2 3 2 + + 3/8 y z - 3/8 y z - 9/8 z y x + 3/2 z y x - 1/8 y + 1/8 y + + 2 3 2 2 2 2 + + 4 y x z - 3 z y x + y z + 3/8 y x + 1/2 y x - 3/2 y x z + + 2 2 2 2 2 2 2 2 2 + - 3/2 y x z + 9/4 y x z - 3 y x z - 3/4 y z + 1/2 y z - 3/8 y x + + 2 3 2 3 3 + - 3/4 y x , COEFF(1, 1, 0) = - 3/4 x y z + x y z + 1/4 x y - 1/2 y + + 2 2 2 2 3 3 2 2 2 + - y x z - 1/2 y x - 9/8 y x z + y z - 3/4 y z + 3/4 y z + + 2 3 2 3 2 3 2 2 + + 9/8 z y x - 3/2 z y x + 1/4 y - 1/4 y - 2 y x z + 3 z y x + + 3 2 2 2 2 2 2 2 2 + - 2 y z - 3/8 y x - 1/4 y x + 3/4 y x z + 3/2 y x z - 9/4 y x z + + 2 2 2 2 2 2 + + 3/2 y x z + 3/2 y z - y z + 3/8 y x + 3/4 y x , COEFF(2, 1, 0) = + + 2 2 2 2 3 2 2 2 2 2 3 + -z y x - 1/2 y x z - 3/8 z y x + 3/8 y x z + 1/24 y - 1/6 y z + + 2 2 3 2 2 2 2 2 + + 1/3 y z + 3/4 y x z + 1/8 y x + 1/6 y z - 1/8 y x - 1/4 y z + + 2 3 2 3 2 2 3 2 + - 1/4 y x + 1/2 z y x - 1/24 y + 1/12 y - 1/8 y z + 1/8 y z , + + 3 2 2 3 2 3 + COEFF(-1, 2, 0) = - 1/9 y z + 1/4 x y z - 1/8 z y x - 1/12 x y + + 3 2 2 3 2 + + 1/3 y x z - 1/3 x y z + 1/8 y x z - 1/36 y + 1/36 y - 1/6 z y x + + 3 2 3 2 2 2 2 + - 1/12 y z + 1/12 y x + 1/6 z y x - 1/4 y x z - 1/24 y x + 1/12 y z + + 3 2 3 2 3 + + 1/24 y x + 1/9 y z, COEFF(0, 2, 0) = 1/8 y z + 1/6 x y + + 3 2 3 2 3 2 2 2 3 2 + - 1/2 x y z - 1/8 y z - 1/8 y x + 1/2 z y x + 3/8 z y x + + 3 2 3 2 2 2 + - 1/2 z y x + 2/3 x y z - 1/24 y - 3/8 y x z - 1/6 y x + 1/8 y x + + 3 2 3 + + 1/24 y - 1/6 y z + 1/2 y x z - 2/3 y x z + 1/6 y z, COEFF(1, 2, 0) = + + 2 2 2 3 2 3 2 3 2 3 2 + 3/8 y x z - 3/8 z y x + 1/4 x y z + 1/8 y x - 1/12 y - 1/4 y z + + 3 2 2 + + 1/3 y x z - 1/3 y z - 1/8 y x + 1/12 y + 1/12 y x - 1/2 z y x + + 3 3 2 2 3 2 3 + - 1/12 x y + 1/2 z y x + 1/3 y z - 1/4 y x z + 1/4 y z - 1/3 x y z, + + 3 2 3 2 2 + COEFF(2, 2, 0) = - 1/24 y z + 1/18 y z - 1/8 y x z - 1/72 y + + 2 3 2 3 3 2 3 2 2 + + 1/8 z y x - 1/18 y z + 1/72 y - 1/6 z y x - 1/24 y x + 1/24 y z + + 2 2 3 2 3 + + 1/6 z y x + 1/24 y x , COEFF(-1, -1, 1) = 1/4 x y z - 1/6 x y z + + 3 2 2 2 2 3 + - 1/6 x y + 1/9 y + 1/2 y x z - 1/3 y x + 3/8 y x z + 1/18 y z + + 3 2 2 2 2 3 2 3 2 3 2 + - 1/12 y z + 1/4 y z - 1/8 z y x + 1/12 z y x + 1/18 y - 1/6 y + + 2 3 2 2 2 2 + - 1/3 y x z + 1/6 z y x + 1/9 y z + 1/12 y x + 1/2 y x - 3/4 y x z + + 2 2 2 2 2 2 2 2 2 + - 1/4 y x z - 1/4 y x z + 1/2 y x z - 1/6 y z - 1/6 y z - 1/4 y x + + 2 3 2 3 3 + + 1/6 y x , COEFF(0, -1, 1) = - 1/2 x y z + 1/3 x y z + 1/3 x y + + 2 2 2 2 3 3 2 + + 1/6 y - y x z + 2/3 y x - 9/8 y x z + 1/12 y z - 1/8 y z + + 2 2 2 3 2 3 2 3 2 + + 3/8 y z + 3/8 z y x - 1/4 z y x + 1/12 y - 1/4 y + 2/3 y x z + + 2 3 2 2 2 2 2 2 + - 1/2 z y x + 1/6 y z - 1/4 y x - y x + 3/2 y x z + 3/4 y x z + + 2 2 2 2 2 2 2 2 + + 3/4 y x z - y x z - 1/4 y z - 1/4 y z + 3/4 y x - 1/2 y x , + + 3 2 3 3 2 + COEFF(1, -1, 1) = 1/4 x y z - 1/6 x y z - 1/6 x y - 1/3 y + 1/2 y x z + + 2 2 2 3 3 2 2 2 2 3 2 + - 1/3 y x + 9/8 y x z - 1/6 y z + 1/4 y z - 3/4 y z - 3/8 z y x + + 3 2 3 2 2 + + 1/4 z y x - 1/6 y + 1/2 y - 1/3 y x z + 1/2 z y x - 1/3 y z + + 3 2 2 2 2 2 2 2 2 + + 1/4 y x + 1/2 y x - 3/4 y x z - 3/4 y x z - 3/4 y x z + + 2 2 2 2 2 2 + + 1/2 y x z + 1/2 y z + 1/2 y z - 3/4 y x + 1/2 y x , COEFF(2, -1, 1) + + 2 2 2 2 2 2 2 2 3 + = 1/4 y x z + 1/4 y x z + 1/18 y - 1/6 y x - 3/8 y x z + 1/36 y z + + 3 2 2 2 3 2 2 3 2 + - 1/12 y x - 1/12 y - 1/6 z y x - 1/12 z y x + 1/8 z y x + + 2 2 3 2 3 2 2 2 + + 1/18 y z + 1/8 y z - 1/24 y z + 1/36 y + 1/4 y x - 1/12 y z + + 2 3 2 3 3 + - 1/12 y z , COEFF(-1, 0, 1) = - 3/4 x y z + 1/2 x y z + x + 1/2 x y + + 2 2 2 2 3 3 2 + + 1/6 y - 1/3 z - y x z - 1/2 y x - 3/4 y x z - 1/6 y z + 1/4 y z + + 2 2 2 3 2 3 2 2 2 3 + - 1/2 y z + 3/8 z y x - 1/4 z y x + 3/4 x z - 1/6 y - 1/3 + + 2 2 2 2 3 2 + + 1/3 y + 1/2 z - 1/2 x - 1/2 y x z + 1/4 z y x + 1/6 y z - 1/4 y x + + 2 2 2 2 2 2 2 2 2 + - y x + 3/2 y x z + 1/2 y x z - 3/8 y x z + 3/4 y x z - 1/4 y z + + 2 2 2 2 2 2 + + 1/3 y z + x z - 1/2 x z - 3/2 x z + 1/2 y x + 1/4 y x , + + 3 2 3 3 + COEFF(0, 0, 1) = 3/2 x y z - x y z - 2 x - x y - 1/2 + 1/4 y - 1/2 z + + 2 2 2 2 3 3 2 2 2 + + 2 y x z + y x + 9/4 y x z - 1/4 y z + 3/8 y z - 3/4 y z + + 2 3 2 3 2 2 2 3 2 2 + - 9/8 z y x + 3/4 z y x - 9/4 x z - 1/4 y + 1/2 y + 3/4 z + + 2 2 3 2 2 2 2 + + 3/2 x + y x z - 3/4 z y x + 1/4 y z + 3/4 y x + 2 y x - 3 y x z + + 2 2 2 2 2 2 2 + - 3/2 y x z + 9/8 y x z - 3/2 y x z - 3/8 y z + 1/2 y z - 2 x z + + 2 2 2 2 2 + + 3/2 x z + 3 x z - 3/2 y x - 3/4 y x , COEFF(1, 0, 1) = 1 + + 3 2 3 3 2 + - 3/4 x y z + 1/2 x y z + x + 1/2 x y - 1/2 y + z - y x z - 1/2 y x + + 2 2 2 3 3 2 2 2 2 3 2 + - 9/4 y x z + 1/2 y z - 3/4 y z + 3/2 y z + 9/8 z y x + + 3 2 2 2 3 2 2 2 + - 3/4 z y x + 9/4 x z + 1/2 y - y - 3/2 z - 3/2 x - 1/2 y x z + + 2 3 2 2 2 2 2 2 + + 3/4 z y x - 1/2 y z - 3/4 y x - y x + 3/2 y x z + 3/2 y x z + + 2 2 2 2 2 2 2 + - 9/8 y x z + 3/4 y x z + 3/4 y z - y z + x z - 3/2 x z - 3/2 x z + + 2 2 2 3 2 2 + + 3/2 y x + 3/4 y x , COEFF(2, 0, 1) = 1/4 y x + 1/6 y + 1/12 y + + 3 2 2 2 2 2 2 3 2 3 + - 1/12 y + 3/4 y x z + 1/2 x + 3/8 y x z + 1/4 z y x - 1/12 y z + + 2 2 3 2 2 2 3 2 + - 1/6 z - 1/6 + 1/2 x z - 3/8 z y x - 1/2 y x z + 1/8 y z + + 2 2 2 2 2 2 2 + - 1/2 y x - 1/4 y z + 1/12 y z + 1/6 y z + 1/4 z - 1/4 y x + + 2 2 2 2 3 2 + - 1/8 y z - 1/4 z y x - 3/4 x z , COEFF(-1, 1, 1) = 3/4 x y z + + 3 3 2 2 2 2 + - 1/2 x y z - 1/2 x y - 1/3 y + 1/2 y x z + y x + 3/8 y x z + + 3 3 2 2 2 2 3 2 3 2 3 + + 1/6 y z - 1/4 y z + 1/4 y z - 3/8 z y x + 1/4 z y x + 1/6 y + + 2 2 3 2 2 + - 1/6 y + y x z - 1/2 z y x - 1/3 y z + 1/4 y x + 1/2 y x + + 2 2 2 2 2 2 2 2 + - 3/4 y x z - 1/4 y x z + 3/4 y x z - 3/2 y x z + 1/2 y z + + 2 2 2 2 3 2 3 + - 1/6 y z - 1/4 y x - 1/2 y x , COEFF(0, 1, 1) = - 3/2 x y z + x y z + + 3 2 2 2 2 3 3 2 + + x y - 1/2 y - y x z - 2 y x - 9/8 y x z + 1/4 y z - 3/8 y z + + 2 2 2 3 2 3 2 3 2 + + 3/8 y z + 9/8 z y x - 3/4 z y x + 1/4 y - 1/4 y - 2 y x z + + 2 3 2 2 2 2 2 2 + + 3/2 z y x - 1/2 y z - 3/4 y x - y x + 3/2 y x z + 3/4 y x z + + 2 2 2 2 2 2 2 2 + - 9/4 y x z + 3 y x z + 3/4 y z - 1/4 y z + 3/4 y x + 3/2 y x , + + 3 2 3 3 2 + COEFF(1, 1, 1) = 3/4 x y z - 1/2 x y z - 1/2 x y + y + 1/2 y x z + y x + + 2 2 2 3 3 2 2 2 2 3 2 + + 9/8 y x z - 1/2 y z + 3/4 y z - 3/4 y z - 9/8 z y x + + 3 2 3 2 2 3 2 + + 3/4 z y x - 1/2 y + 1/2 y + y x z - 3/2 z y x + y z + 3/4 y x + + 2 2 2 2 2 2 2 2 + + 1/2 y x - 3/4 y x z - 3/4 y x z + 9/4 y x z - 3/2 y x z + + 2 2 2 2 2 3 + - 3/2 y z + 1/2 y z - 3/4 y x - 3/2 y x , COEFF(2, 1, 1) = 1/12 y z + + 2 2 2 2 2 2 2 3 2 + - 1/6 y - 1/12 y + 1/2 y x + 1/8 y z - 3/4 y x z + 3/8 z y x + + 3 2 3 3 2 3 2 2 2 2 + - 1/8 y z + 1/12 y - 1/4 z y x - 1/4 y x + 1/4 y z + 1/4 y x z + + 2 2 2 2 2 2 2 + - 3/8 y x z - 1/12 y z + 1/2 z y x + 1/4 y x - 1/6 y z, + + 3 2 2 3 3 + COEFF(-1, 2, 1) = 1/12 y z - 1/12 y z + 1/18 y - 1/18 y z + 1/6 x y + + 2 3 2 2 + + 1/12 z y x + 1/18 y z + 1/6 x y z + 1/4 y x z + 1/12 y x - 1/6 y x z + + 3 2 2 3 2 3 2 2 + - 1/12 y x - 1/6 y x + 1/8 z y x - 1/18 y - 1/8 y x z + + 3 2 3 2 3 2 2 + - 1/4 x y z - 1/12 z y x , COEFF(0, 2, 1) = 1/4 y x - 1/4 y x + + 2 3 2 3 2 3 + - 1/8 y z + 1/8 y z - 1/12 y z + 1/3 y x - 1/4 z y x - 1/3 x y + + 2 3 2 3 2 3 2 + - 1/2 y x z - 1/3 x y z - 3/8 z y x + 1/2 x y z + 1/12 y z + 1/12 y + + 2 2 3 2 3 + + 1/3 y x z + 3/8 y x z + 1/4 z y x - 1/12 y , COEFF(1, 2, 1) = + + 3 2 3 2 2 + 1/6 x y - 1/6 y x + 1/4 y x z - 1/6 y z - 1/4 y z + 1/4 y z + + 3 2 2 2 3 2 3 2 + - 1/4 z y x + 1/4 y x + 1/4 z y x - 1/4 x y z - 1/4 y x + + 2 3 2 3 3 2 2 3 + + 3/8 z y x + 1/6 y z + 1/6 x y z - 1/6 y x z - 3/8 y x z + 1/6 y + + 2 3 2 3 3 2 + - 1/6 y, COEFF(2, 2, 1) = - 1/8 z y x - 1/36 y z + 1/24 y z + 1/36 y + + 2 2 3 2 2 2 + - 1/12 z y x - 1/24 y z + 1/36 y z - 1/36 y - 1/12 y x + 1/8 y x z + + 3 2 3 2 2 2 2 + + 1/12 z y x + 1/12 y x , COEFF(-1, -1, 2) = - 1/36 y x - 1/12 y z + + 2 3 2 2 3 3 2 + + 1/18 y z + 1/36 y z - 1/12 y x + 1/36 x y - 1/72 y x + + 3 2 2 3 2 3 2 2 + - 1/12 x y z + 1/24 z y x - 1/108 y - 1/6 y x z + 1/36 y + + 2 2 2 2 2 2 2 + + 1/18 y x - 1/8 y x z - 1/54 y + 1/4 y x z + 1/24 y x + + 2 2 2 2 3 2 2 2 + + 1/12 y x z , COEFF(0, -1, 2) = - 1/8 y x + 1/6 x y z - 1/2 y x z + + 2 2 2 2 2 3 + - 1/36 y + 1/12 y z - 1/9 y x + 3/8 y x z + 1/3 y x z - 1/18 x y + + 3 2 2 2 2 2 2 2 3 2 + + 1/24 y x + 1/6 y x - 1/4 y x z + 1/24 y + 1/12 y x - 1/8 z y x + + 3 2 3 2 2 3 + + 1/24 y z - 1/72 y - 1/8 y z , COEFF(1, -1, 2) = 1/18 y + 1/36 y + + 3 2 3 2 2 2 2 2 + - 1/12 x y z + 1/36 x y - 1/12 y - 3/8 y x z - 1/12 y x + + 2 2 3 2 2 2 2 2 2 2 + + 1/4 y z - 1/12 y z + 1/4 y x z - 1/6 y z - 1/12 y x + 1/8 y x + + 2 2 3 2 3 2 2 2 + - 1/6 y x z + 1/18 y x + 1/8 z y x - 1/24 y x + 1/4 y x z , + + 2 3 2 2 3 2 2 2 2 + COEFF(2, -1, 2) = 1/72 y + 1/72 y x - 1/24 z y x + 1/8 y x z + + 2 2 2 2 3 2 2 2 + + 1/36 y x - 1/24 y x + 1/36 y z + 1/72 y z - 1/24 y z - 1/108 y + + 3 2 2 2 2 + - 1/216 y - 1/12 y x z , COEFF(-1, 0, 2) = 1/12 y x + 1/6 y z + + 2 2 2 2 2 2 2 2 2 + - 1/2 y x z + 1/8 y x z - 1/6 x + 1/4 y x z - 1/4 x z + + 2 2 3 2 2 + - 1/12 y x - 1/12 x y + 1/12 y z + 1/18 - 1/36 y - 1/18 y + + 3 2 2 2 2 3 2 + + 1/24 y x + 1/2 x z - 1/24 y x + 1/6 y x + 1/36 y - 1/4 y x z + + 2 3 2 2 3 2 2 3 2 + + 1/12 x - 1/12 y z - 1/6 z + 1/4 x y z - 1/8 z y x , + + 2 2 3 2 2 2 3 2 2 + COEFF(0, 0, 2) = 1/4 y x - 1/8 y z + y x z + 1/6 x y + 3/4 x z + + 2 2 2 2 2 2 2 3 2 + + 1/4 y z - 3/8 y x z - 1/12 y - x z + 1/3 x - 1/4 z - 1/2 x y z + + 3 2 2 2 2 + - 1/8 y x + 1/12 - 1/3 y x - 1/6 y x + 1/2 y x z + 1/8 y x + + 2 2 2 2 3 2 2 2 3 + - 3/4 y x z + 3/8 z y x - 1/24 y - 1/4 x + 1/8 y z + 1/24 y , + + 3 2 2 2 2 2 2 2 + COEFF(1, 0, 2) = 1/8 y x - 1/6 + 3/4 y x z + 3/8 y x z - 1/4 y z + + 3 2 2 2 2 2 3 2 2 + - 1/12 x y - 1/2 y z + 1/4 x - 1/6 x - 1/4 y x - 1/12 y - 3/4 x z + + 3 2 2 2 2 + + 1/4 x y z + 1/12 y + 1/2 z + 1/2 x z - 1/4 y x z + 1/12 y x + + 2 2 2 2 2 3 2 2 3 2 + - 1/2 y x z + 1/6 y x - 1/8 y x + 1/6 y + 1/4 y z - 3/8 z y x , + + 3 2 2 2 2 2 2 + COEFF(2, 0, 2) = - 1/24 y x + 1/4 x z - 1/72 y + 1/12 y z - 1/12 x + + 3 2 3 2 2 2 3 2 2 + - 1/24 y z + 1/72 y - 1/8 y x z + 1/8 z y x - 1/12 z + + 2 2 2 2 2 2 2 2 + - 1/4 y x z + 1/12 y x + 1/36 + 1/24 y z + 1/24 y x - 1/36 y , + + 2 2 3 2 2 2 + COEFF(-1, 1, 2) = 1/4 y x z - 1/24 y x + 1/18 y + 1/24 y x + + 3 2 2 2 2 2 2 2 2 2 + + 1/12 y z - 1/12 y z + 1/12 y x + 1/36 y - 1/8 y x z - 1/6 y z + + 3 2 2 2 2 3 2 3 + + 1/12 x y - 1/12 y x - 1/4 y x z + 1/8 z y x - 1/36 y - 1/6 y x + + 2 3 2 3 3 2 + + 1/2 y x z - 1/4 x y z , COEFF(0, 1, 2) = - 1/24 y + 1/2 x y z + + 3 2 2 2 2 2 2 3 2 + - 1/6 x y - y x z - 1/2 y x z + 3/8 y x z + 1/12 y + 1/8 y x + + 2 2 2 2 3 2 2 2 2 + - 1/8 y z - 1/4 y x + 1/6 y x + 1/8 y z + 3/4 y x z - 1/4 y z + + 2 2 2 3 2 2 + - 1/8 y x + 1/3 y x - 3/8 z y x + 1/24 y , COEFF(1, 1, 2) = + + 2 3 2 2 2 2 2 2 3 2 3 2 2 + 3/8 z y x + 1/8 y x - 3/8 y x z - 1/8 y x - 1/4 y z - 1/12 y + + 3 2 2 2 3 2 2 + - 1/6 y x + 1/12 x y - 1/12 y x + 1/4 y z - 1/4 x y z + 1/4 y x + + 2 2 2 2 3 2 2 + + 1/4 y x z - 1/6 y + 1/2 y x z + 1/2 y z + 1/12 y - 3/4 y x z , + + 2 3 2 2 2 3 2 + COEFF(2, 1, 2) = - 1/8 z y x - 1/24 y x - 1/72 y + 1/36 y - 1/12 y z + + 2 2 2 2 3 2 2 2 + - 1/24 y z + 1/72 y - 1/12 y x + 1/24 y x + 1/4 y x z + + 2 2 2 3 2 3 2 + + 1/8 y x z + 1/24 y z , COEFF(-1, 2, 2) = - 1/36 y z - 1/108 y + + 2 2 2 3 2 3 + - 1/72 y x + 1/36 y z - 1/24 z y x + 1/36 y x + 1/108 y + + 2 3 3 2 3 2 2 2 + - 1/12 y x z - 1/36 x y + 1/72 y x + 1/12 x y z + 1/24 y x z , + + 3 3 3 2 2 + COEFF(0, 2, 2) = 1/18 x y + 1/72 y - 1/72 y - 1/24 y z + 1/24 y x + + 2 3 2 3 2 2 2 + + 1/8 z y x - 1/6 x y z - 1/18 y x + 1/6 y x z + 1/24 y z + + 3 2 2 2 3 2 2 3 2 + - 1/24 y x - 1/8 y x z , COEFF(1, 2, 2) = 1/12 x y z - 1/8 z y x + + 3 2 3 3 2 3 + + 1/12 y z - 1/36 x y + 1/24 y x + 1/36 y x + 1/36 y - 1/36 y + + 2 2 2 2 2 + - 1/12 y z + 1/8 y x z - 1/12 y x z - 1/24 y x , COEFF(2, 2, 2) = + + 2 2 2 3 2 3 2 2 2 + 1/72 y z + 1/72 y x + 1/24 z y x - 1/72 y x - 1/216 y - 1/24 y x z + + 3 2 3 + - 1/72 y z + 1/216 y ] + +> print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxz.compute.c"); +bytes used=7274949596, alloc=10549364, time=773.96 +bytes used=7275949780, alloc=10549364, time=774.03 +bytes used=7276950268, alloc=10549364, time=774.12 +bytes used=7277952708, alloc=10549364, time=774.20 +bytes used=7278952960, alloc=10549364, time=774.28 +bytes used=7279953680, alloc=10549364, time=774.37 +bytes used=7280954036, alloc=10549364, time=774.46 +bytes used=7281954268, alloc=10549364, time=774.55 +bytes used=7282954512, alloc=10549364, time=774.75 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used=7533408664, alloc=10549364, time=826.67 +bytes used=7534434360, alloc=10549364, time=830.78 +bytes used=7535434544, alloc=10549364, time=831.96 +bytes used=7536434860, alloc=10549364, time=832.74 +bytes used=7537435324, alloc=10549364, time=832.83 +bytes used=7538435628, alloc=10549364, time=832.91 +bytes used=7539436092, alloc=10549364, time=832.98 +bytes used=7540436384, alloc=10549364, time=833.05 +bytes used=7541436668, alloc=10549364, time=833.12 +bytes used=7542437084, alloc=10549364, time=833.20 +bytes used=7543437324, alloc=10549364, time=833.29 +bytes used=7544437816, alloc=10549364, time=833.35 +bytes used=7545438008, alloc=10549364, time=833.43 +bytes used=7546438260, alloc=10549364, time=833.51 +bytes used=7547438528, alloc=10549364, time=833.60 +bytes used=7548439404, alloc=10549364, time=833.84 +bytes used=7549439632, alloc=10549364, time=834.03 +bytes used=7550439880, alloc=10549364, time=834.24 +bytes used=7551440140, alloc=10549364, time=834.45 +bytes used=7552441492, alloc=10549364, time=834.61 +bytes used=7553441704, alloc=10549364, time=834.73 +bytes used=7554441888, alloc=10549364, time=834.85 +bytes used=7555442084, alloc=10549364, time=834.97 +bytes used=7556442352, alloc=10549364, time=836.24 +bytes used=7557442596, alloc=10549364, time=840.26 +bytes used=7558442804, alloc=10549364, time=841.44 +bytes used=7559443316, alloc=10549364, time=842.20 +bytes used=7560443592, alloc=10549364, time=842.47 +bytes used=7561443972, alloc=10549364, time=842.62 +bytes used=7562444756, alloc=10549364, time=842.68 +bytes used=7563444928, alloc=10549364, time=842.84 +bytes used=7564445300, alloc=10549364, time=843.05 +bytes used=7565445588, alloc=10549364, time=843.27 +> +# d^2/dy^2 +> simplify( diff(interp_3d_cube_order3_smooth0,y,y) ); +bytes used=7566784908, alloc=10549364, time=843.39 +bytes used=7567785112, alloc=10549364, time=843.47 +bytes used=7568785248, alloc=10549364, time=843.54 +bytes used=7569785392, alloc=10549364, time=843.62 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DATA(1, 1, 1) + 1/6 x z DATA(1, 0, 2) + +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=7577850224, alloc=10549364, time=844.32 +bytes used=7578885412, alloc=10549364, time=844.40 +bytes used=7579885612, alloc=10549364, time=844.49 +bytes used=7580924316, alloc=10549364, time=844.59 +bytes used=7582011040, alloc=10549364, time=844.67 +bytes used=7583021552, alloc=10549364, time=844.76 +bytes used=7584042612, alloc=10549364, time=844.85 +bytes used=7585074368, alloc=10549364, time=844.95 +bytes used=7586074588, alloc=10549364, time=845.04 +bytes used=7587076764, alloc=10549364, time=845.13 +bytes used=7588084520, alloc=10549364, time=845.20 +bytes used=7589110508, alloc=10549364, time=845.26 + 2 2 2 2 3 2 2 +[COEFF(-1, -1, -1) = 1/4 x z + 1/6 y x z + 1/12 z y x - 1/4 y x z + + 2 3 2 3 2 3 3 + - 1/12 z x - 1/9 y x z - 1/6 x z - 1/12 z x + 1/9 x z + 1/36 z x + + 2 3 3 3 2 3 + - 1/6 x z - 1/36 z y x - 1/18 z y x + 1/6 z y x + 1/18 x z + + 3 3 2 3 2 + - 1/18 y x z + 1/12 z y x + 1/18 z x , COEFF(0, -1, -1) = 1/3 x z + + 3 3 3 3 3 3 + - 1/6 y x z - 1/12 z x - 1/12 y x z + 1/12 z y x + 1/6 z y x + + 3 3 2 2 2 2 3 2 + - 1/6 z + 1/6 z x - 1/2 y z - 1/3 z y x - 1/4 z y x - 1/4 x z + + 2 3 3 2 3 2 2 3 + + 1/4 z x - 1/6 z y x + 1/12 x z + 1/3 y z + 1/2 y x z + 1/6 y z + + 2 3 2 2 2 + + 1/4 y x z + 1/6 x z - 1/6 z x - 1/2 x z - 1/3 z + 1/2 z , + + 3 2 2 2 3 3 + COEFF(1, -1, -1) = 1/12 z y x - 1/4 y x z + 1/3 y x z - 1/12 z y x + + 3 2 2 3 3 2 2 + - 1/12 z x + 1/4 z y x + 1/6 y x z - 1/3 x z + 1/6 z y x - 1/6 x z + + 2 3 2 3 2 3 3 3 + - 1/4 z x - 1/2 y x z - 1/6 x z + 1/2 x z + 1/12 z x + 1/6 z x + + 3 2 2 3 3 3 3 + - 1/6 z y x + 1/4 x z , COEFF(2, -1, -1) = 1/36 z y x - 1/36 z x + + 3 3 2 3 2 + - 1/36 y x z + 1/36 x z - 1/12 x z - 1/18 z x + 1/12 y x z + 1/18 x z + + 3 2 3 2 3 + + 1/18 z y x - 1/12 z y x - 1/18 y x z + 1/12 z x , COEFF(-1, 0, -1) + + 3 2 2 3 3 2 3 + = - 2/9 x z + 1/6 z x - 1/2 y x z + 1/6 z y x - 1/4 z y x - 1/9 x z + + 2 2 2 2 3 3 + - 1/2 z y x + 3/4 y x z + 1/3 y x z - 1/4 z y x + 1/6 y x z + + 2 3 3 2 2 3 3 2 2 3 + + 1/3 x z + 1/12 z y x - 1/2 x z - 1/18 z x + 1/3 x z + 1/6 z x + + 3 3 2 3 2 3 + - 1/9 z x , COEFF(0, 0, -1) = 1/4 y x z - 1/2 z x - 2/3 x z - 1/6 x z + + 3 3 3 2 2 2 2 3 3 + - y z - 1/4 z y x - 1/3 z x - 3/2 y x z + 3/2 y z + 1/6 z x + + 3 2 2 2 2 2 3 3 + + 1/2 z y x + 1/2 x z - 3/4 y x z + x z - 1/2 z y x + 1/3 z + + 2 2 3 2 3 + + z y x - z + 1/3 z x + 3/4 z y x + 2/3 z + 1/2 y x z - 1/3 x z + + 3 2 3 2 3 3 + - 1/2 y z , COEFF(1, 0, -1) = - 3/4 z y x - y x z + 1/2 z x + 1/3 x z + + 3 2 2 3 3 2 2 3 2 + - 1/2 y x z - 1/2 z y x + 1/3 x z - 1/6 z x - 1/2 x z - 1/4 z y x + + 3 3 2 2 2 3 3 + + 2/3 x z + 1/2 z y x + 1/6 z x - x z + 3/2 y x z + 1/4 z y x + + 2 2 3 2 3 + + 3/4 y x z - 1/3 z x , COEFF(2, 0, -1) = 1/6 y x z - 1/6 z x + + 2 2 3 3 3 3 3 + + 1/6 x z + 1/4 z y x + 1/9 z x - 1/12 z y x + 1/12 y x z + + 3 3 2 3 3 + - 1/6 z y x - 1/18 x z - 1/4 y x z + 1/18 z x - 1/9 x z, + + 3 3 2 2 2 3 + COEFF(-1, 1, -1) = 1/36 z x + 1/9 x z + 1/4 x z + 1/4 z y x + + 3 2 2 3 3 2 2 + + 1/4 z y x + 1/2 y x z - 1/12 z y x - 1/6 x z + 1/2 z y x + + 3 2 3 2 2 3 2 + + 1/18 z x - 1/6 x z - 1/3 y x z - 1/6 y x z - 3/4 y x z - 1/12 z x + + 2 3 3 3 3 + - 1/12 z x + 1/18 x z - 1/6 z y x , COEFF(0, 1, -1) = - 1/6 z x + + 2 2 3 2 2 2 3 + - 1/2 x z + 1/2 y z - 3/2 y z - 1/3 z + 3/2 y x z + 1/2 z y x + + 3 2 3 2 3 3 2 2 + - 1/2 z y x - 1/6 z + 1/4 z x + 1/12 x z + 3/4 y x z - 1/4 x z + + 2 2 3 3 3 2 + + 1/3 x z - 1/2 y x z - 3/4 z y x + 1/4 z y x + y z - z y x + + 2 3 2 3 3 3 + + 1/6 x z + 1/2 z + 1/6 z x - 1/4 y x z - 1/12 z x , COEFF(1, 1, -1) + + 2 3 2 3 2 2 2 + = - 1/4 z x + 1/2 z y x + 1/2 y x z - 3/4 y x z - 1/6 x z + + 3 3 2 2 3 2 + + 1/12 z x + y x z + 1/2 x z + 3/4 z y x - 3/2 y x z - 1/3 x z + + 3 2 3 3 3 3 2 3 2 2 + - 1/12 z x - 1/6 x z - 1/4 z y x + 1/4 z y x + 1/6 z x + 1/4 x z + + 3 3 3 2 + - 1/2 z y x , COEFF(2, 1, -1) = - 1/18 z x - 1/12 y x z - 1/12 x z + + 3 3 3 3 + + 1/12 z y x - 1/6 y x z + 1/36 x z + 1/6 z y x + 1/18 x z + + 3 3 2 2 3 2 3 + - 1/36 z x + 1/4 y x z - 1/4 z y x + 1/12 z x , COEFF(-1, 2, -1) = + + 3 2 2 2 3 + - 1/12 z y x + 1/9 y x z - 1/6 y x z - 1/6 z y x + 1/18 y x z + + 3 2 2 3 3 2 3 + + 1/18 z y x + 1/4 y x z + 1/36 z y x - 1/12 z y x , COEFF(0, 2, -1) + + 2 3 2 2 3 3 + = 1/4 z y x + 1/2 y z + 1/3 z y x + 1/12 y x z - 1/6 y z + + 2 2 3 2 + - 1/2 y x z - 1/3 y z - 1/6 z y x + 1/6 y x z - 1/4 y x z + + 3 3 3 2 3 + - 1/12 z y x + 1/6 z y x , COEFF(1, 2, -1) = - 1/6 y x z + + 3 2 2 2 2 3 3 + - 1/12 z y x + 1/4 y x z - 1/3 y x z - 1/6 z y x + 1/12 z y x + + 2 3 2 3 3 + - 1/4 z y x + 1/2 y x z + 1/6 z y x , COEFF(2, 2, -1) = 1/36 y x z + + 2 3 3 3 2 3 + - 1/12 y x z - 1/18 z y x - 1/36 z y x + 1/12 z y x + 1/18 y x z, + + 2 3 2 3 + COEFF(-1, -1, 0) = 1/3 x z - 1/6 x z + 1/2 x - 1/6 y x z + 1/6 y x + + 2 3 2 3 3 + - 1/2 y x + 1/6 x z - 1/3 x - 1/4 z y x - 1/6 x - 1/12 z y x + + 3 3 2 2 3 3 3 3 + + 1/3 y x - 1/12 z x - 1/2 x z + 1/12 z x + 1/6 y x z + 1/12 z y x + + 2 3 2 2 2 2 2 + - 1/6 z y x - 1/3 y x z + 1/2 y x z - 1/4 x z + 1/4 z y x + + 2 3 3 2 3 3 + + 1/6 z x + 1/4 z x , COEFF(0, -1, 0) = 1 - 1/2 y z + 1/4 y x z + + 3 3 3 3 2 3 + - 1/2 y x - 1/2 x - y - 1/2 z + 1/4 z y x - 1/4 z y x + 1/2 z y x + + 3 2 2 3 3 3 2 2 3 3 + + 1/2 y x - 1/2 z x - 1/2 z x + 1/4 z x + x z - 1/4 z x + 1/2 z + + 3 2 2 3 2 2 2 + + 1/2 x - z - x - 1/4 x z - 1/4 y x z - 1/2 z y x + 1/2 y z - y x z + + 2 2 2 2 3 2 2 + - 1/2 y x z + y z + 1/4 x z + 1/2 x z + 1/2 x z + 1/2 z y x + y x , + + 2 3 3 3 2 + COEFF(1, -1, 0) = - 1/4 x z + 1/4 z x - 1/2 y x z + 1/2 y x + 1/2 x + + 2 3 3 3 3 2 2 3 2 + + 1/2 z x - 1/2 x + 1/4 z y x + 1/2 y x z + 1/2 y x z - 1/4 z y x + + 3 2 2 3 2 3 + - 1/2 x z + 1/4 z x + y x z + 1/2 x z - x z - 1/4 z y x - y x + + 2 3 3 2 3 2 2 2 + + 1/4 z y x - 1/4 z x - 1/2 z y x - 1/2 y x - 1/2 x z + x, + + 2 3 3 + COEFF(2, -1, 0) = 1/6 y x - 1/6 y x z - 1/6 y x + 1/12 y x z + + 2 3 3 3 3 2 + + 1/6 z y x + 1/12 x z - 1/12 y x z + 1/12 z x - 1/12 x z + 1/6 x z + + 3 3 3 3 2 3 3 + - 1/6 x - 1/12 z x + 1/6 x - 1/12 z y x - 1/6 z x + 1/12 z y x , + + 3 3 3 2 3 2 + COEFF(-1, 0, 0) = - 1/4 z y x + 1/3 x z + 1/2 z y x + 3/2 y x + + 2 2 3 3 3 2 2 3 + + 1/2 x z - 1/3 z x - 1/2 y x + 1/4 z y x + x z + 1/3 x + 2/3 x + + 3 2 3 2 2 3 3 + + 3/4 z y x - 1/6 z x - y x + y x z - 3/4 z y x + 1/6 z x + + 2 2 3 3 2 2 + - 3/2 y x z + 1/2 y x z - 1/3 x z - 1/2 y x z - 1/2 z x - 2/3 x z + + 2 3 3 3 + - x , COEFF(0, 0, 0) = -2 + 3/2 y z - 3/4 y x z + 3/2 y x + x + 3 y + z + + 3 3 3 2 3 3 2 2 3 + - 3/4 z y x + 3/4 z y x - 3/2 z y x - 3/2 y x + z x + z x + + 3 3 2 2 3 3 3 2 2 3 + - 1/2 z x - 2 x z + 1/2 z x - z - x + 2 z + 2 x + 1/2 x z + + 2 2 2 2 2 + + 3/4 y x z + 3/2 z y x - 3/2 y z + 3 y x z + 3/2 y x z - 3 y z + + 2 2 3 2 2 3 + - 1/2 x z - x z - x z - 3/2 z y x - 3 y x , COEFF(1, 0, 0) = x + + 3 3 2 2 2 2 2 + - 3/2 y x - 2 x + 3 y x + 3/4 z y x + 2 x z - 3/2 y x z + x z + + 2 2 3 3 3 2 3 + + 3/2 y x + 3/2 z y x - 3/4 z y x + x z - 3/4 z y x - 1/2 z x + + 3 3 3 2 3 3 2 2 3 + + 1/2 z x + 3/2 y x z - 3 y x z - x z + 3/4 z y x - z x + + 2 2 3 2 3 + - 3/2 y x z + 1/2 x z - x - 1/2 z x , COEFF(2, 0, 0) = 1/6 z x + 1/3 x + + 2 3 2 3 3 3 3 2 + - 1/2 z y x + 1/3 z x - 1/6 x z - 1/4 y x z + 1/4 z y x - 1/3 x z + + 2 3 3 3 + + 1/2 y x z - 1/2 y x + 1/4 y x z - 1/4 z y x + 1/2 y x + 1/6 x z + + 3 3 3 2 2 3 3 + - 1/3 x - 1/6 z x , COEFF(-1, 1, 0) = - 3/2 y x + 1/6 z x - 1/6 x z + + 3 2 2 3 3 2 3 2 + + 1/12 z x + 3/2 y x z - 1/4 z y x + 1/2 y x z - 1/4 x z + 1/4 z x + + 2 2 3 3 2 3 + - 1/2 x z - 1/3 x - 1/6 x - 1/2 y x z + y x + 1/2 y x - 1/2 z y x + + 3 3 2 3 3 2 3 2 2 + - 1/12 z x + 1/3 x z + 1/4 z y x + 3/4 z y x - 3/4 z y x - y x z + + 2 3 3 3 + + 1/6 x z + 1/2 x , COEFF(0, 1, 0) = 1 - 3/2 y z + 3/4 y x z - 3/2 y x + + 3 3 3 2 3 + - 1/2 x - 3 y - 1/2 z + 3/4 z y x - 3/4 z y x + 3/2 z y x + 3/2 y x + + 3 2 2 3 3 3 2 2 3 3 3 + - 1/2 z x - 1/2 z x + 1/4 z x + x z - 1/4 z x + 1/2 z + 1/2 x + + 2 2 3 2 2 2 + - z - x - 1/4 x z - 3/4 y x z - 3/2 z y x + 3/2 y z - 3 y x z + + 2 2 2 2 3 2 + - 3/2 y x z + 3 y z + 1/4 x z + 1/2 x z + 1/2 x z + 3/2 z y x + + 2 2 2 3 3 3 + + 3 y x , COEFF(1, 1, 0) = 1/2 x + 3/4 z y x - 1/4 z x + x + 3/2 y x + + 3 2 3 2 3 2 2 + + 3/2 y x z + 1/4 z x + 1/4 z x - 3/2 z y x + 3/2 y x z + + 3 3 2 2 2 2 + - 3/2 y x z - 3 y x - 3/4 z y x - 1/4 x z - x z - 3/2 y x + + 3 3 3 2 2 2 3 3 + - 3/4 z y x + 1/2 x z - 1/2 x + 3 y x z - 1/2 x z + 3/4 z y x + + 2 3 3 2 3 + + 1/2 z x - 1/2 x z, COEFF(2, 1, 0) = 1/4 y x z + 1/6 x z - 1/12 z x + + 3 2 2 3 3 3 2 3 + - 1/6 x - 1/2 y x - 1/2 y x z - 1/6 z x - 1/4 z y x + 1/2 z y x + + 3 3 3 3 3 + + 1/12 z x - 1/12 x z + 1/12 x z + 1/4 z y x + 1/2 y x + 1/6 x + + 3 2 + - 1/4 y x z, COEFF(-1, 2, 0) = - 1/6 y x z + 1/3 y x z + 1/6 y x z + + 3 3 2 3 2 3 3 + - 1/6 y x - 1/3 y x + 1/12 z y x + 1/2 y x + 1/4 z y x - 1/12 z y x + + 2 2 2 3 2 2 3 + - 1/2 y x z + 1/6 z y x - 1/4 z y x , COEFF(0, 2, 0) = y - 1/2 z y x + + 2 2 3 3 3 3 3 + + 1/2 y x z + 1/2 z y x + 1/4 z y x - 1/4 y x z + 1/2 y x + 1/2 y z + + 3 2 2 2 2 + - 1/4 z y x - 1/2 y x - y x + 1/4 y x z + y x z - y z - 1/2 y z + + 3 2 3 3 3 + - 1/2 z y x , COEFF(1, 2, 0) = - 1/2 y x z - 1/4 z y x + 1/2 y x z + + 2 3 3 2 2 3 2 2 + - y x z + 1/4 z y x + y x + 1/4 z y x + 1/2 z y x - 1/2 y x z + + 3 2 2 3 + - 1/2 y x - 1/4 z y x + 1/2 y x , COEFF(2, 2, 0) = 1/6 y x + + 3 3 2 3 3 2 3 + + 1/12 z y x - 1/6 z y x - 1/12 y x z + 1/6 y x z - 1/12 z y x + + 3 2 3 + - 1/6 y x + 1/12 y x z, COEFF(-1, -1, 1) = - 1/6 z x + 1/12 z y x + + 2 3 2 3 3 3 3 3 2 + + 1/2 x z + 1/4 z y x - 1/12 z y x + 1/12 z x - 1/4 z x + + 3 3 3 2 2 2 + + 1/6 x z - 1/6 y x z + 1/6 z y x + 1/4 x z + 1/3 y x z - 1/6 x z + + 2 2 3 2 2 2 + - 1/3 x z + 1/6 y x z - 1/12 z x - 1/4 y x z - 1/2 z y x , + + 2 2 3 3 3 3 + COEFF(0, -1, 1) = 1/2 z - 1/2 y z - 1/4 z x - 1/2 z - 1/4 y x z + + 3 2 3 3 3 2 2 2 2 + - 1/2 z y x + 1/4 z y x + 1/2 z x + z + 1/4 y x z + 1/2 y x z + + 3 2 2 3 2 3 2 + - 1/2 z y x - 1/2 x z + 1/2 y z + 1/4 z x - 1/2 x z - x z + + 2 3 2 3 3 2 + - 1/4 z y x - 1/4 x z + 1/2 z x + 1/4 x z + z y x + 1/2 y x z - y z, + + 3 2 2 2 3 + COEFF(1, -1, 1) = - 1/2 x z - 1/4 y x z - 1/2 y x z - 1/2 z x + + 2 3 2 3 2 3 3 2 + + 1/4 z y x + 1/2 x z - y x z + 1/4 z y x - 1/4 z y x + 1/2 x z + + 3 3 2 3 3 3 2 3 + + 1/4 z x + x z - 1/4 z x + 1/2 z y x - 1/4 z x + 1/2 y x z + + 2 2 2 2 2 3 + + 1/4 x z - 1/2 z y x , COEFF(2, -1, 1) = - 1/12 x z + 1/12 z x + + 2 3 3 3 3 + + 1/12 y x z - 1/12 z x - 1/6 x z - 1/12 y x z + 1/6 z x + + 2 3 3 3 3 3 + - 1/12 z y x + 1/12 x z + 1/12 z y x + 1/6 y x z - 1/6 z y x , + + 2 3 3 2 2 + COEFF(-1, 0, 1) = 3/2 z y x + 1/4 z y x - 1/2 y x z - x z - y x z + + 2 3 2 3 3 2 2 3 3 + - 1/4 z y x + 1/6 z x - 1/2 z y x + 2/3 x z + 3/4 y x z - 1/6 z x + + 2 2 3 2 3 2 2 3 3 + - 1/2 x z + 1/2 z x - 3/4 z y x + 1/3 x z + 1/2 y x z + 1/3 z x + + 3 3 3 3 2 2 3 2 + - 1/3 x z , COEFF(0, 0, 1) = - 3/2 y z + 1/2 z x - 3/2 y x z - z x + + 2 2 3 3 2 3 3 3 2 + - 3/4 y x z - z - 2 z - z x + 3/2 z y x - 3/4 z y x + z + 1/2 x z + + 3 2 3 2 3 2 2 + + 3/2 z y x + 3/2 y z + 3/4 y x z + 3/4 z y x + x z + x z + + 2 3 2 3 2 + - 1/2 z x - 3/2 y x z - 3 z y x - 1/2 x z + 2 x z + 3 y z, + + 2 3 2 2 2 3 2 3 + COEFF(1, 0, 1) = 1/2 z x - x z - 1/2 x z - 3/4 z y x - 3/2 y x z + + 2 3 3 2 3 2 3 + + 3/2 z y x - 1/2 z x - 3/4 z y x + 3 y x z + 3/2 y x z + z x + + 3 2 3 3 2 2 2 3 3 + + x z - x z - 2 x z - 3/2 z y x + 1/2 z x + 3/4 y x z + 3/4 z y x + + 2 3 3 2 + , COEFF(2, 0, 1) = - 1/4 y x z - 1/3 z x + 1/4 y x z + 1/6 x z + + 3 3 2 3 3 3 3 + - 1/2 y x z - 1/4 z y x + 1/3 x z - 1/6 z x + 1/2 z y x + 1/6 z x + + 2 3 3 2 3 + + 1/4 z y x - 1/6 x z , COEFF(-1, 1, 1) = 1/2 x z - 1/6 z x + + 2 3 3 2 3 2 3 3 2 + - 1/12 z x - 1/4 z x + 3/4 z y x + 1/12 z x + 1/2 y x z + + 2 2 3 3 3 2 3 + + 1/4 x z + 1/6 x z - 1/4 z y x + 1/4 z y x - 1/3 x z + y x z + + 2 2 2 2 3 3 + - 3/2 z y x - 3/4 y x z - 1/6 x z - 1/2 y x z + 1/2 z y x , + + 3 2 2 3 2 2 2 2 + COEFF(0, 1, 1) = 1/2 z x - x z + 3/2 y z - 1/2 x z + 3/2 y x z + + 2 3 3 2 3 3 2 3 + + 1/4 z x - 3/2 z y x + 3/4 z y x + 3/4 y x z - 1/2 z + 3/2 y x z + + 2 3 2 2 3 2 + + 1/2 z - 3/4 y x z + 3 z y x - 3 y z + z - 3/4 z y x - 3/2 y z + + 3 3 3 3 2 3 + - 3/2 z y x - 1/4 z x + 1/2 z x - 1/2 x z - 1/4 x z + 1/4 x z , + + 3 2 3 3 + COEFF(1, 1, 1) = - 1/2 z x - 3/2 z y x - 3 y x z + 1/4 z x + + 3 2 3 3 2 2 3 2 2 + + 3/4 z y x - 1/2 x z - 1/4 z x + 3/4 z y x - 3/4 y x z + + 2 3 2 2 2 3 3 3 + + 1/2 x z + 3/2 y x z + 1/4 x z - 1/4 z x + x z - 3/4 z y x + + 2 2 3 2 + - 3/2 y x z + 1/2 x z + 3/2 z y x , COEFF(2, 1, 1) = 1/4 y x z + + 3 3 3 3 3 2 3 + - 1/12 z x - 1/4 y x z + 1/6 z x - 1/2 z y x + 1/12 z x - 1/6 x z + + 2 3 3 3 2 3 + - 1/4 z y x + 1/2 y x z + 1/4 z y x - 1/12 x z + 1/12 x z , + + 2 2 3 2 + COEFF(-1, 2, 1) = 1/2 z y x - 1/6 y x z - 1/3 y x z - 1/4 z y x + + 3 3 3 3 2 2 2 3 + + 1/12 z y x + 1/6 y x z - 1/6 z y x + 1/4 y x z - 1/12 z y x , + + 2 2 3 2 + COEFF(0, 2, 1) = - 1/2 y x z - 1/2 y x z - 1/2 y z - 1/4 y x z + + 3 3 3 2 3 3 2 3 + - 1/4 z y x + 1/2 z y x + 1/4 y x z + 1/2 z y x + y z + 1/4 z y x + + 2 2 2 3 2 + + 1/2 y z - z y x , COEFF(1, 2, 1) = 1/2 y x z - 1/4 z y x + + 3 2 2 3 2 3 + - 1/2 y x z + 1/4 y x z - 1/2 z y x - 1/4 z y x + y x z + + 3 3 2 3 3 2 3 + + 1/4 z y x + 1/2 z y x , COEFF(2, 2, 1) = - 1/12 z y x + 1/12 z y x + + 2 3 3 + - 1/12 y x z + 1/6 z y x + 1/12 y x z - 1/6 y x z, COEFF(-1, -1, 2) = + + 3 3 3 2 2 3 3 + 1/36 z y x + 1/12 z x - 1/12 x z - 1/36 z y x + 1/36 z x + + 3 3 2 3 3 2 + - 1/18 y x z + 1/18 y x z - 1/12 z y x - 1/36 z x + 1/12 z y x + + 3 3 3 + - 1/18 x z + 1/18 x z, COEFF(0, -1, 2) = 1/12 y x z + 1/12 z y x + + 3 3 3 2 2 3 + - 1/12 y x z + 1/6 z + 1/12 z x - 1/6 z y x + 1/6 x z - 1/12 z x + + 3 2 3 2 3 3 3 + - 1/6 z - 1/6 z x + 1/6 z y x + 1/6 y z - 1/12 z y x - 1/6 y z + + 3 3 + - 1/12 x z + 1/12 x z, COEFF(1, -1, 2) = - 1/6 x z + 1/6 x z + + 3 3 3 3 3 3 + - 1/12 z x - 1/12 z y x + 1/12 z x + 1/6 y x z + 1/12 z y x + + 3 2 3 2 2 3 2 + + 1/12 z x - 1/6 y x z - 1/12 x z + 1/12 z y x - 1/12 z y x , + + 3 3 3 3 3 3 + COEFF(2, -1, 2) = 1/36 y x z - 1/36 z y x + 1/36 z x - 1/36 x z + + 3 3 + - 1/36 y x z + 1/36 z y x + 1/36 x z - 1/36 z x , COEFF(-1, 0, 2) = + + 3 3 3 3 3 3 2 3 2 + - 1/18 z x + 1/18 z x - 1/12 z y x - 1/6 z x + 1/4 z y x + + 3 3 2 2 3 + + 1/12 z y x + 1/9 x z + 1/6 x z - 1/4 z y x - 1/6 y x z + 1/6 y x z + + 3 3 2 + - 1/9 x z, COEFF(0, 0, 2) = - 1/4 z y x - 1/2 z y x - 1/2 y z + + 3 3 3 2 2 3 + + 1/4 z y x - 1/3 z - 1/3 x z + 1/2 z y x - 1/6 x z - 1/4 y x z + + 3 3 3 2 3 3 + + 1/6 z x + 1/2 y z + 1/3 z x + 1/4 y x z - 1/6 z x + 1/3 z + + 3 3 3 3 2 + + 1/6 x z , COEFF(1, 0, 2) = 1/2 y x z + 1/3 x z + 1/4 z y x - 1/6 z x + + 3 3 2 3 3 3 2 + - 1/4 z y x - 1/4 z y x - 1/3 x z - 1/6 z x - 1/2 y x z + 1/4 z y x + + 3 3 2 3 3 3 3 + + 1/6 z x + 1/6 x z, COEFF(2, 0, 2) = - 1/18 z x + 1/12 z y x + + 3 3 3 + - 1/12 y x z + 1/18 x z + 1/12 y x z - 1/18 x z - 1/12 z y x + + 3 3 3 3 + + 1/18 z x , COEFF(-1, 1, 2) = - 1/36 z x - 1/6 y x z + 1/6 y x z + + 3 3 2 3 2 + - 1/18 x z - 1/12 z y x + 1/18 x z + 1/4 z y x - 1/4 z y x + + 3 2 3 3 2 3 + + 1/12 z x + 1/12 z y x - 1/12 x z + 1/36 z x , COEFF(0, 1, 2) = + + 3 3 3 2 3 + - 1/12 z x + 1/12 z x - 1/2 z y x + 1/2 y z - 1/4 y x z + 1/4 y x z + + 3 2 2 3 2 3 3 + - 1/6 z x + 1/6 x z - 1/6 z + 1/2 z y x + 1/6 z - 1/2 y z + + 3 3 3 3 + + 1/4 z y x - 1/4 z y x + 1/12 x z - 1/12 x z , COEFF(1, 1, 2) = + + 3 3 2 3 2 + - 1/2 y x z + 1/12 z x - 1/6 x z + 1/2 y x z + 1/4 z y x + 1/12 z x + + 3 3 3 2 3 3 3 2 + + 1/6 x z - 1/12 z x - 1/12 x z + 1/4 z y x - 1/4 z y x + + 3 3 3 3 3 + - 1/4 z y x , COEFF(2, 1, 2) = 1/12 y x z + 1/12 z y x + 1/36 z x + + 3 3 3 3 + - 1/36 z x - 1/36 x z + 1/36 x z - 1/12 z y x - 1/12 y x z, + + 3 2 2 3 + COEFF(-1, 2, 2) = 1/12 z y x + 1/18 y x z - 1/12 z y x - 1/18 y x z + + 3 3 3 3 + - 1/36 z y x + 1/36 z y x , COEFF(0, 2, 2) = - 1/12 y x z - 1/6 y z + + 3 3 3 3 2 3 2 + + 1/6 y z + 1/12 z y x - 1/12 z y x + 1/6 z y x - 1/6 z y x + + 2 3 + + 1/12 y x z, COEFF(1, 2, 2) = - 1/6 y x z - 1/12 z y x + 1/6 y x z + + 3 2 3 3 3 + + 1/12 z y x + 1/12 z y x - 1/12 z y x , + + 3 3 3 3 + COEFF(2, 2, 2) = 1/36 z y x - 1/36 z y x + 1/36 y x z - 1/36 y x z ] + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dyy.compute.c"); +bytes used=7590110864, alloc=10549364, time=845.32 +bytes used=7591111036, alloc=10549364, time=845.40 +bytes used=7592111208, alloc=10549364, time=845.47 +bytes used=7593111532, alloc=10549364, time=845.57 +bytes used=7594112008, alloc=10549364, time=845.65 +bytes used=7595112256, alloc=10549364, time=845.74 +bytes used=7596112492, alloc=10549364, time=845.91 +bytes used=7597112780, alloc=10549364, time=845.99 +bytes used=7598112976, alloc=10549364, time=846.08 +bytes used=7599117908, alloc=10549364, time=846.17 +bytes used=7600159308, alloc=10549364, time=846.25 +bytes used=7601223860, alloc=10549364, time=846.31 +bytes used=7602259180, alloc=10549364, time=846.38 +bytes used=7603276320, alloc=10549364, time=846.44 +bytes used=7604354888, alloc=10549364, 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used=7758015224, alloc=10549364, time=882.27 +bytes used=7759015416, alloc=10549364, time=882.45 +bytes used=7760015608, alloc=10549364, time=882.58 +bytes used=7761015840, alloc=10549364, time=882.68 +bytes used=7762016100, alloc=10549364, time=882.79 +bytes used=7763016288, alloc=10549364, time=882.90 +bytes used=7764016512, alloc=10549364, time=883.82 +bytes used=7765016744, alloc=10549364, time=886.97 +bytes used=7766017000, alloc=10549364, time=888.20 +bytes used=7767017348, alloc=10549364, time=889.03 +bytes used=7768018596, alloc=10549364, time=889.24 +bytes used=7769018988, alloc=10549364, time=889.37 +bytes used=7770019228, alloc=10549364, time=889.45 +bytes used=7771019500, alloc=10549364, time=889.58 +bytes used=7772019780, alloc=10549364, time=889.78 +> +# d^2/dydz +> simplify( diff(interp_3d_cube_order3_smooth0,y,z) ); +bytes used=7773551976, alloc=10549364, time=889.92 +bytes used=7774552192, alloc=10549364, time=890.00 +bytes used=7775552328, alloc=10549364, time=890.08 +bytes used=7776553548, alloc=10549364, time=890.16 +bytes used=7777553964, alloc=10549364, time=890.24 +bytes used=7778554160, alloc=10549364, time=890.32 +bytes used=7779554352, alloc=10549364, time=890.41 +bytes used=7780554932, alloc=10549364, time=890.49 +bytes used=7781555132, alloc=10549364, time=890.58 +bytes used=7782556208, alloc=10549364, time=890.66 +bytes used=7783556488, alloc=10549364, time=890.75 +bytes used=7784557364, alloc=10549364, time=890.85 +bytes used=7785557504, alloc=10549364, time=890.94 +bytes used=7786558024, alloc=10549364, time=891.02 +bytes used=7787558164, alloc=10549364, time=891.11 + 3 2 +1/6 DATA(0, 0, -1) + 1/24 x DATA(2, 0, 0) + 1/6 x z DATA(-1, 2, 0) + + 2 2 + - 1/12 x z DATA(1, 2, 1) + 1/6 x z DATA(0, 2, 1) - 1/3 DATA(0, 1, -1) + + 3 3 + + 1/4 x DATA(1, 1, 0) + 1/6 DATA(0, -1, 0) + 1/8 x DATA(0, 0, 0) + + 3 2 2 + - 1/3 DATA(0, -1, 1) - 1/4 x DATA(0, 1, 0) - 1/4 y x z DATA(-1, 1, -1) + + + 1/4 DATA(0, 0, 0) - 1/2 DATA(0, 1, 0) - 1/2 DATA(0, 0, 1) + + 2 3 + + DATA(0, 1, 1) - 1/4 x DATA(1, 1, 0) + 1/4 z x DATA(1, 0, 1) + + 3 3 + + 1/18 z x DATA(-1, -1, -1) - 1/6 z x DATA(-1, 1, -1) + + 3 3 + - 1/2 z x DATA(1, 1, -1) + 1/4 z x DATA(1, 0, -1) + + 3 3 + - 1/6 z x DATA(-1, 1, 1) + 1/12 z x DATA(-1, 0, 1) + + 3 3 + + 1/6 z x DATA(1, -1, 1) + 1/18 z x DATA(-1, -1, 1) + + 3 2 3 + + 1/6 z x DATA(2, 1, -1) - 1/12 z x DATA(2, 1, -1) + + 2 3 2 3 + + 1/24 z x DATA(2, 0, -1) + 1/8 z x DATA(2, 0, 1) + + 2 3 2 3 + + 1/12 z x DATA(2, -1, 1) + 1/4 z x DATA(2, 1, 0) + + 2 3 2 3 + + 1/8 z x DATA(0, 0, -1) - 1/4 z x DATA(0, 1, -1) + + 2 3 2 3 + + 1/4 z x DATA(0, -1, 1) + 3/8 z x DATA(0, 0, 1) + + 2 3 2 3 + - 3/4 z x DATA(0, 1, 1) + 1/12 z x DATA(0, -1, -1) + + 2 3 2 3 + - 1/12 z x DATA(1, -1, -1) - 1/24 z x DATA(-1, 0, -1) + + 2 3 3 + - 1/4 z x DATA(0, -1, 0) + 1/3 z x DATA(0, -1, 0) + + 3 3 + - 1/9 z x DATA(-1, -1, 0) + 1/3 z x DATA(-1, 1, 0) + + 3 3 + - 1/6 z x DATA(-1, 0, 0) - 1/3 z x DATA(1, -1, 0) + + 2 2 + + 1/2 x z DATA(1, -1, 1) - 1/6 x z DATA(-1, -1, 1) + + 2 3 2 3 + - 1/4 z x DATA(-1, 1, 0) + 1/8 z x DATA(-1, 0, 0) + + 2 3 2 + + 1/4 z x DATA(1, -1, 0) - 1/12 x z DATA(2, -1, 1) + + 2 2 + + 1/4 x z DATA(2, 1, 1) - 1/18 x z DATA(-1, -1, -1) + + 2 2 + + 1/6 x z DATA(-1, 1, -1) - 1/2 x z DATA(1, 1, -1) + + 2 2 + + 1/2 x z DATA(-1, 1, 1) - 3/2 x z DATA(1, 1, 1) + + 2 2 + - 1/36 x z DATA(2, -1, -1) + 1/12 x z DATA(2, 1, -1) + + 2 2 + - 1/24 x z DATA(2, 0, -1) - 1/8 x z DATA(2, 0, 1) + + 2 2 + + 1/12 x z DATA(2, -1, 0) - 3/4 x z DATA(0, 1, 0) + + 2 2 2 + + 3/2 x z DATA(1, 1, 0) + 1/8 x z DATA(2, 0, 0) - 1/4 x z DATA(2, 1, 0) + + 2 2 + + 1/4 x z DATA(0, 1, -1) - 1/4 x z DATA(0, -1, 1) + + 2 2 3 + + 3/2 y x z DATA(-1, 0, 1) - 1/12 z x DATA(2, 0, 1) + + 3 3 + + 1/6 z x DATA(2, 1, 1) - 1/12 z x DATA(2, 0, -1) + + 3 3 + - 1/2 z x DATA(1, 0, 0) - 1/2 z x DATA(1, 1, 1) + + 3 3 + - 1/18 z x DATA(2, -1, -1) - 1/6 z x DATA(0, -1, -1) + + 3 3 + + 1/6 z x DATA(1, -1, -1) + 1/12 z x DATA(-1, 0, -1) + + 3 3 3 + + 1/9 z x DATA(2, -1, 0) - z 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1/4 y x DATA(1, 0, -1) + 1/2 y x DATA(0, -1, 1) + + 2 2 2 2 + - 3/4 y x DATA(0, 1, 0) - 3/2 y x DATA(0, 0, 1) + + 2 2 2 2 + - 1/4 y x DATA(1, -1, 1) + 1/4 y x DATA(0, 2, 0) + + 2 2 2 2 + + 3/4 y x DATA(1, 0, 1) + 1/4 y x DATA(1, 1, -1) + + 2 2 2 2 + - 3/8 y x DATA(-1, 0, 0) + 1/8 y x DATA(1, -1, 0) + + 2 2 2 2 + + 3/8 y x DATA(-1, 1, 0) + 1/8 y x DATA(-1, -1, 0) + + 2 2 2 2 + - 3/4 y x DATA(-1, 1, 1) - 1/6 y x DATA(0, -1, -1) + + 2 2 2 2 + - 3/8 y x DATA(1, 0, 0) + 3/8 y x DATA(1, 1, 0) + + 2 2 2 2 + - 3/4 y x DATA(1, 1, 1) - 1/12 y x DATA(1, 2, -1) + + 2 2 3 2 2 3 + + 1/8 z y x DATA(0, -1, -1) + 1/8 z y x DATA(2, 1, -1) + + 2 2 3 2 2 3 + + 3/8 z y x DATA(0, 0, 2) - 1/24 z y x DATA(-1, 2, 2) + + 2 2 3 2 2 3 + - 1/8 z y x DATA(-1, 0, 2) - 1/8 z y x DATA(2, -1, 0) + + 2 + + 1/2 x z DATA(1, 1, 1) + +> coeffs_as_lc_of_data(%, posn_list_3d_size4); +bytes used=7788558312, alloc=10549364, time=891.19 +bytes used=7789700388, alloc=10549364, time=891.28 +bytes used=7790700848, alloc=10549364, time=891.36 +bytes used=7791773636, alloc=10549364, time=891.45 +bytes used=7792923284, alloc=10549364, time=891.54 +bytes used=7794011412, alloc=10549364, time=891.63 +bytes used=7795046336, alloc=10549364, time=891.71 +bytes used=7796082832, alloc=10549364, time=891.79 +bytes used=7797131908, alloc=10549364, time=891.90 +bytes used=7798151008, alloc=10549364, time=891.99 +bytes used=7799243176, alloc=10549364, time=892.08 +bytes used=7800314280, alloc=10549364, time=892.18 +bytes used=7801315492, alloc=10549364, time=892.29 +bytes used=7802363904, alloc=10549364, time=892.37 +bytes used=7803364952, alloc=10549364, time=892.43 +bytes used=7804366296, alloc=10549364, time=892.49 + 3 3 2 3 +[COEFF(-1, -1, -1) = 1/18 y x - 1/27 x - 1/6 z y x + 1/12 z y x + + 2 2 2 2 2 3 2 2 + + 1/6 y x z + 1/9 y x + 1/8 y x z - 1/36 z x + 1/12 x z + + 3 3 2 3 2 2 + + 1/18 z x - 1/54 x - 1/36 y x + 1/18 x - 1/3 y x z + 1/2 z y x + + 2 3 2 2 3 2 2 2 2 2 + + 1/12 z y x - 1/24 z y x - 1/18 y x - 1/12 y x z - 1/4 y x z + + 2 2 2 2 2 2 2 + - 1/4 y x z + 1/6 y x z + 1/9 x z - 1/6 x z - 1/18 x z + 1/12 y x + + 2 3 + - 1/6 y x , COEFF(0, -1, -1) = - 1/6 y x - 1/18 x - 1/3 y - 1/3 z + + 3 2 3 2 2 2 2 + + 1/2 z y x - 1/4 z y x + 1/4 y x z + 1/6 y x - 1/4 y x z + + 2 3 2 2 3 3 2 3 2 + + 1/12 z x - 1/6 x z - 1/6 z x + 1/18 x + 1/12 y x + 1/6 y + + 2 2 2 2 3 2 2 3 + + 1/6 z - 1/9 x - 1/2 y x z - z y x - 1/4 z y x + 1/8 z y x + 1/9 + + 2 2 2 2 2 2 2 2 + + y z - 1/12 y x - 1/8 y x z + 1/2 y x z + 1/2 y x z + 1/4 y x z + + 2 2 2 2 2 2 + - 1/2 y z + 1/4 y z - 1/2 y z + 1/6 x z + 1/3 x z - 1/12 x z + + 2 2 2 3 3 + - 1/6 y x + 1/3 y x , COEFF(1, -1, -1) = 1/6 y x + 1/9 x - 1/2 z y x + + 2 3 2 2 2 2 2 3 + + 1/4 z y x - 1/2 y x z - 1/3 y x + 1/8 y x z - 1/12 z x + + 2 2 3 3 2 3 2 + + 1/12 x z + 1/6 z x - 1/18 x - 1/12 y x + 1/18 x + y x z + + 2 2 3 2 2 3 2 2 2 + + 1/2 z y x + 1/4 z y x - 1/8 z y x + 1/6 y x + 1/4 y x z + + 2 2 2 2 2 2 2 + - 1/4 y x z - 1/4 y x z - 1/2 y x z - 1/3 x z - 1/6 x z + 1/6 x z + + 2 2 2 3 2 2 + + 1/12 y x - 1/6 y x , COEFF(2, -1, -1) = 1/54 x - 1/24 y x z + + 2 3 3 2 + - 1/12 z y x + 1/18 y x - 1/6 y x z - 1/18 z x + 1/12 y x z + + 2 2 2 2 3 2 3 2 3 + + 1/12 y x z - 1/36 y x + 1/24 z y x - 1/12 z y x + 1/36 y x + + 3 3 2 3 2 + + 1/18 x z - 1/54 x - 1/18 y x + 1/6 z y x + 1/36 z x - 1/36 x z , + + 3 3 2 3 + COEFF(-1, 0, -1) = - 1/9 y x - 1/18 x + 1/3 z y x - 1/6 z y x + + 2 2 2 2 2 3 2 2 3 + - 1/2 y x z - 2/9 y x - 3/8 y x z - 1/24 z x + 1/8 x z + 1/12 z x + + 3 2 3 2 2 2 3 + - 1/36 x + 1/12 y x + 1/12 x + 2/3 y x z - z y x - 1/4 z y x + + 2 2 3 2 2 2 2 2 2 2 + + 1/8 z y x + 1/6 y x + 1/4 y x z + 3/4 y x z + 1/2 y x z + + 2 2 2 2 2 2 + - 1/3 y x z + 1/6 x z - 1/4 x z - 1/12 x z - 1/4 y x + 1/3 y x , + + 3 3 2 3 + COEFF(0, 0, -1) = 1/3 y x - 1/12 x + 2/3 y - 1/2 z - z y x + 1/2 z y x + + 2 2 2 2 2 3 2 2 3 + - 3/4 y x z - 1/3 y x + 3/4 y x z + 1/8 z x - 1/4 x z - 1/4 z x + + 3 2 3 2 2 2 2 + + 1/12 x + 1/6 - 1/4 y x - 1/2 y + 1/4 z - 1/6 x + y x z + 2 z y x + + 2 3 2 2 3 2 2 2 + + 3/4 z y x - 3/8 z y x - 2 y z + 1/4 y x + 3/8 y x z + + 2 2 2 2 2 2 2 2 2 + - 3/2 y x z - y x z - 1/2 y x z + 3/2 y z - 3/4 y z + y z + + 2 2 2 2 2 + + 1/4 x z + 1/2 x z - 1/8 x z + 1/2 y x - 2/3 y x , COEFF(1, 0, -1) = + + 3 3 2 3 2 + - 1/3 y x + 1/6 x + z y x - 1/2 z y x + 3/2 y x z + 2/3 y x + + 2 2 2 2 3 2 2 3 3 2 3 + - 3/8 y x z - 1/8 z x + 1/8 x z + 1/4 z x - 1/12 x + 1/4 y x + + 2 2 2 3 2 2 3 2 + + 1/12 x - 2 y x z - z y x - 3/4 z y x + 3/8 z y x - 1/2 y x + + 2 2 2 2 2 2 2 2 + - 3/4 y x z + 3/4 y x z + 1/2 y x z + y x z - 1/2 x z - 1/4 x z + + 2 2 2 2 3 + + 1/4 x z - 1/4 y x + 1/3 y x , COEFF(2, 0, -1) = 1/9 y x - 1/9 y x + + 3 2 2 2 3 + + 1/36 x - 1/4 y x z - 1/36 x + 1/12 x z + 1/8 y x z - 1/12 z x + + 2 2 3 2 2 3 2 2 3 + - 1/8 z y x + 1/12 y x + 1/24 z x - 1/6 y x z - 1/12 y x + + 2 2 3 2 3 3 + - 1/24 x z + 1/6 z y x + 1/3 y x z + 1/4 z y x - 1/3 z y x , + + 3 3 2 3 + COEFF(-1, 1, -1) = 1/18 y x + 1/9 x - 1/6 z y x + 1/12 z y x + + 2 2 2 2 2 3 2 2 3 + + 1/2 y x z + 1/9 y x + 3/8 y x z + 1/12 z x - 1/4 x z - 1/6 z x + + 3 2 3 2 2 2 3 + + 1/18 x - 1/12 y x - 1/6 x - 1/3 y x z + 1/2 z y x + 1/4 z y x + + 2 2 3 2 2 2 2 2 2 2 + - 1/8 z y x - 1/6 y x - 1/4 y x z - 3/4 y x z - 1/4 y x z + + 2 2 2 2 2 2 + + 1/6 y x z - 1/3 x z + 1/2 x z + 1/6 x z + 1/4 y x - 1/6 y x , + + 3 3 2 3 + COEFF(0, 1, -1) = - 1/6 y x + 1/6 x - 1/3 y + z + 1/2 z y x - 1/4 z y x + + 2 2 2 2 2 3 2 2 3 + + 3/4 y x z + 1/6 y x - 3/4 y x z - 1/4 z x + 1/2 x z + 1/2 z x + + 3 2 3 2 2 2 2 + - 1/6 x - 1/3 + 1/4 y x + 1/2 y - 1/2 z + 1/3 x - 1/2 y x z - z y x + + 2 3 2 2 3 2 2 2 2 2 + - 3/4 z y x + 3/8 z y x + y z - 1/4 y x - 3/8 y x z + 3/2 y x z + + 2 2 2 2 2 2 2 + + 1/2 y x z + 1/4 y x z - 3/2 y z + 3/4 y z - 1/2 y z - 1/2 x z + + 2 2 2 2 2 3 + - x z + 1/4 x z - 1/2 y x + 1/3 y x , COEFF(1, 1, -1) = 1/6 y x + + 3 2 3 2 2 2 2 + - 1/3 x - 1/2 z y x + 1/4 z y x - 3/2 y x z - 1/3 y x + 3/8 y x z + + 2 3 2 2 3 3 2 3 2 + + 1/4 z x - 1/4 x z - 1/2 z x + 1/6 x - 1/4 y x - 1/6 x + y x z + + 2 2 3 2 2 3 2 2 2 + + 1/2 z y x + 3/4 z y x - 3/8 z y x + 1/2 y x + 3/4 y x z + + 2 2 2 2 2 2 2 + - 3/4 y x z - 1/4 y x z - 1/2 y x z + x z + 1/2 x z - 1/2 x z + + 2 2 2 3 2 3 + + 1/4 y x - 1/6 y x , COEFF(2, 1, -1) = 1/6 z x + 1/12 y x + + 2 3 3 2 3 2 + - 1/12 z x - 1/18 y x + 1/18 y x - 1/6 x z - 1/12 z y x + 1/12 x z + + 2 3 2 2 3 2 2 2 + - 1/4 z y x + 1/8 z y x + 1/18 x - 1/8 y x z - 1/12 y x + + 2 3 2 3 + + 1/12 y x z + 1/6 z y x + 1/4 y x z - 1/18 x - 1/6 y x z, + + 2 2 2 2 2 2 3 + COEFF(-1, 2, -1) = 1/18 y x - 1/8 y x z + 1/24 x z - 1/108 x + + 2 3 2 2 2 2 3 2 3 2 + - 1/12 z y x + 1/4 y x z + 1/24 z y x + 1/36 y x - 1/12 x z + + 2 2 2 2 2 2 + + 1/12 y x z + 1/18 x z + 1/36 x - 1/54 x - 1/36 x z - 1/12 y x + + 2 3 2 3 2 3 + - 1/6 y x z + 1/36 z x - 1/72 z x , COEFF(0, 2, -1) = 1/4 z y x + + 2 2 2 2 2 2 2 3 2 3 + + 1/4 y x z + 1/8 y x z - 1/8 z y x - 1/18 x + 1/36 x + + 2 2 2 2 3 2 2 + + 1/12 y x - 1/2 y x z + 1/18 + 1/24 z x + 1/6 y x - 1/36 x + + 2 2 2 3 2 2 2 + + 1/2 y z + 1/12 x z + 1/6 x z - 1/12 y x + 1/12 z - 1/12 x z + + 2 2 2 3 2 2 + - 1/24 x z - 1/4 y z - 1/12 z x - 1/4 y x z - 1/6 y - 1/6 z, + + 2 2 3 2 3 + COEFF(1, 2, -1) = - 1/12 x z - 1/24 z x + 1/12 x z - 1/36 x + + 2 2 2 2 3 2 3 2 2 3 + - 1/12 y x + 1/8 z y x + 1/12 y x - 1/6 y x - 1/4 z y x + + 2 2 2 2 2 2 2 2 2 + - 1/4 y x z + 1/18 x + 1/24 x z - 1/6 x z - 1/8 y x z + 1/4 y x z + + 2 3 2 2 + + 1/36 x + 1/12 z x + 1/2 y x z, COEFF(2, 2, -1) = 1/36 y x + + 2 3 3 2 3 2 + - 1/36 y x + 1/108 x - 1/12 y x z + 1/36 x z - 1/36 z x - 1/72 x z + + 2 3 2 3 2 2 3 2 2 + + 1/12 z y x + 1/72 z x - 1/24 z y x + 1/24 y x z - 1/108 x, + + 3 3 2 3 + COEFF(-1, -1, 0) = 1/12 y x - 1/18 x + 1/3 z y x - 1/4 z y x + + 2 2 2 2 2 3 2 2 3 + - 1/3 y x z + 1/6 y x - 3/8 y x z + 1/12 z x - 1/4 x z - 1/9 z x + + 3 2 3 2 2 2 3 + - 1/36 x - 1/24 y x + 1/12 x + 2/3 y x z - z y x - 1/6 z y x + + 2 2 3 2 2 2 2 2 2 2 + + 1/8 z y x - 1/12 y x + 1/4 y x z + 1/2 y x z + 3/4 y x z + + 2 2 2 2 2 2 + - 1/2 y x z - 2/9 x z + 1/3 x z + 1/6 x z + 1/8 y x - 1/4 y x , + + 3 3 + COEFF(0, -1, 0) = - 1/4 y x - 1/12 x - 1/2 y + 2/3 z - z y x + + 2 3 2 2 2 2 2 3 + + 3/4 z y x - 1/2 y x z + 1/4 y x + 3/4 y x z - 1/4 z x + + 2 2 3 3 2 3 2 2 + + 1/2 x z + 1/3 z x + 1/12 x + 1/6 + 1/8 y x + 1/4 y - 1/2 z + + 2 2 2 3 2 2 3 + - 1/6 x + y x z + 2 z y x + 1/2 z y x - 3/8 z y x - 2 y z + + 2 2 2 2 2 2 2 2 2 + - 1/8 y x + 3/8 y x z - y x z - 3/2 y x z - 3/4 y x z + y z + + 2 2 2 2 2 2 2 + - 3/4 y z + 3/2 y z - 1/3 x z - 2/3 x z + 1/4 x z - 1/4 y x + + 2 3 3 2 3 + + 1/2 y x , COEFF(1, -1, 0) = 1/4 y x + 1/6 x + z y x - 3/4 z y x + + 2 2 2 2 2 3 2 2 3 + + y x z - 1/2 y x - 3/8 y x z + 1/4 z x - 1/4 x z - 1/3 z x + + 3 2 3 2 2 2 3 + - 1/12 x - 1/8 y x + 1/12 x - 2 y x z - z y x - 1/2 z y x + + 2 2 3 2 2 2 2 2 2 2 + + 3/8 z y x + 1/4 y x - 3/4 y x z + 1/2 y x z + 3/4 y x z + + 2 2 2 2 2 2 + + 3/2 y x z + 2/3 x z + 1/3 x z - 1/2 x z + 1/8 y x - 1/4 y x , + + 2 3 2 2 2 3 + COEFF(2, -1, 0) = 1/4 z y x - 1/6 y x z + 1/3 y x z - 1/8 z y x + + 3 2 2 3 2 3 + + 1/12 y x - 1/9 x z + 1/9 z x + 1/12 x z + 1/24 y x - 1/12 z x + + 3 2 2 2 3 2 3 + + 1/36 x - 1/36 x + 1/8 y x z - 1/4 y x z - 1/12 y x + 1/6 z y x + + 3 2 3 + - 1/3 z y x - 1/24 y x, COEFF(-1, 0, 0) = - 1/6 y x - 1/12 x + + 3 2 3 2 2 2 2 2 3 + - 2/3 z y x + 1/2 z y x + y x z - 1/3 y x + 9/8 y x z + 1/8 z x + + 2 2 3 3 2 3 2 + - 3/8 x z - 1/6 z x - 1/24 x + 1/8 y x + 1/8 x - 4/3 y x z + + 2 2 3 2 2 3 2 2 2 + + 2 z y x + 1/2 z y x - 3/8 z y x + 1/4 y x - 3/4 y x z + + 2 2 2 2 2 2 2 + - 3/2 y x z - 3/2 y x z + y x z - 1/3 x z + 1/2 x z + 1/4 x z + + 2 2 2 3 + - 3/8 y x + 1/2 y x , COEFF(0, 0, 0) = 1/2 y x - 1/8 x + 1/4 + y + z + + 3 2 3 2 2 2 2 2 3 + + 2 z y x - 3/2 z y x + 3/2 y x z - 1/2 y x - 9/4 y x z - 3/8 z x + + 2 2 3 3 2 3 2 2 2 + + 3/4 x z + 1/2 z x + 1/8 x - 3/8 y x - 3/4 y - 3/4 z - 1/4 x + + 2 2 3 2 2 3 2 + - 2 y x z - 4 z y x - 3/2 z y x + 9/8 z y x + 4 y z + 3/8 y x + + 2 2 2 2 2 2 2 2 2 2 + - 9/8 y x z + 3 y x z + 3 y x z + 3/2 y x z - 3 y z + 9/4 y z + + 2 2 2 2 2 2 + - 3 y z - 1/2 x z - x z + 3/8 x z + 3/4 y x - y x , COEFF(1, 0, 0) = + + 3 3 2 3 2 2 2 2 + - 1/2 y x + 1/4 x - 2 z y x + 3/2 z y x - 3 y x z + y x + 9/8 y x z + + 2 3 2 2 3 3 2 3 2 + + 3/8 z x - 3/8 x z - 1/2 z x - 1/8 x + 3/8 y x + 1/8 x + 4 y x z + + 2 2 3 2 2 3 2 2 2 + + 2 z y x + 3/2 z y x - 9/8 z y x - 3/4 y x + 9/4 y x z + + 2 2 2 2 2 2 2 + - 3/2 y x z - 3/2 y x z - 3 y x z + x z + 1/2 x z - 3/4 x z + + 2 2 2 3 3 2 2 3 + - 3/8 y x + 1/2 y x , COEFF(2, 0, 0) = 1/6 z x + 1/24 x + 3/8 z y x + + 2 2 2 3 2 + + 1/2 y x z + 1/8 x z - 1/6 y x - 1/8 z x + 1/8 y x - 1/24 x + + 2 2 3 2 3 2 2 3 + - 3/8 y x z + 1/6 y x - 1/2 z y x + 1/2 y x z - 1/2 z y x + + 2 3 3 + - 1/6 x z - 2/3 y x z - 1/8 y x + 2/3 z y x , COEFF(-1, 1, 0) = + + 3 3 2 3 2 + 1/12 y x + 1/6 x + 1/3 z y x - 1/4 z y x - y x z + 1/6 y x + + 2 2 2 2 3 2 2 3 3 2 3 + - 9/8 y x z - 1/4 z x + 3/4 x z + 1/3 z x + 1/12 x - 1/8 y x + + 2 2 2 3 2 2 3 2 + - 1/4 x + 2/3 y x z - z y x - 1/2 z y x + 3/8 z y x - 1/4 y x + + 2 2 2 2 2 2 2 2 + + 3/4 y x z + 3/2 y x z + 3/4 y x z - 1/2 y x z + 2/3 x z - x z + + 2 2 2 2 3 + - 1/2 x z + 3/8 y x - 1/4 y x , COEFF(0, 1, 0) = - 1/4 y x + 1/4 x + + 3 2 3 2 + - 1/2 - 1/2 y - 2 z - z y x + 3/4 z y x - 3/2 y x z + 1/4 y x + + 2 2 2 2 3 2 2 3 3 2 3 + + 9/4 y x z + 3/4 z x - 3/2 x z - z x - 1/4 x + 3/8 y x + + 2 2 2 2 2 3 2 2 3 + + 3/4 y + 3/2 z + 1/2 x + y x z + 2 z y x + 3/2 z y x - 9/8 z y x + + 2 2 2 2 2 2 2 2 + - 2 y z - 3/8 y x + 9/8 y x z - 3 y x z - 3/2 y x z - 3/4 y x z + + 2 2 2 2 2 2 2 2 + + 3 y z - 9/4 y z + 3/2 y z + x z + 2 x z - 3/4 x z - 3/4 y x + + 2 3 3 2 3 + + 1/2 y x , COEFF(1, 1, 0) = 1/4 y x - 1/2 x + z y x - 3/4 z y x + + 2 2 2 2 2 3 2 2 3 + + 3 y x z - 1/2 y x - 9/8 y x z - 3/4 z x + 3/4 x z + z x + + 3 2 3 2 2 2 3 + + 1/4 x - 3/8 y x - 1/4 x - 2 y x z - z y x - 3/2 z y x + + 2 2 3 2 2 2 2 2 2 2 + + 9/8 z y x + 3/4 y x - 9/4 y x z + 3/2 y x z + 3/4 y x z + + 2 2 2 2 2 2 + + 3/2 y x z - 2 x z - x z + 3/2 x z + 3/8 y x - 1/4 y x , + + 2 3 2 3 2 3 3 + COEFF(2, 1, 0) = 1/4 z y x + 1/8 y x + 1/4 z x - 1/12 y x + 1/3 x z + + 2 2 2 2 2 + + 3/8 y x z + 1/3 y x z - 1/4 x z - 1/4 y x z + 1/12 y x - 1/8 y x + + 2 3 2 2 3 2 3 3 + - 1/2 y x z - 1/3 z x + 1/12 x - 3/8 z y x + 1/2 z y x - 1/3 z y x + + 3 2 3 2 3 + - 1/12 x , COEFF(-1, 2, 0) = - 1/9 x z + 1/6 z y x - 1/36 x + 1/24 y x + + 2 2 2 2 2 3 3 2 2 2 + - 1/2 y x z + 3/8 y x z - 1/72 x - 1/18 z x - 1/8 y x + 1/12 y x + + 2 2 2 3 2 2 3 2 2 + + 1/24 x + 1/3 y x z + 1/24 z x - 1/8 z y x - 1/8 x z + + 2 2 2 2 + - 1/4 y x z + 1/6 x z + 1/12 x z , COEFF(0, 2, 0) = - 1/6 x z + + 2 3 2 2 2 2 2 3 + - 1/2 z y x + 1/2 y x z - 1/24 x - 1/3 x z + 1/4 x z - 1/8 y x + + 3 2 2 2 3 2 2 2 + + 1/6 z x + 1/3 z + 1/8 x z + 3/8 z y x + 1/8 y x + 1/4 y x + + 2 2 2 3 2 2 2 2 2 2 + + y x z - 1/8 z x + 1/12 - 1/4 z - 1/12 x + 3/4 y z - 3/8 y x z + + 2 3 2 2 2 2 + - 1/4 y + 1/24 x - y z - 3/4 y x z , COEFF(1, 2, 0) = 1/3 x z + + 2 2 3 2 2 3 2 3 2 3 + - y x z + 1/8 y x - 3/8 z y x + 1/2 z y x + 1/12 x + 1/8 z x + + 2 3 2 2 2 2 2 2 2 + + 1/6 x z - 1/24 x - 1/4 y x - 1/2 y x z - 1/8 y x - 1/8 x z + + 2 3 2 2 2 2 2 2 + - 1/4 x z - 1/6 z x + 3/4 y x z + 1/24 x + 3/8 y x z , + + 2 3 3 2 + COEFF(2, 2, 0) = - 1/6 z y x - 1/72 x + 1/18 z x - 1/18 x z + 1/24 y x + + 2 2 3 2 2 3 2 2 2 3 + + 1/8 z y x + 1/24 x z - 1/24 y x - 1/8 y x z - 1/24 z x + + 3 2 3 3 + + 1/72 x + 1/6 y x z, COEFF(-1, -1, 1) = - 1/6 y x + 1/9 x - 1/6 z y x + + 2 3 2 2 2 2 2 3 + + 1/4 z y x + 1/6 y x z - 1/3 y x + 3/8 y x z - 1/12 z x + + 2 2 3 3 2 3 2 + + 1/4 x z + 1/18 z x + 1/18 x + 1/12 y x - 1/6 x - 1/3 y x z + + 2 2 3 2 2 3 2 2 2 + + 1/2 z y x + 1/12 z y x - 1/8 z y x + 1/6 y x - 1/4 y x z + + 2 2 2 2 2 2 2 + - 1/4 y x z - 3/4 y x z + 1/2 y x z + 1/9 x z - 1/6 x z - 1/6 x z + + 2 2 2 3 + - 1/4 y x + 1/2 y x , COEFF(0, -1, 1) = 1/2 y x + 1/6 x + y - 1/3 z + + 3 2 3 2 2 2 2 + + 1/2 z y x - 3/4 z y x + 1/4 y x z - 1/2 y x - 3/4 y x z + + 2 3 2 2 3 3 2 3 2 + + 1/4 z x - 1/2 x z - 1/6 z x - 1/6 x - 1/3 - 1/4 y x - 1/2 y + + 2 2 2 2 3 2 2 3 + + 1/2 z + 1/3 x - 1/2 y x z - z y x - 1/4 z y x + 3/8 z y x + y z + + 2 2 2 2 2 2 2 2 + + 1/4 y x - 3/8 y x z + 1/2 y x z + 3/2 y x z + 3/4 y x z + + 2 2 2 2 2 2 + - 1/2 y z + 3/4 y z - 3/2 y z + 1/6 x z + 1/3 x z - 1/4 x z + + 2 2 2 3 3 + + 1/2 y x - y x , COEFF(1, -1, 1) = - 1/2 y x - 1/3 x - 1/2 z y x + + 2 3 2 2 2 2 2 3 2 2 + + 3/4 z y x - 1/2 y x z + y x + 3/8 y x z - 1/4 z x + 1/4 x z + + 3 3 2 3 2 2 + + 1/6 z x + 1/6 x + 1/4 y x - 1/6 x + y x z + 1/2 z y x + + 2 3 2 2 3 2 2 2 2 2 + + 1/4 z y x - 3/8 z y x - 1/2 y x + 3/4 y x z - 1/4 y x z + + 2 2 2 2 2 2 2 + - 3/4 y x z - 3/2 y x z - 1/3 x z - 1/6 x z + 1/2 x z - 1/4 y x + + 2 2 2 2 3 3 + + 1/2 y x , COEFF(2, -1, 1) = 1/12 y x z + 1/8 z y x + 1/6 y x + + 3 2 2 2 3 2 + - 1/6 y x + 1/6 z y x - 1/8 y x z - 1/12 z y x - 1/12 x z + + 3 2 2 3 2 3 + - 1/18 z x + 1/12 y x + 1/18 x z - 1/12 y x + 1/4 y x z - 1/18 x + + 2 3 2 3 + + 1/18 x - 1/4 z y x + 1/12 z x - 1/6 y x z, COEFF(-1, 0, 1) = + + 3 3 2 3 2 + 1/3 y x + 1/6 x + 1/3 z y x - 1/2 z y x - 1/2 y x z + 2/3 y x + + 2 2 2 2 3 2 2 3 3 2 3 + - 9/8 y x z - 1/8 z x + 3/8 x z + 1/12 z x + 1/12 x - 1/4 y x + + 2 2 2 3 2 2 3 2 + - 1/4 x + 2/3 y x z - z y x - 1/4 z y x + 3/8 z y x - 1/2 y x + + 2 2 2 2 2 2 2 2 + + 3/4 y x z + 3/4 y x z + 3/2 y x z - y x z + 1/6 x z - 1/4 x z + + 2 2 2 2 3 + - 1/4 x z + 3/4 y x - y x , COEFF(0, 0, 1) = -y x + 1/4 x - 1/2 - 2 y + + 3 2 3 2 2 2 2 + - 1/2 z - z y x + 3/2 z y x - 3/4 y x z + y x + 9/4 y x z + + 2 3 2 2 3 3 2 3 2 2 + + 3/8 z x - 3/4 x z - 1/4 z x - 1/4 x + 3/4 y x + 3/2 y + 3/4 z + + 2 2 2 3 2 2 3 + + 1/2 x + y x z + 2 z y x + 3/4 z y x - 9/8 z y x - 2 y z + + 2 2 2 2 2 2 2 2 2 + - 3/4 y x + 9/8 y x z - 3/2 y x z - 3 y x z - 3/2 y x z + 3/2 y z + + 2 2 2 2 2 2 2 2 + - 9/4 y z + 3 y z + 1/4 x z + 1/2 x z - 3/8 x z - 3/2 y x + 2 y x , + + 3 3 2 3 2 + COEFF(1, 0, 1) = y x - 1/2 x + z y x - 3/2 z y x + 3/2 y x z - 2 y x + + 2 2 2 2 3 2 2 3 3 2 3 + - 9/8 y x z - 3/8 z x + 3/8 x z + 1/4 z x + 1/4 x - 3/4 y x + + 2 2 2 3 2 2 3 2 + - 1/4 x - 2 y x z - z y x - 3/4 z y x + 9/8 z y x + 3/2 y x + + 2 2 2 2 2 2 2 2 + - 9/4 y x z + 3/4 y x z + 3/2 y x z + 3 y x z - 1/2 x z - 1/4 x z + + 2 2 2 2 2 3 + + 3/4 x z + 3/4 y x - y x , COEFF(2, 0, 1) = 1/3 y x + 1/4 z y x + + 3 2 2 2 2 3 + - 1/3 y x + 3/8 y x z - 1/4 y x z + 1/8 z x + 1/3 y x z + + 2 2 3 2 3 2 + - 3/8 z y x + 1/12 x + 1/12 x z - 1/8 x z - 1/12 z x - 1/4 y x + + 2 3 3 2 3 2 3 + - 1/2 y x z - 1/12 x - 1/3 z y x + 1/4 y x + 1/2 z y x , + + 3 3 2 3 + COEFF(-1, 1, 1) = - 1/6 y x - 1/3 x - 1/6 z y x + 1/4 z y x + + 2 2 2 2 2 3 2 2 3 + + 1/2 y x z - 1/3 y x + 9/8 y x z + 1/4 z x - 3/4 x z - 1/6 z x + + 3 2 3 2 2 2 3 + - 1/6 x + 1/4 y x + 1/2 x - 1/3 y x z + 1/2 z y x + 1/4 z y x + + 2 2 3 2 2 2 2 2 2 2 + - 3/8 z y x + 1/2 y x - 3/4 y x z - 3/4 y x z - 3/4 y x z + + 2 2 2 2 2 2 + + 1/2 y x z - 1/3 x z + 1/2 x z + 1/2 x z - 3/4 y x + 1/2 y x , + + 3 3 2 3 + COEFF(0, 1, 1) = 1 + 1/2 y x - 1/2 x + y + z + 1/2 z y x - 3/4 z y x + + 2 2 2 2 2 3 2 2 3 + + 3/4 y x z - 1/2 y x - 9/4 y x z - 3/4 z x + 3/2 x z + 1/2 z x + + 3 2 3 2 2 2 2 + + 1/2 x - 3/4 y x - 3/2 y - 3/2 z - x - 1/2 y x z - z y x + + 2 3 2 2 3 2 2 2 2 2 + - 3/4 z y x + 9/8 z y x + y z + 3/4 y x - 9/8 y x z + 3/2 y x z + + 2 2 2 2 2 2 2 + + 3/2 y x z + 3/4 y x z - 3/2 y z + 9/4 y z - 3/2 y z - 1/2 x z + + 2 2 2 2 2 3 + - x z + 3/4 x z + 3/2 y x - y x , COEFF(1, 1, 1) = - 1/2 y x + x + + 3 2 3 2 2 2 2 2 3 + - 1/2 z y x + 3/4 z y x - 3/2 y x z + y x + 9/8 y x z + 3/4 z x + + 2 2 3 3 2 3 2 2 + - 3/4 x z - 1/2 z x - 1/2 x + 3/4 y x + 1/2 x + y x z + 1/2 z y x + + 2 3 2 2 3 2 2 2 2 2 + + 3/4 z y x - 9/8 z y x - 3/2 y x + 9/4 y x z - 3/4 y x z + + 2 2 2 2 2 2 2 + - 3/4 y x z - 3/2 y x z + x z + 1/2 x z - 3/2 x z - 3/4 y x + + 2 2 2 2 3 2 + + 1/2 y x , COEFF(2, 1, 1) = 1/4 y x z - 1/6 x + 3/8 z y x + 1/4 x z + + 2 2 2 3 2 3 3 + - 1/6 x z - 3/8 y x z + 1/4 y x z + 1/6 z x - 1/4 z x + 1/6 y x + + 2 3 3 2 3 + - 1/4 z y x + 1/6 z y x - 1/6 y x z + 1/4 y x - 1/6 y x + 1/6 x + + 2 3 2 3 2 2 2 3 + - 1/4 y x - 1/4 z y x , COEFF(-1, 2, 1) = 1/8 x z - 1/24 z x + + 2 2 2 2 2 3 + + 1/18 x + 1/18 x z - 1/6 y x z - 1/12 x z - 3/8 y x z + 1/36 z x + + 2 2 2 2 3 2 2 2 3 + + 1/4 y x + 1/8 z y x - 1/12 x - 1/6 y x - 1/12 z y x + + 2 2 2 2 2 3 3 2 + + 1/4 y x z + 1/4 y x z - 1/12 y x + 1/36 x - 1/12 x z, + + 2 2 2 2 2 2 2 + COEFF(0, 2, 1) = - 3/4 y z + 3/8 y x z - 1/4 x z - 1/4 y x z + + 3 2 2 2 2 2 2 3 2 3 + - 1/12 z x + 1/4 z + 3/4 y x z - 3/8 z y x + 1/4 z y x - 1/6 z + + 2 3 2 2 3 3 2 + + 1/8 z x - 1/8 x z + 1/4 y x - 1/12 x - 1/6 + 1/2 y z + 1/12 x z + + 2 2 2 2 2 2 2 2 + + 1/12 x - 1/2 y x - 1/4 y x + 1/2 y + 1/6 x z + 1/6 x - 1/2 y x z + + 2 2 2 2 2 2 + , COEFF(1, 2, 1) = - 1/6 x z + 1/8 x z + 1/4 x z - 3/8 y x z + + 2 3 2 2 2 2 2 2 + - 1/12 x + 1/12 z x - 1/12 x z - 3/4 y x z + 1/4 y x z + 1/2 y x z + + 2 3 2 2 3 3 2 3 2 3 + - 1/6 x - 1/4 z y x + 3/8 z y x + 1/12 x - 1/4 y x - 1/8 z x + + 2 2 2 2 2 3 2 + + 1/2 y x + 1/4 y x , COEFF(2, 2, 1) = 1/36 x - 1/8 z y x - 1/24 x z + + 2 2 2 2 2 3 + + 1/36 x z - 1/12 y x + 1/8 y x z - 1/12 y x z + 1/24 z x + + 2 3 2 3 3 3 + + 1/12 z y x + 1/12 y x - 1/36 x - 1/36 z x , COEFF(-1, -1, 2) = + + 2 2 2 2 3 2 2 + - 1/12 y x - 1/6 y x z + 1/18 y x + 1/36 x - 1/12 z y x - 1/12 x z + + 2 2 3 3 2 2 2 + + 1/24 z y x - 1/108 x - 1/54 x + 1/12 y x z - 1/36 y x + + 2 2 2 2 2 2 2 3 3 + + 1/24 y x - 1/8 y x z + 1/18 x z - 1/72 y x + 1/36 y x + + 2 3 2 2 2 2 + + 1/36 z x + 1/4 y x z , COEFF(0, -1, 2) = 1/6 y x + 1/12 y + + 2 2 2 2 2 3 2 2 2 2 + - 1/12 y x - 1/4 y z + 1/24 y x + 1/12 x z + 1/4 y x z + + 2 2 3 2 2 3 + + 1/8 y x z + 1/12 y x + 1/36 x - 1/6 z - 1/36 x + 1/4 z y x + + 2 2 2 2 3 2 2 3 2 2 2 + + 1/6 x z - 1/18 x - 1/12 z x - 1/8 z y x - 1/2 y x z + 1/2 y z + + 2 3 2 + - 1/24 y x - 1/12 y x - 1/4 y x z - 1/6 y + 1/18, COEFF(1, -1, 2) = + + 2 2 2 2 2 2 2 2 2 3 + - 1/8 y x z - 1/6 y x - 1/4 y x z + 1/36 x + 1/24 y x + 1/12 z x + + 2 2 3 2 2 3 + + 1/18 x + 1/12 y x - 1/4 z y x + 1/2 y x z - 1/6 x z + 1/12 y x + + 2 2 2 2 2 3 2 2 3 2 + + 1/4 y x z - 1/12 x z - 1/24 y x + 1/8 z y x - 1/12 y x + + 3 2 3 3 3 + - 1/36 x , COEFF(2, -1, 2) = - 1/36 z x - 1/36 y x + 1/108 x + + 2 3 2 2 2 2 3 2 + + 1/12 z y x + 1/24 y x z - 1/24 z y x + 1/36 y x + 1/36 x z + + 2 2 3 2 + - 1/72 y x + 1/72 y x - 1/12 y x z - 1/108 x, COEFF(-1, 0, 2) = + + 2 2 2 2 2 3 2 2 2 3 + 3/8 y x z + 1/6 y x + 1/24 z x - 1/4 y x z + 1/3 y x z - 1/18 y x + + 2 2 3 2 3 2 2 2 + - 1/8 x z - 1/72 x + 1/6 z y x - 1/9 y x + 1/24 x - 1/2 y x z + + 2 2 3 2 2 2 3 2 2 + - 1/8 z y x + 1/12 y x + 1/12 x z + 1/24 y x - 1/36 x - 1/8 y x , + + 2 2 2 2 3 2 2 + COEFF(0, 0, 2) = 1/4 y x + 1/2 y x z - 1/8 y x + 1/8 y x - 1/4 y + + 2 2 2 2 2 2 2 3 + - 1/6 y x - 3/8 y x z + y x z + 1/12 + 1/4 x z - 1/3 y x + 1/6 y x + + 2 2 2 2 2 3 + + 1/3 y - 1/12 x - 1/4 z - 1/24 x - y z + 1/8 x z - 1/2 z y x + + 2 3 2 2 3 2 2 3 2 2 2 + - 1/8 z x + 3/8 z y x + 3/4 y z + 1/24 x - 3/4 y x z , + + 2 2 2 2 3 2 + COEFF(1, 0, 2) = - 1/4 y x - 1/2 y x z + 1/12 x + 1/8 y x - y x z + + 3 2 2 2 3 2 2 3 2 3 + - 1/24 x + 1/3 y x - 1/8 x z + 1/8 z x - 3/8 z y x + 1/2 z y x + + 2 2 2 2 2 2 2 2 2 3 + + 3/8 y x z - 1/4 x z + 1/6 y x - 1/8 y x + 3/4 y x z - 1/6 y x + + 2 2 3 3 2 + + 1/24 x , COEFF(2, 0, 2) = - 1/24 y x + 1/72 x + 1/6 y x z + + 2 3 2 2 2 3 + - 1/6 z y x + 1/24 x z - 1/8 y x z + 1/18 y x - 1/18 y x + + 2 2 3 2 3 2 + + 1/8 z y x - 1/72 x - 1/24 z x + 1/24 y x, COEFF(-1, 1, 2) = 1/18 x + + 2 3 2 2 2 2 2 3 2 2 + - 1/24 y x + 1/4 y x z - 1/12 x + 1/4 y x z + 1/36 x + 1/4 x z + + 2 2 3 2 2 2 3 + + 1/8 z y x + 1/18 y x - 1/6 x z - 1/12 y x - 1/12 y x + 1/36 y x + + 2 3 2 2 2 3 2 2 2 2 + - 1/12 z x + 1/8 y x - 1/12 z y x - 1/6 y x z - 3/8 y x z , + + 2 3 2 2 2 + COEFF(0, 1, 2) = 1/2 y z - 1/12 y x + 1/2 z - 1/6 y - 1/2 y x z + + 2 2 2 3 2 + + 1/4 y - 1/4 y x z + 1/12 x + 1/12 y x + 1/4 z x - 1/8 y x + + 2 3 2 2 2 2 2 2 3 2 + + 1/4 z y x + 3/4 y x z - 1/6 + 1/6 x - 3/8 z y x - 1/4 x z + + 2 2 2 3 2 2 2 2 2 3 + + 3/8 y x z + 1/8 y x - 3/4 y z - 1/4 y x + 1/6 y x - 1/12 x + + 2 2 2 2 2 2 2 2 2 + - 1/2 x z , COEFF(1, 1, 2) = - 3/8 y x z + 1/4 x z + 1/4 y x z + + 2 2 2 3 2 2 2 3 2 + + 1/4 y x + 3/8 z y x - 3/4 y x z - 1/6 y x - 1/8 y x - 1/12 x + + 2 2 2 3 2 3 2 2 + - 1/12 y x + 1/2 y x z - 1/4 z y x - 1/4 z x - 1/6 x + 1/8 y x + + 2 3 3 2 3 + + 1/2 x z + 1/12 y x + 1/12 x , COEFF(2, 1, 2) = 1/36 y x + 1/24 y x + + 2 2 3 3 2 2 3 + + 1/36 x - 1/24 y x + 1/12 z y x - 1/36 x - 1/12 x z + 1/12 z x + + 3 2 2 2 3 2 2 + - 1/36 y x - 1/12 y x z - 1/8 z y x + 1/8 y x z , COEFF(-1, 2, 2) = + + 2 2 3 2 2 3 2 2 2 + - 1/24 z y x + 1/36 y x + 1/72 z x - 1/108 x + 1/8 y x z + + 2 2 2 2 2 3 2 3 2 + - 1/24 x z - 1/12 y x z + 1/72 x - 1/216 x + 1/72 y x + 1/36 x z + + 2 2 2 2 3 2 2 3 + - 1/24 y x , COEFF(0, 2, 2) = 1/8 z y x + 1/36 - 1/12 z - 1/24 y x + + 2 3 2 2 2 2 2 2 + - 1/24 z x - 1/12 y + 1/24 y x + 1/4 y z - 1/8 y x z - 1/72 x + + 3 2 2 2 2 2 2 2 2 2 + + 1/72 x + 1/24 x z - 1/4 y x z - 1/36 x + 1/12 x z + 1/12 y x , + + 2 2 2 3 2 3 2 2 3 + COEFF(1, 2, 2) = 1/72 x - 1/8 z y x + 1/24 z x - 1/24 x z - 1/72 x + + 2 2 2 2 2 2 2 2 + + 1/4 y x z + 1/8 y x z + 1/36 x - 1/12 x z - 1/24 y x + + 2 3 2 3 2 + + 1/24 y x - 1/12 y x, COEFF(2, 2, 2) = 1/216 x - 1/216 x + 1/72 x z + + 2 2 2 2 3 2 3 2 2 3 + - 1/24 y x z + 1/24 z y x - 1/72 z x + 1/72 y x - 1/72 y x ] + +> print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dyz.compute.c"); +bytes used=7805366468, alloc=10549364, time=892.55 +bytes used=7806366692, alloc=10549364, time=892.61 +bytes used=7807366876, alloc=10549364, time=892.70 +bytes used=7808367048, alloc=10549364, time=892.79 +bytes used=7809367584, alloc=10549364, time=892.88 +bytes used=7810367908, alloc=10549364, time=892.97 +bytes used=7811368376, alloc=10549364, time=893.04 +bytes used=7812368724, alloc=10549364, time=893.13 +bytes used=7813368896, alloc=10549364, time=893.32 +bytes used=7814369092, alloc=10549364, time=893.39 +bytes used=7815369344, alloc=10549364, time=893.48 +bytes used=7816369560, 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alloc=10549364, time=949.51 +bytes used=8066782184, alloc=10549364, time=949.59 +bytes used=8067782396, alloc=10549364, time=949.81 +bytes used=8068782576, alloc=10549364, time=950.02 +bytes used=8069782812, alloc=10549364, time=950.22 +bytes used=8070783064, alloc=10549364, time=950.38 +bytes used=8071783240, alloc=10549364, time=950.55 +bytes used=8072783496, alloc=10549364, time=950.73 +bytes used=8073783780, alloc=10549364, time=950.85 +bytes used=8074786104, alloc=10549364, time=950.96 +bytes used=8075786280, alloc=10549364, time=951.07 +bytes used=8076786520, alloc=10549364, time=951.19 +bytes used=8077786728, alloc=10549364, time=953.70 +bytes used=8078786908, alloc=10549364, time=957.76 +bytes used=8079787092, alloc=10549364, time=959.19 +bytes used=8080787368, alloc=10549364, time=960.30 +bytes used=8081787652, alloc=10549364, time=960.40 +bytes used=8082787856, alloc=10549364, time=960.47 +bytes used=8083788104, alloc=10549364, time=960.55 +bytes used=8084788464, alloc=10549364, time=960.62 +bytes used=8085788968, alloc=10549364, time=960.70 +bytes used=8086789484, alloc=10549364, time=960.78 +bytes used=8087789908, alloc=10549364, time=960.86 +bytes used=8088790384, alloc=10549364, time=960.93 +bytes used=8089790688, alloc=10549364, time=961.01 +bytes used=8090791064, alloc=10549364, time=961.09 +bytes used=8091791336, alloc=10549364, time=961.17 +bytes used=8092791540, alloc=10549364, time=961.34 +bytes used=8093791736, alloc=10549364, time=961.59 +bytes used=8094792864, alloc=10549364, time=961.79 +bytes used=8095793076, alloc=10549364, time=961.97 +bytes used=8096794984, alloc=10549364, time=962.14 +bytes used=8097795184, alloc=10549364, time=962.32 +bytes used=8098795384, alloc=10549364, time=962.43 +bytes used=8099795628, alloc=10549364, time=962.55 +bytes used=8100795852, alloc=10549364, time=962.66 +bytes used=8101796056, alloc=10549364, time=962.77 +bytes used=8102796244, alloc=10549364, time=966.72 +bytes used=8103796476, alloc=10549364, time=969.91 +bytes used=8104796664, alloc=10549364, time=971.05 +bytes used=8105798456, alloc=10549364, time=971.75 +bytes used=8106798940, alloc=10549364, time=972.00 +bytes used=8107799740, alloc=10549364, time=972.13 +bytes used=8108799936, alloc=10549364, time=972.18 +bytes used=8109800116, alloc=10549364, time=972.42 +bytes used=8110800296, alloc=10549364, time=972.60 +bytes used=8111800520, alloc=10549364, time=972.75 +> +# d^2/dz^2 +> simplify( diff(interp_3d_cube_order3_smooth0,z,z) ); +bytes used=8113000400, alloc=10549364, time=972.89 +bytes used=8114000608, alloc=10549364, time=972.96 +bytes used=8115001632, alloc=10549364, time=973.04 +bytes used=8116001848, alloc=10549364, time=973.13 +bytes used=8117002028, alloc=10549364, time=973.21 +bytes used=8118002196, alloc=10549364, time=973.30 +bytes used=8119002532, alloc=10549364, time=973.38 +bytes used=8120003496, alloc=10549364, time=973.46 +bytes used=8121003748, alloc=10549364, time=973.55 +bytes 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1/3 y z + + 2 3 3 2 2 + - 1/6 y x z + 1/4 y x z - 1/6 y x - 1/12 z y x - 1/2 y x + + 2 2 3 2 3 2 + + 1/2 y x z, COEFF(1, -1, -1) = 1/12 z y x + 1/6 z y x - 1/2 y x z + + 2 2 3 3 2 2 2 + + 1/6 z y x - 1/6 y x - 1/6 y x + 1/3 y x z - 1/12 y x + 1/4 y x + + 2 2 2 3 2 3 2 3 + + 1/2 y x - 1/3 y x - 1/4 y x z + 1/6 y x + 1/4 z y x - 1/4 y x + + 3 3 3 3 3 + - 1/12 z y x + 1/12 y x - 1/6 z y x , COEFF(2, -1, -1) = - 1/18 y x z + + 3 3 2 2 3 2 3 3 3 + + 1/36 z y x - 1/12 y x - 1/12 z y x + 1/12 y x - 1/36 y x + + 3 3 2 3 + - 1/18 y x - 1/36 z y x + 1/12 y x z + 1/36 y x + 1/18 y x + + 3 2 3 3 3 + + 1/18 z y x , COEFF(-1, 0, -1) = 1/6 y x + 1/12 y x + 1/6 z x + + 3 2 3 3 3 2 + - 1/6 y x - 1/6 z y x + 1/6 y x + 1/3 x z - 1/12 z y x - 1/4 z y x + + 3 2 2 3 2 + - 1/6 x - 1/4 y x + 1/4 z y x - 1/6 y x z - 1/3 x + 1/4 y x + + 3 3 3 3 2 2 2 2 2 + - 1/12 y x + 1/12 z y x + 1/2 x + 1/2 y x z - 1/2 y x + + 3 2 2 2 + + 1/6 z y x - 1/2 x z - 1/3 y x z + 1/3 y x, COEFF(0, 0, -1) = 1 + + 3 3 2 + - 1/4 y x - 1/2 x - 1/2 y - z + 1/4 z y x - 1/2 y x z + 1/4 y x + + 3 3 3 3 3 2 3 2 + - 1/2 z x + 1/2 y + 1/2 x - 1/4 y x - 1/2 z y - 1/2 y x - y + + 3 2 3 3 2 3 3 2 3 3 + - 1/2 y x + 1/4 z y x + 1/2 z y x + 1/4 y x - x - 1/4 z y x + + 2 2 3 2 2 2 + - 1/4 y x z - 1/2 z y x + 1/2 z y x + 1/2 y z + 1/2 y x - y x z + + 2 2 2 2 2 + + y z + 1/2 x z + x z + y x + 1/2 y x , COEFF(1, 0, -1) = 1/2 y x z + + 2 3 2 3 3 3 2 2 + + 1/2 y x - 1/2 x z - 1/2 z y x - 1/4 y x + 1/4 z y x + 1/2 x + + 2 3 2 3 2 3 3 + - 1/2 y x - 1/2 z y x + x - 1/4 y x - 1/4 z y x + 1/2 z x + 1/4 y x + + 3 2 3 2 2 3 2 2 + + 1/4 y x + 1/2 y x + 1/2 y x z - 1/4 z y x - x z + y x z - y x + + 3 3 3 2 2 2 2 3 + - 1/2 x + 1/4 z y x - 1/2 y x , COEFF(2, 0, -1) = 1/6 y x - 1/6 y x + + 3 3 3 3 2 2 3 + + 1/12 z y x + 1/6 x + 1/12 y x - 1/6 y x z + 1/6 z y x + 1/12 y x + + 3 3 3 3 3 3 + - 1/6 x - 1/12 y x - 1/12 y x - 1/12 z y x - 1/6 z x + 1/12 z y x + + 3 3 3 + - 1/12 y x z + 1/6 x z, COEFF(-1, 1, -1) = - 1/6 z y x - 1/12 z y x + + 3 2 2 3 3 3 2 3 + + 1/6 y x + 1/2 y x + 1/6 y x z + 1/12 y x + 1/4 z y x - 1/6 y x + + 2 2 2 3 2 2 3 + - 1/2 z y x - 1/6 y x - 1/3 y x + 1/12 z y x + 1/4 y x + 1/6 z y x + + 2 3 3 2 2 2 + - 1/12 y x - 1/4 y x - 1/4 y x z + 1/3 y x z, COEFF(0, 1, -1) = + + 3 2 2 3 2 2 3 3 2 3 3 + 1/2 y x - 1/4 z y x - 1/2 y x - 1/4 y x + 1/4 y x + 1/2 y x + + 3 2 2 2 2 2 + - 1/4 z y x + 1/2 y x z + 1/2 y - 1/2 y x - 1/4 y x + 1/4 y x z + + 3 3 3 2 3 + + 1/2 y x z - y z - 1/2 z y x + 1/4 z y x - 1/2 y z - 1/2 y + + 3 3 2 3 2 2 + + 1/4 y x - 1/2 z y x + y + 1/2 z y + z y x - y x , COEFF(1, 1, -1) + + 3 2 3 2 3 3 3 2 + = 1/2 z y x + 1/2 y x + 1/2 z y x + 1/4 z y x - 1/2 y x - 1/4 y x + + 2 3 2 2 3 3 3 2 + - y x z - 1/4 y x + 1/2 y x - 1/2 z y x + 1/4 y x + 1/4 z y x + + 2 3 3 2 2 3 2 2 + - 1/2 y x z - 1/4 z y x + 1/4 y x + y x - 1/2 y x - 1/4 y x z, + + 3 2 3 2 + COEFF(2, 1, -1) = - 1/12 z y x - 1/12 z y x + 1/12 y x z - 1/6 y x + + 2 3 3 3 2 3 3 + - 1/12 y x - 1/6 z y x - 1/12 y x + 1/12 y x + 1/6 y x + + 3 3 3 + + 1/12 z y x + 1/12 y x + 1/6 y x z, COEFF(-1, 2, -1) = 1/18 y x + + 3 2 2 3 2 3 3 + + 1/12 y x - 1/12 y x + 1/36 y x + 1/12 z y x + 1/36 z y x + + 3 3 2 3 3 + + 1/18 z y x - 1/12 z y x - 1/18 y x z - 1/36 z y x - 1/18 y x + + 3 3 3 2 2 + - 1/36 y x , COEFF(0, 2, -1) = - 1/6 y x - 1/6 z y x - 1/12 y x z + + 3 2 3 3 3 + + 1/12 z y x + 1/6 y x - 1/12 y x + 1/6 y z + 1/12 y x - 1/6 y + + 3 2 3 3 3 3 3 + + 1/6 z y x - 1/12 y x - 1/12 z y x - 1/6 z y + 1/6 y + 1/12 y x + + 3 3 3 3 3 + + 1/12 z y x, COEFF(1, 2, -1) = 1/6 y x z + 1/12 z y x - 1/12 y x + + 2 3 2 3 3 2 3 + + 1/12 z y x + 1/12 y x + 1/12 y x - 1/6 z y x - 1/12 y x + 1/6 y x + + 3 2 3 3 + - 1/12 z y x - 1/6 y x - 1/12 z y x , COEFF(2, 2, -1) = 1/36 z y x + + 3 3 3 3 3 3 + - 1/36 y x - 1/36 z y x - 1/36 y x z - 1/36 y x + 1/36 y x + + 3 3 2 3 + + 1/36 y x + 1/36 z y x , COEFF(-1, -1, 0) = - 1/4 z y x - 1/9 y x + + 3 3 2 3 3 3 2 3 + - 1/9 y x + 1/6 y x + 1/6 z y x + 1/12 z y x + 1/6 y x + + 3 2 2 2 2 + + 1/6 z y x - 2/9 y x + 1/3 y x - 1/2 z y x + 1/3 y x z + 3/4 y x z + + 2 3 3 2 3 2 2 2 + - 1/2 y x z - 1/18 y x - 1/4 z y x + 1/3 y x - 1/2 y x , + + 2 3 2 3 2 3 + COEFF(0, -1, 0) = 3/4 z y x + 1/2 y x + 1/2 z y x - 1/2 z y x + + 2 2 2 3 3 2 3 + - 3/4 y x z - y z - 3/2 y x z - 1/4 z y x + 3/2 y z + 1/3 y x + + 3 2 2 3 2 2 3 3 3 + - 1/2 z y + y x - 1/3 y x - 1/2 y x - 1/6 y x + 2/3 y + 1/3 y + + 3 3 3 2 2 2 + + 1/6 y x + 1/4 z y x + 1/2 y x z - 2/3 y x + z y x - 1/3 y x - y , + + 3 2 3 2 2 2 2 + COEFF(1, -1, 0) = 1/6 y x - 1/4 z y x + 3/2 y x z + 3/4 y x z + + 3 2 3 2 2 3 3 + - 1/3 y x + 1/2 y x + 1/3 y x - y x + 2/3 y x + 1/4 z y x + + 3 2 3 3 3 2 2 3 + - 1/2 z y x - 3/4 z y x - y x z - 1/6 y x - 1/2 y x + 1/3 y x + + 2 3 2 3 3 + - 1/2 z y x + 1/2 z y x , COEFF(2, -1, 0) = 1/4 z y x - 1/18 y x + + 2 3 3 3 + - 1/4 y x z + 1/6 y x z + 1/18 y x + 1/12 z y x - 1/9 y x + + 3 3 3 2 3 2 3 + - 1/12 z y x + 1/9 y x - 1/6 y x + 1/6 y x - 1/6 z y x , + + 2 2 3 3 3 3 3 + COEFF(-1, 0, 0) = 3/2 x z + 1/2 z y x - 1/4 z y x + 1/6 y x + + 2 3 2 2 3 3 + - 2/3 y x + 2/3 x + 1/3 y x + 1/2 y x - 3/4 z y x + 1/3 x - 1/6 y x + + 2 2 3 3 2 3 2 + + y x + 1/4 z y x + 3/4 z y x + 1/2 y x z - 1/3 y x - x z - 1/2 y x + + 2 2 3 3 2 2 2 3 + + y x z - 1/3 y x - 1/2 z x - 3/2 y x z - x - 1/2 z y x, + + 3 3 2 + COEFF(0, 0, 0) = -2 + 1/2 y x + x + y + 3 z - 3/4 z y x + 3/2 y x z + + 3 3 3 3 3 2 3 2 + - 1/2 y x + 3/2 z x - y - x + 1/2 y x + 3/2 z y + y x + 2 y + + 3 2 3 3 2 3 3 2 3 3 + + y x - 3/4 z y x - 3/2 z y x - 1/2 y x + 2 x + 3/4 z y x + + 2 2 3 2 2 2 + + 3/4 y x z + 3/2 z y x - 3/2 z y x - 3/2 y z - y x + 3 y x z + + 2 2 2 2 2 + - 3 y z - 3/2 x z - 3 x z - 2 y x - y x , COEFF(1, 0, 0) = y x + 3 x z + + 2 3 2 2 2 2 2 2 3 2 + - x + 3/4 z y x - 3/2 y x z + y x - 3 y x z - 1/2 y x + + 3 3 3 2 3 2 3 3 3 + + 1/2 y x - 2 x + x + 2 y x + 3/4 z y x - y x - 3/4 z y x + + 2 3 3 3 2 + - 3/4 z y x - 3/2 y x z - 3/2 z x - 1/2 y x - y x + 1/2 y x + + 2 3 3 2 + + 3/2 z y x + 3/2 z y x + 3/2 x z, COEFF(2, 0, 0) = - 1/6 y x + + 2 2 3 2 3 3 + - 1/3 y x + 1/2 y x z - 1/4 z y x + 1/3 y x + 1/6 y x + 1/4 y x z + + 3 3 3 3 2 3 3 3 + + 1/3 x + 1/6 y x + 1/4 z y x + 1/2 z x - 1/2 z y x - 1/6 y x + + 3 3 2 3 2 + - 1/4 z y x - 1/3 x - 1/2 x z, COEFF(-1, 1, 0) = 1/3 y x + 1/2 y x + + 2 3 3 3 2 2 3 3 + + 1/6 y x + 1/4 z y x + 3/4 y x z + 1/2 z y x - 1/2 z y x + + 2 2 3 2 3 2 2 + + 3/2 z y x - y x - 3/4 z y x + 1/3 y x - y x z - 1/2 y x + + 3 3 3 2 3 2 + - 1/3 y x + 2/3 y x - 1/6 y x - 1/4 z y x - 1/2 y x z, + + 3 2 2 3 + COEFF(0, 1, 0) = 3/2 z y x - 3 z y x + y - 3/2 y x z + 3 y z - 2 y + + 2 2 2 2 3 2 2 2 + - 3/2 y x z + y x + 3/4 z y x + 3/2 y z + 1/2 y x + 2 y x + + 3 3 3 3 3 2 3 3 2 3 + - 3/4 z y x + 1/2 y x - y x + 3/4 z y x + y x - y x - 3/2 z y + + 2 3 2 3 2 3 + - y - 1/2 y x - 1/2 y x - 3/4 y x z + 3/2 z y x , COEFF(1, 1, 0) = + + 3 2 3 3 3 3 3 2 3 2 + - 3/4 z y x - 1/2 y x + 3/4 z y x + y x + 1/2 y x - y x + + 2 3 2 2 3 2 3 + - 3/4 z y x + 3/2 y x z + 3/2 z y x + 1/2 y x - 3/2 z y x + + 2 2 2 3 3 2 2 + + 3/4 y x z - y x - 2 y x - 3/2 z y x + 3 y x z + y x - 1/2 y x , + + 3 3 3 2 + COEFF(2, 1, 0) = - 1/6 y x + 1/3 y x - 1/2 y x z + 1/6 y x - 1/4 y x z + + 2 3 3 3 3 2 3 2 3 + + 1/6 y x - 1/3 y x - 1/4 z y x + 1/2 z y x + 1/4 z y x - 1/6 y x + + 3 3 3 3 + + 1/4 z y x, COEFF(-1, 2, 0) = - 1/12 z y x + 1/9 y x + 1/6 y x z + + 3 3 2 3 2 3 3 + + 1/18 y x - 1/9 y x + 1/6 y x - 1/6 y x + 1/12 z y x - 1/6 z y x + + 2 3 3 2 + - 1/4 z y x - 1/18 y x + 1/4 z y x , COEFF(0, 2, 0) = - 1/6 y x + + 2 3 3 3 3 2 3 3 + - 1/3 y x + 1/2 z y - 1/6 y x + 1/3 y x - 1/4 z y x + 1/6 y x + + 3 3 2 + + 1/4 y x z - 1/3 y - 1/4 z y x + 1/3 y - 1/2 y z + 1/2 z y x + + 3 3 3 3 2 3 3 + + 1/4 z y x + 1/6 y x - 1/2 z y x , COEFF(1, 2, 0) = 1/6 y x + + 3 3 2 2 3 2 3 3 + - 1/3 y x + 1/4 z y x - 1/4 z y x + 1/3 y x - 1/6 y x - 1/4 z y x + + 3 2 3 3 + + 1/2 z y x - 1/2 y x z + 1/6 y x + 1/4 z y x - 1/6 y x , + + 3 3 3 + COEFF(2, 2, 0) = 1/18 y x - 1/12 z y x - 1/12 z y x - 1/18 y x + + 3 3 3 3 3 + + 1/12 z y x + 1/18 y x + 1/12 y x z - 1/18 y x , COEFF(-1, -1, 1) = + + 3 3 3 3 2 3 3 + 1/18 y x + 1/18 y x - 1/6 z y x - 1/3 y x z + 1/4 z y x - 1/12 z y x + + 2 2 3 2 2 3 3 2 3 + - 1/6 y x + 1/4 z y x + 1/2 z y x - 1/6 y x + 1/36 y x - 1/12 y x + + 3 2 2 3 2 2 2 2 + - 1/12 y x + 1/2 y x z - 1/6 z y x + 1/9 y x + 1/4 y x - 3/4 y x z + + 2 3 3 2 3 2 3 + , COEFF(0, -1, 1) = 1/2 y - 1/12 y x - z y x - 1/2 z y x + 1/2 z y x + + 2 2 2 3 2 3 3 2 + - 1/2 y x + 1/4 y x + y z - 3/4 z y x - 1/3 y + 1/6 y x + + 2 2 3 3 3 2 + + 3/4 y x z - 1/4 y x + 1/2 z y + 1/4 z y x + 1/6 y x + 1/3 y x + + 3 3 2 2 3 3 + - 1/6 y x - 1/4 z y x - 1/2 y x z + 3/2 y x z + 1/12 y x - 1/6 y + + 2 2 2 3 2 3 + - 3/2 y z, COEFF(1, -1, 1) = - 3/4 y x z - 1/12 y x - 1/6 y x + + 2 3 3 2 3 3 3 2 + - 1/6 y x + 1/12 y x + y x z + 1/2 z y x - 1/4 z y x + 1/4 z y x + + 2 3 2 3 2 2 2 3 + - 1/4 y x + 1/2 y x + 1/6 y x - 3/2 y x z + 1/4 y x + 1/2 z y x + + 2 3 3 2 + + 3/4 z y x - 1/3 y x - 1/2 z y x , COEFF(2, -1, 1) = 1/4 y x z + + 3 3 3 3 2 3 + + 1/18 y x + 1/36 y x + 1/6 z y x - 1/36 y x - 1/6 y x z - 1/4 z y x + + 2 3 3 2 3 3 3 + - 1/12 y x + 1/12 z y x + 1/12 y x - 1/12 z y x - 1/18 y x , + + 3 2 2 3 2 3 2 2 2 + COEFF(-1, 0, 1) = 1/4 y x - 1/2 z y x + 1/6 y x - 1/2 y x + 1/2 x + + 3 3 3 3 2 2 3 + - 1/3 x + 1/4 z y x - 1/12 y x + 3/2 y x z - 1/6 x - 1/2 y x z + + 2 3 3 2 2 3 3 + + 1/3 y x + 1/2 z x - 3/4 z y x + 3/4 z y x + 1/12 y x - 1/4 z y x + + 3 2 3 2 2 + + 1/2 z y x + 1/6 y x - 3/2 x z - 1/6 y x - 1/4 y x + x z - y x z, + + 3 3 + COEFF(0, 0, 1) = 1 - 1/4 y x - 1/2 x - 1/2 y - 3 z + 3/4 z y x + + 2 3 3 3 3 3 + - 3/2 y x z + 1/4 y x - 3/2 z x + 1/2 y + 1/2 x - 1/4 y x - 3/2 z y + + 2 3 2 3 2 3 3 2 3 3 2 + - 1/2 y x - y - 1/2 y x + 3/4 z y x + 3/2 z y x + 1/4 y x - x + + 3 3 2 2 3 2 + - 3/4 z y x - 3/4 y x z - 3/2 z y x + 3/2 z y x + 3/2 y z + 1/2 y x + + 2 2 2 2 2 2 2 + - 3 y x z + 3 y z + 3/2 x z + 3 x z + y x + 1/2 y x , COEFF(1, 0, 1) + + 2 2 3 3 2 2 2 3 2 + = - 3/2 x z + 1/2 y x - 1/2 x + 3/2 y x z - 3/2 z y x - 1/4 y x + + 2 2 3 3 2 + - 1/2 y x - 3/2 z y x - 3/4 z y x - y x - 3 x z - 1/2 y x + + 3 3 2 3 3 3 3 3 2 + + 3/4 z y x + 1/2 x + 1/2 y x - 1/4 y x + x + 3/2 z x + 1/4 y x + + 2 3 2 2 3 + + 3/4 z y x - 3/4 z y x + 3 y x z + 1/4 y x + 3/2 y x z, + + 2 3 + COEFF(2, 0, 1) = - 1/2 y x z - 1/6 x - 1/12 y x + 1/12 y x - 1/4 y x z + + 2 3 3 3 2 3 3 2 3 + - 1/6 y x - 1/4 z y x + 1/2 z y x + 1/4 z y x + 1/6 y x - 1/2 z x + + 3 3 3 3 3 + + 1/2 x z + 1/6 x + 1/12 y x - 1/12 y x + 1/4 z y x, COEFF(-1, 1, 1) + + 2 2 2 2 2 3 3 + = - 1/6 y x + 1/2 y x z + 1/4 y x - 1/3 y x + 1/4 z y x + 1/2 z y x + + 3 2 3 2 2 2 3 2 + - 1/2 z y x - 1/12 y x - 3/2 z y x - 3/4 y x z + y x z - 1/4 y x + + 3 3 3 3 2 3 2 3 3 + - 1/4 z y x + 1/6 y x - 1/6 y x + 1/2 y x + 3/4 z y x + 1/12 y x , + + 2 2 3 2 3 3 3 + COEFF(0, 1, 1) = - 1/2 y x - 3/2 z y x - 1/2 y - 1/4 y x - 1/2 y x + + 2 3 2 2 2 3 2 3 2 + + 1/4 y x + 3/2 y x z + 1/2 y - 3/4 z y x - 3/2 y z + 1/2 y x + + 3 2 2 2 3 + - 3 y z + 1/4 y x + 3 z y x + 3/2 y x z - 1/4 y x - 3/4 z y x + + 3 2 3 3 2 3 3 + + 3/2 z y + 3/4 y x z + y + 3/4 z y x - y x + 1/2 y x - 3/2 z y x , + + 2 2 2 2 3 + COEFF(1, 1, 1) = - 3/4 y x z - 3/2 y x z + 1/2 y x - 1/2 y x + y x + + 2 3 2 2 3 2 3 3 2 + + 3/4 z y x + 1/4 y x - 1/4 y x + 3/2 z y x - 3 y x z + 3/4 z y x + + 3 3 2 3 3 2 3 3 2 + - 3/4 z y x - 1/4 y x + 3/2 z y x + 1/2 y x + 1/4 y x - 3/2 z y x + + 3 2 3 3 3 + - 1/2 y x , COEFF(2, 1, 1) = - 1/12 y x + 1/4 z y x - 1/4 z y x + + 2 3 2 3 3 3 + + 1/12 y x + 1/4 y x z - 1/2 z y x + 1/2 y x z - 1/12 y x + + 3 3 2 3 + + 1/12 y x + 1/6 y x - 1/4 z y x - 1/6 y x, COEFF(-1, 2, 1) = + + 3 3 3 3 3 2 + - 1/36 y x - 1/12 z y x - 1/18 y x + 1/12 y x + 1/18 y x - 1/6 y x z + + 2 3 2 3 3 2 + - 1/12 y x + 1/36 y x + 1/4 z y x + 1/6 z y x - 1/4 z y x + + 3 3 3 3 + + 1/12 z y x , COEFF(0, 2, 1) = - 1/12 y x + 1/2 y z + 1/4 z y x + + 2 3 2 3 3 3 2 3 + - 1/2 z y x + 1/2 z y x - 1/6 y + 1/12 y x - 1/6 y x + 1/6 y + + 3 3 2 3 3 3 + + 1/12 y x + 1/4 z y x - 1/2 z y + 1/6 y x - 1/4 z y x - 1/12 y x + + 3 2 3 3 + - 1/4 y x z, COEFF(1, 2, 1) = - 1/4 z y x - 1/2 z y x + 1/6 y x + + 3 3 3 2 2 3 3 + + 1/4 z y x + 1/12 y x + 1/2 y x z - 1/12 y x - 1/12 y x + + 2 3 3 + + 1/4 z y x - 1/4 z y x + 1/12 y x - 1/6 y x, COEFF(2, 2, 1) = + + 3 3 3 3 + - 1/12 y x z + 1/36 y x - 1/36 y x - 1/36 y x - 1/12 z y x + + 3 3 3 3 2 2 + + 1/12 z y x + 1/12 z y x + 1/36 y x , COEFF(-1, -1, 2) = 1/4 y x z + + 3 3 3 2 3 3 + + 1/18 z y x + 1/18 z y x - 1/12 z y x + 1/9 y x z + 1/36 z y x + + 2 2 2 3 3 3 + - 1/6 z y x - 1/6 y x z - 1/12 z y x , COEFF(0, -1, 2) = - 1/12 z y x + + 2 2 2 3 3 3 + - 1/4 y x z - 1/3 y z + 1/2 y z + 1/4 z y x - 1/6 z y - 1/6 z y x + + 3 2 2 3 2 2 + + 1/12 z y x - 1/2 y x z + 1/6 z y x + 1/6 y x z + 1/3 z y x , + + 3 3 3 2 + COEFF(1, -1, 2) = - 1/6 z y x + 1/12 z y x - 1/3 y x z - 1/6 z y x + + 3 2 3 2 3 2 2 2 + - 1/12 z y x + 1/6 z y x - 1/4 z y x + 1/2 y x z + 1/4 y x z, + + 2 3 3 3 3 + COEFF(2, -1, 2) = - 1/12 y x z + 1/36 z y x - 1/36 z y x - 1/18 z y x + + 2 3 2 2 3 + + 1/12 z y x + 1/18 y x z, COEFF(-1, 0, 2) = - 1/4 z y x + 1/6 z y x + + 3 3 2 3 3 2 + - 1/6 z y x - 1/3 x z - 1/6 z x + 1/3 y x z - 1/12 z y x + 1/2 x z + + 3 2 3 2 2 + + 1/4 z y x + 1/12 z y x - 1/2 y x z + 1/6 y x z, COEFF(0, 0, 2) = + + 3 3 2 2 2 3 + - 1/4 z y x - 1/2 z y x + 1/2 y x z - y z - 1/2 x z + 1/2 z y + + 3 2 2 3 + - 1/4 z y x + 1/2 z y x + z - x z - 1/2 y z + 1/4 y x z + 1/2 z x + + 3 3 2 3 2 2 2 + + 1/4 z y x - 1/2 z y x + y x z, COEFF(1, 0, 2) = x z - y x z + + 3 2 2 3 3 2 + + 1/4 z y x - 1/2 y x z - 1/4 z y x + 1/2 z y x + 1/4 z y x + + 2 2 3 2 3 3 3 + - 1/2 y x z + 1/2 z y x + 1/2 x z - 1/2 z x - 1/4 z y x , + + 3 3 2 3 3 + COEFF(2, 0, 2) = 1/6 z x - 1/12 z y x - 1/6 z y x - 1/12 z y x + + 2 3 3 + - 1/6 x z + 1/12 y x z + 1/6 y x z + 1/12 z y x , COEFF(-1, 1, 2) = + + 3 3 2 2 3 3 2 2 + 1/12 z y x + 1/4 y x z + 1/6 z y x - 1/4 z y x + 1/2 z y x + + 2 2 3 3 + - 1/6 y x z - 1/12 z y x - 1/3 y x z - 1/6 z y x , COEFF(0, 1, 2) = + + 2 3 3 3 2 2 2 3 + 1/2 y z - 1/2 z y - 1/4 z y x - 1/2 y x z - 1/4 y x z + 1/2 z y x + + 2 3 3 2 3 2 + - 1/2 y x z + 1/4 z y x + 1/4 z y x - z y x + 1/2 z y x + y z, + + 2 3 3 2 + COEFF(1, 1, 2) = - 1/4 z y x - 1/2 z y x + y x z + 1/2 z y x + + 2 2 3 3 3 2 3 2 + + 1/4 y x z + 1/4 z y x - 1/2 z y x + 1/2 y x z - 1/4 z y x , + + 3 2 3 3 2 + COEFF(2, 1, 2) = 1/6 z y x + 1/12 z y x + 1/12 z y x - 1/12 y x z + + 3 3 3 2 + - 1/12 z y x - 1/6 y x z, COEFF(-1, 2, 2) = 1/18 y x z + 1/12 z y x + + 3 3 3 2 3 + - 1/18 z y x - 1/36 z y x - 1/12 z y x + 1/36 z y x , COEFF(0, 2, 2) + + 3 3 2 2 3 + = 1/6 z y - 1/6 z y x + 1/12 y x z + 1/6 z y x - 1/6 y z - 1/12 z y x + + 3 3 3 2 + + 1/12 z y x - 1/12 z y x , COEFF(1, 2, 2) = - 1/12 z y x + + 3 2 3 3 3 3 + + 1/12 z y x - 1/6 y x z + 1/6 z y x + 1/12 z y x - 1/12 z y x , + + 3 3 3 3 + COEFF(2, 2, 2) = 1/36 z y x - 1/36 z y x + 1/36 y x z - 1/36 z y x ] + +> print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp", +> "3d.coeffs/3d.cube.order3.smooth0/coeffs-dzz.compute.c"); +bytes used=8136209400, alloc=10549364, time=974.77 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alloc=10549364, time=1369.12 +bytes used=11795046620, alloc=10549364, time=1369.20 +bytes used=11796105204, alloc=10549364, time=1369.28 +bytes used=11797320656, alloc=10549364, time=1369.39 +interp_3d_cube_order4_smooth0 := (- 1/36 DATA(-1, 1, 0) - 1/36 DATA(1, -1, 0) + + + 1/36 DATA(-1, -1, 0) + 1/36 DATA(1, 1, 0) + 1/72 DATA(2, -1, 0) + + + 1/144 DATA(2, 2, 0) - 1/72 DATA(1, 2, 0) + 1/72 DATA(-1, 2, 0) + + - 1/72 DATA(2, 1, 0) - 1/72 DATA(-1, -2, 0) + 1/144 DATA(-2, -2, 0) + + + 1/72 DATA(1, -2, 0) - 1/144 DATA(2, -2, 0) - 1/72 DATA(-2, -1, 0) + + 3 3 + + 1/72 DATA(-2, 1, 0) - 1/144 DATA(-2, 2, 0)) x y + (1/6 DATA(0, 0, -1) + + - 1/9 DATA(0, 1, -1) + 5/24 DATA(0, -1, 0) - 1/9 DATA(0, -1, 1) + + - 5/16 DATA(0, 0, 0) + 5/24 DATA(0, 1, 0) + 1/6 DATA(0, 0, 1) + + - 1/9 DATA(0, 1, 1) - 1/576 DATA(0, -2, -2) - 1/576 DATA(0, -2, 2) + + + 1/144 DATA(0, -1, -2) + 1/36 DATA(0, 2, -1) - 1/96 DATA(0, 0, -2) + + - 5/96 DATA(0, 2, 0) + 1/144 DATA(0, 1, -2) - 1/576 DATA(0, 2, -2) + + + 1/36 DATA(0, 2, 1) - 1/96 DATA(0, 0, 2) + 1/36 DATA(0, -2, -1) + + + 1/144 DATA(0, -1, 2) + 1/144 DATA(0, 1, 2) - 1/576 DATA(0, 2, 2) + + 4 2 + - 1/9 DATA(0, -1, -1) - 5/96 DATA(0, -2, 0) + 1/36 DATA(0, -2, 1)) y z + + + (1/9 DATA(0, 1, -1) + 1/9 DATA(0, -1, 1) - 1/9 DATA(0, 1, 1) + + - 1/144 DATA(0, -2, -2) + 1/144 DATA(0, -2, 2) + 1/72 DATA(0, -1, -2) + + - 1/18 DATA(0, 2, -1) - 1/72 DATA(0, 1, -2) + 1/144 DATA(0, 2, -2) + + + 1/18 DATA(0, 2, 1) + 1/18 DATA(0, -2, -1) - 1/72 DATA(0, -1, 2) + + + 1/72 DATA(0, 1, 2) - 1/144 DATA(0, 2, 2) - 1/9 DATA(0, -1, -1) + + 3 + - 1/18 DATA(0, -2, 1)) y z + (- 1/9 DATA(-1, 0, -1) + 1/9 DATA(1, 0, -1) + + + 1/9 DATA(-1, 0, 1) - 1/9 DATA(1, 0, 1) - 1/72 DATA(-2, 0, 1) + + + 1/18 DATA(-1, 0, -2) - 1/144 DATA(-2, 0, -2) - 1/72 DATA(2, 0, -1) + + + 1/144 DATA(2, 0, -2) - 1/18 DATA(1, 0, -2) + 1/72 DATA(2, 0, 1) + + - 1/18 DATA(-1, 0, 2) - 1/144 DATA(2, 0, 2) + 1/18 DATA(1, 0, 2) + + 3 + + 1/72 DATA(-2, 0, -1) + 1/144 DATA(-2, 0, 2)) x z + ( + + - 1/36 DATA(-1, 0, -1) + 1/36 DATA(1, 0, -1) + 1/24 DATA(-1, 0, 0) + + - 1/36 DATA(-1, 0, 1) - 1/24 DATA(1, 0, 0) + 1/36 DATA(1, 0, 1) + + + 1/72 DATA(-2, 0, 1) + 1/144 DATA(-1, 0, -2) - 1/288 DATA(-2, 0, -2) + + - 1/72 DATA(2, 0, -1) + 1/48 DATA(2, 0, 0) + 1/288 DATA(2, 0, -2) + + - 1/144 DATA(1, 0, -2) - 1/72 DATA(2, 0, 1) + 1/144 DATA(-1, 0, 2) + + + 1/288 DATA(2, 0, 2) - 1/144 DATA(1, 0, 2) + 1/72 DATA(-2, 0, -1) + + 3 4 + - 1/288 DATA(-2, 0, 2) - 1/48 DATA(-2, 0, 0)) x z + (5/24 DATA(0, 0, -1) + + - 1/9 DATA(0, 1, -1) + 1/6 DATA(0, -1, 0) - 1/9 DATA(0, -1, 1) + + - 5/16 DATA(0, 0, 0) + 1/6 DATA(0, 1, 0) + 5/24 DATA(0, 0, 1) + + - 1/9 DATA(0, 1, 1) - 1/576 DATA(0, -2, -2) - 1/576 DATA(0, -2, 2) + + + 1/36 DATA(0, -1, -2) + 1/144 DATA(0, 2, -1) - 5/96 DATA(0, 0, -2) + + - 1/96 DATA(0, 2, 0) + 1/36 DATA(0, 1, -2) - 1/576 DATA(0, 2, -2) + + + 1/144 DATA(0, 2, 1) - 5/96 DATA(0, 0, 2) + 1/144 DATA(0, -2, -1) + + + 1/36 DATA(0, -1, 2) + 1/36 DATA(0, 1, 2) - 1/576 DATA(0, 2, 2) + + 2 4 + - 1/9 DATA(0, -1, -1) - 1/96 DATA(0, -2, 0) + 1/144 DATA(0, -2, 1)) y z + + + (- 4/9 DATA(0, 1, -1) - 4/9 DATA(0, -1, 1) + 4/9 DATA(0, 1, 1) + + + 1/144 DATA(0, -2, -2) - 1/144 DATA(0, -2, 2) - 1/18 DATA(0, -1, -2) + + + 1/18 DATA(0, 2, -1) + 1/18 DATA(0, 1, -2) - 1/144 DATA(0, 2, -2) + + - 1/18 DATA(0, 2, 1) - 1/18 DATA(0, -2, -1) + 1/18 DATA(0, -1, 2) + + - 1/18 DATA(0, 1, 2) + 1/144 DATA(0, 2, 2) + 4/9 DATA(0, -1, -1) + + + 1/18 DATA(0, -2, 1)) y z + (4/9 DATA(-1, 0, -1) - 4/9 DATA(1, 0, -1) + + - 4/9 DATA(-1, 0, 1) + 4/9 DATA(1, 0, 1) + 1/18 DATA(-2, 0, 1) + + - 1/18 DATA(-1, 0, -2) + 1/144 DATA(-2, 0, -2) + 1/18 DATA(2, 0, -1) + + - 1/144 DATA(2, 0, -2) + 1/18 DATA(1, 0, -2) - 1/18 DATA(2, 0, 1) + + + 1/18 DATA(-1, 0, 2) + 1/144 DATA(2, 0, 2) - 1/18 DATA(1, 0, 2) + + - 1/18 DATA(-2, 0, -1) - 1/144 DATA(-2, 0, 2)) x z + (- 4/9 DATA(-1, 1, 0) + + - 4/9 DATA(1, -1, 0) + 4/9 DATA(-1, -1, 0) + 4/9 DATA(1, 1, 0) + + + 1/18 DATA(2, -1, 0) + 1/144 DATA(2, 2, 0) - 1/18 DATA(1, 2, 0) + + + 1/18 DATA(-1, 2, 0) - 1/18 DATA(2, 1, 0) - 1/18 DATA(-1, -2, 0) + + + 1/144 DATA(-2, -2, 0) + 1/18 DATA(1, -2, 0) - 1/144 DATA(2, -2, 0) + + - 1/18 DATA(-2, -1, 0) + 1/18 DATA(-2, 1, 0) - 1/144 DATA(-2, 2, 0)) x y + + / + + |- 5/6 DATA(0, 0, -1) + 4/9 DATA(0, 1, -1) - 5/6 DATA(0, -1, 0) + \ + + 25 + + 4/9 DATA(0, -1, 1) + -- DATA(0, 0, 0) - 5/6 DATA(0, 1, 0) + 16 + + - 5/6 DATA(0, 0, 1) + 4/9 DATA(0, 1, 1) + 1/576 DATA(0, -2, -2) + + + 1/576 DATA(0, -2, 2) - 1/36 DATA(0, -1, -2) - 1/36 DATA(0, 2, -1) + + + 5/96 DATA(0, 0, -2) + 5/96 DATA(0, 2, 0) - 1/36 DATA(0, 1, -2) + + + 1/576 DATA(0, 2, -2) - 1/36 DATA(0, 2, 1) + 5/96 DATA(0, 0, 2) + + - 1/36 DATA(0, -2, -1) - 1/36 DATA(0, -1, 2) - 1/36 DATA(0, 1, 2) + + + 1/576 DATA(0, 2, 2) + 4/9 DATA(0, -1, -1) + 5/96 DATA(0, -2, 0) + + \ 2 2 + - 1/36 DATA(0, -2, 1)| y z + (4/9 DATA(0, 1, -1) + 5/6 DATA(0, -1, 0) + / + + - 4/9 DATA(0, -1, 1) - 5/6 DATA(0, 1, 0) + 4/9 DATA(0, 1, 1) + + - 1/288 DATA(0, -2, -2) - 1/288 DATA(0, -2, 2) + 1/36 DATA(0, -1, -2) + + - 1/18 DATA(0, 2, -1) + 5/48 DATA(0, 2, 0) - 1/36 DATA(0, 1, -2) + + + 1/288 DATA(0, 2, -2) - 1/18 DATA(0, 2, 1) + 1/18 DATA(0, -2, -1) + + + 1/36 DATA(0, -1, 2) - 1/36 DATA(0, 1, 2) + 1/288 DATA(0, 2, 2) + + 2 + - 4/9 DATA(0, -1, -1) - 5/48 DATA(0, -2, 0) + 1/18 DATA(0, -2, 1)) y z + + + (- 4/9 DATA(-1, 0, -1) + 4/9 DATA(1, 0, -1) + 5/6 DATA(-1, 0, 0) + + - 4/9 DATA(-1, 0, 1) - 5/6 DATA(1, 0, 0) + 4/9 DATA(1, 0, 1) + + + 1/18 DATA(-2, 0, 1) + 1/36 DATA(-1, 0, -2) - 1/288 DATA(-2, 0, -2) + + - 1/18 DATA(2, 0, -1) + 5/48 DATA(2, 0, 0) + 1/288 DATA(2, 0, -2) + + - 1/36 DATA(1, 0, -2) - 1/18 DATA(2, 0, 1) + 1/36 DATA(-1, 0, 2) + + + 1/288 DATA(2, 0, 2) - 1/36 DATA(1, 0, 2) + 1/18 DATA(-2, 0, -1) + + 2 / + - 1/288 DATA(-2, 0, 2) - 5/48 DATA(-2, 0, 0)) x z + |- 5/6 DATA(0, 0, -1) + \ + + + 4/9 DATA(-1, 0, -1) + 4/9 DATA(1, 0, -1) - 5/6 DATA(-1, 0, 0) + + 25 + + 4/9 DATA(-1, 0, 1) + -- DATA(0, 0, 0) - 5/6 DATA(1, 0, 0) + 16 + + - 5/6 DATA(0, 0, 1) + 4/9 DATA(1, 0, 1) - 1/36 DATA(-2, 0, 1) + + - 1/36 DATA(-1, 0, -2) + 5/96 DATA(0, 0, -2) + 1/576 DATA(-2, 0, -2) + + - 1/36 DATA(2, 0, -1) + 5/96 DATA(2, 0, 0) + 1/576 DATA(2, 0, -2) + + - 1/36 DATA(1, 0, -2) - 1/36 DATA(2, 0, 1) - 1/36 DATA(-1, 0, 2) + + + 5/96 DATA(0, 0, 2) + 1/576 DATA(2, 0, 2) - 1/36 DATA(1, 0, 2) + + \ 2 2 + - 1/36 DATA(-2, 0, -1) + 1/576 DATA(-2, 0, 2) + 5/96 DATA(-2, 0, 0)| x z + / + + + (5/6 DATA(0, 0, -1) - 4/9 DATA(0, 1, -1) + 4/9 DATA(0, -1, 1) + + - 5/6 DATA(0, 0, 1) + 4/9 DATA(0, 1, 1) - 1/288 DATA(0, -2, -2) + + + 1/288 DATA(0, -2, 2) + 1/18 DATA(0, -1, -2) + 1/36 DATA(0, 2, -1) + + - 5/48 DATA(0, 0, -2) + 1/18 DATA(0, 1, -2) - 1/288 DATA(0, 2, -2) + + - 1/36 DATA(0, 2, 1) + 5/48 DATA(0, 0, 2) + 1/36 DATA(0, -2, -1) + + - 1/18 DATA(0, -1, 2) - 1/18 DATA(0, 1, 2) + 1/288 DATA(0, 2, 2) + + 2 + - 4/9 DATA(0, -1, -1) - 1/36 DATA(0, -2, 1)) y z + (5/6 DATA(0, 0, -1) + + - 4/9 DATA(-1, 0, -1) - 4/9 DATA(1, 0, -1) + 4/9 DATA(-1, 0, 1) + + - 5/6 DATA(0, 0, 1) + 4/9 DATA(1, 0, 1) - 1/36 DATA(-2, 0, 1) + + + 1/18 DATA(-1, 0, -2) - 5/48 DATA(0, 0, -2) - 1/288 DATA(-2, 0, -2) + + + 1/36 DATA(2, 0, -1) - 1/288 DATA(2, 0, -2) + 1/18 DATA(1, 0, -2) + + - 1/36 DATA(2, 0, 1) - 1/18 DATA(-1, 0, 2) + 5/48 DATA(0, 0, 2) + + + 1/288 DATA(2, 0, 2) - 1/18 DATA(1, 0, 2) + 1/36 DATA(-2, 0, -1) + + 2 + + 1/288 DATA(-2, 0, 2)) x z + (- 4/9 DATA(-1, 1, 0) + 5/6 DATA(-1, 0, 0) + + + 4/9 DATA(1, -1, 0) - 4/9 DATA(-1, -1, 0) - 5/6 DATA(1, 0, 0) + + + 4/9 DATA(1, 1, 0) + 5/48 DATA(2, 0, 0) - 1/18 DATA(2, -1, 0) + + + 1/288 DATA(2, 2, 0) - 1/36 DATA(1, 2, 0) + 1/36 DATA(-1, 2, 0) + + - 1/18 DATA(2, 1, 0) + 1/36 DATA(-1, -2, 0) - 1/288 DATA(-2, -2, 0) + + - 1/36 DATA(1, -2, 0) + 1/288 DATA(2, -2, 0) + 1/18 DATA(-2, -1, 0) + + 2 + - 5/48 DATA(-2, 0, 0) + 1/18 DATA(-2, 1, 0) - 1/288 DATA(-2, 2, 0)) x y + + / + + |4/9 DATA(-1, 1, 0) - 5/6 DATA(-1, 0, 0) + 4/9 DATA(1, -1, 0) + \ + + 25 + - 5/6 DATA(0, -1, 0) + 4/9 DATA(-1, -1, 0) + -- DATA(0, 0, 0) + 16 + + - 5/6 DATA(1, 0, 0) - 5/6 DATA(0, 1, 0) + 4/9 DATA(1, 1, 0) + + + 5/96 DATA(2, 0, 0) - 1/36 DATA(2, -1, 0) + 1/576 DATA(2, 2, 0) + + - 1/36 DATA(1, 2, 0) + 5/96 DATA(0, 2, 0) - 1/36 DATA(-1, 2, 0) + + - 1/36 DATA(2, 1, 0) - 1/36 DATA(-1, -2, 0) + 5/96 DATA(0, -2, 0) + + + 1/576 DATA(-2, -2, 0) - 1/36 DATA(1, -2, 0) + 1/576 DATA(2, -2, 0) + + - 1/36 DATA(-2, -1, 0) + 5/96 DATA(-2, 0, 0) - 1/36 DATA(-2, 1, 0) + + \ 2 2 + + 1/576 DATA(-2, 2, 0)| x y + (4/9 DATA(-1, 1, 0) - 4/9 DATA(1, -1, 0) + / + + + 5/6 DATA(0, -1, 0) - 4/9 DATA(-1, -1, 0) - 5/6 DATA(0, 1, 0) + + + 4/9 DATA(1, 1, 0) + 1/36 DATA(2, -1, 0) + 1/288 DATA(2, 2, 0) + + - 1/18 DATA(1, 2, 0) + 5/48 DATA(0, 2, 0) - 1/18 DATA(-1, 2, 0) + + - 1/36 DATA(2, 1, 0) + 1/18 DATA(-1, -2, 0) - 5/48 DATA(0, -2, 0) + + - 1/288 DATA(-2, -2, 0) + 1/18 DATA(1, -2, 0) - 1/288 DATA(2, -2, 0) + + 2 + + 1/36 DATA(-2, -1, 0) - 1/36 DATA(-2, 1, 0) + 1/288 DATA(-2, 2, 0)) x y + + + (- 1/36 DATA(0, 1, -1) - 1/36 DATA(0, -1, 1) + 1/36 DATA(0, 1, 1) + + + 1/144 DATA(0, -2, -2) - 1/144 DATA(0, -2, 2) - 1/72 DATA(0, -1, -2) + + + 1/72 DATA(0, 2, -1) + 1/72 DATA(0, 1, -2) - 1/144 DATA(0, 2, -2) + + - 1/72 DATA(0, 2, 1) - 1/72 DATA(0, -2, -1) + 1/72 DATA(0, -1, 2) + + - 1/72 DATA(0, 1, 2) + 1/144 DATA(0, 2, 2) + 1/36 DATA(0, -1, -1) + + 3 3 + + 1/72 DATA(0, -2, 1)) y z + (- 5/24 DATA(0, 0, -1) + 1/9 DATA(0, 1, -1) + + - 1/9 DATA(0, -1, 1) + 5/24 DATA(0, 0, 1) - 1/9 DATA(0, 1, 1) + + + 1/288 DATA(0, -2, -2) - 1/288 DATA(0, -2, 2) - 1/18 DATA(0, -1, -2) + + - 1/144 DATA(0, 2, -1) + 5/48 DATA(0, 0, -2) - 1/18 DATA(0, 1, -2) + + + 1/288 DATA(0, 2, -2) + 1/144 DATA(0, 2, 1) - 5/48 DATA(0, 0, 2) + + - 1/144 DATA(0, -2, -1) + 1/18 DATA(0, -1, 2) + 1/18 DATA(0, 1, 2) + + 2 3 + - 1/288 DATA(0, 2, 2) + 1/9 DATA(0, -1, -1) + 1/144 DATA(0, -2, 1)) y z + + + (1/9 DATA(0, 1, -1) + 1/9 DATA(0, -1, 1) - 1/9 DATA(0, 1, 1) + + - 1/144 DATA(0, -2, -2) + 1/144 DATA(0, -2, 2) + 1/18 DATA(0, -1, -2) + + - 1/72 DATA(0, 2, -1) - 1/18 DATA(0, 1, -2) + 1/144 DATA(0, 2, -2) + + + 1/72 DATA(0, 2, 1) + 1/72 DATA(0, -2, -1) - 1/18 DATA(0, -1, 2) + + + 1/18 DATA(0, 1, 2) - 1/144 DATA(0, 2, 2) - 1/9 DATA(0, -1, -1) + + 3 + - 1/72 DATA(0, -2, 1)) y z + (- 5/24 DATA(0, 0, -1) + 1/9 DATA(-1, 0, -1) + + + 1/9 DATA(1, 0, -1) - 1/9 DATA(-1, 0, 1) + 5/24 DATA(0, 0, 1) + + - 1/9 DATA(1, 0, 1) + 1/144 DATA(-2, 0, 1) - 1/18 DATA(-1, 0, -2) + + + 5/48 DATA(0, 0, -2) + 1/288 DATA(-2, 0, -2) - 1/144 DATA(2, 0, -1) + + + 1/288 DATA(2, 0, -2) - 1/18 DATA(1, 0, -2) + 1/144 DATA(2, 0, 1) + + + 1/18 DATA(-1, 0, 2) - 5/48 DATA(0, 0, 2) - 1/288 DATA(2, 0, 2) + + 2 3 + + 1/18 DATA(1, 0, 2) - 1/144 DATA(-2, 0, -1) - 1/288 DATA(-2, 0, 2)) x z + + + (1/36 DATA(-1, 0, -1) - 1/36 DATA(1, 0, -1) - 1/36 DATA(-1, 0, 1) + + + 1/36 DATA(1, 0, 1) + 1/72 DATA(-2, 0, 1) - 1/72 DATA(-1, 0, -2) + + + 1/144 DATA(-2, 0, -2) + 1/72 DATA(2, 0, -1) - 1/144 DATA(2, 0, -2) + + + 1/72 DATA(1, 0, -2) - 1/72 DATA(2, 0, 1) + 1/72 DATA(-1, 0, 2) + + + 1/144 DATA(2, 0, 2) - 1/72 DATA(1, 0, 2) - 1/72 DATA(-2, 0, -1) + + 3 3 + - 1/144 DATA(-2, 0, 2)) x z + (- 1/9 DATA(0, 1, -1) + + - 5/24 DATA(0, -1, 0) + 1/9 DATA(0, -1, 1) + 5/24 DATA(0, 1, 0) + + - 1/9 DATA(0, 1, 1) + 1/288 DATA(0, -2, -2) + 1/288 DATA(0, -2, 2) + + - 1/144 DATA(0, -1, -2) + 1/18 DATA(0, 2, -1) - 5/48 DATA(0, 2, 0) + + + 1/144 DATA(0, 1, -2) - 1/288 DATA(0, 2, -2) + 1/18 DATA(0, 2, 1) + + - 1/18 DATA(0, -2, -1) - 1/144 DATA(0, -1, 2) + 1/144 DATA(0, 1, 2) + + - 1/288 DATA(0, 2, 2) + 1/9 DATA(0, -1, -1) + 5/48 DATA(0, -2, 0) + + 3 2 + - 1/18 DATA(0, -2, 1)) y z + (1/9 DATA(-1, 0, -1) - 1/9 DATA(1, 0, -1) + + - 5/24 DATA(-1, 0, 0) + 1/9 DATA(-1, 0, 1) + 5/24 DATA(1, 0, 0) + + - 1/9 DATA(1, 0, 1) - 1/18 DATA(-2, 0, 1) - 1/144 DATA(-1, 0, -2) + + + 1/288 DATA(-2, 0, -2) + 1/18 DATA(2, 0, -1) - 5/48 DATA(2, 0, 0) + + - 1/288 DATA(2, 0, -2) + 1/144 DATA(1, 0, -2) + 1/18 DATA(2, 0, 1) + + - 1/144 DATA(-1, 0, 2) - 1/288 DATA(2, 0, 2) + 1/144 DATA(1, 0, 2) + + 3 2 + - 1/18 DATA(-2, 0, -1) + 1/288 DATA(-2, 0, 2) + 5/48 DATA(-2, 0, 0)) x z + + + (- 1/9 DATA(-1, 0, -1) + 1/9 DATA(1, 0, -1) + 1/9 DATA(-1, 0, 1) + + - 1/9 DATA(1, 0, 1) - 1/18 DATA(-2, 0, 1) + 1/72 DATA(-1, 0, -2) + + - 1/144 DATA(-2, 0, -2) - 1/18 DATA(2, 0, -1) + 1/144 DATA(2, 0, -2) + + - 1/72 DATA(1, 0, -2) + 1/18 DATA(2, 0, 1) - 1/72 DATA(-1, 0, 2) + + - 1/144 DATA(2, 0, 2) + 1/72 DATA(1, 0, 2) + 1/18 DATA(-2, 0, -1) + + 3 + + 1/144 DATA(-2, 0, 2)) x z + (1/9 DATA(-1, 1, 0) + 1/9 DATA(1, -1, 0) + + - 1/9 DATA(-1, -1, 0) - 1/9 DATA(1, 1, 0) - 1/72 DATA(2, -1, 0) + + - 1/144 DATA(2, 2, 0) + 1/18 DATA(1, 2, 0) - 1/18 DATA(-1, 2, 0) + + + 1/72 DATA(2, 1, 0) + 1/18 DATA(-1, -2, 0) - 1/144 DATA(-2, -2, 0) + + - 1/18 DATA(1, -2, 0) + 1/144 DATA(2, -2, 0) + 1/72 DATA(-2, -1, 0) + + 3 + - 1/72 DATA(-2, 1, 0) + 1/144 DATA(-2, 2, 0)) x y + (- 1/9 DATA(-1, 1, 0) + + + 1/9 DATA(1, -1, 0) - 5/24 DATA(0, -1, 0) + 1/9 DATA(-1, -1, 0) + + + 5/24 DATA(0, 1, 0) - 1/9 DATA(1, 1, 0) - 1/144 DATA(2, -1, 0) + + - 1/288 DATA(2, 2, 0) + 1/18 DATA(1, 2, 0) - 5/48 DATA(0, 2, 0) + + + 1/18 DATA(-1, 2, 0) + 1/144 DATA(2, 1, 0) - 1/18 DATA(-1, -2, 0) + + + 5/48 DATA(0, -2, 0) + 1/288 DATA(-2, -2, 0) - 1/18 DATA(1, -2, 0) + + + 1/288 DATA(2, -2, 0) - 1/144 DATA(-2, -1, 0) + 1/144 DATA(-2, 1, 0) + + 2 3 + - 1/288 DATA(-2, 2, 0)) x y + (1/9 DATA(-1, 1, 0) - 5/24 DATA(-1, 0, 0) + + - 1/9 DATA(1, -1, 0) + 1/9 DATA(-1, -1, 0) + 5/24 DATA(1, 0, 0) + + - 1/9 DATA(1, 1, 0) - 5/48 DATA(2, 0, 0) + 1/18 DATA(2, -1, 0) + + - 1/288 DATA(2, 2, 0) + 1/144 DATA(1, 2, 0) - 1/144 DATA(-1, 2, 0) + + + 1/18 DATA(2, 1, 0) - 1/144 DATA(-1, -2, 0) + 1/288 DATA(-2, -2, 0) + + + 1/144 DATA(1, -2, 0) - 1/288 DATA(2, -2, 0) - 1/18 DATA(-2, -1, 0) + + 3 2 + + 5/48 DATA(-2, 0, 0) - 1/18 DATA(-2, 1, 0) + 1/288 DATA(-2, 2, 0)) x y + + + (1/9 DATA(-1, 1, 0) + 1/9 DATA(1, -1, 0) - 1/9 DATA(-1, -1, 0) + + - 1/9 DATA(1, 1, 0) - 1/18 DATA(2, -1, 0) - 1/144 DATA(2, 2, 0) + + + 1/72 DATA(1, 2, 0) - 1/72 DATA(-1, 2, 0) + 1/18 DATA(2, 1, 0) + + + 1/72 DATA(-1, -2, 0) - 1/144 DATA(-2, -2, 0) - 1/72 DATA(1, -2, 0) 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1/96 DATA(2, 0, 0) - 1/576 DATA(2, 0, -2) + 1/36 DATA(1, 0, -2) + + + 1/144 DATA(2, 0, 1) + 1/36 DATA(-1, 0, 2) - 5/96 DATA(0, 0, 2) + + - 1/576 DATA(2, 0, 2) + 1/36 DATA(1, 0, 2) + 1/144 DATA(-2, 0, -1) + + 2 4 + - 1/576 DATA(-2, 0, 2) - 1/96 DATA(-2, 0, 0)) x z + ( + + - 1/24 DATA(0, 0, -1) + 1/36 DATA(-1, 0, -1) + 1/36 DATA(1, 0, -1) + + - 1/24 DATA(-1, 0, 0) + 1/36 DATA(-1, 0, 1) + 1/16 DATA(0, 0, 0) + + - 1/24 DATA(1, 0, 0) - 1/24 DATA(0, 0, 1) + 1/36 DATA(1, 0, 1) + + - 1/144 DATA(-2, 0, 1) - 1/144 DATA(-1, 0, -2) + 1/96 DATA(0, 0, -2) + + + 1/576 DATA(-2, 0, -2) - 1/144 DATA(2, 0, -1) + 1/96 DATA(2, 0, 0) + + + 1/576 DATA(2, 0, -2) - 1/144 DATA(1, 0, -2) - 1/144 DATA(2, 0, 1) + + - 1/144 DATA(-1, 0, 2) + 1/96 DATA(0, 0, 2) + 1/576 DATA(2, 0, 2) + + - 1/144 DATA(1, 0, 2) - 1/144 DATA(-2, 0, -1) + 1/576 DATA(-2, 0, 2) + + 4 4 + + 1/96 DATA(-2, 0, 0)) x z + (1/24 DATA(0, 0, -1) - 1/36 DATA(0, 1, -1) + + + 1/36 DATA(0, -1, 1) - 1/24 DATA(0, 0, 1) + 1/36 DATA(0, 1, 1) + + - 1/288 DATA(0, -2, -2) + 1/288 DATA(0, -2, 2) + 1/72 DATA(0, -1, -2) + + + 1/144 DATA(0, 2, -1) - 1/48 DATA(0, 0, -2) + 1/72 DATA(0, 1, -2) + + - 1/288 DATA(0, 2, -2) - 1/144 DATA(0, 2, 1) + 1/48 DATA(0, 0, 2) + + + 1/144 DATA(0, -2, -1) - 1/72 DATA(0, -1, 2) - 1/72 DATA(0, 1, 2) + + 4 3 + + 1/288 DATA(0, 2, 2) - 1/36 DATA(0, -1, -1) - 1/144 DATA(0, -2, 1)) y z + + + (1/24 DATA(0, 0, -1) - 1/36 DATA(-1, 0, -1) - 1/36 DATA(1, 0, -1) + + + 1/36 DATA(-1, 0, 1) - 1/24 DATA(0, 0, 1) + 1/36 DATA(1, 0, 1) + + - 1/144 DATA(-2, 0, 1) + 1/72 DATA(-1, 0, -2) - 1/48 DATA(0, 0, -2) + + - 1/288 DATA(-2, 0, -2) + 1/144 DATA(2, 0, -1) - 1/288 DATA(2, 0, -2) + + + 1/72 DATA(1, 0, -2) - 1/144 DATA(2, 0, 1) - 1/72 DATA(-1, 0, 2) + + + 1/48 DATA(0, 0, 2) + 1/288 DATA(2, 0, 2) - 1/72 DATA(1, 0, 2) + + 4 3 + + 1/144 DATA(-2, 0, -1) + 1/288 DATA(-2, 0, 2)) x z + ( + + 1/6 DATA(0, 0, -1) - 1/9 DATA(-1, 0, -1) - 1/9 DATA(1, 0, -1) + + + 5/24 DATA(-1, 0, 0) - 1/9 DATA(-1, 0, 1) - 5/16 DATA(0, 0, 0) + + + 5/24 DATA(1, 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DATA(-1, 0, 1) + 1/6 DATA(0, 0, 1) - 1/9 DATA(1, 0, 1) + + + 1/36 DATA(-2, 0, 1) - 1/72 DATA(-1, 0, -2) + 1/48 DATA(0, 0, -2) + + + 1/288 DATA(-2, 0, -2) - 1/36 DATA(2, 0, -1) + 1/288 DATA(2, 0, -2) + + - 1/72 DATA(1, 0, -2) + 1/36 DATA(2, 0, 1) + 1/72 DATA(-1, 0, 2) + + - 1/48 DATA(0, 0, 2) - 1/288 DATA(2, 0, 2) + 1/72 DATA(1, 0, 2) + + 4 + - 1/36 DATA(-2, 0, -1) - 1/288 DATA(-2, 0, 2)) x z + (1/9 DATA(-1, 1, 0) + + - 1/6 DATA(-1, 0, 0) - 1/9 DATA(1, -1, 0) + 1/9 DATA(-1, -1, 0) + + + 1/6 DATA(1, 0, 0) - 1/9 DATA(1, 1, 0) - 1/48 DATA(2, 0, 0) + + + 1/72 DATA(2, -1, 0) - 1/288 DATA(2, 2, 0) + 1/36 DATA(1, 2, 0) + + - 1/36 DATA(-1, 2, 0) + 1/72 DATA(2, 1, 0) - 1/36 DATA(-1, -2, 0) + + + 1/288 DATA(-2, -2, 0) + 1/36 DATA(1, -2, 0) - 1/288 DATA(2, -2, 0) + + - 1/72 DATA(-2, -1, 0) + 1/48 DATA(-2, 0, 0) - 1/72 DATA(-2, 1, 0) + + 4 + + 1/288 DATA(-2, 2, 0)) x y + (- 1/9 DATA(-1, 1, 0) + 1/6 DATA(-1, 0, 0) + + - 1/9 DATA(1, -1, 0) + 5/24 DATA(0, -1, 0) - 1/9 DATA(-1, -1, 0) + + - 5/16 DATA(0, 0, 0) + 1/6 DATA(1, 0, 0) + 5/24 DATA(0, 1, 0) + + - 1/9 DATA(1, 1, 0) - 1/96 DATA(2, 0, 0) + 1/144 DATA(2, -1, 0) + + - 1/576 DATA(2, 2, 0) + 1/36 DATA(1, 2, 0) - 5/96 DATA(0, 2, 0) + + + 1/36 DATA(-1, 2, 0) + 1/144 DATA(2, 1, 0) + 1/36 DATA(-1, -2, 0) + + - 5/96 DATA(0, -2, 0) - 1/576 DATA(-2, -2, 0) + 1/36 DATA(1, -2, 0) + + - 1/576 DATA(2, -2, 0) + 1/144 DATA(-2, -1, 0) - 1/96 DATA(-2, 0, 0) + + 2 4 + + 1/144 DATA(-2, 1, 0) - 1/576 DATA(-2, 2, 0)) x y + ( + + - 1/36 DATA(-1, 1, 0) + 1/24 DATA(-1, 0, 0) + 1/36 DATA(1, -1, 0) + + - 1/36 DATA(-1, -1, 0) - 1/24 DATA(1, 0, 0) + 1/36 DATA(1, 1, 0) + + + 1/48 DATA(2, 0, 0) - 1/72 DATA(2, -1, 0) + 1/288 DATA(2, 2, 0) + + - 1/144 DATA(1, 2, 0) + 1/144 DATA(-1, 2, 0) - 1/72 DATA(2, 1, 0) + + + 1/144 DATA(-1, -2, 0) - 1/288 DATA(-2, -2, 0) - 1/144 DATA(1, -2, 0) + + + 1/288 DATA(2, -2, 0) + 1/72 DATA(-2, -1, 0) - 1/48 DATA(-2, 0, 0) + + 3 4 + + 1/72 DATA(-2, 1, 0) - 1/288 DATA(-2, 2, 0)) x y + (1/36 DATA(-1, 1, 0) + + - 1/24 DATA(-1, 0, 0) + 1/36 DATA(1, -1, 0) - 1/24 DATA(0, -1, 0) + + + 1/36 DATA(-1, -1, 0) + 1/16 DATA(0, 0, 0) - 1/24 DATA(1, 0, 0) + + - 1/24 DATA(0, 1, 0) + 1/36 DATA(1, 1, 0) + 1/96 DATA(2, 0, 0) + + - 1/144 DATA(2, -1, 0) + 1/576 DATA(2, 2, 0) - 1/144 DATA(1, 2, 0) + + + 1/96 DATA(0, 2, 0) - 1/144 DATA(-1, 2, 0) - 1/144 DATA(2, 1, 0) + + - 1/144 DATA(-1, -2, 0) + 1/96 DATA(0, -2, 0) + 1/576 DATA(-2, -2, 0) + + - 1/144 DATA(1, -2, 0) + 1/576 DATA(2, -2, 0) - 1/144 DATA(-2, -1, 0) + + 4 4 + + 1/96 DATA(-2, 0, 0) - 1/144 DATA(-2, 1, 0) + 1/576 DATA(-2, 2, 0)) x y + + + (1/36 DATA(-1, 1, 0) - 1/36 DATA(1, -1, 0) + 1/24 DATA(0, -1, 0) + + - 1/36 DATA(-1, -1, 0) - 1/24 DATA(0, 1, 0) + 1/36 DATA(1, 1, 0) + + - 1/144 DATA(-2, 1, 0) + 1/144 DATA(2, -1, 0) + 1/288 DATA(2, 2, 0) + + - 1/72 DATA(1, 2, 0) + 1/48 DATA(0, 2, 0) - 1/72 DATA(-1, 2, 0) + + - 1/144 DATA(2, 1, 0) + 1/72 DATA(-1, -2, 0) - 1/48 DATA(0, -2, 0) + + - 1/288 DATA(-2, -2, 0) + 1/72 DATA(1, -2, 0) - 1/288 DATA(2, -2, 0) + + 4 3 + + 1/144 DATA(-2, -1, 0) + 1/288 DATA(-2, 2, 0)) x y + ( + + - 1/9 DATA(-1, 1, 0) + 5/24 DATA(-1, 0, 0) - 1/9 DATA(1, -1, 0) + + + 1/6 DATA(0, -1, 0) - 1/9 DATA(-1, -1, 0) - 5/16 DATA(0, 0, 0) + + + 5/24 DATA(1, 0, 0) + 1/6 DATA(0, 1, 0) - 1/9 DATA(1, 1, 0) + + - 5/96 DATA(2, 0, 0) + 1/36 DATA(2, -1, 0) - 1/576 DATA(2, 2, 0) + + + 1/144 DATA(1, 2, 0) - 1/96 DATA(0, 2, 0) + 1/144 DATA(-1, 2, 0) + + + 1/36 DATA(2, 1, 0) + 1/144 DATA(-1, -2, 0) - 1/96 DATA(0, -2, 0) + + - 1/576 DATA(-2, -2, 0) + 1/144 DATA(1, -2, 0) - 1/576 DATA(2, -2, 0) + + + 1/36 DATA(-2, -1, 0) - 5/96 DATA(-2, 0, 0) + 1/36 DATA(-2, 1, 0) + + 4 2 + - 1/576 DATA(-2, 2, 0)) x y + (- 1/9 DATA(-1, 1, 0) + 1/9 DATA(1, -1, 0) + + - 1/6 DATA(0, -1, 0) + 1/9 DATA(-1, -1, 0) + 1/6 DATA(0, 1, 0) + + - 1/9 DATA(1, 1, 0) - 1/36 DATA(2, -1, 0) - 1/288 DATA(2, 2, 0) + + + 1/72 DATA(1, 2, 0) - 1/48 DATA(0, 2, 0) + 1/72 DATA(-1, 2, 0) + + + 1/36 DATA(2, 1, 0) - 1/72 DATA(-1, -2, 0) + 1/48 DATA(0, -2, 0) + + + 1/288 DATA(-2, -2, 0) - 1/72 DATA(1, -2, 0) + 1/288 DATA(2, -2, 0) + + 4 + - 1/36 DATA(-2, -1, 0) + 1/36 DATA(-2, 1, 0) - 1/288 DATA(-2, 2, 0)) x y + + + DATA(0, 0, 0) + (1/9 DATA(-1, 0, -1) - 1/9 DATA(1, 0, -1) + + - 1/6 DATA(-1, 0, 0) + 1/9 DATA(-1, 0, 1) + 1/6 DATA(1, 0, 0) + + - 1/9 DATA(1, 0, 1) - 1/72 DATA(-2, 0, 1) - 1/36 DATA(-1, 0, -2) + + + 1/288 DATA(-2, 0, -2) + 1/72 DATA(2, 0, -1) - 1/48 DATA(2, 0, 0) + + - 1/288 DATA(2, 0, -2) + 1/36 DATA(1, 0, -2) + 1/72 DATA(2, 0, 1) + + - 1/36 DATA(-1, 0, 2) - 1/288 DATA(2, 0, 2) + 1/36 DATA(1, 0, 2) + + 4 + - 1/72 DATA(-2, 0, -1) + 1/288 DATA(-2, 0, 2) + 1/48 DATA(-2, 0, 0)) x z + + + (- 1/108 DATA(1, -2, 1) - 2/27 DATA(1, -1, -1) + 1/3456 DATA(-2, 2, 2) + + + 2/27 DATA(-1, 1, -1) + 2/27 DATA(1, 1, -1) - 5/36 DATA(0, 1, -1) + + - 2/27 DATA(-1, 1, 1) + 2/27 DATA(1, -1, 1) - 5/36 DATA(0, -1, 1) + + + 2/27 DATA(-1, -1, 1) + 5/36 DATA(0, 1, 1) - 2/27 DATA(1, 1, 1) + + - 1/3456 DATA(-2, -2, 2) + 1/216 DATA(-1, -2, 2) + 5/576 DATA(0, -2, -2) + + - 1/216 DATA(-1, -2, 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DATA(-2, -1, 0) + 1/1728 DATA(-2, 1, 2) + + + 1/216 DATA(-2, 2, 1) + 5/288 DATA(-2, 1, 0) + 1/108 DATA(-2, -1, 1) + + - 5/576 DATA(-2, 2, 0) - 1/216 DATA(-2, -2, 1) + 1/27 DATA(-1, -2, 1)) x + + 3 2 / + y z + |- 1/27 DATA(1, -2, 1) + 2/27 DATA(1, -1, -1) + \ + + + 1/6912 DATA(-2, 2, 2) - 2/27 DATA(-1, 1, -1) - 2/27 DATA(1, 1, -1) + + + 5/36 DATA(0, 1, -1) + 5/36 DATA(-1, 1, 0) - 5/36 DATA(1, -1, 0) + + 25 + + -- DATA(0, -1, 0) - 5/36 DATA(-1, -1, 0) - 2/27 DATA(-1, 1, 1) + 96 + + + 2/27 DATA(1, -1, 1) - 5/36 DATA(0, -1, 1) + 2/27 DATA(-1, -1, 1) + + 25 + - -- DATA(0, 1, 0) + 5/36 DATA(1, 1, 0) + 5/36 DATA(0, 1, 1) + 96 + + - 2/27 DATA(1, 1, 1) - 1/6912 DATA(-2, -2, 2) + 1/432 DATA(-1, -2, 2) + + - 5/1152 DATA(0, -2, -2) + 1/432 DATA(-1, -2, -2) - 5/1152 DATA(0, -2, 2) + + - 1/6912 DATA(-2, -2, -2) + 1/3456 DATA(-2, -1, -2) + + - 1/6912 DATA(2, -2, -2) + 1/432 DATA(1, -2, -2) - 1/216 DATA(1, -1, -2) + + - 1/216 DATA(2, -1, -1) + 1/216 DATA(-2, 1, 1) + 1/432 DATA(1, -2, 2) + + + 5/576 DATA(0, -1, -2) - 1/216 DATA(-1, -1, -2) + 1/27 DATA(1, 2, -1) + + - 5/72 DATA(0, 2, -1) + 1/27 DATA(-1, 2, -1) + 1/216 DATA(2, 1, -1) + + + 1/3456 DATA(2, -1, -2) + 1/216 DATA(-1, 1, -2) - 1/3456 DATA(-2, 1, -2) + + + 5/576 DATA(2, -1, 0) - 1/432 DATA(2, 2, -1) + 1/432 DATA(2, -2, 1) + + + 5/1152 DATA(2, 2, 0) - 1/3456 DATA(2, 1, -2) - 5/72 DATA(1, 2, 0) + + 25 + + --- DATA(0, 2, 0) + 1/216 DATA(1, 1, -2) - 5/72 DATA(-1, 2, 0) + 192 + + - 5/576 DATA(2, 1, 0) - 5/576 DATA(0, 1, -2) - 1/6912 DATA(2, -2, 2) + + + 5/1152 DATA(0, 2, -2) - 1/432 DATA(-1, 2, -2) - 1/216 DATA(2, -1, 1) + + + 1/6912 DATA(-2, 2, -2) + 1/432 DATA(-2, -2, -1) - 1/432 DATA(2, 2, 1) + + + 1/27 DATA(1, 2, 1) + 1/6912 DATA(2, 2, -2) - 5/72 DATA(0, 2, 1) + + + 1/27 DATA(-1, 2, 1) + 1/3456 DATA(-2, -1, 2) + 1/216 DATA(2, 1, 1) + + - 1/432 DATA(1, 2, -2) + 5/72 DATA(0, -2, -1) + 1/3456 DATA(2, -1, 2) + + - 1/27 DATA(-1, -2, -1) - 1/216 DATA(1, -1, 2) + 5/576 DATA(0, -1, 2) + + - 1/216 DATA(-1, -1, 2) - 1/3456 DATA(2, 1, 2) + 1/432 DATA(2, -2, -1) + + + 1/216 DATA(1, 1, 2) - 5/576 DATA(0, 1, 2) + 1/216 DATA(-1, 1, 2) + + + 2/27 DATA(-1, -1, -1) - 1/27 DATA(1, -2, -1) + 1/6912 DATA(2, 2, 2) + + - 1/432 DATA(1, 2, 2) + 5/1152 DATA(0, 2, 2) - 1/216 DATA(-2, -1, -1) + + - 1/432 DATA(-1, 2, 2) - 5/36 DATA(0, -1, -1) + 1/216 DATA(-2, 1, -1) + + 25 + - 1/432 DATA(-2, 2, -1) + 5/72 DATA(-1, -2, 0) - --- DATA(0, -2, 0) + 192 + + - 5/1152 DATA(-2, -2, 0) + 5/72 DATA(1, -2, 0) - 5/1152 DATA(2, -2, 0) + + + 5/576 DATA(-2, -1, 0) - 1/3456 DATA(-2, 1, 2) - 1/432 DATA(-2, 2, 1) + + - 5/576 DATA(-2, 1, 0) - 1/216 DATA(-2, -1, 1) + 5/1152 DATA(-2, 2, 0) + + \ 2 + + 1/432 DATA(-2, -2, 1) - 1/27 DATA(-1, -2, 1) + 5/72 DATA(0, -2, 1)| x + / + + 3 2 + y z + (1/108 DATA(1, -2, 1) - 1/54 DATA(1, -1, -1) + + + 1/3456 DATA(-2, 2, 2) - 1/54 DATA(-1, 1, -1) + 1/54 DATA(1, 1, -1) + + + 5/144 DATA(-1, 1, 0) + 5/144 DATA(1, -1, 0) - 5/144 DATA(-1, -1, 0) + + - 1/54 DATA(-1, 1, 1) - 1/54 DATA(1, -1, 1) + 1/54 DATA(-1, -1, 1) + + - 5/144 DATA(1, 1, 0) + 1/54 DATA(1, 1, 1) - 1/3456 DATA(-2, -2, 2) + + + 1/1728 DATA(-1, -2, 2) + 1/1728 DATA(-1, -2, -2) + + - 1/3456 DATA(-2, -2, -2) + 1/1728 DATA(-2, -1, -2) + + + 1/3456 DATA(2, -2, -2) - 1/1728 DATA(1, -2, -2) + 1/864 DATA(1, -1, -2) + + + 1/108 DATA(2, -1, -1) + 1/108 DATA(-2, 1, 1) - 1/1728 DATA(1, -2, 2) + + - 1/864 DATA(-1, -1, -2) - 1/108 DATA(1, 2, -1) + 1/108 DATA(-1, 2, -1) + + - 1/108 DATA(2, 1, -1) - 1/1728 DATA(2, -1, -2) + 1/864 DATA(-1, 1, -2) + + - 1/1728 DATA(-2, 1, -2) - 5/288 DATA(2, -1, 0) + 1/216 DATA(2, 2, -1) + + - 1/216 DATA(2, -2, 1) - 5/576 DATA(2, 2, 0) + 1/1728 DATA(2, 1, -2) + + + 5/288 DATA(1, 2, 0) - 1/864 DATA(1, 1, -2) - 5/288 DATA(-1, 2, 0) + + + 5/288 DATA(2, 1, 0) + 1/3456 DATA(2, -2, 2) - 1/1728 DATA(-1, 2, -2) + + + 1/108 DATA(2, -1, 1) + 1/3456 DATA(-2, 2, -2) + 1/216 DATA(-2, -2, -1) + + + 1/216 DATA(2, 2, 1) - 1/108 DATA(1, 2, 1) - 1/3456 DATA(2, 2, -2) + + + 1/108 DATA(-1, 2, 1) + 1/1728 DATA(-2, -1, 2) - 1/108 DATA(2, 1, 1) 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5/36 DATA(-1, -1, 0) + 2/27 DATA(-1, 1, 1) + + - 5/36 DATA(-1, 0, 1) - 2/27 DATA(1, -1, 1) + 2/27 DATA(-1, -1, 1) + + 25 + - -- DATA(1, 0, 0) + 5/36 DATA(1, 1, 0) + 5/36 DATA(1, 0, 1) + 96 + + - 2/27 DATA(1, 1, 1) + 5/72 DATA(-2, 0, 1) - 1/6912 DATA(-2, -2, 2) + + + 1/3456 DATA(-1, -2, 2) + 1/3456 DATA(-1, -2, -2) + + - 1/6912 DATA(-2, -2, -2) + 1/432 DATA(-2, -1, -2) + + + 1/6912 DATA(2, -2, -2) - 1/3456 DATA(1, -2, -2) + 1/216 DATA(1, -1, -2) + + + 1/27 DATA(2, -1, -1) - 1/27 DATA(-2, 1, 1) - 1/3456 DATA(1, -2, 2) + + - 1/216 DATA(-1, -1, -2) + 1/216 DATA(1, 2, -1) + 5/576 DATA(-1, 0, -2) + + - 1/216 DATA(-1, 2, -1) + 1/27 DATA(2, 1, -1) - 5/1152 DATA(-2, 0, -2) + + - 1/432 DATA(2, -1, -2) - 5/72 DATA(2, 0, -1) - 1/216 DATA(-1, 1, -2) + + 25 + + --- DATA(2, 0, 0) + 1/432 DATA(-2, 1, -2) - 5/72 DATA(2, -1, 0) + 192 + + + 5/1152 DATA(2, 0, -2) - 5/576 DATA(1, 0, -2) - 1/432 DATA(2, 2, -1) + + - 1/432 DATA(2, -2, 1) + 5/1152 DATA(2, 2, 0) - 1/432 DATA(2, 1, -2) + + - 5/576 DATA(1, 2, 0) 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DATA(1, -2, -2) + 1/27 DATA(1, -1, -2) + + + 1/108 DATA(2, -1, -1) - 1/108 DATA(-2, 1, 1) + 1/216 DATA(1, -2, 2) + + - 1/27 DATA(-1, -1, -2) - 1/108 DATA(1, 2, -1) + 1/108 DATA(-1, 2, -1) + + - 1/108 DATA(2, 1, -1) - 1/216 DATA(2, -1, -2) + 1/27 DATA(-1, 1, -2) + + - 1/216 DATA(-2, 1, -2) + 1/864 DATA(2, 2, -1) + 1/864 DATA(2, -2, 1) + + + 1/216 DATA(2, 1, -2) - 1/27 DATA(1, 1, -2) - 1/1728 DATA(2, -2, 2) + + - 1/216 DATA(-1, 2, -2) - 1/108 DATA(2, -1, 1) + 1/1728 DATA(-2, 2, -2) + + + 1/864 DATA(-2, -2, -1) - 1/864 DATA(2, 2, 1) + 1/108 DATA(1, 2, 1) + + - 1/1728 DATA(2, 2, -2) - 1/108 DATA(-1, 2, 1) - 1/216 DATA(-2, -1, 2) + + + 1/108 DATA(2, 1, 1) + 1/216 DATA(1, 2, -2) + 1/216 DATA(2, -1, 2) + + - 1/108 DATA(-1, -2, -1) - 1/27 DATA(1, -1, 2) + 1/27 DATA(-1, -1, 2) + + - 1/216 DATA(2, 1, 2) - 1/864 DATA(2, -2, -1) + 1/27 DATA(1, 1, 2) + + - 1/27 DATA(-1, 1, 2) + 2/27 DATA(-1, -1, -1) + 1/108 DATA(1, -2, -1) + + + 1/1728 DATA(2, 2, 2) - 1/216 DATA(1, 2, 2) - 1/108 DATA(-2, -1, -1) + 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DATA(1, -2, 2) + + + 5/72 DATA(0, -1, -2) - 1/27 DATA(-1, -1, -2) - 1/216 DATA(1, 2, -1) + + 25 + + 5/576 DATA(0, 2, -1) + 5/72 DATA(-1, 0, -2) - --- DATA(0, 0, -2) + 192 + + - 1/216 DATA(-1, 2, -1) - 1/216 DATA(2, 1, -1) - 5/1152 DATA(-2, 0, -2) + + + 1/432 DATA(2, -1, -2) + 5/576 DATA(2, 0, -1) - 1/27 DATA(-1, 1, -2) + + + 1/432 DATA(-2, 1, -2) - 5/1152 DATA(2, 0, -2) + 5/72 DATA(1, 0, -2) + + + 1/3456 DATA(2, 2, -1) - 1/3456 DATA(2, -2, 1) + 1/432 DATA(2, 1, -2) + + - 1/27 DATA(1, 1, -2) + 5/72 DATA(0, 1, -2) + 1/6912 DATA(2, -2, 2) + + - 5/1152 DATA(0, 2, -2) - 5/576 DATA(2, 0, 1) + 1/432 DATA(-1, 2, -2) + + + 1/216 DATA(2, -1, 1) - 1/6912 DATA(-2, 2, -2) + 1/3456 DATA(-2, -2, -1) + + - 1/3456 DATA(2, 2, 1) + 1/216 DATA(1, 2, 1) - 1/6912 DATA(2, 2, -2) + + - 5/576 DATA(0, 2, 1) + 1/216 DATA(-1, 2, 1) - 1/432 DATA(-2, -1, 2) + + + 1/216 DATA(2, 1, 1) + 1/432 DATA(1, 2, -2) - 5/72 DATA(-1, 0, 2) + + 25 + + --- DATA(0, 0, 2) + 5/576 DATA(0, -2, -1) - 1/432 DATA(2, -1, 2) + 192 + + - 1/216 DATA(-1, -2, -1) + 1/27 DATA(1, -1, 2) - 5/72 DATA(0, -1, 2) + + + 1/27 DATA(-1, -1, 2) - 1/432 DATA(2, 1, 2) + 1/3456 DATA(2, -2, -1) + + + 1/27 DATA(1, 1, 2) - 5/72 DATA(0, 1, 2) + 1/27 DATA(-1, 1, 2) + + + 2/27 DATA(-1, -1, -1) - 1/216 DATA(1, -2, -1) + 5/1152 DATA(2, 0, 2) + + - 5/72 DATA(1, 0, 2) + 1/6912 DATA(2, 2, 2) - 1/432 DATA(1, 2, 2) + + + 5/1152 DATA(0, 2, 2) - 1/216 DATA(-2, -1, -1) - 1/432 DATA(-1, 2, 2) + + + 5/576 DATA(-2, 0, -1) - 5/36 DATA(0, -1, -1) - 1/216 DATA(-2, 1, -1) + + + 1/3456 DATA(-2, 2, -1) + 5/1152 DATA(-2, 0, 2) - 1/432 DATA(-2, 1, 2) + + - 1/3456 DATA(-2, 2, 1) + 1/216 DATA(-2, -1, 1) - 1/3456 DATA(-2, -2, 1) + + \ 2 2 3 / + + 1/216 DATA(-1, -2, 1) - 5/576 DATA(0, -2, 1)| x y z + | + / \ + + - 1/54 DATA(1, -2, 1) + 8/27 DATA(1, -1, -1) + 1/6912 DATA(-2, 2, 2) + + + 5/9 DATA(-1, 0, -1) - 8/27 DATA(-1, 1, -1) + 8/27 DATA(1, 1, -1) + + 25 + - 5/9 DATA(1, 0, -1) + 5/9 DATA(-1, 1, 0) - -- DATA(-1, 0, 0) + 24 + + - 5/9 DATA(1, -1, 0) + 5/9 DATA(-1, -1, 0) - 8/27 DATA(-1, 1, 1) + + + 5/9 DATA(-1, 0, 1) + 8/27 DATA(1, -1, 1) - 8/27 DATA(-1, -1, 1) + + 25 + + -- DATA(1, 0, 0) - 5/9 DATA(1, 1, 0) - 5/9 DATA(1, 0, 1) + 24 + + + 8/27 DATA(1, 1, 1) - 5/72 DATA(-2, 0, 1) + 1/6912 DATA(-2, -2, 2) + + - 1/864 DATA(-1, -2, 2) - 1/864 DATA(-1, -2, -2) + 1/6912 DATA(-2, -2, -2) + + - 1/432 DATA(-2, -1, -2) - 1/6912 DATA(2, -2, -2) + 1/864 DATA(1, -2, -2) + + - 1/54 DATA(1, -1, -2) - 1/27 DATA(2, -1, -1) + 1/27 DATA(-2, 1, 1) + + + 1/864 DATA(1, -2, 2) + 1/54 DATA(-1, -1, -2) - 1/54 DATA(1, 2, -1) + + - 5/144 DATA(-1, 0, -2) + 1/54 DATA(-1, 2, -1) - 1/27 DATA(2, 1, -1) + + + 5/1152 DATA(-2, 0, -2) + 1/432 DATA(2, -1, -2) + 5/72 DATA(2, 0, -1) + + 25 + + 1/54 DATA(-1, 1, -2) - --- DATA(2, 0, 0) - 1/432 DATA(-2, 1, -2) + 192 + + + 5/72 DATA(2, -1, 0) - 5/1152 DATA(2, 0, -2) + 5/144 DATA(1, 0, -2) + + + 1/432 DATA(2, 2, -1) + 1/432 DATA(2, -2, 1) - 5/1152 DATA(2, 2, 0) + + + 1/432 DATA(2, 1, -2) + 5/144 DATA(1, 2, 0) - 1/54 DATA(1, 1, -2) + + - 5/144 DATA(-1, 2, 0) + 5/72 DATA(2, 1, 0) - 1/6912 DATA(2, -2, 2) + + + 5/72 DATA(2, 0, 1) - 1/864 DATA(-1, 2, -2) - 1/27 DATA(2, -1, 1) + + + 1/6912 DATA(-2, 2, -2) - 1/432 DATA(-2, -2, -1) + 1/432 DATA(2, 2, 1) + + - 1/54 DATA(1, 2, 1) - 1/6912 DATA(2, 2, -2) + 1/54 DATA(-1, 2, 1) + + - 1/432 DATA(-2, -1, 2) - 1/27 DATA(2, 1, 1) + 1/864 DATA(1, 2, -2) + + - 5/144 DATA(-1, 0, 2) + 1/432 DATA(2, -1, 2) + 1/54 DATA(-1, -2, -1) + + - 1/54 DATA(1, -1, 2) + 1/54 DATA(-1, -1, 2) + 1/432 DATA(2, 1, 2) + + + 1/432 DATA(2, -2, -1) - 1/54 DATA(1, 1, 2) + 1/54 DATA(-1, 1, 2) + + - 8/27 DATA(-1, -1, -1) - 1/54 DATA(1, -2, -1) - 5/1152 DATA(2, 0, 2) + + + 5/144 DATA(1, 0, 2) - 1/6912 DATA(2, 2, 2) + 1/864 DATA(1, 2, 2) + + + 1/27 DATA(-2, -1, -1) - 1/864 DATA(-1, 2, 2) - 5/72 DATA(-2, 0, -1) + + + 1/27 DATA(-2, 1, -1) - 1/432 DATA(-2, 2, -1) + 5/1152 DATA(-2, 0, 2) + + - 5/144 DATA(-1, -2, 0) + 5/1152 DATA(-2, -2, 0) + 5/144 DATA(1, -2, 0) + + 25 + - 5/1152 DATA(2, -2, 0) - 5/72 DATA(-2, -1, 0) + --- DATA(-2, 0, 0) + 192 + + - 1/432 DATA(-2, 1, 2) - 1/432 DATA(-2, 2, 1) - 5/72 DATA(-2, 1, 0) + + + 1/27 DATA(-2, -1, 1) + 5/1152 DATA(-2, 2, 0) - 1/432 DATA(-2, -2, 1) + + \ 2 2 / + + 1/54 DATA(-1, -2, 1)| x y z + |- 1/54 DATA(1, -2, 1) + / \ + + 25 + + 8/27 DATA(1, -1, -1) + -- DATA(0, 0, -1) - 1/13824 DATA(-2, 2, 2) + 24 + + - 5/9 DATA(-1, 0, -1) + 8/27 DATA(-1, 1, -1) + 8/27 DATA(1, 1, -1) + + - 5/9 DATA(0, 1, -1) - 5/9 DATA(1, 0, -1) - 5/9 DATA(-1, 1, 0) + + 25 25 + + -- DATA(-1, 0, 0) - 5/9 DATA(1, -1, 0) + -- DATA(0, -1, 0) + 24 24 + + - 5/9 DATA(-1, -1, 0) + 8/27 DATA(-1, 1, 1) - 5/9 DATA(-1, 0, 1) + + + 8/27 DATA(1, -1, 1) - 5/9 DATA(0, -1, 1) + 8/27 DATA(-1, -1, 1) + + 125 25 25 + - --- DATA(0, 0, 0) + -- DATA(1, 0, 0) + -- DATA(0, 1, 0) + 64 24 24 + + 25 + - 5/9 DATA(1, 1, 0) + -- DATA(0, 0, 1) - 5/9 DATA(1, 0, 1) + 24 + + - 5/9 DATA(0, 1, 1) + 8/27 DATA(1, 1, 1) + 5/144 DATA(-2, 0, 1) + + - 1/13824 DATA(-2, -2, 2) + 1/864 DATA(-1, -2, 2) - 5/2304 DATA(0, -2, -2) + + + 1/864 DATA(-1, -2, -2) - 5/2304 DATA(0, -2, 2) + + - 1/13824 DATA(-2, -2, -2) + 1/864 DATA(-2, -1, -2) + + - 1/13824 DATA(2, -2, -2) + 1/864 DATA(1, -2, -2) - 1/54 DATA(1, -1, -2) + + - 1/54 DATA(2, -1, -1) - 1/54 DATA(-2, 1, 1) + 1/864 DATA(1, -2, 2) + + + 5/144 DATA(0, -1, -2) - 1/54 DATA(-1, -1, -2) - 1/54 DATA(1, 2, -1) + + 25 + + 5/144 DATA(0, 2, -1) + 5/144 DATA(-1, 0, -2) - --- DATA(0, 0, -2) + 384 + + - 1/54 DATA(-1, 2, -1) - 1/54 DATA(2, 1, -1) - 5/2304 DATA(-2, 0, -2) + + + 1/864 DATA(2, -1, -2) + 5/144 DATA(2, 0, -1) - 1/54 DATA(-1, 1, -2) + + 25 + - --- DATA(2, 0, 0) + 1/864 DATA(-2, 1, -2) + 5/144 DATA(2, -1, 0) + 384 + + - 5/2304 DATA(2, 0, -2) + 5/144 DATA(1, 0, -2) + 1/864 DATA(2, 2, -1) + + + 1/864 DATA(2, -2, 1) - 5/2304 DATA(2, 2, 0) + 1/864 DATA(2, 1, -2) + + 25 + + 5/144 DATA(1, 2, 0) - --- DATA(0, 2, 0) - 1/54 DATA(1, 1, -2) + 384 + + + 5/144 DATA(-1, 2, 0) + 5/144 DATA(2, 1, 0) + 5/144 DATA(0, 1, -2) + + - 1/13824 DATA(2, -2, 2) - 5/2304 DATA(0, 2, -2) + 5/144 DATA(2, 0, 1) + + + 1/864 DATA(-1, 2, -2) - 1/54 DATA(2, -1, 1) - 1/13824 DATA(-2, 2, -2) + + + 1/864 DATA(-2, -2, -1) + 1/864 DATA(2, 2, 1) - 1/54 DATA(1, 2, 1) + + - 1/13824 DATA(2, 2, -2) + 5/144 DATA(0, 2, 1) - 1/54 DATA(-1, 2, 1) + + + 1/864 DATA(-2, -1, 2) - 1/54 DATA(2, 1, 1) + 1/864 DATA(1, 2, -2) + + 25 + + 5/144 DATA(-1, 0, 2) - --- DATA(0, 0, 2) + 5/144 DATA(0, -2, -1) + 384 + + + 1/864 DATA(2, -1, 2) - 1/54 DATA(-1, -2, -1) - 1/54 DATA(1, -1, 2) + + + 5/144 DATA(0, -1, 2) - 1/54 DATA(-1, -1, 2) + 1/864 DATA(2, 1, 2) + + + 1/864 DATA(2, -2, -1) - 1/54 DATA(1, 1, 2) + 5/144 DATA(0, 1, 2) + + - 1/54 DATA(-1, 1, 2) + 8/27 DATA(-1, -1, -1) - 1/54 DATA(1, -2, -1) + + - 5/2304 DATA(2, 0, 2) + 5/144 DATA(1, 0, 2) - 1/13824 DATA(2, 2, 2) + + + 1/864 DATA(1, 2, 2) - 5/2304 DATA(0, 2, 2) - 1/54 DATA(-2, -1, -1) + + + 1/864 DATA(-1, 2, 2) + 5/144 DATA(-2, 0, -1) - 5/9 DATA(0, -1, -1) + + - 1/54 DATA(-2, 1, -1) + 1/864 DATA(-2, 2, -1) - 5/2304 DATA(-2, 0, 2) + + 25 + + 5/144 DATA(-1, -2, 0) - 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- 1/3456 y x z - 1/3456 x y z - 1/1728 z y x + + 3 2 3 3 2 + + 1/3456 z y x + 1/1728 z y x + 1/1728 y x z - 1/3456 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + + 1/3456 z y x - 1/6912 z y x - 1/13824 x y z + 1/6912 x y z + + 3 3 4 2 2 3 3 3 4 3 + + 1/1728 y x z + 1/13824 x y z - 1/1728 y x z - 1/3456 x y z + + 4 2 2 4 2 2 2 2 2 + - 1/6912 x y z + 1/13824 x y z + 1/6912 y x z + 1/6912 y x z + + 2 2 2 3 2 3 4 3 3 + + 1/6912 y x z - 1/3456 y x z - 1/3456 y x z + 1/3456 x y z + + 4 2 3 3 4 3 4 4 3 4 + + 1/6912 x y z + 1/3456 x y z - 1/6912 x y z + 1/3456 y x z + + 2 4 3 4 4 4 4 3 + - 1/6912 y x z - 1/3456 y x z + 1/6912 x y z - 1/3456 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + + 1/6912 x y z - 1/13824 x y z + 1/13824 y x z + 1/6912 y x z + + 3 3 4 2 4 4 3 4 + + 1/3456 y x z , COEFF(-1, -2, -2) = 1/864 y x z + 1/1728 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/3456 x y z - 1/3456 x y z - 1/432 x y z + 1/432 x y z + + 3 4 4 4 3 3 4 4 + + 1/1728 x y z - 1/1728 x y z + 1/216 y x z + 1/3456 x y z + + 3 2 4 3 2 3 4 2 + - 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+ 1/3456 x y z - 1/864 y x z + + 2 3 4 3 3 4 4 3 4 + - 1/3456 y x z - 1/1728 y x z , COEFF(0, -2, -2) = - 1/1152 x y z + + 4 4 4 2 4 4 4 3 2 4 + + 1/2304 x y z - 5/1152 x y z + 1/1152 x y z + 5/1152 y x z + + 4 2 2 4 4 2 2 2 2 2 3 + - 1/1152 x y z - 5/2304 x y z - 5/2304 y x z - 5/1152 y x z + + 4 4 2 2 3 3 2 2 + + 1/576 x y z - 1/1152 x y z + 5/576 y x z - 5/1152 y x z + + 4 3 3 3 2 2 + - 1/576 x y z - 1/144 z y + 5/576 z y x - 5/576 z y x + + 4 4 2 4 3 2 4 2 2 + - 1/2304 x y z + 1/144 y z + 1/1152 x y z + 1/2304 x y z + + 4 3 2 4 2 2 2 2 2 + - 1/576 x y z + 5/2304 x y z + 5/1152 y x z + 5/1152 y x z + + 2 3 2 3 4 3 3 4 2 3 + - 1/288 y z - 5/576 y x z + 1/576 x y z + 1/1152 x y z + + 4 4 3 3 2 3 3 3 4 + - 1/1152 x y z - 1/144 y z + 1/288 y z + 1/144 y z + 1/288 y z + + 3 4 4 4 3 2 2 4 4 2 + - 1/288 y z + 1/576 y z + 1/288 y z - 5/1152 y x z - 1/576 y z + + 4 2 2 4 4 4 2 2 + + 1/288 y z - 1/288 y z - 1/576 y z + 1/1152 x y z + 1/576 y z + + 4 3 2 4 3 4 2 4 2 2 4 + - 1/288 y z + 5/1152 x y z - 1/2304 x y z + 5/2304 y x z , + + 2 4 4 3 4 3 4 2 + COEFF(1, -2, -2) = - 1/864 y x z + 1/1728 x y z + 1/3456 x y z + + 4 4 4 4 2 4 3 4 + - 1/3456 x y z + 1/432 x y z + 1/432 x y z - 1/1728 x y z + + 4 4 3 3 4 4 3 2 4 + - 1/1728 x y z - 1/216 y x z - 1/3456 x y z - 1/432 y x z + + 3 2 3 4 2 3 4 + - 1/864 z y x + 1/1728 z y x + 1/1728 x y z - 1/432 y x z + + 2 2 3 2 4 4 4 4 + - 1/432 y x z + 1/432 y x z + 1/864 x y z + 1/864 x y z + + 2 2 2 3 2 2 2 3 4 + + 1/864 y x z + 1/432 y x z + 1/432 y x z - 1/864 x y z + + 4 2 3 3 3 3 2 2 3 + + 1/1728 x y z + 1/864 y x z - 1/1728 y x z - 1/216 y x z + + 3 2 2 2 3 3 4 3 3 + + 1/432 y x z - 1/1728 y x z + 1/864 x y z - 1/216 z y x + + 3 2 3 3 2 + - 1/216 z y x + 1/864 z y x + 1/216 y x z + 1/216 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + + 1/1728 z y x - 1/3456 z y x + 1/3456 x y z - 1/1728 x y z + + 3 3 4 2 2 3 3 3 4 3 + + 1/216 y x z - 1/3456 x y z - 1/864 y x z + 1/864 x y z + + 4 2 2 4 2 2 2 2 2 + - 1/864 x y z - 1/864 x y z + 1/864 y x z - 1/432 y x z + + 2 2 2 3 2 3 4 3 3 + - 1/432 y x z - 1/432 y x z + 1/216 y x z - 1/864 x y z + + 4 2 3 3 4 3 4 4 3 4 + - 1/1728 x y z + 1/1728 x y z + 1/1728 x y z + 1/432 y x z + + 2 4 3 4 4 4 4 3 + + 1/432 y x z - 1/1728 y x z - 1/1728 x y z - 1/432 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + - 1/432 x y z + 1/3456 x y z - 1/864 y x z + 1/3456 y x z + + 3 3 4 2 4 4 3 4 + + 1/1728 y x z , COEFF(2, -2, -2) = 1/6912 y x z - 1/6912 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/6912 x y z + 1/13824 x y z - 1/3456 x y z - 1/6912 x y z + + 3 4 4 4 3 3 4 4 + + 1/3456 x y z + 1/6912 x y z + 1/1728 y x z + 1/6912 x y z + + 3 2 4 3 2 3 4 2 + + 1/6912 y x z + 1/1728 z y x - 1/3456 z y x - 1/6912 x y z + + 3 4 2 2 3 2 4 4 + + 1/3456 y x z + 1/3456 y x z - 1/3456 y x z - 1/13824 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/6912 x y z - 1/13824 y x z - 1/3456 y x z - 1/6912 y x z + + 4 4 2 3 3 3 3 2 + + 1/3456 x y z - 1/6912 x y z - 1/1728 y x z + 1/3456 y x z + + 2 3 3 2 2 2 3 3 4 3 + + 1/3456 y x z - 1/6912 y x z + 1/3456 y x z - 1/3456 x y z + + 3 3 2 3 3 + + 1/1728 z y x + 1/3456 z y x - 1/1728 z y x - 1/1728 y x z + + 2 2 3 2 2 3 4 4 2 + - 1/3456 z y x - 1/3456 z y x + 1/6912 z y x - 1/13824 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + + 1/6912 x y z - 1/1728 y x z + 1/13824 x y z + 1/1728 y x z + + 4 3 4 2 2 4 2 2 2 + - 1/3456 x y z + 1/6912 x y z + 1/13824 x y z - 1/6912 y x z + + 2 2 2 2 2 3 2 3 + + 1/6912 y x z + 1/6912 y x z + 1/3456 y x z - 1/3456 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + + 1/3456 x y z + 1/6912 x y z - 1/3456 x y z - 1/6912 x y z + + 4 2 4 3 4 4 4 + - 1/3456 y x z - 1/6912 y x z + 1/3456 y x z + 1/6912 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + + 1/3456 x y z + 1/6912 x y z - 1/13824 x y z + 1/13824 y x z + + 2 3 4 3 3 4 2 4 + - 1/6912 y x z - 1/3456 y x z , COEFF(-2, -1, -2) = 1/432 y x z + + 4 3 4 3 4 2 4 4 4 4 + + 1/3456 x y z - 1/1728 x y z - 1/3456 x y z - 1/864 x y z + + 2 4 3 4 4 4 3 + + 1/1728 x y z + 1/864 x y z - 1/1728 x y z + 1/216 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/1728 x y z - 1/3456 y x z + 1/216 z y x - 1/432 z y x + + 4 2 3 4 2 2 3 + + 1/864 x y z + 1/1728 y x z + 1/216 y x z - 1/216 y x z + + 2 4 4 4 4 2 2 2 3 2 + + 1/3456 x y z - 1/1728 x y z + 1/864 y x z - 1/1728 y x z + + 2 2 3 4 4 2 3 3 + + 1/432 y x z - 1/432 x y z + 1/432 x y z - 1/216 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + + 1/1728 y x z - 1/432 y x z + 1/3456 y x z + 1/216 y x z + + 4 3 3 3 2 3 3 + + 1/1728 x y z + 1/864 z y x - 1/1728 z y x - 1/864 z y x + + 2 2 3 2 2 3 + - 1/216 y x z + 1/432 z y x - 1/216 z y x + 1/432 z y x + + 4 4 2 4 3 2 3 3 4 2 2 + + 1/3456 x y z - 1/3456 x y z - 1/864 y x z - 1/864 x y z + + 3 3 3 4 3 4 2 2 4 2 + + 1/864 y x z + 1/432 x y z + 1/1728 x y z - 1/3456 x y z + + 2 2 2 2 2 2 2 + - 1/432 y x z - 1/432 y x z - 1/864 y x z + 1/432 y x z + + 3 2 3 4 3 3 4 2 3 3 4 3 + + 1/1728 y x z - 1/1728 x y z - 1/432 x y z - 1/864 x y z + + 4 4 3 4 2 4 3 4 + + 1/1728 x y z - 1/432 y x z + 1/864 y x z + 1/432 y x z + + 4 4 4 3 2 4 3 4 2 4 + - 1/864 x y z + 1/864 x y z - 1/1728 x y z + 1/864 x y z + + 2 2 4 2 3 4 3 3 4 + - 1/864 y x z - 1/432 y x z - 1/1728 y x z , COEFF(-1, -1, -2) = + + 2 4 4 3 4 3 4 2 4 4 4 + - 1/54 y x z - 1/864 x y z + 1/864 x y z + 1/864 x y z + + 4 2 4 3 4 4 4 + + 1/108 x y z - 1/108 x y z - 1/432 x y z + 1/432 x y z + + 3 3 4 4 3 2 4 3 + - 1/27 y x z - 1/864 x y z + 1/216 y x z - 1/108 z y x + + 2 3 4 2 3 4 2 + + 1/216 z y x - 1/216 x y z - 1/216 y x z - 1/27 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/27 y x z - 1/216 x y z + 1/216 x y z - 1/54 y x z + + 3 2 2 2 3 4 4 2 + + 1/216 y x z - 1/27 y x z + 1/108 x y z - 1/108 x y z + + 3 3 3 3 2 2 3 3 2 2 + + 1/108 y x z - 1/864 y x z + 1/27 y x z - 1/216 y x z + + 2 3 3 4 3 3 3 2 + - 1/108 y x z - 1/432 x y z - 1/108 z y x + 1/108 z y x + + 3 3 2 2 3 + + 1/432 z y x + 1/27 y x z - 1/27 z y x + 1/108 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + - 1/216 z y x - 1/864 x y z + 1/864 x y z + 1/108 y x z + + 4 2 2 3 3 3 4 3 4 2 + + 1/216 x y z - 1/432 y x z - 1/108 x y z - 1/216 x y z + + 2 4 2 2 2 2 2 2 2 + + 1/216 x y z + 1/54 y x z + 1/27 y x z + 1/54 y x z + + 2 3 2 3 4 3 3 4 2 3 + - 1/54 y x z - 1/108 y x z + 1/432 x y z + 1/108 x y z + + 3 4 3 4 4 3 4 2 4 + + 1/432 x y z - 1/432 x y z + 1/54 y x z - 1/54 y x z + + 3 4 4 4 4 3 2 4 3 + - 1/216 y x z + 1/216 x y z - 1/108 x y z + 1/108 x y z + + 4 2 4 2 2 4 2 3 4 3 3 4 + - 1/216 x y z + 1/54 y x z + 1/216 y x z + 1/864 y x z , + + 4 3 4 4 4 4 2 4 + COEFF(0, -1, -2) = 1/576 x y z - 1/576 x y z + 5/288 x y z + + 4 4 3 2 4 4 2 2 4 4 + - 1/288 x y z - 5/576 y x z + 1/144 x y z + 5/576 x y z + + 2 2 2 2 2 3 4 4 2 + + 5/144 y x z + 5/72 y x z - 1/72 x y z + 1/72 x y z + + 2 3 3 2 2 4 3 3 + - 5/72 y x z + 5/576 y x z + 1/288 x y z + 1/72 z y + + 3 2 2 4 4 2 4 3 2 + - 5/288 z y x + 5/72 z y x + 1/576 x y z - 1/18 y z - 1/576 x y z + + 4 2 2 4 3 2 4 2 2 2 + - 1/144 x y z + 1/72 x y z - 5/576 x y z - 5/72 y x z + + 2 2 2 3 2 3 4 3 3 + - 5/144 y x z + 1/18 y z + 5/288 y x z - 1/288 x y z + + 4 2 3 4 4 3 3 2 3 3 3 + - 1/72 x y z + 1/288 x y z + 1/18 y z - 1/18 y z - 1/72 y z + + 4 3 4 4 4 3 2 2 4 + - 1/36 y z + 1/144 y z - 1/144 y z - 1/144 y z + 5/144 y x z + + 4 2 4 2 2 4 4 4 + + 1/144 y z - 1/72 y z + 1/36 y z + 1/36 y z - 1/144 x y z + + 2 2 4 3 2 4 3 4 2 4 + - 1/36 y z + 1/72 y z - 5/288 x y z + 1/144 x y z + + 2 2 4 2 4 4 3 4 + - 5/144 y x z , COEFF(1, -1, -2) = 1/54 y x z - 1/864 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/864 x y z + 1/864 x y z - 1/108 x y z - 1/108 x y z + + 3 4 4 4 3 3 4 4 + + 1/432 x y z + 1/432 x y z + 1/27 y x z + 1/864 x y z + + 3 2 4 3 2 3 4 2 + + 1/216 y x z + 1/108 z y x - 1/216 z y x - 1/216 x y z + + 3 4 2 2 3 2 4 4 + + 1/216 y x z + 1/27 y x z - 1/27 y x z - 1/216 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/216 x y z - 1/54 y x z - 1/216 y x z - 1/27 y x z + + 4 4 2 3 3 3 3 2 + + 1/108 x y z - 1/108 x y z - 1/108 y x z + 1/864 y x z + + 2 3 3 2 2 2 3 3 4 3 + + 1/27 y x z - 1/216 y x z + 1/108 y x z - 1/432 x y z + + 3 3 2 3 3 2 + + 1/108 z y x + 1/108 z y x - 1/432 z y x - 1/27 y x z - 1/27 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + - 1/108 z y x + 1/216 z y x - 1/864 x y z + 1/864 x y z + + 3 3 4 2 2 3 3 3 4 3 + - 1/108 y x z + 1/216 x y z + 1/432 y x z - 1/108 x y z + + 4 2 2 4 2 2 2 2 2 + + 1/216 x y z + 1/216 x y z - 1/54 y x z + 1/27 y x z + + 2 2 2 3 2 3 4 3 3 + + 1/54 y x z + 1/54 y x z - 1/108 y x z + 1/432 x y z + + 4 2 3 3 4 3 4 4 3 4 + + 1/108 x y z - 1/432 x y z - 1/432 x y z - 1/54 y x z + + 2 4 3 4 4 4 4 3 + - 1/54 y x z + 1/216 y x z + 1/216 x y z + 1/108 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + + 1/108 x y z - 1/216 x y z + 1/54 y x z - 1/216 y x z + + 3 3 4 2 4 4 3 4 + - 1/864 y x z , COEFF(2, -1, -2) = - 1/432 y x z + 1/3456 x y z + + 3 4 2 4 4 4 4 2 4 + + 1/1728 x y z - 1/3456 x y z + 1/864 x y z + 1/1728 x y z + + 3 4 4 4 3 3 4 4 + - 1/864 x y z - 1/1728 x y z - 1/216 y x z - 1/1728 x y z + + 3 2 4 3 2 3 4 2 + - 1/3456 y x z - 1/216 z y x + 1/432 z y x + 1/864 x y z + + 3 4 2 2 3 2 4 4 + - 1/1728 y x z - 1/216 y x z + 1/216 y x z + 1/3456 x y z + + 4 4 2 2 2 3 2 2 2 3 + + 1/1728 x y z + 1/864 y x z + 1/1728 y x z + 1/432 y x z + + 4 4 2 3 3 3 3 2 + - 1/432 x y z + 1/432 x y z + 1/216 y x z - 1/1728 y x z + + 2 3 3 2 2 2 3 3 4 3 + - 1/432 y x z + 1/3456 y x z - 1/216 y x z + 1/1728 x y z + + 3 3 2 3 3 + - 1/864 z y x - 1/1728 z y x + 1/864 z y x + 1/216 y x z + + 2 2 3 2 2 3 4 4 2 + + 1/432 z y x + 1/216 z y x - 1/432 z y x + 1/3456 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + - 1/3456 x y z + 1/864 y x z - 1/864 x y z - 1/864 y x z + + 4 3 4 2 2 4 2 2 2 + + 1/432 x y z - 1/1728 x y z - 1/3456 x y z + 1/432 y x z + + 2 2 2 2 2 3 2 3 + - 1/432 y x z - 1/864 y x z - 1/432 y x z + 1/1728 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + - 1/1728 x y z - 1/432 x y z + 1/864 x y z + 1/1728 x y z + + 4 2 4 3 4 4 4 + + 1/432 y x z + 1/864 y x z - 1/432 y x z - 1/864 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + - 1/864 x y z - 1/1728 x y z + 1/864 x y z - 1/864 y x z + + 2 3 4 3 3 4 2 4 + + 1/432 y x z + 1/1728 y x z , COEFF(-2, 0, -2) = - 5/1152 y x z + + 3 4 2 4 4 4 4 2 4 + + 1/1152 x y z + 1/2304 x y z + 1/576 x y z - 1/1152 x y z + + 3 4 4 4 3 4 4 2 + - 1/576 x y z + 1/1152 x y z - 1/1152 x y z - 5/576 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 5/576 y x z - 1/2304 x y z + 1/1152 x y z - 5/2304 y x z + + 2 2 3 4 2 3 2 3 3 + - 5/1152 y x z - 5/1152 x y z - 1/144 z x - 5/576 y x z + + 2 3 2 2 3 4 4 2 4 2 2 + + 5/576 z y x - 5/1152 z y x - 1/2304 x y z + 5/2304 x y z + + 4 2 2 4 2 2 2 2 2 + - 1/1152 x y z + 1/2304 x y z + 5/1152 y x z + 5/1152 y x z + + 4 2 3 2 3 4 3 + + 1/144 x z + 5/1152 x y z - 1/288 x z + 1/576 x y z + + 4 4 3 3 3 2 3 4 3 2 4 + - 1/1152 x y z + 1/144 x z + 1/288 x z - 1/288 x z - 1/576 x z + + 3 4 4 4 2 3 4 + - 1/144 x z + 1/288 x z + 1/288 x z - 1/576 x z - 1/288 x z + + 2 2 2 4 4 3 2 4 3 + + 1/576 x z - 1/288 x z + 1/576 x z + 1/288 x z - 1/576 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + + 1/1152 x y z - 5/2304 x y z + 5/2304 y x z + 5/1152 y x z , + + 2 4 3 4 2 4 4 4 + COEFF(-1, 0, -2) = 5/144 y x z - 1/576 x y z - 1/576 x y z + + 4 2 4 3 4 4 4 + - 1/72 x y z + 1/72 x y z + 1/288 x y z - 1/288 x y z + + 3 4 4 2 2 3 2 4 4 + + 1/576 x y z + 5/72 y x z - 5/72 y x z + 1/144 x y z + + 4 4 2 2 2 2 2 3 4 2 + - 1/144 x y z + 5/144 y x z + 5/72 y x z + 5/288 x y z + + 3 2 3 3 2 3 2 2 3 + + 1/72 z x + 5/288 y x z - 5/288 z y x + 5/576 z y x + + 4 4 2 4 2 2 4 2 2 4 2 + + 1/576 x y z - 5/576 x y z + 1/144 x y z - 1/144 x y z + + 2 2 2 2 4 2 3 2 + - 5/144 y x z - 5/72 y x z - 1/18 x z - 5/288 x y z + 1/18 x z + + 3 4 3 4 4 3 3 3 2 3 4 3 + - 1/288 x y z + 1/288 x y z - 1/72 x z - 1/18 x z + 1/72 x z + + 2 4 3 4 4 4 2 + + 1/36 x z + 1/18 x z - 1/36 x z - 1/72 x z + 1/144 x z + + 3 4 2 2 2 4 4 3 2 + + 1/144 x z - 1/36 x z + 1/36 x z - 1/144 x z - 1/144 x z + + 4 3 2 4 3 4 2 4 2 2 4 + + 1/72 x y z - 1/72 x y z + 5/576 x y z - 5/144 y x z + + 2 3 4 4 4 4 2 4 + - 5/576 y x z , COEFF(0, 0, -2) = 1/384 x y z - 5/192 x y z + + 4 4 2 4 4 25 2 2 2 25 2 2 3 + + 1/192 x y z + 1/12 z - 5/384 x y z - --- y x z - --- y x z + 384 192 + + 4 2 4 3 2 4 4 2 + - 5/192 x y z + 1/24 z - 1/12 z - 1/24 z - 1/384 x y z + + 4 2 2 2 4 2 25 2 2 2 + + 5/384 x y z + 5/384 x y z + --- y x z - 5/48 y z + 192 + + 4 2 3 2 4 4 3 2 3 2 3 + + 5/192 x y z - 5/48 x z - 1/192 x y z + 5/48 y z + 5/48 x z + + 4 3 4 4 2 4 4 2 4 + - 1/48 x z + 1/96 y z - 5/96 x z - 1/96 y z + 1/48 y z + + 4 4 2 2 2 4 4 2 4 + + 1/48 x z - 1/96 x z + 5/96 x z + 1/96 x z - 5/96 y z + + 2 2 4 3 2 4 3 4 2 4 25 2 2 4 + + 5/96 y z - 1/48 y z + 5/192 x y z - 5/384 x y z + --- y x z + 384 + + 2 4 3 4 2 4 4 4 + , COEFF(1, 0, -2) = - 5/144 y x z + 1/576 x y z - 1/576 x y z + + 4 2 4 3 4 4 4 + + 1/72 x y z + 1/72 x y z - 1/288 x y z - 1/288 x y z + + 3 4 4 2 2 3 2 4 4 + - 1/576 x y z - 5/72 y x z + 5/72 y x z + 1/144 x y z + + 4 4 2 2 2 2 2 3 4 2 + + 1/144 x y z + 5/144 y x z + 5/72 y x z + 5/288 x y z + + 3 2 3 3 2 3 2 2 3 + - 1/72 z x - 5/288 y x z + 5/288 z y x - 5/576 z y x + + 4 4 2 4 2 2 4 2 2 4 2 + + 1/576 x y z - 5/576 x y z - 1/144 x y z - 1/144 x y z + + 2 2 2 2 4 2 3 2 + + 5/144 y x z - 5/72 y x z + 1/18 x z - 5/288 x y z + 1/18 x z + + 3 4 3 4 4 3 3 3 2 3 4 3 + + 1/288 x y z + 1/288 x y z + 1/72 x z - 1/18 x z + 1/72 x z + + 2 4 3 4 4 4 2 + + 1/36 x z - 1/18 x z + 1/36 x z - 1/72 x z + 1/144 x z + + 3 4 2 2 2 4 4 3 2 + - 1/144 x z - 1/36 x z - 1/36 x z - 1/144 x z + 1/144 x z + + 4 3 2 4 3 4 2 4 2 2 4 + - 1/72 x y z - 1/72 x y z + 5/576 x y z - 5/144 y x z + + 2 3 4 2 4 3 4 2 + + 5/576 y x z , COEFF(2, 0, -2) = 5/1152 y x z - 1/1152 x y z + + 4 4 4 4 2 4 3 4 + + 1/2304 x y z - 1/576 x y z - 1/1152 x y z + 1/576 x y z + + 4 4 3 4 4 2 2 3 + + 1/1152 x y z + 1/1152 x y z + 5/576 y x z - 5/576 y x z + + 2 4 4 4 4 2 2 2 2 2 3 + - 1/2304 x y z - 1/1152 x y z - 5/2304 y x z - 5/1152 y x z + + 4 2 3 2 3 3 2 3 + - 5/1152 x y z + 1/144 z x + 5/576 y x z - 5/576 z y x + + 2 2 3 4 4 2 4 2 2 4 2 + + 5/1152 z y x - 1/2304 x y z + 5/2304 x y z + 1/1152 x y z + + 2 4 2 2 2 2 2 + + 1/2304 x y z - 5/1152 y x z + 5/1152 y x z - 1/144 x z + + 4 2 3 2 3 4 3 4 4 3 + + 5/1152 x y z - 1/288 x z - 1/576 x y z - 1/1152 x y z + + 3 3 2 3 4 3 2 4 3 + - 1/144 x z + 1/288 x z - 1/288 x z - 1/576 x z + 1/144 x z + + 4 4 4 2 3 4 2 2 + - 1/288 x z + 1/288 x z - 1/576 x z + 1/288 x z + 1/576 x z + + 2 4 4 3 2 4 3 2 4 3 + + 1/288 x z + 1/576 x z - 1/288 x z + 1/576 x y z + 1/1152 x y z + + 4 2 4 2 2 4 2 3 4 + - 5/2304 x y z + 5/2304 y x z - 5/1152 y x z , COEFF(-2, 1, -2) = + + 2 4 4 3 4 3 4 2 4 4 4 + 1/432 y x z - 1/3456 x y z - 1/1728 x y z - 1/3456 x y z + + 4 2 4 3 4 4 4 + - 1/864 x y z + 1/1728 x y z + 1/864 x y z - 1/1728 x y z + + 3 3 4 4 3 2 4 3 + - 1/216 y x z + 1/1728 x y z + 1/3456 y x z - 1/216 z y x + + 2 3 4 2 3 4 2 + + 1/432 z y x - 1/864 x y z - 1/1728 y x z + 1/216 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/216 y x z + 1/3456 x y z - 1/1728 x y z + 1/864 y x z + + 3 2 2 2 3 4 4 2 + + 1/1728 y x z + 1/432 y x z + 1/432 x y z + 1/432 x y z + + 3 3 3 3 2 2 3 3 2 2 + + 1/216 y x z - 1/1728 y x z + 1/432 y x z - 1/3456 y x z + + 2 3 3 4 3 3 3 2 + + 1/216 y x z - 1/1728 x y z - 1/864 z y x + 1/1728 z y x + + 3 3 2 2 3 + + 1/864 z y x + 1/216 y x z - 1/432 z y x - 1/216 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + + 1/432 z y x + 1/3456 x y z + 1/3456 x y z + 1/864 y x z + + 4 2 2 3 3 3 4 3 4 2 + - 1/864 x y z - 1/864 y x z - 1/432 x y z + 1/1728 x y z + + 2 4 2 2 2 2 2 2 2 + - 1/3456 x y z - 1/432 y x z - 1/432 y x z + 1/864 y x z + + 2 3 2 3 4 3 3 4 2 3 + - 1/432 y x z - 1/1728 y x z + 1/1728 x y z - 1/432 x y z + + 3 4 3 4 4 3 4 2 4 + - 1/864 x y z + 1/1728 x y z + 1/432 y x z - 1/864 y x z + + 3 4 4 4 4 3 2 4 3 + - 1/432 y x z + 1/864 x y z + 1/864 x y z - 1/1728 x y z + + 4 2 4 2 2 4 2 3 4 3 3 4 + + 1/864 x y z - 1/864 y x z - 1/432 y x z + 1/1728 y x z , + + 2 4 4 3 4 3 4 2 + COEFF(-1, 1, -2) = - 1/54 y x z + 1/864 x y z + 1/864 x y z + + 4 4 4 4 2 4 3 4 + + 1/864 x y z + 1/108 x y z - 1/108 x y z - 1/432 x y z + + 4 4 3 3 4 4 3 2 4 + + 1/432 x y z + 1/27 y x z - 1/864 x y z - 1/216 y x z + + 3 2 3 4 2 3 4 + + 1/108 z y x - 1/216 z y x + 1/216 x y z + 1/216 y x z + + 2 2 3 2 4 4 4 4 + - 1/27 y x z + 1/27 y x z - 1/216 x y z + 1/216 x y z + + 2 2 2 3 2 2 2 3 4 + - 1/54 y x z - 1/216 y x z - 1/27 y x z - 1/108 x y z + + 4 2 3 3 3 3 2 2 3 + - 1/108 x y z - 1/108 y x z + 1/864 y x z - 1/27 y x z + + 3 2 2 2 3 3 4 3 3 + + 1/216 y x z - 1/108 y x z + 1/432 x y z + 1/108 z y x + + 3 2 3 3 2 2 3 + - 1/108 z y x - 1/432 z y x - 1/27 y x z + 1/27 z y x + 1/108 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + - 1/216 z y x - 1/864 x y z - 1/864 x y z - 1/108 y x z + + 4 2 2 3 3 3 4 3 4 2 + + 1/216 x y z + 1/432 y x z + 1/108 x y z - 1/216 x y z + + 2 4 2 2 2 2 2 2 2 + + 1/216 x y z + 1/54 y x z + 1/27 y x z - 1/54 y x z + + 2 3 2 3 4 3 3 4 2 3 + + 1/54 y x z + 1/108 y x z - 1/432 x y z + 1/108 x y z + + 3 4 3 4 4 3 4 2 4 + + 1/432 x y z - 1/432 x y z - 1/54 y x z + 1/54 y x z + + 3 4 4 4 4 3 2 4 3 + + 1/216 y x z - 1/216 x y z - 1/108 x y z + 1/108 x y z + + 4 2 4 2 2 4 2 3 4 3 3 4 + - 1/216 x y z + 1/54 y x z + 1/216 y x z - 1/864 y x z , + + 4 3 4 4 4 4 2 4 + COEFF(0, 1, -2) = - 1/576 x y z - 1/576 x y z + 5/288 x y z + + 4 4 3 2 4 4 2 2 4 4 + - 1/288 x y z + 5/576 y x z - 1/144 x y z + 5/576 x y z + + 2 2 2 2 2 3 4 4 2 + + 5/144 y x z + 5/72 y x z + 1/72 x y z + 1/72 x y z + + 2 3 3 2 2 4 3 3 + + 5/72 y x z - 5/576 y x z - 1/288 x y z - 1/72 z y + + 3 2 2 4 4 2 4 3 2 + + 5/288 z y x - 5/72 z y x + 1/576 x y z + 1/18 y z + 1/576 x y z + + 4 2 2 4 3 2 4 2 2 2 + - 1/144 x y z - 1/72 x y z - 5/576 x y z - 5/72 y x z + + 2 2 2 3 2 3 4 3 3 + + 5/144 y x z + 1/18 y z - 5/288 y x z + 1/288 x y z + + 4 2 3 4 4 3 3 2 3 3 3 + - 1/72 x y z + 1/288 x y z - 1/18 y z - 1/18 y z + 1/72 y z + + 4 3 4 4 4 3 2 2 4 + + 1/36 y z - 1/144 y z - 1/144 y z + 1/144 y z - 5/144 y x z + + 4 2 4 2 2 4 4 4 + + 1/144 y z - 1/72 y z - 1/36 y z + 1/36 y z + 1/144 x y z + + 2 2 4 3 2 4 3 4 2 4 + - 1/36 y z + 1/72 y z - 5/288 x y z + 1/144 x y z + + 2 2 4 2 4 4 3 4 + - 5/144 y x z , COEFF(1, 1, -2) = 1/54 y x z + 1/864 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/864 x y z + 1/864 x y z - 1/108 x y z - 1/108 x y z + + 3 4 4 4 3 3 4 4 + + 1/432 x y z + 1/432 x y z - 1/27 y x z + 1/864 x y z + + 3 2 4 3 2 3 4 2 + - 1/216 y x z - 1/108 z y x + 1/216 z y x + 1/216 x y z + + 3 4 2 2 3 2 4 4 + - 1/216 y x z + 1/27 y x z - 1/27 y x z - 1/216 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/216 x y z - 1/54 y x z + 1/216 y x z - 1/27 y x z + + 4 4 2 3 3 3 3 2 + - 1/108 x y z - 1/108 x y z + 1/108 y x z - 1/864 y x z + + 2 3 3 2 2 2 3 3 4 3 + - 1/27 y x z + 1/216 y x z + 1/108 y x z + 1/432 x y z + + 3 3 2 3 3 2 + - 1/108 z y x - 1/108 z y x + 1/432 z y x + 1/27 y x z + 1/27 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + - 1/108 z y x + 1/216 z y x - 1/864 x y z - 1/864 x y z + + 3 3 4 2 2 3 3 3 4 3 + + 1/108 y x z + 1/216 x y z - 1/432 y x z + 1/108 x y z + + 4 2 2 4 2 2 2 2 2 + + 1/216 x y z + 1/216 x y z - 1/54 y x z + 1/27 y x z + + 2 2 2 3 2 3 4 3 3 + - 1/54 y x z - 1/54 y x z + 1/108 y x z - 1/432 x y z + + 4 2 3 3 4 3 4 4 3 4 + + 1/108 x y z - 1/432 x y z - 1/432 x y z + 1/54 y x z + + 2 4 3 4 4 4 4 3 + + 1/54 y x z - 1/216 y x z - 1/216 x y z + 1/108 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + + 1/108 x y z - 1/216 x y z + 1/54 y x z - 1/216 y x z + + 3 3 4 2 4 4 3 4 + + 1/864 y x z , COEFF(2, 1, -2) = - 1/432 y x z - 1/3456 x y z + + 3 4 2 4 4 4 4 2 4 + + 1/1728 x y z - 1/3456 x y z + 1/864 x y z + 1/1728 x y z + + 3 4 4 4 3 3 4 4 + - 1/864 x y z - 1/1728 x y z + 1/216 y x z - 1/1728 x y z + + 3 2 4 3 2 3 4 2 + + 1/3456 y x z + 1/216 z y x - 1/432 z y x - 1/864 x y z + + 3 4 2 2 3 2 4 4 + + 1/1728 y x z - 1/216 y x z + 1/216 y x z + 1/3456 x y z + + 4 4 2 2 2 3 2 2 2 3 + + 1/1728 x y z + 1/864 y x z - 1/1728 y x z + 1/432 y x z + + 4 4 2 3 3 3 3 2 + + 1/432 x y z + 1/432 x y z - 1/216 y x z + 1/1728 y x z + + 2 3 3 2 2 2 3 3 4 3 + + 1/432 y x z - 1/3456 y x z - 1/216 y x z - 1/1728 x y z + + 3 3 2 3 3 + + 1/864 z y x + 1/1728 z y x - 1/864 z y x - 1/216 y x z + + 2 2 3 2 2 3 4 4 2 + - 1/432 z y x + 1/216 z y x - 1/432 z y x + 1/3456 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + + 1/3456 x y z - 1/864 y x z - 1/864 x y z + 1/864 y x z + + 4 3 4 2 2 4 2 2 2 + - 1/432 x y z - 1/1728 x y z - 1/3456 x y z + 1/432 y x z + + 2 2 2 2 2 3 2 3 + - 1/432 y x z + 1/864 y x z + 1/432 y x z - 1/1728 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + + 1/1728 x y z - 1/432 x y z + 1/864 x y z + 1/1728 x y z + + 4 2 4 3 4 4 4 + - 1/432 y x z - 1/864 y x z + 1/432 y x z + 1/864 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + - 1/864 x y z - 1/1728 x y z + 1/864 x y z - 1/864 y x z + + 2 3 4 3 3 4 2 4 + + 1/432 y x z - 1/1728 y x z , COEFF(-2, 2, -2) = - 1/6912 y x z + + 4 3 4 3 4 2 4 4 4 4 + + 1/6912 x y z + 1/6912 x y z + 1/13824 x y z + 1/3456 x y z + + 2 4 3 4 4 4 3 + - 1/6912 x y z - 1/3456 x y z + 1/6912 x y z + 1/1728 y x z + + 3 4 4 3 2 4 3 2 3 + - 1/6912 x y z - 1/6912 y x z + 1/1728 z y x - 1/3456 z y x + + 4 2 3 4 2 2 3 + + 1/6912 x y z + 1/3456 y x z - 1/3456 y x z + 1/3456 y x z + + 2 4 4 4 4 2 2 2 3 2 + - 1/13824 x y z + 1/6912 x y z - 1/13824 y x z - 1/3456 y x z + + 2 2 3 4 4 2 3 3 + - 1/6912 y x z - 1/3456 x y z - 1/6912 x y z - 1/1728 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + + 1/3456 y x z - 1/3456 y x z + 1/6912 y x z - 1/3456 y x z + + 4 3 3 3 2 3 3 + + 1/3456 x y z + 1/1728 z y x - 1/3456 z y x - 1/1728 z y x + + 2 2 3 2 2 3 + - 1/1728 y x z + 1/3456 z y x + 1/3456 z y x - 1/6912 z y x + + 4 4 2 4 3 2 3 3 4 2 2 + - 1/13824 x y z - 1/6912 x y z - 1/1728 y x z + 1/13824 x y z + + 3 3 3 4 3 4 2 2 4 2 + + 1/1728 y x z + 1/3456 x y z - 1/6912 x y z + 1/13824 x y z + + 2 2 2 2 2 2 2 + + 1/6912 y x z + 1/6912 y x z - 1/6912 y x z + 1/3456 y x z + + 3 2 3 4 3 3 4 2 3 3 4 3 + + 1/3456 y x z - 1/3456 x y z + 1/6912 x y z + 1/3456 x y z + + 4 4 3 4 2 4 3 4 + - 1/6912 x y z - 1/3456 y x z + 1/6912 y x z + 1/3456 y x z + + 4 4 4 3 2 4 3 4 2 4 + - 1/6912 x y z - 1/3456 x y z + 1/6912 x y z - 1/13824 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/13824 y x z + 1/6912 y x z - 1/3456 y x z , COEFF(-1, 2, -2) + + 2 4 4 3 4 3 4 2 4 4 4 + = 1/864 y x z - 1/1728 x y z - 1/3456 x y z - 1/3456 x y z + + 4 2 4 3 4 4 4 + - 1/432 x y z + 1/432 x y z + 1/1728 x y z - 1/1728 x y z + + 3 3 4 4 3 2 4 3 + - 1/216 y x z + 1/3456 x y z + 1/432 y x z - 1/864 z y x + + 2 3 4 2 3 4 2 + + 1/1728 z y x - 1/1728 x y z - 1/432 y x z + 1/432 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/432 y x z + 1/864 x y z - 1/864 x y z + 1/864 y x z + + 3 2 2 2 3 4 4 2 + + 1/432 y x z + 1/432 y x z + 1/864 x y z + 1/1728 x y z + + 3 3 3 3 2 2 3 3 2 2 + + 1/864 y x z - 1/1728 y x z + 1/216 y x z - 1/432 y x z + + 2 3 3 4 3 3 3 2 + + 1/1728 y x z - 1/864 x y z - 1/216 z y x + 1/216 z y x + + 3 3 2 2 3 + + 1/864 z y x + 1/216 y x z - 1/216 z y x - 1/1728 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + + 1/3456 z y x + 1/3456 x y z + 1/1728 x y z + 1/216 y x z + + 4 2 2 3 3 3 4 3 4 2 + - 1/3456 x y z - 1/864 y x z - 1/864 x y z + 1/864 x y z + + 2 4 2 2 2 2 2 2 2 + - 1/864 x y z - 1/864 y x z - 1/432 y x z + 1/432 y x z + + 2 3 2 3 4 3 3 4 2 3 + - 1/432 y x z - 1/216 y x z + 1/864 x y z - 1/1728 x y z + + 3 4 3 4 4 3 4 2 4 + - 1/1728 x y z + 1/1728 x y z + 1/432 y x z - 1/432 y x z + + 3 4 4 4 4 3 2 4 3 + - 1/1728 y x z + 1/1728 x y z + 1/432 x y z - 1/432 x y z + + 4 2 4 2 2 4 2 3 4 3 3 4 + + 1/3456 x y z - 1/864 y x z - 1/3456 y x z + 1/1728 y x z , + + 4 3 4 4 4 4 2 4 + COEFF(0, 2, -2) = 1/1152 x y z + 1/2304 x y z - 5/1152 x y z + + 4 4 3 2 4 4 2 2 4 4 + + 1/1152 x y z - 5/1152 y x z + 1/1152 x y z - 5/2304 x y z + + 2 2 2 2 2 3 4 4 2 + - 5/2304 y x z - 5/1152 y x z - 1/576 x y z - 1/1152 x y z + + 2 3 3 2 2 4 3 3 + - 5/576 y x z + 5/1152 y x z + 1/576 x y z + 1/144 z y + + 3 2 2 4 4 2 + - 5/576 z y x + 5/576 z y x - 1/2304 x y z - 1/144 y z + + 4 3 2 4 2 2 4 3 2 4 2 + - 1/1152 x y z + 1/2304 x y z + 1/576 x y z + 5/2304 x y z + + 2 2 2 2 2 3 2 3 + + 5/1152 y x z - 5/1152 y x z - 1/288 y z + 5/576 y x z + + 4 3 3 4 2 3 4 4 3 3 + - 1/576 x y z + 1/1152 x y z - 1/1152 x y z + 1/144 y z + + 2 3 3 3 4 3 4 4 4 + + 1/288 y z - 1/144 y z - 1/288 y z + 1/288 y z + 1/576 y z + + 3 2 2 4 4 2 4 2 + - 1/288 y z + 5/1152 y x z - 1/576 y z + 1/288 y z + 1/288 y z + + 2 4 4 4 2 2 4 3 + - 1/576 y z - 1/1152 x y z + 1/576 y z - 1/288 y z + + 2 4 3 4 2 4 2 2 4 + + 5/1152 x y z - 1/2304 x y z + 5/2304 y x z , COEFF(1, 2, -2) = + + 2 4 4 3 4 3 4 2 4 4 4 + - 1/864 y x z - 1/1728 x y z + 1/3456 x y z - 1/3456 x y z + + 4 2 4 3 4 4 4 + + 1/432 x y z + 1/432 x y z - 1/1728 x y z - 1/1728 x y z + + 3 3 4 4 3 2 4 3 + + 1/216 y x z - 1/3456 x y z + 1/432 y x z + 1/864 z y x + + 2 3 4 2 3 4 2 + - 1/1728 z y x - 1/1728 x y z + 1/432 y x z - 1/432 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/432 y x z + 1/864 x y z + 1/864 x y z + 1/864 y x z + + 3 2 2 2 3 4 4 2 + - 1/432 y x z + 1/432 y x z + 1/864 x y z + 1/1728 x y z + + 3 3 3 3 2 2 3 3 2 2 + - 1/864 y x z + 1/1728 y x z + 1/216 y x z - 1/432 y x z + + 2 3 3 4 3 3 3 2 + - 1/1728 y x z - 1/864 x y z + 1/216 z y x + 1/216 z y x + + 3 3 2 2 3 + - 1/864 z y x - 1/216 y x z - 1/216 z y x + 1/1728 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + - 1/3456 z y x + 1/3456 x y z + 1/1728 x y z - 1/216 y x z + + 4 2 2 3 3 3 4 3 4 2 + - 1/3456 x y z + 1/864 y x z - 1/864 x y z - 1/864 x y z + + 2 4 2 2 2 2 2 2 2 + - 1/864 x y z + 1/864 y x z - 1/432 y x z + 1/432 y x z + + 2 3 2 3 4 3 3 4 2 3 + + 1/432 y x z - 1/216 y x z + 1/864 x y z - 1/1728 x y z + + 3 4 3 4 4 3 4 2 4 + + 1/1728 x y z + 1/1728 x y z - 1/432 y x z - 1/432 y x z + + 3 4 4 4 4 3 2 4 3 + + 1/1728 y x z + 1/1728 x y z - 1/432 x y z - 1/432 x y z + + 4 2 4 2 2 4 2 3 4 3 3 4 + + 1/3456 x y z - 1/864 y x z + 1/3456 y x z - 1/1728 y x z , + + 2 4 4 3 4 3 4 2 + COEFF(2, 2, -2) = 1/6912 y x z + 1/6912 x y z - 1/6912 x y z + + 4 4 4 4 2 4 3 4 + + 1/13824 x y z - 1/3456 x y z - 1/6912 x y z + 1/3456 x y z + + 4 4 3 3 4 4 3 2 4 + + 1/6912 x y z - 1/1728 y x z + 1/6912 x y z - 1/6912 y x z + + 3 2 3 4 2 3 4 + - 1/1728 z y x + 1/3456 z y x + 1/6912 x y z - 1/3456 y x z + + 2 2 3 2 4 4 4 4 + + 1/3456 y x z - 1/3456 y x z - 1/13824 x y z - 1/6912 x y z + + 2 2 2 3 2 2 2 3 4 + - 1/13824 y x z + 1/3456 y x z - 1/6912 y x z - 1/3456 x y z + + 4 2 3 3 3 3 2 2 3 + - 1/6912 x y z + 1/1728 y x z - 1/3456 y x z - 1/3456 y x z + + 3 2 2 2 3 3 4 3 3 + + 1/6912 y x z + 1/3456 y x z + 1/3456 x y z - 1/1728 z y x + + 3 2 3 3 2 + - 1/3456 z y x + 1/1728 z y x + 1/1728 y x z + 1/3456 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + - 1/3456 z y x + 1/6912 z y x - 1/13824 x y z - 1/6912 x y z + + 3 3 4 2 2 3 3 3 4 3 + + 1/1728 y x z + 1/13824 x y z - 1/1728 y x z + 1/3456 x y z + + 4 2 2 4 2 2 2 2 2 + + 1/6912 x y z + 1/13824 x y z - 1/6912 y x z + 1/6912 y x z + + 2 2 2 3 2 3 4 3 3 + - 1/6912 y x z - 1/3456 y x z + 1/3456 y x z - 1/3456 x y z + + 4 2 3 3 4 3 4 4 3 4 + + 1/6912 x y z - 1/3456 x y z - 1/6912 x y z + 1/3456 y x z + + 2 4 3 4 4 4 4 3 + + 1/6912 y x z - 1/3456 y x z - 1/6912 x y z + 1/3456 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + + 1/6912 x y z - 1/13824 x y z + 1/13824 y x z - 1/6912 y x z + + 3 3 4 2 4 4 3 4 + + 1/3456 y x z , COEFF(-2, -2, -1) = 1/1728 y x z + 1/1728 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/432 x y z - 1/3456 x y z - 1/432 x y z + 1/864 x y z + + 3 4 4 4 3 3 4 4 + + 1/432 x y z - 1/864 x y z + 1/864 y x z + 1/1728 x y z + + 3 2 4 3 2 3 4 2 + - 1/1728 y x z + 1/216 z y x - 1/216 z y x + 1/432 x y z + + 3 4 2 2 3 2 4 4 + + 1/864 y x z + 1/432 y x z - 1/1728 y x z + 1/3456 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/1728 x y z + 1/864 y x z - 1/216 y x z + 1/3456 y x z + + 4 4 2 3 3 3 3 2 + - 1/432 x y z + 1/864 x y z - 1/864 y x z + 1/216 y x z + + 2 3 3 2 2 2 3 3 4 3 + - 1/1728 y x z + 1/432 y x z + 1/1728 y x z + 1/432 x y z + + 3 3 2 3 3 + + 1/216 z y x - 1/432 z y x - 1/216 z y x - 1/216 y x z + + 2 2 3 2 2 3 4 4 2 + + 1/432 z y x - 1/432 z y x + 1/432 z y x + 1/864 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + - 1/432 x y z - 1/864 y x z - 1/864 x y z + 1/864 y x z + + 4 3 4 2 2 4 2 2 2 + + 1/1728 x y z + 1/432 x y z - 1/864 x y z - 1/432 y x z + + 2 2 2 2 2 3 2 3 + - 1/864 y x z - 1/432 y x z + 1/216 y x z + 1/1728 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + - 1/1728 x y z - 1/3456 x y z - 1/1728 x y z + 1/3456 x y z + + 4 2 4 3 4 4 4 + - 1/864 y x z + 1/1728 y x z + 1/864 y x z - 1/1728 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + + 1/1728 x y z - 1/3456 x y z + 1/3456 x y z - 1/3456 y x z + + 2 3 4 3 3 4 2 4 + - 1/1728 y x z - 1/864 y x z , COEFF(-1, -2, -1) = - 1/216 y x z + + 4 3 4 3 4 2 4 4 4 4 + - 1/432 x y z + 1/216 x y z + 1/864 x y z + 1/54 x y z + + 2 4 3 4 4 4 3 + - 1/54 x y z - 1/216 x y z + 1/216 x y z - 1/108 y x z + + 3 4 4 3 2 4 3 2 3 + - 1/864 x y z + 1/108 y x z - 1/108 z y x + 1/108 z y x + + 4 2 3 4 2 2 3 + - 1/108 x y z - 1/108 y x z - 1/54 y x z + 1/216 y x z + + 2 4 4 4 4 2 2 2 3 2 + - 1/216 x y z + 1/216 x y z - 1/54 y x z + 1/27 y x z + + 2 2 3 4 4 2 3 3 + - 1/216 y x z + 1/108 x y z - 1/216 x y z + 1/432 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + - 1/108 y x z + 1/108 y x z - 1/27 y x z - 1/864 y x z + + 4 3 3 3 2 3 3 + - 1/108 x y z - 1/27 z y x + 1/27 z y x + 1/108 z y x + 1/27 y x z + + 2 2 3 2 2 3 4 4 2 + - 1/27 z y x + 1/216 z y x - 1/216 z y x - 1/216 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + + 1/108 x y z + 1/108 y x z + 1/216 x y z - 1/432 y x z + + 4 3 4 2 2 4 2 2 2 + - 1/432 x y z - 1/54 x y z + 1/54 x y z + 1/54 y x z + + 2 2 2 2 2 3 2 3 + + 1/54 y x z + 1/27 y x z - 1/27 y x z - 1/108 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + + 1/432 x y z + 1/864 x y z + 1/864 x y z - 1/864 x y z + + 4 2 4 3 4 4 4 + + 1/108 y x z - 1/108 y x z - 1/432 y x z + 1/432 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + - 1/216 x y z + 1/216 x y z - 1/864 x y z + 1/216 y x z + + 2 3 4 3 3 4 4 3 4 + + 1/864 y x z + 1/432 y x z , COEFF(0, -2, -1) = 1/288 x y z + + 4 4 4 2 4 4 4 3 2 4 + - 1/576 x y z + 5/144 x y z - 1/144 x y z - 5/288 y x z + + 4 2 2 4 4 2 2 2 2 2 3 + + 1/72 x y z + 5/576 x y z + 5/144 y x z + 5/576 y x z + + 4 4 2 2 3 3 2 2 + - 1/72 x y z + 1/144 x y z - 5/288 y x z + 5/72 y x z + + 4 3 3 3 2 2 4 4 2 + + 1/72 x y z + 1/18 z y - 5/72 z y x + 5/72 z y x + 1/144 x y z + + 4 3 2 4 2 2 4 3 + - 1/18 y z - 1/72 x y z - 1/144 x y z + 1/288 x y z + + 2 4 2 2 2 2 2 2 + - 5/144 x y z - 5/144 y x z - 5/72 y x z + 1/36 y z + + 3 2 3 4 3 3 4 2 3 4 4 3 + + 5/288 y x z - 1/288 x y z - 1/576 x y z + 1/576 x y z + + 3 2 3 3 3 4 3 4 + + 1/72 y z - 1/144 y z - 1/72 y z - 1/72 y z + 1/72 y z + + 4 4 3 2 2 4 4 2 4 + - 1/144 y z - 1/18 y z + 5/288 y x z + 1/36 y z - 1/36 y z + + 2 2 4 4 4 2 2 4 3 + + 1/18 y z + 1/144 y z - 1/288 x y z - 1/36 y z + 1/144 y z + + 2 4 3 4 2 4 2 2 4 + - 5/576 x y z + 1/576 x y z - 5/576 y x z , COEFF(1, -2, -1) = + + 2 4 4 3 4 3 4 2 4 4 4 + 1/216 y x z - 1/432 x y z - 1/216 x y z + 1/864 x y z + + 4 2 4 3 4 4 4 + - 1/54 x y z - 1/54 x y z + 1/216 x y z + 1/216 x y z + + 3 3 4 4 3 2 4 3 + + 1/108 y x z + 1/864 x y z + 1/108 y x z + 1/108 z y x + + 2 3 4 2 3 4 2 + - 1/108 z y x - 1/108 x y z + 1/108 y x z + 1/54 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/216 y x z - 1/216 x y z - 1/216 x y z - 1/54 y x z + + 3 2 2 2 3 4 4 2 + - 1/27 y x z - 1/216 y x z + 1/108 x y z - 1/216 x y z + + 3 3 3 3 2 2 3 3 2 2 + - 1/432 y x z + 1/108 y x z + 1/108 y x z - 1/27 y x z + + 2 3 3 4 3 3 3 2 + + 1/864 y x z - 1/108 x y z + 1/27 z y x + 1/27 z y x + + 3 3 2 2 3 + - 1/108 z y x - 1/27 y x z - 1/27 z y x - 1/216 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + + 1/216 z y x - 1/216 x y z + 1/108 x y z - 1/108 y x z + + 4 2 2 3 3 3 4 3 4 2 + + 1/216 x y z + 1/432 y x z - 1/432 x y z + 1/54 x y z + + 2 4 2 2 2 2 2 2 2 2 + + 1/54 x y z - 1/54 y x z + 1/54 y x z + 1/27 y x z + 1/27 y x z + + 3 2 3 4 3 3 4 2 3 3 4 3 + - 1/108 y x z + 1/432 x y z + 1/864 x y z - 1/864 x y z + + 4 4 3 4 2 4 3 4 + - 1/864 x y z - 1/108 y x z - 1/108 y x z + 1/432 y x z + + 4 4 4 3 2 4 3 4 2 4 + + 1/432 x y z + 1/216 x y z + 1/216 x y z - 1/864 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/216 y x z - 1/864 y x z - 1/432 y x z , COEFF(2, -2, -1) = + + 2 4 4 3 4 3 4 2 4 4 4 + - 1/1728 y x z + 1/1728 x y z + 1/432 x y z - 1/3456 x y z + + 4 2 4 3 4 4 4 + + 1/432 x y z + 1/864 x y z - 1/432 x y z - 1/864 x y z + + 3 3 4 4 3 2 4 3 + - 1/864 y x z - 1/1728 x y z - 1/1728 y x z - 1/216 z y x + + 2 3 4 2 3 4 2 + + 1/216 z y x + 1/432 x y z - 1/864 y x z - 1/432 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/1728 y x z + 1/3456 x y z + 1/1728 x y z + 1/864 y x z + + 3 2 2 2 3 4 4 2 + + 1/216 y x z + 1/3456 y x z - 1/432 x y z + 1/864 x y z + + 3 3 3 3 2 2 3 3 2 2 + + 1/864 y x z - 1/216 y x z - 1/1728 y x z + 1/432 y x z + + 2 3 3 4 3 3 3 2 + - 1/1728 y x z + 1/432 x y z - 1/216 z y x - 1/432 z y x + + 3 3 2 2 3 + + 1/216 z y x + 1/216 y x z + 1/432 z y x + 1/432 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + - 1/432 z y x + 1/864 x y z - 1/432 x y z + 1/864 y x z + + 4 2 2 3 3 3 4 3 4 2 + - 1/864 x y z - 1/864 y x z + 1/1728 x y z - 1/432 x y z + + 2 4 2 2 2 2 2 2 2 + - 1/864 x y z + 1/432 y x z - 1/864 y x z - 1/432 y x z + + 2 3 2 3 4 3 3 4 2 3 + - 1/216 y x z + 1/1728 y x z - 1/1728 x y z - 1/3456 x y z + + 3 4 3 4 4 3 4 2 4 + + 1/1728 x y z + 1/3456 x y z + 1/864 y x z + 1/1728 y x z + + 3 4 4 4 4 3 2 4 3 + - 1/864 y x z - 1/1728 x y z - 1/1728 x y z - 1/3456 x y z + + 4 2 4 2 2 4 2 3 4 3 3 4 + + 1/3456 x y z - 1/3456 y x z + 1/1728 y x z + 1/864 y x z , + + 2 4 4 3 4 3 4 2 + COEFF(-2, -1, -1) = - 1/108 y x z - 1/864 x y z + 1/108 x y z + + 4 4 4 4 2 4 3 4 + + 1/864 x y z + 1/108 x y z - 1/216 x y z - 1/108 x y z + + 4 4 3 3 4 4 3 2 4 + + 1/216 x y z - 1/108 y x z - 1/432 x y z + 1/864 y x z + + 3 2 3 4 2 3 4 2 + - 1/27 z y x + 1/27 z y x - 1/54 x y z - 1/432 y x z - 1/27 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/108 y x z - 1/864 x y z + 1/432 x y z - 1/54 y x z + + 3 2 2 2 3 4 4 2 + + 1/108 y x z - 1/216 y x z + 1/54 x y z - 1/54 x y z + + 3 3 3 3 2 2 3 3 2 2 + + 1/108 y x z - 1/108 y x z + 1/216 y x z - 1/216 y x z + + 2 3 3 4 3 3 3 2 + - 1/108 y x z - 1/216 x y z - 1/108 z y x + 1/216 z y x + + 3 3 2 2 3 2 2 3 + + 1/108 z y x + 1/27 y x z - 1/54 z y x + 1/27 z y x - 1/27 z y x + + 4 4 2 4 3 2 3 3 4 2 2 + - 1/216 x y z + 1/216 x y z + 1/432 y x z + 1/54 x y z + + 3 3 3 4 3 4 2 2 4 2 + - 1/432 y x z - 1/216 x y z - 1/108 x y z + 1/216 x y z + + 2 2 2 2 2 2 2 + + 1/27 y x z + 1/54 y x z + 1/54 y x z - 1/27 y x z + + 3 2 3 4 3 3 4 2 3 3 4 3 + - 1/864 y x z + 1/864 x y z + 1/216 x y z + 1/432 x y z + + 4 4 3 4 2 4 3 4 + - 1/864 x y z + 1/108 y x z - 1/216 y x z - 1/108 y x z + + 4 4 4 3 2 4 3 4 2 4 + + 1/216 x y z - 1/432 x y z + 1/864 x y z - 1/216 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/216 y x z + 1/108 y x z + 1/432 y x z , COEFF(-1, -1, -1) = + + 2 4 4 3 4 3 4 2 4 4 4 + 2/27 y x z + 1/216 x y z - 1/54 x y z - 1/216 x y z + + 4 2 4 3 4 4 4 3 + - 2/27 x y z + 2/27 x y z + 1/54 x y z - 1/54 x y z + 2/27 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/216 x y z - 1/54 y x z + 2/27 z y x - 2/27 z y x + + 4 2 3 4 2 2 3 2 4 4 + + 2/27 x y z + 1/54 y x z + 8/27 y x z - 2/27 y x z + 1/54 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/54 x y z + 8/27 y x z - 2/27 y x z + 2/27 y x z + + 4 4 2 3 3 3 3 2 2 3 + - 2/27 x y z + 2/27 x y z - 1/54 y x z + 1/54 y x z - 2/27 y x z + + 3 2 2 2 3 3 4 3 3 + + 2/27 y x z + 1/54 y x z + 1/54 x y z + 2/27 z y x + + 3 2 3 3 2 2 3 + - 2/27 z y x - 1/54 z y x - 8/27 y x z + 8/27 z y x - 2/27 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + + 2/27 z y x + 1/54 x y z - 1/54 x y z - 1/54 y x z + + 4 2 2 3 3 3 4 3 4 2 + - 2/27 x y z + 1/216 y x z + 1/54 x y z + 2/27 x y z + + 2 4 2 2 2 2 2 2 2 2 + - 2/27 x y z - 8/27 y x z - 8/27 y x z - 8/27 y x z + 8/27 y x z + + 3 2 3 4 3 3 4 2 3 3 4 3 + + 1/54 y x z - 1/216 x y z - 1/54 x y z - 1/216 x y z + + 4 4 3 4 2 4 3 4 + + 1/216 x y z - 2/27 y x z + 2/27 y x z + 1/54 y x z + + 4 4 4 3 2 4 3 4 2 4 + - 1/54 x y z + 1/54 x y z - 1/54 x y z + 1/54 x y z + + 2 2 4 2 3 4 3 3 4 + - 2/27 y x z - 1/54 y x z - 1/216 y x z , COEFF(0, -1, -1) = + + 4 3 4 4 4 4 2 4 4 4 + - 1/144 x y z + 1/144 x y z - 5/36 x y z + 1/36 x y z + + 3 2 4 4 2 2 4 4 2 2 2 + + 5/144 y x z - 1/9 x y z - 5/144 x y z - 5/9 y x z + + 2 2 3 4 4 2 2 3 3 2 2 + - 5/36 y x z + 1/9 x y z - 1/9 x y z + 5/36 y x z - 5/36 y x z + + 4 3 3 3 2 2 4 4 2 + - 1/36 x y z - 1/9 z y + 5/36 z y x - 5/9 z y x - 1/36 x y z + + 4 3 2 4 2 2 4 3 2 4 2 + + 4/9 y z + 1/36 x y z + 1/9 x y z - 1/36 x y z + 5/36 x y z + + 2 2 2 2 2 3 2 3 4 3 3 + + 5/9 y x z + 5/9 y x z - 4/9 y z - 5/144 y x z + 1/144 x y z + + 4 2 3 4 4 3 3 2 3 3 3 + + 1/36 x y z - 1/144 x y z - 1/9 y z + 1/9 y z + 1/36 y z + + 4 3 4 4 4 3 2 2 4 + + 1/9 y z - 1/36 y z + 1/36 y z + 1/9 y z - 5/36 y x z + + 4 2 4 2 2 4 4 4 2 2 + - 1/9 y z + 1/9 y z - 4/9 y z - 1/9 y z + 1/36 x y z + 4/9 y z + + 4 3 2 4 3 4 2 4 2 2 4 + - 1/36 y z + 5/144 x y z - 1/36 x y z + 5/36 y x z , + + 2 4 4 3 4 3 4 2 + COEFF(1, -1, -1) = - 2/27 y x z + 1/216 x y z + 1/54 x y z + + 4 4 4 4 2 4 3 4 + - 1/216 x y z + 2/27 x y z + 2/27 x y z - 1/54 x y z + + 4 4 3 3 4 4 3 2 4 + - 1/54 x y z - 2/27 y x z - 1/216 x y z - 1/54 y x z + + 3 2 3 4 2 3 4 2 + - 2/27 z y x + 2/27 z y x + 2/27 x y z - 1/54 y x z - 8/27 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 2/27 y x z + 1/54 x y z + 1/54 x y z + 8/27 y x z + + 3 2 2 2 3 4 4 2 3 3 + + 2/27 y x z + 2/27 y x z - 2/27 x y z + 2/27 x y z + 1/54 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + - 1/54 y x z - 2/27 y x z + 2/27 y x z - 1/54 y x z + + 4 3 3 3 2 3 3 + + 1/54 x y z - 2/27 z y x - 2/27 z y x + 1/54 z y x + 8/27 y x z + + 2 2 3 2 2 3 4 4 2 + + 8/27 z y x + 2/27 z y x - 2/27 z y x + 1/54 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + - 1/54 x y z + 1/54 y x z - 2/27 x y z - 1/216 y x z + + 4 3 4 2 2 4 2 2 2 + + 1/54 x y z - 2/27 x y z - 2/27 x y z + 8/27 y x z + + 2 2 2 2 2 3 2 3 + - 8/27 y x z - 8/27 y x z - 8/27 y x z + 1/54 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + - 1/216 x y z - 1/54 x y z + 1/216 x y z + 1/216 x y z + + 4 2 4 3 4 4 4 4 3 + + 2/27 y x z + 2/27 y x z - 1/54 y x z - 1/54 x y z - 1/54 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + - 1/54 x y z + 1/54 x y z - 2/27 y x z + 1/54 y x z + + 3 3 4 2 4 4 3 4 + + 1/216 y x z , COEFF(2, -1, -1) = 1/108 y x z - 1/864 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/108 x y z + 1/864 x y z - 1/108 x y z - 1/216 x y z + + 3 4 4 4 3 3 4 4 + + 1/108 x y z + 1/216 x y z + 1/108 y x z + 1/432 x y z + + 3 2 4 3 2 3 4 2 + + 1/864 y x z + 1/27 z y x - 1/27 z y x - 1/54 x y z + + 3 4 2 2 3 2 4 4 + + 1/432 y x z + 1/27 y x z - 1/108 y x z - 1/864 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/432 x y z - 1/54 y x z - 1/108 y x z - 1/216 y x z + + 4 4 2 3 3 3 3 2 + + 1/54 x y z - 1/54 x y z - 1/108 y x z + 1/108 y x z + + 2 3 3 2 2 2 3 3 4 3 + + 1/216 y x z - 1/216 y x z + 1/108 y x z - 1/216 x y z + + 3 3 2 3 3 2 + + 1/108 z y x + 1/216 z y x - 1/108 z y x - 1/27 y x z - 1/54 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + - 1/27 z y x + 1/27 z y x - 1/216 x y z + 1/216 x y z + + 3 3 4 2 2 3 3 3 4 3 + - 1/432 y x z + 1/54 x y z + 1/432 y x z - 1/216 x y z + + 4 2 2 4 2 2 2 2 2 + + 1/108 x y z + 1/216 x y z - 1/27 y x z + 1/54 y x z + + 2 2 2 3 2 3 4 3 3 + + 1/54 y x z + 1/27 y x z - 1/864 y x z + 1/864 x y z + + 4 2 3 3 4 3 4 4 3 4 + + 1/216 x y z - 1/432 x y z - 1/864 x y z - 1/108 y x z + + 2 4 3 4 4 4 4 3 + - 1/216 y x z + 1/108 y x z + 1/216 x y z + 1/432 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + + 1/864 x y z - 1/216 x y z + 1/216 y x z - 1/108 y x z + + 3 3 4 2 4 3 4 2 + - 1/432 y x z , COEFF(-2, 0, -1) = 5/288 y x z - 1/72 x y z + + 4 4 4 4 2 4 3 4 + - 1/576 x y z - 1/72 x y z + 1/144 x y z + 1/72 x y z + + 4 4 3 4 4 2 2 3 + - 1/144 x y z + 1/288 x y z + 5/72 y x z - 5/288 y x z + + 2 4 4 4 4 2 2 2 2 2 3 + + 1/576 x y z - 1/288 x y z + 5/144 y x z + 5/576 y x z + + 4 2 3 2 3 3 2 3 + + 5/144 x y z + 1/18 z x + 5/288 y x z - 5/72 z y x + + 2 2 3 4 4 2 4 2 2 4 2 + + 5/72 z y x + 1/144 x y z - 5/144 x y z + 1/72 x y z + + 2 4 2 2 2 2 2 + - 1/144 x y z - 5/72 y x z - 5/144 y x z - 1/18 x z + + 4 2 3 2 3 4 3 4 4 3 + - 5/576 x y z + 1/36 x z - 1/288 x y z + 1/576 x y z + + 3 3 2 3 4 3 2 4 3 + - 1/72 x z - 1/144 x z + 1/144 x z + 1/144 x z + 1/72 x z + + 4 4 4 2 3 4 2 2 2 + - 1/72 x z - 1/36 x z + 1/36 x z + 1/72 x z - 1/36 x z + 1/18 x z + + 4 4 3 2 4 3 2 4 3 + - 1/144 x z - 1/18 x z + 1/288 x y z - 1/576 x y z + + 4 2 4 2 2 4 2 3 4 + + 5/576 x y z - 5/576 y x z - 5/288 y x z , COEFF(-1, 0, -1) = + + 2 4 3 4 2 4 4 4 4 2 4 + - 5/36 y x z + 1/36 x y z + 1/144 x y z + 1/9 x y z - 1/9 x y z + + 3 4 4 4 3 4 4 2 2 3 + - 1/36 x y z + 1/36 x y z - 1/144 x y z - 5/9 y x z + 5/36 y x z + + 2 4 4 4 4 2 2 2 2 2 3 + - 1/36 x y z + 1/36 x y z - 5/9 y x z - 5/36 y x z + + 4 2 3 2 3 3 2 3 2 2 3 + - 5/36 x y z - 1/9 z x - 5/144 y x z + 5/36 z y x - 5/36 z y x + + 4 4 2 4 2 2 4 2 2 4 2 2 2 + - 1/36 x y z + 5/36 x y z - 1/9 x y z + 1/9 x y z + 5/9 y x z + + 2 2 4 2 3 2 3 4 3 + + 5/9 y x z + 4/9 x z + 5/144 x y z - 4/9 x z + 1/144 x y z + + 4 4 3 3 3 2 3 4 3 2 4 + - 1/144 x y z + 1/36 x z + 1/9 x z - 1/36 x z - 1/9 x z + + 3 4 4 4 2 3 4 2 2 + - 1/9 x z + 1/9 x z + 1/9 x z - 1/9 x z - 1/36 x z + 4/9 x z + + 2 4 4 3 2 4 3 2 4 3 + - 4/9 x z + 1/36 x z + 1/9 x z - 1/36 x y z + 1/36 x y z + + 4 2 4 2 2 4 2 3 4 + - 5/144 x y z + 5/36 y x z + 5/144 y x z , COEFF(0, 0, -1) = + + 4 4 4 2 4 4 4 2 4 4 + - 1/96 x y z + 5/24 x y z - 1/24 x y z - 2/3 z + 5/96 x y z + + 25 2 2 2 25 2 2 3 4 2 4 3 2 + + -- y x z + -- y x z + 5/24 x y z - 1/6 z + 1/6 z + 2/3 z + 24 96 + + 4 4 2 4 2 2 2 4 2 25 2 2 2 + + 1/24 x y z - 5/24 x y z - 5/24 x y z - -- y x z + 5/6 y z + 24 + + 4 2 3 2 4 4 3 2 3 2 3 + - 5/96 x y z + 5/6 x z + 1/96 x y z - 5/24 y z - 5/24 x z + + 4 3 4 4 2 4 4 2 4 4 + + 1/24 x z - 1/24 y z + 5/24 x z + 1/6 y z - 1/6 y z - 1/6 x z + + 4 2 2 2 4 4 2 4 2 2 4 3 + + 1/6 x z - 5/6 x z - 1/24 x z + 5/24 y z - 5/6 y z + 1/24 y z + + 2 4 3 4 2 4 25 2 2 4 + - 5/96 x y z + 5/96 x y z - -- y x z , COEFF(1, 0, -1) = + 96 + + 2 4 3 4 2 4 4 4 4 2 4 + 5/36 y x z - 1/36 x y z + 1/144 x y z - 1/9 x y z - 1/9 x y z + + 3 4 4 4 3 4 4 2 2 3 + + 1/36 x y z + 1/36 x y z + 1/144 x y z + 5/9 y x z - 5/36 y x z + + 2 4 4 4 4 2 2 2 2 2 3 + - 1/36 x y z - 1/36 x y z - 5/9 y x z - 5/36 y x z + + 4 2 3 2 3 3 2 3 2 2 3 + - 5/36 x y z + 1/9 z x + 5/144 y x z - 5/36 z y x + 5/36 z y x + + 4 4 2 4 2 2 4 2 2 4 2 2 2 + - 1/36 x y z + 5/36 x y z + 1/9 x y z + 1/9 x y z - 5/9 y x z + + 2 2 4 2 3 2 3 4 3 + + 5/9 y x z - 4/9 x z + 5/144 x y z - 4/9 x z - 1/144 x y z + + 4 4 3 3 3 2 3 4 3 2 4 + - 1/144 x y z - 1/36 x z + 1/9 x z - 1/36 x z - 1/9 x z + + 3 4 4 4 2 3 4 2 2 + + 1/9 x z - 1/9 x z + 1/9 x z - 1/9 x z + 1/36 x z + 4/9 x z + + 2 4 4 3 2 4 3 2 4 3 + + 4/9 x z + 1/36 x z - 1/9 x z + 1/36 x y z + 1/36 x y z + + 4 2 4 2 2 4 2 3 4 + - 5/144 x y z + 5/36 y x z - 5/144 y x z , COEFF(2, 0, -1) = + + 2 4 3 4 2 4 4 4 4 + - 5/288 y x z + 1/72 x y z - 1/576 x y z + 1/72 x y z + + 2 4 3 4 4 4 3 4 4 + + 1/144 x y z - 1/72 x y z - 1/144 x y z - 1/288 x y z + + 2 2 3 2 4 4 4 4 + - 5/72 y x z + 5/288 y x z + 1/576 x y z + 1/288 x y z + + 2 2 2 2 2 3 4 2 3 + + 5/144 y x z + 5/576 y x z + 5/144 x y z - 1/18 z x + + 2 3 3 2 3 2 2 3 4 4 2 + - 5/288 y x z + 5/72 z y x - 5/72 z y x + 1/144 x y z + + 4 2 2 4 2 2 4 2 2 2 + - 5/144 x y z - 1/72 x y z - 1/144 x y z + 5/72 y x z + + 2 2 4 2 3 2 3 4 3 + - 5/144 y x z + 1/18 x z - 5/576 x y z + 1/36 x z + 1/288 x y z + + 4 4 3 3 3 2 3 4 3 2 4 + + 1/576 x y z + 1/72 x z - 1/144 x z + 1/144 x z + 1/144 x z + + 3 4 4 4 2 3 4 2 2 + - 1/72 x z + 1/72 x z - 1/36 x z + 1/36 x z - 1/72 x z - 1/36 x z + + 2 4 4 3 2 4 3 2 4 3 + - 1/18 x z - 1/144 x z + 1/18 x z - 1/288 x y z - 1/576 x y z + + 4 2 4 2 2 4 2 3 4 + + 5/576 x y z - 5/576 y x z + 5/288 y x z , COEFF(-2, 1, -1) = + + 2 4 4 3 4 3 4 2 4 4 4 + - 1/108 y x z + 1/864 x y z + 1/108 x y z + 1/864 x y z + + 4 2 4 3 4 4 4 + + 1/108 x y z - 1/216 x y z - 1/108 x y z + 1/216 x y z + + 3 3 4 4 3 2 4 3 + + 1/108 y x z - 1/432 x y z - 1/864 y x z + 1/27 z y x + + 2 3 4 2 3 4 2 + - 1/27 z y x + 1/54 x y z + 1/432 y x z - 1/27 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/108 y x z - 1/864 x y z + 1/432 x y z - 1/54 y x z + + 3 2 2 2 3 4 4 2 + - 1/108 y x z - 1/216 y x z - 1/54 x y z - 1/54 x y z + + 3 3 3 3 2 2 3 3 2 2 + - 1/108 y x z + 1/108 y x z - 1/216 y x z + 1/216 y x z + + 2 3 3 4 3 3 3 2 + - 1/108 y x z + 1/216 x y z + 1/108 z y x - 1/216 z y x + + 3 3 2 2 3 2 2 3 + - 1/108 z y x - 1/27 y x z + 1/54 z y x + 1/27 z y x - 1/27 z y x + + 4 4 2 4 3 2 3 3 4 2 2 + - 1/216 x y z - 1/216 x y z - 1/432 y x z + 1/54 x y z + + 3 3 3 4 3 4 2 2 4 2 + + 1/432 y x z + 1/216 x y z - 1/108 x y z + 1/216 x y z + + 2 2 2 2 2 2 2 + + 1/27 y x z + 1/54 y x z - 1/54 y x z + 1/27 y x z + + 3 2 3 4 3 3 4 2 3 3 4 3 + + 1/864 y x z - 1/864 x y z + 1/216 x y z + 1/432 x y z + + 4 4 3 4 2 4 3 4 + - 1/864 x y z - 1/108 y x z + 1/216 y x z + 1/108 y x z + + 4 4 4 3 2 4 3 4 2 4 + - 1/216 x y z - 1/432 x y z + 1/864 x y z - 1/216 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/216 y x z + 1/108 y x z - 1/432 y x z , COEFF(-1, 1, -1) = + + 2 4 4 3 4 3 4 2 4 4 4 + 2/27 y x z - 1/216 x y z - 1/54 x y z - 1/216 x y z + + 4 2 4 3 4 4 4 3 + - 2/27 x y z + 2/27 x y z + 1/54 x y z - 1/54 x y z - 2/27 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/216 x y z + 1/54 y x z - 2/27 z y x + 2/27 z y x + + 4 2 3 4 2 2 3 2 4 4 + - 2/27 x y z - 1/54 y x z + 8/27 y x z - 2/27 y x z + 1/54 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/54 x y z + 8/27 y x z + 2/27 y x z + 2/27 y x z + + 4 4 2 3 3 3 3 2 2 3 + + 2/27 x y z + 2/27 x y z + 1/54 y x z - 1/54 y x z + 2/27 y x z + + 3 2 2 2 3 3 4 3 3 + - 2/27 y x z + 1/54 y x z - 1/54 x y z - 2/27 z y x + + 3 2 3 3 2 2 3 + + 2/27 z y x + 1/54 z y x + 8/27 y x z - 8/27 z y x - 2/27 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + + 2/27 z y x + 1/54 x y z + 1/54 x y z + 1/54 y x z + + 4 2 2 3 3 3 4 3 4 2 + - 2/27 x y z - 1/216 y x z - 1/54 x y z + 2/27 x y z + + 2 4 2 2 2 2 2 2 2 2 + - 2/27 x y z - 8/27 y x z - 8/27 y x z + 8/27 y x z - 8/27 y x z + + 3 2 3 4 3 3 4 2 3 3 4 3 + - 1/54 y x z + 1/216 x y z - 1/54 x y z - 1/216 x y z + + 4 4 3 4 2 4 3 4 + + 1/216 x y z + 2/27 y x z - 2/27 y x z - 1/54 y x z + + 4 4 4 3 2 4 3 4 2 4 + + 1/54 x y z + 1/54 x y z - 1/54 x y z + 1/54 x y z + + 2 2 4 2 3 4 3 3 4 + - 2/27 y x z - 1/54 y x z + 1/216 y x z , COEFF(0, 1, -1) = + + 4 3 4 4 4 4 2 4 4 4 + 1/144 x y z + 1/144 x y z - 5/36 x y z + 1/36 x y z + + 3 2 4 4 2 2 4 4 2 2 2 + - 5/144 y x z + 1/9 x y z - 5/144 x y z - 5/9 y x z + + 2 2 3 4 4 2 2 3 3 2 2 + - 5/36 y x z - 1/9 x y z - 1/9 x y z - 5/36 y x z + 5/36 y x z + + 4 3 3 3 2 2 4 4 2 + + 1/36 x y z + 1/9 z y - 5/36 z y x + 5/9 z y x - 1/36 x y z + + 4 3 2 4 2 2 4 3 2 4 2 + - 4/9 y z - 1/36 x y z + 1/9 x y z + 1/36 x y z + 5/36 x y z + + 2 2 2 2 2 3 2 3 4 3 3 + + 5/9 y x z - 5/9 y x z - 4/9 y z + 5/144 y x z - 1/144 x y z + + 4 2 3 4 4 3 3 2 3 3 3 + + 1/36 x y z - 1/144 x y z + 1/9 y z + 1/9 y z - 1/36 y z + + 4 3 4 4 4 3 2 2 4 + - 1/9 y z + 1/36 y z + 1/36 y z - 1/9 y z + 5/36 y x z + + 4 2 4 2 2 4 4 4 2 2 + - 1/9 y z + 1/9 y z + 4/9 y z - 1/9 y z - 1/36 x y z + 4/9 y z + + 4 3 2 4 3 4 2 4 2 2 4 + - 1/36 y z + 5/144 x y z - 1/36 x y z + 5/36 y x z , + + 2 4 4 3 4 3 4 2 + COEFF(1, 1, -1) = - 2/27 y x z - 1/216 x y z + 1/54 x y z + + 4 4 4 4 2 4 3 4 + - 1/216 x y z + 2/27 x y z + 2/27 x y z - 1/54 x y z + + 4 4 3 3 4 4 3 2 4 + - 1/54 x y z + 2/27 y x z - 1/216 x y z + 1/54 y x z + + 3 2 3 4 2 3 4 2 + + 2/27 z y x - 2/27 z y x - 2/27 x y z + 1/54 y x z - 8/27 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 2/27 y x z + 1/54 x y z + 1/54 x y z + 8/27 y x z + + 3 2 2 2 3 4 4 2 3 3 + - 2/27 y x z + 2/27 y x z + 2/27 x y z + 2/27 x y z - 1/54 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + + 1/54 y x z + 2/27 y x z - 2/27 y x z - 1/54 y x z + + 4 3 3 3 2 3 3 + - 1/54 x y z + 2/27 z y x + 2/27 z y x - 1/54 z y x - 8/27 y x z + + 2 2 3 2 2 3 4 4 2 + - 8/27 z y x + 2/27 z y x - 2/27 z y x + 1/54 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + + 1/54 x y z - 1/54 y x z - 2/27 x y z + 1/216 y x z + + 4 3 4 2 2 4 2 2 2 + - 1/54 x y z - 2/27 x y z - 2/27 x y z + 8/27 y x z + + 2 2 2 2 2 3 2 3 + - 8/27 y x z + 8/27 y x z + 8/27 y x z - 1/54 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + + 1/216 x y z - 1/54 x y z + 1/216 x y z + 1/216 x y z + + 4 2 4 3 4 4 4 4 3 + - 2/27 y x z - 2/27 y x z + 1/54 y x z + 1/54 x y z - 1/54 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + - 1/54 x y z + 1/54 x y z - 2/27 y x z + 1/54 y x z + + 3 3 4 2 4 4 3 4 + - 1/216 y x z , COEFF(2, 1, -1) = 1/108 y x z + 1/864 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/108 x y z + 1/864 x y z - 1/108 x y z - 1/216 x y z + + 3 4 4 4 3 3 4 4 + + 1/108 x y z + 1/216 x y z - 1/108 y x z + 1/432 x y z + + 3 2 4 3 2 3 4 2 + - 1/864 y x z - 1/27 z y x + 1/27 z y x + 1/54 x y z + + 3 4 2 2 3 2 4 4 + - 1/432 y x z + 1/27 y x z - 1/108 y x z - 1/864 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/432 x y z - 1/54 y x z + 1/108 y x z - 1/216 y x z + + 4 4 2 3 3 3 3 2 + - 1/54 x y z - 1/54 x y z + 1/108 y x z - 1/108 y x z + + 2 3 3 2 2 2 3 3 4 3 + - 1/216 y x z + 1/216 y x z + 1/108 y x z + 1/216 x y z + + 3 3 2 3 3 2 + - 1/108 z y x - 1/216 z y x + 1/108 z y x + 1/27 y x z + 1/54 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + - 1/27 z y x + 1/27 z y x - 1/216 x y z - 1/216 x y z + + 3 3 4 2 2 3 3 3 4 3 + + 1/432 y x z + 1/54 x y z - 1/432 y x z + 1/216 x y z + + 4 2 2 4 2 2 2 2 2 + + 1/108 x y z + 1/216 x y z - 1/27 y x z + 1/54 y x z + + 2 2 2 3 2 3 4 3 3 + - 1/54 y x z - 1/27 y x z + 1/864 y x z - 1/864 x y z + + 4 2 3 3 4 3 4 4 3 4 + + 1/216 x y z - 1/432 x y z - 1/864 x y z + 1/108 y x z + + 2 4 3 4 4 4 4 3 + + 1/216 y x z - 1/108 y x z - 1/216 x y z + 1/432 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + + 1/864 x y z - 1/216 x y z + 1/216 y x z - 1/108 y x z + + 3 3 4 2 4 4 3 4 + + 1/432 y x z , COEFF(-2, 2, -1) = 1/1728 y x z - 1/1728 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/432 x y z - 1/3456 x y z - 1/432 x y z + 1/864 x y z + + 3 4 4 4 3 3 4 4 + + 1/432 x y z - 1/864 x y z - 1/864 y x z + 1/1728 x y z + + 3 2 4 3 2 3 4 2 + + 1/1728 y x z - 1/216 z y x + 1/216 z y x - 1/432 x y z + + 3 4 2 2 3 2 4 4 + - 1/864 y x z + 1/432 y x z - 1/1728 y x z + 1/3456 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/1728 x y z + 1/864 y x z + 1/216 y x z + 1/3456 y x z + + 4 4 2 3 3 3 3 2 + + 1/432 x y z + 1/864 x y z + 1/864 y x z - 1/216 y x z + + 2 3 3 2 2 2 3 3 4 3 + + 1/1728 y x z - 1/432 y x z + 1/1728 y x z - 1/432 x y z + + 3 3 2 3 3 + - 1/216 z y x + 1/432 z y x + 1/216 z y x + 1/216 y x z + + 2 2 3 2 2 3 4 4 2 + - 1/432 z y x - 1/432 z y x + 1/432 z y x + 1/864 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + + 1/432 x y z + 1/864 y x z - 1/864 x y z - 1/864 y x z + + 4 3 4 2 2 4 2 2 2 + - 1/1728 x y z + 1/432 x y z - 1/864 x y z - 1/432 y x z + + 2 2 2 2 2 3 2 3 + - 1/864 y x z + 1/432 y x z - 1/216 y x z - 1/1728 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + + 1/1728 x y z - 1/3456 x y z - 1/1728 x y z + 1/3456 x y z + + 4 2 4 3 4 4 4 + + 1/864 y x z - 1/1728 y x z - 1/864 y x z + 1/1728 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + + 1/1728 x y z - 1/3456 x y z + 1/3456 x y z - 1/3456 y x z + + 2 3 4 3 3 4 2 4 + - 1/1728 y x z + 1/864 y x z , COEFF(-1, 2, -1) = - 1/216 y x z + + 4 3 4 3 4 2 4 4 4 4 + + 1/432 x y z + 1/216 x y z + 1/864 x y z + 1/54 x y z + + 2 4 3 4 4 4 3 + - 1/54 x y z - 1/216 x y z + 1/216 x y z + 1/108 y x z + + 3 4 4 3 2 4 3 2 3 + - 1/864 x y z - 1/108 y x z + 1/108 z y x - 1/108 z y x + + 4 2 3 4 2 2 3 + + 1/108 x y z + 1/108 y x z - 1/54 y x z + 1/216 y x z + + 2 4 4 4 4 2 2 2 3 2 + - 1/216 x y z + 1/216 x y z - 1/54 y x z - 1/27 y x z + + 2 2 3 4 4 2 3 3 + - 1/216 y x z - 1/108 x y z - 1/216 x y z - 1/432 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + + 1/108 y x z - 1/108 y x z + 1/27 y x z - 1/864 y x z + + 4 3 3 3 2 3 3 + + 1/108 x y z + 1/27 z y x - 1/27 z y x - 1/108 z y x - 1/27 y x z + + 2 2 3 2 2 3 4 4 2 + + 1/27 z y x + 1/216 z y x - 1/216 z y x - 1/216 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + - 1/108 x y z - 1/108 y x z + 1/216 x y z + 1/432 y x z + + 4 3 4 2 2 4 2 2 2 + + 1/432 x y z - 1/54 x y z + 1/54 x y z + 1/54 y x z + + 2 2 2 2 2 3 2 3 + + 1/54 y x z - 1/27 y x z + 1/27 y x z + 1/108 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + - 1/432 x y z + 1/864 x y z + 1/864 x y z - 1/864 x y z + + 4 2 4 3 4 4 4 + - 1/108 y x z + 1/108 y x z + 1/432 y x z - 1/432 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + - 1/216 x y z + 1/216 x y z - 1/864 x y z + 1/216 y x z + + 2 3 4 3 3 4 4 3 4 + + 1/864 y x z - 1/432 y x z , COEFF(0, 2, -1) = - 1/288 x y z + + 4 4 4 2 4 4 4 3 2 4 + - 1/576 x y z + 5/144 x y z - 1/144 x y z + 5/288 y x z + + 4 2 2 4 4 2 2 2 2 2 3 + - 1/72 x y z + 5/576 x y z + 5/144 y x z + 5/576 y x z + + 4 4 2 2 3 3 2 2 + + 1/72 x y z + 1/144 x y z + 5/288 y x z - 5/72 y x z + + 4 3 3 3 2 2 4 4 2 + - 1/72 x y z - 1/18 z y + 5/72 z y x - 5/72 z y x + 1/144 x y z + + 4 3 2 4 2 2 4 3 + + 1/18 y z + 1/72 x y z - 1/144 x y z - 1/288 x y z + + 2 4 2 2 2 2 2 2 + - 5/144 x y z - 5/144 y x z + 5/72 y x z + 1/36 y z + + 3 2 3 4 3 3 4 2 3 4 4 3 + - 5/288 y x z + 1/288 x y z - 1/576 x y z + 1/576 x y z + + 3 2 3 3 3 4 3 4 + - 1/72 y z - 1/144 y z + 1/72 y z + 1/72 y z - 1/72 y z + + 4 4 3 2 2 4 4 2 4 + - 1/144 y z + 1/18 y z - 5/288 y x z + 1/36 y z - 1/36 y z + + 2 2 4 4 4 2 2 4 3 + - 1/18 y z + 1/144 y z + 1/288 x y z - 1/36 y z + 1/144 y z + + 2 4 3 4 2 4 2 2 4 + - 5/576 x y z + 1/576 x y z - 5/576 y x z , COEFF(1, 2, -1) = + + 2 4 4 3 4 3 4 2 4 4 4 + 1/216 y x z + 1/432 x y z - 1/216 x y z + 1/864 x y z + + 4 2 4 3 4 4 4 + - 1/54 x y z - 1/54 x y z + 1/216 x y z + 1/216 x y z + + 3 3 4 4 3 2 4 3 + - 1/108 y x z + 1/864 x y z - 1/108 y x z - 1/108 z y x + + 2 3 4 2 3 4 2 + + 1/108 z y x + 1/108 x y z - 1/108 y x z + 1/54 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/216 y x z - 1/216 x y z - 1/216 x y z - 1/54 y x z + + 3 2 2 2 3 4 4 2 + + 1/27 y x z - 1/216 y x z - 1/108 x y z - 1/216 x y z + + 3 3 3 3 2 2 3 3 2 2 + + 1/432 y x z - 1/108 y x z - 1/108 y x z + 1/27 y x z + + 2 3 3 4 3 3 3 2 + + 1/864 y x z + 1/108 x y z - 1/27 z y x - 1/27 z y x + + 3 3 2 2 3 + + 1/108 z y x + 1/27 y x z + 1/27 z y x - 1/216 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + + 1/216 z y x - 1/216 x y z - 1/108 x y z + 1/108 y x z + + 4 2 2 3 3 3 4 3 4 2 + + 1/216 x y z - 1/432 y x z + 1/432 x y z + 1/54 x y z + + 2 4 2 2 2 2 2 2 2 2 + + 1/54 x y z - 1/54 y x z + 1/54 y x z - 1/27 y x z - 1/27 y x z + + 3 2 3 4 3 3 4 2 3 3 4 3 + + 1/108 y x z - 1/432 x y z + 1/864 x y z - 1/864 x y z + + 4 4 3 4 2 4 3 4 + - 1/864 x y z + 1/108 y x z + 1/108 y x z - 1/432 y x z + + 4 4 4 3 2 4 3 4 2 4 + - 1/432 x y z + 1/216 x y z + 1/216 x y z - 1/864 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/216 y x z - 1/864 y x z + 1/432 y x z , COEFF(2, 2, -1) = + + 2 4 4 3 4 3 4 2 4 4 4 + - 1/1728 y x z - 1/1728 x y z + 1/432 x y z - 1/3456 x y z + + 4 2 4 3 4 4 4 + + 1/432 x y z + 1/864 x y z - 1/432 x y z - 1/864 x y z + + 3 3 4 4 3 2 4 3 + + 1/864 y x z - 1/1728 x y z + 1/1728 y x z + 1/216 z y x + + 2 3 4 2 3 4 2 + - 1/216 z y x - 1/432 x y z + 1/864 y x z - 1/432 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/1728 y x z + 1/3456 x y z + 1/1728 x y z + 1/864 y x z + + 3 2 2 2 3 4 4 2 + - 1/216 y x z + 1/3456 y x z + 1/432 x y z + 1/864 x y z + + 3 3 3 3 2 2 3 3 2 2 + - 1/864 y x z + 1/216 y x z + 1/1728 y x z - 1/432 y x z + + 2 3 3 4 3 3 3 2 + - 1/1728 y x z - 1/432 x y z + 1/216 z y x + 1/432 z y x + + 3 3 2 2 3 + - 1/216 z y x - 1/216 y x z - 1/432 z y x + 1/432 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + - 1/432 z y x + 1/864 x y z + 1/432 x y z - 1/864 y x z + + 4 2 2 3 3 3 4 3 4 2 + - 1/864 x y z + 1/864 y x z - 1/1728 x y z - 1/432 x y z + + 2 4 2 2 2 2 2 2 2 + - 1/864 x y z + 1/432 y x z - 1/864 y x z + 1/432 y x z + + 2 3 2 3 4 3 3 4 2 3 + + 1/216 y x z - 1/1728 y x z + 1/1728 x y z - 1/3456 x y z + + 3 4 3 4 4 3 4 2 4 + + 1/1728 x y z + 1/3456 x y z - 1/864 y x z - 1/1728 y x z + + 3 4 4 4 4 3 2 4 3 + + 1/864 y x z + 1/1728 x y z - 1/1728 x y z - 1/3456 x y z + + 4 2 4 2 2 4 2 3 4 3 3 4 + + 1/3456 x y z - 1/3456 y x z + 1/1728 y x z - 1/864 y x z , + + 3 2 4 4 3 4 + COEFF(-2, -2, 0) = - 1/144 y x - 1/1152 y x z - 1/1152 x y z + + 3 4 2 4 4 4 3 4 4 3 2 4 + + 5/1152 x y z + 1/2304 x y z - 1/1152 x y z + 1/1152 y x z + + 2 3 4 2 3 4 3 4 + + 5/576 z y x - 5/1152 x y z - 1/576 y x z - 1/288 x y + 1/144 y x + + 2 4 4 4 4 2 2 2 3 2 + - 1/2304 x y z + 1/1152 x y z - 5/2304 y x z + 5/576 y x z + + 3 3 2 3 2 2 3 2 3 + - 5/576 y x z - 5/1152 y x z - 1/144 y x + 1/288 y x + + 3 2 3 3 4 2 2 3 + + 1/288 y x + 1/144 y x + 1/288 x y - 5/1152 z y x + + 4 4 2 4 2 4 3 2 4 4 + - 5/2304 x y z - 1/576 x y + 5/1152 x y z + 1/576 x y + + 4 2 2 4 3 2 4 4 + + 5/2304 x y z - 1/288 x y - 1/576 x y + 1/288 x y + + 4 2 2 2 4 2 2 2 + - 5/1152 x y z - 1/288 y x + 5/2304 x y z + 5/1152 y x z + + 2 2 2 4 2 4 + + 5/1152 y x z - 5/576 y x z + 1/576 y x z - 1/1152 y x z + + 3 4 4 4 2 2 2 + - 1/576 y x z + 1/1152 x y z + 1/576 y x - 1/288 y x + + 4 2 4 2 2 4 2 3 4 3 3 4 + - 1/2304 x y z + 1/2304 y x z + 1/1152 y x z + 1/576 y x z , + + 3 2 4 4 3 4 + COEFF(-1, -2, 0) = 1/72 y x + 1/144 y x z + 1/288 x y z + + 3 4 2 4 4 4 3 4 4 3 2 4 + - 5/576 x y z - 1/576 x y z + 1/576 x y z - 1/72 y x z + + 2 3 4 2 3 4 3 4 + - 5/288 z y x + 5/288 x y z + 1/72 y x z + 1/144 x y - 1/18 y x + + 2 4 4 4 4 2 2 2 3 2 + + 1/144 x y z - 1/144 x y z + 5/144 y x z - 5/72 y x z + + 3 3 2 3 2 2 3 2 3 3 2 + + 5/288 y x z + 5/72 y x z + 1/18 y x - 1/144 y x - 1/18 y x + + 3 3 4 2 2 3 4 4 2 4 2 + - 1/72 y x - 1/72 x y + 5/576 z y x + 5/576 x y z + 1/144 x y + + 4 3 2 4 4 4 2 2 4 3 2 4 + - 5/288 x y z - 1/144 x y - 5/576 x y z + 1/72 x y + 1/36 x y + + 4 4 2 2 2 4 2 2 2 + - 1/36 x y + 5/144 x y z + 1/36 y x - 5/144 x y z - 5/144 y x z + + 2 2 2 4 2 4 3 4 + - 5/72 y x z + 5/72 y x z - 1/72 y x z + 1/72 y x z + 1/288 y x z + + 4 4 2 2 2 4 2 4 2 2 4 + - 1/288 x y z - 1/36 y x + 1/18 y x + 1/576 x y z - 1/144 y x z + + 2 3 4 3 3 4 4 3 4 + - 1/576 y x z - 1/288 y x z , COEFF(0, -2, 0) = - 1/192 x y z + + 4 4 4 3 2 4 4 2 + + 1/384 x y z + 1/12 y + 5/192 y x z - 5/192 x y z + + 2 4 4 4 25 2 2 2 25 3 2 2 3 + - 5/384 x y z + 1/24 y - --- y x z - --- y x z - 1/12 y + 384 192 + + 2 3 2 4 4 4 2 4 2 + - 1/24 y + 5/48 y x + 1/48 x y - 5/384 x y z - 1/96 x y + + 4 3 2 4 4 4 2 2 4 3 2 4 + + 5/192 x y z + 1/96 x y + 5/384 x y z - 1/48 x y - 5/96 x y + + 25 2 4 2 25 2 2 4 3 4 4 4 + + --- x y z + --- y x z + 1/48 y z - 1/48 y z + 1/96 y z + 384 192 + + 3 2 2 4 4 2 2 2 4 + + 5/48 y z - 5/192 y x z - 5/96 y z - 5/48 y z - 1/96 y z + + 4 4 2 2 2 2 2 4 2 4 + + 1/192 x y z + 5/96 y z + 5/96 y x - 5/48 y x - 1/384 x y z + + 2 2 4 3 2 4 + + 5/384 y x z , COEFF(1, -2, 0) = - 1/72 y x - 1/144 y x z + + 4 3 4 3 4 2 4 4 4 3 4 4 + + 1/288 x y z + 5/576 x y z - 1/576 x y z - 1/576 x y z + + 3 2 4 2 3 4 2 3 4 + - 1/72 y x z + 5/288 z y x + 5/288 x y z - 1/72 y x z + + 3 4 2 4 4 4 4 2 2 2 + - 1/144 x y + 1/18 y x + 1/144 x y z + 1/144 x y z + 5/144 y x z + + 3 2 3 3 2 3 2 2 3 2 3 + + 5/72 y x z - 5/288 y x z + 5/72 y x z - 1/18 y x + 1/144 y x + + 3 2 3 3 4 2 2 3 4 4 2 + - 1/18 y x + 1/72 y x - 1/72 x y - 5/576 z y x + 5/576 x y z + + 4 2 4 3 2 4 4 4 2 2 4 3 + + 1/144 x y - 5/288 x y z - 1/144 x y - 5/576 x y z + 1/72 x y + + 2 4 4 4 2 2 2 4 2 + + 1/36 x y + 1/36 x y - 5/144 x y z - 1/36 y x - 5/144 x y z + + 2 2 2 2 2 4 2 4 + + 5/144 y x z - 5/72 y x z - 5/72 y x z + 1/72 y x z + 1/72 y x z + + 3 4 4 4 2 2 2 4 2 4 + - 1/288 y x z - 1/288 x y z - 1/36 y x + 1/18 y x + 1/576 x y z + + 2 2 4 2 3 4 3 3 4 + - 1/144 y x z + 1/576 y x z + 1/288 y x z , COEFF(2, -2, 0) = + + 3 2 4 4 3 4 3 4 2 + 1/144 y x + 1/1152 y x z - 1/1152 x y z - 5/1152 x y z + + 4 4 4 3 4 4 3 2 4 2 3 + + 1/2304 x y z + 1/1152 x y z + 1/1152 y x z - 5/576 z y x + + 4 2 3 4 3 4 + - 5/1152 x y z + 1/576 y x z + 1/288 x y - 1/144 y x + + 2 4 4 4 4 2 2 2 3 2 + - 1/2304 x y z - 1/1152 x y z - 5/2304 y x z - 5/576 y x z + + 3 3 2 3 2 2 3 2 3 + + 5/576 y x z - 5/1152 y x z + 1/144 y x - 1/288 y x + + 3 2 3 3 4 2 2 3 + + 1/288 y x - 1/144 y x + 1/288 x y + 5/1152 z y x + + 4 4 2 4 2 4 3 2 4 4 + - 5/2304 x y z - 1/576 x y + 5/1152 x y z + 1/576 x y + + 4 2 2 4 3 2 4 4 + + 5/2304 x y z - 1/288 x y - 1/576 x y - 1/288 x y + + 4 2 2 2 4 2 2 2 + + 5/1152 x y z + 1/288 y x + 5/2304 x y z - 5/1152 y x z + + 2 2 2 4 2 4 + + 5/1152 y x z + 5/576 y x z - 1/576 y x z - 1/1152 y x z + + 3 4 4 4 2 2 2 + + 1/576 y x z + 1/1152 x y z + 1/576 y x - 1/288 y x + + 4 2 4 2 2 4 2 3 4 3 3 4 + - 1/2304 x y z + 1/2304 y x z - 1/1152 y x z - 1/576 y x z , + + 3 2 4 4 3 4 + COEFF(-2, -1, 0) = 1/18 y x + 1/72 y x z + 1/576 x y z + + 3 4 2 4 4 4 3 4 4 3 2 4 + - 5/288 x y z - 1/576 x y z + 1/288 x y z - 1/576 y x z + + 2 3 4 2 3 4 3 4 + - 5/72 z y x + 5/144 x y z + 1/288 y x z + 1/72 x y - 1/18 y x + + 2 4 4 4 4 2 2 2 3 2 + + 1/576 x y z - 1/288 x y z + 5/144 y x z - 5/288 y x z + + 3 3 2 3 2 2 3 2 3 3 2 + + 5/288 y x z + 5/576 y x z + 1/72 y x - 1/18 y x - 1/144 y x + + 3 3 4 2 2 3 4 4 2 4 2 + - 1/72 y x - 1/36 x y + 5/72 z y x + 5/576 x y z + 1/36 x y + + 4 3 2 4 4 4 2 2 4 3 + - 5/576 x y z - 1/144 x y - 5/144 x y z + 1/144 x y + + 2 4 4 4 2 2 2 4 2 + + 1/144 x y - 1/72 x y + 5/288 x y z + 1/18 y x - 5/576 x y z + + 2 2 2 2 2 4 2 4 + - 5/72 y x z - 5/144 y x z + 5/72 y x z - 1/72 y x z + 1/144 y x z + + 3 4 4 4 2 2 2 4 2 4 + + 1/72 y x z - 1/144 x y z - 1/36 y x + 1/36 y x + 1/144 x y z + + 2 2 4 2 3 4 3 3 4 + - 1/144 y x z - 1/72 y x z - 1/288 y x z , COEFF(-1, -1, 0) = + + 3 2 4 4 3 4 3 4 2 4 4 4 + - 1/9 y x - 1/9 y x z - 1/144 x y z + 5/144 x y z + 1/144 x y z + + 3 4 4 3 2 4 2 3 4 2 + - 1/144 x y z + 1/36 y x z + 5/36 z y x - 5/36 x y z + + 3 4 3 4 2 4 4 4 4 + - 1/36 y x z - 1/36 x y + 4/9 y x - 1/36 x y z + 1/36 x y z + + 2 2 2 3 2 3 3 2 3 2 2 3 + - 5/9 y x z + 5/36 y x z - 5/144 y x z - 5/36 y x z - 1/9 y x + + 2 3 3 2 3 3 4 2 2 3 + + 1/9 y x + 1/9 y x + 1/36 y x + 1/9 x y - 5/36 z y x + + 4 4 2 4 2 4 3 2 4 4 4 2 2 + - 5/144 x y z - 1/9 x y + 5/144 x y z + 1/36 x y + 5/36 x y z + + 4 3 2 4 4 4 2 2 + - 1/36 x y - 1/9 x y + 1/9 x y - 5/36 x y z - 4/9 y x + + 2 4 2 2 2 2 2 2 4 + + 5/36 x y z + 5/9 y x z + 5/9 y x z - 5/9 y x z + 1/9 y x z + + 2 4 3 4 4 4 2 2 2 + - 1/9 y x z - 1/36 y x z + 1/36 x y z + 4/9 y x - 4/9 y x + + 4 2 4 2 2 4 2 3 4 3 3 4 + - 1/36 x y z + 1/9 y x z + 1/36 y x z + 1/144 y x z , + + 4 3 4 4 4 4 3 2 4 + COEFF(0, -1, 0) = 1/96 x y z - 1/96 x y z - 2/3 y - 5/96 y x z + + 4 2 2 4 4 4 25 2 2 2 25 3 2 2 + + 5/24 x y z + 5/96 x y z - 1/6 y + -- y x z + -- y x z + 24 96 + + 3 2 3 2 4 4 4 2 4 2 + + 1/6 y + 2/3 y - 5/24 y x - 1/6 x y + 5/96 x y z + 1/6 x y + + 4 3 2 4 4 4 2 2 4 3 2 4 + - 5/96 x y z - 1/24 x y - 5/24 x y z + 1/24 x y + 5/24 x y + + 25 2 4 2 25 2 2 4 3 4 4 4 + - -- x y z - -- y x z - 1/6 y z + 1/24 y z - 1/24 y z + 96 24 + + 3 2 2 4 4 2 2 2 4 + - 5/24 y z + 5/24 y x z + 5/24 y z + 5/6 y z + 1/6 y z + + 4 4 2 2 2 2 2 4 2 4 + - 1/24 x y z - 5/6 y z - 5/6 y x + 5/6 y x + 1/24 x y z + + 2 2 4 3 2 4 4 3 4 + - 5/24 y x z , COEFF(1, -1, 0) = 1/9 y x + 1/9 y x z - 1/144 x y z + + 3 4 2 4 4 4 3 4 4 3 2 4 + - 5/144 x y z + 1/144 x y z + 1/144 x y z + 1/36 y x z + + 2 3 4 2 3 4 3 4 + - 5/36 z y x - 5/36 x y z + 1/36 y x z + 1/36 x y - 4/9 y x + + 2 4 4 4 4 2 2 2 3 2 + - 1/36 x y z - 1/36 x y z - 5/9 y x z - 5/36 y x z + + 3 3 2 3 2 2 3 2 3 3 2 + + 5/144 y x z - 5/36 y x z + 1/9 y x - 1/9 y x + 1/9 y x + + 3 3 4 2 2 3 4 4 2 4 2 + - 1/36 y x + 1/9 x y + 5/36 z y x - 5/144 x y z - 1/9 x y + + 4 3 2 4 4 4 2 2 4 3 2 4 + + 5/144 x y z + 1/36 x y + 5/36 x y z - 1/36 x y - 1/9 x y + + 4 4 2 2 2 4 2 2 2 + - 1/9 x y + 5/36 x y z + 4/9 y x + 5/36 x y z - 5/9 y x z + + 2 2 2 4 2 4 3 4 + + 5/9 y x z + 5/9 y x z - 1/9 y x z - 1/9 y x z + 1/36 y x z + + 4 4 2 2 2 4 2 4 2 2 4 + + 1/36 x y z + 4/9 y x - 4/9 y x - 1/36 x y z + 1/9 y x z + + 2 3 4 3 3 4 3 + - 1/36 y x z - 1/144 y x z , COEFF(2, -1, 0) = - 1/18 y x + + 2 4 4 3 4 3 4 2 4 4 4 + - 1/72 y x z + 1/576 x y z + 5/288 x y z - 1/576 x y z + + 3 4 4 3 2 4 2 3 4 2 + - 1/288 x y z - 1/576 y x z + 5/72 z y x + 5/144 x y z + + 3 4 3 4 2 4 4 4 4 + - 1/288 y x z - 1/72 x y + 1/18 y x + 1/576 x y z + 1/288 x y z + + 2 2 2 3 2 3 3 2 3 2 2 + + 5/144 y x z + 5/288 y x z - 5/288 y x z + 5/576 y x z + + 3 2 3 3 2 3 3 4 + - 1/72 y x + 1/18 y x - 1/144 y x + 1/72 y x - 1/36 x y + + 2 2 3 4 4 2 4 2 4 3 2 + - 5/72 z y x + 5/576 x y z + 1/36 x y - 5/576 x y z + + 4 4 4 2 2 4 3 2 4 4 + - 1/144 x y - 5/144 x y z + 1/144 x y + 1/144 x y + 1/72 x y + + 4 2 2 2 4 2 2 2 + - 5/288 x y z - 1/18 y x - 5/576 x y z + 5/72 y x z + + 2 2 2 4 2 4 3 4 + - 5/144 y x z - 5/72 y x z + 1/72 y x z + 1/144 y x z - 1/72 y x z + + 4 4 2 2 2 4 2 4 2 2 4 + - 1/144 x y z - 1/36 y x + 1/36 y x + 1/144 x y z - 1/144 y x z + + 2 3 4 3 3 4 2 4 + + 1/72 y x z + 1/288 y x z , COEFF(-2, 0, 0) = 1/12 x - 5/192 y x z + + 3 4 2 4 4 4 4 3 4 4 3 4 + + 5/192 x y z + 1/384 x y z + 1/24 x - 1/192 x y z - 1/48 x y + + 2 4 4 4 4 25 2 2 2 3 2 3 + - 1/384 x y z + 1/192 x y z - --- y x z - 1/12 x + 5/48 y x + 384 + + 2 25 2 2 3 4 4 2 4 2 4 4 + - 1/24 x - --- z y x - 5/384 x y z - 5/96 x y + 1/96 x y + 192 + + 25 4 2 2 2 4 4 4 2 2 + + --- x y z - 1/96 x y + 1/48 x y - 5/192 x y z - 5/48 y x + 384 + + 2 4 2 25 2 2 2 4 4 4 2 + + 5/384 x y z + --- y x z - 1/96 x z + 1/48 x z - 5/96 x z + 192 + + 3 4 2 2 2 4 4 3 2 + - 1/48 x z + 5/96 x z - 5/48 x z + 1/96 x z + 5/48 x z + + 2 2 4 2 4 2 2 4 2 3 4 + + 5/96 y x - 5/384 x y z + 5/384 y x z + 5/192 y x z , + + 2 4 3 4 2 4 4 4 + COEFF(-1, 0, 0) = - 2/3 x + 5/24 y x z - 5/96 x y z - 1/96 x y z + + 4 3 4 4 3 4 2 4 4 4 4 + - 1/6 x + 1/96 x y z + 1/24 x y + 1/24 x y z - 1/24 x y z + + 25 2 2 2 3 2 3 2 25 2 2 3 4 4 2 + + -- y x z + 1/6 x - 5/24 y x + 2/3 x + -- z y x + 5/96 x y z + 24 96 + + 4 2 4 4 25 4 2 2 2 4 4 + + 5/24 x y - 1/24 x y - -- x y z + 1/6 x y - 1/6 x y + 96 + + 4 2 2 2 4 2 25 2 2 2 4 + + 5/24 x y z + 5/6 y x - 5/24 x y z - -- y x z + 1/6 x z + 24 + + 4 4 2 3 4 2 2 2 4 4 + - 1/6 x z + 5/24 x z + 1/24 x z - 5/6 x z + 5/6 x z - 1/24 x z + + 3 2 2 2 4 2 4 2 2 4 2 3 4 + - 5/24 x z - 5/6 y x + 5/96 x y z - 5/24 y x z - 5/96 y x z , + + 4 4 4 4 2 4 4 4 + COEFF(0, 0, 0) = 1 + 1/64 x y z + 1/4 x - 5/64 x y z + 1/4 y + + 125 2 2 2 4 2 2 2 4 4 2 + - --- y x z + 1/4 z - 5/4 y - 5/4 z - 5/4 x - 5/64 x y z + 64 + + 4 2 4 4 25 4 2 2 2 4 25 2 4 2 + - 5/16 x y + 1/16 x y + -- x y z - 5/16 x y + -- x y z + 64 64 + + 4 4 2 4 4 2 4 2 25 2 2 + + 1/16 y z - 5/16 x z - 5/16 y z - 5/16 x z + -- x z + 16 + + 4 4 2 4 25 2 2 25 2 2 4 2 4 + + 1/16 x z - 5/16 y z + -- y z + -- y x - 5/64 x y z + 16 16 + + 25 2 2 4 2 4 3 4 2 + + -- y x z , COEFF(1, 0, 0) = 2/3 x - 5/24 y x z + 5/96 x y z + 64 + + 4 4 4 4 3 4 4 3 4 2 4 4 + - 1/96 x y z - 1/6 x - 1/96 x y z - 1/24 x y + 1/24 x y z + + 4 4 25 2 2 2 3 2 3 2 25 2 2 3 + + 1/24 x y z + -- y x z - 1/6 x + 5/24 y x + 2/3 x - -- z y x + 24 96 + + 4 4 2 4 2 4 4 25 4 2 2 2 4 + + 5/96 x y z + 5/24 x y - 1/24 x y - -- x y z + 1/6 x y + 96 + + 4 4 2 2 2 4 2 25 2 2 + + 1/6 x y - 5/24 x y z - 5/6 y x - 5/24 x y z + -- y x z + 24 + + 2 4 4 4 2 3 4 2 2 2 + + 1/6 x z + 1/6 x z + 5/24 x z - 1/24 x z - 5/6 x z - 5/6 x z + + 4 4 3 2 2 2 4 2 4 2 2 4 + - 1/24 x z + 5/24 x z - 5/6 y x + 5/96 x y z - 5/24 y x z + + 2 3 4 2 4 + + 5/96 y x z , COEFF(2, 0, 0) = - 1/12 x + 5/192 y x z + + 3 4 2 4 4 4 4 3 4 4 3 4 + - 5/192 x y z + 1/384 x y z + 1/24 x + 1/192 x y z + 1/48 x y + + 2 4 4 4 4 25 2 2 2 3 2 3 + - 1/384 x y z - 1/192 x y z - --- y x z + 1/12 x - 5/48 y x + 384 + + 2 25 2 2 3 4 4 2 4 2 4 4 + - 1/24 x + --- z y x - 5/384 x y z - 5/96 x y + 1/96 x y + 192 + + 25 4 2 2 2 4 4 4 2 2 + + --- x y z - 1/96 x y - 1/48 x y + 5/192 x y z + 5/48 y x + 384 + + 2 4 2 25 2 2 2 4 4 4 2 + + 5/384 x y z - --- y x z - 1/96 x z - 1/48 x z - 5/96 x z + 192 + + 3 4 2 2 2 4 4 3 2 + + 1/48 x z + 5/96 x z + 5/48 x z + 1/96 x z - 5/48 x z + + 2 2 4 2 4 2 2 4 2 3 4 + + 5/96 y x - 5/384 x y z + 5/384 y x z - 5/192 y x z , + + 3 2 4 4 3 4 + COEFF(-2, 1, 0) = - 1/18 y x + 1/72 y x z - 1/576 x y z + + 3 4 2 4 4 4 3 4 4 3 2 4 + - 5/288 x y z - 1/576 x y z + 1/288 x y z + 1/576 y x z + + 2 3 4 2 3 4 3 4 + + 5/72 z y x - 5/144 x y z - 1/288 y x z + 1/72 x y + 1/18 y x + + 2 4 4 4 4 2 2 2 3 2 + + 1/576 x y z - 1/288 x y z + 5/144 y x z + 5/288 y x z + + 3 3 2 3 2 2 3 2 3 3 2 + - 5/288 y x z - 5/576 y x z - 1/72 y x - 1/18 y x + 1/144 y x + + 3 3 4 2 2 3 4 4 2 4 2 + + 1/72 y x + 1/36 x y + 5/72 z y x + 5/576 x y z + 1/36 x y + + 4 3 2 4 4 4 2 2 4 3 + + 5/576 x y z - 1/144 x y - 5/144 x y z - 1/144 x y + + 2 4 4 4 2 2 2 4 2 + + 1/144 x y - 1/72 x y + 5/288 x y z + 1/18 y x - 5/576 x y z + + 2 2 2 2 2 4 2 4 + - 5/72 y x z + 5/144 y x z - 5/72 y x z + 1/72 y x z - 1/144 y x z + + 3 4 4 4 2 2 2 4 2 4 + - 1/72 y x z + 1/144 x y z - 1/36 y x - 1/36 y x + 1/144 x y z + + 2 2 4 2 3 4 3 3 4 + - 1/144 y x z - 1/72 y x z + 1/288 y x z , COEFF(-1, 1, 0) = + + 3 2 4 4 3 4 3 4 2 4 4 4 + 1/9 y x - 1/9 y x z + 1/144 x y z + 5/144 x y z + 1/144 x y z + + 3 4 4 3 2 4 2 3 4 2 + - 1/144 x y z - 1/36 y x z - 5/36 z y x + 5/36 x y z + + 3 4 3 4 2 4 4 4 4 + + 1/36 y x z - 1/36 x y - 4/9 y x - 1/36 x y z + 1/36 x y z + + 2 2 2 3 2 3 3 2 3 2 2 3 + - 5/9 y x z - 5/36 y x z + 5/144 y x z + 5/36 y x z + 1/9 y x + + 2 3 3 2 3 3 4 2 2 3 + + 1/9 y x - 1/9 y x - 1/36 y x - 1/9 x y - 5/36 z y x + + 4 4 2 4 2 4 3 2 4 4 4 2 2 + - 5/144 x y z - 1/9 x y - 5/144 x y z + 1/36 x y + 5/36 x y z + + 4 3 2 4 4 4 2 2 + + 1/36 x y - 1/9 x y + 1/9 x y - 5/36 x y z - 4/9 y x + + 2 4 2 2 2 2 2 2 4 + + 5/36 x y z + 5/9 y x z - 5/9 y x z + 5/9 y x z - 1/9 y x z + + 2 4 3 4 4 4 2 2 2 + + 1/9 y x z + 1/36 y x z - 1/36 x y z + 4/9 y x + 4/9 y x + + 4 2 4 2 2 4 2 3 4 3 3 4 + - 1/36 x y z + 1/9 y x z + 1/36 y x z - 1/144 y x z , + + 4 3 4 4 4 4 3 2 4 + COEFF(0, 1, 0) = - 1/96 x y z - 1/96 x y z + 2/3 y + 5/96 y x z + + 4 2 2 4 4 4 25 2 2 2 25 3 2 2 + - 5/24 x y z + 5/96 x y z - 1/6 y + -- y x z - -- y x z + 24 96 + + 3 2 3 2 4 4 4 2 4 2 + - 1/6 y + 2/3 y + 5/24 y x + 1/6 x y + 5/96 x y z + 1/6 x y + + 4 3 2 4 4 4 2 2 4 3 2 4 + + 5/96 x y z - 1/24 x y - 5/24 x y z - 1/24 x y + 5/24 x y + + 25 2 4 2 25 2 2 4 3 4 4 4 + - -- x y z + -- y x z + 1/6 y z - 1/24 y z - 1/24 y z + 96 24 + + 3 2 2 4 4 2 2 2 4 + + 5/24 y z - 5/24 y x z + 5/24 y z - 5/6 y z + 1/6 y z + + 4 4 2 2 2 2 2 4 2 4 + + 1/24 x y z - 5/6 y z - 5/6 y x - 5/6 y x + 1/24 x y z + + 2 2 4 3 2 4 + - 5/24 y x z , COEFF(1, 1, 0) = - 1/9 y x + 1/9 y x z + + 4 3 4 3 4 2 4 4 4 3 4 4 + + 1/144 x y z - 5/144 x y z + 1/144 x y z + 1/144 x y z + + 3 2 4 2 3 4 2 3 4 3 4 + - 1/36 y x z + 5/36 z y x + 5/36 x y z - 1/36 y x z + 1/36 x y + + 2 4 4 4 4 2 2 2 3 2 + + 4/9 y x - 1/36 x y z - 1/36 x y z - 5/9 y x z + 5/36 y x z + + 3 3 2 3 2 2 3 2 3 3 2 + - 5/144 y x z + 5/36 y x z - 1/9 y x - 1/9 y x - 1/9 y x + + 3 3 4 2 2 3 4 4 2 4 2 + + 1/36 y x - 1/9 x y + 5/36 z y x - 5/144 x y z - 1/9 x y + + 4 3 2 4 4 4 2 2 4 3 2 4 + - 5/144 x y z + 1/36 x y + 5/36 x y z + 1/36 x y - 1/9 x y + + 4 4 2 2 2 4 2 2 2 + - 1/9 x y + 5/36 x y z + 4/9 y x + 5/36 x y z - 5/9 y x z + + 2 2 2 4 2 4 3 4 + - 5/9 y x z - 5/9 y x z + 1/9 y x z + 1/9 y x z - 1/36 y x z + + 4 4 2 2 2 4 2 4 2 2 4 + - 1/36 x y z + 4/9 y x + 4/9 y x - 1/36 x y z + 1/9 y x z + + 2 3 4 3 3 4 3 + - 1/36 y x z + 1/144 y x z , COEFF(2, 1, 0) = 1/18 y x + + 2 4 4 3 4 3 4 2 4 4 4 + - 1/72 y x z - 1/576 x y z + 5/288 x y z - 1/576 x y z + + 3 4 4 3 2 4 2 3 4 2 + - 1/288 x y z + 1/576 y x z - 5/72 z y x - 5/144 x y z + + 3 4 3 4 2 4 4 4 4 + + 1/288 y x z - 1/72 x y - 1/18 y x + 1/576 x y z + 1/288 x y z + + 2 2 2 3 2 3 3 2 3 2 2 + + 5/144 y x z - 5/288 y x z + 5/288 y x z - 5/576 y x z + + 3 2 3 3 2 3 3 4 + + 1/72 y x + 1/18 y x + 1/144 y x - 1/72 y x + 1/36 x y + + 2 2 3 4 4 2 4 2 4 3 2 + - 5/72 z y x + 5/576 x y z + 1/36 x y + 5/576 x y z + + 4 4 4 2 2 4 3 2 4 4 + - 1/144 x y - 5/144 x y z - 1/144 x y + 1/144 x y + 1/72 x y + + 4 2 2 2 4 2 2 2 + - 5/288 x y z - 1/18 y x - 5/576 x y z + 5/72 y x z + + 2 2 2 4 2 4 3 4 + + 5/144 y x z + 5/72 y x z - 1/72 y x z - 1/144 y x z + 1/72 y x z + + 4 4 2 2 2 4 2 4 2 2 4 + + 1/144 x y z - 1/36 y x - 1/36 y x + 1/144 x y z - 1/144 y x z + + 2 3 4 3 3 4 3 + + 1/72 y x z - 1/288 y x z , COEFF(-2, 2, 0) = 1/144 y x + + 2 4 4 3 4 3 4 2 4 4 4 + - 1/1152 y x z + 1/1152 x y z + 5/1152 x y z + 1/2304 x y z + + 3 4 4 3 2 4 2 3 4 2 + - 1/1152 x y z - 1/1152 y x z - 5/576 z y x + 5/1152 x y z + + 3 4 3 4 2 4 4 + + 1/576 y x z - 1/288 x y - 1/144 y x - 1/2304 x y z + + 4 4 2 2 2 3 2 3 3 2 + + 1/1152 x y z - 5/2304 y x z - 5/576 y x z + 5/576 y x z + + 3 2 2 3 2 3 3 2 3 3 + + 5/1152 y x z + 1/144 y x + 1/288 y x - 1/288 y x - 1/144 y x + + 4 2 2 3 4 4 2 4 2 + - 1/288 x y - 5/1152 z y x - 5/2304 x y z - 1/576 x y + + 4 3 2 4 4 4 2 2 4 3 + - 5/1152 x y z + 1/576 x y + 5/2304 x y z + 1/288 x y + + 2 4 4 4 2 2 2 4 2 + - 1/576 x y + 1/288 x y - 5/1152 x y z - 1/288 y x + 5/2304 x y z + + 2 2 2 2 2 4 + + 5/1152 y x z - 5/1152 y x z + 5/576 y x z - 1/576 y x z + + 2 4 3 4 4 4 2 2 + + 1/1152 y x z + 1/576 y x z - 1/1152 x y z + 1/576 y x + + 2 4 2 4 2 2 4 2 3 4 + + 1/288 y x - 1/2304 x y z + 1/2304 y x z + 1/1152 y x z + + 3 3 4 3 2 4 + - 1/576 y x z , COEFF(-1, 2, 0) = - 1/72 y x + 1/144 y x z + + 4 3 4 3 4 2 4 4 4 3 4 4 + - 1/288 x y z - 5/576 x y z - 1/576 x y z + 1/576 x y z + + 3 2 4 2 3 4 2 3 4 + + 1/72 y x z + 5/288 z y x - 5/288 x y z - 1/72 y x z + + 3 4 2 4 4 4 4 2 2 2 + + 1/144 x y + 1/18 y x + 1/144 x y z - 1/144 x y z + 5/144 y x z + + 3 2 3 3 2 3 2 2 3 2 3 + + 5/72 y x z - 5/288 y x z - 5/72 y x z - 1/18 y x - 1/144 y x + + 3 2 3 3 4 2 2 3 4 4 2 + + 1/18 y x + 1/72 y x + 1/72 x y + 5/576 z y x + 5/576 x y z + + 4 2 4 3 2 4 4 4 2 2 4 3 + + 1/144 x y + 5/288 x y z - 1/144 x y - 5/576 x y z - 1/72 x y + + 2 4 4 4 2 2 2 4 2 + + 1/36 x y - 1/36 x y + 5/144 x y z + 1/36 y x - 5/144 x y z + + 2 2 2 2 2 4 2 4 + - 5/144 y x z + 5/72 y x z - 5/72 y x z + 1/72 y x z - 1/72 y x z + + 3 4 4 4 2 2 2 4 2 4 + - 1/288 y x z + 1/288 x y z - 1/36 y x - 1/18 y x + 1/576 x y z + + 2 2 4 2 3 4 3 3 4 + - 1/144 y x z - 1/576 y x z + 1/288 y x z , COEFF(0, 2, 0) = + + 4 3 4 4 4 4 3 2 4 4 2 + 1/192 x y z + 1/384 x y z - 1/12 y - 5/192 y x z + 5/192 x y z + + 2 4 4 4 25 2 2 2 25 3 2 2 3 + - 5/384 x y z + 1/24 y - --- y x z + --- y x z + 1/12 y + 384 192 + + 2 3 2 4 4 4 2 4 2 + - 1/24 y - 5/48 y x - 1/48 x y - 5/384 x y z - 1/96 x y + + 4 3 2 4 4 4 2 2 4 3 2 4 + - 5/192 x y z + 1/96 x y + 5/384 x y z + 1/48 x y - 5/96 x y + + 25 2 4 2 25 2 2 4 3 4 4 4 + + --- x y z - --- y x z - 1/48 y z + 1/48 y z + 1/96 y z + 384 192 + + 3 2 2 4 4 2 2 2 4 + - 5/48 y z + 5/192 y x z - 5/96 y z + 5/48 y z - 1/96 y z + + 4 4 2 2 2 2 2 4 2 4 + - 1/192 x y z + 5/96 y z + 5/96 y x + 5/48 y x - 1/384 x y z + + 2 2 4 3 2 4 + + 5/384 y x z , COEFF(1, 2, 0) = 1/72 y x - 1/144 y x z + + 4 3 4 3 4 2 4 4 4 3 4 4 + - 1/288 x y z + 5/576 x y z - 1/576 x y z - 1/576 x y z + + 3 2 4 2 3 4 2 3 4 + + 1/72 y x z - 5/288 z y x - 5/288 x y z + 1/72 y x z + + 3 4 2 4 4 4 4 2 2 2 + - 1/144 x y - 1/18 y x + 1/144 x y z + 1/144 x y z + 5/144 y x z + + 3 2 3 3 2 3 2 2 3 2 3 + - 5/72 y x z + 5/288 y x z - 5/72 y x z + 1/18 y x + 1/144 y x + + 3 2 3 3 4 2 2 3 4 4 2 + + 1/18 y x - 1/72 y x + 1/72 x y - 5/576 z y x + 5/576 x y z + + 4 2 4 3 2 4 4 4 2 2 4 3 + + 1/144 x y + 5/288 x y z - 1/144 x y - 5/576 x y z - 1/72 x y + + 2 4 4 4 2 2 2 4 2 + + 1/36 x y + 1/36 x y - 5/144 x y z - 1/36 y x - 5/144 x y z + + 2 2 2 2 2 4 2 4 + + 5/144 y x z + 5/72 y x z + 5/72 y x z - 1/72 y x z - 1/72 y x z + + 3 4 4 4 2 2 2 4 2 4 + + 1/288 y x z + 1/288 x y z - 1/36 y x - 1/18 y x + 1/576 x y z + + 2 2 4 2 3 4 3 3 4 + - 1/144 y x z + 1/576 y x z - 1/288 y x z , COEFF(2, 2, 0) = + + 3 2 4 4 3 4 3 4 2 + - 1/144 y x + 1/1152 y x z + 1/1152 x y z - 5/1152 x y z + + 4 4 4 3 4 4 3 2 4 2 3 + + 1/2304 x y z + 1/1152 x y z - 1/1152 y x z + 5/576 z y x + + 4 2 3 4 3 4 + + 5/1152 x y z - 1/576 y x z + 1/288 x y + 1/144 y x + + 2 4 4 4 4 2 2 2 3 2 + - 1/2304 x y z - 1/1152 x y z - 5/2304 y x z + 5/576 y x z + + 3 3 2 3 2 2 3 2 3 + - 5/576 y x z + 5/1152 y x z - 1/144 y x - 1/288 y x + + 3 2 3 3 4 2 2 3 + - 1/288 y x + 1/144 y x - 1/288 x y + 5/1152 z y x + + 4 4 2 4 2 4 3 2 4 4 + - 5/2304 x y z - 1/576 x y - 5/1152 x y z + 1/576 x y + + 4 2 2 4 3 2 4 4 + + 5/2304 x y z + 1/288 x y - 1/576 x y - 1/288 x y + + 4 2 2 2 4 2 2 2 + + 5/1152 x y z + 1/288 y x + 5/2304 x y z - 5/1152 y x z + + 2 2 2 4 2 4 + - 5/1152 y x z - 5/576 y x z + 1/576 y x z + 1/1152 y x z + + 3 4 4 4 2 2 2 + - 1/576 y x z - 1/1152 x y z + 1/576 y x + 1/288 y x + + 4 2 4 2 2 4 2 3 4 3 3 4 + - 1/2304 x y z + 1/2304 y x z - 1/1152 y x z + 1/576 y x z , + + 2 4 4 3 4 3 4 2 + COEFF(-2, -2, 1) = 1/1728 y x z + 1/1728 x y z - 1/432 x y z + + 4 4 4 4 2 4 3 4 + - 1/3456 x y z + 1/432 x y z - 1/864 x y z - 1/432 x y z + + 4 4 3 3 4 4 3 2 4 + + 1/864 x y z - 1/864 y x z + 1/1728 x y z - 1/1728 y x z + + 3 2 3 4 2 3 4 + - 1/216 z y x - 1/216 z y x + 1/432 x y z + 1/864 y x z + + 2 2 3 2 4 4 4 4 + - 1/432 y x z + 1/1728 y x z + 1/3456 x y z - 1/1728 x y z + + 2 2 2 3 2 2 2 3 4 + + 1/864 y x z - 1/216 y x z - 1/3456 y x z + 1/432 x y z + + 4 2 3 3 3 3 2 2 3 + - 1/864 x y z + 1/864 y x z + 1/216 y x z + 1/1728 y x z + + 3 2 2 2 3 3 4 3 3 + + 1/432 y x z - 1/1728 y x z - 1/432 x y z - 1/216 z y x + + 3 2 3 3 2 + + 1/432 z y x + 1/216 z y x + 1/216 y x z - 1/432 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + + 1/432 z y x + 1/432 z y x + 1/864 x y z - 1/432 x y z + + 3 3 4 2 2 3 3 3 4 3 + + 1/864 y x z - 1/864 x y z - 1/864 y x z - 1/1728 x y z + + 4 2 2 4 2 2 2 2 2 + + 1/432 x y z - 1/864 x y z - 1/432 y x z + 1/864 y x z + + 2 2 2 3 2 3 4 3 3 + - 1/432 y x z + 1/216 y x z - 1/1728 y x z + 1/1728 x y z + + 4 2 3 3 4 3 4 4 3 4 + + 1/3456 x y z + 1/1728 x y z - 1/3456 x y z - 1/864 y x z + + 2 4 3 4 4 4 4 3 + + 1/1728 y x z + 1/864 y x z - 1/1728 x y z - 1/1728 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + + 1/3456 x y z + 1/3456 x y z - 1/3456 y x z - 1/1728 y x z + + 3 3 4 2 4 4 3 4 + - 1/864 y x z , COEFF(-1, -2, 1) = - 1/216 y x z - 1/432 x y z + + 3 4 2 4 4 4 4 2 4 + + 1/216 x y z + 1/864 x y z - 1/54 x y z + 1/54 x y z + + 3 4 4 4 3 3 4 4 + + 1/216 x y z - 1/216 x y z + 1/108 y x z - 1/864 x y z + + 3 2 4 3 2 3 4 2 + + 1/108 y x z + 1/108 z y x + 1/108 z y x - 1/108 x y z + + 3 4 2 2 3 2 4 4 + - 1/108 y x z + 1/54 y x z - 1/216 y x z - 1/216 x y z + + 4 4 2 2 2 3 2 2 2 3 + + 1/216 x y z - 1/54 y x z + 1/27 y x z + 1/216 y x z + + 4 4 2 3 3 3 3 2 + - 1/108 x y z + 1/216 x y z - 1/432 y x z - 1/108 y x z + + 2 3 3 2 2 2 3 3 4 3 + - 1/108 y x z - 1/27 y x z + 1/864 y x z + 1/108 x y z + + 3 3 2 3 3 2 + + 1/27 z y x - 1/27 z y x - 1/108 z y x - 1/27 y x z + 1/27 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + - 1/216 z y x - 1/216 z y x - 1/216 x y z + 1/108 x y z + + 3 3 4 2 2 3 3 3 4 3 + - 1/108 y x z + 1/216 x y z + 1/432 y x z + 1/432 x y z + + 4 2 2 4 2 2 2 2 2 + - 1/54 x y z + 1/54 x y z + 1/54 y x z - 1/54 y x z + + 2 2 2 3 2 3 4 3 3 + + 1/27 y x z - 1/27 y x z + 1/108 y x z - 1/432 x y z + + 4 2 3 3 4 3 4 4 3 4 + - 1/864 x y z - 1/864 x y z + 1/864 x y z + 1/108 y x z + + 2 4 3 4 4 4 4 3 + - 1/108 y x z - 1/432 y x z + 1/432 x y z + 1/216 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + - 1/216 x y z - 1/864 x y z + 1/216 y x z + 1/864 y x z + + 3 3 4 4 3 4 4 4 4 + + 1/432 y x z , COEFF(0, -2, 1) = 1/288 x y z - 1/576 x y z + + 2 4 4 4 3 2 4 4 2 + - 5/144 x y z + 1/144 x y z - 5/288 y x z + 1/72 x y z + + 2 4 4 2 2 2 2 2 3 4 + + 5/576 x y z + 5/144 y x z - 5/576 y x z + 1/72 x y z + + 4 2 2 3 3 2 2 4 3 3 + - 1/144 x y z + 5/288 y x z + 5/72 y x z - 1/72 x y z - 1/18 z y + + 3 2 2 4 4 2 4 3 2 + + 5/72 z y x - 5/72 z y x + 1/144 x y z + 1/18 y z - 1/72 x y z + + 4 2 2 4 3 2 4 2 2 2 + - 1/144 x y z - 1/288 x y z - 5/144 x y z + 5/144 y x z + + 2 2 2 3 2 3 4 3 3 + - 5/72 y x z - 1/36 y z - 5/288 y x z + 1/288 x y z + + 4 2 3 4 4 3 3 2 3 3 3 + + 1/576 x y z - 1/576 x y z - 1/72 y z + 1/144 y z + 1/72 y z + + 4 3 4 4 4 3 2 2 4 + - 1/72 y z + 1/72 y z - 1/144 y z - 1/18 y z + 5/288 y x z + + 4 2 4 2 2 4 4 4 + + 1/36 y z + 1/36 y z + 1/18 y z + 1/144 y z - 1/288 x y z + + 2 2 4 3 2 4 3 4 2 4 + - 1/36 y z - 1/144 y z + 5/576 x y z + 1/576 x y z + + 2 2 4 2 4 4 3 4 + - 5/576 y x z , COEFF(1, -2, 1) = 1/216 y x z - 1/432 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/216 x y z + 1/864 x y z + 1/54 x y z + 1/54 x y z + + 3 4 4 4 3 3 4 4 + - 1/216 x y z - 1/216 x y z - 1/108 y x z + 1/864 x y z + + 3 2 4 3 2 3 4 2 + + 1/108 y x z - 1/108 z y x - 1/108 z y x - 1/108 x y z + + 3 4 2 2 3 2 4 4 + + 1/108 y x z - 1/54 y x z + 1/216 y x z - 1/216 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/216 x y z - 1/54 y x z - 1/27 y x z + 1/216 y x z + + 4 4 2 3 3 3 3 2 + - 1/108 x y z + 1/216 x y z + 1/432 y x z + 1/108 y x z + + 2 3 3 2 2 2 3 3 4 3 + - 1/108 y x z - 1/27 y x z - 1/864 y x z + 1/108 x y z + + 3 3 2 3 3 2 + - 1/27 z y x - 1/27 z y x + 1/108 z y x + 1/27 y x z + 1/27 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + + 1/216 z y x + 1/216 z y x - 1/216 x y z + 1/108 x y z + + 3 3 4 2 2 3 3 3 4 3 + + 1/108 y x z + 1/216 x y z - 1/432 y x z + 1/432 x y z + + 4 2 2 4 2 2 2 2 2 + + 1/54 x y z + 1/54 x y z - 1/54 y x z - 1/54 y x z + + 2 2 2 3 2 3 4 3 3 + + 1/27 y x z + 1/27 y x z + 1/108 y x z - 1/432 x y z + + 4 2 3 3 4 3 4 4 3 4 + - 1/864 x y z + 1/864 x y z + 1/864 x y z - 1/108 y x z + + 2 4 3 4 4 4 4 3 + - 1/108 y x z + 1/432 y x z + 1/432 x y z - 1/216 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + - 1/216 x y z - 1/864 x y z + 1/216 y x z - 1/864 y x z + + 3 3 4 2 4 4 3 4 + - 1/432 y x z , COEFF(2, -2, 1) = - 1/1728 y x z + 1/1728 x y z + + 3 4 2 4 4 4 4 2 4 + + 1/432 x y z - 1/3456 x y z - 1/432 x y z - 1/864 x y z + + 3 4 4 4 3 3 4 4 + + 1/432 x y z + 1/864 x y z + 1/864 y x z - 1/1728 x y z + + 3 2 4 3 2 3 4 2 + - 1/1728 y x z + 1/216 z y x + 1/216 z y x + 1/432 x y z + + 3 4 2 2 3 2 4 4 + - 1/864 y x z + 1/432 y x z - 1/1728 y x z + 1/3456 x y z + + 4 4 2 2 2 3 2 2 2 3 + + 1/1728 x y z + 1/864 y x z + 1/216 y x z - 1/3456 y x z + + 4 4 2 3 3 3 3 2 + + 1/432 x y z - 1/864 x y z - 1/864 y x z - 1/216 y x z + + 2 3 3 2 2 2 3 3 4 3 + + 1/1728 y x z + 1/432 y x z + 1/1728 y x z - 1/432 x y z + + 3 3 2 3 3 + + 1/216 z y x + 1/432 z y x - 1/216 z y x - 1/216 y x z + + 2 2 3 2 2 3 4 4 2 + - 1/432 z y x - 1/432 z y x - 1/432 z y x + 1/864 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + - 1/432 x y z - 1/864 y x z - 1/864 x y z + 1/864 y x z + + 4 3 4 2 2 4 2 2 2 + - 1/1728 x y z - 1/432 x y z - 1/864 x y z + 1/432 y x z + + 2 2 2 2 2 3 2 3 + + 1/864 y x z - 1/432 y x z - 1/216 y x z - 1/1728 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + + 1/1728 x y z + 1/3456 x y z - 1/1728 x y z - 1/3456 x y z + + 4 2 4 3 4 4 4 + + 1/864 y x z + 1/1728 y x z - 1/864 y x z - 1/1728 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + + 1/1728 x y z + 1/3456 x y z + 1/3456 x y z - 1/3456 y x z + + 2 3 4 3 3 4 2 4 + + 1/1728 y x z + 1/864 y x z , COEFF(-2, -1, 1) = - 1/108 y x z + + 4 3 4 3 4 2 4 4 4 4 + - 1/864 x y z + 1/108 x y z + 1/864 x y z - 1/108 x y z + + 2 4 3 4 4 4 3 + + 1/216 x y z + 1/108 x y z - 1/216 x y z + 1/108 y x z + + 3 4 4 3 2 4 3 2 3 + - 1/432 x y z + 1/864 y x z + 1/27 z y x + 1/27 z y x + + 4 2 3 4 2 2 3 + - 1/54 x y z - 1/432 y x z + 1/27 y x z - 1/108 y x z + + 2 4 4 4 4 2 2 2 3 2 + - 1/864 x y z + 1/432 x y z - 1/54 y x z + 1/108 y x z + + 2 2 3 4 4 2 3 3 + + 1/216 y x z - 1/54 x y z + 1/54 x y z - 1/108 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + - 1/108 y x z - 1/216 y x z - 1/216 y x z + 1/108 y x z + + 4 3 3 3 2 3 3 + + 1/216 x y z + 1/108 z y x - 1/216 z y x - 1/108 z y x + + 2 2 3 2 2 3 4 4 2 + - 1/27 y x z + 1/54 z y x - 1/27 z y x - 1/27 z y x - 1/216 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + + 1/216 x y z - 1/432 y x z + 1/54 x y z + 1/432 y x z + + 4 3 4 2 2 4 2 2 2 + + 1/216 x y z - 1/108 x y z + 1/216 x y z + 1/27 y x z + + 2 2 2 2 2 3 2 3 + - 1/54 y x z + 1/54 y x z - 1/27 y x z + 1/864 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + - 1/864 x y z - 1/216 x y z - 1/432 x y z + 1/864 x y z + + 4 2 4 3 4 4 4 + + 1/108 y x z - 1/216 y x z - 1/108 y x z + 1/216 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + + 1/432 x y z - 1/864 x y z - 1/216 x y z + 1/216 y x z + + 2 3 4 3 3 4 2 4 + + 1/108 y x z + 1/432 y x z , COEFF(-1, -1, 1) = 2/27 y x z + + 4 3 4 3 4 2 4 4 4 4 + + 1/216 x y z - 1/54 x y z - 1/216 x y z + 2/27 x y z + + 2 4 3 4 4 4 3 + - 2/27 x y z - 1/54 x y z + 1/54 x y z - 2/27 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/216 x y z - 1/54 y x z - 2/27 z y x - 2/27 z y x + + 4 2 3 4 2 2 3 2 4 4 + + 2/27 x y z + 1/54 y x z - 8/27 y x z + 2/27 y x z + 1/54 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/54 x y z + 8/27 y x z - 2/27 y x z - 2/27 y x z + + 4 4 2 3 3 3 3 2 2 3 + + 2/27 x y z - 2/27 x y z + 1/54 y x z + 1/54 y x z + 2/27 y x z + + 3 2 2 2 3 3 4 3 3 + + 2/27 y x z - 1/54 y x z - 1/54 x y z - 2/27 z y x + + 3 2 3 3 2 2 3 + + 2/27 z y x + 1/54 z y x + 8/27 y x z - 8/27 z y x + 2/27 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + + 2/27 z y x + 1/54 x y z - 1/54 x y z + 1/54 y x z + + 4 2 2 3 3 3 4 3 4 2 + - 2/27 x y z - 1/216 y x z - 1/54 x y z + 2/27 x y z + + 2 4 2 2 2 2 2 2 2 2 + - 2/27 x y z - 8/27 y x z + 8/27 y x z - 8/27 y x z + 8/27 y x z + + 3 2 3 4 3 3 4 2 3 3 4 3 + - 1/54 y x z + 1/216 x y z + 1/54 x y z + 1/216 x y z + + 4 4 3 4 2 4 3 4 + - 1/216 x y z - 2/27 y x z + 2/27 y x z + 1/54 y x z + + 4 4 4 3 2 4 3 4 2 4 + - 1/54 x y z - 1/54 x y z + 1/54 x y z + 1/54 x y z + + 2 2 4 2 3 4 3 3 4 + - 2/27 y x z - 1/54 y x z - 1/216 y x z , COEFF(0, -1, 1) = + + 4 3 4 4 4 4 2 4 4 4 + - 1/144 x y z + 1/144 x y z + 5/36 x y z - 1/36 x y z + + 3 2 4 4 2 2 4 4 2 2 2 + + 5/144 y x z - 1/9 x y z - 5/144 x y z - 5/9 y x z + + 2 2 3 4 4 2 2 3 3 2 2 + + 5/36 y x z - 1/9 x y z + 1/9 x y z - 5/36 y x z - 5/36 y x z + + 4 3 3 3 2 2 4 4 2 + + 1/36 x y z + 1/9 z y - 5/36 z y x + 5/9 z y x - 1/36 x y z + + 4 3 2 4 2 2 4 3 2 4 2 + - 4/9 y z + 1/36 x y z + 1/9 x y z + 1/36 x y z + 5/36 x y z + + 2 2 2 2 2 3 2 3 4 3 3 + - 5/9 y x z + 5/9 y x z + 4/9 y z + 5/144 y x z - 1/144 x y z + + 4 2 3 4 4 3 3 2 3 3 3 + - 1/36 x y z + 1/144 x y z + 1/9 y z - 1/9 y z - 1/36 y z + + 4 3 4 4 4 3 2 2 4 + + 1/9 y z - 1/36 y z + 1/36 y z + 1/9 y z - 5/36 y x z + + 4 2 4 2 2 4 4 4 2 2 + - 1/9 y z - 1/9 y z - 4/9 y z - 1/9 y z + 1/36 x y z + 4/9 y z + + 4 3 2 4 3 4 2 4 2 2 4 + + 1/36 y z - 5/144 x y z - 1/36 x y z + 5/36 y x z , + + 2 4 4 3 4 3 4 2 + COEFF(1, -1, 1) = - 2/27 y x z + 1/216 x y z + 1/54 x y z + + 4 4 4 4 2 4 3 4 + - 1/216 x y z - 2/27 x y z - 2/27 x y z + 1/54 x y z + + 4 4 3 3 4 4 3 2 4 + + 1/54 x y z + 2/27 y x z - 1/216 x y z - 1/54 y x z + + 3 2 3 4 2 3 4 2 + + 2/27 z y x + 2/27 z y x + 2/27 x y z - 1/54 y x z + 8/27 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 2/27 y x z + 1/54 x y z + 1/54 x y z + 8/27 y x z + + 3 2 2 2 3 4 4 2 3 3 + + 2/27 y x z - 2/27 y x z + 2/27 x y z - 2/27 x y z - 1/54 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + - 1/54 y x z + 2/27 y x z + 2/27 y x z + 1/54 y x z + + 4 3 3 3 2 3 3 + - 1/54 x y z + 2/27 z y x + 2/27 z y x - 1/54 z y x - 8/27 y x z + + 2 2 3 2 2 3 4 4 2 + - 8/27 z y x - 2/27 z y x - 2/27 z y x + 1/54 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + - 1/54 x y z - 1/54 y x z - 2/27 x y z + 1/216 y x z + + 4 3 4 2 2 4 2 2 2 + - 1/54 x y z - 2/27 x y z - 2/27 x y z + 8/27 y x z + + 2 2 2 2 2 3 2 3 + + 8/27 y x z - 8/27 y x z - 8/27 y x z - 1/54 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + + 1/216 x y z + 1/54 x y z - 1/216 x y z - 1/216 x y z + + 4 2 4 3 4 4 4 4 3 + + 2/27 y x z + 2/27 y x z - 1/54 y x z - 1/54 x y z + 1/54 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + + 1/54 x y z + 1/54 x y z - 2/27 y x z + 1/54 y x z + + 3 3 4 2 4 4 3 4 + + 1/216 y x z , COEFF(2, -1, 1) = 1/108 y x z - 1/864 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/108 x y z + 1/864 x y z + 1/108 x y z + 1/216 x y z + + 3 4 4 4 3 3 4 4 + - 1/108 x y z - 1/216 x y z - 1/108 y x z + 1/432 x y z + + 3 2 4 3 2 3 4 2 + + 1/864 y x z - 1/27 z y x - 1/27 z y x - 1/54 x y z + + 3 4 2 2 3 2 4 4 + + 1/432 y x z - 1/27 y x z + 1/108 y x z - 1/864 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/432 x y z - 1/54 y x z - 1/108 y x z + 1/216 y x z + + 4 4 2 3 3 3 3 2 + - 1/54 x y z + 1/54 x y z + 1/108 y x z + 1/108 y x z + + 2 3 3 2 2 2 3 3 4 3 + - 1/216 y x z - 1/216 y x z - 1/108 y x z + 1/216 x y z + + 3 3 2 3 3 2 + - 1/108 z y x - 1/216 z y x + 1/108 z y x + 1/27 y x z + 1/54 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + + 1/27 z y x + 1/27 z y x - 1/216 x y z + 1/216 x y z + + 3 3 4 2 2 3 3 3 4 3 + + 1/432 y x z + 1/54 x y z - 1/432 y x z + 1/216 x y z + + 4 2 2 4 2 2 2 2 2 + + 1/108 x y z + 1/216 x y z - 1/27 y x z - 1/54 y x z + + 2 2 2 3 2 3 4 3 3 + + 1/54 y x z + 1/27 y x z + 1/864 y x z - 1/864 x y z + + 4 2 3 3 4 3 4 4 3 4 + - 1/216 x y z + 1/432 x y z + 1/864 x y z - 1/108 y x z + + 2 4 3 4 4 4 4 3 + - 1/216 y x z + 1/108 y x z + 1/216 x y z - 1/432 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + - 1/864 x y z - 1/216 x y z + 1/216 y x z - 1/108 y x z + + 3 3 4 2 4 3 4 2 + - 1/432 y x z , COEFF(-2, 0, 1) = 5/288 y x z - 1/72 x y z + + 4 4 4 4 2 4 3 4 + - 1/576 x y z + 1/72 x y z - 1/144 x y z - 1/72 x y z + + 4 4 3 4 4 2 2 3 + + 1/144 x y z + 1/288 x y z - 5/72 y x z + 5/288 y x z + + 2 4 4 4 4 2 2 2 2 2 3 + + 1/576 x y z - 1/288 x y z + 5/144 y x z - 5/576 y x z + + 4 2 3 2 3 3 2 3 + - 5/144 x y z - 1/18 z x - 5/288 y x z + 5/72 z y x + + 2 2 3 4 4 2 4 2 2 4 2 + + 5/72 z y x + 1/144 x y z - 5/144 x y z + 1/72 x y z + + 2 4 2 2 2 2 2 + - 1/144 x y z - 5/72 y x z + 5/144 y x z + 1/18 x z + + 4 2 3 2 3 4 3 4 4 3 + + 5/576 x y z - 1/36 x z + 1/288 x y z - 1/576 x y z + + 3 3 2 3 4 3 2 4 3 + + 1/72 x z + 1/144 x z - 1/144 x z + 1/144 x z - 1/72 x z + + 4 4 4 2 3 4 2 2 2 + - 1/72 x z + 1/36 x z + 1/36 x z + 1/72 x z - 1/36 x z + 1/18 x z + + 4 4 3 2 4 3 2 4 3 + - 1/144 x z - 1/18 x z - 1/288 x y z + 1/576 x y z + + 4 2 4 2 2 4 2 3 4 + + 5/576 x y z - 5/576 y x z - 5/288 y x z , COEFF(-1, 0, 1) = + + 2 4 3 4 2 4 4 4 4 2 4 + - 5/36 y x z + 1/36 x y z + 1/144 x y z - 1/9 x y z + 1/9 x y z + + 3 4 4 4 3 4 4 2 2 3 + + 1/36 x y z - 1/36 x y z - 1/144 x y z + 5/9 y x z - 5/36 y x z + + 2 4 4 4 4 2 2 2 2 2 3 + - 1/36 x y z + 1/36 x y z - 5/9 y x z + 5/36 y x z + + 4 2 3 2 3 3 2 3 2 2 3 + + 5/36 x y z + 1/9 z x + 5/144 y x z - 5/36 z y x - 5/36 z y x + + 4 4 2 4 2 2 4 2 2 4 2 2 2 + - 1/36 x y z + 5/36 x y z - 1/9 x y z + 1/9 x y z + 5/9 y x z + + 2 2 4 2 3 2 3 4 3 + - 5/9 y x z - 4/9 x z - 5/144 x y z + 4/9 x z - 1/144 x y z + + 4 4 3 3 3 2 3 4 3 2 4 + + 1/144 x y z - 1/36 x z - 1/9 x z + 1/36 x z - 1/9 x z + + 3 4 4 4 2 3 4 2 2 + + 1/9 x z + 1/9 x z - 1/9 x z - 1/9 x z - 1/36 x z + 4/9 x z + + 2 4 4 3 2 4 3 2 4 3 + - 4/9 x z + 1/36 x z + 1/9 x z + 1/36 x y z - 1/36 x y z + + 4 2 4 2 2 4 2 3 4 + - 5/144 x y z + 5/36 y x z + 5/144 y x z , COEFF(0, 0, 1) = + + 4 4 4 2 4 4 4 2 4 4 + - 1/96 x y z - 5/24 x y z + 1/24 x y z + 2/3 z + 5/96 x y z + + 25 2 2 2 25 2 2 3 4 2 4 3 2 + + -- y x z - -- y x z - 5/24 x y z - 1/6 z - 1/6 z + 2/3 z + 24 96 + + 4 4 2 4 2 2 2 4 2 25 2 2 2 + + 1/24 x y z - 5/24 x y z - 5/24 x y z + -- y x z - 5/6 y z + 24 + + 4 2 3 2 4 4 3 2 3 2 3 + + 5/96 x y z - 5/6 x z - 1/96 x y z + 5/24 y z + 5/24 x z + + 4 3 4 4 2 4 4 2 4 4 + - 1/24 x z - 1/24 y z + 5/24 x z + 1/6 y z + 1/6 y z + 1/6 x z + + 4 2 2 2 4 4 2 4 2 2 4 3 + + 1/6 x z - 5/6 x z - 1/24 x z + 5/24 y z - 5/6 y z - 1/24 y z + + 2 4 3 4 2 4 25 2 2 4 + + 5/96 x y z + 5/96 x y z - -- y x z , COEFF(1, 0, 1) = + 96 + + 2 4 3 4 2 4 4 4 4 2 4 + 5/36 y x z - 1/36 x y z + 1/144 x y z + 1/9 x y z + 1/9 x y z + + 3 4 4 4 3 4 4 2 2 3 + - 1/36 x y z - 1/36 x y z + 1/144 x y z - 5/9 y x z + 5/36 y x z + + 2 4 4 4 4 2 2 2 2 2 3 + - 1/36 x y z - 1/36 x y z - 5/9 y x z + 5/36 y x z + + 4 2 3 2 3 3 2 3 2 2 3 + + 5/36 x y z - 1/9 z x - 5/144 y x z + 5/36 z y x + 5/36 z y x + + 4 4 2 4 2 2 4 2 2 4 2 2 2 + - 1/36 x y z + 5/36 x y z + 1/9 x y z + 1/9 x y z - 5/9 y x z + + 2 2 4 2 3 2 3 4 3 + - 5/9 y x z + 4/9 x z - 5/144 x y z + 4/9 x z + 1/144 x y z + + 4 4 3 3 3 2 3 4 3 2 4 + + 1/144 x y z + 1/36 x z - 1/9 x z + 1/36 x z - 1/9 x z + + 3 4 4 4 2 3 4 2 2 + - 1/9 x z - 1/9 x z - 1/9 x z - 1/9 x z + 1/36 x z + 4/9 x z + + 2 4 4 3 2 4 3 2 4 3 + + 4/9 x z + 1/36 x z - 1/9 x z - 1/36 x y z - 1/36 x y z + + 4 2 4 2 2 4 2 3 4 + - 5/144 x y z + 5/36 y x z - 5/144 y x z , COEFF(2, 0, 1) = + + 2 4 3 4 2 4 4 4 4 + - 5/288 y x z + 1/72 x y z - 1/576 x y z - 1/72 x y z + + 2 4 3 4 4 4 3 4 4 + - 1/144 x y z + 1/72 x y z + 1/144 x y z - 1/288 x y z + + 2 2 3 2 4 4 4 4 + + 5/72 y x z - 5/288 y x z + 1/576 x y z + 1/288 x y z + + 2 2 2 2 2 3 4 2 3 + + 5/144 y x z - 5/576 y x z - 5/144 x y z + 1/18 z x + + 2 3 3 2 3 2 2 3 4 4 2 + + 5/288 y x z - 5/72 z y x - 5/72 z y x + 1/144 x y z + + 4 2 2 4 2 2 4 2 2 2 + - 5/144 x y z - 1/72 x y z - 1/144 x y z + 5/72 y x z + + 2 2 4 2 3 2 3 4 3 + + 5/144 y x z - 1/18 x z + 5/576 x y z - 1/36 x z - 1/288 x y z + + 4 4 3 3 3 2 3 4 3 2 4 + - 1/576 x y z - 1/72 x z + 1/144 x z - 1/144 x z + 1/144 x z + + 3 4 4 4 2 3 4 2 2 + + 1/72 x z + 1/72 x z + 1/36 x z + 1/36 x z - 1/72 x z - 1/36 x z + + 2 4 4 3 2 4 3 2 4 3 + - 1/18 x z - 1/144 x z + 1/18 x z + 1/288 x y z + 1/576 x y z + + 4 2 4 2 2 4 2 3 4 + + 5/576 x y z - 5/576 y x z + 5/288 y x z , COEFF(-2, 1, 1) = + + 2 4 4 3 4 3 4 2 4 4 4 + - 1/108 y x z + 1/864 x y z + 1/108 x y z + 1/864 x y z + + 4 2 4 3 4 4 4 + - 1/108 x y z + 1/216 x y z + 1/108 x y z - 1/216 x y z + + 3 3 4 4 3 2 4 3 + - 1/108 y x z - 1/432 x y z - 1/864 y x z - 1/27 z y x + + 2 3 4 2 3 4 2 + - 1/27 z y x + 1/54 x y z + 1/432 y x z + 1/27 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/108 y x z - 1/864 x y z + 1/432 x y z - 1/54 y x z + + 3 2 2 2 3 4 4 2 + - 1/108 y x z + 1/216 y x z + 1/54 x y z + 1/54 x y z + + 3 3 3 3 2 2 3 3 2 2 + + 1/108 y x z + 1/108 y x z + 1/216 y x z + 1/216 y x z + + 2 3 3 4 3 3 3 2 + + 1/108 y x z - 1/216 x y z - 1/108 z y x + 1/216 z y x + + 3 3 2 2 3 2 2 3 + + 1/108 z y x + 1/27 y x z - 1/54 z y x - 1/27 z y x - 1/27 z y x + + 4 4 2 4 3 2 3 3 4 2 2 + - 1/216 x y z - 1/216 x y z + 1/432 y x z + 1/54 x y z + + 3 3 3 4 3 4 2 2 4 2 + - 1/432 y x z - 1/216 x y z - 1/108 x y z + 1/216 x y z + + 2 2 2 2 2 2 2 + + 1/27 y x z - 1/54 y x z - 1/54 y x z + 1/27 y x z + + 3 2 3 4 3 3 4 2 3 3 4 3 + - 1/864 y x z + 1/864 x y z - 1/216 x y z - 1/432 x y z + + 4 4 3 4 2 4 3 4 + + 1/864 x y z - 1/108 y x z + 1/216 y x z + 1/108 y x z + + 4 4 4 3 2 4 3 4 2 4 + - 1/216 x y z + 1/432 x y z - 1/864 x y z - 1/216 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/216 y x z + 1/108 y x z - 1/432 y x z , COEFF(-1, 1, 1) = + + 2 4 4 3 4 3 4 2 4 4 4 + 2/27 y x z - 1/216 x y z - 1/54 x y z - 1/216 x y z + + 4 2 4 3 4 4 4 3 + + 2/27 x y z - 2/27 x y z - 1/54 x y z + 1/54 x y z + 2/27 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/216 x y z + 1/54 y x z + 2/27 z y x + 2/27 z y x + + 4 2 3 4 2 2 3 2 4 4 + - 2/27 x y z - 1/54 y x z - 8/27 y x z + 2/27 y x z + 1/54 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/54 x y z + 8/27 y x z + 2/27 y x z - 2/27 y x z + + 4 4 2 3 3 3 3 2 2 3 + - 2/27 x y z - 2/27 x y z - 1/54 y x z - 1/54 y x z - 2/27 y x z + + 3 2 2 2 3 3 4 3 3 + - 2/27 y x z - 1/54 y x z + 1/54 x y z + 2/27 z y x + + 3 2 3 3 2 2 3 + - 2/27 z y x - 1/54 z y x - 8/27 y x z + 8/27 z y x + 2/27 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + + 2/27 z y x + 1/54 x y z + 1/54 x y z - 1/54 y x z + + 4 2 2 3 3 3 4 3 4 2 + - 2/27 x y z + 1/216 y x z + 1/54 x y z + 2/27 x y z + + 2 4 2 2 2 2 2 2 2 2 + - 2/27 x y z - 8/27 y x z + 8/27 y x z + 8/27 y x z - 8/27 y x z + + 3 2 3 4 3 3 4 2 3 3 4 3 + + 1/54 y x z - 1/216 x y z + 1/54 x y z + 1/216 x y z + + 4 4 3 4 2 4 3 4 + - 1/216 x y z + 2/27 y x z - 2/27 y x z - 1/54 y x z + + 4 4 4 3 2 4 3 4 2 4 + + 1/54 x y z - 1/54 x y z + 1/54 x y z + 1/54 x y z + + 2 2 4 2 3 4 3 3 4 + - 2/27 y x z - 1/54 y x z + 1/216 y x z , COEFF(0, 1, 1) = + + 4 3 4 4 4 4 2 4 4 4 + 1/144 x y z + 1/144 x y z + 5/36 x y z - 1/36 x y z + + 3 2 4 4 2 2 4 4 2 2 2 + - 5/144 y x z + 1/9 x y z - 5/144 x y z - 5/9 y x z + + 2 2 3 4 4 2 2 3 3 2 2 + + 5/36 y x z + 1/9 x y z + 1/9 x y z + 5/36 y x z + 5/36 y x z + + 4 3 3 3 2 2 4 4 2 + - 1/36 x y z - 1/9 z y + 5/36 z y x - 5/9 z y x - 1/36 x y z + + 4 3 2 4 2 2 4 3 2 4 2 + + 4/9 y z - 1/36 x y z + 1/9 x y z - 1/36 x y z + 5/36 x y z + + 2 2 2 2 2 3 2 3 4 3 3 + - 5/9 y x z - 5/9 y x z + 4/9 y z - 5/144 y x z + 1/144 x y z + + 4 2 3 4 4 3 3 2 3 3 3 + - 1/36 x y z + 1/144 x y z - 1/9 y z - 1/9 y z + 1/36 y z + + 4 3 4 4 4 3 2 2 4 + - 1/9 y z + 1/36 y z + 1/36 y z - 1/9 y z + 5/36 y x z + + 4 2 4 2 2 4 4 4 2 2 + - 1/9 y z - 1/9 y z + 4/9 y z - 1/9 y z - 1/36 x y z + 4/9 y z + + 4 3 2 4 3 4 2 4 2 2 4 + + 1/36 y z - 5/144 x y z - 1/36 x y z + 5/36 y x z , + + 2 4 4 3 4 3 4 2 + COEFF(1, 1, 1) = - 2/27 y x z - 1/216 x y z + 1/54 x y z + + 4 4 4 4 2 4 3 4 + - 1/216 x y z - 2/27 x y z - 2/27 x y z + 1/54 x y z + + 4 4 3 3 4 4 3 2 4 + + 1/54 x y z - 2/27 y x z - 1/216 x y z + 1/54 y x z + + 3 2 3 4 2 3 4 2 + - 2/27 z y x - 2/27 z y x - 2/27 x y z + 1/54 y x z + 8/27 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 2/27 y x z + 1/54 x y z + 1/54 x y z + 8/27 y x z + + 3 2 2 2 3 4 4 2 3 3 + - 2/27 y x z - 2/27 y x z - 2/27 x y z - 2/27 x y z + 1/54 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + + 1/54 y x z - 2/27 y x z - 2/27 y x z + 1/54 y x z + + 4 3 3 3 2 3 3 + + 1/54 x y z - 2/27 z y x - 2/27 z y x + 1/54 z y x + 8/27 y x z + + 2 2 3 2 2 3 4 4 2 + + 8/27 z y x - 2/27 z y x - 2/27 z y x + 1/54 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + + 1/54 x y z + 1/54 y x z - 2/27 x y z - 1/216 y x z + + 4 3 4 2 2 4 2 2 2 + + 1/54 x y z - 2/27 x y z - 2/27 x y z + 8/27 y x z + + 2 2 2 2 2 3 2 3 + + 8/27 y x z + 8/27 y x z + 8/27 y x z + 1/54 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + - 1/216 x y z + 1/54 x y z - 1/216 x y z - 1/216 x y z + + 4 2 4 3 4 4 4 4 3 + - 2/27 y x z - 2/27 y x z + 1/54 y x z + 1/54 x y z + 1/54 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + + 1/54 x y z + 1/54 x y z - 2/27 y x z + 1/54 y x z + + 3 3 4 2 4 4 3 4 + - 1/216 y x z , COEFF(2, 1, 1) = 1/108 y x z + 1/864 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/108 x y z + 1/864 x y z + 1/108 x y z + 1/216 x y z + + 3 4 4 4 3 3 4 4 + - 1/108 x y z - 1/216 x y z + 1/108 y x z + 1/432 x y z + + 3 2 4 3 2 3 4 2 + - 1/864 y x z + 1/27 z y x + 1/27 z y x + 1/54 x y z + + 3 4 2 2 3 2 4 4 + - 1/432 y x z - 1/27 y x z + 1/108 y x z - 1/864 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/432 x y z - 1/54 y x z + 1/108 y x z + 1/216 y x z + + 4 4 2 3 3 3 3 2 + + 1/54 x y z + 1/54 x y z - 1/108 y x z - 1/108 y x z + + 2 3 3 2 2 2 3 3 4 3 + + 1/216 y x z + 1/216 y x z - 1/108 y x z - 1/216 x y z + + 3 3 2 3 3 2 + + 1/108 z y x + 1/216 z y x - 1/108 z y x - 1/27 y x z - 1/54 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + + 1/27 z y x + 1/27 z y x - 1/216 x y z - 1/216 x y z + + 3 3 4 2 2 3 3 3 4 3 + - 1/432 y x z + 1/54 x y z + 1/432 y x z - 1/216 x y z + + 4 2 2 4 2 2 2 2 2 + + 1/108 x y z + 1/216 x y z - 1/27 y x z - 1/54 y x z + + 2 2 2 3 2 3 4 3 3 + - 1/54 y x z - 1/27 y x z - 1/864 y x z + 1/864 x y z + + 4 2 3 3 4 3 4 4 3 4 + - 1/216 x y z + 1/432 x y z + 1/864 x y z + 1/108 y x z + + 2 4 3 4 4 4 4 3 + + 1/216 y x z - 1/108 y x z - 1/216 x y z - 1/432 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + - 1/864 x y z - 1/216 x y z + 1/216 y x z - 1/108 y x z + + 3 3 4 2 4 4 3 4 + + 1/432 y x z , COEFF(-2, 2, 1) = 1/1728 y x z - 1/1728 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/432 x y z - 1/3456 x y z + 1/432 x y z - 1/864 x y z + + 3 4 4 4 3 3 4 4 + - 1/432 x y z + 1/864 x y z + 1/864 y x z + 1/1728 x y z + + 3 2 4 3 2 3 4 2 + + 1/1728 y x z + 1/216 z y x + 1/216 z y x - 1/432 x y z + + 3 4 2 2 3 2 4 4 + - 1/864 y x z - 1/432 y x z + 1/1728 y x z + 1/3456 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/1728 x y z + 1/864 y x z + 1/216 y x z - 1/3456 y x z + + 4 4 2 3 3 3 3 2 + - 1/432 x y z - 1/864 x y z - 1/864 y x z - 1/216 y x z + + 2 3 3 2 2 2 3 3 4 3 + - 1/1728 y x z - 1/432 y x z - 1/1728 y x z + 1/432 x y z + + 3 3 2 3 3 + + 1/216 z y x - 1/432 z y x - 1/216 z y x - 1/216 y x z + + 2 2 3 2 2 3 4 4 2 + + 1/432 z y x + 1/432 z y x + 1/432 z y x + 1/864 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + + 1/432 x y z - 1/864 y x z - 1/864 x y z + 1/864 y x z + + 4 3 4 2 2 4 2 2 2 + + 1/1728 x y z + 1/432 x y z - 1/864 x y z - 1/432 y x z + + 2 2 2 2 2 3 2 3 + + 1/864 y x z + 1/432 y x z - 1/216 y x z + 1/1728 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + - 1/1728 x y z + 1/3456 x y z + 1/1728 x y z - 1/3456 x y z + + 4 2 4 3 4 4 4 + + 1/864 y x z - 1/1728 y x z - 1/864 y x z + 1/1728 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + - 1/1728 x y z + 1/3456 x y z + 1/3456 x y z - 1/3456 y x z + + 2 3 4 3 3 4 2 4 + - 1/1728 y x z + 1/864 y x z , COEFF(-1, 2, 1) = - 1/216 y x z + + 4 3 4 3 4 2 4 4 4 4 + + 1/432 x y z + 1/216 x y z + 1/864 x y z - 1/54 x y z + + 2 4 3 4 4 4 3 + + 1/54 x y z + 1/216 x y z - 1/216 x y z - 1/108 y x z + + 3 4 4 3 2 4 3 2 3 + - 1/864 x y z - 1/108 y x z - 1/108 z y x - 1/108 z y x + + 4 2 3 4 2 2 3 + + 1/108 x y z + 1/108 y x z + 1/54 y x z - 1/216 y x z + + 2 4 4 4 4 2 2 2 3 2 + - 1/216 x y z + 1/216 x y z - 1/54 y x z - 1/27 y x z + + 2 2 3 4 4 2 3 3 + + 1/216 y x z + 1/108 x y z + 1/216 x y z + 1/432 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + + 1/108 y x z + 1/108 y x z + 1/27 y x z + 1/864 y x z + + 4 3 3 3 2 3 3 + - 1/108 x y z - 1/27 z y x + 1/27 z y x + 1/108 z y x + 1/27 y x z + + 2 2 3 2 2 3 4 4 2 + - 1/27 z y x - 1/216 z y x - 1/216 z y x - 1/216 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + - 1/108 x y z + 1/108 y x z + 1/216 x y z - 1/432 y x z + + 4 3 4 2 2 4 2 2 2 + - 1/432 x y z - 1/54 x y z + 1/54 x y z + 1/54 y x z + + 2 2 2 2 2 3 2 3 + - 1/54 y x z - 1/27 y x z + 1/27 y x z - 1/108 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + + 1/432 x y z - 1/864 x y z - 1/864 x y z + 1/864 x y z + + 4 2 4 3 4 4 4 + - 1/108 y x z + 1/108 y x z + 1/432 y x z - 1/432 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + + 1/216 x y z - 1/216 x y z - 1/864 x y z + 1/216 y x z + + 2 3 4 3 3 4 4 3 4 + + 1/864 y x z - 1/432 y x z , COEFF(0, 2, 1) = - 1/288 x y z + + 4 4 4 2 4 4 4 3 2 4 + - 1/576 x y z - 5/144 x y z + 1/144 x y z + 5/288 y x z + + 4 2 2 4 4 2 2 2 2 2 3 + - 1/72 x y z + 5/576 x y z + 5/144 y x z - 5/576 y x z + + 4 4 2 2 3 3 2 2 + - 1/72 x y z - 1/144 x y z - 5/288 y x z - 5/72 y x z + + 4 3 3 3 2 2 4 4 2 + + 1/72 x y z + 1/18 z y - 5/72 z y x + 5/72 z y x + 1/144 x y z + + 4 3 2 4 2 2 4 3 + - 1/18 y z + 1/72 x y z - 1/144 x y z + 1/288 x y z + + 2 4 2 2 2 2 2 2 + - 5/144 x y z + 5/144 y x z + 5/72 y x z - 1/36 y z + + 3 2 3 4 3 3 4 2 3 4 4 3 + + 5/288 y x z - 1/288 x y z + 1/576 x y z - 1/576 x y z + + 3 2 3 3 3 4 3 4 + + 1/72 y z + 1/144 y z - 1/72 y z + 1/72 y z - 1/72 y z + + 4 4 3 2 2 4 4 2 4 + - 1/144 y z + 1/18 y z - 5/288 y x z + 1/36 y z + 1/36 y z + + 2 2 4 4 4 2 2 4 3 + - 1/18 y z + 1/144 y z + 1/288 x y z - 1/36 y z - 1/144 y z + + 2 4 3 4 2 4 2 2 4 + + 5/576 x y z + 1/576 x y z - 5/576 y x z , COEFF(1, 2, 1) = + + 2 4 4 3 4 3 4 2 4 4 4 + 1/216 y x z + 1/432 x y z - 1/216 x y z + 1/864 x y z + + 4 2 4 3 4 4 4 + + 1/54 x y z + 1/54 x y z - 1/216 x y z - 1/216 x y z + + 3 3 4 4 3 2 4 3 + + 1/108 y x z + 1/864 x y z - 1/108 y x z + 1/108 z y x + + 2 3 4 2 3 4 2 + + 1/108 z y x + 1/108 x y z - 1/108 y x z - 1/54 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/216 y x z - 1/216 x y z - 1/216 x y z - 1/54 y x z + + 3 2 2 2 3 4 4 2 + + 1/27 y x z + 1/216 y x z + 1/108 x y z + 1/216 x y z + + 3 3 3 3 2 2 3 3 2 2 + - 1/432 y x z - 1/108 y x z + 1/108 y x z + 1/27 y x z + + 2 3 3 4 3 3 3 2 + - 1/864 y x z - 1/108 x y z + 1/27 z y x + 1/27 z y x + + 3 3 2 2 3 + - 1/108 z y x - 1/27 y x z - 1/27 z y x + 1/216 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + + 1/216 z y x - 1/216 x y z - 1/108 x y z - 1/108 y x z + + 4 2 2 3 3 3 4 3 4 2 + + 1/216 x y z + 1/432 y x z - 1/432 x y z + 1/54 x y z + + 2 4 2 2 2 2 2 2 2 2 + + 1/54 x y z - 1/54 y x z - 1/54 y x z - 1/27 y x z - 1/27 y x z + + 3 2 3 4 3 3 4 2 3 3 4 3 + - 1/108 y x z + 1/432 x y z - 1/864 x y z + 1/864 x y z + + 4 4 3 4 2 4 3 4 + + 1/864 x y z + 1/108 y x z + 1/108 y x z - 1/432 y x z + + 4 4 4 3 2 4 3 4 2 4 + - 1/432 x y z - 1/216 x y z - 1/216 x y z - 1/864 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/216 y x z - 1/864 y x z + 1/432 y x z , COEFF(2, 2, 1) = + + 2 4 4 3 4 3 4 2 4 4 4 + - 1/1728 y x z - 1/1728 x y z + 1/432 x y z - 1/3456 x y z + + 4 2 4 3 4 4 4 + - 1/432 x y z - 1/864 x y z + 1/432 x y z + 1/864 x y z + + 3 3 4 4 3 2 4 3 + - 1/864 y x z - 1/1728 x y z + 1/1728 y x z - 1/216 z y x + + 2 3 4 2 3 4 2 + - 1/216 z y x - 1/432 x y z + 1/864 y x z + 1/432 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/1728 y x z + 1/3456 x y z + 1/1728 x y z + 1/864 y x z + + 3 2 2 2 3 4 4 2 + - 1/216 y x z - 1/3456 y x z - 1/432 x y z - 1/864 x y z + + 3 3 3 3 2 2 3 3 2 2 + + 1/864 y x z + 1/216 y x z - 1/1728 y x z - 1/432 y x z + + 2 3 3 4 3 3 3 2 + + 1/1728 y x z + 1/432 x y z - 1/216 z y x - 1/432 z y x + + 3 3 2 2 3 + + 1/216 z y x + 1/216 y x z + 1/432 z y x - 1/432 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + - 1/432 z y x + 1/864 x y z + 1/432 x y z + 1/864 y x z + + 4 2 2 3 3 3 4 3 4 2 + - 1/864 x y z - 1/864 y x z + 1/1728 x y z - 1/432 x y z + + 2 4 2 2 2 2 2 2 2 + - 1/864 x y z + 1/432 y x z + 1/864 y x z + 1/432 y x z + + 2 3 2 3 4 3 3 4 2 3 + + 1/216 y x z + 1/1728 y x z - 1/1728 x y z + 1/3456 x y z + + 3 4 3 4 4 3 4 2 4 + - 1/1728 x y z - 1/3456 x y z - 1/864 y x z - 1/1728 y x z + + 3 4 4 4 4 3 2 4 3 + + 1/864 y x z + 1/1728 x y z + 1/1728 x y z + 1/3456 x y z + + 4 2 4 2 2 4 2 3 4 3 3 4 + + 1/3456 x y z - 1/3456 y x z + 1/1728 y x z - 1/864 y x z , + + 2 4 4 3 4 3 4 2 + COEFF(-2, -2, 2) = - 1/6912 y x z - 1/6912 x y z + 1/6912 x y z + + 4 4 4 4 2 4 3 4 + + 1/13824 x y z - 1/3456 x y z + 1/6912 x y z + 1/3456 x y z + + 4 4 3 3 4 4 3 2 4 + - 1/6912 x y z + 1/1728 y x z - 1/6912 x y z + 1/6912 y x z + + 3 2 3 4 2 3 4 + + 1/1728 z y x + 1/3456 z y x - 1/6912 x y z - 1/3456 y x z + + 2 2 3 2 4 4 4 4 + + 1/3456 y x z - 1/3456 y x z - 1/13824 x y z + 1/6912 x y z + + 2 2 2 3 2 2 2 3 4 + - 1/13824 y x z + 1/3456 y x z + 1/6912 y x z - 1/3456 x y z + + 4 2 3 3 3 3 2 2 3 + + 1/6912 x y z - 1/1728 y x z - 1/3456 y x z - 1/3456 y x z + + 3 2 2 2 3 3 4 3 3 + - 1/6912 y x z + 1/3456 y x z + 1/3456 x y z + 1/1728 z y x + + 3 2 3 3 2 + - 1/3456 z y x - 1/1728 z y x - 1/1728 y x z + 1/3456 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + - 1/3456 z y x - 1/6912 z y x - 1/13824 x y z + 1/6912 x y z + + 3 3 4 2 2 3 3 3 4 3 + - 1/1728 y x z + 1/13824 x y z + 1/1728 y x z + 1/3456 x y z + + 4 2 2 4 2 2 2 2 2 + - 1/6912 x y z + 1/13824 x y z + 1/6912 y x z - 1/6912 y x z + + 2 2 2 3 2 3 4 3 3 + + 1/6912 y x z - 1/3456 y x z + 1/3456 y x z - 1/3456 x y z + + 4 2 3 3 4 3 4 4 3 4 + - 1/6912 x y z - 1/3456 x y z + 1/6912 x y z + 1/3456 y x z + + 2 4 3 4 4 4 4 3 + - 1/6912 y x z - 1/3456 y x z + 1/6912 x y z + 1/3456 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + - 1/6912 x y z - 1/13824 x y z + 1/13824 y x z + 1/6912 y x z + + 3 3 4 2 4 4 3 4 + + 1/3456 y x z , COEFF(-1, -2, 2) = 1/864 y x z + 1/1728 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/3456 x y z - 1/3456 x y z + 1/432 x y z - 1/432 x y z + + 3 4 4 4 3 3 4 4 + - 1/1728 x y z + 1/1728 x y z - 1/216 y x z + 1/3456 x y z + + 3 2 4 3 2 3 4 2 + - 1/432 y x z - 1/864 z y x - 1/1728 z y x + 1/1728 x y z + + 3 4 2 2 3 2 4 4 + + 1/432 y x z - 1/432 y x z + 1/432 y x z + 1/864 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/864 x y z + 1/864 y x z - 1/432 y x z - 1/432 y x z + + 4 4 2 3 3 3 3 2 + + 1/864 x y z - 1/1728 x y z + 1/864 y x z + 1/1728 y x z + + 2 3 3 2 2 2 3 3 4 3 + + 1/216 y x z + 1/432 y x z - 1/1728 y x z - 1/864 x y z + + 3 3 2 3 3 + - 1/216 z y x + 1/216 z y x + 1/864 z y x + 1/216 y x z + + 2 2 3 2 2 3 4 4 2 + - 1/216 z y x + 1/1728 z y x + 1/3456 z y x + 1/3456 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + - 1/1728 x y z + 1/216 y x z - 1/3456 x y z - 1/864 y x z + + 4 3 4 2 2 4 2 2 2 + - 1/864 x y z + 1/864 x y z - 1/864 x y z - 1/864 y x z + + 2 2 2 2 2 3 2 3 + + 1/432 y x z - 1/432 y x z + 1/432 y x z - 1/216 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + + 1/864 x y z + 1/1728 x y z + 1/1728 x y z - 1/1728 x y z + + 4 2 4 3 4 4 4 + - 1/432 y x z + 1/432 y x z + 1/1728 y x z - 1/1728 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + - 1/432 x y z + 1/432 x y z + 1/3456 x y z - 1/864 y x z + + 2 3 4 3 3 4 4 3 4 + - 1/3456 y x z - 1/1728 y x z , COEFF(0, -2, 2) = - 1/1152 x y z + + 4 4 4 2 4 4 4 3 2 4 + + 1/2304 x y z + 5/1152 x y z - 1/1152 x y z + 5/1152 y x z + + 4 2 2 4 4 2 2 2 2 2 3 + - 1/1152 x y z - 5/2304 x y z - 5/2304 y x z + 5/1152 y x z + + 4 4 2 2 3 3 2 2 + - 1/576 x y z + 1/1152 x y z - 5/576 y x z - 5/1152 y x z + + 4 3 3 3 2 2 + + 1/576 x y z + 1/144 z y - 5/576 z y x + 5/576 z y x + + 4 4 2 4 3 2 4 2 2 + - 1/2304 x y z - 1/144 y z + 1/1152 x y z + 1/2304 x y z + + 4 3 2 4 2 2 2 2 2 + + 1/576 x y z + 5/2304 x y z - 5/1152 y x z + 5/1152 y x z + + 2 3 2 3 4 3 3 4 2 3 + + 1/288 y z + 5/576 y x z - 1/576 x y z - 1/1152 x y z + + 4 4 3 3 2 3 3 3 4 + + 1/1152 x y z + 1/144 y z - 1/288 y z - 1/144 y z + 1/288 y z + + 3 4 4 4 3 2 2 4 4 2 + - 1/288 y z + 1/576 y z + 1/288 y z - 5/1152 y x z - 1/576 y z + + 4 2 2 4 4 4 2 2 + - 1/288 y z - 1/288 y z - 1/576 y z + 1/1152 x y z + 1/576 y z + + 4 3 2 4 3 4 2 4 2 2 4 + + 1/288 y z - 5/1152 x y z - 1/2304 x y z + 5/2304 y x z , + + 2 4 4 3 4 3 4 2 + COEFF(1, -2, 2) = - 1/864 y x z + 1/1728 x y z + 1/3456 x y z + + 4 4 4 4 2 4 3 4 + - 1/3456 x y z - 1/432 x y z - 1/432 x y z + 1/1728 x y z + + 4 4 3 3 4 4 3 2 4 + + 1/1728 x y z + 1/216 y x z - 1/3456 x y z - 1/432 y x z + + 3 2 3 4 2 3 4 + + 1/864 z y x + 1/1728 z y x + 1/1728 x y z - 1/432 y x z + + 2 2 3 2 4 4 4 4 + + 1/432 y x z - 1/432 y x z + 1/864 x y z + 1/864 x y z + + 2 2 2 3 2 2 2 3 4 + + 1/864 y x z + 1/432 y x z - 1/432 y x z + 1/864 x y z + + 4 2 3 3 3 3 2 2 3 + - 1/1728 x y z - 1/864 y x z - 1/1728 y x z + 1/216 y x z + + 3 2 2 2 3 3 4 3 3 + + 1/432 y x z + 1/1728 y x z - 1/864 x y z + 1/216 z y x + + 3 2 3 3 2 + + 1/216 z y x - 1/864 z y x - 1/216 y x z - 1/216 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + - 1/1728 z y x - 1/3456 z y x + 1/3456 x y z - 1/1728 x y z + + 3 3 4 2 2 3 3 3 4 3 + - 1/216 y x z - 1/3456 x y z + 1/864 y x z - 1/864 x y z + + 4 2 2 4 2 2 2 2 2 + - 1/864 x y z - 1/864 x y z + 1/864 y x z + 1/432 y x z + + 2 2 2 3 2 3 4 3 3 + - 1/432 y x z - 1/432 y x z - 1/216 y x z + 1/864 x y z + + 4 2 3 3 4 3 4 4 3 4 + + 1/1728 x y z - 1/1728 x y z - 1/1728 x y z + 1/432 y x z + + 2 4 3 4 4 4 4 3 + + 1/432 y x z - 1/1728 y x z - 1/1728 x y z + 1/432 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + + 1/432 x y z + 1/3456 x y z - 1/864 y x z + 1/3456 y x z + + 3 3 4 2 4 4 3 4 + + 1/1728 y x z , COEFF(2, -2, 2) = 1/6912 y x z - 1/6912 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/6912 x y z + 1/13824 x y z + 1/3456 x y z + 1/6912 x y z + + 3 4 4 4 3 3 4 4 + - 1/3456 x y z - 1/6912 x y z - 1/1728 y x z + 1/6912 x y z + + 3 2 4 3 2 3 4 2 + + 1/6912 y x z - 1/1728 z y x - 1/3456 z y x - 1/6912 x y z + + 3 4 2 2 3 2 4 4 + + 1/3456 y x z - 1/3456 y x z + 1/3456 y x z - 1/13824 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/6912 x y z - 1/13824 y x z - 1/3456 y x z + 1/6912 y x z + + 4 4 2 3 3 3 3 2 + - 1/3456 x y z + 1/6912 x y z + 1/1728 y x z + 1/3456 y x z + + 2 3 3 2 2 2 3 3 4 3 + - 1/3456 y x z - 1/6912 y x z - 1/3456 y x z + 1/3456 x y z + + 3 3 2 3 3 + - 1/1728 z y x - 1/3456 z y x + 1/1728 z y x + 1/1728 y x z + + 2 2 3 2 2 3 4 4 2 + + 1/3456 z y x + 1/3456 z y x + 1/6912 z y x - 1/13824 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + + 1/6912 x y z + 1/1728 y x z + 1/13824 x y z - 1/1728 y x z + + 4 3 4 2 2 4 2 2 2 + + 1/3456 x y z + 1/6912 x y z + 1/13824 x y z - 1/6912 y x z + + 2 2 2 2 2 3 2 3 + - 1/6912 y x z + 1/6912 y x z + 1/3456 y x z + 1/3456 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + - 1/3456 x y z - 1/6912 x y z + 1/3456 x y z + 1/6912 x y z + + 4 2 4 3 4 4 4 + - 1/3456 y x z - 1/6912 y x z + 1/3456 y x z + 1/6912 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + - 1/3456 x y z - 1/6912 x y z - 1/13824 x y z + 1/13824 y x z + + 2 3 4 3 3 4 2 4 + - 1/6912 y x z - 1/3456 y x z , COEFF(-2, -1, 2) = 1/432 y x z + + 4 3 4 3 4 2 4 4 4 4 + + 1/3456 x y z - 1/1728 x y z - 1/3456 x y z + 1/864 x y z + + 2 4 3 4 4 4 3 + - 1/1728 x y z - 1/864 x y z + 1/1728 x y z - 1/216 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/1728 x y z - 1/3456 y x z - 1/216 z y x - 1/432 z y x + + 4 2 3 4 2 2 3 + + 1/864 x y z + 1/1728 y x z - 1/216 y x z + 1/216 y x z + + 2 4 4 4 4 2 2 2 3 2 + + 1/3456 x y z - 1/1728 x y z + 1/864 y x z - 1/1728 y x z + + 2 2 3 4 4 2 3 3 + - 1/432 y x z + 1/432 x y z - 1/432 x y z + 1/216 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + + 1/1728 y x z + 1/432 y x z + 1/3456 y x z - 1/216 y x z + + 4 3 3 3 2 3 3 + - 1/1728 x y z - 1/864 z y x + 1/1728 z y x + 1/864 z y x + + 2 2 3 2 2 3 + + 1/216 y x z - 1/432 z y x + 1/216 z y x + 1/432 z y x + + 4 4 2 4 3 2 3 3 4 2 2 + + 1/3456 x y z - 1/3456 x y z + 1/864 y x z - 1/864 x y z + + 3 3 3 4 3 4 2 2 4 2 + - 1/864 y x z - 1/432 x y z + 1/1728 x y z - 1/3456 x y z + + 2 2 2 2 2 2 2 + - 1/432 y x z + 1/432 y x z - 1/864 y x z + 1/432 y x z + + 3 2 3 4 3 3 4 2 3 3 4 3 + - 1/1728 y x z + 1/1728 x y z + 1/432 x y z + 1/864 x y z + + 4 4 3 4 2 4 3 4 + - 1/1728 x y z - 1/432 y x z + 1/864 y x z + 1/432 y x z + + 4 4 4 3 2 4 3 4 2 4 + - 1/864 x y z - 1/864 x y z + 1/1728 x y z + 1/864 x y z + + 2 2 4 2 3 4 3 3 4 + - 1/864 y x z - 1/432 y x z - 1/1728 y x z , COEFF(-1, -1, 2) = + + 2 4 4 3 4 3 4 2 4 4 4 + - 1/54 y x z - 1/864 x y z + 1/864 x y z + 1/864 x y z + + 4 2 4 3 4 4 4 + - 1/108 x y z + 1/108 x y z + 1/432 x y z - 1/432 x y z + + 3 3 4 4 3 2 4 3 + + 1/27 y x z - 1/864 x y z + 1/216 y x z + 1/108 z y x + + 2 3 4 2 3 4 2 + + 1/216 z y x - 1/216 x y z - 1/216 y x z + 1/27 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/27 y x z - 1/216 x y z + 1/216 x y z - 1/54 y x z + + 3 2 2 2 3 4 4 2 + + 1/216 y x z + 1/27 y x z - 1/108 x y z + 1/108 x y z + + 3 3 3 3 2 2 3 3 2 2 + - 1/108 y x z - 1/864 y x z - 1/27 y x z - 1/216 y x z + + 2 3 3 4 3 3 3 2 + + 1/108 y x z + 1/432 x y z + 1/108 z y x - 1/108 z y x + + 3 3 2 2 3 + - 1/432 z y x - 1/27 y x z + 1/27 z y x - 1/108 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + - 1/216 z y x - 1/864 x y z + 1/864 x y z - 1/108 y x z + + 4 2 2 3 3 3 4 3 4 2 + + 1/216 x y z + 1/432 y x z + 1/108 x y z - 1/216 x y z + + 2 4 2 2 2 2 2 2 2 + + 1/216 x y z + 1/54 y x z - 1/27 y x z + 1/54 y x z + + 2 3 2 3 4 3 3 4 2 3 + - 1/54 y x z + 1/108 y x z - 1/432 x y z - 1/108 x y z + + 3 4 3 4 4 3 4 2 4 + - 1/432 x y z + 1/432 x y z + 1/54 y x z - 1/54 y x z + + 3 4 4 4 4 3 2 4 3 + - 1/216 y x z + 1/216 x y z + 1/108 x y z - 1/108 x y z + + 4 2 4 2 2 4 2 3 4 3 3 4 + - 1/216 x y z + 1/54 y x z + 1/216 y x z + 1/864 y x z , + + 4 3 4 4 4 4 2 4 + COEFF(0, -1, 2) = 1/576 x y z - 1/576 x y z - 5/288 x y z + + 4 4 3 2 4 4 2 2 4 4 + + 1/288 x y z - 5/576 y x z + 1/144 x y z + 5/576 x y z + + 2 2 2 2 2 3 4 4 2 + + 5/144 y x z - 5/72 y x z + 1/72 x y z - 1/72 x y z + + 2 3 3 2 2 4 3 3 + + 5/72 y x z + 5/576 y x z - 1/288 x y z - 1/72 z y + + 3 2 2 4 4 2 4 3 2 + + 5/288 z y x - 5/72 z y x + 1/576 x y z + 1/18 y z - 1/576 x y z + + 4 2 2 4 3 2 4 2 2 2 + - 1/144 x y z - 1/72 x y z - 5/576 x y z + 5/72 y x z + + 2 2 2 3 2 3 4 3 3 + - 5/144 y x z - 1/18 y z - 5/288 y x z + 1/288 x y z + + 4 2 3 4 4 3 3 2 3 3 3 + + 1/72 x y z - 1/288 x y z - 1/18 y z + 1/18 y z + 1/72 y z + + 4 3 4 4 4 3 2 2 4 + - 1/36 y z + 1/144 y z - 1/144 y z - 1/144 y z + 5/144 y x z + + 4 2 4 2 2 4 4 4 + + 1/144 y z + 1/72 y z + 1/36 y z + 1/36 y z - 1/144 x y z + + 2 2 4 3 2 4 3 4 2 4 + - 1/36 y z - 1/72 y z + 5/288 x y z + 1/144 x y z + + 2 2 4 2 4 4 3 4 + - 5/144 y x z , COEFF(1, -1, 2) = 1/54 y x z - 1/864 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/864 x y z + 1/864 x y z + 1/108 x y z + 1/108 x y z + + 3 4 4 4 3 3 4 4 + - 1/432 x y z - 1/432 x y z - 1/27 y x z + 1/864 x y z + + 3 2 4 3 2 3 4 2 + + 1/216 y x z - 1/108 z y x - 1/216 z y x - 1/216 x y z + + 3 4 2 2 3 2 4 4 + + 1/216 y x z - 1/27 y x z + 1/27 y x z - 1/216 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/216 x y z - 1/54 y x z - 1/216 y x z + 1/27 y x z + + 4 4 2 3 3 3 3 2 + - 1/108 x y z + 1/108 x y z + 1/108 y x z + 1/864 y x z + + 2 3 3 2 2 2 3 3 4 3 + - 1/27 y x z - 1/216 y x z - 1/108 y x z + 1/432 x y z + + 3 3 2 3 3 2 + - 1/108 z y x - 1/108 z y x + 1/432 z y x + 1/27 y x z + 1/27 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + + 1/108 z y x + 1/216 z y x - 1/864 x y z + 1/864 x y z + + 3 3 4 2 2 3 3 3 4 3 + + 1/108 y x z + 1/216 x y z - 1/432 y x z + 1/108 x y z + + 4 2 2 4 2 2 2 2 2 + + 1/216 x y z + 1/216 x y z - 1/54 y x z - 1/27 y x z + + 2 2 2 3 2 3 4 3 3 + + 1/54 y x z + 1/54 y x z + 1/108 y x z - 1/432 x y z + + 4 2 3 3 4 3 4 4 3 4 + - 1/108 x y z + 1/432 x y z + 1/432 x y z - 1/54 y x z + + 2 4 3 4 4 4 4 3 + - 1/54 y x z + 1/216 y x z + 1/216 x y z - 1/108 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + - 1/108 x y z - 1/216 x y z + 1/54 y x z - 1/216 y x z + + 3 3 4 2 4 4 3 4 + - 1/864 y x z , COEFF(2, -1, 2) = - 1/432 y x z + 1/3456 x y z + + 3 4 2 4 4 4 4 2 4 + + 1/1728 x y z - 1/3456 x y z - 1/864 x y z - 1/1728 x y z + + 3 4 4 4 3 3 4 4 + + 1/864 x y z + 1/1728 x y z + 1/216 y x z - 1/1728 x y z + + 3 2 4 3 2 3 4 2 + - 1/3456 y x z + 1/216 z y x + 1/432 z y x + 1/864 x y z + + 3 4 2 2 3 2 4 4 + - 1/1728 y x z + 1/216 y x z - 1/216 y x z + 1/3456 x y z + + 4 4 2 2 2 3 2 2 2 3 + + 1/1728 x y z + 1/864 y x z + 1/1728 y x z - 1/432 y x z + + 4 4 2 3 3 3 3 2 + + 1/432 x y z - 1/432 x y z - 1/216 y x z - 1/1728 y x z + + 2 3 3 2 2 2 3 3 4 3 + + 1/432 y x z + 1/3456 y x z + 1/216 y x z - 1/1728 x y z + + 3 3 2 3 3 + + 1/864 z y x + 1/1728 z y x - 1/864 z y x - 1/216 y x z + + 2 2 3 2 2 3 4 4 2 + - 1/432 z y x - 1/216 z y x - 1/432 z y x + 1/3456 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + - 1/3456 x y z - 1/864 y x z - 1/864 x y z + 1/864 y x z + + 4 3 4 2 2 4 2 2 2 + - 1/432 x y z - 1/1728 x y z - 1/3456 x y z + 1/432 y x z + + 2 2 2 2 2 3 2 3 + + 1/432 y x z - 1/864 y x z - 1/432 y x z - 1/1728 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + + 1/1728 x y z + 1/432 x y z - 1/864 x y z - 1/1728 x y z + + 4 2 4 3 4 4 4 + + 1/432 y x z + 1/864 y x z - 1/432 y x z - 1/864 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + + 1/864 x y z + 1/1728 x y z + 1/864 x y z - 1/864 y x z + + 2 3 4 3 3 4 2 4 + + 1/432 y x z + 1/1728 y x z , COEFF(-2, 0, 2) = - 5/1152 y x z + + 3 4 2 4 4 4 4 2 4 + + 1/1152 x y z + 1/2304 x y z - 1/576 x y z + 1/1152 x y z + + 3 4 4 4 3 4 4 2 + + 1/576 x y z - 1/1152 x y z - 1/1152 x y z + 5/576 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 5/576 y x z - 1/2304 x y z + 1/1152 x y z - 5/2304 y x z + + 2 2 3 4 2 3 2 3 3 + + 5/1152 y x z + 5/1152 x y z + 1/144 z x + 5/576 y x z + + 2 3 2 2 3 4 4 2 4 2 2 + - 5/576 z y x - 5/1152 z y x - 1/2304 x y z + 5/2304 x y z + + 4 2 2 4 2 2 2 2 2 + - 1/1152 x y z + 1/2304 x y z + 5/1152 y x z - 5/1152 y x z + + 4 2 3 2 3 4 3 + - 1/144 x z - 5/1152 x y z + 1/288 x z - 1/576 x y z + + 4 4 3 3 3 2 3 4 3 2 4 + + 1/1152 x y z - 1/144 x z - 1/288 x z + 1/288 x z - 1/576 x z + + 3 4 4 4 2 3 4 + + 1/144 x z + 1/288 x z - 1/288 x z - 1/576 x z - 1/288 x z + + 2 2 2 4 4 3 2 4 3 + + 1/576 x z - 1/288 x z + 1/576 x z + 1/288 x z + 1/576 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + - 1/1152 x y z - 5/2304 x y z + 5/2304 y x z + 5/1152 y x z , + + 2 4 3 4 2 4 4 4 + COEFF(-1, 0, 2) = 5/144 y x z - 1/576 x y z - 1/576 x y z + + 4 2 4 3 4 4 4 + + 1/72 x y z - 1/72 x y z - 1/288 x y z + 1/288 x y z + + 3 4 4 2 2 3 2 4 4 + + 1/576 x y z - 5/72 y x z + 5/72 y x z + 1/144 x y z + + 4 4 2 2 2 2 2 3 4 2 + - 1/144 x y z + 5/144 y x z - 5/72 y x z - 5/288 x y z + + 3 2 3 3 2 3 2 2 3 + - 1/72 z x - 5/288 y x z + 5/288 z y x + 5/576 z y x + + 4 4 2 4 2 2 4 2 2 4 2 + + 1/576 x y z - 5/576 x y z + 1/144 x y z - 1/144 x y z + + 2 2 2 2 4 2 3 2 + - 5/144 y x z + 5/72 y x z + 1/18 x z + 5/288 x y z - 1/18 x z + + 3 4 3 4 4 3 3 3 2 3 4 3 + + 1/288 x y z - 1/288 x y z + 1/72 x z + 1/18 x z - 1/72 x z + + 2 4 3 4 4 4 2 + + 1/36 x z - 1/18 x z - 1/36 x z + 1/72 x z + 1/144 x z + + 3 4 2 2 2 4 4 3 2 + + 1/144 x z - 1/36 x z + 1/36 x z - 1/144 x z - 1/144 x z + + 4 3 2 4 3 4 2 4 2 2 4 + - 1/72 x y z + 1/72 x y z + 5/576 x y z - 5/144 y x z + + 2 3 4 4 4 4 2 4 + - 5/576 y x z , COEFF(0, 0, 2) = 1/384 x y z + 5/192 x y z + + 4 4 2 4 4 25 2 2 2 25 2 2 3 + - 1/192 x y z - 1/12 z - 5/384 x y z - --- y x z + --- y x z + 384 192 + + 4 2 4 3 2 4 4 2 + + 5/192 x y z + 1/24 z + 1/12 z - 1/24 z - 1/384 x y z + + 4 2 2 2 4 2 25 2 2 2 + + 5/384 x y z + 5/384 x y z - --- y x z + 5/48 y z + 192 + + 4 2 3 2 4 4 3 2 3 2 3 + - 5/192 x y z + 5/48 x z + 1/192 x y z - 5/48 y z - 5/48 x z + + 4 3 4 4 2 4 4 2 4 + + 1/48 x z + 1/96 y z - 5/96 x z - 1/96 y z - 1/48 y z + + 4 4 2 2 2 4 4 2 4 + - 1/48 x z - 1/96 x z + 5/96 x z + 1/96 x z - 5/96 y z + + 2 2 4 3 2 4 3 4 2 4 25 2 2 4 + + 5/96 y z + 1/48 y z - 5/192 x y z - 5/384 x y z + --- y x z + 384 + + 2 4 3 4 2 4 4 4 + , COEFF(1, 0, 2) = - 5/144 y x z + 1/576 x y z - 1/576 x y z + + 4 2 4 3 4 4 4 + - 1/72 x y z - 1/72 x y z + 1/288 x y z + 1/288 x y z + + 3 4 4 2 2 3 2 4 4 + - 1/576 x y z + 5/72 y x z - 5/72 y x z + 1/144 x y z + + 4 4 2 2 2 2 2 3 4 2 + + 1/144 x y z + 5/144 y x z - 5/72 y x z - 5/288 x y z + + 3 2 3 3 2 3 2 2 3 + + 1/72 z x + 5/288 y x z - 5/288 z y x - 5/576 z y x + + 4 4 2 4 2 2 4 2 2 4 2 + + 1/576 x y z - 5/576 x y z - 1/144 x y z - 1/144 x y z + + 2 2 2 2 4 2 3 2 + + 5/144 y x z + 5/72 y x z - 1/18 x z + 5/288 x y z - 1/18 x z + + 3 4 3 4 4 3 3 3 2 3 4 3 + - 1/288 x y z - 1/288 x y z - 1/72 x z + 1/18 x z - 1/72 x z + + 2 4 3 4 4 4 2 + + 1/36 x z + 1/18 x z + 1/36 x z + 1/72 x z + 1/144 x z + + 3 4 2 2 2 4 4 3 2 + - 1/144 x z - 1/36 x z - 1/36 x z - 1/144 x z + 1/144 x z + + 4 3 2 4 3 4 2 4 2 2 4 + + 1/72 x y z + 1/72 x y z + 5/576 x y z - 5/144 y x z + + 2 3 4 2 4 3 4 2 + + 5/576 y x z , COEFF(2, 0, 2) = 5/1152 y x z - 1/1152 x y z + + 4 4 4 4 2 4 3 4 + + 1/2304 x y z + 1/576 x y z + 1/1152 x y z - 1/576 x y z + + 4 4 3 4 4 2 2 3 + - 1/1152 x y z + 1/1152 x y z - 5/576 y x z + 5/576 y x z + + 2 4 4 4 4 2 2 2 2 2 3 + - 1/2304 x y z - 1/1152 x y z - 5/2304 y x z + 5/1152 y x z + + 4 2 3 2 3 3 2 3 + + 5/1152 x y z - 1/144 z x - 5/576 y x z + 5/576 z y x + + 2 2 3 4 4 2 4 2 2 4 2 + + 5/1152 z y x - 1/2304 x y z + 5/2304 x y z + 1/1152 x y z + + 2 4 2 2 2 2 2 + + 1/2304 x y z - 5/1152 y x z - 5/1152 y x z + 1/144 x z + + 4 2 3 2 3 4 3 4 4 3 + - 5/1152 x y z + 1/288 x z + 1/576 x y z + 1/1152 x y z + + 3 3 2 3 4 3 2 4 3 + + 1/144 x z - 1/288 x z + 1/288 x z - 1/576 x z - 1/144 x z + + 4 4 4 2 3 4 2 2 + - 1/288 x z - 1/288 x z - 1/576 x z + 1/288 x z + 1/576 x z + + 2 4 4 3 2 4 3 2 4 3 + + 1/288 x z + 1/576 x z - 1/288 x z - 1/576 x y z - 1/1152 x y z + + 4 2 4 2 2 4 2 3 4 + - 5/2304 x y z + 5/2304 y x z - 5/1152 y x z , COEFF(-2, 1, 2) = + + 2 4 4 3 4 3 4 2 4 4 4 + 1/432 y x z - 1/3456 x y z - 1/1728 x y z - 1/3456 x y z + + 4 2 4 3 4 4 4 + + 1/864 x y z - 1/1728 x y z - 1/864 x y z + 1/1728 x y z + + 3 3 4 4 3 2 4 3 + + 1/216 y x z + 1/1728 x y z + 1/3456 y x z + 1/216 z y x + + 2 3 4 2 3 4 2 + + 1/432 z y x - 1/864 x y z - 1/1728 y x z - 1/216 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/216 y x z + 1/3456 x y z - 1/1728 x y z + 1/864 y x z + + 3 2 2 2 3 4 4 2 + + 1/1728 y x z - 1/432 y x z - 1/432 x y z - 1/432 x y z + + 3 3 3 3 2 2 3 3 2 2 + - 1/216 y x z - 1/1728 y x z - 1/432 y x z - 1/3456 y x z + + 2 3 3 4 3 3 3 2 + - 1/216 y x z + 1/1728 x y z + 1/864 z y x - 1/1728 z y x + + 3 3 2 2 3 + - 1/864 z y x - 1/216 y x z + 1/432 z y x + 1/216 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + + 1/432 z y x + 1/3456 x y z + 1/3456 x y z - 1/864 y x z + + 4 2 2 3 3 3 4 3 4 2 + - 1/864 x y z + 1/864 y x z + 1/432 x y z + 1/1728 x y z + + 2 4 2 2 2 2 2 2 2 + - 1/3456 x y z - 1/432 y x z + 1/432 y x z + 1/864 y x z + + 2 3 2 3 4 3 3 4 2 3 + - 1/432 y x z + 1/1728 y x z - 1/1728 x y z + 1/432 x y z + + 3 4 3 4 4 3 4 2 4 + + 1/864 x y z - 1/1728 x y z + 1/432 y x z - 1/864 y x z + + 3 4 4 4 4 3 2 4 3 + - 1/432 y x z + 1/864 x y z - 1/864 x y z + 1/1728 x y z + + 4 2 4 2 2 4 2 3 4 3 3 4 + + 1/864 x y z - 1/864 y x z - 1/432 y x z + 1/1728 y x z , + + 2 4 4 3 4 3 4 2 + COEFF(-1, 1, 2) = - 1/54 y x z + 1/864 x y z + 1/864 x y z + + 4 4 4 4 2 4 3 4 + + 1/864 x y z - 1/108 x y z + 1/108 x y z + 1/432 x y z + + 4 4 3 3 4 4 3 2 4 + - 1/432 x y z - 1/27 y x z - 1/864 x y z - 1/216 y x z + + 3 2 3 4 2 3 4 + - 1/108 z y x - 1/216 z y x + 1/216 x y z + 1/216 y x z + + 2 2 3 2 4 4 4 4 + + 1/27 y x z - 1/27 y x z - 1/216 x y z + 1/216 x y z + + 2 2 2 3 2 2 2 3 4 + - 1/54 y x z - 1/216 y x z + 1/27 y x z + 1/108 x y z + + 4 2 3 3 3 3 2 2 3 + + 1/108 x y z + 1/108 y x z + 1/864 y x z + 1/27 y x z + + 3 2 2 2 3 3 4 3 3 + + 1/216 y x z + 1/108 y x z - 1/432 x y z - 1/108 z y x + + 3 2 3 3 2 2 3 + + 1/108 z y x + 1/432 z y x + 1/27 y x z - 1/27 z y x - 1/108 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + - 1/216 z y x - 1/864 x y z - 1/864 x y z + 1/108 y x z + + 4 2 2 3 3 3 4 3 4 2 + + 1/216 x y z - 1/432 y x z - 1/108 x y z - 1/216 x y z + + 2 4 2 2 2 2 2 2 2 + + 1/216 x y z + 1/54 y x z - 1/27 y x z - 1/54 y x z + + 2 3 2 3 4 3 3 4 2 3 + + 1/54 y x z - 1/108 y x z + 1/432 x y z - 1/108 x y z + + 3 4 3 4 4 3 4 2 4 + - 1/432 x y z + 1/432 x y z - 1/54 y x z + 1/54 y x z + + 3 4 4 4 4 3 2 4 3 + + 1/216 y x z - 1/216 x y z + 1/108 x y z - 1/108 x y z + + 4 2 4 2 2 4 2 3 4 3 3 4 + - 1/216 x y z + 1/54 y x z + 1/216 y x z - 1/864 y x z , + + 4 3 4 4 4 4 2 4 + COEFF(0, 1, 2) = - 1/576 x y z - 1/576 x y z - 5/288 x y z + + 4 4 3 2 4 4 2 2 4 4 + + 1/288 x y z + 5/576 y x z - 1/144 x y z + 5/576 x y z + + 2 2 2 2 2 3 4 4 2 + + 5/144 y x z - 5/72 y x z - 1/72 x y z - 1/72 x y z + + 2 3 3 2 2 4 3 3 + - 5/72 y x z - 5/576 y x z + 1/288 x y z + 1/72 z y + + 3 2 2 4 4 2 4 3 2 + - 5/288 z y x + 5/72 z y x + 1/576 x y z - 1/18 y z + 1/576 x y z + + 4 2 2 4 3 2 4 2 2 2 + - 1/144 x y z + 1/72 x y z - 5/576 x y z + 5/72 y x z + + 2 2 2 3 2 3 4 3 3 + + 5/144 y x z - 1/18 y z + 5/288 y x z - 1/288 x y z + + 4 2 3 4 4 3 3 2 3 3 3 + + 1/72 x y z - 1/288 x y z + 1/18 y z + 1/18 y z - 1/72 y z + + 4 3 4 4 4 3 2 2 4 + + 1/36 y z - 1/144 y z - 1/144 y z + 1/144 y z - 5/144 y x z + + 4 2 4 2 2 4 4 4 + + 1/144 y z + 1/72 y z - 1/36 y z + 1/36 y z + 1/144 x y z + + 2 2 4 3 2 4 3 4 2 4 + - 1/36 y z - 1/72 y z + 5/288 x y z + 1/144 x y z + + 2 2 4 2 4 4 3 4 + - 5/144 y x z , COEFF(1, 1, 2) = 1/54 y x z + 1/864 x y z + + 3 4 2 4 4 4 4 2 4 + - 1/864 x y z + 1/864 x y z + 1/108 x y z + 1/108 x y z + + 3 4 4 4 3 3 4 4 + - 1/432 x y z - 1/432 x y z + 1/27 y x z + 1/864 x y z + + 3 2 4 3 2 3 4 2 + - 1/216 y x z + 1/108 z y x + 1/216 z y x + 1/216 x y z + + 3 4 2 2 3 2 4 4 + - 1/216 y x z - 1/27 y x z + 1/27 y x z - 1/216 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/216 x y z - 1/54 y x z + 1/216 y x z + 1/27 y x z + + 4 4 2 3 3 3 3 2 + + 1/108 x y z + 1/108 x y z - 1/108 y x z - 1/864 y x z + + 2 3 3 2 2 2 3 3 4 3 + + 1/27 y x z + 1/216 y x z - 1/108 y x z - 1/432 x y z + + 3 3 2 3 3 2 + + 1/108 z y x + 1/108 z y x - 1/432 z y x - 1/27 y x z - 1/27 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + + 1/108 z y x + 1/216 z y x - 1/864 x y z - 1/864 x y z + + 3 3 4 2 2 3 3 3 4 3 + - 1/108 y x z + 1/216 x y z + 1/432 y x z - 1/108 x y z + + 4 2 2 4 2 2 2 2 2 + + 1/216 x y z + 1/216 x y z - 1/54 y x z - 1/27 y x z + + 2 2 2 3 2 3 4 3 3 + - 1/54 y x z - 1/54 y x z - 1/108 y x z + 1/432 x y z + + 4 2 3 3 4 3 4 4 3 4 + - 1/108 x y z + 1/432 x y z + 1/432 x y z + 1/54 y x z + + 2 4 3 4 4 4 4 3 + + 1/54 y x z - 1/216 y x z - 1/216 x y z - 1/108 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + - 1/108 x y z - 1/216 x y z + 1/54 y x z - 1/216 y x z + + 3 3 4 2 4 4 3 4 + + 1/864 y x z , COEFF(2, 1, 2) = - 1/432 y x z - 1/3456 x y z + + 3 4 2 4 4 4 4 2 4 + + 1/1728 x y z - 1/3456 x y z - 1/864 x y z - 1/1728 x y z + + 3 4 4 4 3 3 4 4 + + 1/864 x y z + 1/1728 x y z - 1/216 y x z - 1/1728 x y z + + 3 2 4 3 2 3 4 2 + + 1/3456 y x z - 1/216 z y x - 1/432 z y x - 1/864 x y z + + 3 4 2 2 3 2 4 4 + + 1/1728 y x z + 1/216 y x z - 1/216 y x z + 1/3456 x y z + + 4 4 2 2 2 3 2 2 2 3 + + 1/1728 x y z + 1/864 y x z - 1/1728 y x z - 1/432 y x z + + 4 4 2 3 3 3 3 2 + - 1/432 x y z - 1/432 x y z + 1/216 y x z + 1/1728 y x z + + 2 3 3 2 2 2 3 3 4 3 + - 1/432 y x z - 1/3456 y x z + 1/216 y x z + 1/1728 x y z + + 3 3 2 3 3 + - 1/864 z y x - 1/1728 z y x + 1/864 z y x + 1/216 y x z + + 2 2 3 2 2 3 4 4 2 + + 1/432 z y x - 1/216 z y x - 1/432 z y x + 1/3456 x y z + + 4 3 2 3 3 4 2 2 3 3 3 + + 1/3456 x y z + 1/864 y x z - 1/864 x y z - 1/864 y x z + + 4 3 4 2 2 4 2 2 2 + + 1/432 x y z - 1/1728 x y z - 1/3456 x y z + 1/432 y x z + + 2 2 2 2 2 3 2 3 + + 1/432 y x z + 1/864 y x z + 1/432 y x z + 1/1728 y x z + + 4 3 3 4 2 3 3 4 3 4 4 3 + - 1/1728 x y z + 1/432 x y z - 1/864 x y z - 1/1728 x y z + + 4 2 4 3 4 4 4 + - 1/432 y x z - 1/864 y x z + 1/432 y x z + 1/864 x y z + + 4 3 2 4 3 4 2 4 2 2 4 + + 1/864 x y z + 1/1728 x y z + 1/864 x y z - 1/864 y x z + + 2 3 4 3 3 4 2 4 + + 1/432 y x z - 1/1728 y x z , COEFF(-2, 2, 2) = - 1/6912 y x z + + 4 3 4 3 4 2 4 4 4 4 + + 1/6912 x y z + 1/6912 x y z + 1/13824 x y z - 1/3456 x y z + + 2 4 3 4 4 4 3 + + 1/6912 x y z + 1/3456 x y z - 1/6912 x y z - 1/1728 y x z + + 3 4 4 3 2 4 3 2 3 + - 1/6912 x y z - 1/6912 y x z - 1/1728 z y x - 1/3456 z y x + + 4 2 3 4 2 2 3 + + 1/6912 x y z + 1/3456 y x z + 1/3456 y x z - 1/3456 y x z + + 2 4 4 4 4 2 2 2 3 2 + - 1/13824 x y z + 1/6912 x y z - 1/13824 y x z - 1/3456 y x z + + 2 2 3 4 4 2 3 3 + + 1/6912 y x z + 1/3456 x y z + 1/6912 x y z + 1/1728 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + + 1/3456 y x z + 1/3456 y x z + 1/6912 y x z + 1/3456 y x z + + 4 3 3 3 2 3 3 + - 1/3456 x y z - 1/1728 z y x + 1/3456 z y x + 1/1728 z y x + + 2 2 3 2 2 3 + + 1/1728 y x z - 1/3456 z y x - 1/3456 z y x - 1/6912 z y x + + 4 4 2 4 3 2 3 3 4 2 2 + - 1/13824 x y z - 1/6912 x y z + 1/1728 y x z + 1/13824 x y z + + 3 3 3 4 3 4 2 2 4 2 + - 1/1728 y x z - 1/3456 x y z - 1/6912 x y z + 1/13824 x y z + + 2 2 2 2 2 2 2 + + 1/6912 y x z - 1/6912 y x z - 1/6912 y x z + 1/3456 y x z + + 3 2 3 4 3 3 4 2 3 3 4 3 + - 1/3456 y x z + 1/3456 x y z - 1/6912 x y z - 1/3456 x y z + + 4 4 3 4 2 4 3 4 + + 1/6912 x y z - 1/3456 y x z + 1/6912 y x z + 1/3456 y x z + + 4 4 4 3 2 4 3 4 2 4 + - 1/6912 x y z + 1/3456 x y z - 1/6912 x y z - 1/13824 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/13824 y x z + 1/6912 y x z - 1/3456 y x z , COEFF(-1, 2, 2) = + + 2 4 4 3 4 3 4 2 4 4 4 + 1/864 y x z - 1/1728 x y z - 1/3456 x y z - 1/3456 x y z + + 4 2 4 3 4 4 4 + + 1/432 x y z - 1/432 x y z - 1/1728 x y z + 1/1728 x y z + + 3 3 4 4 3 2 4 3 + + 1/216 y x z + 1/3456 x y z + 1/432 y x z + 1/864 z y x + + 2 3 4 2 3 4 2 + + 1/1728 z y x - 1/1728 x y z - 1/432 y x z - 1/432 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/432 y x z + 1/864 x y z - 1/864 x y z + 1/864 y x z + + 3 2 2 2 3 4 4 2 + + 1/432 y x z - 1/432 y x z - 1/864 x y z - 1/1728 x y z + + 3 3 3 3 2 2 3 3 2 2 + - 1/864 y x z - 1/1728 y x z - 1/216 y x z - 1/432 y x z + + 2 3 3 4 3 3 3 2 + - 1/1728 y x z + 1/864 x y z + 1/216 z y x - 1/216 z y x + + 3 3 2 2 3 + - 1/864 z y x - 1/216 y x z + 1/216 z y x + 1/1728 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + + 1/3456 z y x + 1/3456 x y z + 1/1728 x y z - 1/216 y x z + + 4 2 2 3 3 3 4 3 4 2 + - 1/3456 x y z + 1/864 y x z + 1/864 x y z + 1/864 x y z + + 2 4 2 2 2 2 2 2 2 + - 1/864 x y z - 1/864 y x z + 1/432 y x z + 1/432 y x z + + 2 3 2 3 4 3 3 4 2 3 + - 1/432 y x z + 1/216 y x z - 1/864 x y z + 1/1728 x y z + + 3 4 3 4 4 3 4 2 4 + + 1/1728 x y z - 1/1728 x y z + 1/432 y x z - 1/432 y x z + + 3 4 4 4 4 3 2 4 3 + - 1/1728 y x z + 1/1728 x y z - 1/432 x y z + 1/432 x y z + + 4 2 4 2 2 4 2 3 4 3 3 4 + + 1/3456 x y z - 1/864 y x z - 1/3456 y x z + 1/1728 y x z , + + 4 3 4 4 4 4 2 4 + COEFF(0, 2, 2) = 1/1152 x y z + 1/2304 x y z + 5/1152 x y z + + 4 4 3 2 4 4 2 2 4 4 + - 1/1152 x y z - 5/1152 y x z + 1/1152 x y z - 5/2304 x y z + + 2 2 2 2 2 3 4 4 2 + - 5/2304 y x z + 5/1152 y x z + 1/576 x y z + 1/1152 x y z + + 2 3 3 2 2 4 3 3 + + 5/576 y x z + 5/1152 y x z - 1/576 x y z - 1/144 z y + + 3 2 2 4 4 2 + + 5/576 z y x - 5/576 z y x - 1/2304 x y z + 1/144 y z + + 4 3 2 4 2 2 4 3 2 4 2 + - 1/1152 x y z + 1/2304 x y z - 1/576 x y z + 5/2304 x y z + + 2 2 2 2 2 3 2 3 + - 5/1152 y x z - 5/1152 y x z + 1/288 y z - 5/576 y x z + + 4 3 3 4 2 3 4 4 3 3 + + 1/576 x y z - 1/1152 x y z + 1/1152 x y z - 1/144 y z + + 2 3 3 3 4 3 4 4 4 + - 1/288 y z + 1/144 y z - 1/288 y z + 1/288 y z + 1/576 y z + + 3 2 2 4 4 2 4 2 + - 1/288 y z + 5/1152 y x z - 1/576 y z - 1/288 y z + 1/288 y z + + 2 4 4 4 2 2 4 3 + - 1/576 y z - 1/1152 x y z + 1/576 y z + 1/288 y z + + 2 4 3 4 2 4 2 2 4 + - 5/1152 x y z - 1/2304 x y z + 5/2304 y x z , COEFF(1, 2, 2) = + + 2 4 4 3 4 3 4 2 4 4 4 + - 1/864 y x z - 1/1728 x y z + 1/3456 x y z - 1/3456 x y z + + 4 2 4 3 4 4 4 + - 1/432 x y z - 1/432 x y z + 1/1728 x y z + 1/1728 x y z + + 3 3 4 4 3 2 4 3 + - 1/216 y x z - 1/3456 x y z + 1/432 y x z - 1/864 z y x + + 2 3 4 2 3 4 2 + - 1/1728 z y x - 1/1728 x y z + 1/432 y x z + 1/432 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/432 y x z + 1/864 x y z + 1/864 x y z + 1/864 y x z + + 3 2 2 2 3 4 4 2 + - 1/432 y x z - 1/432 y x z - 1/864 x y z - 1/1728 x y z + + 3 3 3 3 2 2 3 3 2 2 + + 1/864 y x z + 1/1728 y x z - 1/216 y x z - 1/432 y x z + + 2 3 3 4 3 3 3 2 + + 1/1728 y x z + 1/864 x y z - 1/216 z y x - 1/216 z y x + + 3 3 2 2 3 + + 1/864 z y x + 1/216 y x z + 1/216 z y x - 1/1728 z y x + + 2 2 3 4 4 2 4 3 2 3 3 + - 1/3456 z y x + 1/3456 x y z + 1/1728 x y z + 1/216 y x z + + 4 2 2 3 3 3 4 3 4 2 + - 1/3456 x y z - 1/864 y x z + 1/864 x y z - 1/864 x y z + + 2 4 2 2 2 2 2 2 2 + - 1/864 x y z + 1/864 y x z + 1/432 y x z + 1/432 y x z + + 2 3 2 3 4 3 3 4 2 3 + + 1/432 y x z + 1/216 y x z - 1/864 x y z + 1/1728 x y z + + 3 4 3 4 4 3 4 2 4 + - 1/1728 x y z - 1/1728 x y z - 1/432 y x z - 1/432 y x z + + 3 4 4 4 4 3 2 4 3 + + 1/1728 y x z + 1/1728 x y z + 1/432 x y z + 1/432 x y z + + 4 2 4 2 2 4 2 3 4 3 3 4 + + 1/3456 x y z - 1/864 y x z + 1/3456 y x z - 1/1728 y x z , + + 2 4 4 3 4 3 4 2 + COEFF(2, 2, 2) = 1/6912 y x z + 1/6912 x y z - 1/6912 x y z + + 4 4 4 4 2 4 3 4 + + 1/13824 x y z + 1/3456 x y z + 1/6912 x y z - 1/3456 x y z + + 4 4 3 3 4 4 3 2 4 + - 1/6912 x y z + 1/1728 y x z + 1/6912 x y z - 1/6912 y x z + + 3 2 3 4 2 3 4 + + 1/1728 z y x + 1/3456 z y x + 1/6912 x y z - 1/3456 y x z + + 2 2 3 2 4 4 4 4 + - 1/3456 y x z + 1/3456 y x z - 1/13824 x y z - 1/6912 x y z + + 2 2 2 3 2 2 2 3 4 + - 1/13824 y x z + 1/3456 y x z + 1/6912 y x z + 1/3456 x y z + + 4 2 3 3 3 3 2 2 3 + + 1/6912 x y z - 1/1728 y x z - 1/3456 y x z + 1/3456 y x z + + 3 2 2 2 3 3 4 3 3 + + 1/6912 y x z - 1/3456 y x z - 1/3456 x y z + 1/1728 z y x + + 3 2 3 3 2 + + 1/3456 z y x - 1/1728 z y x - 1/1728 y x z - 1/3456 z y x + + 2 3 2 2 3 4 4 2 4 3 2 + + 1/3456 z y x + 1/6912 z y x - 1/13824 x y z - 1/6912 x y z + + 3 3 4 2 2 3 3 3 4 3 + - 1/1728 y x z + 1/13824 x y z + 1/1728 y x z - 1/3456 x y z + + 4 2 2 4 2 2 2 2 2 + + 1/6912 x y z + 1/13824 x y z - 1/6912 y x z - 1/6912 y x z + + 2 2 2 3 2 3 4 3 3 + - 1/6912 y x z - 1/3456 y x z - 1/3456 y x z + 1/3456 x y z + + 4 2 3 3 4 3 4 4 3 4 + - 1/6912 x y z + 1/3456 x y z + 1/6912 x y z + 1/3456 y x z + + 2 4 3 4 4 4 4 3 + + 1/6912 y x z - 1/3456 y x z - 1/6912 x y z - 1/3456 x y z + + 2 4 3 4 2 4 2 2 4 2 3 4 + - 1/6912 x y z - 1/13824 x y z + 1/13824 y x z - 1/6912 y x z + + 3 3 4 + + 1/3456 y x z ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-I.compute.c"); +bytes used=11913427852, alloc=10942508, time=1381.25 +bytes used=11914428420, alloc=10942508, time=1381.34 +bytes used=11915428592, alloc=10942508, time=1381.42 +bytes used=11916429024, alloc=10942508, time=1381.51 +bytes used=11917429620, alloc=10942508, time=1381.60 +bytes used=11918429804, alloc=10942508, time=1381.68 +bytes used=11919429988, alloc=10942508, time=1381.77 +bytes used=11920430368, alloc=10942508, time=1381.85 +bytes used=11921430792, alloc=10942508, time=1381.94 +bytes used=11922431188, alloc=10942508, time=1382.02 +bytes used=11923431680, alloc=10942508, time=1382.10 +bytes used=11924432244, alloc=10942508, time=1382.17 +bytes used=11925432460, alloc=10942508, time=1382.25 +bytes 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x y z - 1/3456 y z + 1/1152 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/2304 y x z - 1/3456 y x z - 1/1728 y x z , COEFF(-1, -2, -2) + + 2 4 3 4 2 4 2 4 + = - 1/432 y x z + 1/864 x y z + 1/216 x y z + 1/576 x y z + + 3 4 3 3 4 4 3 2 4 + - 1/432 x y z - 1/108 y x z - 1/864 x y z - 1/576 y x z + + 3 2 3 3 4 2 + - 1/216 z y x + 1/432 z y x - 1/216 y x z - 1/216 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/216 y x z + 1/1152 x y z + 1/432 x y z + 1/1152 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/216 y x z + 1/576 y x z + 1/216 y x z - 1/432 y x z + + 2 3 3 2 2 2 3 3 3 + - 1/288 y x z + 1/576 y x z - 1/432 y x z + 1/216 z y + + 3 3 2 3 3 + - 1/108 z y x - 1/288 z y x + 1/216 z y x + 1/108 y x z + + 2 2 3 2 2 3 + + 1/288 z y x + 1/432 z y x - 1/864 z y x - 1/216 y z + + 3 3 3 3 3 4 2 2 4 2 + + 1/108 y x z - 1/216 y x z - 1/432 x y z - 1/1152 x y z + + 2 2 2 2 2 2 2 + + 1/432 y x z - 1/576 y x z - 1/576 y x z - 1/216 y x z + + 2 3 2 3 3 4 3 4 3 + + 1/432 y z + 1/288 y x z + 1/432 x y z + 1/216 y x z + 1/216 y z + + 2 3 3 3 4 3 4 4 4 + - 1/432 y z - 1/216 y z - 1/432 y z + 1/432 y z - 1/864 y z + + 3 2 2 4 4 2 4 2 + - 1/432 y z + 1/576 y x z + 1/864 y z - 1/432 y z + 1/432 y z + + 3 4 2 4 2 2 4 3 4 3 + - 1/432 y x z + 1/864 y z - 1/864 y z - 1/216 x y z + 1/432 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + - 1/576 x y z - 1/1152 y x z + 1/864 y x z + 1/432 y x z , + + 2 4 3 4 2 4 + COEFF(0, -2, -2) = 5/1152 y x z - 1/576 x y z - 5/576 x y z + + 3 4 3 3 4 4 3 + + 1/288 x y z + 5/288 y x z + 1/576 x y z + 1/144 z y x + + 2 3 3 4 2 2 3 + - 1/288 z y x + 5/576 y x z + 5/576 y x z - 5/576 y x z + + 4 4 3 2 3 3 3 3 2 + - 5/1152 x y z - 5/576 y x z - 1/144 y x z + 1/288 y x z + + 2 3 3 3 3 3 + + 1/288 y x z + 5/288 z y x - 1/144 z y x - 5/288 y x z + + 2 3 2 2 3 3 3 3 3 3 + - 1/288 z y x + 1/576 z y x - 5/288 y x z + 1/144 y x z + + 4 2 2 2 2 3 4 3 + + 5/1152 x y z - 5/1152 y x z + 5/576 y x z - 1/288 x y z + + 4 3 4 4 3 2 3 4 + - 5/576 y x z + 1/288 y x z + 5/576 x y z - 1/576 y x z + + 3 3 4 2 4 3 4 2 + - 1/288 y x 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2 4 3 4 3 + + 1/144 x y z + 5/144 x y z - 1/72 x y z - 5/36 y x z + + 3 4 4 3 2 3 3 4 + - 1/144 x y z - 1/18 z y x + 1/36 z y x - 5/288 y x z + + 2 2 3 4 4 3 2 + - 5/36 y x z + 5/36 y x z + 5/288 x y z + 5/288 y x z + + 3 3 3 3 2 2 3 3 3 + + 1/18 y x z - 1/144 y x z - 1/18 y x z - 5/144 z y x + + 3 3 2 3 2 2 3 3 3 + + 1/72 z y x + 5/36 y x z + 1/18 z y x - 1/36 z y x + 5/144 y x z + + 3 3 3 4 2 2 2 2 + - 1/72 y x z - 5/288 x y z + 5/72 y x z - 5/72 y x z + + 3 4 3 4 3 4 4 3 + + 1/72 x y z + 5/72 y x z - 1/36 y x z - 5/144 x y z + + 2 3 4 3 3 4 2 4 + + 1/36 y x z + 1/144 y x z , COEFF(1, -1, -2) = 1/27 y x z + + 3 4 2 4 2 4 3 4 + - 1/216 x y z - 1/54 x y z + 1/144 x y z + 1/108 x y z + + 3 3 4 4 3 2 4 3 + + 2/27 y x z + 1/216 x y z - 1/288 y x z + 1/27 z y x + + 2 3 3 4 2 2 3 + - 1/54 z y x + 1/108 y x z + 2/27 y x z - 2/27 y x z + + 2 4 4 4 4 2 2 2 3 2 + + 1/288 x y z - 1/108 x y z + 1/72 y x z - 1/108 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/36 y x z - 1/27 y x z + 1/216 y x z - 1/36 y x z + + 3 2 2 2 3 3 3 3 + + 1/288 y x z + 1/27 y x z + 1/108 z y + 1/54 z y x + + 3 2 3 3 2 2 3 + - 1/144 z y x - 1/108 z y x - 2/27 y x z + 1/36 z y x - 1/27 z y x + + 2 2 3 3 3 3 3 3 4 2 + + 1/54 z y x - 1/27 y z - 1/54 y x z + 1/108 y x z + 1/108 x y z + + 2 4 2 2 2 2 2 2 2 + - 1/288 x y z - 1/27 y x z - 1/36 y x z - 1/72 y x z + + 2 2 3 2 3 3 4 3 4 + + 1/27 y x z + 1/27 y z + 1/144 y x z - 1/108 x y z - 1/27 y x z + + 3 2 3 3 3 4 3 4 + + 1/27 y z - 1/27 y z - 1/108 y z - 1/54 y z + 1/216 y z + + 4 4 3 2 2 4 4 2 4 + - 1/216 y z - 1/216 y z + 1/72 y x z + 1/216 y z - 1/108 y z + + 2 3 4 2 4 2 2 4 3 + + 1/54 y z + 1/54 y x z + 1/54 y z - 1/54 y z + 1/54 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + + 1/108 y z - 1/144 x y z - 1/72 y x z - 1/54 y x z + + 3 3 4 2 4 3 4 2 + - 1/216 y x z , COEFF(2, -1, -2) = - 1/432 y x z + 1/864 x y z + + 4 2 4 3 4 3 + + 1/864 x y z - 1/288 x y z - 1/432 x y z - 1/216 y x z + + 3 4 4 3 2 4 3 2 3 + - 1/864 x y z + 1/576 y x z - 1/108 z y x + 1/216 z y x + + 3 4 2 2 3 2 4 4 + - 1/1728 y x z - 1/216 y x z + 1/216 y x z - 1/576 x y z + + 4 4 2 2 2 3 2 2 2 3 + + 1/1728 x y z - 1/144 y x z + 1/1728 y x z - 1/72 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 1/108 y x z - 1/864 y x z + 1/72 y x z - 1/576 y x z + + 2 3 3 3 3 3 2 + - 1/108 y x z - 1/864 z y - 1/864 z y x + 1/288 z y x + + 3 3 2 2 3 + + 1/432 z y x + 1/216 y x z - 1/72 z y x + 1/108 z y x + + 2 2 3 3 3 3 3 3 + - 1/216 z y x + 1/216 y z + 1/864 y x z - 1/432 y x z + + 4 2 2 4 2 2 2 2 2 + - 1/1728 x y z + 1/576 x y z + 1/432 y x z + 1/72 y x z + + 2 2 2 2 3 2 3 + + 1/144 y x z - 1/432 y x z - 1/216 y z - 1/288 y x z + + 3 4 3 4 3 2 3 3 3 + + 1/432 x y z + 1/432 y x z - 1/216 y z + 1/216 y z + 1/864 y z + + 4 3 4 4 4 3 2 2 4 + + 1/432 y z - 1/1728 y z + 1/1728 y z + 1/1728 y z - 1/144 y x z + + 4 2 4 2 3 4 2 4 + - 1/1728 y z + 1/864 y z - 1/432 y z - 1/216 y x z - 1/432 y z + + 2 2 4 3 4 3 2 4 3 + + 1/432 y z - 1/864 x y z - 1/864 y z + 1/288 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/144 y x z + 1/216 y x z + 1/864 y x z , COEFF(-2, 0, -2) = + + 2 4 3 4 2 4 2 4 + 5/1152 y x z - 1/576 x y z - 1/576 x y z - 1/192 x y z + + 3 4 3 4 4 2 2 3 + + 1/288 x y z + 1/576 x y z + 1/144 z + 5/576 y x z - 5/576 y x z + + 2 4 4 4 4 2 2 2 2 2 3 + - 1/384 x y z - 1/1152 x y z - 5/384 y x z - 5/192 y x z + + 3 4 2 3 3 3 2 + + 1/72 z x + 1/288 z + 5/288 y x z - 1/144 z - 1/288 z + + 2 3 2 2 3 4 2 2 4 2 + - 5/288 z y x + 5/576 z y x + 1/1152 x y z + 1/384 x y z + + 2 2 2 2 2 2 + - 5/1152 y x z + 5/192 y x z - 5/576 y z - 1/144 x z - 1/48 x z + + 3 4 3 2 3 3 3 2 3 4 4 + - 1/288 x y z + 5/576 y z - 1/72 x z + 1/48 x z + 1/1152 y z + + 2 4 3 4 4 2 4 + - 1/96 x z + 1/144 x z - 1/288 x z - 1/1152 y z + 1/576 y z + + 3 4 2 2 2 3 2 2 4 + + 1/144 x z + 1/96 x z + 1/288 x z - 1/144 x z - 5/1152 y z + + 2 2 4 3 4 3 2 4 3 + + 5/1152 y z + 1/576 x y z - 1/576 y z + 1/192 x y z + + 2 2 4 2 3 4 2 4 + + 5/384 y x z - 5/576 y x z , COEFF(-1, 0, -2) = - 5/72 y x z + + 3 4 2 4 2 4 3 4 + + 1/144 x y z + 1/36 x y z + 1/96 x y z - 1/72 x y z + + 3 4 4 2 2 3 2 4 4 + - 1/144 x y z - 1/18 z - 5/36 y x z + 5/36 y x z + 1/192 x y z + + 4 4 2 2 2 2 2 3 3 4 + + 1/72 x y z + 5/192 y x z + 5/96 y x z - 1/18 z x - 1/36 z + + 2 3 3 3 2 2 3 2 2 3 + - 5/72 y x z + 1/18 z + 1/36 z + 5/72 z y x - 5/144 z y x + + 4 2 2 4 2 2 2 2 2 2 + - 1/72 x y z - 1/192 x y z + 5/72 y x z - 5/96 y x z + 5/72 y z + + 2 3 4 3 2 3 3 3 + + 1/9 x z + 1/24 x z + 1/72 x y z - 5/72 y z + 1/18 x z + + 2 3 4 4 2 4 3 4 + - 1/24 x z - 1/144 y z + 1/48 x z - 1/9 x z + 1/18 x z + + 4 2 4 3 4 2 2 2 + + 1/144 y z - 1/72 y z - 1/36 x z - 1/48 x z - 1/18 x z + + 3 2 2 4 2 2 4 3 4 3 + + 1/36 x z + 5/144 y z - 5/144 y z - 1/36 x y z + 1/72 y z + + 2 4 3 2 2 4 2 3 4 + - 1/96 x y z - 5/192 y x z + 5/144 y x z , COEFF(0, 0, -2) = + + 2 2 3 2 3 4 4 3 2 3 3 + 5/96 z y x - 5/96 y x z - 5/48 x z - 1/24 x z - 1/12 x z + + 25 2 2 2 4 2 3 4 25 2 3 + - --- y x z + 5/48 x z + 5/192 x y z + 1/48 x y z - -- y x z + 192 96 + + 25 2 3 4 4 3 4 4 3 4 2 + + -- y x z + 1/12 z x - 5/192 x y z + 1/96 x y z - 1/96 x y z + 96 + + 3 4 3 4 3 2 3 3 + + 1/24 x z + 5/24 x z + 5/96 x y z - 5/24 x z + 5/48 y x z + + 2 3 3 4 3 4 25 2 4 + - 5/48 z y x - 1/48 x y z - 5/96 x y z + --- y x z , + 192 + + 2 4 3 4 2 4 + COEFF(1, 0, -2) = - 5/72 y x z + 1/144 x y z + 1/36 x y z + + 2 4 3 4 3 4 4 2 + - 1/96 x y z - 1/72 x y z - 1/144 x y z + 1/18 z - 5/36 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 5/36 y x z - 1/192 x y z + 1/72 x y z - 5/192 y x z + + 2 2 3 3 4 2 3 3 3 2 + - 5/96 y x z - 1/18 z x + 1/36 z - 5/72 y x z - 1/18 z - 1/36 z + + 2 3 2 2 3 4 2 2 4 2 + + 5/72 z y x - 5/144 z y x - 1/72 x y z + 1/192 x y z + + 2 2 2 2 2 2 + + 5/72 y x z + 5/96 y x z - 5/72 y z + 1/9 x z - 1/24 x z + + 3 4 3 2 3 3 3 2 3 4 4 + + 1/72 x y z + 5/72 y z + 1/18 x z + 1/24 x z + 1/144 y z + + 2 4 3 4 4 2 4 3 4 + - 1/48 x z - 1/9 x z + 1/18 x z - 1/144 y z + 1/72 y z - 1/36 x z + + 2 2 2 3 2 2 4 2 2 + + 1/48 x z - 1/18 x z + 1/36 x z - 5/144 y z + 5/144 y z + + 4 3 4 3 2 4 3 2 2 4 + - 1/36 x y z - 1/72 y z + 1/96 x y z + 5/192 y x z + + 2 3 4 2 4 3 4 2 + + 5/144 y x z , COEFF(2, 0, -2) = 5/1152 y x z - 1/576 x y z + + 4 2 4 3 4 3 4 4 + - 1/576 x y z + 1/192 x y z + 1/288 x y z + 1/576 x y z - 1/144 z + + 2 2 3 2 4 4 4 4 + + 5/576 y x z - 5/576 y x z + 1/384 x y z - 1/1152 x y z + + 2 2 2 2 2 3 3 4 2 3 3 + + 5/384 y x z + 5/192 y x z + 1/72 z x - 1/288 z + 5/288 y x z + + 3 2 2 3 2 2 3 4 2 + + 1/144 z + 1/288 z - 5/288 z y x + 5/576 z y x + 1/1152 x y z + + 2 4 2 2 2 2 2 2 + - 1/384 x y z - 5/1152 y x z - 5/192 y x z + 5/576 y z - 1/144 x z + + 2 3 4 3 2 3 3 3 2 3 + + 1/48 x z - 1/288 x y z - 5/576 y z - 1/72 x z - 1/48 x z + + 4 4 2 4 3 4 4 2 + - 1/1152 y z + 1/96 x z + 1/144 x z - 1/288 x z + 1/1152 y z + + 4 3 4 2 2 2 3 2 + - 1/576 y z + 1/144 x z - 1/96 x z + 1/288 x z - 1/144 x z + + 2 4 2 2 4 3 4 3 + + 5/1152 y z - 5/1152 y z + 1/576 x y z + 1/576 y z + + 2 4 3 2 2 4 2 3 4 + - 1/192 x y z - 5/384 y x z - 5/576 y x z , COEFF(-2, 1, -2) = + + 2 4 3 4 2 4 2 4 + - 1/432 y x z + 1/864 x y z + 1/864 x y z + 1/288 x y z + + 3 4 3 3 4 4 3 2 4 + - 1/432 x y z + 1/216 y x z - 1/864 x y z + 1/576 y x z + + 3 2 3 3 4 2 + + 1/108 z y x - 1/216 z y x + 1/1728 y x z - 1/216 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/216 y x z + 1/576 x y z + 1/1728 x y z + 1/144 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/1728 y x z + 1/72 y x z - 1/108 y x z + 1/864 y x z + + 2 3 3 2 2 2 3 3 3 + + 1/72 y x z - 1/576 y x z - 1/108 y x z - 1/864 z y + + 3 3 2 3 3 2 + + 1/864 z y x + 1/288 z y x - 1/432 z y x - 1/216 y x z - 1/72 z y x + + 2 3 2 2 3 3 3 + + 1/108 z y x - 1/216 z y x + 1/216 y z - 1/864 y x z + + 3 3 3 4 2 2 4 2 2 2 + + 1/432 y x z - 1/1728 x y z - 1/576 x y z + 1/432 y x z + + 2 2 2 2 2 2 + - 1/72 y x z + 1/144 y x z + 1/432 y x z + 1/216 y z + + 3 2 3 3 4 3 4 3 + - 1/288 y x z + 1/432 x y z - 1/432 y x z - 1/216 y z + + 2 3 3 3 4 3 4 4 4 + - 1/216 y z + 1/864 y z + 1/432 y z - 1/1728 y z - 1/1728 y z + + 3 2 2 4 4 2 4 2 + + 1/1728 y z - 1/144 y x z + 1/1728 y z - 1/864 y z - 1/432 y z + + 3 4 2 4 2 2 4 3 4 3 + + 1/216 y x z + 1/432 y z - 1/432 y z - 1/864 x y z + 1/864 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + - 1/288 x y z - 1/144 y x z + 1/216 y x z - 1/864 y x z , + + 2 4 3 4 2 4 + COEFF(-1, 1, -2) = 1/27 y x z - 1/216 x y z - 1/54 x y z + + 2 4 3 4 3 3 4 4 + - 1/144 x y z + 1/108 x y z - 2/27 y x z + 1/216 x y z + + 3 2 4 3 2 3 3 4 + - 1/288 y x z - 1/27 z y x + 1/54 z y x - 1/108 y x z + + 2 2 3 2 4 4 4 4 + + 2/27 y x z - 2/27 y x z - 1/288 x y z - 1/108 x y z + + 2 2 2 3 2 2 2 3 3 3 + - 1/72 y x z + 1/108 y x z - 1/36 y x z + 1/27 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + - 1/216 y x z - 1/36 y x z + 1/288 y x z + 1/27 y x z + + 3 3 3 2 3 3 + + 1/108 z y - 1/54 z y x - 1/144 z y x + 1/108 z y x + 2/27 y x z + + 2 2 3 2 2 3 3 3 + + 1/36 z y x - 1/27 z y x + 1/54 z y x - 1/27 y z + 1/54 y x z + + 3 3 3 4 2 2 4 2 2 2 + - 1/108 y x z + 1/108 x y z + 1/288 x y z - 1/27 y x z + + 2 2 2 2 2 2 3 2 3 + + 1/36 y x z - 1/72 y x z - 1/27 y x z - 1/27 y z + 1/144 y x z + + 3 4 3 4 3 2 3 3 3 + - 1/108 x y z + 1/27 y x z + 1/27 y z + 1/27 y z - 1/108 y z + + 4 3 4 4 4 3 2 2 4 + - 1/54 y z + 1/216 y z + 1/216 y z - 1/216 y z + 1/72 y x z + + 4 2 4 2 3 4 2 4 + - 1/216 y z + 1/108 y z + 1/54 y z - 1/54 y x z - 1/54 y z + + 2 2 4 3 4 3 2 4 3 2 2 4 + + 1/54 y z + 1/54 x y z - 1/108 y z + 1/144 x y z + 1/72 y x z + + 2 3 4 3 3 4 2 4 + - 1/54 y x z + 1/216 y x z , COEFF(0, 1, -2) = - 5/72 y x z + + 3 4 2 4 3 4 3 + + 1/144 x y z + 5/144 x y z - 1/72 x y z + 5/36 y x z + + 3 4 4 3 2 3 3 4 + - 1/144 x y z + 1/18 z y x - 1/36 z y x + 5/288 y x z + + 2 2 3 4 4 3 2 + - 5/36 y x z + 5/36 y x z + 5/288 x y z - 5/288 y x z + + 3 3 3 3 2 2 3 3 3 + - 1/18 y x z + 1/144 y x z - 1/18 y x z + 5/144 z y x + + 3 3 2 3 2 2 3 3 3 + - 1/72 z y x - 5/36 y x z + 1/18 z y x - 1/36 z y x - 5/144 y x z + + 3 3 3 4 2 2 2 2 + + 1/72 y x z - 5/288 x y z + 5/72 y x z + 5/72 y x z + + 3 4 3 4 3 4 4 3 + + 1/72 x y z - 5/72 y x z + 1/36 y x z - 5/144 x y z + + 2 3 4 3 3 4 2 4 + + 1/36 y x z - 1/144 y x z , COEFF(1, 1, -2) = 1/27 y x z + + 3 4 2 4 2 4 3 4 + - 1/216 x y z - 1/54 x y z + 1/144 x y z + 1/108 x y z + + 3 3 4 4 3 2 4 3 + - 2/27 y x z + 1/216 x y z + 1/288 y x z - 1/27 z y x + + 2 3 3 4 2 2 3 + + 1/54 z y x - 1/108 y x z + 2/27 y x z - 2/27 y x z + + 2 4 4 4 4 2 2 2 3 2 + + 1/288 x y z - 1/108 x y z + 1/72 y x z + 1/108 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/36 y x z + 1/27 y x z - 1/216 y x z + 1/36 y x z + + 3 2 2 2 3 3 3 3 + - 1/288 y x z + 1/27 y x z - 1/108 z y - 1/54 z y x + + 3 2 3 3 2 2 3 + + 1/144 z y x + 1/108 z y x + 2/27 y x z - 1/36 z y x - 1/27 z y x + + 2 2 3 3 3 3 3 3 4 2 + + 1/54 z y x + 1/27 y z + 1/54 y x z - 1/108 y x z + 1/108 x y z + + 2 4 2 2 2 2 2 2 2 + - 1/288 x y z - 1/27 y x z - 1/36 y x z + 1/72 y x z + + 2 2 3 2 3 3 4 3 4 + - 1/27 y x z + 1/27 y z - 1/144 y x z - 1/108 x y z + 1/27 y x z + + 3 2 3 3 3 4 3 4 + - 1/27 y z - 1/27 y z + 1/108 y z + 1/54 y z - 1/216 y z + + 4 4 3 2 2 4 4 2 4 + - 1/216 y z + 1/216 y z - 1/72 y x z + 1/216 y z - 1/108 y z + + 2 3 4 2 4 2 2 4 3 + - 1/54 y z - 1/54 y x z + 1/54 y z - 1/54 y z + 1/54 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + + 1/108 y z - 1/144 x y z - 1/72 y x z - 1/54 y x z + + 3 3 4 2 4 3 4 2 + + 1/216 y x z , COEFF(2, 1, -2) = - 1/432 y x z + 1/864 x y z + + 4 2 4 3 4 3 + + 1/864 x y z - 1/288 x y z - 1/432 x y z + 1/216 y x z + + 3 4 4 3 2 4 3 2 3 + - 1/864 x y z - 1/576 y x z + 1/108 z y x - 1/216 z y x + + 3 4 2 2 3 2 4 4 + + 1/1728 y x z - 1/216 y x z + 1/216 y x z - 1/576 x y z + + 4 4 2 2 2 3 2 2 2 3 + + 1/1728 x y z - 1/144 y x z - 1/1728 y x z - 1/72 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/108 y x z + 1/864 y x z - 1/72 y x z + 1/576 y x z + + 2 3 3 3 3 3 2 + - 1/108 y x z + 1/864 z y + 1/864 z y x - 1/288 z y x + + 3 3 2 2 3 + - 1/432 z y x - 1/216 y x z + 1/72 z y x + 1/108 z y x + + 2 2 3 3 3 3 3 3 + - 1/216 z y x - 1/216 y z - 1/864 y x z + 1/432 y x z + + 4 2 2 4 2 2 2 2 2 + - 1/1728 x y z + 1/576 x y z + 1/432 y x z + 1/72 y x z + + 2 2 2 2 3 2 3 + - 1/144 y x z + 1/432 y x z - 1/216 y z + 1/288 y x z + + 3 4 3 4 3 2 3 3 3 + + 1/432 x y z - 1/432 y x z + 1/216 y z + 1/216 y z - 1/864 y z + + 4 3 4 4 4 3 2 2 4 + - 1/432 y z + 1/1728 y z + 1/1728 y z - 1/1728 y z + 1/144 y x z + + 4 2 4 2 3 4 2 4 + - 1/1728 y z + 1/864 y z + 1/432 y z + 1/216 y x z - 1/432 y z + + 2 2 4 3 4 3 2 4 3 + + 1/432 y z - 1/864 x y z - 1/864 y z + 1/288 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/144 y x z + 1/216 y x z - 1/864 y x z , COEFF(-2, 2, -2) = + + 2 4 3 4 2 4 2 4 + 1/6912 y x z - 1/3456 x y z - 1/3456 x y z - 1/1152 x y z + + 3 4 3 3 4 4 3 2 4 + + 1/1728 x y z - 1/1728 y x z + 1/3456 x y z - 1/1152 y x z + + 3 2 3 3 4 2 + - 1/864 z y x + 1/1728 z y x - 1/3456 y x z + 1/3456 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/3456 y x z - 1/2304 x y z - 1/6912 x y z - 1/2304 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/3456 y x z - 1/1152 y x z + 1/864 y x z - 1/1728 y x z + + 2 3 3 2 2 2 3 3 3 + - 1/576 y x z + 1/1152 y x z + 1/1728 y x z + 1/1728 z y + + 3 3 2 3 3 + - 1/1728 z y x - 1/576 z y x + 1/864 z y x + 1/1728 y x z + + 2 2 3 2 2 3 + + 1/576 z y x - 1/1728 z y x + 1/3456 z y x - 1/1728 y z + + 3 3 3 3 3 4 2 2 4 2 + + 1/1728 y x z - 1/864 y x z + 1/6912 x y z + 1/2304 x y z + + 2 2 2 2 2 2 2 + - 1/6912 y x z + 1/1152 y x z - 1/1152 y x z - 1/3456 y x z + + 2 3 2 3 3 4 3 4 + - 1/3456 y z + 1/576 y x z - 1/1728 x y z + 1/3456 y x z + + 3 2 3 3 3 4 3 4 + + 1/1728 y z + 1/3456 y z - 1/1728 y z - 1/3456 y z + 1/3456 y z + + 4 4 3 2 2 4 4 2 + + 1/6912 y z - 1/3456 y z + 1/1152 y x z - 1/6912 y z + + 4 2 3 4 2 4 2 2 + + 1/3456 y z + 1/3456 y z - 1/1728 y x z - 1/6912 y z + 1/6912 y z + + 4 3 4 3 2 4 3 2 2 4 + + 1/3456 x y z - 1/3456 y z + 1/1152 x y z + 1/2304 y x z + + 2 3 4 3 3 4 2 4 + - 1/3456 y x z + 1/1728 y x z , COEFF(-1, 2, -2) = - 1/432 y x z + + 3 4 2 4 2 4 3 4 + + 1/864 x y z + 1/216 x y z + 1/576 x y z - 1/432 x y z + + 3 3 4 4 3 2 4 3 + + 1/108 y x z - 1/864 x y z + 1/576 y x z + 1/216 z y x + + 2 3 3 4 2 2 3 + - 1/432 z y x + 1/216 y x z - 1/216 y x z + 1/216 y x z + + 2 4 4 4 4 2 2 2 3 2 + + 1/1152 x y z + 1/432 x y z + 1/1152 y x z - 1/216 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/576 y x z - 1/216 y x z + 1/432 y x z + 1/288 y x z + + 3 2 2 2 3 3 3 3 + - 1/576 y x z - 1/432 y x z - 1/216 z y + 1/108 z y x + + 3 2 3 3 2 + + 1/288 z y x - 1/216 z y x - 1/108 y x z - 1/288 z y x + + 2 3 2 2 3 3 3 + + 1/432 z y x - 1/864 z y x + 1/216 y z - 1/108 y x z + + 3 3 3 4 2 2 4 2 2 2 + + 1/216 y x z - 1/432 x y z - 1/1152 x y z + 1/432 y x z + + 2 2 2 2 2 2 + - 1/576 y x z + 1/576 y x z + 1/216 y x z + 1/432 y z + + 3 2 3 3 4 3 4 3 + - 1/288 y x z + 1/432 x y z - 1/216 y x z - 1/216 y z + + 2 3 3 3 4 3 4 4 4 + - 1/432 y z + 1/216 y z + 1/432 y z - 1/432 y z - 1/864 y z + + 3 2 2 4 4 2 4 2 + + 1/432 y z - 1/576 y x z + 1/864 y z - 1/432 y z - 1/432 y z + + 3 4 2 4 2 2 4 3 4 3 + + 1/432 y x z + 1/864 y z - 1/864 y z - 1/216 x y z + 1/432 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + - 1/576 x y z - 1/1152 y x z + 1/864 y x z - 1/432 y x z , + + 2 4 3 4 2 4 + COEFF(0, 2, -2) = 5/1152 y x z - 1/576 x y z - 5/576 x y z + + 3 4 3 3 4 4 3 + + 1/288 x y z - 5/288 y x z + 1/576 x y z - 1/144 z y x + + 2 3 3 4 2 2 3 + + 1/288 z y x - 5/576 y x z + 5/576 y x z - 5/576 y x z + + 4 4 3 2 3 3 3 3 2 + - 5/1152 x y z + 5/576 y x z + 1/144 y x z - 1/288 y x z + + 2 3 3 3 3 3 + + 1/288 y x z - 5/288 z y x + 1/144 z y x + 5/288 y x z + + 2 3 2 2 3 3 3 3 3 3 + - 1/288 z y x + 1/576 z y x + 5/288 y x z - 1/144 y x z + + 4 2 2 2 2 3 4 3 + + 5/1152 x y z - 5/1152 y x z - 5/576 y x z - 1/288 x y z + + 4 3 4 4 3 2 3 4 + + 5/576 y x z - 1/288 y x z + 5/576 x y z - 1/576 y x z + + 3 3 4 2 4 3 4 2 + + 1/288 y x z , COEFF(1, 2, -2) = - 1/432 y x z + 1/864 x y z + + 4 2 4 3 4 3 + + 1/216 x y z - 1/576 x y z - 1/432 x y z + 1/108 y x z + + 3 4 4 3 2 4 3 2 3 + - 1/864 x y z - 1/576 y x z + 1/216 z y x - 1/432 z y x + + 3 4 2 2 3 2 4 4 + + 1/216 y x z - 1/216 y x z + 1/216 y x z - 1/1152 x y z + + 4 4 2 2 2 3 2 2 2 3 + + 1/432 x y z - 1/1152 y x z - 1/216 y x z - 1/576 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/216 y x z + 1/432 y x z - 1/288 y x z + 1/576 y x z + + 2 3 3 3 3 3 2 + - 1/432 y x z + 1/216 z y + 1/108 z y x - 1/288 z y x + + 3 3 2 2 3 + - 1/216 z y x - 1/108 y x z + 1/288 z y x + 1/432 z y x + + 2 2 3 3 3 3 3 3 + - 1/864 z y x - 1/216 y z - 1/108 y x z + 1/216 y x z + + 4 2 2 4 2 2 2 2 2 + - 1/432 x y z + 1/1152 x y z + 1/432 y x z + 1/576 y x z + + 2 2 2 2 3 2 3 + - 1/576 y x z + 1/216 y x z - 1/432 y z + 1/288 y x z + + 3 4 3 4 3 2 3 3 3 + + 1/432 x y z - 1/216 y x z + 1/216 y z + 1/432 y z - 1/216 y z + + 4 3 4 4 4 3 2 2 4 + - 1/432 y z + 1/432 y z + 1/864 y z - 1/432 y z + 1/576 y x z + + 4 2 4 2 3 4 2 4 + - 1/864 y z + 1/432 y z + 1/432 y z + 1/432 y x z - 1/864 y z + + 2 2 4 3 4 3 2 4 3 + + 1/864 y z - 1/216 x y z - 1/432 y z + 1/576 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/1152 y x z + 1/864 y x z - 1/432 y x z , COEFF(2, 2, -2) = + + 2 4 3 4 2 4 2 4 + 1/6912 y x z - 1/3456 x y z - 1/3456 x y z + 1/1152 x y z + + 3 4 3 3 4 4 3 2 4 + + 1/1728 x y z - 1/1728 y x z + 1/3456 x y z + 1/1152 y x z + + 3 2 3 3 4 2 + - 1/864 z y x + 1/1728 z y x - 1/3456 y x z + 1/3456 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/3456 y x z + 1/2304 x y z - 1/6912 x y z + 1/2304 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/3456 y x z + 1/1152 y x z + 1/864 y x z - 1/1728 y x z + + 2 3 3 2 2 2 3 3 3 + + 1/576 y x z - 1/1152 y x z + 1/1728 y x z - 1/1728 z y + + 3 3 2 3 3 + - 1/1728 z y x + 1/576 z y x + 1/864 z y x + 1/1728 y x z + + 2 2 3 2 2 3 + - 1/576 z y x - 1/1728 z y x + 1/3456 z y x + 1/1728 y z + + 3 3 3 3 3 4 2 2 4 2 + + 1/1728 y x z - 1/864 y x z + 1/6912 x y z - 1/2304 x y z + + 2 2 2 2 2 2 2 + - 1/6912 y x z - 1/1152 y x z + 1/1152 y x z - 1/3456 y x z + + 2 3 2 3 3 4 3 4 + + 1/3456 y z - 1/576 y x z - 1/1728 x y z + 1/3456 y x z + + 3 2 3 3 3 4 3 4 + - 1/1728 y z - 1/3456 y z + 1/1728 y z + 1/3456 y z - 1/3456 y z + + 4 4 3 2 2 4 4 2 + - 1/6912 y z + 1/3456 y z - 1/1152 y x z + 1/6912 y z + + 4 2 3 4 2 4 2 2 + - 1/3456 y z - 1/3456 y z - 1/1728 y x z + 1/6912 y z - 1/6912 y z + + 4 3 4 3 2 4 3 2 2 4 + + 1/3456 x y z + 1/3456 y z - 1/1152 x y z - 1/2304 y x z + + 2 3 4 3 3 4 2 4 + - 1/3456 y x z + 1/1728 y x z , COEFF(-2, -2, -1) = - 1/1728 y x z + + 3 4 2 4 2 4 3 4 + + 1/216 x y z + 1/432 x y z + 1/144 x y z - 1/216 x y z + + 3 3 4 4 3 2 4 3 + - 1/864 y x z - 1/864 x y z - 1/288 y x z - 1/108 z y x + + 2 3 3 4 2 2 3 + + 1/108 z y x - 1/864 y x z - 1/432 y x z + 1/1728 y x z + + 2 4 4 4 4 2 2 2 3 2 + + 1/576 x y z + 1/1728 x y z + 1/144 y x z + 1/216 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/576 y x z + 1/432 y x z - 1/108 y x z - 1/288 y x z + + 3 2 2 2 3 3 3 3 + + 1/72 y x z - 1/864 y x z + 1/216 z y - 1/216 z y x + + 3 2 3 3 2 2 3 + - 1/72 z y x + 1/108 z y x + 1/216 y x z + 1/72 z y x + 1/216 z y x + + 2 2 3 3 3 3 3 3 + - 1/216 z y x - 1/216 y z + 1/864 y x z - 1/432 y x z + + 4 2 2 4 2 2 2 2 2 + - 1/432 x y z - 1/144 x y z + 1/432 y x z - 1/144 y x z + + 2 2 2 2 3 2 3 + - 1/72 y x z - 1/216 y x z + 1/432 y z + 1/288 y x z + + 3 4 3 4 3 2 3 3 3 + + 1/864 x y z + 1/864 y x z + 1/864 y z - 1/1728 y z - 1/864 y z + + 4 3 4 4 4 3 2 2 4 + - 1/864 y z + 1/864 y z - 1/1728 y z - 1/216 y z + 1/288 y x z + + 4 2 4 2 3 4 2 4 + + 1/432 y z - 1/432 y z + 1/216 y z - 1/432 y x z + 1/1728 y z + + 2 2 4 3 4 3 2 4 3 + - 1/432 y z - 1/1728 x y z + 1/1728 y z - 1/576 x y z + + 2 2 4 2 3 4 3 3 4 + - 1/576 y x z + 1/864 y x z + 1/432 y x z , COEFF(-1, -2, -1) = + + 2 4 3 4 2 4 2 4 3 4 + 1/108 y x z - 1/54 x y z - 1/27 x y z - 1/72 x y z + 1/54 x y z + + 3 3 4 4 3 2 4 3 + + 1/54 y x z + 1/216 x y z + 1/144 y x z + 1/27 z y x + + 2 3 3 4 2 2 3 + - 1/27 z y x + 1/54 y x z + 1/27 y x z - 1/108 y x z + + 2 4 4 4 4 2 2 2 3 2 + - 1/288 x y z - 1/108 x y z - 1/72 y x z - 2/27 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/288 y x z - 1/108 y x z + 1/27 y x z + 1/144 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/36 y x z + 1/216 y x z - 1/27 z y + 2/27 z y x + 1/36 z y x + + 3 3 2 2 3 2 2 3 + - 1/27 z y x - 2/27 y x z - 1/36 z y x - 1/54 z y x + 1/54 z y x + + 3 3 3 3 3 4 2 2 4 2 + + 1/27 y z - 1/54 y x z + 1/108 y x z + 1/27 x y z + 1/72 x y z + + 2 2 2 2 2 2 2 2 + - 1/27 y x z + 1/72 y x z + 1/36 y x z + 2/27 y x z - 1/54 y z + + 3 2 3 3 4 3 4 3 2 3 + - 1/144 y x z - 1/216 x y z - 1/54 y x z - 1/108 y z + 1/216 y z + + 3 3 4 3 4 4 4 3 2 + + 1/108 y z + 1/108 y z - 1/108 y z + 1/216 y z + 1/27 y z + + 2 4 4 2 4 2 3 4 + - 1/144 y x z - 1/54 y z + 1/54 y z - 1/27 y z + 1/108 y x z + + 2 4 2 2 4 3 4 3 2 4 3 + - 1/216 y z + 1/54 y z + 1/108 x y z - 1/216 y z + 1/288 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/288 y x z - 1/216 y x z - 1/108 y x z , COEFF(0, -2, -1) = + + 2 4 3 4 2 4 3 4 3 + - 5/288 y x z + 1/36 x y z + 5/72 x y z - 1/36 x y z - 5/144 y x z + + 3 4 4 3 2 3 3 4 + - 1/144 x y z - 1/18 z y x + 1/18 z y x - 5/144 y x z + + 2 2 3 4 4 3 2 + - 5/72 y x z + 5/288 y x z + 5/288 x y z + 5/36 y x z + + 3 3 3 3 2 2 3 3 3 + + 1/72 y x z - 1/18 y x z - 1/144 y x z - 5/36 z y x + + 3 3 2 3 2 2 3 3 3 + + 1/18 z y x + 5/36 y x z + 1/36 z y x - 1/36 z y x + 5/144 y x z + + 3 3 3 4 2 2 2 2 + - 1/72 y x z - 5/72 x y z + 5/72 y x z - 5/36 y x z + + 3 4 3 4 3 4 4 3 + + 1/144 x y z + 5/144 y x z - 1/72 y x z - 5/288 x y z + + 2 3 4 3 3 4 2 4 + + 1/144 y x z + 1/72 y x z , COEFF(1, -2, -1) = 1/108 y x z + + 3 4 2 4 2 4 3 4 3 + - 1/54 x y z - 1/27 x y z + 1/72 x y z + 1/54 x y z + 1/54 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/216 x y z - 1/144 y x z + 1/27 z y x - 1/27 z y x + + 3 4 2 2 3 2 4 4 + + 1/54 y x z + 1/27 y x z - 1/108 y x z + 1/288 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/108 x y z + 1/72 y x z - 2/27 y x z + 1/288 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/108 y x z + 1/27 y x z - 1/144 y x z + 1/36 y x z + + 2 3 3 3 3 3 2 3 3 + + 1/216 y x z + 1/27 z y + 2/27 z y x - 1/36 z y x - 1/27 z y x + + 2 2 3 2 2 3 + - 2/27 y x z + 1/36 z y x - 1/54 z y x + 1/54 z y x - 1/27 y z + + 3 3 3 3 3 4 2 2 4 2 + - 1/54 y x z + 1/108 y x z + 1/27 x y z - 1/72 x y z + + 2 2 2 2 2 2 2 2 + - 1/27 y x z - 1/72 y x z - 1/36 y x z + 2/27 y x z + 1/54 y z + + 3 2 3 3 4 3 4 3 2 3 + + 1/144 y x z - 1/216 x y z - 1/54 y x z + 1/108 y z - 1/216 y z + + 3 3 4 3 4 4 4 3 2 + - 1/108 y z - 1/108 y z + 1/108 y z - 1/216 y z - 1/27 y z + + 2 4 4 2 4 2 3 4 + + 1/144 y x z + 1/54 y z - 1/54 y z + 1/27 y z + 1/108 y x z + + 2 4 2 2 4 3 4 3 2 4 3 + + 1/216 y z - 1/54 y z + 1/108 x y z + 1/216 y z - 1/288 x y z + + 2 2 4 2 3 4 3 3 4 + - 1/288 y x z - 1/216 y x z - 1/108 y x z , COEFF(2, -2, -1) = + + 2 4 3 4 2 4 2 4 + - 1/1728 y x z + 1/216 x y z + 1/432 x y z - 1/144 x y z + + 3 4 3 3 4 4 3 2 4 + - 1/216 x y z - 1/864 y x z - 1/864 x y z + 1/288 y x z + + 3 2 3 3 4 2 + - 1/108 z y x + 1/108 z y x - 1/864 y x z - 1/432 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/1728 y x z - 1/576 x y z + 1/1728 x y z - 1/144 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/216 y x z - 1/576 y x z + 1/432 y x z - 1/108 y x z + + 2 3 3 2 2 2 3 3 3 + + 1/288 y x z - 1/72 y x z - 1/864 y x z - 1/216 z y + + 3 3 2 3 3 2 + - 1/216 z y x + 1/72 z y x + 1/108 z y x + 1/216 y x z - 1/72 z y x + + 2 3 2 2 3 3 3 + + 1/216 z y x - 1/216 z y x + 1/216 y z + 1/864 y x z + + 3 3 3 4 2 2 4 2 2 2 + - 1/432 y x z - 1/432 x y z + 1/144 x y z + 1/432 y x z + + 2 2 2 2 2 2 + + 1/144 y x z + 1/72 y x z - 1/216 y x z - 1/432 y z + + 3 2 3 3 4 3 4 3 + - 1/288 y x z + 1/864 x y z + 1/864 y x z - 1/864 y z + + 2 3 3 3 4 3 4 4 4 + + 1/1728 y z + 1/864 y z + 1/864 y z - 1/864 y z + 1/1728 y z + + 3 2 2 4 4 2 4 2 + + 1/216 y z - 1/288 y x z - 1/432 y z + 1/432 y z - 1/216 y z + + 3 4 2 4 2 2 4 3 + - 1/432 y x z - 1/1728 y z + 1/432 y z - 1/1728 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + - 1/1728 y z + 1/576 x y z + 1/576 y x z + 1/864 y x z + + 3 3 4 2 4 3 4 2 + + 1/432 y x z , COEFF(-2, -1, -1) = 1/108 y x z - 1/54 x y z + + 4 2 4 3 4 3 + - 1/108 x y z - 1/36 x y z + 1/54 x y z + 1/108 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/216 x y z + 1/144 y x z + 2/27 z y x - 2/27 z y x + + 3 4 2 2 3 2 4 4 + + 1/432 y x z + 1/27 y x z - 1/108 y x z - 1/144 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/432 x y z - 1/9 y x z - 1/108 y x z - 1/36 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/54 y x z + 1/54 y x z + 1/36 y x z - 1/36 y x z + + 2 3 3 3 3 3 2 3 3 + + 1/54 y x z - 1/108 z y + 1/108 z y x + 1/36 z y x - 1/54 z y x + + 2 2 3 2 2 3 + - 1/27 y x z - 1/9 z y x - 2/27 z y x + 2/27 z y x + 1/27 y z + + 3 3 3 3 3 4 2 2 4 2 + - 1/432 y x z + 1/216 y x z + 1/108 x y z + 1/36 x y z + + 2 2 2 2 2 2 2 2 + - 1/27 y x z + 1/9 y x z + 1/9 y x z + 1/27 y x z - 1/27 y z + + 3 2 3 3 4 3 4 3 + - 1/144 y x z - 1/216 x y z - 1/108 y x z - 1/108 y z + + 2 3 3 3 4 3 4 4 4 + + 1/108 y z + 1/432 y z + 1/108 y z - 1/432 y z + 1/432 y z + + 3 2 2 4 4 2 4 2 + + 1/108 y z - 1/36 y x z - 1/108 y z + 1/108 y z - 1/27 y z + + 3 4 2 4 2 2 4 3 4 3 + + 1/54 y x z - 1/108 y z + 1/27 y z + 1/432 x y z - 1/432 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + + 1/144 x y z + 1/36 y x z - 1/54 y x z - 1/216 y x z , + + 2 4 3 4 2 4 + COEFF(-1, -1, -1) = - 4/27 y x z + 2/27 x y z + 4/27 x y z + + 2 4 3 4 3 3 4 4 + + 1/18 x y z - 2/27 x y z - 4/27 y x z - 1/54 x y z + + 3 2 4 3 2 3 3 4 16 2 + - 1/72 y x z - 8/27 z y x + 8/27 z y x - 1/27 y x z - -- y x z + 27 + + 2 3 2 4 4 4 4 2 2 2 + + 4/27 y x z + 1/72 x y z + 1/27 x y z + 2/9 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 4/27 y x z + 1/18 y x z + 2/27 y x z - 2/27 y x z + + 2 3 3 2 2 2 3 3 3 3 + - 1/18 y x z + 1/18 y x z - 2/27 y x z + 2/27 z y - 4/27 z y x + + 3 2 3 3 16 2 2 3 + - 1/18 z y x + 2/27 z y x + -- y x z + 2/9 z y x + 8/27 z y x + 27 + + 2 2 3 3 3 3 3 3 4 2 + - 8/27 z y x - 8/27 y z + 1/27 y x z - 1/54 y x z - 4/27 x y z + + 2 4 2 16 2 2 2 2 2 2 16 2 + - 1/18 x y z + -- y x z - 2/9 y x z - 2/9 y x z - -- y x z + 27 27 + + 2 3 2 3 3 4 3 4 3 + + 8/27 y z + 1/72 y x z + 1/54 x y z + 4/27 y x z + 2/27 y z + + 2 3 3 3 4 3 4 4 4 + - 2/27 y z - 1/54 y z - 2/27 y z + 1/54 y z - 1/54 y z + + 3 2 2 4 4 2 4 2 + - 2/27 y z + 1/18 y x z + 2/27 y z - 2/27 y z + 8/27 y z + + 3 4 2 4 2 2 4 3 4 3 + - 2/27 y x z + 2/27 y z - 8/27 y z - 1/27 x y z + 1/54 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + - 1/72 x y z - 1/18 y x z + 2/27 y x z + 1/54 y x z , + + 2 4 3 4 2 4 3 4 + COEFF(0, -1, -1) = 5/18 y x z - 1/9 x y z - 5/18 x y z + 1/9 x y z + + 3 3 4 4 3 2 3 3 4 + + 5/18 y x z + 1/36 x y z + 4/9 z y x - 4/9 z y x + 5/72 y x z + + 2 2 3 4 4 3 2 3 3 + + 10/9 y x z - 5/18 y x z - 5/72 x y z - 5/18 y x z - 1/9 y x z + + 3 3 2 2 3 3 3 3 3 + + 1/9 y x z + 1/9 y x z + 5/18 z y x - 1/9 z y x - 10/9 y x z + + 2 3 2 2 3 3 3 3 3 3 4 2 + - 4/9 z y x + 4/9 z y x - 5/72 y x z + 1/36 y x z + 5/18 x y z + + 2 2 2 3 4 3 4 3 4 + - 10/9 y x z + 10/9 y x z - 1/36 x y z - 5/18 y x z + 1/9 y x z + + 4 3 2 3 4 3 3 4 + + 5/72 x y z - 1/9 y x z - 1/36 y x z , COEFF(1, -1, -1) = + + 2 4 3 4 2 4 2 4 3 4 + - 4/27 y x z + 2/27 x y z + 4/27 x y z - 1/18 x y z - 2/27 x y z + + 3 3 4 4 3 2 4 3 2 3 + - 4/27 y x z - 1/54 x y z + 1/72 y x z - 8/27 z y x + 8/27 z y x + + 3 4 16 2 2 3 2 4 4 4 4 + - 1/27 y x z - -- y x z + 4/27 y x z - 1/72 x y z + 1/27 x y z + 27 + + 2 2 2 3 2 2 2 3 3 3 + - 2/9 y x z + 4/27 y x z - 1/18 y x z + 2/27 y x z + + 3 3 2 2 3 3 2 2 2 3 3 3 + - 2/27 y x z + 1/18 y x z - 1/18 y x z - 2/27 y x z - 2/27 z y + + 3 3 2 3 3 16 2 + - 4/27 z y x + 1/18 z y x + 2/27 z y x + -- y x z - 2/9 z y x + 27 + + 2 3 2 2 3 3 3 3 3 3 + + 8/27 z y x - 8/27 z y x + 8/27 y z + 1/27 y x z - 1/54 y x z + + 4 2 2 4 2 16 2 2 2 2 2 2 + - 4/27 x y z + 1/18 x y z + -- y x z + 2/9 y x z + 2/9 y x z + 27 + + 16 2 2 3 2 3 3 4 3 4 + - -- y x z - 8/27 y z - 1/72 y x z + 1/54 x y z + 4/27 y x z + 27 + + 3 2 3 3 3 4 3 4 + - 2/27 y z + 2/27 y z + 1/54 y z + 2/27 y z - 1/54 y z + + 4 4 3 2 2 4 4 2 4 + + 1/54 y z + 2/27 y z - 1/18 y x z - 2/27 y z + 2/27 y z + + 2 3 4 2 4 2 2 4 3 + - 8/27 y z - 2/27 y x z - 2/27 y z + 8/27 y z - 1/27 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + - 1/54 y z + 1/72 x y z + 1/18 y x z + 2/27 y x z + + 3 3 4 2 4 3 4 2 + + 1/54 y x z , COEFF(2, -1, -1) = 1/108 y x z - 1/54 x y z + + 4 2 4 3 4 3 + - 1/108 x y z + 1/36 x y z + 1/54 x y z + 1/108 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/216 x y z - 1/144 y x z + 2/27 z y x - 2/27 z y x + + 3 4 2 2 3 2 4 4 + + 1/432 y x z + 1/27 y x z - 1/108 y x z + 1/144 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/432 x y z + 1/9 y x z - 1/108 y x z + 1/36 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/54 y x z + 1/54 y x z - 1/36 y x z + 1/36 y x z + + 2 3 3 3 3 3 2 3 3 + + 1/54 y x z + 1/108 z y + 1/108 z y x - 1/36 z y x - 1/54 z y x + + 2 2 3 2 2 3 + - 1/27 y x z + 1/9 z y x - 2/27 z y x + 2/27 z y x - 1/27 y z + + 3 3 3 3 3 4 2 2 4 2 + - 1/432 y x z + 1/216 y x z + 1/108 x y z - 1/36 x y z + + 2 2 2 2 2 2 2 2 + - 1/27 y x z - 1/9 y x z - 1/9 y x z + 1/27 y x z + 1/27 y z + + 3 2 3 3 4 3 4 3 + + 1/144 y x z - 1/216 x y z - 1/108 y x z + 1/108 y z + + 2 3 3 3 4 3 4 4 4 + - 1/108 y z - 1/432 y z - 1/108 y z + 1/432 y z - 1/432 y z + + 3 2 2 4 4 2 4 2 + - 1/108 y z + 1/36 y x z + 1/108 y z - 1/108 y z + 1/27 y z + + 3 4 2 4 2 2 4 3 4 3 + + 1/54 y x z + 1/108 y z - 1/27 y z + 1/432 x y z + 1/432 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + - 1/144 x y z - 1/36 y x z - 1/54 y x z - 1/216 y x z , + + 2 4 3 4 2 4 + COEFF(-2, 0, -1) = - 5/288 y x z + 1/36 x y z + 1/72 x y z + + 2 4 3 4 3 4 4 2 + + 1/24 x y z - 1/36 x y z - 1/144 x y z - 1/18 z - 5/72 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 5/288 y x z + 1/96 x y z + 1/288 x y z + 5/24 y x z + + 2 2 3 3 4 2 3 3 3 2 + + 5/96 y x z - 1/9 z x - 1/72 z - 5/144 y x z + 1/72 z + 1/18 z + + 2 3 2 2 3 4 2 2 4 2 + + 5/36 z y x - 5/36 z y x - 1/72 x y z - 1/24 x y z + + 2 2 2 2 2 2 + + 5/72 y x z - 5/24 y x z + 5/72 y z + 1/18 x z + 1/6 x z + + 3 4 3 2 3 3 3 2 3 4 4 + + 1/144 x y z - 5/288 y z + 1/36 x z - 1/24 x z - 1/288 y z + + 2 4 3 4 4 2 4 3 4 + + 1/24 x z - 1/72 x z + 1/72 x z + 1/72 y z - 1/72 y z - 1/36 x z + + 2 2 2 3 2 2 4 2 2 + - 1/6 x z - 1/18 x z + 1/9 x z + 5/288 y z - 5/72 y z + + 4 3 4 3 2 4 3 2 2 4 + - 1/288 x y z + 1/288 y z - 1/96 x y z - 5/96 y x z + + 2 3 4 2 4 3 4 2 + + 5/144 y x z , COEFF(-1, 0, -1) = 5/18 y x z - 1/9 x y z + + 4 2 4 3 4 3 4 4 + - 2/9 x y z - 1/12 x y z + 1/9 x y z + 1/36 x y z + 4/9 z + + 2 2 3 2 4 4 4 4 + + 10/9 y x z - 5/18 y x z - 1/48 x y z - 1/18 x y z + + 2 2 2 2 2 3 3 4 2 3 3 + - 5/12 y x z - 5/48 y x z + 4/9 z x + 1/9 z + 5/36 y x z + + 3 2 2 3 2 2 3 4 2 + - 1/9 z - 4/9 z - 5/9 z y x + 5/9 z y x + 2/9 x y z + + 2 4 2 2 2 2 2 2 + + 1/12 x y z - 10/9 y x z + 5/12 y x z - 5/9 y z - 8/9 x z + + 2 3 4 3 2 3 3 3 2 3 + - 1/3 x z - 1/36 x y z + 5/36 y z - 1/9 x z + 1/12 x z + + 4 4 2 4 3 4 4 2 4 + + 1/36 y z - 1/12 x z + 2/9 x z - 2/9 x z - 1/9 y z + 1/9 y z + + 3 4 2 2 2 3 2 2 4 2 2 + + 1/9 x z + 1/3 x z + 8/9 x z - 4/9 x z - 5/36 y z + 5/9 y z + + 4 3 4 3 2 4 3 2 2 4 + + 1/18 x y z - 1/36 y z + 1/48 x y z + 5/48 y x z + + 2 3 4 3 4 2 25 2 4 25 2 3 + - 5/36 y x z , COEFF(0, 0, -1) = 1/6 x y z - -- y x z + -- y x z + 48 48 + + 2 2 3 4 3 4 3 4 + - 5/6 z y x - 5/48 x y z + 5/12 x y z - 5/12 x z + 5/12 x z + + 3 2 3 4 4 4 2 25 2 2 2 + + 2/3 x z - 1/24 x y z - 5/12 x y z + -- y x z - 5/3 x z + 12 + + 4 4 3 4 3 3 2 3 2 3 4 + + 5/48 x y z + 1/24 x y z - 2/3 z x + 5/6 z y x + 5/24 y x z + + 2 3 3 3 3 25 2 3 4 + - 5/24 y x z + 5/3 x z + 1/6 x z - -- y x z - 1/6 x z + 12 + + 3 4 2 4 3 4 2 4 + - 1/6 x y z, COEFF(1, 0, -1) = 5/18 y x z - 1/9 x y z - 2/9 x y z + + 2 4 3 4 3 4 4 2 + + 1/12 x y z + 1/9 x y z + 1/36 x y z - 4/9 z + 10/9 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 5/18 y x z + 1/48 x y z - 1/18 x y z + 5/12 y x z + + 2 2 3 3 4 2 3 3 3 2 + + 5/48 y x z + 4/9 z x - 1/9 z + 5/36 y x z + 1/9 z + 4/9 z + + 2 3 2 2 3 4 2 2 4 2 2 2 + - 5/9 z y x + 5/9 z y x + 2/9 x y z - 1/12 x y z - 10/9 y x z + + 2 2 2 2 3 4 3 + - 5/12 y x z + 5/9 y z - 8/9 x z + 1/3 x z - 1/36 x y z + + 2 3 3 3 2 3 4 4 2 4 3 + - 5/36 y z - 1/9 x z - 1/12 x z - 1/36 y z + 1/12 x z + 2/9 x z + + 4 4 2 4 3 4 2 2 2 + - 2/9 x z + 1/9 y z - 1/9 y z + 1/9 x z - 1/3 x z + 8/9 x z + + 3 2 2 4 2 2 4 3 4 3 + - 4/9 x z + 5/36 y z - 5/9 y z + 1/18 x y z + 1/36 y z + + 2 4 3 2 2 4 2 3 4 + - 1/48 x y z - 5/48 y x z - 5/36 y x z , COEFF(2, 0, -1) = + + 2 4 3 4 2 4 2 4 3 4 + - 5/288 y x z + 1/36 x y z + 1/72 x y z - 1/24 x y z - 1/36 x y z + + 3 4 4 2 2 3 2 4 4 + - 1/144 x y z + 1/18 z - 5/72 y x z + 5/288 y x z - 1/96 x y z + + 4 4 2 2 2 2 2 3 3 4 + + 1/288 x y z - 5/24 y x z - 5/96 y x z - 1/9 z x + 1/72 z + + 2 3 3 3 2 2 3 2 2 3 + - 5/144 y x z - 1/72 z - 1/18 z + 5/36 z y x - 5/36 z y x + + 4 2 2 4 2 2 2 2 2 2 + - 1/72 x y z + 1/24 x y z + 5/72 y x z + 5/24 y x z - 5/72 y z + + 2 3 4 3 2 3 3 3 + + 1/18 x z - 1/6 x z + 1/144 x y z + 5/288 y z + 1/36 x z + + 2 3 4 4 2 4 3 4 + + 1/24 x z + 1/288 y z - 1/24 x z - 1/72 x z + 1/72 x z + + 4 2 4 3 4 2 2 2 3 2 + - 1/72 y z + 1/72 y z - 1/36 x z + 1/6 x z - 1/18 x z + 1/9 x z + + 2 4 2 2 4 3 4 3 2 4 3 + - 5/288 y z + 5/72 y z - 1/288 x y z - 1/288 y z + 1/96 x y z + + 2 2 4 2 3 4 2 4 + + 5/96 y x z + 5/144 y x z , COEFF(-2, 1, -1) = 1/108 y x z + + 3 4 2 4 2 4 3 4 + - 1/54 x y z - 1/108 x y z - 1/36 x y z + 1/54 x y z + + 3 3 4 4 3 2 4 3 + - 1/108 y x z + 1/216 x y z - 1/144 y x z - 2/27 z y x + + 2 3 3 4 2 2 3 + + 2/27 z y x - 1/432 y x z + 1/27 y x z - 1/108 y x z + + 2 4 4 4 4 2 2 2 3 2 + - 1/144 x y z - 1/432 x y z - 1/9 y x z + 1/108 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/36 y x z + 1/54 y x z - 1/54 y x z - 1/36 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/36 y x z + 1/54 y x z + 1/108 z y - 1/108 z y x - 1/36 z y x + + 3 3 2 2 3 2 2 3 + + 1/54 z y x + 1/27 y x z + 1/9 z y x - 2/27 z y x + 2/27 z y x + + 3 3 3 3 3 4 2 + - 1/27 y z + 1/432 y x z - 1/216 y x z + 1/108 x y z + + 2 4 2 2 2 2 2 2 2 2 + + 1/36 x y z - 1/27 y x z + 1/9 y x z - 1/9 y x z - 1/27 y x z + + 2 3 2 3 3 4 3 4 3 + - 1/27 y z + 1/144 y x z - 1/216 x y z + 1/108 y x z + 1/108 y z + + 2 3 3 3 4 3 4 4 4 + + 1/108 y z - 1/432 y z - 1/108 y z + 1/432 y z + 1/432 y z + + 3 2 2 4 4 2 4 2 + - 1/108 y z + 1/36 y x z - 1/108 y z + 1/108 y z + 1/27 y z + + 3 4 2 4 2 2 4 3 4 3 + - 1/54 y x z - 1/108 y z + 1/27 y z + 1/432 x y z - 1/432 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + + 1/144 x y z + 1/36 y x z - 1/54 y x z + 1/216 y x z , + + 2 4 3 4 2 4 + COEFF(-1, 1, -1) = - 4/27 y x z + 2/27 x y z + 4/27 x y z + + 2 4 3 4 3 3 4 4 + + 1/18 x y z - 2/27 x y z + 4/27 y x z - 1/54 x y z + + 3 2 4 3 2 3 3 4 16 2 + + 1/72 y x z + 8/27 z y x - 8/27 z y x + 1/27 y x z - -- y x z + 27 + + 2 3 2 4 4 4 4 2 2 2 + + 4/27 y x z + 1/72 x y z + 1/27 x y z + 2/9 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 4/27 y x z + 1/18 y x z - 2/27 y x z + 2/27 y x z + + 2 3 3 2 2 2 3 3 3 3 + + 1/18 y x z - 1/18 y x z - 2/27 y x z - 2/27 z y + 4/27 z y x + + 3 2 3 3 16 2 2 3 + + 1/18 z y x - 2/27 z y x - -- y x z - 2/9 z y x + 8/27 z y x + 27 + + 2 2 3 3 3 3 3 3 4 2 + - 8/27 z y x + 8/27 y z - 1/27 y x z + 1/54 y x z - 4/27 x y z + + 2 4 2 16 2 2 2 2 2 2 16 2 + - 1/18 x y z + -- y x z - 2/9 y x z + 2/9 y x z + -- y x z + 27 27 + + 2 3 2 3 3 4 3 4 3 + + 8/27 y z - 1/72 y x z + 1/54 x y z - 4/27 y x z - 2/27 y z + + 2 3 3 3 4 3 4 4 4 + - 2/27 y z + 1/54 y z + 2/27 y z - 1/54 y z - 1/54 y z + + 3 2 2 4 4 2 4 2 + + 2/27 y z - 1/18 y x z + 2/27 y z - 2/27 y z - 8/27 y z + + 3 4 2 4 2 2 4 3 4 3 + + 2/27 y x z + 2/27 y z - 8/27 y z - 1/27 x y z + 1/54 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + - 1/72 x y z - 1/18 y x z + 2/27 y x z - 1/54 y x z , + + 2 4 3 4 2 4 3 4 + COEFF(0, 1, -1) = 5/18 y x z - 1/9 x y z - 5/18 x y z + 1/9 x y z + + 3 3 4 4 3 2 3 3 4 + - 5/18 y x z + 1/36 x y z - 4/9 z y x + 4/9 z y x - 5/72 y x z + + 2 2 3 4 4 3 2 3 3 + + 10/9 y x z - 5/18 y x z - 5/72 x y z + 5/18 y x z + 1/9 y x z + + 3 3 2 2 3 3 3 3 3 + - 1/9 y x z + 1/9 y x z - 5/18 z y x + 1/9 z y x + 10/9 y x z + + 2 3 2 2 3 3 3 3 3 3 4 2 + - 4/9 z y x + 4/9 z y x + 5/72 y x z - 1/36 y x z + 5/18 x y z + + 2 2 2 3 4 3 4 3 4 + - 10/9 y x z - 10/9 y x z - 1/36 x y z + 5/18 y x z - 1/9 y x z + + 4 3 2 3 4 3 3 4 + + 5/72 x y z - 1/9 y x z + 1/36 y x z , COEFF(1, 1, -1) = + + 2 4 3 4 2 4 2 4 3 4 + - 4/27 y x z + 2/27 x y z + 4/27 x y z - 1/18 x y z - 2/27 x y z + + 3 3 4 4 3 2 4 3 2 3 + + 4/27 y x z - 1/54 x y z - 1/72 y x z + 8/27 z y x - 8/27 z y x + + 3 4 16 2 2 3 2 4 4 4 4 + + 1/27 y x z - -- y x z + 4/27 y x z - 1/72 x y z + 1/27 x y z + 27 + + 2 2 2 3 2 2 2 3 3 3 + - 2/9 y x z - 4/27 y x z - 1/18 y x z - 2/27 y x z + + 3 3 2 2 3 3 2 2 2 3 3 3 + + 2/27 y x z - 1/18 y x z + 1/18 y x z - 2/27 y x z + 2/27 z y + + 3 3 2 3 3 16 2 + + 4/27 z y x - 1/18 z y x - 2/27 z y x - -- y x z + 2/9 z y x + 27 + + 2 3 2 2 3 3 3 3 3 3 + + 8/27 z y x - 8/27 z y x - 8/27 y z - 1/27 y x z + 1/54 y x z + + 4 2 2 4 2 16 2 2 2 2 2 2 + - 4/27 x y z + 1/18 x y z + -- y x z + 2/9 y x z - 2/9 y x z + 27 + + 16 2 2 3 2 3 3 4 3 4 + + -- y x z - 8/27 y z + 1/72 y x z + 1/54 x y z - 4/27 y x z + 27 + + 3 2 3 3 3 4 3 4 + + 2/27 y z + 2/27 y z - 1/54 y z - 2/27 y z + 1/54 y z + + 4 4 3 2 2 4 4 2 4 + + 1/54 y z - 2/27 y z + 1/18 y x z - 2/27 y z + 2/27 y z + + 2 3 4 2 4 2 2 4 3 + + 8/27 y z + 2/27 y x z - 2/27 y z + 8/27 y z - 1/27 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + - 1/54 y z + 1/72 x y z + 1/18 y x z + 2/27 y x z + + 3 3 4 2 4 3 4 2 + - 1/54 y x z , COEFF(2, 1, -1) = 1/108 y x z - 1/54 x y z + + 4 2 4 3 4 3 + - 1/108 x y z + 1/36 x y z + 1/54 x y z - 1/108 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/216 x y z + 1/144 y x z - 2/27 z y x + 2/27 z y x + + 3 4 2 2 3 2 4 4 + - 1/432 y x z + 1/27 y x z - 1/108 y x z + 1/144 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/432 x y z + 1/9 y x z + 1/108 y x z + 1/36 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 1/54 y x z - 1/54 y x z + 1/36 y x z - 1/36 y x z + + 2 3 3 3 3 3 2 3 3 + + 1/54 y x z - 1/108 z y - 1/108 z y x + 1/36 z y x + 1/54 z y x + + 2 2 3 2 2 3 + + 1/27 y x z - 1/9 z y x - 2/27 z y x + 2/27 z y x + 1/27 y z + + 3 3 3 3 3 4 2 2 4 2 + + 1/432 y x z - 1/216 y x z + 1/108 x y z - 1/36 x y z + + 2 2 2 2 2 2 2 2 + - 1/27 y x z - 1/9 y x z + 1/9 y x z - 1/27 y x z + 1/27 y z + + 3 2 3 3 4 3 4 3 + - 1/144 y x z - 1/216 x y z + 1/108 y x z - 1/108 y z + + 2 3 3 3 4 3 4 4 4 + - 1/108 y z + 1/432 y z + 1/108 y z - 1/432 y z - 1/432 y z + + 3 2 2 4 4 2 4 2 + + 1/108 y z - 1/36 y x z + 1/108 y z - 1/108 y z - 1/27 y z + + 3 4 2 4 2 2 4 3 4 3 + - 1/54 y x z + 1/108 y z - 1/27 y z + 1/432 x y z + 1/432 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + - 1/144 x y z - 1/36 y x z - 1/54 y x z + 1/216 y x z , + + 2 4 3 4 2 4 + COEFF(-2, 2, -1) = - 1/1728 y x z + 1/216 x y z + 1/432 x y z + + 2 4 3 4 3 3 4 4 + + 1/144 x y z - 1/216 x y z + 1/864 y x z - 1/864 x y z + + 3 2 4 3 2 3 3 4 + + 1/288 y x z + 1/108 z y x - 1/108 z y x + 1/864 y x z + + 2 2 3 2 4 4 4 4 + - 1/432 y x z + 1/1728 y x z + 1/576 x y z + 1/1728 x y z + + 2 2 2 3 2 2 2 3 3 3 + + 1/144 y x z - 1/216 y x z + 1/576 y x z - 1/432 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + + 1/108 y x z + 1/288 y x z - 1/72 y x z - 1/864 y x z + + 3 3 3 2 3 3 + - 1/216 z y + 1/216 z y x + 1/72 z y x - 1/108 z y x - 1/216 y x z + + 2 2 3 2 2 3 3 3 + - 1/72 z y x + 1/216 z y x - 1/216 z y x + 1/216 y z - 1/864 y x z + + 3 3 3 4 2 2 4 2 2 2 + + 1/432 y x z - 1/432 x y z - 1/144 x y z + 1/432 y x z + + 2 2 2 2 2 2 + - 1/144 y x z + 1/72 y x z + 1/216 y x z + 1/432 y z + + 3 2 3 3 4 3 4 3 + - 1/288 y x z + 1/864 x y z - 1/864 y x z - 1/864 y z + + 2 3 3 3 4 3 4 4 4 + - 1/1728 y z + 1/864 y z + 1/864 y z - 1/864 y z - 1/1728 y z + + 3 2 2 4 4 2 4 2 + + 1/216 y z - 1/288 y x z + 1/432 y z - 1/432 y z - 1/216 y z + + 3 4 2 4 2 2 4 3 + + 1/432 y x z + 1/1728 y z - 1/432 y z - 1/1728 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + + 1/1728 y z - 1/576 x y z - 1/576 y x z + 1/864 y x z + + 3 3 4 2 4 3 4 2 + - 1/432 y x z , COEFF(-1, 2, -1) = 1/108 y x z - 1/54 x y z + + 4 2 4 3 4 3 3 4 4 + - 1/27 x y z - 1/72 x y z + 1/54 x y z - 1/54 y x z + 1/216 x y z + + 3 2 4 3 2 3 3 4 2 + - 1/144 y x z - 1/27 z y x + 1/27 z y x - 1/54 y x z + 1/27 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/108 y x z - 1/288 x y z - 1/108 x y z - 1/72 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 2/27 y x z - 1/288 y x z + 1/108 y x z - 1/27 y x z + + 2 3 3 2 2 2 3 3 3 3 + - 1/144 y x z + 1/36 y x z + 1/216 y x z + 1/27 z y - 2/27 z y x + + 3 2 3 3 2 2 3 + - 1/36 z y x + 1/27 z y x + 2/27 y x z + 1/36 z y x - 1/54 z y x + + 2 2 3 3 3 3 3 3 4 2 + + 1/54 z y x - 1/27 y z + 1/54 y x z - 1/108 y x z + 1/27 x y z + + 2 4 2 2 2 2 2 2 2 2 + + 1/72 x y z - 1/27 y x z + 1/72 y x z - 1/36 y x z - 2/27 y x z + + 2 3 2 3 3 4 3 4 3 + - 1/54 y z + 1/144 y x z - 1/216 x y z + 1/54 y x z + 1/108 y z + + 2 3 3 3 4 3 4 4 4 + + 1/216 y z - 1/108 y z - 1/108 y z + 1/108 y z + 1/216 y z + + 3 2 2 4 4 2 4 2 + - 1/27 y z + 1/144 y x z - 1/54 y z + 1/54 y z + 1/27 y z + + 3 4 2 4 2 2 4 3 4 3 + - 1/108 y x z - 1/216 y z + 1/54 y z + 1/108 x y z - 1/216 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + + 1/288 x y z + 1/288 y x z - 1/216 y x z + 1/108 y x z , + + 2 4 3 4 2 4 + COEFF(0, 2, -1) = - 5/288 y x z + 1/36 x y z + 5/72 x y z + + 3 4 3 3 4 4 3 + - 1/36 x y z + 5/144 y x z - 1/144 x y z + 1/18 z y x + + 2 3 3 4 2 2 3 + - 1/18 z y x + 5/144 y x z - 5/72 y x z + 5/288 y x z + + 4 4 3 2 3 3 3 3 2 + + 5/288 x y z - 5/36 y x z - 1/72 y x z + 1/18 y x z + + 2 3 3 3 3 3 2 3 + - 1/144 y x z + 5/36 z y x - 1/18 z y x - 5/36 y x z + 1/36 z y x + + 2 2 3 3 3 3 3 3 4 2 + - 1/36 z y x - 5/144 y x z + 1/72 y x z - 5/72 x y z + + 2 2 2 3 4 3 4 + + 5/72 y x z + 5/36 y x z + 1/144 x y z - 5/144 y x z + + 3 4 4 3 2 3 4 3 3 4 + + 1/72 y x z - 5/288 x y z + 1/144 y x z - 1/72 y x z , + + 2 4 3 4 2 4 + COEFF(1, 2, -1) = 1/108 y x z - 1/54 x y z - 1/27 x y z + + 2 4 3 4 3 3 4 4 + + 1/72 x y z + 1/54 x y z - 1/54 y x z + 1/216 x y z + + 3 2 4 3 2 3 3 4 2 + + 1/144 y x z - 1/27 z y x + 1/27 z y x - 1/54 y x z + 1/27 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/108 y x z + 1/288 x y z - 1/108 x y z + 1/72 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 2/27 y x z + 1/288 y x z + 1/108 y x z - 1/27 y x z + + 2 3 3 2 2 2 3 3 3 3 + + 1/144 y x z - 1/36 y x z + 1/216 y x z - 1/27 z y - 2/27 z y x + + 3 2 3 3 2 2 3 + + 1/36 z y x + 1/27 z y x + 2/27 y x z - 1/36 z y x - 1/54 z y x + + 2 2 3 3 3 3 3 3 4 2 + + 1/54 z y x + 1/27 y z + 1/54 y x z - 1/108 y x z + 1/27 x y z + + 2 4 2 2 2 2 2 2 2 2 + - 1/72 x y z - 1/27 y x z - 1/72 y x z + 1/36 y x z - 2/27 y x z + + 2 3 2 3 3 4 3 4 3 + + 1/54 y z - 1/144 y x z - 1/216 x y z + 1/54 y x z - 1/108 y z + + 2 3 3 3 4 3 4 4 4 + - 1/216 y z + 1/108 y z + 1/108 y z - 1/108 y z - 1/216 y z + + 3 2 2 4 4 2 4 2 + + 1/27 y z - 1/144 y x z + 1/54 y z - 1/54 y z - 1/27 y z + + 3 4 2 4 2 2 4 3 4 3 + - 1/108 y x z + 1/216 y z - 1/54 y z + 1/108 x y z + 1/216 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + - 1/288 x y z - 1/288 y x z - 1/216 y x z + 1/108 y x z , + + 2 4 3 4 2 4 + COEFF(2, 2, -1) = - 1/1728 y x z + 1/216 x y z + 1/432 x y z + + 2 4 3 4 3 3 4 4 + - 1/144 x y z - 1/216 x y z + 1/864 y x z - 1/864 x y z + + 3 2 4 3 2 3 3 4 + - 1/288 y x z + 1/108 z y x - 1/108 z y x + 1/864 y x z + + 2 2 3 2 4 4 4 4 + - 1/432 y x z + 1/1728 y x z - 1/576 x y z + 1/1728 x y z + + 2 2 2 3 2 2 2 3 3 3 + - 1/144 y x z - 1/216 y x z - 1/576 y x z - 1/432 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + + 1/108 y x z - 1/288 y x z + 1/72 y x z - 1/864 y x z + + 3 3 3 2 3 3 + + 1/216 z y + 1/216 z y x - 1/72 z y x - 1/108 z y x - 1/216 y x z + + 2 2 3 2 2 3 3 3 + + 1/72 z y x + 1/216 z y x - 1/216 z y x - 1/216 y z - 1/864 y x z + + 3 3 3 4 2 2 4 2 2 2 + + 1/432 y x z - 1/432 x y z + 1/144 x y z + 1/432 y x z + + 2 2 2 2 2 2 + + 1/144 y x z - 1/72 y x z + 1/216 y x z - 1/432 y z + + 3 2 3 3 4 3 4 3 + + 1/288 y x z + 1/864 x y z - 1/864 y x z + 1/864 y z + + 2 3 3 3 4 3 4 4 4 + + 1/1728 y z - 1/864 y z - 1/864 y z + 1/864 y z + 1/1728 y z + + 3 2 2 4 4 2 4 2 + - 1/216 y z + 1/288 y x z - 1/432 y z + 1/432 y z + 1/216 y z + + 3 4 2 4 2 2 4 3 + + 1/432 y x z - 1/1728 y z + 1/432 y z - 1/1728 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + - 1/1728 y z + 1/576 x y z + 1/576 y x z + 1/864 y x z + + 3 3 4 3 2 4 + - 1/432 y x z , COEFF(-2, -2, 0) = 1/72 y x + 1/1152 y x z + + 3 4 2 3 4 4 3 2 4 + - 5/576 x y z + 1/576 x y z + 1/144 y + 1/192 y x z + + 2 3 3 4 3 4 2 4 4 + - 5/288 z y x + 1/576 y x z + 1/144 x y - 1/144 y x - 1/384 x y z + + 4 4 4 2 2 2 3 2 + + 1/288 y - 1/1152 x y z - 5/384 y x z - 5/576 y x z + + 3 3 2 3 2 2 3 3 2 3 + + 5/288 y x z - 5/192 y x z - 1/144 y + 1/144 y x - 1/144 y x + + 2 3 2 3 3 2 2 3 2 4 + - 1/288 y + 1/48 y x - 1/72 y x + 5/576 z y x - 1/96 x y + + 4 4 2 2 2 4 2 + - 1/288 x y + 5/1152 x y z + 1/288 y x + 5/384 x y z + + 2 2 2 2 2 4 + - 5/1152 y x z + 5/192 y x z + 5/576 y x z - 1/576 y x z + + 4 3 4 4 4 3 2 2 4 + + 1/576 y z - 1/576 y z + 1/1152 y z + 5/576 y z - 1/192 y x z + + 4 2 2 3 4 2 4 2 2 + - 5/1152 y z - 5/576 y z + 1/288 y x z - 1/1152 y z + 5/1152 y z + + 2 2 2 2 2 4 2 3 4 + + 1/96 y x - 1/48 y x + 1/384 y x z - 1/576 y x z + + 3 3 4 3 2 4 + - 1/288 y x z , COEFF(-1, -2, 0) = - 1/18 y x - 1/72 y x z + + 3 4 2 3 4 4 3 2 4 2 3 + + 5/144 x y z - 1/144 x y z - 1/18 y - 1/96 y x z + 5/72 z y x + + 3 4 3 4 2 4 4 4 + - 1/36 y x z - 1/36 x y + 1/9 y x + 1/192 x y z - 1/36 y + + 4 4 2 2 2 3 2 3 3 2 + + 1/72 x y z + 5/192 y x z + 5/36 y x z - 5/72 y x z + + 3 2 2 3 3 2 3 2 3 2 + + 5/96 y x z + 1/18 y - 1/9 y x + 1/36 y x + 1/36 y - 1/24 y x + + 3 3 2 2 3 2 4 4 4 2 + + 1/18 y x - 5/144 z y x + 1/48 x y + 1/18 x y - 5/72 x y z + + 2 2 4 2 2 2 2 2 2 + - 1/18 y x - 5/192 x y z + 5/72 y x z - 5/96 y x z - 5/36 y x z + + 4 4 3 4 4 4 3 2 + + 1/36 y x z - 1/72 y z + 1/72 y z - 1/144 y z - 5/72 y z + + 2 4 4 2 2 3 4 2 4 + + 1/96 y x z + 5/144 y z + 5/72 y z - 1/72 y x z + 1/144 y z + + 2 2 2 2 2 2 2 4 2 3 4 + - 5/144 y z - 1/48 y x + 1/24 y x - 1/192 y x z + 1/144 y x z + + 3 3 4 2 2 3 3 + + 1/72 y x z , COEFF(0, -2, 0) = 5/96 z y x + 1/12 y x + + 2 4 3 3 2 4 2 3 2 3 + + 5/192 y x z + 5/48 y x z - 5/96 y x z - 5/48 z y x - 1/24 y x + + 3 4 3 25 2 3 3 4 + - 5/24 y x + 1/24 x y + 5/24 y x + -- y x z - 1/48 y x z + 96 + + 3 4 4 3 4 2 3 4 2 3 4 + + 1/96 x y z - 5/96 x y z + 5/96 y x z - 1/96 y x z + + 3 3 3 4 4 4 25 4 2 25 2 2 + - 1/12 y x + 1/48 y x z - 5/192 x y z + --- x y z - --- y x z + 192 192 + + 25 3 2 4 2 3 + - -- y x z - 5/48 x y + 5/48 y x, COEFF(1, -2, 0) = - 1/18 y x + 96 + + 2 4 3 4 2 3 4 4 3 2 4 + - 1/72 y x z + 5/144 x y z - 1/144 x y z + 1/18 y + 1/96 y x z + + 2 3 3 4 3 4 2 4 4 + + 5/72 z y x - 1/36 y x z - 1/36 x y + 1/9 y x - 1/192 x y z + + 4 4 4 2 2 2 3 2 3 3 2 + + 1/36 y + 1/72 x y z - 5/192 y x z + 5/36 y x z - 5/72 y x z + + 3 2 2 3 3 2 3 2 3 2 + - 5/96 y x z - 1/18 y - 1/9 y x + 1/36 y x - 1/36 y + 1/24 y x + + 3 3 2 2 3 2 4 4 4 2 + + 1/18 y x - 5/144 z y x - 1/48 x y + 1/18 x y - 5/72 x y z + + 2 2 4 2 2 2 2 2 2 + - 1/18 y x + 5/192 x y z + 5/72 y x z + 5/96 y x z - 5/36 y x z + + 4 4 3 4 4 4 3 2 + + 1/36 y x z + 1/72 y z - 1/72 y z + 1/144 y z + 5/72 y z + + 2 4 4 2 2 3 4 2 4 + - 1/96 y x z - 5/144 y z - 5/72 y z - 1/72 y x z - 1/144 y z + + 2 2 2 2 2 2 2 4 2 3 4 + + 5/144 y z + 1/48 y x - 1/24 y x + 1/192 y x z + 1/144 y x z + + 3 3 4 3 2 4 + + 1/72 y x z , COEFF(2, -2, 0) = 1/72 y x + 1/1152 y x z + + 3 4 2 3 4 4 3 2 4 + - 5/576 x y z + 1/576 x y z - 1/144 y - 1/192 y x z + + 2 3 3 4 3 4 2 4 4 + - 5/288 z y x + 1/576 y x z + 1/144 x y - 1/144 y x + 1/384 x y z + + 4 4 4 2 2 2 3 2 + - 1/288 y - 1/1152 x y z + 5/384 y x z - 5/576 y x z + + 3 3 2 3 2 2 3 3 2 3 + + 5/288 y x z + 5/192 y x z + 1/144 y + 1/144 y x - 1/144 y x + + 2 3 2 3 3 2 2 3 2 4 + + 1/288 y - 1/48 y x - 1/72 y x + 5/576 z y x + 1/96 x y + + 4 4 2 2 2 4 2 + - 1/288 x y + 5/1152 x y z + 1/288 y x - 5/384 x y z + + 2 2 2 2 2 4 + - 5/1152 y x z - 5/192 y x z + 5/576 y x z - 1/576 y x z + + 4 3 4 4 4 3 2 2 4 + - 1/576 y z + 1/576 y z - 1/1152 y z - 5/576 y z + 1/192 y x z + + 4 2 2 3 4 2 4 2 2 + + 5/1152 y z + 5/576 y z + 1/288 y x z + 1/1152 y z - 5/1152 y z + + 2 2 2 2 2 4 2 3 4 + - 1/96 y x + 1/48 y x - 1/384 y x z - 1/576 y x z + + 3 3 4 3 2 4 + - 1/288 y x z , COEFF(-2, -1, 0) = - 1/9 y x - 1/72 y x z + + 3 4 2 3 4 4 3 2 4 2 3 + + 5/144 x y z - 1/144 x y z - 1/18 y - 1/96 y x z + 5/36 z y x + + 3 4 3 4 2 4 4 4 + - 1/288 y x z - 1/36 x y + 1/18 y x + 1/96 x y z - 1/72 y + + 4 4 2 2 2 3 2 3 3 2 + + 1/288 x y z + 5/24 y x z + 5/288 y x z - 5/144 y x z + + 3 2 2 3 3 2 3 2 3 2 + + 5/96 y x z + 1/72 y - 1/72 y x + 1/9 y x + 1/18 y - 1/24 y x + + 3 3 2 2 3 2 4 4 4 2 + + 1/36 y x - 5/36 z y x + 1/24 x y + 1/72 x y - 5/288 x y z + + 2 2 4 2 2 2 2 2 2 + - 1/18 y x - 5/96 x y z + 5/72 y x z - 5/24 y x z - 5/72 y x z + + 4 4 3 4 4 4 3 2 + + 1/72 y x z - 1/72 y z + 1/288 y z - 1/288 y z - 5/288 y z + + 2 4 4 2 2 3 4 2 4 + + 1/24 y x z + 5/288 y z + 5/72 y z - 1/36 y x z + 1/72 y z + + 2 2 2 2 2 2 2 4 2 3 4 + - 5/72 y z - 1/6 y x + 1/6 y x - 1/24 y x z + 1/36 y x z + + 3 3 4 3 2 4 + + 1/144 y x z , COEFF(-1, -1, 0) = 4/9 y x + 2/9 y x z + + 3 4 2 3 4 4 3 2 4 2 3 + - 5/36 x y z + 1/36 x y z + 4/9 y + 1/48 y x z - 5/9 z y x + + 3 4 3 4 2 4 4 4 + + 1/18 y x z + 1/9 x y - 8/9 y x - 1/48 x y z + 1/9 y + + 4 4 2 2 2 3 2 3 3 2 + - 1/18 x y z - 5/12 y x z - 5/18 y x z + 5/36 y x z + + 3 2 2 3 3 2 3 2 3 2 + - 5/48 y x z - 1/9 y + 2/9 y x - 4/9 y x - 4/9 y + 1/12 y x + + 3 3 2 2 3 2 4 4 4 2 + - 1/9 y x + 5/9 z y x - 1/12 x y - 2/9 x y + 5/18 x y z + + 2 2 4 2 2 2 2 2 2 + + 8/9 y x + 5/48 x y z - 10/9 y x z + 5/12 y x z + 10/9 y x z + + 4 4 3 4 4 4 3 2 + - 2/9 y x z + 1/9 y z - 1/36 y z + 1/36 y z + 5/36 y z + + 2 4 4 2 2 3 4 2 4 + - 1/12 y x z - 5/36 y z - 5/9 y z + 1/9 y x z - 1/9 y z + + 2 2 2 2 2 2 2 4 2 3 4 + + 5/9 y z + 1/3 y x - 1/3 y x + 1/12 y x z - 1/9 y x z + + 3 3 4 3 3 4 + - 1/36 y x z , COEFF(0, -1, 0) = - 2/3 y x - 5/48 y x z + 5/3 y x + + 2 3 25 2 3 4 2 4 4 2 3 4 + + 5/6 z y x - -- y x z + 5/24 x y z + 5/48 x y z + 1/6 y x z + 12 + + 3 4 4 2 2 3 2 4 25 3 2 3 + - 1/24 x y z - 5/6 z y x - 5/12 y x z + -- y x z - 5/12 y x + 48 + + 3 4 3 3 3 3 4 2 3 4 2 + - 1/6 x y + 1/6 y x + 1/24 y x z + 2/3 y x + 5/12 x y - 5/3 y x + + 25 4 2 4 3 4 3 3 2 25 2 2 + - -- x y z + 5/12 y x z - 1/6 y x z - 5/24 y x z + -- y x z , + 48 12 + + 3 2 4 3 4 2 3 4 4 + COEFF(1, -1, 0) = 4/9 y x + 2/9 y x z - 5/36 x y z + 1/36 x y z + + 3 2 4 2 3 3 4 3 4 + - 4/9 y - 1/48 y x z - 5/9 z y x + 1/18 y x z + 1/9 x y - 8/9 y x + + 2 4 4 4 4 4 2 2 2 3 2 + + 1/48 x y z - 1/9 y - 1/18 x y z + 5/12 y x z - 5/18 y x z + + 3 3 2 3 2 2 3 3 2 3 2 + + 5/36 y x z + 5/48 y x z + 1/9 y + 2/9 y x - 4/9 y x + 4/9 y + + 3 2 3 3 2 2 3 2 4 4 + - 1/12 y x - 1/9 y x + 5/9 z y x + 1/12 x y - 2/9 x y + + 4 2 2 2 4 2 2 2 2 2 + + 5/18 x y z + 8/9 y x - 5/48 x y z - 10/9 y x z - 5/12 y x z + + 2 4 4 3 4 4 4 + + 10/9 y x z - 2/9 y x z - 1/9 y z + 1/36 y z - 1/36 y z + + 3 2 2 4 4 2 2 3 4 + - 5/36 y z + 1/12 y x z + 5/36 y z + 5/9 y z + 1/9 y x z + + 2 4 2 2 2 2 2 2 2 4 + + 1/9 y z - 5/9 y z - 1/3 y x + 1/3 y x - 1/12 y x z + + 2 3 4 3 3 4 3 + - 1/9 y x z - 1/36 y x z , COEFF(2, -1, 0) = - 1/9 y x + + 2 4 3 4 2 3 4 4 3 2 4 + - 1/72 y x z + 5/144 x y z - 1/144 x y z + 1/18 y + 1/96 y x z + + 2 3 3 4 3 4 2 4 4 + + 5/36 z y x - 1/288 y x z - 1/36 x y + 1/18 y x - 1/96 x y z + + 4 4 4 2 2 2 3 2 3 3 2 + + 1/72 y + 1/288 x y z - 5/24 y x z + 5/288 y x z - 5/144 y x z + + 3 2 2 3 3 2 3 2 3 2 + - 5/96 y x z - 1/72 y - 1/72 y x + 1/9 y x - 1/18 y + 1/24 y x + + 3 3 2 2 3 2 4 4 4 2 + + 1/36 y x - 5/36 z y x - 1/24 x y + 1/72 x y - 5/288 x y z + + 2 2 4 2 2 2 2 2 2 + - 1/18 y x + 5/96 x y z + 5/72 y x z + 5/24 y x z - 5/72 y x z + + 4 4 3 4 4 4 3 2 + + 1/72 y x z + 1/72 y z - 1/288 y z + 1/288 y z + 5/288 y z + + 2 4 4 2 2 3 4 2 4 + - 1/24 y x z - 5/288 y z - 5/72 y z - 1/36 y x z - 1/72 y z + + 2 2 2 2 2 2 2 4 2 3 4 + + 5/72 y z + 1/6 y x - 1/6 y x + 1/24 y x z + 1/36 y x z + + 3 3 4 2 4 + + 1/144 y x z , COEFF(-2, 0, 0) = - 1/12 x + 5/192 y x z + + 3 4 2 3 4 4 3 4 2 4 4 4 + - 5/96 x y z + 1/96 x y z + 1/24 x y - 1/64 x y z + 1/48 y + + 4 4 25 2 2 2 4 3 2 3 + - 1/192 x y z - -- y x z + 1/48 z + 1/6 x + 1/12 - 5/24 y x + 64 + + 2 2 2 25 2 2 3 2 4 4 + - 5/48 y - 5/48 z - 1/4 x + -- z y x - 1/16 x y - 1/48 x y + 96 + + 4 2 2 2 4 2 25 2 2 4 4 + + 5/192 x y z + 5/48 y x + 5/64 x y z - --- y x z + 1/192 y z + 192 + + 2 4 4 4 2 3 4 2 2 + - 1/16 x z - 1/48 x z - 5/192 y z + 1/24 x z + 5/16 x z + + 2 3 2 2 4 25 2 2 2 2 + + 5/48 x z - 5/24 x z - 5/192 y z + --- y z + 5/16 y x + 192 + + 2 2 4 2 3 4 2 4 + + 5/64 y x z - 5/96 y x z , COEFF(-1, 0, 0) = 4/3 x - 5/12 y x z + + 3 4 2 3 4 4 3 4 2 4 4 4 + + 5/24 x y z - 1/24 x y z - 1/6 x y + 1/32 x y z - 1/6 y + + 4 4 25 2 2 2 4 3 2 3 2 + + 1/12 x y z + -- y x z - 1/6 z - 2/3 - 2/3 x + 5/6 y x + 5/6 y + 32 + + 2 2 25 2 2 3 2 4 4 4 2 + + 5/6 z + 1/2 x - -- z y x + 1/8 x y + 1/3 x y - 5/12 x y z + 24 + + 2 2 4 2 25 2 2 4 4 2 4 + - 5/3 y x - 5/32 x y z + -- y x z - 1/24 y z + 1/8 x z + 12 + + 4 4 2 3 4 2 2 2 3 2 + + 1/3 x z + 5/24 y z - 1/6 x z - 5/8 x z - 5/3 x z + 5/6 x z + + 2 4 25 2 2 2 2 2 2 4 2 3 4 + + 5/24 y z - -- y z - 5/8 y x - 5/32 y x z + 5/24 y x z , + 24 + + 25 2 4 2 3 4 2 25 4 2 + COEFF(0, 0, 0) = -- y x z - 5/16 y x z + 25/8 y x + -- x y z + 32 32 + + 4 2 3 4 2 4 4 4 + - 5/8 x z + 25/8 x z - 5/16 x y z - 5/8 x y - 5/2 x - 5/32 x y z + + 3 4 3 4 25 2 2 3 2 3 3 2 + + 1/4 x z + 1/4 x y + -- z y x - 5/4 y x - 5/4 x z + 16 + + 125 2 2 3 4 4 3 2 4 + - --- y x z + 1/16 x y z + x , COEFF(1, 0, 0) = 4/3 x - 5/12 y x z + 32 + + 3 4 2 3 4 4 3 4 2 4 4 4 + + 5/24 x y z - 1/24 x y z - 1/6 x y - 1/32 x y z + 1/6 y + + 4 4 25 2 2 2 4 3 2 3 2 + + 1/12 x y z - -- y x z + 1/6 z + 2/3 - 2/3 x + 5/6 y x - 5/6 y + 32 + + 2 2 25 2 2 3 2 4 4 4 2 + - 5/6 z - 1/2 x - -- z y x - 1/8 x y + 1/3 x y - 5/12 x y z + 24 + + 2 2 4 2 25 2 2 4 4 2 4 + - 5/3 y x + 5/32 x y z + -- y x z + 1/24 y z - 1/8 x z + 12 + + 4 4 2 3 4 2 2 2 3 2 + + 1/3 x z - 5/24 y z - 1/6 x z + 5/8 x z - 5/3 x z + 5/6 x z + + 2 4 25 2 2 2 2 2 2 4 2 3 4 + - 5/24 y z + -- y z + 5/8 y x + 5/32 y x z + 5/24 y x z , + 24 + + 2 4 3 4 2 3 4 4 + COEFF(2, 0, 0) = - 1/12 x + 5/192 y x z - 5/96 x y z + 1/96 x y z + + 3 4 2 4 4 4 4 4 25 2 2 2 + + 1/24 x y + 1/64 x y z - 1/48 y - 1/192 x y z + -- y x z + 64 + + 4 3 2 3 2 2 2 + - 1/48 z + 1/6 x - 1/12 - 5/24 y x + 5/48 y + 5/48 z + 1/4 x + + 25 2 2 3 2 4 4 4 2 2 + + -- z y x + 1/16 x y - 1/48 x y + 5/192 x y z + 5/48 y x + 96 + + 2 4 2 25 2 2 4 4 2 4 4 + - 5/64 x y z - --- y x z - 1/192 y z + 1/16 x z - 1/48 x z + 192 + + 4 2 3 4 2 2 2 3 2 + + 5/192 y z + 1/24 x z - 5/16 x z + 5/48 x z - 5/24 x z + + 2 4 25 2 2 2 2 2 2 4 2 3 4 + + 5/192 y z - --- y z - 5/16 y x - 5/64 y x z - 5/96 y x z , + 192 + + 3 2 4 3 4 2 3 4 4 + COEFF(-2, 1, 0) = 1/9 y x - 1/72 y x z + 5/144 x y z - 1/144 x y z + + 3 2 4 2 3 3 4 3 4 + + 1/18 y + 1/96 y x z - 5/36 z y x + 1/288 y x z - 1/36 x y + + 2 4 4 4 4 4 2 2 2 + - 1/18 y x + 1/96 x y z - 1/72 y + 1/288 x y z + 5/24 y x z + + 3 2 3 3 2 3 2 2 3 3 + - 5/288 y x z + 5/144 y x z - 5/96 y x z - 1/72 y + 1/72 y x + + 2 3 2 3 2 3 3 2 2 3 + + 1/9 y x + 1/18 y + 1/24 y x - 1/36 y x - 5/36 z y x + + 2 4 4 4 2 2 2 4 2 + + 1/24 x y + 1/72 x y - 5/288 x y z - 1/18 y x - 5/96 x y z + + 2 2 2 2 2 4 4 + + 5/72 y x z + 5/24 y x z + 5/72 y x z - 1/72 y x z + 1/72 y z + + 3 4 4 4 3 2 2 4 4 2 + - 1/288 y z - 1/288 y z + 5/288 y z - 1/24 y x z + 5/288 y z + + 2 3 4 2 4 2 2 2 2 + - 5/72 y z + 1/36 y x z + 1/72 y z - 5/72 y z - 1/6 y x + + 2 2 2 4 2 3 4 3 3 4 + - 1/6 y x - 1/24 y x z + 1/36 y x z - 1/144 y x z , + + 3 2 4 3 4 2 3 4 4 + COEFF(-1, 1, 0) = - 4/9 y x + 2/9 y x z - 5/36 x y z + 1/36 x y z + + 3 2 4 2 3 3 4 3 4 + - 4/9 y - 1/48 y x z + 5/9 z y x - 1/18 y x z + 1/9 x y + 8/9 y x + + 2 4 4 4 4 4 2 2 2 3 2 + - 1/48 x y z + 1/9 y - 1/18 x y z - 5/12 y x z + 5/18 y x z + + 3 3 2 3 2 2 3 3 2 3 2 + - 5/36 y x z + 5/48 y x z + 1/9 y - 2/9 y x - 4/9 y x - 4/9 y + + 3 2 3 3 2 2 3 2 4 4 + - 1/12 y x + 1/9 y x + 5/9 z y x - 1/12 x y - 2/9 x y + + 4 2 2 2 4 2 2 2 2 2 + + 5/18 x y z + 8/9 y x + 5/48 x y z - 10/9 y x z - 5/12 y x z + + 2 4 4 3 4 4 4 + - 10/9 y x z + 2/9 y x z - 1/9 y z + 1/36 y z + 1/36 y z + + 3 2 2 4 4 2 2 3 4 + - 5/36 y z + 1/12 y x z - 5/36 y z + 5/9 y z - 1/9 y x z + + 2 4 2 2 2 2 2 2 2 4 + - 1/9 y z + 5/9 y z + 1/3 y x + 1/3 y x + 1/12 y x z + + 2 3 4 3 3 4 2 3 + - 1/9 y x z + 1/36 y x z , COEFF(0, 1, 0) = - 5/6 z y x + + 3 4 25 3 2 3 3 4 2 3 4 + + 5/48 y x z - -- y x z + 5/12 y x + 1/6 y x z + 1/6 y x z + 48 + + 25 2 2 2 4 4 2 3 3 + + -- y x z - 5/12 y x z - 5/12 y x z + 2/3 y x + 2/3 y x + 12 + + 2 3 4 4 4 4 3 3 2 + - 5/3 y x - 1/6 x y + 5/12 x y + 5/48 x y z + 5/24 y x z + + 3 3 4 3 4 2 25 2 2 2 3 + - 1/24 y x z - 5/3 y x + 5/24 x y z + -- y x z - 5/6 z y x + 12 + + 3 3 3 4 4 25 4 2 3 + - 1/6 y x - 1/24 x y z - -- x y z , COEFF(1, 1, 0) = - 4/9 y x + 48 + + 2 4 3 4 2 3 4 4 3 2 4 + + 2/9 y x z - 5/36 x y z + 1/36 x y z + 4/9 y + 1/48 y x z + + 2 3 3 4 3 4 2 4 4 + + 5/9 z y x - 1/18 y x z + 1/9 x y + 8/9 y x + 1/48 x y z + + 4 4 4 2 2 2 3 2 3 3 2 + - 1/9 y - 1/18 x y z + 5/12 y x z + 5/18 y x z - 5/36 y x z + + 3 2 2 3 3 2 3 2 3 2 + - 5/48 y x z - 1/9 y - 2/9 y x - 4/9 y x + 4/9 y + 1/12 y x + + 3 3 2 2 3 2 4 4 4 2 + + 1/9 y x + 5/9 z y x + 1/12 x y - 2/9 x y + 5/18 x y z + + 2 2 4 2 2 2 2 2 2 + + 8/9 y x - 5/48 x y z - 10/9 y x z + 5/12 y x z - 10/9 y x z + + 4 4 3 4 4 4 3 2 + + 2/9 y x z + 1/9 y z - 1/36 y z - 1/36 y z + 5/36 y z + + 2 4 4 2 2 3 4 2 4 + - 1/12 y x z + 5/36 y z - 5/9 y z - 1/9 y x z + 1/9 y z + + 2 2 2 2 2 2 2 4 2 3 4 + - 5/9 y z - 1/3 y x - 1/3 y x - 1/12 y x z - 1/9 y x z + + 3 3 4 3 2 4 3 4 2 + + 1/36 y x z , COEFF(2, 1, 0) = 1/9 y x - 1/72 y x z + 5/144 x y z + + 3 4 4 3 2 4 2 3 3 4 + - 1/144 x y z - 1/18 y - 1/96 y x z - 5/36 z y x + 1/288 y x z + + 3 4 2 4 4 4 4 4 + - 1/36 x y - 1/18 y x - 1/96 x y z + 1/72 y + 1/288 x y z + + 2 2 2 3 2 3 3 2 3 2 2 3 + - 5/24 y x z - 5/288 y x z + 5/144 y x z + 5/96 y x z + 1/72 y + + 3 2 3 2 3 2 3 3 + + 1/72 y x + 1/9 y x - 1/18 y - 1/24 y x - 1/36 y x + + 2 2 3 2 4 4 4 2 2 + - 5/36 z y x - 1/24 x y + 1/72 x y - 5/288 x y z - 1/18 y x + + 2 4 2 2 2 2 2 2 4 + + 5/96 x y z + 5/72 y x z - 5/24 y x z + 5/72 y x z - 1/72 y x z + + 4 3 4 4 4 3 2 2 4 + - 1/72 y z + 1/288 y z + 1/288 y z - 5/288 y z + 1/24 y x z + + 4 2 2 3 4 2 4 2 2 + - 5/288 y z + 5/72 y z + 1/36 y x z - 1/72 y z + 5/72 y z + + 2 2 2 2 2 4 2 3 4 3 3 4 + + 1/6 y x + 1/6 y x + 1/24 y x z + 1/36 y x z - 1/144 y x z , + + 3 2 4 3 4 2 + COEFF(-2, 2, 0) = - 1/72 y x + 1/1152 y x z - 5/576 x y z + + 3 4 4 3 2 4 2 3 + + 1/576 x y z - 1/144 y - 1/192 y x z + 5/288 z y x + + 3 4 3 4 2 4 4 4 + - 1/576 y x z + 1/144 x y + 1/144 y x - 1/384 x y z + 1/288 y + + 4 4 2 2 2 3 2 3 3 2 + - 1/1152 x y z - 5/384 y x z + 5/576 y x z - 5/288 y x z + + 3 2 2 3 3 2 3 2 + + 5/192 y x z + 1/144 y - 1/144 y x - 1/144 y x - 1/288 y + + 3 2 3 3 2 2 3 2 4 4 + - 1/48 y x + 1/72 y x + 5/576 z y x - 1/96 x y - 1/288 x y + + 4 2 2 2 4 2 2 2 + + 5/1152 x y z + 1/288 y x + 5/384 x y z - 5/1152 y x z + + 2 2 2 4 4 3 4 + - 5/192 y x z - 5/576 y x z + 1/576 y x z - 1/576 y z + 1/576 y z + + 4 4 3 2 2 4 4 2 2 + + 1/1152 y z - 5/576 y z + 1/192 y x z - 5/1152 y z + 5/576 y z + + 3 4 2 4 2 2 2 2 2 + - 1/288 y x z - 1/1152 y z + 5/1152 y z + 1/96 y x + 1/48 y x + + 2 2 4 2 3 4 3 3 4 + + 1/384 y x z - 1/576 y x z + 1/288 y x z , COEFF(-1, 2, 0) = + + 3 2 4 3 4 2 3 4 4 + 1/18 y x - 1/72 y x z + 5/144 x y z - 1/144 x y z + 1/18 y + + 3 2 4 2 3 3 4 3 4 + + 1/96 y x z - 5/72 z y x + 1/36 y x z - 1/36 x y - 1/9 y x + + 2 4 4 4 4 4 2 2 2 3 2 + + 1/192 x y z - 1/36 y + 1/72 x y z + 5/192 y x z - 5/36 y x z + + 3 3 2 3 2 2 3 3 2 3 + + 5/72 y x z - 5/96 y x z - 1/18 y + 1/9 y x + 1/36 y x + + 2 3 2 3 3 2 2 3 2 4 + + 1/36 y + 1/24 y x - 1/18 y x - 5/144 z y x + 1/48 x y + + 4 4 2 2 2 4 2 2 2 + + 1/18 x y - 5/72 x y z - 1/18 y x - 5/192 x y z + 5/72 y x z + + 2 2 2 4 4 3 4 + + 5/96 y x z + 5/36 y x z - 1/36 y x z + 1/72 y z - 1/72 y z + + 4 4 3 2 2 4 4 2 2 + - 1/144 y z + 5/72 y z - 1/96 y x z + 5/144 y z - 5/72 y z + + 3 4 2 4 2 2 2 2 2 + + 1/72 y x z + 1/144 y z - 5/144 y z - 1/48 y x - 1/24 y x + + 2 2 4 2 3 4 3 3 4 + - 1/192 y x z + 1/144 y x z - 1/72 y x z , COEFF(0, 2, 0) = + + 3 3 4 2 2 3 2 4 25 4 2 25 2 2 + 1/48 y x z + 5/96 z y x + 5/192 y x z + --- x y z - --- y x z + 192 192 + + 25 3 2 3 3 2 3 3 4 2 3 4 + + -- y x z - 5/48 y x z - 5/24 y x - 5/96 x y z - 5/96 y x z + 96 + + 2 3 3 3 4 3 3 2 + + 5/48 z y x - 1/12 y x + 1/24 x y + 1/12 y x + 5/48 y x + + 2 3 4 4 4 25 2 2 3 4 + - 1/24 y x - 5/48 x y - 5/192 x y z - -- y x z - 1/96 y x z + 96 + + 3 4 3 4 4 4 + - 1/48 y x z + 1/96 x y z + 5/96 y x z + 5/24 y x, COEFF(1, 2, 0) = + + 3 2 4 3 4 2 3 4 4 + 1/18 y x - 1/72 y x z + 5/144 x y z - 1/144 x y z - 1/18 y + + 3 2 4 2 3 3 4 3 4 + - 1/96 y x z - 5/72 z y x + 1/36 y x z - 1/36 x y - 1/9 y x + + 2 4 4 4 4 4 2 2 2 3 2 + - 1/192 x y z + 1/36 y + 1/72 x y z - 5/192 y x z - 5/36 y x z + + 3 3 2 3 2 2 3 3 2 3 + + 5/72 y x z + 5/96 y x z + 1/18 y + 1/9 y x + 1/36 y x + + 2 3 2 3 3 2 2 3 2 4 + - 1/36 y - 1/24 y x - 1/18 y x - 5/144 z y x - 1/48 x y + + 4 4 2 2 2 4 2 2 2 + + 1/18 x y - 5/72 x y z - 1/18 y x + 5/192 x y z + 5/72 y x z + + 2 2 2 4 4 3 4 + - 5/96 y x z + 5/36 y x z - 1/36 y x z - 1/72 y z + 1/72 y z + + 4 4 3 2 2 4 4 2 2 + + 1/144 y z - 5/72 y z + 1/96 y x z - 5/144 y z + 5/72 y z + + 3 4 2 4 2 2 2 2 2 + + 1/72 y x z - 1/144 y z + 5/144 y z + 1/48 y x + 1/24 y x + + 2 2 4 2 3 4 3 3 4 + + 1/192 y x z + 1/144 y x z - 1/72 y x z , COEFF(2, 2, 0) = + + 3 2 4 3 4 2 3 4 4 + - 1/72 y x + 1/1152 y x z - 5/576 x y z + 1/576 x y z + 1/144 y + + 3 2 4 2 3 3 4 3 4 + + 1/192 y x z + 5/288 z y x - 1/576 y x z + 1/144 x y + 1/144 y x + + 2 4 4 4 4 4 2 2 2 + + 1/384 x y z - 1/288 y - 1/1152 x y z + 5/384 y x z + + 3 2 3 3 2 3 2 2 3 3 + + 5/576 y x z - 5/288 y x z - 5/192 y x z - 1/144 y - 1/144 y x + + 2 3 2 3 2 3 3 2 2 3 + - 1/144 y x + 1/288 y + 1/48 y x + 1/72 y x + 5/576 z y x + + 2 4 4 4 2 2 2 4 2 + + 1/96 x y - 1/288 x y + 5/1152 x y z + 1/288 y x - 5/384 x y z + + 2 2 2 2 2 4 + - 5/1152 y x z + 5/192 y x z - 5/576 y x z + 1/576 y x z + + 4 3 4 4 4 3 2 2 4 + + 1/576 y z - 1/576 y z - 1/1152 y z + 5/576 y z - 1/192 y x z + + 4 2 2 3 4 2 4 2 2 + + 5/1152 y z - 5/576 y z - 1/288 y x z + 1/1152 y z - 5/1152 y z + + 2 2 2 2 2 4 2 3 4 + - 1/96 y x - 1/48 y x - 1/384 y x z - 1/576 y x z + + 3 3 4 2 4 3 4 2 + + 1/288 y x z , COEFF(-2, -2, 1) = - 1/1728 y x z + 1/216 x y z + + 4 2 4 3 4 3 + - 1/432 x y z - 1/144 x y z + 1/216 x y z + 1/864 y x z + + 3 4 4 3 2 4 3 2 3 + - 1/864 x y z - 1/288 y x z + 1/108 z y x + 1/108 z y x + + 3 4 2 2 3 2 4 4 + - 1/864 y x z + 1/432 y x z - 1/1728 y x z + 1/576 x y z + + 4 4 2 2 2 3 2 2 2 3 + + 1/1728 x y z + 1/144 y x z + 1/216 y x z - 1/576 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/432 y x z - 1/108 y x z + 1/288 y x z + 1/72 y x z + + 2 3 3 3 3 3 2 + + 1/864 y x z - 1/216 z y + 1/216 z y x + 1/72 z y x + + 3 3 2 2 3 + - 1/108 z y x - 1/216 y x z - 1/72 z y x - 1/216 z y x + + 2 2 3 3 3 3 3 3 + - 1/216 z y x + 1/216 y z - 1/864 y x z + 1/432 y x z + + 4 2 2 4 2 2 2 2 2 + - 1/432 x y z - 1/144 x y z + 1/432 y x z + 1/144 y x z + + 2 2 2 2 3 2 3 + - 1/72 y x z - 1/216 y x z - 1/432 y z - 1/288 y x z + + 3 4 3 4 3 2 3 3 3 + - 1/864 x y z + 1/864 y x z - 1/864 y z + 1/1728 y z + 1/864 y z + + 4 3 4 4 4 3 2 2 4 + - 1/864 y z + 1/864 y z - 1/1728 y z - 1/216 y z + 1/288 y x z + + 4 2 4 2 3 4 2 4 + + 1/432 y z + 1/432 y z + 1/216 y z - 1/432 y x z + 1/1728 y z + + 2 2 4 3 4 3 2 4 3 + - 1/432 y z + 1/1728 x y z - 1/1728 y z + 1/576 x y z + + 2 2 4 2 3 4 3 3 4 + - 1/576 y x z + 1/864 y x z + 1/432 y x z , COEFF(-1, -2, 1) = + + 2 4 3 4 2 4 2 4 3 4 + 1/108 y x z - 1/54 x y z + 1/27 x y z + 1/72 x y z - 1/54 x y z + + 3 3 4 4 3 2 4 3 + - 1/54 y x z + 1/216 x y z + 1/144 y x z - 1/27 z y x + + 2 3 3 4 2 2 3 + - 1/27 z y x + 1/54 y x z - 1/27 y x z + 1/108 y x z + + 2 4 4 4 4 2 2 2 3 2 + - 1/288 x y z - 1/108 x y z - 1/72 y x z - 2/27 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/288 y x z + 1/108 y x z + 1/27 y x z - 1/144 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/36 y x z - 1/216 y x z + 1/27 z y - 2/27 z y x - 1/36 z y x + + 3 3 2 2 3 2 2 3 + + 1/27 z y x + 2/27 y x z + 1/36 z y x + 1/54 z y x + 1/54 z y x + + 3 3 3 3 3 4 2 2 4 2 + - 1/27 y z + 1/54 y x z - 1/108 y x z + 1/27 x y z + 1/72 x y z + + 2 2 2 2 2 2 2 2 + - 1/27 y x z - 1/72 y x z + 1/36 y x z + 2/27 y x z + 1/54 y z + + 3 2 3 3 4 3 4 3 2 3 + + 1/144 y x z + 1/216 x y z - 1/54 y x z + 1/108 y z - 1/216 y z + + 3 3 4 3 4 4 4 3 2 + - 1/108 y z + 1/108 y z - 1/108 y z + 1/216 y z + 1/27 y z + + 2 4 4 2 4 2 3 4 + - 1/144 y x z - 1/54 y z - 1/54 y z - 1/27 y z + 1/108 y x z + + 2 4 2 2 4 3 4 3 2 4 3 + - 1/216 y z + 1/54 y z - 1/108 x y z + 1/216 y z - 1/288 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/288 y x z - 1/216 y x z - 1/108 y x z , COEFF(0, -2, 1) = + + 2 4 3 4 2 4 3 4 3 + - 5/288 y x z + 1/36 x y z - 5/72 x y z + 1/36 x y z + 5/144 y x z + + 3 4 4 3 2 3 3 4 + - 1/144 x y z + 1/18 z y x + 1/18 z y x - 5/144 y x z + + 2 2 3 4 4 3 2 + + 5/72 y x z - 5/288 y x z + 5/288 x y z + 5/36 y x z + + 3 3 3 3 2 2 3 3 3 + - 1/72 y x z - 1/18 y x z + 1/144 y x z + 5/36 z y x + + 3 3 2 3 2 2 3 3 3 + - 1/18 z y x - 5/36 y x z - 1/36 z y x - 1/36 z y x - 5/144 y x z + + 3 3 3 4 2 2 2 2 + + 1/72 y x z - 5/72 x y z + 5/72 y x z - 5/36 y x z + + 3 4 3 4 3 4 4 3 + - 1/144 x y z + 5/144 y x z - 1/72 y x z + 5/288 x y z + + 2 3 4 3 3 4 2 4 + + 1/144 y x z + 1/72 y x z , COEFF(1, -2, 1) = 1/108 y x z + + 3 4 2 4 2 4 3 4 3 + - 1/54 x y z + 1/27 x y z - 1/72 x y z - 1/54 x y z - 1/54 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/216 x y z - 1/144 y x z - 1/27 z y x - 1/27 z y x + + 3 4 2 2 3 2 4 4 + + 1/54 y x z - 1/27 y x z + 1/108 y x z + 1/288 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/108 x y z + 1/72 y x z - 2/27 y x z - 1/288 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 1/108 y x z + 1/27 y x z + 1/144 y x z + 1/36 y x z + + 2 3 3 3 3 3 2 3 3 + - 1/216 y x z - 1/27 z y - 2/27 z y x + 1/36 z y x + 1/27 z y x + + 2 2 3 2 2 3 + + 2/27 y x z - 1/36 z y x + 1/54 z y x + 1/54 z y x + 1/27 y z + + 3 3 3 3 3 4 2 2 4 2 + + 1/54 y x z - 1/108 y x z + 1/27 x y z - 1/72 x y z + + 2 2 2 2 2 2 2 2 + - 1/27 y x z + 1/72 y x z - 1/36 y x z + 2/27 y x z - 1/54 y z + + 3 2 3 3 4 3 4 3 2 3 + - 1/144 y x z + 1/216 x y z - 1/54 y x z - 1/108 y z + 1/216 y z + + 3 3 4 3 4 4 4 3 2 + + 1/108 y z - 1/108 y z + 1/108 y z - 1/216 y z - 1/27 y z + + 2 4 4 2 4 2 3 4 + + 1/144 y x z + 1/54 y z + 1/54 y z + 1/27 y z + 1/108 y x z + + 2 4 2 2 4 3 4 3 2 4 3 + + 1/216 y z - 1/54 y z - 1/108 x y z - 1/216 y z + 1/288 x y z + + 2 2 4 2 3 4 3 3 4 + - 1/288 y x z - 1/216 y x z - 1/108 y x z , COEFF(2, -2, 1) = + + 2 4 3 4 2 4 2 4 + - 1/1728 y x z + 1/216 x y z - 1/432 x y z + 1/144 x y z + + 3 4 3 3 4 4 3 2 4 + + 1/216 x y z + 1/864 y x z - 1/864 x y z + 1/288 y x z + + 3 2 3 3 4 2 + + 1/108 z y x + 1/108 z y x - 1/864 y x z + 1/432 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/1728 y x z - 1/576 x y z + 1/1728 x y z - 1/144 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/216 y x z + 1/576 y x z - 1/432 y x z - 1/108 y x z + + 2 3 3 2 2 2 3 3 3 + - 1/288 y x z - 1/72 y x z + 1/864 y x z + 1/216 z y + + 3 3 2 3 3 2 + + 1/216 z y x - 1/72 z y x - 1/108 z y x - 1/216 y x z + 1/72 z y x + + 2 3 2 2 3 3 3 + - 1/216 z y x - 1/216 z y x - 1/216 y z - 1/864 y x z + + 3 3 3 4 2 2 4 2 2 2 + + 1/432 y x z - 1/432 x y z + 1/144 x y z + 1/432 y x z + + 2 2 2 2 2 2 + - 1/144 y x z + 1/72 y x z - 1/216 y x z + 1/432 y z + + 3 2 3 3 4 3 4 3 + + 1/288 y x z - 1/864 x y z + 1/864 y x z + 1/864 y z + + 2 3 3 3 4 3 4 4 4 + - 1/1728 y z - 1/864 y z + 1/864 y z - 1/864 y z + 1/1728 y z + + 3 2 2 4 4 2 4 2 + + 1/216 y z - 1/288 y x z - 1/432 y z - 1/432 y z - 1/216 y z + + 3 4 2 4 2 2 4 3 + - 1/432 y x z - 1/1728 y z + 1/432 y z + 1/1728 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + + 1/1728 y z - 1/576 x y z + 1/576 y x z + 1/864 y x z + + 3 3 4 2 4 3 4 2 + + 1/432 y x z , COEFF(-2, -1, 1) = 1/108 y x z - 1/54 x y z + + 4 2 4 3 4 3 + + 1/108 x y z + 1/36 x y z - 1/54 x y z - 1/108 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/216 x y z + 1/144 y x z - 2/27 z y x - 2/27 z y x + + 3 4 2 2 3 2 4 4 + + 1/432 y x z - 1/27 y x z + 1/108 y x z - 1/144 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/432 x y z - 1/9 y x z - 1/108 y x z + 1/36 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 1/54 y x z + 1/54 y x z - 1/36 y x z - 1/36 y x z + + 2 3 3 3 3 3 2 3 3 + - 1/54 y x z + 1/108 z y - 1/108 z y x - 1/36 z y x + 1/54 z y x + + 2 2 3 2 2 3 + + 1/27 y x z + 1/9 z y x + 2/27 z y x + 2/27 z y x - 1/27 y z + + 3 3 3 3 3 4 2 2 4 2 + + 1/432 y x z - 1/216 y x z + 1/108 x y z + 1/36 x y z + + 2 2 2 2 2 2 2 2 + - 1/27 y x z - 1/9 y x z + 1/9 y x z + 1/27 y x z + 1/27 y z + + 3 2 3 3 4 3 4 3 + + 1/144 y x z + 1/216 x y z - 1/108 y x z + 1/108 y z + + 2 3 3 3 4 3 4 4 4 + - 1/108 y z - 1/432 y z + 1/108 y z - 1/432 y z + 1/432 y z + + 3 2 2 4 4 2 4 2 + + 1/108 y z - 1/36 y x z - 1/108 y z - 1/108 y z - 1/27 y z + + 3 4 2 4 2 2 4 3 4 3 + + 1/54 y x z - 1/108 y z + 1/27 y z - 1/432 x y z + 1/432 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + - 1/144 x y z + 1/36 y x z - 1/54 y x z - 1/216 y x z , + + 2 4 3 4 2 4 + COEFF(-1, -1, 1) = - 4/27 y x z + 2/27 x y z - 4/27 x y z + + 2 4 3 4 3 3 4 4 + - 1/18 x y z + 2/27 x y z + 4/27 y x z - 1/54 x y z + + 3 2 4 3 2 3 3 4 16 2 + - 1/72 y x z + 8/27 z y x + 8/27 z y x - 1/27 y x z + -- y x z + 27 + + 2 3 2 4 4 4 4 2 2 2 + - 4/27 y x z + 1/72 x y z + 1/27 x y z + 2/9 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 4/27 y x z - 1/18 y x z - 2/27 y x z - 2/27 y x z + + 2 3 3 2 2 2 3 3 3 3 + + 1/18 y x z + 1/18 y x z + 2/27 y x z - 2/27 z y + 4/27 z y x + + 3 2 3 3 16 2 2 3 + + 1/18 z y x - 2/27 z y x - -- y x z - 2/9 z y x - 8/27 z y x + 27 + + 2 2 3 3 3 3 3 3 4 2 + - 8/27 z y x + 8/27 y z - 1/27 y x z + 1/54 y x z - 4/27 x y z + + 2 4 2 16 2 2 2 2 2 2 16 2 + - 1/18 x y z + -- y x z + 2/9 y x z - 2/9 y x z - -- y x z + 27 27 + + 2 3 2 3 3 4 3 4 3 + - 8/27 y z - 1/72 y x z - 1/54 x y z + 4/27 y x z - 2/27 y z + + 2 3 3 3 4 3 4 4 4 + + 2/27 y z + 1/54 y z - 2/27 y z + 1/54 y z - 1/54 y z + + 3 2 2 4 4 2 4 2 + - 2/27 y z + 1/18 y x z + 2/27 y z + 2/27 y z + 8/27 y z + + 3 4 2 4 2 2 4 3 4 3 + - 2/27 y x z + 2/27 y z - 8/27 y z + 1/27 x y z - 1/54 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + + 1/72 x y z - 1/18 y x z + 2/27 y x z + 1/54 y x z , + + 2 4 3 4 2 4 3 4 + COEFF(0, -1, 1) = 5/18 y x z - 1/9 x y z + 5/18 x y z - 1/9 x y z + + 3 3 4 4 3 2 3 3 4 + - 5/18 y x z + 1/36 x y z - 4/9 z y x - 4/9 z y x + 5/72 y x z + + 2 2 3 4 4 3 2 3 3 + - 10/9 y x z + 5/18 y x z - 5/72 x y z - 5/18 y x z + 1/9 y x z + + 3 3 2 2 3 3 3 3 3 + + 1/9 y x z - 1/9 y x z - 5/18 z y x + 1/9 z y x + 10/9 y x z + + 2 3 2 2 3 3 3 3 3 3 4 2 + + 4/9 z y x + 4/9 z y x + 5/72 y x z - 1/36 y x z + 5/18 x y z + + 2 2 2 3 4 3 4 3 4 + - 10/9 y x z + 10/9 y x z + 1/36 x y z - 5/18 y x z + 1/9 y x z + + 4 3 2 3 4 3 3 4 + - 5/72 x y z - 1/9 y x z - 1/36 y x z , COEFF(1, -1, 1) = + + 2 4 3 4 2 4 2 4 3 4 + - 4/27 y x z + 2/27 x y z - 4/27 x y z + 1/18 x y z + 2/27 x y z + + 3 3 4 4 3 2 4 3 2 3 + + 4/27 y x z - 1/54 x y z + 1/72 y x z + 8/27 z y x + 8/27 z y x + + 3 4 16 2 2 3 2 4 4 4 4 + - 1/27 y x z + -- y x z - 4/27 y x z - 1/72 x y z + 1/27 x y z + 27 + + 2 2 2 3 2 2 2 3 3 3 + - 2/9 y x z + 4/27 y x z + 1/18 y x z - 2/27 y x z + + 3 3 2 2 3 3 2 2 2 3 3 3 + - 2/27 y x z - 1/18 y x z - 1/18 y x z + 2/27 y x z + 2/27 z y + + 3 3 2 3 3 16 2 + + 4/27 z y x - 1/18 z y x - 2/27 z y x - -- y x z + 2/9 z y x + 27 + + 2 3 2 2 3 3 3 3 3 3 + - 8/27 z y x - 8/27 z y x - 8/27 y z - 1/27 y x z + 1/54 y x z + + 4 2 2 4 2 16 2 2 2 2 2 2 + - 4/27 x y z + 1/18 x y z + -- y x z - 2/9 y x z + 2/9 y x z + 27 + + 16 2 2 3 2 3 3 4 3 4 + - -- y x z + 8/27 y z + 1/72 y x z - 1/54 x y z + 4/27 y x z + 27 + + 3 2 3 3 3 4 3 4 + + 2/27 y z - 2/27 y z - 1/54 y z + 2/27 y z - 1/54 y z + + 4 4 3 2 2 4 4 2 4 + + 1/54 y z + 2/27 y z - 1/18 y x z - 2/27 y z - 2/27 y z + + 2 3 4 2 4 2 2 4 3 + - 8/27 y z - 2/27 y x z - 2/27 y z + 8/27 y z + 1/27 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + + 1/54 y z - 1/72 x y z + 1/18 y x z + 2/27 y x z + + 3 3 4 2 4 3 4 2 + + 1/54 y x z , COEFF(2, -1, 1) = 1/108 y x z - 1/54 x y z + + 4 2 4 3 4 3 + + 1/108 x y z - 1/36 x y z - 1/54 x y z - 1/108 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/216 x y z - 1/144 y x z - 2/27 z y x - 2/27 z y x + + 3 4 2 2 3 2 4 4 + + 1/432 y x z - 1/27 y x z + 1/108 y x z + 1/144 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/432 x y z + 1/9 y x z - 1/108 y x z - 1/36 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 1/54 y x z + 1/54 y x z + 1/36 y x z + 1/36 y x z + + 2 3 3 3 3 3 2 3 3 + - 1/54 y x z - 1/108 z y - 1/108 z y x + 1/36 z y x + 1/54 z y x + + 2 2 3 2 2 3 + + 1/27 y x z - 1/9 z y x + 2/27 z y x + 2/27 z y x + 1/27 y z + + 3 3 3 3 3 4 2 2 4 2 + + 1/432 y x z - 1/216 y x z + 1/108 x y z - 1/36 x y z + + 2 2 2 2 2 2 2 2 + - 1/27 y x z + 1/9 y x z - 1/9 y x z + 1/27 y x z - 1/27 y z + + 3 2 3 3 4 3 4 3 + - 1/144 y x z + 1/216 x y z - 1/108 y x z - 1/108 y z + + 2 3 3 3 4 3 4 4 4 + + 1/108 y z + 1/432 y z - 1/108 y z + 1/432 y z - 1/432 y z + + 3 2 2 4 4 2 4 2 + - 1/108 y z + 1/36 y x z + 1/108 y z + 1/108 y z + 1/27 y z + + 3 4 2 4 2 2 4 3 4 3 + + 1/54 y x z + 1/108 y z - 1/27 y z - 1/432 x y z - 1/432 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + + 1/144 x y z - 1/36 y x z - 1/54 y x z - 1/216 y x z , + + 2 4 3 4 2 4 + COEFF(-2, 0, 1) = - 5/288 y x z + 1/36 x y z - 1/72 x y z + + 2 4 3 4 3 4 4 2 + - 1/24 x y z + 1/36 x y z - 1/144 x y z + 1/18 z + 5/72 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 5/288 y x z + 1/96 x y z + 1/288 x y z + 5/24 y x z + + 2 2 3 3 4 2 3 3 3 2 + - 5/96 y x z + 1/9 z x - 1/72 z + 5/144 y x z - 1/72 z + 1/18 z + + 2 3 2 2 3 4 2 2 4 2 + - 5/36 z y x - 5/36 z y x - 1/72 x y z - 1/24 x y z + + 2 2 2 2 2 2 + + 5/72 y x z + 5/24 y x z - 5/72 y z - 1/18 x z - 1/6 x z + + 3 4 3 2 3 3 3 2 3 4 4 + - 1/144 x y z + 5/288 y z - 1/36 x z + 1/24 x z - 1/288 y z + + 2 4 3 4 4 2 4 3 4 + + 1/24 x z + 1/72 x z + 1/72 x z + 1/72 y z + 1/72 y z - 1/36 x z + + 2 2 2 3 2 2 4 2 2 + - 1/6 x z - 1/18 x z + 1/9 x z + 5/288 y z - 5/72 y z + + 4 3 4 3 2 4 3 2 2 4 + + 1/288 x y z - 1/288 y z + 1/96 x y z - 5/96 y x z + + 2 3 4 2 4 3 4 2 + + 5/144 y x z , COEFF(-1, 0, 1) = 5/18 y x z - 1/9 x y z + + 4 2 4 3 4 3 4 4 + + 2/9 x y z + 1/12 x y z - 1/9 x y z + 1/36 x y z - 4/9 z + + 2 2 3 2 4 4 4 4 + - 10/9 y x z + 5/18 y x z - 1/48 x y z - 1/18 x y z + + 2 2 2 2 2 3 3 4 2 3 3 + - 5/12 y x z + 5/48 y x z - 4/9 z x + 1/9 z - 5/36 y x z + + 3 2 2 3 2 2 3 4 2 + + 1/9 z - 4/9 z + 5/9 z y x + 5/9 z y x + 2/9 x y z + + 2 4 2 2 2 2 2 2 + + 1/12 x y z - 10/9 y x z - 5/12 y x z + 5/9 y z + 8/9 x z + + 2 3 4 3 2 3 3 3 2 3 + + 1/3 x z + 1/36 x y z - 5/36 y z + 1/9 x z - 1/12 x z + + 4 4 2 4 3 4 4 2 4 + + 1/36 y z - 1/12 x z - 2/9 x z - 2/9 x z - 1/9 y z - 1/9 y z + + 3 4 2 2 2 3 2 2 4 2 2 + + 1/9 x z + 1/3 x z + 8/9 x z - 4/9 x z - 5/36 y z + 5/9 y z + + 4 3 4 3 2 4 3 2 2 4 + - 1/18 x y z + 1/36 y z - 1/48 x y z + 5/48 y x z + + 2 3 4 25 2 2 3 3 + - 5/36 y x z , COEFF(0, 0, 1) = -- y x z + 5/12 x z + 2/3 z x + 12 + + 2 3 4 3 4 3 3 4 + - 5/3 x z - 1/6 x z - 1/24 x y z - 5/3 x z + 1/6 x y z + + 2 2 3 4 3 3 2 25 2 4 4 2 + - 5/6 z y x + 5/48 x y z + 2/3 x z - -- y x z - 5/12 x y z + 48 + + 4 25 2 3 2 3 3 3 3 4 4 + - 5/12 x y z - -- y x z - 5/6 z y x - 1/6 x z - 1/24 x y z + 48 + + 4 4 3 4 2 4 2 3 4 25 2 + + 5/48 x y z + 1/6 x y z + 5/12 x z + 5/24 y x z + -- y x z + 12 + + 2 3 3 2 4 3 4 2 4 + + 5/24 y x z , COEFF(1, 0, 1) = 5/18 y x z - 1/9 x y z + 2/9 x y z + + 2 4 3 4 3 4 4 2 + - 1/12 x y z - 1/9 x y z + 1/36 x y z + 4/9 z - 10/9 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 5/18 y x z + 1/48 x y z - 1/18 x y z + 5/12 y x z + + 2 2 3 3 4 2 3 3 3 2 + - 5/48 y x z - 4/9 z x - 1/9 z - 5/36 y x z - 1/9 z + 4/9 z + + 2 3 2 2 3 4 2 2 4 2 2 2 + + 5/9 z y x + 5/9 z y x + 2/9 x y z - 1/12 x y z - 10/9 y x z + + 2 2 2 2 3 4 3 + + 5/12 y x z - 5/9 y z + 8/9 x z - 1/3 x z + 1/36 x y z + + 2 3 3 3 2 3 4 4 2 4 3 + + 5/36 y z + 1/9 x z + 1/12 x z - 1/36 y z + 1/12 x z - 2/9 x z + + 4 4 2 4 3 4 2 2 2 + - 2/9 x z + 1/9 y z + 1/9 y z + 1/9 x z - 1/3 x z + 8/9 x z + + 3 2 2 4 2 2 4 3 4 3 + - 4/9 x z + 5/36 y z - 5/9 y z - 1/18 x y z - 1/36 y z + + 2 4 3 2 2 4 2 3 4 + + 1/48 x y z - 5/48 y x z - 5/36 y x z , COEFF(2, 0, 1) = + + 2 4 3 4 2 4 2 4 3 4 + - 5/288 y x z + 1/36 x y z - 1/72 x y z + 1/24 x y z + 1/36 x y z + + 3 4 4 2 2 3 2 4 4 + - 1/144 x y z - 1/18 z + 5/72 y x z - 5/288 y x z - 1/96 x y z + + 4 4 2 2 2 2 2 3 3 4 + + 1/288 x y z - 5/24 y x z + 5/96 y x z + 1/9 z x + 1/72 z + + 2 3 3 3 2 2 3 2 2 3 + + 5/144 y x z + 1/72 z - 1/18 z - 5/36 z y x - 5/36 z y x + + 4 2 2 4 2 2 2 2 2 2 + - 1/72 x y z + 1/24 x y z + 5/72 y x z - 5/24 y x z + 5/72 y z + + 2 3 4 3 2 3 3 3 + - 1/18 x z + 1/6 x z - 1/144 x y z - 5/288 y z - 1/36 x z + + 2 3 4 4 2 4 3 4 + - 1/24 x z + 1/288 y z - 1/24 x z + 1/72 x z + 1/72 x z + + 4 2 4 3 4 2 2 2 3 2 + - 1/72 y z - 1/72 y z - 1/36 x z + 1/6 x z - 1/18 x z + 1/9 x z + + 2 4 2 2 4 3 4 3 2 4 3 + - 5/288 y z + 5/72 y z + 1/288 x y z + 1/288 y z - 1/96 x y z + + 2 2 4 2 3 4 2 4 + + 5/96 y x z + 5/144 y x z , COEFF(-2, 1, 1) = 1/108 y x z + + 3 4 2 4 2 4 3 4 + - 1/54 x y z + 1/108 x y z + 1/36 x y z - 1/54 x y z + + 3 3 4 4 3 2 4 3 + + 1/108 y x z + 1/216 x y z - 1/144 y x z + 2/27 z y x + + 2 3 3 4 2 2 3 + + 2/27 z y x - 1/432 y x z - 1/27 y x z + 1/108 y x z + + 2 4 4 4 4 2 2 2 3 2 + - 1/144 x y z - 1/432 x y z - 1/9 y x z + 1/108 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/36 y x z - 1/54 y x z - 1/54 y x z + 1/36 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/36 y x z - 1/54 y x z - 1/108 z y + 1/108 z y x + 1/36 z y x + + 3 3 2 2 3 2 2 3 + - 1/54 z y x - 1/27 y x z - 1/9 z y x + 2/27 z y x + 2/27 z y x + + 3 3 3 3 3 4 2 + + 1/27 y z - 1/432 y x z + 1/216 y x z + 1/108 x y z + + 2 4 2 2 2 2 2 2 2 2 + + 1/36 x y z - 1/27 y x z - 1/9 y x z - 1/9 y x z - 1/27 y x z + + 2 3 2 3 3 4 3 4 3 + + 1/27 y z - 1/144 y x z + 1/216 x y z + 1/108 y x z - 1/108 y z + + 2 3 3 3 4 3 4 4 4 + - 1/108 y z + 1/432 y z - 1/108 y z + 1/432 y z + 1/432 y z + + 3 2 2 4 4 2 4 2 + - 1/108 y z + 1/36 y x z - 1/108 y z - 1/108 y z + 1/27 y z + + 3 4 2 4 2 2 4 3 4 3 + - 1/54 y x z - 1/108 y z + 1/27 y z - 1/432 x y z + 1/432 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + - 1/144 x y z + 1/36 y x z - 1/54 y x z + 1/216 y x z , + + 2 4 3 4 2 4 + COEFF(-1, 1, 1) = - 4/27 y x z + 2/27 x y z - 4/27 x y z + + 2 4 3 4 3 3 4 4 + - 1/18 x y z + 2/27 x y z - 4/27 y x z - 1/54 x y z + + 3 2 4 3 2 3 3 4 16 2 + + 1/72 y x z - 8/27 z y x - 8/27 z y x + 1/27 y x z + -- y x z + 27 + + 2 3 2 4 4 4 4 2 2 2 + - 4/27 y x z + 1/72 x y z + 1/27 x y z + 2/9 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 4/27 y x z - 1/18 y x z + 2/27 y x z + 2/27 y x z + + 2 3 3 2 2 2 3 3 3 3 + - 1/18 y x z - 1/18 y x z + 2/27 y x z + 2/27 z y - 4/27 z y x + + 3 2 3 3 16 2 2 3 + - 1/18 z y x + 2/27 z y x + -- y x z + 2/9 z y x - 8/27 z y x + 27 + + 2 2 3 3 3 3 3 3 4 2 + - 8/27 z y x - 8/27 y z + 1/27 y x z - 1/54 y x z - 4/27 x y z + + 2 4 2 16 2 2 2 2 2 2 16 2 + - 1/18 x y z + -- y x z + 2/9 y x z + 2/9 y x z + -- y x z + 27 27 + + 2 3 2 3 3 4 3 4 3 + - 8/27 y z + 1/72 y x z - 1/54 x y z - 4/27 y x z + 2/27 y z + + 2 3 3 3 4 3 4 4 4 + + 2/27 y z - 1/54 y z + 2/27 y z - 1/54 y z - 1/54 y z + + 3 2 2 4 4 2 4 2 + + 2/27 y z - 1/18 y x z + 2/27 y z + 2/27 y z - 8/27 y z + + 3 4 2 4 2 2 4 3 4 3 + + 2/27 y x z + 2/27 y z - 8/27 y z + 1/27 x y z - 1/54 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + + 1/72 x y z - 1/18 y x z + 2/27 y x z - 1/54 y x z , + + 2 4 3 4 2 4 3 4 + COEFF(0, 1, 1) = 5/18 y x z - 1/9 x y z + 5/18 x y z - 1/9 x y z + + 3 3 4 4 3 2 3 3 4 + + 5/18 y x z + 1/36 x y z + 4/9 z y x + 4/9 z y x - 5/72 y x z + + 2 2 3 4 4 3 2 3 3 + - 10/9 y x z + 5/18 y x z - 5/72 x y z + 5/18 y x z - 1/9 y x z + + 3 3 2 2 3 3 3 3 3 + - 1/9 y x z - 1/9 y x z + 5/18 z y x - 1/9 z y x - 10/9 y x z + + 2 3 2 2 3 3 3 3 3 3 4 2 + + 4/9 z y x + 4/9 z y x - 5/72 y x z + 1/36 y x z + 5/18 x y z + + 2 2 2 3 4 3 4 3 4 + - 10/9 y x z - 10/9 y x z + 1/36 x y z + 5/18 y x z - 1/9 y x z + + 4 3 2 3 4 3 3 4 + - 5/72 x y z - 1/9 y x z + 1/36 y x z , COEFF(1, 1, 1) = + + 2 4 3 4 2 4 2 4 3 4 + - 4/27 y x z + 2/27 x y z - 4/27 x y z + 1/18 x y z + 2/27 x y z + + 3 3 4 4 3 2 4 3 2 3 + - 4/27 y x z - 1/54 x y z - 1/72 y x z - 8/27 z y x - 8/27 z y x + + 3 4 16 2 2 3 2 4 4 4 4 + + 1/27 y x z + -- y x z - 4/27 y x z - 1/72 x y z + 1/27 x y z + 27 + + 2 2 2 3 2 2 2 3 3 3 + - 2/9 y x z - 4/27 y x z + 1/18 y x z + 2/27 y x z + + 3 3 2 2 3 3 2 2 2 3 3 3 + + 2/27 y x z + 1/18 y x z + 1/18 y x z + 2/27 y x z - 2/27 z y + + 3 3 2 3 3 16 2 + - 4/27 z y x + 1/18 z y x + 2/27 z y x + -- y x z - 2/9 z y x + 27 + + 2 3 2 2 3 3 3 3 3 3 + - 8/27 z y x - 8/27 z y x + 8/27 y z + 1/27 y x z - 1/54 y x z + + 4 2 2 4 2 16 2 2 2 2 2 2 + - 4/27 x y z + 1/18 x y z + -- y x z - 2/9 y x z - 2/9 y x z + 27 + + 16 2 2 3 2 3 3 4 3 4 + + -- y x z + 8/27 y z - 1/72 y x z - 1/54 x y z - 4/27 y x z + 27 + + 3 2 3 3 3 4 3 4 + - 2/27 y z - 2/27 y z + 1/54 y z - 2/27 y z + 1/54 y z + + 4 4 3 2 2 4 4 2 4 + + 1/54 y z - 2/27 y z + 1/18 y x z - 2/27 y z - 2/27 y z + + 2 3 4 2 4 2 2 4 3 + + 8/27 y z + 2/27 y x z - 2/27 y z + 8/27 y z + 1/27 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + + 1/54 y z - 1/72 x y z + 1/18 y x z + 2/27 y x z + + 3 3 4 2 4 3 4 2 + - 1/54 y x z , COEFF(2, 1, 1) = 1/108 y x z - 1/54 x y z + + 4 2 4 3 4 3 + + 1/108 x y z - 1/36 x y z - 1/54 x y z + 1/108 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/216 x y z + 1/144 y x z + 2/27 z y x + 2/27 z y x + + 3 4 2 2 3 2 4 4 + - 1/432 y x z - 1/27 y x z + 1/108 y x z + 1/144 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/432 x y z + 1/9 y x z + 1/108 y x z - 1/36 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/54 y x z - 1/54 y x z - 1/36 y x z - 1/36 y x z + + 2 3 3 3 3 3 2 3 3 + - 1/54 y x z + 1/108 z y + 1/108 z y x - 1/36 z y x - 1/54 z y x + + 2 2 3 2 2 3 + - 1/27 y x z + 1/9 z y x + 2/27 z y x + 2/27 z y x - 1/27 y z + + 3 3 3 3 3 4 2 2 4 2 + - 1/432 y x z + 1/216 y x z + 1/108 x y z - 1/36 x y z + + 2 2 2 2 2 2 2 2 + - 1/27 y x z + 1/9 y x z + 1/9 y x z - 1/27 y x z - 1/27 y z + + 3 2 3 3 4 3 4 3 + + 1/144 y x z + 1/216 x y z + 1/108 y x z + 1/108 y z + + 2 3 3 3 4 3 4 4 4 + + 1/108 y z - 1/432 y z + 1/108 y z - 1/432 y z - 1/432 y z + + 3 2 2 4 4 2 4 2 + + 1/108 y z - 1/36 y x z + 1/108 y z + 1/108 y z - 1/27 y z + + 3 4 2 4 2 2 4 3 4 3 + - 1/54 y x z + 1/108 y z - 1/27 y z - 1/432 x y z - 1/432 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + + 1/144 x y z - 1/36 y x z - 1/54 y x z + 1/216 y x z , + + 2 4 3 4 2 4 + COEFF(-2, 2, 1) = - 1/1728 y x z + 1/216 x y z - 1/432 x y z + + 2 4 3 4 3 3 4 4 + - 1/144 x y z + 1/216 x y z - 1/864 y x z - 1/864 x y z + + 3 2 4 3 2 3 3 4 + + 1/288 y x z - 1/108 z y x - 1/108 z y x + 1/864 y x z + + 2 2 3 2 4 4 4 4 + + 1/432 y x z - 1/1728 y x z + 1/576 x y z + 1/1728 x y z + + 2 2 2 3 2 2 2 3 3 3 + + 1/144 y x z - 1/216 y x z - 1/576 y x z + 1/432 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + + 1/108 y x z - 1/288 y x z - 1/72 y x z + 1/864 y x z + + 3 3 3 2 3 3 + + 1/216 z y - 1/216 z y x - 1/72 z y x + 1/108 z y x + 1/216 y x z + + 2 2 3 2 2 3 3 3 + + 1/72 z y x - 1/216 z y x - 1/216 z y x - 1/216 y z + 1/864 y x z + + 3 3 3 4 2 2 4 2 2 2 + - 1/432 y x z - 1/432 x y z - 1/144 x y z + 1/432 y x z + + 2 2 2 2 2 2 + + 1/144 y x z + 1/72 y x z + 1/216 y x z - 1/432 y z + + 3 2 3 3 4 3 4 3 + + 1/288 y x z - 1/864 x y z - 1/864 y x z + 1/864 y z + + 2 3 3 3 4 3 4 4 4 + + 1/1728 y z - 1/864 y z + 1/864 y z - 1/864 y z - 1/1728 y z + + 3 2 2 4 4 2 4 2 + + 1/216 y z - 1/288 y x z + 1/432 y z + 1/432 y z - 1/216 y z + + 3 4 2 4 2 2 4 3 + + 1/432 y x z + 1/1728 y z - 1/432 y z + 1/1728 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + - 1/1728 y z + 1/576 x y z - 1/576 y x z + 1/864 y x z + + 3 3 4 2 4 3 4 2 + - 1/432 y x z , COEFF(-1, 2, 1) = 1/108 y x z - 1/54 x y z + + 4 2 4 3 4 3 3 4 4 + + 1/27 x y z + 1/72 x y z - 1/54 x y z + 1/54 y x z + 1/216 x y z + + 3 2 4 3 2 3 3 4 2 + - 1/144 y x z + 1/27 z y x + 1/27 z y x - 1/54 y x z - 1/27 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/108 y x z - 1/288 x y z - 1/108 x y z - 1/72 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 2/27 y x z + 1/288 y x z - 1/108 y x z - 1/27 y x z + + 2 3 3 2 2 2 3 3 3 3 + + 1/144 y x z + 1/36 y x z - 1/216 y x z - 1/27 z y + 2/27 z y x + + 3 2 3 3 2 2 3 + + 1/36 z y x - 1/27 z y x - 2/27 y x z - 1/36 z y x + 1/54 z y x + + 2 2 3 3 3 3 3 3 4 2 + + 1/54 z y x + 1/27 y z - 1/54 y x z + 1/108 y x z + 1/27 x y z + + 2 4 2 2 2 2 2 2 2 2 + + 1/72 x y z - 1/27 y x z - 1/72 y x z - 1/36 y x z - 2/27 y x z + + 2 3 2 3 3 4 3 4 3 + + 1/54 y z - 1/144 y x z + 1/216 x y z + 1/54 y x z - 1/108 y z + + 2 3 3 3 4 3 4 4 4 + - 1/216 y z + 1/108 y z - 1/108 y z + 1/108 y z + 1/216 y z + + 3 2 2 4 4 2 4 2 + - 1/27 y z + 1/144 y x z - 1/54 y z - 1/54 y z + 1/27 y z + + 3 4 2 4 2 2 4 3 4 3 + - 1/108 y x z - 1/216 y z + 1/54 y z - 1/108 x y z + 1/216 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + - 1/288 x y z + 1/288 y x z - 1/216 y x z + 1/108 y x z , + + 2 4 3 4 2 4 + COEFF(0, 2, 1) = - 5/288 y x z + 1/36 x y z - 5/72 x y z + + 3 4 3 3 4 4 3 + + 1/36 x y z - 5/144 y x z - 1/144 x y z - 1/18 z y x + + 2 3 3 4 2 2 3 + - 1/18 z y x + 5/144 y x z + 5/72 y x z - 5/288 y x z + + 4 4 3 2 3 3 3 3 2 + + 5/288 x y z - 5/36 y x z + 1/72 y x z + 1/18 y x z + + 2 3 3 3 3 3 2 3 + + 1/144 y x z - 5/36 z y x + 1/18 z y x + 5/36 y x z - 1/36 z y x + + 2 2 3 3 3 3 3 3 4 2 + - 1/36 z y x + 5/144 y x z - 1/72 y x z - 5/72 x y z + + 2 2 2 3 4 3 4 + + 5/72 y x z + 5/36 y x z - 1/144 x y z - 5/144 y x z + + 3 4 4 3 2 3 4 3 3 4 + + 1/72 y x z + 5/288 x y z + 1/144 y x z - 1/72 y x z , + + 2 4 3 4 2 4 2 4 + COEFF(1, 2, 1) = 1/108 y x z - 1/54 x y z + 1/27 x y z - 1/72 x y z + + 3 4 3 3 4 4 3 2 4 + - 1/54 x y z + 1/54 y x z + 1/216 x y z + 1/144 y x z + + 3 2 3 3 4 2 2 3 + + 1/27 z y x + 1/27 z y x - 1/54 y x z - 1/27 y x z + 1/108 y x z + + 2 4 4 4 4 2 2 2 3 2 + + 1/288 x y z - 1/108 x y z + 1/72 y x z + 2/27 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/288 y x z - 1/108 y x z - 1/27 y x z - 1/144 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/36 y x z - 1/216 y x z + 1/27 z y + 2/27 z y x - 1/36 z y x + + 3 3 2 2 3 2 2 3 + - 1/27 z y x - 2/27 y x z + 1/36 z y x + 1/54 z y x + 1/54 z y x + + 3 3 3 3 3 4 2 2 4 2 + - 1/27 y z - 1/54 y x z + 1/108 y x z + 1/27 x y z - 1/72 x y z + + 2 2 2 2 2 2 2 2 + - 1/27 y x z + 1/72 y x z + 1/36 y x z - 2/27 y x z - 1/54 y z + + 3 2 3 3 4 3 4 3 2 3 + + 1/144 y x z + 1/216 x y z + 1/54 y x z + 1/108 y z + 1/216 y z + + 3 3 4 3 4 4 4 3 2 + - 1/108 y z + 1/108 y z - 1/108 y z - 1/216 y z + 1/27 y z + + 2 4 4 2 4 2 3 4 + - 1/144 y x z + 1/54 y z + 1/54 y z - 1/27 y z - 1/108 y x z + + 2 4 2 2 4 3 4 3 2 4 3 + + 1/216 y z - 1/54 y z - 1/108 x y z - 1/216 y z + 1/288 x y z + + 2 2 4 2 3 4 3 3 4 + - 1/288 y x z - 1/216 y x z + 1/108 y x z , COEFF(2, 2, 1) = + + 2 4 3 4 2 4 2 4 + - 1/1728 y x z + 1/216 x y z - 1/432 x y z + 1/144 x y z + + 3 4 3 3 4 4 3 2 4 + + 1/216 x y z - 1/864 y x z - 1/864 x y z - 1/288 y x z + + 3 2 3 3 4 2 + - 1/108 z y x - 1/108 z y x + 1/864 y x z + 1/432 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/1728 y x z - 1/576 x y z + 1/1728 x y z - 1/144 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/216 y x z + 1/576 y x z + 1/432 y x z + 1/108 y x z + + 2 3 3 2 2 2 3 3 3 + + 1/288 y x z + 1/72 y x z + 1/864 y x z - 1/216 z y + + 3 3 2 3 3 2 + - 1/216 z y x + 1/72 z y x + 1/108 z y x + 1/216 y x z - 1/72 z y x + + 2 3 2 2 3 3 3 + - 1/216 z y x - 1/216 z y x + 1/216 y z + 1/864 y x z + + 3 3 3 4 2 2 4 2 2 2 + - 1/432 y x z - 1/432 x y z + 1/144 x y z + 1/432 y x z + + 2 2 2 2 2 2 + - 1/144 y x z - 1/72 y x z + 1/216 y x z + 1/432 y z + + 3 2 3 3 4 3 4 3 + - 1/288 y x z - 1/864 x y z - 1/864 y x z - 1/864 y z + + 2 3 3 3 4 3 4 4 4 + - 1/1728 y z + 1/864 y z - 1/864 y z + 1/864 y z + 1/1728 y z + + 3 2 2 4 4 2 4 2 + - 1/216 y z + 1/288 y x z - 1/432 y z - 1/432 y z + 1/216 y z + + 3 4 2 4 2 2 4 3 + + 1/432 y x z - 1/1728 y z + 1/432 y z + 1/1728 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + + 1/1728 y z - 1/576 x y z + 1/576 y x z + 1/864 y x z + + 3 3 4 2 4 3 4 2 + - 1/432 y x z , COEFF(-2, -2, 2) = 1/6912 y x z - 1/3456 x y z + + 4 2 4 3 4 3 + + 1/3456 x y z + 1/1152 x y z - 1/1728 x y z - 1/1728 y x z + + 3 4 4 3 2 4 3 2 3 + + 1/3456 x y z + 1/1152 y x z - 1/864 z y x - 1/1728 z y x + + 3 4 2 2 3 2 4 4 + + 1/3456 y x z - 1/3456 y x z + 1/3456 y x z - 1/2304 x y z + + 4 4 2 2 2 3 2 2 2 3 + - 1/6912 x y z - 1/2304 y x z - 1/3456 y x z + 1/1152 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 1/864 y x z + 1/1728 y x z - 1/576 y x z - 1/1152 y x z + + 2 3 3 3 3 3 2 + - 1/1728 y x z + 1/1728 z y - 1/1728 z y x - 1/576 z y x + + 3 3 2 2 3 + + 1/864 z y x + 1/1728 y x z + 1/576 z y x + 1/1728 z y x + + 2 2 3 3 3 3 3 3 + + 1/3456 z y x - 1/1728 y z + 1/1728 y x z - 1/864 y x z + + 4 2 2 4 2 2 2 2 2 + + 1/6912 x y z + 1/2304 x y z - 1/6912 y x z - 1/1152 y x z + + 2 2 2 2 3 2 3 + + 1/1152 y x z + 1/3456 y x z + 1/3456 y z + 1/576 y x z + + 3 4 3 4 3 2 3 + + 1/1728 x y z - 1/3456 y x z + 1/1728 y z - 1/3456 y z + + 3 3 4 3 4 4 4 3 2 + - 1/1728 y z + 1/3456 y z - 1/3456 y z + 1/6912 y z + 1/3456 y z + + 2 4 4 2 4 2 + - 1/1152 y x z - 1/6912 y z - 1/3456 y z - 1/3456 y z + + 3 4 2 4 2 2 4 3 + + 1/1728 y x z - 1/6912 y z + 1/6912 y z - 1/3456 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + + 1/3456 y z - 1/1152 x y z + 1/2304 y x z - 1/3456 y x z + + 3 3 4 2 4 3 4 2 + - 1/1728 y x z , COEFF(-1, -2, 2) = - 1/432 y x z + 1/864 x y z + + 4 2 4 3 4 3 + - 1/216 x y z - 1/576 x y z + 1/432 x y z + 1/108 y x z + + 3 4 4 3 2 4 3 2 3 + - 1/864 x y z - 1/576 y x z + 1/216 z y x + 1/432 z y x + + 3 4 2 2 3 2 4 4 + - 1/216 y x z + 1/216 y x z - 1/216 y x z + 1/1152 x y z + + 4 4 2 2 2 3 2 2 2 3 + + 1/432 x y z + 1/1152 y x z + 1/216 y x z - 1/576 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/216 y x z - 1/432 y x z + 1/288 y x z + 1/576 y x z + + 2 3 3 3 3 3 2 + + 1/432 y x z - 1/216 z y + 1/108 z y x + 1/288 z y x + + 3 3 2 2 3 + - 1/216 z y x - 1/108 y x z - 1/288 z y x - 1/432 z y x + + 2 2 3 3 3 3 3 3 + - 1/864 z y x + 1/216 y z - 1/108 y x z + 1/216 y x z + + 4 2 2 4 2 2 2 2 2 + - 1/432 x y z - 1/1152 x y z + 1/432 y x z + 1/576 y x z + + 2 2 2 2 3 2 3 + - 1/576 y x z - 1/216 y x z - 1/432 y z - 1/288 y x z + + 3 4 3 4 3 2 3 3 3 + - 1/432 x y z + 1/216 y x z - 1/216 y z + 1/432 y z + 1/216 y z + + 4 3 4 4 4 3 2 2 4 + - 1/432 y z + 1/432 y z - 1/864 y z - 1/432 y z + 1/576 y x z + + 4 2 4 2 3 4 2 4 + + 1/864 y z + 1/432 y z + 1/432 y z - 1/432 y x z + 1/864 y z + + 2 2 4 3 4 3 2 4 3 + - 1/864 y z + 1/216 x y z - 1/432 y z + 1/576 x y z + + 2 2 4 2 3 4 3 3 4 + - 1/1152 y x z + 1/864 y x z + 1/432 y x z , COEFF(0, -2, 2) = + + 2 4 3 4 2 4 3 4 + 5/1152 y x z - 1/576 x y z + 5/576 x y z - 1/288 x y z + + 3 3 4 4 3 2 3 + - 5/288 y x z + 1/576 x y z - 1/144 z y x - 1/288 z y x + + 3 4 2 2 3 4 4 + + 5/576 y x z - 5/576 y x z + 5/576 y x z - 5/1152 x y z + + 3 2 3 3 3 3 2 2 3 3 + - 5/576 y x z + 1/144 y x z + 1/288 y x z - 1/288 y x z + + 3 3 3 2 3 + - 5/288 z y x + 1/144 z y x + 5/288 y x z + 1/288 z y x + + 2 2 3 3 3 3 3 3 4 2 + + 1/576 z y x + 5/288 y x z - 1/144 y x z + 5/1152 x y z + + 2 2 2 3 4 3 4 + - 5/1152 y x z + 5/576 y x z + 1/288 x y z - 5/576 y x z + + 3 4 4 3 2 3 4 3 3 4 + + 1/288 y x z - 5/576 x y z - 1/576 y x z - 1/288 y x z , + + 2 4 3 4 2 4 + COEFF(1, -2, 2) = - 1/432 y x z + 1/864 x y z - 1/216 x y z + + 2 4 3 4 3 3 4 4 + + 1/576 x y z + 1/432 x y z + 1/108 y x z - 1/864 x y z + + 3 2 4 3 2 3 3 4 + + 1/576 y x z + 1/216 z y x + 1/432 z y x - 1/216 y x z + + 2 2 3 2 4 4 4 4 + + 1/216 y x z - 1/216 y x z - 1/1152 x y z + 1/432 x y z + + 2 2 2 3 2 2 2 3 3 3 + - 1/1152 y x z + 1/216 y x z + 1/576 y x z - 1/216 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + - 1/432 y x z - 1/288 y x z - 1/576 y x z + 1/432 y x z + + 3 3 3 2 3 3 + + 1/216 z y + 1/108 z y x - 1/288 z y x - 1/216 z y x - 1/108 y x z + + 2 2 3 2 2 3 + + 1/288 z y x - 1/432 z y x - 1/864 z y x - 1/216 y z + + 3 3 3 3 3 4 2 2 4 2 + - 1/108 y x z + 1/216 y x z - 1/432 x y z + 1/1152 x y z + + 2 2 2 2 2 2 2 + + 1/432 y x z - 1/576 y x z + 1/576 y x z - 1/216 y x z + + 2 3 2 3 3 4 3 4 3 + + 1/432 y z + 1/288 y x z - 1/432 x y z + 1/216 y x z + 1/216 y z + + 2 3 3 3 4 3 4 4 4 + - 1/432 y z - 1/216 y z + 1/432 y z - 1/432 y z + 1/864 y z + + 3 2 2 4 4 2 4 2 + + 1/432 y z - 1/576 y x z - 1/864 y z - 1/432 y z - 1/432 y z + + 3 4 2 4 2 2 4 3 4 3 + - 1/432 y x z - 1/864 y z + 1/864 y z + 1/216 x y z + 1/432 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + - 1/576 x y z + 1/1152 y x z + 1/864 y x z + 1/432 y x z , + + 2 4 3 4 2 4 + COEFF(2, -2, 2) = 1/6912 y x z - 1/3456 x y z + 1/3456 x y z + + 2 4 3 4 3 3 4 4 + - 1/1152 x y z - 1/1728 x y z - 1/1728 y x z + 1/3456 x y z + + 3 2 4 3 2 3 3 4 + - 1/1152 y x z - 1/864 z y x - 1/1728 z y x + 1/3456 y x z + + 2 2 3 2 4 4 4 4 + - 1/3456 y x z + 1/3456 y x z + 1/2304 x y z - 1/6912 x y z + + 2 2 2 3 2 2 2 3 3 3 + + 1/2304 y x z - 1/3456 y x z - 1/1152 y x z + 1/864 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + + 1/1728 y x z + 1/576 y x z + 1/1152 y x z - 1/1728 y x z + + 3 3 3 2 3 3 + - 1/1728 z y - 1/1728 z y x + 1/576 z y x + 1/864 z y x + + 2 2 3 2 2 3 + + 1/1728 y x z - 1/576 z y x + 1/1728 z y x + 1/3456 z y x + + 3 3 3 3 3 4 2 + + 1/1728 y z + 1/1728 y x z - 1/864 y x z + 1/6912 x y z + + 2 4 2 2 2 2 2 2 2 + - 1/2304 x y z - 1/6912 y x z + 1/1152 y x z - 1/1152 y x z + + 2 2 3 2 3 3 4 3 + + 1/3456 y x z - 1/3456 y z - 1/576 y x z + 1/1728 x y z + + 4 3 2 3 3 3 4 + - 1/3456 y x z - 1/1728 y z + 1/3456 y z + 1/1728 y z - 1/3456 y z + + 3 4 4 4 3 2 2 4 + + 1/3456 y z - 1/6912 y z - 1/3456 y z + 1/1152 y x z + + 4 2 4 2 3 4 2 4 + + 1/6912 y z + 1/3456 y z + 1/3456 y z + 1/1728 y x z + 1/6912 y z + + 2 2 4 3 4 3 2 4 3 + - 1/6912 y z - 1/3456 x y z - 1/3456 y z + 1/1152 x y z + + 2 2 4 2 3 4 3 3 4 + - 1/2304 y x z - 1/3456 y x z - 1/1728 y x z , COEFF(-2, -1, 2) = + + 2 4 3 4 2 4 2 4 + - 1/432 y x z + 1/864 x y z - 1/864 x y z - 1/288 x y z + + 3 4 3 3 4 4 3 2 4 + + 1/432 x y z + 1/216 y x z - 1/864 x y z - 1/576 y x z + + 3 2 3 3 4 2 + + 1/108 z y x + 1/216 z y x - 1/1728 y x z + 1/216 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/216 y x z + 1/576 x y z + 1/1728 x y z + 1/144 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/1728 y x z - 1/72 y x z - 1/108 y x z - 1/864 y x z + + 2 3 3 2 2 2 3 3 3 + + 1/72 y x z + 1/576 y x z + 1/108 y x z - 1/864 z y + + 3 3 2 3 3 2 + + 1/864 z y x + 1/288 z y x - 1/432 z y x - 1/216 y x z - 1/72 z y x + + 2 3 2 2 3 3 3 + - 1/108 z y x - 1/216 z y x + 1/216 y z - 1/864 y x z + + 3 3 3 4 2 2 4 2 2 2 + + 1/432 y x z - 1/1728 x y z - 1/576 x y z + 1/432 y x z + + 2 2 2 2 2 2 + + 1/72 y x z - 1/144 y x z - 1/432 y x z - 1/216 y z + + 3 2 3 3 4 3 4 3 + - 1/288 y x z - 1/432 x y z + 1/432 y x z - 1/216 y z + + 2 3 3 3 4 3 4 4 4 + + 1/216 y z + 1/864 y z - 1/432 y z + 1/1728 y z - 1/1728 y z + + 3 2 2 4 4 2 4 2 + - 1/1728 y z + 1/144 y x z + 1/1728 y z + 1/864 y z + 1/432 y z + + 3 4 2 4 2 2 4 3 4 3 + - 1/216 y x z + 1/432 y z - 1/432 y z + 1/864 x y z - 1/864 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + + 1/288 x y z - 1/144 y x z + 1/216 y x z + 1/864 y x z , + + 2 4 3 4 2 4 + COEFF(-1, -1, 2) = 1/27 y x z - 1/216 x y z + 1/54 x y z + + 2 4 3 4 3 3 4 4 + + 1/144 x y z - 1/108 x y z - 2/27 y x z + 1/216 x y z + + 3 2 4 3 2 3 3 4 + + 1/288 y x z - 1/27 z y x - 1/54 z y x + 1/108 y x z + + 2 2 3 2 4 4 4 4 + - 2/27 y x z + 2/27 y x z - 1/288 x y z - 1/108 x y z + + 2 2 2 3 2 2 2 3 3 3 + - 1/72 y x z - 1/108 y x z + 1/36 y x z + 1/27 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + + 1/216 y x z - 1/36 y x z - 1/288 y x z - 1/27 y x z + + 3 3 3 2 3 3 + + 1/108 z y - 1/54 z y x - 1/144 z y x + 1/108 z y x + 2/27 y x z + + 2 2 3 2 2 3 3 3 + + 1/36 z y x + 1/27 z y x + 1/54 z y x - 1/27 y z + 1/54 y x z + + 3 3 3 4 2 2 4 2 2 2 + - 1/108 y x z + 1/108 x y z + 1/288 x y z - 1/27 y x z + + 2 2 2 2 2 2 3 2 3 + - 1/36 y x z + 1/72 y x z + 1/27 y x z + 1/27 y z + 1/144 y x z + + 3 4 3 4 3 2 3 3 3 + + 1/108 x y z - 1/27 y x z + 1/27 y z - 1/27 y z - 1/108 y z + + 4 3 4 4 4 3 2 2 4 + + 1/54 y z - 1/216 y z + 1/216 y z + 1/216 y z - 1/72 y x z + + 4 2 4 2 3 4 2 4 + - 1/216 y z - 1/108 y z - 1/54 y z + 1/54 y x z - 1/54 y z + + 2 2 4 3 4 3 2 4 3 2 2 4 + + 1/54 y z - 1/54 x y z + 1/108 y z - 1/144 x y z + 1/72 y x z + + 2 3 4 3 3 4 2 4 + - 1/54 y x z - 1/216 y x z , COEFF(0, -1, 2) = - 5/72 y x z + + 3 4 2 4 3 4 3 + + 1/144 x y z - 5/144 x y z + 1/72 x y z + 5/36 y x z + + 3 4 4 3 2 3 3 4 + - 1/144 x y z + 1/18 z y x + 1/36 z y x - 5/288 y x z + + 2 2 3 4 4 3 2 + + 5/36 y x z - 5/36 y x z + 5/288 x y z + 5/288 y x z + + 3 3 3 3 2 2 3 3 3 + - 1/18 y x z - 1/144 y x z + 1/18 y x z + 5/144 z y x + + 3 3 2 3 2 2 3 3 3 + - 1/72 z y x - 5/36 y x z - 1/18 z y x - 1/36 z y x - 5/144 y x z + + 3 3 3 4 2 2 2 2 + + 1/72 y x z - 5/288 x y z + 5/72 y x z - 5/72 y x z + + 3 4 3 4 3 4 4 3 + - 1/72 x y z + 5/72 y x z - 1/36 y x z + 5/144 x y z + + 2 3 4 3 3 4 2 4 + + 1/36 y x z + 1/144 y x z , COEFF(1, -1, 2) = 1/27 y x z + + 3 4 2 4 2 4 3 4 + - 1/216 x y z + 1/54 x y z - 1/144 x y z - 1/108 x y z + + 3 3 4 4 3 2 4 3 + - 2/27 y x z + 1/216 x y z - 1/288 y x z - 1/27 z y x + + 2 3 3 4 2 2 3 + - 1/54 z y x + 1/108 y x z - 2/27 y x z + 2/27 y x z + + 2 4 4 4 4 2 2 2 3 2 + + 1/288 x y z - 1/108 x y z + 1/72 y x z - 1/108 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/36 y x z + 1/27 y x z + 1/216 y x z + 1/36 y x z + + 3 2 2 2 3 3 3 3 + + 1/288 y x z - 1/27 y x z - 1/108 z y - 1/54 z y x + + 3 2 3 3 2 2 3 + + 1/144 z y x + 1/108 z y x + 2/27 y x z - 1/36 z y x + 1/27 z y x + + 2 2 3 3 3 3 3 3 4 2 + + 1/54 z y x + 1/27 y z + 1/54 y x z - 1/108 y x z + 1/108 x y z + + 2 4 2 2 2 2 2 2 2 + - 1/288 x y z - 1/27 y x z + 1/36 y x z - 1/72 y x z + + 2 2 3 2 3 3 4 3 4 + + 1/27 y x z - 1/27 y z - 1/144 y x z + 1/108 x y z - 1/27 y x z + + 3 2 3 3 3 4 3 4 + - 1/27 y z + 1/27 y z + 1/108 y z - 1/54 y z + 1/216 y z + + 4 4 3 2 2 4 4 2 4 + - 1/216 y z - 1/216 y z + 1/72 y x z + 1/216 y z + 1/108 y z + + 2 3 4 2 4 2 2 4 3 + + 1/54 y z + 1/54 y x z + 1/54 y z - 1/54 y z - 1/54 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + - 1/108 y z + 1/144 x y z - 1/72 y x z - 1/54 y x z + + 3 3 4 2 4 3 4 2 + - 1/216 y x z , COEFF(2, -1, 2) = - 1/432 y x z + 1/864 x y z + + 4 2 4 3 4 3 + - 1/864 x y z + 1/288 x y z + 1/432 x y z + 1/216 y x z + + 3 4 4 3 2 4 3 2 3 + - 1/864 x y z + 1/576 y x z + 1/108 z y x + 1/216 z y x + + 3 4 2 2 3 2 4 4 + - 1/1728 y x z + 1/216 y x z - 1/216 y x z - 1/576 x y z + + 4 4 2 2 2 3 2 2 2 3 + + 1/1728 x y z - 1/144 y x z + 1/1728 y x z + 1/72 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/108 y x z - 1/864 y x z - 1/72 y x z - 1/576 y x z + + 2 3 3 3 3 3 2 + + 1/108 y x z + 1/864 z y + 1/864 z y x - 1/288 z y x + + 3 3 2 2 3 + - 1/432 z y x - 1/216 y x z + 1/72 z y x - 1/108 z y x + + 2 2 3 3 3 3 3 3 + - 1/216 z y x - 1/216 y z - 1/864 y x z + 1/432 y x z + + 4 2 2 4 2 2 2 2 2 + - 1/1728 x y z + 1/576 x y z + 1/432 y x z - 1/72 y x z + + 2 2 2 2 3 2 3 + + 1/144 y x z - 1/432 y x z + 1/216 y z + 1/288 y x z + + 3 4 3 4 3 2 3 3 3 + - 1/432 x y z + 1/432 y x z + 1/216 y z - 1/216 y z - 1/864 y z + + 4 3 4 4 4 3 2 2 4 + + 1/432 y z - 1/1728 y z + 1/1728 y z + 1/1728 y z - 1/144 y x z + + 4 2 4 2 3 4 2 4 + - 1/1728 y z - 1/864 y z - 1/432 y z - 1/216 y x z - 1/432 y z + + 2 2 4 3 4 3 2 4 3 + + 1/432 y z + 1/864 x y z + 1/864 y z - 1/288 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/144 y x z + 1/216 y x z + 1/864 y x z , COEFF(-2, 0, 2) = + + 2 4 3 4 2 4 2 4 + 5/1152 y x z - 1/576 x y z + 1/576 x y z + 1/192 x y z + + 3 4 3 4 4 2 2 3 + - 1/288 x y z + 1/576 x y z - 1/144 z - 5/576 y x z + 5/576 y x z + + 2 4 4 4 4 2 2 2 2 2 3 + - 1/384 x y z - 1/1152 x y z - 5/384 y x z + 5/192 y x z + + 3 4 2 3 3 3 2 + - 1/72 z x + 1/288 z - 5/288 y x z + 1/144 z - 1/288 z + + 2 3 2 2 3 4 2 2 4 2 + + 5/288 z y x + 5/576 z y x + 1/1152 x y z + 1/384 x y z + + 2 2 2 2 2 2 + - 5/1152 y x z - 5/192 y x z + 5/576 y z + 1/144 x z + 1/48 x z + + 3 4 3 2 3 3 3 2 3 4 4 + + 1/288 x y z - 5/576 y z + 1/72 x z - 1/48 x z + 1/1152 y z + + 2 4 3 4 4 2 4 + - 1/96 x z - 1/144 x z - 1/288 x z - 1/1152 y z - 1/576 y z + + 3 4 2 2 2 3 2 2 4 + + 1/144 x z + 1/96 x z + 1/288 x z - 1/144 x z - 5/1152 y z + + 2 2 4 3 4 3 2 4 3 + + 5/1152 y z - 1/576 x y z + 1/576 y z - 1/192 x y z + + 2 2 4 2 3 4 2 4 + + 5/384 y x z - 5/576 y x z , COEFF(-1, 0, 2) = - 5/72 y x z + + 3 4 2 4 2 4 3 4 + + 1/144 x y z - 1/36 x y z - 1/96 x y z + 1/72 x y z + + 3 4 4 2 2 3 2 4 4 + - 1/144 x y z + 1/18 z + 5/36 y x z - 5/36 y x z + 1/192 x y z + + 4 4 2 2 2 2 2 3 3 4 + + 1/72 x y z + 5/192 y x z - 5/96 y x z + 1/18 z x - 1/36 z + + 2 3 3 3 2 2 3 2 2 3 + + 5/72 y x z - 1/18 z + 1/36 z - 5/72 z y x - 5/144 z y x + + 4 2 2 4 2 2 2 2 2 2 + - 1/72 x y z - 1/192 x y z + 5/72 y x z + 5/96 y x z - 5/72 y z + + 2 3 4 3 2 3 3 3 + - 1/9 x z - 1/24 x z - 1/72 x y z + 5/72 y z - 1/18 x z + + 2 3 4 4 2 4 3 4 + + 1/24 x z - 1/144 y z + 1/48 x z + 1/9 x z + 1/18 x z + + 4 2 4 3 4 2 2 2 + + 1/144 y z + 1/72 y z - 1/36 x z - 1/48 x z - 1/18 x z + + 3 2 2 4 2 2 4 3 4 3 + + 1/36 x z + 5/144 y z - 5/144 y z + 1/36 x y z - 1/72 y z + + 2 4 3 2 2 4 2 3 4 + + 1/96 x y z - 5/192 y x z + 5/144 y x z , COEFF(0, 0, 2) = + + 4 3 4 3 3 4 25 2 4 25 2 2 + 5/96 x y z + 1/48 x y z + 1/24 x z + --- y x z - --- y x z + 192 192 + + 4 3 25 2 2 3 2 3 3 3 4 + - 5/96 x y z - -- y x z + 5/48 z y x - 5/48 y x z - 1/48 x y z + 96 + + 4 3 2 3 4 4 3 3 + - 5/48 x z - 5/24 x z + 5/48 x z + 1/96 x y z + 1/12 x z + + 2 2 3 4 2 4 4 3 2 + + 5/96 z y x + 5/24 x z + 5/192 x y z - 5/192 x y z - 1/24 x z + + 3 4 2 3 2 3 4 25 2 3 + - 1/96 x y z - 1/12 z x - 5/96 y x z + -- y x z , COEFF(1, 0, 2) + 96 + + 2 4 3 4 2 4 2 4 + = - 5/72 y x z + 1/144 x y z - 1/36 x y z + 1/96 x y z + + 3 4 3 4 4 2 2 3 + + 1/72 x y z - 1/144 x y z - 1/18 z + 5/36 y x z - 5/36 y x z + + 2 4 4 4 4 2 2 2 2 2 3 + - 1/192 x y z + 1/72 x y z - 5/192 y x z + 5/96 y x z + + 3 4 2 3 3 3 2 2 3 + + 1/18 z x + 1/36 z + 5/72 y x z + 1/18 z - 1/36 z - 5/72 z y x + + 2 2 3 4 2 2 4 2 2 2 + - 5/144 z y x - 1/72 x y z + 1/192 x y z + 5/72 y x z + + 2 2 2 2 3 4 3 + - 5/96 y x z + 5/72 y z - 1/9 x z + 1/24 x z - 1/72 x y z + + 2 3 3 3 2 3 4 4 2 4 + - 5/72 y z - 1/18 x z - 1/24 x z + 1/144 y z - 1/48 x z + + 3 4 4 2 4 3 4 2 2 + + 1/9 x z + 1/18 x z - 1/144 y z - 1/72 y z - 1/36 x z + 1/48 x z + + 2 3 2 2 4 2 2 4 3 + - 1/18 x z + 1/36 x z - 5/144 y z + 5/144 y z + 1/36 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + + 1/72 y z - 1/96 x y z + 5/192 y x z + 5/144 y x z , + + 2 4 3 4 2 4 + COEFF(2, 0, 2) = 5/1152 y x z - 1/576 x y z + 1/576 x y z + + 2 4 3 4 3 4 4 2 + - 1/192 x y z - 1/288 x y z + 1/576 x y z + 1/144 z - 5/576 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 5/576 y x z + 1/384 x y z - 1/1152 x y z + 5/384 y x z + + 2 2 3 3 4 2 3 3 3 + - 5/192 y x z - 1/72 z x - 1/288 z - 5/288 y x z - 1/144 z + + 2 2 3 2 2 3 4 2 + + 1/288 z + 5/288 z y x + 5/576 z y x + 1/1152 x y z + + 2 4 2 2 2 2 2 2 + - 1/384 x y z - 5/1152 y x z + 5/192 y x z - 5/576 y z + 1/144 x z + + 2 3 4 3 2 3 3 3 2 3 + - 1/48 x z + 1/288 x y z + 5/576 y z + 1/72 x z + 1/48 x z + + 4 4 2 4 3 4 4 2 + - 1/1152 y z + 1/96 x z - 1/144 x z - 1/288 x z + 1/1152 y z + + 4 3 4 2 2 2 3 2 + + 1/576 y z + 1/144 x z - 1/96 x z + 1/288 x z - 1/144 x z + + 2 4 2 2 4 3 4 3 + + 5/1152 y z - 5/1152 y z - 1/576 x y z - 1/576 y z + + 2 4 3 2 2 4 2 3 4 + + 1/192 x y z - 5/384 y x z - 5/576 y x z , COEFF(-2, 1, 2) = + + 2 4 3 4 2 4 2 4 + - 1/432 y x z + 1/864 x y z - 1/864 x y z - 1/288 x y z + + 3 4 3 3 4 4 3 2 4 + + 1/432 x y z - 1/216 y x z - 1/864 x y z + 1/576 y x z + + 3 2 3 3 4 2 + - 1/108 z y x - 1/216 z y x + 1/1728 y x z + 1/216 y x z + + 2 3 2 4 4 4 4 2 2 2 + - 1/216 y x z + 1/576 x y z + 1/1728 x y z + 1/144 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/1728 y x z - 1/72 y x z + 1/108 y x z + 1/864 y x z + + 2 3 3 2 2 2 3 3 3 + - 1/72 y x z - 1/576 y x z + 1/108 y x z + 1/864 z y + + 3 3 2 3 3 2 + - 1/864 z y x - 1/288 z y x + 1/432 z y x + 1/216 y x z + 1/72 z y x + + 2 3 2 2 3 3 3 + - 1/108 z y x - 1/216 z y x - 1/216 y z + 1/864 y x z + + 3 3 3 4 2 2 4 2 2 2 + - 1/432 y x z - 1/1728 x y z - 1/576 x y z + 1/432 y x z + + 2 2 2 2 2 2 + + 1/72 y x z + 1/144 y x z + 1/432 y x z - 1/216 y z + + 3 2 3 3 4 3 4 3 + + 1/288 y x z - 1/432 x y z - 1/432 y x z + 1/216 y z + + 2 3 3 3 4 3 4 4 4 + + 1/216 y z - 1/864 y z + 1/432 y z - 1/1728 y z - 1/1728 y z + + 3 2 2 4 4 2 4 2 + + 1/1728 y z - 1/144 y x z + 1/1728 y z + 1/864 y z - 1/432 y z + + 3 4 2 4 2 2 4 3 4 3 + + 1/216 y x z + 1/432 y z - 1/432 y z + 1/864 x y z - 1/864 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + + 1/288 x y z - 1/144 y x z + 1/216 y x z - 1/864 y x z , + + 2 4 3 4 2 4 + COEFF(-1, 1, 2) = 1/27 y x z - 1/216 x y z + 1/54 x y z + + 2 4 3 4 3 3 4 4 + + 1/144 x y z - 1/108 x y z + 2/27 y x z + 1/216 x y z + + 3 2 4 3 2 3 3 4 + - 1/288 y x z + 1/27 z y x + 1/54 z y x - 1/108 y x z + + 2 2 3 2 4 4 4 4 + - 2/27 y x z + 2/27 y x z - 1/288 x y z - 1/108 x y z + + 2 2 2 3 2 2 2 3 3 3 + - 1/72 y x z + 1/108 y x z + 1/36 y x z - 1/27 y x z + + 3 3 2 2 3 3 2 2 2 3 3 + - 1/216 y x z + 1/36 y x z + 1/288 y x z - 1/27 y x z + + 3 3 3 2 3 3 + - 1/108 z y + 1/54 z y x + 1/144 z y x - 1/108 z y x - 2/27 y x z + + 2 2 3 2 2 3 3 3 + - 1/36 z y x + 1/27 z y x + 1/54 z y x + 1/27 y z - 1/54 y x z + + 3 3 3 4 2 2 4 2 2 2 + + 1/108 y x z + 1/108 x y z + 1/288 x y z - 1/27 y x z + + 2 2 2 2 2 2 3 2 3 + - 1/36 y x z - 1/72 y x z - 1/27 y x z + 1/27 y z - 1/144 y x z + + 3 4 3 4 3 2 3 3 3 + + 1/108 x y z + 1/27 y x z - 1/27 y z - 1/27 y z + 1/108 y z + + 4 3 4 4 4 3 2 2 4 + - 1/54 y z + 1/216 y z + 1/216 y z - 1/216 y z + 1/72 y x z + + 4 2 4 2 3 4 2 4 + - 1/216 y z - 1/108 y z + 1/54 y z - 1/54 y x z - 1/54 y z + + 2 2 4 3 4 3 2 4 3 2 2 4 + + 1/54 y z - 1/54 x y z + 1/108 y z - 1/144 x y z + 1/72 y x z + + 2 3 4 3 3 4 2 4 + - 1/54 y x z + 1/216 y x z , COEFF(0, 1, 2) = - 5/72 y x z + + 3 4 2 4 3 4 3 + + 1/144 x y z - 5/144 x y z + 1/72 x y z - 5/36 y x z + + 3 4 4 3 2 3 3 4 + - 1/144 x y z - 1/18 z y x - 1/36 z y x + 5/288 y x z + + 2 2 3 4 4 3 2 + + 5/36 y x z - 5/36 y x z + 5/288 x y z - 5/288 y x z + + 3 3 3 3 2 2 3 3 3 + + 1/18 y x z + 1/144 y x z + 1/18 y x z - 5/144 z y x + + 3 3 2 3 2 2 3 3 3 + + 1/72 z y x + 5/36 y x z - 1/18 z y x - 1/36 z y x + 5/144 y x z + + 3 3 3 4 2 2 2 2 + - 1/72 y x z - 5/288 x y z + 5/72 y x z + 5/72 y x z + + 3 4 3 4 3 4 4 3 + - 1/72 x y z - 5/72 y x z + 1/36 y x z + 5/144 x y z + + 2 3 4 3 3 4 2 4 + + 1/36 y x z - 1/144 y x z , COEFF(1, 1, 2) = 1/27 y x z + + 3 4 2 4 2 4 3 4 + - 1/216 x y z + 1/54 x y z - 1/144 x y z - 1/108 x y z + + 3 3 4 4 3 2 4 3 + + 2/27 y x z + 1/216 x y z + 1/288 y x z + 1/27 z y x + + 2 3 3 4 2 2 3 + + 1/54 z y x - 1/108 y x z - 2/27 y x z + 2/27 y x z + + 2 4 4 4 4 2 2 2 3 2 + + 1/288 x y z - 1/108 x y z + 1/72 y x z + 1/108 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/36 y x z - 1/27 y x z - 1/216 y x z - 1/36 y x z + + 3 2 2 2 3 3 3 3 + - 1/288 y x z - 1/27 y x z + 1/108 z y + 1/54 z y x + + 3 2 3 3 2 2 3 + - 1/144 z y x - 1/108 z y x - 2/27 y x z + 1/36 z y x + 1/27 z y x + + 2 2 3 3 3 3 3 3 4 2 + + 1/54 z y x - 1/27 y z - 1/54 y x z + 1/108 y x z + 1/108 x y z + + 2 4 2 2 2 2 2 2 2 + - 1/288 x y z - 1/27 y x z + 1/36 y x z + 1/72 y x z + + 2 2 3 2 3 3 4 3 4 + - 1/27 y x z - 1/27 y z + 1/144 y x z + 1/108 x y z + 1/27 y x z + + 3 2 3 3 3 4 3 4 + + 1/27 y z + 1/27 y z - 1/108 y z + 1/54 y z - 1/216 y z + + 4 4 3 2 2 4 4 2 4 + - 1/216 y z + 1/216 y z - 1/72 y x z + 1/216 y z + 1/108 y z + + 2 3 4 2 4 2 2 4 3 + - 1/54 y z - 1/54 y x z + 1/54 y z - 1/54 y z - 1/54 x y z + + 4 3 2 4 3 2 2 4 2 3 4 + - 1/108 y z + 1/144 x y z - 1/72 y x z - 1/54 y x z + + 3 3 4 2 4 3 4 2 + + 1/216 y x z , COEFF(2, 1, 2) = - 1/432 y x z + 1/864 x y z + + 4 2 4 3 4 3 + - 1/864 x y z + 1/288 x y z + 1/432 x y z - 1/216 y x z + + 3 4 4 3 2 4 3 2 3 + - 1/864 x y z - 1/576 y x z - 1/108 z y x - 1/216 z y x + + 3 4 2 2 3 2 4 4 + + 1/1728 y x z + 1/216 y x z - 1/216 y x z - 1/576 x y z + + 4 4 2 2 2 3 2 2 2 3 + + 1/1728 x y z - 1/144 y x z - 1/1728 y x z + 1/72 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 1/108 y x z + 1/864 y x z + 1/72 y x z + 1/576 y x z + + 2 3 3 3 3 3 2 + + 1/108 y x z - 1/864 z y - 1/864 z y x + 1/288 z y x + + 3 3 2 2 3 + + 1/432 z y x + 1/216 y x z - 1/72 z y x - 1/108 z y x + + 2 2 3 3 3 3 3 3 + - 1/216 z y x + 1/216 y z + 1/864 y x z - 1/432 y x z + + 4 2 2 4 2 2 2 2 2 + - 1/1728 x y z + 1/576 x y z + 1/432 y x z - 1/72 y x z + + 2 2 2 2 3 2 3 + - 1/144 y x z + 1/432 y x z + 1/216 y z - 1/288 y x z + + 3 4 3 4 3 2 3 3 3 + - 1/432 x y z - 1/432 y x z - 1/216 y z - 1/216 y z + 1/864 y z + + 4 3 4 4 4 3 2 2 4 + - 1/432 y z + 1/1728 y z + 1/1728 y z - 1/1728 y z + 1/144 y x z + + 4 2 4 2 3 4 2 4 + - 1/1728 y z - 1/864 y z + 1/432 y z + 1/216 y x z - 1/432 y z + + 2 2 4 3 4 3 2 4 3 + + 1/432 y z + 1/864 x y z + 1/864 y z - 1/288 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/144 y x z + 1/216 y x z - 1/864 y x z , COEFF(-2, 2, 2) = + + 2 4 3 4 2 4 2 4 + 1/6912 y x z - 1/3456 x y z + 1/3456 x y z + 1/1152 x y z + + 3 4 3 3 4 4 3 2 4 + - 1/1728 x y z + 1/1728 y x z + 1/3456 x y z - 1/1152 y x z + + 3 2 3 3 4 2 + + 1/864 z y x + 1/1728 z y x - 1/3456 y x z - 1/3456 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/3456 y x z - 1/2304 x y z - 1/6912 x y z - 1/2304 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/3456 y x z + 1/1152 y x z - 1/864 y x z - 1/1728 y x z + + 2 3 3 2 2 2 3 3 3 + + 1/576 y x z + 1/1152 y x z - 1/1728 y x z - 1/1728 z y + + 3 3 2 3 3 + + 1/1728 z y x + 1/576 z y x - 1/864 z y x - 1/1728 y x z + + 2 2 3 2 2 3 + - 1/576 z y x + 1/1728 z y x + 1/3456 z y x + 1/1728 y z + + 3 3 3 3 3 4 2 2 4 2 + - 1/1728 y x z + 1/864 y x z + 1/6912 x y z + 1/2304 x y z + + 2 2 2 2 2 2 2 + - 1/6912 y x z - 1/1152 y x z - 1/1152 y x z - 1/3456 y x z + + 2 3 2 3 3 4 3 4 + + 1/3456 y z - 1/576 y x z + 1/1728 x y z + 1/3456 y x z + + 3 2 3 3 3 4 3 4 + - 1/1728 y z - 1/3456 y z + 1/1728 y z - 1/3456 y z + 1/3456 y z + + 4 4 3 2 2 4 4 2 + + 1/6912 y z - 1/3456 y z + 1/1152 y x z - 1/6912 y z + + 4 2 3 4 2 4 2 2 + - 1/3456 y z + 1/3456 y z - 1/1728 y x z - 1/6912 y z + 1/6912 y z + + 4 3 4 3 2 4 3 2 2 4 + - 1/3456 x y z + 1/3456 y z - 1/1152 x y z + 1/2304 y x z + + 2 3 4 3 3 4 2 4 + - 1/3456 y x z + 1/1728 y x z , COEFF(-1, 2, 2) = - 1/432 y x z + + 3 4 2 4 2 4 3 4 + + 1/864 x y z - 1/216 x y z - 1/576 x y z + 1/432 x y z + + 3 3 4 4 3 2 4 3 + - 1/108 y x z - 1/864 x y z + 1/576 y x z - 1/216 z y x + + 2 3 3 4 2 2 3 + - 1/432 z y x + 1/216 y x z + 1/216 y x z - 1/216 y x z + + 2 4 4 4 4 2 2 2 3 2 + + 1/1152 x y z + 1/432 x y z + 1/1152 y x z - 1/216 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/576 y x z + 1/216 y x z + 1/432 y x z - 1/288 y x z + + 3 2 2 2 3 3 3 3 + - 1/576 y x z + 1/432 y x z + 1/216 z y - 1/108 z y x + + 3 2 3 3 2 + - 1/288 z y x + 1/216 z y x + 1/108 y x z + 1/288 z y x + + 2 3 2 2 3 3 3 + - 1/432 z y x - 1/864 z y x - 1/216 y z + 1/108 y x z + + 3 3 3 4 2 2 4 2 2 2 + - 1/216 y x z - 1/432 x y z - 1/1152 x y z + 1/432 y x z + + 2 2 2 2 2 2 + + 1/576 y x z + 1/576 y x z + 1/216 y x z - 1/432 y z + + 3 2 3 3 4 3 4 3 + + 1/288 y x z - 1/432 x y z - 1/216 y x z + 1/216 y z + + 2 3 3 3 4 3 4 4 4 + + 1/432 y z - 1/216 y z + 1/432 y z - 1/432 y z - 1/864 y z + + 3 2 2 4 4 2 4 2 + + 1/432 y z - 1/576 y x z + 1/864 y z + 1/432 y z - 1/432 y z + + 3 4 2 4 2 2 4 3 4 3 + + 1/432 y x z + 1/864 y z - 1/864 y z + 1/216 x y z - 1/432 y z + + 2 4 3 2 2 4 2 3 4 3 3 4 + + 1/576 x y z - 1/1152 y x z + 1/864 y x z - 1/432 y x z , + + 2 4 3 4 2 4 + COEFF(0, 2, 2) = 5/1152 y x z - 1/576 x y z + 5/576 x y z + + 3 4 3 3 4 4 3 + - 1/288 x y z + 5/288 y x z + 1/576 x y z + 1/144 z y x + + 2 3 3 4 2 2 3 + + 1/288 z y x - 5/576 y x z - 5/576 y x z + 5/576 y x z + + 4 4 3 2 3 3 3 3 2 + - 5/1152 x y z + 5/576 y x z - 1/144 y x z - 1/288 y x z + + 2 3 3 3 3 3 + - 1/288 y x z + 5/288 z y x - 1/144 z y x - 5/288 y x z + + 2 3 2 2 3 3 3 3 3 3 + + 1/288 z y x + 1/576 z y x - 5/288 y x z + 1/144 y x z + + 4 2 2 2 2 3 4 3 + + 5/1152 x y z - 5/1152 y x z - 5/576 y x z + 1/288 x y z + + 4 3 4 4 3 2 3 4 + + 5/576 y x z - 1/288 y x z - 5/576 x y z - 1/576 y x z + + 3 3 4 2 4 3 4 2 + + 1/288 y x z , COEFF(1, 2, 2) = - 1/432 y x z + 1/864 x y z + + 4 2 4 3 4 3 + - 1/216 x y z + 1/576 x y z + 1/432 x y z - 1/108 y x z + + 3 4 4 3 2 4 3 2 3 + - 1/864 x y z - 1/576 y x z - 1/216 z y x - 1/432 z y x + + 3 4 2 2 3 2 4 4 + + 1/216 y x z + 1/216 y x z - 1/216 y x z - 1/1152 x y z + + 4 4 2 2 2 3 2 2 2 3 + + 1/432 x y z - 1/1152 y x z - 1/216 y x z + 1/576 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 1/216 y x z + 1/432 y x z + 1/288 y x z + 1/576 y x z + + 2 3 3 3 3 3 2 + + 1/432 y x z - 1/216 z y - 1/108 z y x + 1/288 z y x + + 3 3 2 2 3 + + 1/216 z y x + 1/108 y x z - 1/288 z y x - 1/432 z y x + + 2 2 3 3 3 3 3 3 + - 1/864 z y x + 1/216 y z + 1/108 y x z - 1/216 y x z + + 4 2 2 4 2 2 2 2 2 + - 1/432 x y z + 1/1152 x y z + 1/432 y x z - 1/576 y x z + + 2 2 2 2 3 2 3 + - 1/576 y x z + 1/216 y x z + 1/432 y z - 1/288 y x z + + 3 4 3 4 3 2 3 3 3 + - 1/432 x y z - 1/216 y x z - 1/216 y z - 1/432 y z + 1/216 y z + + 4 3 4 4 4 3 2 2 4 + - 1/432 y z + 1/432 y z + 1/864 y z - 1/432 y z + 1/576 y x z + + 4 2 4 2 3 4 2 4 + - 1/864 y z - 1/432 y z + 1/432 y z + 1/432 y x z - 1/864 y z + + 2 2 4 3 4 3 2 4 3 + + 1/864 y z + 1/216 x y z + 1/432 y z - 1/576 x y z + + 2 2 4 2 3 4 3 3 4 + + 1/1152 y x z + 1/864 y x z - 1/432 y x z , COEFF(2, 2, 2) = + + 2 4 3 4 2 4 2 4 + 1/6912 y x z - 1/3456 x y z + 1/3456 x y z - 1/1152 x y z + + 3 4 3 3 4 4 3 2 4 + - 1/1728 x y z + 1/1728 y x z + 1/3456 x y z + 1/1152 y x z + + 3 2 3 3 4 2 + + 1/864 z y x + 1/1728 z y x - 1/3456 y x z - 1/3456 y x z + + 2 3 2 4 4 4 4 2 2 2 + + 1/3456 y x z + 1/2304 x y z - 1/6912 x y z + 1/2304 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/3456 y x z - 1/1152 y x z - 1/864 y x z - 1/1728 y x z + + 2 3 3 2 2 2 3 3 3 + - 1/576 y x z - 1/1152 y x z - 1/1728 y x z + 1/1728 z y + + 3 3 2 3 3 + + 1/1728 z y x - 1/576 z y x - 1/864 z y x - 1/1728 y x z + + 2 2 3 2 2 3 + + 1/576 z y x + 1/1728 z y x + 1/3456 z y x - 1/1728 y z + + 3 3 3 3 3 4 2 2 4 2 + - 1/1728 y x z + 1/864 y x z + 1/6912 x y z - 1/2304 x y z + + 2 2 2 2 2 2 2 + - 1/6912 y x z + 1/1152 y x z + 1/1152 y x z - 1/3456 y x z + + 2 3 2 3 3 4 3 4 + - 1/3456 y z + 1/576 y x z + 1/1728 x y z + 1/3456 y x z + + 3 2 3 3 3 4 3 4 + + 1/1728 y z + 1/3456 y z - 1/1728 y z + 1/3456 y z - 1/3456 y z + + 4 4 3 2 2 4 4 2 + - 1/6912 y z + 1/3456 y z - 1/1152 y x z + 1/6912 y z + + 4 2 3 4 2 4 2 2 + + 1/3456 y z - 1/3456 y z - 1/1728 y x z + 1/6912 y z - 1/6912 y z + + 4 3 4 3 2 4 3 2 2 4 + - 1/3456 x y z - 1/3456 y z + 1/1152 x y z - 1/2304 y x z + + 2 3 4 3 3 4 + - 1/3456 y x z + 1/1728 y x z ] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dx.compute.c"); +bytes used=16474676788, alloc=63820376, time=2269.70 +bytes used=16475677264, alloc=63820376, time=2269.80 +bytes used=16476677484, alloc=63820376, time=2269.90 +bytes used=16477677664, alloc=63820376, time=2270.00 +bytes used=16478677844, alloc=63820376, time=2270.11 +bytes used=16479678072, alloc=63820376, time=2270.21 +bytes used=16480681672, alloc=63820376, time=2270.30 +bytes used=16481682004, alloc=63820376, time=2270.40 +bytes used=16482682280, alloc=63820376, time=2270.50 +bytes used=16483682544, alloc=63820376, time=2270.60 +bytes used=16484682720, alloc=63820376, time=2270.70 +bytes used=16485683308, alloc=63820376, time=2270.80 +bytes used=16486683660, alloc=63820376, time=2270.89 +bytes used=16487683832, alloc=63820376, time=2270.99 +bytes 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COEFF(-1, -2, -2) + + 4 2 4 4 4 4 3 4 4 3 + = 1/576 x y z + 1/1728 x y z - 1/864 x y z - 1/432 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/864 x y z + 1/288 x y z - 1/288 x y z + 1/432 x y z + + 4 2 4 3 2 4 4 4 2 2 + - 1/1728 x y z + 1/864 x y z - 1/1728 x z - 1/576 x y z + + 4 3 2 4 4 3 + - 1/864 x y z + 1/144 y x z - 1/864 x z - 1/216 y x z + + 3 2 4 3 2 3 3 4 + + 1/216 y x z - 1/864 z y x + 1/1728 z y x - 1/216 y x z + + 2 2 3 2 2 2 3 2 + + 1/72 y x z - 1/72 y x z + 1/144 y x z + 1/216 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/72 y x z + 1/864 y x z - 1/864 y x z + 1/216 y x z + + 3 3 2 2 2 3 3 4 2 + + 1/864 z x - 1/216 y x z + 1/288 y x z + 1/1728 x z + + 3 3 2 3 3 + - 1/108 z y x + 1/108 z y x + 1/432 z y x + 1/216 y x z + + 2 2 3 2 2 3 3 3 + - 1/216 z y x - 1/288 z y x + 1/576 z y x + 1/108 y x z + + 4 3 3 3 3 2 2 2 2 + + 1/864 x z - 1/432 y x z - 1/144 y x z - 1/72 y x z + + 2 2 2 3 2 3 2 + + 1/432 y x z - 1/432 y x z - 1/108 y x z - 1/216 x z + 1/216 x z + + 4 3 3 2 3 2 4 3 + + 1/432 y x z - 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3 + - 1/72 y x z + 1/432 y x z + 1/432 y x z - 1/108 y x z + 1/216 x z + + 2 4 3 3 2 3 2 4 + + 1/216 x z - 1/432 y x z + 1/864 x z - 1/216 x z + 1/432 x z + + 3 2 4 4 3 4 2 2 + - 1/216 x z - 1/432 y x z + 1/432 x z - 1/1728 x z - 1/432 x z + + 3 4 2 3 2 2 2 4 + + 1/1728 y x z - 1/432 x z + 1/1728 x z - 1/144 y x z + + 2 3 4 3 3 4 4 2 4 + + 1/576 y x z - 1/864 y x z , COEFF(2, -2, -2) = - 1/2304 x y z + + 4 4 4 3 4 4 3 4 + - 1/6912 x y z + 1/3456 x y z + 1/1728 x y z - 1/3456 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/1152 x y z + 1/1152 x y z - 1/1728 x y z + 1/6912 x y z + + 4 3 2 4 4 4 2 2 4 3 + - 1/3456 x y z + 1/6912 x z + 1/2304 x y z + 1/3456 x y z + + 2 4 4 3 3 2 4 + + 1/1152 y x z + 1/3456 x z - 1/1728 y x z - 1/3456 y x z + + 3 2 3 3 4 2 + - 1/1728 z y x + 1/3456 z y x - 1/1728 y x z + 1/576 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/576 y x z - 1/2304 y x z + 1/1728 y x z - 1/1152 y x z + + 3 3 3 3 2 2 3 3 + + 1/1728 y x z - 1/1728 y x z - 1/3456 y x z + 1/1728 z x + + 3 2 2 2 3 3 4 2 3 + 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x z - 1/54 x z + 1/216 x z + 1/72 y x z + + 2 3 4 3 3 4 4 2 4 + + 1/288 y x z - 1/216 y x z , COEFF(0, -1, -2) = 1/192 x y z + + 4 4 4 3 4 4 3 4 + + 1/72 x y z - 1/144 x y z - 1/72 x y z + 1/36 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/96 x y z - 1/96 x y z + 1/72 x y z - 1/72 x y z + + 4 3 2 4 4 4 2 2 4 3 4 + + 1/144 x y z - 1/144 x z - 1/192 x y z - 1/36 x y z - 1/72 x z + + 3 2 4 2 2 2 2 2 3 2 3 + - 1/18 z + 5/144 y x z + 5/192 y x z + 5/96 y x z + 5/36 y x z + + 4 3 2 2 4 2 3 3 2 + - 1/36 z - 5/144 y x z + 1/144 x z + 1/18 z - 1/18 z y + 1/36 z + + 3 2 2 4 3 2 2 + + 5/72 z y x - 5/36 z y x + 1/9 y z + 1/72 x z - 5/96 y x z + + 2 2 2 3 2 3 2 3 + + 5/72 y x z + 1/24 y z - 5/72 y x z + 5/72 x z - 1/9 y z + + 2 3 3 3 2 3 4 3 4 + - 1/24 y z + 1/18 y z - 5/72 x z + 1/18 y z - 1/36 y z + + 3 2 2 4 2 4 2 2 2 + + 1/36 y z + 5/144 x z - 5/72 y x z - 1/18 y z - 5/144 x z + + 2 4 2 2 2 2 4 + + 1/48 y z - 1/48 y z - 5/192 y x z , COEFF(1, -1, -2) = + + 4 2 4 4 4 4 3 4 4 3 + - 1/288 x y z - 1/108 x y z + 1/216 x y z + 1/108 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/54 x y z - 1/144 x y z + 1/144 x y z - 1/108 x y z + + 4 2 4 3 2 4 4 4 2 2 + + 1/108 x y z - 1/216 x y z + 1/216 x z + 1/288 x y z + + 4 3 2 4 4 3 3 2 4 + + 1/54 x y z + 1/72 y x z + 1/108 x z - 2/27 y x z - 1/54 y x z + + 3 2 3 3 4 2 2 3 + - 1/54 z y x + 1/108 z y x - 1/54 y x z + 1/36 y x z - 1/36 y x z + + 2 2 2 3 2 2 2 3 3 3 + - 1/72 y x z + 1/54 y x z - 1/36 y x z + 1/54 y x z + + 3 3 2 2 3 3 3 2 2 + - 1/216 y x z - 2/27 y x z + 1/108 z x + 1/54 y x z + + 2 3 3 4 2 3 3 2 + + 1/144 y x z - 1/216 x z - 1/27 z y x - 1/27 z y x + + 3 3 2 2 3 + + 1/108 z y x + 2/27 y x z + 2/27 z y x - 1/144 z y x + + 2 2 3 3 3 4 3 3 3 3 + + 1/288 z y x + 1/27 y x z - 1/108 x z - 1/108 y x z + + 2 2 2 2 2 2 2 3 2 3 + - 1/72 y x z + 1/36 y x z - 1/27 y x z - 1/27 y x z + 1/27 y x z + + 2 4 3 3 2 3 + - 1/27 x z - 1/27 x z + 1/27 y x z - 1/108 x z + 1/27 x z + + 2 4 3 2 4 4 3 4 + - 1/54 x z + 1/27 x z + 1/27 y x z - 1/54 x z + 1/216 x z + + 2 2 3 4 2 3 2 2 2 4 + + 1/54 x z - 1/108 y x z + 1/54 x z - 1/216 x z + 1/72 y x z + + 2 3 4 3 3 4 4 2 4 + - 1/288 y x z + 1/216 y x z , COEFF(2, -1, -2) = 1/1152 x y z + + 4 4 4 3 4 4 3 4 + + 1/432 x y z - 1/864 x y z - 1/432 x y z + 1/216 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/576 x y z - 1/576 x y z + 1/432 x y z - 1/432 x y z + + 4 3 2 4 4 4 2 2 4 3 + + 1/864 x y z - 1/864 x z - 1/1152 x y z - 1/216 x y z + + 2 4 4 3 3 2 4 + - 1/576 y x z - 1/432 x z + 1/108 y x z + 1/864 y x z + + 3 2 3 3 4 2 + + 1/108 z y x - 1/216 z y x + 1/432 y x z - 1/288 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/288 y x z + 1/1152 y x z - 1/432 y x z + 1/576 y x z + + 3 3 3 3 2 2 3 3 + - 1/108 y x z + 1/432 y x z + 1/216 y x z - 1/216 z x + + 3 2 2 2 3 3 4 2 3 + - 1/864 y x z - 1/288 y x z + 1/864 x z + 1/216 z y x + + 3 2 3 3 2 + + 1/432 z y x - 1/216 z y x - 1/108 y x z - 1/216 z y x + + 2 3 2 2 3 3 3 4 3 + + 1/288 z y x - 1/576 z y x - 1/216 y x z + 1/432 x z + + 3 3 3 2 2 2 2 2 2 + + 1/216 y x z + 1/576 y x z - 1/576 y x z + 1/432 y x z + + 2 3 2 3 2 4 + + 1/216 y x z - 1/432 y x z + 1/216 x z + 1/432 x z - 1/216 y x z + + 3 3 2 3 2 4 3 2 4 + + 1/216 x z - 1/432 x z + 1/864 x z - 1/216 x z - 1/432 y x z + + 4 3 4 2 2 3 4 2 + + 1/432 x z - 1/432 x z - 1/864 x z + 1/216 y x z - 1/432 x z + + 3 2 2 2 4 2 3 4 3 3 4 + + 1/432 x z - 1/1152 y x z + 1/576 y x z - 1/432 y x z , + + 4 4 4 3 4 4 3 + COEFF(-2, 0, -2) = - 5/1152 x y z + 1/576 x y z + 1/288 x y z + + 4 4 3 3 4 2 4 3 2 + - 5/576 x y z - 1/288 x y z + 5/1152 x y z - 1/576 x y z + + 4 3 3 3 2 4 3 + + 5/576 x y z + 5/288 y x z - 1/576 y x z + 5/288 z y x + + 2 3 3 4 3 2 3 3 + - 5/576 z y x + 1/288 y x z - 1/288 y x z - 5/288 y x z + + 3 3 2 2 3 3 2 2 3 + + 1/288 y x z - 5/576 y x z + 1/576 y x z + 1/144 z y x + + 3 2 3 3 2 + - 1/288 z y x - 1/144 z y x - 5/288 y x z + 5/576 z y x + + 3 3 3 3 3 2 2 2 + - 1/144 y x z + 1/144 y x z - 5/1152 y x z + 5/576 y x z + + 3 2 3 4 2 4 3 4 + + 1/288 y x z - 5/576 y x z + 5/1152 y x z + 5/576 y x z + + 3 3 4 4 4 4 3 4 + - 1/288 y x z , COEFF(-1, 0, -2) = 5/288 x y z - 1/144 x y z + + 4 3 4 4 3 3 4 2 + - 1/72 x y z + 5/144 x y z + 1/72 x y z - 5/288 x y z + + 4 3 2 4 3 3 3 2 4 + + 1/144 x y z - 5/144 x y z - 5/36 y x z + 1/36 y x z + + 3 2 3 3 4 3 2 + - 5/144 z y x + 5/288 z y x - 1/36 y x z + 1/36 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 5/144 y x z - 1/144 y x z + 5/36 y x z - 1/36 y x z + + 3 3 2 3 3 2 + - 1/18 z y x + 1/18 z y x + 1/72 z y x + 5/36 y x z - 5/36 z y x + + 3 3 3 3 3 2 2 2 + + 1/18 y x z - 1/72 y x z + 5/72 y x z - 5/72 y x z + + 3 2 3 4 2 4 3 4 + - 1/18 y x z + 5/72 y x z - 5/72 y x z - 5/288 y x z + + 3 3 4 25 2 4 4 + + 1/144 y x z , COEFF(0, 0, -2) = -- z y x - 5/192 x y z + 96 + + 25 2 4 3 4 3 4 3 2 2 4 2 + + --- y x z + 5/24 y z + 1/96 x y z + 5/96 y x z + 5/192 x y z + 192 + + 25 2 3 3 2 4 3 2 3 2 + - 5/24 y z - -- y x z - 5/96 y x z - 1/24 y z - 5/48 z y x + 96 + + 25 2 2 3 4 2 3 4 + - --- y x z + 1/24 y z + 5/48 y z + 1/12 z y - 5/96 x y z + 192 + + 4 3 4 3 4 4 3 3 3 3 + + 5/96 x y z + 1/48 x y z - 5/48 y z - 1/48 x y z - 1/12 y z + + 4 3 2 3 2 3 4 4 + - 1/96 x y z + 5/48 y x z , COEFF(1, 0, -2) = 5/288 x y z + + 4 3 4 4 3 4 4 3 3 + - 1/144 x y z - 1/72 x y z + 5/144 x y z + 1/72 x y z + + 4 2 4 3 2 4 3 3 + - 5/288 x y z + 1/144 x y z - 5/144 x y z + 5/36 y x z + + 3 2 4 3 2 3 3 4 + + 1/36 y x z + 5/144 z y x - 5/288 z y x + 1/36 y x z + + 3 2 3 3 3 3 2 2 3 + - 1/36 y x z - 5/144 y x z + 1/144 y x z + 5/36 y x z + + 3 2 2 3 3 2 3 3 + - 1/36 y x z + 1/18 z y x + 1/18 z y x - 1/72 z y x - 5/36 y x z + + 2 3 3 3 3 3 2 2 2 + - 5/36 z y x - 1/18 y x z + 1/72 y x z + 5/72 y x z + 5/72 y x z + + 3 2 3 4 2 4 3 4 + - 1/18 y x z - 5/72 y x z - 5/72 y x z + 5/288 y x z + + 3 3 4 4 4 4 3 4 + - 1/144 y x z , COEFF(2, 0, -2) = - 5/1152 x y z + 1/576 x y z + + 4 3 4 4 3 3 4 2 + + 1/288 x y z - 5/576 x y z - 1/288 x y z + 5/1152 x y z + + 4 3 2 4 3 3 3 2 4 + - 1/576 x y z + 5/576 x y z - 5/288 y x z - 1/576 y x z + + 3 2 3 3 4 3 2 + - 5/288 z y x + 5/576 z y x - 1/288 y x z + 1/288 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 5/288 y x z - 1/288 y x z - 5/576 y x z + 1/576 y x z + + 3 3 2 3 3 + - 1/144 z y x - 1/288 z y x + 1/144 z y x + 5/288 y x z + + 2 3 3 3 3 3 2 2 + + 5/576 z y x + 1/144 y x z - 1/144 y x z - 5/1152 y x z + + 2 3 2 3 4 2 4 + - 5/576 y x z + 1/288 y x z + 5/576 y x z + 5/1152 y x z + + 3 4 3 3 4 4 2 4 + - 5/576 y x z + 1/288 y x z , COEFF(-2, 1, -2) = - 1/1152 x y z + + 4 4 4 3 4 4 3 4 + + 1/432 x y z - 1/864 x y z - 1/432 x y z + 1/216 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/576 x y z + 1/576 x y z + 1/432 x y z - 1/432 x y z + + 4 3 2 4 4 4 2 2 4 3 + + 1/864 x y z + 1/864 x z + 1/1152 x y z - 1/216 x y z + + 2 4 4 3 3 2 4 + - 1/576 y x z + 1/432 x z - 1/108 y x z + 1/864 y x z + + 3 2 3 3 4 2 + - 1/108 z y x + 1/216 z y x - 1/432 y x z - 1/288 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/288 y x z - 1/1152 y x z + 1/432 y x z - 1/576 y x z + + 3 3 3 3 2 2 3 3 + + 1/108 y x z - 1/432 y x z + 1/216 y x z - 1/216 z x + + 3 2 2 2 3 3 4 2 3 + - 1/864 y x z - 1/288 y x z - 1/864 x z - 1/216 z y x + + 3 2 3 3 2 + + 1/432 z y x + 1/216 z y x + 1/108 y x z - 1/216 z y x + + 2 3 2 2 3 3 3 4 3 + + 1/288 z y x - 1/576 z y x + 1/216 y x z - 1/432 x z + + 3 3 3 2 2 2 2 2 2 + - 1/216 y x z + 1/576 y x z + 1/576 y x z + 1/432 y x z + + 2 3 2 3 2 4 + - 1/216 y x z - 1/432 y x z + 1/216 x z - 1/432 x z + 1/216 y x z + + 3 3 2 3 2 4 3 2 4 + + 1/216 x z + 1/432 x z - 1/864 x z - 1/216 x z - 1/432 y x z + + 4 3 4 2 2 3 4 2 + + 1/432 x z - 1/432 x z + 1/864 x z - 1/216 y x z - 1/432 x z + + 3 2 2 2 4 2 3 4 3 3 4 + + 1/432 x z + 1/1152 y x z + 1/576 y x z + 1/432 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(-1, 1, -2) = 1/288 x y z - 1/108 x y z + 1/216 x y z + + 4 3 4 4 2 4 2 3 + + 1/108 x y z - 1/54 x y z + 1/144 x y z - 1/144 x y z + + 4 3 3 4 2 4 3 2 4 4 + - 1/108 x y z + 1/108 x y z - 1/216 x y z - 1/216 x z + + 4 2 2 4 3 2 4 4 3 + - 1/288 x y z + 1/54 x y z + 1/72 y x z - 1/108 x z + 2/27 y x z + + 3 2 4 3 2 3 3 4 2 + - 1/54 y x z + 1/54 z y x - 1/108 z y x + 1/54 y x z + 1/36 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/36 y x z + 1/72 y x z - 1/54 y x z + 1/36 y x z + + 3 3 3 3 2 2 3 3 + - 1/54 y x z + 1/216 y x z - 2/27 y x z + 1/108 z x + + 3 2 2 2 3 3 4 2 3 + + 1/54 y x z + 1/144 y x z + 1/216 x z + 1/27 z y x + + 3 2 3 3 2 2 3 + - 1/27 z y x - 1/108 z y x - 2/27 y x z + 2/27 z y x - 1/144 z y x + + 2 2 3 3 3 4 3 3 3 3 + + 1/288 z y x - 1/27 y x z + 1/108 x z + 1/108 y x z + + 2 2 2 2 2 2 2 3 2 3 + - 1/72 y x z - 1/36 y x z - 1/27 y x z + 1/27 y x z + 1/27 y x z + + 2 4 3 3 2 3 + - 1/27 x z + 1/27 x z - 1/27 y x z - 1/108 x z - 1/27 x z + + 2 4 3 2 4 4 3 4 + + 1/54 x z + 1/27 x z + 1/27 y x z - 1/54 x z + 1/216 x z + + 2 2 3 4 2 3 2 2 2 4 + - 1/54 x z + 1/108 y x z + 1/54 x z - 1/216 x z - 1/72 y x z + + 2 3 4 3 3 4 4 2 4 + - 1/288 y x z - 1/216 y x z , COEFF(0, 1, -2) = - 1/192 x y z + + 4 4 4 3 4 4 3 4 + + 1/72 x y z - 1/144 x y z - 1/72 x y z + 1/36 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/96 x y z + 1/96 x y z + 1/72 x y z - 1/72 x y z + + 4 3 2 4 4 4 2 2 4 3 4 + + 1/144 x y z + 1/144 x z + 1/192 x y z - 1/36 x y z + 1/72 x z + + 3 2 4 2 2 2 2 2 3 2 3 + + 1/18 z + 5/144 y x z - 5/192 y x z - 5/96 y x z + 5/36 y x z + + 4 3 2 2 4 2 3 3 2 + + 1/36 z - 5/144 y x z - 1/144 x z - 1/18 z - 1/18 z y - 1/36 z + + 3 2 2 4 3 2 2 + + 5/72 z y x - 5/36 z y x + 1/9 y z - 1/72 x z + 5/96 y x z + + 2 2 2 3 2 3 2 3 + + 5/72 y x z - 1/24 y z - 5/72 y x z - 5/72 x z - 1/9 y z + + 2 3 3 3 2 3 4 3 4 + + 1/24 y z + 1/18 y z + 5/72 x z + 1/18 y z - 1/36 y z + + 3 2 2 4 2 4 2 2 2 + + 1/36 y z - 5/144 x z - 5/72 y x z - 1/18 y z + 5/144 x z + + 2 4 2 2 2 2 4 + - 1/48 y z + 1/48 y z + 5/192 y x z , COEFF(1, 1, -2) = + + 4 2 4 4 4 4 3 4 4 3 + 1/288 x y z - 1/108 x y z + 1/216 x y z + 1/108 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/54 x y z + 1/144 x y z - 1/144 x y z - 1/108 x y z + + 4 2 4 3 2 4 4 4 2 2 + + 1/108 x y z - 1/216 x y z - 1/216 x z - 1/288 x y z + + 4 3 2 4 4 3 3 2 4 + + 1/54 x y z - 1/72 y x z - 1/108 x z - 2/27 y x z - 1/54 y x z + + 3 2 3 3 4 2 2 3 + - 1/54 z y x + 1/108 z y x - 1/54 y x z - 1/36 y x z + 1/36 y x z + + 2 2 2 3 2 2 2 3 3 3 + + 1/72 y x z + 1/54 y x z + 1/36 y x z + 1/54 y x z + + 3 3 2 2 3 3 3 2 2 + - 1/216 y x z - 2/27 y x z - 1/108 z x + 1/54 y x z + + 2 3 3 4 2 3 3 2 + - 1/144 y x z + 1/216 x z - 1/27 z y x - 1/27 z y x + + 3 3 2 2 3 + + 1/108 z y x + 2/27 y x z + 2/27 z y x + 1/144 z y x + + 2 2 3 3 3 4 3 3 3 3 + - 1/288 z y x + 1/27 y x z + 1/108 x z - 1/108 y x z + + 2 2 2 2 2 2 2 3 2 3 + + 1/72 y x z - 1/36 y x z - 1/27 y x z - 1/27 y x z + 1/27 y x z + + 2 4 3 3 2 3 + + 1/27 x z + 1/27 x z + 1/27 y x z + 1/108 x z - 1/27 x z + + 2 4 3 2 4 4 3 4 + + 1/54 x z - 1/27 x z + 1/27 y x z + 1/54 x z - 1/216 x z + + 2 2 3 4 2 3 2 2 2 4 + - 1/54 x z - 1/108 y x z - 1/54 x z + 1/216 x z - 1/72 y x z + + 2 3 4 3 3 4 4 2 4 + + 1/288 y x z + 1/216 y x z , COEFF(2, 1, -2) = - 1/1152 x y z + + 4 4 4 3 4 4 3 4 + + 1/432 x y z - 1/864 x y z - 1/432 x y z + 1/216 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/576 x y z + 1/576 x y z + 1/432 x y z - 1/432 x y z + + 4 3 2 4 4 4 2 2 4 3 + + 1/864 x y z + 1/864 x z + 1/1152 x y z - 1/216 x y z + + 2 4 4 3 3 2 4 + + 1/576 y x z + 1/432 x z + 1/108 y x z + 1/864 y x z + + 3 2 3 3 4 2 + + 1/108 z y x - 1/216 z y x + 1/432 y x z + 1/288 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/288 y x z - 1/1152 y x z - 1/432 y x z - 1/576 y x z + + 3 3 3 3 2 2 3 3 + - 1/108 y x z + 1/432 y x z + 1/216 y x z + 1/216 z x + + 3 2 2 2 3 3 4 2 3 + - 1/864 y x z + 1/288 y x z - 1/864 x z + 1/216 z y x + + 3 2 3 3 2 + + 1/432 z y x - 1/216 z y x - 1/108 y x z - 1/216 z y x + + 2 3 2 2 3 3 3 4 3 + - 1/288 z y x + 1/576 z y x - 1/216 y x z - 1/432 x z + + 3 3 3 2 2 2 2 2 2 + + 1/216 y x z - 1/576 y x z + 1/576 y x z + 1/432 y x z + + 2 3 2 3 2 4 + + 1/216 y x z - 1/432 y x z - 1/216 x z - 1/432 x z - 1/216 y x z + + 3 3 2 3 2 4 3 2 4 + - 1/216 x z + 1/432 x z - 1/864 x z + 1/216 x z - 1/432 y x z + + 4 3 4 2 2 3 4 2 + - 1/432 x z + 1/432 x z + 1/864 x z + 1/216 y x z + 1/432 x z + + 3 2 2 2 4 2 3 4 3 3 4 + - 1/432 x z + 1/1152 y x z - 1/576 y x z - 1/432 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(-2, 2, -2) = 1/2304 x y z - 1/6912 x y z + 1/3456 x y z + + 4 3 4 4 2 4 2 3 + + 1/1728 x y z - 1/3456 x y z + 1/1152 x y z - 1/1152 x y z + + 4 3 3 4 2 4 3 2 4 4 + - 1/1728 x y z + 1/6912 x y z - 1/3456 x y z - 1/6912 x z + + 4 2 2 4 3 2 4 4 + - 1/2304 x y z + 1/3456 x y z + 1/1152 y x z - 1/3456 x z + + 3 3 2 4 3 2 3 + + 1/1728 y x z - 1/3456 y x z + 1/1728 z y x - 1/3456 z y x + + 3 4 2 2 3 2 2 2 + + 1/1728 y x z + 1/576 y x z - 1/576 y x z + 1/2304 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/1728 y x z + 1/1152 y x z - 1/1728 y x z + 1/1728 y x z + + 2 3 3 3 2 2 2 3 3 + - 1/3456 y x z + 1/1728 z x + 1/3456 y x z + 1/576 y x z + + 4 2 3 3 2 3 3 + + 1/6912 x z + 1/864 z y x - 1/1728 z y x - 1/864 z y x + + 2 2 3 2 2 3 + - 1/1728 y x z + 1/3456 z y x - 1/576 z y x + 1/1152 z y x + + 3 3 4 3 3 3 3 2 2 + - 1/864 y x z + 1/3456 x z + 1/864 y x z - 1/1152 y x z + + 2 2 2 2 2 3 2 3 + - 1/1152 y x z - 1/6912 y x z + 1/3456 y x z + 1/1728 y x z + + 2 4 3 3 2 3 + - 1/1728 x z + 1/3456 x z - 1/3456 y x z - 1/1728 x z - 1/3456 x z + + 2 4 3 2 4 4 3 4 + + 1/6912 x z + 1/1728 x z + 1/6912 y x z - 1/3456 x z + 1/3456 x z + + 2 2 3 4 2 3 2 + - 1/6912 x z + 1/3456 y x z + 1/3456 x z - 1/3456 x z + + 2 2 4 2 3 4 3 3 4 + - 1/2304 y x z - 1/1152 y x z - 1/1728 y x z , COEFF(-1, 2, -2) = + + 4 2 4 4 4 4 3 4 4 3 + - 1/576 x y z + 1/1728 x y z - 1/864 x y z - 1/432 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/864 x y z - 1/288 x y z + 1/288 x y z + 1/432 x y z + + 4 2 4 3 2 4 4 4 2 2 + - 1/1728 x y z + 1/864 x y z + 1/1728 x z + 1/576 x y z + + 4 3 2 4 4 3 + - 1/864 x y z - 1/144 y x z + 1/864 x z - 1/216 y x z + + 3 2 4 3 2 3 3 4 + + 1/216 y x z - 1/864 z y x + 1/1728 z y x - 1/216 y x z + + 2 2 3 2 2 2 3 2 + - 1/72 y x z + 1/72 y x z - 1/144 y x z + 1/216 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/72 y x z + 1/864 y x z - 1/864 y x z + 1/216 y x z + + 3 3 2 2 2 3 3 4 2 + - 1/864 z x - 1/216 y x z - 1/288 y x z - 1/1728 x z + + 3 3 2 3 3 + - 1/108 z y x + 1/108 z y x + 1/432 z y x + 1/216 y x z + + 2 2 3 2 2 3 3 3 + - 1/216 z y x + 1/288 z y x - 1/576 z y x + 1/108 y x z + + 4 3 3 3 3 2 2 2 2 + - 1/864 x z - 1/432 y x z + 1/144 y x z + 1/72 y x z + + 2 2 2 3 2 3 2 + + 1/432 y x z - 1/432 y x z - 1/108 y x z + 1/216 x z - 1/216 x z + + 4 3 3 2 3 2 4 3 + + 1/432 y x z + 1/864 x z + 1/216 x z - 1/432 x z - 1/216 x z + + 2 4 4 3 4 2 2 3 4 + - 1/432 y x z + 1/432 x z - 1/1728 x z + 1/432 x z - 1/1728 y x z + + 2 3 2 2 2 4 2 3 4 + - 1/432 x z + 1/1728 x z + 1/144 y x z + 1/576 y x z + + 3 3 4 4 2 4 4 4 + + 1/864 y x z , COEFF(0, 2, -2) = 1/384 x y z - 1/1152 x y z + + 4 3 4 4 3 4 4 2 + + 1/576 x y z + 1/288 x y z - 1/576 x y z + 1/192 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/192 x y z - 1/288 x y z + 1/1152 x y z - 1/576 x y z + + 4 4 4 2 2 4 3 4 + - 1/1152 x z - 1/384 x y z + 1/576 x y z - 1/576 x z - 1/144 z + + 3 2 4 2 2 2 2 2 3 2 3 + - 5/576 y x z + 5/384 y x z + 5/192 y x z - 5/576 y x z + + 4 3 2 2 4 2 3 3 + - 1/288 z + 5/576 y x z + 1/1152 x z + 1/144 z + 1/72 z y + + 2 3 2 2 4 3 + + 1/288 z - 5/288 z y x + 5/576 z y x - 1/144 y z + 1/576 x z + + 2 2 2 2 2 3 2 3 2 + - 5/192 y x z - 5/1152 y x z + 1/48 y z + 5/288 y x z + 5/576 x z + + 3 2 3 3 3 2 3 4 + + 1/144 y z - 1/48 y z - 1/72 y z - 5/576 x z - 1/288 y z + + 3 4 3 2 2 4 2 4 2 + + 1/144 y z - 1/144 y z + 5/1152 x z + 5/1152 y x z + 1/288 y z + + 2 2 2 4 2 2 2 2 4 + - 5/1152 x z + 1/96 y z - 1/96 y z - 5/384 y x z , COEFF(1, 2, -2) + + 4 2 4 4 4 4 3 4 4 3 + = - 1/576 x y z + 1/1728 x y z - 1/864 x y z - 1/432 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/864 x y z - 1/288 x y z + 1/288 x y z + 1/432 x y z + + 4 2 4 3 2 4 4 4 2 2 + - 1/1728 x y z + 1/864 x y z + 1/1728 x z + 1/576 x y z + + 4 3 2 4 4 3 + - 1/864 x y z + 1/144 y x z + 1/864 x z + 1/216 y x z + + 3 2 4 3 2 3 3 4 + + 1/216 y x z + 1/864 z y x - 1/1728 z y x + 1/216 y x z + + 2 2 3 2 2 2 3 2 + + 1/72 y x z - 1/72 y x z - 1/144 y x z - 1/216 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/72 y x z - 1/864 y x z + 1/864 y x z + 1/216 y x z + + 3 3 2 2 2 3 3 4 2 + + 1/864 z x - 1/216 y x z + 1/288 y x z - 1/1728 x z + + 3 3 2 3 3 + + 1/108 z y x + 1/108 z y x - 1/432 z y x - 1/216 y x z + + 2 2 3 2 2 3 3 3 + - 1/216 z y x - 1/288 z y x + 1/576 z y x - 1/108 y x z + + 4 3 3 3 3 2 2 2 2 + - 1/864 x z + 1/432 y x z - 1/144 y x z + 1/72 y x z + + 2 2 2 3 2 3 2 + + 1/432 y x z + 1/432 y x z - 1/108 y x z - 1/216 x z - 1/216 x z + + 4 3 3 2 3 2 4 3 + - 1/432 y x z - 1/864 x z + 1/216 x z - 1/432 x z + 1/216 x z + + 2 4 4 3 4 2 2 3 4 + - 1/432 y x z - 1/432 x z + 1/1728 x z + 1/432 x z + 1/1728 y x z + + 2 3 2 2 2 4 2 3 4 + + 1/432 x z - 1/1728 x z + 1/144 y x z - 1/576 y x z + + 3 3 4 4 2 4 4 4 + - 1/864 y x z , COEFF(2, 2, -2) = 1/2304 x y z - 1/6912 x y z + + 4 3 4 4 3 4 4 2 + + 1/3456 x y z + 1/1728 x y z - 1/3456 x y z + 1/1152 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/1152 x y z - 1/1728 x y z + 1/6912 x y z - 1/3456 x y z + + 4 4 4 2 2 4 3 2 4 + - 1/6912 x z - 1/2304 x y z + 1/3456 x y z - 1/1152 y x z + + 4 3 3 2 4 3 + - 1/3456 x z - 1/1728 y x z - 1/3456 y x z - 1/1728 z y x + + 2 3 3 4 2 2 3 + + 1/3456 z y x - 1/1728 y x z - 1/576 y x z + 1/576 y x z + + 2 2 2 3 2 2 2 3 3 3 + + 1/2304 y x z + 1/1728 y x z + 1/1152 y x z + 1/1728 y x z + + 3 3 2 2 3 3 3 2 2 + - 1/1728 y x z - 1/3456 y x z - 1/1728 z x + 1/3456 y x z + + 2 3 3 4 2 3 3 2 + - 1/576 y x z + 1/6912 x z - 1/864 z y x - 1/1728 z y x + + 3 3 2 2 3 + + 1/864 z y x + 1/1728 y x z + 1/3456 z y x + 1/576 z y x + + 2 2 3 3 3 4 3 3 3 3 + - 1/1152 z y x + 1/864 y x z + 1/3456 x z - 1/864 y x z + + 2 2 2 2 2 2 2 + + 1/1152 y x z - 1/1152 y x z - 1/6912 y x z - 1/3456 y x z + + 3 2 3 2 4 + + 1/1728 y x z + 1/1728 x z + 1/3456 x z + 1/3456 y x z + + 3 3 2 3 2 4 3 + + 1/1728 x z - 1/3456 x z + 1/6912 x z - 1/1728 x z + + 2 4 4 3 4 2 2 + + 1/6912 y x z + 1/3456 x z - 1/3456 x z - 1/6912 x z + + 3 4 2 3 2 2 2 4 + - 1/3456 y x z - 1/3456 x z + 1/3456 x z - 1/2304 y x z + + 2 3 4 3 3 4 4 2 4 + + 1/1152 y x z + 1/1728 y x z , COEFF(-2, -2, -1) = 1/576 x y z + + 4 4 4 3 4 4 3 4 + + 1/1728 x y z - 1/864 x y z - 1/216 x y z + 1/432 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/144 x y z - 1/576 x y z + 1/864 x y z - 1/432 x y z + + 4 3 2 4 4 4 2 2 4 3 + + 1/216 x y z - 1/1728 x z - 1/144 x y z - 1/1728 x y z + + 2 4 4 3 3 2 4 + + 1/288 y x z - 1/432 x z - 1/864 y x z + 1/864 y x z + + 3 2 3 3 4 2 + - 1/216 z y x + 1/216 z y x - 1/432 y x z + 1/72 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/288 y x z + 1/144 y x z + 1/108 y x z + 1/576 y x z + + 3 3 3 3 2 2 3 3 + + 1/864 y x z - 1/108 y x z + 1/1728 y x z + 1/216 z x + + 3 2 2 2 3 3 4 2 3 + - 1/216 y x z + 1/288 y x z + 1/432 x z - 1/108 z y x + + 3 2 3 3 2 + + 1/216 z y x + 1/108 z y x + 1/216 y x z - 1/432 z y x + + 2 3 2 2 3 3 3 4 3 + - 1/72 z y x + 1/72 z y x + 1/432 y x z + 1/1728 x z + + 3 3 3 2 2 2 2 2 2 + - 1/432 y x z - 1/72 y x z - 1/144 y x z + 1/432 y x z + + 2 3 2 3 2 4 + - 1/216 y x z - 1/864 y x z - 1/216 x z + 1/432 x z + 1/864 y x z + + 3 3 2 3 2 4 3 2 4 + - 1/864 x z - 1/1728 x z + 1/1728 x z + 1/864 x z - 1/1728 y x z + + 4 3 4 2 2 3 4 2 + - 1/864 x z + 1/864 x z - 1/432 x z - 1/864 y x z + 1/216 x z + + 3 2 2 2 4 2 3 4 3 3 4 + - 1/216 x z - 1/576 y x z - 1/288 y x z + 1/432 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(-1, -2, -1) = - 1/144 x y z - 1/432 x y z + 1/216 x y z + + 4 3 4 4 2 4 2 3 + + 1/54 x y z - 1/108 x y z - 1/36 x y z + 1/144 x y z + + 4 3 3 4 2 4 3 2 4 4 + - 1/216 x y z + 1/108 x y z - 1/54 x y z + 1/432 x z + + 4 2 2 4 3 2 4 4 3 + + 1/36 x y z + 1/432 x y z - 1/36 y x z + 1/108 x z + 1/108 y x z + + 3 2 4 3 2 3 3 4 2 + - 1/54 y x z + 1/108 z y x - 1/108 z y x + 1/54 y x z - 1/9 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/36 y x z - 1/9 y x z - 2/27 y x z - 1/36 y x z + + 3 3 3 3 2 2 3 3 + - 1/432 y x z + 1/54 y x z - 1/108 y x z - 1/108 z x + + 3 2 2 2 3 3 4 2 3 + + 2/27 y x z - 1/144 y x z - 1/108 x z + 2/27 z y x + + 3 2 3 3 2 2 3 + - 2/27 z y x - 1/54 z y x - 1/27 y x z + 1/27 z y x + 1/36 z y x + + 2 2 3 3 3 4 3 3 3 3 + - 1/36 z y x - 1/54 y x z - 1/432 x z + 1/216 y x z + + 2 2 2 2 2 2 2 3 2 3 + + 1/9 y x z + 1/9 y x z - 1/27 y x z + 1/27 y x z + 1/54 y x z + + 2 4 3 3 2 3 + + 1/27 x z - 1/27 x z - 1/108 y x z + 1/432 x z + 1/108 x z + + 2 4 3 2 4 4 3 4 + - 1/108 x z - 1/108 x z + 1/108 y x z + 1/108 x z - 1/432 x z + + 2 2 3 4 2 3 2 2 2 4 + + 1/27 x z + 1/432 y x z - 1/27 x z + 1/108 x z + 1/36 y x z + + 2 3 4 3 3 4 4 2 4 + + 1/144 y x z - 1/216 y x z , COEFF(0, -2, -1) = 1/96 x y z + + 4 4 4 3 4 4 3 4 + + 1/288 x y z - 1/144 x y z - 1/36 x y z + 1/72 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/24 x y z - 1/96 x y z + 1/144 x y z - 1/72 x y z + + 4 3 2 4 4 4 2 2 4 3 4 + + 1/36 x y z - 1/288 x z - 1/24 x y z - 1/288 x y z - 1/72 x z + + 3 2 4 2 2 2 2 2 3 2 3 + - 1/18 z + 5/144 y x z + 5/24 y x z + 5/96 y x z + 5/288 y x z + + 4 3 2 2 4 2 3 3 2 + - 1/72 z - 5/36 y x z + 1/72 x z + 1/72 z - 1/9 z y + 1/18 z + + 3 2 2 4 3 2 2 + + 5/36 z y x - 5/72 z y x + 1/18 y z + 1/288 x z - 5/24 y x z + + 2 2 2 3 2 3 2 3 + + 5/72 y x z + 1/6 y z - 5/144 y x z + 5/72 x z - 1/72 y z + + 2 3 3 3 2 3 4 3 4 + - 1/24 y z + 1/36 y z - 5/288 x z + 1/72 y z - 1/36 y z + + 3 2 2 4 2 4 2 2 2 + + 1/9 y z + 5/288 x z - 5/288 y x z - 1/18 y z - 5/72 x z + + 2 4 2 2 2 2 4 + + 1/24 y z - 1/6 y z - 5/96 y x z , COEFF(1, -2, -1) = + + 4 2 4 4 4 4 3 4 4 3 + - 1/144 x y z - 1/432 x y z + 1/216 x y z + 1/54 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/108 x y z - 1/36 x y z + 1/144 x y z - 1/216 x y z + + 4 2 4 3 2 4 4 4 2 2 + + 1/108 x y z - 1/54 x y z + 1/432 x z + 1/36 x y z + + 4 3 2 4 4 3 3 2 4 + + 1/432 x y z + 1/36 y x z + 1/108 x z - 1/108 y x z - 1/54 y x z + + 3 2 3 3 4 2 2 3 + - 1/108 z y x + 1/108 z y x - 1/54 y x z + 1/9 y x z - 1/36 y x z + + 2 2 2 3 2 2 2 3 3 3 + - 1/9 y x z + 2/27 y x z - 1/36 y x z + 1/432 y x z + + 3 3 2 2 3 3 3 2 2 + - 1/54 y x z - 1/108 y x z + 1/108 z x + 2/27 y x z + + 2 3 3 4 2 3 3 2 3 3 + + 1/144 y x z - 1/108 x z - 2/27 z y x - 2/27 z y x + 1/54 z y x + + 2 2 3 2 2 3 3 3 + + 1/27 y x z + 1/27 z y x - 1/36 z y x + 1/36 z y x + 1/54 y x z + + 4 3 3 3 3 2 2 2 2 2 2 + - 1/432 x z - 1/216 y x z - 1/9 y x z + 1/9 y x z - 1/27 y x z + + 2 3 2 3 2 4 + - 1/27 y x z + 1/54 y x z - 1/27 x z - 1/27 x z + 1/108 y x z + + 3 3 2 3 2 4 3 2 4 + - 1/432 x z + 1/108 x z - 1/108 x z + 1/108 x z + 1/108 y x z + + 4 3 4 2 2 3 4 2 + - 1/108 x z + 1/432 x z + 1/27 x z - 1/432 y x z + 1/27 x z + + 3 2 2 2 4 2 3 4 3 3 4 + - 1/108 x z + 1/36 y x z - 1/144 y x z + 1/216 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(2, -2, -1) = 1/576 x y z + 1/1728 x y z - 1/864 x y z + + 4 3 4 4 2 4 2 3 + - 1/216 x y z + 1/432 x y z + 1/144 x y z - 1/576 x y z + + 4 3 3 4 2 4 3 2 4 4 + + 1/864 x y z - 1/432 x y z + 1/216 x y z - 1/1728 x z + + 4 2 2 4 3 2 4 4 + - 1/144 x y z - 1/1728 x y z - 1/288 y x z - 1/432 x z + + 3 3 2 4 3 2 3 + + 1/864 y x z + 1/864 y x z + 1/216 z y x - 1/216 z y x + + 3 4 2 2 3 2 2 2 + + 1/432 y x z - 1/72 y x z + 1/288 y x z + 1/144 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/108 y x z + 1/576 y x z - 1/864 y x z + 1/108 y x z + + 2 3 3 3 2 2 2 3 3 + + 1/1728 y x z - 1/216 z x - 1/216 y x z - 1/288 y x z + + 4 2 3 3 2 3 3 + + 1/432 x z + 1/108 z y x + 1/216 z y x - 1/108 z y x - 1/216 y x z + + 2 2 3 2 2 3 3 3 + - 1/432 z y x + 1/72 z y x - 1/72 z y x - 1/432 y x z + + 4 3 3 3 3 2 2 2 2 + + 1/1728 x z + 1/432 y x z + 1/72 y x z - 1/144 y x z + + 2 2 2 3 2 3 2 + + 1/432 y x z + 1/216 y x z - 1/864 y x z + 1/216 x z + 1/432 x z + + 4 3 3 2 3 2 4 3 + - 1/864 y x z + 1/864 x z - 1/1728 x z + 1/1728 x z - 1/864 x z + + 2 4 4 3 4 2 2 3 4 + - 1/1728 y x z + 1/864 x z - 1/864 x z - 1/432 x z + 1/864 y x z + + 2 3 2 2 2 4 2 3 4 + - 1/216 x z + 1/216 x z - 1/576 y x z + 1/288 y x z + + 3 3 4 4 2 4 4 4 + - 1/432 y x z , COEFF(-2, -1, -1) = - 1/288 x y z - 1/108 x y z + + 4 3 4 4 3 4 4 2 + + 1/216 x y z + 1/54 x y z - 1/27 x y z - 1/72 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + + 1/288 x y z - 1/216 x y z + 1/27 x y z - 1/54 x y z + + 4 4 4 2 2 4 3 2 4 4 + + 1/216 x z + 1/72 x y z + 1/108 x y z - 1/144 y x z + 1/54 x z + + 3 3 2 4 3 2 3 + + 1/54 y x z - 1/216 y x z + 2/27 z y x - 2/27 z y x + + 3 4 2 2 3 2 2 2 + + 1/108 y x z - 1/36 y x z + 1/144 y x z - 1/72 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/27 y x z - 1/288 y x z - 1/54 y x z + 1/27 y x z + + 2 3 3 3 2 2 2 3 3 4 2 + - 1/108 y x z - 1/27 z x + 1/54 y x z - 1/144 y x z - 1/54 x z + + 3 3 2 3 3 2 + + 1/27 z y x - 1/54 z y x - 1/27 z y x - 2/27 y x z + 1/27 z y x + + 2 3 2 2 3 3 3 4 3 + + 1/36 z y x - 1/36 z y x - 1/108 y x z - 1/216 x z + + 3 3 3 2 2 2 2 2 2 + + 1/108 y x z + 1/36 y x z + 1/72 y x z - 1/27 y x z + + 2 3 2 3 2 4 + + 2/27 y x z + 1/216 y x z + 1/27 x z - 1/54 x z - 1/54 y x z + + 3 3 2 3 2 4 3 2 4 + + 1/108 x z + 1/216 x z - 1/216 x z - 1/108 x z + 1/108 y x z + + 4 3 4 2 2 3 4 2 + + 1/108 x z - 1/108 x z + 1/54 x z + 1/54 y x z - 1/27 x z + + 3 2 2 2 4 2 3 4 3 3 4 + + 1/27 x z + 1/288 y x z + 1/144 y x z - 1/108 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(-1, -1, -1) = 1/72 x y z + 1/27 x y z - 1/54 x y z + + 4 3 4 4 2 4 2 3 + - 2/27 x y z + 4/27 x y z + 1/18 x y z - 1/72 x y z + + 4 3 3 4 2 4 3 2 4 4 + + 1/54 x y z - 4/27 x y z + 2/27 x y z - 1/54 x z + + 4 2 2 4 3 2 4 4 3 + - 1/18 x y z - 1/27 x y z + 1/18 y x z - 2/27 x z - 4/27 y x z + + 3 2 4 3 2 3 3 4 2 + + 2/27 y x z - 4/27 z y x + 4/27 z y x - 2/27 y x z + 2/9 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/18 y x z + 2/9 y x z + 8/27 y x z + 1/18 y x z + + 3 3 3 3 2 2 3 3 3 2 2 + + 1/27 y x z - 2/27 y x z + 4/27 y x z + 2/27 z x - 8/27 y x z + + 2 3 3 4 2 3 3 2 3 3 + + 1/72 y x z + 2/27 x z - 8/27 z y x + 8/27 z y x + 2/27 z y x + + 16 16 2 2 3 2 2 3 3 3 + + -- y x z - -- z y x - 1/18 z y x + 1/18 z y x + 2/27 y x z + 27 27 + + 4 3 3 3 3 2 2 2 2 16 2 2 + + 1/54 x z - 1/54 y x z - 2/9 y x z - 2/9 y x z + -- y x z + 27 + + 16 2 3 2 3 2 4 + - -- y x z - 2/27 y x z - 8/27 x z + 8/27 x z + 4/27 y x z + 27 + + 3 3 2 3 2 4 3 2 4 + - 1/54 x z - 2/27 x z + 2/27 x z + 2/27 x z - 4/27 y x z + + 4 3 4 2 2 3 4 2 + - 2/27 x z + 1/54 x z - 8/27 x z - 1/27 y x z + 8/27 x z + + 3 2 2 2 4 2 3 4 3 3 4 + - 2/27 x z - 1/18 y x z - 1/72 y x z + 1/54 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(0, -1, -1) = - 1/48 x y z - 1/18 x y z + 1/36 x y z + + 4 3 4 4 2 4 2 3 4 3 3 + + 1/9 x y z - 2/9 x y z - 1/12 x y z + 1/48 x y z - 1/36 x y z + + 4 2 4 3 2 4 4 4 2 2 4 3 + + 2/9 x y z - 1/9 x y z + 1/36 x z + 1/12 x y z + 1/18 x y z + + 4 3 2 4 2 2 2 2 2 3 + + 1/9 x z + 4/9 z - 5/36 y x z - 5/12 y x z - 5/48 y x z + + 2 3 4 3 2 2 4 2 3 3 + - 5/18 y x z + 1/9 z + 5/9 y x z - 1/9 x z - 1/9 z + 4/9 z y + + 2 3 2 2 4 3 2 2 + - 4/9 z - 5/9 z y x + 10/9 z y x - 8/9 y z - 1/36 x z + 5/12 y x z + + 2 2 2 3 2 3 2 3 + - 10/9 y x z - 1/3 y z + 5/36 y x z - 5/9 x z + 2/9 y z + + 2 3 3 3 2 3 4 3 4 3 2 + + 1/12 y z - 1/9 y z + 5/36 x z - 2/9 y z + 1/9 y z - 4/9 y z + + 2 4 2 4 2 2 2 2 4 + - 5/36 x z + 5/18 y x z + 8/9 y z + 5/9 x z - 1/12 y z + + 2 2 2 2 4 4 2 4 + + 1/3 y z + 5/48 y x z , COEFF(1, -1, -1) = 1/72 x y z + + 4 4 4 3 4 4 3 4 4 2 + + 1/27 x y z - 1/54 x y z - 2/27 x y z + 4/27 x y z + 1/18 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/72 x y z + 1/54 x y z - 4/27 x y z + 2/27 x y z + + 4 4 4 2 2 4 3 2 4 4 + - 1/54 x z - 1/18 x y z - 1/27 x y z - 1/18 y x z - 2/27 x z + + 3 3 2 4 3 2 3 3 4 + + 4/27 y x z + 2/27 y x z + 4/27 z y x - 4/27 z y x + 2/27 y x z + + 2 2 3 2 2 2 3 2 2 2 3 + - 2/9 y x z + 1/18 y x z + 2/9 y x z - 8/27 y x z + 1/18 y x z + + 3 3 3 3 2 2 3 3 3 2 2 + - 1/27 y x z + 2/27 y x z + 4/27 y x z - 2/27 z x - 8/27 y x z + + 2 3 3 4 2 3 3 2 3 3 + - 1/72 y x z + 2/27 x z + 8/27 z y x + 8/27 z y x - 2/27 z y x + + 16 16 2 2 3 2 2 3 3 3 + - -- y x z - -- z y x + 1/18 z y x - 1/18 z y x - 2/27 y x z + 27 27 + + 4 3 3 3 3 2 2 2 2 16 2 2 + + 1/54 x z + 1/54 y x z + 2/9 y x z - 2/9 y x z + -- y x z + 27 + + 16 2 3 2 3 2 4 + + -- y x z - 2/27 y x z + 8/27 x z + 8/27 x z - 4/27 y x z + 27 + + 3 3 2 3 2 4 3 2 4 + + 1/54 x z - 2/27 x z + 2/27 x z - 2/27 x z - 4/27 y x z + + 4 3 4 2 2 3 4 2 + + 2/27 x z - 1/54 x z - 8/27 x z + 1/27 y x z - 8/27 x z + + 3 2 2 2 4 2 3 4 3 3 4 + + 2/27 x z - 1/18 y x z + 1/72 y x z - 1/54 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(2, -1, -1) = - 1/288 x y z - 1/108 x y z + 1/216 x y z + + 4 3 4 4 2 4 2 3 + + 1/54 x y z - 1/27 x y z - 1/72 x y z + 1/288 x y z + + 4 3 3 4 2 4 3 2 4 4 + - 1/216 x y z + 1/27 x y z - 1/54 x y z + 1/216 x z + + 4 2 2 4 3 2 4 4 3 + + 1/72 x y z + 1/108 x y z + 1/144 y x z + 1/54 x z - 1/54 y x z + + 3 2 4 3 2 3 3 4 + - 1/216 y x z - 2/27 z y x + 2/27 z y x - 1/108 y x z + + 2 2 3 2 2 2 3 2 + + 1/36 y x z - 1/144 y x z - 1/72 y x z + 1/27 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/288 y x z + 1/54 y x z - 1/27 y x z - 1/108 y x z + + 3 3 2 2 2 3 3 4 2 3 + + 1/27 z x + 1/54 y x z + 1/144 y x z - 1/54 x z - 1/27 z y x + + 3 2 3 3 2 2 3 + - 1/54 z y x + 1/27 z y x + 2/27 y x z + 1/27 z y x - 1/36 z y x + + 2 2 3 3 3 4 3 3 3 3 + + 1/36 z y x + 1/108 y x z - 1/216 x z - 1/108 y x z + + 2 2 2 2 2 2 2 + - 1/36 y x z + 1/72 y x z - 1/27 y x z - 2/27 y x z + + 3 2 3 2 4 3 3 + + 1/216 y x z - 1/27 x z - 1/54 x z + 1/54 y x z - 1/108 x z + + 2 3 2 4 3 2 4 4 + + 1/216 x z - 1/216 x z + 1/108 x z + 1/108 y x z - 1/108 x z + + 3 4 2 2 3 4 2 3 2 + + 1/108 x z + 1/54 x z - 1/54 y x z + 1/27 x z - 1/27 x z + + 2 2 4 2 3 4 3 3 4 + + 1/288 y x z - 1/144 y x z + 1/108 y x z , COEFF(-2, 0, -1) = + + 4 4 4 3 4 4 3 4 + 5/288 x y z - 1/144 x y z - 1/36 x y z + 5/72 x y z + + 4 3 3 4 2 4 3 2 4 3 + + 1/144 x y z - 5/72 x y z + 1/36 x y z - 5/288 x y z + + 3 3 2 4 3 2 3 + - 5/144 y x z + 1/144 y x z - 5/36 z y x + 5/36 z y x + + 3 4 3 2 3 3 3 3 2 + - 1/72 y x z + 1/18 y x z + 5/144 y x z - 1/18 y x z + + 2 3 3 2 2 3 3 2 + + 5/288 y x z - 1/36 y x z - 1/18 z y x + 1/36 z y x + + 3 3 2 3 3 3 3 3 + + 1/18 z y x + 5/36 y x z - 5/72 z y x + 1/72 y x z - 1/72 y x z + + 2 2 2 3 2 3 4 + + 5/72 y x z - 5/36 y x z - 1/144 y x z + 5/144 y x z + + 2 4 3 4 3 3 4 + - 5/288 y x z - 5/144 y x z + 1/72 y x z , COEFF(-1, 0, -1) = + + 4 4 4 3 4 4 3 4 4 3 3 + - 5/72 x y z + 1/36 x y z + 1/9 x y z - 5/18 x y z - 1/36 x y z + + 4 2 4 3 2 4 3 3 3 2 4 + + 5/18 x y z - 1/9 x y z + 5/72 x y z + 5/18 y x z - 1/9 y x z + + 3 2 3 3 4 3 2 3 3 + + 5/18 z y x - 5/18 z y x + 1/9 y x z - 4/9 y x z - 5/72 y x z + + 3 3 2 2 3 3 2 2 3 3 2 + + 1/9 y x z - 5/18 y x z + 4/9 y x z + 4/9 z y x - 4/9 z y x + + 3 3 2 3 3 3 3 3 + - 1/9 z y x - 10/9 y x z + 10/9 z y x - 1/9 y x z + 1/36 y x z + + 2 2 2 3 2 3 4 2 4 + - 10/9 y x z + 10/9 y x z + 1/9 y x z - 5/18 y x z + 5/18 y x z + + 3 4 3 3 4 3 3 + + 5/72 y x z - 1/36 y x z , COEFF(0, 0, -1) = 1/6 y z + + 4 3 3 4 3 2 4 4 4 3 2 2 + + 1/24 x y z + 1/6 x y z + 5/48 x y z + 5/12 y z - 5/6 y x z + + 4 4 3 4 25 2 2 3 2 3 3 + + 5/12 x y z - 1/24 x y z + -- y x z - 5/24 y x z - 5/12 y z + 12 + + 2 4 3 25 2 3 3 2 25 2 4 3 + - 5/3 y z - 5/48 x y z + -- y x z + 2/3 y z - -- y x z - 2/3 z y + 48 48 + + 3 2 4 4 3 25 2 3 4 + + 5/3 y z + 5/24 y x z - 1/6 x y z - -- z y x - 1/6 y z + 12 + + 3 2 4 2 4 4 + + 5/6 z y x - 5/12 x y z , COEFF(1, 0, -1) = - 5/72 x y z + + 4 3 4 4 3 4 4 3 3 4 2 + + 1/36 x y z + 1/9 x y z - 5/18 x y z - 1/36 x y z + 5/18 x y z + + 4 3 2 4 3 3 3 2 4 3 + - 1/9 x y z + 5/72 x y z - 5/18 y x z - 1/9 y x z - 5/18 z y x + + 2 3 3 4 3 2 3 3 3 3 2 + + 5/18 z y x - 1/9 y x z + 4/9 y x z + 5/72 y x z - 1/9 y x z + + 2 3 3 2 2 3 3 2 3 3 + - 5/18 y x z + 4/9 y x z - 4/9 z y x - 4/9 z y x + 1/9 z y x + + 2 3 3 3 3 3 2 2 + + 10/9 y x z + 10/9 z y x + 1/9 y x z - 1/36 y x z - 10/9 y x z + + 2 3 2 3 4 2 4 3 4 + - 10/9 y x z + 1/9 y x z + 5/18 y x z + 5/18 y x z - 5/72 y x z + + 3 3 4 4 4 4 3 4 + + 1/36 y x z , COEFF(2, 0, -1) = 5/288 x y z - 1/144 x y z + + 4 3 4 4 3 3 4 2 + - 1/36 x y z + 5/72 x y z + 1/144 x y z - 5/72 x y z + + 4 3 2 4 3 3 3 2 4 + + 1/36 x y z - 5/288 x y z + 5/144 y x z + 1/144 y x z + + 3 2 3 3 4 3 2 3 3 + + 5/36 z y x - 5/36 z y x + 1/72 y x z - 1/18 y x z - 5/144 y x z + + 3 3 2 2 3 3 2 2 3 + + 1/18 y x z + 5/288 y x z - 1/36 y x z + 1/18 z y x + + 3 2 3 3 2 3 3 + + 1/36 z y x - 1/18 z y x - 5/36 y x z - 5/72 z y x - 1/72 y x z + + 3 3 3 2 2 2 3 2 3 + + 1/72 y x z + 5/72 y x z + 5/36 y x z - 1/144 y x z + + 4 2 4 3 4 3 3 4 + - 5/144 y x z - 5/288 y x z + 5/144 y x z - 1/72 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(-2, 1, -1) = 1/288 x y z - 1/108 x y z + 1/216 x y z + + 4 3 4 4 2 4 2 3 + + 1/54 x y z - 1/27 x y z + 1/72 x y z - 1/288 x y z + + 4 3 3 4 2 4 3 2 4 4 + - 1/216 x y z + 1/27 x y z - 1/54 x y z - 1/216 x z + + 4 2 2 4 3 2 4 4 3 + - 1/72 x y z + 1/108 x y z + 1/144 y x z - 1/54 x z + 1/54 y x z + + 3 2 4 3 2 3 3 4 + - 1/216 y x z + 2/27 z y x - 2/27 z y x + 1/108 y x z + + 2 2 3 2 2 2 3 2 + + 1/36 y x z - 1/144 y x z + 1/72 y x z - 1/27 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/288 y x z - 1/54 y x z + 1/27 y x z - 1/108 y x z + + 3 3 2 2 2 3 3 4 2 3 + + 1/27 z x + 1/54 y x z + 1/144 y x z + 1/54 x z + 1/27 z y x + + 3 2 3 3 2 2 3 + - 1/54 z y x - 1/27 z y x - 2/27 y x z + 1/27 z y x - 1/36 z y x + + 2 2 3 3 3 4 3 3 3 3 + + 1/36 z y x - 1/108 y x z + 1/216 x z + 1/108 y x z + + 2 2 2 2 2 2 2 + - 1/36 y x z - 1/72 y x z - 1/27 y x z + 2/27 y x z + + 3 2 3 2 4 3 3 + + 1/216 y x z - 1/27 x z + 1/54 x z - 1/54 y x z - 1/108 x z + + 2 3 2 4 3 2 4 4 + - 1/216 x z + 1/216 x z + 1/108 x z + 1/108 y x z - 1/108 x z + + 3 4 2 2 3 4 2 3 2 + + 1/108 x z - 1/54 x z + 1/54 y x z + 1/27 x z - 1/27 x z + + 2 2 4 2 3 4 3 3 4 + - 1/288 y x z - 1/144 y x z - 1/108 y x z , COEFF(-1, 1, -1) = + + 4 2 4 4 4 4 3 4 4 3 4 + - 1/72 x y z + 1/27 x y z - 1/54 x y z - 2/27 x y z + 4/27 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/18 x y z + 1/72 x y z + 1/54 x y z - 4/27 x y z + + 4 3 2 4 4 4 2 2 4 3 2 4 + + 2/27 x y z + 1/54 x z + 1/18 x y z - 1/27 x y z - 1/18 y x z + + 4 3 3 2 4 3 2 3 + + 2/27 x z - 4/27 y x z + 2/27 y x z - 4/27 z y x + 4/27 z y x + + 3 4 2 2 3 2 2 2 3 2 + - 2/27 y x z - 2/9 y x z + 1/18 y x z - 2/9 y x z + 8/27 y x z + + 2 2 3 3 3 3 3 2 2 3 3 + - 1/18 y x z + 1/27 y x z - 2/27 y x z + 4/27 y x z - 2/27 z x + + 3 2 2 2 3 3 4 2 3 3 2 + - 8/27 y x z - 1/72 y x z - 2/27 x z - 8/27 z y x + 8/27 z y x + + 3 3 16 16 2 2 3 2 2 3 + + 2/27 z y x + -- y x z - -- z y x + 1/18 z y x - 1/18 z y x + 27 27 + + 3 3 4 3 3 3 3 2 2 2 2 + + 2/27 y x z - 1/54 x z - 1/54 y x z + 2/9 y x z + 2/9 y x z + + 16 2 2 16 2 3 2 3 2 + + -- y x z - -- y x z - 2/27 y x z + 8/27 x z - 8/27 x z + 27 27 + + 4 3 3 2 3 2 4 3 + + 4/27 y x z + 1/54 x z + 2/27 x z - 2/27 x z - 2/27 x z + + 2 4 4 3 4 2 2 3 4 + - 4/27 y x z + 2/27 x z - 1/54 x z + 8/27 x z - 1/27 y x z + + 2 3 2 2 2 4 2 3 4 3 3 4 + - 8/27 x z + 2/27 x z + 1/18 y x z + 1/72 y x z + 1/54 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(0, 1, -1) = 1/48 x y z - 1/18 x y z + 1/36 x y z + + 4 3 4 4 2 4 2 3 4 3 3 + + 1/9 x y z - 2/9 x y z + 1/12 x y z - 1/48 x y z - 1/36 x y z + + 4 2 4 3 2 4 4 4 2 2 4 3 + + 2/9 x y z - 1/9 x y z - 1/36 x z - 1/12 x y z + 1/18 x y z + + 4 3 2 4 2 2 2 2 2 3 + - 1/9 x z - 4/9 z - 5/36 y x z + 5/12 y x z + 5/48 y x z + + 2 3 4 3 2 2 4 2 3 3 + - 5/18 y x z - 1/9 z + 5/9 y x z + 1/9 x z + 1/9 z + 4/9 z y + + 2 3 2 2 4 3 2 2 + + 4/9 z - 5/9 z y x + 10/9 z y x - 8/9 y z + 1/36 x z - 5/12 y x z + + 2 2 2 3 2 3 2 3 + - 10/9 y x z + 1/3 y z + 5/36 y x z + 5/9 x z + 2/9 y z + + 2 3 3 3 2 3 4 3 4 3 2 + - 1/12 y z - 1/9 y z - 5/36 x z - 2/9 y z + 1/9 y z - 4/9 y z + + 2 4 2 4 2 2 2 2 4 + + 5/36 x z + 5/18 y x z + 8/9 y z - 5/9 x z + 1/12 y z + + 2 2 2 2 4 4 2 4 + - 1/3 y z - 5/48 y x z , COEFF(1, 1, -1) = - 1/72 x y z + + 4 4 4 3 4 4 3 4 4 2 + + 1/27 x y z - 1/54 x y z - 2/27 x y z + 4/27 x y z - 1/18 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + + 1/72 x y z + 1/54 x y z - 4/27 x y z + 2/27 x y z + + 4 4 4 2 2 4 3 2 4 4 + + 1/54 x z + 1/18 x y z - 1/27 x y z + 1/18 y x z + 2/27 x z + + 3 3 2 4 3 2 3 3 4 + + 4/27 y x z + 2/27 y x z + 4/27 z y x - 4/27 z y x + 2/27 y x z + + 2 2 3 2 2 2 3 2 2 2 3 + + 2/9 y x z - 1/18 y x z - 2/9 y x z - 8/27 y x z - 1/18 y x z + + 3 3 3 3 2 2 3 3 3 2 2 + - 1/27 y x z + 2/27 y x z + 4/27 y x z + 2/27 z x - 8/27 y x z + + 2 3 3 4 2 3 3 2 3 3 + + 1/72 y x z - 2/27 x z + 8/27 z y x + 8/27 z y x - 2/27 z y x + + 16 16 2 2 3 2 2 3 3 3 + - -- y x z - -- z y x - 1/18 z y x + 1/18 z y x - 2/27 y x z + 27 27 + + 4 3 3 3 3 2 2 2 2 16 2 2 + - 1/54 x z + 1/54 y x z - 2/9 y x z + 2/9 y x z + -- y x z + 27 + + 16 2 3 2 3 2 4 + + -- y x z - 2/27 y x z - 8/27 x z - 8/27 x z - 4/27 y x z + 27 + + 3 3 2 3 2 4 3 2 4 + - 1/54 x z + 2/27 x z - 2/27 x z + 2/27 x z - 4/27 y x z + + 4 3 4 2 2 3 4 2 + - 2/27 x z + 1/54 x z + 8/27 x z + 1/27 y x z + 8/27 x z + + 3 2 2 2 4 2 3 4 3 3 4 + - 2/27 x z + 1/18 y x z - 1/72 y x z - 1/54 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(2, 1, -1) = 1/288 x y z - 1/108 x y z + 1/216 x y z + + 4 3 4 4 2 4 2 3 + + 1/54 x y z - 1/27 x y z + 1/72 x y z - 1/288 x y z + + 4 3 3 4 2 4 3 2 4 4 + - 1/216 x y z + 1/27 x y z - 1/54 x y z - 1/216 x z + + 4 2 2 4 3 2 4 4 3 + - 1/72 x y z + 1/108 x y z - 1/144 y x z - 1/54 x z - 1/54 y x z + + 3 2 4 3 2 3 3 4 + - 1/216 y x z - 2/27 z y x + 2/27 z y x - 1/108 y x z + + 2 2 3 2 2 2 3 2 + - 1/36 y x z + 1/144 y x z + 1/72 y x z + 1/27 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/288 y x z + 1/54 y x z - 1/27 y x z - 1/108 y x z + + 3 3 2 2 2 3 3 4 2 3 + - 1/27 z x + 1/54 y x z - 1/144 y x z + 1/54 x z - 1/27 z y x + + 3 2 3 3 2 2 3 + - 1/54 z y x + 1/27 z y x + 2/27 y x z + 1/27 z y x + 1/36 z y x + + 2 2 3 3 3 4 3 3 3 3 + - 1/36 z y x + 1/108 y x z + 1/216 x z - 1/108 y x z + + 2 2 2 2 2 2 2 + + 1/36 y x z - 1/72 y x z - 1/27 y x z - 2/27 y x z + + 3 2 3 2 4 3 3 + + 1/216 y x z + 1/27 x z + 1/54 x z + 1/54 y x z + 1/108 x z + + 2 3 2 4 3 2 4 4 + - 1/216 x z + 1/216 x z - 1/108 x z + 1/108 y x z + 1/108 x z + + 3 4 2 2 3 4 2 3 2 + - 1/108 x z - 1/54 x z - 1/54 y x z - 1/27 x z + 1/27 x z + + 2 2 4 2 3 4 3 3 4 + - 1/288 y x z + 1/144 y x z + 1/108 y x z , COEFF(-2, 2, -1) = + + 4 2 4 4 4 4 3 4 4 3 + - 1/576 x y z + 1/1728 x y z - 1/864 x y z - 1/216 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/432 x y z - 1/144 x y z + 1/576 x y z + 1/864 x y z + + 4 2 4 3 2 4 4 4 2 2 + - 1/432 x y z + 1/216 x y z + 1/1728 x z + 1/144 x y z + + 4 3 2 4 4 3 + - 1/1728 x y z - 1/288 y x z + 1/432 x z - 1/864 y x z + + 3 2 4 3 2 3 3 4 + + 1/864 y x z - 1/216 z y x + 1/216 z y x - 1/432 y x z + + 2 2 3 2 2 2 3 2 + - 1/72 y x z + 1/288 y x z - 1/144 y x z + 1/108 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/576 y x z + 1/864 y x z - 1/108 y x z + 1/1728 y x z + + 3 3 2 2 2 3 3 4 2 + - 1/216 z x - 1/216 y x z - 1/288 y x z - 1/432 x z + + 3 3 2 3 3 + - 1/108 z y x + 1/216 z y x + 1/108 z y x + 1/216 y x z + + 2 2 3 2 2 3 3 3 + - 1/432 z y x + 1/72 z y x - 1/72 z y x + 1/432 y x z + + 4 3 3 3 3 2 2 2 2 + - 1/1728 x z - 1/432 y x z + 1/72 y x z + 1/144 y x z + + 2 2 2 3 2 3 2 + + 1/432 y x z - 1/216 y x z - 1/864 y x z + 1/216 x z - 1/432 x z + + 4 3 3 2 3 2 4 3 + + 1/864 y x z + 1/864 x z + 1/1728 x z - 1/1728 x z - 1/864 x z + + 2 4 4 3 4 2 2 3 4 + - 1/1728 y x z + 1/864 x z - 1/864 x z + 1/432 x z - 1/864 y x z + + 2 3 2 2 2 4 2 3 4 + - 1/216 x z + 1/216 x z + 1/576 y x z + 1/288 y x z + + 3 3 4 4 2 4 4 4 + + 1/432 y x z , COEFF(-1, 2, -1) = 1/144 x y z - 1/432 x y z + + 4 3 4 4 3 4 4 2 + + 1/216 x y z + 1/54 x y z - 1/108 x y z + 1/36 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/144 x y z - 1/216 x y z + 1/108 x y z - 1/54 x y z + + 4 4 4 2 2 4 3 2 4 4 + - 1/432 x z - 1/36 x y z + 1/432 x y z + 1/36 y x z - 1/108 x z + + 3 3 2 4 3 2 3 + + 1/108 y x z - 1/54 y x z + 1/108 z y x - 1/108 z y x + + 3 4 2 2 3 2 2 2 3 2 + + 1/54 y x z + 1/9 y x z - 1/36 y x z + 1/9 y x z - 2/27 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/36 y x z - 1/432 y x z + 1/54 y x z - 1/108 y x z + + 3 3 2 2 2 3 3 4 2 3 + + 1/108 z x + 2/27 y x z + 1/144 y x z + 1/108 x z + 2/27 z y x + + 3 2 3 3 2 2 3 + - 2/27 z y x - 1/54 z y x - 1/27 y x z + 1/27 z y x - 1/36 z y x + + 2 2 3 3 3 4 3 3 3 3 + + 1/36 z y x - 1/54 y x z + 1/432 x z + 1/216 y x z + + 2 2 2 2 2 2 2 3 2 3 + - 1/9 y x z - 1/9 y x z - 1/27 y x z + 1/27 y x z + 1/54 y x z + + 2 4 3 3 2 3 + - 1/27 x z + 1/27 x z - 1/108 y x z - 1/432 x z - 1/108 x z + + 2 4 3 2 4 4 3 4 + + 1/108 x z + 1/108 x z + 1/108 y x z - 1/108 x z + 1/432 x z + + 2 2 3 4 2 3 2 2 2 4 + - 1/27 x z + 1/432 y x z + 1/27 x z - 1/108 x z - 1/36 y x z + + 2 3 4 3 3 4 4 2 4 + - 1/144 y x z - 1/216 y x z , COEFF(0, 2, -1) = - 1/96 x y z + + 4 4 4 3 4 4 3 4 + + 1/288 x y z - 1/144 x y z - 1/36 x y z + 1/72 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/24 x y z + 1/96 x y z + 1/144 x y z - 1/72 x y z + + 4 3 2 4 4 4 2 2 4 3 4 + + 1/36 x y z + 1/288 x z + 1/24 x y z - 1/288 x y z + 1/72 x z + + 3 2 4 2 2 2 2 2 3 2 3 + + 1/18 z + 5/144 y x z - 5/24 y x z - 5/96 y x z + 5/288 y x z + + 4 3 2 2 4 2 3 3 2 + + 1/72 z - 5/36 y x z - 1/72 x z - 1/72 z - 1/9 z y - 1/18 z + + 3 2 2 4 3 2 2 + + 5/36 z y x - 5/72 z y x + 1/18 y z - 1/288 x z + 5/24 y x z + + 2 2 2 3 2 3 2 3 + + 5/72 y x z - 1/6 y z - 5/144 y x z - 5/72 x z - 1/72 y z + + 2 3 3 3 2 3 4 3 4 + + 1/24 y z + 1/36 y z + 5/288 x z + 1/72 y z - 1/36 y z + + 3 2 2 4 2 4 2 2 2 + + 1/9 y z - 5/288 x z - 5/288 y x z - 1/18 y z + 5/72 x z + + 2 4 2 2 2 2 4 4 2 4 + - 1/24 y z + 1/6 y z + 5/96 y x z , COEFF(1, 2, -1) = 1/144 x y z + + 4 4 4 3 4 4 3 4 + - 1/432 x y z + 1/216 x y z + 1/54 x y z - 1/108 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/36 x y z - 1/144 x y z - 1/216 x y z + 1/108 x y z + + 4 3 2 4 4 4 2 2 4 3 + - 1/54 x y z - 1/432 x z - 1/36 x y z + 1/432 x y z + + 2 4 4 3 3 2 4 3 + - 1/36 y x z - 1/108 x z - 1/108 y x z - 1/54 y x z - 1/108 z y x + + 2 3 3 4 2 2 3 2 2 2 + + 1/108 z y x - 1/54 y x z - 1/9 y x z + 1/36 y x z + 1/9 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 2/27 y x z + 1/36 y x z + 1/432 y x z - 1/54 y x z + + 2 3 3 3 2 2 2 3 3 + - 1/108 y x z - 1/108 z x + 2/27 y x z - 1/144 y x z + + 4 2 3 3 2 3 3 + + 1/108 x z - 2/27 z y x - 2/27 z y x + 1/54 z y x + 1/27 y x z + + 2 2 3 2 2 3 3 3 4 3 + + 1/27 z y x + 1/36 z y x - 1/36 z y x + 1/54 y x z + 1/432 x z + + 3 3 3 2 2 2 2 2 2 2 + - 1/216 y x z + 1/9 y x z - 1/9 y x z - 1/27 y x z - 1/27 y x z + + 3 2 3 2 4 3 3 + + 1/54 y x z + 1/27 x z + 1/27 x z + 1/108 y x z + 1/432 x z + + 2 3 2 4 3 2 4 4 + - 1/108 x z + 1/108 x z - 1/108 x z + 1/108 y x z + 1/108 x z + + 3 4 2 2 3 4 2 3 2 + - 1/432 x z - 1/27 x z - 1/432 y x z - 1/27 x z + 1/108 x z + + 2 2 4 2 3 4 3 3 4 + - 1/36 y x z + 1/144 y x z + 1/216 y x z , COEFF(2, 2, -1) = + + 4 2 4 4 4 4 3 4 4 3 + - 1/576 x y z + 1/1728 x y z - 1/864 x y z - 1/216 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/432 x y z - 1/144 x y z + 1/576 x y z + 1/864 x y z + + 4 2 4 3 2 4 4 4 2 2 + - 1/432 x y z + 1/216 x y z + 1/1728 x z + 1/144 x y z + + 4 3 2 4 4 3 + - 1/1728 x y z + 1/288 y x z + 1/432 x z + 1/864 y x z + + 3 2 4 3 2 3 3 4 + + 1/864 y x z + 1/216 z y x - 1/216 z y x + 1/432 y x z + + 2 2 3 2 2 2 3 2 + + 1/72 y x z - 1/288 y x z - 1/144 y x z - 1/108 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/576 y x z - 1/864 y x z + 1/108 y x z + 1/1728 y x z + + 3 3 2 2 2 3 3 4 2 + + 1/216 z x - 1/216 y x z + 1/288 y x z - 1/432 x z + + 3 3 2 3 3 + + 1/108 z y x + 1/216 z y x - 1/108 z y x - 1/216 y x z + + 2 2 3 2 2 3 3 3 + - 1/432 z y x - 1/72 z y x + 1/72 z y x - 1/432 y x z + + 4 3 3 3 3 2 2 2 2 + - 1/1728 x z + 1/432 y x z - 1/72 y x z + 1/144 y x z + + 2 2 2 3 2 3 2 + + 1/432 y x z + 1/216 y x z - 1/864 y x z - 1/216 x z - 1/432 x z + + 4 3 3 2 3 2 4 3 + - 1/864 y x z - 1/864 x z + 1/1728 x z - 1/1728 x z + 1/864 x z + + 2 4 4 3 4 2 2 3 4 + - 1/1728 y x z - 1/864 x z + 1/864 x z + 1/432 x z + 1/864 y x z + + 2 3 2 2 2 4 2 3 4 + + 1/216 x z - 1/216 x z + 1/576 y x z - 1/288 y x z + + 3 3 4 4 2 4 4 4 + - 1/432 y x z , COEFF(-2, -2, 0) = - 1/384 x y z - 1/1152 x y z + + 4 3 4 4 2 4 3 2 4 4 + + 1/576 x y z + 5/1152 x y z - 5/576 x y z + 1/1152 x z + + 4 2 2 3 2 4 4 + + 5/384 x y z + 1/144 y x + 1/144 x - 1/192 y x z + 1/288 x + + 3 2 4 2 3 3 4 + - 1/576 y x z - 5/576 z y x + 1/288 y x z - 1/144 y x + + 2 2 2 3 2 3 3 2 3 2 2 + - 5/384 y x z - 5/288 y x z + 5/288 y x z + 5/576 y x z + + 4 2 3 3 2 3 3 2 + - 5/1152 x z - 1/144 x + 1/72 y x + 1/48 y x - 1/144 y x + + 3 3 2 2 2 3 2 2 2 + - 1/72 y x - 1/288 x - 5/192 z y x - 1/48 y x + 5/192 y x z + + 2 2 2 4 2 4 + - 5/1152 y x z + 5/576 y x z - 1/576 y x z - 1/1152 x z + + 2 4 4 3 4 2 2 3 4 + + 1/1152 y x z + 1/576 x z - 1/576 x z + 5/1152 x z + 1/576 y x z + + 2 3 2 2 2 2 2 2 4 + - 5/576 x z + 5/576 x z + 1/96 y x + 1/288 y x + 1/384 y x z + + 2 3 4 3 3 4 4 4 2 4 3 + + 1/192 y x z - 1/288 y x z - 1/288 x y - 1/96 x y + 1/144 x y , + + 4 2 4 4 4 4 3 4 + COEFF(-1, -2, 0) = 1/96 x y z + 1/288 x y z - 1/144 x y z + + 4 2 4 3 2 4 4 4 2 2 3 + - 5/288 x y z + 5/144 x y z - 1/288 x z - 5/96 x y z - 1/72 y x + + 2 4 4 3 2 4 2 3 + - 1/18 x + 1/24 y x z - 1/72 x + 1/36 y x z + 5/288 z y x + + 3 4 2 2 2 3 2 3 3 2 + - 1/36 y x z + 1/18 y x + 5/24 y x z + 5/36 y x z - 5/144 y x z + + 3 2 2 4 2 3 3 2 3 + - 5/36 y x z + 5/288 x z + 1/72 x - 1/9 y x - 1/24 y x + + 3 2 3 3 2 2 2 3 2 + + 1/9 y x + 1/36 y x + 1/18 x + 5/96 z y x + 1/6 y x + + 2 2 2 2 2 4 2 4 + - 5/24 y x z + 5/72 y x z - 5/72 y x z + 1/72 y x z + 1/72 x z + + 2 4 4 3 4 2 2 3 4 + - 1/72 y x z - 1/72 x z + 1/288 x z - 5/72 x z - 1/288 y x z + + 2 3 2 2 2 2 2 2 4 + + 5/72 x z - 5/288 x z - 1/6 y x - 1/18 y x - 1/24 y x z + + 2 3 4 3 3 4 4 4 2 4 3 + - 1/96 y x z + 1/144 y x z + 1/72 x y + 1/24 x y - 1/36 x y , + + 4 2 4 4 4 4 3 4 + COEFF(0, -2, 0) = - 1/64 x y z - 1/192 x y z + 1/96 x y z + + 4 2 4 3 2 4 4 4 2 2 4 + + 5/192 x y z - 5/96 x y z + 1/192 x z + 5/64 x y z + 1/48 x + + 3 2 4 25 2 2 2 4 25 3 2 2 + - 1/12 y - 5/96 y x z - -- y x z + 1/48 z + -- y x z + 64 96 + + 4 2 3 2 2 3 2 2 + - 5/192 x z + 1/6 y + 1/12 - 1/4 y - 5/48 z - 5/24 y x - 5/48 x + + 25 2 2 4 3 4 3 2 2 4 + - --- y x z - 1/48 y z + 1/24 y z - 5/24 y z - 5/192 x z + 192 + + 2 4 2 25 2 2 2 4 2 2 + + 5/192 y x z + 5/48 y z + --- x z - 1/16 y z + 5/16 y z + 192 + + 2 2 2 2 2 4 4 4 2 + + 5/16 y x + 5/48 y x + 5/64 y x z - 1/48 x y - 1/16 x y + + 4 3 4 2 4 4 4 + + 1/24 x y , COEFF(1, -2, 0) = 1/96 x y z + 1/288 x y z + + 4 3 4 4 2 4 3 2 4 4 + - 1/144 x y z - 5/288 x y z + 5/144 x y z - 1/288 x z + + 4 2 2 3 2 4 4 + - 5/96 x y z + 1/72 y x + 1/18 x - 1/24 y x z - 1/72 x + + 3 2 4 2 3 3 4 2 2 2 + + 1/36 y x z - 5/288 z y x + 1/36 y x z - 1/18 y x + 5/24 y x z + + 3 2 3 3 2 3 2 2 4 2 3 + - 5/36 y x z + 5/144 y x z - 5/36 y x z + 5/288 x z - 1/72 x + + 3 2 3 3 2 3 3 2 2 2 3 + + 1/9 y x + 1/24 y x + 1/9 y x - 1/36 y x + 1/18 x - 5/96 z y x + + 2 2 2 2 2 2 4 + - 1/6 y x + 5/24 y x z + 5/72 y x z + 5/72 y x z - 1/72 y x z + + 2 4 2 4 4 3 4 2 2 + + 1/72 x z - 1/72 y x z + 1/72 x z - 1/288 x z - 5/72 x z + + 3 4 2 3 2 2 2 2 + + 1/288 y x z - 5/72 x z + 5/288 x z - 1/6 y x - 1/18 y x + + 2 2 4 2 3 4 3 3 4 4 4 2 + - 1/24 y x z + 1/96 y x z - 1/144 y x z + 1/72 x y + 1/24 x y + + 4 3 4 2 4 4 4 + - 1/36 x y , COEFF(2, -2, 0) = - 1/384 x y z - 1/1152 x y z + + 4 3 4 4 2 4 3 2 4 4 + + 1/576 x y z + 5/1152 x y z - 5/576 x y z + 1/1152 x z + + 4 2 2 3 2 4 4 + + 5/384 x y z - 1/144 y x - 1/144 x + 1/192 y x z + 1/288 x + + 3 2 4 2 3 3 4 + - 1/576 y x z + 5/576 z y x - 1/288 y x z + 1/144 y x + + 2 2 2 3 2 3 3 2 3 2 2 + - 5/384 y x z + 5/288 y x z - 5/288 y x z + 5/576 y x z + + 4 2 3 3 2 3 3 2 + - 5/1152 x z + 1/144 x - 1/72 y x - 1/48 y x - 1/144 y x + + 3 3 2 2 2 3 2 2 2 + + 1/72 y x - 1/288 x + 5/192 z y x + 1/48 y x - 5/192 y x z + + 2 2 2 4 2 4 + - 5/1152 y x z - 5/576 y x z + 1/576 y x z - 1/1152 x z + + 2 4 4 3 4 2 2 3 4 + + 1/1152 y x z - 1/576 x z + 1/576 x z + 5/1152 x z - 1/576 y x z + + 2 3 2 2 2 2 2 2 4 + + 5/576 x z - 5/576 x z + 1/96 y x + 1/288 y x + 1/384 y x z + + 2 3 4 3 3 4 4 4 2 4 3 + - 1/192 y x z + 1/288 y x z - 1/288 x y - 1/96 x y + 1/144 x y , + + 4 2 4 4 4 4 3 4 + COEFF(-2, -1, 0) = 1/192 x y z + 1/72 x y z - 1/144 x y z + + 4 2 4 3 2 4 4 4 2 2 3 + - 5/72 x y z + 5/144 x y z - 1/144 x z - 5/192 x y z - 1/9 y x + + 2 4 4 3 2 4 2 3 + - 1/18 x + 1/96 y x z - 1/36 x + 1/144 y x z + 5/36 z y x + + 3 4 2 2 2 3 2 3 3 2 + - 1/72 y x z + 1/9 y x + 5/192 y x z + 5/72 y x z - 5/72 y x z + + 3 2 2 4 2 3 3 2 3 + - 5/144 y x z + 5/144 x z + 1/18 x - 1/18 y x - 1/24 y x + + 3 2 3 3 2 2 2 3 2 + + 1/36 y x + 1/18 y x + 1/36 x + 5/96 z y x + 1/24 y x + + 2 2 2 2 2 4 2 4 + - 5/96 y x z + 5/72 y x z - 5/36 y x z + 1/36 y x z + 1/144 x z + + 2 4 4 3 4 2 2 3 4 + - 1/72 y x z - 1/72 x z + 1/72 x z - 5/144 x z - 1/36 y x z + + 2 3 2 2 2 2 2 2 4 + + 5/72 x z - 5/72 x z - 1/48 y x - 1/18 y x - 1/192 y x z + + 2 3 4 3 3 4 4 4 2 4 3 + - 1/96 y x z + 1/72 y x z + 1/18 x y + 1/48 x y - 1/36 x y , + + 4 2 4 4 4 4 3 4 + COEFF(-1, -1, 0) = - 1/48 x y z - 1/18 x y z + 1/36 x y z + + 4 2 4 3 2 4 4 4 2 2 3 + + 5/18 x y z - 5/36 x y z + 1/36 x z + 5/48 x y z + 2/9 y x + + 2 4 4 3 2 4 2 3 + + 4/9 x - 1/12 y x z + 1/9 x - 1/9 y x z - 5/18 z y x + + 3 4 2 2 2 3 2 3 3 2 + + 1/9 y x z - 8/9 y x - 5/12 y x z - 5/9 y x z + 5/36 y x z + + 3 2 2 4 2 3 3 2 3 3 2 + + 5/9 y x z - 5/36 x z - 1/9 x + 4/9 y x + 1/12 y x - 4/9 y x + + 3 3 2 2 2 3 2 2 2 + - 1/9 y x - 4/9 x - 5/48 z y x - 1/3 y x + 5/12 y x z + + 2 2 2 4 2 4 2 4 + - 10/9 y x z + 10/9 y x z - 2/9 y x z - 1/9 x z + 2/9 y x z + + 4 3 4 2 2 3 4 2 3 2 + + 1/9 x z - 1/36 x z + 5/9 x z + 1/18 y x z - 5/9 x z + 5/36 x z + + 2 2 2 2 2 4 2 3 4 3 3 4 + + 1/3 y x + 8/9 y x + 1/12 y x z + 1/48 y x z - 1/36 y x z + + 4 4 2 4 3 4 2 4 + - 2/9 x y - 1/12 x y + 1/9 x y , COEFF(0, -1, 0) = 1/32 x y z + + 4 4 4 3 4 4 2 4 3 2 4 4 + + 1/12 x y z - 1/24 x y z - 5/12 x y z + 5/24 x y z - 1/24 x z + + 4 2 2 4 3 2 4 25 2 2 2 4 + - 5/32 x y z - 1/6 x + 4/3 y + 5/24 y x z + -- y x z - 1/6 z + 32 + + 25 3 2 2 4 2 3 2 2 3 2 + - -- y x z - 2/3 + 5/24 x z - 2/3 y + 1/2 y + 5/6 z + 5/6 y x + 24 + + 2 25 2 2 4 3 4 3 2 2 4 + + 5/6 x + -- y x z + 1/3 y z - 1/6 y z + 5/6 y z + 5/24 x z + 12 + + 2 4 2 25 2 2 2 4 2 2 2 2 + - 5/12 y x z - 5/3 y z - -- x z + 1/8 y z - 5/8 y z - 5/8 y x + 24 + + 2 2 2 4 4 4 2 4 3 + - 5/3 y x - 5/32 y x z + 1/3 x y + 1/8 x y - 1/6 x y , + + 4 2 4 4 4 4 3 4 + COEFF(1, -1, 0) = - 1/48 x y z - 1/18 x y z + 1/36 x y z + + 4 2 4 3 2 4 4 4 2 2 3 + + 5/18 x y z - 5/36 x y z + 1/36 x z + 5/48 x y z - 2/9 y x + + 2 4 4 3 2 4 2 3 + - 4/9 x + 1/12 y x z + 1/9 x - 1/9 y x z + 5/18 z y x + + 3 4 2 2 2 3 2 3 3 2 + - 1/9 y x z + 8/9 y x - 5/12 y x z + 5/9 y x z - 5/36 y x z + + 3 2 2 4 2 3 3 2 3 3 2 + + 5/9 y x z - 5/36 x z + 1/9 x - 4/9 y x - 1/12 y x - 4/9 y x + + 3 3 2 2 2 3 2 2 2 + + 1/9 y x - 4/9 x + 5/48 z y x + 1/3 y x - 5/12 y x z + + 2 2 2 4 2 4 2 4 + - 10/9 y x z - 10/9 y x z + 2/9 y x z - 1/9 x z + 2/9 y x z + + 4 3 4 2 2 3 4 2 3 2 + - 1/9 x z + 1/36 x z + 5/9 x z - 1/18 y x z + 5/9 x z - 5/36 x z + + 2 2 2 2 2 4 2 3 4 3 3 4 + + 1/3 y x + 8/9 y x + 1/12 y x z - 1/48 y x z + 1/36 y x z + + 4 4 2 4 3 4 2 4 + - 2/9 x y - 1/12 x y + 1/9 x y , COEFF(2, -1, 0) = 1/192 x y z + + 4 4 4 3 4 4 2 4 3 2 + + 1/72 x y z - 1/144 x y z - 5/72 x y z + 5/144 x y z + + 4 4 4 2 2 3 2 4 + - 1/144 x z - 5/192 x y z + 1/9 y x + 1/18 x - 1/96 y x z + + 4 3 2 4 2 3 3 4 + - 1/36 x + 1/144 y x z - 5/36 z y x + 1/72 y x z - 1/9 y x + + 2 2 2 3 2 3 3 2 3 2 2 + + 5/192 y x z - 5/72 y x z + 5/72 y x z - 5/144 y x z + + 4 2 3 3 2 3 3 2 3 3 + + 5/144 x z - 1/18 x + 1/18 y x + 1/24 y x + 1/36 y x - 1/18 y x + + 2 2 2 3 2 2 2 2 2 + + 1/36 x - 5/96 z y x - 1/24 y x + 5/96 y x z + 5/72 y x z + + 2 4 2 4 2 4 4 + + 5/36 y x z - 1/36 y x z + 1/144 x z - 1/72 y x z + 1/72 x z + + 3 4 2 2 3 4 2 3 2 + - 1/72 x z - 5/144 x z + 1/36 y x z - 5/72 x z + 5/72 x z + + 2 2 2 2 2 4 2 3 4 3 3 4 + - 1/48 y x - 1/18 y x - 1/192 y x z + 1/96 y x z - 1/72 y x z + + 4 4 2 4 3 25 2 2 + + 1/18 x y + 1/48 x y - 1/36 x y , COEFF(-2, 0, 0) = - --- y x z + 192 + + 25 4 2 25 2 3 2 4 3 4 + + --- x y z + -- y x z + 1/12 y x + 5/48 y x + 1/96 x y z + 192 96 + + 3 2 4 4 3 4 2 4 + - 1/24 y x - 5/192 x y z + 5/96 y x z + 5/192 y x z + + 4 3 2 3 3 2 3 2 2 3 2 4 + - 5/96 x y z + 5/48 y x z + 5/96 y x z - 1/96 y x z + + 3 3 4 4 25 2 3 4 3 + + 5/24 y x + 1/48 y x z - 5/96 y x z - -- z y x + 1/24 x y + 96 + + 3 3 4 3 3 4 3 2 + - 1/12 y x - 5/48 x y - 1/48 y x z - 5/24 y x - 5/48 y x z , + + 25 2 25 2 3 3 3 4 + COEFF(-1, 0, 0) = 5/3 y x - -- y x z + -- z y x + 1/24 y x z + 12 48 + + 3 3 2 4 4 3 3 2 4 3 2 + - 5/12 y x + 1/6 y x z + 5/12 x y - 5/24 y x z + 5/24 x y z + + 4 3 4 4 4 3 25 4 2 4 + - 1/24 x y z + 5/48 x y z - 2/3 y x - -- x y z + 5/12 y x z + 48 + + 3 2 2 25 2 2 3 4 3 2 + + 2/3 y x - 5/3 y x + -- y x z - 5/48 y x z + 5/6 y x z + 12 + + 3 2 2 4 3 3 4 3 3 2 4 + - 5/6 y x z - 1/6 x y - 1/6 y x z + 1/6 y x - 5/12 y x z , + + 4 3 2 3 2 125 2 2 4 4 + COEFF(0, 0, 0) = - 5/16 x y z - 5/4 y z - --- y x z - 5/32 x y z + 32 + + 4 3 4 25 4 2 3 2 4 4 3 2 + + 1/16 x y z + -- x y z - 5/16 y x z - 5/8 x y - 5/4 y x + 32 + + 25 2 4 25 3 2 2 2 2 3 4 4 3 + + -- y x z + -- y x z + 25/8 y z + 25/8 y x + 1/4 y z + 1/4 x y + 32 16 + + 3 4 4 4 4 3 + + y - 5/2 y - 5/8 y z , COEFF(1, 0, 0) = 5/48 x y z - 1/6 x y + + 3 2 2 3 4 3 2 3 4 + - 5/6 y x z - 5/3 y x + 2/3 y x + 5/24 x y z + 5/48 y x z + + 25 2 3 2 4 3 25 4 2 4 + - -- z y x - 5/12 y x z + 5/12 y x - -- x y z + 5/12 x y + 48 48 + + 4 3 4 25 2 3 2 3 3 2 2 + - 1/24 x y z + -- y x z - 5/6 y x z + 5/24 y x z - 5/3 y x + 12 + + 3 2 4 3 3 25 2 2 3 2 3 3 4 + + 1/6 y x z - 1/6 y x + -- y x z + 2/3 y x - 1/24 y x z + 12 + + 4 3 4 25 4 2 + - 5/12 y x z + 1/6 y x z , COEFF(2, 0, 0) = 5/24 y x + --- x y z + 192 + + 3 4 2 4 3 2 3 2 3 + - 1/48 y x z + 5/192 y x z + 5/48 y x z - 1/24 y x - 5/24 y x + + 25 2 4 3 4 4 3 2 4 4 + - -- y x z + 1/96 x y z - 5/96 x y z - 5/192 x y z + 96 + + 3 2 2 3 4 25 2 2 4 3 + + 5/96 y x z - 1/12 y x - 5/48 x y - --- y x z + 1/24 x y + 192 + + 3 4 2 25 2 3 3 2 4 4 + - 5/96 y x z + 5/48 y x + -- z y x - 1/96 y x z + 5/96 y x z + 96 + + 3 3 2 3 3 4 3 3 + - 5/48 y x z + 1/48 y x z + 1/12 y x , COEFF(-2, 1, 0) = + + 4 2 4 4 4 4 3 4 4 2 + - 1/192 x y z + 1/72 x y z - 1/144 x y z - 5/72 x y z + + 4 3 2 4 4 4 2 2 3 + + 5/144 x y z + 1/144 x z + 5/192 x y z - 1/9 y x + 1/18 x + + 2 4 4 3 2 4 2 3 3 4 + - 1/96 y x z + 1/36 x + 1/144 y x z + 5/36 z y x - 1/72 y x z + + 2 2 2 3 2 3 3 2 3 2 2 + + 1/9 y x - 5/192 y x z + 5/72 y x z - 5/72 y x z - 5/144 y x z + + 4 2 3 3 2 3 3 2 3 3 + - 5/144 x z - 1/18 x - 1/18 y x + 1/24 y x + 1/36 y x + 1/18 y x + + 2 2 2 3 2 2 2 2 2 + - 1/36 x - 5/96 z y x - 1/24 y x + 5/96 y x z + 5/72 y x z + + 2 4 2 4 2 4 4 + - 5/36 y x z + 1/36 y x z - 1/144 x z - 1/72 y x z + 1/72 x z + + 3 4 2 2 3 4 2 3 2 + - 1/72 x z + 5/144 x z - 1/36 y x z - 5/72 x z + 5/72 x z + + 2 2 2 2 2 4 2 3 4 3 3 4 + + 1/48 y x - 1/18 y x + 1/192 y x z + 1/96 y x z + 1/72 y x z + + 4 4 2 4 3 4 2 4 + + 1/18 x y - 1/48 x y - 1/36 x y , COEFF(-1, 1, 0) = 1/48 x y z + + 4 4 4 3 4 4 2 4 3 2 4 4 + - 1/18 x y z + 1/36 x y z + 5/18 x y z - 5/36 x y z - 1/36 x z + + 4 2 2 3 2 4 4 3 2 4 + - 5/48 x y z + 2/9 y x - 4/9 x + 1/12 y x z - 1/9 x - 1/9 y x z + + 2 3 3 4 2 2 2 3 2 + - 5/18 z y x + 1/9 y x z - 8/9 y x + 5/12 y x z - 5/9 y x z + + 3 3 2 3 2 2 4 2 3 3 + + 5/36 y x z + 5/9 y x z + 5/36 x z + 1/9 x + 4/9 y x + + 2 3 3 2 3 3 2 2 2 3 2 + - 1/12 y x - 4/9 y x - 1/9 y x + 4/9 x + 5/48 z y x + 1/3 y x + + 2 2 2 2 2 4 2 4 + - 5/12 y x z - 10/9 y x z + 10/9 y x z - 2/9 y x z + 1/9 x z + + 2 4 4 3 4 2 2 3 4 + + 2/9 y x z - 1/9 x z + 1/36 x z - 5/9 x z + 1/18 y x z + + 2 3 2 2 2 2 2 2 4 + + 5/9 x z - 5/36 x z - 1/3 y x + 8/9 y x - 1/12 y x z + + 2 3 4 3 3 4 4 4 2 4 3 + - 1/48 y x z - 1/36 y x z - 2/9 x y + 1/12 x y + 1/9 x y , + + 4 2 4 4 4 4 3 4 + COEFF(0, 1, 0) = - 1/32 x y z + 1/12 x y z - 1/24 x y z + + 4 2 4 3 2 4 4 4 2 2 4 + - 5/12 x y z + 5/24 x y z + 1/24 x z + 5/32 x y z + 1/6 x + + 3 2 4 25 2 2 2 4 25 3 2 2 4 2 + + 4/3 y + 5/24 y x z - -- y x z + 1/6 z - -- y x z - 5/24 x z + 32 24 + + 3 2 2 3 2 2 25 2 2 + + 2/3 - 2/3 y - 1/2 y - 5/6 z + 5/6 y x - 5/6 x + -- y x z + 12 + + 4 3 4 3 2 2 4 2 4 2 + + 1/3 y z - 1/6 y z + 5/6 y z - 5/24 x z - 5/12 y x z - 5/3 y z + + 25 2 2 2 4 2 2 2 2 2 2 2 4 + + -- x z - 1/8 y z + 5/8 y z + 5/8 y x - 5/3 y x + 5/32 y x z + 24 + + 4 4 2 4 3 4 2 4 + + 1/3 x y - 1/8 x y - 1/6 x y , COEFF(1, 1, 0) = 1/48 x y z + + 4 4 4 3 4 4 2 4 3 2 4 4 + - 1/18 x y z + 1/36 x y z + 5/18 x y z - 5/36 x y z - 1/36 x z + + 4 2 2 3 2 4 4 3 2 4 + - 5/48 x y z - 2/9 y x + 4/9 x - 1/12 y x z - 1/9 x - 1/9 y x z + + 2 3 3 4 2 2 2 3 2 + + 5/18 z y x - 1/9 y x z + 8/9 y x + 5/12 y x z + 5/9 y x z + + 3 3 2 3 2 2 4 2 3 3 + - 5/36 y x z + 5/9 y x z + 5/36 x z - 1/9 x - 4/9 y x + + 2 3 3 2 3 3 2 2 2 3 2 + + 1/12 y x - 4/9 y x + 1/9 y x + 4/9 x - 5/48 z y x - 1/3 y x + + 2 2 2 2 2 4 2 4 + + 5/12 y x z - 10/9 y x z - 10/9 y x z + 2/9 y x z + 1/9 x z + + 2 4 4 3 4 2 2 3 4 + + 2/9 y x z + 1/9 x z - 1/36 x z - 5/9 x z - 1/18 y x z + + 2 3 2 2 2 2 2 2 4 + - 5/9 x z + 5/36 x z - 1/3 y x + 8/9 y x - 1/12 y x z + + 2 3 4 3 3 4 4 4 2 4 3 + + 1/48 y x z + 1/36 y x z - 2/9 x y + 1/12 x y + 1/9 x y , + + 4 2 4 4 4 4 3 4 + COEFF(2, 1, 0) = - 1/192 x y z + 1/72 x y z - 1/144 x y z + + 4 2 4 3 2 4 4 4 2 2 3 + - 5/72 x y z + 5/144 x y z + 1/144 x z + 5/192 x y z + 1/9 y x + + 2 4 4 3 2 4 2 3 + - 1/18 x + 1/96 y x z + 1/36 x + 1/144 y x z - 5/36 z y x + + 3 4 2 2 2 3 2 3 3 2 + + 1/72 y x z - 1/9 y x - 5/192 y x z - 5/72 y x z + 5/72 y x z + + 3 2 2 4 2 3 3 2 3 + - 5/144 y x z - 5/144 x z + 1/18 x + 1/18 y x - 1/24 y x + + 3 2 3 3 2 2 2 3 2 + + 1/36 y x - 1/18 y x - 1/36 x + 5/96 z y x + 1/24 y x + + 2 2 2 2 2 4 2 4 + - 5/96 y x z + 5/72 y x z + 5/36 y x z - 1/36 y x z - 1/144 x z + + 2 4 4 3 4 2 2 3 4 + - 1/72 y x z - 1/72 x z + 1/72 x z + 5/144 x z + 1/36 y x z + + 2 3 2 2 2 2 2 2 4 + + 5/72 x z - 5/72 x z + 1/48 y x - 1/18 y x + 1/192 y x z + + 2 3 4 3 3 4 4 4 2 4 3 + - 1/96 y x z - 1/72 y x z + 1/18 x y - 1/48 x y - 1/36 x y , + + 4 2 4 4 4 4 3 4 + COEFF(-2, 2, 0) = 1/384 x y z - 1/1152 x y z + 1/576 x y z + + 4 2 4 3 2 4 4 4 2 2 + + 5/1152 x y z - 5/576 x y z - 1/1152 x z - 5/384 x y z + + 3 2 4 4 3 2 4 + + 1/144 y x - 1/144 x + 1/192 y x z - 1/288 x - 1/576 y x z + + 2 3 3 4 2 2 2 + - 5/576 z y x + 1/288 y x z - 1/144 y x + 5/384 y x z + + 3 2 3 3 2 3 2 2 4 2 + - 5/288 y x z + 5/288 y x z + 5/576 y x z + 5/1152 x z + + 3 3 2 3 3 2 3 3 2 + + 1/144 x + 1/72 y x - 1/48 y x - 1/144 y x - 1/72 y x + 1/288 x + + 2 2 3 2 2 2 2 2 + + 5/192 z y x + 1/48 y x - 5/192 y x z - 5/1152 y x z + + 2 4 2 4 2 4 4 + + 5/576 y x z - 1/576 y x z + 1/1152 x z + 1/1152 y x z - 1/576 x z + + 3 4 2 2 3 4 2 3 2 + + 1/576 x z - 5/1152 x z + 1/576 y x z + 5/576 x z - 5/576 x z + + 2 2 2 2 2 4 2 3 4 + - 1/96 y x + 1/288 y x - 1/384 y x z - 1/192 y x z + + 3 3 4 4 4 2 4 3 + - 1/288 y x z - 1/288 x y + 1/96 x y + 1/144 x y , COEFF(-1, 2, 0) + + 4 2 4 4 4 4 3 4 4 2 + = - 1/96 x y z + 1/288 x y z - 1/144 x y z - 5/288 x y z + + 4 3 2 4 4 4 2 2 3 + + 5/144 x y z + 1/288 x z + 5/96 x y z - 1/72 y x + 1/18 x + + 2 4 4 3 2 4 2 3 3 4 + - 1/24 y x z + 1/72 x + 1/36 y x z + 5/288 z y x - 1/36 y x z + + 2 2 2 3 2 3 3 2 3 2 2 + + 1/18 y x - 5/24 y x z + 5/36 y x z - 5/144 y x z - 5/36 y x z + + 4 2 3 3 2 3 3 2 3 3 + - 5/288 x z - 1/72 x - 1/9 y x + 1/24 y x + 1/9 y x + 1/36 y x + + 2 2 2 3 2 2 2 2 2 + - 1/18 x - 5/96 z y x - 1/6 y x + 5/24 y x z + 5/72 y x z + + 2 4 2 4 2 4 4 + - 5/72 y x z + 1/72 y x z - 1/72 x z - 1/72 y x z + 1/72 x z + + 3 4 2 2 3 4 2 3 2 + - 1/288 x z + 5/72 x z - 1/288 y x z - 5/72 x z + 5/288 x z + + 2 2 2 2 2 4 2 3 4 3 3 4 + + 1/6 y x - 1/18 y x + 1/24 y x z + 1/96 y x z + 1/144 y x z + + 4 4 2 4 3 4 2 4 + + 1/72 x y - 1/24 x y - 1/36 x y , COEFF(0, 2, 0) = 1/64 x y z + + 4 4 4 3 4 4 2 4 3 2 + - 1/192 x y z + 1/96 x y z + 5/192 x y z - 5/96 x y z + + 4 4 4 2 2 4 3 2 4 + - 1/192 x z - 5/64 x y z - 1/48 x - 1/12 y - 5/96 y x z + + 25 2 2 2 4 25 3 2 2 4 2 3 + + -- y x z - 1/48 z + -- y x z + 5/192 x z + 1/6 y - 1/12 + 64 96 + + 2 2 3 2 2 25 2 2 4 + + 1/4 y + 5/48 z - 5/24 y x + 5/48 x - --- y x z - 1/48 y z + 192 + + 3 4 3 2 2 4 2 4 2 + + 1/24 y z - 5/24 y z + 5/192 x z + 5/192 y x z + 5/48 y z + + 25 2 2 2 4 2 2 2 2 2 + - --- x z + 1/16 y z - 5/16 y z - 5/16 y x + 5/48 y x + 192 + + 2 2 4 4 4 2 4 3 + - 5/64 y x z - 1/48 x y + 1/16 x y + 1/24 x y , COEFF(1, 2, 0) = + + 4 2 4 4 4 4 3 4 4 2 + - 1/96 x y z + 1/288 x y z - 1/144 x y z - 5/288 x y z + + 4 3 2 4 4 4 2 2 3 + + 5/144 x y z + 1/288 x z + 5/96 x y z + 1/72 y x - 1/18 x + + 2 4 4 3 2 4 2 3 3 4 + + 1/24 y x z + 1/72 x + 1/36 y x z - 5/288 z y x + 1/36 y x z + + 2 2 2 3 2 3 3 2 3 2 2 + - 1/18 y x - 5/24 y x z - 5/36 y x z + 5/144 y x z - 5/36 y x z + + 4 2 3 3 2 3 3 2 3 3 + - 5/288 x z + 1/72 x + 1/9 y x - 1/24 y x + 1/9 y x - 1/36 y x + + 2 2 2 3 2 2 2 2 2 + - 1/18 x + 5/96 z y x + 1/6 y x - 5/24 y x z + 5/72 y x z + + 2 4 2 4 2 4 4 + + 5/72 y x z - 1/72 y x z - 1/72 x z - 1/72 y x z - 1/72 x z + + 3 4 2 2 3 4 2 3 2 + + 1/288 x z + 5/72 x z + 1/288 y x z + 5/72 x z - 5/288 x z + + 2 2 2 2 2 4 2 3 4 3 3 4 + + 1/6 y x - 1/18 y x + 1/24 y x z - 1/96 y x z - 1/144 y x z + + 4 4 2 4 3 4 2 4 + + 1/72 x y - 1/24 x y - 1/36 x y , COEFF(2, 2, 0) = 1/384 x y z + + 4 4 4 3 4 4 2 4 3 2 + - 1/1152 x y z + 1/576 x y z + 5/1152 x y z - 5/576 x y z + + 4 4 4 2 2 3 2 4 + - 1/1152 x z - 5/384 x y z - 1/144 y x + 1/144 x - 1/192 y x z + + 4 3 2 4 2 3 3 4 + - 1/288 x - 1/576 y x z + 5/576 z y x - 1/288 y x z + 1/144 y x + + 2 2 2 3 2 3 3 2 3 2 2 + + 5/384 y x z + 5/288 y x z - 5/288 y x z + 5/576 y x z + + 4 2 3 3 2 3 3 2 + + 5/1152 x z - 1/144 x - 1/72 y x + 1/48 y x - 1/144 y x + + 3 3 2 2 2 3 2 2 2 + + 1/72 y x + 1/288 x - 5/192 z y x - 1/48 y x + 5/192 y x z + + 2 2 2 4 2 4 + - 5/1152 y x z - 5/576 y x z + 1/576 y x z + 1/1152 x z + + 2 4 4 3 4 2 2 3 4 + + 1/1152 y x z + 1/576 x z - 1/576 x z - 5/1152 x z - 1/576 y x z + + 2 3 2 2 2 2 2 2 4 + - 5/576 x z + 5/576 x z - 1/96 y x + 1/288 y x - 1/384 y x z + + 2 3 4 3 3 4 4 4 2 4 3 + + 1/192 y x z + 1/288 y x z - 1/288 x y + 1/96 x y + 1/144 x y , + + 4 2 4 4 4 4 3 4 + COEFF(-2, -2, 1) = 1/576 x y z + 1/1728 x y z - 1/864 x y z + + 4 3 4 4 2 4 2 3 + + 1/216 x y z - 1/432 x y z - 1/144 x y z + 1/576 x y z + + 4 3 3 4 2 4 3 2 4 4 + - 1/864 x y z - 1/432 x y z + 1/216 x y z - 1/1728 x z + + 4 2 2 4 3 2 4 4 + - 1/144 x y z + 1/1728 x y z + 1/288 y x z + 1/432 x z + + 3 3 2 4 3 2 3 + + 1/864 y x z + 1/864 y x z + 1/216 z y x + 1/216 z y x + + 3 4 2 2 3 2 2 2 + - 1/432 y x z - 1/72 y x z + 1/288 y x z + 1/144 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/108 y x z - 1/576 y x z - 1/864 y x z - 1/108 y x z + + 2 3 3 3 2 2 2 3 3 + - 1/1728 y x z - 1/216 z x - 1/216 y x z - 1/288 y x z + + 4 2 3 3 2 3 3 + + 1/432 x z + 1/108 z y x - 1/216 z y x - 1/108 z y x - 1/216 y x z + + 2 2 3 2 2 3 3 3 + + 1/432 z y x + 1/72 z y x + 1/72 z y x - 1/432 y x z + + 4 3 3 3 3 2 2 2 2 + - 1/1728 x z + 1/432 y x z - 1/72 y x z + 1/144 y x z + + 2 2 2 3 2 3 2 + + 1/432 y x z - 1/216 y x z + 1/864 y x z + 1/216 x z - 1/432 x z + + 4 3 3 2 3 2 4 3 + + 1/864 y x z + 1/864 x z + 1/1728 x z + 1/1728 x z - 1/864 x z + + 2 4 4 3 4 2 2 3 4 + - 1/1728 y x z - 1/864 x z + 1/864 x z - 1/432 x z - 1/864 y x z + + 2 3 2 2 2 4 2 3 4 + + 1/216 x z - 1/216 x z - 1/576 y x z - 1/288 y x z + + 3 3 4 4 2 4 4 4 + + 1/432 y x z , COEFF(-1, -2, 1) = - 1/144 x y z - 1/432 x y z + + 4 3 4 4 3 4 4 2 + + 1/216 x y z - 1/54 x y z + 1/108 x y z + 1/36 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/144 x y z + 1/216 x y z + 1/108 x y z - 1/54 x y z + + 4 4 4 2 2 4 3 2 4 4 + + 1/432 x z + 1/36 x y z - 1/432 x y z - 1/36 y x z - 1/108 x z + + 3 3 2 4 3 2 3 + - 1/108 y x z - 1/54 y x z - 1/108 z y x - 1/108 z y x + + 3 4 2 2 3 2 2 2 3 2 + + 1/54 y x z + 1/9 y x z - 1/36 y x z - 1/9 y x z - 2/27 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/36 y x z + 1/432 y x z + 1/54 y x z + 1/108 y x z + + 3 3 2 2 2 3 3 4 2 3 + + 1/108 z x + 2/27 y x z + 1/144 y x z - 1/108 x z - 2/27 z y x + + 3 2 3 3 2 2 3 + + 2/27 z y x + 1/54 z y x + 1/27 y x z - 1/27 z y x - 1/36 z y x + + 2 2 3 3 3 4 3 3 3 3 + - 1/36 z y x + 1/54 y x z + 1/432 x z - 1/216 y x z + + 2 2 2 2 2 2 2 3 2 3 + + 1/9 y x z - 1/9 y x z - 1/27 y x z + 1/27 y x z - 1/54 y x z + + 2 4 3 3 2 3 + - 1/27 x z + 1/27 x z - 1/108 y x z - 1/432 x z - 1/108 x z + + 2 4 3 2 4 4 3 4 + - 1/108 x z + 1/108 x z + 1/108 y x z + 1/108 x z - 1/432 x z + + 2 2 3 4 2 3 2 2 2 4 + + 1/27 x z + 1/432 y x z - 1/27 x z + 1/108 x z + 1/36 y x z + + 2 3 4 3 3 4 4 2 4 + + 1/144 y x z - 1/216 y x z , COEFF(0, -2, 1) = 1/96 x y z + + 4 4 4 3 4 4 3 4 + + 1/288 x y z - 1/144 x y z + 1/36 x y z - 1/72 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/24 x y z + 1/96 x y z - 1/144 x y z - 1/72 x y z + + 4 3 2 4 4 4 2 2 4 3 4 + + 1/36 x y z - 1/288 x z - 1/24 x y z + 1/288 x y z + 1/72 x z + + 3 2 4 2 2 2 2 2 3 2 3 + + 1/18 z + 5/144 y x z + 5/24 y x z - 5/96 y x z - 5/288 y x z + + 4 3 2 2 4 2 3 3 2 + - 1/72 z - 5/36 y x z + 1/72 x z - 1/72 z + 1/9 z y + 1/18 z + + 3 2 2 4 3 2 2 + - 5/36 z y x + 5/72 z y x - 1/18 y z - 1/288 x z + 5/24 y x z + + 2 2 2 3 2 3 2 3 + + 5/72 y x z - 1/6 y z + 5/144 y x z - 5/72 x z + 1/72 y z + + 2 3 3 3 2 3 4 3 4 + + 1/24 y z - 1/36 y z + 5/288 x z + 1/72 y z - 1/36 y z + + 3 2 2 4 2 4 2 2 2 + + 1/9 y z + 5/288 x z - 5/288 y x z - 1/18 y z - 5/72 x z + + 2 4 2 2 2 2 4 + + 1/24 y z - 1/6 y z - 5/96 y x z , COEFF(1, -2, 1) = + + 4 2 4 4 4 4 3 4 4 3 + - 1/144 x y z - 1/432 x y z + 1/216 x y z - 1/54 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/108 x y z + 1/36 x y z - 1/144 x y z + 1/216 x y z + + 4 2 4 3 2 4 4 4 2 2 + + 1/108 x y z - 1/54 x y z + 1/432 x z + 1/36 x y z + + 4 3 2 4 4 3 3 2 4 + - 1/432 x y z + 1/36 y x z - 1/108 x z + 1/108 y x z - 1/54 y x z + + 3 2 3 3 4 2 2 3 + + 1/108 z y x + 1/108 z y x - 1/54 y x z - 1/9 y x z + 1/36 y x z + + 2 2 2 3 2 2 2 3 3 3 + - 1/9 y x z + 2/27 y x z + 1/36 y x z - 1/432 y x z + + 3 3 2 2 3 3 3 2 2 + - 1/54 y x z + 1/108 y x z - 1/108 z x + 2/27 y x z + + 2 3 3 4 2 3 3 2 3 3 + - 1/144 y x z - 1/108 x z + 2/27 z y x + 2/27 z y x - 1/54 z y x + + 2 2 3 2 2 3 3 3 + - 1/27 y x z - 1/27 z y x + 1/36 z y x + 1/36 z y x - 1/54 y x z + + 4 3 3 3 3 2 2 2 2 2 2 + + 1/432 x z + 1/216 y x z - 1/9 y x z - 1/9 y x z - 1/27 y x z + + 2 3 2 3 2 4 + - 1/27 y x z - 1/54 y x z + 1/27 x z + 1/27 x z + 1/108 y x z + + 3 3 2 3 2 4 3 2 4 + + 1/432 x z - 1/108 x z - 1/108 x z - 1/108 x z + 1/108 y x z + + 4 3 4 2 2 3 4 2 + - 1/108 x z + 1/432 x z + 1/27 x z - 1/432 y x z + 1/27 x z + + 3 2 2 2 4 2 3 4 3 3 4 + - 1/108 x z + 1/36 y x z - 1/144 y x z + 1/216 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(2, -2, 1) = 1/576 x y z + 1/1728 x y z - 1/864 x y z + + 4 3 4 4 2 4 2 3 + + 1/216 x y z - 1/432 x y z - 1/144 x y z + 1/576 x y z + + 4 3 3 4 2 4 3 2 4 4 + - 1/864 x y z - 1/432 x y z + 1/216 x y z - 1/1728 x z + + 4 2 2 4 3 2 4 4 + - 1/144 x y z + 1/1728 x y z - 1/288 y x z + 1/432 x z + + 3 3 2 4 3 2 3 + - 1/864 y x z + 1/864 y x z - 1/216 z y x - 1/216 z y x + + 3 4 2 2 3 2 2 2 + + 1/432 y x z + 1/72 y x z - 1/288 y x z + 1/144 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/108 y x z - 1/576 y x z + 1/864 y x z + 1/108 y x z + + 2 3 3 3 2 2 2 3 3 + - 1/1728 y x z + 1/216 z x - 1/216 y x z + 1/288 y x z + + 4 2 3 3 2 3 3 + + 1/432 x z - 1/108 z y x - 1/216 z y x + 1/108 z y x + 1/216 y x z + + 2 2 3 2 2 3 3 3 + + 1/432 z y x - 1/72 z y x - 1/72 z y x + 1/432 y x z + + 4 3 3 3 3 2 2 2 2 + - 1/1728 x z - 1/432 y x z + 1/72 y x z + 1/144 y x z + + 2 2 2 3 2 3 2 + + 1/432 y x z + 1/216 y x z + 1/864 y x z - 1/216 x z - 1/432 x z + + 4 3 3 2 3 2 4 3 + - 1/864 y x z - 1/864 x z + 1/1728 x z + 1/1728 x z + 1/864 x z + + 2 4 4 3 4 2 2 3 4 + - 1/1728 y x z + 1/864 x z - 1/864 x z - 1/432 x z + 1/864 y x z + + 2 3 2 2 2 4 2 3 4 + - 1/216 x z + 1/216 x z - 1/576 y x z + 1/288 y x z + + 3 3 4 4 2 4 4 4 + - 1/432 y x z , COEFF(-2, -1, 1) = - 1/288 x y z - 1/108 x y z + + 4 3 4 4 3 4 4 2 + + 1/216 x y z - 1/54 x y z + 1/27 x y z + 1/72 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/288 x y z + 1/216 x y z + 1/27 x y z - 1/54 x y z + + 4 4 4 2 2 4 3 2 4 4 + + 1/216 x z + 1/72 x y z - 1/108 x y z - 1/144 y x z - 1/54 x z + + 3 3 2 4 3 2 3 + - 1/54 y x z - 1/216 y x z - 2/27 z y x - 2/27 z y x + + 3 4 2 2 3 2 2 2 + + 1/108 y x z + 1/36 y x z - 1/144 y x z - 1/72 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/27 y x z + 1/288 y x z + 1/54 y x z + 1/27 y x z + + 2 3 3 3 2 2 2 3 3 4 2 + + 1/108 y x z + 1/27 z x + 1/54 y x z + 1/144 y x z - 1/54 x z + + 3 3 2 3 3 2 + - 1/27 z y x + 1/54 z y x + 1/27 z y x + 2/27 y x z - 1/27 z y x + + 2 3 2 2 3 3 3 4 3 + - 1/36 z y x - 1/36 z y x + 1/108 y x z + 1/216 x z + + 3 3 3 2 2 2 2 2 2 + - 1/108 y x z + 1/36 y x z - 1/72 y x z - 1/27 y x z + + 2 3 2 3 2 4 + + 2/27 y x z - 1/216 y x z - 1/27 x z + 1/54 x z - 1/54 y x z + + 3 3 2 3 2 4 3 2 4 + - 1/108 x z - 1/216 x z - 1/216 x z + 1/108 x z + 1/108 y x z + + 4 3 4 2 2 3 4 2 + + 1/108 x z - 1/108 x z + 1/54 x z + 1/54 y x z - 1/27 x z + + 3 2 2 2 4 2 3 4 3 3 4 + + 1/27 x z + 1/288 y x z + 1/144 y x z - 1/108 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(-1, -1, 1) = 1/72 x y z + 1/27 x y z - 1/54 x y z + + 4 3 4 4 2 4 2 3 + + 2/27 x y z - 4/27 x y z - 1/18 x y z + 1/72 x y z + + 4 3 3 4 2 4 3 2 4 4 + - 1/54 x y z - 4/27 x y z + 2/27 x y z - 1/54 x z + + 4 2 2 4 3 2 4 4 3 + - 1/18 x y z + 1/27 x y z + 1/18 y x z + 2/27 x z + 4/27 y x z + + 3 2 4 3 2 3 3 4 2 + + 2/27 y x z + 4/27 z y x + 4/27 z y x - 2/27 y x z - 2/9 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/18 y x z + 2/9 y x z + 8/27 y x z - 1/18 y x z + + 3 3 3 3 2 2 3 3 3 2 2 + - 1/27 y x z - 2/27 y x z - 4/27 y x z - 2/27 z x - 8/27 y x z + + 2 3 3 4 2 3 3 2 3 3 + - 1/72 y x z + 2/27 x z + 8/27 z y x - 8/27 z y x - 2/27 z y x + + 16 16 2 2 3 2 2 3 3 3 + - -- y x z + -- z y x + 1/18 z y x + 1/18 z y x - 2/27 y x z + 27 27 + + 4 3 3 3 3 2 2 2 2 16 2 2 + - 1/54 x z + 1/54 y x z - 2/9 y x z + 2/9 y x z + -- y x z + 27 + + 16 2 3 2 3 2 4 + - -- y x z + 2/27 y x z + 8/27 x z - 8/27 x z + 4/27 y x z + 27 + + 3 3 2 3 2 4 3 2 4 + + 1/54 x z + 2/27 x z + 2/27 x z - 2/27 x z - 4/27 y x z + + 4 3 4 2 2 3 4 2 + - 2/27 x z + 1/54 x z - 8/27 x z - 1/27 y x z + 8/27 x z + + 3 2 2 2 4 2 3 4 3 3 4 + - 2/27 x z - 1/18 y x z - 1/72 y x z + 1/54 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(0, -1, 1) = - 1/48 x y z - 1/18 x y z + 1/36 x y z + + 4 3 4 4 2 4 2 3 4 3 3 + - 1/9 x y z + 2/9 x y z + 1/12 x y z - 1/48 x y z + 1/36 x y z + + 4 2 4 3 2 4 4 4 2 2 4 3 + + 2/9 x y z - 1/9 x y z + 1/36 x z + 1/12 x y z - 1/18 x y z + + 4 3 2 4 2 2 2 2 2 3 + - 1/9 x z - 4/9 z - 5/36 y x z - 5/12 y x z + 5/48 y x z + + 2 3 4 3 2 2 4 2 3 3 + + 5/18 y x z + 1/9 z + 5/9 y x z - 1/9 x z + 1/9 z - 4/9 z y + + 2 3 2 2 4 3 2 2 + - 4/9 z + 5/9 z y x - 10/9 z y x + 8/9 y z + 1/36 x z - 5/12 y x z + + 2 2 2 3 2 3 2 3 + - 10/9 y x z + 1/3 y z - 5/36 y x z + 5/9 x z - 2/9 y z + + 2 3 3 3 2 3 4 3 4 3 2 + - 1/12 y z + 1/9 y z - 5/36 x z - 2/9 y z + 1/9 y z - 4/9 y z + + 2 4 2 4 2 2 2 2 4 + - 5/36 x z + 5/18 y x z + 8/9 y z + 5/9 x z - 1/12 y z + + 2 2 2 2 4 4 2 4 + + 1/3 y z + 5/48 y x z , COEFF(1, -1, 1) = 1/72 x y z + + 4 4 4 3 4 4 3 4 4 2 + + 1/27 x y z - 1/54 x y z + 2/27 x y z - 4/27 x y z - 1/18 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + + 1/72 x y z - 1/54 x y z - 4/27 x y z + 2/27 x y z + + 4 4 4 2 2 4 3 2 4 4 + - 1/54 x z - 1/18 x y z + 1/27 x y z - 1/18 y x z + 2/27 x z + + 3 3 2 4 3 2 3 3 4 + - 4/27 y x z + 2/27 y x z - 4/27 z y x - 4/27 z y x + 2/27 y x z + + 2 2 3 2 2 2 3 2 2 2 3 + + 2/9 y x z - 1/18 y x z + 2/9 y x z - 8/27 y x z - 1/18 y x z + + 3 3 3 3 2 2 3 3 3 2 2 + + 1/27 y x z + 2/27 y x z - 4/27 y x z + 2/27 z x - 8/27 y x z + + 2 3 3 4 2 3 3 2 3 3 + + 1/72 y x z + 2/27 x z - 8/27 z y x - 8/27 z y x + 2/27 z y x + + 16 16 2 2 3 2 2 3 3 3 + + -- y x z + -- z y x - 1/18 z y x - 1/18 z y x + 2/27 y x z + 27 27 + + 4 3 3 3 3 2 2 2 2 16 2 2 + - 1/54 x z - 1/54 y x z + 2/9 y x z + 2/9 y x z + -- y x z + 27 + + 16 2 3 2 3 2 4 + + -- y x z + 2/27 y x z - 8/27 x z - 8/27 x z - 4/27 y x z + 27 + + 3 3 2 3 2 4 3 2 4 + - 1/54 x z + 2/27 x z + 2/27 x z + 2/27 x z - 4/27 y x z + + 4 3 4 2 2 3 4 2 + + 2/27 x z - 1/54 x z - 8/27 x z + 1/27 y x z - 8/27 x z + + 3 2 2 2 4 2 3 4 3 3 4 + + 2/27 x z - 1/18 y x z + 1/72 y x z - 1/54 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(2, -1, 1) = - 1/288 x y z - 1/108 x y z + 1/216 x y z + + 4 3 4 4 2 4 2 3 + - 1/54 x y z + 1/27 x y z + 1/72 x y z - 1/288 x y z + + 4 3 3 4 2 4 3 2 4 4 + + 1/216 x y z + 1/27 x y z - 1/54 x y z + 1/216 x z + + 4 2 2 4 3 2 4 4 3 + + 1/72 x y z - 1/108 x y z + 1/144 y x z - 1/54 x z + 1/54 y x z + + 3 2 4 3 2 3 3 4 + - 1/216 y x z + 2/27 z y x + 2/27 z y x - 1/108 y x z + + 2 2 3 2 2 2 3 2 + - 1/36 y x z + 1/144 y x z - 1/72 y x z + 1/27 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/288 y x z - 1/54 y x z - 1/27 y x z + 1/108 y x z + + 3 3 2 2 2 3 3 4 2 3 + - 1/27 z x + 1/54 y x z - 1/144 y x z - 1/54 x z + 1/27 z y x + + 3 2 3 3 2 2 3 + + 1/54 z y x - 1/27 z y x - 2/27 y x z - 1/27 z y x + 1/36 z y x + + 2 2 3 3 3 4 3 3 3 3 + + 1/36 z y x - 1/108 y x z + 1/216 x z + 1/108 y x z + + 2 2 2 2 2 2 2 + - 1/36 y x z - 1/72 y x z - 1/27 y x z - 2/27 y x z + + 3 2 3 2 4 3 3 + - 1/216 y x z + 1/27 x z + 1/54 x z + 1/54 y x z + 1/108 x z + + 2 3 2 4 3 2 4 4 + - 1/216 x z - 1/216 x z - 1/108 x z + 1/108 y x z - 1/108 x z + + 3 4 2 2 3 4 2 3 2 + + 1/108 x z + 1/54 x z - 1/54 y x z + 1/27 x z - 1/27 x z + + 2 2 4 2 3 4 3 3 4 + + 1/288 y x z - 1/144 y x z + 1/108 y x z , COEFF(-2, 0, 1) = + + 4 4 4 3 4 4 3 4 + 5/288 x y z - 1/144 x y z + 1/36 x y z - 5/72 x y z + + 4 3 3 4 2 4 3 2 4 3 + - 1/144 x y z - 5/72 x y z + 1/36 x y z + 5/288 x y z + + 3 3 2 4 3 2 3 + + 5/144 y x z + 1/144 y x z + 5/36 z y x + 5/36 z y x + + 3 4 3 2 3 3 3 3 2 + - 1/72 y x z + 1/18 y x z - 5/144 y x z - 1/18 y x z + + 2 3 3 2 2 3 3 2 + - 5/288 y x z - 1/36 y x z + 1/18 z y x - 1/36 z y x + + 3 3 2 3 3 3 3 3 + - 1/18 z y x - 5/36 y x z + 5/72 z y x - 1/72 y x z + 1/72 y x z + + 2 2 2 3 2 3 4 + + 5/72 y x z - 5/36 y x z + 1/144 y x z + 5/144 y x z + + 2 4 3 4 3 3 4 + - 5/288 y x z - 5/144 y x z + 1/72 y x z , COEFF(-1, 0, 1) = + + 4 4 4 3 4 4 3 4 4 3 3 + - 5/72 x y z + 1/36 x y z - 1/9 x y z + 5/18 x y z + 1/36 x y z + + 4 2 4 3 2 4 3 3 3 2 4 + + 5/18 x y z - 1/9 x y z - 5/72 x y z - 5/18 y x z - 1/9 y x z + + 3 2 3 3 4 3 2 3 3 + - 5/18 z y x - 5/18 z y x + 1/9 y x z - 4/9 y x z + 5/72 y x z + + 3 3 2 2 3 3 2 2 3 3 2 + + 1/9 y x z + 5/18 y x z + 4/9 y x z - 4/9 z y x + 4/9 z y x + + 3 3 2 3 3 3 3 3 + + 1/9 z y x + 10/9 y x z - 10/9 z y x + 1/9 y x z - 1/36 y x z + + 2 2 2 3 2 3 4 2 4 + - 10/9 y x z + 10/9 y x z - 1/9 y x z - 5/18 y x z + 5/18 y x z + + 3 4 3 3 4 4 + + 5/72 y x z - 1/36 y x z , COEFF(0, 0, 1) = - 5/3 y z - 5/12 x y z + + 3 2 25 2 4 4 2 4 3 2 3 2 3 + - 5/6 z y x - -- y x z - 5/12 x y z + 1/6 x y z + 5/24 y x z + 48 + + 3 4 4 25 2 3 3 2 4 3 + + 2/3 z y + 5/48 x y z - -- y x z + 2/3 y z + 5/48 x y z + 48 + + 4 3 3 4 3 25 2 3 4 2 + - 1/24 x y z + 5/12 y z + 5/12 y z + -- z y x - 1/6 y z - 5/3 y z + 12 + + 3 2 2 4 3 4 4 3 25 2 2 3 3 + - 5/6 y x z - 1/24 x y z + 1/6 x y z + -- y x z - 1/6 y z + 12 + + 3 2 4 4 4 4 3 4 + + 5/24 y x z , COEFF(1, 0, 1) = - 5/72 x y z + 1/36 x y z + + 4 3 4 4 3 3 4 2 4 3 2 + - 1/9 x y z + 5/18 x y z + 1/36 x y z + 5/18 x y z - 1/9 x y z + + 4 3 3 3 2 4 3 2 3 + - 5/72 x y z + 5/18 y x z - 1/9 y x z + 5/18 z y x + 5/18 z y x + + 3 4 3 2 3 3 3 3 2 2 3 + - 1/9 y x z + 4/9 y x z - 5/72 y x z - 1/9 y x z + 5/18 y x z + + 3 2 2 3 3 2 3 3 + + 4/9 y x z + 4/9 z y x + 4/9 z y x - 1/9 z y x - 10/9 y x z + + 2 3 3 3 3 3 2 2 2 + - 10/9 z y x - 1/9 y x z + 1/36 y x z - 10/9 y x z - 10/9 y x z + + 3 2 3 4 2 4 3 4 3 3 4 + - 1/9 y x z + 5/18 y x z + 5/18 y x z - 5/72 y x z + 1/36 y x z + + 4 4 4 3 4 4 3 + , COEFF(2, 0, 1) = 5/288 x y z - 1/144 x y z + 1/36 x y z + + 4 4 3 3 4 2 4 3 2 + - 5/72 x y z - 1/144 x y z - 5/72 x y z + 1/36 x y z + + 4 3 3 3 2 4 3 + + 5/288 x y z - 5/144 y x z + 1/144 y x z - 5/36 z y x + + 2 3 3 4 3 2 3 3 + - 5/36 z y x + 1/72 y x z - 1/18 y x z + 5/144 y x z + + 3 3 2 2 3 3 2 2 3 + + 1/18 y x z - 5/288 y x z - 1/36 y x z - 1/18 z y x + + 3 2 3 3 2 3 3 + - 1/36 z y x + 1/18 z y x + 5/36 y x z + 5/72 z y x + 1/72 y x z + + 3 3 3 2 2 2 3 2 3 + - 1/72 y x z + 5/72 y x z + 5/36 y x z + 1/144 y x z + + 4 2 4 3 4 3 3 4 + - 5/144 y x z - 5/288 y x z + 5/144 y x z - 1/72 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(-2, 1, 1) = 1/288 x y z - 1/108 x y z + 1/216 x y z + + 4 3 4 4 2 4 2 3 + - 1/54 x y z + 1/27 x y z - 1/72 x y z + 1/288 x y z + + 4 3 3 4 2 4 3 2 4 4 + + 1/216 x y z + 1/27 x y z - 1/54 x y z - 1/216 x z + + 4 2 2 4 3 2 4 4 3 + - 1/72 x y z - 1/108 x y z + 1/144 y x z + 1/54 x z - 1/54 y x z + + 3 2 4 3 2 3 3 4 + - 1/216 y x z - 2/27 z y x - 2/27 z y x + 1/108 y x z + + 2 2 3 2 2 2 3 2 + - 1/36 y x z + 1/144 y x z + 1/72 y x z - 1/27 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/288 y x z + 1/54 y x z + 1/27 y x z + 1/108 y x z + + 3 3 2 2 2 3 3 4 2 3 + - 1/27 z x + 1/54 y x z - 1/144 y x z + 1/54 x z - 1/27 z y x + + 3 2 3 3 2 2 3 + + 1/54 z y x + 1/27 z y x + 2/27 y x z - 1/27 z y x + 1/36 z y x + + 2 2 3 3 3 4 3 3 3 3 + + 1/36 z y x + 1/108 y x z - 1/216 x z - 1/108 y x z + + 2 2 2 2 2 2 2 + - 1/36 y x z + 1/72 y x z - 1/27 y x z + 2/27 y x z + + 3 2 3 2 4 3 3 + - 1/216 y x z + 1/27 x z - 1/54 x z - 1/54 y x z + 1/108 x z + + 2 3 2 4 3 2 4 4 + + 1/216 x z + 1/216 x z - 1/108 x z + 1/108 y x z - 1/108 x z + + 3 4 2 2 3 4 2 3 2 + + 1/108 x z - 1/54 x z + 1/54 y x z + 1/27 x z - 1/27 x z + + 2 2 4 2 3 4 3 3 4 + - 1/288 y x z - 1/144 y x z - 1/108 y x z , COEFF(-1, 1, 1) = + + 4 2 4 4 4 4 3 4 4 3 4 + - 1/72 x y z + 1/27 x y z - 1/54 x y z + 2/27 x y z - 4/27 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/18 x y z - 1/72 x y z - 1/54 x y z - 4/27 x y z + + 4 3 2 4 4 4 2 2 4 3 2 4 + + 2/27 x y z + 1/54 x z + 1/18 x y z + 1/27 x y z - 1/18 y x z + + 4 3 3 2 4 3 2 3 + - 2/27 x z + 4/27 y x z + 2/27 y x z + 4/27 z y x + 4/27 z y x + + 3 4 2 2 3 2 2 2 3 2 + - 2/27 y x z + 2/9 y x z - 1/18 y x z - 2/9 y x z + 8/27 y x z + + 2 2 3 3 3 3 3 2 2 3 3 + + 1/18 y x z - 1/27 y x z - 2/27 y x z - 4/27 y x z + 2/27 z x + + 3 2 2 2 3 3 4 2 3 3 2 + - 8/27 y x z + 1/72 y x z - 2/27 x z + 8/27 z y x - 8/27 z y x + + 3 3 16 16 2 2 3 2 2 3 + - 2/27 z y x - -- y x z + -- z y x - 1/18 z y x - 1/18 z y x + 27 27 + + 3 3 4 3 3 3 3 2 2 2 2 + - 2/27 y x z + 1/54 x z + 1/54 y x z + 2/9 y x z - 2/9 y x z + + 16 2 2 16 2 3 2 3 2 + + -- y x z - -- y x z + 2/27 y x z - 8/27 x z + 8/27 x z + 27 27 + + 4 3 3 2 3 2 4 3 + + 4/27 y x z - 1/54 x z - 2/27 x z - 2/27 x z + 2/27 x z + + 2 4 4 3 4 2 2 3 4 + - 4/27 y x z + 2/27 x z - 1/54 x z + 8/27 x z - 1/27 y x z + + 2 3 2 2 2 4 2 3 4 3 3 4 + - 8/27 x z + 2/27 x z + 1/18 y x z + 1/72 y x z + 1/54 y x z , + + 4 2 4 4 4 4 3 4 4 3 + COEFF(0, 1, 1) = 1/48 x y z - 1/18 x y z + 1/36 x y z - 1/9 x y z + + 4 4 2 4 2 3 4 3 3 4 2 + + 2/9 x y z - 1/12 x y z + 1/48 x y z + 1/36 x y z + 2/9 x y z + + 4 3 2 4 4 4 2 2 4 3 4 + - 1/9 x y z - 1/36 x z - 1/12 x y z - 1/18 x y z + 1/9 x z + + 3 2 4 2 2 2 2 2 3 2 3 + + 4/9 z - 5/36 y x z + 5/12 y x z - 5/48 y x z + 5/18 y x z + + 4 3 2 2 4 2 3 3 2 + - 1/9 z + 5/9 y x z + 1/9 x z - 1/9 z - 4/9 z y + 4/9 z + + 3 2 2 4 3 2 2 + + 5/9 z y x - 10/9 z y x + 8/9 y z - 1/36 x z + 5/12 y x z + + 2 2 2 3 2 3 2 3 + - 10/9 y x z - 1/3 y z - 5/36 y x z - 5/9 x z - 2/9 y z + + 2 3 3 3 2 3 4 3 4 3 2 + + 1/12 y z + 1/9 y z + 5/36 x z - 2/9 y z + 1/9 y z - 4/9 y z + + 2 4 2 4 2 2 2 2 4 + + 5/36 x z + 5/18 y x z + 8/9 y z - 5/9 x z + 1/12 y z + + 2 2 2 2 4 4 2 4 + - 1/3 y z - 5/48 y x z , COEFF(1, 1, 1) = - 1/72 x y z + + 4 4 4 3 4 4 3 4 4 2 + + 1/27 x y z - 1/54 x y z + 2/27 x y z - 4/27 x y z + 1/18 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/72 x y z - 1/54 x y z - 4/27 x y z + 2/27 x y z + + 4 4 4 2 2 4 3 2 4 4 + + 1/54 x z + 1/18 x y z + 1/27 x y z + 1/18 y x z - 2/27 x z + + 3 3 2 4 3 2 3 3 4 + - 4/27 y x z + 2/27 y x z - 4/27 z y x - 4/27 z y x + 2/27 y x z + + 2 2 3 2 2 2 3 2 2 2 3 + - 2/9 y x z + 1/18 y x z - 2/9 y x z - 8/27 y x z + 1/18 y x z + + 3 3 3 3 2 2 3 3 3 2 2 + + 1/27 y x z + 2/27 y x z - 4/27 y x z - 2/27 z x - 8/27 y x z + + 2 3 3 4 2 3 3 2 3 3 + - 1/72 y x z - 2/27 x z - 8/27 z y x - 8/27 z y x + 2/27 z y x + + 16 16 2 2 3 2 2 3 3 3 + + -- y x z + -- z y x + 1/18 z y x + 1/18 z y x + 2/27 y x z + 27 27 + + 4 3 3 3 3 2 2 2 2 16 2 2 + + 1/54 x z - 1/54 y x z - 2/9 y x z - 2/9 y x z + -- y x z + 27 + + 16 2 3 2 3 2 4 + + -- y x z + 2/27 y x z + 8/27 x z + 8/27 x z - 4/27 y x z + 27 + + 3 3 2 3 2 4 3 2 4 + + 1/54 x z - 2/27 x z - 2/27 x z - 2/27 x z - 4/27 y x z + + 4 3 4 2 2 3 4 2 + - 2/27 x z + 1/54 x z + 8/27 x z + 1/27 y x z + 8/27 x z + + 3 2 2 2 4 2 3 4 3 3 4 + - 2/27 x z + 1/18 y x z - 1/72 y x z - 1/54 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(2, 1, 1) = 1/288 x y z - 1/108 x y z + 1/216 x y z + + 4 3 4 4 2 4 2 3 + - 1/54 x y z + 1/27 x y z - 1/72 x y z + 1/288 x y z + + 4 3 3 4 2 4 3 2 4 4 + + 1/216 x y z + 1/27 x y z - 1/54 x y z - 1/216 x z + + 4 2 2 4 3 2 4 4 3 + - 1/72 x y z - 1/108 x y z - 1/144 y x z + 1/54 x z + 1/54 y x z + + 3 2 4 3 2 3 3 4 + - 1/216 y x z + 2/27 z y x + 2/27 z y x - 1/108 y x z + + 2 2 3 2 2 2 3 2 + + 1/36 y x z - 1/144 y x z + 1/72 y x z + 1/27 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/288 y x z - 1/54 y x z - 1/27 y x z + 1/108 y x z + + 3 3 2 2 2 3 3 4 2 3 + + 1/27 z x + 1/54 y x z + 1/144 y x z + 1/54 x z + 1/27 z y x + + 3 2 3 3 2 2 3 + + 1/54 z y x - 1/27 z y x - 2/27 y x z - 1/27 z y x - 1/36 z y x + + 2 2 3 3 3 4 3 3 3 3 + - 1/36 z y x - 1/108 y x z - 1/216 x z + 1/108 y x z + + 2 2 2 2 2 2 2 + + 1/36 y x z + 1/72 y x z - 1/27 y x z - 2/27 y x z + + 3 2 3 2 4 3 3 + - 1/216 y x z - 1/27 x z - 1/54 x z + 1/54 y x z - 1/108 x z + + 2 3 2 4 3 2 4 4 + + 1/216 x z + 1/216 x z + 1/108 x z + 1/108 y x z + 1/108 x z + + 3 4 2 2 3 4 2 3 2 + - 1/108 x z - 1/54 x z - 1/54 y x z - 1/27 x z + 1/27 x z + + 2 2 4 2 3 4 3 3 4 + - 1/288 y x z + 1/144 y x z + 1/108 y x z , COEFF(-2, 2, 1) = + + 4 2 4 4 4 4 3 4 4 3 + - 1/576 x y z + 1/1728 x y z - 1/864 x y z + 1/216 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/432 x y z + 1/144 x y z - 1/576 x y z - 1/864 x y z + + 4 2 4 3 2 4 4 4 2 2 + - 1/432 x y z + 1/216 x y z + 1/1728 x z + 1/144 x y z + + 4 3 2 4 4 3 + + 1/1728 x y z - 1/288 y x z - 1/432 x z + 1/864 y x z + + 3 2 4 3 2 3 3 4 + + 1/864 y x z + 1/216 z y x + 1/216 z y x - 1/432 y x z + + 2 2 3 2 2 2 3 2 + + 1/72 y x z - 1/288 y x z - 1/144 y x z + 1/108 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/576 y x z - 1/864 y x z - 1/108 y x z - 1/1728 y x z + + 3 3 2 2 2 3 3 4 2 + + 1/216 z x - 1/216 y x z + 1/288 y x z - 1/432 x z + + 3 3 2 3 3 + + 1/108 z y x - 1/216 z y x - 1/108 z y x - 1/216 y x z + + 2 2 3 2 2 3 3 3 + + 1/432 z y x - 1/72 z y x - 1/72 z y x - 1/432 y x z + + 4 3 3 3 3 2 2 2 2 + + 1/1728 x z + 1/432 y x z + 1/72 y x z - 1/144 y x z + + 2 2 2 3 2 3 2 + + 1/432 y x z - 1/216 y x z + 1/864 y x z - 1/216 x z + 1/432 x z + + 4 3 3 2 3 2 4 3 + + 1/864 y x z - 1/864 x z - 1/1728 x z - 1/1728 x z + 1/864 x z + + 2 4 4 3 4 2 2 3 4 + - 1/1728 y x z + 1/864 x z - 1/864 x z + 1/432 x z - 1/864 y x z + + 2 3 2 2 2 4 2 3 4 + - 1/216 x z + 1/216 x z + 1/576 y x z + 1/288 y x z + + 3 3 4 4 2 4 4 4 + + 1/432 y x z , COEFF(-1, 2, 1) = 1/144 x y z - 1/432 x y z + + 4 3 4 4 3 4 4 2 + + 1/216 x y z - 1/54 x y z + 1/108 x y z - 1/36 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + + 1/144 x y z + 1/216 x y z + 1/108 x y z - 1/54 x y z + + 4 4 4 2 2 4 3 2 4 4 + - 1/432 x z - 1/36 x y z - 1/432 x y z + 1/36 y x z + 1/108 x z + + 3 3 2 4 3 2 3 + - 1/108 y x z - 1/54 y x z - 1/108 z y x - 1/108 z y x + + 3 4 2 2 3 2 2 2 3 2 + + 1/54 y x z - 1/9 y x z + 1/36 y x z + 1/9 y x z - 2/27 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/36 y x z + 1/432 y x z + 1/54 y x z + 1/108 y x z + + 3 3 2 2 2 3 3 4 2 3 + - 1/108 z x + 2/27 y x z - 1/144 y x z + 1/108 x z - 2/27 z y x + + 3 2 3 3 2 2 3 + + 2/27 z y x + 1/54 z y x + 1/27 y x z - 1/27 z y x + 1/36 z y x + + 2 2 3 3 3 4 3 3 3 3 + + 1/36 z y x + 1/54 y x z - 1/432 x z - 1/216 y x z + + 2 2 2 2 2 2 2 3 2 3 + - 1/9 y x z + 1/9 y x z - 1/27 y x z + 1/27 y x z - 1/54 y x z + + 2 4 3 3 2 3 + + 1/27 x z - 1/27 x z - 1/108 y x z + 1/432 x z + 1/108 x z + + 2 4 3 2 4 4 3 4 + + 1/108 x z - 1/108 x z + 1/108 y x z - 1/108 x z + 1/432 x z + + 2 2 3 4 2 3 2 2 2 4 + - 1/27 x z + 1/432 y x z + 1/27 x z - 1/108 x z - 1/36 y x z + + 2 3 4 3 3 4 4 2 4 + - 1/144 y x z - 1/216 y x z , COEFF(0, 2, 1) = - 1/96 x y z + + 4 4 4 3 4 4 3 4 + + 1/288 x y z - 1/144 x y z + 1/36 x y z - 1/72 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/24 x y z - 1/96 x y z - 1/144 x y z - 1/72 x y z + + 4 3 2 4 4 4 2 2 4 3 4 + + 1/36 x y z + 1/288 x z + 1/24 x y z + 1/288 x y z - 1/72 x z + + 3 2 4 2 2 2 2 2 3 2 3 + - 1/18 z + 5/144 y x z - 5/24 y x z + 5/96 y x z - 5/288 y x z + + 4 3 2 2 4 2 3 3 2 + + 1/72 z - 5/36 y x z - 1/72 x z + 1/72 z + 1/9 z y - 1/18 z + + 3 2 2 4 3 2 2 + - 5/36 z y x + 5/72 z y x - 1/18 y z + 1/288 x z - 5/24 y x z + + 2 2 2 3 2 3 2 3 + + 5/72 y x z + 1/6 y z + 5/144 y x z + 5/72 x z + 1/72 y z + + 2 3 3 3 2 3 4 3 4 + - 1/24 y z - 1/36 y z - 5/288 x z + 1/72 y z - 1/36 y z + + 3 2 2 4 2 4 2 2 2 + + 1/9 y z - 5/288 x z - 5/288 y x z - 1/18 y z + 5/72 x z + + 2 4 2 2 2 2 4 4 2 4 + - 1/24 y z + 1/6 y z + 5/96 y x z , COEFF(1, 2, 1) = 1/144 x y z + + 4 4 4 3 4 4 3 4 + - 1/432 x y z + 1/216 x y z - 1/54 x y z + 1/108 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/36 x y z + 1/144 x y z + 1/216 x y z + 1/108 x y z + + 4 3 2 4 4 4 2 2 4 3 + - 1/54 x y z - 1/432 x z - 1/36 x y z - 1/432 x y z + + 2 4 4 3 3 2 4 3 + - 1/36 y x z + 1/108 x z + 1/108 y x z - 1/54 y x z + 1/108 z y x + + 2 3 3 4 2 2 3 2 2 2 + + 1/108 z y x - 1/54 y x z + 1/9 y x z - 1/36 y x z + 1/9 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 2/27 y x z - 1/36 y x z - 1/432 y x z - 1/54 y x z + + 2 3 3 3 2 2 2 3 3 + + 1/108 y x z + 1/108 z x + 2/27 y x z + 1/144 y x z + + 4 2 3 3 2 3 3 + + 1/108 x z + 2/27 z y x + 2/27 z y x - 1/54 z y x - 1/27 y x z + + 2 2 3 2 2 3 3 3 4 3 + - 1/27 z y x - 1/36 z y x - 1/36 z y x - 1/54 y x z - 1/432 x z + + 3 3 3 2 2 2 2 2 2 2 + + 1/216 y x z + 1/9 y x z + 1/9 y x z - 1/27 y x z - 1/27 y x z + + 3 2 3 2 4 3 3 + - 1/54 y x z - 1/27 x z - 1/27 x z + 1/108 y x z - 1/432 x z + + 2 3 2 4 3 2 4 4 + + 1/108 x z + 1/108 x z + 1/108 x z + 1/108 y x z + 1/108 x z + + 3 4 2 2 3 4 2 3 2 + - 1/432 x z - 1/27 x z - 1/432 y x z - 1/27 x z + 1/108 x z + + 2 2 4 2 3 4 3 3 4 + - 1/36 y x z + 1/144 y x z + 1/216 y x z , COEFF(2, 2, 1) = + + 4 2 4 4 4 4 3 4 4 3 + - 1/576 x y z + 1/1728 x y z - 1/864 x y z + 1/216 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/432 x y z + 1/144 x y z - 1/576 x y z - 1/864 x y z + + 4 2 4 3 2 4 4 4 2 2 + - 1/432 x y z + 1/216 x y z + 1/1728 x z + 1/144 x y z + + 4 3 2 4 4 3 + + 1/1728 x y z + 1/288 y x z - 1/432 x z - 1/864 y x z + + 3 2 4 3 2 3 3 4 + + 1/864 y x z - 1/216 z y x - 1/216 z y x + 1/432 y x z + + 2 2 3 2 2 2 3 2 + - 1/72 y x z + 1/288 y x z - 1/144 y x z - 1/108 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/576 y x z + 1/864 y x z + 1/108 y x z - 1/1728 y x z + + 3 3 2 2 2 3 3 4 2 + - 1/216 z x - 1/216 y x z - 1/288 y x z - 1/432 x z + + 3 3 2 3 3 + - 1/108 z y x - 1/216 z y x + 1/108 z y x + 1/216 y x z + + 2 2 3 2 2 3 3 3 + + 1/432 z y x + 1/72 z y x + 1/72 z y x + 1/432 y x z + + 4 3 3 3 3 2 2 2 2 + + 1/1728 x z - 1/432 y x z - 1/72 y x z - 1/144 y x z + + 2 2 2 3 2 3 2 + + 1/432 y x z + 1/216 y x z + 1/864 y x z + 1/216 x z + 1/432 x z + + 4 3 3 2 3 2 4 3 + - 1/864 y x z + 1/864 x z - 1/1728 x z - 1/1728 x z - 1/864 x z + + 2 4 4 3 4 2 2 3 4 + - 1/1728 y x z - 1/864 x z + 1/864 x z + 1/432 x z + 1/864 y x z + + 2 3 2 2 2 4 2 3 4 + + 1/216 x z - 1/216 x z + 1/576 y x z - 1/288 y x z + + 3 3 4 4 2 4 4 4 + - 1/432 y x z , COEFF(-2, -2, 2) = - 1/2304 x y z - 1/6912 x y z + + 4 3 4 4 3 4 4 2 + + 1/3456 x y z - 1/1728 x y z + 1/3456 x y z + 1/1152 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/1152 x y z + 1/1728 x y z + 1/6912 x y z - 1/3456 x y z + + 4 4 4 2 2 4 3 2 4 + + 1/6912 x z + 1/2304 x y z - 1/3456 x y z - 1/1152 y x z + + 4 3 3 2 4 3 + - 1/3456 x z - 1/1728 y x z - 1/3456 y x z - 1/1728 z y x + + 2 3 3 4 2 2 3 + - 1/3456 z y x + 1/1728 y x z + 1/576 y x z - 1/576 y x z + + 2 2 2 3 2 2 2 3 3 3 + - 1/2304 y x z - 1/1728 y x z + 1/1152 y x z + 1/1728 y x z + + 3 3 2 2 3 3 3 2 2 + + 1/1728 y x z + 1/3456 y x z + 1/1728 z x + 1/3456 y x z + + 2 3 3 4 2 3 3 2 + + 1/576 y x z - 1/6912 x z - 1/864 z y x + 1/1728 z y x + + 3 3 2 2 3 + + 1/864 z y x + 1/1728 y x z - 1/3456 z y x - 1/576 z y x + + 2 2 3 3 3 4 3 3 3 3 + - 1/1152 z y x + 1/864 y x z + 1/3456 x z - 1/864 y x z + + 2 2 2 2 2 2 2 + + 1/1152 y x z - 1/1152 y x z - 1/6912 y x z + 1/3456 y x z + + 3 2 3 2 4 + - 1/1728 y x z - 1/1728 x z + 1/3456 x z - 1/3456 y x z + + 3 3 2 3 2 4 3 + - 1/1728 x z - 1/3456 x z - 1/6912 x z + 1/1728 x z + + 2 4 4 3 4 2 2 + + 1/6912 y x z + 1/3456 x z - 1/3456 x z + 1/6912 x z + + 3 4 2 3 2 2 2 4 + + 1/3456 y x z - 1/3456 x z + 1/3456 x z + 1/2304 y x z + + 2 3 4 3 3 4 4 2 4 + + 1/1152 y x z - 1/1728 y x z , COEFF(-1, -2, 2) = 1/576 x y z + + 4 4 4 3 4 4 3 4 + + 1/1728 x y z - 1/864 x y z + 1/432 x y z - 1/864 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/288 x y z + 1/288 x y z - 1/432 x y z - 1/1728 x y z + + 4 3 2 4 4 4 2 2 4 3 + + 1/864 x y z - 1/1728 x z - 1/576 x y z + 1/864 x y z + + 2 4 4 3 3 2 4 + + 1/144 y x z + 1/864 x z + 1/216 y x z + 1/216 y x z + + 3 2 3 3 4 2 + + 1/864 z y x + 1/1728 z y x - 1/216 y x z - 1/72 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/72 y x z + 1/144 y x z + 1/216 y x z - 1/72 y x z + + 3 3 3 3 2 2 3 3 + - 1/864 y x z - 1/864 y x z - 1/216 y x z - 1/864 z x + + 3 2 2 2 3 3 4 2 3 + - 1/216 y x z - 1/288 y x z + 1/1728 x z + 1/108 z y x + + 3 2 3 3 2 + - 1/108 z y x - 1/432 z y x - 1/216 y x z + 1/216 z y x + + 2 3 2 2 3 3 3 4 3 + + 1/288 z y x + 1/576 z y x - 1/108 y x z - 1/864 x z + + 3 3 3 2 2 2 2 2 2 + + 1/432 y x z - 1/144 y x z + 1/72 y x z + 1/432 y x z + + 2 3 2 3 2 4 + - 1/432 y x z + 1/108 y x z + 1/216 x z - 1/216 x z + 1/432 y x z + + 3 3 2 3 2 4 3 2 4 + + 1/864 x z + 1/216 x z + 1/432 x z - 1/216 x z - 1/432 y x z + + 4 3 4 2 2 3 4 2 + - 1/432 x z + 1/1728 x z - 1/432 x z - 1/1728 y x z + 1/432 x z + + 3 2 2 2 4 2 3 4 3 3 4 + - 1/1728 x z - 1/144 y x z - 1/576 y x z + 1/864 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(0, -2, 2) = - 1/384 x y z - 1/1152 x y z + 1/576 x y z + + 4 3 4 4 2 4 2 3 + - 1/288 x y z + 1/576 x y z + 1/192 x y z - 1/192 x y z + + 4 3 3 4 2 4 3 2 4 4 + + 1/288 x y z + 1/1152 x y z - 1/576 x y z + 1/1152 x z + + 4 2 2 4 3 4 3 2 4 + + 1/384 x y z - 1/576 x y z - 1/576 x z - 1/144 z - 5/576 y x z + + 2 2 2 2 2 3 2 3 4 + - 5/384 y x z + 5/192 y x z + 5/576 y x z + 1/288 z + + 3 2 2 4 2 3 3 2 + + 5/576 y x z - 1/1152 x z + 1/144 z - 1/72 z y - 1/288 z + + 3 2 2 4 3 2 2 + + 5/288 z y x - 5/576 z y x + 1/144 y z + 1/576 x z - 5/192 y x z + + 2 2 2 3 2 3 2 3 + - 5/1152 y x z + 1/48 y z - 5/288 y x z + 5/576 x z - 1/144 y z + + 2 3 3 3 2 3 4 3 4 + - 1/48 y z + 1/72 y z - 5/576 x z - 1/288 y z + 1/144 y z + + 3 2 2 4 2 4 2 2 2 + - 1/144 y z - 5/1152 x z + 5/1152 y x z + 1/288 y z + 5/1152 x z + + 2 4 2 2 2 2 4 + - 1/96 y z + 1/96 y z + 5/384 y x z , COEFF(1, -2, 2) = + + 4 2 4 4 4 4 3 4 4 3 + 1/576 x y z + 1/1728 x y z - 1/864 x y z + 1/432 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/864 x y z - 1/288 x y z + 1/288 x y z - 1/432 x y z + + 4 2 4 3 2 4 4 4 2 2 + - 1/1728 x y z + 1/864 x y z - 1/1728 x z - 1/576 x y z + + 4 3 2 4 4 3 + + 1/864 x y z - 1/144 y x z + 1/864 x z - 1/216 y x z + + 3 2 4 3 2 3 3 4 + + 1/216 y x z - 1/864 z y x - 1/1728 z y x + 1/216 y x z + + 2 2 3 2 2 2 3 2 + + 1/72 y x z - 1/72 y x z + 1/144 y x z - 1/216 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/72 y x z + 1/864 y x z + 1/864 y x z - 1/216 y x z + + 3 3 2 2 2 3 3 4 2 + + 1/864 z x - 1/216 y x z + 1/288 y x z + 1/1728 x z + + 3 3 2 3 3 + - 1/108 z y x - 1/108 z y x + 1/432 z y x + 1/216 y x z + + 2 2 3 2 2 3 3 3 + + 1/216 z y x - 1/288 z y x - 1/576 z y x + 1/108 y x z + + 4 3 3 3 3 2 2 2 2 + - 1/864 x z - 1/432 y x z + 1/144 y x z + 1/72 y x z + + 2 2 2 3 2 3 2 + + 1/432 y x z + 1/432 y x z + 1/108 y x z - 1/216 x z - 1/216 x z + + 4 3 3 2 3 2 4 3 + - 1/432 y x z - 1/864 x z + 1/216 x z + 1/432 x z + 1/216 x z + + 2 4 4 3 4 2 2 3 4 + - 1/432 y x z + 1/432 x z - 1/1728 x z - 1/432 x z + 1/1728 y x z + + 2 3 2 2 2 4 2 3 4 + - 1/432 x z + 1/1728 x z - 1/144 y x z + 1/576 y x z + + 3 3 4 4 2 4 4 4 + - 1/864 y x z , COEFF(2, -2, 2) = - 1/2304 x y z - 1/6912 x y z + + 4 3 4 4 3 4 4 2 + + 1/3456 x y z - 1/1728 x y z + 1/3456 x y z + 1/1152 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/1152 x y z + 1/1728 x y z + 1/6912 x y z - 1/3456 x y z + + 4 4 4 2 2 4 3 2 4 + + 1/6912 x z + 1/2304 x y z - 1/3456 x y z + 1/1152 y x z + + 4 3 3 2 4 3 + - 1/3456 x z + 1/1728 y x z - 1/3456 y x z + 1/1728 z y x + + 2 3 3 4 2 2 3 + + 1/3456 z y x - 1/1728 y x z - 1/576 y x z + 1/576 y x z + + 2 2 2 3 2 2 2 3 3 3 + - 1/2304 y x z + 1/1728 y x z + 1/1152 y x z - 1/1728 y x z + + 3 3 2 2 3 3 3 2 2 + - 1/1728 y x z + 1/3456 y x z - 1/1728 z x + 1/3456 y x z + + 2 3 3 4 2 3 3 2 + - 1/576 y x z - 1/6912 x z + 1/864 z y x + 1/1728 z y x + + 3 3 2 2 3 + - 1/864 z y x - 1/1728 y x z - 1/3456 z y x + 1/576 z y x + + 2 2 3 3 3 4 3 3 3 3 + + 1/1152 z y x - 1/864 y x z + 1/3456 x z + 1/864 y x z + + 2 2 2 2 2 2 2 + - 1/1152 y x z - 1/1152 y x z - 1/6912 y x z - 1/3456 y x z + + 3 2 3 2 4 + - 1/1728 y x z + 1/1728 x z + 1/3456 x z + 1/3456 y x z + + 3 3 2 3 2 4 3 + + 1/1728 x z - 1/3456 x z - 1/6912 x z - 1/1728 x z + + 2 4 4 3 4 2 2 + + 1/6912 y x z - 1/3456 x z + 1/3456 x z + 1/6912 x z + + 3 4 2 3 2 2 2 4 + - 1/3456 y x z + 1/3456 x z - 1/3456 x z + 1/2304 y x z + + 2 3 4 3 3 4 4 2 4 + - 1/1152 y x z + 1/1728 y x z , COEFF(-2, -1, 2) = 1/1152 x y z + + 4 4 4 3 4 4 3 4 + + 1/432 x y z - 1/864 x y z + 1/432 x y z - 1/216 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/576 x y z + 1/576 x y z - 1/432 x y z - 1/432 x y z + + 4 3 2 4 4 4 2 2 4 3 + + 1/864 x y z - 1/864 x z - 1/1152 x y z + 1/216 x y z + + 2 4 4 3 3 2 4 + + 1/576 y x z + 1/432 x z + 1/108 y x z + 1/864 y x z + + 3 2 3 3 4 2 + + 1/108 z y x + 1/216 z y x - 1/432 y x z - 1/288 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/288 y x z + 1/1152 y x z + 1/432 y x z - 1/576 y x z + + 3 3 3 3 2 2 3 3 + - 1/108 y x z - 1/432 y x z - 1/216 y x z - 1/216 z x + + 3 2 2 2 3 3 4 2 3 + - 1/864 y x z - 1/288 y x z + 1/864 x z + 1/216 z y x + + 3 2 3 3 2 + - 1/432 z y x - 1/216 z y x - 1/108 y x z + 1/216 z y x + + 2 3 2 2 3 3 3 4 3 + + 1/288 z y x + 1/576 z y x - 1/216 y x z - 1/432 x z + + 3 3 3 2 2 2 2 2 2 + + 1/216 y x z - 1/576 y x z + 1/576 y x z + 1/432 y x z + + 2 3 2 3 2 4 + - 1/216 y x z + 1/432 y x z + 1/216 x z - 1/432 x z + 1/216 y x z + + 3 3 2 3 2 4 3 2 4 + + 1/216 x z + 1/432 x z + 1/864 x z - 1/216 x z - 1/432 y x z + + 4 3 4 2 2 3 4 2 + - 1/432 x z + 1/432 x z - 1/864 x z - 1/216 y x z + 1/432 x z + + 3 2 2 2 4 2 3 4 3 3 4 + - 1/432 x z - 1/1152 y x z - 1/576 y x z + 1/432 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(-1, -1, 2) = - 1/288 x y z - 1/108 x y z + 1/216 x y z + + 4 3 4 4 2 4 2 3 + - 1/108 x y z + 1/54 x y z + 1/144 x y z - 1/144 x y z + + 4 3 3 4 2 4 3 2 4 4 + + 1/108 x y z + 1/108 x y z - 1/216 x y z + 1/216 x z + + 4 2 2 4 3 2 4 4 3 + + 1/288 x y z - 1/54 x y z - 1/72 y x z - 1/108 x z - 2/27 y x z + + 3 2 4 3 2 3 3 4 2 + - 1/54 y x z - 1/54 z y x - 1/108 z y x + 1/54 y x z + 1/36 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/36 y x z - 1/72 y x z - 1/54 y x z + 1/36 y x z + + 3 3 3 3 2 2 3 3 + + 1/54 y x z + 1/216 y x z + 2/27 y x z + 1/108 z x + + 3 2 2 2 3 3 4 2 3 + + 1/54 y x z + 1/144 y x z - 1/216 x z - 1/27 z y x + + 3 2 3 3 2 2 3 + + 1/27 z y x + 1/108 z y x + 2/27 y x z - 2/27 z y x - 1/144 z y x + + 2 2 3 3 3 4 3 3 3 3 + - 1/288 z y x + 1/27 y x z + 1/108 x z - 1/108 y x z + + 2 2 2 2 2 2 2 3 2 3 + + 1/72 y x z - 1/36 y x z - 1/27 y x z + 1/27 y x z - 1/27 y x z + + 2 4 3 3 2 3 + - 1/27 x z + 1/27 x z - 1/27 y x z - 1/108 x z - 1/27 x z + + 2 4 3 2 4 4 3 4 + - 1/54 x z + 1/27 x z + 1/27 y x z + 1/54 x z - 1/216 x z + + 2 2 3 4 2 3 2 2 2 4 + + 1/54 x z + 1/108 y x z - 1/54 x z + 1/216 x z + 1/72 y x z + + 2 3 4 3 3 4 4 2 4 + + 1/288 y x z - 1/216 y x z , COEFF(0, -1, 2) = 1/192 x y z + + 4 4 4 3 4 4 3 4 + + 1/72 x y z - 1/144 x y z + 1/72 x y z - 1/36 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/96 x y z + 1/96 x y z - 1/72 x y z - 1/72 x y z + + 4 3 2 4 4 4 2 2 4 3 4 + + 1/144 x y z - 1/144 x z - 1/192 x y z + 1/36 x y z + 1/72 x z + + 3 2 4 2 2 2 2 2 3 2 3 + + 1/18 z + 5/144 y x z + 5/192 y x z - 5/96 y x z - 5/36 y x z + + 4 3 2 2 4 2 3 3 2 + - 1/36 z - 5/144 y x z + 1/144 x z - 1/18 z + 1/18 z y + 1/36 z + + 3 2 2 4 3 2 2 + - 5/72 z y x + 5/36 z y x - 1/9 y z - 1/72 x z + 5/96 y x z + + 2 2 2 3 2 3 2 3 + + 5/72 y x z - 1/24 y z + 5/72 y x z - 5/72 x z + 1/9 y z + + 2 3 3 3 2 3 4 3 4 + + 1/24 y z - 1/18 y z + 5/72 x z + 1/18 y z - 1/36 y z + + 3 2 2 4 2 4 2 2 2 + + 1/36 y z + 5/144 x z - 5/72 y x z - 1/18 y z - 5/144 x z + + 2 4 2 2 2 2 4 + + 1/48 y z - 1/48 y z - 5/192 y x z , COEFF(1, -1, 2) = + + 4 2 4 4 4 4 3 4 4 3 + - 1/288 x y z - 1/108 x y z + 1/216 x y z - 1/108 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/54 x y z + 1/144 x y z - 1/144 x y z + 1/108 x y z + + 4 2 4 3 2 4 4 4 2 2 + + 1/108 x y z - 1/216 x y z + 1/216 x z + 1/288 x y z + + 4 3 2 4 4 3 3 2 4 + - 1/54 x y z + 1/72 y x z - 1/108 x z + 2/27 y x z - 1/54 y x z + + 3 2 3 3 4 2 2 3 + + 1/54 z y x + 1/108 z y x - 1/54 y x z - 1/36 y x z + 1/36 y x z + + 2 2 2 3 2 2 2 3 3 3 + - 1/72 y x z + 1/54 y x z + 1/36 y x z - 1/54 y x z + + 3 3 2 2 3 3 3 2 2 + - 1/216 y x z + 2/27 y x z - 1/108 z x + 1/54 y x z + + 2 3 3 4 2 3 3 2 + - 1/144 y x z - 1/216 x z + 1/27 z y x + 1/27 z y x + + 3 3 2 2 3 + - 1/108 z y x - 2/27 y x z - 2/27 z y x + 1/144 z y x + + 2 2 3 3 3 4 3 3 3 3 + + 1/288 z y x - 1/27 y x z + 1/108 x z + 1/108 y x z + + 2 2 2 2 2 2 2 3 2 3 + - 1/72 y x z - 1/36 y x z - 1/27 y x z - 1/27 y x z - 1/27 y x z + + 2 4 3 3 2 3 + + 1/27 x z + 1/27 x z + 1/27 y x z + 1/108 x z - 1/27 x z + + 2 4 3 2 4 4 3 4 + - 1/54 x z - 1/27 x z + 1/27 y x z - 1/54 x z + 1/216 x z + + 2 2 3 4 2 3 2 2 2 4 + + 1/54 x z - 1/108 y x z + 1/54 x z - 1/216 x z + 1/72 y x z + + 2 3 4 3 3 4 4 2 4 + - 1/288 y x z + 1/216 y x z , COEFF(2, -1, 2) = 1/1152 x y z + + 4 4 4 3 4 4 3 4 + + 1/432 x y z - 1/864 x y z + 1/432 x y z - 1/216 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/576 x y z + 1/576 x y z - 1/432 x y z - 1/432 x y z + + 4 3 2 4 4 4 2 2 4 3 + + 1/864 x y z - 1/864 x z - 1/1152 x y z + 1/216 x y z + + 2 4 4 3 3 2 4 + - 1/576 y x z + 1/432 x z - 1/108 y x z + 1/864 y x z + + 3 2 3 3 4 2 + - 1/108 z y x - 1/216 z y x + 1/432 y x z + 1/288 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/288 y x z + 1/1152 y x z - 1/432 y x z - 1/576 y x z + + 3 3 3 3 2 2 3 3 + + 1/108 y x z + 1/432 y x z - 1/216 y x z + 1/216 z x + + 3 2 2 2 3 3 4 2 3 + - 1/864 y x z + 1/288 y x z + 1/864 x z - 1/216 z y x + + 3 2 3 3 2 + - 1/432 z y x + 1/216 z y x + 1/108 y x z + 1/216 z y x + + 2 3 2 2 3 3 3 4 3 + - 1/288 z y x - 1/576 z y x + 1/216 y x z - 1/432 x z + + 3 3 3 2 2 2 2 2 2 + - 1/216 y x z + 1/576 y x z + 1/576 y x z + 1/432 y x z + + 2 3 2 3 2 4 + + 1/216 y x z + 1/432 y x z - 1/216 x z - 1/432 x z - 1/216 y x z + + 3 3 2 3 2 4 3 2 4 + - 1/216 x z + 1/432 x z + 1/864 x z + 1/216 x z - 1/432 y x z + + 4 3 4 2 2 3 4 2 + + 1/432 x z - 1/432 x z - 1/864 x z + 1/216 y x z - 1/432 x z + + 3 2 2 2 4 2 3 4 3 3 4 + + 1/432 x z - 1/1152 y x z + 1/576 y x z - 1/432 y x z , + + 4 4 4 3 4 4 3 + COEFF(-2, 0, 2) = - 5/1152 x y z + 1/576 x y z - 1/288 x y z + + 4 4 3 3 4 2 4 3 2 + + 5/576 x y z + 1/288 x y z + 5/1152 x y z - 1/576 x y z + + 4 3 3 3 2 4 3 + - 5/576 x y z - 5/288 y x z - 1/576 y x z - 5/288 z y x + + 2 3 3 4 3 2 3 3 + - 5/576 z y x + 1/288 y x z - 1/288 y x z + 5/288 y x z + + 3 3 2 2 3 3 2 2 3 + + 1/288 y x z + 5/576 y x z + 1/576 y x z - 1/144 z y x + + 3 2 3 3 2 + + 1/288 z y x + 1/144 z y x + 5/288 y x z - 5/576 z y x + + 3 3 3 3 3 2 2 2 + + 1/144 y x z - 1/144 y x z - 5/1152 y x z + 5/576 y x z + + 3 2 3 4 2 4 3 4 + - 1/288 y x z - 5/576 y x z + 5/1152 y x z + 5/576 y x z + + 3 3 4 4 4 4 3 4 + - 1/288 y x z , COEFF(-1, 0, 2) = 5/288 x y z - 1/144 x y z + + 4 3 4 4 3 3 4 2 + + 1/72 x y z - 5/144 x y z - 1/72 x y z - 5/288 x y z + + 4 3 2 4 3 3 3 2 4 + + 1/144 x y z + 5/144 x y z + 5/36 y x z + 1/36 y x z + + 3 2 3 3 4 3 2 + + 5/144 z y x + 5/288 z y x - 1/36 y x z + 1/36 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 5/144 y x z - 1/144 y x z - 5/36 y x z - 1/36 y x z + + 3 3 2 3 3 2 + + 1/18 z y x - 1/18 z y x - 1/72 z y x - 5/36 y x z + 5/36 z y x + + 3 3 3 3 3 2 2 2 + - 1/18 y x z + 1/72 y x z + 5/72 y x z - 5/72 y x z + + 3 2 3 4 2 4 3 4 + + 1/18 y x z + 5/72 y x z - 5/72 y x z - 5/288 y x z + + 3 3 4 4 3 2 3 2 + + 1/144 y x z , COEFF(0, 0, 2) = - 1/96 x y z + 5/48 z y x + + 25 2 3 2 3 2 3 4 3 4 + + -- y x z + 5/48 y z - 5/48 y x z + 5/24 y z + 1/96 x y z + 96 + + 3 4 3 3 25 2 4 4 2 + + 1/24 y z + 1/12 y z - -- z y x - 5/48 y z + 5/192 x y z + 96 + + 4 4 3 2 4 3 2 2 4 3 2 + - 5/192 x y z - 5/96 y x z + 5/96 y x z + 5/96 x y z - 1/24 y z + + 4 3 25 2 4 4 3 25 2 2 3 + - 5/96 x y z + --- y x z - 1/48 x y z - --- y x z - 1/12 z y + 192 192 + + 4 3 3 3 4 4 + + 1/48 x y z - 5/24 y z , COEFF(1, 0, 2) = 5/288 x y z + + 4 3 4 4 3 4 4 3 3 + - 1/144 x y z + 1/72 x y z - 5/144 x y z - 1/72 x y z + + 4 2 4 3 2 4 3 3 + - 5/288 x y z + 1/144 x y z + 5/144 x y z - 5/36 y x z + + 3 2 4 3 2 3 3 4 + + 1/36 y x z - 5/144 z y x - 5/288 z y x + 1/36 y x z + + 3 2 3 3 3 3 2 2 3 + - 1/36 y x z + 5/144 y x z + 1/144 y x z - 5/36 y x z + + 3 2 2 3 3 2 3 3 + - 1/36 y x z - 1/18 z y x - 1/18 z y x + 1/72 z y x + 5/36 y x z + + 2 3 3 3 3 3 2 2 2 + + 5/36 z y x + 1/18 y x z - 1/72 y x z + 5/72 y x z + 5/72 y x z + + 3 2 3 4 2 4 3 4 + + 1/18 y x z - 5/72 y x z - 5/72 y x z + 5/288 y x z + + 3 3 4 4 4 4 3 4 + - 1/144 y x z , COEFF(2, 0, 2) = - 5/1152 x y z + 1/576 x y z + + 4 3 4 4 3 3 4 2 + - 1/288 x y z + 5/576 x y z + 1/288 x y z + 5/1152 x y z + + 4 3 2 4 3 3 3 2 4 + - 1/576 x y z - 5/576 x y z + 5/288 y x z - 1/576 y x z + + 3 2 3 3 4 3 2 + + 5/288 z y x + 5/576 z y x - 1/288 y x z + 1/288 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 5/288 y x z - 1/288 y x z + 5/576 y x z + 1/576 y x z + + 3 3 2 3 3 + + 1/144 z y x + 1/288 z y x - 1/144 z y x - 5/288 y x z + + 2 3 3 3 3 3 2 2 + - 5/576 z y x - 1/144 y x z + 1/144 y x z - 5/1152 y x z + + 2 3 2 3 4 2 4 + - 5/576 y x z - 1/288 y x z + 5/576 y x z + 5/1152 y x z + + 3 4 3 3 4 4 2 4 + - 5/576 y x z + 1/288 y x z , COEFF(-2, 1, 2) = - 1/1152 x y z + + 4 4 4 3 4 4 3 4 + + 1/432 x y z - 1/864 x y z + 1/432 x y z - 1/216 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/576 x y z - 1/576 x y z - 1/432 x y z - 1/432 x y z + + 4 3 2 4 4 4 2 2 4 3 + + 1/864 x y z + 1/864 x z + 1/1152 x y z + 1/216 x y z + + 2 4 4 3 3 2 4 + - 1/576 y x z - 1/432 x z + 1/108 y x z + 1/864 y x z + + 3 2 3 3 4 2 + + 1/108 z y x + 1/216 z y x - 1/432 y x z + 1/288 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/288 y x z - 1/1152 y x z + 1/432 y x z + 1/576 y x z + + 3 3 3 3 2 2 3 3 + - 1/108 y x z - 1/432 y x z - 1/216 y x z + 1/216 z x + + 3 2 2 2 3 3 4 2 3 + - 1/864 y x z + 1/288 y x z - 1/864 x z + 1/216 z y x + + 3 2 3 3 2 + - 1/432 z y x - 1/216 z y x - 1/108 y x z + 1/216 z y x + + 2 3 2 2 3 3 3 4 3 + - 1/288 z y x - 1/576 z y x - 1/216 y x z + 1/432 x z + + 3 3 3 2 2 2 2 2 2 + + 1/216 y x z + 1/576 y x z - 1/576 y x z + 1/432 y x z + + 2 3 2 3 2 4 + - 1/216 y x z + 1/432 y x z - 1/216 x z + 1/432 x z + 1/216 y x z + + 3 3 2 3 2 4 3 2 4 + - 1/216 x z - 1/432 x z - 1/864 x z + 1/216 x z - 1/432 y x z + + 4 3 4 2 2 3 4 2 + + 1/432 x z - 1/432 x z + 1/864 x z - 1/216 y x z - 1/432 x z + + 3 2 2 2 4 2 3 4 3 3 4 + + 1/432 x z + 1/1152 y x z + 1/576 y x z + 1/432 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(-1, 1, 2) = 1/288 x y z - 1/108 x y z + 1/216 x y z + + 4 3 4 4 2 4 2 3 + - 1/108 x y z + 1/54 x y z - 1/144 x y z + 1/144 x y z + + 4 3 3 4 2 4 3 2 4 4 + + 1/108 x y z + 1/108 x y z - 1/216 x y z - 1/216 x z + + 4 2 2 4 3 2 4 4 3 + - 1/288 x y z - 1/54 x y z + 1/72 y x z + 1/108 x z - 2/27 y x z + + 3 2 4 3 2 3 3 4 2 + - 1/54 y x z - 1/54 z y x - 1/108 z y x + 1/54 y x z - 1/36 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/36 y x z + 1/72 y x z - 1/54 y x z - 1/36 y x z + + 3 3 3 3 2 2 3 3 + + 1/54 y x z + 1/216 y x z + 2/27 y x z - 1/108 z x + + 3 2 2 2 3 3 4 2 3 + + 1/54 y x z - 1/144 y x z + 1/216 x z - 1/27 z y x + + 3 2 3 3 2 2 3 + + 1/27 z y x + 1/108 z y x + 2/27 y x z - 2/27 z y x + 1/144 z y x + + 2 2 3 3 3 4 3 3 3 3 + + 1/288 z y x + 1/27 y x z - 1/108 x z - 1/108 y x z + + 2 2 2 2 2 2 2 3 2 3 + - 1/72 y x z + 1/36 y x z - 1/27 y x z + 1/27 y x z - 1/27 y x z + + 2 4 3 3 2 3 + + 1/27 x z - 1/27 x z - 1/27 y x z + 1/108 x z + 1/27 x z + + 2 4 3 2 4 4 3 4 + + 1/54 x z - 1/27 x z + 1/27 y x z - 1/54 x z + 1/216 x z + + 2 2 3 4 2 3 2 2 2 4 + - 1/54 x z + 1/108 y x z + 1/54 x z - 1/216 x z - 1/72 y x z + + 2 3 4 3 3 4 4 2 4 + - 1/288 y x z - 1/216 y x z , COEFF(0, 1, 2) = - 1/192 x y z + + 4 4 4 3 4 4 3 4 + + 1/72 x y z - 1/144 x y z + 1/72 x y z - 1/36 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/96 x y z - 1/96 x y z - 1/72 x y z - 1/72 x y z + + 4 3 2 4 4 4 2 2 4 3 4 + + 1/144 x y z + 1/144 x z + 1/192 x y z + 1/36 x y z - 1/72 x z + + 3 2 4 2 2 2 2 2 3 2 3 + - 1/18 z + 5/144 y x z - 5/192 y x z + 5/96 y x z - 5/36 y x z + + 4 3 2 2 4 2 3 3 2 + + 1/36 z - 5/144 y x z - 1/144 x z + 1/18 z + 1/18 z y - 1/36 z + + 3 2 2 4 3 2 2 + - 5/72 z y x + 5/36 z y x - 1/9 y z + 1/72 x z - 5/96 y x z + + 2 2 2 3 2 3 2 3 + + 5/72 y x z + 1/24 y z + 5/72 y x z + 5/72 x z + 1/9 y z + + 2 3 3 3 2 3 4 3 4 + - 1/24 y z - 1/18 y z - 5/72 x z + 1/18 y z - 1/36 y z + + 3 2 2 4 2 4 2 2 2 + + 1/36 y z - 5/144 x z - 5/72 y x z - 1/18 y z + 5/144 x z + + 2 4 2 2 2 2 4 + - 1/48 y z + 1/48 y z + 5/192 y x z , COEFF(1, 1, 2) = + + 4 2 4 4 4 4 3 4 4 3 + 1/288 x y z - 1/108 x y z + 1/216 x y z - 1/108 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/54 x y z - 1/144 x y z + 1/144 x y z + 1/108 x y z + + 4 2 4 3 2 4 4 4 2 2 + + 1/108 x y z - 1/216 x y z - 1/216 x z - 1/288 x y z + + 4 3 2 4 4 3 3 2 4 + - 1/54 x y z - 1/72 y x z + 1/108 x z + 2/27 y x z - 1/54 y x z + + 3 2 3 3 4 2 2 3 + + 1/54 z y x + 1/108 z y x - 1/54 y x z + 1/36 y x z - 1/36 y x z + + 2 2 2 3 2 2 2 3 3 3 + + 1/72 y x z + 1/54 y x z - 1/36 y x z - 1/54 y x z + + 3 3 2 2 3 3 3 2 2 + - 1/216 y x z + 2/27 y x z + 1/108 z x + 1/54 y x z + + 2 3 3 4 2 3 3 2 + + 1/144 y x z + 1/216 x z + 1/27 z y x + 1/27 z y x + + 3 3 2 2 3 + - 1/108 z y x - 2/27 y x z - 2/27 z y x - 1/144 z y x + + 2 2 3 3 3 4 3 3 3 3 + - 1/288 z y x - 1/27 y x z - 1/108 x z + 1/108 y x z + + 2 2 2 2 2 2 2 3 2 3 + + 1/72 y x z + 1/36 y x z - 1/27 y x z - 1/27 y x z - 1/27 y x z + + 2 4 3 3 2 3 + - 1/27 x z - 1/27 x z + 1/27 y x z - 1/108 x z + 1/27 x z + + 2 4 3 2 4 4 3 4 + + 1/54 x z + 1/27 x z + 1/27 y x z + 1/54 x z - 1/216 x z + + 2 2 3 4 2 3 2 2 2 4 + - 1/54 x z - 1/108 y x z - 1/54 x z + 1/216 x z - 1/72 y x z + + 2 3 4 3 3 4 4 2 4 + + 1/288 y x z + 1/216 y x z , COEFF(2, 1, 2) = - 1/1152 x y z + + 4 4 4 3 4 4 3 4 + + 1/432 x y z - 1/864 x y z + 1/432 x y z - 1/216 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/576 x y z - 1/576 x y z - 1/432 x y z - 1/432 x y z + + 4 3 2 4 4 4 2 2 4 3 + + 1/864 x y z + 1/864 x z + 1/1152 x y z + 1/216 x y z + + 2 4 4 3 3 2 4 + + 1/576 y x z - 1/432 x z - 1/108 y x z + 1/864 y x z + + 3 2 3 3 4 2 + - 1/108 z y x - 1/216 z y x + 1/432 y x z - 1/288 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/288 y x z - 1/1152 y x z - 1/432 y x z + 1/576 y x z + + 3 3 3 3 2 2 3 3 + + 1/108 y x z + 1/432 y x z - 1/216 y x z - 1/216 z x + + 3 2 2 2 3 3 4 2 3 + - 1/864 y x z - 1/288 y x z - 1/864 x z - 1/216 z y x + + 3 2 3 3 2 + - 1/432 z y x + 1/216 z y x + 1/108 y x z + 1/216 z y x + + 2 3 2 2 3 3 3 4 3 + + 1/288 z y x + 1/576 z y x + 1/216 y x z + 1/432 x z + + 3 3 3 2 2 2 2 2 2 + - 1/216 y x z - 1/576 y x z - 1/576 y x z + 1/432 y x z + + 2 3 2 3 2 4 + + 1/216 y x z + 1/432 y x z + 1/216 x z + 1/432 x z - 1/216 y x z + + 3 3 2 3 2 4 3 2 4 + + 1/216 x z - 1/432 x z - 1/864 x z - 1/216 x z - 1/432 y x z + + 4 3 4 2 2 3 4 2 + - 1/432 x z + 1/432 x z + 1/864 x z + 1/216 y x z + 1/432 x z + + 3 2 2 2 4 2 3 4 3 3 4 + - 1/432 x z + 1/1152 y x z - 1/576 y x z - 1/432 y x z , + + 4 2 4 4 4 4 3 4 + COEFF(-2, 2, 2) = 1/2304 x y z - 1/6912 x y z + 1/3456 x y z + + 4 3 4 4 2 4 2 3 + - 1/1728 x y z + 1/3456 x y z - 1/1152 x y z + 1/1152 x y z + + 4 3 3 4 2 4 3 2 4 4 + + 1/1728 x y z + 1/6912 x y z - 1/3456 x y z - 1/6912 x z + + 4 2 2 4 3 2 4 4 + - 1/2304 x y z - 1/3456 x y z + 1/1152 y x z + 1/3456 x z + + 3 3 2 4 3 2 3 + - 1/1728 y x z - 1/3456 y x z - 1/1728 z y x - 1/3456 z y x + + 3 4 2 2 3 2 2 2 + + 1/1728 y x z - 1/576 y x z + 1/576 y x z + 1/2304 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/1728 y x z - 1/1152 y x z + 1/1728 y x z + 1/1728 y x z + + 2 3 3 3 2 2 2 3 3 + + 1/3456 y x z - 1/1728 z x + 1/3456 y x z - 1/576 y x z + + 4 2 3 3 2 3 3 + + 1/6912 x z - 1/864 z y x + 1/1728 z y x + 1/864 z y x + + 2 2 3 2 2 3 + + 1/1728 y x z - 1/3456 z y x + 1/576 z y x + 1/1152 z y x + + 3 3 4 3 3 3 3 2 2 + + 1/864 y x z - 1/3456 x z - 1/864 y x z - 1/1152 y x z + + 2 2 2 2 2 3 2 3 + + 1/1152 y x z - 1/6912 y x z + 1/3456 y x z - 1/1728 y x z + + 2 4 3 3 2 3 + + 1/1728 x z - 1/3456 x z - 1/3456 y x z + 1/1728 x z + 1/3456 x z + + 2 4 3 2 4 4 3 4 + + 1/6912 x z - 1/1728 x z + 1/6912 y x z - 1/3456 x z + 1/3456 x z + + 2 2 3 4 2 3 2 + - 1/6912 x z + 1/3456 y x z + 1/3456 x z - 1/3456 x z + + 2 2 4 2 3 4 3 3 4 + - 1/2304 y x z - 1/1152 y x z - 1/1728 y x z , COEFF(-1, 2, 2) = + + 4 2 4 4 4 4 3 4 4 3 + - 1/576 x y z + 1/1728 x y z - 1/864 x y z + 1/432 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/864 x y z + 1/288 x y z - 1/288 x y z - 1/432 x y z + + 4 2 4 3 2 4 4 4 2 2 + - 1/1728 x y z + 1/864 x y z + 1/1728 x z + 1/576 x y z + + 4 3 2 4 4 3 + + 1/864 x y z - 1/144 y x z - 1/864 x z + 1/216 y x z + + 3 2 4 3 2 3 3 4 + + 1/216 y x z + 1/864 z y x + 1/1728 z y x - 1/216 y x z + + 2 2 3 2 2 2 3 2 + + 1/72 y x z - 1/72 y x z - 1/144 y x z + 1/216 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/72 y x z - 1/864 y x z - 1/864 y x z - 1/216 y x z + + 3 3 2 2 2 3 3 4 2 + + 1/864 z x - 1/216 y x z + 1/288 y x z - 1/1728 x z + + 3 3 2 3 3 + + 1/108 z y x - 1/108 z y x - 1/432 z y x - 1/216 y x z + + 2 2 3 2 2 3 3 3 + + 1/216 z y x - 1/288 z y x - 1/576 z y x - 1/108 y x z + + 4 3 3 3 3 2 2 2 2 + + 1/864 x z + 1/432 y x z + 1/144 y x z - 1/72 y x z + + 2 2 2 3 2 3 2 + + 1/432 y x z - 1/432 y x z + 1/108 y x z - 1/216 x z + 1/216 x z + + 4 3 3 2 3 2 4 3 + + 1/432 y x z - 1/864 x z - 1/216 x z - 1/432 x z + 1/216 x z + + 2 4 4 3 4 2 2 3 4 + - 1/432 y x z + 1/432 x z - 1/1728 x z + 1/432 x z - 1/1728 y x z + + 2 3 2 2 2 4 2 3 4 + - 1/432 x z + 1/1728 x z + 1/144 y x z + 1/576 y x z + + 3 3 4 4 2 4 4 4 + + 1/864 y x z , COEFF(0, 2, 2) = 1/384 x y z - 1/1152 x y z + + 4 3 4 4 3 4 4 2 + + 1/576 x y z - 1/288 x y z + 1/576 x y z - 1/192 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + + 1/192 x y z + 1/288 x y z + 1/1152 x y z - 1/576 x y z + + 4 4 4 2 2 4 3 4 + - 1/1152 x z - 1/384 x y z - 1/576 x y z + 1/576 x z + 1/144 z + + 3 2 4 2 2 2 2 2 3 2 3 + - 5/576 y x z + 5/384 y x z - 5/192 y x z + 5/576 y x z + + 4 3 2 2 4 2 3 3 + - 1/288 z + 5/576 y x z + 1/1152 x z - 1/144 z - 1/72 z y + + 2 3 2 2 4 3 + + 1/288 z + 5/288 z y x - 5/576 z y x + 1/144 y z - 1/576 x z + + 2 2 2 2 2 3 2 3 2 + + 5/192 y x z - 5/1152 y x z - 1/48 y z - 5/288 y x z - 5/576 x z + + 3 2 3 3 3 2 3 4 + - 1/144 y z + 1/48 y z + 1/72 y z + 5/576 x z - 1/288 y z + + 3 4 3 2 2 4 2 4 2 + + 1/144 y z - 1/144 y z + 5/1152 x z + 5/1152 y x z + 1/288 y z + + 2 2 2 4 2 2 2 2 4 + - 5/1152 x z + 1/96 y z - 1/96 y z - 5/384 y x z , COEFF(1, 2, 2) + + 4 2 4 4 4 4 3 4 4 3 + = - 1/576 x y z + 1/1728 x y z - 1/864 x y z + 1/432 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/864 x y z + 1/288 x y z - 1/288 x y z - 1/432 x y z + + 4 2 4 3 2 4 4 4 2 2 + - 1/1728 x y z + 1/864 x y z + 1/1728 x z + 1/576 x y z + + 4 3 2 4 4 3 + + 1/864 x y z + 1/144 y x z - 1/864 x z - 1/216 y x z + + 3 2 4 3 2 3 3 4 + + 1/216 y x z - 1/864 z y x - 1/1728 z y x + 1/216 y x z + + 2 2 3 2 2 2 3 2 + - 1/72 y x z + 1/72 y x z - 1/144 y x z - 1/216 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/72 y x z + 1/864 y x z + 1/864 y x z - 1/216 y x z + + 3 3 2 2 2 3 3 4 2 + - 1/864 z x - 1/216 y x z - 1/288 y x z - 1/1728 x z + + 3 3 2 3 3 + - 1/108 z y x - 1/108 z y x + 1/432 z y x + 1/216 y x z + + 2 2 3 2 2 3 3 3 + + 1/216 z y x + 1/288 z y x + 1/576 z y x + 1/108 y x z + + 4 3 3 3 3 2 2 2 2 + + 1/864 x z - 1/432 y x z - 1/144 y x z - 1/72 y x z + + 2 2 2 3 2 3 2 + + 1/432 y x z + 1/432 y x z + 1/108 y x z + 1/216 x z + 1/216 x z + + 4 3 3 2 3 2 4 3 + - 1/432 y x z + 1/864 x z - 1/216 x z - 1/432 x z - 1/216 x z + + 2 4 4 3 4 2 2 3 4 + - 1/432 y x z - 1/432 x z + 1/1728 x z + 1/432 x z + 1/1728 y x z + + 2 3 2 2 2 4 2 3 4 + + 1/432 x z - 1/1728 x z + 1/144 y x z - 1/576 y x z + + 3 3 4 4 2 4 4 4 + - 1/864 y x z , COEFF(2, 2, 2) = 1/2304 x y z - 1/6912 x y z + + 4 3 4 4 3 4 4 2 + + 1/3456 x y z - 1/1728 x y z + 1/3456 x y z - 1/1152 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + + 1/1152 x y z + 1/1728 x y z + 1/6912 x y z - 1/3456 x y z + + 4 4 4 2 2 4 3 2 4 + - 1/6912 x z - 1/2304 x y z - 1/3456 x y z - 1/1152 y x z + + 4 3 3 2 4 3 + + 1/3456 x z + 1/1728 y x z - 1/3456 y x z + 1/1728 z y x + + 2 3 3 4 2 2 3 + + 1/3456 z y x - 1/1728 y x z + 1/576 y x z - 1/576 y x z + + 2 2 2 3 2 2 2 3 3 3 + + 1/2304 y x z + 1/1728 y x z - 1/1152 y x z - 1/1728 y x z + + 3 3 2 2 3 3 3 2 2 + - 1/1728 y x z + 1/3456 y x z + 1/1728 z x + 1/3456 y x z + + 2 3 3 4 2 3 3 2 + + 1/576 y x z + 1/6912 x z + 1/864 z y x + 1/1728 z y x + + 3 3 2 2 3 + - 1/864 z y x - 1/1728 y x z - 1/3456 z y x - 1/576 z y x + + 2 2 3 3 3 4 3 3 3 3 + - 1/1152 z y x - 1/864 y x z - 1/3456 x z + 1/864 y x z + + 2 2 2 2 2 2 2 + + 1/1152 y x z + 1/1152 y x z - 1/6912 y x z - 1/3456 y x z + + 3 2 3 2 4 + - 1/1728 y x z - 1/1728 x z - 1/3456 x z + 1/3456 y x z + + 3 3 2 3 2 4 3 + - 1/1728 x z + 1/3456 x z + 1/6912 x z + 1/1728 x z + + 2 4 4 3 4 2 2 + + 1/6912 y x z + 1/3456 x z - 1/3456 x z - 1/6912 x z + + 3 4 2 3 2 2 2 4 + - 1/3456 y x z - 1/3456 x z + 1/3456 x z - 1/2304 y x z + + 2 3 4 3 3 4 + + 1/1152 y x z + 1/1728 y x z ] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dy.compute.c"); +bytes used=20600113680, alloc=64737712, time=3341.53 +bytes used=20601113952, alloc=64737712, time=3341.64 +bytes used=20602114124, alloc=64737712, time=3341.74 +bytes used=20603114456, alloc=64737712, time=3341.84 +bytes used=20604117636, alloc=64737712, time=3341.93 +bytes used=20605117808, alloc=64737712, time=3342.03 +bytes used=20606117980, alloc=64737712, time=3342.14 +bytes used=20607118160, alloc=64737712, time=3342.23 +bytes used=20608118340, alloc=64737712, time=3342.33 +bytes used=20609118772, alloc=64737712, time=3342.43 +bytes used=20610119180, alloc=64737712, time=3342.53 +bytes used=20611119552, alloc=64737712, time=3342.63 +bytes used=20612119728, alloc=64737712, time=3342.73 +bytes used=20613120036, alloc=64737712, time=3342.83 +bytes used=20614120428, alloc=64737712, time=3342.94 +bytes used=20615121012, alloc=64737712, time=3343.04 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1/3456 x y z - 1/1728 x y z + + 4 2 4 3 2 4 2 2 4 3 + - 1/1152 x y z + 1/1152 x y z + 1/2304 x y z + 1/1728 x y z + + 3 4 4 4 2 4 3 + - 1/3456 x y z - 1/6912 z y x + 1/6912 x y z + 1/1728 y x + + 3 3 2 3 2 + - 1/864 y x z - 1/1728 z y x - 1/576 z y x - 1/3456 y x z + + 2 3 3 4 2 2 2 + + 1/1728 y x z - 1/1728 y x + 1/3456 x y - 1/2304 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/576 y x z + 1/3456 y x z + 1/864 y x z + 1/576 y x z + + 2 3 3 2 2 4 2 3 3 + - 1/1728 y x z - 1/1152 y x z - 1/3456 x y - 1/1728 y x z + + 4 4 3 2 3 3 2 3 + + 1/6912 y x + 1/1728 y x - 1/3456 y x + 1/3456 y x - 1/1728 z y x + + 3 2 2 4 3 3 3 3 + - 1/3456 z y x - 1/6912 x y - 1/1728 y x + 1/1728 z y x + + 2 2 3 2 2 3 + + 1/1728 y x z + 1/3456 z y x + 1/3456 z y x + 1/1152 z y x + + 3 3 3 3 3 2 2 2 + + 1/864 y x z - 1/864 y x z + 1/3456 y x - 1/1152 y x z + + 2 2 2 2 2 3 2 3 + - 1/6912 y x z + 1/1152 y x z + 1/576 y x z + 1/1728 y x z + + 2 2 2 4 4 2 4 3 + + 1/6912 y x - 1/3456 y x + 1/3456 x y - 1/6912 x y - 1/3456 x y , + + 4 3 4 2 2 4 2 + COEFF(-2, -1, -2) = 1/864 x y z - 1/288 x y z - 1/576 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + + 1/288 x y z + 1/432 x y z + 1/576 z y x - 1/864 z y x + + 4 3 2 4 3 4 3 4 + - 1/432 x y z + 1/864 x y z - 1/1728 x y z + 1/432 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/432 x y z + 1/216 x y z + 1/864 x y z + 1/144 x y z + + 4 3 2 4 2 2 4 3 3 4 + - 1/576 x y z - 1/144 x y z - 1/216 x y z - 1/864 x y z + + 4 4 2 4 3 3 + + 1/1728 z y x - 1/1728 x y z + 1/216 y x - 1/108 y x z + + 3 2 3 2 2 3 + - 1/216 z y x - 1/72 z y x - 1/216 y x z + 1/108 y x z - 1/216 y x + + 3 4 2 2 2 3 2 2 2 3 + + 1/864 x y + 1/144 y x z - 1/288 y x z - 1/216 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 1/108 y x z + 1/288 y x z + 1/216 y x z + 1/576 y x z + + 4 2 3 3 4 4 3 2 3 + - 1/864 x y - 1/108 y x z - 1/1728 y x + 1/864 y x - 1/216 y x + + 3 2 3 3 2 2 4 + - 1/1728 y x - 1/864 z y x + 1/1728 z y x + 1/1728 x y + + 3 3 3 3 2 2 3 + - 1/864 y x + 1/864 z y x + 1/216 y x z - 1/432 z y x + 1/216 z y x + + 2 2 3 3 3 3 3 3 2 + + 1/72 z y x + 1/432 y x z - 1/432 y x z + 1/216 y x + + 2 2 2 2 2 2 2 + - 1/72 y x z + 1/432 y x z - 1/144 y x z + 1/72 y x z + + 3 2 3 2 2 2 4 4 2 + - 1/864 y x z - 1/432 y x + 1/432 y x - 1/432 x y + 1/432 x y + + 4 3 4 3 4 2 + + 1/1728 x y , COEFF(-1, -1, -2) = - 1/108 x y z + 1/144 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + + 1/36 x y z - 1/36 x y z - 1/216 x y z - 1/144 z y x + + 3 4 4 4 3 2 4 3 4 3 + + 1/216 z y x + 1/54 x y z - 1/54 x y z + 1/432 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/108 x y z + 1/108 x y z - 1/54 x y z - 1/216 x y z + + 4 2 4 3 2 4 2 2 4 3 + - 1/36 x y z + 1/144 x y z + 1/36 x y z + 1/54 x y z + + 3 4 4 4 2 4 3 3 + + 1/432 x y z - 1/432 z y x + 1/108 x y z - 1/108 y x + 2/27 y x z + + 3 2 3 2 2 3 + + 1/108 z y x + 1/36 z y x + 1/27 y x z - 2/27 y x z + 1/27 y x + + 3 4 2 2 2 3 2 2 2 3 3 3 + - 1/432 x y - 1/9 y x z + 1/36 y x z + 2/27 y x z - 1/54 y x z + + 3 3 2 2 3 3 2 2 4 + - 1/144 y x z - 2/27 y x z - 1/36 y x z + 1/108 x y + + 2 3 3 4 4 3 2 3 3 2 + + 1/54 y x z + 1/432 y x - 1/108 y x + 1/108 y x + 1/108 y x + + 3 3 2 2 4 3 3 3 3 + + 1/108 z y x - 1/108 z y x - 1/108 x y + 1/432 y x - 1/432 z y x + + 2 2 3 2 2 3 3 3 + - 1/27 y x z + 1/27 z y x - 1/108 z y x - 1/36 z y x - 1/54 y x z + + 3 3 3 2 2 2 2 2 2 2 + + 1/216 y x z - 1/27 y x + 1/9 y x z - 1/27 y x z + 1/9 y x z + + 2 3 2 3 2 2 2 4 + - 1/9 y x z + 1/54 y x z + 1/27 y x - 1/27 y x + 1/108 x y + + 4 2 4 3 2 4 2 + - 1/108 x y - 1/432 x y , COEFF(0, -1, -2) = - 5/96 x y z + + 2 4 4 3 4 4 2 4 3 4 3 + + 1/96 z y x - 1/144 z y x + 5/144 x y z - 1/288 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/72 x y z - 1/72 x y z + 1/36 x y z + 1/144 x y z + + 4 2 4 3 2 4 2 2 4 3 + + 1/24 x y z - 1/96 x y z - 1/24 x y z - 1/36 x y z + + 4 4 4 3 2 4 4 + + 1/288 z y x - 1/36 y z - 5/288 x y z - 1/18 y - 1/72 y + + 4 2 4 2 2 2 2 2 3 2 3 + + 1/24 y z + 1/72 y z + 5/24 y x z - 5/36 y x z + 5/36 y x z + + 3 2 2 4 4 3 3 2 + + 5/96 y x z - 1/288 y x + 1/72 y - 1/72 z y + 1/18 y + + 3 2 3 2 2 4 2 + - 5/288 y x + 5/288 z y x + 5/288 x y - 5/72 z y x + 1/18 y z + + 2 2 2 2 2 3 2 3 3 + + 5/72 y x z - 5/24 y x z - 1/18 y z - 5/144 y x z - 1/9 y z + + 2 3 3 3 3 2 2 2 2 2 2 + + 1/9 y z + 1/36 y z - 1/24 y z + 1/6 y z - 1/6 y z - 5/72 y x + + 2 4 4 2 4 3 + + 5/72 y x - 1/72 x y + 1/72 x y + 1/288 x y , COEFF(1, -1, -2) = + + 4 3 4 2 2 4 2 4 2 + 1/108 x y z - 1/144 x y z + 1/36 x y z + 1/36 x y z + + 3 4 3 2 4 4 3 4 4 4 3 + + 1/216 x y z - 1/144 z y x + 1/216 z y x - 1/54 x y z + + 2 4 3 4 3 4 4 2 + - 1/54 x y z + 1/432 x y z - 1/108 x y z + 1/108 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/54 x y z - 1/216 x y z - 1/36 x y z + 1/144 x y z + + 4 2 2 4 3 3 4 4 4 + + 1/36 x y z + 1/54 x y z - 1/432 x y z - 1/432 z y x + + 2 4 3 3 3 2 3 + + 1/108 x y z + 1/108 y x - 2/27 y x z - 1/108 z y x - 1/36 z y x + + 2 2 3 3 4 2 2 2 + - 1/27 y x z + 2/27 y x z - 1/27 y x + 1/432 x y - 1/9 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/36 y x z + 2/27 y x z + 1/54 y x z + 1/144 y x z + + 2 3 3 2 2 4 2 3 3 4 4 + - 2/27 y x z - 1/36 y x z - 1/108 x y - 1/54 y x z + 1/432 y x + + 3 2 3 3 2 3 3 2 + + 1/108 y x - 1/108 y x + 1/108 y x - 1/108 z y x - 1/108 z y x + + 2 4 3 3 3 3 2 + - 1/108 x y - 1/432 y x + 1/432 z y x + 1/27 y x z + 1/27 z y x + + 2 3 2 2 3 3 3 3 3 3 + + 1/108 z y x + 1/36 z y x + 1/54 y x z - 1/216 y x z + + 2 2 2 2 2 2 2 2 + + 1/27 y x - 1/9 y x z - 1/27 y x z + 1/9 y x z + 1/9 y x z + + 3 2 3 2 2 2 4 4 2 + + 1/54 y x z + 1/27 y x - 1/27 y x + 1/108 x y - 1/108 x y + + 4 3 4 3 4 2 + - 1/432 x y , COEFF(2, -1, -2) = - 1/864 x y z + 1/288 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + - 1/576 x y z - 1/288 x y z - 1/432 x y z + 1/576 z y x + + 3 4 4 4 3 2 4 3 4 3 + - 1/864 z y x + 1/432 x y z + 1/864 x y z - 1/1728 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/432 x y z - 1/432 x y z + 1/216 x y z + 1/864 x y z + + 4 2 4 3 2 4 2 2 4 3 + + 1/144 x y z - 1/576 x y z - 1/144 x y z - 1/216 x y z + + 3 4 4 4 2 4 3 + + 1/864 x y z + 1/1728 z y x - 1/1728 x y z - 1/216 y x + + 3 3 2 3 2 + + 1/108 y x z + 1/216 z y x + 1/72 z y x + 1/216 y x z + + 2 3 3 4 2 2 2 3 2 + - 1/108 y x z + 1/216 y x - 1/864 x y + 1/144 y x z + 1/288 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/216 y x z - 1/108 y x z - 1/288 y x z + 1/216 y x z + + 3 2 2 4 2 3 3 4 4 3 + + 1/576 y x z + 1/864 x y + 1/108 y x z - 1/1728 y x - 1/864 y x + + 2 3 3 2 3 3 2 + + 1/216 y x - 1/1728 y x + 1/864 z y x + 1/1728 z y x + + 2 4 3 3 3 3 2 + + 1/1728 x y + 1/864 y x - 1/864 z y x - 1/216 y x z - 1/432 z y x + + 2 3 2 2 3 3 3 3 3 3 + - 1/216 z y x - 1/72 z y x - 1/432 y x z + 1/432 y x z + + 2 2 2 2 2 2 2 2 + - 1/216 y x + 1/72 y x z + 1/432 y x z - 1/144 y x z - 1/72 y x z + + 3 2 3 2 2 2 4 4 2 + - 1/864 y x z - 1/432 y x + 1/432 y x - 1/432 x y + 1/432 x y + + 4 3 4 3 4 2 + + 1/1728 x y , COEFF(-2, 0, -2) = - 1/576 x y z + 1/192 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + + 1/384 x y z - 1/192 x y z - 1/288 x y z - 1/384 z y x + + 3 4 4 4 3 2 4 3 4 2 + + 1/576 z y x + 1/288 x y z - 1/576 x y z + 5/1152 x y z + + 4 2 3 4 2 2 3 4 4 4 + - 5/576 x y z + 5/384 x y z + 1/576 x y z - 1/1152 z y x + + 2 4 4 4 2 + + 1/1152 x y z + 1/144 x - 1/288 x z + 1/288 x + 5/576 y x z + + 2 3 3 4 2 2 2 2 2 3 + - 5/288 y x z - 1/576 x y - 5/384 y x z + 5/576 y x z + + 3 4 2 3 3 4 2 4 4 + + 1/144 z x + 1/576 x y + 5/288 y x z - 1/96 x z + 1/1152 y x + + 3 2 3 2 4 2 2 3 + - 1/144 x + 5/576 y x - 1/1152 x y - 1/288 x - 5/576 z y x + + 2 2 3 4 3 2 2 2 + - 5/192 z y x + 1/144 x z - 5/576 y x + 5/192 y x z + + 2 2 2 3 3 2 3 + - 5/1152 y x z - 1/144 x z + 1/288 x z - 1/72 x z - 1/144 x z + + 3 2 2 2 3 2 2 2 + + 1/72 x z + 1/96 x z - 1/48 x z + 1/48 x z + 5/1152 y x + + 4 2 4 3 4 2 + - 5/1152 x y , COEFF(-1, 0, -2) = 1/72 x y z - 1/96 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + - 1/24 x y z + 1/24 x y z + 1/144 x y z + 1/96 z y x + + 3 4 4 4 3 2 4 3 4 2 + - 1/144 z y x - 1/36 x y z + 1/36 x y z - 5/288 x y z + + 4 2 3 4 2 2 3 4 4 4 + + 5/144 x y z - 5/96 x y z - 1/288 x y z + 1/288 z y x + + 2 4 4 4 2 2 3 + - 1/72 x y z - 1/18 x + 1/72 x z - 1/72 x - 5/72 y x z + 5/36 y x z + + 3 4 2 2 2 2 2 3 3 4 + + 1/288 x y + 5/24 y x z - 5/36 y x z - 1/72 z x - 1/72 x y + + 2 3 3 4 2 4 4 3 2 3 + - 5/144 y x z + 1/24 x z - 1/288 y x + 1/72 x - 5/288 y x + + 2 4 2 2 3 2 2 3 4 3 + + 1/72 x y + 1/18 x + 5/288 z y x + 5/96 z y x - 1/36 x z + + 2 2 2 2 2 2 + + 5/72 y x - 5/24 y x z + 5/72 y x z + 1/18 x z - 1/18 x z + + 3 3 2 3 3 2 2 2 3 2 + + 1/36 x z + 1/9 x z - 1/9 x z - 1/6 x z + 1/6 x z - 1/24 x z + + 2 2 4 2 2 4 2 + - 5/72 y x + 5/288 x y , COEFF(0, 0, -2) = 5/64 x y z + + 2 4 4 3 4 4 2 4 3 4 2 + - 1/64 z y x + 1/96 z y x - 5/96 x y z + 5/192 x y z + + 4 2 3 4 2 2 4 4 4 3 + - 5/96 x y z + 5/64 x y z - 1/192 z y x + 1/24 y z + + 2 4 4 4 4 4 2 + + 5/192 x y z - 1/48 x z + 1/48 x - 1/12 z + 1/48 y - 1/16 y z + + 4 25 2 2 2 25 2 2 3 4 2 4 4 + - 1/48 y z - -- y x z + -- y x z - 1/16 x z + 1/192 y x + 64 96 + + 3 2 2 2 4 2 4 3 + + 1/6 z + 1/12 - 5/48 y - 1/4 z - 5/192 x y - 5/48 x + 1/24 x z + + 25 2 2 2 2 2 3 2 3 + - --- y x z + 5/48 y z + 5/48 x z - 5/24 y z - 5/24 x z + 192 + + 2 2 2 2 25 2 2 4 2 + + 5/16 x z + 5/16 y z + --- y x - 5/192 x y , COEFF(1, 0, -2) = + 192 + + 4 3 4 2 2 4 2 4 2 + - 1/72 x y z + 1/96 x y z - 1/24 x y z - 1/24 x y z + + 3 4 3 2 4 4 3 4 4 4 3 + - 1/144 x y z + 1/96 z y x - 1/144 z y x + 1/36 x y z + + 2 4 3 4 2 4 2 3 4 2 2 + + 1/36 x y z - 5/288 x y z + 5/144 x y z - 5/96 x y z + + 3 4 4 4 2 4 4 + + 1/288 x y z + 1/288 z y x - 1/72 x y z + 1/18 x + 1/72 x z + + 4 2 2 3 3 4 2 2 2 + - 1/72 x + 5/72 y x z - 5/36 y x z - 1/288 x y + 5/24 y x z + + 2 2 3 3 4 2 3 3 4 2 + - 5/36 y x z + 1/72 z x + 1/72 x y + 5/144 y x z + 1/24 x z + + 4 4 3 2 3 2 4 2 + - 1/288 y x - 1/72 x + 5/288 y x + 1/72 x y + 1/18 x + + 2 3 2 2 3 4 3 2 2 2 + - 5/288 z y x - 5/96 z y x - 1/36 x z - 5/72 y x + 5/24 y x z + + 2 2 2 3 3 2 3 3 + + 5/72 y x z - 1/18 x z - 1/18 x z - 1/36 x z + 1/9 x z + 1/9 x z + + 2 2 2 3 2 2 2 4 2 + - 1/6 x z - 1/6 x z + 1/24 x z - 5/72 y x + 5/288 x y , + + 4 3 4 2 2 4 2 + COEFF(2, 0, -2) = 1/576 x y z - 1/192 x y z + 1/384 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + + 1/192 x y z + 1/288 x y z - 1/384 z y x + 1/576 z y x + + 4 3 2 4 3 4 2 4 2 3 + - 1/288 x y z - 1/576 x y z + 5/1152 x y z - 5/576 x y z + + 4 2 2 3 4 4 4 2 4 + + 5/384 x y z - 1/576 x y z - 1/1152 z y x + 1/1152 x y z + + 4 4 2 2 3 + - 1/144 x - 1/288 x z + 1/288 x - 5/576 y x z + 5/288 y x z + + 3 4 2 2 2 2 2 3 3 4 + + 1/576 x y - 5/384 y x z + 5/576 y x z - 1/144 z x - 1/576 x y + + 2 3 3 4 2 4 4 3 2 3 + - 5/288 y x z - 1/96 x z + 1/1152 y x + 1/144 x - 5/576 y x + + 2 4 2 2 3 2 2 3 4 3 + - 1/1152 x y - 1/288 x + 5/576 z y x + 5/192 z y x + 1/144 x z + + 2 2 2 2 2 2 + + 5/576 y x - 5/192 y x z - 5/1152 y x z + 1/144 x z + 1/288 x z + + 3 3 2 3 3 2 2 2 + + 1/72 x z - 1/144 x z - 1/72 x z + 1/96 x z + 1/48 x z + + 3 2 2 2 4 2 + - 1/48 x z + 5/1152 y x - 5/1152 x y , COEFF(-2, 1, -2) = + + 4 3 4 2 2 4 2 4 2 + 1/864 x y z - 1/288 x y z - 1/576 x y z + 1/288 x y z + + 3 4 3 2 4 4 3 4 4 4 3 + + 1/432 x y z + 1/576 z y x - 1/864 z y x - 1/432 x y z + + 2 4 3 4 3 4 4 2 + + 1/864 x y z + 1/1728 x y z - 1/432 x y z - 1/432 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + + 1/216 x y z - 1/864 x y z - 1/144 x y z + 1/576 x y z + + 4 2 2 4 3 3 4 4 4 + - 1/144 x y z + 1/216 x y z - 1/864 x y z + 1/1728 z y x + + 2 4 3 3 3 2 3 + - 1/1728 x y z - 1/216 y x + 1/108 y x z + 1/216 z y x + 1/72 z y x + + 2 2 3 3 4 2 2 2 + - 1/216 y x z + 1/108 y x z + 1/216 y x + 1/864 x y + 1/144 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/288 y x z - 1/216 y x z - 1/108 y x z - 1/288 y x z + + 2 3 3 2 2 4 2 3 3 + - 1/216 y x z - 1/576 y x z - 1/864 x y - 1/108 y x z + + 4 4 3 2 3 3 2 3 + - 1/1728 y x - 1/864 y x - 1/216 y x + 1/1728 y x + 1/864 z y x + + 3 2 2 4 3 3 3 3 + - 1/1728 z y x + 1/1728 x y + 1/864 y x - 1/864 z y x + + 2 2 3 2 2 3 + - 1/216 y x z + 1/432 z y x + 1/216 z y x + 1/72 z y x + + 3 3 3 3 3 2 2 2 + - 1/432 y x z + 1/432 y x z + 1/216 y x - 1/72 y x z + + 2 2 2 2 2 3 2 3 + + 1/432 y x z + 1/144 y x z - 1/72 y x z + 1/864 y x z + + 2 2 2 4 4 2 4 3 + - 1/432 y x - 1/432 y x + 1/432 x y + 1/432 x y - 1/1728 x y , + + 4 3 4 2 2 4 2 + COEFF(-1, 1, -2) = - 1/108 x y z + 1/144 x y z + 1/36 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + - 1/36 x y z - 1/216 x y z - 1/144 z y x + 1/216 z y x + + 4 3 2 4 3 4 3 4 + + 1/54 x y z - 1/54 x y z - 1/432 x y z + 1/108 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/108 x y z - 1/54 x y z + 1/216 x y z + 1/36 x y z + + 4 3 2 4 2 2 4 3 3 4 + - 1/144 x y z + 1/36 x y z - 1/54 x y z + 1/432 x y z + + 4 4 2 4 3 3 3 + - 1/432 z y x + 1/108 x y z + 1/108 y x - 2/27 y x z - 1/108 z y x + + 2 3 2 2 3 3 4 + - 1/36 z y x + 1/27 y x z - 2/27 y x z - 1/27 y x - 1/432 x y + + 2 2 2 3 2 2 2 3 3 3 + - 1/9 y x z - 1/36 y x z + 2/27 y x z + 1/54 y x z + + 3 3 2 2 3 3 2 2 4 + + 1/144 y x z + 2/27 y x z + 1/36 y x z + 1/108 x y + + 2 3 3 4 4 3 2 3 3 2 + + 1/54 y x z + 1/432 y x + 1/108 y x + 1/108 y x - 1/108 y x + + 3 3 2 2 4 3 3 3 3 + - 1/108 z y x + 1/108 z y x - 1/108 x y - 1/432 y x + 1/432 z y x + + 2 2 3 2 2 3 3 3 + + 1/27 y x z - 1/27 z y x - 1/108 z y x - 1/36 z y x + 1/54 y x z + + 3 3 3 2 2 2 2 2 2 2 + - 1/216 y x z - 1/27 y x + 1/9 y x z - 1/27 y x z - 1/9 y x z + + 2 3 2 3 2 2 2 4 + + 1/9 y x z - 1/54 y x z + 1/27 y x + 1/27 y x - 1/108 x y + + 4 2 4 3 2 4 2 + - 1/108 x y + 1/432 x y , COEFF(0, 1, -2) = - 5/96 x y z + + 2 4 4 3 4 4 2 4 3 4 3 + + 1/96 z y x - 1/144 z y x + 5/144 x y z + 1/288 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/72 x y z - 1/72 x y z + 1/36 x y z - 1/144 x y z + + 4 2 4 3 2 4 2 2 4 3 + - 1/24 x y z + 1/96 x y z - 1/24 x y z + 1/36 x y z + + 4 4 4 3 2 4 4 + + 1/288 z y x - 1/36 y z - 5/288 x y z + 1/18 y - 1/72 y + + 4 2 4 2 2 2 2 2 3 2 3 + + 1/24 y z + 1/72 y z + 5/24 y x z - 5/36 y x z - 5/36 y x z + + 3 2 2 4 4 3 3 2 + - 5/96 y x z - 1/288 y x - 1/72 y + 1/72 z y + 1/18 y + + 3 2 3 2 2 4 2 + + 5/288 y x - 5/288 z y x + 5/288 x y + 5/72 z y x - 1/18 y z + + 2 2 2 2 2 3 2 3 3 + + 5/72 y x z + 5/24 y x z - 1/18 y z + 5/144 y x z + 1/9 y z + + 2 3 3 3 3 2 2 2 2 2 2 + + 1/9 y z - 1/36 y z + 1/24 y z - 1/6 y z - 1/6 y z - 5/72 y x + + 2 4 4 2 4 3 + - 5/72 y x + 1/72 x y + 1/72 x y - 1/288 x y , COEFF(1, 1, -2) = + + 4 3 4 2 2 4 2 4 2 + 1/108 x y z - 1/144 x y z + 1/36 x y z + 1/36 x y z + + 3 4 3 2 4 4 3 4 4 4 3 + + 1/216 x y z - 1/144 z y x + 1/216 z y x - 1/54 x y z + + 2 4 3 4 3 4 4 2 + - 1/54 x y z - 1/432 x y z + 1/108 x y z + 1/108 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/54 x y z + 1/216 x y z + 1/36 x y z - 1/144 x y z + + 4 2 2 4 3 3 4 4 4 + + 1/36 x y z - 1/54 x y z - 1/432 x y z - 1/432 z y x + + 2 4 3 3 3 2 3 + + 1/108 x y z - 1/108 y x + 2/27 y x z + 1/108 z y x + 1/36 z y x + + 2 2 3 3 4 2 2 2 + - 1/27 y x z + 2/27 y x z + 1/27 y x + 1/432 x y - 1/9 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/36 y x z + 2/27 y x z - 1/54 y x z - 1/144 y x z + + 2 3 3 2 2 4 2 3 3 4 4 + + 2/27 y x z + 1/36 y x z - 1/108 x y - 1/54 y x z + 1/432 y x + + 3 2 3 3 2 3 3 2 + - 1/108 y x - 1/108 y x - 1/108 y x + 1/108 z y x + 1/108 z y x + + 2 4 3 3 3 3 2 + - 1/108 x y + 1/432 y x - 1/432 z y x - 1/27 y x z - 1/27 z y x + + 2 3 2 2 3 3 3 3 3 3 + + 1/108 z y x + 1/36 z y x - 1/54 y x z + 1/216 y x z + + 2 2 2 2 2 2 2 2 + + 1/27 y x - 1/9 y x z - 1/27 y x z - 1/9 y x z - 1/9 y x z + + 3 2 3 2 2 2 4 4 2 + - 1/54 y x z + 1/27 y x + 1/27 y x - 1/108 x y - 1/108 x y + + 4 3 4 3 4 2 + + 1/432 x y , COEFF(2, 1, -2) = - 1/864 x y z + 1/288 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + - 1/576 x y z - 1/288 x y z - 1/432 x y z + 1/576 z y x + + 3 4 4 4 3 2 4 3 4 3 + - 1/864 z y x + 1/432 x y z + 1/864 x y z + 1/1728 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/432 x y z - 1/432 x y z + 1/216 x y z - 1/864 x y z + + 4 2 4 3 2 4 2 2 4 3 + - 1/144 x y z + 1/576 x y z - 1/144 x y z + 1/216 x y z + + 3 4 4 4 2 4 3 + + 1/864 x y z + 1/1728 z y x - 1/1728 x y z + 1/216 y x + + 3 3 2 3 2 + - 1/108 y x z - 1/216 z y x - 1/72 z y x + 1/216 y x z + + 2 3 3 4 2 2 2 3 2 + - 1/108 y x z - 1/216 y x - 1/864 x y + 1/144 y x z - 1/288 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/216 y x z + 1/108 y x z + 1/288 y x z - 1/216 y x z + + 3 2 2 4 2 3 3 4 4 3 + - 1/576 y x z + 1/864 x y + 1/108 y x z - 1/1728 y x + 1/864 y x + + 2 3 3 2 3 3 2 + + 1/216 y x + 1/1728 y x - 1/864 z y x - 1/1728 z y x + + 2 4 3 3 3 3 2 + + 1/1728 x y - 1/864 y x + 1/864 z y x + 1/216 y x z + 1/432 z y x + + 2 3 2 2 3 3 3 3 3 3 + - 1/216 z y x - 1/72 z y x + 1/432 y x z - 1/432 y x z + + 2 2 2 2 2 2 2 2 + - 1/216 y x + 1/72 y x z + 1/432 y x z + 1/144 y x z + 1/72 y x z + + 3 2 3 2 2 2 4 4 2 + + 1/864 y x z - 1/432 y x - 1/432 y x + 1/432 x y + 1/432 x y + + 4 3 4 3 4 2 + - 1/1728 x y , COEFF(-2, 2, -2) = - 1/3456 x y z + 1/1152 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + + 1/2304 x y z - 1/1152 x y z - 1/1728 x y z - 1/2304 z y x + + 3 4 4 4 3 2 4 3 4 3 + + 1/3456 z y x + 1/1728 x y z - 1/3456 x y z - 1/3456 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/3456 x y z + 1/6912 x y z - 1/3456 x y z + 1/1728 x y z + + 4 2 4 3 2 4 2 2 4 3 + + 1/1152 x y z - 1/1152 x y z + 1/2304 x y z - 1/1728 x y z + + 3 4 4 4 2 4 3 + + 1/3456 x y z - 1/6912 z y x + 1/6912 x y z + 1/1728 y x + + 3 3 2 3 2 + - 1/864 y x z - 1/1728 z y x - 1/576 z y x + 1/3456 y x z + + 2 3 3 4 2 2 2 + - 1/1728 y x z - 1/1728 y x - 1/3456 x y - 1/2304 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/576 y x z + 1/3456 y x z + 1/864 y x z + 1/576 y x z + + 2 3 3 2 2 4 2 3 3 + + 1/1728 y x z + 1/1152 y x z + 1/3456 x y + 1/1728 y x z + + 4 4 3 2 3 3 2 3 + + 1/6912 y x + 1/1728 y x + 1/3456 y x - 1/3456 y x - 1/1728 z y x + + 3 2 2 4 3 3 3 3 + + 1/3456 z y x - 1/6912 x y - 1/1728 y x + 1/1728 z y x + + 2 2 3 2 2 3 + + 1/1728 y x z - 1/3456 z y x - 1/3456 z y x - 1/1152 z y x + + 3 3 3 3 3 2 2 2 + + 1/864 y x z - 1/864 y x z - 1/3456 y x + 1/1152 y x z + + 2 2 2 2 2 3 2 3 + - 1/6912 y x z - 1/1152 y x z + 1/576 y x z - 1/1728 y x z + + 2 2 2 4 4 2 4 3 + + 1/6912 y x + 1/3456 y x - 1/3456 x y - 1/6912 x y + 1/3456 x y , + + 4 3 4 2 2 4 2 + COEFF(-1, 2, -2) = 1/432 x y z - 1/576 x y z - 1/144 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + + 1/144 x y z + 1/864 x y z + 1/576 z y x - 1/864 z y x + + 4 3 2 4 3 4 3 4 + - 1/216 x y z + 1/216 x y z + 1/864 x y z - 1/864 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/1728 x y z + 1/864 x y z - 1/432 x y z - 1/288 x y z + + 4 3 2 4 2 2 4 3 3 4 + + 1/288 x y z - 1/576 x y z + 1/432 x y z - 1/1728 x y z + + 4 4 2 4 3 3 + + 1/1728 z y x - 1/432 x y z - 1/864 y x + 1/108 y x z + + 3 2 3 2 2 3 + + 1/864 z y x + 1/288 z y x - 1/432 y x z + 1/216 y x z + 1/216 y x + + 3 4 2 2 2 3 2 2 2 3 + + 1/1728 x y + 1/144 y x z + 1/72 y x z - 1/216 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/432 y x z - 1/288 y x z - 1/108 y x z - 1/72 y x z + + 4 2 3 3 4 4 3 2 3 + - 1/432 x y - 1/864 y x z - 1/1728 y x - 1/216 y x - 1/1728 y x + + 3 2 3 3 2 2 4 3 3 + + 1/216 y x + 1/216 z y x - 1/216 z y x + 1/432 x y + 1/864 y x + + 3 3 2 2 3 + - 1/864 z y x - 1/216 y x z + 1/216 z y x + 1/1728 z y x + + 2 2 3 3 3 3 3 3 2 + + 1/576 z y x - 1/108 y x z + 1/432 y x z + 1/432 y x + + 2 2 2 2 2 2 2 + - 1/144 y x z + 1/432 y x z + 1/72 y x z - 1/72 y x z + + 3 2 3 2 2 2 4 4 2 + + 1/108 y x z - 1/432 y x - 1/216 y x + 1/864 x y + 1/1728 x y + + 4 3 2 4 2 2 4 4 + - 1/864 x y , COEFF(0, 2, -2) = 5/384 x y z - 1/384 z y x + + 3 4 4 2 4 3 4 3 4 + + 1/576 z y x - 5/576 x y z - 1/576 x y z + 1/576 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/1152 x y z - 1/576 x y z + 1/288 x y z + 1/192 x y z + + 4 3 2 4 2 2 4 3 4 4 + - 1/192 x y z + 1/384 x y z - 1/288 x y z - 1/1152 z y x + + 4 3 2 4 4 4 2 + + 1/144 y z + 5/1152 x y z - 1/144 y + 1/288 y - 1/96 y z + + 4 2 2 2 2 2 3 2 3 + - 1/288 y z - 5/384 y x z + 5/576 y x z + 5/288 y x z + + 3 2 2 4 4 3 3 2 + + 5/192 y x z + 1/1152 y x + 1/144 y - 1/144 z y - 1/288 y + + 3 2 3 2 2 4 2 + - 5/576 y x + 5/576 z y x - 5/1152 x y - 5/576 z y x + 1/144 y z + + 2 2 2 2 2 3 2 3 3 + - 5/1152 y x z - 5/192 y x z + 1/288 y z - 5/288 y x z - 1/72 y z + + 2 3 3 3 3 2 2 2 2 + - 1/144 y z + 1/72 y z - 1/48 y z + 1/48 y z + 1/96 y z + + 2 2 2 4 4 2 4 3 + + 5/1152 y x + 5/576 y x - 1/576 x y - 1/1152 x y + 1/576 x y , + + 4 3 4 2 2 4 2 + COEFF(1, 2, -2) = - 1/432 x y z + 1/576 x y z - 1/144 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + - 1/144 x y z - 1/864 x y z + 1/576 z y x - 1/864 z y x + + 4 3 2 4 3 4 3 4 + + 1/216 x y z + 1/216 x y z + 1/864 x y z - 1/864 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/1728 x y z + 1/864 x y z - 1/432 x y z - 1/288 x y z + + 4 3 2 4 2 2 4 3 3 4 + + 1/288 x y z - 1/576 x y z + 1/432 x y z + 1/1728 x y z + + 4 4 2 4 3 3 + + 1/1728 z y x - 1/432 x y z + 1/864 y x - 1/108 y x z + + 3 2 3 2 2 3 + - 1/864 z y x - 1/288 z y x + 1/432 y x z - 1/216 y x z - 1/216 y x + + 3 4 2 2 2 3 2 2 2 3 + - 1/1728 x y + 1/144 y x z - 1/72 y x z - 1/216 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 1/432 y x z + 1/288 y x z - 1/108 y x z - 1/72 y x z + + 4 2 3 3 4 4 3 2 3 + + 1/432 x y + 1/864 y x z - 1/1728 y x + 1/216 y x + 1/1728 y x + + 3 2 3 3 2 2 4 3 3 + + 1/216 y x - 1/216 z y x - 1/216 z y x + 1/432 x y - 1/864 y x + + 3 3 2 2 3 + + 1/864 z y x + 1/216 y x z + 1/216 z y x - 1/1728 z y x + + 2 2 3 3 3 3 3 3 2 + - 1/576 z y x + 1/108 y x z - 1/432 y x z - 1/432 y x + + 2 2 2 2 2 2 2 + + 1/144 y x z + 1/432 y x z + 1/72 y x z + 1/72 y x z + + 3 2 3 2 2 2 4 4 2 + + 1/108 y x z - 1/432 y x - 1/216 y x + 1/864 x y + 1/1728 x y + + 4 3 4 3 4 2 + - 1/864 x y , COEFF(2, 2, -2) = 1/3456 x y z - 1/1152 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + + 1/2304 x y z + 1/1152 x y z + 1/1728 x y z - 1/2304 z y x + + 3 4 4 4 3 2 4 3 4 3 + + 1/3456 z y x - 1/1728 x y z - 1/3456 x y z - 1/3456 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/3456 x y z + 1/6912 x y z - 1/3456 x y z + 1/1728 x y z + + 4 2 4 3 2 4 2 2 4 3 + + 1/1152 x y z - 1/1152 x y z + 1/2304 x y z - 1/1728 x y z + + 3 4 4 4 2 4 3 + - 1/3456 x y z - 1/6912 z y x + 1/6912 x y z - 1/1728 y x + + 3 3 2 3 2 + + 1/864 y x z + 1/1728 z y x + 1/576 z y x - 1/3456 y x z + + 2 3 3 4 2 2 2 + + 1/1728 y x z + 1/1728 y x + 1/3456 x y - 1/2304 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/576 y x z + 1/3456 y x z - 1/864 y x z - 1/576 y x z + + 2 3 3 2 2 4 2 3 3 + + 1/1728 y x z + 1/1152 y x z - 1/3456 x y - 1/1728 y x z + + 4 4 3 2 3 3 2 3 + + 1/6912 y x - 1/1728 y x - 1/3456 y x - 1/3456 y x + 1/1728 z y x + + 3 2 2 4 3 3 3 3 + + 1/3456 z y x - 1/6912 x y + 1/1728 y x - 1/1728 z y x + + 2 2 3 2 2 3 + - 1/1728 y x z - 1/3456 z y x + 1/3456 z y x + 1/1152 z y x + + 3 3 3 3 3 2 2 2 + - 1/864 y x z + 1/864 y x z + 1/3456 y x - 1/1152 y x z + + 2 2 2 2 2 3 2 3 + - 1/6912 y x z - 1/1152 y x z - 1/576 y x z - 1/1728 y x z + + 2 2 2 4 4 2 4 3 + + 1/6912 y x + 1/3456 y x - 1/3456 x y - 1/6912 x y + 1/3456 x y , + + 4 3 4 2 2 4 2 + COEFF(-2, -2, -1) = 1/216 x y z - 1/576 x y z - 1/1152 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + + 1/576 x y z + 1/432 x y z + 1/1152 z y x - 1/864 z y x + + 4 3 2 4 3 4 3 4 + - 1/432 x y z + 1/864 x y z - 1/216 x y z + 1/216 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/432 x y z + 1/864 x y z + 1/432 x y z + 1/576 x y z + + 4 3 2 4 2 2 4 3 3 4 + - 1/576 x y z - 1/1152 x y z - 1/432 x y z - 1/216 x y z + + 4 4 2 4 3 3 3 + + 1/432 z y x - 1/432 x y z + 1/216 y x - 1/216 y x z - 1/108 z y x + + 2 3 2 2 3 3 4 + - 1/288 z y x - 1/216 y x z + 1/432 y x z - 1/216 y x + 1/432 x y + + 2 2 2 3 2 2 2 3 3 3 + + 1/1152 y x z - 1/288 y x z - 1/864 y x z + 1/216 y x z + + 3 3 2 2 3 3 2 2 4 + + 1/288 y x z + 1/432 y x z + 1/576 y x z - 1/432 x y + + 2 3 3 4 4 3 2 3 3 2 + - 1/432 y x z - 1/864 y x + 1/216 y x - 1/432 y x - 1/432 y x + + 3 3 2 2 4 3 3 3 3 + - 1/108 z y x + 1/216 z y x + 1/864 x y - 1/216 y x + 1/108 z y x + + 2 2 3 2 2 3 + + 1/108 y x z - 1/216 z y x + 1/216 z y x + 1/576 z y x + + 3 3 3 3 3 2 2 2 + + 1/216 y x z - 1/216 y x z + 1/432 y x - 1/576 y x z + + 2 2 2 2 2 3 2 3 + + 1/432 y x z - 1/576 y x z + 1/288 y x z - 1/432 y x z + + 2 2 2 4 4 2 4 3 + - 1/864 y x + 1/432 y x - 1/432 x y + 1/864 x y + 1/432 x y , + + 4 3 4 2 2 4 2 + COEFF(-1, -2, -1) = - 1/27 x y z + 1/288 x y z + 1/72 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + - 1/72 x y z - 1/216 x y z - 1/288 z y x + 1/216 z y x + + 4 3 2 4 3 4 3 4 + + 1/54 x y z - 1/54 x y z + 1/54 x y z - 1/54 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/108 x y z - 1/216 x y z - 1/108 x y z - 1/144 x y z + + 4 3 2 4 2 2 4 3 3 4 + + 1/144 x y z + 1/288 x y z + 1/108 x y z + 1/108 x y z + + 4 4 2 4 3 3 3 + - 1/108 z y x + 1/27 x y z - 1/108 y x + 1/27 y x z + 1/54 z y x + + 2 3 2 2 3 3 4 + + 1/144 z y x + 1/27 y x z - 1/54 y x z + 1/27 y x - 1/216 x y + + 2 2 2 3 2 2 2 3 3 3 + - 1/72 y x z + 1/36 y x z + 1/54 y x z - 1/108 y x z + + 3 3 2 2 3 3 2 2 4 + - 1/144 y x z - 1/27 y x z - 1/36 y x z + 1/54 x y + + 2 3 3 4 4 3 2 3 3 2 + + 1/216 y x z + 1/216 y x - 1/27 y x + 1/216 y x + 1/27 y x + + 3 3 2 2 4 3 3 3 3 + + 2/27 z y x - 2/27 z y x - 1/54 x y + 1/108 y x - 1/54 z y x + + 2 2 3 2 2 3 3 3 + - 2/27 y x z + 2/27 z y x - 1/108 z y x - 1/288 z y x - 1/27 y x z + + 3 3 3 2 2 2 2 2 2 2 + + 1/108 y x z - 1/54 y x + 1/72 y x z - 1/27 y x z + 1/36 y x z + + 2 3 2 3 2 2 2 4 + - 1/36 y x z + 1/27 y x z + 1/54 y x - 1/27 y x + 1/108 x y + + 4 2 4 3 2 4 2 + - 1/216 x y - 1/108 x y , COEFF(0, -2, -1) = - 5/192 x y z + + 2 4 4 3 4 4 2 4 3 4 3 + + 1/192 z y x - 1/144 z y x + 5/144 x y z - 1/36 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/36 x y z - 1/72 x y z + 1/144 x y z + 1/72 x y z + + 4 2 4 3 2 4 2 2 4 3 + + 1/96 x y z - 1/96 x y z - 1/192 x y z - 1/72 x y z + + 4 4 4 3 2 4 4 4 2 + + 1/72 z y x - 1/36 y z - 5/72 x y z - 1/18 y - 1/36 y + 1/48 y z + + 4 2 2 2 2 2 3 2 3 + + 1/18 y z + 5/192 y x z - 5/144 y x z + 5/72 y x z + + 3 2 2 4 4 3 3 2 3 2 + + 5/96 y x z - 1/144 y x + 1/18 y - 1/9 z y + 1/36 y - 5/72 y x + + 3 2 2 4 2 2 2 + + 5/36 z y x + 5/144 x y - 5/36 z y x + 1/9 y z + 5/72 y x z + + 2 2 2 3 2 3 3 2 3 + - 5/96 y x z - 1/18 y z - 5/72 y x z - 1/18 y z + 1/36 y z + + 3 3 3 2 2 2 2 2 2 + + 1/18 y z - 1/24 y z + 1/24 y z - 1/48 y z - 5/144 y x + + 2 4 4 2 4 3 + + 5/72 y x - 1/72 x y + 1/144 x y + 1/72 x y , COEFF(1, -2, -1) = + + 4 3 4 2 2 4 2 4 2 + 1/27 x y z - 1/288 x y z + 1/72 x y z + 1/72 x y z + + 3 4 3 2 4 4 3 4 4 4 3 + + 1/216 x y z - 1/288 z y x + 1/216 z y x - 1/54 x y z + + 2 4 3 4 3 4 4 2 + - 1/54 x y z + 1/54 x y z - 1/54 x y z + 1/108 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/216 x y z - 1/108 x y z - 1/144 x y z + 1/144 x y z + + 4 2 2 4 3 3 4 4 4 + + 1/288 x y z + 1/108 x y z - 1/108 x y z - 1/108 z y x + + 2 4 3 3 3 2 3 + + 1/27 x y z + 1/108 y x - 1/27 y x z - 1/54 z y x - 1/144 z y x + + 2 2 3 3 4 2 2 2 + - 1/27 y x z + 1/54 y x z - 1/27 y x + 1/216 x y - 1/72 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/36 y x z + 1/54 y x z + 1/108 y x z + 1/144 y x z + + 2 3 3 2 2 4 2 3 3 4 4 + - 1/27 y x z - 1/36 y x z - 1/54 x y - 1/216 y x z + 1/216 y x + + 3 2 3 3 2 3 3 2 + + 1/27 y x - 1/216 y x + 1/27 y x - 2/27 z y x - 2/27 z y x + + 2 4 3 3 3 3 2 + - 1/54 x y - 1/108 y x + 1/54 z y x + 2/27 y x z + 2/27 z y x + + 2 3 2 2 3 3 3 3 3 3 + + 1/108 z y x + 1/288 z y x + 1/27 y x z - 1/108 y x z + + 2 2 2 2 2 2 2 2 + + 1/54 y x - 1/72 y x z - 1/27 y x z + 1/36 y x z + 1/36 y x z + + 3 2 3 2 2 2 4 4 2 + + 1/27 y x z + 1/54 y x - 1/27 y x + 1/108 x y - 1/216 x y + + 4 3 4 3 4 2 + - 1/108 x y , COEFF(2, -2, -1) = - 1/216 x y z + 1/576 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + - 1/1152 x y z - 1/576 x y z - 1/432 x y z + 1/1152 z y x + + 3 4 4 4 3 2 4 3 4 3 + - 1/864 z y x + 1/432 x y z + 1/864 x y z - 1/216 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/216 x y z - 1/432 x y z + 1/864 x y z + 1/432 x y z + + 4 2 4 3 2 4 2 2 4 3 + + 1/576 x y z - 1/576 x y z - 1/1152 x y z - 1/432 x y z + + 3 4 4 4 2 4 3 + + 1/216 x y z + 1/432 z y x - 1/432 x y z - 1/216 y x + + 3 3 2 3 2 + + 1/216 y x z + 1/108 z y x + 1/288 z y x + 1/216 y x z + + 2 3 3 4 2 2 2 + - 1/432 y x z + 1/216 y x - 1/432 x y + 1/1152 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/288 y x z - 1/864 y x z - 1/216 y x z - 1/288 y x z + + 2 3 3 2 2 4 2 3 3 + + 1/432 y x z + 1/576 y x z + 1/432 x y + 1/432 y x z + + 4 4 3 2 3 3 2 3 + - 1/864 y x - 1/216 y x + 1/432 y x - 1/432 y x + 1/108 z y x + + 3 2 2 4 3 3 3 3 + + 1/216 z y x + 1/864 x y + 1/216 y x - 1/108 z y x - 1/108 y x z + + 2 2 3 2 2 3 3 3 + - 1/216 z y x - 1/216 z y x - 1/576 z y x - 1/216 y x z + + 3 3 3 2 2 2 2 2 + + 1/216 y x z - 1/432 y x + 1/576 y x z + 1/432 y x z + + 2 2 2 3 2 3 2 2 2 + - 1/576 y x z - 1/288 y x z - 1/432 y x z - 1/864 y x + 1/432 y x + + 4 4 2 4 3 + - 1/432 x y + 1/864 x y + 1/432 x y , COEFF(-2, -1, -1) = + + 4 3 4 2 2 4 2 4 2 + - 1/54 x y z + 1/144 x y z + 1/288 x y z - 1/144 x y z + + 3 4 3 2 4 4 3 4 4 4 3 + - 1/108 x y z - 1/288 z y x + 1/216 z y x + 1/108 x y z + + 2 4 3 4 3 4 4 2 + - 1/216 x y z + 1/108 x y z - 1/27 x y z + 1/27 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/54 x y z - 1/216 x y z - 1/72 x y z + 1/288 x y z + + 4 2 2 4 3 3 4 4 4 + + 1/72 x y z + 1/54 x y z + 1/54 x y z - 1/108 z y x + + 2 4 3 3 3 2 3 + + 1/108 x y z - 1/27 y x + 1/27 y x z + 2/27 z y x + 1/36 z y x + + 2 2 3 3 4 2 2 2 + + 2/27 y x z - 1/27 y x z + 1/27 y x - 1/108 x y - 1/72 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/144 y x z + 1/54 y x z - 1/27 y x z - 1/144 y x z + + 2 3 3 2 2 4 2 3 3 4 4 + - 1/54 y x z - 1/288 y x z + 1/108 x y + 1/27 y x z + 1/216 y x + + 3 2 3 3 2 3 3 2 + - 1/108 y x + 1/27 y x + 1/216 y x + 1/54 z y x - 1/108 z y x + + 2 4 3 3 3 3 2 + - 1/216 x y + 1/108 y x - 1/54 z y x - 2/27 y x z + 1/27 z y x + + 2 3 2 2 3 3 3 3 3 3 + - 2/27 z y x - 1/36 z y x - 1/108 y x z + 1/108 y x z + + 2 2 2 2 2 2 2 2 + - 1/27 y x + 1/36 y x z - 1/27 y x z + 1/72 y x z - 1/36 y x z + + 3 2 3 2 2 2 4 4 2 + + 1/216 y x z + 1/54 y x - 1/54 y x + 1/54 x y - 1/54 x y + + 4 3 4 3 4 2 + - 1/216 x y , COEFF(-1, -1, -1) = 4/27 x y z - 1/72 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + - 1/18 x y z + 1/18 x y z + 1/54 x y z + 1/72 z y x + + 3 4 4 4 3 2 4 3 4 3 + - 1/54 z y x - 2/27 x y z + 2/27 x y z - 1/27 x y z + + 4 4 2 4 2 3 4 3 3 + + 4/27 x y z - 4/27 x y z + 2/27 x y z + 1/54 x y z + + 4 2 4 3 2 4 2 2 4 3 + + 1/18 x y z - 1/72 x y z - 1/18 x y z - 2/27 x y z + + 3 4 4 4 2 4 3 3 + - 1/27 x y z + 1/27 z y x - 4/27 x y z + 2/27 y x - 8/27 y x z + + 3 2 3 16 2 2 3 + - 4/27 z y x - 1/18 z y x - -- y x z + 8/27 y x z - 8/27 y x + 27 + + 3 4 2 2 2 3 2 2 2 3 3 3 + + 1/54 x y + 2/9 y x z - 1/18 y x z - 8/27 y x z + 2/27 y x z + + 3 3 2 2 3 3 2 2 4 2 3 3 + + 1/72 y x z + 8/27 y x z + 1/18 y x z - 2/27 x y - 2/27 y x z + + 4 4 3 2 3 3 2 3 + - 1/54 y x + 2/27 y x - 2/27 y x - 2/27 y x - 4/27 z y x + + 3 2 2 4 3 3 3 3 16 + + 4/27 z y x + 2/27 x y - 1/54 y x + 1/27 z y x + -- y x z + 27 + + 16 2 2 3 2 2 3 3 3 3 3 3 + - -- z y x + 4/27 z y x + 1/18 z y x + 2/27 y x z - 1/54 y x z + 27 + + 2 2 2 16 2 2 2 2 2 + + 8/27 y x - 2/9 y x z + -- y x z - 2/9 y x z + 2/9 y x z + 27 + + 3 2 3 2 2 2 4 4 2 + - 2/27 y x z - 8/27 y x + 8/27 y x - 2/27 x y + 2/27 x y + + 4 3 2 4 2 2 4 4 + + 1/54 x y , COEFF(0, -1, -1) = 5/48 x y z - 1/48 z y x + + 3 4 4 2 4 3 4 3 4 4 2 + + 1/36 z y x - 5/36 x y z + 1/18 x y z - 2/9 x y z + 2/9 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/9 x y z - 1/36 x y z - 1/12 x y z + 1/48 x y z + + 4 2 2 4 3 4 4 4 3 2 4 + + 1/12 x y z + 1/9 x y z - 1/18 z y x + 1/9 y z + 5/18 x y z + + 4 4 2 4 2 2 2 2 2 3 + + 4/9 y + 1/9 y - 1/12 y z - 2/9 y z - 5/12 y x z + 5/9 y x z + + 2 3 3 2 2 4 4 3 3 2 + - 5/9 y x z - 5/48 y x z + 1/36 y x - 1/9 y + 2/9 z y - 4/9 y + + 3 2 3 2 2 4 2 + + 5/36 y x - 5/18 z y x - 5/36 x y + 10/9 z y x - 8/9 y z + + 2 2 2 2 2 3 2 3 3 + - 10/9 y x z + 5/12 y x z + 8/9 y z + 5/36 y x z + 4/9 y z + + 2 3 3 3 3 2 2 2 2 2 2 + - 4/9 y z - 1/9 y z + 1/12 y z - 1/3 y z + 1/3 y z + 5/9 y x + + 2 4 4 2 4 3 + - 5/9 y x + 1/9 x y - 1/9 x y - 1/36 x y , COEFF(1, -1, -1) = + + 4 3 4 2 2 4 2 4 2 + - 4/27 x y z + 1/72 x y z - 1/18 x y z - 1/18 x y z + + 3 4 3 2 4 4 3 4 4 4 3 + - 1/54 x y z + 1/72 z y x - 1/54 z y x + 2/27 x y z + + 2 4 3 4 3 4 4 2 + + 2/27 x y z - 1/27 x y z + 4/27 x y z - 4/27 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + + 2/27 x y z + 1/54 x y z + 1/18 x y z - 1/72 x y z + + 4 2 2 4 3 3 4 4 4 + - 1/18 x y z - 2/27 x y z + 1/27 x y z + 1/27 z y x + + 2 4 3 3 3 2 3 + - 4/27 x y z - 2/27 y x + 8/27 y x z + 4/27 z y x + 1/18 z y x + + 16 2 2 3 3 4 2 2 2 + + -- y x z - 8/27 y x z + 8/27 y x - 1/54 x y + 2/9 y x z + 27 + + 3 2 2 2 3 3 3 3 3 2 + + 1/18 y x z - 8/27 y x z - 2/27 y x z - 1/72 y x z + + 2 3 3 2 2 4 2 3 3 4 4 + + 8/27 y x z + 1/18 y x z + 2/27 x y + 2/27 y x z - 1/54 y x + + 3 2 3 3 2 3 3 2 + - 2/27 y x + 2/27 y x - 2/27 y x + 4/27 z y x + 4/27 z y x + + 2 4 3 3 3 3 16 16 2 + + 2/27 x y + 1/54 y x - 1/27 z y x - -- y x z - -- z y x + 27 27 + + 2 3 2 2 3 3 3 3 3 3 2 + - 4/27 z y x - 1/18 z y x - 2/27 y x z + 1/54 y x z - 8/27 y x + + 2 2 16 2 2 2 2 2 3 2 3 + + 2/9 y x z + -- y x z - 2/9 y x z - 2/9 y x z - 2/27 y x z + 27 + + 2 2 2 4 4 2 4 3 + - 8/27 y x + 8/27 y x - 2/27 x y + 2/27 x y + 1/54 x y , + + 4 3 4 2 2 4 2 + COEFF(2, -1, -1) = 1/54 x y z - 1/144 x y z + 1/288 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + + 1/144 x y z + 1/108 x y z - 1/288 z y x + 1/216 z y x + + 4 3 2 4 3 4 3 4 + - 1/108 x y z - 1/216 x y z + 1/108 x y z - 1/27 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/27 x y z - 1/54 x y z - 1/216 x y z - 1/72 x y z + + 4 3 2 4 2 2 4 3 3 4 + + 1/288 x y z + 1/72 x y z + 1/54 x y z - 1/54 x y z + + 4 4 2 4 3 3 3 + - 1/108 z y x + 1/108 x y z + 1/27 y x - 1/27 y x z - 2/27 z y x + + 2 3 2 2 3 3 4 + - 1/36 z y x - 2/27 y x z + 1/27 y x z - 1/27 y x + 1/108 x y + + 2 2 2 3 2 2 2 3 3 3 + - 1/72 y x z - 1/144 y x z + 1/54 y x z + 1/27 y x z + + 3 3 2 2 3 3 2 2 4 + + 1/144 y x z - 1/54 y x z - 1/288 y x z - 1/108 x y + + 2 3 3 4 4 3 2 3 3 2 + - 1/27 y x z + 1/216 y x + 1/108 y x - 1/27 y x + 1/216 y x + + 3 3 2 2 4 3 3 3 3 + - 1/54 z y x - 1/108 z y x - 1/216 x y - 1/108 y x + 1/54 z y x + + 2 2 3 2 2 3 3 3 + + 2/27 y x z + 1/27 z y x + 2/27 z y x + 1/36 z y x + 1/108 y x z + + 3 3 3 2 2 2 2 2 2 2 + - 1/108 y x z + 1/27 y x - 1/36 y x z - 1/27 y x z + 1/72 y x z + + 2 3 2 3 2 2 2 4 + + 1/36 y x z + 1/216 y x z + 1/54 y x - 1/54 y x + 1/54 x y + + 4 2 4 3 4 3 4 2 + - 1/54 x y - 1/216 x y , COEFF(-2, 0, -1) = 1/36 x y z - 1/96 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + - 1/192 x y z + 1/96 x y z + 1/72 x y z + 1/192 z y x + + 3 4 4 4 3 2 4 3 4 2 + - 1/144 z y x - 1/72 x y z + 1/144 x y z - 5/72 x y z + + 4 2 3 4 2 2 3 4 4 4 + + 5/144 x y z - 5/192 x y z - 1/36 x y z + 1/72 z y x + + 2 4 4 4 2 2 3 + - 1/72 x y z - 1/18 x + 1/18 x z - 1/36 x - 5/36 y x z + 5/72 y x z + + 3 4 2 2 2 2 2 3 3 4 + + 1/72 x y + 5/192 y x z - 5/144 y x z - 1/9 z x - 1/72 x y + + 2 3 3 4 2 4 4 3 2 3 + - 5/72 y x z + 1/48 x z - 1/144 y x + 1/18 x - 5/72 y x + + 2 4 2 2 3 2 2 3 4 3 + + 1/144 x y + 1/36 x + 5/36 z y x + 5/96 z y x - 1/36 x z + + 2 2 2 2 2 2 + + 5/72 y x - 5/96 y x z + 5/72 y x z + 1/9 x z - 1/18 x z + + 3 3 2 3 3 2 2 2 + + 1/18 x z + 1/36 x z - 1/18 x z - 1/48 x z + 1/24 x z + + 3 2 2 2 4 2 4 + - 1/24 x z - 5/144 y x + 5/144 x y , COEFF(-1, 0, -1) = - 2/9 x y z + + 3 4 2 2 4 2 4 2 3 4 3 + + 1/48 x y z + 1/12 x y z - 1/12 x y z - 1/36 x y z + + 2 4 4 3 4 4 4 3 2 4 3 + - 1/48 z y x + 1/36 z y x + 1/9 x y z - 1/9 x y z + + 4 2 4 2 3 4 2 2 3 4 + + 5/18 x y z - 5/36 x y z + 5/48 x y z + 1/18 x y z + + 4 4 2 4 4 4 2 + - 1/18 z y x + 2/9 x y z + 4/9 x - 2/9 x z + 1/9 x + 10/9 y x z + + 2 3 3 4 2 2 2 2 2 3 3 + - 5/9 y x z - 1/36 x y - 5/12 y x z + 5/9 y x z + 2/9 z x + + 4 2 3 3 4 2 4 4 3 2 3 + + 1/9 x y + 5/36 y x z - 1/12 x z + 1/36 y x - 1/9 x + 5/36 y x + + 2 4 2 2 3 2 2 3 4 3 2 + - 1/9 x y - 4/9 x - 5/18 z y x - 5/48 z y x + 1/9 x z - 5/9 y x + + 2 2 2 2 2 3 3 2 3 + + 5/12 y x z - 10/9 y x z - 8/9 x z + 8/9 x z - 1/9 x z - 4/9 x z + + 3 2 2 2 3 2 2 2 4 2 + + 4/9 x z + 1/3 x z - 1/3 x z + 1/12 x z + 5/9 y x - 5/36 x y , + + 2 4 2 2 4 4 3 4 4 + COEFF(0, 0, -1) = - 5/32 x y z + 1/32 z y x - 1/24 z y x + + 2 4 3 4 2 4 2 3 4 2 2 + + 5/24 x y z - 5/12 x y z + 5/24 x y z - 5/32 x y z + + 4 4 4 3 2 4 4 4 + + 1/12 z y x - 1/6 y z - 5/12 x y z + 1/3 x z - 1/6 x + 4/3 z + + 4 4 2 4 25 2 2 2 25 2 2 3 + - 1/6 y + 1/8 y z + 1/3 y z + -- y x z - -- y x z - 2/3 + 32 24 + + 4 2 4 4 3 2 2 2 4 2 + + 1/8 x z - 1/24 y x - 2/3 z + 5/6 y + 1/2 z + 5/24 x y + 5/6 x + + 4 3 25 2 2 2 2 2 3 2 3 + - 1/6 x z + -- y x z - 5/3 y z - 5/3 x z + 5/6 y z + 5/6 x z + 12 + + 2 2 2 2 25 2 2 4 2 + - 5/8 x z - 5/8 y z - -- y x + 5/24 x y , COEFF(1, 0, -1) = + 24 + + 4 3 4 2 2 4 2 4 2 3 4 3 + 2/9 x y z - 1/48 x y z + 1/12 x y z + 1/12 x y z + 1/36 x y z + + 2 4 4 3 4 4 4 3 2 4 3 + - 1/48 z y x + 1/36 z y x - 1/9 x y z - 1/9 x y z + + 4 2 4 2 3 4 2 2 3 4 + + 5/18 x y z - 5/36 x y z + 5/48 x y z - 1/18 x y z + + 4 4 2 4 4 4 2 + - 1/18 z y x + 2/9 x y z - 4/9 x - 2/9 x z + 1/9 x - 10/9 y x z + + 2 3 3 4 2 2 2 2 2 3 3 + + 5/9 y x z + 1/36 x y - 5/12 y x z + 5/9 y x z - 2/9 z x + + 4 2 3 3 4 2 4 4 3 2 3 + - 1/9 x y - 5/36 y x z - 1/12 x z + 1/36 y x + 1/9 x - 5/36 y x + + 2 4 2 2 3 2 2 3 4 3 2 + - 1/9 x y - 4/9 x + 5/18 z y x + 5/48 z y x + 1/9 x z + 5/9 y x + + 2 2 2 2 2 3 3 2 3 + - 5/12 y x z - 10/9 y x z + 8/9 x z + 8/9 x z + 1/9 x z - 4/9 x z + + 3 2 2 2 3 2 2 2 4 2 + - 4/9 x z + 1/3 x z + 1/3 x z - 1/12 x z + 5/9 y x - 5/36 x y , + + 4 3 4 2 2 4 2 + COEFF(2, 0, -1) = - 1/36 x y z + 1/96 x y z - 1/192 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + - 1/96 x y z - 1/72 x y z + 1/192 z y x - 1/144 z y x + + 4 3 2 4 3 4 2 4 2 3 + + 1/72 x y z + 1/144 x y z - 5/72 x y z + 5/144 x y z + + 4 2 2 3 4 4 4 2 4 + - 5/192 x y z + 1/36 x y z + 1/72 z y x - 1/72 x y z + 1/18 x + + 4 4 2 2 3 3 4 + + 1/18 x z - 1/36 x + 5/36 y x z - 5/72 y x z - 1/72 x y + + 2 2 2 2 2 3 3 4 2 3 3 + + 5/192 y x z - 5/144 y x z + 1/9 z x + 1/72 x y + 5/72 y x z + + 4 2 4 4 3 2 3 2 4 2 + + 1/48 x z - 1/144 y x - 1/18 x + 5/72 y x + 1/144 x y + 1/36 x + + 2 3 2 2 3 4 3 2 2 2 + - 5/36 z y x - 5/96 z y x - 1/36 x z - 5/72 y x + 5/96 y x z + + 2 2 2 3 3 2 3 3 + + 5/72 y x z - 1/9 x z - 1/18 x z - 1/18 x z + 1/36 x z + 1/18 x z + + 2 2 2 3 2 2 2 4 2 + - 1/48 x z - 1/24 x z + 1/24 x z - 5/144 y x + 5/144 x y , + + 4 3 4 2 2 4 2 + COEFF(-2, 1, -1) = - 1/54 x y z + 1/144 x y z + 1/288 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + - 1/144 x y z - 1/108 x y z - 1/288 z y x + 1/216 z y x + + 4 3 2 4 3 4 3 4 + + 1/108 x y z - 1/216 x y z - 1/108 x y z + 1/27 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/27 x y z - 1/54 x y z + 1/216 x y z + 1/72 x y z + + 4 3 2 4 2 2 4 3 3 4 + - 1/288 x y z + 1/72 x y z - 1/54 x y z + 1/54 x y z + + 4 4 2 4 3 3 3 + - 1/108 z y x + 1/108 x y z + 1/27 y x - 1/27 y x z - 2/27 z y x + + 2 3 2 2 3 3 4 + - 1/36 z y x + 2/27 y x z - 1/27 y x z - 1/27 y x - 1/108 x y + + 2 2 2 3 2 2 2 3 3 3 + - 1/72 y x z - 1/144 y x z + 1/54 y x z + 1/27 y x z + + 3 3 2 2 3 3 2 2 4 + + 1/144 y x z + 1/54 y x z + 1/288 y x z + 1/108 x y + + 2 3 3 4 4 3 2 3 3 2 + + 1/27 y x z + 1/216 y x + 1/108 y x + 1/27 y x - 1/216 y x + + 3 3 2 2 4 3 3 3 3 + - 1/54 z y x + 1/108 z y x - 1/216 x y - 1/108 y x + 1/54 z y x + + 2 2 3 2 2 3 3 3 + + 2/27 y x z - 1/27 z y x - 2/27 z y x - 1/36 z y x + 1/108 y x z + + 3 3 3 2 2 2 2 2 2 2 + - 1/108 y x z - 1/27 y x + 1/36 y x z - 1/27 y x z - 1/72 y x z + + 2 3 2 3 2 2 2 4 + + 1/36 y x z - 1/216 y x z + 1/54 y x + 1/54 y x - 1/54 x y + + 4 2 4 3 4 3 4 2 + - 1/54 x y + 1/216 x y , COEFF(-1, 1, -1) = 4/27 x y z - 1/72 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + - 1/18 x y z + 1/18 x y z + 1/54 x y z + 1/72 z y x + + 3 4 4 4 3 2 4 3 4 3 + - 1/54 z y x - 2/27 x y z + 2/27 x y z + 1/27 x y z + + 4 4 2 4 2 3 4 3 3 + - 4/27 x y z - 4/27 x y z + 2/27 x y z - 1/54 x y z + + 4 2 4 3 2 4 2 2 4 3 + - 1/18 x y z + 1/72 x y z - 1/18 x y z + 2/27 x y z + + 3 4 4 4 2 4 3 3 + - 1/27 x y z + 1/27 z y x - 4/27 x y z - 2/27 y x + 8/27 y x z + + 3 2 3 16 2 2 3 + + 4/27 z y x + 1/18 z y x - -- y x z + 8/27 y x z + 8/27 y x + 27 + + 3 4 2 2 2 3 2 2 2 3 3 3 + + 1/54 x y + 2/9 y x z + 1/18 y x z - 8/27 y x z - 2/27 y x z + + 3 3 2 2 3 3 2 2 4 2 3 3 + - 1/72 y x z - 8/27 y x z - 1/18 y x z - 2/27 x y - 2/27 y x z + + 4 4 3 2 3 3 2 3 + - 1/54 y x - 2/27 y x - 2/27 y x + 2/27 y x + 4/27 z y x + + 3 2 2 4 3 3 3 3 16 + - 4/27 z y x + 2/27 x y + 1/54 y x - 1/27 z y x - -- y x z + 27 + + 16 2 2 3 2 2 3 3 3 3 3 3 + + -- z y x + 4/27 z y x + 1/18 z y x - 2/27 y x z + 1/54 y x z + 27 + + 2 2 2 16 2 2 2 2 2 + + 8/27 y x - 2/9 y x z + -- y x z + 2/9 y x z - 2/9 y x z + 27 + + 3 2 3 2 2 2 4 4 2 + + 2/27 y x z - 8/27 y x - 8/27 y x + 2/27 x y + 2/27 x y + + 4 3 2 4 2 2 4 4 + - 1/54 x y , COEFF(0, 1, -1) = 5/48 x y z - 1/48 z y x + + 3 4 4 2 4 3 4 3 4 4 2 + + 1/36 z y x - 5/36 x y z - 1/18 x y z + 2/9 x y z + 2/9 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/9 x y z + 1/36 x y z + 1/12 x y z - 1/48 x y z + + 4 2 2 4 3 4 4 4 3 2 4 + + 1/12 x y z - 1/9 x y z - 1/18 z y x + 1/9 y z + 5/18 x y z + + 4 4 2 4 2 2 2 2 2 3 + - 4/9 y + 1/9 y - 1/12 y z - 2/9 y z - 5/12 y x z + 5/9 y x z + + 2 3 3 2 2 4 4 3 3 2 + + 5/9 y x z + 5/48 y x z + 1/36 y x + 1/9 y - 2/9 z y - 4/9 y + + 3 2 3 2 2 4 2 + - 5/36 y x + 5/18 z y x - 5/36 x y - 10/9 z y x + 8/9 y z + + 2 2 2 2 2 3 2 3 3 + - 10/9 y x z - 5/12 y x z + 8/9 y z - 5/36 y x z - 4/9 y z + + 2 3 3 3 3 2 2 2 2 2 2 + - 4/9 y z + 1/9 y z - 1/12 y z + 1/3 y z + 1/3 y z + 5/9 y x + + 2 4 4 2 4 3 + + 5/9 y x - 1/9 x y - 1/9 x y + 1/36 x y , COEFF(1, 1, -1) = + + 4 3 4 2 2 4 2 4 2 + - 4/27 x y z + 1/72 x y z - 1/18 x y z - 1/18 x y z + + 3 4 3 2 4 4 3 4 4 4 3 + - 1/54 x y z + 1/72 z y x - 1/54 z y x + 2/27 x y z + + 2 4 3 4 3 4 4 2 + + 2/27 x y z + 1/27 x y z - 4/27 x y z - 4/27 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + + 2/27 x y z - 1/54 x y z - 1/18 x y z + 1/72 x y z + + 4 2 2 4 3 3 4 4 4 + - 1/18 x y z + 2/27 x y z + 1/27 x y z + 1/27 z y x + + 2 4 3 3 3 2 3 + - 4/27 x y z + 2/27 y x - 8/27 y x z - 4/27 z y x - 1/18 z y x + + 16 2 2 3 3 4 2 2 2 + + -- y x z - 8/27 y x z - 8/27 y x - 1/54 x y + 2/9 y x z + 27 + + 3 2 2 2 3 3 3 3 3 2 + - 1/18 y x z - 8/27 y x z + 2/27 y x z + 1/72 y x z + + 2 3 3 2 2 4 2 3 3 4 4 + - 8/27 y x z - 1/18 y x z + 2/27 x y + 2/27 y x z - 1/54 y x + + 3 2 3 3 2 3 3 2 + + 2/27 y x + 2/27 y x + 2/27 y x - 4/27 z y x - 4/27 z y x + + 2 4 3 3 3 3 16 16 2 + + 2/27 x y - 1/54 y x + 1/27 z y x + -- y x z + -- z y x + 27 27 + + 2 3 2 2 3 3 3 3 3 3 2 + - 4/27 z y x - 1/18 z y x + 2/27 y x z - 1/54 y x z - 8/27 y x + + 2 2 16 2 2 2 2 2 3 2 3 + + 2/9 y x z + -- y x z + 2/9 y x z + 2/9 y x z + 2/27 y x z + 27 + + 2 2 2 4 4 2 4 3 + - 8/27 y x - 8/27 y x + 2/27 x y + 2/27 x y - 1/54 x y , + + 4 3 4 2 2 4 2 + COEFF(2, 1, -1) = 1/54 x y z - 1/144 x y z + 1/288 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + + 1/144 x y z + 1/108 x y z - 1/288 z y x + 1/216 z y x + + 4 3 2 4 3 4 3 4 + - 1/108 x y z - 1/216 x y z - 1/108 x y z + 1/27 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/27 x y z - 1/54 x y z + 1/216 x y z + 1/72 x y z + + 4 3 2 4 2 2 4 3 3 4 + - 1/288 x y z + 1/72 x y z - 1/54 x y z - 1/54 x y z + + 4 4 2 4 3 3 3 + - 1/108 z y x + 1/108 x y z - 1/27 y x + 1/27 y x z + 2/27 z y x + + 2 3 2 2 3 3 4 + + 1/36 z y x - 2/27 y x z + 1/27 y x z + 1/27 y x + 1/108 x y + + 2 2 2 3 2 2 2 3 3 3 + - 1/72 y x z + 1/144 y x z + 1/54 y x z - 1/27 y x z + + 3 3 2 2 3 3 2 2 4 + - 1/144 y x z + 1/54 y x z + 1/288 y x z - 1/108 x y + + 2 3 3 4 4 3 2 3 3 2 + - 1/27 y x z + 1/216 y x - 1/108 y x - 1/27 y x - 1/216 y x + + 3 3 2 2 4 3 3 3 3 + + 1/54 z y x + 1/108 z y x - 1/216 x y + 1/108 y x - 1/54 z y x + + 2 2 3 2 2 3 3 3 + - 2/27 y x z - 1/27 z y x + 2/27 z y x + 1/36 z y x - 1/108 y x z + + 3 3 3 2 2 2 2 2 2 2 + + 1/108 y x z + 1/27 y x - 1/36 y x z - 1/27 y x z - 1/72 y x z + + 2 3 2 3 2 2 2 4 + - 1/36 y x z - 1/216 y x z + 1/54 y x + 1/54 y x - 1/54 x y + + 4 2 4 3 4 + - 1/54 x y + 1/216 x y , COEFF(-2, 2, -1) = 1/216 x y z + + 3 4 2 2 4 2 4 2 3 4 3 + - 1/576 x y z - 1/1152 x y z + 1/576 x y z + 1/432 x y z + + 2 4 4 3 4 4 4 3 2 4 3 + + 1/1152 z y x - 1/864 z y x - 1/432 x y z + 1/864 x y z + + 4 3 4 4 2 4 2 3 + + 1/216 x y z - 1/216 x y z - 1/432 x y z + 1/864 x y z + + 4 3 3 4 2 4 3 2 4 2 2 + - 1/432 x y z - 1/576 x y z + 1/576 x y z - 1/1152 x y z + + 4 3 3 4 4 4 2 4 + + 1/432 x y z - 1/216 x y z + 1/432 z y x - 1/432 x y z + + 3 3 3 2 3 2 + - 1/216 y x + 1/216 y x z + 1/108 z y x + 1/288 z y x - 1/216 y x z + + 2 3 3 4 2 2 2 + + 1/432 y x z + 1/216 y x + 1/432 x y + 1/1152 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/288 y x z - 1/864 y x z - 1/216 y x z - 1/288 y x z + + 2 3 3 2 2 4 2 3 3 + - 1/432 y x z - 1/576 y x z - 1/432 x y - 1/432 y x z + + 4 4 3 2 3 3 2 3 + - 1/864 y x - 1/216 y x - 1/432 y x + 1/432 y x + 1/108 z y x + + 3 2 2 4 3 3 3 3 + - 1/216 z y x + 1/864 x y + 1/216 y x - 1/108 z y x - 1/108 y x z + + 2 2 3 2 2 3 3 3 + + 1/216 z y x + 1/216 z y x + 1/576 z y x - 1/216 y x z + + 3 3 3 2 2 2 2 2 + + 1/216 y x z + 1/432 y x - 1/576 y x z + 1/432 y x z + + 2 2 2 3 2 3 2 2 2 + + 1/576 y x z - 1/288 y x z + 1/432 y x z - 1/864 y x - 1/432 y x + + 4 4 2 4 3 4 + + 1/432 x y + 1/864 x y - 1/432 x y , COEFF(-1, 2, -1) = - 1/27 x y z + + 3 4 2 2 4 2 4 2 3 4 3 + + 1/288 x y z + 1/72 x y z - 1/72 x y z - 1/216 x y z + + 2 4 4 3 4 4 4 3 2 4 3 + - 1/288 z y x + 1/216 z y x + 1/54 x y z - 1/54 x y z + + 4 3 4 4 2 4 2 3 + - 1/54 x y z + 1/54 x y z + 1/108 x y z - 1/216 x y z + + 4 3 3 4 2 4 3 2 4 2 2 + + 1/108 x y z + 1/144 x y z - 1/144 x y z + 1/288 x y z + + 4 3 3 4 4 4 2 4 + - 1/108 x y z + 1/108 x y z - 1/108 z y x + 1/27 x y z + + 3 3 3 2 3 2 + + 1/108 y x - 1/27 y x z - 1/54 z y x - 1/144 z y x + 1/27 y x z + + 2 3 3 4 2 2 2 3 2 + - 1/54 y x z - 1/27 y x - 1/216 x y - 1/72 y x z - 1/36 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/54 y x z + 1/108 y x z + 1/144 y x z + 1/27 y x z + + 3 2 2 4 2 3 3 4 4 3 + + 1/36 y x z + 1/54 x y + 1/216 y x z + 1/216 y x + 1/27 y x + + 2 3 3 2 3 3 2 2 4 + + 1/216 y x - 1/27 y x - 2/27 z y x + 2/27 z y x - 1/54 x y + + 3 3 3 3 2 2 3 + - 1/108 y x + 1/54 z y x + 2/27 y x z - 2/27 z y x - 1/108 z y x + + 2 2 3 3 3 3 3 3 2 + - 1/288 z y x + 1/27 y x z - 1/108 y x z - 1/54 y x + + 2 2 2 2 2 2 2 3 2 3 + + 1/72 y x z - 1/27 y x z - 1/36 y x z + 1/36 y x z - 1/27 y x z + + 2 2 2 4 4 2 4 3 + + 1/54 y x + 1/27 y x - 1/108 x y - 1/216 x y + 1/108 x y , + + 2 4 2 2 4 4 3 4 4 + COEFF(0, 2, -1) = - 5/192 x y z + 1/192 z y x - 1/144 z y x + + 2 4 3 4 3 4 4 2 + + 5/144 x y z + 1/36 x y z - 1/36 x y z - 1/72 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + + 1/144 x y z - 1/72 x y z - 1/96 x y z + 1/96 x y z + + 4 2 2 4 3 4 4 4 3 2 4 + - 1/192 x y z + 1/72 x y z + 1/72 z y x - 1/36 y z - 5/72 x y z + + 4 4 2 4 2 2 2 + + 1/18 y - 1/36 y + 1/48 y z + 1/18 y z + 5/192 y x z + + 2 2 3 2 3 3 2 2 4 4 3 + - 5/144 y x z - 5/72 y x z - 5/96 y x z - 1/144 y x - 1/18 y + + 3 2 3 2 3 2 2 4 + + 1/9 z y + 1/36 y + 5/72 y x - 5/36 z y x + 5/144 x y + + 2 2 2 2 2 2 + + 5/36 z y x - 1/9 y z + 5/72 y x z + 5/96 y x z - 1/18 y z + + 3 2 3 3 2 3 3 3 3 2 + + 5/72 y x z + 1/18 y z + 1/36 y z - 1/18 y z + 1/24 y z + + 2 2 2 2 2 2 4 + - 1/24 y z - 1/48 y z - 5/144 y x - 5/72 y x + 1/72 x y + + 4 2 4 3 4 3 4 2 + + 1/144 x y - 1/72 x y , COEFF(1, 2, -1) = 1/27 x y z - 1/288 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + + 1/72 x y z + 1/72 x y z + 1/216 x y z - 1/288 z y x + + 3 4 4 4 3 2 4 3 4 3 + + 1/216 z y x - 1/54 x y z - 1/54 x y z - 1/54 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/54 x y z + 1/108 x y z - 1/216 x y z + 1/108 x y z + + 4 2 4 3 2 4 2 2 4 3 + + 1/144 x y z - 1/144 x y z + 1/288 x y z - 1/108 x y z + + 3 4 4 4 2 4 3 3 + - 1/108 x y z - 1/108 z y x + 1/27 x y z - 1/108 y x + 1/27 y x z + + 3 2 3 2 2 3 + + 1/54 z y x + 1/144 z y x - 1/27 y x z + 1/54 y x z + 1/27 y x + + 3 4 2 2 2 3 2 2 2 3 + + 1/216 x y - 1/72 y x z + 1/36 y x z + 1/54 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/108 y x z - 1/144 y x z + 1/27 y x z + 1/36 y x z + + 4 2 3 3 4 4 3 2 3 + - 1/54 x y - 1/216 y x z + 1/216 y x - 1/27 y x - 1/216 y x + + 3 2 3 3 2 2 4 3 3 + - 1/27 y x + 2/27 z y x + 2/27 z y x - 1/54 x y + 1/108 y x + + 3 3 2 2 3 2 2 3 + - 1/54 z y x - 2/27 y x z - 2/27 z y x + 1/108 z y x + 1/288 z y x + + 3 3 3 3 3 2 2 2 2 2 + - 1/27 y x z + 1/108 y x z + 1/54 y x - 1/72 y x z - 1/27 y x z + + 2 2 2 3 2 3 2 2 2 + - 1/36 y x z - 1/36 y x z - 1/27 y x z + 1/54 y x + 1/27 y x + + 4 4 2 4 3 4 + - 1/108 x y - 1/216 x y + 1/108 x y , COEFF(2, 2, -1) = - 1/216 x y z + + 3 4 2 2 4 2 4 2 3 4 3 + + 1/576 x y z - 1/1152 x y z - 1/576 x y z - 1/432 x y z + + 2 4 4 3 4 4 4 3 2 4 3 + + 1/1152 z y x - 1/864 z y x + 1/432 x y z + 1/864 x y z + + 4 3 4 4 2 4 2 3 + + 1/216 x y z - 1/216 x y z - 1/432 x y z + 1/864 x y z + + 4 3 3 4 2 4 3 2 4 2 2 + - 1/432 x y z - 1/576 x y z + 1/576 x y z - 1/1152 x y z + + 4 3 3 4 4 4 2 4 + + 1/432 x y z + 1/216 x y z + 1/432 z y x - 1/432 x y z + + 3 3 3 2 3 2 + + 1/216 y x - 1/216 y x z - 1/108 z y x - 1/288 z y x + 1/216 y x z + + 2 3 3 4 2 2 2 + - 1/432 y x z - 1/216 y x - 1/432 x y + 1/1152 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/288 y x z - 1/864 y x z + 1/216 y x z + 1/288 y x z + + 2 3 3 2 2 4 2 3 3 + - 1/432 y x z - 1/576 y x z + 1/432 x y + 1/432 y x z + + 4 4 3 2 3 3 2 3 + - 1/864 y x + 1/216 y x + 1/432 y x + 1/432 y x - 1/108 z y x + + 3 2 2 4 3 3 3 3 + - 1/216 z y x + 1/864 x y - 1/216 y x + 1/108 z y x + 1/108 y x z + + 2 2 3 2 2 3 3 3 + + 1/216 z y x - 1/216 z y x - 1/576 z y x + 1/216 y x z + + 3 3 3 2 2 2 2 2 + - 1/216 y x z - 1/432 y x + 1/576 y x z + 1/432 y x z + + 2 2 2 3 2 3 2 2 2 + + 1/576 y x z + 1/288 y x z + 1/432 y x z - 1/864 y x - 1/432 y x + + 4 4 2 4 3 + + 1/432 x y + 1/864 x y - 1/432 x y , COEFF(-2, -2, 0) = + + 4 3 4 3 3 4 4 4 3 + - 5/576 x y z - 1/288 x y z + 1/576 z y x + 1/288 x y z + + 2 4 3 4 3 4 4 2 + - 1/576 x y z + 5/576 x y z - 5/576 x y z + 5/1152 x y z + + 4 2 3 4 3 3 4 3 3 4 + - 1/576 x y z - 1/288 x y z + 1/288 x y z + 5/576 x y z + + 4 4 2 4 3 3 + - 5/1152 z y x + 5/1152 x y z + 1/144 y x z + 5/288 z y x + + 2 2 3 2 2 3 3 3 + + 5/576 y x z - 1/288 y x z + 1/576 y x z - 1/144 y x z + + 2 3 2 3 3 3 3 2 + - 1/288 y x z + 1/288 y x z + 5/288 z y x - 5/576 z y x + + 3 3 2 2 3 + - 5/288 z y x - 5/288 y x z + 5/576 z y x - 5/576 z y x + + 3 3 3 3 3 2 2 3 2 3 + - 1/144 y x z + 1/144 y x z - 5/1152 y x z + 1/288 y x z , + + 4 3 4 3 3 4 4 + COEFF(-1, -2, 0) = 5/72 x y z + 1/144 x y z - 1/144 z y x + + 4 3 2 4 3 4 3 4 + - 1/36 x y z + 1/36 x y z - 5/144 x y z + 5/144 x y z + + 4 2 4 2 3 4 3 3 4 3 + - 5/288 x y z + 1/144 x y z + 1/72 x y z - 1/72 x y z + + 3 4 4 4 2 4 3 + - 5/288 x y z + 5/288 z y x - 5/72 x y z - 1/18 y x z + + 3 2 2 3 2 2 3 3 3 + - 5/144 z y x - 5/72 y x z + 1/36 y x z - 1/36 y x z + 1/72 y x z + + 2 3 2 3 3 3 3 2 + + 1/18 y x z - 1/144 y x z - 5/36 z y x + 5/36 z y x + + 3 3 2 2 3 3 3 + + 5/144 z y x + 5/36 y x z - 5/36 z y x + 5/288 z y x + 1/18 y x z + + 3 3 3 2 2 3 2 3 + - 1/72 y x z + 5/72 y x z - 1/18 y x z , COEFF(0, -2, 0) = + + 4 4 4 2 4 + - 5/192 z y x - 5/96 x y z + 5/48 y z - 5/24 y z - 5/48 y z + + 25 2 4 3 3 2 3 2 2 3 + + -- z y x + 1/24 y z + 1/12 y z - 1/24 y z + 5/96 y x z + 96 + + 3 2 3 4 2 3 4 3 3 25 2 2 + + 5/48 y x z - 1/96 x y z + 1/48 x y z + 5/24 z y - --- y x z + 192 + + 2 4 3 25 2 4 3 4 4 3 3 25 3 2 + - 5/96 x y z + --- x y z + 1/96 z y x - 1/12 y z - -- z y x + 192 96 + + 2 3 4 3 3 4 2 4 3 + - 5/48 y x z - 1/48 x y z + 5/192 x y z + 5/96 x y z, + + 4 3 4 3 3 4 4 + COEFF(1, -2, 0) = - 5/72 x y z - 1/144 x y z - 1/144 z y x + + 4 3 2 4 3 4 3 4 + + 1/36 x y z + 1/36 x y z - 5/144 x y z + 5/144 x y z + + 4 2 4 2 3 4 3 3 4 3 + - 5/288 x y z + 1/144 x y z + 1/72 x y z - 1/72 x y z + + 3 4 4 4 2 4 3 + + 5/288 x y z + 5/288 z y x - 5/72 x y z + 1/18 y x z + + 3 2 2 3 2 2 3 3 3 + + 5/144 z y x + 5/72 y x z - 1/36 y x z - 1/36 y x z - 1/72 y x z + + 2 3 2 3 3 3 3 2 + + 1/18 y x z + 1/144 y x z + 5/36 z y x + 5/36 z y x + + 3 3 2 2 3 3 3 + - 5/144 z y x - 5/36 y x z - 5/36 z y x - 5/288 z y x - 1/18 y x z + + 3 3 3 2 2 3 2 3 + + 1/72 y x z + 5/72 y x z - 1/18 y x z , COEFF(2, -2, 0) = + + 4 3 4 3 3 4 4 4 3 + 5/576 x y z + 1/288 x y z + 1/576 z y x - 1/288 x y z + + 2 4 3 4 3 4 4 2 + - 1/576 x y z + 5/576 x y z - 5/576 x y z + 5/1152 x y z + + 4 2 3 4 3 3 4 3 3 4 + - 1/576 x y z - 1/288 x y z + 1/288 x y z - 5/576 x y z + + 4 4 2 4 3 3 + - 5/1152 z y x + 5/1152 x y z - 1/144 y x z - 5/288 z y x + + 2 2 3 2 2 3 3 3 + - 5/576 y x z + 1/288 y x z + 1/576 y x z + 1/144 y x z + + 2 3 2 3 3 3 3 2 + - 1/288 y x z - 1/288 y x z - 5/288 z y x - 5/576 z y x + + 3 3 2 2 3 + + 5/288 z y x + 5/288 y x z + 5/576 z y x + 5/576 z y x + + 3 3 3 3 3 2 2 3 2 3 + + 1/144 y x z - 1/144 y x z - 5/1152 y x z + 1/288 y x z , + + 4 3 4 3 3 4 4 + COEFF(-2, -1, 0) = 5/144 x y z + 1/72 x y z - 1/144 z y x + + 4 3 2 4 3 4 3 4 + - 1/72 x y z + 1/144 x y z - 5/288 x y z + 5/72 x y z + + 4 2 4 2 3 4 3 3 4 3 + - 5/72 x y z + 1/36 x y z + 1/144 x y z - 1/36 x y z + + 3 4 4 4 2 4 3 + - 5/144 x y z + 5/288 z y x - 5/288 x y z - 1/18 y x z + + 3 2 2 3 2 2 3 3 3 + - 5/36 z y x - 5/36 y x z + 1/18 y x z - 1/36 y x z + 1/18 y x z + + 2 3 2 3 3 3 3 2 + + 1/36 y x z - 1/18 y x z - 5/144 z y x + 5/288 z y x + + 3 3 2 2 3 3 3 + + 5/144 z y x + 5/36 y x z - 5/72 z y x + 5/36 z y x + 1/72 y x z + + 3 3 3 2 2 3 2 3 + - 1/72 y x z + 5/72 y x z - 1/144 y x z , COEFF(-1, -1, 0) = + + 4 3 4 3 3 4 4 4 3 2 4 3 + - 5/18 x y z - 1/36 x y z + 1/36 z y x + 1/9 x y z - 1/9 x y z + + 4 3 4 4 2 4 2 3 4 3 3 + + 5/72 x y z - 5/18 x y z + 5/18 x y z - 1/9 x y z - 1/36 x y z + + 4 3 3 4 4 4 2 4 3 + + 1/9 x y z + 5/72 x y z - 5/72 z y x + 5/18 x y z + 4/9 y x z + + 3 2 2 3 2 2 3 3 3 + + 5/18 z y x + 10/9 y x z - 4/9 y x z + 4/9 y x z - 1/9 y x z + + 2 3 2 3 3 3 3 2 3 3 + - 4/9 y x z + 1/9 y x z + 5/18 z y x - 5/18 z y x - 5/72 z y x + + 2 2 3 3 3 3 3 3 + - 10/9 y x z + 10/9 z y x - 5/18 z y x - 1/9 y x z + 1/36 y x z + + 2 2 3 2 3 25 2 + - 10/9 y x z + 1/9 y x z , COEFF(0, -1, 0) = - -- z y x + 12 + + 3 4 4 2 3 4 4 3 + - 1/24 z y x + 2/3 y z + 5/3 y z + 5/48 z y x - 2/3 y z + + 4 3 2 2 3 25 2 2 2 3 + - 1/6 y z - 5/6 y x z + -- y x z - 5/3 y z - 5/12 z y + 12 + + 4 3 4 4 3 3 3 2 3 25 2 4 + - 1/6 x y z + 5/12 x y z + 1/24 x y z - 5/24 y x z - -- x y z + 48 + + 4 4 2 2 3 4 2 3 3 3 + + 5/12 y z - 5/12 x y z + 5/6 y x z + 1/6 x y z + 1/6 y z + + 4 3 25 3 2 2 4 3 4 + - 5/48 x y z + -- z y x + 5/24 x y z , COEFF(1, -1, 0) = 5/18 x y z + 48 + + 3 4 3 3 4 4 4 3 2 4 3 + + 1/36 x y z + 1/36 z y x - 1/9 x y z - 1/9 x y z + + 4 3 4 4 2 4 2 3 4 3 3 + + 5/72 x y z - 5/18 x y z + 5/18 x y z - 1/9 x y z - 1/36 x y z + + 4 3 3 4 4 4 2 4 3 + + 1/9 x y z - 5/72 x y z - 5/72 z y x + 5/18 x y z - 4/9 y x z + + 3 2 2 3 2 2 3 3 3 + - 5/18 z y x - 10/9 y x z + 4/9 y x z + 4/9 y x z + 1/9 y x z + + 2 3 2 3 3 3 3 2 3 3 + - 4/9 y x z - 1/9 y x z - 5/18 z y x - 5/18 z y x + 5/72 z y x + + 2 2 3 3 3 3 3 3 + + 10/9 y x z + 10/9 z y x + 5/18 z y x + 1/9 y x z - 1/36 y x z + + 2 2 3 2 3 4 + - 10/9 y x z + 1/9 y x z , COEFF(2, -1, 0) = - 5/144 x y z + + 3 4 3 3 4 4 4 3 2 4 3 + - 1/72 x y z - 1/144 z y x + 1/72 x y z + 1/144 x y z + + 4 3 4 4 2 4 2 3 + - 5/288 x y z + 5/72 x y z - 5/72 x y z + 1/36 x y z + + 4 3 3 4 3 3 4 4 4 + + 1/144 x y z - 1/36 x y z + 5/144 x y z + 5/288 z y x + + 2 4 3 3 2 2 3 + - 5/288 x y z + 1/18 y x z + 5/36 z y x + 5/36 y x z - 1/18 y x z + + 2 2 3 3 3 2 3 2 3 3 + - 1/36 y x z - 1/18 y x z + 1/36 y x z + 1/18 y x z + + 3 3 2 3 3 2 + + 5/144 z y x + 5/288 z y x - 5/144 z y x - 5/36 y x z - 5/72 z y x + + 2 3 3 3 3 3 3 2 2 + - 5/36 z y x - 1/72 y x z + 1/72 y x z + 5/72 y x z + + 3 2 3 3 4 4 4 4 + - 1/144 y x z , COEFF(-2, 0, 0) = 1/96 z y x - 5/192 z y x + + 4 3 4 3 3 3 3 4 + - 5/48 x z - 1/48 x y z + 1/12 x z + 5/24 z x + 5/96 x y z + + 2 3 4 25 2 3 4 3 + - 5/48 y x z - 5/24 x z - 5/96 x y z - -- z y x + 1/24 x z + 96 + + 4 2 3 25 4 2 3 3 2 3 3 2 4 + - 5/96 x y z + --- x y z - 1/12 x z + 5/48 y x z + 5/192 x y z + 192 + + 2 3 2 25 2 2 25 2 4 3 + - 1/24 x z + 5/48 x z - --- y x z + -- y x z + 1/48 x y z + 192 96 + + 2 4 3 2 2 3 3 4 + - 1/96 x y z + 5/96 y x z , COEFF(-1, 0, 0) = - 5/48 x y z + + 25 2 3 25 4 2 2 3 2 2 3 2 3 3 + + -- z y x - -- x y z + 2/3 x z - 5/6 y x z - 5/24 y x z + 48 48 + + 3 3 3 4 4 2 4 3 2 3 + + 5/3 x z + 1/6 x z - 1/24 z y x + 1/6 x y z + 5/6 y x z + + 2 4 4 2 3 3 3 4 3 3 + - 5/12 x y z + 5/24 x y z - 5/12 z x + 1/24 x y z - 2/3 x z + + 4 3 4 3 4 4 25 2 4 + - 1/6 x z - 1/6 x y z + 5/48 z y x - -- y x z + 5/12 x y z + 12 + + 4 25 2 2 2 4 3 + + 5/12 x z + -- y x z - 5/3 x z, COEFF(0, 0, 0) = 1/4 x z + 12 + + 3 4 4 4 2 3 4 3 2 3 2 3 + + 1/16 z y x - 5/16 x y z + 1/4 y z - 5/4 y z - 5/4 x z + + 4 2 4 3 3 25 4 2 25 2 4 2 + - 5/8 y z - 5/16 x y z + z + -- x y z + -- x y z + 25/8 y z + 32 32 + + 4 4 4 2 125 2 2 25 2 2 3 + - 5/32 z y x - 5/2 z - 5/8 x z + 25/8 x z - --- y x z + -- y x z , + 32 16 + + 2 2 3 2 4 2 + COEFF(1, 0, 0) = - 5/6 y x z - 5/12 x y z - 5/3 x z - 5/3 x z + + 3 3 3 4 4 3 3 2 3 + - 1/6 x z + 5/48 x y z + 1/6 x y z + 5/12 z x - 5/6 y x z + + 25 2 3 4 3 4 4 2 4 3 25 2 + - -- z y x - 5/12 x y z - 1/24 z y x + 1/6 x y z + -- y x z + 48 12 + + 4 2 3 2 3 3 4 4 4 2 3 + + 5/24 x y z + 5/24 y x z + 5/12 x z + 5/48 z y x + 2/3 x z + + 25 4 2 3 4 3 3 25 2 2 4 3 + - -- x y z - 1/24 x y z + 2/3 x z + -- y x z - 1/6 x z , + 48 12 + + 2 4 3 4 4 25 2 2 3 4 + COEFF(2, 0, 0) = 5/192 x y z + 1/96 z y x - --- y x z - 5/96 x y z + 192 + + 3 25 2 3 2 3 4 25 4 2 + - 1/12 x z + -- z y x - 1/24 x z - 5/48 x z + --- x y z + 96 192 + + 2 3 3 3 2 4 4 3 + + 5/48 y x z + 1/12 x z + 5/48 x z + 5/96 x y z + 1/24 x z + + 4 3 4 2 3 3 25 2 4 4 + - 1/48 x y z - 5/96 x y z - 5/24 z x - -- y x z - 5/192 z y x + 96 + + 3 4 3 2 2 3 2 3 3 2 4 3 + + 1/48 x y z + 5/96 y x z + 5/24 x z - 5/48 y x z - 1/96 x y z + + 4 3 4 3 3 4 4 + , COEFF(-2, 1, 0) = 5/144 x y z + 1/72 x y z - 1/144 z y x + + 4 3 2 4 3 4 3 4 + - 1/72 x y z + 1/144 x y z + 5/288 x y z - 5/72 x y z + + 4 2 4 2 3 4 3 3 4 3 + - 5/72 x y z + 1/36 x y z - 1/144 x y z + 1/36 x y z + + 3 4 4 4 2 4 3 + - 5/144 x y z + 5/288 z y x - 5/288 x y z + 1/18 y x z + + 3 2 2 3 2 2 3 3 3 + + 5/36 z y x - 5/36 y x z + 1/18 y x z - 1/36 y x z - 1/18 y x z + + 2 3 2 3 3 3 3 2 + - 1/36 y x z - 1/18 y x z + 5/144 z y x - 5/288 z y x + + 3 3 2 2 3 3 3 + - 5/144 z y x - 5/36 y x z + 5/72 z y x + 5/36 z y x - 1/72 y x z + + 3 3 3 2 2 3 2 3 + + 1/72 y x z + 5/72 y x z + 1/144 y x z , COEFF(-1, 1, 0) = + + 4 3 4 3 3 4 4 4 3 2 4 3 + - 5/18 x y z - 1/36 x y z + 1/36 z y x + 1/9 x y z - 1/9 x y z + + 4 3 4 4 2 4 2 3 4 3 3 + - 5/72 x y z + 5/18 x y z + 5/18 x y z - 1/9 x y z + 1/36 x y z + + 4 3 3 4 4 4 2 4 3 + - 1/9 x y z + 5/72 x y z - 5/72 z y x + 5/18 x y z - 4/9 y x z + + 3 2 2 3 2 2 3 3 3 + - 5/18 z y x + 10/9 y x z - 4/9 y x z + 4/9 y x z + 1/9 y x z + + 2 3 2 3 3 3 3 2 3 3 + + 4/9 y x z + 1/9 y x z - 5/18 z y x + 5/18 z y x + 5/72 z y x + + 2 2 3 3 3 3 3 3 + + 10/9 y x z - 10/9 z y x - 5/18 z y x + 1/9 y x z - 1/36 y x z + + 2 2 3 2 3 2 2 2 3 + - 10/9 y x z - 1/9 y x z , COEFF(0, 1, 0) = - 5/3 y z - 5/6 y x z + + 25 2 2 3 4 4 4 3 4 3 3 2 3 + + -- y x z - 1/24 z y x - 1/6 y z + 1/6 x y z + 5/24 y x z + 12 + + 4 3 2 3 4 3 3 2 4 3 4 + + 5/48 x y z - 5/6 y x z - 1/24 x y z + 5/24 x y z - 5/12 x y z + + 2 3 4 2 3 3 4 4 2 + + 2/3 y z + 1/6 x y z + 5/12 z y + 5/12 y z - 5/12 x y z + + 3 25 2 4 3 3 25 2 25 3 2 + - 5/3 y z + 2/3 y z - -- x y z - 1/6 y z + -- z y x - -- z y x + 48 12 48 + + 4 4 4 3 4 3 + + 5/48 z y x , COEFF(1, 1, 0) = 5/18 x y z + 1/36 x y z + + 3 4 4 4 3 2 4 3 4 3 4 + + 1/36 z y x - 1/9 x y z - 1/9 x y z - 5/72 x y z + 5/18 x y z + + 4 2 4 2 3 4 3 3 4 3 3 4 + + 5/18 x y z - 1/9 x y z + 1/36 x y z - 1/9 x y z - 5/72 x y z + + 4 4 2 4 3 3 2 + - 5/72 z y x + 5/18 x y z + 4/9 y x z + 5/18 z y x - 10/9 y x z + + 2 3 2 2 3 3 3 2 3 2 3 3 + + 4/9 y x z + 4/9 y x z - 1/9 y x z + 4/9 y x z - 1/9 y x z + + 3 3 2 3 3 2 + + 5/18 z y x + 5/18 z y x - 5/72 z y x - 10/9 y x z - 10/9 z y x + + 2 3 3 3 3 3 3 2 2 3 2 3 + + 5/18 z y x - 1/9 y x z + 1/36 y x z - 10/9 y x z - 1/9 y x z + + 4 3 4 3 3 4 4 + , COEFF(2, 1, 0) = - 5/144 x y z - 1/72 x y z - 1/144 z y x + + 4 3 2 4 3 4 3 4 + + 1/72 x y z + 1/144 x y z + 5/288 x y z - 5/72 x y z + + 4 2 4 2 3 4 3 3 4 3 + - 5/72 x y z + 1/36 x y z - 1/144 x y z + 1/36 x y z + + 3 4 4 4 2 4 3 + + 5/144 x y z + 5/288 z y x - 5/288 x y z - 1/18 y x z + + 3 2 2 3 2 2 3 3 3 + - 5/36 z y x + 5/36 y x z - 1/18 y x z - 1/36 y x z + 1/18 y x z + + 2 3 2 3 3 3 3 2 + - 1/36 y x z + 1/18 y x z - 5/144 z y x - 5/288 z y x + + 3 3 2 2 3 3 3 + + 5/144 z y x + 5/36 y x z + 5/72 z y x - 5/36 z y x + 1/72 y x z + + 3 3 3 2 2 3 2 3 + - 1/72 y x z + 5/72 y x z + 1/144 y x z , COEFF(-2, 2, 0) = + + 4 3 4 3 3 4 4 4 3 + - 5/576 x y z - 1/288 x y z + 1/576 z y x + 1/288 x y z + + 2 4 3 4 3 4 4 2 + - 1/576 x y z - 5/576 x y z + 5/576 x y z + 5/1152 x y z + + 4 2 3 4 3 3 4 3 3 4 + - 1/576 x y z + 1/288 x y z - 1/288 x y z + 5/576 x y z + + 4 4 2 4 3 3 + - 5/1152 z y x + 5/1152 x y z - 1/144 y x z - 5/288 z y x + + 2 2 3 2 2 3 3 3 + + 5/576 y x z - 1/288 y x z + 1/576 y x z + 1/144 y x z + + 2 3 2 3 3 3 3 2 + + 1/288 y x z + 1/288 y x z - 5/288 z y x + 5/576 z y x + + 3 3 2 2 3 + + 5/288 z y x + 5/288 y x z - 5/576 z y x - 5/576 z y x + + 3 3 3 3 3 2 2 3 2 3 + + 1/144 y x z - 1/144 y x z - 5/1152 y x z - 1/288 y x z , + + 4 3 4 3 3 4 4 + COEFF(-1, 2, 0) = 5/72 x y z + 1/144 x y z - 1/144 z y x + + 4 3 2 4 3 4 3 4 + - 1/36 x y z + 1/36 x y z + 5/144 x y z - 5/144 x y z + + 4 2 4 2 3 4 3 3 4 3 + - 5/288 x y z + 1/144 x y z - 1/72 x y z + 1/72 x y z + + 3 4 4 4 2 4 3 + - 5/288 x y z + 5/288 z y x - 5/72 x y z + 1/18 y x z + + 3 2 2 3 2 2 3 3 3 + + 5/144 z y x - 5/72 y x z + 1/36 y x z - 1/36 y x z - 1/72 y x z + + 2 3 2 3 3 3 3 2 + - 1/18 y x z - 1/144 y x z + 5/36 z y x - 5/36 z y x + + 3 3 2 2 3 3 3 + - 5/144 z y x - 5/36 y x z + 5/36 z y x + 5/288 z y x - 1/18 y x z + + 3 3 3 2 2 3 2 3 + + 1/72 y x z + 5/72 y x z + 1/18 y x z , COEFF(0, 2, 0) = + + 4 2 3 2 4 3 4 3 3 4 4 + - 1/96 x y z - 5/96 x y z - 5/96 x y z + 1/96 z y x + + 3 2 3 4 2 3 3 2 3 + - 5/48 y x z + 5/24 y z + 5/192 x y z + 1/12 y z + 5/48 y x z + + 4 4 2 3 2 2 3 4 3 3 3 + - 5/192 z y x - 1/24 y z + 5/96 y x z + 1/48 x y z - 5/24 z y + + 25 2 2 4 3 3 4 3 25 2 + - --- y x z - 1/48 x y z - 1/12 y z + 1/24 y z - -- z y x + 192 96 + + 25 3 2 25 2 4 2 4 4 + + -- z y x + --- x y z + 5/48 y z + 5/96 x y z - 5/48 y z, + 96 192 + + 4 3 4 3 3 4 4 + COEFF(1, 2, 0) = - 5/72 x y z - 1/144 x y z - 1/144 z y x + + 4 3 2 4 3 4 3 4 + + 1/36 x y z + 1/36 x y z + 5/144 x y z - 5/144 x y z + + 4 2 4 2 3 4 3 3 4 3 + - 5/288 x y z + 1/144 x y z - 1/72 x y z + 1/72 x y z + + 3 4 4 4 2 4 3 + + 5/288 x y z + 5/288 z y x - 5/72 x y z - 1/18 y x z + + 3 2 2 3 2 2 3 3 3 + - 5/144 z y x + 5/72 y x z - 1/36 y x z - 1/36 y x z + 1/72 y x z + + 2 3 2 3 3 3 3 2 + - 1/18 y x z + 1/144 y x z - 5/36 z y x - 5/36 z y x + + 3 3 2 2 3 3 3 + + 5/144 z y x + 5/36 y x z + 5/36 z y x - 5/288 z y x + 1/18 y x z + + 3 3 3 2 2 3 2 3 + - 1/72 y x z + 5/72 y x z + 1/18 y x z , COEFF(2, 2, 0) = + + 4 3 4 3 3 4 4 4 3 + 5/576 x y z + 1/288 x y z + 1/576 z y x - 1/288 x y z + + 2 4 3 4 3 4 4 2 + - 1/576 x y z - 5/576 x y z + 5/576 x y z + 5/1152 x y z + + 4 2 3 4 3 3 4 3 3 4 + - 1/576 x y z + 1/288 x y z - 1/288 x y z - 5/576 x y z + + 4 4 2 4 3 3 + - 5/1152 z y x + 5/1152 x y z + 1/144 y x z + 5/288 z y x + + 2 2 3 2 2 3 3 3 + - 5/576 y x z + 1/288 y x z + 1/576 y x z - 1/144 y x z + + 2 3 2 3 3 3 3 2 + + 1/288 y x z - 1/288 y x z + 5/288 z y x + 5/576 z y x + + 3 3 2 2 3 + - 5/288 z y x - 5/288 y x z - 5/576 z y x + 5/576 z y x + + 3 3 3 3 3 2 2 3 2 3 + - 1/144 y x z + 1/144 y x z - 5/1152 y x z - 1/288 y x z , + + 4 3 4 2 2 4 2 + COEFF(-2, -2, 1) = 1/216 x y z + 1/576 x y z + 1/1152 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + - 1/576 x y z + 1/432 x y z - 1/1152 z y x - 1/864 z y x + + 4 3 2 4 3 4 3 4 + - 1/432 x y z + 1/864 x y z - 1/216 x y z + 1/216 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/432 x y z + 1/864 x y z + 1/432 x y z - 1/576 x y z + + 4 3 2 4 2 2 4 3 3 4 + + 1/576 x y z + 1/1152 x y z - 1/432 x y z - 1/216 x y z + + 4 4 2 4 3 3 3 + + 1/432 z y x - 1/432 x y z - 1/216 y x - 1/216 y x z - 1/108 z y x + + 2 3 2 2 3 3 4 + + 1/288 z y x - 1/216 y x z + 1/432 y x z + 1/216 y x - 1/432 x y + + 2 2 2 3 2 2 2 3 3 3 + - 1/1152 y x z + 1/288 y x z - 1/864 y x z + 1/216 y x z + + 3 3 2 2 3 3 2 2 4 + - 1/288 y x z + 1/432 y x z - 1/576 y x z + 1/432 x y + + 2 3 3 4 4 3 2 3 3 2 + - 1/432 y x z + 1/864 y x - 1/216 y x + 1/432 y x + 1/432 y x + + 3 3 2 2 4 3 3 3 3 + - 1/108 z y x + 1/216 z y x - 1/864 x y + 1/216 y x + 1/108 z y x + + 2 2 3 2 2 3 + + 1/108 y x z - 1/216 z y x + 1/216 z y x - 1/576 z y x + + 3 3 3 3 3 2 2 2 + + 1/216 y x z - 1/216 y x z - 1/432 y x + 1/576 y x z + + 2 2 2 2 2 3 2 3 + + 1/432 y x z + 1/576 y x z - 1/288 y x z - 1/432 y x z + + 2 2 2 4 4 2 4 3 + + 1/864 y x - 1/432 y x + 1/432 x y - 1/864 x y - 1/432 x y , + + 4 3 4 2 2 4 2 + COEFF(-1, -2, 1) = - 1/27 x y z - 1/288 x y z - 1/72 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + + 1/72 x y z - 1/216 x y z + 1/288 z y x + 1/216 z y x + + 4 3 2 4 3 4 3 4 + + 1/54 x y z - 1/54 x y z + 1/54 x y z - 1/54 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/108 x y z - 1/216 x y z - 1/108 x y z + 1/144 x y z + + 4 3 2 4 2 2 4 3 3 4 + - 1/144 x y z - 1/288 x y z + 1/108 x y z + 1/108 x y z + + 4 4 2 4 3 3 3 + - 1/108 z y x + 1/27 x y z + 1/108 y x + 1/27 y x z + 1/54 z y x + + 2 3 2 2 3 3 4 + - 1/144 z y x + 1/27 y x z - 1/54 y x z - 1/27 y x + 1/216 x y + + 2 2 2 3 2 2 2 3 3 3 + + 1/72 y x z - 1/36 y x z + 1/54 y x z - 1/108 y x z + + 3 3 2 2 3 3 2 2 4 + + 1/144 y x z - 1/27 y x z + 1/36 y x z - 1/54 x y + + 2 3 3 4 4 3 2 3 3 2 + + 1/216 y x z - 1/216 y x + 1/27 y x - 1/216 y x - 1/27 y x + + 3 3 2 2 4 3 3 3 3 + + 2/27 z y x - 2/27 z y x + 1/54 x y - 1/108 y x - 1/54 z y x + + 2 2 3 2 2 3 3 3 + - 2/27 y x z + 2/27 z y x - 1/108 z y x + 1/288 z y x - 1/27 y x z + + 3 3 3 2 2 2 2 2 2 2 + + 1/108 y x z + 1/54 y x - 1/72 y x z - 1/27 y x z - 1/36 y x z + + 2 3 2 3 2 2 2 4 + + 1/36 y x z + 1/27 y x z - 1/54 y x + 1/27 y x - 1/108 x y + + 4 2 4 3 2 4 2 + + 1/216 x y + 1/108 x y , COEFF(0, -2, 1) = 5/192 x y z + + 2 4 4 3 4 4 2 4 3 4 3 + - 1/192 z y x - 1/144 z y x + 5/144 x y z - 1/36 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/36 x y z - 1/72 x y z + 1/144 x y z + 1/72 x y z + + 4 2 4 3 2 4 2 2 4 3 + - 1/96 x y z + 1/96 x y z + 1/192 x y z - 1/72 x y z + + 4 4 4 3 2 4 4 4 2 + + 1/72 z y x - 1/36 y z - 5/72 x y z + 1/18 y + 1/36 y - 1/48 y z + + 4 2 2 2 2 2 3 2 3 + + 1/18 y z - 5/192 y x z - 5/144 y x z + 5/72 y x z + + 3 2 2 4 4 3 3 2 3 2 + - 5/96 y x z + 1/144 y x - 1/18 y - 1/9 z y - 1/36 y + 5/72 y x + + 3 2 2 4 2 2 2 + + 5/36 z y x - 5/144 x y - 5/36 z y x + 1/9 y z + 5/72 y x z + + 2 2 2 3 2 3 3 2 3 + + 5/96 y x z - 1/18 y z - 5/72 y x z - 1/18 y z + 1/36 y z + + 3 3 3 2 2 2 2 2 2 + + 1/18 y z + 1/24 y z - 1/24 y z + 1/48 y z + 5/144 y x + + 2 4 4 2 4 3 + - 5/72 y x + 1/72 x y - 1/144 x y - 1/72 x y , COEFF(1, -2, 1) = + + 4 3 4 2 2 4 2 4 2 + 1/27 x y z + 1/288 x y z - 1/72 x y z - 1/72 x y z + + 3 4 3 2 4 4 3 4 4 4 3 + + 1/216 x y z + 1/288 z y x + 1/216 z y x - 1/54 x y z + + 2 4 3 4 3 4 4 2 + - 1/54 x y z + 1/54 x y z - 1/54 x y z + 1/108 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/216 x y z - 1/108 x y z + 1/144 x y z - 1/144 x y z + + 4 2 2 4 3 3 4 4 4 + - 1/288 x y z + 1/108 x y z - 1/108 x y z - 1/108 z y x + + 2 4 3 3 3 2 3 + + 1/27 x y z - 1/108 y x - 1/27 y x z - 1/54 z y x + 1/144 z y x + + 2 2 3 3 4 2 2 2 + - 1/27 y x z + 1/54 y x z + 1/27 y x - 1/216 x y + 1/72 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/36 y x z + 1/54 y x z + 1/108 y x z - 1/144 y x z + + 2 3 3 2 2 4 2 3 3 4 4 + - 1/27 y x z + 1/36 y x z + 1/54 x y - 1/216 y x z - 1/216 y x + + 3 2 3 3 2 3 3 2 + - 1/27 y x + 1/216 y x - 1/27 y x - 2/27 z y x - 2/27 z y x + + 2 4 3 3 3 3 2 + + 1/54 x y + 1/108 y x + 1/54 z y x + 2/27 y x z + 2/27 z y x + + 2 3 2 2 3 3 3 3 3 3 + + 1/108 z y x - 1/288 z y x + 1/27 y x z - 1/108 y x z + + 2 2 2 2 2 2 2 2 + - 1/54 y x + 1/72 y x z - 1/27 y x z - 1/36 y x z - 1/36 y x z + + 3 2 3 2 2 2 4 4 2 + + 1/27 y x z - 1/54 y x + 1/27 y x - 1/108 x y + 1/216 x y + + 4 3 4 3 4 2 + + 1/108 x y , COEFF(2, -2, 1) = - 1/216 x y z - 1/576 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + + 1/1152 x y z + 1/576 x y z - 1/432 x y z - 1/1152 z y x + + 3 4 4 4 3 2 4 3 4 3 + - 1/864 z y x + 1/432 x y z + 1/864 x y z - 1/216 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/216 x y z - 1/432 x y z + 1/864 x y z + 1/432 x y z + + 4 2 4 3 2 4 2 2 4 3 + - 1/576 x y z + 1/576 x y z + 1/1152 x y z - 1/432 x y z + + 3 4 4 4 2 4 3 + + 1/216 x y z + 1/432 z y x - 1/432 x y z + 1/216 y x + + 3 3 2 3 2 + + 1/216 y x z + 1/108 z y x - 1/288 z y x + 1/216 y x z + + 2 3 3 4 2 2 2 + - 1/432 y x z - 1/216 y x + 1/432 x y - 1/1152 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/288 y x z - 1/864 y x z - 1/216 y x z + 1/288 y x z + + 2 3 3 2 2 4 2 3 3 + + 1/432 y x z - 1/576 y x z - 1/432 x y + 1/432 y x z + + 4 4 3 2 3 3 2 3 + + 1/864 y x + 1/216 y x - 1/432 y x + 1/432 y x + 1/108 z y x + + 3 2 2 4 3 3 3 3 + + 1/216 z y x - 1/864 x y - 1/216 y x - 1/108 z y x - 1/108 y x z + + 2 2 3 2 2 3 3 3 + - 1/216 z y x - 1/216 z y x + 1/576 z y x - 1/216 y x z + + 3 3 3 2 2 2 2 2 + + 1/216 y x z + 1/432 y x - 1/576 y x z + 1/432 y x z + + 2 2 2 3 2 3 2 2 2 + + 1/576 y x z + 1/288 y x z - 1/432 y x z + 1/864 y x - 1/432 y x + + 4 4 2 4 3 4 + + 1/432 x y - 1/864 x y - 1/432 x y , COEFF(-2, -1, 1) = - 1/54 x y z + + 3 4 2 2 4 2 4 2 3 4 3 + - 1/144 x y z - 1/288 x y z + 1/144 x y z - 1/108 x y z + + 2 4 4 3 4 4 4 3 2 4 3 + + 1/288 z y x + 1/216 z y x + 1/108 x y z - 1/216 x y z + + 4 3 4 4 2 4 2 3 + + 1/108 x y z - 1/27 x y z + 1/27 x y z - 1/54 x y z + + 4 3 3 4 2 4 3 2 4 2 2 + - 1/216 x y z + 1/72 x y z - 1/288 x y z - 1/72 x y z + + 4 3 3 4 4 4 2 4 3 + + 1/54 x y z + 1/54 x y z - 1/108 z y x + 1/108 x y z + 1/27 y x + + 3 3 2 3 2 2 3 + + 1/27 y x z + 2/27 z y x - 1/36 z y x + 2/27 y x z - 1/27 y x z + + 3 4 2 2 2 3 2 2 2 3 + - 1/27 y x + 1/108 x y + 1/72 y x z - 1/144 y x z + 1/54 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/27 y x z + 1/144 y x z - 1/54 y x z + 1/288 y x z + + 4 2 3 3 4 4 3 2 3 + - 1/108 x y + 1/27 y x z - 1/216 y x + 1/108 y x - 1/27 y x + + 3 2 3 3 2 2 4 3 3 + - 1/216 y x + 1/54 z y x - 1/108 z y x + 1/216 x y - 1/108 y x + + 3 3 2 2 3 2 2 3 + - 1/54 z y x - 2/27 y x z + 1/27 z y x - 2/27 z y x + 1/36 z y x + + 3 3 3 3 3 2 2 2 2 2 + - 1/108 y x z + 1/108 y x z + 1/27 y x - 1/36 y x z - 1/27 y x z + + 2 2 2 3 2 3 2 2 2 + - 1/72 y x z + 1/36 y x z + 1/216 y x z - 1/54 y x + 1/54 y x + + 4 4 2 4 3 4 + - 1/54 x y + 1/54 x y + 1/216 x y , COEFF(-1, -1, 1) = 4/27 x y z + + 3 4 2 2 4 2 4 2 3 4 3 + + 1/72 x y z + 1/18 x y z - 1/18 x y z + 1/54 x y z + + 2 4 4 3 4 4 4 3 2 4 3 + - 1/72 z y x - 1/54 z y x - 2/27 x y z + 2/27 x y z + + 4 3 4 4 2 4 2 3 + - 1/27 x y z + 4/27 x y z - 4/27 x y z + 2/27 x y z + + 4 3 3 4 2 4 3 2 4 2 2 + + 1/54 x y z - 1/18 x y z + 1/72 x y z + 1/18 x y z + + 4 3 3 4 4 4 2 4 3 + - 2/27 x y z - 1/27 x y z + 1/27 z y x - 4/27 x y z - 2/27 y x + + 3 3 2 3 16 2 2 3 + - 8/27 y x z - 4/27 z y x + 1/18 z y x - -- y x z + 8/27 y x z + 27 + + 3 4 2 2 2 3 2 2 2 3 + + 8/27 y x - 1/54 x y - 2/9 y x z + 1/18 y x z - 8/27 y x z + + 3 3 3 3 2 2 3 3 2 2 4 + + 2/27 y x z - 1/72 y x z + 8/27 y x z - 1/18 y x z + 2/27 x y + + 2 3 3 4 4 3 2 3 3 2 + - 2/27 y x z + 1/54 y x - 2/27 y x + 2/27 y x + 2/27 y x + + 3 3 2 2 4 3 3 3 3 + - 4/27 z y x + 4/27 z y x - 2/27 x y + 1/54 y x + 1/27 z y x + + 16 16 2 2 3 2 2 3 3 3 + + -- y x z - -- z y x + 4/27 z y x - 1/18 z y x + 2/27 y x z + 27 27 + + 3 3 3 2 2 2 16 2 2 2 2 + - 1/54 y x z - 8/27 y x + 2/9 y x z + -- y x z + 2/9 y x z + 27 + + 2 3 2 3 2 2 2 4 + - 2/9 y x z - 2/27 y x z + 8/27 y x - 8/27 y x + 2/27 x y + + 4 2 4 3 2 4 2 + - 2/27 x y - 1/54 x y , COEFF(0, -1, 1) = - 5/48 x y z + + 2 4 4 3 4 4 2 4 3 4 3 + + 1/48 z y x + 1/36 z y x - 5/36 x y z + 1/18 x y z + + 4 4 2 4 2 3 4 3 3 4 2 + - 2/9 x y z + 2/9 x y z - 1/9 x y z - 1/36 x y z + 1/12 x y z + + 4 3 2 4 2 2 4 3 4 4 4 3 + - 1/48 x y z - 1/12 x y z + 1/9 x y z - 1/18 z y x + 1/9 y z + + 2 4 4 4 2 4 2 2 2 + + 5/18 x y z - 4/9 y - 1/9 y + 1/12 y z - 2/9 y z + 5/12 y x z + + 2 2 3 2 3 3 2 2 4 4 3 + + 5/9 y x z - 5/9 y x z + 5/48 y x z - 1/36 y x + 1/9 y + + 3 2 3 2 3 2 2 4 2 + + 2/9 z y + 4/9 y - 5/36 y x - 5/18 z y x + 5/36 x y + 10/9 z y x + + 2 2 2 2 2 3 2 3 + - 8/9 y z - 10/9 y x z - 5/12 y x z + 8/9 y z + 5/36 y x z + + 3 2 3 3 3 3 2 2 2 2 + + 4/9 y z - 4/9 y z - 1/9 y z - 1/12 y z + 1/3 y z - 1/3 y z + + 2 2 2 4 4 2 4 3 + - 5/9 y x + 5/9 y x - 1/9 x y + 1/9 x y + 1/36 x y , + + 4 3 4 2 2 4 2 + COEFF(1, -1, 1) = - 4/27 x y z - 1/72 x y z + 1/18 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + + 1/18 x y z - 1/54 x y z - 1/72 z y x - 1/54 z y x + + 4 3 2 4 3 4 3 4 4 2 + + 2/27 x y z + 2/27 x y z - 1/27 x y z + 4/27 x y z - 4/27 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + + 2/27 x y z + 1/54 x y z - 1/18 x y z + 1/72 x y z + + 4 2 2 4 3 3 4 4 4 + + 1/18 x y z - 2/27 x y z + 1/27 x y z + 1/27 z y x + + 2 4 3 3 3 2 3 + - 4/27 x y z + 2/27 y x + 8/27 y x z + 4/27 z y x - 1/18 z y x + + 16 2 2 3 3 4 2 2 2 + + -- y x z - 8/27 y x z - 8/27 y x + 1/54 x y - 2/9 y x z + 27 + + 3 2 2 2 3 3 3 3 3 2 + - 1/18 y x z - 8/27 y x z - 2/27 y x z + 1/72 y x z + + 2 3 3 2 2 4 2 3 3 4 4 + + 8/27 y x z - 1/18 y x z - 2/27 x y + 2/27 y x z + 1/54 y x + + 3 2 3 3 2 3 3 2 + + 2/27 y x - 2/27 y x + 2/27 y x + 4/27 z y x + 4/27 z y x + + 2 4 3 3 3 3 16 16 2 + - 2/27 x y - 1/54 y x - 1/27 z y x - -- y x z - -- z y x + 27 27 + + 2 3 2 2 3 3 3 3 3 3 2 + - 4/27 z y x + 1/18 z y x - 2/27 y x z + 1/54 y x z + 8/27 y x + + 2 2 16 2 2 2 2 2 3 2 3 + - 2/9 y x z + -- y x z + 2/9 y x z + 2/9 y x z - 2/27 y x z + 27 + + 2 2 2 4 4 2 4 3 + + 8/27 y x - 8/27 y x + 2/27 x y - 2/27 x y - 1/54 x y , + + 4 3 4 2 2 4 2 + COEFF(2, -1, 1) = 1/54 x y z + 1/144 x y z - 1/288 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + - 1/144 x y z + 1/108 x y z + 1/288 z y x + 1/216 z y x + + 4 3 2 4 3 4 3 4 + - 1/108 x y z - 1/216 x y z + 1/108 x y z - 1/27 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/27 x y z - 1/54 x y z - 1/216 x y z + 1/72 x y z + + 4 3 2 4 2 2 4 3 3 4 + - 1/288 x y z - 1/72 x y z + 1/54 x y z - 1/54 x y z + + 4 4 2 4 3 3 3 + - 1/108 z y x + 1/108 x y z - 1/27 y x - 1/27 y x z - 2/27 z y x + + 2 3 2 2 3 3 4 + + 1/36 z y x - 2/27 y x z + 1/27 y x z + 1/27 y x - 1/108 x y + + 2 2 2 3 2 2 2 3 3 3 + + 1/72 y x z + 1/144 y x z + 1/54 y x z + 1/27 y x z + + 3 3 2 2 3 3 2 2 4 + - 1/144 y x z - 1/54 y x z + 1/288 y x z + 1/108 x y + + 2 3 3 4 4 3 2 3 3 2 + - 1/27 y x z - 1/216 y x - 1/108 y x + 1/27 y x - 1/216 y x + + 3 3 2 2 4 3 3 3 3 + - 1/54 z y x - 1/108 z y x + 1/216 x y + 1/108 y x + 1/54 z y x + + 2 2 3 2 2 3 3 3 + + 2/27 y x z + 1/27 z y x + 2/27 z y x - 1/36 z y x + 1/108 y x z + + 3 3 3 2 2 2 2 2 2 2 + - 1/108 y x z - 1/27 y x + 1/36 y x z - 1/27 y x z - 1/72 y x z + + 2 3 2 3 2 2 2 4 + - 1/36 y x z + 1/216 y x z - 1/54 y x + 1/54 y x - 1/54 x y + + 4 2 4 3 4 3 4 2 + + 1/54 x y + 1/216 x y , COEFF(-2, 0, 1) = 1/36 x y z + 1/96 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + + 1/192 x y z - 1/96 x y z + 1/72 x y z - 1/192 z y x + + 3 4 4 4 3 2 4 3 4 2 + - 1/144 z y x - 1/72 x y z + 1/144 x y z - 5/72 x y z + + 4 2 3 4 2 2 3 4 4 4 + + 5/144 x y z + 5/192 x y z - 1/36 x y z + 1/72 z y x + + 2 4 4 4 2 2 3 + - 1/72 x y z + 1/18 x + 1/18 x z + 1/36 x - 5/36 y x z + 5/72 y x z + + 3 4 2 2 2 2 2 3 3 4 + - 1/72 x y - 5/192 y x z - 5/144 y x z - 1/9 z x + 1/72 x y + + 2 3 3 4 2 4 4 3 2 3 + - 5/72 y x z - 1/48 x z + 1/144 y x - 1/18 x + 5/72 y x + + 2 4 2 2 3 2 2 3 4 3 + - 1/144 x y - 1/36 x + 5/36 z y x - 5/96 z y x - 1/36 x z + + 2 2 2 2 2 2 + - 5/72 y x + 5/96 y x z + 5/72 y x z + 1/9 x z - 1/18 x z + + 3 3 2 3 3 2 2 2 + + 1/18 x z + 1/36 x z - 1/18 x z + 1/48 x z - 1/24 x z + + 3 2 2 2 4 2 4 + + 1/24 x z + 5/144 y x - 5/144 x y , COEFF(-1, 0, 1) = - 2/9 x y z + + 3 4 2 2 4 2 4 2 3 4 3 + - 1/48 x y z - 1/12 x y z + 1/12 x y z - 1/36 x y z + + 2 4 4 3 4 4 4 3 2 4 3 + + 1/48 z y x + 1/36 z y x + 1/9 x y z - 1/9 x y z + + 4 2 4 2 3 4 2 2 3 4 + + 5/18 x y z - 5/36 x y z - 5/48 x y z + 1/18 x y z + + 4 4 2 4 4 4 2 + - 1/18 z y x + 2/9 x y z - 4/9 x - 2/9 x z - 1/9 x + 10/9 y x z + + 2 3 3 4 2 2 2 2 2 3 3 + - 5/9 y x z + 1/36 x y + 5/12 y x z + 5/9 y x z + 2/9 z x + + 4 2 3 3 4 2 4 4 3 2 3 + - 1/9 x y + 5/36 y x z + 1/12 x z - 1/36 y x + 1/9 x - 5/36 y x + + 2 4 2 2 3 2 2 3 4 3 2 + + 1/9 x y + 4/9 x - 5/18 z y x + 5/48 z y x + 1/9 x z + 5/9 y x + + 2 2 2 2 2 3 3 2 3 + - 5/12 y x z - 10/9 y x z - 8/9 x z + 8/9 x z - 1/9 x z - 4/9 x z + + 3 2 2 2 3 2 2 2 4 2 + + 4/9 x z - 1/3 x z + 1/3 x z - 1/12 x z - 5/9 y x + 5/36 x y , + + 2 4 2 2 4 4 3 4 4 + COEFF(0, 0, 1) = 5/32 x y z - 1/32 z y x - 1/24 z y x + + 2 4 3 4 2 4 2 3 4 2 2 + + 5/24 x y z - 5/12 x y z + 5/24 x y z + 5/32 x y z + + 4 4 4 3 2 4 4 4 + + 1/12 z y x - 1/6 y z - 5/12 x y z + 1/3 x z + 1/6 x + 4/3 z + + 4 4 2 4 25 2 2 2 25 2 2 3 4 2 + + 1/6 y - 1/8 y z + 1/3 y z - -- y x z - -- y x z - 1/8 x z + 32 24 + + 4 4 3 2 2 2 4 2 + + 1/24 y x + 2/3 - 2/3 z - 5/6 y - 1/2 z - 5/24 x y - 5/6 x + + 4 3 25 2 2 2 2 2 3 2 3 + - 1/6 x z + -- y x z - 5/3 y z - 5/3 x z + 5/6 y z + 5/6 x z + 12 + + 2 2 2 2 25 2 2 4 2 + + 5/8 x z + 5/8 y z + -- y x - 5/24 x y , COEFF(1, 0, 1) = + 24 + + 4 3 4 2 2 4 2 4 2 3 4 3 + 2/9 x y z + 1/48 x y z - 1/12 x y z - 1/12 x y z + 1/36 x y z + + 2 4 4 3 4 4 4 3 2 4 3 + + 1/48 z y x + 1/36 z y x - 1/9 x y z - 1/9 x y z + + 4 2 4 2 3 4 2 2 3 4 + + 5/18 x y z - 5/36 x y z - 5/48 x y z - 1/18 x y z + + 4 4 2 4 4 4 2 + - 1/18 z y x + 2/9 x y z + 4/9 x - 2/9 x z - 1/9 x - 10/9 y x z + + 2 3 3 4 2 2 2 2 2 3 3 + + 5/9 y x z - 1/36 x y + 5/12 y x z + 5/9 y x z - 2/9 z x + + 4 2 3 3 4 2 4 4 3 2 3 + + 1/9 x y - 5/36 y x z + 1/12 x z - 1/36 y x - 1/9 x + 5/36 y x + + 2 4 2 2 3 2 2 3 4 3 2 + + 1/9 x y + 4/9 x + 5/18 z y x - 5/48 z y x + 1/9 x z - 5/9 y x + + 2 2 2 2 2 3 3 2 3 + + 5/12 y x z - 10/9 y x z + 8/9 x z + 8/9 x z + 1/9 x z - 4/9 x z + + 3 2 2 2 3 2 2 2 4 2 + - 4/9 x z - 1/3 x z - 1/3 x z + 1/12 x z - 5/9 y x + 5/36 x y , + + 4 3 4 2 2 4 2 + COEFF(2, 0, 1) = - 1/36 x y z - 1/96 x y z + 1/192 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + + 1/96 x y z - 1/72 x y z - 1/192 z y x - 1/144 z y x + + 4 3 2 4 3 4 2 4 2 3 + + 1/72 x y z + 1/144 x y z - 5/72 x y z + 5/144 x y z + + 4 2 2 3 4 4 4 2 4 + + 5/192 x y z + 1/36 x y z + 1/72 z y x - 1/72 x y z - 1/18 x + + 4 4 2 2 3 3 4 + + 1/18 x z + 1/36 x + 5/36 y x z - 5/72 y x z + 1/72 x y + + 2 2 2 2 2 3 3 4 2 3 3 + - 5/192 y x z - 5/144 y x z + 1/9 z x - 1/72 x y + 5/72 y x z + + 4 2 4 4 3 2 3 2 4 2 + - 1/48 x z + 1/144 y x + 1/18 x - 5/72 y x - 1/144 x y - 1/36 x + + 2 3 2 2 3 4 3 2 2 2 + - 5/36 z y x + 5/96 z y x - 1/36 x z + 5/72 y x - 5/96 y x z + + 2 2 2 3 3 2 3 3 + + 5/72 y x z - 1/9 x z - 1/18 x z - 1/18 x z + 1/36 x z + 1/18 x z + + 2 2 2 3 2 2 2 4 2 + + 1/48 x z + 1/24 x z - 1/24 x z + 5/144 y x - 5/144 x y , + + 4 3 4 2 2 4 2 + COEFF(-2, 1, 1) = - 1/54 x y z - 1/144 x y z - 1/288 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + + 1/144 x y z - 1/108 x y z + 1/288 z y x + 1/216 z y x + + 4 3 2 4 3 4 3 4 + + 1/108 x y z - 1/216 x y z - 1/108 x y z + 1/27 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/27 x y z - 1/54 x y z + 1/216 x y z - 1/72 x y z + + 4 3 2 4 2 2 4 3 3 4 + + 1/288 x y z - 1/72 x y z - 1/54 x y z + 1/54 x y z + + 4 4 2 4 3 3 3 + - 1/108 z y x + 1/108 x y z - 1/27 y x - 1/27 y x z - 2/27 z y x + + 2 3 2 2 3 3 4 + + 1/36 z y x + 2/27 y x z - 1/27 y x z + 1/27 y x + 1/108 x y + + 2 2 2 3 2 2 2 3 3 3 + + 1/72 y x z + 1/144 y x z + 1/54 y x z + 1/27 y x z + + 3 3 2 2 3 3 2 2 4 + - 1/144 y x z + 1/54 y x z - 1/288 y x z - 1/108 x y + + 2 3 3 4 4 3 2 3 3 2 + + 1/27 y x z - 1/216 y x - 1/108 y x - 1/27 y x + 1/216 y x + + 3 3 2 2 4 3 3 3 3 + - 1/54 z y x + 1/108 z y x + 1/216 x y + 1/108 y x + 1/54 z y x + + 2 2 3 2 2 3 3 3 + + 2/27 y x z - 1/27 z y x - 2/27 z y x + 1/36 z y x + 1/108 y x z + + 3 3 3 2 2 2 2 2 2 2 + - 1/108 y x z + 1/27 y x - 1/36 y x z - 1/27 y x z + 1/72 y x z + + 2 3 2 3 2 2 2 4 + - 1/36 y x z - 1/216 y x z - 1/54 y x - 1/54 y x + 1/54 x y + + 4 2 4 3 4 3 4 2 + + 1/54 x y - 1/216 x y , COEFF(-1, 1, 1) = 4/27 x y z + 1/72 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + + 1/18 x y z - 1/18 x y z + 1/54 x y z - 1/72 z y x + + 3 4 4 4 3 2 4 3 4 3 + - 1/54 z y x - 2/27 x y z + 2/27 x y z + 1/27 x y z + + 4 4 2 4 2 3 4 3 3 + - 4/27 x y z - 4/27 x y z + 2/27 x y z - 1/54 x y z + + 4 2 4 3 2 4 2 2 4 3 + + 1/18 x y z - 1/72 x y z + 1/18 x y z + 2/27 x y z + + 3 4 4 4 2 4 3 3 + - 1/27 x y z + 1/27 z y x - 4/27 x y z + 2/27 y x + 8/27 y x z + + 3 2 3 16 2 2 3 + + 4/27 z y x - 1/18 z y x - -- y x z + 8/27 y x z - 8/27 y x + 27 + + 3 4 2 2 2 3 2 2 2 3 3 3 + - 1/54 x y - 2/9 y x z - 1/18 y x z - 8/27 y x z - 2/27 y x z + + 3 3 2 2 3 3 2 2 4 2 3 3 + + 1/72 y x z - 8/27 y x z + 1/18 y x z + 2/27 x y - 2/27 y x z + + 4 4 3 2 3 3 2 3 + + 1/54 y x + 2/27 y x + 2/27 y x - 2/27 y x + 4/27 z y x + + 3 2 2 4 3 3 3 3 16 + - 4/27 z y x - 2/27 x y - 1/54 y x - 1/27 z y x - -- y x z + 27 + + 16 2 2 3 2 2 3 3 3 3 3 3 + + -- z y x + 4/27 z y x - 1/18 z y x - 2/27 y x z + 1/54 y x z + 27 + + 2 2 2 16 2 2 2 2 2 + - 8/27 y x + 2/9 y x z + -- y x z - 2/9 y x z + 2/9 y x z + 27 + + 3 2 3 2 2 2 4 4 2 + + 2/27 y x z + 8/27 y x + 8/27 y x - 2/27 x y - 2/27 x y + + 4 3 2 4 2 2 4 4 + + 1/54 x y , COEFF(0, 1, 1) = - 5/48 x y z + 1/48 z y x + + 3 4 4 2 4 3 4 3 4 4 2 + + 1/36 z y x - 5/36 x y z - 1/18 x y z + 2/9 x y z + 2/9 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/9 x y z + 1/36 x y z - 1/12 x y z + 1/48 x y z + + 4 2 2 4 3 4 4 4 3 2 4 + - 1/12 x y z - 1/9 x y z - 1/18 z y x + 1/9 y z + 5/18 x y z + + 4 4 2 4 2 2 2 2 2 3 + + 4/9 y - 1/9 y + 1/12 y z - 2/9 y z + 5/12 y x z + 5/9 y x z + + 2 3 3 2 2 4 4 3 3 2 + + 5/9 y x z - 5/48 y x z - 1/36 y x - 1/9 y - 2/9 z y + 4/9 y + + 3 2 3 2 2 4 2 + + 5/36 y x + 5/18 z y x + 5/36 x y - 10/9 z y x + 8/9 y z + + 2 2 2 2 2 3 2 3 3 + - 10/9 y x z + 5/12 y x z + 8/9 y z - 5/36 y x z - 4/9 y z + + 2 3 3 3 3 2 2 2 2 2 2 + - 4/9 y z + 1/9 y z + 1/12 y z - 1/3 y z - 1/3 y z - 5/9 y x + + 2 4 4 2 4 3 + - 5/9 y x + 1/9 x y + 1/9 x y - 1/36 x y , COEFF(1, 1, 1) = + + 4 3 4 2 2 4 2 4 2 + - 4/27 x y z - 1/72 x y z + 1/18 x y z + 1/18 x y z + + 3 4 3 2 4 4 3 4 4 4 3 + - 1/54 x y z - 1/72 z y x - 1/54 z y x + 2/27 x y z + + 2 4 3 4 3 4 4 2 + + 2/27 x y z + 1/27 x y z - 4/27 x y z - 4/27 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + + 2/27 x y z - 1/54 x y z + 1/18 x y z - 1/72 x y z + + 4 2 2 4 3 3 4 4 4 + + 1/18 x y z + 2/27 x y z + 1/27 x y z + 1/27 z y x + + 2 4 3 3 3 2 3 + - 4/27 x y z - 2/27 y x - 8/27 y x z - 4/27 z y x + 1/18 z y x + + 16 2 2 3 3 4 2 2 2 + + -- y x z - 8/27 y x z + 8/27 y x + 1/54 x y - 2/9 y x z + 27 + + 3 2 2 2 3 3 3 3 3 2 + + 1/18 y x z - 8/27 y x z + 2/27 y x z - 1/72 y x z + + 2 3 3 2 2 4 2 3 3 4 4 + - 8/27 y x z + 1/18 y x z - 2/27 x y + 2/27 y x z + 1/54 y x + + 3 2 3 3 2 3 3 2 + - 2/27 y x - 2/27 y x - 2/27 y x - 4/27 z y x - 4/27 z y x + + 2 4 3 3 3 3 16 16 2 + - 2/27 x y + 1/54 y x + 1/27 z y x + -- y x z + -- z y x + 27 27 + + 2 3 2 2 3 3 3 3 3 3 2 + - 4/27 z y x + 1/18 z y x + 2/27 y x z - 1/54 y x z + 8/27 y x + + 2 2 16 2 2 2 2 2 3 2 3 + - 2/9 y x z + -- y x z - 2/9 y x z - 2/9 y x z + 2/27 y x z + 27 + + 2 2 2 4 4 2 4 3 + + 8/27 y x + 8/27 y x - 2/27 x y - 2/27 x y + 1/54 x y , + + 4 3 4 2 2 4 2 + COEFF(2, 1, 1) = 1/54 x y z + 1/144 x y z - 1/288 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + - 1/144 x y z + 1/108 x y z + 1/288 z y x + 1/216 z y x + + 4 3 2 4 3 4 3 4 + - 1/108 x y z - 1/216 x y z - 1/108 x y z + 1/27 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/27 x y z - 1/54 x y z + 1/216 x y z - 1/72 x y z + + 4 3 2 4 2 2 4 3 3 4 + + 1/288 x y z - 1/72 x y z - 1/54 x y z - 1/54 x y z + + 4 4 2 4 3 3 3 + - 1/108 z y x + 1/108 x y z + 1/27 y x + 1/27 y x z + 2/27 z y x + + 2 3 2 2 3 3 4 + - 1/36 z y x - 2/27 y x z + 1/27 y x z - 1/27 y x - 1/108 x y + + 2 2 2 3 2 2 2 3 3 3 + + 1/72 y x z - 1/144 y x z + 1/54 y x z - 1/27 y x z + + 3 3 2 2 3 3 2 2 4 + + 1/144 y x z + 1/54 y x z - 1/288 y x z + 1/108 x y + + 2 3 3 4 4 3 2 3 3 2 + - 1/27 y x z - 1/216 y x + 1/108 y x + 1/27 y x + 1/216 y x + + 3 3 2 2 4 3 3 3 3 + + 1/54 z y x + 1/108 z y x + 1/216 x y - 1/108 y x - 1/54 z y x + + 2 2 3 2 2 3 3 3 + - 2/27 y x z - 1/27 z y x + 2/27 z y x - 1/36 z y x - 1/108 y x z + + 3 3 3 2 2 2 2 2 2 2 + + 1/108 y x z - 1/27 y x + 1/36 y x z - 1/27 y x z + 1/72 y x z + + 2 3 2 3 2 2 2 4 + + 1/36 y x z - 1/216 y x z - 1/54 y x - 1/54 y x + 1/54 x y + + 4 2 4 3 4 + + 1/54 x y - 1/216 x y , COEFF(-2, 2, 1) = 1/216 x y z + + 3 4 2 2 4 2 4 2 3 4 3 + + 1/576 x y z + 1/1152 x y z - 1/576 x y z + 1/432 x y z + + 2 4 4 3 4 4 4 3 2 4 3 + - 1/1152 z y x - 1/864 z y x - 1/432 x y z + 1/864 x y z + + 4 3 4 4 2 4 2 3 + + 1/216 x y z - 1/216 x y z - 1/432 x y z + 1/864 x y z + + 4 3 3 4 2 4 3 2 4 2 2 + - 1/432 x y z + 1/576 x y z - 1/576 x y z + 1/1152 x y z + + 4 3 3 4 4 4 2 4 + + 1/432 x y z - 1/216 x y z + 1/432 z y x - 1/432 x y z + + 3 3 3 2 3 2 + + 1/216 y x + 1/216 y x z + 1/108 z y x - 1/288 z y x - 1/216 y x z + + 2 3 3 4 2 2 2 + + 1/432 y x z - 1/216 y x - 1/432 x y - 1/1152 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/288 y x z - 1/864 y x z - 1/216 y x z + 1/288 y x z + + 2 3 3 2 2 4 2 3 3 + - 1/432 y x z + 1/576 y x z + 1/432 x y - 1/432 y x z + + 4 4 3 2 3 3 2 3 + + 1/864 y x + 1/216 y x + 1/432 y x - 1/432 y x + 1/108 z y x + + 3 2 2 4 3 3 3 3 + - 1/216 z y x - 1/864 x y - 1/216 y x - 1/108 z y x - 1/108 y x z + + 2 2 3 2 2 3 3 3 + + 1/216 z y x + 1/216 z y x - 1/576 z y x - 1/216 y x z + + 3 3 3 2 2 2 2 2 + + 1/216 y x z - 1/432 y x + 1/576 y x z + 1/432 y x z + + 2 2 2 3 2 3 2 2 2 + - 1/576 y x z + 1/288 y x z + 1/432 y x z + 1/864 y x + 1/432 y x + + 4 4 2 4 3 4 + - 1/432 x y - 1/864 x y + 1/432 x y , COEFF(-1, 2, 1) = - 1/27 x y z + + 3 4 2 2 4 2 4 2 3 4 3 + - 1/288 x y z - 1/72 x y z + 1/72 x y z - 1/216 x y z + + 2 4 4 3 4 4 4 3 2 4 3 + + 1/288 z y x + 1/216 z y x + 1/54 x y z - 1/54 x y z + + 4 3 4 4 2 4 2 3 + - 1/54 x y z + 1/54 x y z + 1/108 x y z - 1/216 x y z + + 4 3 3 4 2 4 3 2 4 2 2 + + 1/108 x y z - 1/144 x y z + 1/144 x y z - 1/288 x y z + + 4 3 3 4 4 4 2 4 + - 1/108 x y z + 1/108 x y z - 1/108 z y x + 1/27 x y z + + 3 3 3 2 3 2 + - 1/108 y x - 1/27 y x z - 1/54 z y x + 1/144 z y x + 1/27 y x z + + 2 3 3 4 2 2 2 3 2 + - 1/54 y x z + 1/27 y x + 1/216 x y + 1/72 y x z + 1/36 y x z + + 2 2 3 3 3 3 3 2 2 3 + + 1/54 y x z + 1/108 y x z - 1/144 y x z + 1/27 y x z + + 3 2 2 4 2 3 3 4 4 3 + - 1/36 y x z - 1/54 x y + 1/216 y x z - 1/216 y x - 1/27 y x + + 2 3 3 2 3 3 2 2 4 + - 1/216 y x + 1/27 y x - 2/27 z y x + 2/27 z y x + 1/54 x y + + 3 3 3 3 2 2 3 + + 1/108 y x + 1/54 z y x + 2/27 y x z - 2/27 z y x - 1/108 z y x + + 2 2 3 3 3 3 3 3 2 + + 1/288 z y x + 1/27 y x z - 1/108 y x z + 1/54 y x + + 2 2 2 2 2 2 2 3 2 3 + - 1/72 y x z - 1/27 y x z + 1/36 y x z - 1/36 y x z - 1/27 y x z + + 2 2 2 4 4 2 4 3 + - 1/54 y x - 1/27 y x + 1/108 x y + 1/216 x y - 1/108 x y , + + 2 4 2 2 4 4 3 4 4 + COEFF(0, 2, 1) = 5/192 x y z - 1/192 z y x - 1/144 z y x + + 2 4 3 4 3 4 4 2 + + 5/144 x y z + 1/36 x y z - 1/36 x y z - 1/72 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + + 1/144 x y z - 1/72 x y z + 1/96 x y z - 1/96 x y z + + 4 2 2 4 3 4 4 4 3 2 4 + + 1/192 x y z + 1/72 x y z + 1/72 z y x - 1/36 y z - 5/72 x y z + + 4 4 2 4 2 2 2 + - 1/18 y + 1/36 y - 1/48 y z + 1/18 y z - 5/192 y x z + + 2 2 3 2 3 3 2 2 4 4 3 + - 5/144 y x z - 5/72 y x z + 5/96 y x z + 1/144 y x + 1/18 y + + 3 2 3 2 3 2 2 4 + + 1/9 z y - 1/36 y - 5/72 y x - 5/36 z y x - 5/144 x y + + 2 2 2 2 2 2 + + 5/36 z y x - 1/9 y z + 5/72 y x z - 5/96 y x z - 1/18 y z + + 3 2 3 3 2 3 3 3 3 2 + + 5/72 y x z + 1/18 y z + 1/36 y z - 1/18 y z - 1/24 y z + + 2 2 2 2 2 2 4 + + 1/24 y z + 1/48 y z + 5/144 y x + 5/72 y x - 1/72 x y + + 4 2 4 3 4 3 4 2 + - 1/144 x y + 1/72 x y , COEFF(1, 2, 1) = 1/27 x y z + 1/288 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + - 1/72 x y z - 1/72 x y z + 1/216 x y z + 1/288 z y x + + 3 4 4 4 3 2 4 3 4 3 + + 1/216 z y x - 1/54 x y z - 1/54 x y z - 1/54 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/54 x y z + 1/108 x y z - 1/216 x y z + 1/108 x y z + + 4 2 4 3 2 4 2 2 4 3 + - 1/144 x y z + 1/144 x y z - 1/288 x y z - 1/108 x y z + + 3 4 4 4 2 4 3 3 + - 1/108 x y z - 1/108 z y x + 1/27 x y z + 1/108 y x + 1/27 y x z + + 3 2 3 2 2 3 + + 1/54 z y x - 1/144 z y x - 1/27 y x z + 1/54 y x z - 1/27 y x + + 3 4 2 2 2 3 2 2 2 3 + - 1/216 x y + 1/72 y x z - 1/36 y x z + 1/54 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/108 y x z + 1/144 y x z + 1/27 y x z - 1/36 y x z + + 4 2 3 3 4 4 3 2 3 + + 1/54 x y - 1/216 y x z - 1/216 y x + 1/27 y x + 1/216 y x + + 3 2 3 3 2 2 4 3 3 + + 1/27 y x + 2/27 z y x + 2/27 z y x + 1/54 x y - 1/108 y x + + 3 3 2 2 3 2 2 3 + - 1/54 z y x - 2/27 y x z - 2/27 z y x + 1/108 z y x - 1/288 z y x + + 3 3 3 3 3 2 2 2 2 2 + - 1/27 y x z + 1/108 y x z - 1/54 y x + 1/72 y x z - 1/27 y x z + + 2 2 2 3 2 3 2 2 2 + + 1/36 y x z + 1/36 y x z - 1/27 y x z - 1/54 y x - 1/27 y x + + 4 4 2 4 3 4 + + 1/108 x y + 1/216 x y - 1/108 x y , COEFF(2, 2, 1) = - 1/216 x y z + + 3 4 2 2 4 2 4 2 3 4 3 + - 1/576 x y z + 1/1152 x y z + 1/576 x y z - 1/432 x y z + + 2 4 4 3 4 4 4 3 2 4 3 + - 1/1152 z y x - 1/864 z y x + 1/432 x y z + 1/864 x y z + + 4 3 4 4 2 4 2 3 + + 1/216 x y z - 1/216 x y z - 1/432 x y z + 1/864 x y z + + 4 3 3 4 2 4 3 2 4 2 2 + - 1/432 x y z + 1/576 x y z - 1/576 x y z + 1/1152 x y z + + 4 3 3 4 4 4 2 4 + + 1/432 x y z + 1/216 x y z + 1/432 z y x - 1/432 x y z + + 3 3 3 2 3 2 + - 1/216 y x - 1/216 y x z - 1/108 z y x + 1/288 z y x + 1/216 y x z + + 2 3 3 4 2 2 2 + - 1/432 y x z + 1/216 y x + 1/432 x y - 1/1152 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/288 y x z - 1/864 y x z + 1/216 y x z - 1/288 y x z + + 2 3 3 2 2 4 2 3 3 + - 1/432 y x z + 1/576 y x z - 1/432 x y + 1/432 y x z + + 4 4 3 2 3 3 2 3 + + 1/864 y x - 1/216 y x - 1/432 y x - 1/432 y x - 1/108 z y x + + 3 2 2 4 3 3 3 3 + - 1/216 z y x - 1/864 x y + 1/216 y x + 1/108 z y x + 1/108 y x z + + 2 2 3 2 2 3 3 3 + + 1/216 z y x - 1/216 z y x + 1/576 z y x + 1/216 y x z + + 3 3 3 2 2 2 2 2 + - 1/216 y x z + 1/432 y x - 1/576 y x z + 1/432 y x z + + 2 2 2 3 2 3 2 2 2 + - 1/576 y x z - 1/288 y x z + 1/432 y x z + 1/864 y x + 1/432 y x + + 4 4 2 4 3 + - 1/432 x y - 1/864 x y + 1/432 x y , COEFF(-2, -2, 2) = + + 4 3 4 2 2 4 2 4 2 + - 1/3456 x y z - 1/1152 x y z - 1/2304 x y z + 1/1152 x y z + + 3 4 3 2 4 4 3 4 4 4 3 + - 1/1728 x y z + 1/2304 z y x + 1/3456 z y x + 1/1728 x y z + + 2 4 3 4 3 4 4 2 + - 1/3456 x y z + 1/3456 x y z - 1/3456 x y z + 1/6912 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/3456 x y z - 1/1728 x y z + 1/1152 x y z - 1/1152 x y z + + 4 2 2 4 3 3 4 4 4 + - 1/2304 x y z + 1/1728 x y z + 1/3456 x y z - 1/6912 z y x + + 2 4 3 3 3 + + 1/6912 x y z + 1/1728 y x + 1/864 y x z + 1/1728 z y x + + 2 3 2 2 3 + - 1/576 z y x + 1/3456 y x z - 1/1728 y x z - 1/1728 y x + + 3 4 2 2 2 3 2 2 2 3 + + 1/3456 x y + 1/2304 y x z - 1/576 y x z + 1/3456 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/864 y x z + 1/576 y x z - 1/1728 y x z + 1/1152 y x z + + 4 2 3 3 4 4 3 + - 1/3456 x y + 1/1728 y x z - 1/6912 y x + 1/1728 y x + + 2 3 3 2 3 3 2 + - 1/3456 y x - 1/3456 y x + 1/1728 z y x - 1/3456 z y x + + 2 4 3 3 3 3 + + 1/6912 x y - 1/1728 y x - 1/1728 z y x - 1/1728 y x z + + 2 2 3 2 2 3 3 3 + + 1/3456 z y x - 1/3456 z y x + 1/1152 z y x - 1/864 y x z + + 3 3 3 2 2 2 2 2 + + 1/864 y x z + 1/3456 y x - 1/1152 y x z - 1/6912 y x z + + 2 2 2 3 2 3 2 2 + - 1/1152 y x z + 1/576 y x z + 1/1728 y x z - 1/6912 y x + + 2 4 4 2 4 3 + + 1/3456 y x - 1/3456 x y + 1/6912 x y + 1/3456 x y , + + 4 3 4 2 2 4 2 + COEFF(-1, -2, 2) = 1/432 x y z + 1/576 x y z + 1/144 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + - 1/144 x y z + 1/864 x y z - 1/576 z y x - 1/864 z y x + + 4 3 2 4 3 4 3 4 + - 1/216 x y z + 1/216 x y z - 1/864 x y z + 1/864 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/1728 x y z + 1/864 x y z + 1/432 x y z - 1/288 x y z + + 4 3 2 4 2 2 4 3 3 4 + + 1/288 x y z + 1/576 x y z - 1/432 x y z - 1/1728 x y z + + 4 4 2 4 3 3 + + 1/1728 z y x - 1/432 x y z - 1/864 y x - 1/108 y x z + + 3 2 3 2 2 3 + - 1/864 z y x + 1/288 z y x - 1/432 y x z + 1/216 y x z + 1/216 y x + + 3 4 2 2 2 3 2 2 2 3 + - 1/1728 x y - 1/144 y x z + 1/72 y x z - 1/216 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 1/432 y x z - 1/288 y x z + 1/108 y x z - 1/72 y x z + + 4 2 3 3 4 4 3 2 3 + + 1/432 x y - 1/864 y x z + 1/1728 y x - 1/216 y x + 1/1728 y x + + 3 2 3 3 2 2 4 3 3 + + 1/216 y x - 1/216 z y x + 1/216 z y x - 1/432 x y + 1/864 y x + + 3 3 2 2 3 + + 1/864 z y x + 1/216 y x z - 1/216 z y x + 1/1728 z y x + + 2 2 3 3 3 3 3 3 2 + - 1/576 z y x + 1/108 y x z - 1/432 y x z - 1/432 y x + + 2 2 2 2 2 2 2 + + 1/144 y x z + 1/432 y x z + 1/72 y x z - 1/72 y x z + + 3 2 3 2 2 2 4 4 2 + - 1/108 y x z + 1/432 y x - 1/216 y x + 1/864 x y - 1/1728 x y + + 4 3 2 4 2 2 4 4 + - 1/864 x y , COEFF(0, -2, 2) = - 5/384 x y z + 1/384 z y x + + 3 4 4 2 4 3 4 3 4 + + 1/576 z y x - 5/576 x y z + 1/576 x y z - 1/576 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/1152 x y z - 1/576 x y z - 1/288 x y z + 1/192 x y z + + 4 3 2 4 2 2 4 3 4 4 + - 1/192 x y z - 1/384 x y z + 1/288 x y z - 1/1152 z y x + + 4 3 2 4 4 4 2 + + 1/144 y z + 5/1152 x y z - 1/144 y - 1/288 y + 1/96 y z + + 4 2 2 2 2 2 3 2 3 + - 1/288 y z + 5/384 y x z + 5/576 y x z - 5/288 y x z + + 3 2 2 4 4 3 3 2 + + 5/192 y x z - 1/1152 y x + 1/144 y + 1/144 z y + 1/288 y + + 3 2 3 2 2 4 2 + - 5/576 y x - 5/576 z y x + 5/1152 x y + 5/576 z y x - 1/144 y z + + 2 2 2 2 2 3 2 3 3 + - 5/1152 y x z - 5/192 y x z + 1/288 y z + 5/288 y x z + 1/72 y z + + 2 3 3 3 3 2 2 2 2 + - 1/144 y z - 1/72 y z - 1/48 y z + 1/48 y z - 1/96 y z + + 2 2 2 4 4 2 4 3 + - 5/1152 y x + 5/576 y x - 1/576 x y + 1/1152 x y + 1/576 x y , + + 4 3 4 2 2 4 2 + COEFF(1, -2, 2) = - 1/432 x y z - 1/576 x y z + 1/144 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + + 1/144 x y z - 1/864 x y z - 1/576 z y x - 1/864 z y x + + 4 3 2 4 3 4 3 4 + + 1/216 x y z + 1/216 x y z - 1/864 x y z + 1/864 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/1728 x y z + 1/864 x y z + 1/432 x y z - 1/288 x y z + + 4 3 2 4 2 2 4 3 3 4 + + 1/288 x y z + 1/576 x y z - 1/432 x y z + 1/1728 x y z + + 4 4 2 4 3 3 + + 1/1728 z y x - 1/432 x y z + 1/864 y x + 1/108 y x z + + 3 2 3 2 2 3 + + 1/864 z y x - 1/288 z y x + 1/432 y x z - 1/216 y x z - 1/216 y x + + 3 4 2 2 2 3 2 2 2 3 + + 1/1728 x y - 1/144 y x z - 1/72 y x z - 1/216 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/432 y x z + 1/288 y x z + 1/108 y x z - 1/72 y x z + + 4 2 3 3 4 4 3 2 3 + - 1/432 x y + 1/864 y x z + 1/1728 y x + 1/216 y x - 1/1728 y x + + 3 2 3 3 2 2 4 3 3 + + 1/216 y x + 1/216 z y x + 1/216 z y x - 1/432 x y - 1/864 y x + + 3 3 2 2 3 + - 1/864 z y x - 1/216 y x z - 1/216 z y x - 1/1728 z y x + + 2 2 3 3 3 3 3 3 2 + + 1/576 z y x - 1/108 y x z + 1/432 y x z + 1/432 y x + + 2 2 2 2 2 2 2 + - 1/144 y x z + 1/432 y x z + 1/72 y x z + 1/72 y x z + + 3 2 3 2 2 2 4 4 2 + - 1/108 y x z + 1/432 y x - 1/216 y x + 1/864 x y - 1/1728 x y + + 4 3 4 3 4 2 + - 1/864 x y , COEFF(2, -2, 2) = 1/3456 x y z + 1/1152 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + - 1/2304 x y z - 1/1152 x y z + 1/1728 x y z + 1/2304 z y x + + 3 4 4 4 3 2 4 3 4 3 + + 1/3456 z y x - 1/1728 x y z - 1/3456 x y z + 1/3456 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/3456 x y z + 1/6912 x y z - 1/3456 x y z - 1/1728 x y z + + 4 2 4 3 2 4 2 2 4 3 + + 1/1152 x y z - 1/1152 x y z - 1/2304 x y z + 1/1728 x y z + + 3 4 4 4 2 4 3 + - 1/3456 x y z - 1/6912 z y x + 1/6912 x y z - 1/1728 y x + + 3 3 2 3 2 + - 1/864 y x z - 1/1728 z y x + 1/576 z y x - 1/3456 y x z + + 2 3 3 4 2 2 2 + + 1/1728 y x z + 1/1728 y x - 1/3456 x y + 1/2304 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/576 y x z + 1/3456 y x z + 1/864 y x z - 1/576 y x z + + 2 3 3 2 2 4 2 3 3 + - 1/1728 y x z + 1/1152 y x z + 1/3456 x y - 1/1728 y x z + + 4 4 3 2 3 3 2 3 + - 1/6912 y x - 1/1728 y x + 1/3456 y x - 1/3456 y x - 1/1728 z y x + + 3 2 2 4 3 3 3 3 + - 1/3456 z y x + 1/6912 x y + 1/1728 y x + 1/1728 z y x + + 2 2 3 2 2 3 + + 1/1728 y x z + 1/3456 z y x + 1/3456 z y x - 1/1152 z y x + + 3 3 3 3 3 2 2 2 + + 1/864 y x z - 1/864 y x z - 1/3456 y x + 1/1152 y x z + + 2 2 2 2 2 3 2 3 + - 1/6912 y x z - 1/1152 y x z - 1/576 y x z + 1/1728 y x z + + 2 2 2 4 4 2 4 3 + - 1/6912 y x + 1/3456 y x - 1/3456 x y + 1/6912 x y + 1/3456 x y , + + 4 3 4 2 2 4 2 + COEFF(-2, -1, 2) = 1/864 x y z + 1/288 x y z + 1/576 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + - 1/288 x y z + 1/432 x y z - 1/576 z y x - 1/864 z y x + + 4 3 2 4 3 4 3 4 + - 1/432 x y z + 1/864 x y z - 1/1728 x y z + 1/432 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/432 x y z + 1/216 x y z + 1/864 x y z - 1/144 x y z + + 4 3 2 4 2 2 4 3 3 4 + + 1/576 x y z + 1/144 x y z - 1/216 x y z - 1/864 x y z + + 4 4 2 4 3 3 + + 1/1728 z y x - 1/1728 x y z - 1/216 y x - 1/108 y x z + + 3 2 3 2 2 3 + - 1/216 z y x + 1/72 z y x - 1/216 y x z + 1/108 y x z + 1/216 y x + + 3 4 2 2 2 3 2 2 2 3 + - 1/864 x y - 1/144 y x z + 1/288 y x z - 1/216 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 1/108 y x z - 1/288 y x z + 1/216 y x z - 1/576 y x z + + 4 2 3 3 4 4 3 2 3 + + 1/864 x y - 1/108 y x z + 1/1728 y x - 1/864 y x + 1/216 y x + + 3 2 3 3 2 2 4 + + 1/1728 y x - 1/864 z y x + 1/1728 z y x - 1/1728 x y + + 3 3 3 3 2 2 3 + + 1/864 y x + 1/864 z y x + 1/216 y x z - 1/432 z y x + 1/216 z y x + + 2 2 3 3 3 3 3 3 2 + - 1/72 z y x + 1/432 y x z - 1/432 y x z - 1/216 y x + + 2 2 2 2 2 2 2 + + 1/72 y x z + 1/432 y x z + 1/144 y x z - 1/72 y x z + + 3 2 3 2 2 2 4 4 2 + - 1/864 y x z + 1/432 y x - 1/432 y x + 1/432 x y - 1/432 x y + + 4 3 4 3 4 2 + - 1/1728 x y , COEFF(-1, -1, 2) = - 1/108 x y z - 1/144 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + - 1/36 x y z + 1/36 x y z - 1/216 x y z + 1/144 z y x + + 3 4 4 4 3 2 4 3 4 3 + + 1/216 z y x + 1/54 x y z - 1/54 x y z + 1/432 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/108 x y z + 1/108 x y z - 1/54 x y z - 1/216 x y z + + 4 2 4 3 2 4 2 2 4 3 + + 1/36 x y z - 1/144 x y z - 1/36 x y z + 1/54 x y z + + 3 4 4 4 2 4 3 3 + + 1/432 x y z - 1/432 z y x + 1/108 x y z + 1/108 y x + 2/27 y x z + + 3 2 3 2 2 3 + + 1/108 z y x - 1/36 z y x + 1/27 y x z - 2/27 y x z - 1/27 y x + + 3 4 2 2 2 3 2 2 2 3 3 3 + + 1/432 x y + 1/9 y x z - 1/36 y x z + 2/27 y x z - 1/54 y x z + + 3 3 2 2 3 3 2 2 4 + + 1/144 y x z - 2/27 y x z + 1/36 y x z - 1/108 x y + + 2 3 3 4 4 3 2 3 3 2 + + 1/54 y x z - 1/432 y x + 1/108 y x - 1/108 y x - 1/108 y x + + 3 3 2 2 4 3 3 3 3 + + 1/108 z y x - 1/108 z y x + 1/108 x y - 1/432 y x - 1/432 z y x + + 2 2 3 2 2 3 3 3 + - 1/27 y x z + 1/27 z y x - 1/108 z y x + 1/36 z y x - 1/54 y x z + + 3 3 3 2 2 2 2 2 2 2 + + 1/216 y x z + 1/27 y x - 1/9 y x z - 1/27 y x z - 1/9 y x z + + 2 3 2 3 2 2 2 4 + + 1/9 y x z + 1/54 y x z - 1/27 y x + 1/27 y x - 1/108 x y + + 4 2 4 3 2 4 2 + + 1/108 x y + 1/432 x y , COEFF(0, -1, 2) = 5/96 x y z + + 2 4 4 3 4 4 2 4 3 4 3 + - 1/96 z y x - 1/144 z y x + 5/144 x y z - 1/288 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/72 x y z - 1/72 x y z + 1/36 x y z + 1/144 x y z + + 4 2 4 3 2 4 2 2 4 3 + - 1/24 x y z + 1/96 x y z + 1/24 x y z - 1/36 x y z + + 4 4 4 3 2 4 4 + + 1/288 z y x - 1/36 y z - 5/288 x y z + 1/18 y + 1/72 y + + 4 2 4 2 2 2 2 2 3 2 3 + - 1/24 y z + 1/72 y z - 5/24 y x z - 5/36 y x z + 5/36 y x z + + 3 2 2 4 4 3 3 2 + - 5/96 y x z + 1/288 y x - 1/72 y - 1/72 z y - 1/18 y + + 3 2 3 2 2 4 2 + + 5/288 y x + 5/288 z y x - 5/288 x y - 5/72 z y x + 1/18 y z + + 2 2 2 2 2 3 2 3 3 + + 5/72 y x z + 5/24 y x z - 1/18 y z - 5/144 y x z - 1/9 y z + + 2 3 3 3 3 2 2 2 2 2 2 + + 1/9 y z + 1/36 y z + 1/24 y z - 1/6 y z + 1/6 y z + 5/72 y x + + 2 4 4 2 4 3 + - 5/72 y x + 1/72 x y - 1/72 x y - 1/288 x y , COEFF(1, -1, 2) = + + 4 3 4 2 2 4 2 4 2 + 1/108 x y z + 1/144 x y z - 1/36 x y z - 1/36 x y z + + 3 4 3 2 4 4 3 4 4 4 3 + + 1/216 x y z + 1/144 z y x + 1/216 z y x - 1/54 x y z + + 2 4 3 4 3 4 4 2 + - 1/54 x y z + 1/432 x y z - 1/108 x y z + 1/108 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/54 x y z - 1/216 x y z + 1/36 x y z - 1/144 x y z + + 4 2 2 4 3 3 4 4 4 + - 1/36 x y z + 1/54 x y z - 1/432 x y z - 1/432 z y x + + 2 4 3 3 3 2 3 + + 1/108 x y z - 1/108 y x - 2/27 y x z - 1/108 z y x + 1/36 z y x + + 2 2 3 3 4 2 2 2 + - 1/27 y x z + 2/27 y x z + 1/27 y x - 1/432 x y + 1/9 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/36 y x z + 2/27 y x z + 1/54 y x z - 1/144 y x z + + 2 3 3 2 2 4 2 3 3 4 4 + - 2/27 y x z + 1/36 y x z + 1/108 x y - 1/54 y x z - 1/432 y x + + 3 2 3 3 2 3 3 2 + - 1/108 y x + 1/108 y x - 1/108 y x - 1/108 z y x - 1/108 z y x + + 2 4 3 3 3 3 2 + + 1/108 x y + 1/432 y x + 1/432 z y x + 1/27 y x z + 1/27 z y x + + 2 3 2 2 3 3 3 3 3 3 + + 1/108 z y x - 1/36 z y x + 1/54 y x z - 1/216 y x z + + 2 2 2 2 2 2 2 2 + - 1/27 y x + 1/9 y x z - 1/27 y x z - 1/9 y x z - 1/9 y x z + + 3 2 3 2 2 2 4 4 2 + + 1/54 y x z - 1/27 y x + 1/27 y x - 1/108 x y + 1/108 x y + + 4 3 4 3 4 2 + + 1/432 x y , COEFF(2, -1, 2) = - 1/864 x y z - 1/288 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + + 1/576 x y z + 1/288 x y z - 1/432 x y z - 1/576 z y x + + 3 4 4 4 3 2 4 3 4 3 + - 1/864 z y x + 1/432 x y z + 1/864 x y z - 1/1728 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/432 x y z - 1/432 x y z + 1/216 x y z + 1/864 x y z + + 4 2 4 3 2 4 2 2 4 3 + - 1/144 x y z + 1/576 x y z + 1/144 x y z - 1/216 x y z + + 3 4 4 4 2 4 3 + + 1/864 x y z + 1/1728 z y x - 1/1728 x y z + 1/216 y x + + 3 3 2 3 2 + + 1/108 y x z + 1/216 z y x - 1/72 z y x + 1/216 y x z + + 2 3 3 4 2 2 2 3 2 + - 1/108 y x z - 1/216 y x + 1/864 x y - 1/144 y x z - 1/288 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/216 y x z - 1/108 y x z + 1/288 y x z + 1/216 y x z + + 3 2 2 4 2 3 3 4 4 3 + - 1/576 y x z - 1/864 x y + 1/108 y x z + 1/1728 y x + 1/864 y x + + 2 3 3 2 3 3 2 + - 1/216 y x + 1/1728 y x + 1/864 z y x + 1/1728 z y x + + 2 4 3 3 3 3 2 + - 1/1728 x y - 1/864 y x - 1/864 z y x - 1/216 y x z - 1/432 z y x + + 2 3 2 2 3 3 3 3 3 3 + - 1/216 z y x + 1/72 z y x - 1/432 y x z + 1/432 y x z + + 2 2 2 2 2 2 2 2 + + 1/216 y x - 1/72 y x z + 1/432 y x z + 1/144 y x z + 1/72 y x z + + 3 2 3 2 2 2 4 4 2 + - 1/864 y x z + 1/432 y x - 1/432 y x + 1/432 x y - 1/432 x y + + 4 3 4 3 4 2 + - 1/1728 x y , COEFF(-2, 0, 2) = - 1/576 x y z - 1/192 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + - 1/384 x y z + 1/192 x y z - 1/288 x y z + 1/384 z y x + + 3 4 4 4 3 2 4 3 4 2 + + 1/576 z y x + 1/288 x y z - 1/576 x y z + 5/1152 x y z + + 4 2 3 4 2 2 3 4 4 4 + - 5/576 x y z - 5/384 x y z + 1/576 x y z - 1/1152 z y x + + 2 4 4 4 2 + + 1/1152 x y z - 1/144 x - 1/288 x z - 1/288 x + 5/576 y x z + + 2 3 3 4 2 2 2 2 2 3 + - 5/288 y x z + 1/576 x y + 5/384 y x z + 5/576 y x z + + 3 4 2 3 3 4 2 4 4 + + 1/144 z x - 1/576 x y + 5/288 y x z + 1/96 x z - 1/1152 y x + + 3 2 3 2 4 2 2 3 + + 1/144 x - 5/576 y x + 1/1152 x y + 1/288 x - 5/576 z y x + + 2 2 3 4 3 2 2 2 + + 5/192 z y x + 1/144 x z + 5/576 y x - 5/192 y x z + + 2 2 2 3 3 2 3 + - 5/1152 y x z - 1/144 x z + 1/288 x z - 1/72 x z - 1/144 x z + + 3 2 2 2 3 2 2 2 + + 1/72 x z - 1/96 x z + 1/48 x z - 1/48 x z - 5/1152 y x + + 4 2 4 3 4 2 + + 5/1152 x y , COEFF(-1, 0, 2) = 1/72 x y z + 1/96 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + + 1/24 x y z - 1/24 x y z + 1/144 x y z - 1/96 z y x + + 3 4 4 4 3 2 4 3 4 2 + - 1/144 z y x - 1/36 x y z + 1/36 x y z - 5/288 x y z + + 4 2 3 4 2 2 3 4 4 4 + + 5/144 x y z + 5/96 x y z - 1/288 x y z + 1/288 z y x + + 2 4 4 4 2 2 3 + - 1/72 x y z + 1/18 x + 1/72 x z + 1/72 x - 5/72 y x z + 5/36 y x z + + 3 4 2 2 2 2 2 3 3 4 + - 1/288 x y - 5/24 y x z - 5/36 y x z - 1/72 z x + 1/72 x y + + 2 3 3 4 2 4 4 3 2 3 + - 5/144 y x z - 1/24 x z + 1/288 y x - 1/72 x + 5/288 y x + + 2 4 2 2 3 2 2 3 4 3 + - 1/72 x y - 1/18 x + 5/288 z y x - 5/96 z y x - 1/36 x z + + 2 2 2 2 2 2 + - 5/72 y x + 5/24 y x z + 5/72 y x z + 1/18 x z - 1/18 x z + + 3 3 2 3 3 2 2 2 3 2 + + 1/36 x z + 1/9 x z - 1/9 x z + 1/6 x z - 1/6 x z + 1/24 x z + + 2 2 4 2 2 4 2 + + 5/72 y x - 5/288 x y , COEFF(0, 0, 2) = - 5/64 x y z + + 2 4 4 3 4 4 2 4 3 4 2 + + 1/64 z y x + 1/96 z y x - 5/96 x y z + 5/192 x y z + + 4 2 3 4 2 2 4 4 4 3 + - 5/96 x y z - 5/64 x y z - 1/192 z y x + 1/24 y z + + 2 4 4 4 4 4 2 + + 5/192 x y z - 1/48 x z - 1/48 x - 1/12 z - 1/48 y + 1/16 y z + + 4 25 2 2 2 25 2 2 3 4 2 4 4 + - 1/48 y z + -- y x z + -- y x z + 1/16 x z - 1/192 y x + 64 96 + + 3 2 2 2 4 2 4 3 + + 1/6 z - 1/12 + 5/48 y + 1/4 z + 5/192 x y + 5/48 x + 1/24 x z + + 25 2 2 2 2 2 3 2 3 + - --- y x z + 5/48 y z + 5/48 x z - 5/24 y z - 5/24 x z + 192 + + 2 2 2 2 25 2 2 4 2 + - 5/16 x z - 5/16 y z - --- y x + 5/192 x y , COEFF(1, 0, 2) = + 192 + + 4 3 4 2 2 4 2 4 2 + - 1/72 x y z - 1/96 x y z + 1/24 x y z + 1/24 x y z + + 3 4 3 2 4 4 3 4 4 4 3 + - 1/144 x y z - 1/96 z y x - 1/144 z y x + 1/36 x y z + + 2 4 3 4 2 4 2 3 4 2 2 + + 1/36 x y z - 5/288 x y z + 5/144 x y z + 5/96 x y z + + 3 4 4 4 2 4 4 + + 1/288 x y z + 1/288 z y x - 1/72 x y z - 1/18 x + 1/72 x z + + 4 2 2 3 3 4 2 2 2 + + 1/72 x + 5/72 y x z - 5/36 y x z + 1/288 x y - 5/24 y x z + + 2 2 3 3 4 2 3 3 4 2 + - 5/36 y x z + 1/72 z x - 1/72 x y + 5/144 y x z - 1/24 x z + + 4 4 3 2 3 2 4 2 + + 1/288 y x + 1/72 x - 5/288 y x - 1/72 x y - 1/18 x + + 2 3 2 2 3 4 3 2 2 2 + - 5/288 z y x + 5/96 z y x - 1/36 x z + 5/72 y x - 5/24 y x z + + 2 2 2 3 3 2 3 3 + + 5/72 y x z - 1/18 x z - 1/18 x z - 1/36 x z + 1/9 x z + 1/9 x z + + 2 2 2 3 2 2 2 4 2 + + 1/6 x z + 1/6 x z - 1/24 x z + 5/72 y x - 5/288 x y , + + 4 3 4 2 2 4 2 + COEFF(2, 0, 2) = 1/576 x y z + 1/192 x y z - 1/384 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + - 1/192 x y z + 1/288 x y z + 1/384 z y x + 1/576 z y x + + 4 3 2 4 3 4 2 4 2 3 + - 1/288 x y z - 1/576 x y z + 5/1152 x y z - 5/576 x y z + + 4 2 2 3 4 4 4 2 4 + - 5/384 x y z - 1/576 x y z - 1/1152 z y x + 1/1152 x y z + + 4 4 2 2 3 + + 1/144 x - 1/288 x z - 1/288 x - 5/576 y x z + 5/288 y x z + + 3 4 2 2 2 2 2 3 3 4 + - 1/576 x y + 5/384 y x z + 5/576 y x z - 1/144 z x + 1/576 x y + + 2 3 3 4 2 4 4 3 2 3 + - 5/288 y x z + 1/96 x z - 1/1152 y x - 1/144 x + 5/576 y x + + 2 4 2 2 3 2 2 3 4 3 + + 1/1152 x y + 1/288 x + 5/576 z y x - 5/192 z y x + 1/144 x z + + 2 2 2 2 2 2 + - 5/576 y x + 5/192 y x z - 5/1152 y x z + 1/144 x z + 1/288 x z + + 3 3 2 3 3 2 2 2 + + 1/72 x z - 1/144 x z - 1/72 x z - 1/96 x z - 1/48 x z + + 3 2 2 2 4 2 4 + + 1/48 x z - 5/1152 y x + 5/1152 x y , COEFF(-2, 1, 2) = 1/864 x y z + + 3 4 2 2 4 2 4 2 3 4 3 + + 1/288 x y z + 1/576 x y z - 1/288 x y z + 1/432 x y z + + 2 4 4 3 4 4 4 3 2 4 3 + - 1/576 z y x - 1/864 z y x - 1/432 x y z + 1/864 x y z + + 4 3 4 4 2 4 2 3 + + 1/1728 x y z - 1/432 x y z - 1/432 x y z + 1/216 x y z + + 4 3 3 4 2 4 3 2 4 2 2 + - 1/864 x y z + 1/144 x y z - 1/576 x y z + 1/144 x y z + + 4 3 3 4 4 4 2 4 + + 1/216 x y z - 1/864 x y z + 1/1728 z y x - 1/1728 x y z + + 3 3 3 2 3 2 + + 1/216 y x + 1/108 y x z + 1/216 z y x - 1/72 z y x - 1/216 y x z + + 2 3 3 4 2 2 2 3 2 + + 1/108 y x z - 1/216 y x - 1/864 x y - 1/144 y x z - 1/288 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/216 y x z - 1/108 y x z + 1/288 y x z - 1/216 y x z + + 3 2 2 4 2 3 3 4 4 3 + + 1/576 y x z + 1/864 x y - 1/108 y x z + 1/1728 y x + 1/864 y x + + 2 3 3 2 3 3 2 + + 1/216 y x - 1/1728 y x + 1/864 z y x - 1/1728 z y x + + 2 4 3 3 3 3 2 + - 1/1728 x y - 1/864 y x - 1/864 z y x - 1/216 y x z + 1/432 z y x + + 2 3 2 2 3 3 3 3 3 3 + + 1/216 z y x - 1/72 z y x - 1/432 y x z + 1/432 y x z + + 2 2 2 2 2 2 2 2 + - 1/216 y x + 1/72 y x z + 1/432 y x z - 1/144 y x z + 1/72 y x z + + 3 2 3 2 2 2 4 4 2 + + 1/864 y x z + 1/432 y x + 1/432 y x - 1/432 x y - 1/432 x y + + 4 3 4 3 4 2 + + 1/1728 x y , COEFF(-1, 1, 2) = - 1/108 x y z - 1/144 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + - 1/36 x y z + 1/36 x y z - 1/216 x y z + 1/144 z y x + + 3 4 4 4 3 2 4 3 4 3 + + 1/216 z y x + 1/54 x y z - 1/54 x y z - 1/432 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/108 x y z + 1/108 x y z - 1/54 x y z + 1/216 x y z + + 4 2 4 3 2 4 2 2 4 3 + - 1/36 x y z + 1/144 x y z - 1/36 x y z - 1/54 x y z + + 3 4 4 4 2 4 3 3 + + 1/432 x y z - 1/432 z y x + 1/108 x y z - 1/108 y x - 2/27 y x z + + 3 2 3 2 2 3 + - 1/108 z y x + 1/36 z y x + 1/27 y x z - 2/27 y x z + 1/27 y x + + 3 4 2 2 2 3 2 2 2 3 3 3 + + 1/432 x y + 1/9 y x z + 1/36 y x z + 2/27 y x z + 1/54 y x z + + 3 3 2 2 3 3 2 2 4 + - 1/144 y x z + 2/27 y x z - 1/36 y x z - 1/108 x y + + 2 3 3 4 4 3 2 3 3 2 + + 1/54 y x z - 1/432 y x - 1/108 y x - 1/108 y x + 1/108 y x + + 3 3 2 2 4 3 3 3 3 + - 1/108 z y x + 1/108 z y x + 1/108 x y + 1/432 y x + 1/432 z y x + + 2 2 3 2 2 3 3 3 + + 1/27 y x z - 1/27 z y x - 1/108 z y x + 1/36 z y x + 1/54 y x z + + 3 3 3 2 2 2 2 2 2 2 + - 1/216 y x z + 1/27 y x - 1/9 y x z - 1/27 y x z + 1/9 y x z + + 2 3 2 3 2 2 2 4 + - 1/9 y x z - 1/54 y x z - 1/27 y x - 1/27 y x + 1/108 x y + + 4 2 4 3 2 4 2 + + 1/108 x y - 1/432 x y , COEFF(0, 1, 2) = 5/96 x y z + + 2 4 4 3 4 4 2 4 3 4 3 + - 1/96 z y x - 1/144 z y x + 5/144 x y z + 1/288 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/72 x y z - 1/72 x y z + 1/36 x y z - 1/144 x y z + + 4 2 4 3 2 4 2 2 4 3 + + 1/24 x y z - 1/96 x y z + 1/24 x y z + 1/36 x y z + + 4 4 4 3 2 4 4 + + 1/288 z y x - 1/36 y z - 5/288 x y z - 1/18 y + 1/72 y + + 4 2 4 2 2 2 2 2 3 2 3 + - 1/24 y z + 1/72 y z - 5/24 y x z - 5/36 y x z - 5/36 y x z + + 3 2 2 4 4 3 3 2 + + 5/96 y x z + 1/288 y x + 1/72 y + 1/72 z y - 1/18 y + + 3 2 3 2 2 4 2 + - 5/288 y x - 5/288 z y x - 5/288 x y + 5/72 z y x - 1/18 y z + + 2 2 2 2 2 3 2 3 3 + + 5/72 y x z - 5/24 y x z - 1/18 y z + 5/144 y x z + 1/9 y z + + 2 3 3 3 3 2 2 2 2 2 2 + + 1/9 y z - 1/36 y z - 1/24 y z + 1/6 y z + 1/6 y z + 5/72 y x + + 2 4 4 2 4 3 + + 5/72 y x - 1/72 x y - 1/72 x y + 1/288 x y , COEFF(1, 1, 2) = + + 4 3 4 2 2 4 2 4 2 + 1/108 x y z + 1/144 x y z - 1/36 x y z - 1/36 x y z + + 3 4 3 2 4 4 3 4 4 4 3 + + 1/216 x y z + 1/144 z y x + 1/216 z y x - 1/54 x y z + + 2 4 3 4 3 4 4 2 + - 1/54 x y z - 1/432 x y z + 1/108 x y z + 1/108 x y z + + 4 2 3 4 3 3 4 2 4 3 2 + - 1/54 x y z + 1/216 x y z - 1/36 x y z + 1/144 x y z + + 4 2 2 4 3 3 4 4 4 + - 1/36 x y z - 1/54 x y z - 1/432 x y z - 1/432 z y x + + 2 4 3 3 3 2 3 + + 1/108 x y z + 1/108 y x + 2/27 y x z + 1/108 z y x - 1/36 z y x + + 2 2 3 3 4 2 2 2 + - 1/27 y x z + 2/27 y x z - 1/27 y x - 1/432 x y + 1/9 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/36 y x z + 2/27 y x z - 1/54 y x z + 1/144 y x z + + 2 3 3 2 2 4 2 3 3 4 4 + + 2/27 y x z - 1/36 y x z + 1/108 x y - 1/54 y x z - 1/432 y x + + 3 2 3 3 2 3 3 2 + + 1/108 y x + 1/108 y x + 1/108 y x + 1/108 z y x + 1/108 z y x + + 2 4 3 3 3 3 2 + + 1/108 x y - 1/432 y x - 1/432 z y x - 1/27 y x z - 1/27 z y x + + 2 3 2 2 3 3 3 3 3 3 + + 1/108 z y x - 1/36 z y x - 1/54 y x z + 1/216 y x z + + 2 2 2 2 2 2 2 2 + - 1/27 y x + 1/9 y x z - 1/27 y x z + 1/9 y x z + 1/9 y x z + + 3 2 3 2 2 2 4 4 2 + - 1/54 y x z - 1/27 y x - 1/27 y x + 1/108 x y + 1/108 x y + + 4 3 4 3 4 2 + - 1/432 x y , COEFF(2, 1, 2) = - 1/864 x y z - 1/288 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + + 1/576 x y z + 1/288 x y z - 1/432 x y z - 1/576 z y x + + 3 4 4 4 3 2 4 3 4 3 + - 1/864 z y x + 1/432 x y z + 1/864 x y z + 1/1728 x y z + + 4 4 2 4 2 3 4 3 3 + - 1/432 x y z - 1/432 x y z + 1/216 x y z - 1/864 x y z + + 4 2 4 3 2 4 2 2 4 3 + + 1/144 x y z - 1/576 x y z + 1/144 x y z + 1/216 x y z + + 3 4 4 4 2 4 3 + + 1/864 x y z + 1/1728 z y x - 1/1728 x y z - 1/216 y x + + 3 3 2 3 2 + - 1/108 y x z - 1/216 z y x + 1/72 z y x + 1/216 y x z + + 2 3 3 4 2 2 2 3 2 + - 1/108 y x z + 1/216 y x + 1/864 x y - 1/144 y x z + 1/288 y x z + + 2 2 3 3 3 3 3 2 2 3 + - 1/216 y x z + 1/108 y x z - 1/288 y x z - 1/216 y x z + + 3 2 2 4 2 3 3 4 4 3 + + 1/576 y x z - 1/864 x y + 1/108 y x z + 1/1728 y x - 1/864 y x + + 2 3 3 2 3 3 2 + - 1/216 y x - 1/1728 y x - 1/864 z y x - 1/1728 z y x + + 2 4 3 3 3 3 2 + - 1/1728 x y + 1/864 y x + 1/864 z y x + 1/216 y x z + 1/432 z y x + + 2 3 2 2 3 3 3 3 3 3 + - 1/216 z y x + 1/72 z y x + 1/432 y x z - 1/432 y x z + + 2 2 2 2 2 2 2 2 + + 1/216 y x - 1/72 y x z + 1/432 y x z - 1/144 y x z - 1/72 y x z + + 3 2 3 2 2 2 4 4 2 + + 1/864 y x z + 1/432 y x + 1/432 y x - 1/432 x y - 1/432 x y + + 4 3 4 3 4 2 + + 1/1728 x y , COEFF(-2, 2, 2) = - 1/3456 x y z - 1/1152 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + - 1/2304 x y z + 1/1152 x y z - 1/1728 x y z + 1/2304 z y x + + 3 4 4 4 3 2 4 3 4 3 + + 1/3456 z y x + 1/1728 x y z - 1/3456 x y z - 1/3456 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/3456 x y z + 1/6912 x y z - 1/3456 x y z + 1/1728 x y z + + 4 2 4 3 2 4 2 2 4 3 + - 1/1152 x y z + 1/1152 x y z - 1/2304 x y z - 1/1728 x y z + + 3 4 4 4 2 4 3 + + 1/3456 x y z - 1/6912 z y x + 1/6912 x y z - 1/1728 y x + + 3 3 2 3 2 + - 1/864 y x z - 1/1728 z y x + 1/576 z y x + 1/3456 y x z + + 2 3 3 4 2 2 2 + - 1/1728 y x z + 1/1728 y x + 1/3456 x y + 1/2304 y x z + + 3 2 2 2 3 3 3 3 3 2 + + 1/576 y x z + 1/3456 y x z + 1/864 y x z - 1/576 y x z + + 2 3 3 2 2 4 2 3 3 + + 1/1728 y x z - 1/1152 y x z - 1/3456 x y + 1/1728 y x z + + 4 4 3 2 3 3 2 3 + - 1/6912 y x - 1/1728 y x - 1/3456 y x + 1/3456 y x - 1/1728 z y x + + 3 2 2 4 3 3 3 3 + + 1/3456 z y x + 1/6912 x y + 1/1728 y x + 1/1728 z y x + + 2 2 3 2 2 3 + + 1/1728 y x z - 1/3456 z y x - 1/3456 z y x + 1/1152 z y x + + 3 3 3 3 3 2 2 2 + + 1/864 y x z - 1/864 y x z + 1/3456 y x - 1/1152 y x z + + 2 2 2 2 2 3 2 3 + - 1/6912 y x z + 1/1152 y x z - 1/576 y x z - 1/1728 y x z + + 2 2 2 4 4 2 4 3 + - 1/6912 y x - 1/3456 y x + 1/3456 x y + 1/6912 x y - 1/3456 x y , + + 4 3 4 2 2 4 2 + COEFF(-1, 2, 2) = 1/432 x y z + 1/576 x y z + 1/144 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + - 1/144 x y z + 1/864 x y z - 1/576 z y x - 1/864 z y x + + 4 3 2 4 3 4 3 4 + - 1/216 x y z + 1/216 x y z + 1/864 x y z - 1/864 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/1728 x y z + 1/864 x y z - 1/432 x y z + 1/288 x y z + + 4 3 2 4 2 2 4 3 3 4 + - 1/288 x y z + 1/576 x y z + 1/432 x y z - 1/1728 x y z + + 4 4 2 4 3 3 + + 1/1728 z y x - 1/432 x y z + 1/864 y x + 1/108 y x z + + 3 2 3 2 2 3 + + 1/864 z y x - 1/288 z y x - 1/432 y x z + 1/216 y x z - 1/216 y x + + 3 4 2 2 2 3 2 2 2 3 + - 1/1728 x y - 1/144 y x z - 1/72 y x z - 1/216 y x z + + 3 3 3 3 2 2 3 3 2 2 + - 1/432 y x z + 1/288 y x z - 1/108 y x z + 1/72 y x z + + 4 2 3 3 4 4 3 2 3 + + 1/432 x y - 1/864 y x z + 1/1728 y x + 1/216 y x + 1/1728 y x + + 3 2 3 3 2 2 4 3 3 + - 1/216 y x + 1/216 z y x - 1/216 z y x - 1/432 x y - 1/864 y x + + 3 3 2 2 3 + - 1/864 z y x - 1/216 y x z + 1/216 z y x + 1/1728 z y x + + 2 2 3 3 3 3 3 3 2 + - 1/576 z y x - 1/108 y x z + 1/432 y x z - 1/432 y x + + 2 2 2 2 2 2 2 + + 1/144 y x z + 1/432 y x z - 1/72 y x z + 1/72 y x z + + 3 2 3 2 2 2 4 4 2 + + 1/108 y x z + 1/432 y x + 1/216 y x - 1/864 x y - 1/1728 x y + + 4 3 2 4 2 2 4 4 + + 1/864 x y , COEFF(0, 2, 2) = - 5/384 x y z + 1/384 z y x + + 3 4 4 2 4 3 4 3 4 + + 1/576 z y x - 5/576 x y z - 1/576 x y z + 1/576 x y z + + 4 2 4 2 3 4 3 3 4 2 + + 1/1152 x y z - 1/576 x y z + 1/288 x y z - 1/192 x y z + + 4 3 2 4 2 2 4 3 4 4 + + 1/192 x y z - 1/384 x y z - 1/288 x y z - 1/1152 z y x + + 4 3 2 4 4 4 2 + + 1/144 y z + 5/1152 x y z + 1/144 y - 1/288 y + 1/96 y z + + 4 2 2 2 2 2 3 2 3 + - 1/288 y z + 5/384 y x z + 5/576 y x z + 5/288 y x z + + 3 2 2 4 4 3 3 2 + - 5/192 y x z - 1/1152 y x - 1/144 y - 1/144 z y + 1/288 y + + 3 2 3 2 2 4 2 + + 5/576 y x + 5/576 z y x + 5/1152 x y - 5/576 z y x + 1/144 y z + + 2 2 2 2 2 3 2 3 3 + - 5/1152 y x z + 5/192 y x z + 1/288 y z - 5/288 y x z - 1/72 y z + + 2 3 3 3 3 2 2 2 2 + - 1/144 y z + 1/72 y z + 1/48 y z - 1/48 y z - 1/96 y z + + 2 2 2 4 4 2 4 3 + - 5/1152 y x - 5/576 y x + 1/576 x y + 1/1152 x y - 1/576 x y , + + 4 3 4 2 2 4 2 + COEFF(1, 2, 2) = - 1/432 x y z - 1/576 x y z + 1/144 x y z + + 4 2 3 4 3 2 4 4 3 4 4 + + 1/144 x y z - 1/864 x y z - 1/576 z y x - 1/864 z y x + + 4 3 2 4 3 4 3 4 + + 1/216 x y z + 1/216 x y z + 1/864 x y z - 1/864 x y z + + 4 2 4 2 3 4 3 3 4 2 + - 1/1728 x y z + 1/864 x y z - 1/432 x y z + 1/288 x y z + + 4 3 2 4 2 2 4 3 3 4 + - 1/288 x y z + 1/576 x y z + 1/432 x y z + 1/1728 x y z + + 4 4 2 4 3 3 + + 1/1728 z y x - 1/432 x y z - 1/864 y x - 1/108 y x z + + 3 2 3 2 2 3 + - 1/864 z y x + 1/288 z y x + 1/432 y x z - 1/216 y x z + 1/216 y x + + 3 4 2 2 2 3 2 2 2 3 + + 1/1728 x y - 1/144 y x z + 1/72 y x z - 1/216 y x z + + 3 3 3 3 2 2 3 3 2 2 + + 1/432 y x z - 1/288 y x z - 1/108 y x z + 1/72 y x z + + 4 2 3 3 4 4 3 2 3 + - 1/432 x y + 1/864 y x z + 1/1728 y x - 1/216 y x - 1/1728 y x + + 3 2 3 3 2 2 4 3 3 + - 1/216 y x - 1/216 z y x - 1/216 z y x - 1/432 x y + 1/864 y x + + 3 3 2 2 3 + + 1/864 z y x + 1/216 y x z + 1/216 z y x - 1/1728 z y x + + 2 2 3 3 3 3 3 3 2 + + 1/576 z y x + 1/108 y x z - 1/432 y x z + 1/432 y x + + 2 2 2 2 2 2 2 + - 1/144 y x z + 1/432 y x z - 1/72 y x z - 1/72 y x z + + 3 2 3 2 2 2 4 4 2 + + 1/108 y x z + 1/432 y x + 1/216 y x - 1/864 x y - 1/1728 x y + + 4 3 4 3 4 2 + + 1/864 x y , COEFF(2, 2, 2) = 1/3456 x y z + 1/1152 x y z + + 2 4 2 4 2 3 4 3 2 4 4 + - 1/2304 x y z - 1/1152 x y z + 1/1728 x y z + 1/2304 z y x + + 3 4 4 4 3 2 4 3 4 3 + + 1/3456 z y x - 1/1728 x y z - 1/3456 x y z - 1/3456 x y z + + 4 4 2 4 2 3 4 3 3 + + 1/3456 x y z + 1/6912 x y z - 1/3456 x y z + 1/1728 x y z + + 4 2 4 3 2 4 2 2 4 3 + - 1/1152 x y z + 1/1152 x y z - 1/2304 x y z - 1/1728 x y z + + 3 4 4 4 2 4 3 + - 1/3456 x y z - 1/6912 z y x + 1/6912 x y z + 1/1728 y x + + 3 3 2 3 2 + + 1/864 y x z + 1/1728 z y x - 1/576 z y x - 1/3456 y x z + + 2 3 3 4 2 2 2 + + 1/1728 y x z - 1/1728 y x - 1/3456 x y + 1/2304 y x z + + 3 2 2 2 3 3 3 3 3 2 + - 1/576 y x z + 1/3456 y x z - 1/864 y x z + 1/576 y x z + + 2 3 3 2 2 4 2 3 3 + + 1/1728 y x z - 1/1152 y x z + 1/3456 x y - 1/1728 y x z + + 4 4 3 2 3 3 2 3 + - 1/6912 y x + 1/1728 y x + 1/3456 y x + 1/3456 y x + 1/1728 z y x + + 3 2 2 4 3 3 3 3 + + 1/3456 z y x + 1/6912 x y - 1/1728 y x - 1/1728 z y x + + 2 2 3 2 2 3 + - 1/1728 y x z - 1/3456 z y x + 1/3456 z y x - 1/1152 z y x + + 3 3 3 3 3 2 2 2 + - 1/864 y x z + 1/864 y x z - 1/3456 y x + 1/1152 y x z + + 2 2 2 2 2 3 2 3 + - 1/6912 y x z + 1/1152 y x z + 1/576 y x z - 1/1728 y x z + + 2 2 2 4 4 2 4 3 + - 1/6912 y x - 1/3456 y x + 1/3456 x y + 1/6912 x y - 1/3456 x y ] + +> print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dz.compute.c"); +bytes used=24844042464, alloc=64737712, time=4579.93 +bytes used=24845042836, alloc=64737712, time=4580.03 +bytes used=24846043420, alloc=64737712, time=4580.13 +bytes used=24847043964, alloc=64737712, time=4580.23 +bytes used=24848044144, alloc=64737712, time=4580.33 +bytes used=24849044320, alloc=64737712, time=4580.43 +bytes used=24850044928, alloc=64737712, time=4580.52 +bytes used=24851045100, alloc=64737712, time=4580.63 +bytes used=24852048416, alloc=64737712, time=4580.73 +bytes used=24853050172, alloc=64737712, time=4580.83 +bytes 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z + 1/72 y x z + + 3 2 2 3 4 3 3 3 2 + - 1/144 y x z - 1/216 y z - 1/108 z y - 1/144 z y x + 1/72 z y x + + 4 4 2 3 3 + + 1/432 z y + 1/144 y x z - 1/72 z y x + 1/108 y z + 1/144 y x z + + 2 2 2 2 2 2 2 + + 1/576 y x z + 1/144 y x z + 1/144 y x z - 1/288 y x z + + 2 3 2 3 3 2 3 3 3 + - 1/216 y z - 1/72 y x z - 1/108 y z + 1/216 y z + 1/108 y z + + 3 2 2 2 2 2 4 + + 1/216 y z - 1/216 y z + 1/432 y z , COEFF(0, -2, -2) = 1/96 y x z + + 3 2 4 2 4 2 2 2 4 2 4 3 + - 1/96 y x z - 1/192 x y z - 1/192 y x z - 1/96 x y z + + 4 4 2 2 4 4 3 2 4 4 + + 1/192 z y x + 5/1152 y z + 5/576 y z + 1/96 x y z - 5/576 y z + + 4 2 4 2 2 2 2 2 3 + + 5/1152 y z - 5/576 y z + 1/192 y x z + 1/96 y x z + + 2 3 3 2 2 3 4 3 3 2 + - 1/48 y x z + 1/96 y x z + 5/576 y z + 5/288 z y - 1/48 z y x + + 4 4 2 2 2 2 2 + - 5/1152 z y + 1/48 z y x - 5/288 y z - 1/96 y x z - 1/96 y x z + + 2 3 2 3 3 2 3 3 3 + + 5/576 y z + 1/48 y x z + 5/288 y z - 5/576 y z - 5/288 y z + + 3 2 2 2 2 + - 5/576 y z + 5/576 y z - 5/1152 y z , COEFF(1, -2, -2) = + + 3 4 4 2 4 3 2 4 + 1/288 y x z - 1/288 x y z - 1/144 y x z + 1/144 y x z + + 2 4 2 4 2 4 2 2 2 4 + + 1/576 y x z + 1/288 x y z + 1/576 x y z + 1/288 y x z + + 4 3 2 4 3 4 4 4 + + 1/288 x y z + 1/144 x y z - 1/576 z y x - 1/288 y x z + + 4 4 2 2 4 4 3 2 4 4 + - 1/288 z y x - 1/432 y z - 1/216 y z - 1/144 x y z + 1/216 y z + + 3 2 2 3 4 2 4 + + 1/144 y x z + 1/288 y x z - 1/288 y x z - 1/432 y z + 1/216 y z + + 2 2 2 3 2 2 2 3 2 3 + - 1/288 y x z - 1/288 y x z - 1/144 y x z + 1/72 y x z + + 3 2 2 3 4 3 3 3 2 + - 1/144 y x z - 1/216 y z - 1/108 z y + 1/144 z y x + 1/72 z y x + + 4 4 2 3 3 + + 1/432 z y - 1/144 y x z - 1/72 z y x + 1/108 y z - 1/144 y x z + + 2 2 2 2 2 2 2 + - 1/576 y x z + 1/144 y x z + 1/144 y x z + 1/288 y x z + + 2 3 2 3 3 2 3 3 3 + - 1/216 y z - 1/72 y x z - 1/108 y z + 1/216 y z + 1/108 y z + + 3 2 2 2 2 + + 1/216 y z - 1/216 y z + 1/432 y z , COEFF(2, -2, -2) = + + 3 4 4 2 4 3 2 4 + - 1/576 y x z + 1/576 x y z + 1/576 y x z - 1/576 y x z + + 2 4 2 4 2 4 2 2 2 4 + - 1/1152 y x z - 1/1152 x y z - 1/1152 x y z - 1/1152 y x z + + 4 3 2 4 3 4 4 4 + - 1/576 x y z - 1/576 x y z + 1/1152 z y x + 1/576 y x z + + 4 4 2 2 4 4 3 2 4 + + 1/1152 z y x + 1/6912 y z + 1/3456 y z + 1/576 x y z + + 4 3 2 2 3 4 2 + - 1/3456 y z - 1/288 y x z - 1/576 y x z + 1/576 y x z + 1/6912 y z + + 4 2 2 2 3 2 2 2 3 + - 1/3456 y z + 1/1152 y x z + 1/576 y x z + 1/576 y x z + + 2 3 3 2 2 3 4 3 + - 1/288 y x z + 1/576 y x z + 1/3456 y z + 1/1728 z y + + 3 3 2 4 4 2 + - 1/288 z y x - 1/288 z y x - 1/6912 z y + 1/288 y x z + 1/288 z y x + + 3 3 2 2 2 2 + - 1/1728 y z + 1/288 y x z + 1/1152 y x z - 1/576 y x z + + 2 2 2 2 3 2 3 + - 1/576 y x z - 1/576 y x z + 1/3456 y z + 1/288 y x z + + 3 2 3 3 3 3 2 2 + + 1/1728 y z - 1/3456 y z - 1/1728 y z - 1/3456 y z + 1/3456 y z + + 2 2 3 4 4 + - 1/6912 y z , COEFF(-2, -1, -2) = - 1/288 y x z + 1/144 x y z + + 2 4 3 2 4 2 4 2 4 2 + - 1/72 y x z + 1/288 y x z - 1/72 y x z + 1/288 x y z + + 4 2 2 2 4 4 3 2 4 3 + - 1/288 x y z + 1/72 y x z - 1/144 x y z + 1/144 x y z + + 4 4 4 4 4 2 2 4 4 3 + + 1/288 z y x + 1/72 y x z - 1/288 z y x - 1/432 y z - 1/864 y z + + 2 4 4 3 2 2 3 + - 1/144 x y z + 1/432 y z - 1/36 y x z - 1/36 y x z + 1/36 y x z + + 4 2 4 2 2 2 3 2 + - 1/1728 y z + 1/864 y z - 1/72 y x z + 1/288 y x z + + 2 2 3 2 3 3 2 2 3 4 + - 1/36 y x z + 1/36 y x z - 1/288 y x z - 1/1728 y z + + 3 3 3 2 4 4 + - 1/864 z y - 1/144 z y x + 1/144 z y x + 1/1728 z y + 1/36 y x z + + 2 3 3 2 2 2 2 + - 1/36 z y x + 1/216 y z + 1/144 y x z + 1/72 y x z + 1/36 y x z + + 2 2 2 2 3 2 3 3 + + 1/72 y x z - 1/72 y x z - 1/216 y z - 1/144 y x z - 1/216 y z + + 2 3 3 3 3 2 2 2 2 + + 1/216 y z + 1/864 y z + 1/1728 y z - 1/432 y z + 1/432 y z , + + 3 4 4 2 4 + COEFF(-1, -1, -2) = 1/144 y x z - 1/72 x y z + 1/18 y x z + + 3 2 4 2 4 2 4 2 4 2 + - 1/72 y x z + 1/36 y x z - 1/72 x y z + 1/144 x y z + + 2 2 4 4 3 2 4 3 4 4 + - 1/18 y x z + 1/72 x y z - 1/36 x y z - 1/144 z y x + + 4 4 4 2 2 4 4 3 2 4 + - 1/36 y x z + 1/72 z y x + 1/27 y z + 1/54 y z + 1/36 x y z + + 4 3 2 2 3 4 2 + - 1/27 y z + 1/18 y x z + 1/18 y x z - 1/18 y x z + 1/108 y z + + 4 2 2 2 3 2 2 2 3 2 3 + - 1/54 y z + 1/18 y x z - 1/144 y x z + 1/9 y x z - 1/9 y x z + + 3 2 2 3 4 3 3 3 2 + + 1/72 y x z + 1/108 y z + 1/54 z y + 1/72 z y x - 1/36 z y x + + 4 4 2 3 3 + - 1/108 z y - 1/18 y x z + 1/9 z y x - 2/27 y z - 1/72 y x z + + 2 2 2 2 2 2 2 2 + - 1/36 y x z - 1/9 y x z - 1/18 y x z + 1/36 y x z + 2/27 y z + + 3 2 3 3 2 3 3 3 3 2 + + 1/36 y x z + 2/27 y z - 2/27 y z - 1/54 y z - 1/108 y z + + 2 2 2 2 4 + + 1/27 y z - 1/27 y z , COEFF(0, -1, -2) = - 1/12 y x z + + 3 2 4 2 4 2 2 2 4 2 4 3 + + 1/48 y x z + 1/48 x y z + 1/12 y x z + 1/24 x y z + + 4 4 2 2 4 4 3 2 4 4 + - 1/48 z y x - 5/72 y z - 5/144 y z - 1/24 x y z + 5/72 y z + + 4 2 4 2 2 2 2 2 3 2 3 + - 5/288 y z + 5/144 y z - 1/12 y x z - 1/6 y x z + 1/6 y x z + + 3 2 2 3 4 3 3 2 4 4 + - 1/48 y x z - 5/288 y z - 5/144 z y + 1/24 z y x + 5/288 z y + + 2 2 2 2 2 2 + - 1/6 z y x + 5/36 y z + 1/6 y x z + 1/12 y x z - 5/36 y z + + 3 2 3 3 2 3 3 3 3 2 + - 1/24 y x z - 5/36 y z + 5/36 y z + 5/144 y z + 5/288 y z + + 2 2 2 3 4 4 + - 5/72 y z + 5/72 y z , COEFF(1, -1, -2) = - 1/144 y x z + 1/72 x y z + + 2 4 3 2 4 2 4 2 4 2 + + 1/18 y x z - 1/72 y x z - 1/36 y x z - 1/72 x y z + + 4 2 2 2 4 4 3 2 4 3 + - 1/144 x y z - 1/18 y x z - 1/72 x y z - 1/36 x y z + + 4 4 4 4 4 2 2 4 4 3 + + 1/144 z y x + 1/36 y x z + 1/72 z y x + 1/27 y z + 1/54 y z + + 2 4 4 3 2 2 3 + + 1/36 x y z - 1/27 y z - 1/18 y x z - 1/18 y x z + 1/18 y x z + + 4 2 4 2 2 2 3 2 2 2 3 + + 1/108 y z - 1/54 y z + 1/18 y x z + 1/144 y x z + 1/9 y x z + + 2 3 3 2 2 3 4 3 3 + - 1/9 y x z + 1/72 y x z + 1/108 y z + 1/54 z y - 1/72 z y x + + 3 2 4 4 2 + - 1/36 z y x - 1/108 z y + 1/18 y x z + 1/9 z y x - 2/27 y z + + 3 3 2 2 2 2 2 2 2 + + 1/72 y x z + 1/36 y x z - 1/9 y x z - 1/18 y x z - 1/36 y x z + + 2 3 2 3 3 2 3 3 3 + + 2/27 y z + 1/36 y x z + 2/27 y z - 2/27 y z - 1/54 y z + + 3 2 2 2 2 3 4 + - 1/108 y z + 1/27 y z - 1/27 y z , COEFF(2, -1, -2) = 1/288 y x z + + 4 2 4 3 2 4 2 4 + - 1/144 x y z - 1/72 y x z + 1/288 y x z + 1/72 y x z + + 2 4 2 4 2 2 2 4 4 3 + + 1/288 x y z + 1/288 x y z + 1/72 y x z + 1/144 x y z + + 2 4 3 4 4 4 4 4 2 + + 1/144 x y z - 1/288 z y x - 1/72 y x z - 1/288 z y x + + 2 4 4 3 2 4 4 3 + - 1/432 y z - 1/864 y z - 1/144 x y z + 1/432 y z + 1/36 y x z + + 2 2 3 4 2 4 2 2 2 + + 1/36 y x z - 1/36 y x z - 1/1728 y z + 1/864 y z - 1/72 y x z + + 3 2 2 2 3 2 3 3 2 2 + - 1/288 y x z - 1/36 y x z + 1/36 y x z - 1/288 y x z + + 3 4 3 3 3 2 4 4 + - 1/1728 y z - 1/864 z y + 1/144 z y x + 1/144 z y x + 1/1728 z y + + 2 3 3 2 2 + - 1/36 y x z - 1/36 z y x + 1/216 y z - 1/144 y x z - 1/72 y x z + + 2 2 2 2 2 2 3 2 3 + + 1/36 y x z + 1/72 y x z + 1/72 y x z - 1/216 y z - 1/144 y x z + + 3 2 3 3 3 3 2 2 + - 1/216 y z + 1/216 y z + 1/864 y z + 1/1728 y z - 1/432 y z + + 2 2 4 2 4 + + 1/432 y z , COEFF(-2, 0, -2) = - 1/96 x y z + 5/192 y x z + + 2 4 2 4 2 2 2 4 4 3 + - 1/192 x y z + 1/192 x y z - 5/192 y x z + 1/96 x y z + + 2 4 3 4 4 4 4 2 2 4 + - 1/96 x y z - 1/192 z y x + 1/192 z y x + 5/1152 y z + + 4 3 2 4 4 2 4 + + 1/576 y z + 1/96 x y z - 1/48 x z + 1/48 x z - 1/144 z + + 2 2 3 4 2 4 2 2 2 + + 5/96 y x z - 5/96 y x z + 1/1152 y z - 1/576 y z + 5/192 y x z + + 2 2 3 4 3 2 4 4 + + 5/96 y x z - 1/288 z + 1/144 z + 1/288 z - 1/1152 z y + + 2 2 2 2 2 2 + - 5/192 y x z - 5/96 y x z + 5/576 y z - 1/24 x z + 1/24 x z + + 2 3 2 3 3 2 2 2 + - 5/576 y z - 1/24 x z + 1/24 x z - 1/48 x z + 1/48 x z + + 2 2 4 2 4 + - 5/1152 y z , COEFF(-1, 0, -2) = 1/48 x y z - 5/96 y x z + + 2 4 2 4 2 2 2 4 4 3 + + 1/48 x y z - 1/96 x y z + 5/48 y x z - 1/48 x y z + + 2 4 3 4 4 4 4 2 2 4 4 3 + + 1/24 x y z + 1/96 z y x - 1/48 z y x - 5/72 y z - 1/36 y z + + 2 4 4 2 4 2 + - 1/24 x y z + 1/24 x z - 1/12 x z + 1/9 z - 5/48 y x z + + 2 3 4 2 4 2 2 2 2 2 3 + + 5/48 y x z - 1/72 y z + 1/36 y z - 5/48 y x z - 5/24 y x z + + 4 3 2 4 4 2 2 2 2 + + 1/18 z - 1/9 z - 1/18 z + 1/72 z y + 5/96 y x z + 5/24 y x z + + 2 2 2 3 2 3 3 + - 5/36 y z + 1/12 x z - 1/6 x z + 5/36 y z + 1/6 x z - 1/12 x z + + 2 2 2 2 2 2 4 + + 1/12 x z - 1/24 x z + 5/72 y z , COEFF(0, 0, -2) = 1/8 x z + + 2 4 2 4 4 2 2 2 3 4 2 + - 1/32 x y z - 5/192 z y + 1/4 x z + 5/16 y x z + 5/192 y z + + 25 2 3 25 2 4 4 3 2 2 2 25 2 3 + - -- y z + --- y z + 5/96 y z + 5/32 y x z + -- y z + 5/24 z + 96 192 96 + + 2 4 2 2 4 2 3 2 4 3 + + 1/16 x y z - 5/16 y x z - 5/96 y z - 1/4 x z - 1/16 x y z + + 4 2 2 2 4 25 2 2 4 4 2 + - 5/48 z + 5/48 z - 5/32 y x z - --- y z + 1/32 z y x + 192 + + 2 2 4 2 4 + - 1/8 x z - 5/24 z, COEFF(1, 0, -2) = - 1/48 x y z + 5/96 y x z + + 2 4 2 4 2 2 2 4 4 3 + + 1/48 x y z + 1/96 x y z + 5/48 y x z + 1/48 x y z + + 2 4 3 4 4 4 4 2 2 4 4 3 + + 1/24 x y z - 1/96 z y x - 1/48 z y x - 5/72 y z - 1/36 y z + + 2 4 4 2 4 2 + - 1/24 x y z - 1/24 x z - 1/12 x z + 1/9 z + 5/48 y x z + + 2 3 4 2 4 2 2 2 2 2 3 + - 5/48 y x z - 1/72 y z + 1/36 y z - 5/48 y x z - 5/24 y x z + + 4 3 2 4 4 2 2 2 2 + + 1/18 z - 1/9 z - 1/18 z + 1/72 z y - 5/96 y x z + 5/24 y x z + + 2 2 2 3 2 3 3 + - 5/36 y z - 1/12 x z - 1/6 x z + 5/36 y z + 1/6 x z + 1/12 x z + + 2 2 2 2 2 4 + + 1/12 x z + 1/24 x z + 5/72 y z , COEFF(2, 0, -2) = 1/96 x y z + + 2 4 2 4 2 4 2 2 2 4 + - 5/192 y x z - 1/192 x y z - 1/192 x y z - 5/192 y x z + + 4 3 2 4 3 4 4 4 4 2 + - 1/96 x y z - 1/96 x y z + 1/192 z y x + 1/192 z y x + + 2 4 4 3 2 4 4 2 4 + + 5/1152 y z + 1/576 y z + 1/96 x y z + 1/48 x z + 1/48 x z + + 2 2 3 4 2 4 + - 1/144 z - 5/96 y x z + 5/96 y x z + 1/1152 y z - 1/576 y z + + 2 2 2 2 2 3 4 3 2 + + 5/192 y x z + 5/96 y x z - 1/288 z + 1/144 z + 1/288 z + + 4 4 2 2 2 2 2 + - 1/1152 z y + 5/192 y x z - 5/96 y x z + 5/576 y z + 1/24 x z + + 2 2 3 2 3 3 2 2 + + 1/24 x z - 5/576 y z - 1/24 x z - 1/24 x z - 1/48 x z + + 2 2 2 3 4 + - 1/48 x z - 5/1152 y z , COEFF(-2, 1, -2) = 1/288 y x z + + 4 2 4 3 2 4 2 4 + + 1/144 x y z + 1/72 y x z - 1/288 y x z - 1/72 y x z + + 2 4 2 4 2 2 2 4 4 3 + + 1/288 x y z - 1/288 x y z + 1/72 y x z - 1/144 x y z + + 2 4 3 4 4 4 4 4 2 + + 1/144 x y z + 1/288 z y x - 1/72 y x z - 1/288 z y x + + 2 4 4 3 2 4 4 3 + - 1/432 y z - 1/864 y z - 1/144 x y z - 1/432 y z + 1/36 y x z + + 2 2 3 4 2 4 2 2 2 + - 1/36 y x z + 1/36 y x z - 1/1728 y z + 1/864 y z - 1/72 y x z + + 3 2 2 2 3 2 3 3 2 2 + - 1/288 y x z - 1/36 y x z - 1/36 y x z + 1/288 y x z + + 3 4 3 3 3 2 4 4 + + 1/1728 y z + 1/864 z y + 1/144 z y x - 1/144 z y x + 1/1728 z y + + 2 3 3 2 2 + - 1/36 y x z + 1/36 z y x - 1/216 y z - 1/144 y x z + 1/72 y x z + + 2 2 2 2 2 2 3 2 3 + + 1/36 y x z - 1/72 y x z + 1/72 y x z - 1/216 y z + 1/144 y x z + + 3 2 3 3 3 3 2 2 + + 1/216 y z + 1/216 y z - 1/864 y z - 1/1728 y z + 1/432 y z + + 2 2 3 4 4 + + 1/432 y z , COEFF(-1, 1, -2) = - 1/144 y x z - 1/72 x y z + + 2 4 3 2 4 2 4 2 4 2 + - 1/18 y x z + 1/72 y x z + 1/36 y x z - 1/72 x y z + + 4 2 2 2 4 4 3 2 4 3 + + 1/144 x y z - 1/18 y x z + 1/72 x y z - 1/36 x y z + + 4 4 4 4 4 2 2 4 4 3 + - 1/144 z y x + 1/36 y x z + 1/72 z y x + 1/27 y z + 1/54 y z + + 2 4 4 3 2 2 3 + + 1/36 x y z + 1/27 y z - 1/18 y x z + 1/18 y x z - 1/18 y x z + + 4 2 4 2 2 2 3 2 2 2 3 + + 1/108 y z - 1/54 y z + 1/18 y x z + 1/144 y x z + 1/9 y x z + + 2 3 3 2 2 3 4 3 3 + + 1/9 y x z - 1/72 y x z - 1/108 y z - 1/54 z y - 1/72 z y x + + 3 2 4 4 2 + + 1/36 z y x - 1/108 z y + 1/18 y x z - 1/9 z y x + 2/27 y z + + 3 3 2 2 2 2 2 2 2 + + 1/72 y x z - 1/36 y x z - 1/9 y x z + 1/18 y x z - 1/36 y x z + + 2 3 2 3 3 2 3 3 3 + + 2/27 y z - 1/36 y x z - 2/27 y z - 2/27 y z + 1/54 y z + + 3 2 2 2 2 2 4 + + 1/108 y z - 1/27 y z - 1/27 y z , COEFF(0, 1, -2) = 1/12 y x z + + 3 2 4 2 4 2 2 2 4 2 4 3 + - 1/48 y x z + 1/48 x y z + 1/12 y x z + 1/24 x y z + + 4 4 2 2 4 4 3 2 4 4 + - 1/48 z y x - 5/72 y z - 5/144 y z - 1/24 x y z - 5/72 y z + + 4 2 4 2 2 2 2 2 3 2 3 + - 5/288 y z + 5/144 y z - 1/12 y x z - 1/6 y x z - 1/6 y x z + + 3 2 2 3 4 3 3 2 4 4 + + 1/48 y x z + 5/288 y z + 5/144 z y - 1/24 z y x + 5/288 z y + + 2 2 2 2 2 2 + + 1/6 z y x - 5/36 y z + 1/6 y x z - 1/12 y x z - 5/36 y z + + 3 2 3 3 2 3 3 3 3 2 + + 1/24 y x z + 5/36 y z + 5/36 y z - 5/144 y z - 5/288 y z + + 2 2 2 3 4 4 + + 5/72 y z + 5/72 y z , COEFF(1, 1, -2) = 1/144 y x z + 1/72 x y z + + 2 4 3 2 4 2 4 2 4 2 + - 1/18 y x z + 1/72 y x z - 1/36 y x z - 1/72 x y z + + 4 2 2 2 4 4 3 2 4 3 + - 1/144 x y z - 1/18 y x z - 1/72 x y z - 1/36 x y z + + 4 4 4 4 4 2 2 4 4 3 + + 1/144 z y x - 1/36 y x z + 1/72 z y x + 1/27 y z + 1/54 y z + + 2 4 4 3 2 2 3 + + 1/36 x y z + 1/27 y z + 1/18 y x z - 1/18 y x z + 1/18 y x z + + 4 2 4 2 2 2 3 2 2 2 3 + + 1/108 y z - 1/54 y z + 1/18 y x z - 1/144 y x z + 1/9 y x z + + 2 3 3 2 2 3 4 3 3 + + 1/9 y x z - 1/72 y x z - 1/108 y z - 1/54 z y + 1/72 z y x + + 3 2 4 4 2 + + 1/36 z y x - 1/108 z y - 1/18 y x z - 1/9 z y x + 2/27 y z + + 3 3 2 2 2 2 2 2 2 + - 1/72 y x z + 1/36 y x z - 1/9 y x z + 1/18 y x z + 1/36 y x z + + 2 3 2 3 3 2 3 3 3 + + 2/27 y z - 1/36 y x z - 2/27 y z - 2/27 y z + 1/54 y z + + 3 2 2 2 2 3 4 + + 1/108 y z - 1/27 y z - 1/27 y z , COEFF(2, 1, -2) = - 1/288 y x z + + 4 2 4 3 2 4 2 4 + - 1/144 x y z + 1/72 y x z - 1/288 y x z + 1/72 y x z + + 2 4 2 4 2 2 2 4 4 3 + + 1/288 x y z + 1/288 x y z + 1/72 y x z + 1/144 x y z + + 2 4 3 4 4 4 4 4 2 + + 1/144 x y z - 1/288 z y x + 1/72 y x z - 1/288 z y x + + 2 4 4 3 2 4 4 3 + - 1/432 y z - 1/864 y z - 1/144 x y z - 1/432 y z - 1/36 y x z + + 2 2 3 4 2 4 2 2 2 + + 1/36 y x z - 1/36 y x z - 1/1728 y z + 1/864 y z - 1/72 y x z + + 3 2 2 2 3 2 3 3 2 2 + + 1/288 y x z - 1/36 y x z - 1/36 y x z + 1/288 y x z + + 3 4 3 3 3 2 4 4 + + 1/1728 y z + 1/864 z y - 1/144 z y x - 1/144 z y x + 1/1728 z y + + 2 3 3 2 2 + + 1/36 y x z + 1/36 z y x - 1/216 y z + 1/144 y x z - 1/72 y x z + + 2 2 2 2 2 2 3 2 3 + + 1/36 y x z - 1/72 y x z - 1/72 y x z - 1/216 y z + 1/144 y x z + + 3 2 3 3 3 3 2 2 + + 1/216 y z + 1/216 y z - 1/864 y z - 1/1728 y z + 1/432 y z + + 2 2 3 4 4 + + 1/432 y z , COEFF(-2, 2, -2) = - 1/576 y x z - 1/576 x y z + + 2 4 3 2 4 2 4 2 4 2 + - 1/576 y x z + 1/576 y x z + 1/1152 y x z - 1/1152 x y z + + 4 2 2 2 4 4 3 2 4 3 + + 1/1152 x y z - 1/1152 y x z + 1/576 x y z - 1/576 x y z + + 4 4 4 4 4 2 2 4 + - 1/1152 z y x + 1/576 y x z + 1/1152 z y x + 1/6912 y z + + 4 3 2 4 4 3 2 + + 1/3456 y z + 1/576 x y z + 1/3456 y z - 1/288 y x z + 1/576 y x z + + 2 3 4 2 4 2 2 2 + - 1/576 y x z + 1/6912 y z - 1/3456 y z + 1/1152 y x z + + 3 2 2 2 3 2 3 3 2 2 + + 1/576 y x z + 1/576 y x z + 1/288 y x z - 1/576 y x z + + 3 4 3 3 3 2 4 4 + - 1/3456 y z - 1/1728 z y - 1/288 z y x + 1/288 z y x - 1/6912 z y + + 2 3 3 2 2 + + 1/288 y x z - 1/288 z y x + 1/1728 y z + 1/288 y x z - 1/1152 y x z + + 2 2 2 2 2 2 + - 1/576 y x z + 1/576 y x z - 1/576 y x z + 1/3456 y z + + 3 2 3 3 2 3 3 3 + - 1/288 y x z - 1/1728 y z - 1/3456 y z + 1/1728 y z + + 3 2 2 2 2 + + 1/3456 y z - 1/3456 y z - 1/6912 y z , COEFF(-1, 2, -2) = + + 3 4 4 2 4 3 2 4 + 1/288 y x z + 1/288 x y z + 1/144 y x z - 1/144 y x z + + 2 4 2 4 2 4 2 2 2 4 + - 1/576 y x z + 1/288 x y z - 1/576 x y z + 1/288 y x z + + 4 3 2 4 3 4 4 4 + - 1/288 x y z + 1/144 x y z + 1/576 z y x - 1/288 y x z + + 4 4 2 2 4 4 3 2 4 4 + - 1/288 z y x - 1/432 y z - 1/216 y z - 1/144 x y z - 1/216 y z + + 3 2 2 3 4 2 4 + + 1/144 y x z - 1/288 y x z + 1/288 y x z - 1/432 y z + 1/216 y z + + 2 2 2 3 2 2 2 3 2 3 + - 1/288 y x z - 1/288 y x z - 1/144 y x z - 1/72 y x z + + 3 2 2 3 4 3 3 3 2 + + 1/144 y x z + 1/216 y z + 1/108 z y + 1/144 z y x - 1/72 z y x + + 4 4 2 3 3 + + 1/432 z y - 1/144 y x z + 1/72 z y x - 1/108 y z - 1/144 y x z + + 2 2 2 2 2 2 2 + + 1/576 y x z + 1/144 y x z - 1/144 y x z + 1/288 y x z + + 2 3 2 3 3 2 3 3 3 + - 1/216 y z + 1/72 y x z + 1/108 y z + 1/216 y z - 1/108 y z + + 3 2 2 2 2 2 4 + - 1/216 y z + 1/216 y z + 1/432 y z , COEFF(0, 2, -2) = - 1/96 y x z + + 3 2 4 2 4 2 2 2 4 2 4 3 + + 1/96 y x z - 1/192 x y z - 1/192 y x z - 1/96 x y z + + 4 4 2 2 4 4 3 2 4 4 + + 1/192 z y x + 5/1152 y z + 5/576 y z + 1/96 x y z + 5/576 y z + + 4 2 4 2 2 2 2 2 3 + + 5/1152 y z - 5/576 y z + 1/192 y x z + 1/96 y x z + + 2 3 3 2 2 3 4 3 3 2 + + 1/48 y x z - 1/96 y x z - 5/576 y z - 5/288 z y + 1/48 z y x + + 4 4 2 2 2 2 2 + - 5/1152 z y - 1/48 z y x + 5/288 y z - 1/96 y x z + 1/96 y x z + + 2 3 2 3 3 2 3 3 3 + + 5/576 y z - 1/48 y x z - 5/288 y z - 5/576 y z + 5/288 y z + + 3 2 2 2 2 + + 5/576 y z - 5/576 y z - 5/1152 y z , COEFF(1, 2, -2) = + + 3 4 4 2 4 3 2 4 + - 1/288 y x z - 1/288 x y z + 1/144 y x z - 1/144 y x z + + 2 4 2 4 2 4 2 2 2 4 + + 1/576 y x z + 1/288 x y z + 1/576 x y z + 1/288 y x z + + 4 3 2 4 3 4 4 4 + + 1/288 x y z + 1/144 x y z - 1/576 z y x + 1/288 y x z + + 4 4 2 2 4 4 3 2 4 4 + - 1/288 z y x - 1/432 y z - 1/216 y z - 1/144 x y z - 1/216 y z + + 3 2 2 3 4 2 4 + - 1/144 y x z + 1/288 y x z - 1/288 y x z - 1/432 y z + 1/216 y z + + 2 2 2 3 2 2 2 3 2 3 + - 1/288 y x z + 1/288 y x z - 1/144 y x z - 1/72 y x z + + 3 2 2 3 4 3 3 3 2 + + 1/144 y x z + 1/216 y z + 1/108 z y - 1/144 z y x - 1/72 z y x + + 4 4 2 3 3 + + 1/432 z y + 1/144 y x z + 1/72 z y x - 1/108 y z + 1/144 y x z + + 2 2 2 2 2 2 2 + - 1/576 y x z + 1/144 y x z - 1/144 y x z - 1/288 y x z + + 2 3 2 3 3 2 3 3 3 + - 1/216 y z + 1/72 y x z + 1/108 y z + 1/216 y z - 1/108 y z + + 3 2 2 2 2 3 4 + - 1/216 y z + 1/216 y z + 1/432 y z , COEFF(2, 2, -2) = 1/576 y x z + + 4 2 4 3 2 4 2 4 + + 1/576 x y z - 1/576 y x z + 1/576 y x z - 1/1152 y x z + + 2 4 2 4 2 2 2 4 4 3 + - 1/1152 x y z - 1/1152 x y z - 1/1152 y x z - 1/576 x y z + + 2 4 3 4 4 4 4 4 2 + - 1/576 x y z + 1/1152 z y x - 1/576 y x z + 1/1152 z y x + + 2 4 4 3 2 4 4 3 + + 1/6912 y z + 1/3456 y z + 1/576 x y z + 1/3456 y z + 1/288 y x z + + 2 2 3 4 2 4 + - 1/576 y x z + 1/576 y x z + 1/6912 y z - 1/3456 y z + + 2 2 2 3 2 2 2 3 2 3 + + 1/1152 y x z - 1/576 y x z + 1/576 y x z + 1/288 y x z + + 3 2 2 3 4 3 3 + - 1/576 y x z - 1/3456 y z - 1/1728 z y + 1/288 z y x + + 3 2 4 4 2 + + 1/288 z y x - 1/6912 z y - 1/288 y x z - 1/288 z y x + 1/1728 y z + + 3 3 2 2 2 2 2 2 + - 1/288 y x z + 1/1152 y x z - 1/576 y x z + 1/576 y x z + + 2 2 3 2 3 3 2 3 + + 1/576 y x z + 1/3456 y z - 1/288 y x z - 1/1728 y z - 1/3456 y z + + 3 3 3 2 2 2 2 + + 1/1728 y z + 1/3456 y z - 1/3456 y z - 1/6912 y z , + + 3 4 4 2 4 + COEFF(-2, -2, -1) = - 1/144 y x z + 1/72 x y z - 1/144 y x z + + 3 2 4 2 4 2 4 2 4 2 + + 1/144 y x z - 1/288 y x z + 1/72 x y z - 1/72 x y z + + 2 2 4 4 3 2 4 3 4 4 + + 1/288 y x z - 1/288 x y z + 1/288 x y z + 1/288 z y x + + 4 4 4 2 2 4 4 3 + + 1/144 y x z - 1/288 z y x - 1/1728 y z - 1/1728 y z + + 2 4 4 3 2 2 3 + - 1/72 x y z + 1/864 y z - 1/144 y x z - 1/72 y x z + 1/288 y x z + + 4 2 4 2 2 2 3 2 2 2 3 + - 1/432 y z + 1/432 y z - 1/72 y x z + 1/36 y x z - 1/288 y x z + + 2 3 3 2 2 3 4 3 3 + + 1/144 y x z - 1/36 y x z - 1/864 y z - 1/216 z y - 1/36 z y x + + 3 2 4 4 2 + + 1/36 z y x + 1/1728 z y + 1/36 y x z - 1/36 z y x + 1/216 y z + + 3 3 2 2 2 2 2 2 2 + + 1/144 y x z + 1/72 y x z + 1/72 y x z + 1/36 y x z - 1/36 y x z + + 2 3 2 3 3 2 3 3 3 + - 1/432 y z - 1/144 y x z - 1/864 y z + 1/1728 y z + 1/864 y z + + 3 2 2 2 2 3 4 + + 1/216 y z - 1/216 y z + 1/432 y z , COEFF(-1, -2, -1) = 1/72 y x z + + 4 2 4 3 2 4 2 4 + - 1/36 x y z + 1/36 y x z - 1/36 y x z + 1/144 y x z + + 2 4 2 4 2 2 2 4 4 3 + - 1/18 x y z + 1/36 x y z - 1/72 y x z + 1/144 x y z + + 2 4 3 4 4 4 4 4 2 + - 1/72 x y z - 1/144 z y x - 1/72 y x z + 1/72 z y x + + 2 4 4 3 2 4 4 3 + + 1/108 y z + 1/108 y z + 1/18 x y z - 1/54 y z + 1/72 y x z + + 2 2 3 4 2 4 2 2 2 + + 1/36 y x z - 1/144 y x z + 1/27 y z - 1/27 y z + 1/18 y x z + + 3 2 2 2 3 2 3 3 2 2 3 4 + - 1/18 y x z + 1/72 y x z - 1/36 y x z + 1/9 y x z + 1/54 y z + + 3 3 3 2 4 4 + + 2/27 z y + 1/18 z y x - 1/9 z y x - 1/108 z y - 1/18 y x z + + 2 3 3 2 2 2 2 + + 1/9 z y x - 2/27 y z - 1/72 y x z - 1/36 y x z - 1/18 y x z + + 2 2 2 2 3 2 3 3 + - 1/9 y x z + 1/18 y x z + 1/27 y z + 1/36 y x z + 1/54 y z + + 2 3 3 3 3 2 2 2 2 + - 1/108 y z - 1/54 y z - 2/27 y z + 2/27 y z - 1/27 y z , + + 2 4 3 2 4 2 4 2 + COEFF(0, -2, -1) = - 1/24 y x z + 1/24 y x z + 1/12 x y z + + 2 2 4 2 4 3 4 4 2 2 4 + + 1/48 y x z + 1/48 x y z - 1/48 z y x - 5/288 y z + + 4 3 2 4 4 4 2 4 + - 5/288 y z - 1/12 x y z + 5/144 y z - 5/72 y z + 5/72 y z + + 2 2 2 2 2 3 2 3 3 2 2 + - 1/12 y x z - 1/48 y x z + 1/24 y x z - 1/6 y x z + + 3 4 3 3 2 4 4 2 + - 5/144 y z - 5/36 z y + 1/6 z y x + 5/288 z y - 1/6 z y x + + 2 2 2 2 2 3 2 3 + + 5/36 y z + 1/12 y x z + 1/6 y x z - 5/72 y z - 1/24 y x z + + 3 2 3 3 3 3 2 2 + - 5/144 y z + 5/288 y z + 5/144 y z + 5/36 y z - 5/36 y z + + 2 2 3 4 4 + + 5/72 y z , COEFF(1, -2, -1) = - 1/72 y x z + 1/36 x y z + + 2 4 3 2 4 2 4 2 4 2 + + 1/36 y x z - 1/36 y x z - 1/144 y x z - 1/18 x y z + + 4 2 2 2 4 4 3 2 4 3 + - 1/36 x y z - 1/72 y x z - 1/144 x y z - 1/72 x y z + + 4 4 4 4 4 2 2 4 4 3 + + 1/144 z y x + 1/72 y x z + 1/72 z y x + 1/108 y z + 1/108 y z + + 2 4 4 3 2 2 3 + + 1/18 x y z - 1/54 y z - 1/72 y x z - 1/36 y x z + 1/144 y x z + + 4 2 4 2 2 2 3 2 2 2 3 + + 1/27 y z - 1/27 y z + 1/18 y x z + 1/18 y x z + 1/72 y x z + + 2 3 3 2 2 3 4 3 3 + - 1/36 y x z + 1/9 y x z + 1/54 y z + 2/27 z y - 1/18 z y x + + 3 2 4 4 2 + - 1/9 z y x - 1/108 z y + 1/18 y x z + 1/9 z y x - 2/27 y z + + 3 3 2 2 2 2 2 2 2 + + 1/72 y x z + 1/36 y x z - 1/18 y x z - 1/9 y x z - 1/18 y x z + + 2 3 2 3 3 2 3 3 3 + + 1/27 y z + 1/36 y x z + 1/54 y z - 1/108 y z - 1/54 y z + + 3 2 2 2 2 3 4 + - 2/27 y z + 2/27 y z - 1/27 y z , COEFF(2, -2, -1) = 1/144 y x z + + 4 2 4 3 2 4 2 4 + - 1/72 x y z - 1/144 y x z + 1/144 y x z + 1/288 y x z + + 2 4 2 4 2 2 2 4 4 3 + + 1/72 x y z + 1/72 x y z + 1/288 y x z + 1/288 x y z + + 2 4 3 4 4 4 4 4 2 + + 1/288 x y z - 1/288 z y x - 1/144 y x z - 1/288 z y x + + 2 4 4 3 2 4 4 3 + - 1/1728 y z - 1/1728 y z - 1/72 x y z + 1/864 y z + 1/144 y x z + + 2 2 3 4 2 4 2 2 2 + + 1/72 y x z - 1/288 y x z - 1/432 y z + 1/432 y z - 1/72 y x z + + 3 2 2 2 3 2 3 3 2 2 + - 1/36 y x z - 1/288 y x z + 1/144 y x z - 1/36 y x z + + 3 4 3 3 3 2 4 4 + - 1/864 y z - 1/216 z y + 1/36 z y x + 1/36 z y x + 1/1728 z y + + 2 3 3 2 2 + - 1/36 y x z - 1/36 z y x + 1/216 y z - 1/144 y x z - 1/72 y x z + + 2 2 2 2 2 2 3 2 3 + + 1/72 y x z + 1/36 y x z + 1/36 y x z - 1/432 y z - 1/144 y x z + + 3 2 3 3 3 3 2 2 + - 1/864 y z + 1/1728 y z + 1/864 y z + 1/216 y z - 1/216 y z + + 2 2 3 4 4 + + 1/432 y z , COEFF(-2, -1, -1) = 1/72 y x z - 1/18 x y z + + 2 4 3 2 4 2 4 2 4 2 + + 1/18 y x z - 1/72 y x z + 1/18 y x z - 1/18 x y z + + 4 2 2 2 4 4 3 2 4 3 + + 1/18 x y z - 1/18 y x z + 1/72 x y z - 1/72 x y z + + 4 4 4 4 4 2 2 4 4 3 + - 1/72 z y x - 1/18 y x z + 1/72 z y x + 1/108 y z + 1/432 y z + + 2 4 4 3 2 2 3 + + 1/18 x y z - 1/108 y z + 1/18 y x z + 2/9 y x z - 1/18 y x z + + 4 2 4 2 2 2 3 2 2 2 3 + + 1/108 y z - 1/108 y z + 2/9 y x z - 1/18 y x z + 1/18 y x z + + 2 3 3 2 2 3 4 3 3 + - 1/18 y x z + 1/18 y x z + 1/432 y z + 1/108 z y + 1/18 z y x + + 3 2 4 4 2 + - 1/18 z y x - 1/432 z y - 2/9 y x z + 2/9 z y x - 1/27 y z + + 3 3 2 2 2 2 2 2 2 + - 1/72 y x z - 2/9 y x z - 2/9 y x z - 2/9 y x z + 2/9 y x z + + 2 3 2 3 3 2 3 3 3 + + 1/27 y z + 1/72 y x z + 1/108 y z - 1/108 y z - 1/432 y z + + 3 2 2 2 2 3 4 + - 1/108 y z + 1/27 y z - 1/27 y z , COEFF(-1, -1, -1) = - 1/36 y x z + + 4 2 4 3 2 4 2 4 2 4 2 + + 1/9 x y z - 2/9 y x z + 1/18 y x z - 1/9 y x z + 2/9 x y z + + 4 2 2 2 4 4 3 2 4 3 4 4 + - 1/9 x y z + 2/9 y x z - 1/36 x y z + 1/18 x y z + 1/36 z y x + + 4 4 4 2 2 4 4 3 2 4 + + 1/9 y x z - 1/18 z y x - 4/27 y z - 1/27 y z - 2/9 x y z + + 4 3 2 2 3 4 2 + + 4/27 y z - 1/9 y x z - 4/9 y x z + 1/9 y x z - 4/27 y z + + 4 2 2 2 3 2 2 2 3 2 3 + + 4/27 y z - 8/9 y x z + 1/9 y x z - 2/9 y x z + 2/9 y x z + + 3 2 2 3 4 3 3 3 2 + - 2/9 y x z - 1/27 y z - 4/27 z y - 1/9 z y x + 2/9 z y x + + 4 4 2 16 3 3 + + 1/27 z y + 4/9 y x z - 8/9 z y x + -- y z + 1/36 y x z + 27 + + 2 2 2 2 2 2 2 16 2 + + 4/9 y x z + 8/9 y x z + 8/9 y x z - 4/9 y x z - -- y z + 27 + + 3 2 3 3 2 3 3 3 3 2 + - 1/18 y x z - 4/27 y z + 4/27 y z + 1/27 y z + 4/27 y z + + 16 2 16 2 2 2 4 3 2 4 + - -- y z + -- y z , COEFF(0, -1, -1) = 1/3 y x z - 1/12 y x z + 27 27 + + 2 4 2 2 2 4 2 4 3 4 4 2 2 4 + - 1/3 x y z - 1/3 y x z - 1/12 x y z + 1/12 z y x + 5/18 y z + + 4 3 2 4 4 4 2 4 + + 5/72 y z + 1/3 x y z - 5/18 y z + 5/18 y z - 5/18 y z + + 2 2 2 2 2 3 2 3 3 2 2 3 4 + + 4/3 y x z + 1/3 y x z - 1/3 y x z + 1/3 y x z + 5/72 y z + + 3 3 2 4 4 2 + + 5/18 z y - 1/3 z y x - 5/72 z y + 4/3 z y x - 10/9 y z + + 2 2 2 2 2 3 2 3 3 + - 4/3 y x z - 4/3 y x z + 10/9 y z + 1/12 y x z + 5/18 y z + + 2 3 3 3 3 2 2 2 2 + - 5/18 y z - 5/72 y z - 5/18 y z + 10/9 y z - 10/9 y z , + + 3 4 4 2 4 3 2 4 + COEFF(1, -1, -1) = 1/36 y x z - 1/9 x y z - 2/9 y x z + 1/18 y x z + + 2 4 2 4 2 4 2 2 2 4 4 3 + + 1/9 y x z + 2/9 x y z + 1/9 x y z + 2/9 y x z + 1/36 x y z + + 2 4 3 4 4 4 4 4 2 2 4 + + 1/18 x y z - 1/36 z y x - 1/9 y x z - 1/18 z y x - 4/27 y z + + 4 3 2 4 4 3 2 + - 1/27 y z - 2/9 x y z + 4/27 y z + 1/9 y x z + 4/9 y x z + + 2 3 4 2 4 2 2 2 3 2 + - 1/9 y x z - 4/27 y z + 4/27 y z - 8/9 y x z - 1/9 y x z + + 2 2 3 2 3 3 2 2 3 4 3 + - 2/9 y x z + 2/9 y x z - 2/9 y x z - 1/27 y z - 4/27 z y + + 3 3 2 4 4 2 16 + + 1/9 z y x + 2/9 z y x + 1/27 z y - 4/9 y x z - 8/9 z y x + -- y z + 27 + + 3 3 2 2 2 2 2 2 2 + - 1/36 y x z - 4/9 y x z + 8/9 y x z + 8/9 y x z + 4/9 y x z + + 16 2 3 2 3 3 2 3 3 3 + - -- y z - 1/18 y x z - 4/27 y z + 4/27 y z + 1/27 y z + 27 + + 3 2 16 2 16 2 2 3 4 + + 4/27 y z - -- y z + -- y z , COEFF(2, -1, -1) = - 1/72 y x z + 27 27 + + 4 2 4 3 2 4 2 4 + + 1/18 x y z + 1/18 y x z - 1/72 y x z - 1/18 y x z + + 2 4 2 4 2 2 2 4 4 3 + - 1/18 x y z - 1/18 x y z - 1/18 y x z - 1/72 x y z + + 2 4 3 4 4 4 4 4 2 2 4 + - 1/72 x y z + 1/72 z y x + 1/18 y x z + 1/72 z y x + 1/108 y z + + 4 3 2 4 4 3 2 + + 1/432 y z + 1/18 x y z - 1/108 y z - 1/18 y x z - 2/9 y x z + + 2 3 4 2 4 2 2 2 3 2 + + 1/18 y x z + 1/108 y z - 1/108 y z + 2/9 y x z + 1/18 y x z + + 2 2 3 2 3 3 2 2 3 4 3 + + 1/18 y x z - 1/18 y x z + 1/18 y x z + 1/432 y z + 1/108 z y + + 3 3 2 4 4 2 + - 1/18 z y x - 1/18 z y x - 1/432 z y + 2/9 y x z + 2/9 z y x + + 3 3 2 2 2 2 2 2 + - 1/27 y z + 1/72 y x z + 2/9 y x z - 2/9 y x z - 2/9 y x z + + 2 2 3 2 3 3 2 3 + - 2/9 y x z + 1/27 y z + 1/72 y x z + 1/108 y z - 1/108 y z + + 3 3 3 2 2 2 2 + - 1/432 y z - 1/108 y z + 1/27 y z - 1/27 y z , COEFF(-2, 0, -1) = + + 4 2 4 2 4 2 4 2 2 2 4 + 1/12 x y z - 5/48 y x z + 1/12 x y z - 1/12 x y z + 5/48 y x z + + 4 3 2 4 3 4 4 4 4 2 + - 1/48 x y z + 1/48 x y z + 1/48 z y x - 1/48 z y x + + 2 4 4 3 2 4 4 2 4 + - 5/288 y z - 1/288 y z - 1/12 x y z + 1/12 x z - 1/12 x z + + 2 2 3 4 2 4 + + 1/18 z - 5/12 y x z + 5/48 y x z - 1/72 y z + 1/72 y z + + 2 2 2 2 2 3 4 3 2 + - 5/12 y x z - 5/48 y x z + 1/72 z - 1/72 z - 1/18 z + + 4 4 2 2 2 2 2 + + 1/288 z y + 5/12 y x z + 5/12 y x z - 5/72 y z + 1/3 x z + + 2 2 3 2 3 3 2 2 2 + - 1/3 x z + 5/288 y z + 1/12 x z - 1/12 x z + 1/3 x z - 1/3 x z + + 2 2 4 2 4 + + 5/72 y z , COEFF(-1, 0, -1) = - 1/6 x y z + 5/24 y x z + + 2 4 2 4 2 2 2 4 4 3 + - 1/3 x y z + 1/6 x y z - 5/12 y x z + 1/24 x y z + + 2 4 3 4 4 4 4 2 2 4 4 3 + - 1/12 x y z - 1/24 z y x + 1/12 z y x + 5/18 y z + 1/18 y z + + 2 4 4 2 4 2 2 3 + + 1/3 x y z - 1/6 x z + 1/3 x z - 8/9 z + 5/6 y x z - 5/24 y x z + + 4 2 4 2 2 2 2 2 3 4 3 + + 2/9 y z - 2/9 y z + 5/3 y x z + 5/12 y x z - 2/9 z + 2/9 z + + 2 4 4 2 2 2 2 2 + + 8/9 z - 1/18 z y - 5/6 y x z - 5/3 y x z + 10/9 y z - 2/3 x z + + 2 2 3 2 3 3 2 2 2 + + 4/3 x z - 5/18 y z - 1/3 x z + 1/6 x z - 4/3 x z + 2/3 x z + + 2 2 25 2 3 2 2 2 25 2 4 + - 10/9 y z , COEFF(0, 0, -1) = -- y z - 5/3 z + 5/2 y x z - -- y z + 48 48 + + 3 2 4 3 4 2 2 2 4 4 4 + - 5/12 z + 1/8 x y z + 5/12 y z - 5/2 y x z + 5/48 z y + 5/12 z + + 2 4 2 3 2 4 2 4 2 2 2 4 + - 1/2 x y z + 1/2 x z + 1/2 x y z - 5/12 y z + 5/8 y x z + + 25 2 2 2 3 4 3 25 2 2 4 4 2 + - -- y z - 5/8 y x z - 5/48 y z + -- y z - 1/8 z y x + 5/3 z + 12 12 + + 2 2 2 2 4 4 + + 2 x z - 2 x z - 1/2 x z , COEFF(1, 0, -1) = 1/6 x y z + + 2 4 2 4 2 4 2 2 2 4 4 3 + - 5/24 y x z - 1/3 x y z - 1/6 x y z - 5/12 y x z - 1/24 x y z + + 2 4 3 4 4 4 4 2 2 4 4 3 + - 1/12 x y z + 1/24 z y x + 1/12 z y x + 5/18 y z + 1/18 y z + + 2 4 4 2 4 2 2 3 + + 1/3 x y z + 1/6 x z + 1/3 x z - 8/9 z - 5/6 y x z + 5/24 y x z + + 4 2 4 2 2 2 2 2 3 4 3 + + 2/9 y z - 2/9 y z + 5/3 y x z + 5/12 y x z - 2/9 z + 2/9 z + + 2 4 4 2 2 2 2 2 + + 8/9 z - 1/18 z y + 5/6 y x z - 5/3 y x z + 10/9 y z + 2/3 x z + + 2 2 3 2 3 3 2 2 2 + + 4/3 x z - 5/18 y z - 1/3 x z - 1/6 x z - 4/3 x z - 2/3 x z + + 2 2 4 2 4 + - 10/9 y z , COEFF(2, 0, -1) = - 1/12 x y z + 5/48 y x z + + 2 4 2 4 2 2 2 4 4 3 + + 1/12 x y z + 1/12 x y z + 5/48 y x z + 1/48 x y z + + 2 4 3 4 4 4 4 2 2 4 4 3 + + 1/48 x y z - 1/48 z y x - 1/48 z y x - 5/288 y z - 1/288 y z + + 2 4 4 2 4 2 + - 1/12 x y z - 1/12 x z - 1/12 x z + 1/18 z + 5/12 y x z + + 2 3 4 2 4 2 2 2 2 2 3 + - 5/48 y x z - 1/72 y z + 1/72 y z - 5/12 y x z - 5/48 y x z + + 4 3 2 4 4 2 2 2 2 + + 1/72 z - 1/72 z - 1/18 z + 1/288 z y - 5/12 y x z + 5/12 y x z + + 2 2 2 3 2 3 3 + - 5/72 y z - 1/3 x z - 1/3 x z + 5/288 y z + 1/12 x z + 1/12 x z + + 2 2 2 2 2 3 4 + + 1/3 x z + 1/3 x z + 5/72 y z , COEFF(-2, 1, -1) = - 1/72 y x z + + 4 2 4 3 2 4 2 4 + - 1/18 x y z - 1/18 y x z + 1/72 y x z + 1/18 y x z + + 2 4 2 4 2 2 2 4 4 3 + - 1/18 x y z + 1/18 x y z - 1/18 y x z + 1/72 x y z + + 2 4 3 4 4 4 4 4 2 2 4 + - 1/72 x y z - 1/72 z y x + 1/18 y x z + 1/72 z y x + 1/108 y z + + 4 3 2 4 4 3 2 + + 1/432 y z + 1/18 x y z + 1/108 y z - 1/18 y x z + 2/9 y x z + + 2 3 4 2 4 2 2 2 3 2 + - 1/18 y x z + 1/108 y z - 1/108 y z + 2/9 y x z + 1/18 y x z + + 2 2 3 2 3 3 2 2 3 4 3 + + 1/18 y x z + 1/18 y x z - 1/18 y x z - 1/432 y z - 1/108 z y + + 3 3 2 4 4 2 + - 1/18 z y x + 1/18 z y x - 1/432 z y + 2/9 y x z - 2/9 z y x + + 3 3 2 2 2 2 2 2 + + 1/27 y z + 1/72 y x z - 2/9 y x z - 2/9 y x z + 2/9 y x z + + 2 2 3 2 3 3 2 3 + - 2/9 y x z + 1/27 y z - 1/72 y x z - 1/108 y z - 1/108 y z + + 3 3 3 2 2 2 2 + + 1/432 y z + 1/108 y z - 1/27 y z - 1/27 y z , COEFF(-1, 1, -1) = + + 3 4 4 2 4 3 2 4 2 4 + 1/36 y x z + 1/9 x y z + 2/9 y x z - 1/18 y x z - 1/9 y x z + + 2 4 2 4 2 2 2 4 4 3 2 4 3 + + 2/9 x y z - 1/9 x y z + 2/9 y x z - 1/36 x y z + 1/18 x y z + + 4 4 4 4 4 2 2 4 4 3 + + 1/36 z y x - 1/9 y x z - 1/18 z y x - 4/27 y z - 1/27 y z + + 2 4 4 3 2 2 3 + - 2/9 x y z - 4/27 y z + 1/9 y x z - 4/9 y x z + 1/9 y x z + + 4 2 4 2 2 2 3 2 2 2 3 + - 4/27 y z + 4/27 y z - 8/9 y x z - 1/9 y x z - 2/9 y x z + + 2 3 3 2 2 3 4 3 3 + - 2/9 y x z + 2/9 y x z + 1/27 y z + 4/27 z y + 1/9 z y x + + 3 2 4 4 2 16 + - 2/9 z y x + 1/27 z y - 4/9 y x z + 8/9 z y x - -- y z + 27 + + 3 3 2 2 2 2 2 2 2 + - 1/36 y x z + 4/9 y x z + 8/9 y x z - 8/9 y x z + 4/9 y x z + + 16 2 3 2 3 3 2 3 3 3 + - -- y z + 1/18 y x z + 4/27 y z + 4/27 y z - 1/27 y z + 27 + + 3 2 16 2 16 2 2 2 4 + - 4/27 y z + -- y z + -- y z , COEFF(0, 1, -1) = - 1/3 y x z + 27 27 + + 3 2 4 2 4 2 2 2 4 2 4 3 + + 1/12 y x z - 1/3 x y z - 1/3 y x z - 1/12 x y z + + 4 4 2 2 4 4 3 2 4 4 + + 1/12 z y x + 5/18 y z + 5/72 y z + 1/3 x y z + 5/18 y z + + 4 2 4 2 2 2 2 2 3 2 3 + + 5/18 y z - 5/18 y z + 4/3 y x z + 1/3 y x z + 1/3 y x z + + 3 2 2 3 4 3 3 2 4 4 + - 1/3 y x z - 5/72 y z - 5/18 z y + 1/3 z y x - 5/72 z y + + 2 2 2 2 2 2 + - 4/3 z y x + 10/9 y z - 4/3 y x z + 4/3 y x z + 10/9 y z + + 3 2 3 3 2 3 3 3 3 2 + - 1/12 y x z - 5/18 y z - 5/18 y z + 5/72 y z + 5/18 y z + + 2 2 2 3 4 4 + - 10/9 y z - 10/9 y z , COEFF(1, 1, -1) = - 1/36 y x z - 1/9 x y z + + 2 4 3 2 4 2 4 2 4 2 4 2 + + 2/9 y x z - 1/18 y x z + 1/9 y x z + 2/9 x y z + 1/9 x y z + + 2 2 4 4 3 2 4 3 4 4 4 + + 2/9 y x z + 1/36 x y z + 1/18 x y z - 1/36 z y x + 1/9 y x z + + 4 4 2 2 4 4 3 2 4 4 + - 1/18 z y x - 4/27 y z - 1/27 y z - 2/9 x y z - 4/27 y z + + 3 2 2 3 4 2 4 + - 1/9 y x z + 4/9 y x z - 1/9 y x z - 4/27 y z + 4/27 y z + + 2 2 2 3 2 2 2 3 2 3 3 2 2 + - 8/9 y x z + 1/9 y x z - 2/9 y x z - 2/9 y x z + 2/9 y x z + + 3 4 3 3 3 2 4 4 + + 1/27 y z + 4/27 z y - 1/9 z y x - 2/9 z y x + 1/27 z y + + 2 16 3 3 2 2 + + 4/9 y x z + 8/9 z y x - -- y z + 1/36 y x z - 4/9 y x z + 27 + + 2 2 2 2 2 16 2 3 2 3 + + 8/9 y x z - 8/9 y x z - 4/9 y x z - -- y z + 1/18 y x z + 27 + + 3 2 3 3 3 3 2 16 2 16 2 2 + + 4/27 y z + 4/27 y z - 1/27 y z - 4/27 y z + -- y z + -- y z , + 27 27 + + 3 4 4 2 4 3 2 4 + COEFF(2, 1, -1) = 1/72 y x z + 1/18 x y z - 1/18 y x z + 1/72 y x z + + 2 4 2 4 2 4 2 2 2 4 + - 1/18 y x z - 1/18 x y z - 1/18 x y z - 1/18 y x z + + 4 3 2 4 3 4 4 4 + - 1/72 x y z - 1/72 x y z + 1/72 z y x - 1/18 y x z + + 4 4 2 2 4 4 3 2 4 4 + + 1/72 z y x + 1/108 y z + 1/432 y z + 1/18 x y z + 1/108 y z + + 3 2 2 3 4 2 4 + + 1/18 y x z - 2/9 y x z + 1/18 y x z + 1/108 y z - 1/108 y z + + 2 2 2 3 2 2 2 3 2 3 + + 2/9 y x z - 1/18 y x z + 1/18 y x z + 1/18 y x z + + 3 2 2 3 4 3 3 3 2 + - 1/18 y x z - 1/432 y z - 1/108 z y + 1/18 z y x + 1/18 z y x + + 4 4 2 3 3 + - 1/432 z y - 2/9 y x z - 2/9 z y x + 1/27 y z - 1/72 y x z + + 2 2 2 2 2 2 2 2 + + 2/9 y x z - 2/9 y x z + 2/9 y x z + 2/9 y x z + 1/27 y z + + 3 2 3 3 2 3 3 3 3 2 + - 1/72 y x z - 1/108 y z - 1/108 y z + 1/432 y z + 1/108 y z + + 2 2 2 3 4 4 + - 1/27 y z - 1/27 y z , COEFF(-2, 2, -1) = 1/144 y x z + 1/72 x y z + + 2 4 3 2 4 2 4 2 4 2 + + 1/144 y x z - 1/144 y x z - 1/288 y x z + 1/72 x y z + + 4 2 2 2 4 4 3 2 4 3 + - 1/72 x y z + 1/288 y x z - 1/288 x y z + 1/288 x y z + + 4 4 4 4 4 2 2 4 + + 1/288 z y x - 1/144 y x z - 1/288 z y x - 1/1728 y z + + 4 3 2 4 4 3 2 + - 1/1728 y z - 1/72 x y z - 1/864 y z + 1/144 y x z - 1/72 y x z + + 2 3 4 2 4 2 2 2 3 2 + + 1/288 y x z - 1/432 y z + 1/432 y z - 1/72 y x z - 1/36 y x z + + 2 2 3 2 3 3 2 2 3 4 + - 1/288 y x z - 1/144 y x z + 1/36 y x z + 1/864 y z + + 3 3 3 2 4 4 + + 1/216 z y + 1/36 z y x - 1/36 z y x + 1/1728 z y - 1/36 y x z + + 2 3 3 2 2 2 2 + + 1/36 z y x - 1/216 y z - 1/144 y x z + 1/72 y x z + 1/72 y x z + + 2 2 2 2 3 2 3 3 + - 1/36 y x z + 1/36 y x z - 1/432 y z + 1/144 y x z + 1/864 y z + + 2 3 3 3 3 2 2 2 2 + + 1/1728 y z - 1/864 y z - 1/216 y z + 1/216 y z + 1/432 y z , + + 3 4 4 2 4 + COEFF(-1, 2, -1) = - 1/72 y x z - 1/36 x y z - 1/36 y x z + + 3 2 4 2 4 2 4 2 4 2 + + 1/36 y x z + 1/144 y x z - 1/18 x y z + 1/36 x y z + + 2 2 4 4 3 2 4 3 4 4 + - 1/72 y x z + 1/144 x y z - 1/72 x y z - 1/144 z y x + + 4 4 4 2 2 4 4 3 2 4 + + 1/72 y x z + 1/72 z y x + 1/108 y z + 1/108 y z + 1/18 x y z + + 4 3 2 2 3 4 2 + + 1/54 y z - 1/72 y x z + 1/36 y x z - 1/144 y x z + 1/27 y z + + 4 2 2 2 3 2 2 2 3 2 3 + - 1/27 y z + 1/18 y x z + 1/18 y x z + 1/72 y x z + 1/36 y x z + + 3 2 2 3 4 3 3 3 2 + - 1/9 y x z - 1/54 y z - 2/27 z y - 1/18 z y x + 1/9 z y x + + 4 4 2 3 3 + - 1/108 z y + 1/18 y x z - 1/9 z y x + 2/27 y z + 1/72 y x z + + 2 2 2 2 2 2 2 2 + - 1/36 y x z - 1/18 y x z + 1/9 y x z - 1/18 y x z + 1/27 y z + + 3 2 3 3 2 3 3 3 3 2 + - 1/36 y x z - 1/54 y z - 1/108 y z + 1/54 y z + 2/27 y z + + 2 2 2 2 4 3 2 4 + - 2/27 y z - 1/27 y z , COEFF(0, 2, -1) = 1/24 y x z - 1/24 y x z + + 2 4 2 2 2 4 2 4 3 4 4 2 + + 1/12 x y z + 1/48 y x z + 1/48 x y z - 1/48 z y x + + 2 4 4 3 2 4 4 4 2 + - 5/288 y z - 5/288 y z - 1/12 x y z - 5/144 y z - 5/72 y z + + 4 2 2 2 2 2 3 2 3 3 2 2 + + 5/72 y z - 1/12 y x z - 1/48 y x z - 1/24 y x z + 1/6 y x z + + 3 4 3 3 2 4 4 2 + + 5/144 y z + 5/36 z y - 1/6 z y x + 5/288 z y + 1/6 z y x + + 2 2 2 2 2 3 2 3 + - 5/36 y z + 1/12 y x z - 1/6 y x z - 5/72 y z + 1/24 y x z + + 3 2 3 3 3 3 2 2 + + 5/144 y z + 5/288 y z - 5/144 y z - 5/36 y z + 5/36 y z + + 2 2 3 4 4 2 4 + + 5/72 y z , COEFF(1, 2, -1) = 1/72 y x z + 1/36 x y z - 1/36 y x z + + 3 2 4 2 4 2 4 2 4 2 + + 1/36 y x z - 1/144 y x z - 1/18 x y z - 1/36 x y z + + 2 2 4 4 3 2 4 3 4 4 + - 1/72 y x z - 1/144 x y z - 1/72 x y z + 1/144 z y x + + 4 4 4 2 2 4 4 3 2 4 + - 1/72 y x z + 1/72 z y x + 1/108 y z + 1/108 y z + 1/18 x y z + + 4 3 2 2 3 4 2 + + 1/54 y z + 1/72 y x z - 1/36 y x z + 1/144 y x z + 1/27 y z + + 4 2 2 2 3 2 2 2 3 2 3 + - 1/27 y z + 1/18 y x z - 1/18 y x z + 1/72 y x z + 1/36 y x z + + 3 2 2 3 4 3 3 3 2 + - 1/9 y x z - 1/54 y z - 2/27 z y + 1/18 z y x + 1/9 z y x + + 4 4 2 3 3 + - 1/108 z y - 1/18 y x z - 1/9 z y x + 2/27 y z - 1/72 y x z + + 2 2 2 2 2 2 2 2 + + 1/36 y x z - 1/18 y x z + 1/9 y x z + 1/18 y x z + 1/27 y z + + 3 2 3 3 2 3 3 3 3 2 + - 1/36 y x z - 1/54 y z - 1/108 y z + 1/54 y z + 2/27 y z + + 2 2 2 3 4 4 + - 2/27 y z - 1/27 y z , COEFF(2, 2, -1) = - 1/144 y x z - 1/72 x y z + + 2 4 3 2 4 2 4 2 4 2 + + 1/144 y x z - 1/144 y x z + 1/288 y x z + 1/72 x y z + + 4 2 2 2 4 4 3 2 4 3 + + 1/72 x y z + 1/288 y x z + 1/288 x y z + 1/288 x y z + + 4 4 4 4 4 2 2 4 + - 1/288 z y x + 1/144 y x z - 1/288 z y x - 1/1728 y z + + 4 3 2 4 4 3 2 + - 1/1728 y z - 1/72 x y z - 1/864 y z - 1/144 y x z + 1/72 y x z + + 2 3 4 2 4 2 2 2 3 2 + - 1/288 y x z - 1/432 y z + 1/432 y z - 1/72 y x z + 1/36 y x z + + 2 2 3 2 3 3 2 2 3 4 + - 1/288 y x z - 1/144 y x z + 1/36 y x z + 1/864 y z + + 3 3 3 2 4 4 + + 1/216 z y - 1/36 z y x - 1/36 z y x + 1/1728 z y + 1/36 y x z + + 2 3 3 2 2 2 2 + + 1/36 z y x - 1/216 y z + 1/144 y x z - 1/72 y x z + 1/72 y x z + + 2 2 2 2 3 2 3 3 + - 1/36 y x z - 1/36 y x z - 1/432 y z + 1/144 y x z + 1/864 y z + + 2 3 3 3 3 2 2 2 2 + + 1/1728 y z - 1/864 y z - 1/216 y z + 1/216 y z + 1/432 y z , + + 3 4 2 4 3 2 4 + COEFF(-2, -2, 0) = 1/96 y x z + 1/96 y x z - 1/96 y x z + + 2 4 2 4 2 4 2 2 2 4 + + 1/192 y x z - 5/192 x y z + 5/192 x y z - 1/192 y x z + + 4 4 4 4 4 2 2 4 4 + - 1/192 z y x - 1/96 y x z + 1/192 z y x + 1/1152 y z - 1/576 y z + + 4 4 2 2 2 2 + - 1/144 y - 1/24 y x - 1/288 y + 5/1152 y z + 5/192 y x z + + 3 2 3 2 2 4 3 3 + - 5/96 y x z + 5/96 y x z - 1/48 x y + 1/144 y + 1/24 y x + + 3 4 2 3 2 4 4 2 4 + + 1/576 y z + 1/288 y - 1/24 y x - 1/1152 z y + 1/48 x y + + 2 2 2 2 2 2 3 2 + + 1/48 y x - 5/192 y x z - 5/96 y x z + 5/96 y x z - 5/576 y z + + 2 2 2 2 2 2 + + 5/576 y z - 5/1152 y z - 1/48 y x + 1/24 y x , COEFF(-1, -2, 0) = + + 3 4 2 4 3 2 4 2 4 + - 1/48 y x z - 1/24 y x z + 1/24 y x z - 1/96 y x z + + 2 4 2 4 2 2 2 4 4 4 + + 5/48 x y z - 5/96 x y z + 1/48 y x z + 1/96 z y x + + 4 4 4 2 2 4 4 + + 1/48 y x z - 1/48 z y x - 1/72 y z + 1/36 y z + 1/9 y + 1/12 y x + + 4 4 2 2 2 2 3 2 3 2 2 + + 1/18 y - 5/72 y z - 5/48 y x z + 5/48 y x z - 5/24 y x z + + 4 3 3 3 4 2 3 2 + + 1/24 x y - 1/9 y - 1/12 y x - 1/36 y z - 1/18 y + 1/6 y x + + 4 4 2 4 2 2 2 2 2 + + 1/72 z y - 1/12 x y - 1/24 y x + 5/96 y x z + 5/24 y x z + + 2 3 2 2 2 2 2 2 + - 5/48 y x z + 5/36 y z - 5/36 y z + 5/72 y z + 1/12 y x + + 2 3 4 2 4 2 4 + - 1/6 y x , COEFF(0, -2, 0) = 5/96 y z + 1/16 y x z + 5/192 y z + + 4 2 4 2 2 4 3 2 4 4 + - 5/48 y - 5/32 x y z + 1/8 x y - 1/16 y x z - 5/96 y z + + 4 4 2 25 4 2 2 2 25 2 2 3 2 2 + + 1/32 z y x + --- y z - 5/16 y x z - --- y z + 5/16 y x z + 192 192 + + 2 3 3 2 4 4 2 2 4 25 2 + + 5/48 y + 5/24 y - 1/4 y x - 5/192 z y - 1/32 y x z + -- y z + 96 + + 2 2 2 2 2 2 25 3 2 + - 5/24 y - 1/8 y x + 1/4 y x + 5/32 y x z - -- y z , + 96 + + 3 4 2 4 3 2 4 + COEFF(1, -2, 0) = 1/48 y x z - 1/24 y x z + 1/24 y x z + + 2 4 2 4 2 4 2 2 2 4 + + 1/96 y x z + 5/48 x y z + 5/96 x y z + 1/48 y x z + + 4 4 4 4 4 2 2 4 4 + - 1/96 z y x - 1/48 y x z - 1/48 z y x - 1/72 y z + 1/36 y z + + 4 4 2 2 2 2 3 2 + + 1/9 y - 1/12 y x + 1/18 y - 5/72 y z - 5/48 y x z - 5/48 y x z + + 3 2 2 4 3 3 3 4 2 + - 5/24 y x z - 1/24 x y - 1/9 y + 1/12 y x - 1/36 y z - 1/18 y + + 3 2 4 4 2 4 2 2 2 + + 1/6 y x + 1/72 z y - 1/12 x y + 1/24 y x - 5/96 y x z + + 2 2 2 3 2 2 2 2 + + 5/24 y x z + 5/48 y x z + 5/36 y z - 5/36 y z + 5/72 y z + + 2 2 2 3 4 2 4 + + 1/12 y x - 1/6 y x , COEFF(2, -2, 0) = - 1/96 y x z + 1/96 y x z + + 3 2 4 2 4 2 4 2 4 2 + - 1/96 y x z - 1/192 y x z - 5/192 x y z - 5/192 x y z + + 2 2 4 4 4 4 4 4 2 + - 1/192 y x z + 1/192 z y x + 1/96 y x z + 1/192 z y x + + 2 4 4 4 4 2 + + 1/1152 y z - 1/576 y z - 1/144 y + 1/24 y x - 1/288 y + 5/1152 y z + + 2 2 2 3 2 3 2 2 4 3 + + 5/192 y x z + 5/96 y x z + 5/96 y x z + 1/48 x y + 1/144 y + + 3 3 4 2 3 2 4 4 + - 1/24 y x + 1/576 y z + 1/288 y - 1/24 y x - 1/1152 z y + + 2 4 2 2 2 2 2 2 + + 1/48 x y - 1/48 y x + 5/192 y x z - 5/96 y x z - 5/96 y x z + + 3 2 2 2 2 2 2 2 + - 5/576 y z + 5/576 y z - 5/1152 y z - 1/48 y x + 1/24 y x , + + 3 4 2 4 3 2 4 + COEFF(-2, -1, 0) = - 1/48 y x z - 1/12 y x z + 1/48 y x z + + 2 4 2 4 2 4 2 2 2 4 + - 1/12 y x z + 5/48 x y z - 5/48 x y z + 1/12 y x z + + 4 4 4 4 4 2 2 4 4 + + 1/48 z y x + 1/12 y x z - 1/48 z y x - 1/72 y z + 1/72 y z + + 4 4 2 2 2 2 3 2 + + 1/18 y + 1/3 y x + 1/72 y - 5/288 y z - 5/12 y x z + 5/48 y x z + + 3 2 2 4 3 3 3 4 2 + - 5/48 y x z + 1/12 x y - 1/72 y - 1/12 y x - 1/288 y z - 1/18 y + + 3 2 4 4 2 4 2 2 2 + + 1/12 y x + 1/288 z y - 1/12 x y - 1/3 y x + 5/12 y x z + + 2 2 2 3 2 2 2 2 + + 5/12 y x z - 5/12 y x z + 5/288 y z - 5/72 y z + 5/72 y z + + 2 2 2 3 4 2 4 + + 1/3 y x - 1/3 y x , COEFF(-1, -1, 0) = 1/24 y x z + 1/3 y x z + + 3 2 4 2 4 2 4 2 4 2 + - 1/12 y x z + 1/6 y x z - 5/12 x y z + 5/24 x y z + + 2 2 4 4 4 4 4 4 2 2 4 + - 1/3 y x z - 1/24 z y x - 1/6 y x z + 1/12 z y x + 2/9 y z + + 4 4 4 2 2 2 2 + - 2/9 y z - 8/9 y - 2/3 y x - 2/9 y + 5/18 y z + 5/3 y x z + + 3 2 3 2 2 4 3 3 3 4 + - 5/24 y x z + 5/12 y x z - 1/6 x y + 2/9 y + 1/6 y x + 1/18 y z + + 2 3 2 4 4 2 4 2 2 2 + + 8/9 y - 1/3 y x - 1/18 z y + 1/3 x y + 2/3 y x - 5/6 y x z + + 2 2 2 3 2 2 2 2 + - 5/3 y x z + 5/6 y x z - 5/18 y z + 10/9 y z - 10/9 y z + + 2 2 2 2 4 2 + - 4/3 y x + 4/3 y x , COEFF(0, -1, 0) = - 5/12 y z - 2 y x + + 2 2 2 2 4 2 4 2 4 4 2 + + 5/2 y x z + 1/2 y x z + 5/3 y + 5/8 x y z - 1/8 z y x + + 2 4 4 4 25 4 2 4 4 3 4 + - 1/2 x y + 5/12 y z + 5/12 y - -- y z + 5/48 z y - 5/48 y z + 48 + + 2 4 3 2 3 2 2 2 2 25 3 2 2 + - 1/2 y x z + 1/2 y x - 5/8 y x z + 2 y x + -- y z - 5/3 y + 48 + + 3 2 4 25 2 2 2 2 25 2 2 3 + + 1/8 y x z - -- y z - 5/2 y x z + -- y z - 5/12 y , + 12 12 + + 3 4 2 4 3 2 4 + COEFF(1, -1, 0) = - 1/24 y x z + 1/3 y x z - 1/12 y x z + + 2 4 2 4 2 4 2 2 2 4 4 4 + - 1/6 y x z - 5/12 x y z - 5/24 x y z - 1/3 y x z + 1/24 z y x + + 4 4 4 2 2 4 4 + + 1/6 y x z + 1/12 z y x + 2/9 y z - 2/9 y z - 8/9 y + 2/3 y x + + 4 4 2 2 2 2 3 2 3 2 2 + - 2/9 y + 5/18 y z + 5/3 y x z + 5/24 y x z + 5/12 y x z + + 4 3 3 3 4 2 3 2 + + 1/6 x y + 2/9 y - 1/6 y x + 1/18 y z + 8/9 y - 1/3 y x + + 4 4 2 4 2 2 2 2 2 + - 1/18 z y + 1/3 x y - 2/3 y x + 5/6 y x z - 5/3 y x z + + 2 3 2 2 2 2 2 2 2 + - 5/6 y x z - 5/18 y z + 10/9 y z - 10/9 y z - 4/3 y x + 4/3 y x , + + 3 4 2 4 3 2 4 + COEFF(2, -1, 0) = 1/48 y x z - 1/12 y x z + 1/48 y x z + + 2 4 2 4 2 4 2 2 2 4 + + 1/12 y x z + 5/48 x y z + 5/48 x y z + 1/12 y x z + + 4 4 4 4 4 2 2 4 4 + - 1/48 z y x - 1/12 y x z - 1/48 z y x - 1/72 y z + 1/72 y z + + 4 4 2 2 2 2 3 2 + + 1/18 y - 1/3 y x + 1/72 y - 5/288 y z - 5/12 y x z - 5/48 y x z + + 3 2 2 4 3 3 3 4 2 + - 5/48 y x z - 1/12 x y - 1/72 y + 1/12 y x - 1/288 y z - 1/18 y + + 3 2 4 4 2 4 2 2 2 + + 1/12 y x + 1/288 z y - 1/12 x y + 1/3 y x - 5/12 y x z + + 2 2 2 3 2 2 2 2 + + 5/12 y x z + 5/12 y x z + 5/288 y z - 5/72 y z + 5/72 y z + + 2 2 2 2 4 2 4 2 + + 1/3 y x - 1/3 y x , COEFF(-2, 0, 0) = 5/32 y x z - 5/32 x y z + + 4 2 2 2 4 4 4 4 4 2 + + 5/32 x y z - 5/32 y x z - 1/32 z y x + 1/32 z y x + + 2 4 4 2 4 4 4 2 + + 5/192 y z - 1/2 x - 1/8 x z + 1/8 x z - 1/48 y + 5/192 y z + + 25 2 2 2 4 4 2 2 + + -- y x z - 1/48 z - 1/8 x y - 1/12 + 5/48 y + 5/48 z + 32 + + 4 4 2 4 2 2 25 2 2 2 2 + - 1/192 z y + 1/8 x y + 1/2 x + 5/8 y x - -- y x z - 5/8 x z + 32 + + 2 25 2 2 2 2 2 4 + + 5/8 x z - --- y z - 5/8 y x , COEFF(-1, 0, 0) = - 5/16 y x z + 192 + + 2 4 2 4 2 2 2 4 4 4 4 4 2 + + 5/8 x y z - 5/16 x y z + 5/8 y x z + 1/16 z y x - 1/8 z y x + + 2 4 4 2 4 4 4 2 + - 5/12 y z + x + 1/4 x z - 1/2 x z + 1/3 y - 5/12 y z + + 2 2 2 4 4 2 2 4 4 + - 25/8 y x z + 1/3 z + 1/4 x y - 5/3 y - 5/3 z + 1/12 z y + + 2 4 2 2 25 2 2 2 2 2 + - 1/2 x y - 2 x - 5/4 y x + -- y x z + 4/3 + 5/2 x z - 5/4 x z + 16 + + 25 2 2 2 2 2 4 4 4 + + -- y z + 5/2 y x , COEFF(0, 0, 0) = 25/8 z - 5/32 z y - 5/8 z + 12 + + 4 15 2 4 2 15 2 2 4 2 2 125 2 2 + - 5/8 y - -- x y z - -- y x z - 15/4 x z - --- y z + 16 16 32 + + 75 2 2 2 25 4 2 2 25 2 4 2 2 + + -- y x z + -- y z + 25/8 y - 5/2 + -- y z - 15/4 y x + 16 32 32 + + 4 4 2 2 4 2 4 2 + + 3/16 z y x + 3/4 x z + 3/4 x y + 3 x , COEFF(1, 0, 0) = + + 2 4 2 4 2 4 2 2 2 4 4 4 + 5/16 y x z + 5/8 x y z + 5/16 x y z + 5/8 y x z - 1/16 z y x + + 4 4 2 2 4 4 2 4 4 + - 1/8 z y x - 5/12 y z - x - 1/4 x z - 1/2 x z + 1/3 y + + 4 2 2 2 2 4 4 2 2 + - 5/12 y z - 25/8 y x z + 1/3 z - 1/4 x y - 5/3 y - 5/3 z + + 4 4 2 4 2 2 25 2 2 2 2 + + 1/12 z y - 1/2 x y - 2 x + 5/4 y x - -- y x z + 4/3 + 5/2 x z + 16 + + 2 25 2 2 2 2 2 4 + + 5/4 x z + -- y z + 5/2 y x , COEFF(2, 0, 0) = - 5/32 y x z + 12 + + 2 4 2 4 2 2 2 4 4 4 + - 5/32 x y z - 5/32 x y z - 5/32 y x z + 1/32 z y x + + 4 4 2 2 4 4 2 4 4 + + 1/32 z y x + 5/192 y z + 1/2 x + 1/8 x z + 1/8 x z - 1/48 y + + 4 2 25 2 2 2 4 4 2 + + 5/192 y z + -- y x z - 1/48 z + 1/8 x y - 1/12 + 5/48 y + 32 + + 2 4 4 2 4 2 2 25 2 2 + + 5/48 z - 1/192 z y + 1/8 x y + 1/2 x - 5/8 y x + -- y x z + 32 + + 2 2 2 25 2 2 2 2 + - 5/8 x z - 5/8 x z - --- y z - 5/8 y x , COEFF(-2, 1, 0) = + 192 + + 3 4 2 4 3 2 4 2 4 2 4 2 + 1/48 y x z + 1/12 y x z - 1/48 y x z - 1/12 y x z + 5/48 x y z + + 4 2 2 2 4 4 4 4 + - 5/48 x y z + 1/12 y x z + 1/48 z y x - 1/12 y x z + + 4 4 2 2 4 4 4 + - 1/48 z y x - 1/72 y z - 1/72 y z - 1/18 y - 1/3 y x + 1/72 y + + 4 2 2 2 2 3 2 3 2 2 4 + - 5/288 y z - 5/12 y x z - 5/48 y x z + 5/48 y x z + 1/12 x y + + 3 3 3 4 2 3 2 4 4 + + 1/72 y + 1/12 y x + 1/288 y z - 1/18 y - 1/12 y x + 1/288 z y + + 2 4 2 2 2 2 2 2 + - 1/12 x y - 1/3 y x + 5/12 y x z - 5/12 y x z + 5/12 y x z + + 3 2 2 2 2 2 2 2 + - 5/288 y z + 5/72 y z + 5/72 y z + 1/3 y x + 1/3 y x , + + 3 4 2 4 3 2 4 + COEFF(-1, 1, 0) = - 1/24 y x z - 1/3 y x z + 1/12 y x z + + 2 4 2 4 2 4 2 2 2 4 4 4 + + 1/6 y x z - 5/12 x y z + 5/24 x y z - 1/3 y x z - 1/24 z y x + + 4 4 4 2 2 4 4 + + 1/6 y x z + 1/12 z y x + 2/9 y z + 2/9 y z + 8/9 y + 2/3 y x + + 4 4 2 2 2 2 3 2 3 2 2 + - 2/9 y + 5/18 y z + 5/3 y x z + 5/24 y x z - 5/12 y x z + + 4 3 3 3 4 2 3 2 + - 1/6 x y - 2/9 y - 1/6 y x - 1/18 y z + 8/9 y + 1/3 y x + + 4 4 2 4 2 2 2 2 2 + - 1/18 z y + 1/3 x y + 2/3 y x - 5/6 y x z + 5/3 y x z + + 2 3 2 2 2 2 2 2 2 + - 5/6 y x z + 5/18 y z - 10/9 y z - 10/9 y z - 4/3 y x - 4/3 y x , + + 2 2 25 4 2 3 2 3 4 3 2 4 + COEFF(0, 1, 0) = 2 y x - -- y z - 1/2 y x + 5/48 y z - 1/8 y x z + 48 + + 2 2 3 2 2 4 2 4 25 2 2 + - 5/2 y x z + 5/8 y x z - 5/12 y z - 5/3 y + 5/12 y + -- y z + 12 + + 4 4 2 4 2 2 4 2 4 2 4 + + 5/48 z y - 5/12 y z + 1/2 y x z + 1/2 y x z - 5/3 y - 1/2 x y + + 2 2 2 2 3 2 4 2 25 3 2 25 2 + - 5/2 y x z + 2 y x + 5/12 y + 5/8 x y z - -- y z + -- y z + 48 12 + + 4 4 2 3 4 2 4 + - 1/8 z y x , COEFF(1, 1, 0) = 1/24 y x z - 1/3 y x z + + 3 2 4 2 4 2 4 2 4 2 + + 1/12 y x z - 1/6 y x z - 5/12 x y z - 5/24 x y z + + 2 2 4 4 4 4 4 4 2 2 4 + - 1/3 y x z + 1/24 z y x - 1/6 y x z + 1/12 z y x + 2/9 y z + + 4 4 4 2 2 2 2 + + 2/9 y z + 8/9 y - 2/3 y x - 2/9 y + 5/18 y z + 5/3 y x z + + 3 2 3 2 2 4 3 3 3 4 + - 5/24 y x z - 5/12 y x z + 1/6 x y - 2/9 y + 1/6 y x - 1/18 y z + + 2 3 2 4 4 2 4 2 2 2 + + 8/9 y + 1/3 y x - 1/18 z y + 1/3 x y - 2/3 y x + 5/6 y x z + + 2 2 2 3 2 2 2 2 + + 5/3 y x z + 5/6 y x z + 5/18 y z - 10/9 y z - 10/9 y z + + 2 2 2 3 4 2 4 + - 4/3 y x - 4/3 y x , COEFF(2, 1, 0) = - 1/48 y x z + 1/12 y x z + + 3 2 4 2 4 2 4 2 4 2 + - 1/48 y x z + 1/12 y x z + 5/48 x y z + 5/48 x y z + + 2 2 4 4 4 4 4 4 2 2 4 + + 1/12 y x z - 1/48 z y x + 1/12 y x z - 1/48 z y x - 1/72 y z + + 4 4 4 2 2 2 2 + - 1/72 y z - 1/18 y + 1/3 y x + 1/72 y - 5/288 y z - 5/12 y x z + + 3 2 3 2 2 4 3 3 + + 5/48 y x z + 5/48 y x z - 1/12 x y + 1/72 y - 1/12 y x + + 3 4 2 3 2 4 4 2 4 2 + + 1/288 y z - 1/18 y - 1/12 y x + 1/288 z y - 1/12 x y + 1/3 y x + + 2 2 2 2 2 3 2 2 + - 5/12 y x z - 5/12 y x z - 5/12 y x z - 5/288 y z + 5/72 y z + + 2 2 2 2 2 3 4 + + 5/72 y z + 1/3 y x + 1/3 y x , COEFF(-2, 2, 0) = - 1/96 y x z + + 2 4 3 2 4 2 4 2 4 2 + - 1/96 y x z + 1/96 y x z + 1/192 y x z - 5/192 x y z + + 4 2 2 2 4 4 4 4 + + 5/192 x y z - 1/192 y x z - 1/192 z y x + 1/96 y x z + + 4 4 2 2 4 4 + + 1/192 z y x + 1/1152 y z + 1/576 y z + 1/144 y + 1/24 y x + + 4 4 2 2 2 2 3 2 3 2 2 + - 1/288 y + 5/1152 y z + 5/192 y x z + 5/96 y x z - 5/96 y x z + + 4 3 3 3 4 2 3 2 + - 1/48 x y - 1/144 y - 1/24 y x - 1/576 y z + 1/288 y + 1/24 y x + + 4 4 2 4 2 2 2 2 2 + - 1/1152 z y + 1/48 x y + 1/48 y x - 5/192 y x z + 5/96 y x z + + 2 3 2 2 2 2 2 2 + - 5/96 y x z + 5/576 y z - 5/576 y z - 5/1152 y z - 1/48 y x + + 2 3 4 2 4 3 2 4 + - 1/24 y x , COEFF(-1, 2, 0) = 1/48 y x z + 1/24 y x z - 1/24 y x z + + 2 4 2 4 2 4 2 2 2 4 + - 1/96 y x z + 5/48 x y z - 5/96 x y z + 1/48 y x z + + 4 4 4 4 4 2 2 4 4 + + 1/96 z y x - 1/48 y x z - 1/48 z y x - 1/72 y z - 1/36 y z + + 4 4 2 2 2 2 3 2 + - 1/9 y - 1/12 y x + 1/18 y - 5/72 y z - 5/48 y x z - 5/48 y x z + + 3 2 2 4 3 3 3 4 2 + + 5/24 y x z + 1/24 x y + 1/9 y + 1/12 y x + 1/36 y z - 1/18 y + + 3 2 4 4 2 4 2 2 2 + - 1/6 y x + 1/72 z y - 1/12 x y - 1/24 y x + 5/96 y x z + + 2 2 2 3 2 2 2 2 + - 5/24 y x z + 5/48 y x z - 5/36 y z + 5/36 y z + 5/72 y z + + 2 2 2 25 2 2 4 + + 1/12 y x + 1/6 y x , COEFF(0, 2, 0) = - --- y z + 5/96 y z + 192 + + 2 25 2 2 4 2 4 2 4 4 2 + - 1/4 y x - -- y z + 5/192 y z - 5/32 x y z + 1/32 z y x + 96 + + 3 3 2 2 2 2 25 3 2 3 2 4 + + 5/24 y - 5/24 y - 5/16 y x z - 1/8 y x + -- y z + 1/16 y x z + 96 + + 2 2 4 25 4 2 3 2 3 4 4 4 + - 1/32 y x z + --- y z + 1/4 y x - 5/96 y z - 5/192 z y + 192 + + 2 2 2 2 4 2 2 2 4 + + 5/48 y + 5/32 y x z - 5/48 y + 5/16 y x z + 1/8 x y + + 2 4 3 4 2 4 + - 1/16 y x z , COEFF(1, 2, 0) = - 1/48 y x z + 1/24 y x z + + 3 2 4 2 4 2 4 2 4 2 + - 1/24 y x z + 1/96 y x z + 5/48 x y z + 5/96 x y z + + 2 2 4 4 4 4 4 4 2 2 4 + + 1/48 y x z - 1/96 z y x + 1/48 y x z - 1/48 z y x - 1/72 y z + + 4 4 4 2 2 2 2 + - 1/36 y z - 1/9 y + 1/12 y x + 1/18 y - 5/72 y z - 5/48 y x z + + 3 2 3 2 2 4 3 3 + + 5/48 y x z + 5/24 y x z - 1/24 x y + 1/9 y - 1/12 y x + + 3 4 2 3 2 4 4 2 4 2 + + 1/36 y z - 1/18 y - 1/6 y x + 1/72 z y - 1/12 x y + 1/24 y x + + 2 2 2 2 2 3 2 2 + - 5/96 y x z - 5/24 y x z - 5/48 y x z - 5/36 y z + 5/36 y z + + 2 2 2 2 2 3 4 + + 5/72 y z + 1/12 y x + 1/6 y x , COEFF(2, 2, 0) = 1/96 y x z + + 2 4 3 2 4 2 4 2 4 2 + - 1/96 y x z + 1/96 y x z - 1/192 y x z - 5/192 x y z + + 4 2 2 2 4 4 4 4 + - 5/192 x y z - 1/192 y x z + 1/192 z y x - 1/96 y x z + + 4 4 2 2 4 4 + + 1/192 z y x + 1/1152 y z + 1/576 y z + 1/144 y - 1/24 y x + + 4 4 2 2 2 2 3 2 3 2 2 + - 1/288 y + 5/1152 y z + 5/192 y x z - 5/96 y x z - 5/96 y x z + + 4 3 3 3 4 2 3 2 + + 1/48 x y - 1/144 y + 1/24 y x - 1/576 y z + 1/288 y + 1/24 y x + + 4 4 2 4 2 2 2 2 2 + - 1/1152 z y + 1/48 x y - 1/48 y x + 5/192 y x z + 5/96 y x z + + 2 3 2 2 2 2 2 2 + + 5/96 y x z + 5/576 y z - 5/576 y z - 5/1152 y z - 1/48 y x + + 2 3 4 4 + - 1/24 y x , COEFF(-2, -2, 1) = - 1/144 y x z - 1/72 x y z + + 2 4 3 2 4 2 4 2 4 2 + - 1/144 y x z + 1/144 y x z - 1/288 y x z + 1/72 x y z + + 4 2 2 2 4 4 3 2 4 3 + - 1/72 x y z + 1/288 y x z + 1/288 x y z - 1/288 x y z + + 4 4 4 4 4 2 2 4 + + 1/288 z y x + 1/144 y x z - 1/288 z y x - 1/1728 y z + + 4 3 2 4 4 3 2 + + 1/1728 y z + 1/72 x y z + 1/864 y z + 1/144 y x z + 1/72 y x z + + 2 3 4 2 4 2 2 2 3 2 + - 1/288 y x z - 1/432 y z - 1/432 y z - 1/72 y x z + 1/36 y x z + + 2 2 3 2 3 3 2 2 3 4 + + 1/288 y x z - 1/144 y x z - 1/36 y x z - 1/864 y z + + 3 3 3 2 4 4 + + 1/216 z y + 1/36 z y x - 1/36 z y x + 1/1728 z y - 1/36 y x z + + 2 3 3 2 2 2 2 + + 1/36 z y x - 1/216 y z - 1/144 y x z + 1/72 y x z - 1/72 y x z + + 2 2 2 2 3 2 3 3 + + 1/36 y x z - 1/36 y x z + 1/432 y z + 1/144 y x z + 1/864 y z + + 2 3 3 3 3 2 2 2 2 + - 1/1728 y z - 1/864 y z + 1/216 y z - 1/216 y z + 1/432 y z , + + 3 4 4 2 4 + COEFF(-1, -2, 1) = 1/72 y x z + 1/36 x y z + 1/36 y x z + + 3 2 4 2 4 2 4 2 4 2 + - 1/36 y x z + 1/144 y x z - 1/18 x y z + 1/36 x y z + + 2 2 4 4 3 2 4 3 4 4 + - 1/72 y x z - 1/144 x y z + 1/72 x y z - 1/144 z y x + + 4 4 4 2 2 4 4 3 2 4 + - 1/72 y x z + 1/72 z y x + 1/108 y z - 1/108 y z - 1/18 x y z + + 4 3 2 2 3 4 2 + - 1/54 y z - 1/72 y x z - 1/36 y x z + 1/144 y x z + 1/27 y z + + 4 2 2 2 3 2 2 2 3 2 3 + + 1/27 y z + 1/18 y x z - 1/18 y x z - 1/72 y x z + 1/36 y x z + + 3 2 2 3 4 3 3 3 2 + + 1/9 y x z + 1/54 y z - 2/27 z y - 1/18 z y x + 1/9 z y x + + 4 4 2 3 3 + - 1/108 z y + 1/18 y x z - 1/9 z y x + 2/27 y z + 1/72 y x z + + 2 2 2 2 2 2 2 2 + - 1/36 y x z + 1/18 y x z - 1/9 y x z + 1/18 y x z - 1/27 y z + + 3 2 3 3 2 3 3 3 3 2 + - 1/36 y x z - 1/54 y z + 1/108 y z + 1/54 y z - 2/27 y z + + 2 2 2 2 4 3 2 4 + + 2/27 y z - 1/27 y z , COEFF(0, -2, 1) = - 1/24 y x z + 1/24 y x z + + 2 4 2 2 2 4 2 4 3 4 4 2 + + 1/12 x y z + 1/48 y x z - 1/48 x y z - 1/48 z y x + + 2 4 4 3 2 4 4 4 2 + - 5/288 y z + 5/288 y z + 1/12 x y z + 5/144 y z - 5/72 y z + + 4 2 2 2 2 2 3 2 3 3 2 2 + - 5/72 y z - 1/12 y x z + 1/48 y x z - 1/24 y x z - 1/6 y x z + + 3 4 3 3 2 4 4 2 + - 5/144 y z + 5/36 z y - 1/6 z y x + 5/288 z y + 1/6 z y x + + 2 2 2 2 2 3 2 3 + - 5/36 y z - 1/12 y x z + 1/6 y x z + 5/72 y z + 1/24 y x z + + 3 2 3 3 3 3 2 2 + + 5/144 y z - 5/288 y z - 5/144 y z + 5/36 y z - 5/36 y z + + 2 2 3 4 4 + + 5/72 y z , COEFF(1, -2, 1) = - 1/72 y x z - 1/36 x y z + + 2 4 3 2 4 2 4 2 4 2 + + 1/36 y x z - 1/36 y x z - 1/144 y x z - 1/18 x y z + + 4 2 2 2 4 4 3 2 4 3 + - 1/36 x y z - 1/72 y x z + 1/144 x y z + 1/72 x y z + + 4 4 4 4 4 2 2 4 4 3 + + 1/144 z y x + 1/72 y x z + 1/72 z y x + 1/108 y z - 1/108 y z + + 2 4 4 3 2 2 3 + - 1/18 x y z - 1/54 y z + 1/72 y x z + 1/36 y x z - 1/144 y x z + + 4 2 4 2 2 2 3 2 2 2 3 + + 1/27 y z + 1/27 y z + 1/18 y x z + 1/18 y x z - 1/72 y x z + + 2 3 3 2 2 3 4 3 3 + + 1/36 y x z + 1/9 y x z + 1/54 y z - 2/27 z y + 1/18 z y x + + 3 2 4 4 2 + + 1/9 z y x - 1/108 z y - 1/18 y x z - 1/9 z y x + 2/27 y z + + 3 3 2 2 2 2 2 2 2 + - 1/72 y x z + 1/36 y x z + 1/18 y x z - 1/9 y x z - 1/18 y x z + + 2 3 2 3 3 2 3 3 3 + - 1/27 y z - 1/36 y x z - 1/54 y z + 1/108 y z + 1/54 y z + + 3 2 2 2 2 3 4 + - 2/27 y z + 2/27 y z - 1/27 y z , COEFF(2, -2, 1) = 1/144 y x z + + 4 2 4 3 2 4 2 4 + + 1/72 x y z - 1/144 y x z + 1/144 y x z + 1/288 y x z + + 2 4 2 4 2 2 2 4 4 3 + + 1/72 x y z + 1/72 x y z + 1/288 y x z - 1/288 x y z + + 2 4 3 4 4 4 4 4 2 + - 1/288 x y z - 1/288 z y x - 1/144 y x z - 1/288 z y x + + 2 4 4 3 2 4 4 3 + - 1/1728 y z + 1/1728 y z + 1/72 x y z + 1/864 y z - 1/144 y x z + + 2 2 3 4 2 4 2 2 2 + - 1/72 y x z + 1/288 y x z - 1/432 y z - 1/432 y z - 1/72 y x z + + 3 2 2 2 3 2 3 3 2 2 + - 1/36 y x z + 1/288 y x z - 1/144 y x z - 1/36 y x z + + 3 4 3 3 3 2 4 4 + - 1/864 y z + 1/216 z y - 1/36 z y x - 1/36 z y x + 1/1728 z y + + 2 3 3 2 2 + + 1/36 y x z + 1/36 z y x - 1/216 y z + 1/144 y x z - 1/72 y x z + + 2 2 2 2 2 2 3 2 3 + - 1/72 y x z + 1/36 y x z + 1/36 y x z + 1/432 y z + 1/144 y x z + + 3 2 3 3 3 3 2 2 + + 1/864 y z - 1/1728 y z - 1/864 y z + 1/216 y z - 1/216 y z + + 2 2 3 4 4 + + 1/432 y z , COEFF(-2, -1, 1) = 1/72 y x z + 1/18 x y z + + 2 4 3 2 4 2 4 2 4 2 + + 1/18 y x z - 1/72 y x z + 1/18 y x z - 1/18 x y z + + 4 2 2 2 4 4 3 2 4 3 + + 1/18 x y z - 1/18 y x z - 1/72 x y z + 1/72 x y z + + 4 4 4 4 4 2 2 4 4 3 + - 1/72 z y x - 1/18 y x z + 1/72 z y x + 1/108 y z - 1/432 y z + + 2 4 4 3 2 2 3 + - 1/18 x y z - 1/108 y z - 1/18 y x z - 2/9 y x z + 1/18 y x z + + 4 2 4 2 2 2 3 2 2 2 3 + + 1/108 y z + 1/108 y z + 2/9 y x z - 1/18 y x z - 1/18 y x z + + 2 3 3 2 2 3 4 3 3 + + 1/18 y x z + 1/18 y x z + 1/432 y z - 1/108 z y - 1/18 z y x + + 3 2 4 4 2 + + 1/18 z y x - 1/432 z y + 2/9 y x z - 2/9 z y x + 1/27 y z + + 3 3 2 2 2 2 2 2 2 + + 1/72 y x z - 2/9 y x z + 2/9 y x z - 2/9 y x z + 2/9 y x z + + 2 3 2 3 3 2 3 3 3 + - 1/27 y z - 1/72 y x z - 1/108 y z + 1/108 y z + 1/432 y z + + 3 2 2 2 2 3 4 + - 1/108 y z + 1/27 y z - 1/27 y z , COEFF(-1, -1, 1) = - 1/36 y x z + + 4 2 4 3 2 4 2 4 2 4 2 + - 1/9 x y z - 2/9 y x z + 1/18 y x z - 1/9 y x z + 2/9 x y z + + 4 2 2 2 4 4 3 2 4 3 4 4 + - 1/9 x y z + 2/9 y x z + 1/36 x y z - 1/18 x y z + 1/36 z y x + + 4 4 4 2 2 4 4 3 2 4 + + 1/9 y x z - 1/18 z y x - 4/27 y z + 1/27 y z + 2/9 x y z + + 4 3 2 2 3 4 2 + + 4/27 y z + 1/9 y x z + 4/9 y x z - 1/9 y x z - 4/27 y z + + 4 2 2 2 3 2 2 2 3 2 3 + - 4/27 y z - 8/9 y x z + 1/9 y x z + 2/9 y x z - 2/9 y x z + + 3 2 2 3 4 3 3 3 2 + - 2/9 y x z - 1/27 y z + 4/27 z y + 1/9 z y x - 2/9 z y x + + 4 4 2 16 3 3 + + 1/27 z y - 4/9 y x z + 8/9 z y x - -- y z - 1/36 y x z + 27 + + 2 2 2 2 2 2 2 16 2 + + 4/9 y x z - 8/9 y x z + 8/9 y x z - 4/9 y x z + -- y z + 27 + + 3 2 3 3 2 3 3 3 3 2 + + 1/18 y x z + 4/27 y z - 4/27 y z - 1/27 y z + 4/27 y z + + 16 2 16 2 2 2 4 3 2 4 + - -- y z + -- y z , COEFF(0, -1, 1) = 1/3 y x z - 1/12 y x z + 27 27 + + 2 4 2 2 2 4 2 4 3 4 4 2 2 4 + - 1/3 x y z - 1/3 y x z + 1/12 x y z + 1/12 z y x + 5/18 y z + + 4 3 2 4 4 4 2 4 + - 5/72 y z - 1/3 x y z - 5/18 y z + 5/18 y z + 5/18 y z + + 2 2 2 2 2 3 2 3 3 2 2 3 4 + + 4/3 y x z - 1/3 y x z + 1/3 y x z + 1/3 y x z + 5/72 y z + + 3 3 2 4 4 2 + - 5/18 z y + 1/3 z y x - 5/72 z y - 4/3 z y x + 10/9 y z + + 2 2 2 2 2 3 2 3 3 + + 4/3 y x z - 4/3 y x z - 10/9 y z - 1/12 y x z - 5/18 y z + + 2 3 3 3 3 2 2 2 2 + + 5/18 y z + 5/72 y z - 5/18 y z + 10/9 y z - 10/9 y z , + + 3 4 4 2 4 3 2 4 + COEFF(1, -1, 1) = 1/36 y x z + 1/9 x y z - 2/9 y x z + 1/18 y x z + + 2 4 2 4 2 4 2 2 2 4 4 3 + + 1/9 y x z + 2/9 x y z + 1/9 x y z + 2/9 y x z - 1/36 x y z + + 2 4 3 4 4 4 4 4 2 2 4 + - 1/18 x y z - 1/36 z y x - 1/9 y x z - 1/18 z y x - 4/27 y z + + 4 3 2 4 4 3 2 + + 1/27 y z + 2/9 x y z + 4/27 y z - 1/9 y x z - 4/9 y x z + + 2 3 4 2 4 2 2 2 3 2 + + 1/9 y x z - 4/27 y z - 4/27 y z - 8/9 y x z - 1/9 y x z + + 2 2 3 2 3 3 2 2 3 4 3 + + 2/9 y x z - 2/9 y x z - 2/9 y x z - 1/27 y z + 4/27 z y + + 3 3 2 4 4 2 16 + - 1/9 z y x - 2/9 z y x + 1/27 z y + 4/9 y x z + 8/9 z y x - -- y z + 27 + + 3 3 2 2 2 2 2 2 2 + + 1/36 y x z - 4/9 y x z - 8/9 y x z + 8/9 y x z + 4/9 y x z + + 16 2 3 2 3 3 2 3 3 3 + + -- y z + 1/18 y x z + 4/27 y z - 4/27 y z - 1/27 y z + 27 + + 3 2 16 2 16 2 2 3 4 + + 4/27 y z - -- y z + -- y z , COEFF(2, -1, 1) = - 1/72 y x z + 27 27 + + 4 2 4 3 2 4 2 4 + - 1/18 x y z + 1/18 y x z - 1/72 y x z - 1/18 y x z + + 2 4 2 4 2 2 2 4 4 3 + - 1/18 x y z - 1/18 x y z - 1/18 y x z + 1/72 x y z + + 2 4 3 4 4 4 4 4 2 2 4 + + 1/72 x y z + 1/72 z y x + 1/18 y x z + 1/72 z y x + 1/108 y z + + 4 3 2 4 4 3 2 + - 1/432 y z - 1/18 x y z - 1/108 y z + 1/18 y x z + 2/9 y x z + + 2 3 4 2 4 2 2 2 3 2 + - 1/18 y x z + 1/108 y z + 1/108 y z + 2/9 y x z + 1/18 y x z + + 2 2 3 2 3 3 2 2 3 4 3 + - 1/18 y x z + 1/18 y x z + 1/18 y x z + 1/432 y z - 1/108 z y + + 3 3 2 4 4 2 + + 1/18 z y x + 1/18 z y x - 1/432 z y - 2/9 y x z - 2/9 z y x + + 3 3 2 2 2 2 2 2 + + 1/27 y z - 1/72 y x z + 2/9 y x z + 2/9 y x z - 2/9 y x z + + 2 2 3 2 3 3 2 3 + - 2/9 y x z - 1/27 y z - 1/72 y x z - 1/108 y z + 1/108 y z + + 3 3 3 2 2 2 2 + + 1/432 y z - 1/108 y z + 1/27 y z - 1/27 y z , COEFF(-2, 0, 1) = + + 4 2 4 2 4 2 4 2 2 2 4 + - 1/12 x y z - 5/48 y x z + 1/12 x y z - 1/12 x y z + 5/48 y x z + + 4 3 2 4 3 4 4 4 4 2 + + 1/48 x y z - 1/48 x y z + 1/48 z y x - 1/48 z y x + + 2 4 4 3 2 4 4 2 4 + - 5/288 y z + 1/288 y z + 1/12 x y z + 1/12 x z - 1/12 x z + + 2 2 3 4 2 4 + - 1/18 z + 5/12 y x z - 5/48 y x z - 1/72 y z - 1/72 y z + + 2 2 2 2 2 3 4 3 2 + - 5/12 y x z + 5/48 y x z + 1/72 z + 1/72 z - 1/18 z + + 4 4 2 2 2 2 2 + + 1/288 z y + 5/12 y x z - 5/12 y x z + 5/72 y z - 1/3 x z + + 2 2 3 2 3 3 2 2 2 + + 1/3 x z - 5/288 y z - 1/12 x z + 1/12 x z + 1/3 x z - 1/3 x z + + 2 2 4 2 4 2 4 2 + + 5/72 y z , COEFF(-1, 0, 1) = 1/6 x y z + 5/24 y x z - 1/3 x y z + + 4 2 2 2 4 4 3 2 4 3 + + 1/6 x y z - 5/12 y x z - 1/24 x y z + 1/12 x y z + + 4 4 4 4 2 2 4 4 3 2 4 + - 1/24 z y x + 1/12 z y x + 5/18 y z - 1/18 y z - 1/3 x y z + + 4 2 4 2 2 3 4 2 + - 1/6 x z + 1/3 x z + 8/9 z - 5/6 y x z + 5/24 y x z + 2/9 y z + + 4 2 2 2 2 2 3 4 3 2 + + 2/9 y z + 5/3 y x z - 5/12 y x z - 2/9 z - 2/9 z + 8/9 z + + 4 4 2 2 2 2 2 2 + - 1/18 z y - 5/6 y x z + 5/3 y x z - 10/9 y z + 2/3 x z - 4/3 x z + + 2 3 2 3 3 2 2 2 2 2 + + 5/18 y z + 1/3 x z - 1/6 x z - 4/3 x z + 2/3 x z - 10/9 y z , + + 4 3 2 2 2 3 2 4 2 2 + COEFF(0, 0, 1) = 5/48 y z + 2 x z - 1/2 x z + 1/2 x y z - 5/3 z + + 2 2 3 25 2 2 4 2 2 2 2 2 4 + + 5/8 y x z + -- y z - 5/12 y z - 5/2 y x z + 5/8 y x z + 12 + + 2 2 2 4 4 2 3 4 2 + - 5/2 y x z + 2 x z - 1/8 z y x + 5/12 z - 5/3 z - 5/12 y z + + 25 2 4 4 4 2 4 3 25 2 3 25 2 4 + - -- y z + 5/48 z y - 1/8 x y z - -- y z + -- y z + 5/12 z + 48 48 12 + + 2 4 2 4 4 2 4 + - 1/2 x z + 1/2 x y z, COEFF(1, 0, 1) = - 1/6 x y z - 5/24 y x z + + 2 4 2 4 2 2 2 4 4 3 + - 1/3 x y z - 1/6 x y z - 5/12 y x z + 1/24 x y z + + 2 4 3 4 4 4 4 2 2 4 4 3 + + 1/12 x y z + 1/24 z y x + 1/12 z y x + 5/18 y z - 1/18 y z + + 2 4 4 2 4 2 2 3 + - 1/3 x y z + 1/6 x z + 1/3 x z + 8/9 z + 5/6 y x z - 5/24 y x z + + 4 2 4 2 2 2 2 2 3 4 3 + + 2/9 y z + 2/9 y z + 5/3 y x z - 5/12 y x z - 2/9 z - 2/9 z + + 2 4 4 2 2 2 2 2 + + 8/9 z - 1/18 z y + 5/6 y x z + 5/3 y x z - 10/9 y z - 2/3 x z + + 2 2 3 2 3 3 2 2 2 + - 4/3 x z + 5/18 y z + 1/3 x z + 1/6 x z - 4/3 x z - 2/3 x z + + 2 2 4 2 4 2 4 2 + - 10/9 y z , COEFF(2, 0, 1) = 1/12 x y z + 5/48 y x z + 1/12 x y z + + 4 2 2 2 4 4 3 2 4 3 + + 1/12 x y z + 5/48 y x z - 1/48 x y z - 1/48 x y z + + 4 4 4 4 2 2 4 4 3 2 4 + - 1/48 z y x - 1/48 z y x - 5/288 y z + 1/288 y z + 1/12 x y z + + 4 2 4 2 2 3 + - 1/12 x z - 1/12 x z - 1/18 z - 5/12 y x z + 5/48 y x z + + 4 2 4 2 2 2 2 2 3 4 + - 1/72 y z - 1/72 y z - 5/12 y x z + 5/48 y x z + 1/72 z + + 3 2 4 4 2 2 2 2 + + 1/72 z - 1/18 z + 1/288 z y - 5/12 y x z - 5/12 y x z + + 2 2 2 3 2 3 3 + + 5/72 y z + 1/3 x z + 1/3 x z - 5/288 y z - 1/12 x z - 1/12 x z + + 2 2 2 2 2 3 4 + + 1/3 x z + 1/3 x z + 5/72 y z , COEFF(-2, 1, 1) = - 1/72 y x z + + 4 2 4 3 2 4 2 4 + + 1/18 x y z - 1/18 y x z + 1/72 y x z + 1/18 y x z + + 2 4 2 4 2 2 2 4 4 3 + - 1/18 x y z + 1/18 x y z - 1/18 y x z - 1/72 x y z + + 2 4 3 4 4 4 4 4 2 2 4 + + 1/72 x y z - 1/72 z y x + 1/18 y x z + 1/72 z y x + 1/108 y z + + 4 3 2 4 4 3 2 + - 1/432 y z - 1/18 x y z + 1/108 y z + 1/18 y x z - 2/9 y x z + + 2 3 4 2 4 2 2 2 3 2 + + 1/18 y x z + 1/108 y z + 1/108 y z + 2/9 y x z + 1/18 y x z + + 2 2 3 2 3 3 2 2 3 4 3 + - 1/18 y x z - 1/18 y x z - 1/18 y x z - 1/432 y z + 1/108 z y + + 3 3 2 4 4 2 + + 1/18 z y x - 1/18 z y x - 1/432 z y - 2/9 y x z + 2/9 z y x + + 3 3 2 2 2 2 2 2 + - 1/27 y z - 1/72 y x z - 2/9 y x z + 2/9 y x z + 2/9 y x z + + 2 2 3 2 3 3 2 3 + - 2/9 y x z - 1/27 y z + 1/72 y x z + 1/108 y z + 1/108 y z + + 3 3 3 2 2 2 2 + - 1/432 y z + 1/108 y z - 1/27 y z - 1/27 y z , COEFF(-1, 1, 1) = + + 3 4 4 2 4 3 2 4 2 4 + 1/36 y x z - 1/9 x y z + 2/9 y x z - 1/18 y x z - 1/9 y x z + + 2 4 2 4 2 2 2 4 4 3 2 4 3 + + 2/9 x y z - 1/9 x y z + 2/9 y x z + 1/36 x y z - 1/18 x y z + + 4 4 4 4 4 2 2 4 4 3 + + 1/36 z y x - 1/9 y x z - 1/18 z y x - 4/27 y z + 1/27 y z + + 2 4 4 3 2 2 3 + + 2/9 x y z - 4/27 y z - 1/9 y x z + 4/9 y x z - 1/9 y x z + + 4 2 4 2 2 2 3 2 2 2 3 + - 4/27 y z - 4/27 y z - 8/9 y x z - 1/9 y x z + 2/9 y x z + + 2 3 3 2 2 3 4 3 3 + + 2/9 y x z + 2/9 y x z + 1/27 y z - 4/27 z y - 1/9 z y x + + 3 2 4 4 2 16 + + 2/9 z y x + 1/27 z y + 4/9 y x z - 8/9 z y x + -- y z + 27 + + 3 3 2 2 2 2 2 2 2 + + 1/36 y x z + 4/9 y x z - 8/9 y x z - 8/9 y x z + 4/9 y x z + + 16 2 3 2 3 3 2 3 3 3 + + -- y z - 1/18 y x z - 4/27 y z - 4/27 y z + 1/27 y z + 27 + + 3 2 16 2 16 2 2 2 4 + - 4/27 y z + -- y z + -- y z , COEFF(0, 1, 1) = - 1/3 y x z + 27 27 + + 3 2 4 2 4 2 2 2 4 2 4 3 + + 1/12 y x z - 1/3 x y z - 1/3 y x z + 1/12 x y z + + 4 4 2 2 4 4 3 2 4 4 + + 1/12 z y x + 5/18 y z - 5/72 y z - 1/3 x y z + 5/18 y z + + 4 2 4 2 2 2 2 2 3 2 3 + + 5/18 y z + 5/18 y z + 4/3 y x z - 1/3 y x z - 1/3 y x z + + 3 2 2 3 4 3 3 2 4 4 + - 1/3 y x z - 5/72 y z + 5/18 z y - 1/3 z y x - 5/72 z y + + 2 2 2 2 2 2 + + 4/3 z y x - 10/9 y z + 4/3 y x z + 4/3 y x z - 10/9 y z + + 3 2 3 3 2 3 3 3 3 2 + + 1/12 y x z + 5/18 y z + 5/18 y z - 5/72 y z + 5/18 y z + + 2 2 2 3 4 4 + - 10/9 y z - 10/9 y z , COEFF(1, 1, 1) = - 1/36 y x z + 1/9 x y z + + 2 4 3 2 4 2 4 2 4 2 4 2 + + 2/9 y x z - 1/18 y x z + 1/9 y x z + 2/9 x y z + 1/9 x y z + + 2 2 4 4 3 2 4 3 4 4 4 + + 2/9 y x z - 1/36 x y z - 1/18 x y z - 1/36 z y x + 1/9 y x z + + 4 4 2 2 4 4 3 2 4 4 + - 1/18 z y x - 4/27 y z + 1/27 y z + 2/9 x y z - 4/27 y z + + 3 2 2 3 4 2 4 + + 1/9 y x z - 4/9 y x z + 1/9 y x z - 4/27 y z - 4/27 y z + + 2 2 2 3 2 2 2 3 2 3 3 2 2 + - 8/9 y x z + 1/9 y x z + 2/9 y x z + 2/9 y x z + 2/9 y x z + + 3 4 3 3 3 2 4 4 + + 1/27 y z - 4/27 z y + 1/9 z y x + 2/9 z y x + 1/27 z y + + 2 16 3 3 2 2 + - 4/9 y x z - 8/9 z y x + -- y z - 1/36 y x z - 4/9 y x z + 27 + + 2 2 2 2 2 16 2 3 2 3 + - 8/9 y x z - 8/9 y x z - 4/9 y x z + -- y z - 1/18 y x z + 27 + + 3 2 3 3 3 3 2 16 2 16 2 2 + - 4/27 y z - 4/27 y z + 1/27 y z - 4/27 y z + -- y z + -- y z , + 27 27 + + 3 4 4 2 4 3 2 4 + COEFF(2, 1, 1) = 1/72 y x z - 1/18 x y z - 1/18 y x z + 1/72 y x z + + 2 4 2 4 2 4 2 2 2 4 + - 1/18 y x z - 1/18 x y z - 1/18 x y z - 1/18 y x z + + 4 3 2 4 3 4 4 4 + + 1/72 x y z + 1/72 x y z + 1/72 z y x - 1/18 y x z + + 4 4 2 2 4 4 3 2 4 4 + + 1/72 z y x + 1/108 y z - 1/432 y z - 1/18 x y z + 1/108 y z + + 3 2 2 3 4 2 4 + - 1/18 y x z + 2/9 y x z - 1/18 y x z + 1/108 y z + 1/108 y z + + 2 2 2 3 2 2 2 3 2 3 + + 2/9 y x z - 1/18 y x z - 1/18 y x z - 1/18 y x z + + 3 2 2 3 4 3 3 3 2 + - 1/18 y x z - 1/432 y z + 1/108 z y - 1/18 z y x - 1/18 z y x + + 4 4 2 3 3 + - 1/432 z y + 2/9 y x z + 2/9 z y x - 1/27 y z + 1/72 y x z + + 2 2 2 2 2 2 2 2 + + 2/9 y x z + 2/9 y x z + 2/9 y x z + 2/9 y x z - 1/27 y z + + 3 2 3 3 2 3 3 3 3 2 + + 1/72 y x z + 1/108 y z + 1/108 y z - 1/432 y z + 1/108 y z + + 2 2 2 3 4 4 + - 1/27 y z - 1/27 y z , COEFF(-2, 2, 1) = 1/144 y x z - 1/72 x y z + + 2 4 3 2 4 2 4 2 4 2 + + 1/144 y x z - 1/144 y x z - 1/288 y x z + 1/72 x y z + + 4 2 2 2 4 4 3 2 4 3 + - 1/72 x y z + 1/288 y x z + 1/288 x y z - 1/288 x y z + + 4 4 4 4 4 2 2 4 + + 1/288 z y x - 1/144 y x z - 1/288 z y x - 1/1728 y z + + 4 3 2 4 4 3 2 + + 1/1728 y z + 1/72 x y z - 1/864 y z - 1/144 y x z + 1/72 y x z + + 2 3 4 2 4 2 2 2 3 2 + - 1/288 y x z - 1/432 y z - 1/432 y z - 1/72 y x z - 1/36 y x z + + 2 2 3 2 3 3 2 2 3 4 + + 1/288 y x z + 1/144 y x z + 1/36 y x z + 1/864 y z + + 3 3 3 2 4 4 + - 1/216 z y - 1/36 z y x + 1/36 z y x + 1/1728 z y + 1/36 y x z + + 2 3 3 2 2 2 2 + - 1/36 z y x + 1/216 y z + 1/144 y x z + 1/72 y x z - 1/72 y x z + + 2 2 2 2 3 2 3 3 + - 1/36 y x z + 1/36 y x z + 1/432 y z - 1/144 y x z - 1/864 y z + + 2 3 3 3 3 2 2 2 2 + - 1/1728 y z + 1/864 y z - 1/216 y z + 1/216 y z + 1/432 y z , + + 3 4 4 2 4 + COEFF(-1, 2, 1) = - 1/72 y x z + 1/36 x y z - 1/36 y x z + + 3 2 4 2 4 2 4 2 4 2 + + 1/36 y x z + 1/144 y x z - 1/18 x y z + 1/36 x y z + + 2 2 4 4 3 2 4 3 4 4 + - 1/72 y x z - 1/144 x y z + 1/72 x y z - 1/144 z y x + + 4 4 4 2 2 4 4 3 2 4 + + 1/72 y x z + 1/72 z y x + 1/108 y z - 1/108 y z - 1/18 x y z + + 4 3 2 2 3 4 2 + + 1/54 y z + 1/72 y x z - 1/36 y x z + 1/144 y x z + 1/27 y z + + 4 2 2 2 3 2 2 2 3 2 3 + + 1/27 y z + 1/18 y x z + 1/18 y x z - 1/72 y x z - 1/36 y x z + + 3 2 2 3 4 3 3 3 2 + - 1/9 y x z - 1/54 y z + 2/27 z y + 1/18 z y x - 1/9 z y x + + 4 4 2 3 3 + - 1/108 z y - 1/18 y x z + 1/9 z y x - 2/27 y z - 1/72 y x z + + 2 2 2 2 2 2 2 2 + - 1/36 y x z + 1/18 y x z + 1/9 y x z - 1/18 y x z - 1/27 y z + + 3 2 3 3 2 3 3 3 3 2 + + 1/36 y x z + 1/54 y z + 1/108 y z - 1/54 y z + 2/27 y z + + 2 2 2 2 4 3 2 4 + - 2/27 y z - 1/27 y z , COEFF(0, 2, 1) = 1/24 y x z - 1/24 y x z + + 2 4 2 2 2 4 2 4 3 4 4 2 + + 1/12 x y z + 1/48 y x z - 1/48 x y z - 1/48 z y x + + 2 4 4 3 2 4 4 4 2 + - 5/288 y z + 5/288 y z + 1/12 x y z - 5/144 y z - 5/72 y z + + 4 2 2 2 2 2 3 2 3 3 2 2 + - 5/72 y z - 1/12 y x z + 1/48 y x z + 1/24 y x z + 1/6 y x z + + 3 4 3 3 2 4 4 2 + + 5/144 y z - 5/36 z y + 1/6 z y x + 5/288 z y - 1/6 z y x + + 2 2 2 2 2 3 2 3 + + 5/36 y z - 1/12 y x z - 1/6 y x z + 5/72 y z - 1/24 y x z + + 3 2 3 3 3 3 2 2 + - 5/144 y z - 5/288 y z + 5/144 y z - 5/36 y z + 5/36 y z + + 2 2 3 4 4 2 4 + + 5/72 y z , COEFF(1, 2, 1) = 1/72 y x z - 1/36 x y z - 1/36 y x z + + 3 2 4 2 4 2 4 2 4 2 + + 1/36 y x z - 1/144 y x z - 1/18 x y z - 1/36 x y z + + 2 2 4 4 3 2 4 3 4 4 + - 1/72 y x z + 1/144 x y z + 1/72 x y z + 1/144 z y x + + 4 4 4 2 2 4 4 3 2 4 + - 1/72 y x z + 1/72 z y x + 1/108 y z - 1/108 y z - 1/18 x y z + + 4 3 2 2 3 4 2 + + 1/54 y z - 1/72 y x z + 1/36 y x z - 1/144 y x z + 1/27 y z + + 4 2 2 2 3 2 2 2 3 2 3 + + 1/27 y z + 1/18 y x z - 1/18 y x z - 1/72 y x z - 1/36 y x z + + 3 2 2 3 4 3 3 3 2 + - 1/9 y x z - 1/54 y z + 2/27 z y - 1/18 z y x - 1/9 z y x + + 4 4 2 3 3 + - 1/108 z y + 1/18 y x z + 1/9 z y x - 2/27 y z + 1/72 y x z + + 2 2 2 2 2 2 2 2 + + 1/36 y x z + 1/18 y x z + 1/9 y x z + 1/18 y x z - 1/27 y z + + 3 2 3 3 2 3 3 3 3 2 + + 1/36 y x z + 1/54 y z + 1/108 y z - 1/54 y z + 2/27 y z + + 2 2 2 3 4 4 + - 2/27 y z - 1/27 y z , COEFF(2, 2, 1) = - 1/144 y x z + 1/72 x y z + + 2 4 3 2 4 2 4 2 4 2 + + 1/144 y x z - 1/144 y x z + 1/288 y x z + 1/72 x y z + + 4 2 2 2 4 4 3 2 4 3 + + 1/72 x y z + 1/288 y x z - 1/288 x y z - 1/288 x y z + + 4 4 4 4 4 2 2 4 + - 1/288 z y x + 1/144 y x z - 1/288 z y x - 1/1728 y z + + 4 3 2 4 4 3 2 + + 1/1728 y z + 1/72 x y z - 1/864 y z + 1/144 y x z - 1/72 y x z + + 2 3 4 2 4 2 2 2 3 2 + + 1/288 y x z - 1/432 y z - 1/432 y z - 1/72 y x z + 1/36 y x z + + 2 2 3 2 3 3 2 2 3 4 + + 1/288 y x z + 1/144 y x z + 1/36 y x z + 1/864 y z + + 3 3 3 2 4 4 + - 1/216 z y + 1/36 z y x + 1/36 z y x + 1/1728 z y - 1/36 y x z + + 2 3 3 2 2 2 2 + - 1/36 z y x + 1/216 y z - 1/144 y x z - 1/72 y x z - 1/72 y x z + + 2 2 2 2 3 2 3 3 + - 1/36 y x z - 1/36 y x z + 1/432 y z - 1/144 y x z - 1/864 y z + + 2 3 3 3 3 2 2 2 2 + - 1/1728 y z + 1/864 y z - 1/216 y z + 1/216 y z + 1/432 y z , + + 3 4 4 2 4 + COEFF(-2, -2, 2) = 1/576 y x z + 1/576 x y z + 1/576 y x z + + 3 2 4 2 4 2 4 2 4 2 + - 1/576 y x z + 1/1152 y x z - 1/1152 x y z + 1/1152 x y z + + 2 2 4 4 3 2 4 3 4 4 + - 1/1152 y x z - 1/576 x y z + 1/576 x y z - 1/1152 z y x + + 4 4 4 2 2 4 4 3 + - 1/576 y x z + 1/1152 z y x + 1/6912 y z - 1/3456 y z + + 2 4 4 3 2 + - 1/576 x y z - 1/3456 y z - 1/288 y x z - 1/576 y x z + + 2 3 4 2 4 2 2 2 + + 1/576 y x z + 1/6912 y z + 1/3456 y z + 1/1152 y x z + + 3 2 2 2 3 2 3 3 2 2 + - 1/576 y x z - 1/576 y x z + 1/288 y x z + 1/576 y x z + + 3 4 3 3 3 2 4 4 + + 1/3456 y z - 1/1728 z y - 1/288 z y x + 1/288 z y x - 1/6912 z y + + 2 3 3 2 2 + + 1/288 y x z - 1/288 z y x + 1/1728 y z + 1/288 y x z - 1/1152 y x z + + 2 2 2 2 2 2 + + 1/576 y x z - 1/576 y x z + 1/576 y x z - 1/3456 y z + + 3 2 3 3 2 3 3 3 + - 1/288 y x z - 1/1728 y z + 1/3456 y z + 1/1728 y z + + 3 2 2 2 2 + - 1/3456 y z + 1/3456 y z - 1/6912 y z , COEFF(-1, -2, 2) = + + 3 4 4 2 4 3 2 4 + - 1/288 y x z - 1/288 x y z - 1/144 y x z + 1/144 y x z + + 2 4 2 4 2 4 2 2 2 4 + - 1/576 y x z + 1/288 x y z - 1/576 x y z + 1/288 y x z + + 4 3 2 4 3 4 4 4 + + 1/288 x y z - 1/144 x y z + 1/576 z y x + 1/288 y x z + + 4 4 2 2 4 4 3 2 4 4 + - 1/288 z y x - 1/432 y z + 1/216 y z + 1/144 x y z + 1/216 y z + + 3 2 2 3 4 2 4 + + 1/144 y x z + 1/288 y x z - 1/288 y x z - 1/432 y z - 1/216 y z + + 2 2 2 3 2 2 2 3 2 3 + - 1/288 y x z + 1/288 y x z + 1/144 y x z - 1/72 y x z + + 3 2 2 3 4 3 3 3 2 + - 1/144 y x z - 1/216 y z + 1/108 z y + 1/144 z y x - 1/72 z y x + + 4 4 2 3 3 + + 1/432 z y - 1/144 y x z + 1/72 z y x - 1/108 y z - 1/144 y x z + + 2 2 2 2 2 2 2 + + 1/576 y x z - 1/144 y x z + 1/144 y x z - 1/288 y x z + + 2 3 2 3 3 2 3 3 3 + + 1/216 y z + 1/72 y x z + 1/108 y z - 1/216 y z - 1/108 y z + + 3 2 2 2 2 2 4 + + 1/216 y z - 1/216 y z + 1/432 y z , COEFF(0, -2, 2) = 1/96 y x z + + 3 2 4 2 4 2 2 2 4 2 4 3 + - 1/96 y x z - 1/192 x y z - 1/192 y x z + 1/96 x y z + + 4 4 2 2 4 4 3 2 4 4 + + 1/192 z y x + 5/1152 y z - 5/576 y z - 1/96 x y z - 5/576 y z + + 4 2 4 2 2 2 2 2 3 + + 5/1152 y z + 5/576 y z + 1/192 y x z - 1/96 y x z + + 2 3 3 2 2 3 4 3 3 2 + + 1/48 y x z + 1/96 y x z + 5/576 y z - 5/288 z y + 1/48 z y x + + 4 4 2 2 2 2 2 + - 5/1152 z y - 1/48 z y x + 5/288 y z + 1/96 y x z - 1/96 y x z + + 2 3 2 3 3 2 3 3 3 + - 5/576 y z - 1/48 y x z - 5/288 y z + 5/576 y z + 5/288 y z + + 3 2 2 2 2 3 4 + - 5/576 y z + 5/576 y z - 5/1152 y z , COEFF(1, -2, 2) = 1/288 y x z + + 4 2 4 3 2 4 2 4 + + 1/288 x y z - 1/144 y x z + 1/144 y x z + 1/576 y x z + + 2 4 2 4 2 2 2 4 4 3 + + 1/288 x y z + 1/576 x y z + 1/288 y x z - 1/288 x y z + + 2 4 3 4 4 4 4 4 2 + - 1/144 x y z - 1/576 z y x - 1/288 y x z - 1/288 z y x + + 2 4 4 3 2 4 4 3 + - 1/432 y z + 1/216 y z + 1/144 x y z + 1/216 y z - 1/144 y x z + + 2 2 3 4 2 4 2 2 2 + - 1/288 y x z + 1/288 y x z - 1/432 y z - 1/216 y z - 1/288 y x z + + 3 2 2 2 3 2 3 3 2 2 + - 1/288 y x z + 1/144 y x z - 1/72 y x z - 1/144 y x z + + 3 4 3 3 3 2 4 4 + - 1/216 y z + 1/108 z y - 1/144 z y x - 1/72 z y x + 1/432 z y + + 2 3 3 2 2 + + 1/144 y x z + 1/72 z y x - 1/108 y z + 1/144 y x z - 1/576 y x z + + 2 2 2 2 2 2 + - 1/144 y x z + 1/144 y x z + 1/288 y x z + 1/216 y z + + 3 2 3 3 2 3 3 3 3 2 + + 1/72 y x z + 1/108 y z - 1/216 y z - 1/108 y z + 1/216 y z + + 2 2 2 3 4 + - 1/216 y z + 1/432 y z , COEFF(2, -2, 2) = - 1/576 y x z + + 4 2 4 3 2 4 2 4 + - 1/576 x y z + 1/576 y x z - 1/576 y x z - 1/1152 y x z + + 2 4 2 4 2 2 2 4 4 3 + - 1/1152 x y z - 1/1152 x y z - 1/1152 y x z + 1/576 x y z + + 2 4 3 4 4 4 4 4 2 + + 1/576 x y z + 1/1152 z y x + 1/576 y x z + 1/1152 z y x + + 2 4 4 3 2 4 4 3 + + 1/6912 y z - 1/3456 y z - 1/576 x y z - 1/3456 y z + 1/288 y x z + + 2 2 3 4 2 4 + + 1/576 y x z - 1/576 y x z + 1/6912 y z + 1/3456 y z + + 2 2 2 3 2 2 2 3 2 3 + + 1/1152 y x z + 1/576 y x z - 1/576 y x z + 1/288 y x z + + 3 2 2 3 4 3 3 + + 1/576 y x z + 1/3456 y z - 1/1728 z y + 1/288 z y x + + 3 2 4 4 2 + + 1/288 z y x - 1/6912 z y - 1/288 y x z - 1/288 z y x + 1/1728 y z + + 3 3 2 2 2 2 2 2 + - 1/288 y x z + 1/1152 y x z + 1/576 y x z - 1/576 y x z + + 2 2 3 2 3 3 2 3 + - 1/576 y x z - 1/3456 y z - 1/288 y x z - 1/1728 y z + 1/3456 y z + + 3 3 3 2 2 2 2 + + 1/1728 y z - 1/3456 y z + 1/3456 y z - 1/6912 y z , + + 3 4 4 2 4 + COEFF(-2, -1, 2) = - 1/288 y x z - 1/144 x y z - 1/72 y x z + + 3 2 4 2 4 2 4 2 4 2 + + 1/288 y x z - 1/72 y x z + 1/288 x y z - 1/288 x y z + + 2 2 4 4 3 2 4 3 4 4 + + 1/72 y x z + 1/144 x y z - 1/144 x y z + 1/288 z y x + + 4 4 4 2 2 4 4 3 2 4 + + 1/72 y x z - 1/288 z y x - 1/432 y z + 1/864 y z + 1/144 x y z + + 4 3 2 2 3 4 2 + + 1/432 y z + 1/36 y x z + 1/36 y x z - 1/36 y x z - 1/1728 y z + + 4 2 2 2 3 2 2 2 3 + - 1/864 y z - 1/72 y x z + 1/288 y x z + 1/36 y x z + + 2 3 3 2 2 3 4 3 3 + - 1/36 y x z - 1/288 y x z - 1/1728 y z + 1/864 z y + 1/144 z y x + + 3 2 4 4 2 + - 1/144 z y x + 1/1728 z y - 1/36 y x z + 1/36 z y x - 1/216 y z + + 3 3 2 2 2 2 2 2 2 + - 1/144 y x z + 1/72 y x z - 1/36 y x z + 1/72 y x z - 1/72 y x z + + 2 3 2 3 3 2 3 3 3 + + 1/216 y z + 1/144 y x z + 1/216 y z - 1/216 y z - 1/864 y z + + 3 2 2 2 2 + + 1/1728 y z - 1/432 y z + 1/432 y z , COEFF(-1, -1, 2) = + + 3 4 4 2 4 3 2 4 2 4 + 1/144 y x z + 1/72 x y z + 1/18 y x z - 1/72 y x z + 1/36 y x z + + 2 4 2 4 2 2 2 4 4 3 + - 1/72 x y z + 1/144 x y z - 1/18 y x z - 1/72 x y z + + 2 4 3 4 4 4 4 4 2 2 4 + + 1/36 x y z - 1/144 z y x - 1/36 y x z + 1/72 z y x + 1/27 y z + + 4 3 2 4 4 3 2 + - 1/54 y z - 1/36 x y z - 1/27 y z - 1/18 y x z - 1/18 y x z + + 2 3 4 2 4 2 2 2 3 2 + + 1/18 y x z + 1/108 y z + 1/54 y z + 1/18 y x z - 1/144 y x z + + 2 2 3 2 3 3 2 2 3 4 3 + - 1/9 y x z + 1/9 y x z + 1/72 y x z + 1/108 y z - 1/54 z y + + 3 3 2 4 4 2 + - 1/72 z y x + 1/36 z y x - 1/108 z y + 1/18 y x z - 1/9 z y x + + 3 3 2 2 2 2 2 2 + + 2/27 y z + 1/72 y x z - 1/36 y x z + 1/9 y x z - 1/18 y x z + + 2 2 3 2 3 3 2 3 + + 1/36 y x z - 2/27 y z - 1/36 y x z - 2/27 y z + 2/27 y z + + 3 3 3 2 2 2 2 + + 1/54 y z - 1/108 y z + 1/27 y z - 1/27 y z , COEFF(0, -1, 2) = + + 2 4 3 2 4 2 4 2 2 2 4 + - 1/12 y x z + 1/48 y x z + 1/48 x y z + 1/12 y x z + + 2 4 3 4 4 2 2 4 4 3 2 4 + - 1/24 x y z - 1/48 z y x - 5/72 y z + 5/144 y z + 1/24 x y z + + 4 4 2 4 2 2 2 2 2 3 + + 5/72 y z - 5/288 y z - 5/144 y z - 1/12 y x z + 1/6 y x z + + 2 3 3 2 2 3 4 3 3 2 + - 1/6 y x z - 1/48 y x z - 5/288 y z + 5/144 z y - 1/24 z y x + + 4 4 2 2 2 2 2 + + 5/288 z y + 1/6 z y x - 5/36 y z - 1/6 y x z + 1/12 y x z + + 2 3 2 3 3 2 3 3 3 + + 5/36 y z + 1/24 y x z + 5/36 y z - 5/36 y z - 5/144 y z + + 3 2 2 2 2 3 4 + + 5/288 y z - 5/72 y z + 5/72 y z , COEFF(1, -1, 2) = - 1/144 y x z + + 4 2 4 3 2 4 2 4 + - 1/72 x y z + 1/18 y x z - 1/72 y x z - 1/36 y x z + + 2 4 2 4 2 2 2 4 4 3 + - 1/72 x y z - 1/144 x y z - 1/18 y x z + 1/72 x y z + + 2 4 3 4 4 4 4 4 2 2 4 + + 1/36 x y z + 1/144 z y x + 1/36 y x z + 1/72 z y x + 1/27 y z + + 4 3 2 4 4 3 2 + - 1/54 y z - 1/36 x y z - 1/27 y z + 1/18 y x z + 1/18 y x z + + 2 3 4 2 4 2 2 2 3 2 + - 1/18 y x z + 1/108 y z + 1/54 y z + 1/18 y x z + 1/144 y x z + + 2 2 3 2 3 3 2 2 3 4 3 + - 1/9 y x z + 1/9 y x z + 1/72 y x z + 1/108 y z - 1/54 z y + + 3 3 2 4 4 2 + + 1/72 z y x + 1/36 z y x - 1/108 z y - 1/18 y x z - 1/9 z y x + + 3 3 2 2 2 2 2 2 + + 2/27 y z - 1/72 y x z + 1/36 y x z + 1/9 y x z - 1/18 y x z + + 2 2 3 2 3 3 2 3 + - 1/36 y x z - 2/27 y z - 1/36 y x z - 2/27 y z + 2/27 y z + + 3 3 3 2 2 2 2 + + 1/54 y z - 1/108 y z + 1/27 y z - 1/27 y z , COEFF(2, -1, 2) = + + 3 4 4 2 4 3 2 4 2 4 + 1/288 y x z + 1/144 x y z - 1/72 y x z + 1/288 y x z + 1/72 y x z + + 2 4 2 4 2 2 2 4 4 3 + + 1/288 x y z + 1/288 x y z + 1/72 y x z - 1/144 x y z + + 2 4 3 4 4 4 4 4 2 + - 1/144 x y z - 1/288 z y x - 1/72 y x z - 1/288 z y x + + 2 4 4 3 2 4 4 3 + - 1/432 y z + 1/864 y z + 1/144 x y z + 1/432 y z - 1/36 y x z + + 2 2 3 4 2 4 2 2 2 + - 1/36 y x z + 1/36 y x z - 1/1728 y z - 1/864 y z - 1/72 y x z + + 3 2 2 2 3 2 3 3 2 2 + - 1/288 y x z + 1/36 y x z - 1/36 y x z - 1/288 y x z + + 3 4 3 3 3 2 4 4 + - 1/1728 y z + 1/864 z y - 1/144 z y x - 1/144 z y x + 1/1728 z y + + 2 3 3 2 2 + + 1/36 y x z + 1/36 z y x - 1/216 y z + 1/144 y x z - 1/72 y x z + + 2 2 2 2 2 2 3 2 3 + - 1/36 y x z + 1/72 y x z + 1/72 y x z + 1/216 y z + 1/144 y x z + + 3 2 3 3 3 3 2 2 + + 1/216 y z - 1/216 y z - 1/864 y z + 1/1728 y z - 1/432 y z + + 2 2 4 2 4 + + 1/432 y z , COEFF(-2, 0, 2) = 1/96 x y z + 5/192 y x z + + 2 4 2 4 2 2 2 4 4 3 + - 1/192 x y z + 1/192 x y z - 5/192 y x z - 1/96 x y z + + 2 4 3 4 4 4 4 2 2 4 + + 1/96 x y z - 1/192 z y x + 1/192 z y x + 5/1152 y z + + 4 3 2 4 4 2 4 + - 1/576 y z - 1/96 x y z - 1/48 x z + 1/48 x z + 1/144 z + + 2 2 3 4 2 4 2 2 2 + - 5/96 y x z + 5/96 y x z + 1/1152 y z + 1/576 y z + 5/192 y x z + + 2 2 3 4 3 2 4 4 + - 5/96 y x z - 1/288 z - 1/144 z + 1/288 z - 1/1152 z y + + 2 2 2 2 2 2 + - 5/192 y x z + 5/96 y x z - 5/576 y z + 1/24 x z - 1/24 x z + + 2 3 2 3 3 2 2 2 + + 5/576 y z + 1/24 x z - 1/24 x z - 1/48 x z + 1/48 x z + + 2 2 4 2 4 + - 5/1152 y z , COEFF(-1, 0, 2) = - 1/48 x y z - 5/96 y x z + + 2 4 2 4 2 2 2 4 4 3 + + 1/48 x y z - 1/96 x y z + 5/48 y x z + 1/48 x y z + + 2 4 3 4 4 4 4 2 2 4 4 3 + - 1/24 x y z + 1/96 z y x - 1/48 z y x - 5/72 y z + 1/36 y z + + 2 4 4 2 4 2 + + 1/24 x y z + 1/24 x z - 1/12 x z - 1/9 z + 5/48 y x z + + 2 3 4 2 4 2 2 2 2 2 3 + - 5/48 y x z - 1/72 y z - 1/36 y z - 5/48 y x z + 5/24 y x z + + 4 3 2 4 4 2 2 2 2 + + 1/18 z + 1/9 z - 1/18 z + 1/72 z y + 5/96 y x z - 5/24 y x z + + 2 2 2 3 2 3 3 + + 5/36 y z - 1/12 x z + 1/6 x z - 5/36 y z - 1/6 x z + 1/12 x z + + 2 2 2 2 2 2 + + 1/12 x z - 1/24 x z + 5/72 y z , COEFF(0, 0, 2) = 5/48 z + + 2 2 3 4 4 4 2 2 2 25 2 + - 5/16 y x z + 5/96 y z - 5/192 z y + 5/32 y x z - -- y z + 96 + + 2 4 2 25 2 4 2 4 2 4 2 4 3 + - 1/32 x y z + --- y z + 1/8 x z - 1/16 x y z + 1/16 x y z + 192 + + 4 2 3 2 25 2 3 25 2 2 + + 5/192 y z - 5/24 z + 5/24 z - 1/4 x z + -- y z - --- y z + 96 192 + + 2 3 2 2 4 4 4 2 4 2 2 + + 1/4 x z - 5/32 y x z + 1/32 z y x - 5/48 z - 1/8 x z + + 4 3 2 2 4 2 4 + - 5/96 y z + 5/16 y x z, COEFF(1, 0, 2) = 1/48 x y z + 5/96 y x z + + 2 4 2 4 2 2 2 4 4 3 + + 1/48 x y z + 1/96 x y z + 5/48 y x z - 1/48 x y z + + 2 4 3 4 4 4 4 2 2 4 4 3 + - 1/24 x y z - 1/96 z y x - 1/48 z y x - 5/72 y z + 1/36 y z + + 2 4 4 2 4 2 + + 1/24 x y z - 1/24 x z - 1/12 x z - 1/9 z - 5/48 y x z + + 2 3 4 2 4 2 2 2 2 2 3 + + 5/48 y x z - 1/72 y z - 1/36 y z - 5/48 y x z + 5/24 y x z + + 4 3 2 4 4 2 2 2 2 + + 1/18 z + 1/9 z - 1/18 z + 1/72 z y - 5/96 y x z - 5/24 y x z + + 2 2 2 3 2 3 3 + + 5/36 y z + 1/12 x z + 1/6 x z - 5/36 y z - 1/6 x z - 1/12 x z + + 2 2 2 2 2 4 + + 1/12 x z + 1/24 x z + 5/72 y z , COEFF(2, 0, 2) = - 1/96 x y z + + 2 4 2 4 2 4 2 2 2 4 + - 5/192 y x z - 1/192 x y z - 1/192 x y z - 5/192 y x z + + 4 3 2 4 3 4 4 4 4 2 + + 1/96 x y z + 1/96 x y z + 1/192 z y x + 1/192 z y x + + 2 4 4 3 2 4 4 2 4 + + 5/1152 y z - 1/576 y z - 1/96 x y z + 1/48 x z + 1/48 x z + + 2 2 3 4 2 4 + + 1/144 z + 5/96 y x z - 5/96 y x z + 1/1152 y z + 1/576 y z + + 2 2 2 2 2 3 4 3 2 + + 5/192 y x z - 5/96 y x z - 1/288 z - 1/144 z + 1/288 z + + 4 4 2 2 2 2 2 + - 1/1152 z y + 5/192 y x z + 5/96 y x z - 5/576 y z - 1/24 x z + + 2 2 3 2 3 3 2 2 + - 1/24 x z + 5/576 y z + 1/24 x z + 1/24 x z - 1/48 x z + + 2 2 2 3 4 4 + - 1/48 x z - 5/1152 y z , COEFF(-2, 1, 2) = 1/288 y x z - 1/144 x y z + + 2 4 3 2 4 2 4 2 4 2 + + 1/72 y x z - 1/288 y x z - 1/72 y x z + 1/288 x y z + + 4 2 2 2 4 4 3 2 4 3 + - 1/288 x y z + 1/72 y x z + 1/144 x y z - 1/144 x y z + + 4 4 4 4 4 2 2 4 4 3 + + 1/288 z y x - 1/72 y x z - 1/288 z y x - 1/432 y z + 1/864 y z + + 2 4 4 3 2 2 3 + + 1/144 x y z - 1/432 y z - 1/36 y x z + 1/36 y x z - 1/36 y x z + + 4 2 4 2 2 2 3 2 + - 1/1728 y z - 1/864 y z - 1/72 y x z - 1/288 y x z + + 2 2 3 2 3 3 2 2 3 4 + + 1/36 y x z + 1/36 y x z + 1/288 y x z + 1/1728 y z + + 3 3 3 2 4 4 + - 1/864 z y - 1/144 z y x + 1/144 z y x + 1/1728 z y + 1/36 y x z + + 2 3 3 2 2 2 2 + - 1/36 z y x + 1/216 y z + 1/144 y x z + 1/72 y x z - 1/36 y x z + + 2 2 2 2 3 2 3 3 + - 1/72 y x z + 1/72 y x z + 1/216 y z - 1/144 y x z - 1/216 y z + + 2 3 3 3 3 2 2 2 2 + - 1/216 y z + 1/864 y z - 1/1728 y z + 1/432 y z + 1/432 y z , + + 3 4 4 2 4 + COEFF(-1, 1, 2) = - 1/144 y x z + 1/72 x y z - 1/18 y x z + + 3 2 4 2 4 2 4 2 4 2 + + 1/72 y x z + 1/36 y x z - 1/72 x y z + 1/144 x y z + + 2 2 4 4 3 2 4 3 4 4 + - 1/18 y x z - 1/72 x y z + 1/36 x y z - 1/144 z y x + + 4 4 4 2 2 4 4 3 2 4 + + 1/36 y x z + 1/72 z y x + 1/27 y z - 1/54 y z - 1/36 x y z + + 4 3 2 2 3 4 2 + + 1/27 y z + 1/18 y x z - 1/18 y x z + 1/18 y x z + 1/108 y z + + 4 2 2 2 3 2 2 2 3 2 3 + + 1/54 y z + 1/18 y x z + 1/144 y x z - 1/9 y x z - 1/9 y x z + + 3 2 2 3 4 3 3 3 2 + - 1/72 y x z - 1/108 y z + 1/54 z y + 1/72 z y x - 1/36 z y x + + 4 4 2 3 3 + - 1/108 z y - 1/18 y x z + 1/9 z y x - 2/27 y z - 1/72 y x z + + 2 2 2 2 2 2 2 2 + - 1/36 y x z + 1/9 y x z + 1/18 y x z - 1/36 y x z - 2/27 y z + + 3 2 3 3 2 3 3 3 3 2 + + 1/36 y x z + 2/27 y z + 2/27 y z - 1/54 y z + 1/108 y z + + 2 2 2 2 4 3 2 4 + - 1/27 y z - 1/27 y z , COEFF(0, 1, 2) = 1/12 y x z - 1/48 y x z + + 2 4 2 2 2 4 2 4 3 4 4 2 + + 1/48 x y z + 1/12 y x z - 1/24 x y z - 1/48 z y x + + 2 4 4 3 2 4 4 4 2 + - 5/72 y z + 5/144 y z + 1/24 x y z - 5/72 y z - 5/288 y z + + 4 2 2 2 2 2 3 2 3 3 2 2 + - 5/144 y z - 1/12 y x z + 1/6 y x z + 1/6 y x z + 1/48 y x z + + 3 4 3 3 2 4 4 2 + + 5/288 y z - 5/144 z y + 1/24 z y x + 5/288 z y - 1/6 z y x + + 2 2 2 2 2 3 2 3 + + 5/36 y z - 1/6 y x z - 1/12 y x z + 5/36 y z - 1/24 y x z + + 3 2 3 3 3 3 2 2 + - 5/36 y z - 5/36 y z + 5/144 y z - 5/288 y z + 5/72 y z + + 2 2 3 4 4 2 4 + + 5/72 y z , COEFF(1, 1, 2) = 1/144 y x z - 1/72 x y z - 1/18 y x z + + 3 2 4 2 4 2 4 2 4 2 + + 1/72 y x z - 1/36 y x z - 1/72 x y z - 1/144 x y z + + 2 2 4 4 3 2 4 3 4 4 + - 1/18 y x z + 1/72 x y z + 1/36 x y z + 1/144 z y x + + 4 4 4 2 2 4 4 3 2 4 + - 1/36 y x z + 1/72 z y x + 1/27 y z - 1/54 y z - 1/36 x y z + + 4 3 2 2 3 4 2 + + 1/27 y z - 1/18 y x z + 1/18 y x z - 1/18 y x z + 1/108 y z + + 4 2 2 2 3 2 2 2 3 2 3 + + 1/54 y z + 1/18 y x z - 1/144 y x z - 1/9 y x z - 1/9 y x z + + 3 2 2 3 4 3 3 3 2 + - 1/72 y x z - 1/108 y z + 1/54 z y - 1/72 z y x - 1/36 z y x + + 4 4 2 3 3 + - 1/108 z y + 1/18 y x z + 1/9 z y x - 2/27 y z + 1/72 y x z + + 2 2 2 2 2 2 2 2 + + 1/36 y x z + 1/9 y x z + 1/18 y x z + 1/36 y x z - 2/27 y z + + 3 2 3 3 2 3 3 3 3 2 + + 1/36 y x z + 2/27 y z + 2/27 y z - 1/54 y z + 1/108 y z + + 2 2 2 3 4 4 + - 1/27 y z - 1/27 y z , COEFF(2, 1, 2) = - 1/288 y x z + 1/144 x y z + + 2 4 3 2 4 2 4 2 4 2 + + 1/72 y x z - 1/288 y x z + 1/72 y x z + 1/288 x y z + + 4 2 2 2 4 4 3 2 4 3 + + 1/288 x y z + 1/72 y x z - 1/144 x y z - 1/144 x y z + + 4 4 4 4 4 2 2 4 4 3 + - 1/288 z y x + 1/72 y x z - 1/288 z y x - 1/432 y z + 1/864 y z + + 2 4 4 3 2 2 3 + + 1/144 x y z - 1/432 y z + 1/36 y x z - 1/36 y x z + 1/36 y x z + + 4 2 4 2 2 2 3 2 + - 1/1728 y z - 1/864 y z - 1/72 y x z + 1/288 y x z + + 2 2 3 2 3 3 2 2 3 4 + + 1/36 y x z + 1/36 y x z + 1/288 y x z + 1/1728 y z + + 3 3 3 2 4 4 + - 1/864 z y + 1/144 z y x + 1/144 z y x + 1/1728 z y - 1/36 y x z + + 2 3 3 2 2 2 2 + - 1/36 z y x + 1/216 y z - 1/144 y x z - 1/72 y x z - 1/36 y x z + + 2 2 2 2 3 2 3 3 + - 1/72 y x z - 1/72 y x z + 1/216 y z - 1/144 y x z - 1/216 y z + + 2 3 3 3 3 2 2 2 2 + - 1/216 y z + 1/864 y z - 1/1728 y z + 1/432 y z + 1/432 y z , + + 3 4 4 2 4 + COEFF(-2, 2, 2) = - 1/576 y x z + 1/576 x y z - 1/576 y x z + + 3 2 4 2 4 2 4 2 4 2 + + 1/576 y x z + 1/1152 y x z - 1/1152 x y z + 1/1152 x y z + + 2 2 4 4 3 2 4 3 4 4 + - 1/1152 y x z - 1/576 x y z + 1/576 x y z - 1/1152 z y x + + 4 4 4 2 2 4 4 3 + + 1/576 y x z + 1/1152 z y x + 1/6912 y z - 1/3456 y z + + 2 4 4 3 2 + - 1/576 x y z + 1/3456 y z + 1/288 y x z - 1/576 y x z + + 2 3 4 2 4 2 2 2 + + 1/576 y x z + 1/6912 y z + 1/3456 y z + 1/1152 y x z + + 3 2 2 2 3 2 3 3 2 2 + + 1/576 y x z - 1/576 y x z - 1/288 y x z - 1/576 y x z + + 3 4 3 3 3 2 4 4 + - 1/3456 y z + 1/1728 z y + 1/288 z y x - 1/288 z y x - 1/6912 z y + + 2 3 3 2 2 + - 1/288 y x z + 1/288 z y x - 1/1728 y z - 1/288 y x z - 1/1152 y x z + + 2 2 2 2 2 2 + + 1/576 y x z + 1/576 y x z - 1/576 y x z - 1/3456 y z + + 3 2 3 3 2 3 3 3 + + 1/288 y x z + 1/1728 y z + 1/3456 y z - 1/1728 y z + + 3 2 2 2 2 + + 1/3456 y z - 1/3456 y z - 1/6912 y z , COEFF(-1, 2, 2) = + + 3 4 4 2 4 3 2 4 + 1/288 y x z - 1/288 x y z + 1/144 y x z - 1/144 y x z + + 2 4 2 4 2 4 2 2 2 4 + - 1/576 y x z + 1/288 x y z - 1/576 x y z + 1/288 y x z + + 4 3 2 4 3 4 4 4 + + 1/288 x y z - 1/144 x y z + 1/576 z y x - 1/288 y x z + + 4 4 2 2 4 4 3 2 4 4 + - 1/288 z y x - 1/432 y z + 1/216 y z + 1/144 x y z - 1/216 y z + + 3 2 2 3 4 2 4 + - 1/144 y x z + 1/288 y x z - 1/288 y x z - 1/432 y z - 1/216 y z + + 2 2 2 3 2 2 2 3 2 3 + - 1/288 y x z - 1/288 y x z + 1/144 y x z + 1/72 y x z + + 3 2 2 3 4 3 3 3 2 + + 1/144 y x z + 1/216 y z - 1/108 z y - 1/144 z y x + 1/72 z y x + + 4 4 2 3 3 + + 1/432 z y + 1/144 y x z - 1/72 z y x + 1/108 y z + 1/144 y x z + + 2 2 2 2 2 2 2 + + 1/576 y x z - 1/144 y x z - 1/144 y x z + 1/288 y x z + + 2 3 2 3 3 2 3 3 3 + + 1/216 y z - 1/72 y x z - 1/108 y z - 1/216 y z + 1/108 y z + + 3 2 2 2 2 2 4 + - 1/216 y z + 1/216 y z + 1/432 y z , COEFF(0, 2, 2) = - 1/96 y x z + + 3 2 4 2 4 2 2 2 4 2 4 3 + + 1/96 y x z - 1/192 x y z - 1/192 y x z + 1/96 x y z + + 4 4 2 2 4 4 3 2 4 4 + + 1/192 z y x + 5/1152 y z - 5/576 y z - 1/96 x y z + 5/576 y z + + 4 2 4 2 2 2 2 2 3 + + 5/1152 y z + 5/576 y z + 1/192 y x z - 1/96 y x z + + 2 3 3 2 2 3 4 3 3 2 + - 1/48 y x z - 1/96 y x z - 5/576 y z + 5/288 z y - 1/48 z y x + + 4 4 2 2 2 2 2 + - 5/1152 z y + 1/48 z y x - 5/288 y z + 1/96 y x z + 1/96 y x z + + 2 3 2 3 3 2 3 3 3 + - 5/576 y z + 1/48 y x z + 5/288 y z + 5/576 y z - 5/288 y z + + 3 2 2 2 2 + + 5/576 y z - 5/576 y z - 5/1152 y z , COEFF(1, 2, 2) = + + 3 4 4 2 4 3 2 4 + - 1/288 y x z + 1/288 x y z + 1/144 y x z - 1/144 y x z + + 2 4 2 4 2 4 2 2 2 4 + + 1/576 y x z + 1/288 x y z + 1/576 x y z + 1/288 y x z + + 4 3 2 4 3 4 4 4 + - 1/288 x y z - 1/144 x y z - 1/576 z y x + 1/288 y x z + + 4 4 2 2 4 4 3 2 4 4 + - 1/288 z y x - 1/432 y z + 1/216 y z + 1/144 x y z - 1/216 y z + + 3 2 2 3 4 2 4 + + 1/144 y x z - 1/288 y x z + 1/288 y x z - 1/432 y z - 1/216 y z + + 2 2 2 3 2 2 2 3 2 3 + - 1/288 y x z + 1/288 y x z + 1/144 y x z + 1/72 y x z + + 3 2 2 3 4 3 3 3 2 + + 1/144 y x z + 1/216 y z - 1/108 z y + 1/144 z y x + 1/72 z y x + + 4 4 2 3 3 + + 1/432 z y - 1/144 y x z - 1/72 z y x + 1/108 y z - 1/144 y x z + + 2 2 2 2 2 2 2 + - 1/576 y x z - 1/144 y x z - 1/144 y x z - 1/288 y x z + + 2 3 2 3 3 2 3 3 3 + + 1/216 y z - 1/72 y x z - 1/108 y z - 1/216 y z + 1/108 y z + + 3 2 2 2 2 3 4 + - 1/216 y z + 1/216 y z + 1/432 y z , COEFF(2, 2, 2) = 1/576 y x z + + 4 2 4 3 2 4 2 4 + - 1/576 x y z - 1/576 y x z + 1/576 y x z - 1/1152 y x z + + 2 4 2 4 2 2 2 4 4 3 + - 1/1152 x y z - 1/1152 x y z - 1/1152 y x z + 1/576 x y z + + 2 4 3 4 4 4 4 4 2 + + 1/576 x y z + 1/1152 z y x - 1/576 y x z + 1/1152 z y x + + 2 4 4 3 2 4 4 3 + + 1/6912 y z - 1/3456 y z - 1/576 x y z + 1/3456 y z - 1/288 y x z + + 2 2 3 4 2 4 + + 1/576 y x z - 1/576 y x z + 1/6912 y z + 1/3456 y z + + 2 2 2 3 2 2 2 3 2 3 + + 1/1152 y x z - 1/576 y x z - 1/576 y x z - 1/288 y x z + + 3 2 2 3 4 3 3 + - 1/576 y x z - 1/3456 y z + 1/1728 z y - 1/288 z y x + + 3 2 4 4 2 + - 1/288 z y x - 1/6912 z y + 1/288 y x z + 1/288 z y x - 1/1728 y z + + 3 3 2 2 2 2 2 2 + + 1/288 y x z + 1/1152 y x z + 1/576 y x z + 1/576 y x z + + 2 2 3 2 3 3 2 3 + + 1/576 y x z - 1/3456 y z + 1/288 y x z + 1/1728 y z + 1/3456 y z + + 3 3 3 2 2 2 2 + - 1/1728 y z + 1/3456 y z - 1/3456 y z - 1/6912 y z ] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxx.compute.c"); +bytes used=28983607036, alloc=64737712, time=5906.59 +bytes used=28984607472, alloc=64737712, time=5906.68 +bytes 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1/3456 x z + 1/1152 y z + 1/864 z x , COEFF(-1, -2, -2) = + + 3 4 2 4 3 2 4 2 4 + 1/108 y x z - 1/576 y x z + 1/288 y x z - 1/72 y x z + + 3 3 4 3 3 3 3 2 2 4 + - 1/216 y x z + 1/432 z y x + 1/108 y x z - 1/192 y x z + + 4 4 2 3 2 3 3 2 3 + - 1/216 y x z + 1/144 z y x - 1/72 y x z + 1/72 z y x + + 3 4 3 3 3 3 2 2 4 + + 1/216 z y x - 1/216 z y x + 1/216 y x z + 1/144 y z + + 2 2 3 2 3 3 3 3 2 + - 1/144 z y x - 1/432 z y x - 1/108 z y x + 1/432 x z + + 3 3 4 3 4 4 2 4 + + 1/216 x z - 1/432 z x + 1/432 y z + 1/216 x z + 1/576 x z + + 3 2 2 3 2 2 2 + + 1/108 y x z - 1/216 z - 1/36 y x z + 1/36 y x z + 1/192 y x z + + 3 2 2 2 3 2 3 4 + - 1/108 y x z + 1/96 y x z + 1/288 y x z - 1/432 z + + 3 2 2 3 3 4 3 2 + - 1/288 y x z + 1/216 z - 1/216 y z - 1/108 z y + 1/432 z + + 3 3 2 2 + + 1/54 z y x + 1/144 z y x - 1/108 y x z - 1/288 z y x + 1/216 y z + + 3 3 2 2 2 2 2 2 + - 1/54 y x z + 1/72 y x z - 1/96 y x z + 1/576 y x z + + 2 2 3 2 3 2 + + 1/216 y x z + 1/72 y z - 1/144 y x z + 1/108 x z + 1/288 x z + + 3 2 3 3 3 2 3 3 2 + - 1/216 y z - 1/72 y z + 1/108 y z - 1/288 x z + 1/216 y z + + 3 2 2 2 2 2 2 + - 1/108 x z - 1/432 y z - 1/576 x z - 1/216 x z - 1/144 y z + + 3 3 4 2 4 + - 1/216 z x , COEFF(0, -2, -2) = - 5/288 y x z + 5/192 y x z + + 3 3 4 3 3 3 3 4 + + 1/144 y x z - 1/288 z y x - 1/72 y x z + 5/576 y x z + + 4 2 3 2 3 3 2 3 3 + - 1/96 z y x + 1/48 y x z - 1/48 z y x - 1/144 z y x + + 4 3 3 3 3 2 2 2 3 2 3 + + 1/144 z y x - 1/144 y x z + 1/96 z y x + 1/288 z y x + + 3 3 3 2 3 3 4 3 4 + + 1/72 z y x - 1/288 x z - 1/144 x z + 1/288 z x - 5/576 x z + + 3 2 2 3 3 2 3 + - 5/288 y x z + 5/96 y x z - 5/96 y x z + 5/288 y x z - 5/144 z y x + + 3 3 2 2 2 + + 5/288 y x z + 5/144 y x z - 5/192 y x z - 5/576 y x z - 5/288 x z + + 3 2 3 3 4 + + 5/288 x z + 5/576 x z + 1/144 z x , COEFF(1, -2, -2) = 1/108 y x z + + 2 4 3 2 4 2 4 3 3 + + 1/576 y x z - 1/288 y x z - 1/72 y x z - 1/216 y x z + + 4 3 3 3 3 2 2 4 4 + + 1/432 z y x + 1/108 y x z + 1/192 y x z - 1/216 y x z + + 4 2 3 2 3 3 2 3 3 + + 1/144 z y x - 1/72 y x z + 1/72 z y x + 1/216 z y x + + 4 3 3 3 3 2 2 4 2 2 3 + - 1/216 z y x + 1/216 y x z - 1/144 y z - 1/144 z y x + + 2 3 3 3 3 2 3 3 4 3 + - 1/432 z y x - 1/108 z y x + 1/432 x z + 1/216 x z - 1/432 z x + + 4 4 2 4 3 + - 1/432 y z + 1/216 x z - 1/576 x z + 1/108 y x z + 1/216 z + + 2 2 3 2 2 2 3 2 + - 1/36 y x z + 1/36 y x z - 1/192 y x z - 1/108 y x z + + 2 2 3 2 3 4 3 2 2 3 + - 1/96 y x z - 1/288 y x z + 1/432 z + 1/288 y x z - 1/216 z + + 3 4 3 2 3 3 2 + + 1/216 y z + 1/108 z y - 1/432 z + 1/54 z y x - 1/144 z y x + + 2 3 3 2 2 + - 1/108 y x z + 1/288 z y x - 1/216 y z - 1/54 y x z + 1/72 y x z + + 2 2 2 2 2 2 3 2 3 + + 1/96 y x z - 1/576 y x z + 1/216 y x z - 1/72 y z + 1/144 y x z + + 2 3 2 3 3 3 + + 1/108 x z - 1/288 x z + 1/216 y z + 1/72 y z - 1/108 y z + + 2 3 3 2 3 2 2 2 + + 1/288 x z - 1/216 y z - 1/108 x z + 1/432 y z + 1/576 x z + + 2 2 2 3 + - 1/216 x z + 1/144 y z - 1/216 z x , COEFF(2, -2, -2) = + + 3 4 2 4 3 2 4 2 4 + - 1/1728 y x z - 1/1152 y x z + 1/576 y x z + 1/1152 y x z + + 3 3 4 3 3 3 3 2 2 4 + + 1/864 y x z - 1/1728 z y x - 1/432 y x z - 1/384 y x z + + 4 4 2 3 2 3 3 2 3 + + 1/3456 y x z - 1/576 z y x + 1/288 y x z - 1/288 z y x + + 3 4 3 3 3 3 2 2 4 + - 1/864 z y x + 1/864 z y x - 1/864 y x z + 1/1152 y z + + 2 2 3 2 3 3 3 3 2 + + 1/576 z y x + 1/1728 z y x + 1/432 z y x - 1/1728 x z + + 3 3 4 3 4 4 2 4 + - 1/864 x z + 1/1728 z x + 1/3456 y z - 1/3456 x z + 1/1152 x z + + 3 2 2 3 2 2 2 + - 1/1728 y x z - 1/1728 z + 1/576 y x z - 1/576 y x z + 1/384 y x z + + 3 2 2 2 3 2 3 4 + + 1/1728 y x z + 1/192 y x z + 1/576 y x z - 1/3456 z + + 3 2 2 3 3 4 3 2 + - 1/576 y x z + 1/1728 z - 1/1728 y z - 1/864 z y + 1/3456 z + + 3 3 2 2 + - 1/864 z y x + 1/288 z y x + 1/1728 y x z - 1/576 z y x + 1/1728 y z + + 3 3 2 2 2 2 2 2 + + 1/864 y x z - 1/1152 y x z - 1/192 y x z + 1/1152 y x z + + 2 2 3 2 3 2 + - 1/3456 y x z + 1/576 y z - 1/288 y x z - 1/1728 x z + 1/576 x z + + 3 2 3 3 3 2 3 3 2 + - 1/1728 y z - 1/576 y z + 1/864 y z - 1/576 x z + 1/1728 y z + + 3 2 2 2 2 2 2 + + 1/1728 x z - 1/3456 y z - 1/1152 x z + 1/3456 x z - 1/1152 y z + + 3 3 4 2 4 + + 1/864 z x , COEFF(-2, -1, -2) = 1/432 y x z - 1/72 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/144 y x z - 1/576 y x z - 1/54 y x z + 1/108 z y x + + 3 3 3 2 2 4 4 4 2 3 + + 1/108 y x z - 1/192 y x z - 1/216 y x z + 1/288 z y x + + 2 3 3 2 3 3 4 3 3 + - 1/144 y x z + 1/144 z y x + 1/54 z y x - 1/216 z y x + + 3 3 2 2 4 2 2 3 2 3 + + 1/216 y x z + 1/576 y z - 1/288 z y x - 1/108 z y x + + 3 3 3 2 3 3 4 3 4 + - 1/108 z y x + 1/216 x z + 1/108 x z - 1/216 z x + 1/216 y z + + 4 2 4 3 2 + + 1/432 x z + 1/144 x z + 1/108 y x z - 1/216 z - 1/288 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/288 y x z + 1/192 y x z - 1/432 y x z + 1/96 y x z + + 2 3 4 3 2 2 3 3 4 + + 1/36 y x z - 1/432 z - 1/144 y x z + 1/216 z - 1/432 y z + + 3 2 3 3 2 + - 1/216 z y + 1/432 z + 1/216 z y x + 1/72 z y x - 1/108 y x z + + 2 3 3 2 2 2 2 + - 1/36 z y x + 1/108 y z - 1/216 y x z + 1/576 y x z - 1/96 y x z + + 2 2 2 2 3 2 3 + + 1/72 y x z + 1/216 y x z + 1/288 y z - 1/72 y x z + 1/216 x z + + 2 3 2 3 3 3 2 3 + + 1/72 x z - 1/108 y z - 1/288 y z + 1/216 y z - 1/72 x z + + 3 2 3 2 2 2 2 + + 1/432 y z - 1/216 x z - 1/216 y z - 1/144 x z - 1/432 x z + + 2 2 3 3 4 + - 1/576 y z - 1/108 z x , COEFF(-1, -1, -2) = - 1/27 y x z + + 2 4 3 2 4 2 4 3 3 + + 1/36 y x z - 1/72 y x z + 1/36 y x z + 2/27 y x z + + 4 3 3 3 3 2 2 4 4 + - 1/27 z y x - 1/27 y x z + 1/96 y x z + 2/27 y x z + + 4 2 3 2 3 3 2 3 3 + - 1/72 z y x + 1/36 y x z - 1/36 z y x - 2/27 z y x + + 4 3 3 3 3 2 2 4 2 2 3 + + 1/54 z y x - 1/54 y x z - 1/72 y z + 1/72 z y x + + 2 3 3 3 3 2 3 3 4 3 + + 1/27 z y x + 1/27 z y x - 1/54 x z - 1/27 x z + 1/54 z x + + 4 4 2 4 3 2 + - 1/27 y z - 1/27 x z - 1/72 x z - 4/27 y x z + 1/27 z + 1/18 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/18 y x z - 1/96 y x z + 1/27 y x z - 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/18 y x z + 1/54 z + 1/72 y x z - 1/27 z + 1/54 y z + + 3 2 3 3 2 + + 1/27 z y - 1/54 z - 2/27 z y x - 1/36 z y x + 4/27 y x z + + 2 3 3 2 2 2 2 + + 1/18 z y x - 2/27 y z + 2/27 y x z - 1/36 y x z + 1/48 y x z + + 2 2 2 2 3 2 3 + - 1/36 y x z - 2/27 y x z - 1/36 y z + 1/36 y x z - 2/27 x z + + 2 3 2 3 3 3 2 3 + - 1/36 x z + 2/27 y z + 1/36 y z - 1/27 y z + 1/36 x z + + 3 2 3 2 2 2 2 2 2 + - 1/54 y z + 2/27 x z + 1/27 y z + 1/72 x z + 1/27 x z + 1/72 y z + + 3 3 4 2 4 3 3 + + 1/27 z x , COEFF(0, -1, -2) = 5/72 y x z - 5/96 y x z - 1/9 y x z + + 4 3 3 3 3 4 4 2 3 + + 1/18 z y x + 1/18 y x z - 5/36 y x z + 1/48 z y x + + 2 3 3 2 3 3 4 3 3 + - 1/24 y x z + 1/24 z y x + 1/9 z y x - 1/36 z y x + + 3 3 2 2 2 3 2 3 3 3 3 2 + + 1/36 y x z - 1/48 z y x - 1/18 z y x - 1/18 z y x + 1/36 x z + + 3 3 4 3 4 3 2 + + 1/18 x z - 1/36 z x + 5/72 x z + 5/18 y x z - 5/48 y x z + + 2 3 3 2 3 3 3 + + 5/48 y x z - 5/72 y x z + 5/36 z y x - 5/18 y x z - 5/36 y x z + + 2 2 2 3 2 + + 5/96 y x z + 5/36 y x z + 5/36 x z - 5/36 x z - 5/72 x z + + 3 3 4 2 4 + - 1/18 z x , COEFF(1, -1, -2) = - 1/27 y x z - 1/36 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/72 y x z + 1/36 y x z + 2/27 y x z - 1/27 z y x + + 3 3 3 2 2 4 4 4 2 3 + - 1/27 y x z - 1/96 y x z + 2/27 y x z - 1/72 z y x + + 2 3 3 2 3 3 4 3 3 + + 1/36 y x z - 1/36 z y x - 2/27 z y x + 1/54 z y x + + 3 3 2 2 4 2 2 3 2 3 3 3 + - 1/54 y x z + 1/72 y z + 1/72 z y x + 1/27 z y x + 1/27 z y x + + 3 2 3 3 4 3 4 4 + - 1/54 x z - 1/27 x z + 1/54 z x + 1/27 y z - 1/27 x z + + 2 4 3 2 2 3 + + 1/72 x z - 4/27 y x z - 1/27 z + 1/18 y x z - 1/18 y x z + + 2 2 2 3 2 2 2 3 2 3 4 + + 1/96 y x z + 1/27 y x z + 1/48 y x z + 1/18 y x z - 1/54 z + + 3 2 2 3 3 4 3 2 3 + - 1/72 y x z + 1/27 z - 1/54 y z - 1/27 z y + 1/54 z - 2/27 z y x + + 3 2 2 3 3 + + 1/36 z y x + 4/27 y x z - 1/18 z y x + 2/27 y z + 2/27 y x z + + 2 2 2 2 2 2 2 2 + - 1/36 y x z - 1/48 y x z + 1/36 y x z - 2/27 y x z + 1/36 y z + + 3 2 3 2 3 2 3 + - 1/36 y x z - 2/27 x z + 1/36 x z - 2/27 y z - 1/36 y z + + 3 3 2 3 3 2 3 2 + + 1/27 y z - 1/36 x z + 1/54 y z + 2/27 x z - 1/27 y z + + 2 2 2 2 2 3 + - 1/72 x z + 1/27 x z - 1/72 y z + 1/27 z x , COEFF(2, -1, -2) = + + 3 4 2 4 3 2 4 2 4 + 1/432 y x z + 1/72 y x z - 1/144 y x z - 1/576 y x z + + 3 3 4 3 3 3 3 2 2 4 + - 1/54 y x z + 1/108 z y x + 1/108 y x z + 1/192 y x z + + 4 4 2 3 2 3 3 2 3 + - 1/216 y x z + 1/288 z y x - 1/144 y x z + 1/144 z y x + + 3 4 3 3 3 3 2 2 4 + + 1/54 z y x - 1/216 z y x + 1/216 y x z - 1/576 y z + + 2 2 3 2 3 3 3 3 2 + - 1/288 z y x - 1/108 z y x - 1/108 z y x + 1/216 x z + + 3 3 4 3 4 4 2 4 + + 1/108 x z - 1/216 z x - 1/216 y z + 1/432 x z - 1/144 x z + + 3 2 2 3 2 2 2 + + 1/108 y x z + 1/216 z - 1/288 y x z + 1/288 y x z - 1/192 y x z + + 3 2 2 2 3 2 3 4 3 2 2 + - 1/432 y x z - 1/96 y x z - 1/36 y x z + 1/432 z + 1/144 y x z + + 3 3 4 3 2 3 + - 1/216 z + 1/432 y z + 1/216 z y - 1/432 z + 1/216 z y x + + 3 2 2 3 3 + - 1/72 z y x - 1/108 y x z + 1/36 z y x - 1/108 y z - 1/216 y x z + + 2 2 2 2 2 2 2 2 + + 1/576 y x z + 1/96 y x z - 1/72 y x z + 1/216 y x z - 1/288 y z + + 3 2 3 2 3 2 3 + + 1/72 y x z + 1/216 x z - 1/72 x z + 1/108 y z + 1/288 y z + + 3 3 2 3 3 2 3 2 + - 1/216 y z + 1/72 x z - 1/432 y z - 1/216 x z + 1/216 y z + + 2 2 2 2 2 3 + + 1/144 x z - 1/432 x z + 1/576 y z - 1/108 z x , COEFF(-2, 0, -2) = + + 3 4 2 4 3 2 4 3 3 + - 1/288 y x z + 5/192 y x z - 1/96 y x z + 5/144 y x z + + 4 3 3 3 3 4 3 + - 5/288 z y x - 1/72 y x z + 5/576 y x z - 5/144 z y x + + 4 3 3 3 3 2 2 3 3 3 + + 1/144 z y x - 1/144 y x z + 5/288 z y x + 1/72 z y x + + 4 3 3 2 2 3 3 2 2 + - 5/576 y z - 5/288 y x z + 1/288 y x z - 5/96 y x z + 1/96 y x z + + 3 4 3 3 3 2 + + 1/288 y z + 1/144 z y - 1/144 z y x - 1/48 z y x + 5/288 y x z + + 2 3 3 2 2 2 + + 5/96 z y x - 5/288 y z + 1/144 y x z - 5/192 y x z - 5/576 y x z + + 3 2 3 3 3 3 3 2 2 + + 1/48 y x z + 5/288 y z - 1/144 y z - 1/288 y z + 5/576 y z , + + 3 4 2 4 3 2 4 + COEFF(-1, 0, -2) = 1/18 y x z - 5/96 y x z + 1/48 y x z + + 3 3 4 3 3 3 3 4 3 + - 5/36 y x z + 5/72 z y x + 1/18 y x z - 5/36 y x z + 5/36 z y x + + 4 3 3 3 3 2 2 3 3 3 4 + - 1/36 z y x + 1/36 y x z - 5/72 z y x - 1/18 z y x + 5/72 y z + + 3 3 2 2 3 3 2 2 3 4 + + 5/18 y x z - 1/18 y x z + 5/48 y x z - 1/48 y x z - 1/36 y z + + 3 3 3 2 2 + - 1/18 z y + 1/9 z y x + 1/24 z y x - 5/18 y x z - 5/48 z y x + + 3 3 2 2 2 3 2 3 + + 5/36 y z - 1/9 y x z + 5/96 y x z + 5/36 y x z - 1/24 y x z + + 3 3 3 3 2 2 + - 5/36 y z + 1/18 y z + 1/36 y z - 5/72 y z , COEFF(0, 0, -2) = + + 3 3 4 3 3 3 3 3 3 3 + - 5/24 z y x - 5/48 y x z + 5/24 y x z - 1/12 y x z + 5/24 y x z + + 4 3 3 2 3 25 3 3 3 3 2 + + 1/24 z y x + 5/48 z y x - -- y x z + 1/12 z y x + 5/48 y x z + 48 + + 25 4 3 4 3 25 2 25 + + -- y x z - 5/24 z y x - 5/48 z y x - -- y x z + -- y x z + 96 96 48 + + 3 3 2 3 4 2 4 + - 1/24 y x z , COEFF(1, 0, -2) = 1/18 y x z + 5/96 y x z + + 3 2 4 3 3 4 3 3 3 3 + - 1/48 y x z - 5/36 y x z + 5/72 z y x + 1/18 y x z + + 4 3 4 3 3 3 3 2 2 3 + - 5/36 y x z + 5/36 z y x - 1/36 z y x + 1/36 y x z - 5/72 z y x + + 3 3 4 3 3 2 2 3 + - 1/18 z y x - 5/72 y z + 5/18 y x z - 1/18 y x z - 5/48 y x z + + 3 2 2 3 4 3 3 3 2 + + 1/48 y x z + 1/36 y z + 1/18 z y + 1/9 z y x - 1/24 z y x + + 2 3 3 2 2 + - 5/18 y x z + 5/48 z y x - 5/36 y z - 1/9 y x z - 5/96 y x z + + 2 3 2 3 3 3 3 3 2 + + 5/36 y x z + 1/24 y x z + 5/36 y z - 1/18 y z - 1/36 y z + + 2 3 4 2 4 + + 5/72 y z , COEFF(2, 0, -2) = - 1/288 y x z - 5/192 y x z + + 3 2 4 3 3 4 3 3 3 3 + + 1/96 y x z + 5/144 y x z - 5/288 z y x - 1/72 y x z + + 4 3 4 3 3 3 3 2 + + 5/576 y x z - 5/144 z y x + 1/144 z y x - 1/144 y x z + + 2 3 3 3 4 3 3 2 + + 5/288 z y x + 1/72 z y x + 5/576 y z - 5/288 y x z + 1/288 y x z + + 2 3 3 2 2 3 4 3 3 + + 5/96 y x z - 1/96 y x z - 1/288 y z - 1/144 z y - 1/144 z y x + + 3 2 2 3 3 + + 1/48 z y x + 5/288 y x z - 5/96 z y x + 5/288 y z + 1/144 y x z + + 2 2 2 3 2 3 3 3 3 + + 5/192 y x z - 5/576 y x z - 1/48 y x z - 5/288 y z + 1/144 y z + + 3 2 2 3 4 + + 1/288 y z - 5/576 y z , COEFF(-2, 1, -2) = 1/432 y x z + + 2 4 3 2 4 2 4 3 3 + - 1/72 y x z + 1/144 y x z + 1/576 y x z - 1/54 y x z + + 4 3 3 3 3 2 2 4 4 + + 1/108 z y x + 1/108 y x z + 1/192 y x z - 1/216 y x z + + 4 2 3 2 3 3 2 3 3 + - 1/288 z y x + 1/144 y x z - 1/144 z y x + 1/54 z y x + + 4 3 3 3 3 2 2 4 2 2 3 + - 1/216 z y x + 1/216 y x z - 1/576 y z + 1/288 z y x + + 2 3 3 3 3 2 3 3 4 3 + - 1/108 z y x - 1/108 z y x - 1/216 x z - 1/108 x z + 1/216 z x + + 4 4 2 4 3 + + 1/216 y z - 1/432 x z - 1/144 x z + 1/108 y x z + 1/216 z + + 2 2 3 2 2 2 3 2 + + 1/288 y x z - 1/288 y x z - 1/192 y x z - 1/432 y x z + + 2 2 3 2 3 4 3 2 2 3 + - 1/96 y x z + 1/36 y x z + 1/432 z - 1/144 y x z - 1/216 z + + 3 4 3 2 3 3 2 + - 1/432 y z - 1/216 z y - 1/432 z + 1/216 z y x + 1/72 z y x + + 2 3 3 2 2 + - 1/108 y x z - 1/36 z y x + 1/108 y z - 1/216 y x z - 1/576 y x z + + 2 2 2 2 2 2 3 2 3 + + 1/96 y x z + 1/72 y x z + 1/216 y x z - 1/288 y z - 1/72 y x z + + 2 3 2 3 3 3 + - 1/216 x z - 1/72 x z - 1/108 y z + 1/288 y z + 1/216 y z + + 2 3 3 2 3 2 2 2 + + 1/72 x z + 1/432 y z + 1/216 x z - 1/216 y z + 1/144 x z + + 2 2 2 3 3 4 + + 1/432 x z + 1/576 y z + 1/108 z x , COEFF(-1, 1, -2) = - 1/27 y x z + + 2 4 3 2 4 2 4 3 3 + + 1/36 y x z - 1/72 y x z - 1/36 y x z + 2/27 y x z + + 4 3 3 3 3 2 2 4 4 + - 1/27 z y x - 1/27 y x z - 1/96 y x z + 2/27 y x z + + 4 2 3 2 3 3 2 3 3 + + 1/72 z y x - 1/36 y x z + 1/36 z y x - 2/27 z y x + + 4 3 3 3 3 2 2 4 2 2 3 + + 1/54 z y x - 1/54 y x z + 1/72 y z - 1/72 z y x + + 2 3 3 3 3 2 3 3 4 3 + + 1/27 z y x + 1/27 z y x + 1/54 x z + 1/27 x z - 1/54 z x + + 4 4 2 4 3 2 + - 1/27 y z + 1/27 x z + 1/72 x z - 4/27 y x z - 1/27 z - 1/18 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/18 y x z + 1/96 y x z + 1/27 y x z + 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/18 y x z - 1/54 z + 1/72 y x z + 1/27 z + 1/54 y z + + 3 2 3 3 2 + + 1/27 z y + 1/54 z - 2/27 z y x - 1/36 z y x + 4/27 y x z + + 2 3 3 2 2 2 2 + + 1/18 z y x - 2/27 y z + 2/27 y x z + 1/36 y x z - 1/48 y x z + + 2 2 2 2 3 2 3 + - 1/36 y x z - 2/27 y x z + 1/36 y z + 1/36 y x z + 2/27 x z + + 2 3 2 3 3 3 2 3 + + 1/36 x z + 2/27 y z - 1/36 y z - 1/27 y z - 1/36 x z + + 3 2 3 2 2 2 2 2 2 + - 1/54 y z - 2/27 x z + 1/27 y z - 1/72 x z - 1/27 x z - 1/72 y z + + 3 3 4 2 4 3 3 + - 1/27 z x , COEFF(0, 1, -2) = 5/72 y x z + 5/96 y x z - 1/9 y x z + + 4 3 3 3 3 4 4 2 3 + + 1/18 z y x + 1/18 y x z - 5/36 y x z - 1/48 z y x + + 2 3 3 2 3 3 4 3 3 + + 1/24 y x z - 1/24 z y x + 1/9 z y x - 1/36 z y x + + 3 3 2 2 2 3 2 3 3 3 3 2 + + 1/36 y x z + 1/48 z y x - 1/18 z y x - 1/18 z y x - 1/36 x z + + 3 3 4 3 4 3 2 + - 1/18 x z + 1/36 z x - 5/72 x z + 5/18 y x z + 5/48 y x z + + 2 3 3 2 3 3 3 + - 5/48 y x z - 5/72 y x z + 5/36 z y x - 5/18 y x z - 5/36 y x z + + 2 2 2 3 2 + - 5/96 y x z + 5/36 y x z - 5/36 x z + 5/36 x z + 5/72 x z + + 3 3 4 2 4 + + 1/18 z x , COEFF(1, 1, -2) = - 1/27 y x z - 1/36 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/72 y x z - 1/36 y x z + 2/27 y x z - 1/27 z y x + + 3 3 3 2 2 4 4 4 2 3 + - 1/27 y x z + 1/96 y x z + 2/27 y x z + 1/72 z y x + + 2 3 3 2 3 3 4 3 3 + - 1/36 y x z + 1/36 z y x - 2/27 z y x + 1/54 z y x + + 3 3 2 2 4 2 2 3 2 3 3 3 + - 1/54 y x z - 1/72 y z - 1/72 z y x + 1/27 z y x + 1/27 z y x + + 3 2 3 3 4 3 4 4 + + 1/54 x z + 1/27 x z - 1/54 z x + 1/27 y z + 1/27 x z + + 2 4 3 2 2 3 + - 1/72 x z - 4/27 y x z + 1/27 z - 1/18 y x z + 1/18 y x z + + 2 2 2 3 2 2 2 3 2 3 4 + - 1/96 y x z + 1/27 y x z - 1/48 y x z + 1/18 y x z + 1/54 z + + 3 2 2 3 3 4 3 2 3 + - 1/72 y x z - 1/27 z - 1/54 y z - 1/27 z y - 1/54 z - 2/27 z y x + + 3 2 2 3 3 + + 1/36 z y x + 4/27 y x z - 1/18 z y x + 2/27 y z + 2/27 y x z + + 2 2 2 2 2 2 2 2 + + 1/36 y x z + 1/48 y x z + 1/36 y x z - 2/27 y x z - 1/36 y z + + 3 2 3 2 3 2 3 + - 1/36 y x z + 2/27 x z - 1/36 x z - 2/27 y z + 1/36 y z + + 3 3 2 3 3 2 3 2 + + 1/27 y z + 1/36 x z + 1/54 y z - 2/27 x z - 1/27 y z + + 2 2 2 2 2 3 + + 1/72 x z - 1/27 x z + 1/72 y z - 1/27 z x , COEFF(2, 1, -2) = + + 3 4 2 4 3 2 4 2 4 + 1/432 y x z + 1/72 y x z - 1/144 y x z + 1/576 y x z + + 3 3 4 3 3 3 3 2 2 4 + - 1/54 y x z + 1/108 z y x + 1/108 y x z - 1/192 y x z + + 4 4 2 3 2 3 3 2 3 + - 1/216 y x z - 1/288 z y x + 1/144 y x z - 1/144 z y x + + 3 4 3 3 3 3 2 2 4 + + 1/54 z y x - 1/216 z y x + 1/216 y x z + 1/576 y z + + 2 2 3 2 3 3 3 3 2 + + 1/288 z y x - 1/108 z y x - 1/108 z y x - 1/216 x z + + 3 3 4 3 4 4 2 4 + - 1/108 x z + 1/216 z x - 1/216 y z - 1/432 x z + 1/144 x z + + 3 2 2 3 2 2 2 + + 1/108 y x z - 1/216 z + 1/288 y x z - 1/288 y x z + 1/192 y x z + + 3 2 2 2 3 2 3 4 3 2 2 + - 1/432 y x z + 1/96 y x z - 1/36 y x z - 1/432 z + 1/144 y x z + + 3 3 4 3 2 3 + + 1/216 z + 1/432 y z + 1/216 z y + 1/432 z + 1/216 z y x + + 3 2 2 3 3 + - 1/72 z y x - 1/108 y x z + 1/36 z y x - 1/108 y z - 1/216 y x z + + 2 2 2 2 2 2 2 2 + - 1/576 y x z - 1/96 y x z - 1/72 y x z + 1/216 y x z + 1/288 y z + + 3 2 3 2 3 2 3 + + 1/72 y x z - 1/216 x z + 1/72 x z + 1/108 y z - 1/288 y z + + 3 3 2 3 3 2 3 2 + - 1/216 y z - 1/72 x z - 1/432 y z + 1/216 x z + 1/216 y z + + 2 2 2 2 2 3 + - 1/144 x z + 1/432 x z - 1/576 y z + 1/108 z x , COEFF(-2, 2, -2) = + + 3 4 2 4 3 2 4 2 4 + - 1/1728 y x z + 1/1152 y x z - 1/576 y x z - 1/1152 y x z + + 3 3 4 3 3 3 3 2 2 4 + + 1/864 y x z - 1/1728 z y x - 1/432 y x z - 1/384 y x z + + 4 4 2 3 2 3 3 2 3 + + 1/3456 y x z + 1/576 z y x - 1/288 y x z + 1/288 z y x + + 3 4 3 3 3 3 2 2 4 + - 1/864 z y x + 1/864 z y x - 1/864 y x z + 1/1152 y z + + 2 2 3 2 3 3 3 3 2 + - 1/576 z y x + 1/1728 z y x + 1/432 z y x + 1/1728 x z + + 3 3 4 3 4 4 2 4 + + 1/864 x z - 1/1728 z x - 1/3456 y z + 1/3456 x z + 1/1152 x z + + 3 2 2 3 2 2 2 + - 1/1728 y x z - 1/1728 z - 1/576 y x z + 1/576 y x z + 1/384 y x z + + 3 2 2 2 3 2 3 4 + + 1/1728 y x z + 1/192 y x z - 1/576 y x z - 1/3456 z + + 3 2 2 3 3 4 3 2 + + 1/576 y x z + 1/1728 z + 1/1728 y z + 1/864 z y + 1/3456 z + + 3 3 2 2 + - 1/864 z y x - 1/288 z y x + 1/1728 y x z + 1/576 z y x - 1/1728 y z + + 3 3 2 2 2 2 2 2 + + 1/864 y x z + 1/1152 y x z - 1/192 y x z - 1/1152 y x z + + 2 2 3 2 3 2 + - 1/3456 y x z + 1/576 y z + 1/288 y x z + 1/1728 x z + 1/576 x z + + 3 2 3 3 3 2 3 3 2 + + 1/1728 y z - 1/576 y z - 1/864 y z - 1/576 x z - 1/1728 y z + + 3 2 2 2 2 2 2 + - 1/1728 x z + 1/3456 y z - 1/1152 x z - 1/3456 x z - 1/1152 y z + + 3 3 4 2 4 + - 1/864 z x , COEFF(-1, 2, -2) = 1/108 y x z - 1/576 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/288 y x z + 1/72 y x z - 1/216 y x z + 1/432 z y x + + 3 3 3 2 2 4 4 4 2 3 + + 1/108 y x z + 1/192 y x z - 1/216 y x z - 1/144 z y x + + 2 3 3 2 3 3 4 3 3 + + 1/72 y x z - 1/72 z y x + 1/216 z y x - 1/216 z y x + + 3 3 2 2 4 2 2 3 2 3 + + 1/216 y x z - 1/144 y z + 1/144 z y x - 1/432 z y x + + 3 3 3 2 3 3 4 3 4 + - 1/108 z y x - 1/432 x z - 1/216 x z + 1/432 z x + 1/432 y z + + 4 2 4 3 2 + - 1/216 x z - 1/576 x z + 1/108 y x z + 1/216 z + 1/36 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/36 y x z - 1/192 y x z - 1/108 y x z - 1/96 y x z + + 2 3 4 3 2 2 3 3 4 + + 1/288 y x z + 1/432 z - 1/288 y x z - 1/216 z - 1/216 y z + + 3 2 3 3 2 + - 1/108 z y - 1/432 z + 1/54 z y x + 1/144 z y x - 1/108 y x z + + 2 3 3 2 2 2 2 + - 1/288 z y x + 1/216 y z - 1/54 y x z - 1/72 y x z + 1/96 y x z + + 2 2 2 2 3 2 3 + + 1/576 y x z + 1/216 y x z - 1/72 y z - 1/144 y x z - 1/108 x z + + 2 3 2 3 3 3 2 3 + - 1/288 x z - 1/216 y z + 1/72 y z + 1/108 y z + 1/288 x z + + 3 2 3 2 2 2 2 + + 1/216 y z + 1/108 x z - 1/432 y z + 1/576 x z + 1/216 x z + + 2 2 3 3 4 + + 1/144 y z + 1/216 z x , COEFF(0, 2, -2) = - 5/288 y x z + + 2 4 3 3 4 3 3 3 3 + - 5/192 y x z + 1/144 y x z - 1/288 z y x - 1/72 y x z + + 4 4 2 3 2 3 3 2 3 + + 5/576 y x z + 1/96 z y x - 1/48 y x z + 1/48 z y x + + 3 4 3 3 3 3 2 2 2 3 + - 1/144 z y x + 1/144 z y x - 1/144 y x z - 1/96 z y x + + 2 3 3 3 3 2 3 3 4 3 + + 1/288 z y x + 1/72 z y x + 1/288 x z + 1/144 x z - 1/288 z x + + 4 3 2 2 3 3 2 + + 5/576 x z - 5/288 y x z - 5/96 y x z + 5/96 y x z + 5/288 y x z + + 3 3 3 2 2 + - 5/144 z y x + 5/288 y x z + 5/144 y x z + 5/192 y x z + + 2 3 2 3 + - 5/576 y x z + 5/288 x z - 5/288 x z - 5/576 x z - 1/144 z x , + + 3 4 2 4 3 2 4 + COEFF(1, 2, -2) = 1/108 y x z + 1/576 y x z - 1/288 y x z + + 2 4 3 3 4 3 3 3 3 + + 1/72 y x z - 1/216 y x z + 1/432 z y x + 1/108 y x z + + 2 2 4 4 4 2 3 2 3 3 + - 1/192 y x z - 1/216 y x z - 1/144 z y x + 1/72 y x z + + 2 3 3 4 3 3 3 3 2 + - 1/72 z y x + 1/216 z y x - 1/216 z y x + 1/216 y x z + + 2 4 2 2 3 2 3 3 3 + + 1/144 y z + 1/144 z y x - 1/432 z y x - 1/108 z y x + + 3 2 3 3 4 3 4 4 + - 1/432 x z - 1/216 x z + 1/432 z x - 1/432 y z - 1/216 x z + + 2 4 3 2 2 3 + + 1/576 x z + 1/108 y x z - 1/216 z + 1/36 y x z - 1/36 y x z + + 2 2 2 3 2 2 2 3 2 3 + + 1/192 y x z - 1/108 y x z + 1/96 y x z - 1/288 y x z + + 4 3 2 2 3 3 4 3 + - 1/432 z + 1/288 y x z + 1/216 z + 1/216 y z + 1/108 z y + + 2 3 3 2 2 + + 1/432 z + 1/54 z y x - 1/144 z y x - 1/108 y x z + 1/288 z y x + + 3 3 2 2 2 2 2 2 + - 1/216 y z - 1/54 y x z - 1/72 y x z - 1/96 y x z - 1/576 y x z + + 2 2 3 2 3 2 + + 1/216 y x z + 1/72 y z + 1/144 y x z - 1/108 x z + 1/288 x z + + 3 2 3 3 3 2 3 3 2 + + 1/216 y z - 1/72 y z - 1/108 y z - 1/288 x z - 1/216 y z + + 3 2 2 2 2 2 2 + + 1/108 x z + 1/432 y z - 1/576 x z + 1/216 x z - 1/144 y z + + 3 3 4 2 4 + + 1/216 z x , COEFF(2, 2, -2) = - 1/1728 y x z - 1/1152 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/576 y x z - 1/1152 y x z + 1/864 y x z - 1/1728 z y x + + 3 3 3 2 2 4 4 4 2 3 + - 1/432 y x z + 1/384 y x z + 1/3456 y x z + 1/576 z y x + + 2 3 3 2 3 3 4 3 3 + - 1/288 y x z + 1/288 z y x - 1/864 z y x + 1/864 z y x + + 3 3 2 2 4 2 2 3 2 3 + - 1/864 y x z - 1/1152 y z - 1/576 z y x + 1/1728 z y x + + 3 3 3 2 3 3 4 3 4 + + 1/432 z y x + 1/1728 x z + 1/864 x z - 1/1728 z x + 1/3456 y z + + 4 2 4 3 2 + + 1/3456 x z - 1/1152 x z - 1/1728 y x z + 1/1728 z - 1/576 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/576 y x z - 1/384 y x z + 1/1728 y x z - 1/192 y x z + + 2 3 4 3 2 2 3 3 4 + + 1/576 y x z + 1/3456 z - 1/576 y x z - 1/1728 z - 1/1728 y z + + 3 2 3 3 2 + - 1/864 z y - 1/3456 z - 1/864 z y x + 1/288 z y x + 1/1728 y x z + + 2 3 3 2 2 + - 1/576 z y x + 1/1728 y z + 1/864 y x z + 1/1152 y x z + + 2 2 2 2 2 2 + + 1/192 y x z + 1/1152 y x z - 1/3456 y x z - 1/576 y z + + 3 2 3 2 3 2 3 + - 1/288 y x z + 1/1728 x z - 1/576 x z - 1/1728 y z + 1/576 y z + + 3 3 2 3 3 2 3 2 + + 1/864 y z + 1/576 x z + 1/1728 y z - 1/1728 x z - 1/3456 y z + + 2 2 2 2 2 3 + + 1/1152 x z - 1/3456 x z + 1/1152 y z - 1/864 z x , + + 3 4 2 4 3 2 4 + COEFF(-2, -2, -1) = 1/432 y x z - 1/288 y x z + 1/144 y x z + + 2 4 3 3 4 3 3 3 3 + - 1/288 y x z - 1/432 y x z + 1/432 z y x + 1/216 y x z + + 2 2 4 4 4 2 3 2 3 3 + - 1/96 y x z - 1/864 y x z + 1/144 z y x - 1/144 y x z + + 2 3 3 4 3 3 3 3 2 + + 1/36 z y x + 1/108 z y x - 1/216 z y x + 1/54 y x z + + 2 4 2 2 3 2 3 3 3 3 2 + + 1/288 y z - 1/36 z y x - 1/108 z y x - 1/54 z y x + 1/108 x z + + 3 3 4 3 4 4 2 4 + + 1/432 x z - 1/432 z x + 1/864 y z + 1/864 x z + 1/288 x z + + 3 2 2 3 2 2 2 + + 1/864 y x z - 1/216 z - 1/72 y x z + 1/288 y x z + 1/24 y x z + + 3 2 2 2 3 2 3 4 3 2 2 + - 1/108 y x z + 1/96 y x z + 1/288 y x z - 1/864 z - 1/36 y x z + + 3 3 4 3 2 3 + + 1/864 z - 1/432 y z - 1/108 z y + 1/216 z + 1/108 z y x + + 3 2 2 3 3 + + 1/36 z y x - 1/216 y x z - 1/72 z y x + 1/216 y z - 1/432 y x z + + 2 2 2 2 2 2 2 2 + + 1/72 y x z - 1/24 y x z + 1/72 y x z + 1/216 y x z + 1/72 y z + + 3 2 3 2 3 2 3 + - 1/144 y x z + 1/216 x z + 1/72 x z - 1/864 y z - 1/288 y z + + 3 3 2 3 3 2 3 2 + + 1/432 y z - 1/288 x z + 1/108 y z - 1/864 x z - 1/216 y z + + 2 2 2 2 2 3 + - 1/72 x z - 1/216 x z - 1/72 y z - 1/108 z x , COEFF(-1, -2, -1) = + + 3 4 2 4 3 2 4 2 4 + - 1/27 y x z + 1/144 y x z - 1/72 y x z + 1/18 y x z + + 3 3 4 3 3 3 3 2 2 4 + + 1/108 y x z - 1/108 z y x - 1/54 y x z + 1/48 y x z + + 4 4 2 3 2 3 3 2 3 3 + + 1/54 y x z - 1/36 z y x + 1/36 y x z - 1/9 z y x - 1/27 z y x + + 4 3 3 3 3 2 2 4 2 2 3 2 3 + + 1/54 z y x - 2/27 y x z - 1/36 y z + 1/9 z y x + 1/27 z y x + + 3 3 3 2 3 3 4 3 4 + + 2/27 z y x - 1/27 x z - 1/108 x z + 1/108 z x - 1/108 y z + + 4 2 4 3 2 + - 1/54 x z - 1/144 x z - 1/54 y x z + 1/27 z + 2/9 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/18 y x z - 1/12 y x z + 4/27 y x z - 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/144 y x z + 1/108 z + 1/18 y x z - 1/108 z + 1/54 y z + + 3 2 3 3 2 + + 2/27 z y - 1/27 z - 4/27 z y x - 1/18 z y x + 2/27 y x z + + 2 3 3 2 2 2 2 + + 1/36 z y x - 1/27 y z + 1/27 y x z - 2/9 y x z + 1/12 y x z + + 2 2 2 2 3 2 3 + - 1/36 y x z - 2/27 y x z - 1/9 y z + 1/72 y x z - 2/27 x z + + 2 3 2 3 3 3 2 3 + - 1/36 x z + 1/108 y z + 1/36 y z - 1/54 y z + 1/144 x z + + 3 2 3 2 2 2 2 2 2 + - 2/27 y z + 1/54 x z + 1/27 y z + 1/36 x z + 2/27 x z + 1/9 y z + + 3 3 4 2 4 3 3 + + 1/27 z x , COEFF(0, -2, -1) = 5/72 y x z - 5/48 y x z - 1/72 y x z + + 4 3 3 3 3 4 4 2 3 + + 1/72 z y x + 1/36 y x z - 5/144 y x z + 1/24 z y x + + 2 3 3 2 3 3 4 3 3 3 3 2 + - 1/24 y x z + 1/6 z y x + 1/18 z y x - 1/36 z y x + 1/9 y x z + + 2 2 3 2 3 3 3 3 2 3 3 + - 1/6 z y x - 1/18 z y x - 1/9 z y x + 1/18 x z + 1/72 x z + + 4 3 4 3 2 2 3 + - 1/72 z x + 5/144 x z + 5/144 y x z - 5/12 y x z + 5/48 y x z + + 3 2 3 3 3 2 2 + - 5/18 y x z + 5/18 z y x - 5/36 y x z - 5/72 y x z + 5/12 y x z + + 2 3 2 3 + + 5/36 y x z + 5/36 x z - 5/144 x z - 5/36 x z - 1/18 z x , + + 3 4 2 4 3 2 4 + COEFF(1, -2, -1) = - 1/27 y x z - 1/144 y x z + 1/72 y x z + + 2 4 3 3 4 3 3 3 3 + + 1/18 y x z + 1/108 y x z - 1/108 z y x - 1/54 y x z + + 2 2 4 4 4 2 3 2 3 3 + - 1/48 y x z + 1/54 y x z - 1/36 z y x + 1/36 y x z + + 2 3 3 4 3 3 3 3 2 2 4 + - 1/9 z y x - 1/27 z y x + 1/54 z y x - 2/27 y x z + 1/36 y z + + 2 2 3 2 3 3 3 3 2 3 3 + + 1/9 z y x + 1/27 z y x + 2/27 z y x - 1/27 x z - 1/108 x z + + 4 3 4 4 2 4 3 + + 1/108 z x + 1/108 y z - 1/54 x z + 1/144 x z - 1/54 y x z + + 2 2 3 2 2 2 3 2 + - 1/27 z + 2/9 y x z - 1/18 y x z + 1/12 y x z + 4/27 y x z + + 2 2 3 2 3 4 3 2 2 3 + + 1/48 y x z + 1/144 y x z - 1/108 z - 1/18 y x z + 1/108 z + + 3 4 3 2 3 3 2 + - 1/54 y z - 2/27 z y + 1/27 z - 4/27 z y x + 1/18 z y x + + 2 3 3 2 2 + + 2/27 y x z - 1/36 z y x + 1/27 y z + 1/27 y x z - 2/9 y x z + + 2 2 2 2 2 2 3 2 3 + - 1/12 y x z + 1/36 y x z - 2/27 y x z + 1/9 y z - 1/72 y x z + + 2 3 2 3 3 3 + - 2/27 x z + 1/36 x z - 1/108 y z - 1/36 y z + 1/54 y z + + 2 3 3 2 3 2 2 2 + - 1/144 x z + 2/27 y z + 1/54 x z - 1/27 y z - 1/36 x z + + 2 2 2 3 3 4 + + 2/27 x z - 1/9 y z + 1/27 z x , COEFF(2, -2, -1) = 1/432 y x z + + 2 4 3 2 4 2 4 3 3 + + 1/288 y x z - 1/144 y x z - 1/288 y x z - 1/432 y x z + + 4 3 3 3 3 2 2 4 4 + + 1/432 z y x + 1/216 y x z + 1/96 y x z - 1/864 y x z + + 4 2 3 2 3 3 2 3 3 + + 1/144 z y x - 1/144 y x z + 1/36 z y x + 1/108 z y x + + 4 3 3 3 3 2 2 4 2 2 3 + - 1/216 z y x + 1/54 y x z - 1/288 y z - 1/36 z y x + + 2 3 3 3 3 2 3 3 4 3 + - 1/108 z y x - 1/54 z y x + 1/108 x z + 1/432 x z - 1/432 z x + + 4 4 2 4 3 + - 1/864 y z + 1/864 x z - 1/288 x z + 1/864 y x z + 1/216 z + + 2 2 3 2 2 2 3 2 + - 1/72 y x z + 1/288 y x z - 1/24 y x z - 1/108 y x z + + 2 2 3 2 3 4 3 2 2 3 + - 1/96 y x z - 1/288 y x z + 1/864 z + 1/36 y x z - 1/864 z + + 3 4 3 2 3 3 2 + + 1/432 y z + 1/108 z y - 1/216 z + 1/108 z y x - 1/36 z y x + + 2 3 3 2 2 + - 1/216 y x z + 1/72 z y x - 1/216 y z - 1/432 y x z + 1/72 y x z + + 2 2 2 2 2 2 3 2 3 + + 1/24 y x z - 1/72 y x z + 1/216 y x z - 1/72 y z + 1/144 y x z + + 2 3 2 3 3 3 + + 1/216 x z - 1/72 x z + 1/864 y z + 1/288 y z - 1/432 y z + + 2 3 3 2 3 2 2 2 + + 1/288 x z - 1/108 y z - 1/864 x z + 1/216 y z + 1/72 x z + + 2 2 2 3 + - 1/216 x z + 1/72 y z - 1/108 z x , COEFF(-2, -1, -1) = + + 3 4 2 4 3 2 4 2 4 + - 1/108 y x z + 1/18 y x z - 1/36 y x z + 1/144 y x z + + 3 3 4 3 3 3 3 2 2 4 + + 1/27 y x z - 1/27 z y x - 1/54 y x z + 1/48 y x z + + 4 4 2 3 2 3 3 2 3 3 + + 1/54 y x z - 1/72 z y x + 1/72 y x z - 1/18 z y x - 4/27 z y x + + 4 3 3 3 3 2 2 4 2 2 3 + + 1/54 z y x - 2/27 y x z - 1/144 y z + 1/18 z y x + + 2 3 3 3 3 2 3 3 4 3 + + 4/27 z y x + 2/27 z y x - 2/27 x z - 1/54 x z + 1/54 z x + + 4 4 2 4 3 2 + - 1/54 y z - 1/108 x z - 1/36 x z - 1/54 y x z + 1/27 z + 1/36 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/144 y x z - 1/12 y x z + 1/27 y x z - 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/18 y x z + 1/108 z + 1/9 y x z - 1/108 z + 1/108 y z + + 3 2 3 3 2 + + 1/27 z y - 1/27 z - 1/27 z y x - 1/9 z y x + 2/27 y x z + + 2 3 3 2 2 2 2 + + 2/9 z y x - 2/27 y z + 1/108 y x z - 1/36 y x z + 1/12 y x z + + 2 2 2 2 3 2 3 + - 2/9 y x z - 2/27 y x z - 1/36 y z + 1/36 y x z - 1/27 x z + + 2 3 2 3 3 3 2 3 + - 1/9 x z + 1/54 y z + 1/144 y z - 1/108 y z + 1/36 x z + + 3 2 3 2 2 2 2 2 2 + - 1/27 y z + 1/108 x z + 2/27 y z + 1/9 x z + 1/27 x z + 1/36 y z + + 3 3 4 2 4 + + 2/27 z x , COEFF(-1, -1, -1) = 4/27 y x z - 1/9 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/18 y x z - 1/9 y x z - 4/27 y x z + 4/27 z y x + + 3 3 3 2 2 4 4 4 2 3 + + 2/27 y x z - 1/24 y x z - 8/27 y x z + 1/18 z y x + + 2 3 3 2 3 16 3 4 3 3 3 3 2 + - 1/18 y x z + 2/9 z y x + -- z y x - 2/27 z y x + 8/27 y x z + 27 + + 2 4 2 2 3 16 2 3 3 3 3 2 + + 1/18 y z - 2/9 z y x - -- z y x - 8/27 z y x + 8/27 x z + 27 + + 3 3 4 3 4 4 2 4 + + 2/27 x z - 2/27 z x + 4/27 y z + 4/27 x z + 1/18 x z + + 3 2 2 3 2 2 2 + + 8/27 y x z - 8/27 z - 4/9 y x z + 1/9 y x z + 1/6 y x z + + 16 3 2 2 2 3 2 3 4 3 2 2 + - -- y x z + 1/24 y x z + 1/9 y x z - 2/27 z - 2/9 y x z + 27 + + 3 3 4 3 2 16 3 3 2 + + 2/27 z - 2/27 y z - 8/27 z y + 8/27 z + -- z y x + 2/9 z y x + 27 + + 32 2 16 3 3 2 2 + - -- y x z - 4/9 z y x + -- y z - 4/27 y x z + 4/9 y x z + 27 27 + + 2 2 2 2 32 2 2 3 2 3 + - 1/6 y x z + 4/9 y x z + -- y x z + 2/9 y z - 1/18 y x z + 27 + + 16 2 3 2 3 3 3 2 3 + + -- x z + 2/9 x z - 4/27 y z - 1/18 y z + 2/27 y z - 1/18 x z + 27 + + 3 2 3 16 2 2 2 16 2 2 2 + + 8/27 y z - 4/27 x z - -- y z - 2/9 x z - -- x z - 2/9 y z + 27 27 + + 3 3 4 2 4 + - 8/27 z x , COEFF(0, -1, -1) = - 5/18 y x z + 5/24 y x z + + 3 3 4 3 3 3 3 4 4 2 3 + + 2/9 y x z - 2/9 z y x - 1/9 y x z + 5/9 y x z - 1/12 z y x + + 2 3 3 2 3 3 4 3 3 3 3 2 + + 1/12 y x z - 1/3 z y x - 8/9 z y x + 1/9 z y x - 4/9 y x z + + 2 2 3 2 3 3 3 3 2 3 3 + + 1/3 z y x + 8/9 z y x + 4/9 z y x - 4/9 x z - 1/9 x z + + 4 3 4 3 2 2 3 + + 1/9 z x - 5/18 x z - 5/9 y x z + 5/6 y x z - 5/24 y x z + + 3 2 3 3 3 2 2 + + 10/9 y x z - 10/9 z y x + 20/9 y x z + 5/18 y x z - 5/6 y x z + + 2 3 2 3 + - 20/9 y x z - 10/9 x z + 5/18 x z + 10/9 x z + 4/9 z x , + + 3 4 2 4 3 2 4 2 4 + COEFF(1, -1, -1) = 4/27 y x z + 1/9 y x z - 1/18 y x z - 1/9 y x z + + 3 3 4 3 3 3 3 2 2 4 + - 4/27 y x z + 4/27 z y x + 2/27 y x z + 1/24 y x z + + 4 4 2 3 2 3 3 2 3 16 3 + - 8/27 y x z + 1/18 z y x - 1/18 y x z + 2/9 z y x + -- z y x + 27 + + 4 3 3 3 3 2 2 4 2 2 3 16 2 3 + - 2/27 z y x + 8/27 y x z - 1/18 y z - 2/9 z y x - -- z y x + 27 + + 3 3 3 2 3 3 4 3 4 + - 8/27 z y x + 8/27 x z + 2/27 x z - 2/27 z x - 4/27 y z + + 4 2 4 3 2 2 3 + + 4/27 x z - 1/18 x z + 8/27 y x z + 8/27 z - 4/9 y x z + 1/9 y x z + + 2 2 2 16 3 2 2 2 3 2 3 4 + - 1/6 y x z - -- y x z - 1/24 y x z - 1/9 y x z + 2/27 z + 27 + + 3 2 2 3 3 4 3 2 16 3 + + 2/9 y x z - 2/27 z + 2/27 y z + 8/27 z y - 8/27 z + -- z y x + 27 + + 3 2 32 2 16 3 3 + - 2/9 z y x - -- y x z + 4/9 z y x - -- y z - 4/27 y x z + 27 27 + + 2 2 2 2 2 2 32 2 2 + + 4/9 y x z + 1/6 y x z - 4/9 y x z + -- y x z - 2/9 y z + 27 + + 3 2 3 16 2 3 2 3 3 3 + + 1/18 y x z + -- x z - 2/9 x z + 4/27 y z + 1/18 y z - 2/27 y z + 27 + + 2 3 3 2 3 16 2 2 2 16 2 + + 1/18 x z - 8/27 y z - 4/27 x z + -- y z + 2/9 x z - -- x z + 27 27 + + 2 2 3 3 4 2 4 + + 2/9 y z - 8/27 z x , COEFF(2, -1, -1) = - 1/108 y x z - 1/18 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/36 y x z + 1/144 y x z + 1/27 y x z - 1/27 z y x + + 3 3 3 2 2 4 4 4 2 3 + - 1/54 y x z - 1/48 y x z + 1/54 y x z - 1/72 z y x + + 2 3 3 2 3 3 4 3 3 + + 1/72 y x z - 1/18 z y x - 4/27 z y x + 1/54 z y x + + 3 3 2 2 4 2 2 3 2 3 + - 2/27 y x z + 1/144 y z + 1/18 z y x + 4/27 z y x + + 3 3 3 2 3 3 4 3 4 + + 2/27 z y x - 2/27 x z - 1/54 x z + 1/54 z x + 1/54 y z + + 4 2 4 3 2 + - 1/108 x z + 1/36 x z - 1/54 y x z - 1/27 z + 1/36 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/144 y x z + 1/12 y x z + 1/27 y x z + 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + + 1/18 y x z - 1/108 z - 1/9 y x z + 1/108 z - 1/108 y z + + 3 2 3 3 2 + - 1/27 z y + 1/27 z - 1/27 z y x + 1/9 z y x + 2/27 y x z + + 2 3 3 2 2 2 2 + - 2/9 z y x + 2/27 y z + 1/108 y x z - 1/36 y x z - 1/12 y x z + + 2 2 2 2 3 2 3 + + 2/9 y x z - 2/27 y x z + 1/36 y z - 1/36 y x z - 1/27 x z + + 2 3 2 3 3 3 2 3 + + 1/9 x z - 1/54 y z - 1/144 y z + 1/108 y z - 1/36 x z + + 3 2 3 2 2 2 2 2 2 + + 1/27 y z + 1/108 x z - 2/27 y z - 1/9 x z + 1/27 x z - 1/36 y z + + 3 3 4 2 4 + + 2/27 z x , COEFF(-2, 0, -1) = 1/72 y x z - 5/48 y x z + + 3 2 4 3 3 4 3 3 3 3 + + 1/24 y x z - 5/72 y x z + 5/72 z y x + 1/36 y x z + + 4 3 4 3 3 3 3 2 2 3 + - 5/144 y x z + 5/18 z y x - 1/36 z y x + 1/9 y x z - 5/18 z y x + + 3 3 4 3 3 2 2 3 + - 1/9 z y x + 5/144 y z + 5/144 y x z - 1/18 y x z + 5/48 y x z + + 3 2 2 3 4 3 3 3 2 + - 1/6 y x z - 1/72 y z - 1/18 z y + 1/18 z y x + 1/6 z y x + + 2 3 3 2 2 + - 5/36 y x z - 5/12 z y x + 5/36 y z - 1/72 y x z + 5/12 y x z + + 2 3 2 3 3 3 3 3 2 + + 5/36 y x z - 1/24 y x z - 5/144 y z + 1/72 y z + 1/18 y z + + 2 3 4 2 4 + - 5/36 y z , COEFF(-1, 0, -1) = - 2/9 y x z + 5/24 y x z + + 3 2 4 3 3 4 3 3 3 3 4 + - 1/12 y x z + 5/18 y x z - 5/18 z y x - 1/9 y x z + 5/9 y x z + + 3 4 3 3 3 3 2 2 3 3 3 + - 10/9 z y x + 1/9 z y x - 4/9 y x z + 10/9 z y x + 4/9 z y x + + 4 3 3 2 2 3 3 2 2 + - 5/18 y z - 5/9 y x z + 8/9 y x z - 5/24 y x z + 1/3 y x z + + 3 4 3 3 3 2 + + 1/9 y z + 4/9 z y - 8/9 z y x - 1/3 z y x + 20/9 y x z + + 2 3 3 2 2 2 + + 5/6 z y x - 10/9 y z + 2/9 y x z - 5/6 y x z - 20/9 y x z + + 3 2 3 3 3 3 3 2 2 + + 1/12 y x z + 5/18 y z - 1/9 y z - 4/9 y z + 10/9 y z , + + 25 3 2 3 3 3 3 + COEFF(0, 0, -1) = -- y x z + 25/6 y x z - 5/12 y x z - 2/3 z y x + 24 + + 3 4 3 3 3 4 3 3 3 3 2 + + 5/3 z y x + 5/12 z y x - 5/12 y x z - 1/6 z y x + 2/3 y x z + + 25 4 3 2 3 4 3 3 3 3 + - -- y x z - 5/3 y x z + 5/12 y x z + 5/3 z y x + 1/6 y x z + 24 + + 2 3 3 4 2 4 + - 25/6 y x z - 5/3 z y x , COEFF(1, 0, -1) = - 2/9 y x z - 5/24 y x z + + 3 2 4 3 3 4 3 3 3 3 4 + + 1/12 y x z + 5/18 y x z - 5/18 z y x - 1/9 y x z + 5/9 y x z + + 3 4 3 3 3 3 2 2 3 3 3 + - 10/9 z y x + 1/9 z y x - 4/9 y x z + 10/9 z y x + 4/9 z y x + + 4 3 3 2 2 3 3 2 2 + + 5/18 y z - 5/9 y x z + 8/9 y x z + 5/24 y x z - 1/3 y x z + + 3 4 3 3 3 2 + - 1/9 y z - 4/9 z y - 8/9 z y x + 1/3 z y x + 20/9 y x z + + 2 3 3 2 2 2 + - 5/6 z y x + 10/9 y z + 2/9 y x z + 5/6 y x z - 20/9 y x z + + 3 2 3 3 3 3 3 2 2 + - 1/12 y x z - 5/18 y z + 1/9 y z + 4/9 y z - 10/9 y z , + + 3 4 2 4 3 2 4 + COEFF(2, 0, -1) = 1/72 y x z + 5/48 y x z - 1/24 y x z + + 3 3 4 3 3 3 3 4 3 + - 5/72 y x z + 5/72 z y x + 1/36 y x z - 5/144 y x z + 5/18 z y x + + 4 3 3 3 3 2 2 3 3 3 4 + - 1/36 z y x + 1/9 y x z - 5/18 z y x - 1/9 z y x - 5/144 y z + + 3 3 2 2 3 3 2 2 3 4 + + 5/144 y x z - 1/18 y x z - 5/48 y x z + 1/6 y x z + 1/72 y z + + 3 3 3 2 2 + + 1/18 z y + 1/18 z y x - 1/6 z y x - 5/36 y x z + 5/12 z y x + + 3 3 2 2 2 3 2 3 + - 5/36 y z - 1/72 y x z - 5/12 y x z + 5/36 y x z + 1/24 y x z + + 3 3 3 3 2 2 + + 5/144 y z - 1/72 y z - 1/18 y z + 5/36 y z , COEFF(-2, 1, -1) = + + 3 4 2 4 3 2 4 2 4 + - 1/108 y x z + 1/18 y x z - 1/36 y x z - 1/144 y x z + + 3 3 4 3 3 3 3 2 2 4 + + 1/27 y x z - 1/27 z y x - 1/54 y x z - 1/48 y x z + + 4 4 2 3 2 3 3 2 3 3 + + 1/54 y x z + 1/72 z y x - 1/72 y x z + 1/18 z y x - 4/27 z y x + + 4 3 3 3 3 2 2 4 2 2 3 + + 1/54 z y x - 2/27 y x z + 1/144 y z - 1/18 z y x + + 2 3 3 3 3 2 3 3 4 3 + + 4/27 z y x + 2/27 z y x + 2/27 x z + 1/54 x z - 1/54 z x + + 4 4 2 4 3 2 + - 1/54 y z + 1/108 x z + 1/36 x z - 1/54 y x z - 1/27 z - 1/36 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/144 y x z + 1/12 y x z + 1/27 y x z + 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/18 y x z - 1/108 z + 1/9 y x z + 1/108 z + 1/108 y z + + 3 2 3 3 2 + + 1/27 z y + 1/27 z - 1/27 z y x - 1/9 z y x + 2/27 y x z + + 2 3 3 2 2 2 2 + + 2/9 z y x - 2/27 y z + 1/108 y x z + 1/36 y x z - 1/12 y x z + + 2 2 2 2 3 2 3 + - 2/9 y x z - 2/27 y x z + 1/36 y z + 1/36 y x z + 1/27 x z + + 2 3 2 3 3 3 2 3 + + 1/9 x z + 1/54 y z - 1/144 y z - 1/108 y z - 1/36 x z + + 3 2 3 2 2 2 2 2 2 + - 1/27 y z - 1/108 x z + 2/27 y z - 1/9 x z - 1/27 x z - 1/36 y z + + 3 3 4 2 4 3 2 4 + - 2/27 z x , COEFF(-1, 1, -1) = 4/27 y x z - 1/9 y x z + 1/18 y x z + + 2 4 3 3 4 3 3 3 3 + + 1/9 y x z - 4/27 y x z + 4/27 z y x + 2/27 y x z + + 2 2 4 4 4 2 3 2 3 3 + + 1/24 y x z - 8/27 y x z - 1/18 z y x + 1/18 y x z + + 2 3 16 3 4 3 3 3 3 2 2 4 + - 2/9 z y x + -- z y x - 2/27 z y x + 8/27 y x z - 1/18 y z + 27 + + 2 2 3 16 2 3 3 3 3 2 3 3 + + 2/9 z y x - -- z y x - 8/27 z y x - 8/27 x z - 2/27 x z + 27 + + 4 3 4 4 2 4 3 + + 2/27 z x + 4/27 y z - 4/27 x z - 1/18 x z + 8/27 y x z + 8/27 z + + 2 2 3 2 2 2 16 3 2 2 2 3 + + 4/9 y x z - 1/9 y x z - 1/6 y x z - -- y x z - 1/24 y x z + 27 + + 2 3 4 3 2 2 3 3 4 3 + + 1/9 y x z + 2/27 z - 2/9 y x z - 2/27 z - 2/27 y z - 8/27 z y + + 2 16 3 3 2 32 2 16 + - 8/27 z + -- z y x + 2/9 z y x - -- y x z - 4/9 z y x + -- y z + 27 27 27 + + 3 3 2 2 2 2 2 2 32 2 + - 4/27 y x z - 4/9 y x z + 1/6 y x z + 4/9 y x z + -- y x z + 27 + + 2 3 2 3 16 2 3 2 3 + - 2/9 y z - 1/18 y x z - -- x z - 2/9 x z - 4/27 y z + 1/18 y z + 27 + + 3 3 2 3 3 2 3 16 2 2 2 + + 2/27 y z + 1/18 x z + 8/27 y z + 4/27 x z - -- y z + 2/9 x z + 27 + + 16 2 2 2 3 3 4 + + -- x z + 2/9 y z + 8/27 z x , COEFF(0, 1, -1) = - 5/18 y x z + 27 + + 2 4 3 3 4 3 3 3 3 4 + - 5/24 y x z + 2/9 y x z - 2/9 z y x - 1/9 y x z + 5/9 y x z + + 4 2 3 2 3 3 2 3 3 4 3 3 + + 1/12 z y x - 1/12 y x z + 1/3 z y x - 8/9 z y x + 1/9 z y x + + 3 3 2 2 2 3 2 3 3 3 3 2 + - 4/9 y x z - 1/3 z y x + 8/9 z y x + 4/9 z y x + 4/9 x z + + 3 3 4 3 4 3 2 + + 1/9 x z - 1/9 z x + 5/18 x z - 5/9 y x z - 5/6 y x z + + 2 3 3 2 3 3 3 + + 5/24 y x z + 10/9 y x z - 10/9 z y x + 20/9 y x z + 5/18 y x z + + 2 2 2 3 2 3 + + 5/6 y x z - 20/9 y x z + 10/9 x z - 5/18 x z - 10/9 x z - 4/9 z x , + + 3 4 2 4 3 2 4 2 4 + COEFF(1, 1, -1) = 4/27 y x z + 1/9 y x z - 1/18 y x z + 1/9 y x z + + 3 3 4 3 3 3 3 2 2 4 + - 4/27 y x z + 4/27 z y x + 2/27 y x z - 1/24 y x z + + 4 4 2 3 2 3 3 2 3 16 3 + - 8/27 y x z - 1/18 z y x + 1/18 y x z - 2/9 z y x + -- z y x + 27 + + 4 3 3 3 3 2 2 4 2 2 3 16 2 3 + - 2/27 z y x + 8/27 y x z + 1/18 y z + 2/9 z y x - -- z y x + 27 + + 3 3 3 2 3 3 4 3 4 + - 8/27 z y x - 8/27 x z - 2/27 x z + 2/27 z x - 4/27 y z + + 4 2 4 3 2 2 3 + - 4/27 x z + 1/18 x z + 8/27 y x z - 8/27 z + 4/9 y x z - 1/9 y x z + + 2 2 2 16 3 2 2 2 3 2 3 4 + + 1/6 y x z - -- y x z + 1/24 y x z - 1/9 y x z - 2/27 z + 27 + + 3 2 2 3 3 4 3 2 16 3 + + 2/9 y x z + 2/27 z + 2/27 y z + 8/27 z y + 8/27 z + -- z y x + 27 + + 3 2 32 2 16 3 3 + - 2/9 z y x - -- y x z + 4/9 z y x - -- y z - 4/27 y x z + 27 27 + + 2 2 2 2 2 2 32 2 2 + - 4/9 y x z - 1/6 y x z - 4/9 y x z + -- y x z + 2/9 y z + 27 + + 3 2 3 16 2 3 2 3 3 3 + + 1/18 y x z - -- x z + 2/9 x z + 4/27 y z - 1/18 y z - 2/27 y z + 27 + + 2 3 3 2 3 16 2 2 2 16 2 + - 1/18 x z - 8/27 y z + 4/27 x z + -- y z - 2/9 x z + -- x z + 27 27 + + 2 2 3 3 4 2 4 + - 2/9 y z + 8/27 z x , COEFF(2, 1, -1) = - 1/108 y x z - 1/18 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/36 y x z - 1/144 y x z + 1/27 y x z - 1/27 z y x + + 3 3 3 2 2 4 4 4 2 3 + - 1/54 y x z + 1/48 y x z + 1/54 y x z + 1/72 z y x + + 2 3 3 2 3 3 4 3 3 + - 1/72 y x z + 1/18 z y x - 4/27 z y x + 1/54 z y x + + 3 3 2 2 4 2 2 3 2 3 + - 2/27 y x z - 1/144 y z - 1/18 z y x + 4/27 z y x + + 3 3 3 2 3 3 4 3 4 + + 2/27 z y x + 2/27 x z + 1/54 x z - 1/54 z x + 1/54 y z + + 4 2 4 3 2 + + 1/108 x z - 1/36 x z - 1/54 y x z + 1/27 z - 1/36 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/144 y x z - 1/12 y x z + 1/27 y x z - 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + + 1/18 y x z + 1/108 z - 1/9 y x z - 1/108 z - 1/108 y z + + 3 2 3 3 2 + - 1/27 z y - 1/27 z - 1/27 z y x + 1/9 z y x + 2/27 y x z + + 2 3 3 2 2 2 2 + - 2/9 z y x + 2/27 y z + 1/108 y x z + 1/36 y x z + 1/12 y x z + + 2 2 2 2 3 2 3 + + 2/9 y x z - 2/27 y x z - 1/36 y z - 1/36 y x z + 1/27 x z + + 2 3 2 3 3 3 2 3 + - 1/9 x z - 1/54 y z + 1/144 y z + 1/108 y z + 1/36 x z + + 3 2 3 2 2 2 2 2 2 + + 1/27 y z - 1/108 x z - 2/27 y z + 1/9 x z - 1/27 x z + 1/36 y z + + 3 3 4 2 4 + - 2/27 z x , COEFF(-2, 2, -1) = 1/432 y x z - 1/288 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/144 y x z + 1/288 y x z - 1/432 y x z + 1/432 z y x + + 3 3 3 2 2 4 4 4 2 3 + + 1/216 y x z + 1/96 y x z - 1/864 y x z - 1/144 z y x + + 2 3 3 2 3 3 4 3 3 + + 1/144 y x z - 1/36 z y x + 1/108 z y x - 1/216 z y x + + 3 3 2 2 4 2 2 3 2 3 + + 1/54 y x z - 1/288 y z + 1/36 z y x - 1/108 z y x + + 3 3 3 2 3 3 4 3 4 + - 1/54 z y x - 1/108 x z - 1/432 x z + 1/432 z x + 1/864 y z + + 4 2 4 3 2 + - 1/864 x z - 1/288 x z + 1/864 y x z + 1/216 z + 1/72 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/288 y x z - 1/24 y x z - 1/108 y x z - 1/96 y x z + + 2 3 4 3 2 2 3 3 4 + + 1/288 y x z + 1/864 z - 1/36 y x z - 1/864 z - 1/432 y z + + 3 2 3 3 2 + - 1/108 z y - 1/216 z + 1/108 z y x + 1/36 z y x - 1/216 y x z + + 2 3 3 2 2 2 2 + - 1/72 z y x + 1/216 y z - 1/432 y x z - 1/72 y x z + 1/24 y x z + + 2 2 2 2 3 2 3 + + 1/72 y x z + 1/216 y x z - 1/72 y z - 1/144 y x z - 1/216 x z + + 2 3 2 3 3 3 2 3 + - 1/72 x z - 1/864 y z + 1/288 y z + 1/432 y z + 1/288 x z + + 3 2 3 2 2 2 2 + + 1/108 y z + 1/864 x z - 1/216 y z + 1/72 x z + 1/216 x z + + 2 2 3 3 4 + + 1/72 y z + 1/108 z x , COEFF(-1, 2, -1) = - 1/27 y x z + + 2 4 3 2 4 2 4 3 3 + + 1/144 y x z - 1/72 y x z - 1/18 y x z + 1/108 y x z + + 4 3 3 3 3 2 2 4 4 + - 1/108 z y x - 1/54 y x z - 1/48 y x z + 1/54 y x z + + 4 2 3 2 3 3 2 3 3 + + 1/36 z y x - 1/36 y x z + 1/9 z y x - 1/27 z y x + + 4 3 3 3 3 2 2 4 2 2 3 2 3 + + 1/54 z y x - 2/27 y x z + 1/36 y z - 1/9 z y x + 1/27 z y x + + 3 3 3 2 3 3 4 3 4 + + 2/27 z y x + 1/27 x z + 1/108 x z - 1/108 z x - 1/108 y z + + 4 2 4 3 2 + + 1/54 x z + 1/144 x z - 1/54 y x z - 1/27 z - 2/9 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/18 y x z + 1/12 y x z + 4/27 y x z + 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/144 y x z - 1/108 z + 1/18 y x z + 1/108 z + 1/54 y z + + 3 2 3 3 2 + + 2/27 z y + 1/27 z - 4/27 z y x - 1/18 z y x + 2/27 y x z + + 2 3 3 2 2 2 2 + + 1/36 z y x - 1/27 y z + 1/27 y x z + 2/9 y x z - 1/12 y x z + + 2 2 2 2 3 2 3 + - 1/36 y x z - 2/27 y x z + 1/9 y z + 1/72 y x z + 2/27 x z + + 2 3 2 3 3 3 2 3 + + 1/36 x z + 1/108 y z - 1/36 y z - 1/54 y z - 1/144 x z + + 3 2 3 2 2 2 2 2 2 + - 2/27 y z - 1/54 x z + 1/27 y z - 1/36 x z - 2/27 x z - 1/9 y z + + 3 3 4 2 4 3 3 + - 1/27 z x , COEFF(0, 2, -1) = 5/72 y x z + 5/48 y x z - 1/72 y x z + + 4 3 3 3 3 4 4 2 3 + + 1/72 z y x + 1/36 y x z - 5/144 y x z - 1/24 z y x + + 2 3 3 2 3 3 4 3 3 3 3 2 + + 1/24 y x z - 1/6 z y x + 1/18 z y x - 1/36 z y x + 1/9 y x z + + 2 2 3 2 3 3 3 3 2 3 3 + + 1/6 z y x - 1/18 z y x - 1/9 z y x - 1/18 x z - 1/72 x z + + 4 3 4 3 2 2 3 + + 1/72 z x - 5/144 x z + 5/144 y x z + 5/12 y x z - 5/48 y x z + + 3 2 3 3 3 2 2 + - 5/18 y x z + 5/18 z y x - 5/36 y x z - 5/72 y x z - 5/12 y x z + + 2 3 2 3 + + 5/36 y x z - 5/36 x z + 5/144 x z + 5/36 x z + 1/18 z x , + + 3 4 2 4 3 2 4 + COEFF(1, 2, -1) = - 1/27 y x z - 1/144 y x z + 1/72 y x z + + 2 4 3 3 4 3 3 3 3 + - 1/18 y x z + 1/108 y x z - 1/108 z y x - 1/54 y x z + + 2 2 4 4 4 2 3 2 3 3 + + 1/48 y x z + 1/54 y x z + 1/36 z y x - 1/36 y x z + + 2 3 3 4 3 3 3 3 2 2 4 + + 1/9 z y x - 1/27 z y x + 1/54 z y x - 2/27 y x z - 1/36 y z + + 2 2 3 2 3 3 3 3 2 3 3 + - 1/9 z y x + 1/27 z y x + 2/27 z y x + 1/27 x z + 1/108 x z + + 4 3 4 4 2 4 3 + - 1/108 z x + 1/108 y z + 1/54 x z - 1/144 x z - 1/54 y x z + + 2 2 3 2 2 2 3 2 + + 1/27 z - 2/9 y x z + 1/18 y x z - 1/12 y x z + 4/27 y x z + + 2 2 3 2 3 4 3 2 2 3 + - 1/48 y x z + 1/144 y x z + 1/108 z - 1/18 y x z - 1/108 z + + 3 4 3 2 3 3 2 + - 1/54 y z - 2/27 z y - 1/27 z - 4/27 z y x + 1/18 z y x + + 2 3 3 2 2 + + 2/27 y x z - 1/36 z y x + 1/27 y z + 1/27 y x z + 2/9 y x z + + 2 2 2 2 2 2 3 2 3 + + 1/12 y x z + 1/36 y x z - 2/27 y x z - 1/9 y z - 1/72 y x z + + 2 3 2 3 3 3 + + 2/27 x z - 1/36 x z - 1/108 y z + 1/36 y z + 1/54 y z + + 2 3 3 2 3 2 2 2 + + 1/144 x z + 2/27 y z - 1/54 x z - 1/27 y z + 1/36 x z + + 2 2 2 3 3 4 + - 2/27 x z + 1/9 y z - 1/27 z x , COEFF(2, 2, -1) = 1/432 y x z + + 2 4 3 2 4 2 4 3 3 + + 1/288 y x z - 1/144 y x z + 1/288 y x z - 1/432 y x z + + 4 3 3 3 3 2 2 4 4 + + 1/432 z y x + 1/216 y x z - 1/96 y x z - 1/864 y x z + + 4 2 3 2 3 3 2 3 3 + - 1/144 z y x + 1/144 y x z - 1/36 z y x + 1/108 z y x + + 4 3 3 3 3 2 2 4 2 2 3 + - 1/216 z y x + 1/54 y x z + 1/288 y z + 1/36 z y x + + 2 3 3 3 3 2 3 3 4 3 + - 1/108 z y x - 1/54 z y x - 1/108 x z - 1/432 x z + 1/432 z x + + 4 4 2 4 3 + - 1/864 y z - 1/864 x z + 1/288 x z + 1/864 y x z - 1/216 z + + 2 2 3 2 2 2 3 2 + + 1/72 y x z - 1/288 y x z + 1/24 y x z - 1/108 y x z + + 2 2 3 2 3 4 3 2 2 3 + + 1/96 y x z - 1/288 y x z - 1/864 z + 1/36 y x z + 1/864 z + + 3 4 3 2 3 3 2 + + 1/432 y z + 1/108 z y + 1/216 z + 1/108 z y x - 1/36 z y x + + 2 3 3 2 2 + - 1/216 y x z + 1/72 z y x - 1/216 y z - 1/432 y x z - 1/72 y x z + + 2 2 2 2 2 2 3 2 3 + - 1/24 y x z - 1/72 y x z + 1/216 y x z + 1/72 y z + 1/144 y x z + + 2 3 2 3 3 3 + - 1/216 x z + 1/72 x z + 1/864 y z - 1/288 y z - 1/432 y z + + 2 3 3 2 3 2 2 2 + - 1/288 x z - 1/108 y z + 1/864 x z + 1/216 y z - 1/72 x z + + 2 2 2 3 3 4 + + 1/216 x z - 1/72 y z + 1/108 z x , COEFF(-2, -2, 0) = - 1/288 y x z + + 2 4 3 2 4 2 4 4 3 + + 1/192 y x z - 1/96 y x z + 1/192 y x z - 1/288 z y x + + 2 2 4 4 4 2 3 4 3 3 + + 1/64 y x z + 1/576 y x z - 1/96 z y x + 1/144 z y x + + 3 3 2 2 4 2 2 3 3 2 3 + - 5/144 y x z - 1/192 y z + 5/96 z y x - 1/72 y x + 5/288 z y x + + 3 2 4 3 4 4 + - 5/288 x z - 1/144 x + 1/288 z x - 1/576 y z - 1/576 x z + + 2 4 2 2 2 3 2 + - 1/192 x z - 1/144 y + 1/144 y x - 5/64 y x z + 5/288 y x z + + 4 3 2 2 3 3 3 3 4 + + 1/576 z + 5/96 y x z + 1/72 y + 1/72 x - 1/72 y x + 1/288 y z + + 2 2 3 2 2 2 2 2 + - 1/48 y - 5/576 z - 1/24 y x - 1/48 x + 1/48 y x - 5/192 y x z + + 2 2 2 3 2 2 2 2 + - 5/192 y x z - 5/576 y x z - 5/288 y z + 5/576 y z + 5/192 x z + + 2 2 2 2 2 2 2 3 + + 5/576 x z + 5/192 y z + 1/16 y x + 1/48 y x + 1/144 - 1/24 y x + + 3 3 3 4 2 4 + + 1/36 y x , COEFF(-1, -2, 0) = 1/18 y x z - 1/96 y x z + + 3 2 4 2 4 4 3 2 2 4 + + 1/48 y x z - 1/12 y x z + 1/72 z y x - 1/32 y x z + + 4 4 2 3 4 3 3 3 3 2 2 4 + - 1/36 y x z + 1/24 z y x - 1/36 z y x + 5/36 y x z + 1/24 y z + + 2 2 3 3 2 3 3 2 + - 5/24 z y x + 1/18 y x - 5/72 z y x + 5/72 x z + 1/9 x + + 4 3 4 4 2 4 + - 1/72 z x + 1/72 y z + 1/36 x z + 1/96 x z + 1/18 y - 1/9 y x + + 2 2 2 3 2 4 3 2 2 3 + + 5/32 y x z - 5/18 y x z - 1/72 z - 5/48 y x z - 1/9 y + + 3 3 3 4 2 2 3 2 + - 1/18 x + 2/9 y x - 1/36 y z + 1/6 y + 5/72 z + 1/12 y x + + 2 2 2 2 2 2 2 + + 1/24 x - 1/3 y x + 5/12 y x z + 5/96 y x z + 5/36 y x z - 1/18 + + 3 2 2 2 2 2 2 2 2 2 + + 5/36 y z - 5/72 y z - 5/96 x z - 5/36 x z - 5/24 y z - 1/8 y x + + 2 2 3 3 3 2 4 + - 1/24 y x + 1/6 y x - 1/9 y x , COEFF(0, -2, 0) = 5/32 y x z + + 4 3 3 3 2 4 3 3 3 2 4 + + 1/24 z y x - 5/48 x z + 1/48 z x - 5/24 y x z - 5/96 x z + + 2 3 3 4 3 4 2 2 3 + + 5/48 z y x - 1/12 y x + 5/96 y x z - 5/48 y x z + 5/16 z y x + + 4 2 3 25 2 4 3 2 + - 1/16 z y x - -- y x z - 1/48 z y x - 5/24 x + 5/8 y x + 96 + + 25 3 2 25 2 2 2 3 3 3 3 + + -- y x z - -- y x z + 5/24 y x - 1/4 y x + 1/12 x + 1/6 y x + 48 32 + + 25 2 3 3 4 2 4 + + -- x z - 5/12 y x, COEFF(1, -2, 0) = 1/18 y x z + 1/96 y x z + 96 + + 3 2 4 2 4 4 3 2 2 4 + - 1/48 y x z - 1/12 y x z + 1/72 z y x + 1/32 y x z + + 4 4 2 3 4 3 3 3 3 2 2 4 + - 1/36 y x z + 1/24 z y x - 1/36 z y x + 5/36 y x z - 1/24 y z + + 2 2 3 3 2 3 3 2 + - 5/24 z y x + 1/18 y x - 5/72 z y x + 5/72 x z + 1/9 x + + 4 3 4 4 2 4 + - 1/72 z x - 1/72 y z + 1/36 x z - 1/96 x z - 1/18 y - 1/9 y x + + 2 2 2 3 2 4 3 2 2 3 + - 5/32 y x z - 5/18 y x z + 1/72 z + 5/48 y x z + 1/9 y + + 3 3 3 4 2 2 3 2 + - 1/18 x + 2/9 y x + 1/36 y z - 1/6 y - 5/72 z - 1/12 y x + + 2 2 2 2 2 2 2 + - 1/24 x - 1/3 y x + 5/12 y x z - 5/96 y x z + 5/36 y x z + 1/18 + + 3 2 2 2 2 2 2 2 2 2 + - 5/36 y z + 5/72 y z + 5/96 x z - 5/36 x z + 5/24 y z + 1/8 y x + + 2 2 3 3 3 3 4 + + 1/24 y x + 1/6 y x - 1/9 y x , COEFF(2, -2, 0) = - 1/288 y x z + + 2 4 3 2 4 2 4 4 3 + - 1/192 y x z + 1/96 y x z + 1/192 y x z - 1/288 z y x + + 2 2 4 4 4 2 3 4 3 3 + - 1/64 y x z + 1/576 y x z - 1/96 z y x + 1/144 z y x + + 3 3 2 2 4 2 2 3 3 2 3 + - 5/144 y x z + 1/192 y z + 5/96 z y x - 1/72 y x + 5/288 z y x + + 3 2 4 3 4 4 + - 5/288 x z - 1/144 x + 1/288 z x + 1/576 y z - 1/576 x z + + 2 4 2 2 2 3 2 + + 1/192 x z + 1/144 y + 1/144 y x + 5/64 y x z + 5/288 y x z + + 4 3 2 2 3 3 3 3 4 + - 1/576 z - 5/96 y x z - 1/72 y + 1/72 x - 1/72 y x - 1/288 y z + + 2 2 3 2 2 2 2 2 + + 1/48 y + 5/576 z + 1/24 y x + 1/48 x + 1/48 y x - 5/192 y x z + + 2 2 2 3 2 2 2 2 + + 5/192 y x z - 5/576 y x z + 5/288 y z - 5/576 y z - 5/192 x z + + 2 2 2 2 2 2 2 3 + + 5/576 x z - 5/192 y z - 1/16 y x - 1/48 y x - 1/144 - 1/24 y x + + 3 3 3 4 2 4 + + 1/36 y x , COEFF(-2, -1, 0) = 1/72 y x z - 1/12 y x z + + 3 2 4 2 4 4 3 2 2 4 + + 1/24 y x z - 1/96 y x z + 1/18 z y x - 1/32 y x z + + 4 4 2 3 4 3 3 3 3 2 2 4 + - 1/36 y x z + 1/48 z y x - 1/36 z y x + 5/36 y x z + 1/96 y z + + 2 2 3 3 2 3 3 2 + - 5/48 z y x + 2/9 y x - 5/18 z y x + 5/36 x z + 1/18 x + + 4 3 4 4 2 4 + - 1/36 z x + 1/36 y z + 1/72 x z + 1/24 x z + 1/9 y - 1/9 y x + + 2 2 2 3 2 4 3 2 2 3 + + 5/32 y x z - 5/72 y x z - 1/72 z - 5/24 y x z - 1/18 y + + 3 3 3 4 2 2 3 2 2 + - 1/9 x + 1/18 y x - 1/72 y z + 1/24 y + 5/72 z + 1/6 y x + 1/6 x + + 2 2 2 2 2 2 + - 1/24 y x + 5/96 y x z + 5/12 y x z + 5/36 y x z - 1/18 + + 3 2 2 2 2 2 2 2 2 2 + + 5/72 y z - 5/36 y z - 5/24 x z - 5/72 x z - 5/96 y z - 1/8 y x + + 2 2 3 3 3 3 4 + - 1/3 y x + 1/12 y x - 1/9 y x , COEFF(-1, -1, 0) = - 2/9 y x z + + 2 4 3 2 4 2 4 4 3 2 2 4 + + 1/6 y x z - 1/12 y x z + 1/6 y x z - 2/9 z y x + 1/16 y x z + + 4 4 2 3 4 3 3 3 3 2 2 4 + + 4/9 y x z - 1/12 z y x + 1/9 z y x - 5/9 y x z - 1/12 y z + + 2 2 3 3 2 3 3 2 4 3 + + 5/12 z y x - 8/9 y x + 10/9 z y x - 5/9 x z - 8/9 x + 1/9 z x + + 4 4 2 4 2 2 2 + - 2/9 y z - 2/9 x z - 1/12 x z - 8/9 y + 16/9 y x - 5/16 y x z + + 3 2 4 3 2 2 3 3 3 + + 10/9 y x z + 1/9 z + 5/12 y x z + 4/9 + 4/9 y + 4/9 x - 8/9 y x + + 3 4 2 2 3 2 2 2 + + 1/9 y z - 1/3 y - 5/9 z - 1/3 y x - 1/3 x + 2/3 y x + + 2 2 2 2 2 3 2 2 + - 5/6 y x z - 5/6 y x z - 20/9 y x z - 5/9 y z + 10/9 y z + + 2 2 2 2 2 2 2 2 2 3 + + 5/12 x z + 10/9 x z + 5/12 y z + 1/4 y x + 2/3 y x - 1/3 y x + + 3 3 4 2 3 3 4 3 + + 4/9 y x , COEFF(0, -1, 0) = 1/8 z y x + 5/3 y x - 1/6 z x + + 25 3 2 4 3 3 2 3 3 3 3 2 + - -- y x z + 1/3 z y x + 5/6 x z - 2/3 y x + 5/6 y x z + 12 + + 4 3 4 2 4 4 3 3 + - 5/6 y x z + 5/12 y x z + 5/3 x - 5/16 y x z - 1/6 z y x + + 3 2 3 4 2 2 3 + - 10/3 y x + 4/3 y x + 25/6 y x z - 2/3 x + 5/12 x z - 5/8 z y x + + 2 2 3 25 2 2 3 25 2 2 + - 5/4 y x - 5/3 z y x - -- x z + 1/2 y x + -- y x z , + 12 16 + + 3 4 2 4 3 2 4 2 4 + COEFF(1, -1, 0) = - 2/9 y x z - 1/6 y x z + 1/12 y x z + 1/6 y x z + + 4 3 2 2 4 4 4 2 3 4 3 3 + - 2/9 z y x - 1/16 y x z + 4/9 y x z - 1/12 z y x + 1/9 z y x + + 3 3 2 2 4 2 2 3 3 2 3 + - 5/9 y x z + 1/12 y z + 5/12 z y x - 8/9 y x + 10/9 z y x + + 3 2 4 3 4 4 2 4 + - 5/9 x z - 8/9 x + 1/9 z x + 2/9 y z - 2/9 x z + 1/12 x z + 8/9 y + + 2 2 2 3 2 4 3 2 2 + + 16/9 y x + 5/16 y x z + 10/9 y x z - 1/9 z - 5/12 y x z + + 3 3 3 3 4 2 2 3 2 + - 4/9 y + 4/9 x - 8/9 y x - 1/9 y z + 1/3 y + 5/9 z + 1/3 y x + + 2 2 2 2 2 2 2 + + 1/3 x - 4/9 + 2/3 y x - 5/6 y x z + 5/6 y x z - 20/9 y x z + + 3 2 2 2 2 2 2 2 2 2 + + 5/9 y z - 10/9 y z - 5/12 x z + 10/9 x z - 5/12 y z - 1/4 y x + + 2 2 3 3 3 3 4 + - 2/3 y x - 1/3 y x + 4/9 y x , COEFF(2, -1, 0) = 1/72 y x z + + 2 4 3 2 4 2 4 4 3 + + 1/12 y x z - 1/24 y x z - 1/96 y x z + 1/18 z y x + + 2 2 4 4 4 2 3 4 3 3 + + 1/32 y x z - 1/36 y x z + 1/48 z y x - 1/36 z y x + + 3 3 2 2 4 2 2 3 3 2 3 + + 5/36 y x z - 1/96 y z - 5/48 z y x + 2/9 y x - 5/18 z y x + + 3 2 4 3 4 4 2 4 + + 5/36 x z + 1/18 x - 1/36 z x - 1/36 y z + 1/72 x z - 1/24 x z + + 2 2 2 3 2 4 3 2 2 + - 1/9 y - 1/9 y x - 5/32 y x z - 5/72 y x z + 1/72 z + 5/24 y x z + + 3 3 3 3 4 2 2 + + 1/18 y - 1/9 x + 1/18 y x + 1/72 y z - 1/24 y - 5/72 z + + 3 2 2 2 2 2 2 2 + - 1/6 y x - 1/6 x - 1/24 y x + 5/96 y x z - 5/12 y x z + + 2 3 2 2 2 2 2 + + 5/36 y x z + 1/18 - 5/72 y z + 5/36 y z + 5/24 x z - 5/72 x z + + 2 2 2 2 2 2 3 3 3 + + 5/96 y z + 1/8 y x + 1/3 y x + 1/12 y x - 1/9 y x , + + 3 2 3 2 25 2 2 + COEFF(-2, 0, 0) = - 1/4 y x - 5/24 y - 5/48 y z - -- y x z + 32 + + 3 4 3 2 4 4 3 3 3 2 + - 5/12 y x + 5/96 y x z - 1/16 y x z + 1/24 z y x + 5/48 y x z + + 25 2 3 3 3 2 2 25 2 + - -- y x z + 5/24 y x + 1/12 y - 1/12 y x + 5/16 y x z + -- y z + 96 96 + + 3 3 2 3 3 2 4 3 4 3 4 + - 5/24 y x z + 1/6 y x + 5/32 y x z + 1/48 y z - 1/48 y x z + + 4 3 25 2 3 2 4 + - 5/48 z y x + -- z y x + 5/8 y x - 5/96 y z , COEFF(-1, 0, 0) = + 48 + + 2 4 3 2 4 3 2 2 3 2 4 + - 5/16 y x z + 5/6 y z + 5/12 y z - 5/8 y x z + 1/8 y x z + + 3 4 25 2 3 4 4 3 3 3 + - 1/6 y z - -- z y x - 5/6 y x z + 5/12 z y x - 2/3 y x + 12 + + 3 2 3 4 3 2 3 25 2 2 + + 1/2 y x - 10/3 y x + 1/3 y x z - 5/3 y x z + 4/3 y x + -- y x z + 16 + + 3 2 25 2 3 2 + + 5/3 y x + 5/3 y - 5/4 y x - -- y z - 2/3 y + 25/6 y x z + 12 + + 3 3 2 4 3 3 3 3 2 + + 5/6 y x z - 1/6 z y x , COEFF(0, 0, 0) = - 5/4 y x z + 25/4 y x + + 3 4 3 4 3 3 2 3 25 4 + - 5/2 y x - 5/8 z y x + 1/4 z y x + 25/8 z y x + -- y x z + 16 + + 3 3 2 3 4 125 2 3 3 + - 5/2 y x + 25/8 y x z - 5/8 y x z - --- y x z + y x , + 16 + + 3 2 3 3 3 2 4 3 + COEFF(1, 0, 0) = - 1/2 y x + 4/3 y x - 2/3 y x + 5/16 y x z + 2/3 y + + 3 4 3 2 2 25 2 2 4 3 + + 1/3 y x z - 10/3 y x + 5/8 y x z - -- y x z + 5/12 z y x + 16 + + 3 2 25 2 3 3 4 3 3 2 2 + - 5/3 y - 5/6 y z - -- z y x + 1/6 y z + 5/6 y x z + 25/6 y x z + 12 + + 4 4 3 3 3 2 4 3 3 2 + - 5/12 y z - 1/6 z y x - 1/8 y x z + 5/3 y x - 5/3 y x z + + 2 4 25 2 3 3 2 + + 5/4 y x - 5/6 y x z + -- y z , COEFF(2, 0, 0) = - 5/24 y x z + 12 + + 25 2 2 4 3 4 2 4 3 + + -- y x z + 5/96 y x z - 1/48 y x z - 5/32 y x z - 1/12 y x + 32 + + 4 3 2 25 2 25 2 3 2 + + 5/96 y z + 1/4 y x - -- y x z - -- y z + 5/48 y x z + 5/24 y + 96 96 + + 4 3 3 3 3 3 2 2 + + 1/24 z y x + 5/24 y x + 1/6 y x + 5/48 y z - 5/8 y x + + 3 4 25 2 3 3 3 2 4 4 3 + - 1/48 y z + -- z y x - 5/12 y x + 1/16 y x z - 5/48 z y x + 48 + + 3 3 2 2 3 4 2 4 + - 1/12 y - 5/16 y x z , COEFF(-2, 1, 0) = 1/72 y x z - 1/12 y x z + + 3 2 4 2 4 4 3 2 2 4 + + 1/24 y x z + 1/96 y x z + 1/18 z y x + 1/32 y x z + + 4 4 2 3 4 3 3 3 3 2 2 4 + - 1/36 y x z - 1/48 z y x - 1/36 z y x + 5/36 y x z - 1/96 y z + + 2 2 3 3 2 3 3 2 + + 5/48 z y x + 2/9 y x - 5/18 z y x - 5/36 x z - 1/18 x + + 4 3 4 4 2 4 + + 1/36 z x + 1/36 y z - 1/72 x z - 1/24 x z + 1/9 y - 1/9 y x + + 2 2 2 3 2 4 3 2 2 3 + - 5/32 y x z - 5/72 y x z + 1/72 z - 5/24 y x z - 1/18 y + + 3 3 3 4 2 2 3 2 2 + + 1/9 x + 1/18 y x - 1/72 y z - 1/24 y - 5/72 z + 1/6 y x - 1/6 x + + 2 2 2 2 2 2 + + 1/24 y x - 5/96 y x z + 5/12 y x z + 5/36 y x z + 1/18 + + 3 2 2 2 2 2 2 2 2 2 + + 5/72 y z - 5/36 y z + 5/24 x z + 5/72 x z + 5/96 y z + 1/8 y x + + 2 2 3 3 3 3 4 + - 1/3 y x - 1/12 y x - 1/9 y x , COEFF(-1, 1, 0) = - 2/9 y x z + + 2 4 3 2 4 2 4 4 3 2 2 4 + + 1/6 y x z - 1/12 y x z - 1/6 y x z - 2/9 z y x - 1/16 y x z + + 4 4 2 3 4 3 3 3 3 2 2 4 + + 4/9 y x z + 1/12 z y x + 1/9 z y x - 5/9 y x z + 1/12 y z + + 2 2 3 3 2 3 3 2 4 3 + - 5/12 z y x - 8/9 y x + 10/9 z y x + 5/9 x z + 8/9 x - 1/9 z x + + 4 4 2 4 2 2 2 + - 2/9 y z + 2/9 x z + 1/12 x z - 8/9 y + 16/9 y x + 5/16 y x z + + 3 2 4 3 2 2 3 3 3 + + 10/9 y x z - 1/9 z + 5/12 y x z + 4/9 y - 4/9 x - 8/9 y x + + 3 4 2 2 3 2 2 2 + + 1/9 y z + 1/3 y + 5/9 z - 1/3 y x + 1/3 x - 4/9 - 2/3 y x + + 2 2 2 2 2 3 2 2 + + 5/6 y x z - 5/6 y x z - 20/9 y x z - 5/9 y z + 10/9 y z + + 2 2 2 2 2 2 2 2 2 3 + - 5/12 x z - 10/9 x z - 5/12 y z - 1/4 y x + 2/3 y x + 1/3 y x + + 3 3 3 2 25 2 2 + + 4/9 y x , COEFF(0, 1, 0) = 5/3 y x + 5/4 y x - -- y x z + 16 + + 3 3 2 25 3 2 3 4 25 2 2 + + 5/6 y x z - -- y x z - 5/3 x + 5/12 y x z + -- x z + 25/6 y x z + 12 12 + + 2 2 3 2 4 3 2 3 4 + + 5/8 z y x + 5/16 y x z + 4/3 y x - 5/3 z y x - 5/12 x z + + 2 3 4 3 3 2 3 3 4 3 + - 1/2 y x - 5/6 y x z + 2/3 x - 5/6 x z - 2/3 y x + 1/6 z x + + 4 2 3 4 3 4 3 3 + - 1/8 z y x + 1/3 z y x - 10/3 y x - 1/6 z y x , COEFF(1, 1, 0) = + + 3 4 2 4 3 2 4 2 4 4 3 + - 2/9 y x z - 1/6 y x z + 1/12 y x z - 1/6 y x z - 2/9 z y x + + 2 2 4 4 4 2 3 4 3 3 3 3 2 + + 1/16 y x z + 4/9 y x z + 1/12 z y x + 1/9 z y x - 5/9 y x z + + 2 4 2 2 3 3 2 3 3 2 + - 1/12 y z - 5/12 z y x - 8/9 y x + 10/9 z y x + 5/9 x z + 8/9 x + + 4 3 4 4 2 4 + - 1/9 z x + 2/9 y z + 2/9 x z - 1/12 x z + 8/9 y + 16/9 y x + + 2 2 2 3 2 4 3 2 2 3 + - 5/16 y x z + 10/9 y x z + 1/9 z - 5/12 y x z + 4/9 - 4/9 y + + 3 3 3 4 2 2 3 2 2 + - 4/9 x - 8/9 y x - 1/9 y z - 1/3 y - 5/9 z + 1/3 y x - 1/3 x + + 2 2 2 2 2 2 3 2 + - 2/3 y x + 5/6 y x z + 5/6 y x z - 20/9 y x z + 5/9 y z + + 2 2 2 2 2 2 2 2 2 + - 10/9 y z + 5/12 x z - 10/9 x z + 5/12 y z + 1/4 y x - 2/3 y x + + 2 3 3 3 3 4 2 4 + + 1/3 y x + 4/9 y x , COEFF(2, 1, 0) = 1/72 y x z + 1/12 y x z + + 3 2 4 2 4 4 3 2 2 4 + - 1/24 y x z + 1/96 y x z + 1/18 z y x - 1/32 y x z + + 4 4 2 3 4 3 3 3 3 2 2 4 + - 1/36 y x z - 1/48 z y x - 1/36 z y x + 5/36 y x z + 1/96 y z + + 2 2 3 3 2 3 3 2 + + 5/48 z y x + 2/9 y x - 5/18 z y x - 5/36 x z - 1/18 x + + 4 3 4 4 2 4 + + 1/36 z x - 1/36 y z - 1/72 x z + 1/24 x z - 1/9 y - 1/9 y x + + 2 2 2 3 2 4 3 2 2 3 + + 5/32 y x z - 5/72 y x z - 1/72 z + 5/24 y x z + 1/18 y + + 3 3 3 4 2 2 3 2 2 + + 1/9 x + 1/18 y x + 1/72 y z + 1/24 y + 5/72 z - 1/6 y x + 1/6 x + + 2 2 2 2 2 2 + + 1/24 y x - 5/96 y x z - 5/12 y x z + 5/36 y x z - 1/18 + + 3 2 2 2 2 2 2 2 2 2 + - 5/72 y z + 5/36 y z - 5/24 x z + 5/72 x z - 5/96 y z - 1/8 y x + + 2 2 3 3 3 3 4 + + 1/3 y x - 1/12 y x - 1/9 y x , COEFF(-2, 2, 0) = - 1/288 y x z + + 2 4 3 2 4 2 4 4 3 + + 1/192 y x z - 1/96 y x z - 1/192 y x z - 1/288 z y x + + 2 2 4 4 4 2 3 4 3 3 + - 1/64 y x z + 1/576 y x z + 1/96 z y x + 1/144 z y x + + 3 3 2 2 4 2 2 3 3 2 3 + - 5/144 y x z + 1/192 y z - 5/96 z y x - 1/72 y x + 5/288 z y x + + 3 2 4 3 4 4 + + 5/288 x z + 1/144 x - 1/288 z x - 1/576 y z + 1/576 x z + + 2 4 2 2 2 3 2 + + 1/192 x z - 1/144 y + 1/144 y x + 5/64 y x z + 5/288 y x z + + 4 3 2 2 3 3 3 3 4 + - 1/576 z + 5/96 y x z + 1/72 y - 1/72 x - 1/72 y x + 1/288 y z + + 2 2 3 2 2 2 2 2 + + 1/48 y + 5/576 z - 1/24 y x + 1/48 x - 1/48 y x + 5/192 y x z + + 2 2 2 3 2 2 2 2 + - 5/192 y x z - 5/576 y x z - 5/288 y z + 5/576 y z - 5/192 x z + + 2 2 2 2 2 2 2 3 + - 5/576 x z - 5/192 y z - 1/16 y x + 1/48 y x - 1/144 + 1/24 y x + + 3 3 3 4 2 4 + + 1/36 y x , COEFF(-1, 2, 0) = 1/18 y x z - 1/96 y x z + + 3 2 4 2 4 4 3 2 2 4 + + 1/48 y x z + 1/12 y x z + 1/72 z y x + 1/32 y x z + + 4 4 2 3 4 3 3 3 3 2 2 4 + - 1/36 y x z - 1/24 z y x - 1/36 z y x + 5/36 y x z - 1/24 y z + + 2 2 3 3 2 3 3 2 + + 5/24 z y x + 1/18 y x - 5/72 z y x - 5/72 x z - 1/9 x + + 4 3 4 4 2 4 + + 1/72 z x + 1/72 y z - 1/36 x z - 1/96 x z + 1/18 y - 1/9 y x + + 2 2 2 3 2 4 3 2 2 3 + - 5/32 y x z - 5/18 y x z + 1/72 z - 5/48 y x z - 1/9 y + + 3 3 3 4 2 2 3 2 + + 1/18 x + 2/9 y x - 1/36 y z - 1/6 y - 5/72 z + 1/12 y x + + 2 2 2 2 2 2 2 + - 1/24 x + 1/3 y x - 5/12 y x z + 5/96 y x z + 5/36 y x z + 1/18 + + 3 2 2 2 2 2 2 2 2 2 + + 5/36 y z - 5/72 y z + 5/96 x z + 5/36 x z + 5/24 y z + 1/8 y x + + 2 2 3 3 3 3 3 2 + - 1/24 y x - 1/6 y x - 1/9 y x , COEFF(0, 2, 0) = - 5/24 y x z + + 4 4 2 3 2 4 25 2 2 + + 5/96 x z + 5/24 x + 1/16 z y x - 5/32 y x z + -- y x z + 32 + + 2 3 4 3 3 3 3 2 25 2 + + 1/4 y x + 1/24 z y x - 5/12 y x - 1/12 y x - 5/8 y x - -- x z + 96 + + 3 2 25 3 2 4 3 2 2 3 25 2 + + 5/48 x z + -- y x z - 1/48 z y x - 5/16 z y x - -- y x z + 48 96 + + 2 3 3 3 3 4 3 4 + + 5/48 z y x - 1/12 x + 1/6 y x - 1/48 z x + 5/96 y x z + + 3 4 3 4 2 4 + - 5/48 y x z + 5/24 y x, COEFF(1, 2, 0) = 1/18 y x z + 1/96 y x z + + 3 2 4 2 4 4 3 2 2 4 + - 1/48 y x z + 1/12 y x z + 1/72 z y x - 1/32 y x z + + 4 4 2 3 4 3 3 3 3 2 2 4 + - 1/36 y x z - 1/24 z y x - 1/36 z y x + 5/36 y x z + 1/24 y z + + 2 2 3 3 2 3 3 2 + + 5/24 z y x + 1/18 y x - 5/72 z y x - 5/72 x z - 1/9 x + + 4 3 4 4 2 4 + + 1/72 z x - 1/72 y z - 1/36 x z + 1/96 x z - 1/18 y - 1/9 y x + + 2 2 2 3 2 4 3 2 2 3 + + 5/32 y x z - 5/18 y x z - 1/72 z + 5/48 y x z + 1/9 y + + 3 3 3 4 2 2 3 2 + + 1/18 x + 2/9 y x + 1/36 y z + 1/6 y + 5/72 z - 1/12 y x + + 2 2 2 2 2 2 2 + + 1/24 x + 1/3 y x - 5/12 y x z - 5/96 y x z + 5/36 y x z - 1/18 + + 3 2 2 2 2 2 2 2 2 2 + - 5/36 y z + 5/72 y z - 5/96 x z + 5/36 x z - 5/24 y z - 1/8 y x + + 2 2 3 3 3 3 4 + + 1/24 y x - 1/6 y x - 1/9 y x , COEFF(2, 2, 0) = - 1/288 y x z + + 2 4 3 2 4 2 4 4 3 + - 1/192 y x z + 1/96 y x z - 1/192 y x z - 1/288 z y x + + 2 2 4 4 4 2 3 4 3 3 + + 1/64 y x z + 1/576 y x z + 1/96 z y x + 1/144 z y x + + 3 3 2 2 4 2 2 3 3 2 3 + - 5/144 y x z - 1/192 y z - 5/96 z y x - 1/72 y x + 5/288 z y x + + 3 2 4 3 4 4 + + 5/288 x z + 1/144 x - 1/288 z x + 1/576 y z + 1/576 x z + + 2 4 2 2 2 3 2 + - 1/192 x z + 1/144 y + 1/144 y x - 5/64 y x z + 5/288 y x z + + 4 3 2 2 3 3 3 3 4 + + 1/576 z - 5/96 y x z - 1/72 y - 1/72 x - 1/72 y x - 1/288 y z + + 2 2 3 2 2 2 2 2 + - 1/48 y - 5/576 z + 1/24 y x - 1/48 x - 1/48 y x + 5/192 y x z + + 2 2 2 3 2 2 2 2 + + 5/192 y x z - 5/576 y x z + 5/288 y z - 5/576 y z + 5/192 x z + + 2 2 2 2 2 2 2 3 + - 5/576 x z + 5/192 y z + 1/16 y x - 1/48 y x + 1/144 + 1/24 y x + + 3 3 3 4 2 4 + + 1/36 y x , COEFF(-2, -2, 1) = 1/432 y x z - 1/288 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/144 y x z - 1/288 y x z + 1/432 y x z + 1/432 z y x + + 3 3 3 2 2 4 4 4 2 3 + - 1/216 y x z - 1/96 y x z - 1/864 y x z + 1/144 z y x + + 2 3 3 2 3 3 4 3 3 + + 1/144 y x z - 1/36 z y x - 1/108 z y x - 1/216 z y x + + 3 3 2 2 4 2 2 3 2 3 + + 1/54 y x z + 1/288 y z - 1/36 z y x - 1/108 z y x + + 3 3 3 2 3 3 4 3 4 + + 1/54 z y x + 1/108 x z - 1/432 x z - 1/432 z x + 1/864 y z + + 4 2 4 3 2 + + 1/864 x z + 1/288 x z - 1/864 y x z + 1/216 z + 1/72 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/288 y x z + 1/24 y x z - 1/108 y x z - 1/96 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/288 y x z - 1/864 z - 1/36 y x z - 1/864 z - 1/432 y z + + 3 2 3 3 2 + + 1/108 z y + 1/216 z - 1/108 z y x - 1/36 z y x + 1/216 y x z + + 2 3 3 2 2 2 2 + + 1/72 z y x - 1/216 y z + 1/432 y x z + 1/72 y x z + 1/24 y x z + + 2 2 2 2 3 2 3 + + 1/72 y x z + 1/216 y x z - 1/72 y z + 1/144 y x z - 1/216 x z + + 2 3 2 3 3 3 2 3 + - 1/72 x z + 1/864 y z + 1/288 y z - 1/432 y z + 1/288 x z + + 3 2 3 2 2 2 2 + + 1/108 y z + 1/864 x z - 1/216 y z - 1/72 x z - 1/216 x z + + 2 2 3 3 4 + - 1/72 y z + 1/108 z x , COEFF(-1, -2, 1) = - 1/27 y x z + + 2 4 3 2 4 2 4 3 3 + + 1/144 y x z - 1/72 y x z + 1/18 y x z - 1/108 y x z + + 4 3 3 3 3 2 2 4 4 + - 1/108 z y x + 1/54 y x z + 1/48 y x z + 1/54 y x z + + 4 2 3 2 3 3 2 3 3 + - 1/36 z y x - 1/36 y x z + 1/9 z y x + 1/27 z y x + + 4 3 3 3 3 2 2 4 2 2 3 2 3 + + 1/54 z y x - 2/27 y x z - 1/36 y z + 1/9 z y x + 1/27 z y x + + 3 3 3 2 3 3 4 3 4 + - 2/27 z y x - 1/27 x z + 1/108 x z + 1/108 z x - 1/108 y z + + 4 2 4 3 2 + - 1/54 x z - 1/144 x z + 1/54 y x z - 1/27 z - 2/9 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/18 y x z - 1/12 y x z + 4/27 y x z + 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + + 1/144 y x z + 1/108 z + 1/18 y x z + 1/108 z + 1/54 y z + + 3 2 3 3 2 + - 2/27 z y - 1/27 z + 4/27 z y x + 1/18 z y x - 2/27 y x z + + 2 3 3 2 2 2 2 + - 1/36 z y x + 1/27 y z - 1/27 y x z - 2/9 y x z - 1/12 y x z + + 2 2 2 2 3 2 3 + - 1/36 y x z - 2/27 y x z + 1/9 y z - 1/72 y x z + 2/27 x z + + 2 3 2 3 3 3 2 3 + + 1/36 x z - 1/108 y z - 1/36 y z + 1/54 y z - 1/144 x z + + 3 2 3 2 2 2 2 2 2 + - 2/27 y z - 1/54 x z + 1/27 y z + 1/36 x z + 2/27 x z + 1/9 y z + + 3 3 4 2 4 3 3 + - 1/27 z x , COEFF(0, -2, 1) = 5/72 y x z - 5/48 y x z + 1/72 y x z + + 4 3 3 3 3 4 4 2 3 + + 1/72 z y x - 1/36 y x z - 5/144 y x z + 1/24 z y x + + 2 3 3 2 3 3 4 3 3 3 3 2 + + 1/24 y x z - 1/6 z y x - 1/18 z y x - 1/36 z y x + 1/9 y x z + + 2 2 3 2 3 3 3 3 2 3 3 + - 1/6 z y x - 1/18 z y x + 1/9 z y x + 1/18 x z - 1/72 x z + + 4 3 4 3 2 2 3 + - 1/72 z x + 5/144 x z - 5/144 y x z + 5/12 y x z - 5/48 y x z + + 3 2 3 3 3 2 2 + - 5/18 y x z - 5/18 z y x + 5/36 y x z + 5/72 y x z + 5/12 y x z + + 2 3 2 3 + + 5/36 y x z - 5/36 x z + 5/144 x z - 5/36 x z + 1/18 z x , + + 3 4 2 4 3 2 4 + COEFF(1, -2, 1) = - 1/27 y x z - 1/144 y x z + 1/72 y x z + + 2 4 3 3 4 3 3 3 3 + + 1/18 y x z - 1/108 y x z - 1/108 z y x + 1/54 y x z + + 2 2 4 4 4 2 3 2 3 3 + - 1/48 y x z + 1/54 y x z - 1/36 z y x - 1/36 y x z + + 2 3 3 4 3 3 3 3 2 2 4 + + 1/9 z y x + 1/27 z y x + 1/54 z y x - 2/27 y x z + 1/36 y z + + 2 2 3 2 3 3 3 3 2 3 3 + + 1/9 z y x + 1/27 z y x - 2/27 z y x - 1/27 x z + 1/108 x z + + 4 3 4 4 2 4 3 + + 1/108 z x + 1/108 y z - 1/54 x z + 1/144 x z + 1/54 y x z + + 2 2 3 2 2 2 3 2 + + 1/27 z - 2/9 y x z + 1/18 y x z + 1/12 y x z + 4/27 y x z + + 2 2 3 2 3 4 3 2 2 3 + - 1/48 y x z - 1/144 y x z - 1/108 z - 1/18 y x z - 1/108 z + + 3 4 3 2 3 3 2 + - 1/54 y z + 2/27 z y + 1/27 z + 4/27 z y x - 1/18 z y x + + 2 3 3 2 2 + - 2/27 y x z + 1/36 z y x - 1/27 y z - 1/27 y x z - 2/9 y x z + + 2 2 2 2 2 2 3 2 3 + + 1/12 y x z + 1/36 y x z - 2/27 y x z - 1/9 y z + 1/72 y x z + + 2 3 2 3 3 3 + + 2/27 x z - 1/36 x z + 1/108 y z + 1/36 y z - 1/54 y z + + 2 3 3 2 3 2 2 2 + + 1/144 x z + 2/27 y z - 1/54 x z - 1/27 y z - 1/36 x z + + 2 2 2 3 3 4 + + 2/27 x z - 1/9 y z - 1/27 z x , COEFF(2, -2, 1) = 1/432 y x z + + 2 4 3 2 4 2 4 3 3 + + 1/288 y x z - 1/144 y x z - 1/288 y x z + 1/432 y x z + + 4 3 3 3 3 2 2 4 4 + + 1/432 z y x - 1/216 y x z + 1/96 y x z - 1/864 y x z + + 4 2 3 2 3 3 2 3 3 + + 1/144 z y x + 1/144 y x z - 1/36 z y x - 1/108 z y x + + 4 3 3 3 3 2 2 4 2 2 3 + - 1/216 z y x + 1/54 y x z - 1/288 y z - 1/36 z y x + + 2 3 3 3 3 2 3 3 4 3 + - 1/108 z y x + 1/54 z y x + 1/108 x z - 1/432 x z - 1/432 z x + + 4 4 2 4 3 + - 1/864 y z + 1/864 x z - 1/288 x z - 1/864 y x z - 1/216 z + + 2 2 3 2 2 2 3 2 + + 1/72 y x z - 1/288 y x z - 1/24 y x z - 1/108 y x z + + 2 2 3 2 3 4 3 2 2 3 + + 1/96 y x z + 1/288 y x z + 1/864 z + 1/36 y x z + 1/864 z + + 3 4 3 2 3 3 2 + + 1/432 y z - 1/108 z y - 1/216 z - 1/108 z y x + 1/36 z y x + + 2 3 3 2 2 + + 1/216 y x z - 1/72 z y x + 1/216 y z + 1/432 y x z + 1/72 y x z + + 2 2 2 2 2 2 3 2 3 + - 1/24 y x z - 1/72 y x z + 1/216 y x z + 1/72 y z - 1/144 y x z + + 2 3 2 3 3 3 + - 1/216 x z + 1/72 x z - 1/864 y z - 1/288 y z + 1/432 y z + + 2 3 3 2 3 2 2 2 + - 1/288 x z - 1/108 y z + 1/864 x z + 1/216 y z + 1/72 x z + + 2 2 2 3 3 4 + - 1/216 x z + 1/72 y z + 1/108 z x , COEFF(-2, -1, 1) = - 1/108 y x z + + 2 4 3 2 4 2 4 3 3 + + 1/18 y x z - 1/36 y x z + 1/144 y x z - 1/27 y x z + + 4 3 3 3 3 2 2 4 4 + - 1/27 z y x + 1/54 y x z + 1/48 y x z + 1/54 y x z + + 4 2 3 2 3 3 2 3 3 + - 1/72 z y x - 1/72 y x z + 1/18 z y x + 4/27 z y x + + 4 3 3 3 3 2 2 4 2 2 3 + + 1/54 z y x - 2/27 y x z - 1/144 y z + 1/18 z y x + + 2 3 3 3 3 2 3 3 4 3 + + 4/27 z y x - 2/27 z y x - 2/27 x z + 1/54 x z + 1/54 z x + + 4 4 2 4 3 2 + - 1/54 y z - 1/108 x z - 1/36 x z + 1/54 y x z - 1/27 z - 1/36 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/144 y x z - 1/12 y x z + 1/27 y x z + 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + + 1/18 y x z + 1/108 z + 1/9 y x z + 1/108 z + 1/108 y z + + 3 2 3 3 2 + - 1/27 z y - 1/27 z + 1/27 z y x + 1/9 z y x - 2/27 y x z + + 2 3 3 2 2 2 2 + - 2/9 z y x + 2/27 y z - 1/108 y x z - 1/36 y x z - 1/12 y x z + + 2 2 2 2 3 2 3 + - 2/9 y x z - 2/27 y x z + 1/36 y z - 1/36 y x z + 1/27 x z + + 2 3 2 3 3 3 2 3 + + 1/9 x z - 1/54 y z - 1/144 y z + 1/108 y z - 1/36 x z + + 3 2 3 2 2 2 2 2 2 + - 1/27 y z - 1/108 x z + 2/27 y z + 1/9 x z + 1/27 x z + 1/36 y z + + 3 3 4 2 4 3 2 4 + - 2/27 z x , COEFF(-1, -1, 1) = 4/27 y x z - 1/9 y x z + 1/18 y x z + + 2 4 3 3 4 3 3 3 3 + - 1/9 y x z + 4/27 y x z + 4/27 z y x - 2/27 y x z + + 2 2 4 4 4 2 3 2 3 3 + - 1/24 y x z - 8/27 y x z + 1/18 z y x + 1/18 y x z + + 2 3 16 3 4 3 3 3 3 2 2 4 + - 2/9 z y x - -- z y x - 2/27 z y x + 8/27 y x z + 1/18 y z + 27 + + 2 2 3 16 2 3 3 3 3 2 3 3 + - 2/9 z y x - -- z y x + 8/27 z y x + 8/27 x z - 2/27 x z + 27 + + 4 3 4 4 2 4 3 + - 2/27 z x + 4/27 y z + 4/27 x z + 1/18 x z - 8/27 y x z + 8/27 z + + 2 2 3 2 2 2 16 3 2 2 2 3 + + 4/9 y x z - 1/9 y x z + 1/6 y x z - -- y x z - 1/24 y x z + 27 + + 2 3 4 3 2 2 3 3 4 3 + - 1/9 y x z - 2/27 z - 2/9 y x z - 2/27 z - 2/27 y z + 8/27 z y + + 2 16 3 3 2 32 2 16 + + 8/27 z - -- z y x - 2/9 z y x + -- y x z + 4/9 z y x - -- y z + 27 27 27 + + 3 3 2 2 2 2 2 2 32 2 + + 4/27 y x z + 4/9 y x z + 1/6 y x z + 4/9 y x z + -- y x z + 27 + + 2 3 2 3 16 2 3 2 3 + - 2/9 y z + 1/18 y x z - -- x z - 2/9 x z + 4/27 y z + 1/18 y z + 27 + + 3 3 2 3 3 2 3 16 2 2 2 + - 2/27 y z + 1/18 x z + 8/27 y z + 4/27 x z - -- y z - 2/9 x z + 27 + + 16 2 2 2 3 3 4 + - -- x z - 2/9 y z + 8/27 z x , COEFF(0, -1, 1) = - 5/18 y x z + 27 + + 2 4 3 3 4 3 3 3 3 4 + + 5/24 y x z - 2/9 y x z - 2/9 z y x + 1/9 y x z + 5/9 y x z + + 4 2 3 2 3 3 2 3 3 4 3 3 + - 1/12 z y x - 1/12 y x z + 1/3 z y x + 8/9 z y x + 1/9 z y x + + 3 3 2 2 2 3 2 3 3 3 3 2 + - 4/9 y x z + 1/3 z y x + 8/9 z y x - 4/9 z y x - 4/9 x z + + 3 3 4 3 4 3 2 + + 1/9 x z + 1/9 z x - 5/18 x z + 5/9 y x z - 5/6 y x z + + 2 3 3 2 3 3 3 + + 5/24 y x z + 10/9 y x z + 10/9 z y x - 20/9 y x z - 5/18 y x z + + 2 2 2 3 2 3 + - 5/6 y x z - 20/9 y x z + 10/9 x z - 5/18 x z + 10/9 x z - 4/9 z x , + + 3 4 2 4 3 2 4 2 4 + COEFF(1, -1, 1) = 4/27 y x z + 1/9 y x z - 1/18 y x z - 1/9 y x z + + 3 3 4 3 3 3 3 2 2 4 + + 4/27 y x z + 4/27 z y x - 2/27 y x z + 1/24 y x z + + 4 4 2 3 2 3 3 2 3 16 3 + - 8/27 y x z + 1/18 z y x + 1/18 y x z - 2/9 z y x - -- z y x + 27 + + 4 3 3 3 3 2 2 4 2 2 3 16 2 3 + - 2/27 z y x + 8/27 y x z - 1/18 y z - 2/9 z y x - -- z y x + 27 + + 3 3 3 2 3 3 4 3 4 + + 8/27 z y x + 8/27 x z - 2/27 x z - 2/27 z x - 4/27 y z + + 4 2 4 3 2 2 3 + + 4/27 x z - 1/18 x z - 8/27 y x z - 8/27 z + 4/9 y x z - 1/9 y x z + + 2 2 2 16 3 2 2 2 3 2 3 4 + - 1/6 y x z - -- y x z + 1/24 y x z + 1/9 y x z + 2/27 z + 27 + + 3 2 2 3 3 4 3 2 16 3 + + 2/9 y x z + 2/27 z + 2/27 y z - 8/27 z y - 8/27 z - -- z y x + 27 + + 3 2 32 2 16 3 3 + + 2/9 z y x + -- y x z - 4/9 z y x + -- y z + 4/27 y x z + 27 27 + + 2 2 2 2 2 2 32 2 2 + + 4/9 y x z - 1/6 y x z - 4/9 y x z + -- y x z + 2/9 y z + 27 + + 3 2 3 16 2 3 2 3 3 3 + - 1/18 y x z - -- x z + 2/9 x z - 4/27 y z - 1/18 y z + 2/27 y z + 27 + + 2 3 3 2 3 16 2 2 2 16 2 + - 1/18 x z - 8/27 y z + 4/27 x z + -- y z + 2/9 x z - -- x z + 27 27 + + 2 2 3 3 4 2 4 + + 2/9 y z + 8/27 z x , COEFF(2, -1, 1) = - 1/108 y x z - 1/18 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/36 y x z + 1/144 y x z - 1/27 y x z - 1/27 z y x + + 3 3 3 2 2 4 4 4 2 3 + + 1/54 y x z - 1/48 y x z + 1/54 y x z - 1/72 z y x + + 2 3 3 2 3 3 4 3 3 + - 1/72 y x z + 1/18 z y x + 4/27 z y x + 1/54 z y x + + 3 3 2 2 4 2 2 3 2 3 + - 2/27 y x z + 1/144 y z + 1/18 z y x + 4/27 z y x + + 3 3 3 2 3 3 4 3 4 + - 2/27 z y x - 2/27 x z + 1/54 x z + 1/54 z x + 1/54 y z + + 4 2 4 3 2 + - 1/108 x z + 1/36 x z + 1/54 y x z + 1/27 z - 1/36 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/144 y x z + 1/12 y x z + 1/27 y x z - 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/18 y x z - 1/108 z - 1/9 y x z - 1/108 z - 1/108 y z + + 3 2 3 3 2 + + 1/27 z y + 1/27 z + 1/27 z y x - 1/9 z y x - 2/27 y x z + + 2 3 3 2 2 2 2 + + 2/9 z y x - 2/27 y z - 1/108 y x z - 1/36 y x z + 1/12 y x z + + 2 2 2 2 3 2 3 + + 2/9 y x z - 2/27 y x z - 1/36 y z + 1/36 y x z + 1/27 x z + + 2 3 2 3 3 3 2 3 + - 1/9 x z + 1/54 y z + 1/144 y z - 1/108 y z + 1/36 x z + + 3 2 3 2 2 2 2 2 2 + + 1/27 y z - 1/108 x z - 2/27 y z - 1/9 x z + 1/27 x z - 1/36 y z + + 3 3 4 2 4 3 2 4 + - 2/27 z x , COEFF(-2, 0, 1) = 1/72 y x z - 5/48 y x z + 1/24 y x z + + 3 3 4 3 3 3 3 4 3 + + 5/72 y x z + 5/72 z y x - 1/36 y x z - 5/144 y x z - 5/18 z y x + + 4 3 3 3 3 2 2 3 3 3 4 + - 1/36 z y x + 1/9 y x z - 5/18 z y x + 1/9 z y x + 5/144 y z + + 3 3 2 2 3 3 2 2 3 4 + - 5/144 y x z - 1/18 y x z - 5/48 y x z - 1/6 y x z - 1/72 y z + + 3 3 3 2 2 + + 1/18 z y - 1/18 z y x - 1/6 z y x + 5/36 y x z + 5/12 z y x + + 3 3 2 2 2 3 2 3 + - 5/36 y z + 1/72 y x z + 5/12 y x z + 5/36 y x z + 1/24 y x z + + 3 3 3 3 2 2 + + 5/144 y z - 1/72 y z + 1/18 y z - 5/36 y z , COEFF(-1, 0, 1) = + + 3 4 2 4 3 2 4 3 3 4 3 + - 2/9 y x z + 5/24 y x z - 1/12 y x z - 5/18 y x z - 5/18 z y x + + 3 3 3 4 3 4 3 3 3 3 2 + + 1/9 y x z + 5/9 y x z + 10/9 z y x + 1/9 z y x - 4/9 y x z + + 2 3 3 3 4 3 3 2 + + 10/9 z y x - 4/9 z y x - 5/18 y z + 5/9 y x z + 8/9 y x z + + 2 3 3 2 2 3 4 3 3 + + 5/24 y x z + 1/3 y x z + 1/9 y z - 4/9 z y + 8/9 z y x + + 3 2 2 3 3 + + 1/3 z y x - 20/9 y x z - 5/6 z y x + 10/9 y z - 2/9 y x z + + 2 2 2 3 2 3 3 3 3 + - 5/6 y x z - 20/9 y x z - 1/12 y x z - 5/18 y z + 1/9 y z + + 3 2 2 3 3 3 + - 4/9 y z + 10/9 y z , COEFF(0, 0, 1) = - 5/3 z y x + 2/3 z y x + + 3 3 2 4 3 25 3 3 3 3 + + 2/3 y x z + 25/6 y x z + 5/12 z y x - -- y x z - 1/6 y x z + 24 + + 3 3 3 2 3 4 4 3 3 2 + + 5/12 y x z - 5/3 y x z + 5/12 y x z - 1/6 z y x + 25/6 y x z + + 3 3 3 25 4 2 3 + + 5/12 y x z - 5/3 z y x - -- y x z - 5/3 z y x , COEFF(1, 0, 1) = + 24 + + 3 4 2 4 3 2 4 3 3 4 3 + - 2/9 y x z - 5/24 y x z + 1/12 y x z - 5/18 y x z - 5/18 z y x + + 3 3 3 4 3 4 3 3 3 3 2 + + 1/9 y x z + 5/9 y x z + 10/9 z y x + 1/9 z y x - 4/9 y x z + + 2 3 3 3 4 3 3 2 + + 10/9 z y x - 4/9 z y x + 5/18 y z + 5/9 y x z + 8/9 y x z + + 2 3 3 2 2 3 4 3 3 + - 5/24 y x z - 1/3 y x z - 1/9 y z + 4/9 z y + 8/9 z y x + + 3 2 2 3 3 + - 1/3 z y x - 20/9 y x z + 5/6 z y x - 10/9 y z - 2/9 y x z + + 2 2 2 3 2 3 3 3 3 + + 5/6 y x z - 20/9 y x z + 1/12 y x z + 5/18 y z - 1/9 y z + + 3 2 2 3 4 2 4 + + 4/9 y z - 10/9 y z , COEFF(2, 0, 1) = 1/72 y x z + 5/48 y x z + + 3 2 4 3 3 4 3 3 3 3 + - 1/24 y x z + 5/72 y x z + 5/72 z y x - 1/36 y x z + + 4 3 4 3 3 3 3 2 2 3 + - 5/144 y x z - 5/18 z y x - 1/36 z y x + 1/9 y x z - 5/18 z y x + + 3 3 4 3 3 2 2 3 + + 1/9 z y x - 5/144 y z - 5/144 y x z - 1/18 y x z + 5/48 y x z + + 3 2 2 3 4 3 3 3 2 + + 1/6 y x z + 1/72 y z - 1/18 z y - 1/18 z y x + 1/6 z y x + + 2 3 3 2 2 + + 5/36 y x z - 5/12 z y x + 5/36 y z + 1/72 y x z - 5/12 y x z + + 2 3 2 3 3 3 3 3 2 + + 5/36 y x z - 1/24 y x z - 5/144 y z + 1/72 y z - 1/18 y z + + 2 3 4 2 4 + + 5/36 y z , COEFF(-2, 1, 1) = - 1/108 y x z + 1/18 y x z + + 3 2 4 2 4 3 3 4 3 + - 1/36 y x z - 1/144 y x z - 1/27 y x z - 1/27 z y x + + 3 3 3 2 2 4 4 4 2 3 + + 1/54 y x z - 1/48 y x z + 1/54 y x z + 1/72 z y x + + 2 3 3 2 3 3 4 3 3 + + 1/72 y x z - 1/18 z y x + 4/27 z y x + 1/54 z y x + + 3 3 2 2 4 2 2 3 2 3 + - 2/27 y x z + 1/144 y z - 1/18 z y x + 4/27 z y x + + 3 3 3 2 3 3 4 3 4 + - 2/27 z y x + 2/27 x z - 1/54 x z - 1/54 z x - 1/54 y z + + 4 2 4 3 2 + + 1/108 x z + 1/36 x z + 1/54 y x z + 1/27 z + 1/36 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/144 y x z + 1/12 y x z + 1/27 y x z - 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + + 1/18 y x z - 1/108 z + 1/9 y x z - 1/108 z + 1/108 y z + + 3 2 3 3 2 + - 1/27 z y + 1/27 z + 1/27 z y x + 1/9 z y x - 2/27 y x z + + 2 3 3 2 2 2 2 + - 2/9 z y x + 2/27 y z - 1/108 y x z + 1/36 y x z + 1/12 y x z + + 2 2 2 2 3 2 3 + - 2/9 y x z - 2/27 y x z - 1/36 y z - 1/36 y x z - 1/27 x z + + 2 3 2 3 3 3 2 3 + - 1/9 x z - 1/54 y z + 1/144 y z + 1/108 y z + 1/36 x z + + 3 2 3 2 2 2 2 2 2 + - 1/27 y z + 1/108 x z + 2/27 y z - 1/9 x z - 1/27 x z - 1/36 y z + + 3 3 4 2 4 3 2 4 + + 2/27 z x , COEFF(-1, 1, 1) = 4/27 y x z - 1/9 y x z + 1/18 y x z + + 2 4 3 3 4 3 3 3 3 + + 1/9 y x z + 4/27 y x z + 4/27 z y x - 2/27 y x z + + 2 2 4 4 4 2 3 2 3 3 + + 1/24 y x z - 8/27 y x z - 1/18 z y x - 1/18 y x z + + 2 3 16 3 4 3 3 3 3 2 2 4 + + 2/9 z y x - -- z y x - 2/27 z y x + 8/27 y x z - 1/18 y z + 27 + + 2 2 3 16 2 3 3 3 3 2 3 3 + + 2/9 z y x - -- z y x + 8/27 z y x - 8/27 x z + 2/27 x z + 27 + + 4 3 4 4 2 4 3 + + 2/27 z x + 4/27 y z - 4/27 x z - 1/18 x z - 8/27 y x z - 8/27 z + + 2 2 3 2 2 2 16 3 2 2 2 3 + - 4/9 y x z + 1/9 y x z - 1/6 y x z - -- y x z + 1/24 y x z + 27 + + 2 3 4 3 2 2 3 3 4 3 + - 1/9 y x z + 2/27 z - 2/9 y x z + 2/27 z - 2/27 y z + 8/27 z y + + 2 16 3 3 2 32 2 16 + - 8/27 z - -- z y x - 2/9 z y x + -- y x z + 4/9 z y x - -- y z + 27 27 27 + + 3 3 2 2 2 2 2 2 32 2 + + 4/27 y x z - 4/9 y x z - 1/6 y x z + 4/9 y x z + -- y x z + 27 + + 2 3 2 3 16 2 3 2 3 + + 2/9 y z + 1/18 y x z + -- x z + 2/9 x z + 4/27 y z - 1/18 y z + 27 + + 3 3 2 3 3 2 3 16 2 2 2 + - 2/27 y z - 1/18 x z + 8/27 y z - 4/27 x z - -- y z + 2/9 x z + 27 + + 16 2 2 2 3 3 4 + + -- x z + 2/9 y z - 8/27 z x , COEFF(0, 1, 1) = - 5/18 y x z + 27 + + 2 4 3 3 4 3 3 3 3 4 + - 5/24 y x z - 2/9 y x z - 2/9 z y x + 1/9 y x z + 5/9 y x z + + 4 2 3 2 3 3 2 3 3 4 3 3 + + 1/12 z y x + 1/12 y x z - 1/3 z y x + 8/9 z y x + 1/9 z y x + + 3 3 2 2 2 3 2 3 3 3 3 2 + - 4/9 y x z - 1/3 z y x + 8/9 z y x - 4/9 z y x + 4/9 x z + + 3 3 4 3 4 3 2 + - 1/9 x z - 1/9 z x + 5/18 x z + 5/9 y x z + 5/6 y x z + + 2 3 3 2 3 3 3 + - 5/24 y x z + 10/9 y x z + 10/9 z y x - 20/9 y x z - 5/18 y x z + + 2 2 2 3 2 3 + + 5/6 y x z - 20/9 y x z - 10/9 x z + 5/18 x z - 10/9 x z + 4/9 z x , + + 3 4 2 4 3 2 4 2 4 + COEFF(1, 1, 1) = 4/27 y x z + 1/9 y x z - 1/18 y x z + 1/9 y x z + + 3 3 4 3 3 3 3 2 2 4 + + 4/27 y x z + 4/27 z y x - 2/27 y x z - 1/24 y x z + + 4 4 2 3 2 3 3 2 3 16 3 + - 8/27 y x z - 1/18 z y x - 1/18 y x z + 2/9 z y x - -- z y x + 27 + + 4 3 3 3 3 2 2 4 2 2 3 16 2 3 + - 2/27 z y x + 8/27 y x z + 1/18 y z + 2/9 z y x - -- z y x + 27 + + 3 3 3 2 3 3 4 3 4 + + 8/27 z y x - 8/27 x z + 2/27 x z + 2/27 z x - 4/27 y z + + 4 2 4 3 2 2 3 + - 4/27 x z + 1/18 x z - 8/27 y x z + 8/27 z - 4/9 y x z + 1/9 y x z + + 2 2 2 16 3 2 2 2 3 2 3 4 + + 1/6 y x z - -- y x z - 1/24 y x z + 1/9 y x z - 2/27 z + 27 + + 3 2 2 3 3 4 3 2 16 3 + + 2/9 y x z - 2/27 z + 2/27 y z - 8/27 z y + 8/27 z - -- z y x + 27 + + 3 2 32 2 16 3 3 + + 2/9 z y x + -- y x z - 4/9 z y x + -- y z + 4/27 y x z + 27 27 + + 2 2 2 2 2 2 32 2 2 + - 4/9 y x z + 1/6 y x z - 4/9 y x z + -- y x z - 2/9 y z + 27 + + 3 2 3 16 2 3 2 3 3 3 + - 1/18 y x z + -- x z - 2/9 x z - 4/27 y z + 1/18 y z + 2/27 y z + 27 + + 2 3 3 2 3 16 2 2 2 16 2 + + 1/18 x z - 8/27 y z - 4/27 x z + -- y z - 2/9 x z + -- x z + 27 27 + + 2 2 3 3 4 2 4 + - 2/9 y z - 8/27 z x , COEFF(2, 1, 1) = - 1/108 y x z - 1/18 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/36 y x z - 1/144 y x z - 1/27 y x z - 1/27 z y x + + 3 3 3 2 2 4 4 4 2 3 + + 1/54 y x z + 1/48 y x z + 1/54 y x z + 1/72 z y x + + 2 3 3 2 3 3 4 3 3 + + 1/72 y x z - 1/18 z y x + 4/27 z y x + 1/54 z y x + + 3 3 2 2 4 2 2 3 2 3 + - 2/27 y x z - 1/144 y z - 1/18 z y x + 4/27 z y x + + 3 3 3 2 3 3 4 3 4 + - 2/27 z y x + 2/27 x z - 1/54 x z - 1/54 z x + 1/54 y z + + 4 2 4 3 2 + + 1/108 x z - 1/36 x z + 1/54 y x z - 1/27 z + 1/36 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/144 y x z - 1/12 y x z + 1/27 y x z + 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/18 y x z + 1/108 z - 1/9 y x z + 1/108 z - 1/108 y z + + 3 2 3 3 2 + + 1/27 z y - 1/27 z + 1/27 z y x - 1/9 z y x - 2/27 y x z + + 2 3 3 2 2 2 2 + + 2/9 z y x - 2/27 y z - 1/108 y x z + 1/36 y x z - 1/12 y x z + + 2 2 2 2 3 2 3 + + 2/9 y x z - 2/27 y x z + 1/36 y z + 1/36 y x z - 1/27 x z + + 2 3 2 3 3 3 2 3 + + 1/9 x z + 1/54 y z - 1/144 y z - 1/108 y z - 1/36 x z + + 3 2 3 2 2 2 2 2 2 + + 1/27 y z + 1/108 x z - 2/27 y z + 1/9 x z - 1/27 x z + 1/36 y z + + 3 3 4 2 4 + + 2/27 z x , COEFF(-2, 2, 1) = 1/432 y x z - 1/288 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/144 y x z + 1/288 y x z + 1/432 y x z + 1/432 z y x + + 3 3 3 2 2 4 4 4 2 3 + - 1/216 y x z + 1/96 y x z - 1/864 y x z - 1/144 z y x + + 2 3 3 2 3 3 4 3 3 + - 1/144 y x z + 1/36 z y x - 1/108 z y x - 1/216 z y x + + 3 3 2 2 4 2 2 3 2 3 + + 1/54 y x z - 1/288 y z + 1/36 z y x - 1/108 z y x + + 3 3 3 2 3 3 4 3 4 + + 1/54 z y x - 1/108 x z + 1/432 x z + 1/432 z x + 1/864 y z + + 4 2 4 3 2 + - 1/864 x z - 1/288 x z - 1/864 y x z - 1/216 z - 1/72 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/288 y x z - 1/24 y x z - 1/108 y x z + 1/96 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/288 y x z + 1/864 z - 1/36 y x z + 1/864 z - 1/432 y z + + 3 2 3 3 2 + + 1/108 z y - 1/216 z - 1/108 z y x - 1/36 z y x + 1/216 y x z + + 2 3 3 2 2 2 2 + + 1/72 z y x - 1/216 y z + 1/432 y x z - 1/72 y x z - 1/24 y x z + + 2 2 2 2 3 2 3 + + 1/72 y x z + 1/216 y x z + 1/72 y z + 1/144 y x z + 1/216 x z + + 2 3 2 3 3 3 2 3 + + 1/72 x z + 1/864 y z - 1/288 y z - 1/432 y z - 1/288 x z + + 3 2 3 2 2 2 2 + + 1/108 y z - 1/864 x z - 1/216 y z + 1/72 x z + 1/216 x z + + 2 2 3 3 4 + + 1/72 y z - 1/108 z x , COEFF(-1, 2, 1) = - 1/27 y x z + + 2 4 3 2 4 2 4 3 3 + + 1/144 y x z - 1/72 y x z - 1/18 y x z - 1/108 y x z + + 4 3 3 3 3 2 2 4 4 + - 1/108 z y x + 1/54 y x z - 1/48 y x z + 1/54 y x z + + 4 2 3 2 3 3 2 3 3 + + 1/36 z y x + 1/36 y x z - 1/9 z y x + 1/27 z y x + + 4 3 3 3 3 2 2 4 2 2 3 2 3 + + 1/54 z y x - 2/27 y x z + 1/36 y z - 1/9 z y x + 1/27 z y x + + 3 3 3 2 3 3 4 3 4 + - 2/27 z y x + 1/27 x z - 1/108 x z - 1/108 z x - 1/108 y z + + 4 2 4 3 2 + + 1/54 x z + 1/144 x z + 1/54 y x z + 1/27 z + 2/9 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/18 y x z + 1/12 y x z + 4/27 y x z - 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + + 1/144 y x z - 1/108 z + 1/18 y x z - 1/108 z + 1/54 y z + + 3 2 3 3 2 + - 2/27 z y + 1/27 z + 4/27 z y x + 1/18 z y x - 2/27 y x z + + 2 3 3 2 2 2 2 + - 1/36 z y x + 1/27 y z - 1/27 y x z + 2/9 y x z + 1/12 y x z + + 2 2 2 2 3 2 3 + - 1/36 y x z - 2/27 y x z - 1/9 y z - 1/72 y x z - 2/27 x z + + 2 3 2 3 3 3 2 3 + - 1/36 x z - 1/108 y z + 1/36 y z + 1/54 y z + 1/144 x z + + 3 2 3 2 2 2 2 2 2 + - 2/27 y z + 1/54 x z + 1/27 y z - 1/36 x z - 2/27 x z - 1/9 y z + + 3 3 4 2 4 3 3 + + 1/27 z x , COEFF(0, 2, 1) = 5/72 y x z + 5/48 y x z + 1/72 y x z + + 4 3 3 3 3 4 4 2 3 + + 1/72 z y x - 1/36 y x z - 5/144 y x z - 1/24 z y x + + 2 3 3 2 3 3 4 3 3 3 3 2 + - 1/24 y x z + 1/6 z y x - 1/18 z y x - 1/36 z y x + 1/9 y x z + + 2 2 3 2 3 3 3 3 2 3 3 + + 1/6 z y x - 1/18 z y x + 1/9 z y x - 1/18 x z + 1/72 x z + + 4 3 4 3 2 2 3 + + 1/72 z x - 5/144 x z - 5/144 y x z - 5/12 y x z + 5/48 y x z + + 3 2 3 3 3 2 2 + - 5/18 y x z - 5/18 z y x + 5/36 y x z + 5/72 y x z - 5/12 y x z + + 2 3 2 3 + + 5/36 y x z + 5/36 x z - 5/144 x z + 5/36 x z - 1/18 z x , + + 3 4 2 4 3 2 4 + COEFF(1, 2, 1) = - 1/27 y x z - 1/144 y x z + 1/72 y x z + + 2 4 3 3 4 3 3 3 3 + - 1/18 y x z - 1/108 y x z - 1/108 z y x + 1/54 y x z + + 2 2 4 4 4 2 3 2 3 3 + + 1/48 y x z + 1/54 y x z + 1/36 z y x + 1/36 y x z + + 2 3 3 4 3 3 3 3 2 2 4 + - 1/9 z y x + 1/27 z y x + 1/54 z y x - 2/27 y x z - 1/36 y z + + 2 2 3 2 3 3 3 3 2 3 3 + - 1/9 z y x + 1/27 z y x - 2/27 z y x + 1/27 x z - 1/108 x z + + 4 3 4 4 2 4 3 + - 1/108 z x + 1/108 y z + 1/54 x z - 1/144 x z + 1/54 y x z + + 2 2 3 2 2 2 3 2 + - 1/27 z + 2/9 y x z - 1/18 y x z - 1/12 y x z + 4/27 y x z + + 2 2 3 2 3 4 3 2 2 3 + + 1/48 y x z - 1/144 y x z + 1/108 z - 1/18 y x z + 1/108 z + + 3 4 3 2 3 3 2 + - 1/54 y z + 2/27 z y - 1/27 z + 4/27 z y x - 1/18 z y x + + 2 3 3 2 2 + - 2/27 y x z + 1/36 z y x - 1/27 y z - 1/27 y x z + 2/9 y x z + + 2 2 2 2 2 2 3 2 3 + - 1/12 y x z + 1/36 y x z - 2/27 y x z + 1/9 y z + 1/72 y x z + + 2 3 2 3 3 3 + - 2/27 x z + 1/36 x z + 1/108 y z - 1/36 y z - 1/54 y z + + 2 3 3 2 3 2 2 2 + - 1/144 x z + 2/27 y z + 1/54 x z - 1/27 y z + 1/36 x z + + 2 2 2 3 3 4 + - 2/27 x z + 1/9 y z + 1/27 z x , COEFF(2, 2, 1) = 1/432 y x z + + 2 4 3 2 4 2 4 3 3 + + 1/288 y x z - 1/144 y x z + 1/288 y x z + 1/432 y x z + + 4 3 3 3 3 2 2 4 4 + + 1/432 z y x - 1/216 y x z - 1/96 y x z - 1/864 y x z + + 4 2 3 2 3 3 2 3 3 + - 1/144 z y x - 1/144 y x z + 1/36 z y x - 1/108 z y x + + 4 3 3 3 3 2 2 4 2 2 3 + - 1/216 z y x + 1/54 y x z + 1/288 y z + 1/36 z y x + + 2 3 3 3 3 2 3 3 4 3 + - 1/108 z y x + 1/54 z y x - 1/108 x z + 1/432 x z + 1/432 z x + + 4 4 2 4 3 + - 1/864 y z - 1/864 x z + 1/288 x z - 1/864 y x z + 1/216 z + + 2 2 3 2 2 2 3 2 + - 1/72 y x z + 1/288 y x z + 1/24 y x z - 1/108 y x z + + 2 2 3 2 3 4 3 2 2 3 + - 1/96 y x z + 1/288 y x z - 1/864 z + 1/36 y x z - 1/864 z + + 3 4 3 2 3 3 2 + + 1/432 y z - 1/108 z y + 1/216 z - 1/108 z y x + 1/36 z y x + + 2 3 3 2 2 + + 1/216 y x z - 1/72 z y x + 1/216 y z + 1/432 y x z - 1/72 y x z + + 2 2 2 2 2 2 3 2 3 + + 1/24 y x z - 1/72 y x z + 1/216 y x z - 1/72 y z - 1/144 y x z + + 2 3 2 3 3 3 + + 1/216 x z - 1/72 x z - 1/864 y z + 1/288 y z + 1/432 y z + + 2 3 3 2 3 2 2 2 + + 1/288 x z - 1/108 y z - 1/864 x z + 1/216 y z - 1/72 x z + + 2 2 2 3 + + 1/216 x z - 1/72 y z - 1/108 z x , COEFF(-2, -2, 2) = + + 3 4 2 4 3 2 4 2 4 + - 1/1728 y x z + 1/1152 y x z - 1/576 y x z + 1/1152 y x z + + 3 3 4 3 3 3 3 2 2 4 + - 1/864 y x z - 1/1728 z y x + 1/432 y x z + 1/384 y x z + + 4 4 2 3 2 3 3 2 3 + + 1/3456 y x z - 1/576 z y x - 1/288 y x z + 1/288 z y x + + 3 4 3 3 3 3 2 2 4 + + 1/864 z y x + 1/864 z y x - 1/864 y x z - 1/1152 y z + + 2 2 3 2 3 3 3 3 2 + + 1/576 z y x + 1/1728 z y x - 1/432 z y x - 1/1728 x z + + 3 3 4 3 4 4 2 4 + + 1/864 x z + 1/1728 z x - 1/3456 y z - 1/3456 x z - 1/1152 x z + + 3 2 2 3 2 2 2 + + 1/1728 y x z - 1/1728 z - 1/576 y x z + 1/576 y x z - 1/384 y x z + + 3 2 2 2 3 2 3 4 + + 1/1728 y x z + 1/192 y x z + 1/576 y x z + 1/3456 z + + 3 2 2 3 3 4 3 2 + + 1/576 y x z + 1/1728 z + 1/1728 y z - 1/864 z y - 1/3456 z + + 3 3 2 2 + + 1/864 z y x + 1/288 z y x - 1/1728 y x z - 1/576 z y x + 1/1728 y z + + 3 3 2 2 2 2 2 2 + - 1/864 y x z - 1/1152 y x z - 1/192 y x z - 1/1152 y x z + + 2 2 3 2 3 2 + - 1/3456 y x z + 1/576 y z - 1/288 y x z + 1/1728 x z + 1/576 x z + + 3 2 3 3 3 2 3 3 2 + - 1/1728 y z - 1/576 y z + 1/864 y z - 1/576 x z - 1/1728 y z + + 3 2 2 2 2 2 2 + - 1/1728 x z + 1/3456 y z + 1/1152 x z + 1/3456 x z + 1/1152 y z + + 3 3 4 2 4 + - 1/864 z x , COEFF(-1, -2, 2) = 1/108 y x z - 1/576 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/288 y x z - 1/72 y x z + 1/216 y x z + 1/432 z y x + + 3 3 3 2 2 4 4 4 2 3 + - 1/108 y x z - 1/192 y x z - 1/216 y x z + 1/144 z y x + + 2 3 3 2 3 3 4 3 3 + + 1/72 y x z - 1/72 z y x - 1/216 z y x - 1/216 z y x + + 3 3 2 2 4 2 2 3 2 3 + + 1/216 y x z + 1/144 y z - 1/144 z y x - 1/432 z y x + + 3 3 3 2 3 3 4 3 4 + + 1/108 z y x + 1/432 x z - 1/216 x z - 1/432 z x + 1/432 y z + + 4 2 4 3 2 + + 1/216 x z + 1/576 x z - 1/108 y x z + 1/216 z + 1/36 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/36 y x z + 1/192 y x z - 1/108 y x z - 1/96 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/288 y x z - 1/432 z - 1/288 y x z - 1/216 z - 1/216 y z + + 3 2 3 3 2 + + 1/108 z y + 1/432 z - 1/54 z y x - 1/144 z y x + 1/108 y x z + + 2 3 3 2 2 2 2 + + 1/288 z y x - 1/216 y z + 1/54 y x z + 1/72 y x z + 1/96 y x z + + 2 2 2 2 3 2 3 + + 1/576 y x z + 1/216 y x z - 1/72 y z + 1/144 y x z - 1/108 x z + + 2 3 2 3 3 3 2 3 + - 1/288 x z + 1/216 y z + 1/72 y z - 1/108 y z + 1/288 x z + + 3 2 3 2 2 2 2 + + 1/216 y z + 1/108 x z - 1/432 y z - 1/576 x z - 1/216 x z + + 2 2 3 3 4 + - 1/144 y z + 1/216 z x , COEFF(0, -2, 2) = - 5/288 y x z + + 2 4 3 3 4 3 3 3 3 + + 5/192 y x z - 1/144 y x z - 1/288 z y x + 1/72 y x z + + 4 4 2 3 2 3 3 2 3 + + 5/576 y x z - 1/96 z y x - 1/48 y x z + 1/48 z y x + + 3 4 3 3 3 3 2 2 2 3 + + 1/144 z y x + 1/144 z y x - 1/144 y x z + 1/96 z y x + + 2 3 3 3 3 2 3 3 4 3 + + 1/288 z y x - 1/72 z y x - 1/288 x z + 1/144 x z + 1/288 z x + + 4 3 2 2 3 3 2 + - 5/576 x z + 5/288 y x z - 5/96 y x z + 5/96 y x z + 5/288 y x z + + 3 3 3 2 2 + + 5/144 z y x - 5/288 y x z - 5/144 y x z - 5/192 y x z + + 2 3 2 3 + - 5/576 y x z + 5/288 x z - 5/288 x z + 5/576 x z - 1/144 z x , + + 3 4 2 4 3 2 4 + COEFF(1, -2, 2) = 1/108 y x z + 1/576 y x z - 1/288 y x z + + 2 4 3 3 4 3 3 3 3 + - 1/72 y x z + 1/216 y x z + 1/432 z y x - 1/108 y x z + + 2 2 4 4 4 2 3 2 3 3 + + 1/192 y x z - 1/216 y x z + 1/144 z y x + 1/72 y x z + + 2 3 3 4 3 3 3 3 2 + - 1/72 z y x - 1/216 z y x - 1/216 z y x + 1/216 y x z + + 2 4 2 2 3 2 3 3 3 + - 1/144 y z - 1/144 z y x - 1/432 z y x + 1/108 z y x + + 3 2 3 3 4 3 4 4 + + 1/432 x z - 1/216 x z - 1/432 z x - 1/432 y z + 1/216 x z + + 2 4 3 2 2 3 + - 1/576 x z - 1/108 y x z - 1/216 z + 1/36 y x z - 1/36 y x z + + 2 2 2 3 2 2 2 3 2 3 + - 1/192 y x z - 1/108 y x z + 1/96 y x z + 1/288 y x z + + 4 3 2 2 3 3 4 3 + + 1/432 z + 1/288 y x z + 1/216 z + 1/216 y z - 1/108 z y + + 2 3 3 2 2 + - 1/432 z - 1/54 z y x + 1/144 z y x + 1/108 y x z - 1/288 z y x + + 3 3 2 2 2 2 2 2 + + 1/216 y z + 1/54 y x z + 1/72 y x z - 1/96 y x z - 1/576 y x z + + 2 2 3 2 3 2 + + 1/216 y x z + 1/72 y z - 1/144 y x z - 1/108 x z + 1/288 x z + + 3 2 3 3 3 2 3 3 2 + - 1/216 y z - 1/72 y z + 1/108 y z - 1/288 x z - 1/216 y z + + 3 2 2 2 2 2 2 + + 1/108 x z + 1/432 y z + 1/576 x z - 1/216 x z + 1/144 y z + + 3 3 4 2 4 + + 1/216 z x , COEFF(2, -2, 2) = - 1/1728 y x z - 1/1152 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/576 y x z + 1/1152 y x z - 1/864 y x z - 1/1728 z y x + + 3 3 3 2 2 4 4 4 2 3 + + 1/432 y x z - 1/384 y x z + 1/3456 y x z - 1/576 z y x + + 2 3 3 2 3 3 4 3 3 + - 1/288 y x z + 1/288 z y x + 1/864 z y x + 1/864 z y x + + 3 3 2 2 4 2 2 3 2 3 + - 1/864 y x z + 1/1152 y z + 1/576 z y x + 1/1728 z y x + + 3 3 3 2 3 3 4 3 4 + - 1/432 z y x - 1/1728 x z + 1/864 x z + 1/1728 z x + 1/3456 y z + + 4 2 4 3 2 + - 1/3456 x z + 1/1152 x z + 1/1728 y x z + 1/1728 z - 1/576 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/576 y x z + 1/384 y x z + 1/1728 y x z - 1/192 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/576 y x z - 1/3456 z - 1/576 y x z - 1/1728 z - 1/1728 y z + + 3 2 3 3 2 + + 1/864 z y + 1/3456 z + 1/864 z y x - 1/288 z y x - 1/1728 y x z + + 2 3 3 2 2 + + 1/576 z y x - 1/1728 y z - 1/864 y x z - 1/1152 y x z + + 2 2 2 2 2 2 + + 1/192 y x z + 1/1152 y x z - 1/3456 y x z - 1/576 y z + + 3 2 3 2 3 2 3 + + 1/288 y x z + 1/1728 x z - 1/576 x z + 1/1728 y z + 1/576 y z + + 3 3 2 3 3 2 3 2 + - 1/864 y z + 1/576 x z + 1/1728 y z - 1/1728 x z - 1/3456 y z + + 2 2 2 2 2 3 + - 1/1152 x z + 1/3456 x z - 1/1152 y z - 1/864 z x , COEFF(-2, -1, 2) + + 3 4 2 4 3 2 4 2 4 + = 1/432 y x z - 1/72 y x z + 1/144 y x z - 1/576 y x z + + 3 3 4 3 3 3 3 2 2 4 + + 1/54 y x z + 1/108 z y x - 1/108 y x z - 1/192 y x z + + 4 4 2 3 2 3 3 2 3 + - 1/216 y x z + 1/288 z y x + 1/144 y x z - 1/144 z y x + + 3 4 3 3 3 3 2 2 4 + - 1/54 z y x - 1/216 z y x + 1/216 y x z + 1/576 y z + + 2 2 3 2 3 3 3 3 2 + - 1/288 z y x - 1/108 z y x + 1/108 z y x + 1/216 x z + + 3 3 4 3 4 4 2 4 + - 1/108 x z - 1/216 z x + 1/216 y z + 1/432 x z + 1/144 x z + + 3 2 2 3 2 2 2 + - 1/108 y x z + 1/216 z + 1/288 y x z - 1/288 y x z + 1/192 y x z + + 3 2 2 2 3 2 3 4 3 2 2 + - 1/432 y x z - 1/96 y x z - 1/36 y x z - 1/432 z - 1/144 y x z + + 3 3 4 3 2 3 + - 1/216 z - 1/432 y z + 1/216 z y + 1/432 z - 1/216 z y x + + 3 2 2 3 3 + - 1/72 z y x + 1/108 y x z + 1/36 z y x - 1/108 y z + 1/216 y x z + + 2 2 2 2 2 2 2 2 + + 1/576 y x z + 1/96 y x z + 1/72 y x z + 1/216 y x z - 1/288 y z + + 3 2 3 2 3 2 3 + + 1/72 y x z - 1/216 x z - 1/72 x z + 1/108 y z + 1/288 y z + + 3 3 2 3 3 2 3 2 + - 1/216 y z + 1/72 x z + 1/432 y z + 1/216 x z - 1/216 y z + + 2 2 2 2 2 3 + - 1/144 x z - 1/432 x z - 1/576 y z + 1/108 z x , COEFF(-1, -1, 2) = + + 3 4 2 4 3 2 4 2 4 3 3 + - 1/27 y x z + 1/36 y x z - 1/72 y x z + 1/36 y x z - 2/27 y x z + + 4 3 3 3 3 2 2 4 4 + - 1/27 z y x + 1/27 y x z + 1/96 y x z + 2/27 y x z + + 4 2 3 2 3 3 2 3 3 + - 1/72 z y x - 1/36 y x z + 1/36 z y x + 2/27 z y x + + 4 3 3 3 3 2 2 4 2 2 3 + + 1/54 z y x - 1/54 y x z - 1/72 y z + 1/72 z y x + + 2 3 3 3 3 2 3 3 4 3 + + 1/27 z y x - 1/27 z y x - 1/54 x z + 1/27 x z + 1/54 z x + + 4 4 2 4 3 2 + - 1/27 y z - 1/27 x z - 1/72 x z + 4/27 y x z - 1/27 z - 1/18 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/18 y x z - 1/96 y x z + 1/27 y x z + 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + + 1/18 y x z + 1/54 z + 1/72 y x z + 1/27 z + 1/54 y z + + 3 2 3 3 2 + - 1/27 z y - 1/54 z + 2/27 z y x + 1/36 z y x - 4/27 y x z + + 2 3 3 2 2 2 2 + - 1/18 z y x + 2/27 y z - 2/27 y x z - 1/36 y x z - 1/48 y x z + + 2 2 2 2 3 2 3 + - 1/36 y x z - 2/27 y x z + 1/36 y z - 1/36 y x z + 2/27 x z + + 2 3 2 3 3 3 2 3 + + 1/36 x z - 2/27 y z - 1/36 y z + 1/27 y z - 1/36 x z + + 3 2 3 2 2 2 2 2 2 + - 1/54 y z - 2/27 x z + 1/27 y z + 1/72 x z + 1/27 x z + 1/72 y z + + 3 3 4 2 4 3 3 + - 1/27 z x , COEFF(0, -1, 2) = 5/72 y x z - 5/96 y x z + 1/9 y x z + + 4 3 3 3 3 4 4 2 3 + + 1/18 z y x - 1/18 y x z - 5/36 y x z + 1/48 z y x + + 2 3 3 2 3 3 4 3 3 + + 1/24 y x z - 1/24 z y x - 1/9 z y x - 1/36 z y x + + 3 3 2 2 2 3 2 3 3 3 3 2 + + 1/36 y x z - 1/48 z y x - 1/18 z y x + 1/18 z y x + 1/36 x z + + 3 3 4 3 4 3 2 + - 1/18 x z - 1/36 z x + 5/72 x z - 5/18 y x z + 5/48 y x z + + 2 3 3 2 3 3 3 + - 5/48 y x z - 5/72 y x z - 5/36 z y x + 5/18 y x z + 5/36 y x z + + 2 2 2 3 2 + + 5/96 y x z + 5/36 y x z - 5/36 x z + 5/36 x z - 5/72 x z + + 3 3 4 2 4 + + 1/18 z x , COEFF(1, -1, 2) = - 1/27 y x z - 1/36 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/72 y x z + 1/36 y x z - 2/27 y x z - 1/27 z y x + + 3 3 3 2 2 4 4 4 2 3 + + 1/27 y x z - 1/96 y x z + 2/27 y x z - 1/72 z y x + + 2 3 3 2 3 3 4 3 3 + - 1/36 y x z + 1/36 z y x + 2/27 z y x + 1/54 z y x + + 3 3 2 2 4 2 2 3 2 3 3 3 + - 1/54 y x z + 1/72 y z + 1/72 z y x + 1/27 z y x - 1/27 z y x + + 3 2 3 3 4 3 4 4 + - 1/54 x z + 1/27 x z + 1/54 z x + 1/27 y z - 1/27 x z + + 2 4 3 2 2 3 + + 1/72 x z + 4/27 y x z + 1/27 z - 1/18 y x z + 1/18 y x z + + 2 2 2 3 2 2 2 3 2 3 4 + + 1/96 y x z + 1/27 y x z - 1/48 y x z - 1/18 y x z - 1/54 z + + 3 2 2 3 3 4 3 2 3 + - 1/72 y x z - 1/27 z - 1/54 y z + 1/27 z y + 1/54 z + 2/27 z y x + + 3 2 2 3 3 + - 1/36 z y x - 4/27 y x z + 1/18 z y x - 2/27 y z - 2/27 y x z + + 2 2 2 2 2 2 2 2 + - 1/36 y x z + 1/48 y x z + 1/36 y x z - 2/27 y x z - 1/36 y z + + 3 2 3 2 3 2 3 + + 1/36 y x z + 2/27 x z - 1/36 x z + 2/27 y z + 1/36 y z + + 3 3 2 3 3 2 3 2 + - 1/27 y z + 1/36 x z + 1/54 y z - 2/27 x z - 1/27 y z + + 2 2 2 2 2 3 + - 1/72 x z + 1/27 x z - 1/72 y z - 1/27 z x , COEFF(2, -1, 2) = + + 3 4 2 4 3 2 4 2 4 + 1/432 y x z + 1/72 y x z - 1/144 y x z - 1/576 y x z + + 3 3 4 3 3 3 3 2 2 4 + + 1/54 y x z + 1/108 z y x - 1/108 y x z + 1/192 y x z + + 4 4 2 3 2 3 3 2 3 + - 1/216 y x z + 1/288 z y x + 1/144 y x z - 1/144 z y x + + 3 4 3 3 3 3 2 2 4 + - 1/54 z y x - 1/216 z y x + 1/216 y x z - 1/576 y z + + 2 2 3 2 3 3 3 3 2 + - 1/288 z y x - 1/108 z y x + 1/108 z y x + 1/216 x z + + 3 3 4 3 4 4 2 4 + - 1/108 x z - 1/216 z x - 1/216 y z + 1/432 x z - 1/144 x z + + 3 2 2 3 2 2 2 + - 1/108 y x z - 1/216 z + 1/288 y x z - 1/288 y x z - 1/192 y x z + + 3 2 2 2 3 2 3 4 3 2 2 + - 1/432 y x z + 1/96 y x z + 1/36 y x z + 1/432 z + 1/144 y x z + + 3 3 4 3 2 3 + + 1/216 z + 1/432 y z - 1/216 z y - 1/432 z - 1/216 z y x + + 3 2 2 3 3 + + 1/72 z y x + 1/108 y x z - 1/36 z y x + 1/108 y z + 1/216 y x z + + 2 2 2 2 2 2 2 2 + + 1/576 y x z - 1/96 y x z - 1/72 y x z + 1/216 y x z + 1/288 y z + + 3 2 3 2 3 2 3 + - 1/72 y x z - 1/216 x z + 1/72 x z - 1/108 y z - 1/288 y z + + 3 3 2 3 3 2 3 2 + + 1/216 y z - 1/72 x z - 1/432 y z + 1/216 x z + 1/216 y z + + 2 2 2 2 2 3 + + 1/144 x z - 1/432 x z + 1/576 y z + 1/108 z x , COEFF(-2, 0, 2) = + + 3 4 2 4 3 2 4 3 3 + - 1/288 y x z + 5/192 y x z - 1/96 y x z - 5/144 y x z + + 4 3 3 3 3 4 3 + - 5/288 z y x + 1/72 y x z + 5/576 y x z + 5/144 z y x + + 4 3 3 3 3 2 2 3 3 3 + + 1/144 z y x - 1/144 y x z + 5/288 z y x - 1/72 z y x + + 4 3 3 2 2 3 3 2 2 + - 5/576 y z + 5/288 y x z + 1/288 y x z + 5/96 y x z + 1/96 y x z + + 3 4 3 3 3 2 + + 1/288 y z - 1/144 z y + 1/144 z y x + 1/48 z y x - 5/288 y x z + + 2 3 3 2 2 2 + - 5/96 z y x + 5/288 y z - 1/144 y x z - 5/192 y x z - 5/576 y x z + + 3 2 3 3 3 3 3 2 2 + - 1/48 y x z - 5/288 y z + 1/144 y z - 1/288 y z + 5/576 y z , + + 3 4 2 4 3 2 4 + COEFF(-1, 0, 2) = 1/18 y x z - 5/96 y x z + 1/48 y x z + + 3 3 4 3 3 3 3 4 3 + + 5/36 y x z + 5/72 z y x - 1/18 y x z - 5/36 y x z - 5/36 z y x + + 4 3 3 3 3 2 2 3 3 3 4 + - 1/36 z y x + 1/36 y x z - 5/72 z y x + 1/18 z y x + 5/72 y z + + 3 3 2 2 3 3 2 2 3 4 + - 5/18 y x z - 1/18 y x z - 5/48 y x z - 1/48 y x z - 1/36 y z + + 3 3 3 2 2 + + 1/18 z y - 1/9 z y x - 1/24 z y x + 5/18 y x z + 5/48 z y x + + 3 3 2 2 2 3 2 3 + - 5/36 y z + 1/9 y x z + 5/96 y x z + 5/36 y x z + 1/24 y x z + + 3 3 3 3 2 2 + + 5/36 y z - 1/18 y z + 1/36 y z - 5/72 y z , COEFF(0, 0, 2) = + + 4 3 3 3 3 3 3 4 25 4 3 3 + 1/24 z y x + 1/12 y x z - 5/48 y x z + -- y x z - 1/12 z y x + 96 + + 3 25 3 3 4 3 2 3 + + 5/24 z y x - -- y x z - 5/24 y x z - 5/48 z y x + 5/48 z y x + 48 + + 25 3 3 3 3 25 2 3 2 + + -- y x z + 5/24 z y x - 5/24 y x z - -- y x z + 5/48 y x z + 48 96 + + 3 3 2 3 4 2 4 + - 1/24 y x z , COEFF(1, 0, 2) = 1/18 y x z + 5/96 y x z + + 3 2 4 3 3 4 3 3 3 3 + - 1/48 y x z + 5/36 y x z + 5/72 z y x - 1/18 y x z + + 4 3 4 3 3 3 3 2 2 3 + - 5/36 y x z - 5/36 z y x - 1/36 z y x + 1/36 y x z - 5/72 z y x + + 3 3 4 3 3 2 2 3 + + 1/18 z y x - 5/72 y z - 5/18 y x z - 1/18 y x z + 5/48 y x z + + 3 2 2 3 4 3 3 3 2 + + 1/48 y x z + 1/36 y z - 1/18 z y - 1/9 z y x + 1/24 z y x + + 2 3 3 2 2 + + 5/18 y x z - 5/48 z y x + 5/36 y z + 1/9 y x z - 5/96 y x z + + 2 3 2 3 3 3 3 3 2 + + 5/36 y x z - 1/24 y x z - 5/36 y z + 1/18 y z - 1/36 y z + + 2 3 4 2 4 + + 5/72 y z , COEFF(2, 0, 2) = - 1/288 y x z - 5/192 y x z + + 3 2 4 3 3 4 3 3 3 3 + + 1/96 y x z - 5/144 y x z - 5/288 z y x + 1/72 y x z + + 4 3 4 3 3 3 3 2 + + 5/576 y x z + 5/144 z y x + 1/144 z y x - 1/144 y x z + + 2 3 3 3 4 3 3 2 + + 5/288 z y x - 1/72 z y x + 5/576 y z + 5/288 y x z + 1/288 y x z + + 2 3 3 2 2 3 4 3 3 + - 5/96 y x z - 1/96 y x z - 1/288 y z + 1/144 z y + 1/144 z y x + + 3 2 2 3 3 + - 1/48 z y x - 5/288 y x z + 5/96 z y x - 5/288 y z - 1/144 y x z + + 2 2 2 3 2 3 3 3 3 + + 5/192 y x z - 5/576 y x z + 1/48 y x z + 5/288 y z - 1/144 y z + + 3 2 2 3 4 2 4 + + 1/288 y z - 5/576 y z , COEFF(-2, 1, 2) = 1/432 y x z - 1/72 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/144 y x z + 1/576 y x z + 1/54 y x z + 1/108 z y x + + 3 3 3 2 2 4 4 4 2 3 + - 1/108 y x z + 1/192 y x z - 1/216 y x z - 1/288 z y x + + 2 3 3 2 3 3 4 3 3 + - 1/144 y x z + 1/144 z y x - 1/54 z y x - 1/216 z y x + + 3 3 2 2 4 2 2 3 2 3 + + 1/216 y x z - 1/576 y z + 1/288 z y x - 1/108 z y x + + 3 3 3 2 3 3 4 3 4 + + 1/108 z y x - 1/216 x z + 1/108 x z + 1/216 z x + 1/216 y z + + 4 2 4 3 2 + - 1/432 x z - 1/144 x z - 1/108 y x z - 1/216 z - 1/288 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/288 y x z - 1/192 y x z - 1/432 y x z + 1/96 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/36 y x z + 1/432 z - 1/144 y x z + 1/216 z - 1/432 y z + + 3 2 3 3 2 + + 1/216 z y - 1/432 z - 1/216 z y x - 1/72 z y x + 1/108 y x z + + 2 3 3 2 2 2 2 + + 1/36 z y x - 1/108 y z + 1/216 y x z - 1/576 y x z - 1/96 y x z + + 2 2 2 2 3 2 3 + + 1/72 y x z + 1/216 y x z + 1/288 y z + 1/72 y x z + 1/216 x z + + 2 3 2 3 3 3 2 3 + + 1/72 x z + 1/108 y z - 1/288 y z - 1/216 y z - 1/72 x z + + 3 2 3 2 2 2 2 + + 1/432 y z - 1/216 x z - 1/216 y z + 1/144 x z + 1/432 x z + + 2 2 3 3 4 + + 1/576 y z - 1/108 z x , COEFF(-1, 1, 2) = - 1/27 y x z + + 2 4 3 2 4 2 4 3 3 + + 1/36 y x z - 1/72 y x z - 1/36 y x z - 2/27 y x z + + 4 3 3 3 3 2 2 4 4 + - 1/27 z y x + 1/27 y x z - 1/96 y x z + 2/27 y x z + + 4 2 3 2 3 3 2 3 3 + + 1/72 z y x + 1/36 y x z - 1/36 z y x + 2/27 z y x + + 4 3 3 3 3 2 2 4 2 2 3 + + 1/54 z y x - 1/54 y x z + 1/72 y z - 1/72 z y x + + 2 3 3 3 3 2 3 3 4 3 + + 1/27 z y x - 1/27 z y x + 1/54 x z - 1/27 x z - 1/54 z x + + 4 4 2 4 3 2 + - 1/27 y z + 1/27 x z + 1/72 x z + 4/27 y x z + 1/27 z + 1/18 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/18 y x z + 1/96 y x z + 1/27 y x z - 1/48 y x z + + 2 3 4 3 2 2 3 3 4 + + 1/18 y x z - 1/54 z + 1/72 y x z - 1/27 z + 1/54 y z + + 3 2 3 3 2 + - 1/27 z y + 1/54 z + 2/27 z y x + 1/36 z y x - 4/27 y x z + + 2 3 3 2 2 2 2 + - 1/18 z y x + 2/27 y z - 2/27 y x z + 1/36 y x z + 1/48 y x z + + 2 2 2 2 3 2 3 + - 1/36 y x z - 2/27 y x z - 1/36 y z - 1/36 y x z - 2/27 x z + + 2 3 2 3 3 3 2 3 + - 1/36 x z - 2/27 y z + 1/36 y z + 1/27 y z + 1/36 x z + + 3 2 3 2 2 2 2 2 2 + - 1/54 y z + 2/27 x z + 1/27 y z - 1/72 x z - 1/27 x z - 1/72 y z + + 3 3 4 2 4 3 3 + + 1/27 z x , COEFF(0, 1, 2) = 5/72 y x z + 5/96 y x z + 1/9 y x z + + 4 3 3 3 3 4 4 2 3 + + 1/18 z y x - 1/18 y x z - 5/36 y x z - 1/48 z y x + + 2 3 3 2 3 3 4 3 3 + - 1/24 y x z + 1/24 z y x - 1/9 z y x - 1/36 z y x + + 3 3 2 2 2 3 2 3 3 3 3 2 + + 1/36 y x z + 1/48 z y x - 1/18 z y x + 1/18 z y x - 1/36 x z + + 3 3 4 3 4 3 2 + + 1/18 x z + 1/36 z x - 5/72 x z - 5/18 y x z - 5/48 y x z + + 2 3 3 2 3 3 3 + + 5/48 y x z - 5/72 y x z - 5/36 z y x + 5/18 y x z + 5/36 y x z + + 2 2 2 3 2 + - 5/96 y x z + 5/36 y x z + 5/36 x z - 5/36 x z + 5/72 x z + + 3 3 4 2 4 + - 1/18 z x , COEFF(1, 1, 2) = - 1/27 y x z - 1/36 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/72 y x z - 1/36 y x z - 2/27 y x z - 1/27 z y x + + 3 3 3 2 2 4 4 4 2 3 + + 1/27 y x z + 1/96 y x z + 2/27 y x z + 1/72 z y x + + 2 3 3 2 3 3 4 3 3 + + 1/36 y x z - 1/36 z y x + 2/27 z y x + 1/54 z y x + + 3 3 2 2 4 2 2 3 2 3 3 3 + - 1/54 y x z - 1/72 y z - 1/72 z y x + 1/27 z y x - 1/27 z y x + + 3 2 3 3 4 3 4 4 + + 1/54 x z - 1/27 x z - 1/54 z x + 1/27 y z + 1/27 x z + + 2 4 3 2 2 3 + - 1/72 x z + 4/27 y x z - 1/27 z + 1/18 y x z - 1/18 y x z + + 2 2 2 3 2 2 2 3 2 3 4 + - 1/96 y x z + 1/27 y x z + 1/48 y x z - 1/18 y x z + 1/54 z + + 3 2 2 3 3 4 3 2 3 + - 1/72 y x z + 1/27 z - 1/54 y z + 1/27 z y - 1/54 z + 2/27 z y x + + 3 2 2 3 3 + - 1/36 z y x - 4/27 y x z + 1/18 z y x - 2/27 y z - 2/27 y x z + + 2 2 2 2 2 2 2 2 + + 1/36 y x z - 1/48 y x z + 1/36 y x z - 2/27 y x z + 1/36 y z + + 3 2 3 2 3 2 3 + + 1/36 y x z - 2/27 x z + 1/36 x z + 2/27 y z - 1/36 y z + + 3 3 2 3 3 2 3 2 + - 1/27 y z - 1/36 x z + 1/54 y z + 2/27 x z - 1/27 y z + + 2 2 2 2 2 3 + + 1/72 x z - 1/27 x z + 1/72 y z + 1/27 z x , COEFF(2, 1, 2) = + + 3 4 2 4 3 2 4 2 4 + 1/432 y x z + 1/72 y x z - 1/144 y x z + 1/576 y x z + + 3 3 4 3 3 3 3 2 2 4 + + 1/54 y x z + 1/108 z y x - 1/108 y x z - 1/192 y x z + + 4 4 2 3 2 3 3 2 3 + - 1/216 y x z - 1/288 z y x - 1/144 y x z + 1/144 z y x + + 3 4 3 3 3 3 2 2 4 + - 1/54 z y x - 1/216 z y x + 1/216 y x z + 1/576 y z + + 2 2 3 2 3 3 3 3 2 + + 1/288 z y x - 1/108 z y x + 1/108 z y x - 1/216 x z + + 3 3 4 3 4 4 2 4 + + 1/108 x z + 1/216 z x - 1/216 y z - 1/432 x z + 1/144 x z + + 3 2 2 3 2 2 2 + - 1/108 y x z + 1/216 z - 1/288 y x z + 1/288 y x z + 1/192 y x z + + 3 2 2 2 3 2 3 4 3 2 2 + - 1/432 y x z - 1/96 y x z + 1/36 y x z - 1/432 z + 1/144 y x z + + 3 3 4 3 2 3 + - 1/216 z + 1/432 y z - 1/216 z y + 1/432 z - 1/216 z y x + + 3 2 2 3 3 + + 1/72 z y x + 1/108 y x z - 1/36 z y x + 1/108 y z + 1/216 y x z + + 2 2 2 2 2 2 2 2 + - 1/576 y x z + 1/96 y x z - 1/72 y x z + 1/216 y x z - 1/288 y z + + 3 2 3 2 3 2 3 + - 1/72 y x z + 1/216 x z - 1/72 x z - 1/108 y z + 1/288 y z + + 3 3 2 3 3 2 3 2 + + 1/216 y z + 1/72 x z - 1/432 y z - 1/216 x z + 1/216 y z + + 2 2 2 2 2 3 + - 1/144 x z + 1/432 x z - 1/576 y z - 1/108 z x , COEFF(-2, 2, 2) = + + 3 4 2 4 3 2 4 2 4 + - 1/1728 y x z + 1/1152 y x z - 1/576 y x z - 1/1152 y x z + + 3 3 4 3 3 3 3 2 2 4 + - 1/864 y x z - 1/1728 z y x + 1/432 y x z - 1/384 y x z + + 4 4 2 3 2 3 3 2 3 + + 1/3456 y x z + 1/576 z y x + 1/288 y x z - 1/288 z y x + + 3 4 3 3 3 3 2 2 4 + + 1/864 z y x + 1/864 z y x - 1/864 y x z + 1/1152 y z + + 2 2 3 2 3 3 3 3 2 + - 1/576 z y x + 1/1728 z y x - 1/432 z y x + 1/1728 x z + + 3 3 4 3 4 4 2 4 + - 1/864 x z - 1/1728 z x - 1/3456 y z + 1/3456 x z + 1/1152 x z + + 3 2 2 3 2 2 2 + + 1/1728 y x z + 1/1728 z + 1/576 y x z - 1/576 y x z + 1/384 y x z + + 3 2 2 2 3 2 3 4 + + 1/1728 y x z - 1/192 y x z + 1/576 y x z - 1/3456 z + + 3 2 2 3 3 4 3 2 + + 1/576 y x z - 1/1728 z + 1/1728 y z - 1/864 z y + 1/3456 z + + 3 3 2 2 + + 1/864 z y x + 1/288 z y x - 1/1728 y x z - 1/576 z y x + 1/1728 y z + + 3 3 2 2 2 2 2 2 + - 1/864 y x z + 1/1152 y x z + 1/192 y x z - 1/1152 y x z + + 2 2 3 2 3 2 + - 1/3456 y x z - 1/576 y z - 1/288 y x z - 1/1728 x z - 1/576 x z + + 3 2 3 3 3 2 3 3 2 + - 1/1728 y z + 1/576 y z + 1/864 y z + 1/576 x z - 1/1728 y z + + 3 2 2 2 2 2 2 + + 1/1728 x z + 1/3456 y z - 1/1152 x z - 1/3456 x z - 1/1152 y z + + 3 3 4 2 4 + + 1/864 z x , COEFF(-1, 2, 2) = 1/108 y x z - 1/576 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/288 y x z + 1/72 y x z + 1/216 y x z + 1/432 z y x + + 3 3 3 2 2 4 4 4 2 3 + - 1/108 y x z + 1/192 y x z - 1/216 y x z - 1/144 z y x + + 2 3 3 2 3 3 4 3 3 + - 1/72 y x z + 1/72 z y x - 1/216 z y x - 1/216 z y x + + 3 3 2 2 4 2 2 3 2 3 + + 1/216 y x z - 1/144 y z + 1/144 z y x - 1/432 z y x + + 3 3 3 2 3 3 4 3 4 + + 1/108 z y x - 1/432 x z + 1/216 x z + 1/432 z x + 1/432 y z + + 4 2 4 3 2 + - 1/216 x z - 1/576 x z - 1/108 y x z - 1/216 z - 1/36 y x z + + 2 3 2 2 2 3 2 2 2 3 + + 1/36 y x z - 1/192 y x z - 1/108 y x z + 1/96 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/288 y x z + 1/432 z - 1/288 y x z + 1/216 z - 1/216 y z + + 3 2 3 3 2 + + 1/108 z y - 1/432 z - 1/54 z y x - 1/144 z y x + 1/108 y x z + + 2 3 3 2 2 2 2 + + 1/288 z y x - 1/216 y z + 1/54 y x z - 1/72 y x z - 1/96 y x z + + 2 2 2 2 3 2 3 + + 1/576 y x z + 1/216 y x z + 1/72 y z + 1/144 y x z + 1/108 x z + + 2 3 2 3 3 3 2 3 + + 1/288 x z + 1/216 y z - 1/72 y z - 1/108 y z - 1/288 x z + + 3 2 3 2 2 2 2 + + 1/216 y z - 1/108 x z - 1/432 y z + 1/576 x z + 1/216 x z + + 2 2 3 3 4 + + 1/144 y z - 1/216 z x , COEFF(0, 2, 2) = - 5/288 y x z + + 2 4 3 3 4 3 3 3 3 + - 5/192 y x z - 1/144 y x z - 1/288 z y x + 1/72 y x z + + 4 4 2 3 2 3 3 2 3 + + 5/576 y x z + 1/96 z y x + 1/48 y x z - 1/48 z y x + + 3 4 3 3 3 3 2 2 2 3 + + 1/144 z y x + 1/144 z y x - 1/144 y x z - 1/96 z y x + + 2 3 3 3 3 2 3 3 4 3 + + 1/288 z y x - 1/72 z y x + 1/288 x z - 1/144 x z - 1/288 z x + + 4 3 2 2 3 3 2 + + 5/576 x z + 5/288 y x z + 5/96 y x z - 5/96 y x z + 5/288 y x z + + 3 3 3 2 2 + + 5/144 z y x - 5/288 y x z - 5/144 y x z + 5/192 y x z + + 2 3 2 3 + - 5/576 y x z - 5/288 x z + 5/288 x z - 5/576 x z + 1/144 z x , + + 3 4 2 4 3 2 4 + COEFF(1, 2, 2) = 1/108 y x z + 1/576 y x z - 1/288 y x z + + 2 4 3 3 4 3 3 3 3 + + 1/72 y x z + 1/216 y x z + 1/432 z y x - 1/108 y x z + + 2 2 4 4 4 2 3 2 3 3 + - 1/192 y x z - 1/216 y x z - 1/144 z y x - 1/72 y x z + + 2 3 3 4 3 3 3 3 2 + + 1/72 z y x - 1/216 z y x - 1/216 z y x + 1/216 y x z + + 2 4 2 2 3 2 3 3 3 + + 1/144 y z + 1/144 z y x - 1/432 z y x + 1/108 z y x + + 3 2 3 3 4 3 4 4 + - 1/432 x z + 1/216 x z + 1/432 z x - 1/432 y z - 1/216 x z + + 2 4 3 2 2 3 + + 1/576 x z - 1/108 y x z + 1/216 z - 1/36 y x z + 1/36 y x z + + 2 2 2 3 2 2 2 3 2 3 + + 1/192 y x z - 1/108 y x z - 1/96 y x z + 1/288 y x z + + 4 3 2 2 3 3 4 3 + - 1/432 z + 1/288 y x z - 1/216 z + 1/216 y z - 1/108 z y + + 2 3 3 2 2 + + 1/432 z - 1/54 z y x + 1/144 z y x + 1/108 y x z - 1/288 z y x + + 3 3 2 2 2 2 2 2 + + 1/216 y z + 1/54 y x z - 1/72 y x z + 1/96 y x z - 1/576 y x z + + 2 2 3 2 3 2 + + 1/216 y x z - 1/72 y z - 1/144 y x z + 1/108 x z - 1/288 x z + + 3 2 3 3 3 2 3 3 2 + - 1/216 y z + 1/72 y z + 1/108 y z + 1/288 x z - 1/216 y z + + 3 2 2 2 2 2 2 + - 1/108 x z + 1/432 y z - 1/576 x z + 1/216 x z - 1/144 y z + + 3 3 4 2 4 + - 1/216 z x , COEFF(2, 2, 2) = - 1/1728 y x z - 1/1152 y x z + + 3 2 4 2 4 3 3 4 3 + + 1/576 y x z - 1/1152 y x z - 1/864 y x z - 1/1728 z y x + + 3 3 3 2 2 4 4 4 2 3 + + 1/432 y x z + 1/384 y x z + 1/3456 y x z + 1/576 z y x + + 2 3 3 2 3 3 4 3 3 + + 1/288 y x z - 1/288 z y x + 1/864 z y x + 1/864 z y x + + 3 3 2 2 4 2 2 3 2 3 + - 1/864 y x z - 1/1152 y z - 1/576 z y x + 1/1728 z y x + + 3 3 3 2 3 3 4 3 4 + - 1/432 z y x + 1/1728 x z - 1/864 x z - 1/1728 z x + 1/3456 y z + + 4 2 4 3 2 + + 1/3456 x z - 1/1152 x z + 1/1728 y x z - 1/1728 z + 1/576 y x z + + 2 3 2 2 2 3 2 2 2 3 + - 1/576 y x z - 1/384 y x z + 1/1728 y x z + 1/192 y x z + + 2 3 4 3 2 2 3 3 4 + - 1/576 y x z + 1/3456 z - 1/576 y x z + 1/1728 z - 1/1728 y z + + 3 2 3 3 2 + + 1/864 z y - 1/3456 z + 1/864 z y x - 1/288 z y x - 1/1728 y x z + + 2 3 3 2 2 + + 1/576 z y x - 1/1728 y z - 1/864 y x z + 1/1152 y x z + + 2 2 2 2 2 2 + - 1/192 y x z + 1/1152 y x z - 1/3456 y x z + 1/576 y z + + 3 2 3 2 3 2 3 + + 1/288 y x z - 1/1728 x z + 1/576 x z + 1/1728 y z - 1/576 y z + + 3 3 2 3 3 2 3 2 + - 1/864 y z - 1/576 x z + 1/1728 y z + 1/1728 x z - 1/3456 y z + + 2 2 2 2 2 3 + + 1/1152 x z - 1/3456 x z + 1/1152 y z + 1/864 z x ] + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxy.compute.c"); +bytes used=31783606220, alloc=64737712, 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x + + 3 3 2 2 + - 1/1728 z y x - 1/576 z y x + 1/1728 y x z + 1/576 z y x + + 4 3 3 2 2 2 + - 1/3456 y z - 1/1728 y z + 1/864 y x z + 1/3456 y x - 1/1152 y x z + + 4 2 2 2 2 2 2 + - 1/1152 y z - 1/1152 y x z + 1/192 y x z + 1/576 y x z + + 2 3 2 3 2 4 3 2 3 + + 1/3456 y z + 1/288 y x z - 1/1152 x y + 1/864 y z - 1/1728 y z + + 3 3 3 2 2 2 2 2 2 + - 1/864 y z + 1/576 y z - 1/576 y z + 1/1152 y z + 1/1152 y x + + 2 2 3 3 3 + - 1/576 y x - 1/1728 y x - 1/864 y x , COEFF(-1, -2, -2) = + + 4 2 4 2 4 2 2 4 3 + - 1/216 x y z - 1/192 x y z - 1/72 x y z + 1/288 x y z + + 4 3 3 3 3 4 3 3 3 3 + + 1/108 x y z - 1/108 y x z - 1/216 z y x + 1/108 y x z + + 2 4 4 3 2 3 3 2 3 + - 1/576 x y z + 1/432 z y x + 1/216 y x z - 1/432 z y x + + 3 3 3 2 2 2 3 3 + + 1/216 z y x - 1/72 y x z - 1/144 z y x - 1/216 y x + + 2 3 3 3 4 3 2 4 3 + + 1/72 z y x - 1/216 z y x - 1/216 y z + 1/144 z y x + + 4 3 4 3 2 + - 1/432 y x + 1/216 x y + 1/54 y x z - 1/216 y + 1/216 y x z + + 2 3 4 2 2 2 3 2 + - 1/108 y x z + 1/108 y x - 1/432 y + 1/192 y x z + 1/36 y x z + + 2 2 3 2 3 3 2 2 3 3 + - 1/288 y x z + 1/144 y x z + 1/96 y x z + 1/216 y - 1/108 y x + + 3 2 3 2 3 3 2 + - 1/216 z y + 1/432 y - 1/288 y x + 1/108 z y x + 1/288 z y x + + 2 4 3 3 + - 1/108 y x z - 1/288 z y x + 1/432 y z + 1/216 y z - 1/54 y x z + + 2 2 2 4 2 2 2 2 2 + - 1/216 y x + 1/72 y x z + 1/144 y z + 1/576 y x z - 1/96 y x z + + 2 2 3 2 3 2 4 3 + - 1/36 y x z - 1/432 y z - 1/144 y x z + 1/576 x y - 1/108 y z + + 2 3 3 3 3 2 2 2 2 + + 1/216 y z + 1/108 y z - 1/72 y z + 1/72 y z - 1/144 y z + + 2 2 2 2 3 3 3 + - 1/576 y x + 1/288 y x + 1/432 y x + 1/216 y x , COEFF(0, -2, -2) + + 4 4 2 4 3 3 3 + = 5/576 x y z + 5/192 x y z - 5/288 x y z + 1/72 y x z + + 3 4 3 3 3 3 4 3 2 3 3 + + 1/144 z y x - 1/72 y x z - 1/288 z y x - 1/144 y x z + + 2 3 3 3 3 2 2 2 3 + + 1/288 z y x - 1/144 z y x + 1/48 y x z + 1/96 z y x + + 3 2 3 3 3 2 4 3 4 3 + + 1/144 y x - 1/48 z y x + 1/144 z y x - 1/96 z y x + 1/288 y x + + 4 3 2 2 3 + - 5/576 x y - 5/144 y x z - 5/576 y x z + 5/288 y x z - 5/288 y x + + 3 2 3 3 3 3 + - 5/96 y x z + 5/288 y x - 5/288 z y x + 5/288 y x z + 5/144 y x z + + 2 2 2 2 2 3 3 3 + + 5/576 y x - 5/192 y x z + 5/96 y x z - 1/288 y x - 1/144 y x , + + 4 2 4 2 4 2 + COEFF(1, -2, -2) = - 1/216 x y z + 1/192 x y z - 1/72 x y z + + 2 4 3 4 3 3 3 3 4 3 + - 1/288 x y z + 1/108 x y z - 1/108 y x z - 1/216 z y x + + 3 3 3 2 4 4 3 2 3 3 + + 1/108 y x z + 1/576 x y z + 1/432 z y x + 1/216 y x z + + 2 3 3 3 3 2 2 2 3 + - 1/432 z y x + 1/216 z y x - 1/72 y x z - 1/144 z y x + + 3 2 3 3 3 4 3 2 4 3 + - 1/216 y x + 1/72 z y x - 1/216 z y x + 1/216 y z + 1/144 z y x + + 4 3 4 3 2 + - 1/432 y x + 1/216 x y + 1/54 y x z + 1/216 y + 1/216 y x z + + 2 3 4 2 2 2 3 2 + - 1/108 y x z + 1/108 y x + 1/432 y - 1/192 y x z + 1/36 y x z + + 2 2 3 2 3 3 2 2 3 3 + + 1/288 y x z - 1/144 y x z - 1/96 y x z - 1/216 y - 1/108 y x + + 3 2 3 2 3 3 2 + + 1/216 z y - 1/432 y + 1/288 y x + 1/108 z y x - 1/288 z y x + + 2 4 3 3 + - 1/108 y x z + 1/288 z y x - 1/432 y z - 1/216 y z - 1/54 y x z + + 2 2 2 4 2 2 2 2 2 + - 1/216 y x + 1/72 y x z - 1/144 y z - 1/576 y x z + 1/96 y x z + + 2 2 3 2 3 2 4 3 + - 1/36 y x z + 1/432 y z + 1/144 y x z - 1/576 x y + 1/108 y z + + 2 3 3 3 3 2 2 2 2 + - 1/216 y z - 1/108 y z + 1/72 y z - 1/72 y z + 1/144 y z + + 2 2 2 2 3 3 3 + + 1/576 y x - 1/288 y x + 1/432 y x + 1/216 y x , COEFF(2, -2, -2) + + 4 2 4 2 4 2 2 4 3 + = 1/3456 x y z - 1/384 x y z + 1/1152 x y z + 1/576 x y z + + 4 3 3 3 3 4 3 3 3 3 + - 1/1728 x y z + 1/432 y x z + 1/864 z y x - 1/432 y x z + + 2 4 4 3 2 3 3 2 3 + - 1/1152 x y z - 1/1728 z y x - 1/864 y x z + 1/1728 z y x + + 3 3 3 2 2 2 3 3 + - 1/864 z y x + 1/288 y x z + 1/576 z y x + 1/864 y x + + 2 3 3 3 4 3 2 4 3 + - 1/288 z y x + 1/864 z y x - 1/1728 y z - 1/576 z y x + + 4 3 4 3 2 + + 1/1728 y x - 1/3456 x y - 1/864 y x z - 1/1728 y - 1/3456 y x z + + 2 3 4 2 2 2 3 2 + + 1/1728 y x z - 1/1728 y x - 1/3456 y + 1/384 y x z - 1/576 y x z + + 2 2 3 2 3 3 2 2 3 + - 1/576 y x z + 1/288 y x z + 1/192 y x z + 1/1728 y + + 3 3 2 3 2 3 + + 1/1728 y x - 1/1728 z y + 1/3456 y - 1/576 y x - 1/1728 z y x + + 3 2 2 4 + + 1/576 z y x + 1/1728 y x z - 1/576 z y x + 1/3456 y z + 1/1728 y z + + 3 3 2 2 2 4 2 + + 1/864 y x z + 1/3456 y x - 1/1152 y x z + 1/1152 y z + + 2 2 2 2 2 2 + + 1/1152 y x z - 1/192 y x z + 1/576 y x z - 1/3456 y z + + 3 2 3 2 4 3 2 3 3 3 + - 1/288 y x z + 1/1152 x y - 1/864 y z + 1/1728 y z + 1/864 y z + + 3 2 2 2 2 2 2 2 + - 1/576 y z + 1/576 y z - 1/1152 y z - 1/1152 y x + 1/576 y x + + 2 3 3 3 4 + - 1/1728 y x - 1/864 y x , COEFF(-2, -1, -2) = - 1/864 x y z + + 2 4 2 4 2 2 4 3 4 3 + - 1/96 x y z - 1/288 x y z + 1/144 x y z + 1/432 x y z + + 3 3 3 4 3 3 3 3 2 4 + - 1/54 y x z - 1/216 z y x + 1/216 y x z - 1/288 x y z + + 4 3 2 3 3 2 3 3 + + 1/432 z y x + 1/54 y x z - 1/108 z y x + 1/108 z y x + + 3 3 2 2 2 3 3 2 3 + - 1/144 y x z - 1/36 z y x - 1/108 y x + 1/36 z y x + + 3 3 4 3 2 4 3 4 3 4 + - 1/432 z y x - 1/432 y z + 1/144 z y x - 1/432 y x + 1/864 x y + + 3 2 2 3 + + 1/108 y x z - 1/216 y + 1/216 y x z - 1/108 y x z + 1/216 y x + + 4 2 2 2 3 2 2 2 3 2 3 + - 1/864 y + 1/24 y x z + 1/288 y x z - 1/36 y x z + 1/36 y x z + + 3 2 2 3 3 3 2 + + 1/96 y x z + 1/864 y - 1/864 y x - 1/864 z y + 1/216 y + + 3 2 3 3 2 2 + - 1/288 y x + 1/864 z y x + 1/288 z y x - 1/216 y x z - 1/72 z y x + + 4 3 3 2 2 2 + + 1/864 y z + 1/216 y z - 1/432 y x z - 1/216 y x + 1/72 y x z + + 4 2 2 2 2 2 2 2 + + 1/288 y z + 1/72 y x z - 1/24 y x z - 1/72 y x z - 1/216 y z + + 3 2 3 2 4 3 2 3 3 3 + - 1/144 y x z + 1/288 x y - 1/108 y z + 1/108 y z + 1/432 y z + + 3 2 2 2 2 2 2 2 + - 1/288 y z + 1/72 y z - 1/72 y z - 1/72 y x + 1/72 y x + + 2 3 3 3 4 + + 1/108 y x + 1/432 y x , COEFF(-1, -1, -2) = 1/54 x y z + + 2 4 2 4 2 2 4 3 4 3 + + 1/48 x y z + 1/18 x y z - 1/72 x y z - 1/27 x y z + + 3 3 3 4 3 3 3 3 2 4 + + 2/27 y x z + 1/54 z y x - 1/54 y x z + 1/144 x y z + + 4 3 2 3 3 2 3 3 + - 1/108 z y x - 2/27 y x z + 1/27 z y x - 1/27 z y x + + 3 3 2 2 2 3 3 2 3 3 3 + + 1/36 y x z + 1/9 z y x + 1/27 y x - 1/9 z y x + 1/108 z y x + + 4 3 2 4 3 4 3 4 3 + + 1/54 y z - 1/36 z y x + 1/108 y x - 1/54 x y - 4/27 y x z + + 2 2 3 4 + + 1/27 y - 2/27 y x z + 4/27 y x z - 2/27 y x + 1/108 y + + 2 2 2 3 2 2 2 3 2 3 + - 1/12 y x z - 1/18 y x z + 1/18 y x z - 1/18 y x z + + 3 2 2 3 3 3 2 + - 1/48 y x z - 1/108 y + 1/54 y x + 1/108 z y - 1/27 y + + 3 2 3 3 2 2 + + 1/144 y x - 1/54 z y x - 1/144 z y x + 2/27 y x z + 1/36 z y x + + 4 3 3 2 2 2 + - 1/108 y z - 1/27 y z + 1/27 y x z + 2/27 y x - 2/9 y x z + + 4 2 2 2 2 2 2 2 + - 1/36 y z - 1/36 y x z + 1/12 y x z + 2/9 y x z + 1/27 y z + + 3 2 3 2 4 3 2 3 3 3 + + 1/72 y x z - 1/144 x y + 2/27 y z - 2/27 y z - 1/54 y z + + 3 2 2 2 2 2 2 2 2 3 + + 1/36 y z - 1/9 y z + 1/9 y z + 1/36 y x - 1/36 y x - 1/27 y x + + 3 3 4 4 2 + - 1/108 y x , COEFF(0, -1, -2) = - 5/144 x y z - 5/48 x y z + + 4 3 3 3 3 4 3 3 3 3 + + 5/72 x y z - 1/9 y x z - 1/36 z y x + 1/36 y x z + + 4 3 2 3 3 2 3 3 3 3 2 + + 1/72 z y x + 1/9 y x z - 1/18 z y x + 1/18 z y x - 1/24 y x z + + 2 2 3 3 2 3 3 3 2 4 3 + - 1/6 z y x - 1/18 y x + 1/6 z y x - 1/72 z y x + 1/24 z y x + + 4 3 4 3 2 2 3 + - 1/72 y x + 5/144 x y + 5/18 y x z + 5/36 y x z - 5/18 y x z + + 3 2 3 3 + + 5/36 y x + 5/48 y x z - 5/144 y x + 5/144 z y x - 5/36 y x z + + 3 3 2 2 2 2 2 3 + - 5/72 y x z - 5/36 y x + 5/12 y x z - 5/12 y x z + 1/18 y x + + 3 3 4 2 4 2 + + 1/72 y x , COEFF(1, -1, -2) = 1/54 x y z - 1/48 x y z + + 4 2 2 4 3 4 3 3 3 + + 1/18 x y z + 1/72 x y z - 1/27 x y z + 2/27 y x z + + 3 4 3 3 3 3 2 4 4 3 + + 1/54 z y x - 1/54 y x z - 1/144 x y z - 1/108 z y x + + 2 3 3 2 3 3 3 3 2 + - 2/27 y x z + 1/27 z y x - 1/27 z y x + 1/36 y x z + + 2 2 3 3 2 3 3 3 4 3 + + 1/9 z y x + 1/27 y x - 1/9 z y x + 1/108 z y x - 1/54 y z + + 2 4 3 4 3 4 3 + - 1/36 z y x + 1/108 y x - 1/54 x y - 4/27 y x z - 1/27 y + + 2 2 3 4 2 2 2 + - 2/27 y x z + 4/27 y x z - 2/27 y x - 1/108 y + 1/12 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + - 1/18 y x z - 1/18 y x z + 1/18 y x z + 1/48 y x z + 1/108 y + + 3 3 2 3 2 3 + + 1/54 y x - 1/108 z y + 1/27 y - 1/144 y x - 1/54 z y x + + 3 2 2 4 + + 1/144 z y x + 2/27 y x z - 1/36 z y x + 1/108 y z + 1/27 y z + + 3 3 2 2 2 4 2 2 2 + + 1/27 y x z + 2/27 y x - 2/9 y x z + 1/36 y z + 1/36 y x z + + 2 2 2 2 3 2 3 2 4 + - 1/12 y x z + 2/9 y x z - 1/27 y z - 1/72 y x z + 1/144 x y + + 3 2 3 3 3 3 2 2 2 2 + - 2/27 y z + 2/27 y z + 1/54 y z - 1/36 y z + 1/9 y z - 1/9 y z + + 2 2 2 2 3 3 3 + - 1/36 y x + 1/36 y x - 1/27 y x - 1/108 y x , COEFF(2, -1, -2) = + + 4 2 4 2 4 2 2 4 3 + - 1/864 x y z + 1/96 x y z - 1/288 x y z - 1/144 x y z + + 4 3 3 3 3 4 3 3 3 3 + + 1/432 x y z - 1/54 y x z - 1/216 z y x + 1/216 y x z + + 2 4 4 3 2 3 3 2 3 + + 1/288 x y z + 1/432 z y x + 1/54 y x z - 1/108 z y x + + 3 3 3 2 2 2 3 3 + + 1/108 z y x - 1/144 y x z - 1/36 z y x - 1/108 y x + + 2 3 3 3 4 3 2 4 3 + + 1/36 z y x - 1/432 z y x + 1/432 y z + 1/144 z y x + + 4 3 4 3 2 + - 1/432 y x + 1/864 x y + 1/108 y x z + 1/216 y + 1/216 y x z + + 2 3 4 2 2 2 3 2 + - 1/108 y x z + 1/216 y x + 1/864 y - 1/24 y x z + 1/288 y x z + + 2 2 3 2 3 3 2 2 3 3 + + 1/36 y x z - 1/36 y x z - 1/96 y x z - 1/864 y - 1/864 y x + + 3 2 3 2 3 3 2 + + 1/864 z y - 1/216 y + 1/288 y x + 1/864 z y x - 1/288 z y x + + 2 4 3 3 + - 1/216 y x z + 1/72 z y x - 1/864 y z - 1/216 y z - 1/432 y x z + + 2 2 2 4 2 2 2 2 2 + - 1/216 y x + 1/72 y x z - 1/288 y z - 1/72 y x z + 1/24 y x z + + 2 2 3 2 3 2 4 3 + - 1/72 y x z + 1/216 y z + 1/144 y x z - 1/288 x y + 1/108 y z + + 2 3 3 3 3 2 2 2 2 + - 1/108 y z - 1/432 y z + 1/288 y z - 1/72 y z + 1/72 y z + + 2 2 2 2 3 3 3 + + 1/72 y x - 1/72 y x + 1/108 y x + 1/432 y x , COEFF(-2, 0, -2) = + + 4 2 4 2 4 2 2 4 3 + 1/576 x y z + 1/64 x y z + 1/192 x y z - 1/96 x y z + + 4 3 3 4 3 2 4 4 3 + - 1/288 x y z + 1/144 z y x + 1/192 x y z - 1/288 z y x + + 2 3 3 2 3 2 2 3 4 3 + - 5/144 y x z + 5/288 z y x + 5/96 z y x + 1/288 y z + + 2 4 3 3 2 3 3 4 3 + - 1/96 z y x - 1/24 x z + 1/36 x z - 1/144 x + 1/288 y x + + 4 2 2 3 4 + - 1/576 x y - 1/144 z - 5/576 y x z + 5/288 y x z + 1/576 y + + 2 2 2 2 2 3 3 3 2 2 + - 5/64 y x z + 5/96 y x z + 1/72 z + 1/72 x - 5/576 y - 1/48 z + + 2 4 2 2 2 4 2 + - 1/48 x - 1/576 y z + 5/576 y x - 5/192 y x z - 1/192 y z + + 2 2 2 2 2 4 + - 5/192 y x z + 5/576 y z + 1/144 x z + 1/48 x z - 1/192 x y + + 2 3 2 3 3 2 2 2 + - 5/288 y z - 1/24 x z - 1/72 x z + 1/16 x z + 1/48 x z + + 2 2 2 2 3 2 3 + + 5/192 y z + 5/192 y x + 1/144 - 1/72 z x - 5/288 y x , + + 4 2 4 2 4 2 + COEFF(-1, 0, -2) = - 1/36 x y z - 1/32 x y z - 1/12 x y z + + 2 4 3 4 3 3 4 3 2 4 + + 1/48 x y z + 1/18 x y z - 1/36 z y x - 1/96 x y z + + 4 3 2 3 3 2 3 2 2 3 4 3 + + 1/72 z y x + 5/36 y x z - 5/72 z y x - 5/24 z y x - 1/36 y z + + 2 4 3 3 2 3 3 4 3 4 + + 1/24 z y x + 1/6 x z - 1/9 x z + 1/9 x - 1/72 y x + 1/36 x y + + 2 2 3 4 2 2 2 + + 1/18 z + 5/36 y x z - 5/18 y x z - 1/72 y + 5/32 y x z + + 2 2 3 3 3 2 2 2 + - 5/48 y x z - 1/9 z - 1/18 x + 5/72 y + 1/6 z + 1/24 x + + 4 2 2 2 4 2 2 2 + + 1/72 y z - 5/36 y x + 5/12 y x z + 1/24 y z + 5/96 y x z + + 2 2 2 4 2 3 + - 5/72 y z - 1/9 x z - 1/24 x z - 1/18 + 1/96 x y + 5/36 y z + + 2 3 3 2 2 2 2 2 2 2 + + 1/12 x z + 2/9 x z - 1/8 x z - 1/3 x z - 5/24 y z - 5/96 y x + + 3 2 3 2 3 3 4 + + 1/18 z x + 5/72 y x , COEFF(0, 0, -2) = - 5/24 y x z + 5/96 x y z + + 2 3 4 3 2 3 2 2 3 4 3 + + 5/8 x z + 1/24 z y x + 5/48 z y x + 5/16 z y x - 5/48 x y z + + 2 4 3 4 3 4 3 4 2 25 2 + - 1/16 z y x - 1/48 z y x + 1/48 y x + 5/32 x y z + -- y x + 96 + + 25 2 2 3 3 4 25 2 2 + - -- y x z - 5/48 y x - 1/12 z x - 5/96 x y - 5/24 x - -- y x z + 96 32 + + 25 2 3 3 3 3 2 3 3 + + -- y x z + 1/6 x z - 1/4 x z - 5/12 x z + 5/24 x z + 1/12 x , + 48 + + 4 2 4 2 4 2 + COEFF(1, 0, -2) = - 1/36 x y z + 1/32 x y z - 1/12 x y z + + 2 4 3 4 3 3 4 3 2 4 + - 1/48 x y z + 1/18 x y z - 1/36 z y x + 1/96 x y z + + 4 3 2 3 3 2 3 2 2 3 4 3 + + 1/72 z y x + 5/36 y x z - 5/72 z y x - 5/24 z y x + 1/36 y z + + 2 4 3 3 2 3 3 4 3 4 + + 1/24 z y x + 1/6 x z - 1/9 x z + 1/9 x - 1/72 y x + 1/36 x y + + 2 2 3 4 2 2 2 + - 1/18 z + 5/36 y x z - 5/18 y x z + 1/72 y - 5/32 y x z + + 2 2 3 3 3 2 2 2 + + 5/48 y x z + 1/9 z - 1/18 x - 5/72 y - 1/6 z - 1/24 x + + 4 2 2 2 4 2 2 2 + - 1/72 y z - 5/36 y x + 5/12 y x z - 1/24 y z - 5/96 y x z + + 2 2 2 4 2 3 + + 5/72 y z - 1/9 x z + 1/24 x z + 1/18 - 1/96 x y - 5/36 y z + + 2 3 3 2 2 2 2 2 2 2 + - 1/12 x z + 2/9 x z + 1/8 x z - 1/3 x z + 5/24 y z + 5/96 y x + + 3 2 3 4 2 4 2 + + 1/18 z x + 5/72 y x , COEFF(2, 0, -2) = 1/576 x y z - 1/64 x y z + + 4 2 2 4 3 4 3 3 4 3 + + 1/192 x y z + 1/96 x y z - 1/288 x y z + 1/144 z y x + + 2 4 4 3 2 3 3 2 3 + - 1/192 x y z - 1/288 z y x - 5/144 y x z + 5/288 z y x + + 2 2 3 4 3 2 4 3 3 2 3 3 + + 5/96 z y x - 1/288 y z - 1/96 z y x - 1/24 x z + 1/36 x z + + 4 3 4 2 + - 1/144 x + 1/288 y x - 1/576 x y + 1/144 z - 5/576 y x z + + 2 3 4 2 2 2 2 2 3 3 + + 5/288 y x z - 1/576 y + 5/64 y x z - 5/96 y x z - 1/72 z + + 3 2 2 2 4 2 + + 1/72 x + 5/576 y + 1/48 z + 1/48 x + 1/576 y z + 5/576 y x + + 2 2 4 2 2 2 2 + - 5/192 y x z + 1/192 y z + 5/192 y x z - 5/576 y z + 1/144 x z + + 2 2 4 2 3 2 3 3 + - 1/48 x z + 1/192 x y + 5/288 y z + 1/24 x z - 1/72 x z + + 2 2 2 2 2 2 2 3 + - 1/16 x z + 1/48 x z - 5/192 y z - 5/192 y x - 1/144 - 1/72 z x + + 2 3 4 2 4 2 + - 5/288 y x , COEFF(-2, 1, -2) = - 1/864 x y z - 1/96 x y z + + 4 2 2 4 3 4 3 3 3 + - 1/288 x y z + 1/144 x y z + 1/432 x y z + 1/54 y x z + + 3 4 3 3 3 3 2 4 4 3 + - 1/216 z y x - 1/216 y x z - 1/288 x y z + 1/432 z y x + + 2 3 3 2 3 3 3 3 2 + + 1/54 y x z - 1/108 z y x - 1/108 z y x + 1/144 y x z + + 2 2 3 3 2 3 3 3 4 3 + - 1/36 z y x + 1/108 y x - 1/36 z y x + 1/432 z y x - 1/432 y z + + 2 4 3 4 3 4 3 + + 1/144 z y x - 1/432 y x + 1/864 x y - 1/108 y x z + 1/216 y + + 2 2 3 4 2 2 2 + + 1/216 y x z - 1/108 y x z - 1/216 y x - 1/864 y + 1/24 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + - 1/288 y x z - 1/36 y x z - 1/36 y x z - 1/96 y x z - 1/864 y + + 3 3 2 3 2 3 + + 1/864 y x + 1/864 z y + 1/216 y + 1/288 y x - 1/864 z y x + + 3 2 2 4 + - 1/288 z y x + 1/216 y x z + 1/72 z y x + 1/864 y z - 1/216 y z + + 3 3 2 2 2 4 2 2 2 + + 1/432 y x z - 1/216 y x + 1/72 y x z + 1/288 y z + 1/72 y x z + + 2 2 2 2 3 2 3 2 4 + + 1/24 y x z + 1/72 y x z - 1/216 y z + 1/144 y x z + 1/288 x y + + 3 2 3 3 3 3 2 2 + + 1/108 y z + 1/108 y z - 1/432 y z + 1/288 y z - 1/72 y z + + 2 2 2 2 2 2 3 3 3 + - 1/72 y z - 1/72 y x - 1/72 y x + 1/108 y x - 1/432 y x , + + 4 2 4 2 4 2 + COEFF(-1, 1, -2) = 1/54 x y z + 1/48 x y z + 1/18 x y z + + 2 4 3 4 3 3 3 3 4 3 + - 1/72 x y z - 1/27 x y z - 2/27 y x z + 1/54 z y x + + 3 3 3 2 4 4 3 2 3 3 + + 1/54 y x z + 1/144 x y z - 1/108 z y x - 2/27 y x z + + 2 3 3 3 3 2 2 2 3 3 + + 1/27 z y x + 1/27 z y x - 1/36 y x z + 1/9 z y x - 1/27 y x + + 2 3 3 3 4 3 2 4 3 4 3 + + 1/9 z y x - 1/108 z y x + 1/54 y z - 1/36 z y x + 1/108 y x + + 4 3 2 2 3 + - 1/54 x y + 4/27 y x z - 1/27 y - 2/27 y x z + 4/27 y x z + 2/27 y x + + 4 2 2 2 3 2 2 2 3 2 3 + + 1/108 y - 1/12 y x z + 1/18 y x z + 1/18 y x z + 1/18 y x z + + 3 2 2 3 3 3 2 + + 1/48 y x z + 1/108 y - 1/54 y x - 1/108 z y - 1/27 y + + 3 2 3 3 2 2 + - 1/144 y x + 1/54 z y x + 1/144 z y x - 2/27 y x z - 1/36 z y x + + 4 3 3 2 2 2 + - 1/108 y z + 1/27 y z - 1/27 y x z + 2/27 y x - 2/9 y x z + + 4 2 2 2 2 2 2 2 + - 1/36 y z - 1/36 y x z - 1/12 y x z - 2/9 y x z + 1/27 y z + + 3 2 3 2 4 3 2 3 3 3 + - 1/72 y x z - 1/144 x y - 2/27 y z - 2/27 y z + 1/54 y z + + 3 2 2 2 2 2 2 2 2 3 + - 1/36 y z + 1/9 y z + 1/9 y z + 1/36 y x + 1/36 y x - 1/27 y x + + 3 3 4 4 2 + + 1/108 y x , COEFF(0, 1, -2) = - 5/144 x y z - 5/48 x y z + + 4 3 3 3 3 4 3 3 3 3 + + 5/72 x y z + 1/9 y x z - 1/36 z y x - 1/36 y x z + + 4 3 2 3 3 2 3 3 3 3 2 + + 1/72 z y x + 1/9 y x z - 1/18 z y x - 1/18 z y x + 1/24 y x z + + 2 2 3 3 2 3 3 3 2 4 3 + - 1/6 z y x + 1/18 y x - 1/6 z y x + 1/72 z y x + 1/24 z y x + + 4 3 4 3 2 2 3 + - 1/72 y x + 5/144 x y - 5/18 y x z + 5/36 y x z - 5/18 y x z + + 3 2 3 3 + - 5/36 y x - 5/48 y x z + 5/144 y x - 5/144 z y x + 5/36 y x z + + 3 3 2 2 2 2 2 3 + + 5/72 y x z - 5/36 y x + 5/12 y x z + 5/12 y x z + 1/18 y x + + 3 3 4 2 4 2 4 2 + - 1/72 y x , COEFF(1, 1, -2) = 1/54 x y z - 1/48 x y z + 1/18 x y z + + 2 4 3 4 3 3 3 3 4 3 + + 1/72 x y z - 1/27 x y z - 2/27 y x z + 1/54 z y x + + 3 3 3 2 4 4 3 2 3 3 + + 1/54 y x z - 1/144 x y z - 1/108 z y x - 2/27 y x z + + 2 3 3 3 3 2 2 2 3 3 + + 1/27 z y x + 1/27 z y x - 1/36 y x z + 1/9 z y x - 1/27 y x + + 2 3 3 3 4 3 2 4 3 4 3 + + 1/9 z y x - 1/108 z y x - 1/54 y z - 1/36 z y x + 1/108 y x + + 4 3 2 2 3 + - 1/54 x y + 4/27 y x z + 1/27 y - 2/27 y x z + 4/27 y x z + 2/27 y x + + 4 2 2 2 3 2 2 2 3 2 3 + - 1/108 y + 1/12 y x z + 1/18 y x z - 1/18 y x z - 1/18 y x z + + 3 2 2 3 3 3 2 + - 1/48 y x z - 1/108 y - 1/54 y x + 1/108 z y + 1/27 y + + 3 2 3 3 2 2 + + 1/144 y x + 1/54 z y x - 1/144 z y x - 2/27 y x z + 1/36 z y x + + 4 3 3 2 2 2 + + 1/108 y z - 1/27 y z - 1/27 y x z + 2/27 y x - 2/9 y x z + + 4 2 2 2 2 2 2 2 + + 1/36 y z + 1/36 y x z + 1/12 y x z - 2/9 y x z - 1/27 y z + + 3 2 3 2 4 3 2 3 3 3 + + 1/72 y x z + 1/144 x y + 2/27 y z + 2/27 y z - 1/54 y z + + 3 2 2 2 2 2 2 2 2 3 + + 1/36 y z - 1/9 y z - 1/9 y z - 1/36 y x - 1/36 y x - 1/27 y x + + 3 3 4 2 4 2 + + 1/108 y x , COEFF(2, 1, -2) = - 1/864 x y z + 1/96 x y z + + 4 2 2 4 3 4 3 3 3 + - 1/288 x y z - 1/144 x y z + 1/432 x y z + 1/54 y x z + + 3 4 3 3 3 3 2 4 4 3 + - 1/216 z y x - 1/216 y x z + 1/288 x y z + 1/432 z y x + + 2 3 3 2 3 3 3 3 2 + + 1/54 y x z - 1/108 z y x - 1/108 z y x + 1/144 y x z + + 2 2 3 3 2 3 3 3 4 3 + - 1/36 z y x + 1/108 y x - 1/36 z y x + 1/432 z y x + 1/432 y z + + 2 4 3 4 3 4 3 + + 1/144 z y x - 1/432 y x + 1/864 x y - 1/108 y x z - 1/216 y + + 2 2 3 4 2 2 2 + + 1/216 y x z - 1/108 y x z - 1/216 y x + 1/864 y - 1/24 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + - 1/288 y x z + 1/36 y x z + 1/36 y x z + 1/96 y x z + 1/864 y + + 3 3 2 3 2 3 + + 1/864 y x - 1/864 z y - 1/216 y - 1/288 y x - 1/864 z y x + + 3 2 2 4 + + 1/288 z y x + 1/216 y x z - 1/72 z y x - 1/864 y z + 1/216 y z + + 3 3 2 2 2 4 2 2 2 + + 1/432 y x z - 1/216 y x + 1/72 y x z - 1/288 y z - 1/72 y x z + + 2 2 2 2 3 2 3 2 4 + - 1/24 y x z + 1/72 y x z + 1/216 y z - 1/144 y x z - 1/288 x y + + 3 2 3 3 3 3 2 2 + - 1/108 y z - 1/108 y z + 1/432 y z - 1/288 y z + 1/72 y z + + 2 2 2 2 2 2 3 3 3 + + 1/72 y z + 1/72 y x + 1/72 y x + 1/108 y x - 1/432 y x , + + 4 2 4 2 4 2 + COEFF(-2, 2, -2) = 1/3456 x y z + 1/384 x y z + 1/1152 x y z + + 2 4 3 4 3 3 3 3 4 3 + - 1/576 x y z - 1/1728 x y z - 1/432 y x z + 1/864 z y x + + 3 3 3 2 4 4 3 2 3 3 + + 1/432 y x z + 1/1152 x y z - 1/1728 z y x - 1/864 y x z + + 2 3 3 3 3 2 2 2 3 + + 1/1728 z y x + 1/864 z y x - 1/288 y x z + 1/576 z y x + + 3 2 3 3 3 4 3 + - 1/864 y x + 1/288 z y x - 1/864 z y x + 1/1728 y z + + 2 4 3 4 3 4 3 + - 1/576 z y x + 1/1728 y x - 1/3456 x y + 1/864 y x z - 1/1728 y + + 2 2 3 4 2 2 2 + - 1/3456 y x z + 1/1728 y x z + 1/1728 y x + 1/3456 y - 1/384 y x z + + 3 2 2 2 3 2 3 3 2 2 + + 1/576 y x z + 1/576 y x z + 1/288 y x z + 1/192 y x z + + 3 3 3 2 3 2 + + 1/1728 y - 1/1728 y x - 1/1728 z y - 1/3456 y - 1/576 y x + + 3 3 2 2 + + 1/1728 z y x + 1/576 z y x - 1/1728 y x z - 1/576 z y x + + 4 3 3 2 2 2 + - 1/3456 y z + 1/1728 y z - 1/864 y x z + 1/3456 y x - 1/1152 y x z + + 4 2 2 2 2 2 2 + - 1/1152 y z - 1/1152 y x z - 1/192 y x z - 1/576 y x z + + 2 3 2 3 2 4 3 2 3 + + 1/3456 y z - 1/288 y x z - 1/1152 x y - 1/864 y z - 1/1728 y z + + 3 3 3 2 2 2 2 2 2 + + 1/864 y z - 1/576 y z + 1/576 y z + 1/1152 y z + 1/1152 y x + + 2 2 3 3 3 + + 1/576 y x - 1/1728 y x + 1/864 y x , COEFF(-1, 2, -2) = + + 4 2 4 2 4 2 2 4 3 + - 1/216 x y z - 1/192 x y z - 1/72 x y z + 1/288 x y z + + 4 3 3 3 3 4 3 3 3 3 + + 1/108 x y z + 1/108 y x z - 1/216 z y x - 1/108 y x z + + 2 4 4 3 2 3 3 2 3 + - 1/576 x y z + 1/432 z y x + 1/216 y x z - 1/432 z y x + + 3 3 3 2 2 2 3 3 + - 1/216 z y x + 1/72 y x z - 1/144 z y x + 1/216 y x + + 2 3 3 3 4 3 2 4 3 + - 1/72 z y x + 1/216 z y x - 1/216 y z + 1/144 z y x + + 4 3 4 3 2 + - 1/432 y x + 1/216 x y - 1/54 y x z + 1/216 y + 1/216 y x z + + 2 3 4 2 2 2 3 2 + - 1/108 y x z - 1/108 y x - 1/432 y + 1/192 y x z - 1/36 y x z + + 2 2 3 2 3 3 2 2 3 3 + - 1/288 y x z - 1/144 y x z - 1/96 y x z - 1/216 y + 1/108 y x + + 3 2 3 2 3 3 2 + + 1/216 z y + 1/432 y + 1/288 y x - 1/108 z y x - 1/288 z y x + + 2 4 3 3 + + 1/108 y x z + 1/288 z y x + 1/432 y z - 1/216 y z + 1/54 y x z + + 2 2 2 4 2 2 2 2 2 + - 1/216 y x + 1/72 y x z + 1/144 y z + 1/576 y x z + 1/96 y x z + + 2 2 3 2 3 2 4 3 + + 1/36 y x z - 1/432 y z + 1/144 y x z + 1/576 x y + 1/108 y z + + 2 3 3 3 3 2 2 2 2 + + 1/216 y z - 1/108 y z + 1/72 y z - 1/72 y z - 1/144 y z + + 2 2 2 2 3 3 3 + - 1/576 y x - 1/288 y x + 1/432 y x - 1/216 y x , COEFF(0, 2, -2) = + + 4 4 2 4 3 3 3 + 5/576 x y z + 5/192 x y z - 5/288 x y z - 1/72 y x z + + 3 4 3 3 3 3 4 3 2 3 3 + + 1/144 z y x + 1/72 y x z - 1/288 z y x - 1/144 y x z + + 2 3 3 3 3 2 2 2 3 + + 1/288 z y x + 1/144 z y x - 1/48 y x z + 1/96 z y x + + 3 2 3 3 3 2 4 3 4 3 + - 1/144 y x + 1/48 z y x - 1/144 z y x - 1/96 z y x + 1/288 y x + + 4 3 2 2 3 + - 5/576 x y + 5/144 y x z - 5/576 y x z + 5/288 y x z + 5/288 y x + + 3 2 3 3 3 3 + + 5/96 y x z - 5/288 y x + 5/288 z y x - 5/288 y x z - 5/144 y x z + + 2 2 2 2 2 3 3 3 + + 5/576 y x - 5/192 y x z - 5/96 y x z - 1/288 y x + 1/144 y x , + + 4 2 4 2 4 2 + COEFF(1, 2, -2) = - 1/216 x y z + 1/192 x y z - 1/72 x y z + + 2 4 3 4 3 3 3 3 4 3 + - 1/288 x y z + 1/108 x y z + 1/108 y x z - 1/216 z y x + + 3 3 3 2 4 4 3 2 3 3 + - 1/108 y x z + 1/576 x y z + 1/432 z y x + 1/216 y x z + + 2 3 3 3 3 2 2 2 3 + - 1/432 z y x - 1/216 z y x + 1/72 y x z - 1/144 z y x + + 3 2 3 3 3 4 3 2 4 3 + + 1/216 y x - 1/72 z y x + 1/216 z y x + 1/216 y z + 1/144 z y x + + 4 3 4 3 2 + - 1/432 y x + 1/216 x y - 1/54 y x z - 1/216 y + 1/216 y x z + + 2 3 4 2 2 2 3 2 + - 1/108 y x z - 1/108 y x + 1/432 y - 1/192 y x z - 1/36 y x z + + 2 2 3 2 3 3 2 2 3 3 + + 1/288 y x z + 1/144 y x z + 1/96 y x z + 1/216 y + 1/108 y x + + 3 2 3 2 3 3 2 + - 1/216 z y - 1/432 y - 1/288 y x - 1/108 z y x + 1/288 z y x + + 2 4 3 3 + + 1/108 y x z - 1/288 z y x - 1/432 y z + 1/216 y z + 1/54 y x z + + 2 2 2 4 2 2 2 2 2 + - 1/216 y x + 1/72 y x z - 1/144 y z - 1/576 y x z - 1/96 y x z + + 2 2 3 2 3 2 4 3 + + 1/36 y x z + 1/432 y z - 1/144 y x z - 1/576 x y - 1/108 y z + + 2 3 3 3 3 2 2 2 2 + - 1/216 y z + 1/108 y z - 1/72 y z + 1/72 y z + 1/144 y z + + 2 2 2 2 3 3 3 + + 1/576 y x + 1/288 y x + 1/432 y x - 1/216 y x , COEFF(2, 2, -2) = + + 4 2 4 2 4 2 2 4 3 + 1/3456 x y z - 1/384 x y z + 1/1152 x y z + 1/576 x y z + + 4 3 3 3 3 4 3 3 3 3 + - 1/1728 x y z - 1/432 y x z + 1/864 z y x + 1/432 y x z + + 2 4 4 3 2 3 3 2 3 + - 1/1152 x y z - 1/1728 z y x - 1/864 y x z + 1/1728 z y x + + 3 3 3 2 2 2 3 3 + + 1/864 z y x - 1/288 y x z + 1/576 z y x - 1/864 y x + + 2 3 3 3 4 3 2 4 3 + + 1/288 z y x - 1/864 z y x - 1/1728 y z - 1/576 z y x + + 4 3 4 3 2 + + 1/1728 y x - 1/3456 x y + 1/864 y x z + 1/1728 y - 1/3456 y x z + + 2 3 4 2 2 2 3 2 + + 1/1728 y x z + 1/1728 y x - 1/3456 y + 1/384 y x z + 1/576 y x z + + 2 2 3 2 3 3 2 2 3 + - 1/576 y x z - 1/288 y x z - 1/192 y x z - 1/1728 y + + 3 3 2 3 2 3 + - 1/1728 y x + 1/1728 z y + 1/3456 y + 1/576 y x + 1/1728 z y x + + 3 2 2 4 + - 1/576 z y x - 1/1728 y x z + 1/576 z y x + 1/3456 y z - 1/1728 y z + + 3 3 2 2 2 4 2 + - 1/864 y x z + 1/3456 y x - 1/1152 y x z + 1/1152 y z + + 2 2 2 2 2 2 + + 1/1152 y x z + 1/192 y x z - 1/576 y x z - 1/3456 y z + + 3 2 3 2 4 3 2 3 3 3 + + 1/288 y x z + 1/1152 x y + 1/864 y z + 1/1728 y z - 1/864 y z + + 3 2 2 2 2 2 2 2 + + 1/576 y z - 1/576 y z - 1/1152 y z - 1/1152 y x - 1/576 y x + + 2 3 3 3 4 + - 1/1728 y x + 1/864 y x , COEFF(-2, -2, -1) = - 1/216 x y z + + 2 4 2 4 2 2 4 3 4 3 + - 1/192 x y z - 1/576 x y z + 1/144 x y z + 1/432 x y z + + 3 3 3 4 3 3 3 3 2 4 + - 1/108 y x z - 1/216 z y x + 1/108 y x z - 1/72 x y z + + 4 3 2 3 3 2 3 3 + + 1/108 z y x + 1/216 y x z - 1/108 z y x + 1/54 z y x + + 3 3 2 2 2 3 3 2 3 + - 1/144 y x z - 1/288 z y x - 1/108 y x + 1/144 z y x + + 3 3 4 3 2 4 3 4 3 4 + - 1/54 z y x - 1/432 y z + 1/288 z y x - 1/216 y x + 1/432 x y + + 3 2 2 3 + + 1/216 y x z - 1/216 y + 1/216 y x z - 1/432 y x z + 1/216 y x + + 4 2 2 2 3 2 2 2 3 + - 1/432 y + 1/192 y x z + 1/288 y x z - 1/144 y x z + + 2 3 3 2 2 3 3 3 + + 1/72 y x z + 1/96 y x z + 1/216 y - 1/216 y x - 1/108 z y + + 2 3 2 3 3 2 + + 1/432 y - 1/72 y x + 1/108 z y x + 1/36 z y x - 1/108 y x z + + 2 4 3 3 2 + - 1/36 z y x + 1/216 y z + 1/108 y z - 1/216 y x z - 1/432 y x + + 2 2 4 2 2 2 2 2 2 + + 1/576 y x z + 1/576 y z + 1/72 y x z - 1/96 y x z - 1/288 y x z + + 2 3 2 3 2 4 3 2 3 + - 1/216 y z - 1/72 y x z + 1/144 x y - 1/216 y z + 1/432 y z + + 3 3 3 2 2 2 2 2 2 + + 1/216 y z - 1/288 y z + 1/288 y z - 1/576 y z - 1/144 y x + + 2 2 3 3 3 4 + + 1/72 y x + 1/216 y x + 1/108 y x , COEFF(-1, -2, -1) = 2/27 x y z + + 2 4 2 4 2 2 4 3 4 3 + + 1/96 x y z + 1/36 x y z - 1/72 x y z - 1/27 x y z + + 3 3 3 4 3 3 3 3 2 4 + + 1/27 y x z + 1/54 z y x - 1/27 y x z + 1/36 x y z + + 4 3 2 3 3 2 3 3 + - 1/27 z y x - 1/54 y x z + 1/27 z y x - 2/27 z y x + + 3 3 2 2 2 3 3 2 3 3 3 + + 1/36 y x z + 1/72 z y x + 1/27 y x - 1/36 z y x + 2/27 z y x + + 4 3 2 4 3 4 3 4 3 + + 1/54 y z - 1/72 z y x + 1/54 y x - 1/27 x y - 2/27 y x z + + 2 2 3 4 2 2 2 + + 1/27 y - 2/27 y x z + 1/27 y x z - 2/27 y x + 1/54 y - 1/96 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + - 1/18 y x z + 1/72 y x z - 1/36 y x z - 1/48 y x z - 1/27 y + + 3 3 2 3 2 3 + + 2/27 y x + 2/27 z y - 1/54 y + 1/36 y x - 4/27 z y x + + 3 2 2 4 + - 1/18 z y x + 4/27 y x z + 1/18 z y x - 1/27 y z - 2/27 y z + + 3 3 2 2 2 4 2 2 2 + + 2/27 y x z + 1/27 y x - 1/36 y x z - 1/72 y z - 1/36 y x z + + 2 2 2 2 3 2 3 2 4 + + 1/48 y x z + 1/18 y x z + 1/27 y z + 1/36 y x z - 1/72 x y + + 3 2 3 3 3 3 2 2 + + 1/27 y z - 1/54 y z - 1/27 y z + 1/36 y z - 1/36 y z + + 2 2 2 2 2 2 3 3 3 + + 1/72 y z + 1/72 y x - 1/36 y x - 1/54 y x - 1/27 y x , + + 4 4 2 4 3 + COEFF(0, -2, -1) = - 5/36 x y z - 5/96 x y z + 5/72 x y z + + 3 3 3 4 3 3 3 3 4 3 + - 1/18 y x z - 1/36 z y x + 1/18 y x z + 1/18 z y x + + 2 3 3 2 3 3 3 3 2 + + 1/36 y x z - 1/18 z y x + 1/9 z y x - 1/24 y x z + + 2 2 3 3 2 3 3 3 2 4 3 + - 1/48 z y x - 1/18 y x + 1/24 z y x - 1/9 z y x + 1/48 z y x + + 4 3 4 3 2 2 3 + - 1/36 y x + 5/72 x y + 5/36 y x z + 5/36 y x z - 5/72 y x z + + 3 2 3 3 + + 5/36 y x + 5/48 y x z - 5/36 y x + 5/18 z y x - 5/18 y x z + + 3 3 2 2 2 2 2 3 + - 5/36 y x z - 5/72 y x + 5/96 y x z - 5/48 y x z + 1/36 y x + + 3 3 4 2 4 2 + + 1/18 y x , COEFF(1, -2, -1) = 2/27 x y z - 1/96 x y z + + 4 2 2 4 3 4 3 3 3 + + 1/36 x y z + 1/72 x y z - 1/27 x y z + 1/27 y x z + + 3 4 3 3 3 3 2 4 4 3 + + 1/54 z y x - 1/27 y x z - 1/36 x y z - 1/27 z y x + + 2 3 3 2 3 3 3 3 2 + - 1/54 y x z + 1/27 z y x - 2/27 z y x + 1/36 y x z + + 2 2 3 3 2 3 3 3 4 3 + + 1/72 z y x + 1/27 y x - 1/36 z y x + 2/27 z y x - 1/54 y z + + 2 4 3 4 3 4 3 + - 1/72 z y x + 1/54 y x - 1/27 x y - 2/27 y x z - 1/27 y + + 2 2 3 4 2 2 2 + - 2/27 y x z + 1/27 y x z - 2/27 y x - 1/54 y + 1/96 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + - 1/18 y x z - 1/72 y x z + 1/36 y x z + 1/48 y x z + 1/27 y + + 3 3 2 3 2 3 + + 2/27 y x - 2/27 z y + 1/54 y - 1/36 y x - 4/27 z y x + + 3 2 2 4 + + 1/18 z y x + 4/27 y x z - 1/18 z y x + 1/27 y z + 2/27 y z + + 3 3 2 2 2 4 2 2 2 + + 2/27 y x z + 1/27 y x - 1/36 y x z + 1/72 y z + 1/36 y x z + + 2 2 2 2 3 2 3 2 4 + - 1/48 y x z + 1/18 y x z - 1/27 y z - 1/36 y x z + 1/72 x y + + 3 2 3 3 3 3 2 2 + - 1/27 y z + 1/54 y z + 1/27 y z - 1/36 y z + 1/36 y z + + 2 2 2 2 2 2 3 3 3 + - 1/72 y z - 1/72 y x + 1/36 y x - 1/54 y x - 1/27 y x , + + 4 2 4 2 4 2 + COEFF(2, -2, -1) = - 1/216 x y z + 1/192 x y z - 1/576 x y z + + 2 4 3 4 3 3 3 3 4 3 + - 1/144 x y z + 1/432 x y z - 1/108 y x z - 1/216 z y x + + 3 3 3 2 4 4 3 2 3 3 + + 1/108 y x z + 1/72 x y z + 1/108 z y x + 1/216 y x z + + 2 3 3 3 3 2 2 2 3 + - 1/108 z y x + 1/54 z y x - 1/144 y x z - 1/288 z y x + + 3 2 3 3 3 4 3 2 4 3 + - 1/108 y x + 1/144 z y x - 1/54 z y x + 1/432 y z + 1/288 z y x + + 4 3 4 3 2 + - 1/216 y x + 1/432 x y + 1/216 y x z + 1/216 y + 1/216 y x z + + 2 3 4 2 2 2 3 2 + - 1/432 y x z + 1/216 y x + 1/432 y - 1/192 y x z + 1/288 y x z + + 2 2 3 2 3 3 2 2 3 3 + + 1/144 y x z - 1/72 y x z - 1/96 y x z - 1/216 y - 1/216 y x + + 3 2 3 2 3 3 2 + + 1/108 z y - 1/432 y + 1/72 y x + 1/108 z y x - 1/36 z y x + + 2 4 3 3 + - 1/108 y x z + 1/36 z y x - 1/216 y z - 1/108 y z - 1/216 y x z + + 2 2 2 4 2 2 2 2 2 + - 1/432 y x + 1/576 y x z - 1/576 y z - 1/72 y x z + 1/96 y x z + + 2 2 3 2 3 2 4 3 + - 1/288 y x z + 1/216 y z + 1/72 y x z - 1/144 x y + 1/216 y z + + 2 3 3 3 3 2 2 2 2 + - 1/432 y z - 1/216 y z + 1/288 y z - 1/288 y z + 1/576 y z + + 2 2 2 2 3 3 3 + + 1/144 y x - 1/72 y x + 1/216 y x + 1/108 y x , COEFF(-2, -1, -1) + + 4 2 4 2 4 2 2 4 3 + = 1/54 x y z + 1/48 x y z + 1/144 x y z - 1/36 x y z + + 4 3 3 3 3 4 3 3 3 3 + - 1/108 x y z + 2/27 y x z + 1/54 z y x - 1/54 y x z + + 2 4 4 3 2 3 3 2 3 3 + + 1/18 x y z - 1/27 z y x - 2/27 y x z + 4/27 z y x - 4/27 z y x + + 3 3 2 2 2 3 3 2 3 3 3 + + 1/72 y x z + 1/18 z y x + 2/27 y x - 1/18 z y x + 1/27 z y x + + 4 3 2 4 3 4 3 4 3 + + 1/108 y z - 1/72 z y x + 1/54 y x - 1/108 x y - 1/27 y x z + + 2 2 3 4 + + 1/27 y - 2/27 y x z + 1/27 y x z - 1/27 y x + 1/108 y + + 2 2 2 3 2 2 2 3 2 3 + - 1/12 y x z - 1/144 y x z + 1/9 y x z - 1/9 y x z + + 3 2 2 3 3 3 2 3 2 + - 1/48 y x z - 1/108 y + 1/108 y x + 1/54 z y - 1/27 y + 1/36 y x + + 3 3 2 2 4 + - 1/54 z y x - 1/18 z y x + 2/27 y x z + 2/9 z y x - 1/54 y z + + 3 3 2 2 2 4 2 + - 2/27 y z + 1/108 y x z + 1/27 y x - 1/36 y x z - 1/144 y z + + 2 2 2 2 2 2 3 2 3 + - 2/9 y x z + 1/12 y x z + 1/36 y x z + 2/27 y z + 1/36 y x z + + 2 4 3 2 3 3 3 3 2 + - 1/36 x y + 1/27 y z - 1/27 y z - 1/108 y z + 1/144 y z + + 2 2 2 2 2 2 2 3 3 3 + - 1/36 y z + 1/36 y z + 1/9 y x - 1/9 y x - 2/27 y x - 1/54 y x , + + 4 2 4 2 4 2 + COEFF(-1, -1, -1) = - 8/27 x y z - 1/24 x y z - 1/9 x y z + + 2 4 3 4 3 3 3 3 4 3 + + 1/18 x y z + 4/27 x y z - 8/27 y x z - 2/27 z y x + + 3 3 3 2 4 4 3 2 3 3 16 2 3 + + 2/27 y x z - 1/9 x y z + 4/27 z y x + 8/27 y x z - -- z y x + 27 + + 16 3 3 3 2 2 2 3 3 2 3 + + -- z y x - 1/18 y x z - 2/9 z y x - 8/27 y x + 2/9 z y x + 27 + + 3 3 4 3 2 4 3 4 3 4 + - 4/27 z y x - 2/27 y z + 1/18 z y x - 2/27 y x + 4/27 x y + + 16 3 32 2 16 2 3 16 4 + + -- y x z - 8/27 y + -- y x z - -- y x z + -- y x - 2/27 y + 27 27 27 27 + + 2 2 2 3 2 2 2 3 2 3 3 2 2 + + 1/6 y x z + 1/9 y x z - 2/9 y x z + 2/9 y x z + 1/24 y x z + + 3 3 3 2 3 2 3 + + 2/27 y - 4/27 y x - 4/27 z y + 8/27 y - 1/18 y x + 8/27 z y x + + 3 2 32 2 4 16 3 3 + + 1/9 z y x - -- y x z - 4/9 z y x + 4/27 y z + -- y z - 4/27 y x z + 27 27 + + 16 2 2 2 4 2 2 2 2 2 + - -- y x + 4/9 y x z + 1/18 y z + 4/9 y x z - 1/6 y x z + 27 + + 2 16 2 3 2 3 2 4 3 + - 4/9 y x z - -- y z - 1/18 y x z + 1/18 x y - 8/27 y z + 27 + + 2 3 3 3 3 2 2 2 2 2 2 + + 8/27 y z + 2/27 y z - 1/18 y z + 2/9 y z - 2/9 y z - 2/9 y x + + 2 2 3 3 3 4 + + 2/9 y x + 8/27 y x + 2/27 y x , COEFF(0, -1, -1) = 5/9 x y z + + 4 2 4 3 3 3 3 4 3 3 3 3 + + 5/24 x y z - 5/18 x y z + 4/9 y x z + 1/9 z y x - 1/9 y x z + + 4 3 2 3 3 2 3 3 3 3 2 + - 2/9 z y x - 4/9 y x z + 8/9 z y x - 8/9 z y x + 1/12 y x z + + 2 2 3 3 2 3 3 3 2 4 3 + + 1/3 z y x + 4/9 y x - 1/3 z y x + 2/9 z y x - 1/12 z y x + + 4 3 4 3 2 2 3 + + 1/9 y x - 5/18 x y - 10/9 y x z - 20/9 y x z + 10/9 y x z + + 3 2 3 3 + - 10/9 y x - 5/24 y x z + 5/18 y x - 5/9 z y x + 20/9 y x z + + 3 3 2 2 2 2 2 3 + + 5/18 y x z + 10/9 y x - 5/6 y x z + 5/6 y x z - 4/9 y x + + 3 3 4 2 4 2 + - 1/9 y x , COEFF(1, -1, -1) = - 8/27 x y z + 1/24 x y z + + 4 2 2 4 3 4 3 3 3 + - 1/9 x y z - 1/18 x y z + 4/27 x y z - 8/27 y x z + + 3 4 3 3 3 3 2 4 4 3 + - 2/27 z y x + 2/27 y x z + 1/9 x y z + 4/27 z y x + + 2 3 3 16 2 3 16 3 3 3 2 2 2 3 + + 8/27 y x z - -- z y x + -- z y x - 1/18 y x z - 2/9 z y x + 27 27 + + 3 2 3 3 3 4 3 2 4 3 + - 8/27 y x + 2/9 z y x - 4/27 z y x + 2/27 y z + 1/18 z y x + + 4 3 4 16 3 32 2 16 2 3 + - 2/27 y x + 4/27 x y + -- y x z + 8/27 y + -- y x z - -- y x z + 27 27 27 + + 16 4 2 2 2 3 2 2 2 3 + + -- y x + 2/27 y - 1/6 y x z + 1/9 y x z + 2/9 y x z + 27 + + 2 3 3 2 2 3 3 3 2 + - 2/9 y x z - 1/24 y x z - 2/27 y - 4/27 y x + 4/27 z y - 8/27 y + + 3 2 3 3 2 32 2 + + 1/18 y x + 8/27 z y x - 1/9 z y x - -- y x z + 4/9 z y x + 27 + + 4 16 3 3 16 2 2 2 4 2 + - 4/27 y z - -- y z - 4/27 y x z - -- y x + 4/9 y x z - 1/18 y z + 27 27 + + 2 2 2 2 2 16 2 3 2 3 + - 4/9 y x z + 1/6 y x z - 4/9 y x z + -- y z + 1/18 y x z + 27 + + 2 4 3 2 3 3 3 3 2 2 + - 1/18 x y + 8/27 y z - 8/27 y z - 2/27 y z + 1/18 y z - 2/9 y z + + 2 2 2 2 2 2 3 3 3 + + 2/9 y z + 2/9 y x - 2/9 y x + 8/27 y x + 2/27 y x , + + 4 2 4 2 4 2 + COEFF(2, -1, -1) = 1/54 x y z - 1/48 x y z + 1/144 x y z + + 2 4 3 4 3 3 3 3 4 3 + + 1/36 x y z - 1/108 x y z + 2/27 y x z + 1/54 z y x + + 3 3 3 2 4 4 3 2 3 3 + - 1/54 y x z - 1/18 x y z - 1/27 z y x - 2/27 y x z + + 2 3 3 3 3 2 2 2 3 3 + + 4/27 z y x - 4/27 z y x + 1/72 y x z + 1/18 z y x + 2/27 y x + + 2 3 3 3 4 3 2 4 3 4 3 + - 1/18 z y x + 1/27 z y x - 1/108 y z - 1/72 z y x + 1/54 y x + + 4 3 2 2 3 + - 1/108 x y - 1/27 y x z - 1/27 y - 2/27 y x z + 1/27 y x z + + 4 2 2 2 3 2 2 2 3 + - 1/27 y x - 1/108 y + 1/12 y x z - 1/144 y x z - 1/9 y x z + + 2 3 3 2 2 3 3 3 + + 1/9 y x z + 1/48 y x z + 1/108 y + 1/108 y x - 1/54 z y + + 2 3 2 3 3 2 + + 1/27 y - 1/36 y x - 1/54 z y x + 1/18 z y x + 2/27 y x z + + 2 4 3 3 2 + - 2/9 z y x + 1/54 y z + 2/27 y z + 1/108 y x z + 1/27 y x + + 2 2 4 2 2 2 2 2 2 + - 1/36 y x z + 1/144 y z + 2/9 y x z - 1/12 y x z + 1/36 y x z + + 2 3 2 3 2 4 3 2 3 + - 2/27 y z - 1/36 y x z + 1/36 x y - 1/27 y z + 1/27 y z + + 3 3 3 2 2 2 2 2 2 + + 1/108 y z - 1/144 y z + 1/36 y z - 1/36 y z - 1/9 y x + + 2 2 3 3 3 4 + + 1/9 y x - 2/27 y x - 1/54 y x , COEFF(-2, 0, -1) = - 1/36 x y z + + 2 4 2 4 2 2 4 3 4 3 + - 1/32 x y z - 1/96 x y z + 1/24 x y z + 1/72 x y z + + 3 4 3 2 4 4 3 2 3 3 + - 1/36 z y x - 1/12 x y z + 1/18 z y x + 5/36 y x z + + 2 3 2 2 3 4 3 2 4 3 3 2 + - 5/18 z y x - 5/48 z y x - 1/72 y z + 1/48 z y x + 1/12 x z + + 3 3 4 3 4 2 + - 1/9 x z + 1/18 x - 1/36 y x + 1/72 x y + 1/9 z + 5/36 y x z + + 2 3 4 2 2 2 2 2 3 3 + - 5/72 y x z - 1/72 y + 5/32 y x z - 5/24 y x z - 1/18 z + + 3 2 2 2 4 2 + - 1/9 x + 5/72 y + 1/24 z + 1/6 x + 1/36 y z - 5/72 y x + + 2 2 4 2 2 2 2 + + 5/96 y x z + 1/96 y z + 5/12 y x z - 5/36 y z - 1/9 x z + + 2 2 4 2 3 2 3 3 + - 1/3 x z - 1/18 + 1/24 x y + 5/72 y z + 1/6 x z + 1/18 x z + + 2 2 2 2 2 2 2 3 2 3 + - 1/8 x z - 1/24 x z - 5/96 y z - 5/24 y x + 2/9 z x + 5/36 y x , + + 4 2 4 2 4 2 2 4 3 + COEFF(-1, 0, -1) = 4/9 x y z + 1/16 x y z + 1/6 x y z - 1/12 x y z + + 4 3 3 4 3 2 4 4 3 2 3 3 + - 2/9 x y z + 1/9 z y x + 1/6 x y z - 2/9 z y x - 5/9 y x z + + 2 3 2 2 3 4 3 2 4 3 3 2 + + 10/9 z y x + 5/12 z y x + 1/9 y z - 1/12 z y x - 1/3 x z + + 3 3 4 3 4 2 + + 4/9 x z - 8/9 x + 1/9 y x - 2/9 x y - 8/9 z - 20/9 y x z + + 2 3 4 2 2 2 2 2 3 3 + + 10/9 y x z + 1/9 y - 5/16 y x z + 5/12 y x z + 4/9 + 4/9 z + + 3 2 2 2 4 2 2 2 + + 4/9 x - 5/9 y - 1/3 z - 1/3 x - 2/9 y z + 10/9 y x - 5/6 y x z + + 4 2 2 2 2 2 2 4 + - 1/12 y z - 5/6 y x z + 10/9 y z + 16/9 x z + 2/3 x z - 1/12 x y + + 2 3 2 3 3 2 2 2 2 2 + - 5/9 y z - 1/3 x z - 8/9 x z + 1/4 x z + 2/3 x z + 5/12 y z + + 2 2 3 2 3 2 4 3 + + 5/12 y x - 8/9 z x - 5/9 y x , COEFF(0, 0, -1) = 1/8 z y x + + 4 3 2 3 2 3 25 2 4 3 + + 5/12 x y z - 5/4 x z + 5/3 x z - 5/3 z y x - -- y x - 1/6 y x + 12 + + 3 4 3 2 3 4 2 + - 1/6 z y x + 5/6 y x - 5/6 x y z + 5/3 x + 25/6 y x z + + 4 3 2 2 3 4 3 2 + + 1/3 z y x - 5/8 z y x + 5/12 x y - 10/3 x z + 1/2 x z + + 4 2 3 3 3 2 3 3 25 2 2 3 + - 5/16 x y z + 4/3 z x - 2/3 x z + 5/6 y x z + -- y x z - 2/3 x + 16 + + 25 2 3 4 2 4 2 4 2 + - -- y x z , COEFF(1, 0, -1) = 4/9 x y z - 1/16 x y z + 1/6 x y z + 12 + + 2 4 3 4 3 3 4 3 2 4 4 3 + + 1/12 x y z - 2/9 x y z + 1/9 z y x - 1/6 x y z - 2/9 z y x + + 2 3 3 2 3 2 2 3 4 3 2 4 3 + - 5/9 y x z + 10/9 z y x + 5/12 z y x - 1/9 y z - 1/12 z y x + + 3 2 3 3 4 3 4 + - 1/3 x z + 4/9 x z - 8/9 x + 1/9 y x - 2/9 x y + 8/9 z + + 2 2 3 4 2 2 2 2 2 3 + - 20/9 y x z + 10/9 y x z - 1/9 y + 5/16 y x z - 5/12 y x z + + 3 3 2 2 2 4 2 + - 4/9 z + 4/9 x + 5/9 y + 1/3 z + 1/3 x + 2/9 y z - 4/9 + 10/9 y x + + 2 2 4 2 2 2 2 2 + - 5/6 y x z + 1/12 y z + 5/6 y x z - 10/9 y z + 16/9 x z - 2/3 x z + + 2 4 2 3 2 3 3 2 2 2 + + 1/12 x y + 5/9 y z + 1/3 x z - 8/9 x z - 1/4 x z + 2/3 x z + + 2 2 2 2 3 2 3 + - 5/12 y z - 5/12 y x - 8/9 z x - 5/9 y x , COEFF(2, 0, -1) = + + 4 2 4 2 4 2 2 4 3 4 3 + - 1/36 x y z + 1/32 x y z - 1/96 x y z - 1/24 x y z + 1/72 x y z + + 3 4 3 2 4 4 3 2 3 3 + - 1/36 z y x + 1/12 x y z + 1/18 z y x + 5/36 y x z + + 2 3 2 2 3 4 3 2 4 3 3 2 + - 5/18 z y x - 5/48 z y x + 1/72 y z + 1/48 z y x + 1/12 x z + + 3 3 4 3 4 2 + - 1/9 x z + 1/18 x - 1/36 y x + 1/72 x y - 1/9 z + 5/36 y x z + + 2 3 4 2 2 2 2 2 3 3 + - 5/72 y x z + 1/72 y - 5/32 y x z + 5/24 y x z + 1/18 z + + 3 2 2 2 4 2 + - 1/9 x - 5/72 y - 1/24 z - 1/6 x - 1/36 y z - 5/72 y x + + 2 2 4 2 2 2 2 + + 5/96 y x z - 1/96 y z - 5/12 y x z + 5/36 y z - 1/9 x z + + 2 2 4 2 3 2 3 3 + + 1/3 x z + 1/18 - 1/24 x y - 5/72 y z - 1/6 x z + 1/18 x z + + 2 2 2 2 2 2 2 3 2 3 + + 1/8 x z - 1/24 x z + 5/96 y z + 5/24 y x + 2/9 z x + 5/36 y x , + + 4 2 4 2 4 2 + COEFF(-2, 1, -1) = 1/54 x y z + 1/48 x y z + 1/144 x y z + + 2 4 3 4 3 3 3 3 4 3 + - 1/36 x y z - 1/108 x y z - 2/27 y x z + 1/54 z y x + + 3 3 3 2 4 4 3 2 3 3 + + 1/54 y x z + 1/18 x y z - 1/27 z y x - 2/27 y x z + + 2 3 3 3 3 2 2 2 3 3 + + 4/27 z y x + 4/27 z y x - 1/72 y x z + 1/18 z y x - 2/27 y x + + 2 3 3 3 4 3 2 4 3 4 3 + + 1/18 z y x - 1/27 z y x + 1/108 y z - 1/72 z y x + 1/54 y x + + 4 3 2 2 3 + - 1/108 x y + 1/27 y x z - 1/27 y - 2/27 y x z + 1/27 y x z + + 4 2 2 2 3 2 2 2 3 + + 1/27 y x + 1/108 y - 1/12 y x z + 1/144 y x z + 1/9 y x z + + 2 3 3 2 2 3 3 3 + + 1/9 y x z + 1/48 y x z + 1/108 y - 1/108 y x - 1/54 z y + + 2 3 2 3 3 2 + - 1/27 y - 1/36 y x + 1/54 z y x + 1/18 z y x - 2/27 y x z + + 2 4 3 3 2 + - 2/9 z y x - 1/54 y z + 2/27 y z - 1/108 y x z + 1/27 y x + + 2 2 4 2 2 2 2 2 2 + - 1/36 y x z - 1/144 y z - 2/9 y x z - 1/12 y x z - 1/36 y x z + + 2 3 2 3 2 4 3 2 3 + + 2/27 y z - 1/36 y x z - 1/36 x y - 1/27 y z - 1/27 y z + + 3 3 3 2 2 2 2 2 2 + + 1/108 y z - 1/144 y z + 1/36 y z + 1/36 y z + 1/9 y x + + 2 2 3 3 3 4 + + 1/9 y x - 2/27 y x + 1/54 y x , COEFF(-1, 1, -1) = - 8/27 x y z + + 2 4 2 4 2 2 4 3 4 3 + - 1/24 x y z - 1/9 x y z + 1/18 x y z + 4/27 x y z + + 3 3 3 4 3 3 3 3 2 4 + + 8/27 y x z - 2/27 z y x - 2/27 y x z - 1/9 x y z + + 4 3 2 3 3 16 2 3 16 3 3 3 2 + + 4/27 z y x + 8/27 y x z - -- z y x - -- z y x + 1/18 y x z + 27 27 + + 2 2 3 3 2 3 3 3 4 3 + - 2/9 z y x + 8/27 y x - 2/9 z y x + 4/27 z y x - 2/27 y z + + 2 4 3 4 3 4 16 3 32 2 + + 1/18 z y x - 2/27 y x + 4/27 x y - -- y x z + 8/27 y + -- y x z + 27 27 + + 16 2 3 16 4 2 2 2 3 2 + - -- y x z - -- y x - 2/27 y + 1/6 y x z - 1/9 y x z + 27 27 + + 2 2 3 2 3 3 2 2 3 3 + - 2/9 y x z - 2/9 y x z - 1/24 y x z - 2/27 y + 4/27 y x + + 3 2 3 2 3 3 2 32 + + 4/27 z y + 8/27 y + 1/18 y x - 8/27 z y x - 1/9 z y x + -- y x z + 27 + + 2 4 16 3 3 16 2 2 2 + + 4/9 z y x + 4/27 y z - -- y z + 4/27 y x z - -- y x + 4/9 y x z + 27 27 + + 4 2 2 2 2 2 2 16 2 + + 1/18 y z + 4/9 y x z + 1/6 y x z + 4/9 y x z - -- y z + 27 + + 3 2 3 2 4 3 2 3 3 3 + + 1/18 y x z + 1/18 x y + 8/27 y z + 8/27 y z - 2/27 y z + + 3 2 2 2 2 2 2 2 2 3 + + 1/18 y z - 2/9 y z - 2/9 y z - 2/9 y x - 2/9 y x + 8/27 y x + + 3 3 4 4 2 4 3 + - 2/27 y x , COEFF(0, 1, -1) = 5/9 x y z + 5/24 x y z - 5/18 x y z + + 3 3 3 4 3 3 3 3 4 3 2 3 3 + - 4/9 y x z + 1/9 z y x + 1/9 y x z - 2/9 z y x - 4/9 y x z + + 2 3 3 3 3 2 2 2 3 3 + + 8/9 z y x + 8/9 z y x - 1/12 y x z + 1/3 z y x - 4/9 y x + + 2 3 3 3 2 4 3 4 3 4 + + 1/3 z y x - 2/9 z y x - 1/12 z y x + 1/9 y x - 5/18 x y + + 3 2 2 3 3 2 + + 10/9 y x z - 20/9 y x z + 10/9 y x z + 10/9 y x + 5/24 y x z + + 3 3 3 3 2 + - 5/18 y x + 5/9 z y x - 20/9 y x z - 5/18 y x z + 10/9 y x + + 2 2 2 2 3 3 3 + - 5/6 y x z - 5/6 y x z - 4/9 y x + 1/9 y x , COEFF(1, 1, -1) = + + 4 2 4 2 4 2 2 4 3 4 3 + - 8/27 x y z + 1/24 x y z - 1/9 x y z - 1/18 x y z + 4/27 x y z + + 3 3 3 4 3 3 3 3 2 4 + + 8/27 y x z - 2/27 z y x - 2/27 y x z + 1/9 x y z + + 4 3 2 3 3 16 2 3 16 3 3 3 2 + + 4/27 z y x + 8/27 y x z - -- z y x - -- z y x + 1/18 y x z + 27 27 + + 2 2 3 3 2 3 3 3 4 3 + - 2/9 z y x + 8/27 y x - 2/9 z y x + 4/27 z y x + 2/27 y z + + 2 4 3 4 3 4 16 3 32 2 + + 1/18 z y x - 2/27 y x + 4/27 x y - -- y x z - 8/27 y + -- y x z + 27 27 + + 16 2 3 16 4 2 2 2 3 2 + - -- y x z - -- y x + 2/27 y - 1/6 y x z - 1/9 y x z + 27 27 + + 2 2 3 2 3 3 2 2 3 3 + + 2/9 y x z + 2/9 y x z + 1/24 y x z + 2/27 y + 4/27 y x + + 3 2 3 2 3 3 2 32 + - 4/27 z y - 8/27 y - 1/18 y x - 8/27 z y x + 1/9 z y x + -- y x z + 27 + + 2 4 16 3 3 16 2 2 2 + - 4/9 z y x - 4/27 y z + -- y z + 4/27 y x z - -- y x + 4/9 y x z + 27 27 + + 4 2 2 2 2 2 2 16 2 + - 1/18 y z - 4/9 y x z - 1/6 y x z + 4/9 y x z + -- y z + 27 + + 3 2 3 2 4 3 2 3 3 3 + - 1/18 y x z - 1/18 x y - 8/27 y z - 8/27 y z + 2/27 y z + + 3 2 2 2 2 2 2 2 2 3 + - 1/18 y z + 2/9 y z + 2/9 y z + 2/9 y x + 2/9 y x + 8/27 y x + + 3 3 4 2 4 2 + - 2/27 y x , COEFF(2, 1, -1) = 1/54 x y z - 1/48 x y z + + 4 2 2 4 3 4 3 3 3 + + 1/144 x y z + 1/36 x y z - 1/108 x y z - 2/27 y x z + + 3 4 3 3 3 3 2 4 4 3 + + 1/54 z y x + 1/54 y x z - 1/18 x y z - 1/27 z y x + + 2 3 3 2 3 3 3 3 2 + - 2/27 y x z + 4/27 z y x + 4/27 z y x - 1/72 y x z + + 2 2 3 3 2 3 3 3 4 3 + + 1/18 z y x - 2/27 y x + 1/18 z y x - 1/27 z y x - 1/108 y z + + 2 4 3 4 3 4 3 + - 1/72 z y x + 1/54 y x - 1/108 x y + 1/27 y x z + 1/27 y + + 2 2 3 4 2 2 2 + - 2/27 y x z + 1/27 y x z + 1/27 y x - 1/108 y + 1/12 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + + 1/144 y x z - 1/9 y x z - 1/9 y x z - 1/48 y x z - 1/108 y + + 3 3 2 3 2 3 + - 1/108 y x + 1/54 z y + 1/27 y + 1/36 y x + 1/54 z y x + + 3 2 2 4 + - 1/18 z y x - 2/27 y x z + 2/9 z y x + 1/54 y z - 2/27 y z + + 3 3 2 2 2 4 2 2 2 + - 1/108 y x z + 1/27 y x - 1/36 y x z + 1/144 y z + 2/9 y x z + + 2 2 2 2 3 2 3 2 4 + + 1/12 y x z - 1/36 y x z - 2/27 y z + 1/36 y x z + 1/36 x y + + 3 2 3 3 3 3 2 2 + + 1/27 y z + 1/27 y z - 1/108 y z + 1/144 y z - 1/36 y z + + 2 2 2 2 2 2 3 3 3 + - 1/36 y z - 1/9 y x - 1/9 y x - 2/27 y x + 1/54 y x , + + 4 2 4 2 4 2 + COEFF(-2, 2, -1) = - 1/216 x y z - 1/192 x y z - 1/576 x y z + + 2 4 3 4 3 3 3 3 4 3 + + 1/144 x y z + 1/432 x y z + 1/108 y x z - 1/216 z y x + + 3 3 3 2 4 4 3 2 3 3 + - 1/108 y x z - 1/72 x y z + 1/108 z y x + 1/216 y x z + + 2 3 3 3 3 2 2 2 3 + - 1/108 z y x - 1/54 z y x + 1/144 y x z - 1/288 z y x + + 3 2 3 3 3 4 3 2 4 3 + + 1/108 y x - 1/144 z y x + 1/54 z y x - 1/432 y z + 1/288 z y x + + 4 3 4 3 2 + - 1/216 y x + 1/432 x y - 1/216 y x z + 1/216 y + 1/216 y x z + + 2 3 4 2 2 2 3 2 + - 1/432 y x z - 1/216 y x - 1/432 y + 1/192 y x z - 1/288 y x z + + 2 2 3 2 3 3 2 2 3 3 + - 1/144 y x z - 1/72 y x z - 1/96 y x z - 1/216 y + 1/216 y x + + 3 2 3 2 3 3 2 + + 1/108 z y + 1/432 y + 1/72 y x - 1/108 z y x - 1/36 z y x + + 2 4 3 3 + + 1/108 y x z + 1/36 z y x + 1/216 y z - 1/108 y z + 1/216 y x z + + 2 2 2 4 2 2 2 2 2 + - 1/432 y x + 1/576 y x z + 1/576 y z + 1/72 y x z + 1/96 y x z + + 2 2 3 2 3 2 4 3 + + 1/288 y x z - 1/216 y z + 1/72 y x z + 1/144 x y + 1/216 y z + + 2 3 3 3 3 2 2 2 2 + + 1/432 y z - 1/216 y z + 1/288 y z - 1/288 y z - 1/576 y z + + 2 2 2 2 3 3 3 + - 1/144 y x - 1/72 y x + 1/216 y x - 1/108 y x , COEFF(-1, 2, -1) = + + 4 2 4 2 4 2 2 4 3 4 3 + 2/27 x y z + 1/96 x y z + 1/36 x y z - 1/72 x y z - 1/27 x y z + + 3 3 3 4 3 3 3 3 2 4 + - 1/27 y x z + 1/54 z y x + 1/27 y x z + 1/36 x y z + + 4 3 2 3 3 2 3 3 + - 1/27 z y x - 1/54 y x z + 1/27 z y x + 2/27 z y x + + 3 3 2 2 2 3 3 2 3 3 3 + - 1/36 y x z + 1/72 z y x - 1/27 y x + 1/36 z y x - 2/27 z y x + + 4 3 2 4 3 4 3 4 3 + + 1/54 y z - 1/72 z y x + 1/54 y x - 1/27 x y + 2/27 y x z + + 2 2 3 4 2 2 2 + - 1/27 y - 2/27 y x z + 1/27 y x z + 2/27 y x + 1/54 y - 1/96 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + + 1/18 y x z + 1/72 y x z + 1/36 y x z + 1/48 y x z + 1/27 y + + 3 3 2 3 2 3 + - 2/27 y x - 2/27 z y - 1/54 y - 1/36 y x + 4/27 z y x + + 3 2 2 4 + + 1/18 z y x - 4/27 y x z - 1/18 z y x - 1/27 y z + 2/27 y z + + 3 3 2 2 2 4 2 2 2 + - 2/27 y x z + 1/27 y x - 1/36 y x z - 1/72 y z - 1/36 y x z + + 2 2 2 2 3 2 3 2 4 + - 1/48 y x z - 1/18 y x z + 1/27 y z - 1/36 y x z - 1/72 x y + + 3 2 3 3 3 3 2 2 + - 1/27 y z - 1/54 y z + 1/27 y z - 1/36 y z + 1/36 y z + + 2 2 2 2 2 2 3 3 3 + + 1/72 y z + 1/72 y x + 1/36 y x - 1/54 y x + 1/27 y x , + + 4 4 2 4 3 + COEFF(0, 2, -1) = - 5/36 x y z - 5/96 x y z + 5/72 x y z + + 3 3 3 4 3 3 3 3 4 3 + + 1/18 y x z - 1/36 z y x - 1/18 y x z + 1/18 z y x + + 2 3 3 2 3 3 3 3 2 + + 1/36 y x z - 1/18 z y x - 1/9 z y x + 1/24 y x z + + 2 2 3 3 2 3 3 3 2 4 3 + - 1/48 z y x + 1/18 y x - 1/24 z y x + 1/9 z y x + 1/48 z y x + + 4 3 4 3 2 2 3 + - 1/36 y x + 5/72 x y - 5/36 y x z + 5/36 y x z - 5/72 y x z + + 3 2 3 3 + - 5/36 y x - 5/48 y x z + 5/36 y x - 5/18 z y x + 5/18 y x z + + 3 3 2 2 2 2 2 3 + + 5/36 y x z - 5/72 y x + 5/96 y x z + 5/48 y x z + 1/36 y x + + 3 3 4 2 4 2 4 2 + - 1/18 y x , COEFF(1, 2, -1) = 2/27 x y z - 1/96 x y z + 1/36 x y z + + 2 4 3 4 3 3 3 3 4 3 + + 1/72 x y z - 1/27 x y z - 1/27 y x z + 1/54 z y x + + 3 3 3 2 4 4 3 2 3 3 + + 1/27 y x z - 1/36 x y z - 1/27 z y x - 1/54 y x z + + 2 3 3 3 3 2 2 2 3 3 + + 1/27 z y x + 2/27 z y x - 1/36 y x z + 1/72 z y x - 1/27 y x + + 2 3 3 3 4 3 2 4 3 4 3 + + 1/36 z y x - 2/27 z y x - 1/54 y z - 1/72 z y x + 1/54 y x + + 4 3 2 2 3 + - 1/27 x y + 2/27 y x z + 1/27 y - 2/27 y x z + 1/27 y x z + 2/27 y x + + 4 2 2 2 3 2 2 2 3 2 3 + - 1/54 y + 1/96 y x z + 1/18 y x z - 1/72 y x z - 1/36 y x z + + 3 2 2 3 3 3 2 3 2 + - 1/48 y x z - 1/27 y - 2/27 y x + 2/27 z y + 1/54 y + 1/36 y x + + 3 3 2 2 4 + + 4/27 z y x - 1/18 z y x - 4/27 y x z + 1/18 z y x + 1/27 y z + + 3 3 2 2 2 4 2 + - 2/27 y z - 2/27 y x z + 1/27 y x - 1/36 y x z + 1/72 y z + + 2 2 2 2 2 2 3 2 3 + + 1/36 y x z + 1/48 y x z - 1/18 y x z - 1/27 y z + 1/36 y x z + + 2 4 3 2 3 3 3 3 2 + + 1/72 x y + 1/27 y z + 1/54 y z - 1/27 y z + 1/36 y z + + 2 2 2 2 2 2 2 3 + - 1/36 y z - 1/72 y z - 1/72 y x - 1/36 y x - 1/54 y x + + 3 3 4 2 4 2 + + 1/27 y x , COEFF(2, 2, -1) = - 1/216 x y z + 1/192 x y z + + 4 2 2 4 3 4 3 3 3 + - 1/576 x y z - 1/144 x y z + 1/432 x y z + 1/108 y x z + + 3 4 3 3 3 3 2 4 4 3 + - 1/216 z y x - 1/108 y x z + 1/72 x y z + 1/108 z y x + + 2 3 3 2 3 3 3 3 2 + + 1/216 y x z - 1/108 z y x - 1/54 z y x + 1/144 y x z + + 2 2 3 3 2 3 3 3 4 3 + - 1/288 z y x + 1/108 y x - 1/144 z y x + 1/54 z y x + 1/432 y z + + 2 4 3 4 3 4 3 + + 1/288 z y x - 1/216 y x + 1/432 x y - 1/216 y x z - 1/216 y + + 2 2 3 4 2 2 2 + + 1/216 y x z - 1/432 y x z - 1/216 y x + 1/432 y - 1/192 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + - 1/288 y x z + 1/144 y x z + 1/72 y x z + 1/96 y x z + 1/216 y + + 3 3 2 3 2 3 + + 1/216 y x - 1/108 z y - 1/432 y - 1/72 y x - 1/108 z y x + + 3 2 2 4 + + 1/36 z y x + 1/108 y x z - 1/36 z y x - 1/216 y z + 1/108 y z + + 3 3 2 2 2 4 2 2 2 + + 1/216 y x z - 1/432 y x + 1/576 y x z - 1/576 y z - 1/72 y x z + + 2 2 2 2 3 2 3 2 4 + - 1/96 y x z + 1/288 y x z + 1/216 y z - 1/72 y x z - 1/144 x y + + 3 2 3 3 3 3 2 2 + - 1/216 y z - 1/432 y z + 1/216 y z - 1/288 y z + 1/288 y z + + 2 2 2 2 2 2 3 3 3 + + 1/576 y z + 1/144 y x + 1/72 y x + 1/216 y x - 1/108 y x , + + 4 2 4 3 4 3 + COEFF(-2, -2, 0) = 5/576 x y z - 1/96 x y z - 1/288 x y z + + 3 3 3 4 3 3 3 3 2 4 + + 1/72 y x z + 1/144 z y x - 1/72 y x z + 5/192 x y z + + 4 3 2 3 3 2 3 3 + - 5/288 z y x - 1/144 y x z + 5/288 z y x - 5/144 z y x + + 3 3 4 3 3 2 + + 5/144 z y x + 1/288 y z - 1/144 y x z - 5/576 y x z + + 2 3 2 2 3 2 3 3 3 + + 1/288 y x z + 1/96 y x z - 1/48 y x z + 5/288 z y - 5/288 z y x + + 3 2 2 4 + - 5/96 z y x + 5/288 y x z + 5/96 z y x - 5/576 y z - 5/288 y z + + 3 3 2 2 2 3 2 3 3 + + 1/144 y x z - 5/192 y x z + 5/576 y z + 1/48 y x z + 1/144 y z + + 2 3 3 3 4 + - 1/288 y z - 1/144 y z , COEFF(-1, -2, 0) = - 5/36 x y z + + 2 4 3 4 3 3 3 3 4 3 + + 1/48 x y z + 1/18 x y z - 1/18 y x z - 1/36 z y x + + 3 3 3 2 4 4 3 2 3 3 + + 1/18 y x z - 5/96 x y z + 5/72 z y x + 1/36 y x z + + 2 3 3 3 3 4 3 3 + - 5/72 z y x + 5/36 z y x - 5/36 z y x - 1/36 y z + 1/9 y x z + + 2 2 3 2 2 3 2 3 3 + + 5/36 y x z - 1/18 y x z - 1/48 y x z + 1/24 y x z - 5/36 z y + + 3 3 2 2 4 + + 5/18 z y x + 5/48 z y x - 5/18 y x z - 5/48 z y x + 5/72 y z + + 3 3 2 2 2 3 2 3 + + 5/36 y z - 1/9 y x z + 5/96 y x z - 5/72 y z - 1/24 y x z + + 3 2 3 3 3 2 3 + - 1/18 y z + 1/36 y z + 1/18 y z , COEFF(0, -2, 0) = 5/48 z y x + + 4 3 25 3 25 4 25 2 3 + - 5/48 x y z - -- z y x + -- x y z - -- y x z - 5/24 y x z + 48 96 96 + + 3 3 3 3 3 2 3 3 3 + + 1/12 y x z - 1/12 y x z + 5/48 y x z + 5/24 z y x + + 4 3 3 4 3 25 2 3 3 3 3 + - 5/48 z y x + 1/24 z y x + -- y x z - 1/24 y x z + 5/24 y x z + 48 + + 3 4 2 4 3 + - 5/24 z y x , COEFF(1, -2, 0) = - 5/36 x y z - 1/48 x y z + + 4 3 3 3 3 4 3 3 3 3 + + 1/18 x y z - 1/18 y x z - 1/36 z y x + 1/18 y x z + + 2 4 4 3 2 3 3 2 3 3 + + 5/96 x y z + 5/72 z y x + 1/36 y x z - 5/72 z y x + 5/36 z y x + + 3 3 4 3 3 2 2 3 + - 5/36 z y x + 1/36 y z + 1/9 y x z + 5/36 y x z - 1/18 y x z + + 2 2 3 2 3 3 3 3 2 + + 1/48 y x z - 1/24 y x z + 5/36 z y + 5/18 z y x - 5/48 z y x + + 2 4 3 3 + - 5/18 y x z + 5/48 z y x - 5/72 y z - 5/36 y z - 1/9 y x z + + 2 2 2 3 2 3 3 2 3 + - 5/96 y x z + 5/72 y z + 1/24 y x z + 1/18 y z - 1/36 y z + + 3 3 4 2 4 3 + - 1/18 y z , COEFF(2, -2, 0) = 5/576 x y z + 1/96 x y z + + 4 3 3 3 3 4 3 3 3 3 + - 1/288 x y z + 1/72 y x z + 1/144 z y x - 1/72 y x z + + 2 4 4 3 2 3 3 2 3 + - 5/192 x y z - 5/288 z y x - 1/144 y x z + 5/288 z y x + + 3 3 3 4 3 3 2 + - 5/144 z y x + 5/144 z y x - 1/288 y z - 1/144 y x z - 5/576 y x z + + 2 3 2 2 3 2 3 3 3 + + 1/288 y x z - 1/96 y x z + 1/48 y x z - 5/288 z y - 5/288 z y x + + 3 2 2 4 + + 5/96 z y x + 5/288 y x z - 5/96 z y x + 5/576 y z + 5/288 y z + + 3 3 2 2 2 3 2 3 3 + + 1/144 y x z + 5/192 y x z - 5/576 y z - 1/48 y x z - 1/144 y z + + 2 3 3 3 4 + + 1/288 y z + 1/144 y z , COEFF(-2, -1, 0) = - 5/144 x y z + + 2 4 3 4 3 3 3 3 4 3 + + 1/24 x y z + 1/72 x y z - 1/9 y x z - 1/36 z y x + + 3 3 3 2 4 4 3 2 3 3 + + 1/36 y x z - 5/48 x y z + 5/72 z y x + 1/9 y x z + + 2 3 3 3 3 4 3 3 + - 5/18 z y x + 5/18 z y x - 5/72 z y x - 1/72 y z + 1/18 y x z + + 2 2 3 2 2 3 2 3 3 + + 5/36 y x z - 1/18 y x z - 1/6 y x z + 1/6 y x z - 5/144 z y + + 3 3 2 2 4 + + 5/144 z y x + 5/48 z y x - 5/36 y x z - 5/12 z y x + 5/144 y z + + 3 3 2 2 2 3 2 3 + + 5/36 y z - 1/72 y x z + 5/12 y x z - 5/36 y z - 1/24 y x z + + 3 2 3 3 3 4 + - 1/18 y z + 1/18 y z + 1/72 y z , COEFF(-1, -1, 0) = 5/9 x y z + + 2 4 3 4 3 3 3 3 4 3 3 3 3 + - 1/12 x y z - 2/9 x y z + 4/9 y x z + 1/9 z y x - 1/9 y x z + + 2 4 4 3 2 3 3 2 3 3 + + 5/24 x y z - 5/18 z y x - 4/9 y x z + 10/9 z y x - 10/9 z y x + + 3 3 4 3 3 2 2 3 + + 5/18 z y x + 1/9 y z - 8/9 y x z - 20/9 y x z + 8/9 y x z + + 2 2 3 2 3 3 3 3 2 + + 1/3 y x z - 1/3 y x z + 5/18 z y - 5/9 z y x - 5/24 z y x + + 2 4 3 3 + + 20/9 y x z + 5/6 z y x - 5/18 y z - 10/9 y z + 2/9 y x z + + 2 2 2 3 2 3 3 2 3 + - 5/6 y x z + 10/9 y z + 1/12 y x z + 4/9 y z - 4/9 y z + + 3 3 2 3 3 2 3 3 + - 1/9 y z , COEFF(0, -1, 0) = - 5/3 y x z + 5/3 z y x + 2/3 y x z + + 3 3 2 3 3 3 3 25 3 + - 5/12 z y x + 25/6 y x z - 5/12 y x z - 2/3 y x z + -- z y x + 24 + + 4 3 4 3 3 3 3 25 4 + + 5/12 z y x + 5/12 x y z + 1/6 y x z - 25/6 y x z - -- x y z + 24 + + 3 3 4 3 2 3 4 + + 5/3 y x z - 1/6 z y x - 5/3 z y x , COEFF(1, -1, 0) = 5/9 x y z + + 2 4 3 4 3 3 3 3 4 3 3 3 3 + + 1/12 x y z - 2/9 x y z + 4/9 y x z + 1/9 z y x - 1/9 y x z + + 2 4 4 3 2 3 3 2 3 3 + - 5/24 x y z - 5/18 z y x - 4/9 y x z + 10/9 z y x - 10/9 z y x + + 3 3 4 3 3 2 2 3 + + 5/18 z y x - 1/9 y z - 8/9 y x z - 20/9 y x z + 8/9 y x z + + 2 2 3 2 3 3 3 3 2 + - 1/3 y x z + 1/3 y x z - 5/18 z y - 5/9 z y x + 5/24 z y x + + 2 4 3 3 + + 20/9 y x z - 5/6 z y x + 5/18 y z + 10/9 y z + 2/9 y x z + + 2 2 2 3 2 3 3 2 3 + + 5/6 y x z - 10/9 y z - 1/12 y x z - 4/9 y z + 4/9 y z + + 3 3 4 2 4 3 + + 1/9 y z , COEFF(2, -1, 0) = - 5/144 x y z - 1/24 x y z + + 4 3 3 3 3 4 3 3 3 3 + + 1/72 x y z - 1/9 y x z - 1/36 z y x + 1/36 y x z + + 2 4 4 3 2 3 3 2 3 3 + + 5/48 x y z + 5/72 z y x + 1/9 y x z - 5/18 z y x + 5/18 z y x + + 3 3 4 3 3 2 2 3 + - 5/72 z y x + 1/72 y z + 1/18 y x z + 5/36 y x z - 1/18 y x z + + 2 2 3 2 3 3 3 3 2 + + 1/6 y x z - 1/6 y x z + 5/144 z y + 5/144 z y x - 5/48 z y x + + 2 4 3 3 + - 5/36 y x z + 5/12 z y x - 5/144 y z - 5/36 y z - 1/72 y x z + + 2 2 2 3 2 3 3 2 3 + - 5/12 y x z + 5/36 y z + 1/24 y x z + 1/18 y z - 1/18 y z + + 3 3 25 2 25 2 3 4 3 + - 1/72 y z , COEFF(-2, 0, 0) = -- y z + -- z y x - 5/48 z y x + 96 48 + + 3 3 2 3 3 25 2 2 2 4 + + 1/6 x z - 5/24 y x z + 5/24 x z - -- y x z + 5/32 x y z + 32 + + 2 3 2 3 25 2 4 3 2 3 + - 5/48 y z - 1/4 x z - -- y x z + 1/48 y z + 5/8 x z + 1/12 z + 96 + + 3 2 3 4 4 2 2 3 + - 5/12 z x + 5/48 y x z - 5/96 y z + 5/96 x y z + 5/16 y x z + + 2 4 3 3 3 4 3 4 3 + - 5/24 z - 1/16 x y z - 1/12 x z + 1/24 z y x - 1/48 x y z , + + 2 4 3 3 3 3 4 3 + COEFF(-1, 0, 0) = 1/8 x y z - 2/3 z + 5/3 z x - 1/6 z y x + + 2 3 4 3 2 3 2 3 + - 5/3 y x z - 10/3 x z + 5/12 z y x + 5/6 y z + 5/3 z + 1/2 x z + + 2 4 25 2 2 4 3 4 4 3 + - 5/16 x y z + -- y x z - 1/6 y z - 5/6 x y z + 1/3 x y z + 16 + + 2 2 2 3 4 3 2 + - 5/4 x z - 5/8 y x z + 5/12 y z + 4/3 x z + 25/6 y x z + + 2 3 3 25 2 25 2 3 3 3 + + 5/6 y x z - -- y z - -- z y x - 2/3 x z , COEFF(0, 0, 0) = + 12 12 + + 3 125 2 2 3 2 3 3 4 3 + - 5/2 x z - --- y x z + 25/8 z y x - 5/4 y x z - 5/8 z y x + 16 + + 4 3 25 4 3 4 3 2 3 3 3 3 + - 5/8 x y z + -- x y z + 1/4 z y x + 25/8 y x z + x z - 5/2 z x + 16 + + 2 2 3 2 2 3 + + 25/4 x z, COEFF(1, 0, 0) = 5/8 y x z + 25/6 y x z - 1/2 x z + + 2 4 3 3 3 4 25 2 3 + + 5/4 x z + 1/3 x y z - 2/3 x z - 5/12 y z - -- z y x + 12 + + 2 3 3 25 2 2 3 4 2 3 + + 5/6 y x z - -- y x z + 2/3 z - 5/6 x y z - 5/3 z - 5/6 y z + 16 + + 3 3 25 2 2 4 3 3 4 3 + + 4/3 x z + 5/3 z x + -- y z - 1/8 x y z - 10/3 x z - 1/6 z y x + 12 + + 4 3 4 3 2 4 2 3 + + 5/12 z y x + 1/6 y z + 5/16 x y z - 5/3 y x z , COEFF(2, 0, 0) = + + 2 3 3 2 3 3 3 25 2 3 + 5/24 z - 5/24 y x z + 5/48 y z - 5/12 z x - 1/12 z + -- z y x + 48 + + 2 3 3 3 4 3 2 + + 5/48 y x z + 5/24 x z + 1/6 x z - 1/48 x y z - 5/8 x z + + 2 3 3 4 2 2 3 25 2 2 + + 1/4 x z - 1/12 x z + 5/96 x y z - 5/16 y x z + -- y x z + 32 + + 3 4 3 25 2 4 3 4 3 2 4 + + 1/24 z y x - -- y x z - 5/48 z y x - 1/48 y z - 5/32 x y z + 96 + + 2 4 3 25 2 4 4 + + 1/16 x y z - -- y z + 5/96 y z, COEFF(-2, 1, 0) = - 5/144 x y z + 96 + + 2 4 3 4 3 3 3 3 4 3 + + 1/24 x y z + 1/72 x y z + 1/9 y x z - 1/36 z y x + + 3 3 3 2 4 4 3 2 3 3 + - 1/36 y x z - 5/48 x y z + 5/72 z y x + 1/9 y x z + + 2 3 3 3 3 4 3 3 + - 5/18 z y x - 5/18 z y x + 5/72 z y x - 1/72 y z - 1/18 y x z + + 2 2 3 2 2 3 2 3 3 + + 5/36 y x z - 1/18 y x z - 1/6 y x z - 1/6 y x z + 5/144 z y + + 3 3 2 2 4 + - 5/144 z y x - 5/48 z y x + 5/36 y x z + 5/12 z y x + 5/144 y z + + 3 3 2 2 2 3 2 3 + - 5/36 y z + 1/72 y x z + 5/12 y x z - 5/36 y z + 1/24 y x z + + 3 2 3 3 3 4 + + 1/18 y z + 1/18 y z - 1/72 y z , COEFF(-1, 1, 0) = 5/9 x y z + + 2 4 3 4 3 3 3 3 4 3 3 3 3 + - 1/12 x y z - 2/9 x y z - 4/9 y x z + 1/9 z y x + 1/9 y x z + + 2 4 4 3 2 3 3 2 3 3 + + 5/24 x y z - 5/18 z y x - 4/9 y x z + 10/9 z y x + 10/9 z y x + + 3 3 4 3 3 2 2 3 + - 5/18 z y x + 1/9 y z + 8/9 y x z - 20/9 y x z + 8/9 y x z + + 2 2 3 2 3 3 3 3 2 + + 1/3 y x z + 1/3 y x z - 5/18 z y + 5/9 z y x + 5/24 z y x + + 2 4 3 3 + - 20/9 y x z - 5/6 z y x - 5/18 y z + 10/9 y z - 2/9 y x z + + 2 2 2 3 2 3 3 2 3 + - 5/6 y x z + 10/9 y z - 1/12 y x z - 4/9 y z - 4/9 y z + + 3 3 2 3 3 + + 1/9 y z , COEFF(0, 1, 0) = 25/6 y x z + 25/6 y x z + 2/3 y x z + + 2 3 3 2 3 4 3 3 + - 5/3 z y x - 5/3 y x z - 5/3 y x z + 5/12 x y z - 5/3 z y x + + 2 3 3 3 3 25 3 3 3 3 3 3 + + 2/3 y x z + 5/12 y x z - -- z y x - 1/6 y x z + 5/12 z y x + 24 + + 25 4 4 3 3 4 3 4 + - -- x y z + 5/12 z y x - 1/6 z y x , COEFF(1, 1, 0) = 5/9 x y z + 24 + + 2 4 3 4 3 3 3 3 4 3 3 3 3 + + 1/12 x y z - 2/9 x y z - 4/9 y x z + 1/9 z y x + 1/9 y x z + + 2 4 4 3 2 3 3 2 3 3 + - 5/24 x y z - 5/18 z y x - 4/9 y x z + 10/9 z y x + 10/9 z y x + + 3 3 4 3 3 2 2 3 + - 5/18 z y x - 1/9 y z + 8/9 y x z - 20/9 y x z + 8/9 y x z + + 2 2 3 2 3 3 3 3 2 + - 1/3 y x z - 1/3 y x z + 5/18 z y + 5/9 z y x - 5/24 z y x + + 2 4 3 3 + - 20/9 y x z + 5/6 z y x + 5/18 y z - 10/9 y z - 2/9 y x z + + 2 2 2 3 2 3 3 2 3 + + 5/6 y x z - 10/9 y z + 1/12 y x z + 4/9 y z + 4/9 y z + + 3 3 4 2 4 3 + - 1/9 y z , COEFF(2, 1, 0) = - 5/144 x y z - 1/24 x y z + + 4 3 3 3 3 4 3 3 3 3 + + 1/72 x y z + 1/9 y x z - 1/36 z y x - 1/36 y x z + + 2 4 4 3 2 3 3 2 3 3 + + 5/48 x y z + 5/72 z y x + 1/9 y x z - 5/18 z y x - 5/18 z y x + + 3 3 4 3 3 2 2 3 + + 5/72 z y x + 1/72 y z - 1/18 y x z + 5/36 y x z - 1/18 y x z + + 2 2 3 2 3 3 3 3 2 + + 1/6 y x z + 1/6 y x z - 5/144 z y - 5/144 z y x + 5/48 z y x + + 2 4 3 3 + + 5/36 y x z - 5/12 z y x - 5/144 y z + 5/36 y z + 1/72 y x z + + 2 2 2 3 2 3 3 2 3 + - 5/12 y x z + 5/36 y z - 1/24 y x z - 1/18 y z - 1/18 y z + + 3 3 4 2 4 3 + + 1/72 y z , COEFF(-2, 2, 0) = 5/576 x y z - 1/96 x y z + + 4 3 3 3 3 4 3 3 3 3 + - 1/288 x y z - 1/72 y x z + 1/144 z y x + 1/72 y x z + + 2 4 4 3 2 3 3 2 3 + + 5/192 x y z - 5/288 z y x - 1/144 y x z + 5/288 z y x + + 3 3 3 4 3 3 2 + + 5/144 z y x - 5/144 z y x + 1/288 y z + 1/144 y x z - 5/576 y x z + + 2 3 2 2 3 2 3 3 3 + + 1/288 y x z + 1/96 y x z + 1/48 y x z - 5/288 z y + 5/288 z y x + + 3 2 2 4 + + 5/96 z y x - 5/288 y x z - 5/96 z y x - 5/576 y z + 5/288 y z + + 3 3 2 2 2 3 2 3 3 + - 1/144 y x z - 5/192 y x z + 5/576 y z - 1/48 y x z - 1/144 y z + + 2 3 3 3 4 + - 1/288 y z + 1/144 y z , COEFF(-1, 2, 0) = - 5/36 x y z + + 2 4 3 4 3 3 3 3 4 3 + + 1/48 x y z + 1/18 x y z + 1/18 y x z - 1/36 z y x + + 3 3 3 2 4 4 3 2 3 3 + - 1/18 y x z - 5/96 x y z + 5/72 z y x + 1/36 y x z + + 2 3 3 3 3 4 3 3 + - 5/72 z y x - 5/36 z y x + 5/36 z y x - 1/36 y z - 1/9 y x z + + 2 2 3 2 2 3 2 3 3 + + 5/36 y x z - 1/18 y x z - 1/48 y x z - 1/24 y x z + 5/36 z y + + 3 3 2 2 4 + - 5/18 z y x - 5/48 z y x + 5/18 y x z + 5/48 z y x + 5/72 y z + + 3 3 2 2 2 3 2 3 + - 5/36 y z + 1/9 y x z + 5/96 y x z - 5/72 y z + 1/24 y x z + + 3 2 3 3 3 4 3 + + 1/18 y z + 1/36 y z - 1/18 y z , COEFF(0, 2, 0) = - 5/48 x y z + + 2 3 3 3 3 3 3 25 4 3 3 + + 5/48 z y x - 1/12 y x z + 1/12 y x z + -- x y z - 5/24 z y x + 96 + + 4 3 25 25 3 3 3 + - 5/48 z y x - -- y x z + -- z y x + 5/24 y x z + 5/24 z y x + 48 48 + + 3 3 2 3 3 25 2 3 4 3 2 3 + - 5/24 y x z - 1/24 y x z - -- y x z + 1/24 z y x + 5/48 y x z , + 96 + + 4 2 4 3 4 3 + COEFF(1, 2, 0) = - 5/36 x y z - 1/48 x y z + 1/18 x y z + + 3 3 3 4 3 3 3 3 2 4 + + 1/18 y x z - 1/36 z y x - 1/18 y x z + 5/96 x y z + + 4 3 2 3 3 2 3 3 3 3 + + 5/72 z y x + 1/36 y x z - 5/72 z y x - 5/36 z y x + 5/36 z y x + + 4 3 3 2 2 3 2 2 3 + + 1/36 y z - 1/9 y x z + 5/36 y x z - 1/18 y x z + 1/48 y x z + + 2 3 3 3 3 2 + + 1/24 y x z - 5/36 z y - 5/18 z y x + 5/48 z y x + 5/18 y x z + + 2 4 3 3 2 2 + - 5/48 z y x - 5/72 y z + 5/36 y z + 1/9 y x z - 5/96 y x z + + 2 3 2 3 3 2 3 3 3 + + 5/72 y z - 1/24 y x z - 1/18 y z - 1/36 y z + 1/18 y z , + + 4 2 4 3 4 3 + COEFF(2, 2, 0) = 5/576 x y z + 1/96 x y z - 1/288 x y z + + 3 3 3 4 3 3 3 3 2 4 + - 1/72 y x z + 1/144 z y x + 1/72 y x z - 5/192 x y z + + 4 3 2 3 3 2 3 3 + - 5/288 z y x - 1/144 y x z + 5/288 z y x + 5/144 z y x + + 3 3 4 3 3 2 + - 5/144 z y x - 1/288 y z + 1/144 y x z - 5/576 y x z + + 2 3 2 2 3 2 3 3 3 + + 1/288 y x z - 1/96 y x z - 1/48 y x z + 5/288 z y + 5/288 z y x + + 3 2 2 4 + - 5/96 z y x - 5/288 y x z + 5/96 z y x + 5/576 y z - 5/288 y z + + 3 3 2 2 2 3 2 3 3 + - 1/144 y x z + 5/192 y x z - 5/576 y z + 1/48 y x z + 1/144 y z + + 2 3 3 3 4 + + 1/288 y z - 1/144 y z , COEFF(-2, -2, 1) = - 1/216 x y z + + 2 4 2 4 2 2 4 3 4 3 + + 1/192 x y z + 1/576 x y z + 1/144 x y z + 1/432 x y z + + 3 3 3 4 3 3 3 3 2 4 + - 1/108 y x z - 1/216 z y x + 1/108 y x z - 1/72 x y z + + 4 3 2 3 3 2 3 3 + + 1/108 z y x + 1/216 y x z - 1/108 z y x + 1/54 z y x + + 3 3 2 2 2 3 3 2 3 + + 1/144 y x z + 1/288 z y x + 1/108 y x - 1/144 z y x + + 3 3 4 3 2 4 3 4 3 4 + - 1/54 z y x - 1/432 y z - 1/288 z y x + 1/216 y x - 1/432 x y + + 3 2 2 3 + + 1/216 y x z + 1/216 y + 1/216 y x z - 1/432 y x z - 1/216 y x + + 4 2 2 2 3 2 2 2 3 + + 1/432 y - 1/192 y x z - 1/288 y x z - 1/144 y x z + + 2 3 3 2 2 3 3 3 + + 1/72 y x z - 1/96 y x z - 1/216 y + 1/216 y x - 1/108 z y + + 2 3 2 3 3 2 + - 1/432 y + 1/72 y x + 1/108 z y x + 1/36 z y x - 1/108 y x z + + 2 4 3 3 2 + - 1/36 z y x + 1/216 y z + 1/108 y z - 1/216 y x z + 1/432 y x + + 2 2 4 2 2 2 2 2 2 + - 1/576 y x z - 1/576 y z + 1/72 y x z + 1/96 y x z + 1/288 y x z + + 2 3 2 3 2 4 3 2 3 + - 1/216 y z - 1/72 y x z - 1/144 x y - 1/216 y z + 1/432 y z + + 3 3 3 2 2 2 2 2 2 + + 1/216 y z + 1/288 y z - 1/288 y z + 1/576 y z + 1/144 y x + + 2 2 3 3 3 4 + - 1/72 y x - 1/216 y x - 1/108 y x , COEFF(-1, -2, 1) = 2/27 x y z + + 2 4 2 4 2 2 4 3 4 3 + - 1/96 x y z - 1/36 x y z - 1/72 x y z - 1/27 x y z + + 3 3 3 4 3 3 3 3 2 4 + + 1/27 y x z + 1/54 z y x - 1/27 y x z + 1/36 x y z + + 4 3 2 3 3 2 3 3 + - 1/27 z y x - 1/54 y x z + 1/27 z y x - 2/27 z y x + + 3 3 2 2 2 3 3 2 3 3 3 + - 1/36 y x z - 1/72 z y x - 1/27 y x + 1/36 z y x + 2/27 z y x + + 4 3 2 4 3 4 3 4 3 + + 1/54 y z + 1/72 z y x - 1/54 y x + 1/27 x y - 2/27 y x z + + 2 2 3 4 2 2 2 + - 1/27 y - 2/27 y x z + 1/27 y x z + 2/27 y x - 1/54 y + 1/96 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + + 1/18 y x z + 1/72 y x z - 1/36 y x z + 1/48 y x z + 1/27 y + + 3 3 2 3 2 3 + - 2/27 y x + 2/27 z y + 1/54 y - 1/36 y x - 4/27 z y x + + 3 2 2 4 + - 1/18 z y x + 4/27 y x z + 1/18 z y x - 1/27 y z - 2/27 y z + + 3 3 2 2 2 4 2 2 2 + + 2/27 y x z - 1/27 y x + 1/36 y x z + 1/72 y z - 1/36 y x z + + 2 2 2 2 3 2 3 2 4 + - 1/48 y x z - 1/18 y x z + 1/27 y z + 1/36 y x z + 1/72 x y + + 3 2 3 3 3 3 2 2 + + 1/27 y z - 1/54 y z - 1/27 y z - 1/36 y z + 1/36 y z + + 2 2 2 2 2 2 3 3 3 + - 1/72 y z - 1/72 y x + 1/36 y x + 1/54 y x + 1/27 y x , + + 4 4 2 4 3 + COEFF(0, -2, 1) = - 5/36 x y z + 5/96 x y z + 5/72 x y z + + 3 3 3 4 3 3 3 3 4 3 + - 1/18 y x z - 1/36 z y x + 1/18 y x z + 1/18 z y x + + 2 3 3 2 3 3 3 3 2 + + 1/36 y x z - 1/18 z y x + 1/9 z y x + 1/24 y x z + + 2 2 3 3 2 3 3 3 2 4 3 + + 1/48 z y x + 1/18 y x - 1/24 z y x - 1/9 z y x - 1/48 z y x + + 4 3 4 3 2 2 3 + + 1/36 y x - 5/72 x y + 5/36 y x z + 5/36 y x z - 5/72 y x z + + 3 2 3 3 + - 5/36 y x - 5/48 y x z + 5/36 y x + 5/18 z y x - 5/18 y x z + + 3 3 2 2 2 2 2 3 + - 5/36 y x z + 5/72 y x - 5/96 y x z + 5/48 y x z - 1/36 y x + + 3 3 4 2 4 2 4 2 + - 1/18 y x , COEFF(1, -2, 1) = 2/27 x y z + 1/96 x y z - 1/36 x y z + + 2 4 3 4 3 3 3 3 4 3 + + 1/72 x y z - 1/27 x y z + 1/27 y x z + 1/54 z y x + + 3 3 3 2 4 4 3 2 3 3 + - 1/27 y x z - 1/36 x y z - 1/27 z y x - 1/54 y x z + + 2 3 3 3 3 2 2 2 3 3 + + 1/27 z y x - 2/27 z y x - 1/36 y x z - 1/72 z y x - 1/27 y x + + 2 3 3 3 4 3 2 4 3 4 3 + + 1/36 z y x + 2/27 z y x - 1/54 y z + 1/72 z y x - 1/54 y x + + 4 3 2 2 3 + + 1/27 x y - 2/27 y x z + 1/27 y - 2/27 y x z + 1/27 y x z + 2/27 y x + + 4 2 2 2 3 2 2 2 3 2 3 + + 1/54 y - 1/96 y x z + 1/18 y x z - 1/72 y x z + 1/36 y x z + + 3 2 2 3 3 3 2 3 2 + - 1/48 y x z - 1/27 y - 2/27 y x - 2/27 z y - 1/54 y + 1/36 y x + + 3 3 2 2 4 + - 4/27 z y x + 1/18 z y x + 4/27 y x z - 1/18 z y x + 1/27 y z + + 3 3 2 2 2 4 2 + + 2/27 y z + 2/27 y x z - 1/27 y x + 1/36 y x z - 1/72 y z + + 2 2 2 2 2 2 3 2 3 + + 1/36 y x z + 1/48 y x z - 1/18 y x z - 1/27 y z - 1/36 y x z + + 2 4 3 2 3 3 3 3 2 + - 1/72 x y - 1/27 y z + 1/54 y z + 1/27 y z + 1/36 y z + + 2 2 2 2 2 2 2 3 + - 1/36 y z + 1/72 y z + 1/72 y x - 1/36 y x + 1/54 y x + + 3 3 4 2 4 2 + + 1/27 y x , COEFF(2, -2, 1) = - 1/216 x y z - 1/192 x y z + + 4 2 2 4 3 4 3 3 3 + + 1/576 x y z - 1/144 x y z + 1/432 x y z - 1/108 y x z + + 3 4 3 3 3 3 2 4 4 3 + - 1/216 z y x + 1/108 y x z + 1/72 x y z + 1/108 z y x + + 2 3 3 2 3 3 3 3 2 + + 1/216 y x z - 1/108 z y x + 1/54 z y x + 1/144 y x z + + 2 2 3 3 2 3 3 3 4 3 + + 1/288 z y x + 1/108 y x - 1/144 z y x - 1/54 z y x + 1/432 y z + + 2 4 3 4 3 4 3 + - 1/288 z y x + 1/216 y x - 1/432 x y + 1/216 y x z - 1/216 y + + 2 2 3 4 2 2 2 + + 1/216 y x z - 1/432 y x z - 1/216 y x - 1/432 y + 1/192 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + - 1/288 y x z + 1/144 y x z - 1/72 y x z + 1/96 y x z + 1/216 y + + 3 3 2 3 2 3 + + 1/216 y x + 1/108 z y + 1/432 y - 1/72 y x + 1/108 z y x + + 3 2 2 4 + - 1/36 z y x - 1/108 y x z + 1/36 z y x - 1/216 y z - 1/108 y z + + 3 3 2 2 2 4 2 2 2 + - 1/216 y x z + 1/432 y x - 1/576 y x z + 1/576 y z - 1/72 y x z + + 2 2 2 2 3 2 3 2 4 + - 1/96 y x z + 1/288 y x z + 1/216 y z + 1/72 y x z + 1/144 x y + + 3 2 3 3 3 3 2 2 + + 1/216 y z - 1/432 y z - 1/216 y z - 1/288 y z + 1/288 y z + + 2 2 2 2 2 2 3 3 3 + - 1/576 y z - 1/144 y x + 1/72 y x - 1/216 y x - 1/108 y x , + + 4 2 4 2 4 2 + COEFF(-2, -1, 1) = 1/54 x y z - 1/48 x y z - 1/144 x y z + + 2 4 3 4 3 3 3 3 4 3 + - 1/36 x y z - 1/108 x y z + 2/27 y x z + 1/54 z y x + + 3 3 3 2 4 4 3 2 3 3 + - 1/54 y x z + 1/18 x y z - 1/27 z y x - 2/27 y x z + + 2 3 3 3 3 2 2 2 3 3 + + 4/27 z y x - 4/27 z y x - 1/72 y x z - 1/18 z y x - 2/27 y x + + 2 3 3 3 4 3 2 4 3 4 3 + + 1/18 z y x + 1/27 z y x + 1/108 y z + 1/72 z y x - 1/54 y x + + 4 3 2 2 3 + + 1/108 x y - 1/27 y x z - 1/27 y - 2/27 y x z + 1/27 y x z + + 4 2 2 2 3 2 2 2 3 + + 1/27 y x - 1/108 y + 1/12 y x z + 1/144 y x z + 1/9 y x z + + 2 3 3 2 2 3 3 3 + - 1/9 y x z + 1/48 y x z + 1/108 y - 1/108 y x + 1/54 z y + + 2 3 2 3 3 2 + + 1/27 y - 1/36 y x - 1/54 z y x - 1/18 z y x + 2/27 y x z + + 2 4 3 3 2 + + 2/9 z y x - 1/54 y z - 2/27 y z + 1/108 y x z - 1/27 y x + + 2 2 4 2 2 2 2 2 2 + + 1/36 y x z + 1/144 y z - 2/9 y x z - 1/12 y x z - 1/36 y x z + + 2 3 2 3 2 4 3 2 3 + + 2/27 y z + 1/36 y x z + 1/36 x y + 1/27 y z - 1/27 y z + + 3 3 3 2 2 2 2 2 2 + - 1/108 y z - 1/144 y z + 1/36 y z - 1/36 y z - 1/9 y x + + 2 2 3 3 3 4 + + 1/9 y x + 2/27 y x + 1/54 y x , COEFF(-1, -1, 1) = - 8/27 x y z + + 2 4 2 4 2 2 4 3 4 3 + + 1/24 x y z + 1/9 x y z + 1/18 x y z + 4/27 x y z + + 3 3 3 4 3 3 3 3 2 4 + - 8/27 y x z - 2/27 z y x + 2/27 y x z - 1/9 x y z + + 4 3 2 3 3 16 2 3 16 3 3 3 2 + + 4/27 z y x + 8/27 y x z - -- z y x + -- z y x + 1/18 y x z + 27 27 + + 2 2 3 3 2 3 3 3 4 3 + + 2/9 z y x + 8/27 y x - 2/9 z y x - 4/27 z y x - 2/27 y z + + 2 4 3 4 3 4 16 3 32 2 + - 1/18 z y x + 2/27 y x - 4/27 x y + -- y x z + 8/27 y + -- y x z + 27 27 + + 16 2 3 16 4 2 2 2 3 2 + - -- y x z - -- y x + 2/27 y - 1/6 y x z - 1/9 y x z + 27 27 + + 2 2 3 2 3 3 2 2 3 3 + - 2/9 y x z + 2/9 y x z - 1/24 y x z - 2/27 y + 4/27 y x + + 3 2 3 2 3 3 2 32 + - 4/27 z y - 8/27 y + 1/18 y x + 8/27 z y x + 1/9 z y x - -- y x z + 27 + + 2 4 16 3 3 16 2 2 2 + - 4/9 z y x + 4/27 y z + -- y z - 4/27 y x z + -- y x - 4/9 y x z + 27 27 + + 4 2 2 2 2 2 2 16 2 + - 1/18 y z + 4/9 y x z + 1/6 y x z + 4/9 y x z - -- y z + 27 + + 3 2 3 2 4 3 2 3 3 3 + - 1/18 y x z - 1/18 x y - 8/27 y z + 8/27 y z + 2/27 y z + + 3 2 2 2 2 2 2 2 2 3 + + 1/18 y z - 2/9 y z + 2/9 y z + 2/9 y x - 2/9 y x - 8/27 y x + + 3 3 4 4 2 4 3 + - 2/27 y x , COEFF(0, -1, 1) = 5/9 x y z - 5/24 x y z - 5/18 x y z + + 3 3 3 4 3 3 3 3 4 3 2 3 3 + + 4/9 y x z + 1/9 z y x - 1/9 y x z - 2/9 z y x - 4/9 y x z + + 2 3 3 3 3 2 2 2 3 3 + + 8/9 z y x - 8/9 z y x - 1/12 y x z - 1/3 z y x - 4/9 y x + + 2 3 3 3 2 4 3 4 3 4 + + 1/3 z y x + 2/9 z y x + 1/12 z y x - 1/9 y x + 5/18 x y + + 3 2 2 3 3 2 + - 10/9 y x z - 20/9 y x z + 10/9 y x z + 10/9 y x + 5/24 y x z + + 3 3 3 3 2 + - 5/18 y x - 5/9 z y x + 20/9 y x z + 5/18 y x z - 10/9 y x + + 2 2 2 2 3 3 3 + + 5/6 y x z - 5/6 y x z + 4/9 y x + 1/9 y x , COEFF(1, -1, 1) = + + 4 2 4 2 4 2 2 4 3 4 3 + - 8/27 x y z - 1/24 x y z + 1/9 x y z - 1/18 x y z + 4/27 x y z + + 3 3 3 4 3 3 3 3 2 4 + - 8/27 y x z - 2/27 z y x + 2/27 y x z + 1/9 x y z + + 4 3 2 3 3 16 2 3 16 3 3 3 2 + + 4/27 z y x + 8/27 y x z - -- z y x + -- z y x + 1/18 y x z + 27 27 + + 2 2 3 3 2 3 3 3 4 3 + + 2/9 z y x + 8/27 y x - 2/9 z y x - 4/27 z y x + 2/27 y z + + 2 4 3 4 3 4 16 3 32 2 + - 1/18 z y x + 2/27 y x - 4/27 x y + -- y x z - 8/27 y + -- y x z + 27 27 + + 16 2 3 16 4 2 2 2 3 2 + - -- y x z - -- y x - 2/27 y + 1/6 y x z - 1/9 y x z + 27 27 + + 2 2 3 2 3 3 2 2 3 3 + + 2/9 y x z - 2/9 y x z + 1/24 y x z + 2/27 y + 4/27 y x + + 3 2 3 2 3 3 2 32 + + 4/27 z y + 8/27 y - 1/18 y x + 8/27 z y x - 1/9 z y x - -- y x z + 27 + + 2 4 16 3 3 16 2 2 2 + + 4/9 z y x - 4/27 y z - -- y z - 4/27 y x z + -- y x - 4/9 y x z + 27 27 + + 4 2 2 2 2 2 2 16 2 + + 1/18 y z - 4/9 y x z - 1/6 y x z + 4/9 y x z + -- y z + 27 + + 3 2 3 2 4 3 2 3 3 3 + + 1/18 y x z + 1/18 x y + 8/27 y z - 8/27 y z - 2/27 y z + + 3 2 2 2 2 2 2 2 2 3 + - 1/18 y z + 2/9 y z - 2/9 y z - 2/9 y x + 2/9 y x - 8/27 y x + + 3 3 4 2 4 2 + - 2/27 y x , COEFF(2, -1, 1) = 1/54 x y z + 1/48 x y z + + 4 2 2 4 3 4 3 3 3 + - 1/144 x y z + 1/36 x y z - 1/108 x y z + 2/27 y x z + + 3 4 3 3 3 3 2 4 4 3 + + 1/54 z y x - 1/54 y x z - 1/18 x y z - 1/27 z y x + + 2 3 3 2 3 3 3 3 2 + - 2/27 y x z + 4/27 z y x - 4/27 z y x - 1/72 y x z + + 2 2 3 3 2 3 3 3 4 3 + - 1/18 z y x - 2/27 y x + 1/18 z y x + 1/27 z y x - 1/108 y z + + 2 4 3 4 3 4 3 + + 1/72 z y x - 1/54 y x + 1/108 x y - 1/27 y x z + 1/27 y + + 2 2 3 4 2 2 2 + - 2/27 y x z + 1/27 y x z + 1/27 y x + 1/108 y - 1/12 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + + 1/144 y x z - 1/9 y x z + 1/9 y x z - 1/48 y x z - 1/108 y + + 3 3 2 3 2 3 + - 1/108 y x - 1/54 z y - 1/27 y + 1/36 y x - 1/54 z y x + + 3 2 2 4 + + 1/18 z y x + 2/27 y x z - 2/9 z y x + 1/54 y z + 2/27 y z + + 3 3 2 2 2 4 2 2 2 + + 1/108 y x z - 1/27 y x + 1/36 y x z - 1/144 y z + 2/9 y x z + + 2 2 2 2 3 2 3 2 4 + + 1/12 y x z - 1/36 y x z - 2/27 y z - 1/36 y x z - 1/36 x y + + 3 2 3 3 3 3 2 2 + - 1/27 y z + 1/27 y z + 1/108 y z + 1/144 y z - 1/36 y z + + 2 2 2 2 2 2 3 3 3 + + 1/36 y z + 1/9 y x - 1/9 y x + 2/27 y x + 1/54 y x , + + 4 2 4 2 4 2 + COEFF(-2, 0, 1) = - 1/36 x y z + 1/32 x y z + 1/96 x y z + + 2 4 3 4 3 3 4 3 2 4 + + 1/24 x y z + 1/72 x y z - 1/36 z y x - 1/12 x y z + + 4 3 2 3 3 2 3 2 2 3 4 3 + + 1/18 z y x + 5/36 y x z - 5/18 z y x + 5/48 z y x - 1/72 y z + + 2 4 3 3 2 3 3 4 3 4 + - 1/48 z y x - 1/12 x z - 1/9 x z - 1/18 x + 1/36 y x - 1/72 x y + + 2 2 3 4 2 2 2 + + 1/9 z + 5/36 y x z - 5/72 y x z + 1/72 y - 5/32 y x z + + 2 2 3 3 3 2 2 2 + - 5/24 y x z - 1/18 z + 1/9 x - 5/72 y - 1/24 z - 1/6 x + + 4 2 2 2 4 2 2 2 + + 1/36 y z + 5/72 y x - 5/96 y x z - 1/96 y z + 5/12 y x z + + 2 2 2 4 2 3 + - 5/36 y z - 1/9 x z - 1/3 x z + 1/18 - 1/24 x y + 5/72 y z + + 2 3 3 2 2 2 2 2 2 2 + + 1/6 x z + 1/18 x z + 1/8 x z + 1/24 x z + 5/96 y z + 5/24 y x + + 3 2 3 4 2 4 2 + + 2/9 z x - 5/36 y x , COEFF(-1, 0, 1) = 4/9 x y z - 1/16 x y z + + 4 2 2 4 3 4 3 3 4 3 2 4 + - 1/6 x y z - 1/12 x y z - 2/9 x y z + 1/9 z y x + 1/6 x y z + + 4 3 2 3 3 2 3 2 2 3 4 3 + - 2/9 z y x - 5/9 y x z + 10/9 z y x - 5/12 z y x + 1/9 y z + + 2 4 3 3 2 3 3 4 3 4 + + 1/12 z y x + 1/3 x z + 4/9 x z + 8/9 x - 1/9 y x + 2/9 x y + + 2 2 3 4 2 2 2 + - 8/9 z - 20/9 y x z + 10/9 y x z - 1/9 y + 5/16 y x z + + 2 2 3 3 3 2 2 2 4 + + 5/12 y x z + 4/9 z - 4/9 x + 5/9 y + 1/3 z + 1/3 x - 2/9 y z + + 2 2 2 4 2 2 2 2 + - 4/9 - 10/9 y x + 5/6 y x z + 1/12 y z - 5/6 y x z + 10/9 y z + + 2 2 4 2 3 2 3 3 + + 16/9 x z + 2/3 x z + 1/12 x y - 5/9 y z - 1/3 x z - 8/9 x z + + 2 2 2 2 2 2 2 3 2 3 + - 1/4 x z - 2/3 x z - 5/12 y z - 5/12 y x - 8/9 z x + 5/9 y x , + + 3 4 2 3 3 3 4 3 + COEFF(0, 0, 1) = 2/3 x + 5/16 x y z - 2/3 x z - 1/6 z y x + + 4 25 2 3 2 2 3 25 2 3 2 + - 5/12 x y + -- y x - 1/2 x z - 5/6 y x - -- y x z + 5/4 x z + 12 12 + + 2 4 3 2 2 3 4 3 4 + - 1/8 z y x + 5/8 z y x + 5/12 x y z - 5/3 x - 5/6 x y z + + 4 3 2 2 3 4 3 + + 1/6 y x + 25/6 y x z - 10/3 x z - 5/3 z y x + 1/3 z y x + + 2 3 3 3 3 25 2 2 + + 5/6 y x z + 4/3 z x + 5/3 x z - -- y x z , COEFF(1, 0, 1) = + 16 + + 4 2 4 2 4 2 2 4 3 4 3 + 4/9 x y z + 1/16 x y z - 1/6 x y z + 1/12 x y z - 2/9 x y z + + 3 4 3 2 4 4 3 2 3 3 2 3 + + 1/9 z y x - 1/6 x y z - 2/9 z y x - 5/9 y x z + 10/9 z y x + + 2 2 3 4 3 2 4 3 3 2 3 3 + - 5/12 z y x - 1/9 y z + 1/12 z y x + 1/3 x z + 4/9 x z + + 4 3 4 2 2 3 + + 8/9 x - 1/9 y x + 2/9 x y + 8/9 z - 20/9 y x z + 10/9 y x z + + 4 2 2 2 2 2 3 3 3 2 + + 1/9 y - 5/16 y x z - 5/12 y x z + 4/9 - 4/9 z - 4/9 x - 5/9 y + + 2 2 4 2 2 2 4 2 + - 1/3 z - 1/3 x + 2/9 y z - 10/9 y x + 5/6 y x z - 1/12 y z + + 2 2 2 2 2 4 2 3 + + 5/6 y x z - 10/9 y z + 16/9 x z - 2/3 x z - 1/12 x y + 5/9 y z + + 2 3 3 2 2 2 2 2 2 2 + + 1/3 x z - 8/9 x z + 1/4 x z - 2/3 x z + 5/12 y z + 5/12 y x + + 3 2 3 4 2 4 2 + - 8/9 z x + 5/9 y x , COEFF(2, 0, 1) = - 1/36 x y z - 1/32 x y z + + 4 2 2 4 3 4 3 3 4 3 + + 1/96 x y z - 1/24 x y z + 1/72 x y z - 1/36 z y x + + 2 4 4 3 2 3 3 2 3 + + 1/12 x y z + 1/18 z y x + 5/36 y x z - 5/18 z y x + + 2 2 3 4 3 2 4 3 3 2 3 3 + + 5/48 z y x + 1/72 y z - 1/48 z y x - 1/12 x z - 1/9 x z + + 4 3 4 2 2 3 + - 1/18 x + 1/36 y x - 1/72 x y - 1/9 z + 5/36 y x z - 5/72 y x z + + 4 2 2 2 2 2 3 3 3 2 + - 1/72 y + 5/32 y x z + 5/24 y x z + 1/18 z + 1/9 x + 5/72 y + + 2 2 4 2 2 2 4 2 + + 1/24 z + 1/6 x - 1/36 y z + 5/72 y x - 5/96 y x z + 1/96 y z + + 2 2 2 2 2 4 + - 5/12 y x z + 5/36 y z - 1/9 x z + 1/3 x z - 1/18 + 1/24 x y + + 2 3 2 3 3 2 2 2 2 2 + - 5/72 y z - 1/6 x z + 1/18 x z - 1/8 x z + 1/24 x z - 5/96 y z + + 2 2 3 2 3 4 + - 5/24 y x + 2/9 z x - 5/36 y x , COEFF(-2, 1, 1) = 1/54 x y z + + 2 4 2 4 2 2 4 3 4 3 + - 1/48 x y z - 1/144 x y z - 1/36 x y z - 1/108 x y z + + 3 3 3 4 3 3 3 3 2 4 + - 2/27 y x z + 1/54 z y x + 1/54 y x z + 1/18 x y z + + 4 3 2 3 3 2 3 3 + - 1/27 z y x - 2/27 y x z + 4/27 z y x + 4/27 z y x + + 3 3 2 2 2 3 3 2 3 3 3 + + 1/72 y x z - 1/18 z y x + 2/27 y x - 1/18 z y x - 1/27 z y x + + 4 3 2 4 3 4 3 4 3 + + 1/108 y z + 1/72 z y x - 1/54 y x + 1/108 x y + 1/27 y x z + + 2 2 3 4 + + 1/27 y - 2/27 y x z + 1/27 y x z - 1/27 y x - 1/108 y + + 2 2 2 3 2 2 2 3 2 3 + + 1/12 y x z - 1/144 y x z + 1/9 y x z + 1/9 y x z + + 3 2 2 3 3 3 2 3 2 + - 1/48 y x z - 1/108 y + 1/108 y x - 1/54 z y + 1/27 y + 1/36 y x + + 3 3 2 2 4 + + 1/54 z y x + 1/18 z y x - 2/27 y x z - 2/9 z y x - 1/54 y z + + 3 3 2 2 2 4 2 + + 2/27 y z - 1/108 y x z - 1/27 y x + 1/36 y x z + 1/144 y z + + 2 2 2 2 2 2 3 2 3 + - 2/9 y x z + 1/12 y x z + 1/36 y x z + 2/27 y z - 1/36 y x z + + 2 4 3 2 3 3 3 3 2 + + 1/36 x y - 1/27 y z - 1/27 y z + 1/108 y z + 1/144 y z + + 2 2 2 2 2 2 2 3 3 3 + - 1/36 y z - 1/36 y z - 1/9 y x - 1/9 y x + 2/27 y x - 1/54 y x , + + 4 2 4 2 4 2 + COEFF(-1, 1, 1) = - 8/27 x y z + 1/24 x y z + 1/9 x y z + + 2 4 3 4 3 3 3 3 4 3 + + 1/18 x y z + 4/27 x y z + 8/27 y x z - 2/27 z y x + + 3 3 3 2 4 4 3 2 3 3 16 2 3 + - 2/27 y x z - 1/9 x y z + 4/27 z y x + 8/27 y x z - -- z y x + 27 + + 16 3 3 3 2 2 2 3 3 2 3 + - -- z y x - 1/18 y x z + 2/9 z y x - 8/27 y x + 2/9 z y x + 27 + + 3 3 4 3 2 4 3 4 3 4 + + 4/27 z y x - 2/27 y z - 1/18 z y x + 2/27 y x - 4/27 x y + + 16 3 32 2 16 2 3 16 4 + - -- y x z - 8/27 y + -- y x z - -- y x z + -- y x + 2/27 y + 27 27 27 27 + + 2 2 2 3 2 2 2 3 2 3 3 2 2 + - 1/6 y x z + 1/9 y x z - 2/9 y x z - 2/9 y x z + 1/24 y x z + + 3 3 3 2 3 2 3 + + 2/27 y - 4/27 y x + 4/27 z y - 8/27 y - 1/18 y x - 8/27 z y x + + 3 2 32 2 4 16 3 3 + - 1/9 z y x + -- y x z + 4/9 z y x + 4/27 y z - -- y z + 4/27 y x z + 27 27 + + 16 2 2 2 4 2 2 2 2 2 + + -- y x - 4/9 y x z - 1/18 y z + 4/9 y x z - 1/6 y x z + 27 + + 2 16 2 3 2 3 2 4 3 + - 4/9 y x z - -- y z + 1/18 y x z - 1/18 x y + 8/27 y z + 27 + + 2 3 3 3 3 2 2 2 2 2 2 + + 8/27 y z - 2/27 y z - 1/18 y z + 2/9 y z + 2/9 y z + 2/9 y x + + 2 2 3 3 3 4 + + 2/9 y x - 8/27 y x + 2/27 y x , COEFF(0, 1, 1) = 5/9 x y z + + 4 2 4 3 3 3 3 4 3 3 3 3 + - 5/24 x y z - 5/18 x y z - 4/9 y x z + 1/9 z y x + 1/9 y x z + + 4 3 2 3 3 2 3 3 3 3 2 + - 2/9 z y x - 4/9 y x z + 8/9 z y x + 8/9 z y x + 1/12 y x z + + 2 2 3 3 2 3 3 3 2 4 3 + - 1/3 z y x + 4/9 y x - 1/3 z y x - 2/9 z y x + 1/12 z y x + + 4 3 4 3 2 2 3 + - 1/9 y x + 5/18 x y + 10/9 y x z - 20/9 y x z + 10/9 y x z + + 3 2 3 3 + - 10/9 y x - 5/24 y x z + 5/18 y x + 5/9 z y x - 20/9 y x z + + 3 3 2 2 2 2 2 3 + - 5/18 y x z - 10/9 y x + 5/6 y x z + 5/6 y x z + 4/9 y x + + 3 3 4 2 4 2 4 2 + - 1/9 y x , COEFF(1, 1, 1) = - 8/27 x y z - 1/24 x y z + 1/9 x y z + + 2 4 3 4 3 3 3 3 4 3 + - 1/18 x y z + 4/27 x y z + 8/27 y x z - 2/27 z y x + + 3 3 3 2 4 4 3 2 3 3 16 2 3 + - 2/27 y x z + 1/9 x y z + 4/27 z y x + 8/27 y x z - -- z y x + 27 + + 16 3 3 3 2 2 2 3 3 2 3 + - -- z y x - 1/18 y x z + 2/9 z y x - 8/27 y x + 2/9 z y x + 27 + + 3 3 4 3 2 4 3 4 3 4 + + 4/27 z y x + 2/27 y z - 1/18 z y x + 2/27 y x - 4/27 x y + + 16 3 32 2 16 2 3 16 4 + - -- y x z + 8/27 y + -- y x z - -- y x z + -- y x - 2/27 y + 27 27 27 27 + + 2 2 2 3 2 2 2 3 2 3 3 2 2 + + 1/6 y x z + 1/9 y x z + 2/9 y x z + 2/9 y x z - 1/24 y x z + + 3 3 3 2 3 2 3 + - 2/27 y - 4/27 y x - 4/27 z y + 8/27 y + 1/18 y x - 8/27 z y x + + 3 2 32 2 4 16 3 3 + + 1/9 z y x + -- y x z - 4/9 z y x - 4/27 y z + -- y z + 4/27 y x z + 27 27 + + 16 2 2 2 4 2 2 2 2 2 + + -- y x - 4/9 y x z + 1/18 y z - 4/9 y x z + 1/6 y x z + 27 + + 2 16 2 3 2 3 2 4 3 + - 4/9 y x z + -- y z - 1/18 y x z + 1/18 x y - 8/27 y z + 27 + + 2 3 3 3 3 2 2 2 2 2 2 + - 8/27 y z + 2/27 y z + 1/18 y z - 2/9 y z - 2/9 y z - 2/9 y x + + 2 2 3 3 3 4 + - 2/9 y x - 8/27 y x + 2/27 y x , COEFF(2, 1, 1) = 1/54 x y z + + 2 4 2 4 2 2 4 3 4 3 + + 1/48 x y z - 1/144 x y z + 1/36 x y z - 1/108 x y z + + 3 3 3 4 3 3 3 3 2 4 + - 2/27 y x z + 1/54 z y x + 1/54 y x z - 1/18 x y z + + 4 3 2 3 3 2 3 3 + - 1/27 z y x - 2/27 y x z + 4/27 z y x + 4/27 z y x + + 3 3 2 2 2 3 3 2 3 3 3 + + 1/72 y x z - 1/18 z y x + 2/27 y x - 1/18 z y x - 1/27 z y x + + 4 3 2 4 3 4 3 4 3 + - 1/108 y z + 1/72 z y x - 1/54 y x + 1/108 x y + 1/27 y x z + + 2 2 3 4 + - 1/27 y - 2/27 y x z + 1/27 y x z - 1/27 y x + 1/108 y + + 2 2 2 3 2 2 2 3 2 3 + - 1/12 y x z - 1/144 y x z - 1/9 y x z - 1/9 y x z + + 3 2 2 3 3 3 2 3 2 + + 1/48 y x z + 1/108 y + 1/108 y x + 1/54 z y - 1/27 y - 1/36 y x + + 3 3 2 2 4 + + 1/54 z y x - 1/18 z y x - 2/27 y x z + 2/9 z y x + 1/54 y z + + 3 3 2 2 2 4 2 + - 2/27 y z - 1/108 y x z - 1/27 y x + 1/36 y x z - 1/144 y z + + 2 2 2 2 2 2 3 2 3 + + 2/9 y x z - 1/12 y x z + 1/36 y x z - 2/27 y z + 1/36 y x z + + 2 4 3 2 3 3 3 3 2 + - 1/36 x y + 1/27 y z + 1/27 y z - 1/108 y z - 1/144 y z + + 2 2 2 2 2 2 2 3 3 3 + + 1/36 y z + 1/36 y z + 1/9 y x + 1/9 y x + 2/27 y x - 1/54 y x , + + 4 2 4 2 4 2 + COEFF(-2, 2, 1) = - 1/216 x y z + 1/192 x y z + 1/576 x y z + + 2 4 3 4 3 3 3 3 4 3 + + 1/144 x y z + 1/432 x y z + 1/108 y x z - 1/216 z y x + + 3 3 3 2 4 4 3 2 3 3 + - 1/108 y x z - 1/72 x y z + 1/108 z y x + 1/216 y x z + + 2 3 3 3 3 2 2 2 3 + - 1/108 z y x - 1/54 z y x - 1/144 y x z + 1/288 z y x + + 3 2 3 3 3 4 3 2 4 3 + - 1/108 y x + 1/144 z y x + 1/54 z y x - 1/432 y z - 1/288 z y x + + 4 3 4 3 2 + + 1/216 y x - 1/432 x y - 1/216 y x z - 1/216 y + 1/216 y x z + + 2 3 4 2 2 2 3 2 + - 1/432 y x z + 1/216 y x + 1/432 y - 1/192 y x z + 1/288 y x z + + 2 2 3 2 3 3 2 2 3 3 + - 1/144 y x z - 1/72 y x z + 1/96 y x z + 1/216 y - 1/216 y x + + 3 2 3 2 3 3 2 + + 1/108 z y - 1/432 y - 1/72 y x - 1/108 z y x - 1/36 z y x + + 2 4 3 3 + + 1/108 y x z + 1/36 z y x + 1/216 y z - 1/108 y z + 1/216 y x z + + 2 2 2 4 2 2 2 2 2 + + 1/432 y x - 1/576 y x z - 1/576 y z + 1/72 y x z - 1/96 y x z + + 2 2 3 2 3 2 4 3 + - 1/288 y x z - 1/216 y z + 1/72 y x z - 1/144 x y + 1/216 y z + + 2 3 3 3 3 2 2 2 2 + + 1/432 y z - 1/216 y z - 1/288 y z + 1/288 y z + 1/576 y z + + 2 2 2 2 3 3 3 + + 1/144 y x + 1/72 y x - 1/216 y x + 1/108 y x , COEFF(-1, 2, 1) = + + 4 2 4 2 4 2 2 4 3 4 3 + 2/27 x y z - 1/96 x y z - 1/36 x y z - 1/72 x y z - 1/27 x y z + + 3 3 3 4 3 3 3 3 2 4 + - 1/27 y x z + 1/54 z y x + 1/27 y x z + 1/36 x y z + + 4 3 2 3 3 2 3 3 + - 1/27 z y x - 1/54 y x z + 1/27 z y x + 2/27 z y x + + 3 3 2 2 2 3 3 2 3 3 3 + + 1/36 y x z - 1/72 z y x + 1/27 y x - 1/36 z y x - 2/27 z y x + + 4 3 2 4 3 4 3 4 3 + + 1/54 y z + 1/72 z y x - 1/54 y x + 1/27 x y + 2/27 y x z + + 2 2 3 4 2 2 2 + + 1/27 y - 2/27 y x z + 1/27 y x z - 2/27 y x - 1/54 y + 1/96 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + - 1/18 y x z + 1/72 y x z + 1/36 y x z - 1/48 y x z - 1/27 y + + 3 3 2 3 2 3 + + 2/27 y x - 2/27 z y + 1/54 y + 1/36 y x + 4/27 z y x + + 3 2 2 4 + + 1/18 z y x - 4/27 y x z - 1/18 z y x - 1/27 y z + 2/27 y z + + 3 3 2 2 2 4 2 2 2 + - 2/27 y x z - 1/27 y x + 1/36 y x z + 1/72 y z - 1/36 y x z + + 2 2 2 2 3 2 3 2 4 + + 1/48 y x z + 1/18 y x z + 1/27 y z - 1/36 y x z + 1/72 x y + + 3 2 3 3 3 3 2 2 + - 1/27 y z - 1/54 y z + 1/27 y z + 1/36 y z - 1/36 y z + + 2 2 2 2 2 2 3 3 3 + - 1/72 y z - 1/72 y x - 1/36 y x + 1/54 y x - 1/27 y x , + + 4 4 2 4 3 3 3 + COEFF(0, 2, 1) = - 5/36 x y z + 5/96 x y z + 5/72 x y z + 1/18 y x z + + 3 4 3 3 3 3 4 3 2 3 3 + - 1/36 z y x - 1/18 y x z + 1/18 z y x + 1/36 y x z + + 2 3 3 3 3 2 2 2 3 3 + - 1/18 z y x - 1/9 z y x - 1/24 y x z + 1/48 z y x - 1/18 y x + + 2 3 3 3 2 4 3 4 3 4 + + 1/24 z y x + 1/9 z y x - 1/48 z y x + 1/36 y x - 5/72 x y + + 3 2 2 3 3 2 + - 5/36 y x z + 5/36 y x z - 5/72 y x z + 5/36 y x + 5/48 y x z + + 3 3 3 3 2 + - 5/36 y x - 5/18 z y x + 5/18 y x z + 5/36 y x z + 5/72 y x + + 2 2 2 2 3 3 3 + - 5/96 y x z - 5/48 y x z - 1/36 y x + 1/18 y x , COEFF(1, 2, 1) = + + 4 2 4 2 4 2 2 4 3 4 3 + 2/27 x y z + 1/96 x y z - 1/36 x y z + 1/72 x y z - 1/27 x y z + + 3 3 3 4 3 3 3 3 2 4 + - 1/27 y x z + 1/54 z y x + 1/27 y x z - 1/36 x y z + + 4 3 2 3 3 2 3 3 + - 1/27 z y x - 1/54 y x z + 1/27 z y x + 2/27 z y x + + 3 3 2 2 2 3 3 2 3 3 3 + + 1/36 y x z - 1/72 z y x + 1/27 y x - 1/36 z y x - 2/27 z y x + + 4 3 2 4 3 4 3 4 3 + - 1/54 y z + 1/72 z y x - 1/54 y x + 1/27 x y + 2/27 y x z + + 2 2 3 4 2 2 2 + - 1/27 y - 2/27 y x z + 1/27 y x z - 2/27 y x + 1/54 y - 1/96 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + - 1/18 y x z - 1/72 y x z - 1/36 y x z + 1/48 y x z + 1/27 y + + 3 3 2 3 2 3 + + 2/27 y x + 2/27 z y - 1/54 y - 1/36 y x + 4/27 z y x + + 3 2 2 4 + - 1/18 z y x - 4/27 y x z + 1/18 z y x + 1/27 y z - 2/27 y z + + 3 3 2 2 2 4 2 2 2 + - 2/27 y x z - 1/27 y x + 1/36 y x z - 1/72 y z + 1/36 y x z + + 2 2 2 2 3 2 3 2 4 + - 1/48 y x z + 1/18 y x z - 1/27 y z + 1/36 y x z - 1/72 x y + + 3 2 3 3 3 3 2 2 + + 1/27 y z + 1/54 y z - 1/27 y z - 1/36 y z + 1/36 y z + + 2 2 2 2 2 2 3 3 3 + + 1/72 y z + 1/72 y x + 1/36 y x + 1/54 y x - 1/27 y x , + + 4 2 4 2 4 2 + COEFF(2, 2, 1) = - 1/216 x y z - 1/192 x y z + 1/576 x y z + + 2 4 3 4 3 3 3 3 4 3 + - 1/144 x y z + 1/432 x y z + 1/108 y x z - 1/216 z y x + + 3 3 3 2 4 4 3 2 3 3 + - 1/108 y x z + 1/72 x y z + 1/108 z y x + 1/216 y x z + + 2 3 3 3 3 2 2 2 3 + - 1/108 z y x - 1/54 z y x - 1/144 y x z + 1/288 z y x + + 3 2 3 3 3 4 3 2 4 3 + - 1/108 y x + 1/144 z y x + 1/54 z y x + 1/432 y z - 1/288 z y x + + 4 3 4 3 2 + + 1/216 y x - 1/432 x y - 1/216 y x z + 1/216 y + 1/216 y x z + + 2 3 4 2 2 2 3 2 + - 1/432 y x z + 1/216 y x - 1/432 y + 1/192 y x z + 1/288 y x z + + 2 2 3 2 3 3 2 2 3 3 + + 1/144 y x z + 1/72 y x z - 1/96 y x z - 1/216 y - 1/216 y x + + 3 2 3 2 3 3 2 + - 1/108 z y + 1/432 y + 1/72 y x - 1/108 z y x + 1/36 z y x + + 2 4 3 3 + + 1/108 y x z - 1/36 z y x - 1/216 y z + 1/108 y z + 1/216 y x z + + 2 2 2 4 2 2 2 2 2 + + 1/432 y x - 1/576 y x z + 1/576 y z - 1/72 y x z + 1/96 y x z + + 2 2 3 2 3 2 4 3 + - 1/288 y x z + 1/216 y z - 1/72 y x z + 1/144 x y - 1/216 y z + + 2 3 3 3 3 2 2 2 2 + - 1/432 y z + 1/216 y z + 1/288 y z - 1/288 y z - 1/576 y z + + 2 2 2 2 3 3 3 + - 1/144 y x - 1/72 y x - 1/216 y x + 1/108 y x , COEFF(-2, -2, 2) = + + 4 2 4 2 4 2 2 4 3 + 1/3456 x y z - 1/384 x y z - 1/1152 x y z - 1/576 x y z + + 4 3 3 3 3 4 3 3 3 3 + - 1/1728 x y z + 1/432 y x z + 1/864 z y x - 1/432 y x z + + 2 4 4 3 2 3 3 2 3 + + 1/1152 x y z - 1/1728 z y x - 1/864 y x z + 1/1728 z y x + + 3 3 3 2 2 2 3 3 + - 1/864 z y x - 1/288 y x z - 1/576 z y x - 1/864 y x + + 2 3 3 3 4 3 2 4 3 + + 1/288 z y x + 1/864 z y x + 1/1728 y z + 1/576 z y x + + 4 3 4 3 2 + - 1/1728 y x + 1/3456 x y - 1/864 y x z - 1/1728 y - 1/3456 y x z + + 2 3 4 2 2 2 3 2 + + 1/1728 y x z + 1/1728 y x - 1/3456 y + 1/384 y x z + 1/576 y x z + + 2 2 3 2 3 3 2 2 3 + + 1/576 y x z - 1/288 y x z + 1/192 y x z + 1/1728 y + + 3 3 2 3 2 3 + - 1/1728 y x + 1/1728 z y + 1/3456 y - 1/576 y x - 1/1728 z y x + + 3 2 2 4 + - 1/576 z y x + 1/1728 y x z + 1/576 z y x - 1/3456 y z - 1/1728 y z + + 3 3 2 2 2 4 2 + + 1/864 y x z - 1/3456 y x + 1/1152 y x z + 1/1152 y z + + 2 2 2 2 2 2 + - 1/1152 y x z - 1/192 y x z - 1/576 y x z + 1/3456 y z + + 3 2 3 2 4 3 2 3 3 3 + + 1/288 y x z + 1/1152 x y + 1/864 y z - 1/1728 y z - 1/864 y z + + 3 2 2 2 2 2 2 2 + - 1/576 y z + 1/576 y z - 1/1152 y z - 1/1152 y x + 1/576 y x + + 2 3 3 3 4 + + 1/1728 y x + 1/864 y x , COEFF(-1, -2, 2) = - 1/216 x y z + + 2 4 2 4 2 2 4 3 4 3 + + 1/192 x y z + 1/72 x y z + 1/288 x y z + 1/108 x y z + + 3 3 3 4 3 3 3 3 2 4 + - 1/108 y x z - 1/216 z y x + 1/108 y x z - 1/576 x y z + + 4 3 2 3 3 2 3 3 + + 1/432 z y x + 1/216 y x z - 1/432 z y x + 1/216 z y x + + 3 3 2 2 2 3 3 2 3 + + 1/72 y x z + 1/144 z y x + 1/216 y x - 1/72 z y x + + 3 3 4 3 2 4 3 4 3 4 + - 1/216 z y x - 1/216 y z - 1/144 z y x + 1/432 y x - 1/216 x y + + 3 2 2 3 + + 1/54 y x z + 1/216 y + 1/216 y x z - 1/108 y x z - 1/108 y x + + 4 2 2 2 3 2 2 2 3 + + 1/432 y - 1/192 y x z - 1/36 y x z - 1/288 y x z + + 2 3 3 2 2 3 3 3 + + 1/144 y x z - 1/96 y x z - 1/216 y + 1/108 y x - 1/216 z y + + 2 3 2 3 3 2 + - 1/432 y + 1/288 y x + 1/108 z y x + 1/288 z y x - 1/108 y x z + + 2 4 3 3 2 + - 1/288 z y x + 1/432 y z + 1/216 y z - 1/54 y x z + 1/216 y x + + 2 2 4 2 2 2 2 2 2 + - 1/72 y x z - 1/144 y z + 1/576 y x z + 1/96 y x z + 1/36 y x z + + 2 3 2 3 2 4 3 2 3 + - 1/432 y z - 1/144 y x z - 1/576 x y - 1/108 y z + 1/216 y z + + 3 3 3 2 2 2 2 2 2 + + 1/108 y z + 1/72 y z - 1/72 y z + 1/144 y z + 1/576 y x + + 2 2 3 3 3 4 + - 1/288 y x - 1/432 y x - 1/216 y x , COEFF(0, -2, 2) = 5/576 x y z + + 4 2 4 3 3 3 3 4 3 + - 5/192 x y z - 5/288 x y z + 1/72 y x z + 1/144 z y x + + 3 3 3 4 3 2 3 3 2 3 + - 1/72 y x z - 1/288 z y x - 1/144 y x z + 1/288 z y x + + 3 3 3 2 2 2 3 3 2 3 + - 1/144 z y x - 1/48 y x z - 1/96 z y x - 1/144 y x + 1/48 z y x + + 3 3 2 4 3 4 3 4 3 + + 1/144 z y x + 1/96 z y x - 1/288 y x + 5/576 x y - 5/144 y x z + + 2 2 3 3 2 3 + - 5/576 y x z + 5/288 y x z + 5/288 y x + 5/96 y x z - 5/288 y x + + 3 3 3 2 2 2 + - 5/288 z y x + 5/288 y x z + 5/144 y x z - 5/576 y x + 5/192 y x z + + 2 2 3 3 3 + - 5/96 y x z + 1/288 y x + 1/144 y x , COEFF(1, -2, 2) = + + 4 2 4 2 4 2 2 4 3 + - 1/216 x y z - 1/192 x y z + 1/72 x y z - 1/288 x y z + + 4 3 3 3 3 4 3 3 3 3 + + 1/108 x y z - 1/108 y x z - 1/216 z y x + 1/108 y x z + + 2 4 4 3 2 3 3 2 3 + + 1/576 x y z + 1/432 z y x + 1/216 y x z - 1/432 z y x + + 3 3 3 2 2 2 3 3 + + 1/216 z y x + 1/72 y x z + 1/144 z y x + 1/216 y x + + 2 3 3 3 4 3 2 4 3 + - 1/72 z y x - 1/216 z y x + 1/216 y z - 1/144 z y x + + 4 3 4 3 2 + + 1/432 y x - 1/216 x y + 1/54 y x z - 1/216 y + 1/216 y x z + + 2 3 4 2 2 2 3 2 + - 1/108 y x z - 1/108 y x - 1/432 y + 1/192 y x z - 1/36 y x z + + 2 2 3 2 3 3 2 2 3 3 + + 1/288 y x z - 1/144 y x z + 1/96 y x z + 1/216 y + 1/108 y x + + 3 2 3 2 3 3 2 + + 1/216 z y + 1/432 y - 1/288 y x + 1/108 z y x - 1/288 z y x + + 2 4 3 3 + - 1/108 y x z + 1/288 z y x - 1/432 y z - 1/216 y z - 1/54 y x z + + 2 2 2 4 2 2 2 2 2 + + 1/216 y x - 1/72 y x z + 1/144 y z - 1/576 y x z - 1/96 y x z + + 2 2 3 2 3 2 4 3 + + 1/36 y x z + 1/432 y z + 1/144 y x z + 1/576 x y + 1/108 y z + + 2 3 3 3 3 2 2 2 2 + - 1/216 y z - 1/108 y z - 1/72 y z + 1/72 y z - 1/144 y z + + 2 2 2 2 3 3 3 + - 1/576 y x + 1/288 y x - 1/432 y x - 1/216 y x , COEFF(2, -2, 2) = + + 4 2 4 2 4 2 2 4 3 + 1/3456 x y z + 1/384 x y z - 1/1152 x y z + 1/576 x y z + + 4 3 3 3 3 4 3 3 3 3 + - 1/1728 x y z + 1/432 y x z + 1/864 z y x - 1/432 y x z + + 2 4 4 3 2 3 3 2 3 + - 1/1152 x y z - 1/1728 z y x - 1/864 y x z + 1/1728 z y x + + 3 3 3 2 2 2 3 3 + - 1/864 z y x - 1/288 y x z - 1/576 z y x - 1/864 y x + + 2 3 3 3 4 3 2 4 3 + + 1/288 z y x + 1/864 z y x - 1/1728 y z + 1/576 z y x + + 4 3 4 3 2 + - 1/1728 y x + 1/3456 x y - 1/864 y x z + 1/1728 y - 1/3456 y x z + + 2 3 4 2 2 2 3 2 + + 1/1728 y x z + 1/1728 y x + 1/3456 y - 1/384 y x z + 1/576 y x z + + 2 2 3 2 3 3 2 2 3 + - 1/576 y x z + 1/288 y x z - 1/192 y x z - 1/1728 y + + 3 3 2 3 2 3 + - 1/1728 y x - 1/1728 z y - 1/3456 y + 1/576 y x - 1/1728 z y x + + 3 2 2 4 + + 1/576 z y x + 1/1728 y x z - 1/576 z y x + 1/3456 y z + 1/1728 y z + + 3 3 2 2 2 4 2 + + 1/864 y x z - 1/3456 y x + 1/1152 y x z - 1/1152 y z + + 2 2 2 2 2 2 + + 1/1152 y x z + 1/192 y x z - 1/576 y x z - 1/3456 y z + + 3 2 3 2 4 3 2 3 3 3 + - 1/288 y x z - 1/1152 x y - 1/864 y z + 1/1728 y z + 1/864 y z + + 3 2 2 2 2 2 2 2 + + 1/576 y z - 1/576 y z + 1/1152 y z + 1/1152 y x - 1/576 y x + + 2 3 3 3 4 + + 1/1728 y x + 1/864 y x , COEFF(-2, -1, 2) = - 1/864 x y z + + 2 4 2 4 2 2 4 3 4 3 + + 1/96 x y z + 1/288 x y z + 1/144 x y z + 1/432 x y z + + 3 3 3 4 3 3 3 3 2 4 + - 1/54 y x z - 1/216 z y x + 1/216 y x z - 1/288 x y z + + 4 3 2 3 3 2 3 3 + + 1/432 z y x + 1/54 y x z - 1/108 z y x + 1/108 z y x + + 3 3 2 2 2 3 3 2 3 + + 1/144 y x z + 1/36 z y x + 1/108 y x - 1/36 z y x + + 3 3 4 3 2 4 3 4 3 4 + - 1/432 z y x - 1/432 y z - 1/144 z y x + 1/432 y x - 1/864 x y + + 3 2 2 3 + + 1/108 y x z + 1/216 y + 1/216 y x z - 1/108 y x z - 1/216 y x + + 4 2 2 2 3 2 2 2 3 2 3 + + 1/864 y - 1/24 y x z - 1/288 y x z - 1/36 y x z + 1/36 y x z + + 3 2 2 3 3 3 2 + - 1/96 y x z - 1/864 y + 1/864 y x - 1/864 z y - 1/216 y + + 3 2 3 3 2 2 + + 1/288 y x + 1/864 z y x + 1/288 z y x - 1/216 y x z - 1/72 z y x + + 4 3 3 2 2 2 + + 1/864 y z + 1/216 y z - 1/432 y x z + 1/216 y x - 1/72 y x z + + 4 2 2 2 2 2 2 2 + - 1/288 y z + 1/72 y x z + 1/24 y x z + 1/72 y x z - 1/216 y z + + 3 2 3 2 4 3 2 3 3 3 + - 1/144 y x z - 1/288 x y - 1/108 y z + 1/108 y z + 1/432 y z + + 3 2 2 2 2 2 2 2 + + 1/288 y z - 1/72 y z + 1/72 y z + 1/72 y x - 1/72 y x + + 2 3 3 3 4 + - 1/108 y x - 1/432 y x , COEFF(-1, -1, 2) = 1/54 x y z + + 2 4 2 4 2 2 4 3 4 3 + - 1/48 x y z - 1/18 x y z - 1/72 x y z - 1/27 x y z + + 3 3 3 4 3 3 3 3 2 4 + + 2/27 y x z + 1/54 z y x - 1/54 y x z + 1/144 x y z + + 4 3 2 3 3 2 3 3 + - 1/108 z y x - 2/27 y x z + 1/27 z y x - 1/27 z y x + + 3 3 2 2 2 3 3 2 3 3 3 + - 1/36 y x z - 1/9 z y x - 1/27 y x + 1/9 z y x + 1/108 z y x + + 4 3 2 4 3 4 3 4 3 + + 1/54 y z + 1/36 z y x - 1/108 y x + 1/54 x y - 4/27 y x z + + 2 2 3 4 + - 1/27 y - 2/27 y x z + 4/27 y x z + 2/27 y x - 1/108 y + + 2 2 2 3 2 2 2 3 2 3 + + 1/12 y x z + 1/18 y x z + 1/18 y x z - 1/18 y x z + + 3 2 2 3 3 3 2 + + 1/48 y x z + 1/108 y - 1/54 y x + 1/108 z y + 1/27 y + + 3 2 3 3 2 2 + - 1/144 y x - 1/54 z y x - 1/144 z y x + 2/27 y x z + 1/36 z y x + + 4 3 3 2 2 2 + - 1/108 y z - 1/27 y z + 1/27 y x z - 2/27 y x + 2/9 y x z + + 4 2 2 2 2 2 2 2 + + 1/36 y z - 1/36 y x z - 1/12 y x z - 2/9 y x z + 1/27 y z + + 3 2 3 2 4 3 2 3 3 3 + + 1/72 y x z + 1/144 x y + 2/27 y z - 2/27 y z - 1/54 y z + + 3 2 2 2 2 2 2 2 2 3 + - 1/36 y z + 1/9 y z - 1/9 y z - 1/36 y x + 1/36 y x + 1/27 y x + + 3 3 4 4 2 + + 1/108 y x , COEFF(0, -1, 2) = - 5/144 x y z + 5/48 x y z + + 4 3 3 3 3 4 3 3 3 3 + + 5/72 x y z - 1/9 y x z - 1/36 z y x + 1/36 y x z + + 4 3 2 3 3 2 3 3 3 3 2 + + 1/72 z y x + 1/9 y x z - 1/18 z y x + 1/18 z y x + 1/24 y x z + + 2 2 3 3 2 3 3 3 2 4 3 + + 1/6 z y x + 1/18 y x - 1/6 z y x - 1/72 z y x - 1/24 z y x + + 4 3 4 3 2 2 3 + + 1/72 y x - 5/144 x y + 5/18 y x z + 5/36 y x z - 5/18 y x z + + 3 2 3 3 + - 5/36 y x - 5/48 y x z + 5/144 y x + 5/144 z y x - 5/36 y x z + + 3 3 2 2 2 2 2 3 + - 5/72 y x z + 5/36 y x - 5/12 y x z + 5/12 y x z - 1/18 y x + + 3 3 4 2 4 2 4 2 + - 1/72 y x , COEFF(1, -1, 2) = 1/54 x y z + 1/48 x y z - 1/18 x y z + + 2 4 3 4 3 3 3 3 4 3 + + 1/72 x y z - 1/27 x y z + 2/27 y x z + 1/54 z y x + + 3 3 3 2 4 4 3 2 3 3 + - 1/54 y x z - 1/144 x y z - 1/108 z y x - 2/27 y x z + + 2 3 3 3 3 2 2 2 3 3 + + 1/27 z y x - 1/27 z y x - 1/36 y x z - 1/9 z y x - 1/27 y x + + 2 3 3 3 4 3 2 4 3 4 3 + + 1/9 z y x + 1/108 z y x - 1/54 y z + 1/36 z y x - 1/108 y x + + 4 3 2 2 3 + + 1/54 x y - 4/27 y x z + 1/27 y - 2/27 y x z + 4/27 y x z + 2/27 y x + + 4 2 2 2 3 2 2 2 3 2 3 + + 1/108 y - 1/12 y x z + 1/18 y x z - 1/18 y x z + 1/18 y x z + + 3 2 2 3 3 3 2 + - 1/48 y x z - 1/108 y - 1/54 y x - 1/108 z y - 1/27 y + + 3 2 3 3 2 2 + + 1/144 y x - 1/54 z y x + 1/144 z y x + 2/27 y x z - 1/36 z y x + + 4 3 3 2 2 2 + + 1/108 y z + 1/27 y z + 1/27 y x z - 2/27 y x + 2/9 y x z + + 4 2 2 2 2 2 2 2 + - 1/36 y z + 1/36 y x z + 1/12 y x z - 2/9 y x z - 1/27 y z + + 3 2 3 2 4 3 2 3 3 3 + - 1/72 y x z - 1/144 x y - 2/27 y z + 2/27 y z + 1/54 y z + + 3 2 2 2 2 2 2 2 2 3 + + 1/36 y z - 1/9 y z + 1/9 y z + 1/36 y x - 1/36 y x + 1/27 y x + + 3 3 4 2 4 2 + + 1/108 y x , COEFF(2, -1, 2) = - 1/864 x y z - 1/96 x y z + + 4 2 2 4 3 4 3 3 3 + + 1/288 x y z - 1/144 x y z + 1/432 x y z - 1/54 y x z + + 3 4 3 3 3 3 2 4 4 3 + - 1/216 z y x + 1/216 y x z + 1/288 x y z + 1/432 z y x + + 2 3 3 2 3 3 3 3 2 + + 1/54 y x z - 1/108 z y x + 1/108 z y x + 1/144 y x z + + 2 2 3 3 2 3 3 3 4 3 + + 1/36 z y x + 1/108 y x - 1/36 z y x - 1/432 z y x + 1/432 y z + + 2 4 3 4 3 4 3 + - 1/144 z y x + 1/432 y x - 1/864 x y + 1/108 y x z - 1/216 y + + 2 2 3 4 2 2 2 + + 1/216 y x z - 1/108 y x z - 1/216 y x - 1/864 y + 1/24 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + - 1/288 y x z + 1/36 y x z - 1/36 y x z + 1/96 y x z + 1/864 y + + 3 3 2 3 2 3 + + 1/864 y x + 1/864 z y + 1/216 y - 1/288 y x + 1/864 z y x + + 3 2 2 4 + - 1/288 z y x - 1/216 y x z + 1/72 z y x - 1/864 y z - 1/216 y z + + 3 3 2 2 2 4 2 2 2 + - 1/432 y x z + 1/216 y x - 1/72 y x z + 1/288 y z - 1/72 y x z + + 2 2 2 2 3 2 3 2 4 + - 1/24 y x z + 1/72 y x z + 1/216 y z + 1/144 y x z + 1/288 x y + + 3 2 3 3 3 3 2 2 + + 1/108 y z - 1/108 y z - 1/432 y z - 1/288 y z + 1/72 y z + + 2 2 2 2 2 2 3 3 3 + - 1/72 y z - 1/72 y x + 1/72 y x - 1/108 y x - 1/432 y x , + + 4 2 4 2 4 2 + COEFF(-2, 0, 2) = 1/576 x y z - 1/64 x y z - 1/192 x y z + + 2 4 3 4 3 3 4 3 2 4 + - 1/96 x y z - 1/288 x y z + 1/144 z y x + 1/192 x y z + + 4 3 2 3 3 2 3 2 2 3 + - 1/288 z y x - 5/144 y x z + 5/288 z y x - 5/96 z y x + + 4 3 2 4 3 3 2 3 3 + + 1/288 y z + 1/96 z y x + 1/24 x z + 1/36 x z + 1/144 x + + 4 3 4 2 2 3 + - 1/288 y x + 1/576 x y - 1/144 z - 5/576 y x z + 5/288 y x z + + 4 2 2 2 2 2 3 3 3 2 + - 1/576 y + 5/64 y x z + 5/96 y x z + 1/72 z - 1/72 x + 5/576 y + + 2 2 4 2 2 2 + + 1/48 z + 1/48 x - 1/576 y z - 5/576 y x + 5/192 y x z + + 4 2 2 2 2 2 + + 1/192 y z - 5/192 y x z + 5/576 y z + 1/144 x z + 1/48 x z + + 2 4 2 3 2 3 3 2 2 + + 1/192 x y - 5/288 y z - 1/24 x z - 1/72 x z - 1/16 x z + + 2 2 2 2 2 3 2 3 + - 1/48 x z - 5/192 y z - 5/192 y x - 1/144 - 1/72 z x + 5/288 y x , + + 4 2 4 2 4 2 + COEFF(-1, 0, 2) = - 1/36 x y z + 1/32 x y z + 1/12 x y z + + 2 4 3 4 3 3 4 3 2 4 + + 1/48 x y z + 1/18 x y z - 1/36 z y x - 1/96 x y z + + 4 3 2 3 3 2 3 2 2 3 4 3 + + 1/72 z y x + 5/36 y x z - 5/72 z y x + 5/24 z y x - 1/36 y z + + 2 4 3 3 2 3 3 4 3 4 + - 1/24 z y x - 1/6 x z - 1/9 x z - 1/9 x + 1/72 y x - 1/36 x y + + 2 2 3 4 2 2 2 + + 1/18 z + 5/36 y x z - 5/18 y x z + 1/72 y - 5/32 y x z + + 2 2 3 3 3 2 2 2 + - 5/48 y x z - 1/9 z + 1/18 x - 5/72 y - 1/6 z - 1/24 x + + 4 2 2 2 4 2 2 2 + + 1/72 y z + 5/36 y x - 5/12 y x z - 1/24 y z + 5/96 y x z + + 2 2 2 4 2 3 + - 5/72 y z - 1/9 x z - 1/24 x z + 1/18 - 1/96 x y + 5/36 y z + + 2 3 3 2 2 2 2 2 2 2 + + 1/12 x z + 2/9 x z + 1/8 x z + 1/3 x z + 5/24 y z + 5/96 y x + + 3 2 3 2 2 3 2 3 3 + + 1/18 z x - 5/72 y x , COEFF(0, 0, 2) = - 5/16 z y x - 5/24 y x z + + 3 4 3 3 4 2 4 3 + + 1/24 z y x - 1/12 z x + 5/96 x y z + 5/24 x z + 1/16 z y x + + 25 2 4 3 25 2 3 4 3 + - -- y x z + 5/96 x y - 1/12 x + -- y x z - 5/48 x y z + 96 48 + + 2 3 4 2 3 2 3 + + 5/48 z y x - 5/32 x y z - 5/12 x z + 5/48 y x + 5/24 x + + 3 3 2 4 3 25 2 3 2 4 3 + + 1/6 x z - 5/8 x z - 1/48 y x - -- y x + 1/4 x z - 1/48 z y x + 96 + + 25 2 2 4 2 4 2 + + -- y x z , COEFF(1, 0, 2) = - 1/36 x y z - 1/32 x y z + 32 + + 4 2 2 4 3 4 3 3 4 3 + + 1/12 x y z - 1/48 x y z + 1/18 x y z - 1/36 z y x + + 2 4 4 3 2 3 3 2 3 + + 1/96 x y z + 1/72 z y x + 5/36 y x z - 5/72 z y x + + 2 2 3 4 3 2 4 3 3 2 3 3 + + 5/24 z y x + 1/36 y z - 1/24 z y x - 1/6 x z - 1/9 x z + + 4 3 4 2 2 3 + - 1/9 x + 1/72 y x - 1/36 x y - 1/18 z + 5/36 y x z - 5/18 y x z + + 4 2 2 2 2 2 3 3 3 2 + - 1/72 y + 5/32 y x z + 5/48 y x z + 1/9 z + 1/18 x + 5/72 y + + 2 2 4 2 2 2 4 2 + + 1/6 z + 1/24 x - 1/72 y z + 5/36 y x - 5/12 y x z + 1/24 y z + + 2 2 2 2 2 4 + - 5/96 y x z + 5/72 y z - 1/9 x z + 1/24 x z - 1/18 + 1/96 x y + + 2 3 2 3 3 2 2 2 2 2 + - 5/36 y z - 1/12 x z + 2/9 x z - 1/8 x z + 1/3 x z - 5/24 y z + + 2 2 3 2 3 4 + - 5/96 y x + 1/18 z x - 5/72 y x , COEFF(2, 0, 2) = 1/576 x y z + + 2 4 2 4 2 2 4 3 4 3 + + 1/64 x y z - 1/192 x y z + 1/96 x y z - 1/288 x y z + + 3 4 3 2 4 4 3 2 3 3 + + 1/144 z y x - 1/192 x y z - 1/288 z y x - 5/144 y x z + + 2 3 2 2 3 4 3 2 4 3 3 2 + + 5/288 z y x - 5/96 z y x - 1/288 y z + 1/96 z y x + 1/24 x z + + 3 3 4 3 4 2 + + 1/36 x z + 1/144 x - 1/288 y x + 1/576 x y + 1/144 z - 5/576 y x z + + 2 3 4 2 2 2 2 2 3 3 + + 5/288 y x z + 1/576 y - 5/64 y x z - 5/96 y x z - 1/72 z + + 3 2 2 2 4 2 + - 1/72 x - 5/576 y - 1/48 z - 1/48 x + 1/576 y z - 5/576 y x + + 2 2 4 2 2 2 2 + + 5/192 y x z - 1/192 y z + 5/192 y x z - 5/576 y z + 1/144 x z + + 2 2 4 2 3 2 3 3 + - 1/48 x z - 1/192 x y + 5/288 y z + 1/24 x z - 1/72 x z + + 2 2 2 2 2 2 2 3 + + 1/16 x z - 1/48 x z + 5/192 y z + 5/192 y x + 1/144 - 1/72 z x + + 2 3 4 2 4 2 + + 5/288 y x , COEFF(-2, 1, 2) = - 1/864 x y z + 1/96 x y z + + 4 2 2 4 3 4 3 3 3 + + 1/288 x y z + 1/144 x y z + 1/432 x y z + 1/54 y x z + + 3 4 3 3 3 3 2 4 4 3 + - 1/216 z y x - 1/216 y x z - 1/288 x y z + 1/432 z y x + + 2 3 3 2 3 3 3 3 2 + + 1/54 y x z - 1/108 z y x - 1/108 z y x - 1/144 y x z + + 2 2 3 3 2 3 3 3 4 3 + + 1/36 z y x - 1/108 y x + 1/36 z y x + 1/432 z y x - 1/432 y z + + 2 4 3 4 3 4 3 + - 1/144 z y x + 1/432 y x - 1/864 x y - 1/108 y x z - 1/216 y + + 2 2 3 4 2 2 2 + + 1/216 y x z - 1/108 y x z + 1/216 y x + 1/864 y - 1/24 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + + 1/288 y x z - 1/36 y x z - 1/36 y x z + 1/96 y x z + 1/864 y + + 3 3 2 3 2 3 + - 1/864 y x + 1/864 z y - 1/216 y - 1/288 y x - 1/864 z y x + + 3 2 2 4 + - 1/288 z y x + 1/216 y x z + 1/72 z y x + 1/864 y z - 1/216 y z + + 3 3 2 2 2 4 2 2 2 + + 1/432 y x z + 1/216 y x - 1/72 y x z - 1/288 y z + 1/72 y x z + + 2 2 2 2 3 2 3 2 4 + - 1/24 y x z - 1/72 y x z - 1/216 y z + 1/144 y x z - 1/288 x y + + 3 2 3 3 3 3 2 2 + + 1/108 y z + 1/108 y z - 1/432 y z - 1/288 y z + 1/72 y z + + 2 2 2 2 2 2 3 3 3 + + 1/72 y z + 1/72 y x + 1/72 y x - 1/108 y x + 1/432 y x , + + 4 2 4 2 4 2 + COEFF(-1, 1, 2) = 1/54 x y z - 1/48 x y z - 1/18 x y z + + 2 4 3 4 3 3 3 3 4 3 + - 1/72 x y z - 1/27 x y z - 2/27 y x z + 1/54 z y x + + 3 3 3 2 4 4 3 2 3 3 + + 1/54 y x z + 1/144 x y z - 1/108 z y x - 2/27 y x z + + 2 3 3 3 3 2 2 2 3 3 + + 1/27 z y x + 1/27 z y x + 1/36 y x z - 1/9 z y x + 1/27 y x + + 2 3 3 3 4 3 2 4 3 4 3 + - 1/9 z y x - 1/108 z y x + 1/54 y z + 1/36 z y x - 1/108 y x + + 4 3 2 2 3 + + 1/54 x y + 4/27 y x z + 1/27 y - 2/27 y x z + 4/27 y x z - 2/27 y x + + 4 2 2 2 3 2 2 2 3 2 3 + - 1/108 y + 1/12 y x z - 1/18 y x z + 1/18 y x z + 1/18 y x z + + 3 2 2 3 3 3 2 + - 1/48 y x z - 1/108 y + 1/54 y x - 1/108 z y + 1/27 y + + 3 2 3 3 2 2 + + 1/144 y x + 1/54 z y x + 1/144 z y x - 2/27 y x z - 1/36 z y x + + 4 3 3 2 2 2 + - 1/108 y z + 1/27 y z - 1/27 y x z - 2/27 y x + 2/9 y x z + + 4 2 2 2 2 2 2 2 + + 1/36 y z - 1/36 y x z + 1/12 y x z + 2/9 y x z + 1/27 y z + + 3 2 3 2 4 3 2 3 3 3 + - 1/72 y x z + 1/144 x y - 2/27 y z - 2/27 y z + 1/54 y z + + 3 2 2 2 2 2 2 2 2 3 + + 1/36 y z - 1/9 y z - 1/9 y z - 1/36 y x - 1/36 y x + 1/27 y x + + 3 3 4 4 2 + - 1/108 y x , COEFF(0, 1, 2) = - 5/144 x y z + 5/48 x y z + + 4 3 3 3 3 4 3 3 3 3 + + 5/72 x y z + 1/9 y x z - 1/36 z y x - 1/36 y x z + + 4 3 2 3 3 2 3 3 3 3 2 + + 1/72 z y x + 1/9 y x z - 1/18 z y x - 1/18 z y x - 1/24 y x z + + 2 2 3 3 2 3 3 3 2 4 3 + + 1/6 z y x - 1/18 y x + 1/6 z y x + 1/72 z y x - 1/24 z y x + + 4 3 4 3 2 2 3 + + 1/72 y x - 5/144 x y - 5/18 y x z + 5/36 y x z - 5/18 y x z + + 3 2 3 3 + + 5/36 y x + 5/48 y x z - 5/144 y x - 5/144 z y x + 5/36 y x z + + 3 3 2 2 2 2 2 3 + + 5/72 y x z + 5/36 y x - 5/12 y x z - 5/12 y x z - 1/18 y x + + 3 3 4 2 4 2 4 2 + + 1/72 y x , COEFF(1, 1, 2) = 1/54 x y z + 1/48 x y z - 1/18 x y z + + 2 4 3 4 3 3 3 3 4 3 + + 1/72 x y z - 1/27 x y z - 2/27 y x z + 1/54 z y x + + 3 3 3 2 4 4 3 2 3 3 + + 1/54 y x z - 1/144 x y z - 1/108 z y x - 2/27 y x z + + 2 3 3 3 3 2 2 2 3 3 + + 1/27 z y x + 1/27 z y x + 1/36 y x z - 1/9 z y x + 1/27 y x + + 2 3 3 3 4 3 2 4 3 4 3 + - 1/9 z y x - 1/108 z y x - 1/54 y z + 1/36 z y x - 1/108 y x + + 4 3 2 2 3 + + 1/54 x y + 4/27 y x z - 1/27 y - 2/27 y x z + 4/27 y x z - 2/27 y x + + 4 2 2 2 3 2 2 2 3 2 3 + + 1/108 y - 1/12 y x z - 1/18 y x z - 1/18 y x z - 1/18 y x z + + 3 2 2 3 3 3 2 + + 1/48 y x z + 1/108 y + 1/54 y x + 1/108 z y - 1/27 y + + 3 2 3 3 2 2 + - 1/144 y x + 1/54 z y x - 1/144 z y x - 2/27 y x z + 1/36 z y x + + 4 3 3 2 2 2 + + 1/108 y z - 1/27 y z - 1/27 y x z - 2/27 y x + 2/9 y x z + + 4 2 2 2 2 2 2 2 + - 1/36 y z + 1/36 y x z - 1/12 y x z + 2/9 y x z - 1/27 y z + + 3 2 3 2 4 3 2 3 3 3 + + 1/72 y x z - 1/144 x y + 2/27 y z + 2/27 y z - 1/54 y z + + 3 2 2 2 2 2 2 2 2 3 + - 1/36 y z + 1/9 y z + 1/9 y z + 1/36 y x + 1/36 y x + 1/27 y x + + 3 3 4 2 4 2 + - 1/108 y x , COEFF(2, 1, 2) = - 1/864 x y z - 1/96 x y z + + 4 2 2 4 3 4 3 3 3 + + 1/288 x y z - 1/144 x y z + 1/432 x y z + 1/54 y x z + + 3 4 3 3 3 3 2 4 4 3 + - 1/216 z y x - 1/216 y x z + 1/288 x y z + 1/432 z y x + + 2 3 3 2 3 3 3 3 2 + + 1/54 y x z - 1/108 z y x - 1/108 z y x - 1/144 y x z + + 2 2 3 3 2 3 3 3 4 3 + + 1/36 z y x - 1/108 y x + 1/36 z y x + 1/432 z y x + 1/432 y z + + 2 4 3 4 3 4 3 + - 1/144 z y x + 1/432 y x - 1/864 x y - 1/108 y x z + 1/216 y + + 2 2 3 4 2 2 2 + + 1/216 y x z - 1/108 y x z + 1/216 y x - 1/864 y + 1/24 y x z + + 3 2 2 2 3 2 3 3 2 2 3 + + 1/288 y x z + 1/36 y x z + 1/36 y x z - 1/96 y x z - 1/864 y + + 3 3 2 3 2 3 + - 1/864 y x - 1/864 z y + 1/216 y + 1/288 y x - 1/864 z y x + + 3 2 2 4 + + 1/288 z y x + 1/216 y x z - 1/72 z y x - 1/864 y z + 1/216 y z + + 3 3 2 2 2 4 2 2 2 + + 1/432 y x z + 1/216 y x - 1/72 y x z + 1/288 y z - 1/72 y x z + + 2 2 2 2 3 2 3 2 4 + + 1/24 y x z - 1/72 y x z + 1/216 y z - 1/144 y x z + 1/288 x y + + 3 2 3 3 3 3 2 2 + - 1/108 y z - 1/108 y z + 1/432 y z + 1/288 y z - 1/72 y z + + 2 2 2 2 2 2 3 3 3 + - 1/72 y z - 1/72 y x - 1/72 y x - 1/108 y x + 1/432 y x , + + 4 2 4 2 4 2 + COEFF(-2, 2, 2) = 1/3456 x y z - 1/384 x y z - 1/1152 x y z + + 2 4 3 4 3 3 3 3 4 3 + - 1/576 x y z - 1/1728 x y z - 1/432 y x z + 1/864 z y x + + 3 3 3 2 4 4 3 2 3 3 + + 1/432 y x z + 1/1152 x y z - 1/1728 z y x - 1/864 y x z + + 2 3 3 3 3 2 2 2 3 + + 1/1728 z y x + 1/864 z y x + 1/288 y x z - 1/576 z y x + + 3 2 3 3 3 4 3 + + 1/864 y x - 1/288 z y x - 1/864 z y x + 1/1728 y z + + 2 4 3 4 3 4 3 + + 1/576 z y x - 1/1728 y x + 1/3456 x y + 1/864 y x z + 1/1728 y + + 2 2 3 4 2 2 2 + - 1/3456 y x z + 1/1728 y x z - 1/1728 y x - 1/3456 y + 1/384 y x z + + 3 2 2 2 3 2 3 3 2 2 + - 1/576 y x z + 1/576 y x z + 1/288 y x z - 1/192 y x z + + 3 3 3 2 3 2 + - 1/1728 y + 1/1728 y x - 1/1728 z y + 1/3456 y + 1/576 y x + + 3 3 2 2 + + 1/1728 z y x + 1/576 z y x - 1/1728 y x z - 1/576 z y x + + 4 3 3 2 2 2 + - 1/3456 y z + 1/1728 y z - 1/864 y x z - 1/3456 y x + 1/1152 y x z + + 4 2 2 2 2 2 2 + + 1/1152 y z - 1/1152 y x z + 1/192 y x z + 1/576 y x z + + 2 3 2 3 2 4 3 2 3 + + 1/3456 y z - 1/288 y x z + 1/1152 x y - 1/864 y z - 1/1728 y z + + 3 3 3 2 2 2 2 2 2 + + 1/864 y z + 1/576 y z - 1/576 y z - 1/1152 y z - 1/1152 y x + + 2 2 3 3 3 + - 1/576 y x + 1/1728 y x - 1/864 y x , COEFF(-1, 2, 2) = + + 4 2 4 2 4 2 2 4 3 + - 1/216 x y z + 1/192 x y z + 1/72 x y z + 1/288 x y z + + 4 3 3 3 3 4 3 3 3 3 + + 1/108 x y z + 1/108 y x z - 1/216 z y x - 1/108 y x z + + 2 4 4 3 2 3 3 2 3 + - 1/576 x y z + 1/432 z y x + 1/216 y x z - 1/432 z y x + + 3 3 3 2 2 2 3 3 + - 1/216 z y x - 1/72 y x z + 1/144 z y x - 1/216 y x + + 2 3 3 3 4 3 2 4 3 + + 1/72 z y x + 1/216 z y x - 1/216 y z - 1/144 z y x + + 4 3 4 3 2 + + 1/432 y x - 1/216 x y - 1/54 y x z - 1/216 y + 1/216 y x z + + 2 3 4 2 2 2 3 2 + - 1/108 y x z + 1/108 y x + 1/432 y - 1/192 y x z + 1/36 y x z + + 2 2 3 2 3 3 2 2 3 3 + - 1/288 y x z - 1/144 y x z + 1/96 y x z + 1/216 y - 1/108 y x + + 3 2 3 2 3 3 2 + + 1/216 z y - 1/432 y - 1/288 y x - 1/108 z y x - 1/288 z y x + + 2 4 3 3 + + 1/108 y x z + 1/288 z y x + 1/432 y z - 1/216 y z + 1/54 y x z + + 2 2 2 4 2 2 2 2 2 + + 1/216 y x - 1/72 y x z - 1/144 y z + 1/576 y x z - 1/96 y x z + + 2 2 3 2 3 2 4 3 + - 1/36 y x z - 1/432 y z + 1/144 y x z - 1/576 x y + 1/108 y z + + 2 3 3 3 3 2 2 2 2 + + 1/216 y z - 1/108 y z - 1/72 y z + 1/72 y z + 1/144 y z + + 2 2 2 2 3 3 3 + + 1/576 y x + 1/288 y x - 1/432 y x + 1/216 y x , COEFF(0, 2, 2) = + + 4 4 2 4 3 3 3 + 5/576 x y z - 5/192 x y z - 5/288 x y z - 1/72 y x z + + 3 4 3 3 3 3 4 3 2 3 3 + + 1/144 z y x + 1/72 y x z - 1/288 z y x - 1/144 y x z + + 2 3 3 3 3 2 2 2 3 + + 1/288 z y x + 1/144 z y x + 1/48 y x z - 1/96 z y x + + 3 2 3 3 3 2 4 3 4 3 + + 1/144 y x - 1/48 z y x - 1/144 z y x + 1/96 z y x - 1/288 y x + + 4 3 2 2 3 + + 5/576 x y + 5/144 y x z - 5/576 y x z + 5/288 y x z - 5/288 y x + + 3 2 3 3 3 3 + - 5/96 y x z + 5/288 y x + 5/288 z y x - 5/288 y x z - 5/144 y x z + + 2 2 2 2 2 3 3 3 + - 5/576 y x + 5/192 y x z + 5/96 y x z + 1/288 y x - 1/144 y x , + + 4 2 4 2 4 2 + COEFF(1, 2, 2) = - 1/216 x y z - 1/192 x y z + 1/72 x y z + + 2 4 3 4 3 3 3 3 4 3 + - 1/288 x y z + 1/108 x y z + 1/108 y x z - 1/216 z y x + + 3 3 3 2 4 4 3 2 3 3 + - 1/108 y x z + 1/576 x y z + 1/432 z y x + 1/216 y x z + + 2 3 3 3 3 2 2 2 3 + - 1/432 z y x - 1/216 z y x - 1/72 y x z + 1/144 z y x + + 3 2 3 3 3 4 3 2 4 3 + - 1/216 y x + 1/72 z y x + 1/216 z y x + 1/216 y z - 1/144 z y x + + 4 3 4 3 2 + + 1/432 y x - 1/216 x y - 1/54 y x z + 1/216 y + 1/216 y x z + + 2 3 4 2 2 2 3 2 + - 1/108 y x z + 1/108 y x - 1/432 y + 1/192 y x z + 1/36 y x z + + 2 2 3 2 3 3 2 2 3 3 + + 1/288 y x z + 1/144 y x z - 1/96 y x z - 1/216 y - 1/108 y x + + 3 2 3 2 3 3 2 + - 1/216 z y + 1/432 y + 1/288 y x - 1/108 z y x + 1/288 z y x + + 2 4 3 3 + + 1/108 y x z - 1/288 z y x - 1/432 y z + 1/216 y z + 1/54 y x z + + 2 2 2 4 2 2 2 2 2 + + 1/216 y x - 1/72 y x z + 1/144 y z - 1/576 y x z + 1/96 y x z + + 2 2 3 2 3 2 4 3 + - 1/36 y x z + 1/432 y z - 1/144 y x z + 1/576 x y - 1/108 y z + + 2 3 3 3 3 2 2 2 2 + - 1/216 y z + 1/108 y z + 1/72 y z - 1/72 y z - 1/144 y z + + 2 2 2 2 3 3 3 + - 1/576 y x - 1/288 y x - 1/432 y x + 1/216 y x , COEFF(2, 2, 2) = + + 4 2 4 2 4 2 2 4 3 + 1/3456 x y z + 1/384 x y z - 1/1152 x y z + 1/576 x y z + + 4 3 3 3 3 4 3 3 3 3 + - 1/1728 x y z - 1/432 y x z + 1/864 z y x + 1/432 y x z + + 2 4 4 3 2 3 3 2 3 + - 1/1152 x y z - 1/1728 z y x - 1/864 y x z + 1/1728 z y x + + 3 3 3 2 2 2 3 3 + + 1/864 z y x + 1/288 y x z - 1/576 z y x + 1/864 y x + + 2 3 3 3 4 3 2 4 3 + - 1/288 z y x - 1/864 z y x - 1/1728 y z + 1/576 z y x + + 4 3 4 3 2 + - 1/1728 y x + 1/3456 x y + 1/864 y x z - 1/1728 y - 1/3456 y x z + + 2 3 4 2 2 2 3 2 + + 1/1728 y x z - 1/1728 y x + 1/3456 y - 1/384 y x z - 1/576 y x z + + 2 2 3 2 3 3 2 2 3 + - 1/576 y x z - 1/288 y x z + 1/192 y x z + 1/1728 y + + 3 3 2 3 2 3 + + 1/1728 y x + 1/1728 z y - 1/3456 y - 1/576 y x + 1/1728 z y x + + 3 2 2 4 + - 1/576 z y x - 1/1728 y x z + 1/576 z y x + 1/3456 y z - 1/1728 y z + + 3 3 2 2 2 4 2 + - 1/864 y x z - 1/3456 y x + 1/1152 y x z - 1/1152 y z + + 2 2 2 2 2 2 + + 1/1152 y x z - 1/192 y x z + 1/576 y x z - 1/3456 y z + + 3 2 3 2 4 3 2 3 3 3 + + 1/288 y x z - 1/1152 x y + 1/864 y z + 1/1728 y z - 1/864 y z + + 3 2 2 2 2 2 2 2 + - 1/576 y z + 1/576 y z + 1/1152 y z + 1/1152 y x + 1/576 y x + + 2 3 3 3 + + 1/1728 y x - 1/864 y x ] + +> print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxz.compute.c"); +bytes used=35189804772, alloc=64737712, time=8227.64 +bytes used=35190804948, alloc=64737712, time=8227.74 +bytes used=35191805144, alloc=64737712, time=8227.84 +bytes used=35192805432, alloc=64737712, time=8227.93 +bytes used=35193805976, alloc=64737712, time=8228.03 +bytes used=35194806420, alloc=64737712, time=8228.12 +bytes used=35195806668, alloc=64737712, time=8228.22 +bytes used=35196806860, alloc=64737712, time=8228.32 +bytes used=35197807252, alloc=64737712, time=8228.42 +bytes used=35198807832, alloc=64737712, time=8228.51 +bytes used=35199808020, alloc=64737712, time=8228.61 +bytes used=35200808412, alloc=64737712, time=8228.71 +bytes used=35201808592, alloc=64737712, time=8228.81 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2 2 3 2 2 2 + + 1/288 y x z + 1/288 y x z - 1/288 y x z + 1/1152 y x z + + 2 2 3 2 3 2 + + 1/576 y x z - 1/576 y x z - 1/288 y x z + 1/576 z y x + + 4 4 2 2 2 2 + - 1/3456 x z - 1/3456 z x - 1/576 y x z - 1/576 y x z + + 2 2 2 2 2 3 + - 1/1152 y x z + 1/576 y x z - 1/1728 x z + 1/3456 x z - 1/3456 x z + + 3 2 2 2 4 4 2 4 + + 1/1728 x z - 1/6912 x z + 1/3456 x z - 1/6912 z x + 1/6912 z x + + 3 4 3 4 3 + + 1/3456 z x + 1/1728 z x + 1/3456 z x , COEFF(-1, -2, -2) = + + 2 2 4 4 4 3 3 2 2 4 + 1/72 y x z + 1/288 z y x + 1/144 y x z + 1/288 z y x + + 4 4 4 2 4 2 3 3 + + 1/144 z y x + 1/72 y x z - 1/288 z y x - 1/144 y x z + + 2 3 3 2 4 2 2 3 + + 1/144 z y x - 1/144 z y x - 1/72 y x z - 1/288 z y x + + 2 3 2 4 2 4 3 4 + + 1/288 z y x - 1/432 x z - 1/144 z y x - 1/144 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/288 z y x - 1/288 z y x + 1/144 z y x + 1/288 z y x + + 2 4 3 2 3 3 3 2 + - 1/72 y x z + 1/1728 x z + 1/864 x z - 1/36 y x z - 1/36 y x z + + 2 3 2 2 2 2 2 3 2 3 + + 1/36 y x z - 1/72 y x z - 1/36 y x z + 1/36 y x z + 1/36 y x z + + 2 4 4 2 2 2 2 + - 1/36 z y x + 1/432 x z + 1/864 z x + 1/72 y x z + 1/36 y x z + + 2 2 2 2 2 3 + + 1/72 y x z - 1/72 y x z + 1/216 x z - 1/216 x z + 1/216 x z + + 3 2 2 2 4 4 2 4 + - 1/216 x z + 1/432 x z - 1/432 x z + 1/1728 z x - 1/1728 z x + + 3 4 3 4 3 + - 1/864 z x - 1/864 z x - 1/1728 z x , COEFF(0, -2, -2) = + + 2 2 4 4 4 2 2 4 4 + - 5/192 y x z - 1/192 z y x - 1/192 z y x - 1/96 z y x + + 4 2 4 2 4 2 4 3 4 + + 1/192 z y x + 5/1152 x z + 1/96 z y x + 1/96 z y x + + 2 4 3 2 4 2 4 2 2 2 + + 1/192 z y x - 1/96 z y x + 5/192 y x z - 1/144 z + 5/192 y x z + + 2 2 3 2 3 4 3 2 4 + + 5/96 y x z - 5/96 y x z - 1/288 z + 1/144 z + 1/48 y z + + 4 2 2 4 + - 1/48 y z + 1/288 z + 5/96 z y x - 1/24 y z - 1/576 z x + + 2 2 2 2 2 2 3 + - 5/96 y x z - 5/192 y x z + 1/24 y z + 5/576 x z + 1/24 y z + + 2 3 2 3 2 2 2 4 4 + - 1/24 y z - 5/576 x z + 1/48 y z - 5/1152 x z - 1/1152 z x + + 2 2 2 4 3 4 + - 1/48 y z + 1/1152 z x + 1/576 z x , COEFF(1, -2, -2) = + + 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z y x + 1/576 y x z + 1/1152 z y x - 1/288 y x z + + 2 3 3 2 4 2 2 3 + + 1/288 z y x - 1/288 z y x - 1/576 y x z - 1/576 z y x + + 2 3 2 4 2 4 3 4 + + 1/576 z y x + 1/6912 x z + 1/576 z y x + 1/576 z y x + + 2 4 4 3 3 2 4 4 2 3 + + 1/1152 z y x - 1/576 z y x - 1/576 z y x + 1/576 z y x + + 2 4 3 2 3 3 3 + + 1/1152 y x z + 1/3456 x z + 1/1728 x z - 1/288 y x z + + 2 2 3 2 2 2 2 2 3 + - 1/288 y x z + 1/288 y x z + 1/1152 y x z + 1/576 y x z + + 2 3 2 4 4 + - 1/576 y x z + 1/288 y x z + 1/576 z y x + 1/3456 x z - 1/3456 z x + + 2 2 2 2 2 2 2 + + 1/576 y x z - 1/576 y x z - 1/1152 y x z - 1/576 y x z + + 2 2 3 3 2 2 + + 1/1728 x z + 1/3456 x z - 1/3456 x z - 1/1728 x z - 1/6912 x z + + 2 4 4 2 4 3 4 3 + - 1/3456 x z - 1/6912 z x + 1/6912 z x + 1/3456 z x - 1/1728 z x + + 4 3 2 2 4 4 4 + - 1/3456 z x , COEFF(-2, -1, -2) = 1/288 y x z + 1/576 z y x + + 3 3 2 2 4 4 4 + + 1/144 y x z + 1/288 z y x + 1/288 z y x + 1/288 y x z + + 4 2 4 2 3 3 2 3 3 + - 1/288 z y x - 1/72 y x z + 1/72 z y x - 1/144 z y x + + 2 4 2 2 3 2 3 2 4 + - 1/144 y x z - 1/144 z y x + 1/288 z y x - 1/432 x z + + 2 4 3 4 2 4 4 3 + - 1/144 z y x - 1/288 z y x - 1/576 z y x - 1/288 z y x + + 3 2 4 4 2 3 2 4 3 2 + + 1/144 z y x + 1/144 z y x - 1/576 y x z + 1/216 x z + + 3 3 3 2 2 3 2 2 2 + + 1/108 x z - 1/144 y x z - 1/72 y x z + 1/72 y x z - 1/288 y x z + + 2 2 3 2 3 2 4 + - 1/144 y x z + 1/288 y x z + 1/144 y x z - 1/288 z y x + 1/216 x z + + 4 2 2 2 2 2 2 + + 1/216 z x + 1/144 y x z + 1/144 y x z + 1/576 y x z + + 2 2 2 3 3 + - 1/288 y x z + 1/108 x z - 1/216 x z + 1/216 x z - 1/108 x z + + 2 2 2 4 4 2 4 3 4 + + 1/432 x z - 1/216 x z + 1/432 z x - 1/432 z x - 1/216 z x + + 3 4 3 2 2 4 + - 1/108 z x - 1/216 z x , COEFF(-1, -1, -2) = - 1/18 y x z + + 4 4 3 3 2 2 4 4 4 + - 1/144 z y x - 1/72 y x z - 1/72 z y x - 1/72 z y x - 1/36 y x z + + 4 2 4 2 3 3 2 3 3 + + 1/72 z y x + 1/36 y x z - 1/36 z y x + 1/72 z y x + + 2 4 2 2 3 2 3 2 4 2 4 + + 1/18 y x z + 1/72 z y x - 1/144 z y x + 1/27 x z + 1/36 z y x + + 3 4 2 4 4 3 3 2 4 + + 1/72 z y x + 1/144 z y x + 1/144 z y x - 1/36 z y x + + 4 2 3 2 4 3 2 3 3 3 + - 1/72 z y x + 1/36 y x z - 1/108 x z - 1/54 x z + 1/18 y x z + + 2 2 3 2 2 2 2 2 3 2 3 + + 1/9 y x z - 1/9 y x z + 1/18 y x z + 1/9 y x z - 1/18 y x z + + 2 4 4 2 2 + - 1/18 y x z + 1/18 z y x - 1/27 x z - 1/54 z x - 1/18 y x z + + 2 2 2 2 2 2 + - 1/9 y x z - 1/36 y x z + 1/36 y x z - 2/27 x z + 2/27 x z + + 2 3 3 2 2 2 4 4 + - 2/27 x z + 2/27 x z - 1/27 x z + 1/27 x z - 1/108 z x + + 2 4 3 4 3 4 3 + + 1/108 z x + 1/54 z x + 1/54 z x + 1/108 z x , COEFF(0, -1, -2) = + + 2 2 4 4 4 2 2 4 4 4 2 4 + 5/48 y x z + 1/96 z y x + 1/48 z y x + 1/48 z y x - 1/48 z y x + + 2 4 2 4 3 4 2 4 3 2 4 + - 5/72 x z - 1/24 z y x - 1/48 z y x - 1/96 z y x + 1/24 z y x + + 2 4 2 2 2 2 2 3 2 3 + - 5/96 y x z + 1/9 z - 5/48 y x z - 5/24 y x z + 5/48 y x z + + 4 3 2 4 4 2 2 + + 1/18 z - 1/9 z - 1/12 y z + 1/24 y z - 1/18 z - 5/48 z y x + + 4 2 2 2 2 2 + + 1/12 y z + 1/36 z x + 5/24 y x z + 5/96 y x z - 1/6 y z + + 2 3 2 3 2 3 2 2 2 + - 5/36 x z - 1/12 y z + 1/6 y z + 5/36 x z - 1/24 y z + 5/72 x z + + 4 4 2 2 2 4 3 4 + + 1/72 z x + 1/12 y z - 1/72 z x - 1/36 z x , COEFF(1, -1, -2) = + + 2 2 4 4 4 3 3 2 2 4 + - 1/18 y x z - 1/144 z y x + 1/72 y x z - 1/72 z y x + + 4 4 4 2 4 2 3 3 2 3 + - 1/72 z y x + 1/36 y x z + 1/72 z y x - 1/36 y x z + 1/36 z y x + + 3 2 4 2 2 3 2 3 2 4 + - 1/72 z y x - 1/18 y x z - 1/72 z y x + 1/144 z y x + 1/27 x z + + 2 4 3 4 2 4 4 3 + + 1/36 z y x + 1/72 z y x + 1/144 z y x - 1/144 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + - 1/36 z y x + 1/72 z y x + 1/36 y x z + 1/108 x z + 1/54 x z + + 3 2 2 3 2 2 2 2 2 3 + - 1/18 y x z - 1/9 y x z + 1/9 y x z + 1/18 y x z + 1/9 y x z + + 2 3 2 4 4 + - 1/18 y x z + 1/18 y x z + 1/18 z y x + 1/27 x z - 1/54 z x + + 2 2 2 2 2 2 2 + + 1/18 y x z - 1/9 y x z - 1/36 y x z - 1/36 y x z + 2/27 x z + + 2 2 3 3 2 2 2 + + 2/27 x z - 2/27 x z - 2/27 x z - 1/27 x z - 1/27 x z + + 4 4 2 4 3 4 3 4 3 + - 1/108 z x + 1/108 z x + 1/54 z x - 1/54 z x - 1/108 z x , + + 2 2 4 4 4 3 3 + COEFF(2, -1, -2) = 1/288 y x z + 1/576 z y x - 1/144 y x z + + 2 2 4 4 4 4 2 4 + + 1/288 z y x + 1/288 z y x - 1/288 y x z - 1/288 z y x + + 2 3 3 2 3 3 2 4 + + 1/72 y x z - 1/72 z y x + 1/144 z y x + 1/144 y x z + + 2 2 3 2 3 2 4 2 4 + + 1/144 z y x - 1/288 z y x - 1/432 x z - 1/144 z y x + + 3 4 2 4 4 3 3 2 4 + - 1/288 z y x - 1/576 z y x + 1/288 z y x + 1/144 z y x + + 4 2 3 2 4 3 2 3 3 + - 1/144 z y x - 1/576 y x z - 1/216 x z - 1/108 x z + + 3 2 2 3 2 2 2 + + 1/144 y x z + 1/72 y x z - 1/72 y x z - 1/288 y x z + + 2 2 3 2 3 2 4 + - 1/144 y x z + 1/288 y x z - 1/144 y x z - 1/288 z y x - 1/216 x z + + 4 2 2 2 2 2 2 + + 1/216 z x - 1/144 y x z + 1/144 y x z + 1/576 y x z + + 2 2 2 3 3 + + 1/288 y x z - 1/108 x z - 1/216 x z + 1/216 x z + 1/108 x z + + 2 2 2 4 4 2 4 3 4 + + 1/432 x z + 1/216 x z + 1/432 z x - 1/432 z x - 1/216 z x + + 3 4 3 2 2 4 + + 1/108 z x + 1/216 z x , COEFF(-2, 0, -2) = - 1/192 y x z + + 2 2 4 4 2 4 2 3 3 2 3 + - 1/192 z y x + 1/192 z y x + 1/48 y x z - 1/48 z y x + + 2 4 2 2 3 2 4 2 4 + + 1/96 y x z + 1/96 z y x + 5/1152 x z + 1/96 z y x + + 3 2 4 4 2 3 3 2 3 3 2 + - 1/96 z y x - 1/96 z y x - 5/576 x z - 5/288 x z + 1/48 y x z + + 2 3 2 2 2 2 2 3 4 4 + - 1/48 y x z + 1/192 y x z + 1/96 y x z - 5/576 x z - 5/576 z x + + 2 2 2 2 2 2 3 + - 1/96 y x z - 1/96 y x z - 5/288 x z + 5/576 x z - 5/576 x z + + 3 2 2 2 4 4 2 4 + + 5/288 x z - 5/1152 x z + 5/576 x z - 5/1152 z x + 5/1152 z x + + 3 4 3 4 3 2 2 4 + + 5/576 z x + 5/288 z x + 5/576 z x , COEFF(-1, 0, -2) = 1/12 y x z + + 2 2 4 4 2 4 2 3 3 2 3 + + 1/48 z y x - 1/48 z y x - 1/24 y x z + 1/24 z y x + + 2 4 2 2 3 2 4 2 4 3 2 4 + - 1/12 y x z - 1/48 z y x - 5/72 x z - 1/24 z y x + 1/24 z y x + + 4 2 3 3 2 3 3 2 2 3 + + 1/48 z y x + 5/288 x z + 5/144 x z - 1/6 y x z + 1/6 y x z + + 2 2 2 2 2 3 4 4 2 2 + - 1/12 y x z - 1/6 y x z + 5/72 x z + 5/144 z x + 1/12 y x z + + 2 2 2 2 3 3 2 2 + + 1/6 y x z + 5/36 x z - 5/36 x z + 5/36 x z - 5/36 x z + 5/72 x z + + 2 4 4 2 4 3 4 3 + - 5/72 x z + 5/288 z x - 5/288 z x - 5/144 z x - 5/144 z x + + 4 3 2 4 4 4 4 + - 5/288 z x , COEFF(0, 0, -2) = 1/8 y z - 5/192 z x - 5/48 z + + 4 3 2 4 2 4 2 2 4 25 2 4 + - 5/96 z x - 1/16 z y x + 5/192 z x - 5/32 y x z + --- x z + 192 + + 25 2 2 2 4 4 2 4 2 3 4 + - --- x z + 1/16 z y x + 1/32 z y x + 5/48 z + 5/96 z x + 192 + + 25 2 3 2 2 2 2 2 + + -- x z + 5/24 z + 1/4 y z - 5/16 y x z - 5/24 z - 1/8 y z + 96 + + 2 2 3 2 2 4 25 2 3 2 3 2 2 2 + + 5/16 y x z - 1/32 z y x - -- x z - 1/4 y z + 5/32 y x z , + 96 + + 2 2 4 2 2 4 4 2 4 + COEFF(1, 0, -2) = 1/12 y x z + 1/48 z y x - 1/48 z y x + + 2 3 3 2 3 2 4 2 2 3 2 4 + + 1/24 y x z - 1/24 z y x + 1/12 y x z + 1/48 z y x - 5/72 x z + + 2 4 3 2 4 4 2 3 3 2 3 3 + - 1/24 z y x + 1/24 z y x - 1/48 z y x - 5/288 x z - 5/144 x z + + 2 2 3 2 2 2 2 2 3 4 + + 1/6 y x z - 1/6 y x z - 1/12 y x z - 1/6 y x z - 5/72 x z + + 4 2 2 2 2 2 + + 5/144 z x - 1/12 y x z + 1/6 y x z - 5/36 x z - 5/36 x z + + 2 3 3 2 2 2 4 4 + + 5/36 x z + 5/36 x z + 5/72 x z + 5/72 x z + 5/288 z x + + 2 4 3 4 3 4 3 + - 5/288 z x - 5/144 z x + 5/144 z x + 5/288 z x , COEFF(2, 0, -2) = + + 2 2 4 2 2 4 4 2 4 2 3 3 + - 1/192 y x z - 1/192 z y x + 1/192 z y x - 1/48 y x z + + 2 3 2 4 2 2 3 2 4 + + 1/48 z y x - 1/96 y x z - 1/96 z y x + 5/1152 x z + + 2 4 3 2 4 4 2 3 3 2 3 3 + + 1/96 z y x - 1/96 z y x + 1/96 z y x + 5/576 x z + 5/288 x z + + 2 2 3 2 2 2 2 2 3 4 + - 1/48 y x z + 1/48 y x z + 1/192 y x z + 1/96 y x z + 5/576 x z + + 4 2 2 2 2 2 + - 5/576 z x + 1/96 y x z - 1/96 y x z + 5/288 x z + 5/576 x z + + 2 3 3 2 2 2 4 4 + - 5/576 x z - 5/288 x z - 5/1152 x z - 5/576 x z - 5/1152 z x + + 2 4 3 4 3 4 3 + + 5/1152 z x + 5/576 z x - 5/288 z x - 5/576 z x , COEFF(-2, 1, -2) + + 2 2 4 4 4 3 3 2 2 4 + = 1/288 y x z - 1/576 z y x - 1/144 y x z + 1/288 z y x + + 4 4 4 2 4 2 3 3 + - 1/288 z y x - 1/288 y x z - 1/288 z y x - 1/72 y x z + + 2 3 3 2 4 2 2 3 + + 1/72 z y x + 1/144 z y x - 1/144 y x z - 1/144 z y x + + 2 3 2 4 2 4 3 4 + - 1/288 z y x - 1/432 x z - 1/144 z y x + 1/288 z y x + + 2 4 4 3 3 2 4 4 2 3 + + 1/576 z y x + 1/288 z y x + 1/144 z y x + 1/144 z y x + + 2 4 3 2 3 3 3 2 + + 1/576 y x z + 1/216 x z + 1/108 x z + 1/144 y x z - 1/72 y x z + + 2 3 2 2 2 2 2 3 2 3 + + 1/72 y x z - 1/288 y x z - 1/144 y x z - 1/288 y x z + + 2 4 4 2 2 + - 1/144 y x z + 1/288 z y x + 1/216 x z + 1/216 z x + 1/144 y x z + + 2 2 2 2 2 2 + + 1/144 y x z - 1/576 y x z + 1/288 y x z + 1/108 x z - 1/216 x z + + 2 3 3 2 2 2 4 4 + + 1/216 x z - 1/108 x z + 1/432 x z - 1/216 x z + 1/432 z x + + 2 4 3 4 3 4 3 + - 1/432 z x - 1/216 z x - 1/108 z x - 1/216 z x , COEFF(-1, 1, -2) + + 2 2 4 4 4 3 3 2 2 4 + = - 1/18 y x z + 1/144 z y x + 1/72 y x z - 1/72 z y x + + 4 4 4 2 4 2 3 3 2 3 + + 1/72 z y x + 1/36 y x z + 1/72 z y x + 1/36 y x z - 1/36 z y x + + 3 2 4 2 2 3 2 3 2 4 + - 1/72 z y x + 1/18 y x z + 1/72 z y x + 1/144 z y x + 1/27 x z + + 2 4 3 4 2 4 4 3 + + 1/36 z y x - 1/72 z y x - 1/144 z y x - 1/144 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + - 1/36 z y x - 1/72 z y x - 1/36 y x z - 1/108 x z - 1/54 x z + + 3 2 2 3 2 2 2 2 2 3 + - 1/18 y x z + 1/9 y x z - 1/9 y x z + 1/18 y x z + 1/9 y x z + + 2 3 2 4 4 + + 1/18 y x z + 1/18 y x z - 1/18 z y x - 1/27 x z - 1/54 z x + + 2 2 2 2 2 2 2 + - 1/18 y x z - 1/9 y x z + 1/36 y x z - 1/36 y x z - 2/27 x z + + 2 2 3 3 2 2 2 + + 2/27 x z - 2/27 x z + 2/27 x z - 1/27 x z + 1/27 x z + + 4 4 2 4 3 4 3 4 3 + - 1/108 z x + 1/108 z x + 1/54 z x + 1/54 z x + 1/108 z x , + + 2 2 4 4 4 2 2 4 + COEFF(0, 1, -2) = 5/48 y x z - 1/96 z y x + 1/48 z y x + + 4 4 2 4 2 4 2 4 3 4 + - 1/48 z y x - 1/48 z y x - 5/72 x z - 1/24 z y x + 1/48 z y x + + 2 4 3 2 4 2 4 2 2 2 + + 1/96 z y x + 1/24 z y x + 5/96 y x z + 1/9 z - 5/48 y x z + + 2 2 3 2 3 4 3 2 4 4 + - 5/24 y x z - 5/48 y x z + 1/18 z - 1/9 z - 1/12 y z - 1/24 y z + + 2 2 4 2 2 + - 1/18 z + 5/48 z y x - 1/12 y z + 1/36 z x + 5/24 y x z + + 2 2 2 2 3 2 3 2 3 + - 5/96 y x z - 1/6 y z - 5/36 x z + 1/12 y z + 1/6 y z + 5/36 x z + + 2 2 2 4 4 2 2 2 4 + + 1/24 y z + 5/72 x z + 1/72 z x + 1/12 y z - 1/72 z x + + 3 4 2 2 4 4 4 + - 1/36 z x , COEFF(1, 1, -2) = - 1/18 y x z + 1/144 z y x + + 3 3 2 2 4 4 4 4 2 4 + - 1/72 y x z - 1/72 z y x + 1/72 z y x - 1/36 y x z + 1/72 z y x + + 2 3 3 2 3 3 2 4 + - 1/36 y x z + 1/36 z y x + 1/72 z y x - 1/18 y x z + + 2 2 3 2 3 2 4 2 4 3 4 + - 1/72 z y x - 1/144 z y x + 1/27 x z + 1/36 z y x - 1/72 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/144 z y x + 1/144 z y x - 1/36 z y x + 1/72 z y x + + 2 4 3 2 3 3 3 2 + - 1/36 y x z + 1/108 x z + 1/54 x z + 1/18 y x z - 1/9 y x z + + 2 3 2 2 2 2 2 3 2 3 + + 1/9 y x z + 1/18 y x z + 1/9 y x z + 1/18 y x z - 1/18 y x z + + 2 4 4 2 2 2 2 + - 1/18 z y x + 1/27 x z - 1/54 z x + 1/18 y x z - 1/9 y x z + + 2 2 2 2 2 3 + + 1/36 y x z + 1/36 y x z + 2/27 x z + 2/27 x z - 2/27 x z + + 3 2 2 2 4 4 2 4 + - 2/27 x z - 1/27 x z - 1/27 x z - 1/108 z x + 1/108 z x + + 3 4 3 4 3 2 2 4 + + 1/54 z x - 1/54 z x - 1/108 z x , COEFF(2, 1, -2) = 1/288 y x z + + 4 4 3 3 2 2 4 4 + - 1/576 z y x + 1/144 y x z + 1/288 z y x - 1/288 z y x + + 4 4 2 4 2 3 3 2 3 + + 1/288 y x z - 1/288 z y x + 1/72 y x z - 1/72 z y x + + 3 2 4 2 2 3 2 3 + - 1/144 z y x + 1/144 y x z + 1/144 z y x + 1/288 z y x + + 2 4 2 4 3 4 2 4 + - 1/432 x z - 1/144 z y x + 1/288 z y x + 1/576 z y x + + 4 3 3 2 4 4 2 3 2 4 + - 1/288 z y x + 1/144 z y x - 1/144 z y x + 1/576 y x z + + 3 2 3 3 3 2 2 3 + - 1/216 x z - 1/108 x z - 1/144 y x z + 1/72 y x z - 1/72 y x z + + 2 2 2 2 2 3 2 3 + - 1/288 y x z - 1/144 y x z - 1/288 y x z + 1/144 y x z + + 2 4 4 2 2 2 2 + + 1/288 z y x - 1/216 x z + 1/216 z x - 1/144 y x z + 1/144 y x z + + 2 2 2 2 2 3 + - 1/576 y x z - 1/288 y x z - 1/108 x z - 1/216 x z + 1/216 x z + + 3 2 2 2 4 4 2 4 + + 1/108 x z + 1/432 x z + 1/216 x z + 1/432 z x - 1/432 z x + + 3 4 3 4 3 + - 1/216 z x + 1/108 z x + 1/216 z x , COEFF(-2, 2, -2) = + + 2 2 4 4 4 3 3 2 2 4 + - 1/1152 y x z + 1/1152 z y x + 1/288 y x z - 1/1152 z y x + + 4 4 4 2 4 2 3 3 + + 1/576 z y x + 1/576 y x z + 1/1152 z y x + 1/288 y x z + + 2 3 3 2 4 2 2 3 + - 1/288 z y x - 1/288 z y x + 1/576 y x z + 1/576 z y x + + 2 3 2 4 2 4 3 4 + + 1/576 z y x + 1/6912 x z + 1/576 z y x - 1/576 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/1152 z y x - 1/576 z y x - 1/576 z y x - 1/576 z y x + + 2 4 3 2 3 3 3 + - 1/1152 y x z - 1/3456 x z - 1/1728 x z - 1/288 y x z + + 2 2 3 2 2 2 2 2 3 + + 1/288 y x z - 1/288 y x z + 1/1152 y x z + 1/576 y x z + + 2 3 2 4 4 + + 1/576 y x z + 1/288 y x z - 1/576 z y x - 1/3456 x z - 1/3456 z x + + 2 2 2 2 2 2 2 + - 1/576 y x z - 1/576 y x z + 1/1152 y x z - 1/576 y x z + + 2 2 3 3 2 2 + - 1/1728 x z + 1/3456 x z - 1/3456 x z + 1/1728 x z - 1/6912 x z + + 2 4 4 2 4 3 4 3 + + 1/3456 x z - 1/6912 z x + 1/6912 z x + 1/3456 z x + 1/1728 z x + + 4 3 2 2 4 4 4 + + 1/3456 z x , COEFF(-1, 2, -2) = 1/72 y x z - 1/288 z y x + + 3 3 2 2 4 4 4 + - 1/144 y x z + 1/288 z y x - 1/144 z y x - 1/72 y x z + + 4 2 4 2 3 3 2 3 3 + - 1/288 z y x - 1/144 y x z + 1/144 z y x + 1/144 z y x + + 2 4 2 2 3 2 3 2 4 + - 1/72 y x z - 1/288 z y x - 1/288 z y x - 1/432 x z + + 2 4 3 4 2 4 4 3 + - 1/144 z y x + 1/144 z y x + 1/288 z y x + 1/288 z y x + + 3 2 4 4 2 3 2 4 3 2 + + 1/144 z y x + 1/288 z y x + 1/72 y x z + 1/1728 x z + + 3 3 3 2 2 3 2 2 2 + + 1/864 x z + 1/36 y x z - 1/36 y x z + 1/36 y x z - 1/72 y x z + + 2 2 3 2 3 2 4 + - 1/36 y x z - 1/36 y x z - 1/36 y x z + 1/36 z y x + 1/432 x z + + 4 2 2 2 2 2 2 2 + + 1/864 z x + 1/72 y x z + 1/36 y x z - 1/72 y x z + 1/72 y x z + + 2 2 3 3 2 2 + + 1/216 x z - 1/216 x z + 1/216 x z - 1/216 x z + 1/432 x z + + 2 4 4 2 4 3 4 3 + - 1/432 x z + 1/1728 z x - 1/1728 z x - 1/864 z x - 1/864 z x + + 4 3 2 2 4 4 4 + - 1/1728 z x , COEFF(0, 2, -2) = - 5/192 y x z + 1/192 z y x + + 2 2 4 4 4 2 4 2 4 + - 1/192 z y x + 1/96 z y x + 1/192 z y x + 5/1152 x z + + 2 4 3 4 2 4 3 2 4 + + 1/96 z y x - 1/96 z y x - 1/192 z y x - 1/96 z y x + + 2 4 2 2 2 2 2 3 2 3 + - 5/192 y x z - 1/144 z + 5/192 y x z + 5/96 y x z + 5/96 y x z + + 4 3 2 4 4 2 2 + - 1/288 z + 1/144 z + 1/48 y z + 1/48 y z + 1/288 z - 5/96 z y x + + 4 2 2 2 2 2 + + 1/24 y z - 1/576 z x - 5/96 y x z + 5/192 y x z + 1/24 y z + + 2 3 2 3 2 3 2 + + 5/576 x z - 1/24 y z - 1/24 y z - 5/576 x z - 1/48 y z + + 2 2 4 4 2 2 2 4 3 4 + - 5/1152 x z - 1/1152 z x - 1/48 y z + 1/1152 z x + 1/576 z x , + + 2 2 4 4 4 3 3 + COEFF(1, 2, -2) = 1/72 y x z - 1/288 z y x + 1/144 y x z + + 2 2 4 4 4 4 2 4 + + 1/288 z y x - 1/144 z y x + 1/72 y x z - 1/288 z y x + + 2 3 3 2 3 3 2 4 + + 1/144 y x z - 1/144 z y x - 1/144 z y x + 1/72 y x z + + 2 2 3 2 3 2 4 2 4 + + 1/288 z y x + 1/288 z y x - 1/432 x z - 1/144 z y x + + 3 4 2 4 4 3 3 2 4 + + 1/144 z y x + 1/288 z y x - 1/288 z y x + 1/144 z y x + + 4 2 3 2 4 3 2 3 3 3 + - 1/288 z y x + 1/72 y x z - 1/1728 x z - 1/864 x z - 1/36 y x z + + 2 2 3 2 2 2 2 2 3 + + 1/36 y x z - 1/36 y x z - 1/72 y x z - 1/36 y x z + + 2 3 2 4 4 + - 1/36 y x z + 1/36 y x z + 1/36 z y x - 1/432 x z + 1/864 z x + + 2 2 2 2 2 2 2 + - 1/72 y x z + 1/36 y x z - 1/72 y x z - 1/72 y x z - 1/216 x z + + 2 2 3 3 2 2 2 + - 1/216 x z + 1/216 x z + 1/216 x z + 1/432 x z + 1/432 x z + + 4 4 2 4 3 4 3 4 3 + + 1/1728 z x - 1/1728 z x - 1/864 z x + 1/864 z x + 1/1728 z x , + + 2 2 4 4 4 3 3 + COEFF(2, 2, -2) = - 1/1152 y x z + 1/1152 z y x - 1/288 y x z + + 2 2 4 4 4 4 2 4 + - 1/1152 z y x + 1/576 z y x - 1/576 y x z + 1/1152 z y x + + 2 3 3 2 3 3 2 4 + - 1/288 y x z + 1/288 z y x + 1/288 z y x - 1/576 y x z + + 2 2 3 2 3 2 4 2 4 + - 1/576 z y x - 1/576 z y x + 1/6912 x z + 1/576 z y x + + 3 4 2 4 4 3 3 2 4 + - 1/576 z y x - 1/1152 z y x + 1/576 z y x - 1/576 z y x + + 4 2 3 2 4 3 2 3 3 + + 1/576 z y x - 1/1152 y x z + 1/3456 x z + 1/1728 x z + + 3 2 2 3 2 2 2 + + 1/288 y x z - 1/288 y x z + 1/288 y x z + 1/1152 y x z + + 2 2 3 2 3 2 + + 1/576 y x z + 1/576 y x z - 1/288 y x z - 1/576 z y x + + 4 4 2 2 2 2 + + 1/3456 x z - 1/3456 z x + 1/576 y x z - 1/576 y x z + + 2 2 2 2 2 3 + + 1/1152 y x z + 1/576 y x z + 1/1728 x z + 1/3456 x z - 1/3456 x z + + 3 2 2 2 4 4 2 4 + - 1/1728 x z - 1/6912 x z - 1/3456 x z - 1/6912 z x + 1/6912 z x + + 3 4 3 4 3 + + 1/3456 z x - 1/1728 z x - 1/3456 z x , COEFF(-2, -2, -1) = + + 2 2 4 4 4 3 3 2 2 4 + 1/288 y x z + 1/288 z y x + 1/144 y x z + 1/72 z y x + + 4 4 4 2 4 2 3 3 + + 1/72 z y x + 1/144 y x z - 1/288 z y x - 1/144 y x z + + 2 3 3 2 4 2 2 3 + + 1/36 z y x - 1/36 z y x - 1/144 y x z - 1/36 z y x + + 2 3 2 4 2 4 3 4 + + 1/36 z y x - 1/1728 x z - 1/72 z y x - 1/288 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/72 z y x - 1/144 z y x + 1/288 z y x + 1/144 z y x + + 2 4 3 2 3 3 3 2 + - 1/288 y x z + 1/216 x z + 1/864 x z - 1/144 y x z - 1/36 y x z + + 2 3 2 2 2 2 2 3 2 3 + + 1/144 y x z - 1/72 y x z - 1/288 y x z + 1/288 y x z + + 2 4 4 2 2 + + 1/36 y x z - 1/72 z y x + 1/864 x z + 1/432 z x + 1/36 y x z + + 2 2 2 2 2 2 + + 1/72 y x z + 1/72 y x z - 1/36 y x z + 1/216 x z - 1/432 x z + + 2 3 3 2 2 2 4 4 + + 1/1728 x z - 1/864 x z + 1/432 x z - 1/216 x z + 1/1728 z x + + 2 4 3 4 3 4 3 + - 1/432 z x - 1/1728 z x - 1/216 z x - 1/864 z x , COEFF(-1, -2, -1) + + 2 2 4 4 4 3 3 2 2 4 + = - 1/18 y x z - 1/72 z y x - 1/72 y x z - 1/18 z y x + + 4 4 4 2 4 2 3 3 2 3 + - 1/18 z y x - 1/18 y x z + 1/72 z y x + 1/72 y x z - 1/18 z y x + + 3 2 4 2 2 3 2 3 2 4 + + 1/18 z y x + 1/18 y x z + 1/18 z y x - 1/18 z y x + 1/108 x z + + 2 4 3 4 2 4 4 3 + + 1/18 z y x + 1/72 z y x + 1/18 z y x + 1/72 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + - 1/72 z y x - 1/72 z y x + 1/18 y x z - 1/108 x z - 1/432 x z + + 3 2 2 3 2 2 2 2 2 3 + + 1/18 y x z + 2/9 y x z - 1/18 y x z + 2/9 y x z + 1/18 y x z + + 2 3 2 4 4 + - 1/18 y x z - 2/9 y x z + 2/9 z y x - 1/108 x z - 1/108 z x + + 2 2 2 2 2 2 2 + - 2/9 y x z - 2/9 y x z - 2/9 y x z + 2/9 y x z - 1/27 x z + + 2 2 3 3 2 2 2 + + 1/27 x z - 1/108 x z + 1/108 x z - 1/27 x z + 1/27 x z + + 4 4 2 4 3 4 3 4 3 + - 1/432 z x + 1/108 z x + 1/432 z x + 1/108 z x + 1/432 z x , + + 2 2 4 4 4 2 2 4 + COEFF(0, -2, -1) = 5/48 y x z + 1/48 z y x + 1/12 z y x + + 4 4 2 4 2 4 2 4 3 4 + + 1/12 z y x - 1/48 z y x - 5/288 x z - 1/12 z y x - 1/48 z y x + + 2 4 3 2 4 2 4 2 2 2 + - 1/12 z y x + 1/48 z y x - 5/48 y x z + 1/18 z - 5/12 y x z + + 2 2 3 2 3 4 3 2 4 + - 5/48 y x z + 5/48 y x z + 1/72 z - 1/72 z - 1/12 y z + + 4 2 2 4 2 2 + + 1/12 y z - 1/18 z - 5/12 z y x + 1/3 y z + 1/72 z x + 5/12 y x z + + 2 2 2 2 3 2 3 + + 5/12 y x z - 1/3 y z - 5/72 x z - 1/12 y z + 1/12 y z + + 2 3 2 2 2 4 4 2 2 + + 5/288 x z - 1/3 y z + 5/72 x z + 1/288 z x + 1/3 y z + + 2 4 3 4 2 2 4 + - 1/72 z x - 1/288 z x , COEFF(1, -2, -1) = - 1/18 y x z + + 4 4 3 3 2 2 4 4 4 + - 1/72 z y x + 1/72 y x z - 1/18 z y x - 1/18 z y x + 1/18 y x z + + 4 2 4 2 3 3 2 3 3 + + 1/72 z y x - 1/72 y x z + 1/18 z y x - 1/18 z y x + + 2 4 2 2 3 2 3 2 4 2 4 + - 1/18 y x z - 1/18 z y x + 1/18 z y x + 1/108 x z + 1/18 z y x + + 3 4 2 4 4 3 3 2 4 + + 1/72 z y x + 1/18 z y x - 1/72 z y x - 1/72 z y x + + 4 2 3 2 4 3 2 3 3 3 + + 1/72 z y x + 1/18 y x z + 1/108 x z + 1/432 x z - 1/18 y x z + + 2 2 3 2 2 2 2 2 3 2 3 + - 2/9 y x z + 1/18 y x z + 2/9 y x z + 1/18 y x z - 1/18 y x z + + 2 4 4 2 2 + + 2/9 y x z + 2/9 z y x + 1/108 x z - 1/108 z x + 2/9 y x z + + 2 2 2 2 2 2 + - 2/9 y x z - 2/9 y x z - 2/9 y x z + 1/27 x z + 1/27 x z + + 2 3 3 2 2 2 4 4 + - 1/108 x z - 1/108 x z - 1/27 x z - 1/27 x z - 1/432 z x + + 2 4 3 4 3 4 3 + + 1/108 z x + 1/432 z x - 1/108 z x - 1/432 z x , COEFF(2, -2, -1) + + 2 2 4 4 4 3 3 2 2 4 + = 1/288 y x z + 1/288 z y x - 1/144 y x z + 1/72 z y x + + 4 4 4 2 4 2 3 3 + + 1/72 z y x - 1/144 y x z - 1/288 z y x + 1/144 y x z + + 2 3 3 2 4 2 2 3 + - 1/36 z y x + 1/36 z y x + 1/144 y x z + 1/36 z y x + + 2 3 2 4 2 4 3 4 + - 1/36 z y x - 1/1728 x z - 1/72 z y x - 1/288 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/72 z y x + 1/144 z y x + 1/288 z y x - 1/144 z y x + + 2 4 3 2 3 3 3 2 + - 1/288 y x z - 1/216 x z - 1/864 x z + 1/144 y x z + 1/36 y x z + + 2 3 2 2 2 2 2 3 2 3 + - 1/144 y x z - 1/72 y x z - 1/288 y x z + 1/288 y x z + + 2 4 4 2 2 + - 1/36 y x z - 1/72 z y x - 1/864 x z + 1/432 z x - 1/36 y x z + + 2 2 2 2 2 2 + + 1/72 y x z + 1/72 y x z + 1/36 y x z - 1/216 x z - 1/432 x z + + 2 3 3 2 2 2 4 4 + + 1/1728 x z + 1/864 x z + 1/432 x z + 1/216 x z + 1/1728 z x + + 2 4 3 4 3 4 3 + - 1/432 z x - 1/1728 z x + 1/216 z x + 1/864 z x , COEFF(-2, -1, -1) + + 2 2 4 4 4 3 3 2 2 4 + = - 1/72 y x z - 1/144 z y x - 1/72 y x z - 1/18 z y x + + 4 4 4 2 4 2 3 3 2 3 + - 1/36 z y x - 1/72 y x z + 1/72 z y x + 1/36 y x z - 1/9 z y x + + 3 2 4 2 2 3 2 3 2 4 + + 1/18 z y x + 1/36 y x z + 1/9 z y x - 1/18 z y x + 1/108 x z + + 2 4 3 4 2 4 4 3 + + 1/18 z y x + 1/144 z y x + 1/36 z y x + 1/72 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + - 1/72 z y x - 1/36 z y x + 1/144 y x z - 2/27 x z - 1/54 x z + + 3 2 2 3 2 2 2 2 2 3 + + 1/72 y x z + 1/9 y x z - 1/36 y x z + 1/18 y x z + 1/72 y x z + + 2 3 2 4 4 + - 1/144 y x z - 1/18 y x z + 1/36 z y x - 1/54 x z - 1/27 z x + + 2 2 2 2 2 2 2 + - 1/9 y x z - 1/18 y x z - 1/36 y x z + 1/18 y x z - 2/27 x z + + 2 2 3 3 2 2 2 + + 1/27 x z - 1/108 x z + 1/54 x z - 1/27 x z + 2/27 x z + + 4 4 2 4 3 4 3 4 3 + - 1/108 z x + 1/27 z x + 1/108 z x + 2/27 z x + 1/54 z x , + + 2 2 4 4 4 3 3 + COEFF(-1, -1, -1) = 2/9 y x z + 1/36 z y x + 1/36 y x z + + 2 2 4 4 4 4 2 4 2 3 3 + + 2/9 z y x + 1/9 z y x + 1/9 y x z - 1/18 z y x - 1/18 y x z + + 2 3 3 2 4 2 2 3 2 3 + + 2/9 z y x - 1/9 z y x - 2/9 y x z - 2/9 z y x + 1/9 z y x + + 2 4 2 4 3 4 2 4 4 3 + - 4/27 x z - 2/9 z y x - 1/36 z y x - 1/9 z y x - 1/36 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + + 1/18 z y x + 1/18 z y x - 1/9 y x z + 4/27 x z + 1/27 x z + + 3 2 2 3 2 2 2 2 2 3 + - 1/9 y x z - 8/9 y x z + 2/9 y x z - 8/9 y x z - 2/9 y x z + + 2 3 2 4 4 + + 1/9 y x z + 4/9 y x z - 4/9 z y x + 4/27 x z + 4/27 z x + + 2 2 2 2 2 2 2 16 16 2 + + 8/9 y x z + 8/9 y x z + 4/9 y x z - 4/9 y x z + -- x z - -- x z + 27 27 + + 2 3 3 16 2 2 16 2 4 4 2 4 + + 4/27 x z - 4/27 x z + -- x z - -- x z + 1/27 z x - 4/27 z x + 27 27 + + 3 4 3 4 3 2 2 4 + - 1/27 z x - 4/27 z x - 1/27 z x , COEFF(0, -1, -1) = - 5/12 y x z + + 4 4 2 2 4 4 4 2 4 2 4 + - 1/24 z y x - 1/3 z y x - 1/6 z y x + 1/12 z y x + 5/18 x z + + 2 4 3 4 2 4 3 2 4 2 4 + + 1/3 z y x + 1/24 z y x + 1/6 z y x - 1/12 z y x + 5/24 y x z + + 2 2 2 2 2 3 2 3 4 3 + - 8/9 z + 5/3 y x z + 5/12 y x z - 5/24 y x z - 2/9 z + 2/9 z + + 2 4 4 2 2 4 + + 1/3 y z - 1/6 y z + 8/9 z + 5/6 z y x - 2/3 y z - 2/9 z x + + 2 2 2 2 2 2 3 2 3 + - 5/3 y x z - 5/6 y x z + 4/3 y z + 10/9 x z + 1/6 y z - 1/3 y z + + 2 3 2 2 2 4 4 2 2 2 4 + - 5/18 x z + 2/3 y z - 10/9 x z - 1/18 z x - 4/3 y z + 2/9 z x + + 3 4 2 2 4 4 4 + + 1/18 z x , COEFF(1, -1, -1) = 2/9 y x z + 1/36 z y x + + 3 3 2 2 4 4 4 4 2 4 + - 1/36 y x z + 2/9 z y x + 1/9 z y x - 1/9 y x z - 1/18 z y x + + 2 3 3 2 3 3 2 4 2 2 3 + + 1/18 y x z - 2/9 z y x + 1/9 z y x + 2/9 y x z + 2/9 z y x + + 2 3 2 4 2 4 3 4 2 4 + - 1/9 z y x - 4/27 x z - 2/9 z y x - 1/36 z y x - 1/9 z y x + + 4 3 3 2 4 4 2 3 2 4 3 2 + + 1/36 z y x + 1/18 z y x - 1/18 z y x - 1/9 y x z - 4/27 x z + + 3 3 3 2 2 3 2 2 2 + - 1/27 x z + 1/9 y x z + 8/9 y x z - 2/9 y x z - 8/9 y x z + + 2 2 3 2 3 2 4 + - 2/9 y x z + 1/9 y x z - 4/9 y x z - 4/9 z y x - 4/27 x z + + 4 2 2 2 2 2 2 2 + + 4/27 z x - 8/9 y x z + 8/9 y x z + 4/9 y x z + 4/9 y x z + + 16 16 2 2 3 3 16 2 2 16 2 + - -- x z - -- x z + 4/27 x z + 4/27 x z + -- x z + -- x z + 27 27 27 27 + + 4 4 2 4 3 4 3 4 3 + + 1/27 z x - 4/27 z x - 1/27 z x + 4/27 z x + 1/27 z x , + + 2 2 4 4 4 3 3 + COEFF(2, -1, -1) = - 1/72 y x z - 1/144 z y x + 1/72 y x z + + 2 2 4 4 4 4 2 4 + - 1/18 z y x - 1/36 z y x + 1/72 y x z + 1/72 z y x + + 2 3 3 2 3 3 2 4 2 2 3 + - 1/36 y x z + 1/9 z y x - 1/18 z y x - 1/36 y x z - 1/9 z y x + + 2 3 2 4 2 4 3 4 2 4 + + 1/18 z y x + 1/108 x z + 1/18 z y x + 1/144 z y x + 1/36 z y x + + 4 3 3 2 4 4 2 3 2 4 + - 1/72 z y x - 1/72 z y x + 1/36 z y x + 1/144 y x z + + 3 2 3 3 3 2 2 3 + + 2/27 x z + 1/54 x z - 1/72 y x z - 1/9 y x z + 1/36 y x z + + 2 2 2 2 2 3 2 3 2 + + 1/18 y x z + 1/72 y x z - 1/144 y x z + 1/18 y x z + 1/36 z y x + + 4 4 2 2 2 2 2 2 + + 1/54 x z - 1/27 z x + 1/9 y x z - 1/18 y x z - 1/36 y x z + + 2 2 2 3 3 + - 1/18 y x z + 2/27 x z + 1/27 x z - 1/108 x z - 1/54 x z + + 2 2 2 4 4 2 4 3 4 + - 1/27 x z - 2/27 x z - 1/108 z x + 1/27 z x + 1/108 z x + + 3 4 3 2 2 4 2 2 4 + - 2/27 z x - 1/54 z x , COEFF(-2, 0, -1) = 1/48 y x z + 1/12 z y x + + 4 2 4 2 3 3 2 3 2 4 + - 1/48 z y x - 1/24 y x z + 1/6 z y x - 1/24 y x z + + 2 2 3 2 4 2 4 3 2 4 + - 1/6 z y x - 5/288 x z - 1/12 z y x + 1/48 z y x + + 4 2 3 3 2 3 3 2 2 3 + + 1/24 z y x + 5/36 x z + 5/144 x z - 1/6 y x z + 1/24 y x z + + 2 2 2 2 2 3 4 4 2 2 + - 1/12 y x z - 1/48 y x z + 5/144 x z + 5/72 z x + 1/6 y x z + + 2 2 2 2 3 3 + + 1/12 y x z + 5/36 x z - 5/72 x z + 5/288 x z - 5/144 x z + + 2 2 2 4 4 2 4 3 4 + + 5/72 x z - 5/36 x z + 5/288 z x - 5/72 z x - 5/288 z x + + 3 4 3 2 2 4 + - 5/36 z x - 5/144 z x , COEFF(-1, 0, -1) = - 1/3 y x z + + 2 2 4 4 2 4 2 3 3 2 3 2 4 + - 1/3 z y x + 1/12 z y x + 1/12 y x z - 1/3 z y x + 1/3 y x z + + 2 2 3 2 4 2 4 3 2 4 4 2 3 + + 1/3 z y x + 5/18 x z + 1/3 z y x - 1/12 z y x - 1/12 z y x + + 3 2 3 3 2 2 3 2 2 2 + - 5/18 x z - 5/72 x z + 4/3 y x z - 1/3 y x z + 4/3 y x z + + 2 2 3 4 4 2 2 2 2 + + 1/3 y x z - 5/18 x z - 5/18 z x - 4/3 y x z - 4/3 y x z + + 2 2 3 3 2 2 2 + - 10/9 x z + 10/9 x z - 5/18 x z + 5/18 x z - 10/9 x z + 10/9 x z + + 4 4 2 4 3 4 3 4 3 + - 5/72 z x + 5/18 z x + 5/72 z x + 5/18 z x + 5/72 z x , + + 2 2 4 3 2 4 25 2 4 2 + COEFF(0, 0, -1) = 1/2 z y x - 5/12 z - 1/2 z y x - -- x z - 2 y z + 48 + + 2 4 3 4 3 2 4 2 2 2 2 3 + - 1/2 y z - 5/48 z x + 1/8 z y x + 5/2 y x z - 5/8 y x z + + 2 25 2 3 2 2 4 4 4 2 2 2 + - 5/3 z + -- x z + 2 y z + 5/12 z + 5/48 z x - 5/2 y x z + 48 + + 25 2 25 2 2 2 2 4 2 4 4 2 3 + - -- x z + -- x z + 5/8 y x z - 5/12 z x + 5/12 z x + 1/2 y z + 12 12 + + 4 2 4 2 2 4 2 2 4 + + 5/3 z - 1/8 z y x , COEFF(1, 0, -1) = - 1/3 y x z - 1/3 z y x + + 4 2 4 2 3 3 2 3 2 4 2 2 3 + + 1/12 z y x - 1/12 y x z + 1/3 z y x - 1/3 y x z - 1/3 z y x + + 2 4 2 4 3 2 4 4 2 3 3 2 + + 5/18 x z + 1/3 z y x - 1/12 z y x + 1/12 z y x + 5/18 x z + + 3 3 2 2 3 2 2 2 2 2 3 + + 5/72 x z - 4/3 y x z + 1/3 y x z + 4/3 y x z + 1/3 y x z + + 4 4 2 2 2 2 2 + + 5/18 x z - 5/18 z x + 4/3 y x z - 4/3 y x z + 10/9 x z + 10/9 x z + + 2 3 3 2 2 2 4 4 + - 5/18 x z - 5/18 x z - 10/9 x z - 10/9 x z - 5/72 z x + + 2 4 3 4 3 4 3 + + 5/18 z x + 5/72 z x - 5/18 z x - 5/72 z x , COEFF(2, 0, -1) = + + 2 2 4 2 2 4 4 2 4 2 3 3 2 3 + 1/48 y x z + 1/12 z y x - 1/48 z y x + 1/24 y x z - 1/6 z y x + + 2 4 2 2 3 2 4 2 4 3 2 4 + + 1/24 y x z + 1/6 z y x - 5/288 x z - 1/12 z y x + 1/48 z y x + + 4 2 3 3 2 3 3 2 2 3 + - 1/24 z y x - 5/36 x z - 5/144 x z + 1/6 y x z - 1/24 y x z + + 2 2 2 2 2 3 4 4 2 2 + - 1/12 y x z - 1/48 y x z - 5/144 x z + 5/72 z x - 1/6 y x z + + 2 2 2 2 3 3 + + 1/12 y x z - 5/36 x z - 5/72 x z + 5/288 x z + 5/144 x z + + 2 2 2 4 4 2 4 3 4 + + 5/72 x z + 5/36 x z + 5/288 z x - 5/72 z x - 5/288 z x + + 3 4 3 2 2 4 + + 5/36 z x + 5/144 z x , COEFF(-2, 1, -1) = - 1/72 y x z + + 4 4 3 3 2 2 4 4 4 + + 1/144 z y x + 1/72 y x z - 1/18 z y x + 1/36 z y x + 1/72 y x z + + 4 2 4 2 3 3 2 3 3 2 4 + + 1/72 z y x + 1/36 y x z - 1/9 z y x - 1/18 z y x + 1/36 y x z + + 2 2 3 2 3 2 4 2 4 3 4 + + 1/9 z y x + 1/18 z y x + 1/108 x z + 1/18 z y x - 1/144 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/36 z y x - 1/72 z y x - 1/72 z y x - 1/36 z y x + + 2 4 3 2 3 3 3 2 + - 1/144 y x z - 2/27 x z - 1/54 x z - 1/72 y x z + 1/9 y x z + + 2 3 2 2 2 2 2 3 2 3 + - 1/36 y x z + 1/18 y x z + 1/72 y x z + 1/144 y x z + + 2 4 4 2 2 + + 1/18 y x z - 1/36 z y x - 1/54 x z - 1/27 z x - 1/9 y x z + + 2 2 2 2 2 2 + - 1/18 y x z + 1/36 y x z - 1/18 y x z - 2/27 x z + 1/27 x z + + 2 3 3 2 2 2 4 4 + - 1/108 x z + 1/54 x z - 1/27 x z + 2/27 x z - 1/108 z x + + 2 4 3 4 3 4 3 + + 1/27 z x + 1/108 z x + 2/27 z x + 1/54 z x , COEFF(-1, 1, -1) = + + 2 2 4 4 4 3 3 2 2 4 4 + 2/9 y x z - 1/36 z y x - 1/36 y x z + 2/9 z y x - 1/9 z y x + + 4 4 2 4 2 3 3 2 3 3 + - 1/9 y x z - 1/18 z y x - 1/18 y x z + 2/9 z y x + 1/9 z y x + + 2 4 2 2 3 2 3 2 4 2 4 + - 2/9 y x z - 2/9 z y x - 1/9 z y x - 4/27 x z - 2/9 z y x + + 3 4 2 4 4 3 3 2 4 + + 1/36 z y x + 1/9 z y x + 1/36 z y x + 1/18 z y x + + 4 2 3 2 4 3 2 3 3 3 + + 1/18 z y x + 1/9 y x z + 4/27 x z + 1/27 x z + 1/9 y x z + + 2 2 3 2 2 2 2 2 3 2 3 + - 8/9 y x z + 2/9 y x z - 8/9 y x z - 2/9 y x z - 1/9 y x z + + 2 4 4 2 2 + - 4/9 y x z + 4/9 z y x + 4/27 x z + 4/27 z x + 8/9 y x z + + 2 2 2 2 2 16 16 2 2 3 + + 8/9 y x z - 4/9 y x z + 4/9 y x z + -- x z - -- x z + 4/27 x z + 27 27 + + 3 16 2 2 16 2 4 4 2 4 3 4 + - 4/27 x z + -- x z - -- x z + 1/27 z x - 4/27 z x - 1/27 z x + 27 27 + + 3 4 3 2 2 4 4 4 + - 4/27 z x - 1/27 z x , COEFF(0, 1, -1) = - 5/12 y x z + 1/24 z y x + + 2 2 4 4 4 2 4 2 4 2 4 + - 1/3 z y x + 1/6 z y x + 1/12 z y x + 5/18 x z + 1/3 z y x + + 3 4 2 4 3 2 4 2 4 + - 1/24 z y x - 1/6 z y x - 1/12 z y x - 5/24 y x z - 8/9 z + + 2 2 2 2 2 3 2 3 4 3 + + 5/3 y x z + 5/12 y x z + 5/24 y x z - 2/9 z + 2/9 z + + 2 4 4 2 2 4 + + 1/3 y z + 1/6 y z + 8/9 z - 5/6 z y x + 2/3 y z - 2/9 z x + + 2 2 2 2 2 2 3 2 3 + - 5/3 y x z + 5/6 y x z + 4/3 y z + 10/9 x z - 1/6 y z - 1/3 y z + + 2 3 2 2 2 4 4 2 2 2 4 + - 5/18 x z - 2/3 y z - 10/9 x z - 1/18 z x - 4/3 y z + 2/9 z x + + 3 4 2 2 4 4 4 3 3 + + 1/18 z x , COEFF(1, 1, -1) = 2/9 y x z - 1/36 z y x + 1/36 y x z + + 2 2 4 4 4 4 2 4 2 3 3 + + 2/9 z y x - 1/9 z y x + 1/9 y x z - 1/18 z y x + 1/18 y x z + + 2 3 3 2 4 2 2 3 2 3 + - 2/9 z y x - 1/9 z y x + 2/9 y x z + 2/9 z y x + 1/9 z y x + + 2 4 2 4 3 4 2 4 4 3 + - 4/27 x z - 2/9 z y x + 1/36 z y x + 1/9 z y x - 1/36 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + + 1/18 z y x - 1/18 z y x + 1/9 y x z - 4/27 x z - 1/27 x z + + 3 2 2 3 2 2 2 2 2 3 + - 1/9 y x z + 8/9 y x z - 2/9 y x z - 8/9 y x z - 2/9 y x z + + 2 3 2 4 4 + - 1/9 y x z + 4/9 y x z + 4/9 z y x - 4/27 x z + 4/27 z x + + 2 2 2 2 2 2 2 16 16 2 + - 8/9 y x z + 8/9 y x z - 4/9 y x z - 4/9 y x z - -- x z - -- x z + 27 27 + + 2 3 3 16 2 2 16 2 4 4 2 4 + + 4/27 x z + 4/27 x z + -- x z + -- x z + 1/27 z x - 4/27 z x + 27 27 + + 3 4 3 4 3 2 2 4 + - 1/27 z x + 4/27 z x + 1/27 z x , COEFF(2, 1, -1) = - 1/72 y x z + + 4 4 3 3 2 2 4 4 4 + + 1/144 z y x - 1/72 y x z - 1/18 z y x + 1/36 z y x - 1/72 y x z + + 4 2 4 2 3 3 2 3 3 2 4 + + 1/72 z y x - 1/36 y x z + 1/9 z y x + 1/18 z y x - 1/36 y x z + + 2 2 3 2 3 2 4 2 4 3 4 + - 1/9 z y x - 1/18 z y x + 1/108 x z + 1/18 z y x - 1/144 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/36 z y x + 1/72 z y x - 1/72 z y x + 1/36 z y x + + 2 4 3 2 3 3 3 2 + - 1/144 y x z + 2/27 x z + 1/54 x z + 1/72 y x z - 1/9 y x z + + 2 3 2 2 2 2 2 3 2 3 + + 1/36 y x z + 1/18 y x z + 1/72 y x z + 1/144 y x z + + 2 4 4 2 2 + - 1/18 y x z - 1/36 z y x + 1/54 x z - 1/27 z x + 1/9 y x z + + 2 2 2 2 2 2 + - 1/18 y x z + 1/36 y x z + 1/18 y x z + 2/27 x z + 1/27 x z + + 2 3 3 2 2 2 4 4 + - 1/108 x z - 1/54 x z - 1/27 x z - 2/27 x z - 1/108 z x + + 2 4 3 4 3 4 3 + + 1/27 z x + 1/108 z x - 2/27 z x - 1/54 z x , COEFF(-2, 2, -1) = + + 2 2 4 4 4 3 3 2 2 4 + 1/288 y x z - 1/288 z y x - 1/144 y x z + 1/72 z y x + + 4 4 4 2 4 2 3 3 + - 1/72 z y x - 1/144 y x z - 1/288 z y x - 1/144 y x z + + 2 3 3 2 4 2 2 3 + + 1/36 z y x + 1/36 z y x - 1/144 y x z - 1/36 z y x + + 2 3 2 4 2 4 3 4 + - 1/36 z y x - 1/1728 x z - 1/72 z y x + 1/288 z y x + + 2 4 4 3 3 2 4 4 2 3 + + 1/72 z y x + 1/144 z y x + 1/288 z y x + 1/144 z y x + + 2 4 3 2 3 3 3 2 + + 1/288 y x z + 1/216 x z + 1/864 x z + 1/144 y x z - 1/36 y x z + + 2 3 2 2 2 2 2 3 2 3 + + 1/144 y x z - 1/72 y x z - 1/288 y x z - 1/288 y x z + + 2 4 4 2 2 + - 1/36 y x z + 1/72 z y x + 1/864 x z + 1/432 z x + 1/36 y x z + + 2 2 2 2 2 2 + + 1/72 y x z - 1/72 y x z + 1/36 y x z + 1/216 x z - 1/432 x z + + 2 3 3 2 2 2 4 4 + + 1/1728 x z - 1/864 x z + 1/432 x z - 1/216 x z + 1/1728 z x + + 2 4 3 4 3 4 3 + - 1/432 z x - 1/1728 z x - 1/216 z x - 1/864 z x , COEFF(-1, 2, -1) + + 2 2 4 4 4 3 3 2 2 4 + = - 1/18 y x z + 1/72 z y x + 1/72 y x z - 1/18 z y x + + 4 4 4 2 4 2 3 3 2 3 + + 1/18 z y x + 1/18 y x z + 1/72 z y x + 1/72 y x z - 1/18 z y x + + 3 2 4 2 2 3 2 3 2 4 + - 1/18 z y x + 1/18 y x z + 1/18 z y x + 1/18 z y x + 1/108 x z + + 2 4 3 4 2 4 4 3 + + 1/18 z y x - 1/72 z y x - 1/18 z y x - 1/72 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + - 1/72 z y x - 1/72 z y x - 1/18 y x z - 1/108 x z - 1/432 x z + + 3 2 2 3 2 2 2 2 2 3 + - 1/18 y x z + 2/9 y x z - 1/18 y x z + 2/9 y x z + 1/18 y x z + + 2 3 2 4 4 + + 1/18 y x z + 2/9 y x z - 2/9 z y x - 1/108 x z - 1/108 z x + + 2 2 2 2 2 2 2 + - 2/9 y x z - 2/9 y x z + 2/9 y x z - 2/9 y x z - 1/27 x z + + 2 2 3 3 2 2 2 + + 1/27 x z - 1/108 x z + 1/108 x z - 1/27 x z + 1/27 x z + + 4 4 2 4 3 4 3 4 3 + - 1/432 z x + 1/108 z x + 1/432 z x + 1/108 z x + 1/432 z x , + + 2 2 4 4 4 2 2 4 + COEFF(0, 2, -1) = 5/48 y x z - 1/48 z y x + 1/12 z y x + + 4 4 2 4 2 4 2 4 3 4 + - 1/12 z y x - 1/48 z y x - 5/288 x z - 1/12 z y x + 1/48 z y x + + 2 4 3 2 4 2 4 2 2 2 + + 1/12 z y x + 1/48 z y x + 5/48 y x z + 1/18 z - 5/12 y x z + + 2 2 3 2 3 4 3 2 4 + - 5/48 y x z - 5/48 y x z + 1/72 z - 1/72 z - 1/12 y z + + 4 2 2 4 2 2 + - 1/12 y z - 1/18 z + 5/12 z y x - 1/3 y z + 1/72 z x + 5/12 y x z + + 2 2 2 2 3 2 3 + - 5/12 y x z - 1/3 y z - 5/72 x z + 1/12 y z + 1/12 y z + + 2 3 2 2 2 4 4 2 2 + + 5/288 x z + 1/3 y z + 5/72 x z + 1/288 z x + 1/3 y z + + 2 4 3 4 2 2 4 + - 1/72 z x - 1/288 z x , COEFF(1, 2, -1) = - 1/18 y x z + + 4 4 3 3 2 2 4 4 4 + + 1/72 z y x - 1/72 y x z - 1/18 z y x + 1/18 z y x - 1/18 y x z + + 4 2 4 2 3 3 2 3 3 + + 1/72 z y x - 1/72 y x z + 1/18 z y x + 1/18 z y x + + 2 4 2 2 3 2 3 2 4 2 4 + - 1/18 y x z - 1/18 z y x - 1/18 z y x + 1/108 x z + 1/18 z y x + + 3 4 2 4 4 3 3 2 4 + - 1/72 z y x - 1/18 z y x + 1/72 z y x - 1/72 z y x + + 4 2 3 2 4 3 2 3 3 3 + + 1/72 z y x - 1/18 y x z + 1/108 x z + 1/432 x z + 1/18 y x z + + 2 2 3 2 2 2 2 2 3 2 3 + - 2/9 y x z + 1/18 y x z + 2/9 y x z + 1/18 y x z + 1/18 y x z + + 2 4 4 2 2 + - 2/9 y x z - 2/9 z y x + 1/108 x z - 1/108 z x + 2/9 y x z + + 2 2 2 2 2 2 + - 2/9 y x z + 2/9 y x z + 2/9 y x z + 1/27 x z + 1/27 x z + + 2 3 3 2 2 2 4 4 + - 1/108 x z - 1/108 x z - 1/27 x z - 1/27 x z - 1/432 z x + + 2 4 3 4 3 4 3 + + 1/108 z x + 1/432 z x - 1/108 z x - 1/432 z x , COEFF(2, 2, -1) = + + 2 2 4 4 4 3 3 2 2 4 + 1/288 y x z - 1/288 z y x + 1/144 y x z + 1/72 z y x + + 4 4 4 2 4 2 3 3 + - 1/72 z y x + 1/144 y x z - 1/288 z y x + 1/144 y x z + + 2 3 3 2 4 2 2 3 + - 1/36 z y x - 1/36 z y x + 1/144 y x z + 1/36 z y x + + 2 3 2 4 2 4 3 4 + + 1/36 z y x - 1/1728 x z - 1/72 z y x + 1/288 z y x + + 2 4 4 3 3 2 4 4 2 3 + + 1/72 z y x - 1/144 z y x + 1/288 z y x - 1/144 z y x + + 2 4 3 2 3 3 3 2 + + 1/288 y x z - 1/216 x z - 1/864 x z - 1/144 y x z + 1/36 y x z + + 2 3 2 2 2 2 2 3 2 3 + - 1/144 y x z - 1/72 y x z - 1/288 y x z - 1/288 y x z + + 2 4 4 2 2 + + 1/36 y x z + 1/72 z y x - 1/864 x z + 1/432 z x - 1/36 y x z + + 2 2 2 2 2 2 + + 1/72 y x z - 1/72 y x z - 1/36 y x z - 1/216 x z - 1/432 x z + + 2 3 3 2 2 2 4 4 + + 1/1728 x z + 1/864 x z + 1/432 x z + 1/216 x z + 1/1728 z x + + 2 4 3 4 3 4 3 + - 1/432 z x - 1/1728 z x + 1/216 z x + 1/864 z x , COEFF(-2, -2, 0) + + 2 2 4 4 4 2 2 4 4 + = - 1/192 y x z - 1/192 z y x - 5/192 z y x - 1/96 y x z + + 4 2 4 2 4 2 2 3 3 2 3 + + 1/192 z y x + 1/96 y x z + 5/96 z y x + 1/24 y x - 5/96 z y x + + 2 4 2 4 4 3 4 2 3 + + 1/1152 x z + 5/192 z y x + 1/96 z y x - 1/96 z y x + + 2 4 3 2 4 + + 1/192 y x z - 5/576 x z - 1/144 x - 1/288 x - 1/24 y x + + 2 2 2 3 2 4 2 + + 5/192 y x z + 1/144 x + 1/288 x - 1/576 x z + 1/24 y x + + 2 2 2 2 2 2 2 2 + - 5/96 y x z - 5/192 y x z + 5/96 y x z - 5/1152 x z + 5/576 x z + + 4 4 2 2 2 2 4 4 3 + - 1/1152 z x - 1/48 y x + 1/48 y x + 5/1152 z x + 1/576 z x + + 4 2 4 2 3 2 2 4 + - 1/48 y x + 1/48 y x - 1/24 y x , COEFF(-1, -2, 0) = 1/12 y x z + + 4 4 2 2 4 4 4 2 4 + + 1/48 z y x + 5/48 z y x + 1/12 y x z - 1/48 z y x + + 2 4 2 2 3 3 2 3 2 4 + - 1/12 y x z - 5/48 z y x - 1/12 y x + 5/48 z y x - 1/72 x z + + 2 4 4 3 4 2 3 2 4 3 2 + - 5/48 z y x - 1/48 z y x + 1/48 z y x - 1/12 y x z + 5/288 x z + + 4 2 2 2 3 2 + + 1/18 x + 1/72 x + 1/3 y x - 5/12 y x z - 1/72 x - 1/18 x + + 4 2 2 2 2 2 2 + + 1/72 x z - 1/3 y x + 5/12 y x z + 5/12 y x z - 5/12 y x z + + 2 2 2 4 4 2 2 2 + + 5/72 x z - 5/72 x z + 1/288 z x + 1/3 y x - 1/3 y x + + 2 4 4 3 4 2 4 2 3 + - 5/288 z x - 1/288 z x + 1/12 y x - 1/12 y x + 1/12 y x , + + 2 2 4 4 4 2 2 4 + COEFF(0, -2, 0) = - 5/32 y x z - 1/32 z y x - 5/32 z y x + + 4 2 4 2 4 2 4 2 4 4 + + 1/32 z y x + 5/192 x z + 5/32 z y x + 5/32 y x z - 1/48 x + + 25 2 2 2 4 2 4 4 2 + - 1/2 y + -- y x z - 1/48 z + 1/8 y z - 1/12 - 1/8 y z + 1/2 y + 32 + + 2 2 25 2 2 2 25 2 2 4 4 + + 5/48 z + 5/48 x - -- y x z + 5/8 y z - --- x z - 1/192 z x + 32 192 + + 2 2 2 2 2 2 4 4 2 4 + - 5/8 y z - 5/8 y x + 5/8 y x + 5/192 z x - 1/8 y x + 1/8 y x , + + 2 2 4 4 4 2 2 4 + COEFF(1, -2, 0) = 1/12 y x z + 1/48 z y x + 5/48 z y x + + 4 4 2 4 2 4 2 2 3 3 + - 1/12 y x z - 1/48 z y x + 1/12 y x z + 5/48 z y x + 1/12 y x + + 2 3 2 4 2 4 4 3 4 2 3 + - 5/48 z y x - 1/72 x z - 5/48 z y x + 1/48 z y x - 1/48 z y x + + 2 4 3 2 4 2 2 2 + - 1/12 y x z - 5/288 x z - 1/18 x + 1/72 x - 1/3 y x - 5/12 y x z + + 3 2 4 2 2 2 2 2 + + 1/72 x - 1/18 x - 1/72 x z + 1/3 y x - 5/12 y x z + 5/12 y x z + + 2 2 2 2 4 4 2 2 + + 5/12 y x z + 5/72 x z + 5/72 x z + 1/288 z x + 1/3 y x + + 2 2 4 4 3 4 2 4 + - 1/3 y x - 5/288 z x + 1/288 z x + 1/12 y x - 1/12 y x + + 2 3 2 2 4 4 4 + - 1/12 y x , COEFF(2, -2, 0) = - 1/192 y x z - 1/192 z y x + + 2 2 4 4 4 2 4 2 4 + - 5/192 z y x + 1/96 y x z + 1/192 z y x - 1/96 y x z + + 2 2 3 3 2 3 2 4 2 4 + - 5/96 z y x - 1/24 y x + 5/96 z y x + 1/1152 x z + 5/192 z y x + + 4 3 4 2 3 2 4 3 2 + - 1/96 z y x + 1/96 z y x + 1/192 y x z + 5/576 x z + 1/144 x + + 4 2 2 2 3 2 4 + - 1/288 x + 1/24 y x + 5/192 y x z - 1/144 x + 1/288 x + 1/576 x z + + 2 2 2 2 2 2 2 2 + - 1/24 y x + 5/96 y x z - 5/192 y x z - 5/96 y x z - 5/1152 x z + + 2 4 4 2 2 2 2 4 + - 5/576 x z - 1/1152 z x - 1/48 y x + 1/48 y x + 5/1152 z x + + 4 3 4 2 4 2 3 + - 1/576 z x - 1/48 y x + 1/48 y x + 1/24 y x , COEFF(-2, -1, 0) = + + 2 2 4 4 4 2 2 4 4 4 2 4 + 1/48 y x z + 1/96 z y x + 5/48 z y x + 1/48 y x z - 1/48 z y x + + 2 4 2 2 3 3 2 3 2 4 + - 1/24 y x z - 5/24 z y x - 1/12 y x + 5/48 z y x - 1/72 x z + + 2 4 4 3 4 2 3 2 4 3 2 + - 5/96 z y x - 1/48 z y x + 1/24 z y x - 1/96 y x z + 5/36 x z + + 4 2 2 2 3 2 + + 1/9 x + 1/18 x + 1/12 y x - 5/48 y x z - 1/9 x - 1/18 x + + 4 2 2 2 2 2 2 + + 1/36 x z - 1/6 y x + 5/24 y x z + 5/96 y x z - 5/48 y x z + + 2 2 2 4 4 2 2 2 + + 5/72 x z - 5/36 x z + 1/72 z x + 1/12 y x - 1/24 y x + + 2 4 4 3 4 2 4 2 3 + - 5/72 z x - 1/36 z x + 1/24 y x - 1/12 y x + 1/6 y x , + + 2 2 4 4 4 2 2 4 + COEFF(-1, -1, 0) = - 1/3 y x z - 1/24 z y x - 5/12 z y x + + 4 4 2 4 2 4 2 2 3 3 + - 1/6 y x z + 1/12 z y x + 1/3 y x z + 5/12 z y x + 1/6 y x + + 2 3 2 4 2 4 4 3 4 2 3 + - 5/24 z y x + 2/9 x z + 5/24 z y x + 1/24 z y x - 1/12 z y x + + 2 4 3 2 4 2 2 2 + + 1/6 y x z - 5/18 x z - 8/9 x - 2/9 x - 2/3 y x + 5/3 y x z + + 3 2 4 2 2 2 2 2 + + 2/9 x + 8/9 x - 2/9 x z + 4/3 y x - 5/3 y x z - 5/6 y x z + + 2 2 2 2 4 4 2 2 2 + + 5/6 y x z - 10/9 x z + 10/9 x z - 1/18 z x - 4/3 y x + 2/3 y x + + 2 4 4 3 4 2 4 2 3 + + 5/18 z x + 1/18 z x - 1/6 y x + 1/3 y x - 1/3 y x , + + 2 2 4 4 4 2 2 4 4 2 4 + COEFF(0, -1, 0) = 5/8 y x z + 1/16 z y x + 5/8 z y x - 1/8 z y x + + 2 4 2 4 2 4 4 2 2 2 + - 5/12 x z - 5/16 z y x - 5/16 y x z + 1/3 x + y - 25/8 y x z + + 4 2 4 4 2 2 2 + + 1/3 z - 1/2 y z + 1/4 y z - 2 y - 5/3 z - 5/3 x + 4/3 + + 25 2 2 2 25 2 2 4 4 2 2 2 2 + + -- y x z - 5/4 y z + -- x z + 1/12 z x + 5/2 y z + 5/2 y x + 16 12 + + 2 2 4 4 2 4 + - 5/4 y x - 5/12 z x + 1/4 y x - 1/2 y x , COEFF(1, -1, 0) = + + 2 2 4 4 4 2 2 4 4 4 2 4 + - 1/3 y x z - 1/24 z y x - 5/12 z y x + 1/6 y x z + 1/12 z y x + + 2 4 2 2 3 3 2 3 2 4 + - 1/3 y x z - 5/12 z y x - 1/6 y x + 5/24 z y x + 2/9 x z + + 2 4 4 3 4 2 3 2 4 3 2 + + 5/24 z y x - 1/24 z y x + 1/12 z y x + 1/6 y x z + 5/18 x z + + 4 2 2 2 3 2 4 + + 8/9 x - 2/9 x + 2/3 y x + 5/3 y x z - 2/9 x + 8/9 x + 2/9 x z + + 2 2 2 2 2 2 2 2 + - 4/3 y x + 5/3 y x z - 5/6 y x z - 5/6 y x z - 10/9 x z + + 2 4 4 2 2 2 2 4 4 3 + - 10/9 x z - 1/18 z x - 4/3 y x + 2/3 y x + 5/18 z x - 1/18 z x + + 4 2 4 2 3 2 2 4 + - 1/6 y x + 1/3 y x + 1/3 y x , COEFF(2, -1, 0) = 1/48 y x z + + 4 4 2 2 4 4 4 2 4 + + 1/96 z y x + 5/48 z y x - 1/48 y x z - 1/48 z y x + + 2 4 2 2 3 3 2 3 2 4 + + 1/24 y x z + 5/24 z y x + 1/12 y x - 5/48 z y x - 1/72 x z + + 2 4 4 3 4 2 3 2 4 3 2 + - 5/96 z y x + 1/48 z y x - 1/24 z y x - 1/96 y x z - 5/36 x z + + 4 2 2 2 3 2 + - 1/9 x + 1/18 x - 1/12 y x - 5/48 y x z + 1/9 x - 1/18 x + + 4 2 2 2 2 2 2 + - 1/36 x z + 1/6 y x - 5/24 y x z + 5/96 y x z + 5/48 y x z + + 2 2 2 4 4 2 2 2 + + 5/72 x z + 5/36 x z + 1/72 z x + 1/12 y x - 1/24 y x + + 2 4 4 3 4 2 4 2 3 + - 5/72 z x + 1/36 z x + 1/24 y x - 1/12 y x - 1/6 y x , + + 4 2 3 2 4 2 4 + COEFF(-2, 0, 0) = - 5/24 x - 1/16 z y x + 1/4 y x + 1/32 z y x + + 3 2 4 2 4 4 3 2 4 + + 5/24 x + 1/8 y x + 5/48 x - 5/96 x z + 5/96 z x + 1/16 y x z + + 2 2 4 4 25 2 4 2 3 2 2 4 + - 5/16 y x z - 5/192 z x + --- z x - 1/4 y x - 1/32 y x z + 192 + + 25 3 2 2 2 4 4 2 2 2 2 3 25 2 + - -- x z - 5/32 z y x - 5/48 x - 1/8 y x + 5/16 z y x + -- x z + 96 96 + + 2 4 25 2 2 2 2 2 25 3 2 + + 5/192 x z - --- x z + 5/32 y x z , COEFF(-1, 0, 0) = -- x z + 192 48 + + 4 2 3 4 2 4 3 2 2 2 4 + + 1/8 z y x - 1/8 z y x - 5/12 x - 2 y x + 5/8 z y x + + 2 4 25 2 2 4 4 25 2 2 2 3 + - 1/2 y x + -- x z + 5/3 x + 5/48 z x - -- x z - 5/8 z y x + 12 12 + + 25 2 4 4 2 2 2 2 2 4 2 2 4 + - -- z x + 5/12 x z + 5/2 y x z + 2 y x - 5/12 x z + 1/2 y x z + 48 + + 2 2 3 4 4 3 2 4 2 2 2 + - 5/3 x + 1/2 y x + 5/12 x - 5/48 z x - 1/2 y x z - 5/2 y x z , + + 25 2 4 75 2 2 2 15 2 2 4 2 + COEFF(0, 0, 0) = - 5/2 + -- z x + -- y x z - -- z y x + 3 y + 32 16 16 + + 2 4 2 4 2 4 2 4 25 2 4 + + 3/4 y z + 25/8 z + 3/16 z y x + 25/8 x - 5/8 x + -- x z + 32 + + 125 2 2 2 4 4 4 2 2 2 2 4 + - --- x z + 3/4 y x - 5/32 z x - 15/4 y z - 15/4 y x - 5/8 z + 32 + + 15 2 2 4 2 3 25 2 2 + - -- y x z , COEFF(1, 0, 0) = - 1/2 y x + -- x z + 2 y x + 16 12 + + 2 4 2 2 2 2 3 4 4 2 3 + + 1/2 y x z - 5/2 y x z + 5/8 z y x + 5/12 x - 1/8 z y x + + 25 2 4 25 2 2 2 2 4 2 2 2 2 4 + - -- z x + -- x z + 1/2 y x z + 2 y x + 5/8 z y x + 48 12 + + 2 2 2 25 3 2 2 4 3 2 4 4 + - 5/2 y x z - -- x z - 5/3 x + 5/48 z x - 5/12 x z - 5/12 x z + 48 + + 4 2 4 2 4 4 4 3 + - 1/8 z y x - 5/3 x - 1/2 y x + 5/48 z x + 5/12 x , COEFF(2, 0, 0) + + 4 25 2 2 25 2 4 2 2 3 + = 5/96 x z - --- x z + 5/24 x + --- z x - 5/16 z y x + 192 192 + + 4 2 3 2 2 2 2 3 4 3 2 2 4 + + 1/16 z y x + 5/32 y x z + 1/4 y x - 5/96 z x - 1/32 y x z + + 4 4 2 2 4 4 2 4 2 4 4 + - 5/192 z x - 5/32 z y x + 1/32 z y x - 1/16 y x z - 5/48 x + + 25 3 2 2 25 2 2 4 2 2 3 + + -- x z + 5/48 x - -- x z + 5/192 x z - 1/8 y x - 5/24 x + 96 96 + + 2 2 2 2 4 2 2 4 + - 1/4 y x + 5/16 y x z + 1/8 y x , COEFF(-2, 1, 0) = 1/48 y x z + + 4 4 2 2 4 4 4 2 4 + - 1/96 z y x + 5/48 z y x - 1/48 y x z - 1/48 z y x + + 2 4 2 2 3 3 2 3 2 4 + - 1/24 y x z - 5/24 z y x + 1/12 y x - 5/48 z y x - 1/72 x z + + 2 4 4 3 4 2 3 2 4 3 2 + + 5/96 z y x + 1/48 z y x + 1/24 z y x + 1/96 y x z + 5/36 x z + + 4 2 2 2 3 2 + + 1/9 x + 1/18 x - 1/12 y x - 5/48 y x z - 1/9 x - 1/18 x + + 4 2 2 2 2 2 2 + + 1/36 x z - 1/6 y x + 5/24 y x z - 5/96 y x z + 5/48 y x z + + 2 2 2 4 4 2 2 2 + + 5/72 x z - 5/36 x z + 1/72 z x + 1/12 y x + 1/24 y x + + 2 4 4 3 4 2 4 2 3 + - 5/72 z x - 1/36 z x - 1/24 y x - 1/12 y x + 1/6 y x , + + 2 2 4 4 4 2 2 4 + COEFF(-1, 1, 0) = - 1/3 y x z + 1/24 z y x - 5/12 z y x + + 4 4 2 4 2 4 2 2 3 3 + + 1/6 y x z + 1/12 z y x + 1/3 y x z + 5/12 z y x - 1/6 y x + + 2 3 2 4 2 4 4 3 4 2 3 + + 5/24 z y x + 2/9 x z - 5/24 z y x - 1/24 z y x - 1/12 z y x + + 2 4 3 2 4 2 2 2 + - 1/6 y x z - 5/18 x z - 8/9 x - 2/9 x + 2/3 y x + 5/3 y x z + + 3 2 4 2 2 2 2 2 + + 2/9 x + 8/9 x - 2/9 x z + 4/3 y x - 5/3 y x z + 5/6 y x z + + 2 2 2 2 4 4 2 2 2 + - 5/6 y x z - 10/9 x z + 10/9 x z - 1/18 z x - 4/3 y x - 2/3 y x + + 2 4 4 3 4 2 4 2 3 + + 5/18 z x + 1/18 z x + 1/6 y x + 1/3 y x - 1/3 y x , + + 2 2 4 4 4 2 2 4 4 2 4 + COEFF(0, 1, 0) = 5/8 y x z - 1/16 z y x + 5/8 z y x - 1/8 z y x + + 2 4 2 4 2 4 4 2 2 2 + - 5/12 x z + 5/16 z y x + 5/16 y x z + 1/3 x - y - 25/8 y x z + + 4 2 4 4 2 2 2 + + 1/3 z - 1/2 y z - 1/4 y z - 2 y - 5/3 z - 5/3 x + 4/3 + + 25 2 2 2 25 2 2 4 4 2 2 2 2 + - -- y x z + 5/4 y z + -- x z + 1/12 z x + 5/2 y z + 5/2 y x + 16 12 + + 2 2 4 4 2 4 + + 5/4 y x - 5/12 z x - 1/4 y x - 1/2 y x , COEFF(1, 1, 0) = + + 2 2 4 4 4 2 2 4 4 4 2 4 + - 1/3 y x z + 1/24 z y x - 5/12 z y x - 1/6 y x z + 1/12 z y x + + 2 4 2 2 3 3 2 3 2 4 + - 1/3 y x z - 5/12 z y x + 1/6 y x - 5/24 z y x + 2/9 x z + + 2 4 4 3 4 2 3 2 4 3 2 + - 5/24 z y x + 1/24 z y x + 1/12 z y x - 1/6 y x z + 5/18 x z + + 4 2 2 2 3 2 4 + + 8/9 x - 2/9 x - 2/3 y x + 5/3 y x z - 2/9 x + 8/9 x + 2/9 x z + + 2 2 2 2 2 2 2 2 + - 4/3 y x + 5/3 y x z + 5/6 y x z + 5/6 y x z - 10/9 x z + + 2 4 4 2 2 2 2 4 4 3 + - 10/9 x z - 1/18 z x - 4/3 y x - 2/3 y x + 5/18 z x - 1/18 z x + + 4 2 4 2 3 2 2 4 + + 1/6 y x + 1/3 y x + 1/3 y x , COEFF(2, 1, 0) = 1/48 y x z + + 4 4 2 2 4 4 4 2 4 + - 1/96 z y x + 5/48 z y x + 1/48 y x z - 1/48 z y x + + 2 4 2 2 3 3 2 3 2 4 + + 1/24 y x z + 5/24 z y x - 1/12 y x + 5/48 z y x - 1/72 x z + + 2 4 4 3 4 2 3 2 4 3 2 + + 5/96 z y x - 1/48 z y x - 1/24 z y x + 1/96 y x z - 5/36 x z + + 4 2 2 2 3 2 + - 1/9 x + 1/18 x + 1/12 y x - 5/48 y x z + 1/9 x - 1/18 x + + 4 2 2 2 2 2 2 + - 1/36 x z + 1/6 y x - 5/24 y x z - 5/96 y x z - 5/48 y x z + + 2 2 2 4 4 2 2 2 + + 5/72 x z + 5/36 x z + 1/72 z x + 1/12 y x + 1/24 y x + + 2 4 4 3 4 2 4 2 3 + - 5/72 z x + 1/36 z x - 1/24 y x - 1/12 y x - 1/6 y x , + + 2 2 4 4 4 2 2 4 + COEFF(-2, 2, 0) = - 1/192 y x z + 1/192 z y x - 5/192 z y x + + 4 4 2 4 2 4 2 2 3 3 + + 1/96 y x z + 1/192 z y x + 1/96 y x z + 5/96 z y x - 1/24 y x + + 2 3 2 4 2 4 4 3 + + 5/96 z y x + 1/1152 x z - 5/192 z y x - 1/96 z y x + + 4 2 3 2 4 3 2 4 + - 1/96 z y x - 1/192 y x z - 5/576 x z - 1/144 x - 1/288 x + + 2 2 2 3 2 4 2 + + 1/24 y x + 5/192 y x z + 1/144 x + 1/288 x - 1/576 x z + 1/24 y x + + 2 2 2 2 2 2 2 2 + - 5/96 y x z + 5/192 y x z - 5/96 y x z - 5/1152 x z + 5/576 x z + + 4 4 2 2 2 2 4 4 3 + - 1/1152 z x - 1/48 y x - 1/48 y x + 5/1152 z x + 1/576 z x + + 4 2 4 2 3 2 2 4 + + 1/48 y x + 1/48 y x - 1/24 y x , COEFF(-1, 2, 0) = 1/12 y x z + + 4 4 2 2 4 4 4 2 4 + - 1/48 z y x + 5/48 z y x - 1/12 y x z - 1/48 z y x + + 2 4 2 2 3 3 2 3 2 4 + - 1/12 y x z - 5/48 z y x + 1/12 y x - 5/48 z y x - 1/72 x z + + 2 4 4 3 4 2 3 2 4 3 2 + + 5/48 z y x + 1/48 z y x + 1/48 z y x + 1/12 y x z + 5/288 x z + + 4 2 2 2 3 2 + + 1/18 x + 1/72 x - 1/3 y x - 5/12 y x z - 1/72 x - 1/18 x + + 4 2 2 2 2 2 2 + + 1/72 x z - 1/3 y x + 5/12 y x z - 5/12 y x z + 5/12 y x z + + 2 2 2 4 4 2 2 2 + + 5/72 x z - 5/72 x z + 1/288 z x + 1/3 y x + 1/3 y x + + 2 4 4 3 4 2 4 2 3 + - 5/288 z x - 1/288 z x - 1/12 y x - 1/12 y x + 1/12 y x , + + 2 2 4 4 4 2 2 4 + COEFF(0, 2, 0) = - 5/32 y x z + 1/32 z y x - 5/32 z y x + + 4 2 4 2 4 2 4 2 4 4 + + 1/32 z y x + 5/192 x z - 5/32 z y x - 5/32 y x z - 1/48 x + + 25 2 2 2 4 2 4 4 2 + + 1/2 y + -- y x z - 1/48 z + 1/8 y z - 1/12 + 1/8 y z + 1/2 y + 32 + + 2 2 25 2 2 2 25 2 2 4 4 + + 5/48 z + 5/48 x + -- y x z - 5/8 y z - --- x z - 1/192 z x + 32 192 + + 2 2 2 2 2 2 4 4 2 4 + - 5/8 y z - 5/8 y x - 5/8 y x + 5/192 z x + 1/8 y x + 1/8 y x , + + 2 2 4 4 4 2 2 4 4 + COEFF(1, 2, 0) = 1/12 y x z - 1/48 z y x + 5/48 z y x + 1/12 y x z + + 4 2 4 2 4 2 2 3 3 2 3 + - 1/48 z y x + 1/12 y x z + 5/48 z y x - 1/12 y x + 5/48 z y x + + 2 4 2 4 4 3 4 2 3 2 4 + - 1/72 x z + 5/48 z y x - 1/48 z y x - 1/48 z y x + 1/12 y x z + + 3 2 4 2 2 2 3 + - 5/288 x z - 1/18 x + 1/72 x + 1/3 y x - 5/12 y x z + 1/72 x + + 2 4 2 2 2 2 2 + - 1/18 x - 1/72 x z + 1/3 y x - 5/12 y x z - 5/12 y x z + + 2 2 2 2 4 4 2 2 + - 5/12 y x z + 5/72 x z + 5/72 x z + 1/288 z x + 1/3 y x + + 2 2 4 4 3 4 2 4 + + 1/3 y x - 5/288 z x + 1/288 z x - 1/12 y x - 1/12 y x + + 2 3 2 2 4 4 4 + - 1/12 y x , COEFF(2, 2, 0) = - 1/192 y x z + 1/192 z y x + + 2 2 4 4 4 2 4 2 4 + - 5/192 z y x - 1/96 y x z + 1/192 z y x - 1/96 y x z + + 2 2 3 3 2 3 2 4 2 4 + - 5/96 z y x + 1/24 y x - 5/96 z y x + 1/1152 x z - 5/192 z y x + + 4 3 4 2 3 2 4 3 2 + + 1/96 z y x + 1/96 z y x - 1/192 y x z + 5/576 x z + 1/144 x + + 4 2 2 2 3 2 4 + - 1/288 x - 1/24 y x + 5/192 y x z - 1/144 x + 1/288 x + 1/576 x z + + 2 2 2 2 2 2 2 2 + - 1/24 y x + 5/96 y x z + 5/192 y x z + 5/96 y x z - 5/1152 x z + + 2 4 4 2 2 2 2 4 + - 5/576 x z - 1/1152 z x - 1/48 y x - 1/48 y x + 5/1152 z x + + 4 3 4 2 4 2 3 + - 1/576 z x + 1/48 y x + 1/48 y x + 1/24 y x , COEFF(-2, -2, 1) = + + 2 2 4 4 4 3 3 2 2 4 + 1/288 y x z + 1/288 z y x - 1/144 y x z + 1/72 z y x + + 4 4 4 2 4 2 3 3 + - 1/72 z y x + 1/144 y x z - 1/288 z y x + 1/144 y x z + + 2 3 3 2 4 2 2 3 + - 1/36 z y x + 1/36 z y x - 1/144 y x z - 1/36 z y x + + 2 3 2 4 2 4 3 4 + + 1/36 z y x - 1/1728 x z + 1/72 z y x + 1/288 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/72 z y x - 1/144 z y x - 1/288 z y x + 1/144 z y x + + 2 4 3 2 3 3 3 2 + - 1/288 y x z + 1/216 x z - 1/864 x z + 1/144 y x z + 1/36 y x z + + 2 3 2 2 2 2 2 3 2 3 + - 1/144 y x z - 1/72 y x z + 1/288 y x z - 1/288 y x z + + 2 4 4 2 2 + - 1/36 y x z + 1/72 z y x + 1/864 x z - 1/432 z x + 1/36 y x z + + 2 2 2 2 2 2 + - 1/72 y x z + 1/72 y x z - 1/36 y x z - 1/216 x z + 1/432 x z + + 2 3 3 2 2 2 4 4 + - 1/1728 x z + 1/864 x z + 1/432 x z - 1/216 x z + 1/1728 z x + + 2 4 3 4 3 4 3 + - 1/432 z x + 1/1728 z x + 1/216 z x - 1/864 z x , COEFF(-1, -2, 1) + + 2 2 4 4 4 3 3 2 2 4 + = - 1/18 y x z - 1/72 z y x + 1/72 y x z - 1/18 z y x + + 4 4 4 2 4 2 3 3 2 3 + + 1/18 z y x - 1/18 y x z + 1/72 z y x - 1/72 y x z + 1/18 z y x + + 3 2 4 2 2 3 2 3 2 4 + - 1/18 z y x + 1/18 y x z + 1/18 z y x - 1/18 z y x + 1/108 x z + + 2 4 3 4 2 4 4 3 + - 1/18 z y x - 1/72 z y x + 1/18 z y x + 1/72 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + + 1/72 z y x - 1/72 z y x + 1/18 y x z - 1/108 x z + 1/432 x z + + 3 2 2 3 2 2 2 2 2 3 + - 1/18 y x z - 2/9 y x z + 1/18 y x z + 2/9 y x z - 1/18 y x z + + 2 3 2 4 4 + + 1/18 y x z + 2/9 y x z - 2/9 z y x - 1/108 x z + 1/108 z x + + 2 2 2 2 2 2 2 + - 2/9 y x z + 2/9 y x z - 2/9 y x z + 2/9 y x z + 1/27 x z + + 2 2 3 3 2 2 2 + - 1/27 x z + 1/108 x z - 1/108 x z - 1/27 x z + 1/27 x z + + 4 4 2 4 3 4 3 4 3 + - 1/432 z x + 1/108 z x - 1/432 z x - 1/108 z x + 1/432 z x , + + 2 2 4 4 4 2 2 4 + COEFF(0, -2, 1) = 5/48 y x z + 1/48 z y x + 1/12 z y x + + 4 4 2 4 2 4 2 4 3 4 + - 1/12 z y x - 1/48 z y x - 5/288 x z + 1/12 z y x + 1/48 z y x + + 2 4 3 2 4 2 4 2 2 2 + - 1/12 z y x - 1/48 z y x - 5/48 y x z - 1/18 z - 5/12 y x z + + 2 2 3 2 3 4 3 2 4 + + 5/48 y x z - 5/48 y x z + 1/72 z + 1/72 z - 1/12 y z + + 4 2 2 4 2 2 + + 1/12 y z - 1/18 z + 5/12 z y x - 1/3 y z - 1/72 z x - 5/12 y x z + + 2 2 2 2 3 2 3 + + 5/12 y x z + 1/3 y z + 5/72 x z + 1/12 y z - 1/12 y z + + 2 3 2 2 2 4 4 2 2 + - 5/288 x z - 1/3 y z + 5/72 x z + 1/288 z x + 1/3 y z + + 2 4 3 4 2 2 4 + - 1/72 z x + 1/288 z x , COEFF(1, -2, 1) = - 1/18 y x z + + 4 4 3 3 2 2 4 4 4 + - 1/72 z y x - 1/72 y x z - 1/18 z y x + 1/18 z y x + 1/18 y x z + + 4 2 4 2 3 3 2 3 3 + + 1/72 z y x + 1/72 y x z - 1/18 z y x + 1/18 z y x + + 2 4 2 2 3 2 3 2 4 2 4 + - 1/18 y x z - 1/18 z y x + 1/18 z y x + 1/108 x z - 1/18 z y x + + 3 4 2 4 4 3 3 2 4 + - 1/72 z y x + 1/18 z y x - 1/72 z y x + 1/72 z y x + + 4 2 3 2 4 3 2 3 3 3 + + 1/72 z y x + 1/18 y x z + 1/108 x z - 1/432 x z + 1/18 y x z + + 2 2 3 2 2 2 2 2 3 2 3 + + 2/9 y x z - 1/18 y x z + 2/9 y x z - 1/18 y x z + 1/18 y x z + + 2 4 4 2 2 + - 2/9 y x z - 2/9 z y x + 1/108 x z + 1/108 z x + 2/9 y x z + + 2 2 2 2 2 2 + + 2/9 y x z - 2/9 y x z - 2/9 y x z - 1/27 x z - 1/27 x z + + 2 3 3 2 2 2 4 4 + + 1/108 x z + 1/108 x z - 1/27 x z - 1/27 x z - 1/432 z x + + 2 4 3 4 3 4 3 + + 1/108 z x - 1/432 z x + 1/108 z x - 1/432 z x , COEFF(2, -2, 1) = + + 2 2 4 4 4 3 3 2 2 4 + 1/288 y x z + 1/288 z y x + 1/144 y x z + 1/72 z y x + + 4 4 4 2 4 2 3 3 + - 1/72 z y x - 1/144 y x z - 1/288 z y x - 1/144 y x z + + 2 3 3 2 4 2 2 3 + + 1/36 z y x - 1/36 z y x + 1/144 y x z + 1/36 z y x + + 2 3 2 4 2 4 3 4 + - 1/36 z y x - 1/1728 x z + 1/72 z y x + 1/288 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/72 z y x + 1/144 z y x - 1/288 z y x - 1/144 z y x + + 2 4 3 2 3 3 3 2 + - 1/288 y x z - 1/216 x z + 1/864 x z - 1/144 y x z - 1/36 y x z + + 2 3 2 2 2 2 2 3 2 3 + + 1/144 y x z - 1/72 y x z + 1/288 y x z - 1/288 y x z + + 2 4 4 2 2 + + 1/36 y x z + 1/72 z y x - 1/864 x z - 1/432 z x - 1/36 y x z + + 2 2 2 2 2 2 + - 1/72 y x z + 1/72 y x z + 1/36 y x z + 1/216 x z + 1/432 x z + + 2 3 3 2 2 2 4 4 + - 1/1728 x z - 1/864 x z + 1/432 x z + 1/216 x z + 1/1728 z x + + 2 4 3 4 3 4 3 + - 1/432 z x + 1/1728 z x - 1/216 z x + 1/864 z x , COEFF(-2, -1, 1) + + 2 2 4 4 4 3 3 2 2 4 + = - 1/72 y x z - 1/144 z y x + 1/72 y x z - 1/18 z y x + + 4 4 4 2 4 2 3 3 2 3 + + 1/36 z y x - 1/72 y x z + 1/72 z y x - 1/36 y x z + 1/9 z y x + + 3 2 4 2 2 3 2 3 2 4 + - 1/18 z y x + 1/36 y x z + 1/9 z y x - 1/18 z y x + 1/108 x z + + 2 4 3 4 2 4 4 3 + - 1/18 z y x - 1/144 z y x + 1/36 z y x + 1/72 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + + 1/72 z y x - 1/36 z y x + 1/144 y x z - 2/27 x z + 1/54 x z + + 3 2 2 3 2 2 2 2 2 3 + - 1/72 y x z - 1/9 y x z + 1/36 y x z + 1/18 y x z - 1/72 y x z + + 2 3 2 4 4 + + 1/144 y x z + 1/18 y x z - 1/36 z y x - 1/54 x z + 1/27 z x + + 2 2 2 2 2 2 2 + - 1/9 y x z + 1/18 y x z - 1/36 y x z + 1/18 y x z + 2/27 x z + + 2 2 3 3 2 2 2 + - 1/27 x z + 1/108 x z - 1/54 x z - 1/27 x z + 2/27 x z + + 4 4 2 4 3 4 3 4 3 + - 1/108 z x + 1/27 z x - 1/108 z x - 2/27 z x + 1/54 z x , + + 2 2 4 4 4 3 3 + COEFF(-1, -1, 1) = 2/9 y x z + 1/36 z y x - 1/36 y x z + + 2 2 4 4 4 4 2 4 2 3 3 + + 2/9 z y x - 1/9 z y x + 1/9 y x z - 1/18 z y x + 1/18 y x z + + 2 3 3 2 4 2 2 3 2 3 + - 2/9 z y x + 1/9 z y x - 2/9 y x z - 2/9 z y x + 1/9 z y x + + 2 4 2 4 3 4 2 4 4 3 + - 4/27 x z + 2/9 z y x + 1/36 z y x - 1/9 z y x - 1/36 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + - 1/18 z y x + 1/18 z y x - 1/9 y x z + 4/27 x z - 1/27 x z + + 3 2 2 3 2 2 2 2 2 3 + + 1/9 y x z + 8/9 y x z - 2/9 y x z - 8/9 y x z + 2/9 y x z + + 2 3 2 4 4 + - 1/9 y x z - 4/9 y x z + 4/9 z y x + 4/27 x z - 4/27 z x + + 2 2 2 2 2 2 2 16 16 2 + + 8/9 y x z - 8/9 y x z + 4/9 y x z - 4/9 y x z - -- x z + -- x z + 27 27 + + 2 3 3 16 2 2 16 2 4 4 2 4 + - 4/27 x z + 4/27 x z + -- x z - -- x z + 1/27 z x - 4/27 z x + 27 27 + + 3 4 3 4 3 2 2 4 + + 1/27 z x + 4/27 z x - 1/27 z x , COEFF(0, -1, 1) = - 5/12 y x z + + 4 4 2 2 4 4 4 2 4 2 4 + - 1/24 z y x - 1/3 z y x + 1/6 z y x + 1/12 z y x + 5/18 x z + + 2 4 3 4 2 4 3 2 4 2 4 + - 1/3 z y x - 1/24 z y x + 1/6 z y x + 1/12 z y x + 5/24 y x z + + 2 2 2 2 2 3 2 3 4 3 + + 8/9 z + 5/3 y x z - 5/12 y x z + 5/24 y x z - 2/9 z - 2/9 z + + 2 4 4 2 2 4 + + 1/3 y z - 1/6 y z + 8/9 z - 5/6 z y x + 2/3 y z + 2/9 z x + + 2 2 2 2 2 2 3 2 3 + + 5/3 y x z - 5/6 y x z - 4/3 y z - 10/9 x z - 1/6 y z + 1/3 y z + + 2 3 2 2 2 4 4 2 2 2 4 + + 5/18 x z + 2/3 y z - 10/9 x z - 1/18 z x - 4/3 y z + 2/9 z x + + 3 4 2 2 4 4 4 3 3 + - 1/18 z x , COEFF(1, -1, 1) = 2/9 y x z + 1/36 z y x + 1/36 y x z + + 2 2 4 4 4 4 2 4 2 3 3 + + 2/9 z y x - 1/9 z y x - 1/9 y x z - 1/18 z y x - 1/18 y x z + + 2 3 3 2 4 2 2 3 2 3 + + 2/9 z y x - 1/9 z y x + 2/9 y x z + 2/9 z y x - 1/9 z y x + + 2 4 2 4 3 4 2 4 4 3 + - 4/27 x z + 2/9 z y x + 1/36 z y x - 1/9 z y x + 1/36 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + - 1/18 z y x - 1/18 z y x - 1/9 y x z - 4/27 x z + 1/27 x z + + 3 2 2 3 2 2 2 2 2 3 + - 1/9 y x z - 8/9 y x z + 2/9 y x z - 8/9 y x z + 2/9 y x z + + 2 3 2 4 4 + - 1/9 y x z + 4/9 y x z + 4/9 z y x - 4/27 x z - 4/27 z x + + 2 2 2 2 2 2 2 16 16 2 + - 8/9 y x z - 8/9 y x z + 4/9 y x z + 4/9 y x z + -- x z + -- x z + 27 27 + + 2 3 3 16 2 2 16 2 4 4 2 4 + - 4/27 x z - 4/27 x z + -- x z + -- x z + 1/27 z x - 4/27 z x + 27 27 + + 3 4 3 4 3 2 2 4 + + 1/27 z x - 4/27 z x + 1/27 z x , COEFF(2, -1, 1) = - 1/72 y x z + + 4 4 3 3 2 2 4 4 4 + - 1/144 z y x - 1/72 y x z - 1/18 z y x + 1/36 z y x + 1/72 y x z + + 4 2 4 2 3 3 2 3 3 2 4 + + 1/72 z y x + 1/36 y x z - 1/9 z y x + 1/18 z y x - 1/36 y x z + + 2 2 3 2 3 2 4 2 4 3 4 + - 1/9 z y x + 1/18 z y x + 1/108 x z - 1/18 z y x - 1/144 z y x + + 2 4 4 3 3 2 4 4 2 3 + + 1/36 z y x - 1/72 z y x + 1/72 z y x + 1/36 z y x + + 2 4 3 2 3 3 3 2 + + 1/144 y x z + 2/27 x z - 1/54 x z + 1/72 y x z + 1/9 y x z + + 2 3 2 2 2 2 2 3 2 3 + - 1/36 y x z + 1/18 y x z - 1/72 y x z + 1/144 y x z + + 2 4 4 2 2 + - 1/18 y x z - 1/36 z y x + 1/54 x z + 1/27 z x + 1/9 y x z + + 2 2 2 2 2 2 + + 1/18 y x z - 1/36 y x z - 1/18 y x z - 2/27 x z - 1/27 x z + + 2 3 3 2 2 2 4 4 + + 1/108 x z + 1/54 x z - 1/27 x z - 2/27 x z - 1/108 z x + + 2 4 3 4 3 4 3 + + 1/27 z x - 1/108 z x + 2/27 z x - 1/54 z x , COEFF(-2, 0, 1) = + + 2 2 4 2 2 4 4 2 4 2 3 3 2 3 + 1/48 y x z + 1/12 z y x - 1/48 z y x + 1/24 y x z - 1/6 z y x + + 2 4 2 2 3 2 4 2 4 3 2 4 + - 1/24 y x z - 1/6 z y x - 5/288 x z + 1/12 z y x - 1/48 z y x + + 4 2 3 3 2 3 3 2 2 3 + + 1/24 z y x + 5/36 x z - 5/144 x z + 1/6 y x z - 1/24 y x z + + 2 2 2 2 2 3 4 4 2 2 + - 1/12 y x z + 1/48 y x z + 5/144 x z - 5/72 z x + 1/6 y x z + + 2 2 2 2 3 3 + - 1/12 y x z - 5/36 x z + 5/72 x z - 5/288 x z + 5/144 x z + + 2 2 2 4 4 2 4 3 4 + + 5/72 x z - 5/36 x z + 5/288 z x - 5/72 z x + 5/288 z x + + 3 4 3 2 2 4 2 2 4 + + 5/36 z x - 5/144 z x , COEFF(-1, 0, 1) = - 1/3 y x z - 1/3 z y x + + 4 2 4 2 3 3 2 3 2 4 2 2 3 + + 1/12 z y x - 1/12 y x z + 1/3 z y x + 1/3 y x z + 1/3 z y x + + 2 4 2 4 3 2 4 4 2 3 3 2 + + 5/18 x z - 1/3 z y x + 1/12 z y x - 1/12 z y x - 5/18 x z + + 3 3 2 2 3 2 2 2 2 2 3 + + 5/72 x z - 4/3 y x z + 1/3 y x z + 4/3 y x z - 1/3 y x z + + 4 4 2 2 2 2 2 + - 5/18 x z + 5/18 z x - 4/3 y x z + 4/3 y x z + 10/9 x z - 10/9 x z + + 2 3 3 2 2 2 4 4 + + 5/18 x z - 5/18 x z - 10/9 x z + 10/9 x z - 5/72 z x + + 2 4 3 4 3 4 3 + + 5/18 z x - 5/72 z x - 5/18 z x + 5/72 z x , COEFF(0, 0, 1) = + + 3 2 4 2 3 2 4 3 4 4 + - 1/8 z y x - 1/2 y z + 1/2 z y x + 5/48 z x - 5/12 z x + + 2 2 25 2 4 3 4 25 2 2 + - 5/2 y x z - -- x z - 5/3 z + 5/12 z + 5/12 z + -- x z + 48 12 + + 4 4 2 2 4 25 2 2 4 2 2 + + 5/48 z x - 5/3 z - 1/2 y z + -- x z - 5/12 z x + 2 y z + 12 + + 4 2 4 25 2 3 2 2 2 2 2 4 2 2 3 + - 1/8 z y x - -- x z - 5/2 y x z + 5/8 y x z + 5/8 y x z + 48 + + 2 2 4 2 2 2 4 2 2 4 + + 1/2 z y x + 2 y z, COEFF(1, 0, 1) = - 1/3 y x z - 1/3 z y x + + 4 2 4 2 3 3 2 3 2 4 2 2 3 + + 1/12 z y x + 1/12 y x z - 1/3 z y x - 1/3 y x z - 1/3 z y x + + 2 4 2 4 3 2 4 4 2 3 3 2 + + 5/18 x z - 1/3 z y x + 1/12 z y x + 1/12 z y x + 5/18 x z + + 3 3 2 2 3 2 2 2 2 2 3 + - 5/72 x z + 4/3 y x z - 1/3 y x z + 4/3 y x z - 1/3 y x z + + 4 4 2 2 2 2 2 + + 5/18 x z + 5/18 z x + 4/3 y x z + 4/3 y x z - 10/9 x z - 10/9 x z + + 2 3 3 2 2 2 4 4 + + 5/18 x z + 5/18 x z - 10/9 x z - 10/9 x z - 5/72 z x + + 2 4 3 4 3 4 3 + + 5/18 z x - 5/72 z x + 5/18 z x - 5/72 z x , COEFF(2, 0, 1) = + + 2 2 4 2 2 4 4 2 4 2 3 3 2 3 + 1/48 y x z + 1/12 z y x - 1/48 z y x - 1/24 y x z + 1/6 z y x + + 2 4 2 2 3 2 4 2 4 3 2 4 + + 1/24 y x z + 1/6 z y x - 5/288 x z + 1/12 z y x - 1/48 z y x + + 4 2 3 3 2 3 3 2 2 3 + - 1/24 z y x - 5/36 x z + 5/144 x z - 1/6 y x z + 1/24 y x z + + 2 2 2 2 2 3 4 4 2 2 + - 1/12 y x z + 1/48 y x z - 5/144 x z - 5/72 z x - 1/6 y x z + + 2 2 2 2 3 3 + - 1/12 y x z + 5/36 x z + 5/72 x z - 5/288 x z - 5/144 x z + + 2 2 2 4 4 2 4 3 4 + + 5/72 x z + 5/36 x z + 5/288 z x - 5/72 z x + 5/288 z x + + 3 4 3 2 2 4 + - 5/36 z x + 5/144 z x , COEFF(-2, 1, 1) = - 1/72 y x z + + 4 4 3 3 2 2 4 4 4 + + 1/144 z y x - 1/72 y x z - 1/18 z y x - 1/36 z y x + 1/72 y x z + + 4 2 4 2 3 3 2 3 3 2 4 + + 1/72 z y x - 1/36 y x z + 1/9 z y x + 1/18 z y x + 1/36 y x z + + 2 2 3 2 3 2 4 2 4 3 4 + + 1/9 z y x + 1/18 z y x + 1/108 x z - 1/18 z y x + 1/144 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/36 z y x - 1/72 z y x + 1/72 z y x - 1/36 z y x + + 2 4 3 2 3 3 3 2 + - 1/144 y x z - 2/27 x z + 1/54 x z + 1/72 y x z - 1/9 y x z + + 2 3 2 2 2 2 2 3 2 3 + + 1/36 y x z + 1/18 y x z - 1/72 y x z - 1/144 y x z + + 2 4 4 2 2 + - 1/18 y x z + 1/36 z y x - 1/54 x z + 1/27 z x - 1/9 y x z + + 2 2 2 2 2 2 + + 1/18 y x z + 1/36 y x z - 1/18 y x z + 2/27 x z - 1/27 x z + + 2 3 3 2 2 2 4 4 + + 1/108 x z - 1/54 x z - 1/27 x z + 2/27 x z - 1/108 z x + + 2 4 3 4 3 4 3 + + 1/27 z x - 1/108 z x - 2/27 z x + 1/54 z x , COEFF(-1, 1, 1) = + + 2 2 4 4 4 3 3 2 2 4 4 + 2/9 y x z - 1/36 z y x + 1/36 y x z + 2/9 z y x + 1/9 z y x + + 4 4 2 4 2 3 3 2 3 3 + - 1/9 y x z - 1/18 z y x + 1/18 y x z - 2/9 z y x - 1/9 z y x + + 2 4 2 2 3 2 3 2 4 2 4 + - 2/9 y x z - 2/9 z y x - 1/9 z y x - 4/27 x z + 2/9 z y x + + 3 4 2 4 4 3 3 2 4 + - 1/36 z y x + 1/9 z y x + 1/36 z y x - 1/18 z y x + + 4 2 3 2 4 3 2 3 3 3 + + 1/18 z y x + 1/9 y x z + 4/27 x z - 1/27 x z - 1/9 y x z + + 2 2 3 2 2 2 2 2 3 2 3 + + 8/9 y x z - 2/9 y x z - 8/9 y x z + 2/9 y x z + 1/9 y x z + + 2 4 4 2 2 + + 4/9 y x z - 4/9 z y x + 4/27 x z - 4/27 z x + 8/9 y x z + + 2 2 2 2 2 16 16 2 2 3 + - 8/9 y x z - 4/9 y x z + 4/9 y x z - -- x z + -- x z - 4/27 x z + 27 27 + + 3 16 2 2 16 2 4 4 2 4 3 4 + + 4/27 x z + -- x z - -- x z + 1/27 z x - 4/27 z x + 1/27 z x + 27 27 + + 3 4 3 2 2 4 4 4 + + 4/27 z x - 1/27 z x , COEFF(0, 1, 1) = - 5/12 y x z + 1/24 z y x + + 2 2 4 4 4 2 4 2 4 2 4 + - 1/3 z y x - 1/6 z y x + 1/12 z y x + 5/18 x z - 1/3 z y x + + 3 4 2 4 3 2 4 2 4 + + 1/24 z y x - 1/6 z y x + 1/12 z y x - 5/24 y x z + 8/9 z + + 2 2 2 2 2 3 2 3 4 3 + + 5/3 y x z - 5/12 y x z - 5/24 y x z - 2/9 z - 2/9 z + + 2 4 4 2 2 4 + + 1/3 y z + 1/6 y z + 8/9 z + 5/6 z y x - 2/3 y z + 2/9 z x + + 2 2 2 2 2 2 3 2 3 + + 5/3 y x z + 5/6 y x z - 4/3 y z - 10/9 x z + 1/6 y z + 1/3 y z + + 2 3 2 2 2 4 4 2 2 2 4 + + 5/18 x z - 2/3 y z - 10/9 x z - 1/18 z x - 4/3 y z + 2/9 z x + + 3 4 2 2 4 4 4 3 3 + - 1/18 z x , COEFF(1, 1, 1) = 2/9 y x z - 1/36 z y x - 1/36 y x z + + 2 2 4 4 4 4 2 4 2 3 3 + + 2/9 z y x + 1/9 z y x + 1/9 y x z - 1/18 z y x - 1/18 y x z + + 2 3 3 2 4 2 2 3 2 3 + + 2/9 z y x + 1/9 z y x + 2/9 y x z + 2/9 z y x + 1/9 z y x + + 2 4 2 4 3 4 2 4 4 3 + - 4/27 x z + 2/9 z y x - 1/36 z y x + 1/9 z y x - 1/36 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + - 1/18 z y x - 1/18 z y x + 1/9 y x z - 4/27 x z + 1/27 x z + + 3 2 2 3 2 2 2 2 2 3 + + 1/9 y x z - 8/9 y x z + 2/9 y x z - 8/9 y x z + 2/9 y x z + + 2 3 2 4 4 + + 1/9 y x z - 4/9 y x z - 4/9 z y x - 4/27 x z - 4/27 z x + + 2 2 2 2 2 2 2 16 16 2 + - 8/9 y x z - 8/9 y x z - 4/9 y x z - 4/9 y x z + -- x z + -- x z + 27 27 + + 2 3 3 16 2 2 16 2 4 4 2 4 + - 4/27 x z - 4/27 x z + -- x z + -- x z + 1/27 z x - 4/27 z x + 27 27 + + 3 4 3 4 3 2 2 4 + + 1/27 z x - 4/27 z x + 1/27 z x , COEFF(2, 1, 1) = - 1/72 y x z + + 4 4 3 3 2 2 4 4 4 + + 1/144 z y x + 1/72 y x z - 1/18 z y x - 1/36 z y x - 1/72 y x z + + 4 2 4 2 3 3 2 3 3 2 4 + + 1/72 z y x + 1/36 y x z - 1/9 z y x - 1/18 z y x - 1/36 y x z + + 2 2 3 2 3 2 4 2 4 3 4 + - 1/9 z y x - 1/18 z y x + 1/108 x z - 1/18 z y x + 1/144 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/36 z y x + 1/72 z y x + 1/72 z y x + 1/36 z y x + + 2 4 3 2 3 3 3 2 + - 1/144 y x z + 2/27 x z - 1/54 x z - 1/72 y x z + 1/9 y x z + + 2 3 2 2 2 2 2 3 2 3 + - 1/36 y x z + 1/18 y x z - 1/72 y x z - 1/144 y x z + + 2 4 4 2 2 + + 1/18 y x z + 1/36 z y x + 1/54 x z + 1/27 z x + 1/9 y x z + + 2 2 2 2 2 2 + + 1/18 y x z + 1/36 y x z + 1/18 y x z - 2/27 x z - 1/27 x z + + 2 3 3 2 2 2 4 4 + + 1/108 x z + 1/54 x z - 1/27 x z - 2/27 x z - 1/108 z x + + 2 4 3 4 3 4 3 + + 1/27 z x - 1/108 z x + 2/27 z x - 1/54 z x , COEFF(-2, 2, 1) = + + 2 2 4 4 4 3 3 2 2 4 + 1/288 y x z - 1/288 z y x + 1/144 y x z + 1/72 z y x + + 4 4 4 2 4 2 3 3 + + 1/72 z y x - 1/144 y x z - 1/288 z y x + 1/144 y x z + + 2 3 3 2 4 2 2 3 + - 1/36 z y x - 1/36 z y x - 1/144 y x z - 1/36 z y x + + 2 3 2 4 2 4 3 4 + - 1/36 z y x - 1/1728 x z + 1/72 z y x - 1/288 z y x + + 2 4 4 3 3 2 4 4 2 3 + + 1/72 z y x + 1/144 z y x - 1/288 z y x + 1/144 z y x + + 2 4 3 2 3 3 3 2 + + 1/288 y x z + 1/216 x z - 1/864 x z - 1/144 y x z + 1/36 y x z + + 2 3 2 2 2 2 2 3 2 3 + - 1/144 y x z - 1/72 y x z + 1/288 y x z + 1/288 y x z + + 2 4 4 2 2 + + 1/36 y x z - 1/72 z y x + 1/864 x z - 1/432 z x + 1/36 y x z + + 2 2 2 2 2 2 + - 1/72 y x z - 1/72 y x z + 1/36 y x z - 1/216 x z + 1/432 x z + + 2 3 3 2 2 2 4 4 + - 1/1728 x z + 1/864 x z + 1/432 x z - 1/216 x z + 1/1728 z x + + 2 4 3 4 3 4 3 + - 1/432 z x + 1/1728 z x + 1/216 z x - 1/864 z x , COEFF(-1, 2, 1) + + 2 2 4 4 4 3 3 2 2 4 + = - 1/18 y x z + 1/72 z y x - 1/72 y x z - 1/18 z y x + + 4 4 4 2 4 2 3 3 2 3 + - 1/18 z y x + 1/18 y x z + 1/72 z y x - 1/72 y x z + 1/18 z y x + + 3 2 4 2 2 3 2 3 2 4 + + 1/18 z y x + 1/18 y x z + 1/18 z y x + 1/18 z y x + 1/108 x z + + 2 4 3 4 2 4 4 3 + - 1/18 z y x + 1/72 z y x - 1/18 z y x - 1/72 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + + 1/72 z y x - 1/72 z y x - 1/18 y x z - 1/108 x z + 1/432 x z + + 3 2 2 3 2 2 2 2 2 3 + + 1/18 y x z - 2/9 y x z + 1/18 y x z + 2/9 y x z - 1/18 y x z + + 2 3 2 4 4 + - 1/18 y x z - 2/9 y x z + 2/9 z y x - 1/108 x z + 1/108 z x + + 2 2 2 2 2 2 2 + - 2/9 y x z + 2/9 y x z + 2/9 y x z - 2/9 y x z + 1/27 x z + + 2 2 3 3 2 2 2 + - 1/27 x z + 1/108 x z - 1/108 x z - 1/27 x z + 1/27 x z + + 4 4 2 4 3 4 3 4 3 + - 1/432 z x + 1/108 z x - 1/432 z x - 1/108 z x + 1/432 z x , + + 2 2 4 4 4 2 2 4 4 + COEFF(0, 2, 1) = 5/48 y x z - 1/48 z y x + 1/12 z y x + 1/12 z y x + + 4 2 4 2 4 2 4 3 4 2 4 + - 1/48 z y x - 5/288 x z + 1/12 z y x - 1/48 z y x + 1/12 z y x + + 3 2 4 2 4 2 2 2 2 2 3 + - 1/48 z y x + 5/48 y x z - 1/18 z - 5/12 y x z + 5/48 y x z + + 2 3 4 3 2 4 4 2 + + 5/48 y x z + 1/72 z + 1/72 z - 1/12 y z - 1/12 y z - 1/18 z + + 2 4 2 2 2 2 + - 5/12 z y x + 1/3 y z - 1/72 z x - 5/12 y x z - 5/12 y x z + + 2 2 3 2 3 2 3 2 + + 1/3 y z + 5/72 x z - 1/12 y z - 1/12 y z - 5/288 x z + 1/3 y z + + 2 2 4 4 2 2 2 4 3 4 + + 5/72 x z + 1/288 z x + 1/3 y z - 1/72 z x + 1/288 z x , + + 2 2 4 4 4 3 3 + COEFF(1, 2, 1) = - 1/18 y x z + 1/72 z y x + 1/72 y x z + + 2 2 4 4 4 4 2 4 + - 1/18 z y x - 1/18 z y x - 1/18 y x z + 1/72 z y x + + 2 3 3 2 3 3 2 4 + + 1/72 y x z - 1/18 z y x - 1/18 z y x - 1/18 y x z + + 2 2 3 2 3 2 4 2 4 3 4 + - 1/18 z y x - 1/18 z y x + 1/108 x z - 1/18 z y x + 1/72 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/18 z y x + 1/72 z y x + 1/72 z y x + 1/72 z y x + + 2 4 3 2 3 3 3 2 + - 1/18 y x z + 1/108 x z - 1/432 x z - 1/18 y x z + 2/9 y x z + + 2 3 2 2 2 2 2 3 2 3 + - 1/18 y x z + 2/9 y x z - 1/18 y x z - 1/18 y x z + 2/9 y x z + + 2 4 4 2 2 2 2 + + 2/9 z y x + 1/108 x z + 1/108 z x + 2/9 y x z + 2/9 y x z + + 2 2 2 2 2 3 + + 2/9 y x z + 2/9 y x z - 1/27 x z - 1/27 x z + 1/108 x z + + 3 2 2 2 4 4 2 4 + + 1/108 x z - 1/27 x z - 1/27 x z - 1/432 z x + 1/108 z x + + 3 4 3 4 3 2 2 4 + - 1/432 z x + 1/108 z x - 1/432 z x , COEFF(2, 2, 1) = 1/288 y x z + + 4 4 3 3 2 2 4 4 + - 1/288 z y x - 1/144 y x z + 1/72 z y x + 1/72 z y x + + 4 4 2 4 2 3 3 2 3 + + 1/144 y x z - 1/288 z y x - 1/144 y x z + 1/36 z y x + + 3 2 4 2 2 3 2 3 + + 1/36 z y x + 1/144 y x z + 1/36 z y x + 1/36 z y x + + 2 4 2 4 3 4 2 4 + - 1/1728 x z + 1/72 z y x - 1/288 z y x + 1/72 z y x + + 4 3 3 2 4 4 2 3 2 4 + - 1/144 z y x - 1/288 z y x - 1/144 z y x + 1/288 y x z + + 3 2 3 3 3 2 2 3 + - 1/216 x z + 1/864 x z + 1/144 y x z - 1/36 y x z + 1/144 y x z + + 2 2 2 2 2 3 2 3 + - 1/72 y x z + 1/288 y x z + 1/288 y x z - 1/36 y x z + + 2 4 4 2 2 2 2 + - 1/72 z y x - 1/864 x z - 1/432 z x - 1/36 y x z - 1/72 y x z + + 2 2 2 2 2 3 + - 1/72 y x z - 1/36 y x z + 1/216 x z + 1/432 x z - 1/1728 x z + + 3 2 2 2 4 4 2 4 + - 1/864 x z + 1/432 x z + 1/216 x z + 1/1728 z x - 1/432 z x + + 3 4 3 4 3 + + 1/1728 z x - 1/216 z x + 1/864 z x , COEFF(-2, -2, 2) = + + 2 2 4 4 4 3 3 2 2 4 + - 1/1152 y x z - 1/1152 z y x + 1/288 y x z - 1/1152 z y x + + 4 4 4 2 4 2 3 3 + + 1/576 z y x - 1/576 y x z + 1/1152 z y x - 1/288 y x z + + 2 3 3 2 4 2 2 3 + + 1/288 z y x - 1/288 z y x + 1/576 y x z + 1/576 z y x + + 2 3 2 4 2 4 3 4 + - 1/576 z y x + 1/6912 x z - 1/576 z y x - 1/576 z y x + + 2 4 4 3 3 2 4 4 2 3 + + 1/1152 z y x + 1/576 z y x + 1/576 z y x - 1/576 z y x + + 2 4 3 2 3 3 3 + + 1/1152 y x z - 1/3456 x z + 1/1728 x z - 1/288 y x z + + 2 2 3 2 2 2 2 2 3 + - 1/288 y x z + 1/288 y x z + 1/1152 y x z - 1/576 y x z + + 2 3 2 4 4 + + 1/576 y x z + 1/288 y x z - 1/576 z y x - 1/3456 x z + 1/3456 z x + + 2 2 2 2 2 2 2 + - 1/576 y x z + 1/576 y x z - 1/1152 y x z + 1/576 y x z + + 2 2 3 3 2 2 + + 1/1728 x z - 1/3456 x z + 1/3456 x z - 1/1728 x z - 1/6912 x z + + 2 4 4 2 4 3 4 3 + + 1/3456 x z - 1/6912 z x + 1/6912 z x - 1/3456 z x - 1/1728 z x + + 4 3 2 2 4 4 4 + + 1/3456 z x , COEFF(-1, -2, 2) = 1/72 y x z + 1/288 z y x + + 3 3 2 2 4 4 4 + - 1/144 y x z + 1/288 z y x - 1/144 z y x + 1/72 y x z + + 4 2 4 2 3 3 2 3 3 + - 1/288 z y x + 1/144 y x z - 1/144 z y x + 1/144 z y x + + 2 4 2 2 3 2 3 2 4 + - 1/72 y x z - 1/288 z y x + 1/288 z y x - 1/432 x z + + 2 4 3 4 2 4 4 3 + + 1/144 z y x + 1/144 z y x - 1/288 z y x - 1/288 z y x + + 3 2 4 4 2 3 2 4 3 2 + - 1/144 z y x + 1/288 z y x - 1/72 y x z + 1/1728 x z + + 3 3 3 2 2 3 2 2 2 + - 1/864 x z + 1/36 y x z + 1/36 y x z - 1/36 y x z - 1/72 y x z + + 2 2 3 2 3 2 4 + + 1/36 y x z - 1/36 y x z - 1/36 y x z + 1/36 z y x + 1/432 x z + + 4 2 2 2 2 2 2 2 + - 1/864 z x + 1/72 y x z - 1/36 y x z + 1/72 y x z - 1/72 y x z + + 2 2 3 3 2 2 + - 1/216 x z + 1/216 x z - 1/216 x z + 1/216 x z + 1/432 x z + + 2 4 4 2 4 3 4 3 + - 1/432 x z + 1/1728 z x - 1/1728 z x + 1/864 z x + 1/864 z x + + 4 3 2 2 4 4 4 + - 1/1728 z x , COEFF(0, -2, 2) = - 5/192 y x z - 1/192 z y x + + 2 2 4 4 4 2 4 2 4 + - 1/192 z y x + 1/96 z y x + 1/192 z y x + 5/1152 x z + + 2 4 3 4 2 4 3 2 4 + - 1/96 z y x - 1/96 z y x + 1/192 z y x + 1/96 z y x + + 2 4 2 2 2 2 2 3 2 3 + + 5/192 y x z + 1/144 z + 5/192 y x z - 5/96 y x z + 5/96 y x z + + 4 3 2 4 4 2 2 + - 1/288 z - 1/144 z + 1/48 y z - 1/48 y z + 1/288 z - 5/96 z y x + + 4 2 2 2 2 2 + + 1/24 y z + 1/576 z x + 5/96 y x z - 5/192 y x z - 1/24 y z + + 2 3 2 3 2 3 2 + - 5/576 x z - 1/24 y z + 1/24 y z + 5/576 x z + 1/48 y z + + 2 2 4 4 2 2 2 4 3 4 + - 5/1152 x z - 1/1152 z x - 1/48 y z + 1/1152 z x - 1/576 z x , + + 2 2 4 4 4 3 3 + COEFF(1, -2, 2) = 1/72 y x z + 1/288 z y x + 1/144 y x z + + 2 2 4 4 4 4 2 4 + + 1/288 z y x - 1/144 z y x - 1/72 y x z - 1/288 z y x + + 2 3 3 2 3 3 2 4 + - 1/144 y x z + 1/144 z y x - 1/144 z y x + 1/72 y x z + + 2 2 3 2 3 2 4 2 4 + + 1/288 z y x - 1/288 z y x - 1/432 x z + 1/144 z y x + + 3 4 2 4 4 3 3 2 4 + + 1/144 z y x - 1/288 z y x + 1/288 z y x - 1/144 z y x + + 4 2 3 2 4 3 2 3 3 3 + - 1/288 z y x - 1/72 y x z - 1/1728 x z + 1/864 x z - 1/36 y x z + + 2 2 3 2 2 2 2 2 3 + - 1/36 y x z + 1/36 y x z - 1/72 y x z + 1/36 y x z + + 2 3 2 4 4 + - 1/36 y x z + 1/36 y x z + 1/36 z y x - 1/432 x z - 1/864 z x + + 2 2 2 2 2 2 2 + - 1/72 y x z - 1/36 y x z + 1/72 y x z + 1/72 y x z + 1/216 x z + + 2 2 3 3 2 2 2 + + 1/216 x z - 1/216 x z - 1/216 x z + 1/432 x z + 1/432 x z + + 4 4 2 4 3 4 3 4 3 + + 1/1728 z x - 1/1728 z x + 1/864 z x - 1/864 z x + 1/1728 z x , + + 2 2 4 4 4 3 3 + COEFF(2, -2, 2) = - 1/1152 y x z - 1/1152 z y x - 1/288 y x z + + 2 2 4 4 4 4 2 4 + - 1/1152 z y x + 1/576 z y x + 1/576 y x z + 1/1152 z y x + + 2 3 3 2 3 3 2 4 + + 1/288 y x z - 1/288 z y x + 1/288 z y x - 1/576 y x z + + 2 2 3 2 3 2 4 2 4 + - 1/576 z y x + 1/576 z y x + 1/6912 x z - 1/576 z y x + + 3 4 2 4 4 3 3 2 4 + - 1/576 z y x + 1/1152 z y x - 1/576 z y x + 1/576 z y x + + 4 2 3 2 4 3 2 3 3 + + 1/576 z y x + 1/1152 y x z + 1/3456 x z - 1/1728 x z + + 3 2 2 3 2 2 2 + + 1/288 y x z + 1/288 y x z - 1/288 y x z + 1/1152 y x z + + 2 2 3 2 3 2 + - 1/576 y x z + 1/576 y x z - 1/288 y x z - 1/576 z y x + + 4 4 2 2 2 2 + + 1/3456 x z + 1/3456 z x + 1/576 y x z + 1/576 y x z + + 2 2 2 2 2 3 + - 1/1152 y x z - 1/576 y x z - 1/1728 x z - 1/3456 x z + 1/3456 x z + + 3 2 2 2 4 4 2 4 + + 1/1728 x z - 1/6912 x z - 1/3456 x z - 1/6912 z x + 1/6912 z x + + 3 4 3 4 3 + - 1/3456 z x + 1/1728 z x - 1/3456 z x , COEFF(-2, -1, 2) = + + 2 2 4 4 4 3 3 2 2 4 + 1/288 y x z + 1/576 z y x - 1/144 y x z + 1/288 z y x + + 4 4 4 2 4 2 3 3 + - 1/288 z y x + 1/288 y x z - 1/288 z y x + 1/72 y x z + + 2 3 3 2 4 2 2 3 + - 1/72 z y x + 1/144 z y x - 1/144 y x z - 1/144 z y x + + 2 3 2 4 2 4 3 4 + + 1/288 z y x - 1/432 x z + 1/144 z y x + 1/288 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/576 z y x - 1/288 z y x - 1/144 z y x + 1/144 z y x + + 2 4 3 2 3 3 3 2 + - 1/576 y x z + 1/216 x z - 1/108 x z + 1/144 y x z + 1/72 y x z + + 2 3 2 2 2 2 2 3 2 3 + - 1/72 y x z - 1/288 y x z + 1/144 y x z - 1/288 y x z + + 2 4 4 2 2 + - 1/144 y x z + 1/288 z y x + 1/216 x z - 1/216 z x + 1/144 y x z + + 2 2 2 2 2 2 + - 1/144 y x z + 1/576 y x z - 1/288 y x z - 1/108 x z + 1/216 x z + + 2 3 3 2 2 2 4 4 + - 1/216 x z + 1/108 x z + 1/432 x z - 1/216 x z + 1/432 z x + + 2 4 3 4 3 4 3 + - 1/432 z x + 1/216 z x + 1/108 z x - 1/216 z x , COEFF(-1, -1, 2) + + 2 2 4 4 4 3 3 2 2 4 + = - 1/18 y x z - 1/144 z y x + 1/72 y x z - 1/72 z y x + + 4 4 4 2 4 2 3 3 2 3 + + 1/72 z y x - 1/36 y x z + 1/72 z y x - 1/36 y x z + 1/36 z y x + + 3 2 4 2 2 3 2 3 2 4 + - 1/72 z y x + 1/18 y x z + 1/72 z y x - 1/144 z y x + 1/27 x z + + 2 4 3 4 2 4 4 3 + - 1/36 z y x - 1/72 z y x + 1/144 z y x + 1/144 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + + 1/36 z y x - 1/72 z y x + 1/36 y x z - 1/108 x z + 1/54 x z + + 3 2 2 3 2 2 2 2 2 3 + - 1/18 y x z - 1/9 y x z + 1/9 y x z + 1/18 y x z - 1/9 y x z + + 2 3 2 4 4 + + 1/18 y x z + 1/18 y x z - 1/18 z y x - 1/27 x z + 1/54 z x + + 2 2 2 2 2 2 2 + - 1/18 y x z + 1/9 y x z - 1/36 y x z + 1/36 y x z + 2/27 x z + + 2 2 3 3 2 2 2 + - 2/27 x z + 2/27 x z - 2/27 x z - 1/27 x z + 1/27 x z + + 4 4 2 4 3 4 3 4 3 + - 1/108 z x + 1/108 z x - 1/54 z x - 1/54 z x + 1/108 z x , + + 2 2 4 4 4 2 2 4 + COEFF(0, -1, 2) = 5/48 y x z + 1/96 z y x + 1/48 z y x + + 4 4 2 4 2 4 2 4 3 4 + - 1/48 z y x - 1/48 z y x - 5/72 x z + 1/24 z y x + 1/48 z y x + + 2 4 3 2 4 2 4 2 2 2 + - 1/96 z y x - 1/24 z y x - 5/96 y x z - 1/9 z - 5/48 y x z + + 2 2 3 2 3 4 3 2 4 4 + + 5/24 y x z - 5/48 y x z + 1/18 z + 1/9 z - 1/12 y z + 1/24 y z + + 2 2 4 2 2 + - 1/18 z + 5/48 z y x - 1/12 y z - 1/36 z x - 5/24 y x z + + 2 2 2 2 3 2 3 2 3 + + 5/96 y x z + 1/6 y z + 5/36 x z + 1/12 y z - 1/6 y z - 5/36 x z + + 2 2 2 4 4 2 2 2 4 + - 1/24 y z + 5/72 x z + 1/72 z x + 1/12 y z - 1/72 z x + + 3 4 2 2 4 4 4 + + 1/36 z x , COEFF(1, -1, 2) = - 1/18 y x z - 1/144 z y x + + 3 3 2 2 4 4 4 4 2 4 + - 1/72 y x z - 1/72 z y x + 1/72 z y x + 1/36 y x z + 1/72 z y x + + 2 3 3 2 3 3 2 4 + + 1/36 y x z - 1/36 z y x + 1/72 z y x - 1/18 y x z + + 2 2 3 2 3 2 4 2 4 3 4 + - 1/72 z y x + 1/144 z y x + 1/27 x z - 1/36 z y x - 1/72 z y x + + 2 4 4 3 3 2 4 4 2 3 + + 1/144 z y x - 1/144 z y x + 1/36 z y x + 1/72 z y x + + 2 4 3 2 3 3 3 2 + + 1/36 y x z + 1/108 x z - 1/54 x z + 1/18 y x z + 1/9 y x z + + 2 3 2 2 2 2 2 3 2 3 + - 1/9 y x z + 1/18 y x z - 1/9 y x z + 1/18 y x z - 1/18 y x z + + 2 4 4 2 2 2 2 + - 1/18 z y x + 1/27 x z + 1/54 z x + 1/18 y x z + 1/9 y x z + + 2 2 2 2 2 3 + - 1/36 y x z - 1/36 y x z - 2/27 x z - 2/27 x z + 2/27 x z + + 3 2 2 2 4 4 2 4 + + 2/27 x z - 1/27 x z - 1/27 x z - 1/108 z x + 1/108 z x + + 3 4 3 4 3 2 2 4 + - 1/54 z x + 1/54 z x - 1/108 z x , COEFF(2, -1, 2) = 1/288 y x z + + 4 4 3 3 2 2 4 4 + + 1/576 z y x + 1/144 y x z + 1/288 z y x - 1/288 z y x + + 4 4 2 4 2 3 3 2 3 + - 1/288 y x z - 1/288 z y x - 1/72 y x z + 1/72 z y x + + 3 2 4 2 2 3 2 3 + - 1/144 z y x + 1/144 y x z + 1/144 z y x - 1/288 z y x + + 2 4 2 4 3 4 2 4 + - 1/432 x z + 1/144 z y x + 1/288 z y x - 1/576 z y x + + 4 3 3 2 4 4 2 3 2 4 + + 1/288 z y x - 1/144 z y x - 1/144 z y x - 1/576 y x z + + 3 2 3 3 3 2 2 3 + - 1/216 x z + 1/108 x z - 1/144 y x z - 1/72 y x z + 1/72 y x z + + 2 2 2 2 2 3 2 3 + - 1/288 y x z + 1/144 y x z - 1/288 y x z + 1/144 y x z + + 2 4 4 2 2 2 2 + + 1/288 z y x - 1/216 x z - 1/216 z x - 1/144 y x z - 1/144 y x z + + 2 2 2 2 2 3 + + 1/576 y x z + 1/288 y x z + 1/108 x z + 1/216 x z - 1/216 x z + + 3 2 2 2 4 4 2 4 + - 1/108 x z + 1/432 x z + 1/216 x z + 1/432 z x - 1/432 z x + + 3 4 3 4 3 + + 1/216 z x - 1/108 z x + 1/216 z x , COEFF(-2, 0, 2) = + + 2 2 4 2 2 4 4 2 4 2 3 3 + - 1/192 y x z - 1/192 z y x + 1/192 z y x - 1/48 y x z + + 2 3 2 4 2 2 3 2 4 + + 1/48 z y x + 1/96 y x z + 1/96 z y x + 5/1152 x z + + 2 4 3 2 4 4 2 3 3 2 3 3 + - 1/96 z y x + 1/96 z y x - 1/96 z y x - 5/576 x z + 5/288 x z + + 2 2 3 2 2 2 2 2 3 4 + - 1/48 y x z + 1/48 y x z + 1/192 y x z - 1/96 y x z - 5/576 x z + + 4 2 2 2 2 2 + + 5/576 z x - 1/96 y x z + 1/96 y x z + 5/288 x z - 5/576 x z + + 2 3 3 2 2 2 4 4 + + 5/576 x z - 5/288 x z - 5/1152 x z + 5/576 x z - 5/1152 z x + + 2 4 3 4 3 4 3 + + 5/1152 z x - 5/576 z x - 5/288 z x + 5/576 z x , COEFF(-1, 0, 2) + + 2 2 4 2 2 4 4 2 4 2 3 3 + = 1/12 y x z + 1/48 z y x - 1/48 z y x + 1/24 y x z + + 2 3 2 4 2 2 3 2 4 2 4 + - 1/24 z y x - 1/12 y x z - 1/48 z y x - 5/72 x z + 1/24 z y x + + 3 2 4 4 2 3 3 2 3 3 2 + - 1/24 z y x + 1/48 z y x + 5/288 x z - 5/144 x z + 1/6 y x z + + 2 3 2 2 2 2 2 3 4 4 + - 1/6 y x z - 1/12 y x z + 1/6 y x z + 5/72 x z - 5/144 z x + + 2 2 2 2 2 2 3 + + 1/12 y x z - 1/6 y x z - 5/36 x z + 5/36 x z - 5/36 x z + + 3 2 2 2 4 4 2 4 + + 5/36 x z + 5/72 x z - 5/72 x z + 5/288 z x - 5/288 z x + + 3 4 3 4 3 25 2 3 + + 5/144 z x + 5/144 z x - 5/288 z x , COEFF(0, 0, 2) = -- x z + 96 + + 2 3 4 2 4 2 4 3 2 4 4 + + 1/4 y z + 1/32 z y x - 1/16 z y x + 1/16 z y x + 5/96 z x + + 3 25 2 2 2 4 2 4 4 3 4 + - 5/24 z - -- x z - 1/32 z y x + 5/48 z - 5/192 z x - 5/96 z x + 96 + + 2 2 2 2 3 2 2 4 25 2 4 2 + + 5/16 y x z - 5/16 y x z - 5/32 y x z + --- x z - 1/4 y z + 192 + + 4 2 4 2 2 2 4 2 2 2 + + 5/24 z - 5/48 z + 5/192 z x - 1/8 y z + 1/8 y z + 5/32 y x z + + 25 2 2 2 2 4 2 2 4 + - --- x z , COEFF(1, 0, 2) = 1/12 y x z + 1/48 z y x + 192 + + 4 2 4 2 3 3 2 3 2 4 + - 1/48 z y x - 1/24 y x z + 1/24 z y x + 1/12 y x z + + 2 2 3 2 4 2 4 3 2 4 + + 1/48 z y x - 5/72 x z + 1/24 z y x - 1/24 z y x + + 4 2 3 3 2 3 3 2 2 3 + - 1/48 z y x - 5/288 x z + 5/144 x z - 1/6 y x z + 1/6 y x z + + 2 2 2 2 2 3 4 4 2 2 + - 1/12 y x z + 1/6 y x z - 5/72 x z - 5/144 z x - 1/12 y x z + + 2 2 2 2 3 3 2 2 + - 1/6 y x z + 5/36 x z + 5/36 x z - 5/36 x z - 5/36 x z + 5/72 x z + + 2 4 4 2 4 3 4 3 + + 5/72 x z + 5/288 z x - 5/288 z x + 5/144 z x - 5/144 z x + + 4 3 2 2 4 2 2 4 + + 5/288 z x , COEFF(2, 0, 2) = - 1/192 y x z - 1/192 z y x + + 4 2 4 2 3 3 2 3 2 4 + + 1/192 z y x + 1/48 y x z - 1/48 z y x - 1/96 y x z + + 2 2 3 2 4 2 4 3 2 4 + - 1/96 z y x + 5/1152 x z - 1/96 z y x + 1/96 z y x + + 4 2 3 3 2 3 3 2 2 3 + + 1/96 z y x + 5/576 x z - 5/288 x z + 1/48 y x z - 1/48 y x z + + 2 2 2 2 2 3 4 4 2 2 + + 1/192 y x z - 1/96 y x z + 5/576 x z + 5/576 z x + 1/96 y x z + + 2 2 2 2 3 3 + + 1/96 y x z - 5/288 x z - 5/576 x z + 5/576 x z + 5/288 x z + + 2 2 2 4 4 2 4 3 4 + - 5/1152 x z - 5/576 x z - 5/1152 z x + 5/1152 z x - 5/576 z x + + 3 4 3 2 2 4 + + 5/288 z x - 5/576 z x , COEFF(-2, 1, 2) = 1/288 y x z + + 4 4 3 3 2 2 4 4 + - 1/576 z y x + 1/144 y x z + 1/288 z y x + 1/288 z y x + + 4 4 2 4 2 3 3 2 3 + - 1/288 y x z - 1/288 z y x + 1/72 y x z - 1/72 z y x + + 3 2 4 2 2 3 2 3 + - 1/144 z y x - 1/144 y x z - 1/144 z y x - 1/288 z y x + + 2 4 2 4 3 4 2 4 + - 1/432 x z + 1/144 z y x - 1/288 z y x + 1/576 z y x + + 4 3 3 2 4 4 2 3 2 4 + + 1/288 z y x - 1/144 z y x + 1/144 z y x + 1/576 y x z + + 3 2 3 3 3 2 2 3 + + 1/216 x z - 1/108 x z - 1/144 y x z + 1/72 y x z - 1/72 y x z + + 2 2 2 2 2 3 2 3 + - 1/288 y x z + 1/144 y x z + 1/288 y x z + 1/144 y x z + + 2 4 4 2 2 2 2 + - 1/288 z y x + 1/216 x z - 1/216 z x + 1/144 y x z - 1/144 y x z + + 2 2 2 2 2 3 + - 1/576 y x z + 1/288 y x z - 1/108 x z + 1/216 x z - 1/216 x z + + 3 2 2 2 4 4 2 4 + + 1/108 x z + 1/432 x z - 1/216 x z + 1/432 z x - 1/432 z x + + 3 4 3 4 3 + + 1/216 z x + 1/108 z x - 1/216 z x , COEFF(-1, 1, 2) = + + 2 2 4 4 4 3 3 2 2 4 + - 1/18 y x z + 1/144 z y x - 1/72 y x z - 1/72 z y x + + 4 4 4 2 4 2 3 3 2 3 + - 1/72 z y x + 1/36 y x z + 1/72 z y x - 1/36 y x z + 1/36 z y x + + 3 2 4 2 2 3 2 3 2 4 + + 1/72 z y x + 1/18 y x z + 1/72 z y x + 1/144 z y x + 1/27 x z + + 2 4 3 4 2 4 4 3 + - 1/36 z y x + 1/72 z y x - 1/144 z y x - 1/144 z y x + + 3 2 4 4 2 3 2 4 3 2 3 3 + + 1/36 z y x - 1/72 z y x - 1/36 y x z - 1/108 x z + 1/54 x z + + 3 2 2 3 2 2 2 2 2 3 + + 1/18 y x z - 1/9 y x z + 1/9 y x z + 1/18 y x z - 1/9 y x z + + 2 3 2 4 4 + - 1/18 y x z - 1/18 y x z + 1/18 z y x - 1/27 x z + 1/54 z x + + 2 2 2 2 2 2 2 + - 1/18 y x z + 1/9 y x z + 1/36 y x z - 1/36 y x z + 2/27 x z + + 2 2 3 3 2 2 2 + - 2/27 x z + 2/27 x z - 2/27 x z - 1/27 x z + 1/27 x z + + 4 4 2 4 3 4 3 4 3 + - 1/108 z x + 1/108 z x - 1/54 z x - 1/54 z x + 1/108 z x , + + 2 2 4 4 4 2 2 4 4 + COEFF(0, 1, 2) = 5/48 y x z - 1/96 z y x + 1/48 z y x + 1/48 z y x + + 4 2 4 2 4 2 4 3 4 2 4 + - 1/48 z y x - 5/72 x z + 1/24 z y x - 1/48 z y x + 1/96 z y x + + 3 2 4 2 4 2 2 2 2 2 3 + - 1/24 z y x + 5/96 y x z - 1/9 z - 5/48 y x z + 5/24 y x z + + 2 3 4 3 2 4 4 2 + + 5/48 y x z + 1/18 z + 1/9 z - 1/12 y z - 1/24 y z - 1/18 z + + 2 4 2 2 2 2 + - 5/48 z y x + 1/12 y z - 1/36 z x - 5/24 y x z - 5/96 y x z + + 2 2 3 2 3 2 3 2 + + 1/6 y z + 5/36 x z - 1/12 y z - 1/6 y z - 5/36 x z + 1/24 y z + + 2 2 4 4 2 2 2 4 3 4 + + 5/72 x z + 1/72 z x + 1/12 y z - 1/72 z x + 1/36 z x , + + 2 2 4 4 4 3 3 + COEFF(1, 1, 2) = - 1/18 y x z + 1/144 z y x + 1/72 y x z + + 2 2 4 4 4 4 2 4 + - 1/72 z y x - 1/72 z y x - 1/36 y x z + 1/72 z y x + + 2 3 3 2 3 3 2 4 + + 1/36 y x z - 1/36 z y x - 1/72 z y x - 1/18 y x z + + 2 2 3 2 3 2 4 2 4 3 4 + - 1/72 z y x - 1/144 z y x + 1/27 x z - 1/36 z y x + 1/72 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/144 z y x + 1/144 z y x + 1/36 z y x + 1/72 z y x + + 2 4 3 2 3 3 3 2 + - 1/36 y x z + 1/108 x z - 1/54 x z - 1/18 y x z + 1/9 y x z + + 2 3 2 2 2 2 2 3 2 3 + - 1/9 y x z + 1/18 y x z - 1/9 y x z - 1/18 y x z + 1/18 y x z + + 2 4 4 2 2 2 2 + + 1/18 z y x + 1/27 x z + 1/54 z x + 1/18 y x z + 1/9 y x z + + 2 2 2 2 2 3 + + 1/36 y x z + 1/36 y x z - 2/27 x z - 2/27 x z + 2/27 x z + + 3 2 2 2 4 4 2 4 + + 2/27 x z - 1/27 x z - 1/27 x z - 1/108 z x + 1/108 z x + + 3 4 3 4 3 2 2 4 + - 1/54 z x + 1/54 z x - 1/108 z x , COEFF(2, 1, 2) = 1/288 y x z + + 4 4 3 3 2 2 4 4 + - 1/576 z y x - 1/144 y x z + 1/288 z y x + 1/288 z y x + + 4 4 2 4 2 3 3 2 3 + + 1/288 y x z - 1/288 z y x - 1/72 y x z + 1/72 z y x + + 3 2 4 2 2 3 2 3 + + 1/144 z y x + 1/144 y x z + 1/144 z y x + 1/288 z y x + + 2 4 2 4 3 4 2 4 + - 1/432 x z + 1/144 z y x - 1/288 z y x + 1/576 z y x + + 4 3 3 2 4 4 2 3 2 4 + - 1/288 z y x - 1/144 z y x - 1/144 z y x + 1/576 y x z + + 3 2 3 3 3 2 2 3 + - 1/216 x z + 1/108 x z + 1/144 y x z - 1/72 y x z + 1/72 y x z + + 2 2 2 2 2 3 2 3 + - 1/288 y x z + 1/144 y x z + 1/288 y x z - 1/144 y x z + + 2 4 4 2 2 2 2 + - 1/288 z y x - 1/216 x z - 1/216 z x - 1/144 y x z - 1/144 y x z + + 2 2 2 2 2 3 + - 1/576 y x z - 1/288 y x z + 1/108 x z + 1/216 x z - 1/216 x z + + 3 2 2 2 4 4 2 4 + - 1/108 x z + 1/432 x z + 1/216 x z + 1/432 z x - 1/432 z x + + 3 4 3 4 3 + + 1/216 z x - 1/108 z x + 1/216 z x , COEFF(-2, 2, 2) = + + 2 2 4 4 4 3 3 2 2 4 + - 1/1152 y x z + 1/1152 z y x - 1/288 y x z - 1/1152 z y x + + 4 4 4 2 4 2 3 3 + - 1/576 z y x + 1/576 y x z + 1/1152 z y x - 1/288 y x z + + 2 3 3 2 4 2 2 3 + + 1/288 z y x + 1/288 z y x + 1/576 y x z + 1/576 z y x + + 2 3 2 4 2 4 3 4 + + 1/576 z y x + 1/6912 x z - 1/576 z y x + 1/576 z y x + + 2 4 4 3 3 2 4 4 2 3 + - 1/1152 z y x - 1/576 z y x + 1/576 z y x - 1/576 z y x + + 2 4 3 2 3 3 3 + - 1/1152 y x z - 1/3456 x z + 1/1728 x z + 1/288 y x z + + 2 2 3 2 2 2 2 2 3 + - 1/288 y x z + 1/288 y x z + 1/1152 y x z - 1/576 y x z + + 2 3 2 4 4 + - 1/576 y x z - 1/288 y x z + 1/576 z y x - 1/3456 x z + 1/3456 z x + + 2 2 2 2 2 2 2 + - 1/576 y x z + 1/576 y x z + 1/1152 y x z - 1/576 y x z + + 2 2 3 3 2 2 + + 1/1728 x z - 1/3456 x z + 1/3456 x z - 1/1728 x z - 1/6912 x z + + 2 4 4 2 4 3 4 3 + + 1/3456 x z - 1/6912 z x + 1/6912 z x - 1/3456 z x - 1/1728 z x + + 4 3 2 2 4 4 4 + + 1/3456 z x , COEFF(-1, 2, 2) = 1/72 y x z - 1/288 z y x + + 3 3 2 2 4 4 4 + + 1/144 y x z + 1/288 z y x + 1/144 z y x - 1/72 y x z + + 4 2 4 2 3 3 2 3 3 + - 1/288 z y x + 1/144 y x z - 1/144 z y x - 1/144 z y x + + 2 4 2 2 3 2 3 2 4 + - 1/72 y x z - 1/288 z y x - 1/288 z y x - 1/432 x z + + 2 4 3 4 2 4 4 3 + + 1/144 z y x - 1/144 z y x + 1/288 z y x + 1/288 z y x + + 3 2 4 4 2 3 2 4 3 2 + - 1/144 z y x + 1/288 z y x + 1/72 y x z + 1/1728 x z + + 3 3 3 2 2 3 2 2 2 + - 1/864 x z - 1/36 y x z + 1/36 y x z - 1/36 y x z - 1/72 y x z + + 2 2 3 2 3 2 4 + + 1/36 y x z + 1/36 y x z + 1/36 y x z - 1/36 z y x + 1/432 x z + + 4 2 2 2 2 2 2 2 + - 1/864 z x + 1/72 y x z - 1/36 y x z - 1/72 y x z + 1/72 y x z + + 2 2 3 3 2 2 + - 1/216 x z + 1/216 x z - 1/216 x z + 1/216 x z + 1/432 x z + + 2 4 4 2 4 3 4 3 + - 1/432 x z + 1/1728 z x - 1/1728 z x + 1/864 z x + 1/864 z x + + 4 3 2 2 4 4 4 + - 1/1728 z x , COEFF(0, 2, 2) = - 5/192 y x z + 1/192 z y x + + 2 2 4 4 4 2 4 2 4 + - 1/192 z y x - 1/96 z y x + 1/192 z y x + 5/1152 x z + + 2 4 3 4 2 4 3 2 4 + - 1/96 z y x + 1/96 z y x - 1/192 z y x + 1/96 z y x + + 2 4 2 2 2 2 2 3 2 3 + - 5/192 y x z + 1/144 z + 5/192 y x z - 5/96 y x z - 5/96 y x z + + 4 3 2 4 4 2 2 + - 1/288 z - 1/144 z + 1/48 y z + 1/48 y z + 1/288 z + 5/96 z y x + + 4 2 2 2 2 2 + - 1/24 y z + 1/576 z x + 5/96 y x z + 5/192 y x z - 1/24 y z + + 2 3 2 3 2 3 2 + - 5/576 x z + 1/24 y z + 1/24 y z + 5/576 x z - 1/48 y z + + 2 2 4 4 2 2 2 4 3 4 + - 5/1152 x z - 1/1152 z x - 1/48 y z + 1/1152 z x - 1/576 z x , + + 2 2 4 4 4 3 3 + COEFF(1, 2, 2) = 1/72 y x z - 1/288 z y x - 1/144 y x z + + 2 2 4 4 4 4 2 4 + + 1/288 z y x + 1/144 z y x + 1/72 y x z - 1/288 z y x + + 2 3 3 2 3 3 2 4 + - 1/144 y x z + 1/144 z y x + 1/144 z y x + 1/72 y x z + + 2 2 3 2 3 2 4 2 4 + + 1/288 z y x + 1/288 z y x - 1/432 x z + 1/144 z y x + + 3 4 2 4 4 3 3 2 4 + - 1/144 z y x + 1/288 z y x - 1/288 z y x - 1/144 z y x + + 4 2 3 2 4 3 2 3 3 3 + - 1/288 z y x + 1/72 y x z - 1/1728 x z + 1/864 x z + 1/36 y x z + + 2 2 3 2 2 2 2 2 3 + - 1/36 y x z + 1/36 y x z - 1/72 y x z + 1/36 y x z + + 2 3 2 4 4 + + 1/36 y x z - 1/36 y x z - 1/36 z y x - 1/432 x z - 1/864 z x + + 2 2 2 2 2 2 2 + - 1/72 y x z - 1/36 y x z - 1/72 y x z - 1/72 y x z + 1/216 x z + + 2 2 3 3 2 2 2 + + 1/216 x z - 1/216 x z - 1/216 x z + 1/432 x z + 1/432 x z + + 4 4 2 4 3 4 3 4 3 + + 1/1728 z x - 1/1728 z x + 1/864 z x - 1/864 z x + 1/1728 z x , + + 2 2 4 4 4 3 3 + COEFF(2, 2, 2) = - 1/1152 y x z + 1/1152 z y x + 1/288 y x z + + 2 2 4 4 4 4 2 4 + - 1/1152 z y x - 1/576 z y x - 1/576 y x z + 1/1152 z y x + + 2 3 3 2 3 3 2 4 + + 1/288 y x z - 1/288 z y x - 1/288 z y x - 1/576 y x z + + 2 2 3 2 3 2 4 2 4 + - 1/576 z y x - 1/576 z y x + 1/6912 x z - 1/576 z y x + + 3 4 2 4 4 3 3 2 4 + + 1/576 z y x - 1/1152 z y x + 1/576 z y x + 1/576 z y x + + 4 2 3 2 4 3 2 3 3 + + 1/576 z y x - 1/1152 y x z + 1/3456 x z - 1/1728 x z + + 3 2 2 3 2 2 2 + - 1/288 y x z + 1/288 y x z - 1/288 y x z + 1/1152 y x z + + 2 2 3 2 3 2 + - 1/576 y x z - 1/576 y x z + 1/288 y x z + 1/576 z y x + + 4 4 2 2 2 2 + + 1/3456 x z + 1/3456 z x + 1/576 y x z + 1/576 y x z + + 2 2 2 2 2 3 + + 1/1152 y x z + 1/576 y x z - 1/1728 x z - 1/3456 x z + 1/3456 x z + + 3 2 2 2 4 4 2 4 + + 1/1728 x z - 1/6912 x z - 1/3456 x z - 1/6912 z x + 1/6912 z x + + 3 4 3 4 3 + - 1/3456 z x + 1/1728 z x - 1/3456 z x ] + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dyy.compute.c"); +bytes used=38594311484, alloc=64737712, time=9544.01 +bytes used=38595311716, alloc=64737712, time=9544.11 +bytes used=38596312188, alloc=64737712, 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time=10794.67 +bytes used=41138844004, alloc=64737712, time=10794.73 +bytes used=41139844184, alloc=64737712, time=10794.82 +bytes used=41140844412, alloc=64737712, time=10795.01 +bytes used=41141844588, alloc=64737712, time=10795.19 +bytes used=41142844980, alloc=64737712, time=10795.39 +bytes used=41143845196, alloc=64737712, time=10795.57 +bytes used=41144845540, alloc=64737712, time=10795.73 +bytes used=41145845808, alloc=64737712, time=10795.92 +bytes used=41146845988, alloc=64737712, time=10796.14 +> +# d^2/dydz +> simplify( diff(interp_3d_cube_order4_smooth0,y,z) ); +bytes used=41147912688, alloc=64737712, time=10796.33 +bytes used=41149001456, alloc=64737712, time=10796.44 +bytes used=41152259584, alloc=64737712, time=10796.72 +bytes used=41153259844, alloc=64737712, time=10796.82 +bytes used=41154259988, alloc=64737712, time=10796.92 +bytes used=41155260176, alloc=64737712, time=10797.04 +bytes used=41156260564, alloc=64737712, time=10797.16 +bytes used=41157490928, 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+ 2 2 2 2 4 3 4 3 + + 5/192 y x + 5/576 y x + 1/144 - 1/192 z x + 1/288 z x - 1/72 z y + + 4 2 4 3 3 + - 1/576 y x - 1/192 y x , COEFF(1, -2, -2) = 1/432 y x z + + 2 2 4 4 2 3 3 2 3 + - 1/96 z y x - 1/864 z y x + 1/144 y x z - 1/288 z y x + + 3 3 3 3 4 2 2 3 3 + - 1/864 z y x - 1/432 y x - 1/432 y x - 1/96 z y x + 1/864 y x + + 2 3 2 4 3 4 2 4 + - 1/288 z y x - 1/288 z y x + 1/432 z y x - 1/288 z y x + + 3 2 4 3 2 3 3 4 + + 1/144 z y x + 1/288 x z - 1/432 x z + 1/216 x - 1/864 x + + 3 2 2 3 2 2 2 + - 1/108 y x z + 1/72 y x z - 1/36 y x z - 1/216 y x + 1/24 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + + 1/144 z y x + 1/144 y x z - 1/36 y x z + 1/54 y x z + + 3 2 2 3 3 4 3 4 2 3 + - 1/36 y x z - 1/216 z y x + 1/432 z y x - 1/108 y x z + + 3 2 3 2 3 3 3 3 + - 1/108 z y x - 1/36 y x z - 1/216 y x z - 1/108 z y x + + 3 3 3 3 3 2 + + 1/432 z y x + 1/54 y x z - 1/864 x + 1/216 x + 1/216 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x + 1/864 z x - 1/72 y x + 1/24 y x z + 1/72 y x z + + 2 2 2 3 2 3 + + 1/72 y x z + 1/72 y x z + 1/108 y x + 1/108 y x - 1/216 x z + + 2 2 3 3 2 2 2 + - 1/216 x z + 1/108 x z + 1/108 x z - 1/72 x z - 1/72 x z + + 2 2 2 2 4 3 4 3 + - 1/72 y x - 1/216 y x + 1/288 z x - 1/432 z x + 1/864 z x + + 4 2 4 2 3 + + 1/864 y x + 1/288 y x + 1/288 y x , COEFF(2, -2, -2) = + + 3 3 2 2 4 4 2 3 3 + - 1/864 y x z + 1/384 z y x + 1/3456 z y x - 1/288 y x z + + 2 3 3 3 3 3 4 + + 1/576 z y x + 1/1728 z y x + 1/864 y x + 1/1728 y x + + 2 2 3 3 2 3 2 4 + + 1/192 z y x - 1/1728 y x + 1/576 z y x + 1/1152 z y x + + 3 4 2 4 3 2 4 3 2 + - 1/1728 z y x + 1/1152 z y x - 1/576 z y x - 1/576 x z + + 3 3 4 3 2 + + 1/864 x z - 1/1728 x + 1/3456 x + 1/864 y x z - 1/576 y x z + + 2 3 2 2 2 2 3 4 + + 1/288 y x z + 1/1728 y x - 1/384 y x z - 1/576 z y x + + 3 3 2 2 2 3 3 2 3 3 2 2 + - 1/288 y x z + 1/576 y x z - 1/864 y x z + 1/576 y x z + + 3 3 4 3 4 2 3 3 2 + + 1/864 z y x - 1/1728 z y x + 1/1728 y x z + 1/1728 z y x + + 3 2 3 3 3 3 3 3 + + 1/288 y x z + 1/432 y x z + 1/864 z y x - 1/864 z y x + + 3 3 3 2 2 + - 1/432 y x z + 1/1728 x - 1/3456 x - 1/1728 y x z - 1/3456 z y x + + 4 2 2 2 2 2 + - 1/3456 z x + 1/576 y x - 1/192 y x z - 1/1152 y x z + + 2 2 2 3 2 3 + - 1/1152 y x z - 1/576 y x z - 1/1728 y x - 1/864 y x + 1/1728 x z + + 2 2 3 3 2 2 2 + + 1/3456 x z - 1/1728 x z - 1/864 x z + 1/1152 x z + 1/576 x z + + 2 2 2 2 4 3 4 3 + + 1/1152 y x + 1/3456 y x - 1/1152 z x + 1/1728 z x - 1/1728 z x + + 4 2 4 2 3 + - 1/3456 y x - 1/1152 y x - 1/576 y x , COEFF(-2, -1, -2) = + + 3 3 2 2 4 4 2 3 3 + - 1/54 y x z - 1/192 z y x - 1/216 z y x - 1/144 y x z + + 2 3 3 3 3 3 4 2 2 3 + + 1/288 z y x + 1/108 z y x + 1/216 y x - 1/432 y x + 1/96 z y x + + 3 2 3 2 4 3 4 2 4 + - 1/108 y x + 1/36 z y x - 1/576 z y x + 1/108 z y x - 1/72 z y x + + 3 2 4 3 2 3 3 4 + + 1/288 z y x - 1/72 x z + 1/108 x z - 1/216 x - 1/432 x + + 3 2 2 3 2 2 2 + + 1/54 y x z - 1/288 y x z + 1/144 y x z + 1/108 y x + 1/192 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + + 1/144 z y x - 1/72 y x z - 1/288 y x z + 1/216 y x z + + 3 2 2 3 3 4 3 4 2 3 + - 1/144 y x z - 1/216 z y x + 1/432 z y x - 1/108 y x z + + 3 2 3 2 3 3 3 3 + - 1/432 z y x + 1/72 y x z + 1/108 y x z + 1/216 z y x + + 3 3 3 3 3 2 + - 1/216 z y x - 1/108 y x z + 1/216 x + 1/432 x - 1/108 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x + 1/432 z x + 1/288 y x - 1/96 y x z + 1/576 y x z + + 2 2 2 3 2 3 + + 1/72 y x z - 1/36 y x z + 1/432 y x - 1/216 y x + 1/216 x z + + 2 2 3 3 2 2 2 + - 1/432 x z + 1/216 x z - 1/108 x z - 1/144 x z + 1/72 x z + + 2 2 2 2 4 3 4 3 + - 1/576 y x - 1/216 y x + 1/144 z x - 1/216 z x - 1/216 z x + + 4 2 4 2 3 3 3 + + 1/216 y x + 1/576 y x - 1/288 y x , COEFF(-1, -1, -2) = 1/27 y x z + + 2 2 4 4 2 3 3 2 3 + + 1/48 z y x + 1/54 z y x + 1/72 y x z - 1/144 z y x + + 3 3 3 3 4 2 2 3 3 + - 1/54 z y x - 1/108 y x + 1/108 y x - 1/48 z y x + 1/54 y x + + 2 3 2 4 3 4 2 4 + - 1/18 z y x + 1/144 z y x - 1/27 z y x + 1/18 z y x + + 3 2 4 3 2 3 3 4 + - 1/72 z y x + 1/36 x z - 1/54 x z + 1/27 x + 1/108 x + + 3 2 2 3 2 2 2 + - 4/27 y x z + 1/36 y x z - 1/18 y x z - 2/27 y x - 1/12 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + - 1/36 z y x + 1/36 y x z + 1/18 y x z - 2/27 y x z + + 3 2 2 3 3 4 3 4 2 3 + + 1/9 y x z + 1/54 z y x - 1/108 z y x + 4/27 y x z + + 3 2 3 2 3 3 3 3 3 3 + + 1/27 z y x - 1/9 y x z - 1/54 y x z - 1/27 z y x + 1/108 z y x + + 3 3 3 2 2 + + 2/27 y x z - 1/108 x - 1/27 x + 2/27 y x z - 2/27 z y x + + 4 2 2 2 2 2 2 2 + - 1/108 z x - 1/36 y x + 1/12 y x z - 1/36 y x z - 2/9 y x z + + 2 3 2 3 2 2 3 + + 2/9 y x z - 1/27 y x + 1/27 y x - 1/27 x z + 1/27 x z - 2/27 x z + + 3 2 2 2 2 2 2 2 4 + + 2/27 x z + 1/9 x z - 1/9 x z + 1/36 y x + 2/27 y x - 1/36 z x + + 3 4 3 4 2 4 2 3 + + 1/54 z x + 1/108 z x - 1/54 y x - 1/144 y x + 1/144 y x , + + 2 2 4 4 3 4 + COEFF(0, -1, -2) = - 1/32 z y x - 1/36 z y x - 1/72 y x + + 2 4 3 4 2 4 3 2 4 4 + - 1/96 z y x + 1/18 z y x - 1/12 z y x + 1/48 z y x - 1/72 x + + 3 3 2 2 2 2 3 4 + - 1/9 y z + 1/9 y + 1/18 z + 5/32 y x z + 1/24 z y x + + 2 2 3 3 2 3 3 2 2 3 3 4 + - 5/48 y x z + 5/36 y x z - 5/24 y x z - 1/36 z y x + + 3 4 2 3 3 2 3 3 2 + + 1/72 z y x - 5/18 y x z - 5/72 z y x - 1/9 z - 1/18 y + 1/24 y + + 2 2 2 4 2 2 + + 1/6 z + 5/72 x + 5/36 z y x - 1/9 y z + 1/72 z x + 5/96 y x z + + 2 2 3 2 2 3 2 2 + + 5/12 y x z + 5/72 y x - 1/24 y z + 1/6 y z - 5/72 x z - 1/18 + + 3 2 3 2 3 2 2 2 2 2 + + 2/9 y z + 1/12 y z + 5/36 x z - 1/3 y z - 5/24 x z - 1/8 y z + + 2 2 2 2 4 3 4 3 4 + - 5/96 y x - 5/36 y x + 1/24 z x - 1/36 z x + 1/18 z y + 1/36 y x + + 2 4 3 3 2 2 4 + + 1/96 y x , COEFF(1, -1, -2) = - 1/27 y x z + 1/48 z y x + + 4 2 3 3 2 3 3 3 3 + + 1/54 z y x - 1/72 y x z + 1/144 z y x + 1/54 z y x + 1/108 y x + + 3 4 2 2 3 3 2 3 2 4 + + 1/108 y x + 1/48 z y x - 1/54 y x + 1/18 z y x + 1/144 z y x + + 3 4 2 4 3 2 4 3 2 3 3 + - 1/27 z y x + 1/18 z y x - 1/72 z y x - 1/36 x z + 1/54 x z + + 4 3 2 2 3 + - 1/27 x + 1/108 x + 4/27 y x z - 1/36 y x z + 1/18 y x z + 2/27 y x + + 2 2 2 2 3 4 3 3 2 2 2 3 + - 1/12 y x z - 1/36 z y x - 1/36 y x z + 1/18 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 2/27 y x z + 1/9 y x z + 1/54 z y x - 1/108 z y x + + 2 3 3 2 3 2 3 3 3 3 + + 4/27 y x z + 1/27 z y x + 1/9 y x z + 1/54 y x z + 1/27 z y x + + 3 3 3 3 3 2 + - 1/108 z y x - 2/27 y x z + 1/108 x - 1/27 x - 2/27 y x z + + 2 4 2 2 2 2 2 + - 2/27 z y x - 1/108 z x + 1/36 y x - 1/12 y x z - 1/36 y x z + + 2 2 2 3 2 3 2 + - 2/9 y x z - 2/9 y x z - 1/27 y x - 1/27 y x + 1/27 x z + 1/27 x z + + 2 3 3 2 2 2 2 2 2 + - 2/27 x z - 2/27 x z + 1/9 x z + 1/9 x z + 1/36 y x + 2/27 y x + + 2 4 3 4 3 4 2 4 + - 1/36 z x + 1/54 z x - 1/108 z x - 1/54 y x - 1/144 y x + + 2 3 3 3 2 2 4 + - 1/144 y x , COEFF(2, -1, -2) = 1/54 y x z - 1/192 z y x + + 4 2 3 3 2 3 3 + - 1/216 z y x + 1/144 y x z - 1/288 z y x - 1/108 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 1/216 y x - 1/432 y x - 1/96 z y x + 1/108 y x - 1/36 z y x + + 2 4 3 4 2 4 3 2 4 + - 1/576 z y x + 1/108 z y x - 1/72 z y x + 1/288 z y x + + 3 2 3 3 4 3 + + 1/72 x z - 1/108 x z + 1/216 x - 1/432 x - 1/54 y x z + + 2 2 3 2 2 2 + + 1/288 y x z - 1/144 y x z - 1/108 y x + 1/192 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + + 1/144 z y x + 1/72 y x z - 1/288 y x z + 1/216 y x z + + 3 2 2 3 3 4 3 4 2 3 + - 1/144 y x z - 1/216 z y x + 1/432 z y x - 1/108 y x z + + 3 2 3 2 3 3 3 3 + - 1/432 z y x - 1/72 y x z - 1/108 y x z - 1/216 z y x + + 3 3 3 3 3 2 + + 1/216 z y x + 1/108 y x z - 1/216 x + 1/432 x + 1/108 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x + 1/432 z x - 1/288 y x + 1/96 y x z + 1/576 y x z + + 2 2 2 3 2 3 + + 1/72 y x z + 1/36 y x z + 1/432 y x + 1/216 y x - 1/216 x z + + 2 2 3 3 2 2 2 + - 1/432 x z + 1/216 x z + 1/108 x z - 1/144 x z - 1/72 x z + + 2 2 2 2 4 3 4 3 + - 1/576 y x - 1/216 y x + 1/144 z x - 1/216 z x + 1/216 z x + + 4 2 4 2 3 3 3 + + 1/216 y x + 1/576 y x + 1/288 y x , COEFF(-2, 0, -2) = 5/144 y x z + + 4 3 3 3 3 4 3 + + 5/576 z y x - 5/288 z y x - 1/144 y x + 1/288 y x + 5/288 y x + + 2 3 3 4 2 4 3 + - 5/96 z y x - 5/288 z y x + 5/192 z y x - 5/144 y x z - 5/288 y x + + 2 3 4 3 3 2 3 2 3 3 2 2 + - 1/96 z y x + 1/48 y x z - 1/144 y x z + 1/96 y x z + + 3 3 4 3 4 2 3 3 2 + + 1/144 z y x - 1/288 z y x + 5/288 y x z + 1/288 z y x + + 3 2 3 3 3 3 3 3 + - 1/48 y x z - 1/72 y x z - 1/144 z y x + 1/144 z y x + + 3 3 2 2 2 2 + + 1/72 y x z + 5/288 y x z - 5/576 z y x - 5/192 y x z + 5/96 y x z + + 3 2 3 2 4 + - 1/288 y x + 1/144 y x + 5/576 y x - 5/576 y x , COEFF(-1, 0, -2) = + + 3 3 4 3 3 3 3 4 + - 5/72 y x z - 5/144 z y x + 5/144 z y x + 1/72 y x - 1/72 y x + + 3 2 3 3 4 2 4 3 + - 5/144 y x + 5/48 z y x + 5/72 z y x - 5/48 z y x + 5/18 y x z + + 2 3 4 3 3 2 3 2 3 3 2 2 + + 5/36 y x + 1/24 z y x - 1/24 y x z + 1/9 y x z - 1/6 y x z + + 3 3 4 3 4 2 3 3 2 3 2 + - 1/36 z y x + 1/72 z y x - 5/18 y x z - 1/18 z y x + 1/6 y x z + + 3 3 3 3 3 3 3 3 + + 1/36 y x z + 1/18 z y x - 1/72 z y x - 1/9 y x z - 5/36 y x z + + 2 2 2 2 3 2 3 + + 5/36 z y x + 5/12 y x z - 5/12 y x z + 1/18 y x - 1/18 y x + + 2 4 3 4 3 2 + - 5/36 y x + 5/144 y x , COEFF(0, 0, -2) = - 5/48 z y x - 1/4 y z + + 3 3 2 3 4 25 2 4 + + 1/12 y + 5/48 z y x + 1/48 y x - -- z y x + 5/96 z y x + 96 + + 3 3 3 2 3 3 2 3 2 2 2 3 4 + + 1/6 y z - 5/24 y x z - 5/48 y x + 5/16 y x z - 1/16 z y x + + 4 25 2 3 2 3 3 4 + - 5/96 y x + -- y x z + 5/8 y z + 5/24 y z + 1/24 z y x - 5/24 y + 48 + + 3 4 3 25 2 25 2 2 3 + - 1/48 z y x - 1/12 z y + -- y x - -- y x z - 5/12 y z + 96 32 + + 2 4 3 3 4 + + 5/32 z y x , COEFF(1, 0, -2) = 5/72 y x z - 5/144 z y x + + 3 3 3 3 4 3 2 3 + - 5/144 z y x - 1/72 y x - 1/72 y x + 5/144 y x - 5/48 z y x + + 3 4 2 4 3 2 3 4 + + 5/72 z y x - 5/48 z y x - 5/18 y x z - 5/36 y x + 1/24 z y x + + 3 3 2 3 2 3 3 2 2 3 3 4 + + 1/24 y x z + 1/9 y x z - 1/6 y x z - 1/36 z y x + + 3 4 2 3 3 2 3 2 3 3 3 + + 1/72 z y x - 5/18 y x z - 1/18 z y x - 1/6 y x z - 1/36 y x z + + 3 3 3 3 3 2 + - 1/18 z y x + 1/72 z y x + 1/9 y x z + 5/36 y x z + 5/36 z y x + + 2 2 2 3 2 3 2 + + 5/12 y x z + 5/12 y x z + 1/18 y x + 1/18 y x - 5/36 y x + + 4 3 3 4 + + 5/144 y x , COEFF(2, 0, -2) = - 5/144 y x z + 5/576 z y x + + 3 3 3 3 4 3 2 3 + + 5/288 z y x + 1/144 y x + 1/288 y x - 5/288 y x + 5/96 z y x + + 3 4 2 4 3 2 3 4 + - 5/288 z y x + 5/192 z y x + 5/144 y x z + 5/288 y x - 1/96 z y x + + 3 3 2 3 2 3 3 2 2 3 3 4 + - 1/48 y x z - 1/144 y x z + 1/96 y x z + 1/144 z y x + + 3 4 2 3 3 2 3 2 + - 1/288 z y x + 5/288 y x z + 1/288 z y x + 1/48 y x z + + 3 3 3 3 3 3 3 3 + + 1/72 y x z + 1/144 z y x - 1/144 z y x - 1/72 y x z + + 2 2 2 2 3 2 + - 5/288 y x z - 5/576 z y x - 5/192 y x z - 5/96 y x z - 1/288 y x + + 3 2 4 3 3 + - 1/144 y x + 5/576 y x - 5/576 y x , COEFF(-2, 1, -2) = - 1/54 y x z + + 2 2 4 4 2 3 3 2 3 + + 1/192 z y x - 1/216 z y x + 1/144 y x z - 1/288 z y x + + 3 3 3 3 4 2 2 3 3 + + 1/108 z y x + 1/216 y x - 1/432 y x - 1/96 z y x - 1/108 y x + + 2 3 2 4 3 4 2 4 + + 1/36 z y x + 1/576 z y x + 1/108 z y x - 1/72 z y x + + 3 2 4 3 2 3 3 4 + - 1/288 z y x + 1/72 x z - 1/108 x z + 1/216 x + 1/432 x + + 3 2 2 3 2 2 2 + + 1/54 y x z + 1/288 y x z - 1/144 y x z + 1/108 y x - 1/192 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + + 1/144 z y x - 1/72 y x z + 1/288 y x z + 1/216 y x z + + 3 2 2 3 3 4 3 4 2 3 + - 1/144 y x z - 1/216 z y x + 1/432 z y x - 1/108 y x z + + 3 2 3 2 3 3 3 3 + - 1/432 z y x + 1/72 y x z + 1/108 y x z + 1/216 z y x + + 3 3 3 3 3 2 + - 1/216 z y x - 1/108 y x z - 1/216 x - 1/432 x - 1/108 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x - 1/432 z x - 1/288 y x + 1/96 y x z - 1/576 y x z + + 2 2 2 3 2 3 + + 1/72 y x z - 1/36 y x z + 1/432 y x - 1/216 y x - 1/216 x z + + 2 2 3 3 2 2 2 + + 1/432 x z - 1/216 x z + 1/108 x z + 1/144 x z - 1/72 x z + + 2 2 2 2 4 3 4 3 + + 1/576 y x - 1/216 y x - 1/144 z x + 1/216 z x + 1/216 z x + + 4 2 4 2 3 3 3 + + 1/216 y x - 1/576 y x + 1/288 y x , COEFF(-1, 1, -2) = 1/27 y x z + + 2 2 4 4 2 3 3 2 3 + - 1/48 z y x + 1/54 z y x - 1/72 y x z + 1/144 z y x + + 3 3 3 3 4 2 2 3 3 + - 1/54 z y x - 1/108 y x + 1/108 y x + 1/48 z y x + 1/54 y x + + 2 3 2 4 3 4 2 4 + - 1/18 z y x - 1/144 z y x - 1/27 z y x + 1/18 z y x + + 3 2 4 3 2 3 3 4 + + 1/72 z y x - 1/36 x z + 1/54 x z - 1/27 x - 1/108 x + + 3 2 2 3 2 2 2 + - 4/27 y x z - 1/36 y x z + 1/18 y x z - 2/27 y x + 1/12 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + - 1/36 z y x + 1/36 y x z - 1/18 y x z - 2/27 y x z + + 3 2 2 3 3 4 3 4 2 3 + + 1/9 y x z + 1/54 z y x - 1/108 z y x + 4/27 y x z + + 3 2 3 2 3 3 3 3 3 3 + + 1/27 z y x - 1/9 y x z - 1/54 y x z - 1/27 z y x + 1/108 z y x + + 3 3 3 2 2 + + 2/27 y x z + 1/108 x + 1/27 x + 2/27 y x z - 2/27 z y x + + 4 2 2 2 2 2 2 2 + + 1/108 z x + 1/36 y x - 1/12 y x z + 1/36 y x z - 2/9 y x z + + 2 3 2 3 2 2 3 + + 2/9 y x z - 1/27 y x + 1/27 y x + 1/27 x z - 1/27 x z + 2/27 x z + + 3 2 2 2 2 2 2 2 4 + - 2/27 x z - 1/9 x z + 1/9 x z - 1/36 y x + 2/27 y x + 1/36 z x + + 3 4 3 4 2 4 2 3 + - 1/54 z x - 1/108 z x - 1/54 y x + 1/144 y x - 1/144 y x , + + 2 2 4 4 3 4 2 4 + COEFF(0, 1, -2) = 1/32 z y x - 1/36 z y x - 1/72 y x + 1/96 z y x + + 3 4 2 4 3 2 4 4 3 3 + + 1/18 z y x - 1/12 z y x - 1/48 z y x + 1/72 x - 1/9 y z + + 2 2 2 2 3 4 2 2 3 + + 1/9 y - 1/18 z - 5/32 y x z + 1/24 z y x + 5/48 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + + 5/36 y x z - 5/24 y x z - 1/36 z y x + 1/72 z y x + + 2 3 3 2 3 3 2 2 + - 5/18 y x z - 5/72 z y x + 1/9 z - 1/18 y - 1/24 y - 1/6 z + + 2 2 4 2 2 + - 5/72 x + 5/36 z y x - 1/9 y z - 1/72 z x - 5/96 y x z + + 2 2 3 2 2 3 2 2 + + 5/12 y x z + 5/72 y x + 1/24 y z + 1/6 y z + 5/72 x z + 1/18 + + 3 2 3 2 3 2 2 2 2 2 + + 2/9 y z - 1/12 y z - 5/36 x z - 1/3 y z + 5/24 x z + 1/8 y z + + 2 2 2 2 4 3 4 3 4 + + 5/96 y x - 5/36 y x - 1/24 z x + 1/36 z x + 1/18 z y + 1/36 y x + + 2 4 3 3 2 2 4 + - 1/96 y x , COEFF(1, 1, -2) = - 1/27 y x z - 1/48 z y x + + 4 2 3 3 2 3 3 3 3 + + 1/54 z y x + 1/72 y x z - 1/144 z y x + 1/54 z y x + 1/108 y x + + 3 4 2 2 3 3 2 3 2 4 + + 1/108 y x - 1/48 z y x - 1/54 y x + 1/18 z y x - 1/144 z y x + + 3 4 2 4 3 2 4 3 2 3 3 + - 1/27 z y x + 1/18 z y x + 1/72 z y x + 1/36 x z - 1/54 x z + + 4 3 2 2 3 + + 1/27 x - 1/108 x + 4/27 y x z + 1/36 y x z - 1/18 y x z + 2/27 y x + + 2 2 2 2 3 4 3 3 2 2 2 3 + + 1/12 y x z - 1/36 z y x - 1/36 y x z - 1/18 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 2/27 y x z + 1/9 y x z + 1/54 z y x - 1/108 z y x + + 2 3 3 2 3 2 3 3 3 3 + + 4/27 y x z + 1/27 z y x + 1/9 y x z + 1/54 y x z + 1/27 z y x + + 3 3 3 3 3 2 + - 1/108 z y x - 2/27 y x z - 1/108 x + 1/27 x - 2/27 y x z + + 2 4 2 2 2 2 2 + - 2/27 z y x + 1/108 z x - 1/36 y x + 1/12 y x z + 1/36 y x z + + 2 2 2 3 2 3 2 + - 2/9 y x z - 2/9 y x z - 1/27 y x - 1/27 y x - 1/27 x z - 1/27 x z + + 2 3 3 2 2 2 2 2 2 + + 2/27 x z + 2/27 x z - 1/9 x z - 1/9 x z - 1/36 y x + 2/27 y x + + 2 4 3 4 3 4 2 4 + + 1/36 z x - 1/54 z x + 1/108 z x - 1/54 y x + 1/144 y x + + 2 3 3 3 2 2 4 + + 1/144 y x , COEFF(2, 1, -2) = 1/54 y x z + 1/192 z y x + + 4 2 3 3 2 3 3 + - 1/216 z y x - 1/144 y x z + 1/288 z y x - 1/108 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 1/216 y x - 1/432 y x + 1/96 z y x + 1/108 y x - 1/36 z y x + + 2 4 3 4 2 4 3 2 4 + + 1/576 z y x + 1/108 z y x - 1/72 z y x - 1/288 z y x + + 3 2 3 3 4 3 + - 1/72 x z + 1/108 x z - 1/216 x + 1/432 x - 1/54 y x z + + 2 2 3 2 2 2 + - 1/288 y x z + 1/144 y x z - 1/108 y x - 1/192 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + + 1/144 z y x + 1/72 y x z + 1/288 y x z + 1/216 y x z + + 3 2 2 3 3 4 3 4 2 3 + - 1/144 y x z - 1/216 z y x + 1/432 z y x - 1/108 y x z + + 3 2 3 2 3 3 3 3 + - 1/432 z y x - 1/72 y x z - 1/108 y x z - 1/216 z y x + + 3 3 3 3 3 2 + + 1/216 z y x + 1/108 y x z + 1/216 x - 1/432 x + 1/108 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x - 1/432 z x + 1/288 y x - 1/96 y x z - 1/576 y x z + + 2 2 2 3 2 3 + + 1/72 y x z + 1/36 y x z + 1/432 y x + 1/216 y x + 1/216 x z + + 2 2 3 3 2 2 2 + + 1/432 x z - 1/216 x z - 1/108 x z + 1/144 x z + 1/72 x z + + 2 2 2 2 4 3 4 3 + + 1/576 y x - 1/216 y x - 1/144 z x + 1/216 z x - 1/216 z x + + 4 2 4 2 3 3 3 + + 1/216 y x - 1/576 y x - 1/288 y x , COEFF(-2, 2, -2) = 1/864 y x z + + 2 2 4 4 2 3 3 2 3 + - 1/384 z y x + 1/3456 z y x - 1/288 y x z + 1/576 z y x + + 3 3 3 3 4 2 2 3 + - 1/1728 z y x - 1/864 y x + 1/1728 y x + 1/192 z y x + + 3 2 3 2 4 3 4 + + 1/1728 y x - 1/576 z y x - 1/1152 z y x - 1/1728 z y x + + 2 4 3 2 4 3 2 3 3 + + 1/1152 z y x + 1/576 z y x - 1/576 x z + 1/864 x z - 1/1728 x + + 4 3 2 2 3 + - 1/3456 x - 1/864 y x z - 1/576 y x z + 1/288 y x z - 1/1728 y x + + 2 2 2 2 3 4 3 3 2 2 2 3 + + 1/384 y x z - 1/576 z y x + 1/288 y x z - 1/576 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 1/864 y x z + 1/576 y x z + 1/864 z y x - 1/1728 z y x + + 2 3 3 2 3 2 3 3 3 + + 1/1728 y x z + 1/1728 z y x - 1/288 y x z - 1/432 y x z + + 3 3 3 3 3 3 2 + - 1/864 z y x + 1/864 z y x + 1/432 y x z + 1/1728 x + 1/3456 x + + 2 4 2 2 2 + + 1/1728 y x z - 1/3456 z y x + 1/3456 z x + 1/576 y x - 1/192 y x z + + 2 2 2 2 2 3 2 + + 1/1152 y x z - 1/1152 y x z + 1/576 y x z - 1/1728 y x + + 3 2 2 3 3 + + 1/864 y x + 1/1728 x z - 1/3456 x z + 1/1728 x z - 1/864 x z + + 2 2 2 2 2 2 2 4 + - 1/1152 x z + 1/576 x z - 1/1152 y x + 1/3456 y x + 1/1152 z x + + 3 4 3 4 2 4 2 3 + - 1/1728 z x - 1/1728 z x - 1/3456 y x + 1/1152 y x - 1/576 y x , + + 3 3 2 2 4 4 + COEFF(-1, 2, -2) = - 1/432 y x z + 1/96 z y x - 1/864 z y x + + 2 3 3 2 3 3 3 3 + + 1/144 y x z - 1/288 z y x + 1/864 z y x + 1/432 y x + + 3 4 2 2 3 3 2 3 2 4 + - 1/432 y x - 1/96 z y x - 1/864 y x + 1/288 z y x + 1/288 z y x + + 3 4 2 4 3 2 4 3 2 + + 1/432 z y x - 1/288 z y x - 1/144 z y x + 1/288 x z + + 3 3 4 3 2 + - 1/432 x z + 1/216 x + 1/864 x + 1/108 y x z + 1/72 y x z + + 2 3 2 2 2 2 3 4 + - 1/36 y x z + 1/216 y x - 1/24 y x z + 1/144 z y x + + 3 3 2 2 2 3 3 2 3 3 2 2 + - 1/144 y x z + 1/36 y x z + 1/54 y x z - 1/36 y x z + + 3 3 4 3 4 2 3 3 2 + - 1/216 z y x + 1/432 z y x - 1/108 y x z - 1/108 z y x + + 3 2 3 3 3 3 3 3 + + 1/36 y x z + 1/216 y x z + 1/108 z y x - 1/432 z y x + + 3 3 3 2 2 + - 1/54 y x z - 1/864 x - 1/216 x - 1/216 y x z + 1/216 z y x + + 4 2 2 2 2 2 2 2 + - 1/864 z x - 1/72 y x + 1/24 y x z - 1/72 y x z + 1/72 y x z + + 2 3 2 3 2 + - 1/72 y x z + 1/108 y x - 1/108 y x - 1/216 x z + 1/216 x z + + 2 3 3 2 2 2 2 2 + - 1/108 x z + 1/108 x z + 1/72 x z - 1/72 x z + 1/72 y x + + 2 2 4 3 4 3 4 + - 1/216 y x - 1/288 z x + 1/432 z x + 1/864 z x + 1/864 y x + + 2 4 2 3 2 2 4 + - 1/288 y x + 1/288 y x , COEFF(0, 2, -2) = - 1/64 z y x + + 4 3 4 2 4 3 4 + + 1/576 z y x + 1/288 y x - 1/192 z y x - 1/288 z y x + + 2 4 3 2 4 4 3 3 + + 1/192 z y x + 1/96 z y x - 1/576 x + 1/36 y z - 1/144 y + + 2 2 2 2 3 4 2 2 3 3 2 3 + + 1/144 z + 5/64 y x z - 1/96 z y x - 5/96 y x z - 5/144 y x z + + 3 2 2 3 3 4 3 4 2 3 + + 5/96 y x z + 1/144 z y x - 1/288 z y x + 5/288 y x z + + 3 2 3 3 2 2 2 + + 5/288 z y x - 1/72 z + 1/72 y + 1/48 y + 1/48 z + 5/576 x + + 2 4 2 2 2 2 + - 5/576 z y x + 1/144 y z + 1/576 z x + 5/192 y x z - 5/192 y x z + + 3 2 2 3 2 2 3 + - 5/288 y x - 1/48 y z - 1/24 y z - 5/576 x z - 1/72 y z + + 2 3 2 3 2 2 2 2 2 + + 1/24 y z + 5/288 x z + 1/48 y z - 5/192 x z - 1/16 y z + + 2 2 2 2 4 3 4 3 + - 5/192 y x + 5/576 y x - 1/144 + 1/192 z x - 1/288 z x - 1/72 z y + + 4 2 4 3 3 + - 1/576 y x + 1/192 y x , COEFF(1, 2, -2) = 1/432 y x z + + 2 2 4 4 2 3 3 2 3 + + 1/96 z y x - 1/864 z y x - 1/144 y x z + 1/288 z y x + + 3 3 3 3 4 2 2 3 3 + - 1/864 z y x - 1/432 y x - 1/432 y x + 1/96 z y x + 1/864 y x + + 2 3 2 4 3 4 2 4 + - 1/288 z y x + 1/288 z y x + 1/432 z y x - 1/288 z y x + + 3 2 4 3 2 3 3 4 + - 1/144 z y x - 1/288 x z + 1/432 x z - 1/216 x + 1/864 x + + 3 2 2 3 2 2 2 + - 1/108 y x z - 1/72 y x z + 1/36 y x z - 1/216 y x - 1/24 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + + 1/144 z y x + 1/144 y x z + 1/36 y x z + 1/54 y x z + + 3 2 2 3 3 4 3 4 2 3 + - 1/36 y x z - 1/216 z y x + 1/432 z y x - 1/108 y x z + + 3 2 3 2 3 3 3 3 + - 1/108 z y x - 1/36 y x z - 1/216 y x z - 1/108 z y x + + 3 3 3 3 3 2 + + 1/432 z y x + 1/54 y x z + 1/864 x - 1/216 x + 1/216 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x - 1/864 z x + 1/72 y x - 1/24 y x z - 1/72 y x z + + 2 2 2 3 2 3 + + 1/72 y x z + 1/72 y x z + 1/108 y x + 1/108 y x + 1/216 x z + + 2 2 3 3 2 2 2 + + 1/216 x z - 1/108 x z - 1/108 x z + 1/72 x z + 1/72 x z + + 2 2 2 2 4 3 4 3 + + 1/72 y x - 1/216 y x - 1/288 z x + 1/432 z x - 1/864 z x + + 4 2 4 2 3 + + 1/864 y x - 1/288 y x - 1/288 y x , COEFF(2, 2, -2) = + + 3 3 2 2 4 4 2 3 3 + - 1/864 y x z - 1/384 z y x + 1/3456 z y x + 1/288 y x z + + 2 3 3 3 3 3 4 + - 1/576 z y x + 1/1728 z y x + 1/864 y x + 1/1728 y x + + 2 2 3 3 2 3 2 4 + - 1/192 z y x - 1/1728 y x + 1/576 z y x - 1/1152 z y x + + 3 4 2 4 3 2 4 3 2 + - 1/1728 z y x + 1/1152 z y x + 1/576 z y x + 1/576 x z + + 3 3 4 3 2 + - 1/864 x z + 1/1728 x - 1/3456 x + 1/864 y x z + 1/576 y x z + + 2 3 2 2 2 2 3 4 + - 1/288 y x z + 1/1728 y x + 1/384 y x z - 1/576 z y x + + 3 3 2 2 2 3 3 2 3 3 2 2 + - 1/288 y x z - 1/576 y x z - 1/864 y x z + 1/576 y x z + + 3 3 4 3 4 2 3 3 2 + + 1/864 z y x - 1/1728 z y x + 1/1728 y x z + 1/1728 z y x + + 3 2 3 3 3 3 3 3 + + 1/288 y x z + 1/432 y x z + 1/864 z y x - 1/864 z y x + + 3 3 3 2 2 + - 1/432 y x z - 1/1728 x + 1/3456 x - 1/1728 y x z - 1/3456 z y x + + 4 2 2 2 2 2 + + 1/3456 z x - 1/576 y x + 1/192 y x z + 1/1152 y x z + + 2 2 2 3 2 3 + - 1/1152 y x z - 1/576 y x z - 1/1728 y x - 1/864 y x - 1/1728 x z + + 2 2 3 3 2 2 2 + - 1/3456 x z + 1/1728 x z + 1/864 x z - 1/1152 x z - 1/576 x z + + 2 2 2 2 4 3 4 3 + - 1/1152 y x + 1/3456 y x + 1/1152 z x - 1/1728 z x + 1/1728 z x + + 4 2 4 2 3 + - 1/3456 y x + 1/1152 y x + 1/576 y x , COEFF(-2, -2, -1) = + + 3 3 2 2 4 4 2 3 3 + - 1/216 y x z - 1/192 z y x - 1/216 z y x - 1/72 y x z + + 2 3 3 3 3 3 4 2 2 3 + + 1/36 z y x + 1/108 z y x + 1/108 y x - 1/216 y x + 1/96 z y x + + 3 2 3 2 4 3 4 + - 1/216 y x + 1/288 z y x - 1/72 z y x + 1/432 z y x + + 2 4 3 2 4 3 2 3 3 + - 1/576 z y x + 1/144 z y x - 1/288 x z + 1/216 x z - 1/216 x + + 4 3 2 2 3 + - 1/432 x + 1/216 y x z - 1/36 y x z + 1/72 y x z + 1/216 y x + + 2 2 2 2 3 4 3 3 2 2 2 3 + + 1/192 y x z + 1/288 z y x - 1/144 y x z - 1/144 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + + 1/216 y x z - 1/288 y x z - 1/216 z y x + 1/108 z y x + + 2 3 3 2 3 2 3 3 3 + - 1/432 y x z - 1/108 z y x + 1/144 y x z + 1/108 y x z + + 3 3 3 3 3 3 2 + + 1/54 z y x - 1/54 z y x - 1/108 y x z + 1/216 x + 1/432 x + + 2 4 2 2 2 + - 1/108 y x z + 1/216 z y x + 1/216 z x + 1/72 y x - 1/96 y x z + + 2 2 2 2 2 3 2 3 + + 1/72 y x z + 1/576 y x z - 1/288 y x z + 1/216 y x - 1/108 y x + + 2 2 3 3 2 2 + + 1/108 x z - 1/216 x z + 1/432 x z - 1/216 x z - 1/576 x z + + 2 2 2 2 2 4 3 4 + + 1/288 x z - 1/144 y x - 1/432 y x + 1/576 z x - 1/432 z x + + 3 4 2 4 2 3 + - 1/108 z x + 1/432 y x + 1/144 y x - 1/72 y x , COEFF(-1, -2, -1) = + + 3 3 2 2 4 4 2 3 3 2 3 + 1/108 y x z + 1/48 z y x + 1/54 z y x + 1/36 y x z - 1/18 z y x + + 3 3 3 3 4 2 2 3 3 + - 1/54 z y x - 1/54 y x + 1/54 y x - 1/48 z y x + 1/108 y x + + 2 3 2 4 3 4 2 4 + - 1/144 z y x + 1/18 z y x - 1/108 z y x + 1/144 z y x + + 3 2 4 3 2 3 3 4 + - 1/36 z y x + 1/144 x z - 1/108 x z + 1/27 x + 1/108 x + + 3 2 2 3 2 2 2 + - 1/27 y x z + 2/9 y x z - 1/9 y x z - 1/27 y x - 1/12 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + - 1/72 z y x + 1/72 y x z + 1/9 y x z - 2/27 y x z + + 3 2 2 3 3 4 3 4 2 3 + + 1/18 y x z + 1/54 z y x - 1/27 z y x + 1/27 y x z + + 3 2 3 2 3 3 3 3 3 3 + + 4/27 z y x - 1/18 y x z - 1/54 y x z - 4/27 z y x + 1/27 z y x + + 3 3 3 2 2 4 + + 2/27 y x z - 1/108 x - 1/27 x + 2/27 y x z - 2/27 z y x - 1/54 z x + + 2 2 2 2 2 2 2 2 + - 1/9 y x + 1/12 y x z - 2/9 y x z - 1/36 y x z + 1/36 y x z + + 3 2 3 2 2 3 3 + - 2/27 y x + 2/27 y x - 2/27 x z + 2/27 x z - 1/27 x z + 1/27 x z + + 2 2 2 2 2 2 2 4 + + 1/36 x z - 1/36 x z + 1/9 y x + 1/27 y x - 1/144 z x + + 3 4 3 4 2 4 2 3 + + 1/108 z x + 1/54 z x - 1/108 y x - 1/36 y x + 1/36 y x , + + 2 2 4 4 3 4 + COEFF(0, -2, -1) = - 1/32 z y x - 1/36 z y x - 1/36 y x + + 2 4 3 4 2 4 3 2 4 4 + - 1/12 z y x + 1/72 z y x - 1/96 z y x + 1/24 z y x - 1/72 x + + 3 3 2 2 2 2 3 4 + - 1/9 y z + 1/18 y + 1/9 z + 5/32 y x z + 1/48 z y x + + 2 2 3 3 2 3 3 2 2 3 3 4 + - 5/24 y x z + 5/36 y x z - 5/48 y x z - 1/36 z y x + + 3 4 2 3 3 2 3 3 2 + + 1/18 z y x - 5/72 y x z - 5/18 z y x - 1/18 z - 1/9 y + 1/6 y + + 2 2 2 4 2 2 + + 1/24 z + 5/72 x + 5/36 z y x - 1/9 y z + 1/36 z x + 5/12 y x z + + 2 2 3 2 2 3 2 2 + + 5/96 y x z + 5/36 y x - 1/3 y z + 1/12 y z - 5/36 x z - 1/18 + + 3 2 3 2 3 2 2 2 2 2 + + 1/18 y z + 1/6 y z + 5/72 x z - 1/24 y z - 5/96 x z - 1/8 y z + + 2 2 2 2 4 3 4 3 4 + - 5/24 y x - 5/72 y x + 1/96 z x - 1/72 z x + 2/9 z y + 1/72 y x + + 2 4 3 3 2 2 4 + + 1/24 y x , COEFF(1, -2, -1) = - 1/108 y x z + 1/48 z y x + + 4 2 3 3 2 3 3 3 3 + + 1/54 z y x - 1/36 y x z + 1/18 z y x + 1/54 z y x + 1/54 y x + + 3 4 2 2 3 3 2 3 2 4 + + 1/54 y x + 1/48 z y x - 1/108 y x + 1/144 z y x + 1/18 z y x + + 3 4 2 4 3 2 4 3 2 + - 1/108 z y x + 1/144 z y x - 1/36 z y x - 1/144 x z + + 3 3 4 3 2 2 3 + + 1/108 x z - 1/27 x + 1/108 x + 1/27 y x z - 2/9 y x z + 1/9 y x z + + 2 2 2 2 3 4 3 3 2 2 2 3 + + 1/27 y x - 1/12 y x z - 1/72 z y x - 1/72 y x z + 1/9 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 2/27 y x z + 1/18 y x z + 1/54 z y x - 1/27 z y x + + 2 3 3 2 3 2 3 3 3 3 + + 1/27 y x z + 4/27 z y x + 1/18 y x z + 1/54 y x z + 4/27 z y x + + 3 3 3 3 3 2 + - 1/27 z y x - 2/27 y x z + 1/108 x - 1/27 x - 2/27 y x z + + 2 4 2 2 2 2 2 + - 2/27 z y x - 1/54 z x + 1/9 y x - 1/12 y x z - 2/9 y x z + + 2 2 2 3 2 3 + - 1/36 y x z - 1/36 y x z - 2/27 y x - 2/27 y x + 2/27 x z + + 2 2 3 3 2 2 2 2 2 + + 2/27 x z - 1/27 x z - 1/27 x z + 1/36 x z + 1/36 x z + 1/9 y x + + 2 2 4 3 4 3 4 + + 1/27 y x - 1/144 z x + 1/108 z x - 1/54 z x - 1/108 y x + + 2 4 2 3 3 3 + - 1/36 y x - 1/36 y x , COEFF(2, -2, -1) = 1/216 y x z + + 2 2 4 4 2 3 3 2 3 + - 1/192 z y x - 1/216 z y x + 1/72 y x z - 1/36 z y x + + 3 3 3 3 4 2 2 3 3 + - 1/108 z y x - 1/108 y x - 1/216 y x - 1/96 z y x + 1/216 y x + + 2 3 2 4 3 4 2 4 + - 1/288 z y x - 1/72 z y x + 1/432 z y x - 1/576 z y x + + 3 2 4 3 2 3 3 4 + + 1/144 z y x + 1/288 x z - 1/216 x z + 1/216 x - 1/432 x + + 3 2 2 3 2 2 2 + - 1/216 y x z + 1/36 y x z - 1/72 y x z - 1/216 y x + 1/192 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + + 1/288 z y x + 1/144 y x z - 1/144 y x z + 1/216 y x z + + 3 2 2 3 3 4 3 4 2 3 + - 1/288 y x z - 1/216 z y x + 1/108 z y x - 1/432 y x z + + 3 2 3 2 3 3 3 3 + - 1/108 z y x - 1/144 y x z - 1/108 y x z - 1/54 z y x + + 3 3 3 3 3 2 + + 1/54 z y x + 1/108 y x z - 1/216 x + 1/432 x + 1/108 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x + 1/216 z x - 1/72 y x + 1/96 y x z + 1/72 y x z + + 2 2 2 3 2 3 + + 1/576 y x z + 1/288 y x z + 1/216 y x + 1/108 y x - 1/108 x z + + 2 2 3 3 2 2 2 + - 1/216 x z + 1/432 x z + 1/216 x z - 1/576 x z - 1/288 x z + + 2 2 2 2 4 3 4 3 + - 1/144 y x - 1/432 y x + 1/576 z x - 1/432 z x + 1/108 z x + + 4 2 4 2 3 3 3 + + 1/432 y x + 1/144 y x + 1/72 y x , COEFF(-2, -1, -1) = 2/27 y x z + + 2 2 4 4 2 3 3 2 3 3 + + 1/96 z y x + 2/27 z y x + 1/36 y x z - 1/18 z y x - 4/27 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 1/27 y x + 1/54 y x - 1/48 z y x + 2/27 y x - 1/18 z y x + + 2 4 3 4 2 4 3 2 4 3 2 + + 1/36 z y x - 1/27 z y x + 1/36 z y x - 1/72 z y x + 1/36 x z + + 3 3 4 3 2 2 3 + - 1/27 x z + 1/27 x + 1/54 x - 2/27 y x z + 1/18 y x z - 1/36 y x z + + 2 2 2 2 3 4 3 3 2 2 2 3 + - 2/27 y x - 1/96 y x z - 1/72 z y x + 1/36 y x z + 1/72 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 1/54 y x z + 1/72 y x z + 1/54 z y x - 1/27 z y x + + 2 3 3 2 3 2 3 3 3 3 + + 1/27 y x z + 1/27 z y x - 1/36 y x z - 1/27 y x z - 2/27 z y x + + 3 3 3 3 3 2 + + 2/27 z y x + 1/27 y x z - 1/27 x - 1/54 x + 4/27 y x z + + 2 4 2 2 2 2 2 + - 2/27 z y x - 1/27 z x - 1/36 y x + 1/48 y x z - 1/36 y x z + + 2 2 2 3 2 3 + - 1/36 y x z + 1/18 y x z - 1/54 y x + 1/27 y x - 2/27 x z + + 2 2 3 3 2 2 2 2 2 + + 1/27 x z - 1/54 x z + 1/27 x z + 1/72 x z - 1/36 x z + 1/72 y x + + 2 2 4 3 4 3 4 2 4 + + 1/27 y x - 1/72 z x + 1/54 z x + 2/27 z x - 1/27 y x - 1/72 y x + + 2 3 3 3 2 2 4 + + 1/36 y x , COEFF(-1, -1, -1) = - 4/27 y x z - 1/24 z y x + + 4 2 3 3 2 3 3 3 3 + - 8/27 z y x - 1/18 y x z + 1/9 z y x + 8/27 z y x + 2/27 y x + + 3 4 2 2 3 3 2 3 2 4 + - 2/27 y x + 1/24 z y x - 4/27 y x + 1/9 z y x - 1/9 z y x + + 3 4 2 4 3 2 4 3 2 3 3 + + 4/27 z y x - 1/9 z y x + 1/18 z y x - 1/18 x z + 2/27 x z + + 4 16 3 2 2 3 16 + - 8/27 x - 2/27 x + -- y x z - 4/9 y x z + 2/9 y x z + -- y x + 27 27 + + 2 2 2 2 3 4 3 3 2 2 2 3 + + 1/6 y x z + 1/18 z y x - 1/18 y x z - 2/9 y x z + + 3 2 3 3 2 2 3 3 4 3 4 16 2 3 + + 8/27 y x z - 2/9 y x z - 2/27 z y x + 4/27 z y x - -- y x z + 27 + + 16 3 2 3 2 3 3 3 16 3 3 3 + - -- z y x + 2/9 y x z + 2/27 y x z + -- z y x - 4/27 z y x + 27 27 + + 3 3 3 2 32 32 2 4 + - 8/27 y x z + 2/27 x + 8/27 x - -- y x z + -- z y x + 4/27 z x + 27 27 + + 2 2 2 2 2 2 2 2 + + 2/9 y x - 1/6 y x z + 4/9 y x z + 4/9 y x z - 4/9 y x z + + 3 2 3 16 16 2 2 3 3 + + 8/27 y x - 8/27 y x + -- x z - -- x z + 8/27 x z - 8/27 x z + 27 27 + + 2 2 2 2 2 16 2 2 4 3 4 + - 2/9 x z + 2/9 x z - 2/9 y x - -- y x + 1/18 z x - 2/27 z x + 27 + + 3 4 2 4 2 3 + - 4/27 z x + 4/27 y x + 1/18 y x - 1/18 y x , COEFF(0, -1, -1) = + + 2 2 4 4 3 4 2 4 3 4 + 1/16 z y x + 4/9 z y x + 1/9 y x + 1/6 z y x - 2/9 z y x + + 2 4 3 2 4 4 3 3 + + 1/6 z y x - 1/12 z y x + 1/9 x + 4/9 y z - 8/9 y - 8/9 z + + 2 2 2 2 3 4 2 2 3 3 2 3 + - 5/16 y x z - 1/12 z y x + 5/12 y x z - 5/9 y x z + + 3 2 2 3 3 4 3 4 2 3 3 2 + + 5/12 y x z + 1/9 z y x - 2/9 z y x + 10/9 y x z + 10/9 z y x + + 3 3 2 2 2 2 + + 4/9 + 4/9 z + 4/9 y - 1/3 y - 1/3 z - 5/9 x - 20/9 z y x + + 4 2 2 2 2 3 2 2 + + 16/9 y z - 2/9 z x - 5/6 y x z - 5/6 y x z - 5/9 y x + 2/3 y z + + 3 2 2 3 2 3 2 3 2 + - 1/3 y z + 10/9 x z - 8/9 y z - 1/3 y z - 5/9 x z + 2/3 y z + + 2 2 2 2 2 2 2 2 4 3 4 + + 5/12 x z + 1/4 y z + 5/12 y x + 10/9 y x - 1/12 z x + 1/9 z x + + 3 4 2 4 3 3 + - 8/9 z y - 2/9 y x - 1/12 y x , COEFF(1, -1, -1) = 4/27 y x z + + 2 2 4 4 2 3 3 2 3 3 + - 1/24 z y x - 8/27 z y x + 1/18 y x z - 1/9 z y x - 8/27 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 2/27 y x - 2/27 y x - 1/24 z y x + 4/27 y x - 1/9 z y x + + 2 4 3 4 2 4 3 2 4 3 2 + - 1/9 z y x + 4/27 z y x - 1/9 z y x + 1/18 z y x + 1/18 x z + + 3 3 4 16 3 2 2 3 + - 2/27 x z + 8/27 x - 2/27 x - -- y x z + 4/9 y x z - 2/9 y x z + 27 + + 16 2 2 2 2 3 4 3 3 2 2 2 3 + - -- y x + 1/6 y x z + 1/18 z y x + 1/18 y x z - 2/9 y x z + 27 + + 3 2 3 3 2 2 3 3 4 3 4 16 2 3 + + 8/27 y x z - 2/9 y x z - 2/27 z y x + 4/27 z y x - -- y x z + 27 + + 16 3 2 3 2 3 3 3 16 3 3 3 + - -- z y x - 2/9 y x z - 2/27 y x z - -- z y x + 4/27 z y x + 27 27 + + 3 3 3 2 32 32 2 4 + + 8/27 y x z - 2/27 x + 8/27 x + -- y x z + -- z y x + 4/27 z x + 27 27 + + 2 2 2 2 2 2 2 2 + - 2/9 y x + 1/6 y x z + 4/9 y x z + 4/9 y x z + 4/9 y x z + + 3 2 3 16 16 2 2 3 3 + + 8/27 y x + 8/27 y x - -- x z - -- x z + 8/27 x z + 8/27 x z + 27 27 + + 2 2 2 2 2 16 2 2 4 3 4 + - 2/9 x z - 2/9 x z - 2/9 y x - -- y x + 1/18 z x - 2/27 z x + 27 + + 3 4 2 4 2 3 + + 4/27 z x + 4/27 y x + 1/18 y x + 1/18 y x , COEFF(2, -1, -1) = + + 3 3 2 2 4 4 2 3 3 2 3 + - 2/27 y x z + 1/96 z y x + 2/27 z y x - 1/36 y x z + 1/18 z y x + + 3 3 3 3 4 2 2 3 3 + + 4/27 z y x + 1/27 y x + 1/54 y x + 1/48 z y x - 2/27 y x + + 2 3 2 4 3 4 2 4 + + 1/18 z y x + 1/36 z y x - 1/27 z y x + 1/36 z y x + + 3 2 4 3 2 3 3 4 3 + - 1/72 z y x - 1/36 x z + 1/27 x z - 1/27 x + 1/54 x + 2/27 y x z + + 2 2 3 2 2 2 2 3 4 + - 1/18 y x z + 1/36 y x z + 2/27 y x - 1/96 y x z - 1/72 z y x + + 3 3 2 2 2 3 3 2 3 3 2 2 + - 1/36 y x z + 1/72 y x z - 1/54 y x z + 1/72 y x z + + 3 3 4 3 4 2 3 3 2 + + 1/54 z y x - 1/27 z y x + 1/27 y x z + 1/27 z y x + + 3 2 3 3 3 3 3 3 3 3 + + 1/36 y x z + 1/27 y x z + 2/27 z y x - 2/27 z y x - 1/27 y x z + + 3 2 2 4 2 + + 1/27 x - 1/54 x - 4/27 y x z - 2/27 z y x - 1/27 z x + 1/36 y x + + 2 2 2 2 2 2 2 3 2 + - 1/48 y x z - 1/36 y x z - 1/36 y x z - 1/18 y x z - 1/54 y x + + 3 2 2 3 3 2 2 + - 1/27 y x + 2/27 x z + 1/27 x z - 1/54 x z - 1/27 x z + 1/72 x z + + 2 2 2 2 2 4 3 4 3 + + 1/36 x z + 1/72 y x + 1/27 y x - 1/72 z x + 1/54 z x - 2/27 z x + + 4 2 4 2 3 3 3 + - 1/27 y x - 1/72 y x - 1/36 y x , COEFF(-2, 0, -1) = - 5/36 y x z + + 4 3 3 3 3 4 3 + - 5/36 z y x + 5/18 z y x + 1/18 y x - 1/36 y x - 5/36 y x + + 2 3 3 4 2 4 3 + + 5/48 z y x + 5/72 z y x - 5/96 z y x + 5/36 y x z + 5/36 y x + + 2 3 4 3 3 2 3 2 3 3 2 2 + + 1/48 z y x - 1/24 y x z + 1/36 y x z - 1/48 y x z + + 3 3 4 3 4 2 3 3 2 + - 1/36 z y x + 1/18 z y x - 5/72 y x z - 1/18 z y x + + 3 2 3 3 3 3 3 3 3 3 + + 1/24 y x z + 1/18 y x z + 1/9 z y x - 1/9 z y x - 1/18 y x z + + 2 2 2 2 3 2 + - 5/18 y x z + 5/36 z y x + 5/96 y x z - 5/48 y x z + 1/36 y x + + 3 2 4 3 3 + - 1/18 y x - 5/72 y x + 5/72 y x , COEFF(-1, 0, -1) = 5/18 y x z + + 4 3 3 3 3 4 3 + + 5/9 z y x - 5/9 z y x - 1/9 y x + 1/9 y x + 5/18 y x + + 2 3 3 4 2 4 3 + - 5/24 z y x - 5/18 z y x + 5/24 z y x - 10/9 y x z - 10/9 y x + + 2 3 4 3 3 2 3 2 3 3 2 2 + - 1/12 z y x + 1/12 y x z - 4/9 y x z + 1/3 y x z + + 3 3 4 3 4 2 3 3 2 3 2 + + 1/9 z y x - 2/9 z y x + 10/9 y x z + 8/9 z y x - 1/3 y x z + + 3 3 3 3 3 3 3 3 + - 1/9 y x z - 8/9 z y x + 2/9 z y x + 4/9 y x z + 20/9 y x z + + 2 2 2 2 3 2 3 + - 20/9 z y x - 5/6 y x z + 5/6 y x z - 4/9 y x + 4/9 y x + + 2 4 3 2 3 2 + + 10/9 y x - 5/18 y x , COEFF(0, 0, -1) = 5/6 y x - 5/3 z y x + + 3 4 3 4 3 2 3 3 3 4 3 4 + + 1/3 z y x + 5/12 z y x + 5/6 y x z - 1/6 z y x - 1/6 y x + + 2 3 4 3 3 2 3 3 2 2 + + 1/8 z y x - 2/3 y z + 25/6 z y x - 2/3 y - 5/8 y x z + + 25 2 3 2 4 25 2 2 4 3 + - -- y x z - 5/16 z y x + -- y x z + 5/12 y x + 4/3 z y - 10/3 y z + 12 16 + + 2 4 3 2 25 2 3 + - 5/4 y z - 5/6 z y x + 1/2 y z - -- y x + 5/3 y + 5/3 y z , + 12 + + 3 3 4 3 3 3 + COEFF(1, 0, -1) = - 5/18 y x z + 5/9 z y x + 5/9 z y x + 1/9 y x + + 3 4 3 2 3 3 4 2 4 + + 1/9 y x - 5/18 y x + 5/24 z y x - 5/18 z y x + 5/24 z y x + + 3 2 3 4 3 3 2 3 2 3 + + 10/9 y x z + 10/9 y x - 1/12 z y x - 1/12 y x z - 4/9 y x z + + 3 2 2 3 3 4 3 4 2 3 3 2 + + 1/3 y x z + 1/9 z y x - 2/9 z y x + 10/9 y x z + 8/9 z y x + + 3 2 3 3 3 3 3 3 3 3 + + 1/3 y x z + 1/9 y x z + 8/9 z y x - 2/9 z y x - 4/9 y x z + + 2 2 2 2 3 2 + - 20/9 y x z - 20/9 z y x - 5/6 y x z - 5/6 y x z - 4/9 y x + + 3 2 4 3 3 + - 4/9 y x + 10/9 y x - 5/18 y x , COEFF(2, 0, -1) = 5/36 y x z + + 4 3 3 3 3 4 3 + - 5/36 z y x - 5/18 z y x - 1/18 y x - 1/36 y x + 5/36 y x + + 2 3 3 4 2 4 3 + - 5/48 z y x + 5/72 z y x - 5/96 z y x - 5/36 y x z - 5/36 y x + + 2 3 4 3 3 2 3 2 3 3 2 2 + + 1/48 z y x + 1/24 y x z + 1/36 y x z - 1/48 y x z + + 3 3 4 3 4 2 3 3 2 + - 1/36 z y x + 1/18 z y x - 5/72 y x z - 1/18 z y x + + 3 2 3 3 3 3 3 3 3 3 + - 1/24 y x z - 1/18 y x z - 1/9 z y x + 1/9 z y x + 1/18 y x z + + 2 2 2 2 3 2 + + 5/18 y x z + 5/36 z y x + 5/96 y x z + 5/48 y x z + 1/36 y x + + 3 2 4 3 3 + + 1/18 y x - 5/72 y x + 5/72 y x , COEFF(-2, 1, -1) = 2/27 y x z + + 2 2 4 4 2 3 3 2 3 3 + - 1/96 z y x + 2/27 z y x - 1/36 y x z + 1/18 z y x - 4/27 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 1/27 y x + 1/54 y x + 1/48 z y x + 2/27 y x - 1/18 z y x + + 2 4 3 4 2 4 3 2 4 3 2 + - 1/36 z y x - 1/27 z y x + 1/36 z y x + 1/72 z y x - 1/36 x z + + 3 3 4 3 2 2 3 + + 1/27 x z - 1/27 x - 1/54 x - 2/27 y x z - 1/18 y x z + 1/36 y x z + + 2 2 2 2 3 4 3 3 2 2 2 3 + - 2/27 y x + 1/96 y x z - 1/72 z y x + 1/36 y x z - 1/72 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 1/54 y x z + 1/72 y x z + 1/54 z y x - 1/27 z y x + + 2 3 3 2 3 2 3 3 3 3 + + 1/27 y x z + 1/27 z y x - 1/36 y x z - 1/27 y x z - 2/27 z y x + + 3 3 3 3 3 2 + + 2/27 z y x + 1/27 y x z + 1/27 x + 1/54 x + 4/27 y x z + + 2 4 2 2 2 2 2 + - 2/27 z y x + 1/27 z x + 1/36 y x - 1/48 y x z + 1/36 y x z + + 2 2 2 3 2 3 + - 1/36 y x z + 1/18 y x z - 1/54 y x + 1/27 y x + 2/27 x z + + 2 2 3 3 2 2 2 2 2 + - 1/27 x z + 1/54 x z - 1/27 x z - 1/72 x z + 1/36 x z - 1/72 y x + + 2 2 4 3 4 3 4 2 4 + + 1/27 y x + 1/72 z x - 1/54 z x - 2/27 z x - 1/27 y x + 1/72 y x + + 2 3 3 3 2 2 4 + - 1/36 y x , COEFF(-1, 1, -1) = - 4/27 y x z + 1/24 z y x + + 4 2 3 3 2 3 3 3 3 + - 8/27 z y x + 1/18 y x z - 1/9 z y x + 8/27 z y x + 2/27 y x + + 3 4 2 2 3 3 2 3 2 4 + - 2/27 y x - 1/24 z y x - 4/27 y x + 1/9 z y x + 1/9 z y x + + 3 4 2 4 3 2 4 3 2 3 3 + + 4/27 z y x - 1/9 z y x - 1/18 z y x + 1/18 x z - 2/27 x z + + 4 16 3 2 2 3 16 + + 8/27 x + 2/27 x + -- y x z + 4/9 y x z - 2/9 y x z + -- y x + 27 27 + + 2 2 2 2 3 4 3 3 2 2 2 3 + - 1/6 y x z + 1/18 z y x - 1/18 y x z + 2/9 y x z + + 3 2 3 3 2 2 3 3 4 3 4 16 2 3 + + 8/27 y x z - 2/9 y x z - 2/27 z y x + 4/27 z y x - -- y x z + 27 + + 16 3 2 3 2 3 3 3 16 3 3 3 + - -- z y x + 2/9 y x z + 2/27 y x z + -- z y x - 4/27 z y x + 27 27 + + 3 3 3 2 32 32 2 4 + - 8/27 y x z - 2/27 x - 8/27 x - -- y x z + -- z y x - 4/27 z x + 27 27 + + 2 2 2 2 2 2 2 2 + - 2/9 y x + 1/6 y x z - 4/9 y x z + 4/9 y x z - 4/9 y x z + + 3 2 3 16 16 2 2 3 3 + + 8/27 y x - 8/27 y x - -- x z + -- x z - 8/27 x z + 8/27 x z + 27 27 + + 2 2 2 2 2 16 2 2 4 3 4 + + 2/9 x z - 2/9 x z + 2/9 y x - -- y x - 1/18 z x + 2/27 z x + 27 + + 3 4 2 4 2 3 + + 4/27 z x + 4/27 y x - 1/18 y x + 1/18 y x , COEFF(0, 1, -1) = + + 2 2 4 4 3 4 2 4 3 4 + - 1/16 z y x + 4/9 z y x + 1/9 y x - 1/6 z y x - 2/9 z y x + + 2 4 3 2 4 4 3 3 + + 1/6 z y x + 1/12 z y x - 1/9 x + 4/9 y z - 8/9 y + 8/9 z + + 2 2 2 2 3 4 2 2 3 3 2 3 + + 5/16 y x z - 1/12 z y x - 5/12 y x z - 5/9 y x z + + 3 2 2 3 3 4 3 4 2 3 3 2 + + 5/12 y x z + 1/9 z y x - 2/9 z y x + 10/9 y x z + 10/9 z y x + + 3 3 2 2 2 2 + - 4/9 z + 4/9 y + 1/3 y + 1/3 z + 5/9 x - 20/9 z y x + 16/9 y z + + 4 2 2 2 2 3 2 2 + - 4/9 + 2/9 z x + 5/6 y x z - 5/6 y x z - 5/9 y x - 2/3 y z + + 3 2 2 3 2 3 2 3 2 + - 1/3 y z - 10/9 x z - 8/9 y z + 1/3 y z + 5/9 x z + 2/3 y z + + 2 2 2 2 2 2 2 2 4 3 4 + - 5/12 x z - 1/4 y z - 5/12 y x + 10/9 y x + 1/12 z x - 1/9 z x + + 3 4 2 4 3 3 + - 8/9 z y - 2/9 y x + 1/12 y x , COEFF(1, 1, -1) = 4/27 y x z + + 2 2 4 4 2 3 3 2 3 3 + + 1/24 z y x - 8/27 z y x - 1/18 y x z + 1/9 z y x - 8/27 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 2/27 y x - 2/27 y x + 1/24 z y x + 4/27 y x - 1/9 z y x + + 2 4 3 4 2 4 3 2 4 3 2 + + 1/9 z y x + 4/27 z y x - 1/9 z y x - 1/18 z y x - 1/18 x z + + 3 3 4 16 3 2 2 3 + + 2/27 x z - 8/27 x + 2/27 x - -- y x z - 4/9 y x z + 2/9 y x z + 27 + + 16 2 2 2 2 3 4 3 3 2 2 2 3 + - -- y x - 1/6 y x z + 1/18 z y x + 1/18 y x z + 2/9 y x z + 27 + + 3 2 3 3 2 2 3 3 4 3 4 16 2 3 + + 8/27 y x z - 2/9 y x z - 2/27 z y x + 4/27 z y x - -- y x z + 27 + + 16 3 2 3 2 3 3 3 16 3 3 3 + - -- z y x - 2/9 y x z - 2/27 y x z - -- z y x + 4/27 z y x + 27 27 + + 3 3 3 2 32 32 2 4 + + 8/27 y x z + 2/27 x - 8/27 x + -- y x z + -- z y x - 4/27 z x + 27 27 + + 2 2 2 2 2 2 2 2 + + 2/9 y x - 1/6 y x z - 4/9 y x z + 4/9 y x z + 4/9 y x z + + 3 2 3 16 16 2 2 3 3 + + 8/27 y x + 8/27 y x + -- x z + -- x z - 8/27 x z - 8/27 x z + 27 27 + + 2 2 2 2 2 16 2 2 4 3 4 + + 2/9 x z + 2/9 x z + 2/9 y x - -- y x - 1/18 z x + 2/27 z x + 27 + + 3 4 2 4 2 3 + - 4/27 z x + 4/27 y x - 1/18 y x - 1/18 y x , COEFF(2, 1, -1) = + + 3 3 2 2 4 4 2 3 3 2 3 + - 2/27 y x z - 1/96 z y x + 2/27 z y x + 1/36 y x z - 1/18 z y x + + 3 3 3 3 4 2 2 3 3 + + 4/27 z y x + 1/27 y x + 1/54 y x - 1/48 z y x - 2/27 y x + + 2 3 2 4 3 4 2 4 + + 1/18 z y x - 1/36 z y x - 1/27 z y x + 1/36 z y x + + 3 2 4 3 2 3 3 4 3 + + 1/72 z y x + 1/36 x z - 1/27 x z + 1/27 x - 1/54 x + 2/27 y x z + + 2 2 3 2 2 2 2 3 4 + + 1/18 y x z - 1/36 y x z + 2/27 y x + 1/96 y x z - 1/72 z y x + + 3 3 2 2 2 3 3 2 3 3 2 2 + - 1/36 y x z - 1/72 y x z - 1/54 y x z + 1/72 y x z + + 3 3 4 3 4 2 3 3 2 + + 1/54 z y x - 1/27 z y x + 1/27 y x z + 1/27 z y x + + 3 2 3 3 3 3 3 3 3 3 + + 1/36 y x z + 1/27 y x z + 2/27 z y x - 2/27 z y x - 1/27 y x z + + 3 2 2 4 2 + - 1/27 x + 1/54 x - 4/27 y x z - 2/27 z y x + 1/27 z x - 1/36 y x + + 2 2 2 2 2 2 2 3 2 + + 1/48 y x z + 1/36 y x z - 1/36 y x z - 1/18 y x z - 1/54 y x + + 3 2 2 3 3 2 2 + - 1/27 y x - 2/27 x z - 1/27 x z + 1/54 x z + 1/27 x z - 1/72 x z + + 2 2 2 2 2 4 3 4 3 + - 1/36 x z - 1/72 y x + 1/27 y x + 1/72 z x - 1/54 z x + 2/27 z x + + 4 2 4 2 3 3 3 + - 1/27 y x + 1/72 y x + 1/36 y x , COEFF(-2, 2, -1) = - 1/216 y x z + + 2 2 4 4 2 3 3 2 3 + + 1/192 z y x - 1/216 z y x + 1/72 y x z - 1/36 z y x + + 3 3 3 3 4 2 2 3 3 + + 1/108 z y x + 1/108 y x - 1/216 y x - 1/96 z y x - 1/216 y x + + 2 3 2 4 3 4 2 4 + + 1/288 z y x + 1/72 z y x + 1/432 z y x - 1/576 z y x + + 3 2 4 3 2 3 3 4 + - 1/144 z y x + 1/288 x z - 1/216 x z + 1/216 x + 1/432 x + + 3 2 2 3 2 2 2 + + 1/216 y x z + 1/36 y x z - 1/72 y x z + 1/216 y x - 1/192 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + + 1/288 z y x - 1/144 y x z + 1/144 y x z + 1/216 y x z + + 3 2 2 3 3 4 3 4 2 3 + - 1/288 y x z - 1/216 z y x + 1/108 z y x - 1/432 y x z + + 3 2 3 2 3 3 3 3 + - 1/108 z y x + 1/144 y x z + 1/108 y x z + 1/54 z y x + + 3 3 3 3 3 2 + - 1/54 z y x - 1/108 y x z - 1/216 x - 1/432 x - 1/108 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x - 1/216 z x - 1/72 y x + 1/96 y x z - 1/72 y x z + + 2 2 2 3 2 3 + + 1/576 y x z - 1/288 y x z + 1/216 y x - 1/108 y x - 1/108 x z + + 2 2 3 3 2 2 2 + + 1/216 x z - 1/432 x z + 1/216 x z + 1/576 x z - 1/288 x z + + 2 2 2 2 4 3 4 3 + + 1/144 y x - 1/432 y x - 1/576 z x + 1/432 z x + 1/108 z x + + 4 2 4 2 3 3 3 + + 1/432 y x - 1/144 y x + 1/72 y x , COEFF(-1, 2, -1) = 1/108 y x z + + 2 2 4 4 2 3 3 2 3 3 + - 1/48 z y x + 1/54 z y x - 1/36 y x z + 1/18 z y x - 1/54 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 1/54 y x + 1/54 y x + 1/48 z y x + 1/108 y x - 1/144 z y x + + 2 4 3 4 2 4 3 2 4 + - 1/18 z y x - 1/108 z y x + 1/144 z y x + 1/36 z y x + + 3 2 3 3 4 3 2 + - 1/144 x z + 1/108 x z - 1/27 x - 1/108 x - 1/27 y x z - 2/9 y x z + + 2 3 2 2 2 2 3 4 3 3 2 + + 1/9 y x z - 1/27 y x + 1/12 y x z - 1/72 z y x + 1/72 y x z + + 2 2 3 3 2 3 3 2 2 3 3 4 + - 1/9 y x z - 2/27 y x z + 1/18 y x z + 1/54 z y x + + 3 4 2 3 3 2 3 2 + - 1/27 z y x + 1/27 y x z + 4/27 z y x - 1/18 y x z + + 3 3 3 3 3 3 3 3 3 + - 1/54 y x z - 4/27 z y x + 1/27 z y x + 2/27 y x z + 1/108 x + + 2 2 4 2 2 2 + + 1/27 x + 2/27 y x z - 2/27 z y x + 1/54 z x + 1/9 y x - 1/12 y x z + + 2 2 2 2 2 3 2 3 + + 2/9 y x z - 1/36 y x z + 1/36 y x z - 2/27 y x + 2/27 y x + + 2 2 3 3 2 2 2 + + 2/27 x z - 2/27 x z + 1/27 x z - 1/27 x z - 1/36 x z + 1/36 x z + + 2 2 2 2 4 3 4 3 + - 1/9 y x + 1/27 y x + 1/144 z x - 1/108 z x - 1/54 z x + + 4 2 4 2 3 2 2 4 + - 1/108 y x + 1/36 y x - 1/36 y x , COEFF(0, 2, -1) = 1/32 z y x + + 4 3 4 2 4 3 4 2 4 + - 1/36 z y x - 1/36 y x + 1/12 z y x + 1/72 z y x - 1/96 z y x + + 3 2 4 4 3 3 2 2 2 + - 1/24 z y x + 1/72 x - 1/9 y z + 1/18 y - 1/9 z - 5/32 y x z + + 2 3 4 2 2 3 3 2 3 3 2 2 + + 1/48 z y x + 5/24 y x z + 5/36 y x z - 5/48 y x z + + 3 3 4 3 4 2 3 3 2 3 + - 1/36 z y x + 1/18 z y x - 5/72 y x z - 5/18 z y x + 1/18 z + + 3 2 2 2 2 4 + - 1/9 y - 1/6 y - 1/24 z - 5/72 x + 5/36 z y x - 1/9 y z - 1/36 z x + + 2 2 2 2 3 2 2 3 2 + - 5/12 y x z + 5/96 y x z + 5/36 y x + 1/3 y z + 1/12 y z + + 2 3 2 3 2 3 2 + + 5/36 x z + 1/18 + 1/18 y z - 1/6 y z - 5/72 x z - 1/24 y z + + 2 2 2 2 2 2 2 2 4 + + 5/96 x z + 1/8 y z + 5/24 y x - 5/72 y x - 1/96 z x + + 3 4 3 4 2 4 + + 1/72 z x + 2/9 z y + 1/72 y x - 1/24 y x , COEFF(1, 2, -1) = + + 3 3 2 2 4 4 2 3 3 + - 1/108 y x z - 1/48 z y x + 1/54 z y x + 1/36 y x z + + 2 3 3 3 3 3 4 2 2 3 + - 1/18 z y x + 1/54 z y x + 1/54 y x + 1/54 y x - 1/48 z y x + + 3 2 3 2 4 3 4 + - 1/108 y x + 1/144 z y x - 1/18 z y x - 1/108 z y x + + 2 4 3 2 4 3 2 3 3 + + 1/144 z y x + 1/36 z y x + 1/144 x z - 1/108 x z + 1/27 x + + 4 3 2 2 3 + - 1/108 x + 1/27 y x z + 2/9 y x z - 1/9 y x z + 1/27 y x + + 2 2 2 2 3 4 3 3 2 2 2 3 + + 1/12 y x z - 1/72 z y x - 1/72 y x z - 1/9 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 2/27 y x z + 1/18 y x z + 1/54 z y x - 1/27 z y x + + 2 3 3 2 3 2 3 3 3 3 + + 1/27 y x z + 4/27 z y x + 1/18 y x z + 1/54 y x z + 4/27 z y x + + 3 3 3 3 3 2 + - 1/27 z y x - 2/27 y x z - 1/108 x + 1/27 x - 2/27 y x z + + 2 4 2 2 2 2 2 + - 2/27 z y x + 1/54 z x - 1/9 y x + 1/12 y x z + 2/9 y x z + + 2 2 2 3 2 3 + - 1/36 y x z - 1/36 y x z - 2/27 y x - 2/27 y x - 2/27 x z + + 2 2 3 3 2 2 2 2 2 + - 2/27 x z + 1/27 x z + 1/27 x z - 1/36 x z - 1/36 x z - 1/9 y x + + 2 2 4 3 4 3 4 + + 1/27 y x + 1/144 z x - 1/108 z x + 1/54 z x - 1/108 y x + + 2 4 2 3 3 3 + + 1/36 y x + 1/36 y x , COEFF(2, 2, -1) = 1/216 y x z + + 2 2 4 4 2 3 3 2 3 + + 1/192 z y x - 1/216 z y x - 1/72 y x z + 1/36 z y x + + 3 3 3 3 4 2 2 3 3 + - 1/108 z y x - 1/108 y x - 1/216 y x + 1/96 z y x + 1/216 y x + + 2 3 2 4 3 4 2 4 + - 1/288 z y x + 1/72 z y x + 1/432 z y x - 1/576 z y x + + 3 2 4 3 2 3 3 4 + - 1/144 z y x - 1/288 x z + 1/216 x z - 1/216 x + 1/432 x + + 3 2 2 3 2 2 2 + - 1/216 y x z - 1/36 y x z + 1/72 y x z - 1/216 y x - 1/192 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + + 1/288 z y x + 1/144 y x z + 1/144 y x z + 1/216 y x z + + 3 2 2 3 3 4 3 4 2 3 + - 1/288 y x z - 1/216 z y x + 1/108 z y x - 1/432 y x z + + 3 2 3 2 3 3 3 3 + - 1/108 z y x - 1/144 y x z - 1/108 y x z - 1/54 z y x + + 3 3 3 3 3 2 + + 1/54 z y x + 1/108 y x z + 1/216 x - 1/432 x + 1/108 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x - 1/216 z x + 1/72 y x - 1/96 y x z - 1/72 y x z + + 2 2 2 3 2 3 + + 1/576 y x z + 1/288 y x z + 1/216 y x + 1/108 y x + 1/108 x z + + 2 2 3 3 2 2 2 + + 1/216 x z - 1/432 x z - 1/216 x z + 1/576 x z + 1/288 x z + + 2 2 2 2 4 3 4 3 + + 1/144 y x - 1/432 y x - 1/576 z x + 1/432 z x - 1/108 z x + + 4 2 4 2 3 3 3 + + 1/432 y x - 1/144 y x - 1/72 y x , COEFF(-2, -2, 0) = 1/144 y x z + + 4 2 3 3 2 3 3 + + 5/576 z y x + 1/48 y x z - 5/96 z y x - 5/288 z y x + + 2 4 3 4 3 2 4 3 3 + + 5/192 z y x - 1/288 z y x - 1/96 z y x - 1/144 x z + + 3 2 2 3 2 2 3 + - 1/144 y x z + 5/96 y x z - 1/48 y x z + 1/96 y x z + + 3 2 3 3 3 4 3 4 2 3 + - 1/144 y x z + 1/144 z y x - 5/288 z y x + 1/288 y x z + + 3 2 3 3 3 3 3 3 + + 5/288 z y x - 1/72 y x z - 5/144 z y x + 5/144 z y x + + 3 3 2 4 2 2 + + 1/72 y x z + 5/288 y x z - 5/576 z y x - 5/576 z x - 5/192 y x z + + 2 2 3 3 3 4 + - 5/288 x z + 5/576 x z - 1/288 x z + 1/144 x z + 1/288 z x + + 3 3 3 4 + + 5/288 z x , COEFF(-1, -2, 0) = - 1/72 y x z - 5/144 z y x + + 2 3 3 2 3 3 2 4 + - 1/24 y x z + 5/48 z y x + 5/144 z y x - 5/48 z y x + + 3 4 3 2 4 3 3 3 2 + + 1/72 z y x + 1/24 z y x + 1/72 x z + 1/18 y x z - 5/12 y x z + + 2 3 2 2 3 3 2 3 3 3 4 3 4 + + 1/6 y x z - 1/6 y x z + 1/9 y x z - 1/36 z y x + 5/72 z y x + + 2 3 3 2 3 3 3 3 3 3 + - 1/18 y x z - 5/18 z y x + 1/36 y x z + 5/18 z y x - 5/72 z y x + + 3 3 2 4 2 2 + - 1/9 y x z - 5/36 y x z + 5/36 z y x + 5/144 z x + 5/12 y x z + + 2 2 3 3 3 4 3 + + 5/36 x z - 5/36 x z + 1/18 x z - 1/18 x z - 1/72 z x - 5/144 z x , + + 2 3 25 2 3 3 4 2 + COEFF(0, -2, 0) = 5/48 y x z - -- z y x + 1/24 z y x + 5/8 y z + 96 + + 3 2 3 3 4 2 3 4 + + 5/24 y z - 5/24 y x z + 1/48 z x - 5/48 x z - 5/96 z x + + 3 2 4 3 3 25 2 2 3 4 + - 1/16 z y x - 1/12 y z + 1/12 z - -- y x z - 5/48 z y x + 32 + + 2 2 3 2 3 25 3 2 2 4 3 4 + + 5/16 y x z - 1/4 y z + -- z y x + 5/32 z y x - 1/48 z y x + 48 + + 3 3 3 4 25 2 + + 1/6 y z - 5/24 z - 5/12 z y + 5/96 z y x + -- x z, COEFF(1, -2, 0) + 96 + + 3 3 4 2 3 3 2 3 + = 1/72 y x z - 5/144 z y x + 1/24 y x z - 5/48 z y x + + 3 2 4 3 4 3 2 4 3 3 + - 5/144 z y x - 5/48 z y x + 1/72 z y x + 1/24 z y x - 1/72 x z + + 3 2 2 3 2 2 3 3 2 3 + - 1/18 y x z + 5/12 y x z - 1/6 y x z - 1/6 y x z + 1/9 y x z + + 3 3 4 3 4 2 3 3 2 + - 1/36 z y x + 5/72 z y x - 1/18 y x z - 5/18 z y x + + 3 3 3 3 3 3 3 3 + - 1/36 y x z - 5/18 z y x + 5/72 z y x + 1/9 y x z + 5/36 y x z + + 2 4 2 2 2 + + 5/36 z y x + 5/144 z x + 5/12 y x z - 5/36 x z - 5/36 x z + + 2 3 3 3 4 3 + + 1/18 x z + 1/18 x z - 1/72 z x + 5/144 z x , COEFF(2, -2, 0) = + + 3 3 4 2 3 3 2 3 + - 1/144 y x z + 5/576 z y x - 1/48 y x z + 5/96 z y x + + 3 2 4 3 4 3 2 4 + + 5/288 z y x + 5/192 z y x - 1/288 z y x - 1/96 z y x + + 3 3 3 2 2 3 2 2 3 + + 1/144 x z + 1/144 y x z - 5/96 y x z + 1/48 y x z + 1/96 y x z + + 3 2 3 3 3 4 3 4 2 3 + - 1/144 y x z + 1/144 z y x - 5/288 z y x + 1/288 y x z + + 3 2 3 3 3 3 3 3 + + 5/288 z y x + 1/72 y x z + 5/144 z y x - 5/144 z y x + + 3 3 2 4 2 2 + - 1/72 y x z - 5/288 y x z - 5/576 z y x - 5/576 z x - 5/192 y x z + + 2 2 3 3 3 4 + + 5/288 x z + 5/576 x z - 1/288 x z - 1/144 x z + 1/288 z x + + 3 3 3 4 + - 5/288 z x , COEFF(-2, -1, 0) = - 1/9 y x z - 5/36 z y x + + 2 3 3 2 3 3 2 4 3 4 + - 1/24 y x z + 5/48 z y x + 5/18 z y x - 5/96 z y x + 1/18 z y x + + 3 2 4 3 3 3 2 2 3 + + 1/48 z y x + 1/18 x z + 1/9 y x z - 5/48 y x z + 1/24 y x z + + 2 2 3 3 2 3 3 3 4 3 4 + - 1/48 y x z + 1/36 y x z - 1/36 z y x + 5/72 z y x + + 2 3 3 2 3 3 3 3 3 3 + - 1/18 y x z - 5/72 z y x + 1/18 y x z + 5/36 z y x - 5/36 z y x + + 3 3 2 4 2 2 + - 1/18 y x z - 5/18 y x z + 5/36 z y x + 5/72 z x + 5/96 y x z + + 2 2 3 3 3 4 3 + + 5/36 x z - 5/72 x z + 1/36 x z - 1/18 x z - 1/36 z x - 5/36 z x , + + 3 3 4 2 3 3 2 3 + COEFF(-1, -1, 0) = 2/9 y x z + 5/9 z y x + 1/12 y x z - 5/24 z y x + + 3 2 4 3 4 3 2 4 3 3 + - 5/9 z y x + 5/24 z y x - 2/9 z y x - 1/12 z y x - 1/9 x z + + 3 2 2 3 2 2 3 3 2 3 + - 8/9 y x z + 5/6 y x z - 1/3 y x z + 1/3 y x z - 4/9 y x z + + 3 3 4 3 4 2 3 3 2 3 3 3 + + 1/9 z y x - 5/18 z y x + 8/9 y x z + 10/9 z y x - 1/9 y x z + + 3 3 3 3 3 2 + - 10/9 z y x + 5/18 z y x + 4/9 y x z + 20/9 y x z - 20/9 z y x + + 4 2 2 2 2 3 3 + - 5/18 z x - 5/6 y x z - 10/9 x z + 10/9 x z - 4/9 x z + 4/9 x z + + 3 4 3 3 3 3 4 + + 1/9 z x + 5/18 z x , COEFF(0, -1, 0) = 5/3 z - 2/3 z - 1/6 z y x + + 25 2 3 4 4 2 4 3 + - 10/3 y z - -- x z - 1/6 z x + 5/12 z x - 5/16 z y x + 4/3 y z + 12 + + 3 4 25 3 2 2 3 3 2 3 2 3 + + 5/12 z y x - -- z y x + 5/6 x z + 5/6 y x z + 1/2 y z + 12 + + 2 3 2 4 3 3 4 4 + + 25/6 z y x + 1/8 z y x + 5/3 z y + 1/3 z y x - 5/6 z y x + + 2 3 3 2 2 3 2 3 25 2 2 + - 5/4 y z - 2/3 y z - 5/8 y x z - 5/3 y x z + -- y x z, + 16 + + 3 3 4 2 3 3 2 3 + COEFF(1, -1, 0) = - 2/9 y x z + 5/9 z y x - 1/12 y x z + 5/24 z y x + + 3 2 4 3 4 3 2 4 3 3 + + 5/9 z y x + 5/24 z y x - 2/9 z y x - 1/12 z y x + 1/9 x z + + 3 2 2 3 2 2 3 3 2 3 + + 8/9 y x z - 5/6 y x z + 1/3 y x z + 1/3 y x z - 4/9 y x z + + 3 3 4 3 4 2 3 3 2 3 3 3 + + 1/9 z y x - 5/18 z y x + 8/9 y x z + 10/9 z y x + 1/9 y x z + + 3 3 3 3 3 2 + + 10/9 z y x - 5/18 z y x - 4/9 y x z - 20/9 y x z - 20/9 z y x + + 4 2 2 2 2 3 3 + - 5/18 z x - 5/6 y x z + 10/9 x z + 10/9 x z - 4/9 x z - 4/9 x z + + 3 4 3 3 3 4 + + 1/9 z x - 5/18 z x , COEFF(2, -1, 0) = 1/9 y x z - 5/36 z y x + + 2 3 3 2 3 3 2 4 3 4 + + 1/24 y x z - 5/48 z y x - 5/18 z y x - 5/96 z y x + 1/18 z y x + + 3 2 4 3 3 3 2 2 3 + + 1/48 z y x - 1/18 x z - 1/9 y x z + 5/48 y x z - 1/24 y x z + + 2 2 3 3 2 3 3 3 4 3 4 + - 1/48 y x z + 1/36 y x z - 1/36 z y x + 5/72 z y x + + 2 3 3 2 3 3 3 3 3 3 + - 1/18 y x z - 5/72 z y x - 1/18 y x z - 5/36 z y x + 5/36 z y x + + 3 3 2 4 2 2 + + 1/18 y x z + 5/18 y x z + 5/36 z y x + 5/72 z x + 5/96 y x z + + 2 2 3 3 3 4 3 + - 5/36 x z - 5/72 x z + 1/36 x z + 1/18 x z - 1/36 z x + 5/36 z x , + + 3 3 3 2 3 3 4 3 + COEFF(-2, 0, 0) = 5/24 y x z - 1/24 y x z - 5/48 z y x - 5/24 y x z + + 3 3 4 25 4 3 4 3 3 25 3 + + 1/24 z y x + -- z y x - 5/48 z y x + 1/12 y x z - -- z y x + 96 48 + + 3 2 2 3 25 25 2 3 + + 5/48 z y x + 5/48 y x z + -- y x z - -- z y x - 5/24 z y x + 48 96 + + 3 3 3 3 3 25 3 3 2 + - 1/12 y x z + 5/24 z y x , COEFF(-1, 0, 0) = -- z y x - 5/3 z y x + 24 + + 3 3 3 3 2 3 2 3 4 3 4 + + 1/6 y x z + 2/3 y x z + 25/6 z y x + 5/12 z y x + 5/12 z y x + + 3 3 3 3 3 3 2 3 + - 5/12 y x z + 5/3 z y x - 5/12 z y x + 5/3 y x z - 5/3 y x z + + 25 4 3 3 4 3 3 + - -- z y x - 25/6 y x z - 1/6 z y x - 2/3 y x z , COEFF(0, 0, 0) = + 24 + + 3 3 125 2 25 4 3 3 4 3 2 3 3 4 + y z - --- z y x + -- z y x + 1/4 z y x - 5/4 y x z - 5/8 z y x + 16 16 + + 2 3 3 4 3 3 + + 25/8 y x z + 25/4 y z - 5/8 z y x - 5/2 z y - 5/2 y z + + 3 2 3 2 3 4 + + 25/8 z y x , COEFF(1, 0, 0) = - 5/3 z y x + 5/12 z y x + + 3 3 3 3 4 25 3 3 2 + + 5/12 y x z - 1/6 z y x - -- z y x - 5/3 z y x + 25/6 z y x + 24 + + 3 3 3 2 3 25 4 3 4 2 3 + + 5/12 z y x + 2/3 y x z - -- z y x + 5/12 z y x - 5/3 y x z + 24 + + 3 3 3 3 3 3 + - 1/6 y x z - 5/3 y x z + 25/6 y x z + 2/3 y x z , COEFF(2, 0, 0) = + + 2 3 3 2 3 3 4 3 3 3 + 5/48 y x z - 1/24 y x z - 5/48 z y x + 5/24 z y x - 5/24 z y x + + 3 3 3 3 3 4 25 2 25 + - 1/12 y x z - 5/24 y x z - 5/48 z y x - -- z y x - -- y x z + 96 48 + + 3 2 3 3 3 3 3 3 4 25 3 + + 5/48 z y x + 5/24 y x z + 1/12 y x z + 1/24 z y x + -- z y x + 48 + + 25 4 3 3 4 2 3 3 + + -- z y x , COEFF(-2, 1, 0) = - 1/9 y x z - 5/36 z y x + 1/24 y x z + 96 + + 2 3 3 2 4 3 4 3 2 4 + - 5/48 z y x + 5/18 z y x + 5/96 z y x + 1/18 z y x - 1/48 z y x + + 3 3 3 2 2 3 2 2 3 + - 1/18 x z + 1/9 y x z + 5/48 y x z - 1/24 y x z + 1/48 y x z + + 3 2 3 3 3 4 3 4 2 3 + + 1/36 y x z - 1/36 z y x + 5/72 z y x - 1/18 y x z + + 3 2 3 3 3 3 3 3 3 3 + - 5/72 z y x + 1/18 y x z + 5/36 z y x - 5/36 z y x - 1/18 y x z + + 2 4 2 2 + - 5/18 y x z + 5/36 z y x - 5/72 z x - 5/96 y x z - 5/36 x z + + 2 2 3 3 3 4 3 + + 5/72 x z - 1/36 x z + 1/18 x z + 1/36 z x + 5/36 z x , + + 3 3 4 2 3 3 2 3 + COEFF(-1, 1, 0) = 2/9 y x z + 5/9 z y x - 1/12 y x z + 5/24 z y x + + 3 2 4 3 4 3 2 4 3 3 + - 5/9 z y x - 5/24 z y x - 2/9 z y x + 1/12 z y x + 1/9 x z + + 3 2 2 3 2 2 3 3 2 3 + - 8/9 y x z - 5/6 y x z + 1/3 y x z - 1/3 y x z - 4/9 y x z + + 3 3 4 3 4 2 3 3 2 3 3 3 + + 1/9 z y x - 5/18 z y x + 8/9 y x z + 10/9 z y x - 1/9 y x z + + 3 3 3 3 3 2 + - 10/9 z y x + 5/18 z y x + 4/9 y x z + 20/9 y x z - 20/9 z y x + + 4 2 2 2 2 3 3 + + 5/18 z x + 5/6 y x z + 10/9 x z - 10/9 x z + 4/9 x z - 4/9 x z + + 3 4 3 3 4 4 + - 1/9 z x - 5/18 z x , COEFF(0, 1, 0) = 5/12 z y x - 5/12 z x + + 2 3 2 4 2 4 2 3 25 3 2 + + 25/6 z y x - 1/8 z y x + 5/16 z y x - 5/6 x z - -- z y x + 12 + + 3 2 3 3 3 3 2 2 3 4 + + 5/6 y x z - 2/3 y z + 5/3 z y + 5/8 y x z - 5/6 z y x + + 3 4 3 2 3 3 4 2 + + 1/3 z y x + 4/3 y z - 1/2 y z + 1/6 z x - 5/3 z + 5/4 y z + + 2 3 25 2 3 25 2 2 3 3 4 + - 5/3 y x z + -- x z - 10/3 y z + 2/3 z - -- y x z - 1/6 z y x , + 12 16 + + 3 3 4 2 3 3 2 3 + COEFF(1, 1, 0) = - 2/9 y x z + 5/9 z y x + 1/12 y x z - 5/24 z y x + + 3 2 4 3 4 3 2 4 3 3 + + 5/9 z y x - 5/24 z y x - 2/9 z y x + 1/12 z y x - 1/9 x z + + 3 2 2 3 2 2 3 3 2 3 + + 8/9 y x z + 5/6 y x z - 1/3 y x z - 1/3 y x z - 4/9 y x z + + 3 3 4 3 4 2 3 3 2 3 3 3 + + 1/9 z y x - 5/18 z y x + 8/9 y x z + 10/9 z y x + 1/9 y x z + + 3 3 3 3 3 2 + + 10/9 z y x - 5/18 z y x - 4/9 y x z - 20/9 y x z - 20/9 z y x + + 4 2 2 2 2 3 3 + + 5/18 z x + 5/6 y x z - 10/9 x z - 10/9 x z + 4/9 x z + 4/9 x z + + 3 4 3 3 3 4 + - 1/9 z x + 5/18 z x , COEFF(2, 1, 0) = 1/9 y x z - 5/36 z y x + + 2 3 3 2 3 3 2 4 3 4 + - 1/24 y x z + 5/48 z y x - 5/18 z y x + 5/96 z y x + 1/18 z y x + + 3 2 4 3 3 3 2 2 3 + - 1/48 z y x + 1/18 x z - 1/9 y x z - 5/48 y x z + 1/24 y x z + + 2 2 3 3 2 3 3 3 4 3 4 + + 1/48 y x z + 1/36 y x z - 1/36 z y x + 5/72 z y x + + 2 3 3 2 3 3 3 3 3 3 + - 1/18 y x z - 5/72 z y x - 1/18 y x z - 5/36 z y x + 5/36 z y x + + 3 3 2 4 2 2 + + 1/18 y x z + 5/18 y x z + 5/36 z y x - 5/72 z x - 5/96 y x z + + 2 2 3 3 3 4 3 + + 5/36 x z + 5/72 x z - 1/36 x z - 1/18 x z + 1/36 z x - 5/36 z x , + + 3 3 4 2 3 3 + COEFF(-2, 2, 0) = 1/144 y x z + 5/576 z y x - 1/48 y x z + + 2 3 3 2 4 3 4 + + 5/96 z y x - 5/288 z y x - 5/192 z y x - 1/288 z y x + + 3 2 4 3 3 3 2 2 3 + + 1/96 z y x + 1/144 x z - 1/144 y x z - 5/96 y x z + 1/48 y x z + + 2 2 3 3 2 3 3 3 4 3 4 + - 1/96 y x z - 1/144 y x z + 1/144 z y x - 5/288 z y x + + 2 3 3 2 3 3 3 3 + + 1/288 y x z + 5/288 z y x - 1/72 y x z - 5/144 z y x + + 3 3 3 3 2 4 + + 5/144 z y x + 1/72 y x z + 5/288 y x z - 5/576 z y x + 5/576 z x + + 2 2 2 2 3 3 + + 5/192 y x z + 5/288 x z - 5/576 x z + 1/288 x z - 1/144 x z + + 3 4 3 3 3 + - 1/288 z x - 5/288 z x , COEFF(-1, 2, 0) = - 1/72 y x z + + 4 2 3 3 2 3 3 + - 5/144 z y x + 1/24 y x z - 5/48 z y x + 5/144 z y x + + 2 4 3 4 3 2 4 3 3 3 + + 5/48 z y x + 1/72 z y x - 1/24 z y x - 1/72 x z + 1/18 y x z + + 2 2 3 2 2 3 3 2 3 3 3 4 + + 5/12 y x z - 1/6 y x z + 1/6 y x z + 1/9 y x z - 1/36 z y x + + 3 4 2 3 3 2 3 3 3 3 + + 5/72 z y x - 1/18 y x z - 5/18 z y x + 1/36 y x z + 5/18 z y x + + 3 3 3 3 2 4 + - 5/72 z y x - 1/9 y x z - 5/36 y x z + 5/36 z y x - 5/144 z x + + 2 2 2 2 3 3 + - 5/12 y x z - 5/36 x z + 5/36 x z - 1/18 x z + 1/18 x z + + 3 4 3 2 3 4 + + 1/72 z x + 5/144 z x , COEFF(0, 2, 0) = 5/48 x z + 5/96 z x + + 3 3 4 2 3 2 4 + - 1/12 y z - 5/48 z y x + 5/48 y x z - 5/8 y z + 5/96 z y x + + 25 3 2 3 2 4 3 4 3 4 2 4 + + -- z y x + 1/16 z y x - 1/48 z y x - 1/48 z x - 5/32 z y x + 48 + + 25 2 2 2 3 25 2 2 2 3 + - -- x z - 5/16 y x z + -- y x z + 5/24 z + 1/4 y z + 96 32 + + 3 2 3 3 3 3 3 25 2 + - 5/24 y x z + 1/6 y z + 5/24 y z - 5/12 z y - 1/12 z - -- z y x + 96 + + 3 3 4 3 3 4 + + 1/24 z y x , COEFF(1, 2, 0) = 1/72 y x z - 5/144 z y x + + 2 3 3 2 3 3 2 4 + - 1/24 y x z + 5/48 z y x - 5/144 z y x + 5/48 z y x + + 3 4 3 2 4 3 3 3 2 + + 1/72 z y x - 1/24 z y x + 1/72 x z - 1/18 y x z - 5/12 y x z + + 2 3 2 2 3 3 2 3 3 3 4 3 4 + + 1/6 y x z + 1/6 y x z + 1/9 y x z - 1/36 z y x + 5/72 z y x + + 2 3 3 2 3 3 3 3 3 3 + - 1/18 y x z - 5/18 z y x - 1/36 y x z - 5/18 z y x + 5/72 z y x + + 3 3 2 4 2 2 + + 1/9 y x z + 5/36 y x z + 5/36 z y x - 5/144 z x - 5/12 y x z + + 2 2 3 3 3 4 3 + + 5/36 x z + 5/36 x z - 1/18 x z - 1/18 x z + 1/72 z x - 5/144 z x , + + 3 3 4 2 3 3 + COEFF(2, 2, 0) = - 1/144 y x z + 5/576 z y x + 1/48 y x z + + 2 3 3 2 4 3 4 + - 5/96 z y x + 5/288 z y x - 5/192 z y x - 1/288 z y x + + 3 2 4 3 3 3 2 2 3 + + 1/96 z y x - 1/144 x z + 1/144 y x z + 5/96 y x z - 1/48 y x z + + 2 2 3 3 2 3 3 3 4 3 4 + - 1/96 y x z - 1/144 y x z + 1/144 z y x - 5/288 z y x + + 2 3 3 2 3 3 3 3 + + 1/288 y x z + 5/288 z y x + 1/72 y x z + 5/144 z y x + + 3 3 3 3 2 4 + - 5/144 z y x - 1/72 y x z - 5/288 y x z - 5/576 z y x + 5/576 z x + + 2 2 2 2 3 3 + + 5/192 y x z - 5/288 x z - 5/576 x z + 1/288 x z + 1/144 x z + + 3 4 3 3 3 + - 1/288 z x + 5/288 z x , COEFF(-2, -2, 1) = - 1/216 y x z + + 2 2 4 4 2 3 3 2 3 + + 1/192 z y x - 1/216 z y x - 1/72 y x z + 1/36 z y x + + 3 3 3 3 4 2 2 3 3 + + 1/108 z y x - 1/108 y x + 1/216 y x - 1/96 z y x + 1/216 y x + + 2 3 2 4 3 4 2 4 + - 1/288 z y x - 1/72 z y x + 1/432 z y x + 1/576 z y x + + 3 2 4 3 2 3 3 4 + + 1/144 z y x + 1/288 x z + 1/216 x z + 1/216 x + 1/432 x + + 3 2 2 3 2 2 2 + + 1/216 y x z - 1/36 y x z + 1/72 y x z - 1/216 y x - 1/192 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + - 1/288 z y x + 1/144 y x z - 1/144 y x z + 1/216 y x z + + 3 2 2 3 3 4 3 4 2 3 + + 1/288 y x z - 1/216 z y x + 1/108 z y x - 1/432 y x z + + 3 2 3 2 3 3 3 3 + - 1/108 z y x - 1/144 y x z + 1/108 y x z + 1/54 z y x + + 3 3 3 3 3 2 + - 1/54 z y x - 1/108 y x z - 1/216 x - 1/432 x - 1/108 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x + 1/216 z x - 1/72 y x + 1/96 y x z + 1/72 y x z + + 2 2 2 3 2 3 + - 1/576 y x z + 1/288 y x z - 1/216 y x + 1/108 y x + 1/108 x z + + 2 2 3 3 2 2 2 + - 1/216 x z + 1/432 x z - 1/216 x z + 1/576 x z - 1/288 x z + + 2 2 2 2 4 3 4 3 + + 1/144 y x + 1/432 y x - 1/576 z x - 1/432 z x - 1/108 z x + + 4 2 4 2 3 3 3 + - 1/432 y x - 1/144 y x + 1/72 y x , COEFF(-1, -2, 1) = 1/108 y x z + + 2 2 4 4 2 3 3 2 3 3 + - 1/48 z y x + 1/54 z y x + 1/36 y x z - 1/18 z y x - 1/54 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 1/54 y x - 1/54 y x + 1/48 z y x - 1/108 y x + 1/144 z y x + + 2 4 3 4 2 4 3 2 4 + + 1/18 z y x - 1/108 z y x - 1/144 z y x - 1/36 z y x + + 3 2 3 3 4 3 2 + - 1/144 x z - 1/108 x z - 1/27 x - 1/108 x - 1/27 y x z + 2/9 y x z + + 2 3 2 2 2 2 3 4 3 3 2 + - 1/9 y x z + 1/27 y x + 1/12 y x z + 1/72 z y x - 1/72 y x z + + 2 2 3 3 2 3 3 2 2 3 3 4 + + 1/9 y x z - 2/27 y x z - 1/18 y x z + 1/54 z y x + + 3 4 2 3 3 2 3 2 + - 1/27 z y x + 1/27 y x z + 4/27 z y x + 1/18 y x z + + 3 3 3 3 3 3 3 3 3 + - 1/54 y x z - 4/27 z y x + 1/27 z y x + 2/27 y x z + 1/108 x + + 2 2 4 2 2 2 + + 1/27 x + 2/27 y x z - 2/27 z y x - 1/54 z x + 1/9 y x - 1/12 y x z + + 2 2 2 2 2 3 2 3 + - 2/9 y x z + 1/36 y x z - 1/36 y x z + 2/27 y x - 2/27 y x + + 2 2 3 3 2 2 2 + - 2/27 x z + 2/27 x z - 1/27 x z + 1/27 x z - 1/36 x z + 1/36 x z + + 2 2 2 2 4 3 4 3 + - 1/9 y x - 1/27 y x + 1/144 z x + 1/108 z x + 1/54 z x + + 4 2 4 2 3 2 2 4 + + 1/108 y x + 1/36 y x - 1/36 y x , COEFF(0, -2, 1) = 1/32 z y x + + 4 3 4 2 4 3 4 2 4 + - 1/36 z y x + 1/36 y x - 1/12 z y x + 1/72 z y x + 1/96 z y x + + 3 2 4 4 3 3 2 2 2 + + 1/24 z y x + 1/72 x - 1/9 y z - 1/18 y + 1/9 z - 5/32 y x z + + 2 3 4 2 2 3 3 2 3 3 2 2 + - 1/48 z y x - 5/24 y x z + 5/36 y x z + 5/48 y x z + + 3 3 4 3 4 2 3 3 2 3 + - 1/36 z y x + 1/18 z y x - 5/72 y x z - 5/18 z y x - 1/18 z + + 3 2 2 2 2 4 + + 1/9 y - 1/6 y - 1/24 z - 5/72 x + 5/36 z y x - 1/9 y z + 1/36 z x + + 2 2 2 2 3 2 2 3 2 + + 5/12 y x z - 5/96 y x z - 5/36 y x - 1/3 y z - 1/12 y z + + 2 3 2 3 2 3 2 + - 5/36 x z + 1/18 + 1/18 y z + 1/6 y z + 5/72 x z + 1/24 y z + + 2 2 2 2 2 2 2 2 4 + + 5/96 x z + 1/8 y z + 5/24 y x + 5/72 y x - 1/96 z x + + 3 4 3 4 2 4 + - 1/72 z x + 2/9 z y - 1/72 y x - 1/24 y x , COEFF(1, -2, 1) = + + 3 3 2 2 4 4 2 3 3 + - 1/108 y x z - 1/48 z y x + 1/54 z y x - 1/36 y x z + + 2 3 3 3 3 3 4 2 2 3 + + 1/18 z y x + 1/54 z y x - 1/54 y x - 1/54 y x - 1/48 z y x + + 3 2 3 2 4 3 4 + + 1/108 y x - 1/144 z y x + 1/18 z y x - 1/108 z y x + + 2 4 3 2 4 3 2 3 3 + - 1/144 z y x - 1/36 z y x + 1/144 x z + 1/108 x z + 1/27 x + + 4 3 2 2 3 + - 1/108 x + 1/27 y x z - 2/9 y x z + 1/9 y x z - 1/27 y x + + 2 2 2 2 3 4 3 3 2 2 2 3 + + 1/12 y x z + 1/72 z y x + 1/72 y x z + 1/9 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 2/27 y x z - 1/18 y x z + 1/54 z y x - 1/27 z y x + + 2 3 3 2 3 2 3 3 3 3 + + 1/27 y x z + 4/27 z y x - 1/18 y x z + 1/54 y x z + 4/27 z y x + + 3 3 3 3 3 2 + - 1/27 z y x - 2/27 y x z - 1/108 x + 1/27 x - 2/27 y x z + + 2 4 2 2 2 2 2 + - 2/27 z y x - 1/54 z x - 1/9 y x + 1/12 y x z - 2/9 y x z + + 2 2 2 3 2 3 + + 1/36 y x z + 1/36 y x z + 2/27 y x + 2/27 y x + 2/27 x z + + 2 2 3 3 2 2 2 2 2 + + 2/27 x z - 1/27 x z - 1/27 x z - 1/36 x z - 1/36 x z - 1/9 y x + + 2 2 4 3 4 3 4 + - 1/27 y x + 1/144 z x + 1/108 z x - 1/54 z x + 1/108 y x + + 2 4 2 3 3 3 + + 1/36 y x + 1/36 y x , COEFF(2, -2, 1) = 1/216 y x z + + 2 2 4 4 2 3 3 2 3 + + 1/192 z y x - 1/216 z y x + 1/72 y x z - 1/36 z y x + + 3 3 3 3 4 2 2 3 3 + - 1/108 z y x + 1/108 y x + 1/216 y x + 1/96 z y x - 1/216 y x + + 2 3 2 4 3 4 2 4 + + 1/288 z y x - 1/72 z y x + 1/432 z y x + 1/576 z y x + + 3 2 4 3 2 3 3 4 + + 1/144 z y x - 1/288 x z - 1/216 x z - 1/216 x + 1/432 x + + 3 2 2 3 2 2 2 + - 1/216 y x z + 1/36 y x z - 1/72 y x z + 1/216 y x - 1/192 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + - 1/288 z y x - 1/144 y x z - 1/144 y x z + 1/216 y x z + + 3 2 2 3 3 4 3 4 2 3 + + 1/288 y x z - 1/216 z y x + 1/108 z y x - 1/432 y x z + + 3 2 3 2 3 3 3 3 + - 1/108 z y x + 1/144 y x z - 1/108 y x z - 1/54 z y x + + 3 3 3 3 3 2 + + 1/54 z y x + 1/108 y x z + 1/216 x - 1/432 x + 1/108 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x + 1/216 z x + 1/72 y x - 1/96 y x z + 1/72 y x z + + 2 2 2 3 2 3 + - 1/576 y x z - 1/288 y x z - 1/216 y x - 1/108 y x - 1/108 x z + + 2 2 3 3 2 2 2 + - 1/216 x z + 1/432 x z + 1/216 x z + 1/576 x z + 1/288 x z + + 2 2 2 2 4 3 4 3 + + 1/144 y x + 1/432 y x - 1/576 z x - 1/432 z x + 1/108 z x + + 4 2 4 2 3 3 3 + - 1/432 y x - 1/144 y x - 1/72 y x , COEFF(-2, -1, 1) = 2/27 y x z + + 2 2 4 4 2 3 3 2 3 3 + - 1/96 z y x + 2/27 z y x + 1/36 y x z - 1/18 z y x - 4/27 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 1/27 y x - 1/54 y x + 1/48 z y x - 2/27 y x + 1/18 z y x + + 2 4 3 4 2 4 3 2 4 3 2 + + 1/36 z y x - 1/27 z y x - 1/36 z y x - 1/72 z y x - 1/36 x z + + 3 3 4 3 2 2 3 + - 1/27 x z - 1/27 x - 1/54 x - 2/27 y x z + 1/18 y x z - 1/36 y x z + + 2 2 2 2 3 4 3 3 2 2 2 3 + + 2/27 y x + 1/96 y x z + 1/72 z y x - 1/36 y x z + 1/72 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 1/54 y x z - 1/72 y x z + 1/54 z y x - 1/27 z y x + + 2 3 3 2 3 2 3 3 3 3 + + 1/27 y x z + 1/27 z y x + 1/36 y x z - 1/27 y x z - 2/27 z y x + + 3 3 3 3 3 2 + + 2/27 z y x + 1/27 y x z + 1/27 x + 1/54 x + 4/27 y x z + + 2 4 2 2 2 2 2 + - 2/27 z y x - 1/27 z x + 1/36 y x - 1/48 y x z - 1/36 y x z + + 2 2 2 3 2 3 + + 1/36 y x z - 1/18 y x z + 1/54 y x - 1/27 y x - 2/27 x z + + 2 2 3 3 2 2 2 2 2 + + 1/27 x z - 1/54 x z + 1/27 x z - 1/72 x z + 1/36 x z - 1/72 y x + + 2 2 4 3 4 3 4 2 4 + - 1/27 y x + 1/72 z x + 1/54 z x + 2/27 z x + 1/27 y x + 1/72 y x + + 2 3 3 3 2 2 4 + - 1/36 y x , COEFF(-1, -1, 1) = - 4/27 y x z + 1/24 z y x + + 4 2 3 3 2 3 3 3 3 + - 8/27 z y x - 1/18 y x z + 1/9 z y x + 8/27 z y x - 2/27 y x + + 3 4 2 2 3 3 2 3 2 4 + + 2/27 y x - 1/24 z y x + 4/27 y x - 1/9 z y x - 1/9 z y x + + 3 4 2 4 3 2 4 3 2 3 3 + + 4/27 z y x + 1/9 z y x + 1/18 z y x + 1/18 x z + 2/27 x z + + 4 16 3 2 2 3 16 + + 8/27 x + 2/27 x + -- y x z - 4/9 y x z + 2/9 y x z - -- y x + 27 27 + + 2 2 2 2 3 4 3 3 2 2 2 3 + - 1/6 y x z - 1/18 z y x + 1/18 y x z - 2/9 y x z + + 3 2 3 3 2 2 3 3 4 3 4 16 2 3 + + 8/27 y x z + 2/9 y x z - 2/27 z y x + 4/27 z y x - -- y x z + 27 + + 16 3 2 3 2 3 3 3 16 3 3 3 + - -- z y x - 2/9 y x z + 2/27 y x z + -- z y x - 4/27 z y x + 27 27 + + 3 3 3 2 32 32 2 4 + - 8/27 y x z - 2/27 x - 8/27 x - -- y x z + -- z y x + 4/27 z x + 27 27 + + 2 2 2 2 2 2 2 2 + - 2/9 y x + 1/6 y x z + 4/9 y x z - 4/9 y x z + 4/9 y x z + + 3 2 3 16 16 2 2 3 3 + - 8/27 y x + 8/27 y x + -- x z - -- x z + 8/27 x z - 8/27 x z + 27 27 + + 2 2 2 2 2 16 2 2 4 3 4 + + 2/9 x z - 2/9 x z + 2/9 y x + -- y x - 1/18 z x - 2/27 z x + 27 + + 3 4 2 4 2 3 + - 4/27 z x - 4/27 y x - 1/18 y x + 1/18 y x , COEFF(0, -1, 1) = + + 2 2 4 4 3 4 2 4 3 4 + - 1/16 z y x + 4/9 z y x - 1/9 y x + 1/6 z y x - 2/9 z y x + + 2 4 3 2 4 4 3 3 + - 1/6 z y x - 1/12 z y x - 1/9 x + 4/9 y z + 8/9 y - 8/9 z + + 2 2 2 2 3 4 2 2 3 3 2 3 + + 5/16 y x z + 1/12 z y x + 5/12 y x z - 5/9 y x z + + 3 2 2 3 3 4 3 4 2 3 3 2 + - 5/12 y x z + 1/9 z y x - 2/9 z y x + 10/9 y x z + 10/9 z y x + + 3 3 2 2 2 2 + + 4/9 z - 4/9 y + 1/3 y + 1/3 z + 5/9 x - 20/9 z y x + 16/9 y z + + 4 2 2 2 2 3 2 2 + - 4/9 - 2/9 z x - 5/6 y x z + 5/6 y x z + 5/9 y x + 2/3 y z + + 3 2 2 3 2 3 2 3 2 + + 1/3 y z + 10/9 x z - 8/9 y z - 1/3 y z - 5/9 x z - 2/3 y z + + 2 2 2 2 2 2 2 2 4 3 4 + - 5/12 x z - 1/4 y z - 5/12 y x - 10/9 y x + 1/12 z x + 1/9 z x + + 3 4 2 4 3 3 + - 8/9 z y + 2/9 y x + 1/12 y x , COEFF(1, -1, 1) = 4/27 y x z + + 2 2 4 4 2 3 3 2 3 3 + + 1/24 z y x - 8/27 z y x + 1/18 y x z - 1/9 z y x - 8/27 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 2/27 y x + 2/27 y x + 1/24 z y x - 4/27 y x + 1/9 z y x + + 2 4 3 4 2 4 3 2 4 3 2 + - 1/9 z y x + 4/27 z y x + 1/9 z y x + 1/18 z y x - 1/18 x z + + 3 3 4 16 3 2 2 3 + - 2/27 x z - 8/27 x + 2/27 x - -- y x z + 4/9 y x z - 2/9 y x z + 27 + + 16 2 2 2 2 3 4 3 3 2 2 2 3 + + -- y x - 1/6 y x z - 1/18 z y x - 1/18 y x z - 2/9 y x z + 27 + + 3 2 3 3 2 2 3 3 4 3 4 16 2 3 + + 8/27 y x z + 2/9 y x z - 2/27 z y x + 4/27 z y x - -- y x z + 27 + + 16 3 2 3 2 3 3 3 16 3 3 3 + - -- z y x + 2/9 y x z - 2/27 y x z - -- z y x + 4/27 z y x + 27 27 + + 3 3 3 2 32 32 2 4 + + 8/27 y x z + 2/27 x - 8/27 x + -- y x z + -- z y x + 4/27 z x + 27 27 + + 2 2 2 2 2 2 2 2 + + 2/9 y x - 1/6 y x z + 4/9 y x z - 4/9 y x z - 4/9 y x z + + 3 2 3 16 16 2 2 3 3 + - 8/27 y x - 8/27 y x - -- x z - -- x z + 8/27 x z + 8/27 x z + 27 27 + + 2 2 2 2 2 16 2 2 4 3 4 + + 2/9 x z + 2/9 x z + 2/9 y x + -- y x - 1/18 z x - 2/27 z x + 27 + + 3 4 2 4 2 3 + + 4/27 z x - 4/27 y x - 1/18 y x - 1/18 y x , COEFF(2, -1, 1) = + + 3 3 2 2 4 4 2 3 3 2 3 + - 2/27 y x z - 1/96 z y x + 2/27 z y x - 1/36 y x z + 1/18 z y x + + 3 3 3 3 4 2 2 3 3 + + 4/27 z y x - 1/27 y x - 1/54 y x - 1/48 z y x + 2/27 y x + + 2 3 2 4 3 4 2 4 + - 1/18 z y x + 1/36 z y x - 1/27 z y x - 1/36 z y x + + 3 2 4 3 2 3 3 4 3 + - 1/72 z y x + 1/36 x z + 1/27 x z + 1/27 x - 1/54 x + 2/27 y x z + + 2 2 3 2 2 2 2 3 4 + - 1/18 y x z + 1/36 y x z - 2/27 y x + 1/96 y x z + 1/72 z y x + + 3 3 2 2 2 3 3 2 3 3 2 2 + + 1/36 y x z + 1/72 y x z - 1/54 y x z - 1/72 y x z + + 3 3 4 3 4 2 3 3 2 + + 1/54 z y x - 1/27 z y x + 1/27 y x z + 1/27 z y x + + 3 2 3 3 3 3 3 3 3 3 + - 1/36 y x z + 1/27 y x z + 2/27 z y x - 2/27 z y x - 1/27 y x z + + 3 2 2 4 2 + - 1/27 x + 1/54 x - 4/27 y x z - 2/27 z y x - 1/27 z x - 1/36 y x + + 2 2 2 2 2 2 2 3 2 + + 1/48 y x z - 1/36 y x z + 1/36 y x z + 1/18 y x z + 1/54 y x + + 3 2 2 3 3 2 2 + + 1/27 y x + 2/27 x z + 1/27 x z - 1/54 x z - 1/27 x z - 1/72 x z + + 2 2 2 2 2 4 3 4 3 + - 1/36 x z - 1/72 y x - 1/27 y x + 1/72 z x + 1/54 z x - 2/27 z x + + 4 2 4 2 3 3 3 + + 1/27 y x + 1/72 y x + 1/36 y x , COEFF(-2, 0, 1) = - 5/36 y x z + + 4 3 3 3 3 4 3 + - 5/36 z y x + 5/18 z y x - 1/18 y x + 1/36 y x + 5/36 y x + + 2 3 3 4 2 4 3 + - 5/48 z y x + 5/72 z y x + 5/96 z y x + 5/36 y x z - 5/36 y x + + 2 3 4 3 3 2 3 2 3 3 2 2 + - 1/48 z y x + 1/24 y x z + 1/36 y x z + 1/48 y x z + + 3 3 4 3 4 2 3 3 2 + - 1/36 z y x + 1/18 z y x - 5/72 y x z - 1/18 z y x + + 3 2 3 3 3 3 3 3 3 3 + - 1/24 y x z + 1/18 y x z + 1/9 z y x - 1/9 z y x - 1/18 y x z + + 2 2 2 2 3 2 + - 5/18 y x z + 5/36 z y x - 5/96 y x z + 5/48 y x z - 1/36 y x + + 3 2 4 3 3 + + 1/18 y x + 5/72 y x - 5/72 y x , COEFF(-1, 0, 1) = 5/18 y x z + + 4 3 3 3 3 4 3 + + 5/9 z y x - 5/9 z y x + 1/9 y x - 1/9 y x - 5/18 y x + + 2 3 3 4 2 4 3 + + 5/24 z y x - 5/18 z y x - 5/24 z y x - 10/9 y x z + 10/9 y x + + 2 3 4 3 3 2 3 2 3 3 2 2 + + 1/12 z y x - 1/12 y x z - 4/9 y x z - 1/3 y x z + + 3 3 4 3 4 2 3 3 2 3 2 + + 1/9 z y x - 2/9 z y x + 10/9 y x z + 8/9 z y x + 1/3 y x z + + 3 3 3 3 3 3 3 3 + - 1/9 y x z - 8/9 z y x + 2/9 z y x + 4/9 y x z + 20/9 y x z + + 2 2 2 2 3 2 3 + - 20/9 z y x + 5/6 y x z - 5/6 y x z + 4/9 y x - 4/9 y x + + 2 4 3 3 4 4 + - 10/9 y x + 5/18 y x , COEFF(0, 0, 1) = - 1/6 z y x - 5/6 z y x + + 3 3 3 25 2 2 3 2 2 3 4 + + 5/3 y z + 2/3 y + 4/3 z y - -- y x z - 1/2 y z - 1/8 z y x + 16 + + 25 2 3 4 3 4 25 2 + - -- y x z - 5/12 y x + 5/12 z y x - 10/3 y z - 5/3 y + -- y x + 12 12 + + 2 3 2 3 2 3 4 3 2 2 + + 5/4 y z - 5/6 y x - 5/3 z y x + 1/6 y x + 5/8 y x z + + 3 2 3 2 3 3 2 4 3 4 + + 5/6 y x z + 25/6 z y x - 2/3 y z + 5/16 z y x + 1/3 z y x , + + 3 3 4 3 3 3 + COEFF(1, 0, 1) = - 5/18 y x z + 5/9 z y x + 5/9 z y x - 1/9 y x + + 3 4 3 2 3 3 4 2 4 + - 1/9 y x + 5/18 y x - 5/24 z y x - 5/18 z y x - 5/24 z y x + + 3 2 3 4 3 3 2 3 2 3 + + 10/9 y x z - 10/9 y x + 1/12 z y x + 1/12 y x z - 4/9 y x z + + 3 2 2 3 3 4 3 4 2 3 3 2 + - 1/3 y x z + 1/9 z y x - 2/9 z y x + 10/9 y x z + 8/9 z y x + + 3 2 3 3 3 3 3 3 3 3 + - 1/3 y x z + 1/9 y x z + 8/9 z y x - 2/9 z y x - 4/9 y x z + + 2 2 2 2 3 2 + - 20/9 y x z - 20/9 z y x + 5/6 y x z + 5/6 y x z + 4/9 y x + + 3 2 4 3 3 + + 4/9 y x - 10/9 y x + 5/18 y x , COEFF(2, 0, 1) = 5/36 y x z + + 4 3 3 3 3 4 3 + - 5/36 z y x - 5/18 z y x + 1/18 y x + 1/36 y x - 5/36 y x + + 2 3 3 4 2 4 3 + + 5/48 z y x + 5/72 z y x + 5/96 z y x - 5/36 y x z + 5/36 y x + + 2 3 4 3 3 2 3 2 3 3 2 2 + - 1/48 z y x - 1/24 y x z + 1/36 y x z + 1/48 y x z + + 3 3 4 3 4 2 3 3 2 + - 1/36 z y x + 1/18 z y x - 5/72 y x z - 1/18 z y x + + 3 2 3 3 3 3 3 3 3 3 + + 1/24 y x z - 1/18 y x z - 1/9 z y x + 1/9 z y x + 1/18 y x z + + 2 2 2 2 3 2 + + 5/18 y x z + 5/36 z y x - 5/96 y x z - 5/48 y x z - 1/36 y x + + 3 2 4 3 3 + - 1/18 y x + 5/72 y x - 5/72 y x , COEFF(-2, 1, 1) = 2/27 y x z + + 2 2 4 4 2 3 3 2 3 3 + + 1/96 z y x + 2/27 z y x - 1/36 y x z + 1/18 z y x - 4/27 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 1/27 y x - 1/54 y x - 1/48 z y x - 2/27 y x + 1/18 z y x + + 2 4 3 4 2 4 3 2 4 3 2 + - 1/36 z y x - 1/27 z y x - 1/36 z y x + 1/72 z y x + 1/36 x z + + 3 3 4 3 2 2 3 + + 1/27 x z + 1/27 x + 1/54 x - 2/27 y x z - 1/18 y x z + 1/36 y x z + + 2 2 2 2 3 4 3 3 2 2 2 3 + + 2/27 y x - 1/96 y x z + 1/72 z y x - 1/36 y x z - 1/72 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 1/54 y x z - 1/72 y x z + 1/54 z y x - 1/27 z y x + + 2 3 3 2 3 2 3 3 3 3 + + 1/27 y x z + 1/27 z y x + 1/36 y x z - 1/27 y x z - 2/27 z y x + + 3 3 3 3 3 2 + + 2/27 z y x + 1/27 y x z - 1/27 x - 1/54 x + 4/27 y x z + + 2 4 2 2 2 2 2 + - 2/27 z y x + 1/27 z x - 1/36 y x + 1/48 y x z + 1/36 y x z + + 2 2 2 3 2 3 + + 1/36 y x z - 1/18 y x z + 1/54 y x - 1/27 y x + 2/27 x z + + 2 2 3 3 2 2 2 2 2 + - 1/27 x z + 1/54 x z - 1/27 x z + 1/72 x z - 1/36 x z + 1/72 y x + + 2 2 4 3 4 3 4 2 4 + - 1/27 y x - 1/72 z x - 1/54 z x - 2/27 z x + 1/27 y x - 1/72 y x + + 2 3 3 3 2 2 4 + + 1/36 y x , COEFF(-1, 1, 1) = - 4/27 y x z - 1/24 z y x + + 4 2 3 3 2 3 3 3 3 + - 8/27 z y x + 1/18 y x z - 1/9 z y x + 8/27 z y x - 2/27 y x + + 3 4 2 2 3 3 2 3 2 4 + + 2/27 y x + 1/24 z y x + 4/27 y x - 1/9 z y x + 1/9 z y x + + 3 4 2 4 3 2 4 3 2 3 3 + + 4/27 z y x + 1/9 z y x - 1/18 z y x - 1/18 x z - 2/27 x z + + 4 16 3 2 2 3 16 + - 8/27 x - 2/27 x + -- y x z + 4/9 y x z - 2/9 y x z - -- y x + 27 27 + + 2 2 2 2 3 4 3 3 2 2 2 3 + + 1/6 y x z - 1/18 z y x + 1/18 y x z + 2/9 y x z + + 3 2 3 3 2 2 3 3 4 3 4 16 2 3 + + 8/27 y x z + 2/9 y x z - 2/27 z y x + 4/27 z y x - -- y x z + 27 + + 16 3 2 3 2 3 3 3 16 3 3 3 + - -- z y x - 2/9 y x z + 2/27 y x z + -- z y x - 4/27 z y x + 27 27 + + 3 3 3 2 32 32 2 4 + - 8/27 y x z + 2/27 x + 8/27 x - -- y x z + -- z y x - 4/27 z x + 27 27 + + 2 2 2 2 2 2 2 2 + + 2/9 y x - 1/6 y x z - 4/9 y x z - 4/9 y x z + 4/9 y x z + + 3 2 3 16 16 2 2 3 3 + - 8/27 y x + 8/27 y x - -- x z + -- x z - 8/27 x z + 8/27 x z + 27 27 + + 2 2 2 2 2 16 2 2 4 3 4 + - 2/9 x z + 2/9 x z - 2/9 y x + -- y x + 1/18 z x + 2/27 z x + 27 + + 3 4 2 4 2 3 + + 4/27 z x - 4/27 y x + 1/18 y x - 1/18 y x , COEFF(0, 1, 1) = + + 2 2 4 4 3 4 2 4 3 4 + 1/16 z y x + 4/9 z y x - 1/9 y x - 1/6 z y x - 2/9 z y x + + 2 4 3 2 4 4 3 3 + - 1/6 z y x + 1/12 z y x + 1/9 x + 4/9 y z + 8/9 y + 8/9 z + + 2 2 2 2 3 4 2 2 3 3 2 3 + - 5/16 y x z + 1/12 z y x - 5/12 y x z - 5/9 y x z + + 3 2 2 3 3 4 3 4 2 3 3 2 + - 5/12 y x z + 1/9 z y x - 2/9 z y x + 10/9 y x z + 10/9 z y x + + 3 3 2 2 2 2 + + 4/9 - 4/9 z - 4/9 y - 1/3 y - 1/3 z - 5/9 x - 20/9 z y x + + 4 2 2 2 2 3 2 2 + + 16/9 y z + 2/9 z x + 5/6 y x z + 5/6 y x z + 5/9 y x - 2/3 y z + + 3 2 2 3 2 3 2 3 2 + + 1/3 y z - 10/9 x z - 8/9 y z + 1/3 y z + 5/9 x z - 2/3 y z + + 2 2 2 2 2 2 2 2 4 3 4 + + 5/12 x z + 1/4 y z + 5/12 y x - 10/9 y x - 1/12 z x - 1/9 z x + + 3 4 2 4 3 3 + - 8/9 z y + 2/9 y x - 1/12 y x , COEFF(1, 1, 1) = 4/27 y x z + + 2 2 4 4 2 3 3 2 3 3 + - 1/24 z y x - 8/27 z y x - 1/18 y x z + 1/9 z y x - 8/27 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 2/27 y x + 2/27 y x - 1/24 z y x - 4/27 y x + 1/9 z y x + + 2 4 3 4 2 4 3 2 4 3 2 + + 1/9 z y x + 4/27 z y x + 1/9 z y x - 1/18 z y x + 1/18 x z + + 3 3 4 16 3 2 2 3 + + 2/27 x z + 8/27 x - 2/27 x - -- y x z - 4/9 y x z + 2/9 y x z + 27 + + 16 2 2 2 2 3 4 3 3 2 2 2 3 + + -- y x + 1/6 y x z - 1/18 z y x - 1/18 y x z + 2/9 y x z + 27 + + 3 2 3 3 2 2 3 3 4 3 4 16 2 3 + + 8/27 y x z + 2/9 y x z - 2/27 z y x + 4/27 z y x - -- y x z + 27 + + 16 3 2 3 2 3 3 3 16 3 3 3 + - -- z y x + 2/9 y x z - 2/27 y x z - -- z y x + 4/27 z y x + 27 27 + + 3 3 3 2 32 32 2 4 + + 8/27 y x z - 2/27 x + 8/27 x + -- y x z + -- z y x - 4/27 z x + 27 27 + + 2 2 2 2 2 2 2 2 + - 2/9 y x + 1/6 y x z - 4/9 y x z - 4/9 y x z - 4/9 y x z + + 3 2 3 16 16 2 2 3 3 + - 8/27 y x - 8/27 y x + -- x z + -- x z - 8/27 x z - 8/27 x z + 27 27 + + 2 2 2 2 2 16 2 2 4 3 4 + - 2/9 x z - 2/9 x z - 2/9 y x + -- y x + 1/18 z x + 2/27 z x + 27 + + 3 4 2 4 2 3 + - 4/27 z x - 4/27 y x + 1/18 y x + 1/18 y x , COEFF(2, 1, 1) = + + 3 3 2 2 4 4 2 3 3 2 3 + - 2/27 y x z + 1/96 z y x + 2/27 z y x + 1/36 y x z - 1/18 z y x + + 3 3 3 3 4 2 2 3 3 + + 4/27 z y x - 1/27 y x - 1/54 y x + 1/48 z y x + 2/27 y x + + 2 3 2 4 3 4 2 4 + - 1/18 z y x - 1/36 z y x - 1/27 z y x - 1/36 z y x + + 3 2 4 3 2 3 3 4 3 + + 1/72 z y x - 1/36 x z - 1/27 x z - 1/27 x + 1/54 x + 2/27 y x z + + 2 2 3 2 2 2 2 3 4 + + 1/18 y x z - 1/36 y x z - 2/27 y x - 1/96 y x z + 1/72 z y x + + 3 3 2 2 2 3 3 2 3 3 2 2 + + 1/36 y x z - 1/72 y x z - 1/54 y x z - 1/72 y x z + + 3 3 4 3 4 2 3 3 2 + + 1/54 z y x - 1/27 z y x + 1/27 y x z + 1/27 z y x + + 3 2 3 3 3 3 3 3 3 3 + - 1/36 y x z + 1/27 y x z + 2/27 z y x - 2/27 z y x - 1/27 y x z + + 3 2 2 4 2 + + 1/27 x - 1/54 x - 4/27 y x z - 2/27 z y x + 1/27 z x + 1/36 y x + + 2 2 2 2 2 2 2 3 2 + - 1/48 y x z + 1/36 y x z + 1/36 y x z + 1/18 y x z + 1/54 y x + + 3 2 2 3 3 2 2 + + 1/27 y x - 2/27 x z - 1/27 x z + 1/54 x z + 1/27 x z + 1/72 x z + + 2 2 2 2 2 4 3 4 3 + + 1/36 x z + 1/72 y x - 1/27 y x - 1/72 z x - 1/54 z x + 2/27 z x + + 4 2 4 2 3 3 3 + + 1/27 y x - 1/72 y x - 1/36 y x , COEFF(-2, 2, 1) = - 1/216 y x z + + 2 2 4 4 2 3 3 2 3 + - 1/192 z y x - 1/216 z y x + 1/72 y x z - 1/36 z y x + + 3 3 3 3 4 2 2 3 3 + + 1/108 z y x - 1/108 y x + 1/216 y x + 1/96 z y x + 1/216 y x + + 2 3 2 4 3 4 2 4 + - 1/288 z y x + 1/72 z y x + 1/432 z y x + 1/576 z y x + + 3 2 4 3 2 3 3 4 + - 1/144 z y x - 1/288 x z - 1/216 x z - 1/216 x - 1/432 x + + 3 2 2 3 2 2 2 + + 1/216 y x z + 1/36 y x z - 1/72 y x z - 1/216 y x + 1/192 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + - 1/288 z y x + 1/144 y x z + 1/144 y x z + 1/216 y x z + + 3 2 2 3 3 4 3 4 2 3 + + 1/288 y x z - 1/216 z y x + 1/108 z y x - 1/432 y x z + + 3 2 3 2 3 3 3 3 + - 1/108 z y x - 1/144 y x z + 1/108 y x z + 1/54 z y x + + 3 3 3 3 3 2 + - 1/54 z y x - 1/108 y x z + 1/216 x + 1/432 x - 1/108 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x - 1/216 z x + 1/72 y x - 1/96 y x z - 1/72 y x z + + 2 2 2 3 2 3 + - 1/576 y x z + 1/288 y x z - 1/216 y x + 1/108 y x - 1/108 x z + + 2 2 3 3 2 2 2 + + 1/216 x z - 1/432 x z + 1/216 x z - 1/576 x z + 1/288 x z + + 2 2 2 2 4 3 4 3 + - 1/144 y x + 1/432 y x + 1/576 z x + 1/432 z x + 1/108 z x + + 4 2 4 2 3 3 3 + - 1/432 y x + 1/144 y x - 1/72 y x , COEFF(-1, 2, 1) = 1/108 y x z + + 2 2 4 4 2 3 3 2 3 3 + + 1/48 z y x + 1/54 z y x - 1/36 y x z + 1/18 z y x - 1/54 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 1/54 y x - 1/54 y x - 1/48 z y x - 1/108 y x + 1/144 z y x + + 2 4 3 4 2 4 3 2 4 + - 1/18 z y x - 1/108 z y x - 1/144 z y x + 1/36 z y x + + 3 2 3 3 4 3 2 + + 1/144 x z + 1/108 x z + 1/27 x + 1/108 x - 1/27 y x z - 2/9 y x z + + 2 3 2 2 2 2 3 4 3 3 2 + + 1/9 y x z + 1/27 y x - 1/12 y x z + 1/72 z y x - 1/72 y x z + + 2 2 3 3 2 3 3 2 2 3 3 4 + - 1/9 y x z - 2/27 y x z - 1/18 y x z + 1/54 z y x + + 3 4 2 3 3 2 3 2 + - 1/27 z y x + 1/27 y x z + 4/27 z y x + 1/18 y x z + + 3 3 3 3 3 3 3 3 3 + - 1/54 y x z - 4/27 z y x + 1/27 z y x + 2/27 y x z - 1/108 x + + 2 2 4 2 2 2 + - 1/27 x + 2/27 y x z - 2/27 z y x + 1/54 z x - 1/9 y x + 1/12 y x z + + 2 2 2 2 2 3 2 3 + + 2/9 y x z + 1/36 y x z - 1/36 y x z + 2/27 y x - 2/27 y x + + 2 2 3 3 2 2 2 + + 2/27 x z - 2/27 x z + 1/27 x z - 1/27 x z + 1/36 x z - 1/36 x z + + 2 2 2 2 4 3 4 3 + + 1/9 y x - 1/27 y x - 1/144 z x - 1/108 z x - 1/54 z x + + 4 2 4 2 3 2 2 4 + + 1/108 y x - 1/36 y x + 1/36 y x , COEFF(0, 2, 1) = - 1/32 z y x + + 4 3 4 2 4 3 4 2 4 + - 1/36 z y x + 1/36 y x + 1/12 z y x + 1/72 z y x + 1/96 z y x + + 3 2 4 4 3 3 2 2 2 + - 1/24 z y x - 1/72 x - 1/9 y z - 1/18 y - 1/9 z + 5/32 y x z + + 2 3 4 2 2 3 3 2 3 3 2 2 + - 1/48 z y x + 5/24 y x z + 5/36 y x z + 5/48 y x z + + 3 3 4 3 4 2 3 3 2 3 + - 1/36 z y x + 1/18 z y x - 5/72 y x z - 5/18 z y x + 1/18 z + + 3 2 2 2 2 4 + + 1/9 y + 1/6 y + 1/24 z + 5/72 x + 5/36 z y x - 1/9 y z - 1/36 z x + + 2 2 2 2 3 2 2 3 2 + - 5/12 y x z - 5/96 y x z - 5/36 y x + 1/3 y z - 1/12 y z + + 2 3 2 3 2 3 2 + + 5/36 x z - 1/18 + 1/18 y z - 1/6 y z - 5/72 x z + 1/24 y z + + 2 2 2 2 2 2 2 2 4 + - 5/96 x z - 1/8 y z - 5/24 y x + 5/72 y x + 1/96 z x + + 3 4 3 4 2 4 + + 1/72 z x + 2/9 z y - 1/72 y x + 1/24 y x , COEFF(1, 2, 1) = + + 3 3 2 2 4 4 2 3 3 + - 1/108 y x z + 1/48 z y x + 1/54 z y x + 1/36 y x z + + 2 3 3 3 3 3 4 2 2 3 + - 1/18 z y x + 1/54 z y x - 1/54 y x - 1/54 y x + 1/48 z y x + + 3 2 3 2 4 3 4 + + 1/108 y x - 1/144 z y x - 1/18 z y x - 1/108 z y x + + 2 4 3 2 4 3 2 3 3 + - 1/144 z y x + 1/36 z y x - 1/144 x z - 1/108 x z - 1/27 x + + 4 3 2 2 3 + + 1/108 x + 1/27 y x z + 2/9 y x z - 1/9 y x z - 1/27 y x + + 2 2 2 2 3 4 3 3 2 2 2 3 + - 1/12 y x z + 1/72 z y x + 1/72 y x z - 1/9 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 2/27 y x z - 1/18 y x z + 1/54 z y x - 1/27 z y x + + 2 3 3 2 3 2 3 3 3 3 + + 1/27 y x z + 4/27 z y x - 1/18 y x z + 1/54 y x z + 4/27 z y x + + 3 3 3 3 3 2 + - 1/27 z y x - 2/27 y x z + 1/108 x - 1/27 x - 2/27 y x z + + 2 4 2 2 2 2 2 + - 2/27 z y x + 1/54 z x + 1/9 y x - 1/12 y x z + 2/9 y x z + + 2 2 2 3 2 3 + + 1/36 y x z + 1/36 y x z + 2/27 y x + 2/27 y x - 2/27 x z + + 2 2 3 3 2 2 2 2 2 + - 2/27 x z + 1/27 x z + 1/27 x z + 1/36 x z + 1/36 x z + 1/9 y x + + 2 2 4 3 4 3 4 + - 1/27 y x - 1/144 z x - 1/108 z x + 1/54 z x + 1/108 y x + + 2 4 2 3 3 3 2 2 4 + - 1/36 y x - 1/36 y x , COEFF(2, 2, 1) = 1/216 y x z - 1/192 z y x + + 4 2 3 3 2 3 3 3 3 + - 1/216 z y x - 1/72 y x z + 1/36 z y x - 1/108 z y x + 1/108 y x + + 3 4 2 2 3 3 2 3 2 4 + + 1/216 y x - 1/96 z y x - 1/216 y x + 1/288 z y x + 1/72 z y x + + 3 4 2 4 3 2 4 3 2 + + 1/432 z y x + 1/576 z y x - 1/144 z y x + 1/288 x z + + 3 3 4 3 2 + + 1/216 x z + 1/216 x - 1/432 x - 1/216 y x z - 1/36 y x z + + 2 3 2 2 2 2 3 4 + + 1/72 y x z + 1/216 y x + 1/192 y x z - 1/288 z y x + + 3 3 2 2 2 3 3 2 3 3 2 2 + - 1/144 y x z + 1/144 y x z + 1/216 y x z + 1/288 y x z + + 3 3 4 3 4 2 3 3 2 + - 1/216 z y x + 1/108 z y x - 1/432 y x z - 1/108 z y x + + 3 2 3 3 3 3 3 3 + + 1/144 y x z - 1/108 y x z - 1/54 z y x + 1/54 z y x + + 3 3 3 2 2 + + 1/108 y x z - 1/216 x + 1/432 x + 1/108 y x z + 1/216 z y x + + 4 2 2 2 2 2 2 2 + - 1/216 z x - 1/72 y x + 1/96 y x z - 1/72 y x z - 1/576 y x z + + 2 3 2 3 2 + - 1/288 y x z - 1/216 y x - 1/108 y x + 1/108 x z + 1/216 x z + + 2 3 3 2 2 2 2 2 + - 1/432 x z - 1/216 x z - 1/576 x z - 1/288 x z - 1/144 y x + + 2 2 4 3 4 3 4 + + 1/432 y x + 1/576 z x + 1/432 z x - 1/108 z x - 1/432 y x + + 2 4 2 3 3 3 + + 1/144 y x + 1/72 y x , COEFF(-2, -2, 2) = 1/864 y x z + + 2 2 4 4 2 3 3 2 3 + - 1/384 z y x + 1/3456 z y x + 1/288 y x z - 1/576 z y x + + 3 3 3 3 4 2 2 3 + - 1/1728 z y x + 1/864 y x - 1/1728 y x + 1/192 z y x + + 3 2 3 2 4 3 4 + - 1/1728 y x + 1/576 z y x + 1/1152 z y x - 1/1728 z y x + + 2 4 3 2 4 3 2 3 3 + - 1/1152 z y x - 1/576 z y x - 1/576 x z - 1/864 x z - 1/1728 x + + 4 3 2 2 3 + - 1/3456 x - 1/864 y x z + 1/576 y x z - 1/288 y x z + 1/1728 y x + + 2 2 2 2 3 4 3 3 2 2 2 3 + + 1/384 y x z + 1/576 z y x - 1/288 y x z + 1/576 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 1/864 y x z - 1/576 y x z + 1/864 z y x - 1/1728 z y x + + 2 3 3 2 3 2 3 3 3 + + 1/1728 y x z + 1/1728 z y x + 1/288 y x z - 1/432 y x z + + 3 3 3 3 3 3 2 + - 1/864 z y x + 1/864 z y x + 1/432 y x z + 1/1728 x + 1/3456 x + + 2 4 2 2 2 + + 1/1728 y x z - 1/3456 z y x - 1/3456 z x + 1/576 y x - 1/192 y x z + + 2 2 2 2 2 3 2 + - 1/1152 y x z + 1/1152 y x z - 1/576 y x z + 1/1728 y x + + 3 2 2 3 3 + - 1/864 y x - 1/1728 x z + 1/3456 x z - 1/1728 x z + 1/864 x z + + 2 2 2 2 2 2 2 4 + - 1/1152 x z + 1/576 x z - 1/1152 y x - 1/3456 y x + 1/1152 z x + + 3 4 3 4 2 4 2 3 + + 1/1728 z x + 1/1728 z x + 1/3456 y x + 1/1152 y x - 1/576 y x , + + 3 3 2 2 4 4 + COEFF(-1, -2, 2) = - 1/432 y x z + 1/96 z y x - 1/864 z y x + + 2 3 3 2 3 3 3 3 + - 1/144 y x z + 1/288 z y x + 1/864 z y x - 1/432 y x + + 3 4 2 2 3 3 2 3 2 4 + + 1/432 y x - 1/96 z y x + 1/864 y x - 1/288 z y x - 1/288 z y x + + 3 4 2 4 3 2 4 3 2 + + 1/432 z y x + 1/288 z y x + 1/144 z y x + 1/288 x z + + 3 3 4 3 2 + + 1/432 x z + 1/216 x + 1/864 x + 1/108 y x z - 1/72 y x z + + 2 3 2 2 2 2 3 4 + + 1/36 y x z - 1/216 y x - 1/24 y x z - 1/144 z y x + + 3 3 2 2 2 3 3 2 3 3 2 2 + + 1/144 y x z - 1/36 y x z + 1/54 y x z + 1/36 y x z + + 3 3 4 3 4 2 3 3 2 + - 1/216 z y x + 1/432 z y x - 1/108 y x z - 1/108 z y x + + 3 2 3 3 3 3 3 3 + - 1/36 y x z + 1/216 y x z + 1/108 z y x - 1/432 z y x + + 3 3 3 2 2 + - 1/54 y x z - 1/864 x - 1/216 x - 1/216 y x z + 1/216 z y x + + 4 2 2 2 2 2 2 2 + + 1/864 z x - 1/72 y x + 1/24 y x z + 1/72 y x z - 1/72 y x z + + 2 3 2 3 2 + + 1/72 y x z - 1/108 y x + 1/108 y x + 1/216 x z - 1/216 x z + + 2 3 3 2 2 2 2 2 + + 1/108 x z - 1/108 x z + 1/72 x z - 1/72 x z + 1/72 y x + + 2 2 4 3 4 3 4 + + 1/216 y x - 1/288 z x - 1/432 z x - 1/864 z x - 1/864 y x + + 2 4 2 3 2 2 4 + - 1/288 y x + 1/288 y x , COEFF(0, -2, 2) = - 1/64 z y x + + 4 3 4 2 4 3 4 + + 1/576 z y x - 1/288 y x + 1/192 z y x - 1/288 z y x + + 2 4 3 2 4 4 3 3 + - 1/192 z y x - 1/96 z y x - 1/576 x + 1/36 y z + 1/144 y + + 2 2 2 2 3 4 2 2 3 3 2 3 + - 1/144 z + 5/64 y x z + 1/96 z y x + 5/96 y x z - 5/144 y x z + + 3 2 2 3 3 4 3 4 2 3 + - 5/96 y x z + 1/144 z y x - 1/288 z y x + 5/288 y x z + + 3 2 3 3 2 2 2 + + 5/288 z y x + 1/72 z - 1/72 y + 1/48 y + 1/48 z + 5/576 x + + 2 4 2 2 2 2 + - 5/576 z y x + 1/144 y z - 1/576 z x - 5/192 y x z + 5/192 y x z + + 3 2 2 3 2 2 3 + + 5/288 y x + 1/48 y z + 1/24 y z + 5/576 x z - 1/72 y z + + 2 3 2 3 2 2 2 2 2 + - 1/24 y z - 5/288 x z - 1/48 y z - 5/192 x z - 1/16 y z + + 2 2 2 2 4 3 4 3 + - 5/192 y x - 5/576 y x - 1/144 + 1/192 z x + 1/288 z x - 1/72 z y + + 4 2 4 3 3 + + 1/576 y x + 1/192 y x , COEFF(1, -2, 2) = 1/432 y x z + + 2 2 4 4 2 3 3 2 3 + + 1/96 z y x - 1/864 z y x + 1/144 y x z - 1/288 z y x + + 3 3 3 3 4 2 2 3 3 + - 1/864 z y x + 1/432 y x + 1/432 y x + 1/96 z y x - 1/864 y x + + 2 3 2 4 3 4 2 4 + + 1/288 z y x - 1/288 z y x + 1/432 z y x + 1/288 z y x + + 3 2 4 3 2 3 3 4 + + 1/144 z y x - 1/288 x z - 1/432 x z - 1/216 x + 1/864 x + + 3 2 2 3 2 2 2 + - 1/108 y x z + 1/72 y x z - 1/36 y x z + 1/216 y x - 1/24 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + - 1/144 z y x - 1/144 y x z - 1/36 y x z + 1/54 y x z + + 3 2 2 3 3 4 3 4 2 3 + + 1/36 y x z - 1/216 z y x + 1/432 z y x - 1/108 y x z + + 3 2 3 2 3 3 3 3 + - 1/108 z y x + 1/36 y x z - 1/216 y x z - 1/108 z y x + + 3 3 3 3 3 2 + + 1/432 z y x + 1/54 y x z + 1/864 x - 1/216 x + 1/216 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x + 1/864 z x + 1/72 y x - 1/24 y x z + 1/72 y x z + + 2 2 2 3 2 3 + - 1/72 y x z - 1/72 y x z - 1/108 y x - 1/108 y x - 1/216 x z + + 2 2 3 3 2 2 2 + - 1/216 x z + 1/108 x z + 1/108 x z + 1/72 x z + 1/72 x z + + 2 2 2 2 4 3 4 3 + + 1/72 y x + 1/216 y x - 1/288 z x - 1/432 z x + 1/864 z x + + 4 2 4 2 3 + - 1/864 y x - 1/288 y x - 1/288 y x , COEFF(2, -2, 2) = + + 3 3 2 2 4 4 2 3 3 + - 1/864 y x z - 1/384 z y x + 1/3456 z y x - 1/288 y x z + + 2 3 3 3 3 3 4 + + 1/576 z y x + 1/1728 z y x - 1/864 y x - 1/1728 y x + + 2 2 3 3 2 3 2 4 + - 1/192 z y x + 1/1728 y x - 1/576 z y x + 1/1152 z y x + + 3 4 2 4 3 2 4 3 2 + - 1/1728 z y x - 1/1152 z y x - 1/576 z y x + 1/576 x z + + 3 3 4 3 2 + + 1/864 x z + 1/1728 x - 1/3456 x + 1/864 y x z - 1/576 y x z + + 2 3 2 2 2 2 3 4 + + 1/288 y x z - 1/1728 y x + 1/384 y x z + 1/576 z y x + + 3 3 2 2 2 3 3 2 3 3 2 2 + + 1/288 y x z + 1/576 y x z - 1/864 y x z - 1/576 y x z + + 3 3 4 3 4 2 3 3 2 + + 1/864 z y x - 1/1728 z y x + 1/1728 y x z + 1/1728 z y x + + 3 2 3 3 3 3 3 3 + - 1/288 y x z + 1/432 y x z + 1/864 z y x - 1/864 z y x + + 3 3 3 2 2 + - 1/432 y x z - 1/1728 x + 1/3456 x - 1/1728 y x z - 1/3456 z y x + + 4 2 2 2 2 2 + - 1/3456 z x - 1/576 y x + 1/192 y x z - 1/1152 y x z + + 2 2 2 3 2 3 + + 1/1152 y x z + 1/576 y x z + 1/1728 y x + 1/864 y x + 1/1728 x z + + 2 2 3 3 2 2 2 + + 1/3456 x z - 1/1728 x z - 1/864 x z - 1/1152 x z - 1/576 x z + + 2 2 2 2 4 3 4 3 + - 1/1152 y x - 1/3456 y x + 1/1152 z x + 1/1728 z x - 1/1728 z x + + 4 2 4 2 3 + + 1/3456 y x + 1/1152 y x + 1/576 y x , COEFF(-2, -1, 2) = + + 3 3 2 2 4 4 2 3 3 + - 1/54 y x z + 1/192 z y x - 1/216 z y x - 1/144 y x z + + 2 3 3 3 3 3 4 2 2 3 + + 1/288 z y x + 1/108 z y x - 1/216 y x + 1/432 y x - 1/96 z y x + + 3 2 3 2 4 3 4 2 4 + + 1/108 y x - 1/36 z y x - 1/576 z y x + 1/108 z y x + 1/72 z y x + + 3 2 4 3 2 3 3 4 + + 1/288 z y x + 1/72 x z + 1/108 x z + 1/216 x + 1/432 x + + 3 2 2 3 2 2 2 + + 1/54 y x z - 1/288 y x z + 1/144 y x z - 1/108 y x - 1/192 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + - 1/144 z y x + 1/72 y x z - 1/288 y x z + 1/216 y x z + + 3 2 2 3 3 4 3 4 2 3 + + 1/144 y x z - 1/216 z y x + 1/432 z y x - 1/108 y x z + + 3 2 3 2 3 3 3 3 + - 1/432 z y x - 1/72 y x z + 1/108 y x z + 1/216 z y x + + 3 3 3 3 3 2 + - 1/216 z y x - 1/108 y x z - 1/216 x - 1/432 x - 1/108 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x + 1/432 z x - 1/288 y x + 1/96 y x z + 1/576 y x z + + 2 2 2 3 2 3 + - 1/72 y x z + 1/36 y x z - 1/432 y x + 1/216 y x + 1/216 x z + + 2 2 3 3 2 2 2 + - 1/432 x z + 1/216 x z - 1/108 x z + 1/144 x z - 1/72 x z + + 2 2 2 2 4 3 4 3 + + 1/576 y x + 1/216 y x - 1/144 z x - 1/216 z x - 1/216 z x + + 4 2 4 2 3 3 3 + - 1/216 y x - 1/576 y x + 1/288 y x , COEFF(-1, -1, 2) = 1/27 y x z + + 2 2 4 4 2 3 3 2 3 + - 1/48 z y x + 1/54 z y x + 1/72 y x z - 1/144 z y x + + 3 3 3 3 4 2 2 3 3 + - 1/54 z y x + 1/108 y x - 1/108 y x + 1/48 z y x - 1/54 y x + + 2 3 2 4 3 4 2 4 + + 1/18 z y x + 1/144 z y x - 1/27 z y x - 1/18 z y x + + 3 2 4 3 2 3 3 4 + - 1/72 z y x - 1/36 x z - 1/54 x z - 1/27 x - 1/108 x + + 3 2 2 3 2 2 2 + - 4/27 y x z + 1/36 y x z - 1/18 y x z + 2/27 y x + 1/12 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + + 1/36 z y x - 1/36 y x z + 1/18 y x z - 2/27 y x z + + 3 2 2 3 3 4 3 4 2 3 + - 1/9 y x z + 1/54 z y x - 1/108 z y x + 4/27 y x z + + 3 2 3 2 3 3 3 3 3 3 + + 1/27 z y x + 1/9 y x z - 1/54 y x z - 1/27 z y x + 1/108 z y x + + 3 3 3 2 2 + + 2/27 y x z + 1/108 x + 1/27 x + 2/27 y x z - 2/27 z y x + + 4 2 2 2 2 2 2 2 + - 1/108 z x + 1/36 y x - 1/12 y x z - 1/36 y x z + 2/9 y x z + + 2 3 2 3 2 2 3 + - 2/9 y x z + 1/27 y x - 1/27 y x - 1/27 x z + 1/27 x z - 2/27 x z + + 3 2 2 2 2 2 2 2 4 + + 2/27 x z - 1/9 x z + 1/9 x z - 1/36 y x - 2/27 y x + 1/36 z x + + 3 4 3 4 2 4 2 3 + + 1/54 z x + 1/108 z x + 1/54 y x + 1/144 y x - 1/144 y x , + + 2 2 4 4 3 4 2 4 + COEFF(0, -1, 2) = 1/32 z y x - 1/36 z y x + 1/72 y x - 1/96 z y x + + 3 4 2 4 3 2 4 4 3 3 + + 1/18 z y x + 1/12 z y x + 1/48 z y x + 1/72 x - 1/9 y z + + 2 2 2 2 3 4 2 2 3 + - 1/9 y + 1/18 z - 5/32 y x z - 1/24 z y x - 5/48 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + + 5/36 y x z + 5/24 y x z - 1/36 z y x + 1/72 z y x + + 2 3 3 2 3 3 2 2 + - 5/18 y x z - 5/72 z y x - 1/9 z + 1/18 y - 1/24 y - 1/6 z + + 2 2 4 2 2 + - 5/72 x + 5/36 z y x - 1/9 y z + 1/72 z x + 5/96 y x z + + 2 2 3 2 2 3 2 2 + - 5/12 y x z - 5/72 y x - 1/24 y z - 1/6 y z - 5/72 x z + 1/18 + + 3 2 3 2 3 2 2 2 2 2 + + 2/9 y z + 1/12 y z + 5/36 x z + 1/3 y z + 5/24 x z + 1/8 y z + + 2 2 2 2 4 3 4 3 4 + + 5/96 y x + 5/36 y x - 1/24 z x - 1/36 z x + 1/18 z y - 1/36 y x + + 2 4 3 3 2 2 4 + - 1/96 y x , COEFF(1, -1, 2) = - 1/27 y x z - 1/48 z y x + + 4 2 3 3 2 3 3 3 3 + + 1/54 z y x - 1/72 y x z + 1/144 z y x + 1/54 z y x - 1/108 y x + + 3 4 2 2 3 3 2 3 2 4 + - 1/108 y x - 1/48 z y x + 1/54 y x - 1/18 z y x + 1/144 z y x + + 3 4 2 4 3 2 4 3 2 3 3 + - 1/27 z y x - 1/18 z y x - 1/72 z y x + 1/36 x z + 1/54 x z + + 4 3 2 2 3 + + 1/27 x - 1/108 x + 4/27 y x z - 1/36 y x z + 1/18 y x z - 2/27 y x + + 2 2 2 2 3 4 3 3 2 2 2 3 + + 1/12 y x z + 1/36 z y x + 1/36 y x z + 1/18 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 2/27 y x z - 1/9 y x z + 1/54 z y x - 1/108 z y x + + 2 3 3 2 3 2 3 3 3 3 + + 4/27 y x z + 1/27 z y x - 1/9 y x z + 1/54 y x z + 1/27 z y x + + 3 3 3 3 3 2 + - 1/108 z y x - 2/27 y x z - 1/108 x + 1/27 x - 2/27 y x z + + 2 4 2 2 2 2 2 + - 2/27 z y x - 1/108 z x - 1/36 y x + 1/12 y x z - 1/36 y x z + + 2 2 2 3 2 3 2 + + 2/9 y x z + 2/9 y x z + 1/27 y x + 1/27 y x + 1/27 x z + 1/27 x z + + 2 3 3 2 2 2 2 2 2 + - 2/27 x z - 2/27 x z - 1/9 x z - 1/9 x z - 1/36 y x - 2/27 y x + + 2 4 3 4 3 4 2 4 + + 1/36 z x + 1/54 z x - 1/108 z x + 1/54 y x + 1/144 y x + + 2 3 3 3 2 2 4 + + 1/144 y x , COEFF(2, -1, 2) = 1/54 y x z + 1/192 z y x + + 4 2 3 3 2 3 3 + - 1/216 z y x + 1/144 y x z - 1/288 z y x - 1/108 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 1/216 y x + 1/432 y x + 1/96 z y x - 1/108 y x + 1/36 z y x + + 2 4 3 4 2 4 3 2 4 + - 1/576 z y x + 1/108 z y x + 1/72 z y x + 1/288 z y x + + 3 2 3 3 4 3 + - 1/72 x z - 1/108 x z - 1/216 x + 1/432 x - 1/54 y x z + + 2 2 3 2 2 2 + + 1/288 y x z - 1/144 y x z + 1/108 y x - 1/192 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + - 1/144 z y x - 1/72 y x z - 1/288 y x z + 1/216 y x z + + 3 2 2 3 3 4 3 4 2 3 + + 1/144 y x z - 1/216 z y x + 1/432 z y x - 1/108 y x z + + 3 2 3 2 3 3 3 3 + - 1/432 z y x + 1/72 y x z - 1/108 y x z - 1/216 z y x + + 3 3 3 3 3 2 + + 1/216 z y x + 1/108 y x z + 1/216 x - 1/432 x + 1/108 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x + 1/432 z x + 1/288 y x - 1/96 y x z + 1/576 y x z + + 2 2 2 3 2 3 + - 1/72 y x z - 1/36 y x z - 1/432 y x - 1/216 y x - 1/216 x z + + 2 2 3 3 2 2 2 + - 1/432 x z + 1/216 x z + 1/108 x z + 1/144 x z + 1/72 x z + + 2 2 2 2 4 3 4 3 + + 1/576 y x + 1/216 y x - 1/144 z x - 1/216 z x + 1/216 z x + + 4 2 4 2 3 3 3 + - 1/216 y x - 1/576 y x - 1/288 y x , COEFF(-2, 0, 2) = 5/144 y x z + + 4 3 3 3 3 4 3 + + 5/576 z y x - 5/288 z y x + 1/144 y x - 1/288 y x - 5/288 y x + + 2 3 3 4 2 4 3 + + 5/96 z y x - 5/288 z y x - 5/192 z y x - 5/144 y x z + 5/288 y x + + 2 3 4 3 3 2 3 2 3 3 2 2 + + 1/96 z y x - 1/48 y x z - 1/144 y x z - 1/96 y x z + + 3 3 4 3 4 2 3 3 2 + + 1/144 z y x - 1/288 z y x + 5/288 y x z + 1/288 z y x + + 3 2 3 3 3 3 3 3 + + 1/48 y x z - 1/72 y x z - 1/144 z y x + 1/144 z y x + + 3 3 2 2 2 2 + + 1/72 y x z + 5/288 y x z - 5/576 z y x + 5/192 y x z - 5/96 y x z + + 3 2 3 2 4 + + 1/288 y x - 1/144 y x - 5/576 y x + 5/576 y x , COEFF(-1, 0, 2) = + + 3 3 4 3 3 3 3 4 + - 5/72 y x z - 5/144 z y x + 5/144 z y x - 1/72 y x + 1/72 y x + + 3 2 3 3 4 2 4 3 + + 5/144 y x - 5/48 z y x + 5/72 z y x + 5/48 z y x + 5/18 y x z + + 2 3 4 3 3 2 3 2 3 3 2 2 + - 5/36 y x - 1/24 z y x + 1/24 y x z + 1/9 y x z + 1/6 y x z + + 3 3 4 3 4 2 3 3 2 3 2 + - 1/36 z y x + 1/72 z y x - 5/18 y x z - 1/18 z y x - 1/6 y x z + + 3 3 3 3 3 3 3 3 + + 1/36 y x z + 1/18 z y x - 1/72 z y x - 1/9 y x z - 5/36 y x z + + 2 2 2 2 3 2 3 + + 5/36 z y x - 5/12 y x z + 5/12 y x z - 1/18 y x + 1/18 y x + + 2 4 3 2 3 4 + + 5/36 y x - 5/144 y x , COEFF(0, 0, 2) = 5/48 z y x - 1/48 y x + + 25 2 3 3 2 3 4 25 2 + - -- z y x - 1/12 z y + 5/24 y - 5/24 y x z + 5/96 z y x - -- y x + 96 96 + + 3 4 3 25 2 3 2 3 4 25 2 2 + - 5/48 z y x - 1/12 y + -- y x z + 1/16 z y x + -- y x z + 48 32 + + 3 2 2 4 2 3 + + 5/48 y x - 5/32 z y x - 5/8 y z - 5/12 y z + 5/24 y z + + 3 2 2 4 3 2 3 3 3 3 4 + - 5/16 y x z + 5/96 y x + 1/4 y z + 1/6 y z + 1/24 z y x + + 3 4 3 3 4 + - 1/48 z y x , COEFF(1, 0, 2) = 5/72 y x z - 5/144 z y x + + 3 3 3 3 4 3 2 3 + - 5/144 z y x + 1/72 y x + 1/72 y x - 5/144 y x + 5/48 z y x + + 3 4 2 4 3 2 3 4 + + 5/72 z y x + 5/48 z y x - 5/18 y x z + 5/36 y x - 1/24 z y x + + 3 3 2 3 2 3 3 2 2 3 3 4 + - 1/24 y x z + 1/9 y x z + 1/6 y x z - 1/36 z y x + + 3 4 2 3 3 2 3 2 3 3 3 + + 1/72 z y x - 5/18 y x z - 1/18 z y x + 1/6 y x z - 1/36 y x z + + 3 3 3 3 3 2 + - 1/18 z y x + 1/72 z y x + 1/9 y x z + 5/36 y x z + 5/36 z y x + + 2 2 2 3 2 3 2 + - 5/12 y x z - 5/12 y x z - 1/18 y x - 1/18 y x + 5/36 y x + + 4 3 3 4 + - 5/144 y x , COEFF(2, 0, 2) = - 5/144 y x z + 5/576 z y x + + 3 3 3 3 4 3 2 3 + + 5/288 z y x - 1/144 y x - 1/288 y x + 5/288 y x - 5/96 z y x + + 3 4 2 4 3 2 3 4 + - 5/288 z y x - 5/192 z y x + 5/144 y x z - 5/288 y x + 1/96 z y x + + 3 3 2 3 2 3 3 2 2 3 3 4 + + 1/48 y x z - 1/144 y x z - 1/96 y x z + 1/144 z y x + + 3 4 2 3 3 2 3 2 + - 1/288 z y x + 5/288 y x z + 1/288 z y x - 1/48 y x z + + 3 3 3 3 3 3 3 3 + + 1/72 y x z + 1/144 z y x - 1/144 z y x - 1/72 y x z + + 2 2 2 2 3 2 + - 5/288 y x z - 5/576 z y x + 5/192 y x z + 5/96 y x z + 1/288 y x + + 3 2 4 3 3 + + 1/144 y x - 5/576 y x + 5/576 y x , COEFF(-2, 1, 2) = - 1/54 y x z + + 2 2 4 4 2 3 3 2 3 + - 1/192 z y x - 1/216 z y x + 1/144 y x z - 1/288 z y x + + 3 3 3 3 4 2 2 3 3 + + 1/108 z y x - 1/216 y x + 1/432 y x + 1/96 z y x + 1/108 y x + + 2 3 2 4 3 4 2 4 + - 1/36 z y x + 1/576 z y x + 1/108 z y x + 1/72 z y x + + 3 2 4 3 2 3 3 4 + - 1/288 z y x - 1/72 x z - 1/108 x z - 1/216 x - 1/432 x + + 3 2 2 3 2 2 2 + + 1/54 y x z + 1/288 y x z - 1/144 y x z - 1/108 y x + 1/192 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + - 1/144 z y x + 1/72 y x z + 1/288 y x z + 1/216 y x z + + 3 2 2 3 3 4 3 4 2 3 + + 1/144 y x z - 1/216 z y x + 1/432 z y x - 1/108 y x z + + 3 2 3 2 3 3 3 3 + - 1/432 z y x - 1/72 y x z + 1/108 y x z + 1/216 z y x + + 3 3 3 3 3 2 + - 1/216 z y x - 1/108 y x z + 1/216 x + 1/432 x - 1/108 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x - 1/432 z x + 1/288 y x - 1/96 y x z - 1/576 y x z + + 2 2 2 3 2 3 + - 1/72 y x z + 1/36 y x z - 1/432 y x + 1/216 y x - 1/216 x z + + 2 2 3 3 2 2 2 + + 1/432 x z - 1/216 x z + 1/108 x z - 1/144 x z + 1/72 x z + + 2 2 2 2 4 3 4 3 + - 1/576 y x + 1/216 y x + 1/144 z x + 1/216 z x + 1/216 z x + + 4 2 4 2 3 3 3 + - 1/216 y x + 1/576 y x - 1/288 y x , COEFF(-1, 1, 2) = 1/27 y x z + + 2 2 4 4 2 3 3 2 3 + + 1/48 z y x + 1/54 z y x - 1/72 y x z + 1/144 z y x + + 3 3 3 3 4 2 2 3 3 + - 1/54 z y x + 1/108 y x - 1/108 y x - 1/48 z y x - 1/54 y x + + 2 3 2 4 3 4 2 4 + + 1/18 z y x - 1/144 z y x - 1/27 z y x - 1/18 z y x + + 3 2 4 3 2 3 3 4 + + 1/72 z y x + 1/36 x z + 1/54 x z + 1/27 x + 1/108 x + + 3 2 2 3 2 2 2 + - 4/27 y x z - 1/36 y x z + 1/18 y x z + 2/27 y x - 1/12 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + + 1/36 z y x - 1/36 y x z - 1/18 y x z - 2/27 y x z + + 3 2 2 3 3 4 3 4 2 3 + - 1/9 y x z + 1/54 z y x - 1/108 z y x + 4/27 y x z + + 3 2 3 2 3 3 3 3 3 3 + + 1/27 z y x + 1/9 y x z - 1/54 y x z - 1/27 z y x + 1/108 z y x + + 3 3 3 2 2 + + 2/27 y x z - 1/108 x - 1/27 x + 2/27 y x z - 2/27 z y x + + 4 2 2 2 2 2 2 2 + + 1/108 z x - 1/36 y x + 1/12 y x z + 1/36 y x z + 2/9 y x z + + 2 3 2 3 2 2 3 + - 2/9 y x z + 1/27 y x - 1/27 y x + 1/27 x z - 1/27 x z + 2/27 x z + + 3 2 2 2 2 2 2 2 4 + - 2/27 x z + 1/9 x z - 1/9 x z + 1/36 y x - 2/27 y x - 1/36 z x + + 3 4 3 4 2 4 2 3 + - 1/54 z x - 1/108 z x + 1/54 y x - 1/144 y x + 1/144 y x , + + 2 2 4 4 3 4 2 4 + COEFF(0, 1, 2) = - 1/32 z y x - 1/36 z y x + 1/72 y x + 1/96 z y x + + 3 4 2 4 3 2 4 4 3 3 + + 1/18 z y x + 1/12 z y x - 1/48 z y x - 1/72 x - 1/9 y z + + 2 2 2 2 3 4 2 2 3 + - 1/9 y - 1/18 z + 5/32 y x z - 1/24 z y x + 5/48 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + + 5/36 y x z + 5/24 y x z - 1/36 z y x + 1/72 z y x + + 2 3 3 2 3 3 2 2 + - 5/18 y x z - 5/72 z y x + 1/9 z + 1/18 y + 1/24 y + 1/6 z + + 2 2 4 2 2 + + 5/72 x + 5/36 z y x - 1/9 y z - 1/72 z x - 5/96 y x z + + 2 2 3 2 2 3 2 2 + - 5/12 y x z - 5/72 y x + 1/24 y z - 1/6 y z + 5/72 x z - 1/18 + + 3 2 3 2 3 2 2 2 2 2 + + 2/9 y z - 1/12 y z - 5/36 x z + 1/3 y z - 5/24 x z - 1/8 y z + + 2 2 2 2 4 3 4 3 4 + - 5/96 y x + 5/36 y x + 1/24 z x + 1/36 z x + 1/18 z y - 1/36 y x + + 2 4 3 3 2 2 4 + + 1/96 y x , COEFF(1, 1, 2) = - 1/27 y x z + 1/48 z y x + + 4 2 3 3 2 3 3 3 3 + + 1/54 z y x + 1/72 y x z - 1/144 z y x + 1/54 z y x - 1/108 y x + + 3 4 2 2 3 3 2 3 2 4 + - 1/108 y x + 1/48 z y x + 1/54 y x - 1/18 z y x - 1/144 z y x + + 3 4 2 4 3 2 4 3 2 3 3 + - 1/27 z y x - 1/18 z y x + 1/72 z y x - 1/36 x z - 1/54 x z + + 4 3 2 2 3 + - 1/27 x + 1/108 x + 4/27 y x z + 1/36 y x z - 1/18 y x z - 2/27 y x + + 2 2 2 2 3 4 3 3 2 2 2 3 + - 1/12 y x z + 1/36 z y x + 1/36 y x z - 1/18 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 2/27 y x z - 1/9 y x z + 1/54 z y x - 1/108 z y x + + 2 3 3 2 3 2 3 3 3 3 + + 4/27 y x z + 1/27 z y x - 1/9 y x z + 1/54 y x z + 1/27 z y x + + 3 3 3 3 3 2 + - 1/108 z y x - 2/27 y x z + 1/108 x - 1/27 x - 2/27 y x z + + 2 4 2 2 2 2 2 + - 2/27 z y x + 1/108 z x + 1/36 y x - 1/12 y x z + 1/36 y x z + + 2 2 2 3 2 3 2 + + 2/9 y x z + 2/9 y x z + 1/27 y x + 1/27 y x - 1/27 x z - 1/27 x z + + 2 3 3 2 2 2 2 2 2 + + 2/27 x z + 2/27 x z + 1/9 x z + 1/9 x z + 1/36 y x - 2/27 y x + + 2 4 3 4 3 4 2 4 + - 1/36 z x - 1/54 z x + 1/108 z x + 1/54 y x - 1/144 y x + + 2 3 3 3 2 2 4 + - 1/144 y x , COEFF(2, 1, 2) = 1/54 y x z - 1/192 z y x + + 4 2 3 3 2 3 3 + - 1/216 z y x - 1/144 y x z + 1/288 z y x - 1/108 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 1/216 y x + 1/432 y x - 1/96 z y x - 1/108 y x + 1/36 z y x + + 2 4 3 4 2 4 3 2 4 + + 1/576 z y x + 1/108 z y x + 1/72 z y x - 1/288 z y x + + 3 2 3 3 4 3 + + 1/72 x z + 1/108 x z + 1/216 x - 1/432 x - 1/54 y x z + + 2 2 3 2 2 2 + - 1/288 y x z + 1/144 y x z + 1/108 y x + 1/192 y x z + + 2 3 4 3 3 2 2 2 3 3 2 3 + - 1/144 z y x - 1/72 y x z + 1/288 y x z + 1/216 y x z + + 3 2 2 3 3 4 3 4 2 3 + + 1/144 y x z - 1/216 z y x + 1/432 z y x - 1/108 y x z + + 3 2 3 2 3 3 3 3 + - 1/432 z y x + 1/72 y x z - 1/108 y x z - 1/216 z y x + + 3 3 3 3 3 2 + + 1/216 z y x + 1/108 y x z - 1/216 x + 1/432 x + 1/108 y x z + + 2 4 2 2 2 2 2 + + 1/216 z y x - 1/432 z x - 1/288 y x + 1/96 y x z - 1/576 y x z + + 2 2 2 3 2 3 + - 1/72 y x z - 1/36 y x z - 1/432 y x - 1/216 y x + 1/216 x z + + 2 2 3 3 2 2 2 + + 1/432 x z - 1/216 x z - 1/108 x z - 1/144 x z - 1/72 x z + + 2 2 2 2 4 3 4 3 + - 1/576 y x + 1/216 y x + 1/144 z x + 1/216 z x - 1/216 z x + + 4 2 4 2 3 3 3 + - 1/216 y x + 1/576 y x + 1/288 y x , COEFF(-2, 2, 2) = 1/864 y x z + + 2 2 4 4 2 3 3 2 3 + + 1/384 z y x + 1/3456 z y x - 1/288 y x z + 1/576 z y x + + 3 3 3 3 4 2 2 3 + - 1/1728 z y x + 1/864 y x - 1/1728 y x - 1/192 z y x + + 3 2 3 2 4 3 4 + - 1/1728 y x + 1/576 z y x - 1/1152 z y x - 1/1728 z y x + + 2 4 3 2 4 3 2 3 3 + - 1/1152 z y x + 1/576 z y x + 1/576 x z + 1/864 x z + 1/1728 x + + 4 3 2 2 3 + + 1/3456 x - 1/864 y x z - 1/576 y x z + 1/288 y x z + 1/1728 y x + + 2 2 2 2 3 4 3 3 2 2 2 3 + - 1/384 y x z + 1/576 z y x - 1/288 y x z - 1/576 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 1/864 y x z - 1/576 y x z + 1/864 z y x - 1/1728 z y x + + 2 3 3 2 3 2 3 3 3 + + 1/1728 y x z + 1/1728 z y x + 1/288 y x z - 1/432 y x z + + 3 3 3 3 3 3 2 + - 1/864 z y x + 1/864 z y x + 1/432 y x z - 1/1728 x - 1/3456 x + + 2 4 2 2 2 + + 1/1728 y x z - 1/3456 z y x + 1/3456 z x - 1/576 y x + 1/192 y x z + + 2 2 2 2 2 3 2 + + 1/1152 y x z + 1/1152 y x z - 1/576 y x z + 1/1728 y x + + 3 2 2 3 3 + - 1/864 y x + 1/1728 x z - 1/3456 x z + 1/1728 x z - 1/864 x z + + 2 2 2 2 2 2 2 4 + + 1/1152 x z - 1/576 x z + 1/1152 y x - 1/3456 y x - 1/1152 z x + + 3 4 3 4 2 4 2 3 + - 1/1728 z x - 1/1728 z x + 1/3456 y x - 1/1152 y x + 1/576 y x , + + 3 3 2 2 4 4 + COEFF(-1, 2, 2) = - 1/432 y x z - 1/96 z y x - 1/864 z y x + + 2 3 3 2 3 3 3 3 + + 1/144 y x z - 1/288 z y x + 1/864 z y x - 1/432 y x + + 3 4 2 2 3 3 2 3 2 4 + + 1/432 y x + 1/96 z y x + 1/864 y x - 1/288 z y x + 1/288 z y x + + 3 4 2 4 3 2 4 3 2 + + 1/432 z y x + 1/288 z y x - 1/144 z y x - 1/288 x z + + 3 3 4 3 2 + - 1/432 x z - 1/216 x - 1/864 x + 1/108 y x z + 1/72 y x z + + 2 3 2 2 2 2 3 4 + - 1/36 y x z - 1/216 y x + 1/24 y x z - 1/144 z y x + + 3 3 2 2 2 3 3 2 3 3 2 2 + + 1/144 y x z + 1/36 y x z + 1/54 y x z + 1/36 y x z + + 3 3 4 3 4 2 3 3 2 + - 1/216 z y x + 1/432 z y x - 1/108 y x z - 1/108 z y x + + 3 2 3 3 3 3 3 3 + - 1/36 y x z + 1/216 y x z + 1/108 z y x - 1/432 z y x + + 3 3 3 2 2 + - 1/54 y x z + 1/864 x + 1/216 x - 1/216 y x z + 1/216 z y x + + 4 2 2 2 2 2 2 2 + - 1/864 z x + 1/72 y x - 1/24 y x z - 1/72 y x z - 1/72 y x z + + 2 3 2 3 2 + + 1/72 y x z - 1/108 y x + 1/108 y x - 1/216 x z + 1/216 x z + + 2 3 3 2 2 2 2 2 + - 1/108 x z + 1/108 x z - 1/72 x z + 1/72 x z - 1/72 y x + + 2 2 4 3 4 3 4 + + 1/216 y x + 1/288 z x + 1/432 z x + 1/864 z x - 1/864 y x + + 2 4 2 3 2 2 4 4 + + 1/288 y x - 1/288 y x , COEFF(0, 2, 2) = 1/64 z y x + 1/576 z y x + + 3 4 2 4 3 4 2 4 + - 1/288 y x - 1/192 z y x - 1/288 z y x - 1/192 z y x + + 3 2 4 4 3 3 + + 1/96 z y x + 1/576 x + 1/36 y z + 1/144 y + 1/144 z + + 2 2 2 2 3 4 2 2 3 3 2 3 + - 5/64 y x z + 1/96 z y x - 5/96 y x z - 5/144 y x z + + 3 2 2 3 3 4 3 4 2 3 + - 5/96 y x z + 1/144 z y x - 1/288 z y x + 5/288 y x z + + 3 2 3 3 2 2 2 + + 5/288 z y x - 1/72 z - 1/72 y - 1/48 y - 1/48 z - 5/576 x + + 2 4 2 2 2 2 + - 5/576 z y x + 1/144 y z + 1/576 z x + 5/192 y x z + 5/192 y x z + + 3 2 2 3 2 2 3 + + 5/288 y x - 1/48 y z + 1/24 y z - 5/576 x z - 1/72 y z + + 2 3 2 3 2 2 2 2 2 + + 1/24 y z + 5/288 x z - 1/48 y z + 5/192 x z + 1/16 y z + + 2 2 2 2 4 3 4 3 + + 5/192 y x - 5/576 y x + 1/144 - 1/192 z x - 1/288 z x - 1/72 z y + + 4 2 4 3 3 2 2 4 + + 1/576 y x - 1/192 y x , COEFF(1, 2, 2) = 1/432 y x z - 1/96 z y x + + 4 2 3 3 2 3 3 + - 1/864 z y x - 1/144 y x z + 1/288 z y x - 1/864 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 1/432 y x + 1/432 y x - 1/96 z y x - 1/864 y x + 1/288 z y x + + 2 4 3 4 2 4 3 2 4 + + 1/288 z y x + 1/432 z y x + 1/288 z y x - 1/144 z y x + + 3 2 3 3 4 3 + + 1/288 x z + 1/432 x z + 1/216 x - 1/864 x - 1/108 y x z + + 2 2 3 2 2 2 2 3 4 + - 1/72 y x z + 1/36 y x z + 1/216 y x + 1/24 y x z - 1/144 z y x + + 3 3 2 2 2 3 3 2 3 3 2 2 + - 1/144 y x z + 1/36 y x z + 1/54 y x z + 1/36 y x z + + 3 3 4 3 4 2 3 3 2 + - 1/216 z y x + 1/432 z y x - 1/108 y x z - 1/108 z y x + + 3 2 3 3 3 3 3 3 + + 1/36 y x z - 1/216 y x z - 1/108 z y x + 1/432 z y x + + 3 3 3 2 2 + + 1/54 y x z - 1/864 x + 1/216 x + 1/216 y x z + 1/216 z y x + + 4 2 2 2 2 2 2 2 + - 1/864 z x - 1/72 y x + 1/24 y x z - 1/72 y x z - 1/72 y x z + + 2 3 2 3 2 + - 1/72 y x z - 1/108 y x - 1/108 y x + 1/216 x z + 1/216 x z + + 2 3 3 2 2 2 2 2 + - 1/108 x z - 1/108 x z - 1/72 x z - 1/72 x z - 1/72 y x + + 2 2 4 3 4 3 4 + + 1/216 y x + 1/288 z x + 1/432 z x - 1/864 z x - 1/864 y x + + 2 4 2 3 3 3 + + 1/288 y x + 1/288 y x , COEFF(2, 2, 2) = - 1/864 y x z + + 2 2 4 4 2 3 3 2 3 + + 1/384 z y x + 1/3456 z y x + 1/288 y x z - 1/576 z y x + + 3 3 3 3 4 2 2 3 + + 1/1728 z y x - 1/864 y x - 1/1728 y x + 1/192 z y x + + 3 2 3 2 4 3 4 + + 1/1728 y x - 1/576 z y x - 1/1152 z y x - 1/1728 z y x + + 2 4 3 2 4 3 2 3 3 + - 1/1152 z y x + 1/576 z y x - 1/576 x z - 1/864 x z - 1/1728 x + + 4 3 2 2 3 + + 1/3456 x + 1/864 y x z + 1/576 y x z - 1/288 y x z - 1/1728 y x + + 2 2 2 2 3 4 3 3 2 2 2 3 + - 1/384 y x z + 1/576 z y x + 1/288 y x z - 1/576 y x z + + 3 2 3 3 2 2 3 3 4 3 4 + - 1/864 y x z - 1/576 y x z + 1/864 z y x - 1/1728 z y x + + 2 3 3 2 3 2 3 3 3 + + 1/1728 y x z + 1/1728 z y x - 1/288 y x z + 1/432 y x z + + 3 3 3 3 3 3 2 + + 1/864 z y x - 1/864 z y x - 1/432 y x z + 1/1728 x - 1/3456 x + + 2 4 2 2 2 + - 1/1728 y x z - 1/3456 z y x + 1/3456 z x + 1/576 y x - 1/192 y x z + + 2 2 2 2 2 3 2 + + 1/1152 y x z + 1/1152 y x z + 1/576 y x z + 1/1728 y x + + 3 2 2 3 3 + + 1/864 y x - 1/1728 x z - 1/3456 x z + 1/1728 x z + 1/864 x z + + 2 2 2 2 2 2 2 4 + + 1/1152 x z + 1/576 x z + 1/1152 y x - 1/3456 y x - 1/1152 z x + + 3 4 3 4 2 4 2 3 + - 1/1728 z x + 1/1728 z x + 1/3456 y x - 1/1152 y x - 1/576 y x ] + +> print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp", +> "3d.coeffs/3d.cube.order4.smooth0/coeffs-dyz.compute.c"); +bytes 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+ 1/3456 y x + 1/576 z y x + + 3 2 3 2 4 2 4 + + 1/1728 y x - 1/288 z y x + 1/1152 z y x + 1/576 z y x + + 2 2 2 2 2 3 4 + + 1/576 y x z - 1/1728 y x + 1/1152 y x z - 1/576 z y x + + 3 3 2 3 2 2 3 4 3 2 + + 1/288 y x z + 1/576 y x z + 1/576 z y x - 1/576 z y x + + 3 2 4 4 3 3 3 + - 1/288 y x z - 1/6912 y x + 1/288 z y x - 1/288 z y x + + 2 4 3 2 2 2 + - 1/288 y x z + 1/576 z y x + 1/3456 y x + 1/3456 y x - 1/576 y x z + + 2 2 2 2 2 3 2 + - 1/1152 y x z - 1/576 y x z + 1/288 y x z - 1/3456 y x + + 4 3 2 2 2 4 2 + - 1/3456 y x + 1/1728 y x - 1/6912 y x + 1/3456 y x + 1/6912 y x + + 4 2 4 2 3 + - 1/3456 y x + 1/6912 y x - 1/3456 y x , COEFF(-1, -2, -2) = + + 2 4 3 4 3 2 4 2 2 4 4 + 1/288 z y x - 1/288 z y x + 1/72 z y x - 1/72 z y x + 1/72 z y x + + 4 2 2 4 4 4 4 2 2 4 + - 1/72 z y x - 1/288 z y x + 1/288 z y x + 1/288 z y x + + 4 2 3 3 3 3 3 4 + + 1/144 z y x + 1/288 z y x - 1/144 z y x + 1/864 y x - 1/864 y x + + 2 2 3 3 2 3 2 4 + - 1/288 z y x - 1/864 y x + 1/144 z y x - 1/288 z y x + + 2 4 2 2 2 2 2 3 4 + - 1/144 z y x - 1/72 y x z + 1/216 y x - 1/72 y x z + 1/144 z y x + + 3 3 2 3 2 2 3 4 3 2 + - 1/144 y x z - 1/36 y x z - 1/144 z y x + 1/36 z y x + + 3 2 4 4 3 3 3 + + 1/36 y x z + 1/1728 y x - 1/36 z y x + 1/144 z y x + 1/36 y x z + + 2 4 3 2 2 2 2 2 + - 1/36 z y x - 1/1728 y x - 1/432 y x + 1/72 y x z + 1/72 y x z + + 2 2 2 3 2 4 3 + + 1/36 y x z - 1/36 y x z + 1/216 y x + 1/432 y x - 1/216 y x + + 2 2 2 4 2 4 2 4 + + 1/432 y x - 1/216 y x - 1/432 y x + 1/864 y x - 1/1728 y x + + 2 3 2 4 2 4 2 + + 1/1728 y x , COEFF(0, -2, -2) = - 5/192 z y x + 5/192 z y x + + 2 4 4 4 4 2 2 4 4 + + 1/192 z y x - 1/192 z y x - 1/192 z y x - 1/96 z y x + + 3 4 2 4 2 4 4 + + 1/576 y x + 1/192 z y x + 1/96 z y x - 1/144 y - 1/288 y + + 2 2 2 2 3 4 4 3 2 2 + + 5/192 y x z - 1/96 z y x - 1/48 z y + 5/96 y x z + + 3 4 2 4 3 2 4 4 3 + + 1/96 z y x + 1/48 z y - 5/96 z y x - 1/1152 y x + 1/144 y + + 2 2 2 2 2 2 + + 1/288 y + 5/96 z y x - 1/24 y z - 5/192 y x z - 5/96 y x z + + 3 2 2 3 2 2 2 2 + - 5/576 y x + 1/48 y z - 1/24 y z + 1/24 y z - 1/48 y z + + 2 2 2 4 2 3 4 + - 5/1152 y x + 5/576 y x + 5/1152 y x + 1/24 z y - 1/576 y x + + 2 4 2 4 3 4 3 + + 1/1152 y x , COEFF(1, -2, -2) = - 1/288 z y x + 1/288 z y x + + 2 4 2 2 4 4 4 2 + + 1/72 z y x + 1/72 z y x - 1/72 z y x - 1/72 z y x + + 2 4 4 4 4 2 2 4 4 + - 1/288 z y x + 1/288 z y x + 1/288 z y x + 1/144 z y x + + 2 3 3 3 3 3 4 + - 1/288 z y x + 1/144 z y x - 1/864 y x - 1/864 y x + + 2 2 3 3 2 3 2 4 + + 1/288 z y x + 1/864 y x - 1/144 z y x - 1/288 z y x + + 2 4 2 2 2 2 2 3 4 + - 1/144 z y x + 1/72 y x z - 1/216 y x - 1/72 y x z + 1/144 z y x + + 3 3 2 3 2 2 3 4 3 2 + + 1/144 y x z - 1/36 y x z - 1/144 z y x + 1/36 z y x + + 3 2 4 4 3 3 3 + - 1/36 y x z + 1/1728 y x + 1/36 z y x - 1/144 z y x - 1/36 y x z + + 2 4 3 2 2 2 2 2 + - 1/36 z y x + 1/1728 y x + 1/432 y x - 1/72 y x z + 1/72 y x z + + 2 2 2 3 2 4 3 + + 1/36 y x z + 1/36 y x z + 1/216 y x - 1/432 y x + 1/216 y x + + 2 2 2 4 2 4 2 4 + + 1/432 y x - 1/216 y x - 1/432 y x + 1/864 y x - 1/1728 y x + + 2 3 2 4 3 4 3 + - 1/1728 y x , COEFF(2, -2, -2) = 1/576 z y x - 1/576 z y x + + 2 4 2 2 4 4 4 2 + - 1/1152 z y x - 1/576 z y x + 1/576 z y x + 1/1152 z y x + + 2 4 4 4 4 2 2 4 4 + + 1/1152 z y x - 1/1152 z y x - 1/1152 z y x - 1/576 z y x + + 2 3 3 3 3 3 4 + + 1/576 z y x - 1/288 z y x + 1/1728 y x + 1/3456 y x + + 2 2 3 3 2 3 2 4 + - 1/576 z y x - 1/1728 y x + 1/288 z y x + 1/1152 z y x + + 2 4 2 2 2 2 + + 1/576 z y x - 1/576 y x z + 1/1728 y x + 1/1152 y x z + + 2 3 4 3 3 2 3 2 2 3 4 + - 1/576 z y x - 1/288 y x z + 1/576 y x z + 1/576 z y x + + 3 2 3 2 4 4 3 + - 1/576 z y x + 1/288 y x z - 1/6912 y x - 1/288 z y x + + 3 3 2 4 3 2 + + 1/288 z y x + 1/288 y x z + 1/576 z y x - 1/3456 y x - 1/3456 y x + + 2 2 2 2 2 2 2 + + 1/576 y x z - 1/1152 y x z - 1/576 y x z - 1/288 y x z + + 3 2 4 3 2 2 2 + - 1/3456 y x + 1/3456 y x - 1/1728 y x - 1/6912 y x + 1/3456 y x + + 4 2 4 2 4 2 3 + + 1/6912 y x - 1/3456 y x + 1/6912 y x + 1/3456 y x , + + 2 4 3 4 3 2 4 2 + COEFF(-2, -1, -2) = 1/144 z y x - 1/144 z y x + 1/288 z y x + + 2 4 4 4 2 2 4 4 + - 1/144 z y x + 1/144 z y x - 1/288 z y x - 1/288 z y x + + 4 4 2 2 4 4 2 3 3 + + 1/288 z y x + 1/72 z y x + 1/72 z y x + 1/36 z y x - 1/36 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 1/864 y x - 1/1728 y x - 1/36 z y x - 1/216 y x + 1/36 z y x + + 2 4 2 4 2 2 2 2 + - 1/72 z y x - 1/72 z y x - 1/36 y x z + 1/216 y x - 1/72 y x z + + 2 3 4 3 3 2 3 2 2 3 4 + + 1/288 z y x - 1/144 y x z - 1/288 y x z - 1/288 z y x + + 3 2 3 2 4 4 3 + + 1/288 z y x + 1/144 y x z + 1/1728 y x - 1/144 z y x + + 3 3 2 4 3 2 + + 1/144 z y x + 1/36 y x z - 1/72 z y x - 1/864 y x - 1/216 y x + + 2 2 2 2 2 2 2 3 2 + + 1/36 y x z + 1/72 y x z + 1/72 y x z - 1/36 y x z + 1/1728 y x + + 4 3 2 2 2 4 2 + + 1/864 y x - 1/864 y x + 1/432 y x - 1/432 y x - 1/1728 y x + + 4 2 4 2 3 + + 1/432 y x - 1/432 y x + 1/216 y x , COEFF(-1, -1, -2) = + + 2 4 3 4 3 2 4 2 2 4 4 + - 1/72 z y x + 1/72 z y x - 1/18 z y x + 1/18 z y x - 1/18 z y x + + 4 2 2 4 4 4 4 2 2 4 + + 1/18 z y x + 1/72 z y x - 1/72 z y x - 1/18 z y x + + 4 2 3 3 3 3 3 4 + - 1/18 z y x - 1/18 z y x + 1/18 z y x - 1/432 y x + 1/432 y x + + 2 2 3 3 2 3 2 4 2 4 + + 1/18 z y x + 1/108 y x - 1/18 z y x + 1/18 z y x + 1/18 z y x + + 2 2 2 2 2 3 4 3 3 2 + + 2/9 y x z - 1/27 y x + 2/9 y x z - 1/72 z y x + 1/72 y x z + + 3 2 2 3 4 3 2 3 2 4 4 + + 1/18 y x z + 1/72 z y x - 1/18 z y x - 1/18 y x z - 1/432 y x + + 3 3 3 2 4 3 + + 1/18 z y x - 1/72 z y x - 2/9 y x z + 2/9 z y x + 1/432 y x + + 2 2 2 2 2 2 2 2 + + 1/27 y x - 2/9 y x z - 2/9 y x z - 2/9 y x z + 2/9 y x z + + 3 2 4 3 2 2 2 + - 1/108 y x - 1/108 y x + 1/108 y x - 1/27 y x + 1/27 y x + + 4 2 4 2 4 2 3 + + 1/108 y x - 1/108 y x + 1/108 y x - 1/108 y x , COEFF(0, -1, -2) + + 2 4 2 4 2 2 4 4 4 4 + = 5/48 z y x - 5/48 z y x - 1/48 z y x + 1/48 z y x + + 2 2 4 4 3 4 2 4 2 4 + + 1/12 z y x + 1/12 z y x - 1/288 y x - 1/12 z y x - 1/12 z y x + + 4 2 2 2 2 3 4 4 + + 1/18 y + 1/72 y - 5/12 y x z + 1/48 z y x + 1/12 z y + + 3 2 2 3 4 2 4 3 2 4 4 + - 5/48 y x z - 1/48 z y x - 1/12 z y + 5/48 z y x + 1/288 y x + + 3 2 2 2 2 2 2 + - 1/72 y - 1/18 y - 5/12 z y x + 1/3 y z + 5/12 y x z + 5/12 y x z + + 3 2 2 3 2 2 2 2 2 2 + + 5/288 y x - 1/3 y z + 1/12 y z - 1/3 y z + 1/3 y z + 5/72 y x + + 2 4 2 3 4 2 4 + - 5/72 y x - 5/288 y x - 1/12 z y + 1/72 y x - 1/72 y x , + + 2 4 3 4 3 2 4 2 + COEFF(1, -1, -2) = 1/72 z y x - 1/72 z y x - 1/18 z y x + + 2 4 4 4 2 2 4 4 4 4 + - 1/18 z y x + 1/18 z y x + 1/18 z y x + 1/72 z y x - 1/72 z y x + + 2 2 4 4 2 3 3 3 3 + - 1/18 z y x - 1/18 z y x + 1/18 z y x - 1/18 z y x + 1/432 y x + + 3 4 2 2 3 3 2 3 2 4 + + 1/432 y x - 1/18 z y x - 1/108 y x + 1/18 z y x + 1/18 z y x + + 2 4 2 2 2 2 2 3 4 + + 1/18 z y x - 2/9 y x z + 1/27 y x + 2/9 y x z - 1/72 z y x + + 3 3 2 3 2 2 3 4 3 2 + - 1/72 y x z + 1/18 y x z + 1/72 z y x - 1/18 z y x + + 3 2 4 4 3 3 3 + + 1/18 y x z - 1/432 y x - 1/18 z y x + 1/72 z y x + 2/9 y x z + + 2 4 3 2 2 2 2 2 + + 2/9 z y x - 1/432 y x - 1/27 y x + 2/9 y x z - 2/9 y x z + + 2 2 2 3 2 4 3 + - 2/9 y x z - 2/9 y x z - 1/108 y x + 1/108 y x - 1/108 y x + + 2 2 2 4 2 4 2 4 + - 1/27 y x + 1/27 y x + 1/108 y x - 1/108 y x + 1/108 y x + + 2 3 2 4 3 4 3 + + 1/108 y x , COEFF(2, -1, -2) = - 1/144 z y x + 1/144 z y x + + 2 4 2 2 4 4 4 2 + + 1/288 z y x + 1/144 z y x - 1/144 z y x - 1/288 z y x + + 2 4 4 4 4 2 2 4 4 + - 1/288 z y x + 1/288 z y x + 1/72 z y x + 1/72 z y x + + 2 3 3 3 3 3 4 2 2 3 + - 1/36 z y x + 1/36 z y x - 1/864 y x - 1/1728 y x + 1/36 z y x + + 3 2 3 2 4 2 4 2 + + 1/216 y x - 1/36 z y x - 1/72 z y x - 1/72 z y x + 1/36 y x z + + 2 2 2 2 3 4 3 3 2 + - 1/216 y x - 1/72 y x z + 1/288 z y x + 1/144 y x z + + 3 2 2 3 4 3 2 3 2 + - 1/288 y x z - 1/288 z y x + 1/288 z y x - 1/144 y x z + + 4 4 3 3 3 2 + + 1/1728 y x + 1/144 z y x - 1/144 z y x - 1/36 y x z - 1/72 z y x + + 4 3 2 2 2 2 2 2 2 + + 1/864 y x + 1/216 y x - 1/36 y x z + 1/72 y x z + 1/72 y x z + + 2 3 2 4 3 2 2 + + 1/36 y x z + 1/1728 y x - 1/864 y x + 1/864 y x + 1/432 y x + + 2 4 2 4 2 4 2 3 + - 1/432 y x - 1/1728 y x + 1/432 y x - 1/432 y x - 1/216 y x , + + 2 4 3 4 3 2 4 2 + COEFF(-2, 0, -2) = - 1/96 z y x + 1/96 z y x - 1/192 z y x + + 2 4 4 4 2 2 4 4 + + 1/96 z y x - 1/96 z y x + 1/192 z y x + 1/192 z y x + + 4 4 2 2 4 2 3 2 2 3 + - 1/192 z y x - 5/192 z y x - 5/96 z y x + 5/96 z y x + + 2 4 3 2 4 2 + + 5/192 z y x - 1/24 x z - 1/144 x - 1/288 x + 5/96 y x z + + 2 2 2 4 4 3 2 4 3 + + 5/192 y x z - 1/1152 y x + 1/144 x + 1/288 x + 1/576 y x + + 4 2 2 2 2 2 4 + - 1/48 z x + 5/576 y x - 5/96 y x z - 5/192 y x z - 1/576 y x + + 2 2 2 2 2 2 + - 1/24 x z + 1/48 x z - 1/48 x z + 1/24 x z - 5/1152 y x + + 4 2 2 4 3 2 4 2 3 + + 1/1152 y x + 1/48 z x + 1/24 z x + 5/1152 y x - 5/576 y x , + + 2 4 3 4 3 2 4 2 + COEFF(-1, 0, -2) = 1/48 z y x - 1/48 z y x + 1/12 z y x + + 2 4 4 4 2 2 4 4 4 4 + - 1/12 z y x + 1/12 z y x - 1/12 z y x - 1/48 z y x + 1/48 z y x + + 2 2 4 2 3 2 2 3 2 4 3 2 + + 5/48 z y x + 5/48 z y x - 5/48 z y x - 5/48 z y x + 1/12 x z + + 4 2 2 2 2 4 4 3 + + 1/18 x + 1/72 x - 5/12 y x z - 5/12 y x z + 1/288 y x - 1/72 x + + 2 4 3 4 2 2 2 + - 1/18 x - 1/288 y x + 1/12 z x - 5/72 y x + 5/12 y x z + + 2 2 4 2 2 2 2 + + 5/12 y x z + 1/72 y x + 1/3 x z - 1/3 x z + 1/3 x z - 1/3 x z + + 2 2 4 2 2 4 3 2 4 + + 5/72 y x - 1/72 y x - 1/12 z x - 1/12 z x - 5/288 y x + + 2 3 2 4 2 4 2 + + 5/288 y x , COEFF(0, 0, -2) = - 5/32 z y x + 5/32 z y x + + 2 4 4 4 4 2 2 4 2 4 4 + + 1/32 z y x - 1/32 z y x - 5/32 z y x + 5/32 z y x - 1/48 x + + 4 25 2 2 2 4 2 4 4 4 + - 1/2 z - 1/48 y + -- y x z - 1/8 z y + 1/8 z y - 1/192 y x + 32 + + 2 2 2 4 25 2 2 2 + - 1/12 + 5/48 y + 1/2 z + 5/48 x - 1/8 z x - -- y x z + 5/8 y z + 32 + + 2 2 2 2 2 25 2 2 4 2 2 4 + + 5/8 x z - 5/8 x z - 5/8 y z - --- y x + 5/192 y x + 1/8 z x + 192 + + 2 4 2 4 3 4 3 + + 5/192 y x , COEFF(1, 0, -2) = - 1/48 z y x + 1/48 z y x + + 2 4 2 2 4 4 4 2 + + 1/12 z y x + 1/12 z y x - 1/12 z y x - 1/12 z y x + + 2 4 4 4 4 2 2 4 2 3 + - 1/48 z y x + 1/48 z y x + 5/48 z y x - 5/48 z y x + + 2 2 3 2 4 3 2 4 + + 5/48 z y x - 5/48 z y x - 1/12 x z - 1/18 x + 1/72 x + + 2 2 2 2 4 4 3 2 + + 5/12 y x z - 5/12 y x z + 1/288 y x + 1/72 x - 1/18 x + + 4 3 4 2 2 2 2 2 + + 1/288 y x + 1/12 z x + 5/72 y x - 5/12 y x z + 5/12 y x z + + 4 2 2 2 2 2 2 + - 1/72 y x - 1/3 x z - 1/3 x z + 1/3 x z + 1/3 x z + 5/72 y x + + 4 2 2 4 3 2 4 2 3 + - 1/72 y x - 1/12 z x + 1/12 z x - 5/288 y x - 5/288 y x , + + 2 4 3 4 3 2 4 2 + COEFF(2, 0, -2) = 1/96 z y x - 1/96 z y x - 1/192 z y x + + 2 4 4 4 2 2 4 4 + - 1/96 z y x + 1/96 z y x + 1/192 z y x + 1/192 z y x + + 4 4 2 2 4 2 3 2 2 3 + - 1/192 z y x - 5/192 z y x + 5/96 z y x - 5/96 z y x + + 2 4 3 2 4 2 + + 5/192 z y x + 1/24 x z + 1/144 x - 1/288 x - 5/96 y x z + + 2 2 2 4 4 3 2 4 3 + + 5/192 y x z - 1/1152 y x - 1/144 x + 1/288 x - 1/576 y x + + 4 2 2 2 2 2 4 + - 1/48 z x - 5/576 y x + 5/96 y x z - 5/192 y x z + 1/576 y x + + 2 2 2 2 2 2 + + 1/24 x z + 1/48 x z - 1/48 x z - 1/24 x z - 5/1152 y x + + 4 2 2 4 3 2 4 2 3 + + 1/1152 y x + 1/48 z x - 1/24 z x + 5/1152 y x + 5/576 y x , + + 2 4 3 4 3 2 4 2 + COEFF(-2, 1, -2) = 1/144 z y x - 1/144 z y x + 1/288 z y x + + 2 4 4 4 2 2 4 4 + - 1/144 z y x + 1/144 z y x - 1/288 z y x - 1/288 z y x + + 4 4 2 2 4 4 2 3 3 + + 1/288 z y x + 1/72 z y x - 1/72 z y x + 1/36 z y x + 1/36 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 1/864 y x + 1/1728 y x - 1/36 z y x + 1/216 y x - 1/36 z y x + + 2 4 2 4 2 2 2 2 + - 1/72 z y x + 1/72 z y x - 1/36 y x z - 1/216 y x - 1/72 y x z + + 2 3 4 3 3 2 3 2 2 3 4 + - 1/288 z y x + 1/144 y x z + 1/288 y x z + 1/288 z y x + + 3 2 3 2 4 4 3 + - 1/288 z y x - 1/144 y x z + 1/1728 y x + 1/144 z y x + + 3 3 2 4 3 2 + - 1/144 z y x - 1/36 y x z + 1/72 z y x - 1/864 y x - 1/216 y x + + 2 2 2 2 2 2 2 3 2 + + 1/36 y x z + 1/72 y x z - 1/72 y x z + 1/36 y x z - 1/1728 y x + + 4 3 2 2 2 4 2 + + 1/864 y x + 1/864 y x + 1/432 y x + 1/432 y x - 1/1728 y x + + 4 2 4 2 3 + - 1/432 y x - 1/432 y x + 1/216 y x , COEFF(-1, 1, -2) = + + 2 4 3 4 3 2 4 2 2 4 4 + - 1/72 z y x + 1/72 z y x - 1/18 z y x + 1/18 z y x - 1/18 z y x + + 4 2 2 4 4 4 4 2 2 4 + + 1/18 z y x + 1/72 z y x - 1/72 z y x - 1/18 z y x + + 4 2 3 3 3 3 3 4 + + 1/18 z y x - 1/18 z y x - 1/18 z y x + 1/432 y x - 1/432 y x + + 2 2 3 3 2 3 2 4 2 4 + + 1/18 z y x - 1/108 y x + 1/18 z y x + 1/18 z y x - 1/18 z y x + + 2 2 2 2 2 3 4 3 3 2 + + 2/9 y x z + 1/27 y x + 2/9 y x z + 1/72 z y x - 1/72 y x z + + 3 2 2 3 4 3 2 3 2 4 4 + - 1/18 y x z - 1/72 z y x + 1/18 z y x + 1/18 y x z - 1/432 y x + + 3 3 3 2 4 3 + - 1/18 z y x + 1/72 z y x + 2/9 y x z - 2/9 z y x + 1/432 y x + + 2 2 2 2 2 2 2 2 + + 1/27 y x - 2/9 y x z - 2/9 y x z + 2/9 y x z - 2/9 y x z + + 3 2 4 3 2 2 2 + + 1/108 y x - 1/108 y x - 1/108 y x - 1/27 y x - 1/27 y x + + 4 2 4 2 4 2 3 + + 1/108 y x + 1/108 y x + 1/108 y x - 1/108 y x , COEFF(0, 1, -2) = + + 2 4 2 4 2 2 4 4 4 4 2 2 4 + 5/48 z y x - 5/48 z y x - 1/48 z y x + 1/48 z y x + 1/12 z y x + + 4 3 4 2 4 2 4 + - 1/12 z y x + 1/288 y x - 1/12 z y x + 1/12 z y x - 1/18 y + + 4 2 2 2 2 3 4 4 3 2 2 + + 1/72 y - 5/12 y x z - 1/48 z y x + 1/12 z y + 5/48 y x z + + 3 4 2 4 3 2 4 4 3 + + 1/48 z y x - 1/12 z y - 5/48 z y x + 1/288 y x + 1/72 y + + 2 2 2 2 2 2 + - 1/18 y + 5/12 z y x - 1/3 y z + 5/12 y x z - 5/12 y x z + + 3 2 2 3 2 2 2 2 2 2 + - 5/288 y x - 1/3 y z - 1/12 y z + 1/3 y z + 1/3 y z + 5/72 y x + + 2 4 2 3 4 2 4 + + 5/72 y x - 5/288 y x + 1/12 z y - 1/72 y x - 1/72 y x , + + 2 4 3 4 3 2 4 2 + COEFF(1, 1, -2) = 1/72 z y x - 1/72 z y x - 1/18 z y x + + 2 4 4 4 2 2 4 4 4 4 + - 1/18 z y x + 1/18 z y x + 1/18 z y x + 1/72 z y x - 1/72 z y x + + 2 2 4 4 2 3 3 3 3 + - 1/18 z y x + 1/18 z y x + 1/18 z y x + 1/18 z y x - 1/432 y x + + 3 4 2 2 3 3 2 3 2 4 + - 1/432 y x - 1/18 z y x + 1/108 y x - 1/18 z y x + 1/18 z y x + + 2 4 2 2 2 2 2 3 4 + - 1/18 z y x - 2/9 y x z - 1/27 y x + 2/9 y x z + 1/72 z y x + + 3 3 2 3 2 2 3 4 3 2 + + 1/72 y x z - 1/18 y x z - 1/72 z y x + 1/18 z y x + + 3 2 4 4 3 3 3 + - 1/18 y x z - 1/432 y x + 1/18 z y x - 1/72 z y x - 2/9 y x z + + 2 4 3 2 2 2 2 2 + - 2/9 z y x - 1/432 y x - 1/27 y x + 2/9 y x z - 2/9 y x z + + 2 2 2 3 2 4 3 + + 2/9 y x z + 2/9 y x z + 1/108 y x + 1/108 y x + 1/108 y x + + 2 2 2 4 2 4 2 4 + - 1/27 y x - 1/27 y x + 1/108 y x + 1/108 y x + 1/108 y x + + 2 3 2 4 3 4 3 + + 1/108 y x , COEFF(2, 1, -2) = - 1/144 z y x + 1/144 z y x + + 2 4 2 2 4 4 4 2 + + 1/288 z y x + 1/144 z y x - 1/144 z y x - 1/288 z y x + + 2 4 4 4 4 2 2 4 4 + - 1/288 z y x + 1/288 z y x + 1/72 z y x - 1/72 z y x + + 2 3 3 3 3 3 4 2 2 3 + - 1/36 z y x - 1/36 z y x + 1/864 y x + 1/1728 y x + 1/36 z y x + + 3 2 3 2 4 2 4 2 + - 1/216 y x + 1/36 z y x - 1/72 z y x + 1/72 z y x + 1/36 y x z + + 2 2 2 2 3 4 3 3 2 + + 1/216 y x - 1/72 y x z - 1/288 z y x - 1/144 y x z + + 3 2 2 3 4 3 2 3 2 + + 1/288 y x z + 1/288 z y x - 1/288 z y x + 1/144 y x z + + 4 4 3 3 3 2 + + 1/1728 y x - 1/144 z y x + 1/144 z y x + 1/36 y x z + 1/72 z y x + + 4 3 2 2 2 2 2 2 2 + + 1/864 y x + 1/216 y x - 1/36 y x z + 1/72 y x z - 1/72 y x z + + 2 3 2 4 3 2 2 + - 1/36 y x z - 1/1728 y x - 1/864 y x - 1/864 y x + 1/432 y x + + 2 4 2 4 2 4 2 3 + + 1/432 y x - 1/1728 y x - 1/432 y x - 1/432 y x - 1/216 y x , + + 2 4 3 4 3 2 4 2 + COEFF(-2, 2, -2) = - 1/576 z y x + 1/576 z y x - 1/1152 z y x + + 2 4 4 4 2 2 4 4 + + 1/576 z y x - 1/576 z y x + 1/1152 z y x + 1/1152 z y x + + 4 4 2 2 4 4 2 3 + - 1/1152 z y x - 1/1152 z y x + 1/576 z y x - 1/576 z y x + + 3 3 3 3 4 2 2 3 + - 1/288 z y x + 1/1728 y x - 1/3456 y x + 1/576 z y x + + 3 2 3 2 4 2 4 + - 1/1728 y x + 1/288 z y x + 1/1152 z y x - 1/576 z y x + + 2 2 2 2 2 3 4 + + 1/576 y x z + 1/1728 y x + 1/1152 y x z + 1/576 z y x + + 3 3 2 3 2 2 3 4 3 2 + - 1/288 y x z - 1/576 y x z - 1/576 z y x + 1/576 z y x + + 3 2 4 4 3 3 3 + + 1/288 y x z - 1/6912 y x - 1/288 z y x + 1/288 z y x + + 2 4 3 2 2 2 + + 1/288 y x z - 1/576 z y x + 1/3456 y x + 1/3456 y x - 1/576 y x z + + 2 2 2 2 2 3 2 + - 1/1152 y x z + 1/576 y x z - 1/288 y x z + 1/3456 y x + + 4 3 2 2 2 4 2 + - 1/3456 y x - 1/1728 y x - 1/6912 y x - 1/3456 y x + 1/6912 y x + + 4 2 4 2 3 + + 1/3456 y x + 1/6912 y x - 1/3456 y x , COEFF(-1, 2, -2) = + + 2 4 3 4 3 2 4 2 2 4 4 + 1/288 z y x - 1/288 z y x + 1/72 z y x - 1/72 z y x + 1/72 z y x + + 4 2 2 4 4 4 4 2 2 4 + - 1/72 z y x - 1/288 z y x + 1/288 z y x + 1/288 z y x + + 4 2 3 3 3 3 3 4 + - 1/144 z y x + 1/288 z y x + 1/144 z y x - 1/864 y x + 1/864 y x + + 2 2 3 3 2 3 2 4 + - 1/288 z y x + 1/864 y x - 1/144 z y x - 1/288 z y x + + 2 4 2 2 2 2 2 3 4 + + 1/144 z y x - 1/72 y x z - 1/216 y x - 1/72 y x z - 1/144 z y x + + 3 3 2 3 2 2 3 4 3 2 + + 1/144 y x z + 1/36 y x z + 1/144 z y x - 1/36 z y x + + 3 2 4 4 3 3 3 + - 1/36 y x z + 1/1728 y x + 1/36 z y x - 1/144 z y x - 1/36 y x z + + 2 4 3 2 2 2 2 2 + + 1/36 z y x - 1/1728 y x - 1/432 y x + 1/72 y x z + 1/72 y x z + + 2 2 2 3 2 4 3 + - 1/36 y x z + 1/36 y x z - 1/216 y x + 1/432 y x + 1/216 y x + + 2 2 2 4 2 4 2 4 + + 1/432 y x + 1/216 y x - 1/432 y x - 1/864 y x - 1/1728 y x + + 2 3 2 4 2 4 2 + + 1/1728 y x , COEFF(0, 2, -2) = - 5/192 z y x + 5/192 z y x + + 2 4 4 4 4 2 2 4 4 + + 1/192 z y x - 1/192 z y x - 1/192 z y x + 1/96 z y x + + 3 4 2 4 2 4 4 + - 1/576 y x + 1/192 z y x - 1/96 z y x + 1/144 y - 1/288 y + + 2 2 2 2 3 4 4 3 2 2 + + 5/192 y x z + 1/96 z y x - 1/48 z y - 5/96 y x z + + 3 4 2 4 3 2 4 4 3 + - 1/96 z y x + 1/48 z y + 5/96 z y x - 1/1152 y x - 1/144 y + + 2 2 2 2 2 2 + + 1/288 y - 5/96 z y x + 1/24 y z - 5/192 y x z + 5/96 y x z + + 3 2 2 3 2 2 2 2 + + 5/576 y x + 1/48 y z + 1/24 y z - 1/24 y z - 1/48 y z + + 2 2 2 4 2 3 4 + - 5/1152 y x - 5/576 y x + 5/1152 y x - 1/24 z y + 1/576 y x + + 2 4 2 4 3 4 3 + + 1/1152 y x , COEFF(1, 2, -2) = - 1/288 z y x + 1/288 z y x + + 2 4 2 2 4 4 4 2 + + 1/72 z y x + 1/72 z y x - 1/72 z y x - 1/72 z y x + + 2 4 4 4 4 2 2 4 4 + - 1/288 z y x + 1/288 z y x + 1/288 z y x - 1/144 z y x + + 2 3 3 3 3 3 4 + - 1/288 z y x - 1/144 z y x + 1/864 y x + 1/864 y x + + 2 2 3 3 2 3 2 4 + + 1/288 z y x - 1/864 y x + 1/144 z y x - 1/288 z y x + + 2 4 2 2 2 2 2 3 4 + + 1/144 z y x + 1/72 y x z + 1/216 y x - 1/72 y x z - 1/144 z y x + + 3 3 2 3 2 2 3 4 3 2 + - 1/144 y x z + 1/36 y x z + 1/144 z y x - 1/36 z y x + + 3 2 4 4 3 3 3 + + 1/36 y x z + 1/1728 y x - 1/36 z y x + 1/144 z y x + 1/36 y x z + + 2 4 3 2 2 2 2 2 + + 1/36 z y x + 1/1728 y x + 1/432 y x - 1/72 y x z + 1/72 y x z + + 2 2 2 3 2 4 3 + - 1/36 y x z - 1/36 y x z - 1/216 y x - 1/432 y x - 1/216 y x + + 2 2 2 4 2 4 2 4 + + 1/432 y x + 1/216 y x - 1/432 y x - 1/864 y x - 1/1728 y x + + 2 3 2 4 3 4 3 + - 1/1728 y x , COEFF(2, 2, -2) = 1/576 z y x - 1/576 z y x + + 2 4 2 2 4 4 4 2 + - 1/1152 z y x - 1/576 z y x + 1/576 z y x + 1/1152 z y x + + 2 4 4 4 4 2 2 4 4 + + 1/1152 z y x - 1/1152 z y x - 1/1152 z y x + 1/576 z y x + + 2 3 3 3 3 3 4 + + 1/576 z y x + 1/288 z y x - 1/1728 y x - 1/3456 y x + + 2 2 3 3 2 3 2 4 + - 1/576 z y x + 1/1728 y x - 1/288 z y x + 1/1152 z y x + + 2 4 2 2 2 2 + - 1/576 z y x - 1/576 y x z - 1/1728 y x + 1/1152 y x z + + 2 3 4 3 3 2 3 2 2 3 4 + + 1/576 z y x + 1/288 y x z - 1/576 y x z - 1/576 z y x + + 3 2 3 2 4 4 3 + + 1/576 z y x - 1/288 y x z - 1/6912 y x + 1/288 z y x + + 3 3 2 4 3 2 + - 1/288 z y x - 1/288 y x z - 1/576 z y x - 1/3456 y x - 1/3456 y x + + 2 2 2 2 2 2 2 + + 1/576 y x z - 1/1152 y x z + 1/576 y x z + 1/288 y x z + + 3 2 4 3 2 2 2 + + 1/3456 y x + 1/3456 y x + 1/1728 y x - 1/6912 y x - 1/3456 y x + + 4 2 4 2 4 2 3 + + 1/6912 y x + 1/3456 y x + 1/6912 y x + 1/3456 y x , + + 2 4 3 4 3 2 4 2 + COEFF(-2, -2, -1) = 1/144 z y x - 1/288 z y x + 1/288 z y x + + 2 4 4 4 2 2 4 4 + - 1/144 z y x + 1/288 z y x - 1/576 z y x - 1/288 z y x + + 4 4 2 2 4 4 2 3 + + 1/576 z y x + 1/288 z y x + 1/288 z y x + 1/288 z y x + + 3 3 3 3 4 2 2 3 3 + - 1/144 z y x + 1/108 y x - 1/216 y x - 1/144 z y x - 1/108 y x + + 2 3 2 4 2 4 2 + + 1/72 z y x - 1/576 z y x - 1/144 z y x - 1/288 y x z + 1/108 y x + + 2 2 2 2 3 4 3 3 2 3 2 2 + - 1/288 y x z + 1/144 z y x - 1/72 y x z - 1/144 y x z + + 3 4 3 2 3 2 4 4 + - 1/288 z y x + 1/288 z y x + 1/72 y x z + 1/432 y x + + 3 3 3 2 4 3 + - 1/144 z y x + 1/144 z y x + 1/144 y x z - 1/288 z y x - 1/216 y x + + 2 2 2 2 2 2 2 2 + - 1/216 y x + 1/144 y x z + 1/576 y x z + 1/144 y x z - 1/72 y x z + + 3 2 4 3 2 2 2 + + 1/216 y x + 1/216 y x - 1/108 y x + 1/432 y x - 1/216 y x + + 4 2 4 2 4 2 3 + - 1/432 y x + 1/216 y x - 1/432 y x + 1/216 y x , COEFF(-1, -2, -1) + + 2 4 3 4 3 2 4 2 2 4 + = - 1/72 z y x + 1/144 z y x - 1/18 z y x + 1/18 z y x + + 4 4 2 2 4 4 4 4 + - 1/36 z y x + 1/36 z y x + 1/72 z y x - 1/144 z y x + + 2 2 4 4 2 3 3 3 3 + - 1/72 z y x - 1/72 z y x - 1/144 z y x + 1/72 z y x - 1/54 y x + + 3 4 2 2 3 3 2 3 2 4 + + 1/54 y x + 1/72 z y x + 1/54 y x - 1/36 z y x + 1/144 z y x + + 2 4 2 2 2 2 2 3 4 + + 1/36 z y x + 1/36 y x z - 2/27 y x + 1/18 y x z - 1/36 z y x + + 3 3 2 3 2 2 3 4 3 2 3 2 + + 1/36 y x z + 1/9 y x z + 1/72 z y x - 1/18 z y x - 1/9 y x z + + 4 4 3 3 3 2 + - 1/108 y x + 1/18 z y x - 1/72 z y x - 1/18 y x z + 1/18 z y x + + 4 3 2 2 2 2 2 2 2 + + 1/108 y x + 1/27 y x - 1/18 y x z - 1/36 y x z - 1/9 y x z + + 2 3 2 4 3 2 2 2 + + 1/9 y x z - 2/27 y x - 1/27 y x + 2/27 y x - 1/27 y x + 2/27 y x + + 4 2 4 2 4 2 3 + + 1/27 y x - 1/54 y x + 1/108 y x - 1/108 y x , COEFF(0, -2, -1) = + + 2 4 2 4 2 2 4 4 4 4 2 2 4 + 5/48 z y x - 5/96 z y x - 1/48 z y x + 1/96 z y x + 1/48 z y x + + 4 3 4 2 4 2 4 4 + + 1/48 z y x - 1/36 y x - 1/96 z y x - 1/24 z y x + 1/9 y + 1/18 y + + 2 2 2 2 3 4 4 3 2 2 3 4 + - 5/48 y x z + 1/24 z y x + 1/24 z y - 5/24 y x z - 1/48 z y x + + 2 4 3 2 4 4 3 2 2 + - 1/12 z y + 5/48 z y x + 1/72 y x - 1/9 y - 1/18 y - 5/48 z y x + + 2 2 2 2 3 2 2 + + 1/12 y z + 5/96 y x z + 5/24 y x z + 5/36 y x - 1/24 y z + + 3 2 2 2 2 2 2 2 4 2 + + 1/6 y z - 1/6 y z + 1/12 y z + 5/72 y x - 5/36 y x - 5/72 y x + + 3 4 2 4 2 4 3 + - 1/12 z y + 1/36 y x - 1/72 y x , COEFF(1, -2, -1) = 1/72 z y x + + 4 3 2 4 2 2 4 4 + - 1/144 z y x - 1/18 z y x - 1/18 z y x + 1/36 z y x + + 4 2 2 4 4 4 4 2 2 4 + + 1/36 z y x + 1/72 z y x - 1/144 z y x - 1/72 z y x + + 4 2 3 3 3 3 3 4 + - 1/72 z y x + 1/144 z y x - 1/72 z y x + 1/54 y x + 1/54 y x + + 2 2 3 3 2 3 2 4 2 4 + - 1/72 z y x - 1/54 y x + 1/36 z y x + 1/144 z y x + 1/36 z y x + + 2 2 2 2 2 3 4 3 3 2 + - 1/36 y x z + 2/27 y x + 1/18 y x z - 1/36 z y x - 1/36 y x z + + 3 2 2 3 4 3 2 3 2 4 4 + + 1/9 y x z + 1/72 z y x - 1/18 z y x + 1/9 y x z - 1/108 y x + + 3 3 3 2 4 3 + - 1/18 z y x + 1/72 z y x + 1/18 y x z + 1/18 z y x - 1/108 y x + + 2 2 2 2 2 2 2 2 + - 1/27 y x + 1/18 y x z - 1/36 y x z - 1/9 y x z - 1/9 y x z + + 3 2 4 3 2 2 2 4 2 + - 2/27 y x + 1/27 y x - 2/27 y x - 1/27 y x + 2/27 y x + 1/27 y x + + 4 2 4 2 3 + - 1/54 y x + 1/108 y x + 1/108 y x , COEFF(2, -2, -1) = + + 2 4 3 4 3 2 4 2 2 4 + - 1/144 z y x + 1/288 z y x + 1/288 z y x + 1/144 z y x + + 4 4 2 2 4 4 4 4 + - 1/288 z y x - 1/576 z y x - 1/288 z y x + 1/576 z y x + + 2 2 4 4 2 3 3 + + 1/288 z y x + 1/288 z y x - 1/288 z y x + 1/144 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 1/108 y x - 1/216 y x + 1/144 z y x + 1/108 y x - 1/72 z y x + + 2 4 2 4 2 + - 1/576 z y x - 1/144 z y x + 1/288 y x z - 1/108 y x + + 2 2 2 2 3 4 3 3 2 3 2 2 + - 1/288 y x z + 1/144 z y x + 1/72 y x z - 1/144 y x z + + 3 4 3 2 3 2 4 4 + - 1/288 z y x + 1/288 z y x - 1/72 y x z + 1/432 y x + + 3 3 3 2 4 3 + + 1/144 z y x - 1/144 z y x - 1/144 y x z - 1/288 z y x + 1/216 y x + + 2 2 2 2 2 2 2 2 + + 1/216 y x - 1/144 y x z + 1/576 y x z + 1/144 y x z + 1/72 y x z + + 3 2 4 3 2 2 2 + + 1/216 y x - 1/216 y x + 1/108 y x + 1/432 y x - 1/216 y x + + 4 2 4 2 4 2 3 + - 1/432 y x + 1/216 y x - 1/432 y x - 1/216 y x , COEFF(-2, -1, -1) + + 2 4 3 4 3 2 4 2 2 4 + = - 1/36 z y x + 1/72 z y x - 1/72 z y x + 1/36 z y x + + 4 4 2 2 4 4 4 4 + - 1/72 z y x + 1/144 z y x + 1/72 z y x - 1/144 z y x + + 2 2 4 4 2 3 3 3 3 + - 1/18 z y x - 1/36 z y x - 1/18 z y x + 1/18 z y x - 1/54 y x + + 3 4 2 2 3 3 2 3 2 4 + + 1/108 y x + 1/9 z y x + 2/27 y x - 1/9 z y x + 1/36 z y x + + 2 4 2 2 2 2 2 3 4 + + 1/18 z y x + 1/18 y x z - 2/27 y x + 1/18 y x z - 1/72 z y x + + 3 3 2 3 2 2 3 4 3 2 + + 1/36 y x z + 1/72 y x z + 1/144 z y x - 1/144 z y x + + 3 2 4 4 3 3 3 + - 1/36 y x z - 1/108 y x + 1/72 z y x - 1/72 z y x - 1/18 y x z + + 2 4 3 2 2 2 2 2 + + 1/36 z y x + 1/54 y x + 2/27 y x - 1/9 y x z - 1/36 y x z + + 2 2 2 3 2 4 3 + - 1/18 y x z + 1/9 y x z - 1/108 y x - 1/54 y x + 1/54 y x + + 2 2 2 4 2 4 2 4 + - 1/27 y x + 1/27 y x + 1/108 y x - 1/27 y x + 1/27 y x + + 2 3 2 4 3 4 3 + - 2/27 y x , COEFF(-1, -1, -1) = 1/18 z y x - 1/36 z y x + + 2 4 2 2 4 4 4 2 2 4 4 + + 2/9 z y x - 2/9 z y x + 1/9 z y x - 1/9 z y x - 1/18 z y x + + 4 4 2 2 4 4 2 3 3 + + 1/36 z y x + 2/9 z y x + 1/9 z y x + 1/9 z y x - 1/9 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 1/27 y x - 1/27 y x - 2/9 z y x - 4/27 y x + 2/9 z y x + + 2 4 2 4 2 16 2 2 2 + - 1/9 z y x - 2/9 z y x - 4/9 y x z + -- y x - 8/9 y x z + 27 + + 2 3 4 3 3 2 3 2 2 3 4 + + 1/18 z y x - 1/18 y x z - 2/9 y x z - 1/36 z y x + + 3 2 3 2 4 4 3 3 3 + + 1/9 z y x + 2/9 y x z + 1/27 y x - 1/9 z y x + 1/36 z y x + + 2 4 3 16 2 2 2 + + 4/9 y x z - 4/9 z y x - 1/27 y x - -- y x + 8/9 y x z + 27 + + 2 2 2 2 2 3 2 4 + + 4/9 y x z + 8/9 y x z - 8/9 y x z + 4/27 y x + 4/27 y x + + 3 16 2 2 16 2 4 2 4 2 4 + - 4/27 y x + -- y x - -- y x - 4/27 y x + 4/27 y x - 4/27 y x + 27 27 + + 2 3 2 4 2 4 2 + + 4/27 y x , COEFF(0, -1, -1) = - 5/12 z y x + 5/24 z y x + + 2 4 4 4 4 2 2 4 4 3 4 + + 1/12 z y x - 1/24 z y x - 1/3 z y x - 1/6 z y x + 1/18 y x + + 2 4 2 4 4 2 2 2 + + 1/6 z y x + 1/3 z y x - 8/9 y - 2/9 y + 5/3 y x z + + 2 3 4 4 3 2 2 3 4 2 4 + - 1/12 z y x - 1/6 z y + 5/12 y x z + 1/24 z y x + 1/3 z y + + 3 2 4 4 3 2 2 + - 5/24 z y x - 1/18 y x + 2/9 y + 8/9 y + 5/6 z y x - 2/3 y z + + 2 2 2 2 3 2 2 3 2 2 + - 5/6 y x z - 5/3 y x z - 5/18 y x + 2/3 y z - 1/3 y z + 4/3 y z + + 2 2 2 2 2 4 2 3 4 + - 4/3 y z - 10/9 y x + 10/9 y x + 5/18 y x + 1/6 z y - 2/9 y x + + 2 4 2 4 3 4 3 + + 2/9 y x , COEFF(1, -1, -1) = - 1/18 z y x + 1/36 z y x + + 2 4 2 2 4 4 4 2 2 4 4 + + 2/9 z y x + 2/9 z y x - 1/9 z y x - 1/9 z y x - 1/18 z y x + + 4 4 2 2 4 4 2 3 3 + + 1/36 z y x + 2/9 z y x + 1/9 z y x - 1/9 z y x + 1/9 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 1/27 y x - 1/27 y x + 2/9 z y x + 4/27 y x - 2/9 z y x + + 2 4 2 4 2 16 2 2 2 + - 1/9 z y x - 2/9 z y x + 4/9 y x z - -- y x - 8/9 y x z + 27 + + 2 3 4 3 3 2 3 2 2 3 4 + + 1/18 z y x + 1/18 y x z - 2/9 y x z - 1/36 z y x + + 3 2 3 2 4 4 3 3 3 + + 1/9 z y x - 2/9 y x z + 1/27 y x + 1/9 z y x - 1/36 z y x + + 2 4 3 16 2 2 2 + - 4/9 y x z - 4/9 z y x + 1/27 y x + -- y x - 8/9 y x z + 27 + + 2 2 2 2 2 3 2 4 + + 4/9 y x z + 8/9 y x z + 8/9 y x z + 4/27 y x - 4/27 y x + + 3 16 2 2 16 2 4 2 4 2 4 + + 4/27 y x + -- y x - -- y x - 4/27 y x + 4/27 y x - 4/27 y x + 27 27 + + 2 3 2 4 3 4 3 + - 4/27 y x , COEFF(2, -1, -1) = 1/36 z y x - 1/72 z y x + + 2 4 2 2 4 4 4 2 + - 1/72 z y x - 1/36 z y x + 1/72 z y x + 1/144 z y x + + 2 4 4 4 4 2 2 4 4 + + 1/72 z y x - 1/144 z y x - 1/18 z y x - 1/36 z y x + + 2 3 3 3 3 3 4 2 2 3 + + 1/18 z y x - 1/18 z y x + 1/54 y x + 1/108 y x - 1/9 z y x + + 3 2 3 2 4 2 4 2 + - 2/27 y x + 1/9 z y x + 1/36 z y x + 1/18 z y x - 1/18 y x z + + 2 2 2 2 3 4 3 3 2 3 2 2 + + 2/27 y x + 1/18 y x z - 1/72 z y x - 1/36 y x z + 1/72 y x z + + 3 4 3 2 3 2 4 4 3 + + 1/144 z y x - 1/144 z y x + 1/36 y x z - 1/108 y x - 1/72 z y x + + 3 3 2 4 3 2 + + 1/72 z y x + 1/18 y x z + 1/36 z y x - 1/54 y x - 2/27 y x + + 2 2 2 2 2 2 2 3 2 + + 1/9 y x z - 1/36 y x z - 1/18 y x z - 1/9 y x z - 1/108 y x + + 4 3 2 2 2 4 2 4 + + 1/54 y x - 1/54 y x - 1/27 y x + 1/27 y x + 1/108 y x - 1/27 y x + + 2 4 2 3 2 4 3 4 3 + + 1/27 y x + 2/27 y x , COEFF(-2, 0, -1) = 1/24 z y x - 1/48 z y x + + 2 4 2 2 4 4 4 2 + + 1/48 z y x - 1/24 z y x + 1/48 z y x - 1/96 z y x + + 2 4 4 4 4 2 2 4 2 3 + - 1/48 z y x + 1/96 z y x + 5/48 z y x + 5/48 z y x + + 2 2 3 2 4 3 2 4 2 + - 5/24 z y x - 5/96 z y x + 1/6 x z + 1/9 x + 1/18 x - 5/48 y x z + + 2 2 2 4 4 3 2 4 3 4 + - 5/48 y x z + 1/72 y x - 1/9 x - 1/18 x - 1/36 y x + 1/24 z x + + 2 2 2 2 2 4 + - 5/36 y x + 5/24 y x z + 5/96 y x z + 1/36 y x + 1/12 x z + + 2 2 2 2 2 2 4 2 2 4 + - 1/24 x z + 1/12 x z - 1/6 x z + 5/72 y x - 1/72 y x - 1/12 z x + + 3 2 4 2 3 2 4 3 + - 1/12 z x - 5/72 y x + 5/36 y x , COEFF(-1, 0, -1) = - 1/12 z y x + + 4 3 2 4 2 2 4 4 4 2 + + 1/24 z y x - 1/3 z y x + 1/3 z y x - 1/6 z y x + 1/6 z y x + + 2 4 4 4 4 2 2 4 2 3 + + 1/12 z y x - 1/24 z y x - 5/12 z y x - 5/24 z y x + + 2 2 3 2 4 3 2 4 2 + + 5/12 z y x + 5/24 z y x - 1/3 x z - 8/9 x - 2/9 x + 5/6 y x z + + 2 2 2 4 4 3 2 4 3 4 + + 5/3 y x z - 1/18 y x + 2/9 x + 8/9 x + 1/18 y x - 1/6 z x + + 2 2 2 2 2 4 2 + + 10/9 y x - 5/3 y x z - 5/6 y x z - 2/9 y x - 2/3 x z + 2/3 x z + + 2 2 2 2 2 4 2 2 4 3 + - 4/3 x z + 4/3 x z - 10/9 y x + 2/9 y x + 1/3 z x + 1/6 z x + + 2 4 2 3 2 4 2 4 2 + + 5/18 y x - 5/18 y x , COEFF(0, 0, -1) = 5/8 z y x - 5/16 z y x + + 2 4 4 4 4 2 2 4 2 4 4 + - 1/8 z y x + 1/16 z y x + 5/8 z y x - 5/16 z y x + 1/3 x + z + + 4 2 2 2 4 2 4 4 4 2 + + 1/3 y - 25/8 y x z + 1/4 z y - 1/2 z y + 1/12 y x - 5/3 y + + 2 2 4 25 2 2 2 2 + - 2 z - 5/3 x + 1/4 z x + 4/3 + -- y x z - 5/4 y z - 5/4 x z + 16 + + 2 2 2 2 25 2 2 4 2 2 4 2 4 + + 5/2 x z + 5/2 y z + -- y x - 5/12 y x - 1/2 z x - 5/12 y x , + 12 + + 2 4 3 4 3 2 4 2 2 4 + COEFF(1, 0, -1) = 1/12 z y x - 1/24 z y x - 1/3 z y x - 1/3 z y x + + 4 4 2 2 4 4 4 4 2 2 4 + + 1/6 z y x + 1/6 z y x + 1/12 z y x - 1/24 z y x - 5/12 z y x + + 2 3 2 2 3 2 4 3 2 4 + + 5/24 z y x - 5/12 z y x + 5/24 z y x + 1/3 x z + 8/9 x - 2/9 x + + 2 2 2 2 4 4 3 2 4 3 + - 5/6 y x z + 5/3 y x z - 1/18 y x - 2/9 x + 8/9 x - 1/18 y x + + 4 2 2 2 2 2 4 + - 1/6 z x - 10/9 y x + 5/3 y x z - 5/6 y x z + 2/9 y x + 2/3 x z + + 2 2 2 2 2 2 4 2 2 4 + + 2/3 x z - 4/3 x z - 4/3 x z - 10/9 y x + 2/9 y x + 1/3 z x + + 3 2 4 2 3 2 4 3 + - 1/6 z x + 5/18 y x + 5/18 y x , COEFF(2, 0, -1) = - 1/24 z y x + + 4 3 2 4 2 2 4 4 4 2 + + 1/48 z y x + 1/48 z y x + 1/24 z y x - 1/48 z y x - 1/96 z y x + + 2 4 4 4 4 2 2 4 2 3 + - 1/48 z y x + 1/96 z y x + 5/48 z y x - 5/48 z y x + + 2 2 3 2 4 3 2 4 2 + + 5/24 z y x - 5/96 z y x - 1/6 x z - 1/9 x + 1/18 x + 5/48 y x z + + 2 2 2 4 4 3 2 4 3 4 + - 5/48 y x z + 1/72 y x + 1/9 x - 1/18 x + 1/36 y x + 1/24 z x + + 2 2 2 2 2 4 + + 5/36 y x - 5/24 y x z + 5/96 y x z - 1/36 y x - 1/12 x z + + 2 2 2 2 2 2 4 2 2 4 + - 1/24 x z + 1/12 x z + 1/6 x z + 5/72 y x - 1/72 y x - 1/12 z x + + 3 2 4 2 3 2 4 3 + + 1/12 z x - 5/72 y x - 5/36 y x , COEFF(-2, 1, -1) = - 1/36 z y x + + 4 3 2 4 2 2 4 4 + + 1/72 z y x - 1/72 z y x + 1/36 z y x - 1/72 z y x + + 4 2 2 4 4 4 4 2 2 4 + + 1/144 z y x + 1/72 z y x - 1/144 z y x - 1/18 z y x + + 4 2 3 3 3 3 3 4 + + 1/36 z y x - 1/18 z y x - 1/18 z y x + 1/54 y x - 1/108 y x + + 2 2 3 3 2 3 2 4 2 4 + + 1/9 z y x - 2/27 y x + 1/9 z y x + 1/36 z y x - 1/18 z y x + + 2 2 2 2 2 3 4 3 3 2 + + 1/18 y x z + 2/27 y x + 1/18 y x z + 1/72 z y x - 1/36 y x z + + 3 2 2 3 4 3 2 3 2 + - 1/72 y x z - 1/144 z y x + 1/144 z y x + 1/36 y x z + + 4 4 3 3 3 2 + - 1/108 y x - 1/72 z y x + 1/72 z y x + 1/18 y x z - 1/36 z y x + + 4 3 2 2 2 2 2 2 2 + + 1/54 y x + 2/27 y x - 1/9 y x z - 1/36 y x z + 1/18 y x z + + 2 3 2 4 3 2 2 + - 1/9 y x z + 1/108 y x - 1/54 y x - 1/54 y x - 1/27 y x + + 2 4 2 4 2 4 2 3 + - 1/27 y x + 1/108 y x + 1/27 y x + 1/27 y x - 2/27 y x , + + 2 4 3 4 3 2 4 2 + COEFF(-1, 1, -1) = 1/18 z y x - 1/36 z y x + 2/9 z y x + + 2 4 4 4 2 2 4 4 4 4 + - 2/9 z y x + 1/9 z y x - 1/9 z y x - 1/18 z y x + 1/36 z y x + + 2 2 4 4 2 3 3 3 3 + + 2/9 z y x - 1/9 z y x + 1/9 z y x + 1/9 z y x - 1/27 y x + + 3 4 2 2 3 3 2 3 2 4 + + 1/27 y x - 2/9 z y x + 4/27 y x - 2/9 z y x - 1/9 z y x + + 2 4 2 16 2 2 2 2 3 4 + + 2/9 z y x - 4/9 y x z - -- y x - 8/9 y x z - 1/18 z y x + 27 + + 3 3 2 3 2 2 3 4 3 2 3 2 + + 1/18 y x z + 2/9 y x z + 1/36 z y x - 1/9 z y x - 2/9 y x z + + 4 4 3 3 3 2 + + 1/27 y x + 1/9 z y x - 1/36 z y x - 4/9 y x z + 4/9 z y x + + 4 3 16 2 2 2 2 2 2 2 + - 1/27 y x - -- y x + 8/9 y x z + 4/9 y x z - 8/9 y x z + 27 + + 2 3 2 4 3 16 2 2 16 2 + + 8/9 y x z - 4/27 y x + 4/27 y x + 4/27 y x + -- y x + -- y x + 27 27 + + 4 2 4 2 4 2 3 + - 4/27 y x - 4/27 y x - 4/27 y x + 4/27 y x , COEFF(0, 1, -1) = + + 2 4 2 4 2 2 4 4 4 4 + - 5/12 z y x + 5/24 z y x + 1/12 z y x - 1/24 z y x + + 2 2 4 4 3 4 2 4 2 4 + - 1/3 z y x + 1/6 z y x - 1/18 y x + 1/6 z y x - 1/3 z y x + + 4 2 2 2 2 3 4 4 3 2 2 + + 8/9 y - 2/9 y + 5/3 y x z + 1/12 z y x - 1/6 z y - 5/12 y x z + + 3 4 2 4 3 2 4 4 3 2 + - 1/24 z y x + 1/3 z y + 5/24 z y x - 1/18 y x - 2/9 y + 8/9 y + + 2 2 2 2 2 3 2 2 + - 5/6 z y x + 2/3 y z - 5/6 y x z + 5/3 y x z + 5/18 y x + 2/3 y z + + 3 2 2 2 2 2 2 2 4 2 + + 1/3 y z - 4/3 y z - 4/3 y z - 10/9 y x - 10/9 y x + 5/18 y x + + 3 4 2 4 2 4 3 + - 1/6 z y + 2/9 y x + 2/9 y x , COEFF(1, 1, -1) = - 1/18 z y x + + 4 3 2 4 2 2 4 4 4 2 + + 1/36 z y x + 2/9 z y x + 2/9 z y x - 1/9 z y x - 1/9 z y x + + 2 4 4 4 4 2 2 4 4 2 3 + - 1/18 z y x + 1/36 z y x + 2/9 z y x - 1/9 z y x - 1/9 z y x + + 3 3 3 3 4 2 2 3 3 + - 1/9 z y x + 1/27 y x + 1/27 y x + 2/9 z y x - 4/27 y x + + 2 3 2 4 2 4 2 16 + + 2/9 z y x - 1/9 z y x + 2/9 z y x + 4/9 y x z + -- y x + 27 + + 2 2 2 2 3 4 3 3 2 3 2 2 + - 8/9 y x z - 1/18 z y x - 1/18 y x z + 2/9 y x z + + 3 4 3 2 3 2 4 4 3 + + 1/36 z y x - 1/9 z y x + 2/9 y x z + 1/27 y x - 1/9 z y x + + 3 3 2 4 3 16 2 + + 1/36 z y x + 4/9 y x z + 4/9 z y x + 1/27 y x + -- y x + 27 + + 2 2 2 2 2 2 2 3 2 + - 8/9 y x z + 4/9 y x z - 8/9 y x z - 8/9 y x z - 4/27 y x + + 4 3 16 2 2 16 2 4 2 4 + - 4/27 y x - 4/27 y x + -- y x + -- y x - 4/27 y x - 4/27 y x + 27 27 + + 2 4 2 3 2 4 3 4 3 + - 4/27 y x - 4/27 y x , COEFF(2, 1, -1) = 1/36 z y x - 1/72 z y x + + 2 4 2 2 4 4 4 2 + - 1/72 z y x - 1/36 z y x + 1/72 z y x + 1/144 z y x + + 2 4 4 4 4 2 2 4 4 + + 1/72 z y x - 1/144 z y x - 1/18 z y x + 1/36 z y x + + 2 3 3 3 3 3 4 2 2 3 + + 1/18 z y x + 1/18 z y x - 1/54 y x - 1/108 y x - 1/9 z y x + + 3 2 3 2 4 2 4 2 + + 2/27 y x - 1/9 z y x + 1/36 z y x - 1/18 z y x - 1/18 y x z + + 2 2 2 2 3 4 3 3 2 3 2 2 + - 2/27 y x + 1/18 y x z + 1/72 z y x + 1/36 y x z - 1/72 y x z + + 3 4 3 2 3 2 4 4 3 + - 1/144 z y x + 1/144 z y x - 1/36 y x z - 1/108 y x + 1/72 z y x + + 3 3 2 4 3 2 + - 1/72 z y x - 1/18 y x z - 1/36 z y x - 1/54 y x - 2/27 y x + + 2 2 2 2 2 2 2 3 2 + + 1/9 y x z - 1/36 y x z + 1/18 y x z + 1/9 y x z + 1/108 y x + + 4 3 2 2 2 4 2 4 + + 1/54 y x + 1/54 y x - 1/27 y x - 1/27 y x + 1/108 y x + 1/27 y x + + 2 4 2 3 2 4 3 + + 1/27 y x + 2/27 y x , COEFF(-2, 2, -1) = 1/144 z y x + + 4 3 2 4 2 2 4 4 + - 1/288 z y x + 1/288 z y x - 1/144 z y x + 1/288 z y x + + 4 2 2 4 4 4 4 2 2 4 + - 1/576 z y x - 1/288 z y x + 1/576 z y x + 1/288 z y x + + 4 2 3 3 3 3 3 4 + - 1/288 z y x + 1/288 z y x + 1/144 z y x - 1/108 y x + 1/216 y x + + 2 2 3 3 2 3 2 4 + - 1/144 z y x + 1/108 y x - 1/72 z y x - 1/576 z y x + + 2 4 2 2 2 2 + + 1/144 z y x - 1/288 y x z - 1/108 y x - 1/288 y x z + + 2 3 4 3 3 2 3 2 2 3 4 + - 1/144 z y x + 1/72 y x z + 1/144 y x z + 1/288 z y x + + 3 2 3 2 4 4 3 + - 1/288 z y x - 1/72 y x z + 1/432 y x + 1/144 z y x + + 3 3 2 4 3 2 + - 1/144 z y x - 1/144 y x z + 1/288 z y x - 1/216 y x - 1/216 y x + + 2 2 2 2 2 2 2 + + 1/144 y x z + 1/576 y x z - 1/144 y x z + 1/72 y x z + + 3 2 4 3 2 2 2 + - 1/216 y x + 1/216 y x + 1/108 y x + 1/432 y x + 1/216 y x + + 4 2 4 2 4 2 3 + - 1/432 y x - 1/216 y x - 1/432 y x + 1/216 y x , COEFF(-1, 2, -1) + + 2 4 3 4 3 2 4 2 2 4 + = - 1/72 z y x + 1/144 z y x - 1/18 z y x + 1/18 z y x + + 4 4 2 2 4 4 4 4 + - 1/36 z y x + 1/36 z y x + 1/72 z y x - 1/144 z y x + + 2 2 4 4 2 3 3 3 3 + - 1/72 z y x + 1/72 z y x - 1/144 z y x - 1/72 z y x + 1/54 y x + + 3 4 2 2 3 3 2 3 2 4 + - 1/54 y x + 1/72 z y x - 1/54 y x + 1/36 z y x + 1/144 z y x + + 2 4 2 2 2 2 2 3 4 + - 1/36 z y x + 1/36 y x z + 2/27 y x + 1/18 y x z + 1/36 z y x + + 3 3 2 3 2 2 3 4 3 2 3 2 + - 1/36 y x z - 1/9 y x z - 1/72 z y x + 1/18 z y x + 1/9 y x z + + 4 4 3 3 3 2 + - 1/108 y x - 1/18 z y x + 1/72 z y x + 1/18 y x z - 1/18 z y x + + 4 3 2 2 2 2 2 2 2 + + 1/108 y x + 1/27 y x - 1/18 y x z - 1/36 y x z + 1/9 y x z + + 2 3 2 4 3 2 2 2 + - 1/9 y x z + 2/27 y x - 1/27 y x - 2/27 y x - 1/27 y x - 2/27 y x + + 4 2 4 2 4 2 3 + + 1/27 y x + 1/54 y x + 1/108 y x - 1/108 y x , COEFF(0, 2, -1) = + + 2 4 2 4 2 2 4 4 4 4 2 2 4 + 5/48 z y x - 5/96 z y x - 1/48 z y x + 1/96 z y x + 1/48 z y x + + 4 3 4 2 4 2 4 4 + - 1/48 z y x + 1/36 y x - 1/96 z y x + 1/24 z y x - 1/9 y + 1/18 y + + 2 2 2 2 3 4 4 3 2 2 3 4 + - 5/48 y x z - 1/24 z y x + 1/24 z y + 5/24 y x z + 1/48 z y x + + 2 4 3 2 4 4 3 2 2 + - 1/12 z y - 5/48 z y x + 1/72 y x + 1/9 y - 1/18 y + 5/48 z y x + + 2 2 2 2 3 2 2 + - 1/12 y z + 5/96 y x z - 5/24 y x z - 5/36 y x - 1/24 y z + + 3 2 2 2 2 2 2 2 4 2 + - 1/6 y z + 1/6 y z + 1/12 y z + 5/72 y x + 5/36 y x - 5/72 y x + + 3 4 2 4 2 4 3 + + 1/12 z y - 1/36 y x - 1/72 y x , COEFF(1, 2, -1) = 1/72 z y x + + 4 3 2 4 2 2 4 4 + - 1/144 z y x - 1/18 z y x - 1/18 z y x + 1/36 z y x + + 4 2 2 4 4 4 4 2 2 4 + + 1/36 z y x + 1/72 z y x - 1/144 z y x - 1/72 z y x + + 4 2 3 3 3 3 3 4 + + 1/72 z y x + 1/144 z y x + 1/72 z y x - 1/54 y x - 1/54 y x + + 2 2 3 3 2 3 2 4 2 4 + - 1/72 z y x + 1/54 y x - 1/36 z y x + 1/144 z y x - 1/36 z y x + + 2 2 2 2 2 3 4 3 3 2 + - 1/36 y x z - 2/27 y x + 1/18 y x z + 1/36 z y x + 1/36 y x z + + 3 2 2 3 4 3 2 3 2 4 4 + - 1/9 y x z - 1/72 z y x + 1/18 z y x - 1/9 y x z - 1/108 y x + + 3 3 3 2 4 3 + + 1/18 z y x - 1/72 z y x - 1/18 y x z - 1/18 z y x - 1/108 y x + + 2 2 2 2 2 2 2 2 + - 1/27 y x + 1/18 y x z - 1/36 y x z + 1/9 y x z + 1/9 y x z + + 3 2 4 3 2 2 2 4 2 + + 2/27 y x + 1/27 y x + 2/27 y x - 1/27 y x - 2/27 y x + 1/27 y x + + 4 2 4 2 3 + + 1/54 y x + 1/108 y x + 1/108 y x , COEFF(2, 2, -1) = + + 2 4 3 4 3 2 4 2 2 4 + - 1/144 z y x + 1/288 z y x + 1/288 z y x + 1/144 z y x + + 4 4 2 2 4 4 4 4 + - 1/288 z y x - 1/576 z y x - 1/288 z y x + 1/576 z y x + + 2 2 4 4 2 3 3 + + 1/288 z y x - 1/288 z y x - 1/288 z y x - 1/144 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 1/108 y x + 1/216 y x + 1/144 z y x - 1/108 y x + 1/72 z y x + + 2 4 2 4 2 + - 1/576 z y x + 1/144 z y x + 1/288 y x z + 1/108 y x + + 2 2 2 2 3 4 3 3 2 3 2 2 + - 1/288 y x z - 1/144 z y x - 1/72 y x z + 1/144 y x z + + 3 4 3 2 3 2 4 4 + + 1/288 z y x - 1/288 z y x + 1/72 y x z + 1/432 y x + + 3 3 3 2 4 3 + - 1/144 z y x + 1/144 z y x + 1/144 y x z + 1/288 z y x + 1/216 y x + + 2 2 2 2 2 2 2 2 + + 1/216 y x - 1/144 y x z + 1/576 y x z - 1/144 y x z - 1/72 y x z + + 3 2 4 3 2 2 2 + - 1/216 y x - 1/216 y x - 1/108 y x + 1/432 y x + 1/216 y x + + 4 2 4 2 4 2 3 + - 1/432 y x - 1/216 y x - 1/432 y x - 1/216 y x , COEFF(-2, -2, 0) + + 2 4 3 2 4 2 2 4 2 4 4 + = - 1/96 z y x - 1/192 z y x + 1/96 z y x + 1/192 z y x + + 2 2 4 3 3 3 4 2 2 3 3 + - 1/192 z y x - 5/288 y x + 5/576 y x + 1/96 z y x + 5/288 y x + + 2 3 2 4 2 2 2 2 3 4 + - 1/48 z y x + 1/96 z y x - 5/288 y x + 1/192 y x z - 1/96 z y x + + 3 3 2 3 2 2 3 2 4 4 + + 1/48 y x z + 1/96 y x z - 1/48 y x z - 5/1152 y x + + 4 3 2 2 2 2 2 2 + + 5/576 y x + 5/576 y x - 1/96 y x z - 1/96 y x z + 1/48 y x z + + 3 2 4 3 2 2 2 + - 5/576 y x - 5/576 y x + 5/288 y x - 5/1152 y x + 5/576 y x + + 4 2 4 2 4 2 3 + + 5/1152 y x - 5/576 y x + 5/1152 y x - 5/576 y x , COEFF(-1, -2, 0) + + 2 4 3 2 4 2 2 4 2 4 4 + = 1/48 z y x + 1/12 z y x - 1/12 z y x - 1/48 z y x + + 2 2 4 3 3 3 4 2 2 3 3 + + 1/48 z y x + 5/144 y x - 5/144 y x - 1/48 z y x - 5/144 y x + + 2 3 2 4 2 2 2 2 3 4 + + 1/24 z y x - 1/24 z y x + 5/36 y x - 1/12 y x z + 1/24 z y x + + 3 3 2 3 2 2 3 2 4 4 4 3 + - 1/24 y x z - 1/6 y x z + 1/6 y x z + 5/288 y x - 5/288 y x + + 2 2 2 2 2 2 3 2 + - 5/72 y x + 1/12 y x z + 1/6 y x z - 1/6 y x z + 5/36 y x + + 4 3 2 2 2 4 2 4 + + 5/72 y x - 5/36 y x + 5/72 y x - 5/36 y x - 5/72 y x + 5/144 y x + + 2 4 2 3 2 2 4 2 + - 5/288 y x + 5/288 y x , COEFF(0, -2, 0) = 5/48 y - 5/32 z y x + + 25 2 2 25 3 2 3 2 4 2 2 2 + - --- y x - -- y x - 1/4 y z - 5/96 y x - 5/24 y + 5/32 y x z + 192 96 + + 2 2 4 2 4 4 2 2 4 2 2 + - 1/32 z y x + 1/32 z y x + 1/4 y z + 5/192 y x - 1/8 y z + + 2 3 4 25 4 2 3 2 2 4 4 2 2 + - 1/16 z y x + --- y x + 5/16 y x z - 5/192 y x - 5/16 y x z + 192 + + 25 2 2 4 2 4 3 4 3 4 + + -- y x + 1/16 z y x + 1/8 z y + 5/24 y - 5/48 y + 5/96 y x , + 96 + + 2 4 3 2 4 2 2 4 + COEFF(1, -2, 0) = - 1/48 z y x + 1/12 z y x + 1/12 z y x + + 2 4 4 2 2 4 3 3 3 4 + - 1/48 z y x + 1/48 z y x - 5/144 y x - 5/144 y x + + 2 2 3 3 2 3 2 4 + + 1/48 z y x + 5/144 y x - 1/24 z y x - 1/24 z y x - 5/36 y x + + 2 2 2 2 3 4 3 3 2 3 2 2 + - 1/12 y x z + 1/24 z y x + 1/24 y x z - 1/6 y x z + + 3 2 4 4 4 3 2 2 2 + - 1/6 y x z + 5/288 y x + 5/288 y x + 5/72 y x - 1/12 y x z + + 2 2 2 3 2 4 3 + + 1/6 y x z + 1/6 y x z + 5/36 y x - 5/72 y x + 5/36 y x + + 2 2 2 4 2 4 2 4 + + 5/72 y x - 5/36 y x - 5/72 y x + 5/144 y x - 5/288 y x + + 2 3 2 4 3 2 4 2 + - 5/288 y x , COEFF(2, -2, 0) = 1/96 z y x - 1/192 z y x + + 2 4 2 4 4 2 2 4 3 3 + - 1/96 z y x + 1/192 z y x - 1/192 z y x + 5/288 y x + + 3 4 2 2 3 3 2 3 2 4 + + 5/576 y x - 1/96 z y x - 5/288 y x + 1/48 z y x + 1/96 z y x + + 2 2 2 2 3 4 3 3 2 + + 5/288 y x + 1/192 y x z - 1/96 z y x - 1/48 y x z + + 3 2 2 3 2 4 4 4 3 2 + + 1/96 y x z + 1/48 y x z - 5/1152 y x - 5/576 y x - 5/576 y x + + 2 2 2 2 2 3 2 4 + + 1/96 y x z - 1/96 y x z - 1/48 y x z - 5/576 y x + 5/576 y x + + 3 2 2 2 4 2 4 + - 5/288 y x - 5/1152 y x + 5/576 y x + 5/1152 y x - 5/576 y x + + 2 4 2 3 2 4 3 + + 5/1152 y x + 5/576 y x , COEFF(-2, -1, 0) = 1/24 z y x + + 2 4 2 2 4 2 4 4 2 2 4 + + 1/48 z y x - 1/24 z y x - 1/48 z y x + 1/12 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 5/144 y x - 5/288 y x - 1/6 z y x - 5/36 y x + 1/6 z y x + + 2 4 2 2 2 2 3 4 3 3 2 + - 1/12 z y x + 5/36 y x - 1/12 y x z + 1/48 z y x - 1/24 y x z + + 3 2 2 3 2 4 4 4 3 2 + - 1/48 y x z + 1/24 y x z + 5/288 y x - 5/144 y x - 5/36 y x + + 2 2 2 2 2 3 2 4 + + 1/6 y x z + 1/12 y x z - 1/6 y x z + 5/288 y x + 5/144 y x + + 3 2 2 2 4 2 4 + - 5/144 y x + 5/72 y x - 5/72 y x - 5/288 y x + 5/72 y x + + 2 4 2 3 2 4 3 + - 5/72 y x + 5/36 y x , COEFF(-1, -1, 0) = - 1/12 z y x + + 2 4 2 2 4 2 4 4 2 2 4 3 3 + - 1/3 z y x + 1/3 z y x + 1/12 z y x - 1/3 z y x - 5/72 y x + + 3 4 2 2 3 3 2 3 2 4 + + 5/72 y x + 1/3 z y x + 5/18 y x - 1/3 z y x + 1/3 z y x + + 2 2 2 2 3 4 3 3 2 3 2 2 + - 10/9 y x + 4/3 y x z - 1/12 z y x + 1/12 y x z + 1/3 y x z + + 3 2 4 4 4 3 2 2 2 + - 1/3 y x z - 5/72 y x + 5/72 y x + 10/9 y x - 4/3 y x z + + 2 2 2 3 2 4 3 + - 4/3 y x z + 4/3 y x z - 5/18 y x - 5/18 y x + 5/18 y x + + 2 2 2 4 2 4 2 4 + - 10/9 y x + 10/9 y x + 5/18 y x - 5/18 y x + 5/18 y x + + 2 3 2 3 2 2 + - 5/18 y x , COEFF(0, -1, 0) = - 5/3 y + 5/3 y - 5/8 y x z + + 2 4 4 4 2 3 2 4 2 2 2 + - 1/2 z y + 5/48 y x - 2 y z - 5/12 y + 5/8 z y x + 5/2 y x z + + 2 2 25 2 2 4 4 25 2 2 2 2 4 + + 2 y z - -- y x - 1/8 z y x + -- y x + 1/2 z y x + 12 12 + + 2 2 2 3 2 2 4 4 25 4 2 + - 5/2 y x z + 1/2 y z - 5/12 y x + 5/12 y x - -- y x + 48 + + 3 4 2 4 25 3 2 4 2 3 4 + - 5/48 y x - 1/2 z y x + -- y x + 5/12 y + 1/8 z y x , + 48 + + 2 4 3 2 4 2 2 4 + COEFF(1, -1, 0) = 1/12 z y x - 1/3 z y x - 1/3 z y x + + 2 4 4 2 2 4 3 3 3 4 2 2 3 + + 1/12 z y x - 1/3 z y x + 5/72 y x + 5/72 y x - 1/3 z y x + + 3 2 3 2 4 2 2 2 + - 5/18 y x + 1/3 z y x + 1/3 z y x + 10/9 y x + 4/3 y x z + + 2 3 4 3 3 2 3 2 2 3 2 4 4 + - 1/12 z y x - 1/12 y x z + 1/3 y x z + 1/3 y x z - 5/72 y x + + 4 3 2 2 2 2 2 2 + - 5/72 y x - 10/9 y x + 4/3 y x z - 4/3 y x z - 4/3 y x z + + 3 2 4 3 2 2 2 4 2 + - 5/18 y x + 5/18 y x - 5/18 y x - 10/9 y x + 10/9 y x + 5/18 y x + + 4 2 4 2 3 2 4 3 + - 5/18 y x + 5/18 y x + 5/18 y x , COEFF(2, -1, 0) = - 1/24 z y x + + 2 4 2 2 4 2 4 4 2 2 4 + + 1/48 z y x + 1/24 z y x - 1/48 z y x + 1/12 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 5/144 y x - 5/288 y x + 1/6 z y x + 5/36 y x - 1/6 z y x + + 2 4 2 2 2 2 3 4 3 3 2 + - 1/12 z y x - 5/36 y x - 1/12 y x z + 1/48 z y x + 1/24 y x z + + 3 2 2 3 2 4 4 4 3 2 + - 1/48 y x z - 1/24 y x z + 5/288 y x + 5/144 y x + 5/36 y x + + 2 2 2 2 2 3 2 4 + - 1/6 y x z + 1/12 y x z + 1/6 y x z + 5/288 y x - 5/144 y x + + 3 2 2 2 4 2 4 + + 5/144 y x + 5/72 y x - 5/72 y x - 5/288 y x + 5/72 y x + + 2 4 2 3 4 4 2 2 + - 5/72 y x - 5/36 y x , COEFF(-2, 0, 0) = - 5/192 y x - 1/8 x z + + 2 2 4 4 4 3 2 3 2 + - 5/32 z y x - 5/96 y x - 5/24 x + 5/96 y x + 5/48 x - 1/4 x z + + 2 2 4 25 2 3 4 2 2 4 2 + - 5/16 y x z - 5/48 x - -- y x + 5/192 y x - 1/32 z y x + 96 + + 25 2 4 2 2 4 4 2 2 2 25 2 2 + + --- y x + 1/4 x z + 1/32 z y x + 5/32 y x z - --- y x + 192 192 + + 2 2 3 3 2 4 25 2 2 4 + + 5/16 z y x + 5/24 x + 1/8 z x + -- y x + 1/16 z y x + 96 + + 2 4 3 4 4 2 4 2 2 + - 1/16 z y x , COEFF(-1, 0, 0) = 5/48 y x - 1/2 z x + 5/2 y x z + + 2 4 2 4 3 2 4 25 2 2 3 + + 1/2 z y x - 5/48 y x - 1/2 z y x + -- y x - 5/12 x + 12 + + 2 2 4 25 2 3 4 4 25 2 + + 5/8 z y x + -- y x + 5/12 y x + 5/12 x + 5/3 x - -- y x + 48 12 + + 2 2 2 2 2 2 2 2 4 4 3 2 + + 2 x z - 2 x z - 5/3 x - 5/2 y x z - 1/8 z y x + 1/2 x z + + 2 2 3 2 4 3 4 2 25 2 4 + - 5/8 z y x + 1/8 z y x - 5/12 y x - -- y x , COEFF(0, 0, 0) = + 48 + + 2 15 2 2 4 2 2 4 25 2 4 4 + 25/8 x - -- z y x - 15/4 y z - 5/8 x + -- y x - 5/8 y + 16 32 + + 4 4 2 125 2 2 2 4 2 2 + - 5/32 y x - 5/2 + 25/8 y - --- y x + 3/4 z y - 15/4 x z + 32 + + 2 4 4 25 4 2 15 2 4 2 75 2 2 2 2 2 4 + + 3/16 z y x + -- y x - -- z y x + -- y x z + 3 z + 3/4 z x , + 32 16 16 + + 2 4 4 25 2 3 4 2 2 4 + COEFF(1, 0, 0) = - 1/8 z y x - -- y x + 5/12 x + 5/8 z y x + 48 + + 2 4 2 2 2 4 2 4 3 2 + + 1/2 z y x - 5/2 y x z - 5/12 y x - 1/2 z x - 1/2 x z + + 2 2 2 2 2 4 3 25 2 2 4 2 + - 5/2 y x z + 2 x z - 1/8 z y x + -- y x - 5/12 y x - 5/3 x + 12 + + 2 4 2 4 3 2 25 2 4 25 2 2 + + 1/2 z y x + 5/48 y x - 5/3 x - -- y x + -- y x + 2 x z + 48 12 + + 4 4 2 2 3 3 3 2 + + 5/48 y x + 5/8 z y x + 5/12 x , COEFF(2, 0, 0) = 1/4 x z + + 4 2 4 4 3 2 2 2 + + 5/96 y x - 1/16 z y x + 5/24 x - 5/96 y x + 5/32 y x z + + 2 4 2 2 4 2 25 2 2 25 2 3 + - 1/32 z y x + 5/48 x + 5/192 y x - --- y x + -- y x + 192 96 + + 2 2 4 4 4 2 4 4 4 25 2 + - 5/32 z y x - 5/192 y x + 1/32 z y x - 5/48 x - -- y x + 96 + + 2 2 3 2 4 3 2 4 25 2 4 2 2 + - 5/16 z y x + 1/16 z y x + 1/8 z x + --- y x - 1/8 x z + 192 + + 3 2 2 2 2 4 3 + - 5/24 x - 1/4 x z + 5/16 y x z , COEFF(-2, 1, 0) = 1/24 z y x + + 2 4 2 2 4 2 4 4 2 2 4 + + 1/48 z y x - 1/24 z y x - 1/48 z y x + 1/12 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 5/144 y x + 5/288 y x - 1/6 z y x + 5/36 y x - 1/6 z y x + + 2 4 2 2 2 2 3 4 3 3 2 + + 1/12 z y x - 5/36 y x - 1/12 y x z - 1/48 z y x + 1/24 y x z + + 3 2 2 3 2 4 4 4 3 2 + + 1/48 y x z - 1/24 y x z + 5/288 y x - 5/144 y x - 5/36 y x + + 2 2 2 2 2 3 2 4 + + 1/6 y x z - 1/12 y x z + 1/6 y x z - 5/288 y x + 5/144 y x + + 3 2 2 2 4 2 4 + + 5/144 y x + 5/72 y x + 5/72 y x - 5/288 y x - 5/72 y x + + 2 4 2 3 2 4 3 + - 5/72 y x + 5/36 y x , COEFF(-1, 1, 0) = - 1/12 z y x + + 2 4 2 2 4 2 4 4 2 2 4 3 3 + - 1/3 z y x + 1/3 z y x + 1/12 z y x - 1/3 z y x + 5/72 y x + + 3 4 2 2 3 3 2 3 2 4 + - 5/72 y x + 1/3 z y x - 5/18 y x + 1/3 z y x - 1/3 z y x + + 2 2 2 2 3 4 3 3 2 3 2 2 + + 10/9 y x + 4/3 y x z + 1/12 z y x - 1/12 y x z - 1/3 y x z + + 3 2 4 4 4 3 2 2 2 + + 1/3 y x z - 5/72 y x + 5/72 y x + 10/9 y x - 4/3 y x z + + 2 2 2 3 2 4 3 + + 4/3 y x z - 4/3 y x z + 5/18 y x - 5/18 y x - 5/18 y x + + 2 2 2 4 2 4 2 4 + - 10/9 y x - 10/9 y x + 5/18 y x + 5/18 y x + 5/18 y x + + 2 3 2 2 4 2 4 + - 5/18 y x , COEFF(0, 1, 0) = - 5/3 y - 5/12 y x - 1/2 z y + + 2 2 2 25 3 2 2 4 2 4 2 4 + - 5/2 y x z - -- y x + 5/8 z y x + 5/12 y + 1/2 z y x + 48 + + 4 25 2 3 2 2 25 4 2 25 2 2 2 2 + - 5/12 y x + -- y x + 5/8 y x z - -- y x + -- y x - 5/2 y x z + 12 48 12 + + 2 2 2 2 3 4 3 4 2 2 4 + - 5/3 y + 2 y z + 2 y z - 1/8 z y x + 5/48 y x + 1/2 z y x + + 3 4 4 3 2 2 4 4 + + 5/12 y + 5/48 y x - 1/2 y z - 1/8 z y x , COEFF(1, 1, 0) = + + 2 4 3 2 4 2 2 4 2 4 4 2 2 4 + 1/12 z y x - 1/3 z y x - 1/3 z y x + 1/12 z y x - 1/3 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 5/72 y x - 5/72 y x - 1/3 z y x + 5/18 y x - 1/3 z y x + + 2 4 2 2 2 2 3 4 3 3 2 + - 1/3 z y x - 10/9 y x + 4/3 y x z + 1/12 z y x + 1/12 y x z + + 3 2 2 3 2 4 4 4 3 2 + - 1/3 y x z - 1/3 y x z - 5/72 y x - 5/72 y x - 10/9 y x + + 2 2 2 2 2 3 2 4 + + 4/3 y x z + 4/3 y x z + 4/3 y x z + 5/18 y x + 5/18 y x + + 3 2 2 2 4 2 4 2 4 + + 5/18 y x - 10/9 y x - 10/9 y x + 5/18 y x + 5/18 y x + 5/18 y x + + 2 3 2 4 3 2 4 2 + + 5/18 y x , COEFF(2, 1, 0) = - 1/24 z y x + 1/48 z y x + + 2 4 2 4 4 2 2 4 3 3 3 4 + + 1/24 z y x - 1/48 z y x + 1/12 z y x + 5/144 y x + 5/288 y x + + 2 2 3 3 2 3 2 4 + + 1/6 z y x - 5/36 y x + 1/6 z y x + 1/12 z y x + 5/36 y x + + 2 2 2 2 3 4 3 3 2 3 2 2 + - 1/12 y x z - 1/48 z y x - 1/24 y x z + 1/48 y x z + + 3 2 4 4 4 3 2 2 2 + + 1/24 y x z + 5/288 y x + 5/144 y x + 5/36 y x - 1/6 y x z + + 2 2 2 3 2 4 3 + - 1/12 y x z - 1/6 y x z - 5/288 y x - 5/144 y x - 5/144 y x + + 2 2 2 4 2 4 2 4 + + 5/72 y x + 5/72 y x - 5/288 y x - 5/72 y x - 5/72 y x + + 2 3 2 4 3 2 4 2 + - 5/36 y x , COEFF(-2, 2, 0) = - 1/96 z y x - 1/192 z y x + + 2 4 2 4 4 2 2 4 3 3 + + 1/96 z y x + 1/192 z y x - 1/192 z y x + 5/288 y x + + 3 4 2 2 3 3 2 3 2 4 + - 5/576 y x + 1/96 z y x - 5/288 y x + 1/48 z y x - 1/96 z y x + + 2 2 2 2 3 4 3 3 2 + + 5/288 y x + 1/192 y x z + 1/96 z y x - 1/48 y x z + + 3 2 2 3 2 4 4 4 3 2 + - 1/96 y x z + 1/48 y x z - 5/1152 y x + 5/576 y x + 5/576 y x + + 2 2 2 2 2 3 2 4 + - 1/96 y x z + 1/96 y x z - 1/48 y x z + 5/576 y x - 5/576 y x + + 3 2 2 2 4 2 4 + - 5/288 y x - 5/1152 y x - 5/576 y x + 5/1152 y x + 5/576 y x + + 2 4 2 3 2 4 3 + + 5/1152 y x - 5/576 y x , COEFF(-1, 2, 0) = 1/48 z y x + + 2 4 2 2 4 2 4 4 2 2 4 + + 1/12 z y x - 1/12 z y x - 1/48 z y x + 1/48 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 5/144 y x + 5/144 y x - 1/48 z y x + 5/144 y x - 1/24 z y x + + 2 4 2 2 2 2 3 4 3 3 2 + + 1/24 z y x - 5/36 y x - 1/12 y x z - 1/24 z y x + 1/24 y x z + + 3 2 2 3 2 4 4 4 3 2 + + 1/6 y x z - 1/6 y x z + 5/288 y x - 5/288 y x - 5/72 y x + + 2 2 2 2 2 3 2 4 + + 1/12 y x z - 1/6 y x z + 1/6 y x z - 5/36 y x + 5/72 y x + + 3 2 2 2 4 2 4 + + 5/36 y x + 5/72 y x + 5/36 y x - 5/72 y x - 5/144 y x + + 2 4 2 3 2 2 2 + - 5/288 y x + 5/288 y x , COEFF(0, 2, 0) = - 1/8 y z + 5/48 y + + 2 4 4 3 2 4 2 2 2 2 2 4 + + 1/32 z y x + 1/4 y z + 5/96 y x + 5/32 y x z - 1/32 z y x + + 25 3 2 4 4 3 2 2 3 2 + + -- y x - 5/192 y x - 5/16 y x z - 5/24 y - 1/4 y z + 96 + + 2 4 25 2 2 2 4 2 3 4 4 + - 1/16 z y x - --- y x + 5/192 y x + 1/16 z y x - 5/48 y + 192 + + 2 4 2 25 2 2 4 25 4 2 2 2 + - 5/32 z y x - -- y x + 1/8 z y + --- y x + 5/16 y x z + 96 192 + + 3 4 2 4 3 2 4 2 + - 5/96 y x + 5/24 y, COEFF(1, 2, 0) = - 1/48 z y x + 1/12 z y x + + 2 4 2 4 4 2 2 4 3 3 3 4 + + 1/12 z y x - 1/48 z y x + 1/48 z y x + 5/144 y x + 5/144 y x + + 2 2 3 3 2 3 2 4 + + 1/48 z y x - 5/144 y x + 1/24 z y x + 1/24 z y x + 5/36 y x + + 2 2 2 2 3 4 3 3 2 3 2 2 + - 1/12 y x z - 1/24 z y x - 1/24 y x z + 1/6 y x z + + 3 2 4 4 4 3 2 2 2 + + 1/6 y x z + 5/288 y x + 5/288 y x + 5/72 y x - 1/12 y x z + + 2 2 2 3 2 4 3 + - 1/6 y x z - 1/6 y x z - 5/36 y x - 5/72 y x - 5/36 y x + + 2 2 2 4 2 4 2 4 + + 5/72 y x + 5/36 y x - 5/72 y x - 5/144 y x - 5/288 y x + + 2 3 2 4 3 2 4 2 + - 5/288 y x , COEFF(2, 2, 0) = 1/96 z y x - 1/192 z y x + + 2 4 2 4 4 2 2 4 3 3 + - 1/96 z y x + 1/192 z y x - 1/192 z y x - 5/288 y x + + 3 4 2 2 3 3 2 3 2 4 + - 5/576 y x - 1/96 z y x + 5/288 y x - 1/48 z y x - 1/96 z y x + + 2 2 2 2 3 4 3 3 2 + - 5/288 y x + 1/192 y x z + 1/96 z y x + 1/48 y x z + + 3 2 2 3 2 4 4 4 3 2 + - 1/96 y x z - 1/48 y x z - 5/1152 y x - 5/576 y x - 5/576 y x + + 2 2 2 2 2 3 2 4 + + 1/96 y x z + 1/96 y x z + 1/48 y x z + 5/576 y x + 5/576 y x + + 3 2 2 2 4 2 4 + + 5/288 y x - 5/1152 y x - 5/576 y x + 5/1152 y x + 5/576 y x + + 2 4 2 3 2 4 3 + + 5/1152 y x + 5/576 y x , COEFF(-2, -2, 1) = 1/144 z y x + + 4 3 2 4 2 2 4 4 + + 1/288 z y x + 1/288 z y x - 1/144 z y x - 1/288 z y x + + 4 2 2 4 4 4 4 2 2 4 + + 1/576 z y x - 1/288 z y x - 1/576 z y x + 1/288 z y x + + 4 2 3 3 3 3 3 4 + - 1/288 z y x - 1/288 z y x + 1/144 z y x + 1/108 y x - 1/216 y x + + 2 2 3 3 2 3 2 4 + - 1/144 z y x - 1/108 y x + 1/72 z y x + 1/576 z y x + + 2 4 2 2 2 2 + - 1/144 z y x + 1/288 y x z + 1/108 y x - 1/288 y x z + + 2 3 4 3 3 2 3 2 2 3 4 + + 1/144 z y x - 1/72 y x z - 1/144 y x z + 1/288 z y x + + 3 2 3 2 4 4 3 + - 1/288 z y x + 1/72 y x z + 1/432 y x + 1/144 z y x + + 3 3 2 4 3 2 + - 1/144 z y x - 1/144 y x z + 1/288 z y x - 1/216 y x - 1/216 y x + + 2 2 2 2 2 2 2 + + 1/144 y x z - 1/576 y x z + 1/144 y x z - 1/72 y x z + + 3 2 4 3 2 2 2 + + 1/216 y x + 1/216 y x - 1/108 y x + 1/432 y x - 1/216 y x + + 4 2 4 2 4 2 3 + - 1/432 y x + 1/216 y x - 1/432 y x + 1/216 y x , COEFF(-1, -2, 1) + + 2 4 3 4 3 2 4 2 2 4 + = - 1/72 z y x - 1/144 z y x - 1/18 z y x + 1/18 z y x + + 4 4 2 2 4 4 4 4 + + 1/36 z y x - 1/36 z y x + 1/72 z y x + 1/144 z y x + + 2 2 4 4 2 3 3 3 3 + - 1/72 z y x + 1/72 z y x + 1/144 z y x - 1/72 z y x - 1/54 y x + + 3 4 2 2 3 3 2 3 2 4 + + 1/54 y x + 1/72 z y x + 1/54 y x - 1/36 z y x - 1/144 z y x + + 2 4 2 2 2 2 2 3 4 + + 1/36 z y x - 1/36 y x z - 2/27 y x + 1/18 y x z - 1/36 z y x + + 3 3 2 3 2 2 3 4 3 2 3 2 + + 1/36 y x z + 1/9 y x z - 1/72 z y x + 1/18 z y x - 1/9 y x z + + 4 4 3 3 3 2 + - 1/108 y x - 1/18 z y x + 1/72 z y x + 1/18 y x z - 1/18 z y x + + 4 3 2 2 2 2 2 2 2 + + 1/108 y x + 1/27 y x - 1/18 y x z + 1/36 y x z - 1/9 y x z + + 2 3 2 4 3 2 2 2 + + 1/9 y x z - 2/27 y x - 1/27 y x + 2/27 y x - 1/27 y x + 2/27 y x + + 4 2 4 2 4 2 3 + + 1/27 y x - 1/54 y x + 1/108 y x - 1/108 y x , COEFF(0, -2, 1) = + + 2 4 2 4 2 2 4 4 4 4 2 2 4 + 5/48 z y x + 5/96 z y x - 1/48 z y x - 1/96 z y x + 1/48 z y x + + 4 3 4 2 4 2 4 4 + - 1/48 z y x - 1/36 y x + 1/96 z y x - 1/24 z y x + 1/9 y + 1/18 y + + 2 2 2 2 3 4 4 3 2 2 3 4 + - 5/48 y x z + 1/24 z y x - 1/24 z y - 5/24 y x z + 1/48 z y x + + 2 4 3 2 4 4 3 2 2 + - 1/12 z y - 5/48 z y x + 1/72 y x - 1/9 y - 1/18 y + 5/48 z y x + + 2 2 2 2 3 2 2 + - 1/12 y z - 5/96 y x z + 5/24 y x z + 5/36 y x + 1/24 y z + + 3 2 2 2 2 2 2 2 4 2 + + 1/6 y z - 1/6 y z + 1/12 y z + 5/72 y x - 5/36 y x - 5/72 y x + + 3 4 2 4 2 4 3 + + 1/12 z y + 1/36 y x - 1/72 y x , COEFF(1, -2, 1) = 1/72 z y x + + 4 3 2 4 2 2 4 4 + + 1/144 z y x - 1/18 z y x - 1/18 z y x - 1/36 z y x + + 4 2 2 4 4 4 4 2 2 4 + - 1/36 z y x + 1/72 z y x + 1/144 z y x - 1/72 z y x + + 4 2 3 3 3 3 3 4 + + 1/72 z y x - 1/144 z y x + 1/72 z y x + 1/54 y x + 1/54 y x + + 2 2 3 3 2 3 2 4 2 4 + - 1/72 z y x - 1/54 y x + 1/36 z y x - 1/144 z y x + 1/36 z y x + + 2 2 2 2 2 3 4 3 3 2 + + 1/36 y x z + 2/27 y x + 1/18 y x z - 1/36 z y x - 1/36 y x z + + 3 2 2 3 4 3 2 3 2 4 4 + + 1/9 y x z - 1/72 z y x + 1/18 z y x + 1/9 y x z - 1/108 y x + + 3 3 3 2 4 3 + + 1/18 z y x - 1/72 z y x - 1/18 y x z - 1/18 z y x - 1/108 y x + + 2 2 2 2 2 2 2 2 + - 1/27 y x + 1/18 y x z + 1/36 y x z - 1/9 y x z - 1/9 y x z + + 3 2 4 3 2 2 2 4 2 + - 2/27 y x + 1/27 y x - 2/27 y x - 1/27 y x + 2/27 y x + 1/27 y x + + 4 2 4 2 3 + - 1/54 y x + 1/108 y x + 1/108 y x , COEFF(2, -2, 1) = + + 2 4 3 4 3 2 4 2 2 4 + - 1/144 z y x - 1/288 z y x + 1/288 z y x + 1/144 z y x + + 4 4 2 2 4 4 4 4 + + 1/288 z y x + 1/576 z y x - 1/288 z y x - 1/576 z y x + + 2 2 4 4 2 3 3 + + 1/288 z y x - 1/288 z y x + 1/288 z y x - 1/144 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 1/108 y x - 1/216 y x + 1/144 z y x + 1/108 y x - 1/72 z y x + + 2 4 2 4 2 + + 1/576 z y x - 1/144 z y x - 1/288 y x z - 1/108 y x + + 2 2 2 2 3 4 3 3 2 3 2 2 + - 1/288 y x z + 1/144 z y x + 1/72 y x z - 1/144 y x z + + 3 4 3 2 3 2 4 4 + + 1/288 z y x - 1/288 z y x - 1/72 y x z + 1/432 y x + + 3 3 3 2 4 3 + - 1/144 z y x + 1/144 z y x + 1/144 y x z + 1/288 z y x + 1/216 y x + + 2 2 2 2 2 2 2 2 + + 1/216 y x - 1/144 y x z - 1/576 y x z + 1/144 y x z + 1/72 y x z + + 3 2 4 3 2 2 2 + + 1/216 y x - 1/216 y x + 1/108 y x + 1/432 y x - 1/216 y x + + 4 2 4 2 4 2 3 + - 1/432 y x + 1/216 y x - 1/432 y x - 1/216 y x , COEFF(-2, -1, 1) + + 2 4 3 4 3 2 4 2 2 4 + = - 1/36 z y x - 1/72 z y x - 1/72 z y x + 1/36 z y x + + 4 4 2 2 4 4 4 4 + + 1/72 z y x - 1/144 z y x + 1/72 z y x + 1/144 z y x + + 2 2 4 4 2 3 3 3 3 + - 1/18 z y x + 1/36 z y x + 1/18 z y x - 1/18 z y x - 1/54 y x + + 3 4 2 2 3 3 2 3 2 4 + + 1/108 y x + 1/9 z y x + 2/27 y x - 1/9 z y x - 1/36 z y x + + 2 4 2 2 2 2 2 3 4 + + 1/18 z y x - 1/18 y x z - 2/27 y x + 1/18 y x z - 1/72 z y x + + 3 3 2 3 2 2 3 4 3 2 + + 1/36 y x z + 1/72 y x z - 1/144 z y x + 1/144 z y x + + 3 2 4 4 3 3 3 + - 1/36 y x z - 1/108 y x - 1/72 z y x + 1/72 z y x + 1/18 y x z + + 2 4 3 2 2 2 2 2 + - 1/36 z y x + 1/54 y x + 2/27 y x - 1/9 y x z + 1/36 y x z + + 2 2 2 3 2 4 3 + - 1/18 y x z + 1/9 y x z - 1/108 y x - 1/54 y x + 1/54 y x + + 2 2 2 4 2 4 2 4 + - 1/27 y x + 1/27 y x + 1/108 y x - 1/27 y x + 1/27 y x + + 2 3 2 4 3 4 3 + - 2/27 y x , COEFF(-1, -1, 1) = 1/18 z y x + 1/36 z y x + + 2 4 2 2 4 4 4 2 2 4 4 + + 2/9 z y x - 2/9 z y x - 1/9 z y x + 1/9 z y x - 1/18 z y x + + 4 4 2 2 4 4 2 3 3 + - 1/36 z y x + 2/9 z y x - 1/9 z y x - 1/9 z y x + 1/9 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 1/27 y x - 1/27 y x - 2/9 z y x - 4/27 y x + 2/9 z y x + + 2 4 2 4 2 16 2 2 2 + + 1/9 z y x - 2/9 z y x + 4/9 y x z + -- y x - 8/9 y x z + 27 + + 2 3 4 3 3 2 3 2 2 3 4 + + 1/18 z y x - 1/18 y x z - 2/9 y x z + 1/36 z y x + + 3 2 3 2 4 4 3 3 3 + - 1/9 z y x + 2/9 y x z + 1/27 y x + 1/9 z y x - 1/36 z y x + + 2 4 3 16 2 2 2 + - 4/9 y x z + 4/9 z y x - 1/27 y x - -- y x + 8/9 y x z + 27 + + 2 2 2 2 2 3 2 4 + - 4/9 y x z + 8/9 y x z - 8/9 y x z + 4/27 y x + 4/27 y x + + 3 16 2 2 16 2 4 2 4 2 4 + - 4/27 y x + -- y x - -- y x - 4/27 y x + 4/27 y x - 4/27 y x + 27 27 + + 2 3 2 4 2 4 2 + + 4/27 y x , COEFF(0, -1, 1) = - 5/12 z y x - 5/24 z y x + + 2 4 4 4 4 2 2 4 4 3 4 + + 1/12 z y x + 1/24 z y x - 1/3 z y x + 1/6 z y x + 1/18 y x + + 2 4 2 4 4 2 2 2 + - 1/6 z y x + 1/3 z y x - 8/9 y - 2/9 y + 5/3 y x z + + 2 3 4 4 3 2 2 3 4 2 4 + - 1/12 z y x + 1/6 z y + 5/12 y x z - 1/24 z y x + 1/3 z y + + 3 2 4 4 3 2 2 + + 5/24 z y x - 1/18 y x + 2/9 y + 8/9 y - 5/6 z y x + 2/3 y z + + 2 2 2 2 3 2 2 3 2 2 + + 5/6 y x z - 5/3 y x z - 5/18 y x - 2/3 y z - 1/3 y z + 4/3 y z + + 2 2 2 2 2 4 2 3 4 + - 4/3 y z - 10/9 y x + 10/9 y x + 5/18 y x - 1/6 z y - 2/9 y x + + 2 4 2 4 3 4 3 + + 2/9 y x , COEFF(1, -1, 1) = - 1/18 z y x - 1/36 z y x + + 2 4 2 2 4 4 4 2 2 4 4 + + 2/9 z y x + 2/9 z y x + 1/9 z y x + 1/9 z y x - 1/18 z y x + + 4 4 2 2 4 4 2 3 3 + - 1/36 z y x + 2/9 z y x - 1/9 z y x + 1/9 z y x - 1/9 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 1/27 y x - 1/27 y x + 2/9 z y x + 4/27 y x - 2/9 z y x + + 2 4 2 4 2 16 2 2 2 + + 1/9 z y x - 2/9 z y x - 4/9 y x z - -- y x - 8/9 y x z + 27 + + 2 3 4 3 3 2 3 2 2 3 4 + + 1/18 z y x + 1/18 y x z - 2/9 y x z + 1/36 z y x + + 3 2 3 2 4 4 3 3 3 + - 1/9 z y x - 2/9 y x z + 1/27 y x - 1/9 z y x + 1/36 z y x + + 2 4 3 16 2 2 2 + + 4/9 y x z + 4/9 z y x + 1/27 y x + -- y x - 8/9 y x z + 27 + + 2 2 2 2 2 3 2 4 + - 4/9 y x z + 8/9 y x z + 8/9 y x z + 4/27 y x - 4/27 y x + + 3 16 2 2 16 2 4 2 4 2 4 + + 4/27 y x + -- y x - -- y x - 4/27 y x + 4/27 y x - 4/27 y x + 27 27 + + 2 3 2 4 3 4 3 + - 4/27 y x , COEFF(2, -1, 1) = 1/36 z y x + 1/72 z y x + + 2 4 2 2 4 4 4 2 + - 1/72 z y x - 1/36 z y x - 1/72 z y x - 1/144 z y x + + 2 4 4 4 4 2 2 4 4 + + 1/72 z y x + 1/144 z y x - 1/18 z y x + 1/36 z y x + + 2 3 3 3 3 3 4 2 2 3 + - 1/18 z y x + 1/18 z y x + 1/54 y x + 1/108 y x - 1/9 z y x + + 3 2 3 2 4 2 4 2 + - 2/27 y x + 1/9 z y x - 1/36 z y x + 1/18 z y x + 1/18 y x z + + 2 2 2 2 3 4 3 3 2 3 2 2 + + 2/27 y x + 1/18 y x z - 1/72 z y x - 1/36 y x z + 1/72 y x z + + 3 4 3 2 3 2 4 4 3 + - 1/144 z y x + 1/144 z y x + 1/36 y x z - 1/108 y x + 1/72 z y x + + 3 3 2 4 3 2 + - 1/72 z y x - 1/18 y x z - 1/36 z y x - 1/54 y x - 2/27 y x + + 2 2 2 2 2 2 2 3 2 + + 1/9 y x z + 1/36 y x z - 1/18 y x z - 1/9 y x z - 1/108 y x + + 4 3 2 2 2 4 2 4 + + 1/54 y x - 1/54 y x - 1/27 y x + 1/27 y x + 1/108 y x - 1/27 y x + + 2 4 2 3 2 4 3 4 3 + + 1/27 y x + 2/27 y x , COEFF(-2, 0, 1) = 1/24 z y x + 1/48 z y x + + 2 4 2 2 4 4 4 2 + + 1/48 z y x - 1/24 z y x - 1/48 z y x + 1/96 z y x + + 2 4 4 4 4 2 2 4 2 3 + - 1/48 z y x - 1/96 z y x + 5/48 z y x - 5/48 z y x + + 2 2 3 2 4 3 2 4 2 + - 5/24 z y x + 5/96 z y x + 1/6 x z + 1/9 x + 1/18 x + 5/48 y x z + + 2 2 2 4 4 3 2 4 3 4 + - 5/48 y x z + 1/72 y x - 1/9 x - 1/18 x - 1/36 y x - 1/24 z x + + 2 2 2 2 2 4 + - 5/36 y x + 5/24 y x z - 5/96 y x z + 1/36 y x - 1/12 x z + + 2 2 2 2 2 2 4 2 2 4 + + 1/24 x z + 1/12 x z - 1/6 x z + 5/72 y x - 1/72 y x - 1/12 z x + + 3 2 4 2 3 2 4 3 + + 1/12 z x - 5/72 y x + 5/36 y x , COEFF(-1, 0, 1) = - 1/12 z y x + + 4 3 2 4 2 2 4 4 4 2 + - 1/24 z y x - 1/3 z y x + 1/3 z y x + 1/6 z y x - 1/6 z y x + + 2 4 4 4 4 2 2 4 2 3 + + 1/12 z y x + 1/24 z y x - 5/12 z y x + 5/24 z y x + + 2 2 3 2 4 3 2 4 2 + + 5/12 z y x - 5/24 z y x - 1/3 x z - 8/9 x - 2/9 x - 5/6 y x z + + 2 2 2 4 4 3 2 4 3 4 + + 5/3 y x z - 1/18 y x + 2/9 x + 8/9 x + 1/18 y x + 1/6 z x + + 2 2 2 2 2 4 2 + + 10/9 y x - 5/3 y x z + 5/6 y x z - 2/9 y x + 2/3 x z - 2/3 x z + + 2 2 2 2 2 4 2 2 4 3 + - 4/3 x z + 4/3 x z - 10/9 y x + 2/9 y x + 1/3 z x - 1/6 z x + + 2 4 2 3 2 4 2 4 2 + + 5/18 y x - 5/18 y x , COEFF(0, 0, 1) = 5/8 z y x + 5/16 z y x + + 2 4 4 4 4 2 2 4 2 4 4 + - 1/8 z y x - 1/16 z y x + 5/8 z y x + 5/16 z y x + 1/3 x - z + + 4 2 2 2 4 2 4 4 4 2 + + 1/3 y - 25/8 y x z - 1/4 z y - 1/2 z y + 1/12 y x - 5/3 y + + 2 2 4 25 2 2 2 2 + - 2 z - 5/3 x - 1/4 z x + 4/3 - -- y x z + 5/4 y z + 5/4 x z + 16 + + 2 2 2 2 25 2 2 4 2 2 4 2 4 + + 5/2 x z + 5/2 y z + -- y x - 5/12 y x - 1/2 z x - 5/12 y x , + 12 + + 2 4 3 4 3 2 4 2 2 4 + COEFF(1, 0, 1) = 1/12 z y x + 1/24 z y x - 1/3 z y x - 1/3 z y x + + 4 4 2 2 4 4 4 4 2 2 4 + - 1/6 z y x - 1/6 z y x + 1/12 z y x + 1/24 z y x - 5/12 z y x + + 2 3 2 2 3 2 4 3 2 4 + - 5/24 z y x - 5/12 z y x - 5/24 z y x + 1/3 x z + 8/9 x - 2/9 x + + 2 2 2 2 4 4 3 2 4 3 + + 5/6 y x z + 5/3 y x z - 1/18 y x - 2/9 x + 8/9 x - 1/18 y x + + 4 2 2 2 2 2 4 + + 1/6 z x - 10/9 y x + 5/3 y x z + 5/6 y x z + 2/9 y x - 2/3 x z + + 2 2 2 2 2 2 4 2 2 4 + - 2/3 x z - 4/3 x z - 4/3 x z - 10/9 y x + 2/9 y x + 1/3 z x + + 3 2 4 2 3 2 4 3 + + 1/6 z x + 5/18 y x + 5/18 y x , COEFF(2, 0, 1) = - 1/24 z y x + + 4 3 2 4 2 2 4 4 4 2 + - 1/48 z y x + 1/48 z y x + 1/24 z y x + 1/48 z y x + 1/96 z y x + + 2 4 4 4 4 2 2 4 2 3 + - 1/48 z y x - 1/96 z y x + 5/48 z y x + 5/48 z y x + + 2 2 3 2 4 3 2 4 2 + + 5/24 z y x + 5/96 z y x - 1/6 x z - 1/9 x + 1/18 x - 5/48 y x z + + 2 2 2 4 4 3 2 4 3 4 + - 5/48 y x z + 1/72 y x + 1/9 x - 1/18 x + 1/36 y x - 1/24 z x + + 2 2 2 2 2 4 + + 5/36 y x - 5/24 y x z - 5/96 y x z - 1/36 y x + 1/12 x z + + 2 2 2 2 2 2 4 2 2 4 + + 1/24 x z + 1/12 x z + 1/6 x z + 5/72 y x - 1/72 y x - 1/12 z x + + 3 2 4 2 3 2 4 3 + - 1/12 z x - 5/72 y x - 5/36 y x , COEFF(-2, 1, 1) = - 1/36 z y x + + 4 3 2 4 2 2 4 4 + - 1/72 z y x - 1/72 z y x + 1/36 z y x + 1/72 z y x + + 4 2 2 4 4 4 4 2 2 4 + - 1/144 z y x + 1/72 z y x + 1/144 z y x - 1/18 z y x + + 4 2 3 3 3 3 3 4 + - 1/36 z y x + 1/18 z y x + 1/18 z y x + 1/54 y x - 1/108 y x + + 2 2 3 3 2 3 2 4 2 4 + + 1/9 z y x - 2/27 y x + 1/9 z y x - 1/36 z y x - 1/18 z y x + + 2 2 2 2 2 3 4 3 3 2 + - 1/18 y x z + 2/27 y x + 1/18 y x z + 1/72 z y x - 1/36 y x z + + 3 2 2 3 4 3 2 3 2 + - 1/72 y x z + 1/144 z y x - 1/144 z y x + 1/36 y x z + + 4 4 3 3 3 2 + - 1/108 y x + 1/72 z y x - 1/72 z y x - 1/18 y x z + 1/36 z y x + + 4 3 2 2 2 2 2 2 2 + + 1/54 y x + 2/27 y x - 1/9 y x z + 1/36 y x z + 1/18 y x z + + 2 3 2 4 3 2 2 + - 1/9 y x z + 1/108 y x - 1/54 y x - 1/54 y x - 1/27 y x + + 2 4 2 4 2 4 2 3 + - 1/27 y x + 1/108 y x + 1/27 y x + 1/27 y x - 2/27 y x , + + 2 4 3 4 3 2 4 2 2 4 + COEFF(-1, 1, 1) = 1/18 z y x + 1/36 z y x + 2/9 z y x - 2/9 z y x + + 4 4 2 2 4 4 4 4 2 2 4 + - 1/9 z y x + 1/9 z y x - 1/18 z y x - 1/36 z y x + 2/9 z y x + + 4 2 3 3 3 3 3 4 + + 1/9 z y x - 1/9 z y x - 1/9 z y x - 1/27 y x + 1/27 y x + + 2 2 3 3 2 3 2 4 2 4 + - 2/9 z y x + 4/27 y x - 2/9 z y x + 1/9 z y x + 2/9 z y x + + 2 16 2 2 2 2 3 4 3 3 2 + + 4/9 y x z - -- y x - 8/9 y x z - 1/18 z y x + 1/18 y x z + 27 + + 3 2 2 3 4 3 2 3 2 4 4 + + 2/9 y x z - 1/36 z y x + 1/9 z y x - 2/9 y x z + 1/27 y x + + 3 3 3 2 4 3 + - 1/9 z y x + 1/36 z y x + 4/9 y x z - 4/9 z y x - 1/27 y x + + 16 2 2 2 2 2 2 2 2 + - -- y x + 8/9 y x z - 4/9 y x z - 8/9 y x z + 8/9 y x z + 27 + + 3 2 4 3 16 2 2 16 2 4 2 + - 4/27 y x + 4/27 y x + 4/27 y x + -- y x + -- y x - 4/27 y x + 27 27 + + 4 2 4 2 3 2 4 2 + - 4/27 y x - 4/27 y x + 4/27 y x , COEFF(0, 1, 1) = - 5/12 z y x + + 4 2 2 4 4 4 4 2 2 4 4 + - 5/24 z y x + 1/12 z y x + 1/24 z y x - 1/3 z y x - 1/6 z y x + + 3 4 2 4 2 4 4 2 2 2 + - 1/18 y x - 1/6 z y x - 1/3 z y x + 8/9 y - 2/9 y + 5/3 y x z + + 2 3 4 4 3 2 2 3 4 2 4 + + 1/12 z y x + 1/6 z y - 5/12 y x z + 1/24 z y x + 1/3 z y + + 3 2 4 4 3 2 2 + - 5/24 z y x - 1/18 y x - 2/9 y + 8/9 y + 5/6 z y x - 2/3 y z + + 2 2 2 2 3 2 2 3 2 2 + + 5/6 y x z + 5/3 y x z + 5/18 y x - 2/3 y z + 1/3 y z - 4/3 y z + + 2 2 2 2 2 4 2 3 4 + - 4/3 y z - 10/9 y x - 10/9 y x + 5/18 y x + 1/6 z y + 2/9 y x + + 2 4 2 4 3 4 3 + + 2/9 y x , COEFF(1, 1, 1) = - 1/18 z y x - 1/36 z y x + + 2 4 2 2 4 4 4 2 2 4 4 + + 2/9 z y x + 2/9 z y x + 1/9 z y x + 1/9 z y x - 1/18 z y x + + 4 4 2 2 4 4 2 3 3 + - 1/36 z y x + 2/9 z y x + 1/9 z y x + 1/9 z y x + 1/9 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 1/27 y x + 1/27 y x + 2/9 z y x - 4/27 y x + 2/9 z y x + + 2 4 2 4 2 16 2 2 2 + + 1/9 z y x + 2/9 z y x - 4/9 y x z + -- y x - 8/9 y x z + 27 + + 2 3 4 3 3 2 3 2 2 3 4 + - 1/18 z y x - 1/18 y x z + 2/9 y x z - 1/36 z y x + + 3 2 3 2 4 4 3 3 3 + + 1/9 z y x + 2/9 y x z + 1/27 y x + 1/9 z y x - 1/36 z y x + + 2 4 3 16 2 2 2 + - 4/9 y x z - 4/9 z y x + 1/27 y x + -- y x - 8/9 y x z + 27 + + 2 2 2 2 2 3 2 4 + - 4/9 y x z - 8/9 y x z - 8/9 y x z - 4/27 y x - 4/27 y x + + 3 16 2 2 16 2 4 2 4 2 4 + - 4/27 y x + -- y x + -- y x - 4/27 y x - 4/27 y x - 4/27 y x + 27 27 + + 2 3 2 4 3 4 3 + - 4/27 y x , COEFF(2, 1, 1) = 1/36 z y x + 1/72 z y x + + 2 4 2 2 4 4 4 2 + - 1/72 z y x - 1/36 z y x - 1/72 z y x - 1/144 z y x + + 2 4 4 4 4 2 2 4 4 + + 1/72 z y x + 1/144 z y x - 1/18 z y x - 1/36 z y x + + 2 3 3 3 3 3 4 2 2 3 + - 1/18 z y x - 1/18 z y x - 1/54 y x - 1/108 y x - 1/9 z y x + + 3 2 3 2 4 2 4 2 + + 2/27 y x - 1/9 z y x - 1/36 z y x - 1/18 z y x + 1/18 y x z + + 2 2 2 2 3 4 3 3 2 3 2 2 + - 2/27 y x + 1/18 y x z + 1/72 z y x + 1/36 y x z - 1/72 y x z + + 3 4 3 2 3 2 4 4 3 + + 1/144 z y x - 1/144 z y x - 1/36 y x z - 1/108 y x - 1/72 z y x + + 3 3 2 4 3 2 + + 1/72 z y x + 1/18 y x z + 1/36 z y x - 1/54 y x - 2/27 y x + + 2 2 2 2 2 2 2 3 2 + + 1/9 y x z + 1/36 y x z + 1/18 y x z + 1/9 y x z + 1/108 y x + + 4 3 2 2 2 4 2 4 + + 1/54 y x + 1/54 y x - 1/27 y x - 1/27 y x + 1/108 y x + 1/27 y x + + 2 4 2 3 2 4 3 + + 1/27 y x + 2/27 y x , COEFF(-2, 2, 1) = 1/144 z y x + + 4 3 2 4 2 2 4 4 + + 1/288 z y x + 1/288 z y x - 1/144 z y x - 1/288 z y x + + 4 2 2 4 4 4 4 2 2 4 + + 1/576 z y x - 1/288 z y x - 1/576 z y x + 1/288 z y x + + 4 2 3 3 3 3 3 4 + + 1/288 z y x - 1/288 z y x - 1/144 z y x - 1/108 y x + 1/216 y x + + 2 2 3 3 2 3 2 4 + - 1/144 z y x + 1/108 y x - 1/72 z y x + 1/576 z y x + + 2 4 2 2 2 2 + + 1/144 z y x + 1/288 y x z - 1/108 y x - 1/288 y x z + + 2 3 4 3 3 2 3 2 2 3 4 + - 1/144 z y x + 1/72 y x z + 1/144 y x z - 1/288 z y x + + 3 2 3 2 4 4 3 + + 1/288 z y x - 1/72 y x z + 1/432 y x - 1/144 z y x + + 3 3 2 4 3 2 + + 1/144 z y x + 1/144 y x z - 1/288 z y x - 1/216 y x - 1/216 y x + + 2 2 2 2 2 2 2 + + 1/144 y x z - 1/576 y x z - 1/144 y x z + 1/72 y x z + + 3 2 4 3 2 2 2 + - 1/216 y x + 1/216 y x + 1/108 y x + 1/432 y x + 1/216 y x + + 4 2 4 2 4 2 3 + - 1/432 y x - 1/216 y x - 1/432 y x + 1/216 y x , COEFF(-1, 2, 1) = + + 2 4 3 4 3 2 4 2 2 4 + - 1/72 z y x - 1/144 z y x - 1/18 z y x + 1/18 z y x + + 4 4 2 2 4 4 4 4 + + 1/36 z y x - 1/36 z y x + 1/72 z y x + 1/144 z y x + + 2 2 4 4 2 3 3 3 3 + - 1/72 z y x - 1/72 z y x + 1/144 z y x + 1/72 z y x + 1/54 y x + + 3 4 2 2 3 3 2 3 2 4 + - 1/54 y x + 1/72 z y x - 1/54 y x + 1/36 z y x - 1/144 z y x + + 2 4 2 2 2 2 2 3 4 + - 1/36 z y x - 1/36 y x z + 2/27 y x + 1/18 y x z + 1/36 z y x + + 3 3 2 3 2 2 3 4 3 2 3 2 + - 1/36 y x z - 1/9 y x z + 1/72 z y x - 1/18 z y x + 1/9 y x z + + 4 4 3 3 3 2 + - 1/108 y x + 1/18 z y x - 1/72 z y x - 1/18 y x z + 1/18 z y x + + 4 3 2 2 2 2 2 2 2 + + 1/108 y x + 1/27 y x - 1/18 y x z + 1/36 y x z + 1/9 y x z + + 2 3 2 4 3 2 2 2 + - 1/9 y x z + 2/27 y x - 1/27 y x - 2/27 y x - 1/27 y x - 2/27 y x + + 4 2 4 2 4 2 3 + + 1/27 y x + 1/54 y x + 1/108 y x - 1/108 y x , COEFF(0, 2, 1) = + + 2 4 2 4 2 2 4 4 4 4 2 2 4 + 5/48 z y x + 5/96 z y x - 1/48 z y x - 1/96 z y x + 1/48 z y x + + 4 3 4 2 4 2 4 4 + + 1/48 z y x + 1/36 y x + 1/96 z y x + 1/24 z y x - 1/9 y + 1/18 y + + 2 2 2 2 3 4 4 3 2 2 3 4 + - 5/48 y x z - 1/24 z y x - 1/24 z y + 5/24 y x z - 1/48 z y x + + 2 4 3 2 4 4 3 2 2 + - 1/12 z y + 5/48 z y x + 1/72 y x + 1/9 y - 1/18 y - 5/48 z y x + + 2 2 2 2 3 2 2 + + 1/12 y z - 5/96 y x z - 5/24 y x z - 5/36 y x + 1/24 y z + + 3 2 2 2 2 2 2 2 4 2 + - 1/6 y z + 1/6 y z + 1/12 y z + 5/72 y x + 5/36 y x - 5/72 y x + + 3 4 2 4 2 4 3 + - 1/12 z y - 1/36 y x - 1/72 y x , COEFF(1, 2, 1) = 1/72 z y x + + 4 3 2 4 2 2 4 4 + + 1/144 z y x - 1/18 z y x - 1/18 z y x - 1/36 z y x + + 4 2 2 4 4 4 4 2 2 4 + - 1/36 z y x + 1/72 z y x + 1/144 z y x - 1/72 z y x + + 4 2 3 3 3 3 3 4 + - 1/72 z y x - 1/144 z y x - 1/72 z y x - 1/54 y x - 1/54 y x + + 2 2 3 3 2 3 2 4 2 4 + - 1/72 z y x + 1/54 y x - 1/36 z y x - 1/144 z y x - 1/36 z y x + + 2 2 2 2 2 3 4 3 3 2 + + 1/36 y x z - 2/27 y x + 1/18 y x z + 1/36 z y x + 1/36 y x z + + 3 2 2 3 4 3 2 3 2 4 4 + - 1/9 y x z + 1/72 z y x - 1/18 z y x - 1/9 y x z - 1/108 y x + + 3 3 3 2 4 3 + - 1/18 z y x + 1/72 z y x + 1/18 y x z + 1/18 z y x - 1/108 y x + + 2 2 2 2 2 2 2 2 + - 1/27 y x + 1/18 y x z + 1/36 y x z + 1/9 y x z + 1/9 y x z + + 3 2 4 3 2 2 2 4 2 + + 2/27 y x + 1/27 y x + 2/27 y x - 1/27 y x - 2/27 y x + 1/27 y x + + 4 2 4 2 3 2 4 3 + + 1/54 y x + 1/108 y x + 1/108 y x , COEFF(2, 2, 1) = - 1/144 z y x + + 4 3 2 4 2 2 4 4 + - 1/288 z y x + 1/288 z y x + 1/144 z y x + 1/288 z y x + + 4 2 2 4 4 4 4 2 2 4 + + 1/576 z y x - 1/288 z y x - 1/576 z y x + 1/288 z y x + + 4 2 3 3 3 3 3 4 + + 1/288 z y x + 1/288 z y x + 1/144 z y x + 1/108 y x + 1/216 y x + + 2 2 3 3 2 3 2 4 + + 1/144 z y x - 1/108 y x + 1/72 z y x + 1/576 z y x + + 2 4 2 2 2 2 + + 1/144 z y x - 1/288 y x z + 1/108 y x - 1/288 y x z + + 2 3 4 3 3 2 3 2 2 3 4 + - 1/144 z y x - 1/72 y x z + 1/144 y x z - 1/288 z y x + + 3 2 3 2 4 4 3 + + 1/288 z y x + 1/72 y x z + 1/432 y x + 1/144 z y x + + 3 3 2 4 3 2 + - 1/144 z y x - 1/144 y x z - 1/288 z y x + 1/216 y x + 1/216 y x + + 2 2 2 2 2 2 2 + - 1/144 y x z - 1/576 y x z - 1/144 y x z - 1/72 y x z + + 3 2 4 3 2 2 2 + - 1/216 y x - 1/216 y x - 1/108 y x + 1/432 y x + 1/216 y x + + 4 2 4 2 4 2 3 + - 1/432 y x - 1/216 y x - 1/432 y x - 1/216 y x , COEFF(-2, -2, 2) + + 2 4 3 4 3 2 4 2 2 4 + = - 1/576 z y x - 1/576 z y x - 1/1152 z y x + 1/576 z y x + + 4 4 2 2 4 4 4 4 + + 1/576 z y x - 1/1152 z y x + 1/1152 z y x + 1/1152 z y x + + 2 2 4 4 2 3 3 + - 1/1152 z y x + 1/576 z y x + 1/576 z y x - 1/288 z y x + + 3 3 3 4 2 2 3 3 + - 1/1728 y x + 1/3456 y x + 1/576 z y x + 1/1728 y x + + 2 3 2 4 2 4 2 + - 1/288 z y x - 1/1152 z y x + 1/576 z y x - 1/576 y x z + + 2 2 2 2 3 4 3 3 2 + - 1/1728 y x + 1/1152 y x z - 1/576 z y x + 1/288 y x z + + 3 2 2 3 4 3 2 3 2 + + 1/576 y x z - 1/576 z y x + 1/576 z y x - 1/288 y x z + + 4 4 3 3 3 2 + - 1/6912 y x - 1/288 z y x + 1/288 z y x + 1/288 y x z - 1/576 z y x + + 4 3 2 2 2 2 2 + + 1/3456 y x + 1/3456 y x - 1/576 y x z + 1/1152 y x z + + 2 2 2 3 2 4 3 + - 1/576 y x z + 1/288 y x z - 1/3456 y x - 1/3456 y x + 1/1728 y x + + 2 2 2 4 2 4 2 4 + - 1/6912 y x + 1/3456 y x + 1/6912 y x - 1/3456 y x + 1/6912 y x + + 2 3 2 4 3 4 3 + - 1/3456 y x , COEFF(-1, -2, 2) = 1/288 z y x + 1/288 z y x + + 2 4 2 2 4 4 4 2 + + 1/72 z y x - 1/72 z y x - 1/72 z y x + 1/72 z y x + + 2 4 4 4 4 2 2 4 4 + - 1/288 z y x - 1/288 z y x + 1/288 z y x - 1/144 z y x + + 2 3 3 3 3 3 4 + - 1/288 z y x + 1/144 z y x + 1/864 y x - 1/864 y x + + 2 2 3 3 2 3 2 4 + - 1/288 z y x - 1/864 y x + 1/144 z y x + 1/288 z y x + + 2 4 2 2 2 2 2 3 4 + - 1/144 z y x + 1/72 y x z + 1/216 y x - 1/72 y x z + 1/144 z y x + + 3 3 2 3 2 2 3 4 3 2 + - 1/144 y x z - 1/36 y x z + 1/144 z y x - 1/36 z y x + + 3 2 4 4 3 3 3 + + 1/36 y x z + 1/1728 y x + 1/36 z y x - 1/144 z y x - 1/36 y x z + + 2 4 3 2 2 2 2 2 + + 1/36 z y x - 1/1728 y x - 1/432 y x + 1/72 y x z - 1/72 y x z + + 2 2 2 3 2 4 3 + + 1/36 y x z - 1/36 y x z + 1/216 y x + 1/432 y x - 1/216 y x + + 2 2 2 4 2 4 2 4 + + 1/432 y x - 1/216 y x - 1/432 y x + 1/864 y x - 1/1728 y x + + 2 3 2 4 2 4 2 + + 1/1728 y x , COEFF(0, -2, 2) = - 5/192 z y x - 5/192 z y x + + 2 4 4 4 4 2 2 4 4 + + 1/192 z y x + 1/192 z y x - 1/192 z y x + 1/96 z y x + + 3 4 2 4 2 4 4 + + 1/576 y x - 1/192 z y x + 1/96 z y x - 1/144 y - 1/288 y + + 2 2 2 2 3 4 4 3 2 2 + + 5/192 y x z - 1/96 z y x + 1/48 z y + 5/96 y x z + + 3 4 2 4 3 2 4 4 3 + - 1/96 z y x + 1/48 z y + 5/96 z y x - 1/1152 y x + 1/144 y + + 2 2 2 2 2 2 + + 1/288 y - 5/96 z y x + 1/24 y z + 5/192 y x z - 5/96 y x z + + 3 2 2 3 2 2 2 2 + - 5/576 y x - 1/48 y z - 1/24 y z + 1/24 y z - 1/48 y z + + 2 2 2 4 2 3 4 + - 5/1152 y x + 5/576 y x + 5/1152 y x - 1/24 z y - 1/576 y x + + 2 4 2 4 3 4 3 + + 1/1152 y x , COEFF(1, -2, 2) = - 1/288 z y x - 1/288 z y x + + 2 4 2 2 4 4 4 2 + + 1/72 z y x + 1/72 z y x + 1/72 z y x + 1/72 z y x + + 2 4 4 4 4 2 2 4 4 + - 1/288 z y x - 1/288 z y x + 1/288 z y x - 1/144 z y x + + 2 3 3 3 3 3 4 + + 1/288 z y x - 1/144 z y x - 1/864 y x - 1/864 y x + + 2 2 3 3 2 3 2 4 + + 1/288 z y x + 1/864 y x - 1/144 z y x + 1/288 z y x + + 2 4 2 2 2 2 2 3 4 + - 1/144 z y x - 1/72 y x z - 1/216 y x - 1/72 y x z + 1/144 z y x + + 3 3 2 3 2 2 3 4 3 2 + + 1/144 y x z - 1/36 y x z + 1/144 z y x - 1/36 z y x + + 3 2 4 4 3 3 3 + - 1/36 y x z + 1/1728 y x - 1/36 z y x + 1/144 z y x + 1/36 y x z + + 2 4 3 2 2 2 2 2 + + 1/36 z y x + 1/1728 y x + 1/432 y x - 1/72 y x z - 1/72 y x z + + 2 2 2 3 2 4 3 + + 1/36 y x z + 1/36 y x z + 1/216 y x - 1/432 y x + 1/216 y x + + 2 2 2 4 2 4 2 4 + + 1/432 y x - 1/216 y x - 1/432 y x + 1/864 y x - 1/1728 y x + + 2 3 2 4 3 4 3 + - 1/1728 y x , COEFF(2, -2, 2) = 1/576 z y x + 1/576 z y x + + 2 4 2 2 4 4 4 2 + - 1/1152 z y x - 1/576 z y x - 1/576 z y x - 1/1152 z y x + + 2 4 4 4 4 2 2 4 4 + + 1/1152 z y x + 1/1152 z y x - 1/1152 z y x + 1/576 z y x + + 2 3 3 3 3 3 4 + - 1/576 z y x + 1/288 z y x + 1/1728 y x + 1/3456 y x + + 2 2 3 3 2 3 2 4 + - 1/576 z y x - 1/1728 y x + 1/288 z y x - 1/1152 z y x + + 2 4 2 2 2 2 + + 1/576 z y x + 1/576 y x z + 1/1728 y x + 1/1152 y x z + + 2 3 4 3 3 2 3 2 2 3 4 + - 1/576 z y x - 1/288 y x z + 1/576 y x z - 1/576 z y x + + 3 2 3 2 4 4 3 + + 1/576 z y x + 1/288 y x z - 1/6912 y x + 1/288 z y x + + 3 3 2 4 3 2 + - 1/288 z y x - 1/288 y x z - 1/576 z y x - 1/3456 y x - 1/3456 y x + + 2 2 2 2 2 2 2 + + 1/576 y x z + 1/1152 y x z - 1/576 y x z - 1/288 y x z + + 3 2 4 3 2 2 2 + - 1/3456 y x + 1/3456 y x - 1/1728 y x - 1/6912 y x + 1/3456 y x + + 4 2 4 2 4 2 3 + + 1/6912 y x - 1/3456 y x + 1/6912 y x + 1/3456 y x , + + 2 4 3 4 3 2 4 2 + COEFF(-2, -1, 2) = 1/144 z y x + 1/144 z y x + 1/288 z y x + + 2 4 4 4 2 2 4 4 + - 1/144 z y x - 1/144 z y x + 1/288 z y x - 1/288 z y x + + 4 4 2 2 4 4 2 3 3 + - 1/288 z y x + 1/72 z y x - 1/72 z y x - 1/36 z y x + 1/36 z y x + + 3 3 3 4 2 2 3 3 2 3 + + 1/864 y x - 1/1728 y x - 1/36 z y x - 1/216 y x + 1/36 z y x + + 2 4 2 4 2 2 2 2 + + 1/72 z y x - 1/72 z y x + 1/36 y x z + 1/216 y x - 1/72 y x z + + 2 3 4 3 3 2 3 2 2 3 4 + + 1/288 z y x - 1/144 y x z - 1/288 y x z + 1/288 z y x + + 3 2 3 2 4 4 3 + - 1/288 z y x + 1/144 y x z + 1/1728 y x + 1/144 z y x + + 3 3 2 4 3 2 + - 1/144 z y x - 1/36 y x z + 1/72 z y x - 1/864 y x - 1/216 y x + + 2 2 2 2 2 2 2 3 2 + + 1/36 y x z - 1/72 y x z + 1/72 y x z - 1/36 y x z + 1/1728 y x + + 4 3 2 2 2 4 2 + + 1/864 y x - 1/864 y x + 1/432 y x - 1/432 y x - 1/1728 y x + + 4 2 4 2 3 + + 1/432 y x - 1/432 y x + 1/216 y x , COEFF(-1, -1, 2) = + + 2 4 3 4 3 2 4 2 2 4 4 + - 1/72 z y x - 1/72 z y x - 1/18 z y x + 1/18 z y x + 1/18 z y x + + 4 2 2 4 4 4 4 2 2 4 + - 1/18 z y x + 1/72 z y x + 1/72 z y x - 1/18 z y x + + 4 2 3 3 3 3 3 4 + + 1/18 z y x + 1/18 z y x - 1/18 z y x - 1/432 y x + 1/432 y x + + 2 2 3 3 2 3 2 4 2 4 + + 1/18 z y x + 1/108 y x - 1/18 z y x - 1/18 z y x + 1/18 z y x + + 2 2 2 2 2 3 4 3 3 2 + - 2/9 y x z - 1/27 y x + 2/9 y x z - 1/72 z y x + 1/72 y x z + + 3 2 2 3 4 3 2 3 2 4 4 + + 1/18 y x z - 1/72 z y x + 1/18 z y x - 1/18 y x z - 1/432 y x + + 3 3 3 2 4 3 + - 1/18 z y x + 1/72 z y x + 2/9 y x z - 2/9 z y x + 1/432 y x + + 2 2 2 2 2 2 2 2 + + 1/27 y x - 2/9 y x z + 2/9 y x z - 2/9 y x z + 2/9 y x z + + 3 2 4 3 2 2 2 + - 1/108 y x - 1/108 y x + 1/108 y x - 1/27 y x + 1/27 y x + + 4 2 4 2 4 2 3 + + 1/108 y x - 1/108 y x + 1/108 y x - 1/108 y x , COEFF(0, -1, 2) = + + 2 4 2 4 2 2 4 4 4 4 2 2 4 + 5/48 z y x + 5/48 z y x - 1/48 z y x - 1/48 z y x + 1/12 z y x + + 4 3 4 2 4 2 4 + - 1/12 z y x - 1/288 y x + 1/12 z y x - 1/12 z y x + 1/18 y + + 4 2 2 2 2 3 4 4 3 2 2 + + 1/72 y - 5/12 y x z + 1/48 z y x - 1/12 z y - 5/48 y x z + + 3 4 2 4 3 2 4 4 3 + + 1/48 z y x - 1/12 z y - 5/48 z y x + 1/288 y x - 1/72 y + + 2 2 2 2 2 2 + - 1/18 y + 5/12 z y x - 1/3 y z - 5/12 y x z + 5/12 y x z + + 3 2 2 3 2 2 2 2 2 2 + + 5/288 y x + 1/3 y z + 1/12 y z - 1/3 y z + 1/3 y z + 5/72 y x + + 2 4 2 3 4 2 4 + - 5/72 y x - 5/288 y x + 1/12 z y + 1/72 y x - 1/72 y x , + + 2 4 3 4 3 2 4 2 + COEFF(1, -1, 2) = 1/72 z y x + 1/72 z y x - 1/18 z y x + + 2 4 4 4 2 2 4 4 4 4 + - 1/18 z y x - 1/18 z y x - 1/18 z y x + 1/72 z y x + 1/72 z y x + + 2 2 4 4 2 3 3 3 3 + - 1/18 z y x + 1/18 z y x - 1/18 z y x + 1/18 z y x + 1/432 y x + + 3 4 2 2 3 3 2 3 2 4 + + 1/432 y x - 1/18 z y x - 1/108 y x + 1/18 z y x - 1/18 z y x + + 2 4 2 2 2 2 2 3 4 + + 1/18 z y x + 2/9 y x z + 1/27 y x + 2/9 y x z - 1/72 z y x + + 3 3 2 3 2 2 3 4 3 2 + - 1/72 y x z + 1/18 y x z - 1/72 z y x + 1/18 z y x + + 3 2 4 4 3 3 3 + + 1/18 y x z - 1/432 y x + 1/18 z y x - 1/72 z y x - 2/9 y x z + + 2 4 3 2 2 2 2 2 + - 2/9 z y x - 1/432 y x - 1/27 y x + 2/9 y x z + 2/9 y x z + + 2 2 2 3 2 4 3 + - 2/9 y x z - 2/9 y x z - 1/108 y x + 1/108 y x - 1/108 y x + + 2 2 2 4 2 4 2 4 + - 1/27 y x + 1/27 y x + 1/108 y x - 1/108 y x + 1/108 y x + + 2 3 2 4 3 4 3 + + 1/108 y x , COEFF(2, -1, 2) = - 1/144 z y x - 1/144 z y x + + 2 4 2 2 4 4 4 2 + + 1/288 z y x + 1/144 z y x + 1/144 z y x + 1/288 z y x + + 2 4 4 4 4 2 2 4 4 + - 1/288 z y x - 1/288 z y x + 1/72 z y x - 1/72 z y x + + 2 3 3 3 3 3 4 2 2 3 + + 1/36 z y x - 1/36 z y x - 1/864 y x - 1/1728 y x + 1/36 z y x + + 3 2 3 2 4 2 4 2 + + 1/216 y x - 1/36 z y x + 1/72 z y x - 1/72 z y x - 1/36 y x z + + 2 2 2 2 3 4 3 3 2 + - 1/216 y x - 1/72 y x z + 1/288 z y x + 1/144 y x z + + 3 2 2 3 4 3 2 3 2 + - 1/288 y x z + 1/288 z y x - 1/288 z y x - 1/144 y x z + + 4 4 3 3 3 2 + + 1/1728 y x - 1/144 z y x + 1/144 z y x + 1/36 y x z + 1/72 z y x + + 4 3 2 2 2 2 2 2 2 + + 1/864 y x + 1/216 y x - 1/36 y x z - 1/72 y x z + 1/72 y x z + + 2 3 2 4 3 2 2 + + 1/36 y x z + 1/1728 y x - 1/864 y x + 1/864 y x + 1/432 y x + + 2 4 2 4 2 4 2 3 + - 1/432 y x - 1/1728 y x + 1/432 y x - 1/432 y x - 1/216 y x , + + 2 4 3 4 3 2 4 2 + COEFF(-2, 0, 2) = - 1/96 z y x - 1/96 z y x - 1/192 z y x + + 2 4 4 4 2 2 4 4 + + 1/96 z y x + 1/96 z y x - 1/192 z y x + 1/192 z y x + + 4 4 2 2 4 2 3 2 2 3 + + 1/192 z y x - 5/192 z y x + 5/96 z y x + 5/96 z y x + + 2 4 3 2 4 2 + - 5/192 z y x - 1/24 x z - 1/144 x - 1/288 x - 5/96 y x z + + 2 2 2 4 4 3 2 4 3 + + 5/192 y x z - 1/1152 y x + 1/144 x + 1/288 x + 1/576 y x + + 4 2 2 2 2 2 4 + + 1/48 z x + 5/576 y x - 5/96 y x z + 5/192 y x z - 1/576 y x + + 2 2 2 2 2 2 + + 1/24 x z - 1/48 x z - 1/48 x z + 1/24 x z - 5/1152 y x + + 4 2 2 4 3 2 4 2 3 + + 1/1152 y x + 1/48 z x - 1/24 z x + 5/1152 y x - 5/576 y x , + + 2 4 3 4 3 2 4 2 + COEFF(-1, 0, 2) = 1/48 z y x + 1/48 z y x + 1/12 z y x + + 2 4 4 4 2 2 4 4 4 4 + - 1/12 z y x - 1/12 z y x + 1/12 z y x - 1/48 z y x - 1/48 z y x + + 2 2 4 2 3 2 2 3 2 4 3 2 + + 5/48 z y x - 5/48 z y x - 5/48 z y x + 5/48 z y x + 1/12 x z + + 4 2 2 2 2 4 4 3 + + 1/18 x + 1/72 x + 5/12 y x z - 5/12 y x z + 1/288 y x - 1/72 x + + 2 4 3 4 2 2 2 + - 1/18 x - 1/288 y x - 1/12 z x - 5/72 y x + 5/12 y x z + + 2 2 4 2 2 2 2 + - 5/12 y x z + 1/72 y x - 1/3 x z + 1/3 x z + 1/3 x z - 1/3 x z + + 2 2 4 2 2 4 3 2 4 + + 5/72 y x - 1/72 y x - 1/12 z x + 1/12 z x - 5/288 y x + + 2 3 2 4 2 4 2 + + 5/288 y x , COEFF(0, 0, 2) = - 5/32 z y x - 5/32 z y x + + 2 4 4 4 4 2 2 4 2 4 4 + + 1/32 z y x + 1/32 z y x - 5/32 z y x - 5/32 z y x - 1/48 x + + 4 25 2 2 2 4 2 4 4 4 + + 1/2 z - 1/48 y + -- y x z + 1/8 z y + 1/8 z y - 1/192 y x + 32 + + 2 2 2 4 25 2 2 2 + - 1/12 + 5/48 y + 1/2 z + 5/48 x + 1/8 z x + -- y x z - 5/8 y z + 32 + + 2 2 2 2 2 25 2 2 4 2 2 4 + - 5/8 x z - 5/8 x z - 5/8 y z - --- y x + 5/192 y x + 1/8 z x + 192 + + 2 4 2 4 3 4 3 + + 5/192 y x , COEFF(1, 0, 2) = - 1/48 z y x - 1/48 z y x + + 2 4 2 2 4 4 4 2 + + 1/12 z y x + 1/12 z y x + 1/12 z y x + 1/12 z y x + + 2 4 4 4 4 2 2 4 2 3 + - 1/48 z y x - 1/48 z y x + 5/48 z y x + 5/48 z y x + + 2 2 3 2 4 3 2 4 + + 5/48 z y x + 5/48 z y x - 1/12 x z - 1/18 x + 1/72 x + + 2 2 2 2 4 4 3 2 + - 5/12 y x z - 5/12 y x z + 1/288 y x + 1/72 x - 1/18 x + + 4 3 4 2 2 2 2 2 + + 1/288 y x - 1/12 z x + 5/72 y x - 5/12 y x z - 5/12 y x z + + 4 2 2 2 2 2 2 + - 1/72 y x + 1/3 x z + 1/3 x z + 1/3 x z + 1/3 x z + 5/72 y x + + 4 2 2 4 3 2 4 2 3 + - 1/72 y x - 1/12 z x - 1/12 z x - 5/288 y x - 5/288 y x , + + 2 4 3 4 3 2 4 2 + COEFF(2, 0, 2) = 1/96 z y x + 1/96 z y x - 1/192 z y x + + 2 4 4 4 2 2 4 4 + - 1/96 z y x - 1/96 z y x - 1/192 z y x + 1/192 z y x + + 4 4 2 2 4 2 3 2 2 3 + + 1/192 z y x - 5/192 z y x - 5/96 z y x - 5/96 z y x + + 2 4 3 2 4 2 + - 5/192 z y x + 1/24 x z + 1/144 x - 1/288 x + 5/96 y x z + + 2 2 2 4 4 3 2 4 3 + + 5/192 y x z - 1/1152 y x - 1/144 x + 1/288 x - 1/576 y x + + 4 2 2 2 2 2 4 + + 1/48 z x - 5/576 y x + 5/96 y x z + 5/192 y x z + 1/576 y x + + 2 2 2 2 2 2 + - 1/24 x z - 1/48 x z - 1/48 x z - 1/24 x z - 5/1152 y x + + 4 2 2 4 3 2 4 2 3 + + 1/1152 y x + 1/48 z x + 1/24 z x + 5/1152 y x + 5/576 y x , + + 2 4 3 4 3 2 4 2 + COEFF(-2, 1, 2) = 1/144 z y x + 1/144 z y x + 1/288 z y x + + 2 4 4 4 2 2 4 4 + - 1/144 z y x - 1/144 z y x + 1/288 z y x - 1/288 z y x + + 4 4 2 2 4 4 2 3 3 + - 1/288 z y x + 1/72 z y x + 1/72 z y x - 1/36 z y x - 1/36 z y x + + 3 3 3 4 2 2 3 3 2 3 + - 1/864 y x + 1/1728 y x - 1/36 z y x + 1/216 y x - 1/36 z y x + + 2 4 2 4 2 2 2 2 + + 1/72 z y x + 1/72 z y x + 1/36 y x z - 1/216 y x - 1/72 y x z + + 2 3 4 3 3 2 3 2 2 3 4 + - 1/288 z y x + 1/144 y x z + 1/288 y x z - 1/288 z y x + + 3 2 3 2 4 4 3 + + 1/288 z y x - 1/144 y x z + 1/1728 y x - 1/144 z y x + + 3 3 2 4 3 2 + + 1/144 z y x + 1/36 y x z - 1/72 z y x - 1/864 y x - 1/216 y x + + 2 2 2 2 2 2 2 3 2 + + 1/36 y x z - 1/72 y x z - 1/72 y x z + 1/36 y x z - 1/1728 y x + + 4 3 2 2 2 4 2 + + 1/864 y x + 1/864 y x + 1/432 y x + 1/432 y x - 1/1728 y x + + 4 2 4 2 3 + - 1/432 y x - 1/432 y x + 1/216 y x , COEFF(-1, 1, 2) = + + 2 4 3 4 3 2 4 2 2 4 4 + - 1/72 z y x - 1/72 z y x - 1/18 z y x + 1/18 z y x + 1/18 z y x + + 4 2 2 4 4 4 4 2 2 4 + - 1/18 z y x + 1/72 z y x + 1/72 z y x - 1/18 z y x + + 4 2 3 3 3 3 3 4 + - 1/18 z y x + 1/18 z y x + 1/18 z y x + 1/432 y x - 1/432 y x + + 2 2 3 3 2 3 2 4 2 4 + + 1/18 z y x - 1/108 y x + 1/18 z y x - 1/18 z y x - 1/18 z y x + + 2 2 2 2 2 3 4 3 3 2 + - 2/9 y x z + 1/27 y x + 2/9 y x z + 1/72 z y x - 1/72 y x z + + 3 2 2 3 4 3 2 3 2 4 4 + - 1/18 y x z + 1/72 z y x - 1/18 z y x + 1/18 y x z - 1/432 y x + + 3 3 3 2 4 3 + + 1/18 z y x - 1/72 z y x - 2/9 y x z + 2/9 z y x + 1/432 y x + + 2 2 2 2 2 2 2 2 + + 1/27 y x - 2/9 y x z + 2/9 y x z + 2/9 y x z - 2/9 y x z + + 3 2 4 3 2 2 2 + + 1/108 y x - 1/108 y x - 1/108 y x - 1/27 y x - 1/27 y x + + 4 2 4 2 4 2 3 + + 1/108 y x + 1/108 y x + 1/108 y x - 1/108 y x , COEFF(0, 1, 2) = + + 2 4 2 4 2 2 4 4 4 4 2 2 4 + 5/48 z y x + 5/48 z y x - 1/48 z y x - 1/48 z y x + 1/12 z y x + + 4 3 4 2 4 2 4 + + 1/12 z y x + 1/288 y x + 1/12 z y x + 1/12 z y x - 1/18 y + + 4 2 2 2 2 3 4 4 3 2 2 + + 1/72 y - 5/12 y x z - 1/48 z y x - 1/12 z y + 5/48 y x z + + 3 4 2 4 3 2 4 4 3 + - 1/48 z y x - 1/12 z y + 5/48 z y x + 1/288 y x + 1/72 y + + 2 2 2 2 2 2 + - 1/18 y - 5/12 z y x + 1/3 y z - 5/12 y x z - 5/12 y x z + + 3 2 2 3 2 2 2 2 2 2 + - 5/288 y x + 1/3 y z - 1/12 y z + 1/3 y z + 1/3 y z + 5/72 y x + + 2 4 2 3 4 2 4 + + 5/72 y x - 5/288 y x - 1/12 z y - 1/72 y x - 1/72 y x , + + 2 4 3 4 3 2 4 2 + COEFF(1, 1, 2) = 1/72 z y x + 1/72 z y x - 1/18 z y x + + 2 4 4 4 2 2 4 4 4 4 + - 1/18 z y x - 1/18 z y x - 1/18 z y x + 1/72 z y x + 1/72 z y x + + 2 2 4 4 2 3 3 3 3 + - 1/18 z y x - 1/18 z y x - 1/18 z y x - 1/18 z y x - 1/432 y x + + 3 4 2 2 3 3 2 3 2 4 + - 1/432 y x - 1/18 z y x + 1/108 y x - 1/18 z y x - 1/18 z y x + + 2 4 2 2 2 2 2 3 4 + - 1/18 z y x + 2/9 y x z - 1/27 y x + 2/9 y x z + 1/72 z y x + + 3 3 2 3 2 2 3 4 3 2 + + 1/72 y x z - 1/18 y x z + 1/72 z y x - 1/18 z y x + + 3 2 4 4 3 3 3 + - 1/18 y x z - 1/432 y x - 1/18 z y x + 1/72 z y x + 2/9 y x z + + 2 4 3 2 2 2 2 2 + + 2/9 z y x - 1/432 y x - 1/27 y x + 2/9 y x z + 2/9 y x z + + 2 2 2 3 2 4 3 + + 2/9 y x z + 2/9 y x z + 1/108 y x + 1/108 y x + 1/108 y x + + 2 2 2 4 2 4 2 4 + - 1/27 y x - 1/27 y x + 1/108 y x + 1/108 y x + 1/108 y x + + 2 3 2 4 3 4 3 + + 1/108 y x , COEFF(2, 1, 2) = - 1/144 z y x - 1/144 z y x + + 2 4 2 2 4 4 4 2 + + 1/288 z y x + 1/144 z y x + 1/144 z y x + 1/288 z y x + + 2 4 4 4 4 2 2 4 4 + - 1/288 z y x - 1/288 z y x + 1/72 z y x + 1/72 z y x + + 2 3 3 3 3 3 4 2 2 3 + + 1/36 z y x + 1/36 z y x + 1/864 y x + 1/1728 y x + 1/36 z y x + + 3 2 3 2 4 2 4 2 + - 1/216 y x + 1/36 z y x + 1/72 z y x + 1/72 z y x - 1/36 y x z + + 2 2 2 2 3 4 3 3 2 + + 1/216 y x - 1/72 y x z - 1/288 z y x - 1/144 y x z + + 3 2 2 3 4 3 2 3 2 + + 1/288 y x z - 1/288 z y x + 1/288 z y x + 1/144 y x z + + 4 4 3 3 3 2 + + 1/1728 y x + 1/144 z y x - 1/144 z y x - 1/36 y x z - 1/72 z y x + + 4 3 2 2 2 2 2 2 2 + + 1/864 y x + 1/216 y x - 1/36 y x z - 1/72 y x z - 1/72 y x z + + 2 3 2 4 3 2 2 + - 1/36 y x z - 1/1728 y x - 1/864 y x - 1/864 y x + 1/432 y x + + 2 4 2 4 2 4 2 3 + + 1/432 y x - 1/1728 y x - 1/432 y x - 1/432 y x - 1/216 y x , + + 2 4 3 4 3 2 4 2 + COEFF(-2, 2, 2) = - 1/576 z y x - 1/576 z y x - 1/1152 z y x + + 2 4 4 4 2 2 4 4 + + 1/576 z y x + 1/576 z y x - 1/1152 z y x + 1/1152 z y x + + 4 4 2 2 4 4 2 3 + + 1/1152 z y x - 1/1152 z y x - 1/576 z y x + 1/576 z y x + + 3 3 3 3 4 2 2 3 + + 1/288 z y x + 1/1728 y x - 1/3456 y x + 1/576 z y x + + 3 2 3 2 4 2 4 + - 1/1728 y x + 1/288 z y x - 1/1152 z y x - 1/576 z y x + + 2 2 2 2 2 3 4 + - 1/576 y x z + 1/1728 y x + 1/1152 y x z + 1/576 z y x + + 3 3 2 3 2 2 3 4 3 2 + - 1/288 y x z - 1/576 y x z + 1/576 z y x - 1/576 z y x + + 3 2 4 4 3 3 3 + + 1/288 y x z - 1/6912 y x + 1/288 z y x - 1/288 z y x + + 2 4 3 2 2 2 + - 1/288 y x z + 1/576 z y x + 1/3456 y x + 1/3456 y x - 1/576 y x z + + 2 2 2 2 2 3 2 + + 1/1152 y x z + 1/576 y x z - 1/288 y x z + 1/3456 y x + + 4 3 2 2 2 4 2 + - 1/3456 y x - 1/1728 y x - 1/6912 y x - 1/3456 y x + 1/6912 y x + + 4 2 4 2 3 + + 1/3456 y x + 1/6912 y x - 1/3456 y x , COEFF(-1, 2, 2) = + + 2 4 3 4 3 2 4 2 2 4 4 + 1/288 z y x + 1/288 z y x + 1/72 z y x - 1/72 z y x - 1/72 z y x + + 4 2 2 4 4 4 4 2 2 4 + + 1/72 z y x - 1/288 z y x - 1/288 z y x + 1/288 z y x + + 4 2 3 3 3 3 3 4 + + 1/144 z y x - 1/288 z y x - 1/144 z y x - 1/864 y x + 1/864 y x + + 2 2 3 3 2 3 2 4 + - 1/288 z y x + 1/864 y x - 1/144 z y x + 1/288 z y x + + 2 4 2 2 2 2 2 3 4 + + 1/144 z y x + 1/72 y x z - 1/216 y x - 1/72 y x z - 1/144 z y x + + 3 3 2 3 2 2 3 4 3 2 + + 1/144 y x z + 1/36 y x z - 1/144 z y x + 1/36 z y x + + 3 2 4 4 3 3 3 + - 1/36 y x z + 1/1728 y x - 1/36 z y x + 1/144 z y x + 1/36 y x z + + 2 4 3 2 2 2 2 2 + - 1/36 z y x - 1/1728 y x - 1/432 y x + 1/72 y x z - 1/72 y x z + + 2 2 2 3 2 4 3 + - 1/36 y x z + 1/36 y x z - 1/216 y x + 1/432 y x + 1/216 y x + + 2 2 2 4 2 4 2 4 + + 1/432 y x + 1/216 y x - 1/432 y x - 1/864 y x - 1/1728 y x + + 2 3 2 4 2 4 2 + + 1/1728 y x , COEFF(0, 2, 2) = - 5/192 z y x - 5/192 z y x + + 2 4 4 4 4 2 2 4 4 + + 1/192 z y x + 1/192 z y x - 1/192 z y x - 1/96 z y x + + 3 4 2 4 2 4 4 + - 1/576 y x - 1/192 z y x - 1/96 z y x + 1/144 y - 1/288 y + + 2 2 2 2 3 4 4 3 2 2 + + 5/192 y x z + 1/96 z y x + 1/48 z y - 5/96 y x z + + 3 4 2 4 3 2 4 4 3 + + 1/96 z y x + 1/48 z y - 5/96 z y x - 1/1152 y x - 1/144 y + + 2 2 2 2 2 2 + + 1/288 y + 5/96 z y x - 1/24 y z + 5/192 y x z + 5/96 y x z + + 3 2 2 3 2 2 2 2 + + 5/576 y x - 1/48 y z + 1/24 y z - 1/24 y z - 1/48 y z + + 2 2 2 4 2 3 4 + - 5/1152 y x - 5/576 y x + 5/1152 y x + 1/24 z y + 1/576 y x + + 2 4 2 4 3 4 3 + + 1/1152 y x , COEFF(1, 2, 2) = - 1/288 z y x - 1/288 z y x + + 2 4 2 2 4 4 4 2 + + 1/72 z y x + 1/72 z y x + 1/72 z y x + 1/72 z y x + + 2 4 4 4 4 2 2 4 4 + - 1/288 z y x - 1/288 z y x + 1/288 z y x + 1/144 z y x + + 2 3 3 3 3 3 4 + + 1/288 z y x + 1/144 z y x + 1/864 y x + 1/864 y x + + 2 2 3 3 2 3 2 4 + + 1/288 z y x - 1/864 y x + 1/144 z y x + 1/288 z y x + + 2 4 2 2 2 2 2 3 4 + + 1/144 z y x - 1/72 y x z + 1/216 y x - 1/72 y x z - 1/144 z y x + + 3 3 2 3 2 2 3 4 3 2 + - 1/144 y x z + 1/36 y x z - 1/144 z y x + 1/36 z y x + + 3 2 4 4 3 3 3 + + 1/36 y x z + 1/1728 y x + 1/36 z y x - 1/144 z y x - 1/36 y x z + + 2 4 3 2 2 2 2 2 + - 1/36 z y x + 1/1728 y x + 1/432 y x - 1/72 y x z - 1/72 y x z + + 2 2 2 3 2 4 3 + - 1/36 y x z - 1/36 y x z - 1/216 y x - 1/432 y x - 1/216 y x + + 2 2 2 4 2 4 2 4 + + 1/432 y x + 1/216 y x - 1/432 y x - 1/864 y x - 1/1728 y x + + 2 3 2 4 3 4 3 + - 1/1728 y x , COEFF(2, 2, 2) = 1/576 z y x + 1/576 z y x + + 2 4 2 2 4 4 4 2 + - 1/1152 z y x - 1/576 z y x - 1/576 z y x - 1/1152 z y x + + 2 4 4 4 4 2 2 4 4 + + 1/1152 z y x + 1/1152 z y x - 1/1152 z y x - 1/576 z y x + + 2 3 3 3 3 3 4 + - 1/576 z y x - 1/288 z y x - 1/1728 y x - 1/3456 y x + + 2 2 3 3 2 3 2 4 + - 1/576 z y x + 1/1728 y x - 1/288 z y x - 1/1152 z y x + + 2 4 2 2 2 2 + - 1/576 z y x + 1/576 y x z - 1/1728 y x + 1/1152 y x z + + 2 3 4 3 3 2 3 2 2 3 4 + + 1/576 z y x + 1/288 y x z - 1/576 y x z + 1/576 z y x + + 3 2 3 2 4 4 3 + - 1/576 z y x - 1/288 y x z - 1/6912 y x - 1/288 z y x + + 3 3 2 4 3 2 + + 1/288 z y x + 1/288 y x z + 1/576 z y x - 1/3456 y x - 1/3456 y x + + 2 2 2 2 2 2 2 + + 1/576 y x z + 1/1152 y x z + 1/576 y x z + 1/288 y x z + + 3 2 4 3 2 2 2 + + 1/3456 y x + 1/3456 y x + 1/1728 y x - 1/6912 y x - 1/3456 y x + + 4 2 4 2 4 2 3 + + 1/6912 y x + 1/3456 y x + 1/6912 y x + 1/3456 y x ] + +> print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp", +> 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used=47412219624, alloc=64737712, time=13767.88 +bytes used=47413220772, alloc=64737712, time=13768.23 +bytes used=47414221212, alloc=64737712, time=13768.45 +bytes used=47415221528, alloc=64737712, time=13768.52 +bytes used=47416222168, alloc=64737712, time=13768.58 +bytes used=47417222480, alloc=64737712, time=13768.65 +bytes used=47418222696, alloc=64737712, time=13768.84 +bytes used=47419222872, alloc=64737712, time=13769.07 +bytes used=47420223084, alloc=64737712, time=13769.22 +bytes used=47421223308, alloc=64737712, time=13769.41 +bytes used=47422223484, alloc=64737712, time=13769.57 +bytes used=47423223804, alloc=64737712, time=13769.76 +bytes used=47424224076, alloc=64737712, time=13769.95 +> +################################################################################ +> quit +bytes used=47425027532, alloc=64737712, time=13770.11 diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.maple b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.maple new file mode 100644 index 0000000..5d44fb2 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/3d.maple @@ -0,0 +1,248 @@ +# 3d.maple -- compute Lagrange interpolation coefficients in 3-D +# $Header$ + +################################################################################ + +# +# 3d, cube, order=1, smoothing=0 (size=2) +# + +# interpolating polynomial +interp_3d_cube_order1_smooth0 + := Lagrange_polynomial_interpolant(fn_3d_order1, coeffs_list_3d_order1, + coords_list_3d, posn_list_3d_size2); + +# I +coeffs_as_lc_of_data(%, posn_list_3d_size2); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "3d.coeffs/3d.cube.order1.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_3d_cube_order1_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_3d_size2); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "3d.coeffs/3d.cube.order1.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_3d_cube_order1_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size2); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "3d.coeffs/3d.cube.order1.smooth0/coeffs-dy.compute.c"); + +# d/dz +simplify( diff(interp_3d_cube_order1_smooth0,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size2); +print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", + "3d.coeffs/3d.cube.order1.smooth0/coeffs-dz.compute.c"); + +################################################################################ + +# +# 3d, cube, order=2, smoothing=0 (size=3) +# + +# interpolating polynomial +interp_3d_cube_order2_smooth0 + := Lagrange_polynomial_interpolant(fn_3d_order2, coeffs_list_3d_order2, + coords_list_3d, posn_list_3d_size3); + +# I +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_3d_cube_order2_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_3d_cube_order2_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dy.compute.c"); + +# d/dz +simplify( diff(interp_3d_cube_order2_smooth0,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dz.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_3d_cube_order2_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_3d_cube_order2_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxy.compute.c"); + +# d^2/dxdz +simplify( diff(interp_3d_cube_order2_smooth0,x,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dxz.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_3d_cube_order2_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dyy.compute.c"); + +# d^2/dydz +simplify( diff(interp_3d_cube_order2_smooth0,y,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dyz.compute.c"); + +# d^2/dz^2 +simplify( diff(interp_3d_cube_order2_smooth0,z,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size3); +print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp", + "3d.coeffs/3d.cube.order2.smooth0/coeffs-dzz.compute.c"); + +################################################################################ + +# +# 3d, cube, order=3, smoothing=0 (size=4) +# + +# interpolating polynomial +interp_3d_cube_order3_smooth0 + := Lagrange_polynomial_interpolant(fn_3d_order3, coeffs_list_3d_order3, + coords_list_3d, posn_list_3d_size4); + +# I +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_3d_cube_order3_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_3d_cube_order3_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dy.compute.c"); + +# d/dz +simplify( diff(interp_3d_cube_order3_smooth0,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dz.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_3d_cube_order3_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_3d_cube_order3_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxy.compute.c"); + +# d^2/dxdz +simplify( diff(interp_3d_cube_order3_smooth0,x,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dxz.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_3d_cube_order3_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dyy.compute.c"); + +# d^2/dydz +simplify( diff(interp_3d_cube_order3_smooth0,y,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dyz.compute.c"); + +# d^2/dz^2 +simplify( diff(interp_3d_cube_order3_smooth0,z,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size4); +print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp", + "3d.coeffs/3d.cube.order3.smooth0/coeffs-dzz.compute.c"); + +################################################################################ + +# +# 3d, cube, order=4, smoothing=0 (size=5) +# + +# interpolating polynomial +interp_3d_cube_order4_smooth0 + := Lagrange_polynomial_interpolant(fn_3d_order4, coeffs_list_3d_order4, + coords_list_3d, posn_list_3d_size5); + +# I +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-I.compute.c"); + +# d/dx +simplify( diff(interp_3d_cube_order4_smooth0,x) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dx.compute.c"); + +# d/dy +simplify( diff(interp_3d_cube_order4_smooth0,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dy.compute.c"); + +# d/dz +simplify( diff(interp_3d_cube_order4_smooth0,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dz->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dz.compute.c"); + +# d^2/dx^2 +simplify( diff(interp_3d_cube_order4_smooth0,x,x) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxx.compute.c"); + +# d^2/dxdy +simplify( diff(interp_3d_cube_order4_smooth0,x,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxy.compute.c"); + +# d^2/dxdz +simplify( diff(interp_3d_cube_order4_smooth0,x,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dxz->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dxz.compute.c"); + +# d^2/dy^2 +simplify( diff(interp_3d_cube_order4_smooth0,y,y) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dyy.compute.c"); + +# d^2/dydz +simplify( diff(interp_3d_cube_order4_smooth0,y,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dyz->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dyz.compute.c"); + +# d^2/dz^2 +simplify( diff(interp_3d_cube_order4_smooth0,z,z) ); +coeffs_as_lc_of_data(%, posn_list_3d_size5); +print_coeffs__lc_of_data(%, "coeffs_dzz->coeff_", "fp", + "3d.coeffs/3d.cube.order4.smooth0/coeffs-dzz.compute.c"); + +################################################################################ diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/README b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/README new file mode 100644 index 0000000..1fd04dd --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/README @@ -0,0 +1,62 @@ +$Header$ + +This directory contains code for Lagrange polynomial interpolation, +using the tensor-product definition for multiple dimensions. + +makefile + This has targets to create the subdirectories for the + Maple-generated coefficient files, and to run Maple to + generated those files. + +make.code.defn + This tells the Cactus build system which files to compile. + +[123]d.maple + These files contain the Maple code to generate the interpolation + coefficients. + +fns.maple + These files define the interpolation functions, coefficients, etc, + for the Maple code in [123]d.maple + +[123]d.cube.order?.smooth?.c + These files are the individual cases for the interpolation. + Each file defines a separate function. Each file just #defines + a bunch of macros, then #includes "../template.c" to get the + actual interpolation code. Unfortunately, the ISO C standard + only guarantees 31 characters for function names (in fact, it + doesn't even guarantee that for external names -- they may be + limited by a system linker -- but I quietly ignore that and + assume I can use 31), so the functions are named in a somewhat + cryptic manner: + 123456789 123456789 123456789 1 + LocalInterp_U_LagrTP_1dcube_10 + LocalInterp_U_LagrTP_1dcube_20 + LocalInterp_U_LagrTP_1dcube_30 + LocalInterp_U_LagrTP_1dcube_40 + LocalInterp_U_LagrTP_1dcube_50 + LocalInterp_U_LagrTP_1dcube_60 + LocalInterp_U_LagrTP_2dcube_10 + LocalInterp_U_LagrTP_2dcube_20 + LocalInterp_U_LagrTP_2dcube_30 + LocalInterp_U_LagrTP_2dcube_40 + LocalInterp_U_LagrTP_3dcube_10 + LocalInterp_U_LagrTP_3dcube_20 + LocalInterp_U_LagrTP_3dcube_30 + LocalInterp_U_LagrTP_3dcube_40 + The naming convention is as follows (eg for the last function) + LocalInterp name of this thorn + U these functions are all for the + CCTK_InterpLocalUniform() API + Lagr_TP these functions are all for the + "Lagrange polynomial interpolation (tensor product)" + interpolation operator + 3d this function does 3-d interpolation + cube this function uses a cube-shaped + interpolation molecule + 4 this function does 4th order interpolation + 0 this function does smoothing=0 interpolation + +all_prototypes.h + This file contains C prototypes for each of the functions + in [123]d.cube.order?.smooth0.c. diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/all_prototypes.h b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/all_prototypes.h new file mode 100644 index 0000000..23e6f37 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/all_prototypes.h @@ -0,0 +1,72 @@ +/* all-prototypes.h -- C prototypes for all template-generated functions */ +/* $Header$ */ + +/* + * 1D + */ + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrTP_1d_cube10 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrTP_1d_cube20 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrTP_1d_cube30 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrTP_1d_cube40 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrTP_1d_cube50 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrTP_1d_cube60 +#include "template.h" + + +/* + * 2D + */ + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrTP_2d_cube10 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrTP_2d_cube20 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrTP_2d_cube30 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrTP_2d_cube40 +#include "template.h" + + +/* + * 3D + */ + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrTP_3d_cube10 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrTP_3d_cube20 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrTP_3d_cube30 +#include "template.h" + +#undef FUNCTION_NAME +#define FUNCTION_NAME LocalInterp_U_LagrTP_3d_cube40 +#include "template.h" diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/fns.maple b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/fns.maple new file mode 100644 index 0000000..e363b10 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/fns.maple @@ -0,0 +1,306 @@ +# Maple code to define Lagrange interpolating functions/coords/coeffs +# $Header$ + +################################################################################ + +# +# 1-D interpolating functions +# + +fn_1d_order1 := +proc(x) ++ c0 + c1*x +end proc; + +fn_1d_order2 := +proc(x) ++ c0 + c1*x + c2*x^2 +end proc; + +fn_1d_order3 := +proc(x) ++ c0 + c1*x + c2*x^2 + c3*x^3 +end proc; + +fn_1d_order4 := +proc(x) ++ c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 +end; + +fn_1d_order5 := +proc(x) ++ c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 +end; + +fn_1d_order6 := +proc(x) ++ c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 +end; + +######################################## + +# coordinates for 1-D interpolating functions +coords_list_1d := [x]; + +######################################## + +# +# coefficients in 1-D interpolating functions +# + +coeffs_list_1d_order1 := [c0, c1]; +coeffs_list_1d_order2 := [c0, c1, c2]; +coeffs_list_1d_order3 := [c0, c1, c2, c3]; +coeffs_list_1d_order4 := [c0, c1, c2, c3, c4]; +coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5]; +coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6]; + +################################################################################ + +# +# 2-D interpolating functions (tensor-product) +# + +fn_2d_order1 := +proc(x,y) ++ c01*y + c11*x*y ++ c00 + c10*x +end proc; + +fn_2d_order2 := +proc(x,y) ++ c02*y^2 + c12*x*y^2 + c22*x^2*y^2 ++ c01*y + c11*x*y + c21*x^2*y ++ c00 + c10*x + c20*x^2 +end proc; + +fn_2d_order3 := +proc(x,y) ++ c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 ++ c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 ++ c01*y + c11*x*y + c21*x^2*y + c31*x^3*y ++ c00 + c10*x + c20*x^2 + c30*x^3 +end proc; + +fn_2d_order4 := +proc(x,y) ++ c04*y^4 + c14*x*y^4 + c24*x^2*y^4 + c34*x^3*y^4 + c44*x^4*y^4 ++ c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c43*x^4*y^3 ++ c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 + c42*x^4*y^2 ++ c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + c41*x^4*y ++ c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 +end; + +######################################## + +# coordinates for 2-D interpolating functions +coords_list_2d := [x,y]; + +######################################## + +# +# coefficients in 2-D interpolating functions (tensor-product) +# + +coeffs_list_2d_order1 := [ + c01, c11, + c00, c10 + ]; +coeffs_list_2d_order2 := [ + c02, c12, c22, + c01, c11, c21, + c00, c10, c20 + ]; +coeffs_list_2d_order3 := [ + c03, c13, c23, c33, + c02, c12, c22, c23, + c01, c11, c21, c13, + c00, c10, c20, c30 + ]; +coeffs_list_2d_order4 := [ + c04, c14, c24, c34, c44, + c03, c13, c23, c33, c43, + c02, c12, c22, c32, c42, + c01, c11, c21, c31, c41, + c00, c10, c20, c30, c40 + ]; + +################################################################################ + +# +# 3-D interpolating functions (tensor-product) +# + +fn_3d_order1 := +proc(x,y,z) +# z^1 ------------------- ++ c011 *y*z + c111*x*y*z ++ c001 *z + c101*x *z +# z^0 ------------------- ++ c010 *y + c110*x*y ++ c000 + c100*x +end proc; + +fn_3d_order2 := +proc(x,y,z) +# z^2 -------------------------------------------------- ++ c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 ++ c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 ++ c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 +# z -------------------------------------------------- ++ c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z ++ c011 *y *z + c111*x *y *z + c211*x^2*y *z ++ c001 *z + c101*x *z + c201*x^2 *z +# z^0 ------------------------------------------------ ++ c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 ++ c010 *y + c110*x *y + c210*x^2*y ++ c000 + c100*x + c200*x^2 +end proc; + +fn_3d_order3 := +proc(x,y,z) +# z^3 --------------------------------------------------------------------- ++ c033 *y^3*z^3 + c133*x *y^3*z^3 + c233*x^2*y^3*z^3 + c333*x^3*y^3*z^3 ++ c023 *y^2*z^3 + c123*x *y^2*z^3 + c223*x^2*y^2*z^3 + c323*x^3*y^2*z^3 ++ c013 *y *z^3 + c113*x *y *z^3 + c213*x^2*y *z^3 + c313*x^3*y *z^3 ++ c003 *z^3 + c103*x *z^3 + c203*x^2 *z^3 + c303*x^3 *z^3 +# z^2 --------------------------------------------------------------------- ++ c032 *y^3*z^2 + c132*x *y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 ++ c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 + c322*x^3*y^2*z^2 ++ c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 + c312*x^3*y *z^2 ++ c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 + c302*x^3 *z^2 +# z --------------------------------------------------------------------- ++ c031 *y^3*z + c131*x *y^3*z + c231*x^2*y^3*z + c331*x^3*y^3*z ++ c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z + c321*x^3*y^2*z ++ c011 *y *z + c111*x *y *z + c211*x^2*y *z + c311*x^3*y *z ++ c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z +# z^0 --------------------------------------------------------------------- ++ c030 *y^3 + c130*x *y^3 + c230*x^2*y^3 + c330*x^3*y^3 ++ c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 + c320*x^3*y^2 ++ c010 *y + c110*x *y + c210*x^2*y + c310*x^3*y ++ c000 + c100*x + c200*x^2 + c300*x^3 +end proc; + +fn_3d_order4 := +proc(x,y,z) +# z^4 ---------------------------------------------------------------------------------------- ++ c044 *y^4*z^4 + c144*x *y^4*z^4 + c244*x^2*y^4*z^4 + c344*x^3*y^4*z^4 + c444*x^4*y^4*z^4 ++ c034 *y^3*z^4 + c134*x *y^3*z^4 + c234*x^2*y^3*z^4 + c334*x^3*y^3*z^4 + c434*x^4*y^3*z^4 ++ c024 *y^2*z^4 + c124*x *y^2*z^4 + c224*x^2*y^2*z^4 + c324*x^3*y^2*z^4 + c424*x^4*y^2*z^4 ++ c014 *y *z^4 + c114*x *y *z^4 + c214*x^2*y *z^4 + c314*x^3*y *z^4 + c414*x^4*y *z^4 ++ c004 *z^4 + c104*x *z^4 + c204*x^2 *z^4 + c304*x^3 *z^4 + c404*x^4 *z^4 +# z^3 ---------------------------------------------------------------------------------------- ++ c043 *y^4*z^3 + c143*x *y^4*z^3 + c243*x^2*y^4*z^3 + c343*x^3*y^4*z^3 + c443*x^4*y^4*z^3 ++ c033 *y^3*z^3 + c133*x *y^3*z^3 + c233*x^2*y^3*z^3 + c333*x^3*y^3*z^3 + c433*x^4*y^3*z^3 ++ c023 *y^2*z^3 + c123*x *y^2*z^3 + c223*x^2*y^2*z^3 + c323*x^3*y^2*z^3 + c423*x^4*y^2*z^3 ++ c013 *y *z^3 + c113*x *y *z^3 + c213*x^2*y *z^3 + c313*x^3*y *z^3 + c413*x^4*y *z^3 ++ c003 *z^3 + c103*x *z^3 + c203*x^2 *z^3 + c303*x^3 *z^3 + c403*x^4 *z^3 +# z^2 ---------------------------------------------------------------------------------------- ++ c042 *y^4*z^2 + c142*x *y^4*z^2 + c242*x^2*y^4*z^2 + c342*x^3*y^4*z^2 + c442*x^4*y^4*z^2 ++ c032 *y^3*z^2 + c132*x *y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 + c432*x^4*y^3*z^2 ++ c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 + c322*x^3*y^2*z^2 + c422*x^4*y^2*z^2 ++ c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 + c312*x^3*y *z^2 + c412*x^4*y *z^2 ++ c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 + c302*x^3 *z^2 + c402*x^4 *z^2 +# z ---------------------------------------------------------------------------------------- ++ c041 *y^4*z + c141*x *y^4*z + c241*x^2*y^4*z + c341*x^3*y^4*z + c441*x^4*y^4*z ++ c031 *y^3*z + c131*x *y^3*z + c231*x^2*y^3*z + c331*x^3*y^3*z + c431*x^4*y^3*z ++ c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z + c321*x^3*y^2*z + c421*x^4*y^2*z ++ c011 *y *z + c111*x *y *z + c211*x^2*y *z + c311*x^3*y *z + c411*x^4*y *z ++ c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z + c401*x^4 *z +# z^0 ---------------------------------------------------------------------------------------- ++ c040 *y^4 + c140*x *y^4 + c240*x^2*y^4 + c340*x^3*y^4 + c440*x^4*y^4 ++ c030 *y^3 + c130*x *y^3 + c230*x^2*y^3 + c330*x^3*y^3 + c430*x^4*y^3 ++ c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 + c320*x^3*y^2 + c420*x^4*y^2 ++ c010 *y + c110*x *y + c210*x^2*y + c310*x^3*y + c410*x^4*y ++ c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 +end; + +######################################## + +# coordinates for 3-D interpolating functions +coords_list_3d := [x,y,z]; + +######################################## + +# +# coefficients in 3-D interpolating functions +# + +coeffs_list_3d_order1 := [ + # z^1 ----- + c011, c111, + c001, c101, + # z^0 ----- + c010, c110, + c000, c100 + ]; +coeffs_list_3d_order2 := [ + # z^2 ----------- + c022, c122, c222, + c012, c112, c212, + c002, c102, c202, + # z^1 ----------- + c021, c121, c221, + c011, c111, c211, + c001, c101, c201, + # z^0 ----------- + c020, c120, c220, + c010, c110, c210, + c000, c100, c200 + ]; +coeffs_list_3d_order3 := [ + # z^3 ----------------- + c033, c133, c233, c333, + c023, c123, c223, c323, + c013, c113, c213, c313, + c003, c103, c203, c303, + # z^2 ----------------- + c032, c132, c232, c332, + c022, c122, c222, c322, + c012, c112, c212, c312, + c002, c102, c202, c302, + # z^1 ----------------- + c031, c131, c231, c331, + c021, c121, c221, c321, + c011, c111, c211, c311, + c001, c101, c201, c301, + # z^0 ----------------- + c030, c130, c230, c330, + c020, c120, c220, c320, + c010, c110, c210, c310, + c000, c100, c200, c300 + ]; +coeffs_list_3d_order4 := [ + # z^4 ----------------------- + c044, c144, c244, c344, c444, + c034, c134, c234, c334, c434, + c024, c124, c224, c324, c424, + c014, c114, c214, c314, c414, + c004, c104, c204, c304, c404, + # z^3 ----------------------- + c043, c143, c243, c343, c443, + c033, c133, c233, c333, c433, + c023, c123, c223, c323, c423, + c013, c113, c213, c313, c413, + c003, c103, c203, c303, c403, + # z^2 ----------------------- + c042, c142, c242, c342, c442, + c032, c132, c232, c332, c432, + c022, c122, c222, c322, c422, + c012, c112, c212, c312, c412, + c002, c102, c202, c302, c402, + # z^1 ----------------------- + c041, c141, c241, c341, c441, + c031, c131, c231, c331, c431, + c021, c121, c221, c321, c421, + c011, c111, c211, c311, c411, + c001, c101, c201, c301, c401, + # z^0 ----------------------- + c040, c140, c240, c340, c440, + c030, c130, c230, c330, c430, + c020, c120, c220, c320, c420, + c010, c110, c210, c310, c410, + c000, c100, c200, c300, c400 + ]; + +################################################################################ diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/make.code.defn b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/make.code.defn new file mode 100644 index 0000000..c656453 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/make.code.defn @@ -0,0 +1,22 @@ +# make.code.defn file for Lagrange polynomial interpolation +# $Header$ + +# Source files in this directory +SRCS = \ + 1d.cube.order1.smooth0.c \ + 1d.cube.order2.smooth0.c \ + 1d.cube.order3.smooth0.c \ + 1d.cube.order4.smooth0.c \ + 1d.cube.order5.smooth0.c \ + 1d.cube.order6.smooth0.c \ + \ + 2d.cube.order1.smooth0.c \ + 2d.cube.order2.smooth0.c \ + 2d.cube.order3.smooth0.c \ + 2d.cube.order4.smooth0.c \ + \ + 3d.cube.order1.smooth0.c \ + 3d.cube.order2.smooth0.c \ + 3d.cube.order3.smooth0.c \ + 3d.cube.order4.smooth0.c \ + # end of list diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/makefile b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/makefile new file mode 100644 index 0000000..e07e5b0 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/makefile @@ -0,0 +1,72 @@ +# $Header: /mnt/data2/cvs2svn/cvs-repositories/arrangements/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/makefile,v 1.1 2003-04-15 17:12:57 jthorn Exp $ + +.PHONY : no-default-target +no-default-target: + @echo 'there is (deliberately) no default target in this makefile,' + @echo 'because (re)generating all the coefficients is quite slow :(' + @echo '==> see the makefile to find out about explicit targets' + +# +# main targets: rebuild machine-generated coefficient files +# + +.PHONY : 1d +1d : + -rm -f 1d.coeffs/*/*.c + cat ../util.maple ../interpolate.maple \ + ../common/cube_posns.maple fns.maple 1d.maple \ + | maple 2>&1 >1d.log + +# with Maple 7, this takes about 40 seconds on a 1.7GHz P4 +.PHONY : 2d +2d : + -rm -f 2d.coeffs/*/*.c + cat ../util.maple ../interpolate.maple \ + ../common/cube_posns.maple fns.maple 2d.maple \ + | maple 2>&1 >2d.log + +# with Maple 7, this takes about 20 minutes on a 1.7GHz P4 +.PHONY : 3d +3d : + -rm -f 3d.coeffs/*/*.c + cat ../util.maple ../interpolate.maple \ + ../common/cube_posns.maple fns.maple 3d.maple \ + | maple 2>&1 >3d.log + +################################################################################ + +# +# targets to initially create directories for machine-generated coefficients +# these only need to be run if you're setting up a new interpolator, +# i.e. if you don't already have the directories in cvs +# (you still have to add them to cvs by hand) +# + +.PHONY : 1d.dirs +1d.dirs: + -rm -rf 1d.coeffs + mkdir 1d.coeffs + cd 1d.coeffs && mkdir 1d.cube.order1.smooth0 + cd 1d.coeffs && mkdir 1d.cube.order2.smooth0 + cd 1d.coeffs && mkdir 1d.cube.order3.smooth0 + cd 1d.coeffs && mkdir 1d.cube.order4.smooth0 + cd 1d.coeffs && mkdir 1d.cube.order5.smooth0 + cd 1d.coeffs && mkdir 1d.cube.order6.smooth0 + +.PHONY : 2d.dirs +2d.dirs: + -rm -rf 2d.coeffs + mkdir 2d.coeffs + cd 2d.coeffs && mkdir 2d.cube.order1.smooth0 + cd 2d.coeffs && mkdir 2d.cube.order2.smooth0 + cd 2d.coeffs && mkdir 2d.cube.order3.smooth0 + cd 2d.coeffs && mkdir 2d.cube.order4.smooth0 + +.PHONY : 3d.dirs +3d.dirs: + -rm -rf 3d.coeffs + mkdir 3d.coeffs + cd 3d.coeffs && mkdir 3d.cube.order1.smooth0 + cd 3d.coeffs && mkdir 3d.cube.order2.smooth0 + cd 3d.coeffs && mkdir 3d.cube.order3.smooth0 + cd 3d.coeffs && mkdir 3d.cube.order4.smooth0 -- cgit v1.2.3