add $Header:$ lines, switch a few $Id:$ --> $Header:$

git-svn-id: http://svn.cactuscode.org/arrangements/CactusBase/LocalInterp/trunk@92 df1f8a13-aa1d-4dd4-9681-27ded5b42416

37 files changed, 3409 insertions, 3122 deletions

diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order1.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order1.smooth0.c
index b56d181..e2a82fa 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order1.smooth0.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order1.smooth0.c
@@ -1,3 +1,5 @@
+/* $Header$ */
+
 #include <math.h>
 #include <limits.h>
 #include <stdlib.h>
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order2.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order2.smooth0.c
index 8622079..c5f9a9c 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order2.smooth0.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order2.smooth0.c
@@ -1,3 +1,5 @@
+/* $Header$ */
+
 #include <math.h>
 #include <limits.h>
 #include <stdlib.h>
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order3.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order3.smooth0.c
index 5042abe..8ff3ce1 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order3.smooth0.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order3.smooth0.c
@@ -1,3 +1,5 @@
+/* $Header$ */
+
 #include <math.h>
 #include <limits.h>
 #include <stdlib.h>
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order4.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order4.smooth0.c
index d8c5b5a..ea211aa 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order4.smooth0.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order4.smooth0.c
@@ -1,3 +1,5 @@
+/* $Header$ */
+
 #include <math.h>
 #include <limits.h>
 #include <stdlib.h>
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order5.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order5.smooth0.c
index 474bb58..559af52 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order5.smooth0.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order5.smooth0.c
@@ -1,3 +1,5 @@
+/* $Header$ */
+
 #include <math.h>
 #include <limits.h>
 #include <stdlib.h>
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order6.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order6.smooth0.c
index b9dba51..1b44efd 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order6.smooth0.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/1d.cube.order6.smooth0.c
@@ -1,3 +1,5 @@
+/* $Header$ */
+
 #include <math.h>
 #include <limits.h>
 #include <stdlib.h>
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/1d.maple b/src/GeneralizedPolynomial-Uniform/Lagrange/1d.maple
index c564b80..e9ac5d6 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/1d.maple
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/1d.maple
@@ -1,5 +1,5 @@
 # 1d.maple -- compute Lagrange interpolation coefficients in 1-D
-# $Id$
+# $Header$
 
 ################################################################################
 
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-I.compute.c
index 34f402b..52b6d48 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-I.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-I.compute.c
@@ -1,49 +1,53 @@
-fp t25,
-   t28,
-   t20,
-   t27,
+fp t27,
+   t26,
    t18,
+   t28,
+   t21,
    t34,
    t33,
    t23,
+   t15,
    t22,
-   t17,
    t32,
-   t15,
+   t17,
    t31,
+   t14,
    t30,
+   t25,
+   t20,
    t29,
-   t26,
-   t21,
    t19,
    t16,
-   t14;
-      t25 = RATIONAL(1.0,6.0);
-      t28 = y*y;
-      t20 = t25*t28;
+   t13,
+   t12;
       t27 = x*x;
-      t18 = t25*t27;
-      t34 = t20+RATIONAL(-1.0,9.0)+t18;
+      t26 = RATIONAL(1.0,6.0);
+      t18 = t26*t27;
+      t28 = y*y;
+      t21 = t26*t28;
+      t34 = t18+t21+RATIONAL(-1.0,9.0);
       t33 = x*y;
-      t23 = RATIONAL(2.0,9.0);
-      t22 = RATIONAL(-1.0,3.0);
-      t17 = t22*t27;
-      t32 = t20+t23+t17;
-      t15 = t22*t28;
-      t31 = t15+t23+t18;
-      t30 = RATIONAL(-1.0,4.0)*t33+t34;
-      t29 = RATIONAL(1.0,4.0)*t33+t34;
-      t26 = RATIONAL(-1.0,6.0);
-      t21 = t26*y;
-      t19 = t26*x;
-      t16 = t25*x;
-      t14 = t25*y;
-      coeff_I_m1_m1 = t21+t19+t29;
-      coeff_I_0_m1 = t21+t32;
-      coeff_I_p1_m1 = t21+t16+t30;
-      coeff_I_m1_0 = t19+t31;
-      coeff_I_0_0 = t15+t17+RATIONAL(5.0,9.0);
-      coeff_I_p1_0 = t16+t31;
-      coeff_I_m1_p1 = t14+t19+t30;
-      coeff_I_0_p1 = t14+t32;
-      coeff_I_p1_p1 = t14+t16+t29;
+      t23 = RATIONAL(-1.0,3.0);
+      t15 = t23*t28;
+      t22 = RATIONAL(2.0,9.0);
+      t32 = t15+t18+t22;
+      t17 = t23*t27;
+      t31 = t17+t21+t22;
+      t14 = t26*y;
+      t30 = t14+t34;
+      t25 = RATIONAL(-1.0,6.0);
+      t20 = t25*y;
+      t29 = t20+t34;
+      t19 = t25*x;
+      t16 = t26*x;
+      t13 = RATIONAL(1.0,4.0)*t33;
+      t12 = RATIONAL(-1.0,4.0)*t33;
+      coeff_I_m1_m1 = t13+t19+t29;
+      coeff_I_0_m1 = t20+t31;
+      coeff_I_p1_m1 = t12+t16+t29;
+      coeff_I_m1_0 = t19+t32;
+      coeff_I_0_0 = t15+RATIONAL(5.0,9.0)+t17;
+      coeff_I_p1_0 = t16+t32;
+      coeff_I_m1_p1 = t19+t12+t30;
+      coeff_I_0_p1 = t14+t31;
+      coeff_I_p1_p1 = t16+t13+t30;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dx.compute.c
index 22a3439..14b1a1c 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dx.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dx.compute.c
@@ -3,19 +3,19 @@ fp t37,
    t41,
    t40,
    t39,
-   t35;
+   t36;
       t37 = RATIONAL(1.0,3.0)*x;
-      t42 = t37+RATIONAL(1.0,4.0)*y;
-      t41 = RATIONAL(-1.0,4.0)*y+t37;
-      t40 = RATIONAL(-1.0,6.0);
-      t39 = RATIONAL(1.0,6.0);
-      t35 = RATIONAL(-2.0,3.0)*x;
-      coeff_dx_m1_m1 = t40+t42;
-      coeff_dx_0_m1 = t35;
-      coeff_dx_p1_m1 = t39+t41;
-      coeff_dx_m1_0 = t40+t37;
-      coeff_dx_0_0 = t35;
-      coeff_dx_p1_0 = t39+t37;
-      coeff_dx_m1_p1 = t40+t41;
-      coeff_dx_0_p1 = t35;
-      coeff_dx_p1_p1 = t39+t42;
+      t42 = RATIONAL(1.0,4.0)*y+t37;
+      t41 = t37+RATIONAL(-1.0,4.0)*y;
+      t40 = RATIONAL(1.0,6.0);
+      t39 = RATIONAL(-1.0,6.0);
+      t36 = RATIONAL(-2.0,3.0)*x;
+      coeff_dx_m1_m1 = t39+t42;
+      coeff_dx_0_m1 = t36;
+      coeff_dx_p1_m1 = t40+t41;
+      coeff_dx_m1_0 = t39+t37;
+      coeff_dx_0_0 = t36;
+      coeff_dx_p1_0 = t40+t37;
+      coeff_dx_m1_p1 = t39+t41;
+      coeff_dx_0_p1 = t36;
+      coeff_dx_p1_p1 = t40+t42;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dxx.compute.c
index 5f6427a..3381569 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dxx.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dxx.compute.c
@@ -1,13 +1,13 @@
 fp t52,
    t51;
-      t52 = RATIONAL(1.0,3.0);
-      t51 = RATIONAL(-2.0,3.0);
-      coeff_dxx_m1_m1 = t52;
-      coeff_dxx_0_m1 = t51;
-      coeff_dxx_p1_m1 = t52;
-      coeff_dxx_m1_0 = t52;
-      coeff_dxx_0_0 = t51;
-      coeff_dxx_p1_0 = t52;
-      coeff_dxx_m1_p1 = t52;
-      coeff_dxx_0_p1 = t51;
-      coeff_dxx_p1_p1 = t52;
+      t52 = RATIONAL(-2.0,3.0);
+      t51 = RATIONAL(1.0,3.0);
+      coeff_dxx_m1_m1 = t51;
+      coeff_dxx_0_m1 = t52;
+      coeff_dxx_p1_m1 = t51;
+      coeff_dxx_m1_0 = t51;
+      coeff_dxx_0_0 = t52;
+      coeff_dxx_p1_0 = t51;
+      coeff_dxx_m1_p1 = t51;
+      coeff_dxx_0_p1 = t52;
+      coeff_dxx_p1_p1 = t51;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dy.compute.c
index 4afa754..65e74bd 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dy.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dy.compute.c
@@ -5,17 +5,17 @@ fp t46,
    t47,
    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);
+      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;
-      coeff_dy_m1_m1 = t48+t49;
-      coeff_dy_0_m1 = t46+t48;
-      coeff_dy_p1_m1 = t48+t50;
+      coeff_dy_m1_m1 = t47+t50;
+      coeff_dy_0_m1 = t47+t46;
+      coeff_dy_p1_m1 = t47+t49;
       coeff_dy_m1_0 = t43;
       coeff_dy_0_0 = t43;
       coeff_dy_p1_0 = t43;
-      coeff_dy_m1_p1 = t47+t50;
-      coeff_dy_0_p1 = t47+t46;
-      coeff_dy_p1_p1 = t47+t49;
+      coeff_dy_m1_p1 = t48+t49;
+      coeff_dy_0_p1 = t46+t48;
+      coeff_dy_p1_p1 = t48+t50;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dyy.compute.c
index a643108..5d0b896 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dyy.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order2.smooth0/coeff-dyy.compute.c
@@ -1,13 +1,13 @@
 fp t57,
    t56;
-      t57 = RATIONAL(1.0,3.0);
-      t56 = RATIONAL(-2.0,3.0);
-      coeff_dyy_m1_m1 = t57;
-      coeff_dyy_0_m1 = t57;
-      coeff_dyy_p1_m1 = t57;
-      coeff_dyy_m1_0 = t56;
-      coeff_dyy_0_0 = t56;
-      coeff_dyy_p1_0 = t56;
-      coeff_dyy_m1_p1 = t57;
-      coeff_dyy_0_p1 = t57;
-      coeff_dyy_p1_p1 = t57;
+      t57 = RATIONAL(-2.0,3.0);
+      t56 = RATIONAL(1.0,3.0);
+      coeff_dyy_m1_m1 = t56;
+      coeff_dyy_0_m1 = t56;
+      coeff_dyy_p1_m1 = t56;
+      coeff_dyy_m1_0 = t57;
+      coeff_dyy_0_0 = t57;
+      coeff_dyy_p1_0 = t57;
+      coeff_dyy_m1_p1 = t56;
+      coeff_dyy_0_p1 = t56;
+      coeff_dyy_p1_p1 = t56;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-I.compute.c
index 55cc52e..a022b8a 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-I.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-I.compute.c
@@ -1,73 +1,73 @@
 fp t160,
    t131,
    t159,
-   t130,
-   t158,
-   t124,
-   t68,
    t133,
-   t126,
-   t82,
-   t157,
-   t71,
+   t158,
+   t117,
+   t66,
    t132,
-   t83,
-   t156,
-   t121,
-   t70,
    t128,
    t87,
-   t155,
-   t67,
+   t157,
    t129,
-   t86,
+   t84,
+   t156,
+   t124,
+   t68,
+   t130,
+   t116,
+   t77,
+   t155,
+   t126,
+   t70,
+   t125,
+   t83,
    t154,
-   t85,
+   t71,
    t153,
-   t117,
-   t77,
+   t108,
+   t122,
+   t69,
    t152,
-   t127,
-   t62,
    t151,
    t63,
    t150,
-   t125,
-   t64,
+   t67,
+   t86,
    t149,
-   t79,
+   t65,
    t148,
+   t85,
    t147,
+   t79,
    t146,
-   t69,
-   t110,
+   t82,
    t145,
-   t84,
    t144,
    t143,
-   t123,
    t142,
-   t104,
+   t123,
    t141,
+   t101,
    t140,
    t139,
    t138,
    t137,
    t136,
-   t122,
-   t120,
+   t127,
+   t121,
    t119,
-   t116,
-   t114,
+   t118,
+   t115,
    t113,
+   t112,
    t111,
-   t108,
-   t107,
+   t109,
+   t106,
    t105,
    t103,
    t102,
-   t101,
-   t99,
+   t100,
    t98,
    t97,
    t96,
@@ -85,112 +85,112 @@ fp t160,
    t76,
    t75,
    t74,
-   t73;
+   t72;
       t160 = x*y;
-      t131 = y*y;
-      t159 = x*t131;
-      t130 = x*x;
-      t158 = t130*y;
+      t131 = x*x;
+      t159 = t131*y;
+      t133 = y*y;
+      t158 = x*t133;
+      t117 = RATIONAL(1.0,40.0);
+      t66 = t117*t159;
+      t132 = t133*y;
+      t128 = RATIONAL(-1.0,8.0);
+      t87 = t128*t132;
+      t157 = t66+t87;
+      t129 = RATIONAL(1.0,8.0);
+      t84 = t129*t132;
+      t156 = t66+t84;
       t124 = RATIONAL(3.0,40.0);
       t68 = t124*t158;
-      t133 = t131*y;
-      t126 = RATIONAL(-1.0,24.0);
-      t82 = t126*t133;
-      t157 = t68+t82;
+      t130 = t131*x;
+      t116 = RATIONAL(1.0,24.0);
+      t77 = t116*t130;
+      t155 = t68+t77;
+      t126 = RATIONAL(-3.0,40.0);
+      t70 = t126*t159;
+      t125 = RATIONAL(-1.0,24.0);
+      t83 = t125*t132;
+      t154 = t70+t83;
       t71 = t124*t159;
-      t132 = t130*x;
-      t83 = t126*t132;
-      t156 = t71+t83;
-      t121 = RATIONAL(1.0,40.0);
-      t70 = t121*t158;
-      t128 = RATIONAL(-1.0,8.0);
-      t87 = t128*t133;
-      t155 = t70+t87;
-      t67 = t121*t159;
-      t129 = RATIONAL(1.0,8.0);
-      t86 = t129*t132;
-      t154 = t67+t86;
-      t85 = t128*t132;
-      t153 = t67+t85;
-      t117 = RATIONAL(1.0,24.0);
-      t77 = t117*t132;
-      t152 = t71+t77;
-      t127 = RATIONAL(-3.0,40.0);
-      t62 = t127*t158;
-      t151 = t62+t82;
-      t63 = t127*t159;
-      t150 = t63+t77;
-      t125 = RATIONAL(-1.0,40.0);
-      t64 = t125*t159;
-      t149 = t64+t86;
-      t79 = t117*t133;
-      t148 = t68+t79;
-      t147 = t63+t83;
-      t146 = t62+t79;
-      t69 = t125*t158;
-      t110 = RATIONAL(11.0,80.0);
-      t145 = t69+t110*t130;
-      t84 = t129*t133;
-      t144 = t70+t84;
-      t143 = t64+t85;
+      t153 = t71+t83;
+      t108 = RATIONAL(11.0,80.0);
+      t122 = RATIONAL(-1.0,40.0);
+      t69 = t122*t158;
+      t152 = t69+t108*t133;
+      t151 = RATIONAL(-1.0,100.0)*t160+RATIONAL(37.0,200.0);
+      t63 = t122*t159;
+      t150 = t63+t87;
+      t67 = t117*t158;
+      t86 = t129*t130;
+      t149 = t67+t86;
+      t65 = t126*t158;
+      t148 = t65+t77;
+      t85 = t128*t130;
+      t147 = t67+t85;
+      t79 = t116*t132;
+      t146 = t70+t79;
+      t82 = t125*t130;
+      t145 = t68+t82;
+      t144 = t63+t84;
+      t143 = t65+t82;
+      t142 = t71+t79;
       t123 = RATIONAL(-1.0,50.0);
-      t142 = RATIONAL(-13.0,100.0)*t160+t123;
-      t104 = RATIONAL(-17.0,200.0);
-      t141 = RATIONAL(-9.0,100.0)*t160+t104;
-      t140 = t123*t160+RATIONAL(11.0,50.0);
-      t139 = RATIONAL(-1.0,100.0)*t160+RATIONAL(37.0,200.0);
-      t138 = RATIONAL(-2.0,25.0)+RATIONAL(2.0,25.0)*t160;
+      t141 = t123+RATIONAL(-13.0,100.0)*t160;
+      t101 = RATIONAL(-17.0,200.0);
+      t140 = RATIONAL(-9.0,100.0)*t160+t101;
+      t139 = RATIONAL(11.0,50.0)+t123*t160;
+      t138 = RATIONAL(2.0,25.0)*t160+RATIONAL(-2.0,25.0);
       t137 = RATIONAL(7.0,100.0)*t160+RATIONAL(13.0,100.0);
-      t136 = t130+t131;
-      t122 = RATIONAL(9.0,80.0);
-      t120 = RATIONAL(7.0,80.0);
+      t136 = t133+t131;
+      t127 = RATIONAL(1.0,80.0);
+      t121 = RATIONAL(9.0,80.0);
       t119 = RATIONAL(-1.0,80.0);
-      t116 = RATIONAL(3.0,80.0);
-      t114 = RATIONAL(1.0,80.0);
-      t113 = RATIONAL(13.0,80.0);
-      t111 = RATIONAL(-23.0,80.0);
-      t108 = RATIONAL(-19.0,80.0);
-      t107 = RATIONAL(-17.0,80.0);
-      t105 = RATIONAL(-31.0,400.0);
-      t103 = RATIONAL(69.0,400.0);
-      t102 = RATIONAL(-57.0,400.0);
-      t101 = RATIONAL(-63.0,400.0);
-      t99 = RATIONAL(-49.0,400.0);
-      t98 = RATIONAL(43.0,1200.0);
-      t97 = RATIONAL(103.0,400.0);
-      t96 = RATIONAL(111.0,400.0);
+      t118 = RATIONAL(7.0,80.0);
+      t115 = RATIONAL(3.0,80.0);
+      t113 = RATIONAL(-19.0,80.0);
+      t112 = RATIONAL(-17.0,80.0);
+      t111 = RATIONAL(13.0,80.0);
+      t109 = RATIONAL(-23.0,80.0);
+      t106 = RATIONAL(-63.0,400.0);
+      t105 = 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(37.0,1200.0);
-      t94 = RATIONAL(89.0,1200.0);
-      t93 = RATIONAL(117.0,400.0);
+      t94 = RATIONAL(111.0,400.0);
+      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);
-      t81 = t122*t131;
-      t80 = t120*t130;
-      t78 = t120*t131;
-      t76 = t122*t130;
-      t75 = t113*t131;
-      t74 = t113*t130;
-      t73 = t110*t131;
+      t89 = RATIONAL(-149.0,1200.0);
+      t88 = RATIONAL(-131.0,1200.0);
+      t81 = t121*t133;
+      t80 = t118*t131;
+      t78 = t118*t133;
+      t76 = t121*t131;
+      t75 = t111*t131;
+      t74 = t111*t133;
+      t72 = t108*t131;
       coeff_I_m1_m1 = t75+RATIONAL(-23.0,200.0)+t74+t92*y+(t92+RATIONAL(6.0,
-25.0)*y)*x+t147+t151;
-      coeff_I_0_m1 = t111*t130+t105*x+t73+t91*y+t140+t149+t157;
-      coeff_I_p1_m1 = t81+t96*x+t90*y+t80+t142+t153+t157;
-      coeff_I_p2_m1 = t78+t94*y+t89*x+t116*t130+t141+t151+t152;
-      coeff_I_m1_0 = t105*y+t91*x+t111*t131+t84+t140+t145+t156;
-      coeff_I_0_0 = RATIONAL(93.0,200.0)+t102*y+t136*RATIONAL(-21.0,80.0)+(
-RATIONAL(-1.0,25.0)*y+t102)*x+t144+t154;
-      coeff_I_p1_0 = t108*t131+t101*y+t76+t93*x+t139+t143+t144;
-      coeff_I_p2_0 = t107*t131+t114*t130+t99*y+t84+t69+t98*x+t137+t150;
-      coeff_I_m1_p1 = t90*x+t96*y+t78+t76+t142+t155+t156;
-      coeff_I_0_p1 = t69+t101*x+t108*t130+t87+t93*y+t81+t139+t154;
-      coeff_I_p1_p1 = t97*y+t73+t104+t87+(RATIONAL(3.0,50.0)*y+t97)*x+t143+t145
+25.0)*y)*x+t143+t154;
+      coeff_I_0_m1 = t109*t131+t91*y+t86+t103*x+t139+t152+t153;
+      coeff_I_p1_m1 = t81+t94*x+t90*y+t80+t141+t147+t153;
+      coeff_I_p2_m1 = t78+t93*y+t88*x+t115*t131+t140+t154+t155;
+      coeff_I_m1_0 = t72+t109*t133+t91*x+t103*y+t139+t144+t145;
+      coeff_I_0_0 = RATIONAL(93.0,200.0)+t100*y+t136*RATIONAL(-21.0,80.0)+(
+RATIONAL(-1.0,25.0)*y+t100)*x+t149+t156;
+      coeff_I_p1_0 = t69+t76+t98*x+t85+t113*t133+t106*y+t151+t156;
+      coeff_I_p2_0 = t97*x+t127*t131+t105*y+t112*t133+t137+t144+t148;
+      coeff_I_m1_p1 = t76+t90*x+t78+t94*y+t141+t145+t157;
+      coeff_I_0_p1 = t113*t131+t81+t106*x+t98*y+t149+t150+t151;
+      coeff_I_p1_p1 = t72+t101+t96*y+t85+(t96+RATIONAL(3.0,50.0)*y)*x+t150+t152
 ;
-      coeff_I_p2_p1 = t95*x+t119*t130+t75+t103*y+t138+t150+t155;
-      coeff_I_m1_p2 = t116*t131+t94*x+t89*y+t80+t141+t147+t148;
-      coeff_I_0_p2 = t99*x+t98*y+t114*t131+t107*t130+t137+t146+t149;
-      coeff_I_p1_p2 = t103*x+t119*t131+t95*y+t74+t138+t146+t153;
-      coeff_I_p2_p2 = RATIONAL(7.0,200.0)+t88*y+t136*RATIONAL(-3.0,80.0)+(t88+
-RATIONAL(-3.0,50.0)*y)*x+t148+t152;
+      coeff_I_p2_p1 = t102*y+t74+t119*t131+t95*x+t138+t148+t157;
+      coeff_I_m1_p2 = t80+t88*y+t93*x+t115*t133+t140+t142+t143;
+      coeff_I_0_p2 = t127*t133+t86+t97*y+t105*x+t112*t131+t69+t137+t146;
+      coeff_I_p1_p2 = t95*y+t75+t119*t133+t102*x+t138+t146+t147;
+      coeff_I_p2_p2 = t89*y+RATIONAL(7.0,200.0)+t136*RATIONAL(-3.0,80.0)+(t89+
+RATIONAL(-3.0,50.0)*y)*x+t142+t155;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dx.compute.c
index 4650764..5bfa6f4 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dx.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dx.compute.c
@@ -1,95 +1,95 @@
 fp t201,
-   t164,
+   t161,
    t200,
-   t163,
-   t199,
-   t183,
+   t184,
    t188,
-   t173,
+   t174,
    t187,
-   t179,
+   t180,
+   t199,
+   t164,
    t198,
-   t161,
+   t183,
+   t175,
    t197,
    t162,
    t196,
-   t185,
-   t176,
-   t195,
    t181,
+   t195,
    t194,
+   t163,
    t193,
    t186,
-   t177,
+   t176,
    t182,
    t192,
-   t180,
-   t191,
-   t184,
+   t185,
    t172,
+   t191,
+   t179,
    t190,
    t189,
    t178,
-   t175,
-   t170,
-   t168,
+   t177,
+   t169,
+   t167,
    t166,
    t165;
       t201 = x*y;
-      t164 = RATIONAL(-3.0,20.0)*t201;
-      t200 = RATIONAL(13.0,40.0)*x+t164;
-      t163 = RATIONAL(3.0,20.0)*t201;
-      t199 = RATIONAL(7.0,40.0)*x+t163;
-      t183 = RATIONAL(1.0,40.0);
+      t161 = RATIONAL(1.0,20.0)*t201;
+      t200 = t161+RATIONAL(9.0,40.0)*x;
+      t184 = RATIONAL(-1.0,40.0);
       t188 = y*y;
-      t173 = t183*t188;
+      t174 = t184*t188;
       t187 = x*x;
-      t179 = RATIONAL(-3.0,8.0)*t187;
-      t198 = t173+t179;
-      t161 = RATIONAL(1.0,20.0)*t201;
-      t197 = RATIONAL(9.0,40.0)*x+t161;
+      t180 = RATIONAL(-3.0,8.0)*t187;
+      t199 = t174+t180;
+      t164 = RATIONAL(-3.0,20.0)*t201;
+      t198 = t164+RATIONAL(13.0,40.0)*x;
+      t183 = RATIONAL(1.0,40.0);
+      t175 = t183*t188;
+      t197 = t175+t180;
       t162 = RATIONAL(-1.0,20.0)*t201;
-      t196 = RATIONAL(11.0,40.0)*x+t162;
-      t185 = RATIONAL(-1.0,40.0);
-      t176 = t185*t188;
-      t195 = t176+t179;
+      t196 = t162+RATIONAL(11.0,40.0)*x;
       t181 = RATIONAL(3.0,8.0)*t187;
-      t194 = t173+t181;
-      t193 = t176+t181;
+      t195 = t174+t181;
+      t194 = t175+t181;
+      t163 = RATIONAL(3.0,20.0)*t201;
+      t193 = RATIONAL(7.0,40.0)*x+t163;
       t186 = RATIONAL(-3.0,40.0);
-      t177 = t186*t188;
+      t176 = t186*t188;
       t182 = RATIONAL(-1.0,8.0)*t187;
-      t192 = t177+t182;
-      t180 = RATIONAL(1.0,8.0)*t187;
-      t191 = t177+t180;
-      t184 = RATIONAL(3.0,40.0);
-      t172 = t184*t188;
-      t190 = t172+t180;
-      t189 = t172+t182;
+      t192 = t176+t182;
+      t185 = RATIONAL(3.0,40.0);
+      t172 = t185*t188;
+      t191 = t172+t182;
+      t179 = RATIONAL(1.0,8.0)*t187;
+      t190 = t172+t179;
+      t189 = t176+t179;
       t178 = RATIONAL(2.0,25.0)*y;
-      t175 = RATIONAL(-1.0,50.0)*y;
-      t170 = RATIONAL(7.0,100.0)*y;
-      t168 = RATIONAL(-9.0,100.0)*y;
-      t166 = RATIONAL(-1.0,100.0)*y;
+      t177 = RATIONAL(-1.0,50.0)*y;
+      t169 = RATIONAL(-9.0,100.0)*y;
+      t167 = RATIONAL(-1.0,100.0)*y;
+      t166 = RATIONAL(7.0,100.0)*y;
       t165 = RATIONAL(-13.0,100.0)*y;
-      coeff_dx_m1_m1 = RATIONAL(-109.0,1200.0)+RATIONAL(6.0,25.0)*y+t192+t200;
-      coeff_dx_0_m1 = RATIONAL(-31.0,400.0)+RATIONAL(-23.0,40.0)*x+t175+t163+
-t193;
-      coeff_dx_p1_m1 = RATIONAL(111.0,400.0)+t165+t198+t199;
-      coeff_dx_p2_m1 = t168+t164+RATIONAL(-131.0,1200.0)+t184*x+t190;
-      coeff_dx_m1_0 = RATIONAL(-223.0,1200.0)+t175+t189+t196;
-      coeff_dx_0_0 = RATIONAL(-57.0,400.0)+RATIONAL(-21.0,40.0)*x+RATIONAL(-1.0
-,25.0)*y+t161+t194;
-      coeff_dx_p1_0 = RATIONAL(117.0,400.0)+t166+t195+t197;
-      coeff_dx_p2_0 = RATIONAL(43.0,1200.0)+t183*x+t162+t170+t191;
-      coeff_dx_m1_p1 = RATIONAL(-157.0,1200.0)+t165+t189+t197;
-      coeff_dx_0_p1 = RATIONAL(-63.0,400.0)+t166+t162+RATIONAL(-19.0,40.0)*x+
+      coeff_dx_m1_m1 = RATIONAL(-109.0,1200.0)+RATIONAL(6.0,25.0)*y+t192+t198;
+      coeff_dx_0_m1 = RATIONAL(-31.0,400.0)+t177+RATIONAL(-23.0,40.0)*x+t163+
+t195;
+      coeff_dx_p1_m1 = RATIONAL(111.0,400.0)+t165+t193+t197;
+      coeff_dx_p2_m1 = t169+RATIONAL(-131.0,1200.0)+t164+t185*x+t190;
+      coeff_dx_m1_0 = RATIONAL(-223.0,1200.0)+t177+t191+t196;
+      coeff_dx_0_0 = RATIONAL(-1.0,25.0)*y+t161+RATIONAL(-21.0,40.0)*x+RATIONAL
+(-57.0,400.0)+t194;
+      coeff_dx_p1_0 = t167+RATIONAL(117.0,400.0)+t199+t200;
+      coeff_dx_p2_0 = t183*x+t162+RATIONAL(43.0,1200.0)+t166+t189;
+      coeff_dx_m1_p1 = RATIONAL(-157.0,1200.0)+t165+t191+t200;
+      coeff_dx_0_p1 = RATIONAL(-19.0,40.0)*x+RATIONAL(-63.0,400.0)+t162+t167+
 t194;
-      coeff_dx_p1_p1 = RATIONAL(3.0,50.0)*y+RATIONAL(103.0,400.0)+t195+t196;
-      coeff_dx_p2_p1 = t185*x+t161+RATIONAL(37.0,1200.0)+t178+t191;
-      coeff_dx_m1_p2 = t168+RATIONAL(89.0,1200.0)+t192+t199;
-      coeff_dx_0_p2 = t164+t170+RATIONAL(-17.0,40.0)*x+RATIONAL(-49.0,400.0)+
-t193;
-      coeff_dx_p1_p2 = RATIONAL(69.0,400.0)+t178+t198+t200;
+      coeff_dx_p1_p1 = RATIONAL(3.0,50.0)*y+RATIONAL(103.0,400.0)+t196+t199;
+      coeff_dx_p2_p1 = t161+t184*x+RATIONAL(37.0,1200.0)+t178+t189;
+      coeff_dx_m1_p2 = RATIONAL(89.0,1200.0)+t169+t192+t193;
+      coeff_dx_0_p2 = RATIONAL(-17.0,40.0)*x+t166+RATIONAL(-49.0,400.0)+t164+
+t195;
+      coeff_dx_p1_p2 = t178+RATIONAL(69.0,400.0)+t197+t198;
       coeff_dx_p2_p2 = t163+RATIONAL(-149.0,1200.0)+t186*x+RATIONAL(-3.0,50.0)*
 y+t190;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dxx.compute.c
index 395eceb..29b5494 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dxx.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dxx.compute.c
@@ -1,40 +1,40 @@
-fp t243,
+fp t244,
    t258,
-   t245,
-   t257,
    t246,
+   t257,
+   t245,
    t256,
-   t244,
+   t243,
    t255,
    t250,
    t249,
    t248,
    t247;
-      t243 = RATIONAL(1.0,20.0)*y;
-      t258 = t243+RATIONAL(9.0,40.0);
-      t245 = RATIONAL(3.0,20.0)*y;
-      t257 = t245+RATIONAL(7.0,40.0);
-      t246 = RATIONAL(-3.0,20.0)*y;
-      t256 = t246+RATIONAL(13.0,40.0);
-      t244 = RATIONAL(-1.0,20.0)*y;
-      t255 = t244+RATIONAL(11.0,40.0);
-      t250 = RATIONAL(-1.0,4.0)*x;
-      t249 = RATIONAL(3.0,4.0)*x;
-      t248 = RATIONAL(-3.0,4.0)*x;
-      t247 = RATIONAL(1.0,4.0)*x;
-      coeff_dxx_m1_m1 = t250+t256;
-      coeff_dxx_0_m1 = RATIONAL(-23.0,40.0)+t245+t249;
-      coeff_dxx_p1_m1 = t248+t257;
-      coeff_dxx_p2_m1 = t246+t247+RATIONAL(3.0,40.0);
-      coeff_dxx_m1_0 = t250+t255;
-      coeff_dxx_0_0 = t243+RATIONAL(-21.0,40.0)+t249;
-      coeff_dxx_p1_0 = t248+t258;
-      coeff_dxx_p2_0 = RATIONAL(1.0,40.0)+t244+t247;
-      coeff_dxx_m1_p1 = t250+t258;
-      coeff_dxx_0_p1 = t244+RATIONAL(-19.0,40.0)+t249;
-      coeff_dxx_p1_p1 = t248+t255;
-      coeff_dxx_p2_p1 = t243+t247+RATIONAL(-1.0,40.0);
-      coeff_dxx_m1_p2 = t250+t257;
-      coeff_dxx_0_p2 = RATIONAL(-17.0,40.0)+t246+t249;
-      coeff_dxx_p1_p2 = t248+t256;
-      coeff_dxx_p2_p2 = RATIONAL(-3.0,40.0)+t247+t245;
+      t244 = RATIONAL(-3.0,20.0)*y;
+      t258 = t244+RATIONAL(13.0,40.0);
+      t246 = RATIONAL(-1.0,20.0)*y;
+      t257 = RATIONAL(11.0,40.0)+t246;
+      t245 = RATIONAL(1.0,20.0)*y;
+      t256 = RATIONAL(9.0,40.0)+t245;
+      t243 = RATIONAL(3.0,20.0)*y;
+      t255 = t243+RATIONAL(7.0,40.0);
+      t250 = RATIONAL(1.0,4.0)*x;
+      t249 = RATIONAL(-1.0,4.0)*x;
+      t248 = RATIONAL(3.0,4.0)*x;
+      t247 = RATIONAL(-3.0,4.0)*x;
+      coeff_dxx_m1_m1 = t249+t258;
+      coeff_dxx_0_m1 = t248+RATIONAL(-23.0,40.0)+t243;
+      coeff_dxx_p1_m1 = t247+t255;
+      coeff_dxx_p2_m1 = RATIONAL(3.0,40.0)+t250+t244;
+      coeff_dxx_m1_0 = t249+t257;
+      coeff_dxx_0_0 = RATIONAL(-21.0,40.0)+t245+t248;
+      coeff_dxx_p1_0 = t247+t256;
+      coeff_dxx_p2_0 = RATIONAL(1.0,40.0)+t246+t250;
+      coeff_dxx_m1_p1 = t249+t256;
+      coeff_dxx_0_p1 = t248+RATIONAL(-19.0,40.0)+t246;
+      coeff_dxx_p1_p1 = t247+t257;
+      coeff_dxx_p2_p1 = RATIONAL(-1.0,40.0)+t250+t245;
+      coeff_dxx_m1_p2 = t249+t255;
+      coeff_dxx_0_p2 = t244+RATIONAL(-17.0,40.0)+t248;
+      coeff_dxx_p1_p2 = t247+t258;
+      coeff_dxx_p2_p2 = RATIONAL(-3.0,40.0)+t250+t243;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dxy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dxy.compute.c
index b48e5bc..20e2106 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dxy.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dxy.compute.c
@@ -17,36 +17,36 @@ fp t276,
    t260,
    t259;
       t276 = RATIONAL(-1.0,50.0);
-      t275 = RATIONAL(-3.0,20.0);
-      t274 = RATIONAL(3.0,20.0);
-      t273 = RATIONAL(2.0,25.0);
+      t275 = RATIONAL(2.0,25.0);
+      t274 = RATIONAL(-3.0,20.0);
+      t273 = RATIONAL(3.0,20.0);
       t272 = RATIONAL(-1.0,20.0);
       t271 = RATIONAL(1.0,20.0);
       t270 = RATIONAL(-9.0,100.0);
-      t269 = RATIONAL(7.0,100.0);
-      t268 = RATIONAL(-1.0,100.0);
+      t269 = RATIONAL(-1.0,100.0);
+      t268 = RATIONAL(7.0,100.0);
       t267 = RATIONAL(-13.0,100.0);
-      t266 = t275*y;
-      t265 = t274*y;
-      t264 = t275*x;
+      t266 = t272*y;
+      t265 = t271*y;
+      t264 = t273*x;
       t263 = t274*x;
       t262 = t271*x;
       t261 = t272*x;
-      t260 = t272*y;
-      t259 = t271*y;
-      coeff_dxy_m1_m1 = t266+t264+RATIONAL(6.0,25.0);
-      coeff_dxy_0_m1 = t263+t260+t276;
-      coeff_dxy_p1_m1 = t263+t259+t267;
-      coeff_dxy_p2_m1 = t270+t264+t265;
-      coeff_dxy_m1_0 = t276+t261+t265;
-      coeff_dxy_0_0 = RATIONAL(-1.0,25.0)+t259+t262;
-      coeff_dxy_p1_0 = t268+t262+t260;
-      coeff_dxy_p2_0 = t261+t269+t266;
-      coeff_dxy_m1_p1 = t267+t262+t265;
-      coeff_dxy_0_p1 = t261+t268+t259;
-      coeff_dxy_p1_p1 = RATIONAL(3.0,50.0)+t261+t260;
-      coeff_dxy_p2_p1 = t266+t262+t273;
-      coeff_dxy_m1_p2 = t266+t263+t270;
-      coeff_dxy_0_p2 = t269+t264+t260;
-      coeff_dxy_p1_p2 = t264+t259+t273;
-      coeff_dxy_p2_p2 = t263+t265+RATIONAL(-3.0,50.0);
+      t260 = t274*y;
+      t259 = t273*y;
+      coeff_dxy_m1_m1 = t260+RATIONAL(6.0,25.0)+t263;
+      coeff_dxy_0_m1 = t276+t264+t266;
+      coeff_dxy_p1_m1 = t264+t267+t265;
+      coeff_dxy_p2_m1 = t263+t270+t259;
+      coeff_dxy_m1_0 = t276+t259+t261;
+      coeff_dxy_0_0 = t262+RATIONAL(-1.0,25.0)+t265;
+      coeff_dxy_p1_0 = t269+t262+t266;
+      coeff_dxy_p2_0 = t260+t268+t261;
+      coeff_dxy_m1_p1 = t262+t267+t259;
+      coeff_dxy_0_p1 = t269+t265+t261;
+      coeff_dxy_p1_p1 = RATIONAL(3.0,50.0)+t266+t261;
+      coeff_dxy_p2_p1 = t260+t275+t262;
+      coeff_dxy_m1_p2 = t264+t260+t270;
+      coeff_dxy_0_p2 = t268+t263+t266;
+      coeff_dxy_p1_p2 = t263+t275+t265;
+      coeff_dxy_p2_p2 = t259+RATIONAL(-3.0,50.0)+t264;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dy.compute.c
index 678f775..c766157 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dy.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dy.compute.c
@@ -1,95 +1,95 @@
 fp t242,
+   t225,
    t228,
-   t226,
    t212,
    t229,
    t220,
    t241,
-   t224,
-   t213,
+   t203,
    t240,
-   t202,
+   t204,
    t239,
-   t223,
+   t205,
    t238,
-   t204,
+   t224,
+   t213,
    t237,
+   t202,
    t236,
-   t227,
-   t217,
-   t221,
+   t226,
+   t215,
+   t222,
    t235,
-   t205,
+   t227,
+   t218,
    t234,
-   t203,
+   t221,
    t233,
-   t225,
-   t218,
    t232,
-   t222,
+   t223,
    t231,
    t230,
    t219,
-   t214,
+   t217,
    t209,
    t208,
    t207,
    t206;
       t242 = x*y;
+      t225 = RATIONAL(-1.0,40.0);
       t228 = x*x;
-      t226 = RATIONAL(-1.0,40.0);
-      t212 = t226*t228;
+      t212 = t225*t228;
       t229 = y*y;
-      t220 = RATIONAL(3.0,8.0)*t229;
+      t220 = RATIONAL(-3.0,8.0)*t229;
       t241 = t212+t220;
+      t203 = RATIONAL(1.0,20.0)*t242;
+      t240 = t203+RATIONAL(9.0,40.0)*y;
+      t204 = RATIONAL(-1.0,20.0)*t242;
+      t239 = RATIONAL(11.0,40.0)*y+t204;
+      t205 = RATIONAL(-3.0,20.0)*t242;
+      t238 = t205+RATIONAL(13.0,40.0)*y;
       t224 = RATIONAL(1.0,40.0);
       t213 = t224*t228;
-      t240 = t213+t220;
+      t237 = t213+t220;
       t202 = RATIONAL(3.0,20.0)*t242;
-      t239 = t202+RATIONAL(7.0,40.0)*y;
-      t223 = RATIONAL(-3.0,8.0)*t229;
-      t238 = t213+t223;
-      t204 = RATIONAL(1.0,20.0)*t242;
-      t237 = t204+RATIONAL(9.0,40.0)*y;
-      t236 = t212+t223;
+      t236 = RATIONAL(7.0,40.0)*y+t202;
+      t226 = RATIONAL(3.0,40.0);
+      t215 = t226*t228;
+      t222 = RATIONAL(-1.0,8.0)*t229;
+      t235 = t215+t222;
       t227 = RATIONAL(-3.0,40.0);
-      t217 = t227*t228;
-      t221 = RATIONAL(-1.0,8.0)*t229;
-      t235 = t217+t221;
-      t205 = RATIONAL(-3.0,20.0)*t242;
-      t234 = t205+RATIONAL(13.0,40.0)*y;
-      t203 = RATIONAL(-1.0,20.0)*t242;
-      t233 = t203+RATIONAL(11.0,40.0)*y;
-      t225 = RATIONAL(3.0,40.0);
-      t218 = t225*t228;
-      t232 = t218+t221;
-      t222 = RATIONAL(1.0,8.0)*t229;
-      t231 = t218+t222;
-      t230 = t217+t222;
+      t218 = t227*t228;
+      t234 = t218+t222;
+      t221 = RATIONAL(3.0,8.0)*t229;
+      t233 = t212+t221;
+      t232 = t213+t221;
+      t223 = RATIONAL(1.0,8.0)*t229;
+      t231 = t218+t223;
+      t230 = t215+t223;
       t219 = RATIONAL(2.0,25.0)*x;
-      t214 = RATIONAL(-1.0,50.0)*x;
-      t209 = RATIONAL(-1.0,100.0)*x;
-      t208 = RATIONAL(-9.0,100.0)*x;
-      t207 = RATIONAL(7.0,100.0)*x;
+      t217 = RATIONAL(-1.0,50.0)*x;
+      t209 = RATIONAL(-9.0,100.0)*x;
+      t208 = RATIONAL(7.0,100.0)*x;
+      t207 = RATIONAL(-1.0,100.0)*x;
       t206 = RATIONAL(-13.0,100.0)*x;
-      coeff_dy_m1_m1 = RATIONAL(-109.0,1200.0)+RATIONAL(6.0,25.0)*x+t234+t235;
-      coeff_dy_0_m1 = t214+RATIONAL(-223.0,1200.0)+t232+t233;
-      coeff_dy_p1_m1 = t206+RATIONAL(-157.0,1200.0)+t232+t237;
-      coeff_dy_p2_m1 = t208+RATIONAL(89.0,1200.0)+t235+t239;
-      coeff_dy_m1_0 = RATIONAL(-23.0,40.0)*y+t214+RATIONAL(-31.0,400.0)+t202+
-t241;
-      coeff_dy_0_0 = RATIONAL(-21.0,40.0)*y+RATIONAL(-57.0,400.0)+t204+RATIONAL
-(-1.0,25.0)*x+t240;
-      coeff_dy_p1_0 = t209+RATIONAL(-63.0,400.0)+t203+RATIONAL(-19.0,40.0)*y+
-t240;
-      coeff_dy_p2_0 = t207+RATIONAL(-49.0,400.0)+RATIONAL(-17.0,40.0)*y+t205+
-t241;
-      coeff_dy_m1_p1 = RATIONAL(111.0,400.0)+t206+t238+t239;
-      coeff_dy_0_p1 = RATIONAL(117.0,400.0)+t209+t236+t237;
-      coeff_dy_p1_p1 = RATIONAL(103.0,400.0)+RATIONAL(3.0,50.0)*x+t233+t236;
-      coeff_dy_p2_p1 = t219+RATIONAL(69.0,400.0)+t234+t238;
-      coeff_dy_m1_p2 = t225*y+t208+RATIONAL(-131.0,1200.0)+t205+t231;
-      coeff_dy_0_p2 = t207+t203+t224*y+RATIONAL(43.0,1200.0)+t230;
-      coeff_dy_p1_p2 = t219+t226*y+RATIONAL(37.0,1200.0)+t204+t230;
-      coeff_dy_p2_p2 = t202+RATIONAL(-3.0,50.0)*x+RATIONAL(-149.0,1200.0)+t227*
-y+t231;
+      coeff_dy_m1_m1 = RATIONAL(6.0,25.0)*x+RATIONAL(-109.0,1200.0)+t234+t238;
+      coeff_dy_0_m1 = RATIONAL(-223.0,1200.0)+t217+t235+t239;
+      coeff_dy_p1_m1 = t206+RATIONAL(-157.0,1200.0)+t235+t240;
+      coeff_dy_p2_m1 = t209+RATIONAL(89.0,1200.0)+t234+t236;
+      coeff_dy_m1_0 = RATIONAL(-23.0,40.0)*y+t202+RATIONAL(-31.0,400.0)+t217+
+t233;
+      coeff_dy_0_0 = RATIONAL(-1.0,25.0)*x+RATIONAL(-57.0,400.0)+t203+RATIONAL(
+-21.0,40.0)*y+t232;
+      coeff_dy_p1_0 = RATIONAL(-63.0,400.0)+t207+t204+RATIONAL(-19.0,40.0)*y+
+t232;
+      coeff_dy_p2_0 = t205+RATIONAL(-17.0,40.0)*y+RATIONAL(-49.0,400.0)+t208+
+t233;
+      coeff_dy_m1_p1 = RATIONAL(111.0,400.0)+t206+t236+t237;
+      coeff_dy_0_p1 = RATIONAL(117.0,400.0)+t207+t240+t241;
+      coeff_dy_p1_p1 = RATIONAL(3.0,50.0)*x+RATIONAL(103.0,400.0)+t239+t241;
+      coeff_dy_p2_p1 = t219+RATIONAL(69.0,400.0)+t237+t238;
+      coeff_dy_m1_p2 = t209+RATIONAL(-131.0,1200.0)+t205+t226*y+t230;
+      coeff_dy_0_p2 = t204+t208+t224*y+RATIONAL(43.0,1200.0)+t231;
+      coeff_dy_p1_p2 = t225*y+t219+t203+RATIONAL(37.0,1200.0)+t231;
+      coeff_dy_p2_p2 = RATIONAL(-149.0,1200.0)+t202+RATIONAL(-3.0,50.0)*x+t227*
+y+t230;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dyy.compute.c
index dea29f0..b449df9 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dyy.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order3.smooth0/coeff-dyy.compute.c
@@ -1,40 +1,40 @@
-fp t279,
+fp t277,
    t292,
-   t280,
+   t279,
    t291,
-   t278,
+   t280,
    t290,
-   t277,
+   t278,
    t289,
    t284,
    t283,
    t282,
    t281;
+      t277 = RATIONAL(3.0,20.0)*x;
+      t292 = t277+RATIONAL(7.0,40.0);
       t279 = RATIONAL(-1.0,20.0)*x;
-      t292 = t279+RATIONAL(11.0,40.0);
+      t291 = t279+RATIONAL(11.0,40.0);
       t280 = RATIONAL(-3.0,20.0)*x;
-      t291 = RATIONAL(13.0,40.0)+t280;
+      t290 = t280+RATIONAL(13.0,40.0);
       t278 = RATIONAL(1.0,20.0)*x;
-      t290 = t278+RATIONAL(9.0,40.0);
-      t277 = RATIONAL(3.0,20.0)*x;
-      t289 = t277+RATIONAL(7.0,40.0);
+      t289 = t278+RATIONAL(9.0,40.0);
       t284 = RATIONAL(-1.0,4.0)*y;
-      t283 = RATIONAL(1.0,4.0)*y;
-      t282 = RATIONAL(3.0,4.0)*y;
-      t281 = RATIONAL(-3.0,4.0)*y;
-      coeff_dyy_m1_m1 = t284+t291;
-      coeff_dyy_0_m1 = t284+t292;
-      coeff_dyy_p1_m1 = t284+t290;
-      coeff_dyy_p2_m1 = t284+t289;
-      coeff_dyy_m1_0 = t282+RATIONAL(-23.0,40.0)+t277;
-      coeff_dyy_0_0 = RATIONAL(-21.0,40.0)+t278+t282;
-      coeff_dyy_p1_0 = RATIONAL(-19.0,40.0)+t282+t279;
-      coeff_dyy_p2_0 = t280+t282+RATIONAL(-17.0,40.0);
-      coeff_dyy_m1_p1 = t281+t289;
-      coeff_dyy_0_p1 = t281+t290;
-      coeff_dyy_p1_p1 = t281+t292;
-      coeff_dyy_p2_p1 = t281+t291;
-      coeff_dyy_m1_p2 = t280+t283+RATIONAL(3.0,40.0);
-      coeff_dyy_0_p2 = t283+RATIONAL(1.0,40.0)+t279;
-      coeff_dyy_p1_p2 = t278+RATIONAL(-1.0,40.0)+t283;
-      coeff_dyy_p2_p2 = t277+t283+RATIONAL(-3.0,40.0);
+      t283 = RATIONAL(-3.0,4.0)*y;
+      t282 = RATIONAL(1.0,4.0)*y;
+      t281 = RATIONAL(3.0,4.0)*y;
+      coeff_dyy_m1_m1 = t284+t290;
+      coeff_dyy_0_m1 = t284+t291;
+      coeff_dyy_p1_m1 = t284+t289;
+      coeff_dyy_p2_m1 = t284+t292;
+      coeff_dyy_m1_0 = RATIONAL(-23.0,40.0)+t281+t277;
+      coeff_dyy_0_0 = t281+RATIONAL(-21.0,40.0)+t278;
+      coeff_dyy_p1_0 = RATIONAL(-19.0,40.0)+t279+t281;
+      coeff_dyy_p2_0 = t281+RATIONAL(-17.0,40.0)+t280;
+      coeff_dyy_m1_p1 = t283+t292;
+      coeff_dyy_0_p1 = t283+t289;
+      coeff_dyy_p1_p1 = t283+t291;
+      coeff_dyy_p2_p1 = t283+t290;
+      coeff_dyy_m1_p2 = t282+RATIONAL(3.0,40.0)+t280;
+      coeff_dyy_0_p2 = t282+RATIONAL(1.0,40.0)+t279;
+      coeff_dyy_p1_p2 = RATIONAL(-1.0,40.0)+t278+t282;
+      coeff_dyy_p2_p2 = t277+t282+RATIONAL(-3.0,40.0);
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-I.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-I.compute.c
index 49655f0..cfe391a 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-I.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-I.compute.c
@@ -1,239 +1,243 @@
-fp t413,
+fp t417,
    t418,
-   t466,
-   t403,
-   t417,
-   t358,
+   t468,
    t414,
+   t411,
+   t361,
+   t416,
    t373,
-   t438,
-   t444,
-   t465,
-   t405,
-   t364,
+   t435,
+   t446,
+   t467,
+   t410,
    t367,
-   t439,
+   t368,
+   t437,
+   t466,
+   t465,
+   t441,
    t464,
-   t436,
    t463,
-   t410,
-   t359,
-   t442,
-   t409,
-   t318,
-   t392,
-   t462,
-   t411,
-   t360,
-   t441,
+   t395,
+   t445,
    t400,
-   t298,
-   t461,
+   t403,
    t366,
-   t443,
-   t395,
+   t462,
+   t397,
+   t404,
+   t362,
    t401,
+   t461,
+   t389,
+   t409,
+   t316,
    t460,
-   t440,
-   t296,
-   t399,
+   t402,
+   t312,
+   t384,
    t459,
-   t372,
+   t412,
+   t443,
+   t407,
+   t309,
    t458,
-   t333,
+   t295,
+   t399,
+   t442,
    t457,
-   t396,
-   t412,
-   t327,
+   t406,
+   t405,
+   t319,
    t456,
-   t407,
-   t331,
-   t391,
+   t444,
+   t370,
    t455,
-   t402,
-   t313,
-   t397,
+   t315,
    t454,
    t325,
    t453,
-   t324,
+   t358,
+   t398,
+   t294,
    t452,
-   t311,
    t451,
+   t413,
+   t364,
    t450,
-   t387,
-   t398,
+   t357,
+   t380,
+   t381,
    t449,
+   t332,
    t415,
-   t371,
-   t416,
-   t357,
-   t383,
-   t382,
-   t448,
-   t317,
    t356,
+   t448,
    t447,
-   t362,
-   t446,
-   t445,
-   t437,
-   t435,
-   t393,
-   t404,
-   t369,
-   t376,
+   t440,
+   t360,
+   t439,
+   t438,
+   t436,
+   t390,
+   t408,
+   t363,
+   t392,
    t434,
-   t365,
-   t384,
    t386,
+   t374,
    t433,
+   t372,
    t432,
    t431,
+   t317,
    t430,
    t429,
+   t326,
    t428,
    t427,
-   t406,
+   t385,
    t426,
    t425,
-   t408,
+   t388,
    t424,
    t423,
    t394,
-   t389,
-   t388,
-   t385;
-      t413 = x*x;
+   t393,
+   t391,
+   t387;
+      t417 = x*x;
       t418 = y*y;
-      t466 = t418+t413;
-      t403 = RATIONAL(-1.0,60.0);
-      t417 = y*t418;
-      t358 = t403*t417;
-      t414 = t413*x;
-      t373 = t403*t414;
-      t438 = y*t373+x*t358;
-      t444 = x*y;
-      t465 = t438+RATIONAL(37.0,300.0)*t444;
-      t405 = RATIONAL(1.0,60.0);
-      t364 = t405*t414;
-      t367 = t405*t417;
-      t439 = y*t364+x*t367;
-      t464 = t439+RATIONAL(-37.0,300.0)*t444;
-      t436 = t413*t418;
-      t463 = RATIONAL(-99.0,1225.0)+RATIONAL(-1.0,98.0)*t436;
-      t410 = RATIONAL(-1.0,30.0);
-      t359 = t410*t417;
-      t442 = y*t413;
-      t409 = RATIONAL(1.0,70.0);
-      t318 = t409*t442;
-      t392 = RATIONAL(11.0,105.0);
-      t462 = t359+t318+t392*y;
-      t411 = RATIONAL(1.0,30.0);
-      t360 = t411*t417;
-      t441 = y*t414;
-      t400 = RATIONAL(-1.0,120.0);
-      t298 = RATIONAL(-21.0,200.0)*t444;
-      t461 = x*t360+t298+t400*t441;
-      t366 = t410*t414;
-      t443 = x*t418;
-      t395 = RATIONAL(31.0,210.0);
+      t468 = t418+t417;
+      t414 = t417*x;
+      t411 = RATIONAL(1.0,60.0);
+      t361 = t411*t414;
+      t416 = y*t418;
+      t373 = t411*t416;
+      t435 = x*t373+y*t361;
+      t446 = x*y;
+      t467 = RATIONAL(-11.0,150.0)*t446+t435;
+      t410 = RATIONAL(-1.0,60.0);
+      t367 = t410*t416;
+      t368 = t410*t414;
+      t437 = x*t367+y*t368;
+      t466 = RATIONAL(37.0,300.0)*t446+t437;
+      t465 = t437+RATIONAL(11.0,150.0)*t446;
+      t441 = t417*t418;
+      t464 = RATIONAL(-1.0,98.0)*t441+RATIONAL(-99.0,1225.0);
+      t463 = RATIONAL(-37.0,300.0)*t446+t435;
+      t395 = RATIONAL(-31.0,210.0);
+      t445 = x*t418;
+      t400 = RATIONAL(1.0,140.0);
+      t403 = RATIONAL(1.0,30.0);
+      t366 = t403*t414;
+      t462 = t400*t445+t395*x+t366;
+      t397 = RATIONAL(31.0,210.0);
+      t404 = RATIONAL(-1.0,30.0);
+      t362 = t404*t414;
       t401 = RATIONAL(-1.0,140.0);
-      t460 = t395*x+t366+t401*t443;
-      t440 = x*t417;
-      t296 = RATIONAL(21.0,200.0)*t444;
+      t461 = t362+t401*t445+t397*x;
+      t389 = RATIONAL(31.0,420.0);
+      t409 = RATIONAL(-1.0,35.0);
+      t316 = t409*t445;
+      t460 = t389*x+t316+t368;
+      t402 = RATIONAL(1.0,35.0);
+      t312 = t402*t445;
+      t384 = RATIONAL(-31.0,420.0);
+      t459 = t312+t384*x+t361;
+      t412 = RATIONAL(1.0,84.0);
+      t443 = y*t417;
+      t407 = RATIONAL(-1.0,70.0);
+      t309 = t407*t443;
+      t458 = t309+t412*y+t373;
+      t295 = RATIONAL(21.0,200.0)*t446;
       t399 = RATIONAL(1.0,120.0);
-      t459 = t296+y*t366+t399*t440;
-      t372 = t411*t414;
-      t458 = t400*t440+y*t372+t298;
-      t333 = t409*t443;
-      t457 = t366+t333+t392*x;
-      t396 = RATIONAL(-11.0,105.0);
-      t412 = RATIONAL(-1.0,70.0);
-      t327 = t412*t443;
-      t456 = t396*x+t372+t327;
-      t407 = RATIONAL(1.0,35.0);
-      t331 = t407*t442;
-      t391 = RATIONAL(-31.0,420.0);
-      t455 = t331+t391*y+t367;
-      t402 = RATIONAL(-1.0,35.0);
-      t313 = t402*t442;
-      t397 = RATIONAL(31.0,420.0);
-      t454 = t358+t397*y+t313;
-      t325 = t402*t443;
-      t453 = t397*x+t325+t373;
-      t324 = t407*t443;
-      t452 = t364+t324+t391*x;
-      t311 = t412*t442;
-      t451 = t360+t311+t396*y;
-      t450 = x*t359+t296+t399*t441;
-      t387 = RATIONAL(-31.0,210.0);
-      t398 = RATIONAL(1.0,140.0);
-      t449 = t372+t387*x+t398*t443;
-      t415 = t413*t413;
-      t371 = t410*t415;
-      t416 = t418*t418;
-      t357 = t399*t416;
-      t383 = RATIONAL(71.0,5880.0);
-      t382 = RATIONAL(113.0,735.0);
-      t448 = t371+t382*t413+t383*t418+t357+t463;
-      t317 = RATIONAL(1.0,49.0)*t436;
+      t442 = x*t416;
+      t457 = t295+t399*t442+y*t362;
+      t406 = RATIONAL(-1.0,84.0);
+      t405 = RATIONAL(1.0,70.0);
+      t319 = t405*t443;
+      t456 = t406*y+t319+t367;
+      t444 = t414*y;
+      t370 = t404*t416;
+      t455 = t295+t399*t444+x*t370;
+      t315 = t405*t445;
+      t454 = t406*x+t315+t368;
+      t325 = t407*t445;
+      t453 = t361+t412*x+t325;
+      t358 = t403*t416;
+      t398 = RATIONAL(-1.0,120.0);
+      t294 = RATIONAL(-21.0,200.0)*t446;
+      t452 = t398*t444+t294+x*t358;
+      t451 = y*t366+t398*t442+t294;
+      t413 = t417*t417;
+      t364 = t404*t413;
+      t450 = RATIONAL(-24.0,1225.0)+t364+RATIONAL(1.0,196.0)*t441+t468*RATIONAL
+(181.0,1470.0);
+      t357 = t399*t413;
+      t380 = RATIONAL(71.0,5880.0);
+      t381 = RATIONAL(113.0,735.0);
+      t449 = t357+t380*t417+t381*t418+t464;
+      t332 = RATIONAL(1.0,49.0)*t441;
+      t415 = t418*t418;
       t356 = t399*t415;
-      t447 = t317+RATIONAL(51.0,1225.0)+t356+t357+t466*RATIONAL(-289.0,5880.0);
-      t362 = t410*t416;
-      t446 = t382*t418+t356+t383*t413+t362+t463;
-      t445 = t362+RATIONAL(1.0,196.0)*t436+t371+RATIONAL(-24.0,1225.0)+t466*
-RATIONAL(181.0,1470.0);
-      t437 = RATIONAL(-1.0,49.0)*t436+RATIONAL(96.0,1225.0);
-      t435 = RATIONAL(1.0,98.0)*t436+RATIONAL(246.0,1225.0);
-      t393 = RATIONAL(-41.0,196.0);
-      t404 = RATIONAL(1.0,20.0);
-      t369 = t404*t415;
-      t376 = RATIONAL(191.0,5880.0);
-      t434 = t376*t418+t369+t357+t393*t413+t437;
-      t365 = t404*t416;
-      t384 = RATIONAL(-53.0,196.0);
-      t386 = RATIONAL(83.0,735.0);
-      t433 = t365+t371+t384*t418+t386*t413+t435;
-      t432 = t365+t376*t413+t356+t393*t418+t437;
-      t431 = t369+t384*t413+t362+t386*t418+t435;
-      t430 = RATIONAL(-11.0,150.0)*t444+t439+t447;
-      t429 = t359+t395*y+t401*t442+t445;
-      t428 = t360+t387*y+t398*t442+t445;
-      t427 = RATIONAL(11.0,150.0)*t444+t438+t447;
-      t406 = RATIONAL(1.0,84.0);
-      t426 = t367+t311+t406*y+t448;
-      t425 = t364+t406*x+t327+t446;
-      t408 = RATIONAL(-1.0,84.0);
-      t424 = t358+t318+t408*y+t448;
-      t423 = t333+t408*x+t373+t446;
-      t394 = RATIONAL(-17.0,420.0);
-      t389 = RATIONAL(17.0,105.0);
-      t388 = RATIONAL(17.0,420.0);
-      t385 = RATIONAL(-17.0,105.0);
-      coeff_I_m2_m2 = t430+t453+t454;
-      coeff_I_m1_m2 = t424+t456+t459;
-      coeff_I_0_m2 = t331+t394*y+t358+t434;
-      coeff_I_p1_m2 = t424+t457+t458;
-      coeff_I_p2_m2 = t427+t452+t454;
-      coeff_I_m2_m1 = t423+t450+t451;
-      coeff_I_m1_m1 = t428+t449+t465;
-      coeff_I_0_m1 = t360+t385*y+t318+t431;
-      coeff_I_p1_m1 = t428+t460+t464;
-      coeff_I_p2_m1 = t425+t451+t461;
-      coeff_I_m2_0 = t373+t394*x+t324+t432;
-      coeff_I_m1_0 = t385*x+t333+t372+t433;
-      coeff_I_0_0 = t317+t365+t369+RATIONAL(541.0,1225.0)+t466*RATIONAL(-57.0,
+      t448 = RATIONAL(51.0,1225.0)+t357+t332+t356+t468*RATIONAL(-289.0,5880.0);
+      t447 = t380*t418+t364+t381*t417+t356+t464;
+      t440 = RATIONAL(1.0,98.0)*t441+RATIONAL(246.0,1225.0);
+      t360 = t404*t415;
+      t439 = t360+t370;
+      t438 = t358+t360;
+      t436 = RATIONAL(-1.0,49.0)*t441+RATIONAL(96.0,1225.0);
+      t390 = RATIONAL(83.0,735.0);
+      t408 = RATIONAL(1.0,20.0);
+      t363 = t408*t413;
+      t392 = RATIONAL(-53.0,196.0);
+      t434 = t360+t390*t418+t363+t392*t417+t440;
+      t386 = RATIONAL(-41.0,196.0);
+      t374 = RATIONAL(191.0,5880.0);
+      t433 = t386*t417+t374*t418+t363+t356+t436;
+      t372 = t408*t415;
+      t432 = t357+t374*t417+t386*t418+t372+t436;
+      t431 = t364+t392*t418+t390*t417+t372+t440;
+      t317 = t402*t443;
+      t430 = t384*y+t317+t373+t448;
+      t429 = t395*y+t400*t443+t438+t450;
+      t326 = t409*t443;
+      t428 = t389*y+t367+t326+t448;
+      t427 = t397*y+t401*t443+t439+t450;
+      t385 = RATIONAL(11.0,105.0);
+      t426 = t385*x+t315+t362+t447;
+      t425 = t385*y+t319+t439+t449;
+      t388 = RATIONAL(-11.0,105.0);
+      t424 = t388*y+t309+t438+t449;
+      t423 = t388*x+t366+t325+t447;
+      t394 = RATIONAL(17.0,420.0);
+      t393 = RATIONAL(17.0,105.0);
+      t391 = RATIONAL(-17.0,105.0);
+      t387 = RATIONAL(-17.0,420.0);
+      coeff_I_m2_m2 = t428+t460+t467;
+      coeff_I_m1_m2 = t423+t456+t457;
+      coeff_I_0_m2 = t317+t367+t387*y+t433;
+      coeff_I_p1_m2 = t426+t451+t456;
+      coeff_I_p2_m2 = t428+t459+t465;
+      coeff_I_m2_m1 = t424+t454+t455;
+      coeff_I_m1_m1 = t429+t462+t466;
+      coeff_I_0_m1 = t319+t391*y+t358+t434;
+      coeff_I_p1_m1 = t429+t461+t463;
+      coeff_I_p2_m1 = t424+t452+t453;
+      coeff_I_m2_0 = t368+t312+t387*x+t432;
+      coeff_I_m1_0 = t366+t315+t391*x+t431;
+      coeff_I_0_0 = RATIONAL(541.0,1225.0)+t363+t372+t332+t468*RATIONAL(-57.0,
 196.0);
-      coeff_I_p1_0 = t389*x+t327+t366+t433;
-      coeff_I_p2_0 = t325+t364+t388*x+t432;
-      coeff_I_m2_p1 = t423+t461+t462;
-      coeff_I_m1_p1 = t429+t449+t464;
-      coeff_I_0_p1 = t359+t389*y+t311+t431;
-      coeff_I_p1_p1 = t429+t460+t465;
-      coeff_I_p2_p1 = t425+t450+t462;
-      coeff_I_m2_p2 = t427+t453+t455;
-      coeff_I_m1_p2 = t426+t456+t458;
-      coeff_I_0_p2 = t313+t388*y+t367+t434;
-      coeff_I_p1_p2 = t426+t457+t459;
-      coeff_I_p2_p2 = t430+t452+t455;
+      coeff_I_p1_0 = t325+t362+t393*x+t431;
+      coeff_I_p2_0 = t394*x+t316+t361+t432;
+      coeff_I_m2_p1 = t425+t452+t454;
+      coeff_I_m1_p1 = t427+t462+t463;
+      coeff_I_0_p1 = t309+t370+t393*y+t434;
+      coeff_I_p1_p1 = t427+t461+t466;
+      coeff_I_p2_p1 = t425+t453+t455;
+      coeff_I_m2_p2 = t430+t460+t465;
+      coeff_I_m1_p2 = t423+t451+t458;
+      coeff_I_0_p2 = t394*y+t326+t373+t433;
+      coeff_I_p1_p2 = t426+t457+t458;
+      coeff_I_p2_p2 = t430+t459+t467;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dx.compute.c
index 83ba345..e56ee74 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dx.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dx.compute.c
@@ -1,48 +1,54 @@
-fp t531,
-   t534,
-   t535,
-   t513,
-   t570,
-   t508,
-   t569,
+fp t538,
+   t507,
+   t539,
    t537,
+   t559,
+   t573,
+   t560,
+   t572,
+   t514,
+   t554,
+   t571,
+   t526,
    t536,
-   t502,
-   t552,
+   t516,
+   t570,
+   t531,
+   t517,
+   t569,
+   t481,
    t568,
-   t512,
-   t555,
+   t561,
+   t494,
    t567,
-   t556,
+   t495,
    t566,
-   t509,
-   t533,
-   t510,
-   t565,
-   t530,
+   t525,
    t506,
-   t507,
+   t565,
+   t510,
    t564,
+   t511,
    t563,
-   t471,
    t562,
-   t561,
-   t523,
-   t511,
-   t560,
-   t528,
-   t504,
-   t559,
+   t475,
+   t527,
+   t509,
    t558,
+   t513,
    t557,
+   t529,
+   t512,
+   t556,
+   t555,
+   t518,
    t478,
-   t554,
    t553,
-   t516,
-   t476,
+   t479,
+   t552,
    t551,
-   t483,
    t550,
+   t490,
    t549,
    t548,
    t547,
@@ -51,97 +57,99 @@ fp t531,
    t544,
    t543,
    t542,
-   t541,
-   t540,
-   t484,
+   t486,
+   t482,
    t477,
-   t475,
-   t473,
-   t469,
-   t467;
-      t531 = RATIONAL(1.0,30.0);
-      t534 = x*x;
-      t535 = t534*x;
-      t513 = t531*t535;
-      t570 = t513+RATIONAL(71.0,2940.0)*x;
-      t508 = RATIONAL(-2.0,15.0)*t535;
-      t569 = t508+RATIONAL(226.0,735.0)*x;
-      t537 = y*y;
-      t536 = y*t537;
-      t502 = RATIONAL(1.0,20.0)*t534;
-      t552 = RATIONAL(1.0,60.0)*t536+y*t502;
-      t568 = t552+RATIONAL(-37.0,300.0)*y;
-      t512 = RATIONAL(-1.0,20.0)*t534;
-      t555 = y*t512+RATIONAL(-1.0,60.0)*t536;
-      t567 = t555+RATIONAL(37.0,300.0)*y;
-      t556 = x*t537;
-      t566 = t508+RATIONAL(181.0,735.0)*x+RATIONAL(1.0,98.0)*t556;
-      t509 = RATIONAL(1.0,10.0)*t534;
-      t533 = RATIONAL(-1.0,70.0);
-      t510 = t533*t537;
-      t565 = t509+t510+RATIONAL(-11.0,105.0);
-      t530 = RATIONAL(1.0,70.0);
-      t506 = t530*t537;
-      t507 = RATIONAL(-1.0,10.0)*t534;
-      t564 = t506+t507+RATIONAL(11.0,105.0);
-      t563 = t510+RATIONAL(1.0,84.0)+t502;
-      t471 = RATIONAL(2.0,49.0)*t556;
-      t562 = t513+t471+RATIONAL(-289.0,2940.0)*x;
-      t561 = t506+t512+RATIONAL(-1.0,84.0);
-      t523 = RATIONAL(-1.0,35.0);
-      t511 = t523*t537;
-      t560 = t511+t512+RATIONAL(31.0,420.0);
-      t528 = RATIONAL(1.0,35.0);
-      t504 = t528*t537;
-      t559 = RATIONAL(-31.0,420.0)+t502+t504;
-      t558 = x*y;
-      t557 = y*t534;
-      t478 = RATIONAL(-1.0,49.0)*t556;
-      t554 = RATIONAL(-21.0,200.0)*y+t478;
-      t553 = RATIONAL(21.0,200.0)*y+t478;
-      t516 = RATIONAL(1.0,5.0)*t535;
-      t476 = RATIONAL(-2.0,49.0)*t556;
-      t551 = t516+t476+RATIONAL(-41.0,98.0)*x;
-      t483 = RATIONAL(1.0,49.0)*t556;
-      t550 = t516+t483+RATIONAL(-53.0,98.0)*x;
-      t549 = t508+RATIONAL(166.0,735.0)*x+t483;
-      t548 = t513+t476+RATIONAL(191.0,2940.0)*x;
-      t547 = t509+RATIONAL(-31.0,210.0)+RATIONAL(1.0,140.0)*t537+t566;
-      t546 = RATIONAL(11.0,150.0)*y+t555+t562;
-      t545 = y*t509+RATIONAL(-1.0,120.0)*t536+t554+t569;
-      t544 = t507+RATIONAL(31.0,210.0)+RATIONAL(-1.0,140.0)*t537+t566;
-      t543 = y*t507+RATIONAL(1.0,120.0)*t536+t553+t569;
-      t542 = t531*t536+RATIONAL(-1.0,40.0)*t557+t554+t570;
-      t541 = RATIONAL(-11.0,150.0)*y+t552+t562;
-      t540 = RATIONAL(1.0,40.0)*t557+RATIONAL(-1.0,30.0)*t536+t553+t570;
-      t484 = t530*t558;
-      t477 = t528*t558;
-      t475 = RATIONAL(2.0,35.0)*t558;
-      t473 = t533*t558;
-      t469 = RATIONAL(-2.0,35.0)*t558;
-      t467 = t523*t558;
-      coeff_dx_m2_m2 = t469+t541+t560;
-      coeff_dx_m1_m2 = t477+t543+t565;
-      coeff_dx_0_m2 = t475+t551;
-      coeff_dx_p1_m2 = t477+t545+t564;
-      coeff_dx_p2_m2 = t469+t546+t559;
-      coeff_dx_m2_m1 = t467+t540+t561;
-      coeff_dx_m1_m1 = t484+t547+t567;
-      coeff_dx_0_m1 = t477+t550;
-      coeff_dx_p1_m1 = t484+t544+t568;
-      coeff_dx_p2_m1 = t467+t542+t563;
-      coeff_dx_m2_0 = t504+t512+RATIONAL(-17.0,420.0)+t548;
-      coeff_dx_m1_0 = RATIONAL(-17.0,105.0)+t509+t506+t549;
-      coeff_dx_0_0 = RATIONAL(-57.0,98.0)*x+t516+t471;
-      coeff_dx_p1_0 = t510+RATIONAL(17.0,105.0)+t507+t549;
-      coeff_dx_p2_0 = t511+RATIONAL(17.0,420.0)+t502+t548;
-      coeff_dx_m2_p1 = t477+t542+t561;
-      coeff_dx_m1_p1 = t473+t547+t568;
-      coeff_dx_0_p1 = t467+t550;
-      coeff_dx_p1_p1 = t473+t544+t567;
-      coeff_dx_p2_p1 = t477+t540+t563;
-      coeff_dx_m2_p2 = t475+t546+t560;
-      coeff_dx_m1_p2 = t467+t545+t565;
-      coeff_dx_0_p2 = t469+t551;
-      coeff_dx_p1_p2 = t467+t543+t564;
-      coeff_dx_p2_p2 = t475+t541+t559;
+   t474,
+   t471,
+   t469;
+      t538 = x*x;
+      t507 = RATIONAL(1.0,20.0)*t538;
+      t539 = y*y;
+      t537 = y*t539;
+      t559 = y*t507+RATIONAL(1.0,60.0)*t537;
+      t573 = RATIONAL(-37.0,300.0)*y+t559;
+      t560 = x*t539;
+      t572 = RATIONAL(1.0,98.0)*t560+RATIONAL(181.0,735.0)*x;
+      t514 = RATIONAL(-1.0,20.0)*t538;
+      t554 = y*t514+RATIONAL(-1.0,60.0)*t537;
+      t571 = RATIONAL(37.0,300.0)*y+t554;
+      t526 = RATIONAL(1.0,30.0);
+      t536 = x*t538;
+      t516 = t526*t536;
+      t570 = RATIONAL(71.0,2940.0)*x+t516;
+      t531 = RATIONAL(-1.0,35.0);
+      t517 = t531*t539;
+      t569 = RATIONAL(31.0,420.0)+t514+t517;
+      t481 = RATIONAL(2.0,49.0)*t560;
+      t568 = RATIONAL(-289.0,2940.0)*x+t481+t516;
+      t561 = y*t538;
+      t494 = RATIONAL(-21.0,200.0)*y;
+      t567 = RATIONAL(-1.0,40.0)*t561+t494+t526*t537;
+      t495 = RATIONAL(21.0,200.0)*y;
+      t566 = RATIONAL(1.0,40.0)*t561+t495+RATIONAL(-1.0,30.0)*t537;
+      t525 = RATIONAL(1.0,35.0);
+      t506 = t525*t539;
+      t565 = RATIONAL(-31.0,420.0)+t507+t506;
+      t510 = RATIONAL(-1.0,10.0)*t538;
+      t564 = y*t510+t495+RATIONAL(1.0,120.0)*t537;
+      t511 = RATIONAL(1.0,10.0)*t538;
+      t563 = y*t511+t494+RATIONAL(-1.0,120.0)*t537;
+      t562 = x*y;
+      t475 = RATIONAL(-1.0,49.0)*t560;
+      t527 = RATIONAL(1.0,70.0);
+      t509 = t527*t539;
+      t558 = t475+t509;
+      t513 = RATIONAL(-2.0,15.0)*t536;
+      t557 = t510+t513;
+      t529 = RATIONAL(-1.0,70.0);
+      t512 = t529*t539;
+      t556 = t475+t512;
+      t555 = t511+t513;
+      t518 = RATIONAL(1.0,5.0)*t536;
+      t478 = RATIONAL(-2.0,49.0)*t560;
+      t553 = t518+RATIONAL(-41.0,98.0)*x+t478;
+      t479 = RATIONAL(1.0,49.0)*t560;
+      t552 = t518+RATIONAL(-53.0,98.0)*x+t479;
+      t551 = RATIONAL(191.0,2940.0)*x+t478+t516;
+      t550 = RATIONAL(166.0,735.0)*x+t479+t513;
+      t490 = RATIONAL(226.0,735.0)*x;
+      t549 = RATIONAL(11.0,105.0)+t490+t557+t558;
+      t548 = t490+RATIONAL(-11.0,105.0)+t555+t556;
+      t547 = RATIONAL(-31.0,210.0)+RATIONAL(1.0,140.0)*t539+t555+t572;
+      t546 = RATIONAL(31.0,210.0)+RATIONAL(-1.0,140.0)*t539+t557+t572;
+      t545 = RATIONAL(1.0,84.0)+t507+t556+t570;
+      t544 = RATIONAL(-11.0,150.0)*y+t559+t568;
+      t543 = RATIONAL(-1.0,84.0)+t514+t558+t570;
+      t542 = RATIONAL(11.0,150.0)*y+t554+t568;
+      t486 = t525*t562;
+      t482 = RATIONAL(-2.0,35.0)*t562;
+      t477 = RATIONAL(2.0,35.0)*t562;
+      t474 = t531*t562;
+      t471 = t527*t562;
+      t469 = t529*t562;
+      coeff_dx_m2_m2 = t482+t544+t569;
+      coeff_dx_m1_m2 = t486+t548+t564;
+      coeff_dx_0_m2 = t477+t553;
+      coeff_dx_p1_m2 = t486+t549+t563;
+      coeff_dx_p2_m2 = t482+t542+t565;
+      coeff_dx_m2_m1 = t474+t543+t566;
+      coeff_dx_m1_m1 = t471+t547+t571;
+      coeff_dx_0_m1 = t486+t552;
+      coeff_dx_p1_m1 = t471+t546+t573;
+      coeff_dx_p2_m1 = t474+t545+t567;
+      coeff_dx_m2_0 = t514+RATIONAL(-17.0,420.0)+t506+t551;
+      coeff_dx_m1_0 = t511+RATIONAL(-17.0,105.0)+t509+t550;
+      coeff_dx_0_0 = t481+t518+RATIONAL(-57.0,98.0)*x;
+      coeff_dx_p1_0 = RATIONAL(17.0,105.0)+t510+t512+t550;
+      coeff_dx_p2_0 = t507+RATIONAL(17.0,420.0)+t517+t551;
+      coeff_dx_m2_p1 = t486+t543+t567;
+      coeff_dx_m1_p1 = t469+t547+t573;
+      coeff_dx_0_p1 = t474+t552;
+      coeff_dx_p1_p1 = t469+t546+t571;
+      coeff_dx_p2_p1 = t486+t545+t566;
+      coeff_dx_m2_p2 = t477+t542+t569;
+      coeff_dx_m1_p2 = t474+t548+t563;
+      coeff_dx_0_p2 = t482+t553;
+      coeff_dx_p1_p2 = t474+t549+t564;
+      coeff_dx_p2_p2 = t477+t544+t565;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dxx.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dxx.compute.c
index 385d8a7..3ac1e8c 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dxx.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dxx.compute.c
@@ -1,111 +1,107 @@
-fp t712,
-   t692,
-   t707,
-   t711,
-   t693,
-   t729,
+fp t713,
+   t683,
+   t708,
+   t712,
    t687,
+   t730,
+   t696,
+   t729,
    t728,
-   t697,
+   t690,
    t727,
    t726,
-   t725,
+   t697,
    t686,
-   t694,
-   t695,
    t698,
-   t689,
+   t691,
+   t693,
+   t725,
+   t699,
    t724,
-   t681,
+   t682,
    t723,
-   t696,
    t722,
+   t695,
    t721,
-   t688,
    t720,
-   t691,
+   t689,
    t719,
-   t685,
    t718,
    t717,
    t716,
-   t690,
+   t678,
    t715,
+   t676,
    t714,
-   t713,
-   t684,
-   t683,
+   t694,
+   t685,
+   t681,
    t680,
    t679,
-   t678,
-   t677,
-   t676,
-   t675;
-      t712 = y*y;
-      t692 = RATIONAL(2.0,49.0)*t712;
-      t707 = RATIONAL(1.0,10.0);
-      t711 = x*x;
-      t693 = t707*t711;
-      t729 = t692+t693+RATIONAL(-289.0,2940.0);
-      t687 = RATIONAL(-1.0,49.0)*t712;
-      t728 = t693+RATIONAL(71.0,2940.0)+t687;
-      t697 = RATIONAL(-2.0,5.0)*t711;
-      t727 = t697+RATIONAL(226.0,735.0)+t687;
-      t726 = t697+RATIONAL(181.0,735.0)+RATIONAL(1.0,98.0)*t712;
-      t725 = x*y;
-      t686 = t707*x;
-      t694 = RATIONAL(-1.0,10.0)*x;
-      t695 = RATIONAL(-1.0,5.0)*x;
-      t698 = RATIONAL(1.0,5.0)*x;
-      t689 = RATIONAL(-2.0,49.0)*t712;
-      t724 = t693+RATIONAL(191.0,2940.0)+t689;
-      t681 = RATIONAL(1.0,49.0)*t712;
-      t723 = t697+RATIONAL(166.0,735.0)+t681;
-      t696 = RATIONAL(3.0,5.0)*t711;
-      t722 = t696+RATIONAL(-53.0,98.0)+t681;
-      t721 = t696+RATIONAL(-41.0,98.0)+t689;
-      t688 = RATIONAL(2.0,35.0)*y;
-      t720 = t688+t729;
-      t691 = RATIONAL(-2.0,35.0)*y;
-      t719 = t691+t729;
-      t685 = RATIONAL(-1.0,35.0)*y;
-      t718 = t685+t727;
-      t717 = t686+t728;
-      t716 = t695+t726;
-      t690 = RATIONAL(1.0,35.0)*y;
-      t715 = t690+t727;
-      t714 = t698+t726;
-      t713 = t694+t728;
-      t684 = RATIONAL(1.0,70.0)*y;
-      t683 = RATIONAL(-1.0,70.0)*y;
-      t680 = y*t695;
-      t679 = y*t698;
-      t678 = RATIONAL(-1.0,20.0)*t725;
-      t677 = y*t686;
-      t676 = y*t694;
-      t675 = RATIONAL(1.0,20.0)*t725;
-      coeff_dxx_m2_m2 = t677+t694+t719;
-      coeff_dxx_m1_m2 = t680+t698+t715;
-      coeff_dxx_0_m2 = t688+t721;
-      coeff_dxx_p1_m2 = t679+t695+t715;
-      coeff_dxx_p2_m2 = t686+t676+t719;
-      coeff_dxx_m2_m1 = t685+t675+t713;
-      coeff_dxx_m1_m1 = t676+t684+t714;
-      coeff_dxx_0_m1 = t690+t722;
-      coeff_dxx_p1_m1 = t684+t677+t716;
-      coeff_dxx_p2_m1 = t685+t678+t717;
-      coeff_dxx_m2_0 = t694+t724;
-      coeff_dxx_m1_0 = t698+t723;
-      coeff_dxx_0_0 = t692+RATIONAL(-57.0,98.0)+t696;
-      coeff_dxx_p1_0 = t695+t723;
-      coeff_dxx_p2_0 = t686+t724;
-      coeff_dxx_m2_p1 = t690+t678+t713;
-      coeff_dxx_m1_p1 = t677+t683+t714;
-      coeff_dxx_0_p1 = t685+t722;
-      coeff_dxx_p1_p1 = t683+t676+t716;
-      coeff_dxx_p2_p1 = t690+t675+t717;
-      coeff_dxx_m2_p2 = t676+t694+t720;
-      coeff_dxx_m1_p2 = t698+t679+t718;
-      coeff_dxx_0_p2 = t691+t721;
-      coeff_dxx_p1_p2 = t695+t680+t718;
-      coeff_dxx_p2_p2 = t686+t677+t720;
+   t677;
+      t713 = y*y;
+      t683 = RATIONAL(-1.0,49.0)*t713;
+      t708 = RATIONAL(1.0,10.0);
+      t712 = x*x;
+      t687 = t708*t712;
+      t730 = RATIONAL(71.0,2940.0)+t683+t687;
+      t696 = RATIONAL(-2.0,5.0)*t712;
+      t729 = t696+RATIONAL(226.0,735.0)+t683;
+      t728 = t696+RATIONAL(181.0,735.0)+RATIONAL(1.0,98.0)*t713;
+      t690 = RATIONAL(2.0,49.0)*t713;
+      t727 = t690+RATIONAL(-289.0,2940.0)+t687;
+      t726 = x*y;
+      t697 = RATIONAL(1.0,5.0)*x;
+      t686 = RATIONAL(-1.0,10.0)*x;
+      t698 = RATIONAL(-1.0,5.0)*x;
+      t691 = t708*x;
+      t693 = RATIONAL(-2.0,49.0)*t713;
+      t725 = t693+RATIONAL(191.0,2940.0)+t687;
+      t699 = RATIONAL(3.0,5.0)*t712;
+      t724 = t693+t699+RATIONAL(-41.0,98.0);
+      t682 = RATIONAL(1.0,49.0)*t713;
+      t723 = t699+RATIONAL(-53.0,98.0)+t682;
+      t722 = t696+RATIONAL(166.0,735.0)+t682;
+      t695 = RATIONAL(1.0,35.0)*y;
+      t721 = t695+t730;
+      t720 = RATIONAL(-1.0,70.0)*y+t728;
+      t689 = RATIONAL(-1.0,35.0)*y;
+      t719 = t689+t730;
+      t718 = t698+t729;
+      t717 = RATIONAL(1.0,70.0)*y+t728;
+      t716 = t697+t729;
+      t678 = y*t686;
+      t715 = t678+t727;
+      t676 = y*t691;
+      t714 = t676+t727;
+      t694 = RATIONAL(2.0,35.0)*y;
+      t685 = RATIONAL(-2.0,35.0)*y;
+      t681 = y*t697;
+      t680 = y*t698;
+      t679 = RATIONAL(1.0,20.0)*t726;
+      t677 = RATIONAL(-1.0,20.0)*t726;
+      coeff_dxx_m2_m2 = t686+t685+t714;
+      coeff_dxx_m1_m2 = t680+t695+t716;
+      coeff_dxx_0_m2 = t694+t724;
+      coeff_dxx_p1_m2 = t695+t681+t718;
+      coeff_dxx_p2_m2 = t691+t685+t715;
+      coeff_dxx_m2_m1 = t679+t686+t719;
+      coeff_dxx_m1_m1 = t697+t678+t717;
+      coeff_dxx_0_m1 = t695+t723;
+      coeff_dxx_p1_m1 = t698+t676+t717;
+      coeff_dxx_p2_m1 = t691+t677+t719;
+      coeff_dxx_m2_0 = t686+t725;
+      coeff_dxx_m1_0 = t697+t722;
+      coeff_dxx_0_0 = RATIONAL(-57.0,98.0)+t690+t699;
+      coeff_dxx_p1_0 = t698+t722;
+      coeff_dxx_p2_0 = t691+t725;
+      coeff_dxx_m2_p1 = t677+t686+t721;
+      coeff_dxx_m1_p1 = t697+t676+t720;
+      coeff_dxx_0_p1 = t689+t723;
+      coeff_dxx_p1_p1 = t678+t698+t720;
+      coeff_dxx_p2_p1 = t691+t679+t721;
+      coeff_dxx_m2_p2 = t694+t686+t715;
+      coeff_dxx_m1_p2 = t689+t681+t716;
+      coeff_dxx_0_p2 = t685+t724;
+      coeff_dxx_p1_p2 = t680+t689+t718;
+      coeff_dxx_p2_p2 = t694+t691+t714;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dxy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dxy.compute.c
index 9388906..0505d86 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dxy.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dxy.compute.c
@@ -1,119 +1,119 @@
-fp t778,
-   t777,
-   t796,
-   t766,
-   t735,
+fp t779,
+   t778,
+   t797,
    t772,
-   t755,
+   t774,
+   t796,
    t795,
-   t751,
-   t748,
+   t770,
+   t739,
+   t766,
+   t752,
    t794,
+   t742,
+   t759,
    t793,
    t792,
-   t791,
    t733,
+   t791,
    t790,
    t789,
    t788,
    t787,
-   t765,
-   t770,
+   t735,
    t786,
-   t734,
+   t732,
    t785,
-   t767,
-   t771,
+   t773,
+   t777,
    t784,
    t783,
    t782,
-   t730,
    t781,
    t780,
-   t779,
    t776,
-   t775,
-   t773,
-   t769,
-   t756,
-   t754,
+   t771,
+   t768,
+   t767,
+   t758,
+   t757,
+   t755,
    t750,
-   t749,
-   t746,
-   t745,
    t743,
    t738,
-   t732,
+   t737,
+   t736,
+   t734,
    t731;
-      t778 = y*y;
-      t777 = x*x;
-      t796 = t778+t777;
-      t766 = RATIONAL(-1.0,35.0);
-      t735 = t766*x;
-      t772 = RATIONAL(1.0,35.0);
-      t755 = t772*y;
-      t795 = t735+t755;
-      t751 = t766*y;
-      t748 = t772*x;
-      t794 = t751+t748;
-      t793 = t735+t751;
-      t792 = t755+t748;
-      t791 = x*y;
-      t733 = RATIONAL(-2.0,49.0)*t791;
-      t790 = t733+RATIONAL(-21.0,200.0);
-      t789 = t733+RATIONAL(21.0,200.0);
-      t788 = t796*RATIONAL(-1.0,20.0);
-      t787 = t796*RATIONAL(1.0,20.0);
-      t765 = RATIONAL(-1.0,40.0);
-      t770 = RATIONAL(1.0,10.0);
-      t786 = t765*t777+t770*t778+t790;
-      t734 = RATIONAL(4.0,49.0)*t791;
-      t785 = t734+RATIONAL(11.0,150.0)+t788;
-      t767 = RATIONAL(1.0,40.0);
-      t771 = RATIONAL(-1.0,10.0);
-      t784 = t771*t778+t767*t777+t789;
-      t783 = t771*t777+t767*t778+t789;
-      t782 = t734+RATIONAL(-11.0,150.0)+t787;
-      t730 = RATIONAL(1.0,49.0)*t791;
-      t781 = RATIONAL(37.0,300.0)+t730+t788;
-      t780 = RATIONAL(-37.0,300.0)+t730+t787;
-      t779 = t765*t778+t770*t777+t790;
+      t779 = y*y;
+      t778 = x*x;
+      t797 = t778+t779;
+      t772 = RATIONAL(1.0,10.0);
+      t774 = RATIONAL(-1.0,40.0);
+      t796 = t772*t778+t774*t779;
+      t795 = t774*t778+t772*t779;
+      t770 = RATIONAL(-1.0,35.0);
+      t739 = t770*y;
+      t766 = RATIONAL(1.0,35.0);
+      t752 = t766*x;
+      t794 = t739+t752;
+      t742 = t770*x;
+      t759 = t766*y;
+      t793 = t742+t759;
+      t792 = x*y;
+      t733 = RATIONAL(-2.0,49.0)*t792;
+      t791 = t733+RATIONAL(-21.0,200.0);
+      t790 = t797*RATIONAL(-1.0,20.0);
+      t789 = t797*RATIONAL(1.0,20.0);
+      t788 = t733+RATIONAL(21.0,200.0);
+      t787 = t752+t759+t791;
+      t735 = RATIONAL(4.0,49.0)*t792;
+      t786 = t735+RATIONAL(11.0,150.0)+t790;
+      t732 = RATIONAL(1.0,49.0)*t792;
+      t785 = t732+RATIONAL(37.0,300.0)+t790;
+      t773 = RATIONAL(-1.0,10.0);
+      t777 = RATIONAL(1.0,40.0);
+      t784 = t773*t779+t777*t778+t788;
+      t783 = t735+RATIONAL(-11.0,150.0)+t789;
+      t782 = t732+RATIONAL(-37.0,300.0)+t789;
+      t781 = t773*t778+t777*t779+t788;
+      t780 = t739+t742+t791;
       t776 = RATIONAL(-2.0,35.0);
-      t775 = RATIONAL(-1.0,70.0);
-      t773 = RATIONAL(1.0,70.0);
-      t769 = RATIONAL(2.0,35.0);
-      t756 = t776*y;
-      t754 = t769*y;
-      t750 = t776*x;
-      t749 = t775*x;
-      t746 = t773*y;
-      t745 = t775*y;
-      t743 = t769*x;
-      t738 = t773*x;
-      t732 = RATIONAL(-4.0,49.0)*t791;
-      t731 = RATIONAL(2.0,49.0)*t791;
-      coeff_dxy_m2_m2 = t756+t750+t782;
-      coeff_dxy_m1_m2 = t783+t794;
-      coeff_dxy_0_m2 = t743+t732;
-      coeff_dxy_p1_m2 = t779+t792;
-      coeff_dxy_p2_m2 = t750+t754+t785;
-      coeff_dxy_m2_m1 = t784+t795;
-      coeff_dxy_m1_m1 = t738+t746+t781;
-      coeff_dxy_0_m1 = t748+t731;
-      coeff_dxy_p1_m1 = t745+t738+t780;
-      coeff_dxy_p2_m1 = t786+t793;
-      coeff_dxy_m2_0 = t754+t732;
-      coeff_dxy_m1_0 = t755+t731;
-      coeff_dxy_0_0 = t734;
-      coeff_dxy_p1_0 = t751+t731;
-      coeff_dxy_p2_0 = t732+t756;
-      coeff_dxy_m2_p1 = t786+t792;
-      coeff_dxy_m1_p1 = t749+t746+t780;
-      coeff_dxy_0_p1 = t735+t731;
-      coeff_dxy_p1_p1 = t749+t745+t781;
+      t771 = RATIONAL(2.0,35.0);
+      t768 = RATIONAL(-1.0,70.0);
+      t767 = RATIONAL(1.0,70.0);
+      t758 = t771*y;
+      t757 = t768*y;
+      t755 = t776*x;
+      t750 = t771*x;
+      t743 = t767*x;
+      t738 = t767*y;
+      t737 = t776*y;
+      t736 = t768*x;
+      t734 = RATIONAL(-4.0,49.0)*t792;
+      t731 = RATIONAL(2.0,49.0)*t792;
+      coeff_dxy_m2_m2 = t755+t737+t783;
+      coeff_dxy_m1_m2 = t781+t794;
+      coeff_dxy_0_m2 = t750+t734;
+      coeff_dxy_p1_m2 = t787+t796;
+      coeff_dxy_p2_m2 = t758+t755+t786;
+      coeff_dxy_m2_m1 = t784+t793;
+      coeff_dxy_m1_m1 = t738+t743+t785;
+      coeff_dxy_0_m1 = t752+t731;
+      coeff_dxy_p1_m1 = t757+t743+t782;
+      coeff_dxy_p2_m1 = t780+t795;
+      coeff_dxy_m2_0 = t734+t758;
+      coeff_dxy_m1_0 = t731+t759;
+      coeff_dxy_0_0 = t735;
+      coeff_dxy_p1_0 = t731+t739;
+      coeff_dxy_p2_0 = t734+t737;
+      coeff_dxy_m2_p1 = t787+t795;
+      coeff_dxy_m1_p1 = t738+t736+t782;
+      coeff_dxy_0_p1 = t731+t742;
+      coeff_dxy_p1_p1 = t757+t736+t785;
       coeff_dxy_p2_p1 = t784+t794;
-      coeff_dxy_m2_p2 = t743+t756+t785;
-      coeff_dxy_m1_p2 = t779+t793;
-      coeff_dxy_0_p2 = t750+t732;
-      coeff_dxy_p1_p2 = t783+t795;
-      coeff_dxy_p2_p2 = t754+t743+t782;
+      coeff_dxy_m2_p2 = t750+t737+t786;
+      coeff_dxy_m1_p2 = t780+t796;
+      coeff_dxy_0_p2 = t755+t734;
+      coeff_dxy_p1_p2 = t781+t793;
+      coeff_dxy_p2_p2 = t758+t750+t783;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dy.compute.c
index 03c68c3..f4baa3a 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dy.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dy.compute.c
@@ -1,50 +1,51 @@
-fp t641,
-   t611,
-   t638,
-   t639,
-   t657,
+fp t644,
+   t609,
+   t630,
+   t643,
+   t616,
+   t675,
+   t636,
+   t621,
+   t622,
    t674,
-   t608,
-   t656,
-   t673,
    t661,
-   t589,
+   t601,
+   t641,
+   t673,
+   t631,
+   t600,
    t672,
+   t613,
    t671,
-   t635,
-   t640,
-   t609,
+   t662,
+   t642,
+   t611,
    t670,
-   t574,
+   t587,
    t669,
-   t614,
-   t598,
+   t619,
+   t590,
    t668,
-   t632,
-   t615,
-   t667,
    t634,
-   t619,
+   t612,
+   t667,
    t666,
-   t617,
-   t596,
+   t610,
    t665,
-   t627,
-   t606,
+   t632,
+   t618,
    t664,
-   t637,
-   t616,
    t663,
-   t662,
    t660,
-   t618,
    t659,
+   t574,
    t658,
    t586,
+   t657,
+   t623,
+   t656,
    t655,
-   t578,
    t654,
-   t620,
    t653,
    t652,
    t651,
@@ -52,100 +53,95 @@ fp t641,
    t649,
    t648,
    t647,
-   t646,
-   t645,
-   t644,
-   t588,
+   t592,
+   t584,
    t583,
    t582,
-   t579,
-   t576,
-   t572;
-      t641 = y*y;
-      t611 = RATIONAL(1.0,20.0)*t641;
-      t638 = x*x;
-      t639 = t638*x;
-      t657 = RATIONAL(1.0,60.0)*t639+x*t611;
-      t674 = t657+RATIONAL(-37.0,300.0)*x;
-      t608 = RATIONAL(-1.0,20.0)*t641;
-      t656 = RATIONAL(-1.0,60.0)*t639+x*t608;
-      t673 = t656+RATIONAL(37.0,300.0)*x;
-      t661 = y*t638;
-      t589 = RATIONAL(-1.0,49.0)*t661;
-      t672 = t589+RATIONAL(226.0,735.0)*y;
-      t671 = RATIONAL(1.0,98.0)*t661+RATIONAL(181.0,735.0)*y;
-      t635 = RATIONAL(1.0,30.0);
-      t640 = y*t641;
-      t609 = t635*t640;
-      t670 = t589+t609+RATIONAL(71.0,2940.0)*y;
-      t574 = RATIONAL(2.0,49.0)*t661;
-      t669 = RATIONAL(-289.0,2940.0)*y+t574+t609;
-      t614 = RATIONAL(-1.0,10.0)*t641;
-      t598 = RATIONAL(21.0,200.0)*x;
-      t668 = x*t614+RATIONAL(1.0,120.0)*t639+t598;
-      t632 = RATIONAL(1.0,35.0);
-      t615 = t632*t638;
-      t667 = t611+RATIONAL(-31.0,420.0)+t615;
-      t634 = RATIONAL(1.0,70.0);
-      t619 = t634*t638;
-      t666 = t619+RATIONAL(-1.0,84.0)+t608;
-      t617 = RATIONAL(1.0,10.0)*t641;
-      t596 = RATIONAL(-21.0,200.0)*x;
-      t665 = RATIONAL(-1.0,120.0)*t639+x*t617+t596;
-      t627 = RATIONAL(-1.0,35.0);
-      t606 = t627*t638;
-      t664 = RATIONAL(31.0,420.0)+t606+t608;
-      t637 = RATIONAL(-1.0,70.0);
-      t616 = t637*t638;
-      t663 = t611+t616+RATIONAL(1.0,84.0);
-      t662 = x*y;
-      t660 = x*t641;
-      t618 = RATIONAL(-2.0,15.0)*t640;
-      t659 = t617+t618;
-      t658 = t618+t614;
-      t586 = RATIONAL(-2.0,49.0)*t661;
-      t655 = t586+t609+RATIONAL(191.0,2940.0)*y;
-      t578 = RATIONAL(1.0,49.0)*t661;
-      t654 = t618+RATIONAL(166.0,735.0)*y+t578;
-      t620 = RATIONAL(1.0,5.0)*t640;
-      t653 = RATIONAL(-53.0,98.0)*y+t620+t578;
-      t652 = t620+RATIONAL(-41.0,98.0)*y+t586;
-      t651 = RATIONAL(1.0,140.0)*t638+RATIONAL(-31.0,210.0)+t659+t671;
-      t650 = t619+RATIONAL(11.0,105.0)+t658+t672;
-      t649 = RATIONAL(-11.0,150.0)*x+t657+t669;
-      t648 = RATIONAL(11.0,150.0)*x+t656+t669;
-      t647 = t616+RATIONAL(-11.0,105.0)+t659+t672;
-      t646 = t635*t639+RATIONAL(-1.0,40.0)*t660+t596+t670;
-      t645 = RATIONAL(31.0,210.0)+RATIONAL(-1.0,140.0)*t638+t658+t671;
-      t644 = RATIONAL(-1.0,30.0)*t639+RATIONAL(1.0,40.0)*t660+t598+t670;
-      t588 = t627*t662;
-      t583 = t632*t662;
-      t582 = RATIONAL(2.0,35.0)*t662;
-      t579 = t634*t662;
-      t576 = t637*t662;
-      t572 = RATIONAL(-2.0,35.0)*t662;
-      coeff_dy_m2_m2 = t572+t649+t664;
-      coeff_dy_m1_m2 = t588+t644+t666;
-      coeff_dy_0_m2 = RATIONAL(-17.0,420.0)+t615+t608+t655;
-      coeff_dy_p1_m2 = t583+t646+t666;
-      coeff_dy_p2_m2 = t582+t648+t664;
-      coeff_dy_m2_m1 = t583+t647+t668;
-      coeff_dy_m1_m1 = t579+t651+t673;
-      coeff_dy_0_m1 = RATIONAL(-17.0,105.0)+t617+t619+t654;
-      coeff_dy_p1_m1 = t576+t651+t674;
-      coeff_dy_p2_m1 = t588+t647+t665;
-      coeff_dy_m2_0 = t582+t652;
-      coeff_dy_m1_0 = t583+t653;
-      coeff_dy_0_0 = t574+RATIONAL(-57.0,98.0)*y+t620;
-      coeff_dy_p1_0 = t588+t653;
-      coeff_dy_p2_0 = t572+t652;
-      coeff_dy_m2_p1 = t583+t650+t665;
-      coeff_dy_m1_p1 = t579+t645+t674;
-      coeff_dy_0_p1 = RATIONAL(17.0,105.0)+t616+t614+t654;
-      coeff_dy_p1_p1 = t576+t645+t673;
-      coeff_dy_p2_p1 = t588+t650+t668;
-      coeff_dy_m2_p2 = t572+t648+t667;
-      coeff_dy_m1_p2 = t588+t646+t663;
-      coeff_dy_0_p2 = t611+RATIONAL(17.0,420.0)+t606+t655;
-      coeff_dy_p1_p2 = t583+t644+t663;
-      coeff_dy_p2_p2 = t582+t649+t667;
+   t578,
+   t576;
+      t644 = y*y;
+      t609 = RATIONAL(1.0,20.0)*t644;
+      t630 = RATIONAL(1.0,35.0);
+      t643 = x*x;
+      t616 = t630*t643;
+      t675 = t609+t616+RATIONAL(-31.0,420.0);
+      t636 = RATIONAL(-1.0,35.0);
+      t621 = t636*t643;
+      t622 = RATIONAL(-1.0,20.0)*t644;
+      t674 = t621+t622+RATIONAL(31.0,420.0);
+      t661 = x*t644;
+      t601 = RATIONAL(21.0,200.0)*x;
+      t641 = x*t643;
+      t673 = RATIONAL(1.0,40.0)*t661+t601+RATIONAL(-1.0,30.0)*t641;
+      t631 = RATIONAL(1.0,30.0);
+      t600 = RATIONAL(-21.0,200.0)*x;
+      t672 = t600+RATIONAL(-1.0,40.0)*t661+t631*t641;
+      t613 = RATIONAL(1.0,10.0)*t644;
+      t671 = RATIONAL(1.0,140.0)*t643+t613+RATIONAL(-31.0,210.0);
+      t662 = y*t643;
+      t642 = y*t644;
+      t611 = RATIONAL(-2.0,15.0)*t642;
+      t670 = RATIONAL(181.0,735.0)*y+t611+RATIONAL(1.0,98.0)*t662;
+      t587 = RATIONAL(-1.0,49.0)*t662;
+      t669 = RATIONAL(226.0,735.0)*y+t587+t611;
+      t619 = t631*t642;
+      t590 = RATIONAL(2.0,49.0)*t662;
+      t668 = RATIONAL(-289.0,2940.0)*y+t619+t590;
+      t634 = RATIONAL(-1.0,70.0);
+      t612 = t634*t643;
+      t667 = t613+t612+RATIONAL(-11.0,105.0);
+      t666 = RATIONAL(71.0,2940.0)*y+t587+t619;
+      t610 = RATIONAL(-1.0,10.0)*t644;
+      t665 = RATIONAL(31.0,210.0)+RATIONAL(-1.0,140.0)*t643+t610;
+      t632 = RATIONAL(1.0,70.0);
+      t618 = t632*t643;
+      t664 = t610+t618+RATIONAL(11.0,105.0);
+      t663 = x*y;
+      t660 = x*t622+RATIONAL(-1.0,60.0)*t641;
+      t659 = x*t609+RATIONAL(1.0,60.0)*t641;
+      t574 = RATIONAL(1.0,49.0)*t662;
+      t658 = RATIONAL(166.0,735.0)*y+t611+t574;
+      t586 = RATIONAL(-2.0,49.0)*t662;
+      t657 = RATIONAL(191.0,2940.0)*y+t619+t586;
+      t623 = RATIONAL(1.0,5.0)*t642;
+      t656 = RATIONAL(-41.0,98.0)*y+t623+t586;
+      t655 = RATIONAL(-53.0,98.0)*y+t623+t574;
+      t654 = RATIONAL(37.0,300.0)*x+t660+t670;
+      t653 = RATIONAL(11.0,150.0)*x+t660+t668;
+      t652 = RATIONAL(-37.0,300.0)*x+t659+t670;
+      t651 = RATIONAL(-1.0,84.0)+t618+t622+t666;
+      t650 = x*t610+t601+RATIONAL(1.0,120.0)*t641+t669;
+      t649 = RATIONAL(1.0,84.0)+t609+t612+t666;
+      t648 = RATIONAL(-11.0,150.0)*x+t659+t668;
+      t647 = t600+RATIONAL(-1.0,120.0)*t641+x*t613+t669;
+      t592 = RATIONAL(-2.0,35.0)*t663;
+      t584 = t630*t663;
+      t583 = t636*t663;
+      t582 = RATIONAL(2.0,35.0)*t663;
+      t578 = t634*t663;
+      t576 = t632*t663;
+      coeff_dy_m2_m2 = t592+t648+t674;
+      coeff_dy_m1_m2 = t583+t651+t673;
+      coeff_dy_0_m2 = t616+RATIONAL(-17.0,420.0)+t622+t657;
+      coeff_dy_p1_m2 = t584+t651+t672;
+      coeff_dy_p2_m2 = t582+t653+t674;
+      coeff_dy_m2_m1 = t584+t650+t667;
+      coeff_dy_m1_m1 = t576+t654+t671;
+      coeff_dy_0_m1 = t618+t613+RATIONAL(-17.0,105.0)+t658;
+      coeff_dy_p1_m1 = t578+t652+t671;
+      coeff_dy_p2_m1 = t583+t647+t667;
+      coeff_dy_m2_0 = t582+t656;
+      coeff_dy_m1_0 = t584+t655;
+      coeff_dy_0_0 = RATIONAL(-57.0,98.0)*y+t590+t623;
+      coeff_dy_p1_0 = t583+t655;
+      coeff_dy_p2_0 = t592+t656;
+      coeff_dy_m2_p1 = t584+t647+t664;
+      coeff_dy_m1_p1 = t576+t652+t665;
+      coeff_dy_0_p1 = t612+t610+RATIONAL(17.0,105.0)+t658;
+      coeff_dy_p1_p1 = t578+t654+t665;
+      coeff_dy_p2_p1 = t583+t650+t664;
+      coeff_dy_m2_p2 = t592+t653+t675;
+      coeff_dy_m1_p2 = t583+t649+t672;
+      coeff_dy_0_p2 = t621+RATIONAL(17.0,420.0)+t609+t657;
+      coeff_dy_p1_p2 = t584+t649+t673;
+      coeff_dy_p2_p2 = t582+t648+t675;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dyy.compute.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dyy.compute.c
index cc0ccef..9e72985 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dyy.compute.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.coeffs/2d.cube.order4.smooth0/coeff-dyy.compute.c
@@ -1,115 +1,115 @@
-fp t833,
-   t808,
+fp t834,
+   t813,
+   t854,
    t853,
-   t807,
+   t830,
+   t835,
+   t814,
    t852,
-   t834,
-   t818,
+   t816,
    t851,
    t850,
-   t849,
-   t829,
    t815,
-   t817,
-   t806,
+   t808,
+   t818,
    t820,
-   t804,
+   t821,
+   t849,
    t848,
+   t810,
    t847,
-   t812,
+   t804,
    t846,
    t819,
    t845,
-   t803,
    t844,
    t843,
-   t798,
    t842,
    t841,
+   t801,
    t840,
+   t798,
    t839,
    t838,
    t837,
-   t800,
    t836,
-   t835,
-   t816,
-   t814,
+   t817,
+   t812,
    t811,
-   t810,
    t809,
+   t806,
    t805,
+   t803,
    t802,
-   t801,
-   t799,
-   t797;
-      t833 = x*x;
-      t808 = RATIONAL(-1.0,49.0)*t833;
-      t853 = t808+RATIONAL(71.0,2940.0);
-      t807 = RATIONAL(2.0,49.0)*t833;
-      t852 = t807+RATIONAL(-289.0,2940.0);
-      t834 = y*y;
-      t818 = RATIONAL(-2.0,5.0)*t834;
-      t851 = t818+RATIONAL(181.0,735.0)+RATIONAL(1.0,98.0)*t833;
-      t850 = t818+t808+RATIONAL(226.0,735.0);
-      t849 = x*y;
-      t829 = RATIONAL(1.0,10.0);
-      t815 = t829*y;
-      t817 = RATIONAL(-1.0,5.0)*y;
-      t806 = RATIONAL(-1.0,10.0)*y;
+   t800,
+   t799;
+      t834 = x*x;
+      t813 = RATIONAL(-1.0,49.0)*t834;
+      t854 = t813+RATIONAL(226.0,735.0);
+      t853 = RATIONAL(1.0,98.0)*t834+RATIONAL(181.0,735.0);
+      t830 = RATIONAL(1.0,10.0);
+      t835 = y*y;
+      t814 = t830*t835;
+      t852 = t813+t814+RATIONAL(71.0,2940.0);
+      t816 = RATIONAL(2.0,49.0)*t834;
+      t851 = t814+t816+RATIONAL(-289.0,2940.0);
+      t850 = x*y;
+      t815 = RATIONAL(-1.0,10.0)*y;
+      t808 = t830*y;
+      t818 = RATIONAL(-1.0,5.0)*y;
       t820 = RATIONAL(1.0,5.0)*y;
-      t804 = t829*t834;
-      t848 = t815+t804;
-      t847 = t806+t804;
-      t812 = RATIONAL(1.0,49.0)*t833;
-      t846 = t818+RATIONAL(166.0,735.0)+t812;
-      t819 = RATIONAL(3.0,5.0)*t834;
-      t845 = t819+RATIONAL(-53.0,98.0)+t812;
-      t803 = RATIONAL(-2.0,49.0)*t833;
-      t844 = t803+RATIONAL(191.0,2940.0)+t804;
-      t843 = t803+t819+RATIONAL(-41.0,98.0);
+      t821 = RATIONAL(-2.0,5.0)*t835;
+      t849 = t818+t821;
+      t848 = t820+t821;
+      t810 = RATIONAL(-2.0,49.0)*t834;
+      t847 = t810+t814+RATIONAL(191.0,2940.0);
+      t804 = RATIONAL(1.0,49.0)*t834;
+      t846 = t804+t821+RATIONAL(166.0,735.0);
+      t819 = RATIONAL(3.0,5.0)*t835;
+      t845 = t810+t819+RATIONAL(-41.0,98.0);
+      t844 = t804+t819+RATIONAL(-53.0,98.0);
+      t843 = t849+t853;
+      t842 = t848+t853;
+      t841 = t849+t854;
+      t801 = x*t808;
+      t840 = t801+t851;
       t798 = x*t815;
-      t842 = t798+t851;
-      t841 = t848+t853;
-      t840 = t847+t853;
-      t839 = t847+t852;
-      t838 = t820+t850;
-      t837 = t817+t850;
-      t800 = x*t806;
-      t836 = t800+t851;
-      t835 = t848+t852;
-      t816 = RATIONAL(2.0,35.0)*x;
-      t814 = RATIONAL(1.0,70.0)*x;
-      t811 = RATIONAL(-1.0,70.0)*x;
-      t810 = RATIONAL(1.0,35.0)*x;
-      t809 = RATIONAL(-1.0,35.0)*x;
-      t805 = RATIONAL(-2.0,35.0)*x;
-      t802 = x*t817;
-      t801 = x*t820;
-      t799 = RATIONAL(-1.0,20.0)*t849;
-      t797 = RATIONAL(1.0,20.0)*t849;
-      coeff_dyy_m2_m2 = t798+t805+t839;
-      coeff_dyy_m1_m2 = t797+t809+t840;
-      coeff_dyy_0_m2 = t806+t844;
-      coeff_dyy_p1_m2 = t810+t799+t840;
-      coeff_dyy_p2_m2 = t800+t816+t839;
-      coeff_dyy_m2_m1 = t810+t802+t838;
-      coeff_dyy_m1_m1 = t820+t814+t836;
+      t839 = t798+t851;
+      t838 = t808+t852;
+      t837 = t848+t854;
+      t836 = t815+t852;
+      t817 = RATIONAL(-2.0,35.0)*x;
+      t812 = RATIONAL(-1.0,35.0)*x;
+      t811 = RATIONAL(1.0,35.0)*x;
+      t809 = RATIONAL(2.0,35.0)*x;
+      t806 = RATIONAL(1.0,70.0)*x;
+      t805 = RATIONAL(-1.0,70.0)*x;
+      t803 = x*t818;
+      t802 = x*t820;
+      t800 = RATIONAL(1.0,20.0)*t850;
+      t799 = RATIONAL(-1.0,20.0)*t850;
+      coeff_dyy_m2_m2 = t815+t817+t840;
+      coeff_dyy_m1_m2 = t800+t812+t836;
+      coeff_dyy_0_m2 = t815+t847;
+      coeff_dyy_p1_m2 = t799+t811+t836;
+      coeff_dyy_p2_m2 = t815+t809+t839;
+      coeff_dyy_m2_m1 = t803+t811+t837;
+      coeff_dyy_m1_m1 = t806+t798+t842;
       coeff_dyy_0_m1 = t820+t846;
-      coeff_dyy_p1_m1 = t811+t820+t842;
-      coeff_dyy_p2_m1 = t809+t801+t838;
-      coeff_dyy_m2_0 = t816+t843;
-      coeff_dyy_m1_0 = t810+t845;
-      coeff_dyy_0_0 = t819+RATIONAL(-57.0,98.0)+t807;
-      coeff_dyy_p1_0 = t809+t845;
-      coeff_dyy_p2_0 = t805+t843;
-      coeff_dyy_m2_p1 = t810+t801+t837;
-      coeff_dyy_m1_p1 = t817+t814+t842;
-      coeff_dyy_0_p1 = t817+t846;
-      coeff_dyy_p1_p1 = t811+t817+t836;
-      coeff_dyy_p2_p1 = t809+t802+t837;
-      coeff_dyy_m2_p2 = t805+t800+t835;
-      coeff_dyy_m1_p2 = t809+t799+t841;
-      coeff_dyy_0_p2 = t815+t844;
-      coeff_dyy_p1_p2 = t797+t810+t841;
-      coeff_dyy_p2_p2 = t816+t798+t835;
+      coeff_dyy_p1_m1 = t805+t801+t842;
+      coeff_dyy_p2_m1 = t802+t812+t837;
+      coeff_dyy_m2_0 = t809+t845;
+      coeff_dyy_m1_0 = t811+t844;
+      coeff_dyy_0_0 = RATIONAL(-57.0,98.0)+t819+t816;
+      coeff_dyy_p1_0 = t812+t844;
+      coeff_dyy_p2_0 = t817+t845;
+      coeff_dyy_m2_p1 = t802+t811+t841;
+      coeff_dyy_m1_p1 = t806+t801+t843;
+      coeff_dyy_0_p1 = t818+t846;
+      coeff_dyy_p1_p1 = t805+t798+t843;
+      coeff_dyy_p2_p1 = t812+t803+t841;
+      coeff_dyy_m2_p2 = t817+t808+t839;
+      coeff_dyy_m1_p2 = t812+t799+t838;
+      coeff_dyy_0_p2 = t808+t847;
+      coeff_dyy_p1_p2 = t811+t800+t838;
+      coeff_dyy_p2_p2 = t808+t809+t840;
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order1.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order1.smooth0.c
index 75a4c9f..ddfa60b 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order1.smooth0.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order1.smooth0.c
@@ -1,3 +1,5 @@
+/* $Header$ */
+
 #include <math.h>
 #include <limits.h>
 #include <stdlib.h>
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order2.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order2.smooth0.c
index f68477d..d75a198 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order2.smooth0.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order2.smooth0.c
@@ -1,3 +1,5 @@
+/* $Header$ */
+
 #include <math.h>
 #include <limits.h>
 #include <stdlib.h>
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order3.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order3.smooth0.c
index 14c886c..66327bb 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order3.smooth0.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order3.smooth0.c
@@ -1,3 +1,5 @@
+/* $Header$ */
+
 #include <math.h>
 #include <limits.h>
 #include <stdlib.h>
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order4.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order4.smooth0.c
index a28e903..ef531d5 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order4.smooth0.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.cube.order4.smooth0.c
@@ -1,3 +1,5 @@
+/* $Header$ */
+
 #include <math.h>
 #include <limits.h>
 #include <stdlib.h>
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.log b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.log
index 4fa17e7..f356a52 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.log
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.log
@@ -444,12 +444,13 @@ ftruncate :=
 
     proc(file_name::string) fopen(file_name, 'WRITE'); fclose(%); NULL end proc
 
-# interpolate.maple -- compute generalized interpolation formulas/coefficients
-# $Id: interpolate.maple,v 1.4 2002/05/14 15:52:50 jthorn Exp $
+# interpolate.maple -- compute interpolation formulas/coefficients
+# $Id: interpolate.maple,v 1.7 2002/08/19 14:30:43 jthorn Exp $
 > 
 #
 # <<<representation of numbers, data values, etc>>>
-# Lagrange polynomial_interpolant - compute Lagrange polynomial interpolant
+# Lagrange_polynomial_interpolant - compute Lagrange polynomial interpolant
+# Hermite_polynomial_interpolant - compute Hermite polynomial interpolant
 # coeff_as_lc_of_data - coefficients of ... (linear combination of data)
 #
 # print_coeff__lc_of_data - print C code to compute coefficients
@@ -540,6 +541,171 @@ 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_list = 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_coord_list = A list of lists of coordinates specifying which
+#		     derivatives are computed by the deriv_proc_list[]
+#		     procedures, for example
+#			[[x], [y], [x,y]]
+# deriv_proc_list = A list of procedures for computing finite-difference
+#		    derivatives.  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
+#		    example,
+#			[
+#			  proc(i::integer, j::integer)
+#			  - 1/2*DATA(i-1,j) + 1/2*DATA(i+1,j)
+#			  end proc
+#			,
+#			  proc(i::integer, j::integer)
+#			  - 1/2*DATA(i,j-1) + 1/2*DATA(i,j+1)
+#			  end proc
+#			,
+#			  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_list = A list 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_list = A list of positions (each a list of numeric values)
+#		    where the interpolant is to match each possible product
+#		    of 1st derivatives"1st"
+#		    derivatives (actually all derivatives the given data DATA(),
+#		    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_list::list(name), coord_list::list(name),
+>       deriv_coord_list::list(list(name)), fd_deriv_proc_list::list(procedure),
+>       fn_posn_list::list(list(numeric)), deriv_posn_list::list(list(numeric))
+>     )
+> local fn_eset,
+>       fn_expr, deriv_eset;
+> 
+# set of equations {fn(posn) = DATA(posn)}
+> fn_eset := map(
+> 		  # return equation that fn(this point) = DATA(this point)
+> 		  proc(posn::list(integer))
+> 		  fn(op(posn)) = 'DATA'(op(posn));
+> 		  end proc
+> 		,
+> 		  {op(fn_posn_list)}
+> 	      );
+> 
+# set of sets of equations
+#	{
+#	  { deriv1(posn1) = fd_deriv1(posn1),
+#	    deriv2(posn1) = fd_deriv2(posn1),
+#	    ... },
+#	  { deriv1(posn2) = fd_deriv1(posn2),
+#	    deriv2(posn2) = fd_deriv2(posn2),
+#	    ... },
+#	  ...
+#	}
+> fn_expr := fn(op(coord_list));
+> map(
+>        # return set of equations
+>        #	{deriv(posn) = fd_deriv(posn)}
+>        # for this point
+>        proc(posn::list(integer))
+>        {
+> 	op(
+> 	 zip(
+> 		# return equation that
+> 		#	deriv(posn) = fd_deriv(posn)
+> 		# for this deriv and this point
+> 		proc(deriv_coords::list(name), fd_deriv_proc::procedure)
+> 		local fn_deriv_proc;
+> 		fn_deriv_proc := unapply( diff(fn_expr,deriv_coords),
+> 					  op(coord_list) );
+> 		fn_deriv_proc(op(posn)) = fd_deriv_proc(op(posn));
+> 		end proc
+> 	      ,
+> 		[op(deriv_coord_list)]
+> 	      ,
+> 		[op(fd_deriv_proc_list)]
+> 	    )
+> 	  )
+>        }
+>        end proc
+>      ,
+>        {op(deriv_posn_list)}
+>    );
+> 
+# set of equations {deriv-i(posn-j) = fd_deriv-i(posn-j)}
+> deriv_eset := `union`(op(%));
+> 
+# solve equations for coeffs
+> solve(fn_eset union deriv_eset, {op(coeff_list)});
+> 
+# interpolant as a polynomial in the coordinates
+> return subs(%, eval(fn))(op(coord_list));
+> end proc;
+Hermite_polynomial_interpolant := proc(fn::procedure, coeff_list::list(name),
+coord_list::list(name), deriv_coord_list::list(list(name)),
+fd_deriv_proc_list::list(procedure), fn_posn_list::list(list(numeric)),
+deriv_posn_list::list(list(numeric)))
+local fn_eset, fn_expr, deriv_eset;
+    fn_eset := map(
+        proc(posn::list(integer)) fn(op(posn)) = 'DATA'(op(posn)) end proc,
+        {op(fn_posn_list)});
+    fn_expr := fn(op(coord_list));
+    map(proc(posn::list(integer))
+            {op(zip(proc(deriv_coords::list(name), fd_deriv_proc::procedure
+            )
+            local fn_deriv_proc;
+                fn_deriv_proc :=
+                    unapply(diff(fn_expr, deriv_coords), op(coord_list));
+                fn_deriv_proc(op(posn)) = fd_deriv_proc(op(posn))
+            end proc, [op(deriv_coord_list)], [op(fd_deriv_proc_list)]))}
+        end proc, {op(deriv_posn_list)});
+    deriv_eset := `union`(op(%));
+    solve(fn_eset union deriv_eset, {op(coeff_list)});
+    return subs(%, eval(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.
@@ -547,8 +713,7 @@ end proc
 # Arguments:
 # interpolant = The interpolating polynomial (an algebraic expression
 #		in the coordinates and the data values).
-# posn_list = The same list of positions as was used to compute the
-#	      interpolating polynomial.
+# 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
@@ -916,7 +1081,7 @@ data_var_name := proc(posn::list(numeric), name_prefix::string)
 end proc
 
 # Maple code to compute lists of point positions in hypercube-shaped molecules
-# $Id: $
+# $Id: cube_posns.maple,v 1.1.1.1 2002/08/18 15:05:38 jthorn Exp $
 > 
 ################################################################################
 > 
@@ -975,6 +1140,18 @@ posn_list_2d_size5 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [-2, -1],
 
     [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]]
+
 > 
 ################################################################################
 > 
@@ -1069,8 +1246,84 @@ posn_list_3d_size5 := [[-2, -2, -2], [-1, -2, -2], [0, -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
-# $Id: 1d.maple,v 1.4 2002/05/14 15:54:01 jthorn Exp $
+# $Id: fns.maple,v 1.1 2002/08/18 15:12:13 jthorn Exp $
 > 
 ################################################################################
 > 
@@ -1338,12 +1591,12 @@ end proc
 > 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 + c000 + c100*x + c001*z + c020*y^2 + c110*x*y
-     + c011*y*z + c101*x*z + c200*x^2 + c002*z^2 + c030*y^3 + c300*x^3
-     + c003*z^3 + c040*y^4 + c400*x^4 + c004*z^4 + 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
+     + c112*x*y*z^2 + c010*y + c000 + c100*x + c001*z + 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 + 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
 
 > 
@@ -1437,7 +1690,7 @@ coeff_list_3d_order4 := [c040, c030, c130, c020, c120, c220, c010, c110, c210,
 > 
 ################################################################################
 # 2d.maple -- compute Lagrange interpolation coefficients in 2-D
-# $Id: $
+# $Id: 2d.maple,v 1.1 2002/08/18 15:12:03 jthorn Exp $
 > 
 ################################################################################
 > 
@@ -1466,7 +1719,7 @@ interp_2d_cube_order1_smooth0 :=
 
 > print_coeff__lc_of_data(%, "coeff_I_", "fp",
 > 			"2d.coeffs/2d.cube.order1.smooth0/coeff-I.compute.c");
-bytes used=1000160, alloc=917336, time=0.07
+bytes used=1002060, alloc=917336, time=0.10
 > 
 # d/dx
 > simplify( diff(interp_2d_cube_order1_smooth0,x) );
@@ -1483,11 +1736,11 @@ bytes used=1000160, alloc=917336, time=0.07
        1/2 DATA(1, 1) - 1/2 DATA(0, 0) - 1/2 DATA(1, 0) + 1/2 DATA(0, 1)
 
 > coeff_as_lc_of_data(%, posn_list_2d_size2);
+bytes used=2002752, alloc=1376004, time=0.18
  [COEFF(0, 0) = -1/2, COEFF(1, 0) = -1/2, COEFF(0, 1) = 1/2, COEFF(1, 1) = 1/2]
 
 > print_coeff__lc_of_data(%, "coeff_dy_", "fp",
 > 			"2d.coeffs/2d.cube.order1.smooth0/coeff-dy.compute.c");
-bytes used=2000328, alloc=1376004, time=0.15
 > 
 ################################################################################
 > 
@@ -1499,136 +1752,134 @@ bytes used=2000328, alloc=1376004, time=0.15
 > interp_2d_cube_order2_smooth0
 > 	:= Lagrange_polynomial_interpolant(fn_2d_order2, coeff_list_2d_order2,
 > 					   coord_list_2d, posn_list_2d_size3);
-interp_2d_cube_order2_smooth0 := (1/6 DATA(0, -1) + 1/6 DATA(-1, -1)
+interp_2d_cube_order2_smooth0 := (- 1/3 DATA(1, 0) + 1/6 DATA(-1, 1)
 
-     - 1/3 DATA(-1, 0) - 1/3 DATA(1, 0) + 1/6 DATA(1, -1) + 1/6 DATA(-1, 1)
+     + 1/6 DATA(0, 1) + 1/6 DATA(0, -1) - 1/3 DATA(-1, 0) - 1/3 DATA(0, 0)
 
-                                                          2
-     + 1/6 DATA(1, 1) - 1/3 DATA(0, 0) + 1/6 DATA(0, 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(0, 1)
+                                                             2
+     + 1/6 DATA(1, 1) + 1/6 DATA(-1, -1) + 1/6 DATA(1, -1)) y  + (
 
-     + 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)
 
-    (1/4 DATA(1, 1) - 1/4 DATA(1, -1) + 1/4 DATA(-1, -1) - 1/4 DATA(-1, 1)) x y
+     - 1/6 DATA(0, -1) - 1/6 DATA(1, -1)) y +
 
-     + 2/9 DATA(0, -1) - 1/9 DATA(-1, -1) + 2/9 DATA(-1, 0) + 2/9 DATA(1, 0)
+    (- 1/4 DATA(1, -1) - 1/4 DATA(-1, 1) + 1/4 DATA(1, 1) + 1/4 DATA(-1, -1)) x
 
-     - 1/9 DATA(1, -1) - 1/9 DATA(-1, 1) - 1/9 DATA(1, 1) + 5/9 DATA(0, 0)
+    y + 2/9 DATA(1, 0) - 1/9 DATA(-1, 1) + 2/9 DATA(0, 1) + 2/9 DATA(0, -1)
 
-     + 2/9 DATA(0, 1) + (- 1/6 DATA(-1, -1) - 1/6 DATA(-1, 0) + 1/6 DATA(1, 0)
+     + 2/9 DATA(-1, 0) + 5/9 DATA(0, 0) - 1/9 DATA(1, 1) - 1/9 DATA(-1, -1)
 
-     + 1/6 DATA(1, -1) - 1/6 DATA(-1, 1) + 1/6 DATA(1, 1)) x + (
+     - 1/9 DATA(1, -1) + (- 1/6 DATA(-1, 0) + 1/6 DATA(1, 0) - 1/6 DATA(-1, 1)
 
-    1/6 DATA(-1, -1) + 1/6 DATA(-1, 0) + 1/6 DATA(1, 0) + 1/6 DATA(1, -1)
+     + 1/6 DATA(1, 1) - 1/6 DATA(-1, -1) + 1/6 DATA(1, -1)) x + (1/6 DATA(1, 0)
 
-     - 1/3 DATA(0, -1) + 1/6 DATA(-1, 1) + 1/6 DATA(1, 1) - 1/3 DATA(0, 0)
+     + 1/6 DATA(-1, 1) - 1/3 DATA(0, 1) - 1/3 DATA(0, -1) + 1/6 DATA(-1, 0)
 
-                        2
-     - 1/3 DATA(0, 1)) x
+                                                                              2
+     - 1/3 DATA(0, 0) + 1/6 DATA(1, 1) + 1/6 DATA(-1, -1) + 1/6 DATA(1, -1)) x
 
 > 
 # I
 > coeff_as_lc_of_data(%, posn_list_2d_size3);
-                                2                                2
-[COEFF(-1, -1) = - 1/6 y + 1/6 y  - 1/9 - 1/6 x + 1/4 x y + 1/6 x ,
+                                2                              2
+[COEFF(-1, -1) = 1/4 x y + 1/6 y  - 1/6 y - 1/6 x - 1/9 + 1/6 x ,
 
-                                        2        2
-    COEFF(0, -1) = - 1/6 y + 2/9 + 1/6 y  - 1/3 x ,
+                                  2        2
+    COEFF(0, -1) = - 1/6 y - 1/3 x  + 1/6 y  + 2/9,
 
-                                                    2              2
-    COEFF(1, -1) = - 1/6 y - 1/4 x y + 1/6 x + 1/6 y  - 1/9 + 1/6 x ,
+                                                  2        2
+    COEFF(1, -1) = - 1/6 y - 1/9 - 1/4 x y + 1/6 x  + 1/6 y  + 1/6 x,
 
-                          2              2
-    COEFF(-1, 0) = - 1/3 y  + 2/9 + 1/6 x  - 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(0, 0) = - 1/3 y  + 5/9 - 1/3 x ,
 
-                             2        2
-    COEFF(1, 0) = 2/9 - 1/3 y  + 1/6 x  + 1/6 x,
+                             2                2
+    COEFF(1, 0) = 2/9 - 1/3 y  + 1/6 x + 1/6 x ,
 
                         2                2
-    COEFF(-1, 1) = 1/6 y  + 1/6 y + 1/6 x  - 1/4 x y - 1/6 x - 1/9,
+    COEFF(-1, 1) = 1/6 y  - 1/6 x + 1/6 x  + 1/6 y - 1/4 x y - 1/9,
 
-                               2              2
-    COEFF(0, 1) = 1/6 y - 1/3 x  + 2/9 + 1/6 y ,
+                               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 y + 1/6 x  - 1/9 + 1/4 x y + 1/6 x]
+                       2                              2
+    COEFF(1, 1) = 1/6 y  - 1/9 + 1/6 y + 1/6 x + 1/6 x  + 1/4 x y]
 
 > print_coeff__lc_of_data(%, "coeff_I_", "fp",
 > 			"2d.coeffs/2d.cube.order2.smooth0/coeff-I.compute.c");
-bytes used=3000520, alloc=1769148, time=0.22
-bytes used=4002236, alloc=1834672, time=0.30
+bytes used=3002924, alloc=1769148, time=0.25
+bytes used=4003132, alloc=1834672, time=0.32
 > 
 # 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)
+- 1/4 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, -1) - 1/6 DATA(-1, 0) + 1/6 DATA(1, 0) + 1/6 DATA(1, -1)
+     - 1/6 DATA(-1, 0) + 1/6 DATA(1, 0) - 1/6 DATA(-1, 1) + 1/6 DATA(1, 1)
 
-     - 1/6 DATA(-1, 1) + 1/6 DATA(1, 1) + 1/3 x DATA(-1, -1)
+     - 1/6 DATA(-1, -1) + 1/6 DATA(1, -1) + 1/3 x DATA(1, 0)
 
-     + 1/3 x DATA(-1, 0) + 1/3 x DATA(1, 0) + 1/3 x DATA(1, -1)
+     + 1/3 x DATA(-1, 1) - 2/3 x DATA(0, 1) - 2/3 x DATA(0, -1)
 
-     - 2/3 x DATA(0, -1) + 1/3 x DATA(-1, 1) + 1/3 x DATA(1, 1)
+     + 1/3 x DATA(-1, 0) - 2/3 x DATA(0, 0) + 1/3 x DATA(1, 1)
 
-     - 2/3 x DATA(0, 0) - 2/3 x DATA(0, 1)
+     + 1/3 x DATA(-1, -1) + 1/3 x DATA(1, -1)
 
 > coeff_as_lc_of_data(%, posn_list_2d_size3);
-[COEFF(-1, -1) = 1/4 y - 1/6 + 1/3 x, COEFF(0, -1) = - 2/3 x,
+[COEFF(-1, -1) = - 1/6 + 1/4 y + 1/3 x, COEFF(0, -1) = - 2/3 x,
 
-    COEFF(1, -1) = 1/6 + 1/3 x - 1/4 y, COEFF(-1, 0) = - 1/6 + 1/3 x,
+    COEFF(1, -1) = 1/6 - 1/4 y + 1/3 x, COEFF(-1, 0) = - 1/6 + 1/3 x,
 
     COEFF(0, 0) = - 2/3 x, COEFF(1, 0) = 1/6 + 1/3 x,
 
-    COEFF(-1, 1) = - 1/4 y - 1/6 + 1/3 x, COEFF(0, 1) = - 2/3 x,
+    COEFF(-1, 1) = - 1/4 y + 1/3 x - 1/6, COEFF(0, 1) = - 2/3 x,
 
     COEFF(1, 1) = 1/4 y + 1/3 x + 1/6]
 
 > print_coeff__lc_of_data(%, "coeff_dx_", "fp",
 > 			"2d.coeffs/2d.cube.order2.smooth0/coeff-dx.compute.c");
-bytes used=5002436, alloc=1834672, time=0.38
+bytes used=5003368, alloc=1834672, time=0.41
 > 
 # d/dy
 > simplify( diff(interp_2d_cube_order2_smooth0,y) );
-1/3 y DATA(0, -1) + 1/3 y DATA(-1, -1) - 2/3 y DATA(-1, 0) - 2/3 y DATA(1, 0)
+- 2/3 y DATA(1, 0) + 1/3 y DATA(-1, 1) + 1/3 y DATA(0, 1) + 1/3 y DATA(0, -1)
 
-     + 1/3 y DATA(1, -1) + 1/3 y DATA(-1, 1) + 1/3 y DATA(1, 1)
+     - 2/3 y DATA(-1, 0) - 2/3 y DATA(0, 0) + 1/3 y DATA(1, 1)
 
-     - 2/3 y DATA(0, 0) + 1/3 y DATA(0, 1) + 1/6 DATA(-1, 1) - 1/6 DATA(1, -1)
+     + 1/3 y DATA(-1, -1) + 1/3 y DATA(1, -1) - 1/6 DATA(-1, -1)
 
-     - 1/6 DATA(0, -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) + 1/6 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)
+     - 1/6 DATA(1, -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) + 1/4 x DATA(-1, -1)
 
 > coeff_as_lc_of_data(%, posn_list_2d_size3);
-[COEFF(-1, -1) = - 1/6 + 1/4 x + 1/3 y, COEFF(0, -1) = 1/3 y - 1/6,
+[COEFF(-1, -1) = 1/3 y - 1/6 + 1/4 x, COEFF(0, -1) = - 1/6 + 1/3 y,
 
-    COEFF(1, -1) = 1/3 y - 1/6 - 1/4 x, COEFF(-1, 0) = - 2/3 y,
+    COEFF(1, -1) = - 1/4 x + 1/3 y - 1/6, COEFF(-1, 0) = - 2/3 y,
 
     COEFF(0, 0) = - 2/3 y, COEFF(1, 0) = - 2/3 y,
 
-    COEFF(-1, 1) = 1/3 y - 1/4 x + 1/6, COEFF(0, 1) = 1/6 + 1/3 y,
+    COEFF(-1, 1) = 1/3 y + 1/6 - 1/4 x, COEFF(0, 1) = 1/3 y + 1/6,
 
-    COEFF(1, 1) = 1/6 + 1/3 y + 1/4 x]
+    COEFF(1, 1) = 1/6 + 1/4 x + 1/3 y]
 
 > print_coeff__lc_of_data(%, "coeff_dy_", "fp",
 > 			"2d.coeffs/2d.cube.order2.smooth0/coeff-dy.compute.c");
 > 
 # d^2/dx^2
 > simplify( diff(interp_2d_cube_order2_smooth0,x,x) );
-1/3 DATA(-1, -1) + 1/3 DATA(-1, 0) + 1/3 DATA(1, 0) + 1/3 DATA(1, -1)
+bytes used=6003876, alloc=1834672, time=0.51
+1/3 DATA(1, 0) + 1/3 DATA(-1, 1) - 2/3 DATA(0, 1) - 2/3 DATA(0, -1)
 
-     - 2/3 DATA(0, -1) + 1/3 DATA(-1, 1) + 1/3 DATA(1, 1) - 2/3 DATA(0, 0)
+     + 1/3 DATA(-1, 0) - 2/3 DATA(0, 0) + 1/3 DATA(1, 1) + 1/3 DATA(-1, -1)
 
-     - 2/3 DATA(0, 1)
+     + 1/3 DATA(1, -1)
 
 > coeff_as_lc_of_data(%, posn_list_2d_size3);
-bytes used=6002660, alloc=1834672, time=0.47
 [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,
@@ -1640,7 +1891,7 @@ bytes used=6002660, alloc=1834672, time=0.47
 > 
 # 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)
+    - 1/4 DATA(1, -1) - 1/4 DATA(-1, 1) + 1/4 DATA(1, 1) + 1/4 DATA(-1, -1)
 
 > coeff_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,
@@ -1654,11 +1905,11 @@ bytes used=6002660, alloc=1834672, time=0.47
 > 
 # d^2/dy^2
 > simplify( diff(interp_2d_cube_order2_smooth0,y,y) );
-1/3 DATA(0, -1) + 1/3 DATA(-1, -1) - 2/3 DATA(-1, 0) - 2/3 DATA(1, 0)
+- 2/3 DATA(1, 0) + 1/3 DATA(-1, 1) + 1/3 DATA(0, 1) + 1/3 DATA(0, -1)
 
-     + 1/3 DATA(1, -1) + 1/3 DATA(-1, 1) + 1/3 DATA(1, 1) - 2/3 DATA(0, 0)
+     - 2/3 DATA(-1, 0) - 2/3 DATA(0, 0) + 1/3 DATA(1, 1) + 1/3 DATA(-1, -1)
 
-     + 1/3 DATA(0, 1)
+     + 1/3 DATA(1, -1)
 
 > coeff_as_lc_of_data(%, posn_list_2d_size3);
 [COEFF(-1, -1) = 1/3, COEFF(0, -1) = 1/3, COEFF(1, -1) = 1/3,
@@ -1669,6 +1920,7 @@ bytes used=6002660, alloc=1834672, time=0.47
 
 > print_coeff__lc_of_data(%, "coeff_dyy_", "fp",
 > 			"2d.coeffs/2d.cube.order2.smooth0/coeff-dyy.compute.c");
+bytes used=7005040, alloc=1834672, time=0.58
 > 
 ################################################################################
 > 
@@ -1680,828 +1932,832 @@ bytes used=6002660, alloc=1834672, time=0.47
 > interp_2d_cube_order3_smooth0
 > 	:= Lagrange_polynomial_interpolant(fn_2d_order3, coeff_list_2d_order3,
 > 					   coord_list_2d, posn_list_2d_size4);
-bytes used=7003016, alloc=1834672, time=0.54
-bytes used=8003280, alloc=1900196, time=0.60
-bytes used=9003556, alloc=1965720, time=0.67
-bytes used=10003800, alloc=1965720, time=0.74
-bytes used=11003984, alloc=1965720, time=0.80
-interp_2d_cube_order3_smooth0 := (1/40 DATA(0, 0) - 1/40 DATA(1, 0)
+bytes used=8005308, alloc=1900196, time=0.64
+bytes used=9005464, alloc=1900196, time=0.71
+bytes used=10006780, alloc=1965720, time=0.77
+bytes used=11007312, alloc=1965720, time=0.84
+                                 /
+interp_2d_cube_order3_smooth0 := |- 1/25 DATA(0, 0) - 1/100 DATA(1, 0)
+                                 \
+
+     - 1/100 DATA(0, 1) + 3/50 DATA(1, 1) + 2/25 DATA(2, 1) + 7/100 DATA(2, 0)
 
-     + 1/40 DATA(0, 1) - 1/40 DATA(1, 1) + 3/40 DATA(-1, 0) + 1/40 DATA(1, -1)
+     - 9/100 DATA(2, -1) - 3/50 DATA(2, 2) + 2/25 DATA(1, 2) + 7/100 DATA(0, 2)
 
-     - 1/40 DATA(0, -1) - 3/40 DATA(-1, -1) + 3/40 DATA(-1, 1)
+                                              13
+     - 9/100 DATA(-1, 2) - 1/50 DATA(-1, 0) - --- DATA(-1, 1)
+                                              100
+
+                                              13             \
+     + 6/25 DATA(-1, -1) - 1/50 DATA(0, -1) - --- DATA(1, -1)| x y + (
+                                              100            /
 
-     + 1/40 DATA(1, 2) + 3/40 DATA(2, 2) - 3/40 DATA(2, 0) - 3/40 DATA(2, 1)
+    1/40 DATA(0, 0) + 1/40 DATA(1, 0) - 1/40 DATA(0, 1) - 1/40 DATA(1, 1)
 
-                                                                 2   /
-     - 3/40 DATA(-1, 2) - 1/40 DATA(0, 2) + 3/40 DATA(2, -1)) x y  + |
-                                                                     \
+     + 1/40 DATA(2, 1) - 1/40 DATA(2, 0) - 3/40 DATA(2, -1) + 3/40 DATA(2, 2)
 
-    - 1/25 DATA(0, 0) - 1/100 DATA(1, 0) - 1/100 DATA(0, 1) + 3/50 DATA(1, 1)
+     - 3/40 DATA(1, 2) - 3/40 DATA(0, 2) + 3/40 DATA(-1, 2) - 1/40 DATA(-1, 0)
 
-                          13
-     - 1/50 DATA(-1, 0) - --- DATA(1, -1) - 1/50 DATA(0, -1)
-                          100
+     + 1/40 DATA(-1, 1) - 3/40 DATA(-1, -1) + 3/40 DATA(0, -1)
 
-                           13
-     + 6/25 DATA(-1, -1) - --- DATA(-1, 1) + 2/25 DATA(1, 2) - 3/50 DATA(2, 2)
-                           100
+                          2
+     + 3/40 DATA(1, -1)) x  y + (1/40 DATA(0, 0) - 1/40 DATA(1, 0)
 
-     + 7/100 DATA(2, 0) + 2/25 DATA(2, 1) - 9/100 DATA(-1, 2)
+     + 1/40 DATA(0, 1) - 1/40 DATA(1, 1) - 3/40 DATA(2, 1) - 3/40 DATA(2, 0)
 
-                                           \
-     + 7/100 DATA(0, 2) - 9/100 DATA(2, -1)| x y + (1/40 DATA(0, 0)
-                                           /
+     + 3/40 DATA(2, -1) + 3/40 DATA(2, 2) + 1/40 DATA(1, 2) - 1/40 DATA(0, 2)
 
-     + 1/40 DATA(1, 0) - 1/40 DATA(0, 1) - 1/40 DATA(1, 1) - 1/40 DATA(-1, 0)
+     - 3/40 DATA(-1, 2) + 3/40 DATA(-1, 0) + 3/40 DATA(-1, 1)
 
-     + 3/40 DATA(1, -1) + 3/40 DATA(0, -1) - 3/40 DATA(-1, -1)
+                                                                   2
+     - 3/40 DATA(-1, -1) - 1/40 DATA(0, -1) + 1/40 DATA(1, -1)) x y
 
-     + 1/40 DATA(-1, 1) - 3/40 DATA(1, 2) + 3/40 DATA(2, 2) - 1/40 DATA(2, 0)
+       93               37               37               17
+     + --- DATA(0, 0) + --- DATA(1, 0) + --- DATA(0, 1) - --- DATA(1, 1)
+       200              200              200              200
 
-     + 1/40 DATA(2, 1) + 3/40 DATA(-1, 2) - 3/40 DATA(0, 2) - 3/40 DATA(2, -1))
+                         13               17
+     - 2/25 DATA(2, 1) + --- DATA(2, 0) - --- DATA(2, -1) + 7/200 DATA(2, 2)
+                         100              200
 
-     2     93               37               37               17
-    x  y + --- DATA(0, 0) + --- DATA(1, 0) + --- DATA(0, 1) - --- DATA(1, 1)
-           200              200              200              200
+                         13               17                11
+     - 2/25 DATA(1, 2) + --- DATA(0, 2) - --- DATA(-1, 2) + -- DATA(-1, 0)
+                         100              200               50
 
-       11                                  11               23
-     + -- DATA(-1, 0) - 1/50 DATA(1, -1) + -- DATA(0, -1) - --- DATA(-1, -1)
-       50                                  50               200
+                          23                 11
+     - 1/50 DATA(-1, 1) - --- DATA(-1, -1) + -- DATA(0, -1) - 1/50 DATA(1, -1)
+                          200                50
 
-     - 1/50 DATA(-1, 1) + (1/8 DATA(0, 0) + 1/8 DATA(1, 0) - 1/8 DATA(0, 1)
+     + (1/8 DATA(0, 0) + 1/8 DATA(1, 0) - 1/8 DATA(0, 1) - 1/8 DATA(1, 1)
 
-     - 1/8 DATA(1, 1) + 1/8 DATA(-1, 0) - 1/24 DATA(1, -1) - 1/24 DATA(0, -1)
+     - 1/8 DATA(2, 1) + 1/8 DATA(2, 0) - 1/24 DATA(2, -1) + 1/24 DATA(2, 2)
 
-     - 1/24 DATA(-1, -1) - 1/8 DATA(-1, 1) + 1/24 DATA(1, 2) + 1/24 DATA(2, 2)
+     + 1/24 DATA(1, 2) + 1/24 DATA(0, 2) + 1/24 DATA(-1, 2) + 1/8 DATA(-1, 0)
 
-     + 1/8 DATA(2, 0) - 1/8 DATA(2, 1) + 1/24 DATA(-1, 2) + 1/24 DATA(0, 2)
+     - 1/8 DATA(-1, 1) - 1/24 DATA(-1, -1) - 1/24 DATA(0, -1)
 
                           3   /  21              19
-     - 1/24 DATA(2, -1)) y  + |- -- DATA(0, 0) - -- DATA(1, 0)
+     - 1/24 DATA(1, -1)) y  + |- -- DATA(0, 0) - -- DATA(1, 0)
                               \  80              80
 
-                         11              23
-     + 9/80 DATA(0, 1) + -- DATA(1, 1) - -- DATA(-1, 0) + 9/80 DATA(1, -1)
-                         80              80
+                         11              13              17
+     + 9/80 DATA(0, 1) + -- DATA(1, 1) + -- DATA(2, 1) - -- DATA(2, 0)
+                         80              80              80
 
-       11               13
-     + -- DATA(0, -1) + -- DATA(-1, -1) + 7/80 DATA(-1, 1) - 1/80 DATA(1, 2)
-       80               80
+     + 7/80 DATA(2, -1) - 3/80 DATA(2, 2) - 1/80 DATA(1, 2) + 1/80 DATA(0, 2)
 
-                         17              13
-     - 3/80 DATA(2, 2) - -- DATA(2, 0) + -- DATA(2, 1) + 3/80 DATA(-1, 2)
-                         80              80
+                          23                                  13
+     + 3/80 DATA(-1, 2) - -- DATA(-1, 0) + 7/80 DATA(-1, 1) + -- DATA(-1, -1)
+                          80                                  80
 
-                                         \  2   /  57
-     + 1/80 DATA(0, 2) + 7/80 DATA(2, -1)| y  + |- --- DATA(0, 0)
-                                         /      \  400
+       11                               \  2   /  57
+     + -- DATA(0, -1) + 9/80 DATA(1, -1)| y  + |- --- DATA(0, 0)
+       80                               /      \  400
 
-       63               117              103              31
-     - --- DATA(1, 0) + --- DATA(0, 1) + --- DATA(1, 1) - --- DATA(-1, 0)
+       63               117              103              69
+     - --- DATA(1, 0) + --- DATA(0, 1) + --- DATA(1, 1) + --- DATA(2, 1)
        400              400              400              400
 
-       157                223                109
-     - ---- DATA(1, -1) - ---- DATA(0, -1) - ---- DATA(-1, -1)
-       1200               1200               1200
+       49                89                149                37
+     - --- DATA(2, 0) + ---- DATA(2, -1) - ---- DATA(2, 2) + ---- DATA(1, 2)
+       400              1200               1200              1200
 
-       111                37               149               49
-     + --- DATA(-1, 1) + ---- DATA(1, 2) - ---- DATA(2, 2) - --- DATA(2, 0)
-       400               1200              1200              400
+        43               131                31                111
+     + ---- DATA(0, 2) - ---- DATA(-1, 2) - --- DATA(-1, 0) + --- DATA(-1, 1)
+       1200              1200               400               400
 
-       69               131                 43                89             \
-     + --- DATA(2, 1) - ---- DATA(-1, 2) + ---- DATA(0, 2) + ---- DATA(2, -1)|
-       400              1200               1200              1200            /
+       109                 223                157             \     /
+     - ---- DATA(-1, -1) - ---- DATA(0, -1) - ---- DATA(1, -1)| y + |
+       1200                1200               1200            /     \
 
-        /  57               117              63               103
-    y + |- --- DATA(0, 0) + --- DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1)
-        \  400              400              400              400
+      57               117              63               103
+    - --- DATA(0, 0) + --- DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1)
+      400              400              400              400
 
-       223                111               31                109
-     - ---- DATA(-1, 0) + --- DATA(1, -1) - --- DATA(0, -1) - ---- DATA(-1, -1)
-       1200               400               400               1200
+        37                43               131                149
+     + ---- DATA(2, 1) + ---- DATA(2, 0) - ---- DATA(2, -1) - ---- DATA(2, 2)
+       1200              1200              1200               1200
 
-       157                69               149                43
-     - ---- DATA(-1, 1) + --- DATA(1, 2) - ---- DATA(2, 2) + ---- DATA(2, 0)
-       1200               400              1200              1200
+       69               49                89                223
+     + --- DATA(1, 2) - --- DATA(0, 2) + ---- DATA(-1, 2) - ---- DATA(-1, 0)
+       400              400              1200               1200
 
-        37                89                49               131             \
-     + ---- DATA(2, 1) + ---- DATA(-1, 2) - --- DATA(0, 2) - ---- DATA(2, -1)|
-       1200              1200               400              1200            /
+       157                109                 31                111
+     - ---- DATA(-1, 1) - ---- DATA(-1, -1) - --- DATA(0, -1) + --- DATA(1, -1)
+       1200               1200                400               400
 
-        /  21                                19              11
-    x + |- -- DATA(0, 0) + 9/80 DATA(1, 0) - -- DATA(0, 1) + -- DATA(1, 1)
-        \  80                                80              80
+    \     /  21                                19              11
+    | x + |- -- DATA(0, 0) + 9/80 DATA(1, 0) - -- DATA(0, 1) + -- DATA(1, 1)
+    /     \  80                                80              80
 
-       11                                  23               13
-     + -- DATA(-1, 0) + 7/80 DATA(1, -1) - -- DATA(0, -1) + -- DATA(-1, -1)
-       80                                  80               80
+     - 1/80 DATA(2, 1) + 1/80 DATA(2, 0) + 3/80 DATA(2, -1) - 3/80 DATA(2, 2)
 
-                          13
-     + 9/80 DATA(-1, 1) + -- DATA(1, 2) - 3/80 DATA(2, 2) + 1/80 DATA(2, 0)
-                          80
+       13              17                                 11
+     + -- DATA(1, 2) - -- DATA(0, 2) + 7/80 DATA(-1, 2) + -- DATA(-1, 0)
+       80              80                                 80
 
-                                            17                              \
-     - 1/80 DATA(2, 1) + 7/80 DATA(-1, 2) - -- DATA(0, 2) + 3/80 DATA(2, -1)|
-                                            80                              /
+                          13                23                               \
+     + 9/80 DATA(-1, 1) + -- DATA(-1, -1) - -- DATA(0, -1) + 7/80 DATA(1, -1)|
+                          80                80                               /
 
      2
     x  + (1/8 DATA(0, 0) - 1/8 DATA(1, 0) + 1/8 DATA(0, 1) - 1/8 DATA(1, 1)
 
-     - 1/24 DATA(-1, 0) - 1/8 DATA(1, -1) + 1/8 DATA(0, -1) - 1/24 DATA(-1, -1)
+     + 1/24 DATA(2, 1) + 1/24 DATA(2, 0) + 1/24 DATA(2, -1) + 1/24 DATA(2, 2)
 
-     - 1/24 DATA(-1, 1) + 1/24 DATA(2, 1) - 1/8 DATA(1, 2) + 1/24 DATA(2, 2)
+     - 1/8 DATA(1, 2) + 1/8 DATA(0, 2) - 1/24 DATA(-1, 2) - 1/24 DATA(-1, 0)
 
-     + 1/24 DATA(2, 0) - 1/24 DATA(-1, 2) + 1/8 DATA(0, 2) + 1/24 DATA(2, -1))
+     - 1/24 DATA(-1, 1) - 1/24 DATA(-1, -1) + 1/8 DATA(0, -1) - 1/8 DATA(1, -1)
 
-     3                                        13
-    x  - 2/25 DATA(1, 2) + 7/200 DATA(2, 2) + --- DATA(2, 0) - 2/25 DATA(2, 1)
-                                              100
-
-       17                13               17
-     - --- DATA(-1, 2) + --- DATA(0, 2) - --- DATA(2, -1)
-       200               100              200
+       3
+    ) x
 
 > 
 # I
 > coeff_as_lc_of_data(%, posn_list_2d_size4);
-bytes used=12006624, alloc=1965720, time=0.86
-                 13  2         3         2           3              13  2
-[COEFF(-1, -1) = -- y  - 1/24 y  - 3/40 x  y - 1/24 x  + 6/25 x y + -- x
-                 80                                                 80
+bytes used=12010552, alloc=1965720, time=0.91
+                           2   13  2         3   109            3   23    13  2
+[COEFF(-1, -1) = - 3/40 x y  + -- x  - 1/24 x  - ---- x - 1/24 y  - --- + -- y
+                               80                1200               200   80
 
-               2   109      23    109                              2        3
-     - 3/40 x y  - ---- x - --- - ---- y, COEFF(0, -1) = - 1/40 x y  + 1/8 x
-                   1200     200   1200
+             2     109                                                  2
+     - 3/40 x  y - ---- y + 6/25 x y, COEFF(0, -1) = - 1/50 x y + 3/40 x  y
+                   1200
 
-                        2     23  2   11         3   31      11  2   223
-     - 1/50 x y + 3/40 x  y - -- x  + -- - 1/24 y  - --- x + -- y  - ---- y,
-                              80      50             400     80      1200
+       11   23  2   223           3           2   31      11  2         3
+     + -- - -- x  - ---- y + 1/8 x  - 1/40 x y  - --- x + -- y  - 1/24 y ,
+       50   80      1200                          400     80
 
-                         2         2             2         3          111
-    COEFF(1, -1) = 9/80 y  + 3/40 x  y + 1/40 x y  - 1/24 y  - 1/50 + --- x
-                                                                      400
+                         2         2     111     157      13              3
+    COEFF(1, -1) = 9/80 y  + 3/40 x  y + --- x - ---- y - --- x y - 1/24 y
+                                         400     1200     100
 
-       157            2   13             3
-     - ---- y + 7/80 x  - --- x y - 1/8 x , COEFF(2, -1) = - 9/100 x y
-       1200               100
+               2         2               3                       2           2
+     + 1/40 x y  + 7/80 x  - 1/50 - 1/8 x , COEFF(2, -1) = 7/80 y  + 3/40 x y
 
-               2         2         3    89      17          2           3
-     + 3/40 x y  + 7/80 y  - 1/24 y  + ---- y - --- - 3/40 x  y + 1/24 x
-                                       1200     200
+             2           3   17          3    89      131
+     - 3/40 x  y - 1/24 y  - --- + 1/24 x  + ---- y - ---- x - 9/100 x y
+                             200             1200     1200
 
-       131            2                 11              31              2
-     - ---- x + 3/80 x , COEFF(-1, 0) = -- - 1/50 x y - --- y + 3/40 x y
-       1200                             50              400
+             2                         2   11  2   23  2   223            2
+     + 3/80 x , COEFF(-1, 0) = 3/40 x y  + -- x  - -- y  - ---- x - 1/40 x  y
+                                           80      80      1200
 
-       223            3   23  2         2     11  2        3
-     - ---- x - 1/24 x  - -- y  - 1/40 x  y + -- x  + 1/8 y , COEFF(0, 0) =
-       1200               80                  80
+                       3   11         3   31                         2
+     - 1/50 x y + 1/8 y  + -- - 1/24 x  - --- y, COEFF(0, 0) = 1/40 x  y
+                           50             400
 
-                 21  2   21  2        3        3   57      57            2
-    - 1/25 x y - -- y  - -- x  + 1/8 x  + 1/8 y  - --- x - --- y + 1/40 x  y
-                 80      80                        400     400
+               2   21  2        3   21  2        3              57      93
+     + 1/40 x y  - -- y  + 1/8 x  - -- x  + 1/8 y  - 1/25 x y - --- x + ---
+                   80               80                          400     200
 
-               2   93                   19  2   63              2
-     + 1/40 x y  + ---, COEFF(1, 0) = - -- y  - --- y - 1/40 x y  - 1/100 x y
-                   200                  80      400
+       57                             2   37                      2   117
+     - --- y, COEFF(1, 0) = - 1/40 x y  + --- - 1/100 x y + 9/80 x  + --- x
+       400                                200                         400
 
-            3         2   117     37         3         2
-     + 1/8 y  + 9/80 x  + --- x + --- - 1/8 x  + 1/40 x  y, COEFF(2, 0) =
-                          400     200
+            3        3   19  2         2     63
+     + 1/8 y  - 1/8 x  - -- y  + 1/40 x  y - --- y, COEFF(2, 0) = 7/100 x y
+                         80                  400
 
-      17  2         2   49           3         2           3           2
-    - -- y  + 1/80 x  - --- y + 1/8 y  - 1/40 x  y + 1/24 x  - 3/40 x y
-      80                400
+               2         3    43            2           2        3   13
+     - 3/40 x y  + 1/24 x  + ---- x - 1/40 x  y + 1/80 x  + 1/8 y  + ---
+                             1200                                    100
 
-                   13     43                          2            157
-     + 7/100 x y + --- + ---- x, COEFF(-1, 1) = 1/40 x  y - 1/50 - ---- x
-                   100   1200                                      1200
+       49      17  2                       2   13                       2
+     - --- y - -- y , COEFF(-1, 1) = 9/80 x  - --- x y - 1/50 + 3/40 x y
+       400     80                              100
 
-       111           3        3           2   13              2         2
-     + --- y - 1/24 x  - 1/8 y  + 3/40 x y  - --- x y + 7/80 y  + 9/80 x ,
-       400                                    100
+            3   157            3         2   111           2
+     - 1/8 y  - ---- x - 1/24 x  + 7/80 y  + --- y + 1/40 x  y, COEFF(0, 1) =
+                1200                         400
 
-                          2     37         3   63      19  2        3
-    COEFF(0, 1) = - 1/40 x  y + --- + 1/8 x  - --- x - -- x  - 1/8 y
-                                200            400     80
+                  19  2        3        3         2   63            2
+    - 1/100 x y - -- x  - 1/8 y  + 1/8 x  + 9/80 y  - --- x - 1/40 x  y
+                  80                                  400
 
-               2   117           2                            103           2
-     + 1/40 x y  + --- y + 9/80 y  - 1/100 x y, COEFF(1, 1) = --- y - 1/40 x  y
-                   400                                        400
+               2   117     37                         2
+     + 1/40 x y  + --- y + ---, COEFF(1, 1) = - 1/40 x  y + 3/50 x y
+                   400     200
 
-       11  2   11  2              103          3           2   17         3
-     + -- x  + -- y  + 3/50 x y + --- x - 1/8 x  - 1/40 x y  - --- - 1/8 y ,
-       80      80                 400                          200
+               2   17    103     11  2        3   11  2   103          3
+     - 1/40 x y  - --- + --- x + -- x  - 1/8 y  + -- y  + --- y - 1/8 x ,
+                   200   400     80               80      400
 
-                         3         2             2    37            3         2
-    COEFF(2, 1) = - 1/8 y  + 1/40 x  y - 3/40 x y  + ---- x + 1/24 x  - 1/80 x
-                                                     1200
+                        2     69      13  2         3        3         2
+    COEFF(2, 1) = 1/40 x  y + --- y + -- y  + 1/24 x  - 1/8 y  - 1/80 x
+                              400     80
 
-              13  2   69                                     2    89
-     - 2/25 + -- y  + --- y + 2/25 x y, COEFF(-1, 2) = 3/80 y  + ---- x
-              80      400                                        1200
+                          2    37                                 2         2
+     + 2/25 x y - 3/40 x y  + ---- x - 2/25, COEFF(-1, 2) = 7/80 x  + 3/40 x  y
+                              1200
 
-             2     131              2         2         3                     3
-     + 3/40 x  y - ---- y - 3/40 x y  + 7/80 x  + 1/24 y  - 9/100 x y - 1/24 x
-                   1200
+       131       89            3   17                      3         2
+     - ---- y + ---- x + 1/24 y  - --- - 9/100 x y - 1/24 x  + 3/80 y
+       1200     1200               200
 
-       17                   49            3    43            2           2
-     - ---, COEFF(0, 2) = - --- x + 1/24 y  + ---- y - 3/40 x  y + 1/80 y
-       200                  400               1200
+               2                      2        3                     3    43
+     - 3/40 x y , COEFF(0, 2) = 1/80 y  + 1/8 x  + 7/100 x y + 1/24 y  + ---- y
+                                                                         1200
 
-       17  2           2   13                     3                69
-     - -- x  - 1/40 x y  + --- + 7/100 x y + 1/8 x , COEFF(1, 2) = --- x
-       80                  100                                     400
+       49      17  2   13          2             2                        2
+     - --- x - -- x  + --- - 3/40 x  y - 1/40 x y , COEFF(1, 2) = - 3/40 x  y
+       400     80      100
 
-             2           2           2    37                   3   13  2
-     - 3/40 x  y - 1/80 y  + 1/40 x y  + ---- y - 2/25 + 1/24 y  + -- x
-                                         1200                      80
+        37      13  2         2                   3         3          69
+     + ---- y + -- x  - 1/80 y  + 2/25 x y - 1/8 x  + 1/24 y  - 2/25 + --- x
+       1200     80                                                     400
 
-                       3                      2           3         3         2
-     + 2/25 x y - 1/8 x , COEFF(2, 2) = 3/40 x  y + 1/24 x  + 1/24 y  - 3/80 x
+               2                  149              2         2           3
+     + 1/40 x y , COEFF(2, 2) = - ---- y + 3/40 x y  + 3/40 x  y + 1/24 y
+                                  1200
 
-                  149      149              2         2
-     - 3/50 x y - ---- y - ---- x + 3/40 x y  - 3/80 y  + 7/200]
-                  1200     1200
+       149                       2         2         3
+     - ---- x - 3/50 x y - 3/80 x  - 3/80 y  + 1/24 x  + 7/200]
+       1200
 
 > print_coeff__lc_of_data(%, "coeff_I_", "fp",
 > 			"2d.coeffs/2d.cube.order3.smooth0/coeff-I.compute.c");
-bytes used=13006948, alloc=2031244, time=0.93
-bytes used=14011252, alloc=2031244, time=1.01
-bytes used=15011472, alloc=2031244, time=1.11
-bytes used=16011652, alloc=2031244, time=1.19
-bytes used=17011812, alloc=2031244, time=1.29
-bytes used=18012000, alloc=2031244, time=1.39
-bytes used=19012216, alloc=2031244, time=1.50
-bytes used=20012436, alloc=2031244, time=1.62
+bytes used=13010732, alloc=2031244, time=0.98
+bytes used=14014148, alloc=2031244, time=1.07
+bytes used=15014304, alloc=2031244, time=1.17
+bytes used=16014668, alloc=2031244, time=1.25
+bytes used=17019400, alloc=2031244, time=1.35
+bytes used=18019708, alloc=2031244, time=1.44
+bytes used=19019860, alloc=2031244, time=1.54
+bytes used=20020128, alloc=2031244, time=1.65
 > 
 # d/dx
 > simplify( diff(interp_2d_cube_order3_smooth0,x) );
-bytes used=21013024, alloc=2031244, time=1.73
-3/20 x y DATA(-1, 2) + 1/20 x y DATA(0, 0) + 1/20 x y DATA(1, 0)
+bytes used=21023596, alloc=2031244, time=1.74
+  23
+- -- x DATA(0, -1) + 7/40 x DATA(1, -1) + 9/40 x DATA(-1, 1)
+  40
 
-     - 1/20 x y DATA(0, 1) - 1/20 x y DATA(1, 1) - 1/20 x y DATA(-1, 0)
+                                                    57
+     + 3/20 x y DATA(1, -1) - 1/20 x y DATA(0, 1) - --- DATA(0, 0)
+                                                    400
 
-     + 3/20 x y DATA(1, -1) + 3/20 x y DATA(0, -1) - 3/20 x y DATA(-1, -1)
+       117              63               103
+     + --- DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1) + 1/20 x y DATA(2, 1)
+       400              400              400
 
-       57               117              63               103
-     - --- DATA(0, 0) + --- DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1)
-       400              400              400              400
+     - 1/20 x y DATA(2, 0) - 3/20 x y DATA(2, -1) + 3/20 x y DATA(2, 2)
 
-                                                         2
-     + 1/20 x y DATA(-1, 1) - 3/20 x y DATA(1, 2) - 1/8 x  DATA(-1, 2)
+     - 3/20 x y DATA(1, 2) - 3/20 x y DATA(0, 2) + 3/20 x y DATA(-1, 2)
 
-            2                   2                    2
-     + 3/8 x  DATA(0, 2) + 1/8 x  DATA(2, -1) + 1/8 x  DATA(2, 1)
+     - 1/20 x y DATA(-1, 0) + 1/20 x y DATA(-1, 1) - 3/20 x y DATA(-1, -1)
 
-            2
-     + 1/8 x  DATA(2, 0) - 3/20 x y DATA(2, -1) - 3/20 x y DATA(0, 2)
+                               37                43
+     + 3/20 x y DATA(0, -1) + ---- DATA(2, 1) + ---- DATA(2, 0)
+                              1200              1200
 
-     + 1/20 x y DATA(2, 1) - 1/20 x y DATA(2, 0) + 3/20 x y DATA(2, 2)
+       131                149               69               49
+     - ---- DATA(2, -1) - ---- DATA(2, 2) + --- DATA(1, 2) - --- DATA(0, 2)
+       1200               1200              400              400
 
-     + 2/25 y DATA(2, 1) + 7/100 y DATA(2, 0) + 2/25 y DATA(1, 2)
+        89                223                157
+     + ---- DATA(-1, 2) - ---- DATA(-1, 0) - ---- DATA(-1, 1)
+       1200               1200               1200
 
-     - 9/100 y DATA(2, -1) + 7/100 y DATA(0, 2) - 9/100 y DATA(-1, 2)
+       109                 31                111
+     - ---- DATA(-1, -1) - --- DATA(0, -1) + --- DATA(1, -1)
+       1200                400               400
 
-                            13
-     - 1/50 y DATA(0, -1) - --- y DATA(1, -1) - 1/50 y DATA(-1, 0)
-                            100
+     - 1/20 x y DATA(1, 1) - 1/100 y DATA(0, 1) + 3/50 y DATA(1, 1)
 
-                                 2               13
-     - 3/50 y DATA(2, 2) + 3/40 y  DATA(2, -1) - --- y DATA(-1, 1)
-                                                 100
+       13
+     + -- x DATA(-1, -1) + 1/20 x y DATA(1, 0) + 2/25 y DATA(1, 2)
+       40
 
-                                   2
-     + 6/25 y DATA(-1, -1) + 1/40 y  DATA(1, 2) - 1/100 y DATA(0, 1)
+                                  2                    2
+     + 7/100 y DATA(0, 2) + 1/40 y  DATA(0, 1) + 1/40 y  DATA(0, 0)
 
-     - 1/100 y DATA(1, 0) - 1/25 y DATA(0, 0) + 3/50 y DATA(1, 1)
+     + 6/25 y DATA(-1, -1) - 1/50 y DATA(0, -1) + 1/20 x y DATA(0, 0)
 
              2                    2                    2
-     - 1/40 y  DATA(0, 2) - 3/40 y  DATA(2, 1) - 3/40 y  DATA(2, 0)
+     - 1/40 y  DATA(1, 0) - 1/40 y  DATA(1, 1) - 3/40 y  DATA(2, 1)
 
-             2                    2                     2
-     + 3/40 y  DATA(2, 2) - 3/40 y  DATA(-1, 2) + 3/40 y  DATA(-1, 1)
-
-             2                     2                     2
-     - 1/40 y  DATA(0, -1) + 1/40 y  DATA(1, -1) + 3/40 y  DATA(-1, 0)
+             2                    2                    2
+     + 1/40 y  DATA(1, 2) - 3/40 y  DATA(2, 0) + 3/40 y  DATA(2, -1)
 
-             2                      2                    2
-     - 3/40 y  DATA(-1, -1) + 1/40 y  DATA(0, 1) - 1/40 y  DATA(1, 0)
+             2                     2                    2
+     + 3/40 y  DATA(-1, 1) + 3/40 y  DATA(2, 2) - 1/40 y  DATA(0, 2)
 
-             2              11
-     + 1/40 y  DATA(0, 0) + -- x DATA(-1, 0) + 9/40 x DATA(1, 0)
-                            40
+             2                     2                19
+     - 3/40 y  DATA(-1, 2) - 3/40 y  DATA(-1, -1) - -- x DATA(0, 1)
+                                                    40
 
-       19                      2              21                13
-     - -- x DATA(0, 1) - 1/40 y  DATA(1, 1) - -- x DATA(0, 0) + -- x DATA(1, 2)
-       40                                     40                40
+             2                     2                     2
+     + 1/40 y  DATA(1, -1) + 3/40 y  DATA(-1, 0) - 1/40 y  DATA(0, -1)
 
-       23                 13                  11
-     - -- x DATA(0, -1) + -- x DATA(-1, -1) + -- x DATA(1, 1)
-       40                 40                  40
+                           21
+     - 1/40 x DATA(2, 1) - -- x DATA(0, 0) + 9/40 x DATA(1, 0)
+                           40
 
-     + 7/40 x DATA(1, -1) + 9/40 x DATA(-1, 1) - 3/40 x DATA(2, 2)
+     + 1/40 x DATA(2, 0) + 3/40 x DATA(2, -1) - 3/40 x DATA(2, 2)
 
-     + 1/40 x DATA(2, 0) - 1/40 x DATA(2, 1) + 7/40 x DATA(-1, 2)
+       11                13                17
+     + -- x DATA(1, 1) + -- x DATA(1, 2) - -- x DATA(0, 2) + 7/40 x DATA(-1, 2)
+       40                40                40
 
-            2                   2              17
-     - 3/8 x  DATA(1, 0) + 3/8 x  DATA(0, 1) - -- x DATA(0, 2)
-                                               40
+       11
+     + -- x DATA(-1, 0) - 1/25 y DATA(0, 0) - 1/100 y DATA(1, 0)
+       40
 
-                                 2                    2
-     + 3/40 x DATA(2, -1) - 3/8 x  DATA(1, -1) + 3/8 x  DATA(0, -1)
+       13                       2                   2
+     - --- y DATA(1, -1) - 3/8 x  DATA(1, 0) + 3/8 x  DATA(0, 0)
+       100
 
             2                   2                   2
-     + 3/8 x  DATA(0, 0) - 3/8 x  DATA(1, 1) - 1/8 x  DATA(-1, 0)
+     + 1/8 x  DATA(2, 1) + 1/8 x  DATA(2, 0) + 1/8 x  DATA(2, -1)
 
-            2                   2                     2
-     - 3/8 x  DATA(1, 2) - 1/8 x  DATA(-1, -1) - 1/8 x  DATA(-1, 1)
+            2                   2                    2
+     + 1/8 x  DATA(2, 2) - 1/8 x  DATA(-1, 1) + 3/8 x  DATA(0, 2)
 
-            2              223                111               31
-     + 1/8 x  DATA(2, 2) - ---- DATA(-1, 0) + --- DATA(1, -1) - --- DATA(0, -1)
-                           1200               400               400
+            2                    2                    2
+     + 3/8 x  DATA(0, -1) - 1/8 x  DATA(-1, 2) - 1/8 x  DATA(-1, 0)
 
-       109                 157                69               149
-     - ---- DATA(-1, -1) - ---- DATA(-1, 1) + --- DATA(1, 2) - ---- DATA(2, 2)
-       1200                1200               400              1200
+            2                   2                   2
+     - 3/8 x  DATA(1, 2) + 3/8 x  DATA(0, 1) - 3/8 x  DATA(1, 1)
 
-        43                37                89                49
-     + ---- DATA(2, 0) + ---- DATA(2, 1) + ---- DATA(-1, 2) - --- DATA(0, 2)
-       1200              1200              1200               400
+            2                    2
+     - 3/8 x  DATA(1, -1) - 1/8 x  DATA(-1, -1) + 7/100 y DATA(2, 0)
 
-       131
-     - ---- DATA(2, -1)
-       1200
+     - 9/100 y DATA(2, -1) - 3/50 y DATA(2, 2) - 9/100 y DATA(-1, 2)
+
+                            13
+     - 1/50 y DATA(-1, 0) - --- y DATA(-1, 1) + 2/25 y DATA(2, 1)
+                            100
 
 > coeff_as_lc_of_data(%, posn_list_2d_size4);
-bytes used=22015264, alloc=2031244, time=1.80
+bytes used=22023792, alloc=2031244, time=1.80
                  13          2   109                              2
 [COEFF(-1, -1) = -- x - 1/8 x  - ---- + 6/25 y - 3/20 x y - 3/40 y ,
                  40              1200
 
-                     31         2         2   23
-    COEFF(0, -1) = - --- + 3/8 x  - 1/40 y  - -- x - 1/50 y + 3/20 x y,
-                     400                      40
+                     31             23           2                   2
+    COEFF(0, -1) = - --- - 1/50 y - -- x - 1/40 y  + 3/20 x y + 3/8 x ,
+                     400            40
 
-                                    2            111        2   13
-    COEFF(1, -1) = 3/20 x y + 1/40 y  + 7/40 x + --- - 3/8 x  - --- y,
-                                                 400            100
+                   111         2   13                    2
+    COEFF(1, -1) = --- + 1/40 y  - --- y + 7/40 x - 3/8 x  + 3/20 x y,
+                   400             100
 
-                        2                        131          2
-    COEFF(2, -1) = 1/8 x  - 9/100 y - 3/20 x y - ---- + 3/40 y  + 3/40 x,
-                                                 1200
+                                     2   131                             2
+    COEFF(2, -1) = - 9/100 y + 3/40 y  - ---- - 3/20 x y + 3/40 x + 1/8 x ,
+                                         1200
 
-                     223          2                       11          2
-    COEFF(-1, 0) = - ---- + 3/40 y  - 1/20 x y - 1/50 y + -- x - 1/8 x ,
-                     1200                                 40
+                          2         2   11                223
+    COEFF(-1, 0) = - 1/8 x  + 3/40 y  + -- x - 1/20 x y - ---- - 1/50 y,
+                                        40                1200
 
-                    57    21          2                  2
-    COEFF(0, 0) = - --- - -- x + 3/8 x  - 1/25 y + 1/40 y  + 1/20 x y,
-                    400   40
+                                              2        2   21     57
+    COEFF(0, 0) = - 1/25 y + 1/20 x y + 1/40 y  + 3/8 x  - -- x - ---,
+                                                           40     400
 
-                           117         2                  2
-    COEFF(1, 0) = 9/40 x + --- - 1/40 y  - 1/100 y - 3/8 x  + 1/20 x y,
-                           400
+                              117                             2        2
+    COEFF(1, 0) = - 1/100 y + --- + 1/20 x y + 9/40 x - 1/40 y  - 3/8 x ,
+                              400
 
-                       2    43          2
-    COEFF(2, 0) = 1/8 x  + ---- - 3/40 y  + 1/40 x - 1/20 x y + 7/100 y,
-                           1200
+                                            2    43                   2
+    COEFF(2, 0) = 1/40 x - 1/20 x y - 3/40 y  + ---- + 7/100 y + 1/8 x ,
+                                                1200
 
-                                   2            157    13            2
-    COEFF(-1, 1) = 1/20 x y - 1/8 x  + 9/40 x - ---- - --- y + 3/40 y ,
-                                                1200   100
+                     157                    2         2            13
+    COEFF(-1, 1) = - ---- + 1/20 x y - 1/8 x  + 3/40 y  + 9/40 x - --- y,
+                     1200                                          100
 
-                    63                   2              19           2
-    COEFF(0, 1) = - --- - 1/100 y + 3/8 x  - 1/20 x y - -- x + 1/40 y ,
-                    400                                 40
+                    19           2   63         2
+    COEFF(0, 1) = - -- x + 1/40 y  - --- + 3/8 x  - 1/20 x y - 1/100 y,
+                    40               400
 
-                               11           2        2            103
-    COEFF(1, 1) = - 1/20 x y + -- x - 1/40 y  - 3/8 x  + 3/50 y + ---,
-                               40                                 400
+                                            2        2   11     103
+    COEFF(1, 1) = 3/50 y - 1/20 x y - 1/40 y  - 3/8 x  + -- x + ---,
+                                                         40     400
 
-                                             2         2    37
-    COEFF(2, 1) = - 1/40 x + 1/20 x y + 1/8 x  - 3/40 y  + ---- + 2/25 y,
+                          2                            2    37
+    COEFF(2, 1) = - 3/40 y  + 1/20 x y - 1/40 x + 1/8 x  + ---- + 2/25 y,
                                                            1200
 
-                                           89          2                 2
-    COEFF(-1, 2) = - 9/100 y + 3/20 x y + ---- - 3/40 y  + 7/40 x - 1/8 x ,
-                                          1200
+                    89                  2                              2
+    COEFF(-1, 2) = ---- + 7/40 x - 1/8 x  - 9/100 y + 3/20 x y - 3/40 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
+                    17           2             49                    2
+    COEFF(0, 2) = - -- x - 1/40 y  + 7/100 y - --- - 3/20 x y + 3/8 x ,
+                    40                         400
 
-                         2   13     69                              2
-    COEFF(1, 2) = - 3/8 x  + -- x + --- - 3/20 x y + 2/25 y + 1/40 y ,
-                             40     400
+                                            2   69         2   13
+    COEFF(1, 2) = 2/25 y - 3/20 x y + 1/40 y  + --- - 3/8 x  + -- x,
+                                                400            40
 
-                             149         2                  2
-    COEFF(2, 2) = 3/20 x y - ---- + 1/8 x  - 3/40 x + 3/40 y  - 3/50 y]
-                             1200
+                                   2        2   149
+    COEFF(2, 2) = 3/20 x y + 3/40 y  + 1/8 x  - ---- - 3/40 x - 3/50 y]
+                                                1200
 
 > print_coeff__lc_of_data(%, "coeff_dx_", "fp",
 > 			"2d.coeffs/2d.cube.order3.smooth0/coeff-dx.compute.c");
-bytes used=23015460, alloc=2031244, time=1.87
-bytes used=24015620, alloc=2031244, time=1.96
-bytes used=25016144, alloc=2096768, time=2.07
-bytes used=26016296, alloc=2096768, time=2.18
+bytes used=23023968, alloc=2031244, time=1.87
+bytes used=24024120, alloc=2031244, time=1.95
+bytes used=25024508, alloc=2031244, time=2.05
+bytes used=26024664, alloc=2031244, time=2.20
 > 
 # d/dy
 > simplify( diff(interp_2d_cube_order3_smooth0,y) );
-bytes used=27016596, alloc=2096768, time=2.28
-- 3/20 x y DATA(-1, 2) + 1/20 x y DATA(0, 0) - 1/20 x y DATA(1, 0)
+bytes used=27025556, alloc=2031244, time=2.28
+                       13                  13
+- 1/50 x DATA(0, -1) - --- x DATA(1, -1) - --- x DATA(-1, 1)
+                       100                 100
 
-     + 1/20 x y DATA(0, 1) - 1/20 x y DATA(1, 1) + 3/20 x y DATA(-1, 0)
+                                                    57
+     + 1/20 x y DATA(1, -1) + 1/20 x y DATA(0, 1) - --- DATA(0, 0)
+                                                    400
 
-     + 1/20 x y DATA(1, -1) - 1/20 x y DATA(0, -1) - 3/20 x y DATA(-1, -1)
+       63               117              103
+     - --- DATA(1, 0) + --- DATA(0, 1) + --- DATA(1, 1) - 3/20 x y DATA(2, 1)
+       400              400              400
 
-       57               63               117              103
-     - --- DATA(0, 0) - --- DATA(1, 0) + --- DATA(0, 1) + --- DATA(1, 1)
-       400              400              400              400
+     - 3/20 x y DATA(2, 0) + 3/20 x y DATA(2, -1) + 3/20 x y DATA(2, 2)
 
-                                                          2
-     + 3/20 x y DATA(-1, 1) + 1/20 x y DATA(1, 2) + 3/40 x  DATA(-1, 2)
+     + 1/20 x y DATA(1, 2) - 1/20 x y DATA(0, 2) - 3/20 x y DATA(-1, 2)
 
-             2                    2                     2
-     - 3/40 x  DATA(0, 2) - 3/40 x  DATA(2, -1) + 1/40 x  DATA(2, 1)
+     + 3/20 x y DATA(-1, 0) + 3/20 x y DATA(-1, 1) - 3/20 x y DATA(-1, -1)
 
-             2
-     - 1/40 x  DATA(2, 0) + 3/20 x y DATA(2, -1) - 1/20 x y DATA(0, 2)
+                              69               49
+     - 1/20 x y DATA(0, -1) + --- DATA(2, 1) - --- DATA(2, 0)
+                              400              400
 
-     - 3/20 x y DATA(2, 1) - 3/20 x y DATA(2, 0) + 3/20 x y DATA(2, 2)
+        89                149                37                43
+     + ---- DATA(2, -1) - ---- DATA(2, 2) + ---- DATA(1, 2) + ---- DATA(0, 2)
+       1200               1200              1200              1200
 
-       13                17
-     + -- y DATA(2, 1) - -- y DATA(2, 0) - 1/40 y DATA(1, 2)
-       40                40
+       131                31                111               109
+     - ---- DATA(-1, 2) - --- DATA(-1, 0) + --- DATA(-1, 1) - ---- DATA(-1, -1)
+       1200               400               400               1200
 
-     + 7/40 y DATA(2, -1) + 1/40 y DATA(0, 2) + 3/40 y DATA(-1, 2)
+       223                157
+     - ---- DATA(0, -1) - ---- DATA(1, -1) - 1/20 x y DATA(1, 1)
+       1200               1200
 
-       11                                      23
-     + -- y DATA(0, -1) + 9/40 y DATA(1, -1) - -- y DATA(-1, 0)
-       40                                      40
+                           11
+     + 9/40 y DATA(0, 1) + -- y DATA(1, 1) + 6/25 x DATA(-1, -1)
+                           40
 
-                                2
-     - 3/40 y DATA(2, 2) - 1/8 y  DATA(2, -1) + 7/40 y DATA(-1, 1)
+     - 1/20 x y DATA(1, 0) - 1/40 y DATA(1, 2) + 1/40 y DATA(0, 2)
 
-       13                       2
-     + -- y DATA(-1, -1) + 1/8 y  DATA(1, 2) + 9/40 y DATA(0, 1)
-       40
+            2                   2              13
+     - 3/8 y  DATA(0, 1) + 3/8 y  DATA(0, 0) + -- y DATA(-1, -1)
+                                               40
 
-       19                21                11                     2
-     - -- y DATA(1, 0) - -- y DATA(0, 0) + -- y DATA(1, 1) + 1/8 y  DATA(0, 2)
-       40                40                40
+       11                                            2
+     + -- y DATA(0, -1) + 1/20 x y DATA(0, 0) + 3/8 y  DATA(1, 0)
+       40
 
             2                   2                   2
-     - 3/8 y  DATA(2, 1) + 3/8 y  DATA(2, 0) + 1/8 y  DATA(2, 2)
+     - 3/8 y  DATA(1, 1) - 3/8 y  DATA(2, 1) + 1/8 y  DATA(1, 2)
 
-            2                    2                    2
-     + 1/8 y  DATA(-1, 2) - 3/8 y  DATA(-1, 1) - 1/8 y  DATA(0, -1)
-
-            2                    2                    2
-     - 1/8 y  DATA(1, -1) + 3/8 y  DATA(-1, 0) - 1/8 y  DATA(-1, -1)
+            2                   2                    2
+     + 3/8 y  DATA(2, 0) - 1/8 y  DATA(2, -1) - 3/8 y  DATA(-1, 1)
 
             2                   2                   2
-     - 3/8 y  DATA(0, 1) + 3/8 y  DATA(1, 0) + 3/8 y  DATA(0, 0)
+     + 1/8 y  DATA(2, 2) + 1/8 y  DATA(0, 2) + 1/8 y  DATA(-1, 2)
 
-     - 1/50 x DATA(-1, 0) - 1/100 x DATA(1, 0) - 1/100 x DATA(0, 1)
+            2                                          2
+     - 1/8 y  DATA(-1, -1) - 1/100 x DATA(0, 1) - 1/8 y  DATA(1, -1)
 
-            2
-     - 3/8 y  DATA(1, 1) - 1/25 x DATA(0, 0) + 2/25 x DATA(1, 2)
+            2                    2
+     + 3/8 y  DATA(-1, 0) - 1/8 y  DATA(0, -1) + 2/25 x DATA(2, 1)
 
-     - 1/50 x DATA(0, -1) + 6/25 x DATA(-1, -1) + 3/50 x DATA(1, 1)
+     - 1/25 x DATA(0, 0) - 1/100 x DATA(1, 0) + 7/100 x DATA(2, 0)
 
-       13                  13
-     - --- x DATA(1, -1) - --- x DATA(-1, 1) - 3/50 x DATA(2, 2)
-       100                 100
+     - 9/100 x DATA(2, -1) - 3/50 x DATA(2, 2) + 3/50 x DATA(1, 1)
 
-     + 7/100 x DATA(2, 0) + 2/25 x DATA(2, 1) - 9/100 x DATA(-1, 2)
+     + 2/25 x DATA(1, 2) + 7/100 x DATA(0, 2) - 9/100 x DATA(-1, 2)
 
-             2                    2
-     + 1/40 x  DATA(1, 0) - 1/40 x  DATA(0, 1) + 7/100 x DATA(0, 2)
+                            21                19
+     - 1/50 x DATA(-1, 0) - -- y DATA(0, 0) - -- y DATA(1, 0)
+                            40                40
 
-                                   2                     2
-     - 9/100 x DATA(2, -1) + 3/40 x  DATA(1, -1) + 3/40 x  DATA(0, -1)
+                                  2                    2
+     + 9/40 y DATA(1, -1) + 1/40 x  DATA(1, 0) + 1/40 x  DATA(0, 0)
 
              2                    2                    2
-     + 1/40 x  DATA(0, 0) - 1/40 x  DATA(1, 1) - 1/40 x  DATA(-1, 0)
+     + 1/40 x  DATA(2, 1) - 1/40 x  DATA(2, 0) - 3/40 x  DATA(2, -1)
 
-             2                    2                      2
-     - 3/40 x  DATA(1, 2) - 3/40 x  DATA(-1, -1) + 1/40 x  DATA(-1, 1)
+             2                    2                     2
+     + 3/40 x  DATA(2, 2) + 1/40 x  DATA(-1, 1) - 3/40 x  DATA(0, 2)
 
-             2              31                157
-     + 3/40 x  DATA(2, 2) - --- DATA(-1, 0) - ---- DATA(1, -1)
-                            400               1200
+             2                     2                     2
+     + 3/40 x  DATA(0, -1) + 3/40 x  DATA(-1, 2) - 1/40 x  DATA(-1, 0)
 
-       223                109                 111                37
-     - ---- DATA(0, -1) - ---- DATA(-1, -1) + --- DATA(-1, 1) + ---- DATA(1, 2)
-       1200               1200                400               1200
+             2                    2                    2
+     - 3/40 x  DATA(1, 2) - 1/40 x  DATA(0, 1) - 1/40 x  DATA(1, 1)
 
-       149               49               69               131
-     - ---- DATA(2, 2) - --- DATA(2, 0) + --- DATA(2, 1) - ---- DATA(-1, 2)
-       1200              400              400              1200
+             2                     2                17
+     + 3/40 x  DATA(1, -1) - 3/40 x  DATA(-1, -1) - -- y DATA(2, 0)
+                                                    40
 
-        43                89
-     + ---- DATA(0, 2) + ---- DATA(2, -1)
-       1200              1200
+     + 7/40 y DATA(2, -1) - 3/40 y DATA(2, 2) + 3/40 y DATA(-1, 2)
+
+       23                                      13
+     - -- y DATA(-1, 0) + 7/40 y DATA(-1, 1) + -- y DATA(2, 1)
+       40                                      40
 
 > coeff_as_lc_of_data(%, posn_list_2d_size4);
-                        2   109          2   13
-[COEFF(-1, -1) = - 1/8 y  - ---- - 3/40 x  + -- y + 6/25 x - 3/20 x y,
-                            1200             40
+                         2   13                         109         2
+[COEFF(-1, -1) = - 3/40 x  + -- y + 6/25 x - 3/20 x y - ---- - 1/8 y ,
+                             40                         1200
 
-                          2         2            223               11
-    COEFF(0, -1) = - 1/8 y  + 3/40 x  - 1/50 x - ---- - 1/20 x y + -- y,
-                                                 1200              40
+                         2   223                             2   11
+    COEFF(0, -1) = 3/40 x  - ---- - 1/50 x - 1/20 x y - 1/8 y  + -- y,
+                             1200                                40
 
-                     13           2                  2   157
-    COEFF(1, -1) = - --- x - 1/8 y  + 9/40 y + 3/40 x  - ---- + 1/20 x y,
-                     100                                 1200
+                            13      157          2                   2
+    COEFF(1, -1) = 9/40 y - --- x - ---- + 3/40 x  + 1/20 x y - 1/8 y ,
+                            100     1200
 
-                          2                             2              89
-    COEFF(2, -1) = - 1/8 y  + 3/20 x y + 7/40 y - 3/40 x  - 9/100 x + ----,
-                                                                      1200
+                                    2               89                   2
+    COEFF(2, -1) = - 9/100 x - 1/8 y  + 3/20 x y + ---- + 7/40 y - 3/40 x ,
+                                                   1200
 
-                     23                   2   31          2
-    COEFF(-1, 0) = - -- y - 1/50 x + 3/8 y  - --- - 1/40 x  + 3/20 x y,
-                     40                       400
+                     23           2        2              31
+    COEFF(-1, 0) = - -- y - 1/40 x  + 3/8 y  + 3/20 x y - --- - 1/50 x,
+                     40                                   400
 
-                    21     57                             2         2
-    COEFF(0, 0) = - -- y - --- + 1/20 x y - 1/25 x + 3/8 y  + 1/40 x ,
-                    40     400
+                       2                  2   57               21
+    COEFF(0, 0) = 3/8 y  - 1/25 x + 1/40 x  - --- + 1/20 x y - -- y,
+                                              400              40
 
-                                   2   63                     2   19
-    COEFF(1, 0) = - 1/100 x + 3/8 y  - --- - 1/20 x y + 1/40 x  - -- y,
-                                       400                        40
+                       2         2   63                         19
+    COEFF(1, 0) = 3/8 y  + 1/40 x  - --- - 1/100 x - 1/20 x y - -- y,
+                                     400                        40
 
-                       2             49    17           2
-    COEFF(2, 0) = 3/8 y  + 7/100 x - --- - -- y - 1/40 x  - 3/20 x y,
-                                     400   40
+                                    2   17           2   49
+    COEFF(2, 0) = - 3/20 x y + 3/8 y  - -- y - 1/40 x  - --- + 7/100 x,
+                                        40               400
 
-                          2         2              111            13
-    COEFF(-1, 1) = - 3/8 y  + 1/40 x  + 3/20 x y + --- + 7/40 y - --- x,
-                                                   400            100
+                   111              13                    2         2
+    COEFF(-1, 1) = --- + 3/20 x y - --- x + 7/40 y - 3/8 y  + 1/40 x ,
+                   400              100
 
-                  117                   2                            2
-    COEFF(0, 1) = --- - 1/100 x - 1/40 x  + 9/40 y + 1/20 x y - 3/8 y ,
+                  117         2                   2
+    COEFF(0, 1) = --- - 1/40 x  + 1/20 x y - 3/8 y  + 9/40 y - 1/100 x,
                   400
 
-                  11     103        2                  2
-    COEFF(1, 1) = -- y + --- - 3/8 y  + 3/50 x - 1/40 x  - 1/20 x y,
-                  40     400
+                  11          2         2                       103
+    COEFF(1, 1) = -- y - 3/8 y  - 1/40 x  - 1/20 x y + 3/50 x + ---,
+                  40                                            400
 
-                         2         2                       69    13
-    COEFF(2, 1) = - 3/8 y  + 1/40 x  + 2/25 x - 3/20 x y + --- + -- y,
-                                                           400   40
+                        2            69    13                     2
+    COEFF(2, 1) = 1/40 x  + 2/25 x + --- + -- y - 3/20 x y - 3/8 y ,
+                                     400   40
 
-                        2         2                      131
-    COEFF(-1, 2) = 1/8 y  + 3/40 x  + 3/40 y - 9/100 x - ---- - 3/20 x y,
-                                                         1200
+                               131         2                    2
+    COEFF(-1, 2) = - 9/100 x - ---- + 1/8 y  - 3/20 x y + 3/40 x  + 3/40 y,
+                               1200
 
-                                             2             43         2
-    COEFF(0, 2) = 7/100 x - 1/20 x y - 3/40 x  + 1/40 y + ---- + 1/8 y ,
-                                                          1200
+                                               2             43         2
+    COEFF(0, 2) = - 1/20 x y + 7/100 x - 3/40 x  + 1/40 y + ---- + 1/8 y ,
+                                                            1200
 
-                       2                  2             37
-    COEFF(1, 2) = 1/8 y  + 2/25 x - 3/40 x  - 1/40 y + ---- + 1/20 x y,
-                                                       1200
+                          2                                     2    37
+    COEFF(1, 2) = - 3/40 x  - 1/40 y + 2/25 x + 1/20 x y + 1/8 y  + ----,
+                                                                    1200
 
-                       2                             2   149
-    COEFF(2, 2) = 1/8 y  + 3/20 x y - 3/50 x + 3/40 x  - ---- - 3/40 y]
-                                                         1200
+                       2   149                                       2
+    COEFF(2, 2) = 1/8 y  - ---- + 3/20 x y - 3/50 x - 3/40 y + 3/40 x ]
+                           1200
 
 > print_coeff__lc_of_data(%, "coeff_dy_", "fp",
 > 			"2d.coeffs/2d.cube.order3.smooth0/coeff-dy.compute.c");
-bytes used=28017044, alloc=2096768, time=2.36
-bytes used=29017220, alloc=2096768, time=2.45
-bytes used=30017984, alloc=2096768, time=2.55
-bytes used=31018144, alloc=2096768, time=2.67
+bytes used=28025712, alloc=2096768, time=2.36
+bytes used=29025924, alloc=2096768, time=2.45
+bytes used=30026084, alloc=2096768, time=2.55
+bytes used=31026248, alloc=2096768, time=2.66
 > 
 # d^2/dx^2
 > simplify( diff(interp_2d_cube_order3_smooth0,x,x) );
-  21                                19              11
-- -- DATA(0, 0) + 9/40 DATA(1, 0) - -- DATA(0, 1) + -- DATA(1, 1)
-  40                                40              40
+                                                            21
+3/4 x DATA(0, -1) - 3/4 x DATA(1, -1) - 1/4 x DATA(-1, 1) - -- DATA(0, 0)
+                                                            40
 
-     + 1/20 y DATA(2, 1) - 1/20 y DATA(2, 0) - 3/20 y DATA(1, 2)
+                         19              11
+     + 9/40 DATA(1, 0) - -- DATA(0, 1) + -- DATA(1, 1) - 1/40 DATA(2, 1)
+                         40              40
 
-     - 3/20 y DATA(2, -1) - 3/20 y DATA(0, 2) + 3/20 y DATA(-1, 2)
+                                                              13
+     + 1/40 DATA(2, 0) + 3/40 DATA(2, -1) - 3/40 DATA(2, 2) + -- DATA(1, 2)
+                                                              40
 
-     + 3/20 y DATA(0, -1) + 3/20 y DATA(1, -1) - 1/20 y DATA(-1, 0)
+       17                                 11
+     - -- DATA(0, 2) + 7/40 DATA(-1, 2) + -- DATA(-1, 0) + 9/40 DATA(-1, 1)
+       40                                 40
 
-     + 3/20 y DATA(2, 2) + 1/20 y DATA(-1, 1) - 3/20 y DATA(-1, -1)
+       13                23
+     + -- DATA(-1, -1) - -- DATA(0, -1) + 7/40 DATA(1, -1) - 1/20 y DATA(0, 1)
+       40                40
 
-     - 1/20 y DATA(0, 1) + 1/20 y DATA(1, 0) + 1/20 y DATA(0, 0)
+     - 1/20 y DATA(1, 1) - 1/4 x DATA(-1, -1) - 3/20 y DATA(1, 2)
 
-     - 1/20 y DATA(1, 1) - 1/4 x DATA(-1, 0) - 3/4 x DATA(1, 0)
+     - 3/20 y DATA(0, 2) - 3/20 y DATA(-1, -1) + 3/20 y DATA(0, -1)
 
-     + 3/4 x DATA(0, 1) + 3/4 x DATA(0, 0) - 3/4 x DATA(1, 2)
+     + 3/4 x DATA(0, 1) + 1/4 x DATA(2, 1) + 3/4 x DATA(0, 0)
 
-     + 3/4 x DATA(0, -1) - 1/4 x DATA(-1, -1) - 3/4 x DATA(1, 1)
+     - 3/4 x DATA(1, 0) + 1/4 x DATA(2, 0) + 1/4 x DATA(2, -1)
 
-     - 3/4 x DATA(1, -1) - 1/4 x DATA(-1, 1) + 1/4 x DATA(2, 2)
+     + 1/4 x DATA(2, 2) - 3/4 x DATA(1, 1) - 3/4 x DATA(1, 2)
 
-     + 1/4 x DATA(2, 0) + 1/4 x DATA(2, 1) - 1/4 x DATA(-1, 2)
+     + 3/4 x DATA(0, 2) - 1/4 x DATA(-1, 2) - 1/4 x DATA(-1, 0)
 
-                                              11
-     + 3/4 x DATA(0, 2) + 1/4 x DATA(2, -1) + -- DATA(-1, 0) + 7/40 DATA(1, -1)
-                                              40
+     + 1/20 y DATA(0, 0) + 1/20 y DATA(1, 0) + 3/20 y DATA(1, -1)
 
-       23               13                                   13
-     - -- DATA(0, -1) + -- DATA(-1, -1) + 9/40 DATA(-1, 1) + -- DATA(1, 2)
-       40               40                                   40
+     - 1/20 y DATA(2, 0) - 3/20 y DATA(2, -1) + 3/20 y DATA(2, 2)
 
-     - 3/40 DATA(2, 2) + 1/40 DATA(2, 0) - 1/40 DATA(2, 1) + 7/40 DATA(-1, 2)
+     + 3/20 y DATA(-1, 2) - 1/20 y DATA(-1, 0) + 1/20 y DATA(-1, 1)
 
-       17
-     - -- DATA(0, 2) + 3/40 DATA(2, -1)
-       40
+     + 1/20 y DATA(2, 1)
 
 > coeff_as_lc_of_data(%, posn_list_2d_size4);
-bytes used=32018340, alloc=2096768, time=2.81
-                                    13                   23
-[COEFF(-1, -1) = - 3/20 y - 1/4 x + --, COEFF(0, -1) = - -- + 3/20 y + 3/4 x,
-                                    40                   40
+bytes used=32026448, alloc=2096768, time=2.74
+                                    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,
+    COEFF(1, -1) = - 3/4 x + 3/20 y + 7/40,
 
-    COEFF(2, -1) = - 3/20 y + 1/4 x + 3/40,
+                                                                            11
+    COEFF(2, -1) = 3/40 + 1/4 x - 3/20 y, COEFF(-1, 0) = - 1/4 x - 1/20 y + --,
+                                                                            40
 
-                             11                                  21
-    COEFF(-1, 0) = - 1/4 x + -- - 1/20 y, COEFF(0, 0) = 1/20 y - -- + 3/4 x,
-                             40                                  40
+                    21
+    COEFF(0, 0) = - -- + 1/20 y + 3/4 x, COEFF(1, 0) = 9/40 + 1/20 y - 3/4 x,
+                    40
 
-    COEFF(1, 0) = 9/40 + 1/20 y - 3/4 x, COEFF(2, 0) = 1/40 - 1/20 y + 1/4 x,
+    COEFF(2, 0) = 1/40 - 1/20 y + 1/4 x, COEFF(-1, 1) = - 1/4 x + 9/40 + 1/20 y,
 
-                                                                     19
-    COEFF(-1, 1) = - 1/4 x + 1/20 y + 9/40, COEFF(0, 1) = - 1/20 y - -- + 3/4 x,
-                                                                     40
+                          19                                   11
+    COEFF(0, 1) = 3/4 x - -- - 1/20 y, COEFF(1, 1) = - 3/4 x + -- - 1/20 y,
+                          40                                   40
 
-                             11
-    COEFF(1, 1) = - 1/20 y + -- - 3/4 x, COEFF(2, 1) = 1/20 y + 1/4 x - 1/40,
-                             40
+    COEFF(2, 1) = - 1/40 + 1/4 x + 1/20 y, COEFF(-1, 2) = 3/20 y - 1/4 x + 7/40,
 
-                                                          17
-    COEFF(-1, 2) = 3/20 y - 1/4 x + 7/40, COEFF(0, 2) = - -- - 3/20 y + 3/4 x,
-                                                          40
+                             17                                           13
+    COEFF(0, 2) = - 3/20 y - -- + 3/4 x, COEFF(1, 2) = - 3/4 x - 3/20 y + --,
+                             40                                           40
 
-                  13
-    COEFF(1, 2) = -- - 3/20 y - 3/4 x, COEFF(2, 2) = - 3/40 + 1/4 x + 3/20 y]
-                  40
+    COEFF(2, 2) = - 3/40 + 1/4 x + 3/20 y]
 
 > print_coeff__lc_of_data(%, "coeff_dxx_", "fp",
 > 			"2d.coeffs/2d.cube.order3.smooth0/coeff-dxx.compute.c");
-bytes used=33018592, alloc=2096768, time=2.91
+bytes used=33026764, alloc=2096768, time=2.83
 > 
 # d^2/dxdy
 > simplify( diff(interp_2d_cube_order3_smooth0,x,y) );
-bytes used=34018772, alloc=2096768, time=3.02
-- 1/25 DATA(0, 0) - 1/100 DATA(1, 0) - 1/100 DATA(0, 1) + 3/50 DATA(1, 1)
+3/20 x DATA(0, -1) + 3/20 x DATA(1, -1) + 1/20 x DATA(-1, 1) - 1/25 DATA(0, 0)
 
-     - 3/20 y DATA(2, 1) - 3/20 y DATA(2, 0) + 1/20 y DATA(1, 2)
+     - 1/100 DATA(1, 0) - 1/100 DATA(0, 1) + 3/50 DATA(1, 1) + 2/25 DATA(2, 1)
 
-     + 3/20 y DATA(2, -1) - 1/20 y DATA(0, 2) - 3/20 y DATA(-1, 2)
+     + 7/100 DATA(2, 0) - 9/100 DATA(2, -1) - 3/50 DATA(2, 2) + 2/25 DATA(1, 2)
 
-     - 1/20 y DATA(0, -1) + 1/20 y DATA(1, -1) + 3/20 y DATA(-1, 0)
+     + 7/100 DATA(0, 2) - 9/100 DATA(-1, 2) - 1/50 DATA(-1, 0)
 
-     + 3/20 y DATA(2, 2) + 3/20 y DATA(-1, 1) - 3/20 y DATA(-1, -1)
+       13                                                       13
+     - --- DATA(-1, 1) + 6/25 DATA(-1, -1) - 1/50 DATA(0, -1) - --- DATA(1, -1)
+       100                                                      100
 
-     + 1/20 y DATA(0, 1) - 1/20 y DATA(1, 0) + 1/20 y DATA(0, 0)
+     + 1/20 y DATA(0, 1) - 1/20 y DATA(1, 1) - 3/20 x DATA(-1, -1)
 
-     - 1/20 y DATA(1, 1) - 1/20 x DATA(-1, 0) + 1/20 x DATA(1, 0)
+     + 1/20 y DATA(1, 2) - 1/20 y DATA(0, 2) - 3/20 y DATA(-1, -1)
 
-     - 1/20 x DATA(0, 1) + 1/20 x DATA(0, 0) - 3/20 x DATA(1, 2)
+     - 1/20 y DATA(0, -1) - 1/20 x DATA(0, 1) + 1/20 x DATA(2, 1)
 
-     + 3/20 x DATA(0, -1) - 3/20 x DATA(-1, -1) - 1/20 x DATA(1, 1)
+     + 1/20 x DATA(0, 0) + 1/20 x DATA(1, 0) - 1/20 x DATA(2, 0)
 
-     + 3/20 x DATA(1, -1) + 1/20 x DATA(-1, 1) + 3/20 x DATA(2, 2)
+     - 3/20 x DATA(2, -1) + 3/20 x DATA(2, 2) - 1/20 x DATA(1, 1)
 
-     - 1/20 x DATA(2, 0) + 1/20 x DATA(2, 1) + 3/20 x DATA(-1, 2)
+     - 3/20 x DATA(1, 2) - 3/20 x DATA(0, 2) + 3/20 x DATA(-1, 2)
 
-     - 3/20 x DATA(0, 2) - 3/20 x DATA(2, -1) - 1/50 DATA(-1, 0)
+     - 1/20 x DATA(-1, 0) + 1/20 y DATA(0, 0) - 1/20 y DATA(1, 0)
 
-       13                                                       13
-     - --- DATA(1, -1) - 1/50 DATA(0, -1) + 6/25 DATA(-1, -1) - --- DATA(-1, 1)
-       100                                                      100
+     + 1/20 y DATA(1, -1) - 3/20 y DATA(2, 0) + 3/20 y DATA(2, -1)
 
-     + 2/25 DATA(1, 2) - 3/50 DATA(2, 2) + 7/100 DATA(2, 0) + 2/25 DATA(2, 1)
+     + 3/20 y DATA(2, 2) - 3/20 y DATA(-1, 2) + 3/20 y DATA(-1, 0)
 
-     - 9/100 DATA(-1, 2) + 7/100 DATA(0, 2) - 9/100 DATA(2, -1)
+     + 3/20 y DATA(-1, 1) - 3/20 y DATA(2, 1)
 
 > coeff_as_lc_of_data(%, posn_list_2d_size4);
-[COEFF(-1, -1) = - 3/20 y - 3/20 x + 6/25,
+bytes used=34027108, alloc=2096768, time=2.96
+[COEFF(-1, -1) = - 3/20 y + 6/25 - 3/20 x,
 
-                                                                            13
-    COEFF(0, -1) = 3/20 x - 1/20 y - 1/50, COEFF(1, -1) = 3/20 x + 1/20 y - ---,
-                                                                            100
+    COEFF(0, -1) = - 1/50 + 3/20 x - 1/20 y,
 
-    COEFF(2, -1) = - 9/100 - 3/20 x + 3/20 y,
+                            13
+    COEFF(1, -1) = 3/20 x - --- + 1/20 y,
+                            100
 
-    COEFF(-1, 0) = - 1/50 - 1/20 x + 3/20 y,
+    COEFF(2, -1) = - 3/20 x - 9/100 + 3/20 y,
 
-    COEFF(0, 0) = - 1/25 + 1/20 y + 1/20 x,
+    COEFF(-1, 0) = - 1/50 + 3/20 y - 1/20 x,
+
+    COEFF(0, 0) = 1/20 x - 1/25 + 1/20 y,
 
     COEFF(1, 0) = - 1/100 + 1/20 x - 1/20 y,
 
-    COEFF(2, 0) = - 1/20 x + 7/100 - 3/20 y,
+    COEFF(2, 0) = - 3/20 y + 7/100 - 1/20 x,
 
-                     13
-    COEFF(-1, 1) = - --- + 1/20 x + 3/20 y,
-                     100
+                            13
+    COEFF(-1, 1) = 1/20 x - --- + 3/20 y,
+                            100
 
-    COEFF(0, 1) = - 1/20 x - 1/100 + 1/20 y,
+    COEFF(0, 1) = - 1/100 + 1/20 y - 1/20 x,
 
-    COEFF(1, 1) = 3/50 - 1/20 x - 1/20 y,
+    COEFF(1, 1) = 3/50 - 1/20 y - 1/20 x,
 
-    COEFF(2, 1) = - 3/20 y + 1/20 x + 2/25,
+    COEFF(2, 1) = - 3/20 y + 2/25 + 1/20 x,
 
-    COEFF(-1, 2) = - 3/20 y + 3/20 x - 9/100,
+    COEFF(-1, 2) = 3/20 x - 3/20 y - 9/100,
 
     COEFF(0, 2) = 7/100 - 3/20 x - 1/20 y,
 
-    COEFF(1, 2) = - 3/20 x + 1/20 y + 2/25,
+    COEFF(1, 2) = - 3/20 x + 2/25 + 1/20 y,
 
-    COEFF(2, 2) = 3/20 x + 3/20 y - 3/50]
+    COEFF(2, 2) = 3/20 y - 3/50 + 3/20 x]
 
 > print_coeff__lc_of_data(%, "coeff_dxy_", "fp",
 > 			"2d.coeffs/2d.cube.order3.smooth0/coeff-dxy.compute.c");
-bytes used=35018968, alloc=2096768, time=3.11
+bytes used=35027272, alloc=2096768, time=3.05
 > 
 # d^2/dy^2
 > simplify( diff(interp_2d_cube_order3_smooth0,y,y) );
-  21              19                                11
-- -- DATA(0, 0) - -- DATA(1, 0) + 9/40 DATA(0, 1) + -- DATA(1, 1)
-  40              40                                40
+                                                                 21
+- 1/20 x DATA(0, -1) + 1/20 x DATA(1, -1) + 3/20 x DATA(-1, 1) - -- DATA(0, 0)
+                                                                 40
 
-     - 3/4 y DATA(2, 1) + 3/4 y DATA(2, 0) + 1/4 y DATA(1, 2)
+       19                                11              13
+     - -- DATA(1, 0) + 9/40 DATA(0, 1) + -- DATA(1, 1) + -- DATA(2, 1)
+       40                                40              40
 
-     - 1/4 y DATA(2, -1) + 1/4 y DATA(0, 2) + 1/4 y DATA(-1, 2)
+       17
+     - -- DATA(2, 0) + 7/40 DATA(2, -1) - 3/40 DATA(2, 2) - 1/40 DATA(1, 2)
+       40
 
-     - 1/4 y DATA(0, -1) - 1/4 y DATA(1, -1) + 3/4 y DATA(-1, 0)
+                                            23
+     + 1/40 DATA(0, 2) + 3/40 DATA(-1, 2) - -- DATA(-1, 0) + 7/40 DATA(-1, 1)
+                                            40
 
-     + 1/4 y DATA(2, 2) - 3/4 y DATA(-1, 1) - 1/4 y DATA(-1, -1)
+       13                11
+     + -- DATA(-1, -1) + -- DATA(0, -1) + 9/40 DATA(1, -1) - 3/4 y DATA(0, 1)
+       40                40
 
-     - 3/4 y DATA(0, 1) + 3/4 y DATA(1, 0) + 3/4 y DATA(0, 0)
+     - 3/4 y DATA(1, 1) - 3/20 x DATA(-1, -1) + 1/4 y DATA(1, 2)
 
-     - 3/4 y DATA(1, 1) + 3/20 x DATA(-1, 0) - 1/20 x DATA(1, 0)
+     + 1/4 y DATA(0, 2) - 1/4 y DATA(-1, -1) - 1/4 y DATA(0, -1)
 
-     + 1/20 x DATA(0, 1) + 1/20 x DATA(0, 0) + 1/20 x DATA(1, 2)
+     + 1/20 x DATA(0, 1) - 3/20 x DATA(2, 1) + 1/20 x DATA(0, 0)
 
-     - 1/20 x DATA(0, -1) - 3/20 x DATA(-1, -1) - 1/20 x DATA(1, 1)
+     - 1/20 x DATA(1, 0) - 3/20 x DATA(2, 0) + 3/20 x DATA(2, -1)
 
-     + 1/20 x DATA(1, -1) + 3/20 x DATA(-1, 1) + 3/20 x DATA(2, 2)
+     + 3/20 x DATA(2, 2) - 1/20 x DATA(1, 1) + 1/20 x DATA(1, 2)
 
-     - 3/20 x DATA(2, 0) - 3/20 x DATA(2, 1) - 3/20 x DATA(-1, 2)
+     - 1/20 x DATA(0, 2) - 3/20 x DATA(-1, 2) + 3/20 x DATA(-1, 0)
 
-                                                23
-     - 1/20 x DATA(0, 2) + 3/20 x DATA(2, -1) - -- DATA(-1, 0)
-                                                40
+     + 3/4 y DATA(0, 0) + 3/4 y DATA(1, 0) - 1/4 y DATA(1, -1)
 
-                          11               13
-     + 9/40 DATA(1, -1) + -- DATA(0, -1) + -- DATA(-1, -1) + 7/40 DATA(-1, 1)
-                          40               40
+     + 3/4 y DATA(2, 0) - 1/4 y DATA(2, -1) + 1/4 y DATA(2, 2)
 
-                                           17              13
-     - 1/40 DATA(1, 2) - 3/40 DATA(2, 2) - -- DATA(2, 0) + -- DATA(2, 1)
-                                           40              40
+     + 1/4 y DATA(-1, 2) + 3/4 y DATA(-1, 0) - 3/4 y DATA(-1, 1)
 
-     + 3/40 DATA(-1, 2) + 1/40 DATA(0, 2) + 7/40 DATA(2, -1)
+     - 3/4 y DATA(2, 1)
 
 > coeff_as_lc_of_data(%, posn_list_2d_size4);
-bytes used=36019260, alloc=2096768, time=3.25
-                           13                                             11
-[COEFF(-1, -1) = - 1/4 y + -- - 3/20 x, COEFF(0, -1) = - 1/20 x - 1/4 y + --,
-                           40                                             40
+bytes used=36028028, alloc=2096768, time=3.15
+                                    13                 11
+[COEFF(-1, -1) = - 1/4 y - 3/20 x + --, COEFF(0, -1) = -- - 1/20 x - 1/4 y,
+                                    40                 40
 
-    COEFF(1, -1) = - 1/4 y + 1/20 x + 9/40,
+    COEFF(1, -1) = 9/40 + 1/20 x - 1/4 y, COEFF(2, -1) = 3/20 x - 1/4 y + 7/40,
 
-                                                                 23
-    COEFF(2, -1) = 3/20 x - 1/4 y + 7/40, COEFF(-1, 0) = 3/4 y - -- + 3/20 x,
-                                                                 40
-
-                    21                                   19
-    COEFF(0, 0) = - -- + 1/20 x + 3/4 y, COEFF(1, 0) = - -- + 3/4 y - 1/20 x,
-                    40                                   40
+                     23                                         21
+    COEFF(-1, 0) = - -- + 3/4 y + 3/20 x, COEFF(0, 0) = 3/4 y - -- + 1/20 x,
+                     40                                         40
 
-                                     17
-    COEFF(2, 0) = - 3/20 x + 3/4 y - --, COEFF(-1, 1) = 3/20 x - 3/4 y + 7/40,
-                                     40
+                    19                                         17
+    COEFF(1, 0) = - -- - 1/20 x + 3/4 y, COEFF(2, 0) = 3/4 y - -- - 3/20 x,
+                    40                                         40
 
-                                                                  11
-    COEFF(0, 1) = 1/20 x + 9/40 - 3/4 y, COEFF(1, 1) = - 1/20 x + -- - 3/4 y,
-                                                                  40
+    COEFF(-1, 1) = 3/20 x + 7/40 - 3/4 y, COEFF(0, 1) = 1/20 x + 9/40 - 3/4 y,
 
-                             13
-    COEFF(2, 1) = - 3/20 x + -- - 3/4 y, COEFF(-1, 2) = - 3/20 x + 1/4 y + 3/40,
-                             40
+                  11                                 13
+    COEFF(1, 1) = -- - 3/4 y - 1/20 x, COEFF(2, 1) = -- - 3/20 x - 3/4 y,
+                  40                                 40
 
-    COEFF(0, 2) = 1/4 y + 1/40 - 1/20 x, COEFF(1, 2) = 1/20 x - 1/40 + 1/4 y,
+    COEFF(-1, 2) = 1/4 y + 3/40 - 3/20 x, COEFF(0, 2) = 1/4 y + 1/40 - 1/20 x,
 
-    COEFF(2, 2) = 3/20 x + 1/4 y - 3/40]
+    COEFF(1, 2) = - 1/40 + 1/20 x + 1/4 y, COEFF(2, 2) = 3/20 x + 1/4 y - 3/40]
 
 > print_coeff__lc_of_data(%, "coeff_dyy_", "fp",
 > 			"2d.coeffs/2d.cube.order3.smooth0/coeff-dyy.compute.c");
-bytes used=37019440, alloc=2096768, time=3.33
+bytes used=37028452, alloc=2096768, time=3.27
 > 
 ################################################################################
 > 
@@ -2513,1970 +2769,1963 @@ bytes used=37019440, alloc=2096768, time=3.33
 > interp_2d_cube_order4_smooth0
 > 	:= Lagrange_polynomial_interpolant(fn_2d_order4, coeff_list_2d_order4,
 > 					   coord_list_2d, posn_list_2d_size5);
-bytes used=38019764, alloc=2096768, time=3.45
-bytes used=39020548, alloc=2096768, time=3.52
-bytes used=40020708, alloc=2162292, time=3.58
-bytes used=41022132, alloc=2162292, time=3.65
-bytes used=42022568, alloc=2162292, time=3.72
-bytes used=43024680, alloc=2162292, time=3.78
-                                 541               246
-interp_2d_cube_order4_smooth0 := ---- DATA(0, 0) + ---- DATA(1, 0)
-                                 1225              1225
+bytes used=38028660, alloc=2096768, time=3.39
+bytes used=39028828, alloc=2096768, time=3.46
+bytes used=40029048, alloc=2096768, time=3.52
+bytes used=41029524, alloc=2096768, time=3.59
+bytes used=42032252, alloc=2096768, time=3.64
+bytes used=43032424, alloc=2096768, time=3.70
+interp_2d_cube_order4_smooth0 := (- 1/60 DATA(1, 1) - 1/30 DATA(2, 1)
+
+     + 1/30 DATA(2, -1) + 1/60 DATA(2, 2) + 1/120 DATA(1, 2)
 
-       246                24               246                 24
-     + ---- DATA(0, 1) - ---- DATA(1, 1) + ---- DATA(-1, 0) - ---- DATA(1, -1)
-       1225              1225              1225               1225
+     - 1/120 DATA(-1, 2) + 1/60 DATA(-1, 1) - 1/60 DATA(-1, -1)
 
-       246                 24                  24
-     + ---- DATA(0, -1) - ---- DATA(-1, -1) - ---- DATA(-1, 1) + (
-       1225               1225                1225
+     + 1/60 DATA(1, -1) - 1/30 DATA(-2, -1) - 1/60 DATA(2, -2)
 
-    - 1/30 DATA(1, 0) - 1/30 DATA(1, 1) + 1/30 DATA(-1, 0) - 1/30 DATA(1, -1)
+     + 1/60 DATA(-2, -2) + 1/120 DATA(-1, -2) - 1/120 DATA(1, -2)
 
-     + 1/30 DATA(-1, -1) + 1/30 DATA(-1, 1) - 1/30 DATA(1, 2) + 1/60 DATA(2, 2)
+                                               3
+     - 1/60 DATA(-2, 2) + 1/30 DATA(-2, 1)) x y  + (- 1/70 DATA(1, 0)
 
-     + 1/60 DATA(2, 0) + 1/60 DATA(2, 1) + 1/30 DATA(-1, 2) + 1/60 DATA(2, -1)
+     - 1/140 DATA(1, 1) - 1/70 DATA(2, 1) - 1/35 DATA(2, 0) - 1/70 DATA(2, -1)
 
-     - 1/60 DATA(-2, 2) - 1/60 DATA(-2, 1) - 1/60 DATA(-2, -1)
+     + 1/35 DATA(2, 2) + 1/70 DATA(1, 2) - 1/70 DATA(-1, 2) + 1/70 DATA(-1, 0)
 
-     - 1/60 DATA(-2, 0) + 1/60 DATA(2, -2) + 1/30 DATA(-1, -2)
+     + 1/140 DATA(-1, 1) + 1/140 DATA(-1, -1) - 1/140 DATA(1, -1)
 
-                                              3
-     - 1/30 DATA(1, -2) - 1/60 DATA(-2, -2)) x  + (1/20 DATA(0, 0)
+     + 1/70 DATA(-2, -1) + 1/35 DATA(2, -2) - 1/35 DATA(-2, -2)
 
-     - 1/30 DATA(1, 0) + 1/20 DATA(0, 1) - 1/30 DATA(1, 1) - 1/30 DATA(-1, 0)
+     - 1/70 DATA(-1, -2) + 1/70 DATA(1, -2) - 1/35 DATA(-2, 2)
 
-     - 1/30 DATA(1, -1) + 1/20 DATA(0, -1) - 1/30 DATA(-1, -1)
+                                               2
+     + 1/35 DATA(-2, 0) + 1/70 DATA(-2, 1)) x y  + (1/49 DATA(0, 0)
 
-     - 1/30 DATA(-1, 1) - 1/30 DATA(1, 2) + 1/120 DATA(2, 2) + 1/120 DATA(2, 0)
+     + 1/98 DATA(1, 0) + 1/98 DATA(0, 1) + 1/196 DATA(1, 1) - 1/98 DATA(2, 1)
 
-     + 1/120 DATA(2, 1) - 1/30 DATA(-1, 2) + 1/20 DATA(0, 2)
+     - 1/49 DATA(2, 0) - 1/98 DATA(2, -1) + 1/49 DATA(2, 2) - 1/98 DATA(1, 2)
 
-     + 1/120 DATA(2, -1) + 1/120 DATA(-2, 2) + 1/120 DATA(-2, 1)
+     - 1/49 DATA(0, 2) - 1/98 DATA(-1, 2) + 1/98 DATA(-1, 0)
 
-     + 1/120 DATA(-2, -1) + 1/120 DATA(-2, 0) + 1/120 DATA(2, -2)
+     + 1/196 DATA(-1, 1) + 1/196 DATA(-1, -1) + 1/98 DATA(0, -1)
 
-     - 1/30 DATA(-1, -2) + 1/20 DATA(0, -2) - 1/30 DATA(1, -2)
+     + 1/196 DATA(1, -1) - 1/98 DATA(-2, -1) + 1/49 DATA(2, -2)
 
-                            4
-     + 1/120 DATA(-2, -2)) x  + (1/20 DATA(0, 0) + 1/20 DATA(1, 0)
+     + 1/49 DATA(-2, -2) - 1/98 DATA(-1, -2) - 1/49 DATA(0, -2)
 
-     - 1/30 DATA(0, 1) - 1/30 DATA(1, 1) + 1/20 DATA(-1, 0) - 1/30 DATA(1, -1)
+     - 1/98 DATA(1, -2) + 1/49 DATA(-2, 2) - 1/49 DATA(-2, 0)
 
-     - 1/30 DATA(0, -1) - 1/30 DATA(-1, -1) - 1/30 DATA(-1, 1)
+                          2  2   /37               21
+     - 1/98 DATA(-2, 1)) x  y  + |--- DATA(1, 1) + --- DATA(2, 1)
+                                 \300              200
 
-     + 1/120 DATA(1, 2) + 1/120 DATA(2, 2) + 1/20 DATA(2, 0) - 1/30 DATA(2, 1)
+       21                11               21               21
+     - --- DATA(2, -1) - --- DATA(2, 2) + --- DATA(1, 2) - --- DATA(-1, 2)
+       200               150              200              200
 
-     + 1/120 DATA(-1, 2) + 1/120 DATA(0, 2) - 1/30 DATA(2, -1)
+       37                37                 37                21
+     - --- DATA(-1, 1) + --- DATA(-1, -1) - --- DATA(1, -1) + --- DATA(-2, -1)
+       300               300                300               200
 
-     + 1/120 DATA(-2, 2) - 1/30 DATA(-2, 1) - 1/30 DATA(-2, -1)
+       11                11                 21                 21
+     + --- DATA(2, -2) - --- DATA(-2, -2) + --- DATA(-1, -2) - --- DATA(1, -2)
+       150               150                200                200
 
-     + 1/20 DATA(-2, 0) + 1/120 DATA(2, -2) + 1/120 DATA(-1, -2)
+       11                21             \
+     + --- DATA(-2, 2) - --- DATA(-2, 1)| x y + (- 1/70 DATA(0, 1)
+       150               200            /
 
-                                                                    4   /
-     + 1/120 DATA(0, -2) + 1/120 DATA(1, -2) + 1/120 DATA(-2, -2)) y  + |
-                                                                        \
+     - 1/140 DATA(1, 1) + 1/70 DATA(2, 1) - 1/70 DATA(2, -1) + 1/35 DATA(2, 2)
 
-    17               31               31                17
-    --- DATA(0, 1) + --- DATA(1, 1) - --- DATA(1, -1) - --- DATA(0, -1)
-    105              210              210               105
+     - 1/70 DATA(1, 2) - 1/35 DATA(0, 2) - 1/70 DATA(-1, 2) - 1/140 DATA(-1, 1)
 
-       31                 31                                  31
-     - --- DATA(-1, -1) + --- DATA(-1, 1) + 1/84 DATA(1, 2) - --- DATA(2, 2)
-       210                210                                 420
+     + 1/140 DATA(-1, -1) + 1/70 DATA(0, -1) + 1/140 DATA(1, -1)
 
-       11                                  17               11
-     + --- DATA(2, 1) + 1/84 DATA(-1, 2) + --- DATA(0, 2) - --- DATA(2, -1)
-       105                                 420              105
+     - 1/70 DATA(-2, -1) - 1/35 DATA(2, -2) - 1/35 DATA(-2, -2)
 
-       31                11                11                 31
-     - --- DATA(-2, 2) + --- DATA(-2, 1) - --- DATA(-2, -1) + --- DATA(2, -2)
-       420               105               105                420
+     + 1/70 DATA(-1, -2) + 1/35 DATA(0, -2) + 1/70 DATA(1, -2)
 
-                           17
-     - 1/84 DATA(-1, -2) - --- DATA(0, -2) - 1/84 DATA(1, -2)
-                           420
+                                             2
+     + 1/35 DATA(-2, 2) + 1/70 DATA(-2, 1)) x  y + (- 1/60 DATA(1, 1)
 
-       31              \     /17               31               17
-     + --- DATA(-2, -2)| y + |--- DATA(1, 0) + --- DATA(1, 1) - --- DATA(-1, 0)
-       420             /     \105              210              105
+     + 1/120 DATA(2, 1) - 1/120 DATA(2, -1) + 1/60 DATA(2, 2) - 1/30 DATA(1, 2)
 
-       31                31                 31                11
-     + --- DATA(1, -1) - --- DATA(-1, -1) - --- DATA(-1, 1) + --- DATA(1, 2)
-       210               210                210               105
+     + 1/30 DATA(-1, 2) + 1/60 DATA(-1, 1) - 1/60 DATA(-1, -1)
 
-       31               17                                 11
-     - --- DATA(2, 2) + --- DATA(2, 0) + 1/84 DATA(2, 1) - --- DATA(-1, 2)
-       420              420                                105
+     + 1/60 DATA(1, -1) + 1/120 DATA(-2, -1) - 1/60 DATA(2, -2)
 
-                          31
-     + 1/84 DATA(2, -1) + --- DATA(-2, 2) - 1/84 DATA(-2, 1)
-                          420
+     + 1/60 DATA(-2, -2) - 1/30 DATA(-1, -2) + 1/30 DATA(1, -2)
 
-                           17                31                11
-     - 1/84 DATA(-2, -1) - --- DATA(-2, 0) - --- DATA(2, -2) - --- DATA(-1, -2)
-                           420               420               105
+                                              3     /  57
+     - 1/60 DATA(-2, 2) - 1/120 DATA(-2, 1)) x  y + |- --- DATA(0, 0)
+                                                    \  196
 
-       11                31              \     /  57
-     + --- DATA(1, -2) + --- DATA(-2, -2)| x + |- --- DATA(0, 0)
-       105               420             /     \  196
+       83               53               181                71
+     + --- DATA(1, 0) - --- DATA(0, 1) + ---- DATA(1, 1) + ---- DATA(2, 1)
+       735              196              1470              5880
 
-       83               53               181               83
-     + --- DATA(1, 0) - --- DATA(0, 1) + ---- DATA(1, 1) + --- DATA(-1, 0)
-       735              196              1470              735
+       191                71                289               113
+     + ---- DATA(2, 0) + ---- DATA(2, -1) - ---- DATA(2, 2) + --- DATA(1, 2)
+       5880              5880               5880              735
 
-       181                53                181
-     + ---- DATA(1, -1) - --- DATA(0, -1) + ---- DATA(-1, -1)
-       1470               196               1470
+       41               113               83                181
+     - --- DATA(0, 2) + --- DATA(-1, 2) + --- DATA(-1, 0) + ---- DATA(-1, 1)
+       196              735               735               1470
 
-       181                113              289               191
-     + ---- DATA(-1, 1) + --- DATA(1, 2) - ---- DATA(2, 2) + ---- DATA(2, 0)
-       1470               735              5880              5880
+       181                 53                181
+     + ---- DATA(-1, -1) - --- DATA(0, -1) + ---- DATA(1, -1)
+       1470                196               1470
 
-        71               113               41                71
-     + ---- DATA(2, 1) + --- DATA(-1, 2) - --- DATA(0, 2) + ---- DATA(2, -1)
-       5880              735               196              5880
+        71                 289                289
+     + ---- DATA(-2, -1) - ---- DATA(2, -2) - ---- DATA(-2, -2)
+       5880                5880               5880
 
-       289                 71                 71
-     - ---- DATA(-2, 2) + ---- DATA(-2, 1) + ---- DATA(-2, -1)
-       5880               5880               5880
+       113                41                113               289
+     + --- DATA(-1, -2) - --- DATA(0, -2) + --- DATA(1, -2) - ---- DATA(-2, 2)
+       735                196               735               5880
 
-       191                289                113                41
-     + ---- DATA(-2, 0) - ---- DATA(2, -2) + --- DATA(-1, -2) - --- DATA(0, -2)
-       5880               5880               735                196
+       191                 71             \  2
+     + ---- DATA(-2, 0) + ---- DATA(-2, 1)| x  + (1/20 DATA(0, 0)
+       5880               5880            /
 
-       113               289              \  2
-     + --- DATA(1, -2) - ---- DATA(-2, -2)| x  + (- 1/70 DATA(1, 0)
-       735               5880             /
+     + 1/20 DATA(1, 0) - 1/30 DATA(0, 1) - 1/30 DATA(1, 1) - 1/30 DATA(2, 1)
 
-     - 1/140 DATA(1, 1) + 1/70 DATA(-1, 0) - 1/140 DATA(1, -1)
+     + 1/20 DATA(2, 0) - 1/30 DATA(2, -1) + 1/120 DATA(2, 2) + 1/120 DATA(1, 2)
 
-     + 1/140 DATA(-1, -1) + 1/140 DATA(-1, 1) + 1/70 DATA(1, 2)
+     + 1/120 DATA(0, 2) + 1/120 DATA(-1, 2) + 1/20 DATA(-1, 0)
 
-     + 1/35 DATA(2, 2) - 1/35 DATA(2, 0) - 1/70 DATA(2, 1) - 1/70 DATA(-1, 2)
+     - 1/30 DATA(-1, 1) - 1/30 DATA(-1, -1) - 1/30 DATA(0, -1)
 
-     - 1/70 DATA(2, -1) - 1/35 DATA(-2, 2) + 1/70 DATA(-2, 1)
+     - 1/30 DATA(1, -1) - 1/30 DATA(-2, -1) + 1/120 DATA(2, -2)
 
-     + 1/70 DATA(-2, -1) + 1/35 DATA(-2, 0) + 1/35 DATA(2, -2)
+     + 1/120 DATA(-2, -2) + 1/120 DATA(-1, -2) + 1/120 DATA(0, -2)
 
-                                                                    2
-     - 1/70 DATA(-1, -2) + 1/70 DATA(1, -2) - 1/35 DATA(-2, -2)) x y  + (
+     + 1/120 DATA(1, -2) + 1/120 DATA(-2, 2) + 1/20 DATA(-2, 0)
 
-    - 1/60 DATA(1, 1) + 1/60 DATA(1, -1) - 1/60 DATA(-1, -1) + 1/60 DATA(-1, 1)
+                          4   541               246
+     - 1/30 DATA(-2, 1)) y  + ---- DATA(0, 0) + ---- DATA(1, 0)
+                              1225              1225
 
-     + 1/120 DATA(1, 2) + 1/60 DATA(2, 2) - 1/30 DATA(2, 1) - 1/120 DATA(-1, 2)
+       246                24                99                96
+     + ---- DATA(0, 1) - ---- DATA(1, 1) - ---- DATA(2, 1) + ---- DATA(2, 0)
+       1225              1225              1225              1225
 
-     + 1/30 DATA(2, -1) - 1/60 DATA(-2, 2) + 1/30 DATA(-2, 1)
+        99                 51                99                96
+     - ---- DATA(2, -1) + ---- DATA(2, 2) - ---- DATA(1, 2) + ---- DATA(0, 2)
+       1225               1225              1225              1225
 
-     - 1/30 DATA(-2, -1) - 1/60 DATA(2, -2) + 1/120 DATA(-1, -2)
+        99                246                 24
+     - ---- DATA(-1, 2) + ---- DATA(-1, 0) - ---- DATA(-1, 1)
+       1225               1225               1225
 
-                                                 3   /  57
-     - 1/120 DATA(1, -2) + 1/60 DATA(-2, -2)) x y  + |- --- DATA(0, 0)
-                                                     \  196
+        24                 246                 24
+     - ---- DATA(-1, -1) + ---- DATA(0, -1) - ---- DATA(1, -1) + (
+       1225                1225               1225
 
-       53               83               181               53
-     - --- DATA(1, 0) + --- DATA(0, 1) + ---- DATA(1, 1) - --- DATA(-1, 0)
-       196              735              1470              196
+    - 1/30 DATA(1, 0) - 1/30 DATA(1, 1) - 1/60 DATA(-2, -2) + 1/60 DATA(2, 1)
 
-       181                83                181
-     + ---- DATA(1, -1) + --- DATA(0, -1) + ---- DATA(-1, -1)
-       1470               735               1470
+     + 1/60 DATA(2, 0) + 1/60 DATA(2, -1) + 1/60 DATA(2, 2) - 1/30 DATA(1, 2)
 
-       181                 71               289               41
-     + ---- DATA(-1, 1) + ---- DATA(1, 2) - ---- DATA(2, 2) - --- DATA(2, 0)
-       1470               5880              5880              196
+     + 1/30 DATA(-1, 2) + 1/30 DATA(-1, 0) + 1/30 DATA(-1, 1)
 
-       113               71                191               113
-     + --- DATA(2, 1) + ---- DATA(-1, 2) + ---- DATA(0, 2) + --- DATA(2, -1)
-       735              5880               5880              735
+     + 1/30 DATA(-1, -1) - 1/30 DATA(1, -1) - 1/60 DATA(-2, -1)
 
-       289                113               113                41
-     - ---- DATA(-2, 2) + --- DATA(-2, 1) + --- DATA(-2, -1) - --- DATA(-2, 0)
-       5880               735               735                196
+     + 1/60 DATA(2, -2) - 1/60 DATA(-2, 0) + 1/30 DATA(-1, -2)
 
-       289                 71                 191
-     - ---- DATA(2, -2) + ---- DATA(-1, -2) + ---- DATA(0, -2)
-       5880               5880                5880
+                                                                3
+     - 1/30 DATA(1, -2) - 1/60 DATA(-2, 2) - 1/60 DATA(-2, 1)) x  + (
 
-        71                289              \  2
-     + ---- DATA(1, -2) - ---- DATA(-2, -2)| y  + (- 1/30 DATA(0, 1)
-       5880               5880             /
+    1/20 DATA(0, 0) - 1/30 DATA(1, 0) + 1/20 DATA(0, 1) - 1/30 DATA(1, 1)
 
-     - 1/30 DATA(1, 1) + 1/30 DATA(1, -1) + 1/30 DATA(0, -1)
+     + 1/120 DATA(2, 1) + 1/120 DATA(2, 0) + 1/120 DATA(2, -1)
 
-     + 1/30 DATA(-1, -1) - 1/30 DATA(-1, 1) + 1/60 DATA(1, 2) + 1/60 DATA(2, 2)
+     + 1/120 DATA(2, 2) - 1/30 DATA(1, 2) + 1/20 DATA(0, 2) - 1/30 DATA(-1, 2)
 
-     - 1/30 DATA(2, 1) + 1/60 DATA(-1, 2) + 1/60 DATA(0, 2) + 1/30 DATA(2, -1)
+     - 1/30 DATA(-1, 0) - 1/30 DATA(-1, 1) - 1/30 DATA(-1, -1)
 
-     + 1/60 DATA(-2, 2) - 1/30 DATA(-2, 1) + 1/30 DATA(-2, -1)
+     + 1/20 DATA(0, -1) - 1/30 DATA(1, -1) + 1/120 DATA(-2, -1)
 
-     - 1/60 DATA(2, -2) - 1/60 DATA(-1, -2) - 1/60 DATA(0, -2)
+     + 1/120 DATA(2, -2) + 1/120 DATA(-2, -2) - 1/30 DATA(-1, -2)
 
-                                              3
-     - 1/60 DATA(1, -2) - 1/60 DATA(-2, -2)) y  + (1/49 DATA(0, 0)
+     + 1/20 DATA(0, -2) - 1/30 DATA(1, -2) + 1/120 DATA(-2, 2)
 
-     + 1/98 DATA(1, 0) + 1/98 DATA(0, 1) + 1/196 DATA(1, 1) + 1/98 DATA(-1, 0)
+                                               4
+     + 1/120 DATA(-2, 0) + 1/120 DATA(-2, 1)) x  + (1/30 DATA(-2, -1)
 
-     + 1/196 DATA(1, -1) + 1/98 DATA(0, -1) + 1/196 DATA(-1, -1)
+     - 1/30 DATA(0, 1) - 1/30 DATA(1, 1) - 1/30 DATA(2, 1) + 1/30 DATA(2, -1)
 
-     + 1/196 DATA(-1, 1) - 1/98 DATA(1, 2) + 1/49 DATA(2, 2) - 1/49 DATA(2, 0)
+     + 1/60 DATA(2, 2) + 1/60 DATA(1, 2) + 1/60 DATA(0, 2) + 1/60 DATA(-1, 2)
 
-     - 1/98 DATA(2, 1) - 1/98 DATA(-1, 2) - 1/49 DATA(0, 2) - 1/98 DATA(2, -1)
+     - 1/30 DATA(-1, 1) + 1/30 DATA(-1, -1) + 1/30 DATA(0, -1)
 
-     + 1/49 DATA(-2, 2) - 1/98 DATA(-2, 1) - 1/98 DATA(-2, -1)
+     + 1/30 DATA(1, -1) - 1/60 DATA(0, -2) - 1/60 DATA(2, -2)
 
-     - 1/49 DATA(-2, 0) + 1/49 DATA(2, -2) - 1/98 DATA(-1, -2)
+     - 1/60 DATA(-2, -2) - 1/60 DATA(-1, -2) - 1/60 DATA(1, -2)
 
-                                                                 2  2   /
-     - 1/49 DATA(0, -2) - 1/98 DATA(1, -2) + 1/49 DATA(-2, -2)) x  y  + |
-                                                                        \
+                                             3   /  57
+     + 1/60 DATA(-2, 2) - 1/30 DATA(-2, 1)) y  + |- --- DATA(0, 0)
+                                                 \  196
 
-    37               37                37                 37
-    --- DATA(1, 1) - --- DATA(1, -1) + --- DATA(-1, -1) - --- DATA(-1, 1)
-    300              300               300                300
+       53               83               181               113
+     - --- DATA(1, 0) + --- DATA(0, 1) + ---- DATA(1, 1) + --- DATA(2, 1)
+       196              735              1470              735
 
-       21               11               21               21
-     + --- DATA(1, 2) - --- DATA(2, 2) + --- DATA(2, 1) - --- DATA(-1, 2)
-       200              150              200              200
+       41               113               289                71
+     - --- DATA(2, 0) + --- DATA(2, -1) - ---- DATA(2, 2) + ---- DATA(1, 2)
+       196              735               5880              5880
 
-       21                11                21                21
-     - --- DATA(2, -1) + --- DATA(-2, 2) - --- DATA(-2, 1) + --- DATA(-2, -1)
-       200               150               200               200
+       191                71                53                181
+     + ---- DATA(0, 2) + ---- DATA(-1, 2) - --- DATA(-1, 0) + ---- DATA(-1, 1)
+       5880              5880               196               1470
 
-       11                21                 21                11              \
-     + --- DATA(2, -2) + --- DATA(-1, -2) - --- DATA(1, -2) - --- DATA(-2, -2)|
-       150               200                200               150             /
+       181                 83                181
+     + ---- DATA(-1, -1) + --- DATA(0, -1) + ---- DATA(1, -1)
+       1470                735               1470
 
-    x y + (- 1/70 DATA(0, 1) - 1/140 DATA(1, 1) + 1/140 DATA(1, -1)
+       113                289                289
+     + --- DATA(-2, -1) - ---- DATA(2, -2) - ---- DATA(-2, -2)
+       735                5880               5880
 
-     + 1/70 DATA(0, -1) + 1/140 DATA(-1, -1) - 1/140 DATA(-1, 1)
+        71                 191                 71
+     + ---- DATA(-1, -2) + ---- DATA(0, -2) + ---- DATA(1, -2)
+       5880                5880               5880
 
-     - 1/70 DATA(1, 2) + 1/35 DATA(2, 2) + 1/70 DATA(2, 1) - 1/70 DATA(-1, 2)
+       289                41                113            \  2   /
+     - ---- DATA(-2, 2) - --- DATA(-2, 0) + --- DATA(-2, 1)| y  + |
+       5880               196               735            /      \
 
-     - 1/35 DATA(0, 2) - 1/70 DATA(2, -1) + 1/35 DATA(-2, 2) + 1/70 DATA(-2, 1)
+    17               31               11               11
+    --- DATA(0, 1) + --- DATA(1, 1) + --- DATA(2, 1) - --- DATA(2, -1)
+    105              210              105              105
 
-     - 1/70 DATA(-2, -1) - 1/35 DATA(2, -2) + 1/70 DATA(-1, -2)
+       31                                 17
+     - --- DATA(2, 2) + 1/84 DATA(1, 2) + --- DATA(0, 2) + 1/84 DATA(-1, 2)
+       420                                420
 
-                                                                 2
-     + 1/35 DATA(0, -2) + 1/70 DATA(1, -2) - 1/35 DATA(-2, -2)) x  y + (
+       31                31                 17                31
+     + --- DATA(-1, 1) - --- DATA(-1, -1) - --- DATA(0, -1) - --- DATA(1, -1)
+       210               210                105               210
 
-    - 1/60 DATA(1, 1) + 1/60 DATA(1, -1) - 1/60 DATA(-1, -1) + 1/60 DATA(-1, 1)
+       11                 31                31
+     - --- DATA(-2, -1) + --- DATA(2, -2) + --- DATA(-2, -2)
+       105                420               420
 
-     - 1/30 DATA(1, 2) + 1/60 DATA(2, 2) + 1/120 DATA(2, 1) + 1/30 DATA(-1, 2)
+                           17                                   31
+     - 1/84 DATA(-1, -2) - --- DATA(0, -2) - 1/84 DATA(1, -2) - --- DATA(-2, 2)
+                           420                                  420
 
-     - 1/120 DATA(2, -1) - 1/60 DATA(-2, 2) - 1/120 DATA(-2, 1)
+       11             \     /17               31
+     + --- DATA(-2, 1)| y + |--- DATA(1, 0) + --- DATA(1, 1) + 1/84 DATA(2, 1)
+       105            /     \105              210
 
-     + 1/120 DATA(-2, -1) - 1/60 DATA(2, -2) - 1/30 DATA(-1, -2)
+       17                                  31               11
+     + --- DATA(2, 0) + 1/84 DATA(2, -1) - --- DATA(2, 2) + --- DATA(1, 2)
+       420                                 420              105
 
-                                              3      99
-     + 1/30 DATA(1, -2) + 1/60 DATA(-2, -2)) x  y - ---- DATA(1, 2)
-                                                    1225
+       11                17                31                31
+     - --- DATA(-1, 2) - --- DATA(-1, 0) - --- DATA(-1, 1) - --- DATA(-1, -1)
+       105               105               210               210
 
-        51                96                99                99
-     + ---- DATA(2, 2) + ---- DATA(2, 0) - ---- DATA(2, 1) - ---- DATA(-1, 2)
-       1225              1225              1225              1225
+       31                                    31                31
+     + --- DATA(1, -1) - 1/84 DATA(-2, -1) - --- DATA(2, -2) + --- DATA(-2, -2)
+       210                                   420               420
 
-        96                99                 51                 99
-     + ---- DATA(0, 2) - ---- DATA(2, -1) + ---- DATA(-2, 2) - ---- DATA(-2, 1)
-       1225              1225               1225               1225
+       11                 11                31                17
+     - --- DATA(-1, -2) + --- DATA(1, -2) + --- DATA(-2, 2) - --- DATA(-2, 0)
+       105                105               420               420
 
-        99                  96                 51
-     - ---- DATA(-2, -1) + ---- DATA(-2, 0) + ---- DATA(2, -2)
-       1225                1225               1225
+                       \      99                  51
+     - 1/84 DATA(-2, 1)| x - ---- DATA(-2, -1) + ---- DATA(2, -2)
+                       /     1225                1225
 
-        99                  96                 99
-     - ---- DATA(-1, -2) + ---- DATA(0, -2) - ---- DATA(1, -2)
-       1225                1225               1225
+        51                  99                  96
+     + ---- DATA(-2, -2) - ---- DATA(-1, -2) + ---- DATA(0, -2)
+       1225                1225                1225
 
-        51
-     + ---- DATA(-2, -2)
+        99                 51                 96
+     - ---- DATA(1, -2) + ---- DATA(-2, 2) + ---- DATA(-2, 0)
+       1225               1225               1225
+
+        99
+     - ---- DATA(-2, 1)
        1225
 
 > 
 # I
 > coeff_as_lc_of_data(%, posn_list_2d_size5);
-bytes used=44033940, alloc=2162292, time=3.85
-bytes used=45039820, alloc=2162292, time=3.91
-                  51          3            4         3         2             2
-[COEFF(-2, -2) = ---- + 1/60 x  y + 1/120 x  - 1/60 y  - 1/35 x  y - 1/35 x y
-                 1225
+bytes used=44043980, alloc=2096768, time=3.78
+                         3           3         2  2   31              2   31
+[COEFF(-2, -2) = - 1/60 x  + 1/60 x y  + 1/49 x  y  + --- y - 1/35 x y  + --- x
+                                                      420                 420
 
-              4   289   2         2  2   31            3   31      11
-     + 1/120 y  - ---- x  + 1/49 x  y  + --- y - 1/60 x  + --- x - --- x y
-                  5880                   420               420     150
+       289   2          4          4    51          3           3         2
+     - ---- y  + 1/120 x  + 1/120 y  + ---- + 1/60 x  y - 1/60 y  - 1/35 x  y
+       5880                            1225
 
-               3   289   2                  21                2          4
-     + 1/60 x y  - ---- y , COEFF(-1, -2) = --- x y - 1/70 x y  + 1/120 y
-                   5880                     200
+       289   2   11                               3    71   2           2
+     - ---- x  - --- x y, COEFF(-1, -2) = - 1/60 y  + ---- y  - 1/70 x y
+       5880      150                                  5880
 
-                3         3    99    113  2    71   2   11            3
-     + 1/120 x y  + 1/30 x  - ---- + --- x  + ---- y  - --- x - 1/60 y
-                              1225   735      5880      105
+       11      113  2   21              2  2         3          4         3
+     - --- x + --- x  + --- x y - 1/98 x  y  + 1/30 x  + 1/120 y  - 1/30 x  y
+       105     735      200
 
-             4         3                    2  2         2
-     - 1/30 x  - 1/30 x  y - 1/84 y - 1/98 x  y  + 1/70 x  y, COEFF(0, -2) =
+             4         2      99             3
+     - 1/30 x  + 1/70 x  y - ---- + 1/120 x y  - 1/84 y, COEFF(0, -2) =
+                             1225
 
-          2           2  2         4   41   2   17       96           4
-    1/35 x  y - 1/49 x  y  + 1/20 x  - --- x  - --- y + ---- + 1/120 y
-                                       196      420     1225
+            2  2         2     41   2          4   191   2         3         4
+    - 1/49 x  y  + 1/35 x  y - --- x  + 1/120 y  + ---- y  - 1/60 y  + 1/20 x
+                               196                 5880
 
-             3   191   2                         2  2    99
-     - 1/60 y  + ---- y , COEFF(1, -2) = - 1/98 x  y  - ---- - 1/84 y
-                 5880                                   1225
+       17       96                          3                  4            3
+     - --- y + ----, COEFF(1, -2) = - 1/60 y  - 1/84 y - 1/30 x  - 1/120 x y
+       420     1225
 
-               2   113  2            3          4         3           2
-     + 1/70 x y  + --- x  - 1/120 x y  + 1/120 y  + 1/30 x  y + 1/70 x  y
-                   735
+             2           3   113  2   11             4           2    99
+     + 1/70 x  y - 1/30 x  + --- x  + --- x + 1/120 y  + 1/70 x y  - ----
+                             735      105                            1225
 
-       21              4         3    71   2   11            3
-     - --- x y - 1/30 x  - 1/30 x  + ---- y  + --- x - 1/60 y , COEFF(2, -2) =
-       200                           5880      105
+       21         71   2         2  2         3                     31
+     - --- x y + ---- y  - 1/98 x  y  + 1/30 x  y, COEFF(2, -2) = - --- x
+       200       5880                                               420
 
-          2  2          4           3          4   31      31            3
-    1/49 x  y  + 1/120 y  - 1/60 x y  + 1/120 x  + --- y - --- x + 1/60 x
-                                                   420     420
+       11              2      51    289   2         3           2         3
+     + --- x y - 1/35 x  y + ---- - ---- y  - 1/60 y  + 1/35 x y  + 1/60 x
+       150                   1225   5880
 
-             2      51          3           3   11        289   2           2
-     - 1/35 x  y + ---- - 1/60 x  y - 1/60 y  + --- x y - ---- y  + 1/35 x y
-                   1225                         150       5880
+             3     31             4          4         2  2   289   2
+     - 1/60 x  y + --- y + 1/120 x  + 1/120 y  + 1/49 x  y  - ---- x
+                   420                                        5880
 
-       289   2                          2  2           2          4
-     - ---- x , COEFF(-2, -1) = - 1/98 x  y  + 1/70 x y  + 1/120 x
-       5880
+               3                         3     21                2   11
+     - 1/60 x y , COEFF(-2, -1) = 1/120 x  y + --- x y + 1/70 x y  - --- y
+                                               200                   105
 
-              3     11      21         71   2         2           3
-     + 1/120 x  y - --- y + --- x y + ---- x  - 1/70 x  y + 1/30 y  - 1/84 x
-                    105     200       5880
+             4    99    113  2         2  2         2             3
+     - 1/30 y  - ---- + --- y  - 1/98 x  y  - 1/70 x  y - 1/30 x y  - 1/84 x
+                 1225   735
 
-             3           3   113  2         4    99                      24
-     - 1/60 x  - 1/30 x y  + --- y  - 1/30 y  - ----, COEFF(-1, -1) = - ----
-                             735                1225                    1225
+        71   2         3          4         3                         2
+     + ---- x  - 1/60 x  + 1/120 x  + 1/30 y , COEFF(-1, -1) = 1/140 x  y
+       5880
 
-       31            4   181   2          2     31              3         3
-     - --- x - 1/30 y  + ---- x  + 1/140 x  y - --- y - 1/60 x y  + 1/30 y
-       210               1470                   210
+       37               2  2         4           3   181   2            2
+     + --- x y + 1/196 x  y  - 1/30 x  - 1/60 x y  + ---- x  + 1/140 x y
+       300                                           1470
 
-             4         3         3     181   2   37               2  2
-     - 1/30 x  + 1/30 x  - 1/60 x  y + ---- y  + --- x y + 1/196 x  y
-                                       1470      300
+             3    24    31      31            3   181   2         3           4
+     + 1/30 y  - ---- - --- x - --- y + 1/30 x  + ---- y  - 1/60 x  y - 1/30 y
+                 1225   210     210               1470
 
-                2                 246    83   2         3   53   2   17
-     + 1/140 x y , COEFF(0, -1) = ---- + --- y  + 1/30 y  - --- x  - --- y
-                                  1225   735                196      105
+                       53   2         2  2         2     17      83   2   246
+    , COEFF(0, -1) = - --- x  + 1/98 x  y  + 1/70 x  y - --- y + --- y  + ----
+                       196                               105     735      1225
 
-             2           4         2  2         4                 181   2
-     + 1/70 x  y + 1/20 x  + 1/98 x  y  - 1/30 y , COEFF(1, -1) = ---- y
-                                                                  1470
+             4         3         4                        2     37
+     - 1/30 y  + 1/30 y  + 1/20 x , COEFF(1, -1) = 1/140 x  y - --- x y
+                                                                300
 
-             4         4         3         3      24    181   2          2
-     - 1/30 x  - 1/30 y  - 1/30 x  + 1/60 x  y - ---- + ---- x  + 1/140 x  y
-                                                 1225   1470
+                2         3      24          3   31      181   2   181   2
+     - 1/140 x y  + 1/60 x  y - ---- - 1/30 x  + --- x + ---- y  + ---- x
+                                1225             210     1470      1470
 
-       37        31               2         3           3          2  2   31
-     - --- x y - --- y - 1/140 x y  + 1/30 y  + 1/60 x y  + 1/196 x  y  + --- x
-       300       210                                                      210
+             4   31            3         4          2  2           3
+     - 1/30 x  - --- y + 1/30 y  - 1/30 y  + 1/196 x  y  + 1/60 x y ,
+                 210
 
-                             3   21              4           2         2  2
-    , COEFF(2, -1) = 1/30 x y  - --- x y - 1/30 y  - 1/70 x y  - 1/98 x  y
-                                 200
+                            3             3    99          3           2
+    COEFF(2, -1) = - 1/120 x  y + 1/30 x y  - ---- + 1/60 x  - 1/70 x y
+                                              1225
 
-        99             11       71   2   113  2         3         2
-     - ---- + 1/84 x - --- y + ---- x  + --- y  + 1/30 y  - 1/70 x  y
-       1225            105     5880      735
+             4   21                       2  2    71   2         3   11
+     - 1/30 y  - --- x y + 1/84 x - 1/98 x  y  + ---- x  + 1/30 y  - --- y
+                 200                             5880                105
 
-              4          3           3                        4         3
-     + 1/120 x  - 1/120 x  y + 1/60 x , COEFF(-2, 0) = 1/120 x  - 1/60 x
+       113  2         2            4                  96    41   2          4
+     + --- y  - 1/70 x  y + 1/120 x , COEFF(-2, 0) = ---- - --- y  + 1/120 x
+       735                                           1225   196
 
-       191   2   17            2  2         4           2   41   2    96
-     + ---- x  - --- x - 1/49 x  y  + 1/20 y  + 1/35 x y  - --- y  + ----,
-       5880      420                                        196      1225
+             3   191   2         4           2   17            2  2
+     - 1/60 x  + ---- x  + 1/20 y  + 1/35 x y  - --- x - 1/49 x  y ,
+                 5880                            420
 
-                         4   17      83   2   246    53   2         4
-    COEFF(-1, 0) = 1/20 y  - --- x + --- x  + ---- - --- y  - 1/30 x
-                             105     735      1225   196
+                     53   2         4   83   2   246          3           2
+    COEFF(-1, 0) = - --- y  - 1/30 x  + --- x  + ---- + 1/30 x  + 1/70 x y
+                     196                735      1225
 
-               2         3         2  2
-     + 1/70 x y  + 1/30 x  + 1/98 x  y ,
+             4         2  2   17
+     + 1/20 y  + 1/98 x  y  - --- x,
+                              105
 
-                    57   2         4         4   57   2         2  2   541
-    COEFF(0, 0) = - --- x  + 1/20 y  + 1/20 x  - --- y  + 1/49 x  y  + ----,
-                    196                          196                   1225
+                  541    57   2         4         4         2  2   57   2
+    COEFF(0, 0) = ---- - --- y  + 1/20 x  + 1/20 y  + 1/49 x  y  - --- x ,
+                  1225   196                                       196
 
-                  246    17              2   53   2         4         4
-    COEFF(1, 0) = ---- + --- x - 1/70 x y  - --- y  - 1/30 x  + 1/20 y
-                  1225   105                 196
+                          4           2   83   2         2  2   53   2   246
+    COEFF(1, 0) = - 1/30 x  - 1/70 x y  + --- x  + 1/98 x  y  - --- y  + ----
+                                          735                   196      1225
 
-             3   83   2         2  2                          2         4
-     - 1/30 x  + --- x  + 1/98 x  y , COEFF(2, 0) = - 1/35 x y  + 1/20 y
-                 735
+             3   17            4                17            4   191   2
+     - 1/30 x  + --- x + 1/20 y , COEFF(2, 0) = --- x + 1/20 y  + ---- x
+                 105                            420               5880
 
-              4    96          3   17            2  2   41   2   191   2
-     + 1/120 x  + ---- + 1/60 x  + --- x - 1/49 x  y  - --- y  + ---- x ,
-                  1225             420                  196      5880
+              4           2    96    41   2         2  2         3
+     + 1/120 x  - 1/35 x y  + ---- - --- y  - 1/49 x  y  + 1/60 x ,
+                              1225   196
 
-                           2  2         3    99          3         2     11
-    COEFF(-2, 1) = - 1/98 x  y  - 1/60 x  - ---- - 1/30 y  + 1/70 x  y + --- y
-                                            1225                         105
+                   113  2    71   2            21              3           2
+    COEFF(-2, 1) = --- y  + ---- x  - 1/84 x - --- x y - 1/60 x  + 1/70 x y
+                   735      5880               200
 
-               2         4   113  2           3          4          3
-     + 1/70 x y  - 1/30 y  + --- y  + 1/30 x y  + 1/120 x  - 1/120 x  y
-                             735
+              3     11       99          3           3         2  2          4
+     - 1/120 x  y + --- y - ---- - 1/30 y  + 1/30 x y  - 1/98 x  y  + 1/120 x
+                    105     1225
 
-                21         71   2                        2  2         3
-     - 1/84 x - --- x y + ---- x , COEFF(-1, 1) = 1/196 x  y  + 1/30 x
-                200       5880
+             2           4                 181   2         3     37
+     + 1/70 x  y - 1/30 y , COEFF(-1, 1) = ---- y  + 1/60 x  y - --- x y
+                                           1470                  300
 
-               3          2           4         3     37        31      31
-     + 1/60 x y  - 1/140 x  y - 1/30 x  + 1/60 x  y - --- x y - --- x + --- y
-                                                      300       210     210
+              2  2          2           4            2         3         4
+     + 1/196 x  y  - 1/140 x  y - 1/30 x  + 1/140 x y  + 1/30 x  - 1/30 y
 
-       181   2            2         3    24    181   2         4
-     + ---- y  + 1/140 x y  - 1/30 y  - ---- + ---- x  - 1/30 y , COEFF(0, 1)
-       1470                             1225   1470
+       181   2         3   31              3   31       24
+     + ---- x  - 1/30 y  - --- x + 1/60 x y  + --- y - ----, COEFF(0, 1) =
+       1470                210                 210     1225
 
-               3         2  2   53   2   246          4   17            2
-     = - 1/30 y  + 1/98 x  y  - --- x  + ---- - 1/30 y  + --- y - 1/70 x  y
-                                196      1225             105
+            4         2     53   2   83   2         3   246          4
+    - 1/30 y  - 1/70 x  y - --- x  + --- y  - 1/30 y  + ---- + 1/20 x
+                            196      735                1225
 
-             4   83   2                        3    24            3
-     + 1/20 x  + --- y , COEFF(1, 1) = - 1/30 y  - ---- - 1/60 x y
-                 735                               1225
+             2  2   17                              2   31             2
+     + 1/98 x  y  + --- y, COEFF(1, 1) = - 1/140 x y  + --- x - 1/140 x  y
+                    105                                 210
 
-              2  2   37              3     181   2   31            4   31
-     + 1/196 x  y  + --- x y - 1/60 x  y + ---- x  + --- y - 1/30 y  + --- x
-                     300                   1470      210               210
+       181   2   37        181   2         4         3     31       24
+     + ---- x  + --- x y + ---- y  - 1/30 x  - 1/60 x  y + --- y - ----
+       1470      300       1470                            210     1225
 
-             4            2         3   181   2          2
-     - 1/30 x  - 1/140 x y  - 1/30 x  + ---- y  - 1/140 x  y, COEFF(2, 1) =
-                                        1470
+             3          2  2         4         3           3
+     - 1/30 x  + 1/196 x  y  - 1/30 y  - 1/30 y  - 1/60 x y , COEFF(2, 1) =
 
-              3            113  2          3           2  2   21
-    - 1/30 x y  + 1/84 x + --- y  + 1/120 x  y - 1/98 x  y  + --- x y
-                           735                                200
+              2         2  2   113  2         4          4         3
+    - 1/70 x y  - 1/98 x  y  + --- y  - 1/30 y  + 1/120 x  - 1/30 y
+                               735
 
-               2    99          4    71   2         3   11             4
-     - 1/70 x y  - ---- - 1/30 y  + ---- x  + 1/60 x  + --- y + 1/120 x
-                   1225             5880                105
+              3              11            2      99     71   2         3
+     + 1/120 x  y + 1/84 x + --- y + 1/70 x  y - ---- + ---- x  + 1/60 x
+                             105                 1225   5880
 
-             3         2                         2             3   11
-     - 1/30 y  + 1/70 x  y, COEFF(-2, 2) = 1/35 x  y - 1/60 x y  + --- x y
-                                                                   150
+       21                3                        4           2         3
+     + --- x y - 1/30 x y , COEFF(-2, 2) = 1/120 x  - 1/35 x y  - 1/60 x
+       200
 
-               2   31      289   2          4         2  2   289   2   31
-     - 1/35 x y  - --- y - ---- y  + 1/120 y  + 1/49 x  y  - ---- x  + --- x
-                   420     5880                              5880      420
+             3     11        31            2  2   31      289   2         2
+     - 1/60 x  y + --- x y + --- x + 1/49 x  y  - --- y - ---- y  + 1/35 x  y
+                   150       420                  420     5880
 
-             3            4         3    51          3                    99
-     - 1/60 x  y + 1/120 x  + 1/60 y  + ---- - 1/60 x , COEFF(-1, 2) = - ----
-                                        1225                             1225
+              4           3    51    289   2         3
+     + 1/120 y  - 1/60 x y  + ---- - ---- x  + 1/60 y , COEFF(-1, 2) =
+                              1225   5880
 
-                3   21                  71   2         2  2           2
-     - 1/120 x y  - --- x y + 1/84 y + ---- y  - 1/98 x  y  - 1/70 x y
-                    200                5880
+               3    99            2   113  2   11            3         2  2
+    - 1/120 x y  - ---- - 1/70 x y  + --- x  - --- x + 1/60 y  - 1/98 x  y
+                   1225               735      105
 
-       113  2         4         3            4         3   11            3
-     + --- x  - 1/30 x  + 1/30 x  y + 1/120 y  + 1/30 x  - --- x + 1/60 y
-       735                                                 105
+             3                  3      71   2   21              2           4
+     + 1/30 x  + 1/84 y + 1/30 x  y + ---- y  - --- x y - 1/70 x  y - 1/30 x
+                                      5880      200
 
-             2                        4         2     17      41   2   191   2
-     - 1/70 x  y, COEFF(0, 2) = 1/20 x  - 1/35 x  y + --- y - --- x  + ---- y
-                                                      420     196      5880
+              4                 96           4   191   2   17            4
+     + 1/120 y , COEFF(0, 2) = ---- + 1/120 y  + ---- y  + --- y + 1/20 x
+                               1225              5880      420
 
-        96           4         2  2         3                   99
-     + ---- + 1/120 y  - 1/49 x  y  + 1/60 y , COEFF(1, 2) = - ----
-       1225                                                    1225
+             2     41   2         3         2  2                   99
+     - 1/35 x  y - --- x  + 1/60 y  - 1/49 x  y , COEFF(1, 2) = - ----
+                   196                                            1225
 
-             2  2         2           3               71   2            3
-     - 1/98 x  y  - 1/70 x  y - 1/30 x  y + 1/84 y + ---- y  + 1/120 x y
-                                                     5880
+                3    71   2          4                  3         2  2
+     + 1/120 x y  + ---- y  + 1/120 y  + 1/84 y + 1/60 y  - 1/98 x  y
+                    5880
 
-             3         4          4   11      113  2           2   21
-     - 1/30 x  - 1/30 x  + 1/120 y  + --- x + --- x  + 1/70 x y  + --- x y
-                                      105     735                  200
+               2         3           4   21              3   11      113  2
+     + 1/70 x y  - 1/30 x  y - 1/30 x  + --- x y - 1/30 x  + --- x + --- x
+                                         200                 105     735
 
-             3                      2            4         2  2   289   2
-     + 1/60 y , COEFF(2, 2) = 1/35 x  y + 1/120 x  + 1/49 x  y  - ---- y
-                                                                  5880
+             2                         4   289   2         3   289   2
+     - 1/70 x  y, COEFF(2, 2) = 1/120 y  - ---- x  + 1/60 y  - ---- y
+                                           5880                5880
 
-               3         3     31             4   289   2         3           2
-     + 1/60 x y  + 1/60 x  y - --- y + 1/120 y  - ---- x  + 1/60 x  + 1/35 x y
-                               420                5880
+               2   31             4           3         3    51          3
+     + 1/35 x y  - --- y + 1/120 x  + 1/60 x y  + 1/60 x  + ---- + 1/60 x  y
+                   420                                      1225
 
-       11        31       51          3
-     - --- x y - --- x + ---- + 1/60 y ]
-       150       420     1225
+       11              2  2   31            2
+     - --- x y + 1/49 x  y  - --- x + 1/35 x  y]
+       150                    420
 
 > print_coeff__lc_of_data(%, "coeff_I_", "fp",
 > 			"2d.coeffs/2d.cube.order4.smooth0/coeff-I.compute.c");
-bytes used=46039980, alloc=2162292, time=4.00
-bytes used=47040144, alloc=2162292, time=4.08
-bytes used=48048756, alloc=2162292, time=4.16
-bytes used=49050036, alloc=2227816, time=4.23
-bytes used=50050424, alloc=2227816, time=4.33
-bytes used=51050604, alloc=2227816, time=4.48
-bytes used=52050764, alloc=2227816, time=4.55
-bytes used=53052936, alloc=2227816, time=4.64
-bytes used=54053412, alloc=2227816, time=4.74
-bytes used=55053604, alloc=2227816, time=4.89
-bytes used=56053828, alloc=2227816, time=4.95
-bytes used=57054040, alloc=2293340, time=5.07
-bytes used=58054312, alloc=2293340, time=5.26
-bytes used=59054740, alloc=2293340, time=5.33
-bytes used=60054904, alloc=2293340, time=5.43
-bytes used=61055148, alloc=2293340, time=5.58
-bytes used=62055404, alloc=2293340, time=5.65
-bytes used=63058408, alloc=2293340, time=5.83
-bytes used=64058672, alloc=2293340, time=5.89
-bytes used=65058956, alloc=2293340, time=6.08
-bytes used=66059172, alloc=2293340, time=6.16
+bytes used=45045780, alloc=2293340, time=3.86
+bytes used=46046060, alloc=2293340, time=3.93
+bytes used=47046296, alloc=2293340, time=4.01
+bytes used=48063992, alloc=2293340, time=4.08
+bytes used=49068776, alloc=2293340, time=4.17
+bytes used=50068940, alloc=2293340, time=4.33
+bytes used=51069184, alloc=2293340, time=4.41
+bytes used=52069472, alloc=2293340, time=4.49
+bytes used=53070464, alloc=2293340, time=4.59
+bytes used=54078496, alloc=2293340, time=4.74
+bytes used=55078844, alloc=2293340, time=4.86
+bytes used=56084964, alloc=2293340, time=4.95
+bytes used=57090392, alloc=2293340, time=5.12
+bytes used=58090872, alloc=2293340, time=5.24
+bytes used=59091028, alloc=2293340, time=5.31
+bytes used=60091208, alloc=2293340, time=5.48
+bytes used=61091384, alloc=2293340, time=5.56
+bytes used=62091584, alloc=2293340, time=5.65
+bytes used=63092040, alloc=2293340, time=5.82
+bytes used=64092228, alloc=2293340, time=5.91
+bytes used=65092808, alloc=2293340, time=6.08
 > 
 # d/dx
 > simplify( diff(interp_2d_cube_order4_smooth0,x) );
-bytes used=67059496, alloc=2293340, time=6.26
-bytes used=68059676, alloc=2293340, time=6.33
-bytes used=69060256, alloc=2358864, time=6.40
-17               31               17                31
---- DATA(1, 0) + --- DATA(1, 1) - --- DATA(-1, 0) + --- DATA(1, -1)
-105              210              105               210
-
-       31                 31                11               31
-     - --- DATA(-1, -1) - --- DATA(-1, 1) + --- DATA(1, 2) - --- DATA(2, 2)
-       210                210               105              420
+bytes used=66093052, alloc=2293340, time=6.20
+bytes used=67093384, alloc=2424388, time=6.26
+bytes used=68093588, alloc=2424388, time=6.34
+bytes used=69093944, alloc=2424388, time=6.40
+17               31                     3                     3
+--- DATA(1, 0) + --- DATA(1, 1) + 1/30 x  DATA(-2, 2) + 1/30 x  DATA(-2, 0)
+105              210
 
-       17                                 11
-     + --- DATA(2, 0) + 1/84 DATA(2, 1) - --- DATA(-1, 2) + 1/84 DATA(2, -1)
-       420                                105
+             3                    3                     3
+     + 1/30 x  DATA(-2, 1) + 1/5 x  DATA(0, -1) - 2/15 x  DATA(1, -1)
 
-       31                                         2
-     + --- DATA(-2, 2) - 1/84 DATA(-2, 1) - 1/70 y  DATA(2, 1)
-       420
+             3                21                 21
+     + 1/30 x  DATA(-2, -1) + --- y DATA(1, 2) - --- y DATA(-1, 2)
+                              200                200
 
-             2                     2                     2
-     - 1/70 y  DATA(-1, 2) - 1/70 y  DATA(2, -1) - 1/35 y  DATA(-2, 2)
+       37                          2              21
+     - --- y DATA(-1, 1) + 2/49 x y  DATA(0, 0) + --- y DATA(-1, -2)
+       300                                        200
 
-             2                     2                      2
-     + 1/70 y  DATA(-2, 1) + 1/70 y  DATA(-2, -1) + 1/35 y  DATA(-2, 0)
+       21                  11                  37
+     - --- y DATA(1, -2) + --- y DATA(-2, 2) - --- y DATA(1, -1)
+       200                 150                 300
 
-             2                     2                      2
-     + 1/35 y  DATA(2, -2) - 1/70 y  DATA(-1, -2) + 1/35 y  DATA(2, 2)
+       37                 21                 21
+     + --- y DATA(1, 1) + --- y DATA(2, 1) - --- y DATA(2, -1)
+       300                200                200
 
-             2                     2                    2
-     - 1/70 y  DATA(1, 0) - 1/140 y  DATA(1, 1) + 1/70 y  DATA(-1, 0)
+       11                         2                    3
+     - --- y DATA(2, 2) + 1/49 x y  DATA(0, 1) + 1/60 y  DATA(2, 2)
+       150
 
-              2                      2                       2
-     - 1/140 y  DATA(1, -1) + 1/140 y  DATA(-1, -1) + 1/140 y  DATA(-1, 1)
+              3                     3                      2
+     + 1/120 y  DATA(1, 2) - 1/120 y  DATA(-1, 2) + 1/140 y  DATA(-1, 1)
 
-     - 1/35 x y DATA(-1, 2) - 2/35 x y DATA(0, 2) - 1/35 x y DATA(0, 1)
+             2                     2                    2
+     - 1/70 y  DATA(2, -1) + 1/35 y  DATA(2, 2) + 1/70 y  DATA(1, 2)
 
-             2                        2
-     - 1/20 x  y DATA(-1, -1) - 1/20 x  y DATA(1, 1) - 1/35 x y DATA(-2, -1)
+             2                     2                     2
+     - 1/70 y  DATA(-1, 2) - 1/70 y  DATA(1, 0) - 1/140 y  DATA(1, 1)
 
-     - 2/35 x y DATA(2, -2) + 2/35 x y DATA(2, 2) + 1/35 x y DATA(2, 1)
+             2                    2              21
+     - 1/70 y  DATA(2, 1) - 1/35 y  DATA(2, 0) - --- y DATA(-2, 1)
+                                                 200
 
-       37                         2                        2
-     + --- y DATA(1, 1) - 1/49 x y  DATA(-2, -1) + 2/49 x y  DATA(2, -2)
-       300
+       37                   21                   11
+     + --- y DATA(-1, -1) + --- y DATA(-2, -1) + --- y DATA(2, -2)
+       300                  200                  150
 
-               2                        2
-     - 1/49 x y  DATA(-1, -2) - 1/49 x y  DATA(1, -2) - 1/35 x y DATA(2, -1)
+       11                         2                     2
+     - --- y DATA(-2, -2) + 1/70 y  DATA(1, -2) - 1/35 y  DATA(-2, 2)
+       150
 
-                                                     21
-     + 2/35 x y DATA(-2, 2) + 1/35 x y DATA(-2, 1) - --- y DATA(-1, 2)
-                                                     200
+             2                     2                     3
+     + 1/35 y  DATA(-2, 0) + 1/70 y  DATA(-2, 1) - 1/60 y  DATA(1, 1)
 
-       21                  11                  21
-     - --- y DATA(2, -1) + --- y DATA(-2, 2) - --- y DATA(-2, 1)
-       200                 150                 200
+             3                    3                     2
+     - 1/30 y  DATA(2, 1) + 1/30 y  DATA(2, -1) + 1/10 x  DATA(-1, 2)
 
-       21                   11                  21
-     + --- y DATA(-2, -1) + --- y DATA(2, -2) + --- y DATA(-1, -2)
-       200                  150                 200
+             3                      3                     3
+     - 1/30 y  DATA(-2, -1) - 1/60 y  DATA(2, -2) + 1/60 y  DATA(-2, -2)
 
-       21                  11                   37
-     - --- y DATA(1, -2) - --- y DATA(-2, -2) - --- y DATA(1, -1)
-       200                 150                  300
+              3                       3                     3
+     + 1/120 y  DATA(-1, -2) - 1/120 y  DATA(1, -2) - 1/60 y  DATA(-2, 2)
 
-             2                     2                      2
-     + 1/70 y  DATA(1, -2) - 1/35 y  DATA(-2, -2) + 1/70 y  DATA(1, 2)
+             3                     3                      3
+     + 1/60 y  DATA(-1, 1) - 1/60 y  DATA(-1, -1) + 1/60 y  DATA(1, -1)
 
-             2                                              2
-     - 1/35 y  DATA(2, 0) + 1/35 x y DATA(-1, -2) - 2/49 x y  DATA(0, 2)
+             2                      2                       2
+     + 1/70 y  DATA(-1, 0) + 1/140 y  DATA(-1, -1) - 1/140 y  DATA(1, -1)
 
-               2                       2                       2
-     - 2/49 x y  DATA(0, -2) + 1/49 x y  DATA(-1, 0) - 2/49 x y  DATA(2, 0)
+             2                      2                     2
+     + 1/70 y  DATA(-2, -1) + 1/35 y  DATA(2, -2) - 1/35 y  DATA(-2, -2)
 
-               2
-     - 2/49 x y  DATA(-2, 0) + 2/35 x y DATA(0, -2) + 1/35 x y DATA(1, -2)
+             2                      2                     2
+     - 1/70 y  DATA(-1, -2) + 1/10 x  DATA(-1, 0) - 1/20 x  DATA(-2, -2)
 
-                                       2                      2
-     - 2/35 x y DATA(-2, -2) - 1/49 x y  DATA(2, 1) - 1/49 x y  DATA(2, -1)
+             2                    2                    2
+     + 1/20 x  DATA(2, 1) + 1/20 x  DATA(2, 0) + 1/20 x  DATA(2, -1)
 
-               2                       2               37
-     + 2/49 x y  DATA(-2, 2) - 1/49 x y  DATA(-2, 1) + --- y DATA(-1, -1)
-                                                       300
+             2                    2                    2
+     + 1/20 x  DATA(2, 2) - 1/10 x  DATA(1, 2) + 1/20 x  y DATA(2, 2)
 
-             3                     3                     3
-     + 1/30 y  DATA(-2, 1) + 1/60 y  DATA(-1, 1) - 1/60 y  DATA(1, 1)
+             2                      2                     2
+     - 1/20 x  DATA(-2, -1) + 1/20 x  DATA(2, -2) - 1/20 x  DATA(-2, 0)
 
-             3               37                  21
-     + 1/60 y  DATA(1, -1) - --- y DATA(-1, 1) + --- y DATA(1, 2)
-                             300                 200
+             3                     2                    2
+     + 1/30 y  DATA(-2, 1) - 1/10 x  DATA(1, 0) - 1/10 x  DATA(1, 1)
 
-       11                 21                       3
-     - --- y DATA(2, 2) + --- y DATA(2, 1) + 1/60 y  DATA(-2, -2)
-       150                200
+       41                 289                  191
+     - -- x DATA(0, -2) - ---- x DATA(-2, 2) + ---- x DATA(-2, 0)
+       98                 2940                 2940
 
-        71                  289                   71
-     + ---- x DATA(2, -1) - ---- x DATA(-2, 2) + ---- x DATA(-2, 1)
-       2940                 2940                 2940
+       289                       2                      2
+     - ---- x DATA(2, 2) + 1/10 x  DATA(-1, -2) - 1/10 x  DATA(1, -2)
+       2940
 
-        71                   289                  226
-     + ---- x DATA(-2, -1) - ---- x DATA(2, -2) + --- x DATA(-1, -2)
-       2940                  2940                 735
+             2                     2               57
+     - 1/20 x  DATA(-2, 2) - 1/20 x  DATA(-2, 1) - -- x DATA(0, 0)
+                                                   98
 
-       226                 289                   53
-     + --- x DATA(1, -2) - ---- x DATA(-2, -2) - -- x DATA(0, 1)
-       735                 2940                  98
+       53                 71                 191
+     - -- x DATA(0, 1) + ---- x DATA(2, 1) + ---- x DATA(2, 0)
+       98                2940                2940
 
-       53                 41                41
-     - -- x DATA(0, -1) - -- x DATA(0, 2) - -- x DATA(0, -2)
-       98                 98                98
+             2                     2                      2
+     + 1/10 x  DATA(-1, 1) + 1/10 x  DATA(-1, -1) - 1/10 x  DATA(1, -1)
 
-       166                       3                     3
-     + --- x DATA(-1, 0) - 1/60 y  DATA(2, -2) - 1/60 y  DATA(-1, -1)
+       226                       3                    3
+     + --- x DATA(1, -2) - 2/15 x  DATA(1, 1) - 2/15 x  DATA(-1, -2)
        735
 
-              3                    3                    3
-     + 1/120 y  DATA(1, 2) + 1/60 y  DATA(2, 2) - 1/30 y  DATA(2, 1)
+        71                  181                  71
+     + ---- x DATA(-2, 1) + --- x DATA(1, -1) + ---- x DATA(-2, -1)
+       2940                 735                 2940
 
-              3                     3                     3
-     - 1/120 y  DATA(-1, 2) + 1/30 y  DATA(2, -1) - 1/60 y  DATA(-2, 2)
+       289                  289                   226
+     - ---- x DATA(2, -2) - ---- x DATA(-2, -2) + --- x DATA(1, 2)
+       2940                 2940                  735
 
-        71                 191                        3
-     + ---- x DATA(2, 1) + ---- x DATA(-2, 0) - 1/30 y  DATA(-2, -1)
-       2940                2940
+       41                226                 181
+     - -- x DATA(0, 2) + --- x DATA(-1, 2) + --- x DATA(-1, 1)
+       98                735                 735
 
-              3                       3               191
-     + 1/120 y  DATA(-1, -2) - 1/120 y  DATA(1, -2) + ---- x DATA(2, 0)
-                                                      2940
+       53                  71                  166
+     - -- x DATA(0, -1) + ---- x DATA(2, -1) + --- x DATA(1, 0)
+       98                 2940                 735
 
-                           17                      3
-     - 1/84 DATA(-2, -1) - --- DATA(-2, 0) - 2/15 x  DATA(1, -2)
-                           420
+       181                226                        3
+     + --- x DATA(1, 1) + --- x DATA(-1, -2) - 2/15 x  DATA(-1, 1)
+       735                735
 
-             3                     3                   3
-     + 1/30 x  DATA(-2, -2) + 1/5 x  DATA(0, 1) + 1/5 x  DATA(0, -1)
+             3               181                  166
+     - 2/15 x  DATA(-1, 0) + --- x DATA(-1, -1) + --- x DATA(-1, 0)
+                             735                  735
 
-            3                   3                     3
-     + 1/5 x  DATA(0, 2) + 1/5 x  DATA(0, -2) - 2/15 x  DATA(-1, 0)
+            3                   3                    3
+     + 1/5 x  DATA(0, 0) + 1/5 x  DATA(0, 1) + 1/30 x  DATA(2, 1)
 
-             3                    3               57
-     + 1/30 x  DATA(2, 0) + 1/30 x  DATA(-2, 0) - -- x DATA(0, 0)
-                                                  98
+             3                    3                     3
+     + 1/30 x  DATA(2, 0) + 1/30 x  DATA(2, -1) + 1/30 x  DATA(2, 2)
 
-       226                 181                181
-     + --- x DATA(-1, 2) + --- x DATA(1, 1) + --- x DATA(1, -1)
-       735                 735                735
+             3                    3                     3
+     - 2/15 x  DATA(1, 0) - 2/15 x  DATA(-1, -1) + 1/5 x  DATA(0, -2)
 
-       181                  181                 226
-     + --- x DATA(-1, -1) + --- x DATA(-1, 1) + --- x DATA(1, 2)
-       735                  735                 735
+                         17                                  31
+     + 1/84 DATA(2, 1) + --- DATA(2, 0) + 1/84 DATA(2, -1) - --- DATA(2, 2)
+                         420                                 420
 
-       289                 166                      3
-     - ---- x DATA(2, 2) + --- x DATA(1, 0) - 2/15 x  DATA(-1, 2)
-       2940                735
+       11               11                17                31
+     + --- DATA(1, 2) - --- DATA(-1, 2) - --- DATA(-1, 0) - --- DATA(-1, 1)
+       105              105               105               210
 
-             3                    3                     3
-     - 2/15 x  DATA(1, 1) - 2/15 x  DATA(1, -1) - 2/15 x  DATA(-1, -1)
+       31                 31                        2
+     - --- DATA(-1, -1) + --- DATA(1, -1) + 1/49 x y  DATA(0, -1)
+       210                210
 
-             3                     3                    3
-     - 2/15 x  DATA(-1, 1) + 1/30 x  DATA(2, 1) + 1/30 x  DATA(2, -1)
+               2                       2                      2
+     - 2/49 x y  DATA(-2, 0) - 1/49 x y  DATA(1, 2) + 1/98 x y  DATA(-1, 1)
 
-             3                     3                     3
-     + 1/30 x  DATA(-2, 2) + 1/30 x  DATA(-2, 1) + 1/30 x  DATA(-2, -1)
+             2                        2                        2
+     + 1/40 x  y DATA(2, 1) - 1/49 x y  DATA(-2, -1) - 1/49 x y  DATA(2, -1)
 
-             3                     3                      2
-     + 1/30 x  DATA(2, -2) - 2/15 x  DATA(-1, -2) - 1/20 x  DATA(-2, -2)
+               2                      2                       2
+     - 2/49 x y  DATA(0, 2) - 1/49 x y  DATA(1, -2) + 1/49 x y  DATA(1, 0)
 
-             3                    3                    3
-     - 2/15 x  DATA(1, 2) + 1/30 x  DATA(2, 2) - 2/15 x  DATA(1, 0)
+               2                       2                        2
+     + 2/49 x y  DATA(2, -2) - 1/49 x y  DATA(-1, -2) - 2/49 x y  DATA(0, -2)
 
-             2                    2                    2
-     - 1/10 x  DATA(1, 0) - 1/10 x  DATA(1, 1) + 1/10 x  DATA(-1, 0)
+             2                      2                         2
+     - 1/20 x  y DATA(1, 1) - 1/40 x  y DATA(2, -1) - 1/49 x y  DATA(2, 1)
 
-             2                     2                      2
-     - 1/10 x  DATA(1, -1) + 1/10 x  DATA(-1, -1) + 1/10 x  DATA(-1, 1)
+               2                      2                       2
+     - 2/49 x y  DATA(2, 0) + 2/49 x y  DATA(-2, 2) + 2/49 x y  DATA(2, 2)
 
-            3                    2                        2
-     + 1/5 x  DATA(0, 0) - 1/10 x  y DATA(-1, -2) + 1/20 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, -2)
 
-             2                          2                      2
-     + 1/40 x  y DATA(-2, -1) - 1/49 x y  DATA(1, 2) + 2/49 x y  DATA(2, 2)
+             2                       2                        2
+     + 1/20 x  y DATA(1, -1) + 1/40 x  y DATA(-2, -1) - 1/20 x  y DATA(2, -2)
 
-               2                      2                      2
-     + 1/49 x y  DATA(1, 0) + 2/49 x y  DATA(0, 0) - 1/49 x y  DATA(-1, 2)
+             2                        2                        2
+     + 1/20 x  y DATA(-2, -2) - 1/10 x  y DATA(-1, -2) + 1/10 x  y DATA(1, -2)
 
-               2                      2                       2
-     + 1/98 x y  DATA(1, 1) + 1/98 x y  DATA(1, -1) + 1/98 x y  DATA(-1, -1)
+             2                       2
+     - 1/20 x  y DATA(-2, 2) - 1/40 x  y DATA(-2, 1) - 1/35 x y DATA(0, 1)
 
-               2                       2                        2
-     + 1/98 x y  DATA(-1, 1) + 2/49 x y  DATA(-2, -2) + 1/49 x y  DATA(0, 1)
+     + 1/70 x y DATA(-1, -1) - 1/70 x y DATA(1, 1) + 1/35 x y DATA(2, 1)
 
-               2
-     + 1/49 x y  DATA(0, -1) - 1/35 x y DATA(1, 2) + 1/70 x y DATA(1, -1)
+     - 1/35 x y DATA(2, -1) + 2/35 x y DATA(2, 2) - 1/35 x y DATA(1, 2)
 
-                                    2                       2
-     + 1/35 x y DATA(0, -1) + 1/10 x  y DATA(1, -2) + 1/10 x  y DATA(-1, 2)
+                                                          2
+     - 2/35 x y DATA(0, 2) - 1/35 x y DATA(-1, 2) - 1/10 x  y DATA(1, 2)
 
-             2                                       31
-     - 1/40 x  y DATA(-2, 1) - 1/70 x y DATA(1, 1) - --- DATA(2, -2)
-                                                     420
+             2                       2                       2
+     + 1/10 x  y DATA(-1, 2) + 1/20 x  y DATA(-1, 1) - 1/20 x  y DATA(-1, -1)
 
-       11                 11                      2
-     - --- DATA(-1, -2) + --- DATA(1, -2) - 1/40 x  y DATA(2, -1)
-       105                105
+     + 1/35 x y DATA(1, -2) + 2/35 x y DATA(-2, 2) + 1/35 x y DATA(-2, 1)
 
-             2                        2                      2
-     + 1/20 x  y DATA(-2, -2) - 1/10 x  y DATA(1, 2) + 1/40 x  y DATA(2, 1)
+                                      2                        2
+     - 1/70 x y DATA(-1, 1) + 1/98 x y  DATA(-1, -1) + 1/49 x y  DATA(-1, 0)
 
-             2                      2                       2
-     + 1/20 x  y DATA(2, 2) - 1/20 x  y DATA(2, -2) - 1/20 x  y DATA(-2, 2)
+     + 1/35 x y DATA(0, -1) + 1/70 x y DATA(1, -1) - 1/35 x y DATA(-2, -1)
 
-             2
-     + 1/20 x  y DATA(-1, 1) + 1/70 x y DATA(-1, -1) - 1/70 x y DATA(-1, 1)
+     - 2/35 x y DATA(2, -2) - 2/35 x y DATA(-2, -2) + 1/35 x y DATA(-1, -2)
 
-             2                    2                    2
-     - 1/10 x  DATA(1, 2) + 1/20 x  DATA(2, 0) + 1/20 x  DATA(2, 1)
+                                      2                       2
+     + 2/35 x y DATA(0, -2) - 1/49 x y  DATA(-2, 1) - 1/49 x y  DATA(-1, 2)
 
-             2                     2                     2
-     + 1/10 x  DATA(-1, 2) + 1/20 x  DATA(2, -1) + 1/20 x  DATA(2, 2)
+                           31                31
+     - 1/84 DATA(-2, -1) - --- DATA(2, -2) + --- DATA(-2, -2)
+                           420               420
 
-             2                     2                     2
-     - 1/20 x  DATA(-2, 2) - 1/20 x  DATA(-2, 1) - 1/20 x  DATA(-2, -1)
+       11                 11                31                17
+     - --- DATA(-1, -2) + --- DATA(1, -2) + --- DATA(-2, 2) - --- DATA(-2, 0)
+       105                105               420               420
 
-             2                     2                     2
-     - 1/20 x  DATA(-2, 0) + 1/20 x  DATA(2, -2) + 1/10 x  DATA(-1, -2)
+                                3                     3
+     - 1/84 DATA(-2, 1) - 2/15 x  DATA(1, -2) + 1/30 x  DATA(2, -2)
 
-             2               31
-     - 1/10 x  DATA(1, -2) + --- DATA(-2, -2)
-                             420
+             3                      3                   3
+     + 1/30 x  DATA(-2, -2) - 2/15 x  DATA(1, 2) + 1/5 x  DATA(0, 2)
+
+             3
+     - 2/15 x  DATA(-1, 2)
 
 > coeff_as_lc_of_data(%, posn_list_2d_size5);
-bytes used=70063472, alloc=2424388, time=6.47
-                 31          3                      2   11            3
-[COEFF(-2, -2) = --- + 1/60 y  - 2/35 x y + 2/49 x y  - --- y + 1/30 x
-                 420                                    150
+bytes used=70094424, alloc=2424388, time=6.48
+                         2                    2   289            2           3
+[COEFF(-2, -2) = 2/49 x y  - 2/35 x y - 1/35 y  - ---- x + 1/20 x  y + 1/30 x
+                                                  2940
 
-             2         2           2   289                             2
-     - 1/20 x  + 1/20 x  y - 1/35 y  - ---- x, COEFF(-1, -2) = - 1/10 x  y
-                                       2940
+       31    11            2         3                          2           2
+     + --- - --- y - 1/20 x  + 1/60 y , COEFF(-1, -2) = - 1/10 x  y - 1/70 y
+       420   150
 
-             2           2          3         2   226     11
-     - 1/70 y  - 1/49 x y  + 1/120 y  + 1/10 x  + --- x - --- + 1/35 x y
-                                                  735     105
+              3         3                    2   21              2   226
+     + 1/120 y  - 2/15 x  + 1/35 x y + 1/10 x  + --- y - 1/49 x y  + --- x
+                                                 200                 735
 
-       21            3                           2   41          3
-     + --- y - 2/15 x , COEFF(0, -2) = - 2/49 x y  - -- x + 1/5 x  + 2/35 x y,
-       200                                           98
+       11                       3   41                        2
+     - ---, COEFF(0, -2) = 1/5 x  - -- x + 2/35 x y - 2/49 x y , COEFF(1, -2)
+       105                          98
 
-                           3           2          3         2
-    COEFF(1, -2) = - 2/15 x  - 1/49 x y  - 1/120 y  - 1/10 x  + 1/35 x y
+                 2         2                      2         3         2
+     = - 1/49 x y  + 1/10 x  y + 1/35 x y + 1/70 y  - 2/15 x  - 1/10 x
 
-       21      226     11          2           2                 11
-     - --- y + --- x + --- + 1/10 x  y + 1/70 y , COEFF(2, -2) = --- y
-       200     735     105                                       150
+              3   226     11    21                                 31
+     - 1/120 y  + --- x + --- - --- y, COEFF(2, -2) = - 2/35 x y - ---
+                  735     105   200                                420
 
-               2         2         2   31    289            3         3
-     + 2/49 x y  + 1/20 x  + 1/35 y  - --- - ---- x - 1/60 y  + 1/30 x
-                                       420   2940
+             3         2         3         2             2   289            2
+     + 1/30 x  + 1/20 x  - 1/60 y  - 1/20 x  y + 2/49 x y  - ---- x + 1/35 y
+                                                             2940
 
-                        2                          3   21            3
-     - 2/35 x y - 1/20 x  y, COEFF(-2, -1) = 1/30 x  + --- y - 1/30 y
-                                                       200
+       11                               2         3                    2
+     + --- y, COEFF(-2, -1) = - 1/49 x y  - 1/30 y  - 1/35 x y - 1/20 x
+       150
 
-               2                    2           2    71            2
-     - 1/49 x y  - 1/35 x y + 1/40 x  y + 1/70 y  + ---- x - 1/20 x  - 1/84,
-                                                    2940
+             2    71             21            3         2
+     + 1/70 y  + ---- x - 1/84 + --- y + 1/30 x  + 1/40 x  y, COEFF(-1, -1) =
+                 2940            200
 
-                            3   31           2                    3         2
-    COEFF(-1, -1) = - 2/15 x  - --- + 1/140 y  + 1/70 x y - 1/60 y  - 1/20 x  y
-                                210
+                     3           2   37      31          2          2         3
+    1/70 x y - 1/60 y  + 1/98 x y  + --- y - --- + 1/10 x  + 1/140 y  - 2/15 x
+                                     300     210
 
-       37            2           2   181
-     + --- y + 1/10 x  + 1/98 x y  + --- x,
-       300                           735
+       181           2                     53                        2        3
+     + --- x - 1/20 x  y, COEFF(0, -1) = - -- x + 1/35 x y + 1/49 x y  + 1/5 x ,
+       735                                 98
 
-                                   3           2   53                         3
-    COEFF(0, -1) = 1/35 x y + 1/5 x  + 1/49 x y  - -- x, COEFF(1, -1) = 1/60 y
-                                                   98
+                           2   181           2            2         2         3
+    COEFF(1, -1) = 1/98 x y  + --- x + 1/20 x  y - 1/140 y  - 1/10 x  + 1/60 y
+                               735
 
-             3         2           2   31            2   181
-     - 2/15 x  + 1/20 x  y - 1/10 x  + --- + 1/98 x y  + --- x + 1/70 x y
-                                       210               735
+             3   31    37                                 21
+     - 2/15 x  + --- - --- y + 1/70 x y, COEFF(2, -1) = - --- y + 1/84
+                 210   300                                200
 
-              2   37                            2           2
-     - 1/140 y  - --- y, COEFF(2, -1) = - 1/70 y  - 1/49 x y  - 1/35 x y
-                  300
+             3    71            2         2                    3           2
+     + 1/30 y  + ---- x + 1/20 x  - 1/70 y  - 1/35 x y + 1/30 x  - 1/49 x y
+                 2940
 
-       21            2           3         3                2    71
-     - --- y - 1/40 x  y + 1/30 x  + 1/30 y  + 1/84 + 1/20 x  + ---- x,
-       200                                                      2940
+             2
+     - 1/40 x  y,
 
-                             2         2   191            3         2   17
-    COEFF(-2, 0) = - 2/49 x y  + 1/35 y  + ---- x + 1/30 x  - 1/20 x  - ---,
-                                           2940                         420
+                           2           2   191      17          2         3
+    COEFF(-2, 0) = - 1/20 x  - 2/49 x y  + ---- x - --- + 1/35 y  + 1/30 x ,
+                                           2940     420
 
-                           2   17    166           2         2         3
-    COEFF(-1, 0) = 1/49 x y  - --- + --- x + 1/10 x  + 1/70 y  - 2/15 x ,
-                               105   735
+                         2         3           2   166     17          2
+    COEFF(-1, 0) = 1/10 x  - 2/15 x  + 1/49 x y  + --- x - --- + 1/70 y ,
+                                                   735     105
 
-                    57          3           2
-    COEFF(0, 0) = - -- x + 1/5 x  + 2/49 x y ,
-                    98
+                          2        3   57
+    COEFF(0, 0) = 2/49 x y  + 1/5 x  - -- x,
+                                       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
+                          3   17          2   166           2           2
+    COEFF(1, 0) = - 2/15 x  + --- - 1/10 x  + --- x - 1/70 y  + 1/49 x y ,
+                              105             735
 
-                          2           2   17          2         3   191
-    COEFF(2, 0) = - 1/35 y  - 2/49 x y  + --- + 1/20 x  + 1/30 x  + ---- x,
-                                          420                       2940
+                            2   191            3         2   17          2
+    COEFF(2, 0) = - 2/49 x y  + ---- x + 1/30 x  + 1/20 x  + --- - 1/35 y ,
+                                2940                         420
 
-                         3         3           2                    2    71
-    COEFF(-2, 1) = 1/30 y  + 1/30 x  - 1/49 x y  + 1/35 x y + 1/70 y  + ---- x
-                                                                        2940
+                                    3           2         2         2     21
+    COEFF(-2, 1) = 1/35 x y + 1/30 y  - 1/49 x y  + 1/70 y  - 1/40 x  y - --- y
+                                                                          200
 
-             2         2     21                                 2
-     - 1/20 x  - 1/40 x  y - --- y - 1/84, COEFF(-1, 1) = 1/20 x  y - 1/70 x y
-                             200
+             2           71            3                       2           3
+     - 1/20 x  - 1/84 + ---- x + 1/30 x , COEFF(-1, 1) = 1/20 x  y + 1/60 y
+                        2940
 
-             2           2          2   181           3         3   31    37
-     + 1/10 x  + 1/98 x y  + 1/140 y  + --- x - 2/15 x  + 1/60 y  - --- - --- y
-                                        735                         210   300
+       181     37                         2         2         3   31
+     + --- x - --- y - 1/70 x y + 1/98 x y  + 1/10 x  - 2/15 x  - ---
+       735     300                                                210
 
-                      53             2        3                           181
-    , COEFF(0, 1) = - -- x + 1/49 x y  + 1/5 x  - 1/35 x y, COEFF(1, 1) = --- x
-                      98                                                  735
+              2                  53             2        3
+     + 1/140 y , COEFF(0, 1) = - -- x + 1/49 x y  + 1/5 x  - 1/35 x y,
+                                 98
 
-             2         3         3   31    37             2
-     - 1/10 x  - 1/60 y  - 2/15 x  + --- + --- y - 1/140 y  - 1/70 x y
-                                     210   300
+                          3   37                       2   31          3
+    COEFF(1, 1) = - 1/60 y  + --- y - 1/70 x y - 1/10 x  + --- - 2/15 x
+                              300                          210
 
-               2         2                  21            3
-     + 1/98 x y  - 1/20 x  y, COEFF(2, 1) = --- y - 1/30 y  + 1/35 x y
-                                            200
+             2             2   181            2                          2
+     - 1/20 x  y + 1/98 x y  + --- x - 1/140 y , COEFF(2, 1) = - 1/49 x y
+                               735
 
-             2    71            2         3                2             2
-     + 1/20 x  + ---- x - 1/70 y  + 1/30 x  + 1/84 + 1/40 x  y - 1/49 x y ,
-                 2940
+        71                   2           3                    3         2
+     + ---- x + 1/84 + 1/40 x  y + 1/30 x  + 1/35 x y - 1/30 y  - 1/70 y
+       2940
 
-                           2         2           2   11              2
-    COEFF(-2, 2) = - 1/20 x  - 1/20 x  y - 1/35 y  + --- y + 2/49 x y
-                                                     150
+             2   21                    11                       3         2
+     + 1/20 x  + --- y, COEFF(-2, 2) = --- y + 2/35 x y - 1/60 y  - 1/20 x  y
+                 200                   150
 
-             3         3              289      31                          3
-     - 1/60 y  + 1/30 x  + 2/35 x y - ---- x + ---, COEFF(-1, 2) = - 2/15 x
-                                      2940     420
+               2   289            2   31          2         3
+     + 2/49 x y  - ---- x - 1/20 x  + --- - 1/35 y  + 1/30 x , COEFF(-1, 2) =
+                   2940               420
 
-                        2          3         2     21              2   226
-     - 1/35 x y + 1/10 x  - 1/120 y  + 1/10 x  y - --- y - 1/49 x y  + --- x
-                                                   200                 735
+          2            3         2           2              226     11
+    1/10 x  y - 1/120 y  + 1/10 x  - 1/49 x y  - 1/35 x y + --- x - ---
+                                                            735     105
 
-             2   11                                      2   41          3
-     - 1/70 y  - ---, COEFF(0, 2) = - 2/35 x y - 2/49 x y  - -- x + 1/5 x ,
-                 105                                         98
+             3   21            2
+     - 2/15 x  - --- y - 1/70 y ,
+                 200
 
-                  11          2           2         3                    2
-    COEFF(1, 2) = --- - 1/10 x  - 1/49 x y  - 2/15 x  - 1/35 x y + 1/70 y
-                  105
+                       3           2              41
+    COEFF(0, 2) = 1/5 x  - 2/49 x y  - 2/35 x y - -- x, COEFF(1, 2) =
+                                                  98
 
-       21            2            3   226                        2           2
-     + --- y - 1/10 x  y + 1/120 y  + --- x, COEFF(2, 2) = 1/20 x  y + 1/35 y
-       200                            735
+              2         2            3         2   11          3   21
+    - 1/49 x y  - 1/10 x  y + 1/120 y  + 1/70 y  + --- - 2/15 x  + --- y
+                                                   105             200
 
-                  31          2   11            3   289              2
-     + 2/35 x y - --- + 1/20 x  - --- y + 1/30 x  - ---- x + 2/49 x y
-                  420             150               2940
+                  226           2                      2   11            2
+     - 1/35 x y + --- x - 1/10 x , COEFF(2, 2) = 1/20 x  - --- y + 1/35 y
+                  735                                      150
 
-             3
-     + 1/60 y ]
+                        3           2   289            2           3   31
+     + 2/35 x y + 1/30 x  + 2/49 x y  - ---- x + 1/20 x  y + 1/60 y  - ---]
+                                        2940                           420
 
 > print_coeff__lc_of_data(%, "coeff_dx_", "fp",
 > 			"2d.coeffs/2d.cube.order4.smooth0/coeff-dx.compute.c");
-bytes used=71064040, alloc=2424388, time=6.54
-bytes used=72064272, alloc=2424388, time=6.62
-bytes used=73075772, alloc=2424388, time=6.70
-bytes used=74075968, alloc=2424388, time=6.88
-bytes used=75076136, alloc=2424388, time=6.95
-bytes used=76076304, alloc=2424388, time=7.04
-bytes used=77076556, alloc=2424388, time=7.20
-bytes used=78076920, alloc=2424388, time=7.29
-bytes used=79077292, alloc=2424388, time=7.46
-bytes used=80077492, alloc=2424388, time=7.59
-bytes used=81077684, alloc=2424388, time=7.72
+bytes used=71095128, alloc=2424388, time=6.56
+bytes used=72109496, alloc=2424388, time=6.63
+bytes used=73109972, alloc=2424388, time=6.71
+bytes used=74110128, alloc=2424388, time=6.86
+bytes used=75111952, alloc=2424388, time=6.95
+bytes used=76112156, alloc=2424388, time=7.14
+bytes used=77115576, alloc=2424388, time=7.22
+bytes used=78115732, alloc=2424388, time=7.40
+bytes used=79116356, alloc=2424388, time=7.47
+bytes used=80116536, alloc=2424388, time=7.66
 > 
 # d/dy
 > simplify( diff(interp_2d_cube_order4_smooth0,y) );
-bytes used=82108412, alloc=2424388, time=7.80
-bytes used=83108600, alloc=2424388, time=7.88
-                        17               31                     2
-- 2/35 x y DATA(2, 0) + --- DATA(0, 1) + --- DATA(1, 1) + 1/35 x  DATA(0, -2)
-                        105              210
-
-       53                166                166                 57
-     - -- y DATA(1, 0) + --- y DATA(0, 1) + --- y DATA(0, -1) - -- y DATA(0, 0)
-       98                735                735                 98
-
-       191                        2                    2
-     + ---- y DATA(0, -2) + 1/20 y  DATA(0, 2) - 1/20 y  DATA(0, -2)
-       2940
+bytes used=81117572, alloc=2424388, time=7.76
+bytes used=82118060, alloc=2424388, time=7.83
+bytes used=83118724, alloc=2489912, time=7.90
+        2                    2                     2
+- 1/10 y  DATA(0, 1) - 1/20 y  DATA(0, -2) + 1/10 y  DATA(0, -1)
 
-            3                    3                   3
-     + 1/5 y  DATA(-1, 0) + 1/5 y  DATA(2, 0) + 1/5 y  DATA(-2, 0)
+             2                   3                   3
+     + 1/20 y  DATA(0, 2) + 1/5 y  DATA(2, 0) + 1/5 y  DATA(-1, 0)
 
-       53                 41                41
-     - -- y DATA(-1, 0) - -- y DATA(2, 0) - -- y DATA(-2, 0)
-       98                 98                98
+            3              53                       3
+     + 1/5 y  DATA(1, 0) - -- y DATA(-1, 0) + 1/30 y  DATA(0, -2)
+                           98
 
-       191                       2                    2
-     + ---- y DATA(0, 2) - 1/10 y  DATA(0, 1) + 1/10 y  DATA(0, -1)
-       2940
+             3                     3                    3
+     - 2/15 y  DATA(0, -1) + 1/30 y  DATA(0, 2) - 2/15 y  DATA(0, 1)
 
-             2                       2                     2
-     - 2/49 x  y DATA(0, -2) + 1/70 x  DATA(0, -1) - 1/35 x  DATA(0, 2)
+            3                    3              191
+     + 1/5 y  DATA(-2, 0) + 1/5 y  DATA(0, 0) + ---- y DATA(0, -2)
+                                                2940
 
-             3                    3                     3
-     + 1/30 y  DATA(0, 2) + 1/30 y  DATA(0, -2) - 2/15 y  DATA(0, -1)
+       41                53                      2
+     - -- y DATA(2, 0) - -- y DATA(1, 0) - 2/49 x  y DATA(2, 0)
+       98                98
 
-            3                   3                    3
-     + 1/5 y  DATA(0, 0) + 1/5 y  DATA(1, 0) - 2/15 y  DATA(0, 1)
+       166                 191                 166
+     + --- y DATA(0, -1) + ---- y DATA(0, 2) + --- y DATA(0, 1)
+       735                 2940                735
 
-       31                17                31                 31
-     - --- DATA(1, -1) - --- DATA(0, -1) - --- DATA(-1, -1) + --- DATA(-1, 1)
-       210               105               210                210
+             2                    2                    2
+     - 1/70 x  DATA(0, 1) - 1/35 x  DATA(0, 2) + 1/70 x  DATA(0, -1)
 
-                         31               11
-     + 1/84 DATA(1, 2) - --- DATA(2, 2) + --- DATA(2, 1) + 1/84 DATA(-1, 2)
-                         420              105
+                                                         2
+     - 2/35 x y DATA(2, 0) - 1/35 x y DATA(1, 0) + 1/35 x  DATA(0, -2)
 
-       17               11                31                11
-     + --- DATA(0, 2) - --- DATA(2, -1) - --- DATA(-2, 2) + --- DATA(-2, 1)
-       420              105               420               105
+             2                      2                      2
+     + 1/49 x  y DATA(1, 0) - 2/49 x  y DATA(0, 2) + 2/49 x  y DATA(0, 0)
 
-             2                    2                     2
-     - 1/10 y  DATA(2, 1) + 1/20 y  DATA(-1, 2) + 1/10 y  DATA(2, -1)
+             2                       2                       2
+     + 1/49 x  y DATA(0, -1) - 2/49 x  y DATA(0, -2) + 1/49 x  y DATA(-1, 0)
 
-             2                     2                     2
-     + 1/20 y  DATA(-2, 2) - 1/10 y  DATA(-2, 1) + 1/10 y  DATA(-2, -1)
+       57                41                 17               31
+     - -- y DATA(0, 0) - -- y DATA(-2, 0) + --- DATA(0, 1) + --- DATA(1, 1)
+       98                98                 105              210
 
-             2                     2                      2
-     - 1/20 y  DATA(2, -2) - 1/20 y  DATA(-1, -2) + 1/20 y  DATA(2, 2)
+             3                      3                     3
+     - 1/60 x  DATA(-2, 2) - 1/120 x  DATA(-2, 1) + 1/60 x  DATA(1, -1)
 
-             2                    2                     2
-     - 1/10 y  DATA(1, 1) + 1/10 y  DATA(1, -1) + 1/10 y  DATA(-1, -1)
+              3                 71                  71
+     + 1/120 x  DATA(-2, -1) + ---- y DATA(1, 2) + ---- y DATA(-1, 2)
+                               2940                2940
 
-             2                                            2
-     - 1/10 y  DATA(-1, 1) - 1/35 x y DATA(-1, 2) + 1/98 x  y DATA(-1, -1)
+       181                  71                    71
+     + --- y DATA(-1, 1) + ---- y DATA(-1, -2) + ---- y DATA(1, -2)
+       735                 2940                  2940
 
-             2
-     + 1/98 x  y DATA(1, 1) + 1/35 x y DATA(-2, -1) + 2/35 x y DATA(2, -2)
+       289                  181                 181
+     - ---- y DATA(-2, 2) + --- y DATA(1, -1) + --- y DATA(1, 1)
+       2940                 735                 735
 
-                                                   181
-     + 2/35 x y DATA(2, 2) - 1/35 x y DATA(2, 1) + --- y DATA(1, 1)
-                                                   735
+       226                226                 289
+     + --- y DATA(2, 1) + --- y DATA(2, -1) - ---- y DATA(2, 2)
+       735                735                 2940
 
-               2                        2                       2
-     - 1/10 x y  DATA(-2, -1) - 1/20 x y  DATA(2, -2) + 1/40 x y  DATA(-1, -2)
+             3                    3                    3
+     + 1/30 y  DATA(2, 2) + 1/30 y  DATA(1, 2) + 1/30 y  DATA(-1, 2)
 
-               2
-     - 1/40 x y  DATA(1, -2) - 1/35 x y DATA(2, -1) - 2/35 x y DATA(-2, 2)
+             2                     2                     2
+     - 1/10 y  DATA(-1, 1) + 1/10 y  DATA(2, -1) + 1/20 y  DATA(2, 2)
 
-                               71                  226
-     + 1/35 x y DATA(-2, 1) + ---- y DATA(-1, 2) + --- y DATA(2, -1)
-                              2940                 735
+             2                    2                     2
+     + 1/20 y  DATA(1, 2) + 1/20 y  DATA(-1, 2) - 1/10 y  DATA(1, 1)
 
-       289                  226                 226
-     - ---- y DATA(-2, 2) + --- y DATA(-2, 1) + --- y DATA(-2, -1)
-       2940                 735                 735
+             2              226                 181
+     - 1/10 y  DATA(2, 1) + --- y DATA(-2, 1) + --- y DATA(-1, -1)
+                            735                 735
 
-       289                   71                    71
-     - ---- y DATA(2, -2) + ---- y DATA(-1, -2) + ---- y DATA(1, -2)
-       2940                 2940                  2940
+       226                  289                  289
+     + --- y DATA(-2, -1) - ---- y DATA(2, -2) - ---- y DATA(-2, -2)
+       735                  2940                 2940
 
-       289                   181                       2
-     - ---- y DATA(-2, -2) + --- y DATA(1, -1) - 1/20 y  DATA(1, -2)
-       2940                  735
+             2                     2                     2
+     - 1/20 y  DATA(1, -2) + 1/20 y  DATA(-2, 2) - 1/10 y  DATA(-2, 1)
 
-             2                      2
-     - 1/20 y  DATA(-2, -2) + 1/20 y  DATA(1, 2) - 1/35 x y DATA(-1, -2)
+             3                    3                    3
+     - 2/15 y  DATA(1, 1) - 2/15 y  DATA(2, 1) - 2/15 y  DATA(2, -1)
 
-                                                              2
-     + 1/35 x y DATA(1, -2) - 2/35 x y DATA(-2, -2) - 1/10 x y  DATA(2, 1)
+             2                     3                      3
+     - 1/70 x  DATA(-1, 2) - 2/15 y  DATA(-2, -1) + 1/30 y  DATA(2, -2)
 
-               2                       2                       2
-     + 1/10 x y  DATA(2, -1) - 1/20 x y  DATA(-2, 2) + 1/10 x y  DATA(-2, 1)
+             3                      3                      3
+     + 1/30 y  DATA(-2, -2) + 1/30 y  DATA(-1, -2) + 1/30 y  DATA(1, -2)
 
-       181                        3                     3
-     + --- y DATA(-1, -1) - 2/15 y  DATA(-2, 1) - 2/15 y  DATA(-1, 1)
-       735
+             3                     3                     3
+     + 1/30 y  DATA(-2, 2) - 2/15 y  DATA(-1, 1) - 2/15 y  DATA(-1, -1)
 
-             3                    3               181
-     - 2/15 y  DATA(1, 1) - 2/15 y  DATA(1, -1) + --- y DATA(-1, 1)
-                                                  735
+             3                     2                      2
+     - 2/15 y  DATA(1, -1) + 1/10 y  DATA(-1, -1) + 1/10 y  DATA(1, -1)
 
-        71                 289                 226
-     + ---- y DATA(1, 2) - ---- y DATA(2, 2) + --- y DATA(2, 1)
-       2940                2940                735
+             2                      2                     2
+     + 1/10 y  DATA(-2, -1) - 1/20 y  DATA(2, -2) - 1/20 y  DATA(-2, -2)
 
-             3                21                  11
-     + 1/30 y  DATA(-2, -2) - --- x DATA(2, -1) + --- x DATA(-2, 2)
-                              200                 150
+             2                      2                      2
+     - 1/20 y  DATA(-1, -2) - 1/35 x  DATA(-2, -2) + 1/70 x  DATA(2, 1)
 
-       21                  21                   11
-     - --- x DATA(-2, 1) + --- x DATA(-2, -1) + --- x DATA(2, -2)
-       200                 200                  150
+             2                     2                    2
+     - 1/70 x  DATA(2, -1) + 1/35 x  DATA(2, 2) - 1/70 x  DATA(1, 2)
 
-       21                   21                  11
-     + --- x DATA(-1, -2) - --- x DATA(1, -2) - --- x DATA(-2, -2)
-       200                  200                 150
+             2                      2                      2
+     + 2/49 x  y DATA(2, 2) - 1/70 x  DATA(-2, -1) - 1/35 x  DATA(2, -2)
 
-             3                     3                      3
-     + 1/30 y  DATA(2, -2) - 2/15 y  DATA(-1, -1) + 1/30 y  DATA(1, 2)
+             3                      2              11
+     - 2/15 y  DATA(-2, 1) - 1/140 x  DATA(1, 1) + --- x DATA(-2, 2)
+                                                   150
 
-             3                    3                    3
-     + 1/30 y  DATA(2, 2) - 2/15 y  DATA(2, 1) + 1/30 y  DATA(-1, 2)
+       11                       2                      2
+     - --- x DATA(2, 2) + 1/70 x  DATA(-1, -2) + 1/70 x  DATA(1, -2)
+       150
 
-             3                     3               21
-     - 2/15 y  DATA(2, -1) + 1/30 y  DATA(-2, 2) + --- x DATA(2, 1)
+             2                     2               21
+     + 1/35 x  DATA(-2, 2) + 1/70 x  DATA(-2, 1) + --- x DATA(2, 1)
                                                    200
 
-             3                      3                      3
-     - 2/15 y  DATA(-2, -1) + 1/30 y  DATA(-1, -2) + 1/30 y  DATA(1, -2)
+              2                      2                       2
+     - 1/140 x  DATA(-1, 1) + 1/140 x  DATA(-1, -1) + 1/140 x  DATA(1, -1)
 
-       11                       3                     3
-     - --- DATA(-2, -1) + 1/30 x  DATA(1, -2) + 1/60 x  DATA(-2, -2)
-       105
+       21                        3                    3
+     - --- x DATA(1, -2) - 1/60 x  DATA(1, 1) - 1/30 x  DATA(-1, -2)
+       200
 
-       21                  37                 37
-     - --- x DATA(-1, 2) + --- x DATA(1, 1) - --- x DATA(1, -1)
-       200                 300                300
+       21                  37                  21
+     - --- x DATA(-2, 1) - --- x DATA(1, -1) + --- x DATA(-2, -1)
+       200                 300                 200
 
-       37                   37                  21
-     + --- x DATA(-1, -1) - --- x DATA(-1, 1) + --- x DATA(1, 2)
-       300                  300                 200
+       11                  11                   21
+     + --- x DATA(2, -2) - --- x DATA(-2, -2) + --- x DATA(1, 2)
+       150                 150                  200
 
-       11                       3                     3
-     - --- x DATA(2, 2) + 1/30 x  DATA(-1, 2) - 1/60 x  DATA(1, 1)
-       150
+       21                  37                  21
+     - --- x DATA(-1, 2) - --- x DATA(-1, 1) - --- x DATA(2, -1)
+       200                 300                 200
 
-             3                     3                      3
-     + 1/60 x  DATA(1, -1) - 1/60 x  DATA(-1, -1) + 1/60 x  DATA(-1, 1)
+       37                 21                         3
+     + --- x DATA(1, 1) + --- x DATA(-1, -2) + 1/60 x  DATA(-1, 1)
+       300                200
 
-              3                     3                     3
-     + 1/120 x  DATA(2, 1) - 1/120 x  DATA(2, -1) - 1/60 x  DATA(-2, 2)
+       37                          3                     3
+     + --- x DATA(-1, -1) + 1/120 x  DATA(2, 1) - 1/120 x  DATA(2, -1)
+       300
 
-              3                      3                      3
-     - 1/120 x  DATA(-2, 1) + 1/120 x  DATA(-2, -1) - 1/60 x  DATA(2, -2)
+             3                    3                11
+     + 1/60 x  DATA(2, 2) - 1/60 x  DATA(-1, -1) + --- DATA(2, 1)
+                                                   105
 
-             3                      2                      3
-     - 1/30 x  DATA(-1, -2) - 1/35 x  DATA(-2, -2) - 1/30 x  DATA(1, 2)
+       11                31                                 17
+     - --- DATA(2, -1) - --- DATA(2, 2) + 1/84 DATA(1, 2) + --- DATA(0, 2)
+       105               420                                420
 
-             3                     2                     2
-     + 1/60 x  DATA(2, 2) - 1/140 x  DATA(1, 1) + 1/140 x  DATA(1, -1)
+                          31                31                 17
+     + 1/84 DATA(-1, 2) + --- DATA(-1, 1) - --- DATA(-1, -1) - --- DATA(0, -1)
+                          210               210                105
 
-              2                       2                     2
-     + 1/140 x  DATA(-1, -1) - 1/140 x  DATA(-1, 1) - 1/49 x  y DATA(-1, -2)
+       31                        2                      2
+     - --- DATA(1, -1) + 1/40 x y  DATA(1, 2) + 1/20 x y  DATA(-1, 1)
+       210
 
-             2                       2                          2
-     + 1/98 x  y DATA(1, -1) - 1/49 x  y DATA(-2, -1) + 1/40 x y  DATA(1, 2)
+             2                        2                        2
+     - 1/49 x  y DATA(2, 1) - 1/10 x y  DATA(-2, -1) + 1/10 x y  DATA(2, -1)
 
-               2                      2                       2
-     + 1/20 x y  DATA(2, 2) - 1/40 x y  DATA(-1, 2) - 1/20 x y  DATA(1, 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                        2
-     + 1/20 x y  DATA(1, -1) - 1/20 x y  DATA(-1, -1) + 1/20 x y  DATA(-1, 1)
+             2                      2                         2
+     + 1/98 x  y DATA(1, 1) - 1/49 x  y DATA(2, -1) - 1/10 x y  DATA(2, 1)
 
-               2
-     + 1/20 x y  DATA(-2, -2) + 1/35 x y DATA(1, 2) - 1/70 x y DATA(1, -1)
+               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                       2
-     - 1/49 x  y DATA(1, -2) - 1/49 x  y DATA(-1, 2) - 1/49 x  y DATA(-2, 1)
+               2                      2                      2
+     - 1/20 x y  DATA(1, 1) + 1/20 x y  DATA(-2, -2) + 1/98 x  y DATA(1, -1)
 
-                             31
-     - 1/70 x y DATA(1, 1) + --- DATA(2, -2) - 1/84 DATA(-1, -2)
-                             420
+             2                        2                       2
+     - 1/49 x  y DATA(-2, -1) + 2/49 x  y DATA(2, -2) + 2/49 x  y DATA(-2, -2)
 
-       17                                         2
-     - --- DATA(0, -2) - 1/84 DATA(1, -2) - 1/49 x  y DATA(2, -1)
-       420
+             2                        2                       2
+     - 1/49 x  y DATA(-1, -2) - 1/49 x  y DATA(1, -2) + 2/49 x  y DATA(-2, 2)
 
-             2                        2                      2
-     + 2/49 x  y DATA(-2, -2) - 1/49 x  y DATA(1, 2) - 1/49 x  y DATA(2, 1)
+             2
+     - 1/49 x  y DATA(-2, 1) + 1/70 x y DATA(-1, -1) - 1/70 x y DATA(1, 1)
 
-             2                      2                       2
-     + 2/49 x  y DATA(2, 2) + 2/49 x  y DATA(2, -2) + 2/49 x  y DATA(-2, 2)
+     - 1/35 x y DATA(2, 1) - 1/35 x y DATA(2, -1) + 2/35 x y DATA(2, 2)
 
-             2
-     + 1/98 x  y DATA(-1, 1) + 1/70 x y DATA(-1, -1) + 1/70 x y DATA(-1, 1)
+                                                          2
+     + 1/35 x y DATA(1, 2) - 1/35 x y DATA(-1, 2) - 1/49 x  y DATA(1, 2)
 
-             2                    2                    2
-     - 1/70 x  DATA(1, 2) + 1/70 x  DATA(2, 1) - 1/70 x  DATA(-1, 2)
+             2                       2                       2
+     - 1/49 x  y DATA(-1, 2) + 1/98 x  y DATA(-1, 1) + 1/98 x  y DATA(-1, -1)
 
-             2                     2                    2
-     - 1/70 x  DATA(2, -1) + 1/35 x  DATA(2, 2) + 1/35 x  DATA(-2, 2)
+     + 1/35 x y DATA(1, -2) - 2/35 x y DATA(-2, 2) + 1/35 x y DATA(-2, 1)
 
-             2                     2                      2
-     + 1/70 x  DATA(-2, 1) - 1/70 x  DATA(-2, -1) - 1/35 x  DATA(2, -2)
+                                      2
+     + 1/70 x y DATA(-1, 1) - 1/20 x y  DATA(-1, -1) - 1/70 x y DATA(1, -1)
 
-             2                      2               31
-     + 1/70 x  DATA(-1, -2) + 1/70 x  DATA(1, -2) + --- DATA(-2, -2)
-                                                    420
+     + 1/35 x y DATA(-2, -1) + 2/35 x y DATA(2, -2) - 2/35 x y DATA(-2, -2)
 
-                                    2                       2
-     + 2/35 x y DATA(-2, 0) + 1/49 x  y DATA(-1, 0) - 2/49 x  y DATA(2, 0)
+                                       2                       2
+     - 1/35 x y DATA(-1, -2) + 1/10 x y  DATA(-2, 1) - 1/40 x y  DATA(-1, 2)
 
-             2                       2
-     - 2/49 x  y DATA(-2, 0) - 2/49 x  y DATA(0, 2) - 1/35 x y DATA(1, 0)
+       11                 31                31
+     - --- DATA(-2, -1) + --- DATA(2, -2) + --- DATA(-2, -2)
+       105                420               420
 
-                                    2                       2
-     + 1/35 x y DATA(-1, 0) + 1/49 x  y DATA(0, -1) + 2/49 x  y DATA(0, 0)
+                           17                                   31
+     - 1/84 DATA(-1, -2) - --- DATA(0, -2) - 1/84 DATA(1, -2) - --- DATA(-2, 2)
+                           420                                  420
 
-             2                      2                      2
-     + 1/49 x  y DATA(1, 0) + 1/49 x  y DATA(0, 1) - 1/70 x  DATA(0, 1)
+       11                      3                     3
+     + --- DATA(-2, 1) + 1/30 x  DATA(1, -2) - 1/60 x  DATA(2, -2)
+       105
 
-> coeff_as_lc_of_data(%, posn_list_2d_size5);
-bytes used=84109804, alloc=2424388, time=7.95
-                 31          3         2         2   11            3
-[COEFF(-2, -2) = --- + 1/30 y  - 1/35 x  - 1/20 y  - --- x + 1/60 x
-                 420                                 150
+             3                      3                    3
+     + 1/60 x  DATA(-2, -2) - 1/30 x  DATA(1, 2) + 1/30 x  DATA(-1, 2)
 
-             2             2   289                                        2
-     + 2/49 x  y + 1/20 x y  - ---- y - 2/35 x y, COEFF(-1, -2) = - 1/20 y
-                               2940
+             2                       2
+     - 2/49 x  y DATA(-2, 0) + 1/49 x  y DATA(0, 1) + 2/35 x y DATA(-2, 0)
 
-       21            2             2         2           71            3
-     + --- x - 1/49 x  y + 1/40 x y  + 1/70 x  - 1/84 + ---- y - 1/30 x
-       200                                              2940
+     + 1/35 x y DATA(-1, 0)
 
-                        3
-     - 1/35 x y + 1/30 y ,
+> coeff_as_lc_of_data(%, posn_list_2d_size5);
+bytes used=84128420, alloc=2489912, time=7.97
+                   11            3         2         2     289            2
+[COEFF(-2, -2) = - --- x + 1/60 x  - 1/35 x  + 2/49 x  y - ---- y - 1/20 y
+                   150                                     2940
 
-                   191      17          2           2         3         2
-    COEFF(0, -2) = ---- y - --- - 2/49 x  y + 1/35 x  + 1/30 y  - 1/20 y ,
-                   2940     420
+       31            2         3                              71              2
+     + --- + 1/20 x y  + 1/30 y  - 2/35 x y, COEFF(-1, -2) = ---- y + 1/40 x y
+       420                                                   2940
 
-                                    3         2                  2   21
-    COEFF(1, -2) = 1/35 x y + 1/30 x  - 1/49 x  y - 1/84 - 1/20 y  - --- x
-                                                                     200
+             3         3                2           2   21
+     - 1/30 x  + 1/30 y  - 1/84 - 1/49 x  y + 1/70 x  + --- x - 1/35 x y
+                                                        200
 
-             2           2    71            3                         3
-     + 1/70 x  - 1/40 x y  + ---- y + 1/30 y , COEFF(2, -2) = - 1/60 x
-                             2940
+             2
+     - 1/20 y ,
 
-                        2   31    11      289            2         2
-     + 2/35 x y - 1/35 x  + --- + --- x - ---- y - 1/20 y  + 2/49 x  y
-                            420   150     2940
+                         2   17    191            2           3         2
+    COEFF(0, -2) = 1/35 x  - --- + ---- y - 2/49 x  y + 1/30 y  - 1/20 y ,
+                             420   2940
 
-               2         3                  21              2         3   226
-     - 1/20 x y  + 1/30 y , COEFF(-2, -1) = --- x - 1/10 x y  - 2/15 y  + --- y
-                                            200                           735
+                         2               71      21              2
+    COEFF(1, -2) = 1/70 x  + 1/35 x y + ---- y - --- x - 1/40 x y  - 1/84
+                                        2940     200
 
-              3                    2         2   11          2
-     + 1/120 x  + 1/35 x y + 1/10 y  - 1/70 x  - --- - 1/49 x  y, COEFF(-1, -1)
-                                                 105
+             2         3         2           3                         3
+     - 1/20 y  + 1/30 x  - 1/49 x  y + 1/30 y , COEFF(2, -2) = - 1/60 x
 
-                 2              37            2   181           2            2
-     = - 1/20 x y  + 1/70 x y + --- x + 1/10 y  + --- y + 1/98 x  y + 1/140 x
-                                300               735
+             2   11              2   289            2     31          3
+     - 1/20 y  + --- x - 1/20 x y  - ---- y + 2/49 x  y + --- + 1/30 y
+                 150                 2940                 420
 
-             3         3   31
-     - 2/15 y  - 1/60 x  - ---,
-                           210
+                        2                         3         2   21      11
+     + 2/35 x y - 1/35 x , COEFF(-2, -1) = 1/120 x  - 1/70 x  + --- x - ---
+                                                                200     105
 
-                     17          2     166           2         2         3
-    COEFF(0, -1) = - --- + 1/49 x  y + --- y + 1/10 y  + 1/70 x  - 2/15 y ,
-                     105               735
+             2         2             2   226                      3
+     + 1/10 y  - 1/49 x  y - 1/10 x y  + --- y + 1/35 x y - 2/15 y ,
+                                         735
 
-                   181            2         2           2   31          3
-    COEFF(1, -1) = --- y + 1/140 x  + 1/98 x  y + 1/10 y  - --- - 2/15 y
-                   735                                      210
+                           2                    2     181           3         2
+    COEFF(-1, -1) = 1/140 x  + 1/70 x y + 1/98 x  y + --- y - 1/60 x  + 1/10 y
+                                                      735
 
-       37            3                      2                              11
-     - --- x + 1/60 x  - 1/70 x y + 1/20 x y , COEFF(2, -1) = - 1/35 x y - ---
-       300                                                                 105
+       31    37            3           2
+     - --- + --- x - 2/15 y  - 1/20 x y ,
+       210   300
 
-               2   21      226            3         3         2           2
-     + 1/10 x y  - --- x + --- y - 1/120 x  - 2/15 y  - 1/49 x  y + 1/10 y
-                   200     735
+                         2     166           3         2         2   17
+    COEFF(0, -1) = 1/49 x  y + --- y - 2/15 y  + 1/70 x  + 1/10 y  - ---,
+                               735                                   105
 
-             2                      3   41                      2
-     - 1/70 x , COEFF(-2, 0) = 1/5 y  - -- y + 2/35 x y - 2/49 x  y,
-                                        98
+                   181           2         3          2   31          3
+    COEFF(1, -1) = --- y + 1/10 y  - 2/15 y  + 1/140 x  - --- + 1/60 x
+                   735                                    210
 
-                        3   53           2
-    COEFF(-1, 0) = 1/5 y  - -- y + 1/49 x  y + 1/35 x y,
-                            98
+               2   37            2
+     + 1/20 x y  - --- x + 1/98 x  y - 1/70 x y, COEFF(2, -1) = - 1/35 x y
+                   300
 
-                        2     57          3
-    COEFF(0, 0) = 2/49 x  y - -- y + 1/5 y ,
-                              98
+             2          3           2         2     11          3   21
+     - 1/70 x  - 1/120 x  + 1/10 x y  - 1/49 x  y - --- - 2/15 y  - --- x
+                                                    105             200
 
-                       3   53           2
-    COEFF(1, 0) = 1/5 y  - -- y + 1/49 x  y - 1/35 x y,
-                           98
+       226           2                                 3   41           2
+     + --- y + 1/10 y , COEFF(-2, 0) = 2/35 x y + 1/5 y  - -- y - 2/49 x  y,
+       735                                                 98
 
-                       3                    2     41
-    COEFF(2, 0) = 1/5 y  - 2/35 x y - 2/49 x  y - -- y, COEFF(-2, 1) =
-                                                  98
+                                    2          3   53
+    COEFF(-1, 0) = 1/35 x y + 1/49 x  y + 1/5 y  - -- y,
+                                                   98
 
-             3         3   11          2           2              226
-    - 1/120 x  - 2/15 y  + --- - 1/49 x  y + 1/70 x  + 1/35 x y + --- y
-                           105                                    735
+                    57           2          3
+    COEFF(0, 0) = - -- y + 2/49 x  y + 1/5 y ,
+                    98
 
-               2         2   21                      37              2
-     + 1/10 x y  - 1/10 y  - --- x, COEFF(-1, 1) = - --- x + 1/20 x y
-                             200                     300
+                    53          3                    2
+    COEFF(1, 0) = - -- y + 1/5 y  - 1/35 x y + 1/49 x  y,
+                    98
 
-                        3   31           2         2         3         2
-     + 1/70 x y + 1/60 x  + --- - 1/140 x  - 1/10 y  - 2/15 y  + 1/98 x  y
-                            210
+                       3         2     41                                    2
+    COEFF(2, 0) = 1/5 y  - 2/49 x  y - -- y - 2/35 x y, COEFF(-2, 1) = 1/70 x
+                                       98
 
-       181
-     + --- y,
-       735
+             2         2     226     11                       2   21
+     - 1/10 y  - 1/49 x  y + --- y + --- + 1/35 x y + 1/10 x y  - --- x
+                             735     105                          200
+
+              3         3                         2         2     37
+     - 1/120 x  - 2/15 y , COEFF(-1, 1) = 1/20 x y  + 1/98 x  y - --- x
+                                                                  300
+
+             3          2              31          3         2   181
+     + 1/60 x  - 1/140 x  + 1/70 x y + --- - 2/15 y  - 1/10 y  + --- y,
+                                       210                       735
 
-                  17          3         2   166           2         2
-    COEFF(0, 1) = --- - 2/15 y  - 1/70 x  + --- y - 1/10 y  + 1/49 x  y,
-                  105                       735
+                          2         2   166           2     17          3
+    COEFF(0, 1) = - 1/70 x  - 1/10 y  + --- y + 1/49 x  y + --- - 2/15 y ,
+                                        735                 105
 
-                  31          3         3                      2         2
-    COEFF(1, 1) = --- - 1/60 x  - 2/15 y  - 1/70 x y - 1/20 x y  - 1/10 y
-                  210
+                            2         2                    2     181
+    COEFF(1, 1) = - 1/20 x y  - 1/10 y  - 1/70 x y + 1/98 x  y + --- y
+                                                                 735
 
-       181           2     37             2                        2     21
-     + --- y + 1/98 x  y + --- x - 1/140 x , COEFF(2, 1) = - 1/49 x  y + --- x
-       735                 300                                           200
+             3   37            3          2   31                         2
+     - 2/15 y  + --- x - 1/60 x  - 1/140 x  + ---, COEFF(2, 1) = - 1/49 x  y
+                 300                          210
 
-       226           2         2              11            2          3
-     + --- y - 1/10 y  + 1/70 x  - 1/35 x y + --- - 1/10 x y  + 1/120 x
-       735                                    105
+             3         2   226     21            2           2              11
+     - 2/15 y  + 1/70 x  + --- y + --- x - 1/10 y  - 1/10 x y  - 1/35 x y + ---
+                           735     200                                      105
 
-             3                         3         2   289      31          3
-     - 2/15 y , COEFF(-2, 2) = - 1/60 x  + 1/35 x  - ---- y - --- + 1/30 y
-                                                     2940     420
+              3                       2         3         2   289      31
+     + 1/120 x , COEFF(-2, 2) = 1/35 x  + 1/30 y  + 1/20 y  - ---- y - ---
+                                                              2940     420
 
-       11            2                        2         2
-     + --- x + 2/49 x  y - 2/35 x y - 1/20 x y  + 1/20 y , COEFF(-1, 2) =
+       11            3                    2             2
+     + --- x - 1/60 x  - 2/35 x y + 2/49 x  y - 1/20 x y , COEFF(-1, 2) =
        150
 
-      21            2           2    71              2         2
-    - --- x - 1/49 x  y + 1/20 y  + ---- y - 1/40 x y  - 1/70 x  + 1/84
-      200                           2940
+          2         3   21              2         2                    3
+    1/20 y  + 1/30 x  - --- x - 1/40 x y  - 1/70 x  - 1/35 x y + 1/30 y
+                        200
 
-                        3         3
-     - 1/35 x y + 1/30 x  + 1/30 y ,
+             2             71
+     - 1/49 x  y + 1/84 + ---- y,
+                          2940
 
-                        2   17    191            2         3         2
-    COEFF(0, 2) = 1/20 y  + --- + ---- y - 1/35 x  + 1/30 y  - 2/49 x  y,
-                            420   2940
+                          2           2         3   17    191            2
+    COEFF(0, 2) = - 2/49 x  y - 1/35 x  + 1/30 y  + --- + ---- y + 1/20 y ,
+                                                    420   2940
 
-                          2                    2           3         2   21
-    COEFF(1, 2) = - 1/70 x  + 1/35 x y - 1/49 x  y - 1/30 x  + 1/20 y  + --- x
-                                                                         200
+                        3           2         2    71            3
+    COEFF(1, 2) = 1/30 y  + 1/40 x y  - 1/70 x  + ---- y - 1/30 x  + 1/35 x y
+                                                  2940
 
-             3    71                     2                      3   289
-     + 1/30 y  + ---- y + 1/84 + 1/40 x y , COEFF(2, 2) = 1/60 x  - ---- y
-                 2940                                               2940
+       21            2                  2                      3           2
+     + --- x - 1/49 x  y + 1/84 + 1/20 y , COEFF(2, 2) = 1/30 y  + 1/20 x y
+       200
 
-             2         2         3   31          2             2   11
-     + 1/35 x  + 1/20 y  + 1/30 y  - --- + 2/49 x  y + 1/20 x y  - --- x
-                                     420                           150
+                        2         3   31    289            2           2
+     + 2/35 x y + 1/20 y  + 1/60 x  - --- - ---- y + 2/49 x  y + 1/35 x
+                                      420   2940
 
-     + 2/35 x y]
+       11
+     - --- x]
+       150
 
 > print_coeff__lc_of_data(%, "coeff_dy_", "fp",
 > 			"2d.coeffs/2d.cube.order4.smooth0/coeff-dy.compute.c");
-bytes used=85110104, alloc=2424388, time=8.01
-bytes used=86110296, alloc=2424388, time=8.09
-bytes used=87116120, alloc=2424388, time=8.16
-bytes used=88116280, alloc=2424388, time=8.30
-bytes used=89116760, alloc=2424388, time=8.38
-bytes used=90116912, alloc=2424388, time=8.48
-bytes used=91117288, alloc=2424388, time=8.64
-bytes used=92117484, alloc=2424388, time=8.73
-bytes used=93117892, alloc=2424388, time=8.88
-bytes used=94118116, alloc=2424388, time=8.97
-bytes used=95118268, alloc=2424388, time=9.12
+bytes used=85128740, alloc=2489912, time=8.04
+bytes used=86138952, alloc=2489912, time=8.13
+bytes used=87140216, alloc=2489912, time=8.22
+bytes used=88140840, alloc=2489912, time=8.39
+bytes used=89142228, alloc=2489912, time=8.47
+bytes used=90142420, alloc=2489912, time=8.63
+bytes used=91145772, alloc=2489912, time=8.71
+bytes used=92145948, alloc=2489912, time=8.89
+bytes used=93146116, alloc=2489912, time=8.97
+bytes used=94146456, alloc=2489912, time=9.16
 > 
 # d^2/dx^2
 > simplify( diff(interp_2d_cube_order4_smooth0,x,x) );
-bytes used=96118472, alloc=2424388, time=9.19
-  57              166              53              181
-- -- DATA(0, 0) + --- DATA(1, 0) - -- DATA(0, 1) + --- DATA(1, 1)
-  98              735              98              735
+bytes used=95147116, alloc=2489912, time=9.28
+bytes used=96147276, alloc=2489912, time=9.35
+      2                    2                     2
+1/49 y  DATA(0, 1) - 2/49 y  DATA(0, -2) + 1/49 y  DATA(0, -1)
 
-            2
-     + 3/5 x  DATA(0, -2) - 1/35 y DATA(0, 1) + 1/35 y DATA(0, -1)
+             2
+     - 2/49 y  DATA(0, 2) + 2/35 y DATA(0, -2) + 1/35 y DATA(0, -1)
 
-                                  2                    2
-     + 2/35 y DATA(0, -2) - 2/49 y  DATA(0, 2) - 2/49 y  DATA(0, -2)
+                                                    2
+     - 2/35 y DATA(0, 2) - 1/35 y DATA(0, 1) + 3/5 x  DATA(0, 1)
 
-                                 2                    2
-     - 2/35 y DATA(0, 2) + 1/49 y  DATA(0, 1) + 1/49 y  DATA(0, -1)
+            2                   2                    2
+     + 3/5 x  DATA(0, 2) + 3/5 x  DATA(0, -1) + 3/5 x  DATA(0, -2)
 
-            2                    2              166
-     + 3/5 x  DATA(0, -1) + 3/5 x  DATA(0, 2) + --- DATA(-1, 0)
-                                                735
+       57              166              53              181
+     - -- DATA(0, 0) + --- DATA(1, 0) - -- DATA(0, 1) + --- DATA(1, 1)
+       98              735              98              735
 
-       181               53               181                181
-     + --- DATA(1, -1) - -- DATA(0, -1) + --- DATA(-1, -1) + --- DATA(-1, 1)
-       735               98               735                735
+     - 1/35 y DATA(1, 2) - 1/35 y DATA(-1, 2) - 1/70 y DATA(-1, 1)
 
-             2                                          2
-     - 2/49 y  DATA(-2, 0) - 1/10 x DATA(-2, 0) - 2/49 y  DATA(2, 0)
+     + 1/35 y DATA(-1, -2) + 1/35 y DATA(1, -2) + 2/35 y DATA(-2, 2)
 
-             2                    2                    2
-     + 2/49 y  DATA(0, 0) + 1/49 y  DATA(1, 0) + 1/49 y  DATA(-1, 0)
+     + 1/70 y DATA(1, -1) - 1/70 y DATA(1, 1) + 1/35 y DATA(2, 1)
 
-                                2                   2
-     + 1/10 x DATA(2, 0) + 3/5 x  DATA(0, 0) - 2/5 x  DATA(1, 0)
+                                                      2
+     - 1/35 y DATA(2, -1) + 2/35 y DATA(2, 2) + 1/98 y  DATA(-1, 1)
 
-             2                    2                     2
-     + 1/10 x  DATA(-2, 0) - 2/5 x  DATA(-1, 0) + 1/10 x  DATA(2, 0)
+             2                     2                    2
+     - 1/49 y  DATA(2, -1) + 2/49 y  DATA(2, 2) - 1/49 y  DATA(1, 2)
 
-                                              226              289
-     - 1/5 x DATA(1, 0) + 1/5 x DATA(-1, 0) + --- DATA(1, 2) - ---- DATA(2, 2)
-                                              735              2940
+             2                     2                    2
+     - 1/49 y  DATA(-1, 2) + 1/98 y  DATA(1, 1) - 1/49 y  DATA(2, 1)
 
-       191                71               226               41
-     + ---- DATA(2, 0) + ---- DATA(2, 1) + --- DATA(-1, 2) - -- DATA(0, 2)
-       2940              2940              735               98
+     + 1/35 y DATA(-2, 1) + 1/70 y DATA(-1, -1) - 1/35 y DATA(-2, -1)
 
-        71                289                 71
-     + ---- DATA(2, -1) - ---- DATA(-2, 2) + ---- DATA(-2, 1)
-       2940               2940               2940
+                                                        2
+     - 2/35 y DATA(2, -2) - 2/35 y DATA(-2, -2) - 1/49 y  DATA(1, -2)
 
-             2                    2                     2
-     - 1/49 y  DATA(2, 1) - 1/49 y  DATA(-1, 2) - 1/49 y  DATA(2, -1)
+             2                     2                    2
+     + 2/49 y  DATA(-2, 2) - 1/49 y  DATA(-2, 1) - 2/5 x  DATA(-1, 2)
 
-             2                     2                     2
-     + 2/49 y  DATA(-2, 2) - 1/49 y  DATA(-2, 1) - 1/49 y  DATA(-2, -1)
+             2                      2                     2
+     + 1/98 y  DATA(-1, -1) + 1/98 y  DATA(1, -1) - 1/49 y  DATA(-2, -1)
 
              2                     2                      2
-     + 2/49 y  DATA(2, -2) - 1/49 y  DATA(-1, -2) + 2/49 y  DATA(2, 2)
+     + 2/49 y  DATA(2, -2) + 2/49 y  DATA(-2, -2) - 1/49 y  DATA(-1, -2)
 
-             2                    2                     2
-     + 1/98 y  DATA(1, 1) + 1/98 y  DATA(1, -1) + 1/98 y  DATA(-1, -1)
+             2                      2                    2
+     + 1/10 x  DATA(-2, -2) + 1/10 x  DATA(2, 1) + 1/10 x  DATA(2, -1)
 
-             2
-     + 1/98 y  DATA(-1, 1) + 1/5 x y DATA(-1, 2) + 1/20 x y DATA(-2, -1)
+             2                   2                    2
+     + 1/10 x  DATA(2, 2) - 2/5 x  DATA(1, 2) + 1/10 x  DATA(-2, -1)
 
-     - 1/10 x y DATA(2, -2) + 1/10 x y DATA(2, 2) + 1/20 x y DATA(2, 1)
+             2                    2
+     + 1/10 x  DATA(2, -2) - 2/5 x  DATA(1, 1) - 1/10 x DATA(-2, 2)
 
-     - 1/70 y DATA(1, 1) - 1/20 x y DATA(2, -1) - 1/10 x y DATA(-2, 2)
+                                2                     2
+     + 1/10 x DATA(2, 2) - 2/5 x  DATA(-1, -2) - 2/5 x  DATA(1, -2)
 
-     - 1/20 x y DATA(-2, 1) - 1/35 y DATA(-1, 2) - 1/35 y DATA(2, -1)
+             2                     2
+     + 1/10 x  DATA(-2, 2) + 1/10 x  DATA(-2, 1) + 1/10 x DATA(2, 1)
 
-     + 2/35 y DATA(-2, 2) + 1/35 y DATA(-2, 1) - 1/35 y DATA(-2, -1)
+            2                    2                     2
+     - 2/5 x  DATA(-1, 1) - 2/5 x  DATA(-1, -1) - 2/5 x  DATA(1, -1)
 
-     - 2/35 y DATA(2, -2) + 1/35 y DATA(-1, -2) + 1/35 y DATA(1, -2)
+     - 1/5 x DATA(1, -2) - 1/10 x DATA(-2, 1) - 1/5 x DATA(1, -1)
 
-                                                        2
-     - 2/35 y DATA(-2, -2) + 1/70 y DATA(1, -1) - 1/49 y  DATA(1, -2)
+     - 1/10 x DATA(-2, -1) + 1/10 x DATA(2, -2) - 1/10 x DATA(-2, -2)
 
-             2                      2
-     + 2/49 y  DATA(-2, -2) - 1/49 y  DATA(1, 2) - 1/5 x y DATA(-1, -2)
+     - 1/5 x DATA(1, 2) + 1/5 x DATA(-1, 2) + 1/5 x DATA(-1, 1)
 
-     + 1/5 x y DATA(1, -2) + 1/10 x y DATA(-2, -2) + 1/70 y DATA(-1, -1)
+     + 1/10 x DATA(2, -1) - 1/5 x DATA(1, 1) + 1/5 x DATA(-1, -2)
 
-     - 1/70 y DATA(-1, 1) - 1/35 y DATA(1, 2) + 2/35 y DATA(2, 2)
+                             71               191
+     + 1/5 x DATA(-1, -1) + ---- DATA(2, 1) + ---- DATA(2, 0)
+                            2940              2940
 
-     + 1/35 y DATA(2, 1) + 1/10 x DATA(2, -1) - 1/10 x DATA(-2, 2)
+        71                289               226              41
+     + ---- DATA(2, -1) - ---- DATA(2, 2) + --- DATA(1, 2) - -- DATA(0, 2)
+       2940               2940              735              98
 
-     - 1/10 x DATA(-2, 1) - 1/10 x DATA(-2, -1) + 1/10 x DATA(2, -2)
+       226               166               181               181
+     + --- DATA(-1, 2) + --- DATA(-1, 0) + --- DATA(-1, 1) + --- DATA(-1, -1)
+       735               735               735               735
 
-     + 1/5 x DATA(-1, -2) - 1/5 x DATA(1, -2) - 1/10 x DATA(-2, -2)
+       53               181                    2
+     - -- DATA(0, -1) + --- DATA(1, -1) - 2/5 x  DATA(1, 0)
+       98               735
 
-                            71                 191
-     + 1/10 x DATA(2, 1) + ---- DATA(-2, -1) + ---- DATA(-2, 0)
-                           2940                2940
+             2                    2                    2
+     + 1/10 x  DATA(2, 0) + 1/10 x  DATA(-2, 0) + 3/5 x  DATA(0, 0)
 
-     + 1/5 x DATA(-1, 2) - 1/5 x DATA(1, 1) - 1/5 x DATA(1, -1)
+            2                                        2
+     - 2/5 x  DATA(-1, 0) - 1/5 x DATA(1, 0) + 1/49 y  DATA(-1, 0)
 
-     + 1/5 x DATA(-1, -1) + 1/5 x DATA(-1, 1) - 1/5 x DATA(1, 2)
+     - 1/10 x y DATA(-1, -1) - 1/10 x y DATA(1, 1) + 1/20 x y DATA(2, 1)
 
-                                 2                     2
-     + 1/10 x DATA(2, 2) + 1/10 x  DATA(-2, -2) - 2/5 x  DATA(1, 1)
+     - 1/20 x y DATA(2, -1) + 1/10 x y DATA(2, 2) - 1/5 x y DATA(1, 2)
 
-            2                    2                     2
-     - 2/5 x  DATA(1, -1) - 2/5 x  DATA(-1, -1) - 2/5 x  DATA(-1, 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(1, -1) - 1/10 x y DATA(1, 1)
+     - 1/20 x y DATA(-2, 1) + 1/10 x y DATA(-1, 1) + 1/10 x y DATA(1, -1)
 
-       289                226                41               226
-     - ---- DATA(2, -2) + --- DATA(-1, -2) - -- DATA(0, -2) + --- DATA(1, -2)
-       2940               735                98               735
+     + 1/20 x y DATA(-2, -1) - 1/10 x y DATA(2, -2) + 1/10 x y DATA(-2, -2)
 
-                                                           2
-     - 1/10 x y DATA(-1, -1) + 1/10 x y DATA(-1, 1) - 2/5 x  DATA(1, 2)
+                               71                 289
+     - 1/5 x y DATA(-1, -2) + ---- DATA(-2, -1) - ---- DATA(2, -2)
+                              2940                2940
 
-             2                   2                     2
-     + 1/10 x  DATA(2, 1) - 2/5 x  DATA(-1, 2) + 1/10 x  DATA(2, -1)
+       289                 226                41               226
+     - ---- DATA(-2, -2) + --- DATA(-1, -2) - -- DATA(0, -2) + --- DATA(1, -2)
+       2940                735                98               735
 
-             2                    2                     2
-     + 1/10 x  DATA(2, 2) + 1/10 x  DATA(-2, 2) + 1/10 x  DATA(-2, 1)
+       289                191                 71
+     - ---- DATA(-2, 2) + ---- DATA(-2, 0) + ---- DATA(-2, 1)
+       2940               2940               2940
 
-             2                      2                    2
-     + 1/10 x  DATA(-2, -1) + 1/10 x  DATA(2, -2) - 2/5 x  DATA(-1, -2)
+             2                                        2
+     + 1/49 y  DATA(1, 0) + 1/10 x DATA(2, 0) + 2/49 y  DATA(0, 0)
 
-            2               289                      2
-     - 2/5 x  DATA(1, -2) - ---- DATA(-2, -2) + 3/5 x  DATA(0, 1)
-                            2940
+             2                     2
+     - 2/49 y  DATA(-2, 0) - 2/49 y  DATA(2, 0) - 1/10 x DATA(-2, 0)
+
+     + 1/5 x DATA(-1, 0)
 
 > coeff_as_lc_of_data(%, posn_list_2d_size5);
-bytes used=97118648, alloc=2424388, time=9.26
-                                           2   289          2
-[COEFF(-2, -2) = 1/10 x y - 2/35 y + 2/49 y  - ---- + 1/10 x  - 1/10 x,
-                                               2940
+bytes used=97147664, alloc=2489912, time=9.43
+                       2                  2                       289
+[COEFF(-2, -2) = 2/49 y  - 1/10 x + 1/10 x  - 2/35 y + 1/10 x y - ----,
+                                                                  2940
 
-                                     2            226                 2
-    COEFF(-1, -2) = - 1/5 x y - 2/5 x  + 1/35 y + --- + 1/5 x - 1/49 y ,
-                                                  735
+                            2           226        2
+    COEFF(-1, -2) = - 1/49 y  + 1/5 x + --- - 2/5 x  - 1/5 x y + 1/35 y,
+                                        735
 
-                                  2        2   41
-    COEFF(0, -2) = 2/35 y - 2/49 y  + 3/5 x  - --,
+                                 2         2   41
+    COEFF(0, -2) = 2/35 y + 3/5 x  - 2/49 y  - --,
                                                98
 
-                   226        2                                    2
-    COEFF(1, -2) = --- - 2/5 x  + 1/35 y + 1/5 x y - 1/5 x - 1/49 y ,
+                   226                 2                           2
+    COEFF(1, -2) = --- - 1/5 x - 1/49 y  + 1/35 y + 1/5 x y - 2/5 x ,
                    735
 
-                         2   289                   2
-    COEFF(2, -2) = 2/49 y  - ---- - 2/35 y + 1/10 x  + 1/10 x - 1/10 x y,
-                             2940
+                            289          2                  2
+    COEFF(2, -2) = 1/10 x - ---- + 1/10 x  - 2/35 y + 2/49 y  - 1/10 x y,
+                            2940
 
-                                71          2         2
-    COEFF(-2, -1) = - 1/10 x + ---- - 1/49 y  + 1/10 x  - 1/35 y + 1/20 x y,
-                               2940
+                            2    71                              2
+    COEFF(-2, -1) = - 1/49 y  + ---- + 1/20 x y - 1/10 x + 1/10 x  - 1/35 y,
+                                2940
 
-                           2         2           181
-    COEFF(-1, -1) = - 2/5 x  + 1/98 y  + 1/5 x + --- - 1/10 x y + 1/70 y,
-                                                 735
+                             181                            2        2
+    COEFF(-1, -1) = 1/70 y + --- + 1/5 x - 1/10 x y + 1/98 y  - 2/5 x ,
+                             735
 
-                     53                  2        2
-    COEFF(0, -1) = - -- + 1/35 y + 1/49 y  + 3/5 x ,
+                     53                 2         2
+    COEFF(0, -1) = - -- + 1/35 y + 3/5 x  + 1/49 y ,
                      98
 
-                                  2        2                      181
-    COEFF(1, -1) = 1/70 y + 1/98 y  - 2/5 x  - 1/5 x + 1/10 x y + ---,
-                                                                  735
+                                   2              181                 2
+    COEFF(1, -1) = - 1/5 x + 1/98 y  + 1/10 x y + --- + 1/70 y - 2/5 x ,
+                                                  735
 
-                         2                  2             71
-    COEFF(2, -1) = 1/10 x  - 1/35 y - 1/49 y  + 1/10 x + ---- - 1/20 x y,
-                                                         2940
+                         2                      71          2
+    COEFF(2, -1) = 1/10 x  - 1/35 y + 1/10 x + ---- - 1/49 y  - 1/20 x y,
+                                               2940
 
-                                    2         2   191
-    COEFF(-2, 0) = - 1/10 x + 1/10 x  - 2/49 y  + ----,
-                                                  2940
+                         2            191          2
+    COEFF(-2, 0) = 1/10 x  - 1/10 x + ---- - 2/49 y ,
+                                      2940
 
-                          2         2   166
-    COEFF(-1, 0) = - 2/5 x  + 1/49 y  + --- + 1/5 x,
-                                        735
+                         2   166        2
+    COEFF(-1, 0) = 1/49 y  + --- - 2/5 x  + 1/5 x,
+                             735
 
-                        2   57        2
-    COEFF(0, 0) = 2/49 y  - -- + 3/5 x ,
-                            98
+                    57         2        2
+    COEFF(0, 0) = - -- + 2/49 y  + 3/5 x ,
+                    98
 
-                                  2        2   166
-    COEFF(1, 0) = - 1/5 x + 1/49 y  - 2/5 x  + ---,
-                                               735
+                                  2   166        2
+    COEFF(1, 0) = - 1/5 x + 1/49 y  + --- - 2/5 x ,
+                                      735
 
-                                 2   191          2
-    COEFF(2, 0) = 1/10 x - 2/49 y  + ---- + 1/10 x ,
-                                     2940
+                  191          2                  2
+    COEFF(2, 0) = ---- - 2/49 y  + 1/10 x + 1/10 x ,
+                  2940
 
-                    71          2         2
-    COEFF(-2, 1) = ---- - 1/49 y  + 1/10 x  + 1/35 y - 1/20 x y - 1/10 x,
+                    71          2                             2
+    COEFF(-2, 1) = ---- - 1/49 y  - 1/20 x y + 1/35 y + 1/10 x  - 1/10 x,
                    2940
 
-                           181                   2         2
-    COEFF(-1, 1) = 1/5 x + --- + 1/10 x y - 2/5 x  + 1/98 y  - 1/70 y,
-                           735
+                   181                 2         2
+    COEFF(-1, 1) = --- - 1/70 y - 2/5 x  + 1/98 y  + 1/5 x + 1/10 x y,
+                   735
 
-                    53        2         2
-    COEFF(0, 1) = - -- + 3/5 x  + 1/49 y  - 1/35 y,
-                    98
+                       2                  2   53
+    COEFF(0, 1) = 3/5 x  - 1/35 y + 1/49 y  - --,
+                                              98
 
-                  181         2        2
-    COEFF(1, 1) = --- + 1/98 y  - 2/5 x  - 1/70 y - 1/5 x - 1/10 x y,
-                  735
+                             181                   2                 2
+    COEFF(1, 1) = - 1/70 y + --- - 1/10 x y - 2/5 x  - 1/5 x + 1/98 y ,
+                             735
 
-                        2                      71                     2
-    COEFF(2, 1) = 1/10 x  + 1/35 y + 1/10 x + ---- + 1/20 x y - 1/49 y ,
-                                              2940
+                                 2    71                   2
+    COEFF(2, 1) = 1/10 x - 1/49 y  + ---- + 1/35 y + 1/10 x  + 1/20 x y,
+                                     2940
 
-                         2            289                              2
-    COEFF(-2, 2) = 2/49 y  + 2/35 y - ---- - 1/10 x y - 1/10 x + 1/10 x ,
+                                  2   289                     2
+    COEFF(-2, 2) = 2/35 y + 2/49 y  - ---- - 1/10 x y + 1/10 x  - 1/10 x,
                                       2940
 
-                   226        2                           2
-    COEFF(-1, 2) = --- - 2/5 x  + 1/5 x + 1/5 x y - 1/49 y  - 1/35 y,
-                   735
+                                    2        2           226
+    COEFF(-1, 2) = - 1/35 y - 1/49 y  - 2/5 x  + 1/5 x + --- + 1/5 x y,
+                                                         735
 
-                    41                  2        2
-    COEFF(0, 2) = - -- - 2/35 y - 2/49 y  + 3/5 x ,
-                    98
+                       2         2            41
+    COEFF(0, 2) = 3/5 x  - 2/49 y  - 2/35 y - --,
+                                              98
 
-                                 2             226         2
-    COEFF(1, 2) = - 1/5 x - 2/5 x  - 1/5 x y + --- - 1/49 y  - 1/35 y,
-                                               735
+                          2        2                              226
+    COEFF(1, 2) = - 1/49 y  - 2/5 x  - 1/5 x - 1/5 x y - 1/35 y + ---,
+                                                                  735
 
-                                 2   289          2
-    COEFF(2, 2) = 1/10 x + 2/49 y  - ---- + 1/10 x  + 2/35 y + 1/10 x y]
-                                     2940
+                                          2                    2   289
+    COEFF(2, 2) = 2/35 y + 1/10 x + 2/49 y  + 1/10 x y + 1/10 x  - ----]
+                                                                   2940
 
 > print_coeff__lc_of_data(%, "coeff_dxx_", "fp",
 > 			"2d.coeffs/2d.cube.order4.smooth0/coeff-dxx.compute.c");
-bytes used=98118800, alloc=2424388, time=9.34
-bytes used=99118996, alloc=2424388, time=9.43
-bytes used=100119256, alloc=2424388, time=9.58
-bytes used=101122084, alloc=2424388, time=9.74
-bytes used=102122280, alloc=2424388, time=9.85
-bytes used=103122400, alloc=2424388, time=9.97
+bytes used=98147868, alloc=2489912, time=9.52
+bytes used=99148020, alloc=2489912, time=9.68
+bytes used=100148588, alloc=2489912, time=9.76
+bytes used=101148864, alloc=2489912, time=9.92
+bytes used=102149152, alloc=2489912, time=10.09
+bytes used=103149320, alloc=2489912, time=10.25
 > 
 # d^2/dxdy
 > simplify( diff(interp_2d_cube_order4_smooth0,x,y) );
-bytes used=104122552, alloc=2424388, time=10.13
-bytes used=105123136, alloc=2424388, time=10.20
+bytes used=104150048, alloc=2489912, time=10.38
 37
---- DATA(1, 1) - 4/49 x y DATA(-2, 0) - 4/49 x y DATA(0, -2)
+--- DATA(1, 1) + 1/35 y DATA(1, 2) - 1/35 y DATA(-1, 2) + 1/70 y DATA(-1, 1)
 300
 
-     + 4/49 x y DATA(0, 0) + 2/49 x y DATA(0, -1) - 4/49 x y DATA(0, 2)
+     - 1/35 y DATA(-1, -2) + 1/35 y DATA(1, -2) - 2/35 y DATA(-2, 2)
 
-     + 2/49 x y DATA(0, 1) + 2/49 x y DATA(1, 0) - 4/49 x y DATA(2, 0)
+     - 1/70 y DATA(1, -1) - 1/70 y DATA(1, 1) - 1/35 y DATA(2, 1)
 
-     + 2/49 x y DATA(-1, 0) + 1/35 y DATA(-1, 0) + 2/35 y DATA(-2, 0)
+                                                      2
+     - 1/35 y DATA(2, -1) + 2/35 y DATA(2, 2) + 1/20 y  DATA(-1, 1)
 
-       37                37                 37
-     - --- DATA(1, -1) + --- DATA(-1, -1) - --- DATA(-1, 1) - 2/35 y DATA(2, 0)
-       300               300                300
+             2                     2                    2
+     + 1/10 y  DATA(2, -1) + 1/20 y  DATA(2, 2) + 1/40 y  DATA(1, 2)
 
-                                               21               11
-     - 1/35 y DATA(1, 0) - 1/35 x DATA(0, 1) + --- DATA(1, 2) - --- DATA(2, 2)
-                                               200              150
+             2                     2                    2
+     - 1/40 y  DATA(-1, 2) - 1/20 y  DATA(1, 1) - 1/10 y  DATA(2, 1)
 
-       21               21                21                11
-     + --- DATA(2, 1) - --- DATA(-1, 2) - --- DATA(2, -1) + --- DATA(-2, 2)
-       200              200               200               150
+     + 1/35 y DATA(-2, 1) + 1/70 y DATA(-1, -1) + 1/35 y DATA(-2, -1)
 
-       21                      2                    2
-     - --- DATA(-2, 1) - 1/10 y  DATA(2, 1) - 1/40 y  DATA(-1, 2)
-       200
+                                                        2
+     + 2/35 y DATA(2, -2) - 2/35 y DATA(-2, -2) - 1/40 y  DATA(1, -2)
 
              2                     2                     2
-     + 1/10 y  DATA(2, -1) - 1/20 y  DATA(-2, 2) + 1/10 y  DATA(-2, 1)
+     - 1/20 y  DATA(-2, 2) + 1/10 y  DATA(-2, 1) + 1/10 x  DATA(-1, 2)
 
              2                      2                     2
-     - 1/10 y  DATA(-2, -1) - 1/20 y  DATA(2, -2) + 1/40 y  DATA(-1, -2)
+     - 1/20 y  DATA(-1, -1) + 1/20 y  DATA(1, -1) - 1/10 y  DATA(-2, -1)
 
-             2                    2                    2
-     + 1/20 y  DATA(2, 2) - 1/20 y  DATA(1, 1) + 1/20 y  DATA(1, -1)
+             2                     2                      2
+     - 1/20 y  DATA(2, -2) + 1/20 y  DATA(-2, -2) + 1/40 y  DATA(-1, -2)
 
-             2                      2
-     - 1/20 y  DATA(-1, -1) + 1/20 y  DATA(-1, 1) - 2/49 x y DATA(-1, 2)
+             2                      2                    2
+     + 1/20 x  DATA(-2, -2) + 1/40 x  DATA(2, 1) - 1/40 x  DATA(2, -1)
 
-     - 2/49 x y DATA(-2, -1) + 4/49 x y DATA(2, -2) + 4/49 x y DATA(2, 2)
+             2                    2                    2
+     + 1/20 x  DATA(2, 2) - 1/10 x  DATA(1, 2) + 1/40 x  DATA(-2, -1)
 
-     - 2/49 x y DATA(2, 1) - 1/70 y DATA(1, 1) - 2/49 x y DATA(2, -1)
+             2                     2
+     - 1/20 x  DATA(2, -2) - 1/20 x  DATA(1, 1) + 2/35 x DATA(-2, 2)
 
-     + 4/49 x y DATA(-2, 2) - 2/49 x y DATA(-2, 1) - 1/35 y DATA(-1, 2)
+                                 2                      2
+     + 2/35 x DATA(2, 2) - 1/10 x  DATA(-1, -2) + 1/10 x  DATA(1, -2)
 
-     - 1/35 y DATA(2, -1) - 2/35 y DATA(-2, 2) + 1/35 y DATA(-2, 1)
+             2                     2
+     - 1/20 x  DATA(-2, 2) - 1/40 x  DATA(-2, 1) + 1/35 x DATA(2, 1)
 
-     + 1/35 y DATA(-2, -1) + 2/35 y DATA(2, -2) - 1/35 y DATA(-1, -2)
+             2                     2                      2
+     + 1/20 x  DATA(-1, 1) - 1/20 x  DATA(-1, -1) + 1/20 x  DATA(1, -1)
 
-     + 1/35 y DATA(1, -2) - 2/35 y DATA(-2, -2) - 1/70 y DATA(1, -1)
+     + 1/35 x DATA(1, -2) + 1/35 x DATA(-2, 1) + 1/70 x DATA(1, -1)
 
-             2                     2                      2
-     - 1/40 y  DATA(1, -2) + 1/20 y  DATA(-2, -2) + 1/40 y  DATA(1, 2)
+     - 1/35 x DATA(-2, -1) - 2/35 x DATA(2, -2) - 2/35 x DATA(-2, -2)
 
-     - 2/49 x y DATA(-1, -2) - 2/49 x y DATA(1, -2) + 4/49 x y DATA(-2, -2)
+     - 1/35 x DATA(1, 2) - 1/35 x DATA(-1, 2) - 1/70 x DATA(-1, 1)
 
-     + 1/70 y DATA(-1, -1) + 1/70 y DATA(-1, 1) + 1/35 y DATA(1, 2)
+     - 1/35 x DATA(2, -1) - 1/70 x DATA(1, 1) + 1/35 x DATA(-1, -2)
 
-     + 2/35 y DATA(2, 2) - 1/35 y DATA(2, 1) - 1/35 x DATA(2, -1)
+                             21               21                11
+     + 1/70 x DATA(-1, -1) + --- DATA(2, 1) - --- DATA(2, -1) - --- DATA(2, 2)
+                             200              200               150
 
-     + 2/35 x DATA(-2, 2) + 1/35 x DATA(-2, 1) - 1/35 x DATA(-2, -1)
+       21               21                37                37
+     + --- DATA(1, 2) - --- DATA(-1, 2) - --- DATA(-1, 1) + --- DATA(-1, -1)
+       200              200               300               300
 
-     - 2/35 x DATA(2, -2) + 1/35 x DATA(-1, -2) + 1/35 x DATA(1, -2)
+       37
+     - --- DATA(1, -1) - 4/49 x y DATA(0, 2) + 1/49 x y DATA(-1, -1)
+       300
 
-                                                 21
-     - 2/35 x DATA(-2, -2) + 1/35 x DATA(2, 1) + --- DATA(-2, -1)
-                                                 200
+     + 1/49 x y DATA(1, 1) - 2/49 x y DATA(2, 1) - 2/49 x y DATA(2, -1)
 
-     - 1/35 x DATA(-1, 2) - 1/70 x DATA(1, 1) + 1/70 x DATA(1, -1)
+     + 4/49 x y DATA(2, 2) - 2/49 x y DATA(1, 2) - 2/49 x y DATA(-1, 2)
 
-     + 1/70 x DATA(-1, -1) - 1/70 x DATA(-1, 1) - 1/35 x DATA(1, 2)
+     - 1/35 x DATA(0, 1) - 2/35 x DATA(0, 2) + 1/35 x DATA(0, -1)
 
-                                 2                      2
-     + 2/35 x DATA(2, 2) + 1/20 x  DATA(-2, -2) - 1/20 x  DATA(1, 1)
+     + 2/35 x DATA(0, -2) + 4/49 x y DATA(0, 0) + 2/49 x y DATA(1, 0)
 
-             2                     2                      2
-     + 1/20 x  DATA(1, -1) - 1/20 x  DATA(-1, -1) + 1/20 x  DATA(-1, 1)
+     - 4/49 x y DATA(2, 0) + 2/49 x y DATA(-1, 0) - 1/35 y DATA(1, 0)
 
-     - 2/49 x y DATA(1, 2) + 1/49 x y DATA(1, -1) + 1/49 x y DATA(1, 1)
+     + 2/49 x y DATA(0, 1) + 2/49 x y DATA(0, -1) - 4/49 x y DATA(0, -2)
 
-       11                21                 21
-     + --- DATA(2, -2) + --- DATA(-1, -2) - --- DATA(1, -2)
-       150               200                200
+     - 2/35 y DATA(2, 0) + 1/35 y DATA(-1, 0) - 4/49 x y DATA(-2, 0)
 
-                                                            2
-     + 1/49 x y DATA(-1, -1) + 1/49 x y DATA(-1, 1) - 1/10 x  DATA(1, 2)
+     + 2/35 y DATA(-2, 0) - 2/49 x y DATA(1, -2) + 4/49 x y DATA(-2, 2)
 
-             2                    2                     2
-     + 1/40 x  DATA(2, 1) + 1/10 x  DATA(-1, 2) - 1/40 x  DATA(2, -1)
+     - 2/49 x y DATA(-2, 1) + 1/49 x y DATA(-1, 1) + 1/49 x y DATA(1, -1)
 
-             2                    2                     2
-     + 1/20 x  DATA(2, 2) - 1/20 x  DATA(-2, 2) - 1/40 x  DATA(-2, 1)
+     - 2/49 x y DATA(-2, -1) + 4/49 x y DATA(2, -2) + 4/49 x y DATA(-2, -2)
 
-             2                      2                     2
-     + 1/40 x  DATA(-2, -1) - 1/20 x  DATA(2, -2) - 1/10 x  DATA(-1, -2)
+                               21                 11
+     - 2/49 x y DATA(-1, -2) + --- DATA(-2, -1) + --- DATA(2, -2)
+                               200                150
 
-             2               11
-     + 1/10 x  DATA(1, -2) - --- DATA(-2, -2) - 2/35 x DATA(0, 2)
-                             150
+       11                 21                 21                11
+     - --- DATA(-2, -2) + --- DATA(-1, -2) - --- DATA(1, -2) + --- DATA(-2, 2)
+       150                200                200               150
 
-     + 1/35 x DATA(0, -1) + 2/35 x DATA(0, -2)
+       21
+     - --- DATA(-2, 1)
+       200
 
 > coeff_as_lc_of_data(%, posn_list_2d_size5);
-                                  2         2                     11
-[COEFF(-2, -2) = 4/49 x y + 1/20 x  + 1/20 y  - 2/35 y - 2/35 x - ---,
-                                                                  150
+bytes used=105150268, alloc=2489912, time=10.45
+                                  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) = - 2/49 x y - 1/35 y + 1/35 x + 1/40 y  - 1/10 x  + ---,
-                                                                       200
+                          2         2            21
+    COEFF(-1, -2) = 1/40 y  - 1/10 x  + 1/35 x + --- - 2/49 x y - 1/35 y,
+                                                 200
 
     COEFF(0, -2) = 2/35 x - 4/49 x y,
 
-                                               2            21          2
-    COEFF(1, -2) = - 2/49 x y + 1/35 x + 1/10 x  + 1/35 y - --- - 1/40 y ,
-                                                            200
+                                21                   2         2
+    COEFF(1, -2) = - 2/49 x y - --- + 1/35 y - 1/40 y  + 1/10 x  + 1/35 x,
+                                200
 
-                   11          2         2
-    COEFF(2, -2) = --- - 1/20 y  - 1/20 x  - 2/35 x + 4/49 x y + 2/35 y,
-                   150
+                           2                     11          2
+    COEFF(2, -2) = - 1/20 x  + 2/35 y - 2/35 x + --- - 1/20 y  + 4/49 x y,
+                                                 150
 
-                    21                   2                             2
-    COEFF(-2, -1) = --- + 1/35 y - 1/10 y  - 2/49 x y - 1/35 x + 1/40 x ,
-                    200
+                            2                  2            21
+    COEFF(-2, -1) = - 1/10 y  + 1/35 y + 1/40 x  - 1/35 x + --- - 2/49 x y,
+                                                            200
 
-                                     2         2                     37
-    COEFF(-1, -1) = 1/49 x y - 1/20 y  - 1/20 x  + 1/70 x + 1/70 y + ---,
-                                                                     300
+                            2                                      2   37
+    COEFF(-1, -1) = - 1/20 x  + 1/70 y + 1/70 x + 1/49 x y - 1/20 y  + ---,
+                                                                       300
 
     COEFF(0, -1) = 1/35 x + 2/49 x y,
 
-                     37                     2                           2
-    COEFF(1, -1) = - --- + 1/49 x y + 1/20 x  - 1/70 y + 1/70 x + 1/20 y ,
-                     300
+                         2                     37          2
+    COEFF(1, -1) = 1/20 y  - 1/70 y + 1/70 x - --- + 1/20 x  + 1/49 x y,
+                                               300
 
-                                    2                             2   21
-    COEFF(2, -1) = - 1/35 x + 1/10 y  - 2/49 x y - 1/35 y - 1/40 x  - ---,
-                                                                      200
+                                    2            21                     2
+    COEFF(2, -1) = - 1/35 y - 1/40 x  - 1/35 x - --- - 2/49 x y + 1/10 y ,
+                                                 200
 
-    COEFF(-2, 0) = 2/35 y - 4/49 x y, COEFF(-1, 0) = 1/35 y + 2/49 x y,
+    COEFF(-2, 0) = - 4/49 x y + 2/35 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(0, 0) = 4/49 x y, COEFF(1, 0) = 2/49 x y - 1/35 y,
 
     COEFF(2, 0) = - 4/49 x y - 2/35 y,
 
-                                                      2         2   21
-    COEFF(-2, 1) = 1/35 y + 1/35 x - 2/49 x y + 1/10 y  - 1/40 x  - ---,
-                                                                    200
+                     21          2                                      2
+    COEFF(-2, 1) = - --- - 1/40 x  + 1/35 x + 1/35 y - 2/49 x y + 1/10 y ,
+                     200
 
                          2   37                   2
-    COEFF(-1, 1) = 1/20 y  - --- - 1/70 x + 1/20 x  + 1/70 y + 1/49 x y,
+    COEFF(-1, 1) = 1/20 y  - --- + 1/70 y + 1/20 x  - 1/70 x + 1/49 x y,
                              300
 
-    COEFF(0, 1) = - 1/35 x + 2/49 x y,
+    COEFF(0, 1) = 2/49 x y - 1/35 x,
 
-                             37          2                  2
-    COEFF(1, 1) = 1/49 x y + --- - 1/20 y  - 1/70 x - 1/20 x  - 1/70 y,
-                             300
+                  37          2         2
+    COEFF(1, 1) = --- - 1/20 y  - 1/20 x  + 1/49 x y - 1/70 y - 1/70 x,
+                  300
 
-                  21          2         2
-    COEFF(2, 1) = --- + 1/40 x  - 1/10 y  + 1/35 x - 1/35 y - 2/49 x y,
-                  200
+                        2            21                              2
+    COEFF(2, 1) = 1/40 x  + 1/35 x + --- - 1/35 y - 2/49 x y - 1/10 y ,
+                                     200
 
-                           2                             2            11
-    COEFF(-2, 2) = - 1/20 x  + 4/49 x y + 2/35 x - 1/20 y  - 2/35 y + ---,
-                                                                      150
+                           2                  2   11
+    COEFF(-2, 2) = - 1/20 x  + 2/35 x - 1/20 y  + --- - 2/35 y + 4/49 x y,
+                                                  150
 
-                         2                           2   21
-    COEFF(-1, 2) = 1/10 x  - 1/35 y - 1/35 x - 1/40 y  - --- - 2/49 x y,
-                                                         200
+                                    2         2   21
+    COEFF(-1, 2) = - 1/35 y + 1/10 x  - 1/40 y  - --- - 2/49 x y - 1/35 x,
+                                                  200
 
     COEFF(0, 2) = - 2/35 x - 4/49 x y,
 
-                                   2                             2   21
-    COEFF(1, 2) = - 1/35 x + 1/40 y  - 2/49 x y + 1/35 y - 1/10 x  + ---,
-                                                                     200
+                                        21          2         2
+    COEFF(1, 2) = - 1/35 x - 2/49 x y + --- - 1/10 x  + 1/40 y  + 1/35 y,
+                                        200
 
-                                            2   11                   2
-    COEFF(2, 2) = 2/35 y + 4/49 x y + 1/20 x  - --- + 2/35 x + 1/20 y ]
-                                                150
+                                    11                     2         2
+    COEFF(2, 2) = 2/35 y + 2/35 x - --- + 4/49 x y + 1/20 y  + 1/20 x ]
+                                    150
 
 > print_coeff__lc_of_data(%, "coeff_dxy_", "fp",
 > 			"2d.coeffs/2d.cube.order4.smooth0/coeff-dxy.compute.c");
-bytes used=106123844, alloc=2424388, time=10.27
-bytes used=107128472, alloc=2424388, time=10.35
-bytes used=108128708, alloc=2424388, time=10.53
-bytes used=109128920, alloc=2424388, time=10.69
-bytes used=110129208, alloc=2424388, time=10.83
-bytes used=111129472, alloc=2424388, time=11.03
-bytes used=112129776, alloc=2424388, time=11.21
+bytes used=106150484, alloc=2489912, time=10.53
+bytes used=107150764, alloc=2489912, time=10.68
+bytes used=108151004, alloc=2489912, time=10.81
+bytes used=109151492, alloc=2489912, time=10.97
+bytes used=110151712, alloc=2489912, time=11.14
+bytes used=111151948, alloc=2489912, time=11.29
+bytes used=112152148, alloc=2489912, time=11.48
 > 
 # d^2/dy^2
 > simplify( diff(interp_2d_cube_order4_smooth0,y,y) );
-bytes used=113130192, alloc=2424388, time=11.31
-bytes used=114130376, alloc=2424388, time=11.38
+bytes used=113152336, alloc=2489912, time=11.54
   57              53              166              181
 - -- DATA(0, 0) - -- DATA(1, 0) + --- DATA(0, 1) + --- DATA(1, 1)
   98              98              735              735
 
-       53               181               166               181
-     - -- DATA(-1, 0) + --- DATA(1, -1) + --- DATA(0, -1) + --- DATA(-1, -1)
-       98               735               735               735
-
-       181                71               289               41
-     + --- DATA(-1, 1) + ---- DATA(1, 2) - ---- DATA(2, 2) - -- DATA(2, 0)
-       735               2940              2940              98
+     + 1/10 y DATA(1, 2) + 1/10 y DATA(-1, 2) - 1/5 y DATA(-1, 1)
 
-       226               71                191               226
-     + --- DATA(2, 1) + ---- DATA(-1, 2) + ---- DATA(0, 2) + --- DATA(2, -1)
-       735              2940               2940              735
+     - 1/10 y DATA(-1, -2) - 1/10 y DATA(1, -2) + 1/10 y DATA(-2, 2)
 
-       289                226                    2
-     - ---- DATA(-2, 2) + --- DATA(-2, 1) - 2/5 y  DATA(2, 1)
-       2940               735
+     + 1/5 y DATA(1, -1) - 1/5 y DATA(1, 1) - 1/5 y DATA(2, 1)
 
-             2                    2                     2
-     + 1/10 y  DATA(-1, 2) - 2/5 y  DATA(2, -1) + 1/10 y  DATA(-2, 2)
+                                                    2
+     + 1/5 y DATA(2, -1) + 1/10 y DATA(2, 2) - 2/5 y  DATA(-1, 1)
 
-            2                    2                      2
-     - 2/5 y  DATA(-2, 1) - 2/5 y  DATA(-2, -1) + 1/10 y  DATA(2, -2)
+            2                     2                    2
+     - 2/5 y  DATA(2, -1) + 1/10 y  DATA(2, 2) + 1/10 y  DATA(1, 2)
 
-             2                      2                   2
-     + 1/10 y  DATA(-1, -2) + 1/10 y  DATA(2, 2) - 2/5 y  DATA(1, 1)
+             2                    2                   2
+     + 1/10 y  DATA(-1, 2) - 2/5 y  DATA(1, 1) - 2/5 y  DATA(2, 1)
 
-            2                    2                     2
-     - 2/5 y  DATA(1, -1) - 2/5 y  DATA(-1, -1) - 2/5 y  DATA(-1, 1)
+     - 1/5 y DATA(-2, 1) + 1/5 y DATA(-1, -1) + 1/5 y DATA(-2, -1)
 
-     - 1/20 x y DATA(-1, 2) - 1/5 x y DATA(-2, -1) - 1/10 x y DATA(2, -2)
+                                                        2
+     - 1/10 y DATA(2, -2) - 1/10 y DATA(-2, -2) + 1/10 y  DATA(1, -2)
 
-     + 1/10 x y DATA(2, 2) - 1/5 x y DATA(2, 1) - 1/5 y DATA(1, 1)
+             2                    2                     2
+     + 1/10 y  DATA(-2, 2) - 2/5 y  DATA(-2, 1) - 1/49 x  DATA(-1, 2)
 
-     + 1/5 x y DATA(2, -1) - 1/10 x y DATA(-2, 2) + 1/5 x y DATA(-2, 1)
+            2                     2                    2
+     - 2/5 y  DATA(-1, -1) - 2/5 y  DATA(1, -1) - 2/5 y  DATA(-2, -1)
 
-     + 1/10 y DATA(-1, 2) + 1/5 y DATA(2, -1) + 1/10 y DATA(-2, 2)
+             2                     2                      2
+     + 1/10 y  DATA(2, -2) + 1/10 y  DATA(-2, -2) + 1/10 y  DATA(-1, -2)
 
-     - 1/5 y DATA(-2, 1) + 1/5 y DATA(-2, -1) - 1/10 y DATA(2, -2)
+             2                      2                    2
+     + 2/49 x  DATA(-2, -2) - 1/49 x  DATA(2, 1) - 1/49 x  DATA(2, -1)
 
-     - 1/10 y DATA(-1, -2) - 1/10 y DATA(1, -2) - 1/10 y DATA(-2, -2)
+             2                    2                    2
+     + 2/49 x  DATA(2, 2) - 1/49 x  DATA(1, 2) - 1/49 x  DATA(-2, -1)
 
-                                 2                     2
-     + 1/5 y DATA(1, -1) + 1/10 y  DATA(1, -2) + 1/10 y  DATA(-2, -2)
+             2                     2
+     + 2/49 x  DATA(2, -2) + 1/98 x  DATA(1, 1) - 2/35 x DATA(-2, 2)
 
-             2
-     + 1/10 y  DATA(1, 2) + 1/20 x y DATA(-1, -2) - 1/20 x y DATA(1, -2)
+                                 2                      2
+     + 2/35 x DATA(2, 2) - 1/49 x  DATA(-1, -2) - 1/49 x  DATA(1, -2)
 
-     + 1/10 x y DATA(-2, -2) + 1/5 y DATA(-1, -1) - 1/5 y DATA(-1, 1)
+             2                     2
+     + 2/49 x  DATA(-2, 2) - 1/49 x  DATA(-2, 1) - 1/35 x DATA(2, 1)
 
-     + 1/10 y DATA(1, 2) + 1/10 y DATA(2, 2) - 1/5 y DATA(2, 1)
+             2                     2                      2
+     + 1/98 x  DATA(-1, 1) + 1/98 x  DATA(-1, -1) + 1/98 x  DATA(1, -1)
 
-     - 1/35 x DATA(2, -1) - 2/35 x DATA(-2, 2) + 1/35 x DATA(-2, 1)
+     + 1/35 x DATA(1, -2) + 1/35 x DATA(-2, 1) - 1/70 x DATA(1, -1)
 
-     + 1/35 x DATA(-2, -1) + 2/35 x DATA(2, -2) - 1/35 x DATA(-1, -2)
+     + 1/35 x DATA(-2, -1) + 2/35 x DATA(2, -2) - 2/35 x DATA(-2, -2)
 
-     + 1/35 x DATA(1, -2) - 2/35 x DATA(-2, -2) - 1/35 x DATA(2, 1)
+     + 1/35 x DATA(1, 2) - 1/35 x DATA(-1, 2) + 1/70 x DATA(-1, 1)
 
-       226                41
-     + --- DATA(-2, -1) - -- DATA(-2, 0) - 1/35 x DATA(-1, 2)
-       735                98
+     - 1/35 x DATA(2, -1) - 1/70 x DATA(1, 1) - 1/35 x DATA(-1, -2)
 
-     - 1/70 x DATA(1, 1) - 1/70 x DATA(1, -1) + 1/70 x DATA(-1, -1)
+                             226              41              226
+     + 1/70 x DATA(-1, -1) + --- DATA(2, 1) - -- DATA(2, 0) + --- DATA(2, -1)
+                             735              98              735
 
-     + 1/70 x DATA(-1, 1) + 1/35 x DATA(1, 2) + 2/35 x DATA(2, 2)
+                                                289
+     + 1/5 y DATA(0, -1) - 1/10 y DATA(0, -2) - ---- DATA(2, 2)
+                                                2940
 
-             2                      2                    2
-     + 2/49 x  DATA(-2, -2) + 1/98 x  DATA(1, 1) + 1/98 x  DATA(1, -1)
+        71               191                71                53
+     + ---- DATA(1, 2) + ---- DATA(0, 2) + ---- DATA(-1, 2) - -- DATA(-1, 0)
+       2940              2940              2940               98
 
-             2                      2
-     + 1/98 x  DATA(-1, -1) + 1/98 x  DATA(-1, 1) + 1/20 x y DATA(1, 2)
+       181               181                166               181
+     + --- DATA(-1, 1) + --- DATA(-1, -1) + --- DATA(0, -1) + --- DATA(1, -1)
+       735               735                735               735
 
-                                                    289
-     + 1/10 x y DATA(1, -1) - 1/10 x y DATA(1, 1) - ---- DATA(2, -2)
-                                                    2940
+             2                    2                    2
+     - 2/49 x  DATA(2, 0) + 1/49 x  DATA(1, 0) + 1/49 x  DATA(0, -1)
 
-        71                 191                 71
-     + ---- DATA(-1, -2) + ---- DATA(0, -2) + ---- DATA(1, -2)
-       2940                2940               2940
+             2                     2                     2
+     - 2/49 x  DATA(-2, 0) - 2/49 x  DATA(0, -2) + 1/49 x  DATA(-1, 0)
 
-                                                            2
-     - 1/10 x y DATA(-1, -1) + 1/10 x y DATA(-1, 1) - 1/49 x  DATA(1, 2)
+             2                    2                    2
+     - 2/49 x  DATA(0, 2) + 1/49 x  DATA(0, 1) + 2/49 x  DATA(0, 0)
 
-             2                    2                     2
-     - 1/49 x  DATA(2, 1) - 1/49 x  DATA(-1, 2) - 1/49 x  DATA(2, -1)
+     - 1/10 x y DATA(-1, -1) - 1/10 x y DATA(1, 1) - 1/5 x y DATA(2, 1)
 
-             2                    2                     2
-     + 2/49 x  DATA(2, 2) + 2/49 x  DATA(-2, 2) - 1/49 x  DATA(-2, 1)
+     + 1/5 x y DATA(2, -1) + 1/10 x y DATA(2, 2) + 1/20 x y DATA(1, 2)
 
-             2                      2                     2
-     - 1/49 x  DATA(-2, -1) + 2/49 x  DATA(2, -2) - 1/49 x  DATA(-1, -2)
+     - 1/20 x y DATA(-1, 2) - 1/20 x y DATA(1, -2) - 1/10 x y DATA(-2, 2)
 
-             2               289
-     - 1/49 x  DATA(1, -2) - ---- DATA(-2, -2) - 1/35 x DATA(1, 0)
-                             2940
+     + 1/5 x y DATA(-2, 1) + 1/10 x y DATA(-1, 1) + 1/35 x DATA(-1, 0)
 
-     + 1/35 x DATA(-1, 0) + 1/5 y DATA(0, -1) - 2/35 x DATA(2, 0)
+     + 1/10 x y DATA(1, -1) - 1/5 x y DATA(-2, -1) - 1/10 x y DATA(2, -2)
 
-                                                     2
-     + 1/10 y DATA(0, 2) - 1/10 y DATA(0, -2) + 3/5 y  DATA(-2, 0)
+     + 1/10 x y DATA(-2, -2) + 1/20 x y DATA(-1, -2) - 1/35 x DATA(1, 0)
 
-            2                    2
-     + 3/5 y  DATA(-1, 0) + 3/5 y  DATA(1, 0) + 2/35 x DATA(-2, 0)
+                                                226
+     - 2/35 x DATA(2, 0) + 2/35 x DATA(-2, 0) + --- DATA(-2, -1)
+                                                735
 
-            2                   2                   2
-     + 3/5 y  DATA(0, 0) - 2/5 y  DATA(0, 1) - 2/5 y  DATA(0, -1)
+       289                289                  71
+     - ---- DATA(2, -2) - ---- DATA(-2, -2) + ---- DATA(-1, -2)
+       2940               2940                2940
 
-             2                    2                     2
-     + 1/10 y  DATA(0, 2) + 1/10 y  DATA(0, -2) + 1/49 x  DATA(1, 0)
+       191                 71                     2
+     + ---- DATA(0, -2) + ---- DATA(1, -2) - 2/5 y  DATA(0, -1)
+       2940               2940
 
-            2                    2                     2
-     + 3/5 y  DATA(2, 0) - 2/49 x  DATA(-2, 0) + 1/49 x  DATA(-1, 0)
+            2                     2                    2
+     + 3/5 y  DATA(-1, 0) + 1/10 y  DATA(0, -2) + 3/5 y  DATA(-2, 0)
 
-                                2                    2
-     - 1/5 y DATA(0, 1) + 2/49 x  DATA(0, 0) + 1/49 x  DATA(0, 1)
+       289                     2                    2
+     - ---- DATA(-2, 2) - 2/5 y  DATA(0, 1) + 1/10 y  DATA(0, 2)
+       2940
 
-             2                     2                    2
-     + 1/49 x  DATA(0, -1) - 2/49 x  DATA(0, 2) - 2/49 x  DATA(0, -2)
+            2                   2              41               226
+     + 3/5 y  DATA(1, 0) + 3/5 y  DATA(2, 0) - -- DATA(-2, 0) + --- DATA(-2, 1)
+                                               98               735
 
-             2
-     - 2/49 x  DATA(2, 0)
+            2
+     + 3/5 y  DATA(0, 0) - 1/5 y DATA(0, 1) + 1/10 y DATA(0, 2)
 
 > coeff_as_lc_of_data(%, posn_list_2d_size5);
-                       2                             2            289
-[COEFF(-2, -2) = 1/10 y  + 1/10 x y - 2/35 x + 2/49 x  - 1/10 y - ----,
-                                                                  2940
-
-                     71          2                                      2
-    COEFF(-1, -2) = ---- + 1/10 y  + 1/20 x y - 1/10 y - 1/35 x - 1/49 x ,
-                    2940
+bytes used=114153352, alloc=2489912, time=11.61
+                            289          2                  2
+[COEFF(-2, -2) = - 1/10 y - ---- + 2/49 x  - 2/35 x + 1/10 y  + 1/10 x y,
+                            2940
 
-                         2   191          2
-    COEFF(0, -2) = 1/10 y  + ---- - 2/49 x  - 1/10 y,
-                             2940
+                                                       2    71          2
+    COEFF(-1, -2) = 1/20 x y - 1/10 y - 1/35 x + 1/10 y  + ---- - 1/49 x ,
+                                                           2940
 
-                                                        2         2    71
-    COEFF(1, -2) = - 1/10 y + 1/35 x - 1/20 x y - 1/49 x  + 1/10 y  + ----,
-                                                                      2940
+                              191          2         2
+    COEFF(0, -2) = - 1/10 y + ---- + 1/10 y  - 2/49 x ,
+                              2940
 
-                         2   289          2
-    COEFF(2, -2) = 2/49 x  - ---- + 1/10 y  - 1/10 x y + 2/35 x - 1/10 y,
-                             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            226
-    COEFF(-2, -1) = 1/5 y - 2/5 y  - 1/49 x  + 1/35 x + --- - 1/5 x y,
-                                                        735
+                         2                    2   289
+    COEFF(2, -2) = 2/49 x  - 1/10 x y + 1/10 y  - ---- - 1/10 y + 2/35 x,
+                                                  2940
 
-                           2                               181         2
-    COEFF(-1, -1) = - 2/5 y  - 1/10 x y + 1/5 y + 1/70 x + --- + 1/98 x ,
+                                      2                    226        2
+    COEFF(-2, -1) = - 1/5 x y - 1/49 x  + 1/5 y + 1/35 x + --- - 2/5 y ,
                                                            735
 
-                         2        2   166
-    COEFF(0, -1) = 1/49 x  - 2/5 y  + --- + 1/5 y,
-                                      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                    2   181
-    COEFF(1, -1) = - 1/70 x + 1/5 y - 2/5 y  + 1/10 x y + 1/98 x  + ---,
+                         2   166                2
+    COEFF(0, -1) = 1/49 x  + --- + 1/5 y - 2/5 y ,
+                             735
+
+                                                       2        2   181
+    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  + --- - 1/49 x  + 1/5 x y + 1/5 y,
-                                       735
+                                                    2   226        2
+    COEFF(2, -1) = 1/5 y + 1/5 x y - 1/35 x - 1/49 x  + --- - 2/5 y ,
+                                                        735
 
-                     41                  2        2
-    COEFF(-2, 0) = - -- + 2/35 x - 2/49 x  + 3/5 y ,
+                     41        2                  2
+    COEFF(-2, 0) = - -- + 3/5 y  + 2/35 x - 2/49 x ,
                      98
 
-                        2                  2   53
-    COEFF(-1, 0) = 3/5 y  + 1/35 x + 1/49 x  - --,
-                                               98
-
-                       2   57         2
-    COEFF(0, 0) = 3/5 y  - -- + 2/49 x ,
-                           98
-
-                       2         2            53
-    COEFF(1, 0) = 3/5 y  + 1/49 x  - 1/35 x - --,
-                                              98
+                            53         2        2
+    COEFF(-1, 0) = 1/35 x - -- + 1/49 x  + 3/5 y ,
+                            98
 
-                    41         2                 2
-    COEFF(2, 0) = - -- - 2/49 x  - 2/35 x + 3/5 y ,
+                    57        2         2
+    COEFF(0, 0) = - -- + 3/5 y  + 2/49 x ,
                     98
 
-                                    226                  2         2
-    COEFF(-2, 1) = 1/35 x - 1/5 y + --- + 1/5 x y - 2/5 y  - 1/49 x ,
-                                    735
+                                  2         2   53
+    COEFF(1, 0) = - 1/35 x + 3/5 y  + 1/49 x  - --,
+                                                98
 
-                                                      2   181         2
-    COEFF(-1, 1) = - 1/5 y + 1/70 x + 1/10 x y - 2/5 y  + --- + 1/98 x ,
-                                                          735
+                          2                 2   41
+    COEFF(2, 0) = - 2/49 x  - 2/35 x + 3/5 y  - --,
+                                                98
 
-                         2         2           166
-    COEFF(0, 1) = - 2/5 y  + 1/49 x  - 1/5 y + ---,
-                                               735
+                           2                          2            226
+    COEFF(-2, 1) = - 1/49 x  - 1/5 y + 1/5 x y - 2/5 y  + 1/35 x + ---,
+                                                                   735
 
-                             181                    2        2
-    COEFF(1, 1) = - 1/70 x + --- - 1/10 x y + 1/98 x  - 2/5 y  - 1/5 y,
-                             735
+                                 2                    2           181
+    COEFF(-1, 1) = 1/70 x - 2/5 y  + 1/10 x y + 1/98 x  - 1/5 y + ---,
+                                                                  735
+
+                        2           166        2
+    COEFF(0, 1) = 1/49 x  - 1/5 y + --- - 2/5 y ,
+                                    735
 
-                  226                 2                 2
-    COEFF(2, 1) = --- - 1/5 y - 1/49 x  - 1/35 x - 2/5 y  - 1/5 x y,
+                  181                  2                           2
+    COEFF(1, 1) = --- - 1/70 x + 1/98 x  - 1/5 y - 1/10 x y - 2/5 y ,
                   735
 
-                                    2              289                   2
-    COEFF(-2, 2) = - 2/35 x + 2/49 x  - 1/10 x y - ---- + 1/10 y + 1/10 y ,
-                                                   2940
+                          2   226                 2
+    COEFF(2, 1) = - 1/49 x  + --- - 1/35 x - 2/5 y  - 1/5 y - 1/5 x y,
+                              735
 
-                    71          2         2
-    COEFF(-1, 2) = ---- - 1/49 x  + 1/10 y  - 1/35 x + 1/10 y - 1/20 x y,
-                   2940
+                                    2   289                              2
+    COEFF(-2, 2) = - 2/35 x + 2/49 x  - ---- + 1/10 y - 1/10 x y + 1/10 y ,
+                                        2940
 
-                          2         2            191
-    COEFF(0, 2) = - 2/49 x  + 1/10 y  + 1/10 y + ----,
-                                                 2940
+                         2         2                      71
+    COEFF(-1, 2) = 1/10 y  - 1/49 x  - 1/35 x + 1/10 y + ---- - 1/20 x y,
+                                                         2940
+
+                  191          2                  2
+    COEFF(0, 2) = ---- + 1/10 y  + 1/10 y - 2/49 x ,
+                  2940
 
-                   71          2                                      2
-    COEFF(1, 2) = ---- + 1/10 y  + 1/20 x y + 1/10 y + 1/35 x - 1/49 x ,
+                   71                   2                  2
+    COEFF(1, 2) = ---- + 1/10 y - 1/49 x  + 1/35 x + 1/10 y  + 1/20 x y,
                   2940
 
-                    289                   2                             2
-    COEFF(2, 2) = - ---- + 1/10 y + 2/49 x  + 2/35 x + 1/10 x y + 1/10 y ]
+                    289                   2         2
+    COEFF(2, 2) = - ---- + 1/10 y + 2/49 x  + 1/10 y  + 1/10 x y + 2/35 x]
                     2940
 
 > print_coeff__lc_of_data(%, "coeff_dyy_", "fp",
 > 			"2d.coeffs/2d.cube.order4.smooth0/coeff-dyy.compute.c");
-bytes used=115130604, alloc=2424388, time=11.46
-bytes used=116138968, alloc=2424388, time=11.55
-bytes used=117139208, alloc=2424388, time=11.72
-bytes used=118140008, alloc=2424388, time=11.80
-bytes used=119140212, alloc=2424388, time=12.00
-bytes used=120140404, alloc=2424388, time=12.21
-bytes used=121141040, alloc=2424388, time=12.38
+bytes used=115153616, alloc=2489912, time=11.69
+bytes used=116153852, alloc=2489912, time=11.82
+bytes used=117154004, alloc=2489912, time=11.94
+bytes used=118154188, alloc=2489912, time=12.11
+bytes used=119154664, alloc=2489912, time=12.30
+bytes used=120154836, alloc=2489912, time=12.46
 > 
 ################################################################################
 > quit
-bytes used=121567580, alloc=2424388, time=12.41
+bytes used=121070196, alloc=2489912, time=12.59
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.maple b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.maple
index 32b685c..ac402b5 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.maple
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.maple
@@ -1,5 +1,5 @@
 # 2d.maple -- compute Lagrange interpolation coefficients in 2-D
-# $Id$
+# $Header$
 
 ################################################################################
 
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order1.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order1.smooth0.c
index 4f7b89b..f97eb83 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order1.smooth0.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order1.smooth0.c
@@ -1,3 +1,5 @@
+/* $Header$ */
+
 #include <math.h>
 #include <limits.h>
 #include <stdlib.h>
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order2.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order2.smooth0.c
index 8de6d28..5a03269 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order2.smooth0.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order2.smooth0.c
@@ -1,3 +1,5 @@
+/* $Header$ */
+
 #include <math.h>
 #include <limits.h>
 #include <stdlib.h>
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order3.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order3.smooth0.c
index 2d25ba1..5ddab6e 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order3.smooth0.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order3.smooth0.c
@@ -1,3 +1,5 @@
+/* $Header$ */
+
 #include <math.h>
 #include <limits.h>
 #include <stdlib.h>
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order4.smooth0.c b/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order4.smooth0.c
index 9ae7038..7f41b48 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order4.smooth0.c
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/3d.cube.order4.smooth0.c
@@ -1,3 +1,5 @@
+/* $Header$ */
+
 #include <math.h>
 #include <limits.h>
 #include <stdlib.h>
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/3d.maple b/src/GeneralizedPolynomial-Uniform/Lagrange/3d.maple
index 615387d..5167fa8 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/3d.maple
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/3d.maple
@@ -1,5 +1,5 @@
 # 3d.maple -- compute Lagrange interpolation coefficients in 3-D
-# $Id$
+# $Header$
 
 ################################################################################
 
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple b/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple
index 3789cfd..6a6a4e3 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple
@@ -1,5 +1,5 @@
 # Maple code to define Lagrange interpolating functions/coords/coeffs
-# $Id$
+# $Header$
 
 ################################################################################
 
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/makefile b/src/GeneralizedPolynomial-Uniform/Lagrange/makefile
index 26e24c3..6684a83 100644
--- a/src/GeneralizedPolynomial-Uniform/Lagrange/makefile
+++ b/src/GeneralizedPolynomial-Uniform/Lagrange/makefile
@@ -1,3 +1,5 @@
+# $Header: /mnt/data2/cvs2svn/cvs-repositories/arrangements/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/makefile,v 1.2 2002-08-20 16:31:24 jthorn Exp $
+
 .PHONY	: no-default-target
 no-default-target:
 	@echo 'there is (deliberately) no default target in this makefile,'
@@ -23,7 +25,7 @@ no-default-target:
             ../common/cube_posns.maple fns.maple 2d.maple \
            | maple 2>&1 >2d.log
 
-# with Maple 7, this takes about 9.5 minutes on a 1.7GHz P4
+# with Maple 7, this takes about 10 minutes on a 1.7GHz P4
 .PHONY	: 3d
 3d	:
 	-rm 3d.coeffs/*/*.c