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/*@@
@header RICCI_guts.h
@date Jun 98
@author Gabrielle Allen
@desc
Macro to calculate the components of the Ricci tensor.
Requires: Second derivatives of physical metric
Christoffel symbols of first kind
Christoffel symbols of second kind
Upper physical metric
Provides: Components of the physical Ricci tensor
@enddesc
@@*/
#ifndef RICCI_GUTS
#define RICCI_GUTS
#include "UPPERMET_guts.h"
#include "DDG_guts.h"
#include "CHR1_guts.h"
#include "CHR2_guts.h"
#ifdef FCODE
RICCI_RXX = (DXYDG_DXYDGXY+(-DXXDG_DXXDGYY-DYYDG_DYYDGXX)/2 - \
CHR1_XYY*CHR2_XXX +CHR1_XXY*CHR2_XXY-CHR1_YYY*CHR2_YXX + \
CHR1_YXY*CHR2_YXY - CHR1_ZYY*CHR2_ZXX + \
CHR1_ZXY*CHR2_ZXY)*UPPERMET_UYY + (-DXXDG_DXXDGYZ + DXYDG_DXYDGXZ + \
DXZDG_DXZDGXY - DYZDG_DYZDGXX - 2*(CHR1_YYZ*CHR2_YXX + \
CHR1_ZYZ*CHR2_ZXX) + 2*(-(CHR1_XYZ*CHR2_XXX) + CHR1_XXZ*CHR2_XXY + \
CHR1_YXZ*CHR2_YXY + CHR1_ZXZ*CHR2_ZXY))*UPPERMET_UYZ + (DXZDG_DXZDGXZ \
+ (-DXXDG_DXXDGZZ - DZZDG_DZZDGXX)/2 - CHR1_XZZ*CHR2_XXX + \
CHR1_XXZ*CHR2_XXZ - CHR1_YZZ*CHR2_YXX + CHR1_YXZ*CHR2_YXZ - \
CHR1_ZZZ*CHR2_ZXX + CHR1_ZXZ*CHR2_ZXZ)*UPPERMET_UZZ
RICCI_RXY = (-DXYDG_DXYDGXY + (DXXDG_DXXDGYY + DYYDG_DYYDGXX)/2 + \
CHR1_XYY*CHR2_XXX - CHR1_XXY*CHR2_XXY + CHR1_YYY*CHR2_YXX - \
CHR1_YXY*CHR2_YXY + CHR1_ZYY*CHR2_ZXX - \
CHR1_ZXY*CHR2_ZXY)*UPPERMET_UXY + ((DXXDG_DXXDGYZ - DXYDG_DXYDGXZ - \
DXZDG_DXZDGXY + DYZDG_DYZDGXX)/2 + CHR1_XYZ*CHR2_XXX - \
CHR1_XXZ*CHR2_XXY + CHR1_YYZ*CHR2_YXX - CHR1_YXZ*CHR2_YXY + \
CHR1_ZYZ*CHR2_ZXX - CHR1_ZXZ*CHR2_ZXY)*UPPERMET_UXZ + \
((-DXYDG_DXYDGYZ + DXZDG_DXZDGYY + DYYDG_DYYDGXZ - DYZDG_DYZDGXY)/2 - \
CHR1_XYZ*CHR2_XXY + CHR1_XYY*CHR2_XXZ - CHR1_YYZ*CHR2_YXY + \
CHR1_YYY*CHR2_YXZ - CHR1_ZYZ*CHR2_ZXY + \
CHR1_ZYY*CHR2_ZXZ)*UPPERMET_UYZ + ((-DXYDG_DXYDGZZ + DXZDG_DXZDGYZ + \
DYZDG_DYZDGXZ - DZZDG_DZZDGXY)/2 - CHR1_XZZ*CHR2_XXY + \
CHR1_XYZ*CHR2_XXZ - CHR1_YZZ*CHR2_YXY + CHR1_YYZ*CHR2_YXZ - \
CHR1_ZZZ*CHR2_ZXY + CHR1_ZYZ*CHR2_ZXZ)*UPPERMET_UZZ ;
RICCI_RXZ = ((DXXDG_DXXDGYZ - DXYDG_DXYDGXZ - DXZDG_DXZDGXY + \
DYZDG_DYZDGXX)/2 + CHR1_XYZ*CHR2_XXX - CHR1_XXZ*CHR2_XXY + \
CHR1_YYZ*CHR2_YXX - CHR1_YXZ*CHR2_YXY + CHR1_ZYZ*CHR2_ZXX - \
CHR1_ZXZ*CHR2_ZXY)*UPPERMET_UXY + (-DXZDG_DXZDGXZ + (DXXDG_DXXDGZZ + \
DZZDG_DZZDGXX)/2 + CHR1_XZZ*CHR2_XXX - CHR1_XXZ*CHR2_XXZ + \
CHR1_YZZ*CHR2_YXX - CHR1_YXZ*CHR2_YXZ + CHR1_ZZZ*CHR2_ZXX - \
CHR1_ZXZ*CHR2_ZXZ)*UPPERMET_UXZ + ((DXYDG_DXYDGYZ - DXZDG_DXZDGYY - \
DYYDG_DYYDGXZ + DYZDG_DYZDGXY)/2 + CHR1_XYZ*CHR2_XXY - \
CHR1_XYY*CHR2_XXZ + CHR1_YYZ*CHR2_YXY - CHR1_YYY*CHR2_YXZ + \
CHR1_ZYZ*CHR2_ZXY - CHR1_ZYY*CHR2_ZXZ)*UPPERMET_UYY + ((DXYDG_DXYDGZZ \
- DXZDG_DXZDGYZ - DYZDG_DYZDGXZ + DZZDG_DZZDGXY)/2 + CHR1_XZZ*CHR2_XXY \
- CHR1_XYZ*CHR2_XXZ + CHR1_YZZ*CHR2_YXY - CHR1_YYZ*CHR2_YXZ + \
CHR1_ZZZ*CHR2_ZXY - CHR1_ZYZ*CHR2_ZXZ)*UPPERMET_UYZ ;
RICCI_RYY = (DXYDG_DXYDGXY + (-DXXDG_DXXDGYY - DYYDG_DYYDGXX)/2 - \
CHR1_XYY*CHR2_XXX + CHR1_XXY*CHR2_XXY - CHR1_YYY*CHR2_YXX + \
CHR1_YXY*CHR2_YXY - CHR1_ZYY*CHR2_ZXX + \
CHR1_ZXY*CHR2_ZXY)*UPPERMET_UXX + (DXYDG_DXYDGYZ - DXZDG_DXZDGYY - \
DYYDG_DYYDGXZ + DYZDG_DYZDGXY + 2*(CHR1_XYZ*CHR2_XXY - \
CHR1_XYY*CHR2_XXZ + CHR1_YYZ*CHR2_YXY + CHR1_ZYZ*CHR2_ZXY) - \
2*(CHR1_YYY*CHR2_YXZ + CHR1_ZYY*CHR2_ZXZ)) *UPPERMET_UXZ + \
(DYZDG_DYZDGYZ + (-DYYDG_DYYDGZZ - DZZDG_DZZDGYY)/2 - \
CHR1_XZZ*CHR2_XYY + CHR1_XYZ*CHR2_XYZ - CHR1_YZZ*CHR2_YYY + \
CHR1_YYZ*CHR2_YYZ - CHR1_ZZZ*CHR2_ZYY + \
CHR1_ZYZ*CHR2_ZYZ)*UPPERMET_UZZ ;
RICCI_RYZ = ((-DXXDG_DXXDGYZ + DXYDG_DXYDGXZ + DXZDG_DXZDGXY - \
DYZDG_DYZDGXX)/2 - CHR1_XYZ*CHR2_XXX + CHR1_XXZ*CHR2_XXY - \
CHR1_YYZ*CHR2_YXX + CHR1_YXZ*CHR2_YXY - CHR1_ZYZ*CHR2_ZXX + \
CHR1_ZXZ*CHR2_ZXY)*UPPERMET_UXX + ((-DXYDG_DXYDGYZ + DXZDG_DXZDGYY + \
DYYDG_DYYDGXZ - DYZDG_DYZDGXY)/2 - CHR1_XYZ*CHR2_XXY + \
CHR1_XYY*CHR2_XXZ - CHR1_YYZ*CHR2_YXY + CHR1_YYY*CHR2_YXZ - \
CHR1_ZYZ*CHR2_ZXY + CHR1_ZYY*CHR2_ZXZ)*UPPERMET_UXY + ((DXYDG_DXYDGZZ \
- DXZDG_DXZDGYZ - DYZDG_DYZDGXZ + DZZDG_DZZDGXY)/2 + CHR1_XZZ*CHR2_XXY \
- CHR1_XYZ*CHR2_XXZ + CHR1_YZZ*CHR2_YXY - CHR1_YYZ*CHR2_YXZ + \
CHR1_ZZZ*CHR2_ZXY - CHR1_ZYZ*CHR2_ZXZ)*UPPERMET_UXZ + (-DYZDG_DYZDGYZ \
+ (DYYDG_DYYDGZZ + DZZDG_DZZDGYY)/2 + CHR1_XZZ*CHR2_XYY - \
CHR1_XYZ*CHR2_XYZ + CHR1_YZZ*CHR2_YYY - CHR1_YYZ*CHR2_YYZ + \
CHR1_ZZZ*CHR2_ZYY - CHR1_ZYZ*CHR2_ZYZ)*UPPERMET_UYZ ;
RICCI_RZZ = (DXZDG_DXZDGXZ + (-DXXDG_DXXDGZZ - DZZDG_DZZDGXX)/2 - \
CHR1_XZZ*CHR2_XXX + CHR1_XXZ*CHR2_XXZ - CHR1_YZZ*CHR2_YXX + \
CHR1_YXZ*CHR2_YXZ - CHR1_ZZZ*CHR2_ZXX + \
CHR1_ZXZ*CHR2_ZXZ)*UPPERMET_UXX + (-DXYDG_DXYDGZZ + DXZDG_DXZDGYZ + \
DYZDG_DYZDGXZ - DZZDG_DZZDGXY - 2*(CHR1_YZZ*CHR2_YXY + \
CHR1_ZZZ*CHR2_ZXY) + 2*(-(CHR1_XZZ*CHR2_XXY) + CHR1_XYZ*CHR2_XXZ + \
CHR1_YYZ*CHR2_YXZ + CHR1_ZYZ*CHR2_ZXZ))*UPPERMET_UXY + (DYZDG_DYZDGYZ \
+ (-DYYDG_DYYDGZZ - DZZDG_DZZDGYY)/2 - CHR1_XZZ*CHR2_XYY + \
CHR1_XYZ*CHR2_XYZ - CHR1_YZZ*CHR2_YYY + CHR1_YYZ*CHR2_YYZ - \
CHR1_ZZZ*CHR2_ZYY + CHR1_ZYZ*CHR2_ZYZ)*UPPERMET_UYY ;
#endif
#ifdef CCODE
RICCI_RXX = (DXYDG_DXYDGXY+(-DXXDG_DXXDGYY-DYYDG_DYYDGXX)/2 -
CHR1_XYY*CHR2_XXX +CHR1_XXY*CHR2_XXY-CHR1_YYY*CHR2_YXX +
CHR1_YXY*CHR2_YXY - CHR1_ZYY*CHR2_ZXX +
CHR1_ZXY*CHR2_ZXY)*UPPERMET_UYY + (-DXXDG_DXXDGYZ + DXYDG_DXYDGXZ +
DXZDG_DXZDGXY - DYZDG_DYZDGXX - 2*(CHR1_YYZ*CHR2_YXX +
CHR1_ZYZ*CHR2_ZXX) + 2*(-(CHR1_XYZ*CHR2_XXX) + CHR1_XXZ*CHR2_XXY +
CHR1_YXZ*CHR2_YXY + CHR1_ZXZ*CHR2_ZXY))*UPPERMET_UYZ + (DXZDG_DXZDGXZ
+ (-DXXDG_DXXDGZZ - DZZDG_DZZDGXX)/2 - CHR1_XZZ*CHR2_XXX +
CHR1_XXZ*CHR2_XXZ - CHR1_YZZ*CHR2_YXX + CHR1_YXZ*CHR2_YXZ -
CHR1_ZZZ*CHR2_ZXX + CHR1_ZXZ*CHR2_ZXZ)*UPPERMET_UZZ;
RICCI_RXY = (-DXYDG_DXYDGXY + (DXXDG_DXXDGYY + DYYDG_DYYDGXX)/2 +
CHR1_XYY*CHR2_XXX - CHR1_XXY*CHR2_XXY + CHR1_YYY*CHR2_YXX -
CHR1_YXY*CHR2_YXY + CHR1_ZYY*CHR2_ZXX -
CHR1_ZXY*CHR2_ZXY)*UPPERMET_UXY + ((DXXDG_DXXDGYZ - DXYDG_DXYDGXZ -
DXZDG_DXZDGXY + DYZDG_DYZDGXX)/2 + CHR1_XYZ*CHR2_XXX -
CHR1_XXZ*CHR2_XXY + CHR1_YYZ*CHR2_YXX - CHR1_YXZ*CHR2_YXY +
CHR1_ZYZ*CHR2_ZXX - CHR1_ZXZ*CHR2_ZXY)*UPPERMET_UXZ +
((-DXYDG_DXYDGYZ + DXZDG_DXZDGYY + DYYDG_DYYDGXZ - DYZDG_DYZDGXY)/2 -
CHR1_XYZ*CHR2_XXY + CHR1_XYY*CHR2_XXZ - CHR1_YYZ*CHR2_YXY +
CHR1_YYY*CHR2_YXZ - CHR1_ZYZ*CHR2_ZXY +
CHR1_ZYY*CHR2_ZXZ)*UPPERMET_UYZ + ((-DXYDG_DXYDGZZ + DXZDG_DXZDGYZ +
DYZDG_DYZDGXZ - DZZDG_DZZDGXY)/2 - CHR1_XZZ*CHR2_XXY +
CHR1_XYZ*CHR2_XXZ - CHR1_YZZ*CHR2_YXY + CHR1_YYZ*CHR2_YXZ -
CHR1_ZZZ*CHR2_ZXY + CHR1_ZYZ*CHR2_ZXZ)*UPPERMET_UZZ ;
RICCI_RXZ = ((DXXDG_DXXDGYZ - DXYDG_DXYDGXZ - DXZDG_DXZDGXY +
DYZDG_DYZDGXX)/2 + CHR1_XYZ*CHR2_XXX - CHR1_XXZ*CHR2_XXY +
CHR1_YYZ*CHR2_YXX - CHR1_YXZ*CHR2_YXY + CHR1_ZYZ*CHR2_ZXX -
CHR1_ZXZ*CHR2_ZXY)*UPPERMET_UXY + (-DXZDG_DXZDGXZ + (DXXDG_DXXDGZZ +
DZZDG_DZZDGXX)/2 + CHR1_XZZ*CHR2_XXX - CHR1_XXZ*CHR2_XXZ +
CHR1_YZZ*CHR2_YXX - CHR1_YXZ*CHR2_YXZ + CHR1_ZZZ*CHR2_ZXX -
CHR1_ZXZ*CHR2_ZXZ)*UPPERMET_UXZ + ((DXYDG_DXYDGYZ - DXZDG_DXZDGYY -
DYYDG_DYYDGXZ + DYZDG_DYZDGXY)/2 + CHR1_XYZ*CHR2_XXY -
CHR1_XYY*CHR2_XXZ + CHR1_YYZ*CHR2_YXY - CHR1_YYY*CHR2_YXZ +
CHR1_ZYZ*CHR2_ZXY - CHR1_ZYY*CHR2_ZXZ)*UPPERMET_UYY + ((DXYDG_DXYDGZZ
- DXZDG_DXZDGYZ - DYZDG_DYZDGXZ + DZZDG_DZZDGXY)/2 + CHR1_XZZ*CHR2_XXY
- CHR1_XYZ*CHR2_XXZ + CHR1_YZZ*CHR2_YXY - CHR1_YYZ*CHR2_YXZ +
CHR1_ZZZ*CHR2_ZXY - CHR1_ZYZ*CHR2_ZXZ)*UPPERMET_UYZ ;
RICCI_RYY = (DXYDG_DXYDGXY + (-DXXDG_DXXDGYY - DYYDG_DYYDGXX)/2 -
CHR1_XYY*CHR2_XXX + CHR1_XXY*CHR2_XXY - CHR1_YYY*CHR2_YXX +
CHR1_YXY*CHR2_YXY - CHR1_ZYY*CHR2_ZXX +
CHR1_ZXY*CHR2_ZXY)*UPPERMET_UXX + (DXYDG_DXYDGYZ - DXZDG_DXZDGYY -
DYYDG_DYYDGXZ + DYZDG_DYZDGXY + 2*(CHR1_XYZ*CHR2_XXY -
CHR1_XYY*CHR2_XXZ + CHR1_YYZ*CHR2_YXY + CHR1_ZYZ*CHR2_ZXY) -
2*(CHR1_YYY*CHR2_YXZ + CHR1_ZYY*CHR2_ZXZ)) *UPPERMET_UXZ +
(DYZDG_DYZDGYZ + (-DYYDG_DYYDGZZ - DZZDG_DZZDGYY)/2 -
CHR1_XZZ*CHR2_XYY + CHR1_XYZ*CHR2_XYZ - CHR1_YZZ*CHR2_YYY +
CHR1_YYZ*CHR2_YYZ - CHR1_ZZZ*CHR2_ZYY +
CHR1_ZYZ*CHR2_ZYZ)*UPPERMET_UZZ ;
RICCI_RYZ = ((-DXXDG_DXXDGYZ + DXYDG_DXYDGXZ + DXZDG_DXZDGXY -
DYZDG_DYZDGXX)/2 - CHR1_XYZ*CHR2_XXX + CHR1_XXZ*CHR2_XXY -
CHR1_YYZ*CHR2_YXX + CHR1_YXZ*CHR2_YXY - CHR1_ZYZ*CHR2_ZXX +
CHR1_ZXZ*CHR2_ZXY)*UPPERMET_UXX + ((-DXYDG_DXYDGYZ + DXZDG_DXZDGYY +
DYYDG_DYYDGXZ - DYZDG_DYZDGXY)/2 - CHR1_XYZ*CHR2_XXY +
CHR1_XYY*CHR2_XXZ - CHR1_YYZ*CHR2_YXY + CHR1_YYY*CHR2_YXZ -
CHR1_ZYZ*CHR2_ZXY + CHR1_ZYY*CHR2_ZXZ)*UPPERMET_UXY + ((DXYDG_DXYDGZZ
- DXZDG_DXZDGYZ - DYZDG_DYZDGXZ + DZZDG_DZZDGXY)/2 + CHR1_XZZ*CHR2_XXY
- CHR1_XYZ*CHR2_XXZ + CHR1_YZZ*CHR2_YXY - CHR1_YYZ*CHR2_YXZ +
CHR1_ZZZ*CHR2_ZXY - CHR1_ZYZ*CHR2_ZXZ)*UPPERMET_UXZ + (-DYZDG_DYZDGYZ
+ (DYYDG_DYYDGZZ + DZZDG_DZZDGYY)/2 + CHR1_XZZ*CHR2_XYY -
CHR1_XYZ*CHR2_XYZ + CHR1_YZZ*CHR2_YYY - CHR1_YYZ*CHR2_YYZ +
CHR1_ZZZ*CHR2_ZYY - CHR1_ZYZ*CHR2_ZYZ)*UPPERMET_UYZ ;
RICCI_RZZ = (DXZDG_DXZDGXZ + (-DXXDG_DXXDGZZ - DZZDG_DZZDGXX)/2 -
CHR1_XZZ*CHR2_XXX + CHR1_XXZ*CHR2_XXZ - CHR1_YZZ*CHR2_YXX +
CHR1_YXZ*CHR2_YXZ - CHR1_ZZZ*CHR2_ZXX +
CHR1_ZXZ*CHR2_ZXZ)*UPPERMET_UXX + (-DXYDG_DXYDGZZ + DXZDG_DXZDGYZ +
DYZDG_DYZDGXZ - DZZDG_DZZDGXY - 2*(CHR1_YZZ*CHR2_YXY +
CHR1_ZZZ*CHR2_ZXY) + 2*(-(CHR1_XZZ*CHR2_XXY) + CHR1_XYZ*CHR2_XXZ +
CHR1_YYZ*CHR2_YXZ + CHR1_ZYZ*CHR2_ZXZ))*UPPERMET_UXY + (DYZDG_DYZDGYZ
+ (-DYYDG_DYYDGZZ - DZZDG_DZZDGYY)/2 - CHR1_XZZ*CHR2_XYY +
CHR1_XYZ*CHR2_XYZ - CHR1_YZZ*CHR2_YYY + CHR1_YYZ*CHR2_YYZ -
CHR1_ZZZ*CHR2_ZYY + CHR1_ZYZ*CHR2_ZYZ)*UPPERMET_UYY ;
#endif
#endif
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