diff --git a/Z4coo/src/constraint.cxx b/Z4coo/src/constraint.cxx index fcf756b2..af4fd4f2 100644 --- a/Z4coo/src/constraint.cxx +++ b/Z4coo/src/constraint.cxx @@ -9,7 +9,6 @@ #endif #include "derivs.hxx" -#include "physics.hxx" #include #include diff --git a/Z4coo/src/enforce.cxx b/Z4coo/src/enforce.cxx index 0f0c5817..c43cc157 100644 --- a/Z4coo/src/enforce.cxx +++ b/Z4coo/src/enforce.cxx @@ -1,5 +1,3 @@ -#include "physics.hxx" - #include #include #include diff --git a/Z4coo/src/initial1.cxx b/Z4coo/src/initial1.cxx index 3ea96d9f..3160f630 100644 --- a/Z4coo/src/initial1.cxx +++ b/Z4coo/src/initial1.cxx @@ -1,5 +1,3 @@ -#include "physics.hxx" - #include #include #include diff --git a/Z4coo/src/initial2.cxx b/Z4coo/src/initial2.cxx index d2f28cbd..141724cc 100644 --- a/Z4coo/src/initial2.cxx +++ b/Z4coo/src/initial2.cxx @@ -1,5 +1,4 @@ #include "derivs.hxx" -#include "physics.hxx" #include #include @@ -16,6 +15,29 @@ using namespace Arith; using namespace Loop; using namespace std; +template +ARITH_INLINE ARITH_DEVICE ARITH_HOST constexpr vec, D> +calc_gammal(const smat, D> &dg) { + // Gammal_abc + return vec, D>([&](int a) ARITH_INLINE { + return smat([&](int b, int c) ARITH_INLINE { + return (dg(a, b)(c) + dg(a, c)(b) - dg(b, c)(a)) / 2; + }); + }); +} + +template +ARITH_INLINE ARITH_DEVICE ARITH_HOST constexpr vec, D> +calc_gamma(const smat &gu, const vec, D> &Gammal) { + // Gamma^a_bc + return vec, D>([&](int a) ARITH_INLINE { + return smat([&](int b, int c) ARITH_INLINE { + return sum([&](int x) + ARITH_INLINE { return gu(a, x) * Gammal(x)(b, c); }); + }); + }); +} + extern "C" void Z4coo_Initial2(CCTK_ARGUMENTS) { DECLARE_CCTK_ARGUMENTS_Z4coo_Initial2; diff --git a/Z4coo/src/physics.hxx b/Z4coo/src/physics.hxx deleted file mode 100644 index c31de826..00000000 --- a/Z4coo/src/physics.hxx +++ /dev/null @@ -1,99 +0,0 @@ -#ifndef PHYSICS_HXX -#define PHYSICS_HXX - -#include -#include -#include -#include - -namespace Z4coo { -using namespace Arith; - -template -ARITH_INLINE ARITH_DEVICE ARITH_HOST constexpr smat, D> -calc_dgu(const smat &gu, const smat, D> &dg) { - // g_xy = g_xa g_yb g^ab - // g_xy,c = (g_xa g_yb g^ab),c - // = g_xa,c g_yb g^ab + g_xa g_yb,c g^ab + g_xa g_yb g^ab,c - // g_xa g_yb g^ab,c = g_xy,c - g_xa,c g_yb g^ab - g_xa g_yb,c g^ab - // = g_xy,c - g_xy,c - g_xy,c - // = - g_xy,c - // g^ab,c = - g^ax g^by g_xy,c - return smat, D>([&](int a, int b) ARITH_INLINE { - return vec([&](int c) ARITH_INLINE { - // return sum2sym([&](int x, int y) ARITH_INLINE { - // return -gu(a, x) * gu(b, y) * dg(x, y)(c); - // }); - return sum([&](int x) ARITH_INLINE { - return -gu(a, x) * sum([&](int y) ARITH_INLINE { - return gu(b, y) * dg(x, y)(c); - }); - }); - }); - }); -} - -template -ARITH_INLINE ARITH_DEVICE ARITH_HOST constexpr smat, D> -calc_dAu(const smat &gu, const smat, D> &dgu, - const smat &A, const smat, D> &dA) { - // A^ab,c = (g^ax g^by A_xy),c - // = g^ax,c g^by A_xy + g^ax g^by,c A_xy + g^ax g^by A_xy,c - return smat, D>([&](int a, int b) ARITH_INLINE { - return vec([&](int c) ARITH_INLINE { - // return sum2sym([&](int x, int y) ARITH_INLINE { - // return dgu(a, x)(c) * gu(b, y) * A(x, y) // - // + gu(a, x) * dgu(b, y)(c) * A(x, y) // - // + gu(a, x) * gu(b, y) * dA(x, y)(c); - // }); - return sum([&](int x) ARITH_INLINE { - return gu(b, x) * sum([&](int y) ARITH_INLINE { - return dgu(a, y)(c) * A(x, y) // - + dgu(b, y)(c) * A(x, y) // - + gu(b, y) * dA(x, y)(c); - }); - }); - }); - }); -} - -template -ARITH_INLINE ARITH_DEVICE ARITH_HOST constexpr vec, D> -calc_gammal(const smat, D> &dg) { - // Gammal_abc - return vec, D>([&](int a) ARITH_INLINE { - return smat([&](int b, int c) ARITH_INLINE { - return (dg(a, b)(c) + dg(a, c)(b) - dg(b, c)(a)) / 2; - }); - }); -} - -template -ARITH_INLINE ARITH_DEVICE ARITH_HOST constexpr vec, D> -calc_gamma(const smat &gu, const vec, D> &Gammal) { - // Gamma^a_bc - return vec, D>([&](int a) ARITH_INLINE { - return smat([&](int b, int c) ARITH_INLINE { - return sum([&](int x) - ARITH_INLINE { return gu(a, x) * Gammal(x)(b, c); }); - }); - }); -} - -template -ARITH_INLINE ARITH_DEVICE ARITH_HOST constexpr vec, D>, D> -calc_gammalu(const smat &gu, const vec, D> &Gammal) { - // Gamma_ab^c - return vec, D>, D>([&](int a) ARITH_INLINE { - return vec, D>([&](int b) ARITH_INLINE { - return vec([&](int c) ARITH_INLINE { - return sum([&](int x) - ARITH_INLINE { return Gammal(a)(b, x) * gu(x, c); }); - }); - }); - }); -} - -} // namespace Z4coo - -#endif // #ifndef PHYSICS_HXX diff --git a/Z4coo/src/rhs.cxx b/Z4coo/src/rhs.cxx index b0b28ef6..bd466fac 100644 --- a/Z4coo/src/rhs.cxx +++ b/Z4coo/src/rhs.cxx @@ -11,7 +11,6 @@ // #define Power(x, y) (Arith::pown((x), (y))) #include "derivs.hxx" -#include "physics.hxx" #include #include diff --git a/Z4coo/wolfram/Z4coo_set_ADM.hxx b/Z4coo/wolfram/Z4coo_set_ADM.hxx index bd58217a..1a5ad5cd 100644 --- a/Z4coo/wolfram/Z4coo_set_ADM.hxx +++ b/Z4coo/wolfram/Z4coo_set_ADM.hxx @@ -1,6 +1,9 @@ /* Z4coo_set_ADM.hxx */ /* Produced with Mathematica */ +#ifndef Z4COO_SET_ADM_HXX +#define Z4COO_SET_ADM_HXX + const GF3D2 &local_ADMgam11 = gf_ADMgam(0,0); const GF3D2 &local_ADMgam12 = gf_ADMgam(0,1); const GF3D2 &local_ADMgam13 = gf_ADMgam(0,2); @@ -118,4 +121,6 @@ beta3 }); +#endif // #ifndef Z4COO_SET_ADM_HXX + /* Z4coo_set_ADM.hxx */ diff --git a/Z4coo/wolfram/Z4coo_set_ADM.wl b/Z4coo/wolfram/Z4coo_set_ADM.wl deleted file mode 100644 index 902017bf..00000000 --- a/Z4coo/wolfram/Z4coo_set_ADM.wl +++ /dev/null @@ -1,53 +0,0 @@ -(* ::Package:: *) - -(* Z4c_set_rhs.wl *) - -(* (c) Liwei Ji, 07/2024 *) - -Needs["xAct`xCoba`", FileNameJoin[{Environment["GENERATO"], "src/Generato.wl" - }]] - -SetPVerbose[False]; - -SetPrintDate[False]; - -SetGridPointIndex[""]; - -SetTempVariableType["vreal"]; - -DefManifold[M3, 3, IndexRange[a, z]]; - -DefChart[cart, M3, {1, 2, 3}, {X[], Y[], Z[]}, ChartColor -> Blue]; - -(* Define Variables *) - -< "MainOut"}, ADMVarlist]; - pr[]; - - pr["grid.loop_all_device<0, 0, 0, vsize>("]; - pr[" grid.nghostzones, [=] ARITH_DEVICE(const PointDesc &p) ARITH_INLINE {"]; - pr[" const vbool mask = mask_for_loop_tail(p.i, p.imax);"]; - pr[" const GF3D2index index2(layout2, p.I);"]; - pr[]; - - PrintListInitializations[Drop[EvolVarlist, {5}], "gf_", "index2"]; - pr[]; - - PrintInitializations[{Mode -> "MainIn"}, Drop[EvolVarlist, {5}]]; - pr[]; - PrintEquations[{Mode -> "Main"}, ADMVarlist]; - pr[]; - pr["});"]; - ]; - -Import[FileNameJoin[{Environment["GENERATO"], "codes/CarpetX.wl"}]]; diff --git a/Z4coo/wolfram/Z4coo_set_constraint.hxx b/Z4coo/wolfram/Z4coo_set_constraint.hxx index daa5605b..d55de695 100644 --- a/Z4coo/wolfram/Z4coo_set_constraint.hxx +++ b/Z4coo/wolfram/Z4coo_set_constraint.hxx @@ -1,6 +1,9 @@ /* Z4coo_set_constraint.hxx */ /* Produced with Mathematica */ +#ifndef Z4COO_SET_CONSTRAINT_HXX +#define Z4COO_SET_CONSTRAINT_HXX + const GF3D2 &local_ZtC1 = gf_ZtC(0); const GF3D2 &local_ZtC2 = gf_ZtC(1); const GF3D2 &local_ZtC3 = gf_ZtC(2); @@ -43,11 +46,8 @@ const vreal eTt3 = tmp_eTt(2); const vreal eT11 = tmp_eT(0,0); const vreal eT12 = tmp_eT(0,1); const vreal eT13 = tmp_eT(0,2); -const vreal eT21 = tmp_eT(1,0); const vreal eT22 = tmp_eT(1,1); const vreal eT23 = tmp_eT(1,2); -const vreal eT31 = tmp_eT(2,0); -const vreal eT32 = tmp_eT(2,1); const vreal eT33 = tmp_eT(2,2); const vreal chi = tmp_chi + 1; const vreal gamt11 = tmp_gamt(0,0) + 1; @@ -842,20 +842,19 @@ invgam11*R11 + 2*invgam12*R12 + 2*invgam13*R13 + invgam22*R22 + vreal rho = -(Power(beta1,2)*eT11 + beta1*beta2*(eT12 + eT21) + Power(beta2,2)*eT22 + - beta1*beta3*(eT13 + eT31) + beta2*beta3*(eT23 + eT32) + - Power(beta3,2)*eT33 - 2*beta1*eTt1 - 2*beta2*eTt2 - 2*beta3*eTt3 + eTtt)/ - Power(alpha,2) +(Power(beta1,2)*eT11 + Power(beta2,2)*eT22 + 2*beta2*beta3*eT23 + + Power(beta3,2)*eT33 + 2*beta1*(beta2*eT12 + beta3*eT13 - eTt1) - + 2*beta2*eTt2 - 2*beta3*eTt3 + eTtt)/Power(alpha,2) ; vreal Sm1 = -(beta1*eT11 + beta2*eT21 + beta3*eT31 - eTt1)/alpha +(beta1*eT11 + beta2*eT12 + beta3*eT13 - eTt1)/alpha ; vreal Sm2 = -(beta1*eT12 + beta2*eT22 + beta3*eT32 - eTt2)/alpha +(beta1*eT12 + beta2*eT22 + beta3*eT23 - eTt2)/alpha ; vreal Sm3 @@ -1030,4 +1029,6 @@ local_MtC3.store(mask, index2, }); }); +#endif // #ifndef Z4COO_SET_CONSTRAINT_HXX + /* Z4coo_set_constraint.hxx */ diff --git a/Z4coo/wolfram/Z4coo_set_constraint.wl b/Z4coo/wolfram/Z4coo_set_constraint.wl deleted file mode 100644 index 01f89c03..00000000 --- a/Z4coo/wolfram/Z4coo_set_constraint.wl +++ /dev/null @@ -1,76 +0,0 @@ -(* ::Package:: *) - -(* Z4c_set_rhs.wl *) - -(* (c) Liwei Ji, 07/2024 *) - -Needs["xAct`xCoba`", FileNameJoin[{Environment["GENERATO"], "src/Generato.wl" - }]] - -SetPVerbose[False]; - -SetPrintDate[False]; - -SetGridPointIndex[""]; - -SetTempVariableType["vreal"]; - -DefManifold[M3, 3, IndexRange[a, z]]; - -DefChart[cart, M3, {1, 2, 3}, {X[], Y[], Z[]}, ChartColor -> Blue]; - -(* Define Variables *) - -< 1}; (* since we enforced that det(gamt) = 1 *) - (* SetEQNDelayed[detinvgamt[], 1 / Det[Mat] // Simplify]; *) - SetEQNDelayed[invgamt[i_, j_], invMat[[i[[1]], j[[1]]]] // Simplify] -]; - -SetOutputFile[FileNameJoin[{Directory[], "Z4coo_set_constraint.hxx"}]]; - -$MainPrint[] := - Module[{}, - PrintInitializations[{Mode -> "MainOut"}, ConstraintVarlist]; - pr[]; - - pr["noinline([&]() __attribute__((__flatten__, __hot__)) {"]; - pr[" grid.loop_int_device<0, 0, 0, vsize>("]; - pr[" grid.nghostzones, [=] ARITH_DEVICE(const PointDesc &p) ARITH_INLINE {"]; - pr[" const vbool mask = mask_for_loop_tail(p.i, p.imax);"]; - pr[" const GF3D2index index2(layout2, p.I);"]; - pr[" const GF3D5index index5(layout5, p.I);"]; - pr[]; - - PrintListInitializations[TmunuVarlist, "gf_", "index2"]; - PrintListInitializations[EvolVarlist, "tl_", "index5"]; - PrintListInitializations[Drop[dEvolVarlist, -2], "tl_", "index5"]; - PrintListInitializations[Drop[ddEvolVarlist, -2], "tl_", "index5"]; - pr[]; - - PrintInitializations[{Mode -> "MainIn"}, TmunuVarlist]; - PrintInitializations[{Mode -> "MainIn", StorageType -> "Tile"}, - EvolVarlist]; - PrintInitializations[{Mode -> "MainIn", StorageType -> "Tile", TensorType -> "Vect"}, - Drop[dEvolVarlist, -2]]; - PrintInitializations[{Mode -> "MainIn", StorageType -> "Tile", TensorType -> "Smat"}, - Drop[ddEvolVarlist, -2]]; - pr[]; - PrintEquations[{Mode -> "Temp"}, Drop[Drop[IntermediateVarlist, {3}], {-4,-2}]]; - PrintEquations[{Mode -> "Temp"}, Drop[DDVarlist, -1]]; - PrintEquations[{Mode -> "Temp"}, RVarlist]; - PrintEquations[{Mode -> "Temp"}, Drop[MatterVarlist, -2]]; - PrintEquations[{Mode -> "Temp"}, dAtUUVarlist]; - pr[]; - PrintEquations[{Mode -> "Main"}, ConstraintVarlist]; - pr[]; - pr[" });"]; - pr["});"]; - ]; - -Import[FileNameJoin[{Environment["GENERATO"], "codes/CarpetX.wl"}]]; diff --git a/Z4coo/wolfram/Z4coo_set_rhs.hxx b/Z4coo/wolfram/Z4coo_set_rhs.hxx index 4d0fa37c..093ace92 100644 --- a/Z4coo/wolfram/Z4coo_set_rhs.hxx +++ b/Z4coo/wolfram/Z4coo_set_rhs.hxx @@ -1,6 +1,9 @@ /* Z4coo_set_rhs.hxx */ /* Produced with Mathematica */ +#ifndef Z4COO_SET_RHS_HXX +#define Z4COO_SET_RHS_HXX + const GF3D2 &local_dtchi = gf_dtchi; const GF3D2 &local_dtgamt11 = gf_dtgamt(0,0); const GF3D2 &local_dtgamt12 = gf_dtgamt(0,1); @@ -61,11 +64,8 @@ const vreal eTt3 = tmp_eTt(2); const vreal eT11 = tmp_eT(0,0); const vreal eT12 = tmp_eT(0,1); const vreal eT13 = tmp_eT(0,2); -const vreal eT21 = tmp_eT(1,0); const vreal eT22 = tmp_eT(1,1); const vreal eT23 = tmp_eT(1,2); -const vreal eT31 = tmp_eT(2,0); -const vreal eT32 = tmp_eT(2,1); const vreal eT33 = tmp_eT(2,2); const vreal chi = tmp_chi + 1; const vreal gamt11 = tmp_gamt(0,0) + 1; @@ -1208,20 +1208,19 @@ invgam11*R11 + 2*invgam12*R12 + 2*invgam13*R13 + invgam22*R22 + vreal rho = -(Power(beta1,2)*eT11 + beta1*beta2*(eT12 + eT21) + Power(beta2,2)*eT22 + - beta1*beta3*(eT13 + eT31) + beta2*beta3*(eT23 + eT32) + - Power(beta3,2)*eT33 - 2*beta1*eTt1 - 2*beta2*eTt2 - 2*beta3*eTt3 + eTtt)/ - Power(alpha,2) +(Power(beta1,2)*eT11 + Power(beta2,2)*eT22 + 2*beta2*beta3*eT23 + + Power(beta3,2)*eT33 + 2*beta1*(beta2*eT12 + beta3*eT13 - eTt1) - + 2*beta2*eTt2 - 2*beta3*eTt3 + eTtt)/Power(alpha,2) ; vreal Sm1 = -(beta1*eT11 + beta2*eT21 + beta3*eT31 - eTt1)/alpha +(beta1*eT11 + beta2*eT12 + beta3*eT13 - eTt1)/alpha ; vreal Sm2 = -(beta1*eT12 + beta2*eT22 + beta3*eT32 - eTt2)/alpha +(beta1*eT12 + beta2*eT22 + beta3*eT23 - eTt2)/alpha ; vreal Sm3 @@ -1519,4 +1518,6 @@ local_dtbeta3.store(mask, index2, }); }); +#endif // #ifndef Z4COO_SET_RHS_HXX + /* Z4coo_set_rhs.hxx */ diff --git a/Z4coo/wolfram/Z4coo_set_rhs.wl b/Z4coo/wolfram/Z4coo_set_rhs.wl deleted file mode 100644 index cf3ed047..00000000 --- a/Z4coo/wolfram/Z4coo_set_rhs.wl +++ /dev/null @@ -1,75 +0,0 @@ -(* ::Package:: *) - -(* Z4c_set_rhs.wl *) - -(* (c) Liwei Ji, 07/2024 *) - -Needs["xAct`xCoba`", FileNameJoin[{Environment["GENERATO"], "src/Generato.wl" - }]] - -SetPVerbose[False]; - -SetPrintDate[False]; - -SetGridPointIndex[""]; - -SetTempVariableType["vreal"]; - -DefManifold[M3, 3, IndexRange[a, z]]; - -DefChart[cart, M3, {1, 2, 3}, {X[], Y[], Z[]}, ChartColor -> Blue]; - -(* Define Variables *) - -< 1}; (* since we enforced that det(gamt) = 1 *) - (* SetEQNDelayed[detinvgamt[], 1 / Det[Mat] // Simplify]; *) - SetEQNDelayed[invgamt[i_, j_], invMat[[i[[1]], j[[1]]]] // Simplify] -]; - -SetOutputFile[FileNameJoin[{Directory[], "Z4coo_set_rhs.hxx"}]]; - -$MainPrint[] := - Module[{}, - PrintInitializations[{Mode -> "MainOut"}, dtEvolVarlist]; - pr[]; - - pr["noinline([&]() __attribute__((__flatten__, __hot__)) {"]; - pr[" grid.loop_int_device<0, 0, 0, vsize>("]; - pr[" grid.nghostzones, [=] ARITH_DEVICE(const PointDesc &p) ARITH_INLINE {"]; - pr[" const vbool mask = mask_for_loop_tail(p.i, p.imax);"]; - pr[" const GF3D2index index2(layout2, p.I);"]; - pr[" const GF3D5index index5(layout5, p.I);"]; - pr[]; - - PrintListInitializations[TmunuVarlist, "gf_", "index2"]; - PrintListInitializations[EvolVarlist, "tl_", "index5"]; - PrintListInitializations[Drop[dEvolVarlist, {4}], "tl_", "index5"]; - PrintListInitializations[ddEvolVarlist, "tl_", "index5"]; - pr[]; - - PrintInitializations[{Mode -> "MainIn"}, TmunuVarlist]; - PrintInitializations[{Mode -> "MainIn", StorageType -> "Tile"}, - EvolVarlist]; - PrintInitializations[{Mode -> "MainIn", StorageType -> "Tile", TensorType -> "Vect"}, - Drop[dEvolVarlist, {4}]]; - PrintInitializations[{Mode -> "MainIn", StorageType -> "Tile", TensorType -> "Smat"}, - ddEvolVarlist]; - pr[]; - PrintEquations[{Mode -> "Temp"}, IntermediateVarlist]; - PrintEquations[{Mode -> "Temp"}, DDVarlist]; - PrintEquations[{Mode -> "Temp"}, RVarlist]; - PrintEquations[{Mode -> "Temp"}, MatterVarlist]; - pr[]; - PrintEquations[{Mode -> "Main"}, dtEvolVarlist]; - pr[]; - pr[" });"]; - pr["});"]; - ]; - -Import[FileNameJoin[{Environment["GENERATO"], "codes/CarpetX.wl"}]]; diff --git a/Z4coo/wolfram/wl/ADM_rhs.wl b/Z4coo/wolfram/wl/ADM_rhs.wl deleted file mode 100644 index b6c5cc06..00000000 --- a/Z4coo/wolfram/wl/ADM_rhs.wl +++ /dev/null @@ -1,19 +0,0 @@ -(* ::Package:: *) - -(* ADM_rhs.wl *) - -(* (c) Liwei Ji, 07/2024 *) - -(* See arXiv:1212.2901 [gr-qc] *) - -SetEQN[ADMgam[i_, j_], chi[] ^ -1 gamt[i, j]]; - -SetEQN[ADMK[i_, j_], chi[] ^ -1 (exAt[i, j] + 1/3 (exKh[] + 2 Theta[]) gamt[i, j])]; - -SetEQN[ADMalpha[], alpha[]]; - -SetEQN[ADMbeta[i_], beta[i]]; - -SetEQN[ADMdtalpha[], dtalpha[]]; - -SetEQN[ADMdtbeta[i_], dtbeta[i]]; diff --git a/Z4coo/wolfram/wl/ADM_vars.wl b/Z4coo/wolfram/wl/ADM_vars.wl deleted file mode 100644 index 51b343fe..00000000 --- a/Z4coo/wolfram/wl/ADM_vars.wl +++ /dev/null @@ -1,19 +0,0 @@ -(* ::Package:: *) - -(* ADM_vars.wl *) - -(* (c) Liwei Ji, 07/2024 *) - -(* ADM variables *) - -ADMVarlist = - GridTensors[ - {ADMgam[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*SuperscriptBox[\(\[Gamma]\), \((ADM)\)]\)"}, - {ADMK[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*SuperscriptBox[\(K\), \((ADM)\)]\)"}, - {ADMalpha[], PrintAs -> "\!\(\*SuperscriptBox[\(\[Alpha]\), \((ADM)\)]\)"}, - {ADMbeta[i], PrintAs -> "\!\(\*SuperscriptBox[\(\[Beta]\), \((ADM)\)]\)"} - (*, - {ADMdtalpha[], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \\(t\)]\)\!\(\*SuperscriptBox[\(\[Alpha]\), \((ADM)\)]\)"}, - {ADMdtbeta[i], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \\(t\)]\)\!\(\*SuperscriptBox[\(\[Beta]\), \((ADM)\)]\)"} - *) - ]; diff --git a/Z4coo/wolfram/wl/Z4c_rhs.wl b/Z4coo/wolfram/wl/Z4c_rhs.wl deleted file mode 100644 index 76347f86..00000000 --- a/Z4coo/wolfram/wl/Z4c_rhs.wl +++ /dev/null @@ -1,113 +0,0 @@ -(* ::Package:: *) - -(* Z4c_rhs.wl *) - -(* (c) Liwei Ji, 07/2024 *) - -(* See arXiv:1212.2901 [gr-qc] *) - -(****************) - -(* Intermediate *) - -(****************) - -SetEQN[invgam[i_, j_], chi[] invgamt[i, j]]; - -SetEQN[gam[i_, j_], chi[] ^ -1 gamt[i, j]]; - -SetEQN[GtDDD[k_, i_, j_], 1/2 (dgamt[i, j, k] + dgamt[j, k, i] - dgamt[k, i, j])]; - -SetEQN[GtDDU[i_, j_, k_], invgamt[k, l] GtDDD[i, j, -l]]; - -SetEQN[Gt[k_, i_, j_], invgamt[k, l] GtDDD[-l, i, j]]; - -SetEQN[trGtd[i_], invgamt[k, l] Gt[i, -k, -l]]; - -SetEQN[dgam[k_, i_, j_], -chi[] ^ -2 dchi[k] gamt[i, j] + chi[] ^ -1 dgamt[k, i, j]]; - -SetEQN[GamDDD[k_, i_, j_], 1/2 (dgam[i, j, k] + dgam[j, k, i] - dgam[k, i, j])]; - -SetEQN[Gam[k_, i_, j_], invgam[k, l] GamDDD[-l, i, j]]; - -SetEQN[exAtUU[i_, j_], invgamt[i, k] invgamt[j, l] exAt[-k, -l]]; - -SetEQN[tDtDchi[i_, j_], ddchi[i, j] - Gt[k, i, j] dchi[-k]]; - -(*SetEQN[DDalpha[i_, j_], ddalpha[i, j] - Gt[k, i, j] dalpha[-k] + 1/2 chi[] ^ -1 (dchi[i] dalpha[j] + dchi[j] dalpha[i]) - 1/2 gamt[i, j] invgamt[k, l] chi[] ^ -1 dchi[-l] dalpha[-k]];*) - -SetEQN[DDalpha[i_, j_], ddalpha[i, j] - Gam[k, i, j] dalpha[-k]]; - -(* (8) *) - -SetEQN[Rtchi[i_, j_], 1 / (2 chi[]) tDtDchi[i, j] + 1 / (2 chi[]) gamt[i, j] invgamt[k, l] tDtDchi[-k, -l] - 1 / (4 chi[] ^ 2) dchi[i] dchi[j] - 3 / (4 chi[] ^ 2) gamt[i, j] invgamt[k, l] dchi[-k] dchi[-l]]; - -(* (9) *) - -SetEQN[Rt[i_, j_], -(1/2) invgamt[l, m] ddgamt[-l, -m, i, j] + 1/2 (gamt[-k, i] dtrGt[j, k] + gamt[-k, j] dtrGt[i, k]) + 1/2 trGtd[k] (GtDDD[i, j, -k] + GtDDD[j, i, -k]) + ((Gt[k, -l, i] GtDDU[j, -k, l] + Gt[k, -l, j] GtDDU[i, -k, l]) + Gt[k, i, -m] GtDDU[-k, j, m])]; - -(* (10) *) - -SetEQN[R[i_, j_], Rtchi[i, j] + Rt[i, j]]; - -SetEQN[trR[], invgam[k, l] R[-k, -l]]; - -SetEQN[rho[], alpha[] ^ -2 (eTtt[] - 2 beta[j] eTt[-j] + beta[i] beta[j] eT[-i, -j])]; - -SetEQN[Sm[i_], -alpha[] ^ -1 (eTt[i] - beta[k] eT[-k, i])]; - -SetEQN[Ss[i_, j_], eT[i, j]]; - -SetEQN[trSs[], invgam[k, l] Ss[-k, -l]]; - -SetEQN[trdexAtUU[i_], -invgamt[i, l] exAtUU[j, m] dgamt[-j, -l, -m] - invgamt[j, l] exAtUU[i, m] dgamt[-j, -l, -m] + invgamt[i, l] invgamt[j, m] dexAt[-j, -l, -m]]; - -(* (13) *) - -SetEQN[ZtC[i_], (trGt[i] - trGtd[i]) / 2]; - -(* (14) *) - -SetEQN[HC[], trR[] + exAt[-k, -l] exAtUU[k, l] - 2/3 (exKh[] + 2 Theta[]) ^ 2 - 16 cpi rho[]]; - -(* (15) *) - -SetEQN[MtC[i_], trdexAtUU[i] + Gt[i, -j, -k] exAtUU[j, k] - 2/3 invgamt[i, j] (dexKh[-j] + 2 dTheta[-j]) - 2/3 exAtUU[i, j] chi[] ^ -1 dchi[-j] - 8 cpi invgamt[i, j] Sm[-j]]; - -(*******) - -(* EOM *) - -(*******) - -(* (1) *) - -SetEQN[dtchi[], 2/3 chi[] (alpha[] (exKh[] + 2 Theta[]) - dbeta[-i, i])]; - -(* (2) *) - -SetEQN[dtgamt[i_, j_], -2 alpha[] exAt[i, j] + (gamt[-k, i] dbeta[j, k] + gamt[-k, j] dbeta[i, k]) - 2/3 gamt[i, j] dbeta[-k, k]]; - -(* (3) *) - -SetEQN[dtexKh[], -invgam[k, l] DDalpha[-k, -l] + alpha[] (exAt[-k, -l] exAtUU[k, l] + 1/3 (exKh[] + 2 Theta[]) ^ 2) + 4 cpi alpha[] (trSs[] + rho[]) + alpha[] ckappa1 (1 - ckappa2) Theta[]]; - -(* (4) *) - -SetEQN[dtexAt[i_, j_], chi[] ((-DDalpha[i, j] + alpha[] (R[i, j] - 8 cpi Ss[i, j])) - 1/3 gam[i, j] invgam[k, l] (-DDalpha[-k, -l] + alpha[] (R[-k, -l] - 8 cpi Ss[-k, -l]))) + alpha[] ((exKh[] + 2 Theta[]) exAt[i, j] - 2 invgamt[k, l] exAt[-k, i] exAt[-l, j]) + (exAt[-k, i] dbeta[j, k] + exAt[-k, j] dbeta[i, k]) - 2/3 exAt[i, j] dbeta[-k, k]]; - -(* (5) *) - -SetEQN[dttrGt[i_], -2 exAtUU[i, j] dalpha[-j] + 2 alpha[] (Gt[i, -j, -k] exAtUU[j, k] - 3/2 exAtUU[i, j] dchi[-j] / chi[] - 1/3 invgamt[i, j] (2 dexKh[-j] + dTheta[-j]) - 8 cpi invgamt[i, j] Sm[-j]) + invgamt[j, k] ddbeta[-j, -k, i] + 1/3 invgamt[i, j] ddbeta[-j, -k, k] - trGtd[j] dbeta[-j, i] + 2/3 trGtd[i] dbeta[-j, j] - 2 alpha[] ckappa1 (trGt[i] - trGtd[i])]; - -(* (6) *) - -SetEQN[dtTheta[], 1/2 alpha[] (trR[] - exAt[-k, -l] exAtUU[k, l] + 2/3 (exKh[] + 2 Theta[]) ^ 2) - alpha[] (8 cpi rho[] + ckappa1 (2 + ckappa2) Theta[])]; - -(* (11) *) - -SetEQN[dtalpha[], -alpha[] cmuL exKh[]]; - -(* (12) *) - -SetEQN[dtbeta[i_], cmuS trGt[i] - ceta beta[i]]; diff --git a/Z4coo/wolfram/wl/Z4c_vars.wl b/Z4coo/wolfram/wl/Z4c_vars.wl deleted file mode 100644 index 240cb4f4..00000000 --- a/Z4coo/wolfram/wl/Z4c_vars.wl +++ /dev/null @@ -1,144 +0,0 @@ -(* ::Package:: *) - -(* Z4c_vars.wl *) - -(* (c) Liwei Ji, 07/2024 *) - -(***********************) - -(* Evolution Variables *) - -(***********************) - -dtEvolVarlist = - GridTensors[ - {dtchi[], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\[Chi]"}, - {dtgamt[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"}, - {dtexKh[], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\!\(\*OverscriptBox[\(K\), \(^\)]\)"}, - {dtexAt[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\!\(\*OverscriptBox[\(A\), \(~\)]\)"}, - {dttrGt[i], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"}, - {dtTheta[], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\[CapitalTheta]"}, - {dtalpha[], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\[Alpha]"}, - {dtbeta[i], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\[Beta]"} - ]; - -EvolVarlist = - GridTensors[ - {chi[], PrintAs -> "\[Chi]"}, - {gamt[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"}, - {exKh[], PrintAs -> "\!\(\*OverscriptBox[\(K\), \(^\)]\)"}, - {exAt[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(A\), \(~\)]\)"}, - {trGt[i], PrintAs -> "\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"}, - {Theta[], PrintAs -> "\[CapitalTheta]"}, {alpha[], PrintAs -> "\[Alpha]"}, - {beta[i], PrintAs -> "\[Beta]"} - ]; - -(*************************) - -(* Other Input Variables *) - -(*************************) - -dEvolVarlist = - GridTensors[ - {dchi[-k], PrintAs -> "\[PartialD]\[Chi]"}, - {dgamt[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"}, - {dexKh[-k], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(K\), \(^\)]\)"}, - {dexAt[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(A\), \(~\)]\)"}, - {dtrGt[-k, i], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"}, - {dTheta[-k], PrintAs -> "\[PartialD]\[CapitalTheta]"}, - {dalpha[-k], PrintAs -> "\[PartialD]\[Alpha]"}, - {dbeta[-k, i], PrintAs -> "\[PartialD]\[Beta]"} - ]; - -ddEvolVarlist = - GridTensors[ - {ddchi[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[PartialD]\[Chi]"}, - {ddgamt[-l, -m, -i, -j], GenSet[Cycles[{1, 2}], Cycles[{3, 4}]], PrintAs -> "\[PartialD]\[PartialD]\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"}, - {ddalpha[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[PartialD]\[Alpha]"}, - {ddbeta[-i, -j, k], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[PartialD]\[Beta]"} - ]; - -TmunuVarlist = - GridTensors[ - {eTtt[], PrintAs -> "\!\(\*SubscriptBox[\(T\), \(tt\)]\)"}, - {eTt[-i], PrintAs -> "\!\(\*SubscriptBox[\(T\), \(t\)]\)"}, - {eT[-i, -j], PrintAs -> "T"} - ]; - -(**************************) - -(* Intermediate Variables *) - -(**************************) - -IntermediateVarlist = - TempTensors[ - (* {detinvgamt[], PrintAs -> "1/\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"}, *) - {invgamt[i, j], Symmetric[{i, j}], PrintAs -> "\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"}, - {invgam[i, j], Symmetric[{i, j}], PrintAs -> "\[Gamma]"}, - {gam[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[Gamma]"}, - {GtDDD[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"}, - {GtDDU[-k, -i, j], PrintAs -> "\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"}, - {Gt[k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"}, - {trGtd[i], PrintAs -> "(\!\(\*SubscriptBox[OverscriptBox[\(\[CapitalGamma]\), \(~\)], \(d\)]\))"}, - {dgam[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[Gamma]"}, - {GamDDD[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[CapitalGamma]"}, - {Gam[k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[CapitalGamma]"}, - {exAtUU[i, j], Symmetric[{i, j}], PrintAs -> "\!\(\*OverscriptBox[\(A\), \(~\)]\)"} - ]; - -DDVarlist = - TempTensors[ - {tDtDchi[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(D\), \(~\)]\)\!\(\*OverscriptBox[\(D\), \(~\)]\)\[Chi]"}, - {DDalpha[-i, -j], Symmetric[{-i, -j}], PrintAs -> "DD\[Alpha]"} - ]; - -RVarlist = - TempTensors[ - {Rtchi[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*SuperscriptBox[OverscriptBox[\(R\), \(~\)], \(\[Chi]\)]\)"}, - {Rt[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(R\), \(~\)]\)"}, - {R[-i, -j], Symmetric[{-i, -j}]}, {trR[], PrintAs -> "R"} - ]; - -(* Matter *) - -MatterVarlist = - TempTensors[ - {rho[], PrintAs -> "\[Rho]"}, - {Sm[-i], PrintAs -> "S"}, - {Ss[-i, -j], Symmetric[{-i, -j}], PrintAs -> "S"}, - {trSs[], PrintAs -> "S"} - ]; - -(* Constraints *) - -dAtUUVarlist = - TempTensors[ - {trdexAtUU[i], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(A\), \(~\)]\)"} - ]; - -ConstraintVarlist = - GridTensors[ - {ZtC[i], PrintAs -> "\!\(\*OverscriptBox[\(Z\), \(~\)]\)"}, - {HC[], PrintAs -> "H"}, - {MtC[i], PrintAs -> "\!\(\*OverscriptBox[\(M\), \(~\)]\)"} - ]; - -(************) - -(* Constant *) - -(************) - -DefConstantSymbol[cpi, PrintAs -> "\[Pi]"]; - -DefConstantSymbol[ckappa1, PrintAs -> "\!\(\*SubscriptBox[\(\[Kappa]\), \(1\)]\)"]; - -DefConstantSymbol[ckappa2, PrintAs -> "\!\(\*SubscriptBox[\(\[Kappa]\), \(2\)]\)"]; - -DefConstantSymbol[cmuL, PrintAs -> "\!\(\*SubscriptBox[\(\[Mu]\), \(L\)]\)"]; - -DefConstantSymbol[cmuS, PrintAs -> "\!\(\*SubscriptBox[\(\[Mu]\), \(S\)]\)"]; - -DefConstantSymbol[ceta, PrintAs -> "\[Eta]"]; diff --git a/Z4coo/wolfram/wl/Z4c_vars_check.wl b/Z4coo/wolfram/wl/Z4c_vars_check.wl deleted file mode 100644 index cfb42ff3..00000000 --- a/Z4coo/wolfram/wl/Z4c_vars_check.wl +++ /dev/null @@ -1,144 +0,0 @@ -(* ::Package:: *) - -(* Z4c_vars.wl *) - -(* (c) Liwei Ji, 07/2024 *) - -(***********************) - -(* Evolution Variables *) - -(***********************) - -dtEvolVarlist = - DefTensors[ - {dtchi[], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\[Chi]"}, - {dtgamt[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"}, - {dtexKh[], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\!\(\*OverscriptBox[\(K\), \(^\)]\)"}, - {dtexAt[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\!\(\*OverscriptBox[\(A\), \(~\)]\)"}, - {dttrGt[i], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"}, - {dtTheta[], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\[CapitalTheta]"}, - {dtalpha[], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\[Alpha]"}, - {dtbeta[i], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)\[Beta]"} - ]; - -EvolVarlist = - DefTensors[ - {chi[], PrintAs -> "\[Chi]"}, - {gamt[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"}, - {exKh[], PrintAs -> "\!\(\*OverscriptBox[\(K\), \(^\)]\)"}, - {exAt[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(A\), \(~\)]\)"}, - {trGt[i], PrintAs -> "\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"}, - {Theta[], PrintAs -> "\[CapitalTheta]"}, {alpha[], PrintAs -> "\[Alpha]"}, - {beta[i], PrintAs -> "\[Beta]"} - ]; - -(*************************) - -(* Other Input Variables *) - -(*************************) - -dEvolVarlist = - DefTensors[ - {dchi[-k], PrintAs -> "\[PartialD]\[Chi]"}, - {dgamt[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"}, - {dexKh[-k], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(K\), \(^\)]\)"}, - {dexAt[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(A\), \(~\)]\)"}, - {dtrGt[-k, i], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"}, - {dTheta[-k], PrintAs -> "\[PartialD]\[CapitalTheta]"}, - {dalpha[-k], PrintAs -> "\[PartialD]\[Alpha]"}, - {dbeta[-k, i], PrintAs -> "\[PartialD]\[Beta]"} - ]; - -ddEvolVarlist = - DefTensors[ - {ddchi[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[PartialD]\[Chi]"}, - {ddgamt[-l, -m, -i, -j], GenSet[Cycles[{1, 2}], Cycles[{3, 4}]], PrintAs -> "\[PartialD]\[PartialD]\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"}, - {ddalpha[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[PartialD]\[Alpha]"}, - {ddbeta[-i, -j, k], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[PartialD]\[Beta]"} - ]; - -TmunuVarlist = - DefTensors[ - {eTtt[], PrintAs -> "\!\(\*SubscriptBox[\(T\), \(tt\)]\)"}, - {eTt[-i], PrintAs -> "\!\(\*SubscriptBox[\(T\), \(t\)]\)"}, - {eT[-i, -j], PrintAs -> "T"} - ]; - -(**************************) - -(* Intermediate Variables *) - -(**************************) - -IntermediateVarlist = - DefTensors[ - {detinvgamt[], PrintAs -> "1/\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"}, - {invgamt[i, j], Symmetric[{i, j}], PrintAs -> "\!\(\*OverscriptBox[\(\[Gamma]\), \(~\)]\)"}, - {invgam[i, j], Symmetric[{i, j}], PrintAs -> "\[Gamma]"}, - {gam[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[Gamma]"}, - {GtDDD[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"}, - {GtDDU[-k, -i, j], PrintAs -> "\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"}, - {Gt[k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(\[CapitalGamma]\), \(~\)]\)"}, - {trGtd[i], PrintAs -> "(\!\(\*SubscriptBox[OverscriptBox[\(\[CapitalGamma]\), \(~\)], \(d\)]\))"}, - {dgam[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[Gamma]"}, - {GamDDD[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[CapitalGamma]"}, - {Gam[k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[CapitalGamma]"}, - {exAtUU[i, j], Symmetric[{i, j}], PrintAs -> "\!\(\*OverscriptBox[\(A\), \(~\)]\)"} - ]; - -DDVarlist = - DefTensors[ - {tDtDchi[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(D\), \(~\)]\)\!\(\*OverscriptBox[\(D\), \(~\)]\)\[Chi]"}, - {DDalpha[-i, -j], Symmetric[{-i, -j}], PrintAs -> "DD\[Alpha]"} - ]; - -RVarlist = - DefTensors[ - {Rtchi[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*SuperscriptBox[OverscriptBox[\(R\), \(~\)], \(\[Chi]\)]\)"}, - {Rt[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(R\), \(~\)]\)"}, - {R[-i, -j], Symmetric[{-i, -j}]}, {trR[], PrintAs -> "R"} - ]; - -(* Matter *) - -MatterVarlist = - DefTensors[ - {rho[], PrintAs -> "\[Rho]"}, - {Sm[-i], PrintAs -> "S"}, - {Ss[-i, -j], Symmetric[{-i, -j}], PrintAs -> "S"}, - {trSs[], PrintAs -> "S"} - ]; - -(* Constraints *) - -dAtUUVarlist = - DefTensors[ - {trdexAtUU[i], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(A\), \(~\)]\)"} - ]; - -ConstraintVarlist = - DefTensors[ - {ZtC[i], PrintAs -> "\!\(\*OverscriptBox[\(Z\), \(~\)]\)"}, - {HC[], PrintAs -> "H"}, - {MtC[i], PrintAs -> "\!\(\*OverscriptBox[\(M\), \(~\)]\)"} - ]; - -(************) - -(* Constant *) - -(************) - -DefConstantSymbol[cpi, PrintAs -> "\[Pi]"]; - -DefConstantSymbol[ckappa1, PrintAs -> "\!\(\*SubscriptBox[\(\[Kappa]\), \(1\)]\)"]; - -DefConstantSymbol[ckappa2, PrintAs -> "\!\(\*SubscriptBox[\(\[Kappa]\), \(2\)]\)"]; - -DefConstantSymbol[cmuL, PrintAs -> "\!\(\*SubscriptBox[\(\[Mu]\), \(L\)]\)"]; - -DefConstantSymbol[cmuS, PrintAs -> "\!\(\*SubscriptBox[\(\[Mu]\), \(S\)]\)"]; - -DefConstantSymbol[ceta, PrintAs -> "\[Eta]"];