Z4co: add Z4c_vars_check.wl

Z4co/wolfram/wl/Z4c_vars_check.wl

@@ -0,0 +1,117 @@
+(* ::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]\), \(~\)], \(d\)]\))"
+  }, {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]"];