diff --git a/Z4cow/wolfram/wl/Z4c_vars_check.wl b/Z4cow/wolfram/wl/Z4c_vars_check.wl
new file mode 100644
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+++ b/Z4cow/wolfram/wl/Z4c_vars_check.wl
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+(* ::Package:: *)
+
+(* Z4c_vars.wl *)
+
+(* (c) Liwei Ji, 07/2024 *)
+
+(***********************)
+
+(* Evolution Variables *)
+
+(***********************)
+
+dtEvolVarlist =
+  DefTensors[
+    {dtW[], PrintAs -> "\!\(\*SubscriptBox[\(\[PartialD]\), \(t\)]\)W"},
+    {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[
+    {W[], PrintAs -> "W"},
+    {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[
+    {dW[-k], PrintAs -> "\[PartialD]W"},
+    {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[
+    {ddW[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[PartialD]W"},
+    {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], Symmetric[{-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[
+    {tDtDW[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*OverscriptBox[\(D\), \(~\)]\)\!\(\*OverscriptBox[\(D\), \(~\)]\)W"},
+    {DDalpha[-i, -j], Symmetric[{-i, -j}], PrintAs -> "DD\[Alpha]"}
+  ];
+
+RVarlist =
+  DefTensors[
+    {RtW[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*SuperscriptBox[OverscriptBox[\(R\), \(~\)], \(W\)]\)"},
+    {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]"];