Z4co: formatting wl files manually

EinsteinToolkit · Jul 5, 2024 · bc35853 · bc35853
1 parent 66d5ec7
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diff --git a/Z4co/wolfram/wl/Z4c_rhs.wl b/Z4co/wolfram/wl/Z4c_rhs.wl
@@ -16,8 +16,7 @@ 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[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]];
 
@@ -29,56 +28,43 @@ 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] - 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]];
 
 (* (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]];
+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])];
+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[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]];
+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[]];
+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]];
+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]];
 
 (*******)
 
@@ -88,42 +74,27 @@ SetEQN[MtC[i_], trdexAtUU[i] + Gt[i, -j, -k] exAtUU[j, k] - 2/3 invgamt[
 
 (* (1) *)
 
-SetEQN[dtchi[], 2/3 chi[] (alpha[] (exKh[] + 2 Theta[]) - dbeta[-i, i])
-  ];
+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]];
+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[]];
+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]];
+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])];
+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[])];
+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) *)
 

diff --git a/Z4co/wolfram/wl/Z4c_vars.wl b/Z4co/wolfram/wl/Z4c_vars.wl
@@ -10,90 +10,117 @@
 
 (***********************)
 
-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]"}];
+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"}];
+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]\), \(~\)], \(d\)]\))"
-  }, {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"}];
+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]\), \(~\)], \(d\)]\))"},
+    {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"}];
+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[\(A\), \(~\)]\)"
-  }];
+dAtUUVarlist =
+  TempTensors[
+    {trdexAtUU[i], PrintAs -> "\[PartialD]\!\(\*OverscriptBox[\(A\), \(~\)]\)"}
+  ];
 
-ConstraintVarlist = GridTensors[{ZtC[i], PrintAs -> "\!\(\*OverscriptBox[\(Z\), \(~\)]\)"
-  }, {HC[], PrintAs -> "H"}, {MtC[i], PrintAs -> "\!\(\*OverscriptBox[\(M\), \(~\)]\)"
-  }];
+ConstraintVarlist =
+  GridTensors[
+    {ZtC[i], PrintAs -> "\!\(\*OverscriptBox[\(Z\), \(~\)]\)"},
+    {HC[], PrintAs -> "H"},
+    {MtC[i], PrintAs -> "\!\(\*OverscriptBox[\(M\), \(~\)]\)"}
+  ];
 
 (************)
 
@@ -103,16 +130,12 @@ ConstraintVarlist = GridTensors[{ZtC[i], PrintAs -> "\!\(\*OverscriptBox[\(Z\),
 
 DefConstantSymbol[cpi, PrintAs -> "\[Pi]"];
 
-DefConstantSymbol[ckappa1, PrintAs -> "\!\(\*SubscriptBox[\(\[Kappa]\), \(1\)]\)"
-  ];
+DefConstantSymbol[ckappa1, PrintAs -> "\!\(\*SubscriptBox[\(\[Kappa]\), \(1\)]\)"];
 
-DefConstantSymbol[ckappa2, PrintAs -> "\!\(\*SubscriptBox[\(\[Kappa]\), \(2\)]\)"
-  ];
+DefConstantSymbol[ckappa2, PrintAs -> "\!\(\*SubscriptBox[\(\[Kappa]\), \(2\)]\)"];
 
-DefConstantSymbol[cmuL, PrintAs -> "\!\(\*SubscriptBox[\(\[Mu]\), \(L\)]\)"
-  ];
+DefConstantSymbol[cmuL, PrintAs -> "\!\(\*SubscriptBox[\(\[Mu]\), \(L\)]\)"];
 
-DefConstantSymbol[cmuS, PrintAs -> "\!\(\*SubscriptBox[\(\[Mu]\), \(S\)]\)"
-  ];
+DefConstantSymbol[cmuS, PrintAs -> "\!\(\*SubscriptBox[\(\[Mu]\), \(S\)]\)"];
 
 DefConstantSymbol[ceta, PrintAs -> "\[Eta]"];