From 70949f47650e5836b04110eaac7eeed4edb1326d Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Fri, 15 Nov 2024 12:24:44 -0500 Subject: [PATCH 01/37] ADMconstraints: add admconstraints.cxx --- ADMconstraints/src/admconstraints.cxx | 14 ++++++++++++++ 1 file changed, 14 insertions(+) create mode 100644 ADMconstraints/src/admconstraints.cxx diff --git a/ADMconstraints/src/admconstraints.cxx b/ADMconstraints/src/admconstraints.cxx new file mode 100644 index 00000000..586bc73a --- /dev/null +++ b/ADMconstraints/src/admconstraints.cxx @@ -0,0 +1,14 @@ +#include +#include +#include + +namespace ADMconstraints { +using namespace Arith; +using namespace Loop; + +extern "C" void ADMconstraints(CCTK_ARGUMENTS) { + DECLARE_CCTK_ARGUMENTSX_ADMconstraints; + DECLARE_CCTK_PARAMETERS; +} + +} // namespace ADMconstraints From a29c293ad5e1904568aed110358a582ae390216d Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Fri, 15 Nov 2024 15:35:20 -0500 Subject: [PATCH 02/37] ADMconstraints: add ADM_vars.wl --- ADMconstraints/wolfram/wl/ADM_vars.wl | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) create mode 100644 ADMconstraints/wolfram/wl/ADM_vars.wl diff --git a/ADMconstraints/wolfram/wl/ADM_vars.wl b/ADMconstraints/wolfram/wl/ADM_vars.wl new file mode 100644 index 00000000..51b343fe --- /dev/null +++ b/ADMconstraints/wolfram/wl/ADM_vars.wl @@ -0,0 +1,19 @@ +(* ::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]\), \((ADM)\)]\)"} + *) + ]; From 73559430615a4af21056d504dad96f058d25d5eb Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Sun, 17 Nov 2024 20:30:30 -0500 Subject: [PATCH 03/37] ADMconstraints: add ADM_rhs.wl --- ADMconstraints/wolfram/wl/ADM_rhs.wl | 73 ++++++++++++++++++++++++++++ 1 file changed, 73 insertions(+) create mode 100644 ADMconstraints/wolfram/wl/ADM_rhs.wl diff --git a/ADMconstraints/wolfram/wl/ADM_rhs.wl b/ADMconstraints/wolfram/wl/ADM_rhs.wl new file mode 100644 index 00000000..920d8a8f --- /dev/null +++ b/ADMconstraints/wolfram/wl/ADM_rhs.wl @@ -0,0 +1,73 @@ +(* ::Package:: *) + +(* Z4c_rhs.wl *) + +(* (c) Liwei Ji, 07/2024 *) + +(* See arXiv:1212.2901 [gr-qc] *) + +(****************) + +(* Intermediate *) + +(****************) + +SetEQN[dlnW[i_], W[] ^ -1 dW[i]]; + +SetEQN[invgam[i_, j_], W[] ^ 2 invgamt[i, j]]; + +SetEQN[gam[i_, j_], W[] ^ -2 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_], W[] ^ -2 (-2 dlnW[k] gamt[i, j] + 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[tDtDW[i_, j_], ddW[i, j] - Gt[k, i, j] dW[-k]]; + +SetEQN[DDalpha[i_, j_], ddalpha[i, j] - Gam[k, i, j] dalpha[-k]]; + +(* (8) *) + +SetEQN[RtW[i_, j_], 1 / W[] tDtDW[i, j] + 1 / W[] gamt[i, j] invgamt[k, l] tDtDW[-k, -l] - 2 gamt[i, j] invgamt[k, l] dlnW[-k] dlnW[-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_], RtW[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]]; + +(***************) + +(* Constraints *) + +(***************) + +SetEQN[HC[], trR[] - exK[-k, -l] exKUU[k, l] + trexK[] ^ 2 - 16 cpi rho[]]; + +SetEQN[MtC[i_], trdexAtUU[i] + Gt[i, -j, -k] exAtUU[j, k] - 2/3 invgamt[i, j] (dexKh[-j] + 2 dTheta[-j]) - 3 exAtUU[i, j] dlnW[-j] - 8 cpi invgamt[i, j] Sm[-j]]; From d593f56bda019b9d982e55446f875dc38be3a9c0 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Sun, 17 Nov 2024 21:02:51 -0500 Subject: [PATCH 04/37] ADMconstraints: add type_in_rhs.nb --- ADMconstraints/wolfram/wl/type_in_rhs.nb | 1481 ++++++++++++++++++++++ 1 file changed, 1481 insertions(+) create mode 100644 ADMconstraints/wolfram/wl/type_in_rhs.nb diff --git a/ADMconstraints/wolfram/wl/type_in_rhs.nb b/ADMconstraints/wolfram/wl/type_in_rhs.nb new file mode 100644 index 00000000..8f3463f3 --- /dev/null +++ b/ADMconstraints/wolfram/wl/type_in_rhs.nb @@ -0,0 +1,1481 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 14.0' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 61752, 1473] +NotebookOptionsPosition[ 54971, 1362] +NotebookOutlinePosition[ 55364, 1378] +CellTagsIndexPosition[ 55321, 1375] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ +Cell[BoxData[ + RowBox[{"Needs", "[", + RowBox[{"\"\\"", ",", + RowBox[{"FileNameJoin", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"Environment", "[", "\"\\"", "]"}], ",", + "\"\\""}], "}"}], + "]"}]}], "]"}]], "Input", + InitializationCell->True, + CellChangeTimes->{{3.9287793106508217`*^9, 3.928779332282189*^9}, { + 3.928779364042645*^9, 3.928779365849419*^9}}, + CellLabel->"In[1]:=",ExpressionUUID->"9857cbce-1237-4124-83ba-143c7adb15bb"], + +Cell[CellGroupData[{ + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882755363988*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"2d413a8c-afde-4f94-995b-ecb6c78e0d0e"], + +Cell[BoxData[ + InterpretationBox[ + RowBox[{"\<\"Package xAct`xPerm` version \"\>", + "\[InvisibleSpace]", "\<\"1.2.3\"\>", "\[InvisibleSpace]", "\<\", \"\>", + "\[InvisibleSpace]", + RowBox[{"{", + RowBox[{"2015", ",", "8", ",", "23"}], "}"}]}], + SequenceForm["Package xAct`xPerm` version ", "1.2.3", ", ", {2015, 8, 23}], + + Editable->False]], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882755367536*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"5063455d-0819-4426-a7cd-a936ec5a18d3"], + +Cell[BoxData["\<\"CopyRight (C) 2003-2020, Jose M. Martin-Garcia, under the \ +General Public License.\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882755369288*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"b2130651-b020-4f0d-b414-aecb07c8bb51"], + +Cell[BoxData["\<\"Connecting to external mac executable...\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.9408827554485807`*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"21efd890-ca3e-4e48-abfc-2557ed72d15b"], + +Cell[BoxData["\<\"Connection established.\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882755559328*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"443f8edf-6aeb-4b63-bbeb-6392d370114a"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882755562408*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"19b61223-15f8-445c-87a7-05366f0cd520"], + +Cell[BoxData[ + InterpretationBox[ + RowBox[{"\<\"Package xAct`xTensor` version \"\>", + "\[InvisibleSpace]", "\<\"1.2.0\"\>", "\[InvisibleSpace]", "\<\", \"\>", + "\[InvisibleSpace]", + RowBox[{"{", + RowBox[{"2021", ",", "10", ",", "17"}], "}"}]}], + SequenceForm[ + "Package xAct`xTensor` version ", "1.2.0", ", ", {2021, 10, 17}], + Editable->False]], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882755563285*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"98a6bade-745f-40c5-b829-851f4886cc64"], + +Cell[BoxData["\<\"CopyRight (C) 2002-2021, Jose M. Martin-Garcia, under the \ +General Public License.\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.9408827555640182`*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"9c6b1c40-abba-4c22-9ce5-fd0ba270ce6f"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882755578768*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"4268e72f-8cd6-4e23-94b7-639cef899a6b"], + +Cell[BoxData["\<\"These packages come with ABSOLUTELY NO WARRANTY; for \ +details type Disclaimer[]. This is free software, and you are welcome to \ +redistribute it under certain conditions. See the General Public License for \ +details.\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.94088275557968*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"440fa9ee-00bc-4842-9415-8118f94d2fbe"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882755580574*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"1661913c-3e50-4257-a01b-4ea5f1e088ed"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882755763043*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"f20e3e8c-53f4-4d6f-b58c-a1038625751e"], + +Cell[BoxData[ + InterpretationBox[ + RowBox[{"\<\"Package xAct`xCoba` version \"\>", + "\[InvisibleSpace]", "\<\"0.8.6\"\>", "\[InvisibleSpace]", "\<\", \"\>", + "\[InvisibleSpace]", + RowBox[{"{", + RowBox[{"2021", ",", "2", ",", "28"}], "}"}]}], + SequenceForm["Package xAct`xCoba` version ", "0.8.6", ", ", {2021, 2, 28}], + + Editable->False]], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882755763953*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"fb9a748e-d6d4-417b-bf17-777aba62c9f0"], + +Cell[BoxData["\<\"CopyRight (C) 2005-2021, David Yllanes and Jose M. \ +Martin-Garcia, under the General Public License.\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.9408827557647543`*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"7a9a155b-7934-41fe-98de-c5e719313a9d"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.9408827557833977`*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"b23d5798-2957-4ac0-a5d9-b540b832f678"], + +Cell[BoxData["\<\"These packages come with ABSOLUTELY NO WARRANTY; for \ +details type Disclaimer[]. This is free software, and you are welcome to \ +redistribute it under certain conditions. See the General Public License for \ +details.\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.94088275578448*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"0fac0347-f8f8-4061-b0ce-dca9ca5a657b"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882755785578*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"87433911-a72e-42c5-901f-d6d4c55f3e5c"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882756921711*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"7df0469d-be51-40b1-b138-7c20ec4f0ea3"], + +Cell[BoxData["\<\"Package Generato`Basic`, {2024, 1, 11}\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882756922667*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"bdf91799-7d12-4aa6-b728-654417a43d7c"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882756923511*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"1f48e0da-b53c-4634-928d-31dc80e81f67"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882756924354*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"d2f15395-4e3f-4bc7-97c5-57afa904824f"], + +Cell[BoxData["\<\"Package Generato`ParseMode`, {2024, 7, 06}\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882756925179*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"c487e186-0b38-4a9d-8de5-b0e1219da427"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.9408827569260073`*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"f07dd22b-7ecf-4e2f-9c19-c3839154085b"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.9408827569268427`*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"14f387a5-5f53-42c4-a285-efbb64f0713e"], + +Cell[BoxData["\<\"Package Generato`Component`, {2024, 1, 11}\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882756927662*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"71ad03b8-4a27-442d-9c9c-62cee9dc5e26"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.9408827569284887`*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"5f6aa3c6-7bab-4969-abc2-3edc76e474bc"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.9408827569293137`*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"250082e4-2673-4abb-848c-e4dfe11295fa"], + +Cell[BoxData["\<\"Package Generato`Varlist`, {2024, 1, 11}\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.9408827569301243`*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"6d4f5338-4c2e-4237-9c39-6d3d5abb6237"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882756930952*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"46921bd2-d6fe-4a16-b844-a67fbeb98326"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882756931789*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"98432958-fdc5-4b68-bdaa-fa9084fb5d85"], + +Cell[BoxData["\<\"Package Generato`Interface`, {2024, 1, 11}\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.9408827569325647`*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"51ee7a70-3f39-42f5-b499-f8bb8b7bfcd9"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882756933343*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"c6532e3b-c63e-4993-86dd-c058b2b84425"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882756934122*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"dd71a352-e2b7-4f91-947d-746836026c60"], + +Cell[BoxData["\<\"Package Generato`Derivation`, {2024, 1, 18}\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.9408827569349413`*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"c87e12a6-b74f-4713-8e6c-4c4c826d5a49"], + +Cell[BoxData["\<\"------------------------------------------------------------\ +\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.940882756935684*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"edd22973-4785-4732-a954-d69990b4757b"], + +Cell[BoxData["\<\"\"\>"], "Print", + CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, + 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, + 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, + 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, + 3.928792872096545*^9, 3.928792972522664*^9, 3.92879477211884*^9, + 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, + 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, + 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, + 3.9408827569363823`*^9}, + CellLabel-> + "During evaluation of \ +In[1]:=",ExpressionUUID->"ca3387bf-41e7-4600-a4bd-e839cfb8aa92"] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Variable List", "Section", + Editable->False, + CellChangeTimes->{{3.9289221456380796`*^9, 3.928922148281581*^9}, { + 3.928922253905546*^9, + 3.928922256640169*^9}},ExpressionUUID->"d93e9e9c-e043-49bf-adc4-\ +613bb015a823"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"DefManifold", "[", + RowBox[{"M3", ",", "3", ",", + RowBox[{"IndexRange", "[", + RowBox[{"a", ",", "z"}], "]"}]}], "]"}], ";"}]], "Input", + Editable->False, + InitializationCell->True, + CellChangeTimes->{{3.928779387620249*^9, 3.9287794127533712`*^9}}, + CellLabel->"In[2]:=",ExpressionUUID->"dc88cf1b-3b54-44ff-b471-d7efa31651a2"], + +Cell[CellGroupData[{ + +Cell["Input", "Subsection", + Editable->False, + CellChangeTimes->{{3.928786604353549*^9, 3.9287866060181503`*^9}, { + 3.9288194877806473`*^9, + 3.928819488701147*^9}},ExpressionUUID->"8f6e447f-5ad1-4983-a220-\ +4a62c32eb45e"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"DefTensors", "[", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"ADMgam", "[", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], ",", + RowBox[{"Symmetric", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "}"}], "]"}], ",", + RowBox[{ + "PrintAs", "->", + "\"\<\\!\\(\\*SuperscriptBox[\\(\[Gamma]\\), \\((ADM)\\)]\\)\>\""}]}], + "}"}], ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"ADMK", "[", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], ",", + RowBox[{"Symmetric", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "}"}], "]"}], ",", + RowBox[{ + "PrintAs", "->", + "\"\<\\!\\(\\*SuperscriptBox[\\(K\\), \\((ADM)\\)]\\)\>\""}]}], "}"}], + ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"ADMalpha", "[", "]"}], ",", + RowBox[{ + "PrintAs", "->", + "\"\<\\!\\(\\*SuperscriptBox[\\(\[Alpha]\\), \\((ADM)\\)]\\)\>\""}]}], + "}"}], ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"ADMbeta", "[", "i", "]"}], ",", + RowBox[{ + "PrintAs", "->", + "\"\<\\!\\(\\*SuperscriptBox[\\(\[Beta]\\), \\((ADM)\\)]\\)\>\""}]}], + "}"}]}], "\[IndentingNewLine]", "]"}], ";"}]], "Input", + Editable->False, + InitializationCell->True, + CellChangeTimes->{{3.940882996300611*^9, 3.940883045177896*^9}}, + CellLabel->"In[4]:=",ExpressionUUID->"4879eb5d-4927-4d70-8345-bbceb0091220"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"DefTensors", "[", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"dADMgam", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], ",", + RowBox[{"Symmetric", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "}"}], "]"}], ",", + RowBox[{ + "PrintAs", "->", + "\"\<\[PartialD]\\!\\(\\*SuperscriptBox[\\(\[Gamma]\\), \ +\\((ADM)\\)]\\)\>\""}]}], "}"}], ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"dADMK", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], ",", + RowBox[{"Symmetric", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "}"}], "]"}], ",", + RowBox[{ + "PrintAs", "->", + "\"\<\[PartialD]\\!\\(\\*SuperscriptBox[\\(K\\), \ +\\((ADM)\\)]\\)\>\""}]}], "}"}], ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"dADMalpha", "[", + RowBox[{"-", "k"}], "]"}], ",", + RowBox[{ + "PrintAs", "->", + "\"\<\[PartialD]\\!\\(\\*SuperscriptBox[\\(\[Alpha]\\), \ +\\((ADM)\\)]\\)\>\""}]}], "}"}], ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"dADMbeta", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", "i"}], "]"}], ",", + RowBox[{ + "PrintAs", "->", + "\"\<\[PartialD]\\!\\(\\*SuperscriptBox[\\(\[Beta]\\), \\((ADM)\\)]\\)\ +\>\""}]}], "}"}]}], "\[IndentingNewLine]", "]"}], ";"}]], "Input", + Editable->False, + InitializationCell->True, + CellChangeTimes->{{3.940882996300611*^9, 3.940883045177896*^9}, { + 3.940883100223941*^9, 3.940883120316469*^9}, {3.9408831503936157`*^9, + 3.94088315830639*^9}}, + CellLabel->"In[5]:=",ExpressionUUID->"ede93dc0-606a-46a8-bf03-9b4328dc7c60"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"DefTensors", "[", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"eTtt", "[", "]"}], ",", + RowBox[{ + "PrintAs", "->", "\"\<\!\(\*SubscriptBox[\(T\), \(tt\)]\)\>\""}]}], + "}"}], ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"eTt", "[", + RowBox[{"-", "i"}], "]"}], ",", + RowBox[{ + "PrintAs", "->", "\"\<\!\(\*SubscriptBox[\(T\), \(t\)]\)\>\""}]}], + "}"}], ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"eT", "[", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], ",", + RowBox[{"PrintAs", "->", "\"\\""}]}], "}"}]}], + "\[IndentingNewLine]", "]"}], ";"}]], "Input", + Editable->False, + InitializationCell->True, + CellChangeTimes->{{3.928836579943162*^9, 3.928836615491*^9}, { + 3.928836745826116*^9, 3.92883674625337*^9}, {3.928836798904362*^9, + 3.928836841519875*^9}, {3.9288370376345053`*^9, 3.928837039390031*^9}}, + CellLabel->"In[6]:=",ExpressionUUID->"c08588c0-b1be-4279-a26f-ad8578054e37"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Temp", "Subsection", + Editable->False, + CellChangeTimes->{{3.9288195149467583`*^9, + 3.928819526489415*^9}},ExpressionUUID->"1fd445a5-eeab-43da-98f4-\ +96f9414b6b16"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"DefTensors", "[", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"detinvgam", "[", "]"}], ",", + RowBox[{"PrintAs", "->", "\"\<1/\[Gamma]\>\""}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"invgam", "[", + RowBox[{"i", ",", "j"}], "]"}], ",", + RowBox[{"Symmetric", "[", + RowBox[{"{", + RowBox[{"i", ",", "j"}], "}"}], "]"}], ",", + RowBox[{"PrintAs", "->", "\"\<\[Gamma]\>\""}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"GamDDD", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], ",", + RowBox[{"Symmetric", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "}"}], "]"}], ",", + RowBox[{"PrintAs", "->", "\"\<\[CapitalGamma]\>\""}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"Gam", "[", + RowBox[{"k", ",", + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], ",", + RowBox[{"Symmetric", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "}"}], "]"}], ",", + RowBox[{"PrintAs", "->", "\"\<\[CapitalGamma]\>\""}]}], "}"}]}], + "\[IndentingNewLine]", "]"}], ";"}]], "Input", + InitializationCell->True, + CellChangeTimes->{{3.928785928985149*^9, 3.928786087978428*^9}, + 3.928786629457264*^9, {3.928786861878175*^9, 3.928786865635483*^9}, { + 3.928787339845923*^9, 3.928787341802931*^9}, {3.928791406939233*^9, + 3.928791427196692*^9}, {3.928791461188624*^9, 3.928791466510343*^9}, { + 3.928791782168232*^9, 3.928791822282562*^9}, {3.928792263871332*^9, + 3.928792296266157*^9}, {3.928792330242548*^9, 3.928792335728332*^9}, { + 3.928792700494267*^9, 3.9287927326180887`*^9}, {3.928793041602625*^9, + 3.928793075981928*^9}, {3.928794674719866*^9, 3.928794749806027*^9}, { + 3.928796226110096*^9, 3.92879626124386*^9}, {3.9288180654899387`*^9, + 3.9288180744719*^9}, {3.9288182788597717`*^9, 3.928818281304373*^9}, { + 3.928818334058167*^9, 3.928818336847477*^9}, {3.928818901877288*^9, + 3.928818903931491*^9}, {3.928820886470365*^9, 3.928820890394692*^9}, { + 3.9288217145115*^9, 3.928821730690242*^9}, {3.928821785001086*^9, + 3.928821798416621*^9}, 3.928836232745147*^9, {3.928836281224597*^9, + 3.928836281538724*^9}, {3.928920995545884*^9, 3.928921053931546*^9}, { + 3.940883468314411*^9, 3.9408835153619347`*^9}, {3.9408838437513227`*^9, + 3.940883897345069*^9}, {3.940884062866747*^9, + 3.9408840633842583`*^9}},ExpressionUUID->"230e3e3d-ec24-4b15-9bc4-\ +4c66fa656cc7"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"DefTensors", "[", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"R", "[", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], ",", + RowBox[{"Symmetric", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "}"}], "]"}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"trR", "[", "]"}], ",", + RowBox[{"PrintAs", "->", "\"\\""}]}], "}"}]}], + "\[IndentingNewLine]", "]"}], ";"}]], "Input", + InitializationCell->True, + CellChangeTimes->{{3.928836234865031*^9, 3.928836243310957*^9}, { + 3.928838514237761*^9, 3.928838528459001*^9}, {3.940883531168107*^9, + 3.940883542282584*^9}}, + CellLabel->"In[7]:=",ExpressionUUID->"b2cd1bbb-ebc2-4ae5-98e8-1baa91d81aa3"], + +Cell[CellGroupData[{ + +Cell["Matter", "Subsubsection", + Editable->False, + CellChangeTimes->{{3.928836335137689*^9, + 3.928836338355296*^9}},ExpressionUUID->"63c86796-f445-4596-a568-\ +cf6b7233992a"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"DefTensors", "[", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"rho", "[", "]"}], ",", + RowBox[{"PrintAs", "->", "\"\<\[Rho]\>\""}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"Sm", "[", + RowBox[{"-", "i"}], "]"}], ",", + RowBox[{"PrintAs", "->", "\"\\""}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"Ss", "[", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], ",", + RowBox[{"Symmetric", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "}"}], "]"}], ",", + RowBox[{"PrintAs", "->", "\"\\""}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"trSs", "[", "]"}], ",", + RowBox[{"PrintAs", "->", "\"\\""}]}], "}"}]}], + "\[IndentingNewLine]", "]"}], ";"}]], "Input", + Editable->False, + InitializationCell->True, + CellChangeTimes->{{3.928790254224685*^9, 3.928790291322857*^9}, { + 3.928790623947823*^9, 3.928790696710313*^9}, {3.928790869029275*^9, + 3.928790972579005*^9}, 3.92879101482416*^9}, + CellLabel->"In[8]:=",ExpressionUUID->"61eaa4ba-0069-4a97-a6d7-a02ee559a741"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Constraints", "Subsubsection", + Editable->False, + CellChangeTimes->{{3.928838206212228*^9, + 3.928838207562324*^9}},ExpressionUUID->"28d203fe-58c8-4126-8774-\ +88d5a1781306"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"DefTensors", "[", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"HC", "[", "]"}], ",", + RowBox[{"PrintAs", "->", "\"\\""}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"MtC", "[", "i", "]"}], ",", + RowBox[{"PrintAs", "->", "\"\\""}]}], "}"}]}], + "\[IndentingNewLine]", "]"}], ";"}]], "Input", + Editable->False, + InitializationCell->True, + CellChangeTimes->{{3.9288382290069113`*^9, 3.9288383176366997`*^9}, { + 3.940883731867737*^9, 3.940883762152182*^9}}, + CellLabel->"In[9]:=",ExpressionUUID->"5502d63c-b6fc-4a63-a203-12b5cbab9476"] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Constant", "Subsection", + Editable->False, + CellChangeTimes->{{3.928788008646267*^9, + 3.928788014497714*^9}},ExpressionUUID->"ab64c7df-87cb-4c7d-990a-\ +2b0543e709db"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"DefConstantSymbol", "[", + RowBox[{"cpi", ",", + RowBox[{"PrintAs", "->", "\"\<\[Pi]\>\""}]}], "]"}], ";"}]], "Input", + Editable->False, + InitializationCell->True, + CellChangeTimes->{{3.928788017861888*^9, 3.9287880651917562`*^9}, { + 3.928797169707514*^9, 3.928797172450495*^9}, {3.928797313015642*^9, + 3.9287973225423384`*^9}, {3.940883821744501*^9, 3.9408838220365953`*^9}}, + CellLabel->"In[10]:=",ExpressionUUID->"e471a9d0-e772-4737-b68b-dc67e2be03b9"] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["RHS", "Section", + Editable->False, + CellChangeTimes->{{3.928785747144782*^9, + 3.928785747527007*^9}},ExpressionUUID->"519fe4de-6999-4db6-9e6b-\ +17dff89f6b40"], + +Cell[CellGroupData[{ + +Cell["Temp", "Subsection", + Editable->False, + CellChangeTimes->{{3.928818678205492*^9, + 3.928818680253039*^9}},ExpressionUUID->"29fb9a40-8f32-4735-bf46-\ +1b2322d6762f"], + +Cell[BoxData[{ + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"GamDDD", "[", + RowBox[{"k_", ",", "i_", ",", "j_"}], "]"}], ",", + RowBox[{ + FractionBox["1", "2"], + RowBox[{"(", + RowBox[{ + RowBox[{"dADMgam", "[", + RowBox[{"i", ",", "j", ",", "k"}], "]"}], "+", + RowBox[{"dADMgam", "[", + RowBox[{"j", ",", "k", ",", "i"}], "]"}], "-", + RowBox[{"dADMgam", "[", + RowBox[{"k", ",", "i", ",", "j"}], "]"}]}], ")"}]}]}], "]"}], + ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"Gam", "[", + RowBox[{"k_", ",", "i_", ",", "j_"}], "]"}], ",", + RowBox[{ + RowBox[{"invgam", "[", + RowBox[{"k", ",", "l"}], "]"}], + RowBox[{"GamDDD", "[", + RowBox[{ + RowBox[{"-", "l"}], ",", "i", ",", "j"}], "]"}]}]}], "]"}], + ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"trGtd", "[", "i_", "]"}], ",", + RowBox[{ + RowBox[{"invgamt", "[", + RowBox[{"k", ",", "l"}], "]"}], + RowBox[{"Gt", "[", + RowBox[{"i", ",", + RowBox[{"-", "k"}], ",", + RowBox[{"-", "l"}]}], "]"}]}]}], "]"}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"exAtUU", "[", + RowBox[{"i_", ",", "j_"}], "]"}], ",", + RowBox[{ + RowBox[{"invgamt", "[", + RowBox[{"i", ",", "k"}], "]"}], + RowBox[{"invgamt", "[", + RowBox[{"j", ",", "l"}], "]"}], + RowBox[{"exAt", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", + RowBox[{"-", "l"}]}], "]"}]}]}], "]"}], ";"}]}], "Input", + InitializationCell->True, + CellChangeTimes->{{3.92882045451426*^9, 3.928820494015818*^9}, { + 3.92882054464657*^9, 3.928820550091407*^9}, {3.928822389143814*^9, + 3.928822403936602*^9}, {3.928822478660738*^9, 3.9288225192530327`*^9}, { + 3.9288361544164658`*^9, 3.928836162461919*^9}, {3.92892211822755*^9, + 3.928922119069038*^9}, {3.940883914871763*^9, + 3.940884055385359*^9}},ExpressionUUID->"06d87d1d-b673-41db-8089-\ +81c4e3d83936"], + +Cell[BoxData[{ + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"Rtchi", "[", + RowBox[{"i_", ",", "j_"}], "]"}], ",", + RowBox[{ + RowBox[{ + FractionBox["1", + RowBox[{"2", + RowBox[{"chi", "[", "]"}]}]], + RowBox[{"tDtDchi", "[", + RowBox[{"i", ",", "j"}], "]"}]}], "+", + RowBox[{ + FractionBox["1", + RowBox[{"2", + RowBox[{"chi", "[", "]"}]}]], + RowBox[{"gamt", "[", + RowBox[{"i", ",", "j"}], "]"}], + RowBox[{"invgamt", "[", + RowBox[{"k", ",", "l"}], "]"}], + RowBox[{"tDtDchi", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", + RowBox[{"-", "l"}]}], "]"}]}], "-", + RowBox[{ + FractionBox["1", + RowBox[{"4", + SuperscriptBox[ + RowBox[{"chi", "[", "]"}], "2"]}]], + RowBox[{"dchi", "[", "i", "]"}], + RowBox[{"dchi", "[", "j", "]"}]}], "-", + RowBox[{ + FractionBox["3", + RowBox[{"4", + SuperscriptBox[ + RowBox[{"chi", "[", "]"}], "2"]}]], + RowBox[{"gamt", "[", + RowBox[{"i", ",", "j"}], "]"}], + RowBox[{"invgamt", "[", + RowBox[{"k", ",", "l"}], "]"}], + RowBox[{"dchi", "[", + RowBox[{"-", "k"}], "]"}], + RowBox[{"dchi", "[", + RowBox[{"-", "l"}], "]"}]}]}]}], "]"}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"Rt", "[", + RowBox[{"i_", ",", "j_"}], "]"}], ",", + RowBox[{ + RowBox[{ + RowBox[{"-", + FractionBox["1", "2"]}], + RowBox[{"invgamt", "[", + RowBox[{"l", ",", "m"}], "]"}], + RowBox[{"ddgamt", "[", + RowBox[{ + RowBox[{"-", "l"}], ",", + RowBox[{"-", "m"}], ",", "i", ",", "j"}], "]"}]}], "+", + RowBox[{ + FractionBox["1", "2"], + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"gamt", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", "i"}], "]"}], + RowBox[{"dtrGt", "[", + RowBox[{"j", ",", "k"}], "]"}]}], "+", + RowBox[{ + RowBox[{"gamt", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", "j"}], "]"}], + RowBox[{"dtrGt", "[", + RowBox[{"i", ",", "k"}], "]"}]}]}], ")"}]}], "+", + RowBox[{ + FractionBox["1", "2"], + RowBox[{"trGtd", "[", "k", "]"}], + RowBox[{"(", + RowBox[{ + RowBox[{"GtDDD", "[", + RowBox[{"i", ",", "j", ",", + RowBox[{"-", "k"}]}], "]"}], "+", + RowBox[{"GtDDD", "[", + RowBox[{"j", ",", "i", ",", + RowBox[{"-", "k"}]}], "]"}]}], ")"}]}], "+", + RowBox[{"(", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"Gt", "[", + RowBox[{"k", ",", + RowBox[{"-", "l"}], ",", "i"}], "]"}], + RowBox[{"GtDDU", "[", + RowBox[{"j", ",", + RowBox[{"-", "k"}], ",", "l"}], "]"}]}], "+", + RowBox[{ + RowBox[{"Gt", "[", + RowBox[{"k", ",", + RowBox[{"-", "l"}], ",", "j"}], "]"}], + RowBox[{"GtDDU", "[", + RowBox[{"i", ",", + RowBox[{"-", "k"}], ",", "l"}], "]"}]}]}], ")"}], "+", + RowBox[{ + RowBox[{"Gt", "[", + RowBox[{"k", ",", "i", ",", + RowBox[{"-", "m"}]}], "]"}], + RowBox[{"GtDDU", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", "j", ",", "m"}], "]"}]}]}], ")"}]}]}], + "]"}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"R", "[", + RowBox[{"i_", ",", "j_"}], "]"}], ",", + RowBox[{ + RowBox[{"Rtchi", "[", + RowBox[{"i", ",", "j"}], "]"}], "+", + RowBox[{"Rt", "[", + RowBox[{"i", ",", "j"}], "]"}]}]}], "]"}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"trR", "[", "]"}], ",", + RowBox[{ + RowBox[{"invgam", "[", + RowBox[{"k", ",", "l"}], "]"}], + RowBox[{"R", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", + RowBox[{"-", "l"}]}], "]"}]}]}], "]"}], ";"}]}], "Input", + Editable->False, + InitializationCell->True, + CellChangeTimes->{{3.928795055142088*^9, 3.928795097524678*^9}, { + 3.928795285307967*^9, 3.928795396640392*^9}, 3.928795530373377*^9, { + 3.928797033157564*^9, 3.92879703750044*^9}, {3.92881829940282*^9, + 3.928818307012298*^9}, {3.92881836473006*^9, 3.9288183755776*^9}, { + 3.928818924377984*^9, 3.928818932083852*^9}, {3.928821849388647*^9, + 3.928821916271117*^9}, {3.9288227556687393`*^9, 3.928822767114849*^9}, { + 3.92883856377037*^9, 3.92883858232276*^9}}, + CellLabel->"In[37]:=",ExpressionUUID->"761ee28a-77fa-409e-93f8-f3c874c11e4e"], + +Cell[CellGroupData[{ + +Cell["Matter", "Subsubsection", + Editable->False, + CellChangeTimes->{{3.928836325237843*^9, + 3.928836330500912*^9}},ExpressionUUID->"21635a48-b393-484a-82e9-\ +abbe12d2c210"], + +Cell[BoxData[{ + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"rho", "[", "]"}], ",", + RowBox[{ + SuperscriptBox[ + RowBox[{"alpha", "[", "]"}], + RowBox[{"-", "2"}]], + RowBox[{"(", + RowBox[{ + RowBox[{"eTtt", "[", "]"}], "-", + RowBox[{"2", + RowBox[{"beta", "[", "j", "]"}], + RowBox[{"eTt", "[", + RowBox[{"-", "j"}], "]"}]}], "+", + RowBox[{ + RowBox[{"beta", "[", "i", "]"}], + RowBox[{"beta", "[", "j", "]"}], + RowBox[{"eT", "[", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}]}]}], ")"}]}]}], "]"}], + ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"Sm", "[", "i_", "]"}], ",", + RowBox[{ + RowBox[{"-", + SuperscriptBox[ + RowBox[{"alpha", "[", "]"}], + RowBox[{"-", "1"}]]}], + RowBox[{"(", + RowBox[{ + RowBox[{"eTt", "[", "i", "]"}], "-", + RowBox[{ + RowBox[{"beta", "[", "k", "]"}], + RowBox[{"eT", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", "i"}], "]"}]}]}], ")"}]}]}], "]"}], + ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"Ss", "[", + RowBox[{"i_", ",", "j_"}], "]"}], ",", + RowBox[{"eT", "[", + RowBox[{"i", ",", "j"}], "]"}]}], "]"}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"trSs", "[", "]"}], ",", + RowBox[{ + RowBox[{"invgam", "[", + RowBox[{"k", ",", "l"}], "]"}], + RowBox[{"Ss", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", + RowBox[{"-", "l"}]}], "]"}]}]}], "]"}], ";"}]}], "Input", + Editable->False, + InitializationCell->True, + CellChangeTimes->{{3.9288368620865*^9, 3.928836869329986*^9}, { + 3.928836906985135*^9, 3.928836910561809*^9}, {3.928837011184399*^9, + 3.928837024212061*^9}, {3.92883705599408*^9, 3.92883712663377*^9}, { + 3.928837309405642*^9, 3.92883735024449*^9}, 3.928837402423648*^9, { + 3.928837488959302*^9, 3.928837522484947*^9}, {3.928837566001819*^9, + 3.928837587478956*^9}}, + CellLabel->"In[41]:=",ExpressionUUID->"0f3722e5-6cf3-48e0-a39d-b9f9cec7d095"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Constraints", "Subsubsection", + Editable->False, + CellChangeTimes->{{3.928838372391102*^9, + 3.9288383741909857`*^9}},ExpressionUUID->"aea00190-9ff0-4165-bc4a-\ +9094b2949563"], + +Cell[BoxData[{ + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"HC", "[", "]"}], ",", + RowBox[{ + RowBox[{"trR", "[", "]"}], "+", + RowBox[{ + RowBox[{"exAt", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", + RowBox[{"-", "l"}]}], "]"}], + RowBox[{"exAtUU", "[", + RowBox[{"k", ",", "l"}], "]"}]}], "-", + RowBox[{ + FractionBox["2", "3"], + SuperscriptBox[ + RowBox[{"(", + RowBox[{ + RowBox[{"exKh", "[", "]"}], "+", + RowBox[{"2", + RowBox[{"Theta", "[", "]"}]}]}], ")"}], "2"]}], "-", + RowBox[{"16", " ", "cpi", " ", + RowBox[{"rho", "[", "]"}]}]}]}], "]"}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"MtC", "[", "i_", "]"}], ",", + RowBox[{ + RowBox[{"dexAtUU", "[", + RowBox[{ + RowBox[{"-", "j"}], ",", "i", ",", "j"}], "]"}], "+", + RowBox[{ + RowBox[{"Gt", "[", + RowBox[{"i", ",", + RowBox[{"-", "j"}], ",", + RowBox[{"-", "k"}]}], "]"}], + RowBox[{"exAtUU", "[", + RowBox[{"j", ",", "k"}], "]"}]}], "-", + RowBox[{ + FractionBox["2", "3"], + RowBox[{"invgamt", "[", + RowBox[{"i", ",", "j"}], "]"}], + RowBox[{"(", + RowBox[{ + RowBox[{"dexKh", "[", + RowBox[{"-", "j"}], "]"}], "+", + RowBox[{"2", + RowBox[{"dTheta", "[", + RowBox[{"-", "j"}], "]"}]}]}], ")"}]}], "-", + RowBox[{ + FractionBox["2", "3"], + RowBox[{"exAtUU", "[", + RowBox[{"i", ",", "j"}], "]"}], + SuperscriptBox[ + RowBox[{"chi", "[", "]"}], + RowBox[{"-", "1"}]], + RowBox[{"dchi", "[", + RowBox[{"-", "j"}], "]"}]}], "-", + RowBox[{"8", "cpi", " ", + RowBox[{"invgamt", "[", + RowBox[{"i", ",", "j"}], "]"}], + RowBox[{"Sm", "[", + RowBox[{"-", "j"}], "]"}]}]}]}], "]"}], ";"}]}], "Input", + InitializationCell->True, + CellChangeTimes->{{3.928838379343862*^9, 3.928838434795819*^9}, { + 3.928838591512603*^9, 3.9288385946294413`*^9}, {3.92883866676774*^9, + 3.928838768805194*^9}, {3.9288394542052717`*^9, 3.928839458164912*^9}, { + 3.928844309306735*^9, 3.9288445005134497`*^9}, {3.940883629753191*^9, + 3.940883634691943*^9}},ExpressionUUID->"de7d67c1-605e-4f29-b6a7-\ +28029963f3cd"] +}, Open ]] +}, Open ]] +}, Open ]] +}, +WindowSize->{1792, 1067}, +WindowMargins->{{0, Automatic}, {Automatic, 0}}, +FrontEndVersion->"14.1 for Mac OS X x86 (64-bit) (July 16, 2024)", +StyleDefinitions->"Default.nb", +ExpressionUUID->"ebd466d4-c373-4284-afdd-a9043ac1493f" +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{} +*) +(*CellTagsIndex +CellTagsIndex->{} +*) +(*NotebookFileOutline +Notebook[{ +Cell[CellGroupData[{ +Cell[580, 22, 531, 12, 45, "Input",ExpressionUUID->"9857cbce-1237-4124-83ba-143c7adb15bb", + InitializationCell->True], +Cell[CellGroupData[{ +Cell[1136, 38, 773, 13, 23, "Print",ExpressionUUID->"2d413a8c-afde-4f94-995b-ecb6c78e0d0e"], +Cell[1912, 53, 1045, 21, 23, "Print",ExpressionUUID->"5063455d-0819-4426-a7cd-a936ec5a18d3"], +Cell[2960, 76, 794, 13, 23, "Print",ExpressionUUID->"b2130651-b020-4f0d-b414-aecb07c8bb51"], +Cell[3757, 91, 753, 12, 23, "Print",ExpressionUUID->"21efd890-ca3e-4e48-abfc-2557ed72d15b"], +Cell[4513, 105, 734, 12, 23, "Print",ExpressionUUID->"443f8edf-6aeb-4b63-bbeb-6392d370114a"], +Cell[5250, 119, 773, 13, 23, "Print",ExpressionUUID->"19b61223-15f8-445c-87a7-05366f0cd520"], +Cell[6026, 134, 1051, 21, 23, "Print",ExpressionUUID->"98a6bade-745f-40c5-b829-851f4886cc64"], +Cell[7080, 157, 796, 13, 23, "Print",ExpressionUUID->"9c6b1c40-abba-4c22-9ce5-fd0ba270ce6f"], +Cell[7879, 172, 773, 13, 23, "Print",ExpressionUUID->"4268e72f-8cd6-4e23-94b7-639cef899a6b"], +Cell[8655, 187, 927, 15, 23, "Print",ExpressionUUID->"440fa9ee-00bc-4842-9415-8118f94d2fbe"], +Cell[9585, 204, 773, 13, 23, "Print",ExpressionUUID->"1661913c-3e50-4257-a01b-4ea5f1e088ed"], +Cell[10361, 219, 773, 13, 23, "Print",ExpressionUUID->"f20e3e8c-53f4-4d6f-b58c-a1038625751e"], +Cell[11137, 234, 1045, 21, 23, "Print",ExpressionUUID->"fb9a748e-d6d4-417b-bf17-777aba62c9f0"], +Cell[12185, 257, 814, 13, 23, "Print",ExpressionUUID->"7a9a155b-7934-41fe-98de-c5e719313a9d"], +Cell[13002, 272, 775, 13, 23, "Print",ExpressionUUID->"b23d5798-2957-4ac0-a5d9-b540b832f678"], +Cell[13780, 287, 927, 15, 23, "Print",ExpressionUUID->"0fac0347-f8f8-4061-b0ce-dca9ca5a657b"], +Cell[14710, 304, 773, 13, 23, "Print",ExpressionUUID->"87433911-a72e-42c5-901f-d6d4c55f3e5c"], +Cell[15486, 319, 773, 13, 23, "Print",ExpressionUUID->"7df0469d-be51-40b1-b138-7c20ec4f0ea3"], +Cell[16262, 334, 749, 12, 23, "Print",ExpressionUUID->"bdf91799-7d12-4aa6-b728-654417a43d7c"], +Cell[17014, 348, 773, 13, 23, "Print",ExpressionUUID->"1f48e0da-b53c-4634-928d-31dc80e81f67"], +Cell[17790, 363, 773, 13, 23, "Print",ExpressionUUID->"d2f15395-4e3f-4bc7-97c5-57afa904824f"], +Cell[18566, 378, 753, 12, 23, "Print",ExpressionUUID->"c487e186-0b38-4a9d-8de5-b0e1219da427"], +Cell[19322, 392, 775, 13, 23, "Print",ExpressionUUID->"f07dd22b-7ecf-4e2f-9c19-c3839154085b"], +Cell[20100, 407, 775, 13, 23, "Print",ExpressionUUID->"14f387a5-5f53-42c4-a285-efbb64f0713e"], +Cell[20878, 422, 753, 12, 23, "Print",ExpressionUUID->"71ad03b8-4a27-442d-9c9c-62cee9dc5e26"], +Cell[21634, 436, 775, 13, 23, "Print",ExpressionUUID->"5f6aa3c6-7bab-4969-abc2-3edc76e474bc"], +Cell[22412, 451, 775, 13, 23, "Print",ExpressionUUID->"250082e4-2673-4abb-848c-e4dfe11295fa"], +Cell[23190, 466, 753, 12, 23, "Print",ExpressionUUID->"6d4f5338-4c2e-4237-9c39-6d3d5abb6237"], +Cell[23946, 480, 773, 13, 23, "Print",ExpressionUUID->"46921bd2-d6fe-4a16-b844-a67fbeb98326"], +Cell[24722, 495, 773, 13, 23, "Print",ExpressionUUID->"98432958-fdc5-4b68-bdaa-fa9084fb5d85"], +Cell[25498, 510, 755, 12, 23, "Print",ExpressionUUID->"51ee7a70-3f39-42f5-b499-f8bb8b7bfcd9"], +Cell[26256, 524, 773, 13, 23, "Print",ExpressionUUID->"c6532e3b-c63e-4993-86dd-c058b2b84425"], +Cell[27032, 539, 773, 13, 23, "Print",ExpressionUUID->"dd71a352-e2b7-4f91-947d-746836026c60"], +Cell[27808, 554, 756, 12, 23, "Print",ExpressionUUID->"c87e12a6-b74f-4713-8e6c-4c4c826d5a49"], +Cell[28567, 568, 773, 13, 23, "Print",ExpressionUUID->"edd22973-4785-4732-a954-d69990b4757b"], +Cell[29343, 583, 713, 12, 23, "Print",ExpressionUUID->"ca3387bf-41e7-4600-a4bd-e839cfb8aa92"] +}, Open ]] +}, Open ]], +Cell[CellGroupData[{ +Cell[30105, 601, 227, 5, 66, "Section",ExpressionUUID->"d93e9e9c-e043-49bf-adc4-613bb015a823"], +Cell[30335, 608, 373, 9, 45, "Input",ExpressionUUID->"dc88cf1b-3b54-44ff-b471-d7efa31651a2", + InitializationCell->True], +Cell[CellGroupData[{ +Cell[30733, 621, 224, 5, 53, "Subsection",ExpressionUUID->"8f6e447f-5ad1-4983-a220-4a62c32eb45e"], +Cell[30960, 628, 1702, 51, 147, "Input",ExpressionUUID->"4879eb5d-4927-4d70-8345-bbceb0091220", + InitializationCell->True], +Cell[32665, 681, 1982, 58, 147, "Input",ExpressionUUID->"ede93dc0-606a-46a8-bf03-9b4328dc7c60", + InitializationCell->True], +Cell[34650, 741, 1110, 30, 127, "Input",ExpressionUUID->"c08588c0-b1be-4279-a26f-ad8578054e37", + InitializationCell->True] +}, Open ]], +Cell[CellGroupData[{ +Cell[35797, 776, 172, 4, 53, "Subsection",ExpressionUUID->"1fd445a5-eeab-43da-98f4-96f9414b6b16"], +Cell[35972, 782, 2790, 64, 147, "Input",ExpressionUUID->"230e3e3d-ec24-4b15-9bc4-4c66fa656cc7", + InitializationCell->True], +Cell[38765, 848, 880, 25, 106, "Input",ExpressionUUID->"b2cd1bbb-ebc2-4ae5-98e8-1baa91d81aa3", + InitializationCell->True], +Cell[CellGroupData[{ +Cell[39670, 877, 175, 4, 43, "Subsubsection",ExpressionUUID->"63c86796-f445-4596-a568-cf6b7233992a"], +Cell[39848, 883, 1327, 38, 147, "Input",ExpressionUUID->"61eaa4ba-0069-4a97-a6d7-a02ee559a741", + InitializationCell->True] +}, Open ]], +Cell[CellGroupData[{ +Cell[41212, 926, 180, 4, 43, "Subsubsection",ExpressionUUID->"28d203fe-58c8-4126-8774-88d5a1781306"], +Cell[41395, 932, 673, 18, 106, "Input",ExpressionUUID->"5502d63c-b6fc-4a63-a203-12b5cbab9476", + InitializationCell->True] +}, Open ]] +}, Open ]], +Cell[CellGroupData[{ +Cell[42117, 956, 174, 4, 53, "Subsection",ExpressionUUID->"ab64c7df-87cb-4c7d-990a-2b0543e709db"], +Cell[42294, 962, 498, 10, 45, "Input",ExpressionUUID->"e471a9d0-e772-4737-b68b-dc67e2be03b9", + InitializationCell->True] +}, Open ]] +}, Open ]], +Cell[CellGroupData[{ +Cell[42841, 978, 166, 4, 66, "Section",ExpressionUUID->"519fe4de-6999-4db6-9e6b-17dff89f6b40"], +Cell[CellGroupData[{ +Cell[43032, 986, 170, 4, 53, "Subsection",ExpressionUUID->"29fb9a40-8f32-4735-bf46-1b2322d6762f"], +Cell[43205, 992, 2079, 61, 121, "Input",ExpressionUUID->"06d87d1d-b673-41db-8089-81c4e3d83936", + InitializationCell->True], +Cell[45287, 1055, 4683, 143, 169, "Input",ExpressionUUID->"761ee28a-77fa-409e-93f8-f3c874c11e4e", + InitializationCell->True], +Cell[CellGroupData[{ +Cell[49995, 1202, 175, 4, 43, "Subsubsection",ExpressionUUID->"21635a48-b393-484a-82e9-abbe12d2c210"], +Cell[50173, 1208, 2211, 68, 111, "Input",ExpressionUUID->"0f3722e5-6cf3-48e0-a39d-b9f9cec7d095", + InitializationCell->True] +}, Open ]], +Cell[CellGroupData[{ +Cell[52421, 1281, 182, 4, 43, "Subsubsection",ExpressionUUID->"aea00190-9ff0-4165-bc4a-9094b2949563"], +Cell[52606, 1287, 2325, 70, 96, "Input",ExpressionUUID->"de7d67c1-605e-4f29-b6a7-28029963f3cd", + InitializationCell->True] +}, Open ]] +}, Open ]] +}, Open ]] +} +] +*) + From bc80d251bff5f0d39b9624bf5b3238b1746768ee Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Sun, 17 Nov 2024 23:09:30 -0500 Subject: [PATCH 05/37] ADMconstraints: nv type_in_rhs.nb outside wl --- ADMconstraints/wolfram/{wl => }/type_in_rhs.nb | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename ADMconstraints/wolfram/{wl => }/type_in_rhs.nb (100%) diff --git a/ADMconstraints/wolfram/wl/type_in_rhs.nb b/ADMconstraints/wolfram/type_in_rhs.nb similarity index 100% rename from ADMconstraints/wolfram/wl/type_in_rhs.nb rename to ADMconstraints/wolfram/type_in_rhs.nb From 3dc202227e9ab8b1d56ce125a55c098374c768df Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 00:27:40 -0500 Subject: [PATCH 06/37] ADMconstraints: update type_in_rhs.nb --- ADMconstraints/wolfram/type_in_rhs.nb | 844 +++++++++++++------------- 1 file changed, 415 insertions(+), 429 deletions(-) diff --git a/ADMconstraints/wolfram/type_in_rhs.nb b/ADMconstraints/wolfram/type_in_rhs.nb index 8f3463f3..c4a2a6d3 100644 --- a/ADMconstraints/wolfram/type_in_rhs.nb +++ b/ADMconstraints/wolfram/type_in_rhs.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 61752, 1473] -NotebookOptionsPosition[ 54971, 1362] -NotebookOutlinePosition[ 55364, 1378] -CellTagsIndexPosition[ 55321, 1375] +NotebookDataLength[ 63486, 1459] +NotebookOptionsPosition[ 56523, 1349] +NotebookOutlinePosition[ 56915, 1365] +CellTagsIndexPosition[ 56872, 1362] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -46,10 +46,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882755363988*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.9408947819049664`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"2d413a8c-afde-4f94-995b-ecb6c78e0d0e"], +In[1]:=",ExpressionUUID->"960e2aea-3640-4c4b-99d7-ad3552e44aa0"], Cell[BoxData[ InterpretationBox[ @@ -69,10 +70,11 @@ Cell[BoxData[ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882755367536*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894781906104*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"5063455d-0819-4426-a7cd-a936ec5a18d3"], +In[1]:=",ExpressionUUID->"270ddc26-f293-42c7-951b-09ce50057326"], Cell[BoxData["\<\"CopyRight (C) 2003-2020, Jose M. Martin-Garcia, under the \ General Public License.\"\>"], "Print", @@ -84,10 +86,11 @@ General Public License.\"\>"], "Print", 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882755369288*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894781908741*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"b2130651-b020-4f0d-b414-aecb07c8bb51"], +In[1]:=",ExpressionUUID->"9d464697-9d75-4fa0-aa78-7da9b1c04cd5"], Cell[BoxData["\<\"Connecting to external mac executable...\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -98,10 +101,11 @@ Cell[BoxData["\<\"Connecting to external mac executable...\"\>"], "Print", 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.9408827554485807`*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894781987438*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"21efd890-ca3e-4e48-abfc-2557ed72d15b"], +In[1]:=",ExpressionUUID->"9b4426f5-23b4-4c5d-a0b7-0395ab1c3139"], Cell[BoxData["\<\"Connection established.\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -112,10 +116,11 @@ Cell[BoxData["\<\"Connection established.\"\>"], "Print", 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882755559328*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894782100172*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"443f8edf-6aeb-4b63-bbeb-6392d370114a"], +In[1]:=",ExpressionUUID->"2ada16dc-f632-420a-a175-efb109277a65"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -127,10 +132,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882755562408*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.9408947821011877`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"19b61223-15f8-445c-87a7-05366f0cd520"], +In[1]:=",ExpressionUUID->"3d282824-fc17-49e2-ae93-e2849fe46ca4"], Cell[BoxData[ InterpretationBox[ @@ -150,10 +156,11 @@ Cell[BoxData[ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882755563285*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894782101965*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"98a6bade-745f-40c5-b829-851f4886cc64"], +In[1]:=",ExpressionUUID->"6c30165f-4fb9-48d9-ae79-64b2a9530c29"], Cell[BoxData["\<\"CopyRight (C) 2002-2021, Jose M. Martin-Garcia, under the \ General Public License.\"\>"], "Print", @@ -165,10 +172,11 @@ General Public License.\"\>"], "Print", 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.9408827555640182`*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894782102714*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"9c6b1c40-abba-4c22-9ce5-fd0ba270ce6f"], +In[1]:=",ExpressionUUID->"06129bbf-451f-4a59-8ecd-8828b612ccec"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -180,10 +188,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882755578768*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894782118977*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"4268e72f-8cd6-4e23-94b7-639cef899a6b"], +In[1]:=",ExpressionUUID->"9e028197-1d0f-40ae-81ef-4e3180b22a7b"], Cell[BoxData["\<\"These packages come with ABSOLUTELY NO WARRANTY; for \ details type Disclaimer[]. This is free software, and you are welcome to \ @@ -197,10 +206,11 @@ details.\"\>"], "Print", 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.94088275557968*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894782120069*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"440fa9ee-00bc-4842-9415-8118f94d2fbe"], +In[1]:=",ExpressionUUID->"ea8f1a9a-8651-4a02-afdf-a8ce6bf3b3e2"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -212,10 +222,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882755580574*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.9408947821211443`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"1661913c-3e50-4257-a01b-4ea5f1e088ed"], +In[1]:=",ExpressionUUID->"92ac23a6-8e9e-4004-9b2c-ddeaa7e63682"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -227,10 +238,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882755763043*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.94089478230459*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"f20e3e8c-53f4-4d6f-b58c-a1038625751e"], +In[1]:=",ExpressionUUID->"0ead17e8-9122-49f6-b430-625a85989719"], Cell[BoxData[ InterpretationBox[ @@ -250,10 +262,11 @@ Cell[BoxData[ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882755763953*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894782305696*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"fb9a748e-d6d4-417b-bf17-777aba62c9f0"], +In[1]:=",ExpressionUUID->"201d47dc-5727-40a1-94be-e35d5b2de144"], Cell[BoxData["\<\"CopyRight (C) 2005-2021, David Yllanes and Jose M. \ Martin-Garcia, under the General Public License.\"\>"], "Print", @@ -265,10 +278,11 @@ Martin-Garcia, under the General Public License.\"\>"], "Print", 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.9408827557647543`*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.9408947823065357`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"7a9a155b-7934-41fe-98de-c5e719313a9d"], +In[1]:=",ExpressionUUID->"994c931d-0e7a-4613-909d-41610b233d47"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -280,10 +294,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.9408827557833977`*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.94089478232628*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"b23d5798-2957-4ac0-a5d9-b540b832f678"], +In[1]:=",ExpressionUUID->"848bc993-593e-4741-8e7d-5a142245a7b0"], Cell[BoxData["\<\"These packages come with ABSOLUTELY NO WARRANTY; for \ details type Disclaimer[]. This is free software, and you are welcome to \ @@ -297,10 +312,11 @@ details.\"\>"], "Print", 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.94088275578448*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894782327444*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"0fac0347-f8f8-4061-b0ce-dca9ca5a657b"], +In[1]:=",ExpressionUUID->"952c9782-95b6-4f07-96e1-099e03e50874"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -312,10 +328,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882755785578*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894782328567*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"87433911-a72e-42c5-901f-d6d4c55f3e5c"], +In[1]:=",ExpressionUUID->"9c9dfb68-d150-4d47-a3de-5b07fb9a3a87"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -327,10 +344,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882756921711*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784002359*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"7df0469d-be51-40b1-b138-7c20ec4f0ea3"], +In[1]:=",ExpressionUUID->"8b3f770a-ea9f-4341-9b86-39080c653e4e"], Cell[BoxData["\<\"Package Generato`Basic`, {2024, 1, 11}\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -341,10 +359,11 @@ Cell[BoxData["\<\"Package Generato`Basic`, {2024, 1, 11}\"\>"], "Print", 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882756922667*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784003731*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"bdf91799-7d12-4aa6-b728-654417a43d7c"], +In[1]:=",ExpressionUUID->"a7c74cbd-4cee-4108-b3a9-0d8feb4235aa"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -356,10 +375,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882756923511*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784004771*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"1f48e0da-b53c-4634-928d-31dc80e81f67"], +In[1]:=",ExpressionUUID->"df2b13e5-0479-4551-9b3a-35f018113808"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -371,10 +391,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882756924354*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784006069*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"d2f15395-4e3f-4bc7-97c5-57afa904824f"], +In[1]:=",ExpressionUUID->"0aa951e3-0f08-40d0-9000-5a73643e757a"], Cell[BoxData["\<\"Package Generato`ParseMode`, {2024, 7, 06}\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -385,10 +406,11 @@ Cell[BoxData["\<\"Package Generato`ParseMode`, {2024, 7, 06}\"\>"], "Print", 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882756925179*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784007107*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"c487e186-0b38-4a9d-8de5-b0e1219da427"], +In[1]:=",ExpressionUUID->"bc18d4a7-4ac7-44c6-b014-d3b0ef82a60d"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -400,10 +422,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.9408827569260073`*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784008399*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"f07dd22b-7ecf-4e2f-9c19-c3839154085b"], +In[1]:=",ExpressionUUID->"bfeb5f35-c536-4f3f-b7ea-08ccfc0548f6"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -415,10 +438,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.9408827569268427`*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784009321*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"14f387a5-5f53-42c4-a285-efbb64f0713e"], +In[1]:=",ExpressionUUID->"329239f6-e906-499a-88b4-ddecb2ca4fdb"], Cell[BoxData["\<\"Package Generato`Component`, {2024, 1, 11}\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -429,10 +453,11 @@ Cell[BoxData["\<\"Package Generato`Component`, {2024, 1, 11}\"\>"], "Print", 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882756927662*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784010365*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"71ad03b8-4a27-442d-9c9c-62cee9dc5e26"], +In[1]:=",ExpressionUUID->"3d6c0aca-79f5-45e9-b922-332980031e90"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -444,10 +469,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.9408827569284887`*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.9408947840113087`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"5f6aa3c6-7bab-4969-abc2-3edc76e474bc"], +In[1]:=",ExpressionUUID->"ac2d3a49-1392-4515-ab60-ed00a6f40213"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -459,10 +485,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.9408827569293137`*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784012226*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"250082e4-2673-4abb-848c-e4dfe11295fa"], +In[1]:=",ExpressionUUID->"29b4b0fa-b21e-4e7e-bad1-e49884c849fc"], Cell[BoxData["\<\"Package Generato`Varlist`, {2024, 1, 11}\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -473,10 +500,11 @@ Cell[BoxData["\<\"Package Generato`Varlist`, {2024, 1, 11}\"\>"], "Print", 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.9408827569301243`*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784012988*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"6d4f5338-4c2e-4237-9c39-6d3d5abb6237"], +In[1]:=",ExpressionUUID->"21926ba2-2cff-4647-9863-45b4c9f2e258"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -488,10 +516,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882756930952*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784013761*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"46921bd2-d6fe-4a16-b844-a67fbeb98326"], +In[1]:=",ExpressionUUID->"fe4a67af-834b-4964-8169-aaf79083e1bd"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -503,10 +532,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882756931789*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784015128*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"98432958-fdc5-4b68-bdaa-fa9084fb5d85"], +In[1]:=",ExpressionUUID->"550e2ce4-9d3f-46da-9dc9-9440a964036e"], Cell[BoxData["\<\"Package Generato`Interface`, {2024, 1, 11}\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -517,10 +547,11 @@ Cell[BoxData["\<\"Package Generato`Interface`, {2024, 1, 11}\"\>"], "Print", 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.9408827569325647`*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784016077*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"51ee7a70-3f39-42f5-b499-f8bb8b7bfcd9"], +In[1]:=",ExpressionUUID->"1a0551c3-8b39-43c6-ba77-653aee99b6c6"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -532,10 +563,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882756933343*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784016852*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"c6532e3b-c63e-4993-86dd-c058b2b84425"], +In[1]:=",ExpressionUUID->"a2715f91-f297-42fb-94ae-470c03294596"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -547,10 +579,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882756934122*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.9408947840176687`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"dd71a352-e2b7-4f91-947d-746836026c60"], +In[1]:=",ExpressionUUID->"d57fef39-1ed8-42b7-a3de-747a9d668f43"], Cell[BoxData["\<\"Package Generato`Derivation`, {2024, 1, 18}\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -561,10 +594,11 @@ Cell[BoxData["\<\"Package Generato`Derivation`, {2024, 1, 18}\"\>"], "Print", 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.9408827569349413`*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784018437*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"c87e12a6-b74f-4713-8e6c-4c4c826d5a49"], +In[1]:=",ExpressionUUID->"554c32c0-301d-45a4-840f-047e516ba95e"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -576,10 +610,11 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.940882756935684*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.9408947840192013`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"edd22973-4785-4732-a954-d69990b4757b"], +In[1]:=",ExpressionUUID->"ca4a35a5-1968-44fa-8267-9ee12a74f98d"], Cell[BoxData["\<\"\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -590,10 +625,11 @@ Cell[BoxData["\<\"\"\>"], "Print", 3.928796308289264*^9, 3.928819264261452*^9, 3.928819829538828*^9, 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, - 3.9408827569363823`*^9}, + 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, + 3.940894784020018*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"ca3387bf-41e7-4600-a4bd-e839cfb8aa92"] +In[1]:=",ExpressionUUID->"18abfc4f-b472-442b-8225-b8149e7b2952"] }, Open ]] }, Open ]], @@ -677,7 +713,7 @@ Cell[BoxData[ Editable->False, InitializationCell->True, CellChangeTimes->{{3.940882996300611*^9, 3.940883045177896*^9}}, - CellLabel->"In[4]:=",ExpressionUUID->"4879eb5d-4927-4d70-8345-bbceb0091220"], + CellLabel->"In[3]:=",ExpressionUUID->"4879eb5d-4927-4d70-8345-bbceb0091220"], Cell[BoxData[ RowBox[{ @@ -737,7 +773,36 @@ Cell[BoxData[ CellChangeTimes->{{3.940882996300611*^9, 3.940883045177896*^9}, { 3.940883100223941*^9, 3.940883120316469*^9}, {3.9408831503936157`*^9, 3.94088315830639*^9}}, - CellLabel->"In[5]:=",ExpressionUUID->"ede93dc0-606a-46a8-bf03-9b4328dc7c60"], + CellLabel->"In[4]:=",ExpressionUUID->"ede93dc0-606a-46a8-bf03-9b4328dc7c60"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"DefTensors", "[", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"ddADMgam", "[", + RowBox[{ + RowBox[{"-", "l"}], ",", + RowBox[{"-", "m"}], ",", + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], ",", + RowBox[{"GenSet", "[", + RowBox[{ + RowBox[{"Cycles", "[", + RowBox[{"{", + RowBox[{"1", ",", "2"}], "}"}], "]"}], ",", + RowBox[{"Cycles", "[", + RowBox[{"{", + RowBox[{"3", ",", "4"}], "}"}], "]"}]}], "]"}], ",", + RowBox[{"PrintAs", "->", "\"\<\[PartialD]\[PartialD]\[Gamma]\>\""}]}], + "}"}], "\[IndentingNewLine]", "]"}], ";"}]], "Input", + Editable->False, + InitializationCell->True, + CellChangeTimes->{{3.9288169618487673`*^9, 3.92881698006419*^9}, + 3.928818284670382*^9, {3.928819316864279*^9, 3.928819367894333*^9}, { + 3.928819562440492*^9, 3.928819601944265*^9}, {3.928819718902767*^9, + 3.9288197436285753`*^9}, {3.940892654640279*^9, 3.9408926801204033`*^9}}, + CellLabel->"In[5]:=",ExpressionUUID->"2f2a6a6e-f59d-4dc4-8900-9dcb96af2d35"], Cell[BoxData[ RowBox[{ @@ -823,7 +888,52 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", "i"}], ",", RowBox[{"-", "j"}]}], "}"}], "]"}], ",", - RowBox[{"PrintAs", "->", "\"\<\[CapitalGamma]\>\""}]}], "}"}]}], + RowBox[{"PrintAs", "->", "\"\<\[CapitalGamma]\>\""}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"dGam", "[", + RowBox[{ + RowBox[{"-", "m"}], ",", "k", ",", + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], ",", + RowBox[{"Symmetric", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "}"}], "]"}], ",", + RowBox[{"PrintAs", "->", "\"\<\[PartialD]\[CapitalGamma]\>\""}]}], + "}"}], ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"R", "[", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], ",", + RowBox[{"Symmetric", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "}"}], "]"}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"trK", "[", "]"}], ",", + RowBox[{"PrintAs", "->", "\"\\""}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"DADMK", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], ",", + RowBox[{"Symmetric", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "}"}], "]"}], ",", + RowBox[{"PrintAs", "->", "\"\\""}]}], "}"}]}], "\[IndentingNewLine]", "]"}], ";"}]], "Input", InitializationCell->True, CellChangeTimes->{{3.928785928985149*^9, 3.928786087978428*^9}, @@ -842,36 +952,11 @@ Cell[BoxData[ 3.928821798416621*^9}, 3.928836232745147*^9, {3.928836281224597*^9, 3.928836281538724*^9}, {3.928920995545884*^9, 3.928921053931546*^9}, { 3.940883468314411*^9, 3.9408835153619347`*^9}, {3.9408838437513227`*^9, - 3.940883897345069*^9}, {3.940884062866747*^9, - 3.9408840633842583`*^9}},ExpressionUUID->"230e3e3d-ec24-4b15-9bc4-\ -4c66fa656cc7"], - -Cell[BoxData[ - RowBox[{ - RowBox[{"DefTensors", "[", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"R", "[", - RowBox[{ - RowBox[{"-", "i"}], ",", - RowBox[{"-", "j"}]}], "]"}], ",", - RowBox[{"Symmetric", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"-", "i"}], ",", - RowBox[{"-", "j"}]}], "}"}], "]"}]}], "}"}], ",", - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{ - RowBox[{"trR", "[", "]"}], ",", - RowBox[{"PrintAs", "->", "\"\\""}]}], "}"}]}], - "\[IndentingNewLine]", "]"}], ";"}]], "Input", - InitializationCell->True, - CellChangeTimes->{{3.928836234865031*^9, 3.928836243310957*^9}, { - 3.928838514237761*^9, 3.928838528459001*^9}, {3.940883531168107*^9, - 3.940883542282584*^9}}, - CellLabel->"In[7]:=",ExpressionUUID->"b2cd1bbb-ebc2-4ae5-98e8-1baa91d81aa3"], + 3.940883897345069*^9}, {3.940884062866747*^9, 3.9408840633842583`*^9}, { + 3.940892974894392*^9, 3.940893086922902*^9}, {3.940894308123448*^9, + 3.940894312904497*^9}, {3.94089437805265*^9, 3.940894379030416*^9}, { + 3.94089472521984*^9, 3.9408947375365887`*^9}}, + CellLabel->"In[7]:=",ExpressionUUID->"230e3e3d-ec24-4b15-9bc4-4c66fa656cc7"], Cell[CellGroupData[{ @@ -894,32 +979,14 @@ Cell[BoxData[ RowBox[{ RowBox[{"Sm", "[", RowBox[{"-", "i"}], "]"}], ",", - RowBox[{"PrintAs", "->", "\"\\""}]}], "}"}], ",", - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{ - RowBox[{"Ss", "[", - RowBox[{ - RowBox[{"-", "i"}], ",", - RowBox[{"-", "j"}]}], "]"}], ",", - RowBox[{"Symmetric", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"-", "i"}], ",", - RowBox[{"-", "j"}]}], "}"}], "]"}], ",", - RowBox[{"PrintAs", "->", "\"\\""}]}], "}"}], ",", - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{ - RowBox[{"trSs", "[", "]"}], ",", RowBox[{"PrintAs", "->", "\"\\""}]}], "}"}]}], "\[IndentingNewLine]", "]"}], ";"}]], "Input", - Editable->False, InitializationCell->True, CellChangeTimes->{{3.928790254224685*^9, 3.928790291322857*^9}, { 3.928790623947823*^9, 3.928790696710313*^9}, {3.928790869029275*^9, - 3.928790972579005*^9}, 3.92879101482416*^9}, - CellLabel->"In[8]:=",ExpressionUUID->"61eaa4ba-0069-4a97-a6d7-a02ee559a741"] + 3.928790972579005*^9}, 3.92879101482416*^9, {3.940896320864653*^9, + 3.940896329996352*^9}},ExpressionUUID->"61eaa4ba-0069-4a97-a6d7-\ +a02ee559a741"] }, Open ]], Cell[CellGroupData[{ @@ -1022,186 +1089,125 @@ Cell[BoxData[{ RowBox[{ RowBox[{"SetEQN", "[", RowBox[{ - RowBox[{"trGtd", "[", "i_", "]"}], ",", + RowBox[{"dGam", "[", + RowBox[{"m_", ",", "k_", ",", "i_", ",", "j_"}], "]"}], ",", RowBox[{ - RowBox[{"invgamt", "[", - RowBox[{"k", ",", "l"}], "]"}], - RowBox[{"Gt", "[", - RowBox[{"i", ",", - RowBox[{"-", "k"}], ",", - RowBox[{"-", "l"}]}], "]"}]}]}], "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"SetEQN", "[", - RowBox[{ - RowBox[{"exAtUU", "[", - RowBox[{"i_", ",", "j_"}], "]"}], ",", - RowBox[{ - RowBox[{"invgamt", "[", - RowBox[{"i", ",", "k"}], "]"}], - RowBox[{"invgamt", "[", - RowBox[{"j", ",", "l"}], "]"}], - RowBox[{"exAt", "[", - RowBox[{ - RowBox[{"-", "k"}], ",", - RowBox[{"-", "l"}]}], "]"}]}]}], "]"}], ";"}]}], "Input", - InitializationCell->True, + RowBox[{ + FractionBox["1", "2"], + RowBox[{"invgam", "[", + RowBox[{"k", ",", "l"}], "]"}], + RowBox[{"(", + RowBox[{ + RowBox[{"ddADMgam", "[", + RowBox[{"m", ",", "i", ",", "j", ",", + RowBox[{"-", "l"}]}], "]"}], "+", + RowBox[{"ddADMgam", "[", + RowBox[{"m", ",", "j", ",", + RowBox[{"-", "l"}], ",", "i"}], "]"}], "-", + RowBox[{"ddADMgam", "[", + RowBox[{"m", ",", + RowBox[{"-", "l"}], ",", "i", ",", "j"}], "]"}]}], ")"}]}], "-", + RowBox[{ + RowBox[{"invgam", "[", + RowBox[{"k", ",", "p"}], "]"}], + RowBox[{"invgam", "[", + RowBox[{"l", ",", "q"}], "]"}], + RowBox[{"dADMgam", "[", + RowBox[{"m", ",", + RowBox[{"-", "p"}], ",", + RowBox[{"-", "q"}]}], "]"}], + RowBox[{"GamDDD", "[", + RowBox[{ + RowBox[{"-", "l"}], ",", "i", ",", "j"}], "]"}]}]}]}], "]"}], + ";"}]}], "Input", + Editable->False, CellChangeTimes->{{3.92882045451426*^9, 3.928820494015818*^9}, { 3.92882054464657*^9, 3.928820550091407*^9}, {3.928822389143814*^9, 3.928822403936602*^9}, {3.928822478660738*^9, 3.9288225192530327`*^9}, { 3.9288361544164658`*^9, 3.928836162461919*^9}, {3.92892211822755*^9, - 3.928922119069038*^9}, {3.940883914871763*^9, - 3.940884055385359*^9}},ExpressionUUID->"06d87d1d-b673-41db-8089-\ -81c4e3d83936"], + 3.928922119069038*^9}, {3.940883914871763*^9, 3.940884055385359*^9}, { + 3.940893223443261*^9, 3.940893458716525*^9}, {3.940893622642169*^9, + 3.9408937202483683`*^9}, {3.940894063701812*^9, 3.94089406708775*^9}, { + 3.940894251213398*^9, 3.940894253919017*^9}}, + CellLabel->"In[11]:=",ExpressionUUID->"06d87d1d-b673-41db-8089-81c4e3d83936"], -Cell[BoxData[{ +Cell[BoxData[ RowBox[{ RowBox[{"SetEQN", "[", RowBox[{ - RowBox[{"Rtchi", "[", - RowBox[{"i_", ",", "j_"}], "]"}], ",", + RowBox[{"R", "[", + RowBox[{"j_", ",", "k_"}], "]"}], ",", RowBox[{ + RowBox[{"dGam", "[", + RowBox[{ + RowBox[{"-", "i"}], ",", "i", ",", "j", ",", "k"}], "]"}], "-", + RowBox[{"dGam", "[", + RowBox[{"k", ",", "i", ",", "j", ",", + RowBox[{"-", "i"}]}], "]"}], "+", RowBox[{ - FractionBox["1", - RowBox[{"2", - RowBox[{"chi", "[", "]"}]}]], - RowBox[{"tDtDchi", "[", - RowBox[{"i", ",", "j"}], "]"}]}], "+", - RowBox[{ - FractionBox["1", - RowBox[{"2", - RowBox[{"chi", "[", "]"}]}]], - RowBox[{"gamt", "[", - RowBox[{"i", ",", "j"}], "]"}], - RowBox[{"invgamt", "[", - RowBox[{"k", ",", "l"}], "]"}], - RowBox[{"tDtDchi", "[", - RowBox[{ - RowBox[{"-", "k"}], ",", - RowBox[{"-", "l"}]}], "]"}]}], "-", - RowBox[{ - FractionBox["1", - RowBox[{"4", - SuperscriptBox[ - RowBox[{"chi", "[", "]"}], "2"]}]], - RowBox[{"dchi", "[", "i", "]"}], - RowBox[{"dchi", "[", "j", "]"}]}], "-", + RowBox[{"Gam", "[", + RowBox[{"i", ",", + RowBox[{"-", "i"}], ",", + RowBox[{"-", "p"}]}], "]"}], + RowBox[{"Gam", "[", + RowBox[{"p", ",", "j", ",", "k"}], "]"}]}], "-", RowBox[{ - FractionBox["3", - RowBox[{"4", - SuperscriptBox[ - RowBox[{"chi", "[", "]"}], "2"]}]], - RowBox[{"gamt", "[", - RowBox[{"i", ",", "j"}], "]"}], - RowBox[{"invgamt", "[", - RowBox[{"k", ",", "l"}], "]"}], - RowBox[{"dchi", "[", - RowBox[{"-", "k"}], "]"}], - RowBox[{"dchi", "[", - RowBox[{"-", "l"}], "]"}]}]}]}], "]"}], ";"}], "\[IndentingNewLine]", + RowBox[{"Gam", "[", + RowBox[{"i", ",", "j", ",", + RowBox[{"-", "p"}]}], "]"}], + RowBox[{"Gam", "[", + RowBox[{"p", ",", + RowBox[{"-", "i"}], ",", "k"}], "]"}]}]}]}], "]"}], ";"}]], "Input", + Editable->False, + CellLabel->"In[14]:=",ExpressionUUID->"73ae3fe4-58f9-4733-946d-e922b451b632"], + +Cell[BoxData[ RowBox[{ RowBox[{"SetEQN", "[", RowBox[{ - RowBox[{"Rt", "[", - RowBox[{"i_", ",", "j_"}], "]"}], ",", + RowBox[{"trK", "[", "]"}], ",", RowBox[{ - RowBox[{ - RowBox[{"-", - FractionBox["1", "2"]}], - RowBox[{"invgamt", "[", - RowBox[{"l", ",", "m"}], "]"}], - RowBox[{"ddgamt", "[", - RowBox[{ - RowBox[{"-", "l"}], ",", - RowBox[{"-", "m"}], ",", "i", ",", "j"}], "]"}]}], "+", - RowBox[{ - FractionBox["1", "2"], - RowBox[{"(", - RowBox[{ - RowBox[{ - RowBox[{"gamt", "[", - RowBox[{ - RowBox[{"-", "k"}], ",", "i"}], "]"}], - RowBox[{"dtrGt", "[", - RowBox[{"j", ",", "k"}], "]"}]}], "+", - RowBox[{ - RowBox[{"gamt", "[", - RowBox[{ - RowBox[{"-", "k"}], ",", "j"}], "]"}], - RowBox[{"dtrGt", "[", - RowBox[{"i", ",", "k"}], "]"}]}]}], ")"}]}], "+", - RowBox[{ - FractionBox["1", "2"], - RowBox[{"trGtd", "[", "k", "]"}], - RowBox[{"(", - RowBox[{ - RowBox[{"GtDDD", "[", - RowBox[{"i", ",", "j", ",", - RowBox[{"-", "k"}]}], "]"}], "+", - RowBox[{"GtDDD", "[", - RowBox[{"j", ",", "i", ",", - RowBox[{"-", "k"}]}], "]"}]}], ")"}]}], "+", - RowBox[{"(", + RowBox[{"invgam", "[", + RowBox[{"k", ",", "l"}], "]"}], + RowBox[{"ADMK", "[", RowBox[{ - RowBox[{"(", - RowBox[{ - RowBox[{ - RowBox[{"Gt", "[", - RowBox[{"k", ",", - RowBox[{"-", "l"}], ",", "i"}], "]"}], - RowBox[{"GtDDU", "[", - RowBox[{"j", ",", - RowBox[{"-", "k"}], ",", "l"}], "]"}]}], "+", - RowBox[{ - RowBox[{"Gt", "[", - RowBox[{"k", ",", - RowBox[{"-", "l"}], ",", "j"}], "]"}], - RowBox[{"GtDDU", "[", - RowBox[{"i", ",", - RowBox[{"-", "k"}], ",", "l"}], "]"}]}]}], ")"}], "+", - RowBox[{ - RowBox[{"Gt", "[", - RowBox[{"k", ",", "i", ",", - RowBox[{"-", "m"}]}], "]"}], - RowBox[{"GtDDU", "[", - RowBox[{ - RowBox[{"-", "k"}], ",", "j", ",", "m"}], "]"}]}]}], ")"}]}]}], - "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"SetEQN", "[", - RowBox[{ - RowBox[{"R", "[", - RowBox[{"i_", ",", "j_"}], "]"}], ",", - RowBox[{ - RowBox[{"Rtchi", "[", - RowBox[{"i", ",", "j"}], "]"}], "+", - RowBox[{"Rt", "[", - RowBox[{"i", ",", "j"}], "]"}]}]}], "]"}], ";"}], "\[IndentingNewLine]", + RowBox[{"-", "k"}], ",", + RowBox[{"-", "l"}]}], "]"}]}]}], "]"}], ";"}]], "Input", + Editable->False, + CellChangeTimes->{{3.9408947554824867`*^9, 3.940894768665745*^9}, + 3.940894827391893*^9}, + CellLabel->"In[15]:=",ExpressionUUID->"52285f16-cbd6-4f41-8e30-7dc7a405d3f4"], + +Cell[BoxData[ RowBox[{ RowBox[{"SetEQN", "[", RowBox[{ - RowBox[{"trR", "[", "]"}], ",", + RowBox[{"DADMK", "[", + RowBox[{"k_", ",", "i_", ",", "j_"}], "]"}], ",", RowBox[{ - RowBox[{"invgam", "[", - RowBox[{"k", ",", "l"}], "]"}], - RowBox[{"R", "[", - RowBox[{ - RowBox[{"-", "k"}], ",", - RowBox[{"-", "l"}]}], "]"}]}]}], "]"}], ";"}]}], "Input", + RowBox[{"dADMK", "[", + RowBox[{"k", ",", "i", ",", "j"}], "]"}], "-", + RowBox[{ + RowBox[{"Gam", "[", + RowBox[{"l", ",", "k", ",", "i"}], "]"}], + RowBox[{"ADMK", "[", + RowBox[{ + RowBox[{"-", "l"}], ",", "j"}], "]"}]}], "-", + RowBox[{ + RowBox[{"Gam", "[", + RowBox[{"l", ",", "k", ",", "j"}], "]"}], + RowBox[{"ADMK", "[", + RowBox[{ + RowBox[{"-", "l"}], ",", "i"}], "]"}]}]}]}], "]"}], ";"}]], "Input", Editable->False, - InitializationCell->True, - CellChangeTimes->{{3.928795055142088*^9, 3.928795097524678*^9}, { - 3.928795285307967*^9, 3.928795396640392*^9}, 3.928795530373377*^9, { - 3.928797033157564*^9, 3.92879703750044*^9}, {3.92881829940282*^9, - 3.928818307012298*^9}, {3.92881836473006*^9, 3.9288183755776*^9}, { - 3.928818924377984*^9, 3.928818932083852*^9}, {3.928821849388647*^9, - 3.928821916271117*^9}, {3.9288227556687393`*^9, 3.928822767114849*^9}, { - 3.92883856377037*^9, 3.92883858232276*^9}}, - CellLabel->"In[37]:=",ExpressionUUID->"761ee28a-77fa-409e-93f8-f3c874c11e4e"], + CellChangeTimes->{{3.940894268241499*^9, 3.940894277409135*^9}, { + 3.94089432936132*^9, 3.940894347507268*^9}, {3.9408944044767647`*^9, + 3.940894446204462*^9}}, + CellLabel->"In[16]:=",ExpressionUUID->"63c26313-037a-484b-ad0f-4bd8ed3260e8"], Cell[CellGroupData[{ Cell["Matter", "Subsubsection", - Editable->False, CellChangeTimes->{{3.928836325237843*^9, 3.928836330500912*^9}},ExpressionUUID->"21635a48-b393-484a-82e9-\ abbe12d2c210"], @@ -1213,18 +1219,18 @@ Cell[BoxData[{ RowBox[{"rho", "[", "]"}], ",", RowBox[{ SuperscriptBox[ - RowBox[{"alpha", "[", "]"}], + RowBox[{"ADMalpha", "[", "]"}], RowBox[{"-", "2"}]], RowBox[{"(", RowBox[{ RowBox[{"eTtt", "[", "]"}], "-", RowBox[{"2", - RowBox[{"beta", "[", "j", "]"}], + RowBox[{"ADMbeta", "[", "j", "]"}], RowBox[{"eTt", "[", RowBox[{"-", "j"}], "]"}]}], "+", RowBox[{ - RowBox[{"beta", "[", "i", "]"}], - RowBox[{"beta", "[", "j", "]"}], + RowBox[{"ADMbeta", "[", "i", "]"}], + RowBox[{"ADMbeta", "[", "j", "]"}], RowBox[{"eT", "[", RowBox[{ RowBox[{"-", "i"}], ",", @@ -1237,130 +1243,111 @@ Cell[BoxData[{ RowBox[{ RowBox[{"-", SuperscriptBox[ - RowBox[{"alpha", "[", "]"}], + RowBox[{"ADMalpha", "[", "]"}], RowBox[{"-", "1"}]]}], RowBox[{"(", RowBox[{ RowBox[{"eTt", "[", "i", "]"}], "-", RowBox[{ - RowBox[{"beta", "[", "k", "]"}], + RowBox[{"ADMbeta", "[", "k", "]"}], RowBox[{"eT", "[", RowBox[{ RowBox[{"-", "k"}], ",", "i"}], "]"}]}]}], ")"}]}]}], "]"}], - ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"SetEQN", "[", - RowBox[{ - RowBox[{"Ss", "[", - RowBox[{"i_", ",", "j_"}], "]"}], ",", - RowBox[{"eT", "[", - RowBox[{"i", ",", "j"}], "]"}]}], "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"SetEQN", "[", - RowBox[{ - RowBox[{"trSs", "[", "]"}], ",", - RowBox[{ - RowBox[{"invgam", "[", - RowBox[{"k", ",", "l"}], "]"}], - RowBox[{"Ss", "[", - RowBox[{ - RowBox[{"-", "k"}], ",", - RowBox[{"-", "l"}]}], "]"}]}]}], "]"}], ";"}]}], "Input", - Editable->False, - InitializationCell->True, + ";"}]}], "Input", CellChangeTimes->{{3.9288368620865*^9, 3.928836869329986*^9}, { 3.928836906985135*^9, 3.928836910561809*^9}, {3.928837011184399*^9, 3.928837024212061*^9}, {3.92883705599408*^9, 3.92883712663377*^9}, { 3.928837309405642*^9, 3.92883735024449*^9}, 3.928837402423648*^9, { 3.928837488959302*^9, 3.928837522484947*^9}, {3.928837566001819*^9, - 3.928837587478956*^9}}, - CellLabel->"In[41]:=",ExpressionUUID->"0f3722e5-6cf3-48e0-a39d-b9f9cec7d095"] + 3.928837587478956*^9}, {3.940896272791565*^9, + 3.940896315980023*^9}},ExpressionUUID->"0f3722e5-6cf3-48e0-a39d-\ +b9f9cec7d095"] }, Open ]], Cell[CellGroupData[{ Cell["Constraints", "Subsubsection", - Editable->False, CellChangeTimes->{{3.928838372391102*^9, 3.9288383741909857`*^9}},ExpressionUUID->"aea00190-9ff0-4165-bc4a-\ 9094b2949563"], -Cell[BoxData[{ +Cell[BoxData[ RowBox[{ RowBox[{"SetEQN", "[", RowBox[{ RowBox[{"HC", "[", "]"}], ",", RowBox[{ - RowBox[{"trR", "[", "]"}], "+", RowBox[{ - RowBox[{"exAt", "[", + RowBox[{"invgam", "[", + RowBox[{"k", ",", "l"}], "]"}], + RowBox[{"R", "[", RowBox[{ RowBox[{"-", "k"}], ",", - RowBox[{"-", "l"}]}], "]"}], - RowBox[{"exAtUU", "[", - RowBox[{"k", ",", "l"}], "]"}]}], "-", + RowBox[{"-", "l"}]}], "]"}]}], "+", + SuperscriptBox[ + RowBox[{"trK", "[", "]"}], "2"], "-", RowBox[{ - FractionBox["2", "3"], - SuperscriptBox[ - RowBox[{"(", - RowBox[{ - RowBox[{"exKh", "[", "]"}], "+", - RowBox[{"2", - RowBox[{"Theta", "[", "]"}]}]}], ")"}], "2"]}], "-", - RowBox[{"16", " ", "cpi", " ", - RowBox[{"rho", "[", "]"}]}]}]}], "]"}], ";"}], "\[IndentingNewLine]", + RowBox[{"invgam", "[", + RowBox[{"i", ",", "k"}], "]"}], + RowBox[{"invgam", "[", + RowBox[{"j", ",", "l"}], "]"}], + RowBox[{"ADMK", "[", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], + RowBox[{"ADMK", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", + RowBox[{"-", "l"}]}], "]"}]}], "-", + RowBox[{"16", "cpi", " ", + RowBox[{"rho", "[", "]"}]}]}]}], "]"}], ";"}]], "Input", + Editable->False, + CellChangeTimes->{{3.940894573105879*^9, 3.940894687834464*^9}, { + 3.940894857588531*^9, 3.940894884463378*^9}}, + CellLabel->"In[21]:=",ExpressionUUID->"f9d74532-a3f3-452d-a719-7d4935c78d8d"], + +Cell[BoxData[ RowBox[{ RowBox[{"SetEQN", "[", RowBox[{ RowBox[{"MtC", "[", "i_", "]"}], ",", RowBox[{ - RowBox[{"dexAtUU", "[", - RowBox[{ - RowBox[{"-", "j"}], ",", "i", ",", "j"}], "]"}], "+", RowBox[{ - RowBox[{"Gt", "[", - RowBox[{"i", ",", + RowBox[{"-", + RowBox[{"invgam", "[", + RowBox[{"i", ",", "k"}], "]"}]}], + RowBox[{"invgam", "[", + RowBox[{"j", ",", "l"}], "]"}], + RowBox[{"DADMK", "[", + RowBox[{ RowBox[{"-", "j"}], ",", - RowBox[{"-", "k"}]}], "]"}], - RowBox[{"exAtUU", "[", - RowBox[{"j", ",", "k"}], "]"}]}], "-", + RowBox[{"-", "k"}], ",", + RowBox[{"-", "l"}]}], "]"}]}], "-", RowBox[{ - FractionBox["2", "3"], - RowBox[{"invgamt", "[", + RowBox[{"invgam", "[", RowBox[{"i", ",", "j"}], "]"}], - RowBox[{"(", + RowBox[{"invgam", "[", + RowBox[{"k", ",", "l"}], "]"}], + RowBox[{"DADMK", "[", RowBox[{ - RowBox[{"dexKh", "[", - RowBox[{"-", "j"}], "]"}], "+", - RowBox[{"2", - RowBox[{"dTheta", "[", - RowBox[{"-", "j"}], "]"}]}]}], ")"}]}], "-", - RowBox[{ - FractionBox["2", "3"], - RowBox[{"exAtUU", "[", - RowBox[{"i", ",", "j"}], "]"}], - SuperscriptBox[ - RowBox[{"chi", "[", "]"}], - RowBox[{"-", "1"}]], - RowBox[{"dchi", "[", - RowBox[{"-", "j"}], "]"}]}], "-", + RowBox[{"-", "j"}], ",", + RowBox[{"-", "k"}], ",", + RowBox[{"-", "l"}]}], "]"}]}], "-", RowBox[{"8", "cpi", " ", - RowBox[{"invgamt", "[", + RowBox[{"invgam", "[", RowBox[{"i", ",", "j"}], "]"}], RowBox[{"Sm", "[", - RowBox[{"-", "j"}], "]"}]}]}]}], "]"}], ";"}]}], "Input", - InitializationCell->True, - CellChangeTimes->{{3.928838379343862*^9, 3.928838434795819*^9}, { - 3.928838591512603*^9, 3.9288385946294413`*^9}, {3.92883866676774*^9, - 3.928838768805194*^9}, {3.9288394542052717`*^9, 3.928839458164912*^9}, { - 3.928844309306735*^9, 3.9288445005134497`*^9}, {3.940883629753191*^9, - 3.940883634691943*^9}},ExpressionUUID->"de7d67c1-605e-4f29-b6a7-\ -28029963f3cd"] + RowBox[{"-", "j"}], "]"}]}]}]}], "]"}], ";"}]], "Input", + CellChangeTimes->{{3.940895545009609*^9, 3.9408955814025393`*^9}, { + 3.940895640679975*^9, 3.940895667140218*^9}, 3.940896099640127*^9, { + 3.9408961321299467`*^9, 3.940896137732473*^9}, {3.94089619830234*^9, + 3.940896250853101*^9}}, + CellLabel->"In[23]:=",ExpressionUUID->"2539bb21-04c2-456d-9145-83172e324ec1"] }, Open ]] }, Open ]] }, Open ]] }, -WindowSize->{1792, 1067}, +WindowSize->{896, 1067}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, FrontEndVersion->"14.1 for Mac OS X x86 (64-bit) (July 16, 2024)", StyleDefinitions->"Default.nb", @@ -1378,100 +1365,99 @@ CellTagsIndex->{} (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ -Cell[580, 22, 531, 12, 45, "Input",ExpressionUUID->"9857cbce-1237-4124-83ba-143c7adb15bb", +Cell[580, 22, 531, 12, 65, "Input",ExpressionUUID->"9857cbce-1237-4124-83ba-143c7adb15bb", InitializationCell->True], Cell[CellGroupData[{ -Cell[1136, 38, 773, 13, 23, "Print",ExpressionUUID->"2d413a8c-afde-4f94-995b-ecb6c78e0d0e"], -Cell[1912, 53, 1045, 21, 23, "Print",ExpressionUUID->"5063455d-0819-4426-a7cd-a936ec5a18d3"], -Cell[2960, 76, 794, 13, 23, "Print",ExpressionUUID->"b2130651-b020-4f0d-b414-aecb07c8bb51"], -Cell[3757, 91, 753, 12, 23, "Print",ExpressionUUID->"21efd890-ca3e-4e48-abfc-2557ed72d15b"], -Cell[4513, 105, 734, 12, 23, "Print",ExpressionUUID->"443f8edf-6aeb-4b63-bbeb-6392d370114a"], -Cell[5250, 119, 773, 13, 23, "Print",ExpressionUUID->"19b61223-15f8-445c-87a7-05366f0cd520"], -Cell[6026, 134, 1051, 21, 23, "Print",ExpressionUUID->"98a6bade-745f-40c5-b829-851f4886cc64"], -Cell[7080, 157, 796, 13, 23, "Print",ExpressionUUID->"9c6b1c40-abba-4c22-9ce5-fd0ba270ce6f"], -Cell[7879, 172, 773, 13, 23, "Print",ExpressionUUID->"4268e72f-8cd6-4e23-94b7-639cef899a6b"], -Cell[8655, 187, 927, 15, 23, "Print",ExpressionUUID->"440fa9ee-00bc-4842-9415-8118f94d2fbe"], -Cell[9585, 204, 773, 13, 23, "Print",ExpressionUUID->"1661913c-3e50-4257-a01b-4ea5f1e088ed"], -Cell[10361, 219, 773, 13, 23, "Print",ExpressionUUID->"f20e3e8c-53f4-4d6f-b58c-a1038625751e"], -Cell[11137, 234, 1045, 21, 23, "Print",ExpressionUUID->"fb9a748e-d6d4-417b-bf17-777aba62c9f0"], -Cell[12185, 257, 814, 13, 23, "Print",ExpressionUUID->"7a9a155b-7934-41fe-98de-c5e719313a9d"], -Cell[13002, 272, 775, 13, 23, "Print",ExpressionUUID->"b23d5798-2957-4ac0-a5d9-b540b832f678"], -Cell[13780, 287, 927, 15, 23, "Print",ExpressionUUID->"0fac0347-f8f8-4061-b0ce-dca9ca5a657b"], -Cell[14710, 304, 773, 13, 23, "Print",ExpressionUUID->"87433911-a72e-42c5-901f-d6d4c55f3e5c"], -Cell[15486, 319, 773, 13, 23, "Print",ExpressionUUID->"7df0469d-be51-40b1-b138-7c20ec4f0ea3"], -Cell[16262, 334, 749, 12, 23, "Print",ExpressionUUID->"bdf91799-7d12-4aa6-b728-654417a43d7c"], -Cell[17014, 348, 773, 13, 23, "Print",ExpressionUUID->"1f48e0da-b53c-4634-928d-31dc80e81f67"], -Cell[17790, 363, 773, 13, 23, "Print",ExpressionUUID->"d2f15395-4e3f-4bc7-97c5-57afa904824f"], -Cell[18566, 378, 753, 12, 23, "Print",ExpressionUUID->"c487e186-0b38-4a9d-8de5-b0e1219da427"], -Cell[19322, 392, 775, 13, 23, "Print",ExpressionUUID->"f07dd22b-7ecf-4e2f-9c19-c3839154085b"], -Cell[20100, 407, 775, 13, 23, "Print",ExpressionUUID->"14f387a5-5f53-42c4-a285-efbb64f0713e"], -Cell[20878, 422, 753, 12, 23, "Print",ExpressionUUID->"71ad03b8-4a27-442d-9c9c-62cee9dc5e26"], -Cell[21634, 436, 775, 13, 23, "Print",ExpressionUUID->"5f6aa3c6-7bab-4969-abc2-3edc76e474bc"], -Cell[22412, 451, 775, 13, 23, "Print",ExpressionUUID->"250082e4-2673-4abb-848c-e4dfe11295fa"], -Cell[23190, 466, 753, 12, 23, "Print",ExpressionUUID->"6d4f5338-4c2e-4237-9c39-6d3d5abb6237"], -Cell[23946, 480, 773, 13, 23, "Print",ExpressionUUID->"46921bd2-d6fe-4a16-b844-a67fbeb98326"], -Cell[24722, 495, 773, 13, 23, "Print",ExpressionUUID->"98432958-fdc5-4b68-bdaa-fa9084fb5d85"], -Cell[25498, 510, 755, 12, 23, "Print",ExpressionUUID->"51ee7a70-3f39-42f5-b499-f8bb8b7bfcd9"], -Cell[26256, 524, 773, 13, 23, "Print",ExpressionUUID->"c6532e3b-c63e-4993-86dd-c058b2b84425"], -Cell[27032, 539, 773, 13, 23, "Print",ExpressionUUID->"dd71a352-e2b7-4f91-947d-746836026c60"], -Cell[27808, 554, 756, 12, 23, "Print",ExpressionUUID->"c87e12a6-b74f-4713-8e6c-4c4c826d5a49"], -Cell[28567, 568, 773, 13, 23, "Print",ExpressionUUID->"edd22973-4785-4732-a954-d69990b4757b"], -Cell[29343, 583, 713, 12, 23, "Print",ExpressionUUID->"ca3387bf-41e7-4600-a4bd-e839cfb8aa92"] +Cell[1136, 38, 846, 14, 23, "Print",ExpressionUUID->"960e2aea-3640-4c4b-99d7-ad3552e44aa0"], +Cell[1985, 54, 1116, 22, 23, "Print",ExpressionUUID->"270ddc26-f293-42c7-951b-09ce50057326"], +Cell[3104, 78, 865, 14, 23, "Print",ExpressionUUID->"9d464697-9d75-4fa0-aa78-7da9b1c04cd5"], +Cell[3972, 94, 822, 13, 23, "Print",ExpressionUUID->"9b4426f5-23b4-4c5d-a0b7-0395ab1c3139"], +Cell[4797, 109, 805, 13, 23, "Print",ExpressionUUID->"2ada16dc-f632-420a-a175-efb109277a65"], +Cell[5605, 124, 846, 14, 23, "Print",ExpressionUUID->"3d282824-fc17-49e2-ae93-e2849fe46ca4"], +Cell[6454, 140, 1122, 22, 23, "Print",ExpressionUUID->"6c30165f-4fb9-48d9-ae79-64b2a9530c29"], +Cell[7579, 164, 865, 14, 23, "Print",ExpressionUUID->"06129bbf-451f-4a59-8ecd-8828b612ccec"], +Cell[8447, 180, 844, 14, 23, "Print",ExpressionUUID->"9e028197-1d0f-40ae-81ef-4e3180b22a7b"], +Cell[9294, 196, 999, 16, 41, "Print",ExpressionUUID->"ea8f1a9a-8651-4a02-afdf-a8ce6bf3b3e2"], +Cell[10296, 214, 846, 14, 23, "Print",ExpressionUUID->"92ac23a6-8e9e-4004-9b2c-ddeaa7e63682"], +Cell[11145, 230, 843, 14, 23, "Print",ExpressionUUID->"0ead17e8-9122-49f6-b430-625a85989719"], +Cell[11991, 246, 1116, 22, 23, "Print",ExpressionUUID->"201d47dc-5727-40a1-94be-e35d5b2de144"], +Cell[13110, 270, 885, 14, 23, "Print",ExpressionUUID->"994c931d-0e7a-4613-909d-41610b233d47"], +Cell[13998, 286, 843, 14, 23, "Print",ExpressionUUID->"848bc993-593e-4741-8e7d-5a142245a7b0"], +Cell[14844, 302, 999, 16, 41, "Print",ExpressionUUID->"952c9782-95b6-4f07-96e1-099e03e50874"], +Cell[15846, 320, 844, 14, 23, "Print",ExpressionUUID->"9c9dfb68-d150-4d47-a3de-5b07fb9a3a87"], +Cell[16693, 336, 844, 14, 23, "Print",ExpressionUUID->"8b3f770a-ea9f-4341-9b86-39080c653e4e"], +Cell[17540, 352, 820, 13, 23, "Print",ExpressionUUID->"a7c74cbd-4cee-4108-b3a9-0d8feb4235aa"], +Cell[18363, 367, 844, 14, 23, "Print",ExpressionUUID->"df2b13e5-0479-4551-9b3a-35f018113808"], +Cell[19210, 383, 844, 14, 23, "Print",ExpressionUUID->"0aa951e3-0f08-40d0-9000-5a73643e757a"], +Cell[20057, 399, 824, 13, 23, "Print",ExpressionUUID->"bc18d4a7-4ac7-44c6-b014-d3b0ef82a60d"], +Cell[20884, 414, 844, 14, 23, "Print",ExpressionUUID->"bfeb5f35-c536-4f3f-b7ea-08ccfc0548f6"], +Cell[21731, 430, 844, 14, 23, "Print",ExpressionUUID->"329239f6-e906-499a-88b4-ddecb2ca4fdb"], +Cell[22578, 446, 824, 13, 23, "Print",ExpressionUUID->"3d6c0aca-79f5-45e9-b922-332980031e90"], +Cell[23405, 461, 846, 14, 23, "Print",ExpressionUUID->"ac2d3a49-1392-4515-ab60-ed00a6f40213"], +Cell[24254, 477, 844, 14, 23, "Print",ExpressionUUID->"29b4b0fa-b21e-4e7e-bad1-e49884c849fc"], +Cell[25101, 493, 822, 13, 23, "Print",ExpressionUUID->"21926ba2-2cff-4647-9863-45b4c9f2e258"], +Cell[25926, 508, 844, 14, 23, "Print",ExpressionUUID->"fe4a67af-834b-4964-8169-aaf79083e1bd"], +Cell[26773, 524, 844, 14, 23, "Print",ExpressionUUID->"550e2ce4-9d3f-46da-9dc9-9440a964036e"], +Cell[27620, 540, 824, 13, 23, "Print",ExpressionUUID->"1a0551c3-8b39-43c6-ba77-653aee99b6c6"], +Cell[28447, 555, 844, 14, 23, "Print",ExpressionUUID->"a2715f91-f297-42fb-94ae-470c03294596"], +Cell[29294, 571, 846, 14, 23, "Print",ExpressionUUID->"d57fef39-1ed8-42b7-a3de-747a9d668f43"], +Cell[30143, 587, 825, 13, 23, "Print",ExpressionUUID->"554c32c0-301d-45a4-840f-047e516ba95e"], +Cell[30971, 602, 846, 14, 23, "Print",ExpressionUUID->"ca4a35a5-1968-44fa-8267-9ee12a74f98d"], +Cell[31820, 618, 782, 13, 23, "Print",ExpressionUUID->"18abfc4f-b472-442b-8225-b8149e7b2952"] }, Open ]] }, Open ]], Cell[CellGroupData[{ -Cell[30105, 601, 227, 5, 66, "Section",ExpressionUUID->"d93e9e9c-e043-49bf-adc4-613bb015a823"], -Cell[30335, 608, 373, 9, 45, "Input",ExpressionUUID->"dc88cf1b-3b54-44ff-b471-d7efa31651a2", +Cell[32651, 637, 227, 5, 66, "Section",ExpressionUUID->"d93e9e9c-e043-49bf-adc4-613bb015a823"], +Cell[32881, 644, 373, 9, 45, "Input",ExpressionUUID->"dc88cf1b-3b54-44ff-b471-d7efa31651a2", InitializationCell->True], Cell[CellGroupData[{ -Cell[30733, 621, 224, 5, 53, "Subsection",ExpressionUUID->"8f6e447f-5ad1-4983-a220-4a62c32eb45e"], -Cell[30960, 628, 1702, 51, 147, "Input",ExpressionUUID->"4879eb5d-4927-4d70-8345-bbceb0091220", +Cell[33279, 657, 224, 5, 53, "Subsection",ExpressionUUID->"8f6e447f-5ad1-4983-a220-4a62c32eb45e"], +Cell[33506, 664, 1702, 51, 147, "Input",ExpressionUUID->"4879eb5d-4927-4d70-8345-bbceb0091220", + InitializationCell->True], +Cell[35211, 717, 1982, 58, 167, "Input",ExpressionUUID->"ede93dc0-606a-46a8-bf03-9b4328dc7c60", InitializationCell->True], -Cell[32665, 681, 1982, 58, 147, "Input",ExpressionUUID->"ede93dc0-606a-46a8-bf03-9b4328dc7c60", +Cell[37196, 777, 1107, 27, 86, "Input",ExpressionUUID->"2f2a6a6e-f59d-4dc4-8900-9dcb96af2d35", InitializationCell->True], -Cell[34650, 741, 1110, 30, 127, "Input",ExpressionUUID->"c08588c0-b1be-4279-a26f-ad8578054e37", +Cell[38306, 806, 1110, 30, 127, "Input",ExpressionUUID->"c08588c0-b1be-4279-a26f-ad8578054e37", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ -Cell[35797, 776, 172, 4, 53, "Subsection",ExpressionUUID->"1fd445a5-eeab-43da-98f4-96f9414b6b16"], -Cell[35972, 782, 2790, 64, 147, "Input",ExpressionUUID->"230e3e3d-ec24-4b15-9bc4-4c66fa656cc7", - InitializationCell->True], -Cell[38765, 848, 880, 25, 106, "Input",ExpressionUUID->"b2cd1bbb-ebc2-4ae5-98e8-1baa91d81aa3", +Cell[39453, 841, 172, 4, 53, "Subsection",ExpressionUUID->"1fd445a5-eeab-43da-98f4-96f9414b6b16"], +Cell[39628, 847, 4411, 111, 229, "Input",ExpressionUUID->"230e3e3d-ec24-4b15-9bc4-4c66fa656cc7", InitializationCell->True], Cell[CellGroupData[{ -Cell[39670, 877, 175, 4, 43, "Subsubsection",ExpressionUUID->"63c86796-f445-4596-a568-cf6b7233992a"], -Cell[39848, 883, 1327, 38, 147, "Input",ExpressionUUID->"61eaa4ba-0069-4a97-a6d7-a02ee559a741", +Cell[44064, 962, 175, 4, 43, "Subsubsection",ExpressionUUID->"63c86796-f445-4596-a568-cf6b7233992a"], +Cell[44242, 968, 780, 20, 106, "Input",ExpressionUUID->"61eaa4ba-0069-4a97-a6d7-a02ee559a741", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ -Cell[41212, 926, 180, 4, 43, "Subsubsection",ExpressionUUID->"28d203fe-58c8-4126-8774-88d5a1781306"], -Cell[41395, 932, 673, 18, 106, "Input",ExpressionUUID->"5502d63c-b6fc-4a63-a203-12b5cbab9476", +Cell[45059, 993, 180, 4, 43, "Subsubsection",ExpressionUUID->"28d203fe-58c8-4126-8774-88d5a1781306"], +Cell[45242, 999, 673, 18, 106, "Input",ExpressionUUID->"5502d63c-b6fc-4a63-a203-12b5cbab9476", InitializationCell->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ -Cell[42117, 956, 174, 4, 53, "Subsection",ExpressionUUID->"ab64c7df-87cb-4c7d-990a-2b0543e709db"], -Cell[42294, 962, 498, 10, 45, "Input",ExpressionUUID->"e471a9d0-e772-4737-b68b-dc67e2be03b9", +Cell[45964, 1023, 174, 4, 53, "Subsection",ExpressionUUID->"ab64c7df-87cb-4c7d-990a-2b0543e709db"], +Cell[46141, 1029, 498, 10, 45, "Input",ExpressionUUID->"e471a9d0-e772-4737-b68b-dc67e2be03b9", InitializationCell->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ -Cell[42841, 978, 166, 4, 66, "Section",ExpressionUUID->"519fe4de-6999-4db6-9e6b-17dff89f6b40"], +Cell[46688, 1045, 166, 4, 66, "Section",ExpressionUUID->"519fe4de-6999-4db6-9e6b-17dff89f6b40"], Cell[CellGroupData[{ -Cell[43032, 986, 170, 4, 53, "Subsection",ExpressionUUID->"29fb9a40-8f32-4735-bf46-1b2322d6762f"], -Cell[43205, 992, 2079, 61, 121, "Input",ExpressionUUID->"06d87d1d-b673-41db-8089-81c4e3d83936", - InitializationCell->True], -Cell[45287, 1055, 4683, 143, 169, "Input",ExpressionUUID->"761ee28a-77fa-409e-93f8-f3c874c11e4e", - InitializationCell->True], +Cell[46879, 1053, 170, 4, 53, "Subsection",ExpressionUUID->"29fb9a40-8f32-4735-bf46-1b2322d6762f"], +Cell[47052, 1059, 2651, 72, 156, "Input",ExpressionUUID->"06d87d1d-b673-41db-8089-81c4e3d83936"], +Cell[49706, 1133, 935, 28, 49, "Input",ExpressionUUID->"73ae3fe4-58f9-4733-946d-e922b451b632"], +Cell[50644, 1163, 509, 15, 29, "Input",ExpressionUUID->"52285f16-cbd6-4f41-8e30-7dc7a405d3f4"], +Cell[51156, 1180, 903, 25, 29, "Input",ExpressionUUID->"63c26313-037a-484b-ad0f-4bd8ed3260e8"], Cell[CellGroupData[{ -Cell[49995, 1202, 175, 4, 43, "Subsubsection",ExpressionUUID->"21635a48-b393-484a-82e9-abbe12d2c210"], -Cell[50173, 1208, 2211, 68, 111, "Input",ExpressionUUID->"0f3722e5-6cf3-48e0-a39d-b9f9cec7d095", - InitializationCell->True] +Cell[52084, 1209, 157, 3, 43, "Subsubsection",ExpressionUUID->"21635a48-b393-484a-82e9-abbe12d2c210"], +Cell[52244, 1214, 1676, 49, 53, "Input",ExpressionUUID->"0f3722e5-6cf3-48e0-a39d-b9f9cec7d095"] }, Open ]], Cell[CellGroupData[{ -Cell[52421, 1281, 182, 4, 43, "Subsubsection",ExpressionUUID->"aea00190-9ff0-4165-bc4a-9094b2949563"], -Cell[52606, 1287, 2325, 70, 96, "Input",ExpressionUUID->"de7d67c1-605e-4f29-b6a7-28029963f3cd", - InitializationCell->True] +Cell[53957, 1268, 164, 3, 43, "Subsubsection",ExpressionUUID->"aea00190-9ff0-4165-bc4a-9094b2949563"], +Cell[54124, 1273, 1080, 33, 53, "Input",ExpressionUUID->"f9d74532-a3f3-452d-a719-7d4935c78d8d"], +Cell[55207, 1308, 1276, 36, 49, "Input",ExpressionUUID->"2539bb21-04c2-456d-9145-83172e324ec1"] }, Open ]] }, Open ]] }, Open ]] From cc44433063a9dcf287454d61e988dc267014bc63 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 08:30:34 -0500 Subject: [PATCH 07/37] ADMconstraints: update ADM_vars.wl --- ADMconstraints/wolfram/wl/ADM_vars.wl | 74 +++++++++++++++++++++++++-- 1 file changed, 70 insertions(+), 4 deletions(-) diff --git a/ADMconstraints/wolfram/wl/ADM_vars.wl b/ADMconstraints/wolfram/wl/ADM_vars.wl index 51b343fe..c0589b2b 100644 --- a/ADMconstraints/wolfram/wl/ADM_vars.wl +++ b/ADMconstraints/wolfram/wl/ADM_vars.wl @@ -6,14 +6,80 @@ (* ADM variables *) +(*******************) + +(* Input 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]\), \((ADM)\)]\)"} - *) ]; + +dADMVarlist = + GridTensors[ + {dADMgam[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*SuperscriptBox[\(\[Gamma]\), \((ADM)\)]\)"}, + {dADMK[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*SuperscriptBox[\(K\), \((ADM)\)]\)"} + ]; + +ddADMVarlist = + GridTensors[ + {ddADMgam[-k, -l, -i, -j], GenSet[Cycles[{1, 2}], Cycles[{3, 4}]], PrintAs -> "\[PartialD]\!\(\*SuperscriptBox[\(\[Gamma]\), \((ADM)\)]\)"} + ]; + +TmunuVarlist = + GridTensors[ + {eTtt[], PrintAs -> "\!\(\*SubscriptBox[\(T\), \(tt\)]\)"}, + {eTt[-i], PrintAs -> "\!\(\*SubscriptBox[\(T\), \(t\)]\)"}, + {eT[-i, -j], Symmetric[{-i, -j}], PrintAs -> "T"} + ]; + +(**************************) + +(* Intermediate Variables *) + +(**************************) + +IntermediateVarlist = + TempTensors[ + {detinvgam[], PrintAs -> "1/\[Gamma]"}, + {invgam[i, j], Symmetric[{i, j}], PrintAs -> "\[Gamma]"}, + {GamDDD [-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[CapitalGamma]"}, + {Gam [k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[CapitalGamma]"}, + {dGam[-m, k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[CapitalGamma]"}, + {R[-i, -j], Symmetric[{-i, -j}]}, + {trK[], PrintAs -> "K"}, + {DADMK[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[Del]K"} + ]; + +(* Matter *) + +MatterVarlist = + TempTensors[ + {rho[], PrintAs -> "\[Rho]"}, + {Sm[-i], PrintAs -> "S"} + ]; + +(***************) + +(* Constraints *) + +(***************) + +ConstraintVarlist = + GridTensors[ + {HC[], PrintAs -> "H"}, + {MtC[i], PrintAs -> "M"} + ]; + +(************) + +(* Constant *) + +(************) + +DefConstantSymbol[cpi, PrintAs -> "\[Pi]"]; From d508df41343bb2d3e0c108a575506a85f8486654 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 14:05:47 -0500 Subject: [PATCH 08/37] ADMconstraints: update type_in_rhs.nb --- ADMconstraints/wolfram/type_in_rhs.nb | 466 ++++++++++++++++---------- ADMconstraints/wolfram/wl/ADM_vars.wl | 9 +- 2 files changed, 288 insertions(+), 187 deletions(-) diff --git a/ADMconstraints/wolfram/type_in_rhs.nb b/ADMconstraints/wolfram/type_in_rhs.nb index c4a2a6d3..ba45a003 100644 --- a/ADMconstraints/wolfram/type_in_rhs.nb +++ b/ADMconstraints/wolfram/type_in_rhs.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 63486, 1459] -NotebookOptionsPosition[ 56523, 1349] -NotebookOutlinePosition[ 56915, 1365] -CellTagsIndexPosition[ 56872, 1362] +NotebookDataLength[ 67855, 1559] +NotebookOptionsPosition[ 60597, 1446] +NotebookOutlinePosition[ 60990, 1462] +CellTagsIndexPosition[ 60947, 1459] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -47,10 +47,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.9408947819049664`*^9}, + 3.9408947819049664`*^9, 3.940945134483776*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"960e2aea-3640-4c4b-99d7-ad3552e44aa0"], +In[1]:=",ExpressionUUID->"ba6a3bac-2e7c-4d46-9c03-b5f3ba5afa0a"], Cell[BoxData[ InterpretationBox[ @@ -71,10 +71,10 @@ Cell[BoxData[ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894781906104*^9}, + 3.9408947819049664`*^9, 3.940945134485121*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"270ddc26-f293-42c7-951b-09ce50057326"], +In[1]:=",ExpressionUUID->"1e4d304c-2c59-45f8-8518-85d9c941106c"], Cell[BoxData["\<\"CopyRight (C) 2003-2020, Jose M. Martin-Garcia, under the \ General Public License.\"\>"], "Print", @@ -87,10 +87,10 @@ General Public License.\"\>"], "Print", 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894781908741*^9}, + 3.9408947819049664`*^9, 3.9409451344876747`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"9d464697-9d75-4fa0-aa78-7da9b1c04cd5"], +In[1]:=",ExpressionUUID->"4260da05-bfea-41c3-9086-068f84123082"], Cell[BoxData["\<\"Connecting to external mac executable...\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -102,10 +102,10 @@ Cell[BoxData["\<\"Connecting to external mac executable...\"\>"], "Print", 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894781987438*^9}, + 3.9408947819049664`*^9, 3.940945134573299*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"9b4426f5-23b4-4c5d-a0b7-0395ab1c3139"], +In[1]:=",ExpressionUUID->"72c7a15c-9fd0-44d1-8dfa-4136f7bc90b5"], Cell[BoxData["\<\"Connection established.\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -117,10 +117,10 @@ Cell[BoxData["\<\"Connection established.\"\>"], "Print", 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894782100172*^9}, + 3.9408947819049664`*^9, 3.940945134685794*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"2ada16dc-f632-420a-a175-efb109277a65"], +In[1]:=",ExpressionUUID->"5bf5737c-59a6-4a05-b6a4-750a3c4f68b4"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -133,10 +133,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.9408947821011877`*^9}, + 3.9408947819049664`*^9, 3.940945134686883*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"3d282824-fc17-49e2-ae93-e2849fe46ca4"], +In[1]:=",ExpressionUUID->"836920d6-996d-411c-81ae-8a0dd4cf8ea0"], Cell[BoxData[ InterpretationBox[ @@ -157,10 +157,10 @@ Cell[BoxData[ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894782101965*^9}, + 3.9408947819049664`*^9, 3.9409451346876593`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"6c30165f-4fb9-48d9-ae79-64b2a9530c29"], +In[1]:=",ExpressionUUID->"e17827c6-4c8d-4e3a-be69-f656210b3f1d"], Cell[BoxData["\<\"CopyRight (C) 2002-2021, Jose M. Martin-Garcia, under the \ General Public License.\"\>"], "Print", @@ -173,10 +173,10 @@ General Public License.\"\>"], "Print", 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894782102714*^9}, + 3.9408947819049664`*^9, 3.940945134688396*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"06129bbf-451f-4a59-8ecd-8828b612ccec"], +In[1]:=",ExpressionUUID->"2a7ad527-c0af-4c6d-ac66-abffa1da874c"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -189,10 +189,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894782118977*^9}, + 3.9408947819049664`*^9, 3.940945134704289*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"9e028197-1d0f-40ae-81ef-4e3180b22a7b"], +In[1]:=",ExpressionUUID->"ffda4c26-5bca-4dc3-adbb-852d2afabbfb"], Cell[BoxData["\<\"These packages come with ABSOLUTELY NO WARRANTY; for \ details type Disclaimer[]. This is free software, and you are welcome to \ @@ -207,10 +207,10 @@ details.\"\>"], "Print", 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894782120069*^9}, + 3.9408947819049664`*^9, 3.940945134705164*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"ea8f1a9a-8651-4a02-afdf-a8ce6bf3b3e2"], +In[1]:=",ExpressionUUID->"dc5d0a86-f88f-43c2-8504-8db94b1165a3"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -223,10 +223,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.9408947821211443`*^9}, + 3.9408947819049664`*^9, 3.940945134706004*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"92ac23a6-8e9e-4004-9b2c-ddeaa7e63682"], +In[1]:=",ExpressionUUID->"fb899cbd-b6f3-4b6e-904a-a778b4053f9b"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -239,10 +239,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.94089478230459*^9}, + 3.9408947819049664`*^9, 3.940945134936344*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"0ead17e8-9122-49f6-b430-625a85989719"], +In[1]:=",ExpressionUUID->"70617423-e9b2-4fd5-925d-aa065a77e111"], Cell[BoxData[ InterpretationBox[ @@ -263,10 +263,10 @@ Cell[BoxData[ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894782305696*^9}, + 3.9408947819049664`*^9, 3.940945134937449*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"201d47dc-5727-40a1-94be-e35d5b2de144"], +In[1]:=",ExpressionUUID->"0a572555-05f4-461a-88d2-2b2ccb8104ff"], Cell[BoxData["\<\"CopyRight (C) 2005-2021, David Yllanes and Jose M. \ Martin-Garcia, under the General Public License.\"\>"], "Print", @@ -279,10 +279,10 @@ Martin-Garcia, under the General Public License.\"\>"], "Print", 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.9408947823065357`*^9}, + 3.9408947819049664`*^9, 3.940945134938333*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"994c931d-0e7a-4613-909d-41610b233d47"], +In[1]:=",ExpressionUUID->"42ef8c7c-3ff8-4ab2-9c65-b588d809b6c7"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -295,10 +295,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.94089478232628*^9}, + 3.9408947819049664`*^9, 3.9409451349575644`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"848bc993-593e-4741-8e7d-5a142245a7b0"], +In[1]:=",ExpressionUUID->"ffa9c04f-8dfe-40de-8dd6-d3a0223a39bb"], Cell[BoxData["\<\"These packages come with ABSOLUTELY NO WARRANTY; for \ details type Disclaimer[]. This is free software, and you are welcome to \ @@ -313,10 +313,10 @@ details.\"\>"], "Print", 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894782327444*^9}, + 3.9408947819049664`*^9, 3.940945134958641*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"952c9782-95b6-4f07-96e1-099e03e50874"], +In[1]:=",ExpressionUUID->"f429ab13-385a-4d3b-bb2f-a393a57c2061"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -329,10 +329,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894782328567*^9}, + 3.9408947819049664`*^9, 3.9409451349596157`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"9c9dfb68-d150-4d47-a3de-5b07fb9a3a87"], +In[1]:=",ExpressionUUID->"b332e86a-4ec6-4054-ad77-d4a937608b98"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -345,10 +345,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784002359*^9}, + 3.9408947819049664`*^9, 3.940945136985634*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"8b3f770a-ea9f-4341-9b86-39080c653e4e"], +In[1]:=",ExpressionUUID->"73f2d98b-30dd-43c8-8910-e109a366b507"], Cell[BoxData["\<\"Package Generato`Basic`, {2024, 1, 11}\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -360,10 +360,10 @@ Cell[BoxData["\<\"Package Generato`Basic`, {2024, 1, 11}\"\>"], "Print", 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784003731*^9}, + 3.9408947819049664`*^9, 3.940945136986679*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"a7c74cbd-4cee-4108-b3a9-0d8feb4235aa"], +In[1]:=",ExpressionUUID->"ce54eb97-bed1-4441-ba0f-f05fbdc49154"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -376,10 +376,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784004771*^9}, + 3.9408947819049664`*^9, 3.940945136987465*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"df2b13e5-0479-4551-9b3a-35f018113808"], +In[1]:=",ExpressionUUID->"66e2d823-0ba4-432f-9fb6-1a09a9727559"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -392,10 +392,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784006069*^9}, + 3.9408947819049664`*^9, 3.940945136988227*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"0aa951e3-0f08-40d0-9000-5a73643e757a"], +In[1]:=",ExpressionUUID->"205117d5-a3c6-4a06-8b57-8b6cca3ae352"], Cell[BoxData["\<\"Package Generato`ParseMode`, {2024, 7, 06}\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -407,10 +407,10 @@ Cell[BoxData["\<\"Package Generato`ParseMode`, {2024, 7, 06}\"\>"], "Print", 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784007107*^9}, + 3.9408947819049664`*^9, 3.940945136989024*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"bc18d4a7-4ac7-44c6-b014-d3b0ef82a60d"], +In[1]:=",ExpressionUUID->"d1f6eb6f-964f-4fe6-b26c-eccfdc8f274b"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -423,10 +423,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784008399*^9}, + 3.9408947819049664`*^9, 3.940945136989772*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"bfeb5f35-c536-4f3f-b7ea-08ccfc0548f6"], +In[1]:=",ExpressionUUID->"6a139613-191f-47a2-b619-18690dd0f75c"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -439,10 +439,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784009321*^9}, + 3.9408947819049664`*^9, 3.940945136990521*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"329239f6-e906-499a-88b4-ddecb2ca4fdb"], +In[1]:=",ExpressionUUID->"05b3d428-7847-44da-8e73-16da4a259f7f"], Cell[BoxData["\<\"Package Generato`Component`, {2024, 1, 11}\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -454,10 +454,10 @@ Cell[BoxData["\<\"Package Generato`Component`, {2024, 1, 11}\"\>"], "Print", 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784010365*^9}, + 3.9408947819049664`*^9, 3.940945136991404*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"3d6c0aca-79f5-45e9-b922-332980031e90"], +In[1]:=",ExpressionUUID->"dd705f5c-fea0-4255-9450-523ea0e8095d"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -470,10 +470,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.9408947840113087`*^9}, + 3.9408947819049664`*^9, 3.940945136992516*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"ac2d3a49-1392-4515-ab60-ed00a6f40213"], +In[1]:=",ExpressionUUID->"aaf3543e-866f-4d56-8b47-30898cfd75e1"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -486,10 +486,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784012226*^9}, + 3.9408947819049664`*^9, 3.9409451369933167`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"29b4b0fa-b21e-4e7e-bad1-e49884c849fc"], +In[1]:=",ExpressionUUID->"1ad19895-c0b9-42cb-88b4-54d28e5e0b51"], Cell[BoxData["\<\"Package Generato`Varlist`, {2024, 1, 11}\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -501,10 +501,10 @@ Cell[BoxData["\<\"Package Generato`Varlist`, {2024, 1, 11}\"\>"], "Print", 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784012988*^9}, + 3.9408947819049664`*^9, 3.940945136994347*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"21926ba2-2cff-4647-9863-45b4c9f2e258"], +In[1]:=",ExpressionUUID->"1159c3cc-1a75-4554-aba0-0a7fb05168b5"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -517,10 +517,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784013761*^9}, + 3.9408947819049664`*^9, 3.9409451369951887`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"fe4a67af-834b-4964-8169-aaf79083e1bd"], +In[1]:=",ExpressionUUID->"7453d1cb-82a6-45c3-9344-bc1f094117fd"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -533,10 +533,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784015128*^9}, + 3.9408947819049664`*^9, 3.9409451369960623`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"550e2ce4-9d3f-46da-9dc9-9440a964036e"], +In[1]:=",ExpressionUUID->"6b10df87-d187-4412-b800-d26ec6a719f9"], Cell[BoxData["\<\"Package Generato`Interface`, {2024, 1, 11}\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -548,10 +548,10 @@ Cell[BoxData["\<\"Package Generato`Interface`, {2024, 1, 11}\"\>"], "Print", 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784016077*^9}, + 3.9408947819049664`*^9, 3.940945136996851*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"1a0551c3-8b39-43c6-ba77-653aee99b6c6"], +In[1]:=",ExpressionUUID->"c5519c0a-5a1b-4a95-8893-2a6db3f9cef6"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -564,10 +564,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784016852*^9}, + 3.9408947819049664`*^9, 3.940945136997596*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"a2715f91-f297-42fb-94ae-470c03294596"], +In[1]:=",ExpressionUUID->"40c49305-6221-4355-8442-11721afd7347"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -580,10 +580,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.9408947840176687`*^9}, + 3.9408947819049664`*^9, 3.940945136998397*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"d57fef39-1ed8-42b7-a3de-747a9d668f43"], +In[1]:=",ExpressionUUID->"dc10054a-3c73-4dca-bb48-875d6b2a8978"], Cell[BoxData["\<\"Package Generato`Derivation`, {2024, 1, 18}\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -595,10 +595,10 @@ Cell[BoxData["\<\"Package Generato`Derivation`, {2024, 1, 18}\"\>"], "Print", 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784018437*^9}, + 3.9408947819049664`*^9, 3.940945136999214*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"554c32c0-301d-45a4-840f-047e516ba95e"], +In[1]:=",ExpressionUUID->"5a0d67c0-c6f6-40bd-9395-92cf5b37af5f"], Cell[BoxData["\<\"------------------------------------------------------------\ \"\>"], "Print", @@ -611,10 +611,10 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.9408947840192013`*^9}, + 3.9408947819049664`*^9, 3.940945137000165*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"ca4a35a5-1968-44fa-8267-9ee12a74f98d"], +In[1]:=",ExpressionUUID->"900589e3-b704-4273-9722-da1e9810498d"], Cell[BoxData["\<\"\"\>"], "Print", CellChangeTimes->{3.928779369275519*^9, 3.928785921920507*^9, @@ -626,10 +626,10 @@ Cell[BoxData["\<\"\"\>"], "Print", 3.928821943000177*^9, 3.928838600341427*^9, 3.928921219102206*^9, 3.928922529309305*^9, 3.9289227830989847`*^9, 3.9289233884139633`*^9, 3.940882755363988*^9, 3.9408931964849997`*^9, 3.940894397020772*^9, - 3.940894784020018*^9}, + 3.9408947819049664`*^9, 3.940945137000951*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"18abfc4f-b472-442b-8225-b8149e7b2952"] +In[1]:=",ExpressionUUID->"28367d85-f7da-4971-9273-fa485eb9a4d9"] }, Open ]] }, Open ]], @@ -892,9 +892,8 @@ Cell[BoxData[ "\[IndentingNewLine]", RowBox[{"{", RowBox[{ - RowBox[{"dGam", "[", + RowBox[{"tr1dGam", "[", RowBox[{ - RowBox[{"-", "m"}], ",", "k", ",", RowBox[{"-", "i"}], ",", RowBox[{"-", "j"}]}], "]"}], ",", RowBox[{"Symmetric", "[", @@ -902,8 +901,25 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", "i"}], ",", RowBox[{"-", "j"}]}], "}"}], "]"}], ",", - RowBox[{"PrintAs", "->", "\"\<\[PartialD]\[CapitalGamma]\>\""}]}], - "}"}], ",", "\[IndentingNewLine]", + RowBox[{ + "PrintAs", "->", + "\"\<\[PartialD]\!\(\*SuperscriptBox[\(\[CapitalGamma]\), \((tr1)\)]\)\ +\>\""}]}], "}"}], ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"tr2dGam", "[", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "]"}], ",", + RowBox[{"Symmetric", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "i"}], ",", + RowBox[{"-", "j"}]}], "}"}], "]"}], ",", + RowBox[{ + "PrintAs", "->", + "\"\<\[PartialD]\!\(\*SuperscriptBox[\(\[CapitalGamma]\), \((tr2)\)]\)\ +\>\""}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"R", "[", @@ -955,7 +971,8 @@ Cell[BoxData[ 3.940883897345069*^9}, {3.940884062866747*^9, 3.9408840633842583`*^9}, { 3.940892974894392*^9, 3.940893086922902*^9}, {3.940894308123448*^9, 3.940894312904497*^9}, {3.94089437805265*^9, 3.940894379030416*^9}, { - 3.94089472521984*^9, 3.9408947375365887`*^9}}, + 3.94089472521984*^9, 3.9408947375365887`*^9}, {3.940945058246612*^9, + 3.940945078629178*^9}}, CellLabel->"In[7]:=",ExpressionUUID->"230e3e3d-ec24-4b15-9bc4-4c66fa656cc7"], Cell[CellGroupData[{ @@ -985,8 +1002,8 @@ Cell[BoxData[ CellChangeTimes->{{3.928790254224685*^9, 3.928790291322857*^9}, { 3.928790623947823*^9, 3.928790696710313*^9}, {3.928790869029275*^9, 3.928790972579005*^9}, 3.92879101482416*^9, {3.940896320864653*^9, - 3.940896329996352*^9}},ExpressionUUID->"61eaa4ba-0069-4a97-a6d7-\ -a02ee559a741"] + 3.940896329996352*^9}}, + CellLabel->"In[8]:=",ExpressionUUID->"61eaa4ba-0069-4a97-a6d7-a02ee559a741"] }, Open ]], Cell[CellGroupData[{ @@ -1085,13 +1102,39 @@ Cell[BoxData[{ RowBox[{"GamDDD", "[", RowBox[{ RowBox[{"-", "l"}], ",", "i", ",", "j"}], "]"}]}]}], "]"}], - ";"}], "\[IndentingNewLine]", + ";"}]}], "Input", + CellChangeTimes->{{3.92882045451426*^9, 3.928820494015818*^9}, { + 3.92882054464657*^9, 3.928820550091407*^9}, {3.928822389143814*^9, + 3.928822403936602*^9}, {3.928822478660738*^9, 3.9288225192530327`*^9}, { + 3.9288361544164658`*^9, 3.928836162461919*^9}, {3.92892211822755*^9, + 3.928922119069038*^9}, {3.940883914871763*^9, 3.940884055385359*^9}, { + 3.940893223443261*^9, 3.940893458716525*^9}, {3.940893622642169*^9, + 3.9408937202483683`*^9}, {3.940894063701812*^9, 3.94089406708775*^9}, { + 3.940894251213398*^9, 3.940894253919017*^9}, {3.940945100043518*^9, + 3.940945124563795*^9}}, + CellLabel->"In[11]:=",ExpressionUUID->"06d87d1d-b673-41db-8089-81c4e3d83936"], + +Cell[BoxData[ RowBox[{ RowBox[{"SetEQN", "[", RowBox[{ - RowBox[{"dGam", "[", - RowBox[{"m_", ",", "k_", ",", "i_", ",", "j_"}], "]"}], ",", + RowBox[{"tr1dGam", "[", + RowBox[{"i_", ",", "j_"}], "]"}], ",", RowBox[{ + RowBox[{ + RowBox[{"-", + RowBox[{"invgam", "[", + RowBox[{"k", ",", "p"}], "]"}]}], + RowBox[{"invgam", "[", + RowBox[{"l", ",", "q"}], "]"}], + RowBox[{"dADMgam", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", + RowBox[{"-", "p"}], ",", + RowBox[{"-", "q"}]}], "]"}], + RowBox[{"GamDDD", "[", + RowBox[{ + RowBox[{"-", "l"}], ",", "i", ",", "j"}], "]"}]}], "+", RowBox[{ FractionBox["1", "2"], RowBox[{"invgam", "[", @@ -1099,37 +1142,93 @@ Cell[BoxData[{ RowBox[{"(", RowBox[{ RowBox[{"ddADMgam", "[", - RowBox[{"m", ",", "i", ",", "j", ",", + RowBox[{ + RowBox[{"-", "k"}], ",", "i", ",", "j", ",", RowBox[{"-", "l"}]}], "]"}], "+", RowBox[{"ddADMgam", "[", - RowBox[{"m", ",", "j", ",", + RowBox[{ + RowBox[{"-", "k"}], ",", "j", ",", RowBox[{"-", "l"}], ",", "i"}], "]"}], "-", RowBox[{"ddADMgam", "[", + RowBox[{ + RowBox[{"-", "k"}], ",", + RowBox[{"-", "l"}], ",", "i", ",", "j"}], "]"}]}], ")"}]}]}]}], + "]"}], ";"}]], "Input", + CellChangeTimes->{{3.940945125734173*^9, 3.940945266081555*^9}}, + CellLabel->"In[13]:=",ExpressionUUID->"506fc32a-ad2a-4ed5-9784-7056af7b0529"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"tr2dGam", "[", + RowBox[{"m_", ",", "i_"}], "]"}], ",", + RowBox[{ + FractionBox["1", "2"], + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"invgam", "[", + RowBox[{"k", ",", "l"}], "]"}], + RowBox[{"ddADMgam", "[", + RowBox[{"m", ",", "i", ",", + RowBox[{"-", "k"}], ",", + RowBox[{"-", "l"}]}], "]"}]}], "-", + RowBox[{ + RowBox[{"invgam", "[", + RowBox[{"k", ",", "p"}], "]"}], + RowBox[{"invgam", "[", + RowBox[{"l", ",", "q"}], "]"}], + RowBox[{"dADMgam", "[", RowBox[{"m", ",", - RowBox[{"-", "l"}], ",", "i", ",", "j"}], "]"}]}], ")"}]}], "-", + RowBox[{"-", "p"}], ",", + RowBox[{"-", "q"}]}], "]"}], + RowBox[{"dADMgam", "[", + RowBox[{"i", ",", + RowBox[{"-", "k"}], ",", + RowBox[{"-", "l"}]}], "]"}]}]}], ")"}]}]}], "]"}], ";"}]], "Input", + CellChangeTimes->{{3.940945299269793*^9, 3.940945441000251*^9}}, + CellLabel->"In[15]:=",ExpressionUUID->"a8a4e286-548c-48df-ae5f-46c9d3840a6c"], + +Cell[BoxData[ + RowBox[{"(*", + RowBox[{ + RowBox[{"SetEQN", "[", + RowBox[{ + RowBox[{"dGam", "[", + RowBox[{"m_", ",", "k_", ",", "i_", ",", "j_"}], "]"}], ",", RowBox[{ - RowBox[{"invgam", "[", - RowBox[{"k", ",", "p"}], "]"}], - RowBox[{"invgam", "[", - RowBox[{"l", ",", "q"}], "]"}], - RowBox[{"dADMgam", "[", - RowBox[{"m", ",", - RowBox[{"-", "p"}], ",", - RowBox[{"-", "q"}]}], "]"}], - RowBox[{"GamDDD", "[", - RowBox[{ - RowBox[{"-", "l"}], ",", "i", ",", "j"}], "]"}]}]}]}], "]"}], - ";"}]}], "Input", - Editable->False, - CellChangeTimes->{{3.92882045451426*^9, 3.928820494015818*^9}, { - 3.92882054464657*^9, 3.928820550091407*^9}, {3.928822389143814*^9, - 3.928822403936602*^9}, {3.928822478660738*^9, 3.9288225192530327`*^9}, { - 3.9288361544164658`*^9, 3.928836162461919*^9}, {3.92892211822755*^9, - 3.928922119069038*^9}, {3.940883914871763*^9, 3.940884055385359*^9}, { - 3.940893223443261*^9, 3.940893458716525*^9}, {3.940893622642169*^9, - 3.9408937202483683`*^9}, {3.940894063701812*^9, 3.94089406708775*^9}, { - 3.940894251213398*^9, 3.940894253919017*^9}}, - CellLabel->"In[11]:=",ExpressionUUID->"06d87d1d-b673-41db-8089-81c4e3d83936"], + RowBox[{ + FractionBox["1", "2"], + RowBox[{"invgam", "[", + RowBox[{"k", ",", "l"}], "]"}], + RowBox[{"(", + RowBox[{ + RowBox[{"ddADMgam", "[", + RowBox[{"m", ",", "i", ",", "j", ",", + RowBox[{"-", "l"}]}], "]"}], "+", + RowBox[{"ddADMgam", "[", + RowBox[{"m", ",", "j", ",", + RowBox[{"-", "l"}], ",", "i"}], "]"}], "-", + RowBox[{"ddADMgam", "[", + RowBox[{"m", ",", + RowBox[{"-", "l"}], ",", "i", ",", "j"}], "]"}]}], ")"}]}], "-", + RowBox[{ + RowBox[{"invgam", "[", + RowBox[{"k", ",", "p"}], "]"}], + RowBox[{"invgam", "[", + RowBox[{"l", ",", "q"}], "]"}], + RowBox[{"dADMgam", "[", + RowBox[{"m", ",", + RowBox[{"-", "p"}], ",", + RowBox[{"-", "q"}]}], "]"}], + RowBox[{"GamDDD", "[", + RowBox[{ + RowBox[{"-", "l"}], ",", "i", ",", "j"}], "]"}]}]}]}], "]"}], ";"}], + "*)"}]], "Input", + CellChangeTimes->{{3.940945112469769*^9, + 3.9409451152483473`*^9}},ExpressionUUID->"c2eeeb7f-9686-4cc9-b9fc-\ +6b348cb297c3"], Cell[BoxData[ RowBox[{ @@ -1138,12 +1237,10 @@ Cell[BoxData[ RowBox[{"R", "[", RowBox[{"j_", ",", "k_"}], "]"}], ",", RowBox[{ - RowBox[{"dGam", "[", - RowBox[{ - RowBox[{"-", "i"}], ",", "i", ",", "j", ",", "k"}], "]"}], "-", - RowBox[{"dGam", "[", - RowBox[{"k", ",", "i", ",", "j", ",", - RowBox[{"-", "i"}]}], "]"}], "+", + RowBox[{"tr1dGam", "[", + RowBox[{"j", ",", "k"}], "]"}], "-", + RowBox[{"tr2dGam", "[", + RowBox[{"j", ",", "k"}], "]"}], "+", RowBox[{ RowBox[{"Gam", "[", RowBox[{"i", ",", @@ -1158,8 +1255,8 @@ Cell[BoxData[ RowBox[{"Gam", "[", RowBox[{"p", ",", RowBox[{"-", "i"}], ",", "k"}], "]"}]}]}]}], "]"}], ";"}]], "Input", - Editable->False, - CellLabel->"In[14]:=",ExpressionUUID->"73ae3fe4-58f9-4733-946d-e922b451b632"], + CellChangeTimes->{{3.940945459607963*^9, 3.940945480521657*^9}}, + CellLabel->"In[16]:=",ExpressionUUID->"73ae3fe4-58f9-4733-946d-e922b451b632"], Cell[BoxData[ RowBox[{ @@ -1347,8 +1444,8 @@ Cell[BoxData[ }, Open ]] }, Open ]] }, -WindowSize->{896, 1067}, -WindowMargins->{{0, Automatic}, {Automatic, 0}}, +WindowSize->{960, 1027}, +WindowMargins->{{Automatic, 0}, {Automatic, 40}}, FrontEndVersion->"14.1 for Mac OS X x86 (64-bit) (July 16, 2024)", StyleDefinitions->"Default.nb", ExpressionUUID->"ebd466d4-c373-4284-afdd-a9043ac1493f" @@ -1368,96 +1465,99 @@ Cell[CellGroupData[{ Cell[580, 22, 531, 12, 65, "Input",ExpressionUUID->"9857cbce-1237-4124-83ba-143c7adb15bb", InitializationCell->True], Cell[CellGroupData[{ -Cell[1136, 38, 846, 14, 23, "Print",ExpressionUUID->"960e2aea-3640-4c4b-99d7-ad3552e44aa0"], -Cell[1985, 54, 1116, 22, 23, "Print",ExpressionUUID->"270ddc26-f293-42c7-951b-09ce50057326"], -Cell[3104, 78, 865, 14, 23, "Print",ExpressionUUID->"9d464697-9d75-4fa0-aa78-7da9b1c04cd5"], -Cell[3972, 94, 822, 13, 23, "Print",ExpressionUUID->"9b4426f5-23b4-4c5d-a0b7-0395ab1c3139"], -Cell[4797, 109, 805, 13, 23, "Print",ExpressionUUID->"2ada16dc-f632-420a-a175-efb109277a65"], -Cell[5605, 124, 846, 14, 23, "Print",ExpressionUUID->"3d282824-fc17-49e2-ae93-e2849fe46ca4"], -Cell[6454, 140, 1122, 22, 23, "Print",ExpressionUUID->"6c30165f-4fb9-48d9-ae79-64b2a9530c29"], -Cell[7579, 164, 865, 14, 23, "Print",ExpressionUUID->"06129bbf-451f-4a59-8ecd-8828b612ccec"], -Cell[8447, 180, 844, 14, 23, "Print",ExpressionUUID->"9e028197-1d0f-40ae-81ef-4e3180b22a7b"], -Cell[9294, 196, 999, 16, 41, "Print",ExpressionUUID->"ea8f1a9a-8651-4a02-afdf-a8ce6bf3b3e2"], -Cell[10296, 214, 846, 14, 23, "Print",ExpressionUUID->"92ac23a6-8e9e-4004-9b2c-ddeaa7e63682"], -Cell[11145, 230, 843, 14, 23, "Print",ExpressionUUID->"0ead17e8-9122-49f6-b430-625a85989719"], -Cell[11991, 246, 1116, 22, 23, "Print",ExpressionUUID->"201d47dc-5727-40a1-94be-e35d5b2de144"], -Cell[13110, 270, 885, 14, 23, "Print",ExpressionUUID->"994c931d-0e7a-4613-909d-41610b233d47"], -Cell[13998, 286, 843, 14, 23, "Print",ExpressionUUID->"848bc993-593e-4741-8e7d-5a142245a7b0"], -Cell[14844, 302, 999, 16, 41, "Print",ExpressionUUID->"952c9782-95b6-4f07-96e1-099e03e50874"], -Cell[15846, 320, 844, 14, 23, "Print",ExpressionUUID->"9c9dfb68-d150-4d47-a3de-5b07fb9a3a87"], -Cell[16693, 336, 844, 14, 23, "Print",ExpressionUUID->"8b3f770a-ea9f-4341-9b86-39080c653e4e"], -Cell[17540, 352, 820, 13, 23, "Print",ExpressionUUID->"a7c74cbd-4cee-4108-b3a9-0d8feb4235aa"], -Cell[18363, 367, 844, 14, 23, "Print",ExpressionUUID->"df2b13e5-0479-4551-9b3a-35f018113808"], -Cell[19210, 383, 844, 14, 23, "Print",ExpressionUUID->"0aa951e3-0f08-40d0-9000-5a73643e757a"], -Cell[20057, 399, 824, 13, 23, "Print",ExpressionUUID->"bc18d4a7-4ac7-44c6-b014-d3b0ef82a60d"], -Cell[20884, 414, 844, 14, 23, "Print",ExpressionUUID->"bfeb5f35-c536-4f3f-b7ea-08ccfc0548f6"], -Cell[21731, 430, 844, 14, 23, "Print",ExpressionUUID->"329239f6-e906-499a-88b4-ddecb2ca4fdb"], -Cell[22578, 446, 824, 13, 23, "Print",ExpressionUUID->"3d6c0aca-79f5-45e9-b922-332980031e90"], -Cell[23405, 461, 846, 14, 23, "Print",ExpressionUUID->"ac2d3a49-1392-4515-ab60-ed00a6f40213"], -Cell[24254, 477, 844, 14, 23, "Print",ExpressionUUID->"29b4b0fa-b21e-4e7e-bad1-e49884c849fc"], -Cell[25101, 493, 822, 13, 23, "Print",ExpressionUUID->"21926ba2-2cff-4647-9863-45b4c9f2e258"], -Cell[25926, 508, 844, 14, 23, "Print",ExpressionUUID->"fe4a67af-834b-4964-8169-aaf79083e1bd"], -Cell[26773, 524, 844, 14, 23, "Print",ExpressionUUID->"550e2ce4-9d3f-46da-9dc9-9440a964036e"], -Cell[27620, 540, 824, 13, 23, "Print",ExpressionUUID->"1a0551c3-8b39-43c6-ba77-653aee99b6c6"], -Cell[28447, 555, 844, 14, 23, "Print",ExpressionUUID->"a2715f91-f297-42fb-94ae-470c03294596"], -Cell[29294, 571, 846, 14, 23, "Print",ExpressionUUID->"d57fef39-1ed8-42b7-a3de-747a9d668f43"], -Cell[30143, 587, 825, 13, 23, "Print",ExpressionUUID->"554c32c0-301d-45a4-840f-047e516ba95e"], -Cell[30971, 602, 846, 14, 23, "Print",ExpressionUUID->"ca4a35a5-1968-44fa-8267-9ee12a74f98d"], -Cell[31820, 618, 782, 13, 23, "Print",ExpressionUUID->"18abfc4f-b472-442b-8225-b8149e7b2952"] +Cell[1136, 38, 868, 14, 23, "Print",ExpressionUUID->"ba6a3bac-2e7c-4d46-9c03-b5f3ba5afa0a"], +Cell[2007, 54, 1140, 22, 23, "Print",ExpressionUUID->"1e4d304c-2c59-45f8-8518-85d9c941106c"], +Cell[3150, 78, 891, 14, 23, "Print",ExpressionUUID->"4260da05-bfea-41c3-9086-068f84123082"], +Cell[4044, 94, 846, 13, 23, "Print",ExpressionUUID->"72c7a15c-9fd0-44d1-8dfa-4136f7bc90b5"], +Cell[4893, 109, 829, 13, 23, "Print",ExpressionUUID->"5bf5737c-59a6-4a05-b6a4-750a3c4f68b4"], +Cell[5725, 124, 868, 14, 23, "Print",ExpressionUUID->"836920d6-996d-411c-81ae-8a0dd4cf8ea0"], +Cell[6596, 140, 1148, 22, 23, "Print",ExpressionUUID->"e17827c6-4c8d-4e3a-be69-f656210b3f1d"], +Cell[7747, 164, 889, 14, 23, "Print",ExpressionUUID->"2a7ad527-c0af-4c6d-ac66-abffa1da874c"], +Cell[8639, 180, 868, 14, 23, "Print",ExpressionUUID->"ffda4c26-5bca-4dc3-adbb-852d2afabbfb"], +Cell[9510, 196, 1023, 16, 41, "Print",ExpressionUUID->"dc5d0a86-f88f-43c2-8504-8db94b1165a3"], +Cell[10536, 214, 868, 14, 23, "Print",ExpressionUUID->"fb899cbd-b6f3-4b6e-904a-a778b4053f9b"], +Cell[11407, 230, 868, 14, 23, "Print",ExpressionUUID->"70617423-e9b2-4fd5-925d-aa065a77e111"], +Cell[12278, 246, 1140, 22, 23, "Print",ExpressionUUID->"0a572555-05f4-461a-88d2-2b2ccb8104ff"], +Cell[13421, 270, 907, 14, 23, "Print",ExpressionUUID->"42ef8c7c-3ff8-4ab2-9c65-b588d809b6c7"], +Cell[14331, 286, 870, 14, 23, "Print",ExpressionUUID->"ffa9c04f-8dfe-40de-8dd6-d3a0223a39bb"], +Cell[15204, 302, 1023, 16, 41, "Print",ExpressionUUID->"f429ab13-385a-4d3b-bb2f-a393a57c2061"], +Cell[16230, 320, 870, 14, 23, "Print",ExpressionUUID->"b332e86a-4ec6-4054-ad77-d4a937608b98"], +Cell[17103, 336, 868, 14, 23, "Print",ExpressionUUID->"73f2d98b-30dd-43c8-8910-e109a366b507"], +Cell[17974, 352, 844, 13, 23, "Print",ExpressionUUID->"ce54eb97-bed1-4441-ba0f-f05fbdc49154"], +Cell[18821, 367, 868, 14, 23, "Print",ExpressionUUID->"66e2d823-0ba4-432f-9fb6-1a09a9727559"], +Cell[19692, 383, 868, 14, 23, "Print",ExpressionUUID->"205117d5-a3c6-4a06-8b57-8b6cca3ae352"], +Cell[20563, 399, 848, 13, 23, "Print",ExpressionUUID->"d1f6eb6f-964f-4fe6-b26c-eccfdc8f274b"], +Cell[21414, 414, 868, 14, 23, "Print",ExpressionUUID->"6a139613-191f-47a2-b619-18690dd0f75c"], +Cell[22285, 430, 868, 14, 23, "Print",ExpressionUUID->"05b3d428-7847-44da-8e73-16da4a259f7f"], +Cell[23156, 446, 848, 13, 23, "Print",ExpressionUUID->"dd705f5c-fea0-4255-9450-523ea0e8095d"], +Cell[24007, 461, 868, 14, 23, "Print",ExpressionUUID->"aaf3543e-866f-4d56-8b47-30898cfd75e1"], +Cell[24878, 477, 870, 14, 23, "Print",ExpressionUUID->"1ad19895-c0b9-42cb-88b4-54d28e5e0b51"], +Cell[25751, 493, 846, 13, 23, "Print",ExpressionUUID->"1159c3cc-1a75-4554-aba0-0a7fb05168b5"], +Cell[26600, 508, 870, 14, 23, "Print",ExpressionUUID->"7453d1cb-82a6-45c3-9344-bc1f094117fd"], +Cell[27473, 524, 870, 14, 23, "Print",ExpressionUUID->"6b10df87-d187-4412-b800-d26ec6a719f9"], +Cell[28346, 540, 848, 13, 23, "Print",ExpressionUUID->"c5519c0a-5a1b-4a95-8893-2a6db3f9cef6"], +Cell[29197, 555, 868, 14, 23, "Print",ExpressionUUID->"40c49305-6221-4355-8442-11721afd7347"], +Cell[30068, 571, 868, 14, 23, "Print",ExpressionUUID->"dc10054a-3c73-4dca-bb48-875d6b2a8978"], +Cell[30939, 587, 849, 13, 23, "Print",ExpressionUUID->"5a0d67c0-c6f6-40bd-9395-92cf5b37af5f"], +Cell[31791, 602, 868, 14, 23, "Print",ExpressionUUID->"900589e3-b704-4273-9722-da1e9810498d"], +Cell[32662, 618, 806, 13, 23, "Print",ExpressionUUID->"28367d85-f7da-4971-9273-fa485eb9a4d9"] }, Open ]] }, Open ]], Cell[CellGroupData[{ -Cell[32651, 637, 227, 5, 66, "Section",ExpressionUUID->"d93e9e9c-e043-49bf-adc4-613bb015a823"], -Cell[32881, 644, 373, 9, 45, "Input",ExpressionUUID->"dc88cf1b-3b54-44ff-b471-d7efa31651a2", +Cell[33517, 637, 227, 5, 66, "Section",ExpressionUUID->"d93e9e9c-e043-49bf-adc4-613bb015a823"], +Cell[33747, 644, 373, 9, 45, "Input",ExpressionUUID->"dc88cf1b-3b54-44ff-b471-d7efa31651a2", InitializationCell->True], Cell[CellGroupData[{ -Cell[33279, 657, 224, 5, 53, "Subsection",ExpressionUUID->"8f6e447f-5ad1-4983-a220-4a62c32eb45e"], -Cell[33506, 664, 1702, 51, 147, "Input",ExpressionUUID->"4879eb5d-4927-4d70-8345-bbceb0091220", +Cell[34145, 657, 224, 5, 53, "Subsection",ExpressionUUID->"8f6e447f-5ad1-4983-a220-4a62c32eb45e"], +Cell[34372, 664, 1702, 51, 147, "Input",ExpressionUUID->"4879eb5d-4927-4d70-8345-bbceb0091220", InitializationCell->True], -Cell[35211, 717, 1982, 58, 167, "Input",ExpressionUUID->"ede93dc0-606a-46a8-bf03-9b4328dc7c60", +Cell[36077, 717, 1982, 58, 147, "Input",ExpressionUUID->"ede93dc0-606a-46a8-bf03-9b4328dc7c60", InitializationCell->True], -Cell[37196, 777, 1107, 27, 86, "Input",ExpressionUUID->"2f2a6a6e-f59d-4dc4-8900-9dcb96af2d35", +Cell[38062, 777, 1107, 27, 86, "Input",ExpressionUUID->"2f2a6a6e-f59d-4dc4-8900-9dcb96af2d35", InitializationCell->True], -Cell[38306, 806, 1110, 30, 127, "Input",ExpressionUUID->"c08588c0-b1be-4279-a26f-ad8578054e37", +Cell[39172, 806, 1110, 30, 127, "Input",ExpressionUUID->"c08588c0-b1be-4279-a26f-ad8578054e37", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ -Cell[39453, 841, 172, 4, 53, "Subsection",ExpressionUUID->"1fd445a5-eeab-43da-98f4-96f9414b6b16"], -Cell[39628, 847, 4411, 111, 229, "Input",ExpressionUUID->"230e3e3d-ec24-4b15-9bc4-4c66fa656cc7", +Cell[40319, 841, 172, 4, 53, "Subsection",ExpressionUUID->"1fd445a5-eeab-43da-98f4-96f9414b6b16"], +Cell[40494, 847, 4948, 128, 258, "Input",ExpressionUUID->"230e3e3d-ec24-4b15-9bc4-4c66fa656cc7", InitializationCell->True], Cell[CellGroupData[{ -Cell[44064, 962, 175, 4, 43, "Subsubsection",ExpressionUUID->"63c86796-f445-4596-a568-cf6b7233992a"], -Cell[44242, 968, 780, 20, 106, "Input",ExpressionUUID->"61eaa4ba-0069-4a97-a6d7-a02ee559a741", +Cell[45467, 979, 175, 4, 43, "Subsubsection",ExpressionUUID->"63c86796-f445-4596-a568-cf6b7233992a"], +Cell[45645, 985, 801, 20, 106, "Input",ExpressionUUID->"61eaa4ba-0069-4a97-a6d7-a02ee559a741", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ -Cell[45059, 993, 180, 4, 43, "Subsubsection",ExpressionUUID->"28d203fe-58c8-4126-8774-88d5a1781306"], -Cell[45242, 999, 673, 18, 106, "Input",ExpressionUUID->"5502d63c-b6fc-4a63-a203-12b5cbab9476", +Cell[46483, 1010, 180, 4, 43, "Subsubsection",ExpressionUUID->"28d203fe-58c8-4126-8774-88d5a1781306"], +Cell[46666, 1016, 673, 18, 106, "Input",ExpressionUUID->"5502d63c-b6fc-4a63-a203-12b5cbab9476", InitializationCell->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ -Cell[45964, 1023, 174, 4, 53, "Subsection",ExpressionUUID->"ab64c7df-87cb-4c7d-990a-2b0543e709db"], -Cell[46141, 1029, 498, 10, 45, "Input",ExpressionUUID->"e471a9d0-e772-4737-b68b-dc67e2be03b9", +Cell[47388, 1040, 174, 4, 53, "Subsection",ExpressionUUID->"ab64c7df-87cb-4c7d-990a-2b0543e709db"], +Cell[47565, 1046, 498, 10, 45, "Input",ExpressionUUID->"e471a9d0-e772-4737-b68b-dc67e2be03b9", InitializationCell->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ -Cell[46688, 1045, 166, 4, 66, "Section",ExpressionUUID->"519fe4de-6999-4db6-9e6b-17dff89f6b40"], +Cell[48112, 1062, 166, 4, 66, "Section",ExpressionUUID->"519fe4de-6999-4db6-9e6b-17dff89f6b40"], Cell[CellGroupData[{ -Cell[46879, 1053, 170, 4, 53, "Subsection",ExpressionUUID->"29fb9a40-8f32-4735-bf46-1b2322d6762f"], -Cell[47052, 1059, 2651, 72, 156, "Input",ExpressionUUID->"06d87d1d-b673-41db-8089-81c4e3d83936"], -Cell[49706, 1133, 935, 28, 49, "Input",ExpressionUUID->"73ae3fe4-58f9-4733-946d-e922b451b632"], -Cell[50644, 1163, 509, 15, 29, "Input",ExpressionUUID->"52285f16-cbd6-4f41-8e30-7dc7a405d3f4"], -Cell[51156, 1180, 903, 25, 29, "Input",ExpressionUUID->"63c26313-037a-484b-ad0f-4bd8ed3260e8"], +Cell[48303, 1070, 170, 4, 53, "Subsection",ExpressionUUID->"29fb9a40-8f32-4735-bf46-1b2322d6762f"], +Cell[48476, 1076, 1553, 38, 64, "Input",ExpressionUUID->"06d87d1d-b673-41db-8089-81c4e3d83936"], +Cell[50032, 1116, 1381, 41, 71, "Input",ExpressionUUID->"506fc32a-ad2a-4ed5-9784-7056af7b0529"], +Cell[51416, 1159, 1077, 31, 71, "Input",ExpressionUUID->"a8a4e286-548c-48df-ae5f-46c9d3840a6c"], +Cell[52496, 1192, 1313, 38, 55, "Input",ExpressionUUID->"c2eeeb7f-9686-4cc9-b9fc-6b348cb297c3"], +Cell[53812, 1232, 903, 26, 80, "Input",ExpressionUUID->"73ae3fe4-58f9-4733-946d-e922b451b632"], +Cell[54718, 1260, 509, 15, 29, "Input",ExpressionUUID->"52285f16-cbd6-4f41-8e30-7dc7a405d3f4"], +Cell[55230, 1277, 903, 25, 29, "Input",ExpressionUUID->"63c26313-037a-484b-ad0f-4bd8ed3260e8"], Cell[CellGroupData[{ -Cell[52084, 1209, 157, 3, 43, "Subsubsection",ExpressionUUID->"21635a48-b393-484a-82e9-abbe12d2c210"], -Cell[52244, 1214, 1676, 49, 53, "Input",ExpressionUUID->"0f3722e5-6cf3-48e0-a39d-b9f9cec7d095"] +Cell[56158, 1306, 157, 3, 43, "Subsubsection",ExpressionUUID->"21635a48-b393-484a-82e9-abbe12d2c210"], +Cell[56318, 1311, 1676, 49, 53, "Input",ExpressionUUID->"0f3722e5-6cf3-48e0-a39d-b9f9cec7d095"] }, Open ]], Cell[CellGroupData[{ -Cell[53957, 1268, 164, 3, 43, "Subsubsection",ExpressionUUID->"aea00190-9ff0-4165-bc4a-9094b2949563"], -Cell[54124, 1273, 1080, 33, 53, "Input",ExpressionUUID->"f9d74532-a3f3-452d-a719-7d4935c78d8d"], -Cell[55207, 1308, 1276, 36, 49, "Input",ExpressionUUID->"2539bb21-04c2-456d-9145-83172e324ec1"] +Cell[58031, 1365, 164, 3, 43, "Subsubsection",ExpressionUUID->"aea00190-9ff0-4165-bc4a-9094b2949563"], +Cell[58198, 1370, 1080, 33, 53, "Input",ExpressionUUID->"f9d74532-a3f3-452d-a719-7d4935c78d8d"], +Cell[59281, 1405, 1276, 36, 49, "Input",ExpressionUUID->"2539bb21-04c2-456d-9145-83172e324ec1"] }, Open ]] }, Open ]] }, Open ]] diff --git a/ADMconstraints/wolfram/wl/ADM_vars.wl b/ADMconstraints/wolfram/wl/ADM_vars.wl index c0589b2b..e692b0ba 100644 --- a/ADMconstraints/wolfram/wl/ADM_vars.wl +++ b/ADMconstraints/wolfram/wl/ADM_vars.wl @@ -15,7 +15,7 @@ ADMVarlist = GridTensors[ {ADMgam[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*SuperscriptBox[\(\[Gamma]\), \((ADM)\)]\)"}, - {ADMK[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*SuperscriptBox[\(K\), \((ADM)\)]\)"}, + {ADMK [-i, -j], Symmetric[{-i, -j}], PrintAs -> "\!\(\*SuperscriptBox[\(K\), \((ADM)\)]\)"}, {ADMalpha[], PrintAs -> "\!\(\*SuperscriptBox[\(\[Alpha]\), \((ADM)\)]\)"}, {ADMbeta[i], PrintAs -> "\!\(\*SuperscriptBox[\(\[Beta]\), \((ADM)\)]\)"} ]; @@ -23,7 +23,7 @@ ADMVarlist = dADMVarlist = GridTensors[ {dADMgam[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*SuperscriptBox[\(\[Gamma]\), \((ADM)\)]\)"}, - {dADMK[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*SuperscriptBox[\(K\), \((ADM)\)]\)"} + {dADMK [-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*SuperscriptBox[\(K\), \((ADM)\)]\)"} ]; ddADMVarlist = @@ -50,8 +50,9 @@ IntermediateVarlist = {invgam[i, j], Symmetric[{i, j}], PrintAs -> "\[Gamma]"}, {GamDDD [-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[CapitalGamma]"}, {Gam [k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[CapitalGamma]"}, - {dGam[-m, k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[CapitalGamma]"}, - {R[-i, -j], Symmetric[{-i, -j}]}, + {tr1dGam[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[CapitalGamma]^(tr1)"}, + {tr2dGam[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[CapitalGamma]^(tr2)"}, + {R[-i, -j], Symmetric[{-i, -j}], PrintAs -> "R"}, {trK[], PrintAs -> "K"}, {DADMK[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[Del]K"} ]; From 73b49e5da09009b343fa6cd99a771275c89fe8b1 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 14:14:03 -0500 Subject: [PATCH 09/37] ADMconstraints: update type_in_rhs.nb --- ADMconstraints/wolfram/type_in_rhs.nb | 22 +++++++++++----------- 1 file changed, 11 insertions(+), 11 deletions(-) diff --git a/ADMconstraints/wolfram/type_in_rhs.nb b/ADMconstraints/wolfram/type_in_rhs.nb index ba45a003..2f445b9b 100644 --- a/ADMconstraints/wolfram/type_in_rhs.nb +++ b/ADMconstraints/wolfram/type_in_rhs.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 67855, 1559] -NotebookOptionsPosition[ 60597, 1446] -NotebookOutlinePosition[ 60990, 1462] -CellTagsIndexPosition[ 60947, 1459] +NotebookDataLength[ 67837, 1559] +NotebookOptionsPosition[ 60579, 1446] +NotebookOutlinePosition[ 60972, 1462] +CellTagsIndexPosition[ 60929, 1459] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -1410,9 +1410,8 @@ Cell[BoxData[ RowBox[{"MtC", "[", "i_", "]"}], ",", RowBox[{ RowBox[{ - RowBox[{"-", - RowBox[{"invgam", "[", - RowBox[{"i", ",", "k"}], "]"}]}], + RowBox[{"invgam", "[", + RowBox[{"i", ",", "k"}], "]"}], RowBox[{"invgam", "[", RowBox[{"j", ",", "l"}], "]"}], RowBox[{"DADMK", "[", @@ -1438,8 +1437,9 @@ Cell[BoxData[ CellChangeTimes->{{3.940895545009609*^9, 3.9408955814025393`*^9}, { 3.940895640679975*^9, 3.940895667140218*^9}, 3.940896099640127*^9, { 3.9408961321299467`*^9, 3.940896137732473*^9}, {3.94089619830234*^9, - 3.940896250853101*^9}}, - CellLabel->"In[23]:=",ExpressionUUID->"2539bb21-04c2-456d-9145-83172e324ec1"] + 3.940896250853101*^9}, + 3.9409460308847523`*^9},ExpressionUUID->"2539bb21-04c2-456d-9145-\ +83172e324ec1"] }, Open ]] }, Open ]] }, Open ]] @@ -1547,7 +1547,7 @@ Cell[48476, 1076, 1553, 38, 64, "Input",ExpressionUUID->"06d87d1d-b673-41db-8089 Cell[50032, 1116, 1381, 41, 71, "Input",ExpressionUUID->"506fc32a-ad2a-4ed5-9784-7056af7b0529"], Cell[51416, 1159, 1077, 31, 71, "Input",ExpressionUUID->"a8a4e286-548c-48df-ae5f-46c9d3840a6c"], Cell[52496, 1192, 1313, 38, 55, "Input",ExpressionUUID->"c2eeeb7f-9686-4cc9-b9fc-6b348cb297c3"], -Cell[53812, 1232, 903, 26, 80, "Input",ExpressionUUID->"73ae3fe4-58f9-4733-946d-e922b451b632"], +Cell[53812, 1232, 903, 26, 29, "Input",ExpressionUUID->"73ae3fe4-58f9-4733-946d-e922b451b632"], Cell[54718, 1260, 509, 15, 29, "Input",ExpressionUUID->"52285f16-cbd6-4f41-8e30-7dc7a405d3f4"], Cell[55230, 1277, 903, 25, 29, "Input",ExpressionUUID->"63c26313-037a-484b-ad0f-4bd8ed3260e8"], Cell[CellGroupData[{ @@ -1557,7 +1557,7 @@ Cell[56318, 1311, 1676, 49, 53, "Input",ExpressionUUID->"0f3722e5-6cf3-48e0-a39d Cell[CellGroupData[{ Cell[58031, 1365, 164, 3, 43, "Subsubsection",ExpressionUUID->"aea00190-9ff0-4165-bc4a-9094b2949563"], Cell[58198, 1370, 1080, 33, 53, "Input",ExpressionUUID->"f9d74532-a3f3-452d-a719-7d4935c78d8d"], -Cell[59281, 1405, 1276, 36, 49, "Input",ExpressionUUID->"2539bb21-04c2-456d-9145-83172e324ec1"] +Cell[59281, 1405, 1258, 36, 49, "Input",ExpressionUUID->"2539bb21-04c2-456d-9145-83172e324ec1"] }, Open ]] }, Open ]] }, Open ]] From 42ad793e72f12fb1453f3bea139394d4558ed545 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 14:19:34 -0500 Subject: [PATCH 10/37] ADMconstraints: update ADM_rhs.wl --- ADMconstraints/wolfram/wl/ADM_rhs.wl | 58 +++++++--------------------- 1 file changed, 13 insertions(+), 45 deletions(-) diff --git a/ADMconstraints/wolfram/wl/ADM_rhs.wl b/ADMconstraints/wolfram/wl/ADM_rhs.wl index 920d8a8f..de3d202f 100644 --- a/ADMconstraints/wolfram/wl/ADM_rhs.wl +++ b/ADMconstraints/wolfram/wl/ADM_rhs.wl @@ -1,10 +1,8 @@ (* ::Package:: *) -(* Z4c_rhs.wl *) +(* ADM_rhs.wl *) -(* (c) Liwei Ji, 07/2024 *) - -(* See arXiv:1212.2901 [gr-qc] *) +(* (c) Liwei Ji, 11/2024 *) (****************) @@ -12,55 +10,25 @@ (****************) -SetEQN[dlnW[i_], W[] ^ -1 dW[i]]; - -SetEQN[invgam[i_, j_], W[] ^ 2 invgamt[i, j]]; - -SetEQN[gam[i_, j_], W[] ^ -2 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_], W[] ^ -2 (-2 dlnW[k] gamt[i, j] + dgamt[k, i, j])]; - -SetEQN[GamDDD[k_, i_, j_], 1/2 (dgam[i, j, k] + dgam[j, k, i] - dgam[k, i, j])]; +SetEQN[GamDDD[k_, i_, j_], 1/2 (dADMgam[i, j, k] + dADMgam[j, k, i] - dADMgam[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[tDtDW[i_, j_], ddW[i, j] - Gt[k, i, j] dW[-k]]; - -SetEQN[DDalpha[i_, j_], ddalpha[i, j] - Gam[k, i, j] dalpha[-k]]; - -(* (8) *) - -SetEQN[RtW[i_, j_], 1 / W[] tDtDW[i, j] + 1 / W[] gamt[i, j] invgamt[k, l] tDtDW[-k, -l] - 2 gamt[i, j] invgamt[k, l] dlnW[-k] dlnW[-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[tr1dGam[i_, j_], -invgam[k, p] invgam[l, q] dADMgam[-k, -p, -q] GamDDD[-l, i, j] + 1/2 invgam[k, l] (ddADMgam[-k, i, j, -l] + ddADMgam[-k, j, -l, i] - ddADMgam[-k, -l, i, j])]; -SetEQN[R[i_, j_], RtW[i, j] + Rt[i, j]]; +SetEQN[tr2dGam[m_, i_], 1/2 (invgam[k, l] ddADMgam[m, i, -k, -l] - invgam[k, p] invgam[l, q] dADMgam[m, -p, -q] dADMgam[i, -k, -l])]; -SetEQN[trR[], invgam[k, l] R[-k, -l]]; +SetEQN[R[j_, k_], tr1dGam[j, k] - tr2dGam[j, k] + Gam[i, -i, -p] Gam[p, j, k] - Gam[i, j, -p] Gam[p, -i, k]]; -SetEQN[rho[], alpha[] ^ -2 (eTtt[] - 2 beta[j] eTt[-j] + beta[i] beta[j] eT[-i, -j])]; +SetEQN[trK[], invgam[k, l] ADMK[-k, -l]]; -SetEQN[Sm[i_], -alpha[] ^ -1 (eTt[i] - beta[k] eT[-k, i])]; +SetEQN[DADMK[k_, i_, j_], dADMK[k, i, j] - Gam[l, k, i] ADMK[-l, j] - Gam[l, k, j] ADMK[-l, i]]; -SetEQN[Ss[i_, j_], eT[i, j]]; +(* matter *) -SetEQN[trSs[], invgam[k, l] Ss[-k, -l]]; +SetEQN[rho[], ADMalpha[]^-2 (eTtt[] - 2 ADMbeta[j] eTt[-j] + ADMbeta[i] ADMbeta[j] eT[-i, -j])]; -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[Sm[i_], -ADMalpha[]^-1 (eTt[i] - ADMbeta[k] eT[-k, i])]; (***************) @@ -68,6 +36,6 @@ SetEQN[trdexAtUU[i_], -invgamt[i, l] exAtUU[j, m] dgamt[-j, -l, -m] - invgamt[j, (***************) -SetEQN[HC[], trR[] - exK[-k, -l] exKUU[k, l] + trexK[] ^ 2 - 16 cpi rho[]]; +SetEQN[HC[], invgam[k, l] R[-k, -l] + trK[]^2 - invgam[i, k] invgam[j, l] ADMK[-i, -j] ADMK[-k, -l] - 16 cpi rho[]]; -SetEQN[MtC[i_], trdexAtUU[i] + Gt[i, -j, -k] exAtUU[j, k] - 2/3 invgamt[i, j] (dexKh[-j] + 2 dTheta[-j]) - 3 exAtUU[i, j] dlnW[-j] - 8 cpi invgamt[i, j] Sm[-j]]; +SetEQN[MtC[i_], (invgam[i, k] invgam[j, l] - invgam[i, j] invgam[k, l]) DADMK[-j, -k, -l] - 8 cpi invgam[i, j] Sm[-j]]; From ca5140266d81d15ecbcaa693c94c16715d6a2a7d Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 15:11:21 -0500 Subject: [PATCH 11/37] ADMconstraints: add check_rhs.ipynb --- ADMconstraints/wolfram/check_rhs.ipynb | 270 +++++++++++++++++++++++++ 1 file changed, 270 insertions(+) create mode 100644 ADMconstraints/wolfram/check_rhs.ipynb diff --git a/ADMconstraints/wolfram/check_rhs.ipynb b/ADMconstraints/wolfram/check_rhs.ipynb new file mode 100644 index 00000000..513f92ab --- /dev/null +++ b/ADMconstraints/wolfram/check_rhs.ipynb @@ -0,0 +1,270 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "a265f5c5-fce9-45ad-b496-8bb1ee1f219b", + "metadata": {}, + "source": [ + "# ADM Equations" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "9642db04-5283-4582-99af-90ffff046096", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "------------------------------------------------------------\n", + "Package xAct`xPerm` version 1.2.3, {2015, 8, 23}\n", + "CopyRight (C) 2003-2020, Jose M. Martin-Garcia, under the General Public\\\n", + " \n", + "> License.\n", + "Connecting to external mac executable...\n", + "Connection established.\n", + "------------------------------------------------------------\n", + "Package xAct`xTensor` version 1.2.0, {2021, 10, 17}\n", + "CopyRight (C) 2002-2021, Jose M. Martin-Garcia, under the General Public\\\n", + " \n", + "> License.\n", + "------------------------------------------------------------\n", + "These packages come with ABSOLUTELY NO WARRANTY; for details type\\\n", + " \n", + "> Disclaimer[]. This is free software, and you are welcome to redistribute\\\n", + " \n", + "> it under certain conditions. See the General Public License for details.\n", + "------------------------------------------------------------\n", + "------------------------------------------------------------\n", + "Package xAct`xCoba` version 0.8.6, {2021, 2, 28}\n", + "CopyRight (C) 2005-2021, David Yllanes and Jose M. Martin-Garcia, under the\\\n", + " \n", + "> General Public License.\n", + "------------------------------------------------------------\n", + "These packages come with ABSOLUTELY NO WARRANTY; for details type\\\n", + " \n", + "> Disclaimer[]. This is free software, and you are welcome to redistribute\\\n", + " \n", + "> it under certain conditions. See the General Public License for details.\n", + "------------------------------------------------------------\n", + "------------------------------------------------------------\n", + "Package Generato`Basic`, {2024, 1, 11}\n", + "------------------------------------------------------------\n", + "------------------------------------------------------------\n", + "Package Generato`ParseMode`, {2024, 7, 06}\n", + "------------------------------------------------------------\n", + "------------------------------------------------------------\n", + "Package Generato`Component`, {2024, 1, 11}\n", + "------------------------------------------------------------\n", + "------------------------------------------------------------\n", + "Package Generato`Varlist`, {2024, 1, 11}\n", + "------------------------------------------------------------\n", + "------------------------------------------------------------\n", + "Package Generato`Interface`, {2024, 1, 11}\n", + "------------------------------------------------------------\n", + "------------------------------------------------------------\n", + "Package Generato`Derivation`, {2024, 1, 18}\n", + "------------------------------------------------------------\n", + "\n" + ] + } + ], + "source": [ + "Needs[\"xAct`xCoba`\", FileNameJoin[{Environment[\"GENERATO\"], \"src/Generato.wl\"}]]" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "ade74516-0ef1-4104-8217-d8968a1fa871", + "metadata": {}, + "outputs": [], + "source": [ + "DefManifold[M3, 3, IndexRange[a, z]];" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "d76d538a-d172-4043-a677-f39b0ba03467", + "metadata": {}, + "outputs": [], + "source": [ + "(* set mode to check equations *)\n", + "SetCheckInputEquations[True];" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "89c3c5eb-f13f-4be9-8117-c9e197d1114e", + "metadata": {}, + "outputs": [], + "source": [ + "<<\"wl/ADM_vars.wl\"" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "396420b3-c92c-49bf-acc6-b02599fffdd0", + "metadata": {}, + "outputs": [], + "source": [ + "<<\"wl/ADM_rhs.wl\"" + ] + }, + { + "cell_type": "markdown", + "id": "789279a3-122b-41b2-a9d7-e852493904d7", + "metadata": {}, + "source": [ + "## Check Expressions" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "07be83aa-230e-44b5-ba16-b6fc7df0626e", + "metadata": {}, + "outputs": [], + "source": [ + "rhsof[var_] := Module[{}, var /. {var[[0]] :> RHSOf[ToString[var[[0]]]]}];\n", + "eqssof[varlist_] := Module[{var}, \n", + " Table[var = varlist[[ivar]][[1]]; var == rhsof[var]//ScreenDollarIndices, {ivar, 1, Length[varlist]}]];" + ] + }, + { + "cell_type": "markdown", + "id": "fe765538-ea4c-48c4-8597-df4256c160c7", + "metadata": {}, + "source": [ + "### Intermediate Variables" + ] + }, + { + "cell_type": "markdown", + "id": "bbb20a49-7fcf-45bc-837c-77948b504af7", + "metadata": {}, + "source": [ + "#### Intermediate" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "de2b21c1-afc1-4772-af17-8b6b1d655f04", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\"Output\"
" + ], + "text/plain": [ + "-Image-" + ] + }, + "execution_count": 10, + "metadata": { + "text/html": [], + "text/plain": [] + }, + "output_type": "execute_result" + } + ], + "source": [ + "Rasterize[Drop[eqssof[IntermediateVarlist], {1,2}]//MatrixForm]" + ] + }, + { + "cell_type": "markdown", + "id": "9ac1d847-e0fa-451c-9f6e-bac3670460e6", + "metadata": {}, + "source": [ + "#### Matter" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "5ddbd250-e7ec-437d-a69a-a1fc753dd032", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\"Output\"
" + ], + "text/plain": [ + "-Image-" + ] + }, + "execution_count": 11, + "metadata": { + "text/html": [], + "text/plain": [] + }, + "output_type": "execute_result" + } + ], + "source": [ + "Rasterize[eqssof[MatterVarlist]//MatrixForm]" + ] + }, + { + "cell_type": "markdown", + "id": "b1c7f63e-2cb3-4340-a0b4-9403f8fe36b6", + "metadata": {}, + "source": [ + "#### Constraint" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "cbb63715-91d1-4e6d-ba35-7b40bf15078e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\"Output\"
" + ], + "text/plain": [ + "-Image-" + ] + }, + "execution_count": 12, + "metadata": { + "text/html": [], + "text/plain": [] + }, + "output_type": "execute_result" + } + ], + "source": [ + "Rasterize[eqssof[ConstraintVarlist]//MatrixForm]" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Wolfram Language 14.1", + "language": "Wolfram Language", + "name": "wolframlanguage14.1" + }, + "language_info": { + "codemirror_mode": "mathematica", + "file_extension": ".m", + "mimetype": "application/vnd.wolfram.m", + "name": "Wolfram Language", + "pygments_lexer": "mathematica", + "version": "12.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 6321a0e10fc6956df3bd54a25d55aef6ac86c2aa Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 15:25:29 -0500 Subject: [PATCH 12/37] ADMconstraints: update check_rhs.ipynb --- ADMconstraints/wolfram/check_rhs.ipynb | 18 +++++++++--------- ADMconstraints/wolfram/wl/ADM_vars.wl | 4 ++-- 2 files changed, 11 insertions(+), 11 deletions(-) diff --git a/ADMconstraints/wolfram/check_rhs.ipynb b/ADMconstraints/wolfram/check_rhs.ipynb index 513f92ab..6ad7c1f1 100644 --- a/ADMconstraints/wolfram/check_rhs.ipynb +++ b/ADMconstraints/wolfram/check_rhs.ipynb @@ -154,20 +154,20 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 9, "id": "de2b21c1-afc1-4772-af17-8b6b1d655f04", "metadata": {}, "outputs": [ { "data": { "text/html": [ - "
\"Output\"
" + "
\"Output\"
" ], "text/plain": [ "-Image-" ] }, - "execution_count": 10, + "execution_count": 9, "metadata": { "text/html": [], "text/plain": [] @@ -189,20 +189,20 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 10, "id": "5ddbd250-e7ec-437d-a69a-a1fc753dd032", "metadata": {}, "outputs": [ { "data": { "text/html": [ - "
\"Output\"
" + "
\"Output\"
" ], "text/plain": [ "-Image-" ] }, - "execution_count": 11, + "execution_count": 10, "metadata": { "text/html": [], "text/plain": [] @@ -224,20 +224,20 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 11, "id": "cbb63715-91d1-4e6d-ba35-7b40bf15078e", "metadata": {}, "outputs": [ { "data": { "text/html": [ - "
\"Output\"
" + "
\"Output\"
" ], "text/plain": [ "-Image-" ] }, - "execution_count": 12, + "execution_count": 11, "metadata": { "text/html": [], "text/plain": [] diff --git a/ADMconstraints/wolfram/wl/ADM_vars.wl b/ADMconstraints/wolfram/wl/ADM_vars.wl index e692b0ba..7e4d2155 100644 --- a/ADMconstraints/wolfram/wl/ADM_vars.wl +++ b/ADMconstraints/wolfram/wl/ADM_vars.wl @@ -50,8 +50,8 @@ IntermediateVarlist = {invgam[i, j], Symmetric[{i, j}], PrintAs -> "\[Gamma]"}, {GamDDD [-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[CapitalGamma]"}, {Gam [k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[CapitalGamma]"}, - {tr1dGam[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[CapitalGamma]^(tr1)"}, - {tr2dGam[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[CapitalGamma]^(tr2)"}, + {tr1dGam[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*SuperscriptBox[\(\[CapitalGamma]\), \((tr1)\)]\)"}, + {tr2dGam[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*SuperscriptBox[\(\[CapitalGamma]\), \((tr2)\)]\)"}, {R[-i, -j], Symmetric[{-i, -j}], PrintAs -> "R"}, {trK[], PrintAs -> "K"}, {DADMK[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[Del]K"} From 88b8d20facc2c32bc9df212127039302d09765b1 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 15:35:17 -0500 Subject: [PATCH 13/37] ADMconstraints: add ADM_set_constraint.wl --- ADMconstraints/wolfram/ADM_set_constraint.wl | 73 ++++++++++++++++++++ 1 file changed, 73 insertions(+) create mode 100644 ADMconstraints/wolfram/ADM_set_constraint.wl diff --git a/ADMconstraints/wolfram/ADM_set_constraint.wl b/ADMconstraints/wolfram/ADM_set_constraint.wl new file mode 100644 index 00000000..7ba5c472 --- /dev/null +++ b/ADMconstraints/wolfram/ADM_set_constraint.wl @@ -0,0 +1,73 @@ +(* ::Package:: *) + +(* ADM_set_constraint.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 *) + +< detinvgam}; + SetEQNDelayed[detinvgam[], 1 / Det[Mat] // Simplify]; + SetEQNDelayed[invgam[i_, j_], invMat[[i[[1]], j[[1]]]] // Simplify] +]; + +SetOutputFile[FileNameJoin[{Directory[], "ADM_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[ADMVarlist, "tl_", "index5"]; + PrintListInitializations[dADMVarlist, "tl_", "index5"]; + PrintListInitializations[ddADMVarlist, "tl_", "index5"]; + pr[]; + + PrintInitializations[{Mode -> "MainIn"}, TmunuVarlist]; + PrintInitializations[{Mode -> "MainIn", StorageType -> "Tile"}, + ADMVarlist]; + PrintInitializations[{Mode -> "MainIn", StorageType -> "Tile", TensorType -> "Vect"}, + dADMVarlist]; + PrintInitializations[{Mode -> "MainIn", StorageType -> "Tile", TensorType -> "Smat"}, + ddADMVarlist]; + pr[]; + PrintEquations[{Mode -> "Temp"}, IntermediateVarlist]; + PrintEquations[{Mode -> "Temp"}, MatterVarlist]; + pr[]; + PrintEquations[{Mode -> "Main"}, ConstraintVarlist]; + pr[]; + pr[" });"]; + pr["});"]; + ]; + +Import[FileNameJoin[{Environment["GENERATO"], "codes/CarpetX.wl"}]]; From a319d14f1f31d537cc13400f814166ff206d0aac Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 15:55:31 -0500 Subject: [PATCH 14/37] ADMconstraints: add ADM_set_constraint.hxx --- ADMconstraints/wolfram/ADM_set_constraint.hxx | 1292 +++++++++++++++++ 1 file changed, 1292 insertions(+) create mode 100644 ADMconstraints/wolfram/ADM_set_constraint.hxx diff --git a/ADMconstraints/wolfram/ADM_set_constraint.hxx b/ADMconstraints/wolfram/ADM_set_constraint.hxx new file mode 100644 index 00000000..267cb3b0 --- /dev/null +++ b/ADMconstraints/wolfram/ADM_set_constraint.hxx @@ -0,0 +1,1292 @@ +/* ADM_set_constraint.hxx */ +/* Produced with Mathematica */ + +#ifndef ADM_SET_CONSTRAINT_HXX +#define ADM_SET_CONSTRAINT_HXX + +const GF3D2 &local_HC = gf_HC; +const GF3D2 &local_MtC1 = gf_MtC(0); +const GF3D2 &local_MtC2 = gf_MtC(1); +const GF3D2 &local_MtC3 = gf_MtC(2); + +noinline([&]() __attribute__((__flatten__, __hot__)) { + grid.loop_int_device<0, 0, 0, vsize>( + grid.nghostzones, [=] ARITH_DEVICE(const PointDesc &p) ARITH_INLINE { + const vbool mask = mask_for_loop_tail(p.i, p.imax); + const GF3D2index index2(layout2, p.I); + const GF3D5index index5(layout5, p.I); + +const auto &tmp_eTtt = gf_eTtt(mask, index2); +const auto &tmp_eTt = gf_eTt(mask, index2); +const auto &tmp_eT = gf_eT(mask, index2); +const auto &tmp_ADMgam = tl_ADMgam(mask, index5); +const auto &tmp_ADMK = tl_ADMK(mask, index5); +const auto &tmp_ADMalpha = tl_ADMalpha(mask, index5); +const auto &tmp_ADMbeta = tl_ADMbeta(mask, index5); +const auto &tmp_dADMgam = tl_dADMgam(mask, index5); +const auto &tmp_dADMK = tl_dADMK(mask, index5); +const auto &tmp_ddADMgam = tl_ddADMgam(mask, index5); + +const vreal eTtt = tmp_eTtt; +const vreal eTt1 = tmp_eTt(0); +const vreal eTt2 = tmp_eTt(1); +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 eT22 = tmp_eT(1,1); +const vreal eT23 = tmp_eT(1,2); +const vreal eT33 = tmp_eT(2,2); +const vreal ADMgam11 = tmp_ADMgam(0,0); +const vreal ADMgam12 = tmp_ADMgam(0,1); +const vreal ADMgam13 = tmp_ADMgam(0,2); +const vreal ADMgam22 = tmp_ADMgam(1,1); +const vreal ADMgam23 = tmp_ADMgam(1,2); +const vreal ADMgam33 = tmp_ADMgam(2,2); +const vreal ADMK11 = tmp_ADMK(0,0); +const vreal ADMK12 = tmp_ADMK(0,1); +const vreal ADMK13 = tmp_ADMK(0,2); +const vreal ADMK22 = tmp_ADMK(1,1); +const vreal ADMK23 = tmp_ADMK(1,2); +const vreal ADMK33 = tmp_ADMK(2,2); +const vreal ADMalpha = tmp_ADMalpha; +const vreal ADMbeta1 = tmp_ADMbeta(0); +const vreal ADMbeta2 = tmp_ADMbeta(1); +const vreal ADMbeta3 = tmp_ADMbeta(2); +const vreal dADMgam111 = tmp_dADMgam(0,0)(0); +const vreal dADMgam112 = tmp_dADMgam(0,1)(0); +const vreal dADMgam113 = tmp_dADMgam(0,2)(0); +const vreal dADMgam122 = tmp_dADMgam(1,1)(0); +const vreal dADMgam123 = tmp_dADMgam(1,2)(0); +const vreal dADMgam133 = tmp_dADMgam(2,2)(0); +const vreal dADMgam211 = tmp_dADMgam(0,0)(1); +const vreal dADMgam212 = tmp_dADMgam(0,1)(1); +const vreal dADMgam213 = tmp_dADMgam(0,2)(1); +const vreal dADMgam222 = tmp_dADMgam(1,1)(1); +const vreal dADMgam223 = tmp_dADMgam(1,2)(1); +const vreal dADMgam233 = tmp_dADMgam(2,2)(1); +const vreal dADMgam311 = tmp_dADMgam(0,0)(2); +const vreal dADMgam312 = tmp_dADMgam(0,1)(2); +const vreal dADMgam313 = tmp_dADMgam(0,2)(2); +const vreal dADMgam322 = tmp_dADMgam(1,1)(2); +const vreal dADMgam323 = tmp_dADMgam(1,2)(2); +const vreal dADMgam333 = tmp_dADMgam(2,2)(2); +const vreal dADMK111 = tmp_dADMK(0,0)(0); +const vreal dADMK112 = tmp_dADMK(0,1)(0); +const vreal dADMK113 = tmp_dADMK(0,2)(0); +const vreal dADMK122 = tmp_dADMK(1,1)(0); +const vreal dADMK123 = tmp_dADMK(1,2)(0); +const vreal dADMK133 = tmp_dADMK(2,2)(0); +const vreal dADMK211 = tmp_dADMK(0,0)(1); +const vreal dADMK212 = tmp_dADMK(0,1)(1); +const vreal dADMK213 = tmp_dADMK(0,2)(1); +const vreal dADMK222 = tmp_dADMK(1,1)(1); +const vreal dADMK223 = tmp_dADMK(1,2)(1); +const vreal dADMK233 = tmp_dADMK(2,2)(1); +const vreal dADMK311 = tmp_dADMK(0,0)(2); +const vreal dADMK312 = tmp_dADMK(0,1)(2); +const vreal dADMK313 = tmp_dADMK(0,2)(2); +const vreal dADMK322 = tmp_dADMK(1,1)(2); +const vreal dADMK323 = tmp_dADMK(1,2)(2); +const vreal dADMK333 = tmp_dADMK(2,2)(2); +const vreal ddADMgam1111 = tmp_ddADMgam(0,0)(0,0); +const vreal ddADMgam1112 = tmp_ddADMgam(0,1)(0,0); +const vreal ddADMgam1113 = tmp_ddADMgam(0,2)(0,0); +const vreal ddADMgam1122 = tmp_ddADMgam(1,1)(0,0); +const vreal ddADMgam1123 = tmp_ddADMgam(1,2)(0,0); +const vreal ddADMgam1133 = tmp_ddADMgam(2,2)(0,0); +const vreal ddADMgam1211 = tmp_ddADMgam(0,0)(0,1); +const vreal ddADMgam1212 = tmp_ddADMgam(0,1)(0,1); +const vreal ddADMgam1213 = tmp_ddADMgam(0,2)(0,1); +const vreal ddADMgam1222 = tmp_ddADMgam(1,1)(0,1); +const vreal ddADMgam1223 = tmp_ddADMgam(1,2)(0,1); +const vreal ddADMgam1233 = tmp_ddADMgam(2,2)(0,1); +const vreal ddADMgam1311 = tmp_ddADMgam(0,0)(0,2); +const vreal ddADMgam1312 = tmp_ddADMgam(0,1)(0,2); +const vreal ddADMgam1313 = tmp_ddADMgam(0,2)(0,2); +const vreal ddADMgam1322 = tmp_ddADMgam(1,1)(0,2); +const vreal ddADMgam1323 = tmp_ddADMgam(1,2)(0,2); +const vreal ddADMgam1333 = tmp_ddADMgam(2,2)(0,2); +const vreal ddADMgam2211 = tmp_ddADMgam(0,0)(1,1); +const vreal ddADMgam2212 = tmp_ddADMgam(0,1)(1,1); +const vreal ddADMgam2213 = tmp_ddADMgam(0,2)(1,1); +const vreal ddADMgam2222 = tmp_ddADMgam(1,1)(1,1); +const vreal ddADMgam2223 = tmp_ddADMgam(1,2)(1,1); +const vreal ddADMgam2233 = tmp_ddADMgam(2,2)(1,1); +const vreal ddADMgam2311 = tmp_ddADMgam(0,0)(1,2); +const vreal ddADMgam2312 = tmp_ddADMgam(0,1)(1,2); +const vreal ddADMgam2313 = tmp_ddADMgam(0,2)(1,2); +const vreal ddADMgam2322 = tmp_ddADMgam(1,1)(1,2); +const vreal ddADMgam2323 = tmp_ddADMgam(1,2)(1,2); +const vreal ddADMgam2333 = tmp_ddADMgam(2,2)(1,2); +const vreal ddADMgam3311 = tmp_ddADMgam(0,0)(2,2); +const vreal ddADMgam3312 = tmp_ddADMgam(0,1)(2,2); +const vreal ddADMgam3313 = tmp_ddADMgam(0,2)(2,2); +const vreal ddADMgam3322 = tmp_ddADMgam(1,1)(2,2); +const vreal ddADMgam3323 = tmp_ddADMgam(1,2)(2,2); +const vreal ddADMgam3333 = tmp_ddADMgam(2,2)(2,2); + +vreal detinvgam += +1/(-(Power(ADMgam13,2)*ADMgam22) + 2*ADMgam12*ADMgam13*ADMgam23 - + ADMgam11*Power(ADMgam23,2) - Power(ADMgam12,2)*ADMgam33 + + ADMgam11*ADMgam22*ADMgam33) +; + +vreal invgam11 += +(-Power(ADMgam23,2) + ADMgam22*ADMgam33)*detinvgam +; + +vreal invgam12 += +(ADMgam13*ADMgam23 - ADMgam12*ADMgam33)*detinvgam +; + +vreal invgam13 += +(-(ADMgam13*ADMgam22) + ADMgam12*ADMgam23)*detinvgam +; + +vreal invgam22 += +(-Power(ADMgam13,2) + ADMgam11*ADMgam33)*detinvgam +; + +vreal invgam23 += +(ADMgam12*ADMgam13 - ADMgam11*ADMgam23)*detinvgam +; + +vreal invgam33 += +(-Power(ADMgam12,2) + ADMgam11*ADMgam22)*detinvgam +; + +vreal GamDDD111 += +dADMgam111/2. +; + +vreal GamDDD112 += +dADMgam211/2. +; + +vreal GamDDD113 += +dADMgam311/2. +; + +vreal GamDDD122 += +-0.5*dADMgam122 + dADMgam212 +; + +vreal GamDDD123 += +(-dADMgam123 + dADMgam213 + dADMgam312)/2. +; + +vreal GamDDD133 += +-0.5*dADMgam133 + dADMgam313 +; + +vreal GamDDD211 += +dADMgam112 - dADMgam211/2. +; + +vreal GamDDD212 += +dADMgam122/2. +; + +vreal GamDDD213 += +(dADMgam123 - dADMgam213 + dADMgam312)/2. +; + +vreal GamDDD222 += +dADMgam222/2. +; + +vreal GamDDD223 += +dADMgam322/2. +; + +vreal GamDDD233 += +-0.5*dADMgam233 + dADMgam323 +; + +vreal GamDDD311 += +dADMgam113 - dADMgam311/2. +; + +vreal GamDDD312 += +(dADMgam123 + dADMgam213 - dADMgam312)/2. +; + +vreal GamDDD313 += +dADMgam133/2. +; + +vreal GamDDD322 += +dADMgam223 - dADMgam322/2. +; + +vreal GamDDD323 += +dADMgam233/2. +; + +vreal GamDDD333 += +dADMgam333/2. +; + +vreal Gam111 += +GamDDD111*invgam11 + GamDDD211*invgam12 + GamDDD311*invgam13 +; + +vreal Gam112 += +GamDDD112*invgam11 + GamDDD212*invgam12 + GamDDD312*invgam13 +; + +vreal Gam113 += +GamDDD113*invgam11 + GamDDD213*invgam12 + GamDDD313*invgam13 +; + +vreal Gam122 += +GamDDD122*invgam11 + GamDDD222*invgam12 + GamDDD322*invgam13 +; + +vreal Gam123 += +GamDDD123*invgam11 + GamDDD223*invgam12 + GamDDD323*invgam13 +; + +vreal Gam133 += +GamDDD133*invgam11 + GamDDD233*invgam12 + GamDDD333*invgam13 +; + +vreal Gam211 += +GamDDD111*invgam12 + GamDDD211*invgam22 + GamDDD311*invgam23 +; + +vreal Gam212 += +GamDDD112*invgam12 + GamDDD212*invgam22 + GamDDD312*invgam23 +; + +vreal Gam213 += +GamDDD113*invgam12 + GamDDD213*invgam22 + GamDDD313*invgam23 +; + +vreal Gam222 += +GamDDD122*invgam12 + GamDDD222*invgam22 + GamDDD322*invgam23 +; + +vreal Gam223 += +GamDDD123*invgam12 + GamDDD223*invgam22 + GamDDD323*invgam23 +; + +vreal Gam233 += +GamDDD133*invgam12 + GamDDD233*invgam22 + GamDDD333*invgam23 +; + +vreal Gam311 += +GamDDD111*invgam13 + GamDDD211*invgam23 + GamDDD311*invgam33 +; + +vreal Gam312 += +GamDDD112*invgam13 + GamDDD212*invgam23 + GamDDD312*invgam33 +; + +vreal Gam313 += +GamDDD113*invgam13 + GamDDD213*invgam23 + GamDDD313*invgam33 +; + +vreal Gam322 += +GamDDD122*invgam13 + GamDDD222*invgam23 + GamDDD322*invgam33 +; + +vreal Gam323 += +GamDDD123*invgam13 + GamDDD223*invgam23 + GamDDD323*invgam33 +; + +vreal Gam333 += +GamDDD133*invgam13 + GamDDD233*invgam23 + GamDDD333*invgam33 +; + +vreal tr1dGam11 += +(ddADMgam1111*invgam11)/2. + ddADMgam1112*invgam12 - + 2*dADMgam112*GamDDD111*invgam11*invgam12 - + dADMgam211*GamDDD111*invgam11*invgam12 - + dADMgam122*GamDDD111*Power(invgam12,2) - + dADMgam212*GamDDD111*Power(invgam12,2) - + dADMgam112*GamDDD211*Power(invgam12,2) - + dADMgam211*GamDDD211*Power(invgam12,2) + ddADMgam1113*invgam13 - + 2*dADMgam113*GamDDD111*invgam11*invgam13 - + dADMgam311*GamDDD111*invgam11*invgam13 - + 2*dADMgam123*GamDDD111*invgam12*invgam13 - + dADMgam213*GamDDD111*invgam12*invgam13 - + dADMgam312*GamDDD111*invgam12*invgam13 - + dADMgam113*GamDDD211*invgam12*invgam13 - + dADMgam311*GamDDD211*invgam12*invgam13 - + dADMgam112*GamDDD311*invgam12*invgam13 - + dADMgam211*GamDDD311*invgam12*invgam13 - + dADMgam133*GamDDD111*Power(invgam13,2) - + dADMgam313*GamDDD111*Power(invgam13,2) - + dADMgam113*GamDDD311*Power(invgam13,2) - + dADMgam311*GamDDD311*Power(invgam13,2) - + dADMgam111*invgam11*(GamDDD111*invgam11 + GamDDD211*invgam12 + + GamDDD311*invgam13) + ddADMgam1212*invgam22 - + (ddADMgam2211*invgam22)/2. - dADMgam212*GamDDD111*invgam11*invgam22 - + dADMgam112*GamDDD211*invgam11*invgam22 - + dADMgam222*GamDDD111*invgam12*invgam22 - + dADMgam122*GamDDD211*invgam12*invgam22 - + 2*dADMgam212*GamDDD211*invgam12*invgam22 - + dADMgam223*GamDDD111*invgam13*invgam22 - + dADMgam123*GamDDD211*invgam13*invgam22 - + dADMgam312*GamDDD211*invgam13*invgam22 - + dADMgam212*GamDDD311*invgam13*invgam22 - + dADMgam222*GamDDD211*Power(invgam22,2) + ddADMgam1213*invgam23 + + ddADMgam1312*invgam23 - ddADMgam2311*invgam23 - + dADMgam213*GamDDD111*invgam11*invgam23 - + dADMgam312*GamDDD111*invgam11*invgam23 - + dADMgam113*GamDDD211*invgam11*invgam23 - + dADMgam112*GamDDD311*invgam11*invgam23 - + dADMgam223*GamDDD111*invgam12*invgam23 - + dADMgam322*GamDDD111*invgam12*invgam23 - + dADMgam123*GamDDD211*invgam12*invgam23 - + 2*dADMgam213*GamDDD211*invgam12*invgam23 - + dADMgam312*GamDDD211*invgam12*invgam23 - + dADMgam122*GamDDD311*invgam12*invgam23 - + dADMgam212*GamDDD311*invgam12*invgam23 - + dADMgam233*GamDDD111*invgam13*invgam23 - + dADMgam323*GamDDD111*invgam13*invgam23 - + dADMgam133*GamDDD211*invgam13*invgam23 - + dADMgam313*GamDDD211*invgam13*invgam23 - + dADMgam123*GamDDD311*invgam13*invgam23 - + dADMgam213*GamDDD311*invgam13*invgam23 - + 2*dADMgam312*GamDDD311*invgam13*invgam23 - + 2*dADMgam223*GamDDD211*invgam22*invgam23 - + dADMgam322*GamDDD211*invgam22*invgam23 - + dADMgam222*GamDDD311*invgam22*invgam23 - + dADMgam233*GamDDD211*Power(invgam23,2) - + dADMgam323*GamDDD211*Power(invgam23,2) - + dADMgam223*GamDDD311*Power(invgam23,2) - + dADMgam322*GamDDD311*Power(invgam23,2) + ddADMgam1313*invgam33 - + (ddADMgam3311*invgam33)/2. - dADMgam313*GamDDD111*invgam11*invgam33 - + dADMgam113*GamDDD311*invgam11*invgam33 - + dADMgam323*GamDDD111*invgam12*invgam33 - + dADMgam313*GamDDD211*invgam12*invgam33 - + dADMgam123*GamDDD311*invgam12*invgam33 - + dADMgam213*GamDDD311*invgam12*invgam33 - + dADMgam333*GamDDD111*invgam13*invgam33 - + dADMgam133*GamDDD311*invgam13*invgam33 - + 2*dADMgam313*GamDDD311*invgam13*invgam33 - + dADMgam323*GamDDD211*invgam22*invgam33 - + dADMgam223*GamDDD311*invgam22*invgam33 - + dADMgam333*GamDDD211*invgam23*invgam33 - + dADMgam233*GamDDD311*invgam23*invgam33 - + 2*dADMgam323*GamDDD311*invgam23*invgam33 - + dADMgam333*GamDDD311*Power(invgam33,2) +; + +vreal tr1dGam12 += +(ddADMgam1211*invgam11 + ddADMgam1122*invgam12 + ddADMgam2211*invgam12 - + 4*dADMgam112*GamDDD112*invgam11*invgam12 - + 2*dADMgam211*GamDDD112*invgam11*invgam12 - + 2*dADMgam122*GamDDD112*Power(invgam12,2) - + 2*dADMgam212*GamDDD112*Power(invgam12,2) - + 2*dADMgam112*GamDDD212*Power(invgam12,2) - + 2*dADMgam211*GamDDD212*Power(invgam12,2) + ddADMgam1123*invgam13 + + ddADMgam1213*invgam13 - ddADMgam1312*invgam13 + ddADMgam2311*invgam13 - + 4*dADMgam113*GamDDD112*invgam11*invgam13 - + 2*dADMgam311*GamDDD112*invgam11*invgam13 - + 4*dADMgam123*GamDDD112*invgam12*invgam13 - + 2*dADMgam213*GamDDD112*invgam12*invgam13 - + 2*dADMgam312*GamDDD112*invgam12*invgam13 - + 2*dADMgam113*GamDDD212*invgam12*invgam13 - + 2*dADMgam311*GamDDD212*invgam12*invgam13 - + 2*dADMgam112*GamDDD312*invgam12*invgam13 - + 2*dADMgam211*GamDDD312*invgam12*invgam13 - + 2*dADMgam133*GamDDD112*Power(invgam13,2) - + 2*dADMgam313*GamDDD112*Power(invgam13,2) - + 2*dADMgam113*GamDDD312*Power(invgam13,2) - + 2*dADMgam311*GamDDD312*Power(invgam13,2) - + 2*dADMgam111*invgam11*(GamDDD112*invgam11 + GamDDD212*invgam12 + + GamDDD312*invgam13) + ddADMgam1222*invgam22 - + 2*dADMgam212*GamDDD112*invgam11*invgam22 - + 2*dADMgam112*GamDDD212*invgam11*invgam22 - + 2*dADMgam222*GamDDD112*invgam12*invgam22 - + 2*dADMgam122*GamDDD212*invgam12*invgam22 - + 4*dADMgam212*GamDDD212*invgam12*invgam22 - + 2*dADMgam223*GamDDD112*invgam13*invgam22 - + 2*dADMgam123*GamDDD212*invgam13*invgam22 - + 2*dADMgam312*GamDDD212*invgam13*invgam22 - + 2*dADMgam212*GamDDD312*invgam13*invgam22 - + 2*dADMgam222*GamDDD212*Power(invgam22,2) + ddADMgam1223*invgam23 + + ddADMgam1322*invgam23 + ddADMgam2213*invgam23 - ddADMgam2312*invgam23 - + 2*dADMgam213*GamDDD112*invgam11*invgam23 - + 2*dADMgam312*GamDDD112*invgam11*invgam23 - + 2*dADMgam113*GamDDD212*invgam11*invgam23 - + 2*dADMgam112*GamDDD312*invgam11*invgam23 - + 2*dADMgam223*GamDDD112*invgam12*invgam23 - + 2*dADMgam322*GamDDD112*invgam12*invgam23 - + 2*dADMgam123*GamDDD212*invgam12*invgam23 - + 4*dADMgam213*GamDDD212*invgam12*invgam23 - + 2*dADMgam312*GamDDD212*invgam12*invgam23 - + 2*dADMgam122*GamDDD312*invgam12*invgam23 - + 2*dADMgam212*GamDDD312*invgam12*invgam23 - + 2*dADMgam233*GamDDD112*invgam13*invgam23 - + 2*dADMgam323*GamDDD112*invgam13*invgam23 - + 2*dADMgam133*GamDDD212*invgam13*invgam23 - + 2*dADMgam313*GamDDD212*invgam13*invgam23 - + 2*dADMgam123*GamDDD312*invgam13*invgam23 - + 2*dADMgam213*GamDDD312*invgam13*invgam23 - + 4*dADMgam312*GamDDD312*invgam13*invgam23 - + 4*dADMgam223*GamDDD212*invgam22*invgam23 - + 2*dADMgam322*GamDDD212*invgam22*invgam23 - + 2*dADMgam222*GamDDD312*invgam22*invgam23 - + 2*dADMgam233*GamDDD212*Power(invgam23,2) - + 2*dADMgam323*GamDDD212*Power(invgam23,2) - + 2*dADMgam223*GamDDD312*Power(invgam23,2) - + 2*dADMgam322*GamDDD312*Power(invgam23,2) + ddADMgam1323*invgam33 + + ddADMgam2313*invgam33 - ddADMgam3312*invgam33 - + 2*dADMgam313*GamDDD112*invgam11*invgam33 - + 2*dADMgam113*GamDDD312*invgam11*invgam33 - + 2*dADMgam323*GamDDD112*invgam12*invgam33 - + 2*dADMgam313*GamDDD212*invgam12*invgam33 - + 2*dADMgam123*GamDDD312*invgam12*invgam33 - + 2*dADMgam213*GamDDD312*invgam12*invgam33 - + 2*dADMgam333*GamDDD112*invgam13*invgam33 - + 2*dADMgam133*GamDDD312*invgam13*invgam33 - + 4*dADMgam313*GamDDD312*invgam13*invgam33 - + 2*dADMgam323*GamDDD212*invgam22*invgam33 - + 2*dADMgam223*GamDDD312*invgam22*invgam33 - + 2*dADMgam333*GamDDD212*invgam23*invgam33 - + 2*dADMgam233*GamDDD312*invgam23*invgam33 - + 4*dADMgam323*GamDDD312*invgam23*invgam33 - + 2*dADMgam333*GamDDD312*Power(invgam33,2))/2. +; + +vreal tr1dGam13 += +(ddADMgam1311*invgam11 + ddADMgam1123*invgam12 - ddADMgam1213*invgam12 + + ddADMgam1312*invgam12 + ddADMgam2311*invgam12 - + 4*dADMgam112*GamDDD113*invgam11*invgam12 - + 2*dADMgam211*GamDDD113*invgam11*invgam12 - + 2*dADMgam122*GamDDD113*Power(invgam12,2) - + 2*dADMgam212*GamDDD113*Power(invgam12,2) - + 2*dADMgam112*GamDDD213*Power(invgam12,2) - + 2*dADMgam211*GamDDD213*Power(invgam12,2) + ddADMgam1133*invgam13 + + ddADMgam3311*invgam13 - 4*dADMgam113*GamDDD113*invgam11*invgam13 - + 2*dADMgam311*GamDDD113*invgam11*invgam13 - + 4*dADMgam123*GamDDD113*invgam12*invgam13 - + 2*dADMgam213*GamDDD113*invgam12*invgam13 - + 2*dADMgam312*GamDDD113*invgam12*invgam13 - + 2*dADMgam113*GamDDD213*invgam12*invgam13 - + 2*dADMgam311*GamDDD213*invgam12*invgam13 - + 2*dADMgam112*GamDDD313*invgam12*invgam13 - + 2*dADMgam211*GamDDD313*invgam12*invgam13 - + 2*dADMgam133*GamDDD113*Power(invgam13,2) - + 2*dADMgam313*GamDDD113*Power(invgam13,2) - + 2*dADMgam113*GamDDD313*Power(invgam13,2) - + 2*dADMgam311*GamDDD313*Power(invgam13,2) - + 2*dADMgam111*invgam11*(GamDDD113*invgam11 + GamDDD213*invgam12 + + GamDDD313*invgam13) + ddADMgam1223*invgam22 - + ddADMgam2213*invgam22 + ddADMgam2312*invgam22 - + 2*dADMgam212*GamDDD113*invgam11*invgam22 - + 2*dADMgam112*GamDDD213*invgam11*invgam22 - + 2*dADMgam222*GamDDD113*invgam12*invgam22 - + 2*dADMgam122*GamDDD213*invgam12*invgam22 - + 4*dADMgam212*GamDDD213*invgam12*invgam22 - + 2*dADMgam223*GamDDD113*invgam13*invgam22 - + 2*dADMgam123*GamDDD213*invgam13*invgam22 - + 2*dADMgam312*GamDDD213*invgam13*invgam22 - + 2*dADMgam212*GamDDD313*invgam13*invgam22 - + 2*dADMgam222*GamDDD213*Power(invgam22,2) + ddADMgam1233*invgam23 + + ddADMgam1323*invgam23 - ddADMgam2313*invgam23 + ddADMgam3312*invgam23 - + 2*dADMgam213*GamDDD113*invgam11*invgam23 - + 2*dADMgam312*GamDDD113*invgam11*invgam23 - + 2*dADMgam113*GamDDD213*invgam11*invgam23 - + 2*dADMgam112*GamDDD313*invgam11*invgam23 - + 2*dADMgam223*GamDDD113*invgam12*invgam23 - + 2*dADMgam322*GamDDD113*invgam12*invgam23 - + 2*dADMgam123*GamDDD213*invgam12*invgam23 - + 4*dADMgam213*GamDDD213*invgam12*invgam23 - + 2*dADMgam312*GamDDD213*invgam12*invgam23 - + 2*dADMgam122*GamDDD313*invgam12*invgam23 - + 2*dADMgam212*GamDDD313*invgam12*invgam23 - + 2*dADMgam233*GamDDD113*invgam13*invgam23 - + 2*dADMgam323*GamDDD113*invgam13*invgam23 - + 2*dADMgam133*GamDDD213*invgam13*invgam23 - + 2*dADMgam313*GamDDD213*invgam13*invgam23 - + 2*dADMgam123*GamDDD313*invgam13*invgam23 - + 2*dADMgam213*GamDDD313*invgam13*invgam23 - + 4*dADMgam312*GamDDD313*invgam13*invgam23 - + 4*dADMgam223*GamDDD213*invgam22*invgam23 - + 2*dADMgam322*GamDDD213*invgam22*invgam23 - + 2*dADMgam222*GamDDD313*invgam22*invgam23 - + 2*dADMgam233*GamDDD213*Power(invgam23,2) - + 2*dADMgam323*GamDDD213*Power(invgam23,2) - + 2*dADMgam223*GamDDD313*Power(invgam23,2) - + 2*dADMgam322*GamDDD313*Power(invgam23,2) + ddADMgam1333*invgam33 - + 2*dADMgam313*GamDDD113*invgam11*invgam33 - + 2*dADMgam113*GamDDD313*invgam11*invgam33 - + 2*dADMgam323*GamDDD113*invgam12*invgam33 - + 2*dADMgam313*GamDDD213*invgam12*invgam33 - + 2*dADMgam123*GamDDD313*invgam12*invgam33 - + 2*dADMgam213*GamDDD313*invgam12*invgam33 - + 2*dADMgam333*GamDDD113*invgam13*invgam33 - + 2*dADMgam133*GamDDD313*invgam13*invgam33 - + 4*dADMgam313*GamDDD313*invgam13*invgam33 - + 2*dADMgam323*GamDDD213*invgam22*invgam33 - + 2*dADMgam223*GamDDD313*invgam22*invgam33 - + 2*dADMgam333*GamDDD213*invgam23*invgam33 - + 2*dADMgam233*GamDDD313*invgam23*invgam33 - + 4*dADMgam323*GamDDD313*invgam23*invgam33 - + 2*dADMgam333*GamDDD313*Power(invgam33,2))/2. +; + +vreal tr1dGam22 += +-0.5*(ddADMgam1122*invgam11) + ddADMgam1212*invgam11 - + dADMgam111*GamDDD122*Power(invgam11,2) + ddADMgam2212*invgam12 - + 2*dADMgam112*GamDDD122*invgam11*invgam12 - + dADMgam211*GamDDD122*invgam11*invgam12 - + dADMgam111*GamDDD222*invgam11*invgam12 - + dADMgam122*GamDDD122*Power(invgam12,2) - + dADMgam212*GamDDD122*Power(invgam12,2) - + dADMgam112*GamDDD222*Power(invgam12,2) - + dADMgam211*GamDDD222*Power(invgam12,2) + ddADMgam1223*invgam13 - + ddADMgam1322*invgam13 + ddADMgam2312*invgam13 - + 2*dADMgam113*GamDDD122*invgam11*invgam13 - + dADMgam311*GamDDD122*invgam11*invgam13 - + dADMgam111*GamDDD322*invgam11*invgam13 - + 2*dADMgam123*GamDDD122*invgam12*invgam13 - + dADMgam213*GamDDD122*invgam12*invgam13 - + dADMgam312*GamDDD122*invgam12*invgam13 - + dADMgam113*GamDDD222*invgam12*invgam13 - + dADMgam311*GamDDD222*invgam12*invgam13 - + dADMgam112*GamDDD322*invgam12*invgam13 - + dADMgam211*GamDDD322*invgam12*invgam13 - + dADMgam133*GamDDD122*Power(invgam13,2) - + dADMgam313*GamDDD122*Power(invgam13,2) - + dADMgam113*GamDDD322*Power(invgam13,2) - + dADMgam311*GamDDD322*Power(invgam13,2) + (ddADMgam2222*invgam22)/2. - + dADMgam212*GamDDD122*invgam11*invgam22 - + dADMgam112*GamDDD222*invgam11*invgam22 - + dADMgam222*GamDDD122*invgam12*invgam22 - + dADMgam122*GamDDD222*invgam12*invgam22 - + 2*dADMgam212*GamDDD222*invgam12*invgam22 - + dADMgam223*GamDDD122*invgam13*invgam22 - + dADMgam123*GamDDD222*invgam13*invgam22 - + dADMgam312*GamDDD222*invgam13*invgam22 - + dADMgam212*GamDDD322*invgam13*invgam22 - + dADMgam222*GamDDD222*Power(invgam22,2) + ddADMgam2223*invgam23 - + dADMgam213*GamDDD122*invgam11*invgam23 - + dADMgam312*GamDDD122*invgam11*invgam23 - + dADMgam113*GamDDD222*invgam11*invgam23 - + dADMgam112*GamDDD322*invgam11*invgam23 - + dADMgam223*GamDDD122*invgam12*invgam23 - + dADMgam322*GamDDD122*invgam12*invgam23 - + dADMgam123*GamDDD222*invgam12*invgam23 - + 2*dADMgam213*GamDDD222*invgam12*invgam23 - + dADMgam312*GamDDD222*invgam12*invgam23 - + dADMgam122*GamDDD322*invgam12*invgam23 - + dADMgam212*GamDDD322*invgam12*invgam23 - + dADMgam233*GamDDD122*invgam13*invgam23 - + dADMgam323*GamDDD122*invgam13*invgam23 - + dADMgam133*GamDDD222*invgam13*invgam23 - + dADMgam313*GamDDD222*invgam13*invgam23 - + dADMgam123*GamDDD322*invgam13*invgam23 - + dADMgam213*GamDDD322*invgam13*invgam23 - + 2*dADMgam312*GamDDD322*invgam13*invgam23 - + 2*dADMgam223*GamDDD222*invgam22*invgam23 - + dADMgam322*GamDDD222*invgam22*invgam23 - + dADMgam222*GamDDD322*invgam22*invgam23 - + dADMgam233*GamDDD222*Power(invgam23,2) - + dADMgam323*GamDDD222*Power(invgam23,2) - + dADMgam223*GamDDD322*Power(invgam23,2) - + dADMgam322*GamDDD322*Power(invgam23,2) + ddADMgam2323*invgam33 - + (ddADMgam3322*invgam33)/2. - dADMgam313*GamDDD122*invgam11*invgam33 - + dADMgam113*GamDDD322*invgam11*invgam33 - + dADMgam323*GamDDD122*invgam12*invgam33 - + dADMgam313*GamDDD222*invgam12*invgam33 - + dADMgam123*GamDDD322*invgam12*invgam33 - + dADMgam213*GamDDD322*invgam12*invgam33 - + dADMgam333*GamDDD122*invgam13*invgam33 - + dADMgam133*GamDDD322*invgam13*invgam33 - + 2*dADMgam313*GamDDD322*invgam13*invgam33 - + dADMgam323*GamDDD222*invgam22*invgam33 - + dADMgam223*GamDDD322*invgam22*invgam33 - + dADMgam333*GamDDD222*invgam23*invgam33 - + dADMgam233*GamDDD322*invgam23*invgam33 - + 2*dADMgam323*GamDDD322*invgam23*invgam33 - + dADMgam333*GamDDD322*Power(invgam33,2) +; + +vreal tr1dGam23 += +(-(ddADMgam1123*invgam11) + ddADMgam1213*invgam11 + ddADMgam1312*invgam11 - + 2*dADMgam111*GamDDD123*Power(invgam11,2) - ddADMgam1223*invgam12 + + ddADMgam1322*invgam12 + ddADMgam2213*invgam12 + ddADMgam2312*invgam12 - + 4*dADMgam112*GamDDD123*invgam11*invgam12 - + 2*dADMgam211*GamDDD123*invgam11*invgam12 - + 2*dADMgam111*GamDDD223*invgam11*invgam12 - + 2*dADMgam122*GamDDD123*Power(invgam12,2) - + 2*dADMgam212*GamDDD123*Power(invgam12,2) - + 2*dADMgam112*GamDDD223*Power(invgam12,2) - + 2*dADMgam211*GamDDD223*Power(invgam12,2) + ddADMgam1233*invgam13 - + ddADMgam1323*invgam13 + ddADMgam2313*invgam13 + ddADMgam3312*invgam13 - + 4*dADMgam113*GamDDD123*invgam11*invgam13 - + 2*dADMgam311*GamDDD123*invgam11*invgam13 - + 2*dADMgam111*GamDDD323*invgam11*invgam13 - + 4*dADMgam123*GamDDD123*invgam12*invgam13 - + 2*dADMgam213*GamDDD123*invgam12*invgam13 - + 2*dADMgam312*GamDDD123*invgam12*invgam13 - + 2*dADMgam113*GamDDD223*invgam12*invgam13 - + 2*dADMgam311*GamDDD223*invgam12*invgam13 - + 2*dADMgam112*GamDDD323*invgam12*invgam13 - + 2*dADMgam211*GamDDD323*invgam12*invgam13 - + 2*dADMgam133*GamDDD123*Power(invgam13,2) - + 2*dADMgam313*GamDDD123*Power(invgam13,2) - + 2*dADMgam113*GamDDD323*Power(invgam13,2) - + 2*dADMgam311*GamDDD323*Power(invgam13,2) + ddADMgam2322*invgam22 - + 2*dADMgam212*GamDDD123*invgam11*invgam22 - + 2*dADMgam112*GamDDD223*invgam11*invgam22 - + 2*dADMgam222*GamDDD123*invgam12*invgam22 - + 2*dADMgam122*GamDDD223*invgam12*invgam22 - + 4*dADMgam212*GamDDD223*invgam12*invgam22 - + 2*dADMgam223*GamDDD123*invgam13*invgam22 - + 2*dADMgam123*GamDDD223*invgam13*invgam22 - + 2*dADMgam312*GamDDD223*invgam13*invgam22 - + 2*dADMgam212*GamDDD323*invgam13*invgam22 - + 2*dADMgam222*GamDDD223*Power(invgam22,2) + ddADMgam2233*invgam23 + + ddADMgam3322*invgam23 - 2*dADMgam213*GamDDD123*invgam11*invgam23 - + 2*dADMgam312*GamDDD123*invgam11*invgam23 - + 2*dADMgam113*GamDDD223*invgam11*invgam23 - + 2*dADMgam112*GamDDD323*invgam11*invgam23 - + 2*dADMgam223*GamDDD123*invgam12*invgam23 - + 2*dADMgam322*GamDDD123*invgam12*invgam23 - + 2*dADMgam123*GamDDD223*invgam12*invgam23 - + 4*dADMgam213*GamDDD223*invgam12*invgam23 - + 2*dADMgam312*GamDDD223*invgam12*invgam23 - + 2*dADMgam122*GamDDD323*invgam12*invgam23 - + 2*dADMgam212*GamDDD323*invgam12*invgam23 - + 2*dADMgam233*GamDDD123*invgam13*invgam23 - + 2*dADMgam323*GamDDD123*invgam13*invgam23 - + 2*dADMgam133*GamDDD223*invgam13*invgam23 - + 2*dADMgam313*GamDDD223*invgam13*invgam23 - + 2*dADMgam123*GamDDD323*invgam13*invgam23 - + 2*dADMgam213*GamDDD323*invgam13*invgam23 - + 4*dADMgam312*GamDDD323*invgam13*invgam23 - + 4*dADMgam223*GamDDD223*invgam22*invgam23 - + 2*dADMgam322*GamDDD223*invgam22*invgam23 - + 2*dADMgam222*GamDDD323*invgam22*invgam23 - + 2*dADMgam233*GamDDD223*Power(invgam23,2) - + 2*dADMgam323*GamDDD223*Power(invgam23,2) - + 2*dADMgam223*GamDDD323*Power(invgam23,2) - + 2*dADMgam322*GamDDD323*Power(invgam23,2) + ddADMgam2333*invgam33 - + 2*dADMgam313*GamDDD123*invgam11*invgam33 - + 2*dADMgam113*GamDDD323*invgam11*invgam33 - + 2*dADMgam323*GamDDD123*invgam12*invgam33 - + 2*dADMgam313*GamDDD223*invgam12*invgam33 - + 2*dADMgam123*GamDDD323*invgam12*invgam33 - + 2*dADMgam213*GamDDD323*invgam12*invgam33 - + 2*dADMgam333*GamDDD123*invgam13*invgam33 - + 2*dADMgam133*GamDDD323*invgam13*invgam33 - + 4*dADMgam313*GamDDD323*invgam13*invgam33 - + 2*dADMgam323*GamDDD223*invgam22*invgam33 - + 2*dADMgam223*GamDDD323*invgam22*invgam33 - + 2*dADMgam333*GamDDD223*invgam23*invgam33 - + 2*dADMgam233*GamDDD323*invgam23*invgam33 - + 4*dADMgam323*GamDDD323*invgam23*invgam33 - + 2*dADMgam333*GamDDD323*Power(invgam33,2))/2. +; + +vreal tr1dGam33 += +-0.5*(ddADMgam1133*invgam11) + ddADMgam1313*invgam11 - + dADMgam111*GamDDD133*Power(invgam11,2) - ddADMgam1233*invgam12 + + ddADMgam1323*invgam12 + ddADMgam2313*invgam12 - + 2*dADMgam112*GamDDD133*invgam11*invgam12 - + dADMgam211*GamDDD133*invgam11*invgam12 - + dADMgam111*GamDDD233*invgam11*invgam12 - + dADMgam122*GamDDD133*Power(invgam12,2) - + dADMgam212*GamDDD133*Power(invgam12,2) - + dADMgam112*GamDDD233*Power(invgam12,2) - + dADMgam211*GamDDD233*Power(invgam12,2) + ddADMgam3313*invgam13 - + 2*dADMgam113*GamDDD133*invgam11*invgam13 - + dADMgam311*GamDDD133*invgam11*invgam13 - + dADMgam111*GamDDD333*invgam11*invgam13 - + 2*dADMgam123*GamDDD133*invgam12*invgam13 - + dADMgam213*GamDDD133*invgam12*invgam13 - + dADMgam312*GamDDD133*invgam12*invgam13 - + dADMgam113*GamDDD233*invgam12*invgam13 - + dADMgam311*GamDDD233*invgam12*invgam13 - + dADMgam112*GamDDD333*invgam12*invgam13 - + dADMgam211*GamDDD333*invgam12*invgam13 - + dADMgam133*GamDDD133*Power(invgam13,2) - + dADMgam313*GamDDD133*Power(invgam13,2) - + dADMgam113*GamDDD333*Power(invgam13,2) - + dADMgam311*GamDDD333*Power(invgam13,2) - (ddADMgam2233*invgam22)/2. + + ddADMgam2323*invgam22 - dADMgam212*GamDDD133*invgam11*invgam22 - + dADMgam112*GamDDD233*invgam11*invgam22 - + dADMgam222*GamDDD133*invgam12*invgam22 - + dADMgam122*GamDDD233*invgam12*invgam22 - + 2*dADMgam212*GamDDD233*invgam12*invgam22 - + dADMgam223*GamDDD133*invgam13*invgam22 - + dADMgam123*GamDDD233*invgam13*invgam22 - + dADMgam312*GamDDD233*invgam13*invgam22 - + dADMgam212*GamDDD333*invgam13*invgam22 - + dADMgam222*GamDDD233*Power(invgam22,2) + ddADMgam3323*invgam23 - + dADMgam213*GamDDD133*invgam11*invgam23 - + dADMgam312*GamDDD133*invgam11*invgam23 - + dADMgam113*GamDDD233*invgam11*invgam23 - + dADMgam112*GamDDD333*invgam11*invgam23 - + dADMgam223*GamDDD133*invgam12*invgam23 - + dADMgam322*GamDDD133*invgam12*invgam23 - + dADMgam123*GamDDD233*invgam12*invgam23 - + 2*dADMgam213*GamDDD233*invgam12*invgam23 - + dADMgam312*GamDDD233*invgam12*invgam23 - + dADMgam122*GamDDD333*invgam12*invgam23 - + dADMgam212*GamDDD333*invgam12*invgam23 - + dADMgam233*GamDDD133*invgam13*invgam23 - + dADMgam323*GamDDD133*invgam13*invgam23 - + dADMgam133*GamDDD233*invgam13*invgam23 - + dADMgam313*GamDDD233*invgam13*invgam23 - + dADMgam123*GamDDD333*invgam13*invgam23 - + dADMgam213*GamDDD333*invgam13*invgam23 - + 2*dADMgam312*GamDDD333*invgam13*invgam23 - + 2*dADMgam223*GamDDD233*invgam22*invgam23 - + dADMgam322*GamDDD233*invgam22*invgam23 - + dADMgam222*GamDDD333*invgam22*invgam23 - + dADMgam233*GamDDD233*Power(invgam23,2) - + dADMgam323*GamDDD233*Power(invgam23,2) - + dADMgam223*GamDDD333*Power(invgam23,2) - + dADMgam322*GamDDD333*Power(invgam23,2) + (ddADMgam3333*invgam33)/2. - + dADMgam313*GamDDD133*invgam11*invgam33 - + dADMgam113*GamDDD333*invgam11*invgam33 - + dADMgam323*GamDDD133*invgam12*invgam33 - + dADMgam313*GamDDD233*invgam12*invgam33 - + dADMgam123*GamDDD333*invgam12*invgam33 - + dADMgam213*GamDDD333*invgam12*invgam33 - + dADMgam333*GamDDD133*invgam13*invgam33 - + dADMgam133*GamDDD333*invgam13*invgam33 - + 2*dADMgam313*GamDDD333*invgam13*invgam33 - + dADMgam323*GamDDD233*invgam22*invgam33 - + dADMgam223*GamDDD333*invgam22*invgam33 - + dADMgam333*GamDDD233*invgam23*invgam33 - + dADMgam233*GamDDD333*invgam23*invgam33 - + 2*dADMgam323*GamDDD333*invgam23*invgam33 - + dADMgam333*GamDDD333*Power(invgam33,2) +; + +vreal tr2dGam11 += +(ddADMgam1111*invgam11 - Power(dADMgam111,2)*Power(invgam11,2) + + 2*ddADMgam1112*invgam12 - 2*Power(dADMgam112,2)*Power(invgam12,2) + + 2*ddADMgam1113*invgam13 - 4*dADMgam112*dADMgam113*invgam12*invgam13 - + 2*Power(dADMgam113,2)*Power(invgam13,2) - + 2*dADMgam111*(2*dADMgam112*invgam11*invgam12 + + dADMgam122*Power(invgam12,2) + + invgam13*(2*dADMgam113*invgam11 + 2*dADMgam123*invgam12 + + dADMgam133*invgam13)) + ddADMgam1122*invgam22 - + 2*Power(dADMgam112,2)*invgam11*invgam22 - + 4*dADMgam112*dADMgam122*invgam12*invgam22 - + 4*dADMgam112*dADMgam123*invgam13*invgam22 - + Power(dADMgam122,2)*Power(invgam22,2) + 2*ddADMgam1123*invgam23 - + 4*dADMgam112*dADMgam113*invgam11*invgam23 - + 4*dADMgam113*dADMgam122*invgam12*invgam23 - + 4*dADMgam112*dADMgam123*invgam12*invgam23 - + 4*dADMgam113*dADMgam123*invgam13*invgam23 - + 4*dADMgam112*dADMgam133*invgam13*invgam23 - + 4*dADMgam122*dADMgam123*invgam22*invgam23 - + 2*Power(dADMgam123,2)*Power(invgam23,2) - + 2*dADMgam122*dADMgam133*Power(invgam23,2) + ddADMgam1133*invgam33 - + 2*Power(dADMgam113,2)*invgam11*invgam33 - + 4*dADMgam113*dADMgam123*invgam12*invgam33 - + 4*dADMgam113*dADMgam133*invgam13*invgam33 - + 2*Power(dADMgam123,2)*invgam22*invgam33 - + 4*dADMgam123*dADMgam133*invgam23*invgam33 - + Power(dADMgam133,2)*Power(invgam33,2))/2. +; + +vreal tr2dGam12 += +(ddADMgam1211*invgam11 + 2*ddADMgam1212*invgam12 - + 2*dADMgam112*dADMgam211*invgam11*invgam12 - + dADMgam122*dADMgam211*Power(invgam12,2) - + 2*dADMgam112*dADMgam212*Power(invgam12,2) + 2*ddADMgam1213*invgam13 - + 2*dADMgam113*dADMgam211*invgam11*invgam13 - + 2*dADMgam123*dADMgam211*invgam12*invgam13 - + 2*dADMgam113*dADMgam212*invgam12*invgam13 - + 2*dADMgam112*dADMgam213*invgam12*invgam13 - + dADMgam133*dADMgam211*Power(invgam13,2) - + 2*dADMgam113*dADMgam213*Power(invgam13,2) - + dADMgam111*(dADMgam211*Power(invgam11,2) + + 2*dADMgam212*invgam11*invgam12 + dADMgam222*Power(invgam12,2) + + 2*dADMgam213*invgam11*invgam13 + 2*dADMgam223*invgam12*invgam13 + + dADMgam233*Power(invgam13,2)) + ddADMgam1222*invgam22 - + 2*dADMgam112*dADMgam212*invgam11*invgam22 - + 2*dADMgam122*dADMgam212*invgam12*invgam22 - + 2*dADMgam112*dADMgam222*invgam12*invgam22 - + 2*dADMgam123*dADMgam212*invgam13*invgam22 - + 2*dADMgam112*dADMgam223*invgam13*invgam22 - + dADMgam122*dADMgam222*Power(invgam22,2) + 2*ddADMgam1223*invgam23 - + 2*dADMgam113*dADMgam212*invgam11*invgam23 - + 2*dADMgam112*dADMgam213*invgam11*invgam23 - + 2*dADMgam123*dADMgam212*invgam12*invgam23 - + 2*dADMgam122*dADMgam213*invgam12*invgam23 - + 2*dADMgam113*dADMgam222*invgam12*invgam23 - + 2*dADMgam112*dADMgam223*invgam12*invgam23 - + 2*dADMgam133*dADMgam212*invgam13*invgam23 - + 2*dADMgam123*dADMgam213*invgam13*invgam23 - + 2*dADMgam113*dADMgam223*invgam13*invgam23 - + 2*dADMgam112*dADMgam233*invgam13*invgam23 - + 2*dADMgam123*dADMgam222*invgam22*invgam23 - + 2*dADMgam122*dADMgam223*invgam22*invgam23 - + dADMgam133*dADMgam222*Power(invgam23,2) - + 2*dADMgam123*dADMgam223*Power(invgam23,2) - + dADMgam122*dADMgam233*Power(invgam23,2) + ddADMgam1233*invgam33 - + 2*dADMgam113*dADMgam213*invgam11*invgam33 - + 2*dADMgam123*dADMgam213*invgam12*invgam33 - + 2*dADMgam113*dADMgam223*invgam12*invgam33 - + 2*dADMgam133*dADMgam213*invgam13*invgam33 - + 2*dADMgam113*dADMgam233*invgam13*invgam33 - + 2*dADMgam123*dADMgam223*invgam22*invgam33 - + 2*dADMgam133*dADMgam223*invgam23*invgam33 - + 2*dADMgam123*dADMgam233*invgam23*invgam33 - + dADMgam133*dADMgam233*Power(invgam33,2))/2. +; + +vreal tr2dGam13 += +(ddADMgam1311*invgam11 + 2*ddADMgam1312*invgam12 - + 2*dADMgam112*dADMgam311*invgam11*invgam12 - + dADMgam122*dADMgam311*Power(invgam12,2) - + 2*dADMgam112*dADMgam312*Power(invgam12,2) + 2*ddADMgam1313*invgam13 - + 2*dADMgam113*dADMgam311*invgam11*invgam13 - + 2*dADMgam123*dADMgam311*invgam12*invgam13 - + 2*dADMgam113*dADMgam312*invgam12*invgam13 - + 2*dADMgam112*dADMgam313*invgam12*invgam13 - + dADMgam133*dADMgam311*Power(invgam13,2) - + 2*dADMgam113*dADMgam313*Power(invgam13,2) - + dADMgam111*(dADMgam311*Power(invgam11,2) + + 2*dADMgam312*invgam11*invgam12 + dADMgam322*Power(invgam12,2) + + 2*dADMgam313*invgam11*invgam13 + 2*dADMgam323*invgam12*invgam13 + + dADMgam333*Power(invgam13,2)) + ddADMgam1322*invgam22 - + 2*dADMgam112*dADMgam312*invgam11*invgam22 - + 2*dADMgam122*dADMgam312*invgam12*invgam22 - + 2*dADMgam112*dADMgam322*invgam12*invgam22 - + 2*dADMgam123*dADMgam312*invgam13*invgam22 - + 2*dADMgam112*dADMgam323*invgam13*invgam22 - + dADMgam122*dADMgam322*Power(invgam22,2) + 2*ddADMgam1323*invgam23 - + 2*dADMgam113*dADMgam312*invgam11*invgam23 - + 2*dADMgam112*dADMgam313*invgam11*invgam23 - + 2*dADMgam123*dADMgam312*invgam12*invgam23 - + 2*dADMgam122*dADMgam313*invgam12*invgam23 - + 2*dADMgam113*dADMgam322*invgam12*invgam23 - + 2*dADMgam112*dADMgam323*invgam12*invgam23 - + 2*dADMgam133*dADMgam312*invgam13*invgam23 - + 2*dADMgam123*dADMgam313*invgam13*invgam23 - + 2*dADMgam113*dADMgam323*invgam13*invgam23 - + 2*dADMgam112*dADMgam333*invgam13*invgam23 - + 2*dADMgam123*dADMgam322*invgam22*invgam23 - + 2*dADMgam122*dADMgam323*invgam22*invgam23 - + dADMgam133*dADMgam322*Power(invgam23,2) - + 2*dADMgam123*dADMgam323*Power(invgam23,2) - + dADMgam122*dADMgam333*Power(invgam23,2) + ddADMgam1333*invgam33 - + 2*dADMgam113*dADMgam313*invgam11*invgam33 - + 2*dADMgam123*dADMgam313*invgam12*invgam33 - + 2*dADMgam113*dADMgam323*invgam12*invgam33 - + 2*dADMgam133*dADMgam313*invgam13*invgam33 - + 2*dADMgam113*dADMgam333*invgam13*invgam33 - + 2*dADMgam123*dADMgam323*invgam22*invgam33 - + 2*dADMgam133*dADMgam323*invgam23*invgam33 - + 2*dADMgam123*dADMgam333*invgam23*invgam33 - + dADMgam133*dADMgam333*Power(invgam33,2))/2. +; + +vreal tr2dGam22 += +(ddADMgam2211*invgam11 - Power(dADMgam211,2)*Power(invgam11,2) + + 2*ddADMgam2212*invgam12 - 2*Power(dADMgam212,2)*Power(invgam12,2) + + 2*ddADMgam2213*invgam13 - 4*dADMgam212*dADMgam213*invgam12*invgam13 - + 2*Power(dADMgam213,2)*Power(invgam13,2) - + 2*dADMgam211*(2*dADMgam212*invgam11*invgam12 + + dADMgam222*Power(invgam12,2) + + invgam13*(2*dADMgam213*invgam11 + 2*dADMgam223*invgam12 + + dADMgam233*invgam13)) + ddADMgam2222*invgam22 - + 2*Power(dADMgam212,2)*invgam11*invgam22 - + 4*dADMgam212*dADMgam222*invgam12*invgam22 - + 4*dADMgam212*dADMgam223*invgam13*invgam22 - + Power(dADMgam222,2)*Power(invgam22,2) + 2*ddADMgam2223*invgam23 - + 4*dADMgam212*dADMgam213*invgam11*invgam23 - + 4*dADMgam213*dADMgam222*invgam12*invgam23 - + 4*dADMgam212*dADMgam223*invgam12*invgam23 - + 4*dADMgam213*dADMgam223*invgam13*invgam23 - + 4*dADMgam212*dADMgam233*invgam13*invgam23 - + 4*dADMgam222*dADMgam223*invgam22*invgam23 - + 2*Power(dADMgam223,2)*Power(invgam23,2) - + 2*dADMgam222*dADMgam233*Power(invgam23,2) + ddADMgam2233*invgam33 - + 2*Power(dADMgam213,2)*invgam11*invgam33 - + 4*dADMgam213*dADMgam223*invgam12*invgam33 - + 4*dADMgam213*dADMgam233*invgam13*invgam33 - + 2*Power(dADMgam223,2)*invgam22*invgam33 - + 4*dADMgam223*dADMgam233*invgam23*invgam33 - + Power(dADMgam233,2)*Power(invgam33,2))/2. +; + +vreal tr2dGam23 += +(ddADMgam2311*invgam11 + 2*ddADMgam2312*invgam12 - + 2*dADMgam212*dADMgam311*invgam11*invgam12 - + dADMgam222*dADMgam311*Power(invgam12,2) - + 2*dADMgam212*dADMgam312*Power(invgam12,2) + 2*ddADMgam2313*invgam13 - + 2*dADMgam213*dADMgam311*invgam11*invgam13 - + 2*dADMgam223*dADMgam311*invgam12*invgam13 - + 2*dADMgam213*dADMgam312*invgam12*invgam13 - + 2*dADMgam212*dADMgam313*invgam12*invgam13 - + dADMgam233*dADMgam311*Power(invgam13,2) - + 2*dADMgam213*dADMgam313*Power(invgam13,2) - + dADMgam211*(dADMgam311*Power(invgam11,2) + + 2*dADMgam312*invgam11*invgam12 + dADMgam322*Power(invgam12,2) + + 2*dADMgam313*invgam11*invgam13 + 2*dADMgam323*invgam12*invgam13 + + dADMgam333*Power(invgam13,2)) + ddADMgam2322*invgam22 - + 2*dADMgam212*dADMgam312*invgam11*invgam22 - + 2*dADMgam222*dADMgam312*invgam12*invgam22 - + 2*dADMgam212*dADMgam322*invgam12*invgam22 - + 2*dADMgam223*dADMgam312*invgam13*invgam22 - + 2*dADMgam212*dADMgam323*invgam13*invgam22 - + dADMgam222*dADMgam322*Power(invgam22,2) + 2*ddADMgam2323*invgam23 - + 2*dADMgam213*dADMgam312*invgam11*invgam23 - + 2*dADMgam212*dADMgam313*invgam11*invgam23 - + 2*dADMgam223*dADMgam312*invgam12*invgam23 - + 2*dADMgam222*dADMgam313*invgam12*invgam23 - + 2*dADMgam213*dADMgam322*invgam12*invgam23 - + 2*dADMgam212*dADMgam323*invgam12*invgam23 - + 2*dADMgam233*dADMgam312*invgam13*invgam23 - + 2*dADMgam223*dADMgam313*invgam13*invgam23 - + 2*dADMgam213*dADMgam323*invgam13*invgam23 - + 2*dADMgam212*dADMgam333*invgam13*invgam23 - + 2*dADMgam223*dADMgam322*invgam22*invgam23 - + 2*dADMgam222*dADMgam323*invgam22*invgam23 - + dADMgam233*dADMgam322*Power(invgam23,2) - + 2*dADMgam223*dADMgam323*Power(invgam23,2) - + dADMgam222*dADMgam333*Power(invgam23,2) + ddADMgam2333*invgam33 - + 2*dADMgam213*dADMgam313*invgam11*invgam33 - + 2*dADMgam223*dADMgam313*invgam12*invgam33 - + 2*dADMgam213*dADMgam323*invgam12*invgam33 - + 2*dADMgam233*dADMgam313*invgam13*invgam33 - + 2*dADMgam213*dADMgam333*invgam13*invgam33 - + 2*dADMgam223*dADMgam323*invgam22*invgam33 - + 2*dADMgam233*dADMgam323*invgam23*invgam33 - + 2*dADMgam223*dADMgam333*invgam23*invgam33 - + dADMgam233*dADMgam333*Power(invgam33,2))/2. +; + +vreal tr2dGam33 += +(ddADMgam3311*invgam11 - Power(dADMgam311,2)*Power(invgam11,2) + + 2*ddADMgam3312*invgam12 - 2*Power(dADMgam312,2)*Power(invgam12,2) + + 2*ddADMgam3313*invgam13 - 4*dADMgam312*dADMgam313*invgam12*invgam13 - + 2*Power(dADMgam313,2)*Power(invgam13,2) - + 2*dADMgam311*(2*dADMgam312*invgam11*invgam12 + + dADMgam322*Power(invgam12,2) + + invgam13*(2*dADMgam313*invgam11 + 2*dADMgam323*invgam12 + + dADMgam333*invgam13)) + ddADMgam3322*invgam22 - + 2*Power(dADMgam312,2)*invgam11*invgam22 - + 4*dADMgam312*dADMgam322*invgam12*invgam22 - + 4*dADMgam312*dADMgam323*invgam13*invgam22 - + Power(dADMgam322,2)*Power(invgam22,2) + 2*ddADMgam3323*invgam23 - + 4*dADMgam312*dADMgam313*invgam11*invgam23 - + 4*dADMgam313*dADMgam322*invgam12*invgam23 - + 4*dADMgam312*dADMgam323*invgam12*invgam23 - + 4*dADMgam313*dADMgam323*invgam13*invgam23 - + 4*dADMgam312*dADMgam333*invgam13*invgam23 - + 4*dADMgam322*dADMgam323*invgam22*invgam23 - + 2*Power(dADMgam323,2)*Power(invgam23,2) - + 2*dADMgam322*dADMgam333*Power(invgam23,2) + ddADMgam3333*invgam33 - + 2*Power(dADMgam313,2)*invgam11*invgam33 - + 4*dADMgam313*dADMgam323*invgam12*invgam33 - + 4*dADMgam313*dADMgam333*invgam13*invgam33 - + 2*Power(dADMgam323,2)*invgam22*invgam33 - + 4*dADMgam323*dADMgam333*invgam23*invgam33 - + Power(dADMgam333,2)*Power(invgam33,2))/2. +; + +vreal R11 += +-(Gam112*Gam211) - Power(Gam212,2) + Gam211*Gam222 - Gam113*Gam311 + + Gam223*Gam311 - 2*Gam213*Gam312 - Power(Gam313,2) + + Gam111*(Gam212 + Gam313) + Gam211*Gam323 + Gam311*Gam333 + tr1dGam11 - + tr2dGam11 +; + +vreal R12 += +-(Gam122*Gam211) - Gam123*Gam311 + Gam112*(Gam212 + Gam313) - + Gam213*Gam322 + Gam212*Gam323 - Gam313*Gam323 + Gam312*Gam333 + + tr1dGam12 - tr2dGam12 +; + +vreal R13 += +-(Gam123*Gam211) + Gam213*Gam222 - Gam212*Gam223 - Gam133*Gam311 - + Gam233*Gam312 + Gam223*Gam313 + Gam113*(Gam212 + Gam313) + tr1dGam13 - + tr2dGam13 +; + +vreal R22 += +-Power(Gam112,2) + Gam111*Gam122 - Gam122*Gam212 + Gam112*Gam222 - + 2*Gam123*Gam312 + Gam122*Gam313 + Gam113*Gam322 - Gam223*Gam322 + + Gam222*Gam323 - Power(Gam323,2) + Gam322*Gam333 + tr1dGam22 - tr2dGam22 +; + +vreal R23 += +Gam111*Gam123 - Gam122*Gam213 + Gam112*(-Gam113 + Gam223) - Gam133*Gam312 - + Gam233*Gam322 + Gam113*Gam323 + Gam223*Gam323 + tr1dGam23 - tr2dGam23 +; + +vreal R33 += +-Power(Gam113,2) + Gam111*Gam133 + Gam133*Gam212 - 2*Gam123*Gam213 - + Power(Gam223,2) + Gam112*Gam233 + Gam222*Gam233 - Gam133*Gam313 - + Gam233*Gam323 + Gam113*Gam333 + Gam223*Gam333 + tr1dGam33 - tr2dGam33 +; + +vreal trK += +ADMK11*invgam11 + 2*ADMK12*invgam12 + 2*ADMK13*invgam13 + ADMK22*invgam22 + + 2*ADMK23*invgam23 + ADMK33*invgam33 +; + +vreal DADMK111 += +dADMK111 - 2*(ADMK11*Gam111 + ADMK12*Gam211 + ADMK13*Gam311) +; + +vreal DADMK112 += +dADMK112 - ADMK11*Gam112 - ADMK22*Gam211 - ADMK12*(Gam111 + Gam212) - + ADMK23*Gam311 - ADMK13*Gam312 +; + +vreal DADMK113 += +dADMK113 - ADMK11*Gam113 - ADMK23*Gam211 - ADMK12*Gam213 - ADMK33*Gam311 - + ADMK13*(Gam111 + Gam313) +; + +vreal DADMK122 += +dADMK122 - 2*(ADMK12*Gam112 + ADMK22*Gam212 + ADMK23*Gam312) +; + +vreal DADMK123 += +dADMK123 - ADMK13*Gam112 - ADMK12*Gam113 - ADMK23*Gam212 - ADMK22*Gam213 - + ADMK33*Gam312 - ADMK23*Gam313 +; + +vreal DADMK133 += +dADMK133 - 2*(ADMK13*Gam113 + ADMK23*Gam213 + ADMK33*Gam313) +; + +vreal DADMK211 += +dADMK211 - 2*(ADMK11*Gam112 + ADMK12*Gam212 + ADMK13*Gam312) +; + +vreal DADMK212 += +dADMK212 - ADMK11*Gam122 - ADMK22*Gam212 - ADMK12*(Gam112 + Gam222) - + ADMK23*Gam312 - ADMK13*Gam322 +; + +vreal DADMK213 += +dADMK213 - ADMK11*Gam123 - ADMK23*Gam212 - ADMK12*Gam223 - ADMK33*Gam312 - + ADMK13*(Gam112 + Gam323) +; + +vreal DADMK222 += +dADMK222 - 2*(ADMK12*Gam122 + ADMK22*Gam222 + ADMK23*Gam322) +; + +vreal DADMK223 += +dADMK223 - ADMK13*Gam122 - ADMK12*Gam123 - ADMK23*Gam222 - ADMK22*Gam223 - + ADMK33*Gam322 - ADMK23*Gam323 +; + +vreal DADMK233 += +dADMK233 - 2*(ADMK13*Gam123 + ADMK23*Gam223 + ADMK33*Gam323) +; + +vreal DADMK311 += +dADMK311 - 2*(ADMK11*Gam113 + ADMK12*Gam213 + ADMK13*Gam313) +; + +vreal DADMK312 += +dADMK312 - ADMK11*Gam123 - ADMK22*Gam213 - ADMK12*(Gam113 + Gam223) - + ADMK23*Gam313 - ADMK13*Gam323 +; + +vreal DADMK313 += +dADMK313 - ADMK11*Gam133 - ADMK23*Gam213 - ADMK12*Gam233 - ADMK33*Gam313 - + ADMK13*(Gam113 + Gam333) +; + +vreal DADMK322 += +dADMK322 - 2*(ADMK12*Gam123 + ADMK22*Gam223 + ADMK23*Gam323) +; + +vreal DADMK323 += +dADMK323 - ADMK13*Gam123 - ADMK12*Gam133 - ADMK23*Gam223 - ADMK22*Gam233 - + ADMK33*Gam323 - ADMK23*Gam333 +; + +vreal DADMK333 += +dADMK333 - 2*(ADMK13*Gam133 + ADMK23*Gam233 + ADMK33*Gam333) +; + +vreal rho += +(Power(ADMbeta1,2)*eT11 + Power(ADMbeta2,2)*eT22 + + 2*ADMbeta2*ADMbeta3*eT23 + Power(ADMbeta3,2)*eT33 + + 2*ADMbeta1*(ADMbeta2*eT12 + ADMbeta3*eT13 - eTt1) - 2*ADMbeta2*eTt2 - + 2*ADMbeta3*eTt3 + eTtt)/Power(ADMalpha,2) +; + +vreal Sm1 += +(ADMbeta1*eT11 + ADMbeta2*eT12 + ADMbeta3*eT13 - eTt1)/ADMalpha +; + +vreal Sm2 += +(ADMbeta1*eT12 + ADMbeta2*eT22 + ADMbeta3*eT23 - eTt2)/ADMalpha +; + +vreal Sm3 += +(ADMbeta1*eT13 + ADMbeta2*eT23 + ADMbeta3*eT33 - eTt3)/ADMalpha +; + + +local_HC.store(mask, index2, +-(Power(ADMK11,2)*Power(invgam11,2)) - 2*Power(ADMK13,2)*Power(invgam13,2) - + 2*ADMK11*(2*ADMK12*invgam11*invgam12 + ADMK22*Power(invgam12,2) + + invgam13*(2*ADMK13*invgam11 + 2*ADMK23*invgam12 + ADMK33*invgam13)) - + Power(ADMK22,2)*Power(invgam22,2) - + 2*Power(ADMK12,2)*(Power(invgam12,2) + invgam11*invgam22) - + 4*ADMK13*ADMK22*invgam12*invgam23 - 4*ADMK13*ADMK23*invgam13*invgam23 - + 4*ADMK22*ADMK23*invgam22*invgam23 - 2*Power(ADMK23,2)*Power(invgam23,2) - + 2*ADMK22*ADMK33*Power(invgam23,2) - + 4*ADMK12*(ADMK13*invgam12*invgam13 + ADMK22*invgam12*invgam22 + + ADMK23*invgam13*invgam22 + ADMK13*invgam11*invgam23 + + ADMK23*invgam12*invgam23 + ADMK33*invgam13*invgam23) - + 2*Power(ADMK13,2)*invgam11*invgam33 - 4*ADMK13*ADMK23*invgam12*invgam33 - + 4*ADMK13*ADMK33*invgam13*invgam33 - 2*Power(ADMK23,2)*invgam22*invgam33 - + 4*ADMK23*ADMK33*invgam23*invgam33 - Power(ADMK33,2)*Power(invgam33,2) + + invgam11*R11 + 2*invgam12*R12 + 2*invgam13*R13 + invgam22*R22 + + 2*invgam23*R23 + invgam33*R33 - 16*cpi*rho + Power(trK,2) +); + +local_MtC1.store(mask, index2, +-(DADMK212*Power(invgam12,2)) + 2*DADMK123*invgam12*invgam13 - + DADMK213*invgam12*invgam13 - DADMK312*invgam12*invgam13 + + DADMK133*Power(invgam13,2) - DADMK313*Power(invgam13,2) + + DADMK212*invgam11*invgam22 + DADMK223*invgam13*invgam22 - + DADMK322*invgam13*invgam22 + + DADMK122*(Power(invgam12,2) - invgam11*invgam22) - + 2*DADMK123*invgam11*invgam23 + DADMK213*invgam11*invgam23 + + DADMK312*invgam11*invgam23 - DADMK223*invgam12*invgam23 + + DADMK322*invgam12*invgam23 + DADMK233*invgam13*invgam23 - + DADMK323*invgam13*invgam23 - DADMK133*invgam11*invgam33 + + DADMK313*invgam11*invgam33 - DADMK233*invgam12*invgam33 + + DADMK323*invgam12*invgam33 - 8*cpi*invgam11*Sm1 - 8*cpi*invgam12*Sm2 - + 8*cpi*invgam13*Sm3 +); + +local_MtC2.store(mask, index2, +-(DADMK112*Power(invgam12,2)) + DADMK211*Power(invgam12,2) - + DADMK113*invgam12*invgam13 + DADMK311*invgam12*invgam13 + + DADMK112*invgam11*invgam22 - DADMK211*invgam11*invgam22 + + DADMK123*invgam13*invgam22 - 2*DADMK213*invgam13*invgam22 + + DADMK312*invgam13*invgam22 + DADMK113*invgam11*invgam23 - + DADMK311*invgam11*invgam23 - DADMK123*invgam12*invgam23 + + 2*DADMK213*invgam12*invgam23 - DADMK312*invgam12*invgam23 + + DADMK133*invgam13*invgam23 - DADMK313*invgam13*invgam23 + + DADMK233*Power(invgam23,2) - DADMK323*Power(invgam23,2) - + DADMK133*invgam12*invgam33 + DADMK313*invgam12*invgam33 - + DADMK233*invgam22*invgam33 + DADMK323*invgam22*invgam33 - + 8*cpi*invgam12*Sm1 - 8*cpi*invgam22*Sm2 - 8*cpi*invgam23*Sm3 +); + +local_MtC3.store(mask, index2, +-(DADMK112*invgam12*invgam13) + DADMK211*invgam12*invgam13 - + DADMK113*Power(invgam13,2) + DADMK311*Power(invgam13,2) - + DADMK122*invgam13*invgam22 + DADMK212*invgam13*invgam22 + + DADMK112*invgam11*invgam23 - DADMK211*invgam11*invgam23 + + DADMK122*invgam12*invgam23 - DADMK212*invgam12*invgam23 - + DADMK123*invgam13*invgam23 - DADMK213*invgam13*invgam23 + + 2*DADMK312*invgam13*invgam23 - DADMK223*Power(invgam23,2) + + DADMK322*Power(invgam23,2) + DADMK113*invgam11*invgam33 - + DADMK311*invgam11*invgam33 + DADMK123*invgam12*invgam33 + + DADMK213*invgam12*invgam33 - 2*DADMK312*invgam12*invgam33 + + DADMK223*invgam22*invgam33 - DADMK322*invgam22*invgam33 - + 8*cpi*invgam13*Sm1 - 8*cpi*invgam23*Sm2 - 8*cpi*invgam33*Sm3 +); + + + }); +}); + +#endif // #ifndef ADM_SET_CONSTRAINT_HXX + +/* ADM_set_constraint.hxx */ From e7ab18be8bbeaf17603aa3fb2df9a76882f5dbbc Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 16:02:15 -0500 Subject: [PATCH 15/37] ADMconstraints: add interface.ccl --- ADMconstraints/interface.ccl | 20 ++++++++++++++++++++ 1 file changed, 20 insertions(+) create mode 100644 ADMconstraints/interface.ccl diff --git a/ADMconstraints/interface.ccl b/ADMconstraints/interface.ccl new file mode 100644 index 00000000..5c0f7a69 --- /dev/null +++ b/ADMconstraints/interface.ccl @@ -0,0 +1,20 @@ +# Interface definition for thorn ADMconstraints + +IMPLEMENTS: ADMconstraints + +INHERITS: ADMBaseX TmunuBaseX + +USES INCLUDE HEADER: defs.hxx +USES INCLUDE HEADER: derivs.hxx +USES INCLUDE HEADER: div.hxx +USES INCLUDE HEADER: dual.hxx +USES INCLUDE HEADER: loop_device.hxx +USES INCLUDE HEADER: mat.hxx +USES INCLUDE HEADER: simd.hxx +USES INCLUDE HEADER: sum.hxx +USES INCLUDE HEADER: vec.hxx +USES INCLUDE HEADER: vect.hxx + +CCTK_REAL HC TYPE=gf TAGS='checkpoint="no"' "H" + +CCTK_REAL MC TYPE=gf TAGS='parities={-1 +1 +1 +1 -1 +1 +1 +1 -1} checkpoint="no"' { MCx MCy MCz } "M" From 76de4baa4e932815b09038e77b5de04038a16b20 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 16:11:37 -0500 Subject: [PATCH 16/37] ADMconstraints: rename MtC to MC --- ADMconstraints/wolfram/ADM_set_constraint.hxx | 12 ++++++------ ADMconstraints/wolfram/check_rhs.ipynb | 6 +++--- ADMconstraints/wolfram/wl/ADM_rhs.wl | 2 +- ADMconstraints/wolfram/wl/ADM_vars.wl | 2 +- 4 files changed, 11 insertions(+), 11 deletions(-) diff --git a/ADMconstraints/wolfram/ADM_set_constraint.hxx b/ADMconstraints/wolfram/ADM_set_constraint.hxx index 267cb3b0..c113f5b9 100644 --- a/ADMconstraints/wolfram/ADM_set_constraint.hxx +++ b/ADMconstraints/wolfram/ADM_set_constraint.hxx @@ -5,9 +5,9 @@ #define ADM_SET_CONSTRAINT_HXX const GF3D2 &local_HC = gf_HC; -const GF3D2 &local_MtC1 = gf_MtC(0); -const GF3D2 &local_MtC2 = gf_MtC(1); -const GF3D2 &local_MtC3 = gf_MtC(2); +const GF3D2 &local_MC1 = gf_MC(0); +const GF3D2 &local_MC2 = gf_MC(1); +const GF3D2 &local_MC3 = gf_MC(2); noinline([&]() __attribute__((__flatten__, __hot__)) { grid.loop_int_device<0, 0, 0, vsize>( @@ -1237,7 +1237,7 @@ local_HC.store(mask, index2, 2*invgam23*R23 + invgam33*R33 - 16*cpi*rho + Power(trK,2) ); -local_MtC1.store(mask, index2, +local_MC1.store(mask, index2, -(DADMK212*Power(invgam12,2)) + 2*DADMK123*invgam12*invgam13 - DADMK213*invgam12*invgam13 - DADMK312*invgam12*invgam13 + DADMK133*Power(invgam13,2) - DADMK313*Power(invgam13,2) + @@ -1253,7 +1253,7 @@ local_MtC1.store(mask, index2, 8*cpi*invgam13*Sm3 ); -local_MtC2.store(mask, index2, +local_MC2.store(mask, index2, -(DADMK112*Power(invgam12,2)) + DADMK211*Power(invgam12,2) - DADMK113*invgam12*invgam13 + DADMK311*invgam12*invgam13 + DADMK112*invgam11*invgam22 - DADMK211*invgam11*invgam22 + @@ -1268,7 +1268,7 @@ local_MtC2.store(mask, index2, 8*cpi*invgam12*Sm1 - 8*cpi*invgam22*Sm2 - 8*cpi*invgam23*Sm3 ); -local_MtC3.store(mask, index2, +local_MC3.store(mask, index2, -(DADMK112*invgam12*invgam13) + DADMK211*invgam12*invgam13 - DADMK113*Power(invgam13,2) + DADMK311*Power(invgam13,2) - DADMK122*invgam13*invgam22 + DADMK212*invgam13*invgam22 + diff --git a/ADMconstraints/wolfram/check_rhs.ipynb b/ADMconstraints/wolfram/check_rhs.ipynb index 6ad7c1f1..ec6dccc1 100644 --- a/ADMconstraints/wolfram/check_rhs.ipynb +++ b/ADMconstraints/wolfram/check_rhs.ipynb @@ -161,7 +161,7 @@ { "data": { "text/html": [ - "
\"Output\"
" + "
\"Output\"
" ], "text/plain": [ "-Image-" @@ -196,7 +196,7 @@ { "data": { "text/html": [ - "
\"Output\"
" + "
\"Output\"
" ], "text/plain": [ "-Image-" @@ -231,7 +231,7 @@ { "data": { "text/html": [ - "
\"Output\"
" + "
\"Output\"
" ], "text/plain": [ "-Image-" diff --git a/ADMconstraints/wolfram/wl/ADM_rhs.wl b/ADMconstraints/wolfram/wl/ADM_rhs.wl index de3d202f..80e25ccc 100644 --- a/ADMconstraints/wolfram/wl/ADM_rhs.wl +++ b/ADMconstraints/wolfram/wl/ADM_rhs.wl @@ -38,4 +38,4 @@ SetEQN[Sm[i_], -ADMalpha[]^-1 (eTt[i] - ADMbeta[k] eT[-k, i])]; SetEQN[HC[], invgam[k, l] R[-k, -l] + trK[]^2 - invgam[i, k] invgam[j, l] ADMK[-i, -j] ADMK[-k, -l] - 16 cpi rho[]]; -SetEQN[MtC[i_], (invgam[i, k] invgam[j, l] - invgam[i, j] invgam[k, l]) DADMK[-j, -k, -l] - 8 cpi invgam[i, j] Sm[-j]]; +SetEQN[MC[i_], (invgam[i, k] invgam[j, l] - invgam[i, j] invgam[k, l]) DADMK[-j, -k, -l] - 8 cpi invgam[i, j] Sm[-j]]; diff --git a/ADMconstraints/wolfram/wl/ADM_vars.wl b/ADMconstraints/wolfram/wl/ADM_vars.wl index 7e4d2155..7488f478 100644 --- a/ADMconstraints/wolfram/wl/ADM_vars.wl +++ b/ADMconstraints/wolfram/wl/ADM_vars.wl @@ -74,7 +74,7 @@ MatterVarlist = ConstraintVarlist = GridTensors[ {HC[], PrintAs -> "H"}, - {MtC[i], PrintAs -> "M"} + {MC[i], PrintAs -> "M"} ]; (************) From 49cf5bf3b3cbced9ab8ff5c4bd83b3f1cb8d21ee Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 16:15:13 -0500 Subject: [PATCH 17/37] ADMconstraints: add param.ccl --- ADMconstraints/param.ccl | 1 + 1 file changed, 1 insertion(+) create mode 100644 ADMconstraints/param.ccl diff --git a/ADMconstraints/param.ccl b/ADMconstraints/param.ccl new file mode 100644 index 00000000..8248a229 --- /dev/null +++ b/ADMconstraints/param.ccl @@ -0,0 +1 @@ +# Parameter definitions for thorn ADMconstraints From e0141d5263a666ccf4fe95832e78cf7105e63bfc Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 16:15:33 -0500 Subject: [PATCH 18/37] ADMconstraints: update admconstraints.cxx --- ADMconstraints/src/admconstraints.cxx | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/ADMconstraints/src/admconstraints.cxx b/ADMconstraints/src/admconstraints.cxx index 586bc73a..6d2dc656 100644 --- a/ADMconstraints/src/admconstraints.cxx +++ b/ADMconstraints/src/admconstraints.cxx @@ -6,6 +6,11 @@ namespace ADMconstraints { using namespace Arith; using namespace Loop; +template +CCTK_DEVICE CCTK_HOST CCTK_ATTRIBUTE_ALWAYS_INLINE inline T Power(T x, int y) { + return (y == 2) ? Arith::pow2(x) : Arith::pown(x, y); +} + extern "C" void ADMconstraints(CCTK_ARGUMENTS) { DECLARE_CCTK_ARGUMENTSX_ADMconstraints; DECLARE_CCTK_PARAMETERS; From 0567e2337123207de45b79575aee58512c91ed1d Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 16:36:10 -0500 Subject: [PATCH 19/37] ADMconstraints: update admconstraints.cxx --- ADMconstraints/src/admconstraints.cxx | 147 ++++++++++++++++++++++++++ 1 file changed, 147 insertions(+) diff --git a/ADMconstraints/src/admconstraints.cxx b/ADMconstraints/src/admconstraints.cxx index 6d2dc656..425fb985 100644 --- a/ADMconstraints/src/admconstraints.cxx +++ b/ADMconstraints/src/admconstraints.cxx @@ -2,6 +2,24 @@ #include #include +#ifdef __CUDACC__ +// Disable CCTK_DEBUG since the debug information takes too much +// parameter space to launch the kernels +#ifdef CCTK_DEBUG +#undef CCTK_DEBUG +#endif +#endif + +#include +#include +#include + +#ifdef __CUDACC__ +#include +#endif + +#include + namespace ADMconstraints { using namespace Arith; using namespace Loop; @@ -14,6 +32,135 @@ CCTK_DEVICE CCTK_HOST CCTK_ATTRIBUTE_ALWAYS_INLINE inline T Power(T x, int y) { extern "C" void ADMconstraints(CCTK_ARGUMENTS) { DECLARE_CCTK_ARGUMENTSX_ADMconstraints; DECLARE_CCTK_PARAMETERS; + + for (int d = 0; d < 3; ++d) + if (cctk_nghostzones[d] < deriv_order / 2) + CCTK_VERROR("Need at least %d ghost zones", deriv_order / 2); + + const vect dx{ + CCTK_DELTA_SPACE(0), + CCTK_DELTA_SPACE(1), + CCTK_DELTA_SPACE(2), + }; + + const array indextype = {0, 0, 0}; + const array nghostzones = {cctk_nghostzones[0], cctk_nghostzones[1], + cctk_nghostzones[2]}; + vect imin, imax; + GridDescBase(cctkGH).box_int<0, 0, 0>(nghostzones, imin, imax); + // suffix 2: with ghost zones, suffix 5: without ghost zones + const GF3D2layout layout2(cctkGH, indextype); + const GF3D5layout layout5(imin, imax); + + // Input grid functions + const GF3D2 &gf_W = W; + const smat, 3> gf_gamt{gammatxx, gammatxy, gammatxz, + gammatyy, gammatyz, gammatzz}; + const GF3D2 &gf_exKh = Kh; + const smat, 3> gf_exAt{Atxx, Atxy, Atxz, + Atyy, Atyz, Atzz}; + const vec, 3> gf_trGt{Gamtx, Gamty, Gamtz}; + const GF3D2 &gf_Theta = Theta; + const GF3D2 &gf_alpha = alphaG; + const vec, 3> gf_beta{betaGx, betaGy, betaGz}; + + // More input grid functions + const GF3D2 &gf_eTtt = eTtt; + const vec, 3> gf_eTt{eTtx, eTty, eTtz}; + const smat, 3> gf_eT{eTxx, eTxy, eTxz, + eTyy, eTyz, eTzz}; + + // Output grid functions + const vec, 3> gf_ZtC{ZtCx, ZtCy, ZtCz}; + const GF3D2 &gf_HC = HC; + const vec, 3> gf_MtC{MtCx, MtCy, MtCz}; + + // Define derivs lambdas + const auto calccopy = [&](const auto &gf, const auto &gf0) { + Derivs::calc_copy<0, 0, 0>(gf, layout5, grid, gf0); + }; + const auto calcderivs = [&](const auto &gf, const auto &dgf, + const auto &gf0) { + Derivs::calc_derivs<0, 0, 0>(gf, dgf, layout5, grid, gf0, dx, deriv_order); + }; + const auto calcderivs2 = [&](const auto &gf, const auto &dgf, + const auto &ddgf, const auto &gf0) { + Derivs::calc_derivs2<0, 0, 0>(gf, dgf, ddgf, layout5, grid, gf0, dx, + deriv_order); + }; + + // Tile variables for derivatives and so on + const int ntmps = 118; + GF3D5vector tmps(layout5, ntmps); + int itmp = 0; + + const auto make_gf = [&]() { return GF3D5(tmps(itmp++)); }; + const auto make_vec = [&](const auto &f) { + return vec, 3>([&](int) { return f(); }); + }; + const auto make_mat = [&](const auto &f) { + return smat, 3>([&](int, int) { return f(); }); + }; + const auto make_vec_gf = [&]() { return make_vec(make_gf); }; + const auto make_mat_gf = [&]() { return make_mat(make_gf); }; + const auto make_vec_vec_gf = [&]() { return make_vec(make_vec_gf); }; + const auto make_mat_vec_gf = [&]() { return make_mat(make_vec_gf); }; + const auto make_mat_mat_gf = [&]() { return make_mat(make_mat_gf); }; + + const GF3D5 tl_W(make_gf()); + const vec, 3> tl_dW(make_vec_gf()); + const smat, 3> tl_ddW(make_mat_gf()); + calcderivs2(tl_W, tl_dW, tl_ddW, gf_W); + + const smat, 3> tl_gamt(make_mat_gf()); + const smat, 3>, 3> tl_dgamt(make_mat_vec_gf()); + const smat, 3>, 3> tl_ddgamt(make_mat_mat_gf()); + calcderivs2(tl_gamt, tl_dgamt, tl_ddgamt, gf_gamt); + + const GF3D5 tl_exKh(make_gf()); + const vec, 3> tl_dexKh(make_vec_gf()); + calcderivs(tl_exKh, tl_dexKh, gf_exKh); + + const smat, 3> tl_exAt(make_mat_gf()); + const smat, 3>, 3> tl_dexAt(make_mat_vec_gf()); + calcderivs(tl_exAt, tl_dexAt, gf_exAt); + + const vec, 3> tl_trGt(make_vec_gf()); + const vec, 3>, 3> tl_dtrGt(make_vec_vec_gf()); + calcderivs(tl_trGt, tl_dtrGt, gf_trGt); + + const GF3D5 tl_Theta(make_gf()); + const vec, 3> tl_dTheta(make_vec_gf()); + calcderivs(tl_Theta, tl_dTheta, gf_Theta); + + const GF3D5 tl_alpha(make_gf()); + calccopy(tl_alpha, gf_alpha); + + const vec, 3> tl_beta(make_vec_gf()); + calccopy(tl_beta, gf_beta); + + if (itmp != ntmps) + CCTK_VERROR("Wrong number of temporary variables: ntmps=%d itmp=%d", ntmps, + itmp); + itmp = -1; + + // simd types + typedef simd vreal; + typedef simdl vbool; + constexpr size_t vsize = tuple_size_v; + + // parameters + const CCTK_REAL cpi = M_PI; + +#ifdef __CUDACC__ + const nvtxRangeId_t range = nvtxRangeStartA("Z4cow_Constraints::constraints"); +#endif + +#include "../wolfram/Z4cow_set_constraint.hxx" + +#ifdef __CUDACC__ + nvtxRangeEnd(range); +#endif } } // namespace ADMconstraints From a51e2e1d6d664a2a04a217c2a52e12875461e618 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 16:51:14 -0500 Subject: [PATCH 20/37] ADMconstraints: remove prefix ADM for variables --- ADMconstraints/wolfram/ADM_set_constraint.hxx | 1753 ++++++++--------- ADMconstraints/wolfram/ADM_set_constraint.wl | 2 +- ADMconstraints/wolfram/check_rhs.ipynb | 6 +- ADMconstraints/wolfram/wl/ADM_rhs.wl | 18 +- ADMconstraints/wolfram/wl/ADM_vars.wl | 18 +- 5 files changed, 892 insertions(+), 905 deletions(-) diff --git a/ADMconstraints/wolfram/ADM_set_constraint.hxx b/ADMconstraints/wolfram/ADM_set_constraint.hxx index c113f5b9..f244272b 100644 --- a/ADMconstraints/wolfram/ADM_set_constraint.hxx +++ b/ADMconstraints/wolfram/ADM_set_constraint.hxx @@ -19,13 +19,13 @@ noinline([&]() __attribute__((__flatten__, __hot__)) { const auto &tmp_eTtt = gf_eTtt(mask, index2); const auto &tmp_eTt = gf_eTt(mask, index2); const auto &tmp_eT = gf_eT(mask, index2); -const auto &tmp_ADMgam = tl_ADMgam(mask, index5); -const auto &tmp_ADMK = tl_ADMK(mask, index5); -const auto &tmp_ADMalpha = tl_ADMalpha(mask, index5); -const auto &tmp_ADMbeta = tl_ADMbeta(mask, index5); -const auto &tmp_dADMgam = tl_dADMgam(mask, index5); -const auto &tmp_dADMK = tl_dADMK(mask, index5); -const auto &tmp_ddADMgam = tl_ddADMgam(mask, index5); +const auto &tmp_gam = tl_gam(mask, index5); +const auto &tmp_exK = tl_exK(mask, index5); +const auto &tmp_alpha = tl_alpha(mask, index5); +const auto &tmp_beta = tl_beta(mask, index5); +const auto &tmp_dgam = tl_dgam(mask, index5); +const auto &tmp_dexK = tl_dexK(mask, index5); +const auto &tmp_ddgam = tl_ddgam(mask, index5); const vreal eTtt = tmp_eTtt; const vreal eTt1 = tmp_eTt(0); @@ -37,220 +37,219 @@ const vreal eT13 = tmp_eT(0,2); const vreal eT22 = tmp_eT(1,1); const vreal eT23 = tmp_eT(1,2); const vreal eT33 = tmp_eT(2,2); -const vreal ADMgam11 = tmp_ADMgam(0,0); -const vreal ADMgam12 = tmp_ADMgam(0,1); -const vreal ADMgam13 = tmp_ADMgam(0,2); -const vreal ADMgam22 = tmp_ADMgam(1,1); -const vreal ADMgam23 = tmp_ADMgam(1,2); -const vreal ADMgam33 = tmp_ADMgam(2,2); -const vreal ADMK11 = tmp_ADMK(0,0); -const vreal ADMK12 = tmp_ADMK(0,1); -const vreal ADMK13 = tmp_ADMK(0,2); -const vreal ADMK22 = tmp_ADMK(1,1); -const vreal ADMK23 = tmp_ADMK(1,2); -const vreal ADMK33 = tmp_ADMK(2,2); -const vreal ADMalpha = tmp_ADMalpha; -const vreal ADMbeta1 = tmp_ADMbeta(0); -const vreal ADMbeta2 = tmp_ADMbeta(1); -const vreal ADMbeta3 = tmp_ADMbeta(2); -const vreal dADMgam111 = tmp_dADMgam(0,0)(0); -const vreal dADMgam112 = tmp_dADMgam(0,1)(0); -const vreal dADMgam113 = tmp_dADMgam(0,2)(0); -const vreal dADMgam122 = tmp_dADMgam(1,1)(0); -const vreal dADMgam123 = tmp_dADMgam(1,2)(0); -const vreal dADMgam133 = tmp_dADMgam(2,2)(0); -const vreal dADMgam211 = tmp_dADMgam(0,0)(1); -const vreal dADMgam212 = tmp_dADMgam(0,1)(1); -const vreal dADMgam213 = tmp_dADMgam(0,2)(1); -const vreal dADMgam222 = tmp_dADMgam(1,1)(1); -const vreal dADMgam223 = tmp_dADMgam(1,2)(1); -const vreal dADMgam233 = tmp_dADMgam(2,2)(1); -const vreal dADMgam311 = tmp_dADMgam(0,0)(2); -const vreal dADMgam312 = tmp_dADMgam(0,1)(2); -const vreal dADMgam313 = tmp_dADMgam(0,2)(2); -const vreal dADMgam322 = tmp_dADMgam(1,1)(2); -const vreal dADMgam323 = tmp_dADMgam(1,2)(2); -const vreal dADMgam333 = tmp_dADMgam(2,2)(2); -const vreal dADMK111 = tmp_dADMK(0,0)(0); -const vreal dADMK112 = tmp_dADMK(0,1)(0); -const vreal dADMK113 = tmp_dADMK(0,2)(0); -const vreal dADMK122 = tmp_dADMK(1,1)(0); -const vreal dADMK123 = tmp_dADMK(1,2)(0); -const vreal dADMK133 = tmp_dADMK(2,2)(0); -const vreal dADMK211 = tmp_dADMK(0,0)(1); -const vreal dADMK212 = tmp_dADMK(0,1)(1); -const vreal dADMK213 = tmp_dADMK(0,2)(1); -const vreal dADMK222 = tmp_dADMK(1,1)(1); -const vreal dADMK223 = tmp_dADMK(1,2)(1); -const vreal dADMK233 = tmp_dADMK(2,2)(1); -const vreal dADMK311 = tmp_dADMK(0,0)(2); -const vreal dADMK312 = tmp_dADMK(0,1)(2); -const vreal dADMK313 = tmp_dADMK(0,2)(2); -const vreal dADMK322 = tmp_dADMK(1,1)(2); -const vreal dADMK323 = tmp_dADMK(1,2)(2); -const vreal dADMK333 = tmp_dADMK(2,2)(2); -const vreal ddADMgam1111 = tmp_ddADMgam(0,0)(0,0); -const vreal ddADMgam1112 = tmp_ddADMgam(0,1)(0,0); -const vreal ddADMgam1113 = tmp_ddADMgam(0,2)(0,0); -const vreal ddADMgam1122 = tmp_ddADMgam(1,1)(0,0); -const vreal ddADMgam1123 = tmp_ddADMgam(1,2)(0,0); -const vreal ddADMgam1133 = tmp_ddADMgam(2,2)(0,0); -const vreal ddADMgam1211 = tmp_ddADMgam(0,0)(0,1); -const vreal ddADMgam1212 = tmp_ddADMgam(0,1)(0,1); -const vreal ddADMgam1213 = tmp_ddADMgam(0,2)(0,1); -const vreal ddADMgam1222 = tmp_ddADMgam(1,1)(0,1); -const vreal ddADMgam1223 = tmp_ddADMgam(1,2)(0,1); -const vreal ddADMgam1233 = tmp_ddADMgam(2,2)(0,1); -const vreal ddADMgam1311 = tmp_ddADMgam(0,0)(0,2); -const vreal ddADMgam1312 = tmp_ddADMgam(0,1)(0,2); -const vreal ddADMgam1313 = tmp_ddADMgam(0,2)(0,2); -const vreal ddADMgam1322 = tmp_ddADMgam(1,1)(0,2); -const vreal ddADMgam1323 = tmp_ddADMgam(1,2)(0,2); -const vreal ddADMgam1333 = tmp_ddADMgam(2,2)(0,2); -const vreal ddADMgam2211 = tmp_ddADMgam(0,0)(1,1); -const vreal ddADMgam2212 = tmp_ddADMgam(0,1)(1,1); -const vreal ddADMgam2213 = tmp_ddADMgam(0,2)(1,1); -const vreal ddADMgam2222 = tmp_ddADMgam(1,1)(1,1); -const vreal ddADMgam2223 = tmp_ddADMgam(1,2)(1,1); -const vreal ddADMgam2233 = tmp_ddADMgam(2,2)(1,1); -const vreal ddADMgam2311 = tmp_ddADMgam(0,0)(1,2); -const vreal ddADMgam2312 = tmp_ddADMgam(0,1)(1,2); -const vreal ddADMgam2313 = tmp_ddADMgam(0,2)(1,2); -const vreal ddADMgam2322 = tmp_ddADMgam(1,1)(1,2); -const vreal ddADMgam2323 = tmp_ddADMgam(1,2)(1,2); -const vreal ddADMgam2333 = tmp_ddADMgam(2,2)(1,2); -const vreal ddADMgam3311 = tmp_ddADMgam(0,0)(2,2); -const vreal ddADMgam3312 = tmp_ddADMgam(0,1)(2,2); -const vreal ddADMgam3313 = tmp_ddADMgam(0,2)(2,2); -const vreal ddADMgam3322 = tmp_ddADMgam(1,1)(2,2); -const vreal ddADMgam3323 = tmp_ddADMgam(1,2)(2,2); -const vreal ddADMgam3333 = tmp_ddADMgam(2,2)(2,2); +const vreal gam11 = tmp_gam(0,0); +const vreal gam12 = tmp_gam(0,1); +const vreal gam13 = tmp_gam(0,2); +const vreal gam22 = tmp_gam(1,1); +const vreal gam23 = tmp_gam(1,2); +const vreal gam33 = tmp_gam(2,2); +const vreal exK11 = tmp_exK(0,0); +const vreal exK12 = tmp_exK(0,1); +const vreal exK13 = tmp_exK(0,2); +const vreal exK22 = tmp_exK(1,1); +const vreal exK23 = tmp_exK(1,2); +const vreal exK33 = tmp_exK(2,2); +const vreal alpha = tmp_alpha; +const vreal beta1 = tmp_beta(0); +const vreal beta2 = tmp_beta(1); +const vreal beta3 = tmp_beta(2); +const vreal dgam111 = tmp_dgam(0,0)(0); +const vreal dgam112 = tmp_dgam(0,1)(0); +const vreal dgam113 = tmp_dgam(0,2)(0); +const vreal dgam122 = tmp_dgam(1,1)(0); +const vreal dgam123 = tmp_dgam(1,2)(0); +const vreal dgam133 = tmp_dgam(2,2)(0); +const vreal dgam211 = tmp_dgam(0,0)(1); +const vreal dgam212 = tmp_dgam(0,1)(1); +const vreal dgam213 = tmp_dgam(0,2)(1); +const vreal dgam222 = tmp_dgam(1,1)(1); +const vreal dgam223 = tmp_dgam(1,2)(1); +const vreal dgam233 = tmp_dgam(2,2)(1); +const vreal dgam311 = tmp_dgam(0,0)(2); +const vreal dgam312 = tmp_dgam(0,1)(2); +const vreal dgam313 = tmp_dgam(0,2)(2); +const vreal dgam322 = tmp_dgam(1,1)(2); +const vreal dgam323 = tmp_dgam(1,2)(2); +const vreal dgam333 = tmp_dgam(2,2)(2); +const vreal dexK111 = tmp_dexK(0,0)(0); +const vreal dexK112 = tmp_dexK(0,1)(0); +const vreal dexK113 = tmp_dexK(0,2)(0); +const vreal dexK122 = tmp_dexK(1,1)(0); +const vreal dexK123 = tmp_dexK(1,2)(0); +const vreal dexK133 = tmp_dexK(2,2)(0); +const vreal dexK211 = tmp_dexK(0,0)(1); +const vreal dexK212 = tmp_dexK(0,1)(1); +const vreal dexK213 = tmp_dexK(0,2)(1); +const vreal dexK222 = tmp_dexK(1,1)(1); +const vreal dexK223 = tmp_dexK(1,2)(1); +const vreal dexK233 = tmp_dexK(2,2)(1); +const vreal dexK311 = tmp_dexK(0,0)(2); +const vreal dexK312 = tmp_dexK(0,1)(2); +const vreal dexK313 = tmp_dexK(0,2)(2); +const vreal dexK322 = tmp_dexK(1,1)(2); +const vreal dexK323 = tmp_dexK(1,2)(2); +const vreal dexK333 = tmp_dexK(2,2)(2); +const vreal ddgam1111 = tmp_ddgam(0,0)(0,0); +const vreal ddgam1112 = tmp_ddgam(0,1)(0,0); +const vreal ddgam1113 = tmp_ddgam(0,2)(0,0); +const vreal ddgam1122 = tmp_ddgam(1,1)(0,0); +const vreal ddgam1123 = tmp_ddgam(1,2)(0,0); +const vreal ddgam1133 = tmp_ddgam(2,2)(0,0); +const vreal ddgam1211 = tmp_ddgam(0,0)(0,1); +const vreal ddgam1212 = tmp_ddgam(0,1)(0,1); +const vreal ddgam1213 = tmp_ddgam(0,2)(0,1); +const vreal ddgam1222 = tmp_ddgam(1,1)(0,1); +const vreal ddgam1223 = tmp_ddgam(1,2)(0,1); +const vreal ddgam1233 = tmp_ddgam(2,2)(0,1); +const vreal ddgam1311 = tmp_ddgam(0,0)(0,2); +const vreal ddgam1312 = tmp_ddgam(0,1)(0,2); +const vreal ddgam1313 = tmp_ddgam(0,2)(0,2); +const vreal ddgam1322 = tmp_ddgam(1,1)(0,2); +const vreal ddgam1323 = tmp_ddgam(1,2)(0,2); +const vreal ddgam1333 = tmp_ddgam(2,2)(0,2); +const vreal ddgam2211 = tmp_ddgam(0,0)(1,1); +const vreal ddgam2212 = tmp_ddgam(0,1)(1,1); +const vreal ddgam2213 = tmp_ddgam(0,2)(1,1); +const vreal ddgam2222 = tmp_ddgam(1,1)(1,1); +const vreal ddgam2223 = tmp_ddgam(1,2)(1,1); +const vreal ddgam2233 = tmp_ddgam(2,2)(1,1); +const vreal ddgam2311 = tmp_ddgam(0,0)(1,2); +const vreal ddgam2312 = tmp_ddgam(0,1)(1,2); +const vreal ddgam2313 = tmp_ddgam(0,2)(1,2); +const vreal ddgam2322 = tmp_ddgam(1,1)(1,2); +const vreal ddgam2323 = tmp_ddgam(1,2)(1,2); +const vreal ddgam2333 = tmp_ddgam(2,2)(1,2); +const vreal ddgam3311 = tmp_ddgam(0,0)(2,2); +const vreal ddgam3312 = tmp_ddgam(0,1)(2,2); +const vreal ddgam3313 = tmp_ddgam(0,2)(2,2); +const vreal ddgam3322 = tmp_ddgam(1,1)(2,2); +const vreal ddgam3323 = tmp_ddgam(1,2)(2,2); +const vreal ddgam3333 = tmp_ddgam(2,2)(2,2); vreal detinvgam = -1/(-(Power(ADMgam13,2)*ADMgam22) + 2*ADMgam12*ADMgam13*ADMgam23 - - ADMgam11*Power(ADMgam23,2) - Power(ADMgam12,2)*ADMgam33 + - ADMgam11*ADMgam22*ADMgam33) +1/(-(Power(gam13,2)*gam22) + 2*gam12*gam13*gam23 - gam11*Power(gam23,2) - + Power(gam12,2)*gam33 + gam11*gam22*gam33) ; vreal invgam11 = -(-Power(ADMgam23,2) + ADMgam22*ADMgam33)*detinvgam +detinvgam*(-Power(gam23,2) + gam22*gam33) ; vreal invgam12 = -(ADMgam13*ADMgam23 - ADMgam12*ADMgam33)*detinvgam +detinvgam*(gam13*gam23 - gam12*gam33) ; vreal invgam13 = -(-(ADMgam13*ADMgam22) + ADMgam12*ADMgam23)*detinvgam +detinvgam*(-(gam13*gam22) + gam12*gam23) ; vreal invgam22 = -(-Power(ADMgam13,2) + ADMgam11*ADMgam33)*detinvgam +detinvgam*(-Power(gam13,2) + gam11*gam33) ; vreal invgam23 = -(ADMgam12*ADMgam13 - ADMgam11*ADMgam23)*detinvgam +detinvgam*(gam12*gam13 - gam11*gam23) ; vreal invgam33 = -(-Power(ADMgam12,2) + ADMgam11*ADMgam22)*detinvgam +detinvgam*(-Power(gam12,2) + gam11*gam22) ; vreal GamDDD111 = -dADMgam111/2. +dgam111/2. ; vreal GamDDD112 = -dADMgam211/2. +dgam211/2. ; vreal GamDDD113 = -dADMgam311/2. +dgam311/2. ; vreal GamDDD122 = --0.5*dADMgam122 + dADMgam212 +-0.5*dgam122 + dgam212 ; vreal GamDDD123 = -(-dADMgam123 + dADMgam213 + dADMgam312)/2. +(-dgam123 + dgam213 + dgam312)/2. ; vreal GamDDD133 = --0.5*dADMgam133 + dADMgam313 +-0.5*dgam133 + dgam313 ; vreal GamDDD211 = -dADMgam112 - dADMgam211/2. +dgam112 - dgam211/2. ; vreal GamDDD212 = -dADMgam122/2. +dgam122/2. ; vreal GamDDD213 = -(dADMgam123 - dADMgam213 + dADMgam312)/2. +(dgam123 - dgam213 + dgam312)/2. ; vreal GamDDD222 = -dADMgam222/2. +dgam222/2. ; vreal GamDDD223 = -dADMgam322/2. +dgam322/2. ; vreal GamDDD233 = --0.5*dADMgam233 + dADMgam323 +-0.5*dgam233 + dgam323 ; vreal GamDDD311 = -dADMgam113 - dADMgam311/2. +dgam113 - dgam311/2. ; vreal GamDDD312 = -(dADMgam123 + dADMgam213 - dADMgam312)/2. +(dgam123 + dgam213 - dgam312)/2. ; vreal GamDDD313 = -dADMgam133/2. +dgam133/2. ; vreal GamDDD322 = -dADMgam223 - dADMgam322/2. +dgam223 - dgam322/2. ; vreal GamDDD323 = -dADMgam233/2. +dgam233/2. ; vreal GamDDD333 = -dADMgam333/2. +dgam333/2. ; vreal Gam111 @@ -345,706 +344,696 @@ GamDDD133*invgam13 + GamDDD233*invgam23 + GamDDD333*invgam33 vreal tr1dGam11 = -(ddADMgam1111*invgam11)/2. + ddADMgam1112*invgam12 - - 2*dADMgam112*GamDDD111*invgam11*invgam12 - - dADMgam211*GamDDD111*invgam11*invgam12 - - dADMgam122*GamDDD111*Power(invgam12,2) - - dADMgam212*GamDDD111*Power(invgam12,2) - - dADMgam112*GamDDD211*Power(invgam12,2) - - dADMgam211*GamDDD211*Power(invgam12,2) + ddADMgam1113*invgam13 - - 2*dADMgam113*GamDDD111*invgam11*invgam13 - - dADMgam311*GamDDD111*invgam11*invgam13 - - 2*dADMgam123*GamDDD111*invgam12*invgam13 - - dADMgam213*GamDDD111*invgam12*invgam13 - - dADMgam312*GamDDD111*invgam12*invgam13 - - dADMgam113*GamDDD211*invgam12*invgam13 - - dADMgam311*GamDDD211*invgam12*invgam13 - - dADMgam112*GamDDD311*invgam12*invgam13 - - dADMgam211*GamDDD311*invgam12*invgam13 - - dADMgam133*GamDDD111*Power(invgam13,2) - - dADMgam313*GamDDD111*Power(invgam13,2) - - dADMgam113*GamDDD311*Power(invgam13,2) - - dADMgam311*GamDDD311*Power(invgam13,2) - - dADMgam111*invgam11*(GamDDD111*invgam11 + GamDDD211*invgam12 + - GamDDD311*invgam13) + ddADMgam1212*invgam22 - - (ddADMgam2211*invgam22)/2. - dADMgam212*GamDDD111*invgam11*invgam22 - - dADMgam112*GamDDD211*invgam11*invgam22 - - dADMgam222*GamDDD111*invgam12*invgam22 - - dADMgam122*GamDDD211*invgam12*invgam22 - - 2*dADMgam212*GamDDD211*invgam12*invgam22 - - dADMgam223*GamDDD111*invgam13*invgam22 - - dADMgam123*GamDDD211*invgam13*invgam22 - - dADMgam312*GamDDD211*invgam13*invgam22 - - dADMgam212*GamDDD311*invgam13*invgam22 - - dADMgam222*GamDDD211*Power(invgam22,2) + ddADMgam1213*invgam23 + - ddADMgam1312*invgam23 - ddADMgam2311*invgam23 - - dADMgam213*GamDDD111*invgam11*invgam23 - - dADMgam312*GamDDD111*invgam11*invgam23 - - dADMgam113*GamDDD211*invgam11*invgam23 - - dADMgam112*GamDDD311*invgam11*invgam23 - - dADMgam223*GamDDD111*invgam12*invgam23 - - dADMgam322*GamDDD111*invgam12*invgam23 - - dADMgam123*GamDDD211*invgam12*invgam23 - - 2*dADMgam213*GamDDD211*invgam12*invgam23 - - dADMgam312*GamDDD211*invgam12*invgam23 - - dADMgam122*GamDDD311*invgam12*invgam23 - - dADMgam212*GamDDD311*invgam12*invgam23 - - dADMgam233*GamDDD111*invgam13*invgam23 - - dADMgam323*GamDDD111*invgam13*invgam23 - - dADMgam133*GamDDD211*invgam13*invgam23 - - dADMgam313*GamDDD211*invgam13*invgam23 - - dADMgam123*GamDDD311*invgam13*invgam23 - - dADMgam213*GamDDD311*invgam13*invgam23 - - 2*dADMgam312*GamDDD311*invgam13*invgam23 - - 2*dADMgam223*GamDDD211*invgam22*invgam23 - - dADMgam322*GamDDD211*invgam22*invgam23 - - dADMgam222*GamDDD311*invgam22*invgam23 - - dADMgam233*GamDDD211*Power(invgam23,2) - - dADMgam323*GamDDD211*Power(invgam23,2) - - dADMgam223*GamDDD311*Power(invgam23,2) - - dADMgam322*GamDDD311*Power(invgam23,2) + ddADMgam1313*invgam33 - - (ddADMgam3311*invgam33)/2. - dADMgam313*GamDDD111*invgam11*invgam33 - - dADMgam113*GamDDD311*invgam11*invgam33 - - dADMgam323*GamDDD111*invgam12*invgam33 - - dADMgam313*GamDDD211*invgam12*invgam33 - - dADMgam123*GamDDD311*invgam12*invgam33 - - dADMgam213*GamDDD311*invgam12*invgam33 - - dADMgam333*GamDDD111*invgam13*invgam33 - - dADMgam133*GamDDD311*invgam13*invgam33 - - 2*dADMgam313*GamDDD311*invgam13*invgam33 - - dADMgam323*GamDDD211*invgam22*invgam33 - - dADMgam223*GamDDD311*invgam22*invgam33 - - dADMgam333*GamDDD211*invgam23*invgam33 - - dADMgam233*GamDDD311*invgam23*invgam33 - - 2*dADMgam323*GamDDD311*invgam23*invgam33 - - dADMgam333*GamDDD311*Power(invgam33,2) +(ddgam1111*invgam11)/2. + ddgam1112*invgam12 - + 2*dgam112*GamDDD111*invgam11*invgam12 - + dgam211*GamDDD111*invgam11*invgam12 - + dgam122*GamDDD111*Power(invgam12,2) - + dgam212*GamDDD111*Power(invgam12,2) - + dgam112*GamDDD211*Power(invgam12,2) - + dgam211*GamDDD211*Power(invgam12,2) + ddgam1113*invgam13 - + 2*dgam113*GamDDD111*invgam11*invgam13 - + dgam311*GamDDD111*invgam11*invgam13 - + 2*dgam123*GamDDD111*invgam12*invgam13 - + dgam213*GamDDD111*invgam12*invgam13 - + dgam312*GamDDD111*invgam12*invgam13 - + dgam113*GamDDD211*invgam12*invgam13 - + dgam311*GamDDD211*invgam12*invgam13 - + dgam112*GamDDD311*invgam12*invgam13 - + dgam211*GamDDD311*invgam12*invgam13 - + dgam133*GamDDD111*Power(invgam13,2) - + dgam313*GamDDD111*Power(invgam13,2) - + dgam113*GamDDD311*Power(invgam13,2) - + dgam311*GamDDD311*Power(invgam13,2) - + dgam111*invgam11*(GamDDD111*invgam11 + GamDDD211*invgam12 + + GamDDD311*invgam13) + ddgam1212*invgam22 - (ddgam2211*invgam22)/2. - + dgam212*GamDDD111*invgam11*invgam22 - + dgam112*GamDDD211*invgam11*invgam22 - + dgam222*GamDDD111*invgam12*invgam22 - + dgam122*GamDDD211*invgam12*invgam22 - + 2*dgam212*GamDDD211*invgam12*invgam22 - + dgam223*GamDDD111*invgam13*invgam22 - + dgam123*GamDDD211*invgam13*invgam22 - + dgam312*GamDDD211*invgam13*invgam22 - + dgam212*GamDDD311*invgam13*invgam22 - + dgam222*GamDDD211*Power(invgam22,2) + ddgam1213*invgam23 + + ddgam1312*invgam23 - ddgam2311*invgam23 - + dgam213*GamDDD111*invgam11*invgam23 - + dgam312*GamDDD111*invgam11*invgam23 - + dgam113*GamDDD211*invgam11*invgam23 - + dgam112*GamDDD311*invgam11*invgam23 - + dgam223*GamDDD111*invgam12*invgam23 - + dgam322*GamDDD111*invgam12*invgam23 - + dgam123*GamDDD211*invgam12*invgam23 - + 2*dgam213*GamDDD211*invgam12*invgam23 - + dgam312*GamDDD211*invgam12*invgam23 - + dgam122*GamDDD311*invgam12*invgam23 - + dgam212*GamDDD311*invgam12*invgam23 - + dgam233*GamDDD111*invgam13*invgam23 - + dgam323*GamDDD111*invgam13*invgam23 - + dgam133*GamDDD211*invgam13*invgam23 - + dgam313*GamDDD211*invgam13*invgam23 - + dgam123*GamDDD311*invgam13*invgam23 - + dgam213*GamDDD311*invgam13*invgam23 - + 2*dgam312*GamDDD311*invgam13*invgam23 - + 2*dgam223*GamDDD211*invgam22*invgam23 - + dgam322*GamDDD211*invgam22*invgam23 - + dgam222*GamDDD311*invgam22*invgam23 - + dgam233*GamDDD211*Power(invgam23,2) - + dgam323*GamDDD211*Power(invgam23,2) - + dgam223*GamDDD311*Power(invgam23,2) - + dgam322*GamDDD311*Power(invgam23,2) + ddgam1313*invgam33 - + (ddgam3311*invgam33)/2. - dgam313*GamDDD111*invgam11*invgam33 - + dgam113*GamDDD311*invgam11*invgam33 - + dgam323*GamDDD111*invgam12*invgam33 - + dgam313*GamDDD211*invgam12*invgam33 - + dgam123*GamDDD311*invgam12*invgam33 - + dgam213*GamDDD311*invgam12*invgam33 - + dgam333*GamDDD111*invgam13*invgam33 - + dgam133*GamDDD311*invgam13*invgam33 - + 2*dgam313*GamDDD311*invgam13*invgam33 - + dgam323*GamDDD211*invgam22*invgam33 - + dgam223*GamDDD311*invgam22*invgam33 - + dgam333*GamDDD211*invgam23*invgam33 - + dgam233*GamDDD311*invgam23*invgam33 - + 2*dgam323*GamDDD311*invgam23*invgam33 - dgam333*GamDDD311*Power(invgam33,2) ; vreal tr1dGam12 = -(ddADMgam1211*invgam11 + ddADMgam1122*invgam12 + ddADMgam2211*invgam12 - - 4*dADMgam112*GamDDD112*invgam11*invgam12 - - 2*dADMgam211*GamDDD112*invgam11*invgam12 - - 2*dADMgam122*GamDDD112*Power(invgam12,2) - - 2*dADMgam212*GamDDD112*Power(invgam12,2) - - 2*dADMgam112*GamDDD212*Power(invgam12,2) - - 2*dADMgam211*GamDDD212*Power(invgam12,2) + ddADMgam1123*invgam13 + - ddADMgam1213*invgam13 - ddADMgam1312*invgam13 + ddADMgam2311*invgam13 - - 4*dADMgam113*GamDDD112*invgam11*invgam13 - - 2*dADMgam311*GamDDD112*invgam11*invgam13 - - 4*dADMgam123*GamDDD112*invgam12*invgam13 - - 2*dADMgam213*GamDDD112*invgam12*invgam13 - - 2*dADMgam312*GamDDD112*invgam12*invgam13 - - 2*dADMgam113*GamDDD212*invgam12*invgam13 - - 2*dADMgam311*GamDDD212*invgam12*invgam13 - - 2*dADMgam112*GamDDD312*invgam12*invgam13 - - 2*dADMgam211*GamDDD312*invgam12*invgam13 - - 2*dADMgam133*GamDDD112*Power(invgam13,2) - - 2*dADMgam313*GamDDD112*Power(invgam13,2) - - 2*dADMgam113*GamDDD312*Power(invgam13,2) - - 2*dADMgam311*GamDDD312*Power(invgam13,2) - - 2*dADMgam111*invgam11*(GamDDD112*invgam11 + GamDDD212*invgam12 + - GamDDD312*invgam13) + ddADMgam1222*invgam22 - - 2*dADMgam212*GamDDD112*invgam11*invgam22 - - 2*dADMgam112*GamDDD212*invgam11*invgam22 - - 2*dADMgam222*GamDDD112*invgam12*invgam22 - - 2*dADMgam122*GamDDD212*invgam12*invgam22 - - 4*dADMgam212*GamDDD212*invgam12*invgam22 - - 2*dADMgam223*GamDDD112*invgam13*invgam22 - - 2*dADMgam123*GamDDD212*invgam13*invgam22 - - 2*dADMgam312*GamDDD212*invgam13*invgam22 - - 2*dADMgam212*GamDDD312*invgam13*invgam22 - - 2*dADMgam222*GamDDD212*Power(invgam22,2) + ddADMgam1223*invgam23 + - ddADMgam1322*invgam23 + ddADMgam2213*invgam23 - ddADMgam2312*invgam23 - - 2*dADMgam213*GamDDD112*invgam11*invgam23 - - 2*dADMgam312*GamDDD112*invgam11*invgam23 - - 2*dADMgam113*GamDDD212*invgam11*invgam23 - - 2*dADMgam112*GamDDD312*invgam11*invgam23 - - 2*dADMgam223*GamDDD112*invgam12*invgam23 - - 2*dADMgam322*GamDDD112*invgam12*invgam23 - - 2*dADMgam123*GamDDD212*invgam12*invgam23 - - 4*dADMgam213*GamDDD212*invgam12*invgam23 - - 2*dADMgam312*GamDDD212*invgam12*invgam23 - - 2*dADMgam122*GamDDD312*invgam12*invgam23 - - 2*dADMgam212*GamDDD312*invgam12*invgam23 - - 2*dADMgam233*GamDDD112*invgam13*invgam23 - - 2*dADMgam323*GamDDD112*invgam13*invgam23 - - 2*dADMgam133*GamDDD212*invgam13*invgam23 - - 2*dADMgam313*GamDDD212*invgam13*invgam23 - - 2*dADMgam123*GamDDD312*invgam13*invgam23 - - 2*dADMgam213*GamDDD312*invgam13*invgam23 - - 4*dADMgam312*GamDDD312*invgam13*invgam23 - - 4*dADMgam223*GamDDD212*invgam22*invgam23 - - 2*dADMgam322*GamDDD212*invgam22*invgam23 - - 2*dADMgam222*GamDDD312*invgam22*invgam23 - - 2*dADMgam233*GamDDD212*Power(invgam23,2) - - 2*dADMgam323*GamDDD212*Power(invgam23,2) - - 2*dADMgam223*GamDDD312*Power(invgam23,2) - - 2*dADMgam322*GamDDD312*Power(invgam23,2) + ddADMgam1323*invgam33 + - ddADMgam2313*invgam33 - ddADMgam3312*invgam33 - - 2*dADMgam313*GamDDD112*invgam11*invgam33 - - 2*dADMgam113*GamDDD312*invgam11*invgam33 - - 2*dADMgam323*GamDDD112*invgam12*invgam33 - - 2*dADMgam313*GamDDD212*invgam12*invgam33 - - 2*dADMgam123*GamDDD312*invgam12*invgam33 - - 2*dADMgam213*GamDDD312*invgam12*invgam33 - - 2*dADMgam333*GamDDD112*invgam13*invgam33 - - 2*dADMgam133*GamDDD312*invgam13*invgam33 - - 4*dADMgam313*GamDDD312*invgam13*invgam33 - - 2*dADMgam323*GamDDD212*invgam22*invgam33 - - 2*dADMgam223*GamDDD312*invgam22*invgam33 - - 2*dADMgam333*GamDDD212*invgam23*invgam33 - - 2*dADMgam233*GamDDD312*invgam23*invgam33 - - 4*dADMgam323*GamDDD312*invgam23*invgam33 - - 2*dADMgam333*GamDDD312*Power(invgam33,2))/2. +(ddgam1211*invgam11 + ddgam1122*invgam12 + ddgam2211*invgam12 - + 4*dgam112*GamDDD112*invgam11*invgam12 - + 2*dgam211*GamDDD112*invgam11*invgam12 - + 2*dgam122*GamDDD112*Power(invgam12,2) - + 2*dgam212*GamDDD112*Power(invgam12,2) - + 2*dgam112*GamDDD212*Power(invgam12,2) - + 2*dgam211*GamDDD212*Power(invgam12,2) + ddgam1123*invgam13 + + ddgam1213*invgam13 - ddgam1312*invgam13 + ddgam2311*invgam13 - + 4*dgam113*GamDDD112*invgam11*invgam13 - + 2*dgam311*GamDDD112*invgam11*invgam13 - + 4*dgam123*GamDDD112*invgam12*invgam13 - + 2*dgam213*GamDDD112*invgam12*invgam13 - + 2*dgam312*GamDDD112*invgam12*invgam13 - + 2*dgam113*GamDDD212*invgam12*invgam13 - + 2*dgam311*GamDDD212*invgam12*invgam13 - + 2*dgam112*GamDDD312*invgam12*invgam13 - + 2*dgam211*GamDDD312*invgam12*invgam13 - + 2*dgam133*GamDDD112*Power(invgam13,2) - + 2*dgam313*GamDDD112*Power(invgam13,2) - + 2*dgam113*GamDDD312*Power(invgam13,2) - + 2*dgam311*GamDDD312*Power(invgam13,2) - + 2*dgam111*invgam11*(GamDDD112*invgam11 + GamDDD212*invgam12 + + GamDDD312*invgam13) + ddgam1222*invgam22 - + 2*dgam212*GamDDD112*invgam11*invgam22 - + 2*dgam112*GamDDD212*invgam11*invgam22 - + 2*dgam222*GamDDD112*invgam12*invgam22 - + 2*dgam122*GamDDD212*invgam12*invgam22 - + 4*dgam212*GamDDD212*invgam12*invgam22 - + 2*dgam223*GamDDD112*invgam13*invgam22 - + 2*dgam123*GamDDD212*invgam13*invgam22 - + 2*dgam312*GamDDD212*invgam13*invgam22 - + 2*dgam212*GamDDD312*invgam13*invgam22 - + 2*dgam222*GamDDD212*Power(invgam22,2) + ddgam1223*invgam23 + + ddgam1322*invgam23 + ddgam2213*invgam23 - ddgam2312*invgam23 - + 2*dgam213*GamDDD112*invgam11*invgam23 - + 2*dgam312*GamDDD112*invgam11*invgam23 - + 2*dgam113*GamDDD212*invgam11*invgam23 - + 2*dgam112*GamDDD312*invgam11*invgam23 - + 2*dgam223*GamDDD112*invgam12*invgam23 - + 2*dgam322*GamDDD112*invgam12*invgam23 - + 2*dgam123*GamDDD212*invgam12*invgam23 - + 4*dgam213*GamDDD212*invgam12*invgam23 - + 2*dgam312*GamDDD212*invgam12*invgam23 - + 2*dgam122*GamDDD312*invgam12*invgam23 - + 2*dgam212*GamDDD312*invgam12*invgam23 - + 2*dgam233*GamDDD112*invgam13*invgam23 - + 2*dgam323*GamDDD112*invgam13*invgam23 - + 2*dgam133*GamDDD212*invgam13*invgam23 - + 2*dgam313*GamDDD212*invgam13*invgam23 - + 2*dgam123*GamDDD312*invgam13*invgam23 - + 2*dgam213*GamDDD312*invgam13*invgam23 - + 4*dgam312*GamDDD312*invgam13*invgam23 - + 4*dgam223*GamDDD212*invgam22*invgam23 - + 2*dgam322*GamDDD212*invgam22*invgam23 - + 2*dgam222*GamDDD312*invgam22*invgam23 - + 2*dgam233*GamDDD212*Power(invgam23,2) - + 2*dgam323*GamDDD212*Power(invgam23,2) - + 2*dgam223*GamDDD312*Power(invgam23,2) - + 2*dgam322*GamDDD312*Power(invgam23,2) + ddgam1323*invgam33 + + ddgam2313*invgam33 - ddgam3312*invgam33 - + 2*dgam313*GamDDD112*invgam11*invgam33 - + 2*dgam113*GamDDD312*invgam11*invgam33 - + 2*dgam323*GamDDD112*invgam12*invgam33 - + 2*dgam313*GamDDD212*invgam12*invgam33 - + 2*dgam123*GamDDD312*invgam12*invgam33 - + 2*dgam213*GamDDD312*invgam12*invgam33 - + 2*dgam333*GamDDD112*invgam13*invgam33 - + 2*dgam133*GamDDD312*invgam13*invgam33 - + 4*dgam313*GamDDD312*invgam13*invgam33 - + 2*dgam323*GamDDD212*invgam22*invgam33 - + 2*dgam223*GamDDD312*invgam22*invgam33 - + 2*dgam333*GamDDD212*invgam23*invgam33 - + 2*dgam233*GamDDD312*invgam23*invgam33 - + 4*dgam323*GamDDD312*invgam23*invgam33 - + 2*dgam333*GamDDD312*Power(invgam33,2))/2. ; vreal tr1dGam13 = -(ddADMgam1311*invgam11 + ddADMgam1123*invgam12 - ddADMgam1213*invgam12 + - ddADMgam1312*invgam12 + ddADMgam2311*invgam12 - - 4*dADMgam112*GamDDD113*invgam11*invgam12 - - 2*dADMgam211*GamDDD113*invgam11*invgam12 - - 2*dADMgam122*GamDDD113*Power(invgam12,2) - - 2*dADMgam212*GamDDD113*Power(invgam12,2) - - 2*dADMgam112*GamDDD213*Power(invgam12,2) - - 2*dADMgam211*GamDDD213*Power(invgam12,2) + ddADMgam1133*invgam13 + - ddADMgam3311*invgam13 - 4*dADMgam113*GamDDD113*invgam11*invgam13 - - 2*dADMgam311*GamDDD113*invgam11*invgam13 - - 4*dADMgam123*GamDDD113*invgam12*invgam13 - - 2*dADMgam213*GamDDD113*invgam12*invgam13 - - 2*dADMgam312*GamDDD113*invgam12*invgam13 - - 2*dADMgam113*GamDDD213*invgam12*invgam13 - - 2*dADMgam311*GamDDD213*invgam12*invgam13 - - 2*dADMgam112*GamDDD313*invgam12*invgam13 - - 2*dADMgam211*GamDDD313*invgam12*invgam13 - - 2*dADMgam133*GamDDD113*Power(invgam13,2) - - 2*dADMgam313*GamDDD113*Power(invgam13,2) - - 2*dADMgam113*GamDDD313*Power(invgam13,2) - - 2*dADMgam311*GamDDD313*Power(invgam13,2) - - 2*dADMgam111*invgam11*(GamDDD113*invgam11 + GamDDD213*invgam12 + - GamDDD313*invgam13) + ddADMgam1223*invgam22 - - ddADMgam2213*invgam22 + ddADMgam2312*invgam22 - - 2*dADMgam212*GamDDD113*invgam11*invgam22 - - 2*dADMgam112*GamDDD213*invgam11*invgam22 - - 2*dADMgam222*GamDDD113*invgam12*invgam22 - - 2*dADMgam122*GamDDD213*invgam12*invgam22 - - 4*dADMgam212*GamDDD213*invgam12*invgam22 - - 2*dADMgam223*GamDDD113*invgam13*invgam22 - - 2*dADMgam123*GamDDD213*invgam13*invgam22 - - 2*dADMgam312*GamDDD213*invgam13*invgam22 - - 2*dADMgam212*GamDDD313*invgam13*invgam22 - - 2*dADMgam222*GamDDD213*Power(invgam22,2) + ddADMgam1233*invgam23 + - ddADMgam1323*invgam23 - ddADMgam2313*invgam23 + ddADMgam3312*invgam23 - - 2*dADMgam213*GamDDD113*invgam11*invgam23 - - 2*dADMgam312*GamDDD113*invgam11*invgam23 - - 2*dADMgam113*GamDDD213*invgam11*invgam23 - - 2*dADMgam112*GamDDD313*invgam11*invgam23 - - 2*dADMgam223*GamDDD113*invgam12*invgam23 - - 2*dADMgam322*GamDDD113*invgam12*invgam23 - - 2*dADMgam123*GamDDD213*invgam12*invgam23 - - 4*dADMgam213*GamDDD213*invgam12*invgam23 - - 2*dADMgam312*GamDDD213*invgam12*invgam23 - - 2*dADMgam122*GamDDD313*invgam12*invgam23 - - 2*dADMgam212*GamDDD313*invgam12*invgam23 - - 2*dADMgam233*GamDDD113*invgam13*invgam23 - - 2*dADMgam323*GamDDD113*invgam13*invgam23 - - 2*dADMgam133*GamDDD213*invgam13*invgam23 - - 2*dADMgam313*GamDDD213*invgam13*invgam23 - - 2*dADMgam123*GamDDD313*invgam13*invgam23 - - 2*dADMgam213*GamDDD313*invgam13*invgam23 - - 4*dADMgam312*GamDDD313*invgam13*invgam23 - - 4*dADMgam223*GamDDD213*invgam22*invgam23 - - 2*dADMgam322*GamDDD213*invgam22*invgam23 - - 2*dADMgam222*GamDDD313*invgam22*invgam23 - - 2*dADMgam233*GamDDD213*Power(invgam23,2) - - 2*dADMgam323*GamDDD213*Power(invgam23,2) - - 2*dADMgam223*GamDDD313*Power(invgam23,2) - - 2*dADMgam322*GamDDD313*Power(invgam23,2) + ddADMgam1333*invgam33 - - 2*dADMgam313*GamDDD113*invgam11*invgam33 - - 2*dADMgam113*GamDDD313*invgam11*invgam33 - - 2*dADMgam323*GamDDD113*invgam12*invgam33 - - 2*dADMgam313*GamDDD213*invgam12*invgam33 - - 2*dADMgam123*GamDDD313*invgam12*invgam33 - - 2*dADMgam213*GamDDD313*invgam12*invgam33 - - 2*dADMgam333*GamDDD113*invgam13*invgam33 - - 2*dADMgam133*GamDDD313*invgam13*invgam33 - - 4*dADMgam313*GamDDD313*invgam13*invgam33 - - 2*dADMgam323*GamDDD213*invgam22*invgam33 - - 2*dADMgam223*GamDDD313*invgam22*invgam33 - - 2*dADMgam333*GamDDD213*invgam23*invgam33 - - 2*dADMgam233*GamDDD313*invgam23*invgam33 - - 4*dADMgam323*GamDDD313*invgam23*invgam33 - - 2*dADMgam333*GamDDD313*Power(invgam33,2))/2. +(ddgam1311*invgam11 + ddgam1123*invgam12 - ddgam1213*invgam12 + + ddgam1312*invgam12 + ddgam2311*invgam12 - + 4*dgam112*GamDDD113*invgam11*invgam12 - + 2*dgam211*GamDDD113*invgam11*invgam12 - + 2*dgam122*GamDDD113*Power(invgam12,2) - + 2*dgam212*GamDDD113*Power(invgam12,2) - + 2*dgam112*GamDDD213*Power(invgam12,2) - + 2*dgam211*GamDDD213*Power(invgam12,2) + ddgam1133*invgam13 + + ddgam3311*invgam13 - 4*dgam113*GamDDD113*invgam11*invgam13 - + 2*dgam311*GamDDD113*invgam11*invgam13 - + 4*dgam123*GamDDD113*invgam12*invgam13 - + 2*dgam213*GamDDD113*invgam12*invgam13 - + 2*dgam312*GamDDD113*invgam12*invgam13 - + 2*dgam113*GamDDD213*invgam12*invgam13 - + 2*dgam311*GamDDD213*invgam12*invgam13 - + 2*dgam112*GamDDD313*invgam12*invgam13 - + 2*dgam211*GamDDD313*invgam12*invgam13 - + 2*dgam133*GamDDD113*Power(invgam13,2) - + 2*dgam313*GamDDD113*Power(invgam13,2) - + 2*dgam113*GamDDD313*Power(invgam13,2) - + 2*dgam311*GamDDD313*Power(invgam13,2) - + 2*dgam111*invgam11*(GamDDD113*invgam11 + GamDDD213*invgam12 + + GamDDD313*invgam13) + ddgam1223*invgam22 - ddgam2213*invgam22 + + ddgam2312*invgam22 - 2*dgam212*GamDDD113*invgam11*invgam22 - + 2*dgam112*GamDDD213*invgam11*invgam22 - + 2*dgam222*GamDDD113*invgam12*invgam22 - + 2*dgam122*GamDDD213*invgam12*invgam22 - + 4*dgam212*GamDDD213*invgam12*invgam22 - + 2*dgam223*GamDDD113*invgam13*invgam22 - + 2*dgam123*GamDDD213*invgam13*invgam22 - + 2*dgam312*GamDDD213*invgam13*invgam22 - + 2*dgam212*GamDDD313*invgam13*invgam22 - + 2*dgam222*GamDDD213*Power(invgam22,2) + ddgam1233*invgam23 + + ddgam1323*invgam23 - ddgam2313*invgam23 + ddgam3312*invgam23 - + 2*dgam213*GamDDD113*invgam11*invgam23 - + 2*dgam312*GamDDD113*invgam11*invgam23 - + 2*dgam113*GamDDD213*invgam11*invgam23 - + 2*dgam112*GamDDD313*invgam11*invgam23 - + 2*dgam223*GamDDD113*invgam12*invgam23 - + 2*dgam322*GamDDD113*invgam12*invgam23 - + 2*dgam123*GamDDD213*invgam12*invgam23 - + 4*dgam213*GamDDD213*invgam12*invgam23 - + 2*dgam312*GamDDD213*invgam12*invgam23 - + 2*dgam122*GamDDD313*invgam12*invgam23 - + 2*dgam212*GamDDD313*invgam12*invgam23 - + 2*dgam233*GamDDD113*invgam13*invgam23 - + 2*dgam323*GamDDD113*invgam13*invgam23 - + 2*dgam133*GamDDD213*invgam13*invgam23 - + 2*dgam313*GamDDD213*invgam13*invgam23 - + 2*dgam123*GamDDD313*invgam13*invgam23 - + 2*dgam213*GamDDD313*invgam13*invgam23 - + 4*dgam312*GamDDD313*invgam13*invgam23 - + 4*dgam223*GamDDD213*invgam22*invgam23 - + 2*dgam322*GamDDD213*invgam22*invgam23 - + 2*dgam222*GamDDD313*invgam22*invgam23 - + 2*dgam233*GamDDD213*Power(invgam23,2) - + 2*dgam323*GamDDD213*Power(invgam23,2) - + 2*dgam223*GamDDD313*Power(invgam23,2) - + 2*dgam322*GamDDD313*Power(invgam23,2) + ddgam1333*invgam33 - + 2*dgam313*GamDDD113*invgam11*invgam33 - + 2*dgam113*GamDDD313*invgam11*invgam33 - + 2*dgam323*GamDDD113*invgam12*invgam33 - + 2*dgam313*GamDDD213*invgam12*invgam33 - + 2*dgam123*GamDDD313*invgam12*invgam33 - + 2*dgam213*GamDDD313*invgam12*invgam33 - + 2*dgam333*GamDDD113*invgam13*invgam33 - + 2*dgam133*GamDDD313*invgam13*invgam33 - + 4*dgam313*GamDDD313*invgam13*invgam33 - + 2*dgam323*GamDDD213*invgam22*invgam33 - + 2*dgam223*GamDDD313*invgam22*invgam33 - + 2*dgam333*GamDDD213*invgam23*invgam33 - + 2*dgam233*GamDDD313*invgam23*invgam33 - + 4*dgam323*GamDDD313*invgam23*invgam33 - + 2*dgam333*GamDDD313*Power(invgam33,2))/2. ; vreal tr1dGam22 = --0.5*(ddADMgam1122*invgam11) + ddADMgam1212*invgam11 - - dADMgam111*GamDDD122*Power(invgam11,2) + ddADMgam2212*invgam12 - - 2*dADMgam112*GamDDD122*invgam11*invgam12 - - dADMgam211*GamDDD122*invgam11*invgam12 - - dADMgam111*GamDDD222*invgam11*invgam12 - - dADMgam122*GamDDD122*Power(invgam12,2) - - dADMgam212*GamDDD122*Power(invgam12,2) - - dADMgam112*GamDDD222*Power(invgam12,2) - - dADMgam211*GamDDD222*Power(invgam12,2) + ddADMgam1223*invgam13 - - ddADMgam1322*invgam13 + ddADMgam2312*invgam13 - - 2*dADMgam113*GamDDD122*invgam11*invgam13 - - dADMgam311*GamDDD122*invgam11*invgam13 - - dADMgam111*GamDDD322*invgam11*invgam13 - - 2*dADMgam123*GamDDD122*invgam12*invgam13 - - dADMgam213*GamDDD122*invgam12*invgam13 - - dADMgam312*GamDDD122*invgam12*invgam13 - - dADMgam113*GamDDD222*invgam12*invgam13 - - dADMgam311*GamDDD222*invgam12*invgam13 - - dADMgam112*GamDDD322*invgam12*invgam13 - - dADMgam211*GamDDD322*invgam12*invgam13 - - dADMgam133*GamDDD122*Power(invgam13,2) - - dADMgam313*GamDDD122*Power(invgam13,2) - - dADMgam113*GamDDD322*Power(invgam13,2) - - dADMgam311*GamDDD322*Power(invgam13,2) + (ddADMgam2222*invgam22)/2. - - dADMgam212*GamDDD122*invgam11*invgam22 - - dADMgam112*GamDDD222*invgam11*invgam22 - - dADMgam222*GamDDD122*invgam12*invgam22 - - dADMgam122*GamDDD222*invgam12*invgam22 - - 2*dADMgam212*GamDDD222*invgam12*invgam22 - - dADMgam223*GamDDD122*invgam13*invgam22 - - dADMgam123*GamDDD222*invgam13*invgam22 - - dADMgam312*GamDDD222*invgam13*invgam22 - - dADMgam212*GamDDD322*invgam13*invgam22 - - dADMgam222*GamDDD222*Power(invgam22,2) + ddADMgam2223*invgam23 - - dADMgam213*GamDDD122*invgam11*invgam23 - - dADMgam312*GamDDD122*invgam11*invgam23 - - dADMgam113*GamDDD222*invgam11*invgam23 - - dADMgam112*GamDDD322*invgam11*invgam23 - - dADMgam223*GamDDD122*invgam12*invgam23 - - dADMgam322*GamDDD122*invgam12*invgam23 - - dADMgam123*GamDDD222*invgam12*invgam23 - - 2*dADMgam213*GamDDD222*invgam12*invgam23 - - dADMgam312*GamDDD222*invgam12*invgam23 - - dADMgam122*GamDDD322*invgam12*invgam23 - - dADMgam212*GamDDD322*invgam12*invgam23 - - dADMgam233*GamDDD122*invgam13*invgam23 - - dADMgam323*GamDDD122*invgam13*invgam23 - - dADMgam133*GamDDD222*invgam13*invgam23 - - dADMgam313*GamDDD222*invgam13*invgam23 - - dADMgam123*GamDDD322*invgam13*invgam23 - - dADMgam213*GamDDD322*invgam13*invgam23 - - 2*dADMgam312*GamDDD322*invgam13*invgam23 - - 2*dADMgam223*GamDDD222*invgam22*invgam23 - - dADMgam322*GamDDD222*invgam22*invgam23 - - dADMgam222*GamDDD322*invgam22*invgam23 - - dADMgam233*GamDDD222*Power(invgam23,2) - - dADMgam323*GamDDD222*Power(invgam23,2) - - dADMgam223*GamDDD322*Power(invgam23,2) - - dADMgam322*GamDDD322*Power(invgam23,2) + ddADMgam2323*invgam33 - - (ddADMgam3322*invgam33)/2. - dADMgam313*GamDDD122*invgam11*invgam33 - - dADMgam113*GamDDD322*invgam11*invgam33 - - dADMgam323*GamDDD122*invgam12*invgam33 - - dADMgam313*GamDDD222*invgam12*invgam33 - - dADMgam123*GamDDD322*invgam12*invgam33 - - dADMgam213*GamDDD322*invgam12*invgam33 - - dADMgam333*GamDDD122*invgam13*invgam33 - - dADMgam133*GamDDD322*invgam13*invgam33 - - 2*dADMgam313*GamDDD322*invgam13*invgam33 - - dADMgam323*GamDDD222*invgam22*invgam33 - - dADMgam223*GamDDD322*invgam22*invgam33 - - dADMgam333*GamDDD222*invgam23*invgam33 - - dADMgam233*GamDDD322*invgam23*invgam33 - - 2*dADMgam323*GamDDD322*invgam23*invgam33 - - dADMgam333*GamDDD322*Power(invgam33,2) +-0.5*(ddgam1122*invgam11) + ddgam1212*invgam11 - + dgam111*GamDDD122*Power(invgam11,2) + ddgam2212*invgam12 - + 2*dgam112*GamDDD122*invgam11*invgam12 - + dgam211*GamDDD122*invgam11*invgam12 - + dgam111*GamDDD222*invgam11*invgam12 - + dgam122*GamDDD122*Power(invgam12,2) - + dgam212*GamDDD122*Power(invgam12,2) - + dgam112*GamDDD222*Power(invgam12,2) - + dgam211*GamDDD222*Power(invgam12,2) + ddgam1223*invgam13 - + ddgam1322*invgam13 + ddgam2312*invgam13 - + 2*dgam113*GamDDD122*invgam11*invgam13 - + dgam311*GamDDD122*invgam11*invgam13 - + dgam111*GamDDD322*invgam11*invgam13 - + 2*dgam123*GamDDD122*invgam12*invgam13 - + dgam213*GamDDD122*invgam12*invgam13 - + dgam312*GamDDD122*invgam12*invgam13 - + dgam113*GamDDD222*invgam12*invgam13 - + dgam311*GamDDD222*invgam12*invgam13 - + dgam112*GamDDD322*invgam12*invgam13 - + dgam211*GamDDD322*invgam12*invgam13 - + dgam133*GamDDD122*Power(invgam13,2) - + dgam313*GamDDD122*Power(invgam13,2) - + dgam113*GamDDD322*Power(invgam13,2) - + dgam311*GamDDD322*Power(invgam13,2) + (ddgam2222*invgam22)/2. - + dgam212*GamDDD122*invgam11*invgam22 - + dgam112*GamDDD222*invgam11*invgam22 - + dgam222*GamDDD122*invgam12*invgam22 - + dgam122*GamDDD222*invgam12*invgam22 - + 2*dgam212*GamDDD222*invgam12*invgam22 - + dgam223*GamDDD122*invgam13*invgam22 - + dgam123*GamDDD222*invgam13*invgam22 - + dgam312*GamDDD222*invgam13*invgam22 - + dgam212*GamDDD322*invgam13*invgam22 - + dgam222*GamDDD222*Power(invgam22,2) + ddgam2223*invgam23 - + dgam213*GamDDD122*invgam11*invgam23 - + dgam312*GamDDD122*invgam11*invgam23 - + dgam113*GamDDD222*invgam11*invgam23 - + dgam112*GamDDD322*invgam11*invgam23 - + dgam223*GamDDD122*invgam12*invgam23 - + dgam322*GamDDD122*invgam12*invgam23 - + dgam123*GamDDD222*invgam12*invgam23 - + 2*dgam213*GamDDD222*invgam12*invgam23 - + dgam312*GamDDD222*invgam12*invgam23 - + dgam122*GamDDD322*invgam12*invgam23 - + dgam212*GamDDD322*invgam12*invgam23 - + dgam233*GamDDD122*invgam13*invgam23 - + dgam323*GamDDD122*invgam13*invgam23 - + dgam133*GamDDD222*invgam13*invgam23 - + dgam313*GamDDD222*invgam13*invgam23 - + dgam123*GamDDD322*invgam13*invgam23 - + dgam213*GamDDD322*invgam13*invgam23 - + 2*dgam312*GamDDD322*invgam13*invgam23 - + 2*dgam223*GamDDD222*invgam22*invgam23 - + dgam322*GamDDD222*invgam22*invgam23 - + dgam222*GamDDD322*invgam22*invgam23 - + dgam233*GamDDD222*Power(invgam23,2) - + dgam323*GamDDD222*Power(invgam23,2) - + dgam223*GamDDD322*Power(invgam23,2) - + dgam322*GamDDD322*Power(invgam23,2) + ddgam2323*invgam33 - + (ddgam3322*invgam33)/2. - dgam313*GamDDD122*invgam11*invgam33 - + dgam113*GamDDD322*invgam11*invgam33 - + dgam323*GamDDD122*invgam12*invgam33 - + dgam313*GamDDD222*invgam12*invgam33 - + dgam123*GamDDD322*invgam12*invgam33 - + dgam213*GamDDD322*invgam12*invgam33 - + dgam333*GamDDD122*invgam13*invgam33 - + dgam133*GamDDD322*invgam13*invgam33 - + 2*dgam313*GamDDD322*invgam13*invgam33 - + dgam323*GamDDD222*invgam22*invgam33 - + dgam223*GamDDD322*invgam22*invgam33 - + dgam333*GamDDD222*invgam23*invgam33 - + dgam233*GamDDD322*invgam23*invgam33 - + 2*dgam323*GamDDD322*invgam23*invgam33 - dgam333*GamDDD322*Power(invgam33,2) ; vreal tr1dGam23 = -(-(ddADMgam1123*invgam11) + ddADMgam1213*invgam11 + ddADMgam1312*invgam11 - - 2*dADMgam111*GamDDD123*Power(invgam11,2) - ddADMgam1223*invgam12 + - ddADMgam1322*invgam12 + ddADMgam2213*invgam12 + ddADMgam2312*invgam12 - - 4*dADMgam112*GamDDD123*invgam11*invgam12 - - 2*dADMgam211*GamDDD123*invgam11*invgam12 - - 2*dADMgam111*GamDDD223*invgam11*invgam12 - - 2*dADMgam122*GamDDD123*Power(invgam12,2) - - 2*dADMgam212*GamDDD123*Power(invgam12,2) - - 2*dADMgam112*GamDDD223*Power(invgam12,2) - - 2*dADMgam211*GamDDD223*Power(invgam12,2) + ddADMgam1233*invgam13 - - ddADMgam1323*invgam13 + ddADMgam2313*invgam13 + ddADMgam3312*invgam13 - - 4*dADMgam113*GamDDD123*invgam11*invgam13 - - 2*dADMgam311*GamDDD123*invgam11*invgam13 - - 2*dADMgam111*GamDDD323*invgam11*invgam13 - - 4*dADMgam123*GamDDD123*invgam12*invgam13 - - 2*dADMgam213*GamDDD123*invgam12*invgam13 - - 2*dADMgam312*GamDDD123*invgam12*invgam13 - - 2*dADMgam113*GamDDD223*invgam12*invgam13 - - 2*dADMgam311*GamDDD223*invgam12*invgam13 - - 2*dADMgam112*GamDDD323*invgam12*invgam13 - - 2*dADMgam211*GamDDD323*invgam12*invgam13 - - 2*dADMgam133*GamDDD123*Power(invgam13,2) - - 2*dADMgam313*GamDDD123*Power(invgam13,2) - - 2*dADMgam113*GamDDD323*Power(invgam13,2) - - 2*dADMgam311*GamDDD323*Power(invgam13,2) + ddADMgam2322*invgam22 - - 2*dADMgam212*GamDDD123*invgam11*invgam22 - - 2*dADMgam112*GamDDD223*invgam11*invgam22 - - 2*dADMgam222*GamDDD123*invgam12*invgam22 - - 2*dADMgam122*GamDDD223*invgam12*invgam22 - - 4*dADMgam212*GamDDD223*invgam12*invgam22 - - 2*dADMgam223*GamDDD123*invgam13*invgam22 - - 2*dADMgam123*GamDDD223*invgam13*invgam22 - - 2*dADMgam312*GamDDD223*invgam13*invgam22 - - 2*dADMgam212*GamDDD323*invgam13*invgam22 - - 2*dADMgam222*GamDDD223*Power(invgam22,2) + ddADMgam2233*invgam23 + - ddADMgam3322*invgam23 - 2*dADMgam213*GamDDD123*invgam11*invgam23 - - 2*dADMgam312*GamDDD123*invgam11*invgam23 - - 2*dADMgam113*GamDDD223*invgam11*invgam23 - - 2*dADMgam112*GamDDD323*invgam11*invgam23 - - 2*dADMgam223*GamDDD123*invgam12*invgam23 - - 2*dADMgam322*GamDDD123*invgam12*invgam23 - - 2*dADMgam123*GamDDD223*invgam12*invgam23 - - 4*dADMgam213*GamDDD223*invgam12*invgam23 - - 2*dADMgam312*GamDDD223*invgam12*invgam23 - - 2*dADMgam122*GamDDD323*invgam12*invgam23 - - 2*dADMgam212*GamDDD323*invgam12*invgam23 - - 2*dADMgam233*GamDDD123*invgam13*invgam23 - - 2*dADMgam323*GamDDD123*invgam13*invgam23 - - 2*dADMgam133*GamDDD223*invgam13*invgam23 - - 2*dADMgam313*GamDDD223*invgam13*invgam23 - - 2*dADMgam123*GamDDD323*invgam13*invgam23 - - 2*dADMgam213*GamDDD323*invgam13*invgam23 - - 4*dADMgam312*GamDDD323*invgam13*invgam23 - - 4*dADMgam223*GamDDD223*invgam22*invgam23 - - 2*dADMgam322*GamDDD223*invgam22*invgam23 - - 2*dADMgam222*GamDDD323*invgam22*invgam23 - - 2*dADMgam233*GamDDD223*Power(invgam23,2) - - 2*dADMgam323*GamDDD223*Power(invgam23,2) - - 2*dADMgam223*GamDDD323*Power(invgam23,2) - - 2*dADMgam322*GamDDD323*Power(invgam23,2) + ddADMgam2333*invgam33 - - 2*dADMgam313*GamDDD123*invgam11*invgam33 - - 2*dADMgam113*GamDDD323*invgam11*invgam33 - - 2*dADMgam323*GamDDD123*invgam12*invgam33 - - 2*dADMgam313*GamDDD223*invgam12*invgam33 - - 2*dADMgam123*GamDDD323*invgam12*invgam33 - - 2*dADMgam213*GamDDD323*invgam12*invgam33 - - 2*dADMgam333*GamDDD123*invgam13*invgam33 - - 2*dADMgam133*GamDDD323*invgam13*invgam33 - - 4*dADMgam313*GamDDD323*invgam13*invgam33 - - 2*dADMgam323*GamDDD223*invgam22*invgam33 - - 2*dADMgam223*GamDDD323*invgam22*invgam33 - - 2*dADMgam333*GamDDD223*invgam23*invgam33 - - 2*dADMgam233*GamDDD323*invgam23*invgam33 - - 4*dADMgam323*GamDDD323*invgam23*invgam33 - - 2*dADMgam333*GamDDD323*Power(invgam33,2))/2. +(-(ddgam1123*invgam11) + ddgam1213*invgam11 + ddgam1312*invgam11 - + 2*dgam111*GamDDD123*Power(invgam11,2) - ddgam1223*invgam12 + + ddgam1322*invgam12 + ddgam2213*invgam12 + ddgam2312*invgam12 - + 4*dgam112*GamDDD123*invgam11*invgam12 - + 2*dgam211*GamDDD123*invgam11*invgam12 - + 2*dgam111*GamDDD223*invgam11*invgam12 - + 2*dgam122*GamDDD123*Power(invgam12,2) - + 2*dgam212*GamDDD123*Power(invgam12,2) - + 2*dgam112*GamDDD223*Power(invgam12,2) - + 2*dgam211*GamDDD223*Power(invgam12,2) + ddgam1233*invgam13 - + ddgam1323*invgam13 + ddgam2313*invgam13 + ddgam3312*invgam13 - + 4*dgam113*GamDDD123*invgam11*invgam13 - + 2*dgam311*GamDDD123*invgam11*invgam13 - + 2*dgam111*GamDDD323*invgam11*invgam13 - + 4*dgam123*GamDDD123*invgam12*invgam13 - + 2*dgam213*GamDDD123*invgam12*invgam13 - + 2*dgam312*GamDDD123*invgam12*invgam13 - + 2*dgam113*GamDDD223*invgam12*invgam13 - + 2*dgam311*GamDDD223*invgam12*invgam13 - + 2*dgam112*GamDDD323*invgam12*invgam13 - + 2*dgam211*GamDDD323*invgam12*invgam13 - + 2*dgam133*GamDDD123*Power(invgam13,2) - + 2*dgam313*GamDDD123*Power(invgam13,2) - + 2*dgam113*GamDDD323*Power(invgam13,2) - + 2*dgam311*GamDDD323*Power(invgam13,2) + ddgam2322*invgam22 - + 2*dgam212*GamDDD123*invgam11*invgam22 - + 2*dgam112*GamDDD223*invgam11*invgam22 - + 2*dgam222*GamDDD123*invgam12*invgam22 - + 2*dgam122*GamDDD223*invgam12*invgam22 - + 4*dgam212*GamDDD223*invgam12*invgam22 - + 2*dgam223*GamDDD123*invgam13*invgam22 - + 2*dgam123*GamDDD223*invgam13*invgam22 - + 2*dgam312*GamDDD223*invgam13*invgam22 - + 2*dgam212*GamDDD323*invgam13*invgam22 - + 2*dgam222*GamDDD223*Power(invgam22,2) + ddgam2233*invgam23 + + ddgam3322*invgam23 - 2*dgam213*GamDDD123*invgam11*invgam23 - + 2*dgam312*GamDDD123*invgam11*invgam23 - + 2*dgam113*GamDDD223*invgam11*invgam23 - + 2*dgam112*GamDDD323*invgam11*invgam23 - + 2*dgam223*GamDDD123*invgam12*invgam23 - + 2*dgam322*GamDDD123*invgam12*invgam23 - + 2*dgam123*GamDDD223*invgam12*invgam23 - + 4*dgam213*GamDDD223*invgam12*invgam23 - + 2*dgam312*GamDDD223*invgam12*invgam23 - + 2*dgam122*GamDDD323*invgam12*invgam23 - + 2*dgam212*GamDDD323*invgam12*invgam23 - + 2*dgam233*GamDDD123*invgam13*invgam23 - + 2*dgam323*GamDDD123*invgam13*invgam23 - + 2*dgam133*GamDDD223*invgam13*invgam23 - + 2*dgam313*GamDDD223*invgam13*invgam23 - + 2*dgam123*GamDDD323*invgam13*invgam23 - + 2*dgam213*GamDDD323*invgam13*invgam23 - + 4*dgam312*GamDDD323*invgam13*invgam23 - + 4*dgam223*GamDDD223*invgam22*invgam23 - + 2*dgam322*GamDDD223*invgam22*invgam23 - + 2*dgam222*GamDDD323*invgam22*invgam23 - + 2*dgam233*GamDDD223*Power(invgam23,2) - + 2*dgam323*GamDDD223*Power(invgam23,2) - + 2*dgam223*GamDDD323*Power(invgam23,2) - + 2*dgam322*GamDDD323*Power(invgam23,2) + ddgam2333*invgam33 - + 2*dgam313*GamDDD123*invgam11*invgam33 - + 2*dgam113*GamDDD323*invgam11*invgam33 - + 2*dgam323*GamDDD123*invgam12*invgam33 - + 2*dgam313*GamDDD223*invgam12*invgam33 - + 2*dgam123*GamDDD323*invgam12*invgam33 - + 2*dgam213*GamDDD323*invgam12*invgam33 - + 2*dgam333*GamDDD123*invgam13*invgam33 - + 2*dgam133*GamDDD323*invgam13*invgam33 - + 4*dgam313*GamDDD323*invgam13*invgam33 - + 2*dgam323*GamDDD223*invgam22*invgam33 - + 2*dgam223*GamDDD323*invgam22*invgam33 - + 2*dgam333*GamDDD223*invgam23*invgam33 - + 2*dgam233*GamDDD323*invgam23*invgam33 - + 4*dgam323*GamDDD323*invgam23*invgam33 - + 2*dgam333*GamDDD323*Power(invgam33,2))/2. ; vreal tr1dGam33 = --0.5*(ddADMgam1133*invgam11) + ddADMgam1313*invgam11 - - dADMgam111*GamDDD133*Power(invgam11,2) - ddADMgam1233*invgam12 + - ddADMgam1323*invgam12 + ddADMgam2313*invgam12 - - 2*dADMgam112*GamDDD133*invgam11*invgam12 - - dADMgam211*GamDDD133*invgam11*invgam12 - - dADMgam111*GamDDD233*invgam11*invgam12 - - dADMgam122*GamDDD133*Power(invgam12,2) - - dADMgam212*GamDDD133*Power(invgam12,2) - - dADMgam112*GamDDD233*Power(invgam12,2) - - dADMgam211*GamDDD233*Power(invgam12,2) + ddADMgam3313*invgam13 - - 2*dADMgam113*GamDDD133*invgam11*invgam13 - - dADMgam311*GamDDD133*invgam11*invgam13 - - dADMgam111*GamDDD333*invgam11*invgam13 - - 2*dADMgam123*GamDDD133*invgam12*invgam13 - - dADMgam213*GamDDD133*invgam12*invgam13 - - dADMgam312*GamDDD133*invgam12*invgam13 - - dADMgam113*GamDDD233*invgam12*invgam13 - - dADMgam311*GamDDD233*invgam12*invgam13 - - dADMgam112*GamDDD333*invgam12*invgam13 - - dADMgam211*GamDDD333*invgam12*invgam13 - - dADMgam133*GamDDD133*Power(invgam13,2) - - dADMgam313*GamDDD133*Power(invgam13,2) - - dADMgam113*GamDDD333*Power(invgam13,2) - - dADMgam311*GamDDD333*Power(invgam13,2) - (ddADMgam2233*invgam22)/2. + - ddADMgam2323*invgam22 - dADMgam212*GamDDD133*invgam11*invgam22 - - dADMgam112*GamDDD233*invgam11*invgam22 - - dADMgam222*GamDDD133*invgam12*invgam22 - - dADMgam122*GamDDD233*invgam12*invgam22 - - 2*dADMgam212*GamDDD233*invgam12*invgam22 - - dADMgam223*GamDDD133*invgam13*invgam22 - - dADMgam123*GamDDD233*invgam13*invgam22 - - dADMgam312*GamDDD233*invgam13*invgam22 - - dADMgam212*GamDDD333*invgam13*invgam22 - - dADMgam222*GamDDD233*Power(invgam22,2) + ddADMgam3323*invgam23 - - dADMgam213*GamDDD133*invgam11*invgam23 - - dADMgam312*GamDDD133*invgam11*invgam23 - - dADMgam113*GamDDD233*invgam11*invgam23 - - dADMgam112*GamDDD333*invgam11*invgam23 - - dADMgam223*GamDDD133*invgam12*invgam23 - - dADMgam322*GamDDD133*invgam12*invgam23 - - dADMgam123*GamDDD233*invgam12*invgam23 - - 2*dADMgam213*GamDDD233*invgam12*invgam23 - - dADMgam312*GamDDD233*invgam12*invgam23 - - dADMgam122*GamDDD333*invgam12*invgam23 - - dADMgam212*GamDDD333*invgam12*invgam23 - - dADMgam233*GamDDD133*invgam13*invgam23 - - dADMgam323*GamDDD133*invgam13*invgam23 - - dADMgam133*GamDDD233*invgam13*invgam23 - - dADMgam313*GamDDD233*invgam13*invgam23 - - dADMgam123*GamDDD333*invgam13*invgam23 - - dADMgam213*GamDDD333*invgam13*invgam23 - - 2*dADMgam312*GamDDD333*invgam13*invgam23 - - 2*dADMgam223*GamDDD233*invgam22*invgam23 - - dADMgam322*GamDDD233*invgam22*invgam23 - - dADMgam222*GamDDD333*invgam22*invgam23 - - dADMgam233*GamDDD233*Power(invgam23,2) - - dADMgam323*GamDDD233*Power(invgam23,2) - - dADMgam223*GamDDD333*Power(invgam23,2) - - dADMgam322*GamDDD333*Power(invgam23,2) + (ddADMgam3333*invgam33)/2. - - dADMgam313*GamDDD133*invgam11*invgam33 - - dADMgam113*GamDDD333*invgam11*invgam33 - - dADMgam323*GamDDD133*invgam12*invgam33 - - dADMgam313*GamDDD233*invgam12*invgam33 - - dADMgam123*GamDDD333*invgam12*invgam33 - - dADMgam213*GamDDD333*invgam12*invgam33 - - dADMgam333*GamDDD133*invgam13*invgam33 - - dADMgam133*GamDDD333*invgam13*invgam33 - - 2*dADMgam313*GamDDD333*invgam13*invgam33 - - dADMgam323*GamDDD233*invgam22*invgam33 - - dADMgam223*GamDDD333*invgam22*invgam33 - - dADMgam333*GamDDD233*invgam23*invgam33 - - dADMgam233*GamDDD333*invgam23*invgam33 - - 2*dADMgam323*GamDDD333*invgam23*invgam33 - - dADMgam333*GamDDD333*Power(invgam33,2) +-0.5*(ddgam1133*invgam11) + ddgam1313*invgam11 - + dgam111*GamDDD133*Power(invgam11,2) - ddgam1233*invgam12 + + ddgam1323*invgam12 + ddgam2313*invgam12 - + 2*dgam112*GamDDD133*invgam11*invgam12 - + dgam211*GamDDD133*invgam11*invgam12 - + dgam111*GamDDD233*invgam11*invgam12 - + dgam122*GamDDD133*Power(invgam12,2) - + dgam212*GamDDD133*Power(invgam12,2) - + dgam112*GamDDD233*Power(invgam12,2) - + dgam211*GamDDD233*Power(invgam12,2) + ddgam3313*invgam13 - + 2*dgam113*GamDDD133*invgam11*invgam13 - + dgam311*GamDDD133*invgam11*invgam13 - + dgam111*GamDDD333*invgam11*invgam13 - + 2*dgam123*GamDDD133*invgam12*invgam13 - + dgam213*GamDDD133*invgam12*invgam13 - + dgam312*GamDDD133*invgam12*invgam13 - + dgam113*GamDDD233*invgam12*invgam13 - + dgam311*GamDDD233*invgam12*invgam13 - + dgam112*GamDDD333*invgam12*invgam13 - + dgam211*GamDDD333*invgam12*invgam13 - + dgam133*GamDDD133*Power(invgam13,2) - + dgam313*GamDDD133*Power(invgam13,2) - + dgam113*GamDDD333*Power(invgam13,2) - + dgam311*GamDDD333*Power(invgam13,2) - (ddgam2233*invgam22)/2. + + ddgam2323*invgam22 - dgam212*GamDDD133*invgam11*invgam22 - + dgam112*GamDDD233*invgam11*invgam22 - + dgam222*GamDDD133*invgam12*invgam22 - + dgam122*GamDDD233*invgam12*invgam22 - + 2*dgam212*GamDDD233*invgam12*invgam22 - + dgam223*GamDDD133*invgam13*invgam22 - + dgam123*GamDDD233*invgam13*invgam22 - + dgam312*GamDDD233*invgam13*invgam22 - + dgam212*GamDDD333*invgam13*invgam22 - + dgam222*GamDDD233*Power(invgam22,2) + ddgam3323*invgam23 - + dgam213*GamDDD133*invgam11*invgam23 - + dgam312*GamDDD133*invgam11*invgam23 - + dgam113*GamDDD233*invgam11*invgam23 - + dgam112*GamDDD333*invgam11*invgam23 - + dgam223*GamDDD133*invgam12*invgam23 - + dgam322*GamDDD133*invgam12*invgam23 - + dgam123*GamDDD233*invgam12*invgam23 - + 2*dgam213*GamDDD233*invgam12*invgam23 - + dgam312*GamDDD233*invgam12*invgam23 - + dgam122*GamDDD333*invgam12*invgam23 - + dgam212*GamDDD333*invgam12*invgam23 - + dgam233*GamDDD133*invgam13*invgam23 - + dgam323*GamDDD133*invgam13*invgam23 - + dgam133*GamDDD233*invgam13*invgam23 - + dgam313*GamDDD233*invgam13*invgam23 - + dgam123*GamDDD333*invgam13*invgam23 - + dgam213*GamDDD333*invgam13*invgam23 - + 2*dgam312*GamDDD333*invgam13*invgam23 - + 2*dgam223*GamDDD233*invgam22*invgam23 - + dgam322*GamDDD233*invgam22*invgam23 - + dgam222*GamDDD333*invgam22*invgam23 - + dgam233*GamDDD233*Power(invgam23,2) - + dgam323*GamDDD233*Power(invgam23,2) - + dgam223*GamDDD333*Power(invgam23,2) - + dgam322*GamDDD333*Power(invgam23,2) + (ddgam3333*invgam33)/2. - + dgam313*GamDDD133*invgam11*invgam33 - + dgam113*GamDDD333*invgam11*invgam33 - + dgam323*GamDDD133*invgam12*invgam33 - + dgam313*GamDDD233*invgam12*invgam33 - + dgam123*GamDDD333*invgam12*invgam33 - + dgam213*GamDDD333*invgam12*invgam33 - + dgam333*GamDDD133*invgam13*invgam33 - + dgam133*GamDDD333*invgam13*invgam33 - + 2*dgam313*GamDDD333*invgam13*invgam33 - + dgam323*GamDDD233*invgam22*invgam33 - + dgam223*GamDDD333*invgam22*invgam33 - + dgam333*GamDDD233*invgam23*invgam33 - + dgam233*GamDDD333*invgam23*invgam33 - + 2*dgam323*GamDDD333*invgam23*invgam33 - dgam333*GamDDD333*Power(invgam33,2) ; vreal tr2dGam11 = -(ddADMgam1111*invgam11 - Power(dADMgam111,2)*Power(invgam11,2) + - 2*ddADMgam1112*invgam12 - 2*Power(dADMgam112,2)*Power(invgam12,2) + - 2*ddADMgam1113*invgam13 - 4*dADMgam112*dADMgam113*invgam12*invgam13 - - 2*Power(dADMgam113,2)*Power(invgam13,2) - - 2*dADMgam111*(2*dADMgam112*invgam11*invgam12 + - dADMgam122*Power(invgam12,2) + - invgam13*(2*dADMgam113*invgam11 + 2*dADMgam123*invgam12 + - dADMgam133*invgam13)) + ddADMgam1122*invgam22 - - 2*Power(dADMgam112,2)*invgam11*invgam22 - - 4*dADMgam112*dADMgam122*invgam12*invgam22 - - 4*dADMgam112*dADMgam123*invgam13*invgam22 - - Power(dADMgam122,2)*Power(invgam22,2) + 2*ddADMgam1123*invgam23 - - 4*dADMgam112*dADMgam113*invgam11*invgam23 - - 4*dADMgam113*dADMgam122*invgam12*invgam23 - - 4*dADMgam112*dADMgam123*invgam12*invgam23 - - 4*dADMgam113*dADMgam123*invgam13*invgam23 - - 4*dADMgam112*dADMgam133*invgam13*invgam23 - - 4*dADMgam122*dADMgam123*invgam22*invgam23 - - 2*Power(dADMgam123,2)*Power(invgam23,2) - - 2*dADMgam122*dADMgam133*Power(invgam23,2) + ddADMgam1133*invgam33 - - 2*Power(dADMgam113,2)*invgam11*invgam33 - - 4*dADMgam113*dADMgam123*invgam12*invgam33 - - 4*dADMgam113*dADMgam133*invgam13*invgam33 - - 2*Power(dADMgam123,2)*invgam22*invgam33 - - 4*dADMgam123*dADMgam133*invgam23*invgam33 - - Power(dADMgam133,2)*Power(invgam33,2))/2. +(ddgam1111*invgam11 - Power(dgam111,2)*Power(invgam11,2) + + 2*ddgam1112*invgam12 - 2*Power(dgam112,2)*Power(invgam12,2) + + 2*ddgam1113*invgam13 - 4*dgam112*dgam113*invgam12*invgam13 - + 2*Power(dgam113,2)*Power(invgam13,2) - + 2*dgam111*(2*dgam112*invgam11*invgam12 + dgam122*Power(invgam12,2) + + invgam13*(2*dgam113*invgam11 + 2*dgam123*invgam12 + + dgam133*invgam13)) + ddgam1122*invgam22 - + 2*Power(dgam112,2)*invgam11*invgam22 - + 4*dgam112*dgam122*invgam12*invgam22 - + 4*dgam112*dgam123*invgam13*invgam22 - + Power(dgam122,2)*Power(invgam22,2) + 2*ddgam1123*invgam23 - + 4*dgam112*dgam113*invgam11*invgam23 - + 4*dgam113*dgam122*invgam12*invgam23 - + 4*dgam112*dgam123*invgam12*invgam23 - + 4*dgam113*dgam123*invgam13*invgam23 - + 4*dgam112*dgam133*invgam13*invgam23 - + 4*dgam122*dgam123*invgam22*invgam23 - + 2*Power(dgam123,2)*Power(invgam23,2) - + 2*dgam122*dgam133*Power(invgam23,2) + ddgam1133*invgam33 - + 2*Power(dgam113,2)*invgam11*invgam33 - + 4*dgam113*dgam123*invgam12*invgam33 - + 4*dgam113*dgam133*invgam13*invgam33 - + 2*Power(dgam123,2)*invgam22*invgam33 - + 4*dgam123*dgam133*invgam23*invgam33 - Power(dgam133,2)*Power(invgam33,2)\ +)/2. ; vreal tr2dGam12 = -(ddADMgam1211*invgam11 + 2*ddADMgam1212*invgam12 - - 2*dADMgam112*dADMgam211*invgam11*invgam12 - - dADMgam122*dADMgam211*Power(invgam12,2) - - 2*dADMgam112*dADMgam212*Power(invgam12,2) + 2*ddADMgam1213*invgam13 - - 2*dADMgam113*dADMgam211*invgam11*invgam13 - - 2*dADMgam123*dADMgam211*invgam12*invgam13 - - 2*dADMgam113*dADMgam212*invgam12*invgam13 - - 2*dADMgam112*dADMgam213*invgam12*invgam13 - - dADMgam133*dADMgam211*Power(invgam13,2) - - 2*dADMgam113*dADMgam213*Power(invgam13,2) - - dADMgam111*(dADMgam211*Power(invgam11,2) + - 2*dADMgam212*invgam11*invgam12 + dADMgam222*Power(invgam12,2) + - 2*dADMgam213*invgam11*invgam13 + 2*dADMgam223*invgam12*invgam13 + - dADMgam233*Power(invgam13,2)) + ddADMgam1222*invgam22 - - 2*dADMgam112*dADMgam212*invgam11*invgam22 - - 2*dADMgam122*dADMgam212*invgam12*invgam22 - - 2*dADMgam112*dADMgam222*invgam12*invgam22 - - 2*dADMgam123*dADMgam212*invgam13*invgam22 - - 2*dADMgam112*dADMgam223*invgam13*invgam22 - - dADMgam122*dADMgam222*Power(invgam22,2) + 2*ddADMgam1223*invgam23 - - 2*dADMgam113*dADMgam212*invgam11*invgam23 - - 2*dADMgam112*dADMgam213*invgam11*invgam23 - - 2*dADMgam123*dADMgam212*invgam12*invgam23 - - 2*dADMgam122*dADMgam213*invgam12*invgam23 - - 2*dADMgam113*dADMgam222*invgam12*invgam23 - - 2*dADMgam112*dADMgam223*invgam12*invgam23 - - 2*dADMgam133*dADMgam212*invgam13*invgam23 - - 2*dADMgam123*dADMgam213*invgam13*invgam23 - - 2*dADMgam113*dADMgam223*invgam13*invgam23 - - 2*dADMgam112*dADMgam233*invgam13*invgam23 - - 2*dADMgam123*dADMgam222*invgam22*invgam23 - - 2*dADMgam122*dADMgam223*invgam22*invgam23 - - dADMgam133*dADMgam222*Power(invgam23,2) - - 2*dADMgam123*dADMgam223*Power(invgam23,2) - - dADMgam122*dADMgam233*Power(invgam23,2) + ddADMgam1233*invgam33 - - 2*dADMgam113*dADMgam213*invgam11*invgam33 - - 2*dADMgam123*dADMgam213*invgam12*invgam33 - - 2*dADMgam113*dADMgam223*invgam12*invgam33 - - 2*dADMgam133*dADMgam213*invgam13*invgam33 - - 2*dADMgam113*dADMgam233*invgam13*invgam33 - - 2*dADMgam123*dADMgam223*invgam22*invgam33 - - 2*dADMgam133*dADMgam223*invgam23*invgam33 - - 2*dADMgam123*dADMgam233*invgam23*invgam33 - - dADMgam133*dADMgam233*Power(invgam33,2))/2. +(ddgam1211*invgam11 + 2*ddgam1212*invgam12 - + 2*dgam112*dgam211*invgam11*invgam12 - + dgam122*dgam211*Power(invgam12,2) - + 2*dgam112*dgam212*Power(invgam12,2) + 2*ddgam1213*invgam13 - + 2*dgam113*dgam211*invgam11*invgam13 - + 2*dgam123*dgam211*invgam12*invgam13 - + 2*dgam113*dgam212*invgam12*invgam13 - + 2*dgam112*dgam213*invgam12*invgam13 - + dgam133*dgam211*Power(invgam13,2) - + 2*dgam113*dgam213*Power(invgam13,2) - + dgam111*(dgam211*Power(invgam11,2) + 2*dgam212*invgam11*invgam12 + + dgam222*Power(invgam12,2) + 2*dgam213*invgam11*invgam13 + + 2*dgam223*invgam12*invgam13 + dgam233*Power(invgam13,2)) + + ddgam1222*invgam22 - 2*dgam112*dgam212*invgam11*invgam22 - + 2*dgam122*dgam212*invgam12*invgam22 - + 2*dgam112*dgam222*invgam12*invgam22 - + 2*dgam123*dgam212*invgam13*invgam22 - + 2*dgam112*dgam223*invgam13*invgam22 - + dgam122*dgam222*Power(invgam22,2) + 2*ddgam1223*invgam23 - + 2*dgam113*dgam212*invgam11*invgam23 - + 2*dgam112*dgam213*invgam11*invgam23 - + 2*dgam123*dgam212*invgam12*invgam23 - + 2*dgam122*dgam213*invgam12*invgam23 - + 2*dgam113*dgam222*invgam12*invgam23 - + 2*dgam112*dgam223*invgam12*invgam23 - + 2*dgam133*dgam212*invgam13*invgam23 - + 2*dgam123*dgam213*invgam13*invgam23 - + 2*dgam113*dgam223*invgam13*invgam23 - + 2*dgam112*dgam233*invgam13*invgam23 - + 2*dgam123*dgam222*invgam22*invgam23 - + 2*dgam122*dgam223*invgam22*invgam23 - + dgam133*dgam222*Power(invgam23,2) - + 2*dgam123*dgam223*Power(invgam23,2) - + dgam122*dgam233*Power(invgam23,2) + ddgam1233*invgam33 - + 2*dgam113*dgam213*invgam11*invgam33 - + 2*dgam123*dgam213*invgam12*invgam33 - + 2*dgam113*dgam223*invgam12*invgam33 - + 2*dgam133*dgam213*invgam13*invgam33 - + 2*dgam113*dgam233*invgam13*invgam33 - + 2*dgam123*dgam223*invgam22*invgam33 - + 2*dgam133*dgam223*invgam23*invgam33 - + 2*dgam123*dgam233*invgam23*invgam33 - dgam133*dgam233*Power(invgam33,2))/ + 2. ; vreal tr2dGam13 = -(ddADMgam1311*invgam11 + 2*ddADMgam1312*invgam12 - - 2*dADMgam112*dADMgam311*invgam11*invgam12 - - dADMgam122*dADMgam311*Power(invgam12,2) - - 2*dADMgam112*dADMgam312*Power(invgam12,2) + 2*ddADMgam1313*invgam13 - - 2*dADMgam113*dADMgam311*invgam11*invgam13 - - 2*dADMgam123*dADMgam311*invgam12*invgam13 - - 2*dADMgam113*dADMgam312*invgam12*invgam13 - - 2*dADMgam112*dADMgam313*invgam12*invgam13 - - dADMgam133*dADMgam311*Power(invgam13,2) - - 2*dADMgam113*dADMgam313*Power(invgam13,2) - - dADMgam111*(dADMgam311*Power(invgam11,2) + - 2*dADMgam312*invgam11*invgam12 + dADMgam322*Power(invgam12,2) + - 2*dADMgam313*invgam11*invgam13 + 2*dADMgam323*invgam12*invgam13 + - dADMgam333*Power(invgam13,2)) + ddADMgam1322*invgam22 - - 2*dADMgam112*dADMgam312*invgam11*invgam22 - - 2*dADMgam122*dADMgam312*invgam12*invgam22 - - 2*dADMgam112*dADMgam322*invgam12*invgam22 - - 2*dADMgam123*dADMgam312*invgam13*invgam22 - - 2*dADMgam112*dADMgam323*invgam13*invgam22 - - dADMgam122*dADMgam322*Power(invgam22,2) + 2*ddADMgam1323*invgam23 - - 2*dADMgam113*dADMgam312*invgam11*invgam23 - - 2*dADMgam112*dADMgam313*invgam11*invgam23 - - 2*dADMgam123*dADMgam312*invgam12*invgam23 - - 2*dADMgam122*dADMgam313*invgam12*invgam23 - - 2*dADMgam113*dADMgam322*invgam12*invgam23 - - 2*dADMgam112*dADMgam323*invgam12*invgam23 - - 2*dADMgam133*dADMgam312*invgam13*invgam23 - - 2*dADMgam123*dADMgam313*invgam13*invgam23 - - 2*dADMgam113*dADMgam323*invgam13*invgam23 - - 2*dADMgam112*dADMgam333*invgam13*invgam23 - - 2*dADMgam123*dADMgam322*invgam22*invgam23 - - 2*dADMgam122*dADMgam323*invgam22*invgam23 - - dADMgam133*dADMgam322*Power(invgam23,2) - - 2*dADMgam123*dADMgam323*Power(invgam23,2) - - dADMgam122*dADMgam333*Power(invgam23,2) + ddADMgam1333*invgam33 - - 2*dADMgam113*dADMgam313*invgam11*invgam33 - - 2*dADMgam123*dADMgam313*invgam12*invgam33 - - 2*dADMgam113*dADMgam323*invgam12*invgam33 - - 2*dADMgam133*dADMgam313*invgam13*invgam33 - - 2*dADMgam113*dADMgam333*invgam13*invgam33 - - 2*dADMgam123*dADMgam323*invgam22*invgam33 - - 2*dADMgam133*dADMgam323*invgam23*invgam33 - - 2*dADMgam123*dADMgam333*invgam23*invgam33 - - dADMgam133*dADMgam333*Power(invgam33,2))/2. +(ddgam1311*invgam11 + 2*ddgam1312*invgam12 - + 2*dgam112*dgam311*invgam11*invgam12 - + dgam122*dgam311*Power(invgam12,2) - + 2*dgam112*dgam312*Power(invgam12,2) + 2*ddgam1313*invgam13 - + 2*dgam113*dgam311*invgam11*invgam13 - + 2*dgam123*dgam311*invgam12*invgam13 - + 2*dgam113*dgam312*invgam12*invgam13 - + 2*dgam112*dgam313*invgam12*invgam13 - + dgam133*dgam311*Power(invgam13,2) - + 2*dgam113*dgam313*Power(invgam13,2) - + dgam111*(dgam311*Power(invgam11,2) + 2*dgam312*invgam11*invgam12 + + dgam322*Power(invgam12,2) + 2*dgam313*invgam11*invgam13 + + 2*dgam323*invgam12*invgam13 + dgam333*Power(invgam13,2)) + + ddgam1322*invgam22 - 2*dgam112*dgam312*invgam11*invgam22 - + 2*dgam122*dgam312*invgam12*invgam22 - + 2*dgam112*dgam322*invgam12*invgam22 - + 2*dgam123*dgam312*invgam13*invgam22 - + 2*dgam112*dgam323*invgam13*invgam22 - + dgam122*dgam322*Power(invgam22,2) + 2*ddgam1323*invgam23 - + 2*dgam113*dgam312*invgam11*invgam23 - + 2*dgam112*dgam313*invgam11*invgam23 - + 2*dgam123*dgam312*invgam12*invgam23 - + 2*dgam122*dgam313*invgam12*invgam23 - + 2*dgam113*dgam322*invgam12*invgam23 - + 2*dgam112*dgam323*invgam12*invgam23 - + 2*dgam133*dgam312*invgam13*invgam23 - + 2*dgam123*dgam313*invgam13*invgam23 - + 2*dgam113*dgam323*invgam13*invgam23 - + 2*dgam112*dgam333*invgam13*invgam23 - + 2*dgam123*dgam322*invgam22*invgam23 - + 2*dgam122*dgam323*invgam22*invgam23 - + dgam133*dgam322*Power(invgam23,2) - + 2*dgam123*dgam323*Power(invgam23,2) - + dgam122*dgam333*Power(invgam23,2) + ddgam1333*invgam33 - + 2*dgam113*dgam313*invgam11*invgam33 - + 2*dgam123*dgam313*invgam12*invgam33 - + 2*dgam113*dgam323*invgam12*invgam33 - + 2*dgam133*dgam313*invgam13*invgam33 - + 2*dgam113*dgam333*invgam13*invgam33 - + 2*dgam123*dgam323*invgam22*invgam33 - + 2*dgam133*dgam323*invgam23*invgam33 - + 2*dgam123*dgam333*invgam23*invgam33 - dgam133*dgam333*Power(invgam33,2))/ + 2. ; vreal tr2dGam22 = -(ddADMgam2211*invgam11 - Power(dADMgam211,2)*Power(invgam11,2) + - 2*ddADMgam2212*invgam12 - 2*Power(dADMgam212,2)*Power(invgam12,2) + - 2*ddADMgam2213*invgam13 - 4*dADMgam212*dADMgam213*invgam12*invgam13 - - 2*Power(dADMgam213,2)*Power(invgam13,2) - - 2*dADMgam211*(2*dADMgam212*invgam11*invgam12 + - dADMgam222*Power(invgam12,2) + - invgam13*(2*dADMgam213*invgam11 + 2*dADMgam223*invgam12 + - dADMgam233*invgam13)) + ddADMgam2222*invgam22 - - 2*Power(dADMgam212,2)*invgam11*invgam22 - - 4*dADMgam212*dADMgam222*invgam12*invgam22 - - 4*dADMgam212*dADMgam223*invgam13*invgam22 - - Power(dADMgam222,2)*Power(invgam22,2) + 2*ddADMgam2223*invgam23 - - 4*dADMgam212*dADMgam213*invgam11*invgam23 - - 4*dADMgam213*dADMgam222*invgam12*invgam23 - - 4*dADMgam212*dADMgam223*invgam12*invgam23 - - 4*dADMgam213*dADMgam223*invgam13*invgam23 - - 4*dADMgam212*dADMgam233*invgam13*invgam23 - - 4*dADMgam222*dADMgam223*invgam22*invgam23 - - 2*Power(dADMgam223,2)*Power(invgam23,2) - - 2*dADMgam222*dADMgam233*Power(invgam23,2) + ddADMgam2233*invgam33 - - 2*Power(dADMgam213,2)*invgam11*invgam33 - - 4*dADMgam213*dADMgam223*invgam12*invgam33 - - 4*dADMgam213*dADMgam233*invgam13*invgam33 - - 2*Power(dADMgam223,2)*invgam22*invgam33 - - 4*dADMgam223*dADMgam233*invgam23*invgam33 - - Power(dADMgam233,2)*Power(invgam33,2))/2. +(ddgam2211*invgam11 - Power(dgam211,2)*Power(invgam11,2) + + 2*ddgam2212*invgam12 - 2*Power(dgam212,2)*Power(invgam12,2) + + 2*ddgam2213*invgam13 - 4*dgam212*dgam213*invgam12*invgam13 - + 2*Power(dgam213,2)*Power(invgam13,2) - + 2*dgam211*(2*dgam212*invgam11*invgam12 + dgam222*Power(invgam12,2) + + invgam13*(2*dgam213*invgam11 + 2*dgam223*invgam12 + + dgam233*invgam13)) + ddgam2222*invgam22 - + 2*Power(dgam212,2)*invgam11*invgam22 - + 4*dgam212*dgam222*invgam12*invgam22 - + 4*dgam212*dgam223*invgam13*invgam22 - + Power(dgam222,2)*Power(invgam22,2) + 2*ddgam2223*invgam23 - + 4*dgam212*dgam213*invgam11*invgam23 - + 4*dgam213*dgam222*invgam12*invgam23 - + 4*dgam212*dgam223*invgam12*invgam23 - + 4*dgam213*dgam223*invgam13*invgam23 - + 4*dgam212*dgam233*invgam13*invgam23 - + 4*dgam222*dgam223*invgam22*invgam23 - + 2*Power(dgam223,2)*Power(invgam23,2) - + 2*dgam222*dgam233*Power(invgam23,2) + ddgam2233*invgam33 - + 2*Power(dgam213,2)*invgam11*invgam33 - + 4*dgam213*dgam223*invgam12*invgam33 - + 4*dgam213*dgam233*invgam13*invgam33 - + 2*Power(dgam223,2)*invgam22*invgam33 - + 4*dgam223*dgam233*invgam23*invgam33 - Power(dgam233,2)*Power(invgam33,2)\ +)/2. ; vreal tr2dGam23 = -(ddADMgam2311*invgam11 + 2*ddADMgam2312*invgam12 - - 2*dADMgam212*dADMgam311*invgam11*invgam12 - - dADMgam222*dADMgam311*Power(invgam12,2) - - 2*dADMgam212*dADMgam312*Power(invgam12,2) + 2*ddADMgam2313*invgam13 - - 2*dADMgam213*dADMgam311*invgam11*invgam13 - - 2*dADMgam223*dADMgam311*invgam12*invgam13 - - 2*dADMgam213*dADMgam312*invgam12*invgam13 - - 2*dADMgam212*dADMgam313*invgam12*invgam13 - - dADMgam233*dADMgam311*Power(invgam13,2) - - 2*dADMgam213*dADMgam313*Power(invgam13,2) - - dADMgam211*(dADMgam311*Power(invgam11,2) + - 2*dADMgam312*invgam11*invgam12 + dADMgam322*Power(invgam12,2) + - 2*dADMgam313*invgam11*invgam13 + 2*dADMgam323*invgam12*invgam13 + - dADMgam333*Power(invgam13,2)) + ddADMgam2322*invgam22 - - 2*dADMgam212*dADMgam312*invgam11*invgam22 - - 2*dADMgam222*dADMgam312*invgam12*invgam22 - - 2*dADMgam212*dADMgam322*invgam12*invgam22 - - 2*dADMgam223*dADMgam312*invgam13*invgam22 - - 2*dADMgam212*dADMgam323*invgam13*invgam22 - - dADMgam222*dADMgam322*Power(invgam22,2) + 2*ddADMgam2323*invgam23 - - 2*dADMgam213*dADMgam312*invgam11*invgam23 - - 2*dADMgam212*dADMgam313*invgam11*invgam23 - - 2*dADMgam223*dADMgam312*invgam12*invgam23 - - 2*dADMgam222*dADMgam313*invgam12*invgam23 - - 2*dADMgam213*dADMgam322*invgam12*invgam23 - - 2*dADMgam212*dADMgam323*invgam12*invgam23 - - 2*dADMgam233*dADMgam312*invgam13*invgam23 - - 2*dADMgam223*dADMgam313*invgam13*invgam23 - - 2*dADMgam213*dADMgam323*invgam13*invgam23 - - 2*dADMgam212*dADMgam333*invgam13*invgam23 - - 2*dADMgam223*dADMgam322*invgam22*invgam23 - - 2*dADMgam222*dADMgam323*invgam22*invgam23 - - dADMgam233*dADMgam322*Power(invgam23,2) - - 2*dADMgam223*dADMgam323*Power(invgam23,2) - - dADMgam222*dADMgam333*Power(invgam23,2) + ddADMgam2333*invgam33 - - 2*dADMgam213*dADMgam313*invgam11*invgam33 - - 2*dADMgam223*dADMgam313*invgam12*invgam33 - - 2*dADMgam213*dADMgam323*invgam12*invgam33 - - 2*dADMgam233*dADMgam313*invgam13*invgam33 - - 2*dADMgam213*dADMgam333*invgam13*invgam33 - - 2*dADMgam223*dADMgam323*invgam22*invgam33 - - 2*dADMgam233*dADMgam323*invgam23*invgam33 - - 2*dADMgam223*dADMgam333*invgam23*invgam33 - - dADMgam233*dADMgam333*Power(invgam33,2))/2. +(ddgam2311*invgam11 + 2*ddgam2312*invgam12 - + 2*dgam212*dgam311*invgam11*invgam12 - + dgam222*dgam311*Power(invgam12,2) - + 2*dgam212*dgam312*Power(invgam12,2) + 2*ddgam2313*invgam13 - + 2*dgam213*dgam311*invgam11*invgam13 - + 2*dgam223*dgam311*invgam12*invgam13 - + 2*dgam213*dgam312*invgam12*invgam13 - + 2*dgam212*dgam313*invgam12*invgam13 - + dgam233*dgam311*Power(invgam13,2) - + 2*dgam213*dgam313*Power(invgam13,2) - + dgam211*(dgam311*Power(invgam11,2) + 2*dgam312*invgam11*invgam12 + + dgam322*Power(invgam12,2) + 2*dgam313*invgam11*invgam13 + + 2*dgam323*invgam12*invgam13 + dgam333*Power(invgam13,2)) + + ddgam2322*invgam22 - 2*dgam212*dgam312*invgam11*invgam22 - + 2*dgam222*dgam312*invgam12*invgam22 - + 2*dgam212*dgam322*invgam12*invgam22 - + 2*dgam223*dgam312*invgam13*invgam22 - + 2*dgam212*dgam323*invgam13*invgam22 - + dgam222*dgam322*Power(invgam22,2) + 2*ddgam2323*invgam23 - + 2*dgam213*dgam312*invgam11*invgam23 - + 2*dgam212*dgam313*invgam11*invgam23 - + 2*dgam223*dgam312*invgam12*invgam23 - + 2*dgam222*dgam313*invgam12*invgam23 - + 2*dgam213*dgam322*invgam12*invgam23 - + 2*dgam212*dgam323*invgam12*invgam23 - + 2*dgam233*dgam312*invgam13*invgam23 - + 2*dgam223*dgam313*invgam13*invgam23 - + 2*dgam213*dgam323*invgam13*invgam23 - + 2*dgam212*dgam333*invgam13*invgam23 - + 2*dgam223*dgam322*invgam22*invgam23 - + 2*dgam222*dgam323*invgam22*invgam23 - + dgam233*dgam322*Power(invgam23,2) - + 2*dgam223*dgam323*Power(invgam23,2) - + dgam222*dgam333*Power(invgam23,2) + ddgam2333*invgam33 - + 2*dgam213*dgam313*invgam11*invgam33 - + 2*dgam223*dgam313*invgam12*invgam33 - + 2*dgam213*dgam323*invgam12*invgam33 - + 2*dgam233*dgam313*invgam13*invgam33 - + 2*dgam213*dgam333*invgam13*invgam33 - + 2*dgam223*dgam323*invgam22*invgam33 - + 2*dgam233*dgam323*invgam23*invgam33 - + 2*dgam223*dgam333*invgam23*invgam33 - dgam233*dgam333*Power(invgam33,2))/ + 2. ; vreal tr2dGam33 = -(ddADMgam3311*invgam11 - Power(dADMgam311,2)*Power(invgam11,2) + - 2*ddADMgam3312*invgam12 - 2*Power(dADMgam312,2)*Power(invgam12,2) + - 2*ddADMgam3313*invgam13 - 4*dADMgam312*dADMgam313*invgam12*invgam13 - - 2*Power(dADMgam313,2)*Power(invgam13,2) - - 2*dADMgam311*(2*dADMgam312*invgam11*invgam12 + - dADMgam322*Power(invgam12,2) + - invgam13*(2*dADMgam313*invgam11 + 2*dADMgam323*invgam12 + - dADMgam333*invgam13)) + ddADMgam3322*invgam22 - - 2*Power(dADMgam312,2)*invgam11*invgam22 - - 4*dADMgam312*dADMgam322*invgam12*invgam22 - - 4*dADMgam312*dADMgam323*invgam13*invgam22 - - Power(dADMgam322,2)*Power(invgam22,2) + 2*ddADMgam3323*invgam23 - - 4*dADMgam312*dADMgam313*invgam11*invgam23 - - 4*dADMgam313*dADMgam322*invgam12*invgam23 - - 4*dADMgam312*dADMgam323*invgam12*invgam23 - - 4*dADMgam313*dADMgam323*invgam13*invgam23 - - 4*dADMgam312*dADMgam333*invgam13*invgam23 - - 4*dADMgam322*dADMgam323*invgam22*invgam23 - - 2*Power(dADMgam323,2)*Power(invgam23,2) - - 2*dADMgam322*dADMgam333*Power(invgam23,2) + ddADMgam3333*invgam33 - - 2*Power(dADMgam313,2)*invgam11*invgam33 - - 4*dADMgam313*dADMgam323*invgam12*invgam33 - - 4*dADMgam313*dADMgam333*invgam13*invgam33 - - 2*Power(dADMgam323,2)*invgam22*invgam33 - - 4*dADMgam323*dADMgam333*invgam23*invgam33 - - Power(dADMgam333,2)*Power(invgam33,2))/2. +(ddgam3311*invgam11 - Power(dgam311,2)*Power(invgam11,2) + + 2*ddgam3312*invgam12 - 2*Power(dgam312,2)*Power(invgam12,2) + + 2*ddgam3313*invgam13 - 4*dgam312*dgam313*invgam12*invgam13 - + 2*Power(dgam313,2)*Power(invgam13,2) - + 2*dgam311*(2*dgam312*invgam11*invgam12 + dgam322*Power(invgam12,2) + + invgam13*(2*dgam313*invgam11 + 2*dgam323*invgam12 + + dgam333*invgam13)) + ddgam3322*invgam22 - + 2*Power(dgam312,2)*invgam11*invgam22 - + 4*dgam312*dgam322*invgam12*invgam22 - + 4*dgam312*dgam323*invgam13*invgam22 - + Power(dgam322,2)*Power(invgam22,2) + 2*ddgam3323*invgam23 - + 4*dgam312*dgam313*invgam11*invgam23 - + 4*dgam313*dgam322*invgam12*invgam23 - + 4*dgam312*dgam323*invgam12*invgam23 - + 4*dgam313*dgam323*invgam13*invgam23 - + 4*dgam312*dgam333*invgam13*invgam23 - + 4*dgam322*dgam323*invgam22*invgam23 - + 2*Power(dgam323,2)*Power(invgam23,2) - + 2*dgam322*dgam333*Power(invgam23,2) + ddgam3333*invgam33 - + 2*Power(dgam313,2)*invgam11*invgam33 - + 4*dgam313*dgam323*invgam12*invgam33 - + 4*dgam313*dgam333*invgam13*invgam33 - + 2*Power(dgam323,2)*invgam22*invgam33 - + 4*dgam323*dgam333*invgam23*invgam33 - Power(dgam333,2)*Power(invgam33,2)\ +)/2. ; vreal R11 @@ -1089,197 +1078,195 @@ vreal R33 Gam233*Gam323 + Gam113*Gam333 + Gam223*Gam333 + tr1dGam33 - tr2dGam33 ; -vreal trK +vreal trexK = -ADMK11*invgam11 + 2*ADMK12*invgam12 + 2*ADMK13*invgam13 + ADMK22*invgam22 + - 2*ADMK23*invgam23 + ADMK33*invgam33 +exK11*invgam11 + 2*exK12*invgam12 + 2*exK13*invgam13 + exK22*invgam22 + + 2*exK23*invgam23 + exK33*invgam33 ; -vreal DADMK111 +vreal DexK111 = -dADMK111 - 2*(ADMK11*Gam111 + ADMK12*Gam211 + ADMK13*Gam311) +dexK111 - 2*(exK11*Gam111 + exK12*Gam211 + exK13*Gam311) ; -vreal DADMK112 +vreal DexK112 = -dADMK112 - ADMK11*Gam112 - ADMK22*Gam211 - ADMK12*(Gam111 + Gam212) - - ADMK23*Gam311 - ADMK13*Gam312 +dexK112 - exK11*Gam112 - exK22*Gam211 - exK12*(Gam111 + Gam212) - + exK23*Gam311 - exK13*Gam312 ; -vreal DADMK113 +vreal DexK113 = -dADMK113 - ADMK11*Gam113 - ADMK23*Gam211 - ADMK12*Gam213 - ADMK33*Gam311 - - ADMK13*(Gam111 + Gam313) +dexK113 - exK11*Gam113 - exK23*Gam211 - exK12*Gam213 - exK33*Gam311 - + exK13*(Gam111 + Gam313) ; -vreal DADMK122 +vreal DexK122 = -dADMK122 - 2*(ADMK12*Gam112 + ADMK22*Gam212 + ADMK23*Gam312) +dexK122 - 2*(exK12*Gam112 + exK22*Gam212 + exK23*Gam312) ; -vreal DADMK123 +vreal DexK123 = -dADMK123 - ADMK13*Gam112 - ADMK12*Gam113 - ADMK23*Gam212 - ADMK22*Gam213 - - ADMK33*Gam312 - ADMK23*Gam313 +dexK123 - exK13*Gam112 - exK12*Gam113 - exK23*Gam212 - exK22*Gam213 - + exK33*Gam312 - exK23*Gam313 ; -vreal DADMK133 +vreal DexK133 = -dADMK133 - 2*(ADMK13*Gam113 + ADMK23*Gam213 + ADMK33*Gam313) +dexK133 - 2*(exK13*Gam113 + exK23*Gam213 + exK33*Gam313) ; -vreal DADMK211 +vreal DexK211 = -dADMK211 - 2*(ADMK11*Gam112 + ADMK12*Gam212 + ADMK13*Gam312) +dexK211 - 2*(exK11*Gam112 + exK12*Gam212 + exK13*Gam312) ; -vreal DADMK212 +vreal DexK212 = -dADMK212 - ADMK11*Gam122 - ADMK22*Gam212 - ADMK12*(Gam112 + Gam222) - - ADMK23*Gam312 - ADMK13*Gam322 +dexK212 - exK11*Gam122 - exK22*Gam212 - exK12*(Gam112 + Gam222) - + exK23*Gam312 - exK13*Gam322 ; -vreal DADMK213 +vreal DexK213 = -dADMK213 - ADMK11*Gam123 - ADMK23*Gam212 - ADMK12*Gam223 - ADMK33*Gam312 - - ADMK13*(Gam112 + Gam323) +dexK213 - exK11*Gam123 - exK23*Gam212 - exK12*Gam223 - exK33*Gam312 - + exK13*(Gam112 + Gam323) ; -vreal DADMK222 +vreal DexK222 = -dADMK222 - 2*(ADMK12*Gam122 + ADMK22*Gam222 + ADMK23*Gam322) +dexK222 - 2*(exK12*Gam122 + exK22*Gam222 + exK23*Gam322) ; -vreal DADMK223 +vreal DexK223 = -dADMK223 - ADMK13*Gam122 - ADMK12*Gam123 - ADMK23*Gam222 - ADMK22*Gam223 - - ADMK33*Gam322 - ADMK23*Gam323 +dexK223 - exK13*Gam122 - exK12*Gam123 - exK23*Gam222 - exK22*Gam223 - + exK33*Gam322 - exK23*Gam323 ; -vreal DADMK233 +vreal DexK233 = -dADMK233 - 2*(ADMK13*Gam123 + ADMK23*Gam223 + ADMK33*Gam323) +dexK233 - 2*(exK13*Gam123 + exK23*Gam223 + exK33*Gam323) ; -vreal DADMK311 +vreal DexK311 = -dADMK311 - 2*(ADMK11*Gam113 + ADMK12*Gam213 + ADMK13*Gam313) +dexK311 - 2*(exK11*Gam113 + exK12*Gam213 + exK13*Gam313) ; -vreal DADMK312 +vreal DexK312 = -dADMK312 - ADMK11*Gam123 - ADMK22*Gam213 - ADMK12*(Gam113 + Gam223) - - ADMK23*Gam313 - ADMK13*Gam323 +dexK312 - exK11*Gam123 - exK22*Gam213 - exK12*(Gam113 + Gam223) - + exK23*Gam313 - exK13*Gam323 ; -vreal DADMK313 +vreal DexK313 = -dADMK313 - ADMK11*Gam133 - ADMK23*Gam213 - ADMK12*Gam233 - ADMK33*Gam313 - - ADMK13*(Gam113 + Gam333) +dexK313 - exK11*Gam133 - exK23*Gam213 - exK12*Gam233 - exK33*Gam313 - + exK13*(Gam113 + Gam333) ; -vreal DADMK322 +vreal DexK322 = -dADMK322 - 2*(ADMK12*Gam123 + ADMK22*Gam223 + ADMK23*Gam323) +dexK322 - 2*(exK12*Gam123 + exK22*Gam223 + exK23*Gam323) ; -vreal DADMK323 +vreal DexK323 = -dADMK323 - ADMK13*Gam123 - ADMK12*Gam133 - ADMK23*Gam223 - ADMK22*Gam233 - - ADMK33*Gam323 - ADMK23*Gam333 +dexK323 - exK13*Gam123 - exK12*Gam133 - exK23*Gam223 - exK22*Gam233 - + exK33*Gam323 - exK23*Gam333 ; -vreal DADMK333 +vreal DexK333 = -dADMK333 - 2*(ADMK13*Gam133 + ADMK23*Gam233 + ADMK33*Gam333) +dexK333 - 2*(exK13*Gam133 + exK23*Gam233 + exK33*Gam333) ; vreal rho = -(Power(ADMbeta1,2)*eT11 + Power(ADMbeta2,2)*eT22 + - 2*ADMbeta2*ADMbeta3*eT23 + Power(ADMbeta3,2)*eT33 + - 2*ADMbeta1*(ADMbeta2*eT12 + ADMbeta3*eT13 - eTt1) - 2*ADMbeta2*eTt2 - - 2*ADMbeta3*eTt3 + eTtt)/Power(ADMalpha,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 = -(ADMbeta1*eT11 + ADMbeta2*eT12 + ADMbeta3*eT13 - eTt1)/ADMalpha +(beta1*eT11 + beta2*eT12 + beta3*eT13 - eTt1)/alpha ; vreal Sm2 = -(ADMbeta1*eT12 + ADMbeta2*eT22 + ADMbeta3*eT23 - eTt2)/ADMalpha +(beta1*eT12 + beta2*eT22 + beta3*eT23 - eTt2)/alpha ; vreal Sm3 = -(ADMbeta1*eT13 + ADMbeta2*eT23 + ADMbeta3*eT33 - eTt3)/ADMalpha +(beta1*eT13 + beta2*eT23 + beta3*eT33 - eTt3)/alpha ; local_HC.store(mask, index2, --(Power(ADMK11,2)*Power(invgam11,2)) - 2*Power(ADMK13,2)*Power(invgam13,2) - - 2*ADMK11*(2*ADMK12*invgam11*invgam12 + ADMK22*Power(invgam12,2) + - invgam13*(2*ADMK13*invgam11 + 2*ADMK23*invgam12 + ADMK33*invgam13)) - - Power(ADMK22,2)*Power(invgam22,2) - - 2*Power(ADMK12,2)*(Power(invgam12,2) + invgam11*invgam22) - - 4*ADMK13*ADMK22*invgam12*invgam23 - 4*ADMK13*ADMK23*invgam13*invgam23 - - 4*ADMK22*ADMK23*invgam22*invgam23 - 2*Power(ADMK23,2)*Power(invgam23,2) - - 2*ADMK22*ADMK33*Power(invgam23,2) - - 4*ADMK12*(ADMK13*invgam12*invgam13 + ADMK22*invgam12*invgam22 + - ADMK23*invgam13*invgam22 + ADMK13*invgam11*invgam23 + - ADMK23*invgam12*invgam23 + ADMK33*invgam13*invgam23) - - 2*Power(ADMK13,2)*invgam11*invgam33 - 4*ADMK13*ADMK23*invgam12*invgam33 - - 4*ADMK13*ADMK33*invgam13*invgam33 - 2*Power(ADMK23,2)*invgam22*invgam33 - - 4*ADMK23*ADMK33*invgam23*invgam33 - Power(ADMK33,2)*Power(invgam33,2) + +-(Power(exK11,2)*Power(invgam11,2)) - 2*Power(exK13,2)*Power(invgam13,2) - + 2*exK11*(2*exK12*invgam11*invgam12 + exK22*Power(invgam12,2) + + invgam13*(2*exK13*invgam11 + 2*exK23*invgam12 + exK33*invgam13)) - + Power(exK22,2)*Power(invgam22,2) - + 2*Power(exK12,2)*(Power(invgam12,2) + invgam11*invgam22) - + 4*exK13*exK22*invgam12*invgam23 - 4*exK13*exK23*invgam13*invgam23 - + 4*exK22*exK23*invgam22*invgam23 - 2*Power(exK23,2)*Power(invgam23,2) - + 2*exK22*exK33*Power(invgam23,2) - + 4*exK12*(exK13*invgam12*invgam13 + exK22*invgam12*invgam22 + + exK23*invgam13*invgam22 + exK13*invgam11*invgam23 + + exK23*invgam12*invgam23 + exK33*invgam13*invgam23) - + 2*Power(exK13,2)*invgam11*invgam33 - 4*exK13*exK23*invgam12*invgam33 - + 4*exK13*exK33*invgam13*invgam33 - 2*Power(exK23,2)*invgam22*invgam33 - + 4*exK23*exK33*invgam23*invgam33 - Power(exK33,2)*Power(invgam33,2) + invgam11*R11 + 2*invgam12*R12 + 2*invgam13*R13 + invgam22*R22 + - 2*invgam23*R23 + invgam33*R33 - 16*cpi*rho + Power(trK,2) + 2*invgam23*R23 + invgam33*R33 - 16*cpi*rho + Power(trexK,2) ); local_MC1.store(mask, index2, --(DADMK212*Power(invgam12,2)) + 2*DADMK123*invgam12*invgam13 - - DADMK213*invgam12*invgam13 - DADMK312*invgam12*invgam13 + - DADMK133*Power(invgam13,2) - DADMK313*Power(invgam13,2) + - DADMK212*invgam11*invgam22 + DADMK223*invgam13*invgam22 - - DADMK322*invgam13*invgam22 + - DADMK122*(Power(invgam12,2) - invgam11*invgam22) - - 2*DADMK123*invgam11*invgam23 + DADMK213*invgam11*invgam23 + - DADMK312*invgam11*invgam23 - DADMK223*invgam12*invgam23 + - DADMK322*invgam12*invgam23 + DADMK233*invgam13*invgam23 - - DADMK323*invgam13*invgam23 - DADMK133*invgam11*invgam33 + - DADMK313*invgam11*invgam33 - DADMK233*invgam12*invgam33 + - DADMK323*invgam12*invgam33 - 8*cpi*invgam11*Sm1 - 8*cpi*invgam12*Sm2 - - 8*cpi*invgam13*Sm3 +-(DexK212*Power(invgam12,2)) + 2*DexK123*invgam12*invgam13 - + DexK213*invgam12*invgam13 - DexK312*invgam12*invgam13 + + DexK133*Power(invgam13,2) - DexK313*Power(invgam13,2) + + DexK212*invgam11*invgam22 + DexK223*invgam13*invgam22 - + DexK322*invgam13*invgam22 + DexK122* + (Power(invgam12,2) - invgam11*invgam22) - 2*DexK123*invgam11*invgam23 + + DexK213*invgam11*invgam23 + DexK312*invgam11*invgam23 - + DexK223*invgam12*invgam23 + DexK322*invgam12*invgam23 + + DexK233*invgam13*invgam23 - DexK323*invgam13*invgam23 - + DexK133*invgam11*invgam33 + DexK313*invgam11*invgam33 - + DexK233*invgam12*invgam33 + DexK323*invgam12*invgam33 - + 8*cpi*invgam11*Sm1 - 8*cpi*invgam12*Sm2 - 8*cpi*invgam13*Sm3 ); local_MC2.store(mask, index2, --(DADMK112*Power(invgam12,2)) + DADMK211*Power(invgam12,2) - - DADMK113*invgam12*invgam13 + DADMK311*invgam12*invgam13 + - DADMK112*invgam11*invgam22 - DADMK211*invgam11*invgam22 + - DADMK123*invgam13*invgam22 - 2*DADMK213*invgam13*invgam22 + - DADMK312*invgam13*invgam22 + DADMK113*invgam11*invgam23 - - DADMK311*invgam11*invgam23 - DADMK123*invgam12*invgam23 + - 2*DADMK213*invgam12*invgam23 - DADMK312*invgam12*invgam23 + - DADMK133*invgam13*invgam23 - DADMK313*invgam13*invgam23 + - DADMK233*Power(invgam23,2) - DADMK323*Power(invgam23,2) - - DADMK133*invgam12*invgam33 + DADMK313*invgam12*invgam33 - - DADMK233*invgam22*invgam33 + DADMK323*invgam22*invgam33 - +-(DexK112*Power(invgam12,2)) + DexK211*Power(invgam12,2) - + DexK113*invgam12*invgam13 + DexK311*invgam12*invgam13 + + DexK112*invgam11*invgam22 - DexK211*invgam11*invgam22 + + DexK123*invgam13*invgam22 - 2*DexK213*invgam13*invgam22 + + DexK312*invgam13*invgam22 + DexK113*invgam11*invgam23 - + DexK311*invgam11*invgam23 - DexK123*invgam12*invgam23 + + 2*DexK213*invgam12*invgam23 - DexK312*invgam12*invgam23 + + DexK133*invgam13*invgam23 - DexK313*invgam13*invgam23 + + DexK233*Power(invgam23,2) - DexK323*Power(invgam23,2) - + DexK133*invgam12*invgam33 + DexK313*invgam12*invgam33 - + DexK233*invgam22*invgam33 + DexK323*invgam22*invgam33 - 8*cpi*invgam12*Sm1 - 8*cpi*invgam22*Sm2 - 8*cpi*invgam23*Sm3 ); local_MC3.store(mask, index2, --(DADMK112*invgam12*invgam13) + DADMK211*invgam12*invgam13 - - DADMK113*Power(invgam13,2) + DADMK311*Power(invgam13,2) - - DADMK122*invgam13*invgam22 + DADMK212*invgam13*invgam22 + - DADMK112*invgam11*invgam23 - DADMK211*invgam11*invgam23 + - DADMK122*invgam12*invgam23 - DADMK212*invgam12*invgam23 - - DADMK123*invgam13*invgam23 - DADMK213*invgam13*invgam23 + - 2*DADMK312*invgam13*invgam23 - DADMK223*Power(invgam23,2) + - DADMK322*Power(invgam23,2) + DADMK113*invgam11*invgam33 - - DADMK311*invgam11*invgam33 + DADMK123*invgam12*invgam33 + - DADMK213*invgam12*invgam33 - 2*DADMK312*invgam12*invgam33 + - DADMK223*invgam22*invgam33 - DADMK322*invgam22*invgam33 - +-(DexK112*invgam12*invgam13) + DexK211*invgam12*invgam13 - + DexK113*Power(invgam13,2) + DexK311*Power(invgam13,2) - + DexK122*invgam13*invgam22 + DexK212*invgam13*invgam22 + + DexK112*invgam11*invgam23 - DexK211*invgam11*invgam23 + + DexK122*invgam12*invgam23 - DexK212*invgam12*invgam23 - + DexK123*invgam13*invgam23 - DexK213*invgam13*invgam23 + + 2*DexK312*invgam13*invgam23 - DexK223*Power(invgam23,2) + + DexK322*Power(invgam23,2) + DexK113*invgam11*invgam33 - + DexK311*invgam11*invgam33 + DexK123*invgam12*invgam33 + + DexK213*invgam12*invgam33 - 2*DexK312*invgam12*invgam33 + + DexK223*invgam22*invgam33 - DexK322*invgam22*invgam33 - 8*cpi*invgam13*Sm1 - 8*cpi*invgam23*Sm2 - 8*cpi*invgam33*Sm3 ); diff --git a/ADMconstraints/wolfram/ADM_set_constraint.wl b/ADMconstraints/wolfram/ADM_set_constraint.wl index 7ba5c472..e632a2b8 100644 --- a/ADMconstraints/wolfram/ADM_set_constraint.wl +++ b/ADMconstraints/wolfram/ADM_set_constraint.wl @@ -26,7 +26,7 @@ DefChart[cart, M3, {1, 2, 3}, {X[], Y[], Z[]}, ChartColor -> Blue]; < detinvgam}; SetEQNDelayed[detinvgam[], 1 / Det[Mat] // Simplify]; SetEQNDelayed[invgam[i_, j_], invMat[[i[[1]], j[[1]]]] // Simplify] diff --git a/ADMconstraints/wolfram/check_rhs.ipynb b/ADMconstraints/wolfram/check_rhs.ipynb index ec6dccc1..47319737 100644 --- a/ADMconstraints/wolfram/check_rhs.ipynb +++ b/ADMconstraints/wolfram/check_rhs.ipynb @@ -161,7 +161,7 @@ { "data": { "text/html": [ - "
\"Output\"
" + "
\"Output\"
" ], "text/plain": [ "-Image-" @@ -196,7 +196,7 @@ { "data": { "text/html": [ - "
\"Output\"
" + "
\"Output\"
" ], "text/plain": [ "-Image-" @@ -231,7 +231,7 @@ { "data": { "text/html": [ - "
\"Output\"
" + "
\"Output\"
" ], "text/plain": [ "-Image-" diff --git a/ADMconstraints/wolfram/wl/ADM_rhs.wl b/ADMconstraints/wolfram/wl/ADM_rhs.wl index 80e25ccc..3956190b 100644 --- a/ADMconstraints/wolfram/wl/ADM_rhs.wl +++ b/ADMconstraints/wolfram/wl/ADM_rhs.wl @@ -10,25 +10,25 @@ (****************) -SetEQN[GamDDD[k_, i_, j_], 1/2 (dADMgam[i, j, k] + dADMgam[j, k, i] - dADMgam[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[tr1dGam[i_, j_], -invgam[k, p] invgam[l, q] dADMgam[-k, -p, -q] GamDDD[-l, i, j] + 1/2 invgam[k, l] (ddADMgam[-k, i, j, -l] + ddADMgam[-k, j, -l, i] - ddADMgam[-k, -l, i, j])]; +SetEQN[tr1dGam[i_, j_], -invgam[k, p] invgam[l, q] dgam[-k, -p, -q] GamDDD[-l, i, j] + 1/2 invgam[k, l] (ddgam[-k, i, j, -l] + ddgam[-k, j, -l, i] - ddgam[-k, -l, i, j])]; -SetEQN[tr2dGam[m_, i_], 1/2 (invgam[k, l] ddADMgam[m, i, -k, -l] - invgam[k, p] invgam[l, q] dADMgam[m, -p, -q] dADMgam[i, -k, -l])]; +SetEQN[tr2dGam[m_, i_], 1/2 (invgam[k, l] ddgam[m, i, -k, -l] - invgam[k, p] invgam[l, q] dgam[m, -p, -q] dgam[i, -k, -l])]; SetEQN[R[j_, k_], tr1dGam[j, k] - tr2dGam[j, k] + Gam[i, -i, -p] Gam[p, j, k] - Gam[i, j, -p] Gam[p, -i, k]]; -SetEQN[trK[], invgam[k, l] ADMK[-k, -l]]; +SetEQN[trexK[], invgam[k, l] exK[-k, -l]]; -SetEQN[DADMK[k_, i_, j_], dADMK[k, i, j] - Gam[l, k, i] ADMK[-l, j] - Gam[l, k, j] ADMK[-l, i]]; +SetEQN[DexK[k_, i_, j_], dexK[k, i, j] - Gam[l, k, i] exK[-l, j] - Gam[l, k, j] exK[-l, i]]; (* matter *) -SetEQN[rho[], ADMalpha[]^-2 (eTtt[] - 2 ADMbeta[j] eTt[-j] + ADMbeta[i] ADMbeta[j] eT[-i, -j])]; +SetEQN[rho[], alpha[]^-2 (eTtt[] - 2 beta[j] eTt[-j] + beta[i] beta[j] eT[-i, -j])]; -SetEQN[Sm[i_], -ADMalpha[]^-1 (eTt[i] - ADMbeta[k] eT[-k, i])]; +SetEQN[Sm[i_], -alpha[]^-1 (eTt[i] - beta[k] eT[-k, i])]; (***************) @@ -36,6 +36,6 @@ SetEQN[Sm[i_], -ADMalpha[]^-1 (eTt[i] - ADMbeta[k] eT[-k, i])]; (***************) -SetEQN[HC[], invgam[k, l] R[-k, -l] + trK[]^2 - invgam[i, k] invgam[j, l] ADMK[-i, -j] ADMK[-k, -l] - 16 cpi rho[]]; +SetEQN[HC[], invgam[k, l] R[-k, -l] + trexK[]^2 - invgam[i, k] invgam[j, l] exK[-i, -j] exK[-k, -l] - 16 cpi rho[]]; -SetEQN[MC[i_], (invgam[i, k] invgam[j, l] - invgam[i, j] invgam[k, l]) DADMK[-j, -k, -l] - 8 cpi invgam[i, j] Sm[-j]]; +SetEQN[MC[i_], (invgam[i, k] invgam[j, l] - invgam[i, j] invgam[k, l]) DexK[-j, -k, -l] - 8 cpi invgam[i, j] Sm[-j]]; diff --git a/ADMconstraints/wolfram/wl/ADM_vars.wl b/ADMconstraints/wolfram/wl/ADM_vars.wl index 7488f478..2f8e5a38 100644 --- a/ADMconstraints/wolfram/wl/ADM_vars.wl +++ b/ADMconstraints/wolfram/wl/ADM_vars.wl @@ -14,21 +14,21 @@ 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]\), \((ADM)\)]\)"} + {gam[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[Gamma]"}, + {exK[-i, -j], Symmetric[{-i, -j}], PrintAs -> "K"}, + {alpha[], PrintAs -> "\[Alpha]"}, + {beta[i], PrintAs -> "\[Beta]"} ]; dADMVarlist = GridTensors[ - {dADMgam[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*SuperscriptBox[\(\[Gamma]\), \((ADM)\)]\)"}, - {dADMK [-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*SuperscriptBox[\(K\), \((ADM)\)]\)"} + {dgam[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\[Gamma]"}, + {dexK[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]K"} ]; ddADMVarlist = GridTensors[ - {ddADMgam[-k, -l, -i, -j], GenSet[Cycles[{1, 2}], Cycles[{3, 4}]], PrintAs -> "\[PartialD]\!\(\*SuperscriptBox[\(\[Gamma]\), \((ADM)\)]\)"} + {ddgam[-k, -l, -i, -j], GenSet[Cycles[{1, 2}], Cycles[{3, 4}]], PrintAs -> "\[PartialD]\[PartialD]\[Gamma]"} ]; TmunuVarlist = @@ -53,8 +53,8 @@ IntermediateVarlist = {tr1dGam[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*SuperscriptBox[\(\[CapitalGamma]\), \((tr1)\)]\)"}, {tr2dGam[-i, -j], Symmetric[{-i, -j}], PrintAs -> "\[PartialD]\!\(\*SuperscriptBox[\(\[CapitalGamma]\), \((tr2)\)]\)"}, {R[-i, -j], Symmetric[{-i, -j}], PrintAs -> "R"}, - {trK[], PrintAs -> "K"}, - {DADMK[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "\[Del]K"} + {trexK[], PrintAs -> "K"}, + {DexK[-k, -i, -j], Symmetric[{-i, -j}], PrintAs -> "DK"} ]; (* Matter *) From a0b89558bd91fd06efbb0b9ccd68f96dde3735c6 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 17:00:57 -0500 Subject: [PATCH 21/37] ADMconstraints: update admconstraints.cxx --- ADMconstraints/src/admconstraints.cxx | 50 +++++++-------------------- 1 file changed, 13 insertions(+), 37 deletions(-) diff --git a/ADMconstraints/src/admconstraints.cxx b/ADMconstraints/src/admconstraints.cxx index 425fb985..985250b3 100644 --- a/ADMconstraints/src/admconstraints.cxx +++ b/ADMconstraints/src/admconstraints.cxx @@ -53,16 +53,10 @@ extern "C" void ADMconstraints(CCTK_ARGUMENTS) { const GF3D5layout layout5(imin, imax); // Input grid functions - const GF3D2 &gf_W = W; - const smat, 3> gf_gamt{gammatxx, gammatxy, gammatxz, - gammatyy, gammatyz, gammatzz}; - const GF3D2 &gf_exKh = Kh; - const smat, 3> gf_exAt{Atxx, Atxy, Atxz, - Atyy, Atyz, Atzz}; - const vec, 3> gf_trGt{Gamtx, Gamty, Gamtz}; - const GF3D2 &gf_Theta = Theta; - const GF3D2 &gf_alpha = alphaG; - const vec, 3> gf_beta{betaGx, betaGy, betaGz}; + const smat, 3> gf_gam{gxx, gxy, gxz, gyy, gyz, gzz}; + const smat, 3> gf_exK{Kxx, Kxy, Kxz, Kyy, Kyz, Kzz}; + const GF3D2 &gf_alpha = alp; + const vec, 3> gf_beta{betax, betay, betaz}; // More input grid functions const GF3D2 &gf_eTtt = eTtt; @@ -71,9 +65,8 @@ extern "C" void ADMconstraints(CCTK_ARGUMENTS) { eTyy, eTyz, eTzz}; // Output grid functions - const vec, 3> gf_ZtC{ZtCx, ZtCy, ZtCz}; const GF3D2 &gf_HC = HC; - const vec, 3> gf_MtC{MtCx, MtCy, MtCz}; + const vec, 3> gf_MC{MCx, MCy, MCz}; // Define derivs lambdas const auto calccopy = [&](const auto &gf, const auto &gf0) { @@ -90,7 +83,7 @@ extern "C" void ADMconstraints(CCTK_ARGUMENTS) { }; // Tile variables for derivatives and so on - const int ntmps = 118; + const int ntmps = 88; GF3D5vector tmps(layout5, ntmps); int itmp = 0; @@ -107,31 +100,14 @@ extern "C" void ADMconstraints(CCTK_ARGUMENTS) { const auto make_mat_vec_gf = [&]() { return make_mat(make_vec_gf); }; const auto make_mat_mat_gf = [&]() { return make_mat(make_mat_gf); }; - const GF3D5 tl_W(make_gf()); - const vec, 3> tl_dW(make_vec_gf()); - const smat, 3> tl_ddW(make_mat_gf()); - calcderivs2(tl_W, tl_dW, tl_ddW, gf_W); + const smat, 3> tl_gam(make_mat_gf()); + const smat, 3>, 3> tl_dgam(make_mat_vec_gf()); + const smat, 3>, 3> tl_ddgam(make_mat_mat_gf()); + calcderivs2(tl_gam, tl_dgam, tl_ddgam, gf_gam); - const smat, 3> tl_gamt(make_mat_gf()); - const smat, 3>, 3> tl_dgamt(make_mat_vec_gf()); - const smat, 3>, 3> tl_ddgamt(make_mat_mat_gf()); - calcderivs2(tl_gamt, tl_dgamt, tl_ddgamt, gf_gamt); - - const GF3D5 tl_exKh(make_gf()); - const vec, 3> tl_dexKh(make_vec_gf()); - calcderivs(tl_exKh, tl_dexKh, gf_exKh); - - const smat, 3> tl_exAt(make_mat_gf()); - const smat, 3>, 3> tl_dexAt(make_mat_vec_gf()); - calcderivs(tl_exAt, tl_dexAt, gf_exAt); - - const vec, 3> tl_trGt(make_vec_gf()); - const vec, 3>, 3> tl_dtrGt(make_vec_vec_gf()); - calcderivs(tl_trGt, tl_dtrGt, gf_trGt); - - const GF3D5 tl_Theta(make_gf()); - const vec, 3> tl_dTheta(make_vec_gf()); - calcderivs(tl_Theta, tl_dTheta, gf_Theta); + const smat, 3> tl_exK(make_mat_gf()); + const smat, 3>, 3> tl_dexK(make_mat_vec_gf()); + calcderivs(tl_exK, tl_dexK, gf_exK); const GF3D5 tl_alpha(make_gf()); calccopy(tl_alpha, gf_alpha); From 77bc9fad68d1ed53167e483e2a27441b5d65b09a Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 22:03:39 -0500 Subject: [PATCH 22/37] ADMconstraints: update admconstraints.cxx --- ADMconstraints/src/admconstraints.cxx | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/ADMconstraints/src/admconstraints.cxx b/ADMconstraints/src/admconstraints.cxx index 985250b3..0be8c75c 100644 --- a/ADMconstraints/src/admconstraints.cxx +++ b/ADMconstraints/src/admconstraints.cxx @@ -129,10 +129,10 @@ extern "C" void ADMconstraints(CCTK_ARGUMENTS) { const CCTK_REAL cpi = M_PI; #ifdef __CUDACC__ - const nvtxRangeId_t range = nvtxRangeStartA("Z4cow_Constraints::constraints"); + const nvtxRangeId_t range = nvtxRangeStartA("ADMconstraints::constraints"); #endif -#include "../wolfram/Z4cow_set_constraint.hxx" +#include "../wolfram/ADM_set_constraint.hxx" #ifdef __CUDACC__ nvtxRangeEnd(range); From 848c23f5a746a2a42fbdefba572ca33fc502a978 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 22:05:17 -0500 Subject: [PATCH 23/37] ADMconstraints: add make.code.defn --- ADMconstraints/src/make.code.defn | 8 ++++++++ 1 file changed, 8 insertions(+) create mode 100644 ADMconstraints/src/make.code.defn diff --git a/ADMconstraints/src/make.code.defn b/ADMconstraints/src/make.code.defn new file mode 100644 index 00000000..6ad5ed87 --- /dev/null +++ b/ADMconstraints/src/make.code.defn @@ -0,0 +1,8 @@ +# Main make.code.defn file for thorn Z4c + +# Source files in this directory +SRCS = \ + admconstraints.cxx + +# Subdirectories containing source files +SUBDIRS = From a8441fef2aa5e5a9a89d022479ccb03102d9783e Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 22:07:02 -0500 Subject: [PATCH 24/37] ADMconstraints: add configuration.ccl --- ADMconstraints/configuration.ccl | 3 +++ 1 file changed, 3 insertions(+) create mode 100644 ADMconstraints/configuration.ccl diff --git a/ADMconstraints/configuration.ccl b/ADMconstraints/configuration.ccl new file mode 100644 index 00000000..82a6edea --- /dev/null +++ b/ADMconstraints/configuration.ccl @@ -0,0 +1,3 @@ +# Configuration definitions for thorn ADMconstraints + +REQUIRES Arith Loop Derivs From 3dcbef312ebb57abc5029fe3f2ebe3bda2ab4540 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 22:12:27 -0500 Subject: [PATCH 25/37] ADMconstraints: add schedule.ccl --- ADMconstraints/schedule.ccl | 28 ++++++++++++++++++++++++++++ 1 file changed, 28 insertions(+) create mode 100644 ADMconstraints/schedule.ccl diff --git a/ADMconstraints/schedule.ccl b/ADMconstraints/schedule.ccl new file mode 100644 index 00000000..4f09e108 --- /dev/null +++ b/ADMconstraints/schedule.ccl @@ -0,0 +1,28 @@ +# Schedule definitions for thorn ADMconstraints + +STORAGE: HC +STORAGE: MtC + + + + +SCHEDULE GROUP ADMconstraints_AnalysisGroup AT analysis +{ +} "Analyse Z4c variables" + + +if (calc_constraints) { + SCHEDULE ADMconstraints_Constraints IN ADMconstraints_AnalysisGroup + { + LANG: C + READS: ADMBaseX::metric(everywhere) + READS: ADMBaseX::curv(everywhere) + READS: ADMBaseX::lapse(everywhere) + READS: ADMBaseX::shift(everywhere) + READS: TmunuBaseX::eTtt(interior) + READS: TmunuBaseX::eTti(interior) + READS: TmunuBaseX::eTij(interior) + WRITES: HC(interior) + WRITES: MtC(interior) + } "Calculate ADM Constraints" +} From cd608e9f449e588ca896ec313824ada8a5e58bde Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Mon, 18 Nov 2024 22:25:53 -0500 Subject: [PATCH 26/37] ADMconstraints: make it compile --- ADMconstraints/param.ccl | 12 ++++++++++++ ADMconstraints/schedule.ccl | 6 +++--- ADMconstraints/src/admconstraints.cxx | 6 +++--- 3 files changed, 18 insertions(+), 6 deletions(-) diff --git a/ADMconstraints/param.ccl b/ADMconstraints/param.ccl index 8248a229..82a0491a 100644 --- a/ADMconstraints/param.ccl +++ b/ADMconstraints/param.ccl @@ -1 +1,13 @@ # Parameter definitions for thorn ADMconstraints + +BOOLEAN calc_constraints "Calculate constraints" STEERABLE=recover +{ +} yes + +CCTK_INT deriv_order "Order of spatial finite differencing" STEERABLE=never +{ + 2 :: "Second order finite difference" + 4 :: "Fourth order finite difference" + 6 :: "Sixth order finite difference" + 8 :: "Eighth order finite difference" +} 4 diff --git a/ADMconstraints/schedule.ccl b/ADMconstraints/schedule.ccl index 4f09e108..952c34d3 100644 --- a/ADMconstraints/schedule.ccl +++ b/ADMconstraints/schedule.ccl @@ -1,7 +1,7 @@ # Schedule definitions for thorn ADMconstraints STORAGE: HC -STORAGE: MtC +STORAGE: MC @@ -12,7 +12,7 @@ SCHEDULE GROUP ADMconstraints_AnalysisGroup AT analysis if (calc_constraints) { - SCHEDULE ADMconstraints_Constraints IN ADMconstraints_AnalysisGroup + SCHEDULE ADMconstraints_CalcConstraints IN ADMconstraints_AnalysisGroup { LANG: C READS: ADMBaseX::metric(everywhere) @@ -23,6 +23,6 @@ if (calc_constraints) { READS: TmunuBaseX::eTti(interior) READS: TmunuBaseX::eTij(interior) WRITES: HC(interior) - WRITES: MtC(interior) + WRITES: MC(interior) } "Calculate ADM Constraints" } diff --git a/ADMconstraints/src/admconstraints.cxx b/ADMconstraints/src/admconstraints.cxx index 0be8c75c..8fda10a3 100644 --- a/ADMconstraints/src/admconstraints.cxx +++ b/ADMconstraints/src/admconstraints.cxx @@ -29,8 +29,8 @@ CCTK_DEVICE CCTK_HOST CCTK_ATTRIBUTE_ALWAYS_INLINE inline T Power(T x, int y) { return (y == 2) ? Arith::pow2(x) : Arith::pown(x, y); } -extern "C" void ADMconstraints(CCTK_ARGUMENTS) { - DECLARE_CCTK_ARGUMENTSX_ADMconstraints; +extern "C" void ADMconstraints_CalcConstraints(CCTK_ARGUMENTS) { + DECLARE_CCTK_ARGUMENTSX_ADMconstraints_CalcConstraints; DECLARE_CCTK_PARAMETERS; for (int d = 0; d < 3; ++d) @@ -54,7 +54,7 @@ extern "C" void ADMconstraints(CCTK_ARGUMENTS) { // Input grid functions const smat, 3> gf_gam{gxx, gxy, gxz, gyy, gyz, gzz}; - const smat, 3> gf_exK{Kxx, Kxy, Kxz, Kyy, Kyz, Kzz}; + const smat, 3> gf_exK{kxx, kxy, kxz, kyy, kyz, kzz}; const GF3D2 &gf_alpha = alp; const vec, 3> gf_beta{betax, betay, betaz}; From a880d2094b0b6ac03fb0303a28e3152151d99b7a Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Tue, 19 Nov 2024 10:03:02 -0500 Subject: [PATCH 27/37] ADMconstraints: format ADM_rhs.wl --- ADMconstraints/src/admconstraints.cxx | 1 - ADMconstraints/wolfram/ADM_set_constraint.wl | 11 ++++++++++- ADMconstraints/wolfram/wl/ADM_rhs.wl | 6 +++--- 3 files changed, 13 insertions(+), 5 deletions(-) diff --git a/ADMconstraints/src/admconstraints.cxx b/ADMconstraints/src/admconstraints.cxx index 8fda10a3..e51a7eb2 100644 --- a/ADMconstraints/src/admconstraints.cxx +++ b/ADMconstraints/src/admconstraints.cxx @@ -96,7 +96,6 @@ extern "C" void ADMconstraints_CalcConstraints(CCTK_ARGUMENTS) { }; const auto make_vec_gf = [&]() { return make_vec(make_gf); }; const auto make_mat_gf = [&]() { return make_mat(make_gf); }; - const auto make_vec_vec_gf = [&]() { return make_vec(make_vec_gf); }; const auto make_mat_vec_gf = [&]() { return make_mat(make_vec_gf); }; const auto make_mat_mat_gf = [&]() { return make_mat(make_mat_gf); }; diff --git a/ADMconstraints/wolfram/ADM_set_constraint.wl b/ADMconstraints/wolfram/ADM_set_constraint.wl index e632a2b8..f51ef720 100644 --- a/ADMconstraints/wolfram/ADM_set_constraint.wl +++ b/ADMconstraints/wolfram/ADM_set_constraint.wl @@ -61,7 +61,16 @@ $MainPrint[] := PrintInitializations[{Mode -> "MainIn", StorageType -> "Tile", TensorType -> "Smat"}, ddADMVarlist]; pr[]; - PrintEquations[{Mode -> "Temp"}, IntermediateVarlist]; + PrintEquations[{Mode -> "Temp"}, Drop[IntermediateVarlist, {-1}]]; + + Module[{printDK}, + printDK[kk_,ii_,jj_] := PrintComponentEquations[GetDefaultChart[], + DexK[{kk,-GetDefaultChart[]},{ii,-GetDefaultChart[]},{jj,-GetDefaultChart[]}]]; + SetParsePrintCompEQNMode[{NewVar -> True}]; + Do[If[ii!=jj || ii!=kk || jj!=kk, printDK[kk,ii,jj]], {kk,1,3}, {ii,1,3}, {jj,ii,3}] + ]; + pr[]; + PrintEquations[{Mode -> "Temp"}, MatterVarlist]; pr[]; PrintEquations[{Mode -> "Main"}, ConstraintVarlist]; diff --git a/ADMconstraints/wolfram/wl/ADM_rhs.wl b/ADMconstraints/wolfram/wl/ADM_rhs.wl index 3956190b..2122a532 100644 --- a/ADMconstraints/wolfram/wl/ADM_rhs.wl +++ b/ADMconstraints/wolfram/wl/ADM_rhs.wl @@ -26,9 +26,9 @@ SetEQN[DexK[k_, i_, j_], dexK[k, i, j] - Gam[l, k, i] exK[-l, j] - Gam[l, k, j] (* matter *) -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[Sm[i_], -alpha[] ^ -1 (eTt[i] - beta[k] eT[-k, i])]; (***************) @@ -36,6 +36,6 @@ SetEQN[Sm[i_], -alpha[]^-1 (eTt[i] - beta[k] eT[-k, i])]; (***************) -SetEQN[HC[], invgam[k, l] R[-k, -l] + trexK[]^2 - invgam[i, k] invgam[j, l] exK[-i, -j] exK[-k, -l] - 16 cpi rho[]]; +SetEQN[HC[], invgam[k, l] R[-k, -l] + trexK[] ^ 2 - invgam[i, k] invgam[j, l] exK[-i, -j] exK[-k, -l] - 16 cpi rho[]]; SetEQN[MC[i_], (invgam[i, k] invgam[j, l] - invgam[i, j] invgam[k, l]) DexK[-j, -k, -l] - 8 cpi invgam[i, j] Sm[-j]]; From cb828b1b9b2e41e545154b34a8526e55acd458cf Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Tue, 19 Nov 2024 10:43:36 -0500 Subject: [PATCH 28/37] ADMconstraints: treat DexK separatedly to remove warnings --- ADMconstraints/wolfram/ADM_set_constraint.hxx | 13 ------------- ADMconstraints/wolfram/ADM_set_constraint.wl | 12 +++++------- 2 files changed, 5 insertions(+), 20 deletions(-) diff --git a/ADMconstraints/wolfram/ADM_set_constraint.hxx b/ADMconstraints/wolfram/ADM_set_constraint.hxx index f244272b..b49f76d1 100644 --- a/ADMconstraints/wolfram/ADM_set_constraint.hxx +++ b/ADMconstraints/wolfram/ADM_set_constraint.hxx @@ -1084,10 +1084,6 @@ exK11*invgam11 + 2*exK12*invgam12 + 2*exK13*invgam13 + exK22*invgam22 + 2*exK23*invgam23 + exK33*invgam33 ; -vreal DexK111 -= -dexK111 - 2*(exK11*Gam111 + exK12*Gam211 + exK13*Gam311) -; vreal DexK112 = @@ -1134,11 +1130,6 @@ dexK213 - exK11*Gam123 - exK23*Gam212 - exK12*Gam223 - exK33*Gam312 - exK13*(Gam112 + Gam323) ; -vreal DexK222 -= -dexK222 - 2*(exK12*Gam122 + exK22*Gam222 + exK23*Gam322) -; - vreal DexK223 = dexK223 - exK13*Gam122 - exK12*Gam123 - exK23*Gam222 - exK22*Gam223 - @@ -1178,10 +1169,6 @@ dexK323 - exK13*Gam123 - exK12*Gam133 - exK23*Gam223 - exK22*Gam233 - exK33*Gam323 - exK23*Gam333 ; -vreal DexK333 -= -dexK333 - 2*(exK13*Gam133 + exK23*Gam233 + exK33*Gam333) -; vreal rho = diff --git a/ADMconstraints/wolfram/ADM_set_constraint.wl b/ADMconstraints/wolfram/ADM_set_constraint.wl index f51ef720..61881bd2 100644 --- a/ADMconstraints/wolfram/ADM_set_constraint.wl +++ b/ADMconstraints/wolfram/ADM_set_constraint.wl @@ -4,8 +4,7 @@ (* (c) Liwei Ji, 07/2024 *) -Needs["xAct`xCoba`", FileNameJoin[{Environment["GENERATO"], "src/Generato.wl" - }]] +Needs["xAct`xCoba`", FileNameJoin[{Environment["GENERATO"], "src/Generato.wl"}]] SetPVerbose[False]; @@ -62,15 +61,14 @@ $MainPrint[] := ddADMVarlist]; pr[]; PrintEquations[{Mode -> "Temp"}, Drop[IntermediateVarlist, {-1}]]; - + pr[]; + (* treat DexK separately *) Module[{printDK}, - printDK[kk_,ii_,jj_] := PrintComponentEquations[GetDefaultChart[], - DexK[{kk,-GetDefaultChart[]},{ii,-GetDefaultChart[]},{jj,-GetDefaultChart[]}]]; + printDK[kk_, ii_, jj_] := PrintComponentEquation[GetDefaultChart[], DexK[{kk, -GetDefaultChart[]}, {ii, -GetDefaultChart[]}, {jj, -GetDefaultChart[]}]]; SetParsePrintCompEQNMode[{NewVar -> True}]; - Do[If[ii!=jj || ii!=kk || jj!=kk, printDK[kk,ii,jj]], {kk,1,3}, {ii,1,3}, {jj,ii,3}] + Do[If[ii != jj || ii != kk || jj != kk, printDK[kk, ii, jj]], {kk, 1, 3}, {ii, 1, 3}, {jj, ii, 3}] ]; pr[]; - PrintEquations[{Mode -> "Temp"}, MatterVarlist]; pr[]; PrintEquations[{Mode -> "Main"}, ConstraintVarlist]; From 57670c0e9542b950787c1d32f924d34a98914866 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Tue, 19 Nov 2024 11:06:23 -0500 Subject: [PATCH 29/37] ADMconstraints: treat dexK separatedly to remove warnings --- ADMconstraints/wolfram/ADM_set_constraint.hxx | 3 --- ADMconstraints/wolfram/ADM_set_constraint.wl | 19 ++++++++++++++++++- 2 files changed, 18 insertions(+), 4 deletions(-) diff --git a/ADMconstraints/wolfram/ADM_set_constraint.hxx b/ADMconstraints/wolfram/ADM_set_constraint.hxx index b49f76d1..57514b25 100644 --- a/ADMconstraints/wolfram/ADM_set_constraint.hxx +++ b/ADMconstraints/wolfram/ADM_set_constraint.hxx @@ -71,7 +71,6 @@ const vreal dgam313 = tmp_dgam(0,2)(2); const vreal dgam322 = tmp_dgam(1,1)(2); const vreal dgam323 = tmp_dgam(1,2)(2); const vreal dgam333 = tmp_dgam(2,2)(2); -const vreal dexK111 = tmp_dexK(0,0)(0); const vreal dexK112 = tmp_dexK(0,1)(0); const vreal dexK113 = tmp_dexK(0,2)(0); const vreal dexK122 = tmp_dexK(1,1)(0); @@ -80,7 +79,6 @@ const vreal dexK133 = tmp_dexK(2,2)(0); const vreal dexK211 = tmp_dexK(0,0)(1); const vreal dexK212 = tmp_dexK(0,1)(1); const vreal dexK213 = tmp_dexK(0,2)(1); -const vreal dexK222 = tmp_dexK(1,1)(1); const vreal dexK223 = tmp_dexK(1,2)(1); const vreal dexK233 = tmp_dexK(2,2)(1); const vreal dexK311 = tmp_dexK(0,0)(2); @@ -88,7 +86,6 @@ const vreal dexK312 = tmp_dexK(0,1)(2); const vreal dexK313 = tmp_dexK(0,2)(2); const vreal dexK322 = tmp_dexK(1,1)(2); const vreal dexK323 = tmp_dexK(1,2)(2); -const vreal dexK333 = tmp_dexK(2,2)(2); const vreal ddgam1111 = tmp_ddgam(0,0)(0,0); const vreal ddgam1112 = tmp_ddgam(0,1)(0,0); const vreal ddgam1113 = tmp_ddgam(0,2)(0,0); diff --git a/ADMconstraints/wolfram/ADM_set_constraint.wl b/ADMconstraints/wolfram/ADM_set_constraint.wl index 61881bd2..4fc5498c 100644 --- a/ADMconstraints/wolfram/ADM_set_constraint.wl +++ b/ADMconstraints/wolfram/ADM_set_constraint.wl @@ -56,18 +56,35 @@ $MainPrint[] := PrintInitializations[{Mode -> "MainIn", StorageType -> "Tile"}, ADMVarlist]; PrintInitializations[{Mode -> "MainIn", StorageType -> "Tile", TensorType -> "Vect"}, - dADMVarlist]; + Drop[dADMVarlist, {-1}]]; + + (* treat dexK separately *) + Module[{printdK, varname, symmetry, printname}, + {varname, symmetry, printname} = ParseVar[dADMVarlist[[-1]]]; + printdK[kk_, ii_, jj_] := PrintComponentInitialization[{varname, symmetry}, dexK[{kk, -GetDefaultChart[]}, {ii, -GetDefaultChart[]}, {jj, -GetDefaultChart[]}]]; + SetParsePrintCompInitMode[MainIn -> True]; + SetParsePrintCompInitStorageType[Tile -> True]; + SetParsePrintCompInitTensorType[Vect -> True]; + Do[If[ii != jj || ii != kk || jj != kk, printdK[kk, ii, jj]], {kk, 1, 3}, {ii, 1, 3}, {jj, ii, 3}] + CleanParsePrintCompInitStorageType[]; + CleanParsePrintCompInitTensorType[]; + CleanParsePrintCompInitMode[]; + ]; + PrintInitializations[{Mode -> "MainIn", StorageType -> "Tile", TensorType -> "Smat"}, ddADMVarlist]; pr[]; PrintEquations[{Mode -> "Temp"}, Drop[IntermediateVarlist, {-1}]]; pr[]; + (* treat DexK separately *) Module[{printDK}, printDK[kk_, ii_, jj_] := PrintComponentEquation[GetDefaultChart[], DexK[{kk, -GetDefaultChart[]}, {ii, -GetDefaultChart[]}, {jj, -GetDefaultChart[]}]]; SetParsePrintCompEQNMode[{NewVar -> True}]; Do[If[ii != jj || ii != kk || jj != kk, printDK[kk, ii, jj]], {kk, 1, 3}, {ii, 1, 3}, {jj, ii, 3}] + CleanParsePrintCompEQNMode[]; ]; + pr[]; PrintEquations[{Mode -> "Temp"}, MatterVarlist]; pr[]; From d8d0af19f25e65e8de1c4bca7e31607f4c250a90 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Wed, 20 Nov 2024 10:43:45 -0500 Subject: [PATCH 30/37] ADMconstraints: add lapse mask --- ADMconstraints/param.ccl | 9 +++++++++ ADMconstraints/schedule.ccl | 13 +++++++++++++ ADMconstraints/src/lapsemask.cxx | 27 +++++++++++++++++++++++++++ ADMconstraints/src/make.code.defn | 3 ++- 4 files changed, 51 insertions(+), 1 deletion(-) create mode 100644 ADMconstraints/src/lapsemask.cxx diff --git a/ADMconstraints/param.ccl b/ADMconstraints/param.ccl index 82a0491a..dadc6c36 100644 --- a/ADMconstraints/param.ccl +++ b/ADMconstraints/param.ccl @@ -11,3 +11,12 @@ CCTK_INT deriv_order "Order of spatial finite differencing" STEERABLE=never 6 :: "Sixth order finite difference" 8 :: "Eighth order finite difference" } 4 + +BOOLEAN use_lapse_mask "Exclude the region when lapse is small" STEERABLE=recover +{ +} yes + +CCTK_REAL lapse_mask_cutoff "Exclude the regin when lapse is smaller then the cutoff" STEERABLE=always +{ + *:* :: "" +} 0.3 diff --git a/ADMconstraints/schedule.ccl b/ADMconstraints/schedule.ccl index 952c34d3..dacac6c2 100644 --- a/ADMconstraints/schedule.ccl +++ b/ADMconstraints/schedule.ccl @@ -24,5 +24,18 @@ if (calc_constraints) { READS: TmunuBaseX::eTij(interior) WRITES: HC(interior) WRITES: MC(interior) + SYNC: HC MC } "Calculate ADM Constraints" + + if (use_lapse_mask) { + SCHEDULE ADMconstraints_LapseMask IN ADMconstraints_AnalysisGroup AFTER ADMconstraints_CalcConstraints + { + LANG: C + READS: ADMBaseX::lapse(interior) + READS: HC(interior) + READS: MC(interior) + WRITES: HC(interior) + WRITES: MC(interior) + } "Apply lapse mask" + } } diff --git a/ADMconstraints/src/lapsemask.cxx b/ADMconstraints/src/lapsemask.cxx new file mode 100644 index 00000000..e298891e --- /dev/null +++ b/ADMconstraints/src/lapsemask.cxx @@ -0,0 +1,27 @@ +#include + +#include +#include + +namespace ADMconstraints { +using namespace Arith; +using namespace Loop; + +extern "C" void ADMconstraints_LapseMask(CCTK_ARGUMENTS) { + DECLARE_CCTK_ARGUMENTSX_ADMconstraints_LapseMask; + DECLARE_CCTK_PARAMETERS; + + const CCTK_REAL local_cutoff = lapse_mask_cutoff; + + grid.loop_int_device<0, 0, 0>( + grid.nghostzones, [=] ARITH_DEVICE(const PointDesc &p) ARITH_INLINE { + if (alp(p.I) < local_cutoff) { + HC(p.I) = 0.0; + MCx(p.I) = 0.0; + MCy(p.I) = 0.0; + MCz(p.I) = 0.0; + } + }); +} + +} // namespace ADMconstraints diff --git a/ADMconstraints/src/make.code.defn b/ADMconstraints/src/make.code.defn index 6ad5ed87..c027665f 100644 --- a/ADMconstraints/src/make.code.defn +++ b/ADMconstraints/src/make.code.defn @@ -2,7 +2,8 @@ # Source files in this directory SRCS = \ - admconstraints.cxx + admconstraints.cxx \ + lapsemask.cxx # Subdirectories containing source files SUBDIRS = From 6026cf28c1bc3d2720a38f77bab892d67364a349 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Wed, 20 Nov 2024 11:08:30 -0500 Subject: [PATCH 31/37] ADMconstraints: add extra SYNCs --- ADMconstraints/schedule.ccl | 14 ++++++++++++-- ADMconstraints/src/admconstraints.cxx | 4 ++++ 2 files changed, 16 insertions(+), 2 deletions(-) diff --git a/ADMconstraints/schedule.ccl b/ADMconstraints/schedule.ccl index dacac6c2..5cff5d09 100644 --- a/ADMconstraints/schedule.ccl +++ b/ADMconstraints/schedule.ccl @@ -12,7 +12,17 @@ SCHEDULE GROUP ADMconstraints_AnalysisGroup AT analysis if (calc_constraints) { - SCHEDULE ADMconstraints_CalcConstraints IN ADMconstraints_AnalysisGroup + SCHEDULE ADMconstraints_Sync IN ADMconstraints_AnalysisGroup + { + LANG: C + OPTIONS: global + SYNC: ADMBaseX::metric + SYNC: ADMBaseX::curv + SYNC: ADMBaseX::lapse + SYNC: ADMBaseX::shift + } "Synchronize" + + SCHEDULE ADMconstraints_CalcConstraints IN ADMconstraints_AnalysisGroup AFTER ADMconstraints_Sync { LANG: C READS: ADMBaseX::metric(everywhere) @@ -24,7 +34,6 @@ if (calc_constraints) { READS: TmunuBaseX::eTij(interior) WRITES: HC(interior) WRITES: MC(interior) - SYNC: HC MC } "Calculate ADM Constraints" if (use_lapse_mask) { @@ -36,6 +45,7 @@ if (calc_constraints) { READS: MC(interior) WRITES: HC(interior) WRITES: MC(interior) + SYNC: HC MC } "Apply lapse mask" } } diff --git a/ADMconstraints/src/admconstraints.cxx b/ADMconstraints/src/admconstraints.cxx index e51a7eb2..18abbc2f 100644 --- a/ADMconstraints/src/admconstraints.cxx +++ b/ADMconstraints/src/admconstraints.cxx @@ -29,6 +29,10 @@ CCTK_DEVICE CCTK_HOST CCTK_ATTRIBUTE_ALWAYS_INLINE inline T Power(T x, int y) { return (y == 2) ? Arith::pow2(x) : Arith::pown(x, y); } +extern "C" void ADMconstraints_Sync(CCTK_ARGUMENTS) { + // do nothing +} + extern "C" void ADMconstraints_CalcConstraints(CCTK_ARGUMENTS) { DECLARE_CCTK_ARGUMENTSX_ADMconstraints_CalcConstraints; DECLARE_CCTK_PARAMETERS; From 1dd4228ce6e9d6e8810650d0397807df4ff49a49 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Sat, 23 Nov 2024 20:41:00 -0500 Subject: [PATCH 32/37] ADMconstraints: fix comments in schedule --- ADMconstraints/schedule.ccl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/ADMconstraints/schedule.ccl b/ADMconstraints/schedule.ccl index 5cff5d09..added4d5 100644 --- a/ADMconstraints/schedule.ccl +++ b/ADMconstraints/schedule.ccl @@ -8,7 +8,7 @@ STORAGE: MC SCHEDULE GROUP ADMconstraints_AnalysisGroup AT analysis { -} "Analyse Z4c variables" +} "Analyse ADM variables" if (calc_constraints) { From 56d5bc085132293aa1e9a5ea173786dad1bff9af Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Wed, 25 Dec 2024 00:51:33 -0500 Subject: [PATCH 33/37] ADMconstraints: add par lapse_mask_outer_radius --- ADMconstraints/param.ccl | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/ADMconstraints/param.ccl b/ADMconstraints/param.ccl index dadc6c36..a07cf66b 100644 --- a/ADMconstraints/param.ccl +++ b/ADMconstraints/param.ccl @@ -16,7 +16,12 @@ BOOLEAN use_lapse_mask "Exclude the region when lapse is small" STEERABLE=recove { } yes -CCTK_REAL lapse_mask_cutoff "Exclude the regin when lapse is smaller then the cutoff" STEERABLE=always +CCTK_REAL lapse_mask_cutoff "Exclude the region when lapse is smaller than the cutoff" STEERABLE=always { *:* :: "" } 0.3 + +CCTK_REAL lapse_mask_outer_radius "Exclude the region when the distance to the origin is larger than the radius" STEERABLE=always +{ + *:* :: "" +} 30 From e1be122de753db7d59ede3ee010e27cfb588726a Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Wed, 25 Dec 2024 00:58:19 -0500 Subject: [PATCH 34/37] ADMconstraints: mask out region which is larger than a radius --- ADMconstraints/src/lapsemask.cxx | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/ADMconstraints/src/lapsemask.cxx b/ADMconstraints/src/lapsemask.cxx index e298891e..ef9d2fd2 100644 --- a/ADMconstraints/src/lapsemask.cxx +++ b/ADMconstraints/src/lapsemask.cxx @@ -12,10 +12,12 @@ extern "C" void ADMconstraints_LapseMask(CCTK_ARGUMENTS) { DECLARE_CCTK_PARAMETERS; const CCTK_REAL local_cutoff = lapse_mask_cutoff; + const CCTK_REAL local_outer_radius = lapse_mask_outer_radius; grid.loop_int_device<0, 0, 0>( grid.nghostzones, [=] ARITH_DEVICE(const PointDesc &p) ARITH_INLINE { - if (alp(p.I) < local_cutoff) { + const CCTK_REAL rad = sqrt(p.x * p.x + p.y * p.y + p.z * p.z); + if (alp(p.I) < local_cutoff && rad > local_outer_radius) { HC(p.I) = 0.0; MCx(p.I) = 0.0; MCy(p.I) = 0.0; From 3fa4e9e95f24c557d9b525633f09dc31da69505a Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Wed, 25 Dec 2024 10:16:12 -0500 Subject: [PATCH 35/37] ADMconstraints: fix type of default value for lapse_mask_outer_radius --- ADMconstraints/param.ccl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/ADMconstraints/param.ccl b/ADMconstraints/param.ccl index a07cf66b..a0cc7bd3 100644 --- a/ADMconstraints/param.ccl +++ b/ADMconstraints/param.ccl @@ -24,4 +24,4 @@ CCTK_REAL lapse_mask_cutoff "Exclude the region when lapse is smaller than the c CCTK_REAL lapse_mask_outer_radius "Exclude the region when the distance to the origin is larger than the radius" STEERABLE=always { *:* :: "" -} 30 +} 30.0 From 6e1abbed04cbc6b14bdeb8c232c9d24d65ce8df7 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Wed, 25 Dec 2024 10:17:11 -0500 Subject: [PATCH 36/37] ADMconstraints: use or instead of and when apply mask --- ADMconstraints/src/lapsemask.cxx | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/ADMconstraints/src/lapsemask.cxx b/ADMconstraints/src/lapsemask.cxx index ef9d2fd2..a344c887 100644 --- a/ADMconstraints/src/lapsemask.cxx +++ b/ADMconstraints/src/lapsemask.cxx @@ -17,7 +17,7 @@ extern "C" void ADMconstraints_LapseMask(CCTK_ARGUMENTS) { grid.loop_int_device<0, 0, 0>( grid.nghostzones, [=] ARITH_DEVICE(const PointDesc &p) ARITH_INLINE { const CCTK_REAL rad = sqrt(p.x * p.x + p.y * p.y + p.z * p.z); - if (alp(p.I) < local_cutoff && rad > local_outer_radius) { + if (alp(p.I) < local_cutoff || rad > local_outer_radius) { HC(p.I) = 0.0; MCx(p.I) = 0.0; MCy(p.I) = 0.0; From c5dab75d3fcd3e8a51b368a3988b770aa2f54006 Mon Sep 17 00:00:00 2001 From: Liwei Ji Date: Wed, 25 Dec 2024 11:40:34 -0500 Subject: [PATCH 37/37] ADMconstraints: sync HC and MC after calculation --- ADMconstraints/schedule.ccl | 1 + 1 file changed, 1 insertion(+) diff --git a/ADMconstraints/schedule.ccl b/ADMconstraints/schedule.ccl index added4d5..84a550d4 100644 --- a/ADMconstraints/schedule.ccl +++ b/ADMconstraints/schedule.ccl @@ -34,6 +34,7 @@ if (calc_constraints) { READS: TmunuBaseX::eTij(interior) WRITES: HC(interior) WRITES: MC(interior) + SYNC: HC MC } "Calculate ADM Constraints" if (use_lapse_mask) {