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AngularMomentumTensor.wl
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(* ::Package:: *)
AngularMomentumTensor[(stressEnergyTensor_)[(metricTensor_)[metricMatrixRepresentation_List, coordinates_List,
metricIndex1_, metricIndex2_], matrixRepresentation_List, index1_, index2_]] :=
AngularMomentumTensor[StressEnergyTensor[MetricTensor[metricMatrixRepresentation, coordinates, metricIndex1,
metricIndex2], matrixRepresentation, index1, index2], (Superscript["\[FormalCapitalX]", ToString[#1]] & ) /@
Range[Length[coordinates]], "\[PartialD]\[FormalCapitalOmega]", (Subscript["\[FormalD]\[FormalCapitalSigma]", ToString[coordinates[[#1]], StandardForm]] & ) /@
Range[Length[coordinates]], False, False] /; SymbolName[stressEnergyTensor] === "StressEnergyTensor" &&
SymbolName[metricTensor] === "MetricTensor" && Length[Dimensions[metricMatrixRepresentation]] == 2 &&
Length[coordinates] == Length[metricMatrixRepresentation] && BooleanQ[metricIndex1] && BooleanQ[metricIndex2] &&
Length[Dimensions[matrixRepresentation]] == 2 && Length[coordinates] == Length[matrixRepresentation] &&
BooleanQ[index1] && BooleanQ[index2]
AngularMomentumTensor[(stressEnergyTensor_)[(metricTensor_)[metricMatrixRepresentation_List, coordinates_List,
metricIndex1_, metricIndex2_], matrixRepresentation_List, stressEnergyIndex1_, stressEnergyIndex2_], index1_,
index2_] := AngularMomentumTensor[StressEnergyTensor[MetricTensor[metricMatrixRepresentation, coordinates,
metricIndex1, metricIndex2], matrixRepresentation, stressEnergyIndex1, stressEnergyIndex2],
(Superscript["\[FormalCapitalX]", ToString[#1]] & ) /@ Range[Length[coordinates]], "\[PartialD]\[FormalCapitalOmega]",
(Subscript["\[FormalD]\[FormalCapitalSigma]", ToString[coordinates[[#1]], StandardForm]] & ) /@ Range[Length[coordinates]], index1, index2] /;
SymbolName[stressEnergyTensor] === "StressEnergyTensor" && SymbolName[metricTensor] === "MetricTensor" &&
Length[Dimensions[metricMatrixRepresentation]] == 2 && Length[coordinates] == Length[metricMatrixRepresentation] &&
BooleanQ[metricIndex1] && BooleanQ[metricIndex2] && Length[Dimensions[matrixRepresentation]] == 2 &&
Length[coordinates] == Length[matrixRepresentation] && BooleanQ[stressEnergyIndex1] &&
BooleanQ[stressEnergyIndex2] && BooleanQ[index1] && BooleanQ[index2]
AngularMomentumTensor[(stressEnergyTensor_)[(metricTensor_)[metricMatrixRepresentation_List, coordinates_List,
metricIndex1_, metricIndex2_], matrixRepresentation_List, index1_, index2_], positionVector_List] :=
AngularMomentumTensor[StressEnergyTensor[MetricTensor[metricMatrixRepresentation, coordinates, metricIndex1,
metricIndex2], matrixRepresentation, index1, index2], positionVector, "\[PartialD]\[FormalCapitalOmega]",
(Subscript["\[FormalD]\[FormalCapitalSigma]", ToString[coordinates[[#1]], StandardForm]] & ) /@ Range[Length[coordinates]], False, False] /;
SymbolName[stressEnergyTensor] === "StressEnergyTensor" && SymbolName[metricTensor] === "MetricTensor" &&
Length[Dimensions[metricMatrixRepresentation]] == 2 && Length[coordinates] == Length[metricMatrixRepresentation] &&
BooleanQ[metricIndex1] && BooleanQ[metricIndex2] && Length[Dimensions[matrixRepresentation]] == 2 &&
Length[coordinates] == Length[matrixRepresentation] && BooleanQ[index1] && BooleanQ[index2] &&
Length[coordinates] == Length[positionVector]
AngularMomentumTensor[(stressEnergyTensor_)[(metricTensor_)[metricMatrixRepresentation_List, coordinates_List,
metricIndex1_, metricIndex2_], matrixRepresentation_List, stressEnergyIndex1_, stressEnergyIndex2_],
positionVector_List, index1_, index2_] :=
AngularMomentumTensor[StressEnergyTensor[MetricTensor[metricMatrixRepresentation, coordinates, metricIndex1,
metricIndex2], matrixRepresentation, stressEnergyIndex1, stressEnergyIndex2], positionVector, "\[PartialD]\[FormalCapitalOmega]",
(Subscript["\[FormalD]\[FormalCapitalSigma]", ToString[coordinates[[#1]], StandardForm]] & ) /@ Range[Length[coordinates]], index1, index2] /;
SymbolName[stressEnergyTensor] === "StressEnergyTensor" && SymbolName[metricTensor] === "MetricTensor" &&
Length[Dimensions[metricMatrixRepresentation]] == 2 && Length[coordinates] == Length[metricMatrixRepresentation] &&
BooleanQ[metricIndex1] && BooleanQ[metricIndex2] && Length[Dimensions[matrixRepresentation]] == 2 &&
Length[coordinates] == Length[matrixRepresentation] && BooleanQ[stressEnergyIndex1] &&
BooleanQ[stressEnergyIndex2] && Length[coordinates] == Length[positionVector] && BooleanQ[index1] && BooleanQ[index2]
AngularMomentumTensor[(stressEnergyTensor_)[(metricTensor_)[metricMatrixRepresentation_List, coordinates_List,
metricIndex1_, metricIndex2_], matrixRepresentation_List, index1_, index2_], positionVector_List,
spacetimeBoundary_] := AngularMomentumTensor[StressEnergyTensor[MetricTensor[metricMatrixRepresentation, coordinates,
metricIndex1, metricIndex2], matrixRepresentation, index1, index2], positionVector, spacetimeBoundary,
(Subscript["\[FormalD]\[FormalCapitalSigma]", ToString[coordinates[[#1]], StandardForm]] & ) /@ Range[Length[coordinates]], False, False] /;
SymbolName[stressEnergyTensor] === "StressEnergyTensor" && SymbolName[metricTensor] === "MetricTensor" &&
Length[Dimensions[metricMatrixRepresentation]] == 2 && Length[coordinates] == Length[metricMatrixRepresentation] &&
BooleanQ[metricIndex1] && BooleanQ[metricIndex2] && Length[Dimensions[matrixRepresentation]] == 2 &&
Length[coordinates] == Length[matrixRepresentation] && BooleanQ[index1] && BooleanQ[index2] &&
Length[coordinates] == Length[positionVector]
AngularMomentumTensor[(stressEnergyTensor_)[(metricTensor_)[metricMatrixRepresentation_List, coordinates_List,
metricIndex1_, metricIndex2_], matrixRepresentation_List, stressEnergyIndex1_, stressEnergyIndex2_],
positionVector_List, spacetimeBoundary_, index1_, index2_] :=
AngularMomentumTensor[StressEnergyTensor[MetricTensor[metricMatrixRepresentation, coordinates, metricIndex1,
metricIndex2], matrixRepresentation, stressEnergyIndex1, stressEnergyIndex2], positionVector, spacetimeBoundary,
(Subscript["\[FormalD]\[FormalCapitalSigma]", ToString[coordinates[[#1]], StandardForm]] & ) /@ Range[Length[coordinates]], index1, index2] /;
SymbolName[stressEnergyTensor] === "StressEnergyTensor" && SymbolName[metricTensor] === "MetricTensor" &&
Length[Dimensions[metricMatrixRepresentation]] == 2 && Length[coordinates] == Length[metricMatrixRepresentation] &&
BooleanQ[metricIndex1] && BooleanQ[metricIndex2] && Length[Dimensions[matrixRepresentation]] == 2 &&
Length[coordinates] == Length[matrixRepresentation] && BooleanQ[stressEnergyIndex1] &&
BooleanQ[stressEnergyIndex2] && Length[coordinates] == Length[positionVector] && BooleanQ[index1] && BooleanQ[index2]
AngularMomentumTensor[(stressEnergyTensor_)[(metricTensor_)[metricMatrixRepresentation_List, coordinates_List,
metricIndex1_, metricIndex2_], matrixRepresentation_List, index1_, index2_], positionVector_List,
spacetimeBoundary_, volumeOneForm_List] :=
AngularMomentumTensor[StressEnergyTensor[MetricTensor[metricMatrixRepresentation, coordinates, metricIndex1,
metricIndex2], matrixRepresentation, index1, index2], positionVector, spacetimeBoundary, volumeOneForm, False,
False] /; SymbolName[stressEnergyTensor] === "StressEnergyTensor" && SymbolName[metricTensor] === "MetricTensor" &&
Length[Dimensions[metricMatrixRepresentation]] == 2 && Length[coordinates] == Length[metricMatrixRepresentation] &&
BooleanQ[metricIndex1] && BooleanQ[metricIndex2] && Length[Dimensions[matrixRepresentation]] == 2 &&
Length[coordinates] == Length[matrixRepresentation] && BooleanQ[index1] && BooleanQ[index2] &&
Length[coordinates] == Length[positionVector]
AngularMomentumTensor[(stressEnergyTensor_)[(metricTensor_)[metricMatrixRepresentation_List, coordinates_List,
metricIndex1_, metricIndex2_], matrixRepresentation_List, stressEnergyIndex1_, stressEnergyIndex2_],
positionVector_List, spacetimeBoundary_, volumeOneForm_List, index1_, index2_]["MatrixRepresentation"] :=
Module[{newMetricMatrixRepresentation, newCoordinates, newMatrixRepresentation, angularMomentumDensityTensor,
angularMomentumTensor}, newMetricMatrixRepresentation = metricMatrixRepresentation /.
(#1 -> ToExpression[#1] & ) /@ Select[coordinates, StringQ];
newCoordinates = coordinates /. (#1 -> ToExpression[#1] & ) /@ Select[coordinates, StringQ];
newMatrixRepresentation = matrixRepresentation /. (#1 -> ToExpression[#1] & ) /@ Select[coordinates, StringQ];
angularMomentumDensityTensor =
Normal[SparseArray[(Module[{index = #1}, index -> (newCoordinates[[index[[1]]]] - positionVector[[index[[1]]]])*
newMatrixRepresentation[[index[[2]],index[[3]]]] - (newCoordinates[[index[[2]]]] - positionVector[[
index[[2]]]])*newMatrixRepresentation[[index[[1]],index[[3]]]]] & ) /@
Tuples[Range[Length[newMetricMatrixRepresentation]], 3]]]; angularMomentumTensor =
Normal[SparseArray[(Module[{index = #1}, index -> Quiet[Integrate[Total[(angularMomentumDensityTensor[[index[[1]],
index[[2]],#1]]*volumeOneForm[[#1]] & ) /@ Range[Length[newMetricMatrixRepresentation]]], Element[
newCoordinates, spacetimeBoundary]]]] & ) /@ Tuples[Range[Length[newMetricMatrixRepresentation]], 2]]] /.
(#1 -> ToExpression[#1] & ) /@ Select[coordinates, StringQ]; If[index1 === True && index2 === True,
Normal[SparseArray[(Module[{index = #1}, index -> Total[(metricMatrixRepresentation[[First[index],First[#1]]]*
metricMatrixRepresentation[[Last[#1],Last[index]]]*angularMomentumTensor[[First[#1],Last[#1]]] & ) /@
Tuples[Range[Length[metricMatrixRepresentation]], 2]]] & ) /@
Tuples[Range[Length[metricMatrixRepresentation]], 2]]], If[index1 === False && index2 === False,
angularMomentumTensor, If[index1 === True && index2 === False,
Normal[SparseArray[(Module[{index = #1}, index -> Total[(metricMatrixRepresentation[[First[index],#1]]*
angularMomentumTensor[[#1,Last[index]]] & ) /@ Range[Length[metricMatrixRepresentation]]]] & ) /@
Tuples[Range[Length[metricMatrixRepresentation]], 2]]], If[index1 === False && index2 === True,
Normal[SparseArray[(Module[{index = #1}, index -> Total[(metricMatrixRepresentation[[#1,Last[index]]]*
angularMomentumTensor[[First[index],#1]] & ) /@ Range[Length[metricMatrixRepresentation]]]] & ) /@
Tuples[Range[Length[metricMatrixRepresentation]], 2]]], Indeterminate]]]]] /;
SymbolName[stressEnergyTensor] === "StressEnergyTensor" && SymbolName[metricTensor] === "MetricTensor" &&
Length[Dimensions[metricMatrixRepresentation]] == 2 && Length[coordinates] == Length[metricMatrixRepresentation] &&
BooleanQ[metricIndex1] && BooleanQ[metricIndex2] && Length[Dimensions[matrixRepresentation]] == 2 &&
Length[coordinates] == Length[matrixRepresentation] && BooleanQ[stressEnergyIndex1] &&
BooleanQ[stressEnergyIndex2] && Length[coordinates] == Length[positionVector] &&
Length[coordinates] == Length[volumeOneForm] && BooleanQ[index1] && BooleanQ[index2]
AngularMomentumTensor[(stressEnergyTensor_)[(metricTensor_)[metricMatrixRepresentation_List, coordinates_List,
metricIndex1_, metricIndex2_], matrixRepresentation_List, stressEnergyIndex1_, stressEnergyIndex2_],
positionVector_List, spacetimeBoundary_, volumeOneForm_List, index1_, index2_]["ReducedMatrixRepresentation"] :=
Module[{newMetricMatrixRepresentation, newCoordinates, newMatrixRepresentation, angularMomentumDensityTensor,
angularMomentumTensor}, newMetricMatrixRepresentation = metricMatrixRepresentation /.
(#1 -> ToExpression[#1] & ) /@ Select[coordinates, StringQ];
newCoordinates = coordinates /. (#1 -> ToExpression[#1] & ) /@ Select[coordinates, StringQ];
newMatrixRepresentation = matrixRepresentation /. (#1 -> ToExpression[#1] & ) /@ Select[coordinates, StringQ];
angularMomentumDensityTensor =
Normal[SparseArray[(Module[{index = #1}, index -> (newCoordinates[[index[[1]]]] - positionVector[[index[[1]]]])*
newMatrixRepresentation[[index[[2]],index[[3]]]] - (newCoordinates[[index[[2]]]] - positionVector[[
index[[2]]]])*newMatrixRepresentation[[index[[1]],index[[3]]]]] & ) /@
Tuples[Range[Length[newMetricMatrixRepresentation]], 3]]]; angularMomentumTensor =
Normal[SparseArray[(Module[{index = #1}, index -> Quiet[Integrate[Total[(angularMomentumDensityTensor[[index[[1]],
index[[2]],#1]]*volumeOneForm[[#1]] & ) /@ Range[Length[newMetricMatrixRepresentation]]], Element[
newCoordinates, spacetimeBoundary]]]] & ) /@ Tuples[Range[Length[newMetricMatrixRepresentation]], 2]]] /.
(#1 -> ToExpression[#1] & ) /@ Select[coordinates, StringQ]; If[index1 === True && index2 === True,
FullSimplify[Normal[SparseArray[(Module[{index = #1}, index -> Total[(metricMatrixRepresentation[[First[index],
First[#1]]]*metricMatrixRepresentation[[Last[#1],Last[index]]]*angularMomentumTensor[[First[#1],
Last[#1]]] & ) /@ Tuples[Range[Length[metricMatrixRepresentation]], 2]]] & ) /@
Tuples[Range[Length[metricMatrixRepresentation]], 2]]]], If[index1 === False && index2 === False,
FullSimplify[angularMomentumTensor], If[index1 === True && index2 === False,
FullSimplify[Normal[SparseArray[(Module[{index = #1}, index -> Total[(metricMatrixRepresentation[[First[index],
#1]]*angularMomentumTensor[[#1,Last[index]]] & ) /@ Range[Length[
metricMatrixRepresentation]]]] & ) /@ Tuples[Range[Length[metricMatrixRepresentation]], 2]]]],
If[index1 === False && index2 === True, FullSimplify[
Normal[SparseArray[(Module[{index = #1}, index -> Total[(metricMatrixRepresentation[[#1,Last[index]]]*
angularMomentumTensor[[First[index],#1]] & ) /@ Range[Length[metricMatrixRepresentation]]]] & ) /@
Tuples[Range[Length[metricMatrixRepresentation]], 2]]]], Indeterminate]]]]] /;
SymbolName[stressEnergyTensor] === "StressEnergyTensor" && SymbolName[metricTensor] === "MetricTensor" &&
Length[Dimensions[metricMatrixRepresentation]] == 2 && Length[coordinates] == Length[metricMatrixRepresentation] &&
BooleanQ[metricIndex1] && BooleanQ[metricIndex2] && Length[Dimensions[matrixRepresentation]] == 2 &&
Length[coordinates] == Length[matrixRepresentation] && BooleanQ[stressEnergyIndex1] &&
BooleanQ[stressEnergyIndex2] && Length[coordinates] == Length[positionVector] &&
Length[coordinates] == Length[volumeOneForm] && BooleanQ[index1] && BooleanQ[index2]
AngularMomentumTensor[(stressEnergyTensor_)[(metricTensor_)[metricMatrixRepresentation_List, coordinates_List,
metricIndex1_, metricIndex2_], matrixRepresentation_List, stressEnergyIndex1_, stressEnergyIndex2_],
positionVector_List, spacetimeBoundary_, volumeOneForm_List, index1_, index2_]["SymbolicMatrixRepresentation"] :=
Module[{newMetricMatrixRepresentation, newCoordinates, newMatrixRepresentation, angularMomentumDensityTensor,
angularMomentumTensor}, newMetricMatrixRepresentation = metricMatrixRepresentation /.
(#1 -> ToExpression[#1] & ) /@ Select[coordinates, StringQ];
newCoordinates = coordinates /. (#1 -> ToExpression[#1] & ) /@ Select[coordinates, StringQ];
newMatrixRepresentation = matrixRepresentation /. (#1 -> ToExpression[#1] & ) /@ Select[coordinates, StringQ];
angularMomentumDensityTensor =
Normal[SparseArray[(Module[{index = #1}, index -> (newCoordinates[[index[[1]]]] - positionVector[[index[[1]]]])*
newMatrixRepresentation[[index[[2]],index[[3]]]] - (newCoordinates[[index[[2]]]] - positionVector[[
index[[2]]]])*newMatrixRepresentation[[index[[1]],index[[3]]]]] & ) /@
Tuples[Range[Length[newMetricMatrixRepresentation]], 3]]]; angularMomentumTensor =
Normal[SparseArray[(Module[{index = #1}, index -> Quiet[Inactive[Integrate][Total[
(angularMomentumDensityTensor[[index[[1]],index[[2]],#1]]*volumeOneForm[[#1]] & ) /@
Range[Length[newMetricMatrixRepresentation]]], Element[newCoordinates, spacetimeBoundary]]]] & ) /@
Tuples[Range[Length[newMetricMatrixRepresentation]], 2]]] /. (#1 -> ToExpression[#1] & ) /@
Select[coordinates, StringQ]; If[index1 === True && index2 === True,
Normal[SparseArray[(Module[{index = #1}, index -> Total[(metricMatrixRepresentation[[First[index],First[#1]]]*
metricMatrixRepresentation[[Last[#1],Last[index]]]*angularMomentumTensor[[First[#1],Last[#1]]] & ) /@
Tuples[Range[Length[metricMatrixRepresentation]], 2]]] & ) /@
Tuples[Range[Length[metricMatrixRepresentation]], 2]]], If[index1 === False && index2 === False,
angularMomentumTensor, If[index1 === True && index2 === False,
Normal[SparseArray[(Module[{index = #1}, index -> Total[(metricMatrixRepresentation[[First[index],#1]]*
angularMomentumTensor[[#1,Last[index]]] & ) /@ Range[Length[metricMatrixRepresentation]]]] & ) /@
Tuples[Range[Length[metricMatrixRepresentation]], 2]]], If[index1 === False && index2 === True,
Normal[SparseArray[(Module[{index = #1}, index -> Total[(metricMatrixRepresentation[[#1,Last[index]]]*
angularMomentumTensor[[First[index],#1]] & ) /@ Range[Length[metricMatrixRepresentation]]]] & ) /@
Tuples[Range[Length[metricMatrixRepresentation]], 2]]], Indeterminate]]]]] /;
SymbolName[stressEnergyTensor] === "StressEnergyTensor" && SymbolName[metricTensor] === "MetricTensor" &&
Length[Dimensions[metricMatrixRepresentation]] == 2 && Length[coordinates] == Length[metricMatrixRepresentation] &&
BooleanQ[metricIndex1] && BooleanQ[metricIndex2] && Length[Dimensions[matrixRepresentation]] == 2 &&
Length[coordinates] == Length[matrixRepresentation] && BooleanQ[stressEnergyIndex1] &&
BooleanQ[stressEnergyIndex2] && Length[coordinates] == Length[positionVector] &&
Length[coordinates] == Length[volumeOneForm] && BooleanQ[index1] && BooleanQ[index2]
AngularMomentumTensor[(stressEnergyTensor_)[(metricTensor_)[metricMatrixRepresentation_List, coordinates_List,
metricIndex1_, metricIndex2_], matrixRepresentation_List, stressEnergyIndex1_, stressEnergyIndex2_],
positionVector_List, spacetimeBoundary_, volumeOneForm_List, index1_, index2_]["Symbol"] :=
If[index1 === True && index2 === True, Subscript["\[FormalCapitalM]", "\[FormalMu]\[FormalNu]"], If[index1 === False && index2 === False,
Superscript["\[FormalCapitalM]", "\[FormalMu]\[FormalNu]"], If[index1 === True && index2 === False, Subsuperscript["\[FormalCapitalM]", "\[FormalMu]", "\[FormalNu]"],
If[index1 === False && index2 === True, Subsuperscript["\[FormalCapitalM]", "\[FormalNu]", "\[FormalMu]"], Indeterminate]]]] /;
SymbolName[stressEnergyTensor] === "StressEnergyTensor" && SymbolName[metricTensor] === "MetricTensor" &&
Length[Dimensions[metricMatrixRepresentation]] == 2 && Length[coordinates] == Length[metricMatrixRepresentation] &&
BooleanQ[metricIndex1] && BooleanQ[metricIndex2] && Length[Dimensions[matrixRepresentation]] == 2 &&
Length[coordinates] == Length[matrixRepresentation] && BooleanQ[stressEnergyIndex1] &&
BooleanQ[stressEnergyIndex2] && Length[coordinates] == Length[positionVector] &&
Length[coordinates] == Length[volumeOneForm] && BooleanQ[index1] && BooleanQ[index2]
AngularMomentumTensor /:
MakeBoxes[angularMomentumTensor:AngularMomentumTensor[(stressEnergyTensor_)[
(metricTensor_)[metricMatrixRepresentation_List, coordinates_List, metricIndex1_, metricIndex2_],
matrixRepresentation_List, stressEnergyIndex1_, stressEnergyIndex2_], positionVector_List, spacetimeBoundary_,
volumeOneForm_List, index1_, index2_], format_] :=
Module[{newMetricMatrixRepresentation, newCoordinates, newMatrixRepresentation, angularMomentumDensityTensor,
tensorRepresentation, matrixForm, type, symbol, dimensions, eigenvalues, positiveEigenvalues, negativeEigenvalues,
signature, icon}, newMetricMatrixRepresentation = metricMatrixRepresentation /. (#1 -> ToExpression[#1] & ) /@
Select[coordinates, StringQ]; newCoordinates = coordinates /. (#1 -> ToExpression[#1] & ) /@
Select[coordinates, StringQ]; newMatrixRepresentation = matrixRepresentation /.
(#1 -> ToExpression[#1] & ) /@ Select[coordinates, StringQ]; angularMomentumDensityTensor =
Normal[SparseArray[(Module[{index = #1}, index -> (newCoordinates[[index[[1]]]] - positionVector[[index[[1]]]])*
newMatrixRepresentation[[index[[2]],index[[3]]]] - (newCoordinates[[index[[2]]]] - positionVector[[
index[[2]]]])*newMatrixRepresentation[[index[[1]],index[[3]]]]] & ) /@
Tuples[Range[Length[newMetricMatrixRepresentation]], 3]]]; tensorRepresentation =
Normal[SparseArray[(Module[{index = #1}, index -> Quiet[Integrate[Total[(angularMomentumDensityTensor[[index[[1]],
index[[2]],#1]]*volumeOneForm[[#1]] & ) /@ Range[Length[newMetricMatrixRepresentation]]],
Element[newCoordinates, spacetimeBoundary]]]] & ) /@ Tuples[Range[Length[newMetricMatrixRepresentation]],
2]]] /. (#1 -> ToExpression[#1] & ) /@ Select[coordinates, StringQ]; If[index1 === True && index2 === True,
matrixForm = Normal[SparseArray[(Module[{index = #1}, index -> Total[(metricMatrixRepresentation[[First[index],
First[#1]]]*metricMatrixRepresentation[[Last[#1],Last[index]]]*tensorRepresentation[[First[#1],
Last[#1]]] & ) /@ Tuples[Range[Length[metricMatrixRepresentation]], 2]]] & ) /@
Tuples[Range[Length[metricMatrixRepresentation]], 2]]]; type = "Covariant";
symbol = Subscript["\[FormalCapitalM]", "\[FormalMu]\[FormalNu]"], If[index1 === False && index2 === False, matrixForm = tensorRepresentation;
type = "Contravariant"; symbol = Superscript["\[FormalCapitalM]", "\[FormalMu]\[FormalNu]"], If[index1 === True && index2 === False,
matrixForm = Normal[SparseArray[(Module[{index = #1}, index -> Total[(metricMatrixRepresentation[[First[index],
#1]]*tensorRepresentation[[#1,Last[index]]] & ) /@ Range[Length[
metricMatrixRepresentation]]]] & ) /@ Tuples[Range[Length[metricMatrixRepresentation]], 2]]];
type = "Mixed"; symbol = Subsuperscript["\[FormalCapitalM]", "\[FormalMu]", "\[FormalNu]"], If[index1 === False && index2 === True,
matrixForm = Normal[SparseArray[(Module[{index = #1}, index -> Total[(metricMatrixRepresentation[[#1,
Last[index]]]*tensorRepresentation[[First[index],#1]] & ) /@ Range[Length[
metricMatrixRepresentation]]]] & ) /@ Tuples[Range[Length[metricMatrixRepresentation]], 2]]];
type = "Mixed"; symbol = Subsuperscript["\[FormalCapitalM]", "\[FormalNu]", "\[FormalMu]"],
matrixForm = ConstantArray[Indeterminate, {Length[metricMatrixRepresentation],
Length[metricMatrixRepresentation]}]; type = Indeterminate; symbol = Indeterminate]]]];
dimensions = Length[metricMatrixRepresentation]; eigenvalues = Eigenvalues[metricMatrixRepresentation];
positiveEigenvalues = Select[eigenvalues, #1 > 0 & ]; negativeEigenvalues = Select[eigenvalues, #1 < 0 & ];
If[Length[positiveEigenvalues] + Length[negativeEigenvalues] == Length[metricMatrixRepresentation],
If[Length[positiveEigenvalues] == Length[metricMatrixRepresentation] || Length[negativeEigenvalues] ==
Length[metricMatrixRepresentation], signature = "Riemannian",
If[Length[positiveEigenvalues] == 1 || Length[negativeEigenvalues] == 1, signature = "Lorentzian",
signature = "Pseudo-Riemannian"]], signature = Indeterminate];
icon = MatrixPlot[matrixForm, ImageSize -> Dynamic[{Automatic, 3.5*(CurrentValue["FontCapHeight"]/
AbsoluteCurrentValue[Magnification])}], Frame -> False, FrameTicks -> None];
BoxForm`ArrangeSummaryBox["AngularMomentumTensor", angularMomentumTensor, icon,
{{BoxForm`SummaryItem[{"Type: ", type}], BoxForm`SummaryItem[{"Symbol: ", symbol}]},
{BoxForm`SummaryItem[{"Dimensions: ", dimensions}], BoxForm`SummaryItem[{"Signature: ", signature}]}},
{{BoxForm`SummaryItem[{"Coordinates: ", coordinates}]}}, format, "Interpretable" -> Automatic]] /;
SymbolName[stressEnergyTensor] === "StressEnergyTensor" && SymbolName[metricTensor] === "MetricTensor" &&
Length[Dimensions[metricMatrixRepresentation]] == 2 && Length[coordinates] == Length[metricMatrixRepresentation] &&
BooleanQ[metricIndex1] && BooleanQ[metricIndex2] && Length[Dimensions[matrixRepresentation]] == 2 &&
Length[coordinates] == Length[matrixRepresentation] && BooleanQ[stressEnergyIndex1] &&
BooleanQ[stressEnergyIndex2] && Length[coordinates] == Length[positionVector] &&
Length[coordinates] == Length[volumeOneForm] && BooleanQ[index1] && BooleanQ[index2]