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Added hacks to be able do define & canonicalize forms with symbolic degree. #6

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Added hacks to be able do define & canonicalize forms with symbolic degree. #6

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9 changes: 8 additions & 1 deletion xTerior.m
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -206,6 +206,10 @@
];


(* ::Input::Initialization:: *)
xAct`xTensor`Private`ToObject[xAct`xTensor`Private`AddedSign[(-1)^(deg_),expr_]]:=MapAt[xAct`xTensor`Private`VerbatimProduct[Times][(-1)^(deg),#1]&,xAct`xTensor`Private`ToObject[expr],1];


(* ::Input::Initialization:: *)
Wedge/:GradeOfProduct[Times,Wedge]=0;

Expand Down Expand Up @@ -407,7 +411,10 @@

(* ::Input::Initialization:: *)
DefDiffForm[form_,mani_,deg_,options___?OptionQ]:=
(DefTensor[form,mani,GradeOfTensor->{Wedge->deg},options];
(
(* Hack to be able to define forms with symbolic degree *)
xAct`xTensor`Private`checkgrade[Wedge->deg]:=Null;
DefTensor[form,mani,GradeOfTensor->{Wedge->deg},options]
)


Expand Down
95 changes: 66 additions & 29 deletions xTerior.nb
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -1346,6 +1346,35 @@ Cell[BoxData[
InitializationCell->
True,ExpressionUUID->"7b17f153-4083-4e03-bf8e-39832a80c04f"],

Cell["Hack to work with symbolic grades:", \
"Text",ExpressionUUID->"55a4bf37-309a-4574-b48e-0c68e7c8e18d"],

Cell[BoxData[
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RowBox[{"xAct`xTensor`Private`AddedSign", "[",
RowBox[{
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RowBox[{"-", "1"}], ")"}], "^",
RowBox[{"(", "deg_", ")"}]}], ",", "expr_"}], "]"}], "]"}], ":=",
RowBox[{"MapAt", "[",
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InitializationCell->
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Cell["Relation between Wedge and Times.", \
"Text",ExpressionUUID->"97f007db-ecca-4a86-9e6a-66f201f82378"],

Expand Down Expand Up @@ -1513,8 +1542,8 @@ Cell[BoxData[
"\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"$UseDimensionsQ", "=", "False"}], ";"}], "\n",
"\[IndentingNewLine]",
RowBox[{"$UseDimensionsQ", "=", "False"}], ";"}], "\[IndentingNewLine]",
"\n",
RowBox[{
RowBox[{"$DimensionsZeroForms", "=",
RowBox[{"{", "}"}]}], ";"}], "\n",
Expand All @@ -1541,8 +1570,8 @@ Cell[BoxData[
RowBox[{
RowBox[{"UnsetZeroForm", "[", "form_", "]"}], ":=",
RowBox[{"Unset", "[",
RowBox[{"form", "[", "___", "]"}], "]"}]}], ";"}], "\n",
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{"form", "[", "___", "]"}], "]"}]}], ";"}],
"\[IndentingNewLine]", "\[IndentingNewLine]", "\n",
RowBox[{
RowBox[{"UseDimensionStart", "[", "]"}], ":=",
RowBox[{"Module", "[",
Expand Down Expand Up @@ -1630,7 +1659,7 @@ Cell[BoxData[
RowBox[{"(",
RowBox[{"DimOfManifold", "/@",
RowBox[{"DependenciesOf", "[", "expr", "]"}]}], ")"}]}],
")"}]}], ")"}]}]}], ";"}]}], "]"}]}], "\[IndentingNewLine]", "\n",
")"}]}], ")"}]}]}], ";"}]}], "]"}]}], "\n", "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"UseDimensionStop", "[", "]"}], ":=",
Expand Down Expand Up @@ -1660,7 +1689,7 @@ Cell[BoxData[
RowBox[{"HoldPattern", "@",
RowBox[{"Diff", "[",
RowBox[{"expr_", ",", "covd_"}], "]"}]}], "=."}], ";"}]}], "]"}]}],
"\[IndentingNewLine]", "\n",
"\n", "\[IndentingNewLine]",
RowBox[{"(*", " ", "xTensions", " ", "*)"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
Expand All @@ -1675,8 +1704,8 @@ Cell[BoxData[
RowBox[{"tensor_", "[", "inds___", "]"}], ",", "__"}], "]"}], ":=",
RowBox[{"If", "[",
RowBox[{"$UseDimensionsQ", ",",
RowBox[{"SetZeroForm", "[", "tensor", "]"}]}], "]"}]}], ";"}],
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RowBox[{"SetZeroForm", "[", "tensor", "]"}]}], "]"}]}], ";"}], "\n",
"\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"xTension", "[",
Expand Down Expand Up @@ -1850,8 +1879,8 @@ Cell[BoxData[
RowBox[{"simplifyBasisWedge", "[", "expr_", "]"}], ":=",
RowBox[{"expr", "/.",
RowBox[{"wed_Wedge", "\[RuleDelayed]",
RowBox[{"simplifyBasisWedge1", "[", "wed", "]"}]}]}]}], ";"}], "\n",
"\[IndentingNewLine]",
RowBox[{"simplifyBasisWedge1", "[", "wed", "]"}]}]}]}], ";"}],
"\[IndentingNewLine]", "\n",
RowBox[{"(*",
RowBox[{
RowBox[{
Expand Down Expand Up @@ -1882,7 +1911,7 @@ Cell[BoxData[
RowBox[{"(",
RowBox[{"head", "/@",
RowBox[{"Sort", "[", "indices", "]"}]}], ")"}]}]}]}], "]"}]}],
";"}], "*)"}], "\n", "\[IndentingNewLine]",
";"}], "*)"}], "\[IndentingNewLine]", "\n",
RowBox[{
RowBox[{
RowBox[{"simplifyBasisWedge1", "[",
Expand Down Expand Up @@ -1930,7 +1959,7 @@ Cell[BoxData[
RowBox[{
RowBox[{"CTensorWedge", "[",
RowBox[{"___", ",", "Zero", ",", "___"}], "]"}], ":=", "Zero"}], ";"}],
"\[IndentingNewLine]", "\n",
"\n", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Wedge", "[",
RowBox[{
Expand Down Expand Up @@ -1981,7 +2010,7 @@ Cell[BoxData[{
RowBox[{"Wedge", "[",
RowBox[{"basis", ",", "array"}], "]"}], ",", "bases", ",",
"addweight"}], "]"}], "[", "b", "]"}]}],
"\n"}], "\[IndentingNewLine]",
"\[IndentingNewLine]"}], "\n",
RowBox[{
RowBox[{"Wedge", "[",
RowBox[{
Expand Down Expand Up @@ -2030,7 +2059,7 @@ Cell[BoxData[{
"frame"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "Infinity"}], "}"}]}], "]"}]}], "]"}]}],
"\n"}], "\[IndentingNewLine]",
"\[IndentingNewLine]"}], "\n",
RowBox[{
RowBox[{
RowBox[{"Wedge", "[",
Expand All @@ -2057,7 +2086,7 @@ Cell[BoxData[{
RowBox[{"ctensor", "[", "inds", "]"}]}], "]"}], "/;",
RowBox[{
RowBox[{"Length", "[", "frames", "]"}], "===", "1"}]}]}], "]"}]}],
"\n"}], "\[IndentingNewLine]",
"\[IndentingNewLine]"}], "\n",
RowBox[{
RowBox[{"Wedge", "[",
RowBox[{
Expand Down Expand Up @@ -2186,7 +2215,7 @@ Cell[BoxData[{
"addweight"}], "]"}], "[", "b", "]"}], "/;",
RowBox[{
RowBox[{"FindFreeIndices", "@", "ten"}], "===",
RowBox[{"IndexList", "[", "]"}]}]}]}], "\n"}], "\[IndentingNewLine]",
RowBox[{"IndexList", "[", "]"}]}]}]}], "\[IndentingNewLine]"}], "\n",
RowBox[{
RowBox[{"Wedge", "[",
RowBox[{
Expand Down Expand Up @@ -2549,7 +2578,7 @@ Cell[BoxData[{
RowBox[{
RowBox[{"CTensorCircleTimes", "[",
RowBox[{"___", ",", "Zero", ",", "___"}], "]"}], ":=", "Zero"}], ";"}],
"\[IndentingNewLine]"}], "\n",
"\n"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"CircleTimes", "[",
Expand Down Expand Up @@ -2596,7 +2625,7 @@ Cell[BoxData[{
"addweight"}], "]"}], "[", "b", "]"}], "/;",
RowBox[{
RowBox[{"FindFreeIndices", "@", "ten"}], "===",
RowBox[{"IndexList", "[", "]"}]}]}]}], "\n"}], "\[IndentingNewLine]",
RowBox[{"IndexList", "[", "]"}]}]}]}], "\[IndentingNewLine]"}], "\n",
RowBox[{
RowBox[{"CircleTimes", "[",
RowBox[{
Expand Down Expand Up @@ -2650,14 +2679,23 @@ Cell[BoxData[
RowBox[{"form_", ",", "mani_", ",", "deg_", ",",
RowBox[{"options___", "?", "OptionQ"}]}], "]"}], ":=",
"\[IndentingNewLine]",
RowBox[{"(",
RowBox[{"(", "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
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RowBox[{"Wedge", "\[Rule]", "deg"}], "}"}]}], ",", "options"}],
"]"}]}], "\[IndentingNewLine]", ")"}]}]], "Input",
InitializationCell->
True,ExpressionUUID->"f99f3489-4765-4483-a30a-b041bb1f2021"],

Expand Down Expand Up @@ -4444,7 +4482,7 @@ Cell[BoxData[
RowBox[{"options", ":",
RowBox[{"OptionsPattern", "[", "Integrate", "]"}]}]}], "]"}], ":=",
RowBox[{"Part", "[",
RowBox[{"expr", ",", "1"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\n",
RowBox[{"expr", ",", "1"}], "]"}]}], ";"}], "\n", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"FindPotential", "[",
Expand Down Expand Up @@ -9644,8 +9682,8 @@ any CovD) are adjoints of each other, in the sense that\n \[Integral] ",
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SubscriptBox["\[Star]", "g"],
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" = \[Integral] ",
Cell[BoxData[
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Expand All @@ -9667,8 +9705,8 @@ any CovD) are adjoints of each other, in the sense that\n \[Integral] ",
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SubscriptBox["\[Star]", "g"],
SubsuperscriptBox["\[Star]", "g",
RowBox[{"-", "1"}]]}], "=", "id"}]}], TraditionalForm]],
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". This inverse is\n ",
Cell[BoxData[
FormBox[
Expand Down Expand Up @@ -10284,14 +10322,13 @@ Cell[BoxData[{
},
AutoGeneratedPackage->Automatic,
WindowSize->{1438, 876},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
WindowMargins->{{4, Automatic}, {Automatic, 29}},
PrivateNotebookOptions->{"FileOutlineCache"->False},
ShowSelection->True,
CellLabelAutoDelete->True,
TrackCellChangeTimes->False,
Magnification->1.5,
FrontEndVersion->"11.3 for Mac OS X x86 (32-bit, 64-bit Kernel) (March 5, \
2018)",
FrontEndVersion->"12.0 for Linux x86 (64-bit) (April 8, 2019)",
StyleDefinitions->"Default.nb"
]