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scalarRuleGeneration.m
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175 lines (126 loc) · 7.5 KB
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(* ::Package:: *)
(* ::Subsubsection:: *)
(*Semi-automated Rule generation*)
InnerEoMOrder[]
FindEoMOrder[IntNull[inside_]]:=InnerEoMOrder[inside];
FindEoMOrder[IntNull[inside_]*TimesExpr_]:=InnerEoMOrder[inside];
FindEoMOrder[PD[{0,-Fra}][IntNull[inside_]]*TimesExpr_]:=.0001+InnerEoMOrder[inside];
FindEoMOrder[PD[{0,-Fra}][PD[{0,-Fra}][IntNull[inside_]]]*TimesExpr_]:=.0002+InnerEoMOrder[inside];
FindEoMOrder[PD[{0,-Fra}][PD[{0,-Fra}][PD[{0,-Fra}][IntNull[inside_]]]]*TimesExpr_]:=.0003+InnerEoMOrder[inside];
FindEoMOrder[PD[{0,-Fra}][IntNull[inside_]]]:=.0001+InnerEoMOrder[inside];
FindEoMOrder[PD[{0,-Fra}][PD[{0,-Fra}][IntNull[inside_]]]]:=.0002+InnerEoMOrder[inside];
FindEoMOrder[PD[{0,-Fra}][PD[{0,-Fra}][PD[{0,-Fra}][IntNull[inside_]]]]]:=.0003+InnerEoMOrder[inside];
FindEoMOrder[expr_]:=0;
InnerEoMOrder[Ns[inds2__] expr_]:=Length[{inds2}];
InnerEoMOrder[Ns[inds2__]]:=Length[{inds2}];
(* ::Text:: *)
(*An alternative heuristic - designed to move things as close as possible to being expressed entirely in body parameters. (prioritizes the expression least like a multipole.) - when in doubt, eliminate to fewer Ns and more r[]'s*)
InnerEoMOrder[(SE|SourceDens)[inds__] r[]^nn_ Ns[inds2__] expr_]:=100+Abs[Length[{inds2}]-nn] + .01*Length[{inds2}];
InnerEoMOrder[(SE|SourceDens)[inds__] r[]^nn_ Ns[inds2__]] :=100+Abs[Length[{inds2}]-nn]+ .01*Length[{inds2}];
InnerEoMOrder[(SE|SourceDens)[inds__] r[] Ns[inds2__] expr_] :=100+Abs[Length[{inds2}]-1]+ .01*Length[{inds2}];
InnerEoMOrder[(SE|SourceDens)[inds__] r[] Ns[inds2__]] :=100+Abs[Length[{inds2}]-1]+ .01*Length[{inds2}];
InnerEoMOrder[(SE|SourceDens)[inds__] r[]^nn_ expr_]:=100+nn;
InnerEoMOrder[(SE|SourceDens)[inds__] r[]^nn_ ] :=100+nn;
InnerEoMOrder[(SE|SourceDens)[inds__] r[] expr_] :=100+1;
InnerEoMOrder[(SE|SourceDens)[inds__] r[] ] :=100+1;
InnerEoMOrder[(SE|SourceDens)[inds__] Ns[inds2__] expr_]:=100+Length[{inds2}]+ .01*Length[{inds2}];
InnerEoMOrder[(SE|SourceDens)[inds__] Ns[inds2__]] :=100+Length[{inds2}]+ .01*Length[{inds2}];
InnerEoMOrder[(SE|SourceDens)[inds__] expr_]:=100;
InnerEoMOrder[(SE|SourceDens)[inds__]] :=100;
InnerEoMOrder[(SEpert|SourceDenspert)[LI[o_],inds__] r[]^nn_ Ns[inds2__] expr_]:=(o+1)*100+Abs[Length[{inds2}]-nn] + .01*Length[{inds2}];
InnerEoMOrder[(SEpert|SourceDenspert)[LI[o_],inds__] r[]^nn_ Ns[inds2__]] :=(o+1)*100+Abs[Length[{inds2}]-nn]+ .01*Length[{inds2}];
InnerEoMOrder[(SEpert|SourceDenspert)[LI[o_],inds__] r[] Ns[inds2__] expr_] :=(o+1)*100+Abs[Length[{inds2}]-1]+ .01*Length[{inds2}];
InnerEoMOrder[(SEpert|SourceDenspert)[LI[o_],inds__] r[] Ns[inds2__]] :=(o+1)*100+Abs[Length[{inds2}]-1]+ .01*Length[{inds2}];
InnerEoMOrder[(SEpert|SourceDenspert)[LI[o_],inds__] r[]^nn_ expr_]:=(o+1)*100+nn;
InnerEoMOrder[(SEpert|SourceDenspert)[LI[o_],inds__] r[]^nn_ ] :=(o+1)*100+nn;
InnerEoMOrder[(SEpert|SourceDenspert)[LI[o_],inds__] r[] expr_] :=(o+1)*100+1;
InnerEoMOrder[(SEpert|SourceDenspert)[LI[o_],inds__] r[] ] :=(o+1)*100+1;
InnerEoMOrder[(SEpert|SourceDenspert)[LI[o_],inds__] Ns[inds2__] expr_]:=(o+1)*100+Length[{inds2}]+ .01*Length[{inds2}];
InnerEoMOrder[(SEpert|SourceDenspert)[LI[o_],inds__] Ns[inds2__]] :=(o+1)*100+Length[{inds2}]+ .01*Length[{inds2}];
InnerEoMOrder[(SEpert|SourceDenspert)[LI[o_],inds__] expr_]:=(o+1)*100;
InnerEoMOrder[(SEpert|SourceDenspert)[LI[o_],inds__]] :=(o+1)*100;
InnerEoMOrder[expr_]:=0;
GetNumericCoeff[ex_?NumericQ expr_]:=ex;
GetNumericCoeff[expr_]:=1;
IndicesOfCDeltas[ex_ CDelta[rank1_,rank2_][inds__]]:=IndicesOfCDeltas[ex]~Join~{inds};
IndicesOfCDeltas[ex_]:={};
OtherIndexOfCDelta[expr_ CDelta[rank1_,rank2_][ind1_,ind2_],ind2_]:=ind1;
OtherIndexOfCDelta[expr_ CDelta[rank1_,rank2_][ind1_,ind2_],ind1_]:=ind2;
(* ::Text:: *)
(*Removed routines regarding unprocessed expressions*)
SymmetryEquivalentsOfTensor=xAct`xTensor`Private`SymmetryEquivalentsOfTensor;
MakeSymmetrizedSet[expr_]:=Module[{symTensors,replacementRHS,resultString},
symTensors=Cases[FindAllOfType[expr,Tensor],
tensor_/;(SymmetryGroupOfTensor[tensor]=!=StrongGenSet[{},GenSet[]])];
replacementRHS=Alternatives@@(SymmetryEquivalentsOfTensor[#])&/@symTensors;
resultString=StringReplace[ToString[InputForm[expr]],(ToString[InputForm[symTensors[[#]]]]->"("<>ToString[InputForm[replacementRHS[[#]]]]<>")")&/@Range[Length[symTensors]]];
Return[ToExpression[resultString]]];
ToPatternInds[exp_List]:=ToPatternInds/@exp;
ToPatternInds[a_?BasisQ]:=a;
ToPatternInds[a_]:=ToExpression[ToString[a]<>"_"];
StripBasis[{a_,b_?BasisQ}]:=a;
StripBasis[exp_List]:=StripBasis/@exp;
GenerateSumRulesFromEoM[expr_,OptionsPattern[]]:=
Module[{rawlhs,rawrhs,firstlhs,truelhs,lhsDeltaIndices,NewDeltaIndices1,NewDeltaIndices2,singleMaxPos,
NewIndexList,NewCDeltas,IndexSigns,symmComb=False,FreeIndices,IndicesList,FreePatternIndicesList,
EoMOrderList=FindEoMOrder/@(List@@expr),maxPos},
If[Head@expr===Plus,
maxPos=Position[EoMOrderList,Max[EoMOrderList]];
If[Length[maxPos]>1, (*If the 'best lhs' term is degenerate, we have a Sum rule to generate*)
firstlhs=First@((expr)[[#]]&/@maxPos);
rawlhs=((expr)[[#]]&/@maxPos);
rawrhs=Plus@@Delete[(List@@expr),maxPos];
rawrhs=(-1*rawrhs/GetNumericCoeff[firstlhs])//Expand//GenerateNewDummies;
rawlhs=rawlhs/GetNumericCoeff[firstlhs]//Expand;
IndicesList=DeleteDuplicates[Join@@IndicesOf[Free]/@List@@(rawlhs)/.IndexList->List];
IndicesList=StripBasis[IndicesList];
FreePatternIndicesList=ToPatternInds[IndicesList];
(*For each symmetric tensor in lhs we need either a separate rule or a _separate pattern entry_*)
truelhs=MakeSymmetrizedSet/@(GeneratePatternDummies/@rawlhs);
(*Print[{truelhs,"Goes to",rawrhs}];*)
Return[{(ToExpression["{"<>ToString[InputForm[truelhs]]<>",{"<>
ToString[FreePatternIndicesList]<>","<>ToString[IndicesList]<>"},"<>ToString[InputForm[rawrhs]]<>"}"])}];
,
Return[{}];
];
,
Return[{}];
];
Return[{}];
];
NZSumEoMRules[1]={};
GenerateRulesFromEoM[expr_,OptionsPattern[]]:=
Module[{rawlhs,rawrhs,firstlhs,truelhs,lhsDeltaIndices,NewDeltaIndices1,NewDeltaIndices2,singleMaxPos,
NewIndexList,NewCDeltas,IndexSigns,symmComb=False,FreeIndices,IndicesList,FreePatternIndicesList,
EoMOrderList=FindEoMOrder/@(List@@expr),maxPos},
If[Head@expr===Plus,
maxPos=Position[EoMOrderList,Max[EoMOrderList]];
If[Length[maxPos]>1, (*If the 'best lhs' term is degenerate, we have a Sum rule to generate*)
Return[{}]
,
singleMaxPos=First@(First@maxPos);
rawlhs=expr[[singleMaxPos]];
rawrhs=Delete[expr,singleMaxPos];
];
,
rawlhs=expr;
rawrhs=0;
If[rawlhs===0,Return[{}];];
];
rawrhs=(-1*rawrhs/GetNumericCoeff[rawlhs])//Expand;
rawlhs=rawlhs/GetNumericCoeff[rawlhs]//Expand;
lhsDeltaIndices=Intersection[(IndicesOf[Free][rawlhs]/.IndexList->List),IndicesOfCDeltas[rawlhs]];
NewDeltaIndices1=Expand[-1*lhsDeltaIndices];
NewDeltaIndices2=({Unique[#[[1]]],#[[2]]}&/@(UpIndex/@(OtherIndexOfCDelta[rawlhs,#]&/@lhsDeltaIndices)))*(-1*(BoolToSign/@(UpIndexQ/@(OtherIndexOfCDelta[rawlhs,#]&/@lhsDeltaIndices))));
NewIndexList={NewDeltaIndices1[[#]],NewDeltaIndices2[[#]]}&/@Range[Length[NewDeltaIndices2]];
NewCDeltas = CDelta[#[[1]][[2]],#[[2]][[2]]][Sequence@@#]&/@NewIndexList;
rawlhs=Times[rawlhs,Sequence@@NewCDeltas]//ExpandAll;
rawrhs=Times[rawrhs,Sequence@@NewCDeltas]//ExpandAll;
With[{lhs=rawlhs,rhs=(rawrhs//GenerateNewDummies),dlhs=PD[-{0,Ret}][rawlhs]},
If[OptionValue[Verbose],
Print[rhs];
Print[lhs];
];
Return[MakeRule[{lhs,rhs},MetricOn->None]];
];
];Options[GenerateRulesFromEoM]={Verbose->False};