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(* ::Package:: *)
(* Copyright 2010 Barry Wardell
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
*)
BeginPackage["xTensorKranc`", {"Differencing`", "Kranc`", "KrancGroups`", "xAct`xTensor`", "xAct`xCore`", "xAct`xCoba`"}];
CreateGroupFromTensor::usage = "";
ReflectionSymmetries::usage = "Produce a list of reflection symmetries of a tensor.";
ExpandComponents::usage = "ExpandComponents[expr] converts an expression x containing abstract indices into one containing components instead."
IncludeCharacter::usage = "IncludeCharacter is an option for makeExplicit which specifies whether the character should also be included in the generated variable names."
TensorCharacterString::usage = "TensorCharacterString[tensor[inds]] returns a string consisting of a sequence of U's and D's representing the character of tensor."
Begin["`Private`"];
(* FIXME: Add support for ManualCartesian attribute *)
TensorCharacterString[t_Symbol?xTensorQ[]] := "Scalar";
TensorCharacterString[t_Symbol?xTensorQ[inds___]] := StringJoin[If[UpIndexQ[#],"U","D"]&/@{inds}];
Options[makeExplicit] = {IncludeCharacter -> False};
SetAttributes[makeExplicit, Listable];
e : makeExplicit[_Plus, opts:OptionsPattern[]] := Distribute[Unevaluated[e]];
makeExplicit[x_Times, opts:OptionsPattern[]] := Map[makeExplicit[#, opts]&, x];
makeExplicit[Power[x_,p_], opts:OptionsPattern[]] := Power[makeExplicit[x, opts],p];
makeExplicit[x_?NumericQ, opts:OptionsPattern[]] := x;
makeExplicit[x_, {}, opts:OptionsPattern[]] := makeExplicit[x];
makeExplicit[t_Symbol?xTensorQ[inds___], opts:OptionsPattern[]] := Module[{indexNumbers,character,indexString},
indexNumbers=First/@{inds};
If[OptionValue[IncludeCharacter],
character = TensorCharacterString[t[inds]];
indexString = StringJoin[character,ToString/@indexNumbers],
indexString = StringJoin[ToString/@indexNumbers]
];
SymbolJoin[PrintAs[t],Sequence@@indexString]
];
makeExplicit[x_, opts:OptionsPattern[]] := x;
makeExplicit[(cd_?CovDQ)[ind_][expr_], opts:OptionsPattern[]] := Module[{indexNumbers},
indexNumbers=First/@{ind};
Global`PDstandard2nd[makeExplicit[expr, opts], Sequence@@indexNumbers]
];
Options[ExpandComponents] = Options[ExpandComponents];
ExpandComponents[x_Rule, opts:OptionsPattern[makeExplicit]] := Thread[ExpandComponents[x[[1]], opts] -> ExpandComponents[x[[2]], opts]];
ExpandComponents[dot[x_], opts:OptionsPattern[makeExplicit]] := dot/@ExpandComponents[x, opts];
ExpandComponents[x_List, opts:OptionsPattern[makeExplicit]] := Flatten[Map[ExpandComponents[#, opts]&, x], 1];
ExpandComponents[x_, opts:OptionsPattern[makeExplicit]] :=
Module[{eqs, options},
eqs = ComponentArray[TraceBasisDummy[x]];
options = Evaluate[FilterRules[{opts}, Options[makeExplicit]]];
If[Length[options]==0,
makeExplicit[eqs],
makeExplicit[eqs, options]
]
];
(* Compute the reflection symmetries of a tensor *)
ReflectionSymmetries[t_Symbol?xTensorQ[inds__]] :=
Module[{b=Global`Euclidean, cnums, components, componentIndices, counts},
(* Get the compoent indices of the basis *)
cnums = CNumbersOf[b, VBundleOfBasis[b]];
(* Get a list of components of the tensor t in the basis b *)
components = Flatten[ComponentArray[ToBasis[b][t[inds]]]];
(* Get the indices of each component *)
componentIndices = Map[IndicesOf[b], components];
(* Count the number of instances of each basis index. *)
countInds[expr_, basis_, cinds_] := Map[(Count[expr,{#,basis}]+Count[expr,{#,-basis}])&, cinds];
counts = Map[countInds[#, b, cnums]&, componentIndices];
(* For each instance, multiply by -1 *)
Thread[ExpandComponents[t[inds]] -> (-1)^counts]
];
ReflectionSymmetries[t_Symbol?xTensorQ[]] := t -> {1,1,1};
ReflectionSymmetries[t_] := t -> {1, 1, 1};
(* FIXME: Implement this fully *)
GetTensorAttribute[t_Symbol?xTensorQ, TensorWeight] := WeightOfTensor[t];
CreateGroupFromTensor[t_Symbol?xTensorQ[inds__]] := Module[{tCharString, nInds, tags, vars, group},
InfoMessage[InfoFull, "Creating group from tensor with kernel " <> SymbolName[t] <> " and indices " <> ToString[{inds}]];
(* Get a string representing the character of the tensor *)
tCharString = TensorCharacterString[t[inds]];
InfoMessage[InfoFull, "Tensor character string: ", tCharString];
(* Check if the tensor is symmetric *)
nInds = Length[SlotsOfTensor[t]];
If[SymmetryGroupOfTensor[t] == StrongGenSet[Range[nInds],GenSet[Cycles[Range[nInds]]]],
tCharString = tCharString <> "_sym"];
(* FIXME: Add tensorspecial, cartesianreflectionparities and tensorparity *)
tags = {"tensortypealias" -> tCharString, "tensorweight" -> GetTensorAttribute[t, TensorWeight]};
vars = If[nInds == 0, {t}, {t[inds]}];
group = CreateGroup[SymbolName[t] <> "_group", vars, {Tags -> tags}];
Return[group]
];
ReflectionSymmetries[x___]:= Throw["ReflectionSymmetries error: "<>ToString[x]];
CreateGroupFromTensor[x___]:= Throw["CreateGroupFromTensor error: "<>ToString[x]];
CheckTensors[expr_] := Validate[expr];
End[];
EndPackage[];
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