(* ::Package:: *)

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BeginPackage["Permutations`"]


Permutation::usage = "Permutation[i1,i2,...] represents a permutation mapping 1->i1, 2->i2, ...";


Begin["`Private`"]


Permutation /: PermutationProduct[a_Permutation, b_Permutation, rest___Permutation] := PermutationProduct[b[[List@@a]], rest];


Permutation /: InversePermutation[a_Permutation] := (t=a; Do[t[[a[[i]]]]=i, {i,Length@a}]; t)


Permutation /: PermutationSupport[a_Permutation] := List@@Select[a, #!=a[[#]]&]


Permutation /: PermutationReplace[expr_,a_Permutation] := expr /. Table[i->a[[i]], {i,a}]


End[]; EndPackage[]



