(* ::Package:: *)

BeginPackage["CycleIndicators`","Combinatorica`"];


ClengthEx[\[Sigma]_,n_]:=If[Count[Length /@\[Sigma] ,n] >0,False,True]
Clength[\[Sigma]_]:=Length /@\[Sigma] 
Cord[\[Sigma]_]:= LCM@@Clength[\[Sigma]]
DoPerm[\[Sigma]_,\[Nu]_]:=If[Depth[\[Sigma]]==2,Permute[\[Sigma],\[Nu]],Permute@@(FromCycles /@{\[Sigma],\[Nu]})] 

Powers[\[Sigma]plain_,n_]:= 
Nest[DoPerm[\[Sigma]plain,#]&,\[Sigma]plain,n]//Return;

PowerList[\[Sigma]plain_]:= Table[Powers[\[Sigma]plain,n],{n,0,Cord[ToCycles[\[Sigma]plain]]-2}]

AllPerms[list_]:=Join[list,Apply[DoPerm,#]& /@Tuples[list,{2}]] //DeleteDuplicates

CIS::usage="Calculates CycleIndicator for given set of generators (GenSet)";
CIS[GenSet_]:=Module[{grp,grpQ,ci,poly},
grp =FixedPointList[DeleteDuplicates[AllPerms[#]]&,FromCycles /@GenSet] //Flatten[#,1]&  //DeleteDuplicates;
If[ grp //PermutationGroupQ ==False,Print["Error (no Permutationgroup"]];
ci = CycleIndex[grp,x];
poly= ci /.x[i_]->n;
Return[{ci,poly}//Column];]

EndPackage[]