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#############################################################################
##
#W trans.gd GAP library J. D. Mitchell
##
##
#Y Copyright (C) 1997, Lehrstuhl D für Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y Copyright (C) 2012 The GAP Group
##
# the documentation for the functions declared herein can be found in
# doc/ref/trans.xml
DeclareUserPreference(rec(
name:=["TransformationDisplayLimit", "NotationForTransformations"],
description:=["options for the display of transformations"],
default:=[100, "input"],
check:=function(a, b) return IsPosInt(a)
or (IsString(b) and b in ["input", "fr"]); end));
DeclareOperation("Transformation", [IsList]);
DeclareOperation("Transformation", [IsList, IsList]);
DeclareOperation("TransformationListList", [IsList, IsList]);
DeclareOperation("TransformationList", [IsList]);
DeclareOperation("Transformation", [IsList, IsFunction]);
DeclareOperation("TransformationByImageAndKernel",
[ IsCyclotomicCollection and IsDenseList,
IsCyclotomicCollection and IsDenseList]);
DeclareOperation("NumberTransformation", [IsTransformation, IsZeroCyc]);
DeclareOperation("NumberTransformation", [IsTransformation, IsPosInt]);
DeclareOperation("NumberTransformation", [IsTransformation]);
DeclareOperation("TransformationNumber", [IsPosInt, IsPosInt]);
DeclareAttribute("MovedPoints", IsTransformation);
DeclareAttribute("NrMovedPoints", IsTransformation);
DeclareAttribute("LargestMovedPoint", IsTransformation);
DeclareAttribute("LargestImageOfMovedPoint", IsTransformation);
DeclareAttribute("SmallestMovedPoint", IsTransformation);
DeclareAttribute("SmallestImageOfMovedPoint", IsTransformation);
DeclareAttribute("MovedPoints", IsTransformationCollection);
DeclareAttribute("NrMovedPoints", IsTransformationCollection);
DeclareAttribute("SmallestImageOfMovedPoint", IsTransformationCollection);
DeclareAttribute("LargestImageOfMovedPoint", IsTransformationCollection);
DeclareAttribute("LargestMovedPoint", IsTransformationCollection);
DeclareAttribute("SmallestMovedPoint", IsTransformationCollection);
DeclareAttribute("RankOfTransformation", IsTransformation);
DeclareOperation("RankOfTransformation", [IsTransformation, IsPosInt]);
DeclareOperation("RankOfTransformation", [IsTransformation, IsZeroCyc]);
DeclareOperation("RankOfTransformation", [IsTransformation, IsList]);
DeclareOperation("AsBinaryRelation", [IsTransformation]);
DeclareAttribute("AsPermutation", IsAssociativeElement);
DeclareAttribute("AsTransformation", IsAssociativeElement);
DeclareOperation("AsTransformation", [IsAssociativeElement, IsInt]);
DeclareAttribute("PermutationOfImage", IsTransformation);
DeclareOperation("ConstantTransformation", [IsPosInt, IsPosInt]);
DeclareAttribute("DegreeOfTransformationCollection",
IsTransformationCollection);
DeclareAttribute("FlatKernelOfTransformation", IsTransformation);
DeclareOperation("FlatKernelOfTransformation", [IsTransformation, IsPosInt]);
DeclareOperation("FlatKernelOfTransformation", [IsTransformation, IsZeroCyc]);
DeclareOperation("ImageListOfTransformation", [IsTransformation, IsPosInt]);
DeclareOperation("ImageListOfTransformation", [IsTransformation, IsZeroCyc]);
DeclareOperation("ImageListOfTransformation", [IsTransformation]);
#ImageListOfTransformation(IsTransformation, IsList) is just OnTuples
DeclareSynonym("ListTransformation", ImageListOfTransformation);
DeclareAttribute("ImageSetOfTransformation", IsTransformation);
DeclareOperation("ImageSetOfTransformation", [IsTransformation, IsPosInt]);
DeclareOperation("ImageSetOfTransformation", [IsTransformation, IsZeroCyc]);
#ImageSetOfTransformation(IsTransformation, IsList) is just OnSets
DeclareAttribute("IndexPeriodOfTransformation", IsTransformation);
DeclareOperation("IsInjectiveListTrans", [IsList, IsTransformation]);
DeclareOperation("IsInjectiveListTrans", [IsList, IsList]);
DeclareAttribute("KernelOfTransformation", IsTransformation);
DeclareOperation("KernelOfTransformation", [IsTransformation, IsPosInt,
IsBool]);
DeclareOperation("KernelOfTransformation", [IsTransformation, IsPosInt]);
DeclareOperation("KernelOfTransformation", [IsTransformation, IsZeroCyc]);
DeclareOperation("KernelOfTransformation", [IsTransformation, IsBool]);
DeclareOperation("PermLeftQuoTransformationNC",[IsTransformation,
IsTransformation]);
DeclareOperation("PermLeftQuoTransformation",[IsTransformation,
IsTransformation]);
DeclareOperation("PreImagesOfTransformation",[IsTransformation, IsPosInt]);
DeclareSynonym("PreimagesOfTransformation", PreImagesOfTransformation);
DeclareOperation("RandomTransformation", [IsPosInt]);
DeclareOperation("RandomTransformation", [IsPosInt, IsPosInt]);
DeclareOperation("RestrictedTransformationNC", [IsTransformation, IsList]);
DeclareOperation("RestrictedTransformation", [IsTransformation, IsList]);
DeclareAttribute("SmallestIdempotentPower", IsAssociativeElement);
DeclareOperation("TrimTransformation", [IsTransformation, IsPosInt]);
DeclareOperation("TrimTransformation", [IsTransformation]);
DeclareOperation("Idempotent", [IsCyclotomicCollection,
IsCyclotomicCollection]);
DeclareOperation("TransformationOp", [IsObject, IsList, IsFunction]);
DeclareOperation("TransformationOp", [IsObject, IsDomain, IsFunction]);
DeclareOperation("TransformationOp", [IsObject, IsList]);
DeclareOperation("TransformationOp", [IsObject, IsDomain]);
DeclareOperation("TransformationOpNC", [IsObject, IsList, IsFunction]);
DeclareOperation("TransformationOpNC", [IsObject, IsDomain, IsFunction]);
DeclareOperation("TransformationOpNC", [IsObject, IsList]);
DeclareOperation("TransformationOpNC", [IsObject, IsDomain]);
DeclareOperation("InverseOfTransformation", [IsTransformation]);
DeclareAttribute("ComponentRepsOfTransformation", IsTransformation);
DeclareAttribute("NrComponentsOfTransformation", IsTransformation);
DeclareAttribute("ComponentsOfTransformation", IsTransformation);
DeclareOperation("ComponentTransformationInt",[IsTransformation, IsPosInt]);
DeclareOperation("CycleTransformationInt", [IsTransformation, IsPosInt]);
DeclareAttribute("CyclesOfTransformation", IsTransformation);
DeclareOperation("CyclesOfTransformation", [IsTransformation, IsList]);
DeclareAttribute("LeftOne", IsAssociativeElement);
DeclareAttribute("RightOne", IsAssociativeElement);
DeclareOperation("OnKernelAntiAction", [IsList, IsTransformation]);
BindGlobal("IdentityTransformation", TransformationNC([]));
# for legacy reasons only!
DeclareSynonym("BinaryRelationTransformation", AsBinaryRelation);
DeclareOperation("InverseOp", [IsTransformation]);
#not yet implemented
DeclareGlobalFunction("TransformationAction");
DeclareGlobalFunction("TransformationActionNC");
DeclareGlobalFunction("TransformationActionHomomorphism");
DeclareGlobalFunction("TransformationActionHomomorphismNC");
#EOF
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