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#############################################################################
##
## attributes/attr.gd
## Copyright (C) 2013-2022 James D. Mitchell
##
## Licensing information can be found in the README file of this package.
##
#############################################################################
##
# This file contains declarations for attributes of semigroups.
DeclareOperation("IrredundantGeneratingSubset",
[IsMultiplicativeElementCollection]);
DeclareAttribute("GroupOfUnits", IsSemigroup);
DeclareAttribute("IdempotentGeneratedSubsemigroup", IsSemigroup);
DeclareAttribute("InjectionPrincipalFactor", IsGreensDClass);
DeclareAttribute("InjectionNormalizedPrincipalFactor", IsGreensDClass);
DeclareAttribute("RepresentativeOfMinimalIdeal", IsSemigroup);
DeclareOperation("RepresentativeOfMinimalIdealNC", [IsSemigroup]);
DeclareSynonymAttr("RepresentativeOfMinimalDClass",
RepresentativeOfMinimalIdeal);
DeclareAttribute("MinimalIdeal", IsSemigroup);
DeclareAttribute("PrincipalFactor", IsGreensDClass);
DeclareAttribute("NormalizedPrincipalFactor", IsGreensDClass);
DeclareAttribute("MultiplicativeZero", IsSemigroup);
DeclareAttribute("LengthOfLongestDClassChain", IsSemigroup);
# We use IsListOrCollection here because some collections of semigroup
# generators (such as elements/congruence classes in a quotient semigroup) do
# not satisfy IsMultiplicativeElementCollection (although the classes
# themselves do satisfy IsMultiplicativeElement).
DeclareAttribute("SmallSemigroupGeneratingSet",
IsListOrCollection);
DeclareAttribute("SmallMonoidGeneratingSet",
IsMultiplicativeElementWithOneCollection);
DeclareAttribute("SmallInverseSemigroupGeneratingSet",
IsMultiplicativeElementCollection);
DeclareAttribute("SmallInverseMonoidGeneratingSet",
IsMultiplicativeElementWithOneCollection);
DeclareAttribute("MinimalSemigroupGeneratingSet",
IsSemigroup);
DeclareAttribute("MinimalMonoidGeneratingSet",
IsMonoid);
DeclareAttribute("MinimalInverseSemigroupGeneratingSet",
IsSemigroup);
DeclareAttribute("MinimalInverseMonoidGeneratingSet",
IsMonoid);
DeclareAttribute("SmallestElementSemigroup", IsSemigroup);
DeclareAttribute("LargestElementSemigroup", IsSemigroup);
DeclareAttribute("StructureDescription", IsBrandtSemigroup);
DeclareAttribute("StructureDescription", IsGroupAsSemigroup);
DeclareAttribute("StructureDescriptionMaximalSubgroups",
IsSemigroup);
DeclareAttribute("MaximalDClasses", IsSemigroup);
DeclareAttribute("MaximalLClasses", IsSemigroup);
DeclareAttribute("MaximalRClasses", IsSemigroup);
DeclareAttribute("MinimalDClass", IsSemigroup);
DeclareAttribute("IsGreensDGreaterThanFunc", IsSemigroup);
DeclareAttribute("UnderlyingSemigroupOfSemigroupWithAdjoinedZero",
IsSemigroup);
DeclareOperation("InversesOfSemigroupElementNC",
[IsSemigroup, IsMultiplicativeElement]);
DeclareOperation("OneInverseOfSemigroupElementNC",
[IsSemigroup, IsMultiplicativeElement]);
DeclareOperation("OneInverseOfSemigroupElement",
[IsSemigroup, IsMultiplicativeElement]);
DeclareAttribute("IndecomposableElements", IsSemigroup);
DeclareAttribute("NambooripadLeqRegularSemigroup", IsSemigroup);
DeclareAttribute("NambooripadPartialOrder", IsSemigroup);
DeclareOperation("LeftIdentity", [IsSemigroup, IsMultiplicativeElement]);
DeclareOperation("RightIdentity", [IsSemigroup, IsMultiplicativeElement]);
DeclareAttribute("MultiplicationTableWithCanonicalPositions",
IsSemigroup and CanUseFroidurePin);
DeclareAttribute("TransposedMultiplicationTableWithCanonicalPositions",
IsSemigroup and CanUseFroidurePin);
DeclareAttribute("MinimalFaithfulTransformationDegree", IsSemigroup);
DeclareAttribute("SmallerDegreeTransformationRepresentation", IsSemigroup);
# TODO(later)
# DeclareAttribute("MinimalFaithfulTransformationRepresentation", IsSemigroup);
[ Dauer der Verarbeitung: 0.2 Sekunden
(vorverarbeitet)
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