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#############################################################################
##
## semigroups/semigrp.gd
## Copyright (C) 2013-2022 James D. Mitchell
##
## Licensing information can be found in the README file of this package.
##
#############################################################################
##
# This file contains operations for creating semigroups, subsemigroups, and
# closures.
# The following true method is required since IsInverseSemigroup is a property
# of semigroups and so objectifying something using IsInverseSemigroup does not
# result in a semigroup.
InstallTrueMethod(IsSemigroup, IsInverseSemigroup);
# 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).
DeclareOperation("SemigroupByGenerators",
[IsListOrCollection]);
DeclareOperation("SemigroupByGenerators",
[IsListOrCollection, IsRecord]);
DeclareOperation("MonoidByGenerators",
[IsListOrCollection]);
DeclareOperation("MonoidByGenerators",
[IsListOrCollection, IsRecord]);
DeclareOperation("InverseMonoidByGenerators",
[IsMultiplicativeElementWithOneCollection, IsRecord]);
DeclareOperation("InverseSemigroupByGenerators",
[IsMultiplicativeElementCollection, IsRecord]);
InstallTrueMethod(IsStarSemigroup,
IsAssociativeElementWithStarCollection and
IsInverseSemigroup and IsGeneratorsOfInverseSemigroup);
DeclareOperation("ClosureInverseSemigroup",
[IsInverseSemigroup and IsGeneratorsOfInverseSemigroup,
IsMultiplicativeElementCollection]);
DeclareOperation("ClosureInverseSemigroup",
[IsInverseSemigroup and IsGeneratorsOfInverseSemigroup,
IsMultiplicativeElementCollection,
IsRecord]);
DeclareOperation("ClosureInverseSemigroup",
[IsInverseSemigroup and IsGeneratorsOfInverseSemigroup,
IsListOrCollection and IsEmpty,
IsRecord]);
DeclareOperation("ClosureInverseSemigroup",
[IsInverseSemigroup and IsGeneratorsOfInverseSemigroup,
IsMultiplicativeElement]);
DeclareOperation("ClosureInverseSemigroup",
[IsInverseSemigroup and IsGeneratorsOfInverseSemigroup,
IsMultiplicativeElement, IsRecord]);
DeclareOperation("ClosureInverseMonoid",
[IsInverseMonoid and IsGeneratorsOfInverseSemigroup,
IsMultiplicativeElementCollection]);
DeclareOperation("ClosureInverseMonoid",
[IsInverseMonoid and IsGeneratorsOfInverseSemigroup,
IsMultiplicativeElementCollection,
IsRecord]);
DeclareOperation("ClosureInverseMonoid",
[IsInverseMonoid and IsGeneratorsOfInverseSemigroup,
IsListOrCollection and IsEmpty,
IsRecord]);
DeclareOperation("ClosureInverseMonoid",
[IsInverseMonoid and IsGeneratorsOfInverseSemigroup,
IsMultiplicativeElement]);
DeclareOperation("ClosureInverseMonoid",
[IsInverseMonoid and IsGeneratorsOfInverseSemigroup,
IsMultiplicativeElement, IsRecord]);
DeclareOperation("ClosureInverseSemigroupOrMonoidNC",
[IsFunction, IsSemigroup, IsList and IsFinite, IsRecord]);
# 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).
DeclareOperation("ClosureSemigroup",
[IsSemigroup, IsListOrCollection, IsRecord]);
DeclareOperation("ClosureSemigroup",
[IsSemigroup, IsListOrCollection]);
DeclareOperation("ClosureSemigroup",
[IsSemigroup, IsListOrCollection and IsEmpty, IsRecord]);
DeclareOperation("ClosureSemigroup",
[IsSemigroup, IsMultiplicativeElement, IsRecord]);
DeclareOperation("ClosureSemigroup",
[IsSemigroup, IsMultiplicativeElement]);
DeclareOperation("ClosureMonoid",
[IsMonoid,
IsMultiplicativeElementWithOneCollection,
IsRecord]);
DeclareOperation("ClosureMonoid",
[IsMonoid, IsMultiplicativeElementWithOneCollection]);
DeclareOperation("ClosureMonoid",
[IsMonoid, IsListOrCollection and IsEmpty, IsRecord]);
DeclareOperation("ClosureMonoid",
[IsMonoid, IsMultiplicativeElementWithOne, IsRecord]);
DeclareOperation("ClosureMonoid",
[IsMonoid, IsMultiplicativeElementWithOne]);
DeclareOperation("ClosureSemigroupOrMonoidNC",
[IsFunction, IsSemigroup, IsList and IsFinite, IsRecord]);
DeclareOperation("AsSemigroup", [IsFunction, IsSemigroup]);
DeclareOperation("AsSemigroup", [IsFunction, IsRing, IsSemigroup]);
DeclareOperation("AsSemigroup", [IsFunction, IsPosInt, IsSemigroup]);
DeclareOperation("AsSemigroup", [IsFunction, IsPosInt, IsPosInt, IsSemigroup]);
DeclareConstructor("IsomorphismSemigroup",
[IsSemigroup, IsSemigroup]);
DeclareConstructor("IsomorphismSemigroup",
[IsSemigroup, IsRing, IsSemigroup]);
DeclareConstructor("IsomorphismSemigroup",
[IsSemigroup, IsPosInt, IsSemigroup]);
DeclareConstructor("IsomorphismSemigroup",
[IsSemigroup, IsPosInt, IsPosInt, IsSemigroup]);
DeclareOperation("AsMonoid", [IsFunction, IsSemigroup]);
DeclareOperation("AsMonoid", [IsFunction, IsRing, IsSemigroup]);
DeclareOperation("AsMonoid", [IsFunction, IsPosInt, IsSemigroup]);
DeclareOperation("AsMonoid", [IsFunction, IsPosInt, IsPosInt, IsSemigroup]);
DeclareConstructor("IsomorphismMonoid",
[IsSemigroup, IsSemigroup]);
DeclareConstructor("IsomorphismMonoid",
[IsSemigroup, IsRing, IsSemigroup]);
DeclareConstructor("IsomorphismMonoid",
[IsSemigroup, IsPosInt, IsSemigroup]);
DeclareConstructor("IsomorphismMonoid",
[IsSemigroup, IsPosInt, IsPosInt, IsSemigroup]);
DeclareAttribute("Generators", IsSemigroup);
DeclareGlobalFunction("RandomSemigroup");
DeclareConstructor("RandomSemigroupCons", [IsSemigroup, IsList]);
DeclareGlobalFunction("RandomMonoid");
DeclareConstructor("RandomMonoidCons", [IsMonoid, IsList]);
DeclareGlobalFunction("RandomInverseSemigroup");
DeclareConstructor("RandomInverseSemigroupCons", [IsSemigroup, IsList]);
DeclareGlobalFunction("RandomInverseMonoid");
DeclareConstructor("RandomInverseMonoidCons", [IsMonoid, IsList]);
DeclareConstructor("SEMIGROUPS_ProcessRandomArgsCons",
[IsSemigroup, IsList]);
DeclareOperation("SubsemigroupByProperty", [IsSemigroup, IsFunction]);
DeclareOperation("SubsemigroupByProperty",
[IsSemigroup, IsFunction, IsPosInt]);
DeclareOperation("InverseSubsemigroupByProperty",
[IsSemigroup, IsFunction]);
DeclareOperation("InverseSubsemigroupByProperty",
[IsInverseSemigroup and IsGeneratorsOfInverseSemigroup,
IsFunction,
IsPosInt]);
# undocumented
DeclareGlobalFunction("RegularSemigroup");
[ Dauer der Verarbeitung: 0.21 Sekunden
(vorverarbeitet)
]
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