|
#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Andrew Solomon.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains the declaration for semigroup congruences.
##
## Maintenance and further development by:
## Robert F. Morse
## Andrew Solomon
##
###########################################################################
##
#O SemigroupCongruenceByGeneratingPairs(<s>,<list>)
##
## create a semigroup congruence on <s> generated by the list
## <list> of pairs.
##
DeclareOperation("SemigroupCongruenceByGeneratingPairs",
[IsMagma and IsAssociative, IsList]);
#############################################################################
##
#O RightSemigroupCongruenceByGeneratingPairs(<D>, <pairs> )
##
## The right congruence on <D> generated by <pairs>
##
DeclareOperation( "RightSemigroupCongruenceByGeneratingPairs",
[IsMagma and IsAssociative, IsList ] );
#############################################################################
##
#O LeftSemigroupCongruenceByGeneratingPairs(<D>, <pairs> )
##
## The left congruence generated by pairs
##
DeclareOperation( "LeftSemigroupCongruenceByGeneratingPairs",
[IsMagma and IsAssociative, IsList ] );
#############################################################################
##
#M JoinSemigroupCongruences(<cong1>, <cong2>)
##
## Join of two semigroup congruences
##
DeclareSynonym("JoinSemigroupCongruences", JoinMagmaCongruences);
#############################################################################
##
#M MeetSemigroupCongruences(<cong1>, <cong2>)
##
## Join of two semigroup congruences
##
DeclareSynonym("MeetSemigroupCongruences", MeetMagmaCongruences);
#############################################################################
##
#A GeneratingPairsOfSemigroupCongruence(<cong1>, <cong2>)
##
## <ManSection>
## <Attr Name="GeneratingPairsOfSemigroupCongruence" Arg='cong1, cong2'/>
##
## <Description>
## Generating Pairs of a semigroup congruences
## </Description>
## </ManSection>
##
DeclareSynonym("GeneratingPairsOfSemigroupCongruence",
GeneratingPairsOfMagmaCongruence);
###########################################################################
##
#P IsLeftSemigroupCongruence(<c>)
##
## <ManSection>
## <Prop Name="IsLeftSemigroupCongruence" Arg='c'/>
##
## <Description>
## a left magma congruence <A>c</A> on a semigroup.
## </Description>
## </ManSection>
##
DeclareProperty("IsLeftSemigroupCongruence", IsLeftMagmaCongruence);
###########################################################################
##
#P IsRightSemigroupCongruence(<c>)
##
## <ManSection>
## <Prop Name="IsRightSemigroupCongruence" Arg='c'/>
##
## <Description>
## a right magma congruence <A>c</A> on a semigroup.
## </Description>
## </ManSection>
##
DeclareProperty("IsRightSemigroupCongruence", IsRightMagmaCongruence);
###########################################################################
##
#P IsSemigroupCongruence(<c>)
##
## <#GAPDoc Label="IsSemigroupCongruence">
## <ManSection>
## <Prop Name="IsSemigroupCongruence" Arg='c'/>
##
## <Description>
## a magma congruence <A>c</A> on a semigroup.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty("IsSemigroupCongruence", IsMagmaCongruence);
InstallTrueMethod(IsLeftSemigroupCongruence,IsSemigroupCongruence);
InstallTrueMethod(IsRightSemigroupCongruence,IsSemigroupCongruence);
###########################################################################
##
#P IsReesCongruence(<c>)
##
## <#GAPDoc Label="IsReesCongruence">
## <ManSection>
## <Prop Name="IsReesCongruence" Arg='c'/>
##
## <Description>
## returns <K>true</K> if and only if the congruence <A>c</A> has at most
## one nonsingleton congruence class.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty("IsReesCongruence", IsSemigroupCongruence );
[ Seitenstruktur0.17Drucken
etwas mehr zur Ethik
]
|
