Quelle smgideal.gd Sprache: unbekannt

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##
##  This file is part of GAP, a system for computational discrete algebra.
##  This file's authors include Robert Arthur.
##
##  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 declarations relating to semigroup ideals.
##

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##
#O  SemigroupIdealByGenerators(<S>, <gens>)
##
##  <#GAPDoc Label="SemigroupIdealByGenerators">
##  <ManSection>
##  <Oper Name="SemigroupIdealByGenerators" Arg='S, gens'/>
##
##  <Description>
##  <A>S</A> is a semigroup, <A>gens</A> is a list of elements of <A>S</A>.
##  Returns the two-sided ideal of <A>S</A> generated by <A>gens</A>.
##  </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareSynonym("SemigroupIdealByGenerators", MagmaIdealByGenerators );

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##
#P  IsLeftSemigroupIdeal(<I>)
#P  IsRightSemigroupIdeal(<I>)
#P  IsSemigroupIdeal(<I>)
##
##  <#GAPDoc Label="IsLeftSemigroupIdeal">
##  <ManSection>
##  <Prop Name="IsLeftSemigroupIdeal" Arg='I'/>
##  <Prop Name="IsRightSemigroupIdeal" Arg='I'/>
##  <Prop Name="IsSemigroupIdeal" Arg='I'/>
##
##  <Description>
##  Categories of semigroup ideals.
##  </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareProperty("IsLeftSemigroupIdeal", IsLeftMagmaIdeal );
DeclareProperty("IsRightSemigroupIdeal", IsRightMagmaIdeal );
DeclareProperty("IsSemigroupIdeal", IsMagmaIdeal );

InstallTrueMethod(IsLeftMagmaIdeal, IsLeftSemigroupIdeal);
InstallTrueMethod(IsRightMagmaIdeal, IsRightSemigroupIdeal);
InstallTrueMethod(IsMagmaIdeal, IsSemigroupIdeal);

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##
#A  ReesCongruenceOfSemigroupIdeal( <I> )
##
##  <#GAPDoc Label="ReesCongruenceOfSemigroupIdeal">
##  <ManSection>
##  <Attr Name="ReesCongruenceOfSemigroupIdeal" Arg='I'/>
##
##  <Description>
##  A two sided ideal <A>I</A> of a semigroup <A>S</A>  defines a congruence on
##  <A>S</A> given by <M>\Delta \cup I \times I</M>.
##  </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareAttribute("ReesCongruenceOfSemigroupIdeal", IsMagmaIdeal);

DeclareGlobalFunction( "EnumeratorOfSemigroupIdeal" );
DeclareGlobalFunction( "IsBound_LeftSemigroupIdealEnumerator" );
DeclareGlobalFunction( "IsBound_RightSemigroupIdealEnumerator" );

Quelle smgideal.gd Sprache: unbekannt

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