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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" );
