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#############################################################################
##
#W fpsemi.gd GAP library Andrew Solomon and Isabel Araujo
##
#H @(#)$Id: fpsemi.gd,v 4.13 2002/04/15 10:04:40 sal Exp $
##
#Y Copyright (C) 1997, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St. Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
## This file contains the declarations for finitely
## presented semigroups.
##
Revision.fpsemi_gd :=
"@(#)$Id: fpsemi.gd,v 4.13 2002/04/15 10:04:40 sal Exp $";
#############################################################################
##
#C IsElementOfFpSemigroup(<elm>)
##
## returns true if <elm> is an element of a finitely presented semigroup.
##
DeclareCategory( "IsElementOfFpSemigroup",
IsMultiplicativeElement and IsAssociativeElement );
#############################################################################
##
#O FpSemigroupOfElementOfFpSemigroup( <elm> )
##
## returns the finitely presented semigroup to which <elm> belongs to
##
DeclareOperation( "FpSemigroupOfElementOfFpSemigroup",
[IsElementOfFpSemigroup]);
#############################################################################
##
#C IsElementOfFpSemigroupCollection(<e>)
##
## Created now so that lists of things in the category IsElementOfFpSemigroup
## are given the category CategoryCollections(IsElementOfFpSemigroup)
## Otherwise these lists (and other collections) won't create the
## collections category. See CollectionsCategory in the manual.
##
DeclareCategoryCollections("IsElementOfFpSemigroup");
#############################################################################
##
#A IsSubsemigroupFpSemigroup( <t> )
##
## true if <t> is a finitely presented semigroup or a
## subsemigroup of a finitely presented semigroup
## (generally speaking, such a subsemigroup can be constructed
## with `Semigroup(<gens>)', where <gens> is a list of elements
## of a finitely presented semigroup).
##
DeclareSynonymAttr( "IsSubsemigroupFpSemigroup",
IsSemigroup and IsElementOfFpSemigroupCollection );
#############################################################################
##
#C IsElementOfFpSemigroupFamily
##
DeclareCategoryFamily( "IsElementOfFpSemigroup" );
#############################################################################
##
#F FactorFreeSemigroupByRelations( <f>, <rels> )
##
## for a free semigroup <f> and <rels> is a list of
## pairs of elements of <f>. Returns the finitely presented semigroup
## which is the quotient of <f> by the least congruence on <f> generated by
## the pairs in <rels>.
##
DeclareGlobalFunction("FactorFreeSemigroupByRelations");
#############################################################################
##
#O ElementOfFpSemigroup( <fam>, <w> )
##
## for a family <fam> of elements of a finitely presented semigroup and
## a word <w> in the free generators underlying this finitely presented
## semigroup, this operation creates the element of the finitely
## presented semigroup with the representative <w> in the free semigroup.
##
DeclareOperation( "ElementOfFpSemigroup",
[ IsElementOfFpSemigroupFamily, IsAssocWord ] );
#############################################################################
##
#P IsFpSemigroup(<s>)
##
## is a synonym for `IsSubsemigroupFpSemigroup(<s>)' and
## `IsWholeFamily(<s>)' (this is because a subsemigroup
## of a finitely presented semigroup is not necessarily finitely presented).
##
DeclareSynonym( "IsFpSemigroup",IsSubsemigroupFpSemigroup and IsWholeFamily);
#############################################################################
##
#A FreeGeneratorsOfFpSemigroup( <s> )
##
## returns the underlying free generators corresponding to the
## generators of the finitely presented semigroup <s>.
##
DeclareAttribute("FreeGeneratorsOfFpSemigroup", IsFpSemigroup );
#############################################################################
##
#A FreeSemigroupOfFpSemigroup( <s> )
##
## returns the underlying free semigroup for the finitely presented
## semigroup <s>, ie, the free semigroup over which <s> is defined
## as a quotient
## (this is the free semigroup generated by the free generators provided
## by `FreeGeneratorsOfFpSemigroup(<s>)').
##
DeclareAttribute("FreeSemigroupOfFpSemigroup", IsFpSemigroup);
############################################################################
##
#A RelationsOfFpSemigroup(<s>)
##
## returns the relations of the finitely presented semigroup <s> as
## pairs of words in the free generators provided by
## `FreeGeneratorsOfFpSemigroup(<s>)'.
##
##
DeclareAttribute("RelationsOfFpSemigroup",IsFpSemigroup);
############################################################################
##
#A IsomorphismFpSemigroup( <s> )
##
## for a semigroup <s> returns an isomorphism from <s> to a
## finitely presented semigroup
##
DeclareAttribute("IsomorphismFpSemigroup",IsSemigroup);
############################################################################
##
#O FpGrpMonSmgOfFpGrpMonSmgElement( <elm> )
##
## returns the finitely presented group, monoid or semigroup to which
## <elm> belongs
##
DeclareOperation("FpGrpMonSmgOfFpGrpMonSmgElement",[IsMultiplicativeElement]);
#############################################################################
##
#E
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