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#############################################################################
##
#W rwssmg.gd GAP library Isabel Araujo
##
#H @(#)$Id: rwssmg.gd,v 4.14 2002/04/15 10:05:16 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 semigroups defined by rws.
##
Revision.rwssmg_gd :=
"@(#)$Id: rwssmg.gd,v 4.14 2002/04/15 10:05:16 sal Exp $";
############################################################################
##
#A ReducedConfluentRewritingSystem( <S> )
#A ReducedConfluentRewritingSystem( <S> , <ordering> )
##
## in the first form returns a reduced confluent rewriting system
## of the finitely presented semigroup or monoid <S> with respect
## to the length plus lexicographic ordering on words (also
## called the shortlex ordering; for the definition see for example
## Sims \cite{Sims94}).
##
## In the second form it returns a reduced confluent rewriting system of
## the finitely presented semigroup or monoid <S> with respect to the
## reduction ordering <ordering> (see "Orderings").
##
## Notice that this might not terminate. In particular, if the semigroup or
## monoid <S> does not have a solvable word problem then it this will
## certainly never end.
## Also, in this case, the object returned is an immutable
## rewriting system, because once we have a confluent
## rewriting system for a finitely presented semigroup or monoid we do
## not want to allow it to change (as it was most probably very time
## consuming to get it in the first place). Furthermore, this is also
## an attribute storing object (see "Representation").
##
DeclareAttribute("ReducedConfluentRewritingSystem",IsSemigroup);
#############################################################################
##
#A FreeMonoidOfRewritingSystem(<rws>)
##
## returns the free monoid over which <rws> is
## a rewriting system
##
DeclareAttribute("FreeMonoidOfRewritingSystem",
IsRewritingSystem);
#############################################################################
##
#A FamilyForRewritingSystem(<rws>)
##
## returns the family of words over which <rws> is
## a rewriting system
##
DeclareAttribute("FamilyForRewritingSystem",
IsRewritingSystem);
#############################################################################
##
#A FreeSemigroupOfRewritingSystem(<rws>)
##
## returns the free semigroup over which <rws> is
## a rewriting system
##
DeclareAttribute("FreeSemigroupOfRewritingSystem",
IsRewritingSystem);
#############################################################################
##
#F ReduceLetterRepWordsRewSys(<tzrules>,<w>)
##
## Here <w> is a word of a free monoid or a free semigroup in tz
## represenattion, and <tzrules> are rules in tz representation. This
## function returns the reduced word in tz representation.
##
## All lists in <tzrules> as well as <w> must be plain lists, the entries
## must be small integers. (The behaviour otherwise is unpredictable.)
##
DeclareGlobalFunction("ReduceLetterRepWordsRewSys");
#############################################################################
##
#E
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