  
  
                                     [1X[5XIdRel[0m[1X[0m
  
  
                    [1XA package for Identities among Relators[0m
  
  
                                  Version 2.05
  
  
                                 November 2008
  
  
                                 Anne Heyworth
  
                                 Chris Wensley
  
  
  
  Anne Heyworth
      Email:    [7Xmailto:anne.heyworth@googlemail.com[0m
  Chris Wensley
      Email:    [7Xmailto:c.d.wensley@bangor.ac.uk[0m
      Homepage: [7Xhttp://www.bangor.ac.uk/~mas023/[0m
      Address:  School of Computer Science, Bangor University,
                Dean Street, Bangor, Gwynedd, LL57 1UT, U.K.
  
  
  
  -------------------------------------------------------
  [1XAbstract[0m
  The  [5XIdRel[0m  package  was  originally  implemented  in  1999, using the [5XGAP[0m 3
  language, when the first author was studying for a Ph.D. in Bangor.
  
  This  package  is  designed  to  compute a minimal set of generators for the
  module  of  the  identities  among relators of a group presentation. It does
  this using
  
  --    rewriting and logged rewriting: a self-contained implementation of the
        Knuth-Bendix  process  using the monoid presentation associated to the
        group presentation;
  
  --    monoid polynomials: an implementation of the monoid ring;
  
  --    module  polynomials:  an  implementation of the right module over this
        monoid generated by the relators.
  
  --    Y-sequences:  used  as  a  [13Xrewriting[0m way of representing elements of a
        free  crossed  module  (products  of  conjugates of group relators and
        inverse relators).
  
  Bug  reports,  suggestions  and  comments  are,  of  course, welcome. Please
  contact the second author at [7Xmailto:c.d.wensley@bangor.ac.uk[0m.
  
  
  -------------------------------------------------------
  [1XCopyright[0m
  © 2005-2008 Anne Heyworth and Chris Wensley
  
  
  -------------------------------------------------------
  [1XAcknowledgements[0m
  This  [5Xidrel[0m  package is released under the GNU General Public License (GPL).
  This file is part of [5Xidrel[0m, though as documentation it is released under the
  GNU            Free           Documentation           License           (see
  [7Xhttp://www.gnu.org/licenses/licenses.html#FDL[0m).
  
  [5Xidrel[0m  is  free software; you can redistribute it and/or modify it under the
  terms  of  the  GNU General Public License as published by the Free Software
  Foundation;  either  version 2 of the License, or (at your option) any later
  version.
  
  [5Xidrel[0m  is  distributed  in  the hope that it will be useful, but WITHOUT ANY
  WARRANTY;  without  even  the implied warranty of MERCHANTABILITY or FITNESS
  FOR  A  PARTICULAR  PURPOSE.  See  the  GNU  General Public License for more
  details.
  
  You should have received a copy of the GNU General Public License along with
  [5Xidrel[0m; if not, write to the Free Software Foundation, Inc., 59 Temple Place,
  Suite 330, Boston, MA 02111-1307 USA.
  
  For more details, see [7Xhttp://www.fsf.org/licenses/gpl.html[0m.
  
  This  documentation  was  prepared with the [5XGAPDoc[0m package of Frank L\"ubeck
  and Max Neunh\"offer.
  
  
  -------------------------------------------------------
  
  
  [1XContents (IdRel)[0X
  
  1 Introduction
  2 Rewriting Systems
    2.1 Identity Y-sequences
    2.2 Monoid Presentations of FpGroups
      2.2-1 FreeRelatorGroup
      2.2-2 MonoidPresentationFpGroup
    2.3 Rewriting systems for FpGroups
      2.3-1 RewritingSystemFpGroup
      2.3-2 OnePassReduceWord
      2.3-3 OnePassKB
    2.4 Enumerating elements
      2.4-1 ElementsOfMonoidPresentation
  3 Logged Rewriting Systems
    3.1 Logged Knuth-Bendix Completion
      3.1-1 LoggedOnePassKB
      3.1-2 LoggedKnuthBendix
    3.2 Logged reduction of a word
      3.2-1 LoggedReduceWordKB
      3.2-2 LoggedRewritingSystemFpGroup
  4 Monoid Polynomials
    4.1 Construction of monoid polynomials
      4.1-1 MonoidPolyFromCoeffsWords
    4.2 Components of a polynomial
      4.2-1 Terms
      4.2-2 Monic
      4.2-3 AddTermMonoidPoly
    4.3 Monoid Polynomial Operations
      4.3-1 Length
    4.4 Reduction of a Monoid Polynomial
      4.4-1 ReduceMonoidPoly
  5 Module Polynomials
    5.1 Construction of module polynomials
      5.1-1 ModulePoly
    5.2 Components of a module polynomial
      5.2-1 Terms
    5.3 Module Polynomial Operations
      5.3-1 AddTermModulePoly
    5.4 Identities among relators
      5.4-1 IdentityYSequences
      5.4-2 RootIdentities
  
  
  -------------------------------------------------------
