IdRel
  
  
                    A package for Identities among Relators
  
  
                                  Version 2.05
  
  
                                 November 2008
  
  
                                 Anne Heyworth
  
                                 Chris Wensley
  
  
  
  Anne Heyworth
      Email:    mailto:anne.heyworth@googlemail.com
  Chris Wensley
      Email:    mailto:c.d.wensley@bangor.ac.uk
      Homepage: http://www.bangor.ac.uk/~mas023/
      Address:  School of Computer Science, Bangor University,
                Dean Street, Bangor, Gwynedd, LL57 1UT, U.K.
  
  
  
  -------------------------------------------------------
  Abstract
  The  IdRel  package  was  originally  implemented  in  1999, using the GAP 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  rewriting 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 mailto:c.d.wensley@bangor.ac.uk.
  
  
  -------------------------------------------------------
  Copyright
  © 2005-2008 Anne Heyworth and Chris Wensley
  
  
  -------------------------------------------------------
  Acknowledgements
  This  idrel  package is released under the GNU General Public License (GPL).
  This file is part of idrel, though as documentation it is released under the
  GNU            Free           Documentation           License           (see
  http://www.gnu.org/licenses/licenses.html#FDL).
  
  idrel  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.
  
  idrel  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
  idrel; if not, write to the Free Software Foundation, Inc., 59 Temple Place,
  Suite 330, Boston, MA 02111-1307 USA.
  
  For more details, see http://www.fsf.org/licenses/gpl.html.
  
  This  documentation  was  prepared with the GAPDoc package of Frank L\"ubeck
  and Max Neunh\"offer.
  
  
  -------------------------------------------------------
  
  
  Contents (IdRel)
  
  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
  
  
  -------------------------------------------------------