Gpd
  
  
              Groupoids, graphs of groups, and graphs of groupoids
  
  
                                  Version 1.05
  
  
                                 November 2008
  
  
                                   Emma Moore
  
                                 Chris Wensley
  
  
  
  Emma Moore
      Email:    mailto:emmajmoore@yahoo.co.uk
  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.
  
  
  
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  Abstract
  The  Gpd  package  for  GAP4  provides  functions  for  the computation with
  groupoids  (categories with every arrow invertible) and their morphisms; for
  graphs of groups, and graphs of groupoids.
  
  It  provides  normal  forms  for  Free  Products  with  Amalgamation and for
  HNN-extensions  when  the  initial  groups  have  rewrite  systems  and  the
  subgroups have finite index.
  
  The  Gpd  package  was originally implemented in 2000 (as GraphGpd) when the
  first author was studying for a Ph.D. in Bangor.
  
  The  current  version  is  1.05,  released  on  21st  November 2008, and now
  includes  the  more  basic  structure  of  magma  with objects. It had to be
  released  hurriedly,  due  to the change of website, so some of the function
  are no longer available. A new version will be released as soon as possible.
  
  Bug  reports,  suggestions  and  comments  are,  of  course, welcome. Please
  contact the second author at mailto:c.d.wensley@bangor.ac.uk.
  
  
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  Copyright
  © 2000-2008 Emma Moore and Chris Wensley
  
  
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  Acknowledgements
  This  gpd  package  is  released under the GNU General Public License (GPL).
  This  file  is part of gpd, though as documentation it is released under the
  GNU            Free           Documentation           License           (see
  http://www.gnu.org/licenses/licenses.html#FDL).
  
  gpd  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.
  
  gpd  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
  gpd;  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.
  
  
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  Contents (Gpd)
  
  1 Introduction
  2 Many-object structures
    2.1 Magmas with objects
      2.1-1 MagmaWithObjects
      2.1-2 MultiplicativeElementWithObjects
      2.1-3 IsSinglePiece
  3 Homomorphisms of many-object structures
    3.1 Homomorphisms of magmas with objects
      3.1-1 MagmaWithObjectsHomomorphism
  4 Groupoids
    4.1 Groupoids: their elements and attributes
      4.1-1 SinglePieceGroupoid
      4.1-2 Pieces
      4.1-3 IsPermGroupoid
      4.1-4 GroupoidElement
      4.1-5 IsSinglePiece
    4.2 Subgroupoids
      4.2-1 SubgroupoidByPieces
    4.3 Stars, Costars and Homsets
      4.3-1 ObjectStar
      4.3-2 IdentityElement
    4.4 Left, right and double cosets
      4.4-1 RightCoset
    4.5 Conjugation
      4.5-1 \^
  5 Homomorphisms of Groupoids
    5.1 Homomorphisms to a connected groupoid
      5.1-1 GroupoidHomomorphism
  6 Graphs of Groups and Groupoids
    6.1 Digraphs
      6.1-1 FpWeightedDigraph
    6.2 Graphs of Groups
      6.2-1 GraphOfGroups
      6.2-2 IsGraphOfFpGroups
      6.2-3 RightTransversalsOfGraphOfGroups
    6.3 Words in a Graph of Groups and their normal forms
      6.3-1 GraphOfGroupsWord
      6.3-2 ReducedGraphOfGroupsWord
    6.4 Free products with amalgamation and HNN extensions
      6.4-1 FreeProductWithAmalgamation
      6.4-2 HnnExtension
    6.5 GraphsOfGroupoids and their Words
      6.5-1 GraphOfGroupoids
      6.5-2 GraphOfGroupoidsWord
  7 Development History
    7.1 Versions of the Package
    7.2 What needs to be done next?
  
  
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