  
  
                                      [1X[5XGpd[0m[1X[0m
  
  
              [1XGroupoids, graphs of groups, and graphs of groupoids[0m
  
  
                                  Version 1.05
  
  
                                 November 2008
  
  
                                   Emma Moore
  
                                 Chris Wensley
  
  
  
  Emma Moore
      Email:    [7Xmailto:emmajmoore@yahoo.co.uk[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  [5XGpd[0m  package  for  [5XGAP[0m4  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  [5XGpd[0m  package  was originally implemented in 2000 (as [5XGraphGpd[0m) 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  [13Xmagma  with objects[0m. 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 [7Xmailto:c.d.wensley@bangor.ac.uk[0m.
  
  
  -------------------------------------------------------
  [1XCopyright[0m
  © 2000-2008 Emma Moore and Chris Wensley
  
  
  -------------------------------------------------------
  [1XAcknowledgements[0m
  This  [5Xgpd[0m  package  is  released under the GNU General Public License (GPL).
  This  file  is part of [5Xgpd[0m, though as documentation it is released under the
  GNU            Free           Documentation           License           (see
  [7Xhttp://www.gnu.org/licenses/licenses.html#FDL[0m).
  
  [5Xgpd[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.
  
  [5Xgpd[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
  [5Xgpd[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 (Gpd)[0X
  
  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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