chap0.txt

  
  
                                     SgpViz
  
  
                   A GAP package for semigroup visualisation
  
  
                                Version 0.999.1
  
  
                                 Manuel Delgado
  
                                José João Morais
  
  
  
  Manuel Delgado
      Email:    mailto:[email protected]
      Homepage: http://www.fc.up.pt/cmup/mdelgado
  
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  Copyright
  © 2005 by Manuel Delgado and José João Morais
  
  SgpViz  package  is  free software; you can redistribute it and/or modify it
  under     the     terms     of    the    GNU    General    Public    License
  (http://www.fsf.org/licenses/gpl.html)  as  published  by  the Free Software
  Foundation;  either  version 2 of the License, or (at your option) any later
  version.  For details, see the file 'GPL' included in the package or see the
  FSF's own site.
  
  
  -------------------------------------------------------
  Acknowledgements
  The  first  author acknowledges financial support of FCT, through the Centro
  de Matemática da Universidade do Porto.
  
  The  second  author  acknowledges  financial  support  of  FCT and the POCTI
  program  through a scholarship given by Centro de Matemática da Universidade
  do Porto.
  
  Both  authors  acknowledge Jorge Almeida, Vítor H. Fernandes and Pedro Silva
  for many helpful discussions and comments.
  
  Concerning maintenance:
  
  The maintainer wants to acknowledge partial support by:
  
  FCT   -   Fundação   para  a  Ciência  e  a  Tecnologia  under  the  project
  PTDC/MAT/65481/2006
  
  Centro de Matemática da Universidade do Porto (CMUP), funded by the European
  Regional   Development  Fund  through  the  programme  COMPETE  and  by  the
  Portuguese Government through the FCT project PEst-C/MAT/UI0144/2011.
  
  CMUP  (UID/MAT/00144/2013),  which is funded by FCT (Portugal) with national
  (MEC)  and  European  structural funds through the programs FEDER, under the
  partnership agreement PT2020.
  
  Furthermore,  the  maintainer  wants  to  thank the organisers of GAPDays in
  their  several  editions,  as  well  as  several people (for advises, giving
  feedback,  etc).  Among them I would like to refer: Max Horn, James Mitchel,
  Jan Philipp Wächter, João Araújo, Alfredo Costa and Teresa Melo.
  
  
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  Colophon
  This   manual  describes  the  GAP  package  SgpViz,  Version  0.999.1,  for
  visualising finite semigroups.
  
  Since  Version  0.998  (released  in 2008), the package is maintained by the
  first author.
  
  The  present  package  is  supersede by the GAP package semigroups, by James
  Mitchel,  in  what  concerns  some  aspects  of  semigroup visualisation. We
  strongly  recommend  the  usage  of  that  package,  unless  you find useful
  specific tools available in SgpViz but not in semigroups.
  
  Bug  reports,  suggestions  and comments are, of course, welcome. Please use
  the email address mailto:[email protected] to this effect.
  
  If  you  have  benefited  from  the  use  of  the SgpViz GAP package in your
  research,  please  cite  it  in addition to GAP itself, following the scheme
  proposed in http://www.gap-system.org/Contacts/cite.html.
  
  
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  Contents (SgpViz)
  
  1 Introduction
  2 Basics
    2.1 Examples
    2.2 Some attributes
      2.2-1 HasCommutingIdempotents
      2.2-2 IsInverseSemigroup
    2.3 Some basic functions
      2.3-1 PartialTransformation
      2.3-2 ReduceNumberOfGenerators
      2.3-3 SemigroupFactorization
      2.3-4 GrahamBlocks
    2.4 Cayley graphs
      2.4-1 RightCayleyGraphAsAutomaton
      2.4-2 RightCayleyGraphMonoidAsAutomaton
  3 Drawings of semigroups
    3.1 Drawing the D-class of an element of a semigroup
      3.1-1 DrawDClassOfElement
      3.1-2 DotForDrawingDClassOfElement
    3.2 Drawing the D-classes of a semigroup
      3.2-1 DrawDClasses
      3.2-2 DotForDrawingDClasses
    3.3 Cayley graphs
      3.3-1 DrawRightCayleyGraph
      3.3-2 DrawCayleyGraph
      3.3-3 DotForDrawingRightCayleyGraph
    3.4 Schützenberger graphs
      3.4-1 DrawSchutzenbergerGraphs
    3.5 Drawings output formats
      3.5-1 DrawingsListOfExtraFormats
      3.5-2 DrawingsExtraFormat
      3.5-3 SetDrawingsExtraFormat
    3.6 Drawings extra graph attributes
      3.6-1 DrawingsExtraGraphAttributes
      3.6-2 SetDrawingsExtraGraphAttributes
      3.6-3 ClearDrawingsExtraGraphAttributes
  4 User friendly ways to give semigroups and automata
    4.1 Finite automata
      4.1-1 XAutomaton
    4.2 Finite semigroups
      4.2-1 XSemigroup
      4.2-2 Semigroups given through generators and relations
      4.2-3 Semigroups given by partial transformations
      4.2-4 Syntatic semigroups