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# SgpViz

## A GAP package for semigroup visualisation

Version 0.999.5

Manuel Delgado
Email: mdelgado@fc.up.pt
Homepage: https://www.fc.up.pt/cmup/mdelgado

José João Morais

### 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 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 and UID/MAT/00144/2019), 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.

### Colophon

This manual describes the GAP package SgpViz, Version 0.999.5, for visualising finite semigroups.

Since Version 0.998 (released in 2008), the package is maintained by the first author.

The present package is superseded by the GAP package semigroups, by James Mitchel, in what concerns some aspects of semigroup visualisation.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 mdelgado@fc.up.pt 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 https://www.gap-system.org/Contacts/cite.html.

### Contents

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
3.4-2 DotForDrawingSchutzenbergerGraphs
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
References
Index
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