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# Semigroup visualization

( Version 0.998 )

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

José João Morais
Email: josejoao@fc.up.pt

### Copyright

© 2005 by Manuel Delgado and José João Morais

We adopt the copyright regulations of GAP as detailed in the copyright notice in the GAP manual.

### Acknowledgements

The first author aknowledges 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 helpfull discussions and comments.

### Colophon

Bug reports, suggestions and comments are, of course, welcome. Please use the email address mdelgado@fc.up.pt or josejoao@fc.up.pt to this effect.

### 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
3.2 Drawing the D-classes of a semigroup
3.2-1 DrawDClasses
3.3 Cayley graphs
3.3-1 DrawRightCayleyGraph
3.3-2 DrawCayleyGraph
3.4 Schutzenberger 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
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