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<h1><span class="URL"><a href="https://gap-packages.github.io/sgpviz/">SgpViz</a></span></h1>


<h2>A <strong class="pkg">GAP</strong> package for semigroup visualisation</h2>

<p> Version 0.999.6</p>

</div>
<p><b> Manuel Delgado
    
    
  </b>
<br />Email: <span class="URL"><a href="mailto:mdelgado@fc.up.pt">mdelgado@fc.up.pt</a></span>
<br />Homepage: <span class="URL"><a href="https://www.fc.up.pt/cmup/mdelgado">https://www.fc.up.pt/cmup/mdelgado</a></span>
</p><p><b> José João Morais
  </b>
</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2005 by Manuel Delgado and José João Morais</p>

<p><span class="URL"><a href="https://gap-packages.github.io/sgpviz/">SgpViz</a></span> package is free software; you can redistribute it and/or modify it under the terms of the <span class="URL"><a href="https://www.fsf.org/licenses/gpl.html">GNU General Public License</a></span> 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.



<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>The first author acknowledges financial support of FCT, through the <em>Centro de Matemática da Universidade do Porto</em>.</p>

<p>The second author acknowledges financial support of FCT and the POCTI program through a scholarship given by <em>Centro de Matemática da Universidade do Porto</em>.</p>

<p>Both authors acknowledge Jorge Almeida, Vítor H. Fernandes and Pedro Silva for many helpful discussions and comments.</p>

<p><strong class="button">Concerning maintenance:</strong></p>

<p>The maintainer wants to acknowledge partial support by:</p>

<p>FCT - Fundação para a Ciência e a Tecnologia under the project PTDC/MAT/65481/2006</p>

<p><em>Centro de Matemática da Universidade do Porto</em> (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.</p>

<p>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.</p>

<p>Furthermore, the maintainer wants to thank the organisers of <code class="code">GAPDays</code> 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.</p>

<p><a id="X7982162280BC7A61" name="X7982162280BC7A61"></a></p>
<h3>Colophon</h3>
<p>This manual describes the <strong class="pkg">GAP</strong> package <span class="URL"><a href="https://gap-packages.github.io/sgpviz/">SgpViz</a></span>, Version 0.999.6, for visualising finite semigroups.</p>

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

<p>The present package is superseded by the <strong class="pkg">GAP</strong> package <em>semigroups</em>, 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 <span class="URL"><a href="https://gap-packages.github.io/sgpviz/">SgpViz</a></span> but not in <em>semigroups</em>.</p>

<p>Bug reports, suggestions and comments are, of course, welcome. Please use the email address <span class="URL"><a href="mailto:mdelgado@fc.up.pt">mdelgado@fc.up.pt</a></span> to this effect.</p>

<p>If you have benefited from the use of the <span class="URL"><a href="https://gap-packages.github.io/sgpviz/">SgpViz</a></span> <strong class="pkg">GAP</strong> package in your research, please cite it in addition to <strong class="pkg">GAP</strong> itself, following the scheme proposed in <span class="URL"><a href="https://www.gap-system.org/Contacts/cite.html">https://www.gap-system.org/Contacts/cite.html</a></span>.</p>

<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>

<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">
      Introduction
    </span></a>
</div>
<div class="ContChap"><a href="chap2.html#X868F7BAB7AC2EEBC">2 <span class="Heading">Basics</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7A489A5D79DA9E5C">2.1 <span class="Heading">Examples </span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X85134313846D1A8A">2.2 <span class="Heading">Some attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7F7FAED380682973">2.2-1 HasCommutingIdempotents</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X83F1529479D56665">2.2-2 IsInverseSemigroup</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X78CA2A0D869C51DC">2.3 <span class="Heading">Some basic functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7A65787A83C0F8EF">2.3-1 PartialTransformation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7EEED52C7D38E1CA">2.3-2 ReduceNumberOfGenerators</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7BBEBEE885D05208">2.3-3 SemigroupFactorization</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7FB7633483A45209">2.3-4 GrahamBlocks</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X789D5E5A8558AA07">2.4 <span class="Heading">Cayley graphs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X822983CD7F01B5EA">2.4-1 RightCayleyGraphAsAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X82F7D3E485D615D8">2.4-2 RightCayleyGraphMonoidAsAutomaton</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap3.html#X826F747F81441D2E">3 <span class="Heading">
      Drawings of semigroups
    </span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7F71117D7F0259B8">3.1 <span class="Heading">
        Drawing the D-class of an element of a semigroup
      </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X87448A11856B0F2D">3.1-1 DrawDClassOfElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X78DC47A785011D84">3.1-2 DotForDrawingDClassOfElement</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X81CCF2BB81C4DF6F">3.2 <span class="Heading">
        Drawing the D-classes of a semigroup
      </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7BDBEDA37ADCAADE">3.2-1 DrawDClasses</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X84B611718473E019">3.2-2 DotForDrawingDClasses</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X789D5E5A8558AA07">3.3 <span class="Heading">Cayley graphs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7EB36DB07C6F58A0">3.3-1 DrawRightCayleyGraph</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X86798CC9823D1DB2">3.3-2 DrawCayleyGraph</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8487357A85497320">3.3-3 DotForDrawingRightCayleyGraph</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X79B26A588771144F">3.4 <span class="Heading">Schützenberger graphs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7B7B58B77EA25719">3.4-1 DrawSchutzenbergerGraphs</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7884329D82F6C65B">3.4-2 DotForDrawingSchutzenbergerGraphs</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4.html#X83D3B9D482790646">4 <span class="Heading">User friendly ways to give semigroups and automata</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X811E5FC2849C5644">4.1 <span class="Heading"> 
Finite automata 
      </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8470C731867684DF">4.1-1 XAutomaton</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X836830E97ED27F7F">4.2 <span class="Heading"> Finite semigroups </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7CFD37938771E821">4.2-1 XSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X83397F6B7B44CACD">4.2-2 <span class="Heading"> 
Semigroups given through generators and relations 
      </span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7FCC7AFB793048E2">4.2-3 <span class="Heading"> 
Semigroups given by partial transformations
      </span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X854F0DDF7D612393">4.2-4 <span class="Heading"> 
Syntatic semigroups
      </span></a>
</span>
</div></div>
</div>
<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
<br />
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