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<div class="ChapSects"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
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<h3>1 <span class="Heading">Introduction</span></h3>
<p>Groupoids are mathematical categories in which every arrow is invertible. The <strong class="pkg">Gpd</strong> package provides functions for the computation with groupoids and their morphisms; for graphs of groups and graphs of groupoids. The package is far from complete, and development continues.</p>
<p>It was used by Emma Moore in her thesis <a href="chapBib.html#biBemma-thesis">[Moo01]</a> to calculate normal forms for Free Products with Amalgamation, and for HNN-extensions, when the initial groups have rewrite systems.</p>
<p><strong class="pkg">Gpd</strong> is implemented using <strong class="pkg">GAP</strong> 4.4.</p>
<p>The information parameter <code class="code">InfoGpd</code> takes default value <code class="code">1</code> which, for the benefit of new users, causes more messages to be printed out when operations fail. When raised to a higher value, additional information is printed out.</p>
<p>Help is available in the usual way.</p>
<table class="example">
<tr><td><pre>
gap> LoadPackage( "gpd" );
-----------------------------------------------------------
loading Gpd 1.05 for GAP 4.4 - Emma Moore and Chris Wensley
-----------------------------------------------------------
true
</pre></td></tr></table>
<p>For version 1.05 the package has been completely restructured, starting with <em>magmas with objects</em> and their mappings, and building up to groupoids via semigroups with objects and monoids with objects. This development is ongoing, and this manual does not mention all the available functions. A new version will be released as soon as possible.</p>
<p>Once the package is loaded, it is possible to check the correct installation by running the test suite of the package with the following command. (The test file itself is <code class="file">tst/gpd_manual.tst</code>.)</p>
<table class="example">
<tr><td><pre>
gap> ReadPackage( "gpd", "tst/testall.g" );
+ Testing examples in Chapter 2 of the Gpd manual
+ GAP4stones: 1250
+ Testing examples in Chapter 3 of the Gpd manual
+ GAP4stones: infinity
+ Testing examples in Chapter 4 of the Gpd manual
+ GAP4stones: 416
+ Testing examples in Chapter 5 of the Gpd manual
+ GAP4stones: 2500
+ Testing examples in Chapter 6 of the Gpd manual
+ GAP4stones: 28
</pre></td></tr></table>
<p>You may reference this package by mentioning <a href="chapBib.html#biBBrMoPoWe">[BMPW02]</a> and <a href="chapBib.html#biBemma-thesis">[Moo01]</a>.</p>
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