<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head> <title>GAP (Gpd) - Chapter 1: Introduction</title> <meta http-equiv="content-type" content="text/html; charset=UTF-8" /> <meta name="generator" content="GAPDoc2HTML" /> <link rel="stylesheet" type="text/css" href="manual.css" /> </head> <body> <div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a> <a href="chap1.html">1</a> <a href="chap2.html">2</a> <a href="chap3.html">3</a> <a href="chap4.html">4</a> <a href="chap5.html">5</a> <a href="chap6.html">6</a> <a href="chap7.html">7</a> <a href="chapBib.html">Bib</a> <a href="chapInd.html">Ind</a> </div> <div class="chlinkprevnexttop"> <a href="chap0.html">Top of Book</a> <a href="chap0.html">Previous Chapter</a> <a href="chap2.html">Next Chapter</a> </div> <p><a id="X7DFB63A97E67C0A1" name="X7DFB63A97E67C0A1"></a></p> <div class="ChapSects"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a> </div> <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> <div class="chlinkprevnextbot"> <a href="chap0.html">Top of Book</a> <a href="chap0.html">Previous Chapter</a> <a href="chap2.html">Next Chapter</a> </div> <div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a> <a href="chap1.html">1</a> <a href="chap2.html">2</a> <a href="chap3.html">3</a> <a href="chap4.html">4</a> <a href="chap5.html">5</a> <a href="chap6.html">6</a> <a href="chap7.html">7</a> <a href="chapBib.html">Bib</a> <a href="chapInd.html">Ind</a> </div> <hr /> <p class="foot">generated by <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p> </body> </html>