<!-- ------------------------------------------------------------------- --> <!-- --> <!-- intro.xml Gpd documentation Chris Wensley --> <!-- & Emma Moore --> <!-- --> <!-- $Id: intro.xml,v 1.05 2008/11/21 gap Exp $ --> <!-- --> <!-- ------------------------------------------------------------------- --> <?xml version="1.0" encoding="ISO-8859-1"?> <!-- $Id: intro.xml,v 1.05 Exp $ --> <Chapter Label="intro"> <Heading>Introduction</Heading> Groupoids are mathematical categories in which every arrow is invertible. The &gpd; 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/> It was used by Emma Moore in her thesis <Cite Key="emma-thesis" /> to calculate normal forms for Free Products with Amalgamation, and for HNN-extensions, when the initial groups have rewrite systems. <P/> &gpd; is implemented using &GAP; 4.4. <P/> The information parameter <C>InfoGpd</C> takes default value <C>1</C> 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/> Help is available in the usual way. <P/> <Example> <![CDATA[ gap> LoadPackage( "gpd" ); ----------------------------------------------------------- loading Gpd 1.05 for GAP 4.4 - Emma Moore and Chris Wensley ----------------------------------------------------------- true ]]> </Example> For version 1.05 the package has been completely restructured, starting with <E>magmas with objects</E> 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/> 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 <F>tst/gpd_manual.tst</F>.) <Example> <![CDATA[ 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 ]]> </Example> You may reference this package by mentioning <Cite Key="BrMoPoWe" /> and <Cite Key="emma-thesis" />. </Chapter>