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<!--  intro.xml              Gpd documentation            Chris Wensley  -->
<!--                                                       & Emma Moore  -->
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<!--  $Id: intro.xml,v 1.01 2006/05/16 gap Exp $                         -->
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<?xml version="1.0" encoding="ISO-8859-1"?>
  <!-- $Id: intro.xml,v 1.01  Exp $ -->

<Chapter Label="intro">
<Heading>Introduction</Heading>

Groupoids are mathematical categories in which every arrow is invertible. 
The &gpd; share 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. 
Some of the utility functions in the <Package>XMod</Package> 
share package for crossed modules are used.
<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 XMod 2.007 for GAP 4.4 - Murat Alp and Chris Wensley
------------------------------------------------------------
-----------------------------------------------------------
loading Gpd 1.01 for GAP 4.4 - Emma Moore and Chris Wensley
-----------------------------------------------------------
true
gap> ?Groupoid
Help: several entries match this topic - type ?2 to get match [2]

[1] Gpd: Groupoid
[2] loops (not loaded): groupoid
[3] Gpd: Groupoids
[4] Gpd: Groupoids: their elements and attributes
[5] Gpd: GroupoidByUnion
[6] Gpd: GroupoidElement
[7] Gpd: GroupoidMorphismByComponents
[8] Gpd: GroupoidMorphism
[9] Gpd: GroupoidsOfGraphOfGroupoids
]]>
</Example>

You may reference this package by mentioning <Cite Key="BrMoPoWe" />
and <Cite Key="emma-thesis" />.
</Chapter>
