<?xml version="1.0" encoding="ISO-8859-1"?>

<!-- $Id: manual.xml,v 1.8 2008/01/18 15:54:39 alexk Exp $ -->

<!DOCTYPE Book SYSTEM "gapdoc.dtd"
[<!ENTITY Circle "<Package>Circle</Package>">] >

<Book Name="Circle">

<TitlePage>
  <Title>&Circle;</Title>
  <Subtitle>Adjoint groups of finite rings</Subtitle>
  <Version>Version 1.3.1</Version>

  <Author>Alexander Konovalov
          <Email>konovalov@member.ams.org</Email>
	      <Homepage>http://www.cs.st-andrews.ac.uk/&tilde;alexk/</Homepage>
          <Address>
            School of Computer Science<Br/>
            University of St Andrews<Br/>
            Jack Cole Building, North Haugh,<Br/>
            St Andrews, Fife, KY16 9SX, Scotland
          </Address> 
  </Author>

  <Author>Panagiotis Soules
          <Email>psoules@math.uoa.gr</Email>
          <Address>
            Department of Mathematics<Br/>
            National and Capodistrian University of Athens<Br/>
            Panepistimioupolis, GR-15784, Athens, Greece
          </Address>        
  </Author>

  <Date>January 2008</Date>

<Abstract>

<Index Key="Circle package">&Circle; package</Index> 
The &GAP;4 package &Circle; extends the &GAP; functionality 
for computations in adjoint groups of associative rings.
It provides functionality to construct circle objects that will 
respect the circle multiplication <M> r \cdot s = r + s + rs </M>, 
and to compute adjoint semigroups and adjoint groups of finite rings.
<P/>

</Abstract>

<Copyright>

&copyright; 2006-2008 by Alexander Konovalov and Panagiotis Soules
<P/>

&Circle; is free software; you can redistribute it and/or modify it 
under the terms of the GNU General Public License as published by 
the Free Software Foundation; either version 2 of the License, or 
(at your option) any later version. For details, see the FSF's own site
<URL>http://www.gnu.org/licenses/gpl.html</URL>.
<P/>

If you obtained &Circle;, we would be grateful for a short notification
sent to one of the authors.
<P/>

If you publish a result which was partially obtained with the usage of
&Circle;, please cite it in the following form:
<P/>

A. Konovalov, P. Soules. 
<E>Circle --- Adjoint groups of finite rings, Version 1.3.1;</E> 2008 
(<URL>http://www.cs.st-andrews.ac.uk/&tilde;alexk/circle.htm</URL>).
</Copyright>
  
<Acknowledgements>

We acknowledge very much Alexander Hulpke and James Mitchell 
for their helpful comments and advices, and the referee for 
testing the package and useful suggestions.
<P/> 

</Acknowledgements>

</TitlePage>

<TableOfContents/>

<Body>
<#Include SYSTEM "intro.xml">
<#Include SYSTEM "objects.xml">
<#Include SYSTEM "funct.xml">
<#Include SYSTEM "example.xml">
</Body>

<Bibliography Databases="manual"/>

<TheIndex/>

</Book>