<?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/˜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> ©right; 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/˜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>