<!DOCTYPE Book SYSTEM "gapdoc.dtd"
[ <!ENTITY Circle "Circle">
<#Include Label="PKGVERSIONDATA">
] >
<Book Name="Circle">
<TitlePage>
<Title>&Circle;</Title>
<Subtitle>Adjoint groups of finite rings</Subtitle>
<Version>Version &VERSION;</Version>
<Author>Olexandr Konovalov
<Email>obk1@st-andrews.ac.uk</Email>
<Homepage>https://alex-konovalov.github.io/</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>&RELEASEDATE;</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.
Also it may serve as an example of extending the &GAP; system with
new multiplicative objects.
<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>https://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/>
O. Konovalov, P. Soules.
<E>Circle --- Adjoint groups of finite rings, Version &VERSION;;</E>
&RELEASEYEAR; (<URL>https://gap-packages.github.io/circle/</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>
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