## &Circle;

Adjoint groups of finite rings
Version 1.2
Alexander Konovalov konovalov@member.ams.org http://www.cs.st-andrews.ac.uk/˜alexk/

                School of Computer Science

                University of St Andrews

                Jack Cole Building, North Haugh,

                St Andrews, Fife, KY16 9SX, Scotland

Panagiotis Soules psoules@math.uoa.gr

                Department of Mathematics

                National and Capodistrian University of Athens

                Panepistimioupolis, GR-15784, Athens, Greece

April 2007

&Circle; package 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 r \cdot s = r + s + rs , and to compute adjoint semigroups and adjoint groups of finite rings.

&copyright; 2006-2007 by Alexander Konovalov and Panagiotis Soules

&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 http://www.gnu.org/licenses/gpl.html.

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

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

A. Konovalov, P. Soules. Circle --- Adjoint groups of associative rings, Version 1.2; 2007 (http://www.cs.st-andrews.ac.uk/˜alexk/circle.htm).

We acknowledge very much Alexander Hulpke for helpful comments and advise.

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