Goto Chapter: Top 1 2 3 4 Bib Ind

# Circle

## Adjoint groups of finite rings

Version 1.5.4

8 January 2016

Alexander Konovalov
Email: alexk@mcs.st-andrews.ac.uk
Homepage: 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
Email: psoules@math.uoa.gr
Department of Mathematics
National and Capodistrian University of Athens
Panepistimioupolis, GR-15784, Athens, Greece

### Abstract

The GAP4 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. Also it may serve as an example of extending the GAP system with new multiplicative objects.

© 2006-2016 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 finite rings, Version 1.5.4; 2016 (http://www.cs.st-andrews.ac.uk/~alexk/circle/).

### 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.

Goto Chapter: Top 1 2 3 4 Bib Ind

generated by GAPDoc2HTML