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Coset Enumeration Using Prefix Gröbner Bases: An Experimental Approach

Published online by Cambridge University Press:  01 February 2010

Birgit Reinert  and
Dirk Zeckzer
Birgit Reinert
Affiliation:
Fachbereich Informatik, Universität Kaiserslautern, 67663 Kaiserslautern, Germany, reinert@informatik.uni-kl.de
Dirk Zeckzer
Affiliation:
Fachbereich Informatik, Universität Kaiserslautern, 67663 Kaiserslautern, Germany, zeckzer@informatik.uni-kl.de

Abstract

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The authors study a new method for coset enumeration in finitely presented groups. Their method uses prefix Gröbner basis computation in the monoid ring ${\mathbb{K}}[{\cal M}]$, where ${\mathbb{K}}$ is a computable field and ${\cal M}$ a monoid presented by a convergent string-rewriting system. The method is compared to well-known methods for Todd-Coxeter enumeration, using examples from the literature where studies of these methods are reported. New insights into coset enumeration were gained using three different kinds of orderings, combined with new frameworks and strategies implemented in MRC 1.2.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 4 , 2001 , pp. 74 - 134
Copyright
Copyright © London Mathematical Society 2001

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