Coset Enumeration using Prefix Gröbner Bases in MRC - An Experimental Approach

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

Abstract:

Based on prefix Gröbner bases as implemented in MRC 1.2 (see [13]) we study a new method to enumerate cosets. It is compared to well known methods for Todd-Coxeter enumeration using the examples from [1,3] where studies of these methods are reported. New insights into coset enumeration were gained using three different kinds of orderings combined with the new frameworks and strategies implemented in MRC 1.2.

Keywords
Gröbner bases, monoid and group rings, prefix reduction, coset enumeration