Computational techniques applied to group presentations

Abstract

Designs for a collection of re-usable software modules are developed. The modules are implemented in C and expressed in a tool-kit for the Unix operating system. Each tool is an expert in some aspect of the manipulation by computer of group presentations. The granularity of the tool-kit has been chosen so that common usages of the Todd-Coxeter and Reidemeister-Schreier methods can be expressed in various ways using any tool composition language (eg. shell scripts), and running as a collection of co-operating processes. Data file formats for the interchange of group-theoretic information between processes are described. The tools are tested on well-known examples, and are used to prove a long-standing conjecture. Use of the tools as the basis for a rule-based "expert system" is discussed.