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Bangor University - School of Computer Science

Computational Higher-dimensional Discrete Algebra

University of Wales Crest

CHDA : Introduction to the Bangor GAP Packages

General Introduction

Computational discrete algebra is concerned with algorithms for computing with groups, semigroups, categories, algebras, and related structures, as well as automorphism objects of combinatorial structures.
The two general-purpose CDA packages are GAP and MAGMA.
Work at Bangor is aimed at developing GAP packages implementing many of the new, higher-dimensional, algebra structures which are described in the Algebra and Algebraic Topology pages.

The XMod Package

This package was developed as part of Murat Alp's Ph.D. thesis, and accepted as a GAP3 package in 1996.
A complete conversion for GAP 4.4 was finished in January 2004.

The following structures are implemented:

The Gpd Package

This package formed part of Emma Moore's Ph.D. thesis in December 2000.
It was originally called GraphGpd, but was not made generally available.
Version 1.003 for GAP 4.4 was completed in January 2004.

After extensive revision, concentrating more on the functions for groupoids rather than those for graphs of groups,
version 1.01 of Gpd was made available on 01/06/06.

Gpd became an accepted GAP package in May 2015.

The following structures are implemented:

The Kan Package

This GAP3 package was developed as part of Anne Heyworth's Ph.D. thesis.
The GAP4 version, Kan 0.94, was made available on 02/06/06.
Kan became an accepted GAP package in May 2015.

The functions available at present are those for double coset rewriting systems for finitely presented groups.
Functions from the Automata package are used to compute word acceptors and their languages for these rewrite systems.
KBMAG functions are also used when no finite complete rewriting system is available for the group.

The following structures are implemented:

This package has been made available in support of the Bangor preprint 05.07, now published as J. Symbolic Comp. 41 (2006) 573-590.

For further information see Anne's KAN page.

The IdRel Package

This GAP3 package was developed as part of Anne Heyworth's Ph.D. thesis.
The GAP4 version IdRel 2.02 was made available on 2nd June 2006.
IdRel became an accepted GAP package in June 2015.

The following structures are implemented:

Package releases on GitHub

From November 2016 new releases of these packages can be found on GitHub.

The first versions of the packages released in this way were as follows:

Package repositories on GitHub

All four packages have repositories on GitHub. Users are encouraged to raise issues in the following places:


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Latest modification to this page: 16/11/16