Some GAP programs

Below are links to some GAP programs I have constructed for various purposes. Those marked (*) use the GAP share package GRAPE, by L. H. Soicher. This requires the graph automorphism package nauty, and runs only on UNIX systems (including GNU/Linux!)

Of course, these programs are provided with no guarantee! In addition, they may be updated at any time. Current versions are 25/07/2003 unless otherwise noted.

1. Programs from the book Permutation Groups:
   • Chapter 1
   • Chapter 3 (*)

2. Functions for primitive lambda-roots. A primitive lambda-root of n is an element of maximum order in the group of units mod n. Read the notes by me and D. A. Preece for documentation.

3. Functions for association schemes and permutation groups. Read in conjunction with this the paper

   Peter J. Cameron, Coherent configurations, association schemes, and permutation groups, pp. 55-71 in Groups, Combinatorics and Geometry (ed. A. A. Ivanov, M. W. Liebeck and J. Saxl), World Scientific, Singapore, 2003

   and see also the web page Classification of association schemes with small vertices by A. Hanaki and I. Miyamoto.
   • 2-closure of a transitive group (this is much faster than the inbuilt GAP function) (*)
   • functions for coherent configurations and association schemes (*)
   • functions for testing AS-related properties of a permutation group

4. Functions for Latin squares and Steiner triple systems, using the DESIGN package (*) by L. H. Soicher. The main point of these is to implement the Markov chain method for choosing random Latin squares described in

   M. T. Jacobson and P. Matthews, Generating uniformly distributed random Latin squares, J. Combinatorial Design 4 (1996), 405-437

   and the analogous chain for Steiner triple systems. Some properties (transversals and orthogonal mates for Latin squares, parallel classes and resolutions for STS) are also calculated.
   • Latin squares
   • Steiner triple systems

This page maintained by P.J.Cameron@qmul.ac.uk
Last modified 25 July 2003