ATLAS of Finite Group Representations

Format information

As a general rule, matrices and permutations are stored in Meataxe format, which is fully explained in the Meataxe manuals. Here we give a brief description which should be sufficient for a beginner to get started.

• Each file starts with a header line which contains some information about the content of the file. This can be ignored if you are not using the Meataxe.
• A permutation p is stored in image format, which means that the file consists of a list of the images p(1), p(2), ... of the points 1, 2, ...
• A matrix is written in the usual way, reading across each row in turn. There are line breaks at the end of each row, and after each 80 characters (usually) in each row. There may or may not be space(s) between the individual entries.
• The entries in a matrix come from a finite field, of order pn say. If this is a prime field, then the elements are just the integers 0, 1, 2, ...p-1.
• If the field is not prime, then the labelling of the elements is done by reference to the so-called Conway polynomials Cn(X). Among other things, these polynomials are irreducible of degree n, so by taking the polynomial ring modulo Cn(X) we obtain the field of order pn. A polynomial an-1Xn-1 + ... is then stored as the non-negative integer an-1pn-1 + ... .
Other representations are stored in GAP or MAGMA format. It is hoped eventually to provide automatic translation between various different formats, but this has not yet been implemented.