ATLAS of Finite Group Representations
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.
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.
- 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
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 + ... .
For advanced users only
Most representations are stored not only as ASCII files, but also as
Meataxe binaries. These can be accessed by replacing the directory
/atlasreps/ in the URL by /atlasbin/. They are frequently significantly smaller
than the ASCII files, but as they may be machine- and meataxe-version-
dependent, we cannot guarantee that you will be able to read them.
20th July 1998.