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Dear Forum,

I have put together a collection of programs to investigate and deal

with classical groups over finite fields. These programs will

eventually become part of the new version of GAP (4.1 or 4.2). The

current programs work with GAP 3.4.3 but are still experimental.

However, I hope that you find them useful when dealing with matrix

groups over finite fields. I have put together a tar archive of these

functions which can be used like a share package.

This archive includes functions to recognise SL, SP, SU, SO in a

non-constructive way, to recognise SL, SP in a construtive way, to

construct the full orthogonal group, a slightly changed 'OrderMat',

which will handle matrices over finite fields efficiently, a new

(pseudo) random function for matrix groups (actually for any group,

see the manual entry), a function to compute the spinor norm, a

function to check whether a given matrix is a primitive prime divisor

element, and a function to compute an invariant quadratic form. As

the programs are written completely in GAP, they run under all

operating systems. However, the functions to compute an invariant

bilinear/quadratic form use the share package "meataxe", so you need

UNIX for these functions (this will be changed).

You can find the archive under:

ftp://ftp.math.rwth-aachen.de/pub/incoming/classic-1.1.tar.gz

To install it, go into the directory "gap3r4p3/pkg" and untar the

archive. To print the manual, go into the directory

"gap3r4p3/pkg/classic/doc" and latex the file "latexme.tex". If you

don't have the share package "meataxe" you have to comment out the

last line in "gap3r4p3/pkg/classic/init.g". As this is still a beta

version, please to not contact the GAP forum in case of trouble but

Frank.Celler@Math.RWTH-Aachen.DE

kind regards

Frank

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