> < ^ From:

^ Subject:

I'm in the process of posting a file called moddist.tar.z (gzipped) to the

anonymous ftp site at Aachen

(<ftp://ftp.math.rwth-aachen.de/pub/incoming>). The connection from

Australia to Germany is atrocious, but hopefully the file will get there

within the next day or two.

This package contains various functions for computing information about

modules for matrix algebras. I've included the README file below which

lists most of the important functions, and there are a number of (hopefully

informative) example files included with the code to get people started.

Hope this is of use to someone out there. Comments and suggestions welcome.

Currently there is no user documentation (apart from the README file), but

examining the README file and the example files would be a good first step

for anyone interested in using the package.

Cheers,

Michael.

--------------------------------------------------------------------------- README for GAP modules code Michael J Smith, School of Mathematical Sciences, ANU 21:07 Wed 22 Nov 1995 ---------------------------------------------------------------------------

The files in subdirectory "modules" contain routines for computing with

modules over matrix group algebras. Included are routines for:

(1) defining module records: gap> M := GModule([mat1, mat2, ...]);

(2) computing the decomposition of a module into a direct sum of

indecomposable summands:

gap> computeDecomposition(M);

(3) computing isomorphisms between modules:

gap> X := isomorphismModules(M1, M2);

(4) computing module endomorphism algebra:

gap> E := moduleEndAlgBasis(M);

(5) computing module homomorphism groups: gap> H := moduleHomBasis(M1, M2);

(6) computing module automorphisms; generators for the multiplicative

subgroup of invertible elements of the endomorphism algebra, and the order

of this matrix group:

gap> A := moduleAutGenerators(M);

gap> o := moduleAutOrder(M);

(7) computing the centraliser in GL(n,p) of a subgroup of GL(n,p): gap> U := MatGroup([mat1, mat2, ...], GF(p)); gap> C := MatGroupCentraliser(U); (note that this is equivalent to the computation in (6))

(8) assorted other routines used by the above.

There are a number of example files that demonstrate most of the routines

that are available.

--------------------------------------------------------------------------- INSTALLATION:

The simplest way to use these files is to define a gap variable called

"LOCALNAMEmodules" pointing to the subdirectory "modules", and then to

issue the command

gap> Read(Concatenation(LOCALNAMEmodules, "init.gap"));

For example, with the "modules" directory copied to /home/user/gap/modules/,

issue the following commands to GAP:

gap> LOCALNAMEmodules := "/home/user/gap/modules/";

gap> Read(Concatenation(LOCALNAMEmodules, "init.gap"));

---------------------------------/|-|--|-|--|-Michael-Smith------------------ Michael.Smith@maths.anu.edu.au /-| |\ | | | Mathematics (CMA) -------------------------------/--|-|-\|-|_/|-Australian-National-University-

http://wwwmaths.anu.edu.au/~smith/Michael_Smith.html

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