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Dear Prof. Neil,

in GAP-3.2 there is a package containing programs for working with

Weyl groups and associated Hecke algebras. The latter are certain deformations

of the group ring of the first. There are programs to do computations

in this algebra, e.g. multiplying two basis elements and expressing the

result as a linear combination of the basis vectors. (I am not certain

whether or not GAP has already some built-in functions for comptations

in group rings). Maybe looking at the code or the documented examples

in the chapter 'Weyl group and Hecke algebras' of the manual might help you?

Sincerely yours, Meinolf Geck

(Lehrstuhl D f"ur Mathematik, RWTH Aachen)

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