> < ^ Date: Mon, 20 Aug 2001 15:31:48 +0200
> < ^ From: Thomas Breuer <Thomas.Breuer@Math.RWTH-Aachen.DE >
> ^ Subject: Re: question about determinant

Dear GAP Forum,

Andrea Donafee wrote

We have the integral group ring ZA of the finitely generated abelian
group A. The abelian group is given by means of a presentation,
but will NOT necessarily be a standard presentation. (In practice it
will be the presentation obtained by abelianising a presentation of a
non abelian group G. eg, If G = <x, y; x^5y^3x^2y^-1> then
A = <X, Y ; XY=YX, X^7Y^2> )

We have an m-by-n matrix M with entries from ZA. Then for each
1 < k =< min{m, n}
we want to compute the determinants of all the k-by-k submatrices
of M. Attempting to call the function DeterminantMat for k > 2,
however, produces an error. Can anyone suggest a different
method to find such determinants?

Currently the GAP function `DeterminantMat' assumes that nonzero
elements in the ring spanned by the matrix entries can be inverted.

If this does not hold, as in your example, we know no other method
for computing a determinant than summing certain products over the
symmetric group or writing the determinant recursively in terms of
determinants of smaller matrices.

Currently we are discussing how to make such a method available in
the next version of GAP.
(Of course this will be useful only in small examples.)

Sorry that this answer comes so late,
which is partially because of the technical
and that there are no better news about this problem.

All the best,

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