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Dear Gap-Forum,

Stefan Kohl wrote:

Thomas Breuer wrote:

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.Is only no better method known, or is there in fact a theorem that states

that in 'general', there is no more efficient way to compute the determinant ?Best wishes,

Stefan

There is a polynomial time fraction-free method of computing determinants

due to Bareiss that works in an arbitrary integral domain. It is described

in Sections 9.2, 9.3 of "Algorithms for Computer Algebra" by Geddes,

Czapor and Labahn. I don't have any direct knowledge or experience of it

myself though!

Derek Holt.

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