> < ^ Date: Thu, 10 Feb 1994 23:19:00 -0800
> ^ From: Robert Beals <beals@sisters.cs.uoregon.edu >
> ^ Subject: possible problem with Domain()


I'm having a problem finding the minimal polynomial of a rational
matrix A. MinimalPolynomial(A) first finds D = Domain([A]), and
then applies D.operations.MinimalPolynomial. Unfortunately, if
A is a rational matrix, then Domain([A]) returns Matrices, and
Matrices.operations.MinimalPolynomial is unbound. Is there any
reason why for a rational matrix A, Domain([A]) doesn't return
FieldMatrices? (FieldMatrices.operations.MinimalPolynomial exists.)

I tried to get around this by simply setting

Matrices.operations.MinimalPolynomial :=

This seems to work for rational matrices A, and indeed there is
nothing in the code for FieldMatrices.operations.MinimalPolynomial
that makes any assumptions about the field. However, I also tested
matrices over cyclotomic fields, and ran into difficulties, because
for a cyclotomic field F GAP seems to be unable to compute Euclidean
quotients in F[x] (that is, the ring of polynomials in x over the
field F, not the xth element of the list F). This is puzzling,
but since I'm mainly interested in rational matrices I didn't chase
it down any further.

Any help or advice would be greatly appreciated.

-- Robert Beals

P.S. I'm using version 3 release 3.

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