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
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.