Workaround for linbox charpoly/minpoly issues

[user202729]

As in the title. Fix #37068. Can be removed once the upstream issue linbox-team/linbox#53 is fixed.

It's possible to do a more expensive check (e.g. check if the matrix satisfy the minpoly with something like Freivalds' algorithm), but I guess this suffice (and it's very cheap).

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[orlitzky]

If that (leading? last?) coefficient guaranteed to be != 1 if the algorithm fails?

I think the "linbox is unreliable" comments would be more helpful around while True, since that's the unexpected part.

[user202729]

If that (leading? last?) coefficient guaranteed to be != 1 if the algorithm fails?

my understanding is that the algorithm fails if it incorrectly choose a prime that makes the minpoly mod that prime's degree less than the minpoly over ℤ's degree. If that happens (and at least a good prime is selected) then the leading coefficient must be ≡ 1 mod the good primes and ≡ 0 mod the bad prime, so it cannot be 1.

A corner case I can think of is what if all primes selected are bad, but I think this is impossible because of the Hadamard bound.

[orlitzky]

So the size of the coefficient list is known beforehand? I was thinking it might still output a monic polynomial but of a lesser degree, which, if the zeros are omitted, could still have lc() == 1.

Regardless, this can't be any worse, and fixes the reproducible case that we have. Let's try it.