Minpoly and charpoly don't check their arguments correctly

[Snark]

The following fails in sage (likewise with charpoly):

k=CyclotomicField(10)
U=matrix(k, 1,1,[1])
var('t')
U.minpoly(t)

The error is in a call that the function makes to PolynomialRing? :

TypeError: invalid input (Cyclotomic Field of order 10 and degree 4, t, None) to PolynomialRing function; please see the docstring for that function

Strangely, if you use :

k=CyclotomicField(10)
U=matrix(k, 1,1,[1])
var('t')
U.minpoly('t')

everything is fine.

In any case, I would expect charpoly/minpoly to complain themselves if I don't call them correctly (which isn't clear at all!) -- it's definitely not normal (and upsetting for newbies) that another function reacts.

This is with sage-5.1.beta6.

[aapitzsch]

The attached patch fixes the problem and contains some code clean-up.

[Snark]

Eh, just moving that piece of code around is enough? Good!

Five hours between the report and the patch? Excellent!

Thanks!

[robertwb]

Yep, that looks like a good fix to me. Lots of style changes (improvements) in this patch as well, but that's fine.