We can't use the _rational_algebra to get minimal polynomials like we
do with characteristic ones. The secret with the charpolys is that the
(irrational) coordinates of the element are hidden behind polynomial
variables. With the minimal polynomial, we'd need to operate on them
directly... but we can't, in a rational algebra.
could easily cache the identity and charpoly coefficients using
the nontrivial factor. On the other hand, it's nice that we can
test out some alternate code paths...
-
-4. Can we hit "x" with the deortho matrix and delegate to the
- _rational_algebra to speed up minimal_polynomial?