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. Add dimension bounds on any tests over AA that compute element
+ subalgebras.
+
+5. The rational_algebra() stuff doesn't really belong in classes that
+ don't derive from RationalBasisEJA or its as-yet-nonexistent
+ element class.