1. Add references and start citing them.

2. Profile (and fix?) any remaining slow operations.

3. When we take a Cartesian product involving a trivial algebra, we
   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. Conjecture: if x = (x1,x2), then det(x) = det(x1)det(x2).