-1. Add CartesianProductEJA.
+1. Add references and start citing them.
-2. Check the axioms in the constructor when check != False?
+2. Profile (and fix?) any remaining slow operations.
-3. Add references and start citing them.
+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. Implement the octonion simple EJA.
+4. Add dimension bounds on any tests over AA that compute element
+ subalgebras.
-5. Factor out the Jordan axiom and norm tests once all of the
- algebras pass.
-
-6. Create Element subclasses for the matrix EJAs, and then override
- their characteristic_polynomial() method to create a new algebra
- over the rationals (with a non-normalized basis). We can then
- compute the charpoly quickly by passing the natural representation
- of the given element into the new algebra and computing its charpoly
- there. (Relies on the theory to ensure that the charpolys are equal.)
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+5. The rational_algebra() stuff doesn't really belong in classes that
+ don't derive from RationalBasisEJA or its as-yet-nonexistent
+ element class.