+0. Add tests for orthogonality in the Peirce decomposition.
+
1. Add CartesianProductEJA.
2. Check the axioms in the constructor when check != False?
5. Factor out the unit-norm basis (and operator symmetry) 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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+6. Can we make the minimal and characteristic polynomial tests work
+ for trivial algebras, too? Then we wouldn't need the "nontrivial"
+ argument to random_eja(). This would also allow us to potentially
+ pass a "size" of zero to the other constructors in random_eja() --
+ a code path that is basically untested right now.