-0. Add tests for orthogonality in the Peirce decomposition.
+1. Add references and start citing them.
-1. Add CartesianProductEJA.
+2. Profile (and fix?) any remaining slow operations.
-2. Check the axioms in the constructor when check != False?
+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...
-3. Add references and start citing them.
-
-4. Implement the octonion simple EJA.
-
-5. Factor out the unit-norm basis (and operator symmetry) tests once
- all of the algebras pass.
-
-6. The EJA random element method only returns two summands by default.
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+4. Conjecture: if x = (x1,x2), then det(x) = det(x1)det(x2). This
+ should be used to fix the fact that det(x) is monstrously slow in
+ Cartesian product algebras, and thus randomly in the doctests.