-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. Can we hit "x" with the deortho matrix and delegate to the
+ _rational_algebra to speed up minimal_polynomial?
-5. Factor out the unit-norm basis (and operator symmetry) tests once
- all of the algebras pass.
-
-6. Implement spectral projector decomposition for EJA operators
- using jordan_form() or eigenmatrix_right(). I suppose we can
- ignore the problem of base rings for now and just let it crash
- if we're not using AA as our base field.
-
-7. Do we really need to orthonormalize the basis in a subalgebra?
- So long as we can decompose the operator (which is invariant
- under changes of basis), who cares?
-
-8. Ensure that we can construct all algebras over both AA and RR.
-
-9. Check that our field is a subring of RLF.
+5. In CartesianProductEJA we already know the multiplication table and
+ inner product matrix. Refactor things until it's no longer
+ necessary to duplicate that work.