4. Implement the octonion simple EJA.
-5. Factor out the Jordan axiom and norm tests once all of the
- algebras pass.
+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.)
\ No newline at end of file
+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?