-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. Every once in a long while, the test
-4. Implement the octonion simple EJA.
+ sage: set_random_seed()
+ sage: x = random_eja().random_element()
+ sage: x.is_invertible() == (x.det() != 0)
-5. Factor out the unit-norm basis (and operator symmetry) tests once
- all of the algebras pass.
+ in eja_element.py returns False. Example:
-6. Refactor the current ungodly fast charpoly hack (relies on the
- theory to ensure that the charpolys are equal.)
+ sage: J1 = ComplexHermitianEJA(2)
+ sage: J2 = TrivialEJA()
+ sage: J = cartesian_product([J1,J2])
+ sage: x = J.from_vector(vector(QQ, [-1, -1/2, -1/2, -1/2]))
+ sage: x.is_invertible()
+ True
+ sage: x.det()
+ 0
-7. If we factor out a "matrix algebra" class, then it would make sense
- to replace the custom embedding/unembedding functions with static
- _real_embedding() and _real_unembedding() methods.
-
-8. Implement random_instance() for the main EJA class.
-
-9. Implement random_instance() for the subalgebra class.
+4. 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...