-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. Every once in a long while, the test
-3. Add references and start citing them.
+ sage: set_random_seed()
+ sage: x = random_eja().random_element()
+ sage: x.is_invertible() == (x.det() != 0)
-4. Implement the octonion simple EJA.
+ in eja_element.py returns False. Example:
-5. Factor out the unit-norm basis (and operator symmetry) tests once
- all of the algebras pass.
+ 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
-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.
+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...