-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. 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.
+ 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. 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. Check that our field is a subring of RLF.
+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...