-3. Profile the construction of "large" matrix algebras (like the
- 15-dimensional QuaternionHermitianAlgebra(3)) to find out why
- they're so slow.
-
-4. Instead of storing a basis multiplication matrix, just make
- product_on_basis() a cached method and manually cache its
- entries. The cython cached method lookup should be faster than a
- python-based matrix lookup anyway. NOTE: we should still be able
- to recompute the table somehow. Is this worth it?
-
-5. What the ever-loving fuck is this shit?
-
- sage: O = Octonions(QQ)
- sage: e0 = O.monomial(0)
- sage: e0*[[[[]]]]
- [[[[]]]]*e0
-
-6. Can we convert the complex/quaternion algebras to avoid real-
- (un)embeddings? Quaternions would need their own
- QuaternionMatrixAlgebra, since Sage matrices have to have entries
- in a commutative ring. Those and the octonion stuff could be moved
- to hurwitz.py along with the HurwitzMatrixAlgebra.
-
-7. Every once in a long while, the test
-
- sage: set_random_seed()
- sage: x = random_eja().random_element()
- sage: x.is_invertible() == (x.det() != 0)
-
- in eja_element.py returns False.