-5. Profile the construction of "large" matrix algebras (like the
- 15-dimensional QuaternionHermitianAlgebra(3)) to find out why
- they're so slow.
-
-6. 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.
-
-7. What the ever-loving fuck is this shit?
-
- sage: O = Octonions(QQ)
- sage: e0 = O.monomial(0)
- sage: e0*[[[[]]]]
- [[[[]]]]*e0
-
-8. Factor out a class for matrices with real embeddings (i.e. not the
- octonions).
-
-9. In fact, could my octonion matrix algebra be generalized for any
- algebra of matrices over the reals whose entries are not real? Then
- we wouldn't need real embeddings at all. They might even be fricking
- vector spaces if I did that...
-
-10. Add HurwitzMatrixAlgebra subclass between MatrixAlgebra and
- OctonionMatrixAlgebra.
+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...