sage: e0*[[[[]]]]
[[[[]]]]*e0
-6. Figure out how to make OctonionHermitianEJA a RationalBasisEJA,
- and then convert the complex/quaternion algebras to avoid real-
- (un)embeddings.
+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.
7. Every once in a long while, the test
sage: x.is_invertible() == (x.det() != 0)
in eja_element.py returns False.
+
+8. The definition of product_on_basis() and the element constructor
+ for MatrixAlgebra are totally wrong. There's no reason to expect
+ a product of monomials to again be plus/minus a monomial.