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...