-7. Drop the element-subalgebra in favor of a regular subalgebra. The
- cached "one" can be set in the method.
+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