interface, we must also support at least the usual SageMath vectors
and matrices.
+Note: this has one less-than-obvious consequence: we have to assume
+that the user has supplied an entirely-correct basis (with entries in
+the correct structure). We generally cannot mess witht the entries of
+his basis, or use them to figure out what (for example) the ambient
+scalar ring is. None of these are insurmountable obstacles; we just
+have to be a little careful distinguishing between what's inside the
+algebra elements and what's outside them.
+
Basis normalization
-------------------
For performance reasons, we prefer the algebra constructors to