+ # Check commutativity of the Jordan product (symmetry of
+ # the multiplication table) and the commutativity of the
+ # inner-product (symmetry of the inner-product table)
+ # first if we're going to check them at all.. This has to
+ # be done before we define product_on_basis(), because
+ # that method assumes that self._multiplication_table is
+ # symmetric. And it has to be done before we build
+ # self._inner_product_matrix, because the process used to
+ # construct it assumes symmetry as well.