Trace inner product tests:

            TESTS:

            The trace inner product is commutative::

            sage: set_random_seed()
            sage: J = random_eja()
            sage: x = J.random_element(); y = J.random_element()
            sage: x.trace_inner_product(y) == y.trace_inner_product(x)
            True

            The trace inner product is bilinear::

            sage: set_random_seed()
            sage: J = random_eja()
            sage: x = J.random_element()
            sage: y = J.random_element()
            sage: z = J.random_element()
            sage: a = QQ.random_element();
            sage: actual = (a*(x+z)).trace_inner_product(y)
            sage: expected = a*x.trace_inner_product(y) + a*z.trace_inner_product(y)
            sage: actual == expected
            True
            sage: actual = x.trace_inner_product(a*(y+z))
            sage: expected = a*x.trace_inner_product(y) +  a*x.trace_inner_product(z)
            sage: actual == expected
            True

            The trace inner product is associative::

            sage: pass

            The trace inner product satisfies the compatibility
            condition in the definition of a Euclidean Jordan algebra:

            sage: set_random_seed()
            sage: J = random_eja()
            sage: x = J.random_element()
            sage: y = J.random_element()
            sage: z = J.random_element()
            sage: (x*y).trace_inner_product(z) == y.trace_inner_product(x*z)
            True