+ We can change the generator prefix::
+
+ sage: QuaternionHermitianEJA(2, prefix='a').gens()
+ (a0, a1, a2, a3, a4, a5)
+
+ Our inner product satisfies the Jordan axiom::
+
+ sage: set_random_seed()
+ sage: n = ZZ.random_element(1,5)
+ sage: J = QuaternionHermitianEJA(n)
+ sage: x = J.random_element()
+ sage: y = J.random_element()
+ sage: z = J.random_element()
+ sage: (x*y).inner_product(z) == y.inner_product(x*z)
+ True
+