1. Finish DirectSumEJA: add to_matrix(), random_instance(),
   one()... methods. Make it subclass RationalBasisEuclideanJordanAlgebra.
   This is not a general direct sum / cartesian product implementation,
   it's used only with the other rationalbasis algebras (to make non-
   simple EJAs out of the simple ones).

2. Add references and start citing them.

3. Implement the octonion simple EJA.

4. Pre-cache charpoly for some small algebras?

RealSymmetricEJA(4):

sage: F = J.base_ring()
sage: a0 = (1/4)*X[4]**2*X[6]**2 - (1/2)*X[2]*X[5]*X[6]**2 - (1/2)*X[3]*X[4]*X[6]*X[7] + (F(2).sqrt()/2)*X[1]*X[5]*X[6]*X[7] + (1/4)*X[3]**2*X[7]**2 - (1/2)*X[0]*X[5]*X[7]**2 + (F(2).sqrt()/2)*X[2]*X[3]*X[6]*X[8] - (1/2)*X[1]*X[4]*X[6*X[8] - (1/2)*X[1]*X[3]*X[7]*X[8] + (F(2).sqrt()/2)*X[0]*X[4]*X[7]*X[8] + (1/4)*X[1]**2*X[8]**2 - (1/2)*X[0]*X[2]*X[8]**2 - (1/2)*X[2]*X[3]**2*X[9] + (F(2).sqrt()/2)*X[1]*X[3]*X[4]*X[9] - (1/2)*X[0]*X[4]**2*X[9] - (1/2)*X[1]**2*X[5]*X[9] + X[0]*X[2]*X[5]*X[9]

5. Compute the scalar in the general natural_inner_product() for
   matrices, so no overrides are necessary.

6. The main EJA element constructor is happy to convert between
   e.g. HadamardEJA(3) and JordanSpinEJA(3).

8. Add back the check_field=False and check_axioms=False parameters
   for the EJAs we've constructed ourselves.