1. Finish CartesisnProductEJA: add to_matrix(), random_instance(),
   one()... methods. This will require rethinking what a "matrix
   representation" and "matrix space" means for a cartesian product
   algebra. Do we want our matrix basis to consist of ordered pairs
   (or triples, or...)? Should the matrix_space() of the algebra
   be the cartesian product of the factors' matrix spaces? Can
   the FDEJA initializer be made to work on tuples, or will it
   need to be overridden?

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

6. Profile the construction of "large" matrix algebras (like the
   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
   they're so slow.