1. Finish CartesianProductEJA: add to_matrix(),
   random_instance(),... 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 we just
   fix the matrix basis/space after we call the FDEJA initializer?

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.