1. Add CartesianProductEJA.

2. Add references and start citing them.

3. Implement the octonion simple EJA.

4. Override random_instance(), one(), et cetera in DirectSumEJA.

5. Switch to QQ in *all* algebras for _charpoly_coefficients().
   This only works when we know that the basis can be rationalized...
   which is the case at least for the concrete EJAs we provide,
   but not in general.

6. Pass already_echelonized (default: False) and echelon_basis
   (default: None) into the subalgebra constructor. The value of
   already_echelonized can be passed to V.span_of_basis() to save
   some time, and using e.g. FreeModule_submodule_with_basis_field
   we may somehow be able to pass the echelon basis straight in to
   save time.

   This may require supporting "basis" as a list of basis vectors
   (as opposed to superalgebra elements) in the subalgebra constructor.

7. The inner product should be an *argument* to the main EJA
   constructor.  Afterwards, the basis normalization step should be
   optional (and enabled by default) for ALL algebras, since any
   algebra can have a nonstandard inner-product and its basis can be
   normalized with respect to that inner- product. For example, the
   HadamardEJA could be equipped with an inner- product that is twice
   the usual one. Then for the basis to be orthonormal, we would need
   to divide e.g. (1,0,0) by <(1,0,0),(1,0,0)> = 2 to normalize it.

8. 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]

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

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

11. Figure out if CombinatorialFreeModule's use of IndexedGenerators
    can be used to replace the matrix_basis().

12. Move the "field" argument to a keyword after basis, jp, and ip.