-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).
+1. Add cartesian products to random_eja().
2. Add references and start citing them.
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
+5. Profile the construction of "large" matrix algebras (like the
15-dimensional QuaternionHermitianAlgebra(3)) to find out why
- they're so slow.
\ No newline at end of file
+ they're so slow.
+
+6. We should compute whether or not the algebra is associative if it
+ is unknown. I guess the "associative" argument should be ternary
+ (True, False, None)? We should also figure out the correct
+ True/False values for the example classes, and of course add an
+ _is_associative() method.