mjo/eja/TODO

   1 1. Add cartesian products to random_eja().
   2
   3 2. Add references and start citing them.
   4
   5 3. Implement the octonion simple EJA.
   6
   7 4. Pre-cache charpoly for some small algebras?
   8
   9 RealSymmetricEJA(4):
  10
  11 sage: F = J.base_ring()
  12 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]
  13
  14 5. Profile the construction of "large" matrix algebras (like the
  15    15-dimensional QuaternionHermitianAlgebra(3)) to find out why
  16    they're so slow.
  17
  18 6. We should compute whether or not the algebra is associative if it
  19    is unknown. I guess the "associative" argument should be ternary
  20    (True, False, None)? We should also figure out the correct
  21    True/False values for the example classes, and of course add an
  22    _is_associative() method.
  23
  24 7. When field=RDF, subalgebra construction is failing because the
  25    inner product isn't associative? Actually, it's the combination
  26    of field=RDF and orthonormalize=True.