mjo/eja/TODO

   1 1. Finish CartesianProductEJA: add to_matrix(), random_instance(),...
   2    methods. I guess we should create a separate class hierarchy for
   3    Cartesian products of RationalBasisEJA? That way we get fast
   4    charpoly and random_instance() defined...
   5
   6 2. Add references and start citing them.
   7
   8 3. Implement the octonion simple EJA.
   9
  10 4. Pre-cache charpoly for some small algebras?
  11
  12 RealSymmetricEJA(4):
  13
  14 sage: F = J.base_ring()
  15 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]
  16
  17 5. The main EJA element constructor is happy to convert between
  18    e.g. HadamardEJA(3) and JordanSpinEJA(3).
  19
  20 6. Profile the construction of "large" matrix algebras (like the
  21    15-dimensional QuaternionHermitianAlgebra(3)) to find out why
  22    they're so slow.
  23
  24 7. Printing of Cartesian product subalgebrasis wrong (it prints the
  25    superalgebra).