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. We don't actually need octonions
   6    for this to work, only their real embedding (some 8x8 monstrosity).
   7
   8 4. Pre-cache charpoly for some small algebras?
   9
  10 RealSymmetricEJA(4):
  11
  12 sage: F = J.base_ring()
  13 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]
  14
  15 5. Profile the construction of "large" matrix algebras (like the
  16    15-dimensional QuaternionHermitianAlgebra(3)) to find out why
  17    they're so slow.
  18
  19 6. Instead of storing a basis multiplication matrix, just make
  20    product_on_basis() a cached method and manually cache its
  21    entries. The cython cached method lookup should be faster than a
  22    python-based matrix lookup anyway.
  23
  24 7. What the ever-loving fuck is this shit?
  25
  26        sage: O = Octonions(QQ)
  27        sage: e0 = O.monomial(0)
  28        sage: e0*[[[[]]]]
  29        [[[[]]]]*e0