mjo/eja/TODO

   1 1. Add references and start citing them.
   2
   3 2. Pre-cache charpoly for some small algebras?
   4
   5 RealSymmetricEJA(4):
   6
   7 sage: F = J.base_ring()
   8 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
  10 3. Profile the construction of "large" matrix algebras (like the
  11    15-dimensional QuaternionHermitianAlgebra(3)) to find out why
  12    they're so slow.
  13
  14 4. Instead of storing a basis multiplication matrix, just make
  15    product_on_basis() a cached method and manually cache its
  16    entries. The cython cached method lookup should be faster than a
  17    python-based matrix lookup anyway. NOTE: we should still be able
  18    to recompute the table somehow. Is this worth it?
  19
  20 5. What the ever-loving fuck is this shit?
  21
  22        sage: O = Octonions(QQ)
  23        sage: e0 = O.monomial(0)
  24        sage: e0*[[[[]]]]
  25        [[[[]]]]*e0
  26
  27 6. In fact, could my octonion matrix algebra be generalized for any
  28    algebra of matrices over the reals whose entries are not real? Then
  29    we wouldn't need real embeddings at all. They might even be fricking
  30    vector spaces if I did that...
  31
  32 7. Every once in a long while, the test
  33
  34        sage: set_random_seed()
  35        sage: x = random_eja().random_element()
  36        sage: x.is_invertible() == (x.det() != 0)
  37
  38    in eja_element.py returns False.