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. Figure out how to make OctonionHermitianEJA a RationalBasisEJA,
  28    and then convert the complex/quaternion algebras to avoid real-
  29    (un)embeddings.
  30
  31 7. Every once in a long while, the test
  32
  33        sage: set_random_seed()
  34        sage: x = random_eja().random_element()
  35        sage: x.is_invertible() == (x.det() != 0)
  36
  37    in eja_element.py returns False.