eja: cache the charpoly coefficients for the AlbertEJA.

[sage.d.git] / mjo / eja / TODO

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 2a13855ac7f3fdfbb61db04adc7649cc200d5fcf..45a9ac06bf2c86020dee102143393e486fa408c5 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,43 +1,22 @@
 1. Add references and start citing them.
 
-2. Implement the octonion simple EJA. We don't actually need octonions
-   for this to work, only their real embedding (some 8x8 monstrosity).
+2. Pre-cache charpoly for some more algebras.
 
-3. Pre-cache charpoly for some small algebras?
-
-RealSymmetricEJA(4):
-
-sage: F = J.base_ring()
-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]
-
-4. Profile the construction of "large" matrix algebras (like the
+3. Profile the construction of "large" matrix algebras (like the
    15-dimensional QuaternionHermitianAlgebra(3)) to find out why
    they're so slow.
 
-5. Instead of storing a basis multiplication matrix, just make
-   product_on_basis() a cached method and manually cache its
-   entries. The cython cached method lookup should be faster than a
-   python-based matrix lookup anyway. NOTE: we should still be able
-   to recompute the table somehow. Is this worth it?
-
-6. What the ever-loving fuck is this shit?
+4. What the ever-loving fuck is this shit?
 
        sage: O = Octonions(QQ)
        sage: e0 = O.monomial(0)
        sage: e0*[[[[]]]]
        [[[[]]]]*e0
 
-7. In fact, could my octonion matrix algebra be generalized for any
-   algebra of matrices over the reals whose entries are not real? Then
-   we wouldn't need real embeddings at all. They might even be fricking
-   vector spaces if I did that...
-
-8. Every once in a long while, the test
+5. Every once in a long while, the test
 
        sage: set_random_seed()
        sage: x = random_eja().random_element()
        sage: x.is_invertible() == (x.det() != 0)
 
    in eja_element.py returns False.
-
-9. Add an alias for AlbertAlgebra.