eja: add the AlbertEJA class.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 900c31c4defccba0b8d2c2a3b83a835f447a81ef..f415681182dd18bf401aba539a66f916e4f0c191 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,37 +1,38 @@
-1. Add cartesian products to random_eja().
+1. Add references and start citing them.
 
-2. Add references and start citing them.
-
-3. Implement the octonion simple EJA. We don't actually need octonions
-   for this to work, only their real embedding (some 8x8 monstrosity).
-
-4. Pre-cache charpoly for some small algebras?
+2. 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]
 
-5. 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.
 
-6. Instead of storing a basis multiplication matrix, just make
+4. 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.
+   python-based matrix lookup anyway. NOTE: we should still be able
+   to recompute the table somehow. Is this worth it?
 
-7. What the ever-loving fuck is this shit?
+5. What the ever-loving fuck is this shit?
 
        sage: O = Octonions(QQ)
        sage: e0 = O.monomial(0)
        sage: e0*[[[[]]]]
        [[[[]]]]*e0
 
-8. Factor out a class for matrices with real embeddings (i.e. not the
-   octonions).
-
-9. In fact, could my octonion matrix algebra be generalized for any
+6. 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...
+
+7. 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.