eja: remove the Octonions from the TODO.

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 2a13855ac7f3fdfbb61db04adc7649cc200d5fcf..2fb5505439e6530cdc7e6c9d31ad06941937918f 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,38 +1,35 @@
 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).
-
-3. 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]
 
-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
+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. NOTE: we should still be able
    to recompute the table somehow. Is this worth it?
 
-6. 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
 
-7. 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...
 
-8. Every once in a long while, the test
+7. Every once in a long while, the test
 
        sage: set_random_seed()
        sage: x = random_eja().random_element()
@@ -40,4 +37,4 @@ 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
 
    in eja_element.py returns False.
 
-9. Add an alias for AlbertAlgebra.
+8. Add an alias for AlbertAlgebra.