X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=9cee421b4f5cacee4e623a6b4d1099c191eeaf72;hb=f0cabe7c6e37781e4f92c9ba0e0c7413a5f6b939;hp=f2e71c8495cd140698d28a88ee515680a997c322;hpb=f56f9cf84a483d4e3b29f65b01bf9287ed6b7844;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index f2e71c8..9cee421 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,43 +1,11 @@
-1. Add cartesian products to random_eja().
+1. Add references and start citing them.
 
-2. Add references and start citing them.
+2. Profile (and fix?) any remaining slow operations.
 
-3. Implement the octonion simple EJA. We don't actually need octonions
-   for this to work, only their real embedding (some 8x8 monstrosity).
+3. When we take a Cartesian product involving a trivial algebra, we
+   could easily cache the identity and charpoly coefficients using
+   the nontrivial factor. On the other hand, it's nice that we can
+   test out some alternate code paths...
 
-4. 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
-   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
-   they're so slow.
-
-6. 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?
-
-7. What the ever-loving fuck is this shit?
-
-       sage: O = Octonions(QQ)
-       sage: e0 = O.monomial(0)
-       sage: e0*[[[[]]]]
-       [[[[]]]]*e0
-
-8. 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...
-
-9. 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.
+4. Add dimension bounds on any tests over AA that compute element
+   subalgebras.