X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=bb2b7f30069dda7ba5b1c63ec7062f1ab397c596;hb=0430a8642776e71ef0c26ab5e186f5a98a5a7433;hp=2fb5505439e6530cdc7e6c9d31ad06941937918f;hpb=07e5949ccb09f26fe6e1bd8e2e135c7eab680466;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 2fb5505..bb2b7f3 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,40 +1,17 @@
 1. Add references and start citing them.
 
-2. Pre-cache charpoly for some small algebras?
+2. Profile (and fix?) any remaining slow operations.
 
-RealSymmetricEJA(4):
+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...
 
-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. Can we hit "x" with the deortho matrix and delegate to the
+   _rational_algebra to speed up minimal_polynomial?
 
-3. Profile the construction of "large" matrix algebras (like the
-   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
-   they're so slow.
+5. In CartesianProductEJA we already know the multiplication table and
+   inner product matrix. Refactor things until it's no longer
+   necessary to duplicate that work.
 
-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?
-
-5. What the ever-loving fuck is this shit?
-
-       sage: O = Octonions(QQ)
-       sage: e0 = O.monomial(0)
-       sage: e0*[[[[]]]]
-       [[[[]]]]*e0
-
-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.
-
-8. Add an alias for AlbertAlgebra.
+6. Eliminate the matrix_space() override in CartesianProductEJA.