X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=421e0e9450bd18bab8fc5b9f0c75c738df099080;hb=7c21799d680433b62d48ca79cc2ea8f27e1cd8da;hp=26ff1e9e7db77b22f3d749056121d094a08f2d8b;hpb=8d91b5b5af605dabe11a024ab030f2fcb2828cde;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 26ff1e9..421e0e9 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,27 +1,10 @@
 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]
-
-3. Profile the construction of "large" matrix algebras (like the
-   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
-   they're so slow.
-
-4. What the ever-loving fuck is this shit?
-
-       sage: O = Octonions(QQ)
-       sage: e0 = O.monomial(0)
-       sage: e0*[[[[]]]]
-       [[[[]]]]*e0
-
-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.
+4. Conjecture: if x = (x1,x2), then det(x) = det(x1)det(x2).