X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=82c49d53d883d40712b66897c115ed1e58fa430f;hb=42571e06964e4a9891614793fb0fc8d7e1dd069d;hp=8f9c17f11c0db462403fdf98faafded920de2839;hpb=cc309b502850fd99abc742ee4ee4e015312f65ac;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 8f9c17f..82c49d5 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,26 +1,15 @@
-1. Finish CartesisnProductEJA: add to_matrix(), random_instance(),
-   one()... methods. This will require rethinking what a "matrix
-   representation" and "matrix space" means for a cartesian product
-   algebra. Do we want our matrix basis to consist of ordered pairs
-   (or triples, or...)? Should the matrix_space() of the algebra
-   be the cartesian product of the factors' matrix spaces? Can
-   the FDEJA initializer be made to work on tuples, or will it
-   need to be overridden?
+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.
+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?
+4. Conjecture: if x = (x1,x2), then det(x) = det(x1)det(x2). This
+   should be used to fix the fact that det(x) is monstrously slow in
+   Cartesian product algebras, and thus randomly in the doctests.
 
-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. The main EJA element constructor is happy to convert between
-   e.g. HadamardEJA(3) and JordanSpinEJA(3).
-
-6. Profile the construction of "large" matrix algebras (like the
-   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
-   they're so slow.
+5. Add dimension bounds on any tests over AA that compute element
+   subalgebras.