eja: fix cartesian_factors() for EJA elements.

[sage.d.git] / mjo / eja / TODO

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 67f390ba24f06e6d0f419609ddb8654afd0a65bf..421e0e9450bd18bab8fc5b9f0c75c738df099080 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,17 +1,10 @@
-1. Add CartesianProductEJA.
+1. Add references and start citing them.
 
-2. Check the axioms in the constructor when check != False?
+2. Profile (and fix?) any remaining slow operations.
 
-3. Add references and start citing them.
+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. Implement the octonion simple EJA.
-
-5. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
-
-6. Create Element subclasses for the matrix EJAs, and then override
-   their characteristic_polynomial() method to create a new algebra
-   over the rationals (with a non-normalized basis). We can then
-   compute the charpoly quickly by passing the natural representation
-   of the given element into the new algebra and computing its charpoly
-   there. (Relies on the theory to ensure that the charpolys are equal.)
\ No newline at end of file
+4. Conjecture: if x = (x1,x2), then det(x) = det(x1)det(x2).