eja: update a half-completed TODO.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 58cab5a83423e8f6aa29bf945950ee099ef848bf..67f390ba24f06e6d0f419609ddb8654afd0a65bf 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -6,5 +6,12 @@
 
 4. Implement the octonion simple EJA.
 
-5. Factor out the Jordan axiom and norm tests once all of the
-   algebras pass.
+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