eja: add an optimization to the TODO.

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 58cab5a83423e8f6aa29bf945950ee099ef848bf..382fb6e67d6050dd6e8215ad2d371a5be3022057 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -8,3 +8,10 @@
 
 5. Factor out the Jordan axiom and norm 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