X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=b2495b59f3264e5d638a59f6630daa77214cdb50;hb=5ce914aa8f29ad8d9d80b85b8ea33dd0cd735d4f;hp=382fb6e67d6050dd6e8215ad2d371a5be3022057;hpb=403848519cc35245713ffb96b2372deb1ee1c621;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 382fb6e..b2495b5 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -6,12 +6,14 @@
 
 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
+6. Implement spectral projector decomposition for EJA operators
+   using jordan_form() or eigenmatrix_right(). I suppose we can
+   ignore the problem of base rings for now and just let it crash
+   if we're not using AA as our base field.
+
+7. Do we really need to orthonormalize the basis in a subalgebra?
+   So long as we can decompose the operator (which is invariant
+   under changes of basis), who cares?