X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=38aa85bfe7a5c5ecc4b97c880c05533e42b5ad69;hb=ffabf130fc8fa05e68d9b3d55a1f3ccf89f5e390;hp=b2495b59f3264e5d638a59f6630daa77214cdb50;hpb=5ce914aa8f29ad8d9d80b85b8ea33dd0cd735d4f;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index b2495b5..38aa85b 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,3 +1,8 @@
+A. Add tests for orthogonality in the Peirce decomposition.
+
+B. Add support for a symmetric positive-definite bilinear form in
+   the JordanSpinEJA.
+
 1. Add CartesianProductEJA.
 
 2. Check the axioms in the constructor when check != False?
@@ -9,11 +14,9 @@
 5. Factor out the unit-norm basis (and operator symmetry) tests once
    all of the algebras pass.
 
-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.
+6. Can we make the minimal and characteristic polynomial tests work
+   for trivial algebras, too? Then we wouldn't need the "nontrivial"
+   argument to random_eja().
 
-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?
+7. Solve the charpoly system with A_of_x.solve_right(x_powers[r])
+   rather than dumbass Cramer's rule.