eja: append to an existing TODO.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 98314cea72c13f0d58a54f2e16ad0067e740336b..fb89e5edc905cea8475fb2349b3318e4aad22947 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,23 +1,12 @@
-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. 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?
-
-8. Ensure that we can construct all algebras over both AA and RR.
-
-9. Check that our field is a subring of RLF.
+4. Conjecture: if x = (x1,x2), then det(x) = det(x1)det(x2). This
+   should be used to fix the fact that det(x) is monstrously slow in
+   Cartesian product algebras, and thus randomly in the doctests.