eja: add a performance TODO for Cartesian products with trivial factors.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 98314cea72c13f0d58a54f2e16ad0067e740336b..529f70fd633bf36275c63282a05614f1109a7df0 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,23 +1,25 @@
-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. Every once in a long while, the test
 
-4. Implement the octonion simple EJA.
+       sage: set_random_seed()
+       sage: x = random_eja().random_element()
+       sage: x.is_invertible() == (x.det() != 0)
 
-5. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
+   in eja_element.py returns False. Example:
 
-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.
+       sage: J1 = ComplexHermitianEJA(2)
+       sage: J2 = TrivialEJA()
+       sage: J = cartesian_product([J1,J2])
+       sage: x = J.from_vector(vector(QQ, [-1, -1/2, -1/2, -1/2]))
+       sage: x.is_invertible()
+       True
+       sage: x.det()
+       0
 
-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. 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...