X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=529f70fd633bf36275c63282a05614f1109a7df0;hb=d9b0659df5d8ad61f457674e009180618dffef67;hp=f09191e3890ea4589ccc5fae3da3e27c2a23b6b8;hpb=db5226c4f5478db40d844b99077a5b164ef6d714;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index f09191e..529f70f 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,24 +1,25 @@
-1. Add CartesianProductEJA.
+1. Add references and start citing them.
 
-2. Add references and start citing them.
+2. Profile (and fix?) any remaining slow operations.
 
-3. Implement the octonion simple EJA.
+3. Every once in a long while, the test
 
-4. Override random_instance(), one(), et cetera in DirectSumEJA.
+       sage: set_random_seed()
+       sage: x = random_eja().random_element()
+       sage: x.is_invertible() == (x.det() != 0)
 
-5. Switch to QQ in *all* algebras for _charpoly_coefficients().
-   This only works when we know that the basis can be rationalized...
-   which is the case at least for the concrete EJAs we provide,
-   but not in general.
+   in eja_element.py returns False. Example:
 
-6. Pass already_echelonized (default: False) and echelon_basis
-   (default: None) into the subalgebra constructor. The value of
-   already_echelonized can be passed to V.span_of_basis() to save
-   some time, and usinf e.g. FreeModule_submodule_with_basis_field
-   we may somehow be able to pass the echelon basis straight in to
-   save time.
+       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
 
-   This may require supporting "basis" as a list of basis vectors
-   (as opposed to superalgebra elements) in the subalgebra constructor.
-
-7. Use charpoly for inverse stuff if it's cached.
+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...