X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=45a9ac06bf2c86020dee102143393e486fa408c5;hp=db363ac3facd6c3c7475bf9b426664320c19951b;hb=cf5e64b70869df65c7bb38888de54b1083e60d45;hpb=308d65140d9822b9542fafff0708004b1364368e

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index db363ac..45a9ac0 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,35 +1,22 @@
-1. Add CartesianProductEJA.
+1. Add references and start citing them.
 
-2. Add references and start citing them.
+2. Pre-cache charpoly for some more algebras.
 
-3. Implement the octonion simple EJA.
+3. Profile the construction of "large" matrix algebras (like the
+   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+   they're so slow.
 
-4. Override random_instance(), one(), et cetera in DirectSumEJA.
+4. What the ever-loving fuck is this shit?
 
-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.
+       sage: O = Octonions(QQ)
+       sage: e0 = O.monomial(0)
+       sage: e0*[[[[]]]]
+       [[[[]]]]*e0
 
-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.
+5. Every once in a long while, the test
 
-   This may require supporting "basis" as a list of basis vectors
-   (as opposed to superalgebra elements) in the subalgebra constructor.
+       sage: set_random_seed()
+       sage: x = random_eja().random_element()
+       sage: x.is_invertible() == (x.det() != 0)
 
-7. The inner product should be an *argument* to the main EJA
-   constructor.  Afterwards, the basis normalization step should be
-   optional (and enabled by default) for ALL algebras, since any
-   algebra can have a nonstandard inner-product and its basis can be
-   normalized with respect to that inner- product. For example, the
-   HadamardEJA could be equipped with an inner- product that is twice
-   the usual one. Then for the basis to be orthonormal, we would need
-   to divide e.g. (1,0,0) by <(1,0,0),(1,0,0)> = 2 to normalize it.
-
-8. Use charpoly for inverse itself?
-
-9. Pre-cache charpoly for some small algebras?
+   in eja_element.py returns False.