X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=f248e119acc5c3d0da34fbfaf87999110e0cc406;hb=fe2af66b109e9487a59f21d5b67bb5c4aafdc98d;hp=f6d7743782613d241c50e05eee665d59278bd4b4;hpb=16825a1ceedeb8363b025cda56dc9f65f639f726;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index f6d7743..f248e11 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,21 +1,35 @@
 1. Add CartesianProductEJA.
 
-2. Check the axioms in the constructor when check != False?
+2. Add references and start citing them.
 
-3. Add references and start citing them.
+3. Implement the octonion simple EJA.
 
-4. Implement the octonion simple EJA.
-
-5. Factor out the unit-norm basis (and operator symmetry) tests once
+4. Factor out the unit-norm basis (and operator symmetry) tests once
    all of the algebras pass.
 
-6. Refactor the current ungodly fast charpoly hack (relies on the
-   theory to ensure that the charpolys are equal.)
+5. Override inner_product(), _max_test_case_size(), et cetera in
+   DirectSumEJA.
+
+6. 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.
+
+7. 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.
 
-7. If we factor out a "matrix algebra" class, then it would make sense
-   to replace the custom embedding/unembedding functions with static
-   _real_embedding() and _real_unembedding() methods.
+   This may require supporting "basis" as a list of basis vectors
+   (as opposed to superalgebra elements) in the subalgebra constructor.
 
-8. Implement random_instance() for the main EJA class.
+8. Implement random_instance() for general algebras as random_eja().
+   Copy/paste the "general" construction into the other classes that
+   can use it. The general construction can be something like "call
+   random_instance() on something that inherits me and return the
+   result."
 
-9. Implement random_instance() for the subalgebra class.
+9. Pre-cache the one() method for concrete algebras, and test the general
+   method by clearing the cache.