X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=f248e119acc5c3d0da34fbfaf87999110e0cc406;hb=fe2af66b109e9487a59f21d5b67bb5c4aafdc98d;hp=67f390ba24f06e6d0f419609ddb8654afd0a65bf;hpb=33e3a4deff70731138dafc2857ba811b3c66f5b3;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 67f390b..f248e11 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,17 +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. Create Element subclasses for the matrix EJAs, and then override
-   their characteristic_polynomial() method to create a new algebra
-   over the rationals (with a non-normalized basis). We can then
-   compute the charpoly quickly by passing the natural representation
-   of the given element into the new algebra and computing its charpoly
-   there. (Relies on the theory to ensure that the charpolys are equal.)
\ No newline at end of file
+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.
+
+   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 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. Pre-cache the one() method for concrete algebras, and test the general
+   method by clearing the cache.