X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=f0901ca91b793debc4877a8ee5a670d240fa51fc;hb=f1ddf1e9eee634161aad87b9c2de0194efb17879;hp=87a162c73ab3ccf86623496dee39064e8b96bfb7;hpb=2a3ec0787b28bc35b3624594d921a995c9425d3a;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 87a162c..f0901ca 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -4,28 +4,39 @@
 
 3. Implement the octonion simple EJA.
 
-4. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
+4. Override random_instance(), one(), et cetera in DirectSumEJA.
 
-5. Override random_instance(), one(), et cetera in DirectSumEJA.
-
-6. Switch to QQ in *all* algebras for _charpoly_coefficients().
+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.
 
-7. Pass already_echelonized (default: False) and echelon_basis
+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
+   some time, and using 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."
+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. Pre-cache charpoly for some small algebras?
+
+9. Compute the scalar in the general natural_inner_product() for
+   matrices, so no overrides are necessary.
+
+10. The main EJA element constructor is happy to convert between
+    e.g. HadamardEJA(3) and JordanSpinEJA(3).
+
+11. Figure out if CombinatorialFreeModule's use of IndexedGenerators
+    can be used to replace the matrix_basis().