eja: update todo, and rename "natural" to "matrix".

[sage.d.git] / mjo / eja / TODO

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index ffa4f7c4ca0ccf3e2a72b6bfd996e9c30ec29fde..f0901ca91b793debc4877a8ee5a670d240fa51fc 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -4,30 +4,39 @@
 
 3. Implement the octonion simple EJA.
 
 
 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.
 
    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
    (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.
 
    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).

 
 

-9. Use charpoly for inverse stuff if it's cached.
+11. Figure out if CombinatorialFreeModule's use of IndexedGenerators
+    can be used to replace the matrix_basis().