X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=f0901ca91b793debc4877a8ee5a670d240fa51fc;hb=f1ddf1e9eee634161aad87b9c2de0194efb17879;hp=38aa85bfe7a5c5ecc4b97c880c05533e42b5ad69;hpb=09298a6b80a44847f506961e0eeccb8cdf2ad9d3;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 38aa85b..f0901ca 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,22 +1,42 @@
-A. Add tests for orthogonality in the Peirce decomposition.
+1. Add CartesianProductEJA.
 
-B. Add support for a symmetric positive-definite bilinear form in
-   the JordanSpinEJA.
+2. Add references and start citing them.
 
-1. Add CartesianProductEJA.
+3. Implement the octonion simple EJA.
+
+4. Override random_instance(), one(), et cetera in DirectSumEJA.
+
+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.
+
+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 using e.g. FreeModule_submodule_with_basis_field
+   we may somehow be able to pass the echelon basis straight in to
+   save time.
 
-2. Check the axioms in the constructor when check != False?
+   This may require supporting "basis" as a list of basis vectors
+   (as opposed to superalgebra elements) in the subalgebra constructor.
 
-3. Add references and start citing them.
+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.
 
-4. Implement the octonion simple EJA.
+8. Pre-cache charpoly for some small algebras?
 
-5. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
+9. Compute the scalar in the general natural_inner_product() for
+   matrices, so no overrides are necessary.
 
-6. Can we make the minimal and characteristic polynomial tests work
-   for trivial algebras, too? Then we wouldn't need the "nontrivial"
-   argument to random_eja().
+10. The main EJA element constructor is happy to convert between
+    e.g. HadamardEJA(3) and JordanSpinEJA(3).
 
-7. Solve the charpoly system with A_of_x.solve_right(x_powers[r])
-   rather than dumbass Cramer's rule.
+11. Figure out if CombinatorialFreeModule's use of IndexedGenerators
+    can be used to replace the matrix_basis().