X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=f4b9515c4ed643bd1f9a13c6fc0d6cefa3d32879;hp=cbe1d95801e9a098b36c75cf2548da460750ac03;hb=HEAD;hpb=251e308af6c3a57b418a06546a572af83eade7ec

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index cbe1d95..b0d5378 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,57 +1,20 @@
-1. Add CartesianProductEJA.
+1. Add references and start citing them.
 
-2. Add references and start citing them.
+2. Profile (and fix?) any remaining slow operations.
 
-3. Implement the octonion simple EJA.
+3. When we take a Cartesian product involving a trivial algebra, we
+   could easily cache the identity and charpoly coefficients using
+   the nontrivial factor. On the other hand, it's nice that we can
+   test out some alternate code paths...
 
-4. Override random_instance(), one(), et cetera in DirectSumEJA.
+4. Add dimension bounds on any tests over AA that compute element
+   subalgebras.
 
-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.
+5. The rational_algebra() stuff doesn't really belong in classes that
+   don't derive from RationalBasisEJA or its as-yet-nonexistent
+   element class.
 
-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.
-
-   This may require supporting "basis" as a list of basis vectors
-   (as opposed to superalgebra elements) in the subalgebra constructor.
-
-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?
-
-RealSymmetricEJA(4):
-
-sage: F = J.base_ring()
-sage: a0 = (1/4)*X[4]**2*X[6]**2 - (1/2)*X[2]*X[5]*X[6]**2 - (1/2)*X[3]*X[4]*X[6]*X[7] + (F(2).sqrt()/2)*X[1]*X[5]*X[6]*X[7] + (1/4)*X[3]**2*X[7]**2 - (1/2)*X[0]*X[5]*X[7]**2 + (F(2).sqrt()/2)*X[2]*X[3]*X[6]*X[8] - (1/2)*X[1]*X[4]*X[6*X[8] - (1/2)*X[1]*X[3]*X[7]*X[8] + (F(2).sqrt()/2)*X[0]*X[4]*X[7]*X[8] + (1/4)*X[1]**2*X[8]**2 - (1/2)*X[0]*X[2]*X[8]**2 - (1/2)*X[2]*X[3]**2*X[9] + (F(2).sqrt()/2)*X[1]*X[3]*X[4]*X[9] - (1/2)*X[0]*X[4]**2*X[9] - (1/2)*X[1]**2*X[5]*X[9] + X[0]*X[2]*X[5]*X[9]
-
-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().
-
-12. Don't pass in an n-by-n multiplication/i-p table since only the
-    lower-left half is used.
-
-13. Move the "field" argument to a keyword after basis, jp, and ip.
-
-14. Instead of storing the multiplication and inner-product tables in
-    RationalBasisEuclideanJordanAlgebra, why not just create the
-    algebra over QQ in the constructor and save that? They're globally
-    unique, so we won't wind up with multiple copies.
+6. Add special det/trace method overrides for the algebras where we
+   know them? The only reason this might be tricky is because the
+   obvious solution is to subclass EJAElement, but then we might
+   collide with e.g. the Cartesian product element subclass.