X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=e925c162786ab4da9bb7155ec8086cda0da05464;hb=47671d4a72c9eaed822c066f05a26f63c7301526;hp=2752dc47cd026eb9c000be7301507567c2161dfa;hpb=707c1ace788819d3d0542e61dab0134eabea2159;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 2752dc4..e925c16 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,54 +1,25 @@
-1. Add CartesianProductEJA.
+1. Add cartesian products to random_eja().
 
 2. Add references and start citing them.
 
 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.
-
-   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?
+4. 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().
+5. Profile the construction of "large" matrix algebras (like the
+   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+   they're so slow.
 
-12. Move the "field" argument to a keyword after basis, jp, and ip.
+6. We should compute whether or not the algebra is associative if it
+   is unknown. I guess the "associative" argument should be ternary
+   (True, False, None)? We should also figure out the correct
+   True/False values for the example classes, and of course add an
+   _is_associative() method.
 
-13. 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.
+7. Set check_axioms=False for element-subalgebras outside of once or
+   twice in the test suite.