eja: clean up the TODO list after major refactoring.

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index ed15aa3dd5443c18195d9548c44e4a208a601dd7..db02b276e9a8a427afd3ad2a3e0b9fb77020fb50 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,17 +1,14 @@
-1. Add CartesianProductEJA.
+1. Finish DirectSumEJA: add to_matrix(), random_instance(),
+   one()... methods. Make it subclass RationalBasisEuclideanJordanAlgebra.
+   This is not a general direct sum / cartesian product implementation,
+   it's used only with the other rationalbasis algebras (to make non-
+   simple EJAs out of the simple ones).
 
 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
+4. 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
@@ -21,29 +18,20 @@
    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?
+5. 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
+6. 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).
+7. 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().
+8. Figure out if CombinatorialFreeModule's use of IndexedGenerators
+   can be used to replace the matrix_basis().
 
-12. Move the "field" argument to a keyword after basis, jp, and ip.
+9. Move the "field" argument to a keyword after basis, jp, and ip.