eja: clean up the TODO list after major refactoring.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index f09191e3890ea4589ccc5fae3da3e27c2a23b6b8..db02b276e9a8a427afd3ad2a3e0b9fb77020fb50 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,24 +1,37 @@
-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 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.
 
-7. Use charpoly for inverse stuff if it's cached.
+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]
+
+6. Compute the scalar in the general natural_inner_product() for
+   matrices, so no overrides are necessary.
+
+7. The main EJA element constructor is happy to convert between
+   e.g. HadamardEJA(3) and JordanSpinEJA(3).
+
+8. Figure out if CombinatorialFreeModule's use of IndexedGenerators
+   can be used to replace the matrix_basis().
+
+9. Move the "field" argument to a keyword after basis, jp, and ip.