eja: propagate check_axioms to some other "check" variables.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index e8a2a8d4fc8988b1ad6f744a69daba9cf0582397..c9c264c436b198e02c39f7792307572c5efead7d 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,13 +1,32 @@
-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.
 
 
 2. Add references and start citing them.
 
 3. Implement the octonion simple EJA.
 

-4. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
+4. Pre-cache charpoly for some small algebras?

 
 

-5. Override inner_product(), _max_test_case_size(), et cetera in
-   DirectSumEJA.
+RealSymmetricEJA(4):

 
 

-6. Switch to QQ in *all* algebras for _charpoly_coefficients().
+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]
+
+5. Compute the scalar in the general natural_inner_product() for
+   matrices, so no overrides are necessary.
+
+6. The main EJA element constructor is happy to convert between
+   e.g. HadamardEJA(3) and JordanSpinEJA(3).
+
+7. Figure out if CombinatorialFreeModule's use of IndexedGenerators
+   can be used to replace the matrix_basis().
+
+8. Move the "field" argument to a keyword after basis, jp, and ip.
+
+9. Add back the check_field=False and check_axioms=False parameters
+   for the EJAs we've constructed ourselves. We can probably pass
+   the value of "check_axioms" to <whatever>.span_of_basis() to skip
+   the linear-independence check.