eja: move the "field" argument to (usually passed through) kwargs.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 38aa85bfe7a5c5ecc4b97c880c05533e42b5ad69..08b8e81b22e8b5fde0a368e11840267edab4d250 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,22 +1,28 @@
-A. Add tests for orthogonality in the Peirce decomposition.
+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).
 
-B. Add support for a symmetric positive-definite bilinear form in
-   the JordanSpinEJA.
+2. Add references and start citing them.
 
-1. Add CartesianProductEJA.
+3. Implement the octonion simple EJA.
 
-2. Check the axioms in the constructor when check != False?
+4. Pre-cache charpoly for some small algebras?
 
-3. Add references and start citing them.
+RealSymmetricEJA(4):
 
-4. Implement the octonion simple EJA.
+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. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
+5. Compute the scalar in the general natural_inner_product() for
+   matrices, so no overrides are necessary.
 
-6. Can we make the minimal and characteristic polynomial tests work
-   for trivial algebras, too? Then we wouldn't need the "nontrivial"
-   argument to random_eja().
+6. The main EJA element constructor is happy to convert between
+   e.g. HadamardEJA(3) and JordanSpinEJA(3).
 
-7. Solve the charpoly system with A_of_x.solve_right(x_powers[r])
-   rather than dumbass Cramer's rule.
+7. Figure out if CombinatorialFreeModule's use of IndexedGenerators
+   can be used to replace the matrix_basis().
+
+9. Add back the check_field=False and check_axioms=False parameters
+   for the EJAs we've constructed ourselves.