eja: add another performance TODO.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 87a162c73ab3ccf86623496dee39064e8b96bfb7..c9c264c436b198e02c39f7792307572c5efead7d 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,31 +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.
 
-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 random_instance(), one(), et cetera in DirectSumEJA.
+RealSymmetricEJA(4):
 
-6. 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.
+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]
 
-7. 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
-   we may somehow be able to pass the echelon basis straight in to
-   save time.
+5. Compute the scalar in the general natural_inner_product() for
+   matrices, so no overrides are necessary.
 
-   This may require supporting "basis" as a list of basis vectors
-   (as opposed to superalgebra elements) in the subalgebra constructor.
+6. The main EJA element constructor is happy to convert between
+   e.g. HadamardEJA(3) and JordanSpinEJA(3).
 
-8. Implement random_instance() for general algebras as random_eja().
-   Copy/paste the "general" construction into the other classes that
-   can use it. The general construction can be something like "call
-   random_instance() on something that inherits me and return the
-   result."
+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.