X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=427a9539bb69aa4ab25e0687f0336a09377d57e0;hb=2eb57d9d9487ef2533c177d2771a7c47b2528c4b;hp=f49bde15a52f31f7147481cf4eada29317b091e1;hpb=77a973c0044e70fff2041a76e78a0fde7595bfb8;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index f49bde1..427a953 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,26 +1,24 @@
-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 inner_product(), _max_test_case_size(), 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. Actually, this is
+   probably better implemented as a dimension_over_reals() method
+   that returns 1, 2, or 4.
 
-   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).