X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=cf870aedc40b1901ca81be9442ebf3d5b5f855cd;hb=ea99a21239882d478c1a458a0411b1eb0588b84b;hp=e8a2a8d4fc8988b1ad6f744a69daba9cf0582397;hpb=3e46389a46db107db3fe36ace6fe5f2c2b52f815;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index e8a2a8d..cf870ae 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,13 +1,19 @@
-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().
+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. The main EJA element constructor is happy to convert between
+   e.g. HadamardEJA(3) and JordanSpinEJA(3).