X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=cf870aedc40b1901ca81be9442ebf3d5b5f855cd;hb=ea99a21239882d478c1a458a0411b1eb0588b84b;hp=985e50a8dbbfc2d6f8c8d2e80d445fcd9b3ccd86;hpb=e529e0e2775cf50207c7d01d5907214d03cdff5c;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 985e50a..cf870ae 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,10 +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. Check the axioms in the constructor when check != False?
+2. Add references and start citing them.
 
-3. Add references and start citing them.
+3. Implement the octonion simple EJA.
 
-4. Implement the octonion simple EJA.
+4. Pre-cache charpoly for some small algebras?
 
-5. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
+RealSymmetricEJA(4):
+
+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).