eja: update the TODO again.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 25ef99df92da5f41595c609cdea9ae5d245cd1fe..fe18d5634835c97dcc1ee635c4fadecab25787ea 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,8 +1,10 @@
-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).
+1. Finish CartesianProductEJA: add to_matrix(), random_instance(),
+   one()... methods. This will require rethinking what a "matrix
+   representation" and "matrix space" means for a cartesian product
+   algebra. Do we want our matrix basis to consist of ordered pairs
+   (or triples, or...)? Should the matrix_space() of the algebra be
+   the cartesian product of the factors' matrix spaces? Can we just
+   fix the matrix basis/space after we call the FDEJA initializer?
 
 2. Add references and start citing them.
 
@@ -20,4 +22,4 @@ 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
 
 6. Profile the construction of "large" matrix algebras (like the
    15-dimensional QuaternionHermitianAlgebra(3)) to find out why
-   they're so slow.
\ No newline at end of file
+   they're so slow.