eja: update the TODO.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 0e969cdfe4a2062c6a531b3fa84520c49e88de8f..8f9c17f11c0db462403fdf98faafded920de2839 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,8 +1,11 @@
-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 CartesisnProductEJA: 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
+   the FDEJA initializer be made to work on tuples, or will it
+   need to be overridden?
 
 2. Add references and start citing them.
 
@@ -21,6 +24,3 @@ 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.
-
-7. Drop the element-subalgebra in favor of a regular subalgebra. The
-   cached "one" can be set in the method.