eja: cache one() for Cartesian product algebras.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 0e969cdfe4a2062c6a531b3fa84520c49e88de8f..03bf40459e26805a2b2d6e3bae114779f0de57d3 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(),... 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.
 
@@ -21,6 +23,3 @@ 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.