eja: add another TODO I had forgotten.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index da3e650bf04da611af5d5d54b4fad635b491da9d..0d6edf2500664bbbad54e08b18f9e304765a7b6f 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,17 +1,22 @@
-1. Add CartesianProductEJA.
+1. Add cartesian products to random_eja().
 
-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):
 
-6. Refactor the current ungodly fast charpoly hack (relies on the
-   theory to ensure that the charpolys are equal.)
+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]
 
-7. If we factor out a "matrix algebra" class, then it would make sense
-   to replace the custom embedding/unembedding functions with static
-   _real_embedding() and _real_unembedding() methods.
+5. Profile the construction of "large" matrix algebras (like the
+   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+   they're so slow.
+
+6. We should compute whether or not the algebra is associative if it
+   is unknown. I guess the "associative" argument should be ternary
+   (True, False, None)? We should also figure out the correct
+   True/False values for the example classes, and of course add an
+   _is_associative() method.