X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=90a49d3a120d4914c8b0664f2d2405f6a5b8b8ab;hb=c3b925473fca353cc16b13ab24de6664821ac305;hp=a9158127e857ccea2b430dc60d91a0465b010480;hpb=0d2f419ecd30a2d7899a37ab38ae6b4ff0e3245e;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index a915812..90a49d3 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,18 +1,16 @@
-0. Add tests for orthogonality in the Peirce decomposition.
+1. Add cartesian products to random_eja().
 
-1. Add CartesianProductEJA.
+2. Add references and start citing them.
 
-2. Check the axioms in the constructor when check != False?
+3. Implement the octonion simple EJA.
 
-3. Add references and start citing them.
+4. Pre-cache charpoly for some small algebras?
 
-4. Implement the octonion simple EJA.
+RealSymmetricEJA(4):
 
-5. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
+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]
 
-6. Can we make the minimal and characteristic polynomial tests work
-   for trivial algebras, too? Then we wouldn't need the "nontrivial"
-   argument to random_eja(). This would also allow us to potentially
-   pass a "size" of zero to the other constructors in random_eja() --
-   a code path that is basically untested right now.
+5. Profile the construction of "large" matrix algebras (like the
+   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+   they're so slow.