X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=1407ebdbe83bafab1ef79d881d25d2cf4912e18e;hb=17c1cf361b330252acae5ba18edb3a4fdf8bf9bd;hp=d7db05d092cf03ddf48a84bf4dab995578597122;hpb=2e96d7bbca8b654f79bc63b9cb09fe3ac6717ad4;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index d7db05d..1407ebd 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,16 +1,19 @@
-0. Add tests for orthogonality in the Peirce decomposition.
+1. Finish CartesianProductEJA: add to_matrix(), random_instance(),...
+   methods. I guess we should create a separate class hierarchy for
+   Cartesian products of RationalBasisEJA? That way we get fast
+   charpoly and random_instance() defined...
 
-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().
+5. Profile the construction of "large" matrix algebras (like the
+   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+   they're so slow.