X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=93aa9fb42e6ec6cdba6963db8dacfddd116ba762;hb=21fa036e86711c6c28b6d89af2b1bfe4ceb24b29;hp=b8ceda8fa3defcb3df1a5641ab03eed28c910ee9;hpb=0ed6dd869beb5fecd91e3653243e9c899b12c36b;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index b8ceda8..93aa9fb 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,19 +1,22 @@
-A. 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...
 
-B. Add support for a symmetric positive-definite bilinear form in
-   the JordanSpinEJA.
+2. Add references and start citing them.
 
-1. Add CartesianProductEJA.
+3. Implement the octonion simple EJA.
 
-2. Check the axioms in the constructor when check != False?
+4. Pre-cache charpoly for some small algebras?
 
-3. Add references and start citing them.
+RealSymmetricEJA(4):
 
-4. Implement the octonion simple EJA.
+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]
 
-5. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
+5. The main EJA element constructor is happy to convert between
+   e.g. HadamardEJA(3) and JordanSpinEJA(3).
 
-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().
+6. Profile the construction of "large" matrix algebras (like the
+   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+   they're so slow.