X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=e925c162786ab4da9bb7155ec8086cda0da05464;hb=857eeec29a9b89b0e4f711476771c935757fa8dc;hp=e02257f2b02776f7c19c0ebb54826ffaa82db364;hpb=d3e40bda3f50a2101103192b91b2ab2a911c0311;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index e02257f..e925c16 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,12 +1,25 @@
-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]
+
+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.
+
+7. Set check_axioms=False for element-subalgebras outside of once or
+   twice in the test suite.