X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=26ff1e9e7db77b22f3d749056121d094a08f2d8b;hb=8d91b5b5af605dabe11a024ab030f2fcb2828cde;hp=e02257f2b02776f7c19c0ebb54826ffaa82db364;hpb=309fc28265693c9abd51780ea76f8beec39ce27f;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index e02257f..26ff1e9 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,12 +1,27 @@
-0. Add tests for orthogonality in the Peirce decomposition.
+1. Add references and start citing them.
 
-1. Add CartesianProductEJA.
+2. Pre-cache charpoly for some small algebras?
 
-2. Check the axioms in the constructor when check != False?
+RealSymmetricEJA(4):
 
-3. Add references and start citing them.
+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]
 
-4. Implement the octonion simple EJA.
+3. Profile the construction of "large" matrix algebras (like the
+   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+   they're so slow.
 
-5. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
+4. What the ever-loving fuck is this shit?
+
+       sage: O = Octonions(QQ)
+       sage: e0 = O.monomial(0)
+       sage: e0*[[[[]]]]
+       [[[[]]]]*e0
+
+5. Every once in a long while, the test
+
+       sage: set_random_seed()
+       sage: x = random_eja().random_element()
+       sage: x.is_invertible() == (x.det() != 0)
+
+   in eja_element.py returns False.