X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=45a9ac06bf2c86020dee102143393e486fa408c5;hp=0d6edf2500664bbbad54e08b18f9e304765a7b6f;hb=cf5e64b70869df65c7bb38888de54b1083e60d45;hpb=f904a86173b5f0dab18a409407e8ac708d9efb4b

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 0d6edf2..45a9ac0 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,22 +1,22 @@
-1. Add cartesian products to random_eja().
+1. Add references and start citing them.
 
-2. Add references and start citing them.
+2. Pre-cache charpoly for some more algebras.
 
-3. 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.
 
-4. Pre-cache charpoly for some small algebras?
+4. What the ever-loving fuck is this shit?
 
-RealSymmetricEJA(4):
+       sage: O = Octonions(QQ)
+       sage: e0 = O.monomial(0)
+       sage: e0*[[[[]]]]
+       [[[[]]]]*e0
 
-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. Every once in a long while, the test
 
-5. Profile the construction of "large" matrix algebras (like the
-   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
-   they're so slow.
+       sage: set_random_seed()
+       sage: x = random_eja().random_element()
+       sage: x.is_invertible() == (x.det() != 0)
 
-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.
+   in eja_element.py returns False.