X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=45a9ac06bf2c86020dee102143393e486fa408c5;hb=cf5e64b70869df65c7bb38888de54b1083e60d45;hp=fe18d5634835c97dcc1ee635c4fadecab25787ea;hpb=3cd987f3ace9517518510e985eb7d1996a924a68;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index fe18d56..45a9ac0 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,25 +1,22 @@
-1. Finish CartesianProductEJA: add to_matrix(), random_instance(),
-   one()... methods. This will require rethinking what a "matrix
-   representation" and "matrix space" means for a cartesian product
-   algebra. Do we want our matrix basis to consist of ordered pairs
-   (or triples, or...)? Should the matrix_space() of the algebra be
-   the cartesian product of the factors' matrix spaces? Can we just
-   fix the matrix basis/space after we call the FDEJA initializer?
+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. The main EJA element constructor is happy to convert between
-   e.g. HadamardEJA(3) and JordanSpinEJA(3).
+       sage: set_random_seed()
+       sage: x = random_eja().random_element()
+       sage: x.is_invertible() == (x.det() != 0)
 
-6. Profile the construction of "large" matrix algebras (like the
-   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
-   they're so slow.
+   in eja_element.py returns False.