X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=17422851f81f5196cd47cc159004c326a848b115;hb=d6c744ecba0a22fdd76cb17e663594d323d1bb38;hp=900c31c4defccba0b8d2c2a3b83a835f447a81ef;hpb=a7092a728c3ec12b91afc0ad74d0831ae8153d02;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 900c31c..1742285 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,37 +1,39 @@
-1. Add cartesian products to random_eja().
+1. Add references and start citing them.
 
-2. Add references and start citing them.
-
-3. Implement the octonion simple EJA. We don't actually need octonions
-   for this to work, only their real embedding (some 8x8 monstrosity).
-
-4. Pre-cache charpoly for some small algebras?
+2. Pre-cache charpoly for some small algebras?
 
 RealSymmetricEJA(4):
 
 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
+3. Profile the construction of "large" matrix algebras (like the
    15-dimensional QuaternionHermitianAlgebra(3)) to find out why
    they're so slow.
 
-6. Instead of storing a basis multiplication matrix, just make
+4. Instead of storing a basis multiplication matrix, just make
    product_on_basis() a cached method and manually cache its
    entries. The cython cached method lookup should be faster than a
-   python-based matrix lookup anyway.
+   python-based matrix lookup anyway. NOTE: we should still be able
+   to recompute the table somehow. Is this worth it?
 
-7. What the ever-loving fuck is this shit?
+5. What the ever-loving fuck is this shit?
 
        sage: O = Octonions(QQ)
        sage: e0 = O.monomial(0)
        sage: e0*[[[[]]]]
        [[[[]]]]*e0
 
-8. Factor out a class for matrices with real embeddings (i.e. not the
-   octonions).
+6. Can we convert the complex/quaternion algebras to avoid real-
+   (un)embeddings? Quaternions would need their own
+   QuaternionMatrixAlgebra, since Sage matrices have to have entries
+   in a commutative ring. Those and the octonion stuff could be moved
+   to hurwitz.py along with the HurwitzMatrixAlgebra.
+
+7. 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)
 
-9. In fact, could my octonion matrix algebra be generalized for any
-   algebra of matrices over the reals whose entries are not real? Then
-   we wouldn't need real embeddings at all. They might even be fricking
-   vector spaces if I did that...
+   in eja_element.py returns False.