X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=f34fc34701a214afd3d086a675844b44619e5d9a;hb=23ced4147cf68d9e5d7a00be958ad3c579436f50;hp=103e8d1017eb5589b6bc5eedcc91655eb13d8c0d;hpb=98bb214e8175eb3526d248c69b3fafe8ab694705;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 103e8d1..f34fc34 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,11 +1,9 @@
-1. Finish CartesianProductEJA: add random_instance() method and
-   optimize. I guess I should create a separate class hierarchy for
-   Cartesian products of RationalBasisEJA? That way we get fast
-   charpoly and random_instance() defined...
+1. Add cartesian products to random_eja().
 
 2. Add references and start citing them.
 
-3. Implement the octonion simple EJA.
+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?
 
@@ -17,3 +15,32 @@ 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
 5. 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
+   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. NOTE: we should still be able
+   to recompute the table somehow. Is this worth it?
+
+7. What the ever-loving fuck is this shit?
+
+       sage: O = Octonions(QQ)
+       sage: e0 = O.monomial(0)
+       sage: e0*[[[[]]]]
+       [[[[]]]]*e0
+
+8. 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...
+
+9. Add HurwitzMatrixAlgebra subclass between MatrixAlgebra and
+   OctonionMatrixAlgebra.
+
+10. 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.