X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=900c31c4defccba0b8d2c2a3b83a835f447a81ef;hb=a7092a728c3ec12b91afc0ad74d0831ae8153d02;hp=c92cfc9a62c2424e7ae2ab3be37d7f17f3954630;hpb=86ec96a9ff510b4b3d178998d63b0ce9a374c444;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index c92cfc9..900c31c 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -2,7 +2,8 @@
 
 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?
 
@@ -15,6 +16,22 @@ 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
    15-dimensional QuaternionHermitianAlgebra(3)) to find out why
    they're so slow.
 
-6. The _rational_algebra for a cartesian product should be a cartesian product.
+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.
 
-7. Use super() where it works.
+7. 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).
+
+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...