X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=f2e71c8495cd140698d28a88ee515680a997c322;hb=f56f9cf84a483d4e3b29f65b01bf9287ed6b7844;hp=90a49d3a120d4914c8b0664f2d2405f6a5b8b8ab;hpb=c3b925473fca353cc16b13ab24de6664821ac305;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 90a49d3..f2e71c8 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?
 
@@ -14,3 +15,29 @@ 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. 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.