X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=45a9ac06bf2c86020dee102143393e486fa408c5;hb=86bf0d59519eef1259fa9fb82457148b28c2fa2e;hp=f27df9cdc14c6e94cabd6a067285bc354ecd3cbe;hpb=7bb608efc474092b1c26286924c8d91a1bf51aaa;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index f27df9c..45a9ac0 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,22 +1,22 @@
-1. Add cartesian products to random_eja().
+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. We don't actually need octonions
-   for this to work, only their real embedding (some 8x8 monstrosity).
+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. Profile the construction of "large" matrix algebras (like the
-   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
-   they're so slow.
+       sage: set_random_seed()
+       sage: x = random_eja().random_element()
+       sage: x.is_invertible() == (x.det() != 0)
 
-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.
+   in eja_element.py returns False.