X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=1def3d2e9fd8cf381ae743344ce670a13f226438;hb=cc172fbdcd369542f90cf64e31611cf8698bc05a;hp=2d93ffb38a772f9409ecdff4153e975cb7c02c0b;hpb=28d86108d78f1ea5a93d9cc8d69bad9cc8cd74fd;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 2d93ffb..1def3d2 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,38 +1,20 @@
-1. Add cartesian products to random_eja().
+1. Add references and start citing them.
 
-2. Add references and start citing them.
+2. Profile (and fix?) any remaining slow operations.
 
-3. Implement the octonion simple EJA. We don't actually need octonions
-   for this to work, only their real embedding (some 8x8 monstrosity).
+3. Every once in a long while, the test
 
-4. Pre-cache charpoly for some small algebras?
+       sage: set_random_seed()
+       sage: x = random_eja().random_element()
+       sage: x.is_invertible() == (x.det() != 0)
 
-RealSymmetricEJA(4):
+   in eja_element.py returns False. Example:
 
-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
-   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.
+       sage: J1 = ComplexHermitianEJA(2)
+       sage: J2 = TrivialEJA()
+       sage: J = cartesian_product([J1,J2])
+       sage: x = J.from_vector(vector(QQ, [-1, -1/2, -1/2, -1/2]))
+       sage: x.is_invertible()
+       True
+       sage: x.det()
+       0