X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=2fb5505439e6530cdc7e6c9d31ad06941937918f;hb=07e5949ccb09f26fe6e1bd8e2e135c7eab680466;hp=8f9c17f11c0db462403fdf98faafded920de2839;hpb=cc309b502850fd99abc742ee4ee4e015312f65ac;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 8f9c17f..2fb5505 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,26 +1,40 @@
-1. Finish CartesisnProductEJA: add to_matrix(), random_instance(),
-   one()... methods. This will require rethinking what a "matrix
-   representation" and "matrix space" means for a cartesian product
-   algebra. Do we want our matrix basis to consist of ordered pairs
-   (or triples, or...)? Should the matrix_space() of the algebra
-   be the cartesian product of the factors' matrix spaces? Can
-   the FDEJA initializer be made to work on tuples, or will it
-   need to be overridden?
+1. Add references and start citing them.
 
-2. Add references and start citing them.
-
-3. Implement the octonion simple EJA.
-
-4. Pre-cache charpoly for some small algebras?
+2. Pre-cache charpoly for some small algebras?
 
 RealSymmetricEJA(4):
 
 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. The main EJA element constructor is happy to convert between
-   e.g. HadamardEJA(3) and JordanSpinEJA(3).
-
-6. Profile the construction of "large" matrix algebras (like the
+3. Profile the construction of "large" matrix algebras (like the
    15-dimensional QuaternionHermitianAlgebra(3)) to find out why
    they're so slow.
+
+4. 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?
+
+5. What the ever-loving fuck is this shit?
+
+       sage: O = Octonions(QQ)
+       sage: e0 = O.monomial(0)
+       sage: e0*[[[[]]]]
+       [[[[]]]]*e0
+
+6. 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...
+
+7. 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.
+
+8. Add an alias for AlbertAlgebra.