eja: rename operator_inner_product -> operator_trace inner_product.

[sage.d.git] / mjo / eja / TODO

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index cd516fce68ccd2fb31272d49529ba3c2bc8a468d..b0d5378fab6ed7c7c981aaf0fd9a044ca18a1b07 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,37 +1,20 @@
 1. Add references and start citing them.
 
-2. Pre-cache charpoly for some small algebras?
+2. Profile (and fix?) any remaining slow operations.
 
-RealSymmetricEJA(4):
+3. When we take a Cartesian product involving a trivial algebra, we
+   could easily cache the identity and charpoly coefficients using
+   the nontrivial factor. On the other hand, it's nice that we can
+   test out some alternate code paths...
 
-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]
+4. Add dimension bounds on any tests over AA that compute element
+   subalgebras.
 
-3. Profile the construction of "large" matrix algebras (like the
-   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
-   they're so slow.
+5. The rational_algebra() stuff doesn't really belong in classes that
+   don't derive from RationalBasisEJA or its as-yet-nonexistent
+   element class.
 
-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. Figure out how to make OctonionHermitianEJA a RationalBasisEJA,
-   and then convert the complex/quaternion algebras to avoid real-
-   (un)embeddings.
-
-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.
+6. Add special det/trace method overrides for the algebras where we
+   know them? The only reason this might be tricky is because the
+   obvious solution is to subclass EJAElement, but then we might
+   collide with e.g. the Cartesian product element subclass.