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]
-
-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
-
-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.
+4. Add dimension bounds on any tests over AA that compute element
+ subalgebras.
projects / sage.d.git / blobdiff