-1. Finish CartesianProductEJA: add random_instance() method and
- optimize. I guess I should create a separate class hierarchy for
- Cartesian products of RationalBasisEJA? That way we get fast
- charpoly and random_instance() defined...
+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.
+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...
-4. Pre-cache charpoly for some small algebras?
+4. Add dimension bounds on any tests over AA that compute element
+ subalgebras.
-RealSymmetricEJA(4):
+5. The rational_algebra() stuff doesn't really belong in classes that
+ don't derive from RationalBasisEJA or its as-yet-nonexistent
+ element class.
-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. 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.
projects / sage.d.git / blobdiff