#6583: Implement two descent over QQ natively in Sage using ratpoints
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Reporter: rlm | Owner: rlm
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.3
Component: elliptic curves | Keywords:
Work_issues: | Author: Robert Miller
Upstream: N/A | Reviewer:
Merged: |
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Comment(by rlm):
I was just trying to address your question whether there were examples
where this was better than mwrank. Your second comment, "any enhanced
performance comes from the use of the more recent version of ratpoints" is
very false: if I remove the use of ratpoints altogether, the speedup
factors increase!
{{{
sage: L = []
sage: for E in cremona_optimal_curves(range(200)):
if E.torsion_order()%2 == 0:
A = E.mwrank_curve()
t = walltime()
A.two_descent(verbose=False, selmer_only=True,
second_descent=False)
t = walltime(t)
s = walltime()
_ = two_descent_by_two_isogeny(E, selmer_only=True)
s = walltime(s)
if s > t: print E.label()
else:
L.append(t/s)
....:
sage: sum(L)/len(L)
147.24136054804828
}}}
Thus I argue that this code is definitely worth including, especially
since this exact code was the main motivation for including ratpoints in
Sage in the first place. I don't know what "typical" means regarding the
conductor bound, especially since I'm primarily interested in curves with
small conductor. I spent a long time optimizing this code, and I'd rather
not see that work getting lost to the four winds.
(John-- Maybe I'm just missing your point?)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6583#comment:15>
Sage <http://www.sagemath.org>
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