#4805: [with patch, needs review] S_integral points failure (possible p-adic
precision problem)
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Reporter: cremona | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.4
Component: number theory | Resolution:
Keywords: elliptic curve |
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Changes (by cremona):
* summary: S_integral points failure (possible p-adic precision problem)
=> [with patch, needs review] S_integral points
failure (possible p-adic precision problem)
* milestone: sage-3.4.1 => sage-3.4
Comment:
I worked on this in Dec 08 and while the result is not perfect it does fix
the immediate problems. Mainly, finding the p-adic elliptic log of a
point (on a curve over QQ) to specified precision may require the working
precision to be increased. [Simple example: if the valuation of the
discriminant is N then don't try changing the base field to Qp(N-1) as the
equation will look singular.]
The fixes in the patch do two things: in a few places where it's clear
that the precision must be at least something, then increase it to that
thing. Otherwise there is a lot of try/expect wrapping with the precision
being doubled if necessary, both in the log function itself and in the
(currently only) function which calls it, namely S_integral_points().
This code has been tested by running S_integral_points() on lots of curves
in the database with a variety of sets S.
To help improve the p-adic log function, a new function for points
has_good_reduction(self,P) has been defined.
The patch (trac_4805.patch) is based on 3.2.3.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4805#comment:1>
Sage <http://sagemath.org/>
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