#4741: [with new patch, needs review (and work too)] Implement S-integral point
finding for elliptic curves over Q
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Reporter: cremona | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.2.2
Component: number theory | Resolution:
Keywords: |
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Comment (by cremona):
Thanks for the encouragement, Michael!
Here's the strategy I propose. We separate out as an issue the
computation of the p-adic elliptic log (of a point on an elliptic curve
over Q, and later over number fields). A lot of this work does not depend
on the point, only on the curve and the prime (specifically, construction
of the base-change curve over Qp, and the integer f such that
{{{f*E(Qp)\subseteq E^1(Qp)}}}, which is the product of the tamagawa
exponent (already cached) and the exponent of the group mod p). This
could be stored in the local_data class which we already have. The p-adic
part of this would need some work to compute the suitable precision needed
(which may be more than the user asks for).
The second issue is then the S_integral points code itself, where I had
one difficulty. I'll recover the curve which caused that and send it to
tnagel.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4741#comment:29>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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