#4525: [with patch, needs review] LLL-reduction of elliptic curve bases (with
resulting speed enhancement to integral_points())
----------------------------+-----------------------------------------------
Reporter: cremona | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.2.1
Component: number theory | Resolution:
Keywords: elliptic curve |
----------------------------+-----------------------------------------------
Changes (by cremona):
* type: enhancement => defect
Comment:
New patch 10984.patch fixes a bug whereby integral points of the form P+T
where P is integral and with small x, and T is torsion, were missed.
Example: in vanilla 3.2:
{{{
sage: E = EllipticCurve([0,0,0,-1131^2,0])
sage: [P[0] for P in E.integral_points()]
[-1131, -117, 0, 1131, 1392]
}}}
misses x=10933. After the patch:
{{{
sage: E = EllipticCurve([0,0,0,-1131^2,0])
sage: [P[0] for P in E.integral_points()]
[-1131, -117, 0, 1131, 1392, 10933]
}}}
The funny thing is that I only ran this curve to check a claim made in "
Solving the Diophantine equation y2=x(x2−n2)" by Konstantinos Draziotis,
Dimitrios Poulakis which just appeared in Volume 129, Issue 1, Pages
102-121 (January 2009) of the Journal of Number theory; in that paper
they miss x=1392!
I guess this should have been a new ticket, but all three patches affect
the same function and no-one has reviewed them yet anyway...
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4525#comment:5>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en
-~----------~----~----~----~------~----~------~--~---
