#10590: Saturation of elliptic curve points can cause an infinite loop
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Reporter: cremona | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone:
Component: elliptic curves | Keywords: saturation
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Possibly related to #9247.
The method saturation() for sets of points on elliptic curves over Q calls
eclib in a loop which is optimistically headed "while True:".
Unfortunately this really can cause infinite looping. Here's an example
(the curve has conductor 130017):
{{{
E = EllipticCurve([1, 0, 1, -977842, -372252745])
P =
E([-192128125858676194585718821667542660822323528626273/336995568430319276695106602174283479617040716649,
70208213492933395764907328787228427430477177498927549075405076353624188436/195630373799784831667835900062564586429333568841391304129067339731164107,
1])
P.height()
E.saturation([P]) ## OK, saturated
E.saturation([2*P]) ## loops!
}}}
The problem is that there are various different ways in which the
saturation inside the loop (line 2097 of ell_rational_field.py) can fail,
and one -- probably the one here -- is due to a lack of precision. I will
look into how to increase the precision used in eclib from Sage. (In this
example, after mwrank_set_precision(200) it works fine, but not with 150.)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10590>
Sage <http://www.sagemath.org>
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