#15483: Simon 2-descent gives RuntimeError for an elliptic curve over a
quadratic
field
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Reporter: pbruin | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.2
Component: elliptic curves | Resolution:
Keywords: simon_two_descent | Merged in:
Authors: Peter Bruin | Reviewers:
Report Upstream: Workaround found; | Work issues:
Bug reported upstream. | Commit:
Branch: | b662aba98ad4122a82fc135cf9b5dbf58de2ba0e
u/pbruin/15483-two_descent_precision| Stopgaps:
Dependencies: #11005 |
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Comment (by pbruin):
Replying to [comment:20 jdemeyer]:
> Did you get any answer from Denis Simon?
Unfortunately not (yet).
> If not, we should try to implement the `nfsign()` solution ourselves.
If you want to do it, go ahead, but to be honest, it seems a bit pointless
to me at the moment.
Although I agreed above that the increase from 10 to 38 in the precision
check was just a hack, there is actually a reason for the 38. (The
following assumes a 64-bit word length.) For any bound ''n'' < 38 in this
test, a 1-bit error in the result already has catastrophic consequences: a
number that should be negative is taken to be a positive number with 64
bits of precision, due to the precision being only 1 bit, and that bit
being affected by a round-off error). For ''n'' >= 38, the round-off
errors have to accumulate to at least 65 bits of precision for the problem
to occur (wrongly trusting the positivity of a 128-bit number). Of course
that can happen, but it is extremely unlikely and I would be surprised if
you could find any example.
--
Ticket URL: <http://trac.sagemath.org/ticket/15483#comment:21>
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