#15299: Incorrect results for analytic Sha due to low precision
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Reporter: jdemeyer | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.13
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by pbruin):
Replying to [comment:5 cremona]:
> Where does that leave this deriv_at1 function? At the very least it
should come with a huge warning about all this. And it really should
return 0 when the root number is +1 unless the user has made an explicit
assumption (assume_order_of_vanishing_is_positive=True, say) and otherwise
raise a NotImplemented error (or attempt to prove that L(1)=0).
The `Lseries_ell` class has a method `L1_vanishes()`, written by William
Stein. According to the documentation, it is provably correct if the
Manin constant is <= 2 for the optimal quotient in the isogeny class.
This method is used in some places, but not currently in `deriv_at1()`,
where we might use it to check the assumption ''L''(''E'', 1) = 0. If
that is too slow, a `check=False` flag could be added.
--
Ticket URL: <http://trac.sagemath.org/ticket/15299#comment:16>
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