#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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Description changed by jdemeyer:
Old description:
> See [https://groups.google.com/forum/#!topic/sage-support/rYQ4rWyncG4]
>
> {{{
> sage: E=EllipticCurve(QQ,[0, 0, 1, -79, 342]);
> E.sha().an(),E.sha().an_numerical()
> (0, 1.00000000000000)
> sage: E.lseries().deriv_at1(100*sqrt(E.conductor()) + 10) # L1,
> error_bound
> (1.94655218772191e-15, 1.82478252135394e-270)
> }}}
>
> This seems to be due to inappropriate use of Python floats instead of
> more precise real numbers.
New description:
See [https://groups.google.com/forum/#!topic/sage-support/rYQ4rWyncG4]
{{{
sage: E = EllipticCurve(QQ,[0, 0, 1, -79, 342]);
E.sha().an(),E.sha().an_numerical()
(0, 1.00000000000000)
sage: E.lseries().deriv_at1(100*sqrt(E.conductor()) + 10) # L1,
error_bound
(1.94655218772191e-15, 1.82478252135394e-270)
}}}
This seems to be due to inappropriate use of Python floats instead of more
precise real numbers. After the patch:
{{{
sage: E = EllipticCurve(QQ,[0, 0, 1, -79, 342]);
E.sha().an(),E.sha().an_numerical()
(1.00000000000000, 1.00000000000000)
sage: E.lseries().deriv_at1(100*sqrt(E.conductor()) + 10) # L1,
error_bound
(-4.32787398660869448751904675450772492666840247314688171540527473331725818170217268435223462033366791557160872926179439894639315476270837428785657638252738603056742447337636326343956370276624493916496382120766160023620812331280787034239648552009947468067829864968026720015203778821069593806584e-277,
1.82478252137476307223140369768561190028055347258560054363485475966241792307587640145132294203994875344783110100551912347495775160520204557245032474939095251969168953786545612090565728262067746413119194690260652692254781091147749697957445424152473292233020112755190503925812425294821095313979e-270)
}}}
--
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Ticket URL: <http://trac.sagemath.org/ticket/15299#comment:8>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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