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Elliptic curve Sha an documentation misleading about proof #1848

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williamstein opened this issue Jan 19, 2008 · 0 comments
Open

Elliptic curve Sha an documentation misleading about proof #1848

williamstein opened this issue Jan 19, 2008 · 0 comments

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@williamstein
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The sha an function:

sage: E = EllipticCurve('37a')
sage: Sha = E.sha(); Sha
<class 'sage.schemes.elliptic_curves.sha.Sha'>
sage: Sha.an()
1    

has help that at the beginning misleadingly suggests that it is provably correct when the analytic rank is 1. Looking at the code, it is clear that currently it is not provably correct except when the rank is 0 and a Manin constant hypothesis holds (which does hold for Cremona's curves).

Fix:

  1. Have a proof=False flag that keeps the current implementation
  2. Have a proof=True flag that fails if the Manin constant isn't known by a theorem to be <=2, and which runs new provably correct code in the case of analytic rank 1.

CC: @JohnCremona

Component: elliptic curves

Issue created by migration from https://trac.sagemath.org/ticket/1848

@williamstein williamstein added this to the sage-5.11 milestone Jan 19, 2008
@williamstein williamstein self-assigned this Jan 19, 2008
@jdemeyer jdemeyer modified the milestones: sage-5.11, sage-5.12 Aug 13, 2013
@sagetrac-vbraun-spam sagetrac-vbraun-spam mannequin modified the milestones: sage-6.1, sage-6.2 Jan 30, 2014
@sagetrac-vbraun-spam sagetrac-vbraun-spam mannequin modified the milestones: sage-6.2, sage-6.3 May 6, 2014
@sagetrac-vbraun-spam sagetrac-vbraun-spam mannequin modified the milestones: sage-6.3, sage-6.4 Aug 10, 2014
@fchapoton fchapoton modified the milestones: sage-6.4, sage-8.2 Apr 7, 2018
@mkoeppe mkoeppe removed this from the sage-8.2 milestone Dec 29, 2022
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