#6667: bug in newton_polygon() for p-adic polynomials
----------------------------------+---------------------------------
Reporter: AlexGhitza | Owner: roed
Type: defect | Status: positive_review
Priority: major | Milestone: sage-5.12
Component: padics | Resolution:
Keywords: newton polygon | Merged in:
Authors: Xavier Caruso | Reviewers: Frédéric Chapoton
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #14826 | Stopgaps: #12701
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Description changed by jdemeyer:
Old description:
> This is as simple as I can make it at the moment:
>
> {{{
> ----------------------------------------------------------------------
> | Sage Version 4.1.1.rc0, Release Date: 2009-07-29 |
> | Type notebook() for the GUI, and license() for information. |
> ----------------------------------------------------------------------
> **********************************************************************
> * *
> * Warning: this is a prerelease version, and it may be unstable. *
> * *
> **********************************************************************
> sage: K = Qp(2, prec=5)
> sage: P.<x> = K[]
> sage: f = P(x^4 + 2^3*x^3 + 2^13*x^2 + 2^21*x + 2^37)
> sage: f.newton_polygon()
> [(0, 37), (1, 21), (2, 13), (3, 3), (4, 0)]
> }}}
>
> This is wrong, as it's not convex (the point (2,13) should not be there).
> Indeed, note that the sequence of Newton slopes is not non-increasing:
>
> {{{
> sage: f.newton_slopes()
> [16, 8, 10, 3]
> }}}
>
> This should be [16, 9, 9, 3].
New description:
This is as simple as I can make it at the moment:
{{{
----------------------------------------------------------------------
| Sage Version 4.1.1.rc0, Release Date: 2009-07-29 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
**********************************************************************
* *
* Warning: this is a prerelease version, and it may be unstable. *
* *
**********************************************************************
sage: K = Qp(2, prec=5)
sage: P.<x> = K[]
sage: f = P(x^4 + 2^3*x^3 + 2^13*x^2 + 2^21*x + 2^37)
sage: f.newton_polygon()
[(0, 37), (1, 21), (2, 13), (3, 3), (4, 0)]
}}}
This is wrong, as it's not convex (the point (2,13) should not be there).
Indeed, note that the sequence of Newton slopes is not non-increasing:
{{{
sage: f.newton_slopes()
[16, 8, 10, 3]
}}}
This should be [16, 9, 9, 3].
'''Apply''' [attachment:trac_6667_caruso_revised.patch]
--
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Ticket URL: <http://trac.sagemath.org/ticket/6667#comment:16>
Sage <http://www.sagemath.org>
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