#6667: bug in newton_polygon() for p-adic polynomials
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Reporter: AlexGhitza | Owner: roed
Type: defect | Status: new
Priority: major | Milestone:
Component: padics | Keywords: newton polygon
Reviewer: | Author:
Merged: |
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This is as simple as I can make it at the moment:
{{{
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| Sage Version 4.1.1.rc0, Release Date: 2009-07-29 |
| Type notebook() for the GUI, and license() for information. |
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**********************************************************************
* *
* 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].
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6667>
Sage <http://sagemath.org/>
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