#14826: Newton polygons
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       Reporter:  caruso           |         Owner:  roed        
           Type:  enhancement      |        Status:  needs_review
       Priority:  major            |     Milestone:  sage-5.12   
      Component:  padics           |    Resolution:              
       Keywords:  Newton polygons  |   Work issues:              
Report Upstream:  N/A              |     Reviewers:              
        Authors:                   |     Merged in:              
   Dependencies:                   |      Stopgaps:              
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Comment (by caruso):

 Replying to [comment:2 vbraun]:
 > There might be a better place that does not require another global name,
 maybe as method of local fields? At the very least the `NewtonPolygon`
 docstring should make an effort to disambiguate.

 If there is some risk of confusion, the best is probably to remove the
 import of the constructor `NewtonPolygon`. Indeed, as you say, these
 Newton polygons are mainly used for polynomials or series over padics (see
 tickets #14828 and #14830) and the user is definitely supposed to write
 `f.newton_polygon()` if `f` is such a polynomial or a series and not to
 construct a Newton polygon by himself.

 > A less scary way than `_normalize()` to compute the hull is to use some
 of Sage's existing polyhedral computation facilities:

 I wonder if it makes sense to derive the class `NewtonPolygon` (provided
 by this patch) from `Polyhedron_QQ`.

 There are obviously similarities (Newton polygons are polyhedrons in
 '''Q'''^2^) but also differences (the sum of two Newton polygons are their
 convex hull, the product of two Newton polygons are their Minkowski sum).

 What is your opinion?

 > Docstrings frequently need `INPUT` / `OUTPUT`, see the sage developer
 manual
 >
 > PEP 8 spacing, e.g.
 > {{{
 >     def __le__(self,other):    # no
 >     def __le__(self, other):   # yes
 > }}}
 >
 >
 > * `ParentNewtonPolygon.__repr__` should be `_repr_`
 > * `NewtonPolygon_lastslope._repr_` docstring has unused import

 Thanks. I will fix it.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14826#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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