Newton Polygons [HB 62]

Removals and Changes:

• Newton polygons created from a polynomial and a prime will now recognise their creation as being from a polynomial and as such will return a Polynomial and have FaceFunctions. The default faces are consequently the inner faces.

• ValuationsOfRoots replaces NewtonSlopes. This function returns as a sequence of tuples, the valuations of the roots of the polynomial and the number of roots with that valuation.

New Features:

• A parameter Faces can be given to NewtonPolygon to determine which faces will be returned by Faces.

• A polygon can be constructed from a polynomial and a place of an algebraic function field.

• In addition to Slopes, this version makes available the functions InnerSlopes, LowerSlopes, OuterSlopes and AllSlopes are available.