Newton polygons can be used to find the valuations of roots of the polynomial from which the polygon was created at the prime used in the creation (given implicitly or explicitly). The following functions use Newton polygons to calculate the valuations of the roots of the polynomial paired with the number of roots with that valuation.
The valuations of the roots of f, where f is a polynomial over a local ring or a series ring.
The valuations of the roots of f with respect to p where p may be either a prime integer, a prime ideal of a number field or a place of a function field.