Newton Polygons

This page contains an applet created by Clif Presser and Rich Williams. The applet takes a given polynomial f(x) with integer coefficients and a given prime p and constructs the Newton polygon of f(x) with respect to p. The Newton polygon of f(x) with respect to p is defined as follows. If m is a non-zero integer and p is a prime, we define v(m) to be the largest non-negative integer r such that p^r divides m. If the degree of f(x) is n and if the coefficient of x^j is a non-zero integer a_j, then we consider the point (j,v(a_j)). The Newton polygon of f(x) with respect to p is the lower convex hull of the set of all such points. (More details about Newton polygons and their connection to p-adic roots of polynomials will be forthcoming.)

INSTRUCTIONS: Type a polynomial and a prime in the indicated spaces below. The polynomial should have integer coefficients. An example of an admissable form for the polynomial is:

The Newton Polygon Applet

There is no applet here!