**
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:
**

presser@sc.edu williams@math.sc.edu filaseta@math.sc.edu Last modified: Mon Jan 31 15:54:06 EST 1998