Newton polytope

In mathematics, the Newton polytope is an integral polytope associated with a multivariate polynomial. It can be used to analyze the polynomial's behavior when specific variables are considered negligible relative to the others. Specifically, let
where we use the shorthand notation . Then the Newton polytope associated to is the convex hull of the ; that is
The Newton polytope satisfies the following homomorphism-type property: 
where the addition is in the sense of Minkowski.
Newton polytopes are the central object of study in tropical geometry and characterize the Gröbner bases for an ideal.