Multiple Discriminants and Extreme Values of Polynomials in Several Variables

Abstract

An extremal value of a function is the value of the function at one of its extremum points. Each extremum point of a differentiable function of several variables is described by the system of equations expressing the vanishing of all partial derivatives. However, in the general case, one cannot obtain equations for extremal values of the function. The case of polynomials significantly differs from the general case, and in this paper we obtain an equation for extremal values of a given polynomial in several variables.