Resultants and contour integrals

Resultants are important special functions used to describe nonlinear phenomena. The resultant R-r1 ... r(n) determines a consistency condition for a system of n homogeneous polynomials of degrees r (1), ..., r (n) in n variables in precisely the same way as the determinant does for a system of linear equations. Unfortunately, there is a lack of convenient formulas for resultants in the case of a large number of variables. In this paper we use Cauchy contour integrals to obtain a polynomial formula for resultants, which is expected to be useful in applications.