Subresultants and locally nilpotent derivations

Abstract

In this paper we establish a connection between subresultants and locally nilpotent derivations over commutative rings containing the rationals. As consequence of this connection, we prove that for any commutative ring with unit and any polynomials P and Q in A[y] , the ith subresultant of P and Q is the determinant of a matrix, depending only on the degrees of P and Q, whose entries are taken from the list built with P, Q and their successive Hasse derivatives.