Elimination and resultants. Part 2: Multivariate resultants

Abstract

Multivariate resultant expressions which are resultants for systems of three or more equations are described. The dialytic method produces the Sylvester bivariate resultant but it yields multiples of multivariate resultants in which extraneous factors must be identified and discarded to obtain the resultant. Generally, multivariate resultants must be expressed as quotients of two determinants. Also discussed are Dixon bidegree resultants for three bidegree equations and several resultant expressions for three equal degree equations. The Macaulay quotient is explained, together with a description of the μ-resultant.