A note on resultants (Q1094456)

The authors present an algorithm for the determination of the number of common roots of a finite set of polynomials in one indeterminate with the coefficients in a field. The algorithm described is based on Sylvester's resultants of two polynomials in one indeterminate and on Kronecker's elimination. As an application a device is derived that establishes the multiplicities of the roots of a given polynomial. The cases of the cubics and of the quartics are explicitly discussed. The authors compare their algorithm with a result of \textit{S. Barnett} [Linear Multilinear Algebra 8, 271-279 (1980; Zbl 0438.12012)].