An alternative algorithm for computing the pseudo-remainder of multivariate polynomials

This paper presents an alternative method to compute the pseudo-remainder for multivariate polynomials, which plays a very important role in polynomial system solving by many known elimination methods. The efficiency of the new approach dependents heavily on the method for computing the determinant of a matrix. Some examples show that the new algorithm is efficient when one computes the determinants of matrices by using Gaussian elimination in Maple system.