A Practical Method for the Sparse Resultant ( Extended

We propose an eecient method for computing the sparse resultant of a system of n + 1 polynomial equations in n unknowns. Our approach improves upon CE93] and constructs a smaller matrix whose determinant is a non-zero multiple of the resultant and from which the latter is easily recovered. For certain classes of systems, it attains optimality by expressing the resultant as a single determinant. An implementation of the algorithm is described and empirical results presented and compared with those from CE93] and SZ94]. In addition, the important subproblem of computing Mixed Volumes is examined and an eecient algorithm is implemented.