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....

Let K be an ordinary differential field with derivation ∂. Let P be a system of n linear differential polynomial parametric equations in n− 1 differential parameters with implicit ideal ID. Given a nonzero linear differential polynomial A in ID we give necessary and sufficient conditions on A for P to be n − 1 dimensional. We prove the existence of a linear perturbation Pφ of P so that the line...

Constructive methods for matrices of multihomogeneous (or multigraded) resultants for unmixed systems have been studied by Weyman, Zelevinsky, Sturmfels, Dickenstein and Emiris. We generalize these constructions to mixed systems, whose Newton polytopes are scaled copies of one polytope, thus taking a step towards systems with arbitrary supports. First, we specify matrices whose determinant equa...

This paper deals with a method of estimating the parameters and the order of a linear system using differential digital filters and the resultant. From the observed signals of the input and output of an objective system, we extract the differential signals from the zero order to an appropriate high order with the same phase characteristics, using several digital filters. On the assumption that ...