Sparse resultant perturbations

We consider linear infinitesimal perturbations on sparse resultants. This yields a family of projection operators, hence a general method for handling algebraic systems in the presence of "excess" components or other degenerate inputs. The complexity is simply exponential in the dimension and polynomial in the sparse resultant degree. Our perturbation generalizes Canny's Generalized Characteristic Polynomial (GCP) for the homogeneous case, while it provides a new and faster algorithm for computing Rojas' toric perturbation. We illustrate our approach through its Maple implementation applied to specific examples. This work generalizes the linear perturbation schemes proposed in computational geometry and is also applied to the problem of rational implicitization with base points.