  We exhibit a probabilistic symbolic algorithm for solving zero-dimensional
sparse systems. Our algorithm combines a symbolic homotopy procedure, based on
a flat deformation of a certain morphism of affine varieties, with the
polyhedral deformation of Huber and Sturmfels. The complexity of our algorithm
is quadratic in the size of the combinatorial structure of the input system.
This size is mainly represented by the mixed volume of Newton polytopes of the
input polynomials and an arithmetic analogue of the mixed volume associated to
the deformations under consideration.
