Computing isolated roots of sparse polynomial systems in affine space
We present a symbolic probabilistic algorithm to compute the isolated roots in C(n) of sparse polynomial equation systems. As some already known numerical algorithms solving this task, our procedure is based on polyhedral deformations and homotopies, but it amounts to solving a smaller number of square systems of equations and in fewer variables. The output of the algorithm is a geometric resolution of a finite set of points including the isolated roots of the system. The complexity is polynomial in the size of the combinatorial structure of the system supports up to a pre-processing yielding the mixed cells in a subdivision of the family of these supports. (C) 2010 Elsevier B.V. All rights reserved.
sparse polynomial systems algorithms complexity