Solving sparse polynomial equation systems

GABRIELA JERONIMO

Beijing

Otro; Key Laboratory of Mathematics and Mechanization Colloquium; 2010

Chinese Academy of Sciences

We will present symbolic algorithms for the computation of isolated roots of sparse polynomial systems. First, we will describe recent symbolic deformation techniques based on the polyhedral deformation introduced by Huber and Sturmfels that enable us to obtain of all the isolated roots in the torus of a sparse polynomial system of n equations in n variables in time which is polynomial in the combinatorial structure of the problem. Then, we will focus on affine isolated roots of sparse systems and  we will present a new symbolic probabilistic algorithm for the computation of these affine roots within the same complexity bounds.