Title:
  A Special Quantifier Elimination Algorithm for Pham Systems
Author:
  Laureano Gonzalez-Vega and Neila Gonzalez-Campos
  Departamento de Matematicas, Estadistica y Computacion,
  Facultad de Ciencias, Universidad de Cantabria,
  Avenida de los Castros s/n, 39071 Santander, Spain
E_mail:
  gvega@matesco.unican.es  gcampos@matesco.unican.es

Abstract:
  We show how to perform quantifier elimination in an efficient way for
  existential formulae involving a  polynomial system of n equations in n
  variables with parametric coefficients, where the polynomials have a
  particular structure: a Pham system or equivalently a Grobner Bases with
  respect some monomial ordering. The algorithm proceeds first in an
  algebraic manner, computing a partition of the parameter space and
  a finite number of polynomials for every set in the partition; in the
  second phase, the algorithm proceeds in a combinatorial way, selecting,
  among all possible sign conditions on these polynomials, those making
  the considered formula true, using a precise rule.

  The application of this method to the analysis of discretization
  schemes depending on a parameter and to the emptiness checking of a
  hypersurface will be also presented.