On the practical computation of one point in each connected component of a semi-algebraic set defined by a polynomial system of equations and non-strict inequalities - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 2004

On the practical computation of one point in each connected component of a semi-algebraic set defined by a polynomial system of equations and non-strict inequalities

Abstract

Given polynomials f_1, , f_k, g_1, , g_s in , we consider the semi-algebraic set defined by: \begin{array}l f_1== f_k=0 g_10, , g_s0 \end{array} and focus on the problem of computing at least one point in each connected component of . We first study how to solve this problem by considering as the union of solutions sets of polynomial systems of equations and strict inequalities and proceed to the complexity analysis of the underlying algorithm. Then, we improve this approach by proving that computing at least one point in each connected component of can be done by computing at least one point in each connected component of real algebraic sets defined by vanishing the polynomials f_1, , f_k and some of the polynomials g_1, , g_s. The complexity analysis shows that this latter approach is better than the former one. Finally, we present our implementation and use it to solve an application in Pattern Matching.

Domains

Other [cs.OH]
Fichier principal
Vignette du fichier
RR-5079.pdf (295.08 Ko) Télécharger le fichier

Dates and versions

inria-00071504 , version 1 (23-05-2006)

Identifiers

  • HAL Id : inria-00071504 , version 1

Cite

Colas Le Guernic, Mohab Safey El Din. On the practical computation of one point in each connected component of a semi-algebraic set defined by a polynomial system of equations and non-strict inequalities. [Research Report] RR-5079, INRIA. 2004. ⟨inria-00071504⟩
105 View
147 Download

Share

Gmail Facebook Twitter LinkedIn More