On the complexity of computing real radicals of polynomial systems - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2018

On the complexity of computing real radicals of polynomial systems

Mohab Safey El Din
Lihong Zhi
  • Fonction : Auteur
  • PersonId : 863556

Résumé

Let f= (f1, ..., fs) be a sequence of polynomials in Q[X1,...,Xn] of maximal degree D and V⊂ Cn be the algebraic set defined by f and r be its dimension. The real radical re < f > associated to f is the largest ideal which defines the real trace of V . When V is smooth, we show that re < f >, has a finite set of generators with degrees bounded by V. Moreover, we present a probabilistic algorithm of complexity (snDn )O(1) to compute the minimal primes of re < f >. When V is not smooth, we give a probabilistic algorithm of complexity sO(1) (nD)O(nr2r) to compute rational parametrizations for all irreducible components of the real algebraic set V ∩ Rn. Experiments are given to show the efficiency of our approaches.
Fichier principal
Vignette du fichier
SaYaZhi18.pdf (375.03 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01956596 , version 1 (16-12-2018)

Identifiants

Citer

Mohab Safey El Din, Zhi-Hong Yang, Lihong Zhi. On the complexity of computing real radicals of polynomial systems. ISSAC '18 - The 2018 ACM on International Symposium on Symbolic and Algebraic Computation, Jul 2018, New-York, United States. pp.351-358, ⟨10.1145/3208976.3209002⟩. ⟨hal-01956596⟩
70 Consultations
392 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More