Using approximate roots for irreducibility and equi-singularity issues in K[[x]][y]

Abstract : We provide an irreducibility test in the ring K[[x]][y] whose complexity is quasi-linear with respect to the discriminant valuation, assuming the input polynomial F square-free and K a perfect field of characteristic zero or greater than deg(F). The algorithm uses the theory of approximate roots and may be seen as a generalization of Abhyankhar's irreducibility criterion to the case of non algebraically closed residue fields. More generally, we show that we can test within the same complexity if a polynomial is pseudo-irreducible, a larger class of polynomials containing irreducible ones. If F is pseudo-irreducible, the algorithm computes also the discriminant valuation of F and the equisingularity classes of the germs of plane curves defined by F along the fiber x = 0.
Liste complète des métadonnées

Littérature citée [36 références]  Voir  Masquer  Télécharger

https://hal-normandie-univ.archives-ouvertes.fr/hal-02137331
Contributeur : Martin Weimann <>
Soumis le : mercredi 22 mai 2019 - 22:13:54
Dernière modification le : jeudi 21 novembre 2019 - 15:51:11

Fichier

irreducible_approx_roots.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-02137331, version 1

Citation

Adrien Poteaux, Martin Weimann. Using approximate roots for irreducibility and equi-singularity issues in K[[x]][y]. 2019. ⟨hal-02137331v1⟩

Partager

Métriques

Consultations de la notice

53

Téléchargements de fichiers

59