Title :

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

Author(s) :

Poteaux, Adrien [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Weimann, Martin [Auteur]
Université de la Polynésie Française [UPF]
Laboratoire de Géométrie Algébrique et Applications à la Théorie de l'Information [GAATI]
Laboratoire de Mathématiques Nicolas Oresme [LMNO]
Université de Caen Normandie [UNICAEN]

HAL domain(s) :

Mathématiques [math]
Mathématiques [math]/Algèbre commutative [math.AC]
Mathématiques [math]/Géométrie algébrique [math.AG]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL