A quasi-linear irreducibility test in K[[x]][y]
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
A quasi-linear irreducibility test 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]
Laboratoire de Géométrie Algébrique et Applications à la Théorie de l'Information [GAATI]
Université de Caen Normandie [UNICAEN]

Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Weimann, Martin [Auteur]
Laboratoire de Géométrie Algébrique et Applications à la Théorie de l'Information [GAATI]
Université de Caen Normandie [UNICAEN]
Journal title :
Computational Complexity
Publisher :
Springer Verlag
Publication date :
2022
ISSN :
1016-3328
HAL domain(s) :
Mathématiques [math]
Informatique [cs]
Informatique [cs]/Calcul formel [cs.SC]
Mathématiques [math]/Géométrie algébrique [math.AG]
Informatique [cs]
Informatique [cs]/Calcul formel [cs.SC]
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 generalisation of Abhyankhar's irreducibility criterion to the case of non algebraically closed residue fields.Show less >
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 generalisation of Abhyankhar's irreducibility criterion to the case of non algebraically closed residue fields.Show less >
Language :
Anglais
Popular science :
Non
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