Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Complete list of metadatas

Cited literature [36 references]  Display  Hide  Download

https://hal-normandie-univ.archives-ouvertes.fr/hal-02137331
Contributor : Martin Weimann <>
Submitted on : Wednesday, May 22, 2019 - 10:13:54 PM
Last modification on : Tuesday, September 29, 2020 - 12:24:07 PM

File

irreducible_approx_roots.pdf
Files produced by the author(s)

Identifiers

  • 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⟩

Share

Metrics

Record views

57

Files downloads

59