A discriminant criterion of irreducibility

Barroso, Evelia R. García; Gwoździewicz, Janusz

doi:10.2996/kmj/1341401060

“…In some sense, our approach establishes a bridge between the Newton-Puiseux algorithm, the Montes algorithm and Abhyankar's irreducibility criterion. Let us mention also [6,7] where an other irreducibility criterion in K[[x]][y] is given in terms of the Newton polygon of the discriminant curve of F , without complexity estimates.…”

Section: Introductionmentioning

confidence: 99%

A quasi-linear irreducibility test in $$\mathbb{K}[[x]][y]$$

Poteaux

¹

,

Weimann

²

2022

comput. complex.

0

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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.

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“…In some sense, our approach establishes a bridge between the Newton-Puiseux algorithm, the Montes algorithm and Abhyankar's irreducibility criterion. Let us mention also [9,10] where an other irreducibility criterion in K[[x]][y] is given in terms of the Newton polygon of the discriminant curve of F , without complexity estimates, and [20], which provides a good reference for the relations between approximate roots, Puiseux series and resolution of singularities of an irreducible Weierstrass polynomial…”

Section: Introductionmentioning

confidence: 99%

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

Poteaux,

Weimann

2019

Preprint

0

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“…In some sense, our approach establishes a bridge between the Newton-Puiseux algorithm, the Montes algorithm and Abhyankar's irreducibility criterion. Let us mention also [6,7] where an other irreducibility criterion in K[[x]][y] is given in terms of the Newton polygon of the discriminant curve of F , without complexity estimates.…”

Section: Introductionmentioning

confidence: 99%

A quasi-linear irreducibility test in K[[x]][y]

Poteaux¹,

Weimann²

2019

Preprint

0

View full text Add to dashboard Cite

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 abstract

A discriminant criterion of irreducibility

Cited by 7 publications

References 19 publications

A quasi-linear irreducibility test in $$\mathbb{K}[[x]][y]$$

A quasi-linear irreducibility test in $$\mathbb{K}[[x]][y]$$

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

A quasi-linear irreducibility test in K[[x]][y]

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