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Article Dans Une Revue Computational Complexity Année : 2022

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

Résumé

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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hal-02354929 , version 1 (08-11-2019)

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Adrien Poteaux, Martin Weimann. A quasi-linear irreducibility test in K[[x]][y]. Computational Complexity, 2022, ⟨10.1007/s00037-022-00221-w⟩. ⟨hal-02354929⟩
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