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arXiv · 1911.03551

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

Adrien Poteaux·Martin Weimann
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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 generalisation of Abhyankhar's irreducibility criterion to the case of non algebraically closed residue fields.

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Adrien Poteaux, Martin Weimann. 2019-11-05. A quasi-linear irreducibility test in K[[x]][y]. https://arxiv.org/abs/1911.03551

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