A quasi-linear irreducibility test in K[[x]][y]
Number Theory
2019-11-12 v1 Commutative Algebra
Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1911.03551,
title = {A quasi-linear irreducibility test in K[[x]][y]},
author = {Adrien Poteaux and Martin Weimann},
journal= {arXiv preprint arXiv:1911.03551},
year = {2019}
}
Comments
29 pages. arXiv admin note: substantial text overlap with arXiv:1904.00286