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

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 is square-free and K is a perfect field of characteristic not dividing deg ( F ) . The algorithm uses the theory of approximate...

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Vydáno v:Computational complexity Ročník 31; číslo 1
Hlavní autoři: Poteaux, Adrien, Weimann, Martin
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.06.2022
Springer Nature B.V
Springer Verlag
Témata:
Algebraic Geometry
Algorithm Analysis and Problem Complexity
Algorithms
Computational Mathematics and Numerical Analysis
Computer Science
Mathematics
Polynomials
Symbolic Computation
Newton polygon
68W30
11S05
Irreducibility test
Residual polynomial
Approximate roots
14H20
13P05
Algorithm
Puiseux series
Complexity
14B05
ISSN:1016-3328, 1420-8954
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Shrnutí: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 is square-free and K is a perfect field of characteristic not dividing deg ( F ) . The algorithm uses the theory of approximate roots and may be seen as a generalisation of Abhyankar's irreducibility criterion to the case of non-algebraically closed residue fields.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1016-3328
1420-8954
DOI:10.1007/s00037-022-00221-w