Factoring polynomials over function fields

If K / k is a function field in one variable of positive characteristic, we describe a general algorithm to factor one-variable polynomials with coefficients in K . The algorithm is flexible enough to find factors subject to additional restrictions, e.g., to find all roots that belong to a given fin...

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Bibliographic Details
Published inResearch in number theory Vol. 11; no. 1
Main Author Voloch, José Felipe
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2025
Subjects
Mathematics
Mathematics and Statistics
Number Theory
Polynomial factorization
Primary: 12-08
Irreducibility test
Secondary: 11R09
Function fields
List decoding
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ISSN2522-0160
2363-9555
DOI10.1007/s40993-024-00581-y

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Summary:If K / k is a function field in one variable of positive characteristic, we describe a general algorithm to factor one-variable polynomials with coefficients in K . The algorithm is flexible enough to find factors subject to additional restrictions, e.g., to find all roots that belong to a given finite dimensional k -subspace of K , more efficiently. For bounded characteristic, it runs in polynomial time, relative to factorizations over the constant field k and also provides a deterministic polynomial time irreducibility test. We also discuss applications to places of reducible reduction, when k is a global field, and to list decoding of Reed-Solomon codes.
ISSN:2522-0160
2363-9555
DOI:10.1007/s40993-024-00581-y