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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| Published in | Research in number theory Vol. 11; no. 1 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.03.2025
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 2522-0160 2363-9555 |
| DOI | 10.1007/s40993-024-00581-y |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| ArticleNumber | 5 |
| Author | Voloch, José Felipe |
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| Cites_doi | 10.1007/3-540-45455-1_29 10.1006/jsco.2001.0513 10.1090/S0894-0347-2014-00820-1 10.1109/18.887868 10.1109/FOCS46700.2020.00088 10.1090/S0025-5718-1985-0790658-X 10.5802/jtnb.655 10.1007/s10208-016-9318-8 10.1090/conm/767/15402 10.1145/3087604.3087642 10.1006/jcom.1997.0439 10.1007/BF01170848 10.1006/jnth.1999.2381 10.1007/978-3-642-59663-6_12 10.1006/jsco.2002.0564 10.1007/s00200-010-0121-5 10.1016/j.jsc.2005.03.002 10.1112/plms/s3-52.1.1 10.1007/978-1-4757-1810-2 10.1016/j.jsc.2004.09.006 10.1007/s00200-013-0200-5 10.1090/S0025-5718-02-01428-X |
| ContentType | Journal Article |
| Copyright | The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Keywords | Polynomial factorization Primary: 12-08 Irreducibility test Secondary: 11R09 Function fields List decoding |
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| Snippet | 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... |
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| Title | Factoring polynomials over function fields |
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