article

Hensel lifting and bivariate polynomial factorisation over finite fields

Authors:

Alan G. B. LauderAuthors Info & Claims

Mathematics of Computation, Volume 71, Issue 240

Pages 1663 - 1676

https://doi.org/10.1090/S0025-5718-01-01393-X

Published: 01 October 2002 Publication History

Abstract

This paper presents an average time analysis of a Hensel lifting based factorisation algorithm for bivariate polynomials over finite fields. It is shown that the average running time is almost linear in the input size. This explains why the Hensel lifting technique is fast in practice for most polynomials.

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Cited By

Hoppen CRodrigues VTrevisan V(2011)A note on Gao's algorithm for polynomial factorizationTheoretical Computer Science10.1016/j.tcs.2010.11.048412:16(1508-1522)Online publication date: 1-Apr-2011
https://dl.acm.org/doi/10.1016/j.tcs.2010.11.048
von zur Gathen JViola AZiegler K(2010)Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fieldsProceedings of the 9th Latin American conference on Theoretical Informatics10.1007/978-3-642-12200-2_23(243-254)Online publication date: 19-Apr-2010
https://dl.acm.org/doi/10.1007/978-3-642-12200-2_23
von zur Gathen JWang D(2007)Counting reducible and singular bivariate polynomialsProceedings of the 2007 international symposium on Symbolic and algebraic computation10.1145/1277548.1277598(369-376)Online publication date: 29-Jul-2007
https://dl.acm.org/doi/10.1145/1277548.1277598
Show More Cited By

Index Terms

Hensel lifting and bivariate polynomial factorisation over finite fields
1. Mathematics of computing
  1. Mathematical analysis
    1. Nonlinear equations
    2. Numerical analysis

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cover image Mathematics of Computation

Mathematics of Computation Volume 71, Issue 240

October 2002

457 pages

ISSN:0025-5718

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American Mathematical Society

United States

Publication History

Published: 01 October 2002

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Cited By

Hoppen CRodrigues VTrevisan V(2011)A note on Gao's algorithm for polynomial factorizationTheoretical Computer Science10.1016/j.tcs.2010.11.048412:16(1508-1522)Online publication date: 1-Apr-2011
https://dl.acm.org/doi/10.1016/j.tcs.2010.11.048
von zur Gathen JViola AZiegler K(2010)Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fieldsProceedings of the 9th Latin American conference on Theoretical Informatics10.1007/978-3-642-12200-2_23(243-254)Online publication date: 19-Apr-2010
https://dl.acm.org/doi/10.1007/978-3-642-12200-2_23
von zur Gathen JWang D(2007)Counting reducible and singular bivariate polynomialsProceedings of the 2007 international symposium on Symbolic and algebraic computation10.1145/1277548.1277598(369-376)Online publication date: 29-Jul-2007
https://dl.acm.org/doi/10.1145/1277548.1277598
Abu Salem FGao SLauder ASchicho J(2004)Factoring polynomials via polytopesProceedings of the 2004 international symposium on Symbolic and algebraic computation10.1145/1005285.1005289(4-11)Online publication date: 4-Jul-2004
https://dl.acm.org/doi/10.1145/1005285.1005289
Gao SKaltofen ELauder A(2004)Deterministic distinct-degree factorization of polynomials over finite fieldsJournal of Symbolic Computation10.1016/j.jsc.2004.05.00438:6(1461-1470)Online publication date: 1-Dec-2004
https://dl.acm.org/doi/10.1016/j.jsc.2004.05.004
Kaltofen EHong H(2003)Polynomial factorizationProceedings of the 2003 international symposium on Symbolic and algebraic computation10.1145/860854.860857(3-4)Online publication date: 3-Aug-2003
https://dl.acm.org/doi/10.1145/860854.860857

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