Factoring bivariate sparse (lacunary) polynomials
We present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K [x, y] over an algebraic number field K and their multiplicities, whose running time is polynomial over the rationals, in the bit length of the sparse encoding of the input...
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todo:paper_0885064X_v23_n2_p193_Avendano2023-10-03T15:40:39Z Factoring bivariate sparse (lacunary) polynomials Avendaño, M. Krick, T. Sombra, M. Height of points Lacunary (sparse) polynomials Lehmer's problem Polynomial factorization Algebra Degrees of freedom (mechanics) Factorization Problem solving Height of points Lacunary (sparse) polynomials Lehmer's problem Polynomial factorization Polynomials We present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K [x, y] over an algebraic number field K and their multiplicities, whose running time is polynomial over the rationals, in the bit length of the sparse encoding of the input and in d. Moreover, we show that the factors over over(Q, -) of degree ≤ d which are not binomials can also be computed in time polynomial in the sparse length of the input and in d. © 2006 Elsevier Inc. All rights reserved. Fil:Avendaño, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Krick, T. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Sombra, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0885064X_v23_n2_p193_Avendano |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
Height of points Lacunary (sparse) polynomials Lehmer's problem Polynomial factorization Algebra Degrees of freedom (mechanics) Factorization Problem solving Height of points Lacunary (sparse) polynomials Lehmer's problem Polynomial factorization Polynomials |
spellingShingle |
Height of points Lacunary (sparse) polynomials Lehmer's problem Polynomial factorization Algebra Degrees of freedom (mechanics) Factorization Problem solving Height of points Lacunary (sparse) polynomials Lehmer's problem Polynomial factorization Polynomials Avendaño, M. Krick, T. Sombra, M. Factoring bivariate sparse (lacunary) polynomials |
topic_facet |
Height of points Lacunary (sparse) polynomials Lehmer's problem Polynomial factorization Algebra Degrees of freedom (mechanics) Factorization Problem solving Height of points Lacunary (sparse) polynomials Lehmer's problem Polynomial factorization Polynomials |
description |
We present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K [x, y] over an algebraic number field K and their multiplicities, whose running time is polynomial over the rationals, in the bit length of the sparse encoding of the input and in d. Moreover, we show that the factors over over(Q, -) of degree ≤ d which are not binomials can also be computed in time polynomial in the sparse length of the input and in d. © 2006 Elsevier Inc. All rights reserved. |
format |
JOUR |
author |
Avendaño, M. Krick, T. Sombra, M. |
author_facet |
Avendaño, M. Krick, T. Sombra, M. |
author_sort |
Avendaño, M. |
title |
Factoring bivariate sparse (lacunary) polynomials |
title_short |
Factoring bivariate sparse (lacunary) polynomials |
title_full |
Factoring bivariate sparse (lacunary) polynomials |
title_fullStr |
Factoring bivariate sparse (lacunary) polynomials |
title_full_unstemmed |
Factoring bivariate sparse (lacunary) polynomials |
title_sort |
factoring bivariate sparse (lacunary) polynomials |
url |
http://hdl.handle.net/20.500.12110/paper_0885064X_v23_n2_p193_Avendano |
work_keys_str_mv |
AT avendanom factoringbivariatesparselacunarypolynomials AT krickt factoringbivariatesparselacunarypolynomials AT sombram factoringbivariatesparselacunarypolynomials |
_version_ |
1782024785719459840 |