The number of roots of a lacunary bivariate polynomial on a line

Mostrar todas las versiones(3)

We prove that a polynomial f ∈ R [x, y] with t non-zero terms, restricted to a real line y = a x + b, either has at most 6 t - 4 zeros or vanishes over the whole line. As a consequence, we derive an alternative algorithm for deciding whether a linear polynomial y - a x - b ∈ K [x, y] divides a lacun...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autor principal: Avendaño, M.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2009
Materias:
Descartes' rule of signs
Factorization of polynomials
Fewnomials
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_07477171_v44_n9_p1280_Avendano
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_07477171_v44_n9_p1280_Avendano
record_format dspace
spelling paperaa:paper_07477171_v44_n9_p1280_Avendano2023-06-12T16:48:13Z The number of roots of a lacunary bivariate polynomial on a line J. Symb. Comput. 2009;44(9):1280-1284 Avendaño, M. Descartes' rule of signs Factorization of polynomials Fewnomials We prove that a polynomial f ∈ R [x, y] with t non-zero terms, restricted to a real line y = a x + b, either has at most 6 t - 4 zeros or vanishes over the whole line. As a consequence, we derive an alternative algorithm for deciding whether a linear polynomial y - a x - b ∈ K [x, y] divides a lacunary polynomial f ∈ K [x, y], where K is a real number field. The number of bit operations performed by the algorithm is polynomial in the number of non-zero terms of f, in the logarithm of the degree of f, in the degree of the extension K / Q and in the logarithmic height of a, b and f. © 2009 Elsevier Ltd. All rights reserved. Fil:Avendaño, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2009 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_07477171_v44_n9_p1280_Avendano
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Descartes' rule of signs
Factorization of polynomials
Fewnomials
spellingShingle Descartes' rule of signs
Factorization of polynomials
Fewnomials
Avendaño, M.
The number of roots of a lacunary bivariate polynomial on a line
topic_facet Descartes' rule of signs
Factorization of polynomials
Fewnomials
description We prove that a polynomial f ∈ R [x, y] with t non-zero terms, restricted to a real line y = a x + b, either has at most 6 t - 4 zeros or vanishes over the whole line. As a consequence, we derive an alternative algorithm for deciding whether a linear polynomial y - a x - b ∈ K [x, y] divides a lacunary polynomial f ∈ K [x, y], where K is a real number field. The number of bit operations performed by the algorithm is polynomial in the number of non-zero terms of f, in the logarithm of the degree of f, in the degree of the extension K / Q and in the logarithmic height of a, b and f. © 2009 Elsevier Ltd. All rights reserved.
format Artículo
Artículo
publishedVersion
author Avendaño, M.
author_facet Avendaño, M.
author_sort Avendaño, M.
title The number of roots of a lacunary bivariate polynomial on a line
title_short The number of roots of a lacunary bivariate polynomial on a line
title_full The number of roots of a lacunary bivariate polynomial on a line
title_fullStr The number of roots of a lacunary bivariate polynomial on a line
title_full_unstemmed The number of roots of a lacunary bivariate polynomial on a line
title_sort number of roots of a lacunary bivariate polynomial on a line
publishDate 2009
url http://hdl.handle.net/20.500.12110/paper_07477171_v44_n9_p1280_Avendano
work_keys_str_mv AT avendanom thenumberofrootsofalacunarybivariatepolynomialonaline
AT avendanom numberofrootsofalacunarybivariatepolynomialonaline
_version_ 1769810338514993152

Ejemplares similares