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Abstract:

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.

Registro:

Documento: Artículo
Título:The number of roots of a lacunary bivariate polynomial on a line
Autor:Avendaño, M.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Descartes' rule of signs; Factorization of polynomials; Fewnomials
Año:2009
Volumen:44
Número:9
Página de inicio:1280
Página de fin:1284
DOI: http://dx.doi.org/10.1016/j.jsc.2008.02.016
Título revista:Journal of Symbolic Computation
Título revista abreviado:J. Symb. Comput.
ISSN:07477171
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_07477171_v44_n9_p1280_Avendano.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v44_n9_p1280_Avendano

Referencias:

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Citas:

---------- APA ----------
(2009) . The number of roots of a lacunary bivariate polynomial on a line. Journal of Symbolic Computation, 44(9), 1280-1284.
http://dx.doi.org/10.1016/j.jsc.2008.02.016
---------- CHICAGO ----------
Avendaño, M. "The number of roots of a lacunary bivariate polynomial on a line" . Journal of Symbolic Computation 44, no. 9 (2009) : 1280-1284.
http://dx.doi.org/10.1016/j.jsc.2008.02.016
---------- MLA ----------
Avendaño, M. "The number of roots of a lacunary bivariate polynomial on a line" . Journal of Symbolic Computation, vol. 44, no. 9, 2009, pp. 1280-1284.
http://dx.doi.org/10.1016/j.jsc.2008.02.016
---------- VANCOUVER ----------
Avendaño, M. The number of roots of a lacunary bivariate polynomial on a line. J. Symb. Comput. 2009;44(9):1280-1284.
http://dx.doi.org/10.1016/j.jsc.2008.02.016