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

• Autores: Avendaño, M.
• Año de publicación: 2009
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: J. Symb. Comput. 2009;44(9):1280-1284
• Materia: Descartes' rule of signs; Factorization of polynomials; Fewnomials
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

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.