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

• Autores: Martín Avendaño
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 44, Nº 9, 2009, págs. 1280-1284
• Idioma: inglés
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• Resumen

  • We prove that a polynomial with t non-zero terms, restricted to a real line y=ax+b, either has at most 6t-4 zeros or vanishes over the whole line. As a consequence, we derive an alternative algorithm for deciding whether a linear polynomial y-ax-bK[x,y] divides a lacunary polynomial fK[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 and in the logarithmic height of a, b and f.