The number of roots of a lacunary bivariate polynomial on a line |
| |
Authors: | Martí n Avendañ o |
| |
Affiliation: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina |
| |
Abstract: | We prove that a polynomial f∈R[x,y] 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−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. |
| |
Keywords: | Descartes&rsquo rule of signs Fewnomials Factorization of polynomials |
本文献已被 ScienceDirect 等数据库收录! |
|