Factoring bivariate sparse (lacunary) polynomials

Details Factoring bivariate sparse (lacunary) polynomials Factoring bivariate sparse (lacunary) polynomials

2006-02-07

arxiv.org/abs/math/0602145v1

Mathematics

Number Theory

20 pp, Latex 2e. We learned on January 23th, 2006, that a multivariate version of Theorem 1 had independently been achieved by

Scientific paper

We present a deterministic algorithm for computing all irreducible factors of degree $\le d$ of a given bivariate polynomial $f\in K[x,y]$ over an algebraic number field $K$ and their multiplicities, whose running time is polynomial in the bit length of the sparse encoding of the input and in $d$. Moreover, we show that the factors over $\Qbarra$ of degree $\le d$ which are not binomials can also be computed in time polynomial in the sparse length of the input and in $d$.

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