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Factoring bivariate sparse (lacunary) polynomials

Martin Avendano·Teresa Krick·Martin Sombra
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Abstract

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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Martin Avendano, Teresa Krick, Martin Sombra. 2006-02-07. Factoring bivariate sparse (lacunary) polynomials. https://arxiv.org/abs/math/0602145

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