Factoring bivariate sparse (lacunary) polynomials

Martin Avendano; Teresa Krick; Martin Sombra

Factoring bivariate sparse (lacunary) polynomials

Number Theory 2007-05-23 v1

Authors: Martin Avendano , Teresa Krick , Martin Sombra

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 $d$ .

Keywords

polynomials over finite fields computational complexity polynomial theory

Cite

@article{arxiv.math/0602145,
  title  = {Factoring bivariate sparse (lacunary) polynomials},
  author = {Martin Avendano and Teresa Krick and Martin Sombra},
  journal= {arXiv preprint arXiv:math/0602145},
  year   = {2007}
}

Comments

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

Factoring bivariate sparse (lacunary) polynomials

Abstract

Keywords

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