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Pré-Publication, Document De Travail Année : 2023

Factoring sparse polynomials fast

Résumé

Consider a sparse polynomial in several variables given explicitly as a sum of non-zero terms with coefficients in an effective field. In this paper, we present several algorithms for factoring such polynomials and related tasks (such as gcd computation, square-free factorization, content-free factorization, and root extraction). Our methods are all based on sparse interpolation, but follow two main lines of attack: iteration on the number of variables and more direct reductions to the univariate or bivariate case. We present detailed probabilistic complexity bounds in terms of the complexity of sparse interpolation and evaluation.
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Dates et versions

hal-04366390 , version 1 (28-12-2023)
hal-04366390 , version 2 (04-05-2024)

Identifiants

  • HAL Id : hal-04366390 , version 2

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Alexander Demin, Joris van der Hoeven. Factoring sparse polynomials fast. 2023. ⟨hal-04366390v2⟩
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