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Article Dans Une Revue Foundations of Computational Mathematics Année : 2020

On the complexity exponent of polynomial system solving

Résumé

We present a probabilistic Las Vegas algorithm for solving sufficiently generic square polynomial systems over finite fields. We achieve a nearly quadratic running time in the number of solutions, for densely represented input polynomials. We also prove a nearly linear bit complexity bound for polynomial systems with rational coefficients. Our results are obtained using the combination of the Kronecker solver and a new improved algorithm for fast multivariate modular composition.
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Dates et versions

hal-01848572 , version 1 (24-07-2018)
hal-01848572 , version 2 (28-11-2020)

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Joris van der Hoeven, Grégoire Lecerf. On the complexity exponent of polynomial system solving. Foundations of Computational Mathematics, 2020, ⟨10.1007/s10208-020-09453-0⟩. ⟨hal-01848572v2⟩
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