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Theses

Algorithmes pour les polynômes lacunaires

Abstract : The aim of this thesis is to use some results from Diophantine geometry and from algebraic geometry to obtain applications to the the factorization of lacunary polynomials. In the first part, we describe an algorithm which computes a representation of the torsion points of a subvariety of Gn m defined by lacunary polynomials. The complexity of this algorithm is quasi-linear in the logarithm of the degree of the polynomials defining the subvariety. In the second part, we focus on systems of three lacunary polynomial equations in two variables. We describe an algorithm that computes a representation of the common zeroes of those polynomials as a finite union of complete intersections outside an open subset of A2. The complexity of this algorithm is quasi-linear in the logarithm of the degree of the input polynomials. However this algorithm depends on the conjecture of Zilber which is still an open problem.
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https://tel.archives-ouvertes.fr/tel-00580656
Contributor : Louis Leroux <>
Submitted on : Monday, March 28, 2011 - 7:47:21 PM
Last modification on : Monday, April 27, 2020 - 4:14:03 PM
Long-term archiving on: : Wednesday, June 29, 2011 - 3:00:59 AM

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  • HAL Id : tel-00580656, version 1

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Louis Leroux. Algorithmes pour les polynômes lacunaires. Mathématiques [math]. Université de Caen, 2011. Français. ⟨tel-00580656⟩

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