Modular composition via complex roots

Abstract : Modular composition is the problem to compute the composition of two univariate polynomials modulo a third one. For polynomials with coefficients in a finite field, Kedlaya and Umans proved in 2008 that the theoretical complexity for performing this task could be made arbitrarily close to linear. Unfortunately, beyond its major theoretical impact, this result has not led to practically faster implementations yet. In this paper, we explore the particular case when the ground field is the field of computable complex numbers. Ultimately, when the precision becomes sufficiently large, we show that modular compositions may be performed in softly linear time.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01455731
Contributeur : Joris Van Der Hoeven <>
Soumis le : lundi 27 mars 2017 - 11:12:40
Dernière modification le : mercredi 29 mars 2017 - 01:09:19

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zcomp.pdf
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  • HAL Id : hal-01455731, version 2

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Joris Van Der Hoeven, Grégoire Lecerf. Modular composition via complex roots. 2017. <hal-01455731v2>

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