Tuning and Generalizing Van Hoeij's Algorithm
Identifieur interne : 009A16 ( Main/Merge ); précédent : 009A15; suivant : 009A17Tuning and Generalizing Van Hoeij's Algorithm
Auteurs : Karim Belabas ; Guillaume Hanrot [France] ; Paul Zimmermann [France]Source :
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Abstract
Recently, van Hoeij's published a new algorithm for factoring polynomials over the rational integers [11]. This algorithms rests on the same principle as Berlekamp-Zassenhaus [2, 13], but uses lattice basis reduction to improve drastically on the recombination phase. The efficiency of the LLL algorithm is very dependent on fine tuning; in this paper, we present such tuning to achieve better performance. Simultaneously, we describe a generalization of van Hoeij's algorithm to factor polynomials over number fields.
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<front><div type="abstract" xml:lang="en">Recently, van Hoeij's published a new algorithm for factoring polynomials over the rational integers [11]. This algorithms rests on the same principle as Berlekamp-Zassenhaus [2, 13], but uses lattice basis reduction to improve drastically on the recombination phase. The efficiency of the LLL algorithm is very dependent on fine tuning; in this paper, we present such tuning to achieve better performance. Simultaneously, we describe a generalization of van Hoeij's algorithm to factor polynomials over number fields.</div>
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