Tuning and Generalizing Van Hoeij's Algorithm
Identifieur interne : 006C28 ( Hal/Curation ); précédent : 006C27; suivant : 006C29Tuning 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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scheme="mix" xml:lang="en"><term>FACTORIZATION OVER NUMBER FIELDS</term><term>LATTICE BASIS REDUCTION</term><term>LLL ALGORITHM</term><term>POLYNOMIAL FACTORIZATION</term></keywords></textClass></profileDesc></teiHeader><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></front></TEI><hal api="V3"><titleStmt><title xml:lang="nl">Tuning and Generalizing Van Hoeij's Algorithm</title><author role="aut"><persName><forename type="first">Karim</forename><surname>Belabas</surname></persName><email></email><idno type="idhal">karim-belabas</idno><idno type="halauthor">100198</idno><idno type="arXiv">http://arxiv.org/a/au:Belabas_K</idno></author><author role="aut"><persName><forename type="first">Guillaume</forename><surname>Hanrot</surname></persName><email>Guillaume.Hanrot@loria.fr</email><idno type="halauthor">73144</idno><affiliation ref="#struct-2364"></affiliation></author><author role="aut"><persName><forename type="first">Paul</forename><surname>Zimmermann</surname></persName><email></email><idno type="idhal">paul-zimmermann</idno><idno type="halauthor">60829</idno><affiliation ref="#struct-2364"></affiliation></author><editor role="depositor"><persName><forename>Rapport De Recherche</forename><surname>Inria</surname></persName><email>rrrt-editeurs@inria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2006-05-24 10:08:51</date><date type="whenWritten">2001-02</date><date type="whenModified">2016-05-19 01:09:25</date><date type="whenReleased">2006-05-31 14:24:26</date><date type="whenProduced">2001</date><date type="whenEndEmbargoed">2006-05-24</date><ref type="file" target="https://hal.inria.fr/inria-00072504/document"><date notBefore="2006-05-24"></date></ref><ref type="file" n="1" target="https://hal.inria.fr/inria-00072504/file/RR-4124.pdf"><date notBefore="2006-05-24"></date></ref></edition><respStmt><resp>contributor</resp><name key="111068"><persName><forename>Rapport De Recherche</forename><surname>Inria</surname></persName><email>rrrt-editeurs@inria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">inria-00072504</idno><idno type="halUri">https://hal.inria.fr/inria-00072504</idno><idno type="halBibtex">belabas:inria-00072504</idno><idno type="halRefHtml">[Research Report] RR-4124, INRIA. 2001</idno><idno type="halRef">[Research Report] RR-4124, INRIA. 2001</idno></publicationStmt><seriesStmt><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="INRIA-RRRT">Rapports de recherche et Technique de l'Inria</idno><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LABO-LORIA-SET" p="LORIA">LABO-LORIA-SET</idno></seriesStmt><notesStmt><note type="audience" n="0">Not set</note><note type="report" n="6">Research Report</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="nl">Tuning and Generalizing Van Hoeij's Algorithm</title><author role="aut"><persName><forename type="first">Karim</forename><surname>Belabas</surname></persName><idno type="idHal">karim-belabas</idno><idno type="halAuthorId">100198</idno><idno type="arXiv">http://arxiv.org/a/au:Belabas_K</idno></author><author role="aut"><persName><forename type="first">Guillaume</forename><surname>Hanrot</surname></persName><email>Guillaume.Hanrot@loria.fr</email><idno type="halAuthorId">73144</idno><affiliation ref="#struct-2364"></affiliation></author><author role="aut"><persName><forename type="first">Paul</forename><surname>Zimmermann</surname></persName><idno type="idHal">paul-zimmermann</idno><idno type="halAuthorId">60829</idno><affiliation ref="#struct-2364"></affiliation></author></analytic><monogr><idno type="reportNumber">RR-4124</idno><imprint><date type="datePub">2001</date></imprint><authority type="institution">INRIA</authority></monogr></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="en">FACTORIZATION OVER NUMBER FIELDS</term><term xml:lang="en">LLL ALGORITHM</term><term xml:lang="en">POLYNOMIAL FACTORIZATION</term><term xml:lang="en">LATTICE BASIS REDUCTION</term></keywords><classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</classCode><classCode scheme="halTypology" n="REPORT">Reports</classCode></textClass><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.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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