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LINEAR RECURRENCES WITH POLYNOMIAL COEFFICIENTS AND APPLICATION TO INTEGER FACTORIZATION AND CARTIER--MANIN OPERATOR.

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Title: LINEAR RECURRENCES WITH POLYNOMIAL COEFFICIENTS AND APPLICATION TO INTEGER FACTORIZATION AND CARTIER--MANIN OPERATOR.
Authors: Bostan, Alin1 alin.bostan@inria.fr, Gaudry, Pierrick2 gaudry@lix.polytechnique.fr, Schost, Éric2 schost@lix.polytechnique.fr
Source: SIAM Journal on Computing. 2007, Vol. 36 Issue 6, p1777-1806. 30p. 1 Chart.
Subjects: Factorization, Factorization of operators, Computational complexity, Algorithms, Mathematics research
Abstract: We study the complexity of computing one or several terms (not necessarily consecutive) in a recurrence with polynomial coefficients. As applications, we improve the best currently known upper bounds for factoring integers deterministically and for computing the Cartier-Manin operator of hyperelliptic curves. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: LINEAR RECURRENCES WITH POLYNOMIAL COEFFICIENTS AND APPLICATION TO INTEGER FACTORIZATION AND CARTIER--MANIN OPERATOR.
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  Data: <searchLink fieldCode="AR" term="%22Bostan%2C+Alin%22">Bostan, Alin</searchLink><relatesTo>1</relatesTo><i> alin.bostan@inria.fr</i><br /><searchLink fieldCode="AR" term="%22Gaudry%2C+Pierrick%22">Gaudry, Pierrick</searchLink><relatesTo>2</relatesTo><i> gaudry@lix.polytechnique.fr</i><br /><searchLink fieldCode="AR" term="%22Schost%2C+Éric%22">Schost, Éric</searchLink><relatesTo>2</relatesTo><i> schost@lix.polytechnique.fr</i>
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  Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Computing%22">SIAM Journal on Computing</searchLink>. 2007, Vol. 36 Issue 6, p1777-1806. 30p. 1 Chart.
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  Data: <searchLink fieldCode="DE" term="%22Factorization%22">Factorization</searchLink><br /><searchLink fieldCode="DE" term="%22Factorization+of+operators%22">Factorization of operators</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+research%22">Mathematics research</searchLink>
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  Data: We study the complexity of computing one or several terms (not necessarily consecutive) in a recurrence with polynomial coefficients. As applications, we improve the best currently known upper bounds for factoring integers deterministically and for computing the Cartier-Manin operator of hyperelliptic curves. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of SIAM Journal on Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1137/S0097539704443793
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        Text: English
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      – SubjectFull: Factorization
        Type: general
      – SubjectFull: Factorization of operators
        Type: general
      – SubjectFull: Computational complexity
        Type: general
      – SubjectFull: Algorithms
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      – TitleFull: LINEAR RECURRENCES WITH POLYNOMIAL COEFFICIENTS AND APPLICATION TO INTEGER FACTORIZATION AND CARTIER--MANIN OPERATOR.
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            NameFull: Bostan, Alin
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            NameFull: Gaudry, Pierrick
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              Text: 2007
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