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Factoring multivariate polynomials over algebraic number fields

Author:

Arjen K. LenstraAuthors Info & Claims

SIAM Journal on Computing, Volume 16, Issue 3

Pages 591 - 598

https://doi.org/10.1137/0216040

Published: 01 June 1987 Publication History

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Chonev VOuaknine JWorrell J(2023)On the Zeros of Exponential PolynomialsJournal of the ACM10.1145/360354370:4(1-26)Online publication date: 12-Aug-2023
https://dl.acm.org/doi/10.1145/3603543
Grenet B(2016)Bounded-degree factors of lacunary multivariate polynomialsJournal of Symbolic Computation10.1016/j.jsc.2015.11.01375:C(171-192)Online publication date: 1-Jul-2016
https://dl.acm.org/doi/10.1016/j.jsc.2015.11.013
Grześkowiak M(2013)Algorithms for Relatively Cyclotomic PrimesFundamenta Informaticae10.5555/2594934.2594938125:2(161-181)Online publication date: 1-Apr-2013
https://dl.acm.org/doi/10.5555/2594934.2594938
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Index Terms

Factoring multivariate polynomials over algebraic number fields
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on polynomials
      2. Number-theoretic computations

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Finding small degree factors of multivariate supersparse (lacunary) polynomials over algebraic number fields
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We present algorithms that compute all irreducible factors of degree ≤ d of supersparse (lacunary) multivariate polynomials in n variables over an algebraic number field in deterministic polynomial-time in (l+d)ⁿ, where l is the size of the input ...
On factoring parametric multivariate polynomials

This paper presents a new algorithm for the absolute factorization of parametric multivariate polynomials over the field of rational numbers. This algorithm decomposes the parameters space into a finite number of constructible sets. The absolutely ...

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Published In

SIAM Journal on Computing Volume 16, Issue 3

June 1987

178 pages

ISSN:0097-5397

Editor:
S. Rao Kosaraju

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Society for Industrial and Applied Mathematics

United States

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Published: 01 June 1987

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Chonev VOuaknine JWorrell J(2023)On the Zeros of Exponential PolynomialsJournal of the ACM10.1145/360354370:4(1-26)Online publication date: 12-Aug-2023
https://dl.acm.org/doi/10.1145/3603543
Grenet B(2016)Bounded-degree factors of lacunary multivariate polynomialsJournal of Symbolic Computation10.1016/j.jsc.2015.11.01375:C(171-192)Online publication date: 1-Jul-2016
https://dl.acm.org/doi/10.1016/j.jsc.2015.11.013
Grześkowiak M(2013)Algorithms for Relatively Cyclotomic PrimesFundamenta Informaticae10.5555/2594934.2594938125:2(161-181)Online publication date: 1-Apr-2013
https://dl.acm.org/doi/10.5555/2594934.2594938
Chattopadhyay AGrenet BKoiran PPortier NStrozecki YMonagan MCooperman GGiesbrecht M(2013)Factoring bivariate lacunary polynomials without heightsProceedings of the 38th International Symposium on Symbolic and Algebraic Computation10.1145/2465506.2465932(141-148)Online publication date: 26-Jun-2013
https://dl.acm.org/doi/10.1145/2465506.2465932
van Dijk MGentry CHalevi SVaikuntanathan V(2010)Fully homomorphic encryption over the integersProceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques10.1007/978-3-642-13190-5_2(24-43)Online publication date: 30-May-2010
https://dl.acm.org/doi/10.1007/978-3-642-13190-5_2
Chen JFeng YQin XZhang JSasaki TShirayanagi KKotsireas I(2009)Exact polynomial factorization by approximate high degree algebraic numbersProceedings of the 2009 conference on Symbolic numeric computation10.1145/1577190.1577199(21-28)Online publication date: 3-Aug-2009
https://dl.acm.org/doi/10.1145/1577190.1577199
Abu Salem FYang L(2008)Parallel methods for absolute irreducibility testingThe Journal of Supercomputing10.1007/s11227-008-0205-146:3(181-212)Online publication date: 1-Dec-2008
https://dl.acm.org/doi/10.1007/s11227-008-0205-1
Avendaòo MKrick TSombra M(2007)Factoring bivariate sparse (lacunary) polynomialsJournal of Complexity10.1016/j.jco.2006.06.00223:2(193-216)Online publication date: 1-Apr-2007
https://dl.acm.org/doi/10.1016/j.jco.2006.06.002
Gao S(2003)Factoring multivariate polynomials via partial differential equationsMathematics of Computation10.5555/763377.76339272:242(801-822)Online publication date: 1-Apr-2003
https://dl.acm.org/doi/10.5555/763377.763392
Tung S(2003)Skolem functions of arithmetical sentencesInformation and Computation10.1016/S0890-5401(03)00085-3185:1(56-65)Online publication date: 25-Aug-2003
https://dl.acm.org/doi/10.1016/S0890-5401%2803%2900085-3
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Factoring multivariate polynomials over algebraic number fields in MACSYMA

Finding small degree factors of multivariate supersparse (lacunary) polynomials over algebraic number fields

On factoring parametric multivariate polynomials

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