Article

Semi-numerical determination of irreducible branches of a reduced space curve

Authors:

André Galligo,

David RupprechtAuthors Info & Claims

ISSAC '01: Proceedings of the 2001 international symposium on Symbolic and algebraic computation

Pages 137 - 142

https://doi.org/10.1145/384101.384121

Published: 01 July 2001 Publication History

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Abstract

In this paper, we propose a semi-numerical algorithm for computing all irreducible branches of a curve in C³ defined by polynomials with rational coefficients. It is based on some properties appearing after a generic change of coordinate. Using numerical computation, Galois group action and rational approximation, it provides an efficient probabilistic algorithm for medium degrees. Our method generalizes our study on absolute factorization of polynomials ([2, 6]).

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KALTOFEN, E. Fast parallel absolute irreducibility testing. J. of Symbolic Computation 1 (1985), 57-67.

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KALTOFEN, E. Effective noether irreducibility forms and applications. J. Comput. Syst. Sci. 50, 2 (1995), 74-295.

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LAZARD, D. Ideal bases and primary decomposition: case of two variables. Journal of Symbolic Computation 1, 3 (1985), 261-270.

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RUPPRECHT, D. Semi-numerical absolute factorization of polynomials with integer coefficients. Journal of Symbolic Computation (2001).

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VAN HOEIJ, M. Factoring polynomials and the knapsack problem. Journal of Number Theory (2001).

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Leykin AVerschelde J(2009)Decomposing solution sets of polynomial systems: a new parallel monodromy breakup algorithmInternational Journal of Computational Science and Engineering10.1504/IJCSE.2009.0270014:2(94-101)Online publication date: 1-Jul-2009
https://dl.acm.org/doi/10.1504/IJCSE.2009.027001
Cuyt ALee WSasaki TShirayanagi KKotsireas I(2009)Extracting numerical factors of multivariate polynomials from taylor expansionsProceedings of the 2009 conference on Symbolic numeric computation10.1145/1577190.1577201(35-44)Online publication date: 3-Aug-2009
https://dl.acm.org/doi/10.1145/1577190.1577201
Zeng Z(2009)Regularization and Matrix Computation in Numerical Polynomial AlgebraApproximate Commutative Algebra10.1007/978-3-211-99314-9_5(125-162)Online publication date: 21-Aug-2009
https://doi.org/10.1007/978-3-211-99314-9_5
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Index Terms

Semi-numerical determination of irreducible branches of a reduced space curve
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Algebraic algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Nonlinear equations
    2. Numerical analysis
      1. Computations on polynomials
  2. Probability and statistics
    1. Probabilistic algorithms
    2. Probabilistic reasoning algorithms
      1. Markov-chain Monte Carlo methods
      2. Sequential Monte Carlo methods

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ISSAC '01: Proceedings of the 2001 international symposium on Symbolic and algebraic computation

July 2001

345 pages

ISBN:1581134177

DOI:10.1145/384101

Chairmen:
Erich Kaltofen
NCSU, Raleigh, NC
,
Gilles Villard
ENS, Lyon, France

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Published: 01 July 2001

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Leykin AVerschelde J(2009)Decomposing solution sets of polynomial systems: a new parallel monodromy breakup algorithmInternational Journal of Computational Science and Engineering10.1504/IJCSE.2009.0270014:2(94-101)Online publication date: 1-Jul-2009
https://dl.acm.org/doi/10.1504/IJCSE.2009.027001
Cuyt ALee WSasaki TShirayanagi KKotsireas I(2009)Extracting numerical factors of multivariate polynomials from taylor expansionsProceedings of the 2009 conference on Symbolic numeric computation10.1145/1577190.1577201(35-44)Online publication date: 3-Aug-2009
https://dl.acm.org/doi/10.1145/1577190.1577201
Zeng Z(2009)Regularization and Matrix Computation in Numerical Polynomial AlgebraApproximate Commutative Algebra10.1007/978-3-211-99314-9_5(125-162)Online publication date: 21-Aug-2009
https://doi.org/10.1007/978-3-211-99314-9_5
Kaltofen EMay JYang ZZhi L(2008)Approximate factorization of multivariate polynomials using singular value decompositionJournal of Symbolic Computation10.1016/j.jsc.2007.11.00543:5(359-376)Online publication date: 1-May-2008
https://dl.acm.org/doi/10.1016/j.jsc.2007.11.005
Verschelde JSchicho J(2004)Numerical algebraic geometry and symbolic computationProceedings of the 2004 international symposium on Symbolic and algebraic computation10.1145/1005285.1005288(3-3)Online publication date: 4-Jul-2004
https://dl.acm.org/doi/10.1145/1005285.1005288
Kaltofen EMay JHong H(2003)On approximate irreducibility of polynomials in several variablesProceedings of the 2003 international symposium on Symbolic and algebraic computation10.1145/860854.860893(161-168)Online publication date: 3-Aug-2003
https://dl.acm.org/doi/10.1145/860854.860893
Corless RGalligo AKotsireas IWatt SGiusti M(2002)A geometric-numeric algorithm for absolute factorization of multivariate polynomialsProceedings of the 2002 international symposium on Symbolic and algebraic computation10.1145/780506.780512(37-45)Online publication date: 10-Jul-2002
https://dl.acm.org/doi/10.1145/780506.780512
Galligo ARupprecht D(2002)Irreducible Decomposition of CurvesJournal of Symbolic Computation10.1006/jsco.2000.052833:5(661-677)Online publication date: 1-May-2002
https://dl.acm.org/doi/10.1006/jsco.2000.0528

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Convergence and asymptotic behavior of Jackson integrals associated with irreducible reduced root systems

Self-reciprocal irreducible polynomials with prescribed coefficients

Computing the irreducible real factors and components of an algebraicf curve

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Convergence and asymptotic behavior of Jackson integrals associated with irreducible reduced root systems

Self-reciprocal irreducible polynomials with prescribed coefficients

Computing the irreducible real factors and components of an algebraicf curve

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