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Barnett's Theorems About the Greatest Common Divisor of Several Univariate Polynomials Through Bezout-like Matrices

Authors:

Gema M. Diaz-Toca,

Laureano Gonzalez-VegaAuthors Info & Claims

Journal of Symbolic Computation, Volume 34, Issue 1

Pages 59 - 81

https://doi.org/10.1006/jsco.2002.0542

Published: 01 July 2002 Publication History

Abstract

This article provides a new presentation of Barnett s theorems giving the degree (resp. coefficients) of the greatest common divisor of several univariate polynomials with coefficients in an integral domain by means of the rank (resp. linear dependencies of the columns) of several Bezout-like matrices. This new presentation uses Bezout or hybrid Bezout matrices instead of polynomials evaluated in a companion matrix as in the original Barnett s presentation. Moreover, this presentation also allows us to compute the coefficients of the considered greatest common divisor in an easier way than in the original Barnett s theorems.

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Cited By

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Wang WYang J(2023)Two Variants of Bézout Subresultants for Several Univariate PolynomialsComputer Algebra in Scientific Computing10.1007/978-3-031-41724-5_19(350-369)Online publication date: 28-Aug-2023
https://dl.acm.org/doi/10.1007/978-3-031-41724-5_19
Belhaj SAlsulami A(2022)Approximate greatest common divisor of several polynomials from Hankel matricesACM Communications in Computer Algebra10.1145/3511528.351153255:3(77-81)Online publication date: 12-Jan-2022
https://dl.acm.org/doi/10.1145/3511528.3511532
Chi BTerui A(2020)The GPGCD Algorithm with the Bézout MatrixComputer Algebra in Scientific Computing10.1007/978-3-030-60026-6_10(170-187)Online publication date: 14-Sep-2020
https://dl.acm.org/doi/10.1007/978-3-030-60026-6_10
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Index Terms

Barnett's Theorems About the Greatest Common Divisor of Several Univariate Polynomials Through Bezout-like Matrices
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Nonlinear equations
    2. Numerical analysis

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cover image Journal of Symbolic Computation

Journal of Symbolic Computation Volume 34, Issue 1

July 2002

94 pages

ISSN:0747-7171

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Academic Press, Inc.

United States

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Published: 01 July 2002

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Wang WYang J(2023)Two Variants of Bézout Subresultants for Several Univariate PolynomialsComputer Algebra in Scientific Computing10.1007/978-3-031-41724-5_19(350-369)Online publication date: 28-Aug-2023
https://dl.acm.org/doi/10.1007/978-3-031-41724-5_19
Belhaj SAlsulami A(2022)Approximate greatest common divisor of several polynomials from Hankel matricesACM Communications in Computer Algebra10.1145/3511528.351153255:3(77-81)Online publication date: 12-Jan-2022
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Sanuki MSasaki TShirayanagi KKotsireas I(2009)Computing multivariate approximate GCD based on Barnett's theoremProceedings of the 2009 conference on Symbolic numeric computation10.1145/1577190.1577214(149-158)Online publication date: 3-Aug-2009
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Two Variants of Bézout Subresultants for Several Univariate Polynomials

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