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On the greatest common divisor of polynomials which depend on a parameter

Authors:

S. A. Abramov,

K. Yu. KvashenkoAuthors Info & Claims

ISSAC '93: Proceedings of the 1993 international symposium on Symbolic and algebraic computation

Pages 152 - 156

https://doi.org/10.1145/164081.164112

Published: 01 August 1993 Publication History

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Cited By

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Ding XWang DXiao FZheng X(2024)An Algorithm for Computing Greatest Common Right Divisors of Parametric Ore PolynomialsProceedings of the 2024 International Symposium on Symbolic and Algebraic Computation10.1145/3666000.3669694(226-233)Online publication date: 16-Jul-2024
https://dl.acm.org/doi/10.1145/3666000.3669694
Wang DWang HWei JXiao F(2023)An extended GCRD algorithm for parametric univariate polynomial matrices and application to parametric Smith formJournal of Symbolic Computation10.1016/j.jsc.2022.07.006115(248-265)Online publication date: Mar-2023
https://doi.org/10.1016/j.jsc.2022.07.006
Menini LPossieri CTornambè A(2020)Algebraic certificates for the structural properties of parametric linear systemsIFAC-PapersOnLine10.1016/j.ifacol.2020.12.51753:2(4676-4681)Online publication date: 2020
https://doi.org/10.1016/j.ifacol.2020.12.517
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Index Terms

On the greatest common divisor of polynomials which depend on a parameter
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Computer algebra systems
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on polynomials

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On the greatest common right divisor of Ore polynomials with polynomial coefficients which depend on a parameter

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The comrade matrix of a polynomial is an analogue of the companion matrix when the matrix is expressed in terms of a general basis such that the basis is a set of orthogonal polynomials satisfying the three-term recurrence relation. We present the ...
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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 ...

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ISSAC '93: Proceedings of the 1993 international symposium on Symbolic and algebraic computation

August 1993

321 pages

ISBN:0897916042

DOI:10.1145/164081

Editor:
Manuel Bronstein

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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Published: 01 August 1993

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ISSAC93: International Symposium on Symbolic and Algebraic

July 6 - 8, 1993

Kiev, Ukraine

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Ding XWang DXiao FZheng X(2024)An Algorithm for Computing Greatest Common Right Divisors of Parametric Ore PolynomialsProceedings of the 2024 International Symposium on Symbolic and Algebraic Computation10.1145/3666000.3669694(226-233)Online publication date: 16-Jul-2024
https://dl.acm.org/doi/10.1145/3666000.3669694
Wang DWang HWei JXiao F(2023)An extended GCRD algorithm for parametric univariate polynomial matrices and application to parametric Smith formJournal of Symbolic Computation10.1016/j.jsc.2022.07.006115(248-265)Online publication date: Mar-2023
https://doi.org/10.1016/j.jsc.2022.07.006
Menini LPossieri CTornambè A(2020)Algebraic certificates for the structural properties of parametric linear systemsIFAC-PapersOnLine10.1016/j.ifacol.2020.12.51753:2(4676-4681)Online publication date: 2020
https://doi.org/10.1016/j.ifacol.2020.12.517
Kapur DLu DMonagan MSun YWang D(2019)Algorithms for computing greatest common divisors of parametric multivariate polynomialsJournal of Symbolic Computation10.1016/j.jsc.2019.10.006Online publication date: Oct-2019
https://doi.org/10.1016/j.jsc.2019.10.006
Kapur DLu DMonagan MSun YWang DKauers MOvchinnikov ASchost É(2018)An Efficient Algorithm for Computing Parametric Multivariate Polynomial GCDProceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3208976.3208980(239-246)Online publication date: 11-Jul-2018
https://dl.acm.org/doi/10.1145/3208976.3208980
Nagasaka KYap CEl Din M(2017)Parametric Greatest Common Divisors using Comprehensive Gröbner SystemsProceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3087604.3087621(341-348)Online publication date: 23-Jul-2017
https://dl.acm.org/doi/10.1145/3087604.3087621
Abramov SRyabenko A(2013)Linear q-difference equations depending on a parameterJournal of Symbolic Computation10.1016/j.jsc.2011.12.01749(65-77)Online publication date: 1-Feb-2013
https://dl.acm.org/doi/10.1016/j.jsc.2011.12.017
Alcázar J(2012)Computing the shapes arising in a family of space rational curves depending on one parameterComputer Aided Geometric Design10.1016/j.cagd.2012.02.00229:6(315-331)Online publication date: 1-Aug-2012
https://dl.acm.org/doi/10.1016/j.cagd.2012.02.002
Le H(2003)A direct algorithm to construct the minimal Z-pairs for rational functionsAdvances in Applied Mathematics10.5555/775458.77546830:1/2(137-159)Online publication date: 1-Jan-2003
https://dl.acm.org/doi/10.5555/775458.775468
Le H(2003)A direct algorithm to construct the minimal Z-pairs for rational functionsAdvances in Applied Mathematics10.5555/2610293.261035130:1-2(137-159)Online publication date: 1-Feb-2003
https://dl.acm.org/doi/10.5555/2610293.2610351
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On the greatest common right divisor of Ore polynomials with polynomial coefficients which depend on a parameter

Computing the Greatest Common Divisor of Polynomials Using the Comrade Matrix

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

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On the greatest common right divisor of Ore polynomials with polynomial coefficients which depend on a parameter

Computing the Greatest Common Divisor of Polynomials Using the Comrade Matrix

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

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