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Polynomial greatest common divisor

Known as: Greatest common divisor of two polynomials, Euclidean division of polynomials, GCD 
In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a… Expand
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Related topics

Related topics

19 relations
Computer algebra systemEuclidean algorithmExtended Euclidean algorithmFactorization of polynomials
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Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
Highly Cited
2006
Highly Cited
2006
Approximate greatest common divisors of several polynomials with linearly constrained coefficients and singular polynomials
We consider the problem of computing minimal real or complex deformations to the coefficients in a list of relatively prime real… Expand
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2004
2004
Minors of Bezout matrices, subresultants and the parameterization of the degree of the polynomial greatest common divisor
The main purpose of this article is to present algorithms to parameterize the degree of the greatest common divisor of two… Expand
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2000
2000
QR-factorization method for computing the greatest common divisor of polynomials with inexact coefficients
This paper presents a novel means of computing the greatest common divisor (GCD) of two polynomials with real-valued coefficients… Expand
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Highly Cited
1996
Highly Cited
1996
Approximate polynomial greatest common divisors and nearest singular polynomials
The problem of computing the greatest common divisor (gcd) of two polynomials ~, g ~ A[z], A being a unique factorization domain… Expand
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Highly Cited
1990
Highly Cited
1990
Interpolating Polynomials from Their Values
A fundamental technique used by many algorithms in computer algebrais interpolating polynomials from their values. This paper… Expand
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1990
1990
Computing with Polynomials Given By Black Boxes for Their Evaluations: Greatest Common Divisors, Factorization, Separation of Numerators and Denominators
Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with… Expand
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Highly Cited
1988
Highly Cited
1988
Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators
Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with… Expand
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1987
1987
The computation of polynomial greatest common divisors over an algebraic number field
We present an algorithm for computing the greatest common divisor of two polynomials over an algebraic number field. We obtain a… Expand
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1974
1974
Computational aspects of Hensel-type univariate polynomial greatest common divisor algorithms
Two Hensel-type univariate polynomial Greatest Common Divisor (GCD) algorithms are presented and compared. The regular linear… Expand
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1971
1971
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
This paper examines the computation of polynomial greatest common divisors by various generalizations of Euclid's algorithm. The… Expand
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