An elementary proof of Barnett's theorem about the greatest common divisor of several univariate polynomials

DOI10.1016/0024-3795(95)00099-2zbMath0866.12002OpenAlexW2049475925WikidataQ126628474 ScholiaQ126628474MaRDI QIDQ2564953

Laureano Gonzalez-Vega

Publication date: 30 June 1997

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(95)00099-2

zbMATH Keywords

algorithmsubresultantsintegral domaingreatest common divisor of univariate polynomialscomputation of the coefficients

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Polynomials in general fields (irreducibility, etc.) (12E05) Polynomials over commutative rings (13B25) Computational methods for problems pertaining to field theory (12-08) Solving polynomial systems; resultants (13P15)

Related Items (14)

Structured matrix methods computing the greatest common divisor of polynomials ⋮ On the complexity of computing the greatest common divisor of several univariate polynomials ⋮ A geometrical approach to finding multivariate approximate LCMs and GCDs ⋮ Metric problems for quadrics in multidimensional space ⋮ On the Relation Between Matrices and the Greatest Common Divisor of Polynomials ⋮ A structured rank-revealing method for Sylvester matrix ⋮ The computation of the degree of the greatest common divisor of three Bernstein basis polynomials ⋮ Various new expressions for subresultants and their applications ⋮ Squarefree decomposition of univariate polynomials depending on a parameter. Application to the integration of parametric rational functions ⋮ Matrix representation of the shifting operation and numerical properties of the ERES method for computing the greatest common divisor of sets of many polynomials ⋮ On the Bézout construction of the resultant ⋮ Simultaneous elimination by using several tools from real algebraic geometry ⋮ Computing greatest common divisors and squarefree decompositions through matrix methods: the parametric and approximate cases ⋮ Barnett's theorems about the greatest common divisor of several univariate polynomials through Bezout-like matrices

Cites Work

• Division of generalized polynomials using the comrade matrix
• Inertia characteristics of self-adjoint matrix polynomials
• Euclidean remainders for generalized polynomials
• Greatest common divisor of two polynomials
• Spécialisation de la suite de Sturm et sous-résultants (I)
• Greatest common divisors from generalized sylvester resultant matrices
• On the complexity of computing the greatest common divisor of several univariate polynomials
• Some Applications of Matrics in the Theory of Equations
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