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Gröbner basis

In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring K [ x 1 , … , x n ] {\displaystyle K[x_{1},\ldots ,x_{n}]} over a field K {\displaystyle K} . A Gröbner basis allows many important…

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Algorithms and implementations

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Gröbner basis

Nodes141
Edges140
Triples222
Avg. degree1.99
Density0.014184
Components1

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Gröbner basis

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related to Further reading · 86
Gröbner basis → Abramson, ACM SIGSAM Bulletin, Adams, Aequationes Mathematicae, Algebraic Equations, American Mathematical Society, An, An Algorithm, An Algorithmic Criterion, An Introduction, Anatoliĭ, Applications, Aschenbrenner, Basis Elements, Becker, Bernd, BF01844169, Bibcode, Bruno, Bruno Buchberger's PhD
related to External links · 28
Gröbner basis → Bruno Buchberger Bruno BuchbergerWeisstein, Buchberger, Comparative Timings Page, Computer Aided Systems Theory, EMS Press, Encyclopedia, Eric, EUROCAST, F4, Faugère's, Freire, Gröbner, Gröbner Bases, Gröbner Bases Bibliography, Gröbner Bases SoftwareProf, In Moreno-Diaz, International Workshop, ISBN, Mathematics, MathWorld
related to Algorithms and implementations · 15
Gröbner basis → Also, As, Bruno Buchberger, Buchberger's, Chinese, Even, For, GMP, Gröbner, Hensel, In, It, S-polynomials, So, The
related to Elimination · 10
Gröbner basis → Consider, Gröbner, If, Let, Moreover, The, This, X-parts, X-variable, Y-parts
related to Complexity · 7
Gröbner basis → Gröbner, In, More, Omega, On, So, The
related to Intersecting ideals · 7
Gröbner basis → For, Gröbner, If, In, Such, This, With
related to Reduction · 7
Gröbner basis → Euclidean, Gaussian, Gröbner, It, Lead-reduction, The, When
related to Solutions of a system of algebraic equations · 7
Gröbner basis → An, Any, Gröbner, Hilbert's Nullstellensatz, In, Such, The
related to Dimension, degree and Hilbert series · 6
Gröbner basis → Gröbner, In, It, Krull, R/I, The
related to Existence · 6
Gröbner basis → Buchberger's, For, Gröbner, Moreover, S-polynomial, This

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Important terminology

gröbner basis polynomial ideal displaystyle bases polynomials monomial ordering monomials may one reduction reduced algorithm set leading computation elimination algebraic

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SubjectPredicateObjectConfidenceSrc
Gröbner basisis aparticular kind of generating set of an ideal in a polynomial ring K0.90text
Gröbner basisis adirect application of Buchberger's algorithm0.90text
polynomials over principal ideal rings or polynomial ringsinstance ofIt has been generalized to other structures0.80text
and also some classes of non-commutative ringsinstance ofIt has been generalized to other structures0.80text
algebrasinstance ofIt has been generalized to other structures0.80text
like Ore algebrasinstance ofIt has been generalized to other structures0.80text
polynomial factorizationinstance ofalthough it is less convenient for other computations0.80text
polynomial greatest common divisor.If Finstance ofalthough it is less convenient for other computations0.80text
Gröbner basisrelated to Algorithms and implementationsBuchberger's0.60section
Gröbner basisrelated to Algorithms and implementationsGröbner0.60section
Gröbner basisrelated to Algorithms and implementationsIt0.60section
Gröbner basisrelated to Algorithms and implementationsBruno Buchberger0.60section

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