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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:appliesTo
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multivariate polynomials
polynomial rings
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gptkbp:basisFor
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polynomial ideal
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gptkbp:computes
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gptkb:Buchberger's_algorithm
gptkb:F4_algorithm
gptkb:F5_algorithm
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gptkbp:enables
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symbolic computation
algebraic simplification
algorithmic solution of polynomial equations
automatic theorem proving
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gptkbp:field
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gptkb:algebra
gptkb:algebraic_geometry
gptkb:commutative_algebra
computational algebra
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gptkbp:generalizes
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gptkb:Euclidean_algorithm
gptkb:Gaussian_elimination
Gaussian elimination for multivariate polynomials
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gptkbp:hasApplication
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gptkb:algebraic_statistics
coding theory
computational biology
control theory
cryptography
robotics
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gptkbp:hasProperty
|
depends on monomial order
finite for polynomial rings over fields
uniqueness for reduced Gröbner basis
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https://www.w3.org/2000/01/rdf-schema#label
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Gröbner basis
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gptkbp:introduced
|
gptkb:Bruno_Buchberger
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gptkbp:introducedIn
|
1965
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gptkbp:namedAfter
|
gptkb:Wolfgang_Gröbner
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gptkbp:relatedTo
|
gptkb:Hilbert's_Nullstellensatz
gptkb:Buchberger's_algorithm
gptkb:Faugère's_F4_algorithm
gptkb:Faugère's_F5_algorithm
gptkb:Macaulay_matrix
gptkb:S-polynomial
primary decomposition
syzygy
computational algebraic geometry
monomial order
polynomial ideal
reduced Gröbner basis
term order
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gptkbp:usedFor
|
computing dimension of algebraic varieties
elimination theory
ideal membership problem
solving systems of polynomial equations
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gptkbp:bfsParent
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gptkb:commutative_algebra
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gptkbp:bfsLayer
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5
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