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• Hilbert_series_and_Hilbert_polynomial abstract "Given a graded commutative algebra finitely generated over a field, the Hilbert function, Hilbert polynomial, and Hilbert series are three strongly related notions which measure the growth of the dimension of its homogeneous components.These notions have been extended to filtered algebras and graded filtered modules over these algebras.The typical situations where these notions are used are the following: The quotient by a homogeneous ideal of a multivariate polynomial ring, graded by the total degree. The quotient by an ideal of a multivariate polynomial ring, filtered by the total degree. The filtration of a local ring by the powers of its maximal ideal. In this case the Hilbert polynomial is called the Hilbert–Samuel polynomial.The Hilbert series of an algebra or a module is a special case of the Hilbert–Poincaré series of a graded vector space.Hilbert polynomial and Hilbert series are important in computational algebraic geometry, as they are the easiest known way for computing the dimension and the degree of an algebraic variety defined by explicit polynomial equations.".
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• Hilbert_series_and_Hilbert_polynomial wikiPageRevisionID "670803046".
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Algebraic_geometry.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Algebraic_variety.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Artinian_ring.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Binomial_coefficient.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Bxc3xa9zouts_theorem.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Cambridge.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Cambridge_University_Press.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Category:Algebraic_geometry.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Category:Commutative_algebra.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Composition_series.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Computational_complexity_theory.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Computer_algebra_system.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink David_Hilbert.
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• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Field_(mathematics).
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Filtered_algebra.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Formal_power_series.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Formal_series.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink General_position.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Graded_algebra.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Graded_module.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Graded_ring.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Graded_vector_space.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Gröbner_basis.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Hilbert–Poincaré_series.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Hilbert–Samuel_function.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Homogeneous_coordinate_ring.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Homogeneous_ideal.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Ideal_(ring_theory).
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Integer-valued_polynomial.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Jordan-Hölder_theorem.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Kernel_(algebra).
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Krull_dimension.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Local_ring.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Magma_(computer_algebra_system).
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Magma_(software).
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Maple_(software).
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Maximal_ideal.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Modularity.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Modules.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Monomial_order.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Monomial_ordering.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Morphism_of_algebraic_varieties.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Multivariate_polynomial.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Nilpotent_ideal.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Numerical_polynomial.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Polynomial.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Polynomial_ring.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Projective_algebraic_set.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Projective_variety.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Regular_function.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Regular_sequence.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Total_degree.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLink Zero_divisor.
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLinkText "Hilbert function".
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLinkText "Hilbert functions".
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLinkText "Hilbert series and Hilbert polynomial".
• Hilbert_series_and_Hilbert_polynomial wikiPageWikiLinkText "Hilbert series and Hilbert polynomial#Degree of a projective variety and Bézout's theorem".
• Hilbert_series_and_Hilbert_polynomial hasPhotoCollection Hilbert_series_and_Hilbert_polynomial.
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• Hilbert_series_and_Hilbert_polynomial wikiPageUsesTemplate Template:Harv.
• Hilbert_series_and_Hilbert_polynomial wikiPageUsesTemplate Template:Mvar.
• Hilbert_series_and_Hilbert_polynomial subject Category:Algebraic_geometry.
• Hilbert_series_and_Hilbert_polynomial subject Category:Commutative_algebra.
• Hilbert_series_and_Hilbert_polynomial comment "Given a graded commutative algebra finitely generated over a field, the Hilbert function, Hilbert polynomial, and Hilbert series are three strongly related notions which measure the growth of the dimension of its homogeneous components.These notions have been extended to filtered algebras and graded filtered modules over these algebras.The typical situations where these notions are used are the following: The quotient by a homogeneous ideal of a multivariate polynomial ring, graded by the total degree. ".
• Hilbert_series_and_Hilbert_polynomial label "Hilbert series and Hilbert polynomial".
• Hilbert_series_and_Hilbert_polynomial sameAs ヒルベルト多項式.
• Hilbert_series_and_Hilbert_polynomial sameAs 힐베르트_다항식.
• Hilbert_series_and_Hilbert_polynomial sameAs m.0gdrxv.
• Hilbert_series_and_Hilbert_polynomial sameAs Q5761236.
• Hilbert_series_and_Hilbert_polynomial sameAs Q5761236.
• Hilbert_series_and_Hilbert_polynomial wasDerivedFrom Hilbert_series_and_Hilbert_polynomial?oldid=670803046.
• Hilbert_series_and_Hilbert_polynomial isPrimaryTopicOf Hilbert_series_and_Hilbert_polynomial.