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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.".
- Hilbert_series_and_Hilbert_polynomial wikiPageID "6612596".
- Hilbert_series_and_Hilbert_polynomial wikiPageRevisionID "597641962".
- Hilbert_series_and_Hilbert_polynomial hasPhotoCollection Hilbert_series_and_Hilbert_polynomial.
- 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 label "ヒルベルト多項式".
- 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=597641962.
- Hilbert_series_and_Hilbert_polynomial isPrimaryTopicOf Hilbert_series_and_Hilbert_polynomial.