Buchberger's algorithm
In the theory of multivariate polynomials, Buchberger's algorithm is a method for transforming a given set of polynomials into a Gröbner basis, which is another set of polynomials that have the same common zeros and are more convenient for extracting information on these common zeros. It was introduced by Bruno Buchberger simultaneously with the definition of Gröbner bases. For other Gröbner basis algorithms, see Gröbner basis § Algorithms and implementations.
- Comment
- enIn the theory of multivariate polynomials, Buchberger's algorithm is a method for transforming a given set of polynomials into a Gröbner basis, which is another set of polynomials that have the same common zeros and are more convenient for extracting information on these common zeros. It was introduced by Bruno Buchberger simultaneously with the definition of Gröbner bases. For other Gröbner basis algorithms, see Gröbner basis § Algorithms and implementations.
- Has abstract
- enIn the theory of multivariate polynomials, Buchberger's algorithm is a method for transforming a given set of polynomials into a Gröbner basis, which is another set of polynomials that have the same common zeros and are more convenient for extracting information on these common zeros. It was introduced by Bruno Buchberger simultaneously with the definition of Gröbner bases. Euclidean algorithm for polynomial Greatest common divisor computation and Gaussian elimination of linear systems are special cases of Buchberger's algorithm when the number of variables or the degrees of the polynomials are respectively equal to one. For other Gröbner basis algorithms, see Gröbner basis § Algorithms and implementations.
- Id
- enp/b110980
- Is primary topic of
- Buchberger's algorithm
- Label
- enBuchberger's algorithm
- Link from a Wikipage to an external page
- www.scholarpedia.org/article/Buchberger%27s_algorithm
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- Bruno Buchberger
- Category:Algebraic geometry
- Category:Commutative algebra
- Category:Computer algebra
- Category:Rewriting systems
- Critical pair (logic)
- Dickson's lemma
- Euclidean algorithm
- Faugère's F4 and F5 algorithms
- Gaussian elimination
- Greatest common divisor
- Gröbner basis
- Hilbert basis theorem
- Knuth–Bendix completion algorithm
- Least common multiple
- Linear algebra
- Monomial ordering
- Multivariate division algorithm
- Multivariate polynomial
- Quine–McCluskey algorithm
- System of linear equations
- Syzygy (mathematics)
- Time complexity
- Total degree
- Vector space
- SameAs
- 57kTz
- Algorithme de Buchberger
- Algoritmo de Buchberger
- Buchberger's algorithm
- Buchberger-Algorithmus
- m.033jys
- Q997962
- Subject
- Category:Algebraic geometry
- Category:Commutative algebra
- Category:Computer algebra
- Category:Rewriting systems
- Title
- enBuchberger algorithm
- enBuchberger's Algorithm
- Urlname
- enBuchbergersAlgorithm
- WasDerivedFrom
- Buchberger's algorithm?oldid=1123757244&ns=0
- WikiPageLength
- 6280
- Wikipage page ID
- 696317
- Wikipage revision ID
- 1123757244
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