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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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| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Gröbner basis | is a | particular kind of generating set of an ideal in a polynomial ring K | 0.90 | text |
| Gröbner basis | is a | direct application of Buchberger's algorithm | 0.90 | text |
| polynomials over principal ideal rings or polynomial rings | instance of | It has been generalized to other structures | 0.80 | text |
| and also some classes of non-commutative rings | instance of | It has been generalized to other structures | 0.80 | text |
| algebras | instance of | It has been generalized to other structures | 0.80 | text |
| like Ore algebras | instance of | It has been generalized to other structures | 0.80 | text |
| polynomial factorization | instance of | although it is less convenient for other computations | 0.80 | text |
| polynomial greatest common divisor.If F | instance of | although it is less convenient for other computations | 0.80 | text |
| Gröbner basis | related to Algorithms and implementations | Buchberger's | 0.60 | section |
| Gröbner basis | related to Algorithms and implementations | Gröbner | 0.60 | section |
| Gröbner basis | related to Algorithms and implementations | It | 0.60 | section |
| Gröbner basis | related to Algorithms and implementations | Bruno Buchberger | 0.60 | section |
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