• algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring K[x1, ..., xn] over a field K. A Gröbner basis allows many...
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    for this involve Gröbner basis computation. The algorithms which are not based on Gröbner bases use regular chains but may need Gröbner bases in some exceptional...
    61 KB (7,507 words) - 11:08, 14 July 2024
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    Wolfgang Gröbner (11 February 1899 – 20 August 1980) was an Austrian mathematician. His name is best known for the Gröbner basis, used for computations...
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  • only if its reduced Gröbner basis (for any monomial ordering) is 1. The number of the common zeros of the polynomials in a Gröbner basis is strongly related...
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  • For other Gröbner basis algorithms, see Gröbner basis § Algorithms and implementations. A crude version of this algorithm to find a basis for an ideal...
    6 KB (777 words) - 07:25, 8 September 2023
  • generators for the next larger basis: If Gprev is an already computed Gröbner basis (f2, …, fm) and we want to compute a Gröbner basis of (f1) + Gprev then we...
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  • Gröbner basis Hilbert's basis theorem Generating set of a group Base (topology) Change of basis Greedoid Normal basis Polynomial basis Radial basis function...
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  • are most commonly used with Gröbner bases and multivariate division. In particular, the property of being a Gröbner basis is always relative to a specific...
    14 KB (2,070 words) - 18:51, 25 January 2024
  • order of the monomial basis in the multivariate case. For problems which require choosing a total order, such as Gröbner basis computations, one generally...
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  • multi-modular arithmetic include polynomial greatest common divisor, Gröbner basis computation and cryptography. A residue numeral system is defined by...
    13 KB (1,596 words) - 08:28, 9 July 2024