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... 62 KB (9,909 words) - 01:29, 9 May 2024 |
Algebraic geometry (section Gröbner basis) 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... 60 KB (7,405 words) - 19:56, 6 May 2024 |
Hilbert's Nullstellensatz (section Using Gröbner bases) 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... 23 KB (3,811 words) - 16:48, 6 February 2024 |
Wolfgang Gröbner (11 February 1899 – 20 August 1980) was an Austrian mathematician. His name is best known for the Gröbner basis, used for computations... 3 KB (227 words) - 10:50, 28 November 2023 |
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 |
Gröbner basis Hilbert's basis theorem Generating set of a group Base (topology) Change of basis Greedoid Normal basis Polynomial basis Radial basis function... 2 KB (296 words) - 12:20, 25 October 2020 |
( L T ( f ) ∣ f ∈ I ) {\displaystyle LT(I)=(LT(f)\mid f\in I)} . A Gröbner basis for an ideal I ⊂ K [ x 1 , x 2 , … , x n ] {\displaystyle I\subset \mathbb... 10 KB (2,098 words) - 15:22, 5 May 2024 |
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... 4 KB (682 words) - 11:02, 7 May 2024 |
of monomials of an algebra forms a k {\displaystyle k} -basis. It is an extension of Gröbner bases to non-commutative rings. The proof of the lemma gives... 15 KB (3,012 words) - 16:45, 8 April 2024 |
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... 4 KB (479 words) - 18:02, 29 November 2023 |
extending this theory as a Gröbner basis theory for submodules of a free module. This extension allows, for computing a Gröbner basis of a submodule, to use... 22 KB (2,913 words) - 11:08, 9 April 2024 |
generalised to multivariate polynomials with respect to a monomial order, see Gröbner basis § Leading term, coefficient and monomial. In linear algebra, a system... 7 KB (1,095 words) - 20:50, 6 February 2024 |
multi-modular arithmetic include polynomial greatest common divisor, Gröbner basis computation and cryptography. A residue numeral system is defined by... 13 KB (1,595 words) - 14:08, 23 April 2024 |
the denominator of the Hilbert series of A. This allows, through a Gröbner basis computation to compute the dimension of the algebraic set defined by... 10 KB (1,535 words) - 10:08, 18 February 2024 |
by the computation of a Gröbner basis of the left-hand sides of the equations. The system is inconsistent if this Gröbner basis is reduced to 1. The system... 33 KB (4,592 words) - 12:17, 9 April 2024 |
Filter bank (section Using Gröbner bases) Gröbner bases implies that the Module has a unique reduced Gröbner basis for a given order of power products in polynomials. If we define the Gröbner... 39 KB (5,908 words) - 03:15, 26 April 2024 |
cosmos and abiogenic petroleum origin theory Wolfgang Gröbner, mathematician (best known for Gröbner basis) Hans Hahn, mathematician (member of the Vienna Circle)... 10 KB (1,186 words) - 01:32, 28 August 2023 |
works well, but for the large matrices that occur in cryptography and Gröbner basis computation, better algorithms are known, which have roughly the same... 23 KB (3,702 words) - 20:31, 30 April 2024 |
performing Euclidean polynomial division Ruffini's rule Euclidean domain Gröbner basis Greatest common divisor of two polynomials Archived at Ghostarchive... 13 KB (2,188 words) - 16:36, 6 August 2023 |
magazine sometimes referred as F5 Faugère F5 algorithm, for computing the Gröbner basis of an ideal of a multivariate polynomial ring Nikon F5, a camera F5... 2 KB (314 words) - 00:35, 6 May 2024 |
Galois theory Discriminant of a polynomial Resultant Elimination theory Gröbner basis Regular chain Triangular decomposition Sturm's theorem Descartes' rule... 5 KB (441 words) - 01:35, 1 December 2023 |
idea of standard basis in the universal enveloping algebra of a Lie algebra is established by the Poincaré–Birkhoff–Witt theorem. Gröbner bases are also... 7 KB (1,006 words) - 17:48, 12 April 2024 |
of a Gröbner basis, to the same problem for an ideal generated by monomials, which is usually much easier than the computation of the Gröbner basis. The... 23 KB (3,880 words) - 14:57, 9 March 2023 |