Gröbner Bases

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 $K[x_1, \ldots ,x_n]$ over a field $K$ . As an algorithmic problem, given a set of polynomials in $K[x_1, \ldots,x_n]$ , determine a Gröbner basis.

Parameters

$n$ : number of variables in each polynomial
$d$ : maximal total degree of the polynomials

Filters

Computational Model

Randomization

Approximation

Algorithms Table

Displaying 3 of 3 algorithms


Faugère F5 algorithm	2002	$O(\binom{n+D_{reg}}{D_{reg}}^{\omega})$	$O(\binom{n+D_{reg}}{D_{reg}}^2)$
Faugère F4 algorithm	1999	$O(\binom{n+D_{reg}}{D_{reg}}^{\omega})$	$O(\binom{n+D_{reg}}{D_{reg}}^2)$
Buchberger's algorithm	1976	$O(d^{2^{n+o(1)}})$	$d^{2^{n+o(1)}}$

Reductions Table

Insuffient Data to display table

Other relevant algorithms