{{Short description|Algorithm for computing Gröbner bases}}
In computationalthe [[algebraic geometry]] andtheory computationalof [[commutativemultivariate algebrapolynomial]]s, '''Buchberger's algorithm''' is a method of transforming a given set of [[Ideal (ring theory)#Ideal generated by a set|generators]] for a polynomial [[ring ideal|ideal]] into a [[Gröbner basis]] with respect to some [[monomial order]]. It was invented by Austrian [[mathematician]] [[Bruno Buchberger]]. One can view it as a generalization of the [[Euclidean algorithm]] for univariate [[Greatest common divisor|GCD]] computation and of [[Gaussian elimination]] for [[linear system]]s.
