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In computational [[algebraic geometry]] and computational [[commutative algebra]], '''Buchberger's algorithm''' is a method of transforming a given set of 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 systems.
A crude version of this algorithm proceeds as follows:
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