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Line 1: 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 ~~[[Wolfgang Gröbner]] and implemented into highly effective tool in computer algebra by his student~~ [[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 to find a basis for an ideal ''I'' of a ring ''R'' proceeds as follows:

Buchberger's algorithm: Difference between revisions