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Reverted 1 edit by 90.146.117.12 (talk); WP:original research and wrong assertion. (TW) |
The theory of Gröbner bases has been developed by Gröbner (see ''Über die Eliminationstheorie''), D. Lazar removes this ref. which is vandalism! |
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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 [[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:
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