Revision as of 18:44, 18 March 2006 edit Tawkerbot2 (talk \| contribs) 131,306 edits m vandalism from User talk:194.133.131.93 (44387745) - reverted to User talk:Leland McInnes (37166851) ← Previous edit		Revision as of 02:04, 17 May 2006 edit undo Chewie (usurped) (talk \| contribs) 12 edits m GCD capitalization Next edit →
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 [[Bruno Buchberger]]. One can view it as a generalization of the [[Euclidean algorithm]] for univariate [[~~greatest~~Greatest common divisor\|~~gcd~~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