Buchberger's algorithm: Difference between revisions

Revision as of 04:53, 16 December 2024

Revision as of 16:49, 29 January 2025

Line 2:

In the theory of [[multivariate polynomial]]s, '''Buchberger's algorithm''' is a method for transforming a given set of polynomials into a [[Gröbner basis]], which is another set of polynomials that have the same common zeros and are more convenient for extracting information on these common zeros. It was introduced by [[Bruno Buchberger]] simultaneously with the definition of Gröbner bases.

The [[Euclidean algorithm]] for computing the polynomial [[greatest common divisor]] computationis anda special case of Buchberger's algorithm restricted to polynomials of a single variable. [[Gaussian elimination]] of a [[system of linear equations|linear system]]s areis another special casescase of Buchberger's algorithm whenwhere the numberdegree of variables or the degrees of theall polynomials are respectively equal toequals one.

For other Gröbner basis algorithms, see {{slink|Gröbner basis#Algorithms and implementations}}.