##  [Buchberger Algorithm](/buchberger-algorithm) 

  ##  [Buchberger Algorithm](https://puremath.quantumdictionary.io/buchberger-algorithm-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An algorithm that constructs a Gröbner basis from a given finite generating set of a polynomial ideal by iteratively forming S-polynomials of pairs of generators and reducing them modulo the current set until all S-polynomials reduce to zero; termination (over a field with a monomial order) yields a Gröbner basis.