GroebnerBasis -- the class of all Groebner bases

GroebnerBasis -- the class of all Groebner bases

A Groebner basis in Macaulay 2 consists of a Groebner basis computation, and several associated matrices. Normally you don't need to refer to these objects directly, as many operations on matrices and modules create them, and refer to them. For more information, see Groebner bases or computing Groebner bases.

The type GroebnerBasis is a member of the class Type. Each object of class GroebnerBasis is called a Groebner basis. Each Groebner basis is also a member of class MutableHashTable.

Making a Groebner basis :

forceGB -- declare that the columns of a matrix are a Groebner basis

forceGB Matrix

gb -- compute a Groebner basis

gb Ideal

gb Matrix

gb Module

Methods for using a Groebner basis :

GroebnerBasis == GroebnerBasis

Matrix % GroebnerBasis

Matrix // GroebnerBasis

RingElement % GroebnerBasis

RingElement // GroebnerBasis

ZZ % GroebnerBasis

betti GroebnerBasis

generators GroebnerBasis -- -- the Groebner basis matrix

getChangeMatrix GroebnerBasis

mingens GroebnerBasis -- -- a matrix whose columns are minimal generators of the submodule

net GroebnerBasis

stats GroebnerBasis -- -- display some statistics about the computation

syz GroebnerBasis -- -- a matrix whose columns are the syzygies on the columns of the original matrix

toString GroebnerBasis