GroebnerBasis -- the class of all Gröbner bases

Description

A Gröbner basis in Macaulay2 consists of a Gröbner 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 Gröbner bases.

Functions and methods returning a Gröbner basis :

forceGB -- declare that the columns of a matrix are a Gröbner basis
forceGB(Matrix) -- see forceGB -- declare that the columns of a matrix are a Gröbner basis
gb -- compute a Gröbner basis
gb(Ideal) -- see gb -- compute a Gröbner basis
gb(Matrix) -- see gb -- compute a Gröbner basis
gb(Module) -- see gb -- compute a Gröbner basis
markedGB -- see markedGB(Matrix,Matrix) -- make a marked Gröbner basis
markedGB(Matrix,Matrix) -- make a marked Gröbner basis

Methods that use a Gröbner basis :

Number % GroebnerBasis -- see % -- a binary operator, usually used for remainder and reduction
betti(GroebnerBasis) -- see betti -- display or modify a Betti diagram
generators(GroebnerBasis) -- the generator matrix of a Gröbner basis
getChangeMatrix(GroebnerBasis) -- see getChangeMatrix -- get the change of basis matrix
leadTerm(GroebnerBasis) -- see leadTerm(Matrix) -- get the greatest term of each column
Matrix % GroebnerBasis -- calculate the normal form of ring elements and matrices using a (partially computed) Gröbner basis
RingElement % GroebnerBasis -- see Matrix % GroebnerBasis -- calculate the normal form of ring elements and matrices using a (partially computed) Gröbner basis
Matrix // GroebnerBasis -- see Matrix // Matrix -- factor a map through another
RingElement // GroebnerBasis -- see Matrix // Matrix -- factor a map through another
mingens(GroebnerBasis) -- (partially constructed) minimal generator matrix
quotient(Matrix,GroebnerBasis) -- matrix quotient
quotientRemainder(Matrix,GroebnerBasis) -- see quotientRemainder -- matrix quotient and remainder
remainder(Matrix,GroebnerBasis) -- see remainder -- matrix remainder
ring(GroebnerBasis) -- see ring -- get the associated ring of an object
status(GroebnerBasis) -- see status -- status of a resolution computation
syz(GroebnerBasis) -- retrieve the syzygy matrix
target(GroebnerBasis) -- find target of a Gröbner basis

For the programmer

The object GroebnerBasis is a type, with ancestor classes MutableHashTable < HashTable < Thing.