GroebnerBasis -- the class of all 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
• status(GroebnerBasis) -- see gb -- compute a Gröbner basis
• 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
• leadTerm(ZZ,GroebnerBasis) -- see leadTerm(ZZ,Matrix) -- get the matrix of lead polynomials of each column
• Matrix % GroebnerBasis -- compute the normal form of a ring element or matrix using a Gröbner basis
• RingElement % GroebnerBasis -- see Matrix % GroebnerBasis -- compute the normal form of a ring element or matrix using a Gröbner basis
• mingens(GroebnerBasis) -- (partially constructed) minimal generator matrix
• Matrix // GroebnerBasis -- see quotient(Matrix,Matrix) -- factor a map through another with the same target
• quotient(Matrix,GroebnerBasis) -- see quotient(Matrix,Matrix) -- factor a map through another with the same target
• RingElement // GroebnerBasis -- see quotient(Matrix,Matrix) -- factor a map through another with the same target
• 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
• 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.

The source of this document is in Macaulay2Doc/functions/gb-doc.m2:186:0.