generators -- provide matrix or list of generators

Usage:

generators x

gens x
Inputs:
- x
Optional inputs:
- CoefficientRing => ..., default value null, only used if x is a ring
Outputs:
- provides the generators of x in a convenient form, as a list or a matrix, depending on the type

Description

Produces the generators of a Gröbner basis, a polynomial ring, an ideal, a free module, a free group, a submodule given by means of generators (or for which generators have been computed), or a free monoid.

Usually the result is a list of generators, but the generators of a module or Gröbner basis are provided as the columns in a matrix. The matrix is stored in a module M under M.generators, unless the matrix is the identity matrix.

The symbol gens is a synonym for generators.

Ways to use generators:

generators(GroebnerBasis) -- the generator matrix of a Gröbner basis
generators(Ideal) -- the generator matrix of an ideal
generators(MonomialIdeal) -- see generators(Ideal) -- the generator matrix of an ideal
generators(Module) -- the generator matrix of a module
generators(Monoid) -- list of generators
generators(Ring) -- the list of generators of a ring

For the programmer

The object generators is a method function with options.

The source of this document is in Macaulay2Doc/functions/generators-doc.m2:36:0.

generators -- provide matrix or list of generators

Description

See also

Ways to use generators:

For the programmer