Macaulay2 » Documentation
Packages » Macaulay2Doc :: generators

Synopsis

• 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.

See also

• numgens -- the number of generators
• Monoid -- the class of all monoids
• GroebnerBasis -- the class of all Gröbner bases
• Module -- the class of all modules
• relations -- the defining relations
• subquotient -- make a subquotient module