CoCoA:MinGens

MinGens

list minimal generators

Description

If M is an ideal or module, this function returns a list of minimal

generators for M. If M is the quotient of a polynomial ring by an

ideal I or the quotient of a free module by the submodule N, then MinGens returns a set of minimal generators for I or N, respectively.

The coefficient ring must be a field.

The input must be homogeneous. The similar command <ttref>Minimalized</ttref>,

will accept inhomogeneous input.

Example

  Use R ::= Q[x,y,z];
  I := Ideal(x-y,(x-y)^4,z+y,(z+y)^2);
  I;
Ideal(x - y, x^4 - 4x^3y + 6x^2y^2 - 4xy^3 + y^4, y + z, y^2 + 2yz + z^2)
-------------------------------
  MinGens(I);
[y + z, x + z]
-------------------------------
  MinGens(R/I);
[y + z, x + z]
-------------------------------
  M :=Module([x+y,x-y],[(x+y)^2,(x+y)(x-y)]);
  MinGens(M);
[Vector(x + y, x - y)]
-------------------------------
  MinGens(R^2/M);
[Vector(x + y, x - y)]
-------------------------------

Syntax

MinGens(M:IDEAL or MODULE or TAGGED(<quotes>Quotient</quotes>)):LIST

Minimalize

Minimalized

   <type>groebner</type>
   <type>groebner-basic</type>
   <type>ideal</type>
   <type>module</type>
   <type>quotient</type>