CoCoA:Gens

Gens

list of generators of an ideal

Description

This function returns a list of polynomials which generate the ideal

I or the module M. The list is not necessarily minimal. Note that

I.Gens and M.Gens will give the same lists of generators. The advantage of Gens is that its argument can be any expression evaluating to an ideal or module.

Example

  Use R ::= Q[x,y];
  I := Ideal(y^2-x^3,xy);
  Gens(I);
[-x^3 + y^2, xy]
-------------------------------
  I.Gens;
[-x^3 + y^2, xy]
-------------------------------
  Gens(I^2);
[x^6 - 2x^3y^2 + y^4, -x^4y + xy^3, x^2y^2]
-------------------------------

Syntax

Gens(I:IDEAL):LIST
Gens(M:MODULE):LIST

Minimalize

Minimalized

   <type>ideal</type>
   <type>module</type>