CoCoA:Minimalize

Minimalize

remove redundant generators

Description

In the inhomogeneous case it removes redundant generators from the

ideal or module contained in X, storing the result in X, i.e. the

original ideal or module is overwritten.

In the homogeneous case, it obtains a generating set with smallest

possible cardinality. The minimal set of generators found by CoCoA is

not necessarily a subset of the given generators. As with the inhomogeneous case, it overwrites its argument.

The coefficient ring is assumed to be a field.

The similar function <ttref>Minimalized</ttref> performs the same

operation, but returns the minimalized ideal or module and does not

modify the argument.

Example

  Use R ::= Q[x,y,z];
  I := Ideal(x-y^2,z-y^5,x^5-z^2);
  I;
Ideal(-y^2 + x, -y^5 + z, x^5 - z^2)
-------------------------------
  Minimalize(I);
  I;
Ideal(-y^2 + x, -y^5 + z)
-------------------------------
  J := Ideal(x, x-y, y-z, z^2);
  Minimalized(J);
Ideal(y - z, x - z, z)
-------------------------------

Syntax

Minimalize(X:IDEAL):NULL
Minimalize(X:MODULE):NULL

where X is a variable containing an ideal or module.

MinGens

Minimalized

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