Minimalize

Minimalize

remove redundant generators

Syntax


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

where X is a variable containing an ideal or module.

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 Minimalized performs the same operation, but returns the minimalized ideal or module and does not modify the argument.

Example

  Use R ::= QQ[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)
-------------------------------

See Also