Minimalized

Minimalized

remove redundant generators

Syntax


Minimalized(E:IDEAL):IDEAL
Minimalized(E:MODULE):MODULE

where X is a variable containing an ideal or module.

Description

In the inhomogeneous case it returns the ideal or module obtained by removing redundant generators from E.

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. It returns the minimalized ideal or module.

The coefficient ring is assumed to be a field.

The similar function Minimalize performs the same operation, but modifies the argument and returns NULL.

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)
-------------------------------
  Minimalized(I);
Ideal(-y^2 + x, -y^5 + z)
-------------------------------
  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