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Minimalize, Minimalized

Syntax

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

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

where X is a variable containing an ideal or module.
    

Summary

remove redundant generators

Description

In the inhomogeneous case the first form removes redundant generators from the ideal or module contained in X, storing the result in X; the original ideal or module is overwritten.

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

In the homogeneous case, one 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, the first form overwrites the ideal or module contained in X and the second returns the minimalized ideal or module.

The coefficient ring is assumed to be a field.

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)
-------------------------------
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