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.
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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)
-------------------------------
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