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ideal, submodule with minimal generators

minimalized(E: IDEAL): IDEAL
minimalized(E: MODULE): MODULE

It works only in the homogeneous case: for the inhomogeneous case see MinSubsetOfGens .

This function returns the ideal (or submodule) generated by a set of minimal generators of E (with minimal cardinality). The minimal set of generators is not necessarily a subset of the given generators.

The coefficient ring is assumed to be a field.

The similar function minimalize performs the same operation, but modifies the argument ( ref ) and returns NULL.

/**/  use R ::= QQ[x,y,z];
/**/  I := ideal(x^2-y^2, z^4-y^4, x^2-z^2);
/**/  I;
ideal(x^2 -y^2, -y^4 +z^4, x^2 -z^2)
/**/  minimalized(I);
ideal(x^2 -z^2, y^2 -z^2)
/**/  I; -- not modified
ideal(x^2 -y^2, -y^4 +z^4, x^2 -z^2)

See Also