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IdealOfMinGens

ideal generated by minimal generators

Syntax
IdealOfMinGens(I: IDEAL): IDEAL

Description
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.

Example
/**/  Use R ::= QQ[x,y,z];
/**/  I := ideal(x^2-y^2, z^4-y^4, x^2-z^2);
/**/  IdealOfMinGens(I);
ideal(x^2 -z^2,  y^2 -z^2)
/**/  HasGBasis(I);
true

See Also