up previous next
IdealOfMinGens    --    ideal generated by minimal generators

IdealOfMinGens(I: IDEAL): IDEAL

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

This function returns the ideal generated by a minimal set of generators (i.e. with minimal cardinality) of I . The minimal set of generators is not necessarily a subset of the given generators.

The coefficient ring must be a field.

/**/  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);

See Also