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vNumber -- compute the $\text{v}$-number of homogeneous ideal $I$

Synopsis

Description

This method computes the $\text{v}$-number of $I$: $$\text{v}(I)=\min\{\text{deg}(f):f\in S\ \text{is homogeneous, and}\ (I:f)\in\text{Ass}(I)\}.$$

i1 : S = QQ[x_1..x_3];
i2 : I = ideal(x_1*x_2,x_1*x_3,x_2*x_3);

o2 : Ideal of S
i3 : vNumber(I)

o3 = 1
i4 : S = QQ[x_1..x_4];
i5 : I = ideal(x_1^3*x_2+x_3^4,x_1+x_2+x_4,x_3^3);

o5 : Ideal of S
i6 : vNumber(I)

o6 = 5

See also

Ways to use vNumber :

For the programmer

The object vNumber is a method function.