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vNumberP -- compute the $\text{v}_\mathfrak{p}$-number of homogeneous ideal $I$

Synopsis

Description

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

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

o2 = ideal (x x , x x , x x )
             1 2   1 3   2 3

o2 : Ideal of S
i3 : p = ideal(x_1,x_2)

o3 = ideal (x , x )
             1   2

o3 : Ideal of S
i4 : vNumberP(I,p)

o4 = 1
i5 : S = QQ[x_1..x_4];
i6 : I = ideal(x_1^3*x_2+x_3^4,x_1+x_2+x_4,x_3^3);

o6 : Ideal of S
i7 : p = (ass I)#0;

o7 : Ideal of S
i8 : vNumberP(I,p)

o8 = 5

See also

Ways to use vNumberP :

For the programmer

The object vNumberP is a method function.