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

Synopsis

• Usage:

  vNumberP(I,p)

• Inputs:
  • I, an ideal, a homogeneous ideal of polynomial ring $S = \mathbb{K}[x_1,\ldots,x_n]$, $\mathbb{K}$ a field
  • p, an ideal, a associated prime of $I$
• Outputs:
  • k, an integer,

Description

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

• vNumber -- compute the $\text{v}$-number of homogeneous ideal $I$
• vFunctionP -- compute the $\text{v}_\mathfrak{p}$-function of monomial ideal $I$
• vFunction -- compute the $\text{v}$-function of monomial ideal $I$