vFunction -- compute the $\text{v}$-function of monomial ideal $I$

Synopsis

• Usage:

  vFunction I

• Inputs:
  • I, an ideal, a monomial ideal of polynomial ring $S = \mathbb{K}[x_1,\ldots,x_n]$, $\mathbb{K}$ a field
• Optional inputs:
  • control => an integer, default value 2, can be changed to increase reliability
• Outputs:
  • l, a list, the first element represents the slope of the line, while the second represents the $y$-intercept

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 of S

i3 : vFunction I

o3 = {2, -1}

o3 : List

i4 : vFunction(I,control=>3)

o4 = {2, -1}

o4 : List

i5 : S = QQ[x_1..x_3];

i6 : I = ideal(x_1,x_2)*ideal(x_1,x_3)*ideal(x_2,x_3);

o6 : Ideal of S

i7 : vFunction I

o7 = {3, -1}

o7 : List

See also

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