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

Synopsis

Description

For $k\gg0$, the numerical function $k\mapsto\text{v}(I^k)$ is a linear function of the form $mk+q$, with $m=\alpha(I)$ the initial degree of $I$ and $q\ge-1$ an integer. This method computes the pair $(\alpha(I),q)$.

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

Ways to use vFunction :

For the programmer

The object vFunction is a method function with options.