Macaulay2 » Documentation
Packages » VNumber :: vFunctionP
next | previous | forward | backward | up | index | toc

vFunctionP -- compute the $\text{v}_\mathfrak{p}$-function of monomial ideal $I$

Synopsis

Description

For $k\gg0$, the numerical function $k\mapsto\text{v}_\mathfrak{p}(I^k)$ is a linear function of the form $mk+q$, with $m$ and $q$ integers. This method computes the pair $(m,q)$.

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 : p = ideal(x_1,x_2);

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

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 : p = ideal(x_1,x_2,x_3);

o7 : Ideal of S
i8 : vFunctionP(I,p,control=>3)

o8 = {3, -1}

o8 : List

See also

Ways to use vFunctionP :

For the programmer

The object vFunctionP is a method function with options.