waldschmidt(...,SampleSize=>...) -- optional parameter used for approximating asymptotic invariants that are defined as limits.

Usage:

waldschmidt(I,SampleSize=>ZZ)

Description

For ideals that are not monomial, we give an approximation of the Waldschmidt constant by taking the minimum value of $\frac{\alpha(I^{(n)})}{n}$ over a finite number of exponents $n$, namely for $n$ from 1 to the optional parameter SampleSize. Similarly the SampleSize is used to give an approximation for the asymptotic regularity by computing the smallest value of $\frac{reg(I^{(n)})}{n}$ for $n$ from 1 to the SampleSize.

i1 : R = QQ[x,y,z];

i2 : J = ideal (x*(y^3-z^3),y*(z^3-x^3),z*(x^3-y^3));

o2 : Ideal of R

i3 : waldschmidt(J, SampleSize=>5)

o3 = 3

o3 : QQ

Functions with optional argument named SampleSize:

asymptoticRegularity(...,SampleSize=>...) -- optional parameter used for approximating asymptotic invariants that are defined as limits.
lowerBoundResurgence(...,SampleSize=>...) -- optional parameter used for approximating asymptotic invariants that are defined as limits.
waldschmidt(...,SampleSize=>...) -- optional parameter used for approximating asymptotic invariants that are defined as limits.

Further information

Default value: 5
Function: waldschmidt -- computes the Waldschmidt constant for a homogeneous ideal.
Option key: SampleSize -- optional parameter used for approximating asymptotic invariants that are defined as limits.