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 |