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SymbolicPowers :: waldschmidt(...,SampleSize=>...)

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

Synopsis

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

Further information

Functions with optional argument named SampleSize :