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



We give an approximation of the asymptotic regularity by taking the minimum value of $\frac{reg(I^{(n)})}{n}$ over a finite number of exponents $n$, namely for $n$ from 1 to the optional parameter SampleSize; the default value for SampleSize is 10.

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 : asymptoticRegularity(J, SampleSize=>5)

o3 = 4

o3 : QQ

Further information

Functions with optional argument named SampleSize :