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 |
The object asymptoticRegularity is a method function with options.