asymptoticRegularity -- approximates the asymptotic regularity

Synopsis

Usage:

asymptoticRegularity(I,SampleSize=>ZZ)
Optional inputs:
- SampleSize => ..., default value 10, optional parameter used for approximating asymptotic invariants that are defined as limits.

Description

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

Ways to use asymptoticRegularity :

asymptoticRegularity(Ideal)

For the programmer

The object asymptoticRegularity is a method function with options.