# 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 .