# lowerBoundResurgence -- computes a lower bound for the resurgence of a given ideal.

## Synopsis

• Usage:
lowerBoundResurgence(Ideal)
• Inputs:
• Optional inputs:
• SampleSize => ..., default value 5, optional parameter used for approximating asymptotic invariants that are defined as limits.
• UseWaldschmidt => ..., default value false, optional input for computing a lower bound for the resurgence of a given ideal.
• Outputs:

## Description

The resurgence of an ideal $I$, defined by Harbourne and Bocci, is given by $\rho(I) :=$ sup $\lbrace a/b : I^{(a)}$ &nsub; $I^b \rbrace.$

Given an ideal $I$, finds the maximum of the quotients $m/k$ that fail $I^{(m)} \subseteq I^k$ with $k \leq$ the optional input SampleSize.

 i1 : T = QQ[x,y,z]; i2 : I = intersect(ideal"x,y",ideal"x,z",ideal"y,z"); o2 : Ideal of T i3 : lowerBoundResurgence(I) 6 o3 = - 5 o3 : QQ

## Ways to use lowerBoundResurgence :

• "lowerBoundResurgence(Ideal)"

## For the programmer

The object lowerBoundResurgence is .