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SymbolicPowers :: lowerBoundResurgence

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

Synopsis

Usage:

lowerBoundResurgence(Ideal)
Inputs:
- I, an ideal
Optional inputs:
- SampleSize => ..., -- optional parameter used for approximating asymptotic invariants that are defined as limits.
- UseWaldschmidt => ..., -- optional input for computing a lower bound for the resurgence of a given ideal.
Outputs:
- a rational number

Description

The resurgence of an ideal I, defined by Harbourne and Bocci, is given by ρ(I) := sup {a/b : I^(a) ⊄ I^b }.

Given an ideal I, finds the maximum of the quotients m/k that fail I^(m) ⊆I^k with k ≤ 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)