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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 => ..., 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:
- a rational number

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 a method function with options.