# localHilbertRegularity -- regularity of the local Hilbert function of a polynomial ideal

## Synopsis

• Usage:
d = localHilbertRegularity(p,I)
• Inputs:
• Optional inputs:
• Tolerance => ..., default value null, optional argument for numerical tolernace
• Outputs:

## Description

The g-corners of the ideal are computed in order to find the Hilbert polynomial, which is compared to the Hilbert function to find the degree of regularity, which is the degree at which the two become equal.

 i1 : R = CC[x,y]; i2 : I = ideal{x^2,x*y} 2 o2 = ideal (x , x*y) o2 : Ideal of R i3 : d = localHilbertRegularity(origin R, I) -- warning: experimental computation over inexact field begun -- results not reliable (one warning given per session) o3 = 2 i4 : D = truncatedDual(origin R, I, 3) o4 = | 1 y x .5y2 .166667y3 | o4 : DualSpace i5 : L = hilbertFunction({0,1,2,3}, D) o5 = {1, 2, 1, 1} o5 : List