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

Synopsis

• Usage:

  d = localHilbertRegularity(p,I)

• Inputs:
  • p, a point,
  • I, an ideal, or a one-row matrix of generators
• Optional inputs:
  • Tolerance => ..., default value null, optional argument for numerical tolerance
• Outputs:
  • d, an integer,

Description

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