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NoetherianOperators :: localHilbertRegularity

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

Synopsis

Description

The gCorners 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

See also gCorners.

Ways to use localHilbertRegularity :

For the programmer

The object localHilbertRegularity is a method function with options.