Singular

D.4.17 mregular_lib

Library:

mregular.lib

Purpose:

Castelnuovo-Mumford regularity of homogeneous ideals

Authors:

I.Bermejo, ibermejo@ull.es
Ph.Gimenez, pgimenez@agt.uva.es
G.-M.Greuel, greuel@mathematik.uni-kl.de

Overview:

A library for computing the Castelnuovo-Mumford regularity of a homogeneous ideal that DOES NOT require the computation of a minimal graded free resolution of the ideal.
It also determines depth(basering/ideal) and satiety(ideal). The procedures are based on 3 papers by Isabel Bermejo and Philippe Gimenez: 'On Castelnuovo-Mumford regularity of projective curves' Proc.Amer.Math.Soc. 128(5) (2000), 'Computing the Castelnuovo-Mumford regularity of some subschemes of Pn using quotients of monomial ideals', Proceedings of MEGA-2000, J. Pure Appl. Algebra 164 (2001), and 'Saturation and Castelnuovo-Mumford regularity', Preprint (2004).

Procedures:

D.4.17.1 regIdeal		regularity of homogeneous ideal id
D.4.17.2 depthIdeal		depth of S/id with S=basering, id homogeneous ideal
D.4.17.3 satiety		saturation index of homogeneous ideal id
D.4.17.4 regMonCurve		regularity of projective monomial curve defined by li
D.4.17.5 NoetherPosition		Noether normalization of ideal id
D.4.17.6 is_NP		checks whether variables are in Noether position
D.4.17.7 is_nested		checks whether monomial ideal id is of nested type