### D.4.16 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.4.16.1 regIdeal |  | regularity of homogeneous ideal id
> D.4.16.2 depthIdeal |  | depth of S/id with S=basering, id homogeneous ideal
> D.4.16.3 satiety |  | saturation index of homogeneous ideal id
> D.4.16.4 regMonCurve |  | regularity of projective monomial curve defined by li
> D.4.16.5 NoetherPosition |  | Noether normalization of ideal id
> D.4.16.6 is_NP |  | checks whether variables are in Noether position
> D.4.16.7 is_nested |  | checks whether monomial ideal id is of nested type

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