Changeset 8942a5 in git for Singular/LIB/mregular.lib


Ignore:
Timestamp:
Dec 22, 2000, 3:33:13 PM (23 years ago)
Author:
Gert-Martin Greuel <greuel@…>
Branches:
(u'spielwiese', '17f1d200f27c5bd38f5dfc6e8a0879242279d1d8')
Children:
8bb77bfee92151ac9ed599c9d789653dc8a3570c
Parents:
803c5a17d620ffa41d14efaab791dcf17ad1f7a4
Message:
* GMG: Kosmetik


git-svn-id: file:///usr/local/Singular/svn/trunk@4982 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 edited

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  • Singular/LIB/mregular.lib

    r803c5a1 r8942a5  
    1 // $Id: mregular.lib,v 1.3 2000-12-19 14:41:43 anne Exp $
    21// IB/PG/GMG, last modified:  21.7.2000
    32//////////////////////////////////////////////////////////////////////////////
    4 version = "$Id: mregular.lib,v 1.3 2000-12-19 14:41:43 anne Exp $";
     3version = "$Id: mregular.lib,v 1.4 2000-12-22 14:17:21 greuel Exp $";
    54category="Commutative Algebra";
    65info="
    7 LIBRARY: mregular.lib       PROCEDURES FOR THE CASTELNUOVO-MUMFORD REGULARITY
    8 AUTHORS: I.Bermejo, email: ibermejo@ull.es
    9          Ph.Gimenez, email: pgimenez@agt.uva.es
    10          G.-M.Greuel, email: greuel@mathematik.uni-kl.de
     6LIBRARY: mregular.lib   Castelnuovo-Mumford Regularity of CM-Schemes and Curves
     7AUTHORS: I.Bermejo,     ibermejo@ull.es
     8         Ph.Gimenez,   pgimenez@agt.uva.es
     9         G.-M.Greuel,   greuel@mathematik.uni-kl.de
    1110
    12 A library for computing the Castelnuovo-Mumford regularity of a subscheme of
    13 the projective n-space that DOES NOT require the computation of a minimal
    14 graded free resolution of the saturated ideal defining the subscheme.
     11OVERVIEW:
     12 A library for computing the Castelnuovo-Mumford regularity of a subscheme of
     13 the projective n-space that DOES NOT require the computation of a minimal
     14 graded free resolution of the saturated ideal defining the subscheme.
     15 The procedures are based on two papers by Isabel Bermejo and Philippe Gimenez:
     16 'On Castelnuovo-Mumford regularity of projective curves' Proc.Amer.Math.Soc.
     17 128(5) (2000), and 'Computing the Castelnuovo-Mumford regularity of some
     18 subschemes of Pn using quotients of monomial ideals', Proceedings of
     19 MEGA-2000, J. Pure Appl. Algebra (to appear).
     20 The algorithm assumes the variables to be in Noether position.
    1521
    1622PROCEDURES:
    … …  
    1824 reg_curve(id,[,e]); regularity of projective curve V(id_sat) in Pn
    1925 reg_moncurve(li);   regularity of projective monomial curve defined by li
     26";
    2027
    21 REMARK:
    22 The procedures are based on two papers by Isabel Bermejo and Philippe Gimenez:
    23 'On Castelnuovo-Mumford regularity of projective curves'
    24  Proc.Amer.Math.Soc. 128(5) (2000), and
    25 'Computing the Castelnuovo-Mumford regularity of some subschemes of Pn using
    26  quotients of monomial ideals',
    27  Proceedings of MEGA-2000, J. Pure Appl. Algebra (to appear).
    28 
    29 IMPORTANT:
    30 To use the first two procedures, the variables must be in Noether
    31 position, i.e. that the polynomial ring in the last variables must be a
    32 Noether normalization of basering/id.
    33 If it is not the case, you should compute a Noether normalization before,
    34 e.g. by using the procedure noetherNormal from algebra.lib.
    35 ";
    36 //
    3728LIB "general.lib";
    38 LIB "elim.lib";
     29LIB "algebra.lib";
    3930LIB "sing.lib";
    4031LIB "poly.lib";
    4132//////////////////////////////////////////////////////////////////////////////
    42 //
     33
    4334proc reg_CM (ideal i)
    4435"
    … …  
    4839         the field K is infinite, and S/i-sat is Cohen-Macaulay.
    4940         Assume that K[x(n-d),...,x(n)] is a Noether normalization of S/i-sat
    50          where d=dim S/i -1.
     41         where d=dim S/i -1. If this is not the case, compute a Noether
     42         normalization e.g. by using the proc noetherNormal from algebra.lib.
    5143NOTE:    The output is reg(X)=reg(i-sat) where X is the arithmetically
    5244         Cohen-Macaulay subscheme of the projective n-space defined by i.
    … …  
    147139   reg_CM(i);
    148140}
     141
     142///////////////////////////////////////////////////////////////////////////////
    149143/*
    150144Out-commented examples:
    … …  
    195189*/
    196190//////////////////////////////////////////////////////////////////////////////
    197 //
     191
    198192proc reg_curve (ideal i, list #)
    199193"
    … …  
    494488   reg_curve(j);
    495489}
     490
     491///////////////////////////////////////////////////////////////////////////////
    496492/*
    497493Out-commented examples:
    … …  
    552548*/
    553549//////////////////////////////////////////////////////////////////////////////
    554 //
     550
    555551proc reg_moncurve (list #)
    556552"
    … …  
    774770   reg_moncurve(0,1,3,5,6);
    775771}
     772///////////////////////////////////////////////////////////////////////////////
    776773/*
    777774Out-commented examples:
    … …  
    811808//
    812809*/
    813 //
    814810//////////////////////////////////////////////////////////////////////////////
    815 //
     811
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