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


Ignore:
Timestamp:
Dec 22, 2000, 3:33:13 PM (23 years ago)
Author:
Gert-Martin Greuel <greuel@…>
Branches:
(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')
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/primdec.lib

    r803c5a1 r8942a5  
    1 // $Id: primdec.lib,v 1.80 2000-12-19 14:41:44 anne Exp $
    21///////////////////////////////////////////////////////////////////////////////
    3 // primdec.lib                                                               //
    4 // algorithms for primary decomposition based on                             //
    5 // the ideas of Gianni,Trager,Zacharias                                      //
    6 // written by Gerhard Pfister                                                //
    7 //                                                                           //
    8 // algorithms for primary decomposition based on                             //
    9 // the ideas of Shimoyama/Yokoyama                                           //
    10 // written by Wolfram Decker and Hans Schoenemann                            //
    11 ///////////////////////////////////////////////////////////////////////////////
    12 
    13 version="$Id: primdec.lib,v 1.80 2000-12-19 14:41:44 anne Exp $";
     2version="$Id: primdec.lib,v 1.81 2000-12-22 14:24:36 greuel Exp $";
    143category="Commutative Algebra";
    154info="
    16 LIBRARY: primdec.lib   PROCEDURES FOR PRIMARY DECOMPOSITION
     5LIBRARY: primdec.lib   Primary Decomposition and Radical of Ideals
    176AUTHORS:  Gerhard Pfister, email: pfister@mathematik.uni-kl.de (GTZ)
    187          Wolfram Decker, email: decker@math.uni-sb.de         (SY)
    198          Hans Schoenemann, email: hannes@mathematik.uni-kl.de (SY)
    209
     10OVERVIEW:
     11 Algorithms for primary decomposition based on the ideas of
     12 Gianni,Trager,Zacharias was written by Gerhard Pfister.                       
     13 Algorithms for primary decomposition based on the ideas of
     14 Shimoyama/Yokoyama was written by Wolfram Decker and Hans Schoenemann.   
     15 These procedures are implemented to be used in characteristic 0.
     16 @*They also work in positive characteristic >> 0.
     17 @*In small characteristic and for algebraic extensions, primdecGTZ,
     18 minAssGTZ, radical and equiRadical may not terminate and primdecSY and
     19 minAssChar may not give a complete decomposition.
     20
    2121PROCEDURES:
    22   primdecGTZ(I);    complete primary decomposition via Gianni,Trager,Zacharias
    23   primdecSY(I...);  complete primary decomposition via Shimoyama-Yokoyama
    24   minAssGTZ(I);     the minimal associated primes via Gianni,Trager,Zacharias
    25   minAssChar(I...); the minimal associated primes using characteristic sets
    26   testPrimary(L,k); tests the result of the primary decomposition
    27   radical(I);       computes the radical of the ideal I
    28   equiRadical(I);   the radical of the equidimensional part of the ideal I
    29   prepareAss(I);    list of radicals of the equidimensional components of I
    30   equidim(I);       weak equidimensional decomposition of I
    31   equidimMax(I);    equidimensional locus of I
    32   equidimMaxEHV(I); equidimensional locus of I via Eisenbud,Huneke,Vasconcelos
    33   zerodec(I);       zerodimensional decomposition via Monico
    34 
    35 REMARK:
    36 These procedures are implemented to be used in characteristic 0.
    37 @*They also work in positive characteristic >> 0.
    38 @*In small characteristic and for algebraic extensions, primdecGTZ,
    39 minAssGTZ, radical and equiRadical may not terminate and primdecSY and
    40 minAssChar may not give a complete decomposition.  ";
     22 primdecGTZ(I);    complete primary decomposition via Gianni,Trager,Zacharias
     23 primdecSY(I...);  complete primary decomposition via Shimoyama-Yokoyama
     24 minAssGTZ(I);     the minimal associated primes via Gianni,Trager,Zacharias
     25 minAssChar(I...); the minimal associated primes using characteristic sets
     26 testPrimary(L,k); tests the result of the primary decomposition
     27 radical(I);       computes the radical of the ideal I
     28 equiRadical(I);   the radical of the equidimensional part of the ideal I
     29 prepareAss(I);    list of radicals of the equidimensional components of I
     30 equidim(I);       weak equidimensional decomposition of I
     31 equidimMax(I);    equidimensional locus of I
     32 equidimMaxEHV(I); equidimensional locus of I via Eisenbud,Huneke,Vasconcelos
     33 zerodec(I);       zerodimensional decomposition via Monico
     34";
    4135
    4236LIB "general.lib";
    … …  
    47024696RETURN:  a list of primary ideals, the zero-dimensional decomposition of I
    47034697ASSUME:  I is zero-dimensional, the characterisitic of the ground field is 0
    4704 NOTE:    the algorithm,due to C. Monico, works well only good for small total
     4698NOTE:    the algorithm (of C. Monico), works well only for small total
    47054699         number of solutions (i.e. vdim(std(I)) should be < 100)
    4706          and without parameters. In practise, it works also in big
     4700         and without parameters. In practice, it works also in big
    47074701         characteristic p>0 but may fail for small p.
    47084702         If printlevel > 0 (default = 0) additional information is displayed
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