Changeset a073dd in git for Singular/LIB/sagbi.lib


Ignore:
Timestamp:
Jun 7, 2005, 12:05:19 PM (19 years ago)
Author:
Hans Schönemann <hannes@…>
Branches:
(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')
Children:
1992ae09fe5b6131c31c54b22c57a436c72fe412
Parents:
0a5ca730b1b89c3ce6ac8f1f6af48f1029041ad0
Message:
*pfister: name chnages


git-svn-id: file:///usr/local/Singular/svn/trunk@8341 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 edited

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  • Singular/LIB/sagbi.lib

    r0a5ca7 ra073dd  
    11//////////////////////////////////////////////////////////////////////////////
     2version="$Id: sagbi.lib,v 1.4 2005-06-07 10:05:19 Singular Exp $";
    23category="Commutative Algebra";
    34info="
    … …  
    56AUTHORS: Gerhard Pfister,        pfister@mathematik.uni-kl.de,
    67@*       Anen Lakhal,            alakhal@mathematik.uni-kl.de
     8
    79PROCEDURES:
    8  proc reduction(p,I); Perform one step subalgebra reducton (for short S-reduction) of p w.r.t I
    9  proc S_poly(I);      Compute the S-polynomilas of the Subalgebra defined by the genartors of I
    10  proc S_nf(id,I);     Perform iterated S-reductions in order to compute Subalgebras normal forms
    11  proc sagbi(I);       Construct SAGBI basis for the Subalgebra defined by I
    12  proc sagbi1(I);      Construct partial SAGBI basis for the Subalgebra defined by I
     10 proc reduction(p,I);  Perform one step subalgebra reducton (for short S-reduction) of p w.r.t I
     11 proc sagbiSPoly(I);   Compute the S-polynomilas of the Subalgebra defined by the genartors of I
     12 proc sagbiNF(id,I);   Perform iterated S-reductions in order to compute Subalgebras normal forms
     13 proc sagbi(I);        Construct SAGBI basis for the Subalgebra defined by I
     14 proc sagbiPart(I);    Construct partial SAGBI basis for the Subalgebra defined by I
    1315";
    1416
    … …  
    1719
    1820///////////////////////////////////////////////////////////////////////////////
    19 proc S_poly(id ,list #)
    20 "USAGE: S_poly(id [,n]); id ideal, n positive integer.
     21proc sagbiSPoly(id ,list #)
     22"USAGE: sagbiSPoly(id [,n]); id ideal, n positive integer.
    2123RETURN: an ideal
    2224@format
    … …  
    2729        the ideal of algebraic relations.
    2830@end format
    29 EXAMPLE: example S_poly; show an example "
     31EXAMPLE: example sagbiSPoly; show an example "
    3032{
    3133  if(size(#)==0)
    … …  
    9799      map phi=R1,vars,id;
    98100
    99       // the S_polynomials are the image by phi of the generators of kern
     101      // the sagbiSPolynomials are the image by phi of the generators of kern
    100102
    101103      P=simplify(phi(kern),1);
    … …  
    110112
    111113                 dbprint(printlevel-voice+3,"
    112 // 'S_poly' created a ring as 2nd element of the list.
     114// 'sagbiSPoly' created a ring as 2nd element of the list.
    113115// The ring contains the ideal 'kern'  of algebraic relations between the
    114116//leading terms of the generators of I.
    … …  
    127129 poly f1,f2,f3,f4=x2,y2,xy+y,2xy2;
    128130 ideal I=f1,f2,f3,f4;
    129  S_poly(I);
    130  list L=S_poly(I,1);
     131 sagbiSPoly(I);
     132 list L=sagbiSPoly(I,1);
    131133 L[1];
    132134 def S= L[2]; setring S; kern;
    … …  
    198200  if(size(J)==0)
    199201    {
    200       @L =S_poly(I,1);
     202      @L =sagbiSPoly(I,1);
    201203    }
    202204  else
    … …  
    438440///////////////////////////////////////////////////////////////////////////////
    439441
    440 proc S_nf(id,ideal dom,int k,list#)
    441 "USAGE: S_nf(id,dom,k[,n]); id either poly or ideal,dom ideal, k and n positive intergers.
     442proc sagbiNF(id,ideal dom,int k,list#)
     443"USAGE: sagbiNF(id,dom,k[,n]); id either poly or ideal,dom ideal, k and n positive intergers.
    442444RETURN: depends On the type of id; ideal or polynomial.
    443445@format
    … …  
    451453NOTE: computation of Subalgebras normal forms may be performed either
    452454      in polynomial rings or quotient polynomial rings
    453 EXAMPLE: example S_nf; show example "
     455EXAMPLE: example sagbiNF; show example "
    454456{
    455457  int z;
    … …  
    490492{"EXAMPLE:"; echo = 2;
    491493 ring r=0,(x,y),dp;
    492  ideal I x2-xy;
     494 ideal I= x2-xy;
    493495 qring Q=std(I);
    494496 ideal dom =x2,x2y+y,x3y2;
    495497 poly p=x4+x2y+y;
    496  S_nf(p,dom,0);
    497  S_nf(p,dom,1);// tail subalgebra reduction is perofrmed
     498 sagbiNF(p,dom,0);
     499 sagbiNF(p,dom,1);// tail subalgebra reduction is perofrmed
    498500}
    499501
    … …  
    550552      L=Spoly1(L,S,Red,2);
    551553      Red=L[1];
    552       Red=S_nf(Red,S,k,#);
     554      Red=sagbiNF(Red,S,k,#);
    553555      oldS=S;
    554556      S=S+Red;
    … …  
    563565}
    564566///////////////////////////////////////////////////////////////////////////////
    565 proc sagbi1(id,int k,int c,list #)
     567proc sagbiPart(id,int k,int c,list #)
    566568"USAGE: sagbi(id,k,c[,n]); id ideal, k, c and n positive integer.
    567569RETURN: A partial SAGBI basis for the subalgebra defined by the genrators of id.
    … …  
    581583       with infinte SAGBI basis. In this case, by means of this procedure,
    582584       we may check for example, if the elements of this basis have a particular form.
    583 EXAMPLE: example sagbi1; show example "
     585EXAMPLE: example sagbiPart; show example "
    584586{
    585587  degBound=0;
    … …  
    592594      L=Spoly1(L,S,Red,2);
    593595      Red=L[1];
    594       Red=S_nf(Red,S,k,#);
     596      Red=sagbiNF(Red,S,k,#);
    595597      oldS=S;
    596598      S=S+Red;
    … …  
    603605 ring r= 0,(x,y),dp;
    604606 ideal I=x,xy-y2,xy2;//the corresponding Subalgebra has an infinte SAGBI basis
    605  sagbi1(I,1,3)// computations should stop after 3 turns.
     607 sagbiPart(I,1,3);// computations should stop after 3 turns.
    606608}
    607609//////////////////////////////////////////////////////////////////////////////
    608 
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