Changeset d939c1 in git


Ignore:
Timestamp:
Nov 13, 2006, 11:15:50 AM (17 years ago)
Author:
Hans Schönemann <hannes@…>
Branches:
(u'jengelh-datetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', '0604212ebb110535022efecad887940825b97c3f')
Children:
7e6727cb6f504e34aa0527cb245dd36801940f69
Parents:
88c2d0339a4d3951514cf761014a3fc294f8ab2b
Message:
*hannes/gmg: new standard.lib


git-svn-id: file:///usr/local/Singular/svn/trunk@9480 2c84dea3-7e68-4137-9b89-c4e89433aadc
Files:
13 edited

Legend:

Unmodified
Added
Removed

  • Singular/LIB/standard.lib

    r88c2d0 rd939c1  
    11//////////////////////////////////////////////////////////////////////////////
    2 version="$Id: standard.lib,v 1.82 2006-09-20 16:42:01 Singular Exp $";
     2version="$Id: standard.lib,v 1.83 2006-11-13 10:15:34 Singular Exp $";
    33category="Miscellaneous";
    44info="
    … …  
    88 stdfglm(ideal[,ord])   standard basis of ideal via fglm [and ordering ord]
    99 stdhilb(ideal[,h])     standard basis of ideal using the Hilbert function
     10 hilbstd(ideal[,h])     standard basis using (weighted) Hilbert function
    1011 groebner(ideal/module) standard basis using a heuristically chosen method
    1112 res(ideal/module,[i])  free resolution of ideal or module
    … …  
    138139//////////////////////////////////////////////////////////////////////////
    139140
     141proc hilbstd(ideal i,list #)
     142"SYNTAX: @code{stdhilb (} ideal_expression @code{)} @*
     143         @code{stdhilb (} ideal_expression@code{,} intvec_expression @code{)}
     144TYPE:    ideal
     145PURPOSE: Computes a Groebner basis of the homogeneous ideal in the basering.
     146THEORY:  Compute first a standard basis of the (weighted) homogenization
     147         of the ideal, then the (weighted) Hilbert function and finally
     148         a Groebner basis in the original ring by using the computed Hilbert
     149         function@*
     150         An optional second argument will be used as 1st Hilbert function.
     151ASSUME:  The optional second argument is the first Hilbert series as computed
     152         by @code{hilb}.
     153NOTE:    This procedure makes stdhilb obsolet since it is a generalization
     154         to rings with some variables having weights >1. Parameters are kept.
     155SEE ALSO: stdfglm, std, groebner
     156KEYWORDS: Hilbert function
     157EXAMPLE: example hilbstd;  shows an example"
     158{
     159   def R=basering;
     160   list lR = ringlist(R);
     161   intvec v = size(lR[1..size(lR)]);   //size of lists lR[i] in lR
     162   int n = nvars(R);
     163   intvec w;                 //ringweights
     164   int ii, neg;
     165   for(ii=1; ii<=n; ii++)
     166   {
     167     w[ii]=deg(var(ii));
     168     if(w[ii] <= 0)
     169     {neg = 1;}
     170   }
     171//---------- exclude cases to which hilbstd should no be applied  ----------
     172   if( homog(i) || find(ordstr(R),"s") || find(ordstr(R),"M")
     173       || find(ordstr(R),"a") || (neg > 0) )
     174   {
     175      if((size(#)!=0) && homog(i))
     176      {
     177         return(std(i,#[1]));
     178      }
     179      return(std(i));
     180   }
     181
     182//----------- create ring for fast computation of hilbert series --------
     183   list lS=lR;
     184   lS[2]=insert(lR[2],"@t",v[2]);
     185   lS[3]=lR[3][1],lR[3][size(lR[3])];
     186   intvec ww=w,1;
     187   if(w==1)
     188   {
     189     lS[3][1]=list("dp",ww);
     190   }
     191   else
     192   {
     193     lS[3][1]=list("wp",ww);
     194   }
     195
     196   def S = ring(lS);              //ring with one weighted block of variables
     197   setring S;
     198   ideal i = homog(imap(R,i),@t); //weighted homog of i
     199   string s_opt = option();
     200   int p_opt=(find(s_opt, "prot"));
     201   if (p_opt) {"std in " + string(S);}
     202   intvec h = hilb(std(i),1);     //compute weighted hilbert series of i
     203
     204//------------- use hilbert driven std with original ordering  ------------
     205   setring R;                     //can access to lR only in R
     206   lR[2]=lS[2];
     207   lR[3]=insert(lR[3],list("dp",1),v[3]-1);
     208   //insert a last block for homogenizing variabble
     209
     210   def T = ring(lR);             //T = R with 1 homogenizing variable @t
     211   setring T;                    //added to last block with weight 1
     212   ideal i=fetch(S,i);           //homogenized i in T
     213
     214   if (p_opt) {"std with hilb in " + string(T);}
     215   ideal a=std(i,h,ww);           //use h from S and Hilbert driven std in T
     216
     217//-------------------- dehomogenize and simplify -------------------------
     218   a=subst(a,@t,1);              //dehomogenize in T (do not use map!)
     219   a=simplify(a,34);             //keep only a[j] with different leading terms
     220
     221//-------------------- back to original ring -------------------------
     222   setring R;
     223   ideal a = fetch(T,a);
     224   attrib(a,"isSB",1);
     225   return(a);
     226}
     227example
     228{ "EXAMPLE:"; echo = 2;
     229   ring  r=0,(x,y,z),(wp(43),wp(49,56));
     230   ideal i=y3+x2,x2y+x2,x3-x2,z4-x2-y;
     231   ideal i1=hilbstd(i); i1;
     232   // the latter computation is equivalent to:
     233   ring r1=0,(x,y,z),wp(43,49,56);
     234   ideal i = imap(r,i);
     235   intvec v=hilb(std(i),1);
     236   setring r;
     237   ideal i2 = hilbstd(i,v);
     238}
    140239//////////////////////////////////////////////////////////////////////////
     240
    141241proc groebner(def i, list #)
    142242"SYNTAX: @code{groebner (} ideal_expression @code{)} @*
    … …  
    220320            export groebner_error;
    221321          }
    222           "// ** groebner did not finish";
     322          "** groebner did not finish";
    223323          j = system("sh", "kill " + string(pid));
    224324        }
    … …  
    227327      else
    228328      {
    229         "// ** groebner needs int as 2nd arg";
     329        "** groebner needs int as 2nd arg";
    230330      }
    231331    }
    232332    else
    233333    {
    234       "// ** groebner with two args is not supported in this configuration";
     334      "** groebner with two args is not supported in this configuration";
    235335    }
    236336  }
    … …  
    238338  // we are still here -- do the actual computation
    239339  string ordstr_P = ordstr(P);
    240   if ((find(ordstr_P,"s") > 0)
     340  int nvarP = nvars(P);
     341  intvec w;                     //ringweights
     342  int neg,k;
     343  for(k=1;  k<=nvarP; k++)
     344  {
     345     w[k]=deg(var(k));
     346     if(w[k] <= 0) {neg=1;}
     347  }
     348  if ( ( find(ordstr_P,"s") > 0)
    241349  ||(find(ordstr_P,"M") > 0)
    242   ||(find(ordstr_P,"w") > 0)
    243   ||(find(ordstr_P,"W") > 0))
     350  ||(find(ordstr_P,"a") > 0)
     351  ||(neg>0) )
    244352  {
    245353    //spaeter den lokalen fall ueber lp oder aehnlich behandeln
    … …  
    256364     { return(slimgb(i)); }
    257365  }
    258   // for module case, not already handled by slimgb:
     366  // for module case, not already hadled by slimgb:
    259367  if (nrows(i)>1)
    260368  { return(std(i)); }
    … …  
    303411  list BRlist = ringlist(P);
    304412  int add_vars = 0;
    305   int nvarP = nvars(P);
    306   int k;
    307413  ideal Qideal = ideal(P);
    308414
    … …  
    341447  list ord_P = BRlist[3];   // should be ring independent
    342448
    343   // ordering is set to (dp, C)
    344   intvec weight_dp = 1;
    345   for (k=2; k<=nvarP+add_vars; k++) { weight_dp = weight_dp,1; }
     449  //ordering is set to (wp(w,1..1), C) where w are the ringweights
     450    intvec weight_wp = w;
     451  for(k=nvarP+1;  k<=nvarP+add_vars; k++)
     452  {
     453     weight_wp[k]=1;
     454  }
     455
    346456  BRlist[3] = list();
    347   BRlist[3][1]=list("dp",weight_dp);
     457  if(weight_wp==1)
     458  {
     459    BRlist[3][1]=list("dp",weight_wp);
     460  }
     461  else
     462  {
     463    BRlist[3][1]=list("wp",weight_wp);
     464  }
    348465  BRlist[3][2]=list("C",intvec(0));
    349466
    350   // change the ring
     467  //------------ change the ring
    351468  def Phelp = ring(BRlist);
    352469  kill BRlist;
    … …  
    374491  {
    375492    // no additional variables were introduced
    376     setring P; // can immediately change to original ring
    377     // simply compute std with hilbert series in original ring
     493    setring P;  // can immediately change to original ring
     494                // simply compute std with hilbert series in original ring
    378495    if (p_opt)
    379496    {
    380497      "std with hilb in basering";
    381498    }
    382     i = std(i, hi);
     499    if ( w==1 ) { i = std(i,hi); }
     500    else { i = std(i,hi,w); }
     501
    383502  }
    384503  else
    … …  
    388507    list BRlist = ringlist(Phelp);
    389508    BRlist[3] = list();
    390     for (k=1; k<=size(ord_P); k++)
     509    for (k=1; k<=size(ord_P)-1; k++)
    391510    {
    392511      BRlist[3][k] = ord_P[k];
    393512    }
    394513
    395     if ( IsSimple_P && (add_vars==1) && (size(ord_P)==2) && (ord_P[1][1]=="lp") )
     514    if( IsSimple_P && (add_vars==1) && (size(ord_P)==2) && (ord_P[1][1]=="lp"))
    396515    {
    397516      // for lp with at most one parameter, we do not need a block ordering
    398517      intvec OW = BRlist[3][1][2];
    399518      OW = OW,1;
    400       BRlist[3][1][2] = OW;
     519      BRlist[3][1][2] = OW; // extend block1 by 1
     520      BRlist[3][2]=ord_P[2]; // copy block 2
    401521    }
    402522    else
    403523    {
    404       if ( IsSimple_P && (add_vars==1) && (size(ord_P)==2) && (ord_P[2][1]=="lp") )
     524      if( IsSimple_P && (add_vars==1) && (size(ord_P)==2)&&(ord_P[2][1]=="lp"))
    405525      {
    406526        // for lp with at most one parameter, we do not need a block ordering
    407         intvec OW = BRlist[3][2][2];
     527        intvec OW = ord_P[2][2];
    408528        OW = OW,1;
    409         BRlist[3][2][2] = OW;
     529        BRlist[3][2]=ord_P[2];
     530        BRlist[3][2][2] = OW; // extend block 2 by 1
    410531      }
    411532      else
    … …  
    413534        intvec OW = 1;
    414535        for (k=2; k<=add_vars; k++) { OW = OW,1; }
    415         BRlist[3][size(ord_P)+1] = list("dp",OW);
    416       }
    417     }
    418 
     536        BRlist[3][size(ord_P)] = list("dp",OW);
     537        BRlist[3][size(BRlist[3])+1]=ord_P[size(ord_P)];
     538      }
     539    }
    419540    // change to intermediate ring
    420541    def Phelp1 = ring(BRlist);
    … …  
    425546    if (p_opt)
    426547    {
    427       "std with hilb in " + string(Phelp1);
     548      "std with hilb in " + string(Phelp1);;
    428549    }
    429550    // compute std with Hilbert series
    430     qh = std(qh, hi);
     551    if (weight_wp==1) { qh = std(qh, hi);}
     552    else { qh = std(qh, hi, weight_wp);}
     553
    431554    // subst 1 for homogenizing var
    432555    if (!is_homog)
    … …  
    469592}
    470593example
    471 { "EXAMPLE: "; echo=2;
     594{ "EXAMPLE: "; echo=2; // LIB "./standard.lib";
    472595  ring r=0,(a,b,c,d),lp;
    473596  option(prot);
    … …  
    481604  defined(Standard::groebner_error);
    482605}
     606
     607//////////////////////////////////////////////////////////////////////////
    483608
    484609proc res(list #)

  • Tst/Long/groebner_l.res.gz.uu

    r88c2d0 rd939c1  
    11begin 640 groebner_l.res.gz
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    170170`
    171171end

  • Tst/Long/groebner_l.stat

    r88c2d0 rd939c1  
    1 1 >> tst_memory_0 :: 1127844194:2005092711:3-0-0:ix86-Linux:nepomuck:1137640
    2 1 >> tst_memory_1 :: 1127844194:2005092711:3-0-0:ix86-Linux:nepomuck:2906900
    3 1 >> tst_memory_2 :: 1127844194:2005092711:3-0-0:ix86-Linux:nepomuck:2947860
    4 1 >> tst_timer_1 :: 1127844194:2005092711:3-0-0:ix86-Linux:nepomuck:100735
     11 >> tst_memory_0 :: 1163408412:2006111019:3-0-2:ix86-Linux:nepomuck:16009132
     21 >> tst_memory_1 :: 1163408412:2006111019:3-0-2:ix86-Linux:nepomuck:18049532
     31 >> tst_memory_2 :: 1163408412:2006111019:3-0-2:ix86-Linux:nepomuck:18168316
     41 >> tst_timer_1 :: 1163408412:2006111019:3-0-2:ix86-Linux:nepomuck:100470

  • Tst/Old/m141si.res.gz.uu

    r88c2d0 rd939c1  
    11begin 640 m141si.res.gz
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    4 MHXN!5IUN8_%X`#P6NE4XXR.+R1A*A]`'*04TPN4`:^3?YK/.^1RF4[!8H21#
    5 MIH:<"U,5MNKQI71<R5KI:ZXA57I=;?=8&K1>:=%Y^6>WYZN"T'`2M(N@38-V
    6 M%;1+__ZM[8\FO2Z@9,`=D.J&7S9>R8YWC@ONW$Z2PB'S?_'5SP=E47HB]P-Q
    7 K7XY1Q\(UXE98??Y$=Z?TPQI>MQL0_8B9HE)DXZPXF60WT3=5TG]1JP(`````
     2M'XL("&T\6$4``VTQ-#%S:2YR97,`?=(]:\,P$`;@W;_B$!V<4)(Z3EJH:8;0
     3M);1T<?=@H[-]5%9<Z4S2?U^K'S$DBA8-[_,>`NGR]^?M&P`DZ^$@S4!/:1;E
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     8#`@``
    89`
    910end

  • Tst/Old/m141si.stat

    r88c2d0 rd939c1  
    1 1 >> tst_memory_0 :: 1130766917:2005103113:3-0-1:ix86-Linux:nepomuck:166400
    2 1 >> tst_memory_1 :: 1130766917:2005103113:3-0-1:ix86-Linux:nepomuck:724724
    3 1 >> tst_memory_2 :: 1130766917:2005103113:3-0-1:ix86-Linux:nepomuck:724724
    4 1 >> tst_timer_1 :: 1130766917:2005103113:3-0-1:ix86-Linux:nepomuck:5
     11 >> tst_memory_0 :: 1163410541:2006111019:3-0-2:ix86-Linux:nepomuck:173848
     21 >> tst_memory_1 :: 1163410541:2006111019:3-0-2:ix86-Linux:nepomuck:723452
     31 >> tst_memory_2 :: 1163410541:2006111019:3-0-2:ix86-Linux:nepomuck:723452
     41 >> tst_timer_1 :: 1163410541:2006111019:3-0-2:ix86-Linux:nepomuck:5

  • Tst/Old/m24si.res.gz.uu

    r88c2d0 rd939c1  
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    168168`
    169169end

  • Tst/Old/m24si.stat

    r88c2d0 rd939c1  
    1 1 >> tst_memory_0 :: 1130766934:2005103113:3-0-1:ix86-Linux:nepomuck:307728
    2 1 >> tst_memory_1 :: 1130766934:2005103113:3-0-1:ix86-Linux:nepomuck:847604
    3 1 >> tst_memory_2 :: 1130766934:2005103113:3-0-1:ix86-Linux:nepomuck:847604
    4 1 >> tst_timer_1 :: 1130766934:2005103113:3-0-1:ix86-Linux:nepomuck:16
     11 >> tst_memory_0 :: 1163410522:2006111019:3-0-2:ix86-Linux:nepomuck:311168
     21 >> tst_memory_1 :: 1163410522:2006111019:3-0-2:ix86-Linux:nepomuck:846332
     31 >> tst_memory_2 :: 1163410522:2006111019:3-0-2:ix86-Linux:nepomuck:846332
     41 >> tst_timer_1 :: 1163410522:2006111019:3-0-2:ix86-Linux:nepomuck:17

  • Tst/Old/m96si.res.gz.uu

    r88c2d0 rd939c1  
    11begin 640 m96si.res.gz
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    3 M2Q=G$R786'($BNQ(-Y2^?:^18M>+T?FP\=$I3^_'+\88W]-#6V2:[=BV@#)Z
    4 M,KC3MF5NPG3`OC._3$V8#6BKJ_3+50&"?[_!\"F())PTB#2<T./98X5W?U;:
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     2M'XL("$,\6$4``VTY-G-I+G)E<P!5T$%K@S`8!N![?D4H.[27L43MVLEZ*+N4
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     8%8NH!````
    89`
    910end

  • Tst/Old/m96si.stat

    r88c2d0 rd939c1  
    1 1 >> tst_memory_0 :: 1130766844:2005103113:3-0-1:ix86-Linux:nepomuck:280540
    2 1 >> tst_memory_1 :: 1130766844:2005103113:3-0-1:ix86-Linux:nepomuck:818932
    3 1 >> tst_memory_2 :: 1130766844:2005103113:3-0-1:ix86-Linux:nepomuck:818932
    4 1 >> tst_timer_1 :: 1130766844:2005103113:3-0-1:ix86-Linux:nepomuck:2
     11 >> tst_memory_0 :: 1163410499:2006111019:3-0-2:ix86-Linux:nepomuck:284076
     21 >> tst_memory_1 :: 1163410499:2006111019:3-0-2:ix86-Linux:nepomuck:817660
     31 >> tst_memory_2 :: 1163410499:2006111019:3-0-2:ix86-Linux:nepomuck:817660
     41 >> tst_timer_1 :: 1163410499:2006111019:3-0-2:ix86-Linux:nepomuck:3

  • Tst/Old/proc.res.gz.uu

    r88c2d0 rd939c1  
    11begin 640 proc.res.gz
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     15/5/Z9/)_\!\_D4$\($```
    1616`
    1717end

  • Tst/Old/proc.stat

    r88c2d0 rd939c1  
    1 1 >> tst_memory_0 :: 1130766831:2005103113:3-0-1:ix86-Linux:nepomuck:151572
    2 1 >> tst_memory_1 :: 1130766831:2005103113:3-0-1:ix86-Linux:nepomuck:708340
    3 1 >> tst_memory_2 :: 1130766831:2005103113:3-0-1:ix86-Linux:nepomuck:708340
    4 1 >> tst_timer_1 :: 1130766831:2005103113:3-0-1:ix86-Linux:nepomuck:1
     11 >> tst_memory_0 :: 1163410477:2006111019:3-0-2:ix86-Linux:nepomuck:156072
     21 >> tst_memory_1 :: 1163410477:2006111019:3-0-2:ix86-Linux:nepomuck:707068
     31 >> tst_memory_2 :: 1163410477:2006111019:3-0-2:ix86-Linux:nepomuck:707068
     41 >> tst_timer_1 :: 1163410477:2006111019:3-0-2:ix86-Linux:nepomuck:2

  • Tst/Short/bug_43.res.gz.uu

    r88c2d0 rd939c1  
    11begin 640 bug_43.res.gz
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    2320`
    2421end

  • Tst/Short/bug_43.stat

    r88c2d0 rd939c1  
    1 1 >> tst_memory_0 :: 1158855053:2006082119:3-0-2:ix86-Linux:nepomuck:169644
    2 1 >> tst_memory_1 :: 1158855053:2006082119:3-0-2:ix86-Linux:nepomuck:706268
    3 1 >> tst_memory_2 :: 1158855053:2006082119:3-0-2:ix86-Linux:nepomuck:706268
    4 1 >> tst_timer_1 :: 1158855053:2006082119:3-0-2:ix86-Linux:nepomuck:5
     11 >> tst_memory_0 :: 1163410370:2006111019:3-0-2:ix86-Linux:nepomuck:174004
     21 >> tst_memory_1 :: 1163410370:2006111019:3-0-2:ix86-Linux:nepomuck:707068
     31 >> tst_memory_2 :: 1163410370:2006111019:3-0-2:ix86-Linux:nepomuck:707068
     41 >> tst_timer_1 :: 1163410370:2006111019:3-0-2:ix86-Linux:nepomuck:3
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