singular-data 4.0.3+ds-1 / usr / share / singular / LIB / resgraph.lib

////////////////////////////////////////////////////////////////////////////
version="version resgraph.lib 4.0.0.0 Jun_2013 "; // $Id: c9ad90e46bae6ab8da94f0274c0d903107549129 $
category="Visualization";
info="
LIBRARY:  resgraph.lib            Visualization of Resolution Data

AUTHOR: A. Fruehbis-Krueger,  anne@mathematik.uni-kl.de,

NOTE: This library uses the external programs surf, graphviz and imagemagick.
@*    Input data is assumed to originate from resolve.lib and reszeta.lib

PROCEDURES:
InterDiv(M[,name])   dual graph of resolution of a surface (uses graphviz,imagemagick)
ResTree(L,M[,name])  tree of charts of resolution (uses graphviz,imagemagick)
finalCharts(L,...)   pictures of final charts of surface (uses surf)
";

proc InterDiv(intmat M, list #)
"USAGE:  InterDiv(M[,name]);
@*       M = matrix
@*       name = string
ASSUME:  - M is first list entry of output of 'intersectionDiv'
@*         from library reszeta.lib
@*       - write permission in the current directory or in the
@*         directory in which the file with name 'name' resides
CREATE:  file 'name.jpg' containing dual graph of resolution
@*       if filename is given
NOTE:    only available on UNIX-type systems and programs
@*       'display' (imagemagick package) and 'dot' (Graphviz package) need to
@*       be in the standard search PATH
RETURN:  nothing, only generating graphics output in separate window
EXAMPLE: not available (for technical reasons)
"
{
  "Warning: alpha testing version of this procedure";
  int i,j;
  string tempstr;
//---------------------------------------------------------------------------
//  build up temporary filename and open file for writing
//---------------------------------------------------------------------------
  if(size(#)>0)
  {
     if((typeof(#[1])=="string") && (goodFilename(#[1])))
     {
        string @filename=#[1];
     }
     else
     {
        ERROR("Second argument should specify a WRITABLE file");
     }
  }
  if(!defined(@filename))
  {
     string @filename=buildFilename("InterDiv.dot");
  }
  link eing=":w "+@filename;
//--------------------------------------------------------------------------
// write input for external program dot to file
//--------------------------------------------------------------------------
  write(eing,"graph G{");
  for(i=1;i<=ncols(M);i++)
  {
     if(M[i,i]!=-2)
     {
        tempstr=string(i)+"[shape=circle,label=\""+string(M[i,i])+"\"];";
     }
     else
     {
        tempstr=string(i)+"[shape=point,label=\" \"];";
     }
     write(eing,tempstr);
  }
  for(i=1;i<=nrows(M);i++)
  {
     for(j=i+1;j<=ncols(M);j++)
     {
        if(M[i,j]!=0)
        {
           tempstr=string(i) + "--" + string(j) + ";";
           write(eing,tempstr);
        }
     }
  }
  write(eing,"}");
  close(eing);
//---------------------------------------------------------------------------
// produce graphics output using the programs dot and display
//---------------------------------------------------------------------------
  string outfile=@filename + ".jpg";
  if(!find(outfile,"/"))
  {
//--- display needs fully qualified path to file
     outfile=system("getenv","PWD") + "/" + outfile;
  }
  j=system("sh","dot -Tjpg " + @filename + " -o "+ outfile);
  j=system("sh","display " + outfile + " &");
//---------------------------------------------------------------------------
// clean up if necessary
//---------------------------------------------------------------------------
  "Currently showing graphics in separate window";
  "Press <Return> to continue";
  pause();
  if((size(#)==0)&&(find(@filename,"/tmp/")))
  {
//--- do not leave any garbage in the public directories
    j=system("sh","command rm " + outfile + " " + @filename);
  }
  return();
}
///////////////////////////////////////////////////////////////////////////////
//static
proc goodFilename(string datei)
{
//--- check whether the specified file datei is writable for us
  if(!system("sh","touch " + datei + " > /dev/null 2>&1"))
  {
     return(1);
  }
  else
  {
     return(0);
  }
}
//////////////////////////////////////////////////////////////////////////////
//static
proc buildFilename(string datei)
{
  if(goodFilename(datei))
  {
     return(datei);
  }
  if(find(datei,"/"))
  {
     ERROR("Specified directory/file is not writable");
  }
  datei="/tmp/" + datei;
  if(goodFilename(datei))
  {
     return(datei);
  }
//--- not reached
  ERROR("At least /tmp should be writable");
}
///////////////////////////////////////////////////////////////////////////////

proc ResTree(list re, intmat DivMat, list #)
"USAGE:  ResTree(L,M[,name][,mark]);
@*       L = list
@*       M = matrix
@*       name = string
@*       mark = intvec
ASSUME:  - L is the output of 'resolve' from resolve.lib
@*       - M is first entry of output of 'collectDiv(L);' from reszeta.lib
@*       - write permission in the current directory or in the
@*         directory in which the file with name 'name' resides
@*       - mark intvec of size size(L[2])
@*            mark[i]=0 (default) border of box black
@*            mark[i]=1 border of box red
CREATE:  file 'name.jpg' containing the tree of charts of L
@*       if filename is given
NOTE:    only available on UNIX-type systems and programs
@*       'display' (imagemagick package) and 'dot' (Graphviz package) need to
@*       be in the standard search PATH
RETURN:  nothing, only generating graphics output in separate window
EXAMPLE: not available (for technical reasons)
"
{
//-----------------------------------------------------------------------------
// Initialization and definition of the temporary filename
//-----------------------------------------------------------------------------
  int i,j,dimC,jsave;
  string tempstr;
  def R=basering;
  if(size(#)>0)
  {
     if(typeof(#[1])=="string")
     {
        if(goodFilename(#[1]))
        {
           string @filename=#[1];
        }
        else
        {
           ERROR("optional argument of type string "+
                  "should specify a writable file.");
        }
     }
     if(typeof(#[1])=="intvec")
     {
        intvec @rot=#[1];
     }
  }
  if(size(#)>1)
  {
     if((typeof(#[2])=="string")&&(!defined(@filename)))
     {
        if(goodFilename(#[1]))
        {
           string @filename=#[1];
        }
        else
        {
           ERROR("optional argument of type string "+
                  "should specify a writable file.");
        }
     }
     if((typeof(#[2])=="intvec")&&(!defined(@rot)))
     {
        intvec @rot=#[2];
     }
  }
  if(!defined(@filename))
  {
     string @filename=buildFilename("ResTree.dot");
  }
  if(!defined(@rot))
  {
     intvec @rot;
     @rot[size(re[2])]=0;
  }
  link eing=":w "+@filename;
//----------------------------------------------------------------------------
// writing the input to the program dot into a file
//----------------------------------------------------------------------------
  write(eing,"graph G{");
  tempstr="1[shape=box,label=\"chart 1\"];";
  write(eing,tempstr);
  for(i=2;i<=size(re[2]);i++)
  {
     tempstr=string(i)+"[shape=box,label=\"chart " + string(i)
            + "\\nE:"+string(simplify(ideal(DivMat[i,1..ncols(DivMat)]),2))
            + " \"";
     if(@rot[i]==1)
     {
        tempstr=tempstr + "color=\"red\"];";
     }
     else
     {
        tempstr=tempstr + "];";
     }
     write(eing,tempstr);
  }
  for(i=2;i<=size(re[2]);i++)
  {
     def S=re[2][i];
     setring S;
     j=int(leadcoef(path[1,ncols(path)]));
     if(j!=jsave)
     {
        def T=re[2][j];
        setring T;
        dimC=dim(std(BO[1]+cent));
        setring S;
        kill T;
     }
     setring R;
     kill S;
     if(j!=jsave)
     {
        tempstr=string(j) + "--" + string(i) +"[label=\"d=" + string(dimC)
               + "\"];";
        jsave=j;
     }
     else
     {
       tempstr=string(j) + "--" + string(i) +";";
     }
     write(eing,tempstr);
  }
  write(eing,"}");
  close(eing);
//---------------------------------------------------------------------------
// Create the graphics output using the programs dot and display
//---------------------------------------------------------------------------
  string outfile=@filename + ".jpg";
  if(!find(outfile,"/"))
  {
//--- display needs fully qualified path to file
     outfile=system("getenv","PWD") + "/" + outfile;
  }
  j=system("sh", "dot -Tjpg " + @filename + " -o "+ outfile);
  j=system("sh","display " + outfile + "&");
//---------------------------------------------------------------------------
// Clean up public directories if necessary
//---------------------------------------------------------------------------
  "Currently showing graphics in separate window";
  "Press <Return> to continue";
  pause();
  if(find(@filename,"/tmp/"))
  {
//--- do not leave any garbage in the public directories
    j=system("sh","command rm " + @filename + ".jpg "+ @filename);
  }
  return();
}
/////////////////////////////////////////////////////////////////////////////

proc finalCharts(list re, list inter, intvec endiv, list #)
"USAGE:  finalCharts(L1,L2,iv[,name]);
@*       L1 = list
@*       L2 = list
@*       iv = intvec
@*       name = string
ASSUME:  - L1 is the output of 'resolve' from resolve.lib
@*       - L2 is the output of 'intersectionDiv(L1)' from reszeta.lib
@*       - iv is the first entry of the output of 'abstractR(L1)'
@*       - write permission in the current directory or in the
@*         directory in which the file with name 'name' resides
CREATE:  - new windows in which surf-images of the final charts are presented
@*       - several '.ras' files in the directory in which 'name' resides
NOTE:    only available on UNIX-type systems
@*       external programs 'surf' and 'display' (imagemagick package) need to be
@*       in the standard search PATH
RETURN:  nothing, only generating graphics output in separate window
EXAMPLE: not available (for technical reasons)
"
{
//-----------------------------------------------------------------------------
// Initialization and Sanity Checks
//-----------------------------------------------------------------------------
  int i,j,k,a,b,cnt,whichE,offset,haveDcE8;
  def R=basering;
  list endCharts;
  string fname,tempstr;
  for(i=1;i<=size(endiv);i++)
  {
    if(endiv[i]==1)
    {
       endCharts[size(endCharts)+1]=i;
//--- Sanity checks for the chart i
       if(nvars(re[2][i])!=3)
       {
          ERROR("This chart is not embedded in 3-dimensional space");
       }
       if(defined(S)){kill S;}
       def S=re[2][i];
       setring S;
       if(dim(std(BO[1]+BO[2]))!=2)
       {
          ERROR("Strict Transform is not a surface");
       }
       if(size(equidim(BO[1]+BO[2]))!=1)
       {
          ERROR("Strict Transform has lower dimensional components.");
       }
//--- put the missing information into dcE, if necessary
       for(k=1;k<=size(dcE);k++)
       {
          for(j=1;j<=size(dcE[k]);j++)
          {
             if(deg(std(dcE[k][j][1])[1])!=0)
             {
                if(size(dcE[k][j][1]) < 8)
                {
                   setring R;
                   k=prepareDcE(re,inter,endiv);
                   setring S;
                }
                haveDcE8=1;
                break;
             }
          }
          if(haveDcE8!=0) break;
       }
       setring R;
    }
  }
  if(!defined(colorlist))
  {
     list colorlist;
     for(i=1;i<=10;i++)
     {
       colorlist[i]="curve_red = "+string((i-1)*25)+"; curve_green = "+
                     string(255-(i-1)*25)+"; curve_blue = "+
                     string(((i-1) mod 5)*50)+";";
     }
  }
  else
  {
     "Warning!";
     "Using colors specified in variable colorlist. No syntax checks";
     "performed on the content of this list.";
     "If built-in colors should be used, please rename the global";
     "object colorlist";
  }
  if(ncols(inter[1])>size(colorlist))
  {
    ERROR("Too many exceptional curves on this surface.....");
  }
  if((size(endCharts)>20)&&(size(#)==0))
  {
    ERROR("More than 20 final charts...");
  }
//-----------------------------------------------------------------------------
// Determine the basename of the temporary files
//-----------------------------------------------------------------------------
  if(size(#)>0)
  {
     if((typeof(#[1])=="string") && (goodFilename(#[1])))
     {
        string fnamebase=#[1];
     }
     else
     {
        ERROR("Second argument should specify a WRITABLE file");
     }
  }
  if(!defined(@fnamebase))
  {
     string fnamebase=buildFilename("Chart");
  }
//-----------------------------------------------------------------------------
// Go through all final charts and write a separate surf input file for each
//-----------------------------------------------------------------------------
  for(i=1;i<=size(endCharts);i++)
  {
     fname=fnamebase + string(endCharts[i]) + ".surf";
     if(defined(eing)){kill eing;}
     link eing=":w "+fname;
//--- define surf's root finding algorithm
     tempstr="root_finder = d_chain_bisection; epsilon = 0.000000001;";
     write(eing,tempstr);
//--- define image size
     tempstr="int wid = 480;width = wid; height = wid;";
     write(eing,tempstr);
//--- define ambient lighting
     tempstr="ambient=50;";
     write(eing,tempstr);
//--- define background colour: some shade of gray
     tempstr="background_red=200; background_green=200; background_blue=200;";
     write(eing,tempstr);
//--- define surface colour (one side):
     tempstr="surface_red=22; surface_green=150; surface_blue=255;";
     write(eing,tempstr);
//--- define surface colour (other side):
     tempstr="inside_red=255; inside_green=192; inside_blue=0;";
     write(eing,tempstr);
//--- define scaling factor
     tempstr="scale_x=0.5; scale_y=0.5; scale_z=0.5;";
     write(eing,tempstr);
//--- rotate a little bit
     tempstr="rot_y=0.9013941717697173; rot_x=-0.5556596516994916; rot_z=0.103062920202253447;";
     write(eing,tempstr);
//----------------------------------------------------------------------------
// change to the chart and extract the equation of the surface
// then draw the surface
//----------------------------------------------------------------------------
     if(defined(S)){kill S;}
     def S=re[2][endCharts[i]];
     setring S;
//--- define equation of strict transform (hypersurface of dim 2)
     ideal drawJ=simplify(mstd(radical(BO[1]+BO[2]))[2],2);
     if(size(drawJ)>1)
     {
//!!! unnoetig! Da kann man auch surface2,... machen
        ERROR("Did not find generator of principal ideal " + string(drawJ));
     }
     tempstr="poly f = " + map2Surf(string(drawJ[1])) + ";";
     write(eing,tempstr);
     tempstr="surface = f;draw_surface;";
     write(eing,tempstr);
//----------------------------------------------------------------------------
// now consider all exceptional curves in this chart separately
// and draw them
//---------------------------------------------------------------------------
     if(!defined(dcE))
     {
//--- Oups, exceptional curves not yet decomposed in this chart
//--- should not happen in practice
        ERROR("The procedure intersectionDiv has not been used
               on this tree of charts");
     }
     for(j=1;j<=size(dcE);j++)
     {
//--- Run through all exceptional divisors (in the embedded sense)
        for(k=1;k<=size(dcE[j]);k++)
        {
//--- Run through all curves corresponding to the current divisor
           if(deg(std(dcE[j][k][1])[1])==0)
           {
//--- This one is empty - skip it
              k++;
              if(k>size(dcE[j])) {break;}
              continue;
           }
           for(a=1;a<=size(inter[3]);a++)
           {
//--- this curve belongs to which (Q-irred.) divisor in global numbering?
              if(inIVList(intvec(endCharts[i],j,k),inter[3][a])) break;
           }
           if(a>size(inter[3]))
           {
//--- curve not found in list
              ERROR("Inconsistency between data of arguments 1 and 2");
           }
           whichE=a;
           offset=0;
           for(a=1;a<whichE;a++)
           {
//--- count C-irred. divisors up to this (Q-irred. divisor) index
              offset=offset+inter[4][a];
           }
           for(a=1;a<=size(dcE[j][k][7]);a++)
           {
//--- run through all C-irred divisors corresponding to this Q-irred. one
//--- run through all generators of the ideal of the curve
//--- unfortunately the ideal is encoded in a string,
//--- and we need to work to find the generators
              int tempint=find(dcE[j][k][6],",");
              b=0;
              cnt=1;
              while(tempint!=0)
              {
                if(!find(dcE[j][k][7][a],"i"))
                {
//--- 1) surf can only handle real numbers ==> we ignore the other curves
//--- 2) we can only form substrings of named strings:
                  tempstr=dcE[j][k][6];            // give it a name
                  tempstr=tempstr[b+1..tempint-1]; // find correct substring
                  tempstr="poly f" + string(offset+dcE[j][k][8][a])+ "_" +
                       string(b+1) + " = " +
                       map2Surf(plugInNumZero(tempstr,dcE[j][k][7][a])) + ";";
                  write(eing,tempstr);
                  tempstr="cutsurface" + string(cnt) + " = f" +
                       string(offset+dcE[j][k][8][a]) + "_" +string(b+1) + ";";
                  write(eing,tempstr);
                  cnt++;
                }
                b=tempint;                          // save end-mark
                tempint=find(dcE[j][k][6],",",b+1); // next one please
              }
              if(!find(dcE[j][k][7][a],"i"))
              {
                tempstr=dcE[j][k][6];                 // as before, but for last
                tempstr=tempstr[b+1..size(tempstr)];  // fragment
                tempstr="poly f" + string(offset+dcE[j][k][8][a])+ "_" +
                       string(b+1) + " = " +
                       map2Surf(plugInNumZero(tempstr,dcE[j][k][7][a])) + ";";
                write(eing,tempstr);
                tempstr="cutsurface" + string(cnt)+ " = f" +
                       string(offset+dcE[j][k][8][a]) + "_" +string(b+1) + ";";
                write(eing,tempstr);
                cnt++;
              }
//--- draw the curve on the surface
              if(cnt>1)
              {
                 tempstr=colorlist[offset+dcE[j][k][8][a]];
                 write(eing,tempstr);
                 write(eing,"cut_with_surface;");
              }
              kill tempint;
           }
        }
     }
     if(!find(fnamebase,"/"))
     {
//--- display needs fully qualified path to file
         if(defined(outfile)) {kill outfile;}
         string outfile=system("getenv","PWD") + "/" + fnamebase;
     }
     if(!defined(outfile))
     {
       tempstr="filename = \"" + fnamebase + string(endCharts[i]) + ".ras\";";
     }
     else
     {
       tempstr="filename = \"" + outfile + string(endCharts[i]) + ".ras\";";
     }
     write(eing,tempstr);
     tempstr="color_file_format = sun;";
     write(eing,tempstr);
     tempstr="save_color_image;";
     write(eing,tempstr);
     close(eing);
     j=system("sh", "surf -n " + fnamebase +string(endCharts[i]) + ".surf");
     if(!defined(outfile))
     {
        j=system("sh","display " + fnamebase
                       + string(endCharts[i]) + ".ras &");
     }
     else
     {
        j=system("sh","display " + outfile
                       + string(endCharts[i]) + ".ras &");
        kill outfile;
     }
     "Currently showing graphics for chart "+string(endCharts[i])
                    +" in separate window";
     "Press <Return> to continue";
     pause();
  }
  return(0);
}
//////////////////////////////////////////////////////////////////////////////
// static
proc plugInNumZero(string f,string num)
{
  int i;
  string fStr=f;
  i=find(fStr,"t");
  while(i!=0)
  {
    fStr = string(fStr[1..i-1]) + "(" + num + ")"
         + string(fStr[i+1..size(fStr)]);
    i=find(fStr,"t");
  }
  return(fStr);
}
//////////////////////////////////////////////////////////////////////////////
// static
proc replaceInStr(string alles, string alt, string neu)
{
  int i=find(alles,alt);
  while(i!=0)
  {
    if((i-1)<1)
    {
       if(size(alt)==size(alles))
       {
          alles=neu;
       }
       else
       {
          alles=neu + string(alles[i+size(alt)..size(alles)]);
       }
    }
    else
    {
       if(i+size(alt)>size(alles))
       {
          alles=string(alles[1..i-1]) + neu;
       }
       else
       {
          alles=string(alles[1..i-1]) + neu +
                string(alles[i+size(alt)..size(alles)]);
       }
    }
    i=find(alles,alt);
  }
  return(alles);
}
/////////////////////////////////////////////////////////////////////////////
// static
proc map2Surf(string str)
{
  str=replaceInStr(str,string(var(1)),"x");
  str=replaceInStr(str,string(var(2)),"y");
  str=replaceInStr(str,string(var(3)),"z");
  return(str);
}
/////////////////////////////////////////////////////////////////////////////
// static
proc prepareDcE(list re, list inter, list endCharts)
{
   def R=basering;
//---Test whether we are in the irreducible surface case
   def S=re[2][1];
   setring S;
   BO[2]=BO[2]+BO[1];              // make sure we are living in the smooth W
   if(dim(std(BO[2]))!=2)
   {
     ERROR("The given original object is not a surface");
   }
   if(dim(std(slocus(BO[2])))>0)
   {
     ERROR("The given original object has non-isolated singularities.");
   }
   setring R;
//----------------------------------------------------------------------------
// Compute a non-embedded resolution from the given embedded one by
// dropping redundant trailing blow-ups
//----------------------------------------------------------------------------
//--- compute non-embedded resolution
   int ii,j,k,a,b,comPa;
   list abst=abstractR(re);
   intvec endiv=abst[1];
   intvec deleted=abst[2];
//--- identify the divisors in the various final charts
   list iden0=collectDiv(re,deleted)[2];
                                    // list of final divisors
//----------------------------------------------------------------------------
// For each Q-irred. divisor (specified in inter[3]), run through all
// occurrences and identify the different C-components
//----------------------------------------------------------------------------
   for(ii=1;ii<=size(inter[3]);ii++)
   {
//--- run through all Q-irred. curves,
//--- set up the first occurrence for reference
      if(defined(S)) {kill S;}
      def S=re[2][inter[3][ii][1][1]];
                                    // inter[3] = list of Q-irred div.
                                    // inter[3][ii] = ii-th thereof
                                    // inter[3][ii][1] = first occurrence
                                    // inter[3][ii][1][1] = corr. chart index
      setring S;
      dcE[inter[3][ii][1][2]][inter[3][ii][1][3]][8]=
              intvec(1..ncols(dcE[inter[3][ii][1][2]][inter[3][ii][1][3]][4]));
//--- prepare the ideal of the divisor for mapping to different chart
      if(defined(idlist1)){kill idlist1;}
      list idlist1;
      idlist1[1]=dcE[inter[3][ii][1][2]][inter[3][ii][1][3]][6];
      exportto(Top,idlist1);
      for(j=2;j<=size(inter[3][ii]);j++)
      {
//--- now do the comparison with the other occurrences
//--- 1. find a common parent for inter[3][ii][1][1] and inter[3][ii][j][1]
         if(defined(S)){kill S;}
         def S=re[2][inter[3][ii][j][1]];
         setring S;
         if(defined(opath)){kill opath;}
         def opath=imap(re[2][inter[3][ii][1][1]],path);
         k=1;
         while(opath[1,k]==path[1,k])
         {
            k++;
            if((k>ncols(opath))||(k>ncols(path))) break;
         }
         comPa=int(leadcoef(opath[1,k-1]));
//--- 2. use fetchInTree to transfer the C-components
         if(defined(str)) {kill str;}
         if(defined(il)) {kill il;}
         if(defined(mpi)) {kill mpi;}
         if(defined(nulli)) {kill nulli;}
         string str="idlist1";
         attrib(str,"algext",imap(re[2][inter[3][ii][1][1]],dcE)[inter[3][ii][1][2]][inter[3][ii][1][3]][5]);
         list il=fetchInTree(re,inter[3][ii][1][1],comPa,inter[3][ii][j][1],str,iden0,1);
         list nulli=imap(re[2][inter[3][ii][1][1]],dcE)[inter[3][ii][1][2]][inter[3][ii][1][3]][7];
         string mpi=imap(re[2][inter[3][ii][1][1]],dcE)[inter[3][ii][1][2]][inter[3][ii][1][3]][5];
         if(mpi!=dcE[inter[3][ii][j][2]][inter[3][ii][j][3]][5])
         {
            ERROR("Problem identifying the appropriate field extension.!");
         }
         if(defined(ringt)){kill ringt;}
         ring ringt=0,(t),dp;
         if(defined(St)){kill St;}
         def St=S+ringt;
         setring St;
         if(defined(strId)) {kill strId;}
         string strId="ideal id1=" + il[1] + ";";
         execute(strId);
         id1=std(id1);
         strId="ideal idj="
                         + imap(S,dcE)[inter[3][ii][j][2]][inter[3][ii][j][3]][6]
                         +  ";";
         execute(strId);
         idj=std(idj);
         if(defined(nullj)){kill nullj;}
         list nullj=imap(S,dcE)[inter[3][ii][1][2]][inter[3][ii][1][3]][7];
         if(defined(rcomp)){kill rcomp;}
         strId="ring rcomp=complex,(" +varstr(basering) +"),(" +
                           ordstr(basering) + ");";
         execute(strId);
         def id1=imap(St,id1);
         def idj=imap(St,idj);
         ideal id10,idj0;
         if(defined(tintvec)){kill tintvec;}
         intvec tintvec;
         tintvec[size(nullj)]=0;
         for(a=1;a<=size(nullj);a++)
         {
            if(defined(numa)) {kill numa;}
            strId="number numa=" + string(nullj[a]) + ";";
            execute(strId);
            idj0=subst(idj,t,numa);
            for(b=1;b<=size(nulli);b++)
            {
               if(defined(numb)) {kill numb;}
               strId="number numb=" + string(nulli[b]) + ";";
               execute(strId);
               id10=subst(id1,t,numb);
               attrib(id10,"isSB",1);
               if(size(reduce(idj0,id10))==0)
               {
                  tintvec[a]=b;
                  break;
               }
            }
            if(!find(string(tintvec),string(b)))
            {
~;
               ERROR("Problem identifying C-components in different charts.");
            }
         }
         setring S;
         dcE[inter[3][ii][1][2]][inter[3][ii][1][3]][8]=tintvec;
      }
   }
   return(0);
}