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

//////////////////////////////////////////////////////////////////////////////
version="version inout.lib 4.0.0.0 Jun_2013 "; // $Id: f30ec30553869bbe596da3bd3649a0494e59cc09 $
category="General purpose";
info="
LIBRARY:  inout.lib     Printing and Manipulating In- and Output

PROCEDURES:
 allprint(list);        print list if ALLprint is defined, with pause if >0
 lprint(poly/...[,n]);  display poly/... fitting to pagewidth [size n]
 pmat(matrix[,n]);      print form-matrix [first n chars of each colum]
 rMacaulay(string);     read Macaulay_1 output and return its @sc{Singular} format
 show(any);             display any object in a compact format
 showrecursive(id,p);   display id recursively with respect to variables in p
 split(string,n);       split given string into lines of length n
 tab(n);                string of n space tabs
 pause([prompt]);       stop the computation until user input
           (parameters in square brackets [] are optional)
";

///////////////////////////////////////////////////////////////////////////////

proc allprint (list #)
"USAGE:   allprint(L);  L list
DISPLAY: prints L[1], L[2], ... if an integer with name ALLprint is defined.
@*       makes \"pause\",   if ALLprint > 0
RETURN:  no return value
EXAMPLE: example allprint; shows an example
"
{
   if( defined(ALLprint) )
   {
      int i;
      for( i=1; i<=size(#); i=i+1 ) { print(#[i]); }
      if( ALLprint >0 ) { pause(); }
   }
   return();
}
example
{ "EXAMPLE:"; echo = 2;
   ring S;
   matrix M=matrix(freemodule(2),3,3);
   int ALLprint; export ALLprint;
   allprint("M =",M);
   kill ALLprint;
}
///////////////////////////////////////////////////////////////////////////////

proc lprint
"USAGE:   lprint(id[,n]);  id poly/ideal/vector/module/matrix, n integer
RETURN:  string of id in a format fitting into lines of size n, such that no
         monomial gets destroyed, i.e. the new line starts with + or -;
         (default: n = pagewidth).
NOTE:    id is printed columnwise, each column separated by a blank line;
         hence lprint(transpose(id)); displays a matrix id in a format which
         can be used as input.
EXAMPLE: example lprint; shows an example
"
{
   if (size(#)==1) { int n = pagewidth-3; }
   else {int n = #[2]-3; }
   matrix M = matrix(#[1]);
   poly p,h,L; string s1,s,S; int jj,ii,a;
   for (jj=1; jj<=ncols(M); jj=jj+1)
   {
      for (ii=1; ii<=nrows(M); ii=ii+1)
      {
         a=2;
         if (a+size(string(M[ii,jj])) <= n) {s = "  "+string(M[ii,jj]);}
         else
         {
            h = lead(M[ii,jj]); p = M[ii,jj] - h; L = lead(p);
            while (p != 0)
            {
               if (a+size(string(h+L)) > n)
               {
                  s = string(h);
                  if (a != 0) { s = "  "+s; }
                  if (a == 0 and s[1] != "-") { s = "+" + s; }
                  a=0; h=0; S=S+newline+s;
               }
               h = h + L; p = p - L; L = lead(p);
            }
            s = string(h);
            if (a == 0 and s[1] != "-") { s = "+" + s; }
         }
         if (ii != nrows(M)) { s = s+","; S=S+newline+s; }
         else
         {
            if (jj != ncols(M)) { s = s+","; S=S+newline+s+newline;}
            else { S=S+newline+s; }
         }
      }
   }
   return(S[2,size(S)-1]);
}
example
{ "EXAMPLE:"; echo = 2;
   ring r= 0,(x,y,z),ds;
   poly f=((x+y)*(x-y)*(x+z)*(y+z)^2);
   lprint(f,40);
   module m = [f*(x-y)],[0,f*(x-y)];
   string s=lprint(m); s;"";
   execute("matrix M[2][2]="+s+";");      //use the string s as input
   module m1 = transpose(M);              //should be the same as m
   print(matrix(m)-matrix(m1));
}
///////////////////////////////////////////////////////////////////////////////

proc pmat (matrix m, list #)
"USAGE:   pmat(M[,n]);  M matrix, n integer
RETURN: A string representing M in array format if it fits into
        pagewidth; if n is given, only the first n characters of
        each column are shown (n>1 required), where a truncation
        of a column is indicated by two dots (\'..\')
EXAMPLE: example pmat; shows an example
"
{
//------------- main case: input is a matrix, no second argument---------------
   string OUT = "";
   if ( size(#)==0)
   {
      int elems,mlen,slen,c,r;
   //-------------- count maximal size of each column, and sum up -------------
      for ( c=1; c<=ncols(m); c=c+1)
      {  int len(c);
         for (r=1; r<=nrows(m); r=r+1)
         {
            elems = elems+1;
            string s(elems) = string(m[r,c])+",";
            slen = size(s(elems));
            if ( slen>len(c) ) { len(c) = slen; }
         }
         mlen = mlen+len(c);
      }
   //---------------------- print all - except last - rows --------------------
      string aus; string sep = " ";
      if (mlen >= pagewidth) { sep = newline; }
      for (r=1; r<nrows(m); r=r+1)
      {  elems = r; aus = "";
         for (c=1; c<=ncols(m); c=c+1)
         {
            aus = aus + s(elems)[1,len(c)] + sep;
            elems = elems + nrows(m);
         }
         OUT=OUT+aus+newline;
      }
   //--------------- print last row (no comma after last entry) ---------------
      aus = ""; elems = nrows(m);
      for (c=1; c<ncols(m); c=c+1)
      {
         aus = aus + s(elems)[1,len(c)] + sep;
         elems = elems + nrows(m);
      }
      aus = aus + string(m[nrows(m),ncols(m)]);
      OUT=OUT+aus;  return(OUT);
   }
//---------- second case: second argument is given and of type int ------------
   if ( typeof(#[1])=="int" and #[1]>1)
   {  string aus,tmp; int c,r;
   //---------------------- print all - except last - rows --------------------
      for ( r=1; r<nrows(m); r=r+1)
      {  aus = "";
         for (c=1; c<=ncols(m); c=c+1)
         {
            tmp=string(m[r,c]);
            if (size(tmp)>#[1])
            { tmp[#[1]-1]=".";
              tmp[#[1]]  =".";
              aus=aus+tmp[1,#[1]]+", ";
            }
            else
            { tmp=tmp+",";
              aus=aus+tmp[1,#[1]+1]+" ";
            }
         }
         OUT=OUT+aus+newline;
      }
   //--------------- print last row (no comma after last entry) ---------------
      aus = "";
      for (c=1; c<ncols(m); c=c+1)
      { tmp=string(m[r,c]);
        if (size(tmp)>#[1])
        { tmp[#[1]-1]=".";
          tmp[#[1]]  =".";
          aus=aus+tmp[1,#[1]]+", ";
        }
        else
        { tmp=tmp+",";
          aus=aus+tmp[1,#[1]+1]+" ";
        }
      }
      tmp=string(m[nrows(m),ncols(m)]);
      if (size(tmp)>#[1])
      { tmp[#[1]-1]=".";
        tmp[#[1]]  =".";
      }
      aus = aus + tmp[1,#[1]];
      OUT=OUT+aus;  return(OUT);
   }
}
example
{  "EXAMPLE:"; echo = 2;
   ring r=0,(x,y,z),ls;
   ideal i= x,z+3y,x+y,z;
   matrix m[3][3]=i^2;
   pmat(m);
   pmat(m,5);
}
///////////////////////////////////////////////////////////////////////////////

proc rMacaulay
"USAGE:   rMacaulay(s[,n]);  s string, n integer
RETURN:  A string denoting a file which should be readable by Singular
         and it should be produced by Macaulay Classic.
         If a second argument is present the first
         n lines of the file are deleted (which is useful if the file was
         produced e.g. by the putstd command of Macaulay).
NOTE:    This does not always work with 'cut and paste' since the character
         \ is treated differently
EXAMPLE: example rMacaulay; shows an example
"
{
   int n;
   if( size(#)==2 ) { n=#[2]; }
   string s0 = #[1];
//------------------------ delete first n=#[2] lines --------------------------
   int ii=find(s0,newline); int jj;
   for ( jj=1; jj<=n; jj=jj+1)
   {
      s0 = s0[ii+1,size(s0)-ii];
      ii = find(s0,newline);
   }
//--------------- delete blanks and 'newline' at start and end ----------------
   ii = 1;
   while( s0[ii]==" " or s0[ii]==newline ) { ii=ii+1; }
   s0 = s0[ii,size(s0)-ii+1]; ii = size(s0);
   while ( s0[ii]==" " or s0[ii]==newline) { ii=ii-1; }
   s0 = s0[1,ii];
//------------------------- make each line a string ---------------------------
   ii = find(s0,newline); jj=0; int kk;
   while( ii!=0 )
   {  jj = jj+1;  kk = ii+1;
      while( s0[kk]==" " or s0[kk]==newline ) {  kk=kk+1; }
      string s(jj) = s0[1,ii-1];
      s0 = s0[kk,size(s0)-kk+1];
      ii = find(s0,newline);
   }
   jj=jj+1;
   string s(jj) = s0;
//------------ delete blanks and \ at end of each string and add , ------------
   for( ii=1; ii<=jj; ii=ii+1 )
   {  kk = 1;
      while( s(ii)[kk]==" " ) { kk=kk+1; }
      s(ii) = s(ii)[kk,size(s(ii))-kk+1];
      kk = size(s(ii));
      while( s(ii)[kk]==" " or s(ii)[kk]=="\\" or s(ii)[kk]==newline )
         {  kk = kk-1; }
      s(ii) = s(ii)[1,kk]+","+newline;
   }
//------------------------ replace blanks by , and add up ---------------------
   int ll; s0 = ""; string s1,s2;
   for( ii=1; ii<=jj; ii=ii+1 )
   {
      s1 = ""; s2 = s(ii);
      kk = find(s(ii)," "); ll=kk+1;
      while( kk!=0 )
      {
         while( s2[ll]==" ") { ll=ll+1; }
         if( kk!=1 ) { s1=s1+s2[1,kk-1]+","+s2[kk+1,ll-kk]; }
         if( kk==1 ) { s1 = s1+","+s2[kk+1,ll-kk]; }
         s2 = s2[ll+1,size(s2)-ll];
         kk = find(s2," "); ll=kk+1;
      }
      s(ii) = s1+s2; s0 = s0+s(ii);
   }
//---------------------------- replace [] by () -------------------------------
   s1 = ""; s2 = s0;
   ii = find(s2,"[");
   while( ii!=0 )
   {
      s0 = s0[1,ii-1]+"("+s0[ii+1,size(s0)-ii];
      if( ii>2 )
      {
         if(s0[ii-2]!="+" and s0[ii-2]!="-" and s0[ii-2]!="," and s0[ii-2]!=newline)
         {
            s0 = s0[1,ii-2]+"*"+s0[ii-1,size(s0)-ii+2];
         }
      }
      ii = find(s0,"[");
   }
   jj = find(s0,"]");
   while ( jj!=0 )
   {
      s0 = s0[1,jj-1]+")"+s0[jj+1,size(s0)-jj];
      if(s0[jj+1]!="+"and s0[jj+1]!="-" and s0[jj+1]!="," and s0[jj+1]!="*")
         { s0 = s0[1,jj] + "^" + s0[jj+1,size(s0)-jj]; }
      jj = find(s0,"]");
   }
   s0 = s0[1,size(s0)-2];
   return(s0);
}
example
{  "EXAMPLE:"; echo = 2;
   // Assume there exists a file 'Macid' with the following ideal in
   // Macaulay format:"
   // x[0]3-101/74x[0]2x[1]+7371x[0]x[1]2-13/83x[1]3-x[0]2x[2] \
   //     -4/71x[0]x[1]x[2]
   // Read this file into Singular and assign it to the string s1 by:
   // string s1 = read("Macid");
   // This is equivalent to";
   string s1 =
   "x[0]3-101/74x[0]2x[1]+7371x[0]x[1]2-13/83x[1]3-x[0]2x[2]-4/71x[0]x[1]x[2]";
   rMacaulay(s1);
   // You may wish to assign s1 to a Singular ideal id:
   string sid = "ideal id =",rMacaulay(s1),";";
   ring r = 0,x(0..3),dp;
   execute(sid);
   id; "";
   // Now treat a matrix in Macaulay format. Using the execute
   // command, this could be assinged to a Singular matrix as above.
   string s2 = "
   0  0  0  0  0
   a3 0  0  0  0
   0  b3 0  0  0
   0  0  c3 0  0
   0  0  0  d3 0
   0  0  0  0  e3 ";
   rMacaulay(s2);
}

///////////////////////////////////////////////////////////////////////////////

proc show (def @@id, list #)
"USAGE:   show(id);   id any object of basering or of type ring/qring
@*       show(R,s);  R=ring, s=string (s = name of an object belonging to R)
DISPLAY: display id/s in a compact format together with some information
RETURN:  no return value
NOTE:    objects of type string, int, intvec, intmat belong to any ring.
         id may be a ring or a qring. In this case the minimal polynomial is
         displayed, and, for a qring, also the defining ideal.
         id may be of type list but the list must not contain a ring.
@*       show(R,s) does not work inside a procedure!
EXAMPLE: example show; shows an example
"
{
//------------- use funny names in order to avoid name conflicts --------------
   int @li@, @ii;
   string @s@,@@s;
   int @short@=short; short=1;
//----------------------------- check syntax ----------------------------------
   if( size(#)!= 0 )
   {
      if( typeof(#[1])=="int" ) { @li@=#[1]; }
   }
   if ( typeof(@@id)!="list" )
   {
      if( size(#)==0 )
      {
          def @id@ = @@id;
      }
      if( size(#)==1 )
      {
         if( typeof(#[1])=="int" )
         {
             def @id@ = @@id;
         }
         if( typeof(#[1])=="string" )
         {
            if( typeof(@@id)=="ring")
            {
               def @R@ = @@id;
               setring @R@;
               def @id@=`#[1]`;
            }
         }
      }
   }
//----------------------- case: @@id is of type list ----------------------------
   if ( typeof(@@id)=="list" )
   {
//      @@s = tab(@li@)+"// list, "+string(size(@@id))+" element(s):";
      @@s = tab((3*(voice-2)))+"// list, "+string(size(@@id))+" element(s):";
      @@s;
      for ( @ii=1; @ii<=size(@@id); @ii++ )
      {
         if( typeof(@@id[@ii])!="none" )
         {
            def @id(@ii) = @@id[@ii];
            tab(3*(voice-2))+"["+string(@ii)+"]:";
            //           show(@id(@ii),@li@+3*(voice-1));
            show(@id(@ii),3*(voice-1));
         }
         else
         {
            "["+string(@ii)+"]:";
            tab(@li@+2),"//",@@id[@ii];
         }
      }
      short=@short@; return();
    }
   if( defined(@id@)!=voice ) { "// wrong syntax, type help show;";  return();}
//-------------------- case: @id@ belongs to any ring -------------------------
   if( typeof(@id@)=="string" or typeof(@id@)=="int" or typeof(@id@)=="intvec"
       or typeof(@id@)=="intmat" or typeof(@id@)=="list" )
   {
      if( typeof(@id@)!="intmat" )
      {
         @@s = tab(@li@)+"// "+typeof(@id@)+", size "+string(size(@id@));
         @@s;
      }
      if( typeof(@id@)=="intmat" )
      {
         @@s = tab(@li@)+"// "+typeof(@id@)+", "+string(nrows(@id@))+" rows, "
               + string(ncols(@id@))+" columns";
         @@s;
      }
      @id@;
      short=@short@; return();
   }
//-------------------- case: @id@ belongs to basering -------------------------
   if( typeof(@id@)=="poly" or typeof(@id@)=="ideal" or typeof(@id@)=="matrix" )
   {
      @@s = tab(@li@)+"// "+ typeof(@id@);
      if( typeof(@id@)=="ideal" )
      {
         @@s=@@s + ", "+string(ncols(@id@))+" generator(s)";
         @@s;
         print(ideal(@id@));
      }
      if( typeof(@id@)=="poly" )
      {
         @@s=@@s + ", "+string(size(@id@))+" monomial(s)";
         @@s;
         print(poly(@id@));
      }
      if( typeof(@id@)=="matrix")
      {
         @@s=@@s + ", "+string(nrows(@id@))+"x"+string(ncols(@id@));
         @@s;
         print(matrix(@id@));
      }
      short=@short@; return();
   }
   if( typeof(@id@)=="vector" )
   {
      @@s = tab(@li@)+"// "+typeof(@id@);
      @@s;
      print(@id@);
      short=@short@; return();
   }
   if( typeof(@id@)=="module" )
   {
      @s@=", "+string(ncols(@id@))+" generator(s)";
      @@s = tab(@li@)+"// "+ typeof(@id@)+ @s@;
      @@s;
      int @n@;
      for( @n@=1; @n@<=ncols(@id@); @n@=@n@+1 ) { print(@id@[@n@]); }
      short=@short@; return();
   }
   if( typeof(@id@)=="number" or typeof(@id@)=="resolution" )
   {
      @@s = tab(@li@)+"// ", typeof(@id@);
      @@s;
      @id@; short=@short@; return();
   }
   if( typeof(@id@)=="map" )
   {
      def @map = @id@;
      @@s = tab(@li@)+"// i-th variable of preimage ring is mapped to @map[i]";
      @@s;
      if( size(#)==0 ) { type @map; }
      if( size(#)==1 )
      {
         if( typeof(#[1])=="int" )    { type @map; }
         if( typeof(#[1])=="string" ) { type `#[1]`; }
      }
      short=@short@; return();
   }
//---------------------- case: @id@ is a ring/qring ---------------------------
   if( typeof(@id@)=="ring" )
   {
      setring @id@;
      string s="("+charstr(@id@)+"),("+varstr(@id@)+"),("+ordstr(@id@)+");";
      if( typeof(@id@)=="ring" )
      {
         list na@me@s=names(@id@);
         @@s = tab(@li@)+"// ring:"; @@s,s;
         @@s = tab(@li@)+"// minpoly ="; @@s,minpoly;
         if (size(ideal(@id@))>0)
         {
           @@s = tab(@li@)+"// quotient ring from ideal:"; @@s;ideal(@id@);
         }
         kill @id@;
         "// objects belonging to this ring:";
         listvar(poly);listvar(ideal);
         listvar(vector);listvar(module);
         listvar(map);listvar(matrix);
         listvar(number);listvar(resolution);
         for(int names@i=1;names@i<=size(na@me@s);names@i++)
         {
           def @hi@lf@=`na@me@s[names@i]`;
           if ((typeof(@hi@lf@)!="poly") and
               (typeof(@hi@lf@)!="ideal") and
               (typeof(@hi@lf@)!="vector") and
               (typeof(@hi@lf@)!="module") and
               (typeof(@hi@lf@)!="map") and
               (typeof(@hi@lf@)!="matrix") and
               (typeof(@hi@lf@)!="number") and
               (typeof(@hi@lf@)!="resolution"))
           {
             listvar(`na@me@s[names@i]`);
           }
           kill @hi@lf@;
         }
      }
      short=@short@; //return();
   }
}
example
{  "EXAMPLE:"; echo = 2;
    ring r;
    show(r);
    ideal i=x^3+y^5-6*z^3,xy,x3-y2;
    show(i,3);            // introduce 3 space tabs before information
    vector v=x*gen(1)+y*gen(3);
    module m=v,2*v+gen(4);
    list L = i,v,m;
    show(L);
    ring S=(0,T),(a,b,c,d),ws(1,2,3,4);
    minpoly = T^2+1;
    ideal i=a2+b,c2+T^2*d2; i=std(i);
    qring Q=i;
    show(Q);
    map F=r,a2,b^2,3*c3;
    show(F);
// Apply 'show' to i (which does not belong to the basering) by typing
// ring r; ideal i=xy,x3-y2; ring Q; show(r,"i");
}
///////////////////////////////////////////////////////////////////////////////

proc showrecursive (def @@id,poly p,list #)
"USAGE:   showrecursive(id,p[,ord]); id any object of basering, p= product of
         variables and ord=string (any allowed ordstr)
DISPLAY: display 'id' in a recursive format as a polynomial in the variables
         occuring in p with coefficients in the remaining variables. This is
         done by mapping to a ring with parameters [and ordering 'ord',
         if a 3rd argument is present (default: ord=\"dp\")] and applying
         procedure 'show'
RETURN:  no return value
EXAMPLE: example showrecursive; shows an example
"
{
   def P = basering;
   int ii;
   string newchar = charstr(P);
   string neword = "dp";
   if( size(#) == 1 ) { neword = #[1]; }
   string newvar;
   for( ii=1; ii <= nvars(P); ii++ )
   {
      if( p/var(ii) == 0 )
      {
         newchar = newchar + ","+varstr(ii);
      }
      else
      {
         newvar = newvar + ","+varstr(ii);
      }
   }
   newvar = newvar[2,size(newvar)-1];

   execute("ring newP=("+newchar+"),("+newvar+"),("+neword+");");
   def @@id = imap(P,@@id);
   show(@@id);
   return();
}
example
{ "EXAMPLE:"; echo=2;
   ring r=2,(a,b,c,d,x,y),ds;
   poly f=y+ax2+bx3+cx2y2+dxy3;
   showrecursive(f,x);
   showrecursive(f,xy,"lp");
}
///////////////////////////////////////////////////////////////////////////////

proc split (string s, list #)
"USAGE:    split(s[,n]); s string, n integer
RETURN:   same string, split into lines of length n separated by \
          (default: n=pagewidth)
NOTE:     may be used in connection with lprint
EXAMPLE:  example split; shows an example
"
{
   string line,re; int p,l;
   if( size(#)==0 ) { int n=pagewidth; }
   else { int n=#[1]; }
   if( s[size(s),1] != newline ) { s=s+newline; }
   l=size(s);
   while( 1 )
   {
      p=1;
      l=find(s,newline); line=s[1,l];
      while( l>=n )
      {
         re=re+line[p,n-2]+"\\"+newline;
         p=p+n-2; l=l-n+2;
      }
      re=re+line[p,l-1]+"\\"+newline;
      l=size(line);
      if( l>=size(s) ) break;
      s=s[l+1,size(s)-l];
   }
   return (re[1,size(re)-2]);
}
example
{  "EXAMPLE:"; echo = 2;
   ring r= 0,(x,y,z),ds;
   poly f = (x+y+z)^4;
   split(string(f),50);
   split(lprint(f));
}
///////////////////////////////////////////////////////////////////////////////

proc tab (int n)
"USAGE:   tab(n);  n integer
RETURN:  string of n space tabs
EXAMPLE: example tab; shows an example
"
{
   if( n==0 ) { return(""); }
   string s=" ";
   return(s[1,n]);
}
example
{  "EXAMPLE:"; echo = 2;
   for(int n=0; n<=5; n=n+1)
   { tab(5-n)+"*"+tab(n)+"+"+tab(n)+"*"; }
}
///////////////////////////////////////////////////////////////////////////////

proc pause(list #)
"USAGE:    pause([ prompt ])  prompt string
RETURN:   none
PURPOSE:  interrupt the execution of commands, displays prompt or pause
          and waits for user input
NOTE:     pause is useful in procedures in connection with printlevel to
          interrupt the computation and to display intermediate results.
SEE ALSO: read, printlevel
EXAMPLE : example pause; shows an example
"
{
  string pr="pause>";
  if (size(#)!=0)
  {
    pr=#[1];
  }
  pr=read("",pr);
}
example
{ "EXAMPLE:"; echo=2;
  // can only be shown interactively, try the following commands:
  // pause("press <return> to continue");
  // pause();
  // In the following pocedure TTT, xxx is printed and the execution of
  // TTT is stopped until the return-key is pressed, if printlevel>0.
  // xxx may be any result of a previous computation or a comment, etc:
  //
  // proc TTT
  // { int pp = printlevel-voice+2;  //pp=0 if printlevel=0 and if TTT is
  //    ....                         //not called from another procedure
  //    if( pp>0 )
  //    {
  //       print( xxx );
  //       pause("press <return> to continue");
  //    }
  //     ....
  // }
}
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