Ticket #731: latex.lib

//////////////////////////////////////////////////////////////////////////////
version="version latex.lib 4.0.0.0 Jun_2013 "; // $Id: e4a01f52f53834cf5c92156dafc6dd07fd2c3929 $
category="Visualization";
info="
LIBRARY: latex.lib    Typesetting of Singular-Objects in LaTeX2e
AUTHOR: Christian Gorzel, gorzelc@math.uni-muenster.de

GLOBAL VARIABLES:
  TeXwidth, TeXnofrac, TeXbrack, TeXproj, TeXaligned, TeXreplace, NoDollars
  are used to control the typesetting.
  Call @code{texdemo();} to obtain a LaTeX2e file @code{texlibdemo.tex}
  explaining the features of @code{latex.lib} and its global variables.
@format
  @code{TeXwidth} (int) -1, 0, 1..9, >9:  controls breaking of long polynomials
  @code{TeXnofrac} (int) flag:  write 1/2 instead of \\frac@{1@}@{2@}
  @code{TeXbrack} (string) \"@{\", \"(\", \"<\", \"|\", empty string:
                                   controls brackets around ideals and matrices
  @code{TeXproj} (int) flag:  write \":\" instead of \",\" in vectors
  @code{TeXaligned} (int) flag:  write maps (and ideals) aligned
  @code{TeXreplace} (list) list entries = 2 strings:  replacing symbols
  @code{NoDollars} (int) flag:  suppresses surrounding $ signs
@end format
PROCEDURES:
 closetex(fnm)       writes closing line for LaTeX-document
 opentex(fnm)        writes header for LaTeX-file fnm
 tex(fnm)            calls LaTeX2e for LaTeX-file fnm
 texdemo([n])        produces a file explaining the features of this lib
 texfactorize(fnm,f) creates string in LaTeX-format for factors of polynomial f
 texmap(fnm,m,r1,r2) creates string in LaTeX-format for map m:r1->r2
 texname(fnm,s)      creates string in LaTeX-format for identifier
 texobj(l)           creates string in LaTeX-format for any (basic) type
 texpoly(f,n[,l])    creates string in LaTeX-format for poly
 texproc(fnm,p)      creates string in LaTeX-format of text from proc p
 texring(fnm,r[,l])  creates string in LaTeX-format for ring/qring
 rmx(s)              removes .aux and .log files of LaTeX-files
 xdvi(s)             calls xdvi for dvi-files
        (parameters in square brackets [] are optional)
        (Procedures with file output assume sufficient write permissions
        when trying to append existing or create new files.)

";

LIB "inout.lib";  // only needed for pause();

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

proc closetex(string fname, list #)
"USAGE:   closetex(fname); fname string
RETURN:  nothing; writes a LaTeX2e closing line into file @code{<fname>}.
NOTE:    preceding \">>\" are deleted and suffix \".tex\" (if not given)
         is added to @code{fname}.
EXAMPLE: example closetex; shows an example
"
{
  string default = "latex2e";
  string s;
  int i = 1;
  int flag;

  if (size(#)) { default = #[1];}

  if (default=="latex2e" or default == "latex")
   {  s = "\\end{document}"; flag = 1;}
  if (default=="amstex") {s = "\\enddocument"; flag = 1;}
  if (default=="tex") {s = "\\bye"; flag = 1;}
  if (not(flag)) { s = "";}

  if (size(fname))
  {
   while (fname[i]==">"){i++;}
   fname = fname[i,size(fname)-i+1];

   if (size(fname)>=4)               // check if filename is ending with ".tex"
   { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; }
   }
   else {fname = fname + ".tex";}
   write(fname, s);
   write(fname," % - Thanks latex.lib and Singular - ");
  }
  else {return(s);}
}
example
{ "EXAMPLE:"; echo=2;
   opentex("exmpl");
   texobj("exmpl","{\\large \\bf hello}");
   closetex("exmpl");
   echo=0;
}
///////////////////////////////////////////////////////////////////////////////

proc tex(string fname, list #)
"USAGE:   tex(fname); fname string
RETURN:  nothing; calls latex (LaTeX2e) for compiling the file fname
NOTE:    preceding \">>\" are deleted and suffix \".tex\" (if not given)
         is added to @code{fname}.
EXAMPLE: example tex; shows an example
"
{
  string default = "latex2e";
  int retval;
  int i=1;
  if (size(#)) {default = string(#[1]);}
  if (size(fname))
  {
   while (fname[i]==">"){i++;}
   fname = fname[i,size(fname)-i+1];

   if (size(fname)>=4)          // check if filename is ending with ".tex"
   { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; }
   }
   else {fname = fname + ".tex";}
   "calling "+default+" for:",fname,newline;

   if (default=="latex2e")
   {
     retval = system("sh","latex " +  fname);
   }
   else
   {
     retval = system("sh",default + " " +  fname);
   }
  }
  else
  { " // -- Need a filename ";
    return();
  }
}
example
{ "EXAMPLE:"; echo =2;
  ring r;
  ideal I = maxideal(7);
  opentex("exp001");              // open latex2e document
  texobj("exp001","An ideal ",I);
  closetex("exp001");
  tex("exp001");
  echo=0;
  pause("the created files will be deleted after pressing <RETURN>");
  system("sh","rm exp001.*");
}
///////////////////////////////////////////////////////////////////////////////

proc opentex(string fname, list #)
"USAGE:   opentex(fname); fname string
RETURN:  nothing; writes a LaTeX2e header into a new file @code{<fname>}.
NOTE:    preceding \">>\" are deleted and suffix \".tex\" (if not given)
         is added to @code{fname}.
EXAMPLE: example opentex; shows an example
"
{
  string default = "latex2e";
  string s;
  int i =1;
  int flag;

  if (size(#)) { default = #[1];}

  if (default == "latex2e")          // the default  latex2e header
  { s =
      "\\documentclass{article}" + newline +
      "\\usepackage{amsmath,amssymb}" + newline +
     "%\\setlength{\\textwidth}{390pt}" + newline +
      "\\parindent=0pt" + newline +
      "\\newcommand{\\C}{\\mathbb{C}}" + newline +
      "\\newcommand{\\F}{\\mathbb{F}}" + newline +
      "\\newcommand{\\N}{\\mathbb{N}}" + newline +
   // "\\renewcommand{\\P}{{\\Bbb P}}" + newline +
      "\\newcommand{\\Q}{\\mathbb{Q}}" + newline +
      "\\newcommand{\\R}{\\mathbb{R}}" + newline +
      "\\newcommand{\\T}{\\mathbb{T}}" + newline +
      "\\newcommand{\\Z}{\\mathbb{Z}}" + newline + newline +
      "\\begin{document}";
    flag = 1;
  }
  if (default == "latex")
  { s =
      "\\documentstyle[12pt,amstex]{article}" + newline +
      "\\parindent=0pt" + newline +
      "\\newcommand{\\C}{\\mathbb{C}}" + newline +
      "\\newcommand{\\F}{\\mathbb{F}}" + newline +
      "\\newcommand{\\N}{\\mathbb{N}}" + newline +
   // "\\newcommand{\\P}{\\mathbb{P}}" + newline +
      "\\newcommand{\\Q}{\\mathbb{Q}}" + newline +
      "\\newcommand{\\R}{\\mathbb{R}}" + newline +
      "\\newcommand{\\T}{\\mathbb{T}}" + newline +
      "\\newcommand{\\Z}{\\mathbb{Z}}" + newline + newline +
      "\\begin{document}";
    flag = 1;
  }
  if (default == "amstex")
  { s =
     "\\documentstyle{amsppt} " + newline + newline +
     "\\document";
    flag = 1;
  }

  if (default == "tex")
  { s =
     "";
    flag = 1;
  }
  if (default == "own")            // the proper own header
  { s = "";
    flag = 1;
  }
  if (not(flag)) { s = "";}

  if (size(fname))
  {
   while (fname[i]==">"){i++;}
   fname = fname[i,size(fname)-i+1];

   if (size(fname)>=4)               // check if filename is ending with ".tex"
   { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; }
   }
   else {fname = fname + ".tex";}
   fname = ">" + fname;
   write(fname,s);
  }
  else {return(s);}
}
example
{ "EXAMPLE:"; echo=2;
   opentex("exmpl");
   texobj("exmpl","hello");
   closetex("exmpl");
}
///////////////////////////////////////////////////////////////////////////////

proc texdemo(list #)
"USAGE:   texdemo();
RETURN:  nothing; generates a LaTeX2e file called @code{texlibdemo.tex}
         explaining the features of @code{latex.lib} and its global variables.
"
{ int TeXdemostart = system("pid");
  string fname = "texlibdemo";

  if (size(#))
  { if (typeof(#[1])=="int") {TeXdemostart = #[1];}
  }
  system("--random",TeXdemostart);

  //if (size(#) ==2)
  //{ if (typeof(#[2]) == "string") { fname = #[2];}
  //}

    if (size(fname))
    {
     if (size(fname)>=4)           // check if filename is ending with ".tex"
     { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; }
     } else {fname = fname + ".tex";}
    }

  // -------- save global variables ---------
  if (defined(NoDollars)) {int NoDoll=NoDollars; kill NoDollars;}
  if (defined(TeXaligned)) {int Teali=TeXaligned; kill TeXaligned;}
  if (defined(TeXreplace)) {list Terep=TeXreplace; kill TeXreplace;}
  if (defined(TeXwidth)) {int Tewid=TeXwidth; kill TeXwidth;}
  if (defined(TeXbrack)) {string Tebra=TeXbrack; kill TeXbrack;}
  if (defined(TeXnofrac)) {int Tenof=TeXnofrac; kill TeXnofrac;}
  if (defined(TeXproj)) {int Tepro=TeXproj; kill TeXproj;}
  // ----------------------------------------
   print(" Generating demofile .");
   part0(fname); print(" .");
   part1(fname); print(" .");
   part2(fname); print(" .");
   part3(fname); print(" .");
   print(" Demofile generated.");
   if (size(fname))
   {
    print(" Call latex now by tex(\"texlibdemo\");" );
    print(" To view the file, call xdvi by xdvi(\"texlibdemo\");" );
    // print(" Call latex now by tex(\"" + fname + "\");" );
    //print(" To view the file, call xdvi by xdvi(\"" + fname + "\");" );
    print(" .log and .aux files may be deleted with rmx(\"texlibdemo\");");
   }
  // -------- save global variables ---------
  if (defined(NoDoll)) {int NoDollars=NoDoll; export NoDollars; kill NoDoll;}
  if (defined(Teali)) {int TeXaligned=Teali; export TeXaligned; kill Teali;}
  if (defined(Terep)) {list TeXreplace=Terep; export TeXreplace; kill Terep;}
  if (defined(Tewid)) {int TeXwidth=Tewid; export TeXwidth; kill Tewid;}
  if (defined(Tebra)) {string TeXbrack=Tebra; export TeXbrack; kill Tebra;}
  if (defined(Tenof)) {int TeXnofrac=Tenof; export TeXnofrac; kill Tenof;}
  if (defined(Tepro)) {int TeXproj=Tepro; export TeXproj; kill Tepro;}
  // ----------------------------------------

  return();
}
///////////////////////////////////////////////////////////////////////////////

proc texfactorize(string fname, poly f, list #)
"USAGE:   texfactorize(fname,f); fname string, f poly
RETURN:  if @code{fname=\"\"}: string, f as a product of its irreducible
         factors@*
         otherwise: append this string to the file @code{<fname>}, and
         return nothing.
NOTE:    preceding \">>\" are deleted and suffix \".tex\" (if not given)
         is added to @code{fname}.
EXAMPLE: example texfactorize; shows an example
"
{
  def @r = basering;
  list l;
  int i,j,k,Tw,TW,ND;;
  intvec v;
  string s,t;
  string D = "$";
  poly g;

  ND = defined(NoDollars);

  if (!(ND)) {int NoDollars; export NoDollars;}
  else { D = ""; }
  TW = defined(TeXwidth);
  if (TW) {Tw = TeXwidth; TeXwidth = -1;}
  else {int TeXwidth = -1; export TeXwidth;}

   l = factorize(f);
   if (l[1][1]<>1){s = texpoly("",l[1][1]);}
   if (size(l[1])>1)
   {
    if (l[1][1]!=-1 and l[1][1]!=1) { s = texpoly("",l[1][1]); }
    if (l[1][1]==-1) { s = "-";}
   }
   else
   {
     s = texpoly("",l[1]);
   }

   for(i=2;i<=size(l[1]);i++)
   {
    if(size(s) and s!="-"){s = s+"\\cdot ";}
    g = l[1][i];
    v = leadexp(g);
    k=0;
    for(j=1;j<=size(v);j++){k = k + v[j];}
    if(size(g)>1 or (size(g)==1 and k>1))
    { t = "(" + texpoly("",l[1][i]) + ")";}
    else { t =  texpoly("",l[1][i]);}
    if (l[2][i]>1)
    { t = t+"^{" +string(l[2][i]) + "}";}
    s = s + t;
   }
   if (!(ND)) { kill NoDollars;}  // kill Latex::
   s = D + s + D;
   if (TW) {TeXwidth = Tw;}
   if (!TW) {kill TeXwidth;}    // kill Latex::

  if(size(fname))
  { i=1;
    while (fname[i]==">"){i++;}
    fname = fname[i,size(fname)-i+1];

    if (size(fname)>=4)             // check if filename is ending with ".tex"
    { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; }
    }
    else {fname = fname + ".tex";}
    write(fname,s);
  }
  else{return(s);}
}
example
{ "EXAMPLE:"; echo=2;
  ring r2 = 13,(x,y),dp;
  poly f = (x+1+y)^2*x3y*(2x-2y)*y12;
  texfactorize("",f);
  ring R49 = (7,a),x,dp;
  minpoly = a2+a+3;
  poly f = (a24x5+x3)*a2x6*(x+1)^2;
  f;
  texfactorize("",f);
}
///////////////////////////////////////////////////////////////////////////////

proc texmap(string fname, def m, def @r1, def @r2, list #)
"USAGE:   texmap(fname,m,@r1,@r2); fname string, m string/map, @r1,@r2 rings
RETURN:  if @code{fname=\"\"}: string, the map m from @r1 to @r2 (preceded
         by its name if m = string) in TeX-typesetting;@*
         otherwise: append this string to the file @code{<fname>}, and
         return nothing.
NOTE:    preceding \">>\" are deleted in @code{fname}, and suffix \".tex\"
         (if not given) is added to @code{fname}.
         If m is a string then it has to be the name of an existing map
         from @r1 to @r2.
EXAMPLE: example texmap; shows an example
"
{
  int saveDollars= defined(NoDollars);
  int TX = defined(TeXwidth);
  int Tw;
  int i,n;
  string r1str,r2str, varr1str, varr2str;
  string mapname,t,s;
  string D,DD,vrg = "$","$$",",";
  def @r = basering;
  def themap;
  list l1,l2;
  string rr1,rr2 = "@r1","@r2";

// --- store all actual informations
  if(TX) { Tw = TeXwidth; TeXwidth = -1;}
  else { int TeXwidth = -1; export TeXwidth;}
  if (!(saveDollars)) { int  NoDollars; export NoDollars;}
  if (defined(TeXproj)) {vrg = ":";}

  if (size(#))
  { if (typeof(#[1])=="list")
    { l1 = #[1];
      if(size(#)==2) { l2 = #[2];}
    }
    else {l1=#; l2 =#;}
  }
// --- tex the information in preimring r1

  setring(@r1);
  r1str = texring("",@r1,l1);
// --- avoid an execute; hence construct an ideal

  n = nvars(@r1);
  if (n>1) { t = "\\left(";}
  ideal @I = var(1);
  t = t + texpoly("",var(1));
  for(i=2;i<=n;i++)
  { @I = @I + var(i);
    t = t + vrg + texpoly("",var(i));
  }
  if (n>1) { t = t + "\\right)";}
  varr1str = t;

// --- now the things in ring ring r2

  setring(@r2);
 // listvar();

  if (typeof(m)=="string")
  { themap = `m`;
    mapname = m;
    if (defined(TeXreplace))
    {
     //mapname = rp(mapname);   // rp ausschreiben !
     for(int ii=1;ii<=size(TeXreplace);ii++)
     {
      if (TeXreplace[ii][1]==mapname) {mapname= TeXreplace[ii][2]; break;}
     }
    }
    mapname = mapname + ":";
  }
  if (typeof(m)=="map") { themap = m;}

  r2str = texring("",@r2,l2);
  ideal @J  = themap(@I);
  n = size(matrix(@J));
  if (n>1) { t = " \\left(";}
  if (!(defined(TeXaligned)) and (n>1))
      { t = t + newline + "\\begin{array}{c}" + newline;}
  t = t + texpoly("",@J[1]);
  for (i=2;i<=n; i++)
  {if(defined(TeXaligned))
   { t = t + vrg + texpoly("",@J[i]); }
   else { t = t + "\\\\" + newline + texpoly("",@J[i]);}
  }
  if (!(defined(TeXaligned)) and (n>1))
      { t = t + newline + "\\end{array}" + newline;}
  if (n>1) {t = t + "\\right)";}
  varr2str = t;

// --- go back to  ring r1 to kill @I

  setring(@r1);
  kill @I;

// --- now reset the old settings and stick all the information together

  setring(@r);
  if (!(saveDollars)) { kill NoDollars;}  // kill Latex::
  if (TX) {TeXwidth = Tw;}
  else { kill TeXwidth;}   // kill Latex::
  if (defined(NoDollars))
  { D,DD = "",""; }

  if (defined(TeXaligned))
  { s = D + mapname;
    s =  s + r1str + "\\longrightarrow" + r2str + ", \\ " +
        varr1str + "\\longmapsto" + varr2str + D; }
  else
  { s = DD;
    s = s + newline + "\\begin{array}{rcc}" +  newline;
    s = s + mapname + r1str + " & \\longrightarrow & " +  r2str + "\\\\[2mm]"
          + newline;
    s = s + varr1str + " & \\longmapsto & " +  newline + varr2str + newline;
    s = s + "\\end{array}" + newline;
    s = s +  DD;
  }

  if (size(fname))
  { i=1;
    while (fname[i]==">"){i++;}
    fname = fname[i,size(fname)-i+1];

    if (size(fname)>=4)          // check if filename is ending with ".tex"
    { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; }
    }
    else {fname = fname + ".tex";}
    write(fname,s);
  }
  else {return(s);}
}
example
{
  echo=0;
  // -------- prepare for example ---------
  if (defined(TeXaligned)) {int Teali=TeXaligned; kill TeXaligned;}
  if (defined(TeXreplace)) {list Terep=TeXreplace; kill TeXreplace;}
  // -------- the example starts here ---------
  //
  "EXAMPLE:"; echo = 2;
  string fname = "tldemo";
  ring @r1=0,(x,y,z),dp;
  export @r1;
  ring r2=0,(u,v),dp;
  map @phi =(@r1,u2,uv -v,v2); export @phi;
  list TeXreplace;
  TeXreplace[1] = list("@phi","\\phi");    // @phi --> \phi
  export TeXreplace;
  texmap("","@phi",@r1,r2);                // standard form
  //
  int TeXaligned; export TeXaligned;       // map in one line
  texmap("",@phi,@r1,r2);
  //
  kill @r1,TeXreplace,TeXaligned;
  echo = 0;
  //
  // --- restore global variables if previously defined ---
  if (defined(Teali)) {int TeXaligned=Teali; export TeXaligned; kill Teali;}
  if (defined(Terep)) {list TeXreplace=Terep; export TeXreplace; kill Terep;}
}
///////////////////////////////////////////////////////////////////////////////

static proc manipul(string s)
{
  string st;
  int i,anf,end,op,bigch;
  int n;
  if (s[1]=="{") { return(s[2,size(s)-2]);}
  if (s=="") { return(s);}
  s = s + newline;             // add a terminating sign
  anf=1;
  while(s[i]!=newline)
  {
    i =anf;
    while(s[i]<"0" or s[i]>"9" and s[i]!="'" and s[i]!= "_" and s[i]!="~" and
          s[i]!="(" and s[i]!=")" and s[i]!= "[" and s[i]!=newline) {i++;}
    if (s[i]==newline){st = st + s[anf,i-anf]; n = n+10*(i-anf); return(st);}
    st = st + s[anf,i-anf];                        // the starting letters
    if (s[anf]>="A" and s[anf]<="Z") {bigch=1;}
    if (s[i]=="'") { st = st + "'";i++;}
    if (s[i]=="~") { st = "\\tilde{" + st + "}"; i++;}
    if (s[i]=="_") { i++;}
    if (s[i]=="(") { op =1;i++;}
    if (s[i]=="[") { anf = i+1;
    while(s[i]!="]"){i++;}                    // matrices and vectors
    st = st + "_{" + s[anf,i-anf] + "}"; n = n+ 5*(i-anf); i++;
   // besser: while s[i]<> nwline : scan forward: end, return
  }
  if (s[i]==newline) {return(st);}
  anf =i;
  while (s[i]>="0" and s[i]<="9") {i++;}  // parse number after the letters
  if (bigch and not(op)) { st = st + "^{" + s[anf,i-anf] + "}"; bigch =0;}
  else { st = st + "_{" + s[anf,i-anf] + "}";}
  n = n+5*(i-anf);
  anf =i;            // the next text in ( , ) as exponent
  if (op)
  {
    if (s[i]== ","){anf = anf+1;}
    while(s[i] !=")"){ i++;}
    if (i<>anf)
      {
        st = st + "^{" + s[anf,i-anf] + "}"; n = n +5*(i-anf);}
        i++;
      }
    anf =i;
  }
  return(st);
}
///////////////////////////////////////////////////////////////////////////////

proc texname(string fname, string s)
"USAGE:   texname(fname,s);  fname,s  strings
RETURN:  if @code{fname=\"\"}: the transformed string s, for which the
         following rules apply:
@example
      s' + \"~\"             -->  \"\\tilde@{\"+ s' +\"@}\"
     \"_\" + int             -->       \"_@{\" + int +\"@}\"
  \"[\" + s' + \"]\"           -->      \"_@{\" + s' + \"@}\"
   \"A..Z\" + int            --> \"A..Z\" + \"^@{\" + int + \"@}\"
   \"a..z\" + int            --> \"a..z\" + \"_@{\" + int + \"@}\"
\"(\" + int + \",\" + s' + \")\" --> \"_@{\"+ int +\"@}\" + \"^@{\" + s'+\"@}\"
@end example
         Furthermore, strings which begin with a left brace are modified
         by deleting the first and the last character (which is then assumed to
         be a right brace).

         if @code{fname!=\"\"}: append the transformed string s to the file
         @code{<fname>}, and return nothing.
NOTE:    preceding \">>\" are deleted in @code{fname}, and suffix \".tex\"
         (if not given) is added to @code{fname}.
EXAMPLE: example texname; shows an example
"
{
  string st, extr;
  st=manipul(s);
  if (size(fname))
  {
    int i=1;
    while (fname[i]==">"){i++;}
    fname = fname[i,size(fname)-i+1];
    if (size(fname)>=4)            // check if filename is ending with ".tex"
    {
      if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; }
    }
    else {fname = fname + ".tex";}
    write(fname,st);
  }
  else {return(st);}
}
example
{ "EXAMPLE:"; echo =2;
   ring r = 0,(x,y),lp;
   poly f = 3xy4 + 2xy2 + x5y3 + x + y6;
   texname("","{f(10)}");
   texname("","f(10) =");
   texname("","n1");
   texname("","T1_12");
   texname("","g'_11");
   texname("","f23");
   texname("","M[2,3]");
   texname("","A(0,3);");
   texname("","E~(3)");
}
///////////////////////////////////////////////////////////////////////////////

proc texobj(string fname, list #)
"USAGE:   texobj(fname,l); fname string, l list
RETURN:  if @code{fname=\"\"}: string, the entries of l in LaTeX-typesetting;@*
         otherwise: append this string to the file @code{<fname>}, and
         return nothing.
NOTE:    preceding \">>\" are deleted in @code{fname}, and suffix \".tex\"
         (if not given) is added to @code{fname}.
EXAMPLE: example texobj; shows an example
"
{
 int i,j,k,nr,nc,linear,Tw,Dollars;
 int ND = defined(NoDollars);
 int TW = defined(TeXwidth);

 if(defined(basering)){ poly g,h; matrix M;}
 string s,t,l,ineq,sg,Iname;
 string sep= ",";
 string D,DA,DE = "$","$$"+newline,"$$";
 string OB,CB = "(",")";
 if (defined(TeXbrack))
 {// if (TeXbrack=="(") {OB = "("; CB = ")";}
   if (TeXbrack=="<") {OB = "<"; CB = ">";}
   if (TeXbrack=="{") {OB = "{"; CB = "}";}
   if (TeXbrack=="|") {OB = "|"; CB = "|";}
   if (TeXbrack=="" ) {OB = "."; CB = ".";}
 }

 if (!(TW)) { int TeXwidth = -1; export TeXwidth; }
 Tw = TeXwidth;

 if (defined(TeXproj)){ sep = ":";}
 if(ND) { D,DA,DE="","","";}
 else {int NoDollars; export NoDollars;}

 if (size(#)==1)
 { if (typeof(#[1])=="int" or typeof(#[1])=="intvec" or typeof(#[1])=="vector"
    or typeof(#[1])=="number" or typeof(#[1])=="bigint" or defined(TeXaligned))
   { DA = D; DE = D; }
}

 s = DA;

 for (k=1; k<=size(#); k++)
 { def obj = #[k];
   if (typeof(obj) == "string")
   { if (defined(`obj`))
     { if (typeof(`obj`)=="ideal")
       {
         Iname = obj; def e = `obj`;     //convert to correct type ideal
         kill obj; def obj = e; kill e;
       }
       else {s = s + obj + newline;}
     }
    else {s = s + obj + newline;}
   }
   if (typeof(obj) == "int" or typeof(#[1])=="bigint")
   { s = s + "  " + string(obj) + "  ";}

   if (typeof(obj) == "intvec")
   { s = s + " (";
     for(j=1; j<size(obj);j++) { s = s + string(obj[j]) + sep;}
     s = s +  string(obj[j]) + ") ";
   }

   if (typeof(obj) == "number" )
   { s = s + texpoly("",obj) + newline;
   }

   if (typeof(obj) == "poly")
   { int TeXdisplay; export TeXdisplay;
     s = s + "\\begin{array}{rl}" + newline;
     s = s + texpoly("",obj) + "\\\\" + newline;
     s = s + "\\end{array}" + newline;
    kill TeXdisplay;
   }

   if (typeof(obj) == "vector")
   { if (obj==0) { s = s  + "0" ;}
     else
     { if (Tw==0) { TeXwidth = -1;}
      s = s + "\\left" + OB;
      for(j=1; j<nrows(obj); j++) {s = s + texpoly("",obj[j]) + sep;}
      s = s + texpoly("",obj[j])  + "\\right" + CB + newline;
      TeXwidth = Tw;
     }
    }

   if (typeof(obj) == "ideal")
   { if (size(Iname))   // verwende hier align
     { if (Tw==0) {TeXwidth = -1;}

      // Lasse hier TeXwidth == 0 zu !
      // if (!(defined(TeXaligned)))
      //  { untereinander }
      // else { hintereinander }
      //
      //
      //  s = s + Iname + "=" + texpoly("",obj,",");
      //  siehe ebenso noch einmal am Ende : ! (TeXwidth <> 0 !? )

       s =  s + "\\begin{array}{rcl}" + newline;
       for (i=1;i<=size(matrix(obj));i++)
       { s =  s + Iname+ "_{" + string(i) + "} & = & "
               + texpoly("",obj[i]);
         if (i<size(matrix(obj))){ s = s  + "\\\\" + newline;}
       }
       s = s + newline;
       s = s + "\\end{array}" + newline;
       TeXwidth = Tw;
       Iname ="";
     }
     else
     {
      if (TeXwidth==0)
      { TeXwidth = -1;
        obj= simplify(obj,2);
        linear = 1;
        for (j=1;j<=size(obj);j++)
        { if (deg(obj[j])>1){linear =0; break;}
        }
        if (!(linear))
        { s = s + "\\begin{array}{rcl}" + newline;
          for(j=1;j<=size(obj);j++)
          { h = jet(obj[j],0);  // absterm
            ineq = "=" ;
            l = texpoly("",obj[j]-h) + " & " + ineq + " & " + texpoly("",-h);
            if(j<size(obj)) { l = l + " \\\\";}
            s =s+ l + newline;
           }
          s = s + "\\end{array}" + newline;
        }
        else   // linear
        { s = s +
   "\\begin{array}{*{" + string(2*nvars(basering)-1) + "}{c}cr}" + newline;
           for(j=1; j<=size(obj);j++)
           { h = jet(obj[j],0);   // absterm
             ineq = "=";
              l = ""; nc = 0;
              for (i=1; i<=nvars(basering);i++)
              { t = " "; sg ="";
                g = obj[j]-subst(obj[j],var(i),0);
                if (g!=0) { t = texpoly("",g);}
                if (i>1)
                { if (t[1]!="-" and t[1]!= " " and nc ){sg = "+";}
                  if  (t[1]=="-") { sg = "-"; nc =1; t=t[2,size(t)-1];}
                  if (t==" ") {sg ="";}
                  l = l + " & " + sg + " & " + t;
                }
                else { l = t;}
                if (g!=0) {nc = 1;}
               }

               l = l + " & " + ineq + " & " + texpoly("",-h);
             if (j < size(obj)) { l = l + " \\\\";}
             s = s + l + newline;
            } // end for (j)
          s = s + "\\end{array}";
         }  // end else linear
        TeXwidth = 0;
       } // end TeXwidth == 0
   else // TeXwidth <> 0
   { s =  s + "\\left"+ OB;
     if (defined(TeXaligned))
     { s = s + texpoly("",obj,",");
     }
     else
     { s = s + newline + "\\begin{array}{c}" + newline +
               texpoly("",obj,", \\\\" + newline) +
                newline + "\\end{array}" + newline;
     }
    s = s + "\\right" + CB;
    } // end TeXwidth <> 0
   }  // not Iname
// s;
  }

   if (typeof(obj) == "module")
   { M = matrix(obj);
     if (Tw ==0 or Tw > 9) { TeXwidth = -1;}
     s = s + "\\left" + OB + newline;
     if (!(defined(TeXaligned)))
     {  // Naechste Zeile nicht notwendig !
     // s = s + "\\begin{array}{*{"+ string(ncols(M)) + "}{c}}" + newline;
      for(j=1;j<=ncols(M);j++)
      { l = "\\left" + OB + newline + "\\begin{array}{c}" + newline;
        l = l + texpoly("",ideal(M[1..nrows(M),j]), " \\\\" + newline)
              + newline + "\\end{array}" +newline + "\\right" + CB + newline;
        if (j< ncols(M)) { l = l + " , " + newline;}
        s = s + l ;
      }
     }
     else    // TeXaligned
     {
      for(j=1;j<=ncols(M);j++)
      { s = s + "\\left" + OB + newline +
           texpoly("",ideal(M[1..nrows(M),j]),",") + newline + "\\right" + CB;
        if (j<ncols(M)) { s = s + "," + newline; }
      }
     }
    s = s  + "\\right" + CB + newline;
   } // module part

   if (typeof(obj) == "matrix")
   { if (Tw==0 or Tw > 9) {TeXwidth = -1;}
     l = "";
   //  M = transpose(obj);
     s = s + "\\left" + OB + newline +
             "\\begin{array}{*{"+ string(ncols(obj)) + "}{c}" + "}"+ newline;
     for(i=1;i<=nrows(obj);i++)
     { l = l + texpoly("",ideal(obj[i,1..ncols(obj)])," & ");
       if (i<nrows(obj)) { l = l + " \\\\" + newline;}
     }
     l = l + newline;
     s = s + l + "\\end{array}" + newline +
                 "\\right" + CB + newline;
    TeXwidth = Tw;
  }

   if (typeof(obj) == "intmat")
   { nr,nc = nrows(obj),ncols(obj);
     l = "";
     l =  "\\left" + OB + newline +
          "\\begin{array}{*{"+ string(nc) + "}{r}}"+ newline;
     for(i=1;i<=nr;i++)
     { for(j=1;j<=nc;j++)
       { l = l + string(obj[i,j]);
         if (j <nc ) { l = l + " & ";}
         else {if( i < nr) { l = l + "\\\\" + newline;}}
       }
     }
     l = l + newline + "\\end{array}" + newline +
             "\\right" + CB + newline;
    s = s + l;
  }

  if (typeof(obj) == "ring")
  { s = s + D + texring("",obj) + D + newline;}

  kill obj;
 }

 s = s +  DE;// + newline;

 if(!(ND)) { kill NoDollars;}  // kill Latex::
 if(!(TW)) { kill TeXwidth;}   // kill Latex::

 if(size(fname))
 { i=1;
  while (fname[i]==">"){i++;}
  fname = fname[i,size(fname)-i+1];
  if (size(fname)>=4)               // check if filename is ending with ".tex"
  { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; }
  }
  else {fname = fname + ".tex";}
  write(fname,s);
 }
 else {return(s);}
}
example
{
   echo=0;
   // -------- prepare for example ---------
   if (defined(TeXaligned)) {int Teali=TeXaligned; kill TeXaligned;}
   if (defined(TeXbrack)){string Tebra=TeXbrack; kill TeXbrack;}
   "EXAMPLE:"; echo = 2;
   //
   //  --------------  typesetting for polynomials ----------
   ring r = 0,(x,y),lp;
   poly f = x5y3 + 3xy4 + 2xy2 + y6;
   f;
   texobj("",f);
   pause();
   //  --------------  typesetting for ideals ----------
   ideal G = jacob(f);
   G;
   texobj("",G);
   pause();
   //  --------------  variation of typesetting for ideals ----------
   int TeXaligned = 1; export TeXaligned;
   string TeXbrack = "<"; export TeXbrack;
   texobj("",G);
   pause();
   kill TeXaligned, TeXbrack;
   //  --------------  typesetting for matrices ----------
   matrix J = jacob(G);
   texobj("",J);
   pause();
   //  --------------  typesetting for intmats ----------
   intmat m[3][4] = 9,2,4,5,2,5,-2,4,-6,10,-1,2,7;
   texobj("",m);
   echo=0;
   //
   // --- restore global variables if previously defined ---
   if (defined(Teali)){int TeXaligned=Teali; export TeXaligned; kill Teali;}
   if (defined(Tebra)){string TeXbrack=Tebra; export TeXbrack; kill Tebra;}
}
///////////////////////////////////////////////////////////////////////////////

proc texproc(string fname,string pname)
"USAGE:   texproc(fname,pname); fname,pname strings
ASSUME:  @code{`pname`} is a procedure.
RETURN:  if @code{fname=\"\"}: string, the proc @code{`pname`} in a verbatim
         environment in LaTeX-typesetting;@*
         otherwise: append this string to the file @code{<fname>}, and
         return nothing.
NOTE:    preceding \">>\" are deleted in @code{fname}, and suffix \".tex\"
         (if not given) is added to @code{fname}.@*
EXAMPLE: example texproc; shows an example
"
{
  int i,j,k,nl;
  string @p,s,t;

  j = 1;

  if (defined(`pname`))
  { if (typeof(`pname`)=="proc")
    { @p = string(`pname`);
      nl = find(@p,newline);
      s = "\\begin{verbatim}" + newline;
      s = s + "proc " + pname + "(";
      i = find(@p,"parameter");       // collecting the parameters
      k = find(@p,"alias");           // and the alias arguments
      while((i and i < nl) or (k and k < nl))
      {
        if (i and (k==0  or i<k))
        {
         j=find(@p,";",i);
         t = @p[i+10,j-i-10];
         if(i>1){s = s + ",";};
         s = s + t;
        }
        if (k and (i==0  or k<i))
        {
         j=find(@p,";",k);
         t = @p[k,j-k];
         if(k>1){s = s + ",";};
         s = s + t;
        }
        i = find(@p,"parameter",j);
        k = find(@p,"alias",j);
      }
      s = s + ")" + newline;
     j++;                      // skip one for the newline
     i = find(@p,";"+"return();"+newline,j);
     if (!(i))
     { i = find(@p,";"+"RETURN();"+newline,j); }  // j kann hier weg
     s = s + "{" + @p[j,i-j-1] + "}" + newline;
     s = s + "\\end{verbatim}" + newline;
   }
  }
  else
  { print(" // -- Error: No such proc defined");
    return();
  }
  if(size(fname))
  { i=1;
    while (fname[i]==">"){i++;}
    fname = fname[i,size(fname)-i+1];
    if (size(fname)>=4)        // check if filename is ending with ".tex"
    { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; }
    }
    else {fname = fname + ".tex";}
    write(fname,s);
  }
  else{return(s);}
}
example
{ "EXAMPLE:"; echo=2;
  texproc("","texproc");
}

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

static proc tvar(intvec v)
{
  int i,j,ldots;
  string s;
  j = 1;
  s = texpoly("",var(1));

  if (nvars(basering)==1) { return(s);}
  if (nvars(basering)==2) { return(s + "," + texpoly("",var(2)));}
  if (size(v)==1 and v[1] == 1)
     {return(s + ",\\ldots,"+ texpoly("",var(nvars(basering))));}
  if (v[1]==1 and size(v) >1) {j++;}
  for(i=2;i<nvars(basering);i++)
  { if (i<v[j]  and !(ldots))
    { s = s + ",\\ldots";
      ldots =1;
    }
    if (i== v[j])
    { s = s + "," + texpoly("",var(i));
      ldots =0;
      if (j< size(v)) {j++;}
    }
  }
  if (v[j]<nvars(basering)-1) { s = s + ",\\ldots";}
  return(s + "," + texpoly("",var(nvars(basering))));
}
///////////////////////////////////////////////////////////////////////////////

proc texring(string fname, def r, list #)
"USAGE:   texring(fname, r[,L]); fname string, r ring, L list
RETURN:  if @code{fname=\"\"}: string, the ring in TeX-typesetting;@*
         otherwise: append this string to the file @code{<fname>} and
         return nothing.
NOTE:    preceding \">>\" are deleted and suffix \".tex\" (if not given)
         is added to @code{fname}.@*
         The optional list L is assumed to be a list of strings which control,
         for instance the symbol for the field of coefficients.@*
         For more details call @code{texdemo();} (generates a LaTeX2e
         file called @code{texlibdemo.tex} which explains all features of
         @code{texring}).
EXAMPLE: example texring; shows an example
"
{
  int i,galT,intT,flag,mipo,nopar,Dollars,TB,TA;
  string ob,cb,cf,en,s,t,savebrack; //opening bracket, closing br, coef.field
  intvec v;

  setring r;
  if (!(defined(NoDollars))){ Dollars = 1; int NoDollars; export NoDollars;}
  ob,cb = "[","]";
  if (find(ordstr(r),"s")) { ob,cb="[[","]]";}
  if(char(r)==0){cf="\\Q";}
  if(find(charstr(r),"integer"))    // 4.10.10
  {
    intT=1;
    cf="\\Z";
    if (char(r)>0) { cf=cf+"_{"+string(char(r))+"}";}
  }
  if(find(charstr(r),"real")){cf="\\R";}
  if(find(charstr(r),"complex")){cf="\\C"; nopar=1;}   // 28.10.06
  if(char(r)==prime(char(r))){cf="\\Z_{"+string(char(r))+"}";}
  if(char(r)>0 and !intT)
  { i = find(charstr(r),",");
    if(i)
    { t= charstr(r)[1,i-1];
      galT = (t <> string(char(r)));
      if (galT) { cf = "\\F_{"+ t + "}";}
    }
  }     // all other cases are cover already by char(r)=? prime(char)

  if (size(#))
  { if (typeof(#[1])=="list") { # = #[1];}
  }
  for (i=1;i<=size(#);i++)
  { flag =0;
    if(typeof(#[i])=="string")
    {
     if(#[i][1]=="^" or #[i][1]=="_"){en=en+#[i];flag = 1;}
     if(#[i]=="mipo"){mipo=1; flag = 1;}
     if(#[i]=="{"){ob,cb="\\{","\\}";flag=1;}
     if(#[i]=="{{"){ob,cb="\\{\\{","\\}\\}";flag=1;}
     if(#[i]=="["){ob,cb="[","]";flag=1;}
     if(#[i]=="[["){ob,cb="[[","]]";flag=1;}
     if(#[i]=="<"){ob,cb="<",">";flag=1;}
     if(#[i]=="<<"){ob,cb="{\\ll}","{\\gg}";flag=1;}
     if(#[i]=="C"){cf="\\C";flag=1;}
     if(#[i]=="Q"){cf="\\Q";flag=1;}
     if((#[i]=="k" or #[i]=="K" or #[i]=="R") and !(galT))
                   {cf=#[i]; flag=1; nopar=1;}
     if (flag!=1) {cf = #[i];}  // for all the cases not covered here e.g Z_(p)
    }                           // or Q[i]

    if ((typeof(#[i])=="intvec") or
        (typeof(#[i])=="int")){v=#[i];}
   }
  s = cf;
 // now the parameters
 // t;
  if(npars(r) and ((t==string(char(r))) or char(r)==0) and !(nopar))
  {
   s = s + "(";                      // !! mit ideal !!
   for(i=1;i<npars(r);i++) {s = s + texpoly("",par(i)) + ",";}
   s = s + texpoly("",par(npars(r))) + ")";
  }                               // parameters done
  if (!(galT) and mipo and minpoly!=0)
  { s = s + "/" + list(parsp(string(minpoly),0))[1];}
  s = s + ob;
  if (v!=0 and nvars(r)>3)
  { s = s + tvar(v);}
  else
  { s = s + texpoly("",maxideal(1),","); }
   s = s + cb + en;

  if (size(ideal(r))>0) /*qring*/
  { ideal @I = ideal(r);
    if (defined(TeXbrack))
    {
      TB =1; savebrack = TeXbrack;
      if (TeXbrack!= "<" and TeXbrack!="(") { TeXbrack = "<";}
    }
    TA = defined(TeXaligned);
    if (!(TA)) { int TeXaligned; export TeXaligned; }
    t = texobj("",@I);
 //   @I;
 //   t;
    if (TB) { TeXbrack = savebrack;}
    if (!(TA)) { kill TeXaligned;}  // kill Latex::
    s = s + "/" + t;
  }

  if (Dollars)
  { kill NoDollars;   // kill Latex::
    s =  "$" + s + "$";
  }
  if (size(fname))
  { i=1;
     while (fname[i]==">"){i++;}
     fname = fname[i,size(fname)-i+1];

     if (size(fname)>=4)           // check if filename is ending with ".tex"
     { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; }
     }
     else {fname = fname + ".tex";}
     write(fname,s);
  }
  else{return(s);}
}
example
{ "EXAMPLE:"; echo=2;
  ring r0 = 0,(x,y),dp;                // char = 0, polynomial ordering
  texring("",r0);
  //
  ring r7 =7,(x(0..2)),ds;             // char = 7, local ordering
  texring("",r7);
  //
  ring r1 = 0,(x1,x2,y1,y2),wp(1,2,3,4);
  texring("",r1);
  //
  ring rr = real,(x),dp;               // real numbers
  texring("",rr);
  //
  ring rC = complex,x,dp;              // complex coefficients
  texring("",rC);
  //
  pause();

  ring rabc =(0,t1,t2,t3),(x,y),dp;    // ring with parameters
  texring("",rabc);
  //
  ring ralg = (7,a),(x1,x2),ds;        // algebraic extension
  minpoly = a2-a+3;
  texring("",ralg);
  texring("",ralg,"mipo");
  //
  ring r49=(49,a),x,dp;                // Galois field
  texring("",r49);
  //
  setring r0;                          // quotient ring
  ideal i = x2-y3;
  qring q = std(i);
  texring("",q);
  //
  pause();

  // ------------------ additional features -------------------
  ring r9 =0,(x(0..9)),ds;
  texring("",r9,1);
  texring("",r9,"C","{","^G");
  //
  ring rxy = 0,(x(1..5),y(1..6)),ds;
  intvec v = 5,6;
  texring("",rxy,v);
}
///////////////////////////////////////////////////////////////////////////////

proc rmx(string fname)
"USAGE:   rmx(fname); fname string
RETURN:  nothing; removes the @code{.log} and @code{.aux} files associated to
         the LaTeX file <fname>.@*
NOTE:    If @code{fname} ends by @code{\".dvi\"} or @code{\".tex\"}, the
         @code{.dvi} or @code{.tex} file will be deleted, too.
EXAMPLE: example rmx; shows an example
"
{
  int i,suffix= 1,0;
  int retval;

  if (size(fname))
  {
   while (fname[i]==">"){i++;}
   fname = fname[i,size(fname)-i+1];
   if (size(fname)>4)
   { if (fname[size(fname)-3,4]==".tex") { suffix = 2;}
     if (fname[size(fname)-3,4]==".dvi") { suffix = 1; }
     if (suffix) { fname = fname[1,size(fname)-4]; }
   }
   retval = system("sh","rm " + fname + ".aux");
   retval = system("sh","rm " + fname + ".log");
   if (suffix==2) {retval = system("sh","/bin/rm -i " + fname +".tex");}
   if (suffix>=1) {retval = system("sh","/bin/rm -i " + fname +".dvi");}
  }
  else
  {" -- Need a filename ";
    return();
  }
}
example
{ "EXAMPLE:"; echo =2;
  ring r;
  poly f = x+y+z;
  opentex("exp001");              // defaulted latex2e document
  texobj("exp001","A polynom",f);
  closetex("exp001");
  tex("exp001");
  rmx("exp001");   // removes aux and log file of exp001
  echo = 0;
  pause("remaining files will be deleted after pressing <RETURN>");
  echo = 2;
  system("sh","rm exp001.*");
}
///////////////////////////////////////////////////////////////////////////////

proc xdvi(string fname, list #)
"USAGE:   xdvi(fname[,style]); fname,style = string
RETURN:  nothing; displays dvi-file fname.dvi with previewer xdvi
NOTE:    suffix .dvi may be omitted in fname
         style captures the program that will be called instead of the default (xdvi)
EXAMPLE: example xdvi; shows an example
"
{
  int i=1;
  int retval;
  string default = "xdvi";

  if (size(#)) {default = string(#[1]);}

  if (size(fname))
  {
   while (fname[i]==">") {i++;}
   fname = fname[i,size(fname)-i+1];

   if (size(fname)>=4)
   { if(fname[size(fname)-3,4]==".tex") {fname = fname[1,size(fname)-4];}}

   "calling ",default, " for :",fname,newline;

   if (default=="latex2e")
   {
     retval = system("sh","latex " +  fname +" &");
   }
   else
   {
     retval = system("sh",default + " " +  fname +" &");
   }
  }
  else
  { " -- Need a filename ";
    return();
  }
}
example
{ "EXAMPLE:"; echo = 2;
  intmat m[3][4] = 9,2,4,5,2,5,-2,4,-6,10,-1,2,7;
  opentex("exp001");
  texobj("exp001","An intmat:  ",m);
  closetex("exp001");
  tex("exp001");
  xdvi("exp001");
  echo = 0;
  pause("the created files will be deleted after pressing <RETURN>");
  echo = 2;
  system("sh","rm exp001.*");
}
///////////////////////////////////////////////////////////////////////////////

static proc parsr(string s)                     // parse real
{
  string t;
  if (s=="(      Inf)") { return("\\infty",3);}
  if (s=="(     -Inf)") { return("\\-infty",6);}
  if (s[8]=="-"){t ="-";}
  if (s[9]<>"0"){t = t + s[9];}
  if (s[10]<>"0" or s[9]<>"0"){t = t + s[10];}
  if (size(t))
  { if (t=="1") {return(s[1,6]+"\\cdot 10",21);}
    if (size(t)>1) {return(s[1,6]+"\\cdot 10^{"+t+"}",21+2*size(t));}
    else {return(s[1,6]+"\\cdot 10^"+t+")",23);}
  }
  else
  {
    return(s[2,5],12);
  }
}
///////////////////////////////////////////////////////////////////////////////

static proc parsg(string s)                  // parse Galois field
{
  string t;

  if (s=="1") {return("1",5);}
  if (short)
  {
    t =s[1];
    if(size(s)>1) {return(t+"^{" + s[2,size(s)-1] + "}",3+2*(size(s)-1));}
    else{return(t,5);}
  }
  else
  {
    return(parselong(s+"!"));
  }
}
///////////////////////////////////////////////////////////////////////////////

proc texpoly(string fname,def p,list #)
"USAGE:   texpoly(fname,p); fname string, p poly
RETURN:  if @code{fname=\"\"}: string, the polynomial p in LaTeX-typesetting;@*
         otherwise: append this string to the file @code{<fname>}, and
         return nothing.
NOTE:    preceding \">>\" are deleted in @code{fname}, and suffix \".tex\"
         (if not given) is added to @code{fname}.
EXAMPLE: example texpoly; shows an example
"
{
  def @r = basering;

  poly f,monom;
  ideal I;
  number cfm;
  string sign,cfmt,pt,s,bg,t,monomt,lnbreak;
  string sep = newline;
  int i,b,b2,n, msz,linesz, count,k;
  int realT, parT, galT, complT;
  int TW = defined(TeXwidth);

  int C = 2 + defined(TeXdisplay);

  string notvalid = "intvec intmat vector matrix module map";

  if (typeof(p) == "int") { return(p);}
  if (typeof(p)  == "ring")
  { " -- Call  texring  instead "; return();}
  if (find(notvalid,typeof(p)))
  { " -- Call  texobj  instead "; return();}
  if (typeof(p)  == "map")
  { " -- Call  texmap  instead "; return();}
  if (typeof(p)  == "proc")
  { " -- Call  texmap  instead "; return();}
  if (typeof(p)  == "link" or typeof(p) == "list" or typeof(p) == "resolution")
  { ERROR(" // -- Object cannot translated into tex "); return();}

  if (!(defined(TeXdisplay))){ lnbreak = "\\\\[2mm]" + newline;}
  else { lnbreak = "\\\\" + newline;}


  if (defined(TeXdisplay)) { bg = "& ";}
  if (!TW) { int TeXwidth = -1; export TeXwidth;}

// -- Type check

 if (typeof(p)=="string")
  { if(defined(`p`))
    { pt = p + " = ";
      p = `p`;
    }
  }
  if (typeof(p)=="poly" or typeof(p)=="number") {I = p;}

  if (typeof(p)=="ideal")
  { I = p;
    if(size(#)){ sep = #[1];}
  }

  if (I==0)
  { if (!(defined(NoDollars))){return("$0$");}
    else {return("0");}
  }

// -- Type check ende

//---------------------

//------- set flags: --------------------------------------------------------

  if (size(#))
  { if (typeof(#[1])=="int") { linesz = #[1];}
 //   if (typeof(#[1])=="string") { linesz = #[1];}
  }

  parT = npars(@r);
  realT = (charstr(@r)=="real");
  complT = find(charstr(@r),"complex");   // 28.10.06
  if (complT) {parT=0;}
  i = find(charstr(@r),",");
  if (i and !realT and !complT)
  { t = charstr(@r)[1,i-1];
    galT = (t <> string(char(@r)));  // the char is not the same as the ...
  }
  i = 0;

//------- parse the polynomial
  pt = bg;

 for(k=1;k<=ncols(I);k++)
 { i = 0; linesz = 0; count =0;
   sign ="";
   f = I[k];
   if (f==0) { pt = pt + "0";}
  while(f<>0)
  { count++; msz = 0;

// ------ tex the coefficient
    monom = lead(f);
    f = f - monom;
    cfm = leadcoef(monom);
    if (cfm*1 != 0) { monom = leadmonom(monom);} // to conform with integer
    if (defined(TeXreplace)) { short =0;}  // this is essential //31.5.07
    s = string(monom) + "!";              // add a terminating sign
    cfmt = "";

    cfmt = string(cfm);
    if (size(cfmt)>1)                   // check if sign is < 0
    { if (cfmt[2]=="-") { cfm = (-1) *cfm; sign = "-";}}
    if (cfmt[1] == "-") { cfm = (-1) * cfm; sign = "-";}
    if  (cfm!=1 or monom==1) {cfmt = string(cfm);}
    else {cfmt="";}

    if (defined(TeXwidth) and TeXwidth > 0 and TeXwidth <9 and count> TeXwidth)
    { pt = pt + sign + "\\ldots"; break;}
   // ----------------------------------------  linesz ??

    if (size(cfmt))                            // parse the coefficient
    {
     monomt = cfmt;                   // (already a good choice for integers)
     msz = 3*size(cfmt);

     if(realT) { monomt,msz = parsr(cfmt);}
     if (galT) { monomt,msz = parsg(cfmt);}
     b = find(cfmt,"/(");                     // look if fraction  // 31.5.07
     if (b==0) { b = -find(cfmt,")/"); }  // 1.9.15
     b2 = find(cfmt,"/");
     // if (b) {b++;}                         // 31.5.07
     n = size(cfmt);
     if (!(parT) and  !(realT) and !(galT))
     { if( !(b2) or defined(TeXnofrac))
       { monomt = cfmt; msz = 3*size(monomt);}
       else
       { monomt = "\\frac{" + cfmt[1,b2-1] + "}{" + cfmt[b2+1,n-b2] + "}";
          if (n-2*b2>0) {msz = C*(n-b2);}
          else {msz = C*b2;}
       }
     }
     if (parT and !(galT))
     { monomt,msz = parsp(cfmt,b);}
    }
    if (monom!=1 and monomt!="" and parT) // 21.4.10
    { monomt = monomt+"\\cdot ";} // at least a blank is needed for TeXreplace

// -- now parse the monom
    if (monom <> 1)
    { i = 1;
      if(short)
      { while(s[i]<>"!")
        { monomt = monomt + s[i]; i++;
          b = i;
          msz = msz + 3; // it was a single lettered var
          while(s[i]!="!" and s[i]>="0" and s[i]<="9"){i++;}
          if (i-b)
          { monomt = monomt + "^{" + s[b,i-b] + "}";
            msz = msz + 2*(i-b);
          }
        }
      }
      else          //  not short
      { t,i = parselong(s);
        monomt = monomt + t;
        msz = msz + i;
      }
    }

   msz = msz + 6*size(sign);   // Wieso mal 6 ??
//  string(msz) + "  ," + string(linesz) + "  " + string(cfm*monom);

   if (TeXwidth > 10 and (linesz + msz > 3*TeXwidth) and linesz)
   { pt = pt + lnbreak + bg;
     linesz = msz;
   }
   else { linesz = linesz + msz; }  // 3 for sign
    pt = pt + sign + monomt;
   sign = "+";
   monomt = "";
  }

  if (k<ncols(I)){ pt = pt + sep;}
 }

  if (TeXwidth==0 and typeof(p)=="poly"){ pt = pt + "= 0";}
  if (!TW) { kill TeXwidth;}    // kill Latex::
  if (not(defined(NoDollars))) { pt = "$"+pt+"$";}

  if (size(fname))
  { i=1;
    while (fname[i]==">"){i++;}
    fname = fname[i,size(fname)-i+1];

    if (size(fname)>=4)         // check if filename is ending with ".tex"
    { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; }
    }
    else {fname = fname + ".tex";}
    write(fname,pt);
   }
  else {return(pt);}
}
example
{ "EXAMPLE:"; echo =2;
  ring r0=0,(x,y,z),dp;
  poly f = -1x^2 + 2;
  texpoly("",f);
  ring rr= real,(x,y,z),dp;
  texpoly("",2x2y23z);
  ring r7= 7,(x,y,z),dp;
  poly f = 2x2y23z;
  texpoly("",f);
  ring rab =(0,a,b),(x,y,z),dp;
  poly f = (-2a2 +b3 -2)/a * x2y4z5 + (a2+1)*x + a+1;
  f;
  texpoly("",f);
  texpoly("",1/(a2+2)*x2+2/b*x+(a+1)/3);
}
///////////////////////////////////////////////////////////////////////////////

static proc parsp(string cfmt, int b)
{ string mt, nom,denom;
  int fl1,fl2,sz1,sz2,msz;

  if (!(b))
  { mt,fl1 = parst(cfmt,0); msz = size(cfmt)-2;
    if (fl1) { mt = "(" + mt + ")"; msz = msz +1; }
  }
  else
  {
    if (b>0) {
     nom,fl1 = parst(cfmt[1,b-1],1);
     denom,fl2 = parst(cfmt[b+1,size(cfmt)-b],1);
    }
    else {
     b = -b;
     nom,fl1 = parst(cfmt[1,b],1);
     denom,fl2 = parst(cfmt[b+2,size(cfmt)-b-1],1);
    }
    if (defined(TeXnofrac))
    { if(fl1) { nom = "(" + nom + ")"; sz1++;}
      if(fl2) {denom = "(" + denom + ")"; sz2++;}
      mt = "(" + nom+ "/"+ denom+ ")"; msz = sz1+sz2 +1;   //31.5.07
    }
    else
    { mt = "\\frac{" + nom + "}{" + denom + "}";
      if (sz1-sz2) { msz = 5*sz1;}
      else {msz = 5*sz2;}
    }
   }
  return(mt,msz);
}
example
{"EXAMPLE:"; echo =2;
  ring r=(0,a,b),x,dp;
  int i;
  poly f = (a2b12 + 23a2 -b13-1)/(a2+2b -1);
  f;
  string s;
  s= string(f);
  i = find(s,")/(");
  parsp(s,i);
}
///////////////////////////////////////////////////////////////////////////////

static proc parst(string s,int sec)                // parse parameter
// sec parameter to see if in parsp a fraction follows
{
  int i,j =1,-1;
  int b,k,jj,mz,in;                         // begin and end, in for index
  int saveshort=short;
  string t,c,vn,nom,denom,sg;

  if (s[1]=="(") { s = s[2,size(s)-2]; }
  s = s + "!";

  if (short)
  { j = 0;  // 31.5.07
    while(s[i]<>"!")
    { b=i; if (s[i]=="+" or s[i]=="-") {j++;}  // 31.5.07
      while(s[i]>="0" and s[i]<="9" or (s[i]=="+" or s[i]=="-") and s[i]!="!")
      {i++;}     // scan the number
        t =s[b,i-b];
    //  if (t=="-1" and s[i]!="!" and s[i]!="-" and s[i]!="+"){t = "-";}
      if (t=="-1" and (s[i]<="0" or s[i]>="9") and s[i]!= "/" and s[i]!="!")
      {t = "-";}
      if (s[i]=="/")
      { i++;
        sg = "";
        if (t[1]=="+" or t[1]=="-")
        { nom = t[2,size(t)-1];
          sg = t[1];
        }
        else { nom = t;}
        b =i;
        while(s[i]>="0" and s[i]<="9") {i++;}
        denom = s[b,i-b];
        if (!(sec) and (!(defined(TeXaligned))))
        { t = sg + "\\frac{" + nom + "}{" + denom + "}";}
        else
        { t = sg + "(" + nom + "/" + denom + ")";
        }
      }
      c = c + t;
      if(s[i]!="!"){c = c + s[i]; i++;}      // the parameter
      b=i;
      while(s[i]>="0" and s[i]<="9")
      {i++;}  //the exponent
      if(i-b){ c = c + "^{" + s[b,i-b]+"}";}
     }
   }
   else                         // if not short ....
   { while (s[i] <> "!")
   { b=i; j++; in=0;         // 4.10.10
       while(s[i]=="-" or s[i]=="+" or (s[i]>="0" and s[i]<="9")){i++;}
       t = s[b,i-b];
       if (t=="-1" and s[i]=="*" ) {t="-";}
       if (s[i]=="/")
       { i++;
         sg = "";
         if (t[1]=="+" or t[1]=="-")
         { nom = t[2,size(t)-1];
           sg = t[1];
         }
         else { nom = t;}
         b =i;
         while(s[i]>="0" and s[i]<="9") {i++;}
         denom = s[b,i-b];
         if (!(sec) and (!(defined(TeXaligned))))
         { t = sg + "\\frac{" + nom + "}{" + denom + "}";}
         else
         { t = sg + "(" + nom + "/" + denom + ")";
         }
       }
       c = c+t; t="";
       if (s[i]=="*"){i++;}
       b=i;
      //  string(s[1,b]);

       while(s[i]!="+" and s[i]!="-" and s[i]!="!")  //pass a monom
       { // start with letters
        // alternativ:
        //in=0;         // 4.10.10
        while((s[i]>="a" and s[i]<="z") or (s[i]>="A" and s[i]<="Z")){i++;}
        k = i-b;
        vn = s[b,k];
        if (defined(TeXreplace))
        { for (jj=1; jj<= size(TeXreplace);jj++)
         { if (vn == TeXreplace[jj][1])
           {vn = TeXreplace[jj][2]; k=1;
             if (s[i]=="*") {vn = vn + " ";}
            break;} //suppose replacing by a single sign
         }
        }
        t = t + vn;
        mz = mz + 10*k;
        if (s[i]=="_"  or s[i]=="(") {in++; i++;}    // the index is coming
        b = i;
        while(s[i]>="0" and s[i]<="9"){ i++;}
        k = i-b;
        if (k and in<=1) {t = t + "_{";in++;} //and k  i.e. there was an index
        if (k){ t = t +s[b,k];}
        if(s[i]==")") {i++;}
        if(k and s[i]!="(" and s[i]!="_"){ t = t + "}";} // index closed
        if(s[i]=="(" or s[i]=="_") {i++; t = t + ",";in++;}
        if (s[i]=="^")
        { i++; b = i;
          while(s[i]>="0" and s[i]<="9"){ i++;} // for neg. expon.
          if (b-i) { t = t + "^{" + s[b,i-b] + "}";}
        }
        if (i-b > k) { mz = mz + 5*(i-b);}
        else {mz = mz + 5*k;}
        if (s[i]=="*"){i++;in=0;}
        b=i;
       }
       c =c+t;
      }
   }
   short = saveshort;
   return(c,j);
}
example
{ "EXAMPLE:"; echo =2;
  ring r=(0,a,b),x,dp;
  poly f = (a2b12 + 23a2 -b13-1);
  f;
  parst(string(f),0);

  f =(-a +4b2 -2);
  f;
  parst(string(f),0);

  f = a23;
  f;
  parst(string(f),0);
  f = 2a12b3 -4ab15 +2a4b12 -2;
  short =0;
  f;
  parst(string(f),0);
   ring r2=(0,a1,b1),x,dp;
  poly f = 2*a1^12*b1^3 -4*a1*b1^15 +2*a1^4*b1^12 -2;
  f;
  parst(string(f),0);
}
///////////////////////////////////////////////////////////////////////////////

static proc parselong(string s)
{
  int i,j,k,b,mz,in;    // in is a counter for indices
  string t,vn;              // varname

  i = 1;
  while (s[i] <> "!")
  { b=i;

  // -- scan now the letter ...
  //  while(s[i]!="!" and )

// alternativ:
 while((s[i]>="a" and s[i]<="z") or (s[i]>="A" and s[i]<="Z"))
 { i++;}
 // s[i]; i;
   k = i-b;
   vn = s[b,k];

   if (defined(TeXreplace))
   { for (j=1; j<= size(TeXreplace);j++)
     { if (vn == TeXreplace[j][1])
       {vn = TeXreplace[j][2]; k=1;
        if (s[i]=="*") {vn = vn + " ";}
         break;} //suppose replacing by a single sign
     }
   }
   t = t + vn;
   mz = mz + 10*k;
   if (s[i]=="_"  or s[i]=="(") { in++;i++;}    // the index is coming
   b = i;
   while(s[i]>="0" and s[i]<="9" or s[i]=="-"){ i++;}  // "-" for neg indices
   j = i-b;
   // if (j){ t = t + "_{" +s[b,j] + "}";}  // formely
   if (j and in<=1) {t = t + "_{";in++;}  // and j  i.e. there was an index
   if (j){ t = t  +s[b,j];}
   if(s[i]==")") {i++;}
   if(j and s[i]!="(" and s[i]!="_"){ t = t + "}";} // index closed
   if(s[i]=="(" or s[i]=="_") {i++; t = t + ",";in++;}
   if (s[i]=="^")
   { i++; b = i;
     while(s[i]>="0" and s[i]<="9" or s[i]=="-")
     { i++;}  // for neg. expon.
     if (b-i) { t = t + "^{" + s[b,i-b] + "}";}
   }
   if (i-b > j) { mz = mz + 5*(i-b);}
   else {mz = mz + 5*j;}
   if (s[i]=="*"){i++;in=0;}
  }
  return(t,mz);
}
example
{ "EXAMPLE:"; echo =2;
  ring r =(49,a),x,dp;
  number f = a13;
  parsg(string(f));
  list TeXreplace; export TeXreplace;
  TeXreplace[1] = list("b","\\beta");
  TeXreplace[2] = list("a","\\alpha");
  TeXreplace[3] = list("c","\\gamma");
  parselong(string(f)+"!");
}
///////////////////////////////////////////////////////////////////////////////

/* obsolete
static proc tktex (def d)
{
 // calls appropriate proc from latex lib

 string typeofd =typeof(d);
 if (typeofd=="int" or typeofd=="string" or typeofd=="resolution" or typeofd=="map" or typeofd =="list"){ return(d);}

 if (typeofd=="intvec" or typeofd == "intmat" or typeofd =="vector" or
     typeofd=="matrix" or typeofd == "module")   { return(texobj("",d));}
 if (typeofd=="ring") { return(texring("",d));}
 if (typeofd =="ideal") { return(texobj("",d));}
 if (typeofd=="number" or typeofd=="poly" or typeofd=="ideal")
                                                 { return(texpoly("",d));}
 if (typeofd=="link") {return(d);}

}
*/
/////////////////////////////  PART0 //////////////////////////////////////////

static proc part0(string fname)
{
 int texdemopart =0;
 export texdemopart;


// Singular script for generating tldemo.tex

 string nl = newline;
 string nl2 = newline + newline;
 string lb = "\\\\";
 string bv = "\\begin{verbatim}" + newline ;
 string ev = newline + "\\end{verbatim}" +newline ;

// "generating part0 of " + fname  + nl;

 opentex(fname);

write(fname,"\\newcommand{\\Line}{{}\\par\\noindent\\rule{\\textwidth}{0.25mm}\\\\[1mm]}");

   write(fname,"\\centerline{\\textbf{\\large Demo file for latex.lib }}");
   //  write(fname,"\\centerline{\\textbf{\\large Christian Gorzel }}");
   write(fname,"\\centerline{07/10/2010}");
   write(fname,"\\vspace{1cm}");

//--

 write(fname,"","\\section{Introduction}");
 write(fname,"The procedures in \\verb|latex.lib| translate the output of
 {\\sc Singular} into \\LaTeX \\ text.
 This document illustrates the functionality of the library."+"\\\\" +  nl);
 write(fname,"\\begin{tabular}{ll}" + nl +
"LIBRARY: {\\tt latex.lib} &   PROCEDURES FOR TYPESETTING SINGULAR" +
"\\\\" +  nl +
" & OBJECTS IN LATEX2E"+
"\\\\" +  nl +
"{\\tt closetex(fnm);} & writes closing line for \\LaTeX-document"+
"\\\\" +  nl +
"{\\tt  opentex(fnm);} & writes header for \\LaTeX-file fnm"+
"\\\\" +  nl +
"{\\tt  tex(fnm);} & calls \\LaTeX2e for file fnm"+
"\\\\" +  nl +
"{\\tt  texdemo([n]);} & produces a file explaining the features of this lib"+
"\\\\" +  nl +
"{\\tt  texfactorize(fnm,f);} & creates string in \\LaTeX-format for
factors of polynomial f"+ "\\\\" +  nl +
"{\\tt  texmap(fnm,m,r1,r2);} & creates string in \\LaTeX-format for
map m:r1$\\rightarrow$r2"+ "\\\\" +  nl +
"{\\tt  texname(fnm,s);} &      creates string in \\LaTeX-format for
identifier"+ "\\\\" +  nl +
"{\\tt  texobj(l);} &           creates string in \\LaTeX-format for
any (basic) type"+ "\\\\" +  nl +
"{\\tt  texpoly(f,n[,l]);} &    creates string in \\LaTeX-format for poly"+
"\\\\" +  nl +
"{\\tt  texproc(fnm,p);} &      creates string in \\LaTeX-format of
text from proc p"+ "\\\\" +  nl +
"{\\tt  texring(fnm,r[,l]);} &  creates string in \\LaTeX-format for
ring/qring"+ "\\\\" +  nl +
"{\\tt  rmx(s);} &              removes .aux and .log files of \\LaTeX-files"+
"\\\\" +  nl +
"{\\tt  xdvi(s);} &             calls xdvi for dvi-files"+
"\\\\" +  nl +
" \\end{tabular} " + nl2 + "\\vspace{0.2cm}" + nl2 +
"(parameters in square brackets {\\tt [ ]} are optional)"+
"\\\\" +  nl2 + "\\vspace{0.2cm}" + nl2 +
"The global variables {\\tt TeXwidth}, {\\tt TeXnofrac}, {\\tt
 TeXbrack}, {\\tt TeXproj}, {\\tt TeXaligned}, {\\tt TeXreplace}, {\\tt
 NoDollars} are used to control the typesetting: "
);

write(fname,
bv +
"
  TeXwidth   (int) -1, 0, 1..9, >9:  controls breaking of long polynomials
  TeXnofrac  (int) flag:  write 1/2 instead of \\frac{1}{2}
  TeXbrack   (string) \"{\", \"(\", \"<\", \"|\", empty string:
                            controls brackets around ideals and matrices
  TeXproj    (int) flag:  write \":\" instead of \",\" in vectors
  TeXaligned (int) flag:  write mappings (and ideals) aligned
  TeXreplace (list) list entries = 2 strings:  replacing symbols
  NoDollars  (int) flag:  suppresses surrounding $ signs

" +
ev);
write(fname,"Notice that none of these global variables are defined when
loading \\verb|latex.lib|. A flag variable is set as soon as it is defined.");


//% The procs and
//% the global variables

//----------------------- opentex -----------------------------
   write(fname,"","\\section{Opening a \\LaTeX\\ file}");
   write(fname,"","In order to create a \\LaTeX\\ document and write a standard
header into it, use the following command."+ nl +
bv+
"> string fname = \"" + fname + "\";" + nl +
"> texopen(fname);" +
ev);

write(fname,"The variable \\verb|fname| is always the first argument when
calling one of the procedures of \\verb|latex.lib|. If this string is the
empty string, then the output in not written into a file but displayed on
the screen.");

 //% opentex, defaulted to latex, possibly extension are ... and
 //% ``own''


pagewidth = 65;
int TeXwidth = 100; export TeXwidth;
// "part 0 generated " + nl;
} //part0


/////////////////////////////  PART1 //////////////////////////////////////////

static proc part1(string fname)
{

  int st = defined(texdemopart);
  string nl = newline;
  string nl2 = newline + newline;
  string lb = "\\\\";
  string bv = "\\begin{verbatim}" + newline ;
  string ev = newline + "\\end{verbatim}" + newline ;

  if (not(st) or texdemopart>=1)
  { print(" Call part0 first");
    return();
  }
  else { texdemopart=1; }

//"Continuing part1 of " + fname + nl;

write(fname,"","\\section{Rings, polynomials and ideals}","");

// -1a------ a ring in char 0, short varnames and poly. ordering ----------
write(fname,
" A ring in characteristic 0 with short names of variables and polynomial
ordering." +nl);
 ring r0=0,(x,y,z),dp;
 poly g=-x2y+2y13z+1;
write(fname,
bv +
"> ring r0=0,(x,y,z),dp;" +nl+
"> texring(fname,r0);" +
ev);
  texring(fname,r0);
  write(fname,nl2);
write(fname,
bv +
"> poly g=-x2y+2y13z+1;  g;" + nl +
"> texpoly(fname,g);" +
ev);
  texpoly(fname,g);
  write(fname,"\\\\"+nl);

// write(fname,"\\Line");

// -1b------ still in the same ring, a polynomial with rational coefs --------
write(fname,
""," A polynomial with rational coefficients." +nl);
write(fname,
bv +
"> texpoly(fname,g/280);" +
ev
);
  texpoly(fname,g/280);
  kill r0;

write(fname,"\\Line","%-----------------------------------------------------");
// -2-------- a ring in char 7, indexed varnames and series ordering ----------
write(fname,
" A ring in characteristic 7 with indexed names of variables and local
ordering.","");
 ring r1=7,(x1,x2,x3,x4),Ds;
 poly g=-2*x1+x4-1;
write(fname,
bv +
"> ring r1=7,(x1,x2,x3,x4),Ds;" +nl +
"> texring(fname,r1);" +
ev);
texring(fname,r1);


write(fname, bv +
"> poly g=-2*x1+x4-1;  g;" +nl +
"> texpoly(fname,g);" +
ev);

  texpoly(fname,g);

write(fname,"\\Line","%-----------------------------------------------------");

// -3-------- a ring in char 0, indexed varnames and local ordering ----------
write(fname,
" A ring in characteristic 0 with indexed names of variables and local
ordering.
" +nl);
 ring r2=0,(x(1..5),y(1..2)),(ds(5),ls(2));
 poly g=-y(1)^3*x(5) +y(1)*x(2);
write(fname,
bv +
"> ring r2=0,(x(1..5),y(1..2)),(ds(5),ls(2));" + nl +
"> texring(fname,r2);" +
ev);
  texring(fname,r2);

write(fname,
bv +
"> poly g=-y(1)^3*x(5)+y(1)*x(2);  g;" +nl+
 string(g) + nl +
"> texpoly(fname,g);"  +
ev
);
  texpoly(fname,g);

write(fname,"\\Line","%-----------------------------------------------------");

// -4-------- a ring in char 0, indexed varnames and weighted ordering ------
write(fname,
" A ring in characteristic 0 with indexed names of variables and weighted
 ordering." +nl);
 ring r3=0,(x_1,x_2,x_3),wp(3,2,1);
 poly g=-x_1*x_2+2*x_2*x_3+x_1*x_3;
write(fname,
bv +
"> ring r3=0,(x_1,x_2,x_3),wp(3,2,1);" +nl+
"> texring(fname,r3);" +
ev);
  texring(fname,r3);
write(fname,
bv +
"> poly g=-x_1*x_2+2*x_2*x_3+x_1*x_3;  g;" +nl+
  string(g) + nl +
"> texpoly(fname,g);"  +
ev
);
texpoly(fname,g);

write(fname,"\\Line","%-----------------------------------------------------");

// -5-------- a ring with real coeff and matrix ordering -------------------
write(fname,
" A ring with real coefficients and matrix ordering.
" +nl);
 ring rr=real,(x,y),M(1,2,3,4);
 poly g =-1.2e-10*x2+y+1;
write(fname,
bv +
"> ring rr=real,(x,y),M(1,2,3,4);"+nl+
"> texring(fname,rr);"+
ev);
  texring(fname,rr);

write(fname,
bv +
"> poly g=-1.2e-10*x2+y+1;  g;"+nl+
  string(g) + nl +
"> texpoly(fname,g);" +
ev);
  texpoly(fname,g);

write(fname,"\\Line","%-----------------------------------------------------");

// -6a-------- a ring in char 0, and indexed parameters --------- ----------
write(fname,
" A ring in characteristic 0 with parameters.
" +nl);
 ring r0t=(0,s,t),(x,y),dp;
 poly g=8*(-s+2t)/(st+t3)*x+t2*x-1;
write(fname,
bv +
"> ring r0t=(0,s,t),(x,y),dp;" +nl +
"> texring(fname,r0t);" +
ev);
 texring(fname,r0t);
write(fname,
bv +
"> poly g=8*(-s+2t)/(st+t3)*x+t2*x-1;  g;"+nl+
  string(g) +nl +
"> texpoly(fname,g);" +
ev);
  texpoly(fname,g);
write(fname,"\\Line","%-----------------------------------------------------");
write(fname,"\\newpage");

// -6b------- a ring in char 11003, and indexed parameters --------- ----------
write(fname,
" A ring in characteristic 11 and indexed parameters.
" +nl);
 ring rt=(11003,t1,t2,t3),(X,Y),dp;
 poly g=8*(-t1+t2)/(t1+t3)*X+t2*Y-1;
write(fname,
bv +
"> ring rt=(11003,t1,t2,t3),(X,Y),dp;" +nl +
"> texring(fname,rt);" +
ev);
  texring(fname,rt);

write(fname,
bv +
"> poly g=8*(-t1+t2)/(t1+t3)*X+t2*Y-1;  g;" + nl+
 string(g) +nl +
"> texpoly(fname,g);" +
ev);
  texpoly(fname,g);

write(fname,"\\Line","%-----------------------------------------------------");

// -7-------- a ring over an algebraic extension in char 7 ---------------
write(fname," A ring over an algebraic extension in char 7.");

  ring ralg = (7,a),x,dp;
  minpoly = a2-a+3;
  poly g = -(2a13+a)*x2+a2*x-a+1;

write(fname,
bv +
"> ring ralg=(7,a),x,dp;" +nl +
"> minpoly=a2-a+3;" +nl +
"> texring(fname,ralg);" +
ev);
 texring(fname,ralg);

write(fname,
bv +
"> poly g=-(2a13+a)*x2+a2*x-a+1;  g;"+nl+
 string(g) +nl +
"> texpoly(fname,g);" +
ev
);
  texpoly(fname,g);

write(fname,"\\Line","%-----------------------------------------------------");

// -8-------- the same ring a in 7 ralg, defined with gftables -- F_49 -------
write(fname,
" A ring defined with \\verb|gftables|, the same as \\verb|ralg| before, but
with primitive element in the Galois field $\\F_{49}$." +nl);
 ring r49 =(49,a),x,dp;
 poly g=-(2a13+a)*x2+a2*x-a+1;
write(fname,
bv +
"> ring r49 =(49,a),x,dp;" +nl+
"> texring(fname,r49);" +
ev);
 texring(fname,r49);

write(fname,
bv +
"> poly g=-(2a13+a)*x2+a2*x-a+1;  g;" +nl+
 string(g) +nl +
"> texpoly(fname,g);" +
ev);
  texpoly(fname,g);

write(fname,"\\Line","%-----------------------------------------------------");

// -9-------- a ring over the Gaussian numbers  ----------
write(fname,
" A ring over the Gaussian numbers.
" +nl);
 ring ri=(0,i),(x,y,z),ls;
 minpoly=i2+1;
 poly g=-(i+1)*x+2i2y2+i+x;
write(fname,
bv +
"> ring ri=(0,i),(x,y,z),ls;" +nl +
"> minpoly=i2+1;" +nl +
"> texring(fname,ri);" +
ev);
 texring(fname,ri);

write(fname,
bv +
"> poly g=-(i+1)*x+2i2y2+i+x;  g;" +nl+
 string(g) +nl +
"> texpoly(fname,g);" +
ev
);
  texpoly(fname,g);

write(fname,"\\Line","%-----------------------------------------------------");

// -10--------- a quotient ring performed from  ----------
write(fname," A quotient ring performed of \\verb|r0| by an ideal.");
 ring r0=0,(x,y,z),dp;
 ideal I = x2-y, y+z2, xy;
 I = std(I);
string sI = string(I);
 qring qr = I;
write(fname,
bv +
"> setring r0;
> ideal I=x2-y,y+z2, xy;
> I=std(I);
> string(I);" + nl +
string(sI) + nl +
"> qring qr=I;
> texring(fname,qr);" +
ev
);
texring(fname,qr);

//write(fname,"\\Line","%-----------------------------------------------------");

// ------------------------- Features for rings

write(fname,"","\\subsection{Features for rings}");

write(fname,
"In many cases it might be convenient to change the standard typesetting
of rings. This can be done by passing additional arguments to \\verb|texring|."
+nl);

// changing the brackets

write(fname,nl,"In order to change the displayed brackets one has to give
the desired ones as additional argument (accepted brackets are: \\verb|\"\{\"|,
\\verb|\"\{\{\"|,\\verb|\"[\"|,\\verb|\"[[\"|,\\verb|\"<\"|,\\verb|\"<<\"|).");

write(fname,
bv +
"> texring(fname,rr,\"{{\");" +
ev
);

texring(fname,rr,"{{");

write(fname,
bv +
"> texring(fname,r2,\"[\");" +
ev
);

texring(fname,r2,"[");

write(fname,nl+"\\vspace{0.2cm}" + nl2);

write(fname,"The brackets around the ideal in a quotient ring can be
changed by setting  the global variable \\verb|TeXbrack| (see section
{\\tt Ideals}).",nl);

write(fname,
bv +
"> string TeXbrack = \"<\";" +nl +
"> texring(fname,qr);" +
ev
);

  string TeXbrack = "<"; export TeXbrack;
  texring(fname,qr);
  kill TeXbrack;

write(fname,
bv +
"> kill TeXbrack;" +
ev);

//write(fname,"\\Line","%-----------------------------------------------------");

// changing the ground field
// -------------------------------------------------

write(fname,
"It is possible to display a ground field different from the
actual one by passing any letter in \\LaTeX \\ notation as additional
argument.  Predefined values are \\verb|\"\\\\C\"|, \\verb|\"\\\\R\"|,
\\verb|\"k\"|, \\verb|\"K\"| and \\verb|\"R\"|."+nl+
"If for example a ground field of characteristic 0 should be written as
$\\C$ instead of $\\Q$ use this as additional argument.",nl);

write(fname,
bv +
"> texring(fname,r3,\"\\\\C\");" +
ev);

texring(fname,r3,"\\C");
write(fname,nl+ "\\vspace{0.2cm}" + nl2);

write(fname,"The values \\verb|\"k\"|, \\verb|\"K\"|, \\verb|\"R\"| play a
 special role when the ground field is an algebraic extension. In this case
the parameters will be omitted.");

write(fname,
bv +
"> texring(fname,ralg,\"k\");" +
ev
);

texring(fname, ralg,"k");
write(fname,nl+"\\vspace{0.2cm}" + nl2);

write(fname,"If an algebraic extension should be displayed together with
its minimal polynomial the optional parameter \\verb|mipo| has to be used.");

write(fname,
bv +
"> texring(fname,ralg,\"mipo\");" +
ev
);

texring(fname, ralg,"mipo");
write(fname,"\\Line","%-----------------------------------------------------");

// displaying only certain vars

write(fname,"By default all variables of a ring will be displayed. It is
possible to print only certain variables with $\\ldots$ between
them. The positions of the variables which should be displayed have to be
passed to \\verb|texring| as an \\verb|intvec|.");

write(fname,
bv +
"> intvec v=5,6;
> texring(fname,r2,v);" +
ev
);

  intvec v = 5,6;
  texring(fname,r2,v);
  kill v;

write(fname,
bv +
"> kill v;" +
ev
);

write(fname,nl+ "\\vspace{0.2cm}" + nl2);

write(fname,"The first and the last variable will always be printed.
In order to print only these it is sufficient to give a 1 as third argument.");

write(fname,
bv +
"> texring(fname,r1,1);" +
ev
);
texring(fname,r1,1);

write(fname,"\\Line","%-----------------------------------------------------");

// invariant ring under a group action

write(fname,"If you want for example to display a ring as the invariant ring
under a group, additional information starting with \\verb|^| may be added.");

write(fname,
bv +
"> texring(fname,r0,\"^G\");" +
ev
);

texring(fname, r0,"^G");
write(fname,"\\Line","%-----------------------------------------------------");

// passing several optional arguments at once

write(fname,"It is also possible to pass several of the arguments described
above at once (in any order).");


write(fname,
bv +
"> texring(fname,r3,\"\\\\R\",\"{{\",\"^G\");" +
ev
);

texring(fname, r3,"\\R","{{","^G");
//"end part 1" + nl;
}


/////////////////////////////  PART2 //////////////////////////////////////////


static proc part2(string fname)
{

  int st = defined(texdemopart);
  string nl = newline;
  string nl2 = newline + newline;
  string lb = "\\\\";
  string bv = "\\begin{verbatim}" + newline ;
  string ev = newline + "\\end{verbatim}" + newline ;
//  string ev = "\\end{verbatim}" ;

  if (not(st) or texdemopart>=2)
  { print(" Call part1 first");
    return();
  }
  else { texdemopart=2; }

// "Continuing Part2 of " + fname + nl;

//-------------------- texfactorize ------------------------------
write(fname,"","\\subsection{Factorized polynomials}");

write(fname,"The command \\verb|texfactorize| calls internally the
{\\sc Singular} command \\verb|factorize| and returns the product of the
irreducible factors. Note that, at the moment, it is not possible to pass
any optional arguments for \\verb|factorize| through \\verb|texfactorize|.");

  ring r0=0,(x,y,z),dp;
  poly h=(x+1+y)^2*x3y*(2x-2y)*y12;

write(fname,
bv +
"> setring r0;
> poly h=(x+1+y)^2*x3y*(2x-2y)*y12;   h;" +nl+
 string(h) + nl +
"> texfactorize(fname,h);" +
ev);
texfactorize(fname,h);

//  setring ralg;
  ring ralg = (7,a),x,dp;
  minpoly = a2-a+3;
  poly h = (a24x5+x3)*a2x6*(x+1)^2;

write(fname,
bv +
"> setring ralg;
> poly h=(a24x5+x3)*a2x6*(x+1)^2;  h;"+ nl +
 string(h) + nl +
"> texfactorize(fname,h);"+
ev);
texfactorize(fname,h);

//--------------------- features for polynomials -----------------
write(fname,"","\\subsection{Features for polynomials}");

// TeXreplace
// ---------------------------------------------
write(fname,"By setting the global variable \\verb|TeXreplace| it is possible
to define rules for replacing strings or variable names.
\\verb|TeXreplace| has to be a list of twoelemented lists where the first
entry is the text which should be replaced by the second entry.
This may be applied to replace names of variables, but is also used
when calling \\verb|texname| or \\verb|texmap|. Note that it
is necessary to write a double backslash \\verb|\\\\\| at the beginning of
a \\TeX \\ symbol.","");

write(fname,"Let us denote the primitive element of an algebraic extension
by $\\xi$.");

list TeXreplace; export TeXreplace;
TeXreplace[1] = list("a","\\xi");
// setring r49;
  ring r49 =(49,a),x,dp;
  poly g=-(2a13 +a)*x2+a2*x-a+1;
write(fname,
bv +
"> list TeXreplace;" +nl +
"> TeXreplace[1]=list(\"a\",\"\\\\xi\");" +nl+
"> setring r49;" +nl+
"> texpoly(fname,g);"+
ev);

texpoly(fname,g);

write(fname,nl+ "\\vspace{0.2cm}" + nl2);
write(fname,"Now let us write $\\lambda$ and $\\mu$ for deformation
parameters.");
TeXreplace[2]= list("s","\\lambda");
TeXreplace[3]= list("t","\\mu");
// setring(r0t);
  ring r0t=(0,s,t),(x,y),dp;
  poly g=8*(-s+2t)/(st+t3)*x+t2*x-1;
write(fname,
bv +
"> TeXreplace[2]=list(\"s\",\"\\\\lambda\");"+nl+
"> TeXreplace[3]=list(\"t\",\"\\\\mu\");"+nl+
"> setring(r0t);"+nl+
"> texpoly(fname,g);"+
ev);
texpoly(fname,g);

kill TeXreplace;
write(fname,nl+ "\\vspace{0.4cm}");
write(fname,nl+"Note that, if \\verb|TeXreplace| is defined, the translation
into \\LaTeX  code runs a little bit slower, because every polynomial is
compiled in the \\verb|non short| mode."+ lb );

write(fname,nl,"\\Line","%-----------------------------------------------------");

//linebreaking   TeXwdith
//-----------------------------------------------------------------------
write(fname,"The global variable \\verb|TeXwidth| controls the wrapping of
polynomials; possible values are:" + lb);

write(fname,
"\\[ " + nl +
"\\text{\\tt TeXwidth} = ",
"\\begin{cases} ",
" -1 & \\text{no line-breaking} \\\\ ",
"  0 & \\text{print the polynomial as equation } f=0 \\\\ ",
" 1,\\dots,9 & \\text{the first n terms followed by the sign of the next
term} \\\\ ",
" > 9 & \\text{line break after terms of length n (see below)} ",
"\\end{cases}",
"\\]",nl);

write(fname,"Note that the size of terms is calculated with certain
multiplicities.",nl);

//----------------------------------------------------------

write(fname,"\\begin{itemize}");
write(fname,"\\item");

write(fname,
bv +
"> TeXwidth=-1;"+nl+
"> setring r0;"+nl+
"> poly f=g^2;"+nl+
"> texpoly(fname,f);" +
ev);

  setring r0;
  poly g=-x2y+2y13z+1;
  poly f=g^2;
  texpoly(fname,f);

write(fname,"\\item");

write(fname,
bv +
"> TeXwidth=0;
> texpoly(fname,f);"+
ev);
TeXwidth = 0;
texpoly(fname,f);

write(fname,"\\item");
write(fname,
bv +
"> TeXwidth=2;
> texpoly(fname,f);"+
ev);
TeXwidth=2;
texpoly(fname,f);

write(fname,"\\item");
write(fname,
bv +
"> TeXwidth=20;"+nl+
"> texpoly(fname,f);"+
ev);
TeXwidth=20;
texpoly(fname,f);
TeXwidth=-1;

write(fname,"\\end{itemize}");

write(fname,"\\Line","%-----------------------------------------------------");

write(fname,"There are two possibilities to convert a polynomial into
\\LaTeX{} code: either by using \\verb|texpoly| or by calling \\verb|texobj|.
The difference is that \\verb|texpoly| puts the polynomial in text-mode
while \\verb|texobj| uses the display mode."+nl+
"The following examples show the different outputs:");

write(fname,
bv +
"> setring r3;
> texpoly(fname,g/180);" +
ev);

// setring r3;

  ring r3=0,(x_1,x_2,x_3),wp(3,2,1);
  poly g=-x_1*x_2+2*x_2*x_3+x_1*x_3;
  texpoly(fname,g/180);

write(fname,
bv +
"> texobj(fname,g/180);
" +
ev);

texobj(fname,g/180);

//write(fname,"Some explanation how it works: if \\verb|texobj| is called for
//a polynomial, then it defines a global variable \\verb|TeXdisp| which forces
//\\verb|texpoly| to count fraction with space corresponding
//the displaymode."+lb,nl2);
//---------------------texobj for ideal ---------------

write(fname,"","\\subsection{Ideals}");
write(fname,"By default, ideals are displayed as column vectors.");

  ring r;
  ideal I=3xz5+x2y3-3z,7xz5+y3z+x-z,-xyz2+4yz+2x;

write(fname,
bv +
"> ring r;   // the default ring"+nl+
"> ideal I=3xz5+x2y3-3z,7xz5+y3z+x-z,-xyz2+4yz+2x;"+nl+
"> texobj(fname,I);" +
ev);

texobj(fname,I);

write(fname,"\\Line","%-----------------------------------------------------");
//----------------------------------------------------------------------
write(fname,"If the global variable \\verb|Texaligned| is set then the ideal
is displayed as a row vector.");

write(fname,
bv +
"> int TeXaligned;
> texobj(fname,I);" +
ev);

int TeXaligned; export TeXaligned;
texobj(fname,I);

 write(fname,nl+"\\Line","%-----------------------------------------------------");
//----------------------------------------------------------------------
write(fname,"By setting the global variable \\verb|TeXbrack| it is possible
to change the brackets.");

write(fname,
bv +
"> string TeXbrack=\"<\";"+nl+
"> texobj(fname,I);"+
ev);

string TeXbrack="<";  export TeXbrack;
texobj(fname,I);

write(fname,
bv +
"> kill TeXbrack, TeXaligned;" +
ev);

kill TeXbrack,TeXaligned;
write(fname,"\\Line","%-----------------------------------------------------");
//----------------------------------------------------------------------
write(fname,
" If \\verb|TeXwidth| is 0, an ideal is displayed as a system of
equations.");

// ------------- a linear equation system

  ring r5=0,x(1..5),dp;
  ideal I=-x(1)+2*x(3)+x(5), x(2)-x(4)+2*x(5)-1, 8*x(1)+x(4)+2;
  TeXwidth=0;

write(fname,
bv +
"> ring r5=0,x(1..5),dp;"+nl+
"> ideal I=-x(1)+2*x(3)+x(5), x(2)-x(4)+2*x(5)-1, 8*x(1)+x(4)+2;"+nl+
"> TeXwidth=0;"+nl+
"> texobj(fname,I);" +
ev);

  texobj(fname,I);

  setring r;
  ideal J=4x4y21+z25y7-y2,x3+y2,y2-z4;

write(fname,
bv +
"> setring r;"+nl+
"> ideal J=4x4y21+z25y7-y2,x3+y2,y2-z4;"+nl+
"> texobj(fname,J);" +
ev
);
  texobj(fname,J);

write(fname,"\\Line","%-----------------------------------------------------");
//-----------------------------------------------------------------------
write(fname,"Call the ideal by its name and it is printed as follows");

write(fname,
bv +
"> setring r;
> ideal I=3xz5+x2y3-3z,7xz5+y3z+x-z,-xyz2+4yz+2x;
> texobj(fname,\"I\");" +
ev);

 setring r; export(I);
 texobj(fname,"I");
 kill I,r;
//" end part 2 " + nl;
}

/////////////////////////////  PART3 //////////////////////////////////////////

static proc part3(string fname)
{
  int st=defined(texdemopart);
  string nl=newline;
  string nl2=newline + newline;
  string lb="\\\\";
  string bv=newline+"\\begin{verbatim}";
//  string ev = newline + "\\end{verbatim}" + newline ;
  string ev="\\end{verbatim}" ;

  if (not(st) or st>=3)

  {
    print(" Call part2 first");
    return();
  }
  else { texdemopart=3; }

// " Continuing part 3 of " + fname +
// " : map,matrices,vectors,intvec,intmats,proc";

//---------------------- texmap ------------------------------
write(fname,"","\\section{Typesetting maps between rings}");
write(fname,"By default, maps are displayed in the following way:");

write(fname,
bv,
"> ring r4=0,(x,y,z),dp;
> ring r5=0,(u,v),dp;
> map phi=r1,u2,uv -v,v2;
> texmap(fname,phi,r4,r5);",
ev);

  ring @r4_h=0,(x,y,z),dp;
  export @r4_h;
  ring r5=0,(u,v),dp;
  map @phi_h=@r4_h,u2,uv -v,v2;  export @phi_h;
  texmap(fname,@phi_h,@r4_h,r5);

write(fname,"\\Line","%-----------------------------------------------------");
//--------------------------------------------------------------------

write(fname,"If the global variable \\verb|TeXaligned| is set, then the
map is displayed in one line.");

write(fname,
bv,
"> int TeXaligned;
> texmap(fname,phi,r4,r5,\"\\\\C\");",
ev );

  int TeXaligned; export TeXaligned;
  texmap(fname,@phi_h,@r4_h,r5,"\\C");

write(fname,nl+"\\Line","%-----------------------------------------------------");
//--------------------------------------------------------------------

write(fname,"It is possible to pass the same additional arguments to
\\verb|texmap| as to \\verb|texring| (see section {\\tt Rings}). This can
be done by calling \\verb|texmap| with two lists as additional parameters,
where the first list contains the optional parameters for the source and
the second one contains the parameters for the domain. Note that if only one
list is present then it is applied to both of the rings.");

write(fname,
bv,
"> texmap(fname,phi,r4,r5,\"\\\\C\",\"{\");",
ev );
  texmap(fname,@phi_h,@r4_h,r5,"\\C","{");

write(fname,nl+ "\\vspace{0.2cm}" + nl);
write(fname,"The next example shows how to format the two rings in different
ways.");

write(fname,
bv,
"> texmap(fname,phi,r4,r5,list(),list(\"{\"));",
ev );

 texmap(fname,@phi_h,@r4_h,r5,list(),list("{"));

write(fname,"\\Line","%-----------------------------------------------------");
//--------------------------------------------------------------------

write(fname,"If the map is called by its name then \\verb|texmap| displays,
in addition, also the name of the map.");

write(fname,
bv,
"> list TeXreplace;
> TeXreplace[1]=list(\"phi\",\"\\\\phi\");
> texmap(fname,\"phi\",r4,r5);",
ev);

  list TeXreplace;
  TeXreplace[1]=list("@phi_h","\\phi");
  export TeXreplace;
  texmap(fname,"@phi_h",@r4_h,r5);
  kill @phi_h,@r4_h,r5,TeXreplace,TeXaligned;

write(fname,
bv,
      "> kill phi,r4,r5,TeXreplace,TeXaligned;",
ev);


//% the texobj part
write(fname,"","\\section{Typesetting composed data structures}");
//=======================================================================

write(fname, "Complex data structures such as matrices, vectors or modules
can be displayed by using the procedure \\verb|texobj|.");

write(fname,"","\\subsection{Matrices and vectors}");
//=======================================================================

write(fname,"The following example shows how to typeset the Hessian of a
polynomial.");

write(fname,
bv,
"> ring r;
> poly h=2xy3-x2z+x4z7+y4z2;
> matrix H=jacob(jacob(h));
> texobj(fname,H);",
ev );

ring r;
poly h=2xy3-x2z+x4z7+y4z2;
matrix H=jacob(jacob(h));
texobj(fname,H);

write(fname,"By default, \\verb|vectors| are written as row vectors:");

vector V = H[2];

write(fname,
bv,
"> vector V=H[2];
> texobj(fname,V);",
ev );

texobj(fname,V);

write(fname,nl+"\\vspace{0.2cm}"+nl);
write(fname,"In order to transpose it, it has to be converted into a
matrix.");
write(fname,
bv,
"> texobj(fname,matrix(V));",
ev );

texobj(fname,matrix(V));

write(fname,nl+"\\Line","%-----------------------------------------------------");
//------------------------------------------------------------------------

write(fname,"All the features for typesetting polynomials work also for
matrices or vectors with polynomial entries.");
write(fname,nl+ "\\vspace{0.2cm}" + nl);
write(fname,"By setting the global variable \\verb|TeXwidth| it is possible
to display only the first terms of the polynomials.");

write(fname,bv,
"> TeXwidth=1;
> texobj(fname,H);
> TeXwidth=-1;",
ev );

TeXwidth = 1;
texobj(fname,H);
TeXwidth = -1;

write(fname,nl,"\\Line","%-----------------------------------------------------");
//------------------------------------------------------------------------
write(fname,"The flag variable \\verb|TeXnofrac| controls the typesetting
of fractions.");

write(fname,
bv,
"> ring R0=0,x,dp;
> matrix M[2][3]=1/2, 0, 1/2, 0, 1/3, 2/3;
> texobj(fname,M);",
ev);


ring R0 = 0,x,dp;
matrix M[2][3] = 1/2, 0, 1/2, 0, 1/3, 2/3;
texobj(fname,M);

write(fname,bv,
"> int TeXnofrac;
> texobj(fname,M);",
ev );

  int TeXnofrac; export TeXnofrac;
  texobj(fname,M);
  kill TeXnofrac;

write(fname,bv,
"> kill TeXnofrac;",
ev );

write(fname,nl,"\\Line","%-----------------------------------------------------");
//------------------------------------------------------------------------

write(fname,"Printing a vector with homogeneous coordinates can be done by
setting \\verb|TeXproj|.");
write(fname,bv +
"> setring r;
> int TeXproj;
> texobj(fname,V);",
ev );

  setring r;
  ideal I=3xz5+x2y3-3z,7xz5+y3z+x-z,-xyz2+4yz+2x;
  int TeXproj; export TeXproj;

  texobj(fname,V);
  kill TeXproj;

write(fname,
bv,
      "> kill TeXproj;",
ev);

write(fname,"","\\subsection{Modules}");

write(fname,"By default, modules are displayed in the following way:");
write(fname,
bv,
"> setring r;
> module md=module(H);
> texobj(fname,md);",
ev );

setring r;
module md = module(H);
texobj(fname,md);

write(fname,"\\Line","%-----------------------------------------------------");
//------------------------------------------------------------------------

write(fname,"In order to write the generators of a module aligned, the flag
variable \\verb|TeXaligned| has to be defined.");

write(fname,bv,
"> int TeXaligned;
> texobj(fname,md);",
ev );

int TeXaligned; export TeXaligned;
texobj(fname,md);
kill TeXaligned;
write(fname,bv,
"> kill TeXaligned;",
ev );

//----------------------------------------------------------------
write(fname,"","\\subsection{Integer matrices and vectors}");

write(fname,"Integer matrices are displayed in the following way.");

intmat m[3][4]=-1,3,5,2,-2,8,6,0,2,5,8,7;

write(fname,
bv,
"> intmat m[3][4]=-1,3,5,2,-2,8,6,0,2,5,8,7;
> m;" + nl +
string(m) + nl +
"> texobj(fname,m);",
ev );

texobj(fname,m);
write(fname,nl+ "\\vspace{0.2cm}" + nl);
write(fname,"Integer vectors are displayed as row vectors.");
intvec v = 1..4;
write(fname,
bv,
"> intvec v=1..4;
> v;" + nl +
string(v) + nl +
"> texobj(fname,v);",
ev );

texobj(fname,v);

write(fname,nl+ "\\vspace{0.2cm}" + nl);
write(fname,"To typeset the transposed vector, it has to be converted into
an integer matrix."+
bv,
"> texobj(fname,intmat(v));",
ev );

texobj(fname,intmat(v));

write(fname,nl+ "\\vspace{0.2cm}" + nl);

write(fname,"The following example shows how to typeset the multiplication of
a matrix with a vector.");
write(fname,
bv,
"> texobj(fname,intmat(m*v),\"=\",m,\"*\",intmat(v));",
ev );

texobj(fname,intmat(m*v),"=",m,"*",intmat(v));

//-----------------------------------------------------------------
write(fname,"\\Line","%-----------------------------------------------------");

write(fname,"Of course, the brackets of a \\verb|intmat| can be changed
by setting \\verb|TeXbrack|.");

write(fname,
bv,
"> intmat mat[3][3]=1,2,3,4,5,6,7,8,9;
> string TeXbrack=\"|\";
> texobj(fname,mat,\" = \",det(mat)); ",
ev );

intmat mat[3][3] = 1,2,3,4,5,6,7,8,9;
string TeXbrack = "|"; export TeXbrack;
texobj(fname,mat," = ",det(mat));
kill TeXbrack;

//----------------------------------texname-------------------

//write(fname,"\\section{Names of identifiers}");


//write(fname,"The proc \\verb|texname| is used to write indexed names in a
//correct way"+lb,nl);



// ------------------------------- texproc -------------------------------
  proc milnor_number (poly p)
  {
    ideal i = std(jacob(p));
    int m_nr = vdim(i);
    if (m_nr<0)
    {
      "//--  not an isolated singularity";
    }
    return(m_nr);
  }
  export(milnor_number);

write(fname,"","\\section{Typesetting procedures}");
write(fname,"The following procedure allows to include the source code
of procedures into a \\LaTeX document.");
write(fname,
bv,
"> texproc(fname,\"milnor\_number\");",
ev);

 texproc(fname,"milnor_number");

  kill milnor_number;

// ------------------------------ closing the tex file -------------------
write(fname,"","\\section{Closing the \\LaTeX\\ file}");
write(fname,"To close the file use \\verb|closetex(fname);|. It should now
contain pure \\LaTeX \\ code and may be compiled with " +
"\\verb|tex(fname)| and displayed with \\verb|xdvi(fname)|.");

// write(fname,"\\section{Remarks}");
closetex(fname);
//"end of part3" + nl;

pagewidth =80;
kill texdemopart,TeXwidth;
}
///////////////////////////////////////////////////////////////////////////////

/*

   texring extended for Z,Z_m,real,complex

// Test for new functionality:
// texring:
  ring rZ = integer,x,dp;
  texring("",rZ);
  ring rZ8 = (integer,8),x,dp;
  texring("",rZ8);

  ring rR = real,x,dp;
  texring("",rR);

  ring rR2010 = (real,20,10),x,dp;
  texring("",rR2010);

  ring rC = complex,x,dp;
  texring("",rC);

  ring rC2010 = (complex,20,10),x,dp;
  texring("",rC2010);

// multi-indexed parameters and variables

  ring rmultind34 = 0,(a(1..3)(1..4)),dp;
  texring("",r34);
  matrix A[3][4] = maxideal(1);
  texobj("",A);

  ring rmultind2 = 0,(x1_2,y_1_1,z),ds;
  texring("",rmultind2);

  ring rmultind3 = 0,(x(-1..1)(0)(3..4)),ds;
  texobj("",maxideal(1));

  ring rmultind4 = (0,b1(0..2),b2_1(3)),x,ds;
  texpoly("",par(1)*par(2)*par(3)+par(4)*x);

*/
// last changed 10/10/10
///////////////////////// end of latex.lib ////////////////////////////////////