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

////////////////////////////////////////////////////////////////////////////
version="version surf.lib 4.0.0.0 Jun_2013 "; // $Id: 4941ace9657fdbc969215d0661db113cf540815e $
category="Visualization";
info="
LIBRARY: surf.lib    Procedures for Graphics with Surf
AUTHOR: Hans Schoenemann, Frank Seelisch

NOTE:
 @texinfo
 Using this library requires the program @code{surf} to be installed.
 You can download @code{surf} either from
  @uref{http://sourceforge.net/projects/surf}
  or from @uref{ftp://www.mathematik.uni-kl.de/pub/Math/Singular/utils/}.
 The procedure surfer requires the program @code{surfer} to be installed.
 You can download @code{surfer} from
  @uref{http://www.imaginary2008.de/surfer.imaginary2008.de}
 @*Under Windows, version 159 or newer of @code{surfer} is required.
 Under Mac OS X please move SURFER.app from http://www.mathematik.uni-kl.de/~motsak/files/SURFER.dmg
 under your /Applications.
 @end texinfo

SEE ALSO: surfex_lib

PROCEDURES:
 plot(I);    plots plane curves and surfaces
 surfer(I);  plots surfaces interactivly
";

///////////////////////////////////////////////////////////////////////////////
proc num_of_vars(ideal I)
"USAGE: num_of_vars(ideal I)

RETURN: an intvec containing one entry for each ring variable.
each contains the sums of all degrees in this variable of all monomials
occuring in the ideal.
An entry is zero if and only if the corresponding variable does not occur in the ideal.
"
{
  intvec v;
  int i;
  poly p;
  for(i=ncols(I);i>0;i--)
  {
    p=I[i];
    while(p!=0)
    {
      v=v+leadexp(p);
      p=p-lead(p);
    }
  }
  return(v);
}
example
{
  "EXAMPLE:"; echo = 2;
  ring r = 0, (x,y,z),dp;
  ideal j0 = x^2-x*y;
  num_of_vars(j0);
  ideal j1 = x^2-x*y-y;
  num_of_vars(j1);
  ideal j2 = x^2-x*y-y, x^3-2*y;
  num_of_vars(j2);
}

proc plot(ideal I,list #)
"USAGE:   plot(I);  I ideal or poly
ASSUME: I defines a plane curve or a surface given by one equation
RETURN: nothing
NOTE: requires the external program `surf` to be installed,
      to close the graphical interface just press `Q`
EXAMPLE: example plot; shows an example
"
{
  string l = "/tmp/surf" + string(system("pid"));
  string err_mes; // string containing error messages
  def base=basering;
  intvec v=num_of_vars(I);
  int i,j,n;
  for(i=size(v);i>0;i--)
  {
    if (v[i]!=0) { n++; }
  }
  if (n==0 or n>3)
  {
    err_mes="Cannot plot equations with "+string(n)+" variables";
    ERROR(err_mes);
  }
  ring r=0,(x,y,z),dp;
  short=0;
  map phi=base,0;
  j=1;
  for(i=1;i<=size(v);i++)
  {
    if (v[i]!=0)
    {
      phi[i]=var(j);
      j++;
      if(j==4) break;
    }
  }
  ideal I=simplify(phi(I),2);
  if (leadcoef(I[1]) <0) { I[1]=-I[1]; }
  if (ncols(I)==1 and n<=2 and nvars(base)!=3) // curve
  {
    write(":w "+l,"clip=none;");
      write(l, "width=500; height=500; set_size; do_background=yes;
               background_red=255; background_green=255;
               background_blue=255;");
    write(l,
    "root_finder=d_chain_bisection;epsilon=0.0000000001;iterations=20000;");
    write(l, "curve_green=0; curve_blue=0; curve_width=1.5;");
    if (size(#)>0)
    {
      write(l,#[1]);
    }
    write(l,"curve=",I[1],";");
    write(l,"draw_curve;");
  }
  else
  {
    if (ncols(I)==1 and (n==3 or nvars(base)==3)) // surface
    {
      write(":w " + l,
            "root_finder=d_chain_bisection;epsilon=0.0000000001;iterations=20000;");
      write(l, "width=500; height=500; set_size; do_background=yes; background_red=255; background_green=255; background_blue=255;");
      write(l, "rot_x=0.14; rot_y=-0.3;");
      if (size(#) > 0)
      {
          write(l, #[1]);
      }
      write(l, "surface=",I[1],";");
      write(l, "draw_surface;");
    }
    else
    {
      err_mes = "cannot plot " + string(ncols(I)) + " equations in "
              + string(n) + " variables";
      ERROR(err_mes);
    }
  }

  string surf_call; i = 0;
  if (isWindows())
  {
    string surferPath = getShellOutput("which surfer");
    if (find(surferPath, "no surfer in") != 0)
    { /* did not find surfer: either not installed or
         not yet included in $PATH variable */
      err_mes = "calling `surfer` failed" + newline
      + " (Either the program Surfer is not installed," + newline
      + "  or it has not yet been included in $PATH.)";
      ERROR(err_mes);
    }
    else
    {
      surf_call = "((xwin -multiwindow -clipboard -silent-dup-error";
      surf_call = surf_call + " >/dev/null 2>&1 &) && sleep 5 && (sinngularsurf ";
      surf_call = surf_call + l + ">/dev/null 2>&1))";
      surf_call = surf_call + "&& command rm " + l;
      "Press q to exit from `surf`.";
        " (You may leave the XServer running for further" + newline
      + "  invocations of `plot`.)";
      i = system("sh", surf_call);
      if (i != 0)
      {
        err_mes = "calling `surf` failed" + newline
                + " (The shell returned the error code "
                + string(i) + "." + newline
                + "  Perhaps the XServer was not properly set up, so" + newline
                + "  try your plot command again. If `plot` fails" + newline
                + "  again, then make sure that the program Surfer" + newline
                + "  is installed and included in your $PATH variable.)";
        ERROR(err_mes);
      }
    }
  }
  else
  {
    surf_call = "singularsurf ";
    surf_call = surf_call + l + " >/dev/null 2>&1";
    "Close window to exit from `singularsurf`.";

    i = system("sh", surf_call);
    if (i != 0)
    {
      err_mes = "calling `surf` failed" + newline
              + " (The shell returned the error code "
              + string(i) + ".";
      ERROR(err_mes);
    }
  }
  system("sh", "command rm " + l);
}
example
{ "EXAMPLE:"; echo = 2;
  // ---------  plane curves ------------
  ring rr0 = 0,(x1,x2),dp;

  ideal I = x1^3 - x2^2;
  plot(I);

  ring rr1 = 0,(x,y,z),dp;
  ideal I(1) = 2x2-1/2x3 +1-y+1;
  plot(I(1));

  //  ---- Singular Logo --------------
  poly logo = ((x+3)^3 + 2*(x+3)^2 - y^2)*(x^3 - y^2)*((x-3)^3-2*(x-3)^2-y^2);
  plot(logo);

  // Steiner surface
  ideal J(2) = x^2*y^2+x^2*z^2+y^2*z^2-17*x*y*z;
  plot(J(2));

  // --------------------
  plot(x*(x2-y2)+z2);

  // E7
  plot(x^3-x*y^3+z^2);

  // Whitney umbrella
  plot(z^2-x^2*y);

}

proc surfer(ideal I)
"USAGE:   surfer(f);  f poly
ASSUME: f defines a surface given by one equation
RETURN: nothing
NOTE: requires the external program `surfer` to be installed,
      to close the graphical interface just close the window of surfer
EXAMPLE: example surfer; shows an example
"
{
  string lForWindows = "surfer" + string(system("pid"));
  string l = "./" + lForWindows;
  string err_mes; // string containing error messages
  def base=basering;
  intvec v=num_of_vars(I);
  int i,j,n;
  for(i=size(v);i>0;i--)
  {
    if (v[i]!=0) { n++; }
  }
  if (n==0 or n>3)
  {
    err_mes="Cannot plot equations with "+string(n)+" variables";
    ERROR(err_mes);
  }
  ring r=0,(x,y,z),dp;
  short=0;
  map phi=base,0;
  j=1;
  for(i=1;i<=size(v);i++)
  {
    if (v[i]!=0)
    {
      phi[i]=var(j);
      j++;
      if(j==4) break;
    }
  }
  ideal I=simplify(phi(I),2);
  if (leadcoef(I[1]) <0) { I[1]=-I[1]; }
  if (ncols(I)==1 and (n==3 or nvars(base)==3)) // surface
  {
    write(":w " + l, "surface=" + string(I[1]) + ";");
  }
  else
  {
    err_mes = "cannot plot " + string(ncols(I)) + " equations in "
            + string(n) + " variables";
    ERROR(err_mes);
  }

  string surf_call; i = 0;

  if (isWindows())
  {
    string surferPath = getShellOutput("which surfer");
    if (find(surferPath, "no surfer in") != 0)
    { /* did not find surfer: either not installed or
         not yet included in $PATH variable */
      err_mes = "calling `surfer` failed" + newline
      + " (Either the program Surfer is not installed," + newline
      + "  or it has not yet been included in $PATH.)";
      ERROR(err_mes);
    }
    else
    {
      string singularPath = getShellOutput("pwd");
      surferPath = windowsCorrection(surferPath);
      surferPath = surferPath[1..size(surferPath)-size("/surfer")];
      singularPath = windowsCorrection(singularPath);
      link ll = "|: cygpath -w " + singularPath;
      singularPath = "'\""+read(ll)+"\"'"; close(ll);
      surf_call = "cygstart -w -d " + surferPath + " ";
      surf_call = surf_call + surferPath + "/surfer ";
      surf_call = surf_call + singularPath + "/" + lForWindows;
      "Close window to exit from `surfer`.";
      i = system("sh", surf_call);
    }
  }
  else
  {
    surf_call = "surfer";
    surf_call = surf_call + " " + l + " >/dev/null 2>&1";
    "Close window to exit from `surfer`.";
    i = system("sh", surf_call);

    if ( (i != 0) && isMacOSX() )
    {
      "*!* Sorry: calling `surfer` failed ['"+surf_call+"']" + newline
      + " (The shell returned the error code " + string(i) + "." + newline
      + "But since we are on Mac OS X, let us try to open SURFER.app instead..." + newline
      + "Appropriate SURFER.app is available for instance at http://www.mathematik.uni-kl.de/~motsak/files/SURFER.dmg";

      // fallback, will only work if SURFER.app is available (e.g. in /Applications)
      // get SURFER.app e.g. from http://www.mathematik.uni-kl.de/~motsak/files/SURFER.dmg
      // note that the newer (Java-based) variant of Surfer may not support command line usage yet :(

      surf_call = "open -a SURFER -W --args -t -s";
      surf_call = surf_call + " " + l + " >/dev/null 2>&1";
      "Close window to exit from `surfer`.";
      i = system("sh", surf_call);
    }



  }
  system("sh", "command rm " + l);

  if (i != 0)
  {
    err_mes = "calling `surfer` failed" + newline
              + " (The shell returned the error code "
              + string(i) + ".";
    ERROR(err_mes);
  }
}
example
{ "EXAMPLE:"; echo = 2;
  ring rr1 = 0,(x,y,z),dp;
  // Steiner surface
  ideal J(2) = x^2*y^2+x^2*z^2+y^2*z^2-17*x*y*z;
  surfer(J(2));

  // --------------------
  surfer(x*(x2-y2)+z2);

  // E7
  surfer(x^3-x*y^3+z^2);

  // Whitney umbrella
  surfer(z^2-x^2*y);
}

static proc isWindows()
"returns 1 if this SINGULAR instance runs under (some) Windows OS;
0 otherwise"
{
  string s = system("uname");
  for (int i = 1; i <= size(s)-2; i = i + 1)
  {
    if (s[i] == "W")
    {
      if (s[i+1] == "i")
      {
        if (s[i+2] == "n")
        {
          return (1);
        }
      }
    }
  }
  return (0);
}

static proc isMacOSX()
"returns 1 if this SINGULAR instance runs under (some) Mac OS X;
0 otherwise"
{
  string s = system("uname");

  for (int i = 1; i <= size(s)-2; i = i + 1)
  {
    if (s[i] == "d" or s[i] == "D")
    {
      if (s[i+1] == "a" or s[i+1] == "A")
      {
        if (s[i+2] == "r" or s[i+2] == "R")
        {
          return (1);
        }
      }
    }
  }
  return (0);
}

static proc getShellOutput(string shellCommand)
"returns the console output when executing the given shellCommand"
{
   int s;
   string tempFilename = "tmp" + string(system("pid"));
   s = system("sh", shellCommand + " > " + tempFilename + " 2>&1");
   string r1 = read(tempFilename);
   s = size(r1) - 1;
   string r2 = r1[1..s];
   s = system("sh", "command rm " + tempFilename);
   return (r2);
}

static proc windowsCorrection(string windowsPath)
"puts a backslash in front of each space and each special character
and returns the resulting string"
{
  string s = ""; int i;
  for (i = 1; i <= size(windowsPath); i++)
  {
    if (find(" ()", windowsPath[i]) != 0)
    {
      s = s + "\\";
    }
    s = s + windowsPath[i];
  }
  return (s);
}
///////////////////////////////////////////////////////////////////////////////