source: git/Singular/LIB/surf.lib @ 4173c7

///////////////////////////////////////////////////////////////////////////////
version="$Id: surf.lib 13499 2010-10-15 09:55:26Z hannes $";
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.
 @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 extra_surf_opts=" -x --auto-resize "; // remove this line for surf 0.9
  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 && (surf";
      if (defined(extra_surf_opts))
      {
        surf_call = surf_call + " " + extra_surf_opts;
      }
      surf_call = surf_call + l + ">/dev/null 2>&1))";
      surf_call = surf_call + "&& /bin/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 = "surf ";
    if (defined(extra_surf_opts))
    {
      surf_call = surf_call + " " + extra_surf_opts;
    }
    surf_call = surf_call + l + " >/dev/null 2>&1";

    if (system("uname") == "ppcMac-darwin")
    {
       surf_call = surf_call + " || " + "singularsurf "
                   + extra_surf_opts + " " + l + " >/dev/null 2>&1";
    }

    "Press q to exit from `surf`.";
    i = system("sh", surf_call);
    if (i != 0)
    {
      err_mes = "calling `surf` failed" + newline
              + " (The shell returned the error code "
              + string(i) + "." + newline
              + "  Make sure that the program Surfer is installed.)";
      ERROR(err_mes);
    }
  }
  system("sh", "/bin/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);
      singularPath = "c:"
         + singularPath[size("/cygdrive/c/")..size(singularPath)];
      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 " + l + " >/dev/null 2>&1";
    "Close window to exit from `surfer`.";
    i = system("sh", surf_call);
  }
  system("sh", "/bin/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 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", "/bin/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);
}
///////////////////////////////////////////////////////////////////////////////