// last modified 21.07.2005, Oliver Wienand
///////////////////////////////////////////////////////////////////////////////
version="$Id: surf.lib,v 1.32 2009-02-17 11:47:48 Singular Exp $";
category="Visualization";
info="
LIBRARY: surf.lib    Procedures for Graphics with Surf
AUTHOR: Hans Schoenemann,
        the program surf is written by Stefan Endrass

NOTE:
 @texinfo
 To use 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.php}
 @*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
";

///////////////////////////////////////////////////////////////////////////////
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 iff 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;
  surf_call = "surf ";
  if (defined(extra_surf_opts))
  {
    surf_call = surf_call + " " + extra_surf_opts;
  }
  surf_call =surf_call + l + " >/dev/null 2>&1";

  "Press q to exit from 'surf'";
  if ("ppcMac-darwin" != system("uname"))
  {
     i=system("sh", surf_call);
  }
  else
  {
     surf_call = surf_call + " || " + "singularsurf "
                 + extra_surf_opts + " " + l +" >/dev/null 2>&1";
     i = system("sh", surf_call);
  }

  if (i != 0)
  {
    err_mes = "calling `surf` failed. (the shell return the error code "
          + string(i) + ")." + newline +
          "probably the executable `surf` is not found.";
    ERROR(err_mes);
  }
  i = 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 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==3 or nvars(base)==3)) // surface
  {
    write(":w " + l, "surface=",I[1],";");
  }
  else
  {
    err_mes = "cannot plot " + string(ncols(I)) + " equations in "
            + string(n) + " variables";
    ERROR(err_mes);
  }
  string surf_call;
  surf_call ="surfer " + l + " >/dev/null 2>&1";

  "Close window to exit from 'surfer'";
  i=system("sh", surf_call);

  if (i != 0)
  {
    err_mes = "calling `surfer` failed. (the shell return the error code "
          + string(i) + ")." + newline +
          "probably the executable `surfer` is not found.";
    ERROR(err_mes);
  }
  i = system("sh", "/bin/rm "+l);
}
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);

}
///////////////////////////////////////////////////////////////////////////////