// $Id: spectrum.lib,v 1.8 2000-12-19 15:05:37 anne Exp $
///////////////////////////////////////////////////////////////////////////////

version="$Id: spectrum.lib,v 1.8 2000-12-19 15:05:37 anne Exp $";
category="Singularities";
info="
LIBRARY:  spectrum.lib   PROCEDURES FOR COMPUTING SINGULARITY SPECTRA

PROCEDURES:
 spectrum(poly[,1]);    spectrum of a isolated singularity (with/without tests)
 semic(s1,s2[,1]);      tests if s2 is semicontinous for s1 using
                        half open intervalls
                        (and open intervalls for a 3rd paramater 1)
 semicqh(s1,s2[,1]);    tests if s2 is semicontinous for s1 using
                        open and half open intervalls
 spadd(s1,s2);          sum of two spectra s1 and s2
 spmul(s,k);            multiplies the spectrum s with the int k
          (parameters in square brackets [] are optional)
";

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

proc spectrum (poly f, list #)
"USAGE:  spectrum(f[,1]);  f polynomial
         computes the spectrum of f
	 if a second argument 1 is given, 
	 no test for a degenerate principal part will be done
RETURN:  list
EXAMPLE: example spectrum; shows examples
"
{
  if(size(#)==0)
  {  return(system("spectrum",f)); }
  return (system("spectrum",f,#[1]));
}
example
{ "EXAMPLE:"; echo = 2;
  ring r=0,(x,y),ds;
  poly f=x^31+x^6*y^7+x^2*y^12+x^13*y^2+y^29;
  spectrum(f);
}
///////////////////////////////////////////////////////////////////////////////

proc semic (list s, list ss, list #)
"USAGE:  semic(s,ss[,i]);  s, ss spectra, i int
         tests if ss is semicontinous for s using half open intervalls
         (and open intervalls for a 3rd paramater 1)
RETURN:  int
EXAMPLE: example semic; shows examples
"
{
  if(size(#)==0)
  {  return(system("semic",s,ss)); }
  return (system("semic",s,ss,#[1]));
}
example
{ "EXAMPLE:"; echo = 2;
}
///////////////////////////////////////////////////////////////////////////////
proc semicsqh (list s, list ss)
"USAGE: semicsqh(s,ss);  s, ss spectra, i int
        tests if ss is semicontinous for s using open and half open intervalls
RETURN: int
EXAMPLE: example semicsqh; shows examples
"
{
  return (system("semic",s,ss,1));
}
example
{ "EXAMPLE:"; echo = 2;
}
///////////////////////////////////////////////////////////////////////////////
proc spadd (list s1, list s2)
"USAGE:  spadd(s1,s2);  s1, s2 spectra
         sum of two spectra s1 and s2
RETURN:  list
EXAMPLE: example spadd; shows examples
"
{
  return (system("spadd",s1,s2));
}
example
{ "EXAMPLE:"; echo = 2;
}
///////////////////////////////////////////////////////////////////////////////
proc spmul (list s, int k)
"USAGE:  spmul(s,k);  s spectrum, k int
         multiplies the spectrum s with the int k
RETURN:  list
EXAMPLE: example spmul; shows examples
"
{
  return (system("spmul",s,k));
}
example
{ "EXAMPLE:"; echo = 2;
}
///////////////////////////////////////////////////////////////////////////////