///////////////////////////////////////////////////////////////////////////////
version="$Id: spectrum.lib,v 1.12 2001-02-02 16:21:37 mschulze Exp $";
category="Singularities";
info="
LIBRARY:  spectrum.lib  Singularity Spectrum for Nondegenerate Singularities
AUTHOR:   S. Endrass

PROCEDURES:
 spectrumnd(poly[,1]);   spectrum of a nondegenerate isolated singularity
 semicont(s1,s2[,1]);    tests if s2 is semicontinous for s1
 semicontqh(s1,s2);      semicontinuity test using open and half open intervals
 spadd(s1,s2);           sum of two spectra s1 and s2
 spmul(s,k);             product of spectrum s with integer k
";

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proc spectrumnd (poly f, list #)
"USAGE:   spectrumnd(f[,1]);  f poly
ASSUME:  f has nondegenerate principal part
RETURN:  a list containing the spectrum of f
NOTE     if a second argument 1 is given,
         no test for a degenerate principal part will be done
EXAMPLE: example spectrumnd; 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;
  spectrumnd(f);
}
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proc semicont (list s, list ss, list #)
"USAGE:   semicont(s,ss[,1]);  s, ss list
RETURN:  1 if ss is semicontinous for s using half open intervals, 0 otherwise
NOTE:    if a third argument 1 is given, open intervals are used
EXAMPLE: example semicont; shows examples
"
{
  if(size(#)==0)
  {  return(system("semic",s,ss)); }
  return (system("semic",s,ss,#[1]));
}
example
{ "EXAMPLE:"; echo = 2;
}
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proc semicontsqh (list s, list ss)
"USAGE: semicontsqh(s,ss);  s, ss list
RETURN: 1 if ss is semicontinous for s using open and half open intervals,
        0 otherwise
EXAMPLE: example semicontsqh; shows examples
"
{
  return (system("semic",s,ss,1));
}
example
{ "EXAMPLE:"; echo = 2;
}
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proc spadd (list s1, list s2)
"USAGE:  spadd(s1,s2);  s1, s2 list
RETURN:  a list containing the sum of the two spectra s1 and s2
EXAMPLE: example spadd; shows examples
"
{
  return (system("spadd",s1,s2));
}
example
{ "EXAMPLE:"; echo = 2;
}
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proc spmul (list s, int k)
"USAGE:  spmul(s,k);  s list, k int
RETURN:  a list containing the product of the spectrum s with the integer k
EXAMPLE: example spmul; shows examples
"
{
  return (system("spmul",s,k));
}
example
{ "EXAMPLE:"; echo = 2;
}
///////////////////////////////////////////////////////////////////////////////