source: git/Singular/LIB/spectrum.lib @ 3686937

////////////////////////////////////////////////////////////////////////////
version="version spectrum.lib 4.0.0.0 Jun_2013 "; // $Id$
category="Singularities";
info="
LIBRARY:  spectrum.lib  Singularity Spectrum for Nondegenerate Singularities
AUTHOR:   S. Endrass

PROCEDURES:
 spectrumnd(poly f[,1]);  spectrum of nondegenerate isolated singularity f
";

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proc spectrumnd (poly f,list #)
"USAGE:    spectrumnd(f[,1]); poly f
ASSUME:   basering has characteristic 0 and local ordering,
          f has isolated singularity at 0 and nondegenerate principal part
RETURN:
@format
list S:
  ideal S[1]: spectral numbers in increasing order
  intvec S[2]:
    int S[2][i]: multiplicity of spectral number S[1][i]
@end format
NOTE:     if a second argument 1 is given,
          no test for a degenerate principal part will be done
SEE_ALSO: gmssing_lib
KEYWORDS: singularities; Gauss-Manin connection; spectrum
EXAMPLE:  example spectrumnd; shows an example
"
{
  if(charstr(basering)!="0")
  {
    ERROR("characteristic 0 expected");
  }
  if(size(#)==0)
  {
    list S=system("spectrum",f);
  }
  else
  {
    list S=system("spectrum",f,#[1]);
  }
  ideal a=number(S[4][1])/S[5][1]-1;
  int i;
  for(i=S[3];i>1;i--)
  {
    a[i]=number(S[4][i])/S[5][i]-1;
  }
  return(list(a,S[6]));
}
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;
  list s=spectrumnd(f);
  size(s[1]);
  s[1][22];
  s[2][22];
}
///////////////////////////////////////////////////////////////////////////////