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D.5.11.1 spectrumnd

Procedure from library spectrum.lib (see spectrum_lib).

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:
 
list S:
  ideal S[1]: spectral numbers in increasing order
  intvec S[2]:
    int S[2][i]: multiplicity of spectral number S[1][i]

Note:
if a second argument 1 is given,
no test for a degenerate principal part will be done
SEE_ALSO: gmssing_lib

Example:
 
LIB "spectrum.lib";
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);
==> [1]:
==>    _[1]=-67/79
==>    _[2]=-62/79
==>    _[3]=-45/58
==>    _[4]=-57/79
==>    _[5]=-41/58
==>    _[6]=-55/79
==>    _[7]=-52/79
==>    _[8]=-37/58
==>    _[9]=-50/79
==>    _[10]=-18/29
==>    _[11]=-47/79
==>    _[12]=-45/79
==>    _[13]=-33/58
==>    _[14]=-16/29
==>    _[15]=-43/79
==>    _[16]=-42/79
==>    _[17]=-40/79
==>    _[18]=-1/2
==>    _[19]=-15/31
==>    _[20]=-14/29
==>    _[21]=-38/79
==>    _[22]=-27/58
==>    _[23]=-14/31
==>    _[24]=-35/79
==>    _[25]=-25/58
==>    _[26]=-13/31
==>    _[27]=-33/79
==>    _[28]=-12/29
==>    _[29]=-23/58
==>    _[30]=-31/79
==>    _[31]=-12/31
==>    _[32]=-30/79
==>    _[33]=-21/58
==>    _[34]=-11/31
==>    _[35]=-28/79
==>    _[36]=-10/29
==>    _[37]=-26/79
==>    _[38]=-19/58
==>    _[39]=-10/31
==>    _[40]=-25/79
==>    _[41]=-9/29
==>    _[42]=-17/58
==>    _[43]=-23/79
==>    _[44]=-9/31
==>    _[45]=-8/29
==>    _[46]=-21/79
==>    _[47]=-15/58
==>    _[48]=-8/31
==>    _[49]=-20/79
==>    _[50]=-7/29
==>    _[51]=-19/79
==>    _[52]=-18/79
==>    _[53]=-7/31
==>    _[54]=-13/58
==>    _[55]=-6/29
==>    _[56]=-16/79
==>    _[57]=-6/31
==>    _[58]=-15/79
==>    _[59]=-11/58
==>    _[60]=-14/79
==>    _[61]=-5/29
==>    _[62]=-13/79
==>    _[63]=-5/31
==>    _[64]=-9/58
==>    _[65]=-11/79
==>    _[66]=-4/29
==>    _[67]=-4/31
==>    _[68]=-10/79
==>    _[69]=-7/58
==>    _[70]=-9/79
==>    _[71]=-3/29
==>    _[72]=-8/79
==>    _[73]=-3/31
==>    _[74]=-7/79
==>    _[75]=-5/58
==>    _[76]=-6/79
==>    _[77]=-2/29
==>    _[78]=-2/31
==>    _[79]=-5/79
==>    _[80]=-3/58
==>    _[81]=-4/79
==>    _[82]=-3/79
==>    _[83]=-1/29
==>    _[84]=-1/31
==>    _[85]=-2/79
==>    _[86]=-1/58
==>    _[87]=-1/79
==>    _[88]=0
==>    _[89]=1/79
==>    _[90]=1/58
==>    _[91]=2/79
==>    _[92]=1/31
==>    _[93]=1/29
==>    _[94]=3/79
==>    _[95]=4/79
==>    _[96]=3/58
==>    _[97]=5/79
==>    _[98]=2/31
==>    _[99]=2/29
==>    _[100]=6/79
==>    _[101]=5/58
==>    _[102]=7/79
==>    _[103]=3/31
==>    _[104]=8/79
==>    _[105]=3/29
==>    _[106]=9/79
==>    _[107]=7/58
==>    _[108]=10/79
==>    _[109]=4/31
==>    _[110]=4/29
==>    _[111]=11/79
==>    _[112]=9/58
==>    _[113]=5/31
==>    _[114]=13/79
==>    _[115]=5/29
==>    _[116]=14/79
==>    _[117]=11/58
==>    _[118]=15/79
==>    _[119]=6/31
==>    _[120]=16/79
==>    _[121]=6/29
==>    _[122]=13/58
==>    _[123]=7/31
==>    _[124]=18/79
==>    _[125]=19/79
==>    _[126]=7/29
==>    _[127]=20/79
==>    _[128]=8/31
==>    _[129]=15/58
==>    _[130]=21/79
==>    _[131]=8/29
==>    _[132]=9/31
==>    _[133]=23/79
==>    _[134]=17/58
==>    _[135]=9/29
==>    _[136]=25/79
==>    _[137]=10/31
==>    _[138]=19/58
==>    _[139]=26/79
==>    _[140]=10/29
==>    _[141]=28/79
==>    _[142]=11/31
==>    _[143]=21/58
==>    _[144]=30/79
==>    _[145]=12/31
==>    _[146]=31/79
==>    _[147]=23/58
==>    _[148]=12/29
==>    _[149]=33/79
==>    _[150]=13/31
==>    _[151]=25/58
==>    _[152]=35/79
==>    _[153]=14/31
==>    _[154]=27/58
==>    _[155]=38/79
==>    _[156]=14/29
==>    _[157]=15/31
==>    _[158]=1/2
==>    _[159]=40/79
==>    _[160]=42/79
==>    _[161]=43/79
==>    _[162]=16/29
==>    _[163]=33/58
==>    _[164]=45/79
==>    _[165]=47/79
==>    _[166]=18/29
==>    _[167]=50/79
==>    _[168]=37/58
==>    _[169]=52/79
==>    _[170]=55/79
==>    _[171]=41/58
==>    _[172]=57/79
==>    _[173]=45/58
==>    _[174]=62/79
==>    _[175]=67/79
==> [2]:
==>    1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,\
   1,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1\
   ,1,1,2,1,1,1,1,2,1,1,1,1,1,2,1,4,1,2,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,2,1,\
   1,1,1,2,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1\
   ,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

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