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D.5.10.1 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]
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- Note:
- if a second argument 1 is given,
no test for a degenerate principal part will be done
SEE_ALSO: gaussman_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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