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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]- 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 |