ring R=0,(x,y,z),ds;
poly f=x7+y7+z7+x2y2z2;
LIB "sing.lib";
milnor(f);
==>
167
LIB "gaussman.lib";
sppairs(f);
==>
[1]:
_[1]=-1/2 _[2]=-5/14 _[3]=-3/14 _[4]=-3/14 _[5]=-1/14 _[6]=-1/14
_[7]=0 _[8]=1/14 _[9]=1/14 _[10]=1/7 _[11]=3/14 _[12]=3/14
_[13]=2/7 _[14]=5/14 _[15]=5/14 _[16]=3/7 _[17]=1/2 _[18]=4/7
_[19]=9/14 _[20]=9/14 _[21]=5/7 _[22]=11/14 _[23]=11/14 _[24]=6/7
_[25]=13/14 _[26]=13/14 _[27]=1 _[28]=15/14 _[29]=15/14 _[30]=17/14
_[31]=17/14 _[32]=19/14 _[33]=3/2
[2]:
4,3,3,2,3,2,3,3,2,2,3, 2,2,3, 2,2, 2,2, 2,1,2, 2,1,2,2,1,1,2,1,2,1,1,0
[3]:
1,3,3,3,3,6,1,3,9,3,3,12,3,3,15,3,19,3,15,3,3,12,3,3,9,3,1,6,3,3,3,3,1
^ ^ ^
In particular, we find a 3 x 3 Jordan
block of the
monodromy (with eigenvalue -1, belonging to the pairs (-1/2,4),
(3/2,0) and one of the pairs (1/2,2)), while the 18 other Jordan
blocks with eigenvalue -1 are of size 1 (belonging to the 18 remaining
pairs (1/2,2)).