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Spectrum and V-Filtration
LIB "gaussman.lib";
ring r=0,(x,y),ds;
poly f=x5+x2y2+y5;
The command vfilt(f) returns a list:
_[1] contains the spectral numbers a[i] in increasing
order.
_[2] contains vector space bases for
GrVa[i]
(H''/H').
vfilt(f);
==> [1]:
_[1]=-1/2
_[2]=-3/10
_[3]=-1/10
_[4]=0
==>
_[5]=1/10
_[6]=3/10
_[7]=1/2
==>
==> [2]:
==> [1]:
_[1]=1
==> [2]:
_[1]=x
_[2]=y
==> [3]:
_[1]=x2
_[2]=y2
==> [4]:
_[1]=xy
==> [5]:
_[1]=x3
_[2]=y3
==> [6]:
_[1]=x4
_[2]=y4
==> [7]:
_[1]=y5
|
| 0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 7 |
0 |
0 |
0 |
0 |
0 |
0 |
| 6 |
0 |
0 |
0 |
0 |
0 |
0 |
| 5 |
0 |
0 |
0 |
0 |
0 |
0 |
| 3 |
0 |
0 |
0 |
0 |
0 |
0 |
| 2 |
4 |
0 |
0 |
0 |
0 |
0 |
| 1 |
2 |
3 |
5 |
6 |
0 |
0 |
|
Interpret:
xayb =
[xayb dx ^ dy]
in
H''/H'.
|
|