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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'.


Paris 7-2-01 http://www.singular.uni-kl.de