Singular Manual: vfilt

D.6.9.8 vfilt

Procedure from library gmssing.lib (see gmssing_lib).

Usage:

vfilt(t); poly t

Assume:

characteristic 0; local degree ordering;
isolated critical point 0 of t

Return:

list v;  V-filtration on H''/s*H''
  ideal v[1];
    number v[1][i];  V-filtration index of i-th spectral number
  intvec v[2];
    int v[2][i];  multiplicity of i-th spectral number
  list v[3];
    module v[3][i];  vector space of i-th graded part in terms of v[4]
  ideal v[4];  monomial vector space basis of H''/s*H''
  ideal v[5];  standard basis of Jacobian ideal

Example:

LIB "gmssing.lib";
ring R=0,(x,y),ds;
poly t=x5+x2y2+y5;
vfilt(t);
==> [1]:
==>    _[1]=-1/2
==>    _[2]=-3/10
==>    _[3]=-1/10
==>    _[4]=0
==>    _[5]=1/10
==>    _[6]=3/10
==>    _[7]=1/2
==> [2]:
==>    1,2,2,1,2,2,1
==> [3]:
==>    [1]:
==>       _[1]=gen(11)
==>    [2]:
==>       _[1]=gen(10)
==>       _[2]=gen(6)
==>    [3]:
==>       _[1]=gen(9)
==>       _[2]=gen(4)
==>    [4]:
==>       _[1]=gen(5)
==>    [5]:
==>       _[1]=gen(3)
==>       _[2]=gen(8)
==>    [6]:
==>       _[1]=gen(2)
==>       _[2]=gen(7)
==>    [7]:
==>       _[1]=gen(1)
==> [4]:
==>    _[1]=y5
==>    _[2]=y4
==>    _[3]=y3
==>    _[4]=y2
==>    _[5]=xy
==>    _[6]=y
==>    _[7]=x4
==>    _[8]=x3
==>    _[9]=x2
==>    _[10]=x
==>    _[11]=1
==> [5]:
==>    _[1]=2x2y+5y4
==>    _[2]=5x5-5y5
==>    _[3]=2xy2+5x4
==>    _[4]=10y6+25x3y4