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D.5.4.10 vfilt

Procedure from library gaussman.lib (see section gaussman_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 "gaussman.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]=2xy2+5x4
→    _[3]=5x5-5y5
→    _[4]=10y6+25x3y4

See also: spectrum_lib.


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            User manual for Singular version 2-0-4, October 2002, generated by texinfo.