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D.6.13.9 vwfilt

Procedure from library gmssing.lib (see gmssing_lib).

Usage:
vwfilt(t); poly t

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

Return:
 
list vw;  weighted V-filtration on H''/s*H''
  ideal vw[1];
    number vw[1][i];  V-filtration index of i-th spectral pair
  intvec vw[2];
    int vw[2][i];  weight filtration index of i-th spectral pair
  intvec vw[3];
    int vw[3][i];  multiplicity of i-th spectral pair
  list vw[4];
    module vw[4][i];  vector space of i-th graded part in terms of vw[5]
  ideal vw[5];  monomial vector space basis of H''/s*H''
  ideal vw[6];  standard basis of Jacobian ideal

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


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