Singular Manual: endvfilt

D.6.13.11 endvfilt

Procedure from library gmssing.lib (see gmssing_lib).

Usage:

endvfilt(v); list v

Assume:

v returned by vfilt

Return:

list ev;  V-filtration on Jacobian algebra
  ideal ev[1];
    number ev[1][i];  i-th V-filtration index
  intvec ev[2];
    int ev[2][i];  i-th multiplicity
  list ev[3];
    module ev[3][i];  vector space of i-th graded part in terms of ev[4]
  ideal ev[4];  monomial vector space basis of Jacobian algebra
  ideal ev[5];  standard basis of Jacobian ideal

Example:

LIB "gmssing.lib";
ring R=0,(x,y),ds;
poly t=x5+x2y2+y5;
endvfilt(vfilt(t));
==> [1]:
==>    _[1]=0
==>    _[2]=1/5
==>    _[3]=2/5
==>    _[4]=1/2
==>    _[5]=3/5
==>    _[6]=4/5
==>    _[7]=1
==> [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(8)
==>       _[2]=gen(3)
==>    [6]:
==>       _[1]=gen(7)
==>       _[2]=gen(2)
==>    [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

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