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D.5.4.3 vfiltjacalg

Procedure from library gaussman.lib (see gaussman_lib).

Usage:
vfiltjacalg(vfiltration(f)); poly f

Assume:
basering has local ordering, f has isolated singularity at 0

Return:
 
list l:
  ideal l[1]: spectral numbers of the V-filtration
              on the Jacobian algebra in increasing order
  intvec l[2]:
    int l[2][i]: multiplicity of spectral number l[1][i]
  list l[3]:
  module l[3][i]: vector space basis of the l[1][i]-th graded part
                  of the V-filtration on the Jacobian algebra
                  in terms of l[4]
  ideal l[4]: monomial vector space basis of the Jacobian algebra
  ideal l[5]: standard basis of the Jacobian ideal

Example:
 
LIB "gaussman.lib";
ring R=0,(x,y),ds;
poly f=x5+x2y2+y5;
vfiltjacalg(vfiltration(f));
==> [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


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