Top
Back: monodromy
Forward: vfiltjacalg
FastBack: equising_lib
FastForward: hnoether_lib
Up: gaussman_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.5.4.2 vfiltration

Procedure from library gaussman.lib (see gaussman_lib).

Usage:
vfiltration(f[,mode]); poly f, int mode

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

Return:
 
list l:
if mode=0 or mode=1:
  ideal l[1]: spectral numbers in increasing order
  intvec l[2]:
    int l[2][i]: multiplicity of spectral number l[1][i]
if mode=1:
  list l[3]:
  module l[3][i]: vector space basis of l[1][i]-th graded part
                  of the V-filtration on H''/H' in terms of l[4]
  ideal l[4]: monomial vector space basis of H''/H'
  ideal l[5]: standard basis of the Jacobian ideal
default: mode=1

Note:
H' and H" denote the Brieskorn lattices

Example:
 
LIB "gaussman.lib";
ring R=0,(x,y),ds;
poly f=x5+x2y2+y5;
list l=vfiltration(f);
print(l);
==> [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(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]=2xy2+5x4
==>    _[3]=x5-y5
==>    _[4]=2y6
See also: spectrum_lib.


Top Back: monodromy Forward: vfiltjacalg FastBack: equising_lib FastForward: hnoether_lib Up: gaussman_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 2-0-0, February 2001, generated by texi2html.