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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
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- 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.
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