# Singular

#### D.6.9.8 vfilt

Procedure from library `gmssing.lib` (see gmssing_lib).

Usage:
vfilt(t); poly t

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

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

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