# Singular

#### D.6.7.11 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 ```