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D.5.4.13 endvfilt
Procedure from library gaussman.lib (see gaussman_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 "gaussman.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]=2xy2+5x4 → _[3]=5x5-5y5 → _[4]=10y6+25x3y4 |