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D.5.4.10 vfilt
Procedure from library gaussman.lib (see gaussman_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 "gaussman.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]=2xy2+5x4 → _[3]=5x5-5y5 → _[4]=10y6+25x3y4 |
See also: spectrum_lib.