We first test whether by the bound b or the range of degrees the restricted unfolding leads to a smoothing family over a finite field. If yes and with Verbose>0 then the degrees of the parameters of the parameters of the smoothing family are printed. In a second step we try to lift the example to characteristic 0 and check smoothness again.
i1 : L=(toDoList 8)_0
o1 = {6, 7, 9, 17}
o1 : List
|
i2 : (smooth,fib)=getSmoothingFamily(L,12,Verbose=>1)
number of components = 1, codimension of components = {0}
smoothing components numbers = {}
o2 = (false, )
o2 : Sequence
|
i3 : (smooth,fib)=getSmoothingFamily(L,11,Verbose=>1)
number of components = 2, codimension of components = {1, 2}
semigroup = {6, 7, 9, 17}
dim and degree singF = (0, 4)
smoothing components numbers = {1}
3 2 12 3 2 15 2 17
o3 = (true, ideal (x - x - x z , x - x x - x z , x x - x x - x z ,
0 3 0 1 0 3 0 1 3 0 5 0
2 15 17 2 2 2 12 17 3 2
x x - x x + x z - x z , x x - x x - x z - x z , x x - x +
0 3 1 5 3 1 0 1 3 5 1 3 1 3 5
2 15 17 27 34
x x z - 2x z - x z - z ))
0 1 5 1
o3 : Sequence
|
i4 : range=makeRange(L,{4})
o4 = {4, 8, 12, 16, 20, 24, 28, 32}
o4 : List
|
i5 : (smooth,fib, comps)=getSmoothingFamily(L,range,Verbose=>1)
time to decompose J1 :
component number = 0
component number = 1
deformation weights = {{12}, {8}, {8}, {4}, {4}, {4}}
semigroup = {6, 7, 9, 17}
dim and degree singF = (0, 8)
smoothing components numbers = {1}
flat = true
3 2 2 4 12 3 2 4 8 12
o5 = (true, ideal (x - x - x z + x z , x - x x - x z - x x z - x z ,
0 3 1 0 1 0 3 5 0 1 3
2 2 4 8 16 2 8 2 12
x x - x x - x x z - x x z - x z , x x - x x - 2x x z - x z ,
1 3 0 5 0 1 0 3 1 0 3 1 5 1 3 0
2 2 4 2 8 20 3 2 4 8
x x - x x - 2x x x z - 2x z + x z , x x - x - x x x z - 3x x z
0 1 3 5 0 1 3 3 0 1 3 5 0 1 5 3 5
12 2 16 28
- 3x x x z - 3x z + x z ), {1})
0 1 3 3 0
o5 : Sequence
|
i6 : (smooth,fib, comps)=getSmoothingFamily(L,range,Verbose=>2)
time to decompose J1 :
number of components = 2, codimension of components = {2, 1}
component number = 0
component number = 1
deformation weights = {{12}, {8}, {8}, {4}, {4}, {4}}
codim J3 = 0, numgens J3 = 0
semigroup = {6, 7, 9, 17}
dim and degree singF = (0, 8)
dim and degree singF = (0, 8)
smoothing components numbers = {1}
flat = true
3 2 2 4 12 3 2 4 8 12
o6 = (true, ideal (x - x - x z + x z , x - x x - x z - x x z - x z ,
0 3 1 0 1 0 3 5 0 1 3
2 2 4 8 16 2 8 2 12
x x - x x - x x z - x x z - x z , x x - x x - 2x x z - x z ,
1 3 0 5 0 1 0 3 1 0 3 1 5 1 3 0
2 2 4 2 8 20 3 2 4 8
x x - x x - 2x x x z - 2x z + x z , x x - x - x x x z - 3x x z
0 1 3 5 0 1 3 3 0 1 3 5 0 1 5 3 5
12 2 16 28
- 3x x x z - 3x z + x z ), {1})
0 1 3 3 0
o6 : Sequence
|