We check whether there exists a smoothing component for the restricted unfolding with variables of degree >b (or degree congruent 0 mod d for some d in congruences or variable with degree in the range). If the answer is yes, then we compute such smoothing family over QQ. This however might fail if the coefficient size is too small or the random choices in solvingFlatteningRelations are bad. In that case J will be null.
i1 : L={7,8,17,19,20}
o1 = {7, 8, 17, 19, 20}
o1 : List
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i2 : (answer,J,comp)=testBound(L,12)
# of coordinate linear subspace of the base = 21
# of linear subsets which leading to a point =21
3 16 17 2 13 19
o2 = (true, ideal (x - x x + x z + x z , x x - x x + x z + x z -
1 0 3 1 0 1 5 0 6 0 1
20 4 13 2 14 20 2 2 14 16
x z , x - x x + x x z + x z - x z , x x - x x - x z + x z
0 0 1 6 0 1 0 1 1 3 0 5 5 3
2 17 18 2 19 2 2 3 13 14 2 18 19
+ x z + x x z + x z , x - x x + x z - x z + x z + 2x x z
1 0 1 0 3 0 6 0 6 1 0 1
2 20 27 34 2 2 13 16 17 19
- x z + x z - 2z , x x - x x + x x z - x z - x z + x z -
0 0 3 5 1 6 0 1 6 5 3
2 20 29 36 3 2 13 2 14 3 16 17
x z + x z - 2z , x x - x x + x x z + x x z + x z + x z -
1 0 0 1 3 6 0 3 0 1 0 6
20 37 3 2 2 16 3 17 18 31 38 2
x z + z , x x - x + x x z + x z + x z - x z + 2z , x x x
3 0 3 5 0 1 0 6 0 0 1 3
13 2 16 2 17 3 18 19 20 39 3
- x x + x x z + x x z + x x z + x z + x z - x z + z , x x
5 6 0 5 0 1 0 1 0 6 5 0 5
2 13 14 3 19 20 2 26 33 40
- x + 2x x z + x x z + x z - 2x z - x z + 3x z - z ), {0})
6 0 6 0 5 0 6 0 0
o2 : Sequence
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i3 : range=drop(flatten getRangeOfOneParameterFamily J,-5)
o3 = {13, 14, 16, 17, 18, 19, 20, 26, 27, 29, 31, 33, 34}
o3 : List
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i4 : (answer1,J1,comp)=testRange(L,range,CoeffSize=>2)
# of coordinate linear subspace of the base = 6
# of linear subsets which leading to a point =4
3 16 17 2 13 4
o4 = (true, ideal (2x - 2x x + 6x z + 3x z , x x - x x + 3x z , x -
1 0 3 1 0 1 5 0 6 0 0
13 2 14 2 2 13 14 16
x x + 4x x z + 2x z , 8x x - 8x x - 8x z - 16x z + 24x z +
1 6 0 1 0 1 3 0 5 6 5 3
18 2 19 26 2 2 3 13 14 17
27x x z + 18x z + 24x z , 8x - 8x x + 16x z - 16x z - 12x z
0 1 0 0 3 0 6 0 6 3
2 18 19 26 27 2 2 13
+ 27x z + 18x x z - 8x z + 32x z , 2x x - 2x x + 6x x z -
1 0 1 1 0 3 5 1 6 0 1
16 17 29 3 2 13 2 14 3 16
6x z - 3x z + 18x z , 2x x - 2x x + 8x x z + 4x x z + 6x z
6 5 0 0 1 3 6 0 3 0 1 0
17 3 2 2 16 18 19 31
+ 3x z , 8x x - 8x + 24x x z + 27x z + 18x z - 108x z ,
6 0 3 5 0 1 6 5 0
2 13 2 16 3 18 19 3 2
8x x x - 8x x + 24x x z + 24x x z + 27x z + 18x z , x x - x +
0 1 3 5 6 0 5 0 1 0 6 0 5 6
13 14 2 26
7x x z + 2x x z - 12x z ), {0})
0 6 0 5 0
o4 : Sequence
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i5 : J_*/size
o5 = {4, 5, 5, 7, 9, 9, 8, 7, 9, 9}
o5 : List
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i6 : J1_*/size
o6 = {4, 3, 4, 8, 9, 6, 6, 6, 6, 5}
o6 : List
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i7 : congruences={6}
o7 = {6}
o7 : List
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i8 : (answer,J,comp)=testCongruences(L,congruences,Verbose=>2)
o8 = (false, , {})
o8 : Sequence
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