corresponds to the construction in math.AC/0712.1843v2, "Betti Numbers of Graded Modules and Cohomology of Vector Bundles", Section 5.
i1 : L = {0,2,3,9}
o1 = {0, 2, 3, 9}
o1 : List
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i2 : B = pureBettiDiagram L
0 1 2 3
o2 = total: 7 27 21 1
0: 7 . . .
1: . 27 21 .
2: . . . .
3: . . . .
4: . . . .
5: . . . .
6: . . . 1
o2 : BettiTally
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i3 : pureCharFree L
o3 = 56
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i4 : L1 = {0,3,4,6}
o4 = {0, 3, 4, 6}
o4 : List
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i5 : B1 = pureBettiDiagram L1
0 1 2 3
o5 = total: 1 8 9 2
0: 1 . . .
1: . . . .
2: . 8 9 .
3: . . . 2
o5 : BettiTally
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i6 : pureCharFree L1
o6 = 5
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Thus, for large enough multiples m, m*B occurs as the Betti diagram of a module from the pureCharFree construction
i7 : betti res randomSocleModule(L,1)
0 1 2 3
o7 = total: 7 27 21 1
0: 7 . . .
1: . 27 21 .
2: . . . .
3: . . . .
4: . . . .
5: . . . .
6: . . . 1
o7 : BettiTally
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i8 : betti res randomModule(L,1)
0 1 2 3
o8 = total: 7 27 35 15
0: 7 . . .
1: . 27 11 .
2: . . 24 15
o8 : BettiTally
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i9 : betti res randomModule({0,6,7,9},1)
0 1 2 3
o9 = total: 1 21 27 7
0: 1 . . .
1: . . . .
2: . . . .
3: . . . .
4: . . . .
5: . 21 27 .
6: . . . 7
o9 : BettiTally
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i10 : betti res randomSocleModule(L1,1)
0 1 2 3
o10 = total: 1 8 9 2
0: 1 . . .
1: . . . .
2: . 8 9 .
3: . . . 2
o10 : BettiTally
|
i11 : betti res randomModule(L1,1)
0 1 2 3
o11 = total: 1 8 9 2
0: 1 . . .
1: . . . .
2: . 8 9 .
3: . . . 2
o11 : BettiTally
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i12 : betti res randomModule({0,2,3,6},1)
0 1 2 3
o12 = total: 2 9 10 3
0: 2 . . .
1: . 9 7 .
2: . . 3 3
o12 : BettiTally
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i13 : betti res randomSocleModule({0,2,3,6},1)
0 1 2 3
o13 = total: 2 9 8 1
0: 2 . . .
1: . 9 8 .
2: . . . .
3: . . . 1
o13 : BettiTally
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