corresponds to the construction in math.AC/0709.1529v3 "The Existence of Pure Free Resolutions", Section 3.
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 : pureTwoInvariant L
o3 = 196
|
i4 : L1 = {0,4,5,7}
o4 = {0, 4, 5, 7}
o4 : List
|
i5 : B1 = pureBettiDiagram L1
0 1 2 3
o5 = total: 3 35 42 10
0: 3 . . .
1: . . . .
2: . . . .
3: . 35 42 .
4: . . . 10
o5 : BettiTally
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i6 : pureTwoInvariant L1
o6 = 15
|
Thus, for large enough multiples m, m*B occurs as the Betti diagram of a module from the pureTwoInvariant 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
|
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
|
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
|
i10 : betti res randomSocleModule(L1,1)
0 1 2 3
o10 = total: 3 35 42 10
0: 3 . . .
1: . . . .
2: . . . .
3: . 35 42 .
4: . . . 10
o10 : BettiTally
|
i11 : betti res randomModule(L1,1)
0 1 2 3
o11 = total: 3 35 42 10
0: 3 . . .
1: . . . .
2: . . . .
3: . 35 42 .
4: . . . 10
o11 : BettiTally
|
i12 : betti res randomModule({0,2,3,7},1)
0 1 2 3
o12 = total: 10 42 50 18
0: 10 . . .
1: . 42 26 .
2: . . 24 18
o12 : BettiTally
|
i13 : betti res randomSocleModule({0,2,3,7},1)
0 1 2 3
o13 = total: 10 42 35 3
0: 10 . . .
1: . 42 35 .
2: . . . .
3: . . . .
4: . . . 3
o13 : BettiTally
|