Description
pureAll returns all three numbers at one time.
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
|
i4 : pureTwoInvariant L
o4 = 196
|
i5 : pureWeyman L
o5 = 21
|
i6 : pureAll L
o6 = (56, 196, 21)
o6 : Sequence
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i7 : gcd pureAll L
o7 = 7
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Thus, for large enough multiples m, m*B occurs as the Betti diagram of a module.
However, B itself occurs:
i8 : betti res randomSocleModule(L,1)
0 1 2 3
o8 = total: 7 27 21 1
0: 7 . . .
1: . 27 21 .
2: . . . .
3: . . . .
4: . . . .
5: . . . .
6: . . . 1
o8 : BettiTally
|
i9 : betti res randomModule(L,1)
0 1 2 3
o9 = total: 7 27 35 15
0: 7 . . .
1: . 27 11 .
2: . . 24 15
o9 : BettiTally
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i10 : betti res randomModule({0,6,7,9},1)
0 1 2 3
o10 = total: 1 21 27 7
0: 1 . . .
1: . . . .
2: . . . .
3: . . . .
4: . . . .
5: . 21 27 .
6: . . . 7
o10 : BettiTally
|