This is an option that can be passed to either lexBetti or almostLexBetti. If the value of the option is true a BettiTally object will be returned. If it is false, a List of lists will be returned. This latter option is useful if one wishes to obtain the total Betti numbers instead of the graded Betti numbers. This can easily be done using by applying sum to the output with AsTally=>false.
i1 : lexBetti (4, {1,2,3,3,3,3}, AsTally => true)
0 1 2 3
o1 = total: 1 3 3 1
0: 1 2 1 .
1: . . . .
2: . 1 2 1
o1 : BettiTally
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i2 : lexBetti (4, {1,2,3,3,3,3}, AsTally => false)
o2 = {{0, 0, 0, 0}, {2, 1, 0, 0}, {0, 0, 0, 0}, {1, 2, 1, 0}, {0, 0, 0, 0},
------------------------------------------------------------------------
{0, 0, 0, 0}}
o2 : List
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i3 : sum oo
o3 = {3, 3, 1, 0}
o3 : List
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