The numerator P(t) of the Hilbert function of a module whose free resolution has a pure resolution of type L has the form P(t) = b_0 t^(d_0) - b_1 t^(d_1) + ... + (-1)^c b_c t^(d_c), where L = {d_0, ..., d_c}. If (1-t)^c divides P(t), as in the case where the module has codimension c, then the b_0, ..., b_c are determined up to a unique scalar multiple. This routine returns the smallest positive integral solution of these (Herzog-Kuhl) equations.
i1 : makePureBetti{0,2,4,5}
o1 = {3, 10, 15, 8}
o1 : List
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i2 : makePureBetti({0,2,4,5},TableEntries => HerzogKuhl)
1 1 1 1
o2 = {--, --, -, --}
40 12 8 15
o2 : List
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i3 : makePureBetti({0,2,4,5},TableEntries => RealizationModules)
o3 = {3, 10, 15, 8}
o3 : List
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i4 : makePureBetti{0,3,4,5,6,7,10}
o4 = {1, 50, 175, 252, 175, 50, 1}
o4 : List
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i5 : makePureBetti({0,3,4,5,6,7,10},TableEntries => HerzogKuhl)
1 1 1 1 1 1 1
o5 = {-----, ---, ---, ---, ---, ---, -----}
25200 504 144 100 144 504 25200
o5 : List
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i6 : makePureBetti({0,3,4,5,6,7,10},TableEntries => RealizationModules)
o6 = {36, 1800, 6300, 9072, 6300, 1800, 36}
o6 : List
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