Description
A Triplet is a list consisting of three degree sequences, each of which is a list of increasing integers. These three degree sequences fulfill certain compatibility conditions. There are two different but equivalent versions:
1. A degree triplet, see Definition 2.9 in math.AC/1207.2071 "Triplets of pure free squarefree complexes"
2. A homology triplet, see Definition 5.4 in math.AC/1212.3675 "Zipping Tate resolutions and exterior coalgebras"
The routines
isDegreeTriplet and
isHomologyTriplet checks if a triplet fulfills the compatibility conditions for degree and homology triplets, respectively. The routine
toHomology converts from a degree triplet to a homology triplet, and the routine
toDegree converts from a homology triplet to a degree triplet.
i1 : T = triplet({1,2,3}, {0,2}, {0,2,3})
o1 = {{1, 2, 3}, {0, 2}, {0, 2, 3}}
o1 : Triplet
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i2 : instance(T, Triplet)
o2 = true
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i3 : isDegreeTriplet T
o3 = true
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i4 : Th = toHomology T
o4 = {{1, 2, 3}, {1, 3}, {0, 2, 3}}
o4 : Triplet
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i5 : instance(Th, Triplet)
o5 = true
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i6 : isHomologyTriplet Th
o6 = true
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