Triplet -- triplet

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.

Functions and methods returning an object of class Triplet :

rotBack -- see rotBack(Triplet) -- backward cyclic permutation
rotForw -- see rotForw(Triplet) -- forward cyclic permutation
toDegree -- see toDegree(Triplet) -- from homology triplet to degree triplet
toHomology -- see toHomology(Triplet) -- from degree triplet to homology triplet
triplet -- see triplet(List,List,List) -- make a triplet
triplet(List,List,List) -- make a triplet

Methods that use an object of class Triplet :

Betti1(Triplet) -- Betti numbers of first pure complex
Betti3(Triplet) -- Betti numbers of the three pure complexes
BettiDiagram1(Triplet) -- Betti diagram of first pure complex
BettiDiagram3(Triplet) -- Betti diagrams of the three pure complexes
cohMatrix(ZZ,ZZ,Triplet) -- cohomology table in matrix form
cohTable(ZZ,ZZ,Triplet) -- cohomology table
dualHomTriplet(Triplet) -- the dual homology triplet
hilbCoeff(Triplet) -- coefficients of Hilbert polynomial
isDegreeTriplet(Triplet) -- checks if it is a degree triplet
isHomologyTriplet(Triplet) -- checks if it is a homology triplet
rotBack(Triplet) -- backward cyclic permutation
rotForw(Triplet) -- forward cyclic permutation
toDegree(Triplet) -- from homology triplet to degree triplet
toHomology(Triplet) -- from degree triplet to homology triplet
type(Triplet) -- number of variables

For the programmer

The object Triplet is a type, with ancestor classes List < VisibleList < BasicList < Thing.