The Fourier coordinates for a phylogenetic tree model have one coordinate for each consistent coloring of the tree T. A consistent coloring is an assignment of one of the group elements of the model M to each of the leaves of T such that the sum of all the group elements assigned is $0$.
Each variable of the ring is indexed by a sequence representing a consistent coloring with each element of the group represented by an integer between $0$ and $m-1$ where $m$ is the order of the group.
A variable name for the ring can be passed using the optional argument Variable. Otherwise the symbol q is used.
i1 : qRing(4,CFNmodel)
o1 = QQ[q , q , q , q , q , q , q , q ]
0,0,0,0 0,0,1,1 0,1,0,1 0,1,1,0 1,0,0,1 1,0,1,0 1,1,0,0 1,1,1,1
o1 : PolynomialRing
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i2 : qRing(3,JCmodel)
o2 = QQ[q , q , q , q , q , q , q , q , q , q , q , q , q , q , q , q ]
0,0,0 0,1,1 0,2,2 0,3,3 1,0,1 1,1,0 1,2,3 1,3,2 2,0,2 2,1,3 2,2,0 2,3,1 3,0,3 3,1,2 3,2,1 3,3,0
o2 : PolynomialRing
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The object qRing is a method function with options.