For any of the functions that produce phylogenetic invariants in the ring of Fourier coordinates, the ring can be specified with this optional argument. If null is passed then a new ring of Fourier coordinates will be created.
The ring passed can be any polynomial ring with sufficiently many variables. The sufficient number is $k = |G|^{n-1}$ where $G$ is the group of labels used by the model, and $n$ is the number of leaves of the phylogenetic tree. The ring may have more than $k$ variables, in which case only the first $k$ will be used.
i1 : T = leafTree(4,{{0,1}})
o1 = {{0, 1, 2, 3}, {set {0, 1}, set {0}, set {1}, set {2}, set {3}}}
o1 : LeafTree
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i2 : phyloToricFP(T,CFNmodel)
o2 = ideal (- q q + q q , q q -
0,0,1,1 1,1,0,0 0,0,0,0 1,1,1,1 0,0,1,1 1,1,0,0
------------------------------------------------------------------------
q q , q q - q q , -
0,0,0,0 1,1,1,1 0,0,1,1 1,1,0,0 0,0,0,0 1,1,1,1
------------------------------------------------------------------------
q q + q q , - q q +
0,0,1,1 1,1,0,0 0,0,0,0 1,1,1,1 0,1,1,0 1,0,0,1
------------------------------------------------------------------------
q q , q q - q q , q q
0,1,0,1 1,0,1,0 0,1,1,0 1,0,0,1 0,1,0,1 1,0,1,0 0,1,1,0 1,0,0,1
------------------------------------------------------------------------
- q q , - q q + q q )
0,1,0,1 1,0,1,0 0,1,1,0 1,0,0,1 0,1,0,1 1,0,1,0
o2 : Ideal of 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
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i3 : S = QQ[a..h] o3 = S o3 : PolynomialRing |
i4 : phyloToricFP(T,CFNmodel,QRing=>S)
o4 = ideal (- b*g + a*h, b*g - a*h, b*g - a*h, - b*g + a*h, - d*e + c*f, d*e
------------------------------------------------------------------------
- c*f, d*e - c*f, - d*e + c*f)
o4 : Ideal of S
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