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QRing -- optional argument to specify Fourier coordinate ring

Description

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
 
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
 
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

Functions with optional argument named QRing :

For the programmer

The object QRing is a symbol.