phyloToricLinears -- compute the linear invariants of a group-based phylogenetic model

Synopsis

Usage:

phyloToricLinears(T,M)

phyloToricLinears(n,E,M)
Inputs:
- T, an instance of the type LeafTree,
- n, an integer, the number of leaves
- E, a list, the internal edges of the tree, given by one part of the bipartition on leaves
- M, an instance of the type Model,
Optional inputs:
- QRing => ..., default value null, optional argument to specify Fourier coordinate ring
- Random => ..., default value false
Outputs:
- a list, a generating set of the linear invariants

Description

For models such as Jukes-Cantor (JCmodel) and Kimura 2-parameter (K2Pmodel), multiple variables in the Fourier coordinates may map to the same monomial under the monomial map that defines the toric variety of the model. These equivalencies give rise to linear relations in the space of Fourier coordinates.

The number of linear invariants is the codimension of the smallest linear subspace in which the toric variety of the model is contained.

The optional argument QRing can be passed the ring of Fourier coordinates. Otherwise the function will create a new ring.

i1 : T = leafTree(3,{})

o1 = {{0, 1, 2}, {set {0}, set {1}, set {2}}}

o1 : LeafTree

i2 : S = qRing(T, K2Pmodel)

o2 = S

o2 : PolynomialRing

i3 : phyloToricLinears(T, K2Pmodel, QRing=>S)

o3 = {q      - q     , q      - q     , q      - q     , q      - q     ,
       1,2,3    1,3,2   2,1,3    3,1,2   2,3,1    3,2,1   2,2,0    3,3,0 
     ------------------------------------------------------------------------
     q      - q     , q      - q     }
      2,0,2    3,0,3   0,2,2    0,3,3

o3 : List

Ways to use phyloToricLinears :

phyloToricLinears(LeafTree,Model)
phyloToricLinears(ZZ,List,Model)

For the programmer

The object phyloToricLinears is a method function with options.

phyloToricLinears -- compute the linear invariants of a group-based phylogenetic model

Synopsis

Description

See also

Ways to use phyloToricLinears :

For the programmer