phyloToric42 -- compute the invariants of a group-based phylogenetic model with 4ti2

Synopsis

• Usage:

  phyloToric42(n,E,M)

  phyloToric42(G,M)

  phyloToric42(T,M)

• Inputs:
  • T, an instance of the type LeafTree,
  • n, an integer, the number of leaves
  • E, an instance of the type LeafTree, the internal edges of the tree, given by one part of the bipartition on leaves
  • G, an instance of the type Graph, a tree
  • M, an instance of the type Model,
• Optional inputs:
  • QRing => ..., default value null, optional argument to specify Fourier coordinate ring
• Outputs:
  • an ideal,

Description

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 : phyloToric42(T, CFNmodel)

o2 = ideal (- q       q        + q       q       , - q       q        +
               0,1,1,0 1,0,0,1    0,1,0,1 1,0,1,0     0,0,1,1 1,1,0,0  
     ------------------------------------------------------------------------
     q       q       )
      0,0,0,0 1,1,1,1

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

See also

• phyloToricFP -- compute the invariants of a group-based phylogenetic model with toric fiber products