phyloToric42 -- Compute the invariants of a group-based phylogenetic tree model using the 4ti2 package.

Synopsis

• Usage:

  I = phyloToric42(n,E,M)

  I = phyloToric42(G,M)

  I = phyloToric42(T,M)

• Inputs:
  • T, an instance of the type LeafTree, A tree
  • 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, The model (CNFmodel, JCmodel, etc)
• Optional inputs:
  • QRing => ..., default value null, Optional argument to specify Fourier coordinate ring
• Outputs:
  • I, an ideal, The ideal of the generators computed

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        + 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    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 tree model using the toric fiber product structure