next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
PhylogeneticTrees :: leafTree

leafTree -- Construct a LeafTree



A LeafTree is specified by listing its leaves, and for each internal edge, the partition the edge induces on the set of leaves. L is the set of leaves, or if an integer n is input then the leaves will be be named 0,...,n-1. E is a list with one entry for each internal edge. Each entry is a partition specified as a List or Set of the leaves in one side of the partition. Thus each edge can be specified in two possible ways.

A LeafTree can also be constructed from a Graph provided the graph has no cycles.

Here we construct the quartet tree which is the tree with 4 leaves and one internal edge.

i1 : T = leafTree({a,b,c,d},{{a,b}})

o1 = {{a, b, c, d}, {set {a, b}, set {a}, set {b}, set {c}, set {d}}}

o1 : LeafTree
i2 : leaves T

o2 = set {a, b, c, d}

o2 : Set
i3 : edges T

o3 = {set {a, b}, set {a}, set {b}, set {c}, set {d}}

o3 : List

Here is a tree with 5 leaves given as a Graph.

i4 : G = graph{{a,b},{c,b},{b,d},{d,e},{d,f},{f,g},{f,h}}

o4 = Graph{a => {b}      }
           b => {a, c, d}
           c => {b}
           d => {b, e, f}
           e => {d}
           f => {d, g, h}
           g => {f}
           h => {f}

o4 : Graph
i5 : T = leafTree G

o5 = {{a, c, e, g, h}, {set {a, c}, set {a, c, e}, set {a}, set {c}, set {e},
     set {g}, set {h}}}

o5 : LeafTree
i6 : leaves T

o6 = set {a, c, e, g, h}

o6 : Set
i7 : internalEdges T

o7 = {set {a, c}, set {a, c, e}}

o7 : List

Ways to use leafTree :