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Dendriform.jl

Symbolic parser generator for Julia language expressions using REDUCE algebra term rewrite system

Setup

Installation of latest release version using Julia:

julia> Pkg.add("Dendriform")

Provides the types PBTree for planar binary trees, Grove for tree collections of constant degree, and GroveBin to compress grove data. This package defines various essential operations on planar binary trees and groves like ∪ for union; ∨ for graft; left and right for branching; <, >, ≤, ≥ for Tamari's partial ordering; / and \ (i.e. over and under); and the dashv and vdash operations ⊣, ⊢, +, * for dendriform algebra.

Background

Check the README for more background information.

Usage

Basic usage examples:

julia> using Dendriform

julia> Grove(3,7) ⊣ [1,2]∪[2,1]
[1,2,5,1,2] ↦ [3]∅∅[2,5][1,4] ↦ 20/42 or 21807
[1,2,5,2,1] ↦ [3]∅∅[2,4][1,5] ↦ 21/42 or 21906
[2,1,5,1,2] ↦ [3]∅∅[1,5][2,4] ↦ 22/42 or 22797
[2,1,5,2,1] ↦ [3]∅∅[1,4][2,5] ↦ 23/42 or 22896
[1,5,3,1,2] ↦ [2]∅[3][5][1,4] ↦ 27/42 or 30807
[1,5,2,1,3] ↦ [2]∅[5][3][1,4] ↦ 25/42 or 29007
[1,5,1,2,3] ↦ [2]∅[5][4][1,3] ↦ 24/42 or 28908
[1,5,3,2,1] ↦ [2]∅[3][4][1,5] ↦ 28/42 or 30906
[1,5,1,3,1] ↦ [2]∅[4]∅[1,3,5] ↦ 26/42 or 30186
267911168 Y5 #9/42 [0.006092%]

julia> Grove(2,3) * [1,2,3]∪[3,2,1] |> GroveBin
2981131286847743360614880957207748817969 Y6 #30/132 [54.75%]

julia> [2,1,7,4,1,3,1] < [2,1,7,4,3,2,1]
true

References