Dendriform.jl Library
Index
Dendriform.BaseTree
Dendriform.Grove
Dendriform.GroveBin
Dendriform.PBTree
Base.:*
Base.:+
Base.:/
Base.:<
Base.:>
Base.:\
Base.:∪
Base.:≤
Base.:≥
Dendriform.:∨
Dendriform.:⊢
Dendriform.:⊣
Dendriform.:⊴
Dendriform.:⋖
Dendriform.:⋗
Dendriform.GroveError
Dendriform.LeftInherited
Dendriform.PrimitiveTree
Dendriform.RightInherited
Dendriform.TreeBase
Dendriform.TreeInteger
Dendriform.TreeRational
Dendriform.between
Dendriform.dashv
Dendriform.graft
Dendriform.grovebit
Dendriform.grovecheck
Dendriform.grovedisplay
Dendriform.groveindex
Dendriform.grovesort
Dendriform.left
Dendriform.over
Dendriform.posetnext
Dendriform.posetprev
Dendriform.right
Dendriform.treecheck
Dendriform.treeindex
Dendriform.treeshift
Dendriform.under
Dendriform.vdash
Dendriform.σ
Dendriform Types
Dendriform.PBTree
— Type.Planar Binary Tree with Loday's notation
Summary
mutable struct PBTree <: AbstractGrove
Fields
degr::UInt8 Y::Array{UInt8,1}
Dendriform.Grove
— Type.Grove of planar binary trees, matrix equivalence class
Summary
mutable struct Grove <: AbstractGrove
Fields
degr::UInt8 size::Int Y::Array{UInt8,2}
Dendriform.GroveBin
— Type.Compressed binary representation of grove
Summary
mutable struct GroveBin <: AbstractGrove
Fields
degr::UInt8 size::Int gbin::Integer ppos::Float16
Dendriform.BaseTree
— Type.Descending greatest integer search data for grove
Summary
mutable struct BaseTree <: Abstract Grove
Fields
μ::Array{Array{UInt8,1},1}
Dendriform Operators
Base.:∪
— Function.∪(g...)
Returns union of AbstractGrove objects
Branching
Dendriform.graft
— Function.graft(left::AbstractPBTree, right::AbstractPBTree)
Grafts the left and right PBTree with root vertex
Dendriform.:∨
— Function.∨(left::AbstractPBTree, right::AbstractPBTree)
Grafts the left and right AbstractPBTree objects
Dendriform.left
— Function.left(::AbstractPBTree)
Returns the left branch of an AbstractPBTree
Dendriform.right
— Function.right(::AbstractPBTree)
Returns the right branch of an AbstractPBTree
Partial Ordering
Dendriform.posetnext
— Function.posetnext(::AbstractPBTree)
Returns a Grove that covers the given tree
Dendriform.posetprev
— Function.posetprev(::AbstractPBTree)
Returns a Grove that covers the given tree
Dendriform.:⋖
— Function.⋖(a::AbstractPBTree, b::AbstractPBTree)
Returns Bool that tells if b covers a in Tamari partial order
Dendriform.:⋗
— Function.⋗(a::AbstractPBTree, b::AbstractPBTree)
Returns Bool that tells if a covers b in Tamari partial order
Base.:<
— Function.<(a::AbstractPBTree, b::AbstractPBTree)
Returns Bool that tells if a < b in Tamari partial order
Base.:>
— Function.>(a::AbstractPBTree, b::AbstractPBTree)
Returns Bool that tells if a > b in Tamari partial order
Base.:≤
— Function.≤(a::AbstractPBTree, b::AbstractPBTree)
Returns Bool that tells if a ≤ b in Tamari partial order
Base.:≥
— Function.≥(a::AbstractPBTree, b::AbstractPBTree)
Returns Bool that tells if a ≥ b in Tamari partial order
Dendriform.between
— Function.between(a::AbstractPBTree,b::AbstractPBTree)
Returns Grove of trees ordered between a and b
Dendriform.:⊴
— Function.⊴(a::AbstractPBTree,b::AbstractPBTree)
Returns Grove of trees ordered between a and b
Dialgebra Arithmetic
Dendriform.over
— Function.over(a::AbstractPBTree, b::AbstractPBTree)
Returns PBTree obtained from a over b operation
Dendriform.under
— Function.under(a::AbstractPBTree, b::AbstractPBTree)
Returns PBTree obtained from a under b operation
Base.:/
— Function./(a::PBTree, b::PBTree)
Returns PBTree obtained from a over b operation
Base.:\
— Function.\(a::PBTree, b::PBTree)
Returns PBTree obtained from a under b operation
Dendriform.dashv
— Function.dashv(a::AbstractGrove, b::AbstractGrove)
Returns Grove obtained from a ⊣ b operation
Dendriform.vdash
— Function.vdash(a::AbstractGrove, b::AbstractGrove)
Returns Grove obtained from a ⊢ b operation
Dendriform.:⊣
— Function.⊣(a::AbstractGrove, b::AbstractGrove)
Returns Grove obtained from a ⊣ b operation
Dendriform.:⊢
— Function.⊢(a::AbstractGrove, b::AbstractGrove)
Returns Grove obtained from a ⊢ b operation
Base.:+
— Function.+(a::AbstractGrove, b::AbstractGrove)
Returns Grove obtained from a + b operation
Base.:*
— Function.*(a::AbstractGrove, b::AbstractGrove)
Returns Grove obtained from a × b operation
Dendriform Morphisms
Dendriform.σ
— Function.σ(g::AbstractGrove)
Applies the involution to any PBTree or Grove object
Consistency Checks
Dendriform.LeftInherited
— Function.Dendriform.LeftInherited(::AbstractPBTree)
Returns Bool that tells if PBTree is left inherited
Dendriform.RightInherited
— Function.Dendriform.RightInherited(::AbstractPBTree)
Returns Bool that tells if PBTree is right inherited
Dendriform.PrimitiveTree
— Function.Dendriform.PrimitiveTree(::AbstractPBTree)
Returns Bool that tells if PBTree is primitive
Dendriform.treecheck
— Function.treecheck(::AbstractPBTree)
Returns Bool that tells if PBTree is valid
Dendriform.grovecheck
— Function.grovecheck(::AbstractGrove)
Returns Bool that tells if Grove is valid
Dendriform.GroveError
— Function.Dendriform.GroveError(::AbstractGrove)
Returns Array with Grove sorting index error
Index Data
Dendriform.treeindex
— Function.treeindex(::AbstractGrove)
Returns tree indices of any PBTree or Grove
Dendriform.groveindex
— Function.groveindex(::AbstractGrove)
Returns the grove index of any Grove
Dendriform.grovebit
— Function.grovebit(::AbstractGrove)
Returns a BitArray of tree indices
Transformations
Dendriform.TreeBase
— Function.Dendriform.TreeBase(::AbstractGrove)
Returns BaseTree objects for any AbstractGrove
Dendriform.TreeInteger
— Function.Dendriform.TreeInteger(::AbstractGrove)
Returns the tree integers of any AbstractGrove
Dendriform.TreeRational
— Function.Dendriform.TreeRational(::AbstractGrove)
Returns the tree rationals of any AbstractGrove
Tools & Options
Dendriform.grovedisplay
— Function.grovedisplay(::Bool)
Toggles the display output of grove index data (disabled by default)
Dendriform.grovesort
— Function.grovesort(::Bool)
Toggles the grovesort algorithm (enabled by default - RECOMMENDED)
Dendriform.treeshift
— Function.treeshift(::Bool)
Toggles the shift for the tree integers / rationals