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.Grove — Method
Grove(g::AbstractGrove)

Creates Grove object from any NotGrove object

Dendriform.Grove — Method
Grove(g::Array{Int,n})

Creates Grove using Loday label array of dimension 1 or 2

Dendriform.Grove — Method
Grove(degree::Int, index::Integer)

Looks up Grove using degree and grove index

Dendriform.GroveBin — Type

Compressed binary representation of grove

Summary

mutable struct GroveBin <: AbstractGrove

Fields

degr::UInt8 size::Int gbin::Integer ppos::Float16

Dendriform.PBTree — Type

Planar Binary Tree with Loday's notation

Summary

mutable struct PBTree <: AbstractGrove

Fields

degr::UInt8 Y::Array{UInt8,1}

Dendriform.PBTree — Method
PBTree(t::Array{Int,1})

Creates PBTree using Loday label array

Dendriform.PBTree — Method
PBTree(degree::Int, index::Int)

Looks up PBTree using degree and tree index

AbstractLattices.:∨ — Method
∨(left::AbstractPBTree, right::AbstractPBTree)

Grafts the left and right AbstractPBTree objects

Base.:* — Method
*(a::AbstractGrove, b::AbstractGrove)

Returns Grove obtained from a × b operation

Base.:+ — Method
+(a::AbstractGrove, b::AbstractGrove)

Returns Grove obtained from a + b operation

Base.:∪ — Method
∪(g...)

Returns union of AbstractGrove objects

Dendriform.:⊢ — Method
⊢(a::AbstractGrove, b::AbstractGrove)

Returns Grove obtained from a ⊢ b operation

Dendriform.:⊣ — Method
⊣(a::AbstractGrove, b::AbstractGrove)

Returns Grove obtained from a ⊣ b operation

Dendriform.:⊴ — Method
⊴(a::AbstractPBTree,b::AbstractPBTree)

Returns Grove of trees ordered between a and b

Dendriform.:⋖ — Method
⋖(a::AbstractPBTree, b::AbstractPBTree)

Returns Bool that tells if b covers a in Tamari partial order

Dendriform.:⋗ — Method
⋗(a::AbstractPBTree, b::AbstractPBTree)

Returns Bool that tells if a covers b in Tamari partial order

Dendriform.between — Method
between(a::AbstractPBTree,b::AbstractPBTree)

Returns Grove of trees ordered between a and b

Dendriform.dashv — Method
dashv(a::AbstractGrove, b::AbstractGrove)

Returns Grove obtained from a ⊣ b operation

Dendriform.graft — Method
graft(left::AbstractPBTree, right::AbstractPBTree)

Grafts the left and right PBTree with root vertex

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.left — Method
left(::AbstractPBTree)

Returns the left branch of an AbstractPBTree

Dendriform.over — Method
over(a::AbstractPBTree, b::AbstractPBTree)

Returns PBTree obtained from a over b operation

Dendriform.posetnext — Method
posetnext(::AbstractPBTree)

Returns a Grove that covers the given tree

Dendriform.posetprev — Method
posetprev(::AbstractPBTree)

Returns a Grove that covers the given tree

Dendriform.right — Method
right(::AbstractPBTree)

Returns the right branch of an AbstractPBTree

Dendriform.treecheck — Method
treecheck(::AbstractPBTree)

Returns Bool that tells if PBTree is valid

Dendriform.treeindex — Method
treeindex(::AbstractGrove)

Returns tree indices of any PBTree or Grove

Dendriform.treeshift — Function
treeshift(::Bool)

Toggles the shift for the tree integers / rationals

Dendriform.under — Method
under(a::AbstractPBTree, b::AbstractPBTree)

Returns PBTree obtained from a under b operation

Dendriform.vdash — Method
vdash(a::AbstractGrove, b::AbstractGrove)

Returns Grove obtained from a ⊢ b operation

Dendriform.σ — Method
σ(g::AbstractGrove)

Applies the involution to any PBTree or Grove object

Dendriform.BaseTree — Type

Descending greatest integer search data for grove

Summary

mutable struct BaseTree <: Abstract Grove

Fields

μ::Array{Array{UInt8,1},1}

Base.:/ — Method
/(a::PBTree, b::PBTree)

Returns PBTree obtained from a over b operation

Base.:< — Method
<(a::AbstractPBTree, b::AbstractPBTree)

Returns Bool that tells if a < b in Tamari partial order

Base.:> — Method
>(a::AbstractPBTree, b::AbstractPBTree)

Returns Bool that tells if a > b in Tamari partial order

Base.:\ — Method
\(a::PBTree, b::PBTree)

Returns PBTree obtained from a under b operation

Base.:≤ — Method
≤(a::AbstractPBTree, b::AbstractPBTree)

Returns Bool that tells if a ≤ b in Tamari partial order

Base.:≥ — Method
≥(a::AbstractPBTree, b::AbstractPBTree)

Returns Bool that tells if a ≥ b in Tamari partial order

Dendriform.GroveError — Method
Dendriform.GroveError(::AbstractGrove)

Returns Array with Grove sorting index error

Dendriform.LeftInherited — Method
Dendriform.LeftInherited(::AbstractPBTree)

Returns Bool that tells if PBTree is left inherited

Dendriform.PrimitiveTree — Method
Dendriform.PrimitiveTree(::AbstractPBTree)

Returns Bool that tells if PBTree is primitive

Dendriform.RightInherited — Method
Dendriform.RightInherited(::AbstractPBTree)

Returns Bool that tells if PBTree is right inherited

Dendriform.TreeBase — Method
Dendriform.TreeBase(::AbstractGrove)

Returns BaseTree objects for any AbstractGrove

Dendriform.TreeInteger — Method
Dendriform.TreeInteger(::AbstractGrove)

Returns the tree integers of any AbstractGrove

Dendriform.TreeRational — Method
Dendriform.TreeRational(::AbstractGrove)

Returns the tree rationals of any AbstractGrove