Library

Dendriform.jl Library

Index

Dendriform Types

Dendriform.PBTree — Type.

Planar Binary Tree with Loday's notation

Summary

mutable struct PBTree <: AbstractGrove

Fields

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

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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}

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Dendriform.GroveBin — Type.

Compressed binary representation of grove

Summary

mutable struct GroveBin <: AbstractGrove

Fields

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

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Dendriform.BaseTree — Type.

Descending greatest integer search data for grove

Summary

mutable struct BaseTree <: Abstract Grove

Fields

μ::Array{Array{UInt8,1},1}

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Dendriform Operators

Base.:∪ — Function.
∪(g...)

Returns union of AbstractGrove objects

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Branching

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

Grafts the left and right PBTree with root vertex

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Dendriform.:∨ — Function.
∨(left::AbstractPBTree, right::AbstractPBTree)

Grafts the left and right AbstractPBTree objects

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Dendriform.left — Function.
left(::AbstractPBTree)

Returns the left branch of an AbstractPBTree

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Dendriform.right — Function.
right(::AbstractPBTree)

Returns the right branch of an AbstractPBTree

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Partial Ordering

Dendriform.posetnext — Function.
posetnext(::AbstractPBTree)

Returns a Grove that covers the given tree

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Dendriform.posetprev — Function.
posetprev(::AbstractPBTree)

Returns a Grove that covers the given tree

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

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

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

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

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

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

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

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

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

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

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

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

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

Returns Grove of trees ordered between a and b

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

Returns Grove of trees ordered between a and b

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Dialgebra Arithmetic

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

Returns PBTree obtained from a over b operation

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

Returns PBTree obtained from a under b operation

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

Returns PBTree obtained from a over b operation

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

Returns PBTree obtained from a under b operation

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

Returns Grove obtained from a ⊣ b operation

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

Returns Grove obtained from a ⊢ b operation

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

Returns Grove obtained from a ⊣ b operation

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

Returns Grove obtained from a ⊢ b operation

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

Returns Grove obtained from a + b operation

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

Returns Grove obtained from a × b operation

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Dendriform Morphisms

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

Applies the involution to any PBTree or Grove object

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Consistency Checks

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

Returns Bool that tells if PBTree is left inherited

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

Returns Bool that tells if PBTree is right inherited

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

Returns Bool that tells if PBTree is primitive

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Dendriform.treecheck — Function.
treecheck(::AbstractPBTree)

Returns Bool that tells if PBTree is valid

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Dendriform.grovecheck — Function.
grovecheck(::AbstractGrove)

Returns Bool that tells if Grove is valid

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

Returns Array with Grove sorting index error

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Index Data

Dendriform.treeindex — Function.
treeindex(::AbstractGrove)

Returns tree indices of any PBTree or Grove

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Dendriform.groveindex — Function.
groveindex(::AbstractGrove)

Returns the grove index of any Grove

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Dendriform.grovebit — Function.
grovebit(::AbstractGrove)

Returns a BitArray of tree indices

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Transformations

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

Returns BaseTree objects for any AbstractGrove

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

Returns the tree integers of any AbstractGrove

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

Returns the tree rationals of any AbstractGrove

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Tools & Options

Dendriform.grovedisplay — Function.
grovedisplay(::Bool)

Toggles the display output of grove index data (disabled by default)

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Dendriform.grovesort — Function.
grovesort(::Bool)

Toggles the grovesort algorithm (enabled by default - RECOMMENDED)

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Dendriform.treeshift — Function.
treeshift(::Bool)

Toggles the shift for the tree integers / rationals

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