reshuffle AutGroup
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src/AutGroup.jl
241
src/AutGroup.jl
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@ -1,8 +1,9 @@
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export Automorphism, AutGroup, Aut, SAut
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###############################################################################
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#
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# AutSymbol/ AutGroup / Automorphism
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#
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###############################################################################
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struct RTransvect
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i::Int8
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@ -30,70 +31,6 @@ struct AutSymbol <: GSymbol
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fn::Union{LTransvect, RTransvect, PermAut, FlipAut, Identity}
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end
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mutable struct AutGroup{N} <: AbstractFPGroup
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objectGroup::FreeGroup
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gens::Vector{AutSymbol}
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end
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mutable struct Automorphism{N} <: GWord{AutSymbol}
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symbols::Vector{AutSymbol}
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modified::Bool
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savedhash::UInt
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parent::AutGroup{N}
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function Automorphism{N}(f::Vector{AutSymbol}) where {N}
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return new{N}(f, true, zero(UInt))
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end
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end
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export Automorphism, AutGroup, Aut, SAut
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###############################################################################
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#
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# Type and parent object methods
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#
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###############################################################################
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elem_type(::Type{AutGroup{N}}) where N = Automorphism{N}
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parent_type(::Automorphism{N}) where N = AutGroup{N}
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###############################################################################
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#
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# AutSymbol defining functions
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#
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###############################################################################
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function (ϱ::RTransvect)(v, pow::Integer=1)
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append!(v[ϱ.i], v[ϱ.j]^pow)
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freereduce!(v[ϱ.i])
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return v
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end
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function (λ::LTransvect)(v, pow::Integer=1)
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prepend!(v[λ.i], v[λ.j]^pow)
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freereduce!(v[λ.i])
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return v
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end
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function (σ::PermAut)(v, pow::Integer=1)
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w = deepcopy(v)
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s = (σ.perm^pow).d
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@inbounds for k in eachindex(v)
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v[k].symbols = w[s[k]].symbols
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end
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return v
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end
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function (ɛ::FlipAut)(v, pow::Integer=1)
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@inbounds if isodd(pow)
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v[ɛ.i].symbols = inv(v[ɛ.i]).symbols
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end
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return v
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end
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(::Identity)(v, pow::Integer=1) = v
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# taken from ValidatedNumerics, under under the MIT "Expat" License:
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# https://github.com/JuliaIntervals/ValidatedNumerics.jl/blob/master/LICENSE.md
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function subscriptify(n::Integer)
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@ -135,26 +72,54 @@ function AutSymbol(p::Generic.Perm, pow::Integer=1)
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return id_autsymbol()
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end
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function AutSymbol(a::Vector{<:Integer}, pow=1)
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return AutSymbol(Generic.Perm(convert(Vector{Int8}, a)), pow)
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end
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ϱ(i::Integer, j::Integer, pow::Integer=1) = transvection_R(i, j, pow)
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λ(i::Integer, j::Integer, pow::Integer=1) = transvection_L(i, j, pow)
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ε(i::Integer, pow::Integer=1) = flip(i, pow)
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σ(v::Generic.Perm, pow::Integer=1) = AutSymbol(v, pow)
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ϱ(i::Integer, j::Integer, pow::Integer=1) = transvection_R(i, j, pow=pow)
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λ(i::Integer, j::Integer, pow::Integer=1) = transvection_L(i, j, pow=pow)
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ε(i::Integer, pow::Integer=1) = flip(i, pow=pow)
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σ(v, pow=1) = AutSymbol(v, pow=pow)
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function domain(G::AutGroup{N}) where N
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F = G.objectGroup
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gg = gens(F)
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return ntuple(i->gg[i], N)
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function change_pow(s::AutSymbol, n::Integer)
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if n == zero(n)
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return id_autsymbol()
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end
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symbol = s.fn
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if symbol isa FlipAut
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return flip(symbol.i, n)
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elseif symbol isa PermAut
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return AutSymbol(symbol.perm, n)
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elseif symbol isa RTransvect
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return transvection_R(symbol.i, symbol.j, n)
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elseif symbol isa LTransvect
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return transvection_L(symbol.i, symbol.j, n)
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elseif symbol isa Identity
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return s
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else
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throw(DomainError("Unknown type of AutSymbol: $s"))
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end
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end
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###############################################################################
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#
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# AutGroup / Automorphism constructors
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# AutGroup / Automorphism
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#
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###############################################################################
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mutable struct AutGroup{N} <: AbstractFPGroup
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objectGroup::FreeGroup
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gens::Vector{AutSymbol}
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end
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mutable struct Automorphism{N} <: GWord{AutSymbol}
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symbols::Vector{AutSymbol}
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modified::Bool
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savedhash::UInt
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parent::AutGroup{N}
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function Automorphism{N}(f::Vector{AutSymbol}) where {N}
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return new{N}(f, true, zero(UInt))
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end
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end
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elem_type(::Type{AutGroup{N}}) where N = Automorphism{N}
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parent_type(::Type{Automorphism{N}}) where N = AutGroup{N}
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function AutGroup(G::FreeGroup; special=false)
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S = AutSymbol[]
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@ -163,14 +128,14 @@ function AutGroup(G::FreeGroup; special=false)
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indexing = [[i,j] for i in 1:n for j in 1:n if i≠j]
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rmuls = [transvection_R(i,j) for (i,j) in indexing]
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lmuls = [transvection_L(i,j) for (i,j) in indexing]
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rmuls = [ϱ(i,j) for (i,j) in indexing]
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lmuls = [λ(i,j) for (i,j) in indexing]
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append!(S, [rmuls; lmuls])
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if !special
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flips = [flip(i) for i in 1:n]
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syms = [AutSymbol(p) for p in SymmetricGroup(Int8(n))][2:end]
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flips = [ε(i) for i in 1:n]
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syms = [σ(p) for p in SymmetricGroup(Int8(n))][2:end]
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append!(S, [flips; syms])
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end
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@ -180,64 +145,86 @@ end
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Aut(G::Group) = AutGroup(G)
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SAut(G::Group) = AutGroup(G, special=true)
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###############################################################################
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#
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# Types call overloads
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#
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###############################################################################
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Automorphism{N}(s::AutSymbol) where N = Automorphism{N}(AutSymbol[s])
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function (G::AutGroup{N})(f::AutSymbol) where N
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g = Automorphism{N}([f])
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g.parent = G
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setparent!(g, G)
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return g
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end
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function (G::AutGroup{N})(g::Automorphism{N}) where N
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g.parent = G
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return g
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(G::AutGroup{N})(g::Automorphism{N}) where N = (setparent!(g, G); g)
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###############################################################################
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#
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# AutSymbol defining functions && evaluation
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# NOTE: all automorphisms operate on a tuple of FreeWords INPLACE!
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#
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function (ϱ::RTransvect)(v, pow::Integer=1)
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append!(v[ϱ.i], v[ϱ.j]^pow)
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freereduce!(v[ϱ.i])
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return v
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end
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function (λ::LTransvect)(v, pow::Integer=1)
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prepend!(v[λ.i], v[λ.j]^pow)
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freereduce!(v[λ.i])
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return v
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end
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function (σ::PermAut)(v, pow::Integer=1)
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w = deepcopy(v)
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s = (σ.perm^pow).d
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@inbounds for k in eachindex(v)
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v[k].symbols = w[s[k]].symbols
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end
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return v
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end
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function (ɛ::FlipAut)(v, pow::Integer=1)
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@inbounds if isodd(pow)
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v[ɛ.i].symbols = inv(v[ɛ.i]).symbols
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end
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return v
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end
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(::Identity)(v, pow::Integer=1) = v
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###############################################################################
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#
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# Functional call overloads for evaluation of AutSymbol and Automorphism
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#
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###############################################################################
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(s::AutSymbol)(v::NTuple{N, T}) where {N, T} = s.fn(v, s.pow)::NTuple{N, T}
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function (f::Automorphism{N})(v::NTuple{N, T}) where {N, T}
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for s in syllables(f)
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v = s(v)::NTuple{N, T}
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# if iszero(i % 3)
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# freereduce!.(v)
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# end
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end
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# return freereduce!.(v)
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return v
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end
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function domain(G::AutGroup{N}) where N
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F = G.objectGroup
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return ntuple(i->F(F.gens[i]), N)
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end
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evaluate(f::Automorphism) = f(domain(parent(f)))
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###############################################################################
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#
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# Comparison
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# hashing && equality
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#
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###############################################################################
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const HASHINGCONST = 0x7d28276b01874b19 # hash(Automorphism)
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hash(s::AutSymbol, h::UInt) = hash(s.id, hash(s.pow, hash(AutSymbol, h)))
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function hash_internal(g::Automorphism, images = freereduce!.(evaluate(g)),
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h::UInt = HASHINGCONST)
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h::UInt = 0x7d28276b01874b19) # hash(Automorphism)
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return hash(images, hash(parent(g), h))
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end
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function compute_images(g::Automorphism)
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images = reduce!.(evaluate(g))
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g.savedhash = hash_internal(g, images)
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savehash!(g, hash_internal(g, images))
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unsetmodified!(g)
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return images
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end
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@ -268,37 +255,10 @@ function (==)(g::Automorphism{N}, h::Automorphism{N}) where N
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return img == imh
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end
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###############################################################################
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#
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# Basic manipulation
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#
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###############################################################################
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function change_pow(s::AutSymbol, n::Integer)
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if n == zero(n)
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return id_autsymbol()
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end
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symbol = s.fn
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if symbol isa FlipAut
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return flip(symbol.i, n)
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elseif symbol isa PermAut
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return AutSymbol(symbol.perm, n)
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elseif symbol isa RTransvect
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return transvection_R(symbol.i, symbol.j, n)
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elseif symbol isa LTransvect
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return transvection_L(symbol.i, symbol.j, n)
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elseif symbol isa Identity
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return s
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else
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throw(DomainError("Unknown type of AutSymbol: $s"))
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end
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end
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###############################################################################
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#
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# String I/O
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#
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###############################################################################
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function show(io::IO, G::AutGroup)
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print(io, "Automorphism Group of $(G.objectGroup)\n")
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@ -307,21 +267,8 @@ end
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###############################################################################
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#
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# Binary operators
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# Reduction
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#
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###############################################################################
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###############################################################################
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#
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# Inversion
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#
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###############################################################################
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###############################################################################
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#
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# Misc
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#
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###############################################################################
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getperm(s::AutSymbol) = s.fn.perm^s.pow
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