mirror of
https://github.com/kalmarek/Groups.jl.git
synced 2024-12-25 18:15:29 +01:00
reshuffle AutGroup
This commit is contained in:
parent
c1f54ad41e
commit
ebefc7e399
241
src/AutGroup.jl
241
src/AutGroup.jl
@ -1,8 +1,9 @@
|
||||
export Automorphism, AutGroup, Aut, SAut
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# AutSymbol/ AutGroup / Automorphism
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
struct RTransvect
|
||||
i::Int8
|
||||
@ -30,70 +31,6 @@ struct AutSymbol <: GSymbol
|
||||
fn::Union{LTransvect, RTransvect, PermAut, FlipAut, Identity}
|
||||
end
|
||||
|
||||
mutable struct AutGroup{N} <: AbstractFPGroup
|
||||
objectGroup::FreeGroup
|
||||
gens::Vector{AutSymbol}
|
||||
end
|
||||
|
||||
mutable struct Automorphism{N} <: GWord{AutSymbol}
|
||||
symbols::Vector{AutSymbol}
|
||||
modified::Bool
|
||||
savedhash::UInt
|
||||
parent::AutGroup{N}
|
||||
|
||||
function Automorphism{N}(f::Vector{AutSymbol}) where {N}
|
||||
return new{N}(f, true, zero(UInt))
|
||||
end
|
||||
end
|
||||
|
||||
export Automorphism, AutGroup, Aut, SAut
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# Type and parent object methods
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
elem_type(::Type{AutGroup{N}}) where N = Automorphism{N}
|
||||
|
||||
parent_type(::Automorphism{N}) where N = AutGroup{N}
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# AutSymbol defining functions
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
function (ϱ::RTransvect)(v, pow::Integer=1)
|
||||
append!(v[ϱ.i], v[ϱ.j]^pow)
|
||||
freereduce!(v[ϱ.i])
|
||||
return v
|
||||
end
|
||||
|
||||
function (λ::LTransvect)(v, pow::Integer=1)
|
||||
prepend!(v[λ.i], v[λ.j]^pow)
|
||||
freereduce!(v[λ.i])
|
||||
return v
|
||||
end
|
||||
|
||||
function (σ::PermAut)(v, pow::Integer=1)
|
||||
w = deepcopy(v)
|
||||
s = (σ.perm^pow).d
|
||||
@inbounds for k in eachindex(v)
|
||||
v[k].symbols = w[s[k]].symbols
|
||||
end
|
||||
return v
|
||||
end
|
||||
|
||||
function (ɛ::FlipAut)(v, pow::Integer=1)
|
||||
@inbounds if isodd(pow)
|
||||
v[ɛ.i].symbols = inv(v[ɛ.i]).symbols
|
||||
end
|
||||
return v
|
||||
end
|
||||
|
||||
(::Identity)(v, pow::Integer=1) = v
|
||||
|
||||
# taken from ValidatedNumerics, under under the MIT "Expat" License:
|
||||
# https://github.com/JuliaIntervals/ValidatedNumerics.jl/blob/master/LICENSE.md
|
||||
function subscriptify(n::Integer)
|
||||
@ -135,26 +72,54 @@ function AutSymbol(p::Generic.Perm, pow::Integer=1)
|
||||
return id_autsymbol()
|
||||
end
|
||||
|
||||
function AutSymbol(a::Vector{<:Integer}, pow=1)
|
||||
return AutSymbol(Generic.Perm(convert(Vector{Int8}, a)), pow)
|
||||
end
|
||||
ϱ(i::Integer, j::Integer, pow::Integer=1) = transvection_R(i, j, pow)
|
||||
λ(i::Integer, j::Integer, pow::Integer=1) = transvection_L(i, j, pow)
|
||||
ε(i::Integer, pow::Integer=1) = flip(i, pow)
|
||||
σ(v::Generic.Perm, pow::Integer=1) = AutSymbol(v, pow)
|
||||
|
||||
ϱ(i::Integer, j::Integer, pow::Integer=1) = transvection_R(i, j, pow=pow)
|
||||
λ(i::Integer, j::Integer, pow::Integer=1) = transvection_L(i, j, pow=pow)
|
||||
ε(i::Integer, pow::Integer=1) = flip(i, pow=pow)
|
||||
σ(v, pow=1) = AutSymbol(v, pow=pow)
|
||||
|
||||
function domain(G::AutGroup{N}) where N
|
||||
F = G.objectGroup
|
||||
gg = gens(F)
|
||||
return ntuple(i->gg[i], N)
|
||||
function change_pow(s::AutSymbol, n::Integer)
|
||||
if n == zero(n)
|
||||
return id_autsymbol()
|
||||
end
|
||||
symbol = s.fn
|
||||
if symbol isa FlipAut
|
||||
return flip(symbol.i, n)
|
||||
elseif symbol isa PermAut
|
||||
return AutSymbol(symbol.perm, n)
|
||||
elseif symbol isa RTransvect
|
||||
return transvection_R(symbol.i, symbol.j, n)
|
||||
elseif symbol isa LTransvect
|
||||
return transvection_L(symbol.i, symbol.j, n)
|
||||
elseif symbol isa Identity
|
||||
return s
|
||||
else
|
||||
throw(DomainError("Unknown type of AutSymbol: $s"))
|
||||
end
|
||||
end
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# AutGroup / Automorphism constructors
|
||||
# AutGroup / Automorphism
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
mutable struct AutGroup{N} <: AbstractFPGroup
|
||||
objectGroup::FreeGroup
|
||||
gens::Vector{AutSymbol}
|
||||
end
|
||||
|
||||
mutable struct Automorphism{N} <: GWord{AutSymbol}
|
||||
symbols::Vector{AutSymbol}
|
||||
modified::Bool
|
||||
savedhash::UInt
|
||||
parent::AutGroup{N}
|
||||
|
||||
function Automorphism{N}(f::Vector{AutSymbol}) where {N}
|
||||
return new{N}(f, true, zero(UInt))
|
||||
end
|
||||
end
|
||||
|
||||
elem_type(::Type{AutGroup{N}}) where N = Automorphism{N}
|
||||
parent_type(::Type{Automorphism{N}}) where N = AutGroup{N}
|
||||
|
||||
function AutGroup(G::FreeGroup; special=false)
|
||||
S = AutSymbol[]
|
||||
@ -163,14 +128,14 @@ function AutGroup(G::FreeGroup; special=false)
|
||||
|
||||
indexing = [[i,j] for i in 1:n for j in 1:n if i≠j]
|
||||
|
||||
rmuls = [transvection_R(i,j) for (i,j) in indexing]
|
||||
lmuls = [transvection_L(i,j) for (i,j) in indexing]
|
||||
rmuls = [ϱ(i,j) for (i,j) in indexing]
|
||||
lmuls = [λ(i,j) for (i,j) in indexing]
|
||||
|
||||
append!(S, [rmuls; lmuls])
|
||||
|
||||
if !special
|
||||
flips = [flip(i) for i in 1:n]
|
||||
syms = [AutSymbol(p) for p in SymmetricGroup(Int8(n))][2:end]
|
||||
flips = [ε(i) for i in 1:n]
|
||||
syms = [σ(p) for p in SymmetricGroup(Int8(n))][2:end]
|
||||
|
||||
append!(S, [flips; syms])
|
||||
end
|
||||
@ -180,64 +145,86 @@ end
|
||||
Aut(G::Group) = AutGroup(G)
|
||||
SAut(G::Group) = AutGroup(G, special=true)
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# Types call overloads
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
Automorphism{N}(s::AutSymbol) where N = Automorphism{N}(AutSymbol[s])
|
||||
|
||||
function (G::AutGroup{N})(f::AutSymbol) where N
|
||||
g = Automorphism{N}([f])
|
||||
g.parent = G
|
||||
setparent!(g, G)
|
||||
return g
|
||||
end
|
||||
|
||||
function (G::AutGroup{N})(g::Automorphism{N}) where N
|
||||
g.parent = G
|
||||
return g
|
||||
(G::AutGroup{N})(g::Automorphism{N}) where N = (setparent!(g, G); g)
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# AutSymbol defining functions && evaluation
|
||||
# NOTE: all automorphisms operate on a tuple of FreeWords INPLACE!
|
||||
#
|
||||
|
||||
function (ϱ::RTransvect)(v, pow::Integer=1)
|
||||
append!(v[ϱ.i], v[ϱ.j]^pow)
|
||||
freereduce!(v[ϱ.i])
|
||||
return v
|
||||
end
|
||||
|
||||
function (λ::LTransvect)(v, pow::Integer=1)
|
||||
prepend!(v[λ.i], v[λ.j]^pow)
|
||||
freereduce!(v[λ.i])
|
||||
return v
|
||||
end
|
||||
|
||||
function (σ::PermAut)(v, pow::Integer=1)
|
||||
w = deepcopy(v)
|
||||
s = (σ.perm^pow).d
|
||||
@inbounds for k in eachindex(v)
|
||||
v[k].symbols = w[s[k]].symbols
|
||||
end
|
||||
return v
|
||||
end
|
||||
|
||||
function (ɛ::FlipAut)(v, pow::Integer=1)
|
||||
@inbounds if isodd(pow)
|
||||
v[ɛ.i].symbols = inv(v[ɛ.i]).symbols
|
||||
end
|
||||
return v
|
||||
end
|
||||
|
||||
(::Identity)(v, pow::Integer=1) = v
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# Functional call overloads for evaluation of AutSymbol and Automorphism
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
(s::AutSymbol)(v::NTuple{N, T}) where {N, T} = s.fn(v, s.pow)::NTuple{N, T}
|
||||
|
||||
function (f::Automorphism{N})(v::NTuple{N, T}) where {N, T}
|
||||
for s in syllables(f)
|
||||
v = s(v)::NTuple{N, T}
|
||||
# if iszero(i % 3)
|
||||
# freereduce!.(v)
|
||||
# end
|
||||
end
|
||||
# return freereduce!.(v)
|
||||
return v
|
||||
end
|
||||
|
||||
function domain(G::AutGroup{N}) where N
|
||||
F = G.objectGroup
|
||||
return ntuple(i->F(F.gens[i]), N)
|
||||
end
|
||||
|
||||
evaluate(f::Automorphism) = f(domain(parent(f)))
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# Comparison
|
||||
# hashing && equality
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
const HASHINGCONST = 0x7d28276b01874b19 # hash(Automorphism)
|
||||
|
||||
hash(s::AutSymbol, h::UInt) = hash(s.id, hash(s.pow, hash(AutSymbol, h)))
|
||||
|
||||
function hash_internal(g::Automorphism, images = freereduce!.(evaluate(g)),
|
||||
h::UInt = HASHINGCONST)
|
||||
h::UInt = 0x7d28276b01874b19) # hash(Automorphism)
|
||||
return hash(images, hash(parent(g), h))
|
||||
end
|
||||
|
||||
function compute_images(g::Automorphism)
|
||||
images = reduce!.(evaluate(g))
|
||||
g.savedhash = hash_internal(g, images)
|
||||
savehash!(g, hash_internal(g, images))
|
||||
unsetmodified!(g)
|
||||
return images
|
||||
end
|
||||
@ -268,37 +255,10 @@ function (==)(g::Automorphism{N}, h::Automorphism{N}) where N
|
||||
return img == imh
|
||||
end
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# Basic manipulation
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
function change_pow(s::AutSymbol, n::Integer)
|
||||
if n == zero(n)
|
||||
return id_autsymbol()
|
||||
end
|
||||
symbol = s.fn
|
||||
if symbol isa FlipAut
|
||||
return flip(symbol.i, n)
|
||||
elseif symbol isa PermAut
|
||||
return AutSymbol(symbol.perm, n)
|
||||
elseif symbol isa RTransvect
|
||||
return transvection_R(symbol.i, symbol.j, n)
|
||||
elseif symbol isa LTransvect
|
||||
return transvection_L(symbol.i, symbol.j, n)
|
||||
elseif symbol isa Identity
|
||||
return s
|
||||
else
|
||||
throw(DomainError("Unknown type of AutSymbol: $s"))
|
||||
end
|
||||
end
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# String I/O
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
function show(io::IO, G::AutGroup)
|
||||
print(io, "Automorphism Group of $(G.objectGroup)\n")
|
||||
@ -307,21 +267,8 @@ end
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# Binary operators
|
||||
# Reduction
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# Inversion
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# Misc
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
getperm(s::AutSymbol) = s.fn.perm^s.pow
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user