1
0
mirror of https://github.com/kalmarek/Groups.jl.git synced 2024-12-25 02:05:30 +01:00

Parametrise Automorphisms on Integer type

This commit is contained in:
kalmarek 2018-04-09 12:59:24 +02:00
parent d46c5dafcc
commit b8abe64656

View File

@ -4,29 +4,29 @@
# #
############################################################################### ###############################################################################
struct RTransvect struct RTransvect{I<:Integer}
i::Int i::I
j::Int j::I
end end
struct LTransvect struct LTransvect{I<:Integer}
i::Int i::I
j::Int j::I
end end
struct FlipAut struct FlipAut{I<:Integer}
i::Int i::I
end end
struct PermAut struct PermAut{I<:Integer}
perm::Nemo.Generic.perm{Int8} perm::Nemo.Generic.perm{I}
end end
struct Identity end struct Identity end
struct AutSymbol <: GSymbol struct AutSymbol <: GSymbol
str::String str::String
pow::Int pow::Int8
typ::Union{LTransvect, RTransvect, PermAut, FlipAut, Identity} typ::Union{LTransvect, RTransvect, PermAut, FlipAut, Identity}
end end
@ -63,17 +63,17 @@ parent_type(::Automorphism{N}) where N = AutGroup{N}
# #
############################################################################### ###############################################################################
function (ϱ::RTransvect)(v, pow=1::Int) function (ϱ::RTransvect{I})(v, pow::Integer=one(I)) where I
@inbounds Groups.r_multiply!(v[ϱ.i], (v[ϱ.j]^pow).symbols, reduced=false) @inbounds Groups.r_multiply!(v[ϱ.i], (v[ϱ.j]^pow).symbols, reduced=false)
return v return v
end end
function (λ::LTransvect)(v, pow=1::Int) function (λ::LTransvect{I})(v, pow::Integer=one(I)) where I
@inbounds Groups.l_multiply!(v[λ.i], (v[λ.j]^pow).symbols, reduced=false) @inbounds Groups.l_multiply!(v[λ.i], (v[λ.j]^pow).symbols, reduced=false)
return v return v
end end
function (σ::PermAut)(v, pow=1::Int) function (σ::PermAut{I})(v, pow::Integer=one(I)) where I
w = deepcopy(v) w = deepcopy(v)
s = (σ.perm^pow).d s = (σ.perm^pow).d
@inbounds for k in eachindex(v) @inbounds for k in eachindex(v)
@ -82,14 +82,14 @@ function (σ::PermAut)(v, pow=1::Int)
return v return v
end end
function (ɛ::FlipAut)(v, pow=1::Int) function (ɛ::FlipAut{I})(v, pow::Integer=one(I)) where I
@inbounds if isodd(pow) @inbounds if isodd(pow)
v[ɛ.i].symbols = inv(v[ɛ.i]).symbols v[ɛ.i].symbols = inv(v[ɛ.i]).symbols
end end
return v return v
end end
(::Identity)(v, pow=1::Int) = v (::Identity)(v, pow::Integer=zero(Int8)) = v
# taken from ValidatedNumerics, under under the MIT "Expat" License: # taken from ValidatedNumerics, under under the MIT "Expat" License:
# https://github.com/JuliaIntervals/ValidatedNumerics.jl/blob/master/LICENSE.md # https://github.com/JuliaIntervals/ValidatedNumerics.jl/blob/master/LICENSE.md
@ -102,38 +102,39 @@ function id_autsymbol()
return AutSymbol("(id)", 0, Identity()) return AutSymbol("(id)", 0, Identity())
end end
function rmul_autsymbol(i, j; pow::Int=1) function rmul_autsymbol(i::I, j::I; pow::Integer=one(I)) where I<:Integer
str = "ϱ"*subscriptify(i)*subscriptify(j) str = "ϱ"*subscriptify(i)*subscriptify(j)
return AutSymbol(str, pow, RTransvect(i, j)) return AutSymbol(str, I(pow), RTransvect(i, j))
end end
function lmul_autsymbol(i, j; pow::Int=1) function lmul_autsymbol(i::I, j::I; pow::Integer=one(I)) where I<:Integer
str = "λ"*subscriptify(i)*subscriptify(j) str = "λ"*subscriptify(i)*subscriptify(j)
return AutSymbol(str, pow, LTransvect(i, j)) return AutSymbol(str, I(pow), LTransvect(i, j))
end end
function flip_autsymbol(i; pow::Int=1) function flip_autsymbol(i::I; pow::Integer=one(I)) where I<:Integer
pow = (2+pow%2)%2 pow = I((2+pow%2)%2)
if pow == 0 if pow == zero(I)
return id_autsymbol() return id_autsymbol()
else else
str = "ɛ"*subscriptify(i) str = "ɛ"*subscriptify(i)
return AutSymbol(str, pow, FlipAut(i)) return AutSymbol(str, I(pow), FlipAut(i))
end end
end end
function perm_autsymbol(p::Generic.perm{Int8}; pow::Int=1) function perm_autsymbol(p::Generic.perm{I}; pow::Integer=one(I)) where I<:Integer
p = p^pow p = p^pow
if p == parent(p)() for i in eachindex(p.d)
return id_autsymbol() if p.d[i] != i
else
str = "σ"*join([subscriptify(i) for i in p.d]) str = "σ"*join([subscriptify(i) for i in p.d])
return AutSymbol(str, 1, PermAut(p)) return AutSymbol(str, one(I), PermAut(p))
end end
end end
return id_autsymbol()
end
function perm_autsymbol(a::Vector{T}) where T<:Integer function perm_autsymbol(a::Vector{T}) where T<:Integer
G = PermutationGroup(Int8(length(a))) G = PermutationGroup(T(length(a)))
return perm_autsymbol(G(Vector{Int8}(a))) return perm_autsymbol(G(Vector{Int8}(a)))
end end
@ -146,11 +147,13 @@ domain(G::AutGroup)= NTuple{length(G.objectGroup.gens), FreeGroupElem}(gens(G.ob
############################################################################### ###############################################################################
function AutGroup(G::FreeGroup; special=false) function AutGroup(G::FreeGroup; special=false)
n = length(gens(G))
n == 0 && return AutGroup{n}(G, AutSymbol[])
S = AutSymbol[] S = AutSymbol[]
n = length(gens(G))
n == 0 && return AutGroup{n}(G, S)
indexing = [[i,j] for i in 1:n for j in 1:n if i≠j] n = convert(Int8, n)
indexing = [[i,j] for i in Int8(1):n for j in Int8(1):n if i≠j]
rmuls = [rmul_autsymbol(i,j) for (i,j) in indexing] rmuls = [rmul_autsymbol(i,j) for (i,j) in indexing]
lmuls = [lmul_autsymbol(i,j) for (i,j) in indexing] lmuls = [lmul_autsymbol(i,j) for (i,j) in indexing]
@ -159,12 +162,12 @@ function AutGroup(G::FreeGroup; special=false)
if !special if !special
flips = [flip_autsymbol(i) for i in 1:n] flips = [flip_autsymbol(i) for i in 1:n]
syms = [perm_autsymbol(p) for p in elements(PermutationGroup(Int8(n)))][2:end] syms = [perm_autsymbol(p) for p in elements(PermutationGroup(n))][2:end]
append!(S, [flips; syms]) append!(S, [flips; syms])
end end
return AutGroup{n}(G, S) return AutGroup{Int64(n)}(G, S)
end end
############################################################################### ###############################################################################
@ -266,8 +269,8 @@ end
# #
############################################################################### ###############################################################################
function change_pow(s::AutSymbol, n::Int) function change_pow(s::AutSymbol, n::Integer)
if n == 0 if n == zero(n)
return id_autsymbol() return id_autsymbol()
end end
symbol = s.typ symbol = s.typ