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mirror of https://github.com/kalmarek/Groups.jl.git synced 2024-12-24 18:05:27 +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
i::Int
j::Int
struct RTransvect{I<:Integer}
i::I
j::I
end
struct LTransvect
i::Int
j::Int
struct LTransvect{I<:Integer}
i::I
j::I
end
struct FlipAut
i::Int
struct FlipAut{I<:Integer}
i::I
end
struct PermAut
perm::Nemo.Generic.perm{Int8}
struct PermAut{I<:Integer}
perm::Nemo.Generic.perm{I}
end
struct Identity end
struct AutSymbol <: GSymbol
str::String
pow::Int
pow::Int8
typ::Union{LTransvect, RTransvect, PermAut, FlipAut, Identity}
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)
return v
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)
return v
end
function (σ::PermAut)(v, pow=1::Int)
function (σ::PermAut{I})(v, pow::Integer=one(I)) where I
w = deepcopy(v)
s = (σ.perm^pow).d
@inbounds for k in eachindex(v)
@ -82,14 +82,14 @@ function (σ::PermAut)(v, pow=1::Int)
return v
end
function (ɛ::FlipAut)(v, pow=1::Int)
function (ɛ::FlipAut{I})(v, pow::Integer=one(I)) where I
@inbounds if isodd(pow)
v[ɛ.i].symbols = inv(v[ɛ.i]).symbols
end
return v
end
(::Identity)(v, pow=1::Int) = v
(::Identity)(v, pow::Integer=zero(Int8)) = v
# taken from ValidatedNumerics, under under the MIT "Expat" License:
# https://github.com/JuliaIntervals/ValidatedNumerics.jl/blob/master/LICENSE.md
@ -102,38 +102,39 @@ function id_autsymbol()
return AutSymbol("(id)", 0, Identity())
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)
return AutSymbol(str, pow, RTransvect(i, j))
return AutSymbol(str, I(pow), RTransvect(i, j))
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)
return AutSymbol(str, pow, LTransvect(i, j))
return AutSymbol(str, I(pow), LTransvect(i, j))
end
function flip_autsymbol(i; pow::Int=1)
pow = (2+pow%2)%2
if pow == 0
function flip_autsymbol(i::I; pow::Integer=one(I)) where I<:Integer
pow = I((2+pow%2)%2)
if pow == zero(I)
return id_autsymbol()
else
str = "ɛ"*subscriptify(i)
return AutSymbol(str, pow, FlipAut(i))
return AutSymbol(str, I(pow), FlipAut(i))
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
if p == parent(p)()
return id_autsymbol()
else
for i in eachindex(p.d)
if p.d[i] != i
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
return id_autsymbol()
end
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)))
end
@ -146,11 +147,13 @@ domain(G::AutGroup)= NTuple{length(G.objectGroup.gens), FreeGroupElem}(gens(G.ob
###############################################################################
function AutGroup(G::FreeGroup; special=false)
n = length(gens(G))
n == 0 && return AutGroup{n}(G, 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]
lmuls = [lmul_autsymbol(i,j) for (i,j) in indexing]
@ -159,12 +162,12 @@ function AutGroup(G::FreeGroup; special=false)
if !special
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])
end
return AutGroup{n}(G, S)
return AutGroup{Int64(n)}(G, S)
end
###############################################################################
@ -266,8 +269,8 @@ end
#
###############################################################################
function change_pow(s::AutSymbol, n::Int)
if n == 0
function change_pow(s::AutSymbol, n::Integer)
if n == zero(n)
return id_autsymbol()
end
symbol = s.typ