parametrize PropertyTGroups types by N
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@ -1,21 +1,12 @@
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struct SpecialAutomorphismGroup <: SymmetrizedGroup
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struct SpecialAutomorphismGroup{N} <: SymmetrizedGroup
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args::Dict{String,Any}
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group::AutGroup
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group::AutGroup
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N::Int
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function SpecialAutomorphismGroup(args::Dict)
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function SpecialAutomorphismGroup(args::Dict)
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N = args["SAut"]
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return new{args["SAut"]}(AutGroup(FreeGroup(N), special=true))
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return new(args, AutGroup(FreeGroup(N), special=true), N)
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end
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end
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end
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end
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function name(G::SpecialAutomorphismGroup)
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name(G::SpecialAutomorphismGroup{N}) where N = "SAutF$(N)"
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if haskey(G.args, "nosymmetry") && G.args["nosymmetry"]
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return "SAutF$(G.N)"
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else
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return "oSAutF$(G.N)"
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end
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end
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group(G::SpecialAutomorphismGroup) = G.group
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group(G::SpecialAutomorphismGroup) = G.group
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@ -24,8 +15,8 @@ function generatingset(G::SpecialAutomorphismGroup)
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return unique([S; inv.(S)])
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return unique([S; inv.(S)])
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end
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end
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function autS(G::SpecialAutomorphismGroup)
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function autS(G::SpecialAutomorphismGroup{N}) where N
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return WreathProduct(PermutationGroup(2), PermutationGroup(G.N))
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return WreathProduct(PermutationGroup(2), PermutationGroup(N))
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end
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end
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###############################################################################
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###############################################################################
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@ -1,17 +1,14 @@
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struct MappingClassGroup <: GAPGroup
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struct MappingClassGroup{N} <: GAPGroup end
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args::Dict{String,Any}
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N::Int
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MappingClassGroup(args) = new(args, args["MCG"])
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MappingClassGroup(args::Dict) = MappingClassGroup{args["MCG"]}()
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end
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name(G::MappingClassGroup) = "MCG($(G.N))"
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name(G::MappingClassGroup{N}) where N = "MCG(N)"
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function group(G::MappingClassGroup)
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function group(G::MappingClassGroup{N}) where N
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if G.N < 2
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if N < 2
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throw("Genus must be at least 2!")
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throw("Genus must be at least 2!")
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elseif G.N == 2
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elseif N == 2
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MCGroup = Groups.FPGroup(["a1","a2","a3","a4","a5"]);
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MCGroup = Groups.FPGroup(["a1","a2","a3","a4","a5"]);
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S = gens(MCGroup)
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S = gens(MCGroup)
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@ -31,7 +28,7 @@ function group(G::MappingClassGroup)
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return MCGroup
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return MCGroup
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else
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else
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MCGroup = Groups.FPGroup(["a$i" for i in 0:2G.N])
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MCGroup = Groups.FPGroup(["a$i" for i in 0:2N])
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S = gens(MCGroup)
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S = gens(MCGroup)
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a0 = S[1]
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a0 = S[1]
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@ -76,7 +73,7 @@ function group(G::MappingClassGroup)
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(A[2i+3]*A[2i+2]*A[2i+4]*A[2i+3])*( n(i+1)*A[2i+2]*A[2i+1]*A[2i] )
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(A[2i+3]*A[2i+2]*A[2i+4]*A[2i+3])*( n(i+1)*A[2i+2]*A[2i+1]*A[2i] )
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end
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end
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# push!(relations, X*n(G.N)*inv(n(G.N)*X))
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# push!(relations, X*n(N)*inv(n(N)*X))
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relations = [relations; [inv(rel) for rel in relations]]
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relations = [relations; [inv(rel) for rel in relations]]
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Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
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Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
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@ -1,60 +1,44 @@
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struct SpecialLinearGroup <: SymmetrizedGroup
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struct SpecialLinearGroup{N} <: SymmetrizedGroup
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args::Dict{String,Any}
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group::AbstractAlgebra.Group
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group::AbstractAlgebra.Group
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N::Int
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p::Int
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X::Bool
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function SpecialLinearGroup(args::Dict)
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function SpecialLinearGroup(args::Dict)
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n = args["SL"]
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N = args["SL"]
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p = args["p"]
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p = args["p"]
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X = args["X"]
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X = args["X"]
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if p == 0
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if p == 0
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G = MatrixSpace(Nemo.ZZ, n, n)
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G = MatrixSpace(Nemo.ZZ, N, N)
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else
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else
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R = Nemo.NmodRing(UInt(p))
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R = Nemo.NmodRing(UInt(p))
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G = MatrixSpace(R, n, n)
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G = MatrixSpace(R, N, N)
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end
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end
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return new(args, G, n)
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return new{N}(G, p, X)
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end
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end
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end
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end
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function name(G::SpecialLinearGroup)
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function name(G::SpecialLinearGroup{N}) where N
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p = G.args["p"]
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if G.p == 0
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X = G.args["X"]
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R = (G.X ? "Z[x]" : "Z")
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if p == 0
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R = (X ? "Z[x]" : "Z")
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else
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else
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R = "F$p"
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R = "F$(G.p)"
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end
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if haskey(G.args, "nosymmetry") && G.args["nosymmetry"]
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return "SL($(G.N),$R)"
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else
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return "oSL($(G.N),$R)"
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end
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end
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return SL($(G.N),$R)
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end
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end
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group(G::SpecialLinearGroup) = G.group
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group(G::SpecialLinearGroup) = G.group
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function E(i::Int, j::Int, M::MatSpace, val=one(M.base_ring))
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function generatingset(G::SpecialLinearGroup{N}) where N
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@assert i≠j
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G.p > 0 && G.X && throw("SL(n, F_p[x]) not implemented")
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m = one(M)
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m[i,j] = val
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return m
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end
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function generatingset(G::SpecialLinearGroup)
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p = G.args["p"]
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X = G.args["X"]
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p > 0 && X && throw("SL(n, F_p[x]) not implemented")
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SL = group(G)
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SL = group(G)
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r = G.args["radius"]
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return generatingset(SL, G.X)
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return generatingset(SL, r, X)
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end
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end
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# r is the injectivity radius of
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# SL(n, Z[X]) -> SL(n, Z) induced by X -> 100
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function generatingset(SL::MatSpace, radius::Integer, X::Bool=false)
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function generatingset(SL::MatSpace, X::Bool=false, r=5)
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n = SL.cols
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n = SL.cols
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indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
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indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
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@ -66,8 +50,15 @@ function generatingset(SL::MatSpace, radius::Integer, X::Bool=false)
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return unique([S; inv.(S)])
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return unique([S; inv.(S)])
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end
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end
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function autS(G::SpecialLinearGroup)
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function E(i::Int, j::Int, M::MatSpace, val=one(M.base_ring))
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return WreathProduct(PermutationGroup(2), PermutationGroup(G.N))
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@assert i≠j
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m = one(M)
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m[i,j] = val
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return m
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end
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function autS(G::SpecialLinearGroup{N}) where N
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return WreathProduct(PermutationGroup(2), PermutationGroup(N))
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end
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end
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###############################################################################
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###############################################################################
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