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remove unnecessary function arguments annotations
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c1bd866dd4
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21
AutF4.jl
21
AutF4.jl
@ -13,7 +13,6 @@ const N = 4
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const VERBOSE = true
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const VERBOSE = true
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function permutation_matrix(p::Vector{Int})
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function permutation_matrix(p::Vector{Int})
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n = length(p)
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n = length(p)
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sort(p) == collect(1:n) || throw(ArgumentError("Input array must be a permutation of 1:n"))
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sort(p) == collect(1:n) || throw(ArgumentError("Input array must be a permutation of 1:n"))
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@ -21,18 +20,18 @@ function permutation_matrix(p::Vector{Int})
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return A[p,:]
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return A[p,:]
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end
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end
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SymmetricGroup(n::Int) = [nthperm(collect(1:n), k) for k in 1:factorial(n)]
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SymmetricGroup(n) = [nthperm(collect(1:n), k) for k in 1:factorial(n)]
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# const SymmetricGroup = [permutation_matrix(x) for x in SymmetricGroup_perms]
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# const SymmetricGroup = [permutation_matrix(x) for x in SymmetricGroup_perms]
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function E(i::Int, j::Int; dim::Int=N)
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function E(i, j; dim::Int=N)
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@assert i≠j
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@assert i≠j
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k = eye(dim)
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k = eye(dim)
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k[i,j] = 1
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k[i,j] = 1
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return k
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return k
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end
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end
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function eltary_basis_vector(i::Int; dim::Int=N)
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function eltary_basis_vector(i; dim::Int=N)
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result = zeros(dim)
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result = zeros(dim)
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if 0 < i ≤ dim
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if 0 < i ≤ dim
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result[i] = 1
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result[i] = 1
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@ -40,12 +39,12 @@ function eltary_basis_vector(i::Int; dim::Int=N)
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return result
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return result
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end
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end
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v(i::Int; dim=N) = eltary_basis_vector(i,dim=dim)
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v(i; dim=N) = eltary_basis_vector(i,dim=dim)
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ϱ(i::Int,j::Int,n=N) = SemiDirectProductElement(E(i,j,dim=n), v(j,dim=n))
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ϱ(i,j::Int,n=N) = SemiDirectProductElement(E(i,j,dim=n), v(j,dim=n))
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λ(i::Int,j::Int,n=N) = SemiDirectProductElement(E(i,j,dim=n), -v(j,dim=n))
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λ(i,j::Int,n=N) = SemiDirectProductElement(E(i,j,dim=n), -v(j,dim=n))
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function ɛ(i::Int, n::Int=N)
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function ɛ(i, n::Int=N)
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result = eye(n)
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result = eye(n)
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result[i,i] = -1
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result[i,i] = -1
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return SemiDirectProductElement(result)
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return SemiDirectProductElement(result)
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@ -54,7 +53,9 @@ end
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σ(permutation::Vector{Int}) =
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σ(permutation::Vector{Int}) =
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SemiDirectProductElement(permutation_matrix(permutation))
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SemiDirectProductElement(permutation_matrix(permutation))
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function AutF_generating_set(n::Int=N)
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# Standard generating set: 103 elements
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function generatingset_ofAutF(n::Int=N)
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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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ϱs = [ϱ(ij...) for ij in indexing]
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ϱs = [ϱ(ij...) for ij in indexing]
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λs = [λ(ij...) for ij in indexing]
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λs = [λ(ij...) for ij in indexing]
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@ -67,7 +68,7 @@ end
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const ID = eye(N+1)
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const ID = eye(N+1)
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const S₁ = AutF_generating_set(N)
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const S₁ = generatingset_ofAutF(N)
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matrix_S₁ = [matrix_repr(x) for x in S₁]
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matrix_S₁ = [matrix_repr(x) for x in S₁]
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