remove old AutF4.jl

AutF4.jl

@@ -1,120 +0,0 @@
-using Combinatorics
-
-using JuMP
-import SCS: SCSSolver
-import Mosek: MosekSolver
-
-push!(LOAD_PATH, "./")
-using SemiDirectProduct
-using GroupAlgebras
-include("property(T).jl")
-
-const N = 4
-
-const VERBOSE = true
-
-function permutation_matrix(p::Vector{Int})
-    n = length(p)
-    sort(p) == collect(1:n) || throw(ArgumentError("Input array must be a permutation of 1:n"))
-    A = eye(n)
-    return A[p,:]
-end
-
-SymmetricGroup(n) = [nthperm(collect(1:n), k) for k in 1:factorial(n)]
-
-# const SymmetricGroup = [permutation_matrix(x) for x in SymmetricGroup_perms]
-
-function E(i, j; dim::Int=N)
-    @assert i≠j
-    k = eye(dim)
-    k[i,j] = 1
-    return k
-end
-
-function eltary_basis_vector(i; dim::Int=N)
-    result = zeros(dim)
-    if 0 < i ≤ dim
-        result[i] = 1
-    end
-    return result
-end
-
-v(i; dim=N) = eltary_basis_vector(i,dim=dim)
-
-ϱ(i,j::Int,n=N) = SemiDirectProductElement(E(i,j,dim=n), v(j,dim=n))
-λ(i,j::Int,n=N) = SemiDirectProductElement(E(i,j,dim=n), -v(j,dim=n))
-
-function ɛ(i, n::Int=N)
-    result = eye(n)
-    result[i,i] = -1
-    return SemiDirectProductElement(result)
-end
-
-σ(permutation::Vector{Int}) =
-     SemiDirectProductElement(permutation_matrix(permutation))
-
-# Standard generating set: 103 elements
-
-function generatingset_ofAutF(n::Int=N)
-    indexing = [[i,j] for i in 1:n for j in 1:n if i≠j]
-    ϱs = [ϱ(ij...) for ij in indexing]
-    λs = [λ(ij...) for ij in indexing]
-    ɛs = [ɛ(i) for i in 1:N]
-    σs = [σ(perm) for perm in SymmetricGroup(n)]
-    S = vcat(ϱs, λs, ɛs, σs);
-    S = unique(vcat(S, [inv(x) for x in S]));
-    return S
-end
-
-#=
-Note that the element
-    α(i,j,k) = ϱ(i,j)*ϱ(i,k)*inv(ϱ(i,j))*inv(ϱ(i,k)),
-which surely belongs to ball of radius 4 in Aut(F₄) becomes trivial under the representation
-    Aut(F₄) → GL₄(ℤ)⋉ℤ⁴ → GL₅(ℂ).
-Moreover, due to work of Potapchik and Rapinchuk [1] every real representation of Aut(Fₙ) into GLₘ(ℂ) (for m ≤ 2n-2) factors through GLₙ(ℤ)⋉ℤⁿ, so will have the same problem.
-
-We need a different approach!
-=#
-
-const ID = eye(N+1)
-
-const S₁ = generatingset_ofAutF(N)
-
-matrix_S₁ = [matrix_repr(x) for x in S₁]
-
-const TOL=10.0^-7
-
-matrix_S₁[1:10,:][:,1]
-
-Δ, cm = prepare_Laplacian_and_constraints(matrix_S₁)
-
-#solver = SCSSolver(eps=TOL, max_iters=ITERATIONS, verbose=true);
-solver = MosekSolver(MSK_DPAR_INTPNT_CO_TOL_REL_GAP=TOL,
-#                      MSK_DPAR_INTPNT_CO_TOL_PFEAS=1e-15,
-#                      MSK_DPAR_INTPNT_CO_TOL_DFEAS=1e-15,
-#                      MSK_IPAR_PRESOLVE_USE=0,
-                  QUIET=!VERBOSE)
-
-# κ, A = solve_for_property_T(S₁, solver, verbose=VERBOSE)
-
-product_matrix = readdlm("SL₃Z.product_matrix", Int)
-L = readdlm("SL₃Z.Δ.coefficients")[:, 1]
-Δ = GroupAlgebraElement(L, product_matrix)
-
-A = readdlm("matrix.A.Mosek")
-κ = readdlm("kappa.Mosek")[1]
-
-# @show eigvals(A)
-@assert isapprox(eigvals(A), abs(eigvals(A)), atol=TOL)
-@assert A == Symmetric(A)
-
-
-const A_sqrt = real(sqrtm(A))
-
-SOS_EOI_fp_L₁, Ω_fp_dist = check_solution(κ, A_sqrt, Δ)
-
-κ_rational = rationalize(BigInt, κ;)
-A_sqrt_rational = rationalize(BigInt, A_sqrt)
-Δ_rational = rationalize(BigInt, Δ)
-
-SOS_EOI_rat_L₁, Ω_rat_dist = check_solution(κ_rational, A_sqrt_rational, Δ_rational)