using JuMP import SCS: SCSSolver import Mosek: MosekSolver push!(LOAD_PATH, "./") using GroupAlgebras include("property(T).jl") function E(i::Int, j::Int, N::Int=3) @assert i≠j k = eye(N) k[i,j] = 1 return k end function SL_3ZZ_generating_set() S = [E(1,2), E(1,3), E(2,3)]; S = vcat(S, [x' for x in S]); S = vcat(S, [inv(x) for x in S]); return S end const ID = eye(3) const S₁ = SL_3ZZ_generating_set() const TOL=10.0^-7 # const VERBOSE=true #solver = SCSSolver(eps=TOL, max_iters=ITERATIONS, verbose=VERBOSE); # 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.delta.coefficients")[:, 1] Δ = GroupAlgebraElement(L, product_matrix) A = readdlm("SL3Z.SDPmatrixA.Mosek") κ = readdlm("SL3Z.kappa.Mosek")[1] @assert isapprox(eigvals(A), abs(eigvals(A)), atol=TOL) @assert A == Symmetric(A) const A_sqrt = real(sqrtm(A)) SOS_fp_diff, SOS_fp_L₁_distance = check_solution(κ, A_sqrt, Δ) @show SOS_fp_L₁_distance @show GroupAlgebras.ɛ(SOS_fp_diff) κ_rational = rationalize(BigInt, κ;) A_sqrt_rational = rationalize(BigInt, A_sqrt) Δ_rational = rationalize(BigInt, Δ) SOS_rational_diff, SOS_rat_L₁_distance = check_solution(κ_rational, A_sqrt_rational, Δ_rational) @assert isa(SOS_rat_L₁_distance, Rational{BigInt}) @show float(SOS_rat_L₁_distance) @show float(GroupAlgebras.ɛ(SOS_rational_diff)) A_sqrt_augmented = correct_to_augmentation_ideal(A_sqrt_rational) SOS_rational_diff_aug, SOS_rat_L₁_distance_aug = check_solution(κ_rational, A_sqrt_augmented, Δ_rational)