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PropertyT.jl/SL(3,Z).jl

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using JuMP
import SCS: SCSSolver
import Mosek: MosekSolver
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workers_processes = addprocs()
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@everywhere push!(LOAD_PATH, "./")
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using GroupAlgebras
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@everywhere include("property(T).jl")
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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
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# 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)
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# κ, A = solve_for_property_T(S₁, solver, verbose=VERBOSE)
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const product_matrix = readdlm("SL3Z.product_matrix", Int)
const L = readdlm("SL3Z.delta.coefficients")[:, 1]
const Δ = GroupAlgebraElement(L, product_matrix)
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const A = readdlm("SL3Z.SDPmatrixA.Mosek")
const κ = readdlm("SL3Z.kappa.Mosek")[1]
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@assert isapprox(eigvals(A), abs(eigvals(A)), atol=TOL)
@assert A == Symmetric(A)
const A_sqrt = real(sqrtm(A))
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const SOS_fp_diff, SOS_fp_L₁_distance = check_solution(κ, A_sqrt, Δ)
@show SOS_fp_L₁_distance
@show GroupAlgebras.ɛ(SOS_fp_diff)
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const κ_rational = rationalize(BigInt, κ, tol=TOL)
const A_sqrt_rational = rationalize(BigInt, A_sqrt, tol=TOL)
const Δ_rational = rationalize(BigInt, Δ, tol=TOL)
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const 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))
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const A_sqrt_augmented = correct_to_augmentation_ideal(A_sqrt_rational)
const SOS_rational_aug_diff, SOS_aug_rat_L₁_distance = check_solution(κ_rational, A_sqrt_augmented, Δ_rational)
@assert isa(SOS_aug_rat_L₁_distance, Rational{BigInt})
@assert GroupAlgebras.ɛ(SOS_rational_aug_diff) == 0//1
@show float(SOS_aug_rat_L₁_distance)
@show float(κ_rational - 2^3*SOS_aug_rat_L₁_distance)
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rmprocs(workers_processes)