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

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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
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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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product_matrix = readdlm("SL3Z.product_matrix", Int)
L = readdlm("SL3Z.delta.coefficients")[:, 1]
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Δ = GroupAlgebraElement(L, product_matrix)
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A = readdlm("SL3Z.SDPmatrixA.Mosek")
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))
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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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))
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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)