cosmetics

property(T).jl

@@ -131,6 +131,7 @@ function check_solution(κ, sqrt_matrix, Δ; verbose=true, augmented=false)
     eoi_SOS_L₁_dist = norm(SOS_diff,1)
 
     if verbose
+        @show κ
         if augmented
             println("ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) = ", GroupAlgebras.ɛ(SOS_diff))
         else
@@ -162,31 +163,30 @@ function ℚ_distance_to_positive_cone(Δ::GroupAlgebraElement,
 
     @show maximum(A)
     if maximum(A) < 1e-2
-        warn("Solver might not solved the problem successfully and what You're seeing is due to floating-point error, proceeding anyway...")
+        warn("Solver might not solved the problem successfully and the positive solution is due to floating-point error, proceeding anyway...")
     end
 
     @assert isapprox(eigvals(A), abs(eigvals(A)), atol=TOL)
     @assert A == Symmetric(A)
-    println("")
     A_sqrt = real(sqrtm(A))
+    println("")
+
     println("Checking in floating-point arithmetic...")
-    @show κ
     fp_distance = check_solution(κ, A_sqrt, Δ, verbose=VERBOSE)
     println("Distance to positive cone ≈ $(Float64(trunc(fp_distance,8)))")
     println("-------------------------------------------------------------")
     println("")
-    println("Checking in rational arithmetic...")
 
+    println("Checking in rational arithmetic...")
     κ_ℚ = ℚ(trunc(κ,Int(abs(log10(tol)))), TOL)
-    @show κ_ℚ
     @assert κ - κ_ℚ ≥ 0
     A_sqrt_ℚ, Δ_ℚ = ℚ(A_sqrt, TOL), ℚ(Δ, TOL)
-
     ℚ_distance = check_solution(κ_ℚ, A_sqrt_ℚ, Δ_ℚ, verbose=VERBOSE)
     @assert isa(ℚ_distance, Rational)
     println("Distance to positive cone ≈ $(Float64(trunc(ℚ_distance,8)))")
     println("-------------------------------------------------------------")
     println("")
+
     println("Projecting columns of A_sqrt to the augmentation ideal...")
     A_sqrt_ℚ_aug = correct_to_augmentation_ideal(A_sqrt_ℚ)
     ℚ_dist_to_Σ² = check_solution(κ_ℚ, A_sqrt_ℚ_aug, Δ_ℚ, verbose=VERBOSE, augmented=true)