diff --git a/SL(3,Z).jl b/SL(3,Z).jl
index 8489f04..548b7b9 100644
--- a/SL(3,Z).jl
+++ b/SL(3,Z).jl
@@ -55,10 +55,17 @@ A = readdlm("matrix.A.Mosek")
 
 const A_sqrt = real(sqrtm(A))
 
-SOS_EOI_fp_L₁, Ω_fp_dist = check_solution(κ, A_sqrt, Δ)
+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_EOI_rat_L₁, Ω_rat_dist = check_solution(κ_rational, A_sqrt_rational, Δ_rational)
+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))
diff --git a/property(T).jl b/property(T).jl
index 28ce397..c309458 100644
--- a/property(T).jl
+++ b/property(T).jl
@@ -160,7 +160,8 @@ function check_solution{T<:Number}(κ::T,
                                    Δ::GroupAlgebraElement{T})
     eoi = EOI(Δ, κ)
     result = resulting_SOS(sqrt_matrix, Δ)
-    return sum(abs.((result - eoi).coefficients)), sum(result.coefficients)
+    L₁_dist = norm(result - eoi,1)
+    return eoi - result, L₁_dist
 end
 
 function rationalize{T<:Integer, S<:Real}(::Type{T},
@@ -168,4 +169,4 @@ function rationalize{T<:Integer, S<:Real}(::Type{T},
 
     r(x) = rationalize(T, x, tol=tol)
     return r.(X)
-end
+end;