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allow check_distance_to_positive_cone return Interval
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@ -167,6 +167,9 @@ function check_property_T(name::String, generating_set::Function,
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if κ > 0
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spectral_gap = check_distance_to_positive_cone(Δ, κ, A, tol=tol, rational=false)
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if isa(spectral_gap, Interval)
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spectral_gap = spectral_gap.lo
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end
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if spectral_gap > 0
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Kazhdan_κ = sqrt(2*spectral_gap/S)
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Kazhdan_κ = Float64(trunc(Kazhdan_κ, 12))
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@ -144,11 +144,11 @@ function check_distance_to_positive_cone(Δ::GroupAlgebraElement, κ, A;
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A_sqrt_ℚ_augⁱⁿᵗ = Float64.(A_sqrt_ℚ_aug) ± δ
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t = @timed Interval_dist_to_Σ² = distance_to_cone(κ_ℚ, A_sqrt_ℚ_augⁱⁿᵗ, Δ_ℚ)
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info(logger, timed_msg(t))
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info(logger, "The Augmentation-projected actual distance (to positive cone) ≥ $(@sprintf("%.10f", Interval_dist_to_Σ².lo))")
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info(logger, "The Augmentation-projected actual distance (to positive cone) ∈ $(Interval_dist_to_Σ²)")
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info(logger, "------------------------------------------------------------")
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if Interval_dist_to_Σ².lo ≤ 0 || !rational
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return Interval_dist_to_Σ².lo
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return Interval_dist_to_Σ²
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else
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info(logger, "Checking Projected SOS decomposition in exact rational arithmetic...")
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t = @timed ℚ_dist_to_Σ² = distance_to_cone(κ_ℚ, A_sqrt_ℚ_aug, Δ_ℚ)
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