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Actually report Kazhdan constant, not the spectral gap
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@ -124,8 +124,8 @@ function check_property_T(name::String, ID, generate_B₄::Function;
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error(logger, err)
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end
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end
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info(logger, "|S| = $(countnz(Δ.coefficients) - 1)")
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S = countnz(Δ.coefficients) - 1
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info(logger, "|S| = $S")
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info(logger, "length(Δ) = $(length(Δ))")
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info(logger, "size(Δ.product_matrix) = $(size(Δ.product_matrix))")
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@ -146,12 +146,13 @@ function check_property_T(name::String, ID, generate_B₄::Function;
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info(logger, "minimum(A) = $(minimum(A))")
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if κ > 0
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true_kappa = check_distance_to_positive_cone(Δ, κ, A, tol=tol, rational=false)
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true_kappa = Float64(trunc(true_kappa,12))
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spectral_gap = check_distance_to_positive_cone(Δ, κ, A, tol=tol, rational=false)
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Kazhdan_κ = sqrt(2*spectral_gap/S)
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Kazhdan_κ = Float64(trunc(Kazhdan_κ,12))
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if true_kappa > 0
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info(logger, "κ($name, S) ≥ $true_kappa: Group HAS property (T)!")
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info(logger, "κ($name, S) ≥ $Kazhdan_κ: Group HAS property (T)!")
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else
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info(logger, "κ($name, S) ≥ $true_kappa: Group may NOT HAVE property (T)!")
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info(logger, "κ($name, S) ≥ $Kazhdan_κ: Group may NOT HAVE property (T)!")
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end
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else
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info(logger, "κ($name, S) ≥ $κ < 0: Tells us nothing about property (T)")
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