kalmar/PropertyT.jl
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Actually report Kazhdan constant, not the spectral gap

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kalmar 2017-03-16 14:33:41 +01:00
parent d832050c63
commit b1e00bfda5
1 changed files with 7 additions and 6 deletions
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src/PropertyT.jl
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@ -124,8 +124,8 @@ function check_property_T(name::String, ID, generate_B₄::Function;
error(logger, err) error(logger, err)
end end
end end
S = countnz(Δ.coefficients) - 1
info(logger, "|S| = $(countnz(Δ.coefficients) - 1)") info(logger, "|S| = $S")
info(logger, "length(Δ) = $(length(Δ))") info(logger, "length(Δ) = $(length(Δ))")
info(logger, "size(Δ.product_matrix) = $(size(Δ.product_matrix))") info(logger, "size(Δ.product_matrix) = $(size(Δ.product_matrix))")
@ -146,12 +146,13 @@ function check_property_T(name::String, ID, generate_B₄::Function;
info(logger, "minimum(A) = $(minimum(A))") info(logger, "minimum(A) = $(minimum(A))")
if κ > 0 if κ > 0
true_kappa = check_distance_to_positive_cone(Δ, κ, A, tol=tol, rational=false) spectral_gap = check_distance_to_positive_cone(Δ, κ, A, tol=tol, rational=false)
true_kappa = Float64(trunc(true_kappa,12)) Kazhdan_κ = sqrt(2*spectral_gap/S)
Kazhdan_κ = Float64(trunc(Kazhdan_κ,12))
if true_kappa > 0 if true_kappa > 0
info(logger, "κ($name, S) ≥ $true_kappa: Group HAS property (T)!") info(logger, "κ($name, S) ≥ $Kazhdan_κ: Group HAS property (T)!")
else else
info(logger, "κ($name, S) ≥ $true_kappa: Group may NOT HAVE property (T)!") info(logger, "κ($name, S) ≥ $Kazhdan_κ: Group may NOT HAVE property (T)!")
end end
else else
info(logger, "κ($name, S) ≥ $κ < 0: Tells us nothing about property (T)") info(logger, "κ($name, S) ≥ $κ < 0: Tells us nothing about property (T)")