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update Orbit-wise to changes in CheckSolution.jl
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@ -249,8 +249,17 @@ function check_property_T(sett::Settings)
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warn("The solution matrix doesn't seem to be positive definite!")
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if λ > 0
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return check_λ(sett.name, sett.S, λ, P, sett.radius, sett.logger)
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RG = GroupRing(parent(first(sett.S)), load(filename(sett.name, :pm), "pm"))
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Δ = RG(load(filename(name, :Δ), "Δ")[:, 1])
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@logtime logger Q = real(sqrtm(Symmetric(P)))
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sgap = distance_to_cone(Δ, λ, Q, wlen=2*sett.radius, logger=sett.logger)
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Kazhdan_κ = Kazhdan(sgap, length(S))
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if Kazhdan_κ > 0
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info(logger, "κ($name, S) ≥ $Kazhdan_κ: Group HAS property (T)!")
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return true
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end
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info(sett.logger, "κ($(sett.name), S) ≥ $λ < 0: Tells us nothing about property (T)")
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end
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info(LOGGER, "κ($name, S) ≥ $λ < 0: Tells us nothing about property (T)")
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return false
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end
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