update PropertyT.jl top changes in CheckSolution.jl

src/PropertyT.jl

@@ -152,29 +152,7 @@ function λandP(name::String, SDP::JuMP.Model, varλ, varP, warmstart=true)
     return λ, P
 end
 
-Kazhdan_from_sgap(λ,N) = sqrt(2*λ/N)
-
-function check_λ(name, S, λ, P, radius, logger)
-
-    RG = GroupRing(parent(first(S)), load(filename(name, :pm), "pm"))
-    Δ = GroupRingElem(load(filename(name, :Δ), "Δ")[:, 1], RG)
-
-    @logtime logger Q = real(sqrtm(Symmetric(P)))
-
-    sgap = check_distance_to_cone(Δ, λ, Q, 2*radius, logger)
-
-    if sgap > 0
-        info(logger, "λ($name, S) ≥ $(Float64(trunc(sgap,12)))")
-        Kazhdan_κ = Kazhdan_from_sgap(sgap, length(S))
-        Kazhdan_κ = Float64(trunc(Kazhdan_κ, 12))
-        info(logger, "κ($name, S) ≥ $Kazhdan_κ: Group HAS property (T)!")
-        return true
-    else
-        sgap = Float64(trunc(sgap, 12))
-        info(logger, "λ($name, S) ≥ $sgap: Group may NOT HAVE property (T)!")
-        return false
-    end
-end
+Kazhdan(λ::Number,N::Integer) = sqrt(2*λ/N)
 
 function check_property_T(name::String, S, Id, solver, upper_bound, tol, radius, warm::Bool=false)
 
@@ -219,7 +197,17 @@ function check_property_T(name::String, S, Id, solver, upper_bound, tol, radius,
         warn("The solution matrix doesn't seem to be positive definite!")
 
     if λ > 0
-        return check_λ(name, S, λ, P, radius, LOGGER)
+
+        RG = GroupRing(parent(first(S)), load(filename(name, :pm), "pm"))
+        Δ = RG(load(filename(name, :Δ), "Δ")[:, 1])
+        @logtime logger Q = real(sqrtm(Symmetric(P)))
+
+        sgap = distance_to_cone(Δ, λ, Q, wlen=2*radius, logger=LOGGER)
+        Kazhdan_κ = Kazhdan(sgap, length(S))
+        if Kazhdan_κ > 0
+            info(logger, "κ($name, S) ≥ $Kazhdan_κ: Group HAS property (T)!")
+            return true
+        end
     end
     info(LOGGER, "κ($name, S) ≥ $λ < 0: Tells us nothing about property (T)")
     return false