109 lines
3.1 KiB
Julia
109 lines
3.1 KiB
Julia
using ArgParse
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using Nemo
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import SCS.SCSSolver
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using PropertyT
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using Groups
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Nemo.setpermstyle(:cycles)
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#=
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Note that the element
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α(i,j,k) = ϱ(i,j)*ϱ(i,k)*inv(ϱ(i,j))*inv(ϱ(i,k)),
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which surely belongs to ball of radius 4 in Aut(F₄) becomes trivial under the representation
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Aut(F₄) → GL₄(ℤ)⋉ℤ⁴ → GL₅(ℂ).
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Moreover, due to work of Potapchik and Rapinchuk [1] every real representation of Aut(Fₙ) into GLₘ(ℂ) (for m ≤ 2n-2) factors through GLₙ(ℤ)⋉ℤⁿ, so will have the same problem.
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We need a different approach: Here we actually compute in Aut(𝔽₄)
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=#
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function cpuinfo_physicalcores()
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maxcore = -1
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for line in eachline("/proc/cpuinfo")
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if startswith(line, "core id")
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maxcore = max(maxcore, parse(Int, split(line, ':')[2]))
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end
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end
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maxcore < 0 && error("failure to read core ids from /proc/cpuinfo")
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return maxcore + 1
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end
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function parse_commandline()
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s = ArgParseSettings()
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@add_arg_table s begin
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"--tol"
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help = "set numerical tolerance for the SDP solver (default: 1e-5)"
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arg_type = Float64
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default = 1e-5
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"--iterations"
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help = "set maximal number of iterations for the SDP solver (default: 20000)"
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arg_type = Int
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default = 20000
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"--upper-bound"
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help = "Set an upper bound for the spectral gap (default: Inf)"
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arg_type = Float64
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default = Inf
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"--cpus"
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help = "Set number of cpus used by solver (default: auto)"
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arg_type = Int
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required = false
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"-N"
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help = "Consider automorphisms of free group on N generators (default: N=3)"
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arg_type = Int
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default = 2
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end
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return parse_args(s)
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end
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# const name = "SYM$N"
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# const upper_bound=factorial(N)-TOL^(1/5)
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# S() = generating_set_of_Sym(N)
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# name = "AutF$N"
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# S() = generating_set_of_AutF(N)
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function main()
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parsed_args = parse_commandline()
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if parsed_args["cpus"] ≠ nothing
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if parsed_args["cpus"] > cpuinfo_physicalcores()
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warn("Number of specified cores exceeds the physical core cound. Performance will suffer.")
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end
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Blas.set_num_threads(parsed_args["cpus"])
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end
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tol = parsed_args["tol"]
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iterations = parsed_args["iterations"]
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# solver = SCSSolver(eps=tol, max_iters=iterations, verbose=true, linearsolver=SCS.Indirect)
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solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct)
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N = parsed_args["N"]
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upper_bound = parsed_args["upper-bound"]
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radius=2
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name = "SOutF$N"
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name = "$(name)_$(upper_bound)_r=$radius"
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logger = PropertyT.setup_logging(name)
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info(logger, "Group: $name")
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info(logger, "Iterations: $iterations")
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info(logger, "Precision: $tol")
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info(logger, "Upper bound: $upper_bound")
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AutFN = AutGroup(FreeGroup(N), special=true, outer=true)
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S = gens(AutFN);
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S = unique([S; [inv(s) for s in S]])
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Id = AutFN()
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@time PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, 2)
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return 0
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end
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main()
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