GroupsWithPropertyT/AutFn.jl

using ArgParse

###############################################################################
#
#  Parsing command line
#
###############################################################################

function parse_commandline()
    s = ArgParseSettings()

    @add_arg_table s begin
        "--tol"
            help = "set numerical tolerance for the SDP solver"
            arg_type = Float64
            default = 1e-6
        "--iterations"
            help = "set maximal number of iterations for the SDP solver"
            arg_type = Int
            default = 50000
        "--upper-bound"
            help = "Set an upper bound for the spectral gap"
            arg_type = Float64
            default = Inf
        "--cpus"
            help = "Set number of cpus used by solver (default: auto)"
            arg_type = Int
            required = false
        "--radius"
            help = "Radius of ball B_r(e,S) to find solution over"
            arg_type = Int
            default = 2
        "--warmstart"
            help = "Use warmstart.jld as the initial guess for SCS"
            action = :store_true
        "--nosymmetry"
            help = "Don't use symmetries of the Laplacian"
            action = :store_true
        "N"
            help = "Compute for the automorphisms group of the free group on N generators"
            arg_type = Int
            required = true
    end
    return parse_args(s)
end
const PARSEDARGS = parse_commandline()

#=
Note that the element
    α(i,j,k) = ϱ(i,j)*ϱ(i,k)*inv(ϱ(i,j))*inv(ϱ(i,k)),
which surely belongs to ball of radius 4 in Aut(Fₙ) becomes trivial under the representation
    Aut(Fₙ) → GLₙ(ℤ)⋉ℤⁿ → GL_(n+1)(ℂ).
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.

We need a different approach: Here we actually compute in (S)Aut(𝔽ₙ)
=#

include("CPUselect.jl")
set_parallel_mthread(PARSEDARGS, workers=true)

include("main.jl")

G = PropertyTGroups.SpecialAutomorphismGroup(PARSEDARGS)

main(G)