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
        "-N"
            help = "Consider automorphisms of free group on N generators"
            arg_type = Int
            default = 2
        "--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
    end

    return parse_args(s)
end
const PARSEDARGS = parse_commandline()

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

#=
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)
=#

using Nemo
using SCS.SCSSolver
using PropertyT
using Groups

Nemo.setpermstyle(:cycles)

include("groups/autfreegroup.jl")

function main(GROUP, parsed_args)

    radius = parsed_args["radius"]
    tol = parsed_args["tol"]
    iterations = parsed_args["iterations"]
    upper_bound = parsed_args["upper-bound"]
    warm = parsed_args["warmstart"]

    name, N = GROUP.groupname(parsed_args)
    G, S = GROUP.generatingset(parsed_args)

    name = "$(name)_r$radius"
    isdir(name) || mkdir(name)

    logger = PropertyT.setup_logging(joinpath(name, "$(upper_bound)"))

    info(logger, "Group:       $name")
    info(logger, "Iterations:  $iterations")
    info(logger, "Precision:   $tol")
    info(logger, "Upper bound: $upper_bound")
    info(logger, G)
    info(logger, "Symmetric generating set of size $(length(S))")
    info(logger, "Threads:     $(Threads.nthreads())")
    info(logger, "Workers:     $(workers())")

    Id = G()

    solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct, alpha=1.95, acceleration_lookback=1)

    PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, radius, warm)
    return 0
end

main(SpecialAutomorphisms, PARSEDARGS)