standardise usage of GROUP modules
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AutFN.jl
80
AutFN.jl
@ -1,37 +1,5 @@
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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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###############################################################################
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#
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# Generating set
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#
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###############################################################################
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function SOutFN_generating_set(N::Int)
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SOutFN = AutGroup(FreeGroup(N), special=true, outer=true)
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S = gens(SOutFN);
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S = [S; [inv(s) for s in S]]
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return SOutFN, unique(S)
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end
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###############################################################################
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#
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# Parsing command line
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@ -73,37 +41,61 @@ function parse_commandline()
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return parse_args(s)
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end
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const PARSEDARGS = parse_commandline()
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function main()
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include("CPUselect.jl")
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set_parallel_mthread(PARSEDARGS, workers=true)
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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(Fₙ) becomes trivial under the representation
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Aut(Fₙ) → GLₙ(ℤ)⋉ℤⁿ → GL_(n+1)(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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N = parsed_args["N"]
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radius = 2
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We need a different approach: Here we actually compute in (S)Aut(𝔽ₙ)
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=#
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using Nemo
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using 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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include("groups/autfreegroup.jl")
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function main(GROUP, parsed_args)
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radius = parsed_args["radius"]
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tol = parsed_args["tol"]
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iterations = parsed_args["iterations"]
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upper_bound = parsed_args["upper-bound"]
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warm = parsed_args["warmstart"]
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dirname = "SOutF$(N)_$(upper_bound)_r=$radius"
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name, N = GROUP.groupname(parsed_args)
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G, S = GROUP.generatingset(parsed_args)
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logger = PropertyT.setup_logging(dirname)
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name = "$(name)_r$radius"
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isdir(name) || mkdir(name)
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info(logger, "Group: $dirname")
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logger = PropertyT.setup_logging(joinpath(name, "$(upper_bound)"))
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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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G, S = SOutFN_generating_set(N)
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info(logger, G)
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info(logger, "Symmetric generating set of size $(length(S))")
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info(logger, S)
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info(logger, "Threads: $(Threads.nthreads())")
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info(logger, "Workers: $(workers())")
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Id = G()
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solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct)
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solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct, alpha=1.95, acceleration_lookback=1)
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@time PropertyT.check_property_T(dirname, S, Id, solver, upper_bound, tol, 2)
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PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, radius, warm)
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return 0
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end
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main()
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main(SpecialAutomorphisms, PARSEDARGS)
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@ -48,7 +48,8 @@ include("CPUselect.jl")
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set_parallel_mthread(parsed_args, workers=true)
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include("SAutFNs.jl")
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include("groups/autfreegroup.jl")
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include("Orbit.jl")
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main(SAutFNs, parsed_args)
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main(SpecialAutomorphisms, parsed_args)
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10
SL.jl
10
SL.jl
@ -53,12 +53,12 @@ const PARSEDARGS = parse_commandline()
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include("CPUselect.jl")
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set_parallel_mthread(PARSEDARGS, workers=true)
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using SCS.SCSSolver
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using Nemo
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using SCS.SCSSolver
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using PropertyT
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using Groups
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include("SLNs.jl")
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include("groups/speciallinear.jl")
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function main(GROUP, parsed_args)
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@ -87,10 +87,10 @@ function main(GROUP, parsed_args)
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Id = one(G)
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solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct, alpha=1.9, acceleration_lookback=1)
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solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct, alpha=1.95, acceleration_lookback=1)
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PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, radius)
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PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, radius, warm)
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return 0
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end
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main(SLNs, PARSEDARGS)
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main(SpecialLinear, PARSEDARGS)
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@ -55,7 +55,7 @@ include("CPUselect.jl")
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set_parallel_mthread(PARSEDARGS, workers=true)
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include("SLNs.jl")
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include("groups/speciallinear.jl")
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include("Orbit.jl")
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main(SLNs, PARSEDARGS)
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main(SpecialLinear, PARSEDARGS)
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