GroupsWithPropertyT/AutFn.jl

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using ArgParse
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###############################################################################
#
# Parsing command line
#
###############################################################################
function parse_commandline()
s = ArgParseSettings()
@add_arg_table s begin
"--tol"
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help = "set numerical tolerance for the SDP solver"
arg_type = Float64
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default = 1e-6
"--iterations"
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help = "set maximal number of iterations for the SDP solver"
arg_type = Int
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default = 50000
"--upper-bound"
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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
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"--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
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"--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
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const PARSEDARGS = parse_commandline()
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#=
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()ℤⁿ GL_(n+1)().
Moreover, due to work of Potapchik and Rapinchuk [1] every real representation of Aut(Fₙ) into GLₘ() (for m 2n-2) factors through GLₙ()ℤⁿ, so will have the same problem.
We need a different approach: Here we actually compute in (S)Aut(𝔽ₙ)
=#
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include("CPUselect.jl")
set_parallel_mthread(PARSEDARGS, workers=true)
include("main.jl")
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G = PropertyTGroups.SpecialAutomorphismGroup(PARSEDARGS)
main(G)