GroupsWithPropertyT/AutFn.jl

66 lines
2.1 KiB
Julia
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

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(F) becomes trivial under the representation
Aut(F) GL() GL_(n+1)().
Moreover, due to work of Potapchik and Rapinchuk [1] every real representation of Aut(F) into GL() (for m 2n-2) factors through GL(), so will have the same problem.
We need a different approach: Here we actually compute in (S)Aut(𝔽)
=#
include("CPUselect.jl")
set_parallel_mthread(PARSEDARGS, workers=true)
include("main.jl")
G = PropertyTGroups.SpecialAutomorphismGroup(PARSEDARGS)
main(G)