GroupsWithPropertyT/AutFN.jl

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using ArgParse
using Nemo
Nemo.setpermstyle(:cycles)
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using Groups
using GroupRings
using PropertyT
import SCS.SCSSolver
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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(F₄) becomes trivial under the representation
Aut(F₄) GL₄()ℤ⁴ GL₅().
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 Aut(𝔽₄)
=#
function cpuinfo_physicalcores()
maxcore = -1
for line in eachline("/proc/cpuinfo")
if startswith(line, "core id")
maxcore = max(maxcore, parse(Int, split(line, ':')[2]))
end
end
maxcore < 0 && error("failure to read core ids from /proc/cpuinfo")
return maxcore + 1
end
function parse_commandline()
s = ArgParseSettings()
@add_arg_table s begin
"--tol"
help = "set numerical tolerance for the SDP solver (default: 1e-5)"
arg_type = Float64
default = 1e-5
"--iterations"
help = "set maximal number of iterations for the SDP solver (default: 20000)"
arg_type = Int
default = 20000
"--upper-bound"
help = "Set an upper bound for the spectral gap (default: Inf)"
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 (default: N=3)"
arg_type = Int
default = 2
end
return parse_args(s)
end
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# const name = "SYM$N"
# const upper_bound=factorial(N)-TOL^(1/5)
# S() = generating_set_of_Sym(N)
# name = "AutF$N"
# S() = generating_set_of_AutF(N)
function main()
parsed_args = parse_commandline()
if parsed_args["cpus"] nothing
if parsed_args["cpus"] > cpuinfo_physicalcores()
warn("Number of specified cores exceeds the physical core cound. Performance will suffer.")
end
Blas.set_num_threads(parsed_args["cpus"])
end
tol = parsed_args["tol"]
iterations = parsed_args["iterations"]
# solver = SCSSolver(eps=tol, max_iters=iterations, verbose=true, linearsolver=SCS.Indirect)
solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct)
N = parsed_args["N"]
upper_bound = parsed_args["upper-bound"]
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name = "SOutF$N"
name = name*"-$(string(upper_bound))"
logger = PropertyT.setup_logging(name)
info(logger, "Group: $name")
info(logger, "Iterations: $iterations")
info(logger, "Precision: $tol")
info(logger, "Upper bound: $upper_bound")
AutFN = AutGroup(FreeGroup(N), special=true, outer=true)
S = generators(AutFN);
S = unique([S; [inv(s) for s in S]])
Id = AutFN()
@time PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, 2)
return 0
end
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main()