110 lines
3.1 KiB
Julia
110 lines
3.1 KiB
Julia
using ArgParse
|
||
|
||
using Nemo
|
||
Nemo.setpermstyle(:cycles)
|
||
|
||
using Groups
|
||
using GroupRings
|
||
using PropertyT
|
||
|
||
import SCS.SCSSolver
|
||
|
||
#=
|
||
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(ℤ)⋉ℤ⁴ → GL₅(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 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
|
||
|
||
|
||
# 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"]
|
||
|
||
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
|
||
|
||
main()
|