GroupsWithPropertyT/SL.jl

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using ArgParse
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using Nemo
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import SCS.SCSSolver
using PropertyT
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function E(i::Int, j::Int, M::Nemo.MatSpace)
@assert i≠j
m = one(M)
m[i,j] = m[1,1]
return m
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end
function SL_generatingset(n::Int)
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
G = Nemo.MatrixSpace(Nemo.ZZ, n,n)
S = [E(i,j,G) for (i,j) in indexing];
S = vcat(S, [transpose(x) for x in S]);
return unique(S)
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end
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function SLsize(n,p)
result = 1
for k in 0:n-1
result *= p^n - p^k
end
return div(result, p-1)
end
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function SL_generatingset(n::Int, p::Int)
p == 0 && return SL_generatingset(n)
(p > 1 && n > 0) || throw(ArgumentError("Both n and p should be positive integers!"))
println("Size(SL($n,$p)) = $(SLsize(n,p))")
F = Nemo.ResidueRing(Nemo.ZZ, p)
G = Nemo.MatrixSpace(F, n,n)
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indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
S = [E(i, j, G) for (i,j) in indexing]
S = vcat(S, [transpose(x) for x in S])
return unique(S)
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end
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
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function parse_commandline()
s = ArgParseSettings()
@add_arg_table s begin
"--tol"
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help = "set numerical tolerance for the SDP solver (default: 1e-5)"
arg_type = Float64
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default = 1e-5
"--iterations"
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help = "set maximal number of iterations for the SDP solver (default: 20000)"
arg_type = Int
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default = 20000
"--upper-bound"
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help = "Set an upper bound for the spectral gap (default: Inf)"
arg_type = Float64
default = Inf
"--cpus"
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help = "Set number of cpus used by solver (default: auto)"
arg_type = Int
required = false
"-N"
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help = "Consider matrices of size N (default: N=3)"
arg_type = Int
default = 3
"-p"
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help = "Matrices over filed of p-elements (default: p=0 => over ZZ)"
arg_type = Int
default = 0
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"--radius"
help = "Find the decomposition over B_r(e,S)"
arg_type = Int
default = 2
end
return parse_args(s)
end
function main()
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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
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tol = parsed_args["tol"]
iterations = parsed_args["iterations"]
solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct)
N = parsed_args["N"]
upper_bound = parsed_args["upper-bound"]
p = parsed_args["p"]
if p == 0
name = "SL$(N)Z"
else
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name = "SL$(N)_$p"
end
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radius = parsed_args["radius"]
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name = "$(name)_$(upper_bound)_r=$radius"
logger = PropertyT.setup_logging(name)
info(logger, "Group: $name")
info(logger, "Iterations: $iterations")
info(logger, "Precision: $tol")
info(logger, "Upper bound: $upper_bound")
S = SL_generatingset(N, p)
S = unique([S; [inv(s) for s in S]])
Id = one(parent(S[1]))
@time PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, radius)
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return 0
end
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main()