rewrite
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MCG.jl
249
MCG.jl
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@ -1,110 +1,187 @@
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using ArgParse
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using JLD
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using Nemo
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import SCS.SCSSolver
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using PropertyT
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using Groups
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function cpuinfo_physicalcores()
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maxcore = -1
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for line in eachline("/proc/cpuinfo")
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if startswith(line, "core id")
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maxcore = max(maxcore, parse(Int, split(line, ':')[2]))
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end
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end
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maxcore < 0 && error("failure to read core ids from /proc/cpuinfo")
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return maxcore + 1
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end
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function parse_commandline()
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args = ArgParseSettings()
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@add_arg_table args begin
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"--tol"
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help = "set numerical tolerance for the SDP solver"
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arg_type = Float64
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default = 1e-14
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"--iterations"
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help = "set maximal number of iterations for the SDP solver (default: 20000)"
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arg_type = Int
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default = 60000
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"--upper-bound"
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help = "Set an upper bound for the spectral gap"
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arg_type = Float64
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default = Inf
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"--cpus"
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help = "Set number of cpus used by solver (default: auto)"
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arg_type = Int
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required = false
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"-N"
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help = "Consider mapping class group of surface of genus N"
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arg_type = Int
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default = 2
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"--radius"
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help = "Radius of ball B_r(e,S) to find solution over"
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arg_type = Int
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default = 4
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"--warmstart"
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help = "Use warmstart.jl as the initial guess for SCS"
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action = :store_true
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end
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@add_arg_table args begin
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"--tol"
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help = "set numerical tolerance for the SDP solver"
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arg_type = Float64
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default = 1e-14
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"--iterations"
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help = "set maximal number of iterations for the SDP solver (default: 20000)"
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arg_type = Int
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default = 60000
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"--upper-bound"
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help = "Set an upper bound for the spectral gap"
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arg_type = Float64
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default = Inf
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"--cpus"
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help = "Set number of cpus used by solver (default: auto)"
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arg_type = Int
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required = false
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"-N"
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help = "Consider mapping class group of surface of genus N"
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arg_type = Int
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default = 2
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"--radius"
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help = "Radius of ball B_r(e,S) to find solution over"
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arg_type = Int
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default = 4
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"--warmstart"
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help = "Use warmstart.jl as the initial guess for SCS"
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action = :store_true
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end
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return parse_args(args)
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return parse_args(args)
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end
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const PARSEDARGS = parse_commandline()
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include("CPUselect.jl")
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# set_parallel_mthread(PARSEDARGS, workers=true)
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include("FPGroups_GAP.jl")
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include("CPUselect.jl")
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function main()
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module MCGrps
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parsed_args = parse_commandline()
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set_parallel_mthread(parsed_args)
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using Groups
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using Nemo
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tol = parsed_args["tol"]
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iterations = parsed_args["iterations"]
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upper_bound = parsed_args["upper-bound"]
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radius = parsed_args["radius"]
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N = parsed_args["N"]
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Comm(x,y) = x*y*x^-1*y^-1
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prefix = "MCG($N)"
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name = "$(prefix)"
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function Group(N::Int)
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if N == 2
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MCGroup = Groups.FPGroup(["a1","a2","a3","a4","a5"]);
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S = Nemo.gens(MCGroup)
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isdir(name) || mkdir(name)
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N = length(S)
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A = prod(reverse(S))*prod(S)
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prepare_pm_delta(prefix, name, radius)
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relations = [
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[Comm(S[i], S[j]) for i in 1:N for j in 1:N if abs(i-j) > 1]...,
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[S[i]*S[i+1]*S[i]*inv(S[i+1]*S[i]*S[i+1]) for i in 1:N-1]...,
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(S[1]*S[2]*S[3])^4*inv(S[5])^2,
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Comm(A, S[1]),
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A^2
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]
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logger = PropertyT.setup_logging(name)
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relations = [relations; [inv(rel) for rel in relations]]
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Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
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return MCGroup
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info(logger, "Group: $name")
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info(logger, "Iterations: $iterations")
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info(logger, "Precision: $tol")
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info(logger, "Upper bound: $upper_bound")
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elseif N < 2
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throw("Genus must be at least 2!")
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end
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MCGroup = Groups.FPGroup(["a1","a2","a3","a4", "a5"]);
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S = Nemo.gens(MCGroup)
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Comm(x,y) = x*y*x^-1*y^-1
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k = length(S)
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MCGroup = Groups.FPGroup(["a$i" for i in 0:2N])
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S = Nemo.gens(MCGroup)
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relations = [[Comm(S[i], S[j]) for i in 1:k for j in 1:k if abs(i-j) > 1]...,
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[S[i]*S[i+1]*S[i]*inv(S[i+1]*S[i]*S[i+1]) for i in 1:k-1]...,
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(S[1]*S[2]*S[3])^4*inv(S[5])^5,
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Comm(prod(reverse(S))*prod(S), S[1]),
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(prod(reverse(S))*prod(S))^2
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];
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a0 = S[1]
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A = S[2:end]
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k = length(A)
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relations = [relations; [inv(rel) for rel in relations]]
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Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
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relations = [
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[Comm(A[i], A[j]) for i in 1:k for j in 1:k if abs(i-j) > 1]...,
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[Comm(a0, A[i]) for i in 1:k if i != 4]...,
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[A[i]*A[(i+1)]*A[i]*inv(A[i+1]*A[i]*A[i+1]) for i in 1:k-1]...,
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A[4]*a0*A[4]*inv(a0*A[4]*a0)
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]
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S = gens(MCGroup)
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S = unique([S; [inv(s) for s in S]])
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Id = MCGroup()
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solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct, alpha=1.9, acceleration_lookback=1)
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# 3-chain relation
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c = prod(reverse(A[1:4]))*prod(A[1:4])
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b0 = c*a0*inv(c)
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push!(relations, (A[1]*A[2]*A[3])^4*inv(a0*b0))
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@time PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, radius)
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return 0
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# Lantern relation
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b1 = inv(A[4]*A[5]*A[3]*A[4])*a0*(A[4]*A[5]*A[3]*A[4])
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b2 = inv(A[2]*A[3]*A[1]*A[2])*b1*(A[2]*A[3]*A[1]*A[2])
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u = inv(A[6]*A[5])*b1*(A[6]*A[5])
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x = prod(reverse(A[2:6]))*u*prod(inv.(A[1:4]))
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b3 = x*a0*inv(x)
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push!(relations, a0*b2*b1*inv(A[1]*A[3]*A[5]*b3))
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# Hyperelliptic relation
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X = prod(reverse(A))*prod(A)
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function n(i::Int, b=b0)
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if i == 1
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return A[1]
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elseif i == 2
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return b
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else
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return w(i-2)*n(i-2)*w(i-2)
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end
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end
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function w(i::Int)
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(A[2i+4]*A[2i+3]*A[2i+2]* n(i+1))*(A[2i+1]*A[2i] *A[2i+2]*A[2i+1])*
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(A[2i+3]*A[2i+2]*A[2i+4]*A[2i+3])*( n(i+1)*A[2i+2]*A[2i+1]*A[2i] )
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end
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push!(relations, X*n(N)*inv(n(N)*X))
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relations = [relations; [inv(rel) for rel in relations]]
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Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
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@show MCGroup
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return MCGroup
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end
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main()
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###############################################################################
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#
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# Misc
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#
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###############################################################################
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function groupname(parsed_args)
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N = parsed_args["N"]
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return groupname(N), N
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end
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groupname(N::Int) = "MCG$(N)"
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end #of module MCGrps
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using SCS.SCSSolver
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using PropertyT
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function main(GROUP, parsed_args)
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radius = parsed_args["radius"]
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tol = parsed_args["tol"]
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iterations = parsed_args["iterations"]
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upper_bound = parsed_args["upper-bound"]
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warm = parsed_args["warmstart"]
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name, N = GROUP.groupname(parsed_args)
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isdir(name) || mkdir(name)
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G = GROUP.Group(N)
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S = Nemo.gens(G)
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relations = [k*inv(v) for (k,v) in G.rels]
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prepare_pm_delta(name, GAP_groupcode(S, relations), radius)
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S = unique([S; [inv(s) for s in S]])
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Id = G()
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logger = PropertyT.setup_logging(joinpath(name, "$(upper_bound)"))
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info(logger, "Group: $name")
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info(logger, "Iterations: $iterations")
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info(logger, "Precision: $tol")
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info(logger, "Upper bound: $upper_bound")
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info(logger, "Radius: $radius")
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info(logger, G)
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info(logger, "Symmetric generating set of size $(length(S))")
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info(logger, "Threads: $(Threads.nthreads())")
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info(logger, "Workers: $(workers())")
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solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct, alpha=1.9, acceleration_lookback=1)
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PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, radius)
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return 0
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end
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main(MCGrps, PARSEDARGS)
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