add MCG code
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FPGroups_GAP.jl
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155
FPGroups_GAP.jl
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using JLD
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function GAP_code(group_code, dir, R; maxeqns=10_000, infolevel=2)
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code = """
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RequirePackage("kbmag");
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SetInfoLevel(InfoRWS, $infolevel);
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MetricBalls := function(rws, R)
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local l, basis, sizes, i;
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l := EnumerateReducedWords(rws, 0, R);;
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SortBy(l, Length);
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sizes := [1..R];
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Apply(sizes, i -> Number(l, w -> Length(w) <= i));
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return [l, sizes];
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end;;
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ProductMatrix := function(rws, basis, len)
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local result, dict, g, tmpList, t;
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result := [];
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dict := NewDictionary(basis[1], true);
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t := Runtime();
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for g in [1..Length(basis)] do;
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AddDictionary(dict, basis[g], g);
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od;
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Print("Creating dictionary: \t\t", StringTime(Runtime()-t), "\\n");
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for g in basis{[1..len]} do;
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tmpList := List(Inverse(g)*basis{[1..len]}, w->ReducedForm(rws, w));
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#t := Runtime();
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tmpList := List(tmpList, x -> LookupDictionary(dict, x));
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#Print(Runtime()-t, "\\n");
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Assert(1, ForAll(tmpList, x -> x <> fail));
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Add(result, tmpList);
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od;
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return result;
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end;;
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SaveCSV := function(fname, pm)
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local file, i, j, k;
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file := OutputTextFile(fname, false);;
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for i in pm do;
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k := 1;
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for j in i do;
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if k < Length(i) then
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AppendTo(file, j, ", ");
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else
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AppendTo(file, j, "\\n");
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fi;
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k := k+1;
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od;
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od;
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CloseStream(file);
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end;;
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$group_code
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G:= SimplifiedFpGroup(G);
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RWS := KBMAGRewritingSystem(G);
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# ResetRewritingSystem(RWS);
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O:=OptionsRecordOfKBMAGRewritingSystem(RWS);;
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O.maxeqns := $maxeqns;
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#O.maxstoredlen := [100,100];
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before := Runtimes();;
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KnuthBendix(RWS);
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after := Runtimes();;
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delta := after.user_time_children - before.user_time_children;;
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Print("Knuth-Bendix completion: \t", StringTime(delta), "\\n");
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t := Runtime();
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res := MetricBalls(RWS,$(2*R));;
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Print("Metric-Balls generation: \t", StringTime(Runtime()-t), "\\n");
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B := res[1];; sizes := res[2];;
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Print(sizes, "\\n");
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t := Runtime();
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pm := ProductMatrix(RWS, B, sizes[$R]);;
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Print("Computing ProductMatrix: \t", StringTime(Runtime()-t), "\\n");
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S := EnumerateReducedWords(RWS, 1, 1);
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S := List(S, s -> Position(B,s));
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SaveCSV("$(dir)/pm.csv", pm);
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SaveCSV("$(dir)/S.csv", [S]);
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SaveCSV("$(dir)/sizes.csv", [sizes]);
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Print("DONE!\\n");
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quit;""";
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return code
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end
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function GAP_groupcode(S, rels)
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F = "FreeGroup("*join(["\"$v\""for v in S], ", ") *");"
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m = match(r".*(\[.*\])$", string(rels))
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rels = replace(m.captures[1], " ", "\n")
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code = """
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F := $F;
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AssignGeneratorVariables(F);;
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relations := $rels;
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G := F/relations;
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"""
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return code
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end
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function GAP_execute(gap_code, dir)
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isdir(dir) || mkdir(dir)
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GAP_file = joinpath(dir, "GAP_code.g")
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@show dir
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@show GAP_file;
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open(GAP_file, "w") do io
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write(io, gap_code)
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end
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run(`gap -q $(GAP_file)`)
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end
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function prepare_pm_delta_csv(name, group_code, R; maxeqns=10_000, infolevel=2)
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info("Preparing multiplication table using GAP (via kbmag)")
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gap_code = GAP_code(group_code, name, R, maxeqns=maxeqns, infolevel=infolevel)
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o = GAP_execute(gap_code, name)
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return o
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end
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function prepare_pm_delta(name, group_code, R; maxeqns=100_000, infolevel=2)
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pm_fname = joinpath(name, "pm.csv")
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S_fname = joinpath(name, "S.csv")
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sizes_fname = joinpath(name, "sizes.csv")
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delta_fname = joinpath(name, "delta.jld")
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if !isfile(pm_fname) || !isfile(S_fname) || !isfile(sizes_fname)
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prepare_pm_delta_csv(name, group_code, R, maxeqns=maxeqns, infolevel=infolevel)
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end
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if isfile(sizes_fname)
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sizes = readcsv(sizes_fname, Int)[1,:]
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if 2R > length(sizes)
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prepare_pm_delta_csv(name, group_code, R, maxeqns=maxeqns, infolevel=infolevel)
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end
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end
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pm = readcsv(pm_fname, Int)
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S = readcsv(S_fname, Int)[1,:]
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sizes = readcsv(sizes_fname, Int)[1,:]
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Δ = spzeros(sizes[2R])
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Δ[S] .= -1
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Δ[1] = length(S)
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pm = pm[1:sizes[R], 1:sizes[R]]
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save(joinpath(name, "pm.jld"), "pm", pm)
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save(joinpath(name, "delta.jld"), "Δ", Δ)
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end
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115
MCG.jl
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115
MCG.jl
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@ -0,0 +1,115 @@
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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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return parse_args(args)
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end
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include("FPGroups_GAP.jl")
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function main()
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parsed_args = parse_commandline()
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if parsed_args["cpus"] ≠ nothing
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if parsed_args["cpus"] > cpuinfo_physicalcores()
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warn("Number of specified cores exceeds the physical core cound. Performance will suffer.")
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end
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BLAS.set_num_threads(parsed_args["cpus"])
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end
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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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solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct)
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prefix = "MCG($N)"
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name = "$(prefix)"
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isdir(name) || mkdir(name)
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prepare_pm_delta(prefix, name, radius)
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logger = PropertyT.setup_logging(name)
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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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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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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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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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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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@time 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()
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