GroupsWithPropertyT/FPGroups_GAP.jl

using JLD

function GAP_code(group_code, dir, R; maxeqns=10_000, infolevel=2)
    code = """
LogTo("$(dir)/GAP.log");
RequirePackage("kbmag");
SetInfoLevel(InfoRWS, $infolevel);


MetricBalls := function(rws, R)
    local l, basis, sizes, i;
    l := EnumerateReducedWords(rws, 0, R);;
    SortBy(l, Length);
    sizes := [1..R];
    Apply(sizes, i -> Number(l, w -> Length(w) <= i));
    return [l, sizes];
end;;

ProductMatrix := function(rws, basis, len)
    local result, dict, g, tmpList, t;
    result := [];
    dict := NewDictionary(basis[1], true);
    t := Runtime();
    for g in [1..Length(basis)] do;
        AddDictionary(dict, basis[g], g);
    od;
    Print("Creating dictionary: \t\t", StringTime(Runtime()-t), "\\n");
    for g in basis{[1..len]} do;
        tmpList := List(Inverse(g)*basis{[1..len]}, w->ReducedForm(rws, w));
        #t := Runtime();
        tmpList := List(tmpList, x -> LookupDictionary(dict, x));
        #Print(Runtime()-t, "\\n");
        Assert(1, ForAll(tmpList, x -> x <> fail));
        Add(result, tmpList);
    od;
    return result;
end;;

SaveCSV := function(fname, pm)
   local file, i, j, k;
   file := OutputTextFile(fname, false);;
   for i in pm do;
      k := 1;
      for j in i do;
         if k < Length(i) then
            AppendTo(file, j, ", ");
         else
            AppendTo(file, j, "\\n");
         fi;
         k := k+1;
      od;
   od;
   CloseStream(file);
end;;

$group_code

# G:= SimplifiedFpGroup(G);
RWS := KBMAGRewritingSystem(G);
# ResetRewritingSystem(RWS);
O:=OptionsRecordOfKBMAGRewritingSystem(RWS);;
O.maxeqns := $maxeqns;
#O.maxstoredlen := [100,100];

before := Runtimes();;
KnuthBendix(RWS);
after := Runtimes();;
delta := after.user_time_children - before.user_time_children;;
Print("Knuth-Bendix completion: \t", StringTime(delta), "\\n");

t := Runtime();
res := MetricBalls(RWS,$(2*R));;
Print("Metric-Balls generation: \t", StringTime(Runtime()-t), "\\n");
B := res[1];; sizes := res[2];;
Print("Sizes of generated Balls: \t", sizes, "\\n");

t := Runtime();
pm := ProductMatrix(RWS, B, sizes[$R]);;
Print("Computing ProductMatrix: \t", StringTime(Runtime()-t), "\\n");

S := EnumerateReducedWords(RWS, 1, 1);
S := List(S, s -> Position(B,s));

SaveCSV("$(dir)/pm.csv", pm);
SaveCSV("$(dir)/S.csv", [S]);
SaveCSV("$(dir)/sizes.csv", [sizes]);

Print("DONE!\\n");

quit;""";
    return code
end

function GAP_groupcode(S, rels)
    F = "FreeGroup("*join(["\"$v\""for v in S], ", ") *");"
    m = match(r".*(\[.*\])$", string(rels))
    rels = replace(m.captures[1], " ", "\n")
    code = """
F := $F;
AssignGeneratorVariables(F);;
relations := $rels;;
G := F/relations;
    """
    return code
end

function GAP_execute(gap_code, dir)
   isdir(dir) || mkdir(dir)
   GAP_file = joinpath(dir, "GAP_code.g")
   @show dir
   @show GAP_file;

   open(GAP_file, "w") do io
      write(io, gap_code)
   end
   run(pipeline(`cat $(GAP_file)`, `gap -q`))
end

function prepare_pm_delta_csv(name, group_code, R; maxeqns=10_000, infolevel=2)
   info("Preparing multiplication table using GAP (via kbmag)")
   gap_code = GAP_code(group_code, name, R, maxeqns=maxeqns, infolevel=infolevel)
   GAP_execute(gap_code, name)
end

function prepare_pm_delta(name, group_code, R; maxeqns=100_000, infolevel=2)

   pm_fname = joinpath(name, "pm.csv")
   S_fname = joinpath(name, "S.csv")
   sizes_fname = joinpath(name, "sizes.csv")
   delta_fname = joinpath(name, "delta.jld")

   if !isfile(pm_fname) || !isfile(S_fname) || !isfile(sizes_fname)
      prepare_pm_delta_csv(name, group_code, R, maxeqns=maxeqns, infolevel=infolevel)
   end

   if isfile(sizes_fname)
      sizes = readcsv(sizes_fname, Int)[1,:]
      if 2R > length(sizes)
         prepare_pm_delta_csv(name, group_code, R, maxeqns=maxeqns, infolevel=infolevel)
      end
   end

   pm = readcsv(pm_fname, Int)
   S = readcsv(S_fname, Int)[1,:]
   sizes = readcsv(sizes_fname, Int)[1,:]

   Δ = spzeros(sizes[2R])
   Δ[S] .= -1
   Δ[1] = length(S)

   pm = pm[1:sizes[R], 1:sizes[R]]

   save(joinpath(name, "pm.jld"), "pm", pm)
   save(joinpath(name, "delta.jld"), "Δ", Δ)

end