// this script computes all non-cyclic abelian tiling groups 
// for genus  2 <= sigma <= 13

filetitle := "Classification of 2-generator Abelian Triangular Actions on Sufaces from Genus 2 to 13";
SetLogFile("abelian2.log":Overwrite := true);
FW := Open("abelian2.act","w");
FWR := Open("abelian2.rez","w");
print filetitle;
fprintf FW, "%o \n", filetitle;

multiactions := [];
groupBDpairsingenus := [];
kaleidoactionsingenus := [];  
nonkaleidoactionsingenus := [];  
actionsingenus := [];  
totalgroupBDpairs := 0;
totalkaleidoactions := 0;
totalnonkaleidoactions := 0;
totalactions := 0;

load "tileclass.mgm";

for n := 2 to 13 do
  fname := "zpolybd_sig"*IntegerToString(n)*"_tau0_t3.bdat";
  print " ";   print "********** working on " cat fname; print " ";
  FR := Open(fname, "r");
  Insert(~groupBDpairsingenus,n,[n,0]);
  Insert(~actionsingenus,n,[n,0]);
  Insert(~kaleidoactionsingenus,n,[n,0]);
  Insert(~nonkaleidoactionsingenus,n,[n,0]);

  repeat
    s := Gets(FR);
    if not IsEof(s) then
       sig, g, ords, note := ParseBData(s);
       L := Lcm(ords);
       if (Position(note,"is_cyclic")+ Position(note,"not_abelian") eq 0)
          then A2L := AbelianGroups2Gen(g);
          for  A in A2L do
            inv := Invariants(A);
            if (Exponent(A) mod L) gt 0 then continue; end if;
            print " ... ", note; 
            print "abelian (2-gen) group of order ",g;   
            triset, normforms := AbelianGroup2GenTriples(A,sig,g,ords);
            print " "; 
            if #normforms gt 0
               then
               fprintf FW, "\n \n";
               fprintf FW, "bdata: %2o %3o %o \n", sig, g, ords;
               fprintf FW, "G = 2 generator abelian group Z_%-2o x Z_%-2o \n", inv[1],inv[2];
               fprintf FW, "%-2o generating vector(s)\n", #normforms;
               fprintf FW, "%o \n", normforms;
               if IsDefined(multiactions,#normforms)
                  then multiactions[#normforms] := [#normforms, multiactions[#normforms][2]+1];
                  else Insert(~multiactions,#normforms,[#normforms,1]);
                  end if;
               groupBDpairsingenus[n]  := [n, groupBDpairsingenus[n][2]+1];
               kal :=0; nkal :=0;
               for x in normforms do
                   if  x[2] eq true then kal := kal +1; else nkal := nkal +1; 
                       end if;
                   end for;
               kaleidoactionsingenus[n] := [n,kaleidoactionsingenus[n][2]+kal];
               nonkaleidoactionsingenus[n] := [n,nonkaleidoactionsingenus[n][2]+nkal];
               actionsingenus[n] := [n,kaleidoactionsingenus[n][2]+nonkaleidoactionsingenus[n][2]]; 
               totalgroupBDpairs := totalgroupBDpairs +1;
               totalkaleidoactions := totalkaleidoactions + kal;
               totalnonkaleidoactions := totalnonkaleidoactions + nkal;
               totalactions := totalkaleidoactions + totalnonkaleidoactions;
               fprintf FWR, "%2o %3o %14o Z_%-2ox Z_%-2o %2o %2o %2o \n", sig, g, ords,inv[1],inv[2],kal,nkal, kal+nkal;
               end if;
            end for;
         end if;
      end if;
    until IsEof(s);
  end for;

  print "   ";
  print "done computing, summary information to follow";
  print "total groupBDpairs: ", totalgroupBDpairs;
  print "total actions : ", totalactions; 
  print "total kaleidoscopic actions: ", totalkaleidoactions; 
  print "total non kaleidoscopic actions: ", totalnonkaleidoactions; 
  print "multiple actions: ", multiactions;
  print "groupBDpairs in genus: ", groupBDpairsingenus;
  print "actions in genus: ", actionsingenus;
  print "kaleidoscopic actions in genus: ", kaleidoactionsingenus;
  print "non-kaleidoscopic actions in genus: ", nonkaleidoactionsingenus;

  fprintf FW, " \n ### summary #### \n";  
  fprintf FW, "total  groupBDpairs: %o \n\n", totalgroupBDpairs;
  fprintf FW, "total actions: %o \n\n", totalactions; 
  fprintf FW, "total kaleidoscopic actions: %o \n\n", totalkaleidoactions; 
  fprintf FW, "total non kaleidoscopic actions: %o \n\n", totalnonkaleidoactions; 
  fprintf FW, "multiple actions: %o \n\n", multiactions;
  fprintf FW, "groupBDpairs in genus: %o \n\n", groupBDpairsingenus;
  fprintf FW, "actions in genus: %o \n\n", actionsingenus;
  fprintf FW, "kaleidoscopic actions in genus: %o \n\n", kaleidoactionsingenus;
  fprintf FW, "non-kaleidoscopic actions in genus: %o \n\n", nonkaleidoactionsingenus;

  delete FW;
  delete FWR;

UnsetLogFile();