// this script computes all cyclic rotation groups 
// for genus  2 <= sigma <= 13

filetitle := "Classification of Cyclic Triangular Actions on Sufaces from Genus 2 to 13";
SetLogFile("cyclic.log":Overwrite := true);
FW := Open("cyclic.act","w");
FWR := Open("cyclic.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);
       if Position(note,"is_cyclic")+Position(note,"possibly_cyclic") gt 0 then
          print " ... ", note; 
          print "cyclic group of order", g; 
          triset, normforms := CyclicGroupTriples(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 = cyclic group Z_%-2o \n", g;
             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_%-2o %2o %2o %2o \n", sig, g, ords,g,kal,nkal, kal+nkal;
             end if;
       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();