sortfunc := function(L1,L2)
  return Length(L1) < Length(L2);
end; # sortfunc

LargestPoint := function(G)
  local Result,L;
  
  Result := 0;
  L := PermGroupOps.MovedPoints(G);
  
  if Length(L) > 0
  then
    Result := Maximum(L);
  fi;

  return Result;
end; # LargestPoint

TrivialBase := function(G)
  local orbitGroup,orbit,coupledElements,head;
  
  if not IsBound(G.trivialBase)
  then
     G.trivialBase := [];
     if not IsBound(G.orbits)
     then
        G.orbits := Orbits(G,[1..LargestPoint(G)]);
        Sort(G.orbits,sortfunc);
     fi;
     for orbit in [1 .. Length(G.orbits)]
     do
       orbitGroup := Operation(G,G.orbits[orbit]);
       coupledElements := Blocks(orbitGroup,[1..Length(G.orbits[orbit])]);
       for head in [1..Length(coupledElements)]
       do
         Add(G.trivialBase,G.orbits[orbit][coupledElements[head][1]]);
       od;
     od;
  fi;
end; # TrivialBase


StripBase := function(G,L)
  local Result,element;
  
  Result := [];
  TrivialBase(G);
  for element in [1 .. Length(L)]
  do
    if L[element] in G.trivialBase
    then
      Add(Result,L[element]);
    fi;
  od;
  
  return Result;
end; # StripBase

SortByGeneratorsOnOrbits := function(G,L)
  local i,j,genpoints,list,list2,Result1,Result;
  
  genpoints := [];
  Result := [];
  Result1 := [];
  
  for i in [1..Length(G.generators)]
  do
    list := Cycles(G.generators[i],
                   [
                    SmallestMovedPointPerm(G.generators[i])
                    ..
                    LargestMovedPointPerm(G.generators[i]) 
                   ]
                  );
    list2 := [];
    for j in [1..Length(list)]
    do
      if Length(list[j]) > 1
      then
        Add(list2,list[j]);
      fi;
    od;
    list2 := Flat(list2);
    for j in [1..Length(list2)]
    do
      if not list2[j] in Result1
      then
        Add(Result1,list2[j]);
      fi;
    od;
  od;
  
  Result1 := StripBase(G,Result1);
 
  for i in [1..Length(Result1)]
  do
    if Result1[i] in L and not Result1[i] in Result
    then
      Add(Result,Result1[i]);
    fi;
  od;
  
  return Result;
end;