/* element of (projective) order */

ElementOfOrder := function (P, RequiredOrder, Limit : Fct := Order)

   if Type (RequiredOrder) eq RngIntElt then 
      RequiredOrder := {RequiredOrder};
   end if;

   NmrTries := Limit;
   repeat
      g, w := Random (P);
      o := Fct (g);
      NmrTries -:= 1;
      rem := exists (x) {x : x in RequiredOrder | (o mod x eq 0)};
   until rem or (NmrTries eq 0);

   if rem then return g^(o div x), w^(o div x); else return false, _; end if;

end function;