//  Farey fractions, illustration how to define functions

D := Denominator;
N := Numerator;

function farey(n)
     if n eq 1 then
         return [RationalField() | 0, 1 ];
     end if;
     f := farey(n-1);
     i := 0;
     while i lt #f-1 do
         i +:= 1;
         if D(f[i]) + D(f[i+1]) eq n then
             Insert(~f, i+1, (N(f[i]) + N(f[i+1]))/(D(f[i]) + D(f[i+1])));
         end if;
     end while;
     return f;
end function;

time f100 := farey(100);
farey(10);