[ $ "bigrat.qky" loadfile ] now!

  [  rot + dip + reduce ] is mediant ( n/d n/d --> n/d )

  [ 1+ temp put [] swap
    dup size 1 - times
    [ dup i^ peek
      rot over nested join
      unrot over i^ 1+ peek
      join do mediant
      dup temp share < iff
      [ join nested
        rot swap join
        swap ]
      else 2drop ]
    drop
    ' [ [ 1 1 ] ] join
    temp release ]          is nextfarey ( fy n --> fy )

  [ witheach
      [ unpack vulgar$
        echo$ sp ] ]        is echofarey ( fy --> )

  [ 0 swap dup times
      [ i over gcd
        1 = rot + swap ]
      drop ]                is totient ( n --> n )

  [ 0 swap times
      [ i 1+ totient + ] ]  is totientsum ( n --> n )

  [ totientsum 1+ ]         is fareylength ( n --> n )

  say "First eleven Farey series:" cr
  ' [ [ 0 1 ] [ 1 1 ] ]
  10 times
    [ dup echofarey cr
      i^ 2 + nextfarey ]
    echofarey cr
  cr
  say "Length of Farey series 100, 200 ... 1000: "
  [] 10 times
     [ i^ 1+ 100 *
       fareylength join ]
  echo