procedure main()
   limit := 2^19

   write("Perfect numbers up to ",limit," (using rational arithmetic):")
   every write(is_perfect(c := 2 to limit))
   write("End of perfect numbers")

   # verify the rest of the implementation

   zero := makerat(0)          # from integer
   half := makerat(0.5)        # from real
   qtr  := makerat("1/4")      # from strings ...
   one  := makerat("1")
   mone := makerat("-1")

   verifyrat("eqrat",zero,zero)
   verifyrat("ltrat",zero,half)
   verifyrat("ltrat",half,zero)
   verifyrat("gtrat",zero,half)
   verifyrat("gtrat",half,zero)
   verifyrat("nerat",zero,half)
   verifyrat("nerat",zero,zero)
   verifyrat("absrat",mone,)

end

procedure is_perfect(c)       #: test for perfect numbers using rational arithmetic
   rsum := rational(1, c, 1)
   every f := 2 to sqrt(c) do
      if 0 = c % f then
         rsum := addrat(rsum,addrat(rational(1,f,1),rational(1,integer(c/f),1)))
   if rsum.numer = rsum.denom = 1 then
      return c
end