sicp exercise 2.1

; Exercise 2.1.  Define a better version of make-rat that handles both positive
; and negative arguments. Make-rat should normalize the sign so that if the rational
; number is positive, both the numerator and denominator are positive, and if the
; rational number is negative, only the numerator is negative.

(begin
  (define (display-rat rat)
    (display (car rat))
    (display '/)
    (display (cdr rat))
    (newline))
  (define (make-rat num den)
    (define (getsign num)
      (if (> num 0) 1 (- 1)))
    (define (makeplus a)
      (if (> a 0) a (- a)))
    (cons
         (*
            (*
               (getsign num)
               (getsign den))
            (makeplus num))
         (makeplus den)))

  (display-rat (make-rat  2  3))
  (display-rat (make-rat  2 -3))
  (display-rat (make-rat -2  3))
  (display-rat (make-rat -2 -3))
)