exercise2-01.lisp

; (define (make-rat n d) (cons n d))
(define (gcd a b)
  (if (= b 0)
	a
	(gcd b (remainder a b))))
;(define (make-rat n d)
;  (let ((g (gcd n d)))
;	(cons (/ n g) (/ d g))))
(define (make-rat n d)
  (let ((g (gcd n d)))
	(if (< d 0)
	  (make-rat (* -1 n) (* -1 d))
	  (cons (/ n g) (/ d g)))))
(define (numer x) (car x))
(define (denom x) (cdr x))
(define (add-rat x y)
  (make-rat (+ (* (numer x) (denom y))
			   (* (numer y) (denom x)))
			(* (denom x) (denom y))))
(define (sub-rat x y)
  (make-rat (- (* (numer x) (denom y))
			   (* (numer y) (denom x)))
			(* (denom x) (denom y))))
(define (mul-rat x y)
  (make-rat (* (numer x) (numer y))
			(* (denom x) (denom y))))
(define (div-rat x y)
  (make-rat (* (numer x) (denom y))
			(* (denom x) (numer y))))
(define (equal-rat? x y)
  (= (* (numer x) (denom y))
	 (* (numer y) (denom x))))
(define (print-rat x)
  (display (numer x))
  (display "/")
  (display (denom x))
  (newline))

(define one-half (make-rat 1 2))
(print-rat one-half)
(define one-third (make-rat 1 3))
(print-rat (add-rat one-half one-third))
(print-rat (mul-rat one-half one-third))
(print-rat (add-rat one-third one-third))

(print-rat (make-rat -1 -2))
(print-rat (make-rat 1 -2))
(print-rat (make-rat -1 2))