sicp chapter 2

gistfile1.sls

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; 2.1.1
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(define (make-rat n d)
 (cons n d))

(define (numer x)
  (car x))

(define (denom x)
  (cdr x))

(define (print-rat x)
  (newline)
  (display (numer x))
  (display "/")
  (display (denom 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 (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))))


;; exercise 2.1
(define (make-rat n d)
  (cond
   ((and (> n 0) (> d 0)) (cons n d))
   ((and (> n 0) (<= d 0)) (cons (- n) (- d)))
   (else (cons (- n) (- d)))))

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; 2.1.2
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(define (make-rat n d)
  (cons n d))

(define (numer x)
  (let ((g (gcd (car x) (cdr x))))
    (/ (car x) g)))

(define (denom x)
  (let ((g (gcd (car x) (cdr x))))
    (/ (cdr x) g)))

(define hoge (make-rat 2 6))
(numer hoge)
(denom hoge)

;; exercise 2.2 start
(define (make-segment start end)
  (cons start end))

(define (start-segment segment)
  (car segment))

(define (end-segment segment)
  (cdr segment))

(define (make-point x y)
  (cons x y))

(define (x-point point)
  (car point))

(define (y-point point)
  (cdr point))

(define (print-point p)
  (newline)
  (display "(")
  (display (x-point p))
  (display ",")
  (display (y-point p))
  (display ")")
  (newline))
  
(define (midpoint-segment segment)
  (print-point (make-point (/ (+ (x-point (start-segment segment))
                                 (x-point (end-segment segment)))
                              2.0)
                           (/ (+ (y-point (start-segment segment))
                                 (y-point (end-segment segment)))
                              2.0))))

(define point1 (make-point 10 20))
(define point2 (make-point 30 40))
(define segment1 (make-segment point1 point2))
(midpoint-segment segment1)
;; exercise 2.2 end

;; exercise 2.3 start

;; point ver
(define (make-rectangle bottom-left top-right)
  (cons bottom-left top-right))

(define (bottom-left rectangle)
  (car rectangle))

(define (top-right rectangle)
  (cdr rectangle))

(define (x-distance rectangle)
  (abs (- (x-point (top-right rectangle)) (x-point (bottom-left rectangle)))))

(define (y-distance rectangle)
  (abs (- (y-point (top-right rectangle)) (y-point (bottom-left rectangle)))))

(define (perimeter rectangle)
  (* 2.0
     (+ (x-distance rectangle)
        (y-distance rectangle))))

(define (area rectangle)
  (* (x-distance rectangle)
     (y-distance rectangle)))
    
(define rectangle1 (make-rectangle
                    (make-point 10 20)
                    (make-point 30 40)))

(perimeter rectangle1)
(area rectangle1)

;; segment ver
(define (make-rectangle first-point second-point)
  (make-segment first-point second-point))

(define (x-distance rectangle)
  (abs (- (x-point (end-segment rectangle))
          (x-point (start-segment rectangle)))))

(define (y-distance rectangle)
  (abs (- (y-point (end-segment rectangle))
          (y-point (start-segment rectangle)))))

(define rectangle1 (make-rectangle
                    (make-point 10 20)
                    (make-point 30 40)))


(perimeter rectangle1)
(area rectangle1)