Multiple Representations complex number data complex number makefromrealimag

데이타를 여러방식으로 구현할 때 Multiple Representations • 데이터 구현방식마다 꼬리표를 붙이고. • 데이터 속내용 감추기 원리를 유지하면서. • 예를 들어 complex number data 구현방안들을 생각해 보자 – complex number 만들기 • make-from-real-imag: real * real -> complex • make-from-mag-angle: real * real -> complex – complex number 사용하기 • • • is-complex? : -> bool real: complex -> real imag: complex -> real angle: complex -> real

add-complex mul-complex make-from-real-imag make-from-mag-angle real img mag angle is-complex? rectangular representation

(define (make-from-real-imag x y) (cons x y)) (define (make-from-mag-angle m a) (cons (* m (cos a)) (* m (sin a)))) (define (is-complex? c) (and (pair? c) (real? (car c)) (real? (cdr c))) (define (real c) (cond ((not (is-complex? c)) (error)) (else (car c)))) (define (imag c) (cond ((not (is-complex? c) (error)) (else (cdr c)))) (define (mag c) (cond ((not (is-complex? c) (error)) (else (sqrt (+ (square (real c)) (square (imag c))))) )) (define (angle c) (cond ((not (is-complex? c) (error)) (else (atan (imag c) (real c)))))

외부에서는, (define (add-complex c 1 c 2) (make-from-real-imag (+ (real c 1) (real c 2)) (+ (imag c 1) (imag c 2)) )) (define (mul-complex c 1 c 2) (make-from-mag-angle (* (mag c 1) (mag c 2)) (+ (angle c 1) (angle c 2)) ))

add-complex mul-complex make-from-real-imag make-from-mag-angle real imag angle is-complex? make… make … rectangular representation polar representation

• rectagular complex 속내용 감추기data abstraction – – – – make-from-real-imag-rectangular: real * real -> complex make-from-mag-angle-rectangular: real * real -> complex is-rectangular? : complex -> bool real-rectangular: complex -> real imag-rectangular: complex -> real angle-rectangular: complex -> real (define rectangular-tag ‘rectangular) (define (make-from-real-imag-rectangular x y) (cons rectangular-tag (cons x y))) (define (make-from-mag-angle-rectangular m a) (cons rectangular-tag (cons (* m (cos a)) (* m (sin a))))) (define (is-rectangular? c) (equal? (car c) rectangular-tag)) (define (real-rectangular c) (car (cdr c))) (define (imag-rectangular c) (cdr c))) (define (mag-rectangular c) (sqrt (+ (square (real-rectangular c))) (+ (square (imag-rectangular c))))) (define (angle-rectangular c) (atan (imag-rectangular c) (real-rectangular c)))

• polar complex 속내용 감추기data abstraction – – – – make-from-real-imag-polar: real * real -> complex make-from-mag-angle-polar: real * real -> complex is-polar? : complex -> bool real-polar: complex -> real imag-polar: complex -> real angle-polar: complex -> real (define polar-tag ‘polar) (define (make-from-real-imag-polar x y) (cons polar-tag (cons …))) (define (make-from-mag-angle-polar m a) (cons polar-tag (cons m a))) (define (is-polar? c) (equal? (car c) polar-tag)) (define (mag-polar c) (car (cdr c))) (define (angle-polar c) (cdr c))) (define (real-polar c) (* (mag-polar c) (cos (angle-polar c)))) (define (imag-polarr c) (* (mag-polar c) (sin (angle-polar c))))

(define (make-from-real-imag x y) (make-from-real-imag-rectangular x y)) (define (make-from-mag-angle m a) (make-from-mag-angle-polar m a)) (define (is-complex? c) (and (pair? c) (cond ((is-rectangular? c) (and (real? (real-rectangular c)) (real? (imag-rectangular c)))) ((is-polar? c) (and (real? (mag-polar c)) (real? (angle-polar c)))) (else #f)) ))

(define (real c) (cond ((not (is-complex? c)) (error)) ((is-rectangular? c) (real-rectangular c)) ((is-polar? c) (real-polar c)))) (define (imag c) (cond ((not (is-complex? c)) (error)) ((is-rectangular? c) (imag-rectangular c)) ((is-polar? c) (imag-polar c)))) (define (mag c) (cond ((not (is-complex? c)) (error)) ((is-rectangllar? c) (mag-rectangular c)) ((is-polar? c) (mag-polar c)))) (define (angle c) (cond ((not (is-complex? c)) (error)) ((is-rectangular? c) (angle-rectangular c)) ((is-polar? c) (angle-polar c))))

외부에서는, 변함없이 (define (add-complex c 1 c 2) (make-from-real-imag (+ (real c 1) (real c 2)) (+ (imag c 1) (imag c 2)) )) (define (mul-complex c 1 c 2) (make-from-mag-angle (* (mag c 1) (mag c 2)) (+ (angle c 1) (angle c 2)) ))

데이타를 여러방식으로 구현할 때 Multiple Representations • 데이터 구현방식마다 꼬리표를 붙이고. • 데이터 속내용 감추기 원리를 유지하면서. add-complex mul-complex make-from-real-imag make-from-mag-angle real imag angle is-complex? make … make… rectangular representation polar representation

또다른 complex number 구현방식을 품고 있게 하려면? add-complex mul-complex make-from-real-imag make-from-mag-angle real imag angle is-complex? make … make… rectangular representation polar representation make… xyz representation 어디를 어떻게 바꾸어야 할까? 적어도 real, imag, angle, is-complex? 를 확 장해야.

(define (real c) (cond ((not (is-complex? c)) (error)) ((is-rectangular? c) (real-rectangular c)) ((is-polar? c) (real-polar c)) ((is-xyz? c) (real-xyz c)) )) (define (imag c) (cond ((not (is-complex? c)) (error)) ((is-rectangular? c) (imag-rectangular c)) ((is-polar? c) (imag-polar c)) ((is-xyz? c) (imag-xyz c)) )) (define (mag c) (cond ((not (is-complex? c)) (error)) ((is-rectangllar? c) (mag-rectangular c)) ((is-polar? c) (mag-polar c)) ((is-xyz? c) (mag-xyz c)) )) (define (angle c) (cond ((not (is-complex? c)) (error)) ((is-rectangular? c) (angle-rectangular c)) ((is-polar? c) (angle-polar c)) ((is-xyz? c) (angle-xyz c)) ))