;;;  From SICP section 2.4.1: Complex Numbers
;;;  Multiple Representations

(define (add-complex z1 z2)
  (make-from-real-imag
   (+ (real-part z1) (real-part z2))
   (+ (imag-part z1) (imag-part z2))))

(define (sub-complex z1 z2)
  (make-from-real-imag
   (- (real-part z1) (real-part z2))
   (- (imag-part z1) (imag-part z2))))

(define (mul-complex z1 z2)
  (make-from-mag-ang
   (* (magnitude z1) (magnitude z2))
   (+ (angle z1) (angle z2))))

(define (div-complex z1 z2)
  (make-from-mag-ang
   (/ (magnitude z1) (magnitude z2))
   (- (angle z1) (angle z2))))


;; Ben (rectangular)

(define (real-part z) (car z))

(define (imag-part z) (cdr z))

(define (magnitude z)
  (sqrt (+ (square (real-part z))
	   (square (imag-part z)))))

(define (angle z)
  (atan (imag-part z) (real-part z)))

(define (make-from-real-imag x y)
  (cons x y))

(define (make-from-mag-ang r a) 
  (cons (* r (cos a)) (* r (sin a))))

;; Alyssa (polar)

(define (real-part z)
  (* (magnitude z) (cos (angle z))))

(define (imag-part z)
  (* (magnitude z) (sin (angle z))))

(define (magnitude z) (car z))

(define (angle z) (cdr z))

(define (make-from-real-imag x y) 
  (cons (sqrt (+ (square x)
		 (square y)))
        (atan y x)))

(define (make-from-mag-ang r a)
  (cons r a))

;;;From SICP section 2.4.2: Tagged Data

(define (attach-tag type-tag contents)
  (cons type-tag contents))

(define (type-tag datum)
  (if (pair? datum)
      (car datum)
      (error "Bad datum -- TYPE-TAG"
	     datum)))

(define (contents datum)
  (if (pair? datum)
      (cdr datum)
      (error "Bad datum -- CONTENTS"
	     datum)))

;;; Predicates

(define (rectangular? z)
  (eq? (type-tag z) 'rectangular))

(define (polar? z)
  (eq? (type-tag z) 'polar))

;; Ben (rectangular)

(define (real-part-rectangular z)
  (car z))

(define (imag-part-rectangular z)
  (cdr z))

(define (magnitude-rectangular z)
  (sqrt
   (+ (square
       (real-part-rectangular z))
      (square
       (imag-part-rectangular z)))))

(define (angle-rectangular z)
  (atan (imag-part-rectangular z)
        (real-part-rectangular z)))

(define (make-from-real-imag-rectangular x y)
  (attach-tag 'rectangular (cons x y)))

(define (make-from-mag-ang-rectangular r a) 
  (attach-tag 'rectangular
     (cons (* r (cos a))
	   (* r (sin a)))))

;; Alyssa (polar)

(define (real-part-polar z)
  (* (magnitude-polar z)
     (cos (angle-polar z))))

(define (imag-part-polar z)
  (* (magnitude-polar z)
     (sin (angle-polar z))))

(define (magnitude-polar z) (car z))

(define (angle-polar z) (cdr z))

(define (make-from-real-imag-polar x y) 
  (attach-tag 'polar
     (cons (sqrt (+ (square x) (square y)))
	   (atan y x))))

(define (make-from-mag-ang-polar r a)
  (attach-tag 'polar (cons r a)))

;; Generic selectors

(define (real-part z)
  (cond ((rectangular? z) 
         (real-part-rectangular (contents z)))
        ((polar? z)
         (real-part-polar (contents z)))
        (else
	 (error "Unknown -- REAL-PART" z))))

(define (imag-part z)
  (cond ((rectangular? z)
         (imag-part-rectangular (contents z)))
        ((polar? z)
         (imag-part-polar (contents z)))
        (else
	 (error "Unknown -- IMAG-PART" z))))

(define (magnitude z)
  (cond ((rectangular? z)
         (magnitude-rectangular (contents z)))
        ((polar? z)
         (magnitude-polar (contents z)))
        (else
	 (error "Unknown -- MAGNITUDE" z))))

(define (angle z)
  (cond ((rectangular? z)
         (angle-rectangular (contents z)))
        ((polar? z)
         (angle-polar (contents z)))
        (else
	 (error "Unknown -- ANGLE" z))))

;; Constructors for complex numbers

(define (make-from-real-imag x y)
  (make-from-real-imag-rectangular x y))

(define (make-from-mag-ang r a)
  (make-from-mag-ang-polar r a))

;;; SICP section 2.4.3

(define (install-rectangular-package)
  ;; internal procedures
  (define (real-part z) (car z))
  (define (imag-part z) (cdr z))
  (define (make-from-real-imag x y) (cons x y))
  (define (magnitude z)
    (sqrt (+ (square (real-part z))
             (square (imag-part z)))))
  (define (angle z)
    (atan (imag-part z) (real-part z)))
  (define (make-from-mag-ang r a) 
    (cons (* r (cos a)) (* r (sin a))))

  ;; interface to the rest of the system
  (define (tag x) (attach-tag 'rectangular x))
  (put 'real-part '(rectangular) real-part)
  (put 'imag-part '(rectangular) imag-part)
  (put 'magnitude '(rectangular) magnitude)
  (put 'angle '(rectangular) angle)
  (put 'make-from-real-imag 'rectangular
       (lambda (x y)
	 (tag (make-from-real-imag x y))))
  (put 'make-from-mag-ang 'rectangular
       (lambda (r a)
	 (tag (make-from-mag-ang r a))))
  'done)

(define (install-polar-package)
  ;; internal procedures
  (define (magnitude z) (car z))
  (define (angle z) (cdr z))
  (define (make-from-mag-ang r a) (cons r a))
  (define (real-part z)
    (* (magnitude z) (cos (angle z))))
  (define (imag-part z)
    (* (magnitude z) (sin (angle z))))
  (define (make-from-real-imag x y) 
    (cons (sqrt (+ (square x) (square y)))
          (atan y x)))

  ;; interface to the rest of the system
  (define (tag x) (attach-tag 'polar x))
  (put 'real-part '(polar) real-part)
  (put 'imag-part '(polar) imag-part)
  (put 'magnitude '(polar) magnitude)
  (put 'angle '(polar) angle)
  (put 'make-from-real-imag 'polar
       (lambda (x y)
	 (tag (make-from-real-imag x y))))
  (put 'make-from-mag-ang 'polar
       (lambda (r a)
	 (tag (make-from-mag-ang r a))))
  'done)

(define (apply-generic op . args)
  (let ((type-tags (map type-tag args)))
    (let ((proc (get op type-tags)))
      (if proc
          (apply proc (map contents args))
          (error
            "No method -- APPLY-GENERIC"
            (list op type-tags))))))


;; Generic selectors

(define (real-part z)
  (apply-generic 'real-part z))
(define (imag-part z)
  (apply-generic 'imag-part z))
(define (magnitude z)
  (apply-generic 'magnitude z))
(define (angle z)
  (apply-generic 'angle z))


;; Constructors for complex numbers
(define (make-from-real-imag x y)
  ((get 'make-from-real-imag 'rectangular)
   x y))

(define (make-from-mag-ang r a)
  ((get 'make-from-mag-ang 'polar)
   r a))