complnum-tags.scm

; Operations on complex numbers

(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))))


; Tag operations

(define (attach-tag type-tag contents)
  (cons type-tag contents))
(define (type-tag datum)
  (if (pair? datum)
      (car datum)
      (error "Bad tagged datum -- TYPE-TAG" datum)))
(define (contents datum)
  (if (pair? datum)
      (cdr datum)
      (error "Bad tagged datum -- CONTENTS" datum)))

; Data definition for complex numbers

; Ben's definition (uses rectangular form)

(define (real-part-rect z) (car z))
(define (imag-part-rect z) (cdr z))
(define (magnitude-rect z)
  (sqrt (+ (square (real-part-rect z))
	   (square (imag-part-rect z)))))
(define (angle-rect z)
  (atan (imag-part-rect z) (real-part-rect z)))
(define (make-from-real-imag-rect x y)
  (attach-tag 'rectangular (cons x y)))
(define (make-from-mag-ang-rect r a)
  (attach-tag 'rectangular (cons (* r (cos a)) (* r (sin a)))))

; Alyssa's definition (uses polar form)

(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 version

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

(define (real-part z)
  (cond ((rectangular? z) (real-part-rect (contents z)))
	((polar? z) (real-part-polar (contents z)))
	(else (error "Unknown type -- REAL-PART" z))))
(define (imag-part z)
  (cond ((rectangular? z) (imag-part-rect (contents z)))
	((polar? z) (imag-part-polar (contents z)))
	(else (error "Unknown type -- REAL-PART" z))))
(define (magnitude z)
  (cond ((rectangular? z) (magnitude-rect (contents z)))
	((polar? z) (magnitude-polar (contents z)))
	(else (error "Unknown type -- REAL-PART" z))))
(define (angle z)
  (cond ((rectangular? z) (angle-rect (contents z)))
	((polar? z) (angle-polar (contents z)))
	(else (error "Unknown type -- REAL-PART" z))))
(define (make-from-real-imag x y)
  (make-from-real-imag-rect x y))
(define (make-from-mag-ang r a)
  (make-from-mag-ang-polar r a))