;;複素数zがあるとして

;;直交座標形式：実数部を取得
(real-part z)
;;直交座標形式：虚数部を取得
(imag-part z)

;;直交座標形式で複素数を構成するコンストラクタ
(make-from-real-imag (real-part z) (imag-part z))

;;同様に極座標形式のコンストラクタと選択子
(make-from-mag-ang (magnitude z) (angle z))

;;それらを組み合わせて、抽象的な四則演算の手続きを実装する
(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))))

(trace add-complex)
(trace sub-complex)
(trace mul-complex)
(trace div-complex)

;;;;;直交座標形式ベースの実装
(define (square n)
  (* n n))

(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))))

;;テスト
(let ((z (make-from-real-imag 100 50)))
  (let ((z2 (make-from-mag-ang (magnitude z) (angle z))))
    (display z)
    (display z2)))

;;CALL magnitude (100 . 50)
;;RETN magnitude 111.80339887498948
;;CALL angle (100 . 50)
;;RETN angle 0.4636476090008061
;;CALL make-from-mag-ang 111.80339887498948 0.4636476090008061
;;RETN make-from-mag-ang (100.0 . 50.0)
;;z  = (100 . 50)
;;z2 = (100.0 . 50.0)

;;四則演算をテスト
(let ((z1 (make-from-real-imag 100 50))
      (z2 (make-from-real-imag 30 20)))
  (add-complex z1 z2)
  ;;CALL add-complex (100 . 50) (30 . 20)
  ;;RETN add-complex (130 . 70)
  (sub-complex z1 z2)
  ;;CALL sub-complex (100 . 50) (30 . 20)
  ;;RETN sub-complex (70 . 30)
  (mul-complex z1 z2)
  ;;CALL mul-complex (100 . 50) (30 . 20)
  ;;RETN mul-complex (2000.0000000000005 . 3499.999999999999)
  (div-complex z1 z2)
  ;;CALL div-complex (100 . 50) (30 . 20)
  ;;RETN div-complex (3.076923076923077 . -0.3846153846153845)
  )

;;;;;;;;;極座標形式ベースの実装
(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))

;;テスト
(trace imag-part)
(trace real-part)
(let ((z1 (make-from-mag-ang 111.8 0.463)))
  (let ((z2 (make-from-real-imag (real-part z1) (imag-part z1))))
    (display z1)
    (display z2)))

;;CALL real-part (111.8 . 0.463)
;;RETN real-part 100.02931844795427
;;CALL imag-part (111.8 . 0.463)
;;RETN imag-part 49.93371056548626
;;z1 = (111.8 . 0.463)
;;z2 = (111.8 . 0.463)

;;四則演算をテスト
(let ((z1 (make-from-real-imag 100 50))
      (z2 (make-from-real-imag 30 20)))
  (add-complex z1 z2)
  ;;CALL add-complex (111.80...98948 . 0.463...8061) (36.055...63989 . 0.58...5675)
  ;;RETN add-complex (147.648230602334 . 0.49394136891958124)
  (sub-complex z1 z2)
  ;;CALL sub-complex (111.80...98948 . 0.463...8061) (36.055...63989 . 0.58...5675)
  ;;RETN sub-complex (76.15773105863909 . 0.4048917862850835)
  (mul-complex z1 z2)
  ;;CALL mul-complex (111.80...98948 . 0.463...8061) (36.055...63989 . 0.58...5675)
  ;;RETN mul-complex (4031.1288741492745 . 1.0516502125483735)
  (div-complex z1 z2)
  ;;CALL div-complex (111.80...98948 . 0.463...8061) (36.055...63989 . 0.58...5675)
  ;;RETN div-complex (3.1008683647302115 . -0.12435499454676141)
  )

;;確認
(real-part (make-from-mag-ang 147.648230602334 0.49394136891958124))
;;129.99999999999997

(imag-part (make-from-mag-ang 147.648230602334 0.49394136891958124))
;;70.0