;; Die ersten drei Zeilen dieser Datei wurden von DrRacket eingefügt. Sie enthalten Metadaten
;; über die Sprachebene dieser Datei in einer Form, die DrRacket verarbeiten kann.
#reader(lib "DMdA-beginner-reader.ss" "deinprogramm")((modname rat) (read-case-sensitive #f) (teachpacks ()) (deinprogramm-settings #(#f write repeating-decimal #f #t none explicit #f ())))
; Schnittstelle rationaler Zahlen:
(provide rat make-rat rat? rat-numerator rat-denominator +rat *rat)

; Eine rationale Zahl besteht aus
; - einem Zähler (integer)
; - einem Nenner (integer)

(define-record-procedures rat
  make-rat-record   ; Konstruktor
  rat?
  (rat-numerator rat-denominator))

(: make-rat-record (integer integer -> rat))
(: rat? (any -> boolean))
(: rat-numerator (rat -> integer))
(: rat-denominator (rat -> integer))

; Erzeuge rationale Zahl in gekürzter Darstellung:
(: make-rat (integer integer -> rat))
(define make-rat
  (lambda (x y)
    (make-rat-record (/ x (gcd x y))
                     (/ y (gcd x y)))))

(define one-third (make-rat 1 3))
(define two-third (make-rat 2 3))
(define one-ninth (make-rat 1 9))


; Berechne das Produkt zweier rationaler Zahlen
(: *rat (rat rat -> rat))

(check-expect (*rat one-third one-third) one-ninth)

#;(define *rat
  (lambda (r1 r2)
    ...(rat-numerator r1) ...(rat-denominator r1)
    ...(rat-numerator r2) ...(rat-denominator r2)
    ...))

#;(define *rat
  (lambda (r1 r2)
    (make-rat
    ...(rat-numerator r1) ...(rat-denominator r1)
    ...(rat-numerator r2) ...(rat-denominator r2)
    ...)))

(define *rat
  (lambda (r1 r2)
    (make-rat
     (* (rat-numerator r1) (rat-numerator r2))
     (* (rat-denominator r1) (rat-denominator r2)))))

; Berechne die Summer zweier rationaler Zahlen
(: +rat (rat rat -> rat))

(check-expect (+rat one-third one-third) two-third)

#;(define +rat
  (lambda (r1 r2)
    (make-rat
    ...(rat-numerator r1) ...(rat-denominator r1)
    ...(rat-numerator r2) ...(rat-denominator r2)
    ...)))

(define +rat
  (lambda (r1 r2)
    (make-rat
      (+ (* (rat-numerator r1) (rat-denominator r2))
         (* (rat-numerator r2) (rat-denominator r1)))
      (* (rat-denominator r1) (rat-denominator r2)))))