html5-img
1 / 6

(define <rat> <pair>) (define (make-rat <function>) (method ((n <integer>) (d <integer>))

(define <rat> <pair>) (define (make-rat <function>) (method ((n <integer>) (d <integer>)) (if (= d 0) (begin (print "zero denominator") (pair 0 1)) (pair n d)))) (define (numer <function>) head) (define (denom <function>) tail) Why not

noreen
Télécharger la présentation

(define <rat> <pair>) (define (make-rat <function>) (method ((n <integer>) (d <integer>))

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. (define <rat> <pair>) (define (make-rat <function>) (method ((n <integer>) (d <integer>)) (if (= d 0) (begin (print "zero denominator") (pair 0 1)) (pair n d)))) (define (numer <function>) head) (define (denom <function>) tail) Why not (define (make-rat <function>) pair) ?

  2. (define rat-add (method ((r1 <rat>) (r2 <rat>)) (bind ((n1 (numer r1)) (d1 (denom r1)) (n2 (numer r2)) (d2 (denom r2))) (make-rat (+ (* n1 d2) (* n2 d1)) (* d1 d2))))) (define rat-mul (method ((r1 <rat>) (r2 <rat>)) (bind ((n1 (numer r1)) (d1 (denom r1)) (n2 (numer r2)) (d2 (denom r2))) (make-rat (* n1 n2) (* d1 d2)))))

  3. (define rat-eq (method ((r1 <rat>) (r2 <rat>)) (bind ((n1 (numer r1)) (d1 (denom r1)) (n2 (numer r2)) (d2 (denom r2))) (= (* n1 d2) (* n2 d1))))) (define rat-leq (method ((r1 <rat>) (r2 <rat>)) (bind ((n1 (numer r1)) (d1 (denom r1)) (n2 (numer r2)) (d2 (denom r2))) (if (>= (* d1 d2) 0) ;;if d1 and d2 have same sign (<= (* n1 d2) (* n2 d1)) (>= (* n1 d2) (* n2 d1))))))

  4. (rat-eq (make-rat 10 8) (make-rat 5 4)) => #t This is correct, since 10/8 = 5/4 But (numer (make-rat 10 8)) => 10 (denom (make-rat 10 8)) => 8 (numer (make-rat 5 4)) => 5 (denom (make-rat 5 4)) => 4 What if I wanted lowest term representation?

  5. (define (make-rat <function>) (method ((n <integer>) (d <integer>)) (if (= d 0) (begin (print "zero denominator") (pair 0 1)) (bind ((g (gcd n d))) (pair (/ n g) (/ d g)))))) Now we have representation in lowest terms: (numer (make-rat 10 8)) => 5 (denom (make-rat 10 8)) => 4 so we can simplify equality testing if we want (or not, if we don’t want): (define rat-eq (method ((r1 <rat>) (r2 <rat>)) (and (= (numer r1) (numer r2)) (= (denom r1) (denom r2)))))

  6. (define (make-rat <function>) (method ((n <integer>) (d <integer>)) (if (= d 0) (begin (print "zero denominator") (pair 0 1)) (bind ((n (if (> d 0) n (- n))) (d (if (> d 0) d (- d))) (g (gcd n d))) (pair (/ n g) (/ d g)))))) Now we can simplify  testing if we want: (define rat-leq (method ((r1 <rat>) (r2 <rat>)) (bind ((n1 (numer r1)) (d1 (denom r1)) (n2 (numer r2)) (d2 (denom r2))) (<= (* n1 d2) (* n2 d1)))))

More Related