Exercise 2.1
Exercise 2.1: Define a better version of make-rat that handles both positive and negative arguments. make-rat should normalize the sign so that if the rational number is positive, both the numerator and denominator are positive, and if the rational number is negative, only the numerator is negative.
第一章學完了，今天開始學習第二章，目前還沒有遇到什麼問題，這道題也比較簡單，只要注意到“分子分母同時為正，或者分子為負，分母為正，不需要改變符號；分子分母同時為負,或者分子為正,分母為負,分子分母都需要改變符號”這一點，就可以很容易地實現題目要求。
; (make-rat ⟨n⟩ ⟨d ⟩) returns the rational number whose numerator is the integer ⟨n⟩ and whose denominator is the integer ⟨d ⟩.
(define (make-rat n d)
(let ((n (/ n (gcd n d)))
(d (/ d (gcd n d))))
; 分子分母同時為正，或者分子為負，分母為正，不需要改變符號
; 分子分母同時為負,或者分子為正,分母為負,分子分母都需要改變符號
(if (or (and (positive? n) (positive? d))
(and (negative? n) (positive? d)))
(cons n d)
(cons (- 0 n) (- 0 d)))))
; (numer ⟨x⟩) returns the numerator of the rational number ⟨x⟩.
(define (numer x) (car x))
; (denom ⟨x⟩) returns the denominator of the rational number ⟨x⟩.
(define (denom x) (cdr x))
(define (add-rat x y)
(make-rat (+ (* (numer x) (denom y))
(* (numer y) (denom x)))
(* (denom x) (denom y))))
(define (sub-rat x y)
(make-rat (- (* (numer x) (denom y))
(* (numer y) (denom x)))
(* (denom x) (denom y))))
(define (mul-rat x y)
(make-rat (* (numer x) (numer y))
(* (denom x) (denom y))))
(define (div-rat x y)
(make-rat (* (numer x) (denom y))
(* (denom x) (numer y))))
(define (equal-rat? x y)
(= (* (numer x) (denom y))
(* (numer y) (denom x))))
(define (print-rat x)
(newline)
(display (numer x))
(display "/")
(display (denom x)))
(print-rat (make-rat -1 2))
(print-rat (make-rat 1 2))
(define neg-one-half (make-rat -1 2))
(define one-third (make-rat 1 3))
(print-rat (add-rat neg-one-half one-third))
(print-rat (add-rat neg-one-half neg-one-half))
(print-rat (sub-rat neg-one-half one-third))
(print-rat (mul-rat neg-one-half one-third))
(print-rat (div-rat neg-one-half one-third))
; 執行結果
-1/2
1/2
-1/6
-1/1
-5/6
-1/6
-3/2
可以看出這裡還是有改進空間，-1/1 寫成 -1 就行，利用 gcd 就可以實現，不過我暫時不改了，也許後面有道題目會讓做這個事情，到時候再說。