2.1.1 Example: Arithmetic Operations for Rational NumbersをPythonでやってみた

SICPの2.1.1 Example: Arithmetic Operations for Rational NumbersあたりをPythonでやってみた

scheme

(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))))
;;Representing rational numbers
(define (make-rat n d)
  (cons n d))
(define (numer x)
  (car x))
(define (denom x)
  (cdr x))
(define (print-rat x)
  (newline)
  (display (numer x))
  (display "/")
  (display (denom x)))
(define one-half
  (make-rat 1 2))
(print-rat one-half);1/2
(define one-third (make-rat 1 3))
(print-rat (add-rat one-half one-third));5/6
(print-rat (mul-rat one-half one-third));1/6
(print-rat (add-rat one-third one-third));6/9

(define (make-rat n d)
  (let ((g (gcd n d)))
    (cons (/ n g) (/ d g))))

(define (gcd a b)  ;<-- SICP1.2.5  Greatest Common Divisors
  (if (= b 0)
      a
      (gcd b (remainder a b))))
(print-rat (add-rat one-third one-third));2/3

python

def add_rat(x, y):
    return make_rat(numer(x) * denom(y) + numer(y) * denom(x),
                    denom(x) * denom(y))
def sub_rat(x, y):
    return make_rat(numer(x) * denom(y) - numer(y) * denom(x),
                    denom(x) * denom(y))
def mul_rat(x, y):
    return make_rat(numer(x) * numer(y), denom(x) * denom(y))
def div_rat(x, y):
    return make_rat(numer(x) * denom(y), denom(x) * numer(y))
def equal_rat(x, y):
    return numer(x) * denom(y) == denom(x) * numer(y)
#Representing rational numbers
def make_rat(n, d):
    return [n,d]
def numer(x):
    return x[0]
def denom(x):
    return x[1]
def print_rat(x):
    return "%d/%d" % (numer(x), denom(x))
def one_half():
    return make_rat(1, 2)

print print_rat(one_half())#1/2

def one_third():
    return make_rat(1, 3)
# not one_third but one_third()

print print_rat(add_rat(one_half(), one_third()))#5/6
print print_rat(mul_rat(one_half(), one_third()))#1/6
print print_rat(add_rat(one_third(), one_third()))#6/9

def make_rat(n, d):
    g = gcd(n, d)
    return [n / g, d / g]
def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)
print print_rat(add_rat(one_third(), one_third()))#2/3