# Fraction Class in Python

I decided to train myself in OOP with a simple perfect precision Fraction class.

from __future__ import division
import doctest

class Fraction:
"""
Implements a Fraction Class with perfect precision
operations and utility methods. The built-in operators
are overwritten to provide a more natural interface.
"""
def __init__(self,num,den):
if den == 0:
raise ValueError("Denominator must not be zero.")

self.num = num
self.den = den

@staticmethod
def greatest_common_divisor(a,b):
"""
Returns the greatest number 'n' existing such
that a % n == 0 and b % n == 0.
This number may be one if 'a' and 'b' are coprimes.

>>> Fraction.greatest_common_divisor(20,15)
5
"""
def common(a,b):
return [i for i in a if i in b]

def div(n):
return [i for i in range(1,n+1) if n % i == 0]

return max(common(div(a),div(b)))

@staticmethod
def invert(fraction):
"""
Returns a fraction where the numerator is the previous
denominator and vice-versa.

>>> Fraction.invert(Fraction(3,5))
5/3
"""
return Fraction(fraction.den,fraction.num)

def from_string(text):
"""
Generates a Fraction object from a string rapresentation
of two integers seperated by '/'.

>>> Fraction.from_string('4/9') + Fraction.from_string('2/18')
5/9
"""
return Fraction(*[int(i) for i in text.split('/')])

def simplify(self):
"""
Returns an eqivalent but simpler Fraction.

>>> Fraction.simplify(Fraction(210,20))
21/2
"""
fact = self.greatest_common_divisor(self.num,
self.den)
return Fraction(self.num // fact, self.den // fact)

def __mul__(self,fraction):
"""
Fraction multiplication.

>>> Fraction(4,3) * Fraction(1,20)
1/15
"""
return Fraction.simplify(
Fraction(self.num*fraction.num,
self.den*fraction.den))

"""

>>> Fraction(4,9) + Fraction(11,7)
127/63
"""
common_den = self.greatest_common_divisor(
self.den,fraction.den)
num1 = self.num * fraction.den
num2 = fraction.num * self.den
return Fraction.simplify(
Fraction(num1+num2, fraction.den*self.den))

def __sub__(self,fraction):
"""
Fraction subtraction.

>>> Fraction(1,2) - Fraction(1,3)
1/6
"""
return self + Fraction(-fraction.num,
fraction.den)

def __truediv__(self,fraction):
"""
Fraction division.

>>> Fraction(4,8) / Fraction(9,2)
1/9
"""
return self * self.invert(fraction)

def __repr__(self):
"""
Returns a printable representation of the fraction
that can also be fed back into the class via
'Fraction.from_string'.
This method is called automatically on printing.

>>> Fraction(5,8)
5/8
>>> Fraction(2,9)
2/9
"""
return '{}/{}'.format(self.num, self.den)

def main():
doctest.testmod()

if __name__ == "__main__":
main()


The from_string() function is missing a @staticmethod decorator, and thus does not work in Python 2.

Your greatest_common_divisor() function works using brute force: it literally tests every possible divisor and picks the greatest one that is common to both. A much faster method is the Euclidean Algorithm.

@staticmethod
def gcd(a, b):
while b:
a, b = b, a % b
return a


Validation and error handling could be tightened up a bit.

• The rejection of floating-point arguments is inconsistent:

>>> Fraction(3.14, 1)
3.14/1
>>> Fraction.from_string('3.14/1')
Traceback (most recent call last):
[…]
File "fraction.py", line 55, in <listcomp>
return Fraction(*[int(i) for i in text.split('/')])
ValueError: invalid literal for int() with base 10: '3.14'

• Instantiating a Fraction with strings initially appears to work, but fails in an odd way later. Either both of these statements should work, or both should fail.

>>> Fraction('1', '3')
1/3
>>> Fraction('1', '3') + Fraction('2', '3')
Traceback (most recent call last):
[…]
File "fraction.py", line 32, in div
return [i for i in range(1,n+1) if n % i == 0]
TypeError: Can't convert 'int' object to str implicitly

• In Fraction.from_string(), the abstraction is slightly leaky. I would prefer to see a ValueError instead of the following:

>>> Fraction.from_string('1/3/5')
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "fraction.py", line 55, in from_string
return Fraction(*[int(i) for i in text.split('/')])
TypeError: __init__() takes 3 positional arguments but 4 were given

• Personally, I would choose to raise a ZeroDivisionError if the denominator is 0.

>>> Fraction(1, 0)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "fraction.py", line 13, in __init__
raise ValueError("Denominator must not be zero.")
ValueError: Denominator must not be zero.


From the docs:

[__repr__] should look like a valid Python expression that could be used to recreate an object with the same value (given an appropriate environment).

Your current __repr__ should really be renamed __str__, and replaced by something like:

 def __repr__(self):
return 'Fraction({0.num}, {0.den})'.format(self)


invert needs access to the class, so should probably be a @classmethod rather than @staticmethod:

@classmethod
def invert(cls, fraction):
"""
Returns a fraction where the numerator is the previous
denominator and vice-versa.

>>> Fraction.invert(Fraction(3, 5))
5/3
"""
return cls(fraction.den, fraction.num)


This factors out the explicit class name from the function, making it work better with any future inheritance. Note that I've also added some extra spaces; see the style guide. You could alternatively implement it as a standard instance method, then call it like Fraction(3, 5).invert().

Similarly, you can remove the explicit class from from_string by making it a class method (currently it's an instance method without a self parameter, so won't work in Python 2.x):

@classmethod
def from_string(cls, text):
"""
Generates a Fraction object from a string rapresentation
of two integers seperated by '/'.

>>> Fraction.from_string('4/9') + Fraction.from_string('2/18')
5/9
"""
return cls(*[int(i) for i in text.split('/')])


You can also simplify with e.g. cls(*map(int, text.split('/')).

Where you return a new Fraction from an instance method, you can access the class less explicitly with self.__class__(...).

You don't need to implement greatest_common_divisor yourself; Python has fractions.gcd.

• Arguably, reusing fractions.gcd is cheating. You might as well reuse the entire fractions.Fraction class. Commented Mar 6, 2015 at 3:05
• @200_success fair point! But if the objective was learning OOP, implementing gcd isn't really necessary. Commented Mar 6, 2015 at 7:15