2. Object Mutability¶

We can change the state of a mutable object by making an assignment to one of its instance variables. For example, we could change the numerator of the fraction by assigning a new value to self.num. Likewise, we could do the same thing for self.den.

One place where this type of modification makes sense is when we place a fraction in lowest terms. Lowest terms simply means that the numerator and denominator do not share any common factors. For example, 12/16 is a fraction but it is not in lowest terms since 2 can divide into both 12 and 16. In this case, we call 2 a common divisor. If we divide the numerator and the denominator by a common divisor, we get an equivalent fraction. If we divide by the greatest common divisor, we will get the lowest terms representation. In this case 4 would be the greatest common divisor and the lowest terms representation would be 3/4.

There is a very nice iterative method for computing the greatest common divisor of two integers. Try to run the function on a number of different examples.

def find_gcd(numerator, denominator): while numerator % denominator != 0: old_num = numerator old_den = denominator numerator = old_den denominator = old_num % old_den return denominator print(find_gcd(12, 16))

Now that we have a function that can help us with finding the greatest common divisor, we can use that to implement a fraction method called simplify. We will ask the fraction “to put itself in lowest terms”.

The simplify method will pass the numerator and the denominator to the find_gcd function to find the greatest common divisor. It will then modify itself by dividing its num and its den by that value.

def find_gcd(numerator, denominator): while numerator % denominator != 0: old_num = numerator old_den = denominator numerator = old_den denominator = old_num % old_den return denominator class Fraction: def __init__(self, top, bottom): self.num = top # the numerator is on top self.den = bottom # the denominator is on the bottom def __repr__(self): return str(self.num) + "/" + str(self.den) def simplify(self): common = find_gcd(self.num, self.den) self.num = self.num // common self.den = self.den // common def main(): myfraction = Fraction(12, 16) print(myfraction) myfraction.simplify() print(myfraction) if __name__ == "__main__": main()

There are two important things to note about this implementation. First, the find_gcd function is not a method of the Fraction class. It does not belong to Fraction. Instead it is a function that is used by Fraction to assist in a task that needs to be performed. This type of function is often called a helper function. Second, the simplify method does not return anything. Its job is to modify the object itself. This type of method is known as a mutator method because it mutates or changes the internal state of the object.