10.10 Operator Overloading

• Can use operator overloading to define how Python’s operators should handle objects of your own types
• Can overload most operators
• For every overloadable operator, class object defines a special method
  • e.g., __add__ for addition (+) or __mul__ for multiplication (*)
• Overriding these methods enables you to define how a given operator works for objects of your custom class
• Complete list of special methods

  https://docs.python.org/3/reference/datamodel.html#special-method-names

Operator Overloading Restrictions

• Precedence cannot be changed by overloading
• Left-to-right or right-to-left grouping of an operator cannot be changed
• “Arity” of an operator—whether it’s unary or binary—cannot be changed
• Cannot create new operators
• How an operator works on objects of built-in types cannot be changed
• Works only with objects of custom classes or with a mixture of an object of a custom class and an object of a built-in type

Complex Numbers

• We’ll define a class named Complex that represents complex numbers
• Complex numbers, like –3 + 4i and 6.2 – 11.73i, have the form

  realPart `+` imaginaryPart `* i`
  

• i is the square root of -1
• We'll overload + and +=

10.10.1 Test-Driving Class Complex

from complexnumber import Complex

• Create and display a couple of Complex objects

x = Complex(real=2, imaginary=4)

x

(2 + 4i)

y = Complex(real=5, imaginary=-1)

y

(5 - 1i)

• Use the + operator to add the Complex objects x and y
• Adds the real parts of the two operands and the imaginary parts of the two operands, then returns a new Complex object

x + y

(7 + 3i)

• + does not modify either of its operands

x

(2 + 4i)

y

(5 - 1i)

• Use += to add y to x and store the result in x
• += operator modifies its left operand

x += y

x

(7 + 3i)

y

(5 - 1i)

10.10.2 Class Complex Definition

Method __init__

• Initializes the real and imaginary data attributes

# complexnumber.py
"""Complex class with overloaded operators."""

class Complex:
    """Complex class that represents a complex number 
    with real and imaginary parts."""

    def __init__(self, real, imaginary):
        """Initialize Complex class's attributes."""
        self.real = real
        self.imaginary = imaginary

Overloaded + Operator

• Overridden special method __add__ defines how to overload the + operator

def __add__(self, right):
        """Overrides the + operator."""
        return Complex(self.real + right.real, 
                       self.imaginary + right.imaginary)

• Methods that overload binary operators must provide two parameters
  • the first (self) is the left operand
  • the second (right) is the right operand
• We do not modify the contents of either of the original operands
  • Matches our intuitive sense of how this operator should behave

Overloaded += Augmented Assignment

• Override special method __iadd__ to define how += adds two Complex objects

def __iadd__(self, right):
        """Overrides the += operator."""
        self.real += right.real
        self.imaginary += right.imaginary
        return self

• Augmented assignments modify their left operands, so method __iadd__ modifies the self object, which represents the left operand, then returns self

Method __repr__

def __repr__(self):
        """Return string representation for repr()."""
        return (f'({self.real} ' + 
                ('+' if self.imaginary >= 0 else '-') +
                f' {abs(self.imaginary)}i)')

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