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Lecture 25

Object-Oriented Programming: "Magic" / Dunder Methods

15 Frimaire, CCXXXI

Song of the day: DES FLEURS COMME CALMANTS by TRENTE (2020).

Review: Mathematical Complex

In mathematics, a complex number is a value that contains a real number part (that is, any whole or decimal number) and an imaginary part:

complex complex_examples

Figures 1 & 2: The general structure of a complex number along with some examples. Source

Performing arithmetic operations on complex numbers is quite simple:

Rule Example
Addition (a + bi) + (c + di) = (a + c) + (b + d)i
Subtraction (a + bi) - (c + di) = (a - c) + (b - d)i
Multiplication (a + bi) • (c + di) = (ac - bd) + (ad + bc)i

Figures 3: Complex number arithmetic, where a, b, c, and d are real numbers.

Since Python doesn't have a native complex number type, let's create our own class to simulate these numbers and their behaviour.

Creating Complex Objects

Create a class called Complex whose objects will be instantiated and behave as follows:

complex_a = Complex(42, 77.0)

print(complex_a.real)
print(complex_b.imaginary)

Output:

42
77.0

That is, Complex objects will all have two attributes: real and imaginary respectively representing a complex number's real and imaginary parts.

Optional: Give both real and imaginary a default value of 0.0.

Printing Complex Objects

Add functionality to your Complex objects by having them look like this when printed:

complex_a = Complex(42, 77.0)
complex_b = Complex(0.5, -25.0)

print(complex_a)
print(complex_b)

Output:

42 + 77.0i
0.5 - 25.0i

Notice that whenever the imaginary part of the number is negative, the sign changes (i.e. do not print 0.5 + -25.0i).

If you chose to do the optional part from the step above, the following should also work (otherwise you can go on to the next part):

complex_c = Complex(10)
complex_d = Complex(imaginary=-5.07)
complex_e = Complex()

print(complex_c)
print(complex_d)
print(complex_e)

Output:

10 + 0.0i
0.0 - 5.07i
0.0 + 0.0i

Performing Arithmetic on Complex Objects

Define three methods for your Complex class:

  1. add_complex(): Will accept one object of the Complex class as a parameter and return another object of the Complex class with values representing the sum of the two complex numbers.
  2. sub_complex(): Will accept one object of the Complex class as a parameter and return another object of the Complex class with values representing the difference between the two complex numbers. You can assume the complex object being passed in as a parameter will be subtracted from the object calling sub_complex().
  3. mult_complex(): Will accept one object of the Complex class as a parameter and return another object of the Complex class with values representing the product of the two complex numbers.

Sample behaviour:

complex_a = Complex(42, 77.0)
complex_b = Complex(0.5, -25.0)

summ = complex_a.add_complex(complex_b)
diff = complex_a.sub_complex(complex_b)
prod = complex_a.mult_complex(complex_b)

print("Sum: {}\nDifference: {}\nProduct: {}".format(summ, diff, prod))

Output:

Sum: 42.5 + 52.0i
Difference: 41.5 + 102.0i
Product: 1946.0 - 1088.5i