Writing Your Own Class Methods

In the lecture, we went through the basic construction of a Rational class.

However, there is a lot of functionality left to implement. That is left up to you.

Download the example class, and get started.

class Rational:
    """An example Rational class.

    This class attempts to implement rational numbers, as an *exercise*.
    For actual use cases, use the rationals available from software such as sympy,
    sage, or the builtin numbers.Rational class.

    Attributes
    ----------
    numerator : int
        Numerator of the rational.
    denominator : int
        Denominator of the rational.
    """

    def __init__(self,numerator, denominator):
        """Creates a new Rational from numerator and denominator.

        Parameters
        ----------
        numerator : int
            Intended numerator of the rational.
        denominator : int
            Intended denominator of the rational.
        """
        self.numerator = numerator
        self.denominator = denominator


    def __add__(self,other):
        # Note that special "magic" methods (except __init__), by default, don't have docstrings.
        # Their behavior should be apparent from the mathematics of an object-
        # If not, feel free to explain in the class docsting.
        if isinstance(other, Rational):
            new_numerator = self.numerator*other.denominator+self.denominator*other.numerator
            new_denominator = self.denominator*other.denominator
            return Rational(new_numerator, new_denominator)
        if isinstance(other, int):
            new_numerator = self.numerator + other*self.denominator
            return Rational(new_numerator,self.denominator)
        raise NotImplementedError("Cannot Add Types {} and {}".format("Rational",type(other)))

    def __neg__(self):
        return Rational(-self.numerator, self.denominator)

    def __sub__(self,other):
        return self+(-other)

    def __repr__(self):
        return "Rational({numerator},{denominator})".format(**self.__dict__)

    def __radd__(self,other):
        return self+other

    def __rsub__(self,other):
        return -self+other

Graded Assignment: Extend the Rational class with the following behaviors:

String representation as "a/b" for printing

Initializing from Integers - e.g. Rational(5)

Left and Right Multiplication and Division by:

Integers

Rationals

Integer Part - e.g. int(Rational(5,2)) should return the integer 2.

Equality Checking (including == and !=)

All 4 Inequality Checks

Absolute Value

Raising ZeroDivisionError whenever asked to divide by 0, in initialization or arithmetic

Upload a .py file containing your class - and no other code - to Brightspace.

Additional Behaviors

Here is a list of some useful additional behaviors you can practice implementing:

Automatic reducing of fractions (hint: use the statement from math import gcd to get a simple gcd function in your file.)
Initialization from floating point numbers
Conversion to floating point numbers
An implementation to check if an integer, like the floating point .is_integer function
Exponentiation
Modulo operator %
Truthiness with __bool__ - investigate the truthiness of integers to see what behavior would be expected.

If you want even more of a challenge, create your own Gaussian integer class, and your own GaussianRational class - try to design behaviors so you can reuse as much as possible without redefining!