Rational numbers
================

This example introduces a simple class representing rational numbers
and a collection of functions that perform arithmetic and comparisons
on rational numbers.

Files
=====

    Rational.hpp
        Contains the declaration and definition of the Rational class,
        together with the declarations of all functions that operate on
        Rational objects.

    Rational.cpp
        Contains the definitions of the functions declared in
        Rational.hpp.

    main.cpp
        Contains examples demonstrating how to create Rational objects
        and call the functions that operate on them.

The Rational class
==================

A Rational object stores two integers:

    numer_
    denom_

These represent the numerator and denominator of a rational number.

For example,

    Rational p{ 3, 4 };

represents the rational number 3/4.

Functions are provided for operations including:

    - addition,
    - subtraction,
    - multiplication,
    - division,
    - additive inverses,
    - multiplicative inverses,
    - absolute values,
    - comparisons,
    - floating-point approximations, and
    - conversion to a string.

Many of the functions are overloaded so that rational numbers can
also be used with integers. For example,

    add( p, q )
    add( p, 2 )
    add( 2, q )

call three different functions with the same identifier.

Important limitations
=====================

This is a deliberately simple implementation intended to demonstrate
classes and functions.

Rational numbers are not automatically reduced to lowest terms. Thus,
for example, 2/4 may be stored as 2/4 rather than 1/2. The comparison
functions nevertheless compare the values of the rational numbers
rather than simply comparing their stored numerators and denominators.

A valid Rational object must have a non-zero denominator. At this
stage, the class itself does not prevent a programmer from creating
an invalid object such as

    Rational p{ 3, 0 };

Later, constructors can be used to enforce requirements such as this
when an object is created.

Purpose
=======

This example demonstrates classes, function overloading, const
references, assertions, and the reuse of existing functions when
implementing related operations.

Later, these operations could be implemented using member functions
and overloaded operators so that rational-number expressions more
closely resemble ordinary mathematical notation.

Compiling
=========

Compile both main.cpp and Rational.cpp. For example:

    g++ -std=c++17 -Wall -Wextra -pedantic main.cpp Rational.cpp