// This ensures that this file is included at most once
// in any program, as there may be multiple include
// statements.
#pragma once

#include <string>

  ////////////////////////
 // Class declarations //
////////////////////////

class Rational;

  ///////////////////////////
 // Function declarations //
///////////////////////////

// All function definitions are in the file 'Rational.cpp'.

// These functions query their arguments, but do not
// change them.

// Calculate p + q.
Rational add( Rational const &p,
              Rational const &q );

// Calculate p + n.
Rational add( Rational const &p,
              int      const  n );

// Calculate n + q.
Rational add( int      const  n,
              Rational const &q );

// Calculate p - q.
Rational sub( Rational const &p,
              Rational const &q );

// Calculate p - n.
Rational sub( Rational const &p,
              int      const  n );

// Calculate n - q.
Rational sub( int      const  n,
              Rational const &q );

// Calculate p*q.
Rational mul( Rational const &p,
              Rational const &q );

// Calculate p*n.
Rational mul( Rational const &p,
              int      const  n );

// Calculate n*q.
Rational mul( int      const  n,
              Rational const &q );

// Calculate p/q.
Rational div( Rational const &p,
              Rational const &q );

// Calculate p/n.
Rational div( Rational const &p,
              int      const  n );

// Calculate n/p.
Rational div( int      const  n,
              Rational const &p );

// Return the additive inverse -p.
Rational negate( Rational const &p );

// Return the multiplicative inverse 1/p.
Rational inverse( Rational const &p );

// Return the absolute value of p.
Rational abs( Rational const &p );

// Determine whether p == q.
bool equal( Rational const &p,
            Rational const &q );

// Determine whether p == n.
bool equal( Rational const &p,
            int      const  n );

// Determine whether n == p.
bool equal( int      const  n,
            Rational const &p );

// Determine whether p != q.
bool unequal( Rational const &p,
              Rational const &q );

// Determine whether p != n.
bool unequal( Rational const &p,
              int      const  n );

// Determine whether n != p.
bool unequal( int      const  n,
              Rational const &p );

// Determine whether p < q.
bool less_than( Rational const &p,
                Rational const &q );

// Determine whether p < n.
bool less_than( Rational const &p,
                int      const  n );

// Determine whether n < p.
bool less_than( int      const  n,
                Rational const &p );

// Determine whether p <= q.
bool less_than_or_equal( Rational const &p,
                         Rational const &q );

// Determine whether p <= n.
bool less_than_or_equal( Rational const &p,
                         int      const  n );

// Determine whether n <= p.
bool less_than_or_equal( int      const  n,
                         Rational const &p );

// Determine whether p >= q.
bool greater_than_or_equal( Rational const &p,
                            Rational const &q );

// Determine whether p >= n.
bool greater_than_or_equal( Rational const &p,
                            int      const  n );

// Determine whether n >= p.
bool greater_than_or_equal( int      const  n,
                            Rational const &p );

// Determine whether p > q.
bool greater_than( Rational const &p,
                   Rational const &q );

// Determine whether p > n.
bool greater_than( Rational const &p,
                   int      const  n );

// Determine whether n > p.
bool greater_than( int      const  n,
                   Rational const &p );

// Return a floating-point approximation of p.
double real( Rational const &p );

// Return a string representation of p.
std::string to_string( Rational const &p );

  ///////////////////////
 // Class definition  //
///////////////////////

// Store the numerator and denominator of a rational number.
class Rational {
  public:
    int numer_;
    int denom_;
};