CS 3323 Topics in Programming Languages

1. Each rational number should be represented as two integers, the numerator (numer) and the denominator (denom). Thus the fraction 5/6 would be represented as the pair of numbers 5 and 6.
2. A default constructor should initialize each declared rational number to 0, which should be 0/1.
3. There should be constructors with 1 and with 2 parameters, to give a/1 and a/b.
4. The constructors and other functions should prevent a 0 denominator and should prevent a negative denominator. Thus the number -2/3 would be represented by the pair of integers -2 and 3.
5. You should reduce or simplify rationals by dividing out the greatest common divisor.
6. You should overload operators + - * / for the class, using the algorithms from grade school. (Addition does not necessarily have to use the least common multiple, but it could reduce to lowest terms after calculating.)
7. You should overload the operators /TT>< > <= >= != == for the class.
8. You should overload friend functions << and >> to do I/O. The output form should be "17/12". In case the rational number has 1 for a denominator, output in the form 23, rather than 23/1
9. Provide your own copy constructor and your own overloaded assignment operator.
10. Provide a private member function reduce to reduce a fraction to lowest terms.
11. Exercise your code with some interesting examples, including at least a code segment or function that will read an integer n and will calculate the sum, programmed with a loop: 1 - (1/2) + (1/3) - (1/4) + ... + (-1)^(n+1) (1/n) For n = 20 this will be (155685007/232792560).

     // gcd: calculate greatest common divisor or a and b 
     //   assumes both a and b >= 0 
     int gcd(int a, int b)
     {
        if (b == 0) return a;
        return gcd(b, a % b);
     

Rat x; cout << "x = " << x << endl; // should output "x = 0"
Rat y(23); cout << "y = " << y << endl; // should output "y = 23"
Rat z(1769, 551); cout << "z = " << z << endl; // should output "z = 61/19"
Rat w; w = z + z/w; cout << "w = " << w << endl;
Rat u(-858, -492); cout << "u = " << u << endl;
Rat v(z); cout << "z = " << z << endl;

Here is code for a C++ class implementing Complex numbers that is similar to what is needed for this assignment:

1. complexIO3.h
2. complexIO3.cpp
3. complex3.cpp