A short C++/OO tutorial: (I) Polynomials

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We shall illustrate the concept of object orientation from a simple example borrowed from mathematics. Suppose we would like to implement something like a polynomial. In the beginning it is usually a good idea to think of what we would like to be able to do with our new object. Therefore, we start with an application of a (not yet existing) type Polynomial. Consider the following piece of code:

 // use the polynomial
 int main()  // this is the entry of the main program (called by the operating system)
 {
 Polynomial  p(4);   // create a polynomial of 4th degree
     p[0] = 1;   // 1*x^0
     p[4] = 2;   // 2*x^4
 
     cout << "p = " << p << endl;    // print it
     return 0;
 }

We note: The input is freely formatted and everything behind a "//" is ignored as a comment. What does this program do?

Line by line walk through:

Line 1:

A comment

Line 2:

This subroutine is called by the operating system upon start (main program).

Line 3:

The block containing the subroutine starts here.

Line 4:

A new polynomial of degree 4 is declared and created (constructed). All coefficients will be initialized to zero.

Line 5:

The coefficient of the x⁰ monomial is initialized;

Line 6:

The coefficient of the x⁴ monomial is initialized;

Line 8:

Write the polynomial in some useful notation to the standard output stream (terminal).

Line 9:

Return 0 (success) to the operating system.

Line 10:

The block containing the subroutine ends here.

The output of this piece of code shall be:

p = 2*x^4 + 1