Making it useful (i)

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So far, our polynomial is not really useful and there is not much it has in common with a polynomial from mathematics. What is missing? Polynomials may be evaluated. So we want to say: p(3) and get a result for x = 3. How to do that? Obviously some new declarative stuff is necessary. We have to tell the compiler that a polynomial with a following bracket should be evaluated as a function:

 class Polynomial : public vector<double> { 
 public:
     // ...
     // function evaluation
     double operator () (double x) const;
     // ...
 };
 
 double Polynomial::operator () (double x) const
 {
 double  xx = 1; // temporary for powers of x
 double  y = 0;  // will contain the result
     for ( int i=0 ; i<=size()-1 ; ++i )
     {
         y += (*this)[i] * xx;   // add coefficient * x^n
         xx *= x;    // next power
     }
     return y;   // return result
 }
 
 int main()
 {
 Polynomial  p(4);
     p[0] = 1;
     p[4] = 2;
 
     cout << "p = " << p << endl;    // print it
     cout << "p(3.4) = " << p(3.4) << endl;  // evaluate and print it
     return 0;
 }

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We printed only new lines of code with occasionally a few lines of environment to avoid any ambiguities.

Line by line walk through:

Line 5:

Declare: There is a new operator "()" taking one argument of a double returning a double (the second argument is implicit by this)

Line 9:

Implementation of the function evaluation for a polynomial.

Line 28:

Use the function evaluation.

The program will return:

p = 2*x^4 + 1
p(3.4) = 268.267