The Polynom.h file: // IMPORTANT: Do not modify the contents of this file // Pol

Question

The Polynom.h file:

// IMPORTANT: Do not modify the contents of this file   
// Polynom.h
// A simple ploynomial class of degree n
#ifndef POLYNOM_H
#define POLYNOM_H
#include <vector>
#include <iostream>
using namespace std;
class Polynom {
public:
// Postcondition: Creates an "empty" polynomial
Polynom();

// Postcondition: Creates a polynomial with coefficients provided in the vector parameter;   
// the degree of the polynomial is the size of the vector plus 1
Polynom(const vector<int>& coeff);

// Basic arithmetic operations:
// Operator +
// Postcondition: The sum of this polynomial and RHS is returned; this   
// and RHS are unchanged   
const Polynom& operator+(const Polynom& RHS) const;

// Operator -
// Postcondition: The RHS is subtracted from this and the result is returned; this   
// and RHS are unchanged   
const Polynom& operator-(const Polynom& RHS) const;

// Evaluation;   
// Operator ()   
// Postcondition: this polynomial is evaluated at x and the the value
// is returned; this polynomial is unchanged
double operator()(double x) const;

// Set the coefficient of x^k
// Precondition: k >= 0 and k <= n, where n is the degree of this polynomial   
// Postcondition: If precondition is met, then coefficient of x^k is changed to
// c and returns true; otherwise no change is made and returns false;   
bool setCoeff(int k, int c);

// Get the coefficient of x^k
// Precondition: k >= 0 and k <= n, where n is the degree of this polynomial   
// Postcondition: If precondition is met, then the function assigns the
// coefficient of x^k in parameter c and return true;
// otherwise returns false and parameter c remains unchanged
bool getCoeff(int k, int& c);

// Stream insertion   
// Postcondition: Write the polynomial onto stream ostr.
ostream& insert(ostream& ostr);

private:
vector<int> P; // coefficients of the polynomial; P[i] is the coefficient
// of x raised to power i;   

};

// overloaded stream to write the polynomial RHS onto stream Out
ostream& operator<<(ostream& Out, const Polynom& RHS);
#endif

In this assignment you will define, implement, and test a C+ class called Polynom to represent and use polynomials, A polynonial function of independent variable r can be written as The highest power of variable that occurs in the polya (in this case ) is called the degree of the polynomial. The quantities an,do are constants known as coefficients. In this assignment coefficients are int type and can be positive, negative, or 0. A basic operation for polynomials is to evaluate a polynomial at a specific value of r. For example, we can evaluate the quadratic polynomial r) q(z) =12 + 5r + 6 for for r-2, by writing the polynomial in the following form, and then substituting2 to obtain, g(2) ((25)2 +6)-(7)2+6)-(146)-20 We can add two polynomials and subtract one from the other. Examples are shown below p(z) = 3r, + 2r2 +1 + 16, q(1)-12 + 51 + 6 -3r' + 3r2 +6r +22 3+(-4)r+10 p(z) + q(z) _ (3 + 0)rs + (2 + 1):r" + (1 +5)| + (16 + 6) p(r)- g(r)-(3-0)(2 (1-5)(16-6) A simple way to represent a polynomial object of degree n is to use a vector of length n+1 to store the coefficients. For example, the polynomsp and q can be represented by vectors of length 4 and 3, respectively. p: 3 21 16, :1 5 6 It is possible that some of the coefficients in a polynomial are 0. Considr the polynomial r(r) = 5r9 + 2A + 19 where the largest power of is 9 so that we need a vector of length 10 to store the polynomial: r:50000 2000 6 This ament asks you to implement the functions that appear in Polynom.cc according to the specification provided in the decription given above.

Explanation / Answer

#define POLYNOM_H
#include <vector>
#include <iostream>
using namespace std;
class Polynom {
public:
// Postcondition: Creates an "empty" polynomial
Polynom();

// Postcondition: Creates a polynomial with coefficients provided in the vector parameter;   
// the degree of the polynomial is the size of the vector plus 1
Polynom(const vector<int>& coeff);

// Basic arithmetic operations:
// Operator +
// Postcondition: The sum of this polynomial and RHS is returned; this   
// and RHS are unchanged   
const Polynom& operator+(const Polynom& RHS) const;

// Operator -
// Postcondition: The RHS is subtracted from this and the result is returned; this   
// and RHS are unchanged   
const Polynom& operator-(const Polynom& RHS) const;

// Evaluation;   
// Operator ()   
// Postcondition: this polynomial is evaluated at x and the the value
// is returned; this polynomial is unchanged
double operator()(double x) const;

// Set the coefficient of x^k
// Precondition: k >= 0 and k <= n, where n is the degree of this polynomial   
// Postcondition: If precondition is met, then coefficient of x^k is changed to
// c and returns true; otherwise no change is made and returns false;   
bool setCoeff(int k, int c);

// Get the coefficient of x^k
// Precondition: k >= 0 and k <= n, where n is the degree of this polynomial   
// Postcondition: If precondition is met, then the function assigns the
// coefficient of x^k in parameter c and return true;
// otherwise returns false and parameter c remains unchanged
bool getCoeff(int k, int& c);

// Stream insertion   
// Postcondition: Write the polynomial onto stream ostr.
ostream& insert(ostream& ostr);

private:
vector<int> P; // coefficients of the polynomial; P[i] is the coefficient
// of x raised to power i;   

};

// overloaded stream to write the polynomial RHS onto stream Out
ostream& operator<<(ostream& Out, const Polynom& RHS);
#endif

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