# C++ polynomial object project

After doing the object stuff in the C++ course, I tried to make a polynomial object.
I also defined the +, -, * operators and I put in a `static` method.
It’s almost complete … I’ll put it on GitHub when its finished.
I’d love some suggestions on how to improve it.

Here’s part of the code. (It’s not the whole thing.)

#include <iostream> #include <string> #include <sstream> int const MAX_DEGREE = 15; double pow(double num, int exp) { // does integer powers of num bool negative_exponent = (exp < 0); if (exp < 0) { exp = exp * -1; }; if (num == 0) { return 0.0; } else if (exp == 0) { return 1.0; } else if (exp == 1) { return num; } double product = 1.0; int i; for (i = 1; i <= exp; i++) { product = product * num; } if (negative_exponent) { return 1.0 / product; } else { return product; } } double abs(double num) { if (num < 0) { return -1 * num; } else { return num; } } std::string to_string(double num) { // better to_string for doubles std::ostringstream oss; oss << num; return oss.str(); } class Polynomial { public: double coefficient[MAX_DEGREE + 1]; int degree = 0; private: void initializeZeros() { for (int i = 0; i <= MAX_DEGREE; i++) { coefficient[i] = 0.0; } } void copyArray(double array[]) { for (int i = 0; i <= MAX_DEGREE; i++) { coefficient[i] = array[i]; } } void copyArray(double array[], int deg) { if (deg > MAX_DEGREE) { deg = MAX_DEGREE; } for (int i = 0; i <= deg; i++) { coefficient[i] = array[i]; } } protected: void compute_degree() { int deg = 0; for (int i = 0; i <= MAX_DEGREE; i++) { if (coefficient[i] != 0) { deg = i; } } // return deg; degree = deg; } void compute_degree(int max) { int deg = 0; for (int i = 0; i <= max; i++) { if (coefficient[i] != 0) { deg = i; } } // return deg; degree = deg; } public: // constructors: Polynomial(){ initializeZeros(); degree = 0; } Polynomial(double constant) { initializeZeros(); degree = 0; coefficient[0] = constant; } Polynomial(int constant) { initializeZeros(); degree = 0; coefficient[0] = constant; } Polynomial(double numArray[], int deg) { degree = deg; initializeZeros(); copyArray(numArray, deg); } Polynomial(double numArray[]) { copyArray(numArray); compute_degree(); } public: // create polynomial static Polynomial create(double nums[], int deg) { Polynomial created; if (deg > MAX_DEGREE) { deg = MAX_DEGREE; } for (int i = 0; i <= deg; i++) { created.coefficient[i] = nums[deg-i]; } created.compute_degree(deg); return created; } public: // methods // synthetic division Polynomial synthetic_div_by(double divisor) { Polynomial quotient(0.0); if (degree == 0) { return quotient; } quotient.degree = degree - 1; int i = degree; quotient.coefficient[i - 1] = coefficient[i]; i --; while (i > 0) { quotient.coefficient[i - 1] = coefficient[i] + (quotient.coefficient[i] * divisor); i--; } double remainder = coefficient[0] + (quotient.coefficient[0] * divisor); return quotient; } // the polynomial as a function using () double operator() (double x) { double power = 1.0; double total = coefficient[0]; int i = 0; for (i = 1; i <= degree; i++) { power *= x; total += coefficient[i] * power; } return total; } double &operator[] (int index) { return coefficient[index]; } // leading coefficent double leading_coefficient() { return coefficient[degree]; } void set_leading_coefficient(double &a) { coefficient[degree] = a; } // constant term double get_constant() { return coefficient[0]; } double constant() { return coefficient[0]; } void set_constant(double &c) { coefficient[0] = c; } // toString method std::string toString() { int i = degree; std::string text = to_string(coefficient[i]); if (i > 0) { text += "x"; } if (i > 1) { text += "^" + std::to_string(i); } for (i = degree - 1; i >= 0; i--) { if (coefficient[i] != 0) { // only do non-zero terms if (coefficient[i] < 0) { text += " - " + to_string(-1 * coefficient[i]); } else { text += " + " + to_string(coefficient[i]); } if (i > 1) { text += "x^" + std::to_string(i); } else if (i == 1) { text += "x"; } } } return text; } // add polynomials Polynomial operator+(Polynomial& g) { Polynomial sum; if (degree < g.degree) { sum.degree = g.degree; } else { sum.degree = degree; } for (int i = 0; i <= sum.degree; i++) { sum.coefficient[i] = coefficient[i] + g.coefficient[i]; } sum.compute_degree(sum.degree); return sum; } // subtract polynomials Polynomial operator-(Polynomial& g) { Polynomial difference; if (degree < g.degree) { difference.degree = g.degree; } else { difference.degree = degree; } for (int i = 0; i <= difference.degree; i++) { difference.coefficient[i] = coefficient[i] - g.coefficient[i]; } difference.compute_degree(difference.degree); return difference; } // negative of polynomial Polynomial operator-() { Polynomial result(coefficient, degree); for (int i = 0; i <= degree; i++) { result.coefficient[i] = -coefficient[i]; } return result; } // multiply polynomials Polynomial operator*(Polynomial &g) { Polynomial product(0.0); if ((degree == 0) && (coefficient[0] == 0)) { return product; } // zero polynomial if ((g.degree == 0) && (g.coefficient[0] == 0)) { return product; } // zero polynomial product.degree = degree + g.degree; for (int i = 0; i <= degree; i++) { for (int j = 0; j <= g.degree; j++) { product.coefficient[i+j] += (coefficient[i] * g.coefficient[j]); } } return product; } // derivative of polynomial Polynomial prime() { Polynomial derivative; if (degree > 0) { derivative.degree = degree - 1; } else { derivative.degree = 0; } for (int i = 1; i <= degree; i++) { derivative.coefficient[i - 1] = i * coefficient[i]; } return derivative; } double prime(double a) { Polynomial derivative = prime(); return derivative(a); } void increase_degree(int n = 1) { for (int i = degree; i >= 0; i--) { coefficient[i + n] = coefficient[i]; } degree = degree + n; //coefficient[0] = 0.0; for (int j = n - 1; j >= 0; j--) { coefficient[j] = 0.0; } } void decrease_degree(int n = 1) { //int old_constant = coefficient[0]; for (int i = 1; i <= degree; i++) { if ((i - n) >= 0) { coefficient[i - n] = coefficient[i]; } } for (int j = 0; j < n; j++) { coefficient[degree - j] = 0.0; } degree = degree - n; //return coefficient[0]; } // == operator bool operator== (Polynomial g) { //compute_degree(); //g.compute_degree(); bool isEqual = (degree == g.degree); for (int i = 0; i <= degree && isEqual; i++) { isEqual = (isEqual && (coefficient[i] == g.coefficient[i])); } return isEqual; } bool operator== (double num) { //compute_degree(); //if ((degree == negInfinity) && (coefficient[0] == 0.0) && (num == 0.0)) { return true; } return ((degree == 0) && (coefficient[0] == num)); } double operator[] (char c) { /* get coefficient for term using letter, where a gets coefficient of highest power, b gets coefficient of next highest power, and so on ... */ //note: 'a' is 97 and 'A' is 65 as an int int i = (int)c; if (i >= 97) { i = i - 97; } else if (i >= 65) { i = i - 65; } return coefficient[degree - i]; } friend std::ostream& operator<<(std::ostream& os, Polynomial& f); }; using namespace std; // so that I don't need to do std:: ostream& operator<<(ostream& os, Polynomial& f) { char const var = 'x'; int i = f.degree; os << f.coefficient[i]; if (i > 0) { os << var; } if (i > 1) { os << "^" << i; } for (i = f.degree - 1; i >= 0; i--) { if (f.coefficient[i] < 0) { os << " - " << (-1 * f.coefficient[i]); } else { os << " + " << f.coefficient[i]; } if (i > 1) { os << var << "^" << i; } else if (i == 1) { os << var; } } return os; } int main() { double f_coeffs[3] = {-5, -4, 1}; // degree is 2 //Polynomial f = Polynomial(f_coeffs, 2); //replaced Polynomial f(f_coeffs, 2); cout << "For the polynomial f(x) = " << f.toString() << " \n"; cout << "f(2) = " << f(2) << "\n"; int c = 2; // divisor for synthetic division cout << "(" << f << ")" << " / (x - " << c << ")"; cout << "\n"; cout << " = "; cout << f.synthetic_div_by(c).toString(); cout << " + "; cout << f(c) << " / (x - " << c << ")" << " \n"; cout << "f(x) = " << f << "\n"; double x = -1.0; cout << "f(" << x << ")" << " = " << f(x) << "\n"; Polynomial neg = -f; cout << "-f(x) = " << neg.toString() << "\n"; cout << "In the quadratic formula: \n"; cout << "a = " << f['a'] << '\n'; cout << "b = " << f['b'] << '\n'; cout << "c = " << f['c'] << '\n'; cout << "from " << f << " = 0 " << '\n'; double g_coeffs[4] = {2, 5, 3, 1}; // degree is 3 Polynomial g(g_coeffs, 3); cout << "g(x) = " << g << endl; Polynomial dg = g.prime(); cout << "g'(x) = " << dg << endl; Polynomial sum = f + g; cout << "f + g = " << sum << endl; Polynomial difference = f - g; cout << "f - g = " << difference << endl; Polynomial product = f * g; cout << "f * g = " << product << endl; return 0; }

I’ve also done antiderivatives, polynomial long division, and composition of polynomials,
but the code for those is too long for this post.

If anyone finds a bug in the code, please let me know.

Here’s a fuller version of the same project (using a C++ object for a polynomial).