#include #include #include using namespace std; template string toStr(T value) { stringstream sstr; sstr << value; return sstr.str(); } class Polynomial { public: Polynomial(double p[], int l); int getSize(); double getCoeff(int degree); double getResult(double x); Polynomial getDerivative(); double getRoot(double root, double dTol); string getExpression(); double getIntegral(double xf, double xi); private: int sizePol; double* pol = new double[sizePol]; string expression; string buildExpression(); }; Polynomial::Polynomial(double p[], int l):pol(p), sizePol(l) { cout << "Polynomial created!" << endl; cout << "N. of Coefficients: " << sizePol << endl; cout << "Coefficients: "; for (int i=0; i < sizePol-1; i++) { cout << pol[i] << ", "; } cout << pol[sizePol-1] << endl; expression = buildExpression(); cout << getExpression() << endl; } int Polynomial::getSize() { return sizePol; } double Polynomial::getCoeff(int degree) { return pol[degree]; } string Polynomial::buildExpression() { string res = "p(x) = "; for (int i=sizePol-1; i > 0; i--) { if (pol[i]!=0.0) { res += "(" + toStr(pol[i]) + "*x^" + toStr(i) + ") + "; } } res += "(" + toStr(pol[0]) + ")"; return res; } string Polynomial::getExpression() { return expression; } double Polynomial::getResult(double x) { double res = 0.0; for (int i=0; i < sizePol; i++) { res += pol[i]*pow(x,i); } return res; } Polynomial Polynomial::getDerivative() { cout << "\n*** begin of getDerivative: ***\n"; if (sizePol>1){ int sizeRes = sizePol - 1; double* res = new double[sizeRes]; for (int i=1; i < sizePol; i++) { res[i-1] = pol[i]*i; } Polynomial dPol(res,sizeRes); cout << "*** end of getDerivative. ***\n"; return dPol; } double res[1] = {0.0}; Polynomial dPol(res,1); cout << "*** end of getDerivative. ***\n"; return dPol; } double Polynomial::getIntegral(double xf, double xi) { cout << "\n*** begin of getIntegral: ***\n"; if ((pol[0]==0.0) && (sizePol==1)) { cout << "\n*** end of getIntegral. ***\n"; return 0.0; } int sizeInt = sizePol + 1; double arrInt[sizeInt]; arrInt[0] = 0.0; for (int i=1; i<=sizeInt; i++) { arrInt[i] = pol[i-1]/(1.0*i); } Polynomial polInt(arrInt,sizeInt); double res = polInt.getResult(xf) - polInt.getResult(xi); cout << "The integral of " << expression; cout << " between " << xi << " and " << xf; cout << " is " << res << ".\n"; cout << "*** end of getIntegral. ***\n"; return res; } double Polynomial::getRoot(double root, double dTol=1.0e-3) { /* Find the root closest to initial guess by means of Newton-Raphson's method. */ Polynomial dPol = getDerivative(); double root0 = root; double newRoot = root; int nIterations = 0; cout << "\n*** begin of getRoot: ***\n"; cout << "dTol adopted: " << dTol << endl; do { nIterations++; root = newRoot; newRoot = root - getResult(root)/dPol.getResult(root); cout << nIterations; cout << ": " << root << " -> " << newRoot << endl; } while (abs(newRoot - root) > dTol); cout << "The root closest to " << root0; cout << " is " << newRoot << ".\n"; cout << "*** end of getRoot. ***\n"; return newRoot; } int main() { double pol[3] = {3.4,7.0,-12}; Polynomial test(pol,3); test.getRoot(5); test.getIntegral(7.0,-2); return 0; }