// Sample program itayl_ex1.cpp; #include "itaylor.hpp" // Header file of class itaylor #include // Input | output using namespace cxsc; using namespace std; using namespace taylor; int main() { /*------------------------------------------------------------ Inclusions of the Taylor coefficients and derivatives up to order p=5 for P(x) = 2x^4 + x^3 + 4x^2 - 3x +2 at points of expansion x0 included by the interval z. ------------------------------------------------------------*/ int p = 5; // Order of expansion interval z; // Interval to include the point of expansion itaylor P; // Default constructor No. 1. while(1) { cout << endl << "Inclusion of x0; [x0,x0] = ? "; cin >> z; itaylor x(p,z); // Constructor No. 4, P = (((real(2.0)*x + 1) // Polynomial of order 4. *x + 4) *x - real(3.0)) *x + real(2.0); cout << SetPrecision(16,16) << Scientific << endl; print_itaylor(P); // Output of Taylor coefficients. ivector derivative(0,p); // interval vector with // components from index 0 up to the order p. for(int i=0;i<=p; i++) derivative[i] = get_j_derive(P,i); // Derivatives cout << "Inclusions of the derivatives up to order 5 " << endl; for(int i=0; i<=p; i++) // Output of the derivatives cout << i<<"th derivative: " << derivative[i] << endl; } return 0; } // main /*Ausgabe Berechnung der ersten zehn Ableitungen der Funktion f(x)= exp(x)*x+sin(x)+x an der Stelle x=1 Ausgabe itaylor der Ordnung 10 i 0 component: [ 4.559752, 4.559753] i 1 component: [ 6.976865, 6.976866] i 2 component: [ 3.656687, 3.656688] i 3 component: [ 1.722137, 1.722138] i 4 component: [ 0.601370, 0.601371] i 5 component: [ 0.140416, 0.140417] i 6 component: [ 0.025259, 0.025260] i 7 component: [ 0.004207, 0.004208] i 8 component: [ 0.000627, 0.000628] i 9 component: [7.639748E-005,7.639749E-005] i 10 component: [8.008054E-006,8.008055E-006] Einschliessungen der Ableitungen bis Ordnung 10 0-te Ableitung: [ 4.559752, 4.559753] 1-te Ableitung: [ 6.976865, 6.976866] 2-te Ableitung: [ 7.313374, 7.313375] 3-te Ableitung: [ 10.332825, 10.332826] 4-te Ableitung: [ 14.432880, 14.432881] 5-te Ableitung: [ 16.849993, 16.849994] 6-te Ableitung: [ 18.186501, 18.186502] 7-te Ableitung: [ 21.205952, 21.205953] 8-te Ableitung: [ 25.306007, 25.306008] 9-te Ableitung: [ 27.723120, 27.723121] 10-te Ableitung: [ 29.059629, 29.059630] */