x016.h

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#pragma once

#include "x013.h"

namespace nmx::apps::x016 {

using nmx::apps::x013::Polynom;

class QPolynom : public Polynom<double, 2>
{
    using BaseT = Polynom<double, 2>;

public:
    using BaseT::BaseT; // erbe Konstruktoren

    auto real_roots() const {
        double x0, x1; //die Nullstellen
        int countroots = gsl_poly_solve_quadratic(c(2), c(1), c(0), &x0, &x1);

        if (countroots == 0) { //keine reelle Nullstellen, leerer Vektor
            return std::vector<double>{};
        } else if (countroots == 1) { //eine reelle Nullstelle
            return std::vector{ x0 };
        } else { //zwei reelle Nullstelle
            return std::vector{ x0, x1 };
        }
    }

    auto complex_roots() const {
        using CVector = std::vector<std::complex<double>>;
        gsl_complex z0, z1;
        gsl_poly_complex_solve_quadratic(c(2), c(1), c(0), &z0, &z1);
        return CVector{ { GSL_REAL(z0), GSL_IMAG(z0) }, //
                        { GSL_REAL(z1), GSL_IMAG(z1) } };
    }
};

inline void ex1() {
    //lambda Funktion zur Ausgabe eines Polynoms und seiner Nullstellen
    auto showResults = [](const QPolynom &p) {
        std::cout << p << std::endl;
        //suche reelle Nullstellen
        auto roots = p.real_roots();
        if (roots.empty()) { //keine reelle Nullstellen
            std::cout << "no real roots" << std::endl;
            auto croots = p.complex_roots();
            for (const auto &z : croots) {
                std::cout << z << std::endl;
            }
        } else {
            std::cout << "real roots" << std::endl;
            for (const auto &x : roots) {
                std::cout << x << std::endl;
            }
        }
    };

    //3*x^2+2*x+1
    QPolynom p1{ { 1, 2, 3 } };
    auto roots = p1.real_roots();
    showResults(p1);
    std::cout << "-------------------" << std::endl;
    //x^2-3*x+1
    QPolynom p2{ { 1, -3, 1 } };
    showResults(p2);
}

} // namespace nmx::apps::x016