example.cpp

#include <iostream>
#include "zeroin.hpp" // your header with Func, Poly, zero_in

int main()
{
    // --- Test 1: Poly root finding ---
    // p(x) = x^2 - 2, root at sqrt(2) ~ 1.41421356
    Poly<double> p({-2.0, 0.0, 1.0});
    double r1 = zero_in<Func<double>, double>(p, 1.0, 2.0);
    std::cout << "sqrt(2)  ~ " << r1 << "\n";

    // --- Test 2: Trig function ---
    // sin(x) = 0 near x = pi ~ 3.14159
    auto f = Sin<double>();
    double r2 = zero_in<Func<double>, double>(f, 3.0, 3.5);
    std::cout << "pi       ~ " << r2 << "\n";

    // --- Test 3: Composed expression ---
    // sin(x) + cos(x) = 0 near x = 3pi/4 ~ 2.356
    auto g = Sin<double>() + Cos<double>();
    double r3 = zero_in<Func<double>, double>(g, 2.0, 3.0);
    std::cout << "3pi/4    ~ " << r3 << "\n";

    // --- Test 4: Deflation ---
    // p(x) = (x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x - 6
    Poly<double> cubic({-6.0, 11.0, -6.0, 1.0});
    double rem = 0.0;
    double root1 = zero_in<Func<double>, double>(cubic, 0.5, 1.5);
    Poly<double> deflated = cubic.deflate(root1, &rem);
    std::cout << "root1    ~ " << root1 << "  remainder: " << rem << "\n";

    double root2 = zero_in<Func<double>, double>(deflated, 1.5, 2.5);
    Poly<double> deflated2 = deflated.deflate(root2, &rem);
    std::cout << "root2    ~ " << root2 << "  remainder: " << rem << "\n";

    double root3 = zero_in<Func<double>, double>(deflated2, 2.5, 3.5);
    std::cout << "root3    ~ " << root3 << "\n";

    return 0;
}