arithmetics.h

#ifndef CHEMMISOL_ARITHMETICS_H
#define CHEMMISOL_ARITHMETICS_H
 
#include <complex>
#include <list>
#include <iostream>
#include <numbers>
 
namespace chemmisol {
    constexpr double pi = 3.141592653589793238462643383279502884;
 
    template<typename T>
        std::list<std::complex<T>> unit_roots(int n) {
            std::list<std::complex<T>> r;
            std::complex<T> single_root = {
                std::cos(2*pi/n),
                std::sin(2*pi/n),
            };
 
            for(int i = 0; i < n; i++) {
                r.push_back(std::pow(single_root, i));
            }
            return r;
        }
 
    template<typename T>
        std::list<std::complex<T>> roots(const std::complex<T>& c, int n) {
            std::list<std::complex<T>> r;
            T theta = std::arg(c);
            std::complex<T> single_root = 
                std::polar(std::pow(std::abs(c), T(1.0)/n), theta/n);
            auto units = unit_roots<T>(n);
            for(auto unit : units) {
                r.push_back(single_root * unit);
            }
            return r;
        }
}
#endif