main.cpp

import sedenion;

#include <iostream>

int main() {
    using S = Sedenion<double>;
    constexpr double EPS = 1e-7;

    for (int a = 1; a < 8; ++a) {
        for (int b = 8; b < 16; ++b) {
            for (int c = a+1; c < 8; ++c) {
                for (int d = 8; d < 16; ++d) {
                    S x, y;
                    x.set(a, 1); x.set(b, 1);
                    y.set(c, 1); y.set(d, 1);
                    auto product = *(x * y);
                    bool is_zero = true;
                    for (int i = 0; i < 16; ++i)
                        if (std::abs(product.get(i)) >= EPS)
                            is_zero = false;

                    if (is_zero)
                        std::cout << "FOUND: (e" << a << " + e" << b
                                  << ") * (e" << c << " + e" << d << ") == 0\n";
                }
            }
        }
    }
}