Function FindRoots

src/minisketch/src/sketch_impl.h:263–278

 */
template<typename F>
std::vector<typename F::Elem> FindRoots(const std::vector<typename F::Elem>& poly, typename F::Elem basis, const F& field) {
    std::vector<typename F::Elem> roots;
    CHECK_RETURN(poly.size() != 0, {});
    CHECK_RETURN(basis != 0, {});
    if (poly.size() == 1) return roots; // No roots when the polynomial is a constant.
    roots.reserve(poly.size() - 1);
    std::vector<std::vector<typename F::Elem>> stack = {poly};

    // Invoke the recursive factorization algorithm.
    if (!RecFindRoots(stack, 0, roots, false, 0, basis, field)) {
        // Not fully factorizable.
        return {};
    }
    CHECK_RETURN(poly.size() - 1 == roots.size(), {});
    return roots;
}

template<typename F>
std::vector<typename F::Elem> BerlekampMassey(const std::vector<typename F::Elem>& syndromes, size_t max_degree, const F& field) {