// Hilfsfunktion für operator*-Funktion:
    // Multipliziert ein Polynom mit a * (x ^ n)
    Polynomial mul_x(int a, int d) const {
        std::vector<int> v;
        for(int i = 0; i < d; ++i){
            v.push_back(0);
        }

        for(int i = 0; i < (*this).size(); ++i){
            v.push_back(a * a_[i]);
        }

        return Polynomial(v);
    }

    // multipliziert 2 Polynome:
    Polynomial operator*(Polynomial p1) const {
        Polynomial p2 = (*this);
        Polynomial res;
        if((p2.size() < p1.size())){
            for(int i = 0; i < p2.size(); ++i){
                res = res + p1.mul_x(p2.a_[i], i);
            }
            return res;
        }
        else{
            for(int i = 0; i < p1.size(); ++i){
                res = res + p2.mul_x(p1.a_[i], i);
            }
            return res;
        }
    }