Polynomial + - * / %, C++ (gcc)

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#include <iostream>
#include <map>

class Polynomial
{
public:
    Polynomial() {}
    int degree()const { return poly.empty() ? 0 : poly.rbegin()->first; }
    void   set(int degree, double coef) { poly[degree] = coef; }
    double get(int degree)const         { auto it = poly.find(degree); return it == end(poly) ? 0 : it->second; }
    Polynomial& operator+=(const Polynomial& rhs);
    Polynomial& operator-=(const Polynomial& rhs);
    Polynomial& operator*=(const Polynomial& rhs);
    Polynomial& operator/=(const Polynomial& rhs);
    Polynomial& operator%=(const Polynomial& rhs);
    Polynomial operator+(const Polynomial& rhs)const { auto ret = *this; return ret += rhs; }
    Polynomial operator-(const Polynomial& rhs)const { auto ret = *this; return ret -= rhs; }
    Polynomial operator*(const Polynomial& rhs)const { auto ret = *this; return ret *= rhs; }
    Polynomial operator/(const Polynomial& rhs)const { auto ret = *this; return ret /= rhs; }
    Polynomial operator%(const Polynomial& rhs)const { auto ret = *this; return ret %= rhs; }
    static std::pair<Polynomial,Polynomial> div(Polynomial lhs, const Polynomial& rhs);
    friend std::ostream& operator<<(std::ostream& out, const Polynomial& rhs);
private:
    std::map<int,double> poly;
};

int main()
{
    Polynomial p1;
    p1.set(0, 1);
    p1.set(1, 2);
    p1.set(2, 3);
    std::cout << "p1 = " << p1 << "\n";
    
    Polynomial p2;
    p2.set(0, 4);
    p2.set(1, 5);
    p2.set(2, 6);
    p2.set(3, 7);
    std::cout << "p2 = " << p2 << "\n\n";
    
    std::cout << "p1 + p2 = " << p1 + p2 << "\n";
    std::cout << "p1 - p2 = " << p1 - p2 << "\n";
    std::cout << "p1 * p2 = " << p1 * p2 << "\n";
    std::cout << "p1 / p2 = " << p1 / p2 << "\n";
    std::cout << "p1 % p2 = " << p1 % p2 << "\n\n";
    
    std::cout << "p2 + p1 = " << p2 + p1 << "\n";
    std::cout << "p2 - p1 = " << p2 - p1 << "\n";
    std::cout << "p2 * p1 = " << p2 * p1 << "\n";
    std::cout << "p2 / p1 = " << p2 / p1 << "\n";
    std::cout << "p2 % p1 = " << p2 % p1 << "\n";
}

std::ostream& operator<<(std::ostream& out, const Polynomial& rhs)
{
    if (!rhs.degree()) return out << 0;
    auto kv = rhs.poly.begin();
    out << kv->second << "*x^" << kv->first;
    while (++kv != end(rhs.poly)) out << " + " << kv->second << "*x^" << kv->first;
    return out;
}

Polynomial& Polynomial::operator+=(const Polynomial& rhs)
{
    for (auto const& kv : rhs.poly) poly[kv.first] += kv.second;
    return *this;
}

Polynomial& Polynomial::operator-=(const Polynomial& rhs)
{
    for (auto const& kv : rhs.poly) poly[kv.first] -= kv.second;
    return *this;
}

Polynomial& Polynomial::operator*=(const Polynomial& rhs)
{
    decltype(poly) p;
    for (auto const& kv1 : poly) for (auto const& kv2 : rhs.poly)
        p[kv1.first + kv2.first] += kv1.second * kv2.second;
    poly.swap(p);
    return *this;
}

std::pair<Polynomial,Polynomial> Polynomial::div(Polynomial remainder, const Polynomial& divisor)
{
    Polynomial quotient;
    while (remainder.degree() >= divisor.degree())
    {
        int    deg  = remainder.degree() - divisor.degree();
        double coef = remainder.poly.rbegin()->second / divisor.poly.rbegin()->second;
        for (auto const& kv : divisor.poly) remainder.poly[kv.first + deg] -= kv.second * coef;
        quotient.poly[deg] = coef;
        remainder.poly.erase(std::prev(end(remainder.poly)));
    }
    return {quotient,remainder};
}

Polynomial& Polynomial::operator/=(const Polynomial& rhs)
{
    auto qr = div(*this, rhs);
    poly.swap(qr.first.poly);
    return *this;
}

Polynomial& Polynomial::operator%=(const Polynomial& rhs)
{
    auto qr = div(*this, rhs);
    poly.swap(qr.second.poly);
    return *this;
}

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Compilation time: 0.62 sec, absolute running time: 0.15 sec, cpu time: 0 sec, memory peak: 3 Mb, absolute service time: 0,77 sec