在派生类中重新定义基类的友元函数

我想重新定义最初定义为Vector类中的友元operator*函数，在派生类中，BigNum . 具体来说，我想调用operator*的Vector版本，然后在BigNum的运算符*中对该操作的结果执行一些其他操作。 这是结构的片段（再次感谢@lemmes对此的帮助）：

template<typename T>
class Vector
{
private:
  std::vector<T> base;
public:                                                                                                                 
  Vector();                                                                                                                        
  Vector(const std::vector<T> vec);                                                                                                
  Vector(const Vector& vec);
  template<typename T1, typename T2>
  friend auto operator*(const Vector<T1>& lhs, const Vector<T2>& rhs) -> Vector<decltype(std::declval<T1>() * std::declval<T2>())>;
};
template<typename T1, typename T2>
auto operator*(const Vector<T1>& lhs, const Vector<T2>& rhs) -> Vector<decltype(std::declval<T1>() * std::declval<T2>())>
{
  typedef decltype(std::declval<T1>() * std::declval<T2>()) T3;
  assert(lhs.base.size() == rhs.base.size());
  Vector<T3> result;
  result.base.reserve(lhs.base.size());
  std::transform(lhs.base.begin(), lhs.base.end(), rhs.base.begin(), std::back_inserter(result.base),
                 [](const T1& e1, const T2& e2) { return e1 * e2; });
  return result;
}
class BigNum : public Vector<int>
{
 public:
  BigNum();
  BigNum(const std::vector<int> init);
  ~BigNum();
  BigNum operator*(const BigNum& rhs);
};
#endif
BigNum BigNum::operator*(const BigNum& rhs)
{
  // How can I call Vector's operator* (a friend of the Vector class)                                                                            
  // and then do other stuff in here?                                                                                                            
}
#include "BigNum.h"
int main()
{
  int arr1[] = {1,2,3,4,5};
  int arr2[] = {10,20,30,40,50};
  std::vector<int> vec1 (arr1, arr1 + sizeof(arr1) / sizeof(arr1[0]));
  std::vector<int> vec2 (arr2, arr2 + sizeof(arr2) / sizeof(arr2[0]));
  BigNum bn1(vec1), bn2(vec2);
  bn1 * bn2;  // want to call BigNum's operator* here
  return 0;
}

我显然不能做像Vector::operator*这样的事情，因为它是朋友。 提前感谢！