C++ 重载输入/输出运算符，为什么它以这种方式工作？

问题是：我得到一个关于这两个操作符的链接器错误。更具体地说，以下是确切的错误消息：

注：我有一个“有效的解决方案”，如果你读到底我提到它。我不知道为什么它是这样工作的，而不是这样。我更希望这个方法能够工作，因为它看起来更干净，没有在我的声明上面挂起输入/输出操作符。对不起，太长了。我删除了一些不必要的东西，比如我使用的其他重载操作符，因为它们不相关

poly.obj : error LNK2005: "class std::basic_istream<char,struct std::char_traits<char> > & __cdecl operator>>(class std::basic_istream<char,struct std::char_traits<char> > &,class Poly &)" (??5@YAAAV?$basic_istream@DU?$char_traits@D@std@@@std@@AAV01@AAVPoly@@@Z) already defined in lab1.obj
1>poly.obj : error LNK2005: "class std::basic_ostream<char,struct std::char_traits<char> > & __cdecl operator<<(class std::basic_ostream<char,struct std::char_traits<char> > &,class Poly const &)" (??6@YAAAV?$basic_ostream@DU?$char_traits@D@std@@@std@@AAV01@ABVPoly@@@Z) already defined in lab1.obj
1>d:\... fatal error LNK1169: one or more multiply defined symbols found

poly.obj:error LNK2005:“class std:：basic\u istream&\u cdecl操作符>>（class std:：basic\u istream&，class poly&）”（？？5@YAAAV？$basic_istream@DU？$char_traits@D@std@@@std@@AAV01@AAVPoly@@@Z） 已在lab1.obj中定义
1> poly.obj:错误LNK2005:“类std:：basic_ostream&__cdecl运算符（从注释中移动）

如果您编写自由函数的主体（如运算符（从注释移动）

如果您编写自由函数体（如运算符）如果您编写自由函数体（如
operator@MatteoItalia好的，这肯定解决了这个问题。介意解释一下ODR代表什么吗？如果你写一个自由函数的主体（就像你的
operator@MatteoItalia这肯定解决了这个问题。介意解释一下ODR代表什么吗？
//file poly.h

#ifndef POLY_H
#define POLY_H

#include <iostream>
using namespace std;

class Poly {

public:
    Poly(int = 0, int = 0);                     //default constructor
    Poly(const Poly &);                         //copy constructor
    ~Poly();                                    //destructor

    friend ostream& operator<<(ostream& output, const Poly& thePoly);
    friend istream& operator>>(istream& input, Poly& thePoly);

private:
    int* polynomial;
    int maxExponent;
};

istream& operator>>(istream& input, Poly& thePoly) {

    return input;
}

ostream& operator<<(ostream& output, const Poly& thePoly) {
    bool isZero = true;

    for (int i = thePoly.maxExponent; i > 0; i--) {
        if (thePoly.polynomial[i] != 0) {
            if (thePoly.polynomial[i] < 0) {
                output << " -";
            }
            else {
                output << " +";
            }

            output << thePoly.polynomial[i];

            if (i != 0) {
                output << "x";
            }
            if (i != 1) {
                output << "^";
            }

            output << i;
            isZero = false;
        }
    }

    if (isZero) {
        output << " 0";
    }

    return output;
}

#endif

// DO NOT change anything in this file. Your code must compile and give the
// correct output with this main on the linux machines.

// Make sure the file containing the member function source is: poly.cpp
// Use all lowercase in the file names.

// This main does not do a thorough job of testing.  When testing arrays,
// be sure to test the middle and also all the boundary conditions.  Test
// values on the boundary and outside the boundaries, i.e., too big/small.

#include "poly.h"
#include <iostream>
using namespace std;

int main() {
    Poly A(5, 7), B(3, 4), C(2), D(A), X, Y;
    Poly A2, B2, Z1, Z2;

    // set polynomials A and B to desired values
    // A = +5x^7 -4x^3 +10x -2
    // B = +3x^4 +1x^3 
    cout << "Enter terms for polynomial A.  Enter a coefficient " << endl
        << "then exponent for each term. Enter -1 -1 to terminate." << endl;
    cin >> A;                                     // or use a bunch of setCoeff
    cout << "Enter terms for polynomial B.  Enter a coefficient " << endl
        << "then exponent for each term. Enter -1 -1 to terminate." << endl;
    cin >> B;                                     // or use a bunch of setCoeff

    // outputs exactly what is in quotes: "A = +5x^7 -4x^3 +10x -2"
    cout << "A =" << A << endl;
    // outputs exactly what is in quotes: "B = +3x^4 +1x^3"
    cout << "B =" << B << endl << endl;

    return 0;
}

#ifndef POLY_H
#define POLY_H

#include <iostream>
using namespace std;

class Poly {

    friend istream& operator>>(istream& input, Poly& thePoly) {

        return input;
    }

    friend ostream& operator<<(ostream& output, const Poly& thePoly) {
        bool isZero = true;

        for (int i = thePoly.maxExponent; i > 0; i--) {
            if (thePoly.polynomial[i] != 0) {
                if (thePoly.polynomial[i] < 0) {
                    output << " -";
                }
                else {
                    output << " +";
                }

                output << thePoly.polynomial[i];

                if (i != 0) {
                    output << "x";
                }
                if (i != 1) {
                    output << "^";
                }

                output << i;
                isZero = false;
            }
        }

        if (isZero) {
            output << " 0";
        }

        return output;
    }

public:
    Poly(int = 0, int = 0);                     //default constructor
    Poly(const Poly &);                         //copy constructor
    ~Poly();                                    //destructor

private:
    int* polynomial;
    int maxExponent;
};



#endif