重载输入/输出运算符，为什么它以这种方式工作而不是以另一种方式工作

问题：我收到了关于这两个运算符的链接器错误。更具体地说，这里有确切的错误消息：

注意：我有一个"工作解决方案"，如果你读到底部，我会提到它。我不知道为什么它是这样工作的，而不是这样。我更喜欢这个方法，因为它看起来更干净，没有输入/输出操作符挂在我的声明上方。抱歉太长了。我去掉了一些不必要的东西，比如我现有的其他超负荷运营商，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

在我的.h文件中(如下所示)，我将两个所需的操作符都声明为好友，这样他们就可以访问私人成员。我也把它们作为非会员功能，这就是运营商在这个网站上超载的"指南"所说的正确做法。运算符>>不完整，但这与此无关。我有一个想法，这可能与以下事实有关：在两个地方我有"#include iostream"，并且由于.cpp包含.h，所以它会因此而失败吗？不确定这是否是一种正确的预感。这是完整的.h文件：

//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

以下是链接错误中引用的辅助文件：

// 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;
}

奇怪的是(至少对我来说)，如果我放弃声明，将整个函数移到公共声明之上，但仍然在类中，那么程序就会正确编译为什么是这样？？？。。。当然，我还没能测试这种编译是否意味着它能正常工作，因为我需要完成操作符>>，这样我才能输入数据，然后输出。

这就是我所说的上述变化：

#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