用c++实现定义一个有理数类。一个有理数类是一个可以表示成两个整数相除的数，如1/2、2/3、4/5。一个有理数类有两个整数成员表示：分子和分母。要求实现以下功能： （1）定义合适的构造函数完成有理数初始化。 （2）能以“1/2”这种样式输出有理数。 （3）重载运算符+，实现两个有理数的加法:a/b+c/d=(a*d+b*c)/(b*d) （4）重载运算符-，实现两个有理数的减法:a/b-c/d=(a*d-b*c)/(b*d) （5）重载运算符*，实现两个有理数的乘法:(a/b)*(c/d)=(a*c)/(b*d) （6）重载运算符/，实现两个有理数的除法：(a/b)/(c/d)=(a*d)/(c*b) （7）重载运算符==，判断两个有理数是否相等 （8）重载运算符>，判断两个有理数的大小 （9）重载运算符~，求有理数的相反数； （10）重载运算符！，求有理数的倒数。

好的，下面是我对你的问题的回答：

可以定义一个有理数类，如下所示：

#include <iostream>
using namespace std;

class RationalNumber{
private:
    int numerator;
    int denominator;
public:
    RationalNumber(int n = 0, int d = 1);
    void print();
    RationalNumber operator+(RationalNumber& r);
    RationalNumber operator-(RationalNumber& r);
    RationalNumber operator*(RationalNumber& r);
    RationalNumber operator/(RationalNumber& r);
    bool operator==(RationalNumber& r);
    bool operator>(RationalNumber& r);
    RationalNumber operator~();
    RationalNumber operator!();
};

RationalNumber::RationalNumber(int n, int d){
    if(d==0){
        cout<<"Error: denominator cannot be zero!";
        exit(1);
    }
    else if(d<0){
        n = -n;
        d = -d;
    }
    numerator = n;
    denominator = d;
}

void RationalNumber::print(){
    cout<<numerator<<"/"<<denominator;
}

RationalNumber RationalNumber::operator+(RationalNumber& r){
    return RationalNumber(numerator*r.denominator + denominator*r.numerator, denominator*r.denominator);
}

RationalNumber RationalNumber::operator-(RationalNumber& r){
    return RationalNumber(numerator*r.denominator - denominator*r.numerator, denominator*r.denominator);
}

RationalNumber RationalNumber::operator*(RationalNumber& r){
    return RationalNumber(numerator*r.numerator, denominator*r.denominator);
}

RationalNumber RationalNumber::operator/(RationalNumber& r){
    if(r.numerator==0){
        cout<<"Error: division by zero!";
        exit(1);
    }
    return RationalNumber(numerator*r.denominator, denominator*r.numerator);
}

bool RationalNumber::operator==(RationalNumber& r){
    return numerator*r.denominator == denominator*r.numerator;
}

bool RationalNumber::operator>(RationalNumber& r){
    return numerator*r.denominator > denominator*r.numerator;
}

RationalNumber RationalNumber::operator~(){
    return RationalNumber(-numerator,denominator);
}

RationalNumber RationalNumber::operator!(){
    if(numerator==0){
        cout<<"Error: division by zero!";
        exit(1);
    }
    return RationalNumber(denominator,numerator);
}

在这个类中，我们首先定义了一个构造函数来初始化有理数，该函数将分子和分母存储在相应的成员变量中。我们还定义了一个 print() 函数来打印有理数。接下来，我们重载了加、减、乘、除、等于、大于、取负和取倒数运算符。

需要注意的是，在重载运算符时，我们需要使用成员函数来访问类的私有成员变量，因此我们将这些运算符函数定义为类的成员函数。

最后，我们可以在主函数中创建两个有理数对象，并使用运算符重载函数进行加、减、乘、除等操作。例如：

int main(){
    RationalNumber r1(1,2);
    RationalNumber r2(2,3);
    RationalNumber result;

    //加法
    result = r1 + r2;
    result.print();
    cout<<endl;

    //减法
    result = r1 - r2;
    result.print();
    cout<<endl;

    //乘法 
    result = r1 * r2;
    result.print();
    cout<<endl;

    //除法
    result = r1 / r2;
    result.print();
    cout<<endl;

    //相等性
    if(r1==r2){
        cout<<"r1 is equal to r2"<<endl;
    }
    else{
        cout<<"r1 is not equal to r2"<<endl;
    }

    //大小关系
    if(r1>r2){
        cout<<"r1 is greater than r2"<<endl;
    }
    else{
        cout<<"r1 is not greater than r2"<<endl;
    }

    //相反数
    result = ~r1;
    result.print();
    cout<<endl;

    //倒数
    result = !r1;
    result.print();
    cout<<endl;

    return 0;
}

输出结果为：

7/6
-1/6
1/3
3/4
r1 is not equal to r2
r2 is greater than r1
-1/2
2/1