在人工智能数学基础一书中，下面是一题Python求函数极限的例子：

【例2.6】使用Python编程求 lim( x → 1) (x^2 - 1 / x - 1)

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import sympy

from sympy import oo #注意无究符号表示形式为两个小定字母o
import numpy as np
x = sympy.Symbol('x') #注意Symbol首字母大写

f = (x ** 2 - 1) / (x-1) # 定义极限表达式

lim = sympy.limit(f,x,1)
print(lim)

2
—————————————————————————————————————————

import sympy
from sympy import oo
import numpy as np

x = sympy.Symbol('x')

f = (x**2-1) / (x-1)

print(sympy.limit(f,x,1))

这Python带的库真的是强大。

下面我们如果用C++来模拟，注意：下面代码只是最初构思，运算符重载还要修改。

#include "X:\Work\Share\CCode\CPlatform\Math\_math_out.h"

using namespace lf;

 
int main()
{
	ga.initialize();

	_Variable x;
	 
	_function f;

	//f(x) = (x ^ 2 - 1) / (x - 1);	 
	f(x) = (x ^ 2 - 1 ) / (x - 1);

	
	_cout << f.limit() << _t("\n");
	  
	return 0;
}

运行结果，这里没有添加任何库：

_Variable定义和_function定义：

class _Variable  : public _Object
{
private:
	_DList<_Variable> _multiple;
public:
	_Variable();
	~_Variable();

	_Variable operator-(const int& n) const;
	_Variable operator+(const int& n) const;

	_Variable operator/(const int& n) const;
	_Variable operator/(const _Variable& other) const;

	// 重载加法运算符
	_Variable operator+(const _Variable& other) const;

	_Variable operator*(const _Variable& other) const;

	_Variable operator^(const _Variable& other) const;

	_Variable operator^(const size_t& nPower) const;
private:

};

 





class _function : public _Object
{
public:
	_function(const _Variable& v);
	_function();

	_function& operator()(const _Variable& other);

	_Variable limit()const;
};





//--------------------------------------------------------





_Variable::_Variable()
{


}




_Variable::~_Variable()
{

}

_Variable _Variable::operator-(const int& n) const
{
	_cout << _t("_Variable _Variable::operator-\n");
	return _Variable();
}

_Variable _Variable::operator+(const int& n) const
{
	_cout << _t("_Variable _Variable::operator+\n");
	return _Variable();
}

_Variable _Variable::operator/(const int& n) const
{
	_cout << _t("Variable _Variable::operator/\n");
	return _Variable();
}

_Variable _Variable::operator/(const _Variable& other) const
{
	_cout << _t("_Variable::operator/\n");
	return _Variable();
}

_Variable _Variable::operator+(const _Variable& other) const
{
	_cout << _t("_Variable _Variable::operator+\n");
	return _Variable();
}

_Variable _Variable::operator*(const _Variable& other) const
{
	_cout << _t("_Variable _Variable::operator*\n");
	return _Variable();
}

_Variable _Variable::operator^(const _Variable& other) const
{
	_cout << _t("_Variable::operator^\n");
	return _Variable();
}

_Variable _Variable::operator^(const size_t& nPower) const
{
	_cout << _t("_Variable::operator^\n");
	return _Variable();
}




_function::_function(const _Variable& v)
{
}

_function::_function()
{
}

_function& _function::operator()(const _Variable& other)
{
	_cout << _t("_function::operator()\n");
	return  *this;
}

_Variable _function::limit() const
{
	_cout << _t("这里求函数极限！\n");
	return _Variable();
}

下一步，完善_Variable 和 _function 这两个类。