college_computing_final_project/function_limitation_continue.py

from sympy import *
from convert_formula import *

def function_limitation(function, independent_variable, point, direction='+'):
    """
    计算函数在指定点的极限值
    :param function: 函数表达式
    :param independent_variable: 自变量
    :param point: 自变量的取值点
    :return: 极限值
    """
    # 转换函数表达式为SymPy表达式
    function_sympy = sympify(convert_formula(function))
    independent_variable_sympy = symbols(independent_variable)
    # 计算函数在指定点的极限值
    limit_value = limit(function_sympy, independent_variable_sympy, float(point), dir=direction)
    if limit_value == oo or limit_value == -oo:
        return limit_value
    return round(limit_value, 3)

def function_limitation_line(function, independent_variable):
    """
    求函数的渐近线
    :param function: 函数表达式
    :param independent_variable: 自变量
    :return: 渐近线方程
    """
    function1 = '(%s)/%s'%(function, independent_variable)
    k = function_limitation(function1, independent_variable, oo)
    function2 = '%s-%s*%s'%(function, str(k), independent_variable)
    b = function_limitation(function2, independent_variable, oo)
    if k==1:
        k = ''
    if b==0:
        b = ''
    elif b>0:
        b = '+'+str(b)
    if k==0:
        return 'y=%s'%str(b)
    return 'y=%s%s%s'%(str(k), independent_variable, str(b))

def function_continue(function, independent_variable, point):
    """
    判断函数在指定点的连续性
    :param function: 函数表达式
    :param independent_variable: 自变量
    :param point: 自变量的取值点
    :return: 连续性值
    """
    left_limitation=function_limitation(function, independent_variable, point, direction='-')
    right_limitation=function_limitation(function, independent_variable, point, direction='+')
    if left_limitation==right_limitation:
        return '连续'
    else:
        return '不连续'

def test_function_limitation():
    """
    测试 function_limitation 函数
    """
    # 测试函数在指定点的极限值
    result = function_limitation('x**2', 'x', 2)
    assert result == 4.000
    result = function_limitation('1/x', 'x', 0)
    assert result == oo
    # 测试函数在无穷远处的极限值
    result = function_limitation('x**2', 'x', oo)
    assert result == oo
    result = function_limitation('1/x', 'x', oo)
    assert result == 0

def test_function_limitation_line():
    result = function_limitation_line('(2*x^2-3)/(x+1)', 'x')
    assert result == 'y=2x-2'

def test_function_continue():
    # 测试连续的情况
    result = function_continue('x**2', 'x', 2)
    assert result == '连续'
    # 测试不连续的情况
    result = function_continue('1/x', 'x', 0)
    assert result == '不连续'

def UI():
    while True:
        command=input("请选择功能：1.求函数极限 2.求函数渐近线 3.判断函数连续性 4.返回上一层")
        if command=='1':
            function=input("请输入函数表达式：（注：只支持形如f(x)=的表达式，不支持y=的表达式）")
            independent_variable, functions=split_function(function)
            point=input("请输入自变量的取值点（如0，0+，0-）：")
            if point.isdigit():
                points=float(point)
                result=function_limitation(functions, independent_variable, points)
            elif point == 'oo' or point == '-oo':
                result=function_limitation(functions, independent_variable, eval(point))
            else:
                direction=point[-1]
                pointsfloat(point[:-1])
                result=function_limitation(functions, independent_variable, points, direction)
            print("函数在%s=%s的极限值为：%s"%(independent_variable, point, result))
        elif command=='2':
            function=input("请输入函数表达式：（注：只支持形如f(x)=的表达式，不支持y=的表达式）")
            independent_variable, function=split_function(function)
            result=function_limitation_line(function, independent_variable)
            print("函数的渐近线方程为：%s"%result)
        elif command=='3':
            function=input("请输入函数表达式：（注：只支持形如f(x)=的表达式，不支持y=的表达式）")
            independent_variable, function=split_function(function)
            point=float(input("请输入自变量的取值点："))
            result=function_continue(function, independent_variable, point)
            print("函数在该点处的连续性为：%s"%result)
        elif command=='4':
            break
        else:
            print("输入错误，请重新输入")

if __name__ == "__main__":
    test_function_limitation()
    test_function_limitation_line()
    test_function_continue()
    UI()