如何知道一个函数是否与sympy连续? [英] How to know whether a function is continuous with sympy?

问题描述

我需要定义一个函数来检查输入函数在具有 sympy 的点上是否连续.

我用关键字连续性"搜索了 sympy 文档，但没有现有的功能.我想也许我应该考虑有限制地去做，但我不确定如何.

def check_continuity(f, var, a):尝试:f = sympify(f)除了 SymifyError:return("无效输入")别的:x1 = 符号(var，正 = 真)x2 = 符号(var，负 = 真)//我不知道这之后该怎么办

解决方案

是的，您需要使用限制.

某一点连续性的正式定义必须满足三个条件.函数 f(x) 在 x = c if

处连续

• lim x —> c f(x) 存在
• f(c) 存在(也就是说，c 在 f 的域中.)
• lim x —> c f(x) = f(c>)

SymPy 可以使用 limit 函数计算符号限制.

<预><代码>>>>限制(罪(x)/x，x，0)1

参见:https://docs.sympy.org/latest/tutorial/calculus.html#limits

I need to define a function that checks if the input function is continuous at a point with sympy.

I searched the sympy documents with the keyword "continuity" and there is no existing function for that. I think maybe I should consider doing it with limits, but I'm not sure how.

def check_continuity(f, var, a):
    try:
            f = sympify(f)
        except SympifyError:
            return("Invaild input")
        else:
            x1 = Symbol(var, positive = True)
            x2 = Symbol(var, negative = True)
            //I don't know what to do after this

解决方案

Yes, you need to use the limits.

The formal definition of continuity at a point has three conditions that must be met. A function f(x) is continuous at a point where x = c if

• lim x —> c f(x) exists
• f(c) exists (That is, c is in the domain of f.)
• lim x —> c f(x) = f(c)

SymPy can compute symbolic limits with the limit function.

>>> limit(sin(x)/x, x, 0)
1

See: https://docs.sympy.org/latest/tutorial/calculus.html#limits

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