根据用户输入定义任何数学函数

问：

我正在创建一个 python 代码，该代码从用户输入接收数学函数并使用 Newton-Raphson 方法查找指定函数的根。当我尝试在用户输入上使用“def”功能时，问题就出现了。 我需要的是一个指定的函数，然后我可以操作该函数并获取其导数，依此类推。 我试过查看其他人的类似问题，但找不到/不理解解决方案，所以请用简单的术语解释。 请注意，我对编程非常陌生。

这是我试图做的：

from math import *

f = input("Write your equation: ") #e.g. 2x^2+log(x)
f = f.replace('^', '**') #I can't find a way to switch out multiplication with "*"

#My original thought was to do something like this, but even with '*' and '**', it still dosen't work
def f(x):
  return f 

早些时候，我让它仅适用于多项式，使用以下方法：

  f = input("Enter the polynomial: ")
  f = f.replace('^', '**')            #replaces exponentiating
  f = f.replace('x', '*x')  #replaces multiplication with *, but dosen't work if x is alone
  f = f.replace('-*x', '-x')          # ̌
  f = f.replace('+*x', '+x')          # fixes the above issue
  if f.find("*") == 0:                # ^
      listf = list(f)
      listf.pop(0)
      f = "".join(listf)

  def g(x, f):
    f = f.replace('x', f"({str(x)})") #my solution to the original problem
    return eval(f)

  def g_prim(x):                      #defining the first derivative
    h = 0.00001
    return (g(x+h, f)-g(x, f))/h

  def g_biss(x):                      #defining the second derivative
    h = 0.00001
    return (g_prim(x+h)-g_prim(x))/h

  a = []                              #list of maximas

  for i in range(-50, 50, 5):         #finds the maxima and adds ± 0.5
    while abs(g_prim(i)) > 0.00001:
      i = i - g_prim(i)/g_biss(i)
    a.append(round(i+.5,3))
    a.append(round(i-.5,3))

  a = list(dict.fromkeys(a))
  b = []                              #list of roots

  for a in a:                         #Newton-Raphson from every maxima(±0.5)
    while abs(g(a, f)) > 0.00001:
      a = a - g(a, f)/g_prim(a)
    b.append(round(a,1))

  b = list(dict.fromkeys(b))
  print("The roots of the polynomial is:")
  print(b)