ZeroDivisionError：浮点除以零？

Question

def fx(x):
    v = float(x*x*x - 5*x - 7)
    return v


err = int(input("Enter zeroes in approxiamtion in solution: "))
b = float(input("Enter upper limit for root: "))
a = float(input("Enter lower limit for root: "))
c = 0.0
while fx(c) > (1 * 10 ** -err):
    c = b - ((b - a)/(fx(b) - fx(a))) * fx(b)
    print(a, b, c, sep=', ')
    a = b
    b = c
    # c = 0
    print()
print("The root is approximately = ", b)

即使循环给出了正确的值，为什么在执行此代码时为什么会出现零除错误？

编辑：我将^运算符更改为**并删除了c = 0，但现在答案甚至与实际答案并不接近。 ^运算符奇怪地给了我正确答案。

带有**运算符的输出：

Enter zeroes in approxiamtion in solution: 3
Enter upper limit for root: 2
Enter lower limit for root: 1
The root is approximately =  2.0

带有^运算符的输出：

Enter zeroes in approxiamtion in solution: 3
Enter upper limit for root: 2
Enter lower limit for root: 1
1.0, 2.0, 6.5
Traceback (most recent call last):

2.0, 6.5, 2.1658986175115205
  File "C:/Users/anves/PycharmProjects/nt/nt.py", line 46, in <module>

    c = b - (((b - a)/(fx(b) - fx(a))) * fx(b))
6.5, 2.1658986175115205, 2.302797651275858

ZeroDivisionError: float division by zero
2.1658986175115205, 2.302797651275858, 2.934211734811194

2.302797651275858, 2.934211734811194, 2.705017710718186

2.934211734811194, 2.705017710718186, 2.7438299655247143

2.705017710718186, 2.7438299655247143, 2.7474171932954787

2.7438299655247143, 2.7474171932954787, 2.7473464241055843

2.7474171932954787, 2.7473464241055843, 2.7473465403033757

2.7473464241055843, 2.7473465403033757, 2.747346540307211

2.7473465403033757, 2.747346540307211, 2.747346540307211

最后一个值是未打印的正确值？

Answer 1

我刚刚运行了您的代码，发现fx(b)和fx(a)是相同的值。因此，当您计算fx(b)减去fx(a)时，您会得到0希望这会有所帮助。

Terminal -----------------------------------
Enter zeroes in approxiamtion in solution: 5
Enter upper limit for root: 5
Enter lower limit for root: 5
93.0
93.0
Traceback (most recent call last):
  File "d:/PythonScripts/first_python_project/curso_python.py", line 13, in <module>
    c = b - ((b - a)/(fx(b) - fx(a))) * fx(b)
ZeroDivisionError: float division by zero

添加更多：当您达到较低的值时，仅fx(b)和fx(a)会变得非常相似。像这样的东西：

Enter zeroes in approxiamtion in solution: 3
Enter upper limit for root: 5
Enter lower limit for root: 3
93.0
5.0
3.0, 5.0, 2.8863636363636362

2.614751596543952
93.0
5.0, 2.8863636363636362, 2.825218326106125

1.424401534793665
2.614751596543952
2.8863636363636362, 2.825218326106125, 2.7520503761266304

0.08317571970829363
1.424401534793665
2.825218326106125, 2.7520503761266304, 2.747512887487003

0.002935214303143141
0.08317571970829363
2.7520503761266304, 2.747512887487003, 2.747346905212986

6.43830337132556e-06
0.002935214303143141
2.747512887487003, 2.747346905212986, 2.747346540335565

5.002736003234531e-10
6.43830337132556e-06
2.747346905212986, 2.747346540335565, 2.747346540307211

1.7763568394002505e-15
5.002736003234531e-10
2.747346540335565, 2.747346540307211, 2.747346540307211

1.7763568394002505e-15
1.7763568394002505e-15
Traceback (most recent call last):
  File "d:/PythonScripts/first_python_project/curso_python.py", line 13, in <module>
    c = b - ((b - a)/(fx(b) - fx(a))) * fx(b)
ZeroDivisionError: float division by zero

Answer 2

我看到两个问题。一种是表达式（（1 * 10 ^ -err））。 Python中的运算符^表示按位XOR，而10 ^ -err是负整数。因此，在找到根之后，循环不会结束。它应该是abs（10 ** -err）。

第二个问题是c = 0作为根的初始值。它应该在（a，b）间隔之内，而不是零。

Answer 3

您收到此错误，因为在代码中的某些时候

让我们说fx(a)=1.0000000000000001和fy(b)=1.0

而不是fx(a)-fy(b)=0.0000000000000001您得到0.0。

因此出现零除法错误