Why is (-27)**(1.0/3.0) not -3.0 in Python?

Question

In math, you are allowed to take cubic roots of negative numbers, because a negative number multiplied by two other negative numbers results in a negative number. Raising so

Answer 1

The type coercion rules documented by builtin pow apply here, since you're using a float for the exponent.

Just make sure that either the base or the exponent is a complex instance and it works:

>>> (-27+0j)**(1.0/3.0)
(1.5000000000000004+2.598076211353316j)
>>> (-27)**(complex(1.0/3.0))
(1.5000000000000004+2.598076211353316j)

To find all three roots, consider numpy:

>>> import numpy as np
>>> np.roots([1, 0, 0, 27])
array([-3.0+0.j        ,  1.5+2.59807621j,  1.5-2.59807621j])

The list [1, 0, 0, 27] here refers to the coefficients of the equation 1x³ + 0x² + 0x + 27.