python - ValueError: negative number cannot be raised to a fractional power

22
votes

When I tried this in terminal

>>> (-3.66/26.32)**0.2

I got the following error

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: negative number cannot be raised to a fractional power

However, I am able to do this in two steps like,

>>> (-3.66/26.32)
-0.13905775075987842
>>> -0.13905775075987842 ** 0.2
-0.6739676327771593

Why this behaviour? What is the way to solve this in single line?

2
python
(possibly) related: stackoverflow.com/questions/4114740/negative-pow-in-python - TerryA
@Haidro, Yes I have seen the question, but my question is (-1.07) ** 1.3 is throwing error but -1.07 ** 1.3 is not throwing error why ? - John Prawyn
I think this relates to complex numbers. The square root (fractional power) of negative 1 is i. It bales when it thinks it's getting into complex number territory. - Jiminion

2 Answers

19
votes

Raising to a power takes precedence over the unary minus sign.

So you have -(0.13905775075987842 ** 0.2) and not (-0.13905775075987842) ** 0.2 as you expect:

>>> -0.13905775075987842 ** 0.2
-0.6739676327771593
>>> (-0.13905775075987842) ** 0.2
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: negative number cannot be raised to a fractional power

If you want it to work you should write (-3.66/26.32 + 0j)**0.2

>>> (-3.66/26.32 + 0j)**0.2
(0.5452512685753758+0.39614823506888347j)

Or switch Python 3 as noted by @TimPietzcker.

7
votes

Switch to Python 3 which automatically promotes the result to a complex number:

>>> (-3.66/26.32)**0.2
(0.5452512685753758+0.39614823506888347j)