Python中负数的准确根

Question

I'm looking for a way to accurately compute roots of negative numbers in Python. I believe that the inaccuracies I see are related to floating point , but it seems like there should be a way to get the right answer for something as simple as this:

>>(-1+0j)**0.1
(0.9510565162951535+0.3090169943749474j)

The answer I expect in this case is (0+1j) . Though raising Python's response to the tenth does come close to -1, I am looking for an answer obtained from a more precise method, ie, one that when raised to the tenth equals exactly -1, not a number really close to -1.

Is there a way to do this correctly with either a native Python library, or sympy/numpy/scipy etc?

Answer 1

-1 has not one but 10 complex tenth roots. You got only one of them. If a is your returned root, a ** 5 is also a root:

(a ** 5) ** 10 = (a ** 10) ** 5 = (-1) ** 5 = -1

But if you run:

a = (-1 + 0j) ** 0.1
print(a)
print(a ** 5)

you'll get:

(0.951056516295+0.309016994375j)
(1.11022302463e-16+1j)

You see a ** 5 is very close to 1j .