x ** 1/3 in python?

Question

Recently I encountered a problem:

I want to calculate various roots of various numbers like this:

x = x ** 1/y+1

None of the methods I know result in a working code.

Method 1:

x = 54
y = 2
x = x ** 1/y+1
print(x)

Printed value is 28.0 instead of 3.7798

Method 2:

x = 54
y = 2
x = x ** 1/(y+1)
print(x)

Printed value is 18.0 istead of 3.7798

Method 3:

x = 216
y = 2
x = x ** (1/(y+1))
print(x)

Printed value is 5.99 instead of 6

Is there a way that would work with y being up to 20?

Edit:

Another suggested method:

def nth_root(val, n):
    ret = int(val**(1./n))
    return ret + 1 if (ret + 1) ** n == val else ret

y = 1
print(nth_root(19, (y+1)))

prints 4

for starters, https://docs.python.org/3/reference/expressions.html#operator-precedence — njzk2, Jan 27 '16 at 00:22
You should look up "operator precedence" for Python, which would indicate that you need the parentheses as shown in your 3rd attempt. As far as the 5.99 answer is concerned, I did not get that when I tried your example. I suspect there's more context to your scenario than you've described. — lurker, Jan 27 '16 at 00:23
`5.999999999999999` in 3.5 too. I thought 3.x had the intelligent repr thing? — nneonneo, Jan 27 '16 at 00:27

Prune · Answer 1 · 2016-01-27T00:26:52.840

3

You don't seem to understand (yet) order of operations in a programming language. You need parentheses to make sure you add 1 to y, then take the reciprocal, and then use that as an exponent. The "natural" order is the opposite.

x = x ** (1.0/(y+1))

edited Jan 27 '16 at 00:26

answered Jan 27 '16 at 00:23

Prune

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Well, no ... it must have been Python 3, in which division is floating point by default. Or the result would have been different. – Tom Zych Jan 27 '16 at 00:24
x = 216 y = 2 x = x ** (1.0/(y+1)) print(x) still prints 5.9999 – Mantas Kandratavičius Jan 27 '16 at 00:25
@Tom Zych: thanks; I've updated the answer. – Prune Jan 27 '16 at 00:27
There has to be something I'm missing... My last method looks exactly like yours just with .0 added. Even if I add the .0, I still get 5.99 printed. So is it that ,,I don't seem to understand'' or your way doesn't solve my problem either? – Mantas Kandratavičius Jan 27 '16 at 00:32
1

@MantasKandratavicius use [this method](http://stackoverflow.com/a/15978862/645956). – grc Jan 27 '16 at 00:32
@grc Thanks for a new method but it either doesn't work or im doing something wrong again. def nth_root(val, n): ret = int(val**(1./n)) return ret + 1 if (ret + 1) ** n == val else ret y = 1 print(nth_root(19, (y+1))) prints 4 – Mantas Kandratavičius Jan 27 '16 at 00:49
If you want to guarantee exact arithmetic in integer cases, you need to use an integer-preserving algorithm. Binary computers do not perform exact arithmetic: they round to the nearest binary representation, given their precision levels. Trying printing the value of 1.0/3, and you'll see that it's not an infinite series of 3's; this is why the resulting operation comes up a little off your expectation. – Prune Jan 27 '16 at 00:51

Carson · Accepted Answer · 2016-01-27T18:46:47.853

Since everyone else has already told you why your Method 3 is correct, I'll stick to getting you an accurate answer. You can read more about why you're not getting exactly 6, but basically it's because your computer doesn't represent the 1/3 exactly when doing the calculation and makes the final answer off.

So, the easiest solution is to use sympy:

import sympy

y = 216
x = 2
x = sympy.root(y,x+1)
print(x)

score 2 · Answer 3 · edited May 23 '17 at 12:08

2

What you want is this (assuming you are using Python 3):

x = x ** (1/(y+1))

For Python 2, either of the following will work:

from __future__ import division
x = x ** (1/(y+1))

or (also fine on Python 3):

x = x ** (1.0/(y+1))

The issue is you need to apply the parentheses in the correct locations to get the order of operations right.

Method 3 is to do with floating point arithmetic. See: https://docs.python.org/3.5/tutorial/floatingpoint.html

For more info on Python 2 vs. Python 3 division: Division in Python 2.7. and 3.3

edited May 23 '17 at 12:08

Community

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answered Jan 27 '16 at 00:24

vk1011

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if the OP were using python 2, their 3rd example would ouptut 1, not 5.99 – njzk2 Jan 27 '16 at 00:25
Correct. My solutions take that in to account. I will update the solution to clarify the logic errors in the OP's code too. – vk1011 Jan 27 '16 at 00:26
my point being that the op is not using python 2, which your solution assumes – njzk2 Jan 27 '16 at 00:28
Point taken. I'll edit the Python 2 part as reference only. – vk1011 Jan 27 '16 at 00:33

score 0 · Answer 4 · answered Jan 27 '16 at 00:24

0

Only your last code works because ** has higher precedence than / (and / has higher precendence than +).

The value is not exactly 6, because floating point numbers are not perfectly accurate. A third can not be represented as a float.

answered Jan 27 '16 at 00:24

Joonazan

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score 0 · Answer 5 · answered Jan 27 '16 at 00:30

All your values are just as expected. According to the python operator precedence:

x ** 1/y+1 is parsed as ((x ** 1) / y) + 1, and

x ** 1/(y+1) is actually (x ** 1) / (y + 1).

What you probably want is x ** (1. / (y + 1)). Note, that 1. is a floating point number, causing the whole expression to be evaluated as floats. This also means that you will work with finite precision, e.g., getting 5.99999 instead fo 6 is to be expected.

x ** 1/3 in python?

5 Answers5