Re: [R] cube root

From: David Winsemius <dwinsemius_at_comcast.net>
Date: Sun, 17 Apr 2011 01:25:40 -0700 (PDT)

Hey :)

In addition, although (-2)^3 = -8, (-8)^(1/3) != -2, mathematically. A fractional power of a negative number is complex.

_Not_ in addition. The citation of FAQ 7.33 did not address the correct issue since the sequence was enclosed in parens. Yours is the only correct answer. For further discussion about various approaches to fractional powers of negative numbers one can get further approaches by searching the archives.

-- 
David.

And this can be
obtained properly in R:

> (-8+0i)^(1/3)
[1] 1+1.732051i

Cheers,

Tsjerk


>> This is some interesting:
>>
>>> -8^(1/3)
>>
>> [1] -2
>>
>>> x=(-8:8)
>>
>>> y=x^(1/3)
>>
>>> y
>>
>>  [1]      NaN      NaN      NaN      NaN      NaN      NaN      NaN
>> NaN
>> 0.000000 1.000000
>>
>> [11] 1.259921 1.442250 1.587401 1.709976 1.817121 1.912931 2.000000
>> So, can anybody explain this?! (Why is x[1]^(1/3)=y[1]=NaN, but
>> -8^(1/3)=-2?)
>>
> > Operator precedence. > > See R FAQ 7.33 Why are powers of negative numbers wrong? > > > Berend > Tsjerk Wassenaar wrote: > > Hey :) > > In addition, although (-2)^3 = -8, (-8)^(1/3) != -2, mathematically. A > fractional power of a negative number is complex. And this can be > obtained properly in R: >
>> (-8+0i)^(1/3)
> [1] 1+1.732051i > > Cheers, > > Tsjerk >
>>> This is some interesting:
>>>
>>>> -8^(1/3)
>>>
>>> [1] -2
>>>
>>>> x=(-8:8)
>>>
>>>> y=x^(1/3)
>>>
>>>> y
>>>
>>>  [1]      NaN      NaN      NaN      NaN      NaN      NaN      NaN
>>> NaN
>>> 0.000000 1.000000
>>>
>>> [11] 1.259921 1.442250 1.587401 1.709976 1.817121 1.912931 2.000000
>>> So, can anybody explain this?! (Why is x[1]^(1/3)=y[1]=NaN, but
>>> -8^(1/3)=-2?)
>>>
>>
>> Operator precedence.
>>
>> See R FAQ 7.33 Why are powers of negative numbers wrong?
>>
>>
>> Berend
>>
>>
>> --
>> View this message in context:
>> http://r.789695.n4.nabble.com/cube-root-tp3455020p3455027.html
>> Sent from the R help mailing list archive at Nabble.com.
>>
>> ______________________________________________
>> R-help_at_r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
> > > > -- > Tsjerk A. Wassenaar, Ph.D. > > post-doctoral researcher > Molecular Dynamics Group > * Groningen Institute for Biomolecular Research and Biotechnology > * Zernike Institute for Advanced Materials > University of Groningen > The Netherlands > > ______________________________________________ > R-help_at_r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > Tsjerk Wassenaar wrote: > > Hey :) > > In addition, although (-2)^3 = -8, (-8)^(1/3) != -2, mathematically. A > fractional power of a negative number is complex. And this can be > obtained properly in R: >
>> (-8+0i)^(1/3)
> [1] 1+1.732051i > > Cheers, > > Tsjerk >
>>> This is some interesting:
>>>
>>>> -8^(1/3)
>>>
>>> [1] -2
>>>
>>>> x=(-8:8)
>>>
>>>> y=x^(1/3)
>>>
>>>> y
>>>
>>>  [1]      NaN      NaN      NaN      NaN      NaN      NaN      NaN
>>> NaN
>>> 0.000000 1.000000
>>>
>>> [11] 1.259921 1.442250 1.587401 1.709976 1.817121 1.912931 2.000000
>>> So, can anybody explain this?! (Why is x[1]^(1/3)=y[1]=NaN, but
>>> -8^(1/3)=-2?)
>>>
>>
>> Operator precedence.
>>
>> See R FAQ 7.33 Why are powers of negative numbers wrong?
>>
>>
>> Berend
>>
>>
>> --
>> View this message in context:
>> http://r.789695.n4.nabble.com/cube-root-tp3455020p3455027.html
>> Sent from the R help mailing list archive at Nabble.com.
>>
>> ______________________________________________
>> R-help_at_r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
> > > > -- > Tsjerk A. Wassenaar, Ph.D. > > post-doctoral researcher > Molecular Dynamics Group > * Groningen Institute for Biomolecular Research and Biotechnology > * Zernike Institute for Advanced Materials > University of Groningen > The Netherlands > > ______________________________________________ > R-help_at_r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > -- View this message in context: http://r.789695.n4.nabble.com/cube-root-tp3455020p3455118.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help_at_r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Received on Sun 17 Apr 2011 - 08:30:10 GMT

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