with. Again, I know nothing about Python and so do not know if it is
");
Three roots of (-1)**3
[(-1, 0), (1/2, -sqrt(3)/2), (1/2, sqrt(3)/2)]
Lets check root (1/2, -sqrt(3)/2)
In the complex plane the vector length for (1/2, -sqrt(3)/2)
> Jon,
> Here is someone in the SAS discussion group how appears to have done
> it with Python. I don't know anything about Python, yet. Would you
> agree with his solution?
> Stan
>
> %let x=-1;
>
> %utl_submit_py64("
> from sympy import *;
> import pyperclip;
> x = symbols('x');
> x=&x;
> r=x^(1/3);
> pyperclip.copy(r);
> print r;
> ",return=fromPy);
>
> %put Cube root of -1 is &=frompy;
>
> LOG
>
> Cube root of -1 is FROMPY=-1
>
>
>
>
>
> On 11/16/2019 7:32 AM, Jon Peck wrote:
>> I thought it would be interesting to explore negative numbers
>> exponentiated to fractional powers in other systems. Here is what I
>> found. (NaN is a value for not a number. Equivalent to SYSMIS.)
>>
>>
>> SPSS Statistics
>> compute z = (-1)**(1/3).
>> SYSMIS
>> Warning # 523
>> >During the execution of the indicated command, an attempt was made
>> to raise a
>> >non-positive number to a fractional power, e.g. (-3)**2.5.
>>
>> golang
>> output := math.Pow(-1, 1./3.)
>> NaN
>> No warning
>>
>> Python
>> (-1)**(1./3.)
>> no result - calculation is stopped
>> ValueError: negative number cannot be raised to a fractional power
>>
>> R
>> (-1)^(1/3)
>> NaN
>> No warning
>>
>> Although I have not seen the SPSS internal transformation code, I
>> expect that it uses logs to calculate exponentiation with a
>> fractional power, hence the error.
>>
>> The expression could be refactored to get a result in the case where
>> the denominator of the exponent is odd but not as a general
>> solution. Since Statistics, as with most statistical packages, does
>> not support complex numbers in expressions, that solution is not
>> available.
>>
>> From Wikpedia...
>>
>> The powers of negative real numbers are not always defined and are
>> discontinuous even where defined. In fact, they are only defined when
>> the exponent is a rational number with the denominator being an odd
>> integer.
>>
>> If the definition of exponentiation of real numbers is extended to
>> allow negative results then the result is no longer well-behaved.
>>
>> Neither the logarithm method nor the rational exponent method can be
>> used to define /b/^/r/ as a real number for a negative real number
>> /b/ and an arbitrary real number /r/. Indeed, /e/^/r/ is positive
>> for every real number /r/, so ln(/b/) is not defined as a real number
>> for /b/ ≤ 0.
>>
>> The rational exponent method cannot be used for negative values of
>> /b/ because it relies on continuity
>> <
https://en.wikipedia.org/wiki/Continuous_function>. The function
>> /f/(/r/) = /b/^/r/ has a unique continuous extension^[15]
>> <
https://en.wikipedia.org/wiki/Exponentiation#cite_note-Denlinger-15>
>> from the rational numbers to the real numbers for each /b/ > 0. But
>> when /b/ < 0, the function /f/ is not even continuous on the set of
>> rational numbers /r/ for which it is defined.
>>
>> For example, consider /b/ = −1. The /n/th root of −1 is −1 for every
>> odd natural number /n/. So if /n/ is an odd positive integer,
>> (−1)^(/m///n/) = −1 if /m/ is odd, and (−1)^(/m///n/) = 1 if /m/ is
>> even. Thus the set of rational numbers /q/ for which (−1)^/q/ = 1 is
>> dense <
https://en.wikipedia.org/wiki/Dense_set> in the rational
>> numbers, as is the set of /q/ for which (−1)^/q/ = −1. This means
>> that the function (−1)^/q/ is not continuous at any rational number
>> /q/ where it is defined.
>>
>> On the other hand, arbitrary complex powers
>> <
https://en.wikipedia.org/wiki/Exponentiation#Powers_of_complex_numbers> of
>> negative numbers /b/ can be defined by choosing a /complex/ logarithm
>> <
https://en.wikipedia.org/wiki/Complex_logarithm> of /b/.
>>
>>
>>
>>
>> On Fri, Nov 15, 2019 at 10:26 AM Stan Gorodenski
>> <
[hidden email] <mailto:
[hidden email]>> wrote:
>>
>> I don't know if there is any demand, but I think the square root
>> of -1
>> is used in electronics. I'm not into this so I really don't know.
>> I did
>> not pose this question because I have an application for it. I was
>> just
>> curious since it seems that sophisticated software packages like
>> SPSS
>> and SAS should be able to do it. I just sent an email to join the
>> SAS
>> discussion group and will ask them if SAS can do it. I suppose one
>> could
>> write a routine to return a -1 if the the denominator of the
>> exponent is
>> an odd number.
>> Stan
>>
>> On 11/15/2019 10:05 AM, Rich Ulrich wrote:
>> > I wonder - Is there any demand for the exception-coding
>> > that would be necessary? How many people write code
>> > where they want to take the fractional root of a negative
>> > number, where the fraction is the reciprocal of an odd integer?
>> > ( Note, the fraction cannot be expressed EXACTLY on a binary
>> > computer. How is that accommodated?)
>> >
>> > The natural programming solution to non-integer roots is
>> > to use logs. I suppose if there is an area where the problem
>> > comes up, specialized programs for that area might do it.
>> > I suspect the efficient solution might use a special subroutine
>> > call rather than an in-line expression.
>> >
>> > --
>> > Rich Ulrich
>> >
>> >
>> ------------------------------------------------------------------------
>> > *From:* SPSSX(r) Discussion <
[hidden email]
>> <mailto:
[hidden email]>> on behalf of
>> > Bruce Weaver <
[hidden email]
>> <mailto:
[hidden email]>>
>> > *Sent:* Friday, November 15, 2019 11:35 AM
>> > *To:*
[hidden email] <mailto:
[hidden email]>
>> <
[hidden email] <mailto:
[hidden email]>>
>> > *Subject:* Re: Roots
>> >
>>
https://www.ibm.com/support/knowledgecenter/en/SSLVMB_26.0.0/statistics_reference_project_ddita/spss/base/syn_transformation_expressions_domain_errors.html>> >
>> >
>> >
>> > Kirill Orlov wrote
>> > > See DOMAIN ERRORS paragraph in Command Syntax Reference.
>> > >
>> > >
>> > > 15.11.2019 4:53, Stan Gorodenski пишет:
>> > >> compute z = (-1)**(1/3).
>> > >
>> > > =====================
>> > > To manage your subscription to SPSSX-L, send a message to
>> >
>> > > LISTSERV@.UGA
>> >
>> > > (not to SPSSX-L), with no body text except the
>> > > command. To leave the list, send the command
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>> > > For a list of commands to manage subscriptions, send the command
>> > > INFO REFCARD
>> >
>> >
>> >
>> >
>> >
>> > -----
>> > --
>> > Bruce Weaver
>> >
[hidden email] <mailto:
[hidden email]>
>> >
http://sites.google.com/a/lakeheadu.ca/bweaver/>> >
>> > "When all else fails, RTFM."
>> >
>> > NOTE: My Hotmail account is not monitored regularly.
>> > To send me an e-mail, please use the address shown above.
>> >
>> > --
>> > Sent from:
http://spssx-discussion.1045642.n5.nabble.com/>> >
>> > =====================
>> > To manage your subscription to SPSSX-L, send a message to
>> >
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>> > ===================== To manage your subscription to SPSSX-L,
>> send a
>> > message to
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>> > <mailto:
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>> <mailto:
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>> text
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>> > command INFO REFCARD
>>
>> =====================
>> To manage your subscription to SPSSX-L, send a message to
>>
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>>
>>
>> --
>> Jon K Peck
>>
[hidden email] <mailto:
[hidden email]>
>>
>> ===================== To manage your subscription to SPSSX-L, send a
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>> command INFO REFCARD
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
>
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>
command. To leave the list, send the command