Hi, The powerplus package does raise a negative number to a fractional power. Try:
library(powerplus) explus(-.5, 1/5) Klaus. On 17/05/2016 17:55, Albyn Jones wrote: > I think R is doing just what it should do, and the TI has been hacked to > make HS teachers happy :-) > >> log(as.complex(-2))/5 > [1] 0.1386294+0.6283185i >> a <- log(as.complex(-2))/5 >> exp(a)^5 > [1] -2-0i > >> exp(a) > [1] 0.9293165+0.675188i >> (as.complex(-2))^(1/5) > [1] 0.9293165+0.675188i >> 2^(1/5)*cos(pi/5) > [1] 0.9293165 >> 2^(1/5)*sin(pi/5) > [1] 0.675188 > > albyn > > > On Tue, May 17, 2016 at 8:10 AM, Richard M. Heiberger <[email protected]> > wrote: > >> This problem is an example of FAQ 7.31. Floating point numbers >> inside the computer can not represent odd fractions exactly. >> >>> seq(1, 15, 2) >> [1] 1 3 5 7 9 11 13 15 >>> 1/seq(1, 15, 2) >> [1] 1.00000000 0.33333333 0.20000000 0.14285714 0.11111111 0.09090909 >> 0.07692308 >> [8] 0.06666667 >>> print(1/seq(1, 15, 2), digits=18) >> [1] 1.0000000000000000000 0.3333333333333333148 0.2000000000000000111 >> [4] 0.1428571428571428492 0.1111111111111111049 0.0909090909090909116 >> [7] 0.0769230769230769273 0.0666666666666666657 >>> ## except for 1, none of these odd fractions is exactly represented >> inside the computer. >>> ## therefore the power requested is not the exact fraction, and the >> result is not capable of calculation >>> (-2)^(1/seq(1, 15, 2)) >> [1] -2 NaN NaN NaN NaN NaN NaN NaN >> Rich >> >> On Tue, May 17, 2016 at 10:23 AM, [email protected] <[email protected]> >> wrote: >>> Forwarded message: >>>>>> System is working correctly. A negative number cannot be raised to a >>>>>> fractional power: >>>>>> >>>>>>> (-2)^(1/5) >>>>>> [1] NaN >>> Well, maybe we should say that _R_ can't raise a negative number to a >>> fractional power. Neither I nor the TI calculators have any trouble >>> doing it;-) I'd say R is funtioning as designed, but it was designed >>> to respond INcorrectly;-) >>> >>> This R exchange >>> >>>> (-2)^5 >>> [1] -32 >>> >>> shows that -2 is a fifth root of -32 while this exchange >>> >>>> (-32)^(1/5) >>> [1] NaN >>> >>> shows that R cannot find that root. The various suggestions for >>> dealing with this amount to asking R a different question which we >>> know has the same answer as the intended question (which R won't >>> answer). >>> >>> On one level you could view this as a coding/implementation issue. I >>> have not looked at R's code, but the usual computer way to handle >>> exponents involves taking the log of the argument. This does not >>> return the correct answer when the argument is negative. That's >>> annoying. The TI graphing calculators were developed with an >>> incredible amount of input from secondary math. teachers. They >>> complained loudly about calculators returning wrong answers or >>> non-answers to problems to which students knew the right answers. TI >>> did a LOT of work on this. I wish R (and lots of scientific software) >>> would do likewise. >>> >>> On another level, involving exponentiation is not entirely avoidable. >>> For rational numbers like 1/5 we can (and usually do) interpret >>> (-32)^(1/5) as a name for a real number that when raised to the fifth >>> power gives -32. Another name for one such number is -2. But if we want >>> to use an irrational exponent, say (-32)^pi we can't interpret it that >>> way. (How do we multiply pi numbers together?) So eventually we have >>> to either exponentiate or have a funciton that is undefined at many >>> points. At lesat in theory. As far as computers and calculators are >>> concerned, they cannot represent irrational numbers anyway -- >>> eveything is a rational approximation. >>> >>> So I think the defect is in R, not in the original posted question. >>> >>> -------> First-time AP Stats. teacher? Help is on the way! See >>> >> http://courses.ncssm.edu/math/Stat_Inst/Stats2007/Bob%20Hayden/Relief.html >>> _ >>> | | Robert W. Hayden >>> | | 614 Nashua Street #119 >>> / | Milford, New Hampshire 03055 USA >>> | | >>> | | email: bob@ the site below >>> / x | website: http://statland.org >>> | / >>> '''''' >>> >>> _______________________________________________ >>> [email protected] mailing list >>> https://stat.ethz.ch/mailman/listinfo/r-sig-teaching >> _______________________________________________ >> [email protected] mailing list >> https://stat.ethz.ch/mailman/listinfo/r-sig-teaching >> > [[alternative HTML version deleted]] > > _______________________________________________ > [email protected] mailing list > https://stat.ethz.ch/mailman/listinfo/r-sig-teaching -- ---------------------------------------------------- Klaus Langohr Departament d'Estad�stica i Investigaci� Operativa Universitat Polit�cnica de Catalunya Edifici C5 (Campus Nord) C/ Jordi Girona, 1-3 E-08034 Barcelona Tel: (+34) 934 017 034 Fax: (+34) 934 015 855 ---------------------------------------------------- [[alternative HTML version deleted]]
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