Re: Problem with eval. of neg. cube root of neg. #

*To*: mathgroup at smc.vnet.net*Subject*: [mg49918] Re: [mg49894] Problem with eval. of neg. cube root of neg. #*From*: Selwyn Hollis <sh2.7183 at misspelled.erthlink.net>*Date*: Fri, 6 Aug 2004 03:09:35 -0400 (EDT)*References*: <200408051321.JAA05879@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On Aug 5, 2004, at 9:21 AM, Josh wrote: > I am having trouble plotting the following function: > > Plot[x^(1/3)*(x + 4), {x, -10, 10}] > > Mathematica won't plot this function for negative x, although it is > obviously defined for negative x. It seems to be evaluating the > negative part of this function to imaginary numbers for some odd > reason.If I do: > > f[x_] := (x^(1/3))*(x + 4) > > and then: > > f[-5] // N > > I get: > > -0.854988 - 1.48088 \[ImaginaryI] > > when the correct answer is the negative cube root of negative 5, which > is approximately - (-1.70998) = 1.70998 > > I can send a copy of the notebook that shows where this is happening > to anyone who requests it... > > Can anyone explain what is going on here? Is this a bug or am I > missing something? > > Thanks in advance for any help ... > > Josh, This is actually typical behavior of software that do computations with complex numbers. When x is negative, x^(1/3) returns the "principle" cube root of x, which is Abs[x](Cos[Pi/3] + I Sin[Pi/3]). You can verify this as follows: In: ComplexExpand[ (Cos[Pi/3] + I Sin[Pi/3])^3 ] Out: -1 Since you want to get the real cube root, you should use Sign[x]Abs[x]^(1/3) in place of x^(1/3). You might want to use that to define a function with a name analogous to Sqrt: Cbrt[x_]:= Sign[x]Abs[x]^(1/3) ----- Selwyn Hollis http://www.appliedsymbols.com (edit reply-to to reply)

**References**:**Problem with eval. of neg. cube root of neg. #***From:*pootleguard-mathgroup@yahoo.com (Josh)