Re: Re: What to do in v. 6 in place of Miscellaneous`RealOnly

• To: mathgroup at smc.vnet.net
• Subject: [mg76799] Re: [mg76728] Re: What to do in v. 6 in place of Miscellaneous`RealOnly
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sun, 27 May 2007 05:06:36 -0400 (EDT)
• References: <f33ork\$l7l\$1@smc.vnet.net> <f36dbl\$6eo\$1@smc.vnet.net> <200705260840.EAA18695@smc.vnet.net>

```On 26 May 2007, at 17:40, Helen Read wrote:

> David W.Cantrell wrote:
>>> Suppose my calculus students want to plot x^(1/3), for say
>>> {x,-8,8}. The
>>> problem, of course, is that Mathematica returns complex roots for
>>> x<0.
>>> In past versions of Mathematica, we could get the desired real roots
>>> Miscellaneous`RealOnly. I
>>> guess we can still do it that way (and ignore the "obsolete package"
>>> message), but is there a suggested way of doing what we need in 6.0?
>>
>> Perhaps have them define their own
>>
>> realCubeRoot[x_]:= Sign[x] Abs[x]^(1/3)
>>
>> which plots as desired, of course.
>
> Well, yes, but it's kind of a pain to have to define their own root
> functions this way on an individual basis. (Not to mention, it
> completely hoses the derivative. Try realCubeRoot'[x] or
> realCubeRoot'[-8] and see what you get.)
>
> I was hoping for a more convenient way to do this in Mathematica 6.0.
> Surely it *knows* the real nth roots of x for n odd and x<0. It
> would be
> nice to be able to define f[x_]=x^(1/3) or x^(3/5) or whatever and
> just
> set some option to make it return the real value for x<0.
>
> --
> University of Vermont
>

Yes, it knows it, and there is a way of expressing it, but I am sure
you won't like it.

realCubeRoot[x_] := Root[#^3 - x &, 1]

Now,

realCubeRoot[-1]
-1

etc. Plotting is no problem. Moreover you can differentiate, but only
using D !

D[realCubeRoot[x], x] /. x -> 8
1/12

It won't work with Derivative :

realCubeRoot'[x]
0

And just in case anyone thinks of reporting the last output as a bug
to WRI, this has been known ever since RootObject appeared in version
3 of Mathematica.

Andrzej Kozlowski

```

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