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MathGroup Archive 2007

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg76728] Re: What to do in v. 6 in place of Miscellaneous`RealOnly
  • From: Helen Read <read at math.uvm.edu>
  • Date: Sat, 26 May 2007 04:40:38 -0400 (EDT)
  • References: <f33ork$l7l$1@smc.vnet.net> <f36dbl$6eo$1@smc.vnet.net>

David W.Cantrell wrote:
> Helen Read <read at math.uvm.edu> 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
>> (and plot the function) by loading the package 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.

--
Helen Read
University of Vermont


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