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MathGroup Archive 2007

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg76709] Re: [mg76653] Re: What to do in v. 6 in place of Miscellaneous`RealOnly
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Sat, 26 May 2007 04:30:48 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <f33ork$l7l$1@smc.vnet.net> <200705251035.GAA08064@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

That is really not a solution to the problem: the poster undoubtedly 
expects to be able to obtain, and plot, an inverse of the cubing 
function R -> R with that inverse defined on the entire real line R.

One root difficulty here is that a "function" really should consist of 
three things: a set that is its domain, a set that is its codomain, and 
the "rule" for assigning to each element of the domain an element of the 
codomain.

Unfortunately, in ordinary calculus, and before, there is a tacit 
understanding that, given a rule (usually, just a formula involving a 
variable x), the function has as domain all the real values of x that 
produce real values from the formula.  And so if one is given a 
one-to-one function from R to R, its inverse should also be a function 
from R to R.

In Mathematica in many cases a function has tacit domain a subset of the 
  set of complex numbers C -- and at times it is unclear what that 
domain is -- and then the codomain is C.

Another root difficulty is the use of a power function.  That, of 
course, is what makes Mathematica want to use the principal cube root in 
the sense of complex numbers.


Jens-Peer Kuska wrote:
> Hi,
> 
> just try it ...
> 
> Plot[] will remove all not-plotable values and
> 
> Plot[x^(1/3), {x, -2, 2}]
> 
> show nothing on the negative part of the x-axes
> and
> Plot3D[(x + y)^(1/3), {x, -2, 2}, {y, -2, 2}]
> will be cutted along the x==-y line.
> 
> So, do nothing and remove the RealOnly package.
> 
> Regards
>    Jens
> 
> 
> Helen Read 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?
>>
>> --
>> Helen Read
>> University of Vermont
>>
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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