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Re: Newby Q: How to specify reals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110544] Re: Newby Q: How to specify reals
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Fri, 25 Jun 2010 07:25:38 -0400 (EDT)

Comments interspersed in-line below...

On 6/24/2010 4:27 AM, AES wrote:
> In article<hvs7n2$8v0$1 at smc.vnet.net>,
>   "David Park"<djmpark at comcast.net>  wrote:
>
>> When working with complex expressions your best friend is the ComplexExpand
>> command. For some reason, this command doesn't immediately jump to the
>> notice of beginners and this leads to frequent questions on MathGroup.
>
> It doesn't immediately jump to the notice of beginners because:
>
> 1)  Unlike familiar commands or functions or operators such as Sin, Cos,
> Exp, SquareRoot, or even Re[-] or Im[-] or complex conjugate, there is
> no such command or operator in "ordinary mathematics."
>
> No one _says_ "ComplexExpand" in ordinary mathematical discourse, and
> the term would not have been encountered by the ordinary high school or
> even college graduate.

Many complex analysis problems in textbooks ask you to "express you 
answer in a + b i form".  How would YOU name a Mathematical function to 
do that?  I think "ComplexExpand" is a darned good rendering.

>
> 2)  It's bizarrely named.  SeriesExpand _expands_ into a series.
> ComplexExpand[Re[expr]] trims, or selects.
>

I don't find anything "bizarre" about the naming.  Compare, e.g., 
TrigExpand, PiecewiseExpand, PowerExpand.


> 3)  And, because of Mathematica's generally dysfunctional documentation
> -- e.g. "ComplexExpand" is not even mentioned in tutorial/ComplexNumbers
> and if it's mentioned in ref/Conjugate, it's buried somewhere down in
> the nested and closed subsections and therefore cannot be _searched_ for
> using any kind of Find command.
>

to somebody who is determined to prove that the Mathematica 
documentation is "dysfuncional", then probably it is. But somebody who 
wants to make use of the documentation instead of complain about it 
should have little trouble finding out about this.  For example...

   - Open Documentation Center
   - Expand Mathematics and Algorithms
   - Select Numbers & Precision
   - Select Complex Numbers
   - Visually scan what's there
   - See "ComplexExpand - expand symbolic expressions into real
     and imaginary parts"
   - Select that function
   - Read about it: expand the More Information section; look at
     examples
   - From the Tutorials section on the ref/ComplexExpand page, select
     Expressions Involving Complex Variables
   - Read the page

Or,  here's another way, using search!

    - Open Documentation Center
    - do a search for "complex variables"
    - examine the search results
    - directly, or indirectly, select ComplexExpand from its abbreviated
      description; OR instead
    - select "Expressions Involving Complex Variables"

> Would anyone suggest that the occurrence of "frequent questions on
> MathGroup" might indicate a weakness, or even a product defect, in this
> particular Mathematica design decision?

No, I would NOT so suggest.  Rather, I'd suggest an excellent design of 
a huge and complex system by very smart and savvy people coping with the 
limitations of the ordinary mortals who use it.

An analyst I met in graduate school was fond of saying, "There are 
really only two topological spaces in which I believe: the real numbers 
and the complex numbers.  And I'm not so sure about the real numbers!"

-- 
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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