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Re: Conformal Mapping

On Nov 4, 2012, at 8:12 PM, Andrzej Kozlowski <akozlowski at gmail.com> wrote:

>
> On 4 Nov 2012, at 16:29, Murray Eisenberg <murray at math.umass.edu> wrote:
>>
>> As to drawing the region: Yes, of course one can do it with
> out-of-the-box Mathematica. But it seems counterintuitive to have to
> plot a figure involving a complex-valued function of a complex variable
> by breaking complex numbers z apart into their real and imaginary parts
> x and y. After all, for calculations Mathematica "wants" numbers to be
> complex rather than real! What Park's "Presentations" allows is to work
> directly in complex terms for plotting.  the "Presentations" primitive
> ComplexRegionDraw is just the tip of the iceberg in complex facilities
> provided.
>>
>
> Maybe, but every Mathematica user ought to acquire enough basic skill to
> overcome this supposed "counter-intuitiveness". After all, it is hardly
> honest to encourage people to use Mathematica by telling them how
> powerful it is and how much simpler than, say, learning C, and then the
> moment they try to solve a simple mathematical problem tell them that
> the best thing to do is to buy an add-on package because Mathematica
> itself is what =85 too complex for them o learn?
>
> And while you are recommending them to get this package you omit to
> mention that they are not going to be able to share the code they
> produced with its help with anyone who does not have the package, or
> embed it in a CDF, etc. Furthermore, by relying on such a package are
> making themselves dependent on it's author who one day may not want to
> or more likely be able to make it compatible with future versions of
> Mathematica. I would think that these are sufficient reasons to hesitate
> before recommending it to anyone but people who really need it and have
> no other alternative and this case I certainly do not see as belonging
> to this category.


That plotting a complex region or function with bare Mathematica requires resort to real and complex parts just shows an unfortunate shortcoming of Mathematica. And a kind of inconsistency, since by default in algebraic calculations numbers are regarded as complex.

---
Murray Eisenberg                                    
murray at math.umass.edu
Mathematics & Statistics Dept.      
Lederle Graduate Research Tower            phone 413 549-1020 (H)
University of Massachusetts                               413 545-2838 (W)
710 North Pleasant Street                         fax   413 545-1801
Amherst, MA 01003-9305
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