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MathGroup Archive 2012

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Re: Conformal Mapping


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.

Andrzej Kozlowski




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