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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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