On Nov 4, 2012, at 8:12 PM, Andrzej Kozlowski <firstname.lastname@example.org> wrote:
> > On 4 Nov 2012, at 16:29, Murray Eisenberg <email@example.com> 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 firstname.lastname@example.org 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