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Topic: analytic function problem
Replies: 76   Last Post: Oct 28, 1996 11:08 AM

 Messages: [ Previous | Next ]
 David Kastrup Posts: 1,472 Registered: 12/7/04
Re: analytic function problem
Posted: Oct 2, 1996 5:09 AM

tleko@aol.com (Tleko) writes:

> In the article <32500731.1BBE@mailbox.syr.edu>

> : We all agree that f(z) = z^2 is analytic ..
>
> We have, however, for z^2
>
> Real= sqrt((x^2-y^2)^2+(2x*y)^2)*cos((atan(2x*y/(x^2-y^2))+(0 or
> pi))
> and
> Imag= sqrt((x^2-y^2)^2+(2x*y)^2)*sin((atan(2x*y/(x^2-y^2))+(0 or
> pi)) .
>
> Neither Real nor Imaginary part of z^2 is analytic (in real terms) in the
> unit disk.
>
> If you like to see the plots request a fax transmission.

This is too stupid for words. From private correspondance I have
learnt that Tleko has been told by several people that
atan(Im(z)/Re(z)) is *not* equal to arg(z) in computer lingo, and is
at best a very dubious formulation in mathematics. He insists,
however, in doing his plots with atan(Im/Re), like above, instead of
atan2(Im,Re) and gets excited like I know what over the fact that
there is a phase jump for sign changes of x. Hopeless. For a quote
from my correspondance:

Subj: Re: recent correspondence
>Date: 96-10-01 04:00:08 EDT
>From: dak@fsnif.neuroinformatik.ruhr-uni-bochum.de (David Kastrup)
>To: Tleko@aol.com

[written by me, dak, and quoted by Tleko:]
I have looked at the faxes. I could not believe my eyes. I could as
well be writing to /dev/null. Please be so kind and *listen*. Just
replace atan(y./x) in *all* of your programs by atan2(y,x). That is
the mistake in *every* single program of yours, and I have written you
already about 3 times *why* this is an mistake, and what you should do
to amend it.

Replace atan(y./x) by atan2(y,x) in program 1.
Replace atan(y./x) by atan2(y,x) in program 2.
Replace atan(y./x) by atan2(y,x) in program 3.
Replace atan(y./x) by atan2(y,x) in program 4.

The function atan cannot return anything outside the range -pi/2..pi/2,
and therefore is *not* able to return the proper arg of x+iy which
covers the range -pi..pi. It will switch to return values out of phase
by pi when x gets negative, and all your plots show exactly this
effect due to the inappropriate use of atan.

Once you replace atan(y./x) by atan2(y,x), it should be possible for
you to be doing your own correct plots.

--
David Kastrup Institut fuer Neuroinformatik, Ruhr-Universitaet Bochum
Email: dak@neuroinformatik.ruhr-uni-bochum.de Telephon: +49-234-700-5570
-----------------------
[written by Tleko:]

Thank you for the message. atan2 is not an analytic function. Neither are
z=x+iy or z=x-iy. You apparently have not read the earlier postings.

[Complete requote of treatise with mistakenly using atan(y/x) for
arg(z) deleted]

Just want to warn you off investing any more time with this
individual. Better argue with your wallpaper. At least it might
become damp and peel off, which is some reaction.

--
David Kastrup Institut fuer Neuroinformatik, Ruhr-Universitaet Bochum
Email: dak@neuroinformatik.ruhr-uni-bochum.de Telephon: +49-234-700-5570

Date Subject Author
9/30/96 Christopher
9/30/96 David Ullrich
9/30/96 Hunter James D. STA x4202
10/1/96 David Ullrich
9/30/96 ilias kastanas 08-14-90
9/30/96 Dik T. Winter
10/1/96 David Kastrup
10/1/96 Hunter James D. STA x4202
9/30/96 Zdislav V. Kovarik
9/30/96 Anne DeCampo
10/2/96 Christopher
10/1/96 Tleko
10/2/96 David Kastrup
10/3/96 Dik T. Winter
10/3/96 Tleko
10/3/96 David Ullrich
10/3/96 Tleko
10/3/96 Dik T. Winter
10/3/96 Tleko
10/3/96 Zdislav V. Kovarik
10/5/96 Tleko
10/5/96 Dik T. Winter
10/6/96 Tleko
10/6/96 David Ullrich
10/7/96 ilias kastanas 08-14-90
10/7/96 Tleko
10/7/96 Andreas Leitgeb
10/7/96 Andreas Leitgeb
10/7/96 ilias kastanas 08-14-90
10/8/96 Tleko
10/8/96 Zdislav V. Kovarik
10/8/96 ilias kastanas 08-14-90
10/9/96 David Ullrich
10/8/96 Jim Hunter
10/8/96 Tleko
10/9/96 David Kastrup
10/9/96 Ilias Kastanas
10/11/96 Tleko
10/12/96 ilias kastanas 08-14-90
10/12/96 Dik T. Winter
10/11/96 Tleko
10/11/96 Tleko
10/11/96 Tleko
10/11/96 Tleko
10/11/96 Tleko
10/12/96 Tleko
10/12/96 Sue Franklin
10/13/96 Ilias Kastanas
10/13/96 Tleko
10/13/96 Tleko
10/13/96 ilias kastanas 08-14-90
10/14/96 Dik T. Winter
10/13/96 Tleko
10/13/96 Tleko
10/14/96 ilias kastanas 08-14-90
10/14/96 Dik T. Winter
10/15/96 Tleko
10/15/96 David Kastrup
10/15/96 Ilias Kastanas
10/16/96 Tleko
10/16/96 Dik T. Winter
10/17/96 Raymond DeCampo
10/18/96 Ariel Scolnicov
10/19/96 Tleko
10/19/96 Dik T. Winter
10/20/96 Terry Moore
10/21/96 Dik T. Winter
10/22/96 Ariel Scolnicov
10/20/96 Tleko
10/21/96 Terry Moore
10/22/96 David Kastrup
10/23/96 Tleko
10/24/96 Gunter Bengel
10/28/96 David Kastrup
10/28/96 David Ullrich