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

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David Kastrup

Posts: 1,472
Registered: 12/7/04
Re: analytic function problem
Posted: Oct 2, 1996 5:09 AM
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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
Read analytic function problem
Christopher
9/30/96
Read Re: analytic function problem
David Ullrich
9/30/96
Read Re: analytic function problem
Hunter James D. STA x4202
10/1/96
Read Re: analytic function problem
David Ullrich
9/30/96
Read Re: analytic function problem
ilias kastanas 08-14-90
9/30/96
Read Re: analytic function problem
Dik T. Winter
10/1/96
Read Re: analytic function problem
David Kastrup
10/1/96
Read Re: analytic function problem
Hunter James D. STA x4202
9/30/96
Read Re: analytic function problem
Zdislav V. Kovarik
9/30/96
Read Re: analytic function problem
Anne DeCampo
10/2/96
Read Re: analytic function problem
Christopher
10/1/96
Read Re: analytic function problem
Tleko
10/2/96
Read Re: analytic function problem
David Kastrup
10/3/96
Read Re: analytic function problem
Dik T. Winter
10/3/96
Read Re: analytic function problem
Tleko
10/3/96
Read Re: analytic function problem
David Ullrich
10/3/96
Read Re: analytic function problem
Tleko
10/3/96
Read Re: analytic function problem
Dik T. Winter
10/3/96
Read Re: analytic function problem
Tleko
10/3/96
Read Re: analytic function problem
Zdislav V. Kovarik
10/5/96
Read Re: analytic function problem
Tleko
10/5/96
Read Re: analytic function problem
Dik T. Winter
10/6/96
Read Re: analytic function problem
Tleko
10/6/96
Read Re: analytic function problem
David Ullrich
10/7/96
Read Re: analytic function problem
ilias kastanas 08-14-90
10/7/96
Read Re: analytic function problem
Tleko
10/7/96
Read Re: analytic function problem
Andreas Leitgeb
10/7/96
Read Re: analytic function problem
Andreas Leitgeb
10/7/96
Read Re: analytic function problem
ilias kastanas 08-14-90
10/9/96
Read Re: analytic function problem
Simon Read
10/8/96
Read Re: analytic function problem
Tleko
10/8/96
Read Re: analytic function problem
Zdislav V. Kovarik
10/8/96
Read Re: analytic function problem
ilias kastanas 08-14-90
10/9/96
Read Re: analytic function problem
David Ullrich
10/8/96
Read Re: analytic function problem
Jim Hunter
10/8/96
Read Re: analytic function problem
Tleko
10/9/96
Read Re: analytic function problem
David Kastrup
10/9/96
Read Re: analytic function problem
Ilias Kastanas
10/11/96
Read Re: analytic function problem
Tleko
10/12/96
Read Re: analytic function problem
ilias kastanas 08-14-90
10/12/96
Read Re: analytic function problem
Dik T. Winter
10/11/96
Read Re: analytic function problem
Tleko
10/11/96
Read Re: analytic function problem
Tleko
10/11/96
Read Re: analytic function problem
Tleko
10/11/96
Read Re: analytic function problem
Tleko
10/11/96
Read Re: analytic function problem
Tleko
10/12/96
Read Re: analytic function problem
Tleko
10/12/96
Read Re: analytic function problem
Sue Franklin
10/13/96
Read Re: analytic function problem
Ilias Kastanas
10/15/96
Read Re: analytic function problem
Simon Read
10/13/96
Read Re: analytic function problem
Tleko
10/13/96
Read Re: analytic function problem
Tleko
10/13/96
Read Re: analytic function problem
ilias kastanas 08-14-90
10/14/96
Read Re: analytic function problem
Dik T. Winter
10/13/96
Read Re: analytic function problem
Tleko
10/13/96
Read Re: analytic function problem
Tleko
10/14/96
Read Re: analytic function problem
ilias kastanas 08-14-90
10/14/96
Read Re: analytic function problem
Dik T. Winter
10/15/96
Read Re: analytic function problem
Tleko
10/15/96
Read Re: analytic function problem
David Kastrup
10/15/96
Read Re: analytic function problem
Ilias Kastanas
10/16/96
Read Re: analytic function problem
Tleko
10/16/96
Read Re: analytic function problem
Dik T. Winter
10/17/96
Read Re: analytic function problem
Raymond DeCampo
10/18/96
Read Re: analytic function problem
Ariel Scolnicov
10/19/96
Read Re: analytic function problem
Tleko
10/19/96
Read Re: analytic function problem
Dik T. Winter
10/20/96
Read Re: analytic function problem
Terry Moore
10/21/96
Read Re: analytic function problem
Dik T. Winter
10/22/96
Read Re: analytic function problem
Ariel Scolnicov
10/20/96
Read Re: analytic function problem
Tleko
10/21/96
Read Re: analytic function problem
Terry Moore
10/22/96
Read Re: analytic function problem
David Kastrup
10/23/96
Read Re: analytic function problem
Tleko
10/24/96
Read Re: analytic function problem
Gunter Bengel
10/28/96
Read Re: analytic function problem
David Kastrup
10/28/96
Read Re: analytic function problem
David Ullrich

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