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MathGroup Archive 2007

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Re: Difficulties with Complex-Modulus Series

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72763] Re: Difficulties with Complex-Modulus Series
  • From: carlos at colorado.edu
  • Date: Thu, 18 Jan 2007 05:54:26 -0500 (EST)
  • References: <eohtrs$q48$1@smc.vnet.net><eokvok$407$1@smc.vnet.net>

>
> Hi Carlos,
>
> What version of Mathematica and system platform were you using when you
> performed your tests?
>
> I ask because I have been unsuccessful in my attempts to get any
> derivatives of the function *Abs*.


Mathematica 5.0 on a dual processor Mac G5.  Abs[] seems
to be broken in that version so that function better be avoided.
Hopefully it is fixed in newer versions. But in general the
manipulation of complex entities has been very poorly
implemented since the first version I used (2.2 on a
Next machine).  Perhaps it was never given priority.
The main weakness is lack of interoperability.

For the example I was able to get R=1 after some gyrations
involving Re[], Im[], ComplexExpand[] and FullSimplify[].
But the actual complex numbers in my research (getting the
spectral radius expansions of some feedback systems)
are far more complicated, and for those nothing helps.


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