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Re: RealValued functions and their derivatives
*To*: mathgroup at smc.vnet.net
*Subject*: [mg51477] Re: [mg51461] RealValued functions and their derivatives
*From*: "David Park" <djmp at earthlink.net>
*Date*: Tue, 19 Oct 2004 02:55:51 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
Damon,
When working with complex expressions, your real friend will be
ComplexExpand. One has to almost always use it.
Re[f[t] Exp[I w]] // ComplexExpand
Cos[w] f[t]
Re[ f'[t] Exp[I w] ] // ComplexExpand
Cos[w] f'[t]
Check the Help page for ComplexExpand. Quite often you may have to use the
TargetFunctions option.
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: D.J. Wischik [mailto:djw1005 at cus.cam.ac.uk]
To: mathgroup at smc.vnet.net
I would be grateful for some help with Alebra`ReIm`. I can declare a
function to be real-valued (for real-valued arguments) by
<<Algebra`ReIm`
RealValued[f];
Then I can ask Mathematica to reason about real and imaginary
parts of expressions involving f -- for example
Im[t] ^= 0;
Im[w] ^= 0;
Re[f[t] Exp[I w]]
(* correctly returns
Cos[w] f[t] *)
In my application, I then want to differentiate f. If I naively ask for
Re[ f'[t] Exp[I w] ]
(* I get
Cos[w] Re[f'[t]] - Im[f'[t]] Sin[w] *)
Of course, if f is real-valued then f' is real-valued, so I only want the
Cos[w] part. If I try to declare f' to be real-valued by
RealValued[f']
(* I get an error message:
$RecursionLimit::reclim : Recursion depth of 256 exceeded. *)
I obviously haven't worked out the right way to tell Mathematica
that f' is real-valued. Any suggestions? I'm using Mathematica 4.0.
My hack at the moment is to substitute a pure symbol g for f', and to
declare that g is RealValued. However, since my function has four
arguments and I need derivatives up to order 3, this is very cumbersome.
Damon.
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