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How to substitute a function?

• To: mathgroup at smc.vnet.net
• Subject: [mg94082] How to substitute a function?
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Thu, 4 Dec 2008 07:16:17 -0500 (EST)

Dear crew,

I faced a difficulty when trying to substitute a newly represented 
function into an expression containing a sum of differential and 
algebraic terms. The difficulty is namely, that Mathematica 6 
substitutes the new representation into the algebraic, but not into the 
differential part. For example:

(* This is the definition of a simple example of such an expression *)


expr = \!\(
\*SubscriptBox[\(\[PartialD]\), \(x\)]\ \(y[x]\)\) + a*y[x]^2;

(* Here I substitute a new representation of the function  into the \
above expression *)
(* What I expect to get is the following expression: -Exp[-x]*f[x] + \
Exp[-x]*f´[x] + a \[ExponentialE]^(-2 x) f[x]^2  *)
(* Instead I get something else. Please have a look and check:  *)
expr /. y[x] -> Exp[-x]*f[x]



(* This is another approach I could think of with even worse result. *)
\

(* Note however, that within this approach a miracle happened: once \
it *)
(* worked as expected (i.e. the substitution of both terms has been \
performed as desired, but only once *)

FullSimplify[expr, y[x] == Exp[-x]*f[x]]


Do you have idea of how to instruct Mathematica to make the substitution 
everywhere?

Thank you in advance, Alexei

-- 
Alexei Boulbitch, Dr., Habil.
Senior Scientist

IEE S.A.
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• Follow-Ups:
  • Re: How to substitute a function?
    • From: Daniel Lichtblau <danl@wolfram.com>