Re: Simplify using custom function

• To: mathgroup at smc.vnet.net
• Subject: [mg47689] Re: [mg47676] Simplify using custom function
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 22 Apr 2004 02:38:33 -0400 (EDT)
• References: <200404210923.FAA02461@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 21 Apr 2004, at 18:23, Jens wrote:

> What I'm trying to achieve is to find a certain function in a more
> complicated expression:
>
> example:    complicated expression: -1+2 x +2 e^x
> 	    function: f[x_]=x+e^x
>
> 	    Mathematica should return: -1+2 f[x]
>
> I've been looking at TransformationFunctions and FullSimplify, but did
> not succeed in defining a transformation function so far. How do I do
> that? (It's Mathematica 5.0)
>
> Jens
>
>
>
First of all, your problem is not well defined since the answer is not
unique. There are obviously infinitely many ways to "find a certain
function" in a more complicated expression. But, assuming that the
expression you are looking for is a polynomial in your function,  in
cases like your example it can be done with PolynomialReduce::

Last[PolynomialReduce[-1+2 x+2 E^x,f[x]-x-E^x]]

-1+2 f[x]

Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/

```

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