       Re: Re: Problem with transformation rule of a function -- Another one

• To: mathgroup at smc.vnet.net
• Subject: [mg53533] Re: [mg53509] Re: [mg53467] Problem with transformation rule of a function -- Another one
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sat, 15 Jan 2005 21:08:18 -0500 (EST)
• References: <200501150644.BAA25320@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 15 Jan 2005, at 07:44, Alain Cochard wrote:

> Thank you so much to those who answered.  Now, here is another one.
>
> The following works as I expect:
>
>      In:= expr=Integrate[D[g[x,t],t],{x,0,1}]
>
> 			(0,1)
>      Out= Integrate[g     [x, t], {x, 0, 1}]
>
>      In:= g[x_,t_]:= x f[t]
>
>      In:= expr
>
> 	     f'[t]
>      Out= -----
> 	       2
>
> Now I would like to use a transformation rule instead, like in:
>
>      In:= expr=Integrate[D[g[x,t],t],{x,0,1}] ;
>
>      In:= expr/. g[x,t]->x f[t]
>
> 			(0,1)
>      Out= Integrate[g     [x, t], {x, 0, 1}]
>
> I tried various alternatives (with "//", ":>", "Evaluate", using "_"
> or not, with "Hold/ReleaseHold" -- although not in a fully systematic
> way, I admit) without success.  Is it feasible?
>
> Thanks,
> Alain
>
>
>

There are several ways. One is

expr /. Derivative[0, 1][g][x, t] :> D[x*f[t], t]

Derivative[f][t]/2

another, which I prefer, is:

expr /. g -> Function[{x, t}, x*f[t]]

Derivative[f][t]/2

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

```

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