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MathGroup Archive 2005

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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[1]:= expr=Integrate[D[g[x,t],t],{x,0,1}]
>
> 			(0,1)
>      Out[1]= Integrate[g     [x, t], {x, 0, 1}]
>
>      In[2]:= g[x_,t_]:= x f[t]
>
>      In[3]:= expr
>
> 	     f'[t]
>      Out[3]= -----
> 	       2
>
> Now I would like to use a transformation rule instead, like in:
>
>      In[1]:= expr=Integrate[D[g[x,t],t],{x,0,1}] ;
>
>      In[2]:= expr/. g[x,t]->x f[t]
>
> 			(0,1)
>      Out[2]= 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[1][f][t]/2

another, which I prefer, is:

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


Derivative[1][f][t]/2


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


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