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Re: Problem with transformation rule of a function
*To*: mathgroup at smc.vnet.net
*Subject*: [mg53490] Re: [mg53467] Problem with transformation rule of a function
*From*: DrBob <drbob at bigfoot.com>
*Date*: Fri, 14 Jan 2005 08:54:38 -0500 (EST)
*References*: <16858.22033.555637.91757@localhost.localdomain> <200501130812.DAA03785@smc.vnet.net>
*Reply-to*: drbob at bigfoot.com
*Sender*: owner-wri-mathgroup at wolfram.com
Your first attempt fails because M[2][t] doesn't actually appear in the expr's derivative term:
expr = M[1][
t] + M[2][t] + Integrate[M[1][t], t] +
Integrate[M[2][t], t] + D[M[1][t], t] + D[M[2][t], t];
FullForm[expr]
FullForm[Integrate[M[1][t], t] +
Integrate[M[2][t], t] +
M[1][t] + M[2][t] +
Derivative[1][M[1]][t] +
Derivative[1][M[2]][t]]
Look closely, and you'll see where M[2][t] does -- and doesn't -- appear.
The second attempt almost works, but this is what you really want:
expr //. {M[1] -> f, M[2] -> (0 & )}
f[t] + Integrate[f[t], t] + Derivative[1][f][t]
0& is the zero function you meant to use.
Bobby
On Thu, 13 Jan 2005 03:12:10 -0500 (EST), Alain Cochard <alain at geophysik.uni-muenchen.de> wrote:
> I define an expression:
>
> In[1]:= expr=M[1][t] + M[2][t] + Integrate[M[1][t],t] + Integrate[M[2][t],t] + D[M[1][t],t] + D[M[2][t],t];
>
> Out[1]= Integrate[M[1][t], t] + Integrate[M[2][t], t] + M[1][t] + M[2][t] +
>
> > (M[1])'[t] + (M[2])'[t]
>
> and then I try 2 transformation rules on this expression:
>
> In[2]:= vers1=expr/.{M[1][t]->f[t], M[2][t]->0}
>
> Out[2]= f[t] + Integrate[f[t], t] + (M[1])'[t] + (M[2])'[t]
>
> In this first one, I get the output I expect for the function and
> integration terms, but not for the derivative ones.
>
> In[3]:= vers2=expr/.{M[1]->f, M[2]->0}
>
> Out[3]= 0[t] + f[t] + Integrate[0[t], t] + Integrate[f[t], t] + f'[t]
>
> In this second version, I get these 0[t] terms for the function and
> integration terms, with which I further have to deal with to achieve
> what I want:
>
> In[4]:= %/.{0[t]->0}
>
> Out[4]= f[t] + Integrate[f[t], t] + f'[t]
>
>
> I would first like to understand why the derivation and integration
> terms are not treated in an identical way, and then I would like to
> know if there is a more elegant way to do what I want in a single
> step.
>
> Thanks in advance,
> AC
>
>
>
>
--
DrBob at bigfoot.com
www.eclecticdreams.net
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