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Problem with transformation rule of a function

• To: mathgroup at smc.vnet.net
• Subject: [mg53467] Problem with transformation rule of a function
• From: Alain Cochard <alain at geophysik.uni-muenchen.de>
• Date: Thu, 13 Jan 2005 03:12:10 -0500 (EST)
• References: <16858.22033.555637.91757@localhost.localdomain>
• Sender: owner-wri-mathgroup at wolfram.com

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

• Follow-Ups:
  • Re: Problem with transformation rule of a function
    • From: DrBob <drbob@bigfoot.com>