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MathGroup Archive 2005

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Re: Problem with transformation rule of a function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53478] Re: Problem with transformation rule of a function
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Thu, 13 Jan 2005 03:59:51 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <16858.22033.555637.91757@localhost.localdomain> <cs5asu$3r1$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <cs5asu$3r1$1 at smc.vnet.net>,
 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]

f is a (pure) function but 0 is not. In other words 0[x] is not 0. The 
zero function is (0 &) or, alternatively, Function[t,0]. If you enter

   (0 &)[x]

or

  Function[t,0][x]

you get 0.

> 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.

Writing

  expr/.{M[1]->f, M[2]-> (0 &)}

is an elegant way to do what you want in a single step.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 6488 2734
School of Physics, M013                         Fax: +61 8 6488 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul


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