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Re: Which inside Module causes problems with ReplaceAll

  • To: mathgroup at smc.vnet.net
  • Subject: [mg111398] Re: Which inside Module causes problems with ReplaceAll
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Sat, 31 Jul 2010 02:39:08 -0400 (EDT)
  • References: <i2rm29$r6b$1@smc.vnet.net>

[note: message sent to comp.soft-sys.math.mathematica as well]

On 2010.07.29. 12:44, P. Fonseca wrote:
> Hi,
>
> Version 7.0.1
>
> This works:
>
> In[7]:= test[x_]:=Module[{u},
> 	u[t_]:=t^2;
> 	u[x]]
>
> In[8]:= test[t]/.t->3
>
> Out[8]= 9
>
>
>
>
> This doesn't:
>
> In[9]:= test[x_]:=Module[{u},
>
> 	Which[
> 	x==0,0,
>
> 	True,
> 	u[t_]:=t^2;
> 	u[x]
> 	]
> 	]
>
> In[10]:= test[t]/.t->3
>
> During evaluation of In[10]:= Pattern::patvar: First element in
> pattern Pattern[3,_] is not a valid pattern name.>>
> Out[10]= u$670[3]
>
>
>
> What's going on?
>

The key to understanding what happens in cases like this is breaking 
down your expressions and looking at what each part evaluates to.  If 
you evaluate test[t], you get something similar to

Which[t == 0, 0, True, u$743[t_] := t^2; u$743[t]]

This is because Which will only evaluate if the test inside it evaluates 
to either True or False, not something else.

If you replace t in this expression, it gets replaced in t_ (full form: 
Pattern[t, _]) as well, leading to the nonsensical Pattern[3, _].

Hope this explains it,
Szabolcs



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