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Re: Re: Confusing results with N[expr]?

• To: mathgroup at smc.vnet.net
• Subject: [mg62373] Re: [mg62327] Re: Confusing results with N[expr]?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 22 Nov 2005 04:42:20 -0500 (EST)
• References: <dlp320$1bs$1@smc.vnet.net> <200511210854.DAA22039@smc.vnet.net> <7EF1243C-78FD-4926-8E96-72AF496B0E91@mimuw.edu.pl> <E0F8D2A1-44F0-43D6-B55B-671647375C19@mimuw.edu.pl>
• Sender: owner-wri-mathgroup at wolfram.com

On 21 Nov 2005, at 21:46, Andrzej Kozlowski wrote:

>
> On 21 Nov 2005, at 21:09, Andrzej Kozlowski wrote:
>
>>
>> On 21 Nov 2005, at 17:54, Peter Pein wrote:
>>
>>> 2.)
>>> Unprotect[Power];
>>> Power /: N[(x_)^(y_)] := Pow$[N[x], N[y]];
>>> Protect[Power];
>>> $Post = #1 /. Pow$ -> Power & ;
>>>
>>
>> Well, I would not recommend it. As often happens if you change one  
>> of the basic arithmetic functions,  there is be a price to pay if  
>> you do this. Here is an example:
>>
>> In[1]:=
>> Unprotect[Power];
>> Power /: N[(x_)^(y_)] := Pow$[N[x], N[y]];
>> Protect[Power];
>> $Post = #1 /. Pow$ -> Power & ;
>>
>> In[5]:=
>> Solve[N[x^2 - 1 == 0], x]
>>
>> "Inverse functions are
>>     being used
>>       by   so some solutions may not be \
>> found; use Reduce for complete solution information.
>>
>> Out[5]=
>> {}
>>
>> Solving polynomial equations has suddenly become  harder  
>> (although, of course, if you do not use N things will still work  
>> fine).
>>
>> Andrzej Kozlowski
>
>
> Actually, there is more. Try this:
>
>
> Unprotect[Power];
> Power /: N[(x_)^(y_)] := Pow$[N[x], N[y]];
> Protect[Power];
> $Post = #1 /. Pow$ -> Power & ;
>
>
> Plot[1,{x,0,1}]
>
> or for that matter any other Plot. It's a nice puzzle to try work  
> out how this comes about ;-)
>
> Andrzej Kozlowski


Actually, I think Peter's solution above was quite instructive. One  
often hears the advice "do not modify the basic functions like Plus,  
Times, Power...", but quite often even experienced users are tempted  
to do this (I have done so more than once myself) and it is not easy  
to think of convincing examples showing the unexpected things that  
can happen.

Now, I am inclined to think that the functions Plus,Times and Power  
(at least) should be given the attribute "Locked" in addition to the  
attribute "Protected".


Andrzej Kozlowski 
  

• References:
  • Re: Confusing results with N[expr]?
    • From: Peter Pein <petsie@dordos.net>