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Re: Re: Assumptions in Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg20594] Re: [mg20579] Re: [mg20562] Assumptions in Integrate
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Tue, 2 Nov 1999 02:35:29 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

Looking at this again I noticed another problem. The answer given by
Mathematica isn't true for n=0, so there is a bug in Simplify. The correct
command should have been:

In[39]:=
 Simplify[Integrate[Cos[n x], {x, -Pi, Pi},
 Assumptions -> Element[n, Integers]], Element[n, Integers] && n != 0]
Out[39]=
0

Note however that the following does not work, though it should:

In[40]:=
Integrate[Cos[n x], {x, -Pi, Pi},
 Assumptions -> Element[n, Integers] && n != 0]
Out[40]=
            2
2 Sin[Sqrt[n ] Pi]
------------------
           2
     Sqrt[n ]
-- 


> From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
> Date: Sat, 30 Oct 1999 14:54:54 -0400
> To: mathgroup at smc.vnet.net
> Subject: [mg20594] [mg20579] Re: [mg20562] Assumptions in Integrate
> 
> I also think the Assumptions mechanism in Integrate leaves a lot to be
> desired. Probably the best thing one can do right now is something like:
> 
> In[45]:=
> Simplify[Integrate[Cos[n x], {x, -Pi, Pi},
> Assumptions -> Element[n, Integers]], Element[n, Integers]]
> 
> Out[45]=
> 0
> -- 
> 
> 
>> From: Julian Aguirre Estibalez <mtpagesj at lg.ehu.es>
To: mathgroup at smc.vnet.net
>> Organization: Universidad del Pais Vasco/Euskal Herriko Unibertsitatea
>> Date: Sat, 30 Oct 1999 00:14:09 -0400
>> To: mathgroup at smc.vnet.net
>> Subject: [mg20594] [mg20579] [mg20562] Assumptions in Integrate
>> 
>> Dear Math Group,
>> 
>> I find the results of using assumptions in Integrate somewhat
>> stranege. For instance,
>> 
>> In[21]:= Integrate[Cos[n x], {x, -Pi, Pi}]
>> 
>> Out[21]= 2 Sin[n Pi]
>> -----------
>> n
>> 
>> In[22]:= Integrate[Cos[n x], {x, -Pi, Pi},
>> Assumptions -> Element[n, Integers]]
>> 
>> Out[22]=
>> 2
>> 2 Sin[Sqrt[n ] Pi]
>> ------------------
>> 2
>> Sqrt[n ]
>> 
>> In[23]:= $Version
>> 
>> Out[23]= "4.0 for Power Macintosh (July 20, 1999)"
>> 
>> I know I can define my own transformation rules, but one would
>> think that Mathematica should do it directly.
>> 
>> Julian Aguirre            | Voice:  +34 946012659
>> Departamento de Matematicas    | Fax:    +34 944648500
>> Universidad del Pais Vasco    | Postal: Aptdo. 644, 48080 Bilbao, Spain
>> | email:  mtpagesj at lg.ehu.es
>> 
>> 
> 
> 



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