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Re: A question about $Assumptions
*To*: mathgroup at smc.vnet.net
*Subject*: [mg68965] Re: A question about $Assumptions
*From*: Roland Franzius <roland.franzius at uos.de>
*Date*: Fri, 25 Aug 2006 05:35:29 -0400 (EDT)
*Organization*: Universitaet Hannover
*References*: <echdmb$oji$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Led schrieb:
> Mathematica 5.2 (Windows) gives:
>
> In[1]:=
> Integrate[ Cos[m*x] * Cos[n*x] ,{x,0,Pi}]
>
> Out[1]=
> \!\(\(m\ Cos[n\ Ï?]\ Sin[m\ Ï?] - n\ Cos[m\ Ï?]\ Sin[n\ Ï?]\)\/\(m\^2 -
> n\^2\)\)
>
> which is the expected result. But if instead one writes
>
> In[1]:=
> $Assumptions={{m,n}â??Integers};
> Integrate[ Cos[m*x] * Cos[n*x] ,{x,0,Pi}]
>
> Out[1]=
> 0
>
> the result is correct only if m~=n.
>
> What's the problem with $Assumptions?
> Shouldn't it be used that way?
>
The problem is evaluation order. In the general formula setting n
Integer generates zero before a check on m is performed. Calculate the
diagonal and zero cases separately
Integrate[ Cos[n*x] * Cos[n*x] ,{x,0,Pi}]
pi/2
Integrate[ Cos[0*x] * Cos[0*x] ,{x,0,Pi}]
pi
--
Roland Franzius
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