A question about $Assumptions

*To*: mathgroup at smc.vnet.net*Subject*: [mg68909] A question about $Assumptions*From*: "Led" <zep.led at laposte.net>*Date*: Wed, 23 Aug 2006 07:15:22 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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?

**Follow-Ups**:**Re: A question about $Assumptions***From:*Daniel Lichtblau <danl@wolfram.com>