Re: A question about $Assumptions

*To*: mathgroup at smc.vnet.net*Subject*: [mg68958] Re: A question about $Assumptions*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Fri, 25 Aug 2006 05:35:20 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <echdmb$oji$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Led wrote: > [...] > 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. > [...] > Shouldn't it be used that way? No. Rather than modifying directly a system value, it is always better and safer to use one of the following constructs: Block[ { $Assumptions= { m,n}\[Element]Integers}, Integrate[ Cos[ m*x]* Cos[ n*x], { x,0,Pi}]] Integrate[Cos[m*x]*Cos[n*x], {x, 0, Pi}, Assumptions -> {m, n} \[Element] Integers] Assuming[{m, n} \[Element] Integers, Integrate[Cos[m*x]*Cos[n*x], {x, 0, Pi}]] Regards, Jean-Marc