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Re: Simplification question
*To*: mathgroup at smc.vnet.net
*Subject*: [mg59082] Re: [mg59032] Simplification question
*From*: Pratik Desai <pdesai1 at umbc.edu>
*Date*: Thu, 28 Jul 2005 02:27:17 -0400 (EDT)
*References*: <200507270525.BAA19953@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
snoofly wrote:
>Can someone explain this to me please.
>
>Clear[m]
>
>Simplify[Sin[3 m Pi], Assumptions -> m \[Element] Integers]
>0
>
>Simplify[Cos[3 m Pi], Assumptions -> m \[Element] Integers]
>
>Cos[3 m \[Pi]]
>
>I'm not sure why Mathematica cannot deduce that the second simplification
>should be (1)^m.
>
>
>
I think the reason is simple as Cos[even*Pi]=+1 and Cos[odd*Pi]=-1
Hence your expression does not specify whether m is odd or even, hence
Mathematica returns the expression unevaluated
Using a recent reply on a post we can try this
Simplify[Cos[(3*Pi*n)], Assumptions -> Mod[n, 2] == 1]
>>-1
Simplify[Cos[(3*Pi*n)], Assumptions -> Mod[n, 2] == 0]
>>1
Best regards
--
Pratik Desai
Graduate Student
UMBC
Department of Mechanical Engineering
Phone: 410 455 8134
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