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Re: Simplification question
*To*: mathgroup at smc.vnet.net
*Subject*: [mg59085] Re: Simplification question
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Thu, 28 Jul 2005 02:27:33 -0400 (EDT)
*Organization*: The Open University, Milton Keynes, U.K.
*References*: <dc76pp$jvg$1@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.
>
Because it is a wrong answer!
In[1]:=
Simplify[Cos[m*Pi], Assumptions -> m \[Element] Integers]
Out[1]=
(-1)^m
In[2]:=
Simplify[Cos[m*Pi], Assumptions -> m \[Element] Integers] /. m -> 3*m
Out[2]=
(-1)^(3*m)
If m is even then
In[3]:=
Simplify[Cos[2*k*Pi], Assumptions -> k \[Element] Integers]
Out[3]=
1
If m is odd then
In[4]:=
Simplify[Cos[(2*k + 1)*Pi], Assumptions -> k \[Element] Integers]
Out[4]=
-1
Regards,
/J.M.
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