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.