Re: Surprising FullSimplify result

*To*: mathgroup at smc.vnet.net*Subject*: [mg111539] Re: Surprising FullSimplify result*From*: Peter Pein <petsie at dordos.net>*Date*: Wed, 4 Aug 2010 07:33:35 -0400 (EDT)*References*: <i368ne$r79$1@smc.vnet.net>

Am Mon, 2 Aug 2010 11:04:14 +0000 (UTC) schrieb Sam Takoy <sam.takoy at yahoo.com>: > Here's what I am getting > > Cos[theta]^2 + Sin[theta]^2 // FullSimplify > Out[540]= 1 > > Cos[theta]^2 + Sin[theta]^2 + L^2 Cos[theta]^2 // FullSimplify > Out[541]= 1/2 (2 + L^2 + L^2 Cos[2 theta]) > > I'm really surprised that the answer in the latter case is not > > 1+ L^2 Cos[theta]^2 > > Is there an explanation? > > Thanks, > > Sam > Hi Sam, how big might the surprise be when observing the following? In[1]:= expr = Cos[theta]^2 + Sin[theta]^2 + L^2 Cos[theta]^2; LeafCount[longexpr = Times @@ (expr /. L -> L /@ Range[5]) // Expand] Out[2]= 1884 longexpr holds the expanded product of five terms of the same type as expr. In[3]:= longexpr // FullSimplify Out[3]= (1 + Cos[theta]^2 L[1]^2) (1 + Cos[theta]^2 L[2]^2) (1 + Cos[theta]^2 L[3]^2) (1 + Cos[theta]^2 L[4]^2) (1 + Cos[theta]^2 L[5]^2) In this case Mathematica has got no problem simplifying each of the five terms -- strange :-\ Peter