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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



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