       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= 1
>
> Cos[theta]^2 + Sin[theta]^2 + L^2 Cos[theta]^2 // FullSimplify
> Out= 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:= expr = Cos[theta]^2 + Sin[theta]^2 + L^2 Cos[theta]^2;
LeafCount[longexpr = Times @@ (expr /. L ->
L /@ Range) // Expand]
Out= 1884

longexpr holds the expanded product of five terms of the same type as
expr.

In:= longexpr // FullSimplify
Out= (1 + Cos[theta]^2 L^2) (1 + Cos[theta]^2 L^2)
(1 + Cos[theta]^2 L^2) (1 + Cos[theta]^2 L^2)
(1 + Cos[theta]^2 L^2)

In this case Mathematica has got no problem simplifying each of the
five terms -- strange :-\

Peter

```

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