Re: Re: Strange behavior of Simplify

• To: mathgroup at smc.vnet.net
• Subject: [mg40180] Re: Re: Strange behavior of Simplify
• From: Selwyn Hollis <selwynh at earthlink.net>
• Date: Tue, 25 Mar 2003 03:04:06 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Thanks, Bob. This is actually a good example to illustrate the
ComplexityFunction option.

expr = Exp[2*n^2*(Log[1 + t] - Log[1 - t])];
LeafCount[expr]

20

newexpr = (1 + t)^(2*n^2)/(1 - t)^(2*n^2);
LeafCount[newexpr]

21

So with the default ComplexityFunction->LeafCount, expr is already
"simpler" than "newexpr". However...

Depth[expr]

8

Depth[newexpr]

5

So with ComplexityFunction->Depth, newexpr is "simpler" than expr;
thus...

Simplify[expr, ComplexityFunction->Depth]

(1 + t)^(2*n^2)/(1 - t)^(2*n^2)

Very cool!

On Monday, March 24, 2003, at 04:28  AM, Bob Hanlon wrote:

> \$Version
>
> 4.2 for Mac OS X (August 22, 2002)
>
> expr = Exp[2*n^2*(Log[1 + t] - Log[1 - t])];
>
> expr // ExpandAll // Simplify
>
> (1 + t)^(2*n^2)/(1 - t)^(2*n^2)
>
> FullSimplify[expr, ComplexityFunction -> Length]
>
> (1 + t)^(2*n^2)/(1 - t)^(2*n^2)
>
>
> Bob Hanlon
>
> In article <b5jtgf\$mah\$1 at smc.vnet.net>, Selwyn Hollis
> wrote:
>
> << Subject:	Strange behavior of Simplify
> From:		Selwyn Hollis <selwynh at earthlink.net>
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> Date:		Sun, 23 Mar 2003 09:07:27 +0000 (UTC)
>
> I've just run across the following strange behavior of Simplify.
> (Using Mathematica 4.1.5, Mac OS X).
>
> These first two commands work as expected:
>
>         Simplify[Exp[2*n*(Log[1 + t] - Log[1 - t])]]
>
>                        (1 - t)^(-2*n) (1 + t)^(2*n)
>
>         Simplify[Exp[n^2*(Log[1 + t] - Log[1 - t])]]
>
>                        (1 - t)^(-n^2) (1 + t)^(n^2)
>
> But Simplify refuses to do anything with this:
>
>         Simplify[Exp[2*n^2*(Log[1 + t] - Log[1 - t])]]
>
>                       Exp[2*n^2*(Log[1 + t] - Log[1 - t])]
>
> Can anyone shed some light here?  By the way, FullSimplify does the
> same thing. >><BR><BR>
>

```

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