Re: Simplify doesn't factor out 16 :-(

• To: mathgroup at smc.vnet.net
• Subject: [mg43599] Re: [mg43586] Simplify doesn't factor out 16 :-(
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 23 Sep 2003 04:01:43 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```As you can imagine there is no "objective" criterion of what makes on
expression simpler than another. WHen you use Simplify this is
determined by the setting for the option ComplexityFunction. The
default setting is Automatic, which is a bit mysterious since we
(users) do not know exactly  what it is. Often it coincides with
LeafCount but not in this case:

Simplify[-4*(16+4*L^2*(-1+3*u^2))]

-4*(16 + 4*L^2*(-1 + 3*u^2))

LeafCount[%]

16

Simplify[-4*(16+4*L^2*(-1+3*u^2)),ComplexityFunction->LeafCount]

-64 + L^2*(16 - 48*u^2)

LeafCount[%]

13

You can get the expression with 16 factored out by setting
ComplexityFunction to Length:

Simplify[-4*(16+4*L^2*(-1+3*u^2)),ComplexityFunction->Length]

-16*(4 + L^2*(-1 + 3*u^2))

The LeafCount is better than with the default (Automatic) setting but
worse than with the LeafCount setting:

LeafCount[%]

15

Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/

On Monday, September 22, 2003, at 04:14 PM, Pavel Pokorny wrote:

>   Dear Mathematica friends
>
> I can't understand why Simplify in Mathematica 5.0 doesn't factor out
> 16
> in this expression
>
> In[1]:= Simplify[-4*(16 + 4*L^2*(-1 + 3*u^2))]
>
>                     2          2
> Out[1]= -4 (16 + 4 L  (-1 + 3 u ))
>
>
> only after using Expand
>
>
> In[2]:= Expand[%]//Simplify
>
>                   2         2
> Out[2]= 16 (-4 + L  (1 - 3 u ))
>
> Is it a bug or an intention?
>
> Pavel Pokorny
>
>
>

```

• Prev by Date: how import data to mathematica????
• Next by Date: Re: package functions in mathlink
• Previous by thread: Simplify doesn't factor out 16 :-(
• Next by thread: Solve real roots only ?