Re: silly questions?

• To: mathgroup at smc.vnet.net
• Subject: [mg59088] Re: [mg59052] silly questions?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 28 Jul 2005 02:27:42 -0400 (EDT)
• References: <200507270526.BAA20063@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```
On 27 Jul 2005, at 07:26, Kent Holing wrote:

> Why does not (x^5-32)/(x-2)//FullSimplify in Mathematica  work?
> Compare with Factor[x^5-32]//InputForm which returns (-2 + x)*(16 +
> 8*x + 4*x^2 + 2*x^3 + x^4).
> So why does not the first command just return 16 + 8*x + 4*x^2 +
> 2*x^3 + x^4?
> As in a factorization above, how is the easiest way to pick
> automatically (by a function) the factors of say degree >=2,  if any ?
>
> Kent Holing
>
>

Very "simple". What makes you think the cancelled out form is "simpler"?

LeafCount[(x^5-32)/(x-2)]

11

while

LeafCount[Cancel[(x^5-32)/(x-2)]]

18

The cancelled form is much more "complicated", at least as measured
by LeafCount (and Mathematica's default complexity function).

So if you want your answer it is better to make ask Mathematica to
make the expression more "complex":

Simplify[(x^5 - 32)/(x - 2), ComplexityFunction ->
(1/LeafCount[#1] & )]

x^4 + 2*x^3 + 4*x^2 + 8*x + 16

But it is of course much more sensible to just use Cancel.

Andrzej Kozlowski

```

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