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Re: Radicals simplify

• To: mathgroup at smc.vnet.net
• Subject: [mg106378] Re: [mg106361] Radicals simplify
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 11 Jan 2010 05:29:03 -0500 (EST)
• References: <201001100830.DAA05621@smc.vnet.net>

On 10 Jan 2010, at 17:30, francix wrote:

> Hi,
> I am using Matematica 7 and need some help with Radicals.
>
> If I do
> Simplify[(x^4 y^3)^(1/4), x >= 0] I correctly have
>
> x (y^3)^(1/4)
>
> But If I do
>
> Simplify[(x^6 y^3)^(1/4), x >= 0] I get
>
> (x^6 y^3)^(1/4) and not the correct answer  x(x^2 y^3)^(1/4)
>
> Thanks in advanced.
>

The problem is that your desired formula has a higher ComplexityFunction 
than the one returned by Mathematica. Mathematica's default 
ComplexityFunction is close to LeafCount and

LeafCount[x*(x^2*y^3)^(1/4)]

13

while

LeafCount[(x^6*y^3)^(1/4)]

11

The quickest way to get the answer close to the one you want in this 
case is:

Refine[(x^6*y^3)^(1/4), x >= 0]

 x^(3/2)*(y^3)^(1/4)

To get exactly the answer you want you will need to play with 
ComplexityFunction, which in this case will be tricky.

Andrzej Kozlowski

• References:
  • Radicals simplify
    • From: "francix" <fracix@gmail.com>