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Re: Re: Radicals simplify

• To: mathgroup at smc.vnet.net
• Subject: [mg106432] Re: [mg106399] Re: Radicals simplify
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 12 Jan 2010 04:50:15 -0500 (EST)
• References: <hic37h$5ef$1@smc.vnet.net> <hieujs$mtu$1@smc.vnet.net> <201001112352.SAA20940@smc.vnet.net>

On 12 Jan 2010, at 08:52, francix wrote:

>
> "dh" <dh at metrohm.com> ha scritto nel messaggio
> news:hieujs$mtu$1 at smc.vnet.net...
>>
>>
>> Hi,
>>
>> why do you think x(x^2 y^3)^(1/4) is simpler than (x^6 y^3)^(1/4)?
>>
>> Mathematica needs some criterion for this decision. The default criterion is the
>>
>> "LeafCount[..]". If that does not suit you, you must define another
>>
>> criterion.
>>
>> Daniel
>
> Thank you all for your answer.
>
> I understand your explanations, but I have the impression
> that in this case Mathematica uses numbers in a different
> way from letters.
>
> If I do
> Simplify[2 Sqrt[2] + 4 Sqrt[2]]  I get
>
> 6 Sqrt[2]
>
> or
>
> Simplify[5 Sqrt[50] + 6 Sqrt[18]]  I get
>
> 43 Sqrt[2]
>
> Instead if I do
>
> Simplify[5 x Sqrt[x] + 6 x Sqrt[x], x >= 0] or
>
> Simplify[5 Sqrt[x^3] + 6 x Sqrt[x], x >= 0] I get
>
> 11 x^(3/2)  instead of  11xSqrt[x]
>
> As you know the last one is the result
>
> normally found in Algebra books.
>
> So, there is no solution?
>
>

Note that Mathematica automatically transforms

x Sqrt[x]

x^(3/2)

This has nothing to do with Simplify but is the reason why you can never 
get answers like
x Sqrt[x] in Mathematica unless you insert HoldForm somewhere.

There is a very good reason why Mathematica does certain simplifications 
even when you do not use Simplify. They are needed for efficiency and, 
unlike the simplifications that Simplify does, they do not depend on any 
ComplexityFunction. But as a side effect they make it impossible to 
achieve certain output forms without using functions like HoldForm which 
prevent evaluation.

Andrzej Kozlowski

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