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MathGroup Archive 2005

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Re: Re: Simplify


On 14 Jul 2005, at 15:48, Andrzej Kozlowski wrote:

>
> On 13 Jul 2005, at 16:29, paulvonhippel at yahoo wrote:
>
>
>> I'm having some trouble getting an expression to simplify in an
>> obvious
>> way. (There seems to be a long tradition of users posting to this
>> group
>> with similar troubles.)
>>
>> The expression is
>>
>>  poly = p (p - 1) b^2 + s^2
>>  prod = Sqrt [poly] Sqrt[1/poly]
>>  Simplify[prod, {0 < p < 1, s > 0, bϵReals}]
>>
>> which should return one, I think, but doesn't.
>>
>> I'd be grateful for suggestions.
>>
>> Thanks!
>> Paul
>>
>>
>>
>
>
> prod /. {p -> 1/2, s -> 0, b -> 1}
>
>
> -1
>
>
> prod /. {p -> 1/2, s -> 1, b -> 0}
>
>
> 1
>
>
> FullSimplify[Abs[prod], {0 < p < 1, s > 0, bϵReals}]
>
>
> 1
>
>
> Andrzej Kozlowski
>
>


I just noticed that my first example
prod /. {p -> 1/2, s -> 0, b -> 1}
violates the assumption that s>0.

A correct example is


prod /. {p -> 1/2, s -> 1/10, b -> 1}

-1

I find it curious that some people seem to be recommending a "work  
around" (using PowerExpand) that will give the "desired" answer 1  
since this "desired answer" is  simply wrong (of course on the  
assumption that one follows the usual mathematical conventions that  
are needed to make Sqrt (a single valued) function).

Andrzej Kozlowski



  • References:
    • Simplify
      • From: "paulvonhippel at yahoo" <paulvonhippel@yahoo.com>
    • Re: Simplify
      • From: Andrzej Kozlowski <akozlowski@gmail.com>
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