Re: Square root of a square
- To: mathgroup at smc.vnet.net
- Subject: [mg107863] Re: Square root of a square
- From: Christoph Lhotka <lhochr at gmail.com>
- Date: Mon, 1 Mar 2010 04:43:56 -0500 (EST)
hi, this is something, which is really needed to be discussed:
1) Simplify[Sqrt[x^2] == x, x \[Element] Reals]
2) Simplify[Sqrt[x^2] == x, x \[Element] Complexes]
3) Simplify[Sqrt[x^2] == x, x < 0]
works fine, while
1) FullSimplify[Sqrt[x^2] == x, x \[Element] Reals]
2) FullSimplify[Sqrt[x^2] == x, x \[Element] Complexes]
3) FullSimplify[Sqrt[x^2] == x, x < 0]
will return a wrong result in the 2nd case.
The problem seems to be only in version 7, not in version 6 or version 5.
chr
Andrzej Kozlowski wrote:
> On 27 Feb 2010, at 09:13, Mariano Su=E1rez-Alvarez wrote:
>
>
>> Hi all,
>>
>> Mathematica evaluates FullSimplify[Sqrt[x^2]] to Sqrt[x^2], while it
>> tells me that FullSimplify[Sqrt[x^2] == x] is True.
>> Are these the expected answers?
>>
>> -- m
>>
>>
>
> The second certainly not the answer I would expect, in fact this looks
> to me like a serious (perhaps even "shocking") bug. It certainly
> contradicts this answer:
>
> FindInstance[Sqrt[x^2] != x, x]
>
> {{x -> -(109/5) + (11*I)/5}}
>
>
> Andrzej Kozlowski
>
>
>
>
> :