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Message from discussion Square root of a square
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More options Feb 28 2010, 4:52 am
Newsgroups: comp.soft-sys.math.mathematica
From: Adam Strzebonski <ad...@wolfram.com>
Date: Sun, 28 Feb 2010 09:52:26 +0000 (UTC)
Local: Sun, Feb 28 2010 4:52 am
Subject: Re: Square root of a square

Andrzej Kozlowski wrote:
> On 27 Feb 2010, at 09:13, Mariano Su rez-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

It is a bug in V7.0. The function used by FullSimplify to
simplify equations involving holonomic functions does not
handle branch cuts correctly. It can be disabled with

In[1]:= Unprotect[Holonomic`HolonomicFullSimplify];
Clear[Holonomic`HolonomicFullSimplify];

In[2]:= FullSimplify[Sqrt[x^2] == x]

2
Out[2]= Sqrt[x ] == x

Best Regards,

Adam Strzebonski
Wolfram Research

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