Re: Square root of a square
- To: mathgroup at smc.vnet.net
- Subject: [mg108159] Re: Square root of a square
- From: "janjitse at gmail.com" <janjitse at gmail.com>
- Date: Tue, 9 Mar 2010 06:25:25 -0500 (EST)
- References: <201002270813.DAA11868@smc.vnet.net> <4E497595-481A-4F1F-9E33-86865698E172@mimuw.edu.pl>
On Feb 28, 10:52 am, Adam Strzebonski <ad... at wolfram.com> wrote:
> 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
>
> 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
This type of error seems to be more wide-spread in Mathematica.
The following Mathematica code gives two answers, one of which is
incorrect, even after entering the unprotect and clear commands above:
DSolve[{y'[x] == 2 y[x] (x Sqrt[y[x]] - 1), y[0] == 1}, y[x], x]
{{y[x] -> 1/(-1 + 2 E^x - x)^2}, {y[x] -> 1/(1 + x)^2}}
The error appears for me in all Mathematica versions I could test,
that is 5.2, 6.0 and 7.0. The first solution can only be imagined to
be correct if you assume Sqrt[x^2] ==x.
Regards,
Jan Jitse Venselaar
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