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Re: positive square root

• To: mathgroup at smc.vnet.net
• Subject: [mg58691] Re: positive square root
• From: dh <dh at metrohm.ch>
• Date: Fri, 15 Jul 2005 03:02:08 -0400 (EDT)
• References: <db57ne$4no$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi Paul,
Mathematica is correct. You can convince yourselve by considering that 
any  number r may be written in exponential form:
r= a Exp[-I b]
where a (a>=0) is the absolute value of the number and b (real) its 
argument. Taking the square root gives (neglecting multiplicity)
Sqrt[a] Exp[-I b/2]
Taking the absolute value, the exponential disappears. Sqrt[a] is 
positive by definition and we are left with:
Sqrt[a]
Therefore:
Abs[Sqrt[r]] == Sqrt[a] == Sqrt[Abs[r]]

sincerely, Daniel


paulvonhippel at yahoo wrote:
> I work in a world where the square root is always a positive number.
> But Mathematica allows for the possibility of negative square roots.
> Two questions arise:
> 
> (1) Is there a way to tell Mathematica that I'm only interested in
> positive square roots?
> 
> (2) My current solution is to use, e.g., Abs[Sqrt[z]]. But when
> Mathematica echoes this, it puts the Abs function *under* the radical,
> so it looks like Sqrt[Abs[z]]. Is this a bug in the display?
>