       Re: 1 equals 3 (among others)

• To: mathgroup at smc.vnet.net
• Subject: [mg32194] Re: 1 equals 3 (among others)
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Sat, 5 Jan 2002 00:10:32 -0500 (EST)
• References: <a13v7l\$dgb\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Grischa,

Sqrt[x^2] need not be x;
for real x it will be Abs[x]

Forcomplex z,
Sqrt[z^2] is z  if  -Pi/2< Arg[z]<=Pi/2,
otherwise is - z.

These comes from the definition:
z^a = Exp[ a (Log[Abs[z]] +Arg[z] I)],
where Log is the natural logarithm and -Pi<Arg[z] <=Pi
--
Allan

---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Grischa Stegemann" <Stegemann at physikDONOT.SPAMtu-berlin.de> wrote in
message news:a13v7l\$dgb\$1 at smc.vnet.net...
> Dear group
>
> Can anyone explain to me what is going on here? Look at this:
>
> In:=f[x_] = (4 - x + Sqrt[-4*(3 - x) + (x - 4)^2])/2;
> In:=Simplify[-4*(3 - x) + (x - 4)^2]
> Out=(-2 + x)^2
>
> Well, right now we can be pretty sure that f[x]=1 for all x. But
> Mathematica (4.0.2.0X) seems to know better:
>
> In:=Map[f[#1]&, {0, 0.1, 1.7, 2, 2.5, 3}]
> Out={3, 2.9, 1.3, 1, 1., 1}
>
> It took me hours to find this error in my rather complex setting...;-(
>
> Bye, Grischa
> --
> -------------------------------------------------------------------------
>    Grischa Stegemann                     Technische Universität Berlin --
>
>

```

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