       Re: How do I get Mathematica to Simplify this to 1?

• To: mathgroup at smc.vnet.net
• Subject: [mg104460] Re: How do I get Mathematica to Simplify this to 1?
• From: Erik Max Francis <max at alcyone.com>
• Date: Sun, 1 Nov 2009 03:59:33 -0500 (EST)
• References: <hcgpkt\$egn\$1@smc.vnet.net>

```dushan wrote:
> After initially declaring that {w>0, k>0, {z,X,Y} el Reals}, a matrix-
> vector multiplication produces the vector
>
> {(X - w Cos[k z])/Sqrt[z^2 + (X - w Cos[k z])^2 + (Y - w Sin[k z])^2],
>  (Y - w Sin[k z])/Sqrt[z^2 + (X - w Cos[k z])^2 + (Y - w Sin[k z])^2],
>  -(z/Sqrt[  w^2 + X^2 + Y^2 + z^2 - 2 w X Cos[k z] - 2 w Y Sin[k z]])}
>
> The denominators are in fact identical.  When I ask for Norm[%] I get
>
> \[Sqrt](
> Abs[z/Sqrt[w^2 + X^2 + Y^2 + z^2 - 2 w X Cos[k z] - 2 w Y Sin[k z]]]
> ^2  +
> Abs[(X - w Cos[k z])/Sqrt[z^2 + (X - w Cos[k z])^2 + (Y - w Sin[k z])
> ^2]]^2 +
>  Abs[(Y - w Sin[k z])/Sqrt[z^2 + (X - w Cos[k z])^2 + (Y - w Sin[k z])
> ^2]]^2
>         )
>
> and Simplify[%] reproduces this identical result instead of supplying
>
> What am I doing wrong that prevents Mathematica from delivering the

I've never been quite sure why Norm stick the Abs calls in there, since
it's squared anyway.  In these cases I've found it's better to do
Sqrt[%.%] rather than Norm[%]:

In:= Sqrt[%.%] // Simplify

Out= 1

--
Erik Max Francis && max at alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
It's hard to say what I want my legacy to be when I'm long gone.
-- Aaliyah

```

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