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
> the correct answer 1.
>
> What am I doing wrong that prevents Mathematica from delivering the
> right answer?
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[12]:= Sqrt[%.%] // Simplify
Out[12]= 1
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