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How do I get Mathematica to Simplify this to 1?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104437] How do I get Mathematica to Simplify this to 1?
  • From: dushan <dushanm at spinn.net>
  • Date: Sat, 31 Oct 2009 01:54:34 -0500 (EST)

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?

A separate question: Is there available somewhere a short list of
symbols (such as '!!', '&&', "=.", '/@', etc.) and their meanings?  A
Mathematica book index would generally start with such a list, but
having it available as a 1-page crib-sheet would be very helpful to
newbies like me.

Thanks.

- Dushan


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