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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104464] Re: [mg104437] How do I get Mathematica to Simplify this to 1?
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Sun, 1 Nov 2009 04:00:20 -0500 (EST)
  • References: <200910310654.BAA13353@smc.vnet.net>
  • Reply-to: drmajorbob at yahoo.com

Remove colons to see the steps:

one = {(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]])} /.
    Power[any_, r : Rational[_, _]] :> Power[TrigExpand@any, r];
two = Norm@one /. Abs[any_]^2 :> any^2;
three = two /.
    Power[any_, r : Rational[_, _]] :> Power[Together@any, r];
{numerator, denominator} = Through[{Numerator, Denominator}@(three^2)];
numerator = TrigExpand@numerator;
final = Sqrt[numerator/denominator]

1

In this case,

two = Norm@two /. Abs -> Identity;

also works at that step.

Bobby

On Sat, 31 Oct 2009 01:54:34 -0500, dushan <dushanm at spinn.net> 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?
>
> 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
>


-- 
DrMajorBob at yahoo.com


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