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