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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104478] Re: How do I get Mathematica to Simplify this to 1?
  • From: Peter Breitfeld <phbrf at t-online.de>
  • Date: Sun, 1 Nov 2009 04:02:58 -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'll name your expression expr. If you want to simplify with all
variables supposed to be Reals, then use:

Simplify[Norm[expr], Element[_, Reals]]

Out= 1


> 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
>

May be this little palette is a starter:

CreatePalette[{
  Grid[{
    {" f @ x", "f[x]"},
    {" x // f", "f[x]"},
    {" x ~ f ~ y", "f[x, y]"},
    {" f /@ x", "Map[f, x]"},
    {" f //@ x", "MapAll[f, x]"},
    {" f @@ x", "Apply[f, x]"},
    {" f @@@ x", "Apply[f, x, {1}]"},
    {" a && b", "And[a, b]"},
    {" a \[And] b", "And[a, b]"},
    {" a || b", "Or[a, b]"},
    {" a \[Or] b", "Or[a, b]"},
    {" ! a", "Not[a]"},
    {" \[Not] a", "Not[a]"},
    {" a \[Union] b", "Union[a, b]"},
    {" a \[Intersection] b", "Intersection[a, b]"},
    {" a <> b", "StringJoin[a, b]"},
    {" a /. b", "ReplaceAll[a, b]"},
    {" a //. b", "ReplaceRepeated[a, b] "},
    {" a /; b", "Condition[a ,b]"},
    {" a /: x=y", "TagSet[a, x, y]"},
    {" a /: x:=y", "TagSetDelayed[a, x, y] "}
    },
   Alignment -> Left,
         BaseStyle -> {FontFamily -> "Palatino", FontSize -> 12},
   Dividers -> {False, {4 -> Black, 6 -> Black, 8 -> Black, 
      14 -> Black, 16 -> Black, 17 -> Black, 19 -> Black, 
      20 -> Black}}
   ]
  }]

-- 
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de


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