       Re: Manipulate function

• To: mathgroup at smc.vnet.net
• Subject: [mg100935] Re: [mg100926] Manipulate function
• From: John Fultz <jfultz at wolfram.com>
• Date: Thu, 18 Jun 2009 06:18:50 -0400 (EDT)

```On Thu, 18 Jun 2009 04:54:34 -0400 (EDT), Przemyslaw Swatek wrote:
> hi !
>
> I have some problem (Mathematica 6) - when I type
> Manipulate[Plot[If[x < 0, n Sin[x], Cos[x]], {x, -10, 10}], {n, 0, 1}]
> all is ok, but when i try:
>
> M[x_]:=If[x < 0, n Sin[x], Cos[x]], {x, -10, 10}] and then
>
> Manipulate[Plot[M[x], {x, -10, 10}], {n, 0, 1}] it doesn`t work - I
> cannot manipulate varible of n. Whay ?

Manipulate (via DynamicModule) is using lexical scoping, which means that it
only replaces values of 'n' which are literally in the body of the Manipulate
expression.  'n' shows up nowhere in the expression 'M[x]'.  If you tried to do
a similar substitution for values of 'n' using Module or With, you'd run into a
similar problem.  Only Block[], with its use of dynamic scoping, is capable of
doing this.  Look for the following in the help viewer for more info:

tutorial/BlocksComparedWithModules

The correct way to deal with this is to add a second argument to M which
represents the variable 'n'.  I.e.,

M[x_, n_] := If[x < 0, n Sin[x], Cos[x]]

Manipulate[Plot[M[x, n], {x, -10, 10}], {n, 0, 1}]

Sincerely,

John Fultz
jfultz at wolfram.com
User Interface Group
Wolfram Research, Inc.

```

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