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Strange interaction between local symbols of a proc inside the Initialization of Manipulate with control variables

• To: mathgroup at smc.vnet.net
• Subject: [mg84881] Strange interaction between local symbols of a proc inside the Initialization of Manipulate with control variables
• From: "Nasser Abbasi" <nma at 12000.org>
• Date: Thu, 17 Jan 2008 07:03:35 -0500 (EST)

Mathematica 6.0.1 on windoz.

Below are 2 examples. In the first I have a proc in the init of a Manipulate 
which uses Dynamic symbols to obtain the limits of a plot. (the x and y 
limits).

In the first example, I have ONE local symbol called yy in the proc which is 
used as the maximum this dynamic symbol goes to.  This seems to work ok:


(*********** EXAMPLE 1 works ******************)
cc=ContinuousAction->False;

Manipulate[proc[],
  {xMax, 10, ControlType -> None},
  {yMax, 1, ControlType -> None},
  Initialization :>
  {
   proc[] := Module[{yy},
   yy = 2;
   Dynamic[Plot[Sin[x], {x, 0, xMax},
     PlotRange -> {Automatic, {-yMax, yMax}},
     Frame -> True,
     FrameLabel -> {Slider[Dynamic[xMax], {1, 10},cc],
                    VerticalSlider[Dynamic[yMax], {1, 2*yy},cc]},
     RotateLabel -> False
     ]
    ]
   ]
 }
]


Now, I added another local symbol call xx and did the same using it for the 
x-range. Now I get errors. You'd have to move the slides couple of times to 
see the error.

(********** EXAMPLE 2  error *******************)
cc=ContinuousAction->False;

Manipulate[proc[],
  {xMax, 10, ControlType -> None},
  {yMax, 1, ControlType -> None},
  Initialization :>
  {
   proc[] := Module[{yy,xx},
   yy = 2;
   xx = 8;
   Dynamic[Plot[Sin[x], {x, 0, xMax},
     PlotRange -> {Automatic, {-yMax, yMax}},
     Frame -> True,
     FrameLabel -> {Slider[Dynamic[xMax], {1, 2*xx},cc],
                    VerticalSlider[Dynamic[yMax], {1, 2*yy},cc]},
     RotateLabel -> False
     ]
    ]
   ]
 }
]

Why would the first example work, and the second not work?
I can fix the second example, by making yy and xx localized to Manipulate 
and not local symbols to the proc[] as follows

(********** EXAMPLE 3 works *******************)
cc=ContinuousAction->False;

Manipulate[proc[],
  {xMax, 10, ControlType -> None},
  {yMax, 1, ControlType -> None},
  {yy, 1, ControlType -> None},
  {xx, 1, ControlType -> None},

  Initialization :>
  {
   proc[] := Module[{},
   yy = 2;
   xx = 8;
   Dynamic[Plot[Sin[x], {x, 0, xMax},
     PlotRange -> {Automatic, {-yMax, yMax}},
     Frame -> True,
     FrameLabel -> {Slider[Dynamic[xMax], {1, 2*xx},cc],
                    VerticalSlider[Dynamic[yMax], {1, 2*yy},cc]},
     RotateLabel -> False
     ]
    ]
   ]
 }
]


It seems if a local symbol to Manipulate depends on a local symbol to a 
proc[] 'called' by Manipulate as in the first 2 examples above, this will 
result in something not nice.  But I do not understand why the first example 
works, and the second does not. It seems adding a second interaction broke 
something internally by accident?

Any idea? And on the subject, could any one be kind enought and summarize 
what is the visibility scope of a Dynamic symbol in Mathematica?

thanks,
Nasser