       Re: DynamicModule Pure Function

• To: mathgroup at smc.vnet.net
• Subject: [mg121926] Re: DynamicModule Pure Function
• From: "David Park" <djmpark at comcast.net>
• Date: Thu, 6 Oct 2011 04:27:02 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <12261069.93191.1317801418077.JavaMail.root@m06>

```DynamicModule[
{x1 = 0, x2 = 2},
{Slider[Dynamic[
x1, (x1 = #; x2 = Rescale[x1, {0, 1}, {2, 0}]) &], {0, 1}],
Slider[Dynamic[
x2, (x2 = #; x1 = Rescale[x2, {2, 0}, {0, 1}]) &], {0, 2}],
Dynamic[x1], Dynamic[x2]}
]

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

From: Don [mailto:donabc at comcast.net]

Thank you all for instructive insights into this problem of why the
pure function works the way it does.

To see if I understood the points made in the emails, I changed
the original problem very slightly and tried to find
a similar solution to the new problem using a modified pure function
from the original problem.

The new problem is exactly the same as the original problem except
that the range for Slider #2 goes from 0 to 2 instead of 0 to 1.
That is the only modification to the original problem.
The problem is to find an inverse function that will allow Slider #1 to
control Slider #2 throughout its range and vice versa.

To define this modified problem completely:

(1) The starting position of Slider #1 with range 0 to 1 is 0.

(2) The starting position of Slider #2 with range 0 to 2 is 2.

(3) When Slider #1 in moved to the right, over its range from  0 to 1,
Slider #2
should go to the left from 2 to 0.

(4) When Slider #2 is moved to the left, over its range from 2 to 0, Slider
#1
should go to the right from 0 to 1.

I was not able to solve this problem.

The closest I was able to do is to break up the problem
into component parts, hoping to synthesize a solution
from the parts.

The code below works when Slider #1 is controlling both Sliders. That is to
say,
it satisfies the requirements 1, 2 and 3 above:
the starting positions are 0 for Slider #1 and 2 for Slider #2 and when
Slider #1 is moved to the right over its range of 0 to 1, Slider #2 goes to
the left
from   2 to 0.

ap = Appearance->"Labeled";

DynamicModule[{x = 0}, {Slider[Dynamic[x], ap],
Slider[Dynamic[2 - 2 x, (x = 2 - 2 #) &], {0, 2}, ap]}]

But, I was not able to find a function that would satisfy requirements 1, 2
and 4 above
where Slider #2 is controlling the action.

In addition, to solve the problem completely, there would have to be a
synthesis
of both component solutions.

Is there a way to do this?