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This is a minimal example of a more complex problem. I need to build the Manipulate function as below with a variable number of parameters, which is why Manipulate is paired with @@ and Sequence@@allLimits. If possible, I wouldn't want to change that.

allLimits = {{{alpha1, 4Pi/9}, Pi/18, 17Pi/18}, {{alpha2, 4Pi/9}, Pi/18, 17Pi/18}};
Manipulate @@ {values = allLimits[[All, 1, 1]], Sequence @@ allLimits}

My problem is that values works fine within Manipulate but it is kept as a symbolic expression, so when evaluating values outside of Manipulate it gives {alpha1,alpha2} instead of the current numerical values within Manipulate.

In the more complex problem, I need values to replace variables within lists that are too huge to handle analytically within Manipulate, and in the case above that is exactly what happens. So I think it would solve my problem if I were able to actually assign numerical values to values.

As a comparison, if we were to write it out like this:

Manipulate[
 values = {alpha1, alpha2}, {{alpha1, 4Pi/9}, Pi/18, 17Pi/18}, {{alpha2, 4Pi/9}, Pi/18, 17Pi/18}]

then values does have numerical values ({4Pi/9, 4Pi/9}). This is what I would want while keeping the construction above.

Any help is much appreciated!

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You may insert local variables into Manipulate using "With" and then assign these to a global variable glob:

With[{varLoc = {alpha1, alpha2}}, 
 Manipulate[glob = varLoc {alpha1, alpha2}, 
  Evaluate[Sequence @@ allLimits]]]

enter image description here

The value of the changing variable "glob" can be displayed using "Dynamic":

Dynamic[glob]

enter image description here

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  • $\begingroup$ Dear @Daniel Huber, that's great, thanks a lot!! Although the construction is not the same, I can keep the variable number of parameters. Some small comments: the {alpha1, alpha2} after varLoc is not necessary (and is multiplied with varLoc). Also, I think the Dynamic is not required to get the numerical value for glob. Thanks again! $\endgroup$ Commented Jun 4 at 11:09
  • $\begingroup$ You are right, it is a copy paste error. It should read : varLoc = {alpha1, alpha2} or varLoc= allLimits[[All, 1, 1]]. And the "Dynamic" is only there for the demo to show the changing value. $\endgroup$ Commented Jun 4 at 11:28

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