# Why doesn't this expression evaluate inside Manipulate?

Consider this simplified code:

Manipulate[Ceiling[c - w/2], {c, Floor[w/2], 200}, {w, 1, 2, 1}]


It gives me a manipulator, in which I see the following content:

Ceiling[-(1/2) + 0]


But when I copy-paste it into a cell, I get this (after transforming to InputForm):

Ceiling[-1/2 + Dynamic[Floor[w$$/2], ImageSizeCache -> {87.8, {19.3, 28.66}}]]  Apparently, w$$ is a custom-generated name for w by Manipulate. But why isn't it actually evaluated for display? And how do I force final result to appear in the window?

• You can specify an initial value, this forces immediate evaluation: Manipulate[ Ceiling[c - w/2], {{c, 1, "c"}, Floor[w/2], 200}, {w, 1, 2, 1}] – Feyre Dec 11 '16 at 16:44
• @Feyre yes I'm aware of it, but I'd like to know what happens in the case I presented. Also, if I supply the default value, it should be the left border of the range, and I can't do it with expression depending on w for the same reason as why this doesn't work. – Ruslan Dec 11 '16 at 16:52
• Feyre shows the correct way to fix this - just assign a starting value. The Manipulate assigns a temporary variable that needs to be set in order to evaluate the expression. So the answer to your question is: to force the final result to appear in the window, you need to initialize w. This is done exactly as Feyre shows. – bill s Dec 11 '16 at 17:03

I will assume Advanced Dynamic Functionality and Advanced Manipulate Functionality (and their introductory siblings) have been read. In particular the notions that Manipulate creates a DynamicModule, which is an inert piece of code that comes to life only when it is displayed by the Front End; and further, every time it is displayed by the Front End, a new instance is created, with new localized variables etc.

In

Manipulate[Ceiling[c - w/2], {c, Floor[w/2], 200}, {w, 1, 2, 1}]


the variable declaration

{c, Floor[w/2], 200}


initializes c to the expression Floor[w/2] with an uninitialized DynamicModule variable represented by w in the code, but in keeping with such variables, it is coded as the symbol w$$. inside the code Manipulate generates. Since w is a Manipulate variable, Manipulate adds a Dynamic wrapper to it. It does this automatically (and perhaps undocumentedly), and it usually is just what the user wanted (but didn't know was necessary). The symbol w$$ is instantiated when the FE creates an instance of the DynamicModule (that is created by Manipulate), and the name is changed to a localized symbol such as FEw$$1379 in the FE context and with a module number appended. When the expression Ceiling[c - w/2] is displayed inside a Dynamic in the front end, the current values of the localized w and c are shown. They are not subtracted because until you move the slider, c is the expression Dynamic[Floor[w/2]] and not a number. When you copy the expression from the displayed Manipulate, you usually get the values as displayed inside the Dynamic[] that wraps the body of the Manipulate. In this case though, what is inside the Ceiling[] is Dynamic[Floor[w/2]] - w/2 and Dynamic is HoldAll. So what Mathematica decides to copy, is the value of the second w/2 but the whole Dynamic[] expression for the first term. The Dynamic[] code is copied as Dynamic[w$$/2], which is the InputForm and not the temporary, active, Front-End form.

• – Michael E2 Dec 12 '16 at 3:53