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I have been developing a program that requires me to use LocalizedVariables->False for some variables. However, I am having a difficult time redirecting these variables to another context as this command defaults the program to the Global setting.

Is it possible to control the context location of the variables you wish to apply LocalizedVariables->False? Thank you!

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I'll assume you meant LocalizeVariables. You could do it like this:

Remove[x, Test`x]
Begin["Test`"]
`x = 0
{Manipulate[x, {x, 0, 1}, LocalizeVariables -> False], Dynamic[Test`x]}
End[]
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