Is it possible to get a list of all existing managed library expressions, from within Mathematica? Mathematica clearly needs to keep track of which ones exist.
Or do I need to refer to the table of existing objects I keep on the C side?
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As far as I know, there is no built-in way to do this. The kernel data structure that stores the information for all existing managed library expressions is not accessible from top level.
But yes, it is indeed possible to keep track of them on the C side and pass the list of IDs to Mathematica through your own