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The solution to your Eigenvalues function are Root objects, see the documentation. Root[f,k] represents the exact k^(th) root of the polynomial equation f[x]==0. Inside Root is the pure function in the argument #1. If we named this pure function f with argument x, this would correspond to the situation in the above quote with f[x]. Your Matrix $A$ ...


This happens because you never set a as a shared variable before using UnsetShared. That is, you were using UnsetShared in an incorrect manner. In short: make sure you never use UnsetShared on a symbol unless it was shared first! Mathematica in general is pretty forgiving (unlike languages like C) and won't make it possible to mess up its internal state ...


There is another way to view the local symbol directory that you might try. SystemOpen[$LocalSymbolBase] On my system, OS X, this opens a Finder window showing the folder containing the currently existing local symbols.


I know of no better way than to just look in the local symbols directory. While it's not necessarily true that all local symbols are stored there, it should be true of the defaults (that is, those made as LocalSymbol["name"]). Now, $LocalSymbolBase is a string with a protocol prefix (presumably to match it up with $CloudSymbolBase, although since that is a ...

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