`del` on a package has some kind of memory

A package is only read from disk once and then stored in memory as mutable singleton. The second time you import it you get the exact same singleton you have previously imported, and it's still missing its cos. del math merely deletes the local name for it, it doesn't "unimport" the package from Python overall.

I would say that the package is still seen as imported. So performing import math again just redeclares the name, but with old contents.

You could use reload to make sure your module is whole again, except that some versions of python require to remove the entry in sys.modules as well, which makes the use of reload redundant:

import mathdel math.cosdel mathsys.modules.pop("math")   # remove from loaded modulesimport mathprint(math.cos(0))  # 1.0

(this difference between various python versions, reload and import are discussed in a follow-up question: Should importlib.reload restore a deleted attribute in Python 3.6?)

del math does not delete the package at all, it just deletes the local name math in the current module.

Like any other object, if any other references to the math module exist anywhere, then it's kept in memory.

And in particular, sys.modules is always a dictionary of all loaded modules, so at least there's always a reference there.

Edit: But there's a way to actually reload a module, imp.reload.

Unfortunately I can't get it to work for this case, reload needs the random module (probably to create some part of the compiled Python file), the random module needs math.cos, and it's gone. Even with importing random first there is no error, but math.cos doesn't reappear; I don't know why, maybe because it's a builtin module.