how to test if one python module has been imported?

If you want to optimize by not importing things twice, save yourself the hassle because Python already takes care of this.

If you need this to avoid NameErrors or something: Fix your sloppy coding - make sure you don't need this, i.e. define (import) everything before you ever use it (in the case if imports: once, at startup, at module level).

In case you do have a good reason: sys.modules is a dictionary containing all modules already imported somewhere. But it only contains modules, and because of the way from <module> import <variable> works (import the whole module as usual, extract the things you import from it), from sys import path would only add sys to sys.modules (if it wasn't already imported on startup). from pkg import module adds pkg.module as you probably expect.

I feel the answer that has been accepted is not fully correct.

Python still has overhead when importing the same module multiple times. Python handles it without giving you an error, sure, but that doesn't mean it won't slow down your script. As you will see from the URL below, there is significant overhead when importing a module multiple times.

For example, in a situation where you may not need a certain module except under a particular condition, if that module is large or has a high overhead then there is reason to import only on condition. That does not explicitly mean you are a sloppy coder either.

https://wiki.python.org/moin/PythonSpeed/PerformanceTips#Import_Statement_Overhead

from sys import modules
try:
    module = modules[module_name]
except KeyError:
    __import__('m')   

this is my solution of changing code at runtime!