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What is a "default Python installation"?

Upon installing Anaconda / Miniconda, there is a prompt that reads:
Where the second tick box has something about "Register Anaconda3 as my default Python 3._"
The image says 3.8 but that's just because I couldn't find an image that said 3.9.
I'm wondering what exactly this does to my system and what exactly it means by "default Python 3.8". Having selected that option, it doesn't seem like anything on my path is edited, and in fact, calling py in my terminal doesn't default to this unless I actually specify that I want Anaconda in my path, so I'm really unsure as to how this links to any other programs like mentioned, such as PyCharm.
Also, is there a point to having both Anaconda's Python 3.9 installed and having the classic Python 3.9 from the Python website installed at the same time? It seems to me like Anaconda's Python 3.9 is simply a better and more versatile version of the classic Python 3.9, but I could be wrong and am unsure as I'm really new to this. As far as I can see, however, Anaconda gives users the ability to install any other version of Python through the command line and use their own environment manager, which seems to just be an upgraded version of pip if I'm not wrong?

Windows uses a registry to manage system configuration, including entries determining what program will open files with a particular extension. It seems to me that Anaconda is offering to create a registry entry that will associate *.py files with the base Python in your installation.

IDLE and python is different, not able to install modules properly

thanks for reading this. I am using macOS High Sierra. I am not very familiar with terminal or environment variables, but am trying to learn more. From reading other threads and google, it seems like I either have multiple pythons installed, or have pythons running from different paths. However I am not able to find a solution to resolving this, either by re-pathing my IDLE or deleting it entirely.
I do have python, python launcher, and anaconda (not very sure how anaconda works, have it installed a few years back and didn't touch it) installed. I am trying to install pandas (pip install pandas), which tells me that I have it installed, but when I run it on IDLE, it says module not found. Though if i run python3 on terminal and type my code in, it works (so pandas has indeed been installed).
When i run which python on terminal, it returns
/Users/myname/anaconda3/bin/python
(when i enter into this directory from terminal, it shows that in the bin folder, I have python, python.app, python3, python3-config, python3.7, python3.7-config, python3.7m, python3.7m-config)
When i run which idle on terminal, it returns
/usr/bin/idle (im not even sure how to find this directory from the terminal)
When i run import os; print(os.path) on IDLE, it returns module 'posixpath' from '/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/posixpath.py'
Would really appreciate some help to figure out how to ensure that when i install modules from terminal, it would be installed into the same python as the one IDLE is using. Also, I would like to know whether it is possible for me to work on VSCode instead of IDLE. I cant seem to find suitable extensions for data science and its related modules (like statsmodels, pandas etc). Thanks a lot!

First of all, a quick description of anaconda:
Anaconda is meant to help you manage multiple python "environments", each one potentially having its own python version and installed packages (with their own respective versions). This is really useful in cases where you would like multiple python versions for different tasks or when there is some conflict in versions of packages, required by other ones. By default, anaconda creates a "base" environment with a specific python version, IDLE and pip. Also, anaconda provides an improved way (with respect to pip) of installing and managing packages via the command conda install <package-name>.
For the rest, I will be using the word "vanilla" to refer to the python/installation that you manually set up, independent of anaconda.
Explanation of the problem:
Now, the problem arises since you also installed python independently. The details of the problem depend on how exactly you set up both python and anaconda, so I cannot tell you exactly what went wrong. Also, I am not an OSX user, so I have no idea how python is installed and what it downloads/sets alongside.
By your description however, it seems that the "vanilla" python installation did not overwrite neither your anaconda python nor anaconda's pip, but it did install IDLE and set it up to use this new python.
So right now, when you are downloading something via pip, only the python from anaconda is able to see that and not IDLE's python.
Possible solutions:
1. Quick fix:
Just run IDLE via /Users/myname/anaconda3/bin/idle3 every time. This one uses anaconda's python and should be able to see all packages installed via conda install of pip install (*). I get this is tiresome, but you don't have to delete anything. You can also set an "alias" in your ~/.bashrc file to make the command idle specifically linking you there. Let me know with a comment if you would like me to explain how to do that, as this answer will get too long and redundant.
2. Remove conda altogether (not recommended)
You can search google on how to uninstall anaconda along with everything that it has installed. What I do not know at this point is whether your "vanilla" python will become the default, whether you will need to also manually install pip again and whether there is the need to reinstall python in order for everything to work properly.
3. Remove your python "vanilla" installation and only use anaconda
Again, I do not know how python installation works in OSX, but it should be reasonably straightforward to uninstall it. The problem now is that probably you will not have a launcher for IDLE (since I am guessing anaconda doesn't provide one on OSX) but you will be able to use it via the terminal as described in 1..
4. Last resort:
If everything fails, simply uninstall both your vanilla python (which I presume will also uninstall IDLE) and anaconda which will uninstall its own python, pip and idle versions. The relevant documentation should not be difficult to follow. Then, reinstall whichever you want anew.
Finally:
When you solve your problems, any IDE you choose, being VScode (I haven't use that either), pycharm or something else, will probably be able to integrate with your installed python. There is no need to install a new python "bundle" with every IDE.
(*): Since you said that after typing pip install pandas your anaconda's python can import pandas while IDLE cannot, I am implying in my answer that pip is also the one that comes with anaconda. You can make sure this is the case by typing which pip which should point to an anaconda directory, probably /Users/myname/anaconda3/bin/pip

First: This would be a comment if I had enough reputation.
Second: I would just delete python. Everything. And reinstall it.

To repeat and summarized what has been said on various other question answers:
1a. 3rd party packages are installed for a particular python(3).exe binary.
1b. To install multiple packages to multiple binaries, see the option from python -m pip -h.
To find out which python binary is running, execute import sys; print(sys.executable).
3a. For 3rd party package xyz usually installed in some_python/Lib/site-packages, IDLE itself has nothing to do with whether import xyz works. It only matters whether xyz is installed for 'somepython' (see 1a).
3b. To run IDLE with 'somepython', run somepython -m idlelib in a terminal or console.
somepython can be a name recognized by the OS or a path to a python executable.

Modules Not Found - I cannot externally run a .py file developed using PyCharm

I am using PyCharm to develop a python project, which uses an external library called win10toast. I have installed win10toast using PyCharm. However, when I tried to run the .py file using cmd (i.e Externally running the python file), an error shows up:
ModuleNotFoundError: No module named 'win10toast'.
I have python 3.6.4. I installed win10toast using PyCharm.
from win10toast import ToastNotifier
I expect the program to run without any error, but currently I am getting the ModuleNotFound error.

Python can be tricky to run properly because it is sensitive to where you installed your dependencies (such as external libraries and packages). If you installed Python to one directory, but accidentally installed the external library to another directory, when you run your .py program, it will be unable to call from the external library because it doesn't exist in the same library that Python is running from.
Lookup where you installed Python on your computer and then find where you installed the external library. Once your find where you installed the external library, move its entire package content to the same directory where Python is installed. Or better yet, reinstall the external library with pip into the same directory as Python.
If you're on Mac, Python and its related dependencies are usually stored somewhere in /User/bin. If you're on Windows, it will be stored somewhere in your C:// directory (possibly somewhere in C:\Users\username\Local\AppData). If you're on Linux, it will be stored somewhere in /usr/bin. Whatever you do, don't move Python from wherever it is because sometimes that can mess up your system for certain operating systems like Mac, which comes with its own version of Python (Python 2.7 I believe, which is outdated anyway).
Lastly, you may have two different versions of Python on your computer, which is common; Python 2.7 and Python 3+. If you wrote your program in one version, but ran it from the other, the external library can only be called from whichever Python version you installed it to. Try running your .py program with python3 instead of python (or vice versa) and see what happens. If it works with one python version over the other, that tells you that the external library is installed in the other version's directory.
That should solve your issue.

I would suggest that you not use PyCharm to install packages, at least not
if the result deviates in the slightest from doing a "pip install" at the command line. I see no reason to involve PyCharm in configuring Python installations. It's just asking for trouble.
I admit that I'm not familiar with the practice I'm suggesting you avoid. I've been using PyCharm since pretty much the week it came out (was an avid user of the IntelliJ Python plugin before that), and have never once considered doing anything but installing Python modules at the command line. That way, I'm sure right where those modules are going (into which base Python install or venv). Also, I know I'm doing all that I can to minimize the differences that I might see between running code in PyCharm and running it at the command line. I'm making my suggestion based solely on this practice having never gone wrong for me.
I have multiple base Python versions installed, and dozens of venvs defined on top of those. PyCharm is great at allowing me to indicate which of these I want to apply to any project or Run/Debug configuration, and utilizing them seamlessly. But agin, I administer these environments at the command line exclusively.
I still experience issues in switching between the command line and PyCharm in terms of one module referencing others in a single source tree. My company has come up with a simple solution to this that insures that all of our Python scripts still run when moving away from PyCharm and its logic for maintaining the Python Path within a project. I've explained the mechanism before on S.O. I'd be happy to find that if anyone is interested.

The library win10toast installed in the directory: YOUR_PYCHARM_WORKSPACE\PycharmProjects\YOUR_PROJECT_NAME\venv\Lib\site-packages
but when you are running your program using cmd, pycharm interpreter uses site-packages directory that you installed python at there. for Ex: C:\Python27\Lib\site-packages
So, you can install the win10toast library to this windows directory using pip.

Unable to use downloaded third-party library from within PyCharm

I'm working on a script that will plot data onto a map using the Basemap library. I'm trying to import Shapely as well for use in this same script. I'm working with Anaconda2 for Python2.7 in a Windows 7 environment. I used conda install to download the tar.bz2 file from the Conda Packages site (using Windows command line) and it looked like it all installed correctly.
When I open Pycharm and look at my accessible site-packages, I can see this package. However, when I try to use it within my script, I get an error saying that the package does not exist. I ran the script through the debugger to see if it would shed any more light, but I got the same error. Here's a screenshot of my available site packages when I go to Settings-->Project Interpreter from within Pycharm.
Screenshot of PyCharm site packages available
Is there something special I need to do in order to access this package from within a fresh Python file? I was trying to say "import shapely" or "import osx-64-shapely", but both give me the same "package does not exist" error message. I've been able to successfully use other third-party libraries within Python, so I'm not quite sure what the error is here....
I'm new to SO - if you need more details or there's some piece of info I didn't include, please let me know. Thank you for your help!
EDIT: I am NOT asking what the difference is between conda and pip, or how to use pip within PyCharm. I have used both successfully before to install third-party libraries. What I am asking is what might cause a third-party library that appears to have installed successfully from the command line become inaccessible from within PyCharm when I attempt to import it.

I'm not familiar with Shapely but I was astonished to see the name osx-64-shapely as a site-package for your python installation which is in windows 7. Are you sure you downloaded the right file? :)

How do I change the kernel/python version for iPython?

I have installed iPython using pip in OS X 10.10, and it gave me the "ipython" and "ipython2" commands, which run great, but which use OS X's default python version 2.7.9. I downloaded and installed the latest release of Python3.4 and can load it with the command "python3," but cannot find a way to get iPython to use this version of python. The iPython Web site states the package can be used with python versions 3.3 and above, but I cannot find any instruction on how to change the default python version used.
So far I have found that the jupyter package for iPython has a kernel specification in /usr/local/share/jupyter/kernels/, which is just a folder called "python2" containing a json file that points to the system's python 2.7.6, but altering this to point to the new python3.4 installation does not work. My guess is this configuration is for the ipython notebook.
I've also tried the approach here: ipython reads wrong python version
In doing so I've duplicated the ipython2 command in /user/local/bin/ and edited it to use the python3 interpreter located at /Library/Frameworks/Python.framework/Versions/3.4/bin/python3, however, this gives me an error "ImportError: No module named 'IPython'," which suggests the python3 installation does not have ipython installed.
To tackle this, I've tried uninstalling ipython and reinstalling it using pip, but it just targets the system's Python 2.7 installation and does nothing for python3.
Does anyone know how to configure iPython to use a different python version, or even install a separate ipython installation for python3? Ultimately it would be nice to quickly switch back and forth depending on my needs.

I just found the answer. In essence, this stems from not understanding the python installation layout and how resources are separated between installed interpreters. It appears each python version will have its own repository of tools, and the current "pip" command I had installed on the system was mapped for use with python 2.7, so all libraries, tools, and other details it managed where available only to python 2.7. This included iPython.
I thought that installing python3 would make all these libraries available to the new interpreter by default, but it appears the system keeps them all separate (which makes sense). The main issue here was continuing to use "pip" which targeted the old installation, instead of the new "pip3" command included with python3. By using pip3 to reinstall iPython, I was able to get iPython3 installed properly.
Unfortunately this setup means needing to re-download other libraries, but that's not too difficult.
It might seem like a trivial issue in hindsight, but this had me completely stuck. I hope this helps someone else in this situation.