Hello from a newbie, and thank you for Sage and all the work you're putting 
into it!

Thanks on behalf of both the current active developers as well as those of 
us not so active :-) we love new developers.
 

- Start testing with Git.
- Rename the variables in my code from Czech to English.
- Add comments to the code.
- Integrate it into Sage's code structure.


Yes, we have a number of "best practices" regarding documentation, testing, 
etc.  See https://doc.sagemath.org/html/en/developer/ and perhaps 
especially the bottom 
of https://doc.sagemath.org/html/en/developer/coding_basics.html for these 
questions.
 


After that, I'd propose adding a new function, e.g. 
number_of_n_colorings_with_pruning, so that the original pure-recursive 
number_of_n_colorings 
remains unchanged.


As the other post suggests, one could either replace or add algorithms (we 
have examples of both in Sage history).  As they say, f you can put the 
Github issue you open for this in this thread, then people can continue to 
follow it there. 

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