adding a new function to sage

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Briefly, you should create a fork of Sage on your own GitHub account, and create a fork there. Then you can compare that with the standard fork of Sage. I personally find the gh command-line interface to GitHub helpful. For more information and guidance, I suggest posting to the sage-devel Google group, both with details about what you're proposing (for feedback) and for help with the pull request.

I strongly recommend perusing the Sagemath Developer's guide as well as the Sagemath Installation guide, which between them give a lot of information, as a prealable to asking further questions.