Academic code copied by library author

In fact something great happened: Your research did have impact in the real world and seems to be useful - not everyone can say that!

When it comes to legal issues, things are usually complicated and will involve copyright issues (of yours and of the journal / publisher) as well as authorship issues. Those vary between countries and it will be difficult to give an advise without proper juristical background and line by line comparison of your publications and the library code.

But as I understood your question, you are more interested in the academic credit, and therefore I would suggest to contact the authors, tell them you are happy that your work is used by them, and offer to be part of the development team. You might add a phrase like it would be a pleasure to be listed as author of the library - an in most cases they will understand...

Here's how I would view it:

I got to do all the fun work of research and discovery. Somebody else voluntarily did the not-fun work of wrapping this work up in a nice software package. They're even volunteering to maintain it, and they're properly giving me all the credit for inventing what they've implemented! So people can use what I created and I can keep focusing on research, rather than on details of software packaging, distribution, and maintenance.

All I would do is thank them and make sure that their documentation suggests that users cite your papers. I certainly wouldn't be in a hurry to get any lawyers or bureaucrats (e.g. from my university) involved.

This is subjective, but I think many academics would align with this view of things.

The first question is, how complex is the code in your paper? Trivial code may not be protected by copyright. This is somehow related to length, but length is NOT the most important criteria, when you invented something new which did not exist before.

And then the question is who owns the copyright of your paper. Often you transfer the copyright to the journal, so you cannot claim the copyright anyway. The journal may have licenced the paper by a CC-licence (or similar) if it is open access, or hold proprietary rights on the paper.

You usually retain the full copyright and usage rights on your source code, but grant a licence to the publisher, who usually can sublicence your code, e.g., by allowing readers to use the code from your paper.

The next question is, if the library licence is compatible to the paper licence. Again, this is probably a question for the publisher and not for the author.

Code from some separate repo is another issue, as long as they used code which is only in your repository and not in the paper itself.

My question is whether I ought to ask to be an author of the library.

Ask for appropriate acknowledgement, if major parts of the code are from your paper. You should not only be acknowledged by "based on paper ...", but also be in the AUTHORS file (or similar files with author information). Existing licence headers in your source files should be retained.

Be aware, that being listed as an author can mean that users will ask you for support or questions about the library. Maybe you prefer a simple acknowledgement.

Personally, I would ask if some paragraph could be included, that academic users should consider citing your paper.