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What's the best way to access sage from a C program?

I'm new to Python/Sage and confused about what my options are here. I have a C++ program and occasionally I want to process some data with Sage. It would be far too slow to simply have Sage running like a server and then use the C++ program like a client that queries the server.

What I really want to do is write a standalone Python function that uses Sage library functions, convert that function and any relevant portions of Sage into C, and then with my own compiler, compile that C code into a library that my C++ program can call.

I'm confused about how all this could work with Cython and spyx files and so forth. Is this even possible? Would it be possible but slower to instead embed the Python function in the C++ program? Thanks for any help.