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sympy/sympy is an open source project licensed under BSD 3clause "New" or "Revised" License which is an OSI approved license.
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Posts

Is the capitalization of sp.symbols vs sp.Symbol intentional in sympy?
symbols is a function

Python Math Library made in 3 Days as a 14 yearold  libmaths
Now compare that to SymPy: https://github.com/sympy/sympy/blob/9e8f62e059d83178c1d8a1e19acac5473bdbf1c1/sympy/ntheory/primetest.py#L472L634

Ask Anything Monday Weekly Thread
Haven't tried it myself. But maybe this library might work for you https://github.com/sympy/sympy

This is the real answer, although the algorithm used seems to use a sieve rather than a naive check for (x & i == 0)
https://github.com/sympy/sympy/blob/219993505f88a8d6f825db1d...

Doing Symbolic Math with SymPy
The trouble with SymPy is it's, well, buggy. I tried it years ago and as soon as I got serious I quite quickly ran into problems that I reported, some of which I see they apparently still haven't gotten around to addressing. [1] [2]
Symbolic math is hard; they have my sympathies. I don't think I could do better. But as long as bugs like these exist, it's going to be hard to convince people to switch away from better tools like Mathematica.

The totient function.
https://github.com/sympy/sympy/blob/master/sympy/ntheory/factor_.py#L1908

ODE logic in Rust
[1] https://github.com/sympy/sympy

Math in GUI
You can use BytesIO instead of StringIO (see the StringIO deprecation issue and sympy docs for more info).