Symbolica 2.0: Programmable Symbols for Python and Rust

Thanks! I'm hoping to use libraries for this, but unfortunately there aren't many available in Rust yet for those kinds of problems.

Integrating Symbolica would be awesome, but our licenses are incompatible at the moment. If you're willing to relicense parts for Woxi, I'd be happy to work on this together!

Mathics (https://mathics.org/) has been working on a Mathematica clone for years and hasn't had any problems so far. There have been many legal cases establishing that APIs are't copyrightable, and since Woxi shares zero code with Mathematica, it should be fine.

No support for intermediate steps yet, but if there is interest in it, I'd be happy to prioritize it.

For short scripts, it’s often faster because there’s less initialization overhead. In general, though, it largely depends on whether the functions you’re using already have optimized implementations in Woxi. That’s what I’m currently working on, so I’d appreciate any feedback on what doesn’t work for you yet!

Hyperreal doesn't have any f64 mode. All math done with hyperreals is at infinite precision using a Rational of two BigUInts and a recursive real Computable. Real provides a cohesive interface over both allowing for easy scalar math. Computables are handled symbolically through a set of deterministic reduction rules until approximation is required, to preserve precision and reduce complexity. Approximation only happens at explicit public API boundaries like .to_f64_lossy() not used except for IO.

Hyperreal gets performance back through caching observed facts about the numbers it's representing at creation, and through operations, and specializing dispatch for predicates and geometric operations. Using this approach throughout the stack allows us to avoid computing on the full representation or collapsing it into an approximation. Instead asking questions like "do we know if it's definitely zero, definitely not, or unknown?" or "is it rational?" or "does it have a known sign, or unknown?" and so on. Each question specializes dispatch further, and some eliminate the need for it entirely.

Asking questions using the cached facts is approximately as fast as computing with f64s. So we do that whenever possible throughout the stack. But then when you actually need to do the exact computation, hyperreal does that too, and can approximate it out to whatever precision you'd like. f32 and f64 being common, but others being supported as well. The downside is that calculating quickly with them requires this sort specialization, but the work's been done for the geometry functions.

I'll look into DoubleFloat and ErrorPropagatingFloat for benches. I should mention that numerica@128bit beat the other pure rust bignum crates I tested. The benchmarks are mostly just to give me an understanding of the performance shapes of the implementation choices of high precision numeric libraries alongside hyperreal.

Development is pretty much dead other than some bug fixes. It's been long overdue for a major rewrite.

Currently hobbyist is the one that describes me the best. As I am no longer in academia. I did not know that there was a special hobbyist tier. The Academia Tier is realy a bit annoying because if you are a Student you do not have the pull to get a license for this even though you are affiliated.

Additionaly what was one of the reasons why I looked at Symbolica because I would have liked to implement it in for the backend in a FOSS (non Profit) project that I wanted to start back when I was still in Academia. My plans shifted though so Its unlikely I am gonna do it in the short term. But what I originaly wanted is a FOSS alternative to Mathcad. I needed a Symbolic Calculation tool that does the heavy lifting.