Groebner.jl: Fast Gröbner Tracing in Julia

A standard way to control expression swell in computer algebra is to use multi-modular or evaluation-interpolation methods. In computations involving Gr\"obner bases, these techniques typically require repeatedly computing Gr\"obner bases of specializations of the same ideal. These repeated computations can be accelerated through precomputation, notably using Traverso's tracing. We present Groebner.jl (https://github.com/sumiya11/Groebner.jl), a Julia implementation of the F4 algorithm that exposes Traverso's tracing through a reusable public interface. The implementation supports SIMD-friendly coefficient types, such as tuples of machine integers, which Julia compiles to efficient code with little manual intervention. This lets other Julia software leverage tracing to obtain speedups in applications such as structural identifiability of ordinary differential equation models and polynomial system solving.