AI 中文总结
研究如何加速格罗贝纳基计算中的重复运算，核心方法是用 Julia 实现 F4 算法并通过公共接口展示特拉弗索追踪法，支持 SIMD 友好系数类型，主要贡献是让 Julia 软件在相关应用中加速。
AI 中文摘要
在计算机代数中，控制表达式膨胀的标准方法是使用多模或求值插值法。在涉及格罗贝纳基的计算中，这些技术通常需要重复计算同一理想的特殊化的格罗贝纳基。通过预计算，特别是使用特拉弗索追踪法，可以加速这些重复计算。我们展示了这个 http URL（这个 https URL），它是 F4 算法的 Julia 实现，通过可重用的公共接口展示了特拉弗索追踪法。该实现支持 SIMD 友好的系数类型，如机器整数元组，Julia 几乎无需人工干预就能将其编译为高效代码。这使得其他 Julia 软件能够利用追踪法在常微分方程模型的结构可识别性和多项式系统求解等应用中获得加速。
英文摘要
A standard way to control expression swell in computer algebra is to use multi-modular or evaluation-interpolation methods. In computations involving Gröbner bases, these techniques typically require repeatedly computing Gröbner 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.
CommentsIn proceedings of ICMS 2026
