AI 中文总结
介绍用于计算零维多项式系统有理单变量表示的Julia包，核心方法是利用稠密线性代数和高斯消元法，主要贡献是能在数秒内计算出有数千个解的理想的保证正确的参数化。
AI 中文摘要
在本笔记中，我们展示了一个用于计算零维多项式系统有理单变量表示的Julia包。该包在类FGLM阶段使用稠密线性代数和高斯消元法。本贡献旨在支持这一选择并解释将算法转化为实用软件的实现细节。特别地，我们表明我们的实现能够在数秒内计算出具有数千个解的理想的保证正确的参数化。
英文摘要
In this note, we present RationalUnivariateRepresentation$.$jl (https://newrur.gitlabpages.inria.fr/RationalUnivariateRepresentation.jl/), a Julia package for computing rational univariate representations of zero-dimensional polynomial systems. The package uses dense linear algebra and Gaussian elimination for the FGLM-like stage. The purpose of this contribution is to advocate for this choice and explain the implementation details that turn the algorithm into practical software. In particular, we show that our implementation can compute guaranteedly correct parametrizations of ideals with thousands of solutions within seconds.
CommentsIn proceedings of ICMS 2026
