Pushing the limits of computer algebra: From the integer resolution of polynomial systems to the computation of topological closures

突破计算机代数的极限：从多项式系统的整数分辨率到拓扑闭包的计算

• 批准号: RGPIN-2018-06534
• 负责人: MorenoMaza, Marc
• 金额: $ 2.99万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=714302
• 关键词: Pushing; limits; computer; algebra; integer

The proposed themes will expand the scope of computer algebra research into two areas where much remains to be done: computations of limits in mathematical analysis and, computing the integer solutions of systems parametric linear equations and inequalities. These themes will also address important problems in high-performance computing: extending polyhedral compilation techniques to support non-linear expressions and, delivering efficient implementation of multi-precision and arbitrary precision arithmetic on hardware accelerators. Finally, the proposed research will support and enhance our more applied software projects with IBM Canada and Maplesoft, namely the MetaFork compilation framework and the RegularChains library.

拟议的主题将把计算机代数研究的范围扩展到两个仍有待完成的领域：数学分析中极限的计算以及系统参数线性方程和不等式的整数解的计算。 这些主题还将解决高性能计算中的重要问题：扩展多面体编译技术以支持非线性表达式，并在硬件加速器上高效实现多精度和任意精度算术。 最后，拟议的研究将支持和增强我们与 IBM Canada 和 Maplesoft 合作的更多应用软件项目，即 MetaFork 编译框架和 RegularChains 库。