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: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=688343
• 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.

拟议的主题将扩大计算机代数研究的范围到两个领域，还有很多工作要做：数学分析中的极限计算，以及计算系统参数线性方程和不等式的整数解。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，并在硬件加速器上提供多精度和任意精度算法的有效实现。最后，拟议的研究将支持和加强我们与IBM加拿大和Maplesoft的更多应用软件项目，即MetaFork编译框架和RegularChains库。