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.

所提出的主题将将计算机代数研究的范围扩展到两个领域，在这些领域要做很多要做：数学分析中限制的计算，并计算系统参数线性方程和不平等的整数解决方案。 这些主题还将解决高性能计算中的重要问题：扩展多面体汇编技术以支持非线性表达式，并在硬件加速器上提供有效的多先知和任意精确算术。 最后，拟议的研究将支持和增强我们使用加拿大IBM和Maplesoft的更应用的软件项目，即Metafork编译框架和常规链库。