New Algorithms for Computer Algebra, Implementations and Applications

计算机代数新算法、实现和应用

• 批准号: RGPIN-2016-04039
• 负责人: Schost, Eric
• 金额: $ 3.88万
• 依托单位: University of Waterloo
• 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=690416
• 关键词: New; Algorithms; Computer; Algebra; Implementations

My field of research is computer algebra: roughly speaking, this is the study of some mathematical problems with an algebraic flavor, that can be dealt with by means of exact computations. This subject actually covers a spectrum of questions, from algorithm development to complexity analysis, to low-level code optimization techniques.***My broad objective in this proposal is the development of efficient families of algorithmic solutions, with high-performance implementations, for questions at the heart of computer algebra, such as solving systems of equations. The precise questions I will address in this proposal are better algorithms for important families of systems that carry extra structure (which show up for instance in optimization), algorithms for various forms of motion planning and finally algorithms to solve problems inspired by error-correction theory. These are all fundamental questions in computer algebra; their solutions would represent significant progress for the field itself, and also have many applications (as mentioned above, in motion planning or error-correction).**

我的研究领域是计算机代数：粗略地说，这是一些数学问题的研究与代数的味道，可以通过精确的计算来处理。这个主题实际上涵盖了一系列问题，从算法开发到复杂性分析，再到低级代码优化技术。我在这个提案中的广泛目标是开发高效的算法解决方案系列，并具有高性能的实现，用于解决计算机代数的核心问题，例如求解方程组。我将在这个建议中解决的确切问题是，为携带额外结构的重要系统家族（例如在优化中出现）提供更好的算法，为各种形式的运动规划提供算法，最后是解决受纠错理论启发的问题的算法。这些都是计算机代数中的基本问题;它们的解决方案将代表该领域本身的重大进展，并且也有许多应用（如上所述，在运动规划或纠错中）。