Computer Algebra: Algorithms and Applications

计算机代数：算法与应用

• 批准号: RGPIN-2018-06670
• 负责人: Jeffrey, David
• 金额: $ 2.04万
• 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: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=654571
• 关键词: Computer; Algebra; Algorithms; Applications

Computer algebra systems are large software systems that allow scientists, engineers, mathematicians, and any other discipline that uses mathematics, to conduct mathematical calculations easily and efficiently. These systems can do much more than numerical computations. They have been programmed with large amounts of mathematical knowledge, and they can work with symbolic quantities (the high school student's x,y,z) as well as numbers. The system's mathematical knowledge allows them to perform high-level tasks, such as solving equations or simplifying complicated expressions. They can handle lengthy expressions that would take a human mathematician more than a page to write down by hand, and manipulate such large expressions without the errors that a human mathematician would inevitably introduce. Thus they allow scientists and engineers to take advantage of specialist mathematical knowledge that would otherwise not be available to them. Instead of the researcher hunting through the library or internet to learn how to solve some difficult equation, and then having to spend time applying the discovered knowledge to the researcher's particular problem, the algebra system user can refer the problem to the system and benefit from the expert knowledge of generations of developer mathematicians and computer scientists. Scientific investigations can gain greatly in mathematical level and productivity.***One such computer system is Canadian. It is named, appropriately, Maple. The results of research supported in this proposal will be openly published, but the results will relevant to improving Maple. This project will increase the power of existing computer algebra systems by adding to their mathematical knowledge base. The mathematical functions known to the systems will be investigated and new properties discovered that will help systems solve users' problems. Of particular importance to the systems and their users are properties connected with complex numbers. Complex numbers are those built using the square root of negative one. Working with functions of complex numbers, and simplifying the mathematical expressions which arise, is a long standing difficulty, which is still not adequately solved. This project aims to strengthen the abilities of the systems in this area. *****

计算机代数系统是大型软件系统，允许科学家、工程师、数学家和任何其他使用数学的学科轻松有效地进行数学计算。这些系统可以做的不仅仅是数值计算。它们使用了大量的数学知识进行编程，并且可以处理符号量（高中生的 x、y、z）以及数字。该系统的数学知识使它们能够执行高级任务，例如求解方程或简化复杂的表达式。它们可以处理冗长的表达式，而这些表达式需要人类数学家手写一页以上才能写下来，并且可以处理如此大的表达式，而不会出现人类数学家不可避免地会引入的错误。因此，它们使科学家和工程师能够利用他们原本无法获得的专业数学知识。研究人员不必通过图书馆或互联网来学习如何解决一些困难的方程，然后必须花时间将发现的知识应用于研究人员的特定问题，代数系统用户可以将问题提交给系统并从中受益几代开发数学家和计算机科学家的专业知识。科学研究可以大大提高数学水平和生产力。***加拿大就有这样一个计算机系统。它被恰当地命名为枫树。该提案支持的研究结果将公开发布，但结果将与改进 Maple 相关。该项目将通过添加数学知识库来增强现有计算机代数系统的功能。将研究系统已知的数学函数，并发现新的属性，以帮助系统解决用户的问题。对于系统及其用户来说特别重要的是与复数相关的属性。复数是使用负一的平方根构建的数。使用复数函数并简化所产生的数学表达式是一个长期存在的难题，但仍未得到充分解决。该项目旨在加强该领域系统的能力。 *****