Simplifying Algebraic Numbers and Algebraic Functions

简化代数数和代数函数

• 批准号: 0511544
• 负责人: Mark van Hoeij
• 金额: $ 9万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0511544&HistoricalAwards=false
• 关键词: Simplifying; Algebraic; Numbers; Functions

Computer algebra software packages can compute exact solutions formany mathematical problems. However, the answers that such softwarepackages return are often not presented in their simplest form,especially when they involve algebraic numbers or algebraic functions.The goal of this project is to develop algorithms that can reducemathematical expressions to their simplest form. The focus will beon expressions that involve algebraic numbers or algebraic functions.Computer algebra software can be very valuable for research andeducation. However, such software often produces large complicatedanswers. This poses a difficult problem for the application of computeralgebra in education, but also in research, because it can be difficult toreduce a complicated expression to its simplest form. Doing such reductionautomatically will make computer algebra systems easier to use.

计算机代数软件包可以计算出许多数学问题的精确解。然而，这些软件包返回的答案通常不是以最简单的形式呈现的，特别是当它们涉及代数数或代数函数时。这个项目的目标是开发能够将数学表达式简化为最简单形式的算法。重点将放在涉及代数数或代数函数的表达式上。计算机代数软件在研究和教育方面非常有价值。然而，这样的软件通常会产生复杂的大答案。这对计算机代数在教育和研究中的应用提出了一个难题，因为很难将复杂的表达式简化为最简单的形式。自动进行这种简化将使计算机代数系统更容易使用。