Mathematical Sciences: Studies in Commutative Algebra and Its Applications to Computational Algebra

数学科学：交换代数研究及其在计算代数中的应用

• 批准号: 9500786
• 负责人: Wolmer Vasconcelos
• 金额: $ 18万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500786&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Commutative; Algebra

This award supports the study of Cohen-Macaulay structures, in algebra, combinatorics, and geometry and is driven by their wide presence and the opportunities offered in issues of computational complexity. The principal investigator will investigate invariants of blowup algebras for their role in deciding the property of Cohen-Macaulay; will contribute to the ongoing process of algebraization of tangent and secant algebras; will study the role of various measures of complexity in the processing of basic operations of computational algebra; and will develop methods and algorithms that facilitate the efficient processing in large scale computations in cDaljit Ahlu geometry. This project is in the general area of computational algebra and the computer-aided computational aspects of this field. There is a growing interest in using computers to answer theoretical questions in algebra and conversely, algebra is quite useful for the development of algorithms. This research will not only aid in the development of computer programs in commutative algebra but will influence the development of computer programs in other areas. One aspect of this project concerns the development of a computer program which will solve systems of polynomial equations. This is significant in manufacturing both for modeling and for the development of robots.

该奖项支持科恩-麦考利结构在代数、组合学和几何方面的研究，并受到其广泛存在和在计算复杂性问题上提供的机会的推动。主要研究者将研究爆破代数的不变量在决定Cohen-Macaulay性质中的作用；将有助于正在进行的正切代数和正割代数的代数化过程；将学习各种复杂性度量在计算代数基本运算处理中的作用；并将开发方法和算法，以促进cDaljit Ahlu几何中大规模计算的有效处理。这个项目是在计算代数和这个领域的计算机辅助计算方面的一般领域。人们对使用计算机来回答代数中的理论问题越来越感兴趣，相反，代数对算法的发展非常有用。本研究不仅有助于交换代数计算机程序的发展，而且将影响其他领域计算机程序的发展。该项目的一个方面涉及开发一个计算机程序，该程序将求解多项式方程组。这对于机器人的建模和开发都是非常重要的。