Cylindrical Algebraic Decomposition and Quantifier Elimination

圆柱代数分解与量词消去

• 批准号: 9712246
• 负责人: George Collins
• 金额: $ 9.51万
• 依托单位: University of Delaware
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-08-15 至 2001-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9712246&HistoricalAwards=false
• 关键词: Cylindrical; Algebraic; Decomposition; Quantifier; Elimination

This project continues investigation of the cylindrical algebraic decomposition (CAD) technique. This technique, developed in 1975 for quantifier elimination in the elementary theory of real- closed fields, has been continually improved in the last twenty years. A vast number of mathematical problems can be expressed in this theory and, potentially, solved via quantifier elimination. CAD has many applications, including control engineering, connectivity and path finding problems. Major improvements are also being made to the algebraic algorithms needed for CAD, including polynomial resultants and greatest common divisors, polynomial factorization, polynomial root isolation and refinement, and computations with algebraic numbers.

本计画继续研究圆柱代数分解（CAD）技术。 这种方法是1975年为消除真实的闭域的基本理论中的量词而发展起来的，近20年来不断得到改进。 大量的数学问题可以用这个理论来表达，并可能通过量词消除来解决。 CAD有许多应用，包括控制工程，连接和路径查找问题。 计算机辅助设计所需的代数算法也正在得到重大改进，包括多项式结式和最大公约数、多项式因式分解、多项式根分离和细化以及代数数计算。