Mathematical Sciences: Conference on Computational Algebra -May 1992

数学科学：计算代数会议 - 1992 年 5 月

• 批准号: 9116375
• 负责人: Phillippe Loustaunay
• 金额: $ 0.49万
• 依托单位: George Mason University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-02-15 至 1993-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9116375&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Conference; Computational; Algebra

The theory of Groebner bases is the underlying theoretical base of the computational tools being developed in commutative and noncommutative ring theory. Important results have been achieved in commutative algebra and algebraic geometry, including algorithms for polynomial factorization and computation of the greatest common divisor of polynomials. There are algorithms for the primary decomposition of an ideal, the construction of projective resolutions and syzygies, the codimension of an ideal, the Poincare and Hilbert series, and the determination of ideal membership. For noncommutative rings, Groebner bases are becoming increasingly relevant. There are complications here since free algebras and path algebras are not Noetherian in general. Recently, algorithms have been designed for finding syzygies, ideal membership, and computation of the Cartan determinant. The theory itself has led to interesting questions about algorithms and their implementations as programs. Theoretical questions on termination as well as effectiveness are being studied. This project will support a Conference on Computational Algebra to be held in May 1992 at George Mason University. The conference will focus on some theoretical and practical applications of computational algebra, including topics in commutative and noncommutative ring theory which utilize Groebner bases, as well as applications to other fields.

Groebner基的理论是 基础的计算工具正在开发的交换 非交换环理论 重要成果 在交换代数和代数几何中实现，包括 多项式因式分解的算法和计算 多项式的最大公约数 有一些算法 一个理想的初等分解， 射影分解和合合，理想的余维， 庞加莱和希尔伯特级数，以及理想的确定 会员资格 对于非交换环，Groebner基是 变得越来越重要。 这里有些复杂的情况 由于自由代数和路代数在 将军 最近，已经设计了算法来寻找 合冲、理想隶属度和Cartan的计算 行列式 这个理论本身引出了一些有趣的问题 关于算法和它们作为程序的实现。 关于终止和效力的理论问题是 被研究。 该项目将支持计算会议 代数将于1992年5月在乔治梅森大学举行。 的 会议将侧重于一些理论和实践 计算代数的应用，包括 交换和非交换环理论，利用Groebner 基地，以及应用到其他领域。