Algorithms for polynomial systems

多项式系统的算法

• 批准号: 0302549
• 负责人: Shuhong Gao
• 金额: $ 23.8万
• 依托单位: Clemson University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-15 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0302549&HistoricalAwards=false
• 关键词: Algorithms; polynomial; systems

Principal Investigator: Shuhong Gao Proposal Number: 0302549Institution: Clemson UniversityAbstract: Algorithms for polynomial systemsThe proposed research belongs to the interface between mathematics and computer science. Professor Gao will investigate efficient algorithms for polynomial systems. Topics include large systems of linear equations, polynomial factorization, primary decomposition, and Hilbert irreducibility theorems. These topics are closely interrelated and are fundamentally important in algebra, number theory, and symbolic computation.Algebra and number theory are the oldest branches of mathematics, and polynomial systems play an important role throughout the history of mathematics. With the increasing use of computers in science and engineering, efficient solution of various problems related to polynomials are of vital importance. In addition, many cryptographic schemes for protecting sensitive digital information (from cellular phone communications, bank transactions, e-commerce to national security) are based on algebraic structures, and their security relies on various hard problems in algebra and number theory. The current research studies a sample of problems related to these applicati

主要研究者：高淑红提案编号：0302549机构：克莱姆森大学摘要：多项式系统的算法拟议的研究属于数学和计算机科学之间的接口。高教授将研究多项式系统的有效算法。 主题包括大型线性方程组，多项式分解，初等分解和希尔伯特不可约定理。代数和数论是数学中最古老的分支，多项式系统在整个数学史中扮演着重要的角色。 随着计算机在科学和工程中的日益广泛的应用，有效地解决与多项式有关的各种问题是至关重要的。此外，许多用于保护敏感数字信息（从蜂窝电话通信、银行交易、电子商务到国家安全）的密码方案都是基于代数结构的，它们的安全性依赖于代数和数论中的各种难题。目前的研究研究与这些应用相关的问题样本，