Mathematical Sciences: A Software System for Algebraic Geometry Research

数学科学：代数几何研究的软件系统

• 批准号: 9623232
• 负责人: Michael Stillman
• 金额: --
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623232&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Software; System; Algebraic

This awards supports the research of Professor M. Stillman to continue the development of Macaulay 2. This system will enable large scale research computing projects dealing with systems of polynomial equations in many variables. He also hopes to work on the relationship of syzygies of a projective variety to the geometry of the variety. This research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past 10 years, solved problems that have stood for centuries. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields. Moreover it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics. The software being developed here will make many previously difficult or impossible computations in this field possible.

该奖项支持M教授的研究。斯蒂尔曼继续开发麦考利2。该系统将使大规模的研究计算项目处理系统的多项式方程在许多变量。他还希望工作的关系syzygies的投影品种的几何品种。 这项研究是在代数几何领域，这是现代数学最古老的部分之一，但在过去的10年里，它已经发展到解决了几个世纪以来的问题。最初，它处理由最简单的方程，即多项式在平面上定义的图形。今天，该领域使用的方法不仅来自代数，而且来自分析和拓扑学，相反，它被广泛用于这些领域。 此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人学等不同领域都很有用。 这里正在开发的软件将使这个领域中许多以前困难或不可能的计算成为可能。