Mathematical Sciences: A Software System for Algebraic Geometry Research

该奖项支持计算机软件系统的开发，使处理多变量多项式方程系统的大规模研究计算项目成为可能。该项目的结果将是一个可用和高效的计算机程序，该程序执行Groebner基算法，用于计算多项式环上理想和模块的标准基和协同。对现有程序的改进，Macaulay，将包括为用户添加一种良好的编程语言，能够处理更一般的系数环，并提高执行速度。这个项目是在交换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。本项目认真运用符号计算的理论和实践来解决交换代数中的实际问题。

This award supports the development of a computer software system enabling large scale research computing projects dealing with systems of polynomial equations in many variables. The result of the project will be a usable and efficient computer program, which executes the Groebner basis algorithm for computing standard bases and syzygies of ideals and modules over polynomial rings. Improvements over the existing program, Macaulay, will include the addition of a good programming language for the user, the ability to work over more general coefficient rings, and increased speed of execution. This project is in the general area of commutative 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 project makes serious use of both the theory and practice of symbolic calculations to solve real problems in commutative algebra.