Mathematical Sciences: A Software System for Algebraic Geometry Research

该奖项支持计算机软件的开发 系统使大规模研究计算项目能够处理 多变量的多项式方程组。 的 这个项目的结果将是一台可用的、高效率的计算机 程序，它执行Groebner基础算法， 上的理想和模的标准基和合 多项式环 对现有方案的改进， 麦考利，将包括一个很好的编程 语言对于用户来说，工作能力比较一般 系数环，并提高执行速度。 这 项目是在交换代数的一般领域和 计算机辅助计算方面的这一领域。 有一个 越来越多的人对使用计算机回答理论问题感兴趣， 代数中的问题，反过来说，代数是非常有用的， 算法的发展。 该项目认真利用 符号计算的理论和实践，以解决 交换代数中的真实的问题。

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.