Mathematical Sciences: A Software System for Algebraic Geometry Research

该奖项支持计算机软件系统的开发，使大型研究计算项目能够处理多个变量的多项式方程组。该项目的结果将是一个可用的和有效的计算机程序，它执行Groebner基算法来计算多项式环上的理想和模的标准基和合子。对现有程序Macaulay的改进将包括为用户添加良好的编程语言，处理更一般的系数环的能力，以及更快的执行速度。这个项目是在交换代数和该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。这个项目认真地利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.