Collaborative Research: A Software System for Research in Algebraic Geometry, Commutative Algebra, and their Applications

协作研究：代数几何、交换代数及其应用研究的软件系统

基本信息

批准号：
2001367
负责人：
Michael Stillman
金额：
$ 80万
依托单位：
Cornell University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-10-01 至 2025-09-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2001367&HistoricalAwards=false
关键词：
Collaborative Research Software System Algebraic

项目摘要

With the advent of widely available fast computing, computational experiments have become more important in every branch of science and mathematics. Macaulay2 is a software system that leads in facilitating the use of symbolic and symbolic-numeric computation in multidisciplinary investigations. The computations it can perform have uses in many fields of mathematics, computer science, and natural sciences. The research under this project extends the computational methods built into Macaulay2. The project will promote collaborations between Macaulay2 developers from the research community, on the one hand, and applied scientists and pure mathematicians, on the other. This project provides research training opportunities for students.Macaulay2 is an open-source computer algebra system dedicated to solving systems of polynomial equations in many variables as well as computing and processing data that describe the underlying geometry of the solution sets. The three major aspects of this proposal are: research on core mathematical topics and applications outside mathematics; the maintenance and development of Macaulay2 as part of the infrastructure of research; and the development of manpower through training, conferences and collaborations, especially involving young researchers. The impact outside mathematics includes investigating problems from physics, biology, computer vision, and other areas where nonlinear algebra is a key ingredient. The project will maintain and develop Macaulay2 as a major tool for research, especially by improving the core algorithms for Groebner bases and free resolutions and by improving its facilities that combine symbolic and numerical computation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

随着广泛可用的快速计算的出现，在科学和数学的每个分支中，计算实验变得越来越重要。 MacAulay2是一种软件系统，可在多学科研究中促进符号和符号数量计算的使用。它可以执行的计算在许多数学，计算机科学和自然科学领域都有用途。该项目下的研究扩展了Macaulay2内置的计算方法。该项目将一方面促进研究界的MacAulay2开发人员之间的合作，另一方面应用科学家和纯数学家。该项目为学生提供研究培训机会。Macaulay2是一种开源计算机代数系统，致力于在许多变量中解决多项式方程的系统以及描述解决方案集的基本几何形状的计算和处理数据。该提案的三个主要方面是：关于数学以外的核心数学主题和应用的研究； Macaulay2的维护和开发是研究基础设施的一部分；以及通过培训，会议和合作，尤其是涉及年轻研究人员的人力发展。数学之外的影响包括研究物理，生物学，计算机视觉和非线性代数是关键成分的其他领域的问题。该项目将维护和开发MacAulay2作为研究的主要工具，尤其是通过改善Groebner基础和免费决议的核心算法，并通过改进其结合符号和数值计算的设施。这奖反映了NSF的法规使命，并认为通过基金会的知识优点和广泛的评论，它值得通过评估来进行评估，并获得了支持。