Collaborative Research: A Software System for Algebraic Geometry Research

协作研究：代数几何研究的软件系统

• 批准号: 0311806
• 负责人: Michael Stillman
• 金额: $ 58.9万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0311806&HistoricalAwards=false
• 关键词: Collaborative; Research; Software; System; Algebraic

Stillman This is a collaborative project carreied out by Daniel R.Grayson and Michael E. Stillman. Macaulay 2 is a free computeralgebra system dedicated to the qualitative investigation ofsystems of polynomial equations in many variables. Theinvestigators continue development of Macaulay 2. They upgradeexisting algorithms, install more algorithms, develop and publishnew algorithms, implement new algorithms as they are discovered,add symbolic-numeric algorithm support, improve thedocumentation, and make systemic software changes that helpcontributors to write, test, and document code. Areas where newalgorithms can make an impact include the study of numericalsystems, fractions with specified types of denominators, idealfactorization, systems where the multiplication of the variablesdoesn't satisfy the commutative law, geometric optimization, theanalysis of observations of gene expression levels over time, andbioinformatics. Macaulay 2 is part of the infrastructure that supportsmathematical research involving systems of polynomial equationsin many variables. A measure of its impact is that at least 70research papers have cited Macaulay 2, at least sevenmathematicians have contributed code, and books and coursematerials are now using it. The experimental results found withMacaulay 2 are helping in the formulation and development oftractable conjectures. Now that the software is approachingmaturity, the investigators place more emphasis on recruitingdevelopers from the research community and on collaborations withother scientists on both mathematical and interdisciplinaryprojects that exploit Macaulay 2's capabilities. They introducegraduate students and postdocs to the use of computers inresearch mathematics through visits and a 5 day workshop inUrbana. The study of systems of polynomial equations has a longand distinguished history in pure and applied mathematics, withrecent impact on such fields as cryptography and robotics.Increasing computer power, combined with further development ofMacaulay 2, enables scientists to expand dramatically its scope.

斯蒂尔曼 这是由丹尼尔R.格雷森和迈克尔E. 斯蒂尔曼 Macaulay 2是一个免费的计算机代数系统，致力于对多元多项式方程组的定性研究。 研究人员继续开发麦考利2号。 他们更新现有的算法，安装更多的算法，开发和验证新的算法，实现新的算法，添加符号-数字算法支持，改进文档，并进行系统的软件更改，帮助贡献者编写，测试和记录代码。 新出租车可以产生影响的领域包括数字系统的研究，指定类型的分数，理想因式分解，变量乘法不满足交换律的系统，几何优化，随着时间的推移对基因表达水平的观察分析，以及生物信息学。 Macaulay 2是支持涉及多变量多项式方程系统的数学研究的基础设施的一部分。 其影响力的一个衡量标准是，至少有70篇研究论文引用了Macaulay 2，至少有7位数学家贡献了代码，书籍和教材现在都在使用它。Macaulay 2的实验结果有助于制定和开发易于处理的结构。 现在软件已经接近成熟，研究人员更加重视从研究社区招募开发人员，并与其他科学家合作开发利用Macaulay 2功能的数学和跨学科项目。 他们通过参观厄巴纳和为期5天的研讨会，向研究生和博士后介绍计算机在数学研究中的使用。 多项式方程组的研究在纯数学和应用数学中有着悠久而杰出的历史，最近对密码学和机器人学等领域产生了影响。计算机能力的提高，加上Macaulay 2的进一步发展，使科学家能够大大扩展其范围。