Collaborative Research: A Software System for Algebraic Geometry Research

这是丹尼尔·r·格雷森和迈克尔·e·斯蒂尔曼的合作项目。Macaulay 2是一个免费的计算机代数系统，致力于对多变量多项式方程组进行定性研究。研究人员继续开发麦考利2号。他们升级现有的算法，安装更多的算法，开发和发布新的算法，在发现新算法时实现新算法，添加符号-数字算法支持，改进文档，并进行系统的软件更改，以帮助贡献者编写，测试和文档代码。新算法可以产生影响的领域包括数字系统的研究，具有特定类型分母的分数，理想因子分解，变量乘法不满足交换律的系统，几何优化，基因表达水平随时间的观察分析，以及生物信息学。麦考利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。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，书籍和课程材料现在都在使用它，这可以衡量它的影响。麦考利2号的实验结果有助于形成和发展易于处理的猜想。现在该软件已经接近成熟，研究人员更加重视从研究社区招募开发人员，并与其他科学家在数学和跨学科项目上合作，以利用麦考利2的能力。他们通过访问和在厄巴纳举行的为期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应用。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技术等领域产生了影响。不断增强的计算机能力，加上麦考利2号的进一步发展，使科学家们能够极大地扩展它的范围。

Grayson 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.