Mathematical Sciences: Studies in Commutative Algebra and Its Applications to Computational Algebra

该奖项支持科恩-麦考利结构的研究，在代数，组合学和几何学，是由他们的广泛存在和在计算复杂性问题提供的机会驱动。 首席研究员将调查不变量的爆破代数的作用，决定其性质的科恩-麦考利;将有助于代数的切线和割线代数正在进行的过程;将研究的作用，各种措施的复杂性，在处理计算代数的基本操作;并将开发方法和算法，促进cDaljit Ahlu几何中大规模计算的有效处理。 这个项目是在计算代数和计算机辅助计算方面的一般领域。 人们对使用计算机来回答代数中的理论问题越来越感兴趣，相反，代数对于算法的开发非常有用。 这项研究不仅有助于交换代数计算机程序的发展，而且将影响其他领域计算机程序的发展。 这个项目的一个方面是开发一个计算机程序来求解多项式方程组。 这在制造业中对于建模和机器人的开发都很重要。

This award supports the study of Cohen-Macaulay structures, in algebra, combinatorics, and geometry and is driven by their wide presence and the opportunities offered in issues of computational complexity. The principal investigator will investigate invariants of blowup algebras for their role in deciding the property of Cohen-Macaulay; will contribute to the ongoing process of algebraization of tangent and secant algebras; will study the role of various measures of complexity in the processing of basic operations of computational algebra; and will develop methods and algorithms that facilitate the efficient processing in large scale computations in cDaljit Ahlu geometry. This project is in the general area of computational 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 research will not only aid in the development of computer programs in commutative algebra but will influence the development of computer programs in other areas. One aspect of this project concerns the development of a computer program which will solve systems of polynomial equations. This is significant in manufacturing both for modeling and for the development of robots.