Mathematical Sciences: Computer Assisted Studies in Commutative Algebra

本项目的目的是研究Cohen-Macaulay环 和代数，并有效地计算它们的不变量。其 目的是揭示和扩展Koszul同源性在 Cohen-Macaulay奇点的结构理论; 研究线性型代数的结构; 检查符号幂代数的方程;研究 交换李簇的不变量和奇性 代数及其表示;并制定方法和 算法允许非常大规模的计算， 交换代数 这项研究是在一般领域的交换 代数和计算机辅助计算方面， 领域人们对使用计算机回答问题的兴趣越来越大 理论问题。这个项目认真利用了这两个 符号计算的理论和实践，以解决真实的 交换代数中的问题

This project is directed at studying Cohen-Macaulay rings and algebras, and effectively computing their invariants. Its aims are to uncover and extend the role of Koszul homology in the structure theory of Cohen-Macaulay singularities; to investigate the structure of the algebras of linear type; to examine the equations of symbolic power algebras; to study the invariants and singularities of commuting varieties of Lie algebras and their representations; and to develop methods and algorithms that allow for very large scale computations in commutative algebra. This research 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. This project makes serious use of both the theory and practice of symbolic calculations to solve real problems in commutative algebra.