Mathematical Sciences: Second Magma Conference on Computational Algebra; May 12-16, 1996; Milwaukee, WI

9626327斯莱特里研究员和他的同事们组织了第二届计算代数岩浆会议。在过去的几年里，计算代数和数论的几个不同分支取得了许多重大进展。由于不同分支之间的相互依赖性越来越强，一个领域的算法进步往往会对其他领域的算法性能产生重大影响。因此，会议聚集了来自一些关键领域的工作人员，包括从事软件开发的研究人员以及使用这些工具的人。这次会议的目的是让算法设计者和用户了解计算代数、数论和几何相关领域的最新发展，并让关键的理论数学家了解现在可用的计算代数工具所提供的可能性。预计它还将确定在不久的将来将产生重大新应用的可取算法和软件开发。会议促进了计算代数技术在数字信号处理、复杂系统设计、网络设计、密码学、编码理论和应用组合学等应用领域的应用。代数研究世界上关于离散结构和对称性的基本问题。这一数学分支的理论结果帮助化学家理解有机分子的光谱，帮助物理学家组织基本粒子族，帮助工程师解决方程系统。代数不变量被用来回答生物化学家关于DNA打结的问题，人类学家甚至使用代数分类来组织美国西南部的本土人工制品。多年来，数学家们除了想象力和铅笔和纸之外，几乎没有更多的东西来研究代数。但现在，计算机使研究人员能够处理比过去更大、更复杂的情况。计算代数是对这些研究工作的总称。然而，在数学研究中使用计算机需要开发专门的软件--这对典型的研究人员来说可能是一项耗时的任务。解决这一需求的一种方法是通过诸如MAGMA之类的系统，这些系统提供了对许多研究领域的最先进算法的轻松访问。另一个重要的过程是鼓励研究人员通过这样的会议分享他们的经验(甚至是软件)；在会议上的互动通常会导致思想的适应和新方向的发展。这些工具使理论研究人员能够探索更复杂的情况，在不熟悉的环境中获得洞察力，并计算出更大问题的答案。基于计算机的大数素性测试和因式分解工作正显示出对密码学和安全的直接应用。有限几何和设计方面的工作正在为错误检测和数据压缩提供改进的技术。这些都对每个人使用计算机和通信产生了很大影响。

9626327 Slattery The investigator and colleagues organize the Second Magma Conference on Computational Algebra. In the past few years a number of significant advances have taken place in several different branches of computational algebra and number theory. Because of the growing interdependence between the different branches, an algorithmic advance in one area often has a major impact on the performance of algorithms in other areas. Consequently, the meeting brings together workers from some of the key areas, including researchers working on software development as well as those using these tools. The conference is intended to inform algorithm designers and users of recent developments in cognate areas of computational algebra, number theory, and geometry and inform key theoretical mathematicians of the possibilities offered by the computational algebra tools that are now becoming available. It is also expected to identify desirable algorithm and software developments that would result in significant new applications in the near future. The conference promotes the use of the techniques of computational algebra in application areas such as digital signal processing, complex system design, network design, cryptography, coding theory and applied combinatorics. Algebra studies basic questions about discrete structure and symmetry in the world. Theoretical results from this branch of mathematics help chemists understand the spectra of organic molecules, physicists organize families of elementary particles, and engineers solve systems of equations. Algebraic invariants are used to answer biochemists' questions about knotting in DNA and anthropologists have even used algebraic classifications to organize native artifacts in the southwestern U.S. For many years mathematicians have studied algebra with little more than their imaginations and a pencil and paper. But now, computers allow researchers to work with larger and more complicated situations tha n were possible in the past. Computational algebra is the general title given to these research efforts. However, to use a computer in mathematical research requires the development of specialized software -- a task that can be time-consuming for the typical researcher. One way to address this need is through systems such as Magma which provide easy access to state-of-the-art algorithms in a number of fields of study. Another important process is to encourage researchers to share their experiences (and even software) through conferences such as this; the interaction at a conference often leads to adaptation of ideas and development of new directions. These tools enable theoretical researchers to explore more complicated situations, to gain insight in unfamiliar settings, and to compute answers to larger problems. Computer-based work on primality testing and factoring of large numbers is showing direct application to cryptography and security. Work in finite geometries and designs are providing improved techniques for error-detection and data compression. These have a large impact on everyone's use of computers and communications.