第39期学术午餐会的通知——An Effective Framework for Constructing Exponent Lattice Basis of Nonzero Algebraic Numbers
报告人：Tao Zheng (Peking University)
时间：2019-04-22 12:00-13:30
地点：Room 1304, Sciences Building No. 1
各位数院老师和同学：
研究生学术午餐会是在学院领导的大力支持下，由研究生会负责组织的系列学术交流活动。午餐会每次邀请一位同学作为主讲人，面向全院各专业背景的研究生介绍自己科研方向的基本问题、概念和方法，并汇报近期的研究成果和进展，是研究生展示自我、促进交流的学术平台。
研究生会已经举办了三十八期活动，我们将于2019年4月22日周五举办第三十八期学术午餐会活动，欢迎感兴趣的老师和同学积极报名参加。
报告人简介：郑涛，tyc234cc 太阳成集团2016级博士研究生，导师为夏壁灿教授。研究方向为符号计算。
报告摘要：Computing a basis for the exponent lattice of algebraic numbers is a basic problem in the field of computational number theory with applications to many other areas. The bottleneck of the computation of a well-known algorithm (called Findrelations) solving the problem is the computation of the primitive element of the extended field generated by the given algebraic numbers. When the extended field is of large degree, the problem seems intractable by the tool implementing the algorithm. In this paper, a special kind of exponent lattice basis is introduced. An important feature of the basis is that it can be inductively constructed, which allows us to deal with the given algebraic numbers one by one when computing the basis. Based on this, an effective framework for constructing exponent lattice basis is proposed. Through computing a so-called pre-basis first and then solving some linear Diophantine equations, the basis can be efficiently constructed. A new certificate for multiplicative independence and some techniques for decreasing degrees of algebraic numbers are provided to speed up the computation. The new algorithm has been implemented with Mathematica and its effectiveness is verified by testing various examples. Moreover, the algorithm is applied to program verification for finding invariants of linear loops.
报名方式：请有意参加的老师在2019年4月19日（周五）中午12点前发送邮件至smsxueshu@126.com，我们将回复邮件和您确认。邮件报名方式仅限于老师，有意参加的同学请点击链接https://www.wjx.top/jq/37175884.aspx 报名, 谢谢！
