报告题目: Reduction systems and degree bounds for integration

报告人: 杜昊 博士（北京邮电大学）

报告时间：2022年12月28日（星期三）19:00-20:00

报告地点：腾讯视频会议（线上）

会议ID：340-337-334

报告校内联系人：黄辉 副教授  联系方式：huanghui@dlut.edu.cn

报告摘要：We apply Norman's completion process to the Risch-Norman integration method instead of using heuristic degree bounds to find antiderivatives in the differential polynomial ring generated by the given special functions. However, the behaviour of the completion process depends not only on the ring, but also on the ordering selected for terms. It may happen that the completion process does not terminate and yields an infinite number of reductions rules, which makes it hard to determine a complete reduction system. In such a case, one has to find finitely many formulae to denote the infinite number of reduction rules. By fixing adapted orderings, we present complete reduction systems for two families of functions satisfying second-order differential equations. In addition, they allow us to find rigorous weighted degree bounds for the antiderivatives.

报告人简介：杜昊，北京邮电大学讲师。2014年获北京航空航天大学理学学士学位，2019年获中国科学院大学应用数学专业博士学位，导师李子明研究员。2019年8月至2021年6月先后在奥地利科学院RICAM研究所与林茨大学代数研究所从事博士后研究工作，合作导师分别是Christoph Koutschan和Clemens Raab。研究方向为符号计算、微分差分代数等。在符号计算领域旗舰会议 ISSAC 发表论文2篇，海报1篇，在《Journal of Systems Science and Complexity》和《European Journal of Combinatorics》等期刊发表论文3篇。曾任ISSAC 2021短型交流委员会成员，组织举办国际计算机代数应用会议(ACA2021)算法组合分会。