报告名称：Towards a Parallel Summation Algorithm

报告专家：陈绍示

专家所在单位：中科院数学与系统科学研究院

报告时间：2024-3-29日16:30点

报告地点: 数统学院203

专家简介：

陈绍示, 现为中国科学院数学与系统科学研究院副研究员, 博士生导师。主要研究符号计算，机器证明与组合数学。近几年致力于发展多变元幂级数的算术理论。在符号计算旗舰会议ISSAC与数学期刊Selecta Mathematica, Algebra and Number Theory, Mathematische Zeitschrift, Journal of Combinatorial Theory Series A，Journal of Symbolic Computation等发表论文30余篇。目前担任Journal of Symbolic Computation, Annals of Combinatorics, Journal of Difference Equations and Applications, Journal of Systems Science and Complexity, 和《系统科学与数学》等杂志编委。曾获得第二届 “吴文俊计算机数学青年学者奖”(2019)，第46届国际符号与代数计算年会(ISSAC2021)“杰出论文奖”，与国际计算机代数应用大会(ACA2022)“青年学者奖”。

报告摘要：

We propose a summation analog of the paradigm of parallel integration. Using this paradigm, we make some first steps towards an indefinite summation algorithm applicable to summands that rationally depend on the summation index and a P-recursive sequence and its shifts. Under the assumption that the corresponding difference field has no unnatural constants, we are able to compute a bound on the normal part of the denominator of a potential closed form. We can also handle the numerator. Our algorithm is incomplete so far as we cannot predict the special part of the denominator. However, we do have some structural results about special polynomials for the setting under consideration. This is a joint work with Ruyong Feng, Manuel Kauers, and Xiuyun Li.