报告题目：Signature-based standard basis algorithm under the framework of GVW algorithm

报告人：西南交通大学鲁东博士

报告时间：2023年10月13日10:20-11:30

报告地点：立志楼A423

摘要：Cover theorem serves as the theoretical foundation of the GVW algorithm, one of the most important signature-based algorithms, can eliminate a large number of useless J-pairs that are analogous to S-polynomials without any reduction. In this talk, we extend the cover theorem that is applicable for global orders and a special class of local orders to any semigroup order. Because a semigroup order is not necessarily global or local, there may not be a minimal signature in an infinite set, resulting in the difficulty of proving the cover theorem by existing methods. Building upon the pioneering idea of the Mora normal form algorithm, we propose a more comprehensive and general proof for the cover theorem while bypassing the need to choose a minimal signature. Therefore, the algorithm for signature-based standard bases is presented for any semigroup order under the framework of the GVW algorithm. This is a joint work with Dingkang Wang, Fanghui Xiao and Xiaopeng Zheng.

鲁东： 西南交通大学硕士研究生导师、副教授。博士毕业于中国科学院数学与系统科学研究院， 2021年入职西南交通大学数学学院。研究领域为符号计算，主要包括多项式系统的符号求解方法、多元多项式矩阵的分解与等价问题研究，与国内外学者合作发表论文十余篇，现主持国自然青年科学项目一项。