报告人：杨静
时间：2024年5月24日（周五）上午10:15 — 11:00
地点：腾讯会议 163985866
摘要：In this talk, we tackle the following problem: compute the gcd for several univariate polynomials with parametric coefficients. It amounts to partitioning the parameter space into “cells” so that the gcd has a uniform expression over each cell and constructing a uniform expression of gcd in each cell. We tackle the problem as follows. We begin by making a natural and obvious extension of subresultant polynomials of two polynomials to several polynomials. Then we develop the following structural theories about them. 1. We generalize Sylvester’s theory to several polynomials, in order to obtain an elegant relationship between generalized subresultant polynomials and the gcd of several polynomials, yielding an elegant algorithm. 2. We generalize Habicht’s theory to several polynomials, in order to obtain a systematic relationship between generalized subresultant polynomials and pseudo-remainders, yielding an efficient algorithm. Using the generalized theories, we present a simple (structurally elegant) algorithm which is significantly more efficient (both in the output size and computing time) than previous (sub)resultant-based approaches.
报告人简介：杨静，广西民族大学副教授、硕士生导师。2013年获北京航空航天大学基础数学理学博士学位。目前主要在计算机代数、计算几何和组合设计等研究方向开展研究工作。主持国家自然科学基金项目4项，在《Science China: Mathematics》、《Journal of Symbolic Computation》、《Computer Aided Geometric Design》等国内外重要期刊和学术会议发表论文20余篇，参编会议论文集2部。
