報告人：楊靜

時間：2024年5月24日（周五）上午10:15 — 11:00

地點：騰訊會議 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.

報告人簡介：楊靜，廣西民族大學(xué)副教授、碩士生導(dǎo)師。2013年獲北京航空航天大學(xué)基礎(chǔ)數(shù)學(xué)理學(xué)博士學(xué)位。目前主要在計算機代數(shù)、計算幾何和組合設(shè)計等研究方向開展研究工作。主持國家自然科學(xué)基金項目4項，在《Science China: Mathematics》、《Journal of Symbolic Computation》、《Computer Aided Geometric Design》等國內(nèi)外重要期刊和學(xué)術(shù)會議發(fā)表論文20余篇，參編會議論文集2部。