图 书 馆
切线和判别式Tangency and Discriminants |
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| 课程网址: | http://videolectures.net/FPSAC2019_di_rocco_tangency_and_discrimi... |
| 主讲教师: | Sandra Di Rocco |
| 开课单位: | 瑞典皇家理工学院 |
| 开课时间: | 2019-07-19 |
| 课程语种: | 英语 |
| 中文简介: |  具有规定单项式的多项式的判别式是当相应多项式具有多个根时消失的系数中的不可约多项式。它是多项式数值研究中的重要工具，并且描述了相关代数形式的切线的丰富几何形状。我将回顾这种相互作用，并介绍多项式系统的判别式（混合判别式）概念。然后，我将展示导致迭代判别式概念的广义Schäfli方法如何简化混合判别式的分析。该演讲将主要介绍该主题。最新结果是基于与艾丽西亚·狄更斯坦和拉尔夫·莫里森的合作。 |
| 课程简介: | The discriminant of a polynomial with prescribed monomials is an irreducible polynomial in the coefficients vanishing when the corresponding polynomial has multiple roots. It is an important tool in numerical studies of polynomials and describes a rich geometry of tangency of an associated algebraic variety. I will recall this interplay and introduce the notion of discriminant for a system of polynomials (the mixed discriminant). I will then show how a generalised Schäfli method leading to the notion of iterated discriminant can simplify the analysis of mixed discriminants. The talk will mostly be introductory to the subject. The latest results are based on joint work with Alicia Dickenstein and Ralph Morrison. |
| 关 键 词: | 判别式; 不可约多项式; 切线 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2020-11-29：cjy |
| 最后编审: | 2020-11-29：cjy |
| 阅读次数: | 36 |