《计算微分代数引论》课程主页
主讲老师： 李伟 副研究员
课程简介:
本课程为符号计算相关专业博士研究生的专业课。微分代数是用代数方法研究微分方程解的结构的一门学科，是计算代数几何在代数微分方程领域的推广。
课程旨在介绍微分代数的一些基础知识与构造性算法，包括微分簇与微分理想的对应关系，微分Hilbert零点定理，Wu-Ritt特征列方法与微分簇不可约分解算法等。
本课程授课以自写讲义为主，参考书目如下：
J.F. Ritt, Differential Algebra, Amer. Math. Soc., New York, 1950.
I. Kaplansky, An Introduction to Differential Algebra, Paris, Hermann, 1957.
E. R. Kolchin, Differential algebra and algebraic groups, Academic Press, New York-London, 1973.
时间地点:
每周二6-8节(14:20-17:00)；中关村教学楼N306教室。
课程讲义：
- Basic notions of differential algebra
- Differential rings and differential ideals[讲义 1]
- Decomposition of radical differential ideals[讲义 2]
- Differential Polynomial Rings and Differential Varieties
- Differential Characterisitic Sets[讲义 3]
- Ritt-Raudenbush Basis Theorem[讲义 4]
- Differential Algebra-Geomety Dictionary
- Ideal-Variety Correspondence in Differential Algebra
- Differential Hilbert Nullstellensatz [讲义 5]
- Irreducible Decomposition of Differential Varieties[讲义 6]
- Extensions of Differential Fields
- Differential Primitive Theorem[讲义 7]
- Differential Transcendence Degree[讲义 8]
- Applications to Differential Varieties[讲义 9][讲义 10]
- Algorithms and Constructive Methods for Algebraic Ordinary Differential Equations
- Wu-Ritt Well-ordering Principle for differential polynomials [讲义 11]
- Differential decomposition Algorithms[讲义 12]
- Applications to Mechanical Theorem Proving and Discovering[讲义 13]
- Decompostion Algorithms for Algebraic Partial Differential Equations[讲义 14]