The Differential Counting Polynomial

被引：0
作者：
Markus Lange-Hegermann
机构：
[1] Rheinisch-Westfälische Technische Hochschule Aachen,Lehrstuhl B für Mathematik
来源：
Foundations of Computational Mathematics | 2018年 / 18卷
关键词：
Differential algebra; Dimension polynomial; Differential counting polynomial; Thomas decomposition; 12H05; 35A01; 35A10; 34G20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The aim of this paper is a quantitative analysis of the solution set of a system of polynomial nonlinear differential equations, both in the ordinary and partial case. Therefore, we introduce the differential counting polynomial, a common generalization of the dimension polynomial and the (algebraic) counting polynomial. Under mild additional assumptions, the differential counting polynomial decides whether a given set of solutions of a system of differential equations is the complete set of solutions.
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页码：291 / 308
页数：17
相关论文
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