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The Differential Counting Polynomial

Markus Lange-Hegermann,
Jan 2018

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.

Literatur Beschaffung: Springer
@misc{2363,
author= {Lange-Hegermann, Markus},
title= {The Differential Counting Polynomial},
abstract= {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.},
booktitle= {},
year= {2018},
month= {Jan},
publisher= {Springer},
address= {https://arxiv.org/abs/1407.5838},
editor= {},
pages= {},
organisation= {},
}