The Differential Counting Polynomial
arXiv:1407.5838
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 asumptions, the differential counting polynomial decides whether a given set of solutions of a system of differential equations is the complete set of solutions.