The Differential Counting Polynomial
Analysis of PDEs
2015-04-07 v2 Commutative Algebra
Classical Analysis and ODEs
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.
Cite
@article{arxiv.1407.5838,
title = {The Differential Counting Polynomial},
author = {Markus Lange-Hegermann},
journal= {arXiv preprint arXiv:1407.5838},
year = {2015}
}