Foundations of Computational Mathematics

, Volume 18, Issue 2, pp 291–308 | Cite as

The Differential Counting Polynomial

  • Markus Lange-Hegermann


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.


Differential algebra Dimension polynomial Differential counting polynomial Thomas decomposition 

Mathematics Subject Classification

12H05 35A01 35A10 34G20 



The author was partly supported by the DFG Schwerpunkt SPP 1489 and Graduiertenkolleg Experimentelle und konstruktive Algebra of the DFG. His gratitude goes to the anonymous referees for a thorough review with many valuable comments.


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Copyright information

© SFoCM 2018

Authors and Affiliations

  1. 1.Lehrstuhl B für MathematikRheinisch-Westfälische Technische Hochschule AachenAachenGermany

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