The Differential Counting Polynomial
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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.
KeywordsDifferential algebra Dimension polynomial Differential counting polynomial Thomas decomposition
Mathematics Subject Classification12H05 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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