A triangular decomposition algorithm for differential polynomial systems with elementary computation complexity

Wei Zhu, Xiao-Shan Gao

Abstract: In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of polynomials in one step using the theory of multivariate resultant. This seems to be the first differential triangular decomposition algorithm with elementary computation complexity.