On the chordality of ordinary differential triangular decomposition in top-down style

Abstract

In this paper we extend existing theoretical results on chordal graphs in algebraic triangular decomposition in top-down style to the ordinary differential case. We first propose the concept of differential associated graph of an ordinary differential polynomial set, and then for two typical algorithms in top-down style for ordinary differential triangular decomposition based on the pseudo-division and subresultant regular subchain respectively, we prove that when the input differential polynomial set has a chordal differential associated graph G and one perfect elimination ordering of G is used, the differential associated graph of any polynomial set in the decomposition process by these two algorithms is a subgraph of G.