Chordal graphs in triangular decomposition in top-down style

In this paper, we first prove that when the associated graph of a polynomial set is chordal, particular triangular computed by general algorithm in top-down style for computing decomposition has an as subgraph chordal graph. Then Wang's method and subresultant-based regular style, all sets appearing process with any these algorithms have graphs subgraphs These theoretical results can be viewed non-trivial generalization existing ones sparse Gaussian elimination, inspired which further propose making use structure set. The effectiveness proposed decomposition, respect to variables, demonstrated preliminary experimental results.