关于自顶向下三角分解中多项式集的弦性
On the chordality of polynomial sets in triangular decomposition in top-down style
摘要：
本文研究了在自顶向下三角分解中，当待分解的多项式集具有弦关联图时，多项式集的弦图结构。特别是，我们证明了在任何一个自顶向下的三角形分解算法中计算出的一个特定三角形集的关联图是输入多项式集的弦图的子图，并且在一个特定的自顶向下的三角形分解的简单结构算法中，所有的多项式集包括所有计算出的三角形集（Wang方法）具有关联图，这些关联图是输入多项式集合的弦图的子图。这些子图结构的三角分解在自顶向下风格的高斯消除现有的结果的多元推广，并可能导致专门的高效算法和精细的复杂性分析弦多项式集的三角分解。
英文摘要：
In this paper the chordal graph structures of polynomial sets appearing in triangular decomposition in top-down style are studied when the input polynomial set to decompose has a chordal associated graph. In particular, we prove that the associated graph of one specific triangular set computed in any algorithm for triangular decomposition in top-down style is a subgraph of the chordal graph of the input polynomial set and that all the polynomial sets including all the computed triangular sets appearing in one specific simply-structured algorithm for triangular decomposition in top-down style (Wang's method) have associated graphs which are subgraphs of the the chordal graph of the input polynomial set. These subgraph structures in triangular decomposition in top-down style are multivariate generalization of existing results for Gaussian elimination and may lead to specialized efficient algorithms and refined complexity analyses for triangular decomposition of chordal polynomial sets.
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