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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

牟晨琪,北京航空航天大学数学与系统科学学院

Inviter:  
Title:
On the chordality of polynomial sets in triangular decomposition in top-down style
Time & Venue:
2018.4.26 15:00-16:00 N219
Abstract:

In this talk, we show the connections between chordal graphs which permit perfect elimination orderings on their vertexes from graph theory and triangular decomposition which decompose polynomial sets into triangular set from symbolic computation and present the chordal graph structures of polynomial sets appearing in triangular decomposition in top-down style when the input polynomial set has a chordal associated graph. In particular, we show that the associated graph of one specific triangular set in any algorithm for triangular decomposition in top-down style is a subgraph of that chordal graph and that all the triangular sets computed by Wang's method for triangular decomposition have associated graphs which are subgraphs of that chordal graph. Furthermore, the associated graphs of polynomial sets can be used to describe their sparsity with respect to thee variables, and we present a refined algorithm for efficient triangular decomposition for sparse polynomial sets in this sense. This talk is based on the joint work with Yang Bai.

 

 

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