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On the Chordality of Simple Decomposition in Top-Down Style

  • Chenqi MouEmail author
  • Jiahua Lai
Conference paper
  • 18 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11989)

Abstract

Simple decomposition of polynomial sets computes conditionally squarefree triangular sets or systems with certain zero or ideal relationships with the polynomial sets. In this paper we study the chordality of polynomial sets occurring in the process of simple decomposition in top-down style. We first reformulate Wang’s algorithm for simple decomposition in top-down style so that the decomposition process can be described in an inductive way. Then we prove that for a polynomial set whose associated graph is chordal, all the polynomial sets in the process of Wang’s algorithm for computing simple decomposition of this polynomial set have associated graphs which are subgraphs of the input chordal graph.

Keywords

Chordal graph Simple decomposition Top-down style Triangular system 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.LMIB–School of Mathematical SciencesBeihang UniversityBeijingChina
  2. 2.Beijing Advanced Innovation Center for Big Data and Brain ComputingBeihang UniversityBeijingChina

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