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Mathematics in Computer Science

, Volume 6, Issue 4, pp 457–473 | Cite as

On Solving Parametric Polynomial Systems

  • Marc Moreno Maza
  • Bican Xia
  • Rong Xiao
Article

Abstract

Border polynomial and discriminant variety are two important notions related to parametric polynomial system solving, in particular, for partitioning the parameter space into regions where the solutions of the system depend continuously on the parameter values. In this paper, we study the relations between those notions in the case of parametric triangular systems. We also investigate the properties and computation of the non-properness locus of the canonical projection restricted at a parametric regular chain or at its saturated ideal.

Keywords

Parametric polynomial system Border polynomial Discriminant variety Effective boundary Triangular decomposition Regular chain 

Mathematics Subject Classification (2010)

Primary 13P15 Secondary 68W30 

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.University of Western OntarioLondonCanada
  2. 2.Peking UniversityShenzhenChina

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