Decomposing Polynomial Sets Simultaneously into Gröbner Bases and Normal Triangular Sets

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10490)


In this paper we focus on the algorithms and their implementations for decomposing an arbitrary polynomial set simultaneously into pairs of lexicographic Gröbner bases and normal triangular sets with inherent connections in between and associated zero relationship with the polynomial set. In particular, a method by temporarily changing the variable orderings to handle the failure of the variable ordering assumption is proposed to ensure splitting needed for characteristic decomposition. Experimental results of our implementations for (strong) characteristic decomposition with comparisons with available implementations of triangular decomposition are also reported.


Normal triangular set Gröbner basis Characteristic decomposition Variable ordering 



The authors would like to thank the reviewers for their detailed comments which have led to effective improvements on this paper.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.LMIB–SKLSDE–School of Mathematics and Systems ScienceBeihang UniversityBeijingChina

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