Characteristic pairs consist of lexicographical Gr?bner bases and the minimal triangular sets,called W-characteristic sets,contained in them,and they are good representations of multivariate polynomial ideals in terms...Characteristic pairs consist of lexicographical Gr?bner bases and the minimal triangular sets,called W-characteristic sets,contained in them,and they are good representations of multivariate polynomial ideals in terms of Gr?bner bases and triangular sets simultaneously.In this paper,it is studied how to decompose a polynomial set of arbitrary dimensions into characteristic pairs with simple W-characteristic sets,and two algorithms are proposed over fields of characteristic zero and over finite fields respectively.Both of the algorithms rely on the concept of strong regular characteristic divisors,and the one for fields of characteristic zero also uses Lazard lemma to test whether an ideal is radical.Experimental results are presented to illustrate the effectiveness of the proposed algorithms.展开更多
In this paper it is shown how to transform a regular triangular set into a normal triangular set by computing the W-characteristic set of their saturated ideal and an algorithm is proposed for decomposing any polynomi...In this paper it is shown how to transform a regular triangular set into a normal triangular set by computing the W-characteristic set of their saturated ideal and an algorithm is proposed for decomposing any polynomial set into ?nitely many strong characteristic pairs, each of which is formed with the reduced lexicographic Gr?bner basis and the normal W-characteristic set of a characterizable ideal.展开更多
This special topic on Computer Mathematics of Journal of Systems Science&Complexity is the collection of 8 excellent papers presented at the 12th Congress of Computer Mathematics of Chinese Mathematical Society he...This special topic on Computer Mathematics of Journal of Systems Science&Complexity is the collection of 8 excellent papers presented at the 12th Congress of Computer Mathematics of Chinese Mathematical Society held in Guilin,China during June 4–7,2021.To look back its successful convening now,this conference was truly a blessed one at the right timing,at the right place,and with the right people in the up-and-downs of COVID-19 epidemic.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.11971050。
文摘Characteristic pairs consist of lexicographical Gr?bner bases and the minimal triangular sets,called W-characteristic sets,contained in them,and they are good representations of multivariate polynomial ideals in terms of Gr?bner bases and triangular sets simultaneously.In this paper,it is studied how to decompose a polynomial set of arbitrary dimensions into characteristic pairs with simple W-characteristic sets,and two algorithms are proposed over fields of characteristic zero and over finite fields respectively.Both of the algorithms rely on the concept of strong regular characteristic divisors,and the one for fields of characteristic zero also uses Lazard lemma to test whether an ideal is radical.Experimental results are presented to illustrate the effectiveness of the proposed algorithms.
基金supported partially by the National Natural Science Foundation of China under Grant Nos.11771034 and 11401018
文摘In this paper it is shown how to transform a regular triangular set into a normal triangular set by computing the W-characteristic set of their saturated ideal and an algorithm is proposed for decomposing any polynomial set into ?nitely many strong characteristic pairs, each of which is formed with the reduced lexicographic Gr?bner basis and the normal W-characteristic set of a characterizable ideal.
文摘This special topic on Computer Mathematics of Journal of Systems Science&Complexity is the collection of 8 excellent papers presented at the 12th Congress of Computer Mathematics of Chinese Mathematical Society held in Guilin,China during June 4–7,2021.To look back its successful convening now,this conference was truly a blessed one at the right timing,at the right place,and with the right people in the up-and-downs of COVID-19 epidemic.
