Abstract
In this paper, the concepts of quasi-characteristic pair and quasi-characteristic decomposition are introduced. The former is a pair \((\mathcal {G}, \mathcal {C})\) of a reduced lexicographic Gröbner basis \(\mathcal {G}\) and the W-characteristic set \(\mathcal {C}\) which is regular and extracted from \(\mathcal {G}\); the latter is the decomposition of a polynomial set into finitely many quasi-characteristic pairs with associated zero relations. We show that the quasi-characteristic decomposition of any polynomial set can be obtained algorithmically regardless of the variable ordering condition. A new algorithm is presented for computing characteristic decomposition when the variable ordering condition is always satisfied, otherwise it degenerates to compute the quasi one. Some properties of quasi-characteristic pairs and decomposition are proved, and examples are given to illustrate the algorithm.
Keywords
This work was partially supported by the National Natural Science Foundation of China (NSFC 11771034) and the Fundamental Research Funds for the Central Universities in China (YWF-19-BJ-J-324).
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The authors would like to thank the anonymous reviewers for their detailed and helpful comments on an earlier version of this paper.
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Dong, R., Mou, C. (2019). On Characteristic Decomposition and Quasi-characteristic Decomposition. In: England, M., Koepf, W., Sadykov, T., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2019. Lecture Notes in Computer Science(), vol 11661. Springer, Cham. https://doi.org/10.1007/978-3-030-26831-2_9
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