The Smith form of a matrix plays an important role in the equivalence of matrix.It is known that some multivariate polynomial matrices are not equivalent to their Smith forms.In this paper,the authors investigate main...The Smith form of a matrix plays an important role in the equivalence of matrix.It is known that some multivariate polynomial matrices are not equivalent to their Smith forms.In this paper,the authors investigate mainly the Smith forms of multivariate polynomial triangular matrices and testify two upper multivariate polynomial triangular matrices are equivalent to their Smith forms respectively.展开更多
Multivariate(n-D)polynomial matrix factorization is one of important research contents in multidimensional(n-D)systems,circuits,and signal processing.In this paper,several results on n-D polynomial matrices factorizat...Multivariate(n-D)polynomial matrix factorization is one of important research contents in multidimensional(n-D)systems,circuits,and signal processing.In this paper,several results on n-D polynomial matrices factorization over arbitrary coefficient fields are proved.Based on these results,generalizations of some results on general matrix factorization are obtained for given n-D polynomial matrices whose maximal order minors or lower order minors satisfy certain conditions.The proposed results fit for arbitrary coefficient field and have a wide range of application.展开更多
Gao,Volny and Wang(2010) gave a simple criterion for signature-based algorithms to compute Grobner bases.It gives a unified frame work for computing Grobner bases for both ideals and syzygies,the latter is very import...Gao,Volny and Wang(2010) gave a simple criterion for signature-based algorithms to compute Grobner bases.It gives a unified frame work for computing Grobner bases for both ideals and syzygies,the latter is very important in free resolutions in homological algebra.Sun and Wang(2011) later generalized the GVW criterion to a more general situation(to include the F5 Algorithm).Signature-based algorithms have become increasingly popular for computing Grobner bases.The current paper introduces a concept of factor pairs that can be used to detect more useless J-pairs than the generalized GVW criterion,thus improving signature-based algorithms.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11971161 and 11871207。
文摘The Smith form of a matrix plays an important role in the equivalence of matrix.It is known that some multivariate polynomial matrices are not equivalent to their Smith forms.In this paper,the authors investigate mainly the Smith forms of multivariate polynomial triangular matrices and testify two upper multivariate polynomial triangular matrices are equivalent to their Smith forms respectively.
基金supported by the National Natural Science Foundation of China under Grant Nos.11871207and 11971161the Natural Science Foundation of Hunan provincial under Grant No.2017JJ3084the Scientific Research Fund of Education Department of Hunan Province under Grant No.17C0635.
文摘Multivariate(n-D)polynomial matrix factorization is one of important research contents in multidimensional(n-D)systems,circuits,and signal processing.In this paper,several results on n-D polynomial matrices factorization over arbitrary coefficient fields are proved.Based on these results,generalizations of some results on general matrix factorization are obtained for given n-D polynomial matrices whose maximal order minors or lower order minors satisfy certain conditions.The proposed results fit for arbitrary coefficient field and have a wide range of application.
基金supported by the National Natural Science Foundation of China under Grant Nos.11471108,11426101Hunan Provincial Natural Science Foundation of China under Grant Nos.14JJ6027,2015JJ2051Fundamental Research Funds for the Central Universities of Central South University under Grant No.2013zzts008
文摘Gao,Volny and Wang(2010) gave a simple criterion for signature-based algorithms to compute Grobner bases.It gives a unified frame work for computing Grobner bases for both ideals and syzygies,the latter is very important in free resolutions in homological algebra.Sun and Wang(2011) later generalized the GVW criterion to a more general situation(to include the F5 Algorithm).Signature-based algorithms have become increasingly popular for computing Grobner bases.The current paper introduces a concept of factor pairs that can be used to detect more useless J-pairs than the generalized GVW criterion,thus improving signature-based algorithms.
