This paper investigates equivalence of square multivariate polynomial matrices with the determinant being some power of a univariate irreducible polynomial.The authors give a necessary and sufficient condition for thi...This paper investigates equivalence of square multivariate polynomial matrices with the determinant being some power of a univariate irreducible polynomial.The authors give a necessary and sufficient condition for this equivalence.And the authors present an algorithm to reduce a class of multivariate polynomial matrices to their Smith forms.展开更多
A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is presented.The key idea is to establish a relationship between ...A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is presented.The key idea is to establish a relationship between a matrix and any of its full row rank submatrices.Based on the new result,the authors propose an algorithm for factorizing matrices and have implemented it on the computer algebra system Maple.Two examples are given to illustrate the effectiveness of the algorithm,and experimental data shows that the algorithm is efficient.展开更多
基金supported by the Scientific Research Fund of Education Department of Hunan ProvinceChina under Grant Nos.20C0790 and 22A0334+1 种基金the National Natural Science Foundation of China under Grant Nos.11971161,12201204,and 12371507the Natural Science Foundation of Hunan Province under Grant No.2023JJ40275。
文摘This paper investigates equivalence of square multivariate polynomial matrices with the determinant being some power of a univariate irreducible polynomial.The authors give a necessary and sufficient condition for this equivalence.And the authors present an algorithm to reduce a class of multivariate polynomial matrices to their Smith forms.
基金supported by the National Natural Science Foundation of China under Grant Nos.12171469,12001030 and 12201210the National Key Research and Development Program under Grant No.2020YFA0712300the Fundamental Research Funds for the Central Universities under Grant No.2682022CX048。
文摘A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is presented.The key idea is to establish a relationship between a matrix and any of its full row rank submatrices.Based on the new result,the authors propose an algorithm for factorizing matrices and have implemented it on the computer algebra system Maple.Two examples are given to illustrate the effectiveness of the algorithm,and experimental data shows that the algorithm is efficient.
