On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices  

作　　者：LU Dong WANG Dingkang XIAO Fanghui 

机构地区：[1]School of Mathematics,Southwest Jiaotong University,Chengdu 610031,China [2]KLMM,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [3]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China [4]MOE-LCSM,School of Mathematics and Statistics,Hunan Normal University,Changsha 410081,China

出　　处：《Journal of Systems Science & Complexity》2024年第3期1295-1307,共13页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.12171469,12001030 and 12201210;the National Key Research and Development Program under Grant No.2020YFA0712300;the Fundamental Research Funds for the Central Universities under Grant No.2682022CX048。

摘　　要：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.

关 键 词：Free modules Grobner bases minor left prime(MLP) multivariate polynomial matrices polynomial matrix factorizations 

分 类 号：O151.21[理学—数学]