Babbage方程解的进一步讨论  

Further Discussion on Solutions of Babbage Equation

作　　者：刘娜 李松[2] 余志恒 LIU Na;LI Song;YU Zhiheng(School of General Education,Chengdu Industry and Trade College,Chengdu 611731,Sichuan;Mao Yisheng Honors College,Southwest Jiaotong University,Chengdu 611756,Sichuan;School of Mathematics,Southwest Jiaotong University,Chengdu 611756,Sichuan)

机构地区：[1]成都工贸职业技术学院通识教育学院,四川成都611731 [2]西南交通大学茅以升学院,四川成都611756 [3]西南交通大学数学学院,四川成都611756

出　　处：《四川师范大学学报（自然科学版）》2020年第6期781-786,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11701476);中央高校基本科研业务专项经费(2682018CX63);成都市工匠文化研究中心项目(2020ZC17).

摘　　要：在前人研究一维映射的迭代根以及Babbage方程解的工作基础上,进一步讨论Babbage方程的一类不连续解,进而研究平面Babbage方程的解.同时,给出平面Babbage方程存在平面二次多项式解的充要条件,以及解的精确表达式.In this paper,based on previous studies of the iterative roots of one-dimensional mappings and the solutions of the Babbage equation,a class of discontinuous solutions of Babbage equation is further discussed.Furthermore,the solutions of the plane Babbage equation are studied.The necessary and sufficient conditions for the existence of the plane quadratic polynomial solutions of the plane Babbage equation and the expressions of these solutions are given concretely.

关 键 词：Babbage方程 多项式代数 GROBNER基 极小不可约分解 

分 类 号：O178[理学—数学]