ΠΣ-域上一阶线性差分方程的极小万有分母  

Minimal universal denominators for first-order linear difference equations in ΠΣ-fields

作　　者：王晴 WANG Qing(School of Mathematics,Tianjin University,Tianjin 300350)

机构地区：[1]天津大学数学学院,天津300350

出　　处：《首都师范大学学报（自然科学版）》2022年第2期7-13,28,共8页Journal of Capital Normal University：Natural Science Edition

基　　金：国家自然科学基金项目(11771330)。

摘　　要：符号求和的一个关键问题是求解线性差分方程的有理解.解决这类问题的第一步是得到每个有理解分母的界,一旦知道分母界,就可以将有理解的问题简化为多项式解的问题.本文提供了一种用于在ΠΣ-域中寻找多项式系数一阶线性差分方程有理解的极小万有分母的算法,得到的极小万有分母为根据Abramov算法在ΠΣ-域上推广得到的万有分母的因子.A key problem of symbolic summation is to solve the rational solution of linear difference equation.The first step in solving it is to obtain the denominator bound of each rational solution.Once the denominator bound is known,the problem of solving rational solutions is reduced to the problem of solving polynomial solutions.This study provides an algorithm for finding a minimal universal denominator of rational solutions for fist-order linear difference equation with polynomial coefficients inΠΣ-fields,and the minimal universal denominator is a factor of universal denominator obtained by the generalization of the Abramov algorithm inΠΣ-fields.

关 键 词：线性差分方程 极小万有分母 Abramov万有分母 ΠΣ-域 

分 类 号：O157.1[理学—数学]