论文标题
多元合理函数的符号总和
Symbolic Summation of Multivariate Rational Functions
论文作者
论文摘要
作为符号计算的主动研究主题的符号总和提供了有效的算法工具，用于评估和简化由数学，计算机科学，物理和其他领域引起的不同类型的总和。符号总和中的大多数现有算法主要适用于单变量输入的问题。符号计算中的一个长期项目是为多元函数的符号总和开发理论，算法和软件。本文将在多元合理函数的符号总结中为两个具有挑战性的问题提供完整的解决方案，即合理的总结性问题以及用于多元合理函数的望远镜的存在问题。我们的方法基于Sato的各向同性多项式的结构，这使我们能够减少测试多项式的移位等效性的问题。我们的结果为Picard问题的离散类似物提供了一个完整的解决方案，可用于检测Wilf-Zeilberger方法在多元合理函数上的适用性。
Symbolic summation as an active research topic of symbolic computation provides efficient algorithmic tools for evaluating and simplifying different types of sums arising from mathematics, computer science, physics and other areas. Most of existing algorithms in symbolic summation are mainly applicable to the problem with univariate inputs. A long-term project in symbolic computation is to develop theories, algorithms and software for the symbolic summation of multivariate functions. This paper will give complete solutions to two challenging problems in symbolic summation of multivariate rational functions, namely the rational summability problem and the existence problem of telescopers for multivariate rational functions. Our approach is based on the structure of Sato's isotropy groups of polynomials, which enables us to reduce the problems to testing the shift equivalence of polynomials. Our results provide a complete solution to the discrete analogue of Picard's problem on differential forms and can be used to detect the applicability of the Wilf-Zeilberger method to multivariate rational functions.
