Polynomial and rational solutions of holonomic systems
Polynomial and rational solutions of holonomic systems
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DOI：
10.1016/s0022-4049(00)00153-5
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发表时间：
2001-10-24
影响因子：
0.8
通讯作者：
Tsai, H
中科院分区：
文献类型：
--
作者：
Oaku, T;Takayama, N;Tsai, H
本文给出了求Weyl代数D = k下线性微分算子集的完整系统的多项式解和有理解的两种新算法，其中k是复数的可计算子域。这两种算法都基于d模理论，第一种算法通过Grobner变形和b函数获得解的度界，第二种算法通过对偶性和限制来评估解的维数。(C) 2001 Elsevier Science b.v.版权所有
In this article, we give two new algorithms to find the polynomial and rational function solutions of a given holonomic system associated to a set of linear differential operators in the Weyl algebra D = k , where k is a computable subfield of the complex numbers. Both algorithms are based on the theory of D-modules - the first algorithm obtains degree bounds on the solutions through Grobner deformations and b-functions while the second algorithm evaluates the dimension of the solutions through duality and restriction. (C) 2001 Elsevier Science B.V All rights reserved.