Polynomial and rational solutions of holonomic systems

[摘要] 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.

[发布日期] 2001-10-24

[效力级别]  Proceedings Paper