Polynomial and rational solutions of holonomic systems
T. Oaku, N. Takayama, H. Tsai
TL;DR
This paper introduces two new elimination-free algorithms for finding polynomial and rational solutions of holonomic systems defined by linear differential operators in the Weyl algebra, enhancing computational efficiency.
Contribution
The paper presents novel algorithms that eliminate the need for elimination techniques to compute solutions of holonomic systems, improving computational methods in differential algebra.
Findings
Algorithms successfully compute polynomial solutions
Algorithms successfully compute rational solutions
Enhanced efficiency over existing methods
Abstract
The aim of this paper is to give two new algorithms, which are elimination free, to find polynomial and rational solutions for a given holonomic system associated to a set of linear differential operators in the Weyl algebra D = k<x_1, ..., x_n, dx_1, ..., dx_n> where k is a subfield of the complex numbers.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation · Nonlinear Waves and Solitons