Open AccessPosted Content
Partial Denominator Bounds for Partial Linear Difference Equations
Manuel Kauers,Carsten Schneider +1 more
TL;DR: In this paper, the authors investigated which polynomials can possibly occur as factors in the denominators of rational solutions of a given Partial Linear Difference Equation (PLDE).
read more
Abstract: We investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation (PLDE). Two kinds of polynomials are to be distinguished, we call them /periodic/ and /aperiodic/. The main result is a generalization of a well-known denominator bounding technique for univariate equations to PLDEs. This generalization is able to find all the aperiodic factors of the denominators for a given PLDE.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
References
Fast algorithms to search for the rational solutions of linear differential equations with polynomial coefficients
Sergei A. Abramov,K. Yu. Kvansenko +1 more
- 01 Jun 1991
TL;DR: This paper is concerned with some way to improve upon the pure theoretical considerations of computer algebra algorithms with regard to solving the linear ordinary differential equations of the form C1/C2/C3.
54
Valuations of rational solutions of linear difference equations at irreducible polynomials
A. Gheffar,S. A. Abramov +1 more
TL;DR: Two algorithms are discussed which, given a linear difference equation with rational function coefficients over a field k of characteristic 0, construct a finite set M of polynomials, irreducible in k[x], such that if the given equation has a solution F(x)@?k( x) and val"p"("x")F(x).
17
Converging to Gosper's algorithm
TL;DR: A unified approach to computing the universal denominators as given by Gosper's algorithm and Abramov's algorithm for finding rational solutions to linear difference equations with polynomial coefficients is presented.
A Collection of Denominator Bounds To Solve Parameterized Linear Difference Equations in ΠΣ-Fields∗
Carsten Schneider
- 01 Jan 2004
TL;DR: In this paper, the authors provide essential algorithmic building blocks that enable to search for all solutions of all difference equations in a polynomial ring instead of searching for rational function solutions.